id	sid	tid	token	lemma	pos
ejpam-5839	1	1	european	european	PROPN
ejpam-5839	1	2	journal	journal	PROPN
ejpam-5839	1	3	of	of	ADP
ejpam-5839	1	4	pure	pure	ADJ
ejpam-5839	1	5	and	and	CCONJ
ejpam-5839	1	6	applied	applied	ADJ
ejpam-5839	1	7	mathematics	mathematic	NOUN
ejpam-5839	1	8	2025	2025	NUM
ejpam-5839	1	9	,	,	PUNCT
ejpam-5839	1	10	vol	vol	NOUN
ejpam-5839	1	11	.	.	PROPN
ejpam-5839	1	12	18	18	NUM
ejpam-5839	1	13	,	,	PUNCT
ejpam-5839	1	14	issue	issue	NOUN
ejpam-5839	1	15	2	2	NUM
ejpam-5839	1	16	,	,	PUNCT
ejpam-5839	1	17	article	article	NOUN
ejpam-5839	1	18	number	number	NOUN
ejpam-5839	1	19	5839	5839	NUM
ejpam-5839	1	20	issn	issn	VERB
ejpam-5839	1	21	1307	1307	NUM
ejpam-5839	1	22	-	-	SYM
ejpam-5839	1	23	5543	5543	NUM
ejpam-5839	1	24	–	–	PUNCT
ejpam-5839	1	25	ejpam.com	ejpam.com	X
ejpam-5839	1	26	published	publish	VERB
ejpam-5839	1	27	by	by	ADP
ejpam-5839	1	28	new	new	PROPN
ejpam-5839	1	29	york	york	PROPN
ejpam-5839	1	30	business	business	PROPN
ejpam-5839	1	31	global	global	ADJ
ejpam-5839	1	32	key	key	ADJ
ejpam-5839	1	33	characteristics	characteristic	NOUN
ejpam-5839	1	34	of	of	ADP
ejpam-5839	1	35	quadri	quadri	NOUN
ejpam-5839	1	36	-	-	PUNCT
ejpam-5839	1	37	partitioned	partition	VERB
ejpam-5839	1	38	neutrosophic	neutrosophic	ADJ
ejpam-5839	1	39	riemann	riemann	PROPN
ejpam-5839	1	40	integrals	integral	NOUN
ejpam-5839	1	41	and	and	CCONJ
ejpam-5839	1	42	quadri	quadri	NOUN
ejpam-5839	1	43	-	-	PUNCT
ejpam-5839	1	44	partitioned	partition	VERB
ejpam-5839	1	45	neutrosophic	neutrosophic	ADJ
ejpam-5839	1	46	soft	soft	ADJ
ejpam-5839	1	47	topological	topological	ADJ
ejpam-5839	1	48	spaces	space	NOUN
ejpam-5839	1	49	abdallah	abdallah	PROPN
ejpam-5839	1	50	shihadeh1	shihadeh1	PROPN
ejpam-5839	1	51	,	,	PUNCT
ejpam-5839	1	52	mayada	mayada	NOUN
ejpam-5839	1	53	abualhomos2	abualhomos2	PROPN
ejpam-5839	1	54	,	,	PUNCT
ejpam-5839	2	1	alaa	alaa	PROPN
ejpam-5839	2	2	m.	m.	PROPN
ejpam-5839	2	3	abd	abd	PROPN
ejpam-5839	2	4	el	el	PROPN
ejpam-5839	2	5	-	-	PUNCT
ejpam-5839	2	6	latif3,∗	latif3,∗	PROPN
ejpam-5839	2	7	,	,	PUNCT
ejpam-5839	2	8	abdallah	abdallah	PROPN
ejpam-5839	2	9	alhusban4	alhusban4	PROPN
ejpam-5839	2	10	,	,	PUNCT
ejpam-5839	2	11	shaaban	shaaban	ADJ
ejpam-5839	2	12	m.	m.	NOUN
ejpam-5839	2	13	shaaban5	shaaban5	PROPN
ejpam-5839	2	14	,	,	PUNCT
ejpam-5839	2	15	muhammad	muhammad	PROPN
ejpam-5839	2	16	arslan6	arslan6	PROPN
ejpam-5839	2	17	,	,	PUNCT
ejpam-5839	2	18	arif	arif	PROPN
ejpam-5839	2	19	mehmood6	mehmood6	X
ejpam-5839	2	20	1	1	NUM
ejpam-5839	2	21	department	department	NOUN
ejpam-5839	2	22	of	of	ADP
ejpam-5839	2	23	mathematics	mathematic	NOUN
ejpam-5839	2	24	,	,	PUNCT
ejpam-5839	2	25	faculty	faculty	NOUN
ejpam-5839	2	26	of	of	ADP
ejpam-5839	2	27	science	science	NOUN
ejpam-5839	2	28	,	,	PUNCT
ejpam-5839	2	29	the	the	DET
ejpam-5839	2	30	hashemite	hashemite	PROPN
ejpam-5839	2	31	university	university	NOUN
ejpam-5839	2	32	,	,	PUNCT
ejpam-5839	2	33	zarqa	zarqa	NOUN
ejpam-5839	2	34	13133	13133	NUM
ejpam-5839	2	35	,	,	PUNCT
ejpam-5839	2	36	po	po	PROPN
ejpam-5839	2	37	box	box	PROPN
ejpam-5839	2	38	330127	330127	NUM
ejpam-5839	2	39	,	,	PUNCT
ejpam-5839	2	40	jordan	jordan	PROPN
ejpam-5839	2	41	2	2	NUM
ejpam-5839	2	42	applied	apply	VERB
ejpam-5839	2	43	science	science	NOUN
ejpam-5839	2	44	private	private	PROPN
ejpam-5839	2	45	university	university	PROPN
ejpam-5839	2	46	amman	amman	NOUN
ejpam-5839	2	47	,	,	PUNCT
ejpam-5839	2	48	11931	11931	NUM
ejpam-5839	2	49	,	,	PUNCT
ejpam-5839	2	50	jordan	jordan	PROPN
ejpam-5839	2	51	3	3	NUM
ejpam-5839	2	52	mathematics	mathematics	PROPN
ejpam-5839	2	53	department	department	PROPN
ejpam-5839	2	54	,	,	PUNCT
ejpam-5839	2	55	college	college	NOUN
ejpam-5839	2	56	of	of	ADP
ejpam-5839	2	57	science	science	NOUN
ejpam-5839	2	58	,	,	PUNCT
ejpam-5839	2	59	northern	northern	ADJ
ejpam-5839	2	60	border	border	NOUN
ejpam-5839	2	61	university	university	NOUN
ejpam-5839	2	62	,	,	PUNCT
ejpam-5839	2	63	arar	arar	NOUN
ejpam-5839	2	64	91431	91431	NUM
ejpam-5839	2	65	,	,	PUNCT
ejpam-5839	2	66	saudi	saudi	PROPN
ejpam-5839	2	67	arabia	arabia	PROPN
ejpam-5839	2	68	4	4	NUM
ejpam-5839	2	69	department	department	NOUN
ejpam-5839	2	70	of	of	ADP
ejpam-5839	2	71	mathematics	mathematic	NOUN
ejpam-5839	2	72	,	,	PUNCT
ejpam-5839	2	73	faculty	faculty	NOUN
ejpam-5839	2	74	of	of	ADP
ejpam-5839	2	75	science	science	NOUN
ejpam-5839	2	76	and	and	CCONJ
ejpam-5839	2	77	technology	technology	NOUN
ejpam-5839	2	78	,	,	PUNCT
ejpam-5839	2	79	irbid	irbid	VERB
ejpam-5839	2	80	national	national	ADJ
ejpam-5839	2	81	university	university	PROPN
ejpam-5839	2	82	,	,	PUNCT
ejpam-5839	2	83	p.o	p.o	PROPN
ejpam-5839	2	84	.	.	PROPN
ejpam-5839	2	85	box	box	PROPN
ejpam-5839	2	86	:	:	PUNCT
ejpam-5839	2	87	2600	2600	NUM
ejpam-5839	2	88	,	,	PUNCT
ejpam-5839	2	89	irbid	irbid	ADJ
ejpam-5839	2	90	,	,	PUNCT
ejpam-5839	2	91	jordan	jordan	PROPN
ejpam-5839	2	92	jadara	jadara	PROPN
ejpam-5839	2	93	university	university	PROPN
ejpam-5839	2	94	research	research	NOUN
ejpam-5839	2	95	center	center	NOUN
ejpam-5839	2	96	,	,	PUNCT
ejpam-5839	2	97	jadara	jadara	PROPN
ejpam-5839	2	98	university	university	PROPN
ejpam-5839	2	99	,	,	PUNCT
ejpam-5839	2	100	jordan	jordan	PROPN
ejpam-5839	2	101	5	5	NUM
ejpam-5839	2	102	center	center	NOUN
ejpam-5839	2	103	for	for	ADP
ejpam-5839	2	104	scientific	scientific	ADJ
ejpam-5839	2	105	research	research	NOUN
ejpam-5839	2	106	and	and	CCONJ
ejpam-5839	2	107	entrepreneurship	entrepreneurship	NOUN
ejpam-5839	2	108	,	,	PUNCT
ejpam-5839	2	109	northern	northern	ADJ
ejpam-5839	2	110	border	border	NOUN
ejpam-5839	2	111	university	university	NOUN
ejpam-5839	2	112	,	,	PUNCT
ejpam-5839	2	113	arar	arar	PROPN
ejpam-5839	2	114	73213	73213	NUM
ejpam-5839	2	115	,	,	PUNCT
ejpam-5839	2	116	saudi	saudi	PROPN
ejpam-5839	2	117	arabia	arabia	PROPN
ejpam-5839	2	118	6	6	NUM
ejpam-5839	2	119	department	department	NOUN
ejpam-5839	2	120	of	of	ADP
ejpam-5839	2	121	mathematics	mathematics	PROPN
ejpam-5839	2	122	,	,	PUNCT
ejpam-5839	2	123	institute	institute	PROPN
ejpam-5839	2	124	of	of	ADP
ejpam-5839	2	125	numerical	numerical	PROPN
ejpam-5839	2	126	sciences	sciences	PROPN
ejpam-5839	2	127	,	,	PUNCT
ejpam-5839	2	128	gomal	gomal	ADJ
ejpam-5839	2	129	university	university	NOUN
ejpam-5839	2	130	,	,	PUNCT
ejpam-5839	2	131	dera	dera	PROPN
ejpam-5839	2	132	ismail	ismail	PROPN
ejpam-5839	2	133	khan	khan	PROPN
ejpam-5839	2	134	29050	29050	NUM
ejpam-5839	2	135	,	,	PUNCT
ejpam-5839	2	136	kpk	kpk	PROPN
ejpam-5839	2	137	,	,	PUNCT
ejpam-5839	2	138	pakistan	pakistan	PROPN
ejpam-5839	2	139	abstract	abstract	NOUN
ejpam-5839	2	140	.	.	PUNCT
ejpam-5839	3	1	neutrosophic	neutrosophic	ADJ
ejpam-5839	3	2	set	set	NOUN
ejpam-5839	3	3	theory	theory	NOUN
ejpam-5839	3	4	(	(	PUNCT
ejpam-5839	3	5	nst	nst	PROPN
ejpam-5839	3	6	)	)	PUNCT
ejpam-5839	3	7	is	be	AUX
ejpam-5839	3	8	an	an	DET
ejpam-5839	3	9	extension	extension	NOUN
ejpam-5839	3	10	of	of	ADP
ejpam-5839	3	11	intuitionistic	intuitionistic	ADJ
ejpam-5839	3	12	fuzzy	fuzzy	ADJ
ejpam-5839	3	13	set	set	NOUN
ejpam-5839	3	14	theory	theory	NOUN
ejpam-5839	3	15	(	(	PUNCT
ejpam-5839	3	16	ifst	ifst	NOUN
ejpam-5839	3	17	)	)	PUNCT
ejpam-5839	3	18	.	.	PUNCT
ejpam-5839	4	1	while	while	SCONJ
ejpam-5839	4	2	ifst	ifst	NOUN
ejpam-5839	4	3	relies	rely	VERB
ejpam-5839	4	4	on	on	ADP
ejpam-5839	4	5	two	two	NUM
ejpam-5839	4	6	possibilities	possibility	NOUN
ejpam-5839	4	7	for	for	ADP
ejpam-5839	4	8	the	the	DET
ejpam-5839	4	9	complete	complete	ADJ
ejpam-5839	4	10	depiction	depiction	NOUN
ejpam-5839	4	11	of	of	ADP
ejpam-5839	4	12	a	a	DET
ejpam-5839	4	13	set	set	NOUN
ejpam-5839	4	14	,	,	PUNCT
ejpam-5839	4	15	neutrosophic	neutrosophic	ADJ
ejpam-5839	4	16	set	set	NOUN
ejpam-5839	4	17	theory	theory	NOUN
ejpam-5839	4	18	familiarizes	familiarize	VERB
ejpam-5839	4	19	an	an	DET
ejpam-5839	4	20	additional	additional	ADJ
ejpam-5839	4	21	third	third	ADJ
ejpam-5839	4	22	possibility	possibility	NOUN
ejpam-5839	4	23	,	,	PUNCT
ejpam-5839	4	24	thus	thus	ADV
ejpam-5839	4	25	providing	provide	VERB
ejpam-5839	4	26	a	a	DET
ejpam-5839	4	27	more	more	ADV
ejpam-5839	4	28	delicate	delicate	ADJ
ejpam-5839	4	29	representation	representation	NOUN
ejpam-5839	4	30	.	.	PUNCT
ejpam-5839	5	1	our	our	PRON
ejpam-5839	5	2	research	research	NOUN
ejpam-5839	5	3	builds	build	VERB
ejpam-5839	5	4	upon	upon	SCONJ
ejpam-5839	5	5	a	a	DET
ejpam-5839	5	6	further	further	ADJ
ejpam-5839	5	7	extension	extension	NOUN
ejpam-5839	5	8	of	of	ADP
ejpam-5839	5	9	neutrosophic	neutrosophic	ADJ
ejpam-5839	5	10	set	set	NOUN
ejpam-5839	5	11	theory	theory	NOUN
ejpam-5839	5	12	,	,	PUNCT
ejpam-5839	5	13	known	know	VERB
ejpam-5839	5	14	as	as	ADP
ejpam-5839	5	15	quadri	quadri	NOUN
ejpam-5839	5	16	-	-	PUNCT
ejpam-5839	5	17	partitioned	partition	VERB
ejpam-5839	5	18	neutrosophic	neutrosophic	ADJ
ejpam-5839	5	19	set	set	NOUN
ejpam-5839	5	20	theory	theory	NOUN
ejpam-5839	5	21	(	(	PUNCT
ejpam-5839	5	22	qpnst	qpnst	ADJ
ejpam-5839	5	23	)	)	PUNCT
ejpam-5839	5	24	,	,	PUNCT
ejpam-5839	5	25	which	which	PRON
ejpam-5839	5	26	brings	bring	VERB
ejpam-5839	5	27	in	in	ADP
ejpam-5839	5	28	a	a	DET
ejpam-5839	5	29	fourth	fourth	ADJ
ejpam-5839	5	30	possibility	possibility	NOUN
ejpam-5839	5	31	for	for	ADP
ejpam-5839	5	32	a	a	DET
ejpam-5839	5	33	more	more	ADV
ejpam-5839	5	34	detailed	detailed	ADJ
ejpam-5839	5	35	and	and	CCONJ
ejpam-5839	5	36	complete	complete	ADJ
ejpam-5839	5	37	description	description	NOUN
ejpam-5839	5	38	of	of	ADP
ejpam-5839	5	39	sets	set	NOUN
ejpam-5839	5	40	.	.	PUNCT
ejpam-5839	6	1	in	in	ADP
ejpam-5839	6	2	this	this	DET
ejpam-5839	6	3	study	study	NOUN
ejpam-5839	6	4	,	,	PUNCT
ejpam-5839	6	5	we	we	PRON
ejpam-5839	6	6	define	define	VERB
ejpam-5839	6	7	the	the	DET
ejpam-5839	6	8	riemann	riemann	PROPN
ejpam-5839	6	9	integral	integral	ADJ
ejpam-5839	6	10	theory	theory	NOUN
ejpam-5839	6	11	(	(	PUNCT
ejpam-5839	6	12	rit	rit	NOUN
ejpam-5839	6	13	)	)	PUNCT
ejpam-5839	6	14	within	within	ADP
ejpam-5839	6	15	the	the	DET
ejpam-5839	6	16	framework	framework	NOUN
ejpam-5839	6	17	of	of	ADP
ejpam-5839	6	18	qpnst	qpnst	ADJ
ejpam-5839	6	19	.	.	PUNCT
ejpam-5839	7	1	this	this	PRON
ejpam-5839	7	2	opens	open	VERB
ejpam-5839	7	3	new	new	ADJ
ejpam-5839	7	4	doors	door	NOUN
ejpam-5839	7	5	for	for	ADP
ejpam-5839	7	6	probing	probe	VERB
ejpam-5839	7	7	the	the	DET
ejpam-5839	7	8	properties	property	NOUN
ejpam-5839	7	9	and	and	CCONJ
ejpam-5839	7	10	characteristics	characteristic	NOUN
ejpam-5839	7	11	of	of	ADP
ejpam-5839	7	12	the	the	DET
ejpam-5839	7	13	riemann	riemann	PROPN
ejpam-5839	7	14	integral	integral	NOUN
ejpam-5839	7	15	in	in	ADP
ejpam-5839	7	16	this	this	DET
ejpam-5839	7	17	extended	extended	ADJ
ejpam-5839	7	18	context	context	NOUN
ejpam-5839	7	19	.	.	PUNCT
ejpam-5839	8	1	one	one	NUM
ejpam-5839	8	2	strategic	strategic	ADJ
ejpam-5839	8	3	concept	concept	NOUN
ejpam-5839	8	4	that	that	PRON
ejpam-5839	8	5	arises	arise	VERB
ejpam-5839	8	6	in	in	ADP
ejpam-5839	8	7	this	this	DET
ejpam-5839	8	8	work	work	NOUN
ejpam-5839	8	9	is	be	AUX
ejpam-5839	8	10	the	the	DET
ejpam-5839	8	11	level	level	NOUN
ejpam-5839	8	12	cut	cut	NOUN
ejpam-5839	8	13	.	.	PUNCT
ejpam-5839	9	1	in	in	ADP
ejpam-5839	9	2	qpnst	qpnst	NOUN
ejpam-5839	9	3	,	,	PUNCT
ejpam-5839	9	4	the	the	DET
ejpam-5839	9	5	level	level	NOUN
ejpam-5839	9	6	cut	cut	NOUN
ejpam-5839	9	7	is	be	AUX
ejpam-5839	9	8	defined	define	VERB
ejpam-5839	9	9	as	as	ADP
ejpam-5839	9	10	a	a	DET
ejpam-5839	9	11	four	four	NUM
ejpam-5839	9	12	-	-	PUNCT
ejpam-5839	9	13	tuple	tuple	NOUN
ejpam-5839	9	14	(	(	PUNCT
ejpam-5839	9	15	i	i	PROPN
ejpam-5839	9	16	,	,	PUNCT
ejpam-5839	9	17	j	j	PROPN
ejpam-5839	9	18	,	,	PUNCT
ejpam-5839	9	19	k	k	PROPN
ejpam-5839	9	20	,	,	PUNCT
ejpam-5839	9	21	l	l	NOUN
ejpam-5839	9	22	)	)	PUNCT
ejpam-5839	9	23	,	,	PUNCT
ejpam-5839	9	24	which	which	PRON
ejpam-5839	9	25	represents	represent	VERB
ejpam-5839	9	26	the	the	DET
ejpam-5839	9	27	different	different	ADJ
ejpam-5839	9	28	possibilities	possibility	NOUN
ejpam-5839	9	29	inherent	inherent	ADJ
ejpam-5839	9	30	in	in	ADP
ejpam-5839	9	31	the	the	DET
ejpam-5839	9	32	theory	theory	NOUN
ejpam-5839	9	33	.	.	PUNCT
ejpam-5839	10	1	the	the	DET
ejpam-5839	10	2	notion	notion	NOUN
ejpam-5839	10	3	of	of	ADP
ejpam-5839	10	4	the	the	DET
ejpam-5839	10	5	quadri	quadri	NOUN
ejpam-5839	10	6	-	-	PUNCT
ejpam-5839	10	7	partitioned	partition	VERB
ejpam-5839	10	8	neutrosophic	neutrosophic	ADJ
ejpam-5839	10	9	riemann	riemann	PROPN
ejpam-5839	10	10	integral	integral	ADJ
ejpam-5839	10	11	theory	theory	NOUN
ejpam-5839	10	12	(	(	PUNCT
ejpam-5839	10	13	qpnrit	qpnrit	NOUN
ejpam-5839	10	14	)	)	PUNCT
ejpam-5839	10	15	is	be	AUX
ejpam-5839	10	16	explored	explore	VERB
ejpam-5839	10	17	numerically	numerically	ADV
ejpam-5839	10	18	in	in	ADP
ejpam-5839	10	19	this	this	DET
ejpam-5839	10	20	study	study	NOUN
ejpam-5839	10	21	,	,	PUNCT
ejpam-5839	10	22	and	and	CCONJ
ejpam-5839	10	23	the	the	DET
ejpam-5839	10	24	results	result	NOUN
ejpam-5839	10	25	are	be	AUX
ejpam-5839	10	26	systematically	systematically	ADV
ejpam-5839	10	27	presented	present	VERB
ejpam-5839	10	28	in	in	ADP
ejpam-5839	10	29	tabular	tabular	PROPN
ejpam-5839	10	30	form	form	NOUN
ejpam-5839	10	31	.	.	PUNCT
ejpam-5839	11	1	this	this	DET
ejpam-5839	11	2	numerical	numerical	ADJ
ejpam-5839	11	3	approach	approach	NOUN
ejpam-5839	11	4	sheds	shed	VERB
ejpam-5839	11	5	light	light	NOUN
ejpam-5839	11	6	on	on	ADP
ejpam-5839	11	7	the	the	DET
ejpam-5839	11	8	integral	integral	ADJ
ejpam-5839	11	9	’s	’s	PART
ejpam-5839	11	10	properties	property	NOUN
ejpam-5839	11	11	and	and	CCONJ
ejpam-5839	11	12	facilitates	facilitate	VERB
ejpam-5839	11	13	the	the	DET
ejpam-5839	11	14	understanding	understanding	NOUN
ejpam-5839	11	15	of	of	ADP
ejpam-5839	11	16	its	its	PRON
ejpam-5839	11	17	behavior	behavior	NOUN
ejpam-5839	11	18	within	within	ADP
ejpam-5839	11	19	the	the	DET
ejpam-5839	11	20	qpnst	qpnst	ADJ
ejpam-5839	11	21	framework	framework	NOUN
ejpam-5839	11	22	.	.	PUNCT
ejpam-5839	12	1	this	this	DET
ejpam-5839	12	2	study	study	NOUN
ejpam-5839	12	3	explores	explore	NOUN
ejpam-5839	12	4	quadripartitioned	quadripartitione	VERB
ejpam-5839	12	5	neutrosophic	neutrosophic	ADJ
ejpam-5839	12	6	soft	soft	ADJ
ejpam-5839	12	7	topological	topological	ADJ
ejpam-5839	12	8	spaces	space	NOUN
ejpam-5839	12	9	,	,	PUNCT
ejpam-5839	12	10	extending	extend	VERB
ejpam-5839	12	11	neutrosophic	neutrosophic	ADJ
ejpam-5839	12	12	set	set	NOUN
ejpam-5839	12	13	theory	theory	NOUN
ejpam-5839	12	14	(	(	PUNCT
ejpam-5839	12	15	nst	nst	PROPN
ejpam-5839	12	16	)	)	PUNCT
ejpam-5839	12	17	,	,	PUNCT
ejpam-5839	12	18	which	which	PRON
ejpam-5839	12	19	incorporates	incorporate	VERB
ejpam-5839	12	20	three	three	NUM
ejpam-5839	12	21	membership	membership	NOUN
ejpam-5839	12	22	values	value	NOUN
ejpam-5839	12	23	:	:	PUNCT
ejpam-5839	12	24	true	true	ADJ
ejpam-5839	12	25	,	,	PUNCT
ejpam-5839	12	26	false	false	ADJ
ejpam-5839	12	27	,	,	PUNCT
ejpam-5839	12	28	and	and	CCONJ
ejpam-5839	12	29	indeterminacy	indeterminacy	NOUN
ejpam-5839	12	30	.	.	PUNCT
ejpam-5839	13	1	the	the	DET
ejpam-5839	13	2	study	study	NOUN
ejpam-5839	13	3	introduces	introduce	VERB
ejpam-5839	13	4	new	new	ADJ
ejpam-5839	13	5	concepts	concept	NOUN
ejpam-5839	13	6	such	such	ADJ
ejpam-5839	13	7	as	as	ADP
ejpam-5839	13	8	qpns	qpns	NOUN
ejpam-5839	13	9	semi	semi	ADJ
ejpam-5839	13	10	-	-	ADJ
ejpam-5839	13	11	open	open	ADJ
ejpam-5839	13	12	,	,	PUNCT
ejpam-5839	13	13	qpns	qpns	NOUN
ejpam-5839	13	14	pre	pre	ADJ
ejpam-5839	13	15	-	-	ADJ
ejpam-5839	13	16	open	open	ADJ
ejpam-5839	13	17	,	,	PUNCT
ejpam-5839	13	18	and	and	CCONJ
ejpam-5839	13	19	qpns	qpns	NOUN
ejpam-5839	13	20	∗b	∗b	PROPN
ejpam-5839	13	21	open	open	ADJ
ejpam-5839	13	22	sets	set	NOUN
ejpam-5839	13	23	,	,	PUNCT
ejpam-5839	13	24	and	and	CCONJ
ejpam-5839	13	25	builds	build	VERB
ejpam-5839	13	26	on	on	ADP
ejpam-5839	13	27	these	these	PRON
ejpam-5839	13	28	to	to	PART
ejpam-5839	13	29	define	define	VERB
ejpam-5839	13	30	qpns	qpns	NOUN
ejpam-5839	13	31	closure	closure	NOUN
ejpam-5839	13	32	,	,	PUNCT
ejpam-5839	13	33	exterior	exterior	ADJ
ejpam-5839	13	34	,	,	PUNCT
ejpam-5839	13	35	boundary	boundary	ADJ
ejpam-5839	13	36	,	,	PUNCT
ejpam-5839	13	37	and	and	CCONJ
ejpam-5839	13	38	interior	interior	NOUN
ejpam-5839	13	39	.	.	PUNCT
ejpam-5839	14	1	a	a	DET
ejpam-5839	14	2	key	key	ADJ
ejpam-5839	14	3	development	development	NOUN
ejpam-5839	14	4	is	be	AUX
ejpam-5839	14	5	the	the	DET
ejpam-5839	14	6	definition	definition	NOUN
ejpam-5839	14	7	of	of	ADP
ejpam-5839	14	8	a	a	DET
ejpam-5839	14	9	quadripartitioned	quadripartitione	VERB
ejpam-5839	14	10	neutrosophic	neutrosophic	ADJ
ejpam-5839	14	11	soft	soft	ADJ
ejpam-5839	14	12	base	base	NOUN
ejpam-5839	14	13	,	,	PUNCT
ejpam-5839	14	14	which	which	PRON
ejpam-5839	14	15	plays	play	VERB
ejpam-5839	14	16	a	a	DET
ejpam-5839	14	17	central	central	ADJ
ejpam-5839	14	18	role	role	NOUN
ejpam-5839	14	19	in	in	ADP
ejpam-5839	14	20	these	these	DET
ejpam-5839	14	21	topological	topological	ADJ
ejpam-5839	14	22	structures	structure	NOUN
ejpam-5839	14	23	.	.	PUNCT
ejpam-5839	15	1	the	the	DET
ejpam-5839	15	2	paper	paper	NOUN
ejpam-5839	15	3	also	also	ADV
ejpam-5839	15	4	explores	explore	VERB
ejpam-5839	15	5	the	the	DET
ejpam-5839	15	6	concept	concept	NOUN
ejpam-5839	15	7	of	of	ADP
ejpam-5839	15	8	a	a	DET
ejpam-5839	15	9	quadripartitioned	quadripartitione	VERB
ejpam-5839	15	10	neutrosophic	neutrosophic	ADJ
ejpam-5839	15	11	soft	soft	ADJ
ejpam-5839	15	12	sub	sub	NOUN
ejpam-5839	15	13	-	-	NOUN
ejpam-5839	15	14	base	base	NOUN
ejpam-5839	15	15	and	and	CCONJ
ejpam-5839	15	16	discusses	discuss	VERB
ejpam-5839	15	17	local	local	ADJ
ejpam-5839	15	18	bases	basis	NOUN
ejpam-5839	15	19	,	,	PUNCT
ejpam-5839	15	20	as	as	ADV
ejpam-5839	15	21	well	well	ADV
ejpam-5839	15	22	as	as	ADP
ejpam-5839	15	23	the	the	DET
ejpam-5839	15	24	firstand	firstand	NOUN
ejpam-5839	15	25	second	second	ADJ
ejpam-5839	15	26	-	-	PUNCT
ejpam-5839	15	27	countability	countability	NOUN
ejpam-5839	15	28	axioms	axiom	NOUN
ejpam-5839	15	29	.	.	PUNCT
ejpam-5839	16	1	the	the	DET
ejpam-5839	16	2	study	study	NOUN
ejpam-5839	16	3	further	far	ADV
ejpam-5839	16	4	examines	examine	VERB
ejpam-5839	16	5	hereditary	hereditary	ADJ
ejpam-5839	16	6	properties	property	NOUN
ejpam-5839	16	7	of	of	ADP
ejpam-5839	16	8	these	these	DET
ejpam-5839	16	9	spaces	space	NOUN
ejpam-5839	16	10	,	,	PUNCT
ejpam-5839	16	11	distinguishing	distinguish	VERB
ejpam-5839	16	12	between	between	ADP
ejpam-5839	16	13	inherited	inherit	VERB
ejpam-5839	16	14	and	and	CCONJ
ejpam-5839	16	15	non	non	ADJ
ejpam-5839	16	16	-	-	ADJ
ejpam-5839	16	17	inherited	inherited	ADJ
ejpam-5839	16	18	properties	property	NOUN
ejpam-5839	16	19	.	.	PUNCT
ejpam-5839	17	1	key	key	ADJ
ejpam-5839	17	2	results	result	NOUN
ejpam-5839	17	3	include	include	VERB
ejpam-5839	17	4	that	that	SCONJ
ejpam-5839	17	5	a	a	DET
ejpam-5839	17	6	quadripartitioned	quadripartitione	VERB
ejpam-5839	17	7	neutrosophic	neutrosophic	ADJ
ejpam-5839	17	8	soft	soft	ADJ
ejpam-5839	17	9	subspace	subspace	NOUN
ejpam-5839	17	10	of	of	ADP
ejpam-5839	17	11	a	a	DET
ejpam-5839	17	12	first	first	ADJ
ejpam-5839	17	13	-	-	PUNCT
ejpam-5839	17	14	countable	countable	ADJ
ejpam-5839	17	15	space	space	NOUN
ejpam-5839	17	16	is	be	AUX
ejpam-5839	17	17	also	also	ADV
ejpam-5839	17	18	firstcountable	firstcountable	ADJ
ejpam-5839	17	19	,	,	PUNCT
ejpam-5839	17	20	and	and	CCONJ
ejpam-5839	17	21	a	a	DET
ejpam-5839	17	22	second	second	ADJ
ejpam-5839	17	23	-	-	PUNCT
ejpam-5839	17	24	countable	countable	ADJ
ejpam-5839	17	25	subspace	subspace	NOUN
ejpam-5839	17	26	of	of	ADP
ejpam-5839	17	27	a	a	DET
ejpam-5839	17	28	second	second	ADJ
ejpam-5839	17	29	-	-	PUNCT
ejpam-5839	17	30	countable	countable	ADJ
ejpam-5839	17	31	space	space	NOUN
ejpam-5839	17	32	remains	remain	VERB
ejpam-5839	17	33	second	second	ADV
ejpam-5839	17	34	-	-	PUNCT
ejpam-5839	17	35	countable	countable	ADJ
ejpam-5839	17	36	.	.	PUNCT
ejpam-5839	18	1	it	it	PRON
ejpam-5839	18	2	also	also	ADV
ejpam-5839	18	3	highlights	highlight	VERB
ejpam-5839	18	4	the	the	DET
ejpam-5839	18	5	relationship	relationship	NOUN
ejpam-5839	18	6	between	between	ADP
ejpam-5839	18	7	second	second	ADJ
ejpam-5839	18	8	countability	countability	NOUN
ejpam-5839	18	9	and	and	CCONJ
ejpam-5839	18	10	separability	separability	NOUN
ejpam-5839	18	11	in	in	ADP
ejpam-5839	18	12	these	these	DET
ejpam-5839	18	13	spaces	space	NOUN
ejpam-5839	18	14	,	,	PUNCT
ejpam-5839	18	15	asserting	assert	VERB
ejpam-5839	18	16	that	that	SCONJ
ejpam-5839	18	17	a	a	DET
ejpam-5839	18	18	second	second	ADV
ejpam-5839	18	19	-	-	PUNCT
ejpam-5839	18	20	countable	countable	ADJ
ejpam-5839	18	21	quadripartitioned	quadripartitione	VERB
ejpam-5839	18	22	neutrosophic	neutrosophic	ADJ
ejpam-5839	18	23	soft	soft	ADJ
ejpam-5839	18	24	space	space	NOUN
ejpam-5839	18	25	is	be	AUX
ejpam-5839	18	26	separable	separable	ADJ
ejpam-5839	18	27	,	,	PUNCT
ejpam-5839	18	28	though	though	SCONJ
ejpam-5839	18	29	the	the	DET
ejpam-5839	18	30	converse	converse	NOUN
ejpam-5839	18	31	is	be	AUX
ejpam-5839	18	32	not	not	PART
ejpam-5839	18	33	always	always	ADV
ejpam-5839	18	34	true	true	ADJ
ejpam-5839	18	35	.	.	PUNCT
ejpam-5839	19	1	this	this	DET
ejpam-5839	19	2	work	work	NOUN
ejpam-5839	19	3	lays	lay	VERB
ejpam-5839	19	4	the	the	DET
ejpam-5839	19	5	foundation	foundation	NOUN
ejpam-5839	19	6	for	for	ADP
ejpam-5839	19	7	further	further	ADJ
ejpam-5839	19	8	research	research	NOUN
ejpam-5839	19	9	in	in	ADP
ejpam-5839	19	10	neutrosophic	neutrosophic	ADJ
ejpam-5839	19	11	soft	soft	ADJ
ejpam-5839	19	12	topologies	topology	NOUN
ejpam-5839	19	13	.	.	PUNCT
ejpam-5839	20	1	2020	2020	NUM
ejpam-5839	20	2	mathematics	mathematic	NOUN
ejpam-5839	20	3	subject	subject	NOUN
ejpam-5839	20	4	classifications	classification	NOUN
ejpam-5839	20	5	:	:	PUNCT
ejpam-5839	20	6	54a05	54a05	NUM
ejpam-5839	20	7	key	key	ADJ
ejpam-5839	20	8	words	word	NOUN
ejpam-5839	20	9	and	and	CCONJ
ejpam-5839	20	10	phrases	phrase	NOUN
ejpam-5839	20	11	:	:	PUNCT
ejpam-5839	20	12	closed	close	VERB
ejpam-5839	20	13	quadri	quadri	PROPN
ejpam-5839	20	14	-	-	PUNCT
ejpam-5839	20	15	neutrosophic	neutrosophic	ADJ
ejpam-5839	20	16	number	number	NOUN
ejpam-5839	20	17	,	,	PUNCT
ejpam-5839	20	18	bounded	bound	VERB
ejpam-5839	20	19	quadri	quadri	PROPN
ejpam-5839	20	20	-	-	PUNCT
ejpam-5839	20	21	neutrosophic	neutrosophic	ADJ
ejpam-5839	20	22	neutrosophic	neutrosophic	ADJ
ejpam-5839	20	23	number	number	NOUN
ejpam-5839	20	24	,	,	PUNCT
ejpam-5839	20	25	quadrineutrosophic	quadrineutrosophic	ADJ
ejpam-5839	20	26	riemann	riemann	PROPN
ejpam-5839	20	27	integration	integration	NOUN
ejpam-5839	20	28	.	.	PUNCT
ejpam-5839	21	1	quadri	quadri	PROPN
ejpam-5839	21	2	-	-	PUNCT
ejpam-5839	21	3	neutrosophic	neutrosophic	ADJ
ejpam-5839	21	4	neutrosophic	neutrosophic	ADJ
ejpam-5839	21	5	soft	soft	ADJ
ejpam-5839	21	6	set	set	NOUN
ejpam-5839	21	7	∗corresponding	∗corresponde	VERB
ejpam-5839	21	8	author	author	NOUN
ejpam-5839	21	9	.	.	PUNCT
ejpam-5839	22	1	doi	doi	NOUN
ejpam-5839	22	2	:	:	PUNCT
ejpam-5839	22	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5839	https://doi.org/10.29020/nybg.ejpam.v18i2.5839	NOUN
ejpam-5839	22	4	email	email	NOUN
ejpam-5839	22	5	addresses	address	NOUN
ejpam-5839	22	6	:	:	PUNCT
ejpam-5839	23	1	alaa.ali@nbu.edu.sa	alaa.ali@nbu.edu.sa	PROPN
ejpam-5839	23	2	(	(	PUNCT
ejpam-5839	23	3	a.	a.	NOUN
ejpam-5839	23	4	m.	m.	PROPN
ejpam-5839	23	5	abd	abd	PROPN
ejpam-5839	23	6	el	el	PROPN
ejpam-5839	23	7	-	-	PROPN
ejpam-5839	23	8	latif	latif	PROPN
ejpam-5839	23	9	)	)	PUNCT
ejpam-5839	23	10	,	,	PUNCT
ejpam-5839	23	11	mehdaniyal@gmail.com	mehdaniyal@gmail.com	X
ejpam-5839	23	12	(	(	PUNCT
ejpam-5839	23	13	a.	a.	PROPN
ejpam-5839	23	14	mehmood	mehmood	PROPN
ejpam-5839	23	15	)	)	PUNCT
ejpam-5839	23	16	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5839	24	1	1	1	NUM
ejpam-5839	24	2	copyright	copyright	NOUN
ejpam-5839	24	3	:	:	PUNCT
ejpam-5839	24	4	©	©	PROPN
ejpam-5839	24	5	2025	2025	NUM
ejpam-5839	24	6	the	the	DET
ejpam-5839	24	7	author(s	author(s	NOUN
ejpam-5839	24	8	)	)	PUNCT
ejpam-5839	24	9	.	.	PUNCT
ejpam-5839	25	1	(	(	PUNCT
ejpam-5839	25	2	cc	cc	NOUN
ejpam-5839	25	3	by	by	ADP
ejpam-5839	25	4	-	-	PUNCT
ejpam-5839	25	5	nc	nc	PROPN
ejpam-5839	25	6	4.0	4.0	NUM
ejpam-5839	25	7	)	)	PUNCT
ejpam-5839	25	8	a.	a.	NOUN
ejpam-5839	25	9	shihadeh	shihadeh	VERB
ejpam-5839	25	10	et	et	PROPN
ejpam-5839	25	11	al	al	PROPN
ejpam-5839	25	12	.	.	PUNCT
ejpam-5839	25	13	/	/	SYM
ejpam-5839	25	14	eur	eur	PROPN
ejpam-5839	25	15	.	.	PUNCT
ejpam-5839	26	1	j.	j.	PROPN
ejpam-5839	26	2	pure	pure	PROPN
ejpam-5839	26	3	appl	appl	PROPN
ejpam-5839	26	4	.	.	PROPN
ejpam-5839	26	5	math	math	PROPN
ejpam-5839	26	6	,	,	PUNCT
ejpam-5839	26	7	18	18	NUM
ejpam-5839	26	8	(	(	PUNCT
ejpam-5839	26	9	2	2	NUM
ejpam-5839	26	10	)	)	PUNCT
ejpam-5839	26	11	(	(	PUNCT
ejpam-5839	26	12	2025	2025	NUM
ejpam-5839	26	13	)	)	PUNCT
ejpam-5839	26	14	,	,	PUNCT
ejpam-5839	26	15	5839	5839	NUM
ejpam-5839	26	16	2	2	NUM
ejpam-5839	26	17	of	of	ADP
ejpam-5839	26	18	54	54	NUM
ejpam-5839	26	19	1	1	NUM
ejpam-5839	26	20	.	.	PUNCT
ejpam-5839	27	1	introduction	introduction	NOUN
ejpam-5839	27	2	zadeh	zadeh	NOUN
ejpam-5839	27	3	[	[	X
ejpam-5839	27	4	1	1	X
ejpam-5839	27	5	]	]	PUNCT
ejpam-5839	27	6	introduced	introduce	VERB
ejpam-5839	27	7	the	the	DET
ejpam-5839	27	8	concept	concept	NOUN
ejpam-5839	27	9	of	of	ADP
ejpam-5839	27	10	fuzzy	fuzzy	ADJ
ejpam-5839	27	11	set	set	NOUN
ejpam-5839	27	12	theory	theory	NOUN
ejpam-5839	27	13	(	(	PUNCT
ejpam-5839	27	14	fst	fst	NOUN
ejpam-5839	27	15	)	)	PUNCT
ejpam-5839	27	16	,	,	PUNCT
ejpam-5839	27	17	where	where	SCONJ
ejpam-5839	27	18	a	a	DET
ejpam-5839	27	19	set	set	NOUN
ejpam-5839	27	20	is	be	AUX
ejpam-5839	27	21	characterized	characterize	VERB
ejpam-5839	27	22	by	by	ADP
ejpam-5839	27	23	a	a	DET
ejpam-5839	27	24	membership	membership	NOUN
ejpam-5839	27	25	function	function	NOUN
ejpam-5839	27	26	.	.	PUNCT
ejpam-5839	28	1	the	the	DET
ejpam-5839	28	2	foundational	foundational	ADJ
ejpam-5839	28	3	operations	operation	NOUN
ejpam-5839	28	4	—	—	PUNCT
ejpam-5839	28	5	union	union	NOUN
ejpam-5839	28	6	,	,	PUNCT
ejpam-5839	28	7	intersection	intersection	NOUN
ejpam-5839	28	8	,	,	PUNCT
ejpam-5839	28	9	complement	complement	NOUN
ejpam-5839	28	10	,	,	PUNCT
ejpam-5839	28	11	and	and	CCONJ
ejpam-5839	28	12	convexity	convexity	NOUN
ejpam-5839	28	13	—	—	PUNCT
ejpam-5839	28	14	were	be	AUX
ejpam-5839	28	15	established	establish	VERB
ejpam-5839	28	16	.	.	PUNCT
ejpam-5839	29	1	additionally	additionally	ADV
ejpam-5839	29	2	,	,	PUNCT
ejpam-5839	29	3	the	the	DET
ejpam-5839	29	4	separation	separation	NOUN
ejpam-5839	29	5	theorem	theorem	VERB
ejpam-5839	29	6	for	for	ADP
ejpam-5839	29	7	convex	convex	ADJ
ejpam-5839	29	8	fuzzy	fuzzy	ADJ
ejpam-5839	29	9	sets	set	NOUN
ejpam-5839	29	10	was	be	AUX
ejpam-5839	29	11	formulated	formulate	VERB
ejpam-5839	29	12	.	.	PUNCT
ejpam-5839	30	1	zadeh	zadeh	NOUN
ejpam-5839	31	1	[	[	X
ejpam-5839	31	2	2	2	X
ejpam-5839	31	3	]	]	PUNCT
ejpam-5839	31	4	introduced	introduce	VERB
ejpam-5839	31	5	the	the	DET
ejpam-5839	31	6	concept	concept	NOUN
ejpam-5839	31	7	of	of	ADP
ejpam-5839	31	8	linguistic	linguistic	ADJ
ejpam-5839	31	9	variables	variable	NOUN
ejpam-5839	31	10	and	and	CCONJ
ejpam-5839	31	11	their	their	PRON
ejpam-5839	31	12	applications	application	NOUN
ejpam-5839	31	13	within	within	ADP
ejpam-5839	31	14	the	the	DET
ejpam-5839	31	15	context	context	NOUN
ejpam-5839	31	16	of	of	ADP
ejpam-5839	31	17	fst	fst	NOUN
ejpam-5839	31	18	.	.	PUNCT
ejpam-5839	32	1	these	these	DET
ejpam-5839	32	2	variables	variable	NOUN
ejpam-5839	32	3	have	have	AUX
ejpam-5839	32	4	found	find	VERB
ejpam-5839	32	5	widespread	widespread	ADJ
ejpam-5839	32	6	use	use	NOUN
ejpam-5839	32	7	in	in	ADP
ejpam-5839	32	8	various	various	ADJ
ejpam-5839	32	9	fields	field	NOUN
ejpam-5839	32	10	,	,	PUNCT
ejpam-5839	32	11	including	include	VERB
ejpam-5839	32	12	medicine	medicine	NOUN
ejpam-5839	32	13	,	,	PUNCT
ejpam-5839	32	14	law	law	NOUN
ejpam-5839	32	15	,	,	PUNCT
ejpam-5839	32	16	psychology	psychology	NOUN
ejpam-5839	32	17	,	,	PUNCT
ejpam-5839	32	18	economics	economic	NOUN
ejpam-5839	32	19	,	,	PUNCT
ejpam-5839	32	20	and	and	CCONJ
ejpam-5839	32	21	others	other	NOUN
ejpam-5839	32	22	.	.	PUNCT
ejpam-5839	33	1	zadeh	zadeh	NOUN
ejpam-5839	34	1	[	[	X
ejpam-5839	34	2	3	3	NUM
ejpam-5839	34	3	]	]	PUNCT
ejpam-5839	34	4	generalized	generalize	VERB
ejpam-5839	34	5	the	the	DET
ejpam-5839	34	6	ideas	idea	NOUN
ejpam-5839	34	7	presented	present	VERB
ejpam-5839	34	8	in	in	ADP
ejpam-5839	34	9	[	[	X
ejpam-5839	34	10	2	2	NUM
ejpam-5839	34	11	]	]	PUNCT
ejpam-5839	34	12	and	and	CCONJ
ejpam-5839	34	13	introduced	introduce	VERB
ejpam-5839	34	14	the	the	DET
ejpam-5839	34	15	notion	notion	NOUN
ejpam-5839	34	16	of	of	ADP
ejpam-5839	34	17	fuzzy	fuzzy	ADJ
ejpam-5839	34	18	variables	variable	NOUN
ejpam-5839	34	19	.	.	PUNCT
ejpam-5839	35	1	zadeh	zadeh	NOUN
ejpam-5839	36	1	[	[	X
ejpam-5839	36	2	4	4	NUM
ejpam-5839	36	3	]	]	PUNCT
ejpam-5839	36	4	applied	apply	VERB
ejpam-5839	36	5	linguistic	linguistic	ADJ
ejpam-5839	36	6	variables	variable	NOUN
ejpam-5839	36	7	to	to	PART
ejpam-5839	36	8	approximate	approximate	ADJ
ejpam-5839	36	9	reasoning	reasoning	NOUN
ejpam-5839	36	10	.	.	PUNCT
ejpam-5839	37	1	zadeh	zadeh	NOUN
ejpam-5839	38	1	[	[	X
ejpam-5839	38	2	5	5	NUM
ejpam-5839	38	3	]	]	PUNCT
ejpam-5839	38	4	proposed	propose	VERB
ejpam-5839	38	5	the	the	DET
ejpam-5839	38	6	generalized	generalized	ADJ
ejpam-5839	38	7	theory	theory	NOUN
ejpam-5839	38	8	of	of	ADP
ejpam-5839	38	9	uncertainty	uncertainty	NOUN
ejpam-5839	38	10	,	,	PUNCT
ejpam-5839	38	11	which	which	PRON
ejpam-5839	38	12	enables	enable	VERB
ejpam-5839	38	13	a	a	DET
ejpam-5839	38	14	broader	broad	ADJ
ejpam-5839	38	15	perspective	perspective	NOUN
ejpam-5839	38	16	on	on	ADP
ejpam-5839	38	17	uncertainty	uncertainty	NOUN
ejpam-5839	38	18	.	.	PUNCT
ejpam-5839	39	1	ye	ye	PRON
ejpam-5839	40	1	[	[	X
ejpam-5839	40	2	6	6	NUM
ejpam-5839	40	3	]	]	PUNCT
ejpam-5839	40	4	discussed	discuss	VERB
ejpam-5839	40	5	the	the	DET
ejpam-5839	40	6	concept	concept	NOUN
ejpam-5839	40	7	of	of	ADP
ejpam-5839	40	8	simplified	simplified	ADJ
ejpam-5839	40	9	neutrosophic	neutrosophic	ADJ
ejpam-5839	40	10	sets	set	NOUN
ejpam-5839	40	11	(	(	PUNCT
ejpam-5839	40	12	snss	sns	NOUN
ejpam-5839	40	13	)	)	PUNCT
ejpam-5839	40	14	,	,	PUNCT
ejpam-5839	40	15	which	which	PRON
ejpam-5839	40	16	are	be	AUX
ejpam-5839	40	17	a	a	DET
ejpam-5839	40	18	sub	sub	NOUN
ejpam-5839	40	19	-	-	NOUN
ejpam-5839	40	20	class	class	NOUN
ejpam-5839	40	21	of	of	ADP
ejpam-5839	40	22	neutrosophic	neutrosophic	ADJ
ejpam-5839	40	23	sets	set	NOUN
ejpam-5839	40	24	,	,	PUNCT
ejpam-5839	40	25	and	and	CCONJ
ejpam-5839	40	26	explored	explore	VERB
ejpam-5839	40	27	several	several	ADJ
ejpam-5839	40	28	aggregation	aggregation	NOUN
ejpam-5839	40	29	operators	operator	NOUN
ejpam-5839	40	30	.	.	PUNCT
ejpam-5839	41	1	furthermore	furthermore	ADV
ejpam-5839	41	2	,	,	PUNCT
ejpam-5839	41	3	decision	decision	NOUN
ejpam-5839	41	4	-	-	PUNCT
ejpam-5839	41	5	making	make	VERB
ejpam-5839	41	6	techniques	technique	NOUN
ejpam-5839	41	7	were	be	AUX
ejpam-5839	41	8	developed	develop	VERB
ejpam-5839	41	9	.	.	PUNCT
ejpam-5839	42	1	liu	liu	PROPN
ejpam-5839	42	2	and	and	CCONJ
ejpam-5839	42	3	luo	luo	PROPN
ejpam-5839	43	1	[	[	X
ejpam-5839	43	2	7	7	X
ejpam-5839	43	3	]	]	PUNCT
ejpam-5839	43	4	introduced	introduce	VERB
ejpam-5839	43	5	the	the	DET
ejpam-5839	43	6	notion	notion	NOUN
ejpam-5839	43	7	of	of	ADP
ejpam-5839	43	8	multi	multi	ADJ
ejpam-5839	43	9	-	-	ADJ
ejpam-5839	43	10	attribute	attribute	NOUN
ejpam-5839	43	11	group	group	NOUN
ejpam-5839	43	12	decision	decision	NOUN
ejpam-5839	43	13	-	-	PUNCT
ejpam-5839	43	14	making	make	VERB
ejpam-5839	43	15	(	(	PUNCT
ejpam-5839	43	16	magdm	magdm	NOUN
ejpam-5839	43	17	)	)	PUNCT
ejpam-5839	43	18	.	.	PUNCT
ejpam-5839	44	1	atanassov	atanassov	PROPN
ejpam-5839	45	1	[	[	X
ejpam-5839	45	2	8	8	NUM
ejpam-5839	45	3	]	]	PUNCT
ejpam-5839	45	4	introduced	introduce	VERB
ejpam-5839	45	5	intuitionistic	intuitionistic	ADJ
ejpam-5839	45	6	fuzzy	fuzzy	ADJ
ejpam-5839	45	7	sets	set	NOUN
ejpam-5839	45	8	(	(	PUNCT
ejpam-5839	45	9	ifs	ifs	PROPN
ejpam-5839	45	10	)	)	PUNCT
ejpam-5839	45	11	,	,	PUNCT
ejpam-5839	45	12	an	an	DET
ejpam-5839	45	13	extension	extension	NOUN
ejpam-5839	45	14	of	of	ADP
ejpam-5839	45	15	fuzzy	fuzzy	ADJ
ejpam-5839	45	16	sets	set	NOUN
ejpam-5839	45	17	,	,	PUNCT
ejpam-5839	45	18	and	and	CCONJ
ejpam-5839	45	19	described	describe	VERB
ejpam-5839	45	20	the	the	DET
ejpam-5839	45	21	basic	basic	ADJ
ejpam-5839	45	22	operations	operation	NOUN
ejpam-5839	45	23	associated	associate	VERB
ejpam-5839	45	24	with	with	ADP
ejpam-5839	45	25	this	this	DET
ejpam-5839	45	26	theory	theory	NOUN
ejpam-5839	45	27	,	,	PUNCT
ejpam-5839	45	28	as	as	ADV
ejpam-5839	45	29	well	well	ADV
ejpam-5839	45	30	as	as	ADP
ejpam-5839	45	31	the	the	DET
ejpam-5839	45	32	development	development	NOUN
ejpam-5839	45	33	of	of	ADP
ejpam-5839	45	34	topological	topological	ADJ
ejpam-5839	45	35	operators	operator	NOUN
ejpam-5839	45	36	.	.	PUNCT
ejpam-5839	46	1	atanassov	atanassov	PROPN
ejpam-5839	46	2	and	and	CCONJ
ejpam-5839	46	3	gargov	gargov	VERB
ejpam-5839	46	4	[	[	PUNCT
ejpam-5839	46	5	9	9	NUM
ejpam-5839	46	6	]	]	X
ejpam-5839	46	7	advanced	advance	VERB
ejpam-5839	46	8	the	the	DET
ejpam-5839	46	9	concept	concept	NOUN
ejpam-5839	46	10	of	of	ADP
ejpam-5839	46	11	interval	interval	NOUN
ejpam-5839	46	12	-	-	PUNCT
ejpam-5839	46	13	valued	value	VERB
ejpam-5839	46	14	ifss	ifss	NOUN
ejpam-5839	46	15	,	,	PUNCT
ejpam-5839	46	16	utilizing	utilize	VERB
ejpam-5839	46	17	intervals	interval	NOUN
ejpam-5839	46	18	in	in	ADP
ejpam-5839	46	19	their	their	PRON
ejpam-5839	46	20	formulation	formulation	NOUN
ejpam-5839	46	21	.	.	PUNCT
ejpam-5839	47	1	smarandache	smarandache	NOUN
ejpam-5839	48	1	[	[	X
ejpam-5839	48	2	10	10	NUM
ejpam-5839	48	3	,	,	PUNCT
ejpam-5839	48	4	11	11	NUM
ejpam-5839	48	5	]	]	PUNCT
ejpam-5839	48	6	explored	explore	VERB
ejpam-5839	48	7	various	various	ADJ
ejpam-5839	48	8	techniques	technique	NOUN
ejpam-5839	48	9	,	,	PUNCT
ejpam-5839	48	10	including	include	VERB
ejpam-5839	48	11	neutrosophic	neutrosophic	ADJ
ejpam-5839	48	12	probability	probability	NOUN
ejpam-5839	48	13	and	and	CCONJ
ejpam-5839	48	14	neutrosophic	neutrosophic	ADJ
ejpam-5839	48	15	logic	logic	NOUN
ejpam-5839	48	16	.	.	PUNCT
ejpam-5839	49	1	ye	ye	PRON
ejpam-5839	50	1	[	[	X
ejpam-5839	50	2	12	12	NUM
ejpam-5839	50	3	]	]	PUNCT
ejpam-5839	50	4	examined	examine	VERB
ejpam-5839	50	5	applications	application	NOUN
ejpam-5839	50	6	of	of	ADP
ejpam-5839	50	7	neutrosophic	neutrosophic	ADJ
ejpam-5839	50	8	sets	set	NOUN
ejpam-5839	50	9	in	in	ADP
ejpam-5839	50	10	multi	multi	ADJ
ejpam-5839	50	11	-	-	ADJ
ejpam-5839	50	12	criteria	criterion	NOUN
ejpam-5839	50	13	decision	decision	NOUN
ejpam-5839	50	14	-	-	PUNCT
ejpam-5839	50	15	making	make	VERB
ejpam-5839	50	16	problems	problem	NOUN
ejpam-5839	50	17	.	.	PUNCT
ejpam-5839	51	1	techniques	technique	NOUN
ejpam-5839	51	2	based	base	VERB
ejpam-5839	51	3	on	on	ADP
ejpam-5839	51	4	weighted	weight	VERB
ejpam-5839	51	5	distance	distance	NOUN
ejpam-5839	51	6	measures	measure	NOUN
ejpam-5839	51	7	and	and	CCONJ
ejpam-5839	51	8	generalized	generalize	VERB
ejpam-5839	51	9	hybrid	hybrid	NOUN
ejpam-5839	51	10	weighted	weight	VERB
ejpam-5839	51	11	average	average	ADJ
ejpam-5839	51	12	operators	operator	NOUN
ejpam-5839	51	13	,	,	PUNCT
ejpam-5839	51	14	employing	employ	VERB
ejpam-5839	51	15	neutrosophic	neutrosophic	ADJ
ejpam-5839	51	16	hesitant	hesitant	ADJ
ejpam-5839	51	17	sets	set	NOUN
ejpam-5839	51	18	,	,	PUNCT
ejpam-5839	51	19	were	be	AUX
ejpam-5839	51	20	discussed	discuss	VERB
ejpam-5839	51	21	in	in	ADP
ejpam-5839	51	22	[	[	X
ejpam-5839	51	23	13	13	NUM
ejpam-5839	51	24	,	,	PUNCT
ejpam-5839	51	25	14	14	NUM
ejpam-5839	51	26	]	]	PUNCT
ejpam-5839	51	27	,	,	PUNCT
ejpam-5839	51	28	along	along	ADP
ejpam-5839	51	29	with	with	ADP
ejpam-5839	51	30	their	their	PRON
ejpam-5839	51	31	applications	application	NOUN
ejpam-5839	51	32	in	in	ADP
ejpam-5839	51	33	multiple	multiple	ADJ
ejpam-5839	51	34	-	-	PUNCT
ejpam-5839	51	35	attribute	attribute	NOUN
ejpam-5839	51	36	decision	decision	NOUN
ejpam-5839	51	37	-	-	PUNCT
ejpam-5839	51	38	making	making	NOUN
ejpam-5839	51	39	.	.	PUNCT
ejpam-5839	52	1	li	li	PROPN
ejpam-5839	52	2	and	and	CCONJ
ejpam-5839	52	3	luo	luo	PROPN
ejpam-5839	53	1	[	[	X
ejpam-5839	53	2	15	15	NUM
ejpam-5839	53	3	]	]	PUNCT
ejpam-5839	53	4	introduced	introduce	VERB
ejpam-5839	53	5	the	the	DET
ejpam-5839	53	6	super	super	ADV
ejpam-5839	53	7	strong	strong	ADJ
ejpam-5839	53	8	theory	theory	NOUN
ejpam-5839	53	9	,	,	PUNCT
ejpam-5839	53	10	known	know	VERB
ejpam-5839	53	11	as	as	ADP
ejpam-5839	53	12	soft	soft	ADJ
ejpam-5839	53	13	set	set	NOUN
ejpam-5839	53	14	theory	theory	NOUN
ejpam-5839	53	15	(	(	PUNCT
ejpam-5839	53	16	sst	sst	NOUN
ejpam-5839	53	17	)	)	PUNCT
ejpam-5839	53	18	,	,	PUNCT
ejpam-5839	53	19	and	and	CCONJ
ejpam-5839	53	20	defined	define	VERB
ejpam-5839	53	21	its	its	PRON
ejpam-5839	53	22	fundamental	fundamental	ADJ
ejpam-5839	53	23	operations	operation	NOUN
ejpam-5839	53	24	.	.	PUNCT
ejpam-5839	54	1	maji	maji	PROPN
ejpam-5839	54	2	et	et	PROPN
ejpam-5839	54	3	al	al	PROPN
ejpam-5839	54	4	.	.	PUNCT
ejpam-5839	55	1	[	[	X
ejpam-5839	55	2	16	16	NUM
ejpam-5839	55	3	]	]	PUNCT
ejpam-5839	55	4	applied	apply	VERB
ejpam-5839	55	5	sst	sst	NOUN
ejpam-5839	55	6	to	to	ADP
ejpam-5839	55	7	decision	decision	NOUN
ejpam-5839	55	8	-	-	PUNCT
ejpam-5839	55	9	making	make	VERB
ejpam-5839	55	10	problems	problem	NOUN
ejpam-5839	55	11	,	,	PUNCT
ejpam-5839	55	12	redefining	redefine	VERB
ejpam-5839	55	13	key	key	ADJ
ejpam-5839	55	14	operations	operation	NOUN
ejpam-5839	55	15	and	and	CCONJ
ejpam-5839	55	16	illustrating	illustrate	VERB
ejpam-5839	55	17	their	their	PRON
ejpam-5839	55	18	validity	validity	NOUN
ejpam-5839	55	19	with	with	ADP
ejpam-5839	55	20	examples	example	NOUN
ejpam-5839	55	21	.	.	PUNCT
ejpam-5839	56	1	molodtsov	molodtsov	PROPN
ejpam-5839	57	1	[	[	X
ejpam-5839	57	2	17	17	NUM
ejpam-5839	57	3	]	]	PUNCT
ejpam-5839	57	4	established	establish	VERB
ejpam-5839	57	5	a	a	DET
ejpam-5839	57	6	connection	connection	NOUN
ejpam-5839	57	7	between	between	ADP
ejpam-5839	57	8	soft	soft	ADJ
ejpam-5839	57	9	sets	set	NOUN
ejpam-5839	57	10	and	and	CCONJ
ejpam-5839	57	11	fuzzy	fuzzy	ADJ
ejpam-5839	57	12	sets	set	NOUN
ejpam-5839	57	13	,	,	PUNCT
ejpam-5839	57	14	leading	lead	VERB
ejpam-5839	57	15	to	to	ADP
ejpam-5839	57	16	the	the	DET
ejpam-5839	57	17	development	development	NOUN
ejpam-5839	57	18	of	of	ADP
ejpam-5839	57	19	a	a	DET
ejpam-5839	57	20	hybrid	hybrid	ADJ
ejpam-5839	57	21	theory	theory	NOUN
ejpam-5839	57	22	known	know	VERB
ejpam-5839	57	23	as	as	ADP
ejpam-5839	57	24	fuzzy	fuzzy	ADJ
ejpam-5839	57	25	soft	soft	ADJ
ejpam-5839	57	26	set	set	NOUN
ejpam-5839	57	27	theory	theory	NOUN
ejpam-5839	57	28	(	(	PUNCT
ejpam-5839	57	29	fsst	fsst	NOUN
ejpam-5839	57	30	)	)	PUNCT
ejpam-5839	57	31	.	.	PUNCT
ejpam-5839	58	1	wang	wang	PROPN
ejpam-5839	58	2	et	et	PROPN
ejpam-5839	58	3	al	al	PROPN
ejpam-5839	58	4	.	.	PUNCT
ejpam-5839	59	1	[	[	X
ejpam-5839	59	2	18	18	NUM
ejpam-5839	59	3	]	]	PUNCT
ejpam-5839	59	4	introduced	introduce	VERB
ejpam-5839	59	5	the	the	DET
ejpam-5839	59	6	concept	concept	NOUN
ejpam-5839	59	7	of	of	ADP
ejpam-5839	59	8	hfss	hfss	NOUN
ejpam-5839	59	9	and	and	CCONJ
ejpam-5839	59	10	effectively	effectively	ADV
ejpam-5839	59	11	applied	apply	VERB
ejpam-5839	59	12	it	it	PRON
ejpam-5839	59	13	in	in	ADP
ejpam-5839	59	14	multi	multi	ADJ
ejpam-5839	59	15	-	-	ADJ
ejpam-5839	59	16	criteria	criterion	NOUN
ejpam-5839	59	17	decision	decision	NOUN
ejpam-5839	59	18	-	-	PUNCT
ejpam-5839	59	19	making	make	VERB
ejpam-5839	59	20	problems	problem	NOUN
ejpam-5839	59	21	.	.	PUNCT
ejpam-5839	60	1	pei	pei	PROPN
ejpam-5839	60	2	and	and	CCONJ
ejpam-5839	60	3	miao	miao	PROPN
ejpam-5839	61	1	[	[	X
ejpam-5839	61	2	19	19	NUM
ejpam-5839	61	3	]	]	PUNCT
ejpam-5839	61	4	bridged	bridge	VERB
ejpam-5839	61	5	soft	soft	ADJ
ejpam-5839	61	6	sets	set	NOUN
ejpam-5839	61	7	with	with	ADP
ejpam-5839	61	8	information	information	NOUN
ejpam-5839	61	9	theory	theory	NOUN
ejpam-5839	61	10	,	,	PUNCT
ejpam-5839	61	11	discussing	discuss	VERB
ejpam-5839	61	12	their	their	PRON
ejpam-5839	61	13	practical	practical	ADJ
ejpam-5839	61	14	applications	application	NOUN
ejpam-5839	61	15	.	.	PUNCT
ejpam-5839	62	1	john	john	PROPN
ejpam-5839	63	1	[	[	X
ejpam-5839	63	2	20–22	20–22	X
ejpam-5839	63	3	]	]	PUNCT
ejpam-5839	63	4	explored	explore	VERB
ejpam-5839	63	5	various	various	ADJ
ejpam-5839	63	6	structures	structure	NOUN
ejpam-5839	63	7	based	base	VERB
ejpam-5839	63	8	on	on	ADP
ejpam-5839	63	9	sst	sst	NOUN
ejpam-5839	63	10	,	,	PUNCT
ejpam-5839	63	11	offering	offer	VERB
ejpam-5839	63	12	examples	example	NOUN
ejpam-5839	63	13	and	and	CCONJ
ejpam-5839	63	14	applications	application	NOUN
ejpam-5839	63	15	across	across	ADP
ejpam-5839	63	16	different	different	ADJ
ejpam-5839	63	17	areas	area	NOUN
ejpam-5839	63	18	of	of	ADP
ejpam-5839	63	19	mathematics	mathematic	NOUN
ejpam-5839	63	20	.	.	PUNCT
ejpam-5839	64	1	al	al	PROPN
ejpam-5839	64	2	-	-	PUNCT
ejpam-5839	64	3	shami	shami	PROPN
ejpam-5839	64	4	et	et	PROPN
ejpam-5839	64	5	al	al	PROPN
ejpam-5839	64	6	.	.	PUNCT
ejpam-5839	65	1	[	[	X
ejpam-5839	65	2	23	23	NUM
ejpam-5839	65	3	]	]	PUNCT
ejpam-5839	65	4	proposed	propose	VERB
ejpam-5839	65	5	a	a	DET
ejpam-5839	65	6	new	new	ADJ
ejpam-5839	65	7	structure	structure	NOUN
ejpam-5839	65	8	known	know	VERB
ejpam-5839	65	9	as	as	ADP
ejpam-5839	65	10	menger	menger	PROPN
ejpam-5839	65	11	space	space	NOUN
ejpam-5839	65	12	.	.	PUNCT
ejpam-5839	66	1	al	al	PROPN
ejpam-5839	66	2	-	-	PUNCT
ejpam-5839	66	3	shami	shami	PROPN
ejpam-5839	66	4	et	et	PROPN
ejpam-5839	66	5	al	al	PROPN
ejpam-5839	66	6	.	.	PUNCT
ejpam-5839	67	1	[	[	X
ejpam-5839	67	2	24	24	NUM
ejpam-5839	67	3	]	]	PUNCT
ejpam-5839	67	4	investigated	investigate	VERB
ejpam-5839	67	5	the	the	DET
ejpam-5839	67	6	structure	structure	NOUN
ejpam-5839	67	7	of	of	ADP
ejpam-5839	67	8	infra	infra	NOUN
ejpam-5839	67	9	soft	soft	ADJ
ejpam-5839	67	10	topological	topological	ADJ
ejpam-5839	67	11	spaces	space	NOUN
ejpam-5839	67	12	(	(	PUNCT
ejpam-5839	67	13	ists	ist	NOUN
ejpam-5839	67	14	)	)	PUNCT
ejpam-5839	67	15	with	with	ADP
ejpam-5839	67	16	respect	respect	NOUN
ejpam-5839	67	17	to	to	ADP
ejpam-5839	67	18	crisp	crisp	ADJ
ejpam-5839	67	19	points	point	NOUN
ejpam-5839	67	20	.	.	PUNCT
ejpam-5839	68	1	al	al	PROPN
ejpam-5839	68	2	-	-	PUNCT
ejpam-5839	68	3	shami	shami	PROPN
ejpam-5839	68	4	et	et	PROPN
ejpam-5839	68	5	al	al	PROPN
ejpam-5839	68	6	.	.	PUNCT
ejpam-5839	69	1	[	[	X
ejpam-5839	69	2	25	25	NUM
ejpam-5839	69	3	]	]	PUNCT
ejpam-5839	69	4	discussed	discuss	VERB
ejpam-5839	69	5	weak	weak	ADJ
ejpam-5839	69	6	forms	form	NOUN
ejpam-5839	69	7	of	of	ADP
ejpam-5839	69	8	soft	soft	ADJ
ejpam-5839	69	9	separation	separation	NOUN
ejpam-5839	69	10	axioms	axiom	NOUN
ejpam-5839	69	11	and	and	CCONJ
ejpam-5839	69	12	fixed	fix	VERB
ejpam-5839	69	13	points	point	NOUN
ejpam-5839	69	14	.	.	PUNCT
ejpam-5839	70	1	al	al	PROPN
ejpam-5839	70	2	-	-	PUNCT
ejpam-5839	70	3	shami	shami	PROPN
ejpam-5839	70	4	et	et	PROPN
ejpam-5839	70	5	al	al	PROPN
ejpam-5839	70	6	.	.	PUNCT
ejpam-5839	71	1	[	[	X
ejpam-5839	71	2	26	26	NUM
ejpam-5839	71	3	]	]	SYM
ejpam-5839	71	4	defined	define	VERB
ejpam-5839	71	5	concepts	concept	NOUN
ejpam-5839	71	6	of	of	ADP
ejpam-5839	71	7	connectedness	connectedness	NOUN
ejpam-5839	71	8	and	and	CCONJ
ejpam-5839	71	9	local	local	ADJ
ejpam-5839	71	10	connectedness	connectedness	NOUN
ejpam-5839	71	11	within	within	ADP
ejpam-5839	71	12	the	the	DET
ejpam-5839	71	13	context	context	NOUN
ejpam-5839	71	14	of	of	ADP
ejpam-5839	71	15	infra	infra	NOUN
ejpam-5839	71	16	soft	soft	ADJ
ejpam-5839	71	17	topological	topological	ADJ
ejpam-5839	71	18	spaces	space	NOUN
ejpam-5839	71	19	,	,	PUNCT
ejpam-5839	71	20	presenting	present	VERB
ejpam-5839	71	21	several	several	ADJ
ejpam-5839	71	22	results	result	NOUN
ejpam-5839	71	23	related	relate	VERB
ejpam-5839	71	24	to	to	ADP
ejpam-5839	71	25	this	this	DET
ejpam-5839	71	26	strong	strong	ADJ
ejpam-5839	71	27	structure	structure	NOUN
ejpam-5839	71	28	.	.	PUNCT
ejpam-5839	72	1	al	al	PROPN
ejpam-5839	72	2	-	-	PUNCT
ejpam-5839	72	3	shami	shami	PROPN
ejpam-5839	72	4	[	[	X
ejpam-5839	72	5	27	27	NUM
ejpam-5839	72	6	]	]	PUNCT
ejpam-5839	72	7	discussed	discuss	VERB
ejpam-5839	72	8	quantum	quantum	ADJ
ejpam-5839	72	9	mechanics	mechanic	NOUN
ejpam-5839	72	10	(	(	PUNCT
ejpam-5839	72	11	qm	qm	PROPN
ejpam-5839	72	12	)	)	PUNCT
ejpam-5839	72	13	in	in	ADP
ejpam-5839	72	14	the	the	DET
ejpam-5839	72	15	framework	framework	NOUN
ejpam-5839	72	16	of	of	ADP
ejpam-5839	72	17	ists	ist	NOUN
ejpam-5839	72	18	.	.	PUNCT
ejpam-5839	73	1	further	further	ADJ
ejpam-5839	73	2	results	result	NOUN
ejpam-5839	73	3	on	on	ADP
ejpam-5839	73	4	ists	ist	NOUN
ejpam-5839	73	5	and	and	CCONJ
ejpam-5839	73	6	soft	soft	ADJ
ejpam-5839	73	7	topological	topological	ADJ
ejpam-5839	73	8	spaces	space	NOUN
ejpam-5839	73	9	(	(	PUNCT
ejpam-5839	73	10	sts	st	NOUN
ejpam-5839	73	11	)	)	PUNCT
ejpam-5839	73	12	were	be	AUX
ejpam-5839	73	13	examined	examine	VERB
ejpam-5839	73	14	in	in	ADP
ejpam-5839	73	15	[	[	X
ejpam-5839	73	16	28	28	NUM
ejpam-5839	73	17	,	,	PUNCT
ejpam-5839	73	18	29	29	NUM
ejpam-5839	73	19	]	]	PUNCT
ejpam-5839	73	20	.	.	PUNCT
ejpam-5839	74	1	ozturk	ozturk	PROPN
ejpam-5839	74	2	et	et	PROPN
ejpam-5839	74	3	al	al	PROPN
ejpam-5839	74	4	.	.	PUNCT
ejpam-5839	75	1	[	[	X
ejpam-5839	75	2	30	30	NUM
ejpam-5839	75	3	]	]	PUNCT
ejpam-5839	75	4	introduced	introduce	VERB
ejpam-5839	75	5	new	new	ADJ
ejpam-5839	75	6	operators	operator	NOUN
ejpam-5839	75	7	in	in	ADP
ejpam-5839	75	8	neutrosophic	neutrosophic	ADJ
ejpam-5839	75	9	soft	soft	ADJ
ejpam-5839	75	10	topological	topological	ADJ
ejpam-5839	75	11	spaces	space	NOUN
ejpam-5839	75	12	(	(	PUNCT
ejpam-5839	75	13	nsts	nst	NOUN
ejpam-5839	75	14	)	)	PUNCT
ejpam-5839	75	15	,	,	PUNCT
ejpam-5839	75	16	leading	lead	VERB
ejpam-5839	75	17	to	to	ADP
ejpam-5839	75	18	novel	novel	ADJ
ejpam-5839	75	19	approaches	approach	NOUN
ejpam-5839	75	20	to	to	ADP
ejpam-5839	75	21	several	several	ADJ
ejpam-5839	75	22	existing	exist	VERB
ejpam-5839	75	23	results	result	NOUN
ejpam-5839	75	24	,	,	PUNCT
ejpam-5839	75	25	with	with	ADP
ejpam-5839	75	26	numerous	numerous	ADJ
ejpam-5839	75	27	examples	example	NOUN
ejpam-5839	75	28	provided	provide	VERB
ejpam-5839	75	29	for	for	ADP
ejpam-5839	75	30	clarification	clarification	NOUN
ejpam-5839	75	31	.	.	PUNCT
ejpam-5839	76	1	ahmad	ahmad	PROPN
ejpam-5839	76	2	et	et	PROPN
ejpam-5839	76	3	al	al	PROPN
ejpam-5839	76	4	.	.	PUNCT
ejpam-5839	77	1	[	[	X
ejpam-5839	77	2	31	31	NUM
ejpam-5839	77	3	]	]	PUNCT
ejpam-5839	77	4	discussed	discuss	VERB
ejpam-5839	77	5	irreversible	irreversible	ADJ
ejpam-5839	77	6	k	k	ADJ
ejpam-5839	77	7	-	-	PUNCT
ejpam-5839	77	8	threshold	threshold	NOUN
ejpam-5839	77	9	conversion	conversion	NOUN
ejpam-5839	77	10	number	number	NOUN
ejpam-5839	77	11	for	for	ADP
ejpam-5839	77	12	some	some	DET
ejpam-5839	77	13	graph	graph	NOUN
ejpam-5839	77	14	products	product	NOUN
ejpam-5839	77	15	and	and	CCONJ
ejpam-5839	77	16	neutrosophic	neutrosophic	ADJ
ejpam-5839	77	17	graphs	graph	NOUN
ejpam-5839	77	18	.	.	PUNCT
ejpam-5839	78	1	hatamleh	hatamleh	ADJ
ejpam-5839	78	2	et	et	PROPN
ejpam-5839	78	3	al	al	PROPN
ejpam-5839	78	4	.	.	PUNCT
ejpam-5839	79	1	[	[	X
ejpam-5839	79	2	32	32	NUM
ejpam-5839	79	3	]	]	PUNCT
ejpam-5839	79	4	studied	study	VERB
ejpam-5839	79	5	complex	complex	ADJ
ejpam-5839	79	6	tangent	tangent	NOUN
ejpam-5839	79	7	trigonometric	trigonometric	ADJ
ejpam-5839	79	8	approach	approach	NOUN
ejpam-5839	79	9	applied	apply	VERB
ejpam-5839	79	10	to	to	ADP
ejpam-5839	79	11	q	q	ADJ
ejpam-5839	79	12	-	-	PUNCT
ejpam-5839	79	13	rung	rung	ADJ
ejpam-5839	79	14	fuzzy	fuzzy	ADJ
ejpam-5839	79	15	set	set	NOUN
ejpam-5839	79	16	using	use	VERB
ejpam-5839	79	17	weighted	weight	VERB
ejpam-5839	79	18	averaging	averaging	NOUN
ejpam-5839	79	19	,	,	PUNCT
ejpam-5839	79	20	geometric	geometric	ADJ
ejpam-5839	79	21	operators	operator	NOUN
ejpam-5839	79	22	and	and	CCONJ
ejpam-5839	79	23	its	its	PRON
ejpam-5839	79	24	extension	extension	NOUN
ejpam-5839	79	25	.	.	PUNCT
ejpam-5839	80	1	hatamleh	hatamleh	ADJ
ejpam-5839	80	2	et	et	PROPN
ejpam-5839	80	3	al	al	PROPN
ejpam-5839	80	4	.	.	PUNCT
ejpam-5839	81	1	[	[	X
ejpam-5839	81	2	33	33	NUM
ejpam-5839	81	3	]	]	PUNCT
ejpam-5839	81	4	studied	study	VERB
ejpam-5839	81	5	different	different	ADJ
ejpam-5839	81	6	weighted	weight	VERB
ejpam-5839	81	7	operators	operator	NOUN
ejpam-5839	81	8	such	such	ADJ
ejpam-5839	81	9	as	as	ADP
ejpam-5839	81	10	generalized	generalized	ADJ
ejpam-5839	81	11	averaging	averaging	NOUN
ejpam-5839	81	12	and	and	CCONJ
ejpam-5839	81	13	generalized	generalized	ADJ
ejpam-5839	81	14	geometric	geometric	NOUN
ejpam-5839	81	15	based	base	VERB
ejpam-5839	81	16	on	on	ADP
ejpam-5839	81	17	trigonometric	trigonometric	ADJ
ejpam-5839	81	18	p	p	ADJ
ejpam-5839	81	19	-	-	PUNCT
ejpam-5839	81	20	rung	rung	ADJ
ejpam-5839	81	21	interval	interval	NOUN
ejpam-5839	81	22	-	-	PUNCT
ejpam-5839	81	23	valued	value	VERB
ejpam-5839	81	24	approach	approach	NOUN
ejpam-5839	81	25	and	and	CCONJ
ejpam-5839	81	26	in	in	ADP
ejpam-5839	81	27	addition	addition	NOUN
ejpam-5839	81	28	to	to	ADP
ejpam-5839	81	29	this	this	PRON
ejpam-5839	81	30	some	some	DET
ejpam-5839	81	31	examples	example	NOUN
ejpam-5839	81	32	were	be	AUX
ejpam-5839	81	33	given	give	VERB
ejpam-5839	81	34	for	for	ADP
ejpam-5839	81	35	clear	clear	ADJ
ejpam-5839	81	36	understanding	understanding	NOUN
ejpam-5839	81	37	.	.	PUNCT
ejpam-5839	82	1	shihadeh	shihadeh	VERB
ejpam-5839	82	2	et	et	PROPN
ejpam-5839	82	3	al	al	PROPN
ejpam-5839	82	4	.	.	PUNCT
ejpam-5839	83	1	[	[	X
ejpam-5839	83	2	34	34	NUM
ejpam-5839	83	3	]	]	PUNCT
ejpam-5839	83	4	discussed	discuss	VERB
ejpam-5839	83	5	algebraic	algebraic	ADJ
ejpam-5839	83	6	structures	structure	NOUN
ejpam-5839	83	7	towards	towards	ADP
ejpam-5839	83	8	different	different	ADJ
ejpam-5839	83	9	intuitionistic	intuitionistic	ADJ
ejpam-5839	83	10	fuzzy	fuzzy	ADJ
ejpam-5839	83	11	ideals	ideal	NOUN
ejpam-5839	83	12	and	and	CCONJ
ejpam-5839	83	13	its	its	PRON
ejpam-5839	83	14	characterization	characterization	NOUN
ejpam-5839	83	15	of	of	ADP
ejpam-5839	83	16	an	an	DET
ejpam-5839	83	17	ordered	order	VERB
ejpam-5839	83	18	ternary	ternary	ADJ
ejpam-5839	83	19	semigroup	semigroup	NOUN
ejpam-5839	83	20	.	.	PUNCT
ejpam-5839	84	1	hatamleh	hatamleh	PROPN
ejpam-5839	84	2	et	et	PROPN
ejpam-5839	84	3	al	al	PROPN
ejpam-5839	84	4	.	.	PUNCT
ejpam-5839	85	1	[	[	X
ejpam-5839	85	2	35	35	NUM
ejpam-5839	85	3	,	,	PUNCT
ejpam-5839	85	4	36	36	NUM
ejpam-5839	85	5	]	]	PUNCT
ejpam-5839	85	6	studied	study	VERB
ejpam-5839	85	7	operators	operator	NOUN
ejpam-5839	85	8	via	via	ADP
ejpam-5839	85	9	weighted	weighted	ADJ
ejpam-5839	85	10	averaging	averaging	NOUN
ejpam-5839	85	11	and	and	CCONJ
ejpam-5839	85	12	geometric	geometric	ADJ
ejpam-5839	85	13	approach	approach	NOUN
ejpam-5839	85	14	using	use	VERB
ejpam-5839	85	15	trigonometric	trigonometric	ADJ
ejpam-5839	85	16	neutrosophic	neutrosophic	ADJ
ejpam-5839	85	17	interval	interval	NOUN
ejpam-5839	85	18	-	-	PUNCT
ejpam-5839	85	19	valued	value	VERB
ejpam-5839	85	20	set	set	NOUN
ejpam-5839	85	21	and	and	CCONJ
ejpam-5839	85	22	its	its	PRON
ejpam-5839	85	23	extension	extension	NOUN
ejpam-5839	85	24	and	and	CCONJ
ejpam-5839	85	25	characterization	characterization	NOUN
ejpam-5839	85	26	of	of	ADP
ejpam-5839	85	27	interaction	interaction	NOUN
ejpam-5839	85	28	aggregating	aggregate	VERB
ejpam-5839	85	29	operators	operator	NOUN
ejpam-5839	85	30	setting	set	VERB
ejpam-5839	85	31	interval	interval	NOUN
ejpam-5839	85	32	-	-	PUNCT
ejpam-5839	85	33	valued	value	VERB
ejpam-5839	85	34	pythagorean	pythagorean	PROPN
ejpam-5839	85	35	neutrosophic	neutrosophic	PROPN
ejpam-5839	85	36	set	set	PROPN
ejpam-5839	85	37	.	.	PUNCT
ejpam-5839	86	1	hatamleh	hatamleh	PROPN
ejpam-5839	86	2	et	et	PROPN
ejpam-5839	86	3	al	al	PROPN
ejpam-5839	86	4	.	.	PUNCT
ejpam-5839	87	1	[	[	X
ejpam-5839	87	2	37	37	NUM
ejpam-5839	87	3	]	]	PUNCT
ejpam-5839	87	4	discussed	discuss	VERB
ejpam-5839	87	5	applications	application	NOUN
ejpam-5839	87	6	of	of	ADP
ejpam-5839	87	7	complex	complex	ADJ
ejpam-5839	87	8	interval	interval	NOUN
ejpam-5839	87	9	-	-	PUNCT
ejpam-5839	87	10	valued	value	VERB
ejpam-5839	87	11	picture	picture	NOUN
ejpam-5839	87	12	fuzzy	fuzzy	ADJ
ejpam-5839	87	13	soft	soft	ADJ
ejpam-5839	87	14	a.	a.	NOUN
ejpam-5839	87	15	shihadeh	shihadeh	NOUN
ejpam-5839	87	16	et	et	PROPN
ejpam-5839	87	17	al	al	PROPN
ejpam-5839	87	18	.	.	PUNCT
ejpam-5839	87	19	/	/	SYM
ejpam-5839	87	20	eur	eur	PROPN
ejpam-5839	87	21	.	.	PUNCT
ejpam-5839	88	1	j.	j.	PROPN
ejpam-5839	88	2	pure	pure	PROPN
ejpam-5839	88	3	appl	appl	PROPN
ejpam-5839	88	4	.	.	PROPN
ejpam-5839	88	5	math	math	PROPN
ejpam-5839	88	6	,	,	PUNCT
ejpam-5839	88	7	18	18	NUM
ejpam-5839	88	8	(	(	PUNCT
ejpam-5839	88	9	2	2	NUM
ejpam-5839	88	10	)	)	PUNCT
ejpam-5839	88	11	(	(	PUNCT
ejpam-5839	88	12	2025	2025	NUM
ejpam-5839	88	13	)	)	PUNCT
ejpam-5839	88	14	,	,	PUNCT
ejpam-5839	88	15	5839	5839	NUM
ejpam-5839	88	16	3	3	NUM
ejpam-5839	88	17	of	of	ADP
ejpam-5839	88	18	54	54	NUM
ejpam-5839	88	19	relations	relation	NOUN
ejpam-5839	88	20	.	.	PUNCT
ejpam-5839	89	1	el	el	ADJ
ejpam-5839	89	2	-	-	PUNCT
ejpam-5839	89	3	sheikh	sheikh	PROPN
ejpam-5839	89	4	and	and	CCONJ
ejpam-5839	89	5	abd	abd	PROPN
ejpam-5839	89	6	el	el	PROPN
ejpam-5839	89	7	-	-	PROPN
ejpam-5839	89	8	latif	latif	PROPN
ejpam-5839	89	9	[	[	X
ejpam-5839	89	10	38	38	NUM
ejpam-5839	89	11	]	]	PUNCT
ejpam-5839	89	12	discussed	discuss	VERB
ejpam-5839	89	13	decompositions	decomposition	NOUN
ejpam-5839	89	14	of	of	ADP
ejpam-5839	89	15	some	some	DET
ejpam-5839	89	16	types	type	NOUN
ejpam-5839	89	17	of	of	ADP
ejpam-5839	89	18	supra	supra	ADJ
ejpam-5839	89	19	soft	soft	ADJ
ejpam-5839	89	20	sets	set	NOUN
ejpam-5839	89	21	and	and	CCONJ
ejpam-5839	89	22	soft	soft	ADJ
ejpam-5839	89	23	continuity	continuity	NOUN
ejpam-5839	89	24	and	and	CCONJ
ejpam-5839	89	25	cited	cite	VERB
ejpam-5839	89	26	some	some	DET
ejpam-5839	89	27	excellent	excellent	ADJ
ejpam-5839	89	28	examples	example	NOUN
ejpam-5839	89	29	for	for	ADP
ejpam-5839	89	30	clear	clear	ADJ
ejpam-5839	89	31	understanding	understanding	NOUN
ejpam-5839	89	32	of	of	ADP
ejpam-5839	89	33	the	the	DET
ejpam-5839	89	34	concept	concept	NOUN
ejpam-5839	89	35	.	.	PUNCT
ejpam-5839	90	1	abd	abd	PROPN
ejpam-5839	90	2	el	el	PROPN
ejpam-5839	90	3	-	-	PROPN
ejpam-5839	90	4	latif	latif	PROPN
ejpam-5839	90	5	[	[	X
ejpam-5839	90	6	39	39	NUM
ejpam-5839	90	7	]	]	PUNCT
ejpam-5839	90	8	discussed	discuss	VERB
ejpam-5839	90	9	soft	soft	ADJ
ejpam-5839	90	10	supra	supra	ADJ
ejpam-5839	90	11	compactness	compactness	NOUN
ejpam-5839	90	12	in	in	ADP
ejpam-5839	90	13	supra	supra	PROPN
ejpam-5839	90	14	soft	soft	ADJ
ejpam-5839	90	15	topological	topological	ADJ
ejpam-5839	90	16	spaces	space	NOUN
ejpam-5839	90	17	.	.	PUNCT
ejpam-5839	91	1	abd	abd	PROPN
ejpam-5839	91	2	el	el	PROPN
ejpam-5839	91	3	-	-	PROPN
ejpam-5839	91	4	latif	latif	PROPN
ejpam-5839	91	5	and	and	CCONJ
ejpam-5839	91	6	hosny	hosny	PROPN
ejpam-5839	92	1	[	[	X
ejpam-5839	92	2	40	40	NUM
ejpam-5839	92	3	]	]	PUNCT
ejpam-5839	92	4	discussed	discuss	VERB
ejpam-5839	92	5	the	the	DET
ejpam-5839	92	6	eye	eye	NOUN
ejpam-5839	92	7	-	-	PUNCT
ejpam-5839	92	8	catching	catch	VERB
ejpam-5839	92	9	concept	concept	NOUN
ejpam-5839	92	10	of	of	ADP
ejpam-5839	92	11	soft	soft	ADJ
ejpam-5839	92	12	separation	separation	NOUN
ejpam-5839	92	13	axioms	axiom	NOUN
ejpam-5839	92	14	and	and	CCONJ
ejpam-5839	92	15	provided	provide	VERB
ejpam-5839	92	16	examples	example	NOUN
ejpam-5839	92	17	.	.	PUNCT
ejpam-5839	93	1	abd	abd	PROPN
ejpam-5839	93	2	el	el	PROPN
ejpam-5839	93	3	-	-	PROPN
ejpam-5839	93	4	latif	latif	PROPN
ejpam-5839	93	5	and	and	CCONJ
ejpam-5839	93	6	hosny	hosny	PROPN
ejpam-5839	93	7	discussed	discuss	VERB
ejpam-5839	93	8	some	some	DET
ejpam-5839	93	9	more	more	ADJ
ejpam-5839	93	10	structures	structure	NOUN
ejpam-5839	93	11	in	in	ADP
ejpam-5839	93	12	[	[	X
ejpam-5839	93	13	41	41	NUM
ejpam-5839	93	14	,	,	PUNCT
ejpam-5839	93	15	42	42	NUM
ejpam-5839	93	16	]	]	PUNCT
ejpam-5839	93	17	.	.	PUNCT
ejpam-5839	94	1	1.1	1.1	NUM
ejpam-5839	94	2	.	.	PUNCT
ejpam-5839	94	3	research	research	NOUN
ejpam-5839	94	4	gap	gap	NOUN
ejpam-5839	94	5	while	while	SCONJ
ejpam-5839	94	6	neutrosophic	neutrosophic	ADJ
ejpam-5839	94	7	set	set	NOUN
ejpam-5839	94	8	theory	theory	NOUN
ejpam-5839	94	9	(	(	PUNCT
ejpam-5839	94	10	nst	nst	PROPN
ejpam-5839	94	11	)	)	PUNCT
ejpam-5839	94	12	extends	extend	VERB
ejpam-5839	94	13	intuitionistic	intuitionistic	ADJ
ejpam-5839	94	14	fuzzy	fuzzy	ADJ
ejpam-5839	94	15	set	set	NOUN
ejpam-5839	94	16	theory	theory	NOUN
ejpam-5839	94	17	(	(	PUNCT
ejpam-5839	94	18	ifst	ifst	NOUN
ejpam-5839	94	19	)	)	PUNCT
ejpam-5839	94	20	by	by	ADP
ejpam-5839	94	21	introducing	introduce	VERB
ejpam-5839	94	22	a	a	DET
ejpam-5839	94	23	third	third	ADJ
ejpam-5839	94	24	possibility	possibility	NOUN
ejpam-5839	94	25	for	for	ADP
ejpam-5839	94	26	uncertainty	uncertainty	NOUN
ejpam-5839	94	27	representation	representation	NOUN
ejpam-5839	94	28	,	,	PUNCT
ejpam-5839	94	29	the	the	DET
ejpam-5839	94	30	extension	extension	NOUN
ejpam-5839	94	31	to	to	ADP
ejpam-5839	94	32	quadri	quadri	VERB
ejpam-5839	94	33	-	-	PUNCT
ejpam-5839	94	34	partitioned	partition	VERB
ejpam-5839	94	35	neutrosophic	neutrosophic	ADJ
ejpam-5839	94	36	set	set	NOUN
ejpam-5839	94	37	theory	theory	NOUN
ejpam-5839	94	38	(	(	PUNCT
ejpam-5839	94	39	qpnst	qpnst	ADJ
ejpam-5839	94	40	)	)	PUNCT
ejpam-5839	94	41	,	,	PUNCT
ejpam-5839	94	42	which	which	PRON
ejpam-5839	94	43	introduces	introduce	VERB
ejpam-5839	94	44	a	a	DET
ejpam-5839	94	45	fourth	fourth	ADJ
ejpam-5839	94	46	possibility	possibility	NOUN
ejpam-5839	94	47	,	,	PUNCT
ejpam-5839	94	48	remains	remain	VERB
ejpam-5839	94	49	underexplored	underexplored	ADJ
ejpam-5839	94	50	.	.	PUNCT
ejpam-5839	95	1	additionally	additionally	ADV
ejpam-5839	95	2	,	,	PUNCT
ejpam-5839	95	3	the	the	DET
ejpam-5839	95	4	application	application	NOUN
ejpam-5839	95	5	of	of	ADP
ejpam-5839	95	6	qpnst	qpnst	ADJ
ejpam-5839	95	7	to	to	ADP
ejpam-5839	95	8	classical	classical	ADJ
ejpam-5839	95	9	mathematical	mathematical	ADJ
ejpam-5839	95	10	theories	theory	NOUN
ejpam-5839	95	11	,	,	PUNCT
ejpam-5839	95	12	such	such	ADJ
ejpam-5839	95	13	as	as	ADP
ejpam-5839	95	14	the	the	DET
ejpam-5839	95	15	riemann	riemann	PROPN
ejpam-5839	95	16	integral	integral	PROPN
ejpam-5839	95	17	,	,	PUNCT
ejpam-5839	95	18	has	have	AUX
ejpam-5839	95	19	not	not	PART
ejpam-5839	95	20	been	be	AUX
ejpam-5839	95	21	rigorously	rigorously	ADV
ejpam-5839	95	22	studied	study	VERB
ejpam-5839	95	23	.	.	PUNCT
ejpam-5839	96	1	there	there	PRON
ejpam-5839	96	2	is	be	VERB
ejpam-5839	96	3	a	a	DET
ejpam-5839	96	4	lack	lack	NOUN
ejpam-5839	96	5	of	of	ADP
ejpam-5839	96	6	formal	formal	ADJ
ejpam-5839	96	7	mathematical	mathematical	ADJ
ejpam-5839	96	8	analysis	analysis	NOUN
ejpam-5839	96	9	and	and	CCONJ
ejpam-5839	96	10	numerical	numerical	ADJ
ejpam-5839	96	11	exploration	exploration	NOUN
ejpam-5839	96	12	of	of	ADP
ejpam-5839	96	13	the	the	DET
ejpam-5839	96	14	properties	property	NOUN
ejpam-5839	96	15	of	of	ADP
ejpam-5839	96	16	the	the	DET
ejpam-5839	96	17	riemann	riemann	PROPN
ejpam-5839	96	18	integral	integral	NOUN
ejpam-5839	96	19	within	within	ADP
ejpam-5839	96	20	the	the	DET
ejpam-5839	96	21	qpnst	qpnst	ADJ
ejpam-5839	96	22	framework	framework	NOUN
ejpam-5839	96	23	,	,	PUNCT
ejpam-5839	96	24	particularly	particularly	ADV
ejpam-5839	96	25	with	with	ADP
ejpam-5839	96	26	respect	respect	NOUN
ejpam-5839	96	27	to	to	ADP
ejpam-5839	96	28	the	the	DET
ejpam-5839	96	29	behavior	behavior	NOUN
ejpam-5839	96	30	of	of	ADP
ejpam-5839	96	31	the	the	DET
ejpam-5839	96	32	quadri	quadri	NOUN
ejpam-5839	96	33	-	-	PUNCT
ejpam-5839	96	34	partitioned	partition	VERB
ejpam-5839	96	35	neutrosophic	neutrosophic	ADJ
ejpam-5839	96	36	riemann	riemann	PROPN
ejpam-5839	96	37	integral	integral	ADJ
ejpam-5839	96	38	theory	theory	NOUN
ejpam-5839	96	39	(	(	PUNCT
ejpam-5839	96	40	qpnrit	qpnrit	NOUN
ejpam-5839	96	41	)	)	PUNCT
ejpam-5839	96	42	.	.	PUNCT
ejpam-5839	97	1	this	this	DET
ejpam-5839	97	2	research	research	NOUN
ejpam-5839	97	3	gap	gap	NOUN
ejpam-5839	97	4	hinders	hinder	VERB
ejpam-5839	97	5	a	a	DET
ejpam-5839	97	6	deeper	deep	ADJ
ejpam-5839	97	7	understanding	understanding	NOUN
ejpam-5839	97	8	of	of	ADP
ejpam-5839	97	9	how	how	SCONJ
ejpam-5839	97	10	higher	high	ADJ
ejpam-5839	97	11	-	-	PUNCT
ejpam-5839	97	12	order	order	NOUN
ejpam-5839	97	13	uncertainty	uncertainty	NOUN
ejpam-5839	97	14	models	model	NOUN
ejpam-5839	97	15	can	can	AUX
ejpam-5839	97	16	be	be	AUX
ejpam-5839	97	17	integrated	integrate	VERB
ejpam-5839	97	18	into	into	ADP
ejpam-5839	97	19	classical	classical	ADJ
ejpam-5839	97	20	mathematical	mathematical	ADJ
ejpam-5839	97	21	analysis	analysis	NOUN
ejpam-5839	97	22	.	.	PUNCT
ejpam-5839	98	1	1.2	1.2	NUM
ejpam-5839	98	2	.	.	PUNCT
ejpam-5839	99	1	motivation	motivation	VERB
ejpam-5839	99	2	the	the	DET
ejpam-5839	99	3	research	research	NOUN
ejpam-5839	99	4	on	on	ADP
ejpam-5839	99	5	neutrosophic	neutrosophic	ADJ
ejpam-5839	99	6	riemann	riemann	PROPN
ejpam-5839	99	7	integration	integration	NOUN
ejpam-5839	99	8	and	and	CCONJ
ejpam-5839	99	9	its	its	PRON
ejpam-5839	99	10	properties	property	NOUN
ejpam-5839	99	11	[	[	X
ejpam-5839	99	12	43	43	NUM
ejpam-5839	99	13	]	]	PUNCT
ejpam-5839	99	14	,	,	PUNCT
ejpam-5839	99	15	which	which	PRON
ejpam-5839	99	16	delves	delve	VERB
ejpam-5839	99	17	into	into	ADP
ejpam-5839	99	18	neutrosophic	neutrosophic	ADJ
ejpam-5839	99	19	riemann	riemann	PROPN
ejpam-5839	99	20	set	set	PROPN
ejpam-5839	99	21	theory	theory	NOUN
ejpam-5839	99	22	,	,	PUNCT
ejpam-5839	99	23	provided	provide	VERB
ejpam-5839	99	24	a	a	DET
ejpam-5839	99	25	foundational	foundational	ADJ
ejpam-5839	99	26	understanding	understanding	NOUN
ejpam-5839	99	27	of	of	ADP
ejpam-5839	99	28	integrating	integrate	VERB
ejpam-5839	99	29	neutrosophic	neutrosophic	ADJ
ejpam-5839	99	30	functions	function	NOUN
ejpam-5839	99	31	.	.	PUNCT
ejpam-5839	100	1	this	this	DET
ejpam-5839	100	2	exploration	exploration	NOUN
ejpam-5839	100	3	highlighted	highlight	VERB
ejpam-5839	100	4	the	the	DET
ejpam-5839	100	5	limitations	limitation	NOUN
ejpam-5839	100	6	and	and	CCONJ
ejpam-5839	100	7	potential	potential	NOUN
ejpam-5839	100	8	for	for	ADP
ejpam-5839	100	9	further	further	ADJ
ejpam-5839	100	10	development	development	NOUN
ejpam-5839	100	11	in	in	ADP
ejpam-5839	100	12	the	the	DET
ejpam-5839	100	13	field	field	NOUN
ejpam-5839	100	14	.	.	PUNCT
ejpam-5839	101	1	as	as	ADP
ejpam-5839	101	2	a	a	DET
ejpam-5839	101	3	result	result	NOUN
ejpam-5839	101	4	,	,	PUNCT
ejpam-5839	101	5	it	it	PRON
ejpam-5839	101	6	motivated	motivate	VERB
ejpam-5839	101	7	the	the	DET
ejpam-5839	101	8	development	development	NOUN
ejpam-5839	101	9	of	of	ADP
ejpam-5839	101	10	the	the	DET
ejpam-5839	101	11	theory	theory	NOUN
ejpam-5839	101	12	of	of	ADP
ejpam-5839	101	13	quadripartitioned	quadripartitione	VERB
ejpam-5839	101	14	neutrosophic	neutrosophic	ADJ
ejpam-5839	101	15	riemann	riemann	PROPN
ejpam-5839	101	16	integrals	integral	NOUN
ejpam-5839	101	17	,	,	PUNCT
ejpam-5839	101	18	which	which	PRON
ejpam-5839	101	19	extends	extend	VERB
ejpam-5839	101	20	the	the	DET
ejpam-5839	101	21	concept	concept	NOUN
ejpam-5839	101	22	by	by	ADP
ejpam-5839	101	23	introducing	introduce	VERB
ejpam-5839	101	24	a	a	DET
ejpam-5839	101	25	fourth	fourth	ADJ
ejpam-5839	101	26	partition	partition	NOUN
ejpam-5839	101	27	.	.	PUNCT
ejpam-5839	102	1	this	this	DET
ejpam-5839	102	2	new	new	ADJ
ejpam-5839	102	3	extension	extension	NOUN
ejpam-5839	102	4	allows	allow	VERB
ejpam-5839	102	5	for	for	ADP
ejpam-5839	102	6	a	a	DET
ejpam-5839	102	7	more	more	ADV
ejpam-5839	102	8	comprehensive	comprehensive	ADJ
ejpam-5839	102	9	representation	representation	NOUN
ejpam-5839	102	10	of	of	ADP
ejpam-5839	102	11	uncertainty	uncertainty	NOUN
ejpam-5839	102	12	,	,	PUNCT
ejpam-5839	102	13	offering	offer	VERB
ejpam-5839	102	14	greater	great	ADJ
ejpam-5839	102	15	flexibility	flexibility	NOUN
ejpam-5839	102	16	and	and	CCONJ
ejpam-5839	102	17	accuracy	accuracy	NOUN
ejpam-5839	102	18	in	in	ADP
ejpam-5839	102	19	modeling	model	VERB
ejpam-5839	102	20	complex	complex	ADJ
ejpam-5839	102	21	systems	system	NOUN
ejpam-5839	102	22	with	with	ADP
ejpam-5839	102	23	multiple	multiple	ADJ
ejpam-5839	102	24	layers	layer	NOUN
ejpam-5839	102	25	of	of	ADP
ejpam-5839	102	26	uncertainty	uncertainty	NOUN
ejpam-5839	102	27	.	.	PUNCT
ejpam-5839	103	1	1.3	1.3	NUM
ejpam-5839	103	2	.	.	PUNCT
ejpam-5839	103	3	novelty	novelty	NOUN
ejpam-5839	103	4	the	the	DET
ejpam-5839	103	5	novelty	novelty	NOUN
ejpam-5839	103	6	of	of	ADP
ejpam-5839	103	7	neutrosophic	neutrosophic	ADJ
ejpam-5839	103	8	set	set	NOUN
ejpam-5839	103	9	theory	theory	NOUN
ejpam-5839	103	10	(	(	PUNCT
ejpam-5839	103	11	nst	nst	PROPN
ejpam-5839	103	12	)	)	PUNCT
ejpam-5839	103	13	lies	lie	VERB
ejpam-5839	103	14	in	in	ADP
ejpam-5839	103	15	its	its	PRON
ejpam-5839	103	16	extension	extension	NOUN
ejpam-5839	103	17	of	of	ADP
ejpam-5839	103	18	intuitionistic	intuitionistic	ADJ
ejpam-5839	103	19	fuzzy	fuzzy	ADJ
ejpam-5839	103	20	set	set	NOUN
ejpam-5839	103	21	theory	theory	NOUN
ejpam-5839	103	22	(	(	PUNCT
ejpam-5839	103	23	ifst	ifst	NOUN
ejpam-5839	103	24	)	)	PUNCT
ejpam-5839	103	25	.	.	PUNCT
ejpam-5839	104	1	while	while	SCONJ
ejpam-5839	104	2	ifst	ifst	NOUN
ejpam-5839	104	3	provides	provide	VERB
ejpam-5839	104	4	two	two	NUM
ejpam-5839	104	5	possibilities	possibility	NOUN
ejpam-5839	104	6	for	for	ADP
ejpam-5839	104	7	a	a	DET
ejpam-5839	104	8	set	set	NOUN
ejpam-5839	104	9	’s	’s	PART
ejpam-5839	104	10	complete	complete	ADJ
ejpam-5839	104	11	representation	representation	NOUN
ejpam-5839	104	12	,	,	PUNCT
ejpam-5839	104	13	neutrosophic	neutrosophic	ADJ
ejpam-5839	104	14	set	set	NOUN
ejpam-5839	104	15	theory	theory	NOUN
ejpam-5839	104	16	introduces	introduce	VERB
ejpam-5839	104	17	an	an	DET
ejpam-5839	104	18	additional	additional	ADJ
ejpam-5839	104	19	third	third	ADJ
ejpam-5839	104	20	possibility	possibility	NOUN
ejpam-5839	104	21	,	,	PUNCT
ejpam-5839	104	22	allowing	allow	VERB
ejpam-5839	104	23	for	for	ADP
ejpam-5839	104	24	a	a	DET
ejpam-5839	104	25	more	more	ADV
ejpam-5839	104	26	refined	refined	ADJ
ejpam-5839	104	27	and	and	CCONJ
ejpam-5839	104	28	nuanced	nuanced	ADJ
ejpam-5839	104	29	depiction	depiction	NOUN
ejpam-5839	104	30	of	of	ADP
ejpam-5839	104	31	sets	set	NOUN
ejpam-5839	104	32	.	.	PUNCT
ejpam-5839	105	1	building	build	VERB
ejpam-5839	105	2	upon	upon	SCONJ
ejpam-5839	105	3	this	this	PRON
ejpam-5839	105	4	,	,	PUNCT
ejpam-5839	105	5	our	our	PRON
ejpam-5839	105	6	research	research	NOUN
ejpam-5839	105	7	delves	delve	VERB
ejpam-5839	105	8	into	into	ADP
ejpam-5839	105	9	an	an	DET
ejpam-5839	105	10	even	even	ADV
ejpam-5839	105	11	further	further	ADJ
ejpam-5839	105	12	extension	extension	NOUN
ejpam-5839	105	13	of	of	ADP
ejpam-5839	105	14	nst	nst	PROPN
ejpam-5839	105	15	,	,	PUNCT
ejpam-5839	105	16	called	call	VERB
ejpam-5839	105	17	quadri	quadri	NOUN
ejpam-5839	105	18	-	-	PUNCT
ejpam-5839	105	19	partitioned	partition	VERB
ejpam-5839	105	20	neutrosophic	neutrosophic	ADJ
ejpam-5839	105	21	set	set	NOUN
ejpam-5839	105	22	theory	theory	NOUN
ejpam-5839	105	23	(	(	PUNCT
ejpam-5839	105	24	qpnst	qpnst	ADJ
ejpam-5839	105	25	)	)	PUNCT
ejpam-5839	105	26	,	,	PUNCT
ejpam-5839	105	27	which	which	PRON
ejpam-5839	105	28	incorporates	incorporate	VERB
ejpam-5839	105	29	a	a	DET
ejpam-5839	105	30	fourth	fourth	ADJ
ejpam-5839	105	31	possibility	possibility	NOUN
ejpam-5839	105	32	.	.	PUNCT
ejpam-5839	106	1	this	this	DET
ejpam-5839	106	2	additional	additional	ADJ
ejpam-5839	106	3	possibility	possibility	NOUN
ejpam-5839	106	4	enhances	enhance	VERB
ejpam-5839	106	5	the	the	DET
ejpam-5839	106	6	level	level	NOUN
ejpam-5839	106	7	of	of	ADP
ejpam-5839	106	8	detail	detail	NOUN
ejpam-5839	106	9	and	and	CCONJ
ejpam-5839	106	10	completeness	completeness	NOUN
ejpam-5839	106	11	in	in	ADP
ejpam-5839	106	12	the	the	DET
ejpam-5839	106	13	representation	representation	NOUN
ejpam-5839	106	14	of	of	ADP
ejpam-5839	106	15	sets	set	NOUN
ejpam-5839	106	16	.	.	PUNCT
ejpam-5839	107	1	in	in	ADP
ejpam-5839	107	2	this	this	DET
ejpam-5839	107	3	study	study	NOUN
ejpam-5839	107	4	,	,	PUNCT
ejpam-5839	107	5	we	we	PRON
ejpam-5839	107	6	define	define	VERB
ejpam-5839	107	7	the	the	DET
ejpam-5839	107	8	riemann	riemann	PROPN
ejpam-5839	107	9	integral	integral	ADJ
ejpam-5839	107	10	theory	theory	NOUN
ejpam-5839	107	11	(	(	PUNCT
ejpam-5839	107	12	rit	rit	NOUN
ejpam-5839	107	13	)	)	PUNCT
ejpam-5839	107	14	within	within	ADP
ejpam-5839	107	15	the	the	DET
ejpam-5839	107	16	context	context	NOUN
ejpam-5839	107	17	of	of	ADP
ejpam-5839	107	18	qpnst	qpnst	NOUN
ejpam-5839	107	19	,	,	PUNCT
ejpam-5839	107	20	offering	offer	VERB
ejpam-5839	107	21	a	a	DET
ejpam-5839	107	22	novel	novel	ADJ
ejpam-5839	107	23	way	way	NOUN
ejpam-5839	107	24	to	to	PART
ejpam-5839	107	25	explore	explore	VERB
ejpam-5839	107	26	the	the	DET
ejpam-5839	107	27	properties	property	NOUN
ejpam-5839	107	28	and	and	CCONJ
ejpam-5839	107	29	characteristics	characteristic	NOUN
ejpam-5839	107	30	of	of	ADP
ejpam-5839	107	31	the	the	DET
ejpam-5839	107	32	riemann	riemann	PROPN
ejpam-5839	107	33	integral	integral	NOUN
ejpam-5839	107	34	in	in	ADP
ejpam-5839	107	35	this	this	DET
ejpam-5839	107	36	expanded	expand	VERB
ejpam-5839	107	37	framework	framework	NOUN
ejpam-5839	107	38	.	.	PUNCT
ejpam-5839	108	1	a	a	DET
ejpam-5839	108	2	key	key	ADJ
ejpam-5839	108	3	concept	concept	NOUN
ejpam-5839	108	4	that	that	PRON
ejpam-5839	108	5	emerges	emerge	VERB
ejpam-5839	108	6	in	in	ADP
ejpam-5839	108	7	this	this	DET
ejpam-5839	108	8	work	work	NOUN
ejpam-5839	108	9	is	be	AUX
ejpam-5839	108	10	the	the	DET
ejpam-5839	108	11	level	level	NOUN
ejpam-5839	108	12	cut	cut	NOUN
ejpam-5839	108	13	,	,	PUNCT
ejpam-5839	108	14	which	which	PRON
ejpam-5839	108	15	in	in	ADP
ejpam-5839	108	16	the	the	DET
ejpam-5839	108	17	context	context	NOUN
ejpam-5839	108	18	of	of	ADP
ejpam-5839	108	19	qpnst	qpnst	ADJ
ejpam-5839	108	20	is	be	AUX
ejpam-5839	108	21	represented	represent	VERB
ejpam-5839	108	22	as	as	ADP
ejpam-5839	108	23	a	a	DET
ejpam-5839	108	24	four	four	NUM
ejpam-5839	108	25	-	-	PUNCT
ejpam-5839	108	26	tuple	tuple	NOUN
ejpam-5839	108	27	(	(	PUNCT
ejpam-5839	108	28	i	i	PROPN
ejpam-5839	108	29	,	,	PUNCT
ejpam-5839	108	30	j	j	PROPN
ejpam-5839	108	31	,	,	PUNCT
ejpam-5839	108	32	k	k	PROPN
ejpam-5839	108	33	,	,	PUNCT
ejpam-5839	108	34	l	l	NOUN
ejpam-5839	108	35	)	)	PUNCT
ejpam-5839	108	36	,	,	PUNCT
ejpam-5839	108	37	encapsulating	encapsulate	VERB
ejpam-5839	108	38	the	the	DET
ejpam-5839	108	39	various	various	ADJ
ejpam-5839	108	40	possibilities	possibility	NOUN
ejpam-5839	108	41	inherent	inherent	ADJ
ejpam-5839	108	42	in	in	ADP
ejpam-5839	108	43	the	the	DET
ejpam-5839	108	44	theory	theory	NOUN
ejpam-5839	108	45	.	.	PUNCT
ejpam-5839	109	1	we	we	PRON
ejpam-5839	109	2	also	also	ADV
ejpam-5839	109	3	explore	explore	VERB
ejpam-5839	109	4	the	the	DET
ejpam-5839	109	5	quadri	quadri	NOUN
ejpam-5839	109	6	-	-	PUNCT
ejpam-5839	109	7	partitioned	partition	VERB
ejpam-5839	109	8	neutrosophic	neutrosophic	ADJ
ejpam-5839	109	9	riemann	riemann	PROPN
ejpam-5839	109	10	integral	integral	ADJ
ejpam-5839	109	11	theory	theory	NOUN
ejpam-5839	109	12	(	(	PUNCT
ejpam-5839	109	13	qpnrit	qpnrit	NOUN
ejpam-5839	109	14	)	)	PUNCT
ejpam-5839	109	15	,	,	PUNCT
ejpam-5839	109	16	applying	apply	VERB
ejpam-5839	109	17	it	it	PRON
ejpam-5839	109	18	numerically	numerically	ADV
ejpam-5839	109	19	and	and	CCONJ
ejpam-5839	109	20	presenting	present	VERB
ejpam-5839	109	21	the	the	DET
ejpam-5839	109	22	results	result	NOUN
ejpam-5839	109	23	in	in	ADP
ejpam-5839	109	24	tabular	tabular	NOUN
ejpam-5839	109	25	form	form	NOUN
ejpam-5839	109	26	.	.	PUNCT
ejpam-5839	110	1	this	this	DET
ejpam-5839	110	2	numerical	numerical	ADJ
ejpam-5839	110	3	exploration	exploration	NOUN
ejpam-5839	110	4	allows	allow	VERB
ejpam-5839	110	5	us	we	PRON
ejpam-5839	110	6	to	to	PART
ejpam-5839	110	7	investigate	investigate	VERB
ejpam-5839	110	8	the	the	DET
ejpam-5839	110	9	behavior	behavior	NOUN
ejpam-5839	110	10	of	of	ADP
ejpam-5839	110	11	the	the	DET
ejpam-5839	110	12	integral	integral	ADJ
ejpam-5839	110	13	in	in	ADP
ejpam-5839	110	14	the	the	DET
ejpam-5839	110	15	qpnst	qpnst	ADJ
ejpam-5839	110	16	framework	framework	NOUN
ejpam-5839	110	17	,	,	PUNCT
ejpam-5839	110	18	providing	provide	VERB
ejpam-5839	110	19	a	a	DET
ejpam-5839	110	20	deeper	deep	ADJ
ejpam-5839	110	21	understanding	understanding	NOUN
ejpam-5839	110	22	of	of	ADP
ejpam-5839	110	23	its	its	PRON
ejpam-5839	110	24	properties	property	NOUN
ejpam-5839	110	25	and	and	CCONJ
ejpam-5839	110	26	showcasing	showcase	VERB
ejpam-5839	110	27	the	the	DET
ejpam-5839	110	28	potential	potential	NOUN
ejpam-5839	110	29	of	of	ADP
ejpam-5839	110	30	this	this	DET
ejpam-5839	110	31	extended	extend	VERB
ejpam-5839	110	32	theory	theory	NOUN
ejpam-5839	110	33	for	for	ADP
ejpam-5839	110	34	future	future	ADJ
ejpam-5839	110	35	mathematical	mathematical	ADJ
ejpam-5839	110	36	and	and	CCONJ
ejpam-5839	110	37	practical	practical	ADJ
ejpam-5839	110	38	applications	application	NOUN
ejpam-5839	110	39	.	.	PUNCT
ejpam-5839	111	1	1.4	1.4	NUM
ejpam-5839	111	2	.	.	PUNCT
ejpam-5839	111	3	importance	importance	NOUN
ejpam-5839	111	4	of	of	ADP
ejpam-5839	111	5	the	the	DET
ejpam-5839	111	6	study	study	NOUN
ejpam-5839	111	7	a	a	DET
ejpam-5839	111	8	significant	significant	ADJ
ejpam-5839	111	9	development	development	NOUN
ejpam-5839	111	10	in	in	ADP
ejpam-5839	111	11	our	our	PRON
ejpam-5839	111	12	study	study	NOUN
ejpam-5839	111	13	is	be	AUX
ejpam-5839	111	14	the	the	DET
ejpam-5839	111	15	application	application	NOUN
ejpam-5839	111	16	of	of	ADP
ejpam-5839	111	17	the	the	DET
ejpam-5839	111	18	riemann	riemann	PROPN
ejpam-5839	111	19	integral	integral	PROPN
ejpam-5839	111	20	theory	theory	NOUN
ejpam-5839	111	21	(	(	PUNCT
ejpam-5839	111	22	rit	rit	NOUN
ejpam-5839	111	23	)	)	PUNCT
ejpam-5839	111	24	within	within	ADP
ejpam-5839	111	25	the	the	DET
ejpam-5839	111	26	context	context	NOUN
ejpam-5839	111	27	of	of	ADP
ejpam-5839	111	28	qpnst	qpnst	ADJ
ejpam-5839	111	29	.	.	PUNCT
ejpam-5839	112	1	this	this	DET
ejpam-5839	112	2	extension	extension	NOUN
ejpam-5839	112	3	paves	pave	VERB
ejpam-5839	112	4	the	the	DET
ejpam-5839	112	5	way	way	NOUN
ejpam-5839	112	6	for	for	ADP
ejpam-5839	112	7	exploring	explore	VERB
ejpam-5839	112	8	the	the	DET
ejpam-5839	112	9	properties	property	NOUN
ejpam-5839	112	10	and	and	CCONJ
ejpam-5839	112	11	characteristics	characteristic	NOUN
ejpam-5839	112	12	of	of	ADP
ejpam-5839	112	13	the	the	DET
ejpam-5839	112	14	riemann	riemann	PROPN
ejpam-5839	112	15	integral	integral	PROPN
ejpam-5839	112	16	in	in	ADP
ejpam-5839	112	17	a	a	DET
ejpam-5839	112	18	richer	rich	ADJ
ejpam-5839	112	19	and	and	CCONJ
ejpam-5839	112	20	more	more	ADV
ejpam-5839	112	21	nuanced	nuanced	ADJ
ejpam-5839	112	22	mathematical	mathematical	ADJ
ejpam-5839	112	23	setting	setting	NOUN
ejpam-5839	112	24	.	.	PUNCT
ejpam-5839	113	1	a.	a.	NOUN
ejpam-5839	113	2	shihadeh	shihadeh	PROPN
ejpam-5839	113	3	et	et	PROPN
ejpam-5839	113	4	al	al	PROPN
ejpam-5839	113	5	.	.	PUNCT
ejpam-5839	113	6	/	/	SYM
ejpam-5839	113	7	eur	eur	PROPN
ejpam-5839	113	8	.	.	PUNCT
ejpam-5839	114	1	j.	j.	PROPN
ejpam-5839	114	2	pure	pure	PROPN
ejpam-5839	114	3	appl	appl	PROPN
ejpam-5839	114	4	.	.	PROPN
ejpam-5839	114	5	math	math	PROPN
ejpam-5839	114	6	,	,	PUNCT
ejpam-5839	114	7	18	18	NUM
ejpam-5839	114	8	(	(	PUNCT
ejpam-5839	114	9	2	2	NUM
ejpam-5839	114	10	)	)	PUNCT
ejpam-5839	114	11	(	(	PUNCT
ejpam-5839	114	12	2025	2025	NUM
ejpam-5839	114	13	)	)	PUNCT
ejpam-5839	114	14	,	,	PUNCT
ejpam-5839	114	15	5839	5839	NUM
ejpam-5839	114	16	4	4	NUM
ejpam-5839	114	17	of	of	ADP
ejpam-5839	114	18	54	54	NUM
ejpam-5839	114	19	the	the	DET
ejpam-5839	114	20	concept	concept	NOUN
ejpam-5839	114	21	of	of	ADP
ejpam-5839	114	22	the	the	DET
ejpam-5839	114	23	level	level	NOUN
ejpam-5839	114	24	cut	cut	NOUN
ejpam-5839	114	25	,	,	PUNCT
ejpam-5839	114	26	defined	define	VERB
ejpam-5839	114	27	as	as	ADP
ejpam-5839	114	28	a	a	DET
ejpam-5839	114	29	four	four	NUM
ejpam-5839	114	30	-	-	PUNCT
ejpam-5839	114	31	tuple	tuple	NOUN
ejpam-5839	114	32	(	(	PUNCT
ejpam-5839	114	33	i	i	PROPN
ejpam-5839	114	34	,	,	PUNCT
ejpam-5839	114	35	j	j	PROPN
ejpam-5839	114	36	,	,	PUNCT
ejpam-5839	114	37	k	k	PROPN
ejpam-5839	114	38	,	,	PUNCT
ejpam-5839	114	39	l	l	NOUN
ejpam-5839	114	40	)	)	PUNCT
ejpam-5839	114	41	,	,	PUNCT
ejpam-5839	114	42	is	be	AUX
ejpam-5839	114	43	critical	critical	ADJ
ejpam-5839	114	44	in	in	ADP
ejpam-5839	114	45	this	this	DET
ejpam-5839	114	46	work	work	NOUN
ejpam-5839	114	47	as	as	SCONJ
ejpam-5839	114	48	it	it	PRON
ejpam-5839	114	49	captures	capture	VERB
ejpam-5839	114	50	the	the	DET
ejpam-5839	114	51	different	different	ADJ
ejpam-5839	114	52	possibilities	possibility	NOUN
ejpam-5839	114	53	within	within	ADP
ejpam-5839	114	54	the	the	DET
ejpam-5839	114	55	qpnst	qpnst	ADJ
ejpam-5839	114	56	framework	framework	NOUN
ejpam-5839	114	57	,	,	PUNCT
ejpam-5839	114	58	offering	offer	VERB
ejpam-5839	114	59	a	a	DET
ejpam-5839	114	60	unique	unique	ADJ
ejpam-5839	114	61	perspective	perspective	NOUN
ejpam-5839	114	62	for	for	ADP
ejpam-5839	114	63	analyzing	analyze	VERB
ejpam-5839	114	64	integral	integral	ADJ
ejpam-5839	114	65	properties	property	NOUN
ejpam-5839	114	66	.	.	PUNCT
ejpam-5839	115	1	through	through	ADP
ejpam-5839	115	2	the	the	DET
ejpam-5839	115	3	introduction	introduction	NOUN
ejpam-5839	115	4	of	of	ADP
ejpam-5839	115	5	the	the	DET
ejpam-5839	115	6	quadri	quadri	NOUN
ejpam-5839	115	7	-	-	PUNCT
ejpam-5839	115	8	partitioned	partition	VERB
ejpam-5839	115	9	neutrosophic	neutrosophic	ADJ
ejpam-5839	115	10	riemann	riemann	PROPN
ejpam-5839	115	11	integral	integral	ADJ
ejpam-5839	115	12	theory	theory	NOUN
ejpam-5839	115	13	(	(	PUNCT
ejpam-5839	115	14	qpnrit	qpnrit	PROPN
ejpam-5839	115	15	)	)	PUNCT
ejpam-5839	115	16	,	,	PUNCT
ejpam-5839	115	17	our	our	PRON
ejpam-5839	115	18	study	study	NOUN
ejpam-5839	115	19	provides	provide	VERB
ejpam-5839	115	20	numerical	numerical	ADJ
ejpam-5839	115	21	insights	insight	NOUN
ejpam-5839	115	22	into	into	ADP
ejpam-5839	115	23	the	the	DET
ejpam-5839	115	24	behavior	behavior	NOUN
ejpam-5839	115	25	of	of	ADP
ejpam-5839	115	26	integrals	integral	NOUN
ejpam-5839	115	27	within	within	ADP
ejpam-5839	115	28	this	this	DET
ejpam-5839	115	29	extended	extend	VERB
ejpam-5839	115	30	framework	framework	NOUN
ejpam-5839	115	31	.	.	PUNCT
ejpam-5839	116	1	the	the	DET
ejpam-5839	116	2	results	result	NOUN
ejpam-5839	116	3	are	be	AUX
ejpam-5839	116	4	presented	present	VERB
ejpam-5839	116	5	systematically	systematically	ADV
ejpam-5839	116	6	in	in	ADP
ejpam-5839	116	7	tabular	tabular	PROPN
ejpam-5839	116	8	form	form	NOUN
ejpam-5839	116	9	,	,	PUNCT
ejpam-5839	116	10	enhancing	enhance	VERB
ejpam-5839	116	11	the	the	DET
ejpam-5839	116	12	understanding	understanding	NOUN
ejpam-5839	116	13	of	of	ADP
ejpam-5839	116	14	the	the	DET
ejpam-5839	116	15	integrals	integral	NOUN
ejpam-5839	116	16	properties	property	NOUN
ejpam-5839	116	17	and	and	CCONJ
ejpam-5839	116	18	illustrating	illustrate	VERB
ejpam-5839	116	19	how	how	SCONJ
ejpam-5839	116	20	it	it	PRON
ejpam-5839	116	21	behaves	behave	VERB
ejpam-5839	116	22	under	under	ADP
ejpam-5839	116	23	different	different	ADJ
ejpam-5839	116	24	conditions	condition	NOUN
ejpam-5839	116	25	of	of	ADP
ejpam-5839	116	26	uncertainty	uncertainty	NOUN
ejpam-5839	116	27	.	.	PUNCT
ejpam-5839	117	1	this	this	DET
ejpam-5839	117	2	numerical	numerical	ADJ
ejpam-5839	117	3	approach	approach	NOUN
ejpam-5839	117	4	not	not	PART
ejpam-5839	117	5	only	only	ADV
ejpam-5839	117	6	enriches	enrich	VERB
ejpam-5839	117	7	the	the	DET
ejpam-5839	117	8	theoretical	theoretical	ADJ
ejpam-5839	117	9	foundations	foundation	NOUN
ejpam-5839	117	10	of	of	ADP
ejpam-5839	117	11	qpnst	qpnst	ADJ
ejpam-5839	117	12	but	but	CCONJ
ejpam-5839	117	13	also	also	ADV
ejpam-5839	117	14	holds	hold	VERB
ejpam-5839	117	15	promise	promise	NOUN
ejpam-5839	117	16	for	for	ADP
ejpam-5839	117	17	practical	practical	ADJ
ejpam-5839	117	18	applications	application	NOUN
ejpam-5839	117	19	in	in	ADP
ejpam-5839	117	20	fields	field	NOUN
ejpam-5839	117	21	such	such	ADJ
ejpam-5839	117	22	as	as	ADP
ejpam-5839	117	23	engineering	engineering	NOUN
ejpam-5839	117	24	,	,	PUNCT
ejpam-5839	117	25	decisionmaking	decisionmake	VERB
ejpam-5839	117	26	,	,	PUNCT
ejpam-5839	117	27	and	and	CCONJ
ejpam-5839	117	28	data	datum	NOUN
ejpam-5839	117	29	analysis	analysis	NOUN
ejpam-5839	117	30	,	,	PUNCT
ejpam-5839	117	31	where	where	SCONJ
ejpam-5839	117	32	complex	complex	ADJ
ejpam-5839	117	33	uncertainties	uncertainty	NOUN
ejpam-5839	117	34	and	and	CCONJ
ejpam-5839	117	35	ambiguities	ambiguity	NOUN
ejpam-5839	117	36	need	need	VERB
ejpam-5839	117	37	to	to	PART
ejpam-5839	117	38	be	be	AUX
ejpam-5839	117	39	addressed	address	VERB
ejpam-5839	117	40	.	.	PUNCT
ejpam-5839	118	1	1.5	1.5	NUM
ejpam-5839	118	2	.	.	PUNCT
ejpam-5839	119	1	literature	literature	PROPN
ejpam-5839	119	2	review	review	PROPN
ejpam-5839	119	3	ozturk	ozturk	PROPN
ejpam-5839	119	4	et	et	PROPN
ejpam-5839	119	5	al	al	PROPN
ejpam-5839	119	6	.	.	PUNCT
ejpam-5839	120	1	[	[	X
ejpam-5839	120	2	44	44	NUM
ejpam-5839	120	3	]	]	PUNCT
ejpam-5839	120	4	explored	explore	VERB
ejpam-5839	120	5	soft	soft	ADJ
ejpam-5839	120	6	continuous	continuous	ADJ
ejpam-5839	120	7	mappings	mapping	NOUN
ejpam-5839	120	8	.	.	PUNCT
ejpam-5839	121	1	gunduz	gunduz	NOUN
ejpam-5839	121	2	et	et	PROPN
ejpam-5839	121	3	al	al	PROPN
ejpam-5839	121	4	.	.	PUNCT
ejpam-5839	122	1	[	[	X
ejpam-5839	122	2	45	45	NUM
ejpam-5839	122	3	]	]	PUNCT
ejpam-5839	122	4	focused	focus	VERB
ejpam-5839	122	5	on	on	ADP
ejpam-5839	122	6	critical	critical	ADJ
ejpam-5839	122	7	structures	structure	NOUN
ejpam-5839	122	8	within	within	ADP
ejpam-5839	122	9	sts	st	NOUN
ejpam-5839	122	10	,	,	PUNCT
ejpam-5839	122	11	particularly	particularly	ADV
ejpam-5839	122	12	separation	separation	NOUN
ejpam-5839	122	13	axioms	axiom	NOUN
ejpam-5839	122	14	.	.	PUNCT
ejpam-5839	123	1	ozturk	ozturk	NOUN
ejpam-5839	124	1	[	[	X
ejpam-5839	124	2	46	46	NUM
ejpam-5839	124	3	]	]	PUNCT
ejpam-5839	124	4	expanded	expand	VERB
ejpam-5839	124	5	the	the	DET
ejpam-5839	124	6	analysis	analysis	NOUN
ejpam-5839	124	7	of	of	ADP
ejpam-5839	124	8	additional	additional	ADJ
ejpam-5839	124	9	structures	structure	NOUN
ejpam-5839	124	10	within	within	ADP
ejpam-5839	124	11	sts	st	NOUN
ejpam-5839	124	12	.	.	PUNCT
ejpam-5839	125	1	mehmood	mehmood	PROPN
ejpam-5839	125	2	et	et	PROPN
ejpam-5839	125	3	al	al	PROPN
ejpam-5839	125	4	.	.	PUNCT
ejpam-5839	126	1	[	[	X
ejpam-5839	126	2	47	47	NUM
ejpam-5839	126	3	]	]	PUNCT
ejpam-5839	126	4	made	make	VERB
ejpam-5839	126	5	significant	significant	ADJ
ejpam-5839	126	6	contributions	contribution	NOUN
ejpam-5839	126	7	to	to	ADP
ejpam-5839	126	8	neutrosophic	neutrosophic	ADJ
ejpam-5839	126	9	soft	soft	ADJ
ejpam-5839	126	10	bounded	bounded	ADJ
ejpam-5839	126	11	topological	topological	ADJ
ejpam-5839	126	12	spaces	space	NOUN
ejpam-5839	126	13	(	(	PUNCT
ejpam-5839	126	14	nsbts	nsbt	NOUN
ejpam-5839	126	15	)	)	PUNCT
ejpam-5839	126	16	and	and	CCONJ
ejpam-5839	126	17	discussed	discuss	VERB
ejpam-5839	126	18	a	a	DET
ejpam-5839	126	19	comprehensive	comprehensive	ADJ
ejpam-5839	126	20	set	set	NOUN
ejpam-5839	126	21	of	of	ADP
ejpam-5839	126	22	results	result	NOUN
ejpam-5839	126	23	related	relate	VERB
ejpam-5839	126	24	to	to	ADP
ejpam-5839	126	25	crisp	crisp	ADJ
ejpam-5839	126	26	points	point	NOUN
ejpam-5839	126	27	.	.	PUNCT
ejpam-5839	127	1	mehmood	mehmood	PROPN
ejpam-5839	127	2	et	et	PROPN
ejpam-5839	127	3	al	al	PROPN
ejpam-5839	127	4	.	.	PUNCT
ejpam-5839	128	1	[	[	X
ejpam-5839	128	2	48	48	NUM
ejpam-5839	128	3	,	,	PUNCT
ejpam-5839	128	4	49	49	NUM
ejpam-5839	128	5	]	]	PUNCT
ejpam-5839	128	6	presented	present	VERB
ejpam-5839	128	7	results	result	NOUN
ejpam-5839	128	8	on	on	ADP
ejpam-5839	128	9	neutrosophic	neutrosophic	ADJ
ejpam-5839	128	10	soft	soft	ADJ
ejpam-5839	128	11	open	open	ADJ
ejpam-5839	128	12	sets	set	NOUN
ejpam-5839	128	13	(	(	PUNCT
ejpam-5839	128	14	nsoss	nsoss	NOUN
ejpam-5839	128	15	)	)	PUNCT
ejpam-5839	128	16	.	.	PUNCT
ejpam-5839	129	1	mehmood	mehmood	PROPN
ejpam-5839	129	2	et	et	PROPN
ejpam-5839	129	3	al.[50	al.[50	PROPN
ejpam-5839	129	4	]	]	PUNCT
ejpam-5839	129	5	introduced	introduce	VERB
ejpam-5839	129	6	the	the	DET
ejpam-5839	129	7	concept	concept	NOUN
ejpam-5839	129	8	of	of	ADP
ejpam-5839	129	9	neutrosophic	neutrosophic	ADJ
ejpam-5839	129	10	soft	soft	ADJ
ejpam-5839	129	11	quasisets	quasiset	NOUN
ejpam-5839	129	12	(	(	PUNCT
ejpam-5839	129	13	nsqs	nsq	NOUN
ejpam-5839	129	14	)	)	PUNCT
ejpam-5839	129	15	,	,	PUNCT
ejpam-5839	129	16	with	with	ADP
ejpam-5839	129	17	respect	respect	NOUN
ejpam-5839	129	18	to	to	ADP
ejpam-5839	129	19	neutrosophic	neutrosophic	ADJ
ejpam-5839	129	20	soft	soft	ADJ
ejpam-5839	129	21	points	point	NOUN
ejpam-5839	129	22	(	(	PUNCT
ejpam-5839	129	23	nsp	nsp	PROPN
ejpam-5839	129	24	)	)	PUNCT
ejpam-5839	129	25	.	.	PUNCT
ejpam-5839	130	1	mehmood	mehmood	PROPN
ejpam-5839	130	2	et	et	PROPN
ejpam-5839	130	3	al	al	PROPN
ejpam-5839	130	4	.	.	PUNCT
ejpam-5839	131	1	[	[	X
ejpam-5839	131	2	51	51	NUM
ejpam-5839	131	3	]	]	PUNCT
ejpam-5839	131	4	provided	provide	VERB
ejpam-5839	131	5	an	an	DET
ejpam-5839	131	6	in	in	ADP
ejpam-5839	131	7	-	-	PUNCT
ejpam-5839	131	8	depth	depth	NOUN
ejpam-5839	131	9	analysis	analysis	NOUN
ejpam-5839	131	10	of	of	ADP
ejpam-5839	131	11	nsqs	nsq	NOUN
ejpam-5839	131	12	,	,	PUNCT
ejpam-5839	131	13	specifically	specifically	ADV
ejpam-5839	131	14	focusing	focus	VERB
ejpam-5839	131	15	on	on	ADP
ejpam-5839	131	16	soft	soft	ADJ
ejpam-5839	131	17	p	p	NOUN
ejpam-5839	131	18	-	-	PUNCT
ejpam-5839	131	19	open	open	ADJ
ejpam-5839	131	20	sets	set	NOUN
ejpam-5839	131	21	.	.	PUNCT
ejpam-5839	132	1	kim	kim	PROPN
ejpam-5839	132	2	et	et	PROPN
ejpam-5839	132	3	al	al	PROPN
ejpam-5839	132	4	.	.	PUNCT
ejpam-5839	133	1	[	[	X
ejpam-5839	133	2	52	52	NUM
ejpam-5839	133	3	]	]	PUNCT
ejpam-5839	133	4	addressed	address	VERB
ejpam-5839	133	5	several	several	ADJ
ejpam-5839	133	6	differential	differential	ADJ
ejpam-5839	133	7	problems	problem	NOUN
ejpam-5839	133	8	and	and	CCONJ
ejpam-5839	133	9	illustrated	illustrate	VERB
ejpam-5839	133	10	their	their	PRON
ejpam-5839	133	11	solutions	solution	NOUN
ejpam-5839	133	12	with	with	ADP
ejpam-5839	133	13	examples	example	NOUN
ejpam-5839	133	14	.	.	PUNCT
ejpam-5839	134	1	moi	moi	PROPN
ejpam-5839	134	2	et	et	PROPN
ejpam-5839	134	3	al	al	PROPN
ejpam-5839	134	4	.	.	PUNCT
ejpam-5839	135	1	[	[	X
ejpam-5839	135	2	53	53	NUM
ejpam-5839	135	3	]	]	PUNCT
ejpam-5839	135	4	investigated	investigate	VERB
ejpam-5839	135	5	second	second	ADJ
ejpam-5839	135	6	-	-	PUNCT
ejpam-5839	135	7	order	order	NOUN
ejpam-5839	135	8	problems	problem	NOUN
ejpam-5839	135	9	within	within	ADP
ejpam-5839	135	10	the	the	DET
ejpam-5839	135	11	context	context	NOUN
ejpam-5839	135	12	of	of	ADP
ejpam-5839	135	13	nst	nst	PROPN
ejpam-5839	135	14	,	,	PUNCT
ejpam-5839	135	15	enhancing	enhance	VERB
ejpam-5839	135	16	applicability	applicability	NOUN
ejpam-5839	135	17	through	through	ADP
ejpam-5839	135	18	well	well	ADV
ejpam-5839	135	19	-	-	PUNCT
ejpam-5839	135	20	chosen	choose	VERB
ejpam-5839	135	21	examples	example	NOUN
ejpam-5839	135	22	.	.	PUNCT
ejpam-5839	136	1	shami	shami	PROPN
ejpam-5839	136	2	et	et	PROPN
ejpam-5839	136	3	al	al	PROPN
ejpam-5839	136	4	.	.	PUNCT
ejpam-5839	137	1	[	[	X
ejpam-5839	137	2	54	54	NUM
ejpam-5839	137	3	]	]	PUNCT
ejpam-5839	137	4	introduced	introduce	VERB
ejpam-5839	137	5	supra	supra	NOUN
ejpam-5839	137	6	-	-	PUNCT
ejpam-5839	137	7	soft	soft	ADJ
ejpam-5839	137	8	topologically	topologically	ADV
ejpam-5839	137	9	ordered	order	VERB
ejpam-5839	137	10	spaces	space	NOUN
ejpam-5839	137	11	as	as	ADP
ejpam-5839	137	12	an	an	DET
ejpam-5839	137	13	extension	extension	NOUN
ejpam-5839	137	14	of	of	ADP
ejpam-5839	137	15	soft	soft	ADJ
ejpam-5839	137	16	topologically	topologically	ADV
ejpam-5839	137	17	ordered	order	VERB
ejpam-5839	137	18	spaces	space	NOUN
ejpam-5839	137	19	.	.	PUNCT
ejpam-5839	138	1	they	they	PRON
ejpam-5839	138	2	discussed	discuss	VERB
ejpam-5839	138	3	key	key	ADJ
ejpam-5839	138	4	notions	notion	NOUN
ejpam-5839	138	5	like	like	ADP
ejpam-5839	138	6	monotone	monotone	ADJ
ejpam-5839	138	7	interior	interior	ADJ
ejpam-5839	138	8	and	and	CCONJ
ejpam-5839	138	9	closure	closure	NOUN
ejpam-5839	138	10	operators	operator	NOUN
ejpam-5839	138	11	,	,	PUNCT
ejpam-5839	138	12	formulated	formulate	VERB
ejpam-5839	138	13	supra	supra	ADJ
ejpam-5839	138	14	-	-	PUNCT
ejpam-5839	138	15	soft	soft	ADJ
ejpam-5839	138	16	separation	separation	NOUN
ejpam-5839	138	17	axioms	axiom	NOUN
ejpam-5839	138	18	,	,	PUNCT
ejpam-5839	138	19	and	and	CCONJ
ejpam-5839	138	20	explored	explore	VERB
ejpam-5839	138	21	the	the	DET
ejpam-5839	138	22	relationships	relationship	NOUN
ejpam-5839	138	23	between	between	ADP
ejpam-5839	138	24	these	these	DET
ejpam-5839	138	25	concepts	concept	NOUN
ejpam-5839	138	26	and	and	CCONJ
ejpam-5839	138	27	their	their	PRON
ejpam-5839	138	28	parametric	parametric	ADJ
ejpam-5839	138	29	supra	supra	PROPN
ejpam-5839	138	30	topologies	topology	NOUN
ejpam-5839	138	31	.	.	PUNCT
ejpam-5839	139	1	they	they	PRON
ejpam-5839	139	2	also	also	ADV
ejpam-5839	139	3	characterized	characterize	VERB
ejpam-5839	139	4	supra	supra	ADJ
ejpam-5839	139	5	p	p	NOUN
ejpam-5839	139	6	-	-	PUNCT
ejpam-5839	139	7	soft	soft	ADJ
ejpam-5839	139	8	ti	ti	NOUN
ejpam-5839	139	9	-	-	ADJ
ejpam-5839	139	10	ordered	order	VERB
ejpam-5839	139	11	spaces	space	NOUN
ejpam-5839	139	12	,	,	PUNCT
ejpam-5839	139	13	supra	supra	PROPN
ejpam-5839	139	14	p	p	NOUN
ejpam-5839	139	15	-	-	PUNCT
ejpam-5839	139	16	soft	soft	ADJ
ejpam-5839	139	17	regularly	regularly	ADV
ejpam-5839	139	18	ordered	order	VERB
ejpam-5839	139	19	spaces	space	NOUN
ejpam-5839	139	20	,	,	PUNCT
ejpam-5839	139	21	and	and	CCONJ
ejpam-5839	139	22	supra	supra	NOUN
ejpam-5839	139	23	-	-	PUNCT
ejpam-5839	139	24	soft	soft	ADJ
ejpam-5839	139	25	normally	normally	ADV
ejpam-5839	139	26	ordered	order	VERB
ejpam-5839	139	27	spaces	space	NOUN
ejpam-5839	139	28	.	.	PUNCT
ejpam-5839	140	1	t.	t.	PROPN
ejpam-5839	140	2	m.	m.	PROPN
ejpam-5839	140	3	al	al	PROPN
ejpam-5839	140	4	-	-	PUNCT
ejpam-5839	140	5	shami	shami	PROPN
ejpam-5839	140	6	and	and	CCONJ
ejpam-5839	140	7	shafei	shafei	NOUN
ejpam-5839	141	1	[	[	X
ejpam-5839	141	2	55	55	NUM
ejpam-5839	141	3	]	]	PUNCT
ejpam-5839	141	4	discussed	discuss	VERB
ejpam-5839	141	5	two	two	NUM
ejpam-5839	141	6	types	type	NOUN
ejpam-5839	141	7	of	of	ADP
ejpam-5839	141	8	separation	separation	NOUN
ejpam-5839	141	9	axioms	axiom	NOUN
ejpam-5839	141	10	in	in	ADP
ejpam-5839	141	11	supra	supra	ADJ
ejpam-5839	141	12	-	-	PUNCT
ejpam-5839	141	13	soft	soft	ADJ
ejpam-5839	141	14	topological	topological	ADJ
ejpam-5839	141	15	spaces	space	NOUN
ejpam-5839	141	16	and	and	CCONJ
ejpam-5839	141	17	provided	provide	VERB
ejpam-5839	141	18	the	the	DET
ejpam-5839	141	19	best	good	ADJ
ejpam-5839	141	20	examples	example	NOUN
ejpam-5839	141	21	for	for	ADP
ejpam-5839	141	22	better	well	ADJ
ejpam-5839	141	23	understanding	understanding	NOUN
ejpam-5839	141	24	of	of	ADP
ejpam-5839	141	25	the	the	DET
ejpam-5839	141	26	results	result	NOUN
ejpam-5839	141	27	.	.	PUNCT
ejpam-5839	142	1	2	2	X
ejpam-5839	142	2	.	.	X
ejpam-5839	142	3	preliminaries	preliminary	NOUN
ejpam-5839	142	4	definition	definition	NOUN
ejpam-5839	142	5	1	1	NUM
ejpam-5839	142	6	.	.	PUNCT
ejpam-5839	143	1	[	[	X
ejpam-5839	143	2	43	43	NUM
ejpam-5839	143	3	]	]	X
ejpam-5839	143	4	let	let	VERB
ejpam-5839	143	5	u	u	PRON
ejpam-5839	143	6	be	be	AUX
ejpam-5839	143	7	the	the	DET
ejpam-5839	143	8	universal	universal	ADJ
ejpam-5839	143	9	set	set	NOUN
ejpam-5839	143	10	.	.	PUNCT
ejpam-5839	144	1	then	then	ADV
ejpam-5839	144	2	,	,	PUNCT
ejpam-5839	144	3	a	a	DET
ejpam-5839	144	4	single	single	ADV
ejpam-5839	144	5	-	-	PUNCT
ejpam-5839	144	6	valued	value	VERB
ejpam-5839	144	7	neutrosophic	neutrosophic	ADJ
ejpam-5839	144	8	set	set	NOUN
ejpam-5839	144	9	(	(	PUNCT
ejpam-5839	144	10	svns	svns	NOUN
ejpam-5839	144	11	)	)	PUNCT
ejpam-5839	144	12	n	n	NOUN
ejpam-5839	144	13	over	over	ADP
ejpam-5839	144	14	the	the	DET
ejpam-5839	144	15	set	set	NOUN
ejpam-5839	144	16	u	u	NOUN
ejpam-5839	144	17	is	be	AUX
ejpam-5839	144	18	a	a	DET
ejpam-5839	144	19	neutrosophic	neutrosophic	ADJ
ejpam-5839	144	20	set	set	NOUN
ejpam-5839	144	21	over	over	ADP
ejpam-5839	144	22	u	u	NOUN
ejpam-5839	144	23	,	,	PUNCT
ejpam-5839	144	24	but	but	CCONJ
ejpam-5839	144	25	the	the	DET
ejpam-5839	144	26	truth	truth	NOUN
ejpam-5839	144	27	,	,	PUNCT
ejpam-5839	144	28	indeterminacy	indeterminacy	NOUN
ejpam-5839	144	29	,	,	PUNCT
ejpam-5839	144	30	and	and	CCONJ
ejpam-5839	144	31	falsity	falsity	NOUN
ejpam-5839	144	32	membership	membership	NOUN
ejpam-5839	144	33	functions	function	NOUN
ejpam-5839	144	34	are	be	AUX
ejpam-5839	144	35	defined	define	VERB
ejpam-5839	144	36	as	as	ADP
ejpam-5839	144	37	tn	tn	NOUN
ejpam-5839	144	38	:	:	PUNCT
ejpam-5839	144	39	u	u	NOUN
ejpam-5839	144	40	→	→	SYM
ejpam-5839	144	41	[	[	X
ejpam-5839	144	42	0	0	NUM
ejpam-5839	144	43	,	,	PUNCT
ejpam-5839	144	44	1	1	NUM
ejpam-5839	144	45	]	]	PUNCT
ejpam-5839	144	46	,	,	PUNCT
ejpam-5839	144	47	in	in	ADP
ejpam-5839	144	48	:	:	PUNCT
ejpam-5839	144	49	u	u	NOUN
ejpam-5839	144	50	→	→	SYM
ejpam-5839	144	51	[	[	X
ejpam-5839	144	52	0	0	NUM
ejpam-5839	144	53	,	,	PUNCT
ejpam-5839	144	54	1	1	NUM
ejpam-5839	144	55	]	]	PUNCT
ejpam-5839	144	56	,	,	PUNCT
ejpam-5839	144	57	fn	fn	INTJ
ejpam-5839	144	58	:	:	PUNCT
ejpam-5839	144	59	u	u	NOUN
ejpam-5839	144	60	→	→	SYM
ejpam-5839	144	61	[	[	X
ejpam-5839	144	62	0	0	NUM
ejpam-5839	144	63	,	,	PUNCT
ejpam-5839	144	64	1	1	NUM
ejpam-5839	144	65	]	]	NUM
ejpam-5839	144	66	,	,	PUNCT
ejpam-5839	144	67	respectively	respectively	ADV
ejpam-5839	144	68	.	.	PUNCT
ejpam-5839	145	1	definition	definition	NOUN
ejpam-5839	145	2	2	2	NUM
ejpam-5839	145	3	.	.	PUNCT
ejpam-5839	146	1	[	[	X
ejpam-5839	146	2	43	43	NUM
ejpam-5839	146	3	]	]	X
ejpam-5839	146	4	a	a	DET
ejpam-5839	146	5	neutrosophic	neutrosophic	ADJ
ejpam-5839	146	6	set	set	NOUN
ejpam-5839	146	7	n	n	NOUN
ejpam-5839	146	8	over	over	ADP
ejpam-5839	146	9	the	the	DET
ejpam-5839	146	10	universal	universal	ADJ
ejpam-5839	146	11	set	set	NOUN
ejpam-5839	146	12	of	of	ADP
ejpam-5839	146	13	real	real	ADJ
ejpam-5839	146	14	numbers	number	NOUN
ejpam-5839	146	15	r	r	NOUN
ejpam-5839	146	16	is	be	AUX
ejpam-5839	146	17	said	say	VERB
ejpam-5839	146	18	to	to	PART
ejpam-5839	146	19	be	be	AUX
ejpam-5839	146	20	a	a	DET
ejpam-5839	146	21	neutrosophic	neutrosophic	ADJ
ejpam-5839	146	22	number	number	NOUN
ejpam-5839	146	23	if	if	SCONJ
ejpam-5839	146	24	it	it	PRON
ejpam-5839	146	25	satisfies	satisfy	VERB
ejpam-5839	146	26	the	the	DET
ejpam-5839	146	27	following	follow	VERB
ejpam-5839	146	28	conditions	condition	NOUN
ejpam-5839	146	29	:	:	PUNCT
ejpam-5839	146	30	1	1	X
ejpam-5839	146	31	.	.	X
ejpam-5839	146	32	n	n	PRON
ejpam-5839	146	33	is	be	AUX
ejpam-5839	146	34	normal	normal	ADJ
ejpam-5839	146	35	,	,	PUNCT
ejpam-5839	146	36	i.e.	i.e.	X
ejpam-5839	146	37	,	,	PUNCT
ejpam-5839	146	38	there	there	PRON
ejpam-5839	146	39	exists	exist	VERB
ejpam-5839	146	40	x0	x0	PROPN
ejpam-5839	146	41	∈	∈	PROPN
ejpam-5839	146	42	r	r	NOUN
ejpam-5839	146	43	such	such	ADJ
ejpam-5839	146	44	that	that	PRON
ejpam-5839	146	45	:	:	PUNCT
ejpam-5839	146	46	tn	tn	PROPN
ejpam-5839	146	47	(	(	PUNCT
ejpam-5839	146	48	x0	x0	PROPN
ejpam-5839	146	49	)	)	PUNCT
ejpam-5839	146	50	=	=	SYM
ejpam-5839	146	51	1	1	X
ejpam-5839	146	52	,	,	PUNCT
ejpam-5839	146	53	in	in	ADP
ejpam-5839	146	54	(	(	PUNCT
ejpam-5839	146	55	x0	x0	PROPN
ejpam-5839	146	56	)	)	PUNCT
ejpam-5839	146	57	=	=	SYM
ejpam-5839	146	58	0	0	NUM
ejpam-5839	146	59	,	,	PUNCT
ejpam-5839	146	60	fn	fn	ADJ
ejpam-5839	146	61	(	(	PUNCT
ejpam-5839	146	62	x0	x0	PROPN
ejpam-5839	146	63	)	)	PUNCT
ejpam-5839	146	64	=	=	SYM
ejpam-5839	147	1	0	0	NUM
ejpam-5839	147	2	.	.	NOUN
ejpam-5839	148	1	2	2	NUM
ejpam-5839	148	2	.	.	X
ejpam-5839	148	3	n	n	PRON
ejpam-5839	148	4	is	be	AUX
ejpam-5839	148	5	convex	convex	ADJ
ejpam-5839	148	6	for	for	ADP
ejpam-5839	148	7	the	the	DET
ejpam-5839	148	8	truth	truth	NOUN
ejpam-5839	148	9	membership	membership	NOUN
ejpam-5839	148	10	function	function	PROPN
ejpam-5839	148	11	tn	tn	PROPN
ejpam-5839	148	12	(	(	PUNCT
ejpam-5839	148	13	x	x	NOUN
ejpam-5839	148	14	)	)	PUNCT
ejpam-5839	148	15	,	,	PUNCT
ejpam-5839	148	16	i.e.	i.e.	X
ejpam-5839	148	17	,	,	PUNCT
ejpam-5839	148	18	tn	tn	PROPN
ejpam-5839	148	19	(	(	PUNCT
ejpam-5839	148	20	µx1	µx1	NOUN
ejpam-5839	148	21	+	+	CCONJ
ejpam-5839	148	22	(	(	PUNCT
ejpam-5839	148	23	1−	1−	NUM
ejpam-5839	148	24	µ)x2	µ)x2	PROPN
ejpam-5839	148	25	)	)	PUNCT
ejpam-5839	148	26	≥	≥	PROPN
ejpam-5839	148	27	min	min	PROPN
ejpam-5839	148	28	(	(	PUNCT
ejpam-5839	148	29	tn	tn	PROPN
ejpam-5839	148	30	(	(	PUNCT
ejpam-5839	148	31	x1	x1	PROPN
ejpam-5839	148	32	)	)	PUNCT
ejpam-5839	148	33	,	,	PUNCT
ejpam-5839	148	34	tn	tn	PROPN
ejpam-5839	148	35	(	(	PUNCT
ejpam-5839	148	36	x2	x2	PROPN
ejpam-5839	148	37	)	)	PUNCT
ejpam-5839	148	38	)	)	PUNCT
ejpam-5839	148	39	,	,	PUNCT
ejpam-5839	149	1	∀x1,x2	∀x1,x2	ADP
ejpam-5839	149	2	∈	∈	PROPN
ejpam-5839	149	3	r	r	NOUN
ejpam-5839	149	4	,	,	PUNCT
ejpam-5839	149	5	µ	µ	X
ejpam-5839	149	6	∈	∈	NOUN
ejpam-5839	150	1	[	[	X
ejpam-5839	150	2	0	0	NUM
ejpam-5839	150	3	,	,	PUNCT
ejpam-5839	150	4	1	1	NUM
ejpam-5839	150	5	]	]	PUNCT
ejpam-5839	150	6	.	.	PUNCT
ejpam-5839	151	1	3	3	X
ejpam-5839	151	2	.	.	X
ejpam-5839	151	3	n	n	PRON
ejpam-5839	151	4	is	be	AUX
ejpam-5839	151	5	concave	concave	VERB
ejpam-5839	151	6	for	for	ADP
ejpam-5839	151	7	the	the	DET
ejpam-5839	151	8	indeterminacy	indeterminacy	NOUN
ejpam-5839	151	9	and	and	CCONJ
ejpam-5839	151	10	falsity	falsity	NOUN
ejpam-5839	151	11	membership	membership	NOUN
ejpam-5839	151	12	functions	function	NOUN
ejpam-5839	151	13	,	,	PUNCT
ejpam-5839	151	14	in	in	ADP
ejpam-5839	151	15	(	(	PUNCT
ejpam-5839	151	16	x	x	X
ejpam-5839	151	17	)	)	PUNCT
ejpam-5839	151	18	and	and	CCONJ
ejpam-5839	151	19	fn	fn	ADJ
ejpam-5839	151	20	(	(	PUNCT
ejpam-5839	151	21	x	x	NOUN
ejpam-5839	151	22	)	)	PUNCT
ejpam-5839	151	23	,	,	PUNCT
ejpam-5839	151	24	respectively	respectively	ADV
ejpam-5839	151	25	:	:	PUNCT
ejpam-5839	151	26	in	in	ADP
ejpam-5839	151	27	(	(	PUNCT
ejpam-5839	151	28	µx1	µx1	NOUN
ejpam-5839	151	29	+	+	CCONJ
ejpam-5839	151	30	(	(	PUNCT
ejpam-5839	151	31	1−	1−	NUM
ejpam-5839	151	32	µ)x2	µ)x2	PROPN
ejpam-5839	151	33	)	)	PUNCT
ejpam-5839	151	34	≥	≥	PROPN
ejpam-5839	151	35	max	max	PROPN
ejpam-5839	151	36	(	(	PUNCT
ejpam-5839	151	37	in	in	ADP
ejpam-5839	151	38	(	(	PUNCT
ejpam-5839	151	39	x1	x1	PROPN
ejpam-5839	151	40	)	)	PUNCT
ejpam-5839	151	41	,	,	PUNCT
ejpam-5839	151	42	in	in	ADP
ejpam-5839	151	43	(	(	PUNCT
ejpam-5839	151	44	x2	x2	PROPN
ejpam-5839	151	45	)	)	PUNCT
ejpam-5839	151	46	)	)	PUNCT
ejpam-5839	151	47	,	,	PUNCT
ejpam-5839	151	48	a.	a.	NOUN
ejpam-5839	151	49	shihadeh	shihadeh	VERB
ejpam-5839	151	50	et	et	PROPN
ejpam-5839	151	51	al	al	PROPN
ejpam-5839	151	52	.	.	PUNCT
ejpam-5839	151	53	/	/	SYM
ejpam-5839	151	54	eur	eur	PROPN
ejpam-5839	151	55	.	.	PUNCT
ejpam-5839	152	1	j.	j.	PROPN
ejpam-5839	152	2	pure	pure	PROPN
ejpam-5839	152	3	appl	appl	PROPN
ejpam-5839	152	4	.	.	PROPN
ejpam-5839	152	5	math	math	PROPN
ejpam-5839	152	6	,	,	PUNCT
ejpam-5839	152	7	18	18	NUM
ejpam-5839	152	8	(	(	PUNCT
ejpam-5839	152	9	2	2	NUM
ejpam-5839	152	10	)	)	PUNCT
ejpam-5839	152	11	(	(	PUNCT
ejpam-5839	152	12	2025	2025	NUM
ejpam-5839	152	13	)	)	PUNCT
ejpam-5839	152	14	,	,	PUNCT
ejpam-5839	152	15	5839	5839	NUM
ejpam-5839	152	16	5	5	NUM
ejpam-5839	152	17	of	of	ADP
ejpam-5839	152	18	54	54	NUM
ejpam-5839	152	19	fn	fn	NOUN
ejpam-5839	152	20	(	(	PUNCT
ejpam-5839	152	21	µx1	µx1	NOUN
ejpam-5839	152	22	+	+	CCONJ
ejpam-5839	152	23	(	(	PUNCT
ejpam-5839	152	24	1−	1−	NUM
ejpam-5839	152	25	µ)x2	µ)x2	PROPN
ejpam-5839	152	26	)	)	PUNCT
ejpam-5839	152	27	≥	≥	PROPN
ejpam-5839	152	28	max	max	PROPN
ejpam-5839	153	1	(	(	PUNCT
ejpam-5839	153	2	fn	fn	INTJ
ejpam-5839	153	3	(	(	PUNCT
ejpam-5839	153	4	x1	x1	PROPN
ejpam-5839	153	5	)	)	PUNCT
ejpam-5839	153	6	,	,	PUNCT
ejpam-5839	153	7	fn	fn	INTJ
ejpam-5839	153	8	(	(	PUNCT
ejpam-5839	153	9	x2	x2	PROPN
ejpam-5839	153	10	)	)	PUNCT
ejpam-5839	153	11	)	)	PUNCT
ejpam-5839	153	12	,	,	PUNCT
ejpam-5839	153	13	for	for	ADP
ejpam-5839	153	14	all	all	DET
ejpam-5839	153	15	x1,x2	x1,x2	PROPN
ejpam-5839	153	16	∈	∈	PROPN
ejpam-5839	153	17	r	r	NOUN
ejpam-5839	153	18	and	and	CCONJ
ejpam-5839	153	19	µ	µ	PRON
ejpam-5839	153	20	∈	∈	NOUN
ejpam-5839	154	1	[	[	X
ejpam-5839	154	2	0	0	NUM
ejpam-5839	154	3	,	,	PUNCT
ejpam-5839	154	4	1	1	NUM
ejpam-5839	154	5	]	]	PUNCT
ejpam-5839	154	6	.	.	PUNCT
ejpam-5839	155	1	definition	definition	NOUN
ejpam-5839	155	2	3	3	NUM
ejpam-5839	155	3	.	.	PUNCT
ejpam-5839	156	1	[	[	X
ejpam-5839	156	2	43	43	NUM
ejpam-5839	156	3	]	]	PUNCT
ejpam-5839	156	4	a	a	DET
ejpam-5839	156	5	truth	truth	NOUN
ejpam-5839	156	6	,	,	PUNCT
ejpam-5839	156	7	indeterminacy	indeterminacy	NOUN
ejpam-5839	156	8	,	,	PUNCT
ejpam-5839	156	9	and	and	CCONJ
ejpam-5839	156	10	falsity	falsity	NOUN
ejpam-5839	156	11	membership	membership	NOUN
ejpam-5839	156	12	function	function	NOUN
ejpam-5839	156	13	describes	describe	VERB
ejpam-5839	156	14	an	an	DET
ejpam-5839	156	15	interval	interval	NOUN
ejpam-5839	156	16	neutrosophic	neutrosophic	ADV
ejpam-5839	156	17	set	set	VERB
ejpam-5839	156	18	n	n	NOUN
ejpam-5839	156	19	over	over	ADP
ejpam-5839	156	20	the	the	DET
ejpam-5839	156	21	universal	universal	ADJ
ejpam-5839	156	22	set	set	VERB
ejpam-5839	156	23	u	u	NOUN
ejpam-5839	156	24	and	and	CCONJ
ejpam-5839	156	25	is	be	AUX
ejpam-5839	156	26	given	give	VERB
ejpam-5839	156	27	as	as	ADP
ejpam-5839	156	28	tn	tn	PROPN
ejpam-5839	156	29	(	(	PUNCT
ejpam-5839	156	30	x	x	NOUN
ejpam-5839	156	31	)	)	PUNCT
ejpam-5839	156	32	,	,	PUNCT
ejpam-5839	156	33	in	in	ADP
ejpam-5839	156	34	(	(	PUNCT
ejpam-5839	156	35	x	x	NOUN
ejpam-5839	156	36	)	)	PUNCT
ejpam-5839	156	37	,	,	PUNCT
ejpam-5839	156	38	and	and	CCONJ
ejpam-5839	156	39	fn	fn	INTJ
ejpam-5839	156	40	(	(	PUNCT
ejpam-5839	156	41	x	x	NOUN
ejpam-5839	156	42	)	)	PUNCT
ejpam-5839	156	43	,	,	PUNCT
ejpam-5839	156	44	respectively	respectively	ADV
ejpam-5839	156	45	.	.	PUNCT
ejpam-5839	157	1	for	for	ADP
ejpam-5839	157	2	all	all	DET
ejpam-5839	157	3	x	x	SYM
ejpam-5839	157	4	∈	∈	PROPN
ejpam-5839	157	5	u	u	NOUN
ejpam-5839	157	6	,	,	PUNCT
ejpam-5839	157	7	we	we	PRON
ejpam-5839	157	8	have	have	VERB
ejpam-5839	157	9	:	:	PUNCT
ejpam-5839	157	10	tn	tn	PROPN
ejpam-5839	157	11	(	(	PUNCT
ejpam-5839	157	12	x	x	NOUN
ejpam-5839	157	13	)	)	PUNCT
ejpam-5839	157	14	=	=	PUNCT
ejpam-5839	158	1	[	[	X
ejpam-5839	158	2	inf	inf	NOUN
ejpam-5839	158	3	tn	tn	PROPN
ejpam-5839	158	4	(	(	PUNCT
ejpam-5839	158	5	x	x	NOUN
ejpam-5839	158	6	)	)	PUNCT
ejpam-5839	158	7	,	,	PUNCT
ejpam-5839	158	8	suptn	suptn	NOUN
ejpam-5839	158	9	(	(	PUNCT
ejpam-5839	158	10	x	x	X
ejpam-5839	158	11	)	)	PUNCT
ejpam-5839	158	12	]	]	PUNCT
ejpam-5839	158	13	,	,	PUNCT
ejpam-5839	158	14	in	in	ADP
ejpam-5839	158	15	(	(	PUNCT
ejpam-5839	158	16	x	x	X
ejpam-5839	158	17	)	)	PUNCT
ejpam-5839	158	18	=	=	PUNCT
ejpam-5839	159	1	[	[	X
ejpam-5839	159	2	inf	inf	NOUN
ejpam-5839	159	3	in	in	ADP
ejpam-5839	159	4	(	(	PUNCT
ejpam-5839	159	5	x	x	NOUN
ejpam-5839	159	6	)	)	PUNCT
ejpam-5839	159	7	,	,	PUNCT
ejpam-5839	159	8	sup	sup	NOUN
ejpam-5839	159	9	in	in	ADP
ejpam-5839	159	10	(	(	PUNCT
ejpam-5839	159	11	x	x	NOUN
ejpam-5839	159	12	)	)	PUNCT
ejpam-5839	159	13	]	]	PUNCT
ejpam-5839	159	14	,	,	PUNCT
ejpam-5839	159	15	fn	fn	INTJ
ejpam-5839	159	16	(	(	PUNCT
ejpam-5839	159	17	x	x	NOUN
ejpam-5839	159	18	)	)	PUNCT
ejpam-5839	159	19	=	=	PUNCT
ejpam-5839	160	1	[	[	X
ejpam-5839	160	2	inf	inf	NOUN
ejpam-5839	160	3	fn	fn	ADJ
ejpam-5839	160	4	(	(	PUNCT
ejpam-5839	160	5	x	x	NOUN
ejpam-5839	160	6	)	)	PUNCT
ejpam-5839	160	7	,	,	PUNCT
ejpam-5839	160	8	supfn	supfn	X
ejpam-5839	160	9	(	(	PUNCT
ejpam-5839	160	10	x	x	NOUN
ejpam-5839	160	11	)	)	PUNCT
ejpam-5839	160	12	]	]	PUNCT
ejpam-5839	161	1	⊆	⊆	NUM
ejpam-5839	161	2	[	[	X
ejpam-5839	161	3	0	0	NUM
ejpam-5839	161	4	,	,	PUNCT
ejpam-5839	161	5	1	1	NUM
ejpam-5839	161	6	]	]	PUNCT
ejpam-5839	161	7	,	,	PUNCT
ejpam-5839	161	8	∀x	∀x	X
ejpam-5839	161	9	∈	∈	PROPN
ejpam-5839	161	10	u.	u.	NOUN
ejpam-5839	161	11	here	here	ADV
ejpam-5839	161	12	,	,	PUNCT
ejpam-5839	161	13	we	we	PRON
ejpam-5839	161	14	focus	focus	VERB
ejpam-5839	161	15	on	on	ADP
ejpam-5839	161	16	the	the	DET
ejpam-5839	161	17	sub	sub	ADJ
ejpam-5839	161	18	-	-	ADJ
ejpam-5839	161	19	unitary	unitary	ADJ
ejpam-5839	161	20	range	range	NOUN
ejpam-5839	161	21	[	[	X
ejpam-5839	161	22	0	0	NUM
ejpam-5839	161	23	,	,	PUNCT
ejpam-5839	161	24	1	1	NUM
ejpam-5839	161	25	]	]	PUNCT
ejpam-5839	161	26	.	.	PUNCT
ejpam-5839	162	1	let	let	VERB
ejpam-5839	162	2	ñ	ñ	PROPN
ejpam-5839	162	3	=	=	SYM
ejpam-5839	162	4	⟨[tl	⟨[tl	NOUN
ejpam-5839	162	5	ñ	ñ	VERB
ejpam-5839	162	6	,	,	PUNCT
ejpam-5839	162	7	t	t	PROPN
ejpam-5839	162	8	u	u	PRON
ejpam-5839	162	9	ñ	ñ	VERB
ejpam-5839	162	10	]	]	PUNCT
ejpam-5839	162	11	,	,	PUNCT
ejpam-5839	162	12	[	[	X
ejpam-5839	162	13	ilñ	ilñ	NOUN
ejpam-5839	162	14	,	,	PUNCT
ejpam-5839	162	15	i	i	PRON
ejpam-5839	162	16	u	u	PROPN
ejpam-5839	162	17	ñ	ñ	VERB
ejpam-5839	162	18	]	]	PUNCT
ejpam-5839	162	19	,	,	PUNCT
ejpam-5839	163	1	[	[	X
ejpam-5839	163	2	fl	fl	ADP
ejpam-5839	163	3	ñ	ñ	PROPN
ejpam-5839	163	4	,	,	PUNCT
ejpam-5839	163	5	f	f	PROPN
ejpam-5839	163	6	u	u	PROPN
ejpam-5839	163	7	ñ	ñ	PROPN
ejpam-5839	163	8	]	]	PUNCT
ejpam-5839	163	9	⟩	⟩	NOUN
ejpam-5839	163	10	indicate	indicate	VERB
ejpam-5839	163	11	a	a	DET
ejpam-5839	163	12	neutrosophic	neutrosophic	ADJ
ejpam-5839	163	13	interval	interval	NOUN
ejpam-5839	163	14	number	number	NOUN
ejpam-5839	163	15	(	(	PUNCT
ejpam-5839	163	16	inn	inn	PROPN
ejpam-5839	163	17	)	)	PUNCT
ejpam-5839	163	18	,	,	PUNCT
ejpam-5839	163	19	where	where	SCONJ
ejpam-5839	163	20	tl	tl	PROPN
ejpam-5839	163	21	ñ	ñ	PROPN
ejpam-5839	163	22	,	,	PUNCT
ejpam-5839	163	23	t	t	PROPN
ejpam-5839	163	24	u	u	PRON
ejpam-5839	163	25	ñ	ñ	PROPN
ejpam-5839	163	26	,	,	PUNCT
ejpam-5839	163	27	ilñ	ilñ	ADP
ejpam-5839	163	28	,	,	PUNCT
ejpam-5839	163	29	i	i	PRON
ejpam-5839	163	30	u	u	PROPN
ejpam-5839	163	31	ñ	ñ	PROPN
ejpam-5839	163	32	,	,	PUNCT
ejpam-5839	163	33	fl	fl	PROPN
ejpam-5839	163	34	ñ	ñ	PROPN
ejpam-5839	163	35	,	,	PUNCT
ejpam-5839	163	36	and	and	CCONJ
ejpam-5839	163	37	fu	fu	ADJ
ejpam-5839	163	38	ñ	ñ	VERB
ejpam-5839	163	39	denote	denote	NOUN
ejpam-5839	163	40	:	:	PUNCT
ejpam-5839	163	41	inf	inf	PROPN
ejpam-5839	163	42	tñ	tñ	X
ejpam-5839	163	43	(	(	PUNCT
ejpam-5839	163	44	x	x	NOUN
ejpam-5839	163	45	)	)	PUNCT
ejpam-5839	163	46	,	,	PUNCT
ejpam-5839	163	47	suptñ	suptñ	NOUN
ejpam-5839	163	48	(	(	PUNCT
ejpam-5839	163	49	x	x	X
ejpam-5839	163	50	)	)	PUNCT
ejpam-5839	163	51	,	,	PUNCT
ejpam-5839	163	52	inf	inf	NOUN
ejpam-5839	163	53	iñ	iñ	PRON
ejpam-5839	163	54	(	(	PUNCT
ejpam-5839	163	55	x	x	NOUN
ejpam-5839	163	56	)	)	PUNCT
ejpam-5839	163	57	,	,	PUNCT
ejpam-5839	163	58	sup	sup	NOUN
ejpam-5839	163	59	iñ	iñ	PRON
ejpam-5839	163	60	(	(	PUNCT
ejpam-5839	163	61	x	x	NOUN
ejpam-5839	163	62	)	)	PUNCT
ejpam-5839	163	63	,	,	PUNCT
ejpam-5839	163	64	inf	inf	PROPN
ejpam-5839	163	65	fñ	fñ	PROPN
ejpam-5839	163	66	(	(	PUNCT
ejpam-5839	163	67	x	x	NOUN
ejpam-5839	163	68	)	)	PUNCT
ejpam-5839	163	69	,	,	PUNCT
ejpam-5839	163	70	supfñ	supfñ	NUM
ejpam-5839	163	71	(	(	PUNCT
ejpam-5839	163	72	x	x	NOUN
ejpam-5839	163	73	)	)	PUNCT
ejpam-5839	163	74	,	,	PUNCT
ejpam-5839	163	75	respectively	respectively	ADV
ejpam-5839	163	76	.	.	PUNCT
ejpam-5839	164	1	3	3	X
ejpam-5839	164	2	.	.	X
ejpam-5839	164	3	single	single	ADJ
ejpam-5839	164	4	valued	value	VERB
ejpam-5839	164	5	quadri	quadri	PROPN
ejpam-5839	164	6	-	-	PUNCT
ejpam-5839	164	7	partitioned	partition	VERB
ejpam-5839	164	8	neutrosophic	neutrosophic	ADJ
ejpam-5839	164	9	set	set	VERB
ejpam-5839	164	10	this	this	DET
ejpam-5839	164	11	section	section	NOUN
ejpam-5839	164	12	introduces	introduce	VERB
ejpam-5839	164	13	the	the	DET
ejpam-5839	164	14	single	single	ADJ
ejpam-5839	164	15	valued	value	VERB
ejpam-5839	164	16	quadri	quadri	PROPN
ejpam-5839	164	17	-	-	PUNCT
ejpam-5839	164	18	partitioned	partition	VERB
ejpam-5839	164	19	neutrosophic	neutrosophic	ADJ
ejpam-5839	164	20	set	set	NOUN
ejpam-5839	164	21	(	(	PUNCT
ejpam-5839	164	22	svqns	svqns	PROPN
ejpam-5839	164	23	)	)	PUNCT
ejpam-5839	164	24	,	,	PUNCT
ejpam-5839	164	25	characterized	characterize	VERB
ejpam-5839	164	26	by	by	ADP
ejpam-5839	164	27	membership	membership	NOUN
ejpam-5839	164	28	functions	function	NOUN
ejpam-5839	164	29	representing	represent	VERB
ejpam-5839	164	30	absolute	absolute	ADJ
ejpam-5839	164	31	truth	truth	NOUN
ejpam-5839	164	32	,	,	PUNCT
ejpam-5839	164	33	relative	relative	ADJ
ejpam-5839	164	34	truth	truth	NOUN
ejpam-5839	164	35	,	,	PUNCT
ejpam-5839	164	36	absolute	absolute	ADJ
ejpam-5839	164	37	falsehood	falsehood	NOUN
ejpam-5839	164	38	,	,	PUNCT
ejpam-5839	164	39	and	and	CCONJ
ejpam-5839	164	40	relative	relative	ADJ
ejpam-5839	164	41	falsehood	falsehood	NOUN
ejpam-5839	164	42	.	.	PUNCT
ejpam-5839	165	1	we	we	PRON
ejpam-5839	165	2	define	define	VERB
ejpam-5839	165	3	the	the	DET
ejpam-5839	165	4	inclusion	inclusion	NOUN
ejpam-5839	165	5	of	of	ADP
ejpam-5839	165	6	one	one	NUM
ejpam-5839	165	7	svqns	svqns	NOUN
ejpam-5839	165	8	within	within	ADP
ejpam-5839	165	9	another	another	PRON
ejpam-5839	165	10	based	base	VERB
ejpam-5839	165	11	on	on	ADP
ejpam-5839	165	12	membership	membership	NOUN
ejpam-5839	165	13	values	value	NOUN
ejpam-5839	165	14	.	.	PUNCT
ejpam-5839	166	1	the	the	DET
ejpam-5839	166	2	union	union	NOUN
ejpam-5839	166	3	and	and	CCONJ
ejpam-5839	166	4	intersections	intersection	NOUN
ejpam-5839	166	5	are	be	AUX
ejpam-5839	166	6	also	also	ADV
ejpam-5839	166	7	defined	define	VERB
ejpam-5839	166	8	in	in	ADP
ejpam-5839	166	9	this	this	DET
ejpam-5839	166	10	study	study	NOUN
ejpam-5839	166	11	.	.	PUNCT
ejpam-5839	167	1	the	the	DET
ejpam-5839	167	2	quadri	quadri	PROPN
ejpam-5839	167	3	single	single	PROPN
ejpam-5839	167	4	valued	value	VERB
ejpam-5839	167	5	neutrosophic	neutrosophic	ADJ
ejpam-5839	167	6	number	number	NOUN
ejpam-5839	167	7	(	(	PUNCT
ejpam-5839	167	8	qsvnn	qsvnn	ADJ
ejpam-5839	167	9	)	)	PUNCT
ejpam-5839	167	10	is	be	AUX
ejpam-5839	167	11	also	also	ADV
ejpam-5839	167	12	proposed	propose	VERB
ejpam-5839	167	13	,	,	PUNCT
ejpam-5839	167	14	a	a	DET
ejpam-5839	167	15	unique	unique	ADJ
ejpam-5839	167	16	neutrosophic	neutrosophic	ADJ
ejpam-5839	167	17	set	set	NOUN
ejpam-5839	167	18	on	on	ADP
ejpam-5839	167	19	the	the	DET
ejpam-5839	167	20	real	real	ADJ
ejpam-5839	167	21	number	number	NOUN
ejpam-5839	167	22	line	line	NOUN
ejpam-5839	167	23	r	r	NOUN
ejpam-5839	167	24	,	,	PUNCT
ejpam-5839	167	25	incorporating	incorporate	VERB
ejpam-5839	167	26	truth	truth	NOUN
ejpam-5839	167	27	,	,	PUNCT
ejpam-5839	167	28	indeterminacy	indeterminacy	NOUN
ejpam-5839	167	29	,	,	PUNCT
ejpam-5839	167	30	hesitation	hesitation	NOUN
ejpam-5839	167	31	,	,	PUNCT
ejpam-5839	167	32	and	and	CCONJ
ejpam-5839	167	33	falsity	falsity	NOUN
ejpam-5839	167	34	membership	membership	NOUN
ejpam-5839	167	35	functions	function	NOUN
ejpam-5839	167	36	.	.	PUNCT
ejpam-5839	168	1	additionally	additionally	ADV
ejpam-5839	168	2	,	,	PUNCT
ejpam-5839	168	3	we	we	PRON
ejpam-5839	168	4	define	define	VERB
ejpam-5839	168	5	the	the	DET
ejpam-5839	168	6	cut	cut	NOUN
ejpam-5839	168	7	of	of	ADP
ejpam-5839	168	8	a	a	DET
ejpam-5839	168	9	neutrosophic	neutrosophic	ADJ
ejpam-5839	168	10	set	set	NOUN
ejpam-5839	168	11	,	,	PUNCT
ejpam-5839	168	12	providing	provide	VERB
ejpam-5839	168	13	a	a	DET
ejpam-5839	168	14	framework	framework	NOUN
ejpam-5839	168	15	for	for	ADP
ejpam-5839	168	16	analyzing	analyze	VERB
ejpam-5839	168	17	subsets	subset	NOUN
ejpam-5839	168	18	.	.	PUNCT
ejpam-5839	169	1	definition	definition	NOUN
ejpam-5839	169	2	4	4	NUM
ejpam-5839	169	3	.	.	PUNCT
ejpam-5839	170	1	a	a	DET
ejpam-5839	170	2	single	single	ADJ
ejpam-5839	170	3	valued	value	VERB
ejpam-5839	170	4	quadri	quadri	NOUN
ejpam-5839	170	5	-	-	PUNCT
ejpam-5839	170	6	partitioned	partition	VERB
ejpam-5839	170	7	neutrosophic	neutrosophic	ADJ
ejpam-5839	170	8	set	set	NOUN
ejpam-5839	170	9	(	(	PUNCT
ejpam-5839	170	10	svqns	svqns	PROPN
ejpam-5839	170	11	)	)	PUNCT
ejpam-5839	170	12	a	a	PRON
ejpam-5839	170	13	on	on	ADP
ejpam-5839	170	14	the	the	DET
ejpam-5839	170	15	universe	universe	NOUN
ejpam-5839	170	16	of	of	ADP
ejpam-5839	170	17	discourse	discourse	NOUN
ejpam-5839	170	18	x	x	SYM
ejpam-5839	170	19	is	be	AUX
ejpam-5839	170	20	characterized	characterize	VERB
ejpam-5839	170	21	by	by	ADP
ejpam-5839	170	22	the	the	DET
ejpam-5839	170	23	following	follow	VERB
ejpam-5839	170	24	membership	membership	NOUN
ejpam-5839	170	25	functions	function	NOUN
ejpam-5839	170	26	:	:	PUNCT
ejpam-5839	170	27	•	•	NUM
ejpam-5839	170	28	absolute	absolute	ADJ
ejpam-5839	170	29	true	true	ADJ
ejpam-5839	170	30	membership	membership	NOUN
ejpam-5839	170	31	function	function	NOUN
ejpam-5839	170	32	:	:	PUNCT
ejpam-5839	170	33	ta(x	ta(x	NOUN
ejpam-5839	170	34	)	)	PUNCT
ejpam-5839	170	35	,	,	PUNCT
ejpam-5839	170	36	•	•	NUM
ejpam-5839	170	37	relative	relative	ADJ
ejpam-5839	170	38	true	true	ADJ
ejpam-5839	170	39	membership	membership	NOUN
ejpam-5839	170	40	function	function	NOUN
ejpam-5839	170	41	:	:	PUNCT
ejpam-5839	170	42	reta(x	reta(x	PROPN
ejpam-5839	170	43	)	)	PUNCT
ejpam-5839	170	44	,	,	PUNCT
ejpam-5839	170	45	•	•	ADP
ejpam-5839	170	46	absolute	absolute	ADJ
ejpam-5839	170	47	false	false	ADJ
ejpam-5839	170	48	membership	membership	NOUN
ejpam-5839	170	49	function	function	NOUN
ejpam-5839	170	50	:	:	PUNCT
ejpam-5839	170	51	fa(x	fa(x	NOUN
ejpam-5839	170	52	)	)	PUNCT
ejpam-5839	170	53	,	,	PUNCT
ejpam-5839	170	54	•	•	NUM
ejpam-5839	170	55	relative	relative	ADJ
ejpam-5839	170	56	false	false	ADJ
ejpam-5839	170	57	membership	membership	NOUN
ejpam-5839	170	58	function	function	NOUN
ejpam-5839	170	59	:	:	PUNCT
ejpam-5839	170	60	refa(x	refa(x	PROPN
ejpam-5839	170	61	)	)	PUNCT
ejpam-5839	170	62	.	.	PUNCT
ejpam-5839	171	1	these	these	DET
ejpam-5839	171	2	functions	function	NOUN
ejpam-5839	171	3	are	be	AUX
ejpam-5839	171	4	subsets	subset	NOUN
ejpam-5839	171	5	of	of	ADP
ejpam-5839	171	6	]	]	X
ejpam-5839	171	7	0	0	NUM
ejpam-5839	171	8	,	,	PUNCT
ejpam-5839	171	9	1	1	NUM
ejpam-5839	171	10	[	[	X
ejpam-5839	171	11	,	,	PUNCT
ejpam-5839	171	12	i.e.	i.e.	X
ejpam-5839	171	13	,	,	PUNCT
ejpam-5839	171	14	ta(x	ta(x	NOUN
ejpam-5839	171	15	)	)	PUNCT
ejpam-5839	171	16	:	:	PUNCT
ejpam-5839	171	17	x	x	X
ejpam-5839	171	18	→]0	→]0	NOUN
ejpam-5839	171	19	,	,	PUNCT
ejpam-5839	171	20	1	1	NUM
ejpam-5839	171	21	[	[	X
ejpam-5839	171	22	,	,	PUNCT
ejpam-5839	171	23	reta(x	reta(x	PROPN
ejpam-5839	171	24	)	)	PUNCT
ejpam-5839	171	25	:	:	PUNCT
ejpam-5839	171	26	x	x	SYM
ejpam-5839	171	27	→]0	→]0	NOUN
ejpam-5839	171	28	,	,	PUNCT
ejpam-5839	171	29	1	1	NUM
ejpam-5839	171	30	[	[	X
ejpam-5839	171	31	,	,	PUNCT
ejpam-5839	171	32	fa(x	fa(x	NOUN
ejpam-5839	171	33	)	)	PUNCT
ejpam-5839	171	34	:	:	PUNCT
ejpam-5839	172	1	x	x	X
ejpam-5839	172	2	→]0	→]0	NOUN
ejpam-5839	172	3	,	,	PUNCT
ejpam-5839	172	4	1	1	NUM
ejpam-5839	172	5	[	[	X
ejpam-5839	172	6	,	,	PUNCT
ejpam-5839	172	7	refa(x	refa(x	PROPN
ejpam-5839	172	8	)	)	PUNCT
ejpam-5839	172	9	:	:	PUNCT
ejpam-5839	172	10	x	x	SYM
ejpam-5839	172	11	→]0	→]0	NOUN
ejpam-5839	172	12	,	,	PUNCT
ejpam-5839	172	13	1	1	NUM
ejpam-5839	172	14	[	[	PUNCT
ejpam-5839	172	15	with	with	ADP
ejpam-5839	172	16	the	the	DET
ejpam-5839	172	17	condition	condition	NOUN
ejpam-5839	172	18	:	:	PUNCT
ejpam-5839	172	19	0	0	NUM
ejpam-5839	172	20	≤	≤	NUM
ejpam-5839	172	21	supta(x	supta(x	PROPN
ejpam-5839	172	22	)	)	PUNCT
ejpam-5839	172	23	+	+	NUM
ejpam-5839	172	24	supreta(x	supreta(x	PROPN
ejpam-5839	172	25	)	)	PUNCT
ejpam-5839	172	26	+	+	CCONJ
ejpam-5839	172	27	supfa(x	supfa(x	PROPN
ejpam-5839	172	28	)	)	PUNCT
ejpam-5839	172	29	+	+	NUM
ejpam-5839	172	30	suprefa(x	suprefa(x	NUM
ejpam-5839	172	31	)	)	PUNCT
ejpam-5839	172	32	≤	≤	NOUN
ejpam-5839	172	33	4	4	NUM
ejpam-5839	172	34	.	.	PUNCT
ejpam-5839	173	1	thus	thus	ADV
ejpam-5839	173	2	,	,	PUNCT
ejpam-5839	173	3	the	the	DET
ejpam-5839	173	4	svqns	svqns	PROPN
ejpam-5839	173	5	can	can	AUX
ejpam-5839	173	6	be	be	AUX
ejpam-5839	173	7	represented	represent	VERB
ejpam-5839	173	8	as	as	ADP
ejpam-5839	173	9	:	:	PUNCT
ejpam-5839	173	10	a	a	PRON
ejpam-5839	173	11	=	=	X
ejpam-5839	173	12	{	{	PUNCT
ejpam-5839	173	13	⟨x	⟨x	VERB
ejpam-5839	173	14	,	,	PUNCT
ejpam-5839	173	15	ta(x	ta(x	NOUN
ejpam-5839	173	16	)	)	PUNCT
ejpam-5839	173	17	,	,	PUNCT
ejpam-5839	173	18	reta(x	reta(x	PROPN
ejpam-5839	173	19	)	)	PUNCT
ejpam-5839	173	20	,	,	PUNCT
ejpam-5839	173	21	refa(x	refa(x	PROPN
ejpam-5839	173	22	)	)	PUNCT
ejpam-5839	173	23	,	,	PUNCT
ejpam-5839	173	24	fa(x)⟩	fa(x)⟩	NOUN
ejpam-5839	173	25	:	:	PUNCT
ejpam-5839	173	26	x	x	PUNCT
ejpam-5839	173	27	∈	∈	NOUN
ejpam-5839	173	28	x	x	NOUN
ejpam-5839	173	29	}	}	PUNCT
ejpam-5839	173	30	.	.	PUNCT
ejpam-5839	174	1	a.	a.	NOUN
ejpam-5839	174	2	shihadeh	shihadeh	PROPN
ejpam-5839	174	3	et	et	PROPN
ejpam-5839	174	4	al	al	PROPN
ejpam-5839	174	5	.	.	PUNCT
ejpam-5839	174	6	/	/	SYM
ejpam-5839	174	7	eur	eur	PROPN
ejpam-5839	174	8	.	.	PUNCT
ejpam-5839	175	1	j.	j.	PROPN
ejpam-5839	175	2	pure	pure	PROPN
ejpam-5839	175	3	appl	appl	PROPN
ejpam-5839	175	4	.	.	PROPN
ejpam-5839	175	5	math	math	PROPN
ejpam-5839	175	6	,	,	PUNCT
ejpam-5839	175	7	18	18	NUM
ejpam-5839	175	8	(	(	PUNCT
ejpam-5839	175	9	2	2	NUM
ejpam-5839	175	10	)	)	PUNCT
ejpam-5839	175	11	(	(	PUNCT
ejpam-5839	175	12	2025	2025	NUM
ejpam-5839	175	13	)	)	PUNCT
ejpam-5839	175	14	,	,	PUNCT
ejpam-5839	175	15	5839	5839	NUM
ejpam-5839	175	16	6	6	NUM
ejpam-5839	175	17	of	of	ADP
ejpam-5839	175	18	54	54	NUM
ejpam-5839	175	19	definition	definition	NOUN
ejpam-5839	175	20	5	5	NUM
ejpam-5839	175	21	.	.	PUNCT
ejpam-5839	176	1	a	a	DET
ejpam-5839	176	2	single	single	ADJ
ejpam-5839	176	3	valued	value	VERB
ejpam-5839	176	4	quadri	quadri	NOUN
ejpam-5839	176	5	-	-	PUNCT
ejpam-5839	176	6	partitioned	partition	VERB
ejpam-5839	176	7	neutrosophic	neutrosophic	ADJ
ejpam-5839	176	8	set	set	NOUN
ejpam-5839	176	9	a	a	PRON
ejpam-5839	176	10	is	be	AUX
ejpam-5839	176	11	contained	contain	VERB
ejpam-5839	176	12	in	in	ADP
ejpam-5839	176	13	another	another	DET
ejpam-5839	176	14	single	single	ADJ
ejpam-5839	176	15	valued	value	VERB
ejpam-5839	176	16	quadri	quadri	NOUN
ejpam-5839	176	17	-	-	PUNCT
ejpam-5839	176	18	partitioned	partition	VERB
ejpam-5839	176	19	neutrosophic	neutrosophic	ADJ
ejpam-5839	176	20	set	set	NOUN
ejpam-5839	176	21	b	b	NOUN
ejpam-5839	176	22	if	if	SCONJ
ejpam-5839	176	23	the	the	DET
ejpam-5839	176	24	following	follow	VERB
ejpam-5839	176	25	conditions	condition	NOUN
ejpam-5839	176	26	hold	hold	VERB
ejpam-5839	176	27	for	for	ADP
ejpam-5839	176	28	each	each	DET
ejpam-5839	176	29	x	x	SYM
ejpam-5839	176	30	∈	∈	PROPN
ejpam-5839	176	31	x	x	NOUN
ejpam-5839	176	32	:	:	PUNCT
ejpam-5839	176	33	ta(x	ta(x	NOUN
ejpam-5839	176	34	)	)	PUNCT
ejpam-5839	176	35	≤	≤	NOUN
ejpam-5839	176	36	tb(x	tb(x	NUM
ejpam-5839	176	37	)	)	PUNCT
ejpam-5839	176	38	,	,	PUNCT
ejpam-5839	176	39	reta(x	reta(x	PROPN
ejpam-5839	176	40	)	)	PUNCT
ejpam-5839	176	41	≤	≤	NOUN
ejpam-5839	176	42	retb(x	retb(x	PROPN
ejpam-5839	176	43	)	)	PUNCT
ejpam-5839	176	44	,	,	PUNCT
ejpam-5839	176	45	fa(x	fa(x	PROPN
ejpam-5839	176	46	)	)	PUNCT
ejpam-5839	176	47	≥	≥	NOUN
ejpam-5839	176	48	fb(x	fb(x	NUM
ejpam-5839	176	49	)	)	PUNCT
ejpam-5839	176	50	,	,	PUNCT
ejpam-5839	176	51	refa(x	refa(x	PROPN
ejpam-5839	176	52	)	)	PUNCT
ejpam-5839	176	53	≥	≥	NOUN
ejpam-5839	176	54	refb(x	refb(x	PROPN
ejpam-5839	176	55	)	)	PUNCT
ejpam-5839	176	56	.	.	PUNCT
ejpam-5839	177	1	equality	equality	NOUN
ejpam-5839	177	2	of	of	ADP
ejpam-5839	177	3	two	two	NUM
ejpam-5839	177	4	svqnss	svqns	NOUN
ejpam-5839	177	5	is	be	AUX
ejpam-5839	177	6	defined	define	VERB
ejpam-5839	177	7	as	as	ADP
ejpam-5839	177	8	:	:	PUNCT
ejpam-5839	177	9	a	a	DET
ejpam-5839	177	10	=	=	X
ejpam-5839	177	11	b	b	NUM
ejpam-5839	177	12	⇐	⇐	PROPN
ejpam-5839	177	13	⇒	⇒	NOUN
ejpam-5839	177	14	a	a	DET
ejpam-5839	177	15	⊆	⊆	NUM
ejpam-5839	177	16	b	b	NOUN
ejpam-5839	177	17	and	and	CCONJ
ejpam-5839	177	18	b	b	NOUN
ejpam-5839	177	19	⊆	⊆	NUM
ejpam-5839	177	20	a.	a.	NOUN
ejpam-5839	177	21	the	the	DET
ejpam-5839	177	22	complement	complement	NOUN
ejpam-5839	177	23	of	of	ADP
ejpam-5839	177	24	a	a	PRON
ejpam-5839	177	25	,	,	PUNCT
ejpam-5839	177	26	denoted	denote	VERB
ejpam-5839	177	27	as	as	ADP
ejpam-5839	177	28	ac	ac	PROPN
ejpam-5839	177	29	,	,	PUNCT
ejpam-5839	177	30	is	be	AUX
ejpam-5839	177	31	given	give	VERB
ejpam-5839	177	32	by	by	ADP
ejpam-5839	177	33	:	:	PUNCT
ejpam-5839	177	34	ac	ac	PROPN
ejpam-5839	177	35	=	=	PUNCT
ejpam-5839	177	36	{	{	PUNCT
ejpam-5839	177	37	⟨x	⟨x	VERB
ejpam-5839	177	38	,	,	PUNCT
ejpam-5839	177	39	fa(x	fa(x	NOUN
ejpam-5839	177	40	)	)	PUNCT
ejpam-5839	177	41	,	,	PUNCT
ejpam-5839	177	42	refa(x	refa(x	PROPN
ejpam-5839	177	43	)	)	PUNCT
ejpam-5839	177	44	,	,	PUNCT
ejpam-5839	177	45	ta(x	ta(x	NOUN
ejpam-5839	177	46	)	)	PUNCT
ejpam-5839	177	47	,	,	PUNCT
ejpam-5839	177	48	reta(x)⟩	reta(x)⟩	NOUN
ejpam-5839	177	49	:	:	PUNCT
ejpam-5839	178	1	x	x	PUNCT
ejpam-5839	178	2	∈	∈	NOUN
ejpam-5839	178	3	x	x	X
ejpam-5839	178	4	}	}	PUNCT
ejpam-5839	178	5	.	.	PUNCT
ejpam-5839	179	1	definition	definition	NOUN
ejpam-5839	179	2	6	6	NUM
ejpam-5839	179	3	.	.	PUNCT
ejpam-5839	180	1	let	let	VERB
ejpam-5839	180	2	a	a	PRON
ejpam-5839	180	3	and	and	CCONJ
ejpam-5839	180	4	b	b	NOUN
ejpam-5839	180	5	be	be	AUX
ejpam-5839	180	6	two	two	NUM
ejpam-5839	180	7	single	single	ADJ
ejpam-5839	180	8	valued	value	VERB
ejpam-5839	180	9	quadri	quadri	PROPN
ejpam-5839	180	10	-	-	PUNCT
ejpam-5839	180	11	partitioned	partition	VERB
ejpam-5839	180	12	neutrosophic	neutrosophic	ADJ
ejpam-5839	180	13	sets	set	NOUN
ejpam-5839	180	14	on	on	ADP
ejpam-5839	180	15	the	the	DET
ejpam-5839	180	16	universe	universe	NOUN
ejpam-5839	180	17	of	of	ADP
ejpam-5839	180	18	discourse	discourse	NOUN
ejpam-5839	180	19	x	x	NOUN
ejpam-5839	180	20	,	,	PUNCT
ejpam-5839	180	21	then	then	ADV
ejpam-5839	180	22	:	:	PUNCT
ejpam-5839	180	23	(	(	PUNCT
ejpam-5839	180	24	i	i	NOUN
ejpam-5839	180	25	)	)	PUNCT
ejpam-5839	180	26	the	the	DET
ejpam-5839	180	27	union	union	NOUN
ejpam-5839	180	28	of	of	ADP
ejpam-5839	180	29	a	a	PRON
ejpam-5839	180	30	and	and	CCONJ
ejpam-5839	180	31	b	b	NOUN
ejpam-5839	180	32	is	be	AUX
ejpam-5839	180	33	defined	define	VERB
ejpam-5839	180	34	as	as	ADP
ejpam-5839	180	35	:	:	PUNCT
ejpam-5839	180	36	a	a	DET
ejpam-5839	180	37	∪b	∪b	X
ejpam-5839	180	38	=	=	PUNCT
ejpam-5839	180	39	{	{	PUNCT
ejpam-5839	180	40	x	x	NOUN
ejpam-5839	180	41	,	,	PUNCT
ejpam-5839	180	42	[	[	PUNCT
ejpam-5839	180	43	max(ta(x	max(ta(x	PROPN
ejpam-5839	180	44	)	)	PUNCT
ejpam-5839	180	45	,	,	PUNCT
ejpam-5839	180	46	tb(x)),max(reta(x	tb(x)),max(reta(x	PROPN
ejpam-5839	180	47	)	)	PUNCT
ejpam-5839	180	48	,	,	PUNCT
ejpam-5839	180	49	retb(x	retb(x	NOUN
ejpam-5839	180	50	)	)	PUNCT
ejpam-5839	180	51	)	)	PUNCT
ejpam-5839	180	52	,	,	PUNCT
ejpam-5839	180	53	min(refa(x	min(refa(x	NOUN
ejpam-5839	180	54	)	)	PUNCT
ejpam-5839	180	55	,	,	PUNCT
ejpam-5839	180	56	refb(x)),min(fa(x	refb(x)),min(fa(x	NOUN
ejpam-5839	180	57	)	)	PUNCT
ejpam-5839	180	58	,	,	PUNCT
ejpam-5839	180	59	fb(x	fb(x	ADJ
ejpam-5839	180	60	)	)	PUNCT
ejpam-5839	180	61	)	)	PUNCT
ejpam-5839	180	62	]	]	PUNCT
ejpam-5839	181	1	:	:	PUNCT
ejpam-5839	181	2	x	x	X
ejpam-5839	181	3	∈	∈	NOUN
ejpam-5839	181	4	x	x	PUNCT
ejpam-5839	181	5	}	}	PUNCT
ejpam-5839	181	6	.	.	PUNCT
ejpam-5839	182	1	(	(	PUNCT
ejpam-5839	182	2	ii	ii	X
ejpam-5839	182	3	)	)	PUNCT
ejpam-5839	182	4	the	the	DET
ejpam-5839	182	5	intersection	intersection	NOUN
ejpam-5839	182	6	of	of	ADP
ejpam-5839	182	7	a	a	PRON
ejpam-5839	182	8	and	and	CCONJ
ejpam-5839	182	9	b	b	NOUN
ejpam-5839	182	10	is	be	AUX
ejpam-5839	182	11	defined	define	VERB
ejpam-5839	182	12	as	as	ADP
ejpam-5839	182	13	:	:	PUNCT
ejpam-5839	182	14	a	a	DET
ejpam-5839	182	15	∩b	∩b	NOUN
ejpam-5839	182	16	=	=	SYM
ejpam-5839	182	17	{	{	PUNCT
ejpam-5839	182	18	x	x	NOUN
ejpam-5839	182	19	,	,	PUNCT
ejpam-5839	182	20	[	[	PUNCT
ejpam-5839	182	21	min(ta(x	min(ta(x	NOUN
ejpam-5839	182	22	)	)	PUNCT
ejpam-5839	182	23	,	,	PUNCT
ejpam-5839	182	24	tb(x)),min(reta(x	tb(x)),min(reta(x	PROPN
ejpam-5839	182	25	)	)	PUNCT
ejpam-5839	182	26	,	,	PUNCT
ejpam-5839	182	27	retb(x	retb(x	NOUN
ejpam-5839	182	28	)	)	PUNCT
ejpam-5839	182	29	)	)	PUNCT
ejpam-5839	182	30	,	,	PUNCT
ejpam-5839	182	31	max(refa(x	max(refa(x	NOUN
ejpam-5839	182	32	)	)	PUNCT
ejpam-5839	182	33	,	,	PUNCT
ejpam-5839	182	34	refb(x)),max(fa(x	refb(x)),max(fa(x	NOUN
ejpam-5839	182	35	)	)	PUNCT
ejpam-5839	182	36	,	,	PUNCT
ejpam-5839	182	37	fb(x	fb(x	NUM
ejpam-5839	182	38	)	)	PUNCT
ejpam-5839	182	39	)	)	PUNCT
ejpam-5839	182	40	]	]	PUNCT
ejpam-5839	183	1	:	:	PUNCT
ejpam-5839	183	2	x	x	X
ejpam-5839	183	3	∈	∈	NOUN
ejpam-5839	183	4	x	x	PUNCT
ejpam-5839	183	5	}	}	PUNCT
ejpam-5839	183	6	.	.	PUNCT
ejpam-5839	184	1	definition	definition	NOUN
ejpam-5839	184	2	7	7	NUM
ejpam-5839	184	3	.	.	PUNCT
ejpam-5839	184	4	a	a	DET
ejpam-5839	184	5	quadri	quadri	NOUN
ejpam-5839	184	6	-	-	PUNCT
ejpam-5839	184	7	single	single	ADV
ejpam-5839	184	8	-	-	PUNCT
ejpam-5839	184	9	valued	value	VERB
ejpam-5839	184	10	-	-	PUNCT
ejpam-5839	184	11	neutrosophic	neutrosophic	ADJ
ejpam-5839	184	12	-	-	PUNCT
ejpam-5839	184	13	number	number	NOUN
ejpam-5839	184	14	(	(	PUNCT
ejpam-5839	184	15	q	q	NOUN
ejpam-5839	184	16	-	-	PUNCT
ejpam-5839	184	17	svnn	svnn	NOUN
ejpam-5839	184	18	)	)	PUNCT
ejpam-5839	184	19	is	be	AUX
ejpam-5839	184	20	denoted	denote	VERB
ejpam-5839	184	21	as	as	ADP
ejpam-5839	184	22	:	:	PUNCT
ejpam-5839	184	23	n	n	PROPN
ejpam-5839	184	24	=	=	SYM
ejpam-5839	184	25	⟨(p	⟨(p	ADJ
ejpam-5839	184	26	,	,	PUNCT
ejpam-5839	184	27	q	q	NOUN
ejpam-5839	184	28	,	,	PUNCT
ejpam-5839	184	29	r	r	NOUN
ejpam-5839	184	30	,	,	PUNCT
ejpam-5839	184	31	s	s	PART
ejpam-5839	184	32	)	)	PUNCT
ejpam-5839	184	33	;	;	PUNCT
ejpam-5839	184	34	ρn	ρn	INTJ
ejpam-5839	184	35	,	,	PUNCT
ejpam-5839	184	36	υn	υn	INTJ
ejpam-5839	184	37	,	,	PUNCT
ejpam-5839	184	38	κn	κn	NOUN
ejpam-5839	184	39	,	,	PUNCT
ejpam-5839	184	40	τn	τn	ADP
ejpam-5839	184	41	⟩	⟩	NOUN
ejpam-5839	184	42	where	where	SCONJ
ejpam-5839	184	43	n	n	PRON
ejpam-5839	184	44	is	be	AUX
ejpam-5839	184	45	a	a	DET
ejpam-5839	184	46	unique	unique	ADJ
ejpam-5839	184	47	neutrosophic	neutrosophic	ADJ
ejpam-5839	184	48	set	set	NOUN
ejpam-5839	184	49	on	on	ADP
ejpam-5839	184	50	r	r	NOUN
ejpam-5839	184	51	,	,	PUNCT
ejpam-5839	184	52	with	with	ADP
ejpam-5839	184	53	its	its	PRON
ejpam-5839	184	54	truth	truth	NOUN
ejpam-5839	184	55	-	-	PUNCT
ejpam-5839	184	56	membership	membership	NOUN
ejpam-5839	184	57	function	function	NOUN
ejpam-5839	184	58	tn	tn	PROPN
ejpam-5839	184	59	(	(	PUNCT
ejpam-5839	184	60	x	x	NOUN
ejpam-5839	184	61	)	)	PUNCT
ejpam-5839	184	62	defined	define	VERB
ejpam-5839	184	63	as	as	ADP
ejpam-5839	184	64	:	:	PUNCT
ejpam-5839	184	65	tn	tn	PROPN
ejpam-5839	184	66	(	(	PUNCT
ejpam-5839	184	67	x	x	NOUN
ejpam-5839	184	68	)	)	PUNCT
ejpam-5839	184	69	=	=	SYM
ejpam-5839	185	1			NOUN
ejpam-5839	185	2	x−p	x−p	PROPN
ejpam-5839	185	3	q−p	q−p	PROPN
ejpam-5839	185	4	ρn	ρn	INTJ
ejpam-5839	185	5	,	,	PUNCT
ejpam-5839	185	6	for	for	SCONJ
ejpam-5839	185	7	p	p	DET
ejpam-5839	185	8	⪯	⪯	NOUN
ejpam-5839	185	9	x	x	X
ejpam-5839	185	10	⪯	⪯	PROPN
ejpam-5839	185	11	q	q	NOUN
ejpam-5839	185	12	,	,	PUNCT
ejpam-5839	185	13	r−x	r−x	NOUN
ejpam-5839	185	14	r−q	r−q	NOUN
ejpam-5839	185	15	ρn	ρn	INTJ
ejpam-5839	185	16	,	,	PUNCT
ejpam-5839	185	17	for	for	ADP
ejpam-5839	185	18	q	q	PROPN
ejpam-5839	185	19	⪯	⪯	NOUN
ejpam-5839	185	20	x	x	X
ejpam-5839	185	21	⪯	⪯	VERB
ejpam-5839	185	22	r	r	NOUN
ejpam-5839	185	23	,	,	PUNCT
ejpam-5839	185	24	0	0	NUM
ejpam-5839	185	25	,	,	PUNCT
ejpam-5839	185	26	otherwise	otherwise	ADV
ejpam-5839	185	27	.	.	PUNCT
ejpam-5839	186	1	the	the	DET
ejpam-5839	186	2	definitions	definition	NOUN
ejpam-5839	186	3	of	of	ADP
ejpam-5839	186	4	the	the	DET
ejpam-5839	186	5	indeterminacy	indeterminacy	NOUN
ejpam-5839	186	6	-	-	PUNCT
ejpam-5839	186	7	membership	membership	NOUN
ejpam-5839	186	8	,	,	PUNCT
ejpam-5839	186	9	hesitation	hesitation	NOUN
ejpam-5839	186	10	,	,	PUNCT
ejpam-5839	186	11	and	and	CCONJ
ejpam-5839	186	12	falsity	falsity	NOUN
ejpam-5839	186	13	-	-	PUNCT
ejpam-5839	186	14	membership	membership	NOUN
ejpam-5839	186	15	functions	function	NOUN
ejpam-5839	186	16	follow	follow	VERB
ejpam-5839	186	17	a	a	DET
ejpam-5839	186	18	similar	similar	ADJ
ejpam-5839	186	19	structure	structure	NOUN
ejpam-5839	186	20	.	.	PUNCT
ejpam-5839	187	1	in	in	ADP
ejpam-5839	187	2	(	(	PUNCT
ejpam-5839	187	3	x	x	X
ejpam-5839	187	4	)	)	PUNCT
ejpam-5839	187	5	=	=	SYM
ejpam-5839	188	1			PROPN
ejpam-5839	188	2	q−x+υn	q−x+υn	PROPN
ejpam-5839	188	3	(	(	PUNCT
ejpam-5839	188	4	x−p	x−p	NOUN
ejpam-5839	188	5	)	)	PUNCT
ejpam-5839	188	6	q−p	q−p	NOUN
ejpam-5839	188	7	,	,	PUNCT
ejpam-5839	188	8	for	for	ADP
ejpam-5839	188	9	p	p	DET
ejpam-5839	188	10	⪯	⪯	NOUN
ejpam-5839	188	11	x	x	X
ejpam-5839	188	12	⪯	⪯	PROPN
ejpam-5839	188	13	q	q	PROPN
ejpam-5839	188	14	,	,	PUNCT
ejpam-5839	188	15	q−x+υn	q−x+υn	PROPN
ejpam-5839	188	16	(	(	PUNCT
ejpam-5839	188	17	r−x	r−x	NOUN
ejpam-5839	188	18	)	)	PUNCT
ejpam-5839	188	19	r−q	r−q	NOUN
ejpam-5839	188	20	,	,	PUNCT
ejpam-5839	188	21	for	for	ADP
ejpam-5839	188	22	q	q	PROPN
ejpam-5839	188	23	⪯	⪯	NOUN
ejpam-5839	188	24	x	x	X
ejpam-5839	188	25	⪯	⪯	VERB
ejpam-5839	188	26	r	r	NOUN
ejpam-5839	188	27	,	,	PUNCT
ejpam-5839	188	28	0	0	NUM
ejpam-5839	188	29	,	,	PUNCT
ejpam-5839	188	30	otherwise	otherwise	ADV
ejpam-5839	188	31	.	.	PUNCT
ejpam-5839	189	1	hn	hn	PRON
ejpam-5839	189	2	(	(	PUNCT
ejpam-5839	189	3	x	x	X
ejpam-5839	189	4	)	)	PUNCT
ejpam-5839	189	5	=	=	PUNCT
ejpam-5839	190	1			PRON
ejpam-5839	190	2	q−x+κn	q−x+κn	PROPN
ejpam-5839	190	3	(	(	PUNCT
ejpam-5839	190	4	x−p	x−p	NOUN
ejpam-5839	190	5	)	)	PUNCT
ejpam-5839	190	6	q−p	q−p	NOUN
ejpam-5839	190	7	,	,	PUNCT
ejpam-5839	190	8	for	for	ADP
ejpam-5839	190	9	p	p	DET
ejpam-5839	190	10	⪯	⪯	NOUN
ejpam-5839	190	11	x	x	X
ejpam-5839	190	12	⪯	⪯	PROPN
ejpam-5839	190	13	q	q	NOUN
ejpam-5839	190	14	,	,	PUNCT
ejpam-5839	190	15	q−x+κn	q−x+κn	PROPN
ejpam-5839	190	16	(	(	PUNCT
ejpam-5839	190	17	r−x	r−x	NOUN
ejpam-5839	190	18	)	)	PUNCT
ejpam-5839	190	19	r−q	r−q	NOUN
ejpam-5839	190	20	,	,	PUNCT
ejpam-5839	190	21	for	for	ADP
ejpam-5839	190	22	q	q	PROPN
ejpam-5839	190	23	⪯	⪯	NOUN
ejpam-5839	190	24	x	x	X
ejpam-5839	190	25	⪯	⪯	VERB
ejpam-5839	190	26	r	r	NOUN
ejpam-5839	190	27	,	,	PUNCT
ejpam-5839	190	28	0	0	NUM
ejpam-5839	190	29	,	,	PUNCT
ejpam-5839	190	30	otherwise	otherwise	ADV
ejpam-5839	190	31	.	.	PUNCT
ejpam-5839	191	1	a.	a.	NOUN
ejpam-5839	191	2	shihadeh	shihadeh	VERB
ejpam-5839	191	3	et	et	PROPN
ejpam-5839	191	4	al	al	PROPN
ejpam-5839	191	5	.	.	PUNCT
ejpam-5839	191	6	/	/	SYM
ejpam-5839	191	7	eur	eur	PROPN
ejpam-5839	191	8	.	.	PUNCT
ejpam-5839	192	1	j.	j.	PROPN
ejpam-5839	192	2	pure	pure	PROPN
ejpam-5839	192	3	appl	appl	PROPN
ejpam-5839	192	4	.	.	PROPN
ejpam-5839	192	5	math	math	PROPN
ejpam-5839	192	6	,	,	PUNCT
ejpam-5839	192	7	18	18	NUM
ejpam-5839	192	8	(	(	PUNCT
ejpam-5839	192	9	2	2	NUM
ejpam-5839	192	10	)	)	PUNCT
ejpam-5839	192	11	(	(	PUNCT
ejpam-5839	192	12	2025	2025	NUM
ejpam-5839	192	13	)	)	PUNCT
ejpam-5839	192	14	,	,	PUNCT
ejpam-5839	192	15	5839	5839	NUM
ejpam-5839	192	16	7	7	NUM
ejpam-5839	192	17	of	of	ADP
ejpam-5839	192	18	54	54	NUM
ejpam-5839	192	19	fn	fn	NOUN
ejpam-5839	192	20	(	(	PUNCT
ejpam-5839	192	21	x	x	NOUN
ejpam-5839	192	22	)	)	PUNCT
ejpam-5839	192	23	=	=	SYM
ejpam-5839	193	1			PRON
ejpam-5839	193	2	q−x+τn	q−x+τn	NOUN
ejpam-5839	193	3	(	(	PUNCT
ejpam-5839	193	4	x−p	x−p	NOUN
ejpam-5839	193	5	)	)	PUNCT
ejpam-5839	193	6	q−p	q−p	NOUN
ejpam-5839	193	7	,	,	PUNCT
ejpam-5839	193	8	for	for	ADP
ejpam-5839	193	9	p	p	DET
ejpam-5839	193	10	⪯	⪯	NOUN
ejpam-5839	193	11	x	x	X
ejpam-5839	193	12	⪯	⪯	PROPN
ejpam-5839	193	13	q	q	NOUN
ejpam-5839	193	14	,	,	PUNCT
ejpam-5839	193	15	q−x+τn	q−x+τn	PROPN
ejpam-5839	193	16	(	(	PUNCT
ejpam-5839	193	17	r−x	r−x	NOUN
ejpam-5839	193	18	)	)	PUNCT
ejpam-5839	193	19	r−q	r−q	NOUN
ejpam-5839	193	20	,	,	PUNCT
ejpam-5839	193	21	for	for	ADP
ejpam-5839	193	22	q	q	PROPN
ejpam-5839	193	23	⪯	⪯	NOUN
ejpam-5839	193	24	x	x	X
ejpam-5839	193	25	⪯	⪯	VERB
ejpam-5839	193	26	r	r	NOUN
ejpam-5839	193	27	,	,	PUNCT
ejpam-5839	193	28	0	0	NUM
ejpam-5839	193	29	,	,	PUNCT
ejpam-5839	193	30	otherwise	otherwise	ADV
ejpam-5839	193	31	.	.	PUNCT
ejpam-5839	194	1	respectively	respectively	ADV
ejpam-5839	194	2	,	,	PUNCT
ejpam-5839	194	3	these	these	PRON
ejpam-5839	194	4	represent	represent	VERB
ejpam-5839	194	5	the	the	DET
ejpam-5839	194	6	indeterminacy	indeterminacy	NOUN
ejpam-5839	194	7	-	-	PUNCT
ejpam-5839	194	8	membership	membership	NOUN
ejpam-5839	194	9	function	function	NOUN
ejpam-5839	194	10	in	in	ADP
ejpam-5839	194	11	(	(	PUNCT
ejpam-5839	194	12	x	x	NOUN
ejpam-5839	194	13	)	)	PUNCT
ejpam-5839	194	14	,	,	PUNCT
ejpam-5839	194	15	hesitation	hesitation	NOUN
ejpam-5839	194	16	-	-	PUNCT
ejpam-5839	194	17	membership	membership	NOUN
ejpam-5839	194	18	function	function	NOUN
ejpam-5839	194	19	hn	hn	PROPN
ejpam-5839	194	20	(	(	PUNCT
ejpam-5839	194	21	x	x	NOUN
ejpam-5839	194	22	)	)	PUNCT
ejpam-5839	194	23	,	,	PUNCT
ejpam-5839	194	24	and	and	CCONJ
ejpam-5839	194	25	falsity	falsity	NOUN
ejpam-5839	194	26	-	-	PUNCT
ejpam-5839	194	27	membership	membership	NOUN
ejpam-5839	194	28	function	function	NOUN
ejpam-5839	194	29	fn	fn	PROPN
ejpam-5839	194	30	(	(	PUNCT
ejpam-5839	194	31	x	x	NOUN
ejpam-5839	194	32	)	)	PUNCT
ejpam-5839	194	33	.	.	PUNCT
ejpam-5839	195	1	definition	definition	NOUN
ejpam-5839	195	2	8	8	NUM
ejpam-5839	195	3	.	.	PUNCT
ejpam-5839	196	1	a	a	DET
ejpam-5839	196	2	quadri	quadri	NOUN
ejpam-5839	196	3	-	-	PUNCT
ejpam-5839	196	4	single	single	ADV
ejpam-5839	196	5	-	-	PUNCT
ejpam-5839	196	6	valued	value	VERB
ejpam-5839	196	7	-	-	PUNCT
ejpam-5839	196	8	neutrosophic	neutrosophic	ADJ
ejpam-5839	196	9	number	number	NOUN
ejpam-5839	196	10	(	(	PUNCT
ejpam-5839	196	11	q	q	ADJ
ejpam-5839	196	12	-	-	PUNCT
ejpam-5839	196	13	svn	svn	NOUN
ejpam-5839	196	14	number	number	NOUN
ejpam-5839	196	15	)	)	PUNCT
ejpam-5839	196	16	is	be	AUX
ejpam-5839	196	17	defined	define	VERB
ejpam-5839	196	18	as	as	ADP
ejpam-5839	196	19	:	:	PUNCT
ejpam-5839	196	20	n	n	PROPN
ejpam-5839	196	21	=	=	SYM
ejpam-5839	196	22	⟨(p	⟨(p	ADJ
ejpam-5839	196	23	,	,	PUNCT
ejpam-5839	196	24	q	q	NOUN
ejpam-5839	196	25	,	,	PUNCT
ejpam-5839	196	26	r	r	NOUN
ejpam-5839	196	27	,	,	PUNCT
ejpam-5839	196	28	s	s	PART
ejpam-5839	196	29	)	)	PUNCT
ejpam-5839	196	30	;	;	PUNCT
ejpam-5839	196	31	ρn	ρn	INTJ
ejpam-5839	196	32	,	,	PUNCT
ejpam-5839	196	33	υn	υn	INTJ
ejpam-5839	196	34	,	,	PUNCT
ejpam-5839	196	35	κn	κn	NOUN
ejpam-5839	196	36	,	,	PUNCT
ejpam-5839	196	37	τn	τn	ADP
ejpam-5839	196	38	⟩	⟩	NOUN
ejpam-5839	196	39	where	where	SCONJ
ejpam-5839	196	40	n	n	PRON
ejpam-5839	196	41	represents	represent	VERB
ejpam-5839	196	42	a	a	DET
ejpam-5839	196	43	unique	unique	ADJ
ejpam-5839	196	44	neutrosophic	neutrosophic	ADJ
ejpam-5839	196	45	set	set	NOUN
ejpam-5839	196	46	on	on	ADP
ejpam-5839	196	47	r.	r.	PROPN
ejpam-5839	196	48	the	the	DET
ejpam-5839	196	49	corresponding	correspond	VERB
ejpam-5839	196	50	membership	membership	NOUN
ejpam-5839	196	51	functions	function	NOUN
ejpam-5839	196	52	for	for	ADP
ejpam-5839	196	53	truth	truth	NOUN
ejpam-5839	196	54	,	,	PUNCT
ejpam-5839	196	55	indeterminacy	indeterminacy	NOUN
ejpam-5839	196	56	,	,	PUNCT
ejpam-5839	196	57	hesitation	hesitation	NOUN
ejpam-5839	196	58	,	,	PUNCT
ejpam-5839	196	59	and	and	CCONJ
ejpam-5839	196	60	falsity	falsity	NOUN
ejpam-5839	196	61	are	be	AUX
ejpam-5839	196	62	defined	define	VERB
ejpam-5839	196	63	as	as	SCONJ
ejpam-5839	196	64	follows	follow	VERB
ejpam-5839	196	65	.	.	PUNCT
ejpam-5839	197	1	n(x	n(x	X
ejpam-5839	197	2	)	)	PUNCT
ejpam-5839	197	3	=	=	PUNCT
ejpam-5839	197	4			NOUN
ejpam-5839	197	5	x−p	x−p	PROPN
ejpam-5839	197	6	q−p	q−p	PROPN
ejpam-5839	197	7	ρn	ρn	INTJ
ejpam-5839	197	8	,	,	PUNCT
ejpam-5839	197	9	for	for	SCONJ
ejpam-5839	197	10	p	p	DET
ejpam-5839	197	11	⪯	⪯	NOUN
ejpam-5839	197	12	x	x	X
ejpam-5839	197	13	⪯	⪯	PROPN
ejpam-5839	197	14	q	q	NOUN
ejpam-5839	197	15	,	,	PUNCT
ejpam-5839	197	16	s−x	s−x	VERB
ejpam-5839	197	17	s−q	s−q	NOUN
ejpam-5839	197	18	ρn	ρn	INTJ
ejpam-5839	197	19	,	,	PUNCT
ejpam-5839	197	20	for	for	ADP
ejpam-5839	197	21	q	q	PROPN
ejpam-5839	197	22	⪯	⪯	NOUN
ejpam-5839	197	23	x	x	X
ejpam-5839	197	24	⪯	⪯	VERB
ejpam-5839	197	25	r	r	NOUN
ejpam-5839	197	26	,	,	PUNCT
ejpam-5839	197	27	τn	τn	INTJ
ejpam-5839	197	28	,	,	PUNCT
ejpam-5839	197	29	for	for	ADP
ejpam-5839	197	30	r	r	NOUN
ejpam-5839	197	31	⪯	⪯	NOUN
ejpam-5839	197	32	x	x	X
ejpam-5839	197	33	⪯	⪯	NOUN
ejpam-5839	197	34	s	s	NOUN
ejpam-5839	197	35	,	,	PUNCT
ejpam-5839	197	36	0	0	NUM
ejpam-5839	197	37	,	,	PUNCT
ejpam-5839	197	38	otherwise	otherwise	ADV
ejpam-5839	197	39	.	.	PUNCT
ejpam-5839	198	1	tn	tn	NOUN
ejpam-5839	198	2	(	(	PUNCT
ejpam-5839	198	3	x	x	X
ejpam-5839	198	4	)	)	PUNCT
ejpam-5839	198	5	=	=	PUNCT
ejpam-5839	199	1			PROPN
ejpam-5839	199	2	q−x+υn	q−x+υn	PROPN
ejpam-5839	199	3	(	(	PUNCT
ejpam-5839	199	4	x−p	x−p	NOUN
ejpam-5839	199	5	)	)	PUNCT
ejpam-5839	199	6	q−p	q−p	NOUN
ejpam-5839	199	7	,	,	PUNCT
ejpam-5839	199	8	for	for	ADP
ejpam-5839	199	9	p	p	DET
ejpam-5839	199	10	⪯	⪯	NOUN
ejpam-5839	199	11	x	x	X
ejpam-5839	199	12	⪯	⪯	VERB
ejpam-5839	199	13	q	q	PROPN
ejpam-5839	199	14	,	,	PUNCT
ejpam-5839	199	15	x−r+υn	x−r+υn	PROPN
ejpam-5839	199	16	(	(	PUNCT
ejpam-5839	199	17	s−x	s−x	NOUN
ejpam-5839	199	18	)	)	PUNCT
ejpam-5839	199	19	s−r	s−r	NOUN
ejpam-5839	199	20	,	,	PUNCT
ejpam-5839	199	21	for	for	ADP
ejpam-5839	199	22	q	q	PROPN
ejpam-5839	199	23	⪯	⪯	NOUN
ejpam-5839	199	24	x	x	X
ejpam-5839	199	25	⪯	⪯	VERB
ejpam-5839	199	26	r	r	NOUN
ejpam-5839	199	27	,	,	PUNCT
ejpam-5839	199	28	τn	τn	INTJ
ejpam-5839	199	29	,	,	PUNCT
ejpam-5839	199	30	for	for	ADP
ejpam-5839	199	31	r	r	NOUN
ejpam-5839	199	32	⪯	⪯	NOUN
ejpam-5839	199	33	x	x	X
ejpam-5839	199	34	⪯	⪯	NOUN
ejpam-5839	199	35	s	s	NOUN
ejpam-5839	199	36	,	,	PUNCT
ejpam-5839	199	37	0	0	NUM
ejpam-5839	199	38	,	,	PUNCT
ejpam-5839	199	39	otherwise	otherwise	ADV
ejpam-5839	199	40	.	.	PUNCT
ejpam-5839	200	1	fn	fn	INTJ
ejpam-5839	200	2	(	(	PUNCT
ejpam-5839	200	3	x	x	X
ejpam-5839	200	4	)	)	PUNCT
ejpam-5839	200	5	=	=	PUNCT
ejpam-5839	201	1			PROPN
ejpam-5839	201	2	q−x+κn	q−x+κn	PROPN
ejpam-5839	201	3	(	(	PUNCT
ejpam-5839	201	4	x−p	x−p	NOUN
ejpam-5839	201	5	)	)	PUNCT
ejpam-5839	201	6	q−p	q−p	NOUN
ejpam-5839	201	7	,	,	PUNCT
ejpam-5839	201	8	for	for	ADP
ejpam-5839	201	9	p	p	DET
ejpam-5839	201	10	⪯	⪯	NOUN
ejpam-5839	201	11	x	x	X
ejpam-5839	201	12	⪯	⪯	PROPN
ejpam-5839	201	13	q	q	NOUN
ejpam-5839	201	14	,	,	PUNCT
ejpam-5839	201	15	x−r+κn	x−r+κn	PROPN
ejpam-5839	201	16	(	(	PUNCT
ejpam-5839	201	17	s−x	s−x	NOUN
ejpam-5839	201	18	)	)	PUNCT
ejpam-5839	201	19	s−r	s−r	NOUN
ejpam-5839	201	20	,	,	PUNCT
ejpam-5839	201	21	for	for	ADP
ejpam-5839	201	22	q	q	PROPN
ejpam-5839	201	23	⪯	⪯	NOUN
ejpam-5839	201	24	x	x	X
ejpam-5839	201	25	⪯	⪯	VERB
ejpam-5839	201	26	r	r	NOUN
ejpam-5839	201	27	,	,	PUNCT
ejpam-5839	201	28	τn	τn	INTJ
ejpam-5839	201	29	,	,	PUNCT
ejpam-5839	201	30	for	for	ADP
ejpam-5839	201	31	r	r	NOUN
ejpam-5839	201	32	⪯	⪯	NOUN
ejpam-5839	201	33	x	x	X
ejpam-5839	201	34	⪯	⪯	NOUN
ejpam-5839	201	35	s	s	NOUN
ejpam-5839	201	36	,	,	PUNCT
ejpam-5839	201	37	0	0	NUM
ejpam-5839	201	38	,	,	PUNCT
ejpam-5839	201	39	otherwise	otherwise	ADV
ejpam-5839	201	40	.	.	PUNCT
ejpam-5839	202	1	definition	definition	NOUN
ejpam-5839	202	2	9	9	NUM
ejpam-5839	202	3	.	.	PUNCT
ejpam-5839	203	1	the	the	DET
ejpam-5839	203	2	(	(	PUNCT
ejpam-5839	203	3	i	i	PROPN
ejpam-5839	203	4	,	,	PUNCT
ejpam-5839	203	5	j	j	PROPN
ejpam-5839	203	6	,	,	PUNCT
ejpam-5839	203	7	k	k	PROPN
ejpam-5839	203	8	,	,	PUNCT
ejpam-5839	203	9	l)-cut	l)-cut	NOUN
ejpam-5839	203	10	of	of	ADP
ejpam-5839	203	11	a	a	DET
ejpam-5839	203	12	neutrosophic	neutrosophic	ADJ
ejpam-5839	203	13	set	set	NOUN
ejpam-5839	203	14	n	n	PRON
ejpam-5839	203	15	is	be	AUX
ejpam-5839	203	16	denoted	denote	VERB
ejpam-5839	203	17	by	by	ADP
ejpam-5839	203	18	n(i	n(i	PROPN
ejpam-5839	203	19	,	,	PUNCT
ejpam-5839	203	20	j	j	PROPN
ejpam-5839	203	21	,	,	PUNCT
ejpam-5839	203	22	k	k	PROPN
ejpam-5839	203	23	,	,	PUNCT
ejpam-5839	203	24	l	l	NOUN
ejpam-5839	203	25	)	)	PUNCT
ejpam-5839	203	26	,	,	PUNCT
ejpam-5839	204	1	where	where	SCONJ
ejpam-5839	204	2	(	(	PUNCT
ejpam-5839	204	3	i	i	PROPN
ejpam-5839	204	4	,	,	PUNCT
ejpam-5839	204	5	j	j	PROPN
ejpam-5839	204	6	,	,	PUNCT
ejpam-5839	204	7	k	k	PROPN
ejpam-5839	204	8	,	,	PUNCT
ejpam-5839	204	9	l	l	NOUN
ejpam-5839	204	10	)	)	PUNCT
ejpam-5839	204	11	∈	∈	PROPN
ejpam-5839	205	1	[	[	X
ejpam-5839	205	2	0	0	NUM
ejpam-5839	205	3	,	,	PUNCT
ejpam-5839	205	4	1	1	NUM
ejpam-5839	205	5	]	]	PUNCT
ejpam-5839	205	6	.	.	PUNCT
ejpam-5839	206	1	then	then	ADV
ejpam-5839	206	2	,	,	PUNCT
ejpam-5839	206	3	n(i	n(i	PROPN
ejpam-5839	206	4	,	,	PUNCT
ejpam-5839	206	5	j	j	PROPN
ejpam-5839	206	6	,	,	PUNCT
ejpam-5839	206	7	k	k	PROPN
ejpam-5839	206	8	,	,	PUNCT
ejpam-5839	206	9	l	l	NOUN
ejpam-5839	206	10	)	)	PUNCT
ejpam-5839	206	11	=	=	PRON
ejpam-5839	206	12	{	{	PUNCT
ejpam-5839	206	13	⟨tn	⟨tn	PROPN
ejpam-5839	206	14	(	(	PUNCT
ejpam-5839	206	15	x	x	NOUN
ejpam-5839	206	16	)	)	PUNCT
ejpam-5839	206	17	,	,	PUNCT
ejpam-5839	206	18	retn	retn	VERB
ejpam-5839	206	19	(	(	PUNCT
ejpam-5839	206	20	x	x	X
ejpam-5839	206	21	)	)	PUNCT
ejpam-5839	206	22	,	,	PUNCT
ejpam-5839	206	23	refn	refn	X
ejpam-5839	206	24	(	(	PUNCT
ejpam-5839	206	25	x	x	NOUN
ejpam-5839	206	26	)	)	PUNCT
ejpam-5839	206	27	,	,	PUNCT
ejpam-5839	206	28	fn	fn	X
ejpam-5839	206	29	(	(	PUNCT
ejpam-5839	206	30	x)⟩	x)⟩	NOUN
ejpam-5839	206	31	:	:	PUNCT
ejpam-5839	206	32	x	x	SYM
ejpam-5839	206	33	∈	∈	PROPN
ejpam-5839	206	34	u	u	PROPN
ejpam-5839	206	35	,	,	PUNCT
ejpam-5839	206	36	tn	tn	PROPN
ejpam-5839	206	37	(	(	PUNCT
ejpam-5839	206	38	x	x	NOUN
ejpam-5839	206	39	)	)	PUNCT
ejpam-5839	206	40	⪰	⪰	NOUN
ejpam-5839	206	41	i	i	PRON
ejpam-5839	206	42	,	,	PUNCT
ejpam-5839	206	43	retn	retn	ADJ
ejpam-5839	206	44	(	(	PUNCT
ejpam-5839	206	45	x	x	X
ejpam-5839	206	46	)	)	PUNCT
ejpam-5839	206	47	⪯	⪯	PROPN
ejpam-5839	206	48	j	j	PROPN
ejpam-5839	206	49	,	,	PUNCT
ejpam-5839	206	50	refn	refn	PROPN
ejpam-5839	206	51	(	(	PUNCT
ejpam-5839	206	52	x	x	X
ejpam-5839	206	53	)	)	PUNCT
ejpam-5839	206	54	⪯	⪯	PROPN
ejpam-5839	207	1	k	k	NOUN
ejpam-5839	207	2	,	,	PUNCT
ejpam-5839	207	3	fn	fn	PROPN
ejpam-5839	207	4	(	(	PUNCT
ejpam-5839	207	5	x	x	NOUN
ejpam-5839	207	6	)	)	PUNCT
ejpam-5839	207	7	⪯	⪯	NOUN
ejpam-5839	207	8	l	l	NOUN
ejpam-5839	207	9	}	}	PUNCT
ejpam-5839	207	10	.	.	PUNCT
ejpam-5839	208	1	4	4	X
ejpam-5839	208	2	.	.	X
ejpam-5839	208	3	characterization	characterization	NOUN
ejpam-5839	208	4	of	of	ADP
ejpam-5839	208	5	few	few	ADJ
ejpam-5839	208	6	results	result	NOUN
ejpam-5839	208	7	in	in	ADP
ejpam-5839	208	8	quadri	quadri	NOUN
ejpam-5839	208	9	-	-	PUNCT
ejpam-5839	208	10	partitioned	partition	VERB
ejpam-5839	208	11	neutrosophic	neutrosophic	ADJ
ejpam-5839	208	12	space	space	NOUN
ejpam-5839	208	13	in	in	ADP
ejpam-5839	208	14	this	this	DET
ejpam-5839	208	15	section	section	NOUN
ejpam-5839	208	16	,	,	PUNCT
ejpam-5839	208	17	some	some	DET
ejpam-5839	208	18	properties	property	NOUN
ejpam-5839	208	19	of	of	ADP
ejpam-5839	208	20	single	single	ADJ
ejpam-5839	208	21	valued	value	VERB
ejpam-5839	208	22	quadri	quadri	PROPN
ejpam-5839	208	23	-	-	PUNCT
ejpam-5839	208	24	partitioned	partition	VERB
ejpam-5839	208	25	neutrosophic	neutrosophic	ADJ
ejpam-5839	208	26	numbers	number	NOUN
ejpam-5839	208	27	and	and	CCONJ
ejpam-5839	208	28	operations	operation	NOUN
ejpam-5839	208	29	of	of	ADP
ejpam-5839	208	30	single	single	ADJ
ejpam-5839	208	31	valued	value	VERB
ejpam-5839	208	32	quadri	quadri	PROPN
ejpam-5839	208	33	-	-	PUNCT
ejpam-5839	208	34	partitioned	partition	VERB
ejpam-5839	208	35	neutrosophic	neutrosophic	ADJ
ejpam-5839	208	36	numbers	number	NOUN
ejpam-5839	208	37	are	be	AUX
ejpam-5839	208	38	presented	present	VERB
ejpam-5839	208	39	.	.	PUNCT
ejpam-5839	209	1	in	in	ADP
ejpam-5839	209	2	addition	addition	NOUN
ejpam-5839	209	3	to	to	ADP
ejpam-5839	209	4	this	this	DET
ejpam-5839	209	5	few	few	ADJ
ejpam-5839	209	6	results	result	NOUN
ejpam-5839	209	7	are	be	AUX
ejpam-5839	209	8	also	also	ADV
ejpam-5839	209	9	addressed	address	VERB
ejpam-5839	209	10	,	,	PUNCT
ejpam-5839	209	11	which	which	PRON
ejpam-5839	209	12	are	be	AUX
ejpam-5839	209	13	necessary	necessary	ADJ
ejpam-5839	209	14	for	for	ADP
ejpam-5839	209	15	the	the	DET
ejpam-5839	209	16	up	up	ADV
ejpam-5839	209	17	-	-	PUNCT
ejpam-5839	209	18	coming	come	VERB
ejpam-5839	209	19	sections	section	NOUN
ejpam-5839	209	20	.	.	PUNCT
ejpam-5839	210	1	definition	definition	NOUN
ejpam-5839	210	2	10	10	NUM
ejpam-5839	210	3	.	.	PUNCT
ejpam-5839	211	1	(	(	PUNCT
ejpam-5839	211	2	i	i	NOUN
ejpam-5839	211	3	)	)	PUNCT
ejpam-5839	211	4	a	a	DET
ejpam-5839	211	5	neutrosophic	neutrosophic	ADJ
ejpam-5839	211	6	number	number	NOUN
ejpam-5839	211	7	ñ	ñ	VERB
ejpam-5839	211	8	is	be	AUX
ejpam-5839	211	9	called	call	VERB
ejpam-5839	211	10	a	a	DET
ejpam-5839	211	11	closed	closed	ADJ
ejpam-5839	211	12	single	single	ADJ
ejpam-5839	211	13	valued	value	VERB
ejpam-5839	211	14	quadri	quadri	PROPN
ejpam-5839	211	15	-	-	PUNCT
ejpam-5839	211	16	partitioned	partition	VERB
ejpam-5839	211	17	neutrosophic	neutrosophic	ADJ
ejpam-5839	211	18	number	number	NOUN
ejpam-5839	211	19	if	if	SCONJ
ejpam-5839	211	20	ñ	ñ	PROPN
ejpam-5839	211	21	is	be	AUX
ejpam-5839	211	22	a	a	DET
ejpam-5839	211	23	quadri	quadri	NOUN
ejpam-5839	211	24	-	-	PUNCT
ejpam-5839	211	25	partitioned	partition	VERB
ejpam-5839	211	26	neutrosophic	neutrosophic	ADJ
ejpam-5839	211	27	number	number	NOUN
ejpam-5839	211	28	and	and	CCONJ
ejpam-5839	211	29	the	the	DET
ejpam-5839	211	30	truth	truth	NOUN
ejpam-5839	211	31	membership	membership	NOUN
ejpam-5839	211	32	function	function	NOUN
ejpam-5839	211	33	and	and	CCONJ
ejpam-5839	211	34	relative	relative	ADJ
ejpam-5839	211	35	truth	truth	NOUN
ejpam-5839	211	36	membership	membership	NOUN
ejpam-5839	211	37	functions	function	NOUN
ejpam-5839	211	38	are	be	AUX
ejpam-5839	211	39	upper	upper	ADJ
ejpam-5839	211	40	semi	semi	ADJ
ejpam-5839	211	41	-	-	ADJ
ejpam-5839	211	42	continuous	continuous	ADJ
ejpam-5839	211	43	,	,	PUNCT
ejpam-5839	211	44	while	while	SCONJ
ejpam-5839	211	45	the	the	DET
ejpam-5839	211	46	false	false	ADJ
ejpam-5839	211	47	and	and	CCONJ
ejpam-5839	211	48	relative	relative	ADJ
ejpam-5839	211	49	false	false	ADJ
ejpam-5839	211	50	membership	membership	NOUN
ejpam-5839	211	51	functions	function	NOUN
ejpam-5839	211	52	are	be	AUX
ejpam-5839	211	53	lower	low	ADJ
ejpam-5839	211	54	semi	semi	ADJ
ejpam-5839	211	55	-	-	ADJ
ejpam-5839	211	56	continuous	continuous	ADJ
ejpam-5839	211	57	.	.	PUNCT
ejpam-5839	212	1	(	(	PUNCT
ejpam-5839	212	2	ii	ii	NOUN
ejpam-5839	212	3	)	)	PUNCT
ejpam-5839	212	4	a	a	DET
ejpam-5839	212	5	neutrosophic	neutrosophic	ADJ
ejpam-5839	212	6	number	number	NOUN
ejpam-5839	212	7	ñ	ñ	VERB
ejpam-5839	212	8	is	be	AUX
ejpam-5839	212	9	called	call	VERB
ejpam-5839	212	10	a	a	DET
ejpam-5839	212	11	bounded	bounded	ADJ
ejpam-5839	212	12	single	single	ADJ
ejpam-5839	212	13	valued	value	VERB
ejpam-5839	212	14	quadri	quadri	PROPN
ejpam-5839	212	15	-	-	PUNCT
ejpam-5839	212	16	partitioned	partition	VERB
ejpam-5839	212	17	neutrosophic	neutrosophic	ADJ
ejpam-5839	212	18	number	number	NOUN
ejpam-5839	212	19	if	if	SCONJ
ejpam-5839	212	20	ñ	ñ	PROPN
ejpam-5839	212	21	is	be	AUX
ejpam-5839	212	22	a	a	DET
ejpam-5839	212	23	quadri	quadri	NOUN
ejpam-5839	212	24	-	-	PUNCT
ejpam-5839	212	25	partitioned	partition	VERB
ejpam-5839	212	26	neutrosophic	neutrosophic	ADJ
ejpam-5839	212	27	number	number	NOUN
ejpam-5839	212	28	and	and	CCONJ
ejpam-5839	212	29	the	the	DET
ejpam-5839	212	30	truth	truth	NOUN
ejpam-5839	212	31	membership	membership	NOUN
ejpam-5839	212	32	,	,	PUNCT
ejpam-5839	212	33	relative	relative	ADJ
ejpam-5839	212	34	truth	truth	NOUN
ejpam-5839	212	35	membership	membership	NOUN
ejpam-5839	212	36	,	,	PUNCT
ejpam-5839	212	37	relative	relative	ADJ
ejpam-5839	212	38	false	false	ADJ
ejpam-5839	212	39	membership	membership	NOUN
ejpam-5839	212	40	,	,	PUNCT
ejpam-5839	212	41	and	and	CCONJ
ejpam-5839	212	42	false	false	ADJ
ejpam-5839	212	43	membership	membership	NOUN
ejpam-5839	212	44	functions	function	NOUN
ejpam-5839	212	45	have	have	VERB
ejpam-5839	212	46	compact	compact	ADJ
ejpam-5839	212	47	support	support	NOUN
ejpam-5839	212	48	.	.	PUNCT
ejpam-5839	213	1	a.	a.	NOUN
ejpam-5839	213	2	shihadeh	shihadeh	VERB
ejpam-5839	213	3	et	et	PROPN
ejpam-5839	213	4	al	al	PROPN
ejpam-5839	213	5	.	.	PUNCT
ejpam-5839	213	6	/	/	SYM
ejpam-5839	213	7	eur	eur	PROPN
ejpam-5839	213	8	.	.	PUNCT
ejpam-5839	214	1	j.	j.	PROPN
ejpam-5839	214	2	pure	pure	PROPN
ejpam-5839	214	3	appl	appl	PROPN
ejpam-5839	214	4	.	.	PROPN
ejpam-5839	214	5	math	math	PROPN
ejpam-5839	214	6	,	,	PUNCT
ejpam-5839	214	7	18	18	NUM
ejpam-5839	214	8	(	(	PUNCT
ejpam-5839	214	9	2	2	NUM
ejpam-5839	214	10	)	)	PUNCT
ejpam-5839	214	11	(	(	PUNCT
ejpam-5839	214	12	2025	2025	NUM
ejpam-5839	214	13	)	)	PUNCT
ejpam-5839	214	14	,	,	PUNCT
ejpam-5839	214	15	5839	5839	NUM
ejpam-5839	214	16	8	8	NUM
ejpam-5839	214	17	of	of	ADP
ejpam-5839	214	18	54	54	NUM
ejpam-5839	214	19	(	(	PUNCT
ejpam-5839	214	20	iii	iii	NOUN
ejpam-5839	214	21	)	)	PUNCT
ejpam-5839	214	22	let	let	VERB
ejpam-5839	214	23	m̃	m̃	PROPN
ejpam-5839	214	24	and	and	CCONJ
ejpam-5839	214	25	ñ	ñ	PROPN
ejpam-5839	214	26	be	be	VERB
ejpam-5839	214	27	two	two	NUM
ejpam-5839	214	28	single	single	ADJ
ejpam-5839	214	29	valued	value	VERB
ejpam-5839	214	30	quadri	quadri	PROPN
ejpam-5839	214	31	-	-	PUNCT
ejpam-5839	214	32	partitioned	partition	VERB
ejpam-5839	214	33	neutrosophic	neutrosophic	ADJ
ejpam-5839	214	34	numbers	number	NOUN
ejpam-5839	214	35	.	.	PUNCT
ejpam-5839	215	1	then	then	ADV
ejpam-5839	215	2	,	,	PUNCT
ejpam-5839	215	3	m̃	m̃	PROPN
ejpam-5839	215	4	and	and	CCONJ
ejpam-5839	215	5	ñ	ñ	PROPN
ejpam-5839	215	6	are	be	AUX
ejpam-5839	215	7	said	say	VERB
ejpam-5839	215	8	to	to	PART
ejpam-5839	215	9	be	be	AUX
ejpam-5839	215	10	equal	equal	ADJ
ejpam-5839	215	11	,	,	PUNCT
ejpam-5839	215	12	denoted	denote	VERB
ejpam-5839	215	13	as	as	ADP
ejpam-5839	215	14	m̃	m̃	PROPN
ejpam-5839	215	15	=	=	SYM
ejpam-5839	215	16	ñ	ñ	PROPN
ejpam-5839	215	17	,	,	PUNCT
ejpam-5839	215	18	if	if	SCONJ
ejpam-5839	215	19	and	and	CCONJ
ejpam-5839	215	20	only	only	ADV
ejpam-5839	215	21	if	if	SCONJ
ejpam-5839	215	22	m̃(i	m̃(i	PROPN
ejpam-5839	215	23	,	,	PUNCT
ejpam-5839	215	24	j	j	PROPN
ejpam-5839	215	25	,	,	PUNCT
ejpam-5839	215	26	k	k	PROPN
ejpam-5839	215	27	,	,	PUNCT
ejpam-5839	215	28	l	l	NOUN
ejpam-5839	215	29	)	)	PUNCT
ejpam-5839	215	30	and	and	CCONJ
ejpam-5839	215	31	ñ(i	ñ(i	PROPN
ejpam-5839	215	32	,	,	PUNCT
ejpam-5839	215	33	j	j	PROPN
ejpam-5839	215	34	,	,	PUNCT
ejpam-5839	215	35	k	k	PROPN
ejpam-5839	215	36	,	,	PUNCT
ejpam-5839	215	37	l	l	NOUN
ejpam-5839	215	38	)	)	PUNCT
ejpam-5839	215	39	.	.	PUNCT
ejpam-5839	216	1	here	here	ADV
ejpam-5839	216	2	,	,	PUNCT
ejpam-5839	216	3	m̃(i	m̃(i	PROPN
ejpam-5839	216	4	,	,	PUNCT
ejpam-5839	216	5	j	j	PROPN
ejpam-5839	216	6	,	,	PUNCT
ejpam-5839	216	7	k	k	PROPN
ejpam-5839	216	8	,	,	PUNCT
ejpam-5839	216	9	l	l	NOUN
ejpam-5839	216	10	)	)	PUNCT
ejpam-5839	216	11	and	and	CCONJ
ejpam-5839	216	12	ñ(i	ñ(i	PROPN
ejpam-5839	216	13	,	,	PUNCT
ejpam-5839	216	14	j	j	PROPN
ejpam-5839	216	15	,	,	PUNCT
ejpam-5839	216	16	k	k	PROPN
ejpam-5839	216	17	,	,	PUNCT
ejpam-5839	216	18	l	l	NOUN
ejpam-5839	216	19	)	)	PUNCT
ejpam-5839	216	20	denote	denote	VERB
ejpam-5839	216	21	the	the	DET
ejpam-5839	216	22	(	(	PUNCT
ejpam-5839	216	23	i	i	PROPN
ejpam-5839	216	24	,	,	PUNCT
ejpam-5839	216	25	j	j	PROPN
ejpam-5839	216	26	,	,	PUNCT
ejpam-5839	216	27	k	k	PROPN
ejpam-5839	216	28	,	,	PUNCT
ejpam-5839	216	29	l)-cut	l)-cut	NOUN
ejpam-5839	216	30	of	of	ADP
ejpam-5839	216	31	m̃	m̃	PROPN
ejpam-5839	216	32	and	and	CCONJ
ejpam-5839	216	33	ñ	ñ	PROPN
ejpam-5839	216	34	,	,	PUNCT
ejpam-5839	216	35	respectively	respectively	ADV
ejpam-5839	216	36	.	.	PUNCT
ejpam-5839	217	1	m̃(i	m̃(i	PROPN
ejpam-5839	217	2	,	,	PUNCT
ejpam-5839	217	3	j	j	PROPN
ejpam-5839	217	4	,	,	PUNCT
ejpam-5839	217	5	k	k	PROPN
ejpam-5839	217	6	,	,	PUNCT
ejpam-5839	217	7	l	l	NOUN
ejpam-5839	217	8	)	)	PUNCT
ejpam-5839	217	9	=	=	SYM
ejpam-5839	218	1	ñ(i	ñ(i	PROPN
ejpam-5839	218	2	,	,	PUNCT
ejpam-5839	218	3	j	j	PROPN
ejpam-5839	218	4	,	,	PUNCT
ejpam-5839	218	5	k	k	PROPN
ejpam-5839	218	6	,	,	PUNCT
ejpam-5839	218	7	l	l	NOUN
ejpam-5839	218	8	)	)	PUNCT
ejpam-5839	218	9	.	.	PUNCT
ejpam-5839	219	1	proposition	proposition	NOUN
ejpam-5839	219	2	1	1	NUM
ejpam-5839	219	3	.	.	PUNCT
ejpam-5839	220	1	if	if	SCONJ
ejpam-5839	220	2	ñ	ñ	PROPN
ejpam-5839	220	3	is	be	AUX
ejpam-5839	220	4	a	a	DET
ejpam-5839	220	5	closed	closed	ADJ
ejpam-5839	220	6	single	single	ADV
ejpam-5839	220	7	-	-	PUNCT
ejpam-5839	220	8	valued	value	VERB
ejpam-5839	220	9	quadri	quadri	NOUN
ejpam-5839	220	10	-	-	PUNCT
ejpam-5839	220	11	partitioned	partition	VERB
ejpam-5839	220	12	neutrosophic	neutrosophic	ADJ
ejpam-5839	220	13	number	number	NOUN
ejpam-5839	220	14	,	,	PUNCT
ejpam-5839	220	15	then	then	ADV
ejpam-5839	220	16	the	the	DET
ejpam-5839	220	17	(	(	PUNCT
ejpam-5839	220	18	i	i	PROPN
ejpam-5839	220	19	,	,	PUNCT
ejpam-5839	220	20	j	j	PROPN
ejpam-5839	220	21	,	,	PUNCT
ejpam-5839	220	22	k	k	PROPN
ejpam-5839	220	23	,	,	PUNCT
ejpam-5839	220	24	l)-cut	l)-cut	NOUN
ejpam-5839	220	25	of	of	ADP
ejpam-5839	220	26	ñ	ñ	PROPN
ejpam-5839	220	27	,	,	PUNCT
ejpam-5839	220	28	denoted	denote	VERB
ejpam-5839	220	29	as	as	ADP
ejpam-5839	220	30	ñ(i	ñ(i	PROPN
ejpam-5839	220	31	,	,	PUNCT
ejpam-5839	220	32	j	j	PROPN
ejpam-5839	220	33	,	,	PUNCT
ejpam-5839	220	34	k	k	PROPN
ejpam-5839	220	35	,	,	PUNCT
ejpam-5839	220	36	l	l	NOUN
ejpam-5839	220	37	)	)	PUNCT
ejpam-5839	220	38	=	=	SYM
ejpam-5839	221	1	〈	〈	PROPN
ejpam-5839	222	1	[	[	X
ejpam-5839	222	2	ñl	ñl	X
ejpam-5839	222	3	i	i	PRON
ejpam-5839	222	4	,	,	PUNCT
ejpam-5839	222	5	ñ	ñ	VERB
ejpam-5839	222	6	u	u	NOUN
ejpam-5839	222	7	i	i	PRON
ejpam-5839	222	8	]	]	X
ejpam-5839	222	9	,	,	PUNCT
ejpam-5839	222	10	[	[	X
ejpam-5839	222	11	ñ	ñ	VERB
ejpam-5839	222	12	l	l	NOUN
ejpam-5839	222	13	j	j	PROPN
ejpam-5839	222	14	,	,	PUNCT
ejpam-5839	222	15	ñ	ñ	VERB
ejpam-5839	222	16	u	u	X
ejpam-5839	222	17	j	j	X
ejpam-5839	222	18	]	]	X
ejpam-5839	222	19	,	,	PUNCT
ejpam-5839	222	20	[	[	X
ejpam-5839	222	21	ñ	ñ	ADP
ejpam-5839	222	22	l	l	NOUN
ejpam-5839	222	23	k	k	X
ejpam-5839	222	24	,	,	PUNCT
ejpam-5839	222	25	ñ	ñ	PROPN
ejpam-5839	222	26	u	u	X
ejpam-5839	222	27	k	k	X
ejpam-5839	222	28	]	]	X
ejpam-5839	222	29	,	,	PUNCT
ejpam-5839	222	30	[	[	X
ejpam-5839	222	31	ñ	ñ	ADP
ejpam-5839	222	32	l	l	NOUN
ejpam-5839	222	33	l	l	NOUN
ejpam-5839	222	34	,	,	PUNCT
ejpam-5839	222	35	ñ	ñ	ADJ
ejpam-5839	222	36	u	u	NOUN
ejpam-5839	222	37	l	l	NOUN
ejpam-5839	222	38	]	]	PUNCT
ejpam-5839	222	39	〉	〉	NOUN
ejpam-5839	222	40	is	be	AUX
ejpam-5839	222	41	a	a	DET
ejpam-5839	222	42	closed	closed	ADJ
ejpam-5839	222	43	interval	interval	NOUN
ejpam-5839	222	44	quadri	quadri	PROPN
ejpam-5839	222	45	-	-	PUNCT
ejpam-5839	222	46	neutrosophic	neutrosophic	ADJ
ejpam-5839	222	47	single	single	ADJ
ejpam-5839	222	48	number	number	NOUN
ejpam-5839	222	49	(	(	PUNCT
ejpam-5839	222	50	qnsn	qnsn	PROPN
ejpam-5839	222	51	)	)	PUNCT
ejpam-5839	222	52	or	or	CCONJ
ejpam-5839	222	53	interval	interval	NOUN
ejpam-5839	222	54	quadri	quadri	PROPN
ejpam-5839	222	55	-	-	PUNCT
ejpam-5839	222	56	neutrosophic	neutrosophic	ADJ
ejpam-5839	222	57	number	number	NOUN
ejpam-5839	222	58	(	(	PUNCT
ejpam-5839	222	59	iqnn	iqnn	PROPN
ejpam-5839	222	60	)	)	PUNCT
ejpam-5839	222	61	,	,	PUNCT
ejpam-5839	222	62	where	where	SCONJ
ejpam-5839	222	63	[	[	X
ejpam-5839	222	64	ñl	ñl	X
ejpam-5839	222	65	k	k	X
ejpam-5839	222	66	,	,	PUNCT
ejpam-5839	222	67	ñ	ñ	PROPN
ejpam-5839	222	68	u	u	X
ejpam-5839	222	69	k	k	X
ejpam-5839	222	70	]	]	PUNCT
ejpam-5839	222	71	and	and	CCONJ
ejpam-5839	222	72	[	[	X
ejpam-5839	222	73	ñl	ñl	X
ejpam-5839	222	74	l	l	NOUN
ejpam-5839	222	75	,	,	PUNCT
ejpam-5839	222	76	ñ	ñ	ADJ
ejpam-5839	222	77	u	u	X
ejpam-5839	222	78	l	l	NOUN
ejpam-5839	222	79	]	]	PUNCT
ejpam-5839	222	80	are	be	AUX
ejpam-5839	222	81	all	all	PRON
ejpam-5839	222	82	closed	closed	ADJ
ejpam-5839	222	83	intervals	interval	NOUN
ejpam-5839	222	84	.	.	PUNCT
ejpam-5839	223	1	here	here	ADV
ejpam-5839	223	2	,	,	PUNCT
ejpam-5839	223	3	ñl	ñl	VERB
ejpam-5839	223	4	i	i	PRON
ejpam-5839	223	5	,	,	PUNCT
ejpam-5839	223	6	ñ	ñ	ADJ
ejpam-5839	223	7	u	u	NOUN
ejpam-5839	223	8	i	i	PRON
ejpam-5839	223	9	,	,	PUNCT
ejpam-5839	223	10	ñ	ñ	PROPN
ejpam-5839	223	11	l	l	NOUN
ejpam-5839	223	12	j	j	PROPN
ejpam-5839	223	13	,	,	PUNCT
ejpam-5839	223	14	ñ	ñ	PROPN
ejpam-5839	223	15	u	u	X
ejpam-5839	223	16	j	j	PROPN
ejpam-5839	223	17	,	,	PUNCT
ejpam-5839	223	18	ñ	ñ	PROPN
ejpam-5839	223	19	l	l	NOUN
ejpam-5839	223	20	k	k	PROPN
ejpam-5839	223	21	,	,	PUNCT
ejpam-5839	224	1	ñ	ñ	PROPN
ejpam-5839	224	2	u	u	X
ejpam-5839	224	3	k	k	PROPN
ejpam-5839	224	4	,	,	PUNCT
ejpam-5839	224	5	ñ	ñ	PROPN
ejpam-5839	224	6	l	l	NOUN
ejpam-5839	224	7	l	l	NOUN
ejpam-5839	224	8	,	,	PUNCT
ejpam-5839	224	9	ñ	ñ	PROPN
ejpam-5839	224	10	u	u	NOUN
ejpam-5839	224	11	l	l	PROPN
ejpam-5839	224	12	denote	denote	NOUN
ejpam-5839	224	13	inf	inf	PROPN
ejpam-5839	224	14	tñ	tñ	X
ejpam-5839	224	15	(	(	PUNCT
ejpam-5839	224	16	x	x	NOUN
ejpam-5839	224	17	)	)	PUNCT
ejpam-5839	224	18	,	,	PUNCT
ejpam-5839	224	19	suptñ	suptñ	NOUN
ejpam-5839	224	20	(	(	PUNCT
ejpam-5839	224	21	x	x	X
ejpam-5839	224	22	)	)	PUNCT
ejpam-5839	224	23	,	,	PUNCT
ejpam-5839	224	24	inf	inf	NOUN
ejpam-5839	224	25	iñ	iñ	PRON
ejpam-5839	224	26	(	(	PUNCT
ejpam-5839	224	27	x	x	NOUN
ejpam-5839	224	28	)	)	PUNCT
ejpam-5839	224	29	,	,	PUNCT
ejpam-5839	224	30	sup	sup	NOUN
ejpam-5839	224	31	iñ	iñ	PRON
ejpam-5839	224	32	(	(	PUNCT
ejpam-5839	224	33	x	x	NOUN
ejpam-5839	224	34	)	)	PUNCT
ejpam-5839	224	35	,	,	PUNCT
ejpam-5839	224	36	inf	inf	PROPN
ejpam-5839	224	37	fñ	fñ	PROPN
ejpam-5839	224	38	(	(	PUNCT
ejpam-5839	224	39	x	x	NOUN
ejpam-5839	224	40	)	)	PUNCT
ejpam-5839	224	41	,	,	PUNCT
ejpam-5839	224	42	supfñ	supfñ	NUM
ejpam-5839	224	43	(	(	PUNCT
ejpam-5839	224	44	x	x	NOUN
ejpam-5839	224	45	)	)	PUNCT
ejpam-5839	224	46	,	,	PUNCT
ejpam-5839	224	47	infhñ	infhñ	PROPN
ejpam-5839	224	48	(	(	PUNCT
ejpam-5839	224	49	x	x	NOUN
ejpam-5839	224	50	)	)	PUNCT
ejpam-5839	224	51	,	,	PUNCT
ejpam-5839	224	52	and	and	CCONJ
ejpam-5839	224	53	suphñ	suphñ	NOUN
ejpam-5839	224	54	(	(	PUNCT
ejpam-5839	224	55	x	x	NOUN
ejpam-5839	224	56	)	)	PUNCT
ejpam-5839	224	57	,	,	PUNCT
ejpam-5839	224	58	respectively	respectively	ADV
ejpam-5839	224	59	.	.	PUNCT
ejpam-5839	225	1	proof	proof	NOUN
ejpam-5839	225	2	.	.	PUNCT
ejpam-5839	226	1	if	if	SCONJ
ejpam-5839	226	2	tñ	tñ	PRON
ejpam-5839	226	3	(	(	PUNCT
ejpam-5839	226	4	x	x	X
ejpam-5839	226	5	)	)	PUNCT
ejpam-5839	226	6	is	be	AUX
ejpam-5839	226	7	upper	upper	ADJ
ejpam-5839	226	8	semi	semi	ADJ
ejpam-5839	226	9	-	-	ADJ
ejpam-5839	226	10	continuous	continuous	ADJ
ejpam-5839	226	11	,	,	PUNCT
ejpam-5839	226	12	and	and	CCONJ
ejpam-5839	226	13	iñ	iñ	NUM
ejpam-5839	226	14	(	(	PUNCT
ejpam-5839	226	15	x	x	X
ejpam-5839	226	16	)	)	PUNCT
ejpam-5839	226	17	and	and	CCONJ
ejpam-5839	226	18	fñ	fñ	NUM
ejpam-5839	226	19	(	(	PUNCT
ejpam-5839	226	20	x	x	X
ejpam-5839	226	21	)	)	PUNCT
ejpam-5839	226	22	are	be	AUX
ejpam-5839	226	23	lower	low	ADJ
ejpam-5839	226	24	semi	semi	ADJ
ejpam-5839	226	25	-	-	ADJ
ejpam-5839	226	26	continuous	continuous	ADJ
ejpam-5839	226	27	,	,	PUNCT
ejpam-5839	226	28	then	then	ADV
ejpam-5839	226	29	the	the	DET
ejpam-5839	226	30	(	(	PUNCT
ejpam-5839	226	31	i	i	PROPN
ejpam-5839	226	32	,	,	PUNCT
ejpam-5839	226	33	j	j	PROPN
ejpam-5839	226	34	,	,	PUNCT
ejpam-5839	226	35	k	k	PROPN
ejpam-5839	226	36	,	,	PUNCT
ejpam-5839	226	37	l)-level	l)-level	VERB
ejpam-5839	226	38	set	set	NOUN
ejpam-5839	226	39	of	of	ADP
ejpam-5839	226	40	ñ	ñ	PROPN
ejpam-5839	226	41	,	,	PUNCT
ejpam-5839	226	42	i.e.	i.e.	X
ejpam-5839	226	43	,	,	PUNCT
ejpam-5839	226	44	ñ(i	ñ(i	PROPN
ejpam-5839	226	45	,	,	PUNCT
ejpam-5839	226	46	j	j	PROPN
ejpam-5839	226	47	,	,	PUNCT
ejpam-5839	226	48	k	k	PROPN
ejpam-5839	226	49	,	,	PUNCT
ejpam-5839	226	50	l	l	NOUN
ejpam-5839	226	51	)	)	PUNCT
ejpam-5839	227	1	=	=	PRON
ejpam-5839	227	2	{	{	PUNCT
ejpam-5839	227	3	tñ	tñ	NUM
ejpam-5839	227	4	(	(	PUNCT
ejpam-5839	227	5	x	x	NOUN
ejpam-5839	227	6	)	)	PUNCT
ejpam-5839	227	7	⪰	⪰	NOUN
ejpam-5839	227	8	i	i	PRON
ejpam-5839	227	9	,	,	PUNCT
ejpam-5839	227	10	iñ	iñ	PROPN
ejpam-5839	227	11	(	(	PUNCT
ejpam-5839	227	12	x	x	X
ejpam-5839	227	13	)	)	PUNCT
ejpam-5839	227	14	⪯	⪯	PROPN
ejpam-5839	227	15	j	j	PROPN
ejpam-5839	227	16	,	,	PUNCT
ejpam-5839	227	17	fñ	fñ	PROPN
ejpam-5839	227	18	(	(	PUNCT
ejpam-5839	227	19	x	x	X
ejpam-5839	227	20	)	)	PUNCT
ejpam-5839	227	21	⪯	⪯	PROPN
ejpam-5839	228	1	k	k	NOUN
ejpam-5839	228	2	,	,	PUNCT
ejpam-5839	228	3	hñ	hñ	X
ejpam-5839	228	4	(	(	PUNCT
ejpam-5839	228	5	x	x	X
ejpam-5839	228	6	)	)	PUNCT
ejpam-5839	228	7	⪯	⪯	PROPN
ejpam-5839	228	8	l	l	NOUN
ejpam-5839	228	9	,	,	PUNCT
ejpam-5839	228	10	x	x	SYM
ejpam-5839	228	11	∈	∈	NOUN
ejpam-5839	228	12	r	r	NOUN
ejpam-5839	228	13	}	}	PUNCT
ejpam-5839	228	14	is	be	AUX
ejpam-5839	228	15	a	a	DET
ejpam-5839	228	16	closed	closed	ADJ
ejpam-5839	228	17	set	set	NOUN
ejpam-5839	228	18	.	.	PUNCT
ejpam-5839	229	1	then	then	ADV
ejpam-5839	229	2	,	,	PUNCT
ejpam-5839	229	3	from	from	ADP
ejpam-5839	229	4	definition	definition	NOUN
ejpam-5839	229	5	7	7	NUM
ejpam-5839	229	6	,	,	PUNCT
ejpam-5839	229	7	ñ	ñ	PROPN
ejpam-5839	229	8	is	be	AUX
ejpam-5839	229	9	an	an	DET
ejpam-5839	229	10	interval	interval	NOUN
ejpam-5839	229	11	quadri	quadri	PROPN
ejpam-5839	229	12	-	-	PUNCT
ejpam-5839	229	13	neutrosophic	neutrosophic	ADJ
ejpam-5839	229	14	single	single	ADJ
ejpam-5839	229	15	number	number	NOUN
ejpam-5839	229	16	(	(	PUNCT
ejpam-5839	229	17	qnsn	qnsn	PROPN
ejpam-5839	229	18	)	)	PUNCT
ejpam-5839	229	19	,	,	PUNCT
ejpam-5839	229	20	and	and	CCONJ
ejpam-5839	229	21	intervals	interval	NOUN
ejpam-5839	229	22	are	be	AUX
ejpam-5839	229	23	closed	closed	ADJ
ejpam-5839	229	24	intervals	interval	NOUN
ejpam-5839	229	25	.	.	PUNCT
ejpam-5839	230	1	proposition	proposition	NOUN
ejpam-5839	230	2	2	2	NUM
ejpam-5839	230	3	.	.	PUNCT
ejpam-5839	230	4	let	let	VERB
ejpam-5839	230	5	m̃	m̃	PROPN
ejpam-5839	230	6	and	and	CCONJ
ejpam-5839	230	7	ñ	ñ	PROPN
ejpam-5839	230	8	be	be	VERB
ejpam-5839	230	9	two	two	NUM
ejpam-5839	230	10	single	single	ADV
ejpam-5839	230	11	-	-	PUNCT
ejpam-5839	230	12	valued	value	VERB
ejpam-5839	230	13	quadri	quadri	NOUN
ejpam-5839	230	14	-	-	PUNCT
ejpam-5839	230	15	partitioned	partition	VERB
ejpam-5839	230	16	neutrosophic	neutrosophic	ADJ
ejpam-5839	230	17	numbers	number	NOUN
ejpam-5839	230	18	,	,	PUNCT
ejpam-5839	230	19	then	then	ADV
ejpam-5839	230	20	:	:	PUNCT
ejpam-5839	230	21	(	(	PUNCT
ejpam-5839	230	22	i	i	NOUN
ejpam-5839	230	23	)	)	PUNCT
ejpam-5839	230	24	(	(	PUNCT
ejpam-5839	230	25	m̃⊙	m̃⊙	NOUN
ejpam-5839	230	26	ñ)(i	ñ)(i	PROPN
ejpam-5839	230	27	,	,	PUNCT
ejpam-5839	230	28	j	j	PROPN
ejpam-5839	230	29	,	,	PUNCT
ejpam-5839	230	30	k	k	PROPN
ejpam-5839	230	31	,	,	PUNCT
ejpam-5839	230	32	l	l	NOUN
ejpam-5839	230	33	)	)	PUNCT
ejpam-5839	230	34	=	=	SYM
ejpam-5839	230	35	m̃(i	m̃(i	PROPN
ejpam-5839	230	36	,	,	PUNCT
ejpam-5839	230	37	j	j	PROPN
ejpam-5839	230	38	,	,	PUNCT
ejpam-5839	230	39	k	k	PROPN
ejpam-5839	230	40	,	,	PUNCT
ejpam-5839	230	41	l	l	NOUN
ejpam-5839	230	42	)	)	PUNCT
ejpam-5839	230	43	⊙	⊙	NOUN
ejpam-5839	231	1	ñ(i	ñ(i	PROPN
ejpam-5839	231	2	,	,	PUNCT
ejpam-5839	231	3	j	j	PROPN
ejpam-5839	231	4	,	,	PUNCT
ejpam-5839	231	5	k	k	PROPN
ejpam-5839	231	6	,	,	PUNCT
ejpam-5839	231	7	l	l	NOUN
ejpam-5839	231	8	)	)	PUNCT
ejpam-5839	231	9	(	(	PUNCT
ejpam-5839	231	10	ii	ii	NOUN
ejpam-5839	231	11	)	)	PUNCT
ejpam-5839	231	12	(	(	PUNCT
ejpam-5839	231	13	λm̃)(i	λm̃)(i	NOUN
ejpam-5839	231	14	,	,	PUNCT
ejpam-5839	231	15	j	j	PROPN
ejpam-5839	231	16	,	,	PUNCT
ejpam-5839	231	17	k	k	PROPN
ejpam-5839	231	18	,	,	PUNCT
ejpam-5839	231	19	l	l	NOUN
ejpam-5839	231	20	)	)	PUNCT
ejpam-5839	231	21	=	=	SYM
ejpam-5839	231	22	λm̃(i	λm̃(i	NOUN
ejpam-5839	231	23	,	,	PUNCT
ejpam-5839	231	24	j	j	PROPN
ejpam-5839	231	25	,	,	PUNCT
ejpam-5839	231	26	k	k	PROPN
ejpam-5839	231	27	,	,	PUNCT
ejpam-5839	231	28	l	l	NOUN
ejpam-5839	231	29	)	)	PUNCT
ejpam-5839	231	30	,	,	PUNCT
ejpam-5839	231	31	where	where	SCONJ
ejpam-5839	231	32	λ	λ	PROPN
ejpam-5839	231	33	̸=	̸=	PROPN
ejpam-5839	231	34	0	0	NUM
ejpam-5839	231	35	is	be	AUX
ejpam-5839	231	36	any	any	DET
ejpam-5839	231	37	real	real	ADJ
ejpam-5839	231	38	number	number	NOUN
ejpam-5839	231	39	.	.	PUNCT
ejpam-5839	232	1	proof	proof	NOUN
ejpam-5839	232	2	.	.	PUNCT
ejpam-5839	233	1	1	1	NUM
ejpam-5839	234	1	since	since	SCONJ
ejpam-5839	234	2	m̃⊙	m̃⊙	NOUN
ejpam-5839	234	3	ñ	ñ	VERB
ejpam-5839	234	4	=	=	SYM
ejpam-5839	234	5	{	{	PUNCT
ejpam-5839	234	6	z	z	NOUN
ejpam-5839	234	7	,	,	PUNCT
ejpam-5839	234	8	max	max	NOUN
ejpam-5839	234	9	x	x	X
ejpam-5839	234	10	z	z	NOUN
ejpam-5839	234	11	=	=	SYM
ejpam-5839	234	12	(	(	PUNCT
ejpam-5839	234	13	x)⊛	x)⊛	NOUN
ejpam-5839	234	14	y	y	PROPN
ejpam-5839	234	15	{	{	PUNCT
ejpam-5839	234	16	min(tm̃(x	min(tm̃(x	NUM
ejpam-5839	234	17	)	)	PUNCT
ejpam-5839	234	18	,	,	PUNCT
ejpam-5839	234	19	tñ(y	tñ(y	NOUN
ejpam-5839	234	20	)	)	PUNCT
ejpam-5839	234	21	)	)	PUNCT
ejpam-5839	234	22	}	}	PUNCT
ejpam-5839	234	23	,	,	PUNCT
ejpam-5839	234	24	minz	minz	NOUN
ejpam-5839	234	25	=	=	SYM
ejpam-5839	234	26	(	(	PUNCT
ejpam-5839	234	27	x)⊛	x)⊛	NOUN
ejpam-5839	234	28	y	y	PROPN
ejpam-5839	234	29	{	{	PUNCT
ejpam-5839	234	30	max(im̃(x	max(im̃(x	NOUN
ejpam-5839	234	31	)	)	PUNCT
ejpam-5839	234	32	,	,	PUNCT
ejpam-5839	234	33	iñ(y	iñ(y	NOUN
ejpam-5839	234	34	)	)	PUNCT
ejpam-5839	234	35	)	)	PUNCT
ejpam-5839	234	36	}	}	PUNCT
ejpam-5839	234	37	,	,	PUNCT
ejpam-5839	234	38	minz	minz	NOUN
ejpam-5839	234	39	=	=	SYM
ejpam-5839	234	40	(	(	PUNCT
ejpam-5839	234	41	x)⊛	x)⊛	NOUN
ejpam-5839	234	42	y	y	PROPN
ejpam-5839	234	43	{	{	PUNCT
ejpam-5839	234	44	max(fm̃(x	max(fm̃(x	PROPN
ejpam-5839	234	45	)	)	PUNCT
ejpam-5839	234	46	,	,	PUNCT
ejpam-5839	234	47	fñ(y	fñ(y	NOUN
ejpam-5839	234	48	)	)	PUNCT
ejpam-5839	234	49	)	)	PUNCT
ejpam-5839	234	50	}	}	PUNCT
ejpam-5839	234	51	,	,	PUNCT
ejpam-5839	234	52	minz	minz	NOUN
ejpam-5839	234	53	=	=	SYM
ejpam-5839	234	54	(	(	PUNCT
ejpam-5839	234	55	x)⊛	x)⊛	NOUN
ejpam-5839	234	56	y	y	PROPN
ejpam-5839	234	57	{	{	PUNCT
ejpam-5839	234	58	max(hm̃(x	max(hm̃(x	PROPN
ejpam-5839	234	59	)	)	PUNCT
ejpam-5839	234	60	,	,	PUNCT
ejpam-5839	234	61	hñ(y	hñ(y	PROPN
ejpam-5839	234	62	)	)	PUNCT
ejpam-5839	234	63	)	)	PUNCT
ejpam-5839	234	64	}	}	PUNCT
ejpam-5839	234	65	}	}	PUNCT
ejpam-5839	234	66	.	.	PUNCT
ejpam-5839	235	1	and	and	CCONJ
ejpam-5839	235	2	(	(	PUNCT
ejpam-5839	235	3	m̃⊙	m̃⊙	NOUN
ejpam-5839	235	4	ñ)(i	ñ)(i	NOUN
ejpam-5839	235	5	,	,	PUNCT
ejpam-5839	235	6	j	j	PROPN
ejpam-5839	235	7	,	,	PUNCT
ejpam-5839	235	8	k	k	PROPN
ejpam-5839	235	9	,	,	PUNCT
ejpam-5839	235	10	l	l	NOUN
ejpam-5839	235	11	)	)	PUNCT
ejpam-5839	235	12	=	=	SYM
ejpam-5839	235	13	{	{	PUNCT
ejpam-5839	235	14	z	z	NOUN
ejpam-5839	235	15	:	:	PUNCT
ejpam-5839	235	16	tm̃⊙ñ(z	tm̃⊙ñ(z	X
ejpam-5839	235	17	)	)	PUNCT
ejpam-5839	235	18	⪰	⪰	NOUN
ejpam-5839	235	19	i	i	PRON
ejpam-5839	235	20	,	,	PUNCT
ejpam-5839	235	21	im̃⊙ñ(z	im̃⊙ñ(z	PROPN
ejpam-5839	235	22	)	)	PUNCT
ejpam-5839	235	23	⪰	⪰	PROPN
ejpam-5839	235	24	j	j	PROPN
ejpam-5839	235	25	,	,	PUNCT
ejpam-5839	235	26	fm̃⊙ñ(z	fm̃⊙ñ(z	ADJ
ejpam-5839	235	27	)	)	PUNCT
ejpam-5839	235	28	⪰	⪰	NOUN
ejpam-5839	235	29	k	k	PROPN
ejpam-5839	235	30	,	,	PUNCT
ejpam-5839	235	31	hm̃⊙ñ(z	hm̃⊙ñ(z	ADJ
ejpam-5839	235	32	)	)	PUNCT
ejpam-5839	235	33	⪰	⪰	NOUN
ejpam-5839	235	34	l	l	NOUN
ejpam-5839	235	35	}	}	PUNCT
ejpam-5839	235	36	.	.	PUNCT
ejpam-5839	236	1	let	let	VERB
ejpam-5839	236	2	z	z	NOUN
ejpam-5839	236	3	∈	∈	PROPN
ejpam-5839	236	4	(	(	PUNCT
ejpam-5839	236	5	m̃	m̃	PROPN
ejpam-5839	236	6	⊙	⊙	NOUN
ejpam-5839	236	7	ñ)(i	ñ)(i	PROPN
ejpam-5839	236	8	,	,	PUNCT
ejpam-5839	236	9	j	j	PROPN
ejpam-5839	236	10	,	,	PUNCT
ejpam-5839	236	11	k	k	PROPN
ejpam-5839	236	12	,	,	PUNCT
ejpam-5839	236	13	l	l	NOUN
ejpam-5839	236	14	)	)	PUNCT
ejpam-5839	236	15	,	,	PUNCT
ejpam-5839	236	16	then	then	ADV
ejpam-5839	236	17	there	there	PRON
ejpam-5839	236	18	exists	exist	VERB
ejpam-5839	236	19	at	at	ADP
ejpam-5839	236	20	least	least	ADV
ejpam-5839	236	21	one	one	NUM
ejpam-5839	236	22	x	x	SYM
ejpam-5839	236	23	∈	∈	PROPN
ejpam-5839	236	24	m̃	m̃	PROPN
ejpam-5839	236	25	and	and	CCONJ
ejpam-5839	236	26	y	y	PROPN
ejpam-5839	236	27	∈	∈	PROPN
ejpam-5839	237	1	ñ	ñ	VERB
ejpam-5839	237	2	such	such	ADJ
ejpam-5839	237	3	that	that	SCONJ
ejpam-5839	237	4	z	z	NOUN
ejpam-5839	237	5	=	=	NOUN
ejpam-5839	237	6	m̃⊙	m̃⊙	NOUN
ejpam-5839	237	7	ñ.	ñ.	PROPN
ejpam-5839	237	8	then	then	ADV
ejpam-5839	237	9	,	,	PUNCT
ejpam-5839	237	10	tm̃⊙ñ(z	tm̃⊙ñ(z	PUNCT
ejpam-5839	237	11	)	)	PUNCT
ejpam-5839	237	12	=	=	SYM
ejpam-5839	237	13	max	max	PROPN
ejpam-5839	237	14	{	{	PUNCT
ejpam-5839	237	15	min(tm̃(x	min(tm̃(x	NUM
ejpam-5839	237	16	)	)	PUNCT
ejpam-5839	237	17	,	,	PUNCT
ejpam-5839	237	18	tñ(y	tñ(y	NOUN
ejpam-5839	237	19	)	)	PUNCT
ejpam-5839	237	20	)	)	PUNCT
ejpam-5839	237	21	}	}	PUNCT
ejpam-5839	237	22	⪰	⪰	VERB
ejpam-5839	237	23	i.	i.	PROPN
ejpam-5839	237	24	tm̃(x	tm̃(x	PROPN
ejpam-5839	237	25	)	)	PUNCT
ejpam-5839	237	26	⪰	⪰	NOUN
ejpam-5839	237	27	i	i	PRON
ejpam-5839	237	28	and	and	CCONJ
ejpam-5839	237	29	tñ(y	tñ(y	NOUN
ejpam-5839	237	30	)	)	PUNCT
ejpam-5839	237	31	⪰	⪰	NOUN
ejpam-5839	237	32	i	i	PRON
ejpam-5839	237	33	im̃⊙ñ(z	im̃⊙ñ(z	NOUN
ejpam-5839	237	34	)	)	PUNCT
ejpam-5839	238	1	=	=	SYM
ejpam-5839	238	2	min	min	PROPN
ejpam-5839	238	3	{	{	PUNCT
ejpam-5839	238	4	max(im̃(x	max(im̃(x	NOUN
ejpam-5839	238	5	)	)	PUNCT
ejpam-5839	238	6	,	,	PUNCT
ejpam-5839	238	7	iñ(y	iñ(y	NOUN
ejpam-5839	238	8	)	)	PUNCT
ejpam-5839	238	9	)	)	PUNCT
ejpam-5839	238	10	}	}	PUNCT
ejpam-5839	238	11	⪯	⪯	VERB
ejpam-5839	238	12	j	j	PROPN
ejpam-5839	238	13	a.	a.	NOUN
ejpam-5839	238	14	shihadeh	shihadeh	PROPN
ejpam-5839	238	15	et	et	PROPN
ejpam-5839	238	16	al	al	PROPN
ejpam-5839	238	17	.	.	PUNCT
ejpam-5839	238	18	/	/	SYM
ejpam-5839	238	19	eur	eur	PROPN
ejpam-5839	238	20	.	.	PUNCT
ejpam-5839	239	1	j.	j.	PROPN
ejpam-5839	239	2	pure	pure	PROPN
ejpam-5839	239	3	appl	appl	PROPN
ejpam-5839	239	4	.	.	PROPN
ejpam-5839	239	5	math	math	PROPN
ejpam-5839	239	6	,	,	PUNCT
ejpam-5839	239	7	18	18	NUM
ejpam-5839	239	8	(	(	PUNCT
ejpam-5839	239	9	2	2	NUM
ejpam-5839	239	10	)	)	PUNCT
ejpam-5839	239	11	(	(	PUNCT
ejpam-5839	239	12	2025	2025	NUM
ejpam-5839	239	13	)	)	PUNCT
ejpam-5839	239	14	,	,	PUNCT
ejpam-5839	239	15	5839	5839	NUM
ejpam-5839	239	16	9	9	NUM
ejpam-5839	239	17	of	of	ADP
ejpam-5839	239	18	54	54	NUM
ejpam-5839	239	19	im̃(x	im̃(x	ADJ
ejpam-5839	239	20	)	)	PUNCT
ejpam-5839	239	21	⪯	⪯	PROPN
ejpam-5839	239	22	j	j	PROPN
ejpam-5839	239	23	and	and	CCONJ
ejpam-5839	239	24	iñ(y	iñ(y	NOUN
ejpam-5839	239	25	)	)	PUNCT
ejpam-5839	239	26	⪯	⪯	NOUN
ejpam-5839	239	27	j	j	PROPN
ejpam-5839	239	28	fm̃⊙ñ(z	fm̃⊙ñ(z	PROPN
ejpam-5839	239	29	)	)	PUNCT
ejpam-5839	239	30	=	=	SYM
ejpam-5839	239	31	min	min	PROPN
ejpam-5839	239	32	{	{	PUNCT
ejpam-5839	239	33	max(fm̃(x	max(fm̃(x	PROPN
ejpam-5839	239	34	)	)	PUNCT
ejpam-5839	239	35	,	,	PUNCT
ejpam-5839	239	36	fñ(y	fñ(y	NOUN
ejpam-5839	239	37	)	)	PUNCT
ejpam-5839	239	38	)	)	PUNCT
ejpam-5839	239	39	}	}	PUNCT
ejpam-5839	239	40	⪯	⪯	NOUN
ejpam-5839	239	41	k	k	X
ejpam-5839	239	42	fm̃(x	fm̃(x	X
ejpam-5839	239	43	)	)	PUNCT
ejpam-5839	239	44	⪯	⪯	PROPN
ejpam-5839	239	45	k	k	NOUN
ejpam-5839	239	46	and	and	CCONJ
ejpam-5839	239	47	fñ(y	fñ(y	ADJ
ejpam-5839	239	48	)	)	PUNCT
ejpam-5839	239	49	⪯	⪯	NOUN
ejpam-5839	239	50	k	k	PROPN
ejpam-5839	239	51	hm̃⊙ñ(z	hm̃⊙ñ(z	PROPN
ejpam-5839	239	52	)	)	PUNCT
ejpam-5839	240	1	=	=	SYM
ejpam-5839	240	2	min	min	NOUN
ejpam-5839	240	3	{	{	PUNCT
ejpam-5839	240	4	max(hm̃(x	max(hm̃(x	NOUN
ejpam-5839	240	5	)	)	PUNCT
ejpam-5839	240	6	,	,	PUNCT
ejpam-5839	240	7	hñ(y	hñ(y	PROPN
ejpam-5839	240	8	)	)	PUNCT
ejpam-5839	240	9	)	)	PUNCT
ejpam-5839	240	10	}	}	PUNCT
ejpam-5839	240	11	⪯	⪯	VERB
ejpam-5839	240	12	l	l	NOUN
ejpam-5839	240	13	hm̃(x	hm̃(x	X
ejpam-5839	240	14	)	)	PUNCT
ejpam-5839	240	15	⪯	⪯	PROPN
ejpam-5839	240	16	l	l	NOUN
ejpam-5839	240	17	and	and	CCONJ
ejpam-5839	240	18	hñ(y	hñ(y	PROPN
ejpam-5839	240	19	)	)	PUNCT
ejpam-5839	240	20	⪯	⪯	PROPN
ejpam-5839	241	1	l	l	NOUN
ejpam-5839	241	2	this	this	PRON
ejpam-5839	241	3	implies	imply	VERB
ejpam-5839	241	4	x	x	PART
ejpam-5839	241	5	∈	∈	PROPN
ejpam-5839	241	6	m̃(i	m̃(i	PROPN
ejpam-5839	241	7	,	,	PUNCT
ejpam-5839	241	8	j	j	PROPN
ejpam-5839	241	9	,	,	PUNCT
ejpam-5839	241	10	k	k	PROPN
ejpam-5839	241	11	,	,	PUNCT
ejpam-5839	241	12	l	l	NOUN
ejpam-5839	241	13	)	)	PUNCT
ejpam-5839	241	14	and	and	CCONJ
ejpam-5839	241	15	y	y	PROPN
ejpam-5839	241	16	∈	∈	PROPN
ejpam-5839	241	17	ñ(i	ñ(i	PROPN
ejpam-5839	241	18	,	,	PUNCT
ejpam-5839	241	19	j	j	PROPN
ejpam-5839	241	20	,	,	PUNCT
ejpam-5839	241	21	k	k	PROPN
ejpam-5839	241	22	,	,	PUNCT
ejpam-5839	241	23	l	l	NOUN
ejpam-5839	241	24	)	)	PUNCT
ejpam-5839	241	25	.	.	PUNCT
ejpam-5839	242	1	therefore	therefore	ADV
ejpam-5839	242	2	,	,	PUNCT
ejpam-5839	242	3	z	z	NOUN
ejpam-5839	242	4	=	=	SYM
ejpam-5839	242	5	x⊙	x⊙	PROPN
ejpam-5839	242	6	y	y	PROPN
ejpam-5839	242	7	∈	∈	PROPN
ejpam-5839	242	8	m̃(i	m̃(i	PROPN
ejpam-5839	242	9	,	,	PUNCT
ejpam-5839	242	10	j	j	PROPN
ejpam-5839	242	11	,	,	PUNCT
ejpam-5839	242	12	k	k	PROPN
ejpam-5839	242	13	,	,	PUNCT
ejpam-5839	242	14	l)⊙	l)⊙	NOUN
ejpam-5839	242	15	ñ(i	ñ(i	PROPN
ejpam-5839	242	16	,	,	PUNCT
ejpam-5839	242	17	j	j	PROPN
ejpam-5839	242	18	,	,	PUNCT
ejpam-5839	242	19	k	k	PROPN
ejpam-5839	242	20	,	,	PUNCT
ejpam-5839	242	21	l	l	NOUN
ejpam-5839	242	22	)	)	PUNCT
ejpam-5839	242	23	again	again	ADV
ejpam-5839	242	24	,	,	PUNCT
ejpam-5839	242	25	let	let	VERB
ejpam-5839	242	26	z∗	z∗	PROPN
ejpam-5839	242	27	∈	∈	PROPN
ejpam-5839	242	28	m̃(i	m̃(i	PROPN
ejpam-5839	242	29	,	,	PUNCT
ejpam-5839	242	30	j	j	PROPN
ejpam-5839	242	31	,	,	PUNCT
ejpam-5839	242	32	k	k	PROPN
ejpam-5839	242	33	,	,	PUNCT
ejpam-5839	242	34	l)⊙	l)⊙	NOUN
ejpam-5839	242	35	ñ(i	ñ(i	PROPN
ejpam-5839	242	36	,	,	PUNCT
ejpam-5839	242	37	j	j	PROPN
ejpam-5839	242	38	,	,	PUNCT
ejpam-5839	242	39	k	k	PROPN
ejpam-5839	242	40	,	,	PUNCT
ejpam-5839	242	41	l	l	NOUN
ejpam-5839	242	42	)	)	PUNCT
ejpam-5839	242	43	.	.	PUNCT
ejpam-5839	243	1	then	then	ADV
ejpam-5839	243	2	there	there	PRON
ejpam-5839	243	3	exists	exist	VERB
ejpam-5839	243	4	at	at	ADP
ejpam-5839	243	5	least	least	ADV
ejpam-5839	243	6	one	one	NUM
ejpam-5839	243	7	x∗	x∗	PROPN
ejpam-5839	243	8	∈	∈	PROPN
ejpam-5839	243	9	m̃(i	m̃(i	PROPN
ejpam-5839	243	10	,	,	PUNCT
ejpam-5839	243	11	j	j	PROPN
ejpam-5839	243	12	,	,	PUNCT
ejpam-5839	243	13	k	k	PROPN
ejpam-5839	243	14	,	,	PUNCT
ejpam-5839	243	15	l	l	NOUN
ejpam-5839	243	16	)	)	PUNCT
ejpam-5839	243	17	and	and	CCONJ
ejpam-5839	243	18	y∗	y∗	PROPN
ejpam-5839	243	19	∈	∈	PROPN
ejpam-5839	243	20	ñ(i	ñ(i	PROPN
ejpam-5839	243	21	,	,	PUNCT
ejpam-5839	243	22	j	j	PROPN
ejpam-5839	243	23	,	,	PUNCT
ejpam-5839	243	24	k	k	PROPN
ejpam-5839	243	25	,	,	PUNCT
ejpam-5839	243	26	l	l	NOUN
ejpam-5839	243	27	)	)	PUNCT
ejpam-5839	243	28	such	such	ADJ
ejpam-5839	243	29	that	that	DET
ejpam-5839	243	30	z∗	z∗	NOUN
ejpam-5839	243	31	=	=	PUNCT
ejpam-5839	243	32	x∗	x∗	PROPN
ejpam-5839	243	33	⊙	⊙	PROPN
ejpam-5839	243	34	y∗	y∗	PROPN
ejpam-5839	244	1	then	then	ADV
ejpam-5839	244	2	,	,	PUNCT
ejpam-5839	244	3	we	we	PRON
ejpam-5839	244	4	have	have	VERB
ejpam-5839	244	5	tm̃(x∗	tm̃(x∗	NOUN
ejpam-5839	244	6	)	)	PUNCT
ejpam-5839	244	7	⪰	⪰	NOUN
ejpam-5839	244	8	i	i	PRON
ejpam-5839	244	9	and	and	CCONJ
ejpam-5839	244	10	tñ(y	tñ(y	NOUN
ejpam-5839	244	11	∗	∗	NOUN
ejpam-5839	244	12	)	)	PUNCT
ejpam-5839	244	13	⪰	⪰	NOUN
ejpam-5839	244	14	i	i	PRON
ejpam-5839	244	15	im̃(x∗	im̃(x∗	NOUN
ejpam-5839	244	16	)	)	PUNCT
ejpam-5839	244	17	⪯	⪯	PROPN
ejpam-5839	244	18	j	j	PROPN
ejpam-5839	244	19	and	and	CCONJ
ejpam-5839	244	20	iñ(y	iñ(y	ADJ
ejpam-5839	244	21	∗	∗	NOUN
ejpam-5839	244	22	)	)	PUNCT
ejpam-5839	244	23	⪯	⪯	PROPN
ejpam-5839	244	24	j	j	PROPN
ejpam-5839	244	25	fm̃(x∗	fm̃(x∗	ADV
ejpam-5839	244	26	)	)	PUNCT
ejpam-5839	244	27	⪯	⪯	NOUN
ejpam-5839	244	28	k	k	NOUN
ejpam-5839	244	29	and	and	CCONJ
ejpam-5839	244	30	fñ(y	fñ(y	NOUN
ejpam-5839	244	31	∗	∗	NOUN
ejpam-5839	244	32	)	)	PUNCT
ejpam-5839	244	33	⪯	⪯	NOUN
ejpam-5839	244	34	k	k	PROPN
ejpam-5839	244	35	hm̃(x∗	hm̃(x∗	PROPN
ejpam-5839	244	36	)	)	PUNCT
ejpam-5839	244	37	⪯	⪯	PROPN
ejpam-5839	244	38	l	l	NOUN
ejpam-5839	244	39	and	and	CCONJ
ejpam-5839	244	40	hñ(y	hñ(y	PROPN
ejpam-5839	244	41	∗	∗	NOUN
ejpam-5839	244	42	)	)	PUNCT
ejpam-5839	245	1	⪯	⪯	PROPN
ejpam-5839	245	2	l	l	NOUN
ejpam-5839	245	3	this	this	PRON
ejpam-5839	245	4	implies	imply	VERB
ejpam-5839	245	5	that	that	SCONJ
ejpam-5839	245	6	min(tm̃(x∗	min(tm̃(x∗	NOUN
ejpam-5839	245	7	)	)	PUNCT
ejpam-5839	245	8	,	,	PUNCT
ejpam-5839	245	9	tñ(y	tñ(y	X
ejpam-5839	245	10	∗	∗	NOUN
ejpam-5839	245	11	)	)	PUNCT
ejpam-5839	245	12	)	)	PUNCT
ejpam-5839	246	1	⪰	⪰	NOUN
ejpam-5839	246	2	i	i	PRON
ejpam-5839	246	3	,	,	PUNCT
ejpam-5839	246	4	max(im̃(x∗	max(im̃(x∗	PROPN
ejpam-5839	246	5	)	)	PUNCT
ejpam-5839	246	6	,	,	PUNCT
ejpam-5839	246	7	iñ(y	iñ(y	ADJ
ejpam-5839	246	8	∗	∗	NOUN
ejpam-5839	246	9	)	)	PUNCT
ejpam-5839	246	10	)	)	PUNCT
ejpam-5839	247	1	⪯	⪯	PROPN
ejpam-5839	247	2	j	j	PROPN
ejpam-5839	247	3	,	,	PUNCT
ejpam-5839	247	4	max(fm̃(x∗	max(fm̃(x∗	PROPN
ejpam-5839	247	5	)	)	PUNCT
ejpam-5839	247	6	,	,	PUNCT
ejpam-5839	247	7	fñ(y	fñ(y	NOUN
ejpam-5839	247	8	∗	∗	NOUN
ejpam-5839	247	9	)	)	PUNCT
ejpam-5839	247	10	)	)	PUNCT
ejpam-5839	248	1	⪯	⪯	PROPN
ejpam-5839	248	2	k	k	NOUN
ejpam-5839	248	3	,	,	PUNCT
ejpam-5839	248	4	max(hm̃(x∗	max(hm̃(x∗	PROPN
ejpam-5839	248	5	)	)	PUNCT
ejpam-5839	248	6	,	,	PUNCT
ejpam-5839	248	7	hñ(y	hñ(y	PROPN
ejpam-5839	248	8	∗	∗	NOUN
ejpam-5839	248	9	)	)	PUNCT
ejpam-5839	248	10	)	)	PUNCT
ejpam-5839	249	1	⪯	⪯	PROPN
ejpam-5839	249	2	l	l	NOUN
ejpam-5839	249	3	then	then	ADV
ejpam-5839	249	4	,	,	PUNCT
ejpam-5839	249	5	we	we	PRON
ejpam-5839	249	6	have	have	VERB
ejpam-5839	249	7	max	max	PROPN
ejpam-5839	249	8	x	x	X
ejpam-5839	249	9	z∗	z∗	PROPN
ejpam-5839	249	10	=	=	PUNCT
ejpam-5839	249	11	x∗	x∗	PROPN
ejpam-5839	249	12	⊙	⊙	PROPN
ejpam-5839	250	1	y∗	y∗	PROPN
ejpam-5839	250	2	{	{	PUNCT
ejpam-5839	250	3	min(tm̃(x∗	min(tm̃(x∗	NOUN
ejpam-5839	250	4	)	)	PUNCT
ejpam-5839	250	5	,	,	PUNCT
ejpam-5839	250	6	tñ(y	tñ(y	X
ejpam-5839	250	7	∗	∗	NOUN
ejpam-5839	250	8	)	)	PUNCT
ejpam-5839	250	9	)	)	PUNCT
ejpam-5839	250	10	}	}	PUNCT
ejpam-5839	251	1	⪰	⪰	NOUN
ejpam-5839	251	2	i	i	PRON
ejpam-5839	251	3	⇒	⇒	VERB
ejpam-5839	251	4	tm̃⊙ñ(z	tm̃⊙ñ(z	X
ejpam-5839	251	5	∗	∗	NOUN
ejpam-5839	251	6	)	)	PUNCT
ejpam-5839	252	1	=	=	SYM
ejpam-5839	252	2	tm̃⊙ñ(x	tm̃⊙ñ(x	X
ejpam-5839	252	3	∗	∗	PROPN
ejpam-5839	252	4	⊙	⊙	PROPN
ejpam-5839	252	5	y∗	y∗	ADV
ejpam-5839	252	6	)	)	PUNCT
ejpam-5839	252	7	⪰	⪰	NOUN
ejpam-5839	252	8	i	i	PRON
ejpam-5839	252	9	similarly	similarly	ADV
ejpam-5839	252	10	,	,	PUNCT
ejpam-5839	252	11	a.	a.	NOUN
ejpam-5839	252	12	shihadeh	shihadeh	VERB
ejpam-5839	252	13	et	et	PROPN
ejpam-5839	252	14	al	al	PROPN
ejpam-5839	252	15	.	.	PUNCT
ejpam-5839	252	16	/	/	SYM
ejpam-5839	252	17	eur	eur	PROPN
ejpam-5839	252	18	.	.	PUNCT
ejpam-5839	253	1	j.	j.	PROPN
ejpam-5839	253	2	pure	pure	PROPN
ejpam-5839	253	3	appl	appl	PROPN
ejpam-5839	253	4	.	.	PROPN
ejpam-5839	253	5	math	math	PROPN
ejpam-5839	253	6	,	,	PUNCT
ejpam-5839	253	7	18	18	NUM
ejpam-5839	253	8	(	(	PUNCT
ejpam-5839	253	9	2	2	NUM
ejpam-5839	253	10	)	)	PUNCT
ejpam-5839	253	11	(	(	PUNCT
ejpam-5839	253	12	2025	2025	NUM
ejpam-5839	253	13	)	)	PUNCT
ejpam-5839	253	14	,	,	PUNCT
ejpam-5839	253	15	5839	5839	NUM
ejpam-5839	253	16	10	10	NUM
ejpam-5839	253	17	of	of	ADP
ejpam-5839	253	18	54	54	NUM
ejpam-5839	253	19	im̃⊙ñ(z	im̃⊙ñ(z	NUM
ejpam-5839	253	20	∗	∗	NOUN
ejpam-5839	253	21	)	)	PUNCT
ejpam-5839	254	1	=	=	PUNCT
ejpam-5839	254	2	im̃⊙ñ(x	im̃⊙ñ(x	NOUN
ejpam-5839	254	3	∗	∗	PROPN
ejpam-5839	254	4	⊙	⊙	PROPN
ejpam-5839	254	5	y∗	y∗	PROPN
ejpam-5839	254	6	)	)	PUNCT
ejpam-5839	254	7	⪯	⪯	PROPN
ejpam-5839	254	8	j	j	PROPN
ejpam-5839	255	1	fm̃⊙ñ(z	fm̃⊙ñ(z	PROPN
ejpam-5839	255	2	∗	∗	PROPN
ejpam-5839	255	3	)	)	PUNCT
ejpam-5839	256	1	=	=	SYM
ejpam-5839	256	2	fm̃⊙ñ(x	fm̃⊙ñ(x	NOUN
ejpam-5839	257	1	∗	∗	NOUN
ejpam-5839	257	2	⊙	⊙	PROPN
ejpam-5839	257	3	y∗	y∗	PROPN
ejpam-5839	257	4	)	)	PUNCT
ejpam-5839	258	1	⪯	⪯	PROPN
ejpam-5839	258	2	k	k	PROPN
ejpam-5839	258	3	hm̃⊙ñ(z	hm̃⊙ñ(z	PROPN
ejpam-5839	258	4	∗	∗	PROPN
ejpam-5839	258	5	)	)	PUNCT
ejpam-5839	259	1	=	=	SYM
ejpam-5839	259	2	hm̃⊙ñ(x	hm̃⊙ñ(x	NOUN
ejpam-5839	259	3	∗	∗	NOUN
ejpam-5839	259	4	⊙	⊙	PROPN
ejpam-5839	259	5	y∗	y∗	PROPN
ejpam-5839	259	6	)	)	PUNCT
ejpam-5839	259	7	⪯	⪯	PROPN
ejpam-5839	259	8	l	l	NOUN
ejpam-5839	259	9	therefore	therefore	ADV
ejpam-5839	259	10	,	,	PUNCT
ejpam-5839	259	11	z∗	z∗	PROPN
ejpam-5839	259	12	∈	∈	PROPN
ejpam-5839	259	13	(	(	PUNCT
ejpam-5839	259	14	m̃⊙	m̃⊙	NOUN
ejpam-5839	259	15	ñ)(i	ñ)(i	PROPN
ejpam-5839	259	16	,	,	PUNCT
ejpam-5839	259	17	j	j	PROPN
ejpam-5839	259	18	,	,	PUNCT
ejpam-5839	259	19	k	k	PROPN
ejpam-5839	259	20	,	,	PUNCT
ejpam-5839	259	21	l	l	NOUN
ejpam-5839	259	22	)	)	PUNCT
ejpam-5839	259	23	.	.	PUNCT
ejpam-5839	260	1	2	2	NUM
ejpam-5839	260	2	since	since	SCONJ
ejpam-5839	260	3	m̃	m̃	PROPN
ejpam-5839	260	4	=	=	SYM
ejpam-5839	260	5	{	{	PUNCT
ejpam-5839	261	1	z	z	NOUN
ejpam-5839	261	2	|	|	INTJ
ejpam-5839	261	3	max	max	PROPN
ejpam-5839	261	4	ζ	ζ	PROPN
ejpam-5839	261	5	z	z	PROPN
ejpam-5839	261	6	=	=	SYM
ejpam-5839	261	7	λ(ζ)tm̃(ζ),min	λ(ζ)tm̃(ζ),min	PUNCT
ejpam-5839	261	8	ζ	ζ	NOUN
ejpam-5839	261	9	z	z	NOUN
ejpam-5839	261	10	=	=	PUNCT
ejpam-5839	261	11	λ(ζ)im̃(ζ),min	λ(ζ)im̃(ζ),min	PART
ejpam-5839	261	12	ζ	ζ	NOUN
ejpam-5839	261	13	z	z	NOUN
ejpam-5839	261	14	=	=	SYM
ejpam-5839	261	15	λ(ζ)fm̃(ζ),min	λ(ζ)fm̃(ζ),min	PUNCT
ejpam-5839	261	16	ζ	ζ	NOUN
ejpam-5839	261	17	z	z	NOUN
ejpam-5839	261	18	=	=	SYM
ejpam-5839	261	19	λ(ζ)hm̃(ζ	λ(ζ)hm̃(ζ	NOUN
ejpam-5839	261	20	)	)	PUNCT
ejpam-5839	261	21	}	}	PUNCT
ejpam-5839	261	22	let	let	VERB
ejpam-5839	261	23	zλm̃(i	zλm̃(i	PROPN
ejpam-5839	261	24	,	,	PUNCT
ejpam-5839	261	25	j	j	PROPN
ejpam-5839	261	26	,	,	PUNCT
ejpam-5839	261	27	k	k	PROPN
ejpam-5839	261	28	,	,	PUNCT
ejpam-5839	261	29	l	l	NOUN
ejpam-5839	261	30	)	)	PUNCT
ejpam-5839	261	31	=	=	PRON
ejpam-5839	261	32	{	{	PUNCT
ejpam-5839	261	33	z	z	NOUN
ejpam-5839	261	34	|	|	NOUN
ejpam-5839	261	35	tm̃(ζ	tm̃(ζ	NOUN
ejpam-5839	261	36	)	)	PUNCT
ejpam-5839	261	37	⪰	⪰	NOUN
ejpam-5839	261	38	i	i	PRON
ejpam-5839	261	39	,	,	PUNCT
ejpam-5839	261	40	im̃(ζ	im̃(ζ	NOUN
ejpam-5839	261	41	)	)	PUNCT
ejpam-5839	261	42	⪯	⪯	PROPN
ejpam-5839	261	43	j	j	PROPN
ejpam-5839	261	44	,	,	PUNCT
ejpam-5839	261	45	fm̃(ζ	fm̃(ζ	NOUN
ejpam-5839	261	46	)	)	PUNCT
ejpam-5839	261	47	⪯	⪯	PROPN
ejpam-5839	261	48	k	k	NOUN
ejpam-5839	261	49	,	,	PUNCT
ejpam-5839	261	50	hm̃(ζ	hm̃(ζ	NOUN
ejpam-5839	261	51	)	)	PUNCT
ejpam-5839	261	52	⪯	⪯	PROPN
ejpam-5839	261	53	l	l	NOUN
ejpam-5839	261	54	}	}	PUNCT
ejpam-5839	261	55	let	let	VERB
ejpam-5839	261	56	z	z	NOUN
ejpam-5839	261	57	∈	∈	PROPN
ejpam-5839	261	58	(	(	PUNCT
ejpam-5839	261	59	λm	λm	NOUN
ejpam-5839	261	60	)	)	PUNCT
ejpam-5839	261	61	,	,	PUNCT
ejpam-5839	261	62	then	then	ADV
ejpam-5839	261	63	there	there	PRON
ejpam-5839	261	64	exists	exist	VERB
ejpam-5839	261	65	ζ	ζ	PROPN
ejpam-5839	261	66	∈	∈	PROPN
ejpam-5839	261	67	m̃	m̃	PROPN
ejpam-5839	261	68	such	such	ADJ
ejpam-5839	261	69	that	that	SCONJ
ejpam-5839	261	70	z	z	NOUN
ejpam-5839	261	71	=	=	SYM
ejpam-5839	261	72	λ(ζ	λ(ζ	NOUN
ejpam-5839	261	73	)	)	PUNCT
ejpam-5839	261	74	which	which	PRON
ejpam-5839	261	75	implies	imply	VERB
ejpam-5839	261	76	tm̃(ζ	tm̃(ζ	NOUN
ejpam-5839	261	77	)	)	PUNCT
ejpam-5839	261	78	⪰	⪰	NOUN
ejpam-5839	261	79	i	i	PRON
ejpam-5839	261	80	,	,	PUNCT
ejpam-5839	261	81	im̃(ζ	im̃(ζ	NOUN
ejpam-5839	261	82	)	)	PUNCT
ejpam-5839	261	83	⪯	⪯	PROPN
ejpam-5839	261	84	j	j	PROPN
ejpam-5839	261	85	,	,	PUNCT
ejpam-5839	261	86	fm̃(ζ	fm̃(ζ	NOUN
ejpam-5839	261	87	)	)	PUNCT
ejpam-5839	261	88	⪯	⪯	PROPN
ejpam-5839	261	89	k	k	NOUN
ejpam-5839	261	90	,	,	PUNCT
ejpam-5839	261	91	hm̃(ζ	hm̃(ζ	NOUN
ejpam-5839	261	92	)	)	PUNCT
ejpam-5839	261	93	⪯	⪯	PROPN
ejpam-5839	261	94	l	l	PROPN
ejpam-5839	261	95	thus	thus	ADV
ejpam-5839	261	96	,	,	PUNCT
ejpam-5839	261	97	ζ	ζ	PROPN
ejpam-5839	261	98	∈	∈	PROPN
ejpam-5839	261	99	m̃(i	m̃(i	PROPN
ejpam-5839	261	100	,	,	PUNCT
ejpam-5839	261	101	j	j	PROPN
ejpam-5839	261	102	,	,	PUNCT
ejpam-5839	261	103	k	k	PROPN
ejpam-5839	261	104	,	,	PUNCT
ejpam-5839	261	105	l	l	NOUN
ejpam-5839	261	106	)	)	PUNCT
ejpam-5839	261	107	⇒	⇒	NOUN
ejpam-5839	261	108	z	z	NOUN
ejpam-5839	261	109	=	=	SYM
ejpam-5839	261	110	λ(ζ	λ(ζ	PROPN
ejpam-5839	261	111	)	)	PUNCT
ejpam-5839	261	112	∈	∈	PROPN
ejpam-5839	261	113	(	(	PUNCT
ejpam-5839	261	114	λm)(i	λm)(i	PROPN
ejpam-5839	261	115	,	,	PUNCT
ejpam-5839	261	116	j	j	PROPN
ejpam-5839	261	117	,	,	PUNCT
ejpam-5839	261	118	k	k	PROPN
ejpam-5839	261	119	,	,	PUNCT
ejpam-5839	261	120	l	l	NOUN
ejpam-5839	261	121	)	)	PUNCT
ejpam-5839	261	122	again	again	ADV
ejpam-5839	261	123	,	,	PUNCT
ejpam-5839	261	124	let	let	VERB
ejpam-5839	261	125	z∗	z∗	PROPN
ejpam-5839	261	126	∈	∈	PROPN
ejpam-5839	261	127	(	(	PUNCT
ejpam-5839	261	128	λm	λm	NOUN
ejpam-5839	261	129	)	)	PUNCT
ejpam-5839	261	130	,	,	PUNCT
ejpam-5839	261	131	then	then	ADV
ejpam-5839	261	132	there	there	PRON
ejpam-5839	261	133	exists	exist	VERB
ejpam-5839	261	134	ζ∗	ζ∗	PROPN
ejpam-5839	261	135	∈	∈	PROPN
ejpam-5839	261	136	m̃	m̃	PROPN
ejpam-5839	262	1	such	such	ADJ
ejpam-5839	262	2	that	that	DET
ejpam-5839	262	3	z∗	z∗	NOUN
ejpam-5839	262	4	=	=	SYM
ejpam-5839	262	5	λ(ζ∗	λ(ζ∗	CCONJ
ejpam-5839	262	6	)	)	PUNCT
ejpam-5839	262	7	which	which	PRON
ejpam-5839	262	8	implies	imply	VERB
ejpam-5839	262	9	tm̃(ζ∗	tm̃(ζ∗	NUM
ejpam-5839	262	10	)	)	PUNCT
ejpam-5839	262	11	⪰	⪰	NOUN
ejpam-5839	262	12	i	i	PRON
ejpam-5839	262	13	,	,	PUNCT
ejpam-5839	262	14	im̃(ζ∗	im̃(ζ∗	NOUN
ejpam-5839	262	15	)	)	PUNCT
ejpam-5839	262	16	⪯	⪯	PROPN
ejpam-5839	262	17	j	j	PROPN
ejpam-5839	262	18	,	,	PUNCT
ejpam-5839	262	19	fm̃(ζ∗	fm̃(ζ∗	PROPN
ejpam-5839	262	20	)	)	PUNCT
ejpam-5839	262	21	⪯	⪯	NOUN
ejpam-5839	262	22	k	k	X
ejpam-5839	262	23	,	,	PUNCT
ejpam-5839	262	24	hm̃(ζ∗	hm̃(ζ∗	PART
ejpam-5839	262	25	)	)	PUNCT
ejpam-5839	262	26	⪯	⪯	NOUN
ejpam-5839	262	27	l	l	NOUN
ejpam-5839	262	28	then	then	ADV
ejpam-5839	262	29	we	we	PRON
ejpam-5839	262	30	have	have	VERB
ejpam-5839	262	31	z∗	z∗	NOUN
ejpam-5839	262	32	=	=	SYM
ejpam-5839	262	33	λ(ζ)∗	λ(ζ)∗	NOUN
ejpam-5839	262	34	tm̃(ζ∗	tm̃(ζ∗	NOUN
ejpam-5839	262	35	)	)	PUNCT
ejpam-5839	262	36	⪰	⪰	NOUN
ejpam-5839	262	37	i	i	PRON
ejpam-5839	262	38	⇒	⇒	VERB
ejpam-5839	262	39	t	t	PROPN
ejpam-5839	262	40	(	(	PUNCT
ejpam-5839	262	41	λm)m̃(λ(ζ)∗	λm)m̃(λ(ζ)∗	NOUN
ejpam-5839	262	42	)	)	PUNCT
ejpam-5839	262	43	=	=	SYM
ejpam-5839	262	44	t	t	PROPN
ejpam-5839	262	45	(	(	PUNCT
ejpam-5839	262	46	λm)m̃(z∗	λm)m̃(z∗	NOUN
ejpam-5839	262	47	)	)	PUNCT
ejpam-5839	262	48	⪰	⪰	NOUN
ejpam-5839	262	49	i	i	NOUN
ejpam-5839	262	50	z∗	z∗	NOUN
ejpam-5839	262	51	=	=	PUNCT
ejpam-5839	262	52	λ(ζ)∗	λ(ζ)∗	NOUN
ejpam-5839	262	53	im̃(ζ∗	im̃(ζ∗	NOUN
ejpam-5839	262	54	)	)	PUNCT
ejpam-5839	262	55	⪯	⪯	NOUN
ejpam-5839	262	56	j	j	PROPN
ejpam-5839	262	57	⇒	⇒	PROPN
ejpam-5839	262	58	i(λm)m̃(λ(ζ)∗	i(λm)m̃(λ(ζ)∗	PROPN
ejpam-5839	262	59	)	)	PUNCT
ejpam-5839	262	60	=	=	SYM
ejpam-5839	262	61	i(λm)m̃(z∗	i(λm)m̃(z∗	PROPN
ejpam-5839	262	62	)	)	PUNCT
ejpam-5839	262	63	⪯	⪯	NOUN
ejpam-5839	262	64	j	j	PROPN
ejpam-5839	262	65	z∗	z∗	PROPN
ejpam-5839	262	66	=	=	PUNCT
ejpam-5839	262	67	λ(ζ)∗	λ(ζ)∗	NOUN
ejpam-5839	262	68	fm̃(ζ∗	fm̃(ζ∗	PROPN
ejpam-5839	262	69	)	)	PUNCT
ejpam-5839	262	70	⪯	⪯	NOUN
ejpam-5839	262	71	k	k	PROPN
ejpam-5839	262	72	⇒	⇒	PROPN
ejpam-5839	262	73	f	f	PROPN
ejpam-5839	262	74	(	(	PUNCT
ejpam-5839	262	75	λm)m̃(λ(ζ)∗	λm)m̃(λ(ζ)∗	NOUN
ejpam-5839	262	76	)	)	PUNCT
ejpam-5839	262	77	=	=	SYM
ejpam-5839	262	78	f	f	X
ejpam-5839	262	79	(	(	PUNCT
ejpam-5839	262	80	λm)m̃(z∗	λm)m̃(z∗	PROPN
ejpam-5839	262	81	)	)	PUNCT
ejpam-5839	262	82	⪯	⪯	NOUN
ejpam-5839	262	83	k	k	PROPN
ejpam-5839	262	84	a.	a.	NOUN
ejpam-5839	262	85	shihadeh	shihadeh	VERB
ejpam-5839	262	86	et	et	PROPN
ejpam-5839	262	87	al	al	PROPN
ejpam-5839	262	88	.	.	PUNCT
ejpam-5839	262	89	/	/	SYM
ejpam-5839	262	90	eur	eur	PROPN
ejpam-5839	262	91	.	.	PUNCT
ejpam-5839	263	1	j.	j.	PROPN
ejpam-5839	263	2	pure	pure	PROPN
ejpam-5839	263	3	appl	appl	PROPN
ejpam-5839	263	4	.	.	PROPN
ejpam-5839	263	5	math	math	PROPN
ejpam-5839	263	6	,	,	PUNCT
ejpam-5839	263	7	18	18	NUM
ejpam-5839	263	8	(	(	PUNCT
ejpam-5839	263	9	2	2	NUM
ejpam-5839	263	10	)	)	PUNCT
ejpam-5839	263	11	(	(	PUNCT
ejpam-5839	263	12	2025	2025	NUM
ejpam-5839	263	13	)	)	PUNCT
ejpam-5839	263	14	,	,	PUNCT
ejpam-5839	263	15	5839	5839	NUM
ejpam-5839	263	16	11	11	NUM
ejpam-5839	263	17	of	of	ADP
ejpam-5839	263	18	54	54	NUM
ejpam-5839	263	19	z∗	z∗	NOUN
ejpam-5839	263	20	=	=	PUNCT
ejpam-5839	263	21	λ(ζ)∗	λ(ζ)∗	NOUN
ejpam-5839	263	22	hm̃(ζ∗	hm̃(ζ∗	PROPN
ejpam-5839	263	23	)	)	PUNCT
ejpam-5839	263	24	⪯	⪯	NOUN
ejpam-5839	263	25	l	l	PROPN
ejpam-5839	263	26	⇒	⇒	PROPN
ejpam-5839	263	27	h(λm)m̃(λ(ζ)∗	h(λm)m̃(λ(ζ)∗	PROPN
ejpam-5839	263	28	)	)	PUNCT
ejpam-5839	263	29	=	=	SYM
ejpam-5839	263	30	h(λm)m̃(z∗	h(λm)m̃(z∗	PROPN
ejpam-5839	263	31	)	)	PUNCT
ejpam-5839	263	32	⪯	⪯	NOUN
ejpam-5839	263	33	l	l	NOUN
ejpam-5839	264	1	therefore	therefore	ADV
ejpam-5839	264	2	,	,	PUNCT
ejpam-5839	264	3	z∗	z∗	PROPN
ejpam-5839	264	4	∈	∈	PROPN
ejpam-5839	264	5	(	(	PUNCT
ejpam-5839	264	6	λm)m̃(i	λm)m̃(i	PROPN
ejpam-5839	264	7	,	,	PUNCT
ejpam-5839	264	8	j	j	PROPN
ejpam-5839	264	9	,	,	PUNCT
ejpam-5839	264	10	k	k	PROPN
ejpam-5839	264	11	,	,	PUNCT
ejpam-5839	264	12	l	l	NOUN
ejpam-5839	264	13	)	)	PUNCT
ejpam-5839	264	14	proposition	proposition	NOUN
ejpam-5839	264	15	3	3	X
ejpam-5839	264	16	.	.	PUNCT
ejpam-5839	264	17	let	let	VERB
ejpam-5839	264	18	m̃	m̃	PROPN
ejpam-5839	264	19	and	and	CCONJ
ejpam-5839	264	20	ñ	ñ	PROPN
ejpam-5839	264	21	be	be	VERB
ejpam-5839	264	22	two	two	NUM
ejpam-5839	264	23	closed	closed	ADJ
ejpam-5839	264	24	quadri	quadri	NOUN
ejpam-5839	264	25	-	-	PUNCT
ejpam-5839	264	26	partitioned	partition	VERB
ejpam-5839	264	27	neutrosophic	neutrosophic	ADJ
ejpam-5839	264	28	numbers	number	NOUN
ejpam-5839	264	29	.	.	PUNCT
ejpam-5839	265	1	then	then	ADV
ejpam-5839	265	2	,	,	PUNCT
ejpam-5839	265	3	m̃+	m̃+	PROPN
ejpam-5839	265	4	ñ	ñ	PROPN
ejpam-5839	265	5	,	,	PUNCT
ejpam-5839	265	6	m̃−	m̃−	PROPN
ejpam-5839	265	7	ñ	ñ	PROPN
ejpam-5839	265	8	,	,	PUNCT
ejpam-5839	265	9	m̃×	m̃×	PROPN
ejpam-5839	265	10	ñ	ñ	PROPN
ejpam-5839	265	11	,	,	PUNCT
ejpam-5839	265	12	and	and	CCONJ
ejpam-5839	265	13	λm̃	λm̃	NUM
ejpam-5839	265	14	are	be	AUX
ejpam-5839	265	15	also	also	ADV
ejpam-5839	265	16	closed	close	VERB
ejpam-5839	265	17	quadri	quadri	NOUN
ejpam-5839	265	18	-	-	PUNCT
ejpam-5839	265	19	partitioned	partition	VERB
ejpam-5839	265	20	neutrosophic	neutrosophic	ADJ
ejpam-5839	265	21	numbers	number	NOUN
ejpam-5839	265	22	,	,	PUNCT
ejpam-5839	265	23	where	where	SCONJ
ejpam-5839	265	24	0	0	NUM
ejpam-5839	265	25	̸=	̸=	PROPN
ejpam-5839	265	26	λ	λ	X
ejpam-5839	265	27	∈	∈	NOUN
ejpam-5839	265	28	r	r	NOUN
ejpam-5839	265	29	and	and	CCONJ
ejpam-5839	265	30	λ	λ	PROPN
ejpam-5839	265	31	is	be	AUX
ejpam-5839	265	32	any	any	DET
ejpam-5839	265	33	real	real	ADJ
ejpam-5839	265	34	number	number	NOUN
ejpam-5839	265	35	.	.	PUNCT
ejpam-5839	266	1	proof	proof	NOUN
ejpam-5839	266	2	.	.	PUNCT
ejpam-5839	267	1	since	since	SCONJ
ejpam-5839	267	2	tm̃⊙ñ	tm̃⊙ñ	PROPN
ejpam-5839	267	3	and	and	CCONJ
ejpam-5839	267	4	t	t	PROPN
ejpam-5839	267	5	(	(	PUNCT
ejpam-5839	267	6	λm̃	λm̃	NUM
ejpam-5839	267	7	)	)	PUNCT
ejpam-5839	267	8	are	be	AUX
ejpam-5839	267	9	upper	upper	ADJ
ejpam-5839	267	10	semi	semi	ADJ
ejpam-5839	267	11	-	-	ADJ
ejpam-5839	267	12	continuous	continuous	ADJ
ejpam-5839	267	13	,	,	PUNCT
ejpam-5839	267	14	and	and	CCONJ
ejpam-5839	267	15	im̃⊙ñ	im̃⊙ñ	PROPN
ejpam-5839	267	16	and	and	CCONJ
ejpam-5839	267	17	i(λm̃	i(λm̃	PROPN
ejpam-5839	267	18	)	)	PUNCT
ejpam-5839	267	19	are	be	AUX
ejpam-5839	267	20	lower	low	ADJ
ejpam-5839	267	21	semi	semi	ADJ
ejpam-5839	267	22	-	-	ADJ
ejpam-5839	267	23	continuous	continuous	ADJ
ejpam-5839	267	24	,	,	PUNCT
ejpam-5839	267	25	it	it	PRON
ejpam-5839	267	26	follows	follow	VERB
ejpam-5839	267	27	that	that	SCONJ
ejpam-5839	267	28	(	(	PUNCT
ejpam-5839	267	29	m̃⊙	m̃⊙	NOUN
ejpam-5839	267	30	ñ)(i	ñ)(i	PROPN
ejpam-5839	267	31	,	,	PUNCT
ejpam-5839	267	32	j	j	PROPN
ejpam-5839	267	33	,	,	PUNCT
ejpam-5839	267	34	k	k	PROPN
ejpam-5839	267	35	,	,	PUNCT
ejpam-5839	267	36	l	l	NOUN
ejpam-5839	267	37	)	)	PUNCT
ejpam-5839	267	38	and	and	CCONJ
ejpam-5839	267	39	(	(	PUNCT
ejpam-5839	267	40	λm̃)(i	λm̃)(i	NOUN
ejpam-5839	267	41	,	,	PUNCT
ejpam-5839	267	42	j	j	PROPN
ejpam-5839	267	43	,	,	PUNCT
ejpam-5839	267	44	k	k	PROPN
ejpam-5839	267	45	,	,	PUNCT
ejpam-5839	267	46	l	l	NOUN
ejpam-5839	267	47	)	)	PUNCT
ejpam-5839	267	48	,	,	PUNCT
ejpam-5839	267	49	along	along	ADP
ejpam-5839	267	50	with	with	ADP
ejpam-5839	267	51	fm̃⊙ñ	fm̃⊙ñ	NOUN
ejpam-5839	267	52	,	,	PUNCT
ejpam-5839	267	53	f	f	PROPN
ejpam-5839	267	54	(	(	PUNCT
ejpam-5839	267	55	λm̃	λm̃	NUM
ejpam-5839	267	56	)	)	PUNCT
ejpam-5839	267	57	,	,	PUNCT
ejpam-5839	267	58	hm̃⊙ñ	hm̃⊙ñ	PROPN
ejpam-5839	267	59	,	,	PUNCT
ejpam-5839	267	60	and	and	CCONJ
ejpam-5839	267	61	h(λm̃	h(λm̃	PROPN
ejpam-5839	267	62	)	)	PUNCT
ejpam-5839	267	63	,	,	PUNCT
ejpam-5839	267	64	are	be	AUX
ejpam-5839	267	65	closed	close	VERB
ejpam-5839	267	66	sets	set	NOUN
ejpam-5839	267	67	for	for	ADP
ejpam-5839	267	68	all	all	PRON
ejpam-5839	267	69	(	(	PUNCT
ejpam-5839	267	70	i	i	PROPN
ejpam-5839	267	71	,	,	PUNCT
ejpam-5839	267	72	j	j	PROPN
ejpam-5839	267	73	,	,	PUNCT
ejpam-5839	267	74	k	k	PROPN
ejpam-5839	267	75	,	,	PUNCT
ejpam-5839	267	76	l	l	NOUN
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ejpam-5839	267	78	.	.	PUNCT
ejpam-5839	268	1	proposition	proposition	NOUN
ejpam-5839	268	2	4	4	NUM
ejpam-5839	268	3	.	.	PUNCT
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ejpam-5839	269	2	m̃	m̃	PROPN
ejpam-5839	269	3	,	,	PUNCT
ejpam-5839	269	4	ñ	ñ	PROPN
ejpam-5839	269	5	be	be	AUX
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ejpam-5839	269	7	quadri	quadri	NOUN
ejpam-5839	269	8	-	-	PUNCT
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ejpam-5839	269	12	,	,	PUNCT
ejpam-5839	269	13	then	then	ADV
ejpam-5839	269	14	(	(	PUNCT
ejpam-5839	269	15	m̃+ñ)(i	m̃+ñ)(i	NOUN
ejpam-5839	269	16	,	,	PUNCT
ejpam-5839	269	17	j	j	NOUN
ejpam-5839	269	18	,	,	PUNCT
ejpam-5839	269	19	k	k	PROPN
ejpam-5839	269	20	,	,	PUNCT
ejpam-5839	269	21	l	l	NOUN
ejpam-5839	269	22	)	)	PUNCT
ejpam-5839	270	1	=	=	SYM
ejpam-5839	270	2	〈	〈	PROPN
ejpam-5839	270	3	[	[	PUNCT
ejpam-5839	270	4	ml	ml	ADP
ejpam-5839	270	5	i	i	PRON
ejpam-5839	271	1	+	+	CCONJ
ejpam-5839	271	2	nl	nl	NOUN
ejpam-5839	272	1	i	i	PROPN
ejpam-5839	272	2	,	,	PUNCT
ejpam-5839	272	3	m	m	VERB
ejpam-5839	272	4	u	u	NOUN
ejpam-5839	273	1	i	i	X
ejpam-5839	273	2	+	+	X
ejpam-5839	274	1	nu	nu	INTJ
ejpam-5839	274	2	i	i	X
ejpam-5839	274	3	]	]	PUNCT
ejpam-5839	274	4	,	,	PUNCT
ejpam-5839	274	5	[	[	PUNCT
ejpam-5839	274	6	ml	ml	ADP
ejpam-5839	274	7	j	j	PROPN
ejpam-5839	275	1	+	+	CCONJ
ejpam-5839	275	2	nl	nl	PROPN
ejpam-5839	275	3	j	j	PROPN
ejpam-5839	275	4	,	,	PUNCT
ejpam-5839	275	5	m	m	VERB
ejpam-5839	275	6	u	u	NOUN
ejpam-5839	275	7	j	j	PROPN
ejpam-5839	275	8	+	+	CCONJ
ejpam-5839	275	9	nu	nu	PROPN
ejpam-5839	275	10	j	j	PROPN
ejpam-5839	275	11	]	]	PUNCT
ejpam-5839	275	12	,	,	PUNCT
ejpam-5839	275	13	[	[	PUNCT
ejpam-5839	275	14	ml	ml	ADP
ejpam-5839	275	15	k	k	PROPN
ejpam-5839	276	1	+	+	PROPN
ejpam-5839	276	2	nl	nl	PROPN
ejpam-5839	276	3	k	k	PROPN
ejpam-5839	276	4	,	,	PUNCT
ejpam-5839	276	5	m	m	VERB
ejpam-5839	276	6	u	u	NOUN
ejpam-5839	276	7	k	k	PROPN
ejpam-5839	277	1	+	+	PROPN
ejpam-5839	277	2	nu	nu	PROPN
ejpam-5839	277	3	k	k	X
ejpam-5839	277	4	]	]	PUNCT
ejpam-5839	277	5	,	,	PUNCT
ejpam-5839	277	6	[	[	PUNCT
ejpam-5839	277	7	ml	ml	ADP
ejpam-5839	277	8	l	l	NOUN
ejpam-5839	277	9	+	+	NUM
ejpam-5839	277	10	nl	nl	PROPN
ejpam-5839	277	11	l	l	NOUN
ejpam-5839	277	12	,	,	PUNCT
ejpam-5839	277	13	m	m	VERB
ejpam-5839	277	14	u	u	NOUN
ejpam-5839	277	15	l	l	NOUN
ejpam-5839	277	16	+	+	X
ejpam-5839	277	17	nu	nu	PROPN
ejpam-5839	277	18	l	l	NOUN
ejpam-5839	277	19	]	]	X
ejpam-5839	277	20	〉	〉	X
ejpam-5839	277	21	(	(	PUNCT
ejpam-5839	277	22	m̃−ñ)(i	m̃−ñ)(i	PROPN
ejpam-5839	277	23	,	,	PUNCT
ejpam-5839	277	24	j	j	PROPN
ejpam-5839	277	25	,	,	PUNCT
ejpam-5839	277	26	k	k	PROPN
ejpam-5839	277	27	,	,	PUNCT
ejpam-5839	277	28	l	l	NOUN
ejpam-5839	277	29	)	)	PUNCT
ejpam-5839	278	1	=	=	SYM
ejpam-5839	278	2	〈	〈	PROPN
ejpam-5839	278	3	[	[	PUNCT
ejpam-5839	278	4	ml	ml	ADP
ejpam-5839	278	5	i	i	PRON
ejpam-5839	278	6	−	−	PROPN
ejpam-5839	279	1	nl	nl	INTJ
ejpam-5839	279	2	i	i	PROPN
ejpam-5839	279	3	,	,	PUNCT
ejpam-5839	279	4	m	m	VERB
ejpam-5839	279	5	u	u	NOUN
ejpam-5839	279	6	i	i	PRON
ejpam-5839	279	7	−	−	PROPN
ejpam-5839	280	1	nu	nu	INTJ
ejpam-5839	280	2	i	i	X
ejpam-5839	280	3	]	]	PUNCT
ejpam-5839	280	4	,	,	PUNCT
ejpam-5839	280	5	[	[	PUNCT
ejpam-5839	280	6	ml	ml	ADP
ejpam-5839	280	7	j	j	PROPN
ejpam-5839	280	8	−	−	PROPN
ejpam-5839	281	1	nl	nl	PROPN
ejpam-5839	281	2	j	j	PROPN
ejpam-5839	281	3	,	,	PUNCT
ejpam-5839	281	4	m	m	VERB
ejpam-5839	281	5	u	u	NOUN
ejpam-5839	281	6	j	j	NOUN
ejpam-5839	281	7	−	−	PROPN
ejpam-5839	281	8	nu	nu	INTJ
ejpam-5839	281	9	j	j	PROPN
ejpam-5839	281	10	]	]	PUNCT
ejpam-5839	281	11	,	,	PUNCT
ejpam-5839	281	12	[	[	PUNCT
ejpam-5839	281	13	ml	ml	X
ejpam-5839	281	14	k	k	X
ejpam-5839	281	15	−	−	PROPN
ejpam-5839	281	16	nl	nl	PROPN
ejpam-5839	281	17	k	k	PROPN
ejpam-5839	281	18	,	,	PUNCT
ejpam-5839	281	19	m	m	VERB
ejpam-5839	281	20	u	u	NOUN
ejpam-5839	281	21	k	k	NOUN
ejpam-5839	281	22	−	−	PROPN
ejpam-5839	281	23	nu	nu	INTJ
ejpam-5839	281	24	k	k	X
ejpam-5839	281	25	]	]	PUNCT
ejpam-5839	281	26	,	,	PUNCT
ejpam-5839	281	27	[	[	PUNCT
ejpam-5839	281	28	ml	ml	ADP
ejpam-5839	281	29	l	l	NOUN
ejpam-5839	281	30	−	−	PROPN
ejpam-5839	281	31	nl	nl	PROPN
ejpam-5839	281	32	l	l	PROPN
ejpam-5839	281	33	,	,	PUNCT
ejpam-5839	281	34	m	m	VERB
ejpam-5839	281	35	u	u	NOUN
ejpam-5839	281	36	l	l	NOUN
ejpam-5839	281	37	−	−	PROPN
ejpam-5839	281	38	nu	nu	INTJ
ejpam-5839	281	39	l	l	NOUN
ejpam-5839	281	40	]	]	X
ejpam-5839	281	41	〉	〉	X
ejpam-5839	281	42	(	(	PUNCT
ejpam-5839	281	43	λm̃)(i	λm̃)(i	PROPN
ejpam-5839	281	44	,	,	PUNCT
ejpam-5839	281	45	j	j	PROPN
ejpam-5839	281	46	,	,	PUNCT
ejpam-5839	281	47	k	k	PROPN
ejpam-5839	281	48	,	,	PUNCT
ejpam-5839	281	49	l	l	NOUN
ejpam-5839	281	50	)	)	PUNCT
ejpam-5839	281	51	=	=	PRON
ejpam-5839	281	52	{	{	PUNCT
ejpam-5839	281	53	〈	〈	PROPN
ejpam-5839	281	54	[	[	PUNCT
ejpam-5839	281	55	λml	λml	PROPN
ejpam-5839	281	56	i	i	PROPN
ejpam-5839	281	57	,	,	PUNCT
ejpam-5839	281	58	λm	λm	ADP
ejpam-5839	281	59	u	u	INTJ
ejpam-5839	281	60	i	i	X
ejpam-5839	281	61	]	]	PUNCT
ejpam-5839	281	62	,	,	PUNCT
ejpam-5839	281	63	[	[	PUNCT
ejpam-5839	281	64	λml	λml	PROPN
ejpam-5839	281	65	j	j	PROPN
ejpam-5839	281	66	,	,	PUNCT
ejpam-5839	281	67	λm	λm	ADP
ejpam-5839	281	68	u	u	PROPN
ejpam-5839	281	69	j	j	X
ejpam-5839	281	70	]	]	PUNCT
ejpam-5839	281	71	,	,	PUNCT
ejpam-5839	281	72	[	[	PUNCT
ejpam-5839	281	73	λml	λml	NOUN
ejpam-5839	281	74	k	k	PROPN
ejpam-5839	281	75	,	,	PUNCT
ejpam-5839	281	76	λm	λm	ADP
ejpam-5839	281	77	u	u	X
ejpam-5839	281	78	k	k	X
ejpam-5839	281	79	]	]	PUNCT
ejpam-5839	281	80	,	,	PUNCT
ejpam-5839	281	81	[	[	PUNCT
ejpam-5839	281	82	λml	λml	NOUN
ejpam-5839	281	83	l	l	NOUN
ejpam-5839	281	84	,	,	PUNCT
ejpam-5839	281	85	λm	λm	ADP
ejpam-5839	281	86	u	u	X
ejpam-5839	281	87	l	l	NOUN
ejpam-5839	281	88	]	]	PUNCT
ejpam-5839	281	89	〉	〉	NOUN
ejpam-5839	281	90	for	for	ADP
ejpam-5839	281	91	λ	λ	PROPN
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ejpam-5839	281	93	0	0	NUM
ejpam-5839	281	94	〈	〈	PROPN
ejpam-5839	281	95	[	[	PUNCT
ejpam-5839	281	96	λmu	λmu	X
ejpam-5839	282	1	i	i	PRON
ejpam-5839	282	2	,	,	PUNCT
ejpam-5839	282	3	λm	λm	ADP
ejpam-5839	282	4	l	l	NOUN
ejpam-5839	283	1	i	i	X
ejpam-5839	283	2	]	]	PUNCT
ejpam-5839	283	3	,	,	PUNCT
ejpam-5839	283	4	[	[	PUNCT
ejpam-5839	283	5	λmu	λmu	PROPN
ejpam-5839	283	6	j	j	PROPN
ejpam-5839	283	7	,	,	PUNCT
ejpam-5839	283	8	λm	λm	ADP
ejpam-5839	283	9	l	l	PROPN
ejpam-5839	283	10	j	j	X
ejpam-5839	283	11	]	]	PUNCT
ejpam-5839	283	12	,	,	PUNCT
ejpam-5839	283	13	[	[	PUNCT
ejpam-5839	283	14	λmu	λmu	X
ejpam-5839	283	15	k	k	NOUN
ejpam-5839	283	16	,	,	PUNCT
ejpam-5839	283	17	λm	λm	ADP
ejpam-5839	283	18	l	l	NOUN
ejpam-5839	283	19	k	k	X
ejpam-5839	283	20	]	]	PUNCT
ejpam-5839	283	21	,	,	PUNCT
ejpam-5839	283	22	[	[	PUNCT
ejpam-5839	283	23	λmu	λmu	PROPN
ejpam-5839	283	24	l	l	NOUN
ejpam-5839	283	25	,	,	PUNCT
ejpam-5839	283	26	λm	λm	ADP
ejpam-5839	283	27	l	l	NOUN
ejpam-5839	283	28	l	l	NOUN
ejpam-5839	283	29	]	]	X
ejpam-5839	283	30	〉	〉	NOUN
ejpam-5839	283	31	for	for	ADP
ejpam-5839	283	32	λ	λ	X
ejpam-5839	283	33	<	<	X
ejpam-5839	283	34	0	0	PUNCT
ejpam-5839	283	35	since	since	SCONJ
ejpam-5839	283	36	(	(	PUNCT
ejpam-5839	283	37	m̃+	m̃+	PROPN
ejpam-5839	283	38	ñ)(i	ñ)(i	NOUN
ejpam-5839	283	39	,	,	PUNCT
ejpam-5839	283	40	j	j	PROPN
ejpam-5839	283	41	,	,	PUNCT
ejpam-5839	283	42	k	k	PROPN
ejpam-5839	283	43	,	,	PUNCT
ejpam-5839	283	44	l	l	NOUN
ejpam-5839	283	45	)	)	PUNCT
ejpam-5839	283	46	=	=	SYM
ejpam-5839	283	47	(	(	PUNCT
ejpam-5839	283	48	m̃)(i	m̃)(i	NOUN
ejpam-5839	283	49	,	,	PUNCT
ejpam-5839	283	50	j	j	PROPN
ejpam-5839	283	51	,	,	PUNCT
ejpam-5839	283	52	k	k	PROPN
ejpam-5839	283	53	,	,	PUNCT
ejpam-5839	283	54	l	l	NOUN
ejpam-5839	283	55	)	)	PUNCT
ejpam-5839	284	1	+	+	CCONJ
ejpam-5839	284	2	(	(	PUNCT
ejpam-5839	284	3	ñ)(i	ñ)(i	PROPN
ejpam-5839	284	4	,	,	PUNCT
ejpam-5839	284	5	j	j	PROPN
ejpam-5839	284	6	,	,	PUNCT
ejpam-5839	284	7	k	k	PROPN
ejpam-5839	284	8	,	,	PUNCT
ejpam-5839	284	9	l	l	NOUN
ejpam-5839	284	10	)	)	PUNCT
ejpam-5839	285	1	=	=	SYM
ejpam-5839	285	2	〈	〈	PROPN
ejpam-5839	285	3	[	[	PUNCT
ejpam-5839	285	4	ml	ml	ADP
ejpam-5839	285	5	i	i	PRON
ejpam-5839	285	6	,	,	PUNCT
ejpam-5839	285	7	m	m	VERB
ejpam-5839	285	8	u	u	NOUN
ejpam-5839	285	9	i	i	X
ejpam-5839	285	10	]	]	PUNCT
ejpam-5839	285	11	,	,	PUNCT
ejpam-5839	285	12	[	[	PUNCT
ejpam-5839	285	13	ml	ml	ADP
ejpam-5839	285	14	j	j	PROPN
ejpam-5839	285	15	,	,	PUNCT
ejpam-5839	285	16	m	m	VERB
ejpam-5839	285	17	u	u	NOUN
ejpam-5839	285	18	j	j	X
ejpam-5839	285	19	]	]	PUNCT
ejpam-5839	285	20	,	,	PUNCT
ejpam-5839	285	21	[	[	PUNCT
ejpam-5839	285	22	ml	ml	ADP
ejpam-5839	285	23	k	k	PROPN
ejpam-5839	285	24	,	,	PUNCT
ejpam-5839	285	25	m	m	VERB
ejpam-5839	285	26	u	u	NOUN
ejpam-5839	285	27	k	k	X
ejpam-5839	285	28	]	]	PUNCT
ejpam-5839	285	29	,	,	PUNCT
ejpam-5839	285	30	[	[	PUNCT
ejpam-5839	285	31	ml	ml	ADP
ejpam-5839	285	32	l	l	NOUN
ejpam-5839	285	33	,	,	PUNCT
ejpam-5839	285	34	m	m	VERB
ejpam-5839	285	35	u	u	NOUN
ejpam-5839	285	36	l	l	NOUN
ejpam-5839	285	37	]	]	PUNCT
ejpam-5839	285	38	〉	〉	NOUN
ejpam-5839	285	39	+	+	CCONJ
ejpam-5839	285	40	〈	〈	PROPN
ejpam-5839	285	41	[	[	PUNCT
ejpam-5839	285	42	nl	nl	NOUN
ejpam-5839	285	43	i	i	PROPN
ejpam-5839	285	44	,	,	PUNCT
ejpam-5839	285	45	n	n	CCONJ
ejpam-5839	285	46	u	u	NOUN
ejpam-5839	285	47	i	i	X
ejpam-5839	285	48	]	]	PUNCT
ejpam-5839	285	49	,	,	PUNCT
ejpam-5839	285	50	[	[	PUNCT
ejpam-5839	285	51	nl	nl	PROPN
ejpam-5839	285	52	j	j	PROPN
ejpam-5839	285	53	,	,	PUNCT
ejpam-5839	285	54	n	n	CCONJ
ejpam-5839	285	55	u	u	X
ejpam-5839	285	56	j	j	PROPN
ejpam-5839	285	57	]	]	PUNCT
ejpam-5839	285	58	,	,	PUNCT
ejpam-5839	285	59	[	[	PUNCT
ejpam-5839	285	60	nl	nl	NOUN
ejpam-5839	285	61	k	k	PROPN
ejpam-5839	285	62	,	,	PUNCT
ejpam-5839	285	63	n	n	CCONJ
ejpam-5839	285	64	u	u	X
ejpam-5839	285	65	k	k	X
ejpam-5839	285	66	]	]	PUNCT
ejpam-5839	285	67	,	,	PUNCT
ejpam-5839	285	68	[	[	PUNCT
ejpam-5839	285	69	nl	nl	NOUN
ejpam-5839	285	70	l	l	NOUN
ejpam-5839	285	71	,	,	PUNCT
ejpam-5839	285	72	n	n	CCONJ
ejpam-5839	285	73	u	u	NOUN
ejpam-5839	285	74	l	l	NOUN
ejpam-5839	285	75	]	]	X
ejpam-5839	285	76	〉	〉	NOUN
ejpam-5839	285	77	=	=	SYM
ejpam-5839	285	78	〈	〈	PROPN
ejpam-5839	285	79	[	[	PUNCT
ejpam-5839	285	80	ml	ml	ADP
ejpam-5839	285	81	i	i	PRON
ejpam-5839	285	82	+	+	CCONJ
ejpam-5839	286	1	nl	nl	NOUN
ejpam-5839	286	2	i	i	PROPN
ejpam-5839	286	3	,	,	PUNCT
ejpam-5839	286	4	m	m	VERB
ejpam-5839	286	5	u	u	NOUN
ejpam-5839	287	1	i	i	X
ejpam-5839	287	2	+	+	X
ejpam-5839	288	1	nu	nu	INTJ
ejpam-5839	288	2	i	i	X
ejpam-5839	288	3	]	]	PUNCT
ejpam-5839	288	4	,	,	PUNCT
ejpam-5839	288	5	[	[	PUNCT
ejpam-5839	288	6	ml	ml	ADP
ejpam-5839	288	7	j	j	PROPN
ejpam-5839	289	1	+	+	CCONJ
ejpam-5839	289	2	nl	nl	PROPN
ejpam-5839	289	3	j	j	PROPN
ejpam-5839	289	4	,	,	PUNCT
ejpam-5839	289	5	m	m	VERB
ejpam-5839	289	6	u	u	NOUN
ejpam-5839	289	7	j	j	PROPN
ejpam-5839	289	8	+	+	CCONJ
ejpam-5839	289	9	nu	nu	PROPN
ejpam-5839	289	10	j	j	PROPN
ejpam-5839	289	11	]	]	PUNCT
ejpam-5839	289	12	,	,	PUNCT
ejpam-5839	289	13	[	[	PUNCT
ejpam-5839	289	14	ml	ml	ADP
ejpam-5839	289	15	k	k	PROPN
ejpam-5839	290	1	+	+	PROPN
ejpam-5839	290	2	nl	nl	PROPN
ejpam-5839	290	3	k	k	PROPN
ejpam-5839	290	4	,	,	PUNCT
ejpam-5839	290	5	m	m	VERB
ejpam-5839	290	6	u	u	NOUN
ejpam-5839	290	7	k	k	PROPN
ejpam-5839	291	1	+	+	PROPN
ejpam-5839	291	2	nu	nu	PROPN
ejpam-5839	291	3	k	k	X
ejpam-5839	291	4	]	]	PUNCT
ejpam-5839	291	5	,	,	PUNCT
ejpam-5839	291	6	[	[	PUNCT
ejpam-5839	291	7	ml	ml	ADP
ejpam-5839	291	8	l	l	NOUN
ejpam-5839	291	9	+	+	NUM
ejpam-5839	291	10	nl	nl	PROPN
ejpam-5839	291	11	l	l	NOUN
ejpam-5839	291	12	,	,	PUNCT
ejpam-5839	291	13	m	m	VERB
ejpam-5839	291	14	u	u	NOUN
ejpam-5839	291	15	l	l	NOUN
ejpam-5839	291	16	+	+	X
ejpam-5839	291	17	nu	nu	PROPN
ejpam-5839	291	18	l	l	NOUN
ejpam-5839	291	19	]	]	PUNCT
ejpam-5839	291	20	〉	〉	NOUN
ejpam-5839	291	21	let	let	VERB
ejpam-5839	291	22	me	i	PRON
ejpam-5839	291	23	know	know	VERB
ejpam-5839	291	24	if	if	SCONJ
ejpam-5839	291	25	you	you	PRON
ejpam-5839	291	26	need	need	VERB
ejpam-5839	291	27	further	further	ADJ
ejpam-5839	291	28	modifications	modification	NOUN
ejpam-5839	291	29	!	!	PUNCT
ejpam-5839	292	1	proof	proof	NOUN
ejpam-5839	292	2	.	.	PUNCT
ejpam-5839	293	1	trivial	trivial	ADJ
ejpam-5839	293	2	.	.	PUNCT
ejpam-5839	294	1	theorem	theorem	NOUN
ejpam-5839	294	2	1	1	NUM
ejpam-5839	294	3	.	.	PUNCT
ejpam-5839	295	1	let	let	VERB
ejpam-5839	295	2	n	n	PRON
ejpam-5839	295	3	be	be	AUX
ejpam-5839	295	4	a	a	DET
ejpam-5839	295	5	quadri	quadri	NOUN
ejpam-5839	295	6	-	-	PUNCT
ejpam-5839	295	7	partitioned	partition	VERB
ejpam-5839	295	8	neutrosophic	neutrosophic	ADJ
ejpam-5839	295	9	set	set	NOUN
ejpam-5839	295	10	.	.	PUNCT
ejpam-5839	296	1	then	then	ADV
ejpam-5839	296	2	,	,	PUNCT
ejpam-5839	296	3	(	(	PUNCT
ejpam-5839	296	4	n)(i	n)(i	NUM
ejpam-5839	296	5	,	,	PUNCT
ejpam-5839	296	6	j	j	PROPN
ejpam-5839	296	7	,	,	PUNCT
ejpam-5839	296	8	k	k	PROPN
ejpam-5839	296	9	,	,	PUNCT
ejpam-5839	296	10	l	l	NOUN
ejpam-5839	296	11	)	)	PUNCT
ejpam-5839	296	12	=	=	AUX
ejpam-5839	296	13	{	{	PUNCT
ejpam-5839	296	14	(	(	PUNCT
ejpam-5839	296	15	x	x	NOUN
ejpam-5839	296	16	)	)	PUNCT
ejpam-5839	296	17	:	:	PUNCT
ejpam-5839	296	18	tn(x	tn(x	X
ejpam-5839	296	19	)	)	PUNCT
ejpam-5839	296	20	⪰	⪰	NOUN
ejpam-5839	296	21	i	i	PRON
ejpam-5839	296	22	,	,	PUNCT
ejpam-5839	296	23	in(x	in(x	X
ejpam-5839	296	24	)	)	PUNCT
ejpam-5839	296	25	⪯	⪯	PROPN
ejpam-5839	296	26	j	j	PROPN
ejpam-5839	296	27	,	,	PUNCT
ejpam-5839	296	28	fn(x	fn(x	X
ejpam-5839	296	29	)	)	PUNCT
ejpam-5839	296	30	⪯	⪯	PROPN
ejpam-5839	296	31	k	k	NOUN
ejpam-5839	296	32	,	,	PUNCT
ejpam-5839	296	33	hn(x	hn(x	X
ejpam-5839	296	34	)	)	PUNCT
ejpam-5839	296	35	⪯	⪯	NOUN
ejpam-5839	296	36	l	l	NOUN
ejpam-5839	296	37	}	}	PUNCT
ejpam-5839	296	38	1	1	NUM
ejpam-5839	296	39	.	.	X
ejpam-5839	297	1	n(i2	n(i2	NOUN
ejpam-5839	297	2	,	,	PUNCT
ejpam-5839	297	3	j2	j2	PROPN
ejpam-5839	297	4	,	,	PUNCT
ejpam-5839	297	5	k2	k2	NOUN
ejpam-5839	297	6	,	,	PUNCT
ejpam-5839	297	7	l2	l2	NOUN
ejpam-5839	297	8	)	)	PUNCT
ejpam-5839	297	9	⊆	⊆	NUM
ejpam-5839	297	10	n(i1	n(i1	NUM
ejpam-5839	297	11	,	,	PUNCT
ejpam-5839	297	12	j1	j1	PROPN
ejpam-5839	297	13	,	,	PUNCT
ejpam-5839	297	14	k1	k1	PROPN
ejpam-5839	297	15	,	,	PUNCT
ejpam-5839	297	16	l1	l1	PROPN
ejpam-5839	297	17	)	)	PUNCT
ejpam-5839	297	18	where	where	SCONJ
ejpam-5839	297	19	i1	i1	PROPN
ejpam-5839	297	20	≺	≺	NOUN
ejpam-5839	297	21	i2	i2	PROPN
ejpam-5839	297	22	,	,	PUNCT
ejpam-5839	297	23	j1	j1	PROPN
ejpam-5839	297	24	≻	≻	PROPN
ejpam-5839	297	25	j2	j2	PROPN
ejpam-5839	297	26	,	,	PUNCT
ejpam-5839	297	27	k1	k1	PROPN
ejpam-5839	297	28	≻	≻	PROPN
ejpam-5839	297	29	k2	k2	PROPN
ejpam-5839	297	30	,	,	PUNCT
ejpam-5839	297	31	l1	l1	PROPN
ejpam-5839	297	32	≻	≻	PROPN
ejpam-5839	297	33	l2	l2	NOUN
ejpam-5839	297	34	.	.	PUNCT
ejpam-5839	298	1	2	2	X
ejpam-5839	298	2	.	.	X
ejpam-5839	298	3	∞⋂	∞⋂	PROPN
ejpam-5839	298	4	n=1	n=1	PROPN
ejpam-5839	298	5	n(in	n(in	PROPN
ejpam-5839	298	6	,	,	PUNCT
ejpam-5839	298	7	jn	jn	PROPN
ejpam-5839	298	8	,	,	PUNCT
ejpam-5839	298	9	kn	kn	PROPN
ejpam-5839	298	10	,	,	PUNCT
ejpam-5839	298	11	ln	ln	PROPN
ejpam-5839	298	12	)	)	PUNCT
ejpam-5839	298	13	=	=	SYM
ejpam-5839	298	14	(	(	PUNCT
ejpam-5839	298	15	n)(i	n)(i	PROPN
ejpam-5839	298	16	,	,	PUNCT
ejpam-5839	298	17	j	j	PROPN
ejpam-5839	298	18	,	,	PUNCT
ejpam-5839	298	19	k	k	PROPN
ejpam-5839	298	20	,	,	PUNCT
ejpam-5839	298	21	l	l	NOUN
ejpam-5839	298	22	)	)	PUNCT
ejpam-5839	298	23	where	where	SCONJ
ejpam-5839	298	24	i1	i1	PROPN
ejpam-5839	298	25	≺	≺	NOUN
ejpam-5839	298	26	i2	i2	PROPN
ejpam-5839	298	27	,	,	PUNCT
ejpam-5839	298	28	j1	j1	PROPN
ejpam-5839	298	29	≻	≻	PROPN
ejpam-5839	298	30	j2	j2	PROPN
ejpam-5839	298	31	,	,	PUNCT
ejpam-5839	298	32	k1	k1	PROPN
ejpam-5839	298	33	≻	≻	PROPN
ejpam-5839	298	34	k2	k2	PROPN
ejpam-5839	298	35	,	,	PUNCT
ejpam-5839	298	36	l1	l1	PROPN
ejpam-5839	298	37	≻	≻	PROPN
ejpam-5839	298	38	l2	l2	PROPN
ejpam-5839	298	39	.	.	PUNCT
ejpam-5839	299	1	a.	a.	NOUN
ejpam-5839	299	2	shihadeh	shihadeh	VERB
ejpam-5839	299	3	et	et	PROPN
ejpam-5839	299	4	al	al	PROPN
ejpam-5839	299	5	.	.	PUNCT
ejpam-5839	299	6	/	/	SYM
ejpam-5839	299	7	eur	eur	PROPN
ejpam-5839	299	8	.	.	PUNCT
ejpam-5839	300	1	j.	j.	PROPN
ejpam-5839	300	2	pure	pure	PROPN
ejpam-5839	300	3	appl	appl	PROPN
ejpam-5839	300	4	.	.	PROPN
ejpam-5839	300	5	math	math	PROPN
ejpam-5839	300	6	,	,	PUNCT
ejpam-5839	300	7	18	18	NUM
ejpam-5839	300	8	(	(	PUNCT
ejpam-5839	300	9	2	2	NUM
ejpam-5839	300	10	)	)	PUNCT
ejpam-5839	300	11	(	(	PUNCT
ejpam-5839	300	12	2025	2025	NUM
ejpam-5839	300	13	)	)	PUNCT
ejpam-5839	300	14	,	,	PUNCT
ejpam-5839	300	15	5839	5839	NUM
ejpam-5839	300	16	12	12	NUM
ejpam-5839	300	17	of	of	ADP
ejpam-5839	300	18	54	54	NUM
ejpam-5839	300	19	proof	proof	NOUN
ejpam-5839	300	20	.	.	PUNCT
ejpam-5839	301	1	1	1	X
ejpam-5839	301	2	.	.	X
ejpam-5839	301	3	let	let	VERB
ejpam-5839	301	4	(	(	PUNCT
ejpam-5839	301	5	x	x	X
ejpam-5839	301	6	)	)	PUNCT
ejpam-5839	301	7	∈	∈	PROPN
ejpam-5839	301	8	n(i2	n(i2	NOUN
ejpam-5839	301	9	,	,	PUNCT
ejpam-5839	301	10	j2	j2	PROPN
ejpam-5839	301	11	,	,	PUNCT
ejpam-5839	301	12	k2	k2	NOUN
ejpam-5839	301	13	,	,	PUNCT
ejpam-5839	301	14	l2	l2	NOUN
ejpam-5839	301	15	)	)	PUNCT
ejpam-5839	301	16	,	,	PUNCT
ejpam-5839	301	17	then	then	ADV
ejpam-5839	301	18	we	we	PRON
ejpam-5839	301	19	have	have	VERB
ejpam-5839	301	20	:	:	PUNCT
ejpam-5839	301	21	tn(x	tn(x	X
ejpam-5839	301	22	)	)	PUNCT
ejpam-5839	301	23	⪰	⪰	NOUN
ejpam-5839	301	24	i2	i2	NOUN
ejpam-5839	301	25	,	,	PUNCT
ejpam-5839	301	26	in(x	in(x	X
ejpam-5839	301	27	)	)	PUNCT
ejpam-5839	301	28	⪯	⪯	PROPN
ejpam-5839	301	29	j2	j2	PROPN
ejpam-5839	301	30	,	,	PUNCT
ejpam-5839	301	31	fn(x	fn(x	PRON
ejpam-5839	301	32	)	)	PUNCT
ejpam-5839	301	33	⪯	⪯	PROPN
ejpam-5839	301	34	k2	k2	NOUN
ejpam-5839	301	35	,	,	PUNCT
ejpam-5839	301	36	hn(x	hn(x	NUM
ejpam-5839	301	37	)	)	PUNCT
ejpam-5839	301	38	⪯	⪯	NOUN
ejpam-5839	301	39	l2	l2	NOUN
ejpam-5839	301	40	.	.	PUNCT
ejpam-5839	302	1	now	now	ADV
ejpam-5839	302	2	,	,	PUNCT
ejpam-5839	302	3	tn(x	tn(x	ADP
ejpam-5839	302	4	)	)	PUNCT
ejpam-5839	302	5	⪰	⪰	PROPN
ejpam-5839	302	6	i2	i2	PROPN
ejpam-5839	302	7	≻	≻	PROPN
ejpam-5839	302	8	i1	i1	PROPN
ejpam-5839	302	9	,	,	PUNCT
ejpam-5839	302	10	in(x	in(x	X
ejpam-5839	302	11	)	)	PUNCT
ejpam-5839	302	12	⪯	⪯	PROPN
ejpam-5839	302	13	j2	j2	PROPN
ejpam-5839	302	14	≺	≺	NOUN
ejpam-5839	302	15	j1	j1	PROPN
ejpam-5839	302	16	,	,	PUNCT
ejpam-5839	302	17	fn(x	fn(x	PRON
ejpam-5839	302	18	)	)	PUNCT
ejpam-5839	302	19	⪯	⪯	VERB
ejpam-5839	302	20	k2	k2	PROPN
ejpam-5839	302	21	≺	≺	NOUN
ejpam-5839	302	22	k1	k1	NOUN
ejpam-5839	302	23	,	,	PUNCT
ejpam-5839	302	24	hn(x	hn(x	NUM
ejpam-5839	302	25	)	)	PUNCT
ejpam-5839	302	26	⪯	⪯	NOUN
ejpam-5839	302	27	l2	l2	NOUN
ejpam-5839	302	28	≺	≺	NOUN
ejpam-5839	302	29	l1	l1	PROPN
ejpam-5839	302	30	this	this	PRON
ejpam-5839	302	31	implies	imply	VERB
ejpam-5839	302	32	that	that	SCONJ
ejpam-5839	302	33	tn(x	tn(x	PUNCT
ejpam-5839	302	34	)	)	PUNCT
ejpam-5839	302	35	⪰	⪰	PROPN
ejpam-5839	302	36	i1	i1	PROPN
ejpam-5839	302	37	,	,	PUNCT
ejpam-5839	302	38	in(x	in(x	X
ejpam-5839	302	39	)	)	PUNCT
ejpam-5839	302	40	⪯	⪯	PROPN
ejpam-5839	302	41	j1	j1	PROPN
ejpam-5839	302	42	,	,	PUNCT
ejpam-5839	302	43	fn(x	fn(x	PRON
ejpam-5839	302	44	)	)	PUNCT
ejpam-5839	302	45	⪯	⪯	PROPN
ejpam-5839	302	46	k1	k1	PROPN
ejpam-5839	302	47	,	,	PUNCT
ejpam-5839	302	48	hn(x	hn(x	NUM
ejpam-5839	302	49	)	)	PUNCT
ejpam-5839	302	50	⪯	⪯	PROPN
ejpam-5839	302	51	l1	l1	PROPN
ejpam-5839	302	52	therefore	therefore	ADV
ejpam-5839	302	53	,	,	PUNCT
ejpam-5839	302	54	x	x	PROPN
ejpam-5839	302	55	∈	∈	PROPN
ejpam-5839	302	56	n(i1	n(i1	NOUN
ejpam-5839	302	57	,	,	PUNCT
ejpam-5839	302	58	j1	j1	PROPN
ejpam-5839	302	59	,	,	PUNCT
ejpam-5839	302	60	k1	k1	PROPN
ejpam-5839	302	61	,	,	PUNCT
ejpam-5839	302	62	l1	l1	PROPN
ejpam-5839	302	63	)	)	PUNCT
ejpam-5839	302	64	⇒	⇒	PROPN
ejpam-5839	302	65	n(i2	n(i2	PROPN
ejpam-5839	302	66	,	,	PUNCT
ejpam-5839	302	67	j2	j2	PROPN
ejpam-5839	302	68	,	,	PUNCT
ejpam-5839	302	69	k2	k2	NOUN
ejpam-5839	302	70	,	,	PUNCT
ejpam-5839	302	71	l2	l2	NOUN
ejpam-5839	302	72	)	)	PUNCT
ejpam-5839	303	1	⊆	⊆	NUM
ejpam-5839	303	2	n(i1	n(i1	NUM
ejpam-5839	303	3	,	,	PUNCT
ejpam-5839	303	4	j1	j1	PROPN
ejpam-5839	303	5	,	,	PUNCT
ejpam-5839	303	6	k1	k1	NOUN
ejpam-5839	303	7	,	,	PUNCT
ejpam-5839	303	8	l1	l1	PROPN
ejpam-5839	303	9	)	)	PUNCT
ejpam-5839	303	10	.	.	PUNCT
ejpam-5839	304	1	2	2	X
ejpam-5839	304	2	.	.	X
ejpam-5839	304	3	let	let	VERB
ejpam-5839	304	4	x	x	X
ejpam-5839	304	5	∈	∈	PROPN
ejpam-5839	304	6	∞⋂	∞⋂	PROPN
ejpam-5839	304	7	n=1	n=1	PROPN
ejpam-5839	304	8	n(in	n(in	PROPN
ejpam-5839	304	9	,	,	PUNCT
ejpam-5839	304	10	jn	jn	PROPN
ejpam-5839	304	11	,	,	PUNCT
ejpam-5839	304	12	kn	kn	PROPN
ejpam-5839	304	13	,	,	PUNCT
ejpam-5839	304	14	ln	ln	ADJ
ejpam-5839	304	15	)	)	PUNCT
ejpam-5839	304	16	⇒	⇒	NOUN
ejpam-5839	304	17	x	x	SYM
ejpam-5839	304	18	∈	∈	NOUN
ejpam-5839	304	19	n(in	n(in	SYM
ejpam-5839	304	20	,	,	PUNCT
ejpam-5839	304	21	jn	jn	PROPN
ejpam-5839	304	22	,	,	PUNCT
ejpam-5839	304	23	kn	kn	PROPN
ejpam-5839	304	24	,	,	PUNCT
ejpam-5839	304	25	ln	ln	ADJ
ejpam-5839	304	26	)	)	PUNCT
ejpam-5839	304	27	.	.	PUNCT
ejpam-5839	305	1	since	since	SCONJ
ejpam-5839	305	2	lim	lim	PROPN
ejpam-5839	305	3	n→∞	n→∞	PRON
ejpam-5839	305	4	in	in	ADP
ejpam-5839	305	5	=	=	PROPN
ejpam-5839	305	6	i	i	PROPN
ejpam-5839	305	7	,	,	PUNCT
ejpam-5839	305	8	lim	lim	PROPN
ejpam-5839	305	9	n→∞	n→∞	NUM
ejpam-5839	305	10	jn	jn	PROPN
ejpam-5839	305	11	=	=	PROPN
ejpam-5839	305	12	j	j	PROPN
ejpam-5839	305	13	,	,	PUNCT
ejpam-5839	305	14	lim	lim	PROPN
ejpam-5839	305	15	n→∞	n→∞	X
ejpam-5839	306	1	kn	kn	PROPN
ejpam-5839	306	2	=	=	SYM
ejpam-5839	306	3	k	k	PROPN
ejpam-5839	306	4	,	,	PUNCT
ejpam-5839	306	5	lim	lim	PROPN
ejpam-5839	306	6	n→∞	n→∞	X
ejpam-5839	306	7	ln	ln	NOUN
ejpam-5839	306	8	=	=	PUNCT
ejpam-5839	306	9	l	l	NOUN
ejpam-5839	306	10	then	then	ADV
ejpam-5839	306	11	tn(x	tn(x	PUNCT
ejpam-5839	306	12	)	)	PUNCT
ejpam-5839	306	13	⪰	⪰	NOUN
ejpam-5839	306	14	lim	lim	PROPN
ejpam-5839	306	15	n→∞	n→∞	NUM
ejpam-5839	306	16	in	in	ADP
ejpam-5839	306	17	=	=	PROPN
ejpam-5839	306	18	i	i	PROPN
ejpam-5839	306	19	,	,	PUNCT
ejpam-5839	306	20	in(x	in(x	X
ejpam-5839	306	21	)	)	PUNCT
ejpam-5839	306	22	⪯	⪯	PROPN
ejpam-5839	306	23	lim	lim	PROPN
ejpam-5839	306	24	n→∞	n→∞	PROPN
ejpam-5839	307	1	jn	jn	PROPN
ejpam-5839	307	2	=	=	PROPN
ejpam-5839	307	3	j	j	PROPN
ejpam-5839	307	4	,	,	PUNCT
ejpam-5839	307	5	fn(x	fn(x	X
ejpam-5839	307	6	)	)	PUNCT
ejpam-5839	307	7	⪯	⪯	PROPN
ejpam-5839	307	8	lim	lim	PROPN
ejpam-5839	307	9	n→∞	n→∞	PRON
ejpam-5839	308	1	kn	kn	PROPN
ejpam-5839	308	2	=	=	SYM
ejpam-5839	308	3	k	k	PROPN
ejpam-5839	308	4	,	,	PUNCT
ejpam-5839	308	5	hn(x	hn(x	X
ejpam-5839	308	6	)	)	PUNCT
ejpam-5839	308	7	⪯	⪯	PROPN
ejpam-5839	308	8	lim	lim	PROPN
ejpam-5839	308	9	n→∞	n→∞	PRON
ejpam-5839	308	10	ln	ln	NOUN
ejpam-5839	308	11	=	=	NOUN
ejpam-5839	308	12	l	l	NOUN
ejpam-5839	308	13	thus	thus	ADV
ejpam-5839	308	14	,	,	PUNCT
ejpam-5839	308	15	tn(x	tn(x	ADP
ejpam-5839	308	16	)	)	PUNCT
ejpam-5839	308	17	⪰	⪰	NOUN
ejpam-5839	308	18	i	i	PRON
ejpam-5839	308	19	,	,	PUNCT
ejpam-5839	308	20	in(x	in(x	X
ejpam-5839	308	21	)	)	PUNCT
ejpam-5839	308	22	⪯	⪯	PROPN
ejpam-5839	308	23	j	j	PROPN
ejpam-5839	308	24	,	,	PUNCT
ejpam-5839	308	25	fn(x	fn(x	X
ejpam-5839	308	26	)	)	PUNCT
ejpam-5839	308	27	⪯	⪯	PROPN
ejpam-5839	309	1	k	k	NOUN
ejpam-5839	309	2	,	,	PUNCT
ejpam-5839	309	3	hn(x	hn(x	X
ejpam-5839	309	4	)	)	PUNCT
ejpam-5839	309	5	⪯	⪯	NOUN
ejpam-5839	309	6	l	l	NOUN
ejpam-5839	309	7	therefore	therefore	ADV
ejpam-5839	309	8	,	,	PUNCT
ejpam-5839	309	9	x	x	SYM
ejpam-5839	309	10	∈	∈	PROPN
ejpam-5839	309	11	(	(	PUNCT
ejpam-5839	309	12	n)(i	n)(i	NUM
ejpam-5839	309	13	,	,	PUNCT
ejpam-5839	309	14	j	j	PROPN
ejpam-5839	309	15	,	,	PUNCT
ejpam-5839	309	16	k	k	PROPN
ejpam-5839	309	17	,	,	PUNCT
ejpam-5839	309	18	l	l	NOUN
ejpam-5839	309	19	)	)	PUNCT
ejpam-5839	309	20	⇒	⇒	PROPN
ejpam-5839	309	21	n(i1	n(i1	NOUN
ejpam-5839	309	22	,	,	PUNCT
ejpam-5839	309	23	j1	j1	PROPN
ejpam-5839	309	24	,	,	PUNCT
ejpam-5839	309	25	k1	k1	PROPN
ejpam-5839	309	26	,	,	PUNCT
ejpam-5839	309	27	l1	l1	PROPN
ejpam-5839	309	28	)	)	PUNCT
ejpam-5839	309	29	⊆	⊆	NUM
ejpam-5839	309	30	(	(	PUNCT
ejpam-5839	309	31	n)(i	n)(i	NUM
ejpam-5839	309	32	,	,	PUNCT
ejpam-5839	309	33	j	j	PROPN
ejpam-5839	309	34	,	,	PUNCT
ejpam-5839	309	35	k	k	PROPN
ejpam-5839	309	36	,	,	PUNCT
ejpam-5839	309	37	l	l	NOUN
ejpam-5839	309	38	)	)	PUNCT
ejpam-5839	309	39	.	.	PUNCT
ejpam-5839	310	1	again	again	ADV
ejpam-5839	310	2	,	,	PUNCT
ejpam-5839	310	3	let	let	VERB
ejpam-5839	310	4	x	x	X
ejpam-5839	310	5	∈	∈	PROPN
ejpam-5839	310	6	(	(	PUNCT
ejpam-5839	310	7	n)(i	n)(i	NUM
ejpam-5839	310	8	,	,	PUNCT
ejpam-5839	310	9	j	j	PROPN
ejpam-5839	310	10	,	,	PUNCT
ejpam-5839	310	11	k	k	PROPN
ejpam-5839	310	12	,	,	PUNCT
ejpam-5839	310	13	l	l	NOUN
ejpam-5839	310	14	)	)	PUNCT
ejpam-5839	310	15	,	,	PUNCT
ejpam-5839	310	16	then	then	ADV
ejpam-5839	310	17	tn(x	tn(x	PUNCT
ejpam-5839	310	18	)	)	PUNCT
ejpam-5839	310	19	⪰	⪰	NOUN
ejpam-5839	310	20	i	i	PRON
ejpam-5839	310	21	,	,	PUNCT
ejpam-5839	310	22	in(x	in(x	X
ejpam-5839	310	23	)	)	PUNCT
ejpam-5839	310	24	⪯	⪯	PROPN
ejpam-5839	310	25	j	j	PROPN
ejpam-5839	310	26	,	,	PUNCT
ejpam-5839	310	27	fn(x	fn(x	X
ejpam-5839	310	28	)	)	PUNCT
ejpam-5839	310	29	⪯	⪯	PROPN
ejpam-5839	310	30	k	k	NOUN
ejpam-5839	310	31	,	,	PUNCT
ejpam-5839	310	32	hn(x	hn(x	X
ejpam-5839	310	33	)	)	PUNCT
ejpam-5839	310	34	⪯	⪯	NOUN
ejpam-5839	310	35	l	l	NOUN
ejpam-5839	310	36	since	since	SCONJ
ejpam-5839	310	37	in	in	ADP
ejpam-5839	310	38	↑	↑	PROPN
ejpam-5839	310	39	i	i	PROPN
ejpam-5839	310	40	,	,	PUNCT
ejpam-5839	310	41	jn	jn	PROPN
ejpam-5839	310	42	↓	↓	PROPN
ejpam-5839	310	43	j	j	PROPN
ejpam-5839	310	44	,	,	PUNCT
ejpam-5839	310	45	kn	kn	PROPN
ejpam-5839	310	46	↓	↓	PROPN
ejpam-5839	310	47	k	k	PROPN
ejpam-5839	310	48	,	,	PUNCT
ejpam-5839	310	49	ln	ln	ADJ
ejpam-5839	310	50	↓	↓	PROPN
ejpam-5839	310	51	l	l	NOUN
ejpam-5839	310	52	,	,	PUNCT
ejpam-5839	310	53	we	we	PRON
ejpam-5839	310	54	obtain	obtain	VERB
ejpam-5839	310	55	:	:	PUNCT
ejpam-5839	310	56	tn(x	tn(x	X
ejpam-5839	310	57	)	)	PUNCT
ejpam-5839	311	1	⪰	⪰	NOUN
ejpam-5839	311	2	i	i	PRON
ejpam-5839	311	3	⪰	⪰	VERB
ejpam-5839	311	4	in	in	ADP
ejpam-5839	311	5	,	,	PUNCT
ejpam-5839	311	6	in(x	in(x	X
ejpam-5839	311	7	)	)	PUNCT
ejpam-5839	311	8	⪯	⪯	PROPN
ejpam-5839	311	9	j	j	PROPN
ejpam-5839	311	10	⪯	⪯	PROPN
ejpam-5839	311	11	jn	jn	PROPN
ejpam-5839	311	12	,	,	PUNCT
ejpam-5839	311	13	fn(x	fn(x	X
ejpam-5839	311	14	)	)	PUNCT
ejpam-5839	311	15	⪯	⪯	NOUN
ejpam-5839	311	16	k	k	PROPN
ejpam-5839	311	17	⪯	⪯	PROPN
ejpam-5839	311	18	kn	kn	PROPN
ejpam-5839	311	19	,	,	PUNCT
ejpam-5839	311	20	hn(x	hn(x	NUM
ejpam-5839	311	21	)	)	PUNCT
ejpam-5839	311	22	⪯	⪯	NOUN
ejpam-5839	311	23	l	l	PROPN
ejpam-5839	311	24	⪯	⪯	PROPN
ejpam-5839	311	25	ln	ln	ADV
ejpam-5839	311	26	for	for	ADP
ejpam-5839	311	27	all	all	DET
ejpam-5839	311	28	n.	n.	NOUN
ejpam-5839	311	29	this	this	PRON
ejpam-5839	311	30	implies	imply	VERB
ejpam-5839	311	31	that	that	SCONJ
ejpam-5839	311	32	x	x	SYM
ejpam-5839	311	33	∈	∈	PROPN
ejpam-5839	311	34	∞⋂	∞⋂	PROPN
ejpam-5839	311	35	n=1	n=1	PROPN
ejpam-5839	311	36	n(in	n(in	PROPN
ejpam-5839	311	37	,	,	PUNCT
ejpam-5839	311	38	jn	jn	PROPN
ejpam-5839	311	39	,	,	PUNCT
ejpam-5839	311	40	kn	kn	PROPN
ejpam-5839	311	41	,	,	PUNCT
ejpam-5839	311	42	ln	ln	ADJ
ejpam-5839	311	43	)	)	PUNCT
ejpam-5839	311	44	⇒	⇒	NOUN
ejpam-5839	311	45	(	(	PUNCT
ejpam-5839	311	46	n)(i	n)(i	NUM
ejpam-5839	311	47	,	,	PUNCT
ejpam-5839	311	48	j	j	PROPN
ejpam-5839	311	49	,	,	PUNCT
ejpam-5839	311	50	k	k	PROPN
ejpam-5839	311	51	,	,	PUNCT
ejpam-5839	311	52	l	l	NOUN
ejpam-5839	311	53	)	)	PUNCT
ejpam-5839	312	1	⊆	⊆	NUM
ejpam-5839	312	2	n(i1	n(i1	NUM
ejpam-5839	312	3	,	,	PUNCT
ejpam-5839	312	4	j1	j1	PROPN
ejpam-5839	312	5	,	,	PUNCT
ejpam-5839	312	6	k1	k1	PROPN
ejpam-5839	312	7	,	,	PUNCT
ejpam-5839	312	8	l1	l1	PROPN
ejpam-5839	312	9	)	)	PUNCT
ejpam-5839	312	10	thus	thus	ADV
ejpam-5839	312	11	,	,	PUNCT
ejpam-5839	312	12	we	we	PRON
ejpam-5839	312	13	conclude	conclude	VERB
ejpam-5839	312	14	:	:	PUNCT
ejpam-5839	312	15	∞⋂	∞⋂	PROPN
ejpam-5839	312	16	n=1	n=1	PROPN
ejpam-5839	312	17	n(in	n(in	PROPN
ejpam-5839	312	18	,	,	PUNCT
ejpam-5839	312	19	jn	jn	PROPN
ejpam-5839	312	20	,	,	PUNCT
ejpam-5839	312	21	kn	kn	PROPN
ejpam-5839	312	22	,	,	PUNCT
ejpam-5839	312	23	ln	ln	PROPN
ejpam-5839	312	24	)	)	PUNCT
ejpam-5839	312	25	=	=	SYM
ejpam-5839	312	26	(	(	PUNCT
ejpam-5839	312	27	n)(i	n)(i	PROPN
ejpam-5839	312	28	,	,	PUNCT
ejpam-5839	312	29	j	j	PROPN
ejpam-5839	312	30	,	,	PUNCT
ejpam-5839	312	31	k	k	PROPN
ejpam-5839	312	32	,	,	PUNCT
ejpam-5839	312	33	l	l	NOUN
ejpam-5839	312	34	)	)	PUNCT
ejpam-5839	312	35	.	.	PUNCT
ejpam-5839	313	1	proposition	proposition	NOUN
ejpam-5839	313	2	5	5	NUM
ejpam-5839	313	3	.	.	PUNCT
ejpam-5839	314	1	let	let	VERB
ejpam-5839	314	2	n(i	n(i	PROPN
ejpam-5839	314	3	,	,	PUNCT
ejpam-5839	314	4	j	j	PROPN
ejpam-5839	314	5	,	,	PUNCT
ejpam-5839	314	6	k	k	PROPN
ejpam-5839	314	7	,	,	PUNCT
ejpam-5839	314	8	l	l	NOUN
ejpam-5839	314	9	)	)	PUNCT
ejpam-5839	314	10	=	=	SYM
ejpam-5839	314	11	⟨[li	⟨[li	NOUN
ejpam-5839	314	12	,	,	PUNCT
ejpam-5839	314	13	ui	ui	NOUN
ejpam-5839	314	14	]	]	X
ejpam-5839	314	15	,	,	PUNCT
ejpam-5839	315	1	[	[	X
ejpam-5839	315	2	lj	lj	PROPN
ejpam-5839	315	3	,	,	PUNCT
ejpam-5839	315	4	uj	uj	PROPN
ejpam-5839	315	5	]	]	PUNCT
ejpam-5839	315	6	,	,	PUNCT
ejpam-5839	315	7	[	[	X
ejpam-5839	315	8	lk	lk	X
ejpam-5839	315	9	,	,	PUNCT
ejpam-5839	315	10	uk	uk	PROPN
ejpam-5839	315	11	]	]	PUNCT
ejpam-5839	315	12	,	,	PUNCT
ejpam-5839	315	13	[	[	X
ejpam-5839	315	14	ll	ll	NOUN
ejpam-5839	315	15	,	,	PUNCT
ejpam-5839	315	16	ul]⟩	ul]⟩	ADP
ejpam-5839	315	17	,	,	PUNCT
ejpam-5839	315	18	where	where	SCONJ
ejpam-5839	315	19	0	0	NUM
ejpam-5839	315	20	⪯	⪯	NOUN
ejpam-5839	315	21	i	i	PRON
ejpam-5839	315	22	⪯	⪯	VERB
ejpam-5839	315	23	1	1	NUM
ejpam-5839	315	24	,	,	PUNCT
ejpam-5839	315	25	0	0	NUM
ejpam-5839	315	26	⪯	⪯	PROPN
ejpam-5839	315	27	j	j	PROPN
ejpam-5839	315	28	⪯	⪯	PROPN
ejpam-5839	315	29	1	1	NUM
ejpam-5839	315	30	,	,	PUNCT
ejpam-5839	315	31	0	0	NUM
ejpam-5839	315	32	⪯	⪯	PROPN
ejpam-5839	315	33	k	k	PROPN
ejpam-5839	315	34	⪯	⪯	PROPN
ejpam-5839	315	35	1	1	NUM
ejpam-5839	315	36	,	,	PUNCT
ejpam-5839	315	37	0	0	NUM
ejpam-5839	315	38	⪯	⪯	PROPN
ejpam-5839	315	39	l	l	PROPN
ejpam-5839	315	40	⪯	⪯	PROPN
ejpam-5839	315	41	1	1	NUM
ejpam-5839	315	42	be	be	AUX
ejpam-5839	315	43	a	a	DET
ejpam-5839	315	44	domain	domain	NOUN
ejpam-5839	315	45	of	of	ADP
ejpam-5839	315	46	interval	interval	NOUN
ejpam-5839	315	47	quadri	quadri	PROPN
ejpam-5839	315	48	-	-	PUNCT
ejpam-5839	315	49	neutrosophic	neutrosophic	ADJ
ejpam-5839	315	50	sets	set	NOUN
ejpam-5839	315	51	(	(	PUNCT
ejpam-5839	315	52	qns	qns	PROPN
ejpam-5839	315	53	)	)	PUNCT
ejpam-5839	315	54	,	,	PUNCT
ejpam-5839	315	55	and	and	CCONJ
ejpam-5839	315	56	each	each	DET
ejpam-5839	315	57	interval	interval	NOUN
ejpam-5839	316	1	[	[	X
ejpam-5839	316	2	li	li	X
ejpam-5839	316	3	,	,	PUNCT
ejpam-5839	316	4	ui	ui	NOUN
ejpam-5839	316	5	]	]	PUNCT
ejpam-5839	316	6	,	,	PUNCT
ejpam-5839	317	1	[	[	X
ejpam-5839	317	2	lj	lj	PROPN
ejpam-5839	317	3	,	,	PUNCT
ejpam-5839	317	4	uj	uj	PROPN
ejpam-5839	317	5	]	]	PUNCT
ejpam-5839	317	6	,	,	PUNCT
ejpam-5839	317	7	[	[	X
ejpam-5839	317	8	lk	lk	X
ejpam-5839	317	9	,	,	PUNCT
ejpam-5839	317	10	uk	uk	PROPN
ejpam-5839	317	11	]	]	PUNCT
ejpam-5839	317	12	,	,	PUNCT
ejpam-5839	317	13	[	[	X
ejpam-5839	317	14	ll	ll	NOUN
ejpam-5839	317	15	,	,	PUNCT
ejpam-5839	317	16	ul	ul	INTJ
ejpam-5839	317	17	]	]	X
ejpam-5839	317	18	is	be	AUX
ejpam-5839	317	19	closed	closed	ADJ
ejpam-5839	317	20	.	.	PUNCT
ejpam-5839	318	1	suppose	suppose	VERB
ejpam-5839	318	2	n(i	n(i	PROPN
ejpam-5839	318	3	,	,	PUNCT
ejpam-5839	318	4	j	j	PROPN
ejpam-5839	318	5	,	,	PUNCT
ejpam-5839	318	6	k	k	PROPN
ejpam-5839	318	7	,	,	PUNCT
ejpam-5839	318	8	l	l	NOUN
ejpam-5839	318	9	)	)	PUNCT
ejpam-5839	318	10	is	be	AUX
ejpam-5839	318	11	decreasing	decrease	VERB
ejpam-5839	318	12	with	with	ADP
ejpam-5839	318	13	respect	respect	NOUN
ejpam-5839	318	14	to	to	ADP
ejpam-5839	318	15	(	(	PUNCT
ejpam-5839	318	16	i	i	PROPN
ejpam-5839	318	17	,	,	PUNCT
ejpam-5839	318	18	j	j	PROPN
ejpam-5839	318	19	,	,	PUNCT
ejpam-5839	318	20	k	k	PROPN
ejpam-5839	318	21	,	,	PUNCT
ejpam-5839	318	22	l	l	NOUN
ejpam-5839	318	23	)	)	PUNCT
ejpam-5839	318	24	and	and	CCONJ
ejpam-5839	318	25	ñ	ñ	PROPN
ejpam-5839	318	26	is	be	AUX
ejpam-5839	318	27	a	a	DET
ejpam-5839	318	28	closed	closed	ADJ
ejpam-5839	318	29	qnsn	qnsn	NOUN
ejpam-5839	318	30	.	.	PUNCT
ejpam-5839	319	1	then	then	ADV
ejpam-5839	319	2	{	{	PUNCT
ejpam-5839	319	3	n(i	n(i	PROPN
ejpam-5839	319	4	,	,	PUNCT
ejpam-5839	319	5	j	j	PROPN
ejpam-5839	319	6	,	,	PUNCT
ejpam-5839	319	7	k	k	PROPN
ejpam-5839	319	8	,	,	PUNCT
ejpam-5839	319	9	l	l	NOUN
ejpam-5839	319	10	)	)	PUNCT
ejpam-5839	319	11	}	}	PUNCT
ejpam-5839	319	12	can	can	AUX
ejpam-5839	319	13	induce	induce	VERB
ejpam-5839	319	14	ñ	ñ	PROPN
ejpam-5839	319	15	,	,	PUNCT
ejpam-5839	319	16	and	and	CCONJ
ejpam-5839	319	17	ñ(i	ñ(i	PROPN
ejpam-5839	319	18	,	,	PUNCT
ejpam-5839	319	19	j	j	PROPN
ejpam-5839	319	20	,	,	PUNCT
ejpam-5839	319	21	k	k	PROPN
ejpam-5839	319	22	,	,	PUNCT
ejpam-5839	319	23	l	l	NOUN
ejpam-5839	319	24	)	)	PUNCT
ejpam-5839	319	25	=	=	SYM
ejpam-5839	319	26	n(i	n(i	PROPN
ejpam-5839	319	27	,	,	PUNCT
ejpam-5839	319	28	j	j	PROPN
ejpam-5839	319	29	,	,	PUNCT
ejpam-5839	319	30	k	k	PROPN
ejpam-5839	319	31	,	,	PUNCT
ejpam-5839	319	32	l	l	NOUN
ejpam-5839	319	33	)	)	PUNCT
ejpam-5839	319	34	where	where	SCONJ
ejpam-5839	319	35	ñ(i	ñ(i	PROPN
ejpam-5839	319	36	,	,	PUNCT
ejpam-5839	319	37	j	j	PROPN
ejpam-5839	319	38	,	,	PUNCT
ejpam-5839	319	39	k	k	PROPN
ejpam-5839	319	40	,	,	PUNCT
ejpam-5839	319	41	l	l	NOUN
ejpam-5839	319	42	)	)	PUNCT
ejpam-5839	319	43	and	and	CCONJ
ejpam-5839	319	44	n(i	n(i	PROPN
ejpam-5839	319	45	,	,	PUNCT
ejpam-5839	319	46	j	j	PROPN
ejpam-5839	319	47	,	,	PUNCT
ejpam-5839	319	48	k	k	PROPN
ejpam-5839	319	49	,	,	PUNCT
ejpam-5839	319	50	l	l	NOUN
ejpam-5839	319	51	)	)	PUNCT
ejpam-5839	319	52	denote	denote	VERB
ejpam-5839	319	53	the	the	DET
ejpam-5839	319	54	(	(	PUNCT
ejpam-5839	319	55	i	i	PROPN
ejpam-5839	319	56	,	,	PUNCT
ejpam-5839	319	57	j	j	PROPN
ejpam-5839	319	58	,	,	PUNCT
ejpam-5839	319	59	k	k	PROPN
ejpam-5839	319	60	,	,	PUNCT
ejpam-5839	319	61	l)-cut	l)-cut	NOUN
ejpam-5839	319	62	of	of	ADP
ejpam-5839	319	63	ñ	ñ	PROPN
ejpam-5839	319	64	and	and	CCONJ
ejpam-5839	319	65	n	n	CCONJ
ejpam-5839	319	66	,	,	PUNCT
ejpam-5839	319	67	respectively	respectively	ADV
ejpam-5839	319	68	.	.	PUNCT
ejpam-5839	320	1	a.	a.	NOUN
ejpam-5839	320	2	shihadeh	shihadeh	PROPN
ejpam-5839	320	3	et	et	PROPN
ejpam-5839	320	4	al	al	PROPN
ejpam-5839	320	5	.	.	PUNCT
ejpam-5839	320	6	/	/	SYM
ejpam-5839	320	7	eur	eur	PROPN
ejpam-5839	320	8	.	.	PUNCT
ejpam-5839	321	1	j.	j.	PROPN
ejpam-5839	321	2	pure	pure	PROPN
ejpam-5839	321	3	appl	appl	PROPN
ejpam-5839	321	4	.	.	PROPN
ejpam-5839	321	5	math	math	PROPN
ejpam-5839	321	6	,	,	PUNCT
ejpam-5839	321	7	18	18	NUM
ejpam-5839	321	8	(	(	PUNCT
ejpam-5839	321	9	2	2	NUM
ejpam-5839	321	10	)	)	PUNCT
ejpam-5839	321	11	(	(	PUNCT
ejpam-5839	321	12	2025	2025	NUM
ejpam-5839	321	13	)	)	PUNCT
ejpam-5839	321	14	,	,	PUNCT
ejpam-5839	321	15	5839	5839	NUM
ejpam-5839	321	16	13	13	NUM
ejpam-5839	321	17	of	of	ADP
ejpam-5839	321	18	54	54	NUM
ejpam-5839	321	19	proof	proof	NOUN
ejpam-5839	321	20	.	.	PUNCT
ejpam-5839	322	1	let	let	VERB
ejpam-5839	322	2	ñ	ñ	PROPN
ejpam-5839	322	3	be	be	AUX
ejpam-5839	322	4	a	a	DET
ejpam-5839	322	5	single	single	ADV
ejpam-5839	322	6	-	-	PUNCT
ejpam-5839	322	7	valued	value	VERB
ejpam-5839	322	8	quadri	quadri	NOUN
ejpam-5839	322	9	-	-	PUNCT
ejpam-5839	322	10	partitioned	partition	VERB
ejpam-5839	322	11	neutrosophic	neutrosophic	ADJ
ejpam-5839	322	12	number	number	NOUN
ejpam-5839	322	13	,	,	PUNCT
ejpam-5839	322	14	and	and	CCONJ
ejpam-5839	322	15	supposen(i	supposen(i	PROPN
ejpam-5839	322	16	,	,	PUNCT
ejpam-5839	322	17	j	j	PROPN
ejpam-5839	322	18	,	,	PUNCT
ejpam-5839	322	19	k	k	PROPN
ejpam-5839	322	20	,	,	PUNCT
ejpam-5839	322	21	l	l	NOUN
ejpam-5839	322	22	)	)	PUNCT
ejpam-5839	322	23	is	be	AUX
ejpam-5839	322	24	decreasing	decrease	VERB
ejpam-5839	322	25	with	with	ADP
ejpam-5839	322	26	respect	respect	NOUN
ejpam-5839	322	27	to	to	ADP
ejpam-5839	322	28	(	(	PUNCT
ejpam-5839	322	29	i	i	PROPN
ejpam-5839	322	30	,	,	PUNCT
ejpam-5839	322	31	j	j	PROPN
ejpam-5839	322	32	,	,	PUNCT
ejpam-5839	322	33	k	k	PROPN
ejpam-5839	322	34	,	,	PUNCT
ejpam-5839	322	35	l	l	NOUN
ejpam-5839	322	36	)	)	PUNCT
ejpam-5839	322	37	.	.	PUNCT
ejpam-5839	323	1	from	from	ADP
ejpam-5839	323	2	theorem	theorem	NOUN
ejpam-5839	323	3	1	1	NUM
ejpam-5839	323	4	,	,	PUNCT
ejpam-5839	323	5	we	we	PRON
ejpam-5839	323	6	have	have	VERB
ejpam-5839	323	7	∞⋂	∞⋂	PROPN
ejpam-5839	323	8	n=1	n=1	PROPN
ejpam-5839	323	9	n(in	n(in	SYM
ejpam-5839	323	10	,	,	PUNCT
ejpam-5839	323	11	jn	jn	PROPN
ejpam-5839	323	12	,	,	PUNCT
ejpam-5839	323	13	kn	kn	PROPN
ejpam-5839	323	14	,	,	PUNCT
ejpam-5839	323	15	ln	ln	ADJ
ejpam-5839	323	16	)	)	PUNCT
ejpam-5839	323	17	=	=	SYM
ejpam-5839	323	18	n(i	n(i	PROPN
ejpam-5839	323	19	,	,	PUNCT
ejpam-5839	323	20	j	j	PROPN
ejpam-5839	323	21	,	,	PUNCT
ejpam-5839	323	22	k	k	PROPN
ejpam-5839	323	23	,	,	PUNCT
ejpam-5839	323	24	l	l	NOUN
ejpam-5839	323	25	)	)	PUNCT
ejpam-5839	323	26	for	for	ADP
ejpam-5839	323	27	in	in	ADP
ejpam-5839	323	28	↑	↑	PROPN
ejpam-5839	323	29	i	i	PROPN
ejpam-5839	323	30	,	,	PUNCT
ejpam-5839	323	31	jn	jn	PROPN
ejpam-5839	323	32	↓	↓	PROPN
ejpam-5839	323	33	j	j	PROPN
ejpam-5839	323	34	,	,	PUNCT
ejpam-5839	323	35	kn	kn	PROPN
ejpam-5839	323	36	↓	↓	PROPN
ejpam-5839	323	37	k	k	PROPN
ejpam-5839	323	38	,	,	PUNCT
ejpam-5839	323	39	ln	ln	PROPN
ejpam-5839	323	40	↓	↓	PROPN
ejpam-5839	323	41	l.	l.	PROPN
ejpam-5839	323	42	now	now	ADV
ejpam-5839	323	43	,	,	PUNCT
ejpam-5839	323	44	from	from	ADP
ejpam-5839	323	45	definitions	definition	NOUN
ejpam-5839	323	46	2	2	NUM
ejpam-5839	323	47	and	and	CCONJ
ejpam-5839	323	48	3	3	NUM
ejpam-5839	323	49	,	,	PUNCT
ejpam-5839	323	50	it	it	PRON
ejpam-5839	323	51	follows	follow	VERB
ejpam-5839	323	52	that	that	SCONJ
ejpam-5839	323	53	{	{	PUNCT
ejpam-5839	323	54	n(i	n(i	PROPN
ejpam-5839	323	55	,	,	PUNCT
ejpam-5839	323	56	j	j	PROPN
ejpam-5839	323	57	,	,	PUNCT
ejpam-5839	323	58	k	k	PROPN
ejpam-5839	323	59	,	,	PUNCT
ejpam-5839	323	60	l	l	NOUN
ejpam-5839	323	61	)	)	PUNCT
ejpam-5839	323	62	}	}	PUNCT
ejpam-5839	323	63	can	can	AUX
ejpam-5839	323	64	induce	induce	VERB
ejpam-5839	323	65	ñ.	ñ.	PROPN
ejpam-5839	323	66	from	from	ADP
ejpam-5839	323	67	definition	definition	NOUN
ejpam-5839	323	68	4	4	NUM
ejpam-5839	323	69	,	,	PUNCT
ejpam-5839	323	70	we	we	PRON
ejpam-5839	323	71	have	have	VERB
ejpam-5839	323	72	{	{	PUNCT
ejpam-5839	323	73	x	x	NOUN
ejpam-5839	323	74	:	:	PUNCT
ejpam-5839	323	75	tñ(x	tñ(x	X
ejpam-5839	323	76	)	)	PUNCT
ejpam-5839	323	77	⪰	⪰	NOUN
ejpam-5839	323	78	i	i	PRON
ejpam-5839	323	79	,	,	PUNCT
ejpam-5839	323	80	iñ(x	iñ(x	NOUN
ejpam-5839	323	81	)	)	PUNCT
ejpam-5839	323	82	⪯	⪯	PROPN
ejpam-5839	323	83	j	j	PROPN
ejpam-5839	323	84	,	,	PUNCT
ejpam-5839	323	85	fñ(x	fñ(x	X
ejpam-5839	323	86	)	)	PUNCT
ejpam-5839	323	87	⪯	⪯	PROPN
ejpam-5839	323	88	k	k	NOUN
ejpam-5839	323	89	,	,	PUNCT
ejpam-5839	323	90	hñ(x	hñ(x	PROPN
ejpam-5839	323	91	)	)	PUNCT
ejpam-5839	323	92	⪯	⪯	NOUN
ejpam-5839	323	93	l	l	NOUN
ejpam-5839	323	94	}	}	PUNCT
ejpam-5839	323	95	=	=	SYM
ejpam-5839	323	96	n(i	n(i	PROPN
ejpam-5839	323	97	,	,	PUNCT
ejpam-5839	323	98	j	j	PROPN
ejpam-5839	323	99	,	,	PUNCT
ejpam-5839	323	100	k	k	PROPN
ejpam-5839	323	101	,	,	PUNCT
ejpam-5839	323	102	l	l	NOUN
ejpam-5839	323	103	)	)	PUNCT
ejpam-5839	324	1	=	=	SYM
ejpam-5839	324	2	⟨[li	⟨[li	NOUN
ejpam-5839	324	3	,	,	PUNCT
ejpam-5839	324	4	ui	ui	NOUN
ejpam-5839	324	5	]	]	X
ejpam-5839	324	6	,	,	PUNCT
ejpam-5839	325	1	[	[	X
ejpam-5839	325	2	lj	lj	PROPN
ejpam-5839	325	3	,	,	PUNCT
ejpam-5839	325	4	uj	uj	PROPN
ejpam-5839	325	5	]	]	PUNCT
ejpam-5839	325	6	,	,	PUNCT
ejpam-5839	325	7	[	[	X
ejpam-5839	325	8	lk	lk	X
ejpam-5839	325	9	,	,	PUNCT
ejpam-5839	325	10	uk	uk	PROPN
ejpam-5839	325	11	]	]	PUNCT
ejpam-5839	325	12	,	,	PUNCT
ejpam-5839	325	13	[	[	X
ejpam-5839	325	14	ll	ll	NOUN
ejpam-5839	325	15	,	,	PUNCT
ejpam-5839	325	16	ul]⟩	ul]⟩	ADJ
ejpam-5839	325	17	is	be	AUX
ejpam-5839	325	18	a	a	DET
ejpam-5839	325	19	closed	closed	ADJ
ejpam-5839	325	20	single	single	ADV
ejpam-5839	325	21	-	-	PUNCT
ejpam-5839	325	22	valued	value	VERB
ejpam-5839	325	23	quadri	quadri	NOUN
ejpam-5839	325	24	-	-	PUNCT
ejpam-5839	325	25	partitioned	partition	VERB
ejpam-5839	325	26	neutrosophic	neutrosophic	ADJ
ejpam-5839	325	27	number	number	NOUN
ejpam-5839	325	28	.	.	PUNCT
ejpam-5839	326	1	proposition	proposition	NOUN
ejpam-5839	326	2	6	6	NUM
ejpam-5839	326	3	.	.	PUNCT
ejpam-5839	327	1	if	if	SCONJ
ejpam-5839	327	2	ñ	ñ	PROPN
ejpam-5839	327	3	is	be	AUX
ejpam-5839	327	4	a	a	DET
ejpam-5839	327	5	closed	closed	ADJ
ejpam-5839	327	6	single	single	ADV
ejpam-5839	327	7	-	-	PUNCT
ejpam-5839	327	8	valued	value	VERB
ejpam-5839	327	9	quadri	quadri	NOUN
ejpam-5839	327	10	-	-	PUNCT
ejpam-5839	327	11	partitioned	partition	VERB
ejpam-5839	327	12	neutrosophic	neutrosophic	ADJ
ejpam-5839	327	13	number	number	NOUN
ejpam-5839	327	14	,	,	PUNCT
ejpam-5839	327	15	then	then	ADV
ejpam-5839	327	16	ñ	ñ	PROPN
ejpam-5839	327	17	and	and	CCONJ
ejpam-5839	327	18	ñ	ñ	ADJ
ejpam-5839	327	19	u	u	NOUN
ejpam-5839	327	20	↓	↓	NOUN
ejpam-5839	327	21	ñu	ñu	VERB
ejpam-5839	327	22	i	i	PRON
ejpam-5839	327	23	for	for	ADP
ejpam-5839	327	24	in	in	ADP
ejpam-5839	327	25	↑	↑	PROPN
ejpam-5839	327	26	i	i	PROPN
ejpam-5839	327	27	,	,	PUNCT
ejpam-5839	327	28	ñl	ñl	PROPN
ejpam-5839	327	29	jn	jn	PROPN
ejpam-5839	327	30	↑	↑	PROPN
ejpam-5839	327	31	ñl	ñl	NUM
ejpam-5839	327	32	j	j	PROPN
ejpam-5839	327	33	,	,	PUNCT
ejpam-5839	327	34	ñu	ñu	VERB
ejpam-5839	327	35	jn	jn	PROPN
ejpam-5839	327	36	↓	↓	PROPN
ejpam-5839	327	37	ñu	ñu	PROPN
ejpam-5839	327	38	j	j	PROPN
ejpam-5839	327	39	for	for	ADP
ejpam-5839	327	40	jn	jn	PROPN
ejpam-5839	327	41	↓	↓	PROPN
ejpam-5839	327	42	j	j	PROPN
ejpam-5839	327	43	,	,	PUNCT
ejpam-5839	327	44	ñl	ñl	NUM
ejpam-5839	327	45	kn	kn	PROPN
ejpam-5839	327	46	↑	↑	PROPN
ejpam-5839	327	47	ñl	ñl	NUM
ejpam-5839	327	48	k	k	X
ejpam-5839	327	49	,	,	PUNCT
ejpam-5839	327	50	ñu	ñu	VERB
ejpam-5839	327	51	kn	kn	PROPN
ejpam-5839	327	52	↓	↓	PROPN
ejpam-5839	327	53	ñu	ñu	PROPN
ejpam-5839	327	54	k	k	PROPN
ejpam-5839	327	55	for	for	ADP
ejpam-5839	327	56	kn	kn	PROPN
ejpam-5839	327	57	↓	↓	PROPN
ejpam-5839	327	58	k	k	PROPN
ejpam-5839	327	59	,	,	PUNCT
ejpam-5839	327	60	ñl	ñl	X
ejpam-5839	327	61	ln	ln	ADJ
ejpam-5839	327	62	↑	↑	NOUN
ejpam-5839	327	63	ñl	ñl	X
ejpam-5839	327	64	l	l	NOUN
ejpam-5839	327	65	,	,	PUNCT
ejpam-5839	327	66	ñu	ñu	VERB
ejpam-5839	327	67	ln	ln	ADJ
ejpam-5839	327	68	↓	↓	NOUN
ejpam-5839	327	69	ñu	ñu	PROPN
ejpam-5839	327	70	l	l	NOUN
ejpam-5839	327	71	for	for	ADP
ejpam-5839	327	72	ln	ln	ADJ
ejpam-5839	327	73	↓	↓	PROPN
ejpam-5839	327	74	l.	l.	PROPN
ejpam-5839	327	75	proof	proof	PROPN
ejpam-5839	327	76	.	.	PUNCT
ejpam-5839	328	1	since	since	SCONJ
ejpam-5839	328	2	(	(	PUNCT
ejpam-5839	328	3	n)(i	n)(i	NUM
ejpam-5839	328	4	,	,	PUNCT
ejpam-5839	328	5	j	j	PROPN
ejpam-5839	328	6	,	,	PUNCT
ejpam-5839	328	7	k	k	PROPN
ejpam-5839	328	8	,	,	PUNCT
ejpam-5839	328	9	l	l	NOUN
ejpam-5839	328	10	)	)	PUNCT
ejpam-5839	328	11	=	=	SYM
ejpam-5839	328	12	ñ(i	ñ(i	PROPN
ejpam-5839	328	13	,	,	PUNCT
ejpam-5839	328	14	j	j	PROPN
ejpam-5839	328	15	,	,	PUNCT
ejpam-5839	328	16	k	k	PROPN
ejpam-5839	328	17	,	,	PUNCT
ejpam-5839	328	18	l	l	NOUN
ejpam-5839	328	19	)	)	PUNCT
ejpam-5839	328	20	=	=	VERB
ejpam-5839	328	21	⟨[ñl	⟨[ñl	VERB
ejpam-5839	328	22	i	i	PRON
ejpam-5839	328	23	,	,	PUNCT
ejpam-5839	328	24	ñ	ñ	VERB
ejpam-5839	328	25	u	u	NOUN
ejpam-5839	328	26	i	i	PRON
ejpam-5839	328	27	]	]	X
ejpam-5839	328	28	,	,	PUNCT
ejpam-5839	328	29	[	[	X
ejpam-5839	328	30	ñ	ñ	VERB
ejpam-5839	328	31	l	l	NOUN
ejpam-5839	328	32	j	j	PROPN
ejpam-5839	328	33	,	,	PUNCT
ejpam-5839	328	34	ñ	ñ	VERB
ejpam-5839	328	35	u	u	X
ejpam-5839	328	36	j	j	X
ejpam-5839	328	37	]	]	X
ejpam-5839	328	38	,	,	PUNCT
ejpam-5839	328	39	[	[	X
ejpam-5839	328	40	ñ	ñ	ADP
ejpam-5839	328	41	l	l	NOUN
ejpam-5839	328	42	k	k	X
ejpam-5839	328	43	,	,	PUNCT
ejpam-5839	328	44	ñ	ñ	PROPN
ejpam-5839	328	45	u	u	X
ejpam-5839	328	46	k	k	X
ejpam-5839	328	47	]	]	X
ejpam-5839	328	48	,	,	PUNCT
ejpam-5839	328	49	[	[	X
ejpam-5839	328	50	ñ	ñ	ADP
ejpam-5839	328	51	l	l	NOUN
ejpam-5839	328	52	l	l	NOUN
ejpam-5839	328	53	,	,	PUNCT
ejpam-5839	328	54	ñ	ñ	VERB
ejpam-5839	328	55	u	u	NOUN
ejpam-5839	328	56	l	l	X
ejpam-5839	328	57	]	]	X
ejpam-5839	328	58	⟩	⟩	NOUN
ejpam-5839	328	59	,	,	PUNCT
ejpam-5839	328	60	then	then	ADV
ejpam-5839	328	61	(	(	PUNCT
ejpam-5839	328	62	n)(i	n)(i	NUM
ejpam-5839	328	63	,	,	PUNCT
ejpam-5839	328	64	j	j	PROPN
ejpam-5839	328	65	,	,	PUNCT
ejpam-5839	328	66	k	k	PROPN
ejpam-5839	328	67	,	,	PUNCT
ejpam-5839	328	68	l	l	NOUN
ejpam-5839	328	69	)	)	PUNCT
ejpam-5839	328	70	is	be	AUX
ejpam-5839	328	71	decreasing	decrease	VERB
ejpam-5839	328	72	with	with	ADP
ejpam-5839	328	73	respect	respect	NOUN
ejpam-5839	328	74	to	to	ADP
ejpam-5839	328	75	(	(	PUNCT
ejpam-5839	328	76	i	i	PROPN
ejpam-5839	328	77	,	,	PUNCT
ejpam-5839	328	78	j	j	PROPN
ejpam-5839	328	79	,	,	PUNCT
ejpam-5839	328	80	k	k	PROPN
ejpam-5839	328	81	,	,	PUNCT
ejpam-5839	328	82	l	l	NOUN
ejpam-5839	328	83	)	)	PUNCT
ejpam-5839	328	84	.	.	PUNCT
ejpam-5839	329	1	we	we	PRON
ejpam-5839	329	2	have	have	VERB
ejpam-5839	329	3	:	:	PUNCT
ejpam-5839	329	4	lim	lim	PROPN
ejpam-5839	329	5	ñl	ñl	VERB
ejpam-5839	329	6	an	an	DET
ejpam-5839	329	7	⪯	⪯	NOUN
ejpam-5839	329	8	ñl	ñl	NUM
ejpam-5839	330	1	i	i	PROPN
ejpam-5839	330	2	,	,	PUNCT
ejpam-5839	330	3	lim	lim	PROPN
ejpam-5839	330	4	ñu	ñu	VERB
ejpam-5839	330	5	an	an	DET
ejpam-5839	330	6	⪰	⪰	NOUN
ejpam-5839	330	7	ñu	ñu	VERB
ejpam-5839	330	8	i	i	PRON
ejpam-5839	330	9	,	,	PUNCT
ejpam-5839	330	10	lim	lim	PROPN
ejpam-5839	330	11	ñl	ñl	X
ejpam-5839	330	12	jn	jn	PROPN
ejpam-5839	330	13	⪯	⪯	PROPN
ejpam-5839	330	14	ñl	ñl	NUM
ejpam-5839	330	15	j	j	PROPN
ejpam-5839	330	16	,	,	PUNCT
ejpam-5839	330	17	lim	lim	PROPN
ejpam-5839	330	18	ñu	ñu	VERB
ejpam-5839	330	19	jn	jn	PROPN
ejpam-5839	330	20	⪰	⪰	PROPN
ejpam-5839	330	21	ñu	ñu	PROPN
ejpam-5839	330	22	j	j	PROPN
ejpam-5839	330	23	,	,	PUNCT
ejpam-5839	330	24	lim	lim	PROPN
ejpam-5839	330	25	ñl	ñl	NUM
ejpam-5839	330	26	kn	kn	PROPN
ejpam-5839	330	27	⪯	⪯	PROPN
ejpam-5839	330	28	ñl	ñl	PROPN
ejpam-5839	331	1	k	k	PROPN
ejpam-5839	331	2	,	,	PUNCT
ejpam-5839	331	3	lim	lim	PROPN
ejpam-5839	331	4	ñu	ñu	VERB
ejpam-5839	331	5	kn	kn	PROPN
ejpam-5839	331	6	⪰	⪰	NOUN
ejpam-5839	331	7	ñu	ñu	PROPN
ejpam-5839	331	8	k	k	PROPN
ejpam-5839	331	9	,	,	PUNCT
ejpam-5839	331	10	lim	lim	PROPN
ejpam-5839	331	11	ñl	ñl	X
ejpam-5839	331	12	ln	ln	ADJ
ejpam-5839	331	13	⪯	⪯	NOUN
ejpam-5839	331	14	ñl	ñl	NUM
ejpam-5839	331	15	l	l	NOUN
ejpam-5839	331	16	,	,	PUNCT
ejpam-5839	331	17	lim	lim	PROPN
ejpam-5839	331	18	ñu	ñu	VERB
ejpam-5839	331	19	ln	ln	ADJ
ejpam-5839	331	20	⪰	⪰	NOUN
ejpam-5839	331	21	ñu	ñu	PROPN
ejpam-5839	331	22	l	l	NOUN
ejpam-5839	331	23	.	.	PUNCT
ejpam-5839	332	1	this	this	PRON
ejpam-5839	332	2	implies	imply	VERB
ejpam-5839	332	3	that	that	SCONJ
ejpam-5839	332	4	:	:	PUNCT
ejpam-5839	332	5	⟨[lim	⟨[lim	X
ejpam-5839	332	6	ñl	ñl	PRON
ejpam-5839	332	7	an	an	PRON
ejpam-5839	332	8	,	,	PUNCT
ejpam-5839	332	9	lim	lim	PROPN
ejpam-5839	332	10	ñu	ñu	VERB
ejpam-5839	332	11	an	an	PRON
ejpam-5839	332	12	]	]	X
ejpam-5839	332	13	,	,	PUNCT
ejpam-5839	332	14	[	[	X
ejpam-5839	332	15	lim	lim	PROPN
ejpam-5839	332	16	ñl	ñl	X
ejpam-5839	332	17	jn	jn	PROPN
ejpam-5839	332	18	,	,	PUNCT
ejpam-5839	332	19	lim	lim	PROPN
ejpam-5839	332	20	ñu	ñu	VERB
ejpam-5839	332	21	jn	jn	PROPN
ejpam-5839	332	22	]	]	X
ejpam-5839	332	23	,	,	PUNCT
ejpam-5839	333	1	[	[	X
ejpam-5839	333	2	lim	lim	PROPN
ejpam-5839	333	3	ñl	ñl	X
ejpam-5839	333	4	kn	kn	PROPN
ejpam-5839	333	5	,	,	PUNCT
ejpam-5839	333	6	lim	lim	PROPN
ejpam-5839	333	7	ñu	ñu	VERB
ejpam-5839	333	8	kn	kn	PROPN
ejpam-5839	333	9	]	]	X
ejpam-5839	333	10	,	,	PUNCT
ejpam-5839	333	11	[	[	X
ejpam-5839	333	12	lim	lim	PROPN
ejpam-5839	333	13	ñl	ñl	X
ejpam-5839	333	14	ln	ln	PROPN
ejpam-5839	333	15	,	,	PUNCT
ejpam-5839	333	16	lim	lim	PROPN
ejpam-5839	333	17	ñu	ñu	VERB
ejpam-5839	333	18	ln]⟩	ln]⟩	NOUN
ejpam-5839	333	19	⊆	⊆	NUM
ejpam-5839	333	20	⟨[ñl	⟨[ñl	VERB
ejpam-5839	333	21	i	i	PRON
ejpam-5839	333	22	,	,	PUNCT
ejpam-5839	333	23	ñ	ñ	VERB
ejpam-5839	333	24	u	u	NOUN
ejpam-5839	333	25	i	i	PRON
ejpam-5839	333	26	]	]	X
ejpam-5839	333	27	,	,	PUNCT
ejpam-5839	333	28	[	[	X
ejpam-5839	333	29	ñ	ñ	VERB
ejpam-5839	333	30	l	l	NOUN
ejpam-5839	333	31	j	j	PROPN
ejpam-5839	333	32	,	,	PUNCT
ejpam-5839	333	33	ñ	ñ	VERB
ejpam-5839	333	34	u	u	X
ejpam-5839	333	35	j	j	X
ejpam-5839	333	36	]	]	X
ejpam-5839	333	37	,	,	PUNCT
ejpam-5839	333	38	[	[	X
ejpam-5839	333	39	ñ	ñ	ADP
ejpam-5839	333	40	l	l	NOUN
ejpam-5839	333	41	k	k	X
ejpam-5839	333	42	,	,	PUNCT
ejpam-5839	333	43	ñ	ñ	PROPN
ejpam-5839	333	44	u	u	X
ejpam-5839	333	45	k	k	X
ejpam-5839	333	46	]	]	X
ejpam-5839	333	47	,	,	PUNCT
ejpam-5839	333	48	[	[	X
ejpam-5839	333	49	ñ	ñ	ADP
ejpam-5839	333	50	l	l	NOUN
ejpam-5839	333	51	l	l	NOUN
ejpam-5839	333	52	,	,	PUNCT
ejpam-5839	333	53	ñ	ñ	VERB
ejpam-5839	333	54	u	u	X
ejpam-5839	333	55	l	l	NOUN
ejpam-5839	333	56	]	]	X
ejpam-5839	333	57	⟩.	⟩.	NOUN
ejpam-5839	333	58	thus	thus	ADV
ejpam-5839	333	59	,	,	PUNCT
ejpam-5839	333	60	we	we	PRON
ejpam-5839	333	61	conclude	conclude	VERB
ejpam-5839	333	62	:	:	PUNCT
ejpam-5839	333	63	lim	lim	PROPN
ejpam-5839	333	64	ñl	ñl	VERB
ejpam-5839	333	65	an	an	DET
ejpam-5839	333	66	⪰	⪰	NOUN
ejpam-5839	333	67	ñl	ñl	X
ejpam-5839	333	68	i	i	NOUN
ejpam-5839	333	69	,	,	PUNCT
ejpam-5839	333	70	lim	lim	PROPN
ejpam-5839	333	71	ñu	ñu	VERB
ejpam-5839	333	72	an	an	DET
ejpam-5839	333	73	⪯	⪯	NOUN
ejpam-5839	333	74	ñu	ñu	VERB
ejpam-5839	333	75	i	i	PRON
ejpam-5839	333	76	,	,	PUNCT
ejpam-5839	333	77	lim	lim	PROPN
ejpam-5839	333	78	ñl	ñl	X
ejpam-5839	333	79	jn	jn	PROPN
ejpam-5839	333	80	⪰	⪰	PROPN
ejpam-5839	333	81	ñl	ñl	X
ejpam-5839	333	82	j	j	PROPN
ejpam-5839	333	83	,	,	PUNCT
ejpam-5839	333	84	lim	lim	PROPN
ejpam-5839	333	85	ñu	ñu	PROPN
ejpam-5839	333	86	jn	jn	PROPN
ejpam-5839	333	87	⪯	⪯	PROPN
ejpam-5839	333	88	ñu	ñu	VERB
ejpam-5839	333	89	j	j	PROPN
ejpam-5839	333	90	,	,	PUNCT
ejpam-5839	333	91	lim	lim	PROPN
ejpam-5839	333	92	ñl	ñl	NUM
ejpam-5839	333	93	kn	kn	PROPN
ejpam-5839	333	94	⪰	⪰	NOUN
ejpam-5839	333	95	ñl	ñl	X
ejpam-5839	333	96	k	k	PROPN
ejpam-5839	333	97	,	,	PUNCT
ejpam-5839	333	98	lim	lim	PROPN
ejpam-5839	333	99	ñu	ñu	VERB
ejpam-5839	333	100	kn	kn	PROPN
ejpam-5839	333	101	⪯	⪯	PROPN
ejpam-5839	333	102	ñu	ñu	VERB
ejpam-5839	333	103	k	k	PROPN
ejpam-5839	333	104	,	,	PUNCT
ejpam-5839	333	105	lim	lim	PROPN
ejpam-5839	333	106	ñl	ñl	X
ejpam-5839	333	107	ln	ln	ADJ
ejpam-5839	333	108	⪰	⪰	NOUN
ejpam-5839	333	109	ñl	ñl	X
ejpam-5839	333	110	l	l	NOUN
ejpam-5839	333	111	,	,	PUNCT
ejpam-5839	333	112	lim	lim	PROPN
ejpam-5839	333	113	ñu	ñu	VERB
ejpam-5839	333	114	ln	ln	ADJ
ejpam-5839	333	115	⪯	⪯	NOUN
ejpam-5839	333	116	ñu	ñu	VERB
ejpam-5839	333	117	l	l	NOUN
ejpam-5839	333	118	.	.	PUNCT
ejpam-5839	334	1	a.	a.	NOUN
ejpam-5839	334	2	shihadeh	shihadeh	VERB
ejpam-5839	334	3	et	et	PROPN
ejpam-5839	334	4	al	al	PROPN
ejpam-5839	334	5	.	.	PUNCT
ejpam-5839	334	6	/	/	SYM
ejpam-5839	334	7	eur	eur	PROPN
ejpam-5839	334	8	.	.	PUNCT
ejpam-5839	335	1	j.	j.	PROPN
ejpam-5839	335	2	pure	pure	PROPN
ejpam-5839	335	3	appl	appl	PROPN
ejpam-5839	335	4	.	.	PROPN
ejpam-5839	335	5	math	math	PROPN
ejpam-5839	335	6	,	,	PUNCT
ejpam-5839	335	7	18	18	NUM
ejpam-5839	335	8	(	(	PUNCT
ejpam-5839	335	9	2	2	NUM
ejpam-5839	335	10	)	)	PUNCT
ejpam-5839	335	11	(	(	PUNCT
ejpam-5839	335	12	2025	2025	NUM
ejpam-5839	335	13	)	)	PUNCT
ejpam-5839	335	14	,	,	PUNCT
ejpam-5839	335	15	5839	5839	NUM
ejpam-5839	335	16	14	14	NUM
ejpam-5839	335	17	of	of	ADP
ejpam-5839	335	18	54	54	NUM
ejpam-5839	335	19	5	5	NUM
ejpam-5839	335	20	.	.	PUNCT
ejpam-5839	335	21	characterization	characterization	NOUN
ejpam-5839	335	22	of	of	ADP
ejpam-5839	335	23	riemann	riemann	PROPN
ejpam-5839	335	24	integration	integration	NOUN
ejpam-5839	335	25	in	in	ADP
ejpam-5839	335	26	terms	term	NOUN
ejpam-5839	335	27	of	of	ADP
ejpam-5839	335	28	quadri	quadri	NOUN
ejpam-5839	335	29	-	-	PUNCT
ejpam-5839	335	30	partitioned	partition	VERB
ejpam-5839	335	31	neutrosophic	neutrosophic	ADJ
ejpam-5839	335	32	structure	structure	NOUN
ejpam-5839	335	33	this	this	DET
ejpam-5839	335	34	section	section	NOUN
ejpam-5839	335	35	is	be	AUX
ejpam-5839	335	36	devoted	devote	VERB
ejpam-5839	335	37	to	to	ADP
ejpam-5839	335	38	riemann	riemann	PROPN
ejpam-5839	335	39	integral	integral	ADJ
ejpam-5839	335	40	theory	theory	NOUN
ejpam-5839	335	41	based	base	VERB
ejpam-5839	335	42	on	on	ADP
ejpam-5839	335	43	quadri	quadri	NOUN
ejpam-5839	335	44	-	-	PUNCT
ejpam-5839	335	45	partitioned	partition	VERB
ejpam-5839	335	46	neutrosophic	neutrosophic	ADJ
ejpam-5839	335	47	sets	set	NOUN
ejpam-5839	335	48	,	,	PUNCT
ejpam-5839	335	49	and	and	CCONJ
ejpam-5839	335	50	all	all	DET
ejpam-5839	335	51	the	the	DET
ejpam-5839	335	52	fundamentals	fundamental	NOUN
ejpam-5839	335	53	are	be	AUX
ejpam-5839	335	54	defined	define	VERB
ejpam-5839	335	55	according	accord	VERB
ejpam-5839	335	56	to	to	ADP
ejpam-5839	335	57	this	this	DET
ejpam-5839	335	58	new	new	ADJ
ejpam-5839	335	59	theory	theory	NOUN
ejpam-5839	335	60	.	.	PUNCT
ejpam-5839	336	1	some	some	DET
ejpam-5839	336	2	new	new	ADJ
ejpam-5839	336	3	effects	effect	NOUN
ejpam-5839	336	4	are	be	AUX
ejpam-5839	336	5	given	give	VERB
ejpam-5839	336	6	,	,	PUNCT
ejpam-5839	336	7	and	and	CCONJ
ejpam-5839	336	8	this	this	DET
ejpam-5839	336	9	whole	whole	ADJ
ejpam-5839	336	10	scenario	scenario	NOUN
ejpam-5839	336	11	has	have	AUX
ejpam-5839	336	12	been	be	AUX
ejpam-5839	336	13	established	establish	VERB
ejpam-5839	336	14	by	by	ADP
ejpam-5839	336	15	introducing	introduce	VERB
ejpam-5839	336	16	interesting	interesting	ADJ
ejpam-5839	336	17	examples	example	NOUN
ejpam-5839	336	18	.	.	PUNCT
ejpam-5839	337	1	definition	definition	NOUN
ejpam-5839	337	2	11	11	NUM
ejpam-5839	337	3	.	.	PUNCT
ejpam-5839	338	1	let	let	VERB
ejpam-5839	338	2	q	q	NOUN
ejpam-5839	338	3	be	be	AUX
ejpam-5839	338	4	the	the	DET
ejpam-5839	338	5	set	set	NOUN
ejpam-5839	338	6	of	of	ADP
ejpam-5839	338	7	all	all	DET
ejpam-5839	338	8	quadri	quadri	NOUN
ejpam-5839	338	9	-	-	PUNCT
ejpam-5839	338	10	partitioned	partition	VERB
ejpam-5839	338	11	neutrosophic	neutrosophic	ADJ
ejpam-5839	338	12	numbers	number	NOUN
ejpam-5839	338	13	(	(	PUNCT
ejpam-5839	338	14	qnsn	qnsn	NOUN
ejpam-5839	338	15	)	)	PUNCT
ejpam-5839	338	16	,	,	PUNCT
ejpam-5839	338	17	qcl	qcl	PROPN
ejpam-5839	338	18	be	be	AUX
ejpam-5839	338	19	the	the	DET
ejpam-5839	338	20	set	set	NOUN
ejpam-5839	338	21	of	of	ADP
ejpam-5839	338	22	all	all	DET
ejpam-5839	338	23	closed	closed	ADJ
ejpam-5839	338	24	(	(	PUNCT
ejpam-5839	338	25	qnsn	qnsn	NOUN
ejpam-5839	338	26	)	)	PUNCT
ejpam-5839	338	27	,	,	PUNCT
ejpam-5839	338	28	and	and	CCONJ
ejpam-5839	338	29	qb	qb	PROPN
ejpam-5839	338	30	signify	signify	VERB
ejpam-5839	338	31	the	the	DET
ejpam-5839	338	32	set	set	NOUN
ejpam-5839	338	33	of	of	ADP
ejpam-5839	338	34	all	all	DET
ejpam-5839	338	35	bounded	bounded	ADJ
ejpam-5839	338	36	(	(	PUNCT
ejpam-5839	338	37	qnsn	qnsn	NOUN
ejpam-5839	338	38	)	)	PUNCT
ejpam-5839	338	39	.	.	PUNCT
ejpam-5839	339	1	(	(	PUNCT
ejpam-5839	339	2	i	i	NOUN
ejpam-5839	339	3	)	)	PUNCT
ejpam-5839	339	4	f̃q(x	f̃q(x	CCONJ
ejpam-5839	339	5	)	)	PUNCT
ejpam-5839	339	6	is	be	AUX
ejpam-5839	339	7	a	a	DET
ejpam-5839	339	8	q	q	NOUN
ejpam-5839	339	9	-	-	PUNCT
ejpam-5839	339	10	nsvf	nsvf	NOUN
ejpam-5839	339	11	if	if	SCONJ
ejpam-5839	339	12	f̃q	f̃q	VERB
ejpam-5839	339	13	:	:	PUNCT
ejpam-5839	339	14	x	x	X
ejpam-5839	339	15	→	→	SYM
ejpam-5839	339	16	q.	q.	PROPN
ejpam-5839	339	17	(	(	PUNCT
ejpam-5839	339	18	ii	ii	NOUN
ejpam-5839	339	19	)	)	PUNCT
ejpam-5839	339	20	f̃q(x	f̃q(x	CCONJ
ejpam-5839	339	21	)	)	PUNCT
ejpam-5839	339	22	is	be	AUX
ejpam-5839	339	23	a	a	DET
ejpam-5839	339	24	closed	closed	ADJ
ejpam-5839	339	25	q	q	NOUN
ejpam-5839	339	26	-	-	PUNCT
ejpam-5839	339	27	nsvf	nsvf	NOUN
ejpam-5839	339	28	if	if	SCONJ
ejpam-5839	339	29	f̃q	f̃q	VERB
ejpam-5839	339	30	:	:	PUNCT
ejpam-5839	339	31	x	x	X
ejpam-5839	339	32	→	→	SYM
ejpam-5839	339	33	qcl	qcl	NOUN
ejpam-5839	339	34	.	.	PUNCT
ejpam-5839	340	1	(	(	PUNCT
ejpam-5839	340	2	iii	iii	NOUN
ejpam-5839	340	3	)	)	PUNCT
ejpam-5839	340	4	f̃q(x	f̃q(x	CCONJ
ejpam-5839	340	5	)	)	PUNCT
ejpam-5839	340	6	is	be	AUX
ejpam-5839	340	7	a	a	DET
ejpam-5839	340	8	bounded	bounded	ADJ
ejpam-5839	340	9	q	q	NOUN
ejpam-5839	340	10	-	-	PUNCT
ejpam-5839	340	11	nsvf	nsvf	NOUN
ejpam-5839	340	12	if	if	SCONJ
ejpam-5839	340	13	f̃q	f̃q	VERB
ejpam-5839	340	14	:	:	PUNCT
ejpam-5839	340	15	x	x	X
ejpam-5839	340	16	→	→	SYM
ejpam-5839	340	17	qb	qb	PROPN
ejpam-5839	340	18	.	.	PROPN
ejpam-5839	340	19	definition	definition	NOUN
ejpam-5839	340	20	12	12	NUM
ejpam-5839	340	21	.	.	PUNCT
ejpam-5839	341	1	let	let	AUX
ejpam-5839	341	2	f̃q(x	f̃q(x	PART
ejpam-5839	341	3	)	)	PUNCT
ejpam-5839	341	4	be	be	AUX
ejpam-5839	341	5	a	a	DET
ejpam-5839	341	6	closed	closed	ADJ
ejpam-5839	341	7	bounded	bounded	ADJ
ejpam-5839	341	8	q	q	NOUN
ejpam-5839	341	9	-	-	PUNCT
ejpam-5839	341	10	nsvf	nsvf	NOUN
ejpam-5839	341	11	on	on	ADP
ejpam-5839	341	12	a	a	DET
ejpam-5839	341	13	closed	closed	ADJ
ejpam-5839	341	14	interval	interval	NOUN
ejpam-5839	341	15	[	[	X
ejpam-5839	341	16	a1	a1	NOUN
ejpam-5839	341	17	,	,	PUNCT
ejpam-5839	341	18	b1	b1	NOUN
ejpam-5839	341	19	]	]	PUNCT
ejpam-5839	341	20	.	.	PUNCT
ejpam-5839	342	1	let	let	VERB
ejpam-5839	342	2	f̃l	f̃l	PROPN
ejpam-5839	342	3	qi(x	qi(x	NUM
ejpam-5839	342	4	)	)	PUNCT
ejpam-5839	342	5	,	,	PUNCT
ejpam-5839	342	6	f̃u	f̃u	NOUN
ejpam-5839	342	7	qi(x	qi(x	NUM
ejpam-5839	342	8	)	)	PUNCT
ejpam-5839	342	9	,	,	PUNCT
ejpam-5839	342	10	f̃l	f̃l	PROPN
ejpam-5839	342	11	qj(x	qj(x	NUM
ejpam-5839	342	12	)	)	PUNCT
ejpam-5839	342	13	,	,	PUNCT
ejpam-5839	342	14	f̃u	f̃u	NOUN
ejpam-5839	342	15	qj(x	qj(x	PUNCT
ejpam-5839	342	16	)	)	PUNCT
ejpam-5839	342	17	,	,	PUNCT
ejpam-5839	342	18	f̃l	f̃l	PROPN
ejpam-5839	342	19	qk(x	qk(x	NOUN
ejpam-5839	342	20	)	)	PUNCT
ejpam-5839	342	21	,	,	PUNCT
ejpam-5839	342	22	f̃u	f̃u	NOUN
ejpam-5839	342	23	qk(x	qk(x	NOUN
ejpam-5839	342	24	)	)	PUNCT
ejpam-5839	342	25	,	,	PUNCT
ejpam-5839	342	26	f̃l	f̃l	PROPN
ejpam-5839	342	27	ql(x	ql(x	PROPN
ejpam-5839	342	28	)	)	PUNCT
ejpam-5839	342	29	,	,	PUNCT
ejpam-5839	342	30	and	and	CCONJ
ejpam-5839	342	31	f̃u	f̃u	NOUN
ejpam-5839	342	32	ql(x	ql(x	NUM
ejpam-5839	342	33	)	)	PUNCT
ejpam-5839	342	34	are	be	AUX
ejpam-5839	342	35	all	all	PRON
ejpam-5839	342	36	quadri	quadri	PROPN
ejpam-5839	342	37	-	-	PUNCT
ejpam-5839	342	38	neutrosophic	neutrosophic	ADJ
ejpam-5839	342	39	riemann	riemann	PROPN
ejpam-5839	342	40	integrable	integrable	ADJ
ejpam-5839	342	41	(	(	PUNCT
ejpam-5839	342	42	qnri	qnri	NOUN
ejpam-5839	342	43	)	)	PUNCT
ejpam-5839	342	44	on	on	ADP
ejpam-5839	342	45	[	[	X
ejpam-5839	342	46	a1	a1	NOUN
ejpam-5839	342	47	,	,	PUNCT
ejpam-5839	342	48	b1	b1	NOUN
ejpam-5839	342	49	]	]	PUNCT
ejpam-5839	342	50	.	.	PUNCT
ejpam-5839	343	1	for	for	ADP
ejpam-5839	343	2	all	all	PRON
ejpam-5839	343	3	(	(	PUNCT
ejpam-5839	343	4	i	i	PROPN
ejpam-5839	343	5	,	,	PUNCT
ejpam-5839	343	6	j	j	PROPN
ejpam-5839	343	7	,	,	PUNCT
ejpam-5839	343	8	k	k	PROPN
ejpam-5839	343	9	,	,	PUNCT
ejpam-5839	343	10	l	l	NOUN
ejpam-5839	343	11	)	)	PUNCT
ejpam-5839	343	12	,	,	PUNCT
ejpam-5839	343	13	let	let	VERB
ejpam-5839	343	14	i(i	i(i	PROPN
ejpam-5839	343	15	,	,	PUNCT
ejpam-5839	343	16	j	j	PROPN
ejpam-5839	343	17	,	,	PUNCT
ejpam-5839	343	18	k	k	PROPN
ejpam-5839	343	19	,	,	PUNCT
ejpam-5839	343	20	l	l	NOUN
ejpam-5839	343	21	)	)	PUNCT
ejpam-5839	343	22	=	=	SYM
ejpam-5839	343	23			NOUN
ejpam-5839	344	1	[	[	X
ejpam-5839	344	2	∫	∫	X
ejpam-5839	344	3	b1	b1	PROPN
ejpam-5839	344	4	a1	a1	PROPN
ejpam-5839	344	5	f̃l	f̃l	PROPN
ejpam-5839	344	6	qi(x)dx	qi(x)dx	VERB
ejpam-5839	344	7	,	,	PUNCT
ejpam-5839	344	8	∫	∫	PROPN
ejpam-5839	344	9	b1	b1	PROPN
ejpam-5839	344	10	a1	a1	PROPN
ejpam-5839	344	11	f̃u	f̃u	NOUN
ejpam-5839	344	12	qi(x)dx	qi(x)dx	VERB
ejpam-5839	344	13	]	]	PUNCT
ejpam-5839	344	14	,	,	PUNCT
ejpam-5839	344	15	[	[	X
ejpam-5839	344	16	∫	∫	X
ejpam-5839	344	17	b1	b1	PROPN
ejpam-5839	344	18	a1	a1	PROPN
ejpam-5839	344	19	f̃l	f̃l	PROPN
ejpam-5839	344	20	qj(x)dx	qj(x)dx	ADJ
ejpam-5839	344	21	,	,	PUNCT
ejpam-5839	344	22	∫	∫	PROPN
ejpam-5839	344	23	b1	b1	PROPN
ejpam-5839	344	24	a1	a1	PROPN
ejpam-5839	344	25	f̃u	f̃u	NOUN
ejpam-5839	344	26	qj(x)dx	qj(x)dx	ADJ
ejpam-5839	344	27	]	]	PUNCT
ejpam-5839	344	28	,	,	PUNCT
ejpam-5839	344	29	[	[	X
ejpam-5839	344	30	∫	∫	X
ejpam-5839	344	31	b1	b1	PROPN
ejpam-5839	344	32	a1	a1	PROPN
ejpam-5839	344	33	f̃l	f̃l	PROPN
ejpam-5839	344	34	qk(x)dx	qk(x)dx	ADJ
ejpam-5839	344	35	,	,	PUNCT
ejpam-5839	344	36	∫	∫	PROPN
ejpam-5839	344	37	b1	b1	PROPN
ejpam-5839	344	38	a1	a1	PROPN
ejpam-5839	344	39	f̃u	f̃u	NOUN
ejpam-5839	344	40	qk(x)dx	qk(x)dx	VERB
ejpam-5839	344	41	]	]	PUNCT
ejpam-5839	344	42	,	,	PUNCT
ejpam-5839	344	43	[	[	X
ejpam-5839	344	44	∫	∫	X
ejpam-5839	344	45	b1	b1	PROPN
ejpam-5839	344	46	a1	a1	PROPN
ejpam-5839	344	47	f̃l	f̃l	PROPN
ejpam-5839	344	48	ql(x)dx	ql(x)dx	NOUN
ejpam-5839	344	49	,	,	PUNCT
ejpam-5839	344	50	∫	∫	PROPN
ejpam-5839	344	51	b1	b1	PROPN
ejpam-5839	344	52	a1	a1	PROPN
ejpam-5839	344	53	f̃u	f̃u	ADV
ejpam-5839	344	54	ql(x)dx	ql(x)dx	NOUN
ejpam-5839	344	55	]	]	PUNCT
ejpam-5839	344	56			NUM
ejpam-5839	344	57	here	here	ADV
ejpam-5839	344	58	,	,	PUNCT
ejpam-5839	344	59	[	[	PUNCT
ejpam-5839	344	60	f̃l	f̃l	PROPN
ejpam-5839	344	61	qi(x	qi(x	NUM
ejpam-5839	344	62	)	)	PUNCT
ejpam-5839	344	63	,	,	PUNCT
ejpam-5839	344	64	f̃	f̃	PROPN
ejpam-5839	344	65	u	u	PROPN
ejpam-5839	344	66	qi(x	qi(x	NUM
ejpam-5839	344	67	)	)	PUNCT
ejpam-5839	344	68	]	]	PUNCT
ejpam-5839	344	69	,	,	PUNCT
ejpam-5839	344	70	[	[	PUNCT
ejpam-5839	344	71	f̃l	f̃l	PROPN
ejpam-5839	344	72	qj(x	qj(x	NUM
ejpam-5839	344	73	)	)	PUNCT
ejpam-5839	344	74	,	,	PUNCT
ejpam-5839	344	75	f̃	f̃	PROPN
ejpam-5839	344	76	u	u	PROPN
ejpam-5839	344	77	qj(x	qj(x	PUNCT
ejpam-5839	344	78	)	)	PUNCT
ejpam-5839	344	79	]	]	PUNCT
ejpam-5839	344	80	,	,	PUNCT
ejpam-5839	344	81	[	[	PUNCT
ejpam-5839	344	82	f̃l	f̃l	NOUN
ejpam-5839	344	83	qk(x	qk(x	NOUN
ejpam-5839	344	84	)	)	PUNCT
ejpam-5839	344	85	,	,	PUNCT
ejpam-5839	344	86	f̃	f̃	PROPN
ejpam-5839	344	87	u	u	PROPN
ejpam-5839	344	88	qk(x	qk(x	NOUN
ejpam-5839	344	89	)	)	PUNCT
ejpam-5839	344	90	]	]	PUNCT
ejpam-5839	344	91	,	,	PUNCT
ejpam-5839	344	92	and	and	CCONJ
ejpam-5839	344	93	[	[	PUNCT
ejpam-5839	344	94	f̃l	f̃l	PROPN
ejpam-5839	344	95	ql(x	ql(x	NUM
ejpam-5839	344	96	)	)	PUNCT
ejpam-5839	344	97	,	,	PUNCT
ejpam-5839	344	98	f̃	f̃	PROPN
ejpam-5839	344	99	u	u	PROPN
ejpam-5839	344	100	ql(x	ql(x	PROPN
ejpam-5839	344	101	)	)	PUNCT
ejpam-5839	344	102	]	]	PUNCT
ejpam-5839	344	103	denote	denote	VERB
ejpam-5839	344	104	the	the	DET
ejpam-5839	344	105	(	(	PUNCT
ejpam-5839	344	106	i	i	PROPN
ejpam-5839	344	107	,	,	PUNCT
ejpam-5839	344	108	j	j	PROPN
ejpam-5839	344	109	,	,	PUNCT
ejpam-5839	344	110	k	k	PROPN
ejpam-5839	344	111	,	,	PUNCT
ejpam-5839	344	112	l)-cut	l)-cut	NOUN
ejpam-5839	344	113	of	of	ADP
ejpam-5839	344	114	f̃q(x	f̃q(x	PROPN
ejpam-5839	344	115	)	)	PUNCT
ejpam-5839	344	116	,	,	PUNCT
ejpam-5839	344	117	respectively	respectively	ADV
ejpam-5839	344	118	.	.	PUNCT
ejpam-5839	345	1	proposition	proposition	NOUN
ejpam-5839	345	2	7	7	NUM
ejpam-5839	345	3	.	.	PUNCT
ejpam-5839	346	1	[	[	X
ejpam-5839	346	2	56	56	NUM
ejpam-5839	346	3	]	]	X
ejpam-5839	346	4	if	if	SCONJ
ejpam-5839	346	5	g(x	g(x	NOUN
ejpam-5839	346	6	)	)	PUNCT
ejpam-5839	346	7	is	be	AUX
ejpam-5839	346	8	defined	define	VERB
ejpam-5839	346	9	on	on	ADP
ejpam-5839	346	10	[	[	X
ejpam-5839	346	11	a1	a1	NOUN
ejpam-5839	346	12	,	,	PUNCT
ejpam-5839	346	13	b1	b1	NOUN
ejpam-5839	346	14	]	]	PUNCT
ejpam-5839	346	15	and	and	CCONJ
ejpam-5839	346	16	is	be	AUX
ejpam-5839	346	17	a	a	DET
ejpam-5839	346	18	bounded	bounded	ADJ
ejpam-5839	346	19	function	function	NOUN
ejpam-5839	346	20	over	over	ADP
ejpam-5839	346	21	[	[	X
ejpam-5839	346	22	a1	a1	NOUN
ejpam-5839	346	23	,	,	PUNCT
ejpam-5839	346	24	b1	b1	NOUN
ejpam-5839	346	25	]	]	PUNCT
ejpam-5839	346	26	,	,	PUNCT
ejpam-5839	346	27	then	then	ADV
ejpam-5839	346	28	g(x	g(x	NOUN
ejpam-5839	346	29	)	)	PUNCT
ejpam-5839	346	30	is	be	AUX
ejpam-5839	346	31	also	also	ADV
ejpam-5839	346	32	lebesgue	lebesgue	NOUN
ejpam-5839	346	33	integrable	integrable	ADJ
ejpam-5839	346	34	over	over	ADP
ejpam-5839	346	35	[	[	X
ejpam-5839	346	36	a1	a1	NOUN
ejpam-5839	346	37	,	,	PUNCT
ejpam-5839	346	38	b1	b1	NOUN
ejpam-5839	346	39	]	]	PUNCT
ejpam-5839	346	40	.	.	PUNCT
ejpam-5839	347	1	proposition	proposition	NOUN
ejpam-5839	347	2	8	8	NUM
ejpam-5839	347	3	.	.	PUNCT
ejpam-5839	348	1	[	[	X
ejpam-5839	348	2	56	56	NUM
ejpam-5839	348	3	]	]	X
ejpam-5839	348	4	if	if	SCONJ
ejpam-5839	348	5	g(x	g(x	NOUN
ejpam-5839	348	6	)	)	PUNCT
ejpam-5839	348	7	is	be	AUX
ejpam-5839	348	8	a	a	DET
ejpam-5839	348	9	bounded	bounded	ADJ
ejpam-5839	348	10	function	function	NOUN
ejpam-5839	348	11	defined	define	VERB
ejpam-5839	348	12	on	on	ADP
ejpam-5839	348	13	[	[	X
ejpam-5839	348	14	a1	a1	NOUN
ejpam-5839	348	15	,	,	PUNCT
ejpam-5839	348	16	b1	b1	NOUN
ejpam-5839	348	17	]	]	PUNCT
ejpam-5839	348	18	,	,	PUNCT
ejpam-5839	348	19	then	then	ADV
ejpam-5839	348	20	g(x	g(x	NOUN
ejpam-5839	348	21	)	)	PUNCT
ejpam-5839	348	22	is	be	AUX
ejpam-5839	348	23	riemann	riemann	PROPN
ejpam-5839	348	24	integrable	integrable	ADJ
ejpam-5839	348	25	on	on	ADP
ejpam-5839	348	26	[	[	X
ejpam-5839	348	27	a1	a1	NOUN
ejpam-5839	348	28	,	,	PUNCT
ejpam-5839	348	29	b1	b1	NOUN
ejpam-5839	348	30	]	]	PUNCT
ejpam-5839	348	31	if	if	SCONJ
ejpam-5839	348	32	and	and	CCONJ
ejpam-5839	348	33	only	only	ADV
ejpam-5839	348	34	if	if	SCONJ
ejpam-5839	348	35	g(x	g(x	NOUN
ejpam-5839	348	36	)	)	PUNCT
ejpam-5839	348	37	is	be	AUX
ejpam-5839	348	38	continuous	continuous	ADJ
ejpam-5839	348	39	on	on	ADP
ejpam-5839	348	40	the	the	DET
ejpam-5839	348	41	closed	closed	ADJ
ejpam-5839	348	42	bounded	bounded	ADJ
ejpam-5839	348	43	interval	interval	NOUN
ejpam-5839	348	44	[	[	X
ejpam-5839	348	45	a1	a1	NOUN
ejpam-5839	348	46	,	,	PUNCT
ejpam-5839	348	47	b1	b1	NOUN
ejpam-5839	348	48	]	]	PUNCT
ejpam-5839	348	49	.	.	PUNCT
ejpam-5839	349	1	proposition	proposition	NOUN
ejpam-5839	349	2	9	9	NUM
ejpam-5839	349	3	.	.	PUNCT
ejpam-5839	350	1	[	[	X
ejpam-5839	350	2	56	56	NUM
ejpam-5839	350	3	]	]	X
ejpam-5839	350	4	if	if	SCONJ
ejpam-5839	350	5	g(x	g(x	NOUN
ejpam-5839	350	6	)	)	PUNCT
ejpam-5839	350	7	is	be	AUX
ejpam-5839	350	8	riemann	riemann	PROPN
ejpam-5839	350	9	integrable	integrable	ADJ
ejpam-5839	350	10	on	on	ADP
ejpam-5839	350	11	[	[	X
ejpam-5839	350	12	a1	a1	NOUN
ejpam-5839	350	13	,	,	PUNCT
ejpam-5839	350	14	b1	b1	NOUN
ejpam-5839	350	15	]	]	PUNCT
ejpam-5839	350	16	and	and	CCONJ
ejpam-5839	350	17	µ	µ	PRON
ejpam-5839	350	18	∈	∈	PROPN
ejpam-5839	350	19	r	r	NOUN
ejpam-5839	350	20	,	,	PUNCT
ejpam-5839	350	21	then	then	ADV
ejpam-5839	350	22	µg(x	µg(x	PUNCT
ejpam-5839	350	23	)	)	PUNCT
ejpam-5839	351	1	is	be	AUX
ejpam-5839	351	2	also	also	ADV
ejpam-5839	351	3	riemann	riemann	PROPN
ejpam-5839	351	4	integrable	integrable	ADJ
ejpam-5839	351	5	on	on	ADP
ejpam-5839	351	6	[	[	X
ejpam-5839	351	7	a1	a1	NOUN
ejpam-5839	351	8	,	,	PUNCT
ejpam-5839	351	9	b1	b1	NOUN
ejpam-5839	351	10	]	]	PUNCT
ejpam-5839	351	11	and∫	and∫	PROPN
ejpam-5839	351	12	b1	b1	PROPN
ejpam-5839	351	13	a1	a1	NOUN
ejpam-5839	351	14	µg(x	µg(x	ADV
ejpam-5839	351	15	)	)	PUNCT
ejpam-5839	351	16	dx	dx	PROPN
ejpam-5839	352	1	=	=	SYM
ejpam-5839	352	2	µ	µ	X
ejpam-5839	352	3	∫	∫	PROPN
ejpam-5839	352	4	b1	b1	NOUN
ejpam-5839	352	5	a1	a1	PROPN
ejpam-5839	352	6	g(x	g(x	PROPN
ejpam-5839	352	7	)	)	PUNCT
ejpam-5839	352	8	dx	dx	PROPN
ejpam-5839	352	9	.	.	PUNCT
ejpam-5839	352	10	theorem	theorem	PROPN
ejpam-5839	352	11	2	2	NUM
ejpam-5839	352	12	.	.	PUNCT
ejpam-5839	353	1	let	let	AUX
ejpam-5839	353	2	f̃q(x	f̃q(x	PART
ejpam-5839	353	3	)	)	PUNCT
ejpam-5839	353	4	be	be	AUX
ejpam-5839	353	5	a	a	DET
ejpam-5839	353	6	closed	closed	ADJ
ejpam-5839	353	7	bounded	bounded	ADJ
ejpam-5839	353	8	quadri	quadri	PROPN
ejpam-5839	353	9	-	-	PUNCT
ejpam-5839	353	10	neutrosophic	neutrosophic	PROPN
ejpam-5839	353	11	valued	value	VERB
ejpam-5839	353	12	function	function	NOUN
ejpam-5839	353	13	on	on	ADP
ejpam-5839	353	14	the	the	DET
ejpam-5839	353	15	closed	closed	ADJ
ejpam-5839	353	16	quadri	quadri	PROPN
ejpam-5839	353	17	-	-	PUNCT
ejpam-5839	353	18	neutrosophic	neutrosophic	ADJ
ejpam-5839	353	19	bounded	bound	VERB
ejpam-5839	353	20	interval	interval	NOUN
ejpam-5839	353	21	[	[	X
ejpam-5839	353	22	a1	a1	NOUN
ejpam-5839	353	23	,	,	PUNCT
ejpam-5839	353	24	b1	b1	NOUN
ejpam-5839	353	25	]	]	PUNCT
ejpam-5839	353	26	.	.	PUNCT
ejpam-5839	354	1	if	if	SCONJ
ejpam-5839	354	2	f̃q(x	f̃q(x	NUM
ejpam-5839	354	3	)	)	PUNCT
ejpam-5839	354	4	∈	∈	PROPN
ejpam-5839	354	5	qri	qri	NOUN
ejpam-5839	354	6	on	on	ADP
ejpam-5839	354	7	the	the	DET
ejpam-5839	354	8	closed	closed	ADJ
ejpam-5839	354	9	quadri	quadri	PROPN
ejpam-5839	354	10	-	-	PUNCT
ejpam-5839	354	11	neutrosophic	neutrosophic	ADJ
ejpam-5839	354	12	bounded	bound	VERB
ejpam-5839	354	13	interval	interval	NOUN
ejpam-5839	354	14	[	[	X
ejpam-5839	354	15	a1	a1	NOUN
ejpam-5839	354	16	,	,	PUNCT
ejpam-5839	354	17	b1	b1	NOUN
ejpam-5839	354	18	]	]	PUNCT
ejpam-5839	354	19	,	,	PUNCT
ejpam-5839	354	20	then	then	ADV
ejpam-5839	354	21	the	the	DET
ejpam-5839	354	22	quadri	quadri	PROPN
ejpam-5839	354	23	-	-	PUNCT
ejpam-5839	354	24	neutrosophic	neutrosophic	ADJ
ejpam-5839	354	25	riemann	riemann	PROPN
ejpam-5839	354	26	integral∫	integral∫	NOUN
ejpam-5839	354	27	b1	b1	NOUN
ejpam-5839	354	28	a1	a1	NOUN
ejpam-5839	354	29	f̃q(x)dx	f̃q(x)dx	NOUN
ejpam-5839	354	30	is	be	AUX
ejpam-5839	354	31	a	a	DET
ejpam-5839	354	32	closed	closed	ADJ
ejpam-5839	354	33	quadri	quadri	NOUN
ejpam-5839	354	34	-	-	PUNCT
ejpam-5839	354	35	neutrosophic	neutrosophic	ADJ
ejpam-5839	354	36	single	single	ADJ
ejpam-5839	354	37	number	number	NOUN
ejpam-5839	354	38	(	(	PUNCT
ejpam-5839	354	39	qnsn	qnsn	PROPN
ejpam-5839	354	40	)	)	PUNCT
ejpam-5839	354	41	.	.	PUNCT
ejpam-5839	355	1	the	the	PRON
ejpam-5839	355	2	(	(	PUNCT
ejpam-5839	355	3	i	i	PROPN
ejpam-5839	355	4	,	,	PUNCT
ejpam-5839	355	5	j	j	PROPN
ejpam-5839	355	6	,	,	PUNCT
ejpam-5839	355	7	k	k	PROPN
ejpam-5839	355	8	,	,	PUNCT
ejpam-5839	355	9	l)-cut	l)-cut	VERB
ejpam-5839	355	10	of∫	of∫	PROPN
ejpam-5839	355	11	b1	b1	PROPN
ejpam-5839	355	12	a1	a1	PROPN
ejpam-5839	355	13	f̃q(x)dx	f̃q(x)dx	PROPN
ejpam-5839	355	14	a.	a.	NOUN
ejpam-5839	355	15	shihadeh	shihadeh	NOUN
ejpam-5839	355	16	et	et	PROPN
ejpam-5839	355	17	al	al	PROPN
ejpam-5839	355	18	.	.	PUNCT
ejpam-5839	355	19	/	/	SYM
ejpam-5839	355	20	eur	eur	PROPN
ejpam-5839	355	21	.	.	PUNCT
ejpam-5839	356	1	j.	j.	PROPN
ejpam-5839	356	2	pure	pure	PROPN
ejpam-5839	356	3	appl	appl	PROPN
ejpam-5839	356	4	.	.	PROPN
ejpam-5839	356	5	math	math	PROPN
ejpam-5839	356	6	,	,	PUNCT
ejpam-5839	356	7	18	18	NUM
ejpam-5839	356	8	(	(	PUNCT
ejpam-5839	356	9	2	2	NUM
ejpam-5839	356	10	)	)	PUNCT
ejpam-5839	356	11	(	(	PUNCT
ejpam-5839	356	12	2025	2025	NUM
ejpam-5839	356	13	)	)	PUNCT
ejpam-5839	356	14	,	,	PUNCT
ejpam-5839	356	15	5839	5839	NUM
ejpam-5839	356	16	15	15	NUM
ejpam-5839	356	17	of	of	ADP
ejpam-5839	356	18	54	54	NUM
ejpam-5839	356	19	is	be	AUX
ejpam-5839	356	20	given	give	VERB
ejpam-5839	356	21	by	by	ADP
ejpam-5839	356	22	:	:	PUNCT
ejpam-5839	356	23	(	(	PUNCT
ejpam-5839	356	24	∫	∫	PROPN
ejpam-5839	356	25	b1	b1	PROPN
ejpam-5839	356	26	a1	a1	PROPN
ejpam-5839	356	27	f̃q(x)dx	f̃q(x)dx	PROPN
ejpam-5839	356	28	)	)	PUNCT
ejpam-5839	357	1	(	(	PUNCT
ejpam-5839	357	2	i	i	PROPN
ejpam-5839	357	3	,	,	PUNCT
ejpam-5839	357	4	j	j	PROPN
ejpam-5839	357	5	,	,	PUNCT
ejpam-5839	357	6	k	k	PROPN
ejpam-5839	357	7	,	,	PUNCT
ejpam-5839	357	8	l	l	NOUN
ejpam-5839	357	9	)	)	PUNCT
ejpam-5839	357	10	=	=	SYM
ejpam-5839	357	11			NOUN
ejpam-5839	358	1	[	[	X
ejpam-5839	358	2	∫	∫	X
ejpam-5839	358	3	b1	b1	NOUN
ejpam-5839	358	4	a1	a1	PROPN
ejpam-5839	358	5	f̃lqi(x)dx	f̃lqi(x)dx	PROPN
ejpam-5839	358	6	,	,	PUNCT
ejpam-5839	358	7	∫	∫	PROPN
ejpam-5839	358	8	b1	b1	PROPN
ejpam-5839	358	9	a1	a1	PROPN
ejpam-5839	358	10	f̃uqi(x)dx	f̃uqi(x)dx	VERB
ejpam-5839	358	11	]	]	PUNCT
ejpam-5839	358	12	,	,	PUNCT
ejpam-5839	358	13	[	[	X
ejpam-5839	358	14	∫	∫	X
ejpam-5839	358	15	b1	b1	NOUN
ejpam-5839	358	16	a1	a1	NOUN
ejpam-5839	358	17	f̃lqj(x)dx	f̃lqj(x)dx	PROPN
ejpam-5839	358	18	,	,	PUNCT
ejpam-5839	358	19	∫	∫	PROPN
ejpam-5839	358	20	b1	b1	PROPN
ejpam-5839	358	21	a1	a1	PROPN
ejpam-5839	358	22	f̃uqj(x)dx	f̃uqj(x)dx	VERB
ejpam-5839	358	23	]	]	PUNCT
ejpam-5839	358	24	,	,	PUNCT
ejpam-5839	358	25	[	[	X
ejpam-5839	358	26	∫	∫	X
ejpam-5839	358	27	b1	b1	NOUN
ejpam-5839	358	28	a1	a1	NOUN
ejpam-5839	358	29	f̃lqk(x)dx	f̃lqk(x)dx	NOUN
ejpam-5839	358	30	,	,	PUNCT
ejpam-5839	358	31	∫	∫	PROPN
ejpam-5839	358	32	b1	b1	PROPN
ejpam-5839	358	33	a1	a1	PROPN
ejpam-5839	358	34	f̃uqk(x)dx	f̃uqk(x)dx	PROPN
ejpam-5839	358	35	]	]	PUNCT
ejpam-5839	358	36	,	,	PUNCT
ejpam-5839	358	37	[	[	X
ejpam-5839	358	38	∫	∫	X
ejpam-5839	358	39	b1	b1	NOUN
ejpam-5839	358	40	a1	a1	PROPN
ejpam-5839	358	41	f̃lql(x)dx	f̃lql(x)dx	VERB
ejpam-5839	358	42	,	,	PUNCT
ejpam-5839	358	43	∫	∫	PROPN
ejpam-5839	358	44	b1	b1	PROPN
ejpam-5839	358	45	a1	a1	NOUN
ejpam-5839	358	46	f̃uql(x)dx	f̃uql(x)dx	VERB
ejpam-5839	358	47	]	]	PUNCT
ejpam-5839	358	48			NUM
ejpam-5839	358	49	where	where	SCONJ
ejpam-5839	358	50	[	[	X
ejpam-5839	358	51	̃flqi(x	̃flqi(x	NOUN
ejpam-5839	358	52	)	)	PUNCT
ejpam-5839	358	53	,	,	PUNCT
ejpam-5839	358	54	f̃	f̃	PROPN
ejpam-5839	358	55	u	u	PROPN
ejpam-5839	358	56	qi(x	qi(x	NUM
ejpam-5839	358	57	)	)	PUNCT
ejpam-5839	358	58	]	]	PUNCT
ejpam-5839	358	59	,	,	PUNCT
ejpam-5839	358	60	[	[	X
ejpam-5839	358	61	̃f	̃f	PROPN
ejpam-5839	358	62	l	l	NOUN
ejpam-5839	358	63	qj(x	qj(x	NUM
ejpam-5839	358	64	)	)	PUNCT
ejpam-5839	358	65	,	,	PUNCT
ejpam-5839	358	66	f̃	f̃	PROPN
ejpam-5839	358	67	u	u	PROPN
ejpam-5839	358	68	qj(x	qj(x	NUM
ejpam-5839	358	69	)	)	PUNCT
ejpam-5839	358	70	]	]	PUNCT
ejpam-5839	358	71	,	,	PUNCT
ejpam-5839	358	72	[	[	X
ejpam-5839	358	73	̃flqk(x	̃flqk(x	NOUN
ejpam-5839	358	74	)	)	PUNCT
ejpam-5839	358	75	,	,	PUNCT
ejpam-5839	358	76	f̃	f̃	PROPN
ejpam-5839	358	77	u	u	PROPN
ejpam-5839	358	78	qk(x	qk(x	NOUN
ejpam-5839	358	79	)	)	PUNCT
ejpam-5839	358	80	]	]	PUNCT
ejpam-5839	358	81	,	,	PUNCT
ejpam-5839	358	82	and	and	CCONJ
ejpam-5839	358	83	[	[	X
ejpam-5839	358	84	̃flql(x	̃flql(x	X
ejpam-5839	358	85	)	)	PUNCT
ejpam-5839	358	86	,	,	PUNCT
ejpam-5839	358	87	f̃	f̃	PROPN
ejpam-5839	358	88	u	u	PROPN
ejpam-5839	358	89	ql(x	ql(x	PROPN
ejpam-5839	358	90	)	)	PUNCT
ejpam-5839	358	91	]	]	PUNCT
ejpam-5839	359	1	denote	denote	VERB
ejpam-5839	359	2	the	the	DET
ejpam-5839	359	3	(	(	PUNCT
ejpam-5839	359	4	i	i	PROPN
ejpam-5839	359	5	,	,	PUNCT
ejpam-5839	359	6	j	j	PROPN
ejpam-5839	359	7	,	,	PUNCT
ejpam-5839	359	8	k	k	PROPN
ejpam-5839	359	9	,	,	PUNCT
ejpam-5839	359	10	l)cut	l)cut	PROPN
ejpam-5839	359	11	of	of	ADP
ejpam-5839	359	12	f̃q(x	f̃q(x	ADV
ejpam-5839	359	13	)	)	PUNCT
ejpam-5839	359	14	,	,	PUNCT
ejpam-5839	359	15	respectively	respectively	ADV
ejpam-5839	359	16	.	.	PUNCT
ejpam-5839	360	1	proof	proof	NOUN
ejpam-5839	360	2	.	.	PUNCT
ejpam-5839	361	1	let	let	VERB
ejpam-5839	361	2	q(i	q(i	NOUN
ejpam-5839	361	3	,	,	PUNCT
ejpam-5839	361	4	j	j	PROPN
ejpam-5839	361	5	,	,	PUNCT
ejpam-5839	361	6	k	k	PROPN
ejpam-5839	361	7	,	,	PUNCT
ejpam-5839	361	8	l	l	NOUN
ejpam-5839	361	9	)	)	PUNCT
ejpam-5839	361	10	=	=	SYM
ejpam-5839	362	1			NUM
ejpam-5839	362	2	∫	∫	PROPN
ejpam-5839	362	3	f̃	f̃	PROPN
ejpam-5839	362	4	l(x	l(x	PROPN
ejpam-5839	362	5	)	)	PUNCT
ejpam-5839	362	6	qi	qi	PROPN
ejpam-5839	362	7	d(x	d(x	PROPN
ejpam-5839	362	8	)	)	PUNCT
ejpam-5839	362	9	,	,	PUNCT
ejpam-5839	362	10	∫	∫	PROPN
ejpam-5839	362	11	f̃	f̃	PROPN
ejpam-5839	362	12	u(x	u(x	PROPN
ejpam-5839	362	13	)	)	PUNCT
ejpam-5839	362	14	qi	qi	PROPN
ejpam-5839	362	15	d(x)∫	d(x)∫	NOUN
ejpam-5839	362	16	f̃	f̃	PROPN
ejpam-5839	362	17	l(x	l(x	PROPN
ejpam-5839	362	18	)	)	PUNCT
ejpam-5839	362	19	qj	qj	PROPN
ejpam-5839	362	20	d(x	d(x	PROPN
ejpam-5839	362	21	)	)	PUNCT
ejpam-5839	362	22	,	,	PUNCT
ejpam-5839	362	23	∫	∫	PROPN
ejpam-5839	362	24	f̃	f̃	PROPN
ejpam-5839	362	25	u(x	u(x	PROPN
ejpam-5839	362	26	)	)	PUNCT
ejpam-5839	362	27	qj	qj	PROPN
ejpam-5839	362	28	d(x)∫	d(x)∫	NOUN
ejpam-5839	362	29	f̃	f̃	PROPN
ejpam-5839	362	30	l(x	l(x	PROPN
ejpam-5839	362	31	)	)	PUNCT
ejpam-5839	362	32	qk	qk	ADP
ejpam-5839	362	33	d(x	d(x	PROPN
ejpam-5839	362	34	)	)	PUNCT
ejpam-5839	362	35	,	,	PUNCT
ejpam-5839	362	36	∫	∫	PROPN
ejpam-5839	362	37	f̃	f̃	PROPN
ejpam-5839	362	38	u(x	u(x	PROPN
ejpam-5839	362	39	)	)	PUNCT
ejpam-5839	362	40	qk	qk	ADP
ejpam-5839	362	41	d(x)∫	d(x)∫	NOUN
ejpam-5839	362	42	f̃	f̃	PROPN
ejpam-5839	362	43	l(x	l(x	PROPN
ejpam-5839	362	44	)	)	PUNCT
ejpam-5839	362	45	ql	ql	NOUN
ejpam-5839	362	46	d(x	d(x	NOUN
ejpam-5839	362	47	)	)	PUNCT
ejpam-5839	362	48	,	,	PUNCT
ejpam-5839	362	49	∫	∫	PROPN
ejpam-5839	362	50	f̃	f̃	PROPN
ejpam-5839	362	51	u(x	u(x	PROPN
ejpam-5839	362	52	)	)	PUNCT
ejpam-5839	362	53	ql	ql	NOUN
ejpam-5839	362	54	d(x	d(x	NOUN
ejpam-5839	362	55	)	)	PUNCT
ejpam-5839	362	56			NOUN
ejpam-5839	362	57	for	for	ADP
ejpam-5839	362	58	i2	i2	PROPN
ejpam-5839	362	59	≻	≻	PROPN
ejpam-5839	362	60	i1	i1	PROPN
ejpam-5839	362	61	,	,	PUNCT
ejpam-5839	362	62	j2	j2	PROPN
ejpam-5839	362	63	≺	≺	NOUN
ejpam-5839	362	64	j1	j1	PROPN
ejpam-5839	362	65	,	,	PUNCT
ejpam-5839	362	66	k2	k2	ADJ
ejpam-5839	362	67	≺	≺	NOUN
ejpam-5839	362	68	k1	k1	NOUN
ejpam-5839	362	69	,	,	PUNCT
ejpam-5839	362	70	l2	l2	NOUN
ejpam-5839	362	71	≺	≺	NOUN
ejpam-5839	362	72	l1	l1	PROPN
ejpam-5839	362	73	,	,	PUNCT
ejpam-5839	362	74	we	we	PRON
ejpam-5839	362	75	have	have	AUX
ejpam-5839	362	76	:	:	PUNCT
ejpam-5839	362	77	f̃	f̃	PROPN
ejpam-5839	362	78	l(x	l(x	PROPN
ejpam-5839	362	79	)	)	PUNCT
ejpam-5839	362	80	qi1	qi1	NOUN
ejpam-5839	362	81	⪯	⪯	NOUN
ejpam-5839	362	82	f̃	f̃	PROPN
ejpam-5839	362	83	l(x	l(x	PROPN
ejpam-5839	362	84	)	)	PUNCT
ejpam-5839	363	1	qi2	qi2	ADV
ejpam-5839	363	2	,	,	PUNCT
ejpam-5839	363	3	f̃	f̃	PROPN
ejpam-5839	363	4	u(x	u(x	PROPN
ejpam-5839	363	5	)	)	PUNCT
ejpam-5839	363	6	qi1	qi1	NOUN
ejpam-5839	363	7	⪰	⪰	NOUN
ejpam-5839	363	8	f̃	f̃	PROPN
ejpam-5839	363	9	u(x	u(x	PROPN
ejpam-5839	363	10	)	)	PUNCT
ejpam-5839	363	11	qi2	qi2	ADV
ejpam-5839	363	12	,	,	PUNCT
ejpam-5839	363	13	f̃	f̃	PROPN
ejpam-5839	363	14	l(x	l(x	PROPN
ejpam-5839	363	15	)	)	PUNCT
ejpam-5839	363	16	qj1	qj1	NOUN
ejpam-5839	363	17	⪰	⪰	NOUN
ejpam-5839	363	18	f̃	f̃	PROPN
ejpam-5839	363	19	l(x	l(x	PROPN
ejpam-5839	363	20	)	)	PUNCT
ejpam-5839	363	21	qj2	qj2	INTJ
ejpam-5839	363	22	,	,	PUNCT
ejpam-5839	363	23	f̃	f̃	PROPN
ejpam-5839	363	24	u(x	u(x	PROPN
ejpam-5839	363	25	)	)	PUNCT
ejpam-5839	363	26	qj1	qj1	NOUN
ejpam-5839	363	27	⪯	⪯	NOUN
ejpam-5839	363	28	f̃	f̃	PROPN
ejpam-5839	363	29	u(x	u(x	PROPN
ejpam-5839	363	30	)	)	PUNCT
ejpam-5839	363	31	qj2	qj2	ADV
ejpam-5839	363	32	,	,	PUNCT
ejpam-5839	363	33	f̃	f̃	PROPN
ejpam-5839	363	34	l(x	l(x	PROPN
ejpam-5839	363	35	)	)	PUNCT
ejpam-5839	363	36	qk1	qk1	NOUN
ejpam-5839	363	37	⪰	⪰	NOUN
ejpam-5839	363	38	f̃	f̃	PROPN
ejpam-5839	363	39	l(x	l(x	PROPN
ejpam-5839	363	40	)	)	PUNCT
ejpam-5839	363	41	qk2	qk2	NOUN
ejpam-5839	363	42	,	,	PUNCT
ejpam-5839	363	43	f̃	f̃	PROPN
ejpam-5839	363	44	u(x	u(x	PROPN
ejpam-5839	363	45	)	)	PUNCT
ejpam-5839	363	46	qk1	qk1	PROPN
ejpam-5839	363	47	⪯	⪯	NOUN
ejpam-5839	363	48	f̃	f̃	PROPN
ejpam-5839	363	49	u(x	u(x	PROPN
ejpam-5839	363	50	)	)	PUNCT
ejpam-5839	363	51	qk2	qk2	NOUN
ejpam-5839	363	52	,	,	PUNCT
ejpam-5839	363	53	f̃	f̃	PROPN
ejpam-5839	363	54	l(x	l(x	PROPN
ejpam-5839	363	55	)	)	PUNCT
ejpam-5839	363	56	ql1	ql1	NOUN
ejpam-5839	363	57	⪰	⪰	NOUN
ejpam-5839	363	58	f̃	f̃	PROPN
ejpam-5839	363	59	l(x	l(x	PROPN
ejpam-5839	363	60	)	)	PUNCT
ejpam-5839	363	61	ql2	ql2	NOUN
ejpam-5839	363	62	,	,	PUNCT
ejpam-5839	363	63	f̃	f̃	PROPN
ejpam-5839	363	64	u(x	u(x	PROPN
ejpam-5839	363	65	)	)	PUNCT
ejpam-5839	363	66	ql1	ql1	NOUN
ejpam-5839	363	67	⪯	⪯	NOUN
ejpam-5839	363	68	f̃	f̃	PROPN
ejpam-5839	363	69	u(x	u(x	PROPN
ejpam-5839	363	70	)	)	PUNCT
ejpam-5839	363	71	ql2	ql2	NOUN
ejpam-5839	363	72	.	.	PUNCT
ejpam-5839	364	1	then	then	ADV
ejpam-5839	364	2	,	,	PUNCT
ejpam-5839	364	3	q(i2	q(i2	PROPN
ejpam-5839	364	4	,	,	PUNCT
ejpam-5839	364	5	j2	j2	PROPN
ejpam-5839	364	6	,	,	PUNCT
ejpam-5839	364	7	k2	k2	NOUN
ejpam-5839	364	8	,	,	PUNCT
ejpam-5839	364	9	l2	l2	NOUN
ejpam-5839	364	10	)	)	PUNCT
ejpam-5839	364	11	⊆	⊆	NUM
ejpam-5839	364	12	q(i1	q(i1	NOUN
ejpam-5839	364	13	,	,	PUNCT
ejpam-5839	364	14	j1	j1	PROPN
ejpam-5839	364	15	,	,	PUNCT
ejpam-5839	364	16	k1	k1	PROPN
ejpam-5839	364	17	,	,	PUNCT
ejpam-5839	364	18	l1	l1	PROPN
ejpam-5839	364	19	)	)	PUNCT
ejpam-5839	364	20	for	for	ADP
ejpam-5839	364	21	0	0	NUM
ejpam-5839	364	22	⪯	⪯	VERB
ejpam-5839	364	23	in1	in1	PROPN
ejpam-5839	364	24	⪯	⪯	PROPN
ejpam-5839	364	25	1	1	NUM
ejpam-5839	364	26	,	,	PUNCT
ejpam-5839	364	27	we	we	PRON
ejpam-5839	364	28	get	get	VERB
ejpam-5839	364	29	:	:	PUNCT
ejpam-5839	364	30	f̃q0l(x	f̃q0l(x	PROPN
ejpam-5839	364	31	)	)	PUNCT
ejpam-5839	364	32	⪯	⪯	NOUN
ejpam-5839	364	33	f̃qin1	f̃qin1	PROPN
ejpam-5839	364	34	(	(	PUNCT
ejpam-5839	364	35	x	x	X
ejpam-5839	364	36	)	)	PUNCT
ejpam-5839	364	37	⪯	⪯	PROPN
ejpam-5839	364	38	f̃q1l(x	f̃q1l(x	PROPN
ejpam-5839	364	39	)	)	PUNCT
ejpam-5839	364	40	.	.	PUNCT
ejpam-5839	365	1	thus	thus	ADV
ejpam-5839	365	2	,	,	PUNCT
ejpam-5839	365	3	|̃fqin1	|̃fqin1	X
ejpam-5839	365	4	(	(	PUNCT
ejpam-5839	365	5	x)|	x)|	PROPN
ejpam-5839	365	6	⪯	⪯	NOUN
ejpam-5839	365	7	max{|̃fq0l(x)|	max{|̃fq0l(x)|	PROPN
ejpam-5839	365	8	,	,	PUNCT
ejpam-5839	365	9	|̃fq1l(x)|	|̃fq1l(x)|	PROPN
ejpam-5839	365	10	}	}	PUNCT
ejpam-5839	365	11	=	=	SYM
ejpam-5839	365	12	h(x	h(x	PROPN
ejpam-5839	365	13	)	)	PUNCT
ejpam-5839	365	14	.	.	PUNCT
ejpam-5839	366	1	since	since	SCONJ
ejpam-5839	366	2	f̃q0l(x	f̃q0l(x	PROPN
ejpam-5839	366	3	)	)	PUNCT
ejpam-5839	366	4	and	and	CCONJ
ejpam-5839	366	5	f̃q1l(x	f̃q1l(x	NOUN
ejpam-5839	366	6	)	)	PUNCT
ejpam-5839	366	7	are	be	AUX
ejpam-5839	366	8	qudri	qudri	NOUN
ejpam-5839	366	9	-	-	PUNCT
ejpam-5839	366	10	neutrosophic	neutrosophic	ADJ
ejpam-5839	366	11	riemann	riemann	PROPN
ejpam-5839	366	12	integrable	integrable	ADJ
ejpam-5839	366	13	on	on	ADP
ejpam-5839	366	14	[	[	X
ejpam-5839	366	15	a1	a1	NOUN
ejpam-5839	366	16	,	,	PUNCT
ejpam-5839	366	17	b1	b1	NOUN
ejpam-5839	366	18	]	]	PUNCT
ejpam-5839	366	19	,	,	PUNCT
ejpam-5839	366	20	|̃fq0l(x)|	|̃fq0l(x)|	PROPN
ejpam-5839	366	21	,	,	PUNCT
ejpam-5839	366	22	|̃fq1l(x)|	|̃fq1l(x)|	PROPN
ejpam-5839	366	23	,	,	PUNCT
ejpam-5839	366	24	and	and	CCONJ
ejpam-5839	366	25	h(x	h(x	PROPN
ejpam-5839	366	26	)	)	PUNCT
ejpam-5839	366	27	are	be	AUX
ejpam-5839	366	28	also	also	ADV
ejpam-5839	366	29	qudri	qudri	PROPN
ejpam-5839	366	30	-	-	PUNCT
ejpam-5839	366	31	neutrosophic	neutrosophic	ADJ
ejpam-5839	366	32	riemann	riemann	PROPN
ejpam-5839	366	33	integrable	integrable	ADJ
ejpam-5839	366	34	on	on	ADP
ejpam-5839	366	35	[	[	X
ejpam-5839	366	36	a1	a1	NOUN
ejpam-5839	366	37	,	,	PUNCT
ejpam-5839	366	38	b1	b1	NOUN
ejpam-5839	366	39	]	]	PUNCT
ejpam-5839	366	40	.	.	PUNCT
ejpam-5839	367	1	from	from	ADP
ejpam-5839	367	2	proposition	proposition	NOUN
ejpam-5839	367	3	9	9	NUM
ejpam-5839	367	4	,	,	PUNCT
ejpam-5839	367	5	it	it	PRON
ejpam-5839	367	6	follows	follow	VERB
ejpam-5839	367	7	that	that	SCONJ
ejpam-5839	367	8	h(x	h(x	PROPN
ejpam-5839	367	9	)	)	PUNCT
ejpam-5839	367	10	is	be	AUX
ejpam-5839	367	11	qudri	qudri	PROPN
ejpam-5839	367	12	-	-	PUNCT
ejpam-5839	367	13	neutrosophic	neutrosophic	ADJ
ejpam-5839	367	14	lebesgue	lebesgue	NOUN
ejpam-5839	367	15	integrable	integrable	ADJ
ejpam-5839	367	16	on	on	ADP
ejpam-5839	367	17	[	[	X
ejpam-5839	367	18	a1	a1	NOUN
ejpam-5839	367	19	,	,	PUNCT
ejpam-5839	367	20	b1	b1	NOUN
ejpam-5839	367	21	]	]	PUNCT
ejpam-5839	367	22	.	.	PUNCT
ejpam-5839	368	1	now	now	ADV
ejpam-5839	368	2	we	we	PRON
ejpam-5839	368	3	should	should	AUX
ejpam-5839	368	4	apply	apply	VERB
ejpam-5839	368	5	the	the	DET
ejpam-5839	368	6	quadri	quadri	PROPN
ejpam-5839	368	7	-	-	PUNCT
ejpam-5839	368	8	neutrosophic	neutrosophic	ADJ
ejpam-5839	368	9	lebesgue	lebesgue	NOUN
ejpam-5839	368	10	dominated	dominate	VERB
ejpam-5839	368	11	convergence	convergence	NOUN
ejpam-5839	368	12	theorem	theorem	VERB
ejpam-5839	368	13	.	.	PUNCT
ejpam-5839	369	1	for	for	ADP
ejpam-5839	369	2	in1	in1	PROPN
ejpam-5839	369	3	↑	↑	PROPN
ejpam-5839	369	4	i1	i1	PROPN
ejpam-5839	369	5	,	,	PUNCT
ejpam-5839	369	6	we	we	PRON
ejpam-5839	369	7	have	have	VERB
ejpam-5839	369	8	:	:	PUNCT
ejpam-5839	370	1	lim	lim	PROPN
ejpam-5839	370	2	n→∞	n→∞	NUM
ejpam-5839	370	3	∫	∫	PROPN
ejpam-5839	370	4	b1	b1	PROPN
ejpam-5839	370	5	a1	a1	NOUN
ejpam-5839	370	6	f̃lqin1	f̃lqin1	ADP
ejpam-5839	370	7	(	(	PUNCT
ejpam-5839	370	8	x)d(x	x)d(x	NOUN
ejpam-5839	370	9	)	)	PUNCT
ejpam-5839	370	10	=	=	SYM
ejpam-5839	370	11	∫	∫	PROPN
ejpam-5839	370	12	b1	b1	PROPN
ejpam-5839	370	13	a1	a1	NOUN
ejpam-5839	370	14	f̃uqi1(x)d(x	f̃uqi1(x)d(x	NOUN
ejpam-5839	370	15	)	)	PUNCT
ejpam-5839	370	16	.	.	PUNCT
ejpam-5839	371	1	since	since	SCONJ
ejpam-5839	371	2	f̃q(x	f̃q(x	NUM
ejpam-5839	371	3	)	)	PUNCT
ejpam-5839	371	4	is	be	AUX
ejpam-5839	371	5	a	a	DET
ejpam-5839	371	6	closed	closed	ADJ
ejpam-5839	371	7	qnvf	qnvf	ADJ
ejpam-5839	371	8	,	,	PUNCT
ejpam-5839	371	9	we	we	PRON
ejpam-5839	371	10	have	have	VERB
ejpam-5839	371	11	lim	lim	PROPN
ejpam-5839	371	12	n→∞	n→∞	PRON
ejpam-5839	371	13	f̃lqin1	f̃lqin1	ADP
ejpam-5839	371	14	(	(	PUNCT
ejpam-5839	371	15	x	x	NOUN
ejpam-5839	371	16	)	)	PUNCT
ejpam-5839	372	1	=	=	SYM
ejpam-5839	372	2	f̃lqin1	f̃lqin1	ADP
ejpam-5839	372	3	(	(	PUNCT
ejpam-5839	372	4	x	x	NOUN
ejpam-5839	372	5	)	)	PUNCT
ejpam-5839	372	6	,	,	PUNCT
ejpam-5839	372	7	a.	a.	NOUN
ejpam-5839	372	8	shihadeh	shihadeh	VERB
ejpam-5839	372	9	et	et	PROPN
ejpam-5839	372	10	al	al	PROPN
ejpam-5839	372	11	.	.	PUNCT
ejpam-5839	372	12	/	/	SYM
ejpam-5839	372	13	eur	eur	PROPN
ejpam-5839	372	14	.	.	PUNCT
ejpam-5839	373	1	j.	j.	PROPN
ejpam-5839	373	2	pure	pure	PROPN
ejpam-5839	373	3	appl	appl	PROPN
ejpam-5839	373	4	.	.	PROPN
ejpam-5839	373	5	math	math	PROPN
ejpam-5839	373	6	,	,	PUNCT
ejpam-5839	373	7	18	18	NUM
ejpam-5839	373	8	(	(	PUNCT
ejpam-5839	373	9	2	2	NUM
ejpam-5839	373	10	)	)	PUNCT
ejpam-5839	373	11	(	(	PUNCT
ejpam-5839	373	12	2025	2025	NUM
ejpam-5839	373	13	)	)	PUNCT
ejpam-5839	373	14	,	,	PUNCT
ejpam-5839	373	15	5839	5839	NUM
ejpam-5839	373	16	16	16	NUM
ejpam-5839	373	17	of	of	ADP
ejpam-5839	373	18	54	54	NUM
ejpam-5839	373	19	by	by	ADP
ejpam-5839	373	20	definition	definition	NOUN
ejpam-5839	373	21	9	9	NUM
ejpam-5839	373	22	.	.	PUNCT
ejpam-5839	374	1	again	again	ADV
ejpam-5839	374	2	,	,	PUNCT
ejpam-5839	374	3	for	for	ADP
ejpam-5839	374	4	0	0	NUM
ejpam-5839	374	5	⪯	⪯	VERB
ejpam-5839	374	6	in1	in1	PROPN
ejpam-5839	374	7	⪯	⪯	PROPN
ejpam-5839	374	8	1	1	NUM
ejpam-5839	374	9	,	,	PUNCT
ejpam-5839	374	10	we	we	PRON
ejpam-5839	374	11	have	have	VERB
ejpam-5839	374	12	:	:	PUNCT
ejpam-5839	374	13	f̃uq1(x	f̃uq1(x	NUM
ejpam-5839	374	14	)	)	PUNCT
ejpam-5839	374	15	⪯	⪯	NOUN
ejpam-5839	374	16	f̃lqin1	f̃lqin1	ADP
ejpam-5839	374	17	(	(	PUNCT
ejpam-5839	374	18	x	x	NOUN
ejpam-5839	374	19	)	)	PUNCT
ejpam-5839	374	20	⪯	⪯	NOUN
ejpam-5839	374	21	f̃uq0(x	f̃uq0(x	NUM
ejpam-5839	374	22	)	)	PUNCT
ejpam-5839	374	23	.	.	PUNCT
ejpam-5839	375	1	then	then	ADV
ejpam-5839	375	2	,	,	PUNCT
ejpam-5839	375	3	|̃fuqin1	|̃fuqin1	AUX
ejpam-5839	375	4	(	(	PUNCT
ejpam-5839	375	5	x)|	x)|	PROPN
ejpam-5839	375	6	⪯	⪯	PROPN
ejpam-5839	375	7	max{|̃fuq1(x)|	max{|̃fuq1(x)|	NOUN
ejpam-5839	375	8	,	,	PUNCT
ejpam-5839	375	9	|̃fuq0(x)|	|̃fuq0(x)|	VERB
ejpam-5839	375	10	}	}	PUNCT
ejpam-5839	375	11	=	=	SYM
ejpam-5839	375	12	g(x	g(x	NOUN
ejpam-5839	375	13	)	)	PUNCT
ejpam-5839	375	14	.	.	PUNCT
ejpam-5839	376	1	by	by	ADP
ejpam-5839	376	2	a	a	DET
ejpam-5839	376	3	similar	similar	ADJ
ejpam-5839	376	4	fashion	fashion	NOUN
ejpam-5839	376	5	,	,	PUNCT
ejpam-5839	376	6	we	we	PRON
ejpam-5839	376	7	can	can	AUX
ejpam-5839	376	8	argue	argue	VERB
ejpam-5839	376	9	:	:	PUNCT
ejpam-5839	377	1	lim	lim	PROPN
ejpam-5839	377	2	n→∞	n→∞	NUM
ejpam-5839	377	3	∫	∫	PROPN
ejpam-5839	377	4	b1	b1	PROPN
ejpam-5839	377	5	a1	a1	NOUN
ejpam-5839	377	6	f̃uqin1	f̃uqin1	PROPN
ejpam-5839	377	7	(	(	PUNCT
ejpam-5839	377	8	x)d(x	x)d(x	NOUN
ejpam-5839	377	9	)	)	PUNCT
ejpam-5839	377	10	=	=	SYM
ejpam-5839	377	11	∫	∫	PROPN
ejpam-5839	377	12	b1	b1	PROPN
ejpam-5839	377	13	a1	a1	NOUN
ejpam-5839	377	14	f̃uqi1(x)d(x	f̃uqi1(x)d(x	NOUN
ejpam-5839	377	15	)	)	PUNCT
ejpam-5839	377	16	.	.	PUNCT
ejpam-5839	378	1	since	since	SCONJ
ejpam-5839	378	2	f̃q(x	f̃q(x	NUM
ejpam-5839	378	3	)	)	PUNCT
ejpam-5839	378	4	is	be	AUX
ejpam-5839	378	5	a	a	DET
ejpam-5839	378	6	closed	closed	ADJ
ejpam-5839	378	7	qnvf	qnvf	ADJ
ejpam-5839	378	8	,	,	PUNCT
ejpam-5839	378	9	then	then	ADV
ejpam-5839	378	10	:	:	PUNCT
ejpam-5839	378	11	lim	lim	PROPN
ejpam-5839	378	12	n→∞	n→∞	PRON
ejpam-5839	378	13	f̃lqin1	f̃lqin1	ADP
ejpam-5839	378	14	(	(	PUNCT
ejpam-5839	378	15	x	x	NOUN
ejpam-5839	378	16	)	)	PUNCT
ejpam-5839	379	1	=	=	SYM
ejpam-5839	379	2	f̃lqin1	f̃lqin1	ADP
ejpam-5839	379	3	(	(	PUNCT
ejpam-5839	379	4	x	x	NOUN
ejpam-5839	379	5	)	)	PUNCT
ejpam-5839	379	6	.	.	PUNCT
ejpam-5839	380	1	by	by	ADP
ejpam-5839	380	2	a	a	DET
ejpam-5839	380	3	similar	similar	ADJ
ejpam-5839	380	4	process	process	NOUN
ejpam-5839	380	5	,	,	PUNCT
ejpam-5839	380	6	we	we	PRON
ejpam-5839	380	7	have	have	VERB
ejpam-5839	380	8	:	:	PUNCT
ejpam-5839	380	9	lim	lim	PROPN
ejpam-5839	380	10	n→∞	n→∞	NUM
ejpam-5839	380	11	∫	∫	PROPN
ejpam-5839	380	12	b1	b1	PROPN
ejpam-5839	380	13	a1	a1	PROPN
ejpam-5839	380	14	f̃lqjn1	f̃lqjn1	PROPN
ejpam-5839	380	15	(	(	PUNCT
ejpam-5839	380	16	x)d(x	x)d(x	NOUN
ejpam-5839	380	17	)	)	PUNCT
ejpam-5839	380	18	=	=	SYM
ejpam-5839	380	19	∫	∫	PROPN
ejpam-5839	380	20	b1	b1	PROPN
ejpam-5839	380	21	a1	a1	PROPN
ejpam-5839	380	22	f̃lqj1(x)d(x	f̃lqj1(x)d(x	PROPN
ejpam-5839	380	23	)	)	PUNCT
ejpam-5839	380	24	,	,	PUNCT
ejpam-5839	380	25	lim	lim	PROPN
ejpam-5839	380	26	n→∞	n→∞	NUM
ejpam-5839	380	27	∫	∫	PROPN
ejpam-5839	380	28	b1	b1	PROPN
ejpam-5839	380	29	a1	a1	NOUN
ejpam-5839	380	30	f̃uqjn1	f̃uqjn1	NOUN
ejpam-5839	380	31	(	(	PUNCT
ejpam-5839	380	32	x)d(x	x)d(x	NOUN
ejpam-5839	380	33	)	)	PUNCT
ejpam-5839	380	34	=	=	SYM
ejpam-5839	380	35	∫	∫	PROPN
ejpam-5839	380	36	b1	b1	PROPN
ejpam-5839	380	37	a1	a1	PROPN
ejpam-5839	380	38	f̃uqj1(x)d(x	f̃uqj1(x)d(x	NOUN
ejpam-5839	380	39	)	)	PUNCT
ejpam-5839	380	40	,	,	PUNCT
ejpam-5839	380	41	lim	lim	PROPN
ejpam-5839	380	42	n→∞	n→∞	NUM
ejpam-5839	380	43	∫	∫	PROPN
ejpam-5839	380	44	b1	b1	NOUN
ejpam-5839	380	45	a1	a1	NOUN
ejpam-5839	380	46	f̃lqkn1	f̃lqkn1	NOUN
ejpam-5839	380	47	(	(	PUNCT
ejpam-5839	380	48	x)d(x	x)d(x	NOUN
ejpam-5839	380	49	)	)	PUNCT
ejpam-5839	380	50	=	=	SYM
ejpam-5839	381	1	∫	∫	PROPN
ejpam-5839	381	2	b1	b1	PROPN
ejpam-5839	381	3	a1	a1	PROPN
ejpam-5839	381	4	f̃lqk1(x)d(x	f̃lqk1(x)d(x	NOUN
ejpam-5839	381	5	)	)	PUNCT
ejpam-5839	381	6	,	,	PUNCT
ejpam-5839	381	7	lim	lim	PROPN
ejpam-5839	381	8	n→∞	n→∞	NUM
ejpam-5839	381	9	∫	∫	PROPN
ejpam-5839	381	10	b1	b1	PROPN
ejpam-5839	381	11	a1	a1	PROPN
ejpam-5839	381	12	f̃uqkn1	f̃uqkn1	PROPN
ejpam-5839	381	13	(	(	PUNCT
ejpam-5839	381	14	x)d(x	x)d(x	NOUN
ejpam-5839	381	15	)	)	PUNCT
ejpam-5839	381	16	=	=	SYM
ejpam-5839	381	17	∫	∫	PROPN
ejpam-5839	381	18	b1	b1	NOUN
ejpam-5839	381	19	a1	a1	NOUN
ejpam-5839	381	20	f̃uqk1(x)d(x	f̃uqk1(x)d(x	PROPN
ejpam-5839	381	21	)	)	PUNCT
ejpam-5839	381	22	.	.	PUNCT
ejpam-5839	382	1	theorem	theorem	NOUN
ejpam-5839	382	2	3	3	NUM
ejpam-5839	382	3	.	.	PUNCT
ejpam-5839	383	1	if	if	SCONJ
ejpam-5839	383	2	f̃q(x	f̃q(x	NUM
ejpam-5839	383	3	)	)	PUNCT
ejpam-5839	383	4	is	be	AUX
ejpam-5839	383	5	a	a	DET
ejpam-5839	383	6	closed	closed	ADJ
ejpam-5839	383	7	bounded	bound	VERB
ejpam-5839	383	8	qnvf	qnvf	ADV
ejpam-5839	383	9	on	on	ADP
ejpam-5839	383	10	the	the	DET
ejpam-5839	383	11	closed	closed	ADJ
ejpam-5839	383	12	quadri	quadri	PROPN
ejpam-5839	383	13	-	-	PUNCT
ejpam-5839	383	14	neutrosophic	neutrosophic	ADJ
ejpam-5839	383	15	bounded	bound	VERB
ejpam-5839	383	16	interval	interval	NOUN
ejpam-5839	383	17	[	[	X
ejpam-5839	383	18	a1	a1	NOUN
ejpam-5839	383	19	,	,	PUNCT
ejpam-5839	383	20	b1	b1	NOUN
ejpam-5839	383	21	]	]	PUNCT
ejpam-5839	383	22	,	,	PUNCT
ejpam-5839	383	23	and	and	CCONJ
ejpam-5839	383	24	the	the	DET
ejpam-5839	383	25	functions	function	NOUN
ejpam-5839	383	26	f̃lqi	f̃lqi	X
ejpam-5839	383	27	(	(	PUNCT
ejpam-5839	383	28	x	x	NOUN
ejpam-5839	383	29	)	)	PUNCT
ejpam-5839	383	30	,	,	PUNCT
ejpam-5839	383	31	f̃uqi	f̃uqi	PROPN
ejpam-5839	383	32	(	(	PUNCT
ejpam-5839	383	33	x	x	NOUN
ejpam-5839	383	34	)	)	PUNCT
ejpam-5839	383	35	,	,	PUNCT
ejpam-5839	383	36	f̃lqj	f̃lqj	X
ejpam-5839	383	37	(	(	PUNCT
ejpam-5839	383	38	x	x	NOUN
ejpam-5839	383	39	)	)	PUNCT
ejpam-5839	383	40	,	,	PUNCT
ejpam-5839	383	41	f̃uqj	f̃uqj	NOUN
ejpam-5839	383	42	(	(	PUNCT
ejpam-5839	383	43	x	x	NOUN
ejpam-5839	383	44	)	)	PUNCT
ejpam-5839	383	45	,	,	PUNCT
ejpam-5839	383	46	f̃lqk	f̃lqk	PROPN
ejpam-5839	383	47	(	(	PUNCT
ejpam-5839	383	48	x	x	NOUN
ejpam-5839	383	49	)	)	PUNCT
ejpam-5839	383	50	,	,	PUNCT
ejpam-5839	383	51	f̃uqk	f̃uqk	NOUN
ejpam-5839	383	52	(	(	PUNCT
ejpam-5839	383	53	x	x	NOUN
ejpam-5839	383	54	)	)	PUNCT
ejpam-5839	383	55	,	,	PUNCT
ejpam-5839	383	56	f̃lql	f̃lql	NOUN
ejpam-5839	383	57	(	(	PUNCT
ejpam-5839	383	58	x	x	NOUN
ejpam-5839	383	59	)	)	PUNCT
ejpam-5839	383	60	,	,	PUNCT
ejpam-5839	383	61	f̃uql	f̃uql	NOUN
ejpam-5839	383	62	(	(	PUNCT
ejpam-5839	383	63	x	x	NOUN
ejpam-5839	383	64	)	)	PUNCT
ejpam-5839	383	65	are	be	AUX
ejpam-5839	383	66	all	all	ADV
ejpam-5839	383	67	continuous	continuous	ADJ
ejpam-5839	383	68	on	on	ADP
ejpam-5839	383	69	the	the	DET
ejpam-5839	383	70	interval	interval	NOUN
ejpam-5839	383	71	[	[	X
ejpam-5839	383	72	a1	a1	NOUN
ejpam-5839	383	73	,	,	PUNCT
ejpam-5839	383	74	b1	b1	NOUN
ejpam-5839	383	75	]	]	PUNCT
ejpam-5839	383	76	,	,	PUNCT
ejpam-5839	383	77	then	then	ADV
ejpam-5839	383	78	we	we	PRON
ejpam-5839	383	79	have	have	AUX
ejpam-5839	383	80	:	:	PUNCT
ejpam-5839	383	81	f̃q(x	f̃q(x	NUM
ejpam-5839	383	82	)	)	PUNCT
ejpam-5839	383	83	∈	∈	PROPN
ejpam-5839	383	84	qri	qri	NOUN
ejpam-5839	383	85	on	on	ADP
ejpam-5839	383	86	the	the	DET
ejpam-5839	383	87	closed	closed	ADJ
ejpam-5839	383	88	bounded	bounded	ADJ
ejpam-5839	383	89	interval	interval	NOUN
ejpam-5839	383	90	[	[	X
ejpam-5839	383	91	a1	a1	NOUN
ejpam-5839	383	92	,	,	PUNCT
ejpam-5839	383	93	b1	b1	NOUN
ejpam-5839	383	94	]	]	PUNCT
ejpam-5839	383	95	thus	thus	ADV
ejpam-5839	383	96	,	,	PUNCT
ejpam-5839	383	97	the	the	DET
ejpam-5839	383	98	integral	integral	NOUN
ejpam-5839	383	99	is	be	AUX
ejpam-5839	383	100	given	give	VERB
ejpam-5839	383	101	by	by	ADP
ejpam-5839	383	102	:	:	PUNCT
ejpam-5839	383	103	(	(	PUNCT
ejpam-5839	383	104	∫	∫	PROPN
ejpam-5839	383	105	b1	b1	PROPN
ejpam-5839	383	106	a1	a1	PROPN
ejpam-5839	383	107	f̃q(x)dx	f̃q(x)dx	PROPN
ejpam-5839	383	108	)	)	PUNCT
ejpam-5839	384	1	(	(	PUNCT
ejpam-5839	384	2	i	i	PROPN
ejpam-5839	384	3	,	,	PUNCT
ejpam-5839	384	4	j	j	PROPN
ejpam-5839	384	5	,	,	PUNCT
ejpam-5839	384	6	k	k	PROPN
ejpam-5839	384	7	,	,	PUNCT
ejpam-5839	384	8	l	l	NOUN
ejpam-5839	384	9	)	)	PUNCT
ejpam-5839	384	10	=	=	SYM
ejpam-5839	384	11			ADJ
ejpam-5839	384	12	∫	∫	PROPN
ejpam-5839	384	13	b1	b1	PROPN
ejpam-5839	384	14	a1	a1	PROPN
ejpam-5839	384	15	f̃lqi	f̃lqi	NOUN
ejpam-5839	384	16	(	(	PUNCT
ejpam-5839	384	17	x)dx	x)dx	PROPN
ejpam-5839	384	18	,	,	PUNCT
ejpam-5839	384	19	∫	∫	PROPN
ejpam-5839	384	20	b1	b1	PROPN
ejpam-5839	384	21	a1	a1	PROPN
ejpam-5839	384	22	f̃uqi	f̃uqi	PROPN
ejpam-5839	384	23	(	(	PUNCT
ejpam-5839	384	24	x)dx∫	x)dx∫	PROPN
ejpam-5839	384	25	b1	b1	PROPN
ejpam-5839	384	26	a1	a1	PROPN
ejpam-5839	384	27	f̃lqj	f̃lqj	X
ejpam-5839	384	28	(	(	PUNCT
ejpam-5839	384	29	x)dx	x)dx	PROPN
ejpam-5839	384	30	,	,	PUNCT
ejpam-5839	384	31	∫	∫	PROPN
ejpam-5839	384	32	b1	b1	NOUN
ejpam-5839	384	33	a1	a1	NOUN
ejpam-5839	384	34	f̃uqj	f̃uqj	NOUN
ejpam-5839	384	35	(	(	PUNCT
ejpam-5839	384	36	x)dx∫	x)dx∫	PROPN
ejpam-5839	384	37	b1	b1	PROPN
ejpam-5839	384	38	a1	a1	PROPN
ejpam-5839	384	39	f̃lqk	f̃lqk	PROPN
ejpam-5839	384	40	(	(	PUNCT
ejpam-5839	384	41	x)dx	x)dx	PROPN
ejpam-5839	384	42	,	,	PUNCT
ejpam-5839	384	43	∫	∫	PROPN
ejpam-5839	384	44	b1	b1	PROPN
ejpam-5839	384	45	a1	a1	NOUN
ejpam-5839	384	46	f̃uqk	f̃uqk	NOUN
ejpam-5839	384	47	(	(	PUNCT
ejpam-5839	384	48	x)dx∫	x)dx∫	PROPN
ejpam-5839	384	49	b1	b1	NOUN
ejpam-5839	384	50	a1	a1	NOUN
ejpam-5839	384	51	f̃lql	f̃lql	NOUN
ejpam-5839	384	52	(	(	PUNCT
ejpam-5839	384	53	x)dx	x)dx	PROPN
ejpam-5839	384	54	,	,	PUNCT
ejpam-5839	384	55	∫	∫	PROPN
ejpam-5839	384	56	b1	b1	PROPN
ejpam-5839	384	57	a1	a1	PROPN
ejpam-5839	384	58	f̃uql	f̃uql	NOUN
ejpam-5839	384	59	(	(	PUNCT
ejpam-5839	384	60	x)dx	x)dx	NOUN
ejpam-5839	384	61			NOUN
ejpam-5839	384	62	proof	proof	NOUN
ejpam-5839	384	63	.	.	PUNCT
ejpam-5839	385	1	from	from	ADP
ejpam-5839	385	2	proposition	proposition	NOUN
ejpam-5839	385	3	8	8	NUM
ejpam-5839	385	4	,	,	PUNCT
ejpam-5839	385	5	the	the	DET
ejpam-5839	385	6	functions	function	NOUN
ejpam-5839	385	7	f̃l	f̃l	PROPN
ejpam-5839	385	8	qi(x	qi(x	NUM
ejpam-5839	385	9	)	)	PUNCT
ejpam-5839	385	10	,	,	PUNCT
ejpam-5839	385	11	f̃u	f̃u	NOUN
ejpam-5839	385	12	qi(x	qi(x	NUM
ejpam-5839	385	13	)	)	PUNCT
ejpam-5839	385	14	,	,	PUNCT
ejpam-5839	385	15	f̃l	f̃l	PROPN
ejpam-5839	385	16	qj(x	qj(x	NUM
ejpam-5839	385	17	)	)	PUNCT
ejpam-5839	385	18	,	,	PUNCT
ejpam-5839	385	19	f̃u	f̃u	NOUN
ejpam-5839	385	20	qj(x	qj(x	PUNCT
ejpam-5839	385	21	)	)	PUNCT
ejpam-5839	385	22	,	,	PUNCT
ejpam-5839	385	23	f̃l	f̃l	PROPN
ejpam-5839	385	24	qk(x	qk(x	NOUN
ejpam-5839	385	25	)	)	PUNCT
ejpam-5839	385	26	,	,	PUNCT
ejpam-5839	385	27	f̃u	f̃u	NOUN
ejpam-5839	385	28	qk(x	qk(x	NOUN
ejpam-5839	385	29	)	)	PUNCT
ejpam-5839	385	30	,	,	PUNCT
ejpam-5839	385	31	f̃l	f̃l	PROPN
ejpam-5839	385	32	ql(x	ql(x	PROPN
ejpam-5839	385	33	)	)	PUNCT
ejpam-5839	385	34	,	,	PUNCT
ejpam-5839	385	35	f̃u	f̃u	NOUN
ejpam-5839	385	36	ql(x	ql(x	NUM
ejpam-5839	385	37	)	)	PUNCT
ejpam-5839	385	38	are	be	AUX
ejpam-5839	385	39	riemann	riemann	PROPN
ejpam-5839	385	40	integrable	integrable	ADJ
ejpam-5839	385	41	on	on	ADP
ejpam-5839	385	42	[	[	X
ejpam-5839	385	43	a1	a1	NOUN
ejpam-5839	385	44	,	,	PUNCT
ejpam-5839	385	45	b1	b1	NOUN
ejpam-5839	385	46	]	]	PUNCT
ejpam-5839	385	47	.	.	PUNCT
ejpam-5839	386	1	then	then	ADV
ejpam-5839	386	2	,	,	PUNCT
ejpam-5839	386	3	f̃q(x	f̃q(x	CCONJ
ejpam-5839	386	4	)	)	PUNCT
ejpam-5839	386	5	is	be	AUX
ejpam-5839	386	6	riemann	riemann	PROPN
ejpam-5839	386	7	integrable	integrable	ADJ
ejpam-5839	386	8	on	on	ADP
ejpam-5839	386	9	[	[	X
ejpam-5839	386	10	a1	a1	NOUN
ejpam-5839	386	11	,	,	PUNCT
ejpam-5839	386	12	b1	b1	NOUN
ejpam-5839	386	13	]	]	PUNCT
ejpam-5839	386	14	,	,	PUNCT
ejpam-5839	386	15	and	and	CCONJ
ejpam-5839	386	16	we	we	PRON
ejpam-5839	386	17	have	have	VERB
ejpam-5839	386	18	(	(	PUNCT
ejpam-5839	386	19	∫	∫	PROPN
ejpam-5839	386	20	b1	b1	PROPN
ejpam-5839	386	21	a1	a1	PROPN
ejpam-5839	386	22	f̃q(x	f̃q(x	CCONJ
ejpam-5839	386	23	)	)	PUNCT
ejpam-5839	386	24	dx	dx	PROPN
ejpam-5839	386	25	)	)	PUNCT
ejpam-5839	387	1	i	i	PRON
ejpam-5839	387	2	,	,	PUNCT
ejpam-5839	387	3	j	j	PROPN
ejpam-5839	387	4	,	,	PUNCT
ejpam-5839	387	5	k	k	PROPN
ejpam-5839	387	6	,	,	PUNCT
ejpam-5839	387	7	l	l	NOUN
ejpam-5839	387	8	=	=	SYM
ejpam-5839	387	9			NOUN
ejpam-5839	388	1	[	[	X
ejpam-5839	388	2	∫	∫	X
ejpam-5839	388	3	b1	b1	PROPN
ejpam-5839	388	4	a1	a1	PROPN
ejpam-5839	388	5	f̃l	f̃l	PROPN
ejpam-5839	388	6	qi(x	qi(x	NUM
ejpam-5839	388	7	)	)	PUNCT
ejpam-5839	388	8	dx	dx	PROPN
ejpam-5839	388	9	,	,	PUNCT
ejpam-5839	388	10	∫	∫	PROPN
ejpam-5839	388	11	b1	b1	PROPN
ejpam-5839	388	12	a1	a1	PROPN
ejpam-5839	388	13	f̃u	f̃u	NOUN
ejpam-5839	388	14	qi(x	qi(x	NUM
ejpam-5839	388	15	)	)	PUNCT
ejpam-5839	388	16	dx	dx	PROPN
ejpam-5839	388	17	]	]	PUNCT
ejpam-5839	389	1	[	[	X
ejpam-5839	389	2	∫	∫	X
ejpam-5839	389	3	b1	b1	PROPN
ejpam-5839	389	4	a1	a1	PROPN
ejpam-5839	389	5	f̃l	f̃l	PROPN
ejpam-5839	389	6	qj(x	qj(x	NUM
ejpam-5839	389	7	)	)	PUNCT
ejpam-5839	389	8	dx	dx	PROPN
ejpam-5839	389	9	,	,	PUNCT
ejpam-5839	389	10	∫	∫	PROPN
ejpam-5839	389	11	b1	b1	PROPN
ejpam-5839	389	12	a1	a1	PROPN
ejpam-5839	389	13	f̃u	f̃u	NOUN
ejpam-5839	389	14	qj(x	qj(x	PUNCT
ejpam-5839	389	15	)	)	PUNCT
ejpam-5839	389	16	dx	dx	PROPN
ejpam-5839	389	17	]	]	PUNCT
ejpam-5839	390	1	[	[	X
ejpam-5839	390	2	∫	∫	X
ejpam-5839	390	3	b1	b1	PROPN
ejpam-5839	390	4	a1	a1	PROPN
ejpam-5839	390	5	f̃l	f̃l	PROPN
ejpam-5839	390	6	qk(x	qk(x	NOUN
ejpam-5839	390	7	)	)	PUNCT
ejpam-5839	390	8	dx	dx	PROPN
ejpam-5839	390	9	,	,	PUNCT
ejpam-5839	390	10	∫	∫	PROPN
ejpam-5839	390	11	b1	b1	PROPN
ejpam-5839	390	12	a1	a1	PROPN
ejpam-5839	390	13	f̃u	f̃u	NOUN
ejpam-5839	390	14	qk(x	qk(x	NOUN
ejpam-5839	390	15	)	)	PUNCT
ejpam-5839	390	16	dx	dx	PROPN
ejpam-5839	390	17	]	]	PUNCT
ejpam-5839	391	1	[	[	X
ejpam-5839	391	2	∫	∫	X
ejpam-5839	391	3	b1	b1	PROPN
ejpam-5839	391	4	a1	a1	PROPN
ejpam-5839	391	5	f̃l	f̃l	PROPN
ejpam-5839	391	6	ql(x	ql(x	PROPN
ejpam-5839	391	7	)	)	PUNCT
ejpam-5839	391	8	dx	dx	PROPN
ejpam-5839	391	9	,	,	PUNCT
ejpam-5839	391	10	∫	∫	PROPN
ejpam-5839	391	11	b1	b1	PROPN
ejpam-5839	391	12	a1	a1	PROPN
ejpam-5839	391	13	f̃u	f̃u	PROPN
ejpam-5839	391	14	ql(x	ql(x	PROPN
ejpam-5839	391	15	)	)	PUNCT
ejpam-5839	391	16	dx	dx	PROPN
ejpam-5839	391	17	]	]	PUNCT
ejpam-5839	391	18			NUM
ejpam-5839	391	19	a.	a.	NOUN
ejpam-5839	391	20	shihadeh	shihadeh	NOUN
ejpam-5839	391	21	et	et	PROPN
ejpam-5839	391	22	al	al	PROPN
ejpam-5839	391	23	.	.	PUNCT
ejpam-5839	391	24	/	/	SYM
ejpam-5839	391	25	eur	eur	PROPN
ejpam-5839	391	26	.	.	PUNCT
ejpam-5839	392	1	j.	j.	PROPN
ejpam-5839	392	2	pure	pure	PROPN
ejpam-5839	392	3	appl	appl	PROPN
ejpam-5839	392	4	.	.	PROPN
ejpam-5839	392	5	math	math	PROPN
ejpam-5839	392	6	,	,	PUNCT
ejpam-5839	392	7	18	18	NUM
ejpam-5839	392	8	(	(	PUNCT
ejpam-5839	392	9	2	2	NUM
ejpam-5839	392	10	)	)	PUNCT
ejpam-5839	392	11	(	(	PUNCT
ejpam-5839	392	12	2025	2025	NUM
ejpam-5839	392	13	)	)	PUNCT
ejpam-5839	392	14	,	,	PUNCT
ejpam-5839	392	15	5839	5839	NUM
ejpam-5839	392	16	17	17	NUM
ejpam-5839	392	17	of	of	ADP
ejpam-5839	392	18	54	54	NUM
ejpam-5839	392	19	theorem	theorem	NOUN
ejpam-5839	392	20	4	4	NUM
ejpam-5839	392	21	.	.	PUNCT
ejpam-5839	393	1	let	let	VERB
ejpam-5839	393	2	f̃q(x	f̃q(x	PART
ejpam-5839	393	3	)	)	PUNCT
ejpam-5839	393	4	and	and	CCONJ
ejpam-5839	393	5	g̃q(x	g̃q(x	NOUN
ejpam-5839	393	6	)	)	PUNCT
ejpam-5839	393	7	be	be	AUX
ejpam-5839	393	8	closed	close	VERB
ejpam-5839	393	9	bounded	bounded	ADJ
ejpam-5839	393	10	quadri	quadri	PROPN
ejpam-5839	393	11	-	-	PUNCT
ejpam-5839	393	12	neutrosophic	neutrosophic	ADJ
ejpam-5839	393	13	valued	value	VERB
ejpam-5839	393	14	functions	function	NOUN
ejpam-5839	393	15	on	on	ADP
ejpam-5839	393	16	[	[	X
ejpam-5839	393	17	a1	a1	NOUN
ejpam-5839	393	18	,	,	PUNCT
ejpam-5839	393	19	b1	b1	NOUN
ejpam-5839	393	20	]	]	PUNCT
ejpam-5839	393	21	.	.	PUNCT
ejpam-5839	394	1	if	if	SCONJ
ejpam-5839	394	2	f̃q(x	f̃q(x	NUM
ejpam-5839	394	3	)	)	PUNCT
ejpam-5839	395	1	·	·	PUNCT
ejpam-5839	395	2	g̃q(x	g̃q(x	X
ejpam-5839	395	3	)	)	PUNCT
ejpam-5839	395	4	∈	∈	PROPN
ejpam-5839	395	5	qri	qri	NOUN
ejpam-5839	395	6	,	,	PUNCT
ejpam-5839	395	7	then	then	ADV
ejpam-5839	395	8	f̃q(x	f̃q(x	CCONJ
ejpam-5839	395	9	)	)	PUNCT
ejpam-5839	396	1	+	+	CCONJ
ejpam-5839	396	2	g̃q(x	g̃q(x	SYM
ejpam-5839	396	3	)	)	PUNCT
ejpam-5839	396	4	∈	∈	PROPN
ejpam-5839	396	5	qri	qri	NOUN
ejpam-5839	396	6	and	and	CCONJ
ejpam-5839	396	7	f̃q(x)−	f̃q(x)−	NOUN
ejpam-5839	396	8	g̃q(x	g̃q(x	NOUN
ejpam-5839	396	9	)	)	PUNCT
ejpam-5839	396	10	∈	∈	PROPN
ejpam-5839	396	11	qri	qri	NOUN
ejpam-5839	396	12	.	.	PUNCT
ejpam-5839	397	1	moreover	moreover	ADV
ejpam-5839	397	2	,	,	PUNCT
ejpam-5839	397	3	we	we	PRON
ejpam-5839	397	4	have∫	have∫	VERB
ejpam-5839	397	5	b1	b1	NOUN
ejpam-5839	397	6	a1	a1	NOUN
ejpam-5839	397	7	(	(	PUNCT
ejpam-5839	397	8	f̃q(x	f̃q(x	NUM
ejpam-5839	397	9	)	)	PUNCT
ejpam-5839	397	10	+	+	CCONJ
ejpam-5839	397	11	g̃q(x	g̃q(x	NOUN
ejpam-5839	397	12	)	)	PUNCT
ejpam-5839	397	13	)	)	PUNCT
ejpam-5839	398	1	dx	dx	PROPN
ejpam-5839	398	2	=	=	SYM
ejpam-5839	398	3	∫	∫	PROPN
ejpam-5839	398	4	b1	b1	PROPN
ejpam-5839	398	5	a1	a1	PROPN
ejpam-5839	398	6	f̃q(x	f̃q(x	CCONJ
ejpam-5839	398	7	)	)	PUNCT
ejpam-5839	398	8	dx+	dx+	NOUN
ejpam-5839	398	9	∫	∫	PROPN
ejpam-5839	398	10	b1	b1	PROPN
ejpam-5839	398	11	a1	a1	PROPN
ejpam-5839	398	12	g̃q(x	g̃q(x	PROPN
ejpam-5839	398	13	)	)	PUNCT
ejpam-5839	398	14	dx	dx	PROPN
ejpam-5839	398	15	∫	∫	PROPN
ejpam-5839	398	16	b1	b1	PROPN
ejpam-5839	398	17	a1	a1	PROPN
ejpam-5839	398	18	(	(	PUNCT
ejpam-5839	398	19	f̃q(x)−	f̃q(x)−	NOUN
ejpam-5839	398	20	g̃q(x	g̃q(x	PROPN
ejpam-5839	398	21	)	)	PUNCT
ejpam-5839	398	22	)	)	PUNCT
ejpam-5839	399	1	dx	dx	PROPN
ejpam-5839	399	2	=	=	SYM
ejpam-5839	399	3	∫	∫	PROPN
ejpam-5839	399	4	b1	b1	PROPN
ejpam-5839	399	5	a1	a1	PROPN
ejpam-5839	399	6	f̃q(x	f̃q(x	ADV
ejpam-5839	399	7	)	)	PUNCT
ejpam-5839	399	8	dx−	dx−	NUM
ejpam-5839	399	9	∫	∫	PROPN
ejpam-5839	399	10	b1	b1	PROPN
ejpam-5839	399	11	a1	a1	PROPN
ejpam-5839	399	12	g̃q(x	g̃q(x	PROPN
ejpam-5839	399	13	)	)	PUNCT
ejpam-5839	400	1	dx	dx	PROPN
ejpam-5839	400	2	proof	proof	NOUN
ejpam-5839	400	3	.	.	PUNCT
ejpam-5839	401	1	let	let	VERB
ejpam-5839	401	2	h̃q(x	h̃q(x	PRON
ejpam-5839	401	3	)	)	PUNCT
ejpam-5839	401	4	=	=	PUNCT
ejpam-5839	402	1	f̃q(x	f̃q(x	NUM
ejpam-5839	402	2	)	)	PUNCT
ejpam-5839	402	3	+	+	CCONJ
ejpam-5839	402	4	g̃q(x	g̃q(x	NOUN
ejpam-5839	402	5	)	)	PUNCT
ejpam-5839	402	6	,	,	PUNCT
ejpam-5839	402	7	then	then	ADV
ejpam-5839	402	8	h̃q(x	h̃q(x	CCONJ
ejpam-5839	402	9	)	)	PUNCT
ejpam-5839	402	10	is	be	AUX
ejpam-5839	402	11	a	a	DET
ejpam-5839	402	12	closed	closed	ADJ
ejpam-5839	402	13	quadri	quadri	NOUN
ejpam-5839	402	14	-	-	PUNCT
ejpam-5839	402	15	neutrosophic	neutrosophic	PROPN
ejpam-5839	402	16	valued	value	VERB
ejpam-5839	402	17	function.(∫	function.(∫	NUM
ejpam-5839	402	18	b1	b1	NOUN
ejpam-5839	402	19	a1	a1	NOUN
ejpam-5839	402	20	f̃q(x	f̃q(x	NOUN
ejpam-5839	402	21	)	)	PUNCT
ejpam-5839	402	22	dx+	dx+	NOUN
ejpam-5839	402	23	∫	∫	PROPN
ejpam-5839	402	24	b1	b1	PROPN
ejpam-5839	402	25	a1	a1	PROPN
ejpam-5839	402	26	g̃q(x	g̃q(x	PROPN
ejpam-5839	402	27	)	)	PUNCT
ejpam-5839	402	28	dx	dx	PROPN
ejpam-5839	402	29	)	)	PUNCT
ejpam-5839	403	1	(	(	PUNCT
ejpam-5839	403	2	i	i	PROPN
ejpam-5839	403	3	,	,	PUNCT
ejpam-5839	403	4	j	j	PROPN
ejpam-5839	403	5	,	,	PUNCT
ejpam-5839	403	6	k	k	PROPN
ejpam-5839	403	7	,	,	PUNCT
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ejpam-5839	403	12	i	i	PRON
ejpam-5839	403	13	q	q	NOUN
ejpam-5839	403	14	,	,	PUNCT
ejpam-5839	403	15	l(x	l(x	PROPN
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ejpam-5839	403	17	dx	dx	PROPN
ejpam-5839	403	18	,	,	PUNCT
ejpam-5839	403	19	∫	∫	PROPN
ejpam-5839	403	20	b1	b1	PROPN
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ejpam-5839	403	23	,	,	PUNCT
ejpam-5839	403	24	l(x	l(x	PROPN
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ejpam-5839	403	26	dx	dx	PROPN
ejpam-5839	403	27	,	,	PUNCT
ejpam-5839	403	28	∫	∫	PROPN
ejpam-5839	403	29	b1	b1	PROPN
ejpam-5839	403	30	a1	a1	NOUN
ejpam-5839	403	31	f̃	f̃	PROPN
ejpam-5839	403	32	i	i	PRON
ejpam-5839	403	33	q	q	NOUN
ejpam-5839	403	34	,	,	PUNCT
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ejpam-5839	403	36	(	(	PUNCT
ejpam-5839	403	37	x	x	NOUN
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ejpam-5839	403	39	dx	dx	PROPN
ejpam-5839	403	40	,	,	PUNCT
ejpam-5839	403	41	∫	∫	PROPN
ejpam-5839	403	42	b1	b1	PROPN
ejpam-5839	403	43	a1	a1	PROPN
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ejpam-5839	403	45	,	,	PUNCT
ejpam-5839	403	46	u	u	NOUN
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ejpam-5839	403	48	x	x	NOUN
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ejpam-5839	403	50	dx	dx	PROPN
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ejpam-5839	403	52	〉	〉	NOUN
ejpam-5839	403	53	[	[	X
ejpam-5839	403	54	∫	∫	NOUN
ejpam-5839	403	55	b1	b1	NOUN
ejpam-5839	403	56	a1	a1	NOUN
ejpam-5839	403	57	f̃	f̃	PROPN
ejpam-5839	403	58	j	j	PROPN
ejpam-5839	403	59	q	q	PROPN
ejpam-5839	403	60	,	,	PUNCT
ejpam-5839	403	61	l(x	l(x	PROPN
ejpam-5839	403	62	)	)	PUNCT
ejpam-5839	403	63	dx	dx	PROPN
ejpam-5839	403	64	,	,	PUNCT
ejpam-5839	403	65	∫	∫	PROPN
ejpam-5839	403	66	b1	b1	PROPN
ejpam-5839	403	67	a1	a1	PROPN
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ejpam-5839	403	69	,	,	PUNCT
ejpam-5839	403	70	l(x	l(x	PROPN
ejpam-5839	403	71	)	)	PUNCT
ejpam-5839	403	72	dx	dx	PROPN
ejpam-5839	403	73	,	,	PUNCT
ejpam-5839	403	74	∫	∫	PROPN
ejpam-5839	403	75	b1	b1	PROPN
ejpam-5839	403	76	a1	a1	PROPN
ejpam-5839	403	77	f̃	f̃	PROPN
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ejpam-5839	403	79	q	q	PROPN
ejpam-5839	403	80	,	,	PUNCT
ejpam-5839	403	81	u	u	NOUN
ejpam-5839	403	82	(	(	PUNCT
ejpam-5839	403	83	x	x	NOUN
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ejpam-5839	403	85	dx	dx	PROPN
ejpam-5839	403	86	,	,	PUNCT
ejpam-5839	403	87	∫	∫	PROPN
ejpam-5839	403	88	b1	b1	PROPN
ejpam-5839	403	89	a1	a1	PROPN
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ejpam-5839	403	91	,	,	PUNCT
ejpam-5839	403	92	u	u	NOUN
ejpam-5839	403	93	(	(	PUNCT
ejpam-5839	403	94	x	x	X
ejpam-5839	403	95	)	)	PUNCT
ejpam-5839	403	96	dx	dx	PROPN
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ejpam-5839	404	1	[	[	PUNCT
ejpam-5839	404	2	∫	∫	PROPN
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ejpam-5839	404	4	a1	a1	NOUN
ejpam-5839	404	5	f̃	f̃	PROPN
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ejpam-5839	404	7	q	q	PROPN
ejpam-5839	404	8	,	,	PUNCT
ejpam-5839	404	9	l(x	l(x	PROPN
ejpam-5839	404	10	)	)	PUNCT
ejpam-5839	404	11	dx	dx	PROPN
ejpam-5839	404	12	,	,	PUNCT
ejpam-5839	404	13	∫	∫	PROPN
ejpam-5839	404	14	b1	b1	PROPN
ejpam-5839	404	15	a1	a1	PROPN
ejpam-5839	404	16	g̃kq	g̃kq	PROPN
ejpam-5839	404	17	,	,	PUNCT
ejpam-5839	404	18	l(x	l(x	PROPN
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ejpam-5839	404	20	dx	dx	PROPN
ejpam-5839	404	21	,	,	PUNCT
ejpam-5839	404	22	∫	∫	PROPN
ejpam-5839	404	23	b1	b1	PROPN
ejpam-5839	404	24	a1	a1	NOUN
ejpam-5839	404	25	f̃	f̃	PROPN
ejpam-5839	404	26	k	k	PROPN
ejpam-5839	405	1	q	q	PROPN
ejpam-5839	405	2	,	,	PUNCT
ejpam-5839	405	3	u	u	NOUN
ejpam-5839	405	4	(	(	PUNCT
ejpam-5839	405	5	x	x	NOUN
ejpam-5839	405	6	)	)	PUNCT
ejpam-5839	405	7	dx	dx	PROPN
ejpam-5839	405	8	,	,	PUNCT
ejpam-5839	405	9	∫	∫	PROPN
ejpam-5839	405	10	b1	b1	PROPN
ejpam-5839	405	11	a1	a1	PROPN
ejpam-5839	405	12	g̃kq	g̃kq	PROPN
ejpam-5839	405	13	,	,	PUNCT
ejpam-5839	405	14	u	u	NOUN
ejpam-5839	405	15	(	(	PUNCT
ejpam-5839	405	16	x	x	X
ejpam-5839	405	17	)	)	PUNCT
ejpam-5839	405	18	dx	dx	PROPN
ejpam-5839	405	19	]	]	PUNCT
ejpam-5839	406	1	〈	〈	PROPN
ejpam-5839	406	2	[	[	PUNCT
ejpam-5839	406	3	∫	∫	PROPN
ejpam-5839	406	4	b1	b1	NOUN
ejpam-5839	406	5	a1	a1	NOUN
ejpam-5839	406	6	f̃	f̃	PROPN
ejpam-5839	406	7	l	l	PROPN
ejpam-5839	406	8	q	q	PROPN
ejpam-5839	406	9	,	,	PUNCT
ejpam-5839	406	10	l(x	l(x	PROPN
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ejpam-5839	406	12	dx	dx	PROPN
ejpam-5839	406	13	,	,	PUNCT
ejpam-5839	406	14	∫	∫	PROPN
ejpam-5839	406	15	b1	b1	PROPN
ejpam-5839	406	16	a1	a1	PROPN
ejpam-5839	406	17	g̃lq	g̃lq	PROPN
ejpam-5839	406	18	,	,	PUNCT
ejpam-5839	406	19	l(x	l(x	PROPN
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ejpam-5839	406	21	dx	dx	PROPN
ejpam-5839	406	22	,	,	PUNCT
ejpam-5839	406	23	∫	∫	PROPN
ejpam-5839	406	24	b1	b1	PROPN
ejpam-5839	406	25	a1	a1	NOUN
ejpam-5839	406	26	f̃	f̃	PROPN
ejpam-5839	406	27	l	l	PROPN
ejpam-5839	406	28	q	q	PROPN
ejpam-5839	406	29	,	,	PUNCT
ejpam-5839	406	30	u	u	NOUN
ejpam-5839	406	31	(	(	PUNCT
ejpam-5839	406	32	x	x	NOUN
ejpam-5839	406	33	)	)	PUNCT
ejpam-5839	406	34	dx	dx	PROPN
ejpam-5839	406	35	,	,	PUNCT
ejpam-5839	406	36	∫	∫	PROPN
ejpam-5839	406	37	b1	b1	PROPN
ejpam-5839	406	38	a1	a1	PROPN
ejpam-5839	406	39	g̃lq	g̃lq	PROPN
ejpam-5839	406	40	,	,	PUNCT
ejpam-5839	406	41	u	u	NOUN
ejpam-5839	406	42	(	(	PUNCT
ejpam-5839	406	43	x	x	NOUN
ejpam-5839	406	44	)	)	PUNCT
ejpam-5839	406	45	dx	dx	PROPN
ejpam-5839	406	46	]	]	PUNCT
ejpam-5839	406	47	〉	〉	X
ejpam-5839	406	48	(	(	PUNCT
ejpam-5839	406	49	∫	∫	PROPN
ejpam-5839	406	50	b1	b1	PROPN
ejpam-5839	406	51	a1	a1	PROPN
ejpam-5839	406	52	f̃q(x	f̃q(x	CCONJ
ejpam-5839	406	53	)	)	PUNCT
ejpam-5839	406	54	dx+	dx+	NOUN
ejpam-5839	406	55	∫	∫	PROPN
ejpam-5839	406	56	b1	b1	PROPN
ejpam-5839	406	57	a1	a1	PROPN
ejpam-5839	406	58	g̃q(x	g̃q(x	PROPN
ejpam-5839	406	59	)	)	PUNCT
ejpam-5839	406	60	dx	dx	PROPN
ejpam-5839	406	61	)	)	PUNCT
ejpam-5839	407	1	(	(	PUNCT
ejpam-5839	407	2	i	i	PROPN
ejpam-5839	407	3	,	,	PUNCT
ejpam-5839	407	4	j	j	PROPN
ejpam-5839	407	5	,	,	PUNCT
ejpam-5839	407	6	k	k	PROPN
ejpam-5839	407	7	,	,	PUNCT
ejpam-5839	407	8	l	l	NOUN
ejpam-5839	407	9	)	)	PUNCT
ejpam-5839	407	10	[	[	PUNCT
ejpam-5839	407	11	[	[	X
ejpam-5839	407	12	∫	∫	X
ejpam-5839	407	13	b1	b1	NOUN
ejpam-5839	407	14	a1	a1	NOUN
ejpam-5839	407	15	f̃	f̃	PROPN
ejpam-5839	407	16	i	i	PRON
ejpam-5839	407	17	q	q	NOUN
ejpam-5839	407	18	,	,	PUNCT
ejpam-5839	407	19	l(x	l(x	PROPN
ejpam-5839	407	20	)	)	PUNCT
ejpam-5839	407	21	dx+	dx+	NOUN
ejpam-5839	407	22	∫	∫	PROPN
ejpam-5839	407	23	b1	b1	PROPN
ejpam-5839	407	24	a1	a1	PROPN
ejpam-5839	407	25	g̃iq	g̃iq	PROPN
ejpam-5839	407	26	,	,	PUNCT
ejpam-5839	407	27	l(x	l(x	PROPN
ejpam-5839	407	28	)	)	PUNCT
ejpam-5839	407	29	dx	dx	PROPN
ejpam-5839	407	30	,	,	PUNCT
ejpam-5839	407	31	∫	∫	PROPN
ejpam-5839	407	32	b1	b1	PROPN
ejpam-5839	407	33	a1	a1	NOUN
ejpam-5839	407	34	f̃	f̃	PROPN
ejpam-5839	407	35	i	i	PRON
ejpam-5839	407	36	q	q	NOUN
ejpam-5839	407	37	,	,	PUNCT
ejpam-5839	407	38	u	u	NOUN
ejpam-5839	407	39	(	(	PUNCT
ejpam-5839	407	40	x	x	NOUN
ejpam-5839	407	41	)	)	PUNCT
ejpam-5839	407	42	dx+	dx+	ADJ
ejpam-5839	407	43	∫	∫	PROPN
ejpam-5839	407	44	b1	b1	PROPN
ejpam-5839	407	45	a1	a1	PROPN
ejpam-5839	407	46	g̃iq	g̃iq	PROPN
ejpam-5839	407	47	,	,	PUNCT
ejpam-5839	407	48	u	u	NOUN
ejpam-5839	407	49	(	(	PUNCT
ejpam-5839	407	50	x	x	X
ejpam-5839	407	51	)	)	PUNCT
ejpam-5839	407	52	dx	dx	PROPN
ejpam-5839	407	53	]	]	PUNCT
ejpam-5839	407	54	]	]	PUNCT
ejpam-5839	408	1	[	[	X
ejpam-5839	408	2	∫	∫	X
ejpam-5839	408	3	b1	b1	NOUN
ejpam-5839	408	4	a1	a1	NOUN
ejpam-5839	408	5	f̃	f̃	PROPN
ejpam-5839	408	6	j	j	PROPN
ejpam-5839	408	7	q	q	PROPN
ejpam-5839	408	8	,	,	PUNCT
ejpam-5839	408	9	l(x	l(x	PROPN
ejpam-5839	408	10	)	)	PUNCT
ejpam-5839	408	11	dx+	dx+	NOUN
ejpam-5839	408	12	∫	∫	PROPN
ejpam-5839	408	13	b1	b1	PROPN
ejpam-5839	408	14	a1	a1	PROPN
ejpam-5839	408	15	g̃jq	g̃jq	PROPN
ejpam-5839	408	16	,	,	PUNCT
ejpam-5839	408	17	l(x	l(x	PROPN
ejpam-5839	408	18	)	)	PUNCT
ejpam-5839	408	19	dx	dx	PROPN
ejpam-5839	408	20	,	,	PUNCT
ejpam-5839	408	21	∫	∫	PROPN
ejpam-5839	408	22	b1	b1	PROPN
ejpam-5839	408	23	a1	a1	PROPN
ejpam-5839	408	24	f̃	f̃	PROPN
ejpam-5839	408	25	j	j	PROPN
ejpam-5839	408	26	q	q	PROPN
ejpam-5839	408	27	,	,	PUNCT
ejpam-5839	408	28	u	u	NOUN
ejpam-5839	408	29	(	(	PUNCT
ejpam-5839	408	30	x	x	NOUN
ejpam-5839	408	31	)	)	PUNCT
ejpam-5839	408	32	dx+	dx+	ADJ
ejpam-5839	408	33	∫	∫	PROPN
ejpam-5839	408	34	b1	b1	PROPN
ejpam-5839	408	35	a1	a1	PROPN
ejpam-5839	408	36	g̃jq	g̃jq	PROPN
ejpam-5839	408	37	,	,	PUNCT
ejpam-5839	408	38	u	u	NOUN
ejpam-5839	408	39	(	(	PUNCT
ejpam-5839	408	40	x	x	X
ejpam-5839	408	41	)	)	PUNCT
ejpam-5839	408	42	dx	dx	PROPN
ejpam-5839	408	43	]	]	PUNCT
ejpam-5839	409	1	[	[	X
ejpam-5839	409	2	∫	∫	X
ejpam-5839	409	3	b1	b1	NOUN
ejpam-5839	409	4	a1	a1	NOUN
ejpam-5839	409	5	f̃	f̃	PROPN
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ejpam-5839	409	7	q	q	PROPN
ejpam-5839	409	8	,	,	PUNCT
ejpam-5839	409	9	l(x	l(x	PROPN
ejpam-5839	409	10	)	)	PUNCT
ejpam-5839	409	11	dx+	dx+	NOUN
ejpam-5839	409	12	∫	∫	PROPN
ejpam-5839	409	13	b1	b1	PROPN
ejpam-5839	409	14	a1	a1	PROPN
ejpam-5839	409	15	g̃kq	g̃kq	PROPN
ejpam-5839	409	16	,	,	PUNCT
ejpam-5839	409	17	l(x	l(x	PROPN
ejpam-5839	409	18	)	)	PUNCT
ejpam-5839	409	19	dx	dx	PROPN
ejpam-5839	409	20	,	,	PUNCT
ejpam-5839	409	21	∫	∫	PROPN
ejpam-5839	409	22	b1	b1	PROPN
ejpam-5839	409	23	a1	a1	NOUN
ejpam-5839	409	24	f̃	f̃	PROPN
ejpam-5839	409	25	k	k	PROPN
ejpam-5839	410	1	q	q	PROPN
ejpam-5839	410	2	,	,	PUNCT
ejpam-5839	410	3	u	u	NOUN
ejpam-5839	410	4	(	(	PUNCT
ejpam-5839	410	5	x	x	NOUN
ejpam-5839	410	6	)	)	PUNCT
ejpam-5839	410	7	dx+	dx+	ADJ
ejpam-5839	410	8	∫	∫	PROPN
ejpam-5839	410	9	b1	b1	PROPN
ejpam-5839	410	10	a1	a1	PROPN
ejpam-5839	410	11	g̃kq	g̃kq	PROPN
ejpam-5839	410	12	,	,	PUNCT
ejpam-5839	410	13	u	u	NOUN
ejpam-5839	410	14	(	(	PUNCT
ejpam-5839	410	15	x	x	X
ejpam-5839	410	16	)	)	PUNCT
ejpam-5839	410	17	dx	dx	PROPN
ejpam-5839	410	18	]	]	PUNCT
ejpam-5839	411	1	[	[	X
ejpam-5839	411	2	∫	∫	X
ejpam-5839	411	3	b1	b1	NOUN
ejpam-5839	411	4	a1	a1	NOUN
ejpam-5839	411	5	f̃	f̃	PROPN
ejpam-5839	411	6	l	l	PROPN
ejpam-5839	411	7	q	q	PROPN
ejpam-5839	411	8	,	,	PUNCT
ejpam-5839	411	9	l(x	l(x	PROPN
ejpam-5839	411	10	)	)	PUNCT
ejpam-5839	411	11	dx+	dx+	NOUN
ejpam-5839	411	12	∫	∫	PROPN
ejpam-5839	411	13	b1	b1	PROPN
ejpam-5839	411	14	a1	a1	PROPN
ejpam-5839	411	15	g̃lq	g̃lq	PROPN
ejpam-5839	411	16	,	,	PUNCT
ejpam-5839	411	17	l(x	l(x	PROPN
ejpam-5839	411	18	)	)	PUNCT
ejpam-5839	411	19	dx	dx	PROPN
ejpam-5839	411	20	,	,	PUNCT
ejpam-5839	411	21	∫	∫	PROPN
ejpam-5839	411	22	b1	b1	PROPN
ejpam-5839	411	23	a1	a1	NOUN
ejpam-5839	411	24	f̃	f̃	PROPN
ejpam-5839	411	25	l	l	PROPN
ejpam-5839	411	26	q	q	PROPN
ejpam-5839	411	27	,	,	PUNCT
ejpam-5839	411	28	u	u	NOUN
ejpam-5839	411	29	(	(	PUNCT
ejpam-5839	411	30	x	x	NOUN
ejpam-5839	411	31	)	)	PUNCT
ejpam-5839	411	32	dx+	dx+	ADJ
ejpam-5839	411	33	∫	∫	PROPN
ejpam-5839	411	34	b1	b1	PROPN
ejpam-5839	411	35	a1	a1	PROPN
ejpam-5839	411	36	g̃lq	g̃lq	PROPN
ejpam-5839	411	37	,	,	PUNCT
ejpam-5839	411	38	u	u	NOUN
ejpam-5839	411	39	(	(	PUNCT
ejpam-5839	411	40	x	x	X
ejpam-5839	411	41	)	)	PUNCT
ejpam-5839	411	42	dx	dx	PROPN
ejpam-5839	411	43	]	]	PUNCT
ejpam-5839	411	44	⟨	⟨	X
ejpam-5839	411	45	∫	∫	PROPN
ejpam-5839	411	46	b1	b1	PROPN
ejpam-5839	411	47	a1	a1	NOUN
ejpam-5839	411	48	(	(	PUNCT
ejpam-5839	411	49	f̃q(x	f̃q(x	ADV
ejpam-5839	411	50	)	)	PUNCT
ejpam-5839	411	51	+	+	CCONJ
ejpam-5839	412	1	g̃q(x	g̃q(x	NOUN
ejpam-5839	412	2	)	)	PUNCT
ejpam-5839	412	3	)	)	PUNCT
ejpam-5839	413	1	i	i	PRON
ejpam-5839	413	2	l	l	PROPN
ejpam-5839	413	3	dx	dx	PROPN
ejpam-5839	413	4	,	,	PUNCT
ejpam-5839	413	5	∫	∫	PROPN
ejpam-5839	413	6	b1	b1	PROPN
ejpam-5839	413	7	a1	a1	PROPN
ejpam-5839	413	8	(	(	PUNCT
ejpam-5839	413	9	f̃q(x	f̃q(x	ADV
ejpam-5839	413	10	)	)	PUNCT
ejpam-5839	413	11	+	+	CCONJ
ejpam-5839	413	12	g̃q(x	g̃q(x	NOUN
ejpam-5839	413	13	)	)	PUNCT
ejpam-5839	413	14	)	)	PUNCT
ejpam-5839	414	1	i	i	PRON
ejpam-5839	414	2	u	u	PROPN
ejpam-5839	414	3	dx	dx	PROPN
ejpam-5839	414	4	,	,	PUNCT
ejpam-5839	414	5	∫	∫	PROPN
ejpam-5839	414	6	b1	b1	PROPN
ejpam-5839	414	7	a1	a1	PROPN
ejpam-5839	414	8	(	(	PUNCT
ejpam-5839	414	9	f̃q(x	f̃q(x	ADV
ejpam-5839	414	10	)	)	PUNCT
ejpam-5839	414	11	+	+	CCONJ
ejpam-5839	414	12	g̃q(x	g̃q(x	NOUN
ejpam-5839	414	13	)	)	PUNCT
ejpam-5839	414	14	)	)	PUNCT
ejpam-5839	415	1	j	j	PROPN
ejpam-5839	415	2	l	l	PROPN
ejpam-5839	415	3	dx	dx	PROPN
ejpam-5839	415	4	,	,	PUNCT
ejpam-5839	415	5	∫	∫	PROPN
ejpam-5839	415	6	b1	b1	PROPN
ejpam-5839	415	7	a1	a1	PROPN
ejpam-5839	415	8	(	(	PUNCT
ejpam-5839	415	9	f̃q(x	f̃q(x	ADV
ejpam-5839	415	10	)	)	PUNCT
ejpam-5839	415	11	+	+	CCONJ
ejpam-5839	415	12	g̃q(x	g̃q(x	NOUN
ejpam-5839	415	13	)	)	PUNCT
ejpam-5839	415	14	)	)	PUNCT
ejpam-5839	416	1	j	j	PROPN
ejpam-5839	416	2	u	u	PROPN
ejpam-5839	416	3	dx	dx	PROPN
ejpam-5839	416	4	,	,	PUNCT
ejpam-5839	416	5	∫	∫	PROPN
ejpam-5839	416	6	b1	b1	PROPN
ejpam-5839	416	7	a1	a1	PROPN
ejpam-5839	416	8	(	(	PUNCT
ejpam-5839	416	9	f̃q(x	f̃q(x	ADV
ejpam-5839	416	10	)	)	PUNCT
ejpam-5839	416	11	+	+	CCONJ
ejpam-5839	416	12	g̃q(x	g̃q(x	NOUN
ejpam-5839	416	13	)	)	PUNCT
ejpam-5839	416	14	)	)	PUNCT
ejpam-5839	417	1	k	k	PROPN
ejpam-5839	417	2	l	l	PROPN
ejpam-5839	417	3	dx	dx	PROPN
ejpam-5839	417	4	,	,	PUNCT
ejpam-5839	417	5	∫	∫	PROPN
ejpam-5839	417	6	b1	b1	PROPN
ejpam-5839	417	7	a1	a1	PROPN
ejpam-5839	417	8	(	(	PUNCT
ejpam-5839	417	9	f̃q(x	f̃q(x	ADV
ejpam-5839	417	10	)	)	PUNCT
ejpam-5839	417	11	+	+	CCONJ
ejpam-5839	417	12	g̃q(x	g̃q(x	NOUN
ejpam-5839	417	13	)	)	PUNCT
ejpam-5839	417	14	)	)	PUNCT
ejpam-5839	418	1	k	k	PROPN
ejpam-5839	418	2	u	u	PROPN
ejpam-5839	418	3	dx	dx	PROPN
ejpam-5839	418	4	,	,	PUNCT
ejpam-5839	418	5	a.	a.	PROPN
ejpam-5839	418	6	shihadeh	shihadeh	PROPN
ejpam-5839	418	7	et	et	PROPN
ejpam-5839	418	8	al	al	PROPN
ejpam-5839	418	9	.	.	PUNCT
ejpam-5839	418	10	/	/	SYM
ejpam-5839	418	11	eur	eur	PROPN
ejpam-5839	418	12	.	.	PUNCT
ejpam-5839	419	1	j.	j.	PROPN
ejpam-5839	419	2	pure	pure	PROPN
ejpam-5839	419	3	appl	appl	PROPN
ejpam-5839	419	4	.	.	PROPN
ejpam-5839	419	5	math	math	PROPN
ejpam-5839	419	6	,	,	PUNCT
ejpam-5839	419	7	18	18	NUM
ejpam-5839	419	8	(	(	PUNCT
ejpam-5839	419	9	2	2	NUM
ejpam-5839	419	10	)	)	PUNCT
ejpam-5839	419	11	(	(	PUNCT
ejpam-5839	419	12	2025	2025	NUM
ejpam-5839	419	13	)	)	PUNCT
ejpam-5839	419	14	,	,	PUNCT
ejpam-5839	419	15	5839	5839	NUM
ejpam-5839	419	16	18	18	NUM
ejpam-5839	419	17	of	of	ADP
ejpam-5839	419	18	54	54	NUM
ejpam-5839	419	19	∫	∫	NOUN
ejpam-5839	419	20	b1	b1	NOUN
ejpam-5839	419	21	a1	a1	NOUN
ejpam-5839	419	22	(	(	PUNCT
ejpam-5839	419	23	f̃q(x	f̃q(x	ADV
ejpam-5839	419	24	)	)	PUNCT
ejpam-5839	419	25	+	+	CCONJ
ejpam-5839	419	26	g̃q(x	g̃q(x	NOUN
ejpam-5839	419	27	)	)	PUNCT
ejpam-5839	419	28	)	)	PUNCT
ejpam-5839	420	1	l	l	NOUN
ejpam-5839	420	2	l	l	X
ejpam-5839	420	3	dx	dx	PROPN
ejpam-5839	420	4	,	,	PUNCT
ejpam-5839	420	5	∫	∫	PROPN
ejpam-5839	420	6	b1	b1	PROPN
ejpam-5839	420	7	a1	a1	PROPN
ejpam-5839	420	8	(	(	PUNCT
ejpam-5839	420	9	f̃q(x	f̃q(x	ADV
ejpam-5839	420	10	)	)	PUNCT
ejpam-5839	420	11	+	+	CCONJ
ejpam-5839	420	12	g̃q(x	g̃q(x	NOUN
ejpam-5839	420	13	)	)	PUNCT
ejpam-5839	420	14	)	)	PUNCT
ejpam-5839	421	1	l	l	NOUN
ejpam-5839	421	2	u	u	NOUN
ejpam-5839	421	3	dx⟩	dx⟩	NOUN
ejpam-5839	421	4	(	(	PUNCT
ejpam-5839	421	5	∫	∫	PROPN
ejpam-5839	421	6	b1	b1	PROPN
ejpam-5839	421	7	a1	a1	PROPN
ejpam-5839	421	8	f̃q(x	f̃q(x	CCONJ
ejpam-5839	421	9	)	)	PUNCT
ejpam-5839	421	10	dx+	dx+	NOUN
ejpam-5839	421	11	∫	∫	PROPN
ejpam-5839	421	12	b1	b1	PROPN
ejpam-5839	421	13	a1	a1	PROPN
ejpam-5839	421	14	g̃q(x	g̃q(x	PROPN
ejpam-5839	421	15	)	)	PUNCT
ejpam-5839	421	16	dx	dx	PROPN
ejpam-5839	421	17	)	)	PUNCT
ejpam-5839	421	18	(	(	PUNCT
ejpam-5839	421	19	i	i	PROPN
ejpam-5839	421	20	,	,	PUNCT
ejpam-5839	421	21	j	j	PROPN
ejpam-5839	421	22	,	,	PUNCT
ejpam-5839	421	23	k	k	PROPN
ejpam-5839	421	24	,	,	PUNCT
ejpam-5839	421	25	l	l	NOUN
ejpam-5839	421	26	)	)	PUNCT
ejpam-5839	421	27	theorem	theorem	NOUN
ejpam-5839	421	28	5	5	NUM
ejpam-5839	421	29	.	.	PUNCT
ejpam-5839	422	1	let	let	AUX
ejpam-5839	422	2	f̃q(x	f̃q(x	PART
ejpam-5839	422	3	)	)	PUNCT
ejpam-5839	422	4	be	be	AUX
ejpam-5839	422	5	a	a	DET
ejpam-5839	422	6	closed	closed	ADJ
ejpam-5839	422	7	bounded	bounded	ADJ
ejpam-5839	422	8	quadri	quadri	PROPN
ejpam-5839	422	9	-	-	PUNCT
ejpam-5839	422	10	neutrosophic	neutrosophic	PROPN
ejpam-5839	422	11	valued	value	VERB
ejpam-5839	422	12	function	function	NOUN
ejpam-5839	422	13	on	on	ADP
ejpam-5839	422	14	the	the	DET
ejpam-5839	422	15	closed	closed	ADJ
ejpam-5839	422	16	interval	interval	NOUN
ejpam-5839	422	17	[	[	X
ejpam-5839	422	18	a1	a1	NOUN
ejpam-5839	422	19	,	,	PUNCT
ejpam-5839	422	20	b1	b1	NOUN
ejpam-5839	422	21	]	]	PUNCT
ejpam-5839	422	22	.	.	PUNCT
ejpam-5839	423	1	if	if	SCONJ
ejpam-5839	423	2	f̃q(x	f̃q(x	NUM
ejpam-5839	423	3	)	)	PUNCT
ejpam-5839	423	4	∈	∈	PROPN
ejpam-5839	423	5	qri	qri	NOUN
ejpam-5839	423	6	,	,	PUNCT
ejpam-5839	423	7	then	then	ADV
ejpam-5839	423	8	λf̃q(x	λf̃q(x	NUM
ejpam-5839	423	9	)	)	PUNCT
ejpam-5839	423	10	∈	∈	PROPN
ejpam-5839	423	11	qri	qri	NOUN
ejpam-5839	423	12	.	.	PUNCT
ejpam-5839	423	13	moreover,∫	moreover,∫	PROPN
ejpam-5839	423	14	b1	b1	PROPN
ejpam-5839	423	15	a1	a1	NOUN
ejpam-5839	423	16	λf̃q(x	λf̃q(x	X
ejpam-5839	423	17	)	)	PUNCT
ejpam-5839	423	18	dx	dx	PROPN
ejpam-5839	423	19	=	=	SYM
ejpam-5839	423	20	λ	λ	PROPN
ejpam-5839	423	21	∫	∫	PROPN
ejpam-5839	423	22	b1	b1	PROPN
ejpam-5839	423	23	a1	a1	PROPN
ejpam-5839	423	24	f̃q(x	f̃q(x	CCONJ
ejpam-5839	423	25	)	)	PUNCT
ejpam-5839	423	26	dx	dx	PROPN
ejpam-5839	423	27	where	where	SCONJ
ejpam-5839	423	28	λ	λ	PROPN
ejpam-5839	423	29	̸=	̸=	PROPN
ejpam-5839	423	30	0	0	NUM
ejpam-5839	423	31	is	be	AUX
ejpam-5839	423	32	any	any	DET
ejpam-5839	423	33	real	real	ADJ
ejpam-5839	423	34	number	number	NOUN
ejpam-5839	423	35	.	.	PUNCT
ejpam-5839	424	1	proof	proof	NOUN
ejpam-5839	424	2	.	.	PUNCT
ejpam-5839	425	1	for	for	ADP
ejpam-5839	425	2	λ	λ	PROPN
ejpam-5839	425	3	≻	≻	PROPN
ejpam-5839	425	4	0	0	NUM
ejpam-5839	425	5	,	,	PUNCT
ejpam-5839	425	6	let	let	VERB
ejpam-5839	425	7	g̃q(x	g̃q(x	X
ejpam-5839	425	8	)	)	PUNCT
ejpam-5839	425	9	=	=	SYM
ejpam-5839	426	1	λf̃q(x	λf̃q(x	NUM
ejpam-5839	426	2	)	)	PUNCT
ejpam-5839	426	3	.	.	PUNCT
ejpam-5839	427	1	also	also	ADV
ejpam-5839	427	2	,	,	PUNCT
ejpam-5839	427	3	g̃q(x	g̃q(x	PROPN
ejpam-5839	427	4	)	)	PUNCT
ejpam-5839	427	5	is	be	AUX
ejpam-5839	427	6	a	a	DET
ejpam-5839	427	7	closed	closed	ADJ
ejpam-5839	427	8	quadri	quadri	NOUN
ejpam-5839	427	9	-	-	PUNCT
ejpam-5839	427	10	neutrosophic	neutrosophic	ADJ
ejpam-5839	427	11	valued	value	VERB
ejpam-5839	427	12	function	function	NOUN
ejpam-5839	427	13	(	(	PUNCT
ejpam-5839	427	14	qnvf	qnvf	ADV
ejpam-5839	427	15	)	)	PUNCT
ejpam-5839	427	16	.	.	PUNCT
ejpam-5839	428	1	(	(	PUNCT
ejpam-5839	428	2	λ	λ	PROPN
ejpam-5839	428	3	∫	∫	PROPN
ejpam-5839	428	4	b1	b1	PROPN
ejpam-5839	428	5	a1	a1	PROPN
ejpam-5839	428	6	f̃q(x	f̃q(x	CCONJ
ejpam-5839	428	7	)	)	PUNCT
ejpam-5839	428	8	dx	dx	PROPN
ejpam-5839	428	9	)	)	PUNCT
ejpam-5839	429	1	(	(	PUNCT
ejpam-5839	429	2	i	i	PROPN
ejpam-5839	429	3	,	,	PUNCT
ejpam-5839	429	4	j	j	PROPN
ejpam-5839	429	5	,	,	PUNCT
ejpam-5839	429	6	k	k	PROPN
ejpam-5839	429	7	,	,	PUNCT
ejpam-5839	429	8	l	l	NOUN
ejpam-5839	429	9	)	)	PUNCT
ejpam-5839	429	10	〈	〈	PROPN
ejpam-5839	429	11	[	[	PUNCT
ejpam-5839	429	12	λ	λ	PROPN
ejpam-5839	429	13	∫	∫	PROPN
ejpam-5839	429	14	b1	b1	PROPN
ejpam-5839	429	15	a1	a1	PROPN
ejpam-5839	429	16	f̃lqi(x	f̃lqi(x	X
ejpam-5839	429	17	)	)	PUNCT
ejpam-5839	429	18	dx	dx	PROPN
ejpam-5839	429	19	,	,	PUNCT
ejpam-5839	429	20	λ	λ	PROPN
ejpam-5839	429	21	∫	∫	PROPN
ejpam-5839	429	22	b1	b1	PROPN
ejpam-5839	429	23	a1	a1	PROPN
ejpam-5839	429	24	f̃uqi(x	f̃uqi(x	PROPN
ejpam-5839	429	25	)	)	PUNCT
ejpam-5839	429	26	dx	dx	PROPN
ejpam-5839	429	27	]	]	PUNCT
ejpam-5839	429	28	,	,	PUNCT
ejpam-5839	429	29	[	[	PUNCT
ejpam-5839	429	30	λ	λ	X
ejpam-5839	429	31	∫	∫	PROPN
ejpam-5839	429	32	b1	b1	PROPN
ejpam-5839	429	33	a1	a1	PROPN
ejpam-5839	429	34	f̃lqj(x	f̃lqj(x	PROPN
ejpam-5839	429	35	)	)	PUNCT
ejpam-5839	429	36	dx	dx	PROPN
ejpam-5839	429	37	,	,	PUNCT
ejpam-5839	429	38	λ	λ	PROPN
ejpam-5839	429	39	∫	∫	PROPN
ejpam-5839	429	40	b1	b1	PROPN
ejpam-5839	429	41	a1	a1	PROPN
ejpam-5839	429	42	f̃uqj(x	f̃uqj(x	X
ejpam-5839	429	43	)	)	PUNCT
ejpam-5839	429	44	dx	dx	PROPN
ejpam-5839	429	45	]	]	PUNCT
ejpam-5839	429	46	,	,	PUNCT
ejpam-5839	429	47	[	[	PUNCT
ejpam-5839	429	48	λ	λ	X
ejpam-5839	429	49	∫	∫	PROPN
ejpam-5839	429	50	b1	b1	PROPN
ejpam-5839	429	51	a1	a1	PROPN
ejpam-5839	429	52	f̃lqk(x	f̃lqk(x	NOUN
ejpam-5839	429	53	)	)	PUNCT
ejpam-5839	429	54	dx	dx	PROPN
ejpam-5839	429	55	,	,	PUNCT
ejpam-5839	429	56	λ	λ	PROPN
ejpam-5839	429	57	∫	∫	PROPN
ejpam-5839	429	58	b1	b1	PROPN
ejpam-5839	429	59	a1	a1	PROPN
ejpam-5839	429	60	f̃uqk(x	f̃uqk(x	PROPN
ejpam-5839	429	61	)	)	PUNCT
ejpam-5839	429	62	dx	dx	PROPN
ejpam-5839	429	63	]	]	PUNCT
ejpam-5839	429	64	,	,	PUNCT
ejpam-5839	429	65	[	[	PUNCT
ejpam-5839	429	66	λ	λ	X
ejpam-5839	429	67	∫	∫	PROPN
ejpam-5839	429	68	b1	b1	PROPN
ejpam-5839	429	69	a1	a1	PROPN
ejpam-5839	429	70	f̃lql(x	f̃lql(x	PROPN
ejpam-5839	429	71	)	)	PUNCT
ejpam-5839	429	72	dx	dx	PROPN
ejpam-5839	429	73	,	,	PUNCT
ejpam-5839	429	74	λ	λ	PROPN
ejpam-5839	429	75	∫	∫	PROPN
ejpam-5839	429	76	b1	b1	PROPN
ejpam-5839	429	77	a1	a1	PROPN
ejpam-5839	429	78	f̃uql(x	f̃uql(x	PROPN
ejpam-5839	429	79	)	)	PUNCT
ejpam-5839	429	80	dx	dx	PROPN
ejpam-5839	429	81	]	]	PUNCT
ejpam-5839	429	82	〉	〉	NOUN
ejpam-5839	429	83	〈	〈	PROPN
ejpam-5839	429	84	[	[	X
ejpam-5839	429	85	∫	∫	NOUN
ejpam-5839	429	86	b1	b1	NOUN
ejpam-5839	429	87	a1	a1	PROPN
ejpam-5839	429	88	λf̃lqi(x	λf̃lqi(x	NOUN
ejpam-5839	429	89	)	)	PUNCT
ejpam-5839	429	90	dx	dx	PROPN
ejpam-5839	429	91	,	,	PUNCT
ejpam-5839	429	92	∫	∫	PROPN
ejpam-5839	429	93	b1	b1	PROPN
ejpam-5839	429	94	a1	a1	PROPN
ejpam-5839	429	95	λf̃uqi(x	λf̃uqi(x	NOUN
ejpam-5839	429	96	)	)	PUNCT
ejpam-5839	429	97	dx	dx	PROPN
ejpam-5839	429	98	]	]	PUNCT
ejpam-5839	429	99	,	,	PUNCT
ejpam-5839	429	100	[	[	PUNCT
ejpam-5839	429	101	∫	∫	PROPN
ejpam-5839	429	102	b1	b1	NOUN
ejpam-5839	429	103	a1	a1	PROPN
ejpam-5839	429	104	λf̃lqj(x	λf̃lqj(x	PROPN
ejpam-5839	429	105	)	)	PUNCT
ejpam-5839	429	106	dx	dx	PROPN
ejpam-5839	429	107	,	,	PUNCT
ejpam-5839	429	108	∫	∫	PROPN
ejpam-5839	429	109	b1	b1	PROPN
ejpam-5839	429	110	a1	a1	PROPN
ejpam-5839	429	111	λf̃uqj(x	λf̃uqj(x	PROPN
ejpam-5839	429	112	)	)	PUNCT
ejpam-5839	429	113	dx	dx	PROPN
ejpam-5839	429	114	]	]	PUNCT
ejpam-5839	429	115	,	,	PUNCT
ejpam-5839	429	116	[	[	PUNCT
ejpam-5839	429	117	∫	∫	PROPN
ejpam-5839	429	118	b1	b1	NOUN
ejpam-5839	429	119	a1	a1	PROPN
ejpam-5839	429	120	λf̃lqk(x	λf̃lqk(x	NOUN
ejpam-5839	429	121	)	)	PUNCT
ejpam-5839	429	122	dx	dx	PROPN
ejpam-5839	429	123	,	,	PUNCT
ejpam-5839	429	124	∫	∫	PROPN
ejpam-5839	429	125	b1	b1	PROPN
ejpam-5839	429	126	a1	a1	NOUN
ejpam-5839	429	127	λf̃uqk(x	λf̃uqk(x	NOUN
ejpam-5839	429	128	)	)	PUNCT
ejpam-5839	429	129	dx	dx	PROPN
ejpam-5839	429	130	]	]	PUNCT
ejpam-5839	429	131	,	,	PUNCT
ejpam-5839	429	132	[	[	PUNCT
ejpam-5839	429	133	∫	∫	PROPN
ejpam-5839	429	134	b1	b1	PROPN
ejpam-5839	429	135	a1	a1	PROPN
ejpam-5839	429	136	λf̃lql(x	λf̃lql(x	PROPN
ejpam-5839	429	137	)	)	PUNCT
ejpam-5839	429	138	dx	dx	PROPN
ejpam-5839	429	139	,	,	PUNCT
ejpam-5839	429	140	∫	∫	PROPN
ejpam-5839	429	141	b1	b1	PROPN
ejpam-5839	429	142	a1	a1	PROPN
ejpam-5839	429	143	λf̃uql(x	λf̃uql(x	PROPN
ejpam-5839	429	144	)	)	PUNCT
ejpam-5839	429	145	dx	dx	PROPN
ejpam-5839	429	146	]	]	PUNCT
ejpam-5839	429	147	〉	〉	X
ejpam-5839	429	148	(	(	PUNCT
ejpam-5839	429	149	∫	∫	PROPN
ejpam-5839	429	150	b1	b1	NOUN
ejpam-5839	429	151	a1	a1	PROPN
ejpam-5839	429	152	λf̃q(x	λf̃q(x	SYM
ejpam-5839	429	153	)	)	PUNCT
ejpam-5839	429	154	dx	dx	PROPN
ejpam-5839	429	155	)	)	PUNCT
ejpam-5839	429	156	(	(	PUNCT
ejpam-5839	429	157	i	i	PROPN
ejpam-5839	429	158	,	,	PUNCT
ejpam-5839	429	159	j	j	PROPN
ejpam-5839	429	160	,	,	PUNCT
ejpam-5839	429	161	k	k	PROPN
ejpam-5839	429	162	,	,	PUNCT
ejpam-5839	429	163	l	l	NOUN
ejpam-5839	429	164	)	)	PUNCT
ejpam-5839	429	165	since	since	SCONJ
ejpam-5839	429	166	,	,	PUNCT
ejpam-5839	429	167	∫	∫	PROPN
ejpam-5839	429	168	b1	b1	PROPN
ejpam-5839	429	169	a1	a1	PROPN
ejpam-5839	429	170	λf̃q(x	λf̃q(x	X
ejpam-5839	429	171	)	)	PUNCT
ejpam-5839	429	172	dx	dx	PROPN
ejpam-5839	430	1	=	=	SYM
ejpam-5839	430	2	λ	λ	PROPN
ejpam-5839	430	3	∫	∫	PROPN
ejpam-5839	430	4	b1	b1	PROPN
ejpam-5839	430	5	a1	a1	PROPN
ejpam-5839	430	6	f̃q(x	f̃q(x	ADV
ejpam-5839	430	7	)	)	PUNCT
ejpam-5839	430	8	dx	dx	PROPN
ejpam-5839	430	9	the	the	DET
ejpam-5839	430	10	same	same	ADJ
ejpam-5839	430	11	holds	hold	VERB
ejpam-5839	430	12	for	for	ADP
ejpam-5839	430	13	λ	λ	PROPN
ejpam-5839	430	14	≺	≺	NOUN
ejpam-5839	430	15	0	0	NUM
ejpam-5839	430	16	.	.	PUNCT
ejpam-5839	431	1	a.	a.	NOUN
ejpam-5839	431	2	shihadeh	shihadeh	PROPN
ejpam-5839	431	3	et	et	PROPN
ejpam-5839	431	4	al	al	PROPN
ejpam-5839	431	5	.	.	PUNCT
ejpam-5839	431	6	/	/	SYM
ejpam-5839	431	7	eur	eur	PROPN
ejpam-5839	431	8	.	.	PUNCT
ejpam-5839	432	1	j.	j.	PROPN
ejpam-5839	432	2	pure	pure	PROPN
ejpam-5839	432	3	appl	appl	PROPN
ejpam-5839	432	4	.	.	PROPN
ejpam-5839	432	5	math	math	PROPN
ejpam-5839	432	6	,	,	PUNCT
ejpam-5839	432	7	18	18	NUM
ejpam-5839	432	8	(	(	PUNCT
ejpam-5839	432	9	2	2	NUM
ejpam-5839	432	10	)	)	PUNCT
ejpam-5839	432	11	(	(	PUNCT
ejpam-5839	432	12	2025	2025	NUM
ejpam-5839	432	13	)	)	PUNCT
ejpam-5839	432	14	,	,	PUNCT
ejpam-5839	432	15	5839	5839	NUM
ejpam-5839	432	16	19	19	NUM
ejpam-5839	432	17	of	of	ADP
ejpam-5839	432	18	54	54	NUM
ejpam-5839	432	19	example	example	NOUN
ejpam-5839	433	1	1	1	NUM
ejpam-5839	433	2	.	.	PUNCT
ejpam-5839	434	1	if	if	SCONJ
ejpam-5839	434	2	f̃(q(x	f̃(q(x	PROPN
ejpam-5839	434	3	)	)	PUNCT
ejpam-5839	434	4	)	)	PUNCT
ejpam-5839	435	1	=	=	PUNCT
ejpam-5839	435	2	ñ(x)2	ñ(x)2	VERB
ejpam-5839	435	3	on	on	ADP
ejpam-5839	435	4	[	[	X
ejpam-5839	435	5	0	0	NUM
ejpam-5839	435	6	,	,	PUNCT
ejpam-5839	435	7	1	1	NUM
ejpam-5839	435	8	]	]	PUNCT
ejpam-5839	435	9	where	where	SCONJ
ejpam-5839	435	10	ñ	ñ	PROPN
ejpam-5839	435	11	=	=	SYM
ejpam-5839	435	12	〈	〈	PROPN
ejpam-5839	435	13	(	(	PUNCT
ejpam-5839	435	14	0	0	NUM
ejpam-5839	435	15	,	,	PUNCT
ejpam-5839	435	16	1	1	NUM
ejpam-5839	435	17	,	,	PUNCT
ejpam-5839	435	18	2	2	NUM
ejpam-5839	435	19	,	,	PUNCT
ejpam-5839	435	20	3	3	NUM
ejpam-5839	435	21	)	)	PUNCT
ejpam-5839	435	22	;	;	PUNCT
ejpam-5839	435	23	8×	8×	ADP
ejpam-5839	435	24	10−1	10−1	NUM
ejpam-5839	435	25	,	,	PUNCT
ejpam-5839	435	26	6×	6×	NOUN
ejpam-5839	435	27	10−1	10−1	NUM
ejpam-5839	435	28	,	,	PUNCT
ejpam-5839	435	29	4×	4×	NOUN
ejpam-5839	435	30	10−1	10−1	NUM
ejpam-5839	435	31	,	,	PUNCT
ejpam-5839	435	32	4×	4×	NOUN
ejpam-5839	435	33	10−1	10−1	NUM
ejpam-5839	435	34	〉	〉	NOUN
ejpam-5839	435	35	is	be	AUX
ejpam-5839	435	36	a	a	DET
ejpam-5839	435	37	quadri	quadri	PROPN
ejpam-5839	435	38	-	-	PUNCT
ejpam-5839	435	39	neutrosophic	neutrosophic	ADJ
ejpam-5839	435	40	valued	value	VERB
ejpam-5839	435	41	number	number	NOUN
ejpam-5839	435	42	.	.	PUNCT
ejpam-5839	436	1	now	now	ADV
ejpam-5839	436	2	,	,	PUNCT
ejpam-5839	436	3	we	we	PRON
ejpam-5839	436	4	integrate	integrate	VERB
ejpam-5839	436	5	the	the	DET
ejpam-5839	436	6	quadri	quadri	PROPN
ejpam-5839	436	7	-	-	PUNCT
ejpam-5839	436	8	neutrosophic	neutrosophic	PROPN
ejpam-5839	436	9	valued	value	VERB
ejpam-5839	436	10	function	function	NOUN
ejpam-5839	436	11	on	on	ADP
ejpam-5839	436	12	[	[	X
ejpam-5839	436	13	0	0	NUM
ejpam-5839	436	14	,	,	PUNCT
ejpam-5839	436	15	1	1	NUM
ejpam-5839	436	16	]	]	PUNCT
ejpam-5839	436	17	and	and	CCONJ
ejpam-5839	436	18	try	try	VERB
ejpam-5839	436	19	to	to	PART
ejpam-5839	436	20	find	find	VERB
ejpam-5839	436	21	∫	∫	PROPN
ejpam-5839	436	22	1	1	NUM
ejpam-5839	436	23	0	0	NUM
ejpam-5839	436	24	f̃q(x	f̃q(x	NUM
ejpam-5839	436	25	)	)	PUNCT
ejpam-5839	436	26	dx	dx	PROPN
ejpam-5839	436	27	.	.	PUNCT
ejpam-5839	437	1	now	now	ADV
ejpam-5839	437	2	,	,	PUNCT
ejpam-5839	437	3	taking	take	VERB
ejpam-5839	437	4	the	the	DET
ejpam-5839	437	5	(	(	PUNCT
ejpam-5839	437	6	i	i	PROPN
ejpam-5839	437	7	,	,	PUNCT
ejpam-5839	437	8	j	j	PROPN
ejpam-5839	437	9	,	,	PUNCT
ejpam-5839	437	10	k	k	PROPN
ejpam-5839	437	11	,	,	PUNCT
ejpam-5839	437	12	l)-cut	l)-cut	NOUN
ejpam-5839	437	13	of	of	ADP
ejpam-5839	437	14	the	the	DET
ejpam-5839	437	15	integral	integral	ADJ
ejpam-5839	437	16	,	,	PUNCT
ejpam-5839	437	17	we	we	PRON
ejpam-5839	437	18	obtain:(∫	obtain:(∫	VERB
ejpam-5839	437	19	1	1	NUM
ejpam-5839	437	20	0	0	NUM
ejpam-5839	437	21	f̃(q(x	f̃(q(x	NUM
ejpam-5839	437	22	)	)	PUNCT
ejpam-5839	437	23	)	)	PUNCT
ejpam-5839	437	24	dx	dx	PROPN
ejpam-5839	437	25	)	)	PUNCT
ejpam-5839	438	1	(	(	PUNCT
ejpam-5839	438	2	i	i	PROPN
ejpam-5839	438	3	,	,	PUNCT
ejpam-5839	438	4	j	j	PROPN
ejpam-5839	438	5	,	,	PUNCT
ejpam-5839	438	6	k	k	PROPN
ejpam-5839	438	7	,	,	PUNCT
ejpam-5839	438	8	l	l	NOUN
ejpam-5839	438	9	)	)	PUNCT
ejpam-5839	438	10	=	=	SYM
ejpam-5839	438	11	(	(	PUNCT
ejpam-5839	438	12	∫	∫	PROPN
ejpam-5839	438	13	1	1	NUM
ejpam-5839	438	14	0	0	NUM
ejpam-5839	438	15	ñ(x)2	ñ(x)2	NOUN
ejpam-5839	438	16	dx	dx	PROPN
ejpam-5839	438	17	)	)	PUNCT
ejpam-5839	438	18	(	(	PUNCT
ejpam-5839	438	19	i	i	PROPN
ejpam-5839	438	20	,	,	PUNCT
ejpam-5839	438	21	j	j	PROPN
ejpam-5839	438	22	,	,	PUNCT
ejpam-5839	438	23	k	k	PROPN
ejpam-5839	438	24	,	,	PUNCT
ejpam-5839	438	25	l	l	NOUN
ejpam-5839	438	26	)	)	PUNCT
ejpam-5839	438	27	.	.	PUNCT
ejpam-5839	439	1	this	this	PRON
ejpam-5839	439	2	results	result	VERB
ejpam-5839	439	3	in:〈[∫	in:〈[∫	ADJ
ejpam-5839	439	4	1	1	NUM
ejpam-5839	439	5	0	0	NUM
ejpam-5839	439	6	5i	5i	NUM
ejpam-5839	439	7	4	4	NUM
ejpam-5839	439	8	x2	x2	PROPN
ejpam-5839	439	9	dx	dx	PROPN
ejpam-5839	439	10	,	,	PUNCT
ejpam-5839	439	11	∫	∫	PROPN
ejpam-5839	439	12	1	1	NUM
ejpam-5839	439	13	0	0	NUM
ejpam-5839	439	14	8−	8−	NUM
ejpam-5839	439	15	5i	5i	NUM
ejpam-5839	439	16	4	4	NUM
ejpam-5839	440	1	x2	x2	NOUN
ejpam-5839	440	2	dx	dx	PROPN
ejpam-5839	440	3	]	]	PUNCT
ejpam-5839	440	4	,	,	PUNCT
ejpam-5839	440	5	[	[	X
ejpam-5839	440	6	∫	∫	X
ejpam-5839	440	7	1	1	NUM
ejpam-5839	440	8	0	0	NUM
ejpam-5839	440	9	5	5	NUM
ejpam-5839	440	10	2	2	NUM
ejpam-5839	440	11	(	(	PUNCT
ejpam-5839	440	12	1−	1−	NUM
ejpam-5839	440	13	j)x2	j)x2	PROPN
ejpam-5839	440	14	dx	dx	PROPN
ejpam-5839	440	15	,	,	PUNCT
ejpam-5839	440	16	∫	∫	PROPN
ejpam-5839	440	17	1	1	NUM
ejpam-5839	440	18	0	0	NUM
ejpam-5839	440	19	1	1	NUM
ejpam-5839	440	20	2	2	NUM
ejpam-5839	440	21	(	(	PUNCT
ejpam-5839	440	22	5j−	5j−	PROPN
ejpam-5839	440	23	1)x2	1)x2	PROPN
ejpam-5839	440	24	dx	dx	X
ejpam-5839	440	25	]	]	PUNCT
ejpam-5839	440	26	,	,	PUNCT
ejpam-5839	440	27	[	[	X
ejpam-5839	440	28	∫	∫	X
ejpam-5839	440	29	1	1	NUM
ejpam-5839	440	30	0	0	NUM
ejpam-5839	440	31	5	5	NUM
ejpam-5839	440	32	3	3	NUM
ejpam-5839	440	33	(	(	PUNCT
ejpam-5839	440	34	1−	1−	NUM
ejpam-5839	440	35	k)x2	k)x2	PROPN
ejpam-5839	440	36	dx	dx	PROPN
ejpam-5839	440	37	,	,	PUNCT
ejpam-5839	440	38	∫	∫	PROPN
ejpam-5839	440	39	1	1	NUM
ejpam-5839	440	40	0	0	NUM
ejpam-5839	440	41	1	1	NUM
ejpam-5839	440	42	3	3	NUM
ejpam-5839	440	43	(	(	PUNCT
ejpam-5839	440	44	5k−	5k−	NUM
ejpam-5839	440	45	1)x2	1)x2	PROPN
ejpam-5839	440	46	dx	dx	X
ejpam-5839	440	47	]	]	PUNCT
ejpam-5839	440	48	,	,	PUNCT
ejpam-5839	441	1	[	[	X
ejpam-5839	441	2	∫	∫	X
ejpam-5839	441	3	1	1	NUM
ejpam-5839	441	4	0	0	NUM
ejpam-5839	441	5	5	5	NUM
ejpam-5839	441	6	3	3	NUM
ejpam-5839	441	7	(	(	PUNCT
ejpam-5839	441	8	1−	1−	NUM
ejpam-5839	441	9	l)x2	l)x2	PROPN
ejpam-5839	441	10	dx	dx	PROPN
ejpam-5839	441	11	,	,	PUNCT
ejpam-5839	441	12	∫	∫	PROPN
ejpam-5839	441	13	1	1	NUM
ejpam-5839	441	14	0	0	NUM
ejpam-5839	441	15	1	1	NUM
ejpam-5839	441	16	3	3	NUM
ejpam-5839	441	17	(	(	PUNCT
ejpam-5839	441	18	5l−	5l−	PROPN
ejpam-5839	441	19	1)x2	1)x2	PROPN
ejpam-5839	441	20	dx	dx	PROPN
ejpam-5839	441	21	]	]	PUNCT
ejpam-5839	441	22	〉	〉	X
ejpam-5839	441	23	.	.	PUNCT
ejpam-5839	442	1	evaluating	evaluate	VERB
ejpam-5839	442	2	the	the	DET
ejpam-5839	442	3	integrals	integral	NOUN
ejpam-5839	442	4	:	:	PUNCT
ejpam-5839	442	5	〈	〈	PROPN
ejpam-5839	442	6	[	[	PUNCT
ejpam-5839	442	7	5i	5i	NUM
ejpam-5839	442	8	12	12	NUM
ejpam-5839	442	9	,	,	PUNCT
ejpam-5839	442	10	8−	8−	NUM
ejpam-5839	442	11	5i	5i	NUM
ejpam-5839	442	12	12	12	NUM
ejpam-5839	442	13	]	]	PUNCT
ejpam-5839	442	14	,	,	PUNCT
ejpam-5839	442	15	[	[	PUNCT
ejpam-5839	442	16	5	5	NUM
ejpam-5839	442	17	6	6	NUM
ejpam-5839	442	18	(	(	PUNCT
ejpam-5839	442	19	1−	1−	NUM
ejpam-5839	442	20	j	j	NOUN
ejpam-5839	442	21	)	)	PUNCT
ejpam-5839	442	22	,	,	PUNCT
ejpam-5839	442	23	1	1	NUM
ejpam-5839	442	24	6	6	NUM
ejpam-5839	442	25	(	(	PUNCT
ejpam-5839	442	26	5j−	5j−	PROPN
ejpam-5839	442	27	1	1	NUM
ejpam-5839	442	28	)	)	PUNCT
ejpam-5839	442	29	]	]	PUNCT
ejpam-5839	442	30	,	,	PUNCT
ejpam-5839	442	31	[	[	PUNCT
ejpam-5839	442	32	5	5	NUM
ejpam-5839	442	33	9	9	NUM
ejpam-5839	442	34	(	(	PUNCT
ejpam-5839	442	35	1−	1−	NUM
ejpam-5839	442	36	k	k	NOUN
ejpam-5839	442	37	)	)	PUNCT
ejpam-5839	442	38	,	,	PUNCT
ejpam-5839	442	39	1	1	NUM
ejpam-5839	442	40	9	9	NUM
ejpam-5839	442	41	(	(	PUNCT
ejpam-5839	442	42	5k−	5k−	PROPN
ejpam-5839	442	43	1	1	NUM
ejpam-5839	442	44	)	)	PUNCT
ejpam-5839	442	45	]	]	PUNCT
ejpam-5839	442	46	,	,	PUNCT
ejpam-5839	442	47	[	[	PUNCT
ejpam-5839	442	48	5	5	NUM
ejpam-5839	442	49	9	9	NUM
ejpam-5839	442	50	(	(	PUNCT
ejpam-5839	442	51	1−	1−	NUM
ejpam-5839	442	52	l	l	NOUN
ejpam-5839	442	53	)	)	PUNCT
ejpam-5839	442	54	,	,	PUNCT
ejpam-5839	442	55	1	1	NUM
ejpam-5839	442	56	9	9	NUM
ejpam-5839	442	57	(	(	PUNCT
ejpam-5839	442	58	5l−	5l−	PROPN
ejpam-5839	442	59	1	1	NUM
ejpam-5839	442	60	)	)	PUNCT
ejpam-5839	442	61	]	]	PUNCT
ejpam-5839	442	62	〉	〉	NOUN
ejpam-5839	442	63	.	.	PUNCT
ejpam-5839	443	1	thus	thus	ADV
ejpam-5839	443	2	,	,	PUNCT
ejpam-5839	443	3	we	we	PRON
ejpam-5839	443	4	obtain	obtain	VERB
ejpam-5839	443	5	:	:	PUNCT
ejpam-5839	443	6	∫	∫	PROPN
ejpam-5839	443	7	1	1	NUM
ejpam-5839	443	8	0	0	NUM
ejpam-5839	443	9	f̃lqi(x	f̃lqi(x	NOUN
ejpam-5839	443	10	)	)	PUNCT
ejpam-5839	443	11	dx	dx	PROPN
ejpam-5839	444	1	=	=	NOUN
ejpam-5839	444	2	5i	5i	NUM
ejpam-5839	444	3	12	12	NUM
ejpam-5839	444	4	,	,	PUNCT
ejpam-5839	444	5	∫	∫	PROPN
ejpam-5839	444	6	1	1	NUM
ejpam-5839	444	7	0	0	NUM
ejpam-5839	444	8	f̃uqi(x	f̃uqi(x	ADJ
ejpam-5839	444	9	)	)	PUNCT
ejpam-5839	444	10	dx	dx	PROPN
ejpam-5839	445	1	=	=	SYM
ejpam-5839	445	2	8−	8−	NUM
ejpam-5839	445	3	5i	5i	NUM
ejpam-5839	445	4	12	12	NUM
ejpam-5839	445	5	,	,	PUNCT
ejpam-5839	445	6	∫	∫	PROPN
ejpam-5839	445	7	1	1	NUM
ejpam-5839	445	8	0	0	NUM
ejpam-5839	445	9	f̃lqj(x	f̃lqj(x	NOUN
ejpam-5839	445	10	)	)	PUNCT
ejpam-5839	445	11	dx	dx	PROPN
ejpam-5839	446	1	=	=	NOUN
ejpam-5839	446	2	5	5	NUM
ejpam-5839	446	3	6	6	NUM
ejpam-5839	446	4	(	(	PUNCT
ejpam-5839	446	5	1−	1−	NUM
ejpam-5839	446	6	j	j	NOUN
ejpam-5839	446	7	)	)	PUNCT
ejpam-5839	446	8	,	,	PUNCT
ejpam-5839	446	9	∫	∫	PROPN
ejpam-5839	446	10	1	1	NUM
ejpam-5839	446	11	0	0	NUM
ejpam-5839	446	12	f̃uqj(x	f̃uqj(x	NOUN
ejpam-5839	446	13	)	)	PUNCT
ejpam-5839	446	14	dx	dx	PROPN
ejpam-5839	446	15	=	=	NOUN
ejpam-5839	446	16	1	1	NUM
ejpam-5839	446	17	6	6	NUM
ejpam-5839	446	18	(	(	PUNCT
ejpam-5839	446	19	5j−	5j−	PROPN
ejpam-5839	446	20	1).∫	1).∫	NUM
ejpam-5839	446	21	1	1	NUM
ejpam-5839	446	22	0	0	NUM
ejpam-5839	446	23	f̃lqk(x	f̃lqk(x	NOUN
ejpam-5839	446	24	)	)	PUNCT
ejpam-5839	446	25	dx	dx	PROPN
ejpam-5839	446	26	=	=	SYM
ejpam-5839	446	27	5	5	NUM
ejpam-5839	446	28	9	9	NUM
ejpam-5839	446	29	(	(	PUNCT
ejpam-5839	446	30	1−	1−	NUM
ejpam-5839	446	31	k	k	NOUN
ejpam-5839	446	32	)	)	PUNCT
ejpam-5839	446	33	,	,	PUNCT
ejpam-5839	446	34	∫	∫	PROPN
ejpam-5839	446	35	1	1	NUM
ejpam-5839	446	36	0	0	NUM
ejpam-5839	446	37	f̃uqk(x	f̃uqk(x	PROPN
ejpam-5839	446	38	)	)	PUNCT
ejpam-5839	446	39	dx	dx	PROPN
ejpam-5839	447	1	=	=	NOUN
ejpam-5839	447	2	1	1	NUM
ejpam-5839	447	3	9	9	NUM
ejpam-5839	447	4	(	(	PUNCT
ejpam-5839	447	5	5k−	5k−	PROPN
ejpam-5839	447	6	1	1	NUM
ejpam-5839	447	7	)	)	PUNCT
ejpam-5839	447	8	.	.	PUNCT
ejpam-5839	448	1	∫	∫	PROPN
ejpam-5839	448	2	1	1	NUM
ejpam-5839	448	3	0	0	NUM
ejpam-5839	448	4	f̃lql(x	f̃lql(x	PROPN
ejpam-5839	448	5	)	)	PUNCT
ejpam-5839	448	6	dx	dx	PROPN
ejpam-5839	449	1	=	=	NOUN
ejpam-5839	449	2	5	5	NUM
ejpam-5839	449	3	9	9	NUM
ejpam-5839	449	4	(	(	PUNCT
ejpam-5839	449	5	1−	1−	NUM
ejpam-5839	449	6	l	l	NOUN
ejpam-5839	449	7	)	)	PUNCT
ejpam-5839	449	8	,	,	PUNCT
ejpam-5839	449	9	∫	∫	PROPN
ejpam-5839	449	10	1	1	NUM
ejpam-5839	449	11	0	0	NUM
ejpam-5839	449	12	f̃uql(x	f̃uql(x	PROPN
ejpam-5839	449	13	)	)	PUNCT
ejpam-5839	449	14	dx	dx	PROPN
ejpam-5839	449	15	=	=	NOUN
ejpam-5839	450	1	1	1	NUM
ejpam-5839	450	2	9	9	NUM
ejpam-5839	450	3	(	(	PUNCT
ejpam-5839	450	4	5l−	5l−	PROPN
ejpam-5839	450	5	1	1	NUM
ejpam-5839	450	6	)	)	PUNCT
ejpam-5839	450	7	.	.	PUNCT
ejpam-5839	451	1	for	for	ADP
ejpam-5839	451	2	parameter	parameter	NOUN
ejpam-5839	451	3	ranges	range	NOUN
ejpam-5839	451	4	:	:	PUNCT
ejpam-5839	451	5	i	i	PRON
ejpam-5839	451	6	∈	∈	VERB
ejpam-5839	452	1	[	[	X
ejpam-5839	452	2	0	0	NUM
ejpam-5839	452	3	,	,	PUNCT
ejpam-5839	452	4	8×	8×	ADP
ejpam-5839	452	5	10−1	10−1	NUM
ejpam-5839	452	6	]	]	PUNCT
ejpam-5839	452	7	,	,	PUNCT
ejpam-5839	452	8	j	j	PROPN
ejpam-5839	452	9	∈	∈	PROPN
ejpam-5839	453	1	[	[	X
ejpam-5839	453	2	6×	6×	NOUN
ejpam-5839	453	3	10−1	10−1	NUM
ejpam-5839	453	4	,	,	PUNCT
ejpam-5839	453	5	1	1	NUM
ejpam-5839	453	6	]	]	PUNCT
ejpam-5839	453	7	,	,	PUNCT
ejpam-5839	453	8	k	k	PROPN
ejpam-5839	453	9	∈	∈	PROPN
ejpam-5839	454	1	[	[	X
ejpam-5839	454	2	4×	4×	NOUN
ejpam-5839	454	3	10−1	10−1	NUM
ejpam-5839	454	4	,	,	PUNCT
ejpam-5839	454	5	1	1	NUM
ejpam-5839	454	6	]	]	PUNCT
ejpam-5839	454	7	,	,	PUNCT
ejpam-5839	454	8	l	l	PROPN
ejpam-5839	454	9	∈	∈	PROPN
ejpam-5839	454	10	[	[	X
ejpam-5839	454	11	4×	4×	NOUN
ejpam-5839	454	12	10−1	10−1	NUM
ejpam-5839	454	13	,	,	PUNCT
ejpam-5839	454	14	1	1	NUM
ejpam-5839	454	15	]	]	PUNCT
ejpam-5839	454	16	.	.	PUNCT
ejpam-5839	455	1	from	from	ADP
ejpam-5839	455	2	the	the	DET
ejpam-5839	455	3	table	table	NOUN
ejpam-5839	455	4	,	,	PUNCT
ejpam-5839	455	5	it	it	PRON
ejpam-5839	455	6	is	be	AUX
ejpam-5839	455	7	observed	observe	VERB
ejpam-5839	455	8	that	that	SCONJ
ejpam-5839	455	9	as	as	ADP
ejpam-5839	455	10	the	the	DET
ejpam-5839	455	11	value	value	NOUN
ejpam-5839	455	12	of	of	ADP
ejpam-5839	455	13	α	α	PRON
ejpam-5839	455	14	increases	increase	NOUN
ejpam-5839	455	15	,	,	PUNCT
ejpam-5839	455	16	the	the	DET
ejpam-5839	455	17	value	value	NOUN
ejpam-5839	455	18	of∫	of∫	ADJ
ejpam-5839	455	19	1	1	NUM
ejpam-5839	455	20	0	0	NUM
ejpam-5839	455	21	f̃lqi(x	f̃lqi(x	NOUN
ejpam-5839	455	22	)	)	PUNCT
ejpam-5839	455	23	dx	dx	PROPN
ejpam-5839	455	24	also	also	ADV
ejpam-5839	455	25	increases	increase	VERB
ejpam-5839	455	26	,	,	PUNCT
ejpam-5839	455	27	whereas	whereas	SCONJ
ejpam-5839	455	28	the	the	DET
ejpam-5839	455	29	value	value	NOUN
ejpam-5839	455	30	of	of	ADP
ejpam-5839	455	31	∫	∫	PROPN
ejpam-5839	455	32	1	1	NUM
ejpam-5839	455	33	0	0	NUM
ejpam-5839	455	34	f̃uqi(x	f̃uqi(x	ADJ
ejpam-5839	455	35	)	)	PUNCT
ejpam-5839	455	36	dx	dx	PROPN
ejpam-5839	455	37	decreases	decrease	VERB
ejpam-5839	455	38	.	.	PUNCT
ejpam-5839	456	1	at	at	ADP
ejpam-5839	456	2	i	i	PRON
ejpam-5839	456	3	=	=	NOUN
ejpam-5839	456	4	0.8	0.8	NUM
ejpam-5839	456	5	,	,	PUNCT
ejpam-5839	456	6	we	we	PRON
ejpam-5839	456	7	obtain	obtain	VERB
ejpam-5839	456	8	:	:	PUNCT
ejpam-5839	456	9	∫	∫	PROPN
ejpam-5839	456	10	1	1	NUM
ejpam-5839	456	11	0	0	NUM
ejpam-5839	456	12	f̃lqi(x	f̃lqi(x	NOUN
ejpam-5839	456	13	)	)	PUNCT
ejpam-5839	456	14	dx	dx	PROPN
ejpam-5839	456	15	.	.	PUNCT
ejpam-5839	457	1	a.	a.	PROPN
ejpam-5839	457	2	shihadeh	shihadeh	PROPN
ejpam-5839	457	3	et	et	PROPN
ejpam-5839	457	4	al	al	PROPN
ejpam-5839	457	5	.	.	PUNCT
ejpam-5839	457	6	/	/	SYM
ejpam-5839	457	7	eur	eur	PROPN
ejpam-5839	457	8	.	.	PUNCT
ejpam-5839	458	1	j.	j.	PROPN
ejpam-5839	458	2	pure	pure	PROPN
ejpam-5839	458	3	appl	appl	PROPN
ejpam-5839	458	4	.	.	PROPN
ejpam-5839	458	5	math	math	PROPN
ejpam-5839	458	6	,	,	PUNCT
ejpam-5839	458	7	18	18	NUM
ejpam-5839	458	8	(	(	PUNCT
ejpam-5839	458	9	2	2	NUM
ejpam-5839	458	10	)	)	PUNCT
ejpam-5839	458	11	(	(	PUNCT
ejpam-5839	458	12	2025	2025	NUM
ejpam-5839	458	13	)	)	PUNCT
ejpam-5839	458	14	,	,	PUNCT
ejpam-5839	458	15	5839	5839	NUM
ejpam-5839	458	16	20	20	NUM
ejpam-5839	458	17	of	of	ADP
ejpam-5839	458	18	54	54	NUM
ejpam-5839	459	1	i	i	PRON
ejpam-5839	459	2	∫	∫	VERB
ejpam-5839	459	3	1	1	NUM
ejpam-5839	459	4	0	0	NUM
ejpam-5839	459	5	f̃lqi(x)dx	f̃lqi(x)dx	NUM
ejpam-5839	459	6	∫	∫	PROPN
ejpam-5839	459	7	1	1	NUM
ejpam-5839	459	8	0	0	NUM
ejpam-5839	459	9	f̃uqi(x)dx	f̃uqi(x)dx	PROPN
ejpam-5839	459	10	j	j	NOUN
ejpam-5839	459	11	∫	∫	PROPN
ejpam-5839	460	1	1	1	NUM
ejpam-5839	460	2	0	0	NUM
ejpam-5839	460	3	f̃lqj(x)dx	f̃lqj(x)dx	ADJ
ejpam-5839	460	4	∫	∫	NOUN
ejpam-5839	460	5	1	1	NUM
ejpam-5839	460	6	0	0	NUM
ejpam-5839	460	7	f̃uqj(x)dx	f̃uqj(x)dx	NOUN
ejpam-5839	460	8	k	k	NOUN
ejpam-5839	460	9	∫	∫	PROPN
ejpam-5839	460	10	1	1	NUM
ejpam-5839	460	11	0	0	NUM
ejpam-5839	460	12	f̃lqk(x)dx	f̃lqk(x)dx	VERB
ejpam-5839	460	13	∫	∫	PROPN
ejpam-5839	460	14	1	1	NUM
ejpam-5839	460	15	0	0	NUM
ejpam-5839	460	16	f̃uqk(x)dx	f̃uqk(x)dx	PROPN
ejpam-5839	460	17	l	l	NOUN
ejpam-5839	460	18	0×	0×	PROPN
ejpam-5839	461	1	10−1	10−1	PROPN
ejpam-5839	461	2	0×	0×	NUM
ejpam-5839	461	3	10−1	10−1	NUM
ejpam-5839	461	4	0.66667×	0.66667×	X
ejpam-5839	461	5	10−5	10−5	NUM
ejpam-5839	461	6	6×	6×	NOUN
ejpam-5839	461	7	10−1	10−1	NUM
ejpam-5839	461	8	0.33333×	0.33333×	NOUN
ejpam-5839	461	9	10−5	10−5	NUM
ejpam-5839	461	10	0.33333×	0.33333×	NOUN
ejpam-5839	462	1	10−5	10−5	NUM
ejpam-5839	462	2	4×	4×	NOUN
ejpam-5839	462	3	10−1	10−1	NUM
ejpam-5839	462	4	0.33333×	0.33333×	NOUN
ejpam-5839	462	5	10−5	10−5	NUM
ejpam-5839	462	6	0.33333×	0.33333×	NOUN
ejpam-5839	463	1	10−5	10−5	NUM
ejpam-5839	463	2	4×	4×	NOUN
ejpam-5839	463	3	10−1	10−1	NUM
ejpam-5839	463	4	1.6667×	1.6667×	NUM
ejpam-5839	463	5	10−5	10−5	NUM
ejpam-5839	464	1	5×	5×	NOUN
ejpam-5839	464	2	10−1	10−1	NUM
ejpam-5839	464	3	8×	8×	ADP
ejpam-5839	464	4	10−1	10−1	PROPN
ejpam-5839	464	5	0.16667×	0.16667×	NUM
ejpam-5839	464	6	10−5	10−5	NUM
ejpam-5839	464	7	5×	5×	NOUN
ejpam-5839	464	8	10−1	10−1	NUM
ejpam-5839	464	9	6×	6×	NOUN
ejpam-5839	464	10	10−1	10−1	NUM
ejpam-5839	464	11	0.22222×	0.22222×	NOUN
ejpam-5839	464	12	10−5	10−5	NUM
ejpam-5839	464	13	0.44444×	0.44444×	NOUN
ejpam-5839	464	14	10−5	10−5	NUM
ejpam-5839	464	15	6×	6×	NOUN
ejpam-5839	464	16	10−1	10−1	NUM
ejpam-5839	464	17	0.22222×	0.22222×	NOUN
ejpam-5839	464	18	10−5	10−5	NUM
ejpam-5839	464	19	0.44444×	0.44444×	NOUN
ejpam-5839	464	20	10−5	10−5	NUM
ejpam-5839	464	21	6×	6×	NOUN
ejpam-5839	464	22	10−1	10−1	NUM
ejpam-5839	464	23	0.25×	0.25×	NUM
ejpam-5839	464	24	10−2	10−2	NUM
ejpam-5839	464	25	0.41667×	0.41667×	NOUN
ejpam-5839	464	26	10−5	10−5	NUM
ejpam-5839	464	27	9×	9×	NUM
ejpam-5839	464	28	10−1	10−1	NUM
ejpam-5839	464	29	0.08333×	0.08333×	NUM
ejpam-5839	464	30	10−5	10−5	NUM
ejpam-5839	464	31	0.58333×	0.58333×	NOUN
ejpam-5839	464	32	10−5	10−5	NUM
ejpam-5839	465	1	8×	8×	NUM
ejpam-5839	465	2	10−1	10−1	NUM
ejpam-5839	465	3	0.11111×	0.11111×	X
ejpam-5839	465	4	10−5	10−5	NUM
ejpam-5839	465	5	0.66667×	0.66667×	X
ejpam-5839	465	6	10−5	10−5	NUM
ejpam-5839	465	7	8×	8×	NUM
ejpam-5839	465	8	10−1	10−1	NUM
ejpam-5839	465	9	0.11111×	0.11111×	X
ejpam-5839	465	10	10−5	10−5	NUM
ejpam-5839	465	11	0.66667×	0.66667×	NOUN
ejpam-5839	465	12	10−5	10−5	NUM
ejpam-5839	465	13	8×	8×	NUM
ejpam-5839	465	14	10−1	10−1	NUM
ejpam-5839	465	15	0.33333×	0.33333×	X
ejpam-5839	465	16	10−5	10−5	NUM
ejpam-5839	465	17	0.33333×	0.33333×	NOUN
ejpam-5839	466	1	10−5	10−5	NUM
ejpam-5839	466	2	1×	1×	NUM
ejpam-5839	466	3	100	100	NUM
ejpam-5839	466	4	0×	0×	NUM
ejpam-5839	466	5	10−1	10−1	NUM
ejpam-5839	466	6	0.66667×	0.66667×	X
ejpam-5839	466	7	10−5	10−5	NUM
ejpam-5839	466	8	1×	1×	NUM
ejpam-5839	466	9	10−1	10−1	PROPN
ejpam-5839	466	10	table	table	NOUN
ejpam-5839	466	11	1	1	NUM
ejpam-5839	466	12	:	:	PUNCT
ejpam-5839	466	13	solution	solution	NOUN
ejpam-5839	466	14	for	for	ADP
ejpam-5839	466	15	different	different	ADJ
ejpam-5839	466	16	values	value	NOUN
ejpam-5839	466	17	of	of	ADP
ejpam-5839	466	18	i	i	PROPN
ejpam-5839	466	19	,	,	PUNCT
ejpam-5839	466	20	j	j	PROPN
ejpam-5839	466	21	,	,	PUNCT
ejpam-5839	466	22	k	k	PROPN
ejpam-5839	466	23	,	,	PUNCT
ejpam-5839	466	24	l	l	NOUN
ejpam-5839	466	25	for	for	ADP
ejpam-5839	466	26	example	example	NOUN
ejpam-5839	466	27	1	1	NUM
ejpam-5839	466	28	∫	∫	NOUN
ejpam-5839	466	29	1	1	NUM
ejpam-5839	466	30	0	0	NUM
ejpam-5839	466	31	f̃uqi	f̃uqi	NOUN
ejpam-5839	466	32	(	(	PUNCT
ejpam-5839	466	33	x	x	X
ejpam-5839	466	34	)	)	PUNCT
ejpam-5839	466	35	dx	dx	PROPN
ejpam-5839	466	36	gives	give	VERB
ejpam-5839	466	37	the	the	DET
ejpam-5839	466	38	same	same	ADJ
ejpam-5839	466	39	solution	solution	NOUN
ejpam-5839	466	40	.	.	PUNCT
ejpam-5839	467	1	again	again	ADV
ejpam-5839	467	2	,	,	PUNCT
ejpam-5839	467	3	when	when	SCONJ
ejpam-5839	467	4	the	the	DET
ejpam-5839	467	5	value	value	NOUN
ejpam-5839	467	6	of	of	ADP
ejpam-5839	467	7	j	j	PROPN
ejpam-5839	467	8	increases	increase	NOUN
ejpam-5839	467	9	,	,	PUNCT
ejpam-5839	467	10	the	the	DET
ejpam-5839	467	11	value	value	NOUN
ejpam-5839	467	12	of∫	of∫	NOUN
ejpam-5839	467	13	1	1	NUM
ejpam-5839	467	14	0	0	NUM
ejpam-5839	467	15	f̃lqj	f̃lqj	PROPN
ejpam-5839	467	16	(	(	PUNCT
ejpam-5839	467	17	x	x	NOUN
ejpam-5839	467	18	)	)	PUNCT
ejpam-5839	467	19	dx	dx	PROPN
ejpam-5839	467	20	decreased	decrease	VERB
ejpam-5839	467	21	,	,	PUNCT
ejpam-5839	467	22	and	and	CCONJ
ejpam-5839	467	23	the	the	DET
ejpam-5839	467	24	value	value	NOUN
ejpam-5839	467	25	of	of	ADP
ejpam-5839	467	26	∫	∫	PROPN
ejpam-5839	467	27	1	1	NUM
ejpam-5839	467	28	0	0	NUM
ejpam-5839	467	29	f̃uqj	f̃uqj	NOUN
ejpam-5839	467	30	(	(	PUNCT
ejpam-5839	467	31	x	x	X
ejpam-5839	467	32	)	)	PUNCT
ejpam-5839	467	33	dx	dx	PROPN
ejpam-5839	467	34	increased	increase	VERB
ejpam-5839	467	35	.	.	PUNCT
ejpam-5839	468	1	at	at	ADP
ejpam-5839	468	2	j	j	PROPN
ejpam-5839	468	3	=	=	SYM
ejpam-5839	468	4	0.6	0.6	NUM
ejpam-5839	468	5	,	,	PUNCT
ejpam-5839	468	6	∫	∫	PROPN
ejpam-5839	468	7	1	1	NUM
ejpam-5839	468	8	0	0	NUM
ejpam-5839	468	9	f̃lqj	f̃lqj	PROPN
ejpam-5839	468	10	(	(	PUNCT
ejpam-5839	468	11	x	x	NOUN
ejpam-5839	468	12	)	)	PUNCT
ejpam-5839	468	13	dx	dx	PROPN
ejpam-5839	468	14	and	and	CCONJ
ejpam-5839	468	15	∫	∫	PROPN
ejpam-5839	469	1	1	1	NUM
ejpam-5839	469	2	0	0	NUM
ejpam-5839	469	3	f̃uqj	f̃uqj	NOUN
ejpam-5839	469	4	(	(	PUNCT
ejpam-5839	469	5	x	x	X
ejpam-5839	469	6	)	)	PUNCT
ejpam-5839	469	7	dx	dx	PROPN
ejpam-5839	469	8	give	give	VERB
ejpam-5839	469	9	the	the	DET
ejpam-5839	469	10	same	same	ADJ
ejpam-5839	469	11	solution	solution	NOUN
ejpam-5839	469	12	.	.	PUNCT
ejpam-5839	470	1	when	when	SCONJ
ejpam-5839	470	2	k	k	PROPN
ejpam-5839	470	3	increases	increase	VERB
ejpam-5839	470	4	,	,	PUNCT
ejpam-5839	470	5	the	the	DET
ejpam-5839	470	6	value	value	NOUN
ejpam-5839	470	7	of	of	ADP
ejpam-5839	470	8	∫	∫	PROPN
ejpam-5839	470	9	1	1	NUM
ejpam-5839	470	10	0	0	NUM
ejpam-5839	470	11	f̃lq∥	f̃lq∥	NOUN
ejpam-5839	470	12	(	(	PUNCT
ejpam-5839	470	13	x	x	X
ejpam-5839	470	14	)	)	PUNCT
ejpam-5839	470	15	dx	dx	PROPN
ejpam-5839	470	16	decreases	decrease	VERB
ejpam-5839	470	17	,	,	PUNCT
ejpam-5839	470	18	and	and	CCONJ
ejpam-5839	470	19	the	the	DET
ejpam-5839	470	20	value	value	NOUN
ejpam-5839	470	21	of	of	ADP
ejpam-5839	470	22	∫	∫	PROPN
ejpam-5839	470	23	1	1	NUM
ejpam-5839	470	24	0	0	NUM
ejpam-5839	470	25	f̃uq∥	f̃uq∥	ADV
ejpam-5839	470	26	(	(	PUNCT
ejpam-5839	470	27	x	x	X
ejpam-5839	470	28	)	)	PUNCT
ejpam-5839	470	29	dx	dx	PROPN
ejpam-5839	470	30	increases	increase	NOUN
ejpam-5839	470	31	.	.	PUNCT
ejpam-5839	471	1	similarly	similarly	ADV
ejpam-5839	471	2	,	,	PUNCT
ejpam-5839	471	3	when	when	SCONJ
ejpam-5839	471	4	l	l	NOUN
ejpam-5839	471	5	increases	increase	NOUN
ejpam-5839	471	6	,	,	PUNCT
ejpam-5839	471	7	the	the	DET
ejpam-5839	471	8	value	value	NOUN
ejpam-5839	471	9	of∫	of∫	ADJ
ejpam-5839	471	10	1	1	NUM
ejpam-5839	471	11	0	0	NUM
ejpam-5839	471	12	f̃lql	f̃lql	NOUN
ejpam-5839	471	13	(	(	PUNCT
ejpam-5839	471	14	x	x	X
ejpam-5839	471	15	)	)	PUNCT
ejpam-5839	471	16	dx	dx	PROPN
ejpam-5839	471	17	decreases	decrease	VERB
ejpam-5839	471	18	,	,	PUNCT
ejpam-5839	471	19	and	and	CCONJ
ejpam-5839	471	20	the	the	DET
ejpam-5839	471	21	value	value	NOUN
ejpam-5839	471	22	of	of	ADP
ejpam-5839	471	23	∫	∫	PROPN
ejpam-5839	471	24	1	1	NUM
ejpam-5839	471	25	0	0	NUM
ejpam-5839	471	26	f̃uql	f̃uql	NOUN
ejpam-5839	471	27	(	(	PUNCT
ejpam-5839	471	28	x	x	NOUN
ejpam-5839	471	29	)	)	PUNCT
ejpam-5839	471	30	dx	dx	PROPN
ejpam-5839	471	31	increases	increase	NOUN
ejpam-5839	471	32	.	.	PUNCT
ejpam-5839	472	1	this	this	PRON
ejpam-5839	472	2	implies	imply	VERB
ejpam-5839	472	3	that	that	SCONJ
ejpam-5839	472	4	the	the	DET
ejpam-5839	472	5	approximate	approximate	ADJ
ejpam-5839	472	6	solution	solution	NOUN
ejpam-5839	472	7	in	in	ADP
ejpam-5839	472	8	table	table	NOUN
ejpam-5839	472	9	1	1	NUM
ejpam-5839	472	10	provides	provide	VERB
ejpam-5839	472	11	a	a	DET
ejpam-5839	472	12	quadri	quadri	NOUN
ejpam-5839	472	13	-	-	PUNCT
ejpam-5839	472	14	neutrosophicvalued	neutrosophicvalue	VERB
ejpam-5839	472	15	number	number	NOUN
ejpam-5839	472	16	.	.	PUNCT
ejpam-5839	473	1	in	in	ADP
ejpam-5839	473	2	the	the	DET
ejpam-5839	473	3	following	follow	VERB
ejpam-5839	473	4	example	example	NOUN
ejpam-5839	473	5	,	,	PUNCT
ejpam-5839	473	6	we	we	PRON
ejpam-5839	473	7	are	be	AUX
ejpam-5839	473	8	going	go	VERB
ejpam-5839	473	9	to	to	PART
ejpam-5839	473	10	show	show	VERB
ejpam-5839	473	11	that	that	SCONJ
ejpam-5839	473	12	how	how	SCONJ
ejpam-5839	473	13	one	one	PRON
ejpam-5839	473	14	can	can	AUX
ejpam-5839	473	15	use	use	VERB
ejpam-5839	473	16	the	the	DET
ejpam-5839	473	17	existing	exist	VERB
ejpam-5839	473	18	numerical	numerical	ADJ
ejpam-5839	473	19	integration	integration	NOUN
ejpam-5839	473	20	methods	method	NOUN
ejpam-5839	473	21	to	to	PART
ejpam-5839	473	22	solve	solve	VERB
ejpam-5839	473	23	the	the	DET
ejpam-5839	473	24	quadri	quadri	PROPN
ejpam-5839	473	25	-	-	PUNCT
ejpam-5839	473	26	neutrosophic	neutrosophic	ADJ
ejpam-5839	473	27	integral	integral	NOUN
ejpam-5839	473	28	.	.	PUNCT
ejpam-5839	474	1	so	so	ADV
ejpam-5839	474	2	,	,	PUNCT
ejpam-5839	474	3	in	in	ADP
ejpam-5839	474	4	the	the	DET
ejpam-5839	474	5	following	follow	VERB
ejpam-5839	474	6	example	example	NOUN
ejpam-5839	474	7	,	,	PUNCT
ejpam-5839	474	8	we	we	PRON
ejpam-5839	474	9	consider	consider	VERB
ejpam-5839	474	10	the	the	DET
ejpam-5839	474	11	same	same	ADJ
ejpam-5839	474	12	quadri	quadri	PROPN
ejpam-5839	474	13	-	-	PUNCT
ejpam-5839	474	14	neutrosophic	neutrosophic	ADJ
ejpam-5839	474	15	function	function	NOUN
ejpam-5839	474	16	,	,	PUNCT
ejpam-5839	474	17	but	but	CCONJ
ejpam-5839	474	18	the	the	DET
ejpam-5839	474	19	parameter	parameter	NOUN
ejpam-5839	474	20	was	be	AUX
ejpam-5839	474	21	taken	take	VERB
ejpam-5839	474	22	in	in	ADP
ejpam-5839	474	23	the	the	DET
ejpam-5839	474	24	form	form	NOUN
ejpam-5839	474	25	of	of	ADP
ejpam-5839	474	26	trapezoidal	trapezoidal	ADJ
ejpam-5839	474	27	quadri	quadri	PROPN
ejpam-5839	474	28	-	-	PUNCT
ejpam-5839	474	29	neutrosophic	neutrosophic	ADJ
ejpam-5839	474	30	number	number	NOUN
ejpam-5839	474	31	.	.	PUNCT
ejpam-5839	475	1	example	example	NOUN
ejpam-5839	476	1	2	2	NUM
ejpam-5839	476	2	.	.	PUNCT
ejpam-5839	476	3	let	let	VERB
ejpam-5839	476	4	us	we	PRON
ejpam-5839	476	5	consider	consider	VERB
ejpam-5839	476	6	the	the	DET
ejpam-5839	476	7	quadri	quadri	PROPN
ejpam-5839	476	8	-	-	PUNCT
ejpam-5839	476	9	neutrosophic	neutrosophic	ADJ
ejpam-5839	476	10	valued	value	VERB
ejpam-5839	476	11	function	function	NOUN
ejpam-5839	476	12	(	(	PUNCT
ejpam-5839	476	13	qnvf	qnvf	ADV
ejpam-5839	476	14	)	)	PUNCT
ejpam-5839	476	15	given	give	VERB
ejpam-5839	476	16	by	by	ADP
ejpam-5839	476	17	:	:	PUNCT
ejpam-5839	476	18	f̃(q(x	f̃(q(x	NUM
ejpam-5839	476	19	)	)	PUNCT
ejpam-5839	476	20	)	)	PUNCT
ejpam-5839	477	1	=	=	PUNCT
ejpam-5839	477	2	ñ(x)2	ñ(x)2	VERB
ejpam-5839	477	3	on	on	ADP
ejpam-5839	477	4	[	[	X
ejpam-5839	477	5	0	0	NUM
ejpam-5839	477	6	,	,	PUNCT
ejpam-5839	477	7	1	1	NUM
ejpam-5839	477	8	]	]	PUNCT
ejpam-5839	477	9	where	where	SCONJ
ejpam-5839	477	10	ñ	ñ	PROPN
ejpam-5839	477	11	=	=	SYM
ejpam-5839	477	12	⟨(0	⟨(0	NOUN
ejpam-5839	477	13	,	,	PUNCT
ejpam-5839	477	14	1	1	NUM
ejpam-5839	477	15	,	,	PUNCT
ejpam-5839	477	16	2	2	NUM
ejpam-5839	477	17	,	,	PUNCT
ejpam-5839	477	18	2	2	NUM
ejpam-5839	477	19	)	)	PUNCT
ejpam-5839	477	20	;	;	PUNCT
ejpam-5839	477	21	0.8	0.8	NUM
ejpam-5839	477	22	,	,	PUNCT
ejpam-5839	477	23	0.6	0.6	NUM
ejpam-5839	477	24	,	,	PUNCT
ejpam-5839	477	25	0.4	0.4	NUM
ejpam-5839	477	26	,	,	PUNCT
ejpam-5839	477	27	0.4⟩	0.4⟩	NUM
ejpam-5839	477	28	is	be	AUX
ejpam-5839	477	29	a	a	DET
ejpam-5839	477	30	single	single	ADV
ejpam-5839	477	31	-	-	PUNCT
ejpam-5839	477	32	valued	value	VERB
ejpam-5839	477	33	triangular	triangular	NOUN
ejpam-5839	477	34	quadri	quadri	PROPN
ejpam-5839	477	35	-	-	PUNCT
ejpam-5839	477	36	neutrosophic	neutrosophic	ADJ
ejpam-5839	477	37	number	number	NOUN
ejpam-5839	477	38	.	.	PUNCT
ejpam-5839	478	1	a.	a.	NOUN
ejpam-5839	478	2	shihadeh	shihadeh	VERB
ejpam-5839	478	3	et	et	PROPN
ejpam-5839	478	4	al	al	PROPN
ejpam-5839	478	5	.	.	PUNCT
ejpam-5839	478	6	/	/	SYM
ejpam-5839	478	7	eur	eur	PROPN
ejpam-5839	478	8	.	.	PUNCT
ejpam-5839	479	1	j.	j.	PROPN
ejpam-5839	479	2	pure	pure	PROPN
ejpam-5839	479	3	appl	appl	PROPN
ejpam-5839	479	4	.	.	PROPN
ejpam-5839	479	5	math	math	PROPN
ejpam-5839	479	6	,	,	PUNCT
ejpam-5839	479	7	18	18	NUM
ejpam-5839	479	8	(	(	PUNCT
ejpam-5839	479	9	2	2	NUM
ejpam-5839	479	10	)	)	PUNCT
ejpam-5839	479	11	(	(	PUNCT
ejpam-5839	479	12	2025	2025	NUM
ejpam-5839	479	13	)	)	PUNCT
ejpam-5839	479	14	,	,	PUNCT
ejpam-5839	479	15	5839	5839	NUM
ejpam-5839	479	16	21	21	NUM
ejpam-5839	479	17	of	of	ADP
ejpam-5839	479	18	54	54	NUM
ejpam-5839	479	19	now	now	ADV
ejpam-5839	479	20	,	,	PUNCT
ejpam-5839	479	21	we	we	PRON
ejpam-5839	479	22	integrate	integrate	VERB
ejpam-5839	479	23	the	the	DET
ejpam-5839	479	24	quadri	quadri	PROPN
ejpam-5839	479	25	-	-	PUNCT
ejpam-5839	479	26	neutrosophic	neutrosophic	PROPN
ejpam-5839	479	27	valued	value	VERB
ejpam-5839	479	28	function	function	NOUN
ejpam-5839	479	29	over	over	ADP
ejpam-5839	479	30	the	the	DET
ejpam-5839	479	31	interval	interval	NOUN
ejpam-5839	479	32	[	[	X
ejpam-5839	479	33	0	0	NUM
ejpam-5839	479	34	,	,	PUNCT
ejpam-5839	479	35	1	1	NUM
ejpam-5839	479	36	]	]	PUNCT
ejpam-5839	479	37	,	,	PUNCT
ejpam-5839	479	38	aiming	aim	VERB
ejpam-5839	479	39	to	to	PART
ejpam-5839	479	40	find	find	VERB
ejpam-5839	479	41	:	:	PUNCT
ejpam-5839	479	42	∫	∫	PROPN
ejpam-5839	479	43	1	1	NUM
ejpam-5839	479	44	0	0	NUM
ejpam-5839	479	45	f̃(q(x	f̃(q(x	NUM
ejpam-5839	479	46	)	)	PUNCT
ejpam-5839	479	47	)	)	PUNCT
ejpam-5839	480	1	dx	dx	PROPN
ejpam-5839	480	2	next	next	ADV
ejpam-5839	480	3	,	,	PUNCT
ejpam-5839	480	4	we	we	PRON
ejpam-5839	480	5	take	take	VERB
ejpam-5839	480	6	the	the	DET
ejpam-5839	480	7	(	(	PUNCT
ejpam-5839	480	8	i	i	PROPN
ejpam-5839	480	9	,	,	PUNCT
ejpam-5839	480	10	j	j	PROPN
ejpam-5839	480	11	,	,	PUNCT
ejpam-5839	480	12	∥	∥	PROPN
ejpam-5839	480	13	,	,	PUNCT
ejpam-5839	480	14	l)-cut	l)-cut	NOUN
ejpam-5839	480	15	of	of	ADP
ejpam-5839	480	16	the	the	DET
ejpam-5839	480	17	integral:∫	integral:∫	NUM
ejpam-5839	480	18	1	1	NUM
ejpam-5839	480	19	0	0	NUM
ejpam-5839	480	20	f̃(q(x	f̃(q(x	NUM
ejpam-5839	480	21	)	)	PUNCT
ejpam-5839	480	22	)	)	PUNCT
ejpam-5839	481	1	dx	dx	PROPN
ejpam-5839	481	2	then	then	ADV
ejpam-5839	481	3	,	,	PUNCT
ejpam-5839	481	4	we	we	PRON
ejpam-5839	481	5	have	have	VERB
ejpam-5839	481	6	:	:	PUNCT
ejpam-5839	481	7	(	(	PUNCT
ejpam-5839	481	8	∫	∫	PROPN
ejpam-5839	481	9	1	1	NUM
ejpam-5839	481	10	0	0	NUM
ejpam-5839	481	11	f̃(q(x	f̃(q(x	NUM
ejpam-5839	481	12	)	)	PUNCT
ejpam-5839	481	13	)	)	PUNCT
ejpam-5839	481	14	dx	dx	PROPN
ejpam-5839	481	15	)	)	PUNCT
ejpam-5839	482	1	(	(	PUNCT
ejpam-5839	482	2	i	i	PROPN
ejpam-5839	482	3	,	,	PUNCT
ejpam-5839	482	4	j,∥,l	j,∥,l	PROPN
ejpam-5839	482	5	)	)	PUNCT
ejpam-5839	482	6	=	=	PUNCT
ejpam-5839	482	7			NOUN
ejpam-5839	483	1	[	[	X
ejpam-5839	483	2	∫	∫	X
ejpam-5839	483	3	1	1	NUM
ejpam-5839	483	4	0	0	X
ejpam-5839	483	5	f̃qi	f̃qi	PROPN
ejpam-5839	483	6	l(x	l(x	PROPN
ejpam-5839	483	7	)	)	PUNCT
ejpam-5839	483	8	dx	dx	PROPN
ejpam-5839	483	9	,	,	PUNCT
ejpam-5839	483	10	∫	∫	PROPN
ejpam-5839	483	11	1	1	NUM
ejpam-5839	483	12	0	0	X
ejpam-5839	483	13	f̃qi	f̃qi	PROPN
ejpam-5839	483	14	u(x	u(x	PROPN
ejpam-5839	483	15	)	)	PUNCT
ejpam-5839	483	16	dx	dx	PROPN
ejpam-5839	483	17	]	]	PUNCT
ejpam-5839	483	18	,	,	PUNCT
ejpam-5839	483	19	[	[	X
ejpam-5839	483	20	∫	∫	PROPN
ejpam-5839	483	21	1	1	NUM
ejpam-5839	483	22	0	0	NUM
ejpam-5839	483	23	f̃qj	f̃qj	ADJ
ejpam-5839	483	24	l(x	l(x	PROPN
ejpam-5839	483	25	)	)	PUNCT
ejpam-5839	483	26	dx	dx	PROPN
ejpam-5839	483	27	,	,	PUNCT
ejpam-5839	483	28	∫	∫	PROPN
ejpam-5839	483	29	1	1	NUM
ejpam-5839	483	30	0	0	NUM
ejpam-5839	483	31	f̃qj	f̃qj	ADJ
ejpam-5839	483	32	u(x	u(x	NOUN
ejpam-5839	483	33	)	)	PUNCT
ejpam-5839	483	34	dx	dx	PROPN
ejpam-5839	483	35	]	]	PUNCT
ejpam-5839	483	36	,	,	PUNCT
ejpam-5839	483	37	[	[	X
ejpam-5839	483	38	∫	∫	PROPN
ejpam-5839	483	39	1	1	NUM
ejpam-5839	483	40	0	0	NUM
ejpam-5839	483	41	f̃q∥l(x	f̃q∥l(x	PROPN
ejpam-5839	483	42	)	)	PUNCT
ejpam-5839	483	43	dx	dx	PROPN
ejpam-5839	483	44	,	,	PUNCT
ejpam-5839	483	45	∫	∫	PROPN
ejpam-5839	483	46	1	1	NUM
ejpam-5839	483	47	0	0	NUM
ejpam-5839	483	48	f̃q∥u(x	f̃q∥u(x	NOUN
ejpam-5839	483	49	)	)	PUNCT
ejpam-5839	483	50	dx	dx	PROPN
ejpam-5839	483	51	]	]	PUNCT
ejpam-5839	483	52	,	,	PUNCT
ejpam-5839	483	53	[	[	X
ejpam-5839	483	54	∫	∫	PROPN
ejpam-5839	483	55	1	1	NUM
ejpam-5839	483	56	0	0	X
ejpam-5839	483	57	f̃ql	f̃ql	PROPN
ejpam-5839	483	58	l(x	l(x	PROPN
ejpam-5839	483	59	)	)	PUNCT
ejpam-5839	483	60	dx	dx	PROPN
ejpam-5839	483	61	,	,	PUNCT
ejpam-5839	483	62	∫	∫	PROPN
ejpam-5839	483	63	1	1	NUM
ejpam-5839	483	64	0	0	X
ejpam-5839	483	65	f̃ql	f̃ql	PROPN
ejpam-5839	483	66	u(x	u(x	PROPN
ejpam-5839	483	67	)	)	PUNCT
ejpam-5839	483	68	dx	dx	PROPN
ejpam-5839	483	69	]	]	PUNCT
ejpam-5839	483	70			VERB
ejpam-5839	483	71	since	since	SCONJ
ejpam-5839	483	72	each	each	PRON
ejpam-5839	483	73	of	of	ADP
ejpam-5839	483	74	the	the	DET
ejpam-5839	483	75	integral	integral	ADJ
ejpam-5839	483	76	∫	∫	PROPN
ejpam-5839	483	77	1	1	NUM
ejpam-5839	483	78	0	0	X
ejpam-5839	483	79	f̃qi	f̃qi	PROPN
ejpam-5839	483	80	l(x	l(x	PROPN
ejpam-5839	483	81	)	)	PUNCT
ejpam-5839	483	82	dx	dx	PROPN
ejpam-5839	483	83	,	,	PUNCT
ejpam-5839	483	84	∫	∫	PROPN
ejpam-5839	483	85	1	1	NUM
ejpam-5839	483	86	0	0	X
ejpam-5839	483	87	f̃qi	f̃qi	PROPN
ejpam-5839	483	88	u(x	u(x	PROPN
ejpam-5839	483	89	)	)	PUNCT
ejpam-5839	483	90	dx,∫	dx,∫	NOUN
ejpam-5839	483	91	1	1	NUM
ejpam-5839	483	92	0	0	NUM
ejpam-5839	483	93	f̃qj	f̃qj	ADJ
ejpam-5839	483	94	l(x	l(x	PROPN
ejpam-5839	483	95	)	)	PUNCT
ejpam-5839	483	96	dx	dx	PROPN
ejpam-5839	483	97	,	,	PUNCT
ejpam-5839	483	98	∫	∫	PROPN
ejpam-5839	483	99	1	1	NUM
ejpam-5839	483	100	0	0	NUM
ejpam-5839	483	101	f̃qj	f̃qj	ADJ
ejpam-5839	483	102	u(x	u(x	NOUN
ejpam-5839	483	103	)	)	PUNCT
ejpam-5839	483	104	dx,∫	dx,∫	NOUN
ejpam-5839	483	105	1	1	NUM
ejpam-5839	483	106	0	0	NUM
ejpam-5839	483	107	f̃qk	f̃qk	PROPN
ejpam-5839	483	108	l(x	l(x	PROPN
ejpam-5839	483	109	)	)	PUNCT
ejpam-5839	483	110	dx	dx	PROPN
ejpam-5839	483	111	,	,	PUNCT
ejpam-5839	483	112	∫	∫	PROPN
ejpam-5839	483	113	1	1	NUM
ejpam-5839	483	114	0	0	NUM
ejpam-5839	483	115	f̃qk	f̃qk	PROPN
ejpam-5839	483	116	u(x	u(x	NOUN
ejpam-5839	483	117	)	)	PUNCT
ejpam-5839	483	118	dx,∫	dx,∫	NOUN
ejpam-5839	483	119	1	1	NUM
ejpam-5839	483	120	0	0	X
ejpam-5839	483	121	f̃ql	f̃ql	PROPN
ejpam-5839	483	122	l(x	l(x	PROPN
ejpam-5839	483	123	)	)	PUNCT
ejpam-5839	483	124	dx	dx	PROPN
ejpam-5839	483	125	,	,	PUNCT
ejpam-5839	483	126	∫	∫	PROPN
ejpam-5839	483	127	1	1	NUM
ejpam-5839	483	128	0	0	X
ejpam-5839	483	129	f̃ql	f̃ql	PROPN
ejpam-5839	483	130	u(x	u(x	PROPN
ejpam-5839	483	131	)	)	PUNCT
ejpam-5839	483	132	dx	dx	PROPN
ejpam-5839	483	133	are	be	AUX
ejpam-5839	483	134	riemann	riemann	PROPN
ejpam-5839	483	135	integrable	integrable	ADJ
ejpam-5839	483	136	on	on	ADP
ejpam-5839	483	137	[	[	X
ejpam-5839	483	138	0	0	NUM
ejpam-5839	483	139	,	,	PUNCT
ejpam-5839	483	140	1	1	NUM
ejpam-5839	483	141	]	]	PUNCT
ejpam-5839	483	142	.	.	PUNCT
ejpam-5839	484	1	then	then	ADV
ejpam-5839	484	2	we	we	PRON
ejpam-5839	484	3	can	can	AUX
ejpam-5839	484	4	use	use	VERB
ejpam-5839	484	5	the	the	DET
ejpam-5839	484	6	trapezoidal	trapezoidal	ADJ
ejpam-5839	484	7	rule	rule	NOUN
ejpam-5839	484	8	to	to	PART
ejpam-5839	484	9	approximate	approximate	VERB
ejpam-5839	484	10	the	the	DET
ejpam-5839	484	11	integral	integral	ADJ
ejpam-5839	484	12	:	:	PUNCT
ejpam-5839	484	13	∫	∫	PROPN
ejpam-5839	484	14	1	1	NUM
ejpam-5839	484	15	0	0	NUM
ejpam-5839	485	1	x2	x2	PRON
ejpam-5839	485	2	dx	dx	PROPN
ejpam-5839	485	3	with	with	ADP
ejpam-5839	485	4	the	the	DET
ejpam-5839	485	5	help	help	NOUN
ejpam-5839	485	6	of	of	ADP
ejpam-5839	485	7	the	the	DET
ejpam-5839	485	8	trapezoidal	trapezoidal	ADJ
ejpam-5839	485	9	rule	rule	NOUN
ejpam-5839	485	10	.	.	PUNCT
ejpam-5839	486	1	let	let	VERB
ejpam-5839	486	2	p	p	NOUN
ejpam-5839	486	3	=	=	X
ejpam-5839	486	4	{	{	PUNCT
ejpam-5839	486	5	0	0	NUM
ejpam-5839	486	6	,	,	PUNCT
ejpam-5839	486	7	1	1	NUM
ejpam-5839	486	8	4	4	NUM
ejpam-5839	486	9	,	,	PUNCT
ejpam-5839	486	10	1	1	NUM
ejpam-5839	486	11	2	2	NUM
ejpam-5839	486	12	,	,	PUNCT
ejpam-5839	486	13	3	3	NUM
ejpam-5839	486	14	4	4	NUM
ejpam-5839	486	15	,	,	PUNCT
ejpam-5839	486	16	1	1	NUM
ejpam-5839	486	17	}	}	PUNCT
ejpam-5839	486	18	be	be	AUX
ejpam-5839	486	19	the	the	DET
ejpam-5839	486	20	set	set	NOUN
ejpam-5839	486	21	of	of	ADP
ejpam-5839	486	22	all	all	DET
ejpam-5839	486	23	elements	element	NOUN
ejpam-5839	486	24	at	at	ADP
ejpam-5839	486	25	the	the	DET
ejpam-5839	486	26	endpoints	endpoint	NOUN
ejpam-5839	486	27	of	of	ADP
ejpam-5839	486	28	the	the	DET
ejpam-5839	486	29	sub	sub	NOUN
ejpam-5839	486	30	-	-	NOUN
ejpam-5839	486	31	intervals	interval	NOUN
ejpam-5839	486	32	,	,	PUNCT
ejpam-5839	486	33	and	and	CCONJ
ejpam-5839	486	34	∆x	∆x	PROPN
ejpam-5839	486	35	=	=	SYM
ejpam-5839	487	1	1−	1−	NUM
ejpam-5839	487	2	0	0	NUM
ejpam-5839	487	3	4	4	NUM
ejpam-5839	487	4	=	=	SYM
ejpam-5839	487	5	1	1	NUM
ejpam-5839	487	6	4	4	NUM
ejpam-5839	487	7	.	.	PUNCT
ejpam-5839	488	1	then	then	ADV
ejpam-5839	488	2	,	,	PUNCT
ejpam-5839	488	3	∫	∫	PROPN
ejpam-5839	488	4	1	1	NUM
ejpam-5839	488	5	0	0	NUM
ejpam-5839	489	1	x2	x2	PRON
ejpam-5839	489	2	dx	dx	PROPN
ejpam-5839	490	1	≈	≈	NOUN
ejpam-5839	490	2	1	1	NUM
ejpam-5839	490	3	4	4	NUM
ejpam-5839	490	4	×	×	NOUN
ejpam-5839	490	5	1	1	NUM
ejpam-5839	490	6	4	4	NUM
ejpam-5839	490	7	[	[	PUNCT
ejpam-5839	490	8	f(0	f(0	NOUN
ejpam-5839	490	9	)	)	PUNCT
ejpam-5839	490	10	+	+	CCONJ
ejpam-5839	490	11	2f	2f	NUM
ejpam-5839	490	12	(	(	PUNCT
ejpam-5839	490	13	1	1	NUM
ejpam-5839	490	14	4	4	NUM
ejpam-5839	490	15	)	)	PUNCT
ejpam-5839	491	1	+	+	CCONJ
ejpam-5839	491	2	2f	2f	NUM
ejpam-5839	491	3	(	(	PUNCT
ejpam-5839	491	4	1	1	NUM
ejpam-5839	491	5	2	2	NUM
ejpam-5839	491	6	)	)	PUNCT
ejpam-5839	492	1	+	+	CCONJ
ejpam-5839	492	2	2f	2f	NUM
ejpam-5839	492	3	(	(	PUNCT
ejpam-5839	492	4	3	3	NUM
ejpam-5839	492	5	4	4	NUM
ejpam-5839	492	6	)	)	PUNCT
ejpam-5839	492	7	+	+	CCONJ
ejpam-5839	492	8	f(1	f(1	NOUN
ejpam-5839	492	9	)	)	PUNCT
ejpam-5839	492	10	]	]	PUNCT
ejpam-5839	492	11	a.	a.	NOUN
ejpam-5839	492	12	shihadeh	shihadeh	PROPN
ejpam-5839	492	13	et	et	PROPN
ejpam-5839	492	14	al	al	PROPN
ejpam-5839	492	15	.	.	PUNCT
ejpam-5839	492	16	/	/	SYM
ejpam-5839	492	17	eur	eur	PROPN
ejpam-5839	492	18	.	.	PUNCT
ejpam-5839	493	1	j.	j.	PROPN
ejpam-5839	493	2	pure	pure	PROPN
ejpam-5839	493	3	appl	appl	PROPN
ejpam-5839	493	4	.	.	PROPN
ejpam-5839	493	5	math	math	PROPN
ejpam-5839	493	6	,	,	PUNCT
ejpam-5839	493	7	18	18	NUM
ejpam-5839	493	8	(	(	PUNCT
ejpam-5839	493	9	2	2	NUM
ejpam-5839	493	10	)	)	PUNCT
ejpam-5839	493	11	(	(	PUNCT
ejpam-5839	493	12	2025	2025	NUM
ejpam-5839	493	13	)	)	PUNCT
ejpam-5839	493	14	,	,	PUNCT
ejpam-5839	493	15	5839	5839	NUM
ejpam-5839	493	16	22	22	NUM
ejpam-5839	493	17	of	of	ADP
ejpam-5839	493	18	54	54	NUM
ejpam-5839	493	19	=	=	SYM
ejpam-5839	493	20	1	1	NUM
ejpam-5839	493	21	8	8	NUM
ejpam-5839	493	22	(	(	PUNCT
ejpam-5839	493	23	0	0	NUM
ejpam-5839	494	1	+	+	CCONJ
ejpam-5839	494	2	1	1	NUM
ejpam-5839	494	3	8	8	NUM
ejpam-5839	494	4	+	+	CCONJ
ejpam-5839	494	5	1	1	NUM
ejpam-5839	494	6	2	2	NUM
ejpam-5839	494	7	+	+	CCONJ
ejpam-5839	494	8	9	9	NUM
ejpam-5839	494	9	8	8	NUM
ejpam-5839	494	10	+	+	NUM
ejpam-5839	494	11	1	1	NUM
ejpam-5839	494	12	)	)	PUNCT
ejpam-5839	494	13	=	=	PUNCT
ejpam-5839	494	14	11	11	NUM
ejpam-5839	494	15	32	32	NUM
ejpam-5839	494	16	.	.	PUNCT
ejpam-5839	495	1	therefore	therefore	ADV
ejpam-5839	495	2	,	,	PUNCT
ejpam-5839	495	3	(	(	PUNCT
ejpam-5839	495	4	∫	∫	PROPN
ejpam-5839	495	5	1	1	NUM
ejpam-5839	495	6	0	0	NUM
ejpam-5839	495	7	f̃(q(x	f̃(q(x	NUM
ejpam-5839	495	8	)	)	PUNCT
ejpam-5839	495	9	)	)	PUNCT
ejpam-5839	495	10	dx	dx	PROPN
ejpam-5839	495	11	)	)	PUNCT
ejpam-5839	496	1	i	i	PRON
ejpam-5839	496	2	,	,	PUNCT
ejpam-5839	496	3	j	j	PROPN
ejpam-5839	496	4	,	,	PUNCT
ejpam-5839	496	5	k	k	PROPN
ejpam-5839	496	6	,	,	PUNCT
ejpam-5839	496	7	l	l	NOUN
ejpam-5839	496	8	=	=	SYM
ejpam-5839	496	9	(	(	PUNCT
ejpam-5839	496	10	∫	∫	PROPN
ejpam-5839	496	11	1	1	NUM
ejpam-5839	496	12	0	0	NUM
ejpam-5839	496	13	ñ(x)2	ñ(x)2	NOUN
ejpam-5839	496	14	dx	dx	PROPN
ejpam-5839	496	15	)	)	PUNCT
ejpam-5839	497	1	i	i	PRON
ejpam-5839	497	2	,	,	PUNCT
ejpam-5839	497	3	j	j	PROPN
ejpam-5839	497	4	,	,	PUNCT
ejpam-5839	497	5	k	k	PROPN
ejpam-5839	497	6	,	,	PUNCT
ejpam-5839	497	7	l	l	PROPN
ejpam-5839	497	8	∫	∫	PROPN
ejpam-5839	497	9	1	1	NUM
ejpam-5839	497	10	0	0	NUM
ejpam-5839	497	11	5i	5i	NUM
ejpam-5839	497	12	4	4	NUM
ejpam-5839	497	13	(	(	PUNCT
ejpam-5839	497	14	x	x	NOUN
ejpam-5839	497	15	)	)	PUNCT
ejpam-5839	497	16	2	2	NUM
ejpam-5839	497	17	dx	dx	PROPN
ejpam-5839	497	18	,	,	PUNCT
ejpam-5839	497	19	∫	∫	PROPN
ejpam-5839	497	20	1	1	NUM
ejpam-5839	497	21	0	0	NUM
ejpam-5839	497	22	(	(	PUNCT
ejpam-5839	497	23	2−	2−	NUM
ejpam-5839	497	24	5i	5i	NUM
ejpam-5839	497	25	4	4	NUM
ejpam-5839	497	26	)	)	PUNCT
ejpam-5839	497	27	(	(	PUNCT
ejpam-5839	497	28	x)2	x)2	AUX
ejpam-5839	497	29	dx∫	dx∫	VERB
ejpam-5839	497	30	1	1	NUM
ejpam-5839	497	31	0	0	NUM
ejpam-5839	497	32	5	5	NUM
ejpam-5839	497	33	2(1−	2(1−	NUM
ejpam-5839	497	34	j)(x)2	j)(x)2	NOUN
ejpam-5839	497	35	dx	dx	PROPN
ejpam-5839	497	36	,	,	PUNCT
ejpam-5839	497	37	∫	∫	PROPN
ejpam-5839	497	38	1	1	NUM
ejpam-5839	497	39	0	0	NUM
ejpam-5839	497	40	1	1	NUM
ejpam-5839	497	41	2(5j−	2(5j−	NUM
ejpam-5839	497	42	1)(x)2	1)(x)2	NUM
ejpam-5839	497	43	dx∫	dx∫	PROPN
ejpam-5839	497	44	1	1	NUM
ejpam-5839	497	45	0	0	NUM
ejpam-5839	497	46	5	5	NUM
ejpam-5839	497	47	3(1−	3(1−	NUM
ejpam-5839	497	48	k)(x)2	k)(x)2	NOUN
ejpam-5839	497	49	dx	dx	PROPN
ejpam-5839	497	50	,	,	PUNCT
ejpam-5839	497	51	∫	∫	PROPN
ejpam-5839	497	52	1	1	NUM
ejpam-5839	497	53	0	0	NUM
ejpam-5839	497	54	1	1	NUM
ejpam-5839	497	55	3(5k−	3(5k−	NUM
ejpam-5839	497	56	1)(x)2	1)(x)2	NUM
ejpam-5839	497	57	dx∫	dx∫	PROPN
ejpam-5839	497	58	1	1	NUM
ejpam-5839	497	59	0	0	NUM
ejpam-5839	497	60	5	5	NUM
ejpam-5839	497	61	3(1−	3(1−	NUM
ejpam-5839	497	62	l)(x)2	l)(x)2	NOUN
ejpam-5839	497	63	dx	dx	PROPN
ejpam-5839	497	64	,	,	PUNCT
ejpam-5839	497	65	∫	∫	PROPN
ejpam-5839	497	66	1	1	NUM
ejpam-5839	497	67	0	0	NUM
ejpam-5839	497	68	1	1	NUM
ejpam-5839	497	69	3(5l−	3(5l−	NUM
ejpam-5839	497	70	1)(x)2	1)(x)2	NUM
ejpam-5839	498	1	dx	dx	PROPN
ejpam-5839	498	2			PROPN
ejpam-5839	498	3			PROPN
ejpam-5839	498	4	5i	5i	NUM
ejpam-5839	498	5	4	4	NUM
ejpam-5839	498	6	∫	∫	NOUN
ejpam-5839	498	7	1	1	NUM
ejpam-5839	498	8	0	0	NUM
ejpam-5839	498	9	(	(	PUNCT
ejpam-5839	498	10	x	x	NOUN
ejpam-5839	498	11	)	)	PUNCT
ejpam-5839	498	12	2	2	NUM
ejpam-5839	498	13	dx	dx	PROPN
ejpam-5839	498	14	,	,	PUNCT
ejpam-5839	498	15	12−5i	12−5i	NUM
ejpam-5839	498	16	4	4	NUM
ejpam-5839	498	17	∫	∫	NOUN
ejpam-5839	498	18	1	1	NUM
ejpam-5839	498	19	0	0	NUM
ejpam-5839	498	20	(	(	PUNCT
ejpam-5839	498	21	x	x	NOUN
ejpam-5839	498	22	)	)	PUNCT
ejpam-5839	498	23	2	2	NUM
ejpam-5839	498	24	dx	dx	PROPN
ejpam-5839	498	25	5	5	NUM
ejpam-5839	498	26	2(1−	2(1−	PROPN
ejpam-5839	498	27	j	j	PROPN
ejpam-5839	498	28	)	)	PUNCT
ejpam-5839	498	29	∫	∫	PROPN
ejpam-5839	499	1	1	1	NUM
ejpam-5839	499	2	0	0	NUM
ejpam-5839	499	3	(	(	PUNCT
ejpam-5839	499	4	x	x	NOUN
ejpam-5839	499	5	)	)	PUNCT
ejpam-5839	499	6	2	2	NUM
ejpam-5839	499	7	dx	dx	PROPN
ejpam-5839	499	8	,	,	PUNCT
ejpam-5839	499	9	1	1	NUM
ejpam-5839	499	10	2(5j−	2(5j−	NUM
ejpam-5839	499	11	1	1	NUM
ejpam-5839	499	12	)	)	PUNCT
ejpam-5839	499	13	∫	∫	PROPN
ejpam-5839	499	14	1	1	NUM
ejpam-5839	499	15	0	0	NUM
ejpam-5839	499	16	(	(	PUNCT
ejpam-5839	499	17	x	x	NOUN
ejpam-5839	499	18	)	)	PUNCT
ejpam-5839	499	19	2	2	NUM
ejpam-5839	499	20	dx	dx	PROPN
ejpam-5839	499	21	5	5	NUM
ejpam-5839	499	22	3(1−	3(1−	NUM
ejpam-5839	499	23	k	k	X
ejpam-5839	499	24	)	)	PUNCT
ejpam-5839	499	25	∫	∫	PROPN
ejpam-5839	499	26	1	1	NUM
ejpam-5839	499	27	0	0	NUM
ejpam-5839	499	28	(	(	PUNCT
ejpam-5839	499	29	x	x	NOUN
ejpam-5839	499	30	)	)	PUNCT
ejpam-5839	499	31	2	2	NUM
ejpam-5839	499	32	dx	dx	PROPN
ejpam-5839	499	33	,	,	PUNCT
ejpam-5839	499	34	1	1	NUM
ejpam-5839	499	35	3(5k−	3(5k−	NUM
ejpam-5839	499	36	1	1	NUM
ejpam-5839	499	37	)	)	PUNCT
ejpam-5839	499	38	∫	∫	PROPN
ejpam-5839	500	1	1	1	NUM
ejpam-5839	500	2	0	0	NUM
ejpam-5839	500	3	(	(	PUNCT
ejpam-5839	500	4	x	x	NOUN
ejpam-5839	500	5	)	)	PUNCT
ejpam-5839	500	6	2	2	NUM
ejpam-5839	500	7	dx	dx	PROPN
ejpam-5839	500	8	5	5	NUM
ejpam-5839	500	9	3(1−	3(1−	NUM
ejpam-5839	500	10	l	l	NOUN
ejpam-5839	500	11	)	)	PUNCT
ejpam-5839	500	12	∫	∫	PROPN
ejpam-5839	501	1	1	1	NUM
ejpam-5839	501	2	0	0	NUM
ejpam-5839	501	3	(	(	PUNCT
ejpam-5839	501	4	x	x	NOUN
ejpam-5839	501	5	)	)	PUNCT
ejpam-5839	501	6	2	2	NUM
ejpam-5839	501	7	dx	dx	PROPN
ejpam-5839	501	8	,	,	PUNCT
ejpam-5839	501	9	1	1	NUM
ejpam-5839	501	10	3(5l−	3(5l−	NUM
ejpam-5839	501	11	1	1	NUM
ejpam-5839	501	12	)	)	PUNCT
ejpam-5839	501	13	∫	∫	PROPN
ejpam-5839	501	14	1	1	NUM
ejpam-5839	501	15	0	0	NUM
ejpam-5839	501	16	(	(	PUNCT
ejpam-5839	501	17	x	x	NOUN
ejpam-5839	501	18	)	)	PUNCT
ejpam-5839	501	19	2	2	NUM
ejpam-5839	501	20	dx	dx	PROPN
ejpam-5839	501	21			PROPN
ejpam-5839	501	22	∫	∫	PROPN
ejpam-5839	502	1	f̃ql	f̃ql	PROPN
ejpam-5839	503	1	i	i	PRON
ejpam-5839	503	2	(	(	PUNCT
ejpam-5839	503	3	x)dx	x)dx	PROPN
ejpam-5839	503	4	∫	∫	PROPN
ejpam-5839	503	5	f̃qu	f̃qu	PROPN
ejpam-5839	503	6	i	i	PRON
ejpam-5839	503	7	(	(	PUNCT
ejpam-5839	503	8	x)dx	x)dx	PROPN
ejpam-5839	503	9	∫	∫	PROPN
ejpam-5839	504	1	f̃ql	f̃ql	PROPN
ejpam-5839	504	2	j	j	PROPN
ejpam-5839	504	3	(	(	PUNCT
ejpam-5839	504	4	x)dx	x)dx	PROPN
ejpam-5839	504	5	∫	∫	PROPN
ejpam-5839	504	6	f̃qu	f̃qu	PROPN
ejpam-5839	504	7	j	j	PROPN
ejpam-5839	504	8	(	(	PUNCT
ejpam-5839	504	9	x)dx	x)dx	PROPN
ejpam-5839	504	10	∫	∫	PROPN
ejpam-5839	505	1	f̃ql	f̃ql	PROPN
ejpam-5839	505	2	k	k	PROPN
ejpam-5839	505	3	(	(	PUNCT
ejpam-5839	505	4	x)dx	x)dx	PROPN
ejpam-5839	505	5	∫	∫	PROPN
ejpam-5839	506	1	f̃qu	f̃qu	PROPN
ejpam-5839	506	2	k	k	X
ejpam-5839	506	3	(	(	PUNCT
ejpam-5839	506	4	x)dx	x)dx	PROPN
ejpam-5839	506	5	∫	∫	PROPN
ejpam-5839	506	6	f̃ql	f̃ql	ADJ
ejpam-5839	506	7	l	l	NOUN
ejpam-5839	506	8	(	(	PUNCT
ejpam-5839	506	9	x)dx	x)dx	PROPN
ejpam-5839	506	10	∫	∫	PROPN
ejpam-5839	506	11	f̃qu	f̃qu	X
ejpam-5839	506	12	l	l	X
ejpam-5839	506	13	(	(	PUNCT
ejpam-5839	506	14	x)dx	x)dx	PROPN
ejpam-5839	506	15	0	0	NUM
ejpam-5839	506	16	0×	0×	PROPN
ejpam-5839	506	17	10−1	10−1	NUM
ejpam-5839	506	18	0×	0×	NUM
ejpam-5839	506	19	10−1	10−1	NUM
ejpam-5839	506	20	1.03125×	1.03125×	NUM
ejpam-5839	506	21	10−5	10−5	NUM
ejpam-5839	506	22	6×	6×	NUM
ejpam-5839	506	23	10−1	10−1	NUM
ejpam-5839	506	24	0.34375×	0.34375×	ADJ
ejpam-5839	506	25	10−5	10−5	NUM
ejpam-5839	506	26	0.6875×	0.6875×	NOUN
ejpam-5839	506	27	10−4	10−4	NUM
ejpam-5839	506	28	4×	4×	NOUN
ejpam-5839	506	29	10−1	10−1	NUM
ejpam-5839	506	30	0.34375×	0.34375×	NOUN
ejpam-5839	506	31	10−5	10−5	NUM
ejpam-5839	506	32	0.4	0.4	NUM
ejpam-5839	506	33	0.34375×	0.34375×	NOUN
ejpam-5839	506	34	10−5	10−5	NUM
ejpam-5839	506	35	0.6875×	0.6875×	NOUN
ejpam-5839	506	36	10−4	10−4	NUM
ejpam-5839	506	37	4×	4×	NOUN
ejpam-5839	506	38	10−1	10−1	NUM
ejpam-5839	506	39	0.34375×	0.34375×	ADJ
ejpam-5839	506	40	10−5	10−5	NUM
ejpam-5839	506	41	0.6875×	0.6875×	NOUN
ejpam-5839	506	42	10−4	10−4	NUM
ejpam-5839	506	43	4×	4×	NOUN
ejpam-5839	506	44	10−1	10−1	NUM
ejpam-5839	506	45	0.171875×	0.171875×	NOUN
ejpam-5839	507	1	10−6	10−6	NUM
ejpam-5839	507	2	0.859375×	0.859375×	NOUN
ejpam-5839	508	1	10−6	10−6	NUM
ejpam-5839	508	2	0.8	0.8	NUM
ejpam-5839	508	3	0.17185×	0.17185×	NUM
ejpam-5839	508	4	10−5	10−5	NUM
ejpam-5839	508	5	0.859375×	0.859375×	NOUN
ejpam-5839	509	1	10−6	10−6	NUM
ejpam-5839	509	2	6×	6×	NUM
ejpam-5839	509	3	10−1	10−1	NUM
ejpam-5839	509	4	0.229167×	0.229167×	NOUN
ejpam-5839	509	5	10−6	10−6	NUM
ejpam-5839	509	6	0.802083×	0.802083×	ADP
ejpam-5839	510	1	10−6	10−6	NUM
ejpam-5839	510	2	6×	6×	NUM
ejpam-5839	510	3	10−1	10−1	NUM
ejpam-5839	510	4	0.229167×	0.229167×	NOUN
ejpam-5839	510	5	10−6	10−6	NUM
ejpam-5839	510	6	0.802083×	0.802083×	ADP
ejpam-5839	510	7	10−6	10−6	NUM
ejpam-5839	510	8	0.6	0.6	NUM
ejpam-5839	510	9	0.257813×	0.257813×	NOUN
ejpam-5839	510	10	10−6	10−6	NUM
ejpam-5839	510	11	0.773438×	0.773438×	NOUN
ejpam-5839	511	1	10−6	10−6	NUM
ejpam-5839	511	2	9×	9×	NUM
ejpam-5839	511	3	10−1	10−1	NUM
ejpam-5839	511	4	0.0859375×	0.0859375×	NOUN
ejpam-5839	512	1	10−7	10−7	NUM
ejpam-5839	512	2	0.945313×	0.945313×	NOUN
ejpam-5839	513	1	10−6	10−6	NUM
ejpam-5839	514	1	8×	8×	ADP
ejpam-5839	514	2	10−1	10−1	NUM
ejpam-5839	514	3	0.114583×	0.114583×	NOUN
ejpam-5839	514	4	10−6	10−6	NUM
ejpam-5839	514	5	0.916667×	0.916667×	NOUN
ejpam-5839	514	6	10−6	10−6	NUM
ejpam-5839	514	7	0.8	0.8	NUM
ejpam-5839	514	8	0.114583×	0.114583×	NUM
ejpam-5839	514	9	10−6	10−6	NUM
ejpam-5839	514	10	0.916667×	0.916667×	NOUN
ejpam-5839	515	1	10−6	10−6	NUM
ejpam-5839	515	2	8×	8×	NUM
ejpam-5839	515	3	10−1	10−1	NUM
ejpam-5839	515	4	0.34375×	0.34375×	ADJ
ejpam-5839	515	5	10−5	10−5	NUM
ejpam-5839	515	6	0.6875×	0.6875×	NOUN
ejpam-5839	515	7	10−4	10−4	NUM
ejpam-5839	515	8	1×	1×	NUM
ejpam-5839	515	9	10−1	10−1	PROPN
ejpam-5839	515	10	0×	0×	PROPN
ejpam-5839	515	11	10−1	10−1	NUM
ejpam-5839	515	12	1.03125×	1.03125×	NUM
ejpam-5839	515	13	10−5	10−5	NUM
ejpam-5839	515	14	1.0	1.0	NUM
ejpam-5839	515	15	0×	0×	SYM
ejpam-5839	515	16	10−1	10−1	NUM
ejpam-5839	515	17	1.03125×	1.03125×	NUM
ejpam-5839	515	18	10−5	10−5	NUM
ejpam-5839	515	19	1×	1×	NUM
ejpam-5839	515	20	10−1	10−1	PROPN
ejpam-5839	515	21	0×	0×	PROPN
ejpam-5839	515	22	10−1	10−1	NUM
ejpam-5839	515	23	1.03125×	1.03125×	NUM
ejpam-5839	515	24	10−5	10−5	NUM
ejpam-5839	515	25	1×	1×	NUM
ejpam-5839	515	26	10−1	10−1	PROPN
ejpam-5839	515	27	0×	0×	PROPN
ejpam-5839	515	28	10−1	10−1	NUM
ejpam-5839	515	29	1.03125×	1.03125×	NUM
ejpam-5839	515	30	10−5	10−5	NUM
ejpam-5839	515	31	table	table	NOUN
ejpam-5839	515	32	2	2	NUM
ejpam-5839	515	33	:	:	PUNCT
ejpam-5839	515	34	value	value	NOUN
ejpam-5839	515	35	of	of	ADP
ejpam-5839	515	36	example	example	NOUN
ejpam-5839	515	37	2	2	NUM
ejpam-5839	515	38	by	by	ADP
ejpam-5839	515	39	the	the	DET
ejpam-5839	515	40	quadri	quadri	NOUN
ejpam-5839	515	41	-	-	PUNCT
ejpam-5839	515	42	trapezoidal	trapezoidal	ADJ
ejpam-5839	515	43	rule	rule	NOUN
ejpam-5839	515	44	for	for	ADP
ejpam-5839	515	45	different	different	ADJ
ejpam-5839	515	46	values	value	NOUN
ejpam-5839	515	47	of	of	ADP
ejpam-5839	515	48	i	i	PROPN
ejpam-5839	515	49	,	,	PUNCT
ejpam-5839	515	50	j	j	PROPN
ejpam-5839	515	51	,	,	PUNCT
ejpam-5839	515	52	k	k	PROPN
ejpam-5839	515	53	,	,	PUNCT
ejpam-5839	515	54	and	and	CCONJ
ejpam-5839	515	55	l	l	ADJ
ejpam-5839	515	56	55i	55i	PROPN
ejpam-5839	515	57	128	128	NUM
ejpam-5839	515	58	,	,	PUNCT
ejpam-5839	515	59	132−55i	132−55i	NUM
ejpam-5839	515	60	128	128	NUM
ejpam-5839	515	61	55	55	NUM
ejpam-5839	515	62	64(1−	64(1−	PROPN
ejpam-5839	515	63	j	j	PROPN
ejpam-5839	515	64	)	)	PUNCT
ejpam-5839	515	65	,	,	PUNCT
ejpam-5839	515	66	11	11	NUM
ejpam-5839	515	67	64(5j−	64(5j−	NUM
ejpam-5839	515	68	1	1	NUM
ejpam-5839	515	69	)	)	PUNCT
ejpam-5839	515	70	55	55	NUM
ejpam-5839	515	71	96(1−	96(1−	NUM
ejpam-5839	515	72	k	k	X
ejpam-5839	515	73	)	)	PUNCT
ejpam-5839	515	74	,	,	PUNCT
ejpam-5839	515	75	11	11	NUM
ejpam-5839	515	76	96(5k−	96(5k−	NOUN
ejpam-5839	515	77	1	1	NUM
ejpam-5839	515	78	)	)	PUNCT
ejpam-5839	515	79	55	55	NUM
ejpam-5839	515	80	96(1−	96(1−	NUM
ejpam-5839	515	81	l	l	NOUN
ejpam-5839	515	82	)	)	PUNCT
ejpam-5839	515	83	,	,	PUNCT
ejpam-5839	515	84	11	11	NUM
ejpam-5839	515	85	96(5l−	96(5l−	NUM
ejpam-5839	515	86	1	1	NUM
ejpam-5839	515	87	)	)	PUNCT
ejpam-5839	515	88			NOUN
ejpam-5839	515	89	where	where	SCONJ
ejpam-5839	515	90	:	:	PUNCT
ejpam-5839	515	91	∫	∫	PROPN
ejpam-5839	516	1	f̃ql	f̃ql	PROPN
ejpam-5839	516	2	i	i	PRON
ejpam-5839	516	3	(	(	PUNCT
ejpam-5839	516	4	x	x	X
ejpam-5839	516	5	)	)	PUNCT
ejpam-5839	516	6	dx	dx	PROPN
ejpam-5839	516	7	∣∣∣1	∣∣∣1	PROPN
ejpam-5839	516	8	0	0	PUNCT
ejpam-5839	517	1	=	=	SYM
ejpam-5839	517	2	55i	55i	NUM
ejpam-5839	517	3	128	128	NUM
ejpam-5839	517	4	,	,	PUNCT
ejpam-5839	517	5	∫	∫	PROPN
ejpam-5839	517	6	f̃qu	f̃qu	INTJ
ejpam-5839	517	7	i	i	PRON
ejpam-5839	517	8	(	(	PUNCT
ejpam-5839	517	9	x	x	X
ejpam-5839	517	10	)	)	PUNCT
ejpam-5839	517	11	dx	dx	PROPN
ejpam-5839	517	12	∣∣∣1	∣∣∣1	PROPN
ejpam-5839	517	13	0	0	PUNCT
ejpam-5839	518	1	=	=	SYM
ejpam-5839	518	2	132−	132−	NUM
ejpam-5839	518	3	55i	55i	NUM
ejpam-5839	518	4	128∫	128∫	PROPN
ejpam-5839	519	1	f̃ql	f̃ql	PROPN
ejpam-5839	519	2	j	j	PROPN
ejpam-5839	519	3	(	(	PUNCT
ejpam-5839	519	4	x	x	X
ejpam-5839	519	5	)	)	PUNCT
ejpam-5839	519	6	dx	dx	PROPN
ejpam-5839	519	7	∣∣∣1	∣∣∣1	PROPN
ejpam-5839	519	8	0	0	PUNCT
ejpam-5839	520	1	=	=	SYM
ejpam-5839	520	2	55	55	NUM
ejpam-5839	520	3	64	64	NUM
ejpam-5839	520	4	(	(	PUNCT
ejpam-5839	520	5	1−	1−	NUM
ejpam-5839	520	6	j	j	NOUN
ejpam-5839	520	7	)	)	PUNCT
ejpam-5839	520	8	,	,	PUNCT
ejpam-5839	520	9	∫	∫	PROPN
ejpam-5839	520	10	f̃qu	f̃qu	X
ejpam-5839	520	11	j	j	PROPN
ejpam-5839	520	12	(	(	PUNCT
ejpam-5839	520	13	x	x	X
ejpam-5839	520	14	)	)	PUNCT
ejpam-5839	520	15	dx	dx	PROPN
ejpam-5839	520	16	∣∣∣1	∣∣∣1	PROPN
ejpam-5839	520	17	0	0	PUNCT
ejpam-5839	521	1	=	=	SYM
ejpam-5839	521	2	11	11	NUM
ejpam-5839	521	3	64	64	NUM
ejpam-5839	521	4	(	(	PUNCT
ejpam-5839	521	5	5j−	5j−	NOUN
ejpam-5839	521	6	1	1	NUM
ejpam-5839	521	7	)	)	PUNCT
ejpam-5839	521	8	∫	∫	PROPN
ejpam-5839	522	1	f̃ql	f̃ql	PROPN
ejpam-5839	522	2	k	k	PROPN
ejpam-5839	522	3	(	(	PUNCT
ejpam-5839	522	4	x	x	X
ejpam-5839	522	5	)	)	PUNCT
ejpam-5839	522	6	dx	dx	PROPN
ejpam-5839	522	7	∣∣∣1	∣∣∣1	PROPN
ejpam-5839	522	8	0	0	PUNCT
ejpam-5839	523	1	=	=	SYM
ejpam-5839	523	2	55	55	NUM
ejpam-5839	523	3	96	96	NUM
ejpam-5839	523	4	(	(	PUNCT
ejpam-5839	523	5	1−	1−	NUM
ejpam-5839	523	6	k	k	NOUN
ejpam-5839	523	7	)	)	PUNCT
ejpam-5839	523	8	,	,	PUNCT
ejpam-5839	523	9	∫	∫	PROPN
ejpam-5839	523	10	f̃qu	f̃qu	X
ejpam-5839	523	11	k	k	X
ejpam-5839	523	12	(	(	PUNCT
ejpam-5839	523	13	x	x	X
ejpam-5839	523	14	)	)	PUNCT
ejpam-5839	523	15	dx	dx	PROPN
ejpam-5839	523	16	∣∣∣1	∣∣∣1	PROPN
ejpam-5839	523	17	0	0	PUNCT
ejpam-5839	524	1	=	=	SYM
ejpam-5839	524	2	11	11	NUM
ejpam-5839	524	3	96	96	NUM
ejpam-5839	524	4	(	(	PUNCT
ejpam-5839	524	5	5k−	5k−	NOUN
ejpam-5839	524	6	1	1	NUM
ejpam-5839	524	7	)	)	PUNCT
ejpam-5839	524	8	∫	∫	NOUN
ejpam-5839	525	1	f̃ql	f̃ql	PROPN
ejpam-5839	525	2	l	l	NOUN
ejpam-5839	525	3	(	(	PUNCT
ejpam-5839	525	4	x	x	X
ejpam-5839	525	5	)	)	PUNCT
ejpam-5839	525	6	dx	dx	PROPN
ejpam-5839	525	7	∣∣∣1	∣∣∣1	PROPN
ejpam-5839	525	8	0	0	PUNCT
ejpam-5839	526	1	=	=	SYM
ejpam-5839	526	2	55	55	NUM
ejpam-5839	526	3	96	96	NUM
ejpam-5839	526	4	(	(	PUNCT
ejpam-5839	526	5	1−	1−	NUM
ejpam-5839	526	6	l	l	NOUN
ejpam-5839	526	7	)	)	PUNCT
ejpam-5839	526	8	,	,	PUNCT
ejpam-5839	526	9	∫	∫	PROPN
ejpam-5839	526	10	f̃qu	f̃qu	X
ejpam-5839	526	11	l	l	X
ejpam-5839	526	12	(	(	PUNCT
ejpam-5839	526	13	x	x	X
ejpam-5839	526	14	)	)	PUNCT
ejpam-5839	526	15	dx	dx	PROPN
ejpam-5839	526	16	∣∣∣1	∣∣∣1	PROPN
ejpam-5839	526	17	0	0	PUNCT
ejpam-5839	527	1	=	=	SYM
ejpam-5839	527	2	11	11	NUM
ejpam-5839	527	3	96	96	NUM
ejpam-5839	527	4	(	(	PUNCT
ejpam-5839	527	5	5l−	5l−	PROPN
ejpam-5839	527	6	1	1	NUM
ejpam-5839	527	7	)	)	PUNCT
ejpam-5839	527	8	.	.	PUNCT
ejpam-5839	528	1	for	for	ADP
ejpam-5839	528	2	:	:	PUNCT
ejpam-5839	528	3	i	i	PRON
ejpam-5839	528	4	∈	∈	VERB
ejpam-5839	529	1	[	[	X
ejpam-5839	529	2	0	0	NUM
ejpam-5839	529	3	,	,	PUNCT
ejpam-5839	529	4	0.8	0.8	NUM
ejpam-5839	529	5	]	]	PUNCT
ejpam-5839	529	6	,	,	PUNCT
ejpam-5839	529	7	j	j	PROPN
ejpam-5839	529	8	∈	∈	PROPN
ejpam-5839	530	1	[	[	X
ejpam-5839	530	2	0.6	0.6	NUM
ejpam-5839	530	3	,	,	PUNCT
ejpam-5839	530	4	1	1	NUM
ejpam-5839	530	5	]	]	PUNCT
ejpam-5839	530	6	,	,	PUNCT
ejpam-5839	530	7	k	k	PROPN
ejpam-5839	530	8	∈	∈	PROPN
ejpam-5839	531	1	[	[	X
ejpam-5839	531	2	0.4	0.4	NUM
ejpam-5839	531	3	,	,	PUNCT
ejpam-5839	531	4	1	1	NUM
ejpam-5839	531	5	]	]	PUNCT
ejpam-5839	531	6	,	,	PUNCT
ejpam-5839	531	7	l	l	PROPN
ejpam-5839	531	8	∈	∈	PROPN
ejpam-5839	531	9	[	[	X
ejpam-5839	531	10	0.4	0.4	NUM
ejpam-5839	531	11	,	,	PUNCT
ejpam-5839	531	12	1	1	NUM
ejpam-5839	531	13	]	]	PUNCT
ejpam-5839	531	14	a.	a.	NOUN
ejpam-5839	531	15	shihadeh	shihadeh	PROPN
ejpam-5839	531	16	et	et	PROPN
ejpam-5839	531	17	al	al	PROPN
ejpam-5839	531	18	.	.	PUNCT
ejpam-5839	531	19	/	/	SYM
ejpam-5839	531	20	eur	eur	PROPN
ejpam-5839	531	21	.	.	PUNCT
ejpam-5839	532	1	j.	j.	PROPN
ejpam-5839	532	2	pure	pure	PROPN
ejpam-5839	532	3	appl	appl	PROPN
ejpam-5839	532	4	.	.	PROPN
ejpam-5839	532	5	math	math	PROPN
ejpam-5839	532	6	,	,	PUNCT
ejpam-5839	532	7	18	18	NUM
ejpam-5839	532	8	(	(	PUNCT
ejpam-5839	532	9	2	2	NUM
ejpam-5839	532	10	)	)	PUNCT
ejpam-5839	532	11	(	(	PUNCT
ejpam-5839	532	12	2025	2025	NUM
ejpam-5839	532	13	)	)	PUNCT
ejpam-5839	532	14	,	,	PUNCT
ejpam-5839	532	15	5839	5839	NUM
ejpam-5839	532	16	23	23	NUM
ejpam-5839	532	17	of	of	ADP
ejpam-5839	532	18	54	54	NUM
ejpam-5839	532	19	6	6	NUM
ejpam-5839	532	20	.	.	PUNCT
ejpam-5839	533	1	comparative	comparative	ADJ
ejpam-5839	533	2	analysis	analysis	NOUN
ejpam-5839	533	3	the	the	DET
ejpam-5839	533	4	following	follow	VERB
ejpam-5839	533	5	table	table	NOUN
ejpam-5839	533	6	3	3	NUM
ejpam-5839	533	7	provides	provide	VERB
ejpam-5839	533	8	a	a	DET
ejpam-5839	533	9	detailed	detailed	ADJ
ejpam-5839	533	10	comparative	comparative	ADJ
ejpam-5839	533	11	analysis	analysis	NOUN
ejpam-5839	533	12	of	of	ADP
ejpam-5839	533	13	the	the	DET
ejpam-5839	533	14	proposed	propose	VERB
ejpam-5839	533	15	methods	method	NOUN
ejpam-5839	533	16	,	,	PUNCT
ejpam-5839	533	17	contrasting	contrast	VERB
ejpam-5839	533	18	them	they	PRON
ejpam-5839	533	19	with	with	ADP
ejpam-5839	533	20	the	the	DET
ejpam-5839	533	21	established	establish	VERB
ejpam-5839	533	22	techniques	technique	NOUN
ejpam-5839	533	23	discussed	discuss	VERB
ejpam-5839	533	24	in	in	ADP
ejpam-5839	533	25	[	[	X
ejpam-5839	533	26	43	43	NUM
ejpam-5839	533	27	]	]	PUNCT
ejpam-5839	533	28	.	.	PUNCT
ejpam-5839	534	1	this	this	DET
ejpam-5839	534	2	comparison	comparison	NOUN
ejpam-5839	534	3	highlights	highlight	VERB
ejpam-5839	534	4	the	the	DET
ejpam-5839	534	5	strengths	strength	NOUN
ejpam-5839	534	6	and	and	CCONJ
ejpam-5839	534	7	weaknesses	weakness	NOUN
ejpam-5839	534	8	of	of	ADP
ejpam-5839	534	9	each	each	DET
ejpam-5839	534	10	approach	approach	NOUN
ejpam-5839	534	11	,	,	PUNCT
ejpam-5839	534	12	offering	offer	VERB
ejpam-5839	534	13	insights	insight	NOUN
ejpam-5839	534	14	into	into	ADP
ejpam-5839	534	15	how	how	SCONJ
ejpam-5839	534	16	the	the	DET
ejpam-5839	534	17	proposed	propose	VERB
ejpam-5839	534	18	methods	method	NOUN
ejpam-5839	534	19	perform	perform	VERB
ejpam-5839	534	20	relative	relative	ADJ
ejpam-5839	534	21	to	to	ADP
ejpam-5839	534	22	the	the	DET
ejpam-5839	534	23	established	establish	VERB
ejpam-5839	534	24	techniques	technique	NOUN
ejpam-5839	534	25	across	across	ADP
ejpam-5839	534	26	various	various	ADJ
ejpam-5839	534	27	key	key	ADJ
ejpam-5839	534	28	factors	factor	NOUN
ejpam-5839	534	29	.	.	PUNCT
ejpam-5839	535	1	aspect	aspect	NOUN
ejpam-5839	535	2	published	publish	VERB
ejpam-5839	535	3	work	work	NOUN
ejpam-5839	535	4	(	(	PUNCT
ejpam-5839	535	5	reference	reference	NOUN
ejpam-5839	535	6	[	[	X
ejpam-5839	535	7	43	43	NUM
ejpam-5839	535	8	]	]	PUNCT
ejpam-5839	535	9	)	)	PUNCT
ejpam-5839	535	10	proposed	propose	VERB
ejpam-5839	535	11	method	method	NOUN
ejpam-5839	535	12	/	/	SYM
ejpam-5839	535	13	work	work	NOUN
ejpam-5839	535	14	1	1	NUM
ejpam-5839	535	15	.	.	PUNCT
ejpam-5839	536	1	foundation	foundation	NOUN
ejpam-5839	536	2	introduces	introduce	NOUN
ejpam-5839	536	3	neutrosophic	neutrosophic	ADJ
ejpam-5839	536	4	riemann	riemann	PROPN
ejpam-5839	536	5	integration	integration	NOUN
ejpam-5839	536	6	,	,	PUNCT
ejpam-5839	536	7	focusing	focus	VERB
ejpam-5839	536	8	on	on	ADP
ejpam-5839	536	9	neutrosophic	neutrosophic	ADJ
ejpam-5839	536	10	numbers	number	NOUN
ejpam-5839	536	11	and	and	CCONJ
ejpam-5839	536	12	functions	function	NOUN
ejpam-5839	536	13	,	,	PUNCT
ejpam-5839	536	14	extending	extend	VERB
ejpam-5839	536	15	classical	classical	ADJ
ejpam-5839	536	16	integration	integration	NOUN
ejpam-5839	536	17	theory	theory	NOUN
ejpam-5839	536	18	.	.	PUNCT
ejpam-5839	537	1	based	base	VERB
ejpam-5839	537	2	on	on	ADP
ejpam-5839	537	3	quadri	quadri	NOUN
ejpam-5839	537	4	-	-	PUNCT
ejpam-5839	537	5	partitioned	partition	VERB
ejpam-5839	537	6	neutrosophic	neutrosophic	ADJ
ejpam-5839	537	7	set	set	NOUN
ejpam-5839	537	8	theory	theory	NOUN
ejpam-5839	537	9	(	(	PUNCT
ejpam-5839	537	10	qpnst	qpnst	ADJ
ejpam-5839	537	11	)	)	PUNCT
ejpam-5839	537	12	,	,	PUNCT
ejpam-5839	537	13	extending	extend	VERB
ejpam-5839	537	14	neutrosophic	neutrosophic	ADJ
ejpam-5839	537	15	set	set	NOUN
ejpam-5839	537	16	theory	theory	NOUN
ejpam-5839	537	17	(	(	PUNCT
ejpam-5839	537	18	nst	nst	PROPN
ejpam-5839	537	19	)	)	PUNCT
ejpam-5839	537	20	and	and	CCONJ
ejpam-5839	537	21	intuitionistic	intuitionistic	ADJ
ejpam-5839	537	22	fuzzy	fuzzy	ADJ
ejpam-5839	537	23	set	set	NOUN
ejpam-5839	537	24	theory	theory	NOUN
ejpam-5839	537	25	(	(	PUNCT
ejpam-5839	537	26	ifst	ifst	NOUN
ejpam-5839	537	27	)	)	PUNCT
ejpam-5839	537	28	.	.	PUNCT
ejpam-5839	538	1	introduces	introduce	VERB
ejpam-5839	538	2	a	a	DET
ejpam-5839	538	3	fourth	fourth	ADJ
ejpam-5839	538	4	component	component	NOUN
ejpam-5839	538	5	for	for	ADP
ejpam-5839	538	6	refined	refined	ADJ
ejpam-5839	538	7	set	set	NOUN
ejpam-5839	538	8	representation	representation	NOUN
ejpam-5839	538	9	.	.	PUNCT
ejpam-5839	539	1	2	2	X
ejpam-5839	539	2	.	.	X
ejpam-5839	539	3	theoretical	theoretical	ADJ
ejpam-5839	539	4	basis	basis	NOUN
ejpam-5839	539	5	uses	use	VERB
ejpam-5839	539	6	neutrosophic	neutrosophic	ADJ
ejpam-5839	539	7	numbers	number	NOUN
ejpam-5839	539	8	with	with	ADP
ejpam-5839	539	9	three	three	NUM
ejpam-5839	539	10	membership	membership	NOUN
ejpam-5839	539	11	values	value	NOUN
ejpam-5839	539	12	(	(	PUNCT
ejpam-5839	539	13	truth	truth	NOUN
ejpam-5839	539	14	,	,	PUNCT
ejpam-5839	539	15	indeterminacy	indeterminacy	NOUN
ejpam-5839	539	16	,	,	PUNCT
ejpam-5839	539	17	falsity	falsity	NOUN
ejpam-5839	539	18	)	)	PUNCT
ejpam-5839	539	19	and	and	CCONJ
ejpam-5839	539	20	(	(	PUNCT
ejpam-5839	539	21	α	α	NOUN
ejpam-5839	539	22	,	,	PUNCT
ejpam-5839	539	23	β	β	X
ejpam-5839	539	24	,	,	PUNCT
ejpam-5839	539	25	γ)-level	γ)-level	NOUN
ejpam-5839	539	26	sets	set	NOUN
ejpam-5839	539	27	.	.	PUNCT
ejpam-5839	540	1	extends	extend	VERB
ejpam-5839	540	2	nst	nst	INTJ
ejpam-5839	540	3	by	by	ADP
ejpam-5839	540	4	introducing	introduce	VERB
ejpam-5839	540	5	a	a	DET
ejpam-5839	540	6	fourth	fourth	ADJ
ejpam-5839	540	7	component	component	NOUN
ejpam-5839	540	8	,	,	PUNCT
ejpam-5839	540	9	forming	form	VERB
ejpam-5839	540	10	quadri	quadri	NOUN
ejpam-5839	540	11	-	-	PUNCT
ejpam-5839	540	12	partitioned	partition	VERB
ejpam-5839	540	13	neutrosophic	neutrosophic	ADJ
ejpam-5839	540	14	set	set	NOUN
ejpam-5839	540	15	theory	theory	NOUN
ejpam-5839	540	16	(	(	PUNCT
ejpam-5839	540	17	qpnst	qpnst	ADJ
ejpam-5839	540	18	)	)	PUNCT
ejpam-5839	540	19	,	,	PUNCT
ejpam-5839	540	20	with	with	SCONJ
ejpam-5839	540	21	riemann	riemann	PROPN
ejpam-5839	540	22	integral	integral	PROPN
ejpam-5839	540	23	theory	theory	NOUN
ejpam-5839	540	24	(	(	PUNCT
ejpam-5839	540	25	rit	rit	NOUN
ejpam-5839	540	26	)	)	PUNCT
ejpam-5839	540	27	adapted	adapt	VERB
ejpam-5839	540	28	to	to	ADP
ejpam-5839	540	29	a	a	DET
ejpam-5839	540	30	four	four	NUM
ejpam-5839	540	31	-	-	PUNCT
ejpam-5839	540	32	tuple	tuple	NOUN
ejpam-5839	540	33	(	(	PUNCT
ejpam-5839	540	34	i	i	PROPN
ejpam-5839	540	35	,	,	PUNCT
ejpam-5839	540	36	j	j	PROPN
ejpam-5839	540	37	,	,	PUNCT
ejpam-5839	540	38	k	k	PROPN
ejpam-5839	540	39	,	,	PUNCT
ejpam-5839	540	40	l	l	NOUN
ejpam-5839	540	41	)	)	PUNCT
ejpam-5839	540	42	level	level	NOUN
ejpam-5839	540	43	cut	cut	NOUN
ejpam-5839	540	44	.	.	PUNCT
ejpam-5839	541	1	3	3	X
ejpam-5839	541	2	.	.	X
ejpam-5839	541	3	conceptual	conceptual	ADJ
ejpam-5839	541	4	innovation	innovation	NOUN
ejpam-5839	541	5	introduces	introduce	VERB
ejpam-5839	541	6	neutrosophic	neutrosophic	ADJ
ejpam-5839	541	7	riemann	riemann	PROPN
ejpam-5839	541	8	integration	integration	NOUN
ejpam-5839	541	9	to	to	PART
ejpam-5839	541	10	manage	manage	VERB
ejpam-5839	541	11	uncertainty	uncertainty	NOUN
ejpam-5839	541	12	in	in	ADP
ejpam-5839	541	13	classical	classical	ADJ
ejpam-5839	541	14	riemann	riemann	PROPN
ejpam-5839	541	15	integration	integration	NOUN
ejpam-5839	541	16	.	.	PUNCT
ejpam-5839	542	1	proposes	propose	VERB
ejpam-5839	542	2	quadri	quadri	NOUN
ejpam-5839	542	3	-	-	PUNCT
ejpam-5839	542	4	partitioned	partition	VERB
ejpam-5839	542	5	neutrosophic	neutrosophic	ADJ
ejpam-5839	542	6	riemann	riemann	PROPN
ejpam-5839	542	7	integral	integral	ADJ
ejpam-5839	542	8	theory	theory	NOUN
ejpam-5839	542	9	(	(	PUNCT
ejpam-5839	542	10	qpnrit	qpnrit	NOUN
ejpam-5839	542	11	)	)	PUNCT
ejpam-5839	542	12	,	,	PUNCT
ejpam-5839	542	13	adding	add	VERB
ejpam-5839	542	14	a	a	DET
ejpam-5839	542	15	fourth	fourth	ADJ
ejpam-5839	542	16	uncertainty	uncertainty	NOUN
ejpam-5839	542	17	dimension	dimension	NOUN
ejpam-5839	542	18	for	for	ADP
ejpam-5839	542	19	a	a	DET
ejpam-5839	542	20	more	more	ADV
ejpam-5839	542	21	comprehensive	comprehensive	ADJ
ejpam-5839	542	22	uncertainty	uncertainty	NOUN
ejpam-5839	542	23	model	model	NOUN
ejpam-5839	542	24	.	.	PUNCT
ejpam-5839	543	1	4	4	X
ejpam-5839	543	2	.	.	X
ejpam-5839	543	3	integration	integration	NOUN
ejpam-5839	543	4	framework	framework	NOUN
ejpam-5839	543	5	uses	use	VERB
ejpam-5839	543	6	neutrosophic	neutrosophic	ADJ
ejpam-5839	543	7	numbers	number	NOUN
ejpam-5839	543	8	with	with	ADP
ejpam-5839	543	9	(	(	PUNCT
ejpam-5839	543	10	α	α	X
ejpam-5839	543	11	,	,	PUNCT
ejpam-5839	543	12	β	β	NOUN
ejpam-5839	543	13	,	,	PUNCT
ejpam-5839	543	14	γ)level	γ)level	PROPN
ejpam-5839	543	15	sets	set	VERB
ejpam-5839	543	16	to	to	PART
ejpam-5839	543	17	define	define	VERB
ejpam-5839	543	18	neutrosophic	neutrosophic	ADJ
ejpam-5839	543	19	riemann	riemann	PROPN
ejpam-5839	543	20	integration	integration	NOUN
ejpam-5839	543	21	.	.	PUNCT
ejpam-5839	544	1	incorporates	incorporate	VERB
ejpam-5839	544	2	riemann	riemann	PROPN
ejpam-5839	544	3	integral	integral	ADJ
ejpam-5839	544	4	theory	theory	NOUN
ejpam-5839	544	5	(	(	PUNCT
ejpam-5839	544	6	rit	rit	NOUN
ejpam-5839	544	7	)	)	PUNCT
ejpam-5839	544	8	into	into	ADP
ejpam-5839	544	9	quadri	quadri	NOUN
ejpam-5839	544	10	-	-	PUNCT
ejpam-5839	544	11	partitioned	partition	VERB
ejpam-5839	544	12	neutrosophic	neutrosophic	ADJ
ejpam-5839	544	13	set	set	NOUN
ejpam-5839	544	14	theory	theory	NOUN
ejpam-5839	544	15	(	(	PUNCT
ejpam-5839	544	16	qpnst	qpnst	ADJ
ejpam-5839	544	17	)	)	PUNCT
ejpam-5839	544	18	,	,	PUNCT
ejpam-5839	544	19	allowing	allow	VERB
ejpam-5839	544	20	for	for	ADP
ejpam-5839	544	21	four	four	NUM
ejpam-5839	544	22	uncertainty	uncertainty	NOUN
ejpam-5839	544	23	possibilities	possibility	NOUN
ejpam-5839	544	24	(	(	PUNCT
ejpam-5839	544	25	true	true	ADJ
ejpam-5839	544	26	,	,	PUNCT
ejpam-5839	544	27	false	false	ADJ
ejpam-5839	544	28	,	,	PUNCT
ejpam-5839	544	29	indeterminacy	indeterminacy	NOUN
ejpam-5839	544	30	,	,	PUNCT
ejpam-5839	544	31	and	and	CCONJ
ejpam-5839	544	32	a	a	DET
ejpam-5839	544	33	new	new	ADJ
ejpam-5839	544	34	fourth	fourth	ADJ
ejpam-5839	544	35	possibility	possibility	NOUN
ejpam-5839	544	36	)	)	PUNCT
ejpam-5839	544	37	.	.	PUNCT
ejpam-5839	545	1	5	5	X
ejpam-5839	545	2	.	.	X
ejpam-5839	545	3	numerical	numerical	PROPN
ejpam-5839	545	4	approach	approach	PROPN
ejpam-5839	545	5	uses	use	VERB
ejpam-5839	545	6	numerical	numerical	ADJ
ejpam-5839	545	7	methods	method	NOUN
ejpam-5839	545	8	like	like	ADP
ejpam-5839	545	9	the	the	DET
ejpam-5839	545	10	trapezoidal	trapezoidal	ADJ
ejpam-5839	545	11	rule	rule	NOUN
ejpam-5839	545	12	to	to	PART
ejpam-5839	545	13	compute	compute	VERB
ejpam-5839	545	14	neutrosophic	neutrosophic	ADJ
ejpam-5839	545	15	riemann	riemann	PROPN
ejpam-5839	545	16	integrals	integral	NOUN
ejpam-5839	545	17	,	,	PUNCT
ejpam-5839	545	18	validating	validate	VERB
ejpam-5839	545	19	results	result	NOUN
ejpam-5839	545	20	with	with	ADP
ejpam-5839	545	21	examples	example	NOUN
ejpam-5839	545	22	.	.	PUNCT
ejpam-5839	546	1	applies	apply	VERB
ejpam-5839	546	2	numerical	numerical	ADJ
ejpam-5839	546	3	analysis	analysis	NOUN
ejpam-5839	546	4	to	to	ADP
ejpam-5839	546	5	quadripartitioned	quadripartitione	VERB
ejpam-5839	546	6	neutrosophic	neutrosophic	PROPN
ejpam-5839	546	7	riemann	riemann	PROPN
ejpam-5839	546	8	integrals	integral	NOUN
ejpam-5839	546	9	(	(	PUNCT
ejpam-5839	546	10	qpnrit	qpnrit	NOUN
ejpam-5839	546	11	)	)	PUNCT
ejpam-5839	546	12	,	,	PUNCT
ejpam-5839	546	13	presenting	present	VERB
ejpam-5839	546	14	systematic	systematic	ADJ
ejpam-5839	546	15	numerical	numerical	ADJ
ejpam-5839	546	16	results	result	NOUN
ejpam-5839	546	17	in	in	ADP
ejpam-5839	546	18	tables	table	NOUN
ejpam-5839	546	19	to	to	PART
ejpam-5839	546	20	assess	assess	VERB
ejpam-5839	546	21	the	the	DET
ejpam-5839	546	22	impact	impact	NOUN
ejpam-5839	546	23	of	of	ADP
ejpam-5839	546	24	the	the	DET
ejpam-5839	546	25	fourth	fourth	ADJ
ejpam-5839	546	26	possibility	possibility	NOUN
ejpam-5839	546	27	.	.	PUNCT
ejpam-5839	547	1	6	6	NUM
ejpam-5839	547	2	.	.	NOUN
ejpam-5839	547	3	level	level	NOUN
ejpam-5839	547	4	set	set	NOUN
ejpam-5839	547	5	representation	representation	NOUN
ejpam-5839	547	6	uses	use	NOUN
ejpam-5839	547	7	(	(	PUNCT
ejpam-5839	547	8	α	α	X
ejpam-5839	547	9	,	,	PUNCT
ejpam-5839	547	10	β	β	X
ejpam-5839	547	11	,	,	PUNCT
ejpam-5839	547	12	γ)-level	γ)-level	PROPN
ejpam-5839	547	13	sets	set	VERB
ejpam-5839	547	14	to	to	PART
ejpam-5839	547	15	represent	represent	VERB
ejpam-5839	547	16	truth	truth	NOUN
ejpam-5839	547	17	,	,	PUNCT
ejpam-5839	547	18	indeterminacy	indeterminacy	NOUN
ejpam-5839	547	19	,	,	PUNCT
ejpam-5839	547	20	and	and	CCONJ
ejpam-5839	547	21	falsity	falsity	NOUN
ejpam-5839	547	22	in	in	ADP
ejpam-5839	547	23	neutrosophic	neutrosophic	ADJ
ejpam-5839	547	24	numbers	number	NOUN
ejpam-5839	547	25	.	.	PUNCT
ejpam-5839	548	1	introduces	introduce	VERB
ejpam-5839	548	2	a	a	DET
ejpam-5839	548	3	four	four	NUM
ejpam-5839	548	4	-	-	PUNCT
ejpam-5839	548	5	tuple	tuple	NOUN
ejpam-5839	548	6	level	level	NOUN
ejpam-5839	548	7	cut	cut	NOUN
ejpam-5839	548	8	(	(	PUNCT
ejpam-5839	548	9	i	i	PROPN
ejpam-5839	548	10	,	,	PUNCT
ejpam-5839	548	11	j	j	PROPN
ejpam-5839	548	12	,	,	PUNCT
ejpam-5839	548	13	k	k	PROPN
ejpam-5839	548	14	,	,	PUNCT
ejpam-5839	548	15	l	l	NOUN
ejpam-5839	548	16	)	)	PUNCT
ejpam-5839	548	17	,	,	PUNCT
ejpam-5839	548	18	enhancing	enhance	VERB
ejpam-5839	548	19	the	the	DET
ejpam-5839	548	20	representation	representation	NOUN
ejpam-5839	548	21	of	of	ADP
ejpam-5839	548	22	uncertainty	uncertainty	NOUN
ejpam-5839	548	23	within	within	ADP
ejpam-5839	548	24	qpnst	qpnst	NOUN
ejpam-5839	548	25	and	and	CCONJ
ejpam-5839	548	26	providing	provide	VERB
ejpam-5839	548	27	a	a	DET
ejpam-5839	548	28	more	more	ADV
ejpam-5839	548	29	detailed	detailed	ADJ
ejpam-5839	548	30	integral	integral	ADJ
ejpam-5839	548	31	calculation	calculation	NOUN
ejpam-5839	548	32	framework	framework	NOUN
ejpam-5839	548	33	.	.	PUNCT
ejpam-5839	549	1	7	7	X
ejpam-5839	549	2	.	.	X
ejpam-5839	549	3	output	output	NOUN
ejpam-5839	549	4	representation	representation	NOUN
ejpam-5839	549	5	displays	display	VERB
ejpam-5839	549	6	results	result	NOUN
ejpam-5839	549	7	in	in	ADP
ejpam-5839	549	8	tables	table	NOUN
ejpam-5839	549	9	and	and	CCONJ
ejpam-5839	549	10	figures	figure	NOUN
ejpam-5839	549	11	to	to	PART
ejpam-5839	549	12	validate	validate	VERB
ejpam-5839	549	13	neutrosophic	neutrosophic	ADJ
ejpam-5839	549	14	riemann	riemann	PROPN
ejpam-5839	549	15	integration	integration	NOUN
ejpam-5839	549	16	,	,	PUNCT
ejpam-5839	549	17	using	use	VERB
ejpam-5839	549	18	the	the	DET
ejpam-5839	549	19	trapezoidal	trapezoidal	ADJ
ejpam-5839	549	20	rule	rule	NOUN
ejpam-5839	549	21	for	for	ADP
ejpam-5839	549	22	approximation	approximation	NOUN
ejpam-5839	549	23	.	.	PUNCT
ejpam-5839	550	1	presents	present	VERB
ejpam-5839	550	2	quadri	quadri	NOUN
ejpam-5839	550	3	-	-	PUNCT
ejpam-5839	550	4	partitioned	partition	VERB
ejpam-5839	550	5	neutrosophic	neutrosophic	ADJ
ejpam-5839	550	6	riemann	riemann	PROPN
ejpam-5839	550	7	integral	integral	ADJ
ejpam-5839	550	8	theory	theory	NOUN
ejpam-5839	550	9	(	(	PUNCT
ejpam-5839	550	10	qpnrit	qpnrit	NOUN
ejpam-5839	550	11	)	)	PUNCT
ejpam-5839	550	12	results	result	NOUN
ejpam-5839	550	13	in	in	ADP
ejpam-5839	550	14	tables	table	NOUN
ejpam-5839	550	15	,	,	PUNCT
ejpam-5839	550	16	showcasing	showcase	VERB
ejpam-5839	550	17	numerical	numerical	ADJ
ejpam-5839	550	18	insights	insight	NOUN
ejpam-5839	550	19	and	and	CCONJ
ejpam-5839	550	20	the	the	DET
ejpam-5839	550	21	fourth	fourth	ADJ
ejpam-5839	550	22	possibility	possibility	NOUN
ejpam-5839	550	23	’s	’s	PART
ejpam-5839	550	24	impact	impact	NOUN
ejpam-5839	550	25	on	on	ADP
ejpam-5839	550	26	integration	integration	NOUN
ejpam-5839	550	27	.	.	PUNCT
ejpam-5839	551	1	8	8	X
ejpam-5839	551	2	.	.	X
ejpam-5839	551	3	scope	scope	NOUN
ejpam-5839	551	4	and	and	CCONJ
ejpam-5839	551	5	extensiveness	extensiveness	NOUN
ejpam-5839	551	6	introduces	introduce	NOUN
ejpam-5839	551	7	and	and	CCONJ
ejpam-5839	551	8	numerically	numerically	ADV
ejpam-5839	551	9	validates	validate	VERB
ejpam-5839	551	10	neutrosophic	neutrosophic	ADJ
ejpam-5839	551	11	riemann	riemann	PROPN
ejpam-5839	551	12	integration	integration	NOUN
ejpam-5839	551	13	with	with	ADP
ejpam-5839	551	14	graphical	graphical	ADJ
ejpam-5839	551	15	representations	representation	NOUN
ejpam-5839	551	16	.	.	PUNCT
ejpam-5839	552	1	extends	extend	VERB
ejpam-5839	552	2	nst	nst	PROPN
ejpam-5839	552	3	and	and	CCONJ
ejpam-5839	552	4	riemann	riemann	PROPN
ejpam-5839	552	5	integration	integration	NOUN
ejpam-5839	552	6	into	into	ADP
ejpam-5839	552	7	a	a	DET
ejpam-5839	552	8	more	more	ADV
ejpam-5839	552	9	sophisticated	sophisticated	ADJ
ejpam-5839	552	10	framework	framework	NOUN
ejpam-5839	552	11	(	(	PUNCT
ejpam-5839	552	12	qpnst	qpnst	ADJ
ejpam-5839	552	13	)	)	PUNCT
ejpam-5839	552	14	,	,	PUNCT
ejpam-5839	552	15	exploring	explore	VERB
ejpam-5839	552	16	a	a	DET
ejpam-5839	552	17	deeper	deep	ADJ
ejpam-5839	552	18	theoretical	theoretical	ADJ
ejpam-5839	552	19	foundation	foundation	NOUN
ejpam-5839	552	20	with	with	ADP
ejpam-5839	552	21	advanced	advanced	ADJ
ejpam-5839	552	22	numerical	numerical	ADJ
ejpam-5839	552	23	techniques	technique	NOUN
ejpam-5839	552	24	.	.	PUNCT
ejpam-5839	553	1	a.	a.	PROPN
ejpam-5839	553	2	shihadeh	shihadeh	VERB
ejpam-5839	553	3	et	et	PROPN
ejpam-5839	553	4	al	al	PROPN
ejpam-5839	553	5	.	.	PUNCT
ejpam-5839	553	6	/	/	SYM
ejpam-5839	553	7	eur	eur	PROPN
ejpam-5839	553	8	.	.	PUNCT
ejpam-5839	554	1	j.	j.	PROPN
ejpam-5839	554	2	pure	pure	PROPN
ejpam-5839	554	3	appl	appl	PROPN
ejpam-5839	554	4	.	.	PROPN
ejpam-5839	554	5	math	math	PROPN
ejpam-5839	554	6	,	,	PUNCT
ejpam-5839	554	7	18	18	NUM
ejpam-5839	554	8	(	(	PUNCT
ejpam-5839	554	9	2	2	NUM
ejpam-5839	554	10	)	)	PUNCT
ejpam-5839	554	11	(	(	PUNCT
ejpam-5839	554	12	2025	2025	NUM
ejpam-5839	554	13	)	)	PUNCT
ejpam-5839	554	14	,	,	PUNCT
ejpam-5839	554	15	5839	5839	NUM
ejpam-5839	554	16	24	24	NUM
ejpam-5839	554	17	of	of	ADP
ejpam-5839	554	18	54	54	NUM
ejpam-5839	554	19	aspect	aspect	NOUN
ejpam-5839	554	20	published	publish	VERB
ejpam-5839	554	21	work	work	NOUN
ejpam-5839	554	22	(	(	PUNCT
ejpam-5839	554	23	reference	reference	NOUN
ejpam-5839	554	24	[	[	X
ejpam-5839	554	25	43	43	NUM
ejpam-5839	554	26	]	]	PUNCT
ejpam-5839	554	27	)	)	PUNCT
ejpam-5839	554	28	proposed	propose	VERB
ejpam-5839	554	29	method	method	NOUN
ejpam-5839	554	30	/	/	SYM
ejpam-5839	554	31	work	work	NOUN
ejpam-5839	554	32	9	9	NUM
ejpam-5839	554	33	.	.	PUNCT
ejpam-5839	555	1	application	application	NOUN
ejpam-5839	555	2	focus	focus	VERB
ejpam-5839	555	3	the	the	DET
ejpam-5839	555	4	primary	primary	ADJ
ejpam-5839	555	5	application	application	NOUN
ejpam-5839	555	6	in	in	ADP
ejpam-5839	555	7	the	the	DET
ejpam-5839	555	8	published	publish	VERB
ejpam-5839	555	9	work	work	NOUN
ejpam-5839	555	10	is	be	AUX
ejpam-5839	555	11	the	the	DET
ejpam-5839	555	12	numerical	numerical	ADJ
ejpam-5839	555	13	verification	verification	NOUN
ejpam-5839	555	14	of	of	ADP
ejpam-5839	555	15	neutrosophic	neutrosophic	ADJ
ejpam-5839	555	16	riemann	riemann	PROPN
ejpam-5839	555	17	integration	integration	NOUN
ejpam-5839	555	18	,	,	PUNCT
ejpam-5839	555	19	focusing	focus	VERB
ejpam-5839	555	20	on	on	ADP
ejpam-5839	555	21	how	how	SCONJ
ejpam-5839	555	22	the	the	DET
ejpam-5839	555	23	trapezoidal	trapezoidal	ADJ
ejpam-5839	555	24	rule	rule	NOUN
ejpam-5839	555	25	can	can	AUX
ejpam-5839	555	26	be	be	AUX
ejpam-5839	555	27	used	use	VERB
ejpam-5839	555	28	to	to	PART
ejpam-5839	555	29	approximate	approximate	VERB
ejpam-5839	555	30	the	the	DET
ejpam-5839	555	31	neutrosophic	neutrosophic	ADJ
ejpam-5839	555	32	integral	integral	NOUN
ejpam-5839	555	33	.	.	PUNCT
ejpam-5839	556	1	the	the	DET
ejpam-5839	556	2	proposed	propose	VERB
ejpam-5839	556	3	method	method	NOUN
ejpam-5839	556	4	’s	’s	PART
ejpam-5839	556	5	application	application	NOUN
ejpam-5839	556	6	focuses	focus	VERB
ejpam-5839	556	7	on	on	ADP
ejpam-5839	556	8	improving	improve	VERB
ejpam-5839	556	9	the	the	DET
ejpam-5839	556	10	accuracy	accuracy	NOUN
ejpam-5839	556	11	and	and	CCONJ
ejpam-5839	556	12	handling	handling	NOUN
ejpam-5839	556	13	of	of	ADP
ejpam-5839	556	14	uncertainty	uncertainty	NOUN
ejpam-5839	556	15	in	in	ADP
ejpam-5839	556	16	riemann	riemann	PROPN
ejpam-5839	556	17	integration	integration	NOUN
ejpam-5839	556	18	,	,	PUNCT
ejpam-5839	556	19	with	with	ADP
ejpam-5839	556	20	potential	potential	ADJ
ejpam-5839	556	21	applications	application	NOUN
ejpam-5839	556	22	in	in	ADP
ejpam-5839	556	23	decision	decision	NOUN
ejpam-5839	556	24	-	-	PUNCT
ejpam-5839	556	25	making	making	NOUN
ejpam-5839	556	26	,	,	PUNCT
ejpam-5839	556	27	engineering	engineering	NOUN
ejpam-5839	556	28	,	,	PUNCT
ejpam-5839	556	29	economics	economic	NOUN
ejpam-5839	556	30	,	,	PUNCT
ejpam-5839	556	31	and	and	CCONJ
ejpam-5839	556	32	artificial	artificial	ADJ
ejpam-5839	556	33	intelligence	intelligence	NOUN
ejpam-5839	556	34	.	.	PUNCT
ejpam-5839	557	1	it	it	PRON
ejpam-5839	557	2	also	also	ADV
ejpam-5839	557	3	lays	lay	VERB
ejpam-5839	557	4	the	the	DET
ejpam-5839	557	5	groundwork	groundwork	NOUN
ejpam-5839	557	6	for	for	ADP
ejpam-5839	557	7	more	more	ADV
ejpam-5839	557	8	sophisticated	sophisticated	ADJ
ejpam-5839	557	9	models	model	NOUN
ejpam-5839	557	10	and	and	CCONJ
ejpam-5839	557	11	techniques	technique	NOUN
ejpam-5839	557	12	in	in	ADP
ejpam-5839	557	13	multi	multi	ADJ
ejpam-5839	557	14	dimensional	dimensional	ADJ
ejpam-5839	557	15	and	and	CCONJ
ejpam-5839	557	16	dynamic	dynamic	ADJ
ejpam-5839	557	17	systems	system	NOUN
ejpam-5839	557	18	.	.	PUNCT
ejpam-5839	558	1	10	10	NUM
ejpam-5839	558	2	.	.	X
ejpam-5839	559	1	foundation	foundation	VERB
ejpam-5839	559	2	the	the	DET
ejpam-5839	559	3	published	publish	VERB
ejpam-5839	559	4	work	work	NOUN
ejpam-5839	559	5	introduces	introduce	VERB
ejpam-5839	559	6	neutrosophic	neutrosophic	ADJ
ejpam-5839	559	7	riemann	riemann	PROPN
ejpam-5839	559	8	integration	integration	NOUN
ejpam-5839	559	9	for	for	ADP
ejpam-5839	559	10	the	the	DET
ejpam-5839	559	11	first	first	ADJ
ejpam-5839	559	12	time	time	NOUN
ejpam-5839	559	13	,	,	PUNCT
ejpam-5839	559	14	focusing	focus	VERB
ejpam-5839	559	15	on	on	ADP
ejpam-5839	559	16	neutrosophic	neutrosophic	ADJ
ejpam-5839	559	17	numbers	number	NOUN
ejpam-5839	559	18	and	and	CCONJ
ejpam-5839	559	19	functions	function	NOUN
ejpam-5839	559	20	.	.	PUNCT
ejpam-5839	560	1	it	it	PRON
ejpam-5839	560	2	builds	build	VERB
ejpam-5839	560	3	on	on	ADP
ejpam-5839	560	4	the	the	DET
ejpam-5839	560	5	concept	concept	NOUN
ejpam-5839	560	6	of	of	ADP
ejpam-5839	560	7	fuzziness	fuzziness	NOUN
ejpam-5839	560	8	and	and	CCONJ
ejpam-5839	560	9	uncertainty	uncertainty	NOUN
ejpam-5839	560	10	in	in	ADP
ejpam-5839	560	11	classical	classical	ADJ
ejpam-5839	560	12	integration	integration	NOUN
ejpam-5839	560	13	theory	theory	NOUN
ejpam-5839	560	14	.	.	PUNCT
ejpam-5839	561	1	the	the	DET
ejpam-5839	561	2	proposed	propose	VERB
ejpam-5839	561	3	method	method	NOUN
ejpam-5839	561	4	is	be	AUX
ejpam-5839	561	5	grounded	ground	VERB
ejpam-5839	561	6	in	in	ADP
ejpam-5839	561	7	quadri	quadri	NOUN
ejpam-5839	561	8	-	-	PUNCT
ejpam-5839	561	9	partitioned	partition	VERB
ejpam-5839	561	10	neutrosophic	neutrosophic	ADJ
ejpam-5839	561	11	set	set	NOUN
ejpam-5839	561	12	theory	theory	NOUN
ejpam-5839	561	13	(	(	PUNCT
ejpam-5839	561	14	qpnst	qpnst	ADJ
ejpam-5839	561	15	)	)	PUNCT
ejpam-5839	561	16	,	,	PUNCT
ejpam-5839	561	17	an	an	DET
ejpam-5839	561	18	extension	extension	NOUN
ejpam-5839	561	19	of	of	ADP
ejpam-5839	561	20	neutrosophic	neutrosophic	ADJ
ejpam-5839	561	21	set	set	NOUN
ejpam-5839	561	22	theory	theory	NOUN
ejpam-5839	561	23	(	(	PUNCT
ejpam-5839	561	24	nst	nst	PROPN
ejpam-5839	561	25	)	)	PUNCT
ejpam-5839	561	26	,	,	PUNCT
ejpam-5839	561	27	which	which	PRON
ejpam-5839	561	28	itself	itself	PRON
ejpam-5839	561	29	is	be	AUX
ejpam-5839	561	30	an	an	DET
ejpam-5839	561	31	extension	extension	NOUN
ejpam-5839	561	32	of	of	ADP
ejpam-5839	561	33	intuitionistic	intuitionistic	ADJ
ejpam-5839	561	34	fuzzy	fuzzy	ADJ
ejpam-5839	561	35	set	set	NOUN
ejpam-5839	561	36	theory	theory	NOUN
ejpam-5839	561	37	(	(	PUNCT
ejpam-5839	561	38	ifst	ifst	NOUN
ejpam-5839	561	39	)	)	PUNCT
ejpam-5839	561	40	.	.	PUNCT
ejpam-5839	562	1	it	it	PRON
ejpam-5839	562	2	introduces	introduce	VERB
ejpam-5839	562	3	a	a	DET
ejpam-5839	562	4	fourth	fourth	ADJ
ejpam-5839	562	5	possibility	possibility	NOUN
ejpam-5839	562	6	(	(	PUNCT
ejpam-5839	562	7	along	along	ADP
ejpam-5839	562	8	with	with	ADP
ejpam-5839	562	9	true	true	ADJ
ejpam-5839	562	10	,	,	PUNCT
ejpam-5839	562	11	false	false	ADJ
ejpam-5839	562	12	,	,	PUNCT
ejpam-5839	562	13	and	and	CCONJ
ejpam-5839	562	14	indeterminacy	indeterminacy	NOUN
ejpam-5839	562	15	)	)	PUNCT
ejpam-5839	562	16	for	for	ADP
ejpam-5839	562	17	set	set	VERB
ejpam-5839	562	18	representation	representation	NOUN
ejpam-5839	562	19	,	,	PUNCT
ejpam-5839	562	20	allowing	allow	VERB
ejpam-5839	562	21	for	for	ADP
ejpam-5839	562	22	more	more	ADJ
ejpam-5839	562	23	refined	refined	ADJ
ejpam-5839	562	24	descriptions	description	NOUN
ejpam-5839	562	25	of	of	ADP
ejpam-5839	562	26	sets	set	NOUN
ejpam-5839	562	27	and	and	CCONJ
ejpam-5839	562	28	their	their	PRON
ejpam-5839	562	29	behavior	behavior	NOUN
ejpam-5839	562	30	.	.	PUNCT
ejpam-5839	563	1	11	11	NUM
ejpam-5839	563	2	.	.	X
ejpam-5839	564	1	theoretical	theoretical	ADJ
ejpam-5839	564	2	basis	basis	NOUN
ejpam-5839	564	3	integration	integration	NOUN
ejpam-5839	564	4	framed	frame	VERB
ejpam-5839	564	5	within	within	ADP
ejpam-5839	564	6	neutrosophic	neutrosophic	ADJ
ejpam-5839	564	7	numbers	number	NOUN
ejpam-5839	564	8	with	with	ADP
ejpam-5839	564	9	three	three	NUM
ejpam-5839	564	10	membership	membership	NOUN
ejpam-5839	564	11	values	value	NOUN
ejpam-5839	564	12	(	(	PUNCT
ejpam-5839	564	13	truth	truth	NOUN
ejpam-5839	564	14	,	,	PUNCT
ejpam-5839	564	15	indeterminacy	indeterminacy	NOUN
ejpam-5839	564	16	,	,	PUNCT
ejpam-5839	564	17	and	and	CCONJ
ejpam-5839	564	18	falsity	falsity	NOUN
ejpam-5839	564	19	)	)	PUNCT
ejpam-5839	564	20	,	,	PUNCT
ejpam-5839	564	21	using	use	VERB
ejpam-5839	564	22	(	(	PUNCT
ejpam-5839	564	23	α	α	NOUN
ejpam-5839	564	24	,	,	PUNCT
ejpam-5839	564	25	β	β	X
ejpam-5839	564	26	,	,	PUNCT
ejpam-5839	564	27	γ)-level	γ)-level	PROPN
ejpam-5839	564	28	sets	set	VERB
ejpam-5839	564	29	to	to	PART
ejpam-5839	564	30	represent	represent	VERB
ejpam-5839	564	31	fuzzy	fuzzy	ADJ
ejpam-5839	564	32	membership	membership	NOUN
ejpam-5839	564	33	.	.	PUNCT
ejpam-5839	565	1	extends	extend	VERB
ejpam-5839	565	2	nst	nst	PROPN
ejpam-5839	565	3	with	with	ADP
ejpam-5839	565	4	a	a	DET
ejpam-5839	565	5	fourth	fourth	ADJ
ejpam-5839	565	6	possibility	possibility	NOUN
ejpam-5839	565	7	,	,	PUNCT
ejpam-5839	565	8	defining	define	VERB
ejpam-5839	565	9	quadri	quadri	NOUN
ejpam-5839	565	10	-	-	PUNCT
ejpam-5839	565	11	partitioned	partition	VERB
ejpam-5839	565	12	neutrosophic	neutrosophic	ADJ
ejpam-5839	565	13	set	set	NOUN
ejpam-5839	565	14	theory	theory	NOUN
ejpam-5839	565	15	(	(	PUNCT
ejpam-5839	565	16	qpnst	qpnst	ADJ
ejpam-5839	565	17	)	)	PUNCT
ejpam-5839	565	18	.	.	PUNCT
ejpam-5839	566	1	develops	develop	VERB
ejpam-5839	566	2	riemann	riemann	PROPN
ejpam-5839	566	3	integral	integral	ADJ
ejpam-5839	566	4	theory	theory	NOUN
ejpam-5839	566	5	(	(	PUNCT
ejpam-5839	566	6	rit	rit	NOUN
ejpam-5839	566	7	)	)	PUNCT
ejpam-5839	566	8	within	within	ADP
ejpam-5839	566	9	qpnst	qpnst	NOUN
ejpam-5839	566	10	using	use	VERB
ejpam-5839	566	11	a	a	DET
ejpam-5839	566	12	four	four	NUM
ejpam-5839	566	13	-	-	PUNCT
ejpam-5839	566	14	tuple	tuple	NOUN
ejpam-5839	566	15	(	(	PUNCT
ejpam-5839	566	16	i	i	PROPN
ejpam-5839	566	17	,	,	PUNCT
ejpam-5839	566	18	j	j	PROPN
ejpam-5839	566	19	,	,	PUNCT
ejpam-5839	566	20	k	k	PROPN
ejpam-5839	566	21	,	,	PUNCT
ejpam-5839	566	22	l	l	NOUN
ejpam-5839	566	23	)	)	PUNCT
ejpam-5839	566	24	level	level	NOUN
ejpam-5839	566	25	cut	cut	NOUN
ejpam-5839	566	26	.	.	PUNCT
ejpam-5839	567	1	12	12	NUM
ejpam-5839	567	2	.	.	PUNCT
ejpam-5839	568	1	conceptual	conceptual	ADJ
ejpam-5839	568	2	innovation	innovation	NOUN
ejpam-5839	568	3	introduces	introduce	VERB
ejpam-5839	568	4	neutrosophic	neutrosophic	ADJ
ejpam-5839	568	5	riemann	riemann	PROPN
ejpam-5839	568	6	integration	integration	NOUN
ejpam-5839	568	7	,	,	PUNCT
ejpam-5839	568	8	applying	apply	VERB
ejpam-5839	568	9	neutrosophic	neutrosophic	ADJ
ejpam-5839	568	10	numbers	number	NOUN
ejpam-5839	568	11	to	to	PART
ejpam-5839	568	12	handle	handle	VERB
ejpam-5839	568	13	uncertainty	uncertainty	NOUN
ejpam-5839	568	14	in	in	ADP
ejpam-5839	568	15	classical	classical	ADJ
ejpam-5839	568	16	riemann	riemann	PROPN
ejpam-5839	568	17	integration	integration	NOUN
ejpam-5839	568	18	.	.	PUNCT
ejpam-5839	569	1	proposes	propose	VERB
ejpam-5839	569	2	quadri	quadri	NOUN
ejpam-5839	569	3	-	-	PUNCT
ejpam-5839	569	4	partitioned	partition	VERB
ejpam-5839	569	5	neutrosophic	neutrosophic	ADJ
ejpam-5839	569	6	riemann	riemann	PROPN
ejpam-5839	569	7	integral	integral	ADJ
ejpam-5839	569	8	theory	theory	NOUN
ejpam-5839	569	9	(	(	PUNCT
ejpam-5839	569	10	qpnrit	qpnrit	NOUN
ejpam-5839	569	11	)	)	PUNCT
ejpam-5839	569	12	,	,	PUNCT
ejpam-5839	569	13	extending	extend	VERB
ejpam-5839	569	14	neutrosophic	neutrosophic	ADJ
ejpam-5839	569	15	integration	integration	NOUN
ejpam-5839	569	16	by	by	ADP
ejpam-5839	569	17	incorporating	incorporate	VERB
ejpam-5839	569	18	a	a	DET
ejpam-5839	569	19	fourth	fourth	ADJ
ejpam-5839	569	20	dimension	dimension	NOUN
ejpam-5839	569	21	of	of	ADP
ejpam-5839	569	22	uncertainty	uncertainty	NOUN
ejpam-5839	569	23	for	for	ADP
ejpam-5839	569	24	a	a	DET
ejpam-5839	569	25	more	more	ADV
ejpam-5839	569	26	comprehensive	comprehensive	ADJ
ejpam-5839	569	27	uncertainty	uncertainty	NOUN
ejpam-5839	569	28	model	model	NOUN
ejpam-5839	569	29	.	.	PUNCT
ejpam-5839	570	1	13	13	NUM
ejpam-5839	570	2	.	.	PUNCT
ejpam-5839	571	1	integration	integration	NOUN
ejpam-5839	571	2	framework	framework	NOUN
ejpam-5839	571	3	defines	define	VERB
ejpam-5839	571	4	neutrosophic	neutrosophic	ADJ
ejpam-5839	571	5	riemann	riemann	PROPN
ejpam-5839	571	6	integration	integration	NOUN
ejpam-5839	571	7	using	use	VERB
ejpam-5839	571	8	(	(	PUNCT
ejpam-5839	571	9	α	α	NOUN
ejpam-5839	571	10	,	,	PUNCT
ejpam-5839	571	11	β	β	X
ejpam-5839	571	12	,	,	PUNCT
ejpam-5839	571	13	γ)-level	γ)-level	NOUN
ejpam-5839	571	14	sets	set	NOUN
ejpam-5839	571	15	and	and	CCONJ
ejpam-5839	571	16	fuzzy	fuzzy	ADJ
ejpam-5839	571	17	membership	membership	NOUN
ejpam-5839	571	18	functions	function	NOUN
ejpam-5839	571	19	to	to	PART
ejpam-5839	571	20	represent	represent	VERB
ejpam-5839	571	21	uncertainty	uncertainty	NOUN
ejpam-5839	571	22	.	.	PUNCT
ejpam-5839	572	1	incorporates	incorporate	VERB
ejpam-5839	572	2	extended	extend	VERB
ejpam-5839	572	3	riemann	riemann	PROPN
ejpam-5839	572	4	integral	integral	ADJ
ejpam-5839	572	5	theory	theory	NOUN
ejpam-5839	572	6	(	(	PUNCT
ejpam-5839	572	7	rit	rit	NOUN
ejpam-5839	572	8	)	)	PUNCT
ejpam-5839	572	9	within	within	ADP
ejpam-5839	572	10	qpnst	qpnst	NOUN
ejpam-5839	572	11	,	,	PUNCT
ejpam-5839	572	12	enhancing	enhance	VERB
ejpam-5839	572	13	uncertainty	uncertainty	NOUN
ejpam-5839	572	14	modeling	model	VERB
ejpam-5839	572	15	with	with	ADP
ejpam-5839	572	16	four	four	NUM
ejpam-5839	572	17	possibilities	possibility	NOUN
ejpam-5839	572	18	(	(	PUNCT
ejpam-5839	572	19	true	true	ADJ
ejpam-5839	572	20	,	,	PUNCT
ejpam-5839	572	21	false	false	ADJ
ejpam-5839	572	22	,	,	PUNCT
ejpam-5839	572	23	indeterminacy	indeterminacy	NOUN
ejpam-5839	572	24	,	,	PUNCT
ejpam-5839	572	25	and	and	CCONJ
ejpam-5839	572	26	a	a	DET
ejpam-5839	572	27	new	new	ADJ
ejpam-5839	572	28	fourth	fourth	ADJ
ejpam-5839	572	29	possibility	possibility	NOUN
ejpam-5839	572	30	)	)	PUNCT
ejpam-5839	572	31	.	.	PUNCT
ejpam-5839	573	1	14	14	NUM
ejpam-5839	573	2	.	.	PUNCT
ejpam-5839	573	3	numerical	numerical	PROPN
ejpam-5839	573	4	approach	approach	PROPN
ejpam-5839	573	5	uses	use	VERB
ejpam-5839	573	6	numerical	numerical	ADJ
ejpam-5839	573	7	methods	method	NOUN
ejpam-5839	573	8	like	like	ADP
ejpam-5839	573	9	the	the	DET
ejpam-5839	573	10	trapezoidal	trapezoidal	ADJ
ejpam-5839	573	11	rule	rule	NOUN
ejpam-5839	573	12	to	to	PART
ejpam-5839	573	13	calculate	calculate	VERB
ejpam-5839	573	14	neutrosophic	neutrosophic	ADJ
ejpam-5839	573	15	riemann	riemann	PROPN
ejpam-5839	573	16	integrals	integral	NOUN
ejpam-5839	573	17	,	,	PUNCT
ejpam-5839	573	18	validated	validate	VERB
ejpam-5839	573	19	with	with	ADP
ejpam-5839	573	20	numerical	numerical	ADJ
ejpam-5839	573	21	examples	example	NOUN
ejpam-5839	573	22	,	,	PUNCT
ejpam-5839	573	23	tables	table	NOUN
ejpam-5839	573	24	,	,	PUNCT
ejpam-5839	573	25	and	and	CCONJ
ejpam-5839	573	26	figures	figure	NOUN
ejpam-5839	573	27	.	.	PUNCT
ejpam-5839	574	1	conducts	conduct	NOUN
ejpam-5839	574	2	numerical	numerical	ADJ
ejpam-5839	574	3	exploration	exploration	NOUN
ejpam-5839	574	4	of	of	ADP
ejpam-5839	574	5	quadri	quadri	NOUN
ejpam-5839	574	6	-	-	PUNCT
ejpam-5839	574	7	partitioned	partition	VERB
ejpam-5839	574	8	neutrosophic	neutrosophic	ADJ
ejpam-5839	574	9	riemann	riemann	PROPN
ejpam-5839	574	10	integrals	integral	NOUN
ejpam-5839	574	11	(	(	PUNCT
ejpam-5839	574	12	qpnrit	qpnrit	PROPN
ejpam-5839	574	13	)	)	PUNCT
ejpam-5839	574	14	.	.	PUNCT
ejpam-5839	575	1	systematic	systematic	ADJ
ejpam-5839	575	2	numerical	numerical	ADJ
ejpam-5839	575	3	results	result	NOUN
ejpam-5839	575	4	in	in	ADP
ejpam-5839	575	5	tables	table	NOUN
ejpam-5839	575	6	illustrate	illustrate	VERB
ejpam-5839	575	7	the	the	DET
ejpam-5839	575	8	impact	impact	NOUN
ejpam-5839	575	9	of	of	ADP
ejpam-5839	575	10	the	the	DET
ejpam-5839	575	11	fourth	fourth	ADJ
ejpam-5839	575	12	possibility	possibility	NOUN
ejpam-5839	575	13	on	on	ADP
ejpam-5839	575	14	integral	integral	ADJ
ejpam-5839	575	15	computation	computation	NOUN
ejpam-5839	575	16	.	.	PUNCT
ejpam-5839	576	1	15	15	NUM
ejpam-5839	576	2	.	.	X
ejpam-5839	576	3	level	level	NOUN
ejpam-5839	576	4	set	set	NOUN
ejpam-5839	576	5	representation	representation	NOUN
ejpam-5839	576	6	uses	use	NOUN
ejpam-5839	576	7	(	(	PUNCT
ejpam-5839	576	8	α	α	X
ejpam-5839	576	9	,	,	PUNCT
ejpam-5839	576	10	β	β	X
ejpam-5839	576	11	,	,	PUNCT
ejpam-5839	576	12	γ)-level	γ)-level	NOUN
ejpam-5839	576	13	sets	set	NOUN
ejpam-5839	576	14	,	,	PUNCT
ejpam-5839	576	15	where	where	SCONJ
ejpam-5839	576	16	each	each	DET
ejpam-5839	576	17	parameter	parameter	NOUN
ejpam-5839	576	18	represents	represent	VERB
ejpam-5839	576	19	different	different	ADJ
ejpam-5839	576	20	membership	membership	NOUN
ejpam-5839	576	21	degrees	degree	NOUN
ejpam-5839	576	22	(	(	PUNCT
ejpam-5839	576	23	truth	truth	NOUN
ejpam-5839	576	24	,	,	PUNCT
ejpam-5839	576	25	indeterminacy	indeterminacy	NOUN
ejpam-5839	576	26	,	,	PUNCT
ejpam-5839	576	27	falsity	falsity	NOUN
ejpam-5839	576	28	)	)	PUNCT
ejpam-5839	576	29	in	in	ADP
ejpam-5839	576	30	the	the	DET
ejpam-5839	576	31	neutrosophic	neutrosophic	ADJ
ejpam-5839	576	32	number	number	NOUN
ejpam-5839	576	33	.	.	PUNCT
ejpam-5839	577	1	introduces	introduce	NOUN
ejpam-5839	577	2	a	a	DET
ejpam-5839	577	3	more	more	ADV
ejpam-5839	577	4	refined	refined	ADJ
ejpam-5839	577	5	four	four	NUM
ejpam-5839	577	6	-	-	PUNCT
ejpam-5839	577	7	tuple	tuple	NOUN
ejpam-5839	577	8	level	level	NOUN
ejpam-5839	577	9	cut	cut	NOUN
ejpam-5839	577	10	(	(	PUNCT
ejpam-5839	577	11	i	i	PROPN
ejpam-5839	577	12	,	,	PUNCT
ejpam-5839	577	13	j	j	PROPN
ejpam-5839	577	14	,	,	PUNCT
ejpam-5839	577	15	k	k	PROPN
ejpam-5839	577	16	,	,	PUNCT
ejpam-5839	577	17	l	l	NOUN
ejpam-5839	577	18	)	)	PUNCT
ejpam-5839	577	19	,	,	PUNCT
ejpam-5839	577	20	providing	provide	VERB
ejpam-5839	577	21	a	a	DET
ejpam-5839	577	22	more	more	ADV
ejpam-5839	577	23	granular	granular	ADJ
ejpam-5839	577	24	representation	representation	NOUN
ejpam-5839	577	25	of	of	ADP
ejpam-5839	577	26	multiple	multiple	ADJ
ejpam-5839	577	27	possibilities	possibility	NOUN
ejpam-5839	577	28	within	within	ADP
ejpam-5839	577	29	qpnst	qpnst	NOUN
ejpam-5839	577	30	,	,	PUNCT
ejpam-5839	577	31	enhancing	enhance	VERB
ejpam-5839	577	32	neutrosophic	neutrosophic	ADJ
ejpam-5839	577	33	riemann	riemann	PROPN
ejpam-5839	577	34	integral	integral	ADJ
ejpam-5839	577	35	calculation	calculation	NOUN
ejpam-5839	577	36	.	.	PUNCT
ejpam-5839	578	1	a.	a.	NOUN
ejpam-5839	578	2	shihadeh	shihadeh	VERB
ejpam-5839	578	3	et	et	PROPN
ejpam-5839	578	4	al	al	PROPN
ejpam-5839	578	5	.	.	PUNCT
ejpam-5839	578	6	/	/	SYM
ejpam-5839	578	7	eur	eur	PROPN
ejpam-5839	578	8	.	.	PUNCT
ejpam-5839	579	1	j.	j.	PROPN
ejpam-5839	579	2	pure	pure	PROPN
ejpam-5839	579	3	appl	appl	PROPN
ejpam-5839	579	4	.	.	PROPN
ejpam-5839	579	5	math	math	PROPN
ejpam-5839	579	6	,	,	PUNCT
ejpam-5839	579	7	18	18	NUM
ejpam-5839	579	8	(	(	PUNCT
ejpam-5839	579	9	2	2	NUM
ejpam-5839	579	10	)	)	PUNCT
ejpam-5839	579	11	(	(	PUNCT
ejpam-5839	579	12	2025	2025	NUM
ejpam-5839	579	13	)	)	PUNCT
ejpam-5839	579	14	,	,	PUNCT
ejpam-5839	579	15	5839	5839	NUM
ejpam-5839	579	16	25	25	NUM
ejpam-5839	579	17	of	of	ADP
ejpam-5839	579	18	54	54	NUM
ejpam-5839	579	19	aspect	aspect	NOUN
ejpam-5839	579	20	published	publish	VERB
ejpam-5839	579	21	work	work	NOUN
ejpam-5839	579	22	(	(	PUNCT
ejpam-5839	579	23	reference	reference	NOUN
ejpam-5839	579	24	[	[	X
ejpam-5839	579	25	43	43	NUM
ejpam-5839	579	26	]	]	PUNCT
ejpam-5839	579	27	)	)	PUNCT
ejpam-5839	579	28	proposed	propose	VERB
ejpam-5839	579	29	method	method	NOUN
ejpam-5839	579	30	/	/	SYM
ejpam-5839	579	31	work	work	NOUN
ejpam-5839	579	32	16	16	NUM
ejpam-5839	579	33	.	.	PUNCT
ejpam-5839	580	1	output	output	NOUN
ejpam-5839	580	2	representation	representation	NOUN
ejpam-5839	580	3	presents	present	VERB
ejpam-5839	580	4	numerical	numerical	ADJ
ejpam-5839	580	5	results	result	NOUN
ejpam-5839	580	6	in	in	ADP
ejpam-5839	580	7	tables	table	NOUN
ejpam-5839	580	8	and	and	CCONJ
ejpam-5839	580	9	figures	figure	NOUN
ejpam-5839	580	10	to	to	PART
ejpam-5839	580	11	validate	validate	VERB
ejpam-5839	580	12	neutrosophic	neutrosophic	ADJ
ejpam-5839	580	13	riemann	riemann	PROPN
ejpam-5839	580	14	integration	integration	NOUN
ejpam-5839	580	15	,	,	PUNCT
ejpam-5839	580	16	with	with	ADP
ejpam-5839	580	17	the	the	DET
ejpam-5839	580	18	trapezoidal	trapezoidal	ADJ
ejpam-5839	580	19	rule	rule	NOUN
ejpam-5839	580	20	used	use	VERB
ejpam-5839	580	21	for	for	ADP
ejpam-5839	580	22	approximation	approximation	NOUN
ejpam-5839	580	23	.	.	PUNCT
ejpam-5839	581	1	presents	present	VERB
ejpam-5839	581	2	quadri	quadri	NOUN
ejpam-5839	581	3	-	-	PUNCT
ejpam-5839	581	4	partitioned	partition	VERB
ejpam-5839	581	5	neutrosophic	neutrosophic	ADJ
ejpam-5839	581	6	riemann	riemann	PROPN
ejpam-5839	581	7	integral	integral	ADJ
ejpam-5839	581	8	theory	theory	NOUN
ejpam-5839	581	9	(	(	PUNCT
ejpam-5839	581	10	qpnrit	qpnrit	NOUN
ejpam-5839	581	11	)	)	PUNCT
ejpam-5839	581	12	results	result	NOUN
ejpam-5839	581	13	in	in	ADP
ejpam-5839	581	14	tables	table	NOUN
ejpam-5839	581	15	,	,	PUNCT
ejpam-5839	581	16	offering	offer	VERB
ejpam-5839	581	17	advanced	advanced	ADJ
ejpam-5839	581	18	integral	integral	ADJ
ejpam-5839	581	19	representations	representation	NOUN
ejpam-5839	581	20	to	to	PART
ejpam-5839	581	21	analyze	analyze	VERB
ejpam-5839	581	22	the	the	DET
ejpam-5839	581	23	impact	impact	NOUN
ejpam-5839	581	24	of	of	ADP
ejpam-5839	581	25	the	the	DET
ejpam-5839	581	26	fourth	fourth	ADJ
ejpam-5839	581	27	possibility	possibility	NOUN
ejpam-5839	581	28	on	on	ADP
ejpam-5839	581	29	integration	integration	NOUN
ejpam-5839	581	30	.	.	PUNCT
ejpam-5839	582	1	17	17	NUM
ejpam-5839	582	2	.	.	PUNCT
ejpam-5839	582	3	scope	scope	NOUN
ejpam-5839	582	4	and	and	CCONJ
ejpam-5839	582	5	extensiveness	extensiveness	PROPN
ejpam-5839	582	6	focuses	focus	VERB
ejpam-5839	582	7	on	on	ADP
ejpam-5839	582	8	basic	basic	ADJ
ejpam-5839	582	9	introduction	introduction	NOUN
ejpam-5839	582	10	and	and	CCONJ
ejpam-5839	582	11	numerical	numerical	ADJ
ejpam-5839	582	12	validation	validation	NOUN
ejpam-5839	582	13	of	of	ADP
ejpam-5839	582	14	neutrosophic	neutrosophic	ADJ
ejpam-5839	582	15	riemann	riemann	PROPN
ejpam-5839	582	16	integration	integration	NOUN
ejpam-5839	582	17	,	,	PUNCT
ejpam-5839	582	18	including	include	VERB
ejpam-5839	582	19	examples	example	NOUN
ejpam-5839	582	20	and	and	CCONJ
ejpam-5839	582	21	graphical	graphical	ADJ
ejpam-5839	582	22	representations	representation	NOUN
ejpam-5839	582	23	.	.	PUNCT
ejpam-5839	583	1	extends	extend	VERB
ejpam-5839	583	2	neutrosophic	neutrosophic	ADJ
ejpam-5839	583	3	set	set	PROPN
ejpam-5839	583	4	theory	theory	NOUN
ejpam-5839	583	5	within	within	ADP
ejpam-5839	583	6	riemann	riemann	PROPN
ejpam-5839	583	7	integration	integration	NOUN
ejpam-5839	583	8	to	to	ADP
ejpam-5839	583	9	a	a	DET
ejpam-5839	583	10	more	more	ADV
ejpam-5839	583	11	complex	complex	ADJ
ejpam-5839	583	12	framework	framework	NOUN
ejpam-5839	583	13	(	(	PUNCT
ejpam-5839	583	14	qpnst	qpnst	ADJ
ejpam-5839	583	15	)	)	PUNCT
ejpam-5839	583	16	,	,	PUNCT
ejpam-5839	583	17	deepening	deepen	VERB
ejpam-5839	583	18	theoretical	theoretical	ADJ
ejpam-5839	583	19	foundations	foundation	NOUN
ejpam-5839	583	20	and	and	CCONJ
ejpam-5839	583	21	numerical	numerical	ADJ
ejpam-5839	583	22	techniques	technique	NOUN
ejpam-5839	583	23	for	for	ADP
ejpam-5839	583	24	broader	broad	ADJ
ejpam-5839	583	25	applications	application	NOUN
ejpam-5839	583	26	.	.	PUNCT
ejpam-5839	584	1	18	18	NUM
ejpam-5839	584	2	.	.	PUNCT
ejpam-5839	584	3	application	application	NOUN
ejpam-5839	584	4	focus	focus	NOUN
ejpam-5839	584	5	primarily	primarily	ADV
ejpam-5839	584	6	applies	apply	VERB
ejpam-5839	584	7	to	to	ADP
ejpam-5839	584	8	numerical	numerical	ADJ
ejpam-5839	584	9	verification	verification	NOUN
ejpam-5839	584	10	of	of	ADP
ejpam-5839	584	11	neutrosophic	neutrosophic	ADJ
ejpam-5839	584	12	riemann	riemann	PROPN
ejpam-5839	584	13	integration	integration	NOUN
ejpam-5839	584	14	,	,	PUNCT
ejpam-5839	584	15	emphasizing	emphasize	VERB
ejpam-5839	584	16	the	the	DET
ejpam-5839	584	17	trapezoidal	trapezoidal	ADJ
ejpam-5839	584	18	rule	rule	NOUN
ejpam-5839	584	19	for	for	ADP
ejpam-5839	584	20	approximation	approximation	NOUN
ejpam-5839	584	21	.	.	PUNCT
ejpam-5839	585	1	enhances	enhance	NOUN
ejpam-5839	585	2	accuracy	accuracy	NOUN
ejpam-5839	585	3	and	and	CCONJ
ejpam-5839	585	4	uncertainty	uncertainty	NOUN
ejpam-5839	585	5	handling	handle	VERB
ejpam-5839	585	6	in	in	ADP
ejpam-5839	585	7	riemann	riemann	PROPN
ejpam-5839	585	8	integration	integration	NOUN
ejpam-5839	585	9	with	with	ADP
ejpam-5839	585	10	potential	potential	ADJ
ejpam-5839	585	11	applications	application	NOUN
ejpam-5839	585	12	in	in	ADP
ejpam-5839	585	13	decision	decision	NOUN
ejpam-5839	585	14	-	-	PUNCT
ejpam-5839	585	15	making	making	NOUN
ejpam-5839	585	16	,	,	PUNCT
ejpam-5839	585	17	engineering	engineering	NOUN
ejpam-5839	585	18	,	,	PUNCT
ejpam-5839	585	19	economics	economic	NOUN
ejpam-5839	585	20	,	,	PUNCT
ejpam-5839	585	21	and	and	CCONJ
ejpam-5839	585	22	ai	ai	VERB
ejpam-5839	585	23	,	,	PUNCT
ejpam-5839	585	24	forming	form	VERB
ejpam-5839	585	25	the	the	DET
ejpam-5839	585	26	basis	basis	NOUN
ejpam-5839	585	27	for	for	ADP
ejpam-5839	585	28	sophisticated	sophisticated	ADJ
ejpam-5839	585	29	multidimensional	multidimensional	ADJ
ejpam-5839	585	30	and	and	CCONJ
ejpam-5839	585	31	dynamic	dynamic	ADJ
ejpam-5839	585	32	system	system	NOUN
ejpam-5839	585	33	models	model	NOUN
ejpam-5839	585	34	.	.	PUNCT
ejpam-5839	586	1	table	table	NOUN
ejpam-5839	586	2	3	3	NUM
ejpam-5839	586	3	:	:	PUNCT
ejpam-5839	586	4	comparison	comparison	NOUN
ejpam-5839	586	5	between	between	ADP
ejpam-5839	586	6	published	publish	VERB
ejpam-5839	586	7	work	work	NOUN
ejpam-5839	586	8	and	and	CCONJ
ejpam-5839	586	9	proposed	propose	VERB
ejpam-5839	586	10	method	method	NOUN
ejpam-5839	586	11	7	7	NUM
ejpam-5839	586	12	.	.	PUNCT
ejpam-5839	587	1	operations	operation	NOUN
ejpam-5839	587	2	on	on	ADP
ejpam-5839	587	3	quadri	quadri	NOUN
ejpam-5839	587	4	-	-	PUNCT
ejpam-5839	587	5	partitioned	partition	VERB
ejpam-5839	587	6	neutrosophic	neutrosophic	ADJ
ejpam-5839	587	7	soft	soft	ADJ
ejpam-5839	587	8	sets	set	NOUN
ejpam-5839	587	9	neutrosophic	neutrosophic	ADJ
ejpam-5839	587	10	set	set	NOUN
ejpam-5839	587	11	theory	theory	NOUN
ejpam-5839	587	12	(	(	PUNCT
ejpam-5839	587	13	nst	nst	PROPN
ejpam-5839	587	14	)	)	PUNCT
ejpam-5839	587	15	,	,	PUNCT
ejpam-5839	587	16	a	a	DET
ejpam-5839	587	17	generality	generality	NOUN
ejpam-5839	587	18	of	of	ADP
ejpam-5839	587	19	vague	vague	ADJ
ejpam-5839	587	20	set	set	NOUN
ejpam-5839	587	21	theory	theory	NOUN
ejpam-5839	587	22	(	(	PUNCT
ejpam-5839	587	23	vst	vst	PROPN
ejpam-5839	587	24	)	)	PUNCT
ejpam-5839	587	25	,	,	PUNCT
ejpam-5839	587	26	is	be	AUX
ejpam-5839	587	27	regarded	regard	VERB
ejpam-5839	587	28	as	as	ADP
ejpam-5839	587	29	the	the	DET
ejpam-5839	587	30	most	most	ADV
ejpam-5839	587	31	appealing	appealing	ADJ
ejpam-5839	587	32	theory	theory	NOUN
ejpam-5839	587	33	since	since	SCONJ
ejpam-5839	587	34	it	it	PRON
ejpam-5839	587	35	considers	consider	VERB
ejpam-5839	587	36	the	the	DET
ejpam-5839	587	37	three	three	NUM
ejpam-5839	587	38	possible	possible	ADJ
ejpam-5839	587	39	membership	membership	NOUN
ejpam-5839	587	40	values	value	NOUN
ejpam-5839	587	41	:	:	PUNCT
ejpam-5839	587	42	true	true	ADJ
ejpam-5839	587	43	,	,	PUNCT
ejpam-5839	587	44	false	false	ADJ
ejpam-5839	587	45	,	,	PUNCT
ejpam-5839	587	46	and	and	CCONJ
ejpam-5839	587	47	indeterminacy	indeterminacy	NOUN
ejpam-5839	587	48	.	.	PUNCT
ejpam-5839	588	1	the	the	DET
ejpam-5839	588	2	principles	principle	NOUN
ejpam-5839	588	3	are	be	AUX
ejpam-5839	588	4	all	all	ADV
ejpam-5839	588	5	quite	quite	ADV
ejpam-5839	588	6	obvious	obvious	ADJ
ejpam-5839	588	7	,	,	PUNCT
ejpam-5839	588	8	but	but	CCONJ
ejpam-5839	588	9	the	the	DET
ejpam-5839	588	10	third	third	ADJ
ejpam-5839	588	11	one	one	NOUN
ejpam-5839	588	12	is	be	AUX
ejpam-5839	588	13	particularly	particularly	ADV
ejpam-5839	588	14	fascinating	fascinating	ADJ
ejpam-5839	588	15	since	since	SCONJ
ejpam-5839	588	16	it	it	PRON
ejpam-5839	588	17	addresses	address	VERB
ejpam-5839	588	18	uncertainty	uncertainty	NOUN
ejpam-5839	588	19	,	,	PUNCT
ejpam-5839	588	20	which	which	PRON
ejpam-5839	588	21	arises	arise	VERB
ejpam-5839	588	22	in	in	ADP
ejpam-5839	588	23	all	all	DET
ejpam-5839	588	24	aspects	aspect	NOUN
ejpam-5839	588	25	of	of	ADP
ejpam-5839	588	26	daily	daily	ADJ
ejpam-5839	588	27	life	life	NOUN
ejpam-5839	588	28	.	.	PUNCT
ejpam-5839	589	1	one	one	PRON
ejpam-5839	589	2	can	can	AUX
ejpam-5839	589	3	make	make	VERB
ejpam-5839	589	4	the	the	DET
ejpam-5839	589	5	situation	situation	NOUN
ejpam-5839	589	6	more	more	ADV
ejpam-5839	589	7	certain	certain	ADJ
ejpam-5839	589	8	and	and	CCONJ
ejpam-5839	589	9	free	free	ADJ
ejpam-5839	589	10	of	of	ADP
ejpam-5839	589	11	error	error	NOUN
ejpam-5839	589	12	if	if	SCONJ
ejpam-5839	589	13	the	the	DET
ejpam-5839	589	14	indeterminacy	indeterminacy	NOUN
ejpam-5839	589	15	membership	membership	NOUN
ejpam-5839	589	16	is	be	AUX
ejpam-5839	589	17	refined	refine	VERB
ejpam-5839	589	18	.	.	PUNCT
ejpam-5839	590	1	this	this	PRON
ejpam-5839	590	2	can	can	AUX
ejpam-5839	590	3	be	be	AUX
ejpam-5839	590	4	done	do	VERB
ejpam-5839	590	5	by	by	ADP
ejpam-5839	590	6	splitting	split	VERB
ejpam-5839	590	7	the	the	DET
ejpam-5839	590	8	indeterminacy	indeterminacy	NOUN
ejpam-5839	590	9	into	into	ADP
ejpam-5839	590	10	five	five	NUM
ejpam-5839	590	11	pieces	piece	NOUN
ejpam-5839	590	12	that	that	PRON
ejpam-5839	590	13	is	be	AUX
ejpam-5839	590	14	possible	possible	ADJ
ejpam-5839	590	15	values	value	NOUN
ejpam-5839	590	16	.	.	PUNCT
ejpam-5839	591	1	these	these	PRON
ejpam-5839	591	2	are	be	AUX
ejpam-5839	591	3	relative	relative	ADJ
ejpam-5839	591	4	true	true	ADJ
ejpam-5839	591	5	,	,	PUNCT
ejpam-5839	591	6	relative	relative	ADJ
ejpam-5839	591	7	false	false	ADJ
ejpam-5839	591	8	,	,	PUNCT
ejpam-5839	591	9	contradiction	contradiction	NOUN
ejpam-5839	591	10	,	,	PUNCT
ejpam-5839	591	11	unknown	unknown	ADJ
ejpam-5839	591	12	(	(	PUNCT
ejpam-5839	591	13	undefined	undefined	ADJ
ejpam-5839	591	14	)	)	PUNCT
ejpam-5839	591	15	and	and	CCONJ
ejpam-5839	591	16	ignorance	ignorance	NOUN
ejpam-5839	591	17	.	.	PUNCT
ejpam-5839	592	1	this	this	DET
ejpam-5839	592	2	section	section	NOUN
ejpam-5839	592	3	is	be	AUX
ejpam-5839	592	4	devoted	devote	VERB
ejpam-5839	592	5	to	to	ADP
ejpam-5839	592	6	the	the	DET
ejpam-5839	592	7	most	most	ADV
ejpam-5839	592	8	basic	basic	ADJ
ejpam-5839	592	9	operations	operation	NOUN
ejpam-5839	592	10	of	of	ADP
ejpam-5839	592	11	union	union	NOUN
ejpam-5839	592	12	,	,	PUNCT
ejpam-5839	592	13	intersection	intersection	NOUN
ejpam-5839	592	14	,	,	PUNCT
ejpam-5839	592	15	difference	difference	NOUN
ejpam-5839	592	16	,	,	PUNCT
ejpam-5839	592	17	and	and	CCONJ
ejpam-5839	592	18	absolute	absolute	ADJ
ejpam-5839	592	19	null	null	ADJ
ejpam-5839	592	20	,	,	PUNCT
ejpam-5839	592	21	absolute	absolute	ADJ
ejpam-5839	592	22	hpnnns	hpnnn	NOUN
ejpam-5839	592	23	.	.	PUNCT
ejpam-5839	593	1	theorems	theorem	NOUN
ejpam-5839	593	2	and	and	CCONJ
ejpam-5839	593	3	examples	example	NOUN
ejpam-5839	593	4	are	be	AUX
ejpam-5839	593	5	given	give	VERB
ejpam-5839	593	6	for	for	ADP
ejpam-5839	593	7	better	well	ADJ
ejpam-5839	593	8	understanding	understand	VERB
ejpam-5839	593	9	the	the	DET
ejpam-5839	593	10	situation	situation	NOUN
ejpam-5839	593	11	.	.	PUNCT
ejpam-5839	594	1	definition	definition	NOUN
ejpam-5839	594	2	13	13	NUM
ejpam-5839	594	3	.	.	PUNCT
ejpam-5839	595	1	let	let	VERB
ejpam-5839	595	2	ω	ω	NUM
ejpam-5839	595	3	be	be	AUX
ejpam-5839	595	4	the	the	DET
ejpam-5839	595	5	set	set	NOUN
ejpam-5839	595	6	of	of	ADP
ejpam-5839	595	7	parameters	parameter	NOUN
ejpam-5839	595	8	and	and	CCONJ
ejpam-5839	595	9	x	x	ADJ
ejpam-5839	595	10	be	be	AUX
ejpam-5839	595	11	the	the	DET
ejpam-5839	595	12	key	key	ADJ
ejpam-5839	595	13	set	set	NOUN
ejpam-5839	595	14	.	.	PUNCT
ejpam-5839	596	1	let	let	VERB
ejpam-5839	596	2	p	p	NOUN
ejpam-5839	596	3	(	(	PUNCT
ejpam-5839	596	4	x	x	X
ejpam-5839	596	5	)	)	PUNCT
ejpam-5839	596	6	represent	represent	VERB
ejpam-5839	596	7	the	the	DET
ejpam-5839	596	8	power	power	NOUN
ejpam-5839	596	9	set	set	NOUN
ejpam-5839	596	10	of	of	ADP
ejpam-5839	596	11	x.	x.	NOUN
ejpam-5839	596	12	then	then	ADV
ejpam-5839	596	13	,	,	PUNCT
ejpam-5839	596	14	a	a	DET
ejpam-5839	596	15	quadri	quadri	NOUN
ejpam-5839	596	16	-	-	PUNCT
ejpam-5839	596	17	partitioned	partition	VERB
ejpam-5839	596	18	neutrosophic	neutrosophic	ADJ
ejpam-5839	596	19	set	set	NOUN
ejpam-5839	596	20	structure	structure	NOUN
ejpam-5839	596	21	(	(	PUNCT
ejpam-5839	596	22	qpnss	qpnss	NOUN
ejpam-5839	596	23	)	)	PUNCT
ejpam-5839	596	24	(	(	PUNCT
ejpam-5839	596	25	f̃	f̃	PROPN
ejpam-5839	596	26	,	,	PUNCT
ejpam-5839	596	27	ω	ω	NOUN
ejpam-5839	596	28	)	)	PUNCT
ejpam-5839	596	29	over	over	ADV
ejpam-5839	596	30	x	x	PRON
ejpam-5839	596	31	is	be	AUX
ejpam-5839	596	32	a	a	DET
ejpam-5839	596	33	mapping	mapping	NOUN
ejpam-5839	596	34	f̃	f̃	PROPN
ejpam-5839	596	35	:	:	PUNCT
ejpam-5839	597	1	ω	ω	X
ejpam-5839	597	2	→	→	SYM
ejpam-5839	597	3	p	p	X
ejpam-5839	597	4	(	(	PUNCT
ejpam-5839	597	5	x	x	NOUN
ejpam-5839	597	6	)	)	PUNCT
ejpam-5839	597	7	where	where	SCONJ
ejpam-5839	597	8	f̃	f̃	PROPN
ejpam-5839	597	9	is	be	AUX
ejpam-5839	597	10	the	the	DET
ejpam-5839	597	11	function	function	NOUN
ejpam-5839	597	12	of	of	ADP
ejpam-5839	597	13	qpnss	qpnss	NOUN
ejpam-5839	597	14	(	(	PUNCT
ejpam-5839	597	15	f̃	f̃	PROPN
ejpam-5839	597	16	,	,	PUNCT
ejpam-5839	597	17	ω	ω	PROPN
ejpam-5839	597	18	)	)	PUNCT
ejpam-5839	597	19	.	.	PUNCT
ejpam-5839	598	1	symbolically	symbolically	ADV
ejpam-5839	598	2	,	,	PUNCT
ejpam-5839	598	3	(	(	PUNCT
ejpam-5839	598	4	f̃	f̃	PROPN
ejpam-5839	598	5	,	,	PUNCT
ejpam-5839	598	6	ω	ω	NUM
ejpam-5839	598	7	)	)	PUNCT
ejpam-5839	598	8	=	=	PUNCT
ejpam-5839	599	1	[	[	X
ejpam-5839	599	2	(	(	PUNCT
ejpam-5839	599	3	θ	θ	PROPN
ejpam-5839	599	4	,	,	PUNCT
ejpam-5839	599	5	〈	〈	PROPN
ejpam-5839	599	6	x	x	NOUN
ejpam-5839	599	7	,	,	PUNCT
ejpam-5839	599	8	abtf̃	abtf̃	PUNCT
ejpam-5839	599	9	(	(	PUNCT
ejpam-5839	599	10	θ)(x	θ)(x	NOUN
ejpam-5839	599	11	)	)	PUNCT
ejpam-5839	599	12	,	,	PUNCT
ejpam-5839	599	13	retf̃	retf̃	NOUN
ejpam-5839	599	14	(	(	PUNCT
ejpam-5839	599	15	θ)(x	θ)(x	NOUN
ejpam-5839	599	16	)	)	PUNCT
ejpam-5839	599	17	,	,	PUNCT
ejpam-5839	599	18	reff̃	reff̃	PROPN
ejpam-5839	599	19	(	(	PUNCT
ejpam-5839	599	20	θ)(x	θ)(x	NOUN
ejpam-5839	599	21	)	)	PUNCT
ejpam-5839	599	22	,	,	PUNCT
ejpam-5839	599	23	abff̃	abff̃	ADP
ejpam-5839	599	24	(	(	PUNCT
ejpam-5839	599	25	θ)(x	θ)(x	PROPN
ejpam-5839	599	26	)	)	PUNCT
ejpam-5839	599	27	:	:	PUNCT
ejpam-5839	599	28	x	x	PUNCT
ejpam-5839	599	29	∈	∈	NOUN
ejpam-5839	599	30	x	x	SYM
ejpam-5839	599	31	〉	〉	NOUN
ejpam-5839	599	32	)	)	PUNCT
ejpam-5839	599	33	:	:	PUNCT
ejpam-5839	599	34	θ	θ	PROPN
ejpam-5839	599	35	∈	∈	PROPN
ejpam-5839	599	36	ω	ω	X
ejpam-5839	599	37	]	]	PUNCT
ejpam-5839	599	38	.	.	PUNCT
ejpam-5839	600	1	here	here	ADV
ejpam-5839	600	2	,	,	PUNCT
ejpam-5839	600	3	abtf̃	abtf̃	PUNCT
ejpam-5839	600	4	(	(	PUNCT
ejpam-5839	600	5	θ)(x	θ)(x	NOUN
ejpam-5839	600	6	)	)	PUNCT
ejpam-5839	600	7	,	,	PUNCT
ejpam-5839	600	8	retf̃	retf̃	NOUN
ejpam-5839	600	9	(	(	PUNCT
ejpam-5839	600	10	θ)(x	θ)(x	NOUN
ejpam-5839	600	11	)	)	PUNCT
ejpam-5839	600	12	,	,	PUNCT
ejpam-5839	600	13	reff̃	reff̃	PROPN
ejpam-5839	600	14	(	(	PUNCT
ejpam-5839	600	15	θ)(x	θ)(x	NOUN
ejpam-5839	600	16	)	)	PUNCT
ejpam-5839	600	17	,	,	PUNCT
ejpam-5839	600	18	and	and	CCONJ
ejpam-5839	600	19	abff̃	abff̃	ADV
ejpam-5839	600	20	(	(	PUNCT
ejpam-5839	600	21	θ)(x	θ)(x	NOUN
ejpam-5839	600	22	)	)	PUNCT
ejpam-5839	600	23	belong	belong	VERB
ejpam-5839	600	24	to	to	ADP
ejpam-5839	600	25	the	the	DET
ejpam-5839	600	26	interval	interval	NOUN
ejpam-5839	600	27	[	[	X
ejpam-5839	600	28	0	0	NUM
ejpam-5839	600	29	,	,	PUNCT
ejpam-5839	600	30	1	1	NUM
ejpam-5839	600	31	]	]	PUNCT
ejpam-5839	600	32	.	.	PUNCT
ejpam-5839	601	1	these	these	DET
ejpam-5839	601	2	functions	function	NOUN
ejpam-5839	601	3	are	be	AUX
ejpam-5839	601	4	referred	refer	VERB
ejpam-5839	601	5	to	to	ADP
ejpam-5839	601	6	as	as	ADP
ejpam-5839	601	7	:	:	PUNCT
ejpam-5839	601	8	•	•	NUM
ejpam-5839	601	9	abtf̃	abtf̃	PRON
ejpam-5839	601	10	(	(	PUNCT
ejpam-5839	601	11	θ)(x	θ)(x	NOUN
ejpam-5839	601	12	):	):	PUNCT
ejpam-5839	601	13	absolute	absolute	ADJ
ejpam-5839	601	14	true	true	ADJ
ejpam-5839	601	15	-	-	PUNCT
ejpam-5839	601	16	membership	membership	NOUN
ejpam-5839	601	17	function	function	NOUN
ejpam-5839	601	18	,	,	PUNCT
ejpam-5839	601	19	•	•	ADV
ejpam-5839	601	20	retf̃	retf̃	NOUN
ejpam-5839	601	21	(	(	PUNCT
ejpam-5839	601	22	θ)(x	θ)(x	NOUN
ejpam-5839	601	23	):	):	PUNCT
ejpam-5839	601	24	relative	relative	ADJ
ejpam-5839	601	25	true	true	ADJ
ejpam-5839	601	26	-	-	PUNCT
ejpam-5839	601	27	membership	membership	NOUN
ejpam-5839	601	28	function	function	NOUN
ejpam-5839	601	29	,	,	PUNCT
ejpam-5839	601	30	•	•	X
ejpam-5839	601	31	reff̃	reff̃	NOUN
ejpam-5839	601	32	(	(	PUNCT
ejpam-5839	601	33	θ)(x	θ)(x	NOUN
ejpam-5839	601	34	):	):	PUNCT
ejpam-5839	601	35	relative	relative	ADJ
ejpam-5839	601	36	false	false	ADJ
ejpam-5839	601	37	-	-	PUNCT
ejpam-5839	601	38	membership	membership	NOUN
ejpam-5839	601	39	function	function	NOUN
ejpam-5839	601	40	,	,	PUNCT
ejpam-5839	601	41	•	•	X
ejpam-5839	601	42	abff̃	abff̃	PROPN
ejpam-5839	601	43	(	(	PUNCT
ejpam-5839	601	44	θ)(x	θ)(x	NOUN
ejpam-5839	601	45	):	):	PUNCT
ejpam-5839	601	46	absolute	absolute	ADJ
ejpam-5839	601	47	false	false	ADJ
ejpam-5839	601	48	-	-	PUNCT
ejpam-5839	601	49	membership	membership	NOUN
ejpam-5839	601	50	function	function	NOUN
ejpam-5839	601	51	of	of	ADP
ejpam-5839	601	52	f̃	f̃	PROPN
ejpam-5839	601	53	(	(	PUNCT
ejpam-5839	601	54	θ	θ	NOUN
ejpam-5839	601	55	)	)	PUNCT
ejpam-5839	601	56	.	.	PUNCT
ejpam-5839	602	1	a.	a.	PROPN
ejpam-5839	602	2	shihadeh	shihadeh	VERB
ejpam-5839	602	3	et	et	PROPN
ejpam-5839	602	4	al	al	PROPN
ejpam-5839	602	5	.	.	PUNCT
ejpam-5839	602	6	/	/	SYM
ejpam-5839	602	7	eur	eur	PROPN
ejpam-5839	602	8	.	.	PUNCT
ejpam-5839	603	1	j.	j.	PROPN
ejpam-5839	603	2	pure	pure	PROPN
ejpam-5839	603	3	appl	appl	PROPN
ejpam-5839	603	4	.	.	PROPN
ejpam-5839	603	5	math	math	PROPN
ejpam-5839	603	6	,	,	PUNCT
ejpam-5839	603	7	18	18	NUM
ejpam-5839	603	8	(	(	PUNCT
ejpam-5839	603	9	2	2	NUM
ejpam-5839	603	10	)	)	PUNCT
ejpam-5839	603	11	(	(	PUNCT
ejpam-5839	603	12	2025	2025	NUM
ejpam-5839	603	13	)	)	PUNCT
ejpam-5839	603	14	,	,	PUNCT
ejpam-5839	603	15	5839	5839	NUM
ejpam-5839	603	16	26	26	NUM
ejpam-5839	603	17	of	of	ADP
ejpam-5839	603	18	54	54	NUM
ejpam-5839	603	19	since	since	SCONJ
ejpam-5839	603	20	the	the	DET
ejpam-5839	603	21	supremum	supremum	NOUN
ejpam-5839	603	22	of	of	ADP
ejpam-5839	603	23	each	each	DET
ejpam-5839	603	24	function	function	NOUN
ejpam-5839	603	25	is	be	AUX
ejpam-5839	603	26	1	1	NUM
ejpam-5839	603	27	and	and	CCONJ
ejpam-5839	603	28	the	the	DET
ejpam-5839	603	29	infimum	infimum	NOUN
ejpam-5839	603	30	of	of	ADP
ejpam-5839	603	31	each	each	DET
ejpam-5839	603	32	function	function	NOUN
ejpam-5839	603	33	is	be	AUX
ejpam-5839	603	34	0	0	NUM
ejpam-5839	603	35	,	,	PUNCT
ejpam-5839	603	36	the	the	DET
ejpam-5839	603	37	following	follow	VERB
ejpam-5839	603	38	inequality	inequality	NOUN
ejpam-5839	603	39	holds	hold	VERB
ejpam-5839	603	40	automatically	automatically	ADV
ejpam-5839	603	41	:	:	PUNCT
ejpam-5839	603	42	0	0	NUM
ejpam-5839	603	43	≤	≤	NUM
ejpam-5839	603	44	abtf̃	abtf̃	PUNCT
ejpam-5839	603	45	(	(	PUNCT
ejpam-5839	603	46	θ)(x	θ)(x	NOUN
ejpam-5839	603	47	)	)	PUNCT
ejpam-5839	604	1	+	+	NOUN
ejpam-5839	604	2	retf̃	retf̃	NOUN
ejpam-5839	604	3	(	(	PUNCT
ejpam-5839	604	4	θ)(x	θ)(x	NOUN
ejpam-5839	604	5	)	)	PUNCT
ejpam-5839	605	1	+	+	VERB
ejpam-5839	605	2	reff̃	reff̃	NOUN
ejpam-5839	605	3	(	(	PUNCT
ejpam-5839	605	4	θ)(x	θ)(x	NOUN
ejpam-5839	605	5	)	)	PUNCT
ejpam-5839	605	6	+	+	PROPN
ejpam-5839	605	7	abff̃	abff̃	PROPN
ejpam-5839	605	8	(	(	PUNCT
ejpam-5839	605	9	θ)(x	θ)(x	NOUN
ejpam-5839	605	10	)	)	PUNCT
ejpam-5839	605	11	≤	≤	NUM
ejpam-5839	605	12	4	4	NUM
ejpam-5839	605	13	.	.	PUNCT
ejpam-5839	605	14	definition	definition	NOUN
ejpam-5839	605	15	14	14	NUM
ejpam-5839	605	16	.	.	PUNCT
ejpam-5839	606	1	let	let	VERB
ejpam-5839	606	2	(	(	PUNCT
ejpam-5839	606	3	f̃	f̃	PROPN
ejpam-5839	606	4	,	,	PUNCT
ejpam-5839	606	5	ω	ω	PROPN
ejpam-5839	606	6	)	)	PUNCT
ejpam-5839	606	7	be	be	VERB
ejpam-5839	606	8	a	a	DET
ejpam-5839	606	9	quadri	quadri	NOUN
ejpam-5839	606	10	-	-	PUNCT
ejpam-5839	606	11	partitioned	partition	VERB
ejpam-5839	606	12	neutrosophic	neutrosophic	ADJ
ejpam-5839	606	13	soft	soft	ADJ
ejpam-5839	606	14	set	set	NOUN
ejpam-5839	606	15	(	(	PUNCT
ejpam-5839	606	16	qpnss	qpnss	NOUN
ejpam-5839	606	17	)	)	PUNCT
ejpam-5839	606	18	over	over	ADP
ejpam-5839	606	19	the	the	DET
ejpam-5839	606	20	key	key	ADJ
ejpam-5839	606	21	set	set	NOUN
ejpam-5839	606	22	x.	x.	NOUN
ejpam-5839	607	1	then	then	ADV
ejpam-5839	607	2	,	,	PUNCT
ejpam-5839	607	3	the	the	DET
ejpam-5839	607	4	complement	complement	NOUN
ejpam-5839	607	5	of	of	ADP
ejpam-5839	607	6	(	(	PUNCT
ejpam-5839	607	7	f̃	f̃	PROPN
ejpam-5839	607	8	,	,	PUNCT
ejpam-5839	607	9	ω	ω	PROPN
ejpam-5839	607	10	)	)	PUNCT
ejpam-5839	607	11	is	be	AUX
ejpam-5839	607	12	denoted	denote	VERB
ejpam-5839	607	13	by	by	ADP
ejpam-5839	607	14	(	(	PUNCT
ejpam-5839	607	15	f̃	f̃	PROPN
ejpam-5839	607	16	,	,	PUNCT
ejpam-5839	607	17	ω)c	ω)c	NOUN
ejpam-5839	607	18	and	and	CCONJ
ejpam-5839	607	19	is	be	AUX
ejpam-5839	607	20	defined	define	VERB
ejpam-5839	607	21	as	as	SCONJ
ejpam-5839	607	22	follows	follow	VERB
ejpam-5839	607	23	:	:	PUNCT
ejpam-5839	607	24	(	(	PUNCT
ejpam-5839	607	25	f̃	f̃	PROPN
ejpam-5839	607	26	,	,	PUNCT
ejpam-5839	607	27	ω)c	ω)c	NOUN
ejpam-5839	607	28	=	=	PUNCT
ejpam-5839	608	1	[	[	X
ejpam-5839	608	2	(	(	PUNCT
ejpam-5839	608	3	θ	θ	PROPN
ejpam-5839	608	4	,	,	PUNCT
ejpam-5839	608	5	〈	〈	PROPN
ejpam-5839	608	6	x	x	NOUN
ejpam-5839	608	7	,	,	PUNCT
ejpam-5839	608	8	abff̃	abff̃	ADV
ejpam-5839	608	9	(	(	PUNCT
ejpam-5839	608	10	θ)(x	θ)(x	PROPN
ejpam-5839	608	11	)	)	PUNCT
ejpam-5839	608	12	,	,	PUNCT
ejpam-5839	608	13	reff̃	reff̃	PROPN
ejpam-5839	608	14	(	(	PUNCT
ejpam-5839	608	15	θ)(x	θ)(x	PROPN
ejpam-5839	608	16	)	)	PUNCT
ejpam-5839	608	17	,	,	PUNCT
ejpam-5839	608	18	retf̃	retf̃	NOUN
ejpam-5839	608	19	(	(	PUNCT
ejpam-5839	608	20	θ)(x	θ)(x	NOUN
ejpam-5839	608	21	)	)	PUNCT
ejpam-5839	608	22	,	,	PUNCT
ejpam-5839	608	23	abtf̃	abtf̃	PUNCT
ejpam-5839	608	24	(	(	PUNCT
ejpam-5839	608	25	θ)(x	θ)(x	NOUN
ejpam-5839	608	26	)	)	PUNCT
ejpam-5839	608	27	:	:	PUNCT
ejpam-5839	608	28	x	x	PUNCT
ejpam-5839	608	29	∈	∈	NOUN
ejpam-5839	608	30	x	x	SYM
ejpam-5839	608	31	〉	〉	NOUN
ejpam-5839	608	32	)	)	PUNCT
ejpam-5839	608	33	:	:	PUNCT
ejpam-5839	608	34	θ	θ	PROPN
ejpam-5839	608	35	∈	∈	PROPN
ejpam-5839	608	36	ω	ω	X
ejpam-5839	608	37	]	]	PUNCT
ejpam-5839	608	38	furthermore	furthermore	ADV
ejpam-5839	608	39	,	,	PUNCT
ejpam-5839	608	40	the	the	DET
ejpam-5839	608	41	double	double	ADJ
ejpam-5839	608	42	complement	complement	NOUN
ejpam-5839	608	43	satisfies	satisfie	NOUN
ejpam-5839	608	44	:	:	PUNCT
ejpam-5839	608	45	(	(	PUNCT
ejpam-5839	608	46	(	(	PUNCT
ejpam-5839	608	47	f̃	f̃	PROPN
ejpam-5839	608	48	,	,	PUNCT
ejpam-5839	608	49	ω)c	ω)c	NOUN
ejpam-5839	608	50	)	)	PUNCT
ejpam-5839	608	51	c	c	NOUN
ejpam-5839	608	52	=	=	SYM
ejpam-5839	608	53	(	(	PUNCT
ejpam-5839	608	54	f̃	f̃	PROPN
ejpam-5839	608	55	,	,	PUNCT
ejpam-5839	608	56	ω	ω	PROPN
ejpam-5839	608	57	)	)	PUNCT
ejpam-5839	608	58	.	.	PUNCT
ejpam-5839	609	1	definition	definition	NOUN
ejpam-5839	609	2	15	15	NUM
ejpam-5839	609	3	.	.	PUNCT
ejpam-5839	610	1	let	let	VERB
ejpam-5839	610	2	(	(	PUNCT
ejpam-5839	610	3	f̃	f̃	PROPN
ejpam-5839	610	4	,	,	PUNCT
ejpam-5839	610	5	ω	ω	PROPN
ejpam-5839	610	6	)	)	PUNCT
ejpam-5839	610	7	and	and	CCONJ
ejpam-5839	610	8	(	(	PUNCT
ejpam-5839	610	9	g̃,ω	g̃,ω	PROPN
ejpam-5839	610	10	)	)	PUNCT
ejpam-5839	610	11	be	be	AUX
ejpam-5839	610	12	two	two	NUM
ejpam-5839	610	13	quadri	quadri	NOUN
ejpam-5839	610	14	-	-	PUNCT
ejpam-5839	610	15	partitioned	partition	VERB
ejpam-5839	610	16	neutrosophic	neutrosophic	ADJ
ejpam-5839	610	17	soft	soft	ADJ
ejpam-5839	610	18	sets	set	NOUN
ejpam-5839	610	19	(	(	PUNCT
ejpam-5839	610	20	qpnsss	qpnsss	NOUN
ejpam-5839	610	21	)	)	PUNCT
ejpam-5839	610	22	over	over	ADP
ejpam-5839	610	23	the	the	DET
ejpam-5839	610	24	key	key	ADJ
ejpam-5839	610	25	set	set	NOUN
ejpam-5839	610	26	x.	x.	NOUN
ejpam-5839	610	27	then	then	ADV
ejpam-5839	610	28	,	,	PUNCT
ejpam-5839	610	29	(	(	PUNCT
ejpam-5839	610	30	f̃	f̃	PROPN
ejpam-5839	610	31	,	,	PUNCT
ejpam-5839	610	32	ω	ω	PROPN
ejpam-5839	610	33	)	)	PUNCT
ejpam-5839	610	34	⊆	⊆	NUM
ejpam-5839	610	35	(	(	PUNCT
ejpam-5839	610	36	g̃,ω	g̃,ω	NOUN
ejpam-5839	610	37	)	)	PUNCT
ejpam-5839	610	38	if	if	SCONJ
ejpam-5839	610	39	abtf̃	abtf̃	ADV
ejpam-5839	610	40	(	(	PUNCT
ejpam-5839	610	41	θ)(x	θ)(x	NOUN
ejpam-5839	610	42	)	)	PUNCT
ejpam-5839	610	43	⪯	⪯	PROPN
ejpam-5839	610	44	abtg̃(θ)(x	abtg̃(θ)(x	PROPN
ejpam-5839	610	45	)	)	PUNCT
ejpam-5839	610	46	,	,	PUNCT
ejpam-5839	610	47	retf̃	retf̃	NOUN
ejpam-5839	610	48	(	(	PUNCT
ejpam-5839	610	49	θ)(x	θ)(x	NOUN
ejpam-5839	610	50	)	)	PUNCT
ejpam-5839	610	51	⪯	⪯	PROPN
ejpam-5839	610	52	retg̃(θ)(x	retg̃(θ)(x	PROPN
ejpam-5839	610	53	)	)	PUNCT
ejpam-5839	610	54	,	,	PUNCT
ejpam-5839	610	55	reff̃	reff̃	PROPN
ejpam-5839	610	56	(	(	PUNCT
ejpam-5839	610	57	θ)(x	θ)(x	NOUN
ejpam-5839	610	58	)	)	PUNCT
ejpam-5839	610	59	⪰	⪰	NOUN
ejpam-5839	610	60	refg̃(θ)(x	refg̃(θ)(x	NOUN
ejpam-5839	610	61	)	)	PUNCT
ejpam-5839	610	62	,	,	PUNCT
ejpam-5839	610	63	abff̃	abff̃	ADP
ejpam-5839	610	64	(	(	PUNCT
ejpam-5839	610	65	θ)(x	θ)(x	NOUN
ejpam-5839	610	66	)	)	PUNCT
ejpam-5839	610	67	⪰	⪰	NOUN
ejpam-5839	610	68	abfg̃(θ)(x	abfg̃(θ)(x	PROPN
ejpam-5839	610	69	)	)	PUNCT
ejpam-5839	610	70	,	,	PUNCT
ejpam-5839	610	71	for	for	ADP
ejpam-5839	610	72	all	all	DET
ejpam-5839	610	73	θ	θ	PROPN
ejpam-5839	610	74	∈	∈	PROPN
ejpam-5839	610	75	ω	ω	NOUN
ejpam-5839	610	76	and	and	CCONJ
ejpam-5839	610	77	for	for	ADP
ejpam-5839	610	78	all	all	DET
ejpam-5839	610	79	x	x	SYM
ejpam-5839	610	80	∈	∈	PROPN
ejpam-5839	610	81	x.	x.	NOUN
ejpam-5839	611	1	if	if	SCONJ
ejpam-5839	611	2	(	(	PUNCT
ejpam-5839	611	3	f̃	f̃	PROPN
ejpam-5839	611	4	,	,	PUNCT
ejpam-5839	611	5	ω	ω	NUM
ejpam-5839	611	6	)	)	PUNCT
ejpam-5839	611	7	⊆	⊆	NUM
ejpam-5839	611	8	(	(	PUNCT
ejpam-5839	611	9	g̃,ω	g̃,ω	NOUN
ejpam-5839	611	10	)	)	PUNCT
ejpam-5839	611	11	and	and	CCONJ
ejpam-5839	611	12	(	(	PUNCT
ejpam-5839	611	13	f̃	f̃	PROPN
ejpam-5839	611	14	,	,	PUNCT
ejpam-5839	611	15	ω	ω	NUM
ejpam-5839	611	16	)	)	PUNCT
ejpam-5839	611	17	⊇	⊇	NOUN
ejpam-5839	611	18	(	(	PUNCT
ejpam-5839	611	19	g̃,ω	g̃,ω	PROPN
ejpam-5839	611	20	)	)	PUNCT
ejpam-5839	611	21	,	,	PUNCT
ejpam-5839	611	22	then	then	ADV
ejpam-5839	611	23	(	(	PUNCT
ejpam-5839	611	24	f̃	f̃	PROPN
ejpam-5839	611	25	,	,	PUNCT
ejpam-5839	611	26	ω	ω	NUM
ejpam-5839	611	27	)	)	PUNCT
ejpam-5839	611	28	=	=	PUNCT
ejpam-5839	611	29	(	(	PUNCT
ejpam-5839	611	30	g̃,ω	g̃,ω	PROPN
ejpam-5839	611	31	)	)	PUNCT
ejpam-5839	611	32	.	.	PUNCT
ejpam-5839	612	1	definition	definition	NOUN
ejpam-5839	612	2	16	16	NUM
ejpam-5839	612	3	.	.	PUNCT
ejpam-5839	613	1	let	let	VERB
ejpam-5839	613	2	(	(	PUNCT
ejpam-5839	613	3	f̃	f̃	PROPN
ejpam-5839	613	4	,	,	PUNCT
ejpam-5839	613	5	ω	ω	PROPN
ejpam-5839	613	6	)	)	PUNCT
ejpam-5839	613	7	and	and	CCONJ
ejpam-5839	613	8	(	(	PUNCT
ejpam-5839	613	9	g̃,ω	g̃,ω	PROPN
ejpam-5839	613	10	)	)	PUNCT
ejpam-5839	613	11	be	be	AUX
ejpam-5839	613	12	two	two	NUM
ejpam-5839	613	13	qpnsss	qpnsss	NOUN
ejpam-5839	613	14	over	over	ADP
ejpam-5839	613	15	key	key	ADJ
ejpam-5839	613	16	set	set	NOUN
ejpam-5839	613	17	x	x	PUNCT
ejpam-5839	613	18	such	such	ADJ
ejpam-5839	613	19	that	that	PRON
ejpam-5839	613	20	(	(	PUNCT
ejpam-5839	613	21	f̃	f̃	PROPN
ejpam-5839	613	22	,	,	PUNCT
ejpam-5839	613	23	ω	ω	NUM
ejpam-5839	613	24	)	)	PUNCT
ejpam-5839	613	25	̸=	̸=	PROPN
ejpam-5839	613	26	(	(	PUNCT
ejpam-5839	613	27	g̃,ω	g̃,ω	PROPN
ejpam-5839	613	28	)	)	PUNCT
ejpam-5839	613	29	.	.	PUNCT
ejpam-5839	614	1	then	then	ADV
ejpam-5839	614	2	their	their	PRON
ejpam-5839	614	3	union	union	NOUN
ejpam-5839	614	4	is	be	AUX
ejpam-5839	614	5	denoted	denote	VERB
ejpam-5839	614	6	by	by	ADP
ejpam-5839	614	7	(	(	PUNCT
ejpam-5839	614	8	f̃	f̃	PROPN
ejpam-5839	614	9	,	,	PUNCT
ejpam-5839	614	10	ω)∪̃(g̃,ω	ω)∪̃(g̃,ω	NUM
ejpam-5839	614	11	)	)	PUNCT
ejpam-5839	614	12	=	=	PUNCT
ejpam-5839	614	13	(	(	PUNCT
ejpam-5839	614	14	h̃,ω	h̃,ω	PROPN
ejpam-5839	614	15	)	)	PUNCT
ejpam-5839	614	16	and	and	CCONJ
ejpam-5839	614	17	is	be	AUX
ejpam-5839	614	18	defined	define	VERB
ejpam-5839	614	19	as	as	ADP
ejpam-5839	614	20	:	:	PUNCT
ejpam-5839	614	21	(	(	PUNCT
ejpam-5839	614	22	h̃,ω	h̃,ω	NOUN
ejpam-5839	614	23	)	)	PUNCT
ejpam-5839	614	24	=	=	PUNCT
ejpam-5839	615	1	[	[	X
ejpam-5839	615	2	(	(	PUNCT
ejpam-5839	615	3	θ	θ	PROPN
ejpam-5839	615	4	,	,	PUNCT
ejpam-5839	615	5	⟨x	⟨x	NUM
ejpam-5839	615	6	,	,	PUNCT
ejpam-5839	615	7	abth̃(θ)(x	abth̃(θ)(x	PROPN
ejpam-5839	615	8	)	)	PUNCT
ejpam-5839	615	9	,	,	PUNCT
ejpam-5839	615	10	reth̃(θ)(x	reth̃(θ)(x	PROPN
ejpam-5839	615	11	)	)	PUNCT
ejpam-5839	615	12	,	,	PUNCT
ejpam-5839	615	13	refh̃(θ)(x	refh̃(θ)(x	PROPN
ejpam-5839	615	14	)	)	PUNCT
ejpam-5839	615	15	,	,	PUNCT
ejpam-5839	615	16	abfh̃(θ)(x	abfh̃(θ)(x	PROPN
ejpam-5839	615	17	)	)	PUNCT
ejpam-5839	615	18	:	:	PUNCT
ejpam-5839	615	19	x	x	PUNCT
ejpam-5839	615	20	∈	∈	NOUN
ejpam-5839	615	21	x⟩	x⟩	PUNCT
ejpam-5839	615	22	)	)	PUNCT
ejpam-5839	615	23	:	:	PUNCT
ejpam-5839	616	1	θ	θ	PROPN
ejpam-5839	616	2	∈	∈	PROPN
ejpam-5839	616	3	ω	ω	X
ejpam-5839	616	4	]	]	PUNCT
ejpam-5839	616	5	where	where	SCONJ
ejpam-5839	616	6	,	,	PUNCT
ejpam-5839	616	7	abth̃(θ)(x	abth̃(θ)(x	PROPN
ejpam-5839	616	8	)	)	PUNCT
ejpam-5839	616	9	=	=	SYM
ejpam-5839	617	1	max	max	PROPN
ejpam-5839	617	2	[	[	PUNCT
ejpam-5839	617	3	abtf̃	abtf̃	X
ejpam-5839	617	4	(	(	PUNCT
ejpam-5839	617	5	θ)(x	θ)(x	NOUN
ejpam-5839	617	6	)	)	PUNCT
ejpam-5839	617	7	,	,	PUNCT
ejpam-5839	617	8	abtg̃(θ)(x	abtg̃(θ)(x	PROPN
ejpam-5839	617	9	)	)	PUNCT
ejpam-5839	617	10	]	]	PUNCT
ejpam-5839	617	11	,	,	PUNCT
ejpam-5839	617	12	reth̃(θ)(x	reth̃(θ)(x	PROPN
ejpam-5839	617	13	)	)	PUNCT
ejpam-5839	617	14	=	=	SYM
ejpam-5839	617	15	max	max	PROPN
ejpam-5839	617	16	[	[	PUNCT
ejpam-5839	617	17	retf̃	retf̃	NOUN
ejpam-5839	617	18	(	(	PUNCT
ejpam-5839	617	19	θ)(x	θ)(x	NOUN
ejpam-5839	617	20	)	)	PUNCT
ejpam-5839	617	21	,	,	PUNCT
ejpam-5839	617	22	retg̃(θ)(x	retg̃(θ)(x	PROPN
ejpam-5839	617	23	)	)	PUNCT
ejpam-5839	617	24	]	]	PUNCT
ejpam-5839	617	25	,	,	PUNCT
ejpam-5839	617	26	refh̃(θ)(x	refh̃(θ)(x	NOUN
ejpam-5839	617	27	)	)	PUNCT
ejpam-5839	617	28	=	=	SYM
ejpam-5839	618	1	min	min	NOUN
ejpam-5839	618	2	[	[	PUNCT
ejpam-5839	618	3	reff̃	reff̃	NOUN
ejpam-5839	618	4	(	(	PUNCT
ejpam-5839	618	5	θ)(x	θ)(x	NOUN
ejpam-5839	618	6	)	)	PUNCT
ejpam-5839	618	7	,	,	PUNCT
ejpam-5839	618	8	refg̃(θ)(x	refg̃(θ)(x	NOUN
ejpam-5839	618	9	)	)	PUNCT
ejpam-5839	618	10	]	]	PUNCT
ejpam-5839	618	11	,	,	PUNCT
ejpam-5839	618	12	abfh̃(θ)(x	abfh̃(θ)(x	PROPN
ejpam-5839	618	13	)	)	PUNCT
ejpam-5839	618	14	=	=	SYM
ejpam-5839	618	15	min	min	NOUN
ejpam-5839	618	16	[	[	PUNCT
ejpam-5839	618	17	abff̃	abff̃	ADV
ejpam-5839	618	18	(	(	PUNCT
ejpam-5839	618	19	θ)(x	θ)(x	PROPN
ejpam-5839	618	20	)	)	PUNCT
ejpam-5839	618	21	,	,	PUNCT
ejpam-5839	618	22	abfg̃(θ)(x	abfg̃(θ)(x	PROPN
ejpam-5839	618	23	)	)	PUNCT
ejpam-5839	618	24	]	]	PUNCT
ejpam-5839	618	25	.	.	PUNCT
ejpam-5839	619	1	definition	definition	NOUN
ejpam-5839	619	2	17	17	NUM
ejpam-5839	619	3	.	.	PUNCT
ejpam-5839	620	1	let	let	VERB
ejpam-5839	620	2	(	(	PUNCT
ejpam-5839	620	3	f̃	f̃	PROPN
ejpam-5839	620	4	,	,	PUNCT
ejpam-5839	620	5	ω	ω	PROPN
ejpam-5839	620	6	)	)	PUNCT
ejpam-5839	620	7	,	,	PUNCT
ejpam-5839	620	8	(	(	PUNCT
ejpam-5839	620	9	g̃,ω	g̃,ω	PROPN
ejpam-5839	620	10	)	)	PUNCT
ejpam-5839	620	11	be	be	AUX
ejpam-5839	620	12	two	two	NUM
ejpam-5839	620	13	qpnsss	qpnsss	NOUN
ejpam-5839	620	14	over	over	ADP
ejpam-5839	620	15	key	key	ADJ
ejpam-5839	620	16	set	set	NOUN
ejpam-5839	620	17	x	x	PUNCT
ejpam-5839	620	18	such	such	ADJ
ejpam-5839	620	19	that	that	PRON
ejpam-5839	620	20	(	(	PUNCT
ejpam-5839	620	21	f̃	f̃	PROPN
ejpam-5839	620	22	,	,	PUNCT
ejpam-5839	620	23	ω	ω	NUM
ejpam-5839	620	24	)	)	PUNCT
ejpam-5839	620	25	̸=	̸=	PROPN
ejpam-5839	620	26	(	(	PUNCT
ejpam-5839	620	27	g̃,ω	g̃,ω	PROPN
ejpam-5839	620	28	)	)	PUNCT
ejpam-5839	620	29	,	,	PUNCT
ejpam-5839	620	30	then	then	ADV
ejpam-5839	620	31	their	their	PRON
ejpam-5839	620	32	intersection	intersection	NOUN
ejpam-5839	620	33	is	be	AUX
ejpam-5839	620	34	denoted	denote	VERB
ejpam-5839	620	35	by	by	ADP
ejpam-5839	620	36	(	(	PUNCT
ejpam-5839	620	37	f̃	f̃	PROPN
ejpam-5839	620	38	,	,	PUNCT
ejpam-5839	620	39	ω	ω	NOUN
ejpam-5839	620	40	)	)	PUNCT
ejpam-5839	620	41	∩	∩	NOUN
ejpam-5839	620	42	(	(	PUNCT
ejpam-5839	620	43	g̃,ω	g̃,ω	PROPN
ejpam-5839	620	44	)	)	PUNCT
ejpam-5839	620	45	=	=	PUNCT
ejpam-5839	620	46	(	(	PUNCT
ejpam-5839	620	47	h̃,ω	h̃,ω	PROPN
ejpam-5839	620	48	)	)	PUNCT
ejpam-5839	620	49	and	and	CCONJ
ejpam-5839	620	50	is	be	AUX
ejpam-5839	620	51	defined	define	VERB
ejpam-5839	620	52	as	as	ADP
ejpam-5839	620	53	(	(	PUNCT
ejpam-5839	620	54	h̃,ω	h̃,ω	NOUN
ejpam-5839	620	55	)	)	PUNCT
ejpam-5839	620	56	=	=	PUNCT
ejpam-5839	621	1	[	[	X
ejpam-5839	621	2	(	(	PUNCT
ejpam-5839	621	3	θ	θ	PROPN
ejpam-5839	621	4	,	,	PUNCT
ejpam-5839	621	5	⟨x	⟨x	NUM
ejpam-5839	621	6	,	,	PUNCT
ejpam-5839	621	7	abth̃(θ)(x	abth̃(θ)(x	PROPN
ejpam-5839	621	8	)	)	PUNCT
ejpam-5839	621	9	,	,	PUNCT
ejpam-5839	621	10	reth̃(θ)(x	reth̃(θ)(x	PROPN
ejpam-5839	621	11	)	)	PUNCT
ejpam-5839	621	12	,	,	PUNCT
ejpam-5839	621	13	refh̃(θ)(x	refh̃(θ)(x	PROPN
ejpam-5839	621	14	)	)	PUNCT
ejpam-5839	621	15	,	,	PUNCT
ejpam-5839	621	16	abfh̃(θ)(x	abfh̃(θ)(x	PROPN
ejpam-5839	621	17	)	)	PUNCT
ejpam-5839	621	18	:	:	PUNCT
ejpam-5839	621	19	x	x	PUNCT
ejpam-5839	621	20	∈	∈	NOUN
ejpam-5839	621	21	x⟩	x⟩	PUNCT
ejpam-5839	621	22	)	)	PUNCT
ejpam-5839	621	23	:	:	PUNCT
ejpam-5839	622	1	θ	θ	PROPN
ejpam-5839	622	2	∈	∈	PROPN
ejpam-5839	622	3	ω	ω	X
ejpam-5839	622	4	]	]	PUNCT
ejpam-5839	622	5	where	where	SCONJ
ejpam-5839	622	6	,	,	PUNCT
ejpam-5839	622	7	abth̃(θ)(x	abth̃(θ)(x	PROPN
ejpam-5839	622	8	)	)	PUNCT
ejpam-5839	622	9	=	=	SYM
ejpam-5839	622	10	min	min	NOUN
ejpam-5839	622	11	[	[	PUNCT
ejpam-5839	622	12	abtf̃	abtf̃	X
ejpam-5839	622	13	(	(	PUNCT
ejpam-5839	622	14	θ)(x	θ)(x	NOUN
ejpam-5839	622	15	)	)	PUNCT
ejpam-5839	622	16	,	,	PUNCT
ejpam-5839	622	17	abtg̃(θ)(x	abtg̃(θ)(x	PROPN
ejpam-5839	622	18	)	)	PUNCT
ejpam-5839	622	19	]	]	PUNCT
ejpam-5839	622	20	,	,	PUNCT
ejpam-5839	622	21	reth̃(θ)(x	reth̃(θ)(x	PROPN
ejpam-5839	622	22	)	)	PUNCT
ejpam-5839	622	23	=	=	SYM
ejpam-5839	622	24	min	min	NOUN
ejpam-5839	622	25	[	[	PUNCT
ejpam-5839	622	26	retf̃	retf̃	NOUN
ejpam-5839	622	27	(	(	PUNCT
ejpam-5839	622	28	θ)(x	θ)(x	NOUN
ejpam-5839	622	29	)	)	PUNCT
ejpam-5839	622	30	,	,	PUNCT
ejpam-5839	622	31	retg̃(θ)(x	retg̃(θ)(x	PROPN
ejpam-5839	622	32	)	)	PUNCT
ejpam-5839	622	33	]	]	PUNCT
ejpam-5839	622	34	,	,	PUNCT
ejpam-5839	622	35	refh̃(θ)(x	refh̃(θ)(x	NOUN
ejpam-5839	622	36	)	)	PUNCT
ejpam-5839	622	37	=	=	SYM
ejpam-5839	623	1	max	max	PROPN
ejpam-5839	623	2	[	[	PUNCT
ejpam-5839	623	3	reff̃	reff̃	PROPN
ejpam-5839	623	4	(	(	PUNCT
ejpam-5839	623	5	θ)(x	θ)(x	NOUN
ejpam-5839	623	6	)	)	PUNCT
ejpam-5839	623	7	,	,	PUNCT
ejpam-5839	623	8	refg̃(θ)(x	refg̃(θ)(x	NOUN
ejpam-5839	623	9	)	)	PUNCT
ejpam-5839	623	10	]	]	PUNCT
ejpam-5839	623	11	,	,	PUNCT
ejpam-5839	623	12	abfh̃(θ)(x	abfh̃(θ)(x	PROPN
ejpam-5839	623	13	)	)	PUNCT
ejpam-5839	623	14	=	=	SYM
ejpam-5839	623	15	max	max	PROPN
ejpam-5839	623	16	[	[	PUNCT
ejpam-5839	623	17	abff̃	abff̃	ADV
ejpam-5839	623	18	(	(	PUNCT
ejpam-5839	623	19	θ)(x	θ)(x	PROPN
ejpam-5839	623	20	)	)	PUNCT
ejpam-5839	623	21	,	,	PUNCT
ejpam-5839	623	22	abfg̃(θ)(x	abfg̃(θ)(x	PROPN
ejpam-5839	623	23	)	)	PUNCT
ejpam-5839	623	24	]	]	PUNCT
ejpam-5839	623	25	.	.	PUNCT
ejpam-5839	624	1	a.	a.	PROPN
ejpam-5839	624	2	shihadeh	shihadeh	PROPN
ejpam-5839	624	3	et	et	PROPN
ejpam-5839	624	4	al	al	PROPN
ejpam-5839	624	5	.	.	PUNCT
ejpam-5839	624	6	/	/	SYM
ejpam-5839	624	7	eur	eur	PROPN
ejpam-5839	624	8	.	.	PUNCT
ejpam-5839	625	1	j.	j.	PROPN
ejpam-5839	625	2	pure	pure	PROPN
ejpam-5839	625	3	appl	appl	PROPN
ejpam-5839	625	4	.	.	PROPN
ejpam-5839	625	5	math	math	PROPN
ejpam-5839	625	6	,	,	PUNCT
ejpam-5839	625	7	18	18	NUM
ejpam-5839	625	8	(	(	PUNCT
ejpam-5839	625	9	2	2	NUM
ejpam-5839	625	10	)	)	PUNCT
ejpam-5839	625	11	(	(	PUNCT
ejpam-5839	625	12	2025	2025	NUM
ejpam-5839	625	13	)	)	PUNCT
ejpam-5839	625	14	,	,	PUNCT
ejpam-5839	625	15	5839	5839	NUM
ejpam-5839	625	16	27	27	NUM
ejpam-5839	625	17	of	of	ADP
ejpam-5839	625	18	54	54	NUM
ejpam-5839	625	19	definition	definition	NOUN
ejpam-5839	625	20	18	18	NUM
ejpam-5839	625	21	.	.	PUNCT
ejpam-5839	626	1	let	let	VERB
ejpam-5839	626	2	(	(	PUNCT
ejpam-5839	626	3	f̃	f̃	PROPN
ejpam-5839	626	4	,	,	PUNCT
ejpam-5839	626	5	ω	ω	PROPN
ejpam-5839	626	6	)	)	PUNCT
ejpam-5839	626	7	,	,	PUNCT
ejpam-5839	626	8	(	(	PUNCT
ejpam-5839	626	9	g̃,ω	g̃,ω	PROPN
ejpam-5839	626	10	)	)	PUNCT
ejpam-5839	626	11	be	be	AUX
ejpam-5839	626	12	two	two	NUM
ejpam-5839	626	13	qpnsss	qpnsss	NOUN
ejpam-5839	626	14	over	over	ADP
ejpam-5839	626	15	key	key	ADJ
ejpam-5839	626	16	set	set	NOUN
ejpam-5839	626	17	x	x	PUNCT
ejpam-5839	626	18	such	such	ADJ
ejpam-5839	626	19	that	that	PRON
ejpam-5839	626	20	(	(	PUNCT
ejpam-5839	626	21	f̃	f̃	PROPN
ejpam-5839	626	22	,	,	PUNCT
ejpam-5839	626	23	ω	ω	NUM
ejpam-5839	626	24	)	)	PUNCT
ejpam-5839	626	25	̸=	̸=	PROPN
ejpam-5839	626	26	(	(	PUNCT
ejpam-5839	626	27	g̃,ω	g̃,ω	PROPN
ejpam-5839	626	28	)	)	PUNCT
ejpam-5839	626	29	,	,	PUNCT
ejpam-5839	626	30	then	then	ADV
ejpam-5839	626	31	their	their	PRON
ejpam-5839	626	32	difference	difference	NOUN
ejpam-5839	626	33	is	be	AUX
ejpam-5839	626	34	given	give	VERB
ejpam-5839	626	35	by	by	ADP
ejpam-5839	626	36	(	(	PUNCT
ejpam-5839	626	37	h̃,ω	h̃,ω	NOUN
ejpam-5839	626	38	)	)	PUNCT
ejpam-5839	626	39	=	=	PUNCT
ejpam-5839	626	40	(	(	PUNCT
ejpam-5839	626	41	f̃	f̃	PROPN
ejpam-5839	626	42	,	,	PUNCT
ejpam-5839	626	43	ω	ω	NUM
ejpam-5839	626	44	)	)	PUNCT
ejpam-5839	626	45	\	\	PUNCT
ejpam-5839	626	46	(	(	PUNCT
ejpam-5839	626	47	g̃,ω	g̃,ω	PROPN
ejpam-5839	626	48	)	)	PUNCT
ejpam-5839	626	49	and	and	CCONJ
ejpam-5839	626	50	is	be	AUX
ejpam-5839	626	51	defined	define	VERB
ejpam-5839	626	52	as	as	ADP
ejpam-5839	626	53	(	(	PUNCT
ejpam-5839	626	54	h̃,ω	h̃,ω	NOUN
ejpam-5839	626	55	)	)	PUNCT
ejpam-5839	626	56	=	=	PUNCT
ejpam-5839	626	57	(	(	PUNCT
ejpam-5839	626	58	f̃	f̃	PROPN
ejpam-5839	626	59	,	,	PUNCT
ejpam-5839	626	60	ω	ω	NOUN
ejpam-5839	626	61	)	)	PUNCT
ejpam-5839	626	62	∩	∩	NOUN
ejpam-5839	626	63	(	(	PUNCT
ejpam-5839	626	64	g̃,ω)c	g̃,ω)c	VERB
ejpam-5839	626	65	such	such	ADJ
ejpam-5839	626	66	that	that	SCONJ
ejpam-5839	626	67	(	(	PUNCT
ejpam-5839	626	68	h̃,ω	h̃,ω	NOUN
ejpam-5839	626	69	)	)	PUNCT
ejpam-5839	626	70	=	=	PUNCT
ejpam-5839	627	1	[	[	X
ejpam-5839	627	2	(	(	PUNCT
ejpam-5839	627	3	θ	θ	PROPN
ejpam-5839	627	4	,	,	PUNCT
ejpam-5839	627	5	⟨x	⟨x	NUM
ejpam-5839	627	6	,	,	PUNCT
ejpam-5839	627	7	abth̃(θ)(x	abth̃(θ)(x	PROPN
ejpam-5839	627	8	)	)	PUNCT
ejpam-5839	627	9	,	,	PUNCT
ejpam-5839	627	10	reth̃(θ)(x	reth̃(θ)(x	PROPN
ejpam-5839	627	11	)	)	PUNCT
ejpam-5839	627	12	,	,	PUNCT
ejpam-5839	627	13	refh̃(θ)(x	refh̃(θ)(x	PROPN
ejpam-5839	627	14	)	)	PUNCT
ejpam-5839	627	15	,	,	PUNCT
ejpam-5839	627	16	abfh̃(θ)(x	abfh̃(θ)(x	PROPN
ejpam-5839	627	17	)	)	PUNCT
ejpam-5839	627	18	:	:	PUNCT
ejpam-5839	627	19	x	x	PUNCT
ejpam-5839	627	20	∈	∈	NOUN
ejpam-5839	627	21	x⟩	x⟩	PUNCT
ejpam-5839	627	22	)	)	PUNCT
ejpam-5839	627	23	:	:	PUNCT
ejpam-5839	628	1	θ	θ	PROPN
ejpam-5839	628	2	∈	∈	PROPN
ejpam-5839	628	3	ω	ω	X
ejpam-5839	628	4	]	]	PUNCT
ejpam-5839	628	5	where	where	SCONJ
ejpam-5839	628	6	,	,	PUNCT
ejpam-5839	628	7	abth̃(θ)(x	abth̃(θ)(x	PROPN
ejpam-5839	628	8	)	)	PUNCT
ejpam-5839	628	9	=	=	SYM
ejpam-5839	628	10	min	min	NOUN
ejpam-5839	628	11	[	[	PUNCT
ejpam-5839	628	12	abtf̃	abtf̃	X
ejpam-5839	628	13	(	(	PUNCT
ejpam-5839	628	14	θ)(x	θ)(x	NOUN
ejpam-5839	628	15	)	)	PUNCT
ejpam-5839	628	16	,	,	PUNCT
ejpam-5839	628	17	abtg̃(θ)(x	abtg̃(θ)(x	PROPN
ejpam-5839	628	18	)	)	PUNCT
ejpam-5839	628	19	]	]	PUNCT
ejpam-5839	628	20	,	,	PUNCT
ejpam-5839	628	21	reth̃(θ)(x	reth̃(θ)(x	PROPN
ejpam-5839	628	22	)	)	PUNCT
ejpam-5839	628	23	=	=	SYM
ejpam-5839	628	24	min	min	NOUN
ejpam-5839	628	25	[	[	PUNCT
ejpam-5839	628	26	retf̃	retf̃	NOUN
ejpam-5839	628	27	(	(	PUNCT
ejpam-5839	628	28	θ)(x	θ)(x	NOUN
ejpam-5839	628	29	)	)	PUNCT
ejpam-5839	628	30	,	,	PUNCT
ejpam-5839	628	31	retg̃(θ)(x	retg̃(θ)(x	PROPN
ejpam-5839	628	32	)	)	PUNCT
ejpam-5839	628	33	]	]	PUNCT
ejpam-5839	628	34	,	,	PUNCT
ejpam-5839	628	35	refh̃(θ)(x	refh̃(θ)(x	NOUN
ejpam-5839	628	36	)	)	PUNCT
ejpam-5839	628	37	=	=	SYM
ejpam-5839	629	1	max	max	PROPN
ejpam-5839	629	2	[	[	PUNCT
ejpam-5839	629	3	reff̃	reff̃	PROPN
ejpam-5839	629	4	(	(	PUNCT
ejpam-5839	629	5	θ)(x	θ)(x	NOUN
ejpam-5839	629	6	)	)	PUNCT
ejpam-5839	629	7	,	,	PUNCT
ejpam-5839	629	8	refg̃(θ)(x	refg̃(θ)(x	NOUN
ejpam-5839	629	9	)	)	PUNCT
ejpam-5839	629	10	]	]	PUNCT
ejpam-5839	629	11	,	,	PUNCT
ejpam-5839	629	12	abfh̃(θ)(x	abfh̃(θ)(x	PROPN
ejpam-5839	629	13	)	)	PUNCT
ejpam-5839	629	14	=	=	SYM
ejpam-5839	629	15	max	max	PROPN
ejpam-5839	629	16	[	[	PUNCT
ejpam-5839	629	17	abff̃	abff̃	ADV
ejpam-5839	629	18	(	(	PUNCT
ejpam-5839	629	19	θ)(x	θ)(x	PROPN
ejpam-5839	629	20	)	)	PUNCT
ejpam-5839	629	21	,	,	PUNCT
ejpam-5839	629	22	abfg̃(θ)(x	abfg̃(θ)(x	PROPN
ejpam-5839	629	23	)	)	PUNCT
ejpam-5839	629	24	]	]	PUNCT
ejpam-5839	629	25	.	.	PUNCT
ejpam-5839	630	1	definition	definition	NOUN
ejpam-5839	630	2	19	19	NUM
ejpam-5839	630	3	.	.	PUNCT
ejpam-5839	631	1	let	let	VERB
ejpam-5839	631	2	{	{	PUNCT
ejpam-5839	631	3	(	(	PUNCT
ejpam-5839	631	4	f̃i	f̃i	NOUN
ejpam-5839	631	5	,	,	PUNCT
ejpam-5839	631	6	ω	ω	NOUN
ejpam-5839	631	7	)	)	PUNCT
ejpam-5839	631	8	:	:	PUNCT
ejpam-5839	632	1	i	i	PRON
ejpam-5839	632	2	∈	∈	VERB
ejpam-5839	632	3	i	i	PRON
ejpam-5839	632	4	}	}	PUNCT
ejpam-5839	632	5	be	be	VERB
ejpam-5839	632	6	a	a	DET
ejpam-5839	632	7	family	family	NOUN
ejpam-5839	632	8	of	of	ADP
ejpam-5839	632	9	qpnsss	qpnsss	NOUN
ejpam-5839	632	10	over	over	ADP
ejpam-5839	632	11	the	the	DET
ejpam-5839	632	12	key	key	ADJ
ejpam-5839	632	13	set	set	NOUN
ejpam-5839	632	14	x.	x.	PROPN
ejpam-5839	632	15	then,⋃	then,⋃	PROPN
ejpam-5839	632	16	i∈i	i∈i	ADJ
ejpam-5839	632	17	(	(	PUNCT
ejpam-5839	632	18	f̃i	f̃i	NOUN
ejpam-5839	632	19	,	,	PUNCT
ejpam-5839	632	20	ω	ω	NOUN
ejpam-5839	632	21	)	)	PUNCT
ejpam-5839	632	22	∩	∩	NOUN
ejpam-5839	632	23	⋂	⋂	PROPN
ejpam-5839	632	24	i∈i	i∈i	ADJ
ejpam-5839	632	25	(	(	PUNCT
ejpam-5839	632	26	f̃i	f̃i	NOUN
ejpam-5839	632	27	,	,	PUNCT
ejpam-5839	632	28	ω	ω	NOUN
ejpam-5839	632	29	)	)	PUNCT
ejpam-5839	632	30	is	be	AUX
ejpam-5839	632	31	given	give	VERB
ejpam-5839	632	32	by	by	ADP
ejpam-5839	632	33	[	[	PUNCT
ejpam-5839	632	34	θ	θ	PROPN
ejpam-5839	632	35	,	,	PUNCT
ejpam-5839	632	36	(	(	PUNCT
ejpam-5839	632	37	x	x	X
ejpam-5839	632	38	,	,	PUNCT
ejpam-5839	632	39	sup	sup	NOUN
ejpam-5839	632	40	i∈i	i∈i	ADJ
ejpam-5839	632	41	abtf̃i(θ)(x	abtf̃i(θ)(x	PROPN
ejpam-5839	632	42	)	)	PUNCT
ejpam-5839	632	43	,	,	PUNCT
ejpam-5839	632	44	sup	sup	NOUN
ejpam-5839	632	45	i∈i	i∈i	ADJ
ejpam-5839	632	46	retf̃i(θ)(x	retf̃i(θ)(x	PROPN
ejpam-5839	632	47	)	)	PUNCT
ejpam-5839	632	48	,	,	PUNCT
ejpam-5839	632	49	inf	inf	PROPN
ejpam-5839	632	50	i∈i	i∈i	ADJ
ejpam-5839	632	51	reff̃i(θ)(x	reff̃i(θ)(x	NOUN
ejpam-5839	632	52	)	)	PUNCT
ejpam-5839	632	53	,	,	PUNCT
ejpam-5839	632	54	inf	inf	PROPN
ejpam-5839	632	55	i∈i	i∈i	ADJ
ejpam-5839	632	56	abff̃i(θ)(x	abff̃i(θ)(x	PROPN
ejpam-5839	632	57	)	)	PUNCT
ejpam-5839	632	58	)	)	PUNCT
ejpam-5839	632	59	:	:	PUNCT
ejpam-5839	633	1	θ	θ	PROPN
ejpam-5839	633	2	∈	∈	PROPN
ejpam-5839	633	3	ω	ω	PROPN
ejpam-5839	633	4	,	,	PUNCT
ejpam-5839	633	5	x	x	X
ejpam-5839	633	6	∈	∈	PROPN
ejpam-5839	633	7	x	x	X
ejpam-5839	633	8	]	]	PUNCT
ejpam-5839	633	9	.	.	PUNCT
ejpam-5839	634	1	definition	definition	NOUN
ejpam-5839	634	2	20	20	NUM
ejpam-5839	634	3	.	.	PUNCT
ejpam-5839	635	1	a	a	DET
ejpam-5839	635	2	quadripartitioned	quadripartitione	VERB
ejpam-5839	635	3	neutrosophic	neutrosophic	ADJ
ejpam-5839	635	4	soft	soft	ADJ
ejpam-5839	635	5	set	set	NOUN
ejpam-5839	635	6	(	(	PUNCT
ejpam-5839	635	7	f̃	f̃	PROPN
ejpam-5839	635	8	,	,	PUNCT
ejpam-5839	635	9	ω	ω	NOUN
ejpam-5839	635	10	)	)	PUNCT
ejpam-5839	635	11	over	over	ADP
ejpam-5839	635	12	key	key	ADJ
ejpam-5839	635	13	set	set	NOUN
ejpam-5839	635	14	x	x	PUNCT
ejpam-5839	635	15	is	be	AUX
ejpam-5839	635	16	said	say	VERB
ejpam-5839	635	17	to	to	PART
ejpam-5839	635	18	be	be	AUX
ejpam-5839	635	19	a	a	DET
ejpam-5839	635	20	null	null	ADJ
ejpam-5839	635	21	qpnss	qpnss	NOUN
ejpam-5839	635	22	if	if	SCONJ
ejpam-5839	635	23	abtf̃	abtf̃	ADV
ejpam-5839	635	24	(	(	PUNCT
ejpam-5839	635	25	θ)(x	θ)(x	NOUN
ejpam-5839	635	26	)	)	PUNCT
ejpam-5839	635	27	=	=	SYM
ejpam-5839	636	1	0	0	NUM
ejpam-5839	636	2	,	,	PUNCT
ejpam-5839	636	3	retf̃	retf̃	NOUN
ejpam-5839	636	4	(	(	PUNCT
ejpam-5839	636	5	θ)(x	θ)(x	NOUN
ejpam-5839	636	6	)	)	PUNCT
ejpam-5839	636	7	=	=	SYM
ejpam-5839	637	1	0	0	NUM
ejpam-5839	637	2	,	,	PUNCT
ejpam-5839	637	3	∀θ	∀θ	NOUN
ejpam-5839	637	4	∈	∈	PROPN
ejpam-5839	637	5	ω,∀x	ω,∀x	NOUN
ejpam-5839	637	6	∈	∈	PROPN
ejpam-5839	637	7	x	x	NOUN
ejpam-5839	637	8	,	,	PUNCT
ejpam-5839	637	9	reff̃	reff̃	PROPN
ejpam-5839	637	10	(	(	PUNCT
ejpam-5839	637	11	θ)(x	θ)(x	NOUN
ejpam-5839	637	12	)	)	PUNCT
ejpam-5839	637	13	=	=	SYM
ejpam-5839	638	1	1	1	NUM
ejpam-5839	638	2	,	,	PUNCT
ejpam-5839	638	3	abff̃	abff̃	ADV
ejpam-5839	638	4	(	(	PUNCT
ejpam-5839	638	5	θ)(x	θ)(x	NOUN
ejpam-5839	638	6	)	)	PUNCT
ejpam-5839	638	7	=	=	SYM
ejpam-5839	638	8	1	1	NUM
ejpam-5839	638	9	,	,	PUNCT
ejpam-5839	638	10	∀θ	∀θ	NOUN
ejpam-5839	638	11	∈	∈	X
ejpam-5839	638	12	ω,∀x	ω,∀x	NOUN
ejpam-5839	638	13	∈	∈	PROPN
ejpam-5839	638	14	x.	x.	NOUN
ejpam-5839	638	15	it	it	PRON
ejpam-5839	638	16	is	be	AUX
ejpam-5839	638	17	signified	signify	VERB
ejpam-5839	638	18	as	as	ADP
ejpam-5839	638	19	0(x	0(x	NOUN
ejpam-5839	638	20	,	,	PUNCT
ejpam-5839	638	21	ω	ω	NOUN
ejpam-5839	638	22	)	)	PUNCT
ejpam-5839	638	23	.	.	PUNCT
ejpam-5839	639	1	definition	definition	NOUN
ejpam-5839	639	2	21	21	NUM
ejpam-5839	639	3	.	.	PUNCT
ejpam-5839	640	1	a	a	DET
ejpam-5839	640	2	quadripartitioned	quadripartitione	VERB
ejpam-5839	640	3	neutrosophic	neutrosophic	ADJ
ejpam-5839	640	4	soft	soft	ADJ
ejpam-5839	640	5	set	set	NOUN
ejpam-5839	640	6	(	(	PUNCT
ejpam-5839	640	7	f̃	f̃	PROPN
ejpam-5839	640	8	,	,	PUNCT
ejpam-5839	640	9	ω	ω	NOUN
ejpam-5839	640	10	)	)	PUNCT
ejpam-5839	640	11	over	over	ADP
ejpam-5839	640	12	key	key	ADJ
ejpam-5839	640	13	set	set	NOUN
ejpam-5839	640	14	x	x	PUNCT
ejpam-5839	640	15	is	be	AUX
ejpam-5839	640	16	an	an	DET
ejpam-5839	640	17	absolute	absolute	ADJ
ejpam-5839	640	18	qpnss	qpnss	NOUN
ejpam-5839	640	19	if	if	SCONJ
ejpam-5839	640	20	abtf̃	abtf̃	ADV
ejpam-5839	640	21	(	(	PUNCT
ejpam-5839	640	22	θ)(x	θ)(x	NOUN
ejpam-5839	640	23	)	)	PUNCT
ejpam-5839	640	24	=	=	SYM
ejpam-5839	640	25	1	1	NUM
ejpam-5839	640	26	,	,	PUNCT
ejpam-5839	640	27	retf̃	retf̃	NOUN
ejpam-5839	640	28	(	(	PUNCT
ejpam-5839	640	29	θ)(x	θ)(x	NOUN
ejpam-5839	640	30	)	)	PUNCT
ejpam-5839	640	31	=	=	SYM
ejpam-5839	640	32	1	1	NUM
ejpam-5839	640	33	,	,	PUNCT
ejpam-5839	640	34	∀θ	∀θ	NOUN
ejpam-5839	640	35	∈	∈	X
ejpam-5839	640	36	ω,∀x	ω,∀x	NOUN
ejpam-5839	640	37	∈	∈	PROPN
ejpam-5839	640	38	x	x	NOUN
ejpam-5839	640	39	,	,	PUNCT
ejpam-5839	640	40	reff̃	reff̃	PROPN
ejpam-5839	640	41	(	(	PUNCT
ejpam-5839	640	42	θ)(x	θ)(x	NOUN
ejpam-5839	640	43	)	)	PUNCT
ejpam-5839	640	44	=	=	SYM
ejpam-5839	640	45	0	0	NUM
ejpam-5839	640	46	,	,	PUNCT
ejpam-5839	640	47	abff̃	abff̃	ADV
ejpam-5839	640	48	(	(	PUNCT
ejpam-5839	640	49	θ)(x	θ)(x	NOUN
ejpam-5839	640	50	)	)	PUNCT
ejpam-5839	640	51	=	=	SYM
ejpam-5839	640	52	0	0	NUM
ejpam-5839	640	53	,	,	PUNCT
ejpam-5839	640	54	∀θ	∀θ	NOUN
ejpam-5839	640	55	∈	∈	PROPN
ejpam-5839	640	56	ω,∀x	ω,∀x	NOUN
ejpam-5839	640	57	∈	∈	PROPN
ejpam-5839	640	58	x.	x.	NOUN
ejpam-5839	640	59	clearly	clearly	ADV
ejpam-5839	640	60	,	,	PUNCT
ejpam-5839	640	61	0(x	0(x	NOUN
ejpam-5839	640	62	,	,	PUNCT
ejpam-5839	640	63	ω)c	ω)c	NOUN
ejpam-5839	640	64	=	=	SYM
ejpam-5839	640	65	1(x	1(x	NUM
ejpam-5839	640	66	,	,	PUNCT
ejpam-5839	640	67	ω	ω	NOUN
ejpam-5839	640	68	)	)	PUNCT
ejpam-5839	640	69	,	,	PUNCT
ejpam-5839	640	70	1(x	1(x	NUM
ejpam-5839	640	71	,	,	PUNCT
ejpam-5839	640	72	ω)c	ω)c	NOUN
ejpam-5839	640	73	=	=	SYM
ejpam-5839	640	74	0(x	0(x	NOUN
ejpam-5839	640	75	,	,	PUNCT
ejpam-5839	640	76	ω	ω	NOUN
ejpam-5839	640	77	)	)	PUNCT
ejpam-5839	640	78	.	.	PUNCT
ejpam-5839	641	1	definition	definition	NOUN
ejpam-5839	641	2	22	22	NUM
ejpam-5839	641	3	.	.	PUNCT
ejpam-5839	642	1	the	the	DET
ejpam-5839	642	2	family	family	NOUN
ejpam-5839	642	3	of	of	ADP
ejpam-5839	642	4	all	all	DET
ejpam-5839	642	5	quadripartitioned	quadripartitione	VERB
ejpam-5839	642	6	neutrosophic	neutrosophic	ADJ
ejpam-5839	642	7	soft	soft	ADJ
ejpam-5839	642	8	sets	set	NOUN
ejpam-5839	642	9	over	over	ADP
ejpam-5839	642	10	x	x	PUNCT
ejpam-5839	642	11	is	be	AUX
ejpam-5839	642	12	designated	designate	VERB
ejpam-5839	642	13	as	as	ADP
ejpam-5839	642	14	qpnss(x	qpnss(x	PROPN
ejpam-5839	642	15	)	)	PUNCT
ejpam-5839	642	16	.	.	PUNCT
ejpam-5839	643	1	then	then	ADV
ejpam-5839	643	2	,	,	PUNCT
ejpam-5839	643	3	xθ⟨r1	xθ⟨r1	PROPN
ejpam-5839	643	4	,	,	PUNCT
ejpam-5839	643	5	r2	r2	PROPN
ejpam-5839	643	6	,	,	PUNCT
ejpam-5839	643	7	r3	r3	PROPN
ejpam-5839	643	8	,	,	PUNCT
ejpam-5839	643	9	r4⟩	r4⟩	ADV
ejpam-5839	643	10	is	be	AUX
ejpam-5839	643	11	called	call	VERB
ejpam-5839	643	12	a	a	DET
ejpam-5839	643	13	qpns	qpns	NOUN
ejpam-5839	643	14	point	point	NOUN
ejpam-5839	643	15	for	for	ADP
ejpam-5839	643	16	every	every	DET
ejpam-5839	643	17	point	point	NOUN
ejpam-5839	643	18	x	x	X
ejpam-5839	643	19	∈	∈	NOUN
ejpam-5839	643	20	x	x	NOUN
ejpam-5839	643	21	,	,	PUNCT
ejpam-5839	643	22	θ	θ	PROPN
ejpam-5839	643	23	∈	∈	PROPN
ejpam-5839	643	24	ω	ω	PROPN
ejpam-5839	643	25	,	,	PUNCT
ejpam-5839	643	26	and	and	CCONJ
ejpam-5839	643	27	is	be	AUX
ejpam-5839	643	28	defined	define	VERB
ejpam-5839	643	29	as	as	SCONJ
ejpam-5839	643	30	follows	follow	VERB
ejpam-5839	643	31	:	:	PUNCT
ejpam-5839	643	32	xθ⟨r1	xθ⟨r1	PROPN
ejpam-5839	643	33	,	,	PUNCT
ejpam-5839	643	34	r2	r2	PROPN
ejpam-5839	643	35	,	,	PUNCT
ejpam-5839	643	36	r3	r3	PROPN
ejpam-5839	643	37	,	,	PUNCT
ejpam-5839	643	38	r4⟩θ′/(y	r4⟩θ′/(y	PROPN
ejpam-5839	643	39	)	)	PUNCT
ejpam-5839	644	1	=	=	PRON
ejpam-5839	644	2	{	{	PUNCT
ejpam-5839	644	3	⟨r1	⟨r1	PROPN
ejpam-5839	644	4	,	,	PUNCT
ejpam-5839	644	5	r2	r2	PROPN
ejpam-5839	644	6	,	,	PUNCT
ejpam-5839	644	7	r3	r3	PROPN
ejpam-5839	644	8	,	,	PUNCT
ejpam-5839	644	9	r4⟩	r4⟩	ADV
ejpam-5839	644	10	,	,	PUNCT
ejpam-5839	644	11	if	if	SCONJ
ejpam-5839	644	12	θ′	θ′	NOUN
ejpam-5839	644	13	=	=	SYM
ejpam-5839	644	14	θ	θ	PROPN
ejpam-5839	644	15	and	and	CCONJ
ejpam-5839	644	16	y	y	PROPN
ejpam-5839	644	17	=	=	SYM
ejpam-5839	644	18	x	x	PROPN
ejpam-5839	644	19	,	,	PUNCT
ejpam-5839	644	20	(	(	PUNCT
ejpam-5839	644	21	0	0	NUM
ejpam-5839	644	22	,	,	PUNCT
ejpam-5839	644	23	0	0	NUM
ejpam-5839	644	24	,	,	PUNCT
ejpam-5839	644	25	0	0	NUM
ejpam-5839	644	26	,	,	PUNCT
ejpam-5839	644	27	1	1	NUM
ejpam-5839	644	28	)	)	PUNCT
ejpam-5839	644	29	,	,	PUNCT
ejpam-5839	644	30	if	if	SCONJ
ejpam-5839	644	31	θ′	θ′	NOUN
ejpam-5839	644	32	̸=	̸=	PROPN
ejpam-5839	644	33	θ	θ	PROPN
ejpam-5839	644	34	or	or	CCONJ
ejpam-5839	644	35	y	y	PROPN
ejpam-5839	644	36	̸=	̸=	PROPN
ejpam-5839	644	37	x.	x.	NOUN
ejpam-5839	644	38	definition	definition	NOUN
ejpam-5839	644	39	23	23	NUM
ejpam-5839	644	40	.	.	PUNCT
ejpam-5839	645	1	let	let	VERB
ejpam-5839	645	2	(	(	PUNCT
ejpam-5839	645	3	f̃	f̃	PROPN
ejpam-5839	645	4	,	,	PUNCT
ejpam-5839	645	5	ω	ω	PROPN
ejpam-5839	645	6	)	)	PUNCT
ejpam-5839	645	7	be	be	VERB
ejpam-5839	645	8	a	a	DET
ejpam-5839	645	9	quadripartitioned	quadripartitione	VERB
ejpam-5839	645	10	neutrosophic	neutrosophic	ADJ
ejpam-5839	645	11	soft	soft	ADJ
ejpam-5839	645	12	set	set	NOUN
ejpam-5839	645	13	over	over	ADP
ejpam-5839	645	14	key	key	ADJ
ejpam-5839	645	15	set	set	NOUN
ejpam-5839	645	16	x.	x.	NOUN
ejpam-5839	645	17	then	then	ADV
ejpam-5839	645	18	,	,	PUNCT
ejpam-5839	645	19	xθ⟨r1	xθ⟨r1	PROPN
ejpam-5839	645	20	,	,	PUNCT
ejpam-5839	645	21	r2	r2	PROPN
ejpam-5839	645	22	,	,	PUNCT
ejpam-5839	645	23	r3	r3	PROPN
ejpam-5839	645	24	,	,	PUNCT
ejpam-5839	645	25	r4⟩	r4⟩	NOUN
ejpam-5839	645	26	∈	∈	PROPN
ejpam-5839	645	27	qpnss(f̃	qpnss(f̃	PROPN
ejpam-5839	645	28	,	,	PUNCT
ejpam-5839	645	29	ω	ω	NOUN
ejpam-5839	645	30	)	)	PUNCT
ejpam-5839	646	1	if	if	SCONJ
ejpam-5839	646	2	r1	r1	PROPN
ejpam-5839	646	3	⪯	⪯	X
ejpam-5839	646	4	abtf̃	abtf̃	PUNCT
ejpam-5839	646	5	(	(	PUNCT
ejpam-5839	646	6	θ)(x	θ)(x	NOUN
ejpam-5839	646	7	)	)	PUNCT
ejpam-5839	646	8	,	,	PUNCT
ejpam-5839	646	9	r2	r2	PROPN
ejpam-5839	646	10	⪯	⪯	VERB
ejpam-5839	646	11	retf̃	retf̃	NOUN
ejpam-5839	646	12	(	(	PUNCT
ejpam-5839	646	13	θ)(x	θ)(x	NOUN
ejpam-5839	646	14	)	)	PUNCT
ejpam-5839	646	15	,	,	PUNCT
ejpam-5839	646	16	r3	r3	PROPN
ejpam-5839	646	17	⪰	⪰	NOUN
ejpam-5839	646	18	reff̃	reff̃	PROPN
ejpam-5839	646	19	(	(	PUNCT
ejpam-5839	646	20	θ)(x	θ)(x	NOUN
ejpam-5839	646	21	)	)	PUNCT
ejpam-5839	646	22	,	,	PUNCT
ejpam-5839	646	23	r4	r4	VERB
ejpam-5839	646	24	⪰	⪰	NOUN
ejpam-5839	646	25	abff̃	abff̃	ADV
ejpam-5839	646	26	(	(	PUNCT
ejpam-5839	646	27	θ)(x	θ)(x	PROPN
ejpam-5839	646	28	)	)	PUNCT
ejpam-5839	646	29	.	.	PUNCT
ejpam-5839	647	1	a.	a.	NOUN
ejpam-5839	647	2	shihadeh	shihadeh	VERB
ejpam-5839	647	3	et	et	PROPN
ejpam-5839	647	4	al	al	PROPN
ejpam-5839	647	5	.	.	PUNCT
ejpam-5839	647	6	/	/	SYM
ejpam-5839	647	7	eur	eur	PROPN
ejpam-5839	647	8	.	.	PUNCT
ejpam-5839	648	1	j.	j.	PROPN
ejpam-5839	648	2	pure	pure	PROPN
ejpam-5839	648	3	appl	appl	PROPN
ejpam-5839	648	4	.	.	PROPN
ejpam-5839	648	5	math	math	PROPN
ejpam-5839	648	6	,	,	PUNCT
ejpam-5839	648	7	18	18	NUM
ejpam-5839	648	8	(	(	PUNCT
ejpam-5839	648	9	2	2	NUM
ejpam-5839	648	10	)	)	PUNCT
ejpam-5839	648	11	(	(	PUNCT
ejpam-5839	648	12	2025	2025	NUM
ejpam-5839	648	13	)	)	PUNCT
ejpam-5839	648	14	,	,	PUNCT
ejpam-5839	648	15	5839	5839	NUM
ejpam-5839	648	16	28	28	NUM
ejpam-5839	648	17	of	of	ADP
ejpam-5839	648	18	54	54	NUM
ejpam-5839	648	19	theorem	theorem	NOUN
ejpam-5839	648	20	6	6	NUM
ejpam-5839	648	21	.	.	PUNCT
ejpam-5839	649	1	let	let	VERB
ejpam-5839	649	2	(	(	PUNCT
ejpam-5839	649	3	f̃	f̃	PROPN
ejpam-5839	649	4	,	,	PUNCT
ejpam-5839	649	5	ω	ω	PROPN
ejpam-5839	649	6	)	)	PUNCT
ejpam-5839	649	7	,	,	PUNCT
ejpam-5839	649	8	(	(	PUNCT
ejpam-5839	649	9	g̃,ω	g̃,ω	NOUN
ejpam-5839	649	10	)	)	PUNCT
ejpam-5839	649	11	,	,	PUNCT
ejpam-5839	649	12	and	and	CCONJ
ejpam-5839	649	13	(	(	PUNCT
ejpam-5839	649	14	h̃,ω	h̃,ω	NOUN
ejpam-5839	649	15	)	)	PUNCT
ejpam-5839	649	16	be	be	AUX
ejpam-5839	649	17	quadripartitioned	quadripartitione	VERB
ejpam-5839	649	18	neutrosophic	neutrosophic	ADJ
ejpam-5839	649	19	soft	soft	ADJ
ejpam-5839	649	20	sets	set	NOUN
ejpam-5839	649	21	over	over	ADP
ejpam-5839	649	22	key	key	ADJ
ejpam-5839	649	23	set	set	NOUN
ejpam-5839	649	24	x.	x.	NOUN
ejpam-5839	650	1	then	then	ADV
ejpam-5839	650	2	,	,	PUNCT
ejpam-5839	650	3	the	the	DET
ejpam-5839	650	4	following	follow	VERB
ejpam-5839	650	5	properties	property	NOUN
ejpam-5839	650	6	hold	hold	VERB
ejpam-5839	650	7	:	:	PUNCT
ejpam-5839	650	8	(	(	PUNCT
ejpam-5839	650	9	i	i	NOUN
ejpam-5839	650	10	)	)	PUNCT
ejpam-5839	650	11	(	(	PUNCT
ejpam-5839	650	12	f̃	f̃	PROPN
ejpam-5839	650	13	,	,	PUNCT
ejpam-5839	650	14	ω	ω	NUM
ejpam-5839	650	15	)	)	PUNCT
ejpam-5839	650	16	∪∼	∪∼	NOUN
ejpam-5839	650	17	[	[	X
ejpam-5839	650	18	(	(	PUNCT
ejpam-5839	650	19	g̃,ω	g̃,ω	NOUN
ejpam-5839	650	20	)	)	PUNCT
ejpam-5839	650	21	∪∼	∪∼	NOUN
ejpam-5839	650	22	(	(	PUNCT
ejpam-5839	650	23	h̃,ω	h̃,ω	PROPN
ejpam-5839	650	24	)	)	PUNCT
ejpam-5839	650	25	]	]	PUNCT
ejpam-5839	651	1	=	=	PUNCT
ejpam-5839	652	1	[	[	X
ejpam-5839	652	2	(	(	PUNCT
ejpam-5839	652	3	f̃	f̃	PROPN
ejpam-5839	652	4	,	,	PUNCT
ejpam-5839	652	5	ω	ω	NOUN
ejpam-5839	652	6	)	)	PUNCT
ejpam-5839	652	7	∪∼	∪∼	NOUN
ejpam-5839	652	8	(	(	PUNCT
ejpam-5839	652	9	g̃,ω	g̃,ω	PROPN
ejpam-5839	652	10	)	)	PUNCT
ejpam-5839	652	11	]	]	PUNCT
ejpam-5839	652	12	∪∼	∪∼	NOUN
ejpam-5839	652	13	(	(	PUNCT
ejpam-5839	652	14	h̃,ω	h̃,ω	PROPN
ejpam-5839	652	15	)	)	PUNCT
ejpam-5839	652	16	.	.	PUNCT
ejpam-5839	653	1	(	(	PUNCT
ejpam-5839	653	2	ii	ii	NOUN
ejpam-5839	653	3	)	)	PUNCT
ejpam-5839	653	4	(	(	PUNCT
ejpam-5839	653	5	f̃	f̃	PROPN
ejpam-5839	653	6	,	,	PUNCT
ejpam-5839	653	7	ω	ω	PROPN
ejpam-5839	653	8	)	)	PUNCT
ejpam-5839	653	9	∩∼	∩∼	NOUN
ejpam-5839	653	10	[	[	X
ejpam-5839	653	11	(	(	PUNCT
ejpam-5839	653	12	g̃,ω	g̃,ω	PROPN
ejpam-5839	653	13	)	)	PUNCT
ejpam-5839	653	14	∩∼	∩∼	NOUN
ejpam-5839	653	15	(	(	PUNCT
ejpam-5839	653	16	h̃,ω	h̃,ω	NOUN
ejpam-5839	653	17	)	)	PUNCT
ejpam-5839	653	18	]	]	PUNCT
ejpam-5839	654	1	=	=	PUNCT
ejpam-5839	655	1	[	[	X
ejpam-5839	655	2	(	(	PUNCT
ejpam-5839	655	3	f̃	f̃	PROPN
ejpam-5839	655	4	,	,	PUNCT
ejpam-5839	655	5	ω	ω	PROPN
ejpam-5839	655	6	)	)	PUNCT
ejpam-5839	655	7	∩∼	∩∼	NOUN
ejpam-5839	655	8	(	(	PUNCT
ejpam-5839	655	9	g̃,ω	g̃,ω	PROPN
ejpam-5839	655	10	)	)	PUNCT
ejpam-5839	655	11	]	]	PUNCT
ejpam-5839	655	12	∩∼	∩∼	NOUN
ejpam-5839	655	13	(	(	PUNCT
ejpam-5839	655	14	h̃,ω	h̃,ω	NOUN
ejpam-5839	655	15	)	)	PUNCT
ejpam-5839	655	16	.	.	PUNCT
ejpam-5839	656	1	(	(	PUNCT
ejpam-5839	656	2	iii	iii	X
ejpam-5839	656	3	)	)	PUNCT
ejpam-5839	656	4	(	(	PUNCT
ejpam-5839	656	5	f̃	f̃	PROPN
ejpam-5839	656	6	,	,	PUNCT
ejpam-5839	656	7	ω	ω	NUM
ejpam-5839	656	8	)	)	PUNCT
ejpam-5839	656	9	∪∼	∪∼	NOUN
ejpam-5839	656	10	[	[	X
ejpam-5839	656	11	(	(	PUNCT
ejpam-5839	656	12	g̃,ω	g̃,ω	PROPN
ejpam-5839	656	13	)	)	PUNCT
ejpam-5839	656	14	∩∼	∩∼	NOUN
ejpam-5839	656	15	(	(	PUNCT
ejpam-5839	656	16	h̃,ω	h̃,ω	NOUN
ejpam-5839	656	17	)	)	PUNCT
ejpam-5839	656	18	]	]	PUNCT
ejpam-5839	657	1	=	=	PUNCT
ejpam-5839	658	1	[	[	X
ejpam-5839	658	2	(	(	PUNCT
ejpam-5839	658	3	f̃	f̃	PROPN
ejpam-5839	658	4	,	,	PUNCT
ejpam-5839	658	5	ω	ω	NOUN
ejpam-5839	658	6	)	)	PUNCT
ejpam-5839	658	7	∪∼	∪∼	NOUN
ejpam-5839	658	8	(	(	PUNCT
ejpam-5839	658	9	g̃,ω	g̃,ω	PROPN
ejpam-5839	658	10	)	)	PUNCT
ejpam-5839	658	11	]	]	PUNCT
ejpam-5839	658	12	∩∼	∩∼	NOUN
ejpam-5839	658	13	[	[	X
ejpam-5839	658	14	(	(	PUNCT
ejpam-5839	658	15	f̃	f̃	PROPN
ejpam-5839	658	16	,	,	PUNCT
ejpam-5839	658	17	ω	ω	NOUN
ejpam-5839	658	18	)	)	PUNCT
ejpam-5839	658	19	∪∼	∪∼	NOUN
ejpam-5839	658	20	(	(	PUNCT
ejpam-5839	658	21	h̃,ω	h̃,ω	PROPN
ejpam-5839	658	22	)	)	PUNCT
ejpam-5839	658	23	]	]	PUNCT
ejpam-5839	658	24	.	.	PUNCT
ejpam-5839	659	1	(	(	PUNCT
ejpam-5839	659	2	iv	iv	X
ejpam-5839	659	3	)	)	PUNCT
ejpam-5839	659	4	(	(	PUNCT
ejpam-5839	659	5	f̃	f̃	PROPN
ejpam-5839	659	6	,	,	PUNCT
ejpam-5839	659	7	ω	ω	PROPN
ejpam-5839	659	8	)	)	PUNCT
ejpam-5839	659	9	∩∼	∩∼	NOUN
ejpam-5839	659	10	[	[	X
ejpam-5839	659	11	(	(	PUNCT
ejpam-5839	659	12	g̃,ω	g̃,ω	NOUN
ejpam-5839	659	13	)	)	PUNCT
ejpam-5839	659	14	∪∼	∪∼	NOUN
ejpam-5839	659	15	(	(	PUNCT
ejpam-5839	659	16	h̃,ω	h̃,ω	PROPN
ejpam-5839	659	17	)	)	PUNCT
ejpam-5839	659	18	]	]	PUNCT
ejpam-5839	660	1	=	=	PUNCT
ejpam-5839	661	1	[	[	X
ejpam-5839	661	2	(	(	PUNCT
ejpam-5839	661	3	f̃	f̃	PROPN
ejpam-5839	661	4	,	,	PUNCT
ejpam-5839	661	5	ω	ω	PROPN
ejpam-5839	661	6	)	)	PUNCT
ejpam-5839	661	7	∩∼	∩∼	NOUN
ejpam-5839	661	8	(	(	PUNCT
ejpam-5839	661	9	g̃,ω	g̃,ω	PROPN
ejpam-5839	661	10	)	)	PUNCT
ejpam-5839	661	11	]	]	PUNCT
ejpam-5839	661	12	∪∼	∪∼	NOUN
ejpam-5839	661	13	[	[	X
ejpam-5839	661	14	(	(	PUNCT
ejpam-5839	661	15	f̃	f̃	PROPN
ejpam-5839	661	16	,	,	PUNCT
ejpam-5839	661	17	ω	ω	PROPN
ejpam-5839	661	18	)	)	PUNCT
ejpam-5839	661	19	∩∼	∩∼	NOUN
ejpam-5839	661	20	(	(	PUNCT
ejpam-5839	661	21	h̃,ω	h̃,ω	NOUN
ejpam-5839	661	22	)	)	PUNCT
ejpam-5839	661	23	]	]	PUNCT
ejpam-5839	661	24	.	.	PUNCT
ejpam-5839	662	1	(	(	PUNCT
ejpam-5839	662	2	v	v	NOUN
ejpam-5839	662	3	)	)	PUNCT
ejpam-5839	662	4	(	(	PUNCT
ejpam-5839	662	5	f̃	f̃	PROPN
ejpam-5839	662	6	,	,	PUNCT
ejpam-5839	662	7	ω	ω	NOUN
ejpam-5839	662	8	)	)	PUNCT
ejpam-5839	662	9	∪∼	∪∼	PROPN
ejpam-5839	662	10	0(x	0(x	NOUN
ejpam-5839	662	11	,	,	PUNCT
ejpam-5839	662	12	ω	ω	NOUN
ejpam-5839	662	13	)	)	PUNCT
ejpam-5839	662	14	=	=	SYM
ejpam-5839	662	15	(	(	PUNCT
ejpam-5839	662	16	f̃	f̃	PROPN
ejpam-5839	662	17	,	,	PUNCT
ejpam-5839	662	18	ω	ω	PROPN
ejpam-5839	662	19	)	)	PUNCT
ejpam-5839	662	20	.	.	PUNCT
ejpam-5839	663	1	(	(	PUNCT
ejpam-5839	663	2	vi	vi	X
ejpam-5839	663	3	)	)	PUNCT
ejpam-5839	663	4	(	(	PUNCT
ejpam-5839	663	5	f̃	f̃	PROPN
ejpam-5839	663	6	,	,	PUNCT
ejpam-5839	663	7	ω	ω	PROPN
ejpam-5839	663	8	)	)	PUNCT
ejpam-5839	663	9	∩∼	∩∼	NOUN
ejpam-5839	663	10	0(x	0(x	NOUN
ejpam-5839	663	11	,	,	PUNCT
ejpam-5839	663	12	ω	ω	NOUN
ejpam-5839	663	13	)	)	PUNCT
ejpam-5839	663	14	=	=	SYM
ejpam-5839	663	15	0(x	0(x	NOUN
ejpam-5839	663	16	,	,	PUNCT
ejpam-5839	663	17	ω	ω	NOUN
ejpam-5839	663	18	)	)	PUNCT
ejpam-5839	663	19	.	.	PUNCT
ejpam-5839	664	1	(	(	PUNCT
ejpam-5839	664	2	vii	vii	PROPN
ejpam-5839	664	3	)	)	PUNCT
ejpam-5839	664	4	(	(	PUNCT
ejpam-5839	664	5	f̃	f̃	PROPN
ejpam-5839	664	6	,	,	PUNCT
ejpam-5839	664	7	ω	ω	NOUN
ejpam-5839	664	8	)	)	PUNCT
ejpam-5839	664	9	∪∼	∪∼	NOUN
ejpam-5839	664	10	1(x	1(x	NUM
ejpam-5839	664	11	,	,	PUNCT
ejpam-5839	664	12	ω	ω	NOUN
ejpam-5839	664	13	)	)	PUNCT
ejpam-5839	664	14	=	=	SYM
ejpam-5839	664	15	1(x	1(x	NUM
ejpam-5839	664	16	,	,	PUNCT
ejpam-5839	664	17	ω	ω	NOUN
ejpam-5839	664	18	)	)	PUNCT
ejpam-5839	664	19	.	.	PUNCT
ejpam-5839	665	1	(	(	PUNCT
ejpam-5839	665	2	viii	viii	NOUN
ejpam-5839	665	3	)	)	PUNCT
ejpam-5839	665	4	(	(	PUNCT
ejpam-5839	665	5	f̃	f̃	PROPN
ejpam-5839	665	6	,	,	PUNCT
ejpam-5839	665	7	ω	ω	PROPN
ejpam-5839	665	8	)	)	PUNCT
ejpam-5839	665	9	∩∼	∩∼	NOUN
ejpam-5839	665	10	1(x	1(x	NUM
ejpam-5839	665	11	,	,	PUNCT
ejpam-5839	665	12	ω	ω	NOUN
ejpam-5839	665	13	)	)	PUNCT
ejpam-5839	665	14	=	=	SYM
ejpam-5839	665	15	(	(	PUNCT
ejpam-5839	665	16	f̃	f̃	PROPN
ejpam-5839	665	17	,	,	PUNCT
ejpam-5839	665	18	ω	ω	PROPN
ejpam-5839	665	19	)	)	PUNCT
ejpam-5839	665	20	.	.	PUNCT
ejpam-5839	666	1	proof	proof	NOUN
ejpam-5839	666	2	.	.	PUNCT
ejpam-5839	667	1	obvious	obvious	ADJ
ejpam-5839	667	2	.	.	PUNCT
ejpam-5839	668	1	theorem	theorem	VERB
ejpam-5839	668	2	7	7	NUM
ejpam-5839	668	3	.	.	PUNCT
ejpam-5839	669	1	let	let	VERB
ejpam-5839	669	2	(	(	PUNCT
ejpam-5839	669	3	f̃	f̃	PROPN
ejpam-5839	669	4	,	,	PUNCT
ejpam-5839	669	5	ω	ω	PROPN
ejpam-5839	669	6	)	)	PUNCT
ejpam-5839	669	7	and	and	CCONJ
ejpam-5839	669	8	(	(	PUNCT
ejpam-5839	669	9	g̃,ω	g̃,ω	PROPN
ejpam-5839	669	10	)	)	PUNCT
ejpam-5839	669	11	be	be	AUX
ejpam-5839	669	12	qpnsss	qpnsss	NOUN
ejpam-5839	669	13	over	over	ADP
ejpam-5839	669	14	key	key	ADJ
ejpam-5839	669	15	set	set	NOUN
ejpam-5839	669	16	x.	x.	NOUN
ejpam-5839	670	1	then	then	ADV
ejpam-5839	670	2	,	,	PUNCT
ejpam-5839	670	3	the	the	DET
ejpam-5839	670	4	following	follow	VERB
ejpam-5839	670	5	de	de	PROPN
ejpam-5839	670	6	morgan	morgan	PROPN
ejpam-5839	670	7	’s	’s	PART
ejpam-5839	670	8	laws	law	NOUN
ejpam-5839	670	9	hold	hold	VERB
ejpam-5839	670	10	:	:	PUNCT
ejpam-5839	670	11	(	(	PUNCT
ejpam-5839	670	12	i	i	NOUN
ejpam-5839	670	13	)	)	PUNCT
ejpam-5839	671	1	[	[	X
ejpam-5839	671	2	(	(	PUNCT
ejpam-5839	671	3	f̃	f̃	PROPN
ejpam-5839	671	4	,	,	PUNCT
ejpam-5839	671	5	ω	ω	NOUN
ejpam-5839	671	6	)	)	PUNCT
ejpam-5839	671	7	∪∼	∪∼	NOUN
ejpam-5839	671	8	(	(	PUNCT
ejpam-5839	671	9	g̃,ω)]c	g̃,ω)]c	NOUN
ejpam-5839	671	10	=	=	SYM
ejpam-5839	671	11	(	(	PUNCT
ejpam-5839	671	12	f̃	f̃	PROPN
ejpam-5839	671	13	,	,	PUNCT
ejpam-5839	671	14	ω)c	ω)c	VERB
ejpam-5839	671	15	∩∼	∩∼	NOUN
ejpam-5839	671	16	(	(	PUNCT
ejpam-5839	671	17	g̃,ω)c	g̃,ω)c	PROPN
ejpam-5839	671	18	.	.	PUNCT
ejpam-5839	671	19	(	(	PUNCT
ejpam-5839	671	20	ii	ii	NOUN
ejpam-5839	671	21	)	)	PUNCT
ejpam-5839	672	1	[	[	X
ejpam-5839	672	2	(	(	PUNCT
ejpam-5839	672	3	f̃	f̃	PROPN
ejpam-5839	672	4	,	,	PUNCT
ejpam-5839	672	5	ω	ω	PROPN
ejpam-5839	672	6	)	)	PUNCT
ejpam-5839	672	7	∩∼	∩∼	NOUN
ejpam-5839	672	8	(	(	PUNCT
ejpam-5839	672	9	g̃,ω)]c	g̃,ω)]c	NOUN
ejpam-5839	672	10	=	=	SYM
ejpam-5839	672	11	(	(	PUNCT
ejpam-5839	672	12	f̃	f̃	PROPN
ejpam-5839	672	13	,	,	PUNCT
ejpam-5839	672	14	ω)c	ω)c	ADJ
ejpam-5839	672	15	∪∼	∪∼	NOUN
ejpam-5839	672	16	(	(	PUNCT
ejpam-5839	672	17	g̃,ω)c	g̃,ω)c	PROPN
ejpam-5839	672	18	.	.	PUNCT
ejpam-5839	673	1	proof	proof	NOUN
ejpam-5839	673	2	.	.	PUNCT
ejpam-5839	674	1	obvious	obvious	ADJ
ejpam-5839	674	2	.	.	PUNCT
ejpam-5839	675	1	theorem	theorem	VERB
ejpam-5839	675	2	8	8	NUM
ejpam-5839	675	3	.	.	PUNCT
ejpam-5839	676	1	let	let	VERB
ejpam-5839	676	2	(	(	PUNCT
ejpam-5839	676	3	f̃	f̃	PROPN
ejpam-5839	676	4	,	,	PUNCT
ejpam-5839	676	5	ω	ω	PROPN
ejpam-5839	676	6	)	)	PUNCT
ejpam-5839	676	7	and	and	CCONJ
ejpam-5839	676	8	(	(	PUNCT
ejpam-5839	676	9	g̃,ω	g̃,ω	PROPN
ejpam-5839	676	10	)	)	PUNCT
ejpam-5839	676	11	be	be	AUX
ejpam-5839	676	12	qpnsss	qpnsss	NOUN
ejpam-5839	676	13	over	over	ADP
ejpam-5839	676	14	key	key	ADJ
ejpam-5839	676	15	set	set	NOUN
ejpam-5839	676	16	x.	x.	NOUN
ejpam-5839	677	1	then	then	ADV
ejpam-5839	677	2	,	,	PUNCT
ejpam-5839	677	3	the	the	DET
ejpam-5839	677	4	following	follow	VERB
ejpam-5839	677	5	de	de	PROPN
ejpam-5839	677	6	morgan	morgan	PROPN
ejpam-5839	677	7	’s	’s	PART
ejpam-5839	677	8	laws	law	NOUN
ejpam-5839	677	9	hold	hold	VERB
ejpam-5839	677	10	:	:	PUNCT
ejpam-5839	677	11	(	(	PUNCT
ejpam-5839	677	12	i	i	NOUN
ejpam-5839	677	13	)	)	PUNCT
ejpam-5839	678	1	[	[	X
ejpam-5839	678	2	(	(	PUNCT
ejpam-5839	678	3	f̃	f̃	PROPN
ejpam-5839	678	4	,	,	PUNCT
ejpam-5839	678	5	ω	ω	NUM
ejpam-5839	678	6	)	)	PUNCT
ejpam-5839	678	7	∨∼	∨∼	NOUN
ejpam-5839	678	8	(	(	PUNCT
ejpam-5839	678	9	g̃,ω)]c	g̃,ω)]c	NOUN
ejpam-5839	678	10	=	=	SYM
ejpam-5839	678	11	(	(	PUNCT
ejpam-5839	678	12	f̃	f̃	PROPN
ejpam-5839	678	13	,	,	PUNCT
ejpam-5839	678	14	ω)c	ω)c	NOUN
ejpam-5839	678	15	∧∼	∧∼	NOUN
ejpam-5839	678	16	(	(	PUNCT
ejpam-5839	678	17	g̃,ω)c	g̃,ω)c	PROPN
ejpam-5839	678	18	.	.	PUNCT
ejpam-5839	679	1	(	(	PUNCT
ejpam-5839	679	2	ii	ii	NOUN
ejpam-5839	679	3	)	)	PUNCT
ejpam-5839	680	1	[	[	X
ejpam-5839	680	2	(	(	PUNCT
ejpam-5839	680	3	f̃	f̃	PROPN
ejpam-5839	680	4	,	,	PUNCT
ejpam-5839	680	5	ω	ω	PROPN
ejpam-5839	680	6	)	)	PUNCT
ejpam-5839	680	7	∩∼	∩∼	NOUN
ejpam-5839	680	8	(	(	PUNCT
ejpam-5839	680	9	g̃,ω)]c	g̃,ω)]c	NOUN
ejpam-5839	680	10	=	=	SYM
ejpam-5839	680	11	(	(	PUNCT
ejpam-5839	680	12	f̃	f̃	PROPN
ejpam-5839	680	13	,	,	PUNCT
ejpam-5839	680	14	ω)c	ω)c	ADJ
ejpam-5839	680	15	∪∼	∪∼	NOUN
ejpam-5839	680	16	(	(	PUNCT
ejpam-5839	680	17	g̃,ω)c	g̃,ω)c	PROPN
ejpam-5839	680	18	.	.	PUNCT
ejpam-5839	681	1	proof	proof	NOUN
ejpam-5839	681	2	.	.	PUNCT
ejpam-5839	682	1	1	1	X
ejpam-5839	682	2	.	.	X
ejpam-5839	682	3	∀(θ1	∀(θ1	NOUN
ejpam-5839	682	4	,	,	PUNCT
ejpam-5839	682	5	θ2	θ2	PROPN
ejpam-5839	682	6	)	)	PUNCT
ejpam-5839	682	7	∈	∈	PROPN
ejpam-5839	682	8	ω×	ω×	PUNCT
ejpam-5839	682	9	ω,∀x	ω,∀x	NUM
ejpam-5839	682	10	∈	∈	PROPN
ejpam-5839	682	11	x	x	NOUN
ejpam-5839	682	12	,	,	PUNCT
ejpam-5839	682	13	(	(	PUNCT
ejpam-5839	682	14	f̃	f̃	PROPN
ejpam-5839	682	15	,	,	PUNCT
ejpam-5839	682	16	ω	ω	PROPN
ejpam-5839	682	17	)	)	PUNCT
ejpam-5839	682	18	∨	∨	PROPN
ejpam-5839	682	19	(	(	PUNCT
ejpam-5839	682	20	g̃,ω	g̃,ω	PROPN
ejpam-5839	682	21	)	)	PUNCT
ejpam-5839	682	22	=	=	PUNCT
ejpam-5839	682	23	{	{	PUNCT
ejpam-5839	682	24	(	(	PUNCT
ejpam-5839	682	25	x	x	X
ejpam-5839	682	26	,	,	PUNCT
ejpam-5839	682	27	max	max	PROPN
ejpam-5839	682	28	[	[	PUNCT
ejpam-5839	682	29	abtf̃	abtf̃	X
ejpam-5839	682	30	(	(	PUNCT
ejpam-5839	682	31	θ)(x),abtg(θ)(x	θ)(x),abtg(θ)(x	NUM
ejpam-5839	682	32	)	)	PUNCT
ejpam-5839	682	33	]	]	PUNCT
ejpam-5839	682	34	,	,	PUNCT
ejpam-5839	682	35	max	max	PROPN
ejpam-5839	682	36	[	[	PUNCT
ejpam-5839	682	37	retf̃	retf̃	X
ejpam-5839	682	38	(	(	PUNCT
ejpam-5839	682	39	θ)(x),retg(θ)(x	θ)(x),retg(θ)(x	NUM
ejpam-5839	682	40	)	)	PUNCT
ejpam-5839	682	41	]	]	PUNCT
ejpam-5839	682	42	,	,	PUNCT
ejpam-5839	682	43	min	min	X
ejpam-5839	682	44	[	[	PUNCT
ejpam-5839	682	45	reff̃	reff̃	X
ejpam-5839	682	46	(	(	PUNCT
ejpam-5839	682	47	θ)(x),refg(θ)(x	θ)(x),refg(θ)(x	NOUN
ejpam-5839	682	48	)	)	PUNCT
ejpam-5839	682	49	]	]	PUNCT
ejpam-5839	682	50	,	,	PUNCT
ejpam-5839	682	51	min	min	PROPN
ejpam-5839	682	52	[	[	PUNCT
ejpam-5839	682	53	abff̃	abff̃	ADV
ejpam-5839	682	54	(	(	PUNCT
ejpam-5839	682	55	θ)(x),abfg(θ)(x	θ)(x),abfg(θ)(x	NOUN
ejpam-5839	682	56	)	)	PUNCT
ejpam-5839	682	57	]	]	PUNCT
ejpam-5839	682	58	)	)	PUNCT
ejpam-5839	682	59	}	}	PUNCT
ejpam-5839	682	60	.	.	PUNCT
ejpam-5839	683	1	[	[	X
ejpam-5839	683	2	(	(	PUNCT
ejpam-5839	683	3	f̃	f̃	PROPN
ejpam-5839	683	4	,	,	PUNCT
ejpam-5839	683	5	ω	ω	PROPN
ejpam-5839	683	6	)	)	PUNCT
ejpam-5839	683	7	∨	∨	NOUN
ejpam-5839	683	8	(	(	PUNCT
ejpam-5839	683	9	g̃,ω)]c	g̃,ω)]c	NOUN
ejpam-5839	683	10	=	=	SYM
ejpam-5839	683	11	{	{	PUNCT
ejpam-5839	683	12	(	(	PUNCT
ejpam-5839	683	13	x	x	NOUN
ejpam-5839	683	14	,	,	PUNCT
ejpam-5839	683	15	min	min	PROPN
ejpam-5839	683	16	[	[	PUNCT
ejpam-5839	683	17	abff̃	abff̃	ADV
ejpam-5839	683	18	(	(	PUNCT
ejpam-5839	683	19	θ)(x),abfg(θ)(x	θ)(x),abfg(θ)(x	NOUN
ejpam-5839	683	20	)	)	PUNCT
ejpam-5839	683	21	]	]	PUNCT
ejpam-5839	683	22	,	,	PUNCT
ejpam-5839	683	23	min	min	X
ejpam-5839	683	24	[	[	PUNCT
ejpam-5839	683	25	reff̃	reff̃	X
ejpam-5839	683	26	(	(	PUNCT
ejpam-5839	683	27	θ)(x),refg(θ)(x	θ)(x),refg(θ)(x	NOUN
ejpam-5839	683	28	)	)	PUNCT
ejpam-5839	683	29	]	]	PUNCT
ejpam-5839	683	30	,	,	PUNCT
ejpam-5839	683	31	max	max	PROPN
ejpam-5839	683	32	[	[	PUNCT
ejpam-5839	683	33	retf̃	retf̃	X
ejpam-5839	683	34	(	(	PUNCT
ejpam-5839	683	35	θ)(x),retg(θ)(x	θ)(x),retg(θ)(x	NUM
ejpam-5839	683	36	)	)	PUNCT
ejpam-5839	683	37	]	]	PUNCT
ejpam-5839	683	38	,	,	PUNCT
ejpam-5839	683	39	a.	a.	NOUN
ejpam-5839	683	40	shihadeh	shihadeh	PROPN
ejpam-5839	683	41	et	et	PROPN
ejpam-5839	683	42	al	al	PROPN
ejpam-5839	683	43	.	.	PUNCT
ejpam-5839	683	44	/	/	SYM
ejpam-5839	683	45	eur	eur	PROPN
ejpam-5839	683	46	.	.	PUNCT
ejpam-5839	684	1	j.	j.	PROPN
ejpam-5839	684	2	pure	pure	PROPN
ejpam-5839	684	3	appl	appl	PROPN
ejpam-5839	684	4	.	.	PROPN
ejpam-5839	684	5	math	math	PROPN
ejpam-5839	684	6	,	,	PUNCT
ejpam-5839	684	7	18	18	NUM
ejpam-5839	684	8	(	(	PUNCT
ejpam-5839	684	9	2	2	NUM
ejpam-5839	684	10	)	)	PUNCT
ejpam-5839	684	11	(	(	PUNCT
ejpam-5839	684	12	2025	2025	NUM
ejpam-5839	684	13	)	)	PUNCT
ejpam-5839	684	14	,	,	PUNCT
ejpam-5839	684	15	5839	5839	NUM
ejpam-5839	684	16	29	29	NUM
ejpam-5839	684	17	of	of	ADP
ejpam-5839	684	18	54	54	NUM
ejpam-5839	684	19	max	max	NOUN
ejpam-5839	684	20	[	[	PUNCT
ejpam-5839	684	21	abtf̃	abtf̃	X
ejpam-5839	684	22	(	(	PUNCT
ejpam-5839	684	23	θ)(x),abtg(θ)(x	θ)(x),abtg(θ)(x	NUM
ejpam-5839	684	24	)	)	PUNCT
ejpam-5839	684	25	]	]	PUNCT
ejpam-5839	684	26	)	)	PUNCT
ejpam-5839	684	27	}	}	PUNCT
ejpam-5839	684	28	.	.	PUNCT
ejpam-5839	685	1	now	now	ADV
ejpam-5839	685	2	,	,	PUNCT
ejpam-5839	685	3	(	(	PUNCT
ejpam-5839	685	4	f̃	f̃	PROPN
ejpam-5839	685	5	,	,	PUNCT
ejpam-5839	685	6	ω)c	ω)c	NOUN
ejpam-5839	685	7	=	=	X
ejpam-5839	685	8	{	{	PUNCT
ejpam-5839	685	9	⟨x	⟨x	NUM
ejpam-5839	685	10	,	,	PUNCT
ejpam-5839	685	11	abff̃	abff̃	ADV
ejpam-5839	685	12	(	(	PUNCT
ejpam-5839	685	13	θ)(x),reff̃	θ)(x),reff̃	X
ejpam-5839	685	14	(	(	PUNCT
ejpam-5839	685	15	θ)(x),retf̃	θ)(x),retf̃	NOUN
ejpam-5839	685	16	(	(	PUNCT
ejpam-5839	685	17	θ)(x),abtf̃	θ)(x),abtf̃	X
ejpam-5839	685	18	(	(	PUNCT
ejpam-5839	685	19	θ)(x)⟩	θ)(x)⟩	NUM
ejpam-5839	685	20	}	}	PUNCT
ejpam-5839	685	21	,	,	PUNCT
ejpam-5839	685	22	(	(	PUNCT
ejpam-5839	685	23	g̃,ω)c	g̃,ω)c	PROPN
ejpam-5839	685	24	=	=	PUNCT
ejpam-5839	685	25	{	{	PUNCT
ejpam-5839	685	26	⟨x	⟨x	VERB
ejpam-5839	685	27	,	,	PUNCT
ejpam-5839	685	28	abfg̃(θ)(x),refg̃(θ)(x),retg̃(θ)(x),abtg̃(θ)(x)⟩	abfg̃(θ)(x),refg̃(θ)(x),retg̃(θ)(x),abtg̃(θ)(x)⟩	NOUN
ejpam-5839	685	29	}	}	PUNCT
ejpam-5839	685	30	.	.	PUNCT
ejpam-5839	686	1	thus	thus	ADV
ejpam-5839	686	2	,	,	PUNCT
ejpam-5839	686	3	(	(	PUNCT
ejpam-5839	686	4	f̃	f̃	PROPN
ejpam-5839	686	5	,	,	PUNCT
ejpam-5839	686	6	ω)c	ω)c	ADJ
ejpam-5839	686	7	∧	∧	NOUN
ejpam-5839	686	8	(	(	PUNCT
ejpam-5839	686	9	g̃,ω)c	g̃,ω)c	PROPN
ejpam-5839	686	10	=	=	SYM
ejpam-5839	686	11	{	{	PUNCT
ejpam-5839	686	12	(	(	PUNCT
ejpam-5839	686	13	x	x	NOUN
ejpam-5839	686	14	,	,	PUNCT
ejpam-5839	686	15	min	min	PROPN
ejpam-5839	686	16	[	[	PUNCT
ejpam-5839	686	17	abff̃	abff̃	ADV
ejpam-5839	686	18	(	(	PUNCT
ejpam-5839	686	19	θ)(x),abfg(θ)(x	θ)(x),abfg(θ)(x	NOUN
ejpam-5839	686	20	)	)	PUNCT
ejpam-5839	686	21	]	]	PUNCT
ejpam-5839	686	22	,	,	PUNCT
ejpam-5839	686	23	min	min	X
ejpam-5839	686	24	[	[	PUNCT
ejpam-5839	686	25	reff̃	reff̃	X
ejpam-5839	686	26	(	(	PUNCT
ejpam-5839	686	27	θ)(x),refg(θ)(x	θ)(x),refg(θ)(x	NOUN
ejpam-5839	686	28	)	)	PUNCT
ejpam-5839	686	29	]	]	PUNCT
ejpam-5839	686	30	,	,	PUNCT
ejpam-5839	686	31	max	max	PROPN
ejpam-5839	686	32	[	[	PUNCT
ejpam-5839	686	33	retf̃	retf̃	X
ejpam-5839	686	34	(	(	PUNCT
ejpam-5839	686	35	θ)(x),retg(θ)(x	θ)(x),retg(θ)(x	NUM
ejpam-5839	686	36	)	)	PUNCT
ejpam-5839	686	37	]	]	PUNCT
ejpam-5839	686	38	,	,	PUNCT
ejpam-5839	686	39	max	max	PROPN
ejpam-5839	686	40	[	[	PUNCT
ejpam-5839	686	41	abtf̃	abtf̃	X
ejpam-5839	686	42	(	(	PUNCT
ejpam-5839	686	43	θ)(x),abtg(θ)(x	θ)(x),abtg(θ)(x	NUM
ejpam-5839	686	44	)	)	PUNCT
ejpam-5839	686	45	]	]	PUNCT
ejpam-5839	686	46	)	)	PUNCT
ejpam-5839	686	47	}	}	PUNCT
ejpam-5839	686	48	.	.	PUNCT
ejpam-5839	687	1	therefore	therefore	ADV
ejpam-5839	687	2	,	,	PUNCT
ejpam-5839	687	3	[	[	X
ejpam-5839	687	4	(	(	PUNCT
ejpam-5839	687	5	f̃	f̃	PROPN
ejpam-5839	687	6	,	,	PUNCT
ejpam-5839	687	7	ω	ω	PROPN
ejpam-5839	687	8	)	)	PUNCT
ejpam-5839	687	9	∨	∨	NOUN
ejpam-5839	687	10	(	(	PUNCT
ejpam-5839	687	11	g̃,ω)]c	g̃,ω)]c	NOUN
ejpam-5839	687	12	=	=	SYM
ejpam-5839	687	13	(	(	PUNCT
ejpam-5839	687	14	f̃	f̃	PROPN
ejpam-5839	687	15	,	,	PUNCT
ejpam-5839	687	16	ω)c	ω)c	ADJ
ejpam-5839	687	17	∧	∧	NOUN
ejpam-5839	687	18	(	(	PUNCT
ejpam-5839	687	19	g̃,ω)c	g̃,ω)c	PROPN
ejpam-5839	687	20	.	.	PUNCT
ejpam-5839	687	21	2	2	NUM
ejpam-5839	687	22	.	.	X
ejpam-5839	687	23	∀(θ1	∀(θ1	PROPN
ejpam-5839	687	24	,	,	PUNCT
ejpam-5839	687	25	θ2	θ2	PROPN
ejpam-5839	687	26	)	)	PUNCT
ejpam-5839	687	27	∈	∈	PROPN
ejpam-5839	687	28	ω×	ω×	PUNCT
ejpam-5839	687	29	ω,∀x	ω,∀x	NUM
ejpam-5839	687	30	∈	∈	NOUN
ejpam-5839	687	31	x	x	X
ejpam-5839	687	32	(	(	PUNCT
ejpam-5839	687	33	f̃	f̃	PROPN
ejpam-5839	687	34	,	,	PUNCT
ejpam-5839	687	35	ω	ω	NOUN
ejpam-5839	687	36	)	)	PUNCT
ejpam-5839	687	37	∧	∧	PROPN
ejpam-5839	687	38	(	(	PUNCT
ejpam-5839	687	39	g̃,ω	g̃,ω	PROPN
ejpam-5839	687	40	)	)	PUNCT
ejpam-5839	687	41	=	=	PUNCT
ejpam-5839	687	42	{	{	PUNCT
ejpam-5839	687	43	(	(	PUNCT
ejpam-5839	687	44	x	x	NOUN
ejpam-5839	687	45	,	,	PUNCT
ejpam-5839	687	46	min	min	PROPN
ejpam-5839	687	47	[	[	PUNCT
ejpam-5839	687	48	tf̃	tf̃	X
ejpam-5839	687	49	(	(	PUNCT
ejpam-5839	687	50	θ)(x),tg(θ)(x	θ)(x),tg(θ)(x	PROPN
ejpam-5839	687	51	)	)	PUNCT
ejpam-5839	687	52	]	]	PUNCT
ejpam-5839	687	53	,	,	PUNCT
ejpam-5839	687	54	min	min	PROPN
ejpam-5839	687	55	[	[	PUNCT
ejpam-5839	687	56	retf̃	retf̃	X
ejpam-5839	687	57	(	(	PUNCT
ejpam-5839	687	58	θ)(x),retg(θ)(x	θ)(x),retg(θ)(x	NUM
ejpam-5839	687	59	)	)	PUNCT
ejpam-5839	687	60	]	]	PUNCT
ejpam-5839	687	61	,	,	PUNCT
ejpam-5839	687	62	max	max	PROPN
ejpam-5839	687	63	[	[	PUNCT
ejpam-5839	687	64	reff̃	reff̃	X
ejpam-5839	687	65	(	(	PUNCT
ejpam-5839	687	66	θ)(x),refg(θ)(x	θ)(x),refg(θ)(x	NOUN
ejpam-5839	687	67	)	)	PUNCT
ejpam-5839	687	68	]	]	PUNCT
ejpam-5839	687	69	,	,	PUNCT
ejpam-5839	687	70	max	max	PROPN
ejpam-5839	687	71	[	[	PUNCT
ejpam-5839	687	72	abff̃	abff̃	ADV
ejpam-5839	687	73	(	(	PUNCT
ejpam-5839	687	74	θ)(x),abfg(θ)(x	θ)(x),abfg(θ)(x	NOUN
ejpam-5839	687	75	)	)	PUNCT
ejpam-5839	687	76	]	]	PUNCT
ejpam-5839	687	77	)	)	PUNCT
ejpam-5839	687	78	}	}	PUNCT
ejpam-5839	687	79	.	.	PUNCT
ejpam-5839	688	1	[	[	X
ejpam-5839	688	2	(	(	PUNCT
ejpam-5839	688	3	f̃	f̃	PROPN
ejpam-5839	688	4	,	,	PUNCT
ejpam-5839	688	5	ω	ω	NOUN
ejpam-5839	688	6	)	)	PUNCT
ejpam-5839	688	7	∧	∧	PROPN
ejpam-5839	688	8	(	(	PUNCT
ejpam-5839	688	9	g̃,ω)]c	g̃,ω)]c	NOUN
ejpam-5839	688	10	=	=	SYM
ejpam-5839	688	11	{	{	PUNCT
ejpam-5839	688	12	(	(	PUNCT
ejpam-5839	688	13	x	x	X
ejpam-5839	688	14	,	,	PUNCT
ejpam-5839	688	15	max	max	PROPN
ejpam-5839	688	16	[	[	PUNCT
ejpam-5839	688	17	abff̃	abff̃	ADV
ejpam-5839	688	18	(	(	PUNCT
ejpam-5839	688	19	θ)(x),abfg(θ)(x	θ)(x),abfg(θ)(x	NOUN
ejpam-5839	688	20	)	)	PUNCT
ejpam-5839	688	21	]	]	PUNCT
ejpam-5839	688	22	,	,	PUNCT
ejpam-5839	688	23	max	max	PROPN
ejpam-5839	688	24	[	[	PUNCT
ejpam-5839	688	25	reff̃	reff̃	X
ejpam-5839	688	26	(	(	PUNCT
ejpam-5839	688	27	θ)(x),refg(θ)(x	θ)(x),refg(θ)(x	NOUN
ejpam-5839	688	28	)	)	PUNCT
ejpam-5839	688	29	]	]	PUNCT
ejpam-5839	688	30	,	,	PUNCT
ejpam-5839	688	31	min	min	PROPN
ejpam-5839	688	32	[	[	PUNCT
ejpam-5839	688	33	retf̃	retf̃	X
ejpam-5839	688	34	(	(	PUNCT
ejpam-5839	688	35	θ)(x),retg(θ)(x	θ)(x),retg(θ)(x	NUM
ejpam-5839	688	36	)	)	PUNCT
ejpam-5839	688	37	]	]	PUNCT
ejpam-5839	688	38	,	,	PUNCT
ejpam-5839	688	39	min	min	X
ejpam-5839	688	40	[	[	PUNCT
ejpam-5839	688	41	abtf̃	abtf̃	X
ejpam-5839	688	42	(	(	PUNCT
ejpam-5839	688	43	θ)(x),abtg(θ)(x	θ)(x),abtg(θ)(x	NUM
ejpam-5839	688	44	)	)	PUNCT
ejpam-5839	688	45	]	]	PUNCT
ejpam-5839	688	46	)	)	PUNCT
ejpam-5839	688	47	}	}	PUNCT
ejpam-5839	688	48	.	.	PUNCT
ejpam-5839	689	1	now	now	ADV
ejpam-5839	689	2	,	,	PUNCT
ejpam-5839	689	3	(	(	PUNCT
ejpam-5839	689	4	f̃	f̃	PROPN
ejpam-5839	689	5	,	,	PUNCT
ejpam-5839	689	6	ω)c	ω)c	NOUN
ejpam-5839	689	7	=	=	X
ejpam-5839	689	8	{	{	PUNCT
ejpam-5839	689	9	⟨x	⟨x	NUM
ejpam-5839	689	10	,	,	PUNCT
ejpam-5839	689	11	abff̃	abff̃	ADV
ejpam-5839	689	12	(	(	PUNCT
ejpam-5839	689	13	θ)(x),reff̃	θ)(x),reff̃	X
ejpam-5839	689	14	(	(	PUNCT
ejpam-5839	689	15	θ)(x),retf̃	θ)(x),retf̃	NOUN
ejpam-5839	689	16	(	(	PUNCT
ejpam-5839	689	17	θ)(x),abtf̃	θ)(x),abtf̃	X
ejpam-5839	689	18	(	(	PUNCT
ejpam-5839	689	19	θ)(x)⟩	θ)(x)⟩	NUM
ejpam-5839	689	20	}	}	PUNCT
ejpam-5839	689	21	,	,	PUNCT
ejpam-5839	689	22	(	(	PUNCT
ejpam-5839	689	23	g̃,ω)c	g̃,ω)c	PROPN
ejpam-5839	689	24	=	=	PUNCT
ejpam-5839	689	25	{	{	PUNCT
ejpam-5839	689	26	⟨x	⟨x	VERB
ejpam-5839	689	27	,	,	PUNCT
ejpam-5839	689	28	abfg̃(θ)(x),refg̃(θ)(x),retg̃(θ)(x),abtg̃(θ)(x)⟩	abfg̃(θ)(x),refg̃(θ)(x),retg̃(θ)(x),abtg̃(θ)(x)⟩	NOUN
ejpam-5839	689	29	}	}	PUNCT
ejpam-5839	689	30	.	.	PUNCT
ejpam-5839	690	1	thus	thus	ADV
ejpam-5839	690	2	,	,	PUNCT
ejpam-5839	690	3	a.	a.	NOUN
ejpam-5839	690	4	shihadeh	shihadeh	PROPN
ejpam-5839	690	5	et	et	PROPN
ejpam-5839	690	6	al	al	PROPN
ejpam-5839	690	7	.	.	PUNCT
ejpam-5839	690	8	/	/	SYM
ejpam-5839	690	9	eur	eur	PROPN
ejpam-5839	690	10	.	.	PUNCT
ejpam-5839	691	1	j.	j.	PROPN
ejpam-5839	691	2	pure	pure	PROPN
ejpam-5839	691	3	appl	appl	PROPN
ejpam-5839	691	4	.	.	PROPN
ejpam-5839	691	5	math	math	PROPN
ejpam-5839	691	6	,	,	PUNCT
ejpam-5839	691	7	18	18	NUM
ejpam-5839	691	8	(	(	PUNCT
ejpam-5839	691	9	2	2	NUM
ejpam-5839	691	10	)	)	PUNCT
ejpam-5839	691	11	(	(	PUNCT
ejpam-5839	691	12	2025	2025	NUM
ejpam-5839	691	13	)	)	PUNCT
ejpam-5839	691	14	,	,	PUNCT
ejpam-5839	691	15	5839	5839	NUM
ejpam-5839	691	16	30	30	NUM
ejpam-5839	691	17	of	of	ADP
ejpam-5839	691	18	54	54	NUM
ejpam-5839	691	19	(	(	PUNCT
ejpam-5839	691	20	f̃	f̃	PROPN
ejpam-5839	691	21	,	,	PUNCT
ejpam-5839	691	22	ω)c	ω)c	NOUN
ejpam-5839	691	23	∨	∨	NOUN
ejpam-5839	691	24	(	(	PUNCT
ejpam-5839	691	25	g̃,ω)c	g̃,ω)c	PROPN
ejpam-5839	691	26	=	=	SYM
ejpam-5839	691	27	{	{	PUNCT
ejpam-5839	691	28	(	(	PUNCT
ejpam-5839	691	29	x	x	X
ejpam-5839	691	30	,	,	PUNCT
ejpam-5839	691	31	max	max	PROPN
ejpam-5839	691	32	[	[	PUNCT
ejpam-5839	691	33	abff̃	abff̃	ADV
ejpam-5839	691	34	(	(	PUNCT
ejpam-5839	691	35	θ)(x),abfg(θ)(x	θ)(x),abfg(θ)(x	NOUN
ejpam-5839	691	36	)	)	PUNCT
ejpam-5839	691	37	]	]	PUNCT
ejpam-5839	691	38	,	,	PUNCT
ejpam-5839	691	39	max	max	PROPN
ejpam-5839	691	40	[	[	PUNCT
ejpam-5839	691	41	reff̃	reff̃	X
ejpam-5839	691	42	(	(	PUNCT
ejpam-5839	691	43	θ)(x),refg(θ)(x	θ)(x),refg(θ)(x	NOUN
ejpam-5839	691	44	)	)	PUNCT
ejpam-5839	691	45	]	]	PUNCT
ejpam-5839	691	46	,	,	PUNCT
ejpam-5839	691	47	min	min	PROPN
ejpam-5839	691	48	[	[	PUNCT
ejpam-5839	691	49	retf̃	retf̃	X
ejpam-5839	691	50	(	(	PUNCT
ejpam-5839	691	51	θ)(x),retg(θ)(x	θ)(x),retg(θ)(x	NUM
ejpam-5839	691	52	)	)	PUNCT
ejpam-5839	691	53	]	]	PUNCT
ejpam-5839	691	54	,	,	PUNCT
ejpam-5839	691	55	min	min	X
ejpam-5839	691	56	[	[	PUNCT
ejpam-5839	691	57	abtf̃	abtf̃	X
ejpam-5839	691	58	(	(	PUNCT
ejpam-5839	691	59	θ)(x),abtg(θ)(x	θ)(x),abtg(θ)(x	NUM
ejpam-5839	691	60	)	)	PUNCT
ejpam-5839	691	61	]	]	PUNCT
ejpam-5839	691	62	)	)	PUNCT
ejpam-5839	691	63	}	}	PUNCT
ejpam-5839	691	64	.	.	PUNCT
ejpam-5839	692	1	therefore	therefore	ADV
ejpam-5839	692	2	,	,	PUNCT
ejpam-5839	692	3	[	[	X
ejpam-5839	692	4	(	(	PUNCT
ejpam-5839	692	5	f̃	f̃	PROPN
ejpam-5839	692	6	,	,	PUNCT
ejpam-5839	692	7	ω	ω	NOUN
ejpam-5839	692	8	)	)	PUNCT
ejpam-5839	692	9	∧	∧	PROPN
ejpam-5839	692	10	(	(	PUNCT
ejpam-5839	692	11	g̃,ω)]c	g̃,ω)]c	NOUN
ejpam-5839	692	12	=	=	SYM
ejpam-5839	692	13	(	(	PUNCT
ejpam-5839	692	14	f̃	f̃	PROPN
ejpam-5839	692	15	,	,	PUNCT
ejpam-5839	692	16	ω)c	ω)c	NOUN
ejpam-5839	692	17	∨	∨	NOUN
ejpam-5839	692	18	(	(	PUNCT
ejpam-5839	692	19	g̃,ω)c	g̃,ω)c	PROPN
ejpam-5839	692	20	.	.	NOUN
ejpam-5839	692	21	8	8	NUM
ejpam-5839	692	22	.	.	PUNCT
ejpam-5839	693	1	a	a	DET
ejpam-5839	693	2	new	new	ADJ
ejpam-5839	693	3	approach	approach	NOUN
ejpam-5839	693	4	to	to	ADP
ejpam-5839	693	5	operations	operation	NOUN
ejpam-5839	693	6	on	on	ADP
ejpam-5839	693	7	quadripartitioned	quadripartitione	VERB
ejpam-5839	693	8	neutrosophic	neutrosophic	PROPN
ejpam-5839	693	9	soft	soft	ADJ
ejpam-5839	693	10	topological	topological	ADJ
ejpam-5839	693	11	space	space	NOUN
ejpam-5839	693	12	the	the	DET
ejpam-5839	693	13	notion	notion	NOUN
ejpam-5839	693	14	of	of	ADP
ejpam-5839	693	15	qpnsts	qpnst	NOUN
ejpam-5839	693	16	is	be	AUX
ejpam-5839	693	17	presented	present	VERB
ejpam-5839	693	18	in	in	ADP
ejpam-5839	693	19	this	this	DET
ejpam-5839	693	20	section	section	NOUN
ejpam-5839	693	21	.	.	PUNCT
ejpam-5839	694	1	the	the	DET
ejpam-5839	694	2	terms	term	NOUN
ejpam-5839	694	3	qpns	qpns	VERB
ejpam-5839	694	4	semi	semi	ADJ
ejpam-5839	694	5	-	-	ADJ
ejpam-5839	694	6	open	open	ADJ
ejpam-5839	694	7	,	,	PUNCT
ejpam-5839	694	8	qpns	qpns	NOUN
ejpam-5839	694	9	preopen	preopen	ADJ
ejpam-5839	694	10	,	,	PUNCT
ejpam-5839	694	11	and	and	CCONJ
ejpam-5839	694	12	qpns	qpns	NOUN
ejpam-5839	694	13	∗b	∗b	PROPN
ejpam-5839	694	14	-	-	PUNCT
ejpam-5839	694	15	open	open	ADJ
ejpam-5839	694	16	sets	set	NOUN
ejpam-5839	694	17	are	be	AUX
ejpam-5839	694	18	defined	define	VERB
ejpam-5839	694	19	.	.	PUNCT
ejpam-5839	695	1	one	one	NUM
ejpam-5839	695	2	of	of	ADP
ejpam-5839	695	3	these	these	DET
ejpam-5839	695	4	intriguing	intriguing	ADJ
ejpam-5839	695	5	qpns	qpns	NOUN
ejpam-5839	695	6	generalized	generalize	VERB
ejpam-5839	695	7	open	open	ADJ
ejpam-5839	695	8	sets	set	NOUN
ejpam-5839	695	9	,	,	PUNCT
ejpam-5839	695	10	referred	refer	VERB
ejpam-5839	695	11	to	to	ADP
ejpam-5839	695	12	as	as	ADP
ejpam-5839	695	13	the	the	DET
ejpam-5839	695	14	qpns	qpns	NOUN
ejpam-5839	695	15	pre	pre	ADJ
ejpam-5839	695	16	-	-	ADJ
ejpam-5839	695	17	open	open	ADJ
ejpam-5839	695	18	set	set	NOUN
ejpam-5839	695	19	,	,	PUNCT
ejpam-5839	695	20	is	be	AUX
ejpam-5839	695	21	selected	select	VERB
ejpam-5839	695	22	,	,	PUNCT
ejpam-5839	695	23	and	and	CCONJ
ejpam-5839	695	24	certain	certain	ADJ
ejpam-5839	695	25	fundamentals	fundamental	NOUN
ejpam-5839	695	26	are	be	AUX
ejpam-5839	695	27	then	then	ADV
ejpam-5839	695	28	produced	produce	VERB
ejpam-5839	695	29	based	base	VERB
ejpam-5839	695	30	on	on	ADP
ejpam-5839	695	31	this	this	DET
ejpam-5839	695	32	description	description	NOUN
ejpam-5839	695	33	.	.	PUNCT
ejpam-5839	696	1	these	these	DET
ejpam-5839	696	2	consist	consist	NOUN
ejpam-5839	696	3	of	of	ADP
ejpam-5839	696	4	the	the	DET
ejpam-5839	696	5	qpns	qpns	NOUN
ejpam-5839	696	6	closure	closure	NOUN
ejpam-5839	696	7	,	,	PUNCT
ejpam-5839	696	8	qpns	qpns	NOUN
ejpam-5839	696	9	exterior	exterior	NOUN
ejpam-5839	696	10	,	,	PUNCT
ejpam-5839	696	11	qpns	qpns	NOUN
ejpam-5839	696	12	boundary	boundary	NOUN
ejpam-5839	696	13	,	,	PUNCT
ejpam-5839	696	14	and	and	CCONJ
ejpam-5839	696	15	qpns	qpns	NOUN
ejpam-5839	696	16	interior	interior	NOUN
ejpam-5839	696	17	.	.	PUNCT
ejpam-5839	697	1	definition	definition	NOUN
ejpam-5839	697	2	24	24	NUM
ejpam-5839	697	3	.	.	PUNCT
ejpam-5839	698	1	let	let	VERB
ejpam-5839	698	2	qnss(x̃,ω	qnss(x̃,ω	NUM
ejpam-5839	698	3	)	)	PUNCT
ejpam-5839	698	4	be	be	AUX
ejpam-5839	698	5	the	the	DET
ejpam-5839	698	6	family	family	NOUN
ejpam-5839	698	7	of	of	ADP
ejpam-5839	698	8	all	all	DET
ejpam-5839	698	9	qpnsss	qpnsss	NOUN
ejpam-5839	698	10	and	and	CCONJ
ejpam-5839	698	11	τ	τ	PROPN
ejpam-5839	698	12	⊂	⊂	PROPN
ejpam-5839	698	13	qpnss(x̃,ω	qpnss(x̃,ω	X
ejpam-5839	698	14	)	)	PUNCT
ejpam-5839	698	15	,	,	PUNCT
ejpam-5839	698	16	then	then	ADV
ejpam-5839	698	17	τ	τ	PROPN
ejpam-5839	698	18	is	be	AUX
ejpam-5839	698	19	a	a	DET
ejpam-5839	698	20	quadri	quadri	NOUN
ejpam-5839	698	21	-	-	PUNCT
ejpam-5839	698	22	partitioned	partition	VERB
ejpam-5839	698	23	neutrosophic	neutrosophic	ADJ
ejpam-5839	698	24	soft	soft	ADJ
ejpam-5839	698	25	topology	topology	NOUN
ejpam-5839	698	26	(	(	PUNCT
ejpam-5839	698	27	qpnst	qpnst	ADJ
ejpam-5839	698	28	)	)	PUNCT
ejpam-5839	698	29	on	on	ADP
ejpam-5839	698	30	x̃	x̃	PROPN
ejpam-5839	698	31	if	if	SCONJ
ejpam-5839	698	32	(	(	PUNCT
ejpam-5839	698	33	i	i	NOUN
ejpam-5839	698	34	)	)	PUNCT
ejpam-5839	698	35	0(⟨x⟩,ω	0(⟨x⟩,ω	NUM
ejpam-5839	698	36	)	)	PUNCT
ejpam-5839	698	37	,	,	PUNCT
ejpam-5839	698	38	1(⟨x⟩,ω	1(⟨x⟩,ω	X
ejpam-5839	698	39	)	)	PUNCT
ejpam-5839	698	40	∈	∈	PROPN
ejpam-5839	698	41	τ	τ	X
ejpam-5839	698	42	,	,	PUNCT
ejpam-5839	698	43	(	(	PUNCT
ejpam-5839	698	44	ii	ii	NOUN
ejpam-5839	698	45	)	)	PUNCT
ejpam-5839	698	46	the	the	DET
ejpam-5839	698	47	union	union	NOUN
ejpam-5839	698	48	of	of	ADP
ejpam-5839	698	49	any	any	DET
ejpam-5839	698	50	number	number	NOUN
ejpam-5839	698	51	of	of	ADP
ejpam-5839	698	52	qpnsss	qpnsss	NOUN
ejpam-5839	698	53	in	in	ADP
ejpam-5839	698	54	τ	τ	PROPN
ejpam-5839	698	55	belongs	belong	VERB
ejpam-5839	698	56	to	to	ADP
ejpam-5839	698	57	τ	τ	PROPN
ejpam-5839	698	58	,	,	PUNCT
ejpam-5839	698	59	(	(	PUNCT
ejpam-5839	698	60	iii	iii	X
ejpam-5839	698	61	)	)	PUNCT
ejpam-5839	698	62	the	the	DET
ejpam-5839	698	63	intersection	intersection	NOUN
ejpam-5839	698	64	of	of	ADP
ejpam-5839	698	65	a	a	DET
ejpam-5839	698	66	finite	finite	ADJ
ejpam-5839	698	67	number	number	NOUN
ejpam-5839	698	68	of	of	ADP
ejpam-5839	698	69	qpnsss	qpnsss	NOUN
ejpam-5839	698	70	in	in	ADP
ejpam-5839	698	71	τ	τ	PROPN
ejpam-5839	698	72	belongs	belong	VERB
ejpam-5839	698	73	to	to	ADP
ejpam-5839	698	74	τ	τ	PROPN
ejpam-5839	698	75	.	.	PUNCT
ejpam-5839	699	1	then	then	ADV
ejpam-5839	699	2	,	,	PUNCT
ejpam-5839	699	3	(	(	PUNCT
ejpam-5839	699	4	x̃	x̃	PROPN
ejpam-5839	699	5	,	,	PUNCT
ejpam-5839	699	6	τ	τ	PROPN
ejpam-5839	699	7	,	,	PUNCT
ejpam-5839	699	8	ω	ω	NOUN
ejpam-5839	699	9	)	)	PUNCT
ejpam-5839	699	10	is	be	AUX
ejpam-5839	699	11	said	say	VERB
ejpam-5839	699	12	to	to	PART
ejpam-5839	699	13	be	be	AUX
ejpam-5839	699	14	a	a	DET
ejpam-5839	699	15	qpnsts	qpnst	NOUN
ejpam-5839	699	16	over	over	ADP
ejpam-5839	699	17	x̃.	x̃.	ADJ
ejpam-5839	699	18	definition	definition	NOUN
ejpam-5839	699	19	25	25	NUM
ejpam-5839	699	20	.	.	PUNCT
ejpam-5839	700	1	(	(	PUNCT
ejpam-5839	700	2	x̃	x̃	PROPN
ejpam-5839	700	3	,	,	PUNCT
ejpam-5839	700	4	τ	τ	PROPN
ejpam-5839	700	5	,	,	PUNCT
ejpam-5839	700	6	ω	ω	NOUN
ejpam-5839	700	7	)	)	PUNCT
ejpam-5839	700	8	is	be	AUX
ejpam-5839	700	9	a	a	DET
ejpam-5839	700	10	qpnsts	qpnst	NOUN
ejpam-5839	700	11	over	over	ADP
ejpam-5839	700	12	x.	x.	NOUN
ejpam-5839	700	13	a	a	DET
ejpam-5839	700	14	qpnss	qpnss	NOUN
ejpam-5839	700	15	(	(	PUNCT
ejpam-5839	700	16	f̃	f̃	PROPN
ejpam-5839	700	17	,	,	PUNCT
ejpam-5839	700	18	ω	ω	PROPN
ejpam-5839	700	19	)	)	PUNCT
ejpam-5839	700	20	is	be	AUX
ejpam-5839	700	21	a	a	DET
ejpam-5839	700	22	qpns	qpns	NOUN
ejpam-5839	700	23	neighborhood	neighborhood	NOUN
ejpam-5839	700	24	of	of	ADP
ejpam-5839	700	25	a	a	DET
ejpam-5839	700	26	qpns	qpns	NOUN
ejpam-5839	700	27	point	point	NOUN
ejpam-5839	700	28	xλ⟨r1,r2,r3,r4⟩	xλ⟨r1,r2,r3,r4⟩	PROPN
ejpam-5839	700	29	∈	∈	PROPN
ejpam-5839	700	30	(	(	PUNCT
ejpam-5839	700	31	f̃	f̃	PROPN
ejpam-5839	700	32	,	,	PUNCT
ejpam-5839	700	33	ω	ω	PROPN
ejpam-5839	700	34	)	)	PUNCT
ejpam-5839	700	35	,	,	PUNCT
ejpam-5839	700	36	if	if	SCONJ
ejpam-5839	700	37	there	there	PRON
ejpam-5839	700	38	is	be	VERB
ejpam-5839	700	39	a	a	DET
ejpam-5839	700	40	qpns	qpns	NOUN
ejpam-5839	700	41	open	open	ADJ
ejpam-5839	700	42	set	set	NOUN
ejpam-5839	700	43	(	(	PUNCT
ejpam-5839	700	44	g̃,ω	g̃,ω	PROPN
ejpam-5839	700	45	)	)	PUNCT
ejpam-5839	701	1	such	such	ADJ
ejpam-5839	701	2	that	that	SCONJ
ejpam-5839	701	3	xλ⟨r1,r2,r3,r4⟩	xλ⟨r1,r2,r3,r4⟩	PROPN
ejpam-5839	701	4	∈	∈	PROPN
ejpam-5839	701	5	(	(	PUNCT
ejpam-5839	701	6	g̃,ω	g̃,ω	PROPN
ejpam-5839	701	7	)	)	PUNCT
ejpam-5839	701	8	.	.	PUNCT
ejpam-5839	702	1	definition	definition	NOUN
ejpam-5839	702	2	26	26	NUM
ejpam-5839	702	3	.	.	PUNCT
ejpam-5839	703	1	let	let	VERB
ejpam-5839	703	2	(	(	PUNCT
ejpam-5839	703	3	x	x	NOUN
ejpam-5839	703	4	,	,	PUNCT
ejpam-5839	703	5	τ1,ω	τ1,ω	PROPN
ejpam-5839	703	6	)	)	PUNCT
ejpam-5839	703	7	and	and	CCONJ
ejpam-5839	703	8	(	(	PUNCT
ejpam-5839	703	9	x	x	NOUN
ejpam-5839	703	10	,	,	PUNCT
ejpam-5839	703	11	τ2,ω	τ2,ω	PROPN
ejpam-5839	703	12	)	)	PUNCT
ejpam-5839	703	13	be	be	VERB
ejpam-5839	703	14	two	two	NUM
ejpam-5839	703	15	qpnsbtss	qpnsbtss	NOUN
ejpam-5839	703	16	.	.	PUNCT
ejpam-5839	704	1	then	then	ADV
ejpam-5839	704	2	,	,	PUNCT
ejpam-5839	704	3	(	(	PUNCT
ejpam-5839	704	4	x	x	NOUN
ejpam-5839	704	5	,	,	PUNCT
ejpam-5839	704	6	τ1	τ1	NOUN
ejpam-5839	704	7	,	,	PUNCT
ejpam-5839	704	8	τ2,ω	τ2,ω	PROPN
ejpam-5839	704	9	)	)	PUNCT
ejpam-5839	704	10	is	be	AUX
ejpam-5839	704	11	a	a	DET
ejpam-5839	704	12	qpnsbts	qpnsbt	NOUN
ejpam-5839	704	13	.	.	PUNCT
ejpam-5839	705	1	if	if	SCONJ
ejpam-5839	705	2	(	(	PUNCT
ejpam-5839	705	3	x	x	NOUN
ejpam-5839	705	4	,	,	PUNCT
ejpam-5839	705	5	τ1	τ1	NOUN
ejpam-5839	705	6	,	,	PUNCT
ejpam-5839	705	7	τ2,ω	τ2,ω	PROPN
ejpam-5839	705	8	)	)	PUNCT
ejpam-5839	705	9	is	be	AUX
ejpam-5839	705	10	a	a	DET
ejpam-5839	705	11	qpnsbts	qpnsbt	NOUN
ejpam-5839	705	12	,	,	PUNCT
ejpam-5839	705	13	a	a	DET
ejpam-5839	705	14	qpnss	qpnss	NOUN
ejpam-5839	705	15	subset	subset	NOUN
ejpam-5839	705	16	(	(	PUNCT
ejpam-5839	705	17	f̃	f̃	PROPN
ejpam-5839	705	18	,	,	PUNCT
ejpam-5839	705	19	ω	ω	NUM
ejpam-5839	705	20	)	)	PUNCT
ejpam-5839	705	21	is	be	AUX
ejpam-5839	705	22	open	open	ADJ
ejpam-5839	705	23	in	in	ADP
ejpam-5839	705	24	(	(	PUNCT
ejpam-5839	705	25	x	x	NOUN
ejpam-5839	705	26	,	,	PUNCT
ejpam-5839	705	27	τ1	τ1	NOUN
ejpam-5839	705	28	,	,	PUNCT
ejpam-5839	705	29	τ2,ω	τ2,ω	PUNCT
ejpam-5839	705	30	)	)	PUNCT
ejpam-5839	705	31	if	if	SCONJ
ejpam-5839	705	32	there	there	PRON
ejpam-5839	705	33	exists	exist	VERB
ejpam-5839	705	34	a	a	DET
ejpam-5839	705	35	qpnss	qpnss	NOUN
ejpam-5839	705	36	open	open	ADJ
ejpam-5839	705	37	set	set	NOUN
ejpam-5839	705	38	(	(	PUNCT
ejpam-5839	705	39	g̃,ω	g̃,ω	PROPN
ejpam-5839	705	40	)	)	PUNCT
ejpam-5839	705	41	belonging	belong	VERB
ejpam-5839	705	42	to	to	ADP
ejpam-5839	705	43	τ1	τ1	NOUN
ejpam-5839	705	44	and	and	CCONJ
ejpam-5839	705	45	a	a	DET
ejpam-5839	705	46	qpnss	qpnss	NOUN
ejpam-5839	705	47	open	open	ADJ
ejpam-5839	705	48	set	set	NOUN
ejpam-5839	705	49	(	(	PUNCT
ejpam-5839	705	50	h̃,ω	h̃,ω	NOUN
ejpam-5839	705	51	)	)	PUNCT
ejpam-5839	705	52	belonging	belong	VERB
ejpam-5839	705	53	to	to	ADP
ejpam-5839	705	54	τ2	τ2	VERB
ejpam-5839	705	55	such	such	ADJ
ejpam-5839	705	56	that	that	SCONJ
ejpam-5839	705	57	(	(	PUNCT
ejpam-5839	705	58	f̃	f̃	PROPN
ejpam-5839	705	59	,	,	PUNCT
ejpam-5839	705	60	ω	ω	NOUN
ejpam-5839	705	61	)	)	PUNCT
ejpam-5839	705	62	=	=	PUNCT
ejpam-5839	705	63	(	(	PUNCT
ejpam-5839	705	64	g̃,ω	g̃,ω	NOUN
ejpam-5839	705	65	)	)	PUNCT
ejpam-5839	705	66	∪	∪	NOUN
ejpam-5839	705	67	(	(	PUNCT
ejpam-5839	705	68	h̃,ω	h̃,ω	NOUN
ejpam-5839	705	69	)	)	PUNCT
ejpam-5839	705	70	.	.	PUNCT
ejpam-5839	706	1	example	example	NOUN
ejpam-5839	707	1	3	3	X
ejpam-5839	707	2	.	.	PUNCT
ejpam-5839	707	3	let	let	VERB
ejpam-5839	707	4	x	x	PUNCT
ejpam-5839	707	5	=	=	PRON
ejpam-5839	707	6	{	{	PUNCT
ejpam-5839	707	7	x1	x1	PROPN
ejpam-5839	707	8	,	,	PUNCT
ejpam-5839	707	9	x2	x2	PROPN
ejpam-5839	707	10	,	,	PUNCT
ejpam-5839	707	11	x3	x3	ADJ
ejpam-5839	707	12	}	}	PUNCT
ejpam-5839	707	13	and	and	CCONJ
ejpam-5839	707	14	ω	ω	NUM
ejpam-5839	707	15	=	=	SYM
ejpam-5839	707	16	{	{	PUNCT
ejpam-5839	707	17	θ1	θ1	PROPN
ejpam-5839	707	18	,	,	PUNCT
ejpam-5839	707	19	θ2	θ2	PROPN
ejpam-5839	707	20	}	}	PUNCT
ejpam-5839	707	21	,	,	PUNCT
ejpam-5839	707	22	τ1	τ1	NOUN
ejpam-5839	707	23	=	=	SYM
ejpam-5839	707	24	{	{	PUNCT
ejpam-5839	707	25	0(x	0(x	NOUN
ejpam-5839	707	26	,	,	PUNCT
ejpam-5839	707	27	ω	ω	NOUN
ejpam-5839	707	28	)	)	PUNCT
ejpam-5839	707	29	,	,	PUNCT
ejpam-5839	707	30	1(x	1(x	NUM
ejpam-5839	707	31	,	,	PUNCT
ejpam-5839	707	32	ω	ω	NOUN
ejpam-5839	707	33	)	)	PUNCT
ejpam-5839	707	34	,	,	PUNCT
ejpam-5839	707	35	(	(	PUNCT
ejpam-5839	707	36	f̃	f̃	PROPN
ejpam-5839	707	37	,	,	PUNCT
ejpam-5839	707	38	ω	ω	PROPN
ejpam-5839	707	39	)	)	PUNCT
ejpam-5839	707	40	,	,	PUNCT
ejpam-5839	707	41	(	(	PUNCT
ejpam-5839	707	42	g̃,ω	g̃,ω	NOUN
ejpam-5839	707	43	)	)	PUNCT
ejpam-5839	707	44	}	}	PUNCT
ejpam-5839	707	45	and	and	CCONJ
ejpam-5839	707	46	τ2	τ2	NOUN
ejpam-5839	707	47	=	=	SYM
ejpam-5839	707	48	{	{	PUNCT
ejpam-5839	707	49	0(x	0(x	NOUN
ejpam-5839	707	50	,	,	PUNCT
ejpam-5839	707	51	ω	ω	NOUN
ejpam-5839	707	52	)	)	PUNCT
ejpam-5839	707	53	,	,	PUNCT
ejpam-5839	707	54	1(x	1(x	NUM
ejpam-5839	707	55	,	,	PUNCT
ejpam-5839	707	56	ω	ω	NOUN
ejpam-5839	707	57	)	)	PUNCT
ejpam-5839	707	58	,	,	PUNCT
ejpam-5839	707	59	(	(	PUNCT
ejpam-5839	707	60	h̃,ω	h̃,ω	NOUN
ejpam-5839	707	61	)	)	PUNCT
ejpam-5839	707	62	,	,	PUNCT
ejpam-5839	707	63	(	(	PUNCT
ejpam-5839	707	64	ĩ	ĩ	PROPN
ejpam-5839	707	65	,	,	PUNCT
ejpam-5839	707	66	ω	ω	NOUN
ejpam-5839	707	67	)	)	PUNCT
ejpam-5839	707	68	}	}	PUNCT
ejpam-5839	707	69	,	,	PUNCT
ejpam-5839	707	70	where	where	SCONJ
ejpam-5839	707	71	(	(	PUNCT
ejpam-5839	707	72	f̃	f̃	PROPN
ejpam-5839	707	73	,	,	PUNCT
ejpam-5839	707	74	ω	ω	PROPN
ejpam-5839	707	75	)	)	PUNCT
ejpam-5839	707	76	,	,	PUNCT
ejpam-5839	707	77	(	(	PUNCT
ejpam-5839	707	78	g̃,ω	g̃,ω	PROPN
ejpam-5839	707	79	)	)	PUNCT
ejpam-5839	707	80	,	,	PUNCT
ejpam-5839	707	81	(	(	PUNCT
ejpam-5839	707	82	h̃,ω	h̃,ω	NOUN
ejpam-5839	707	83	)	)	PUNCT
ejpam-5839	707	84	,	,	PUNCT
ejpam-5839	707	85	and	and	CCONJ
ejpam-5839	707	86	(	(	PUNCT
ejpam-5839	707	87	ĩ	ĩ	PROPN
ejpam-5839	707	88	,	,	PUNCT
ejpam-5839	707	89	ω	ω	NUM
ejpam-5839	707	90	)	)	PUNCT
ejpam-5839	707	91	being	be	AUX
ejpam-5839	707	92	qpnsss	qpnsss	NOUN
ejpam-5839	707	93	are	be	AUX
ejpam-5839	707	94	as	as	SCONJ
ejpam-5839	707	95	follows	follow	VERB
ejpam-5839	707	96	:	:	PUNCT
ejpam-5839	707	97	(	(	PUNCT
ejpam-5839	707	98	f̃	f̃	PROPN
ejpam-5839	707	99	,	,	PUNCT
ejpam-5839	707	100	ω	ω	NOUN
ejpam-5839	707	101	)	)	PUNCT
ejpam-5839	708	1	=	=	PUNCT
ejpam-5839	708	2	[	[	PUNCT
ejpam-5839	708	3	θ1	θ1	NOUN
ejpam-5839	708	4	=	=	SYM
ejpam-5839	708	5	⟨x1	⟨x1	NOUN
ejpam-5839	708	6	,	,	PUNCT
ejpam-5839	708	7	2	2	NUM
ejpam-5839	708	8	10	10	NUM
ejpam-5839	708	9	,	,	PUNCT
ejpam-5839	708	10	3	3	NUM
ejpam-5839	708	11	10	10	NUM
ejpam-5839	708	12	,	,	PUNCT
ejpam-5839	708	13	7	7	NUM
ejpam-5839	708	14	10	10	NUM
ejpam-5839	708	15	,	,	PUNCT
ejpam-5839	708	16	8	8	NUM
ejpam-5839	708	17	10⟩	10⟩	NUM
ejpam-5839	708	18	,	,	PUNCT
ejpam-5839	708	19	⟨x2	⟨x2	PROPN
ejpam-5839	708	20	,	,	PUNCT
ejpam-5839	708	21	4	4	NUM
ejpam-5839	708	22	10	10	NUM
ejpam-5839	708	23	,	,	PUNCT
ejpam-5839	708	24	4	4	NUM
ejpam-5839	708	25	10	10	NUM
ejpam-5839	708	26	,	,	PUNCT
ejpam-5839	708	27	6	6	NUM
ejpam-5839	708	28	10	10	NUM
ejpam-5839	708	29	,	,	PUNCT
ejpam-5839	708	30	4	4	NUM
ejpam-5839	708	31	10⟩	10⟩	NUM
ejpam-5839	708	32	,	,	PUNCT
ejpam-5839	708	33	⟨x3	⟨x3	NOUN
ejpam-5839	708	34	,	,	PUNCT
ejpam-5839	708	35	2	2	NUM
ejpam-5839	708	36	10	10	NUM
ejpam-5839	708	37	,	,	PUNCT
ejpam-5839	708	38	4	4	NUM
ejpam-5839	708	39	10	10	NUM
ejpam-5839	708	40	,	,	PUNCT
ejpam-5839	708	41	6	6	NUM
ejpam-5839	708	42	10	10	NUM
ejpam-5839	708	43	,	,	PUNCT
ejpam-5839	708	44	2	2	NUM
ejpam-5839	708	45	10⟩	10⟩	NUM
ejpam-5839	708	46	,	,	PUNCT
ejpam-5839	708	47	θ2	θ2	PROPN
ejpam-5839	708	48	=	=	SYM
ejpam-5839	708	49	⟨x1	⟨x1	PROPN
ejpam-5839	708	50	,	,	PUNCT
ejpam-5839	708	51	3	3	NUM
ejpam-5839	708	52	10	10	NUM
ejpam-5839	708	53	,	,	PUNCT
ejpam-5839	708	54	2	2	NUM
ejpam-5839	708	55	10	10	NUM
ejpam-5839	708	56	,	,	PUNCT
ejpam-5839	708	57	6	6	NUM
ejpam-5839	708	58	10	10	NUM
ejpam-5839	708	59	,	,	PUNCT
ejpam-5839	708	60	6	6	NUM
ejpam-5839	708	61	10⟩	10⟩	NUM
ejpam-5839	708	62	,	,	PUNCT
ejpam-5839	708	63	⟨x2	⟨x2	PROPN
ejpam-5839	708	64	,	,	PUNCT
ejpam-5839	708	65	1	1	NUM
ejpam-5839	708	66	10	10	NUM
ejpam-5839	708	67	,	,	PUNCT
ejpam-5839	708	68	5	5	NUM
ejpam-5839	708	69	10	10	NUM
ejpam-5839	708	70	,	,	PUNCT
ejpam-5839	708	71	6	6	NUM
ejpam-5839	708	72	10	10	NUM
ejpam-5839	708	73	,	,	PUNCT
ejpam-5839	708	74	5	5	NUM
ejpam-5839	708	75	10⟩	10⟩	NUM
ejpam-5839	708	76	,	,	PUNCT
ejpam-5839	708	77	⟨x3	⟨x3	NOUN
ejpam-5839	708	78	,	,	PUNCT
ejpam-5839	708	79	4	4	NUM
ejpam-5839	708	80	10	10	NUM
ejpam-5839	708	81	,	,	PUNCT
ejpam-5839	708	82	3	3	NUM
ejpam-5839	708	83	10	10	NUM
ejpam-5839	708	84	,	,	PUNCT
ejpam-5839	708	85	6	6	NUM
ejpam-5839	708	86	10	10	NUM
ejpam-5839	708	87	,	,	PUNCT
ejpam-5839	708	88	5	5	NUM
ejpam-5839	708	89	10⟩	10⟩	NUM
ejpam-5839	708	90	]	]	PUNCT
ejpam-5839	708	91	a.	a.	NOUN
ejpam-5839	708	92	shihadeh	shihadeh	PROPN
ejpam-5839	708	93	et	et	PROPN
ejpam-5839	708	94	al	al	PROPN
ejpam-5839	708	95	.	.	PUNCT
ejpam-5839	708	96	/	/	SYM
ejpam-5839	708	97	eur	eur	PROPN
ejpam-5839	708	98	.	.	PUNCT
ejpam-5839	709	1	j.	j.	PROPN
ejpam-5839	709	2	pure	pure	PROPN
ejpam-5839	709	3	appl	appl	PROPN
ejpam-5839	709	4	.	.	PROPN
ejpam-5839	709	5	math	math	PROPN
ejpam-5839	709	6	,	,	PUNCT
ejpam-5839	709	7	18	18	NUM
ejpam-5839	709	8	(	(	PUNCT
ejpam-5839	709	9	2	2	NUM
ejpam-5839	709	10	)	)	PUNCT
ejpam-5839	709	11	(	(	PUNCT
ejpam-5839	709	12	2025	2025	NUM
ejpam-5839	709	13	)	)	PUNCT
ejpam-5839	709	14	,	,	PUNCT
ejpam-5839	709	15	5839	5839	NUM
ejpam-5839	709	16	31	31	NUM
ejpam-5839	709	17	of	of	ADP
ejpam-5839	709	18	54	54	NUM
ejpam-5839	709	19	(	(	PUNCT
ejpam-5839	709	20	g̃,ω	g̃,ω	PROPN
ejpam-5839	709	21	)	)	PUNCT
ejpam-5839	709	22	=	=	PUNCT
ejpam-5839	710	1	[	[	PUNCT
ejpam-5839	710	2	θ1	θ1	NOUN
ejpam-5839	710	3	=	=	SYM
ejpam-5839	710	4	⟨x1	⟨x1	NOUN
ejpam-5839	710	5	,	,	PUNCT
ejpam-5839	710	6	4	4	NUM
ejpam-5839	710	7	10	10	NUM
ejpam-5839	710	8	,	,	PUNCT
ejpam-5839	710	9	3	3	NUM
ejpam-5839	710	10	10	10	NUM
ejpam-5839	710	11	,	,	PUNCT
ejpam-5839	710	12	6	6	NUM
ejpam-5839	710	13	10	10	NUM
ejpam-5839	710	14	,	,	PUNCT
ejpam-5839	710	15	6	6	NUM
ejpam-5839	710	16	10⟩	10⟩	NUM
ejpam-5839	710	17	,	,	PUNCT
ejpam-5839	710	18	⟨x2	⟨x2	PROPN
ejpam-5839	710	19	,	,	PUNCT
ejpam-5839	710	20	4	4	NUM
ejpam-5839	710	21	10	10	NUM
ejpam-5839	710	22	,	,	PUNCT
ejpam-5839	710	23	5	5	NUM
ejpam-5839	710	24	10	10	NUM
ejpam-5839	710	25	,	,	PUNCT
ejpam-5839	710	26	6	6	NUM
ejpam-5839	710	27	10	10	NUM
ejpam-5839	710	28	,	,	PUNCT
ejpam-5839	710	29	3	3	NUM
ejpam-5839	710	30	10⟩	10⟩	NUM
ejpam-5839	710	31	,	,	PUNCT
ejpam-5839	710	32	⟨x3	⟨x3	PROPN
ejpam-5839	710	33	,	,	PUNCT
ejpam-5839	710	34	3	3	NUM
ejpam-5839	710	35	10	10	NUM
ejpam-5839	710	36	,	,	PUNCT
ejpam-5839	710	37	5	5	NUM
ejpam-5839	710	38	10	10	NUM
ejpam-5839	710	39	,	,	PUNCT
ejpam-5839	710	40	6	6	NUM
ejpam-5839	710	41	10	10	NUM
ejpam-5839	710	42	,	,	PUNCT
ejpam-5839	710	43	2	2	NUM
ejpam-5839	710	44	10⟩	10⟩	NUM
ejpam-5839	710	45	,	,	PUNCT
ejpam-5839	710	46	θ2	θ2	PROPN
ejpam-5839	710	47	=	=	SYM
ejpam-5839	710	48	⟨x1	⟨x1	PROPN
ejpam-5839	710	49	,	,	PUNCT
ejpam-5839	710	50	3	3	NUM
ejpam-5839	710	51	10	10	NUM
ejpam-5839	710	52	,	,	PUNCT
ejpam-5839	710	53	4	4	NUM
ejpam-5839	710	54	10	10	NUM
ejpam-5839	710	55	,	,	PUNCT
ejpam-5839	710	56	6	6	NUM
ejpam-5839	710	57	10	10	NUM
ejpam-5839	710	58	,	,	PUNCT
ejpam-5839	710	59	5	5	NUM
ejpam-5839	710	60	10⟩	10⟩	NUM
ejpam-5839	710	61	,	,	PUNCT
ejpam-5839	710	62	⟨x2	⟨x2	PROPN
ejpam-5839	710	63	,	,	PUNCT
ejpam-5839	710	64	2	2	NUM
ejpam-5839	710	65	10	10	NUM
ejpam-5839	710	66	,	,	PUNCT
ejpam-5839	710	67	6	6	NUM
ejpam-5839	710	68	10	10	NUM
ejpam-5839	710	69	,	,	PUNCT
ejpam-5839	710	70	6	6	NUM
ejpam-5839	710	71	10	10	NUM
ejpam-5839	710	72	,	,	PUNCT
ejpam-5839	710	73	4	4	NUM
ejpam-5839	710	74	10⟩	10⟩	NUM
ejpam-5839	710	75	,	,	PUNCT
ejpam-5839	710	76	⟨x3	⟨x3	NOUN
ejpam-5839	710	77	,	,	PUNCT
ejpam-5839	710	78	4	4	NUM
ejpam-5839	710	79	10	10	NUM
ejpam-5839	710	80	,	,	PUNCT
ejpam-5839	710	81	6	6	NUM
ejpam-5839	710	82	10	10	NUM
ejpam-5839	710	83	,	,	PUNCT
ejpam-5839	710	84	6	6	NUM
ejpam-5839	710	85	10	10	NUM
ejpam-5839	710	86	,	,	PUNCT
ejpam-5839	710	87	3	3	NUM
ejpam-5839	710	88	10⟩	10⟩	NUM
ejpam-5839	710	89	]	]	PUNCT
ejpam-5839	710	90	(	(	PUNCT
ejpam-5839	710	91	h̃,ω	h̃,ω	NOUN
ejpam-5839	710	92	)	)	PUNCT
ejpam-5839	710	93	=	=	PUNCT
ejpam-5839	711	1	[	[	PUNCT
ejpam-5839	711	2	θ1	θ1	NOUN
ejpam-5839	711	3	=	=	SYM
ejpam-5839	711	4	⟨x1	⟨x1	NOUN
ejpam-5839	711	5	,	,	PUNCT
ejpam-5839	711	6	6	6	NUM
ejpam-5839	711	7	10	10	NUM
ejpam-5839	711	8	,	,	PUNCT
ejpam-5839	711	9	6	6	NUM
ejpam-5839	711	10	10	10	NUM
ejpam-5839	711	11	,	,	PUNCT
ejpam-5839	711	12	6	6	NUM
ejpam-5839	711	13	10	10	NUM
ejpam-5839	711	14	,	,	PUNCT
ejpam-5839	711	15	2	2	NUM
ejpam-5839	711	16	10⟩	10⟩	NUM
ejpam-5839	711	17	,	,	PUNCT
ejpam-5839	711	18	⟨x2	⟨x2	PROPN
ejpam-5839	711	19	,	,	PUNCT
ejpam-5839	711	20	6	6	NUM
ejpam-5839	711	21	10	10	NUM
ejpam-5839	711	22	,	,	PUNCT
ejpam-5839	711	23	6	6	NUM
ejpam-5839	711	24	10	10	NUM
ejpam-5839	711	25	,	,	PUNCT
ejpam-5839	711	26	6	6	NUM
ejpam-5839	711	27	10	10	NUM
ejpam-5839	711	28	,	,	PUNCT
ejpam-5839	711	29	2	2	NUM
ejpam-5839	711	30	10⟩	10⟩	NUM
ejpam-5839	711	31	,	,	PUNCT
ejpam-5839	711	32	⟨x3	⟨x3	NOUN
ejpam-5839	711	33	,	,	PUNCT
ejpam-5839	711	34	4	4	NUM
ejpam-5839	711	35	10	10	NUM
ejpam-5839	711	36	,	,	PUNCT
ejpam-5839	711	37	6	6	NUM
ejpam-5839	711	38	10	10	NUM
ejpam-5839	711	39	,	,	PUNCT
ejpam-5839	711	40	6	6	NUM
ejpam-5839	711	41	10	10	NUM
ejpam-5839	711	42	,	,	PUNCT
ejpam-5839	711	43	1	1	NUM
ejpam-5839	711	44	10⟩	10⟩	NUM
ejpam-5839	711	45	,	,	PUNCT
ejpam-5839	711	46	θ2	θ2	PROPN
ejpam-5839	711	47	=	=	SYM
ejpam-5839	711	48	⟨x1	⟨x1	PROPN
ejpam-5839	711	49	,	,	PUNCT
ejpam-5839	711	50	5	5	NUM
ejpam-5839	711	51	10	10	NUM
ejpam-5839	711	52	,	,	PUNCT
ejpam-5839	711	53	6	6	NUM
ejpam-5839	711	54	10	10	NUM
ejpam-5839	711	55	,	,	PUNCT
ejpam-5839	711	56	6	6	NUM
ejpam-5839	711	57	10	10	NUM
ejpam-5839	711	58	,	,	PUNCT
ejpam-5839	711	59	2	2	NUM
ejpam-5839	711	60	10⟩	10⟩	NUM
ejpam-5839	711	61	,	,	PUNCT
ejpam-5839	711	62	⟨x2	⟨x2	PROPN
ejpam-5839	711	63	,	,	PUNCT
ejpam-5839	711	64	6	6	NUM
ejpam-5839	711	65	10	10	NUM
ejpam-5839	711	66	,	,	PUNCT
ejpam-5839	711	67	7	7	NUM
ejpam-5839	711	68	10	10	NUM
ejpam-5839	711	69	,	,	PUNCT
ejpam-5839	711	70	6	6	NUM
ejpam-5839	711	71	10	10	NUM
ejpam-5839	711	72	,	,	PUNCT
ejpam-5839	711	73	2	2	NUM
ejpam-5839	711	74	10⟩	10⟩	NUM
ejpam-5839	711	75	,	,	PUNCT
ejpam-5839	711	76	⟨x3	⟨x3	NOUN
ejpam-5839	711	77	,	,	PUNCT
ejpam-5839	711	78	5	5	NUM
ejpam-5839	711	79	10	10	NUM
ejpam-5839	711	80	,	,	PUNCT
ejpam-5839	711	81	5	5	NUM
ejpam-5839	711	82	10	10	NUM
ejpam-5839	711	83	,	,	PUNCT
ejpam-5839	711	84	6	6	NUM
ejpam-5839	711	85	10	10	NUM
ejpam-5839	711	86	,	,	PUNCT
ejpam-5839	711	87	1	1	NUM
ejpam-5839	711	88	10⟩	10⟩	NUM
ejpam-5839	711	89	]	]	PUNCT
ejpam-5839	711	90	(	(	PUNCT
ejpam-5839	711	91	ĩ	ĩ	PROPN
ejpam-5839	711	92	,	,	PUNCT
ejpam-5839	711	93	ω	ω	NOUN
ejpam-5839	711	94	)	)	PUNCT
ejpam-5839	711	95	=	=	NOUN
ejpam-5839	712	1	[	[	PUNCT
ejpam-5839	712	2	θ1	θ1	NOUN
ejpam-5839	712	3	=	=	SYM
ejpam-5839	712	4	⟨x1	⟨x1	NOUN
ejpam-5839	712	5	,	,	PUNCT
ejpam-5839	712	6	1	1	NUM
ejpam-5839	712	7	10	10	NUM
ejpam-5839	712	8	,	,	PUNCT
ejpam-5839	712	9	2	2	NUM
ejpam-5839	712	10	10	10	NUM
ejpam-5839	712	11	,	,	PUNCT
ejpam-5839	712	12	6	6	NUM
ejpam-5839	712	13	10	10	NUM
ejpam-5839	712	14	,	,	PUNCT
ejpam-5839	712	15	7	7	NUM
ejpam-5839	712	16	10⟩	10⟩	NUM
ejpam-5839	712	17	,	,	PUNCT
ejpam-5839	712	18	⟨x2	⟨x2	PROPN
ejpam-5839	712	19	,	,	PUNCT
ejpam-5839	712	20	4	4	NUM
ejpam-5839	712	21	10	10	NUM
ejpam-5839	712	22	,	,	PUNCT
ejpam-5839	712	23	4	4	NUM
ejpam-5839	712	24	10	10	NUM
ejpam-5839	712	25	,	,	PUNCT
ejpam-5839	712	26	6	6	NUM
ejpam-5839	712	27	10	10	NUM
ejpam-5839	712	28	,	,	PUNCT
ejpam-5839	712	29	3	3	NUM
ejpam-5839	712	30	10⟩	10⟩	NUM
ejpam-5839	712	31	,	,	PUNCT
ejpam-5839	712	32	⟨x3	⟨x3	NOUN
ejpam-5839	712	33	,	,	PUNCT
ejpam-5839	712	34	2	2	NUM
ejpam-5839	712	35	10	10	NUM
ejpam-5839	712	36	,	,	PUNCT
ejpam-5839	712	37	4	4	NUM
ejpam-5839	712	38	10	10	NUM
ejpam-5839	712	39	,	,	PUNCT
ejpam-5839	712	40	6	6	NUM
ejpam-5839	712	41	10	10	NUM
ejpam-5839	712	42	,	,	PUNCT
ejpam-5839	712	43	2	2	NUM
ejpam-5839	712	44	10⟩	10⟩	NUM
ejpam-5839	712	45	,	,	PUNCT
ejpam-5839	712	46	θ2	θ2	PROPN
ejpam-5839	712	47	=	=	SYM
ejpam-5839	712	48	⟨x1	⟨x1	PROPN
ejpam-5839	712	49	,	,	PUNCT
ejpam-5839	712	50	3	3	NUM
ejpam-5839	712	51	10	10	NUM
ejpam-5839	712	52	,	,	PUNCT
ejpam-5839	712	53	2	2	NUM
ejpam-5839	712	54	10	10	NUM
ejpam-5839	712	55	,	,	PUNCT
ejpam-5839	712	56	6	6	NUM
ejpam-5839	712	57	10	10	NUM
ejpam-5839	712	58	,	,	PUNCT
ejpam-5839	712	59	5	5	NUM
ejpam-5839	712	60	10⟩	10⟩	NUM
ejpam-5839	712	61	,	,	PUNCT
ejpam-5839	712	62	⟨x2	⟨x2	PROPN
ejpam-5839	712	63	,	,	PUNCT
ejpam-5839	712	64	1	1	NUM
ejpam-5839	712	65	10	10	NUM
ejpam-5839	712	66	,	,	PUNCT
ejpam-5839	712	67	5	5	NUM
ejpam-5839	712	68	10	10	NUM
ejpam-5839	712	69	,	,	PUNCT
ejpam-5839	712	70	6	6	NUM
ejpam-5839	712	71	10	10	NUM
ejpam-5839	712	72	,	,	PUNCT
ejpam-5839	712	73	5	5	NUM
ejpam-5839	712	74	10⟩	10⟩	NUM
ejpam-5839	712	75	,	,	PUNCT
ejpam-5839	712	76	⟨x3	⟨x3	NOUN
ejpam-5839	712	77	,	,	PUNCT
ejpam-5839	712	78	4	4	NUM
ejpam-5839	712	79	10	10	NUM
ejpam-5839	712	80	,	,	PUNCT
ejpam-5839	712	81	3	3	NUM
ejpam-5839	712	82	10	10	NUM
ejpam-5839	712	83	,	,	PUNCT
ejpam-5839	712	84	6	6	NUM
ejpam-5839	712	85	10	10	NUM
ejpam-5839	712	86	,	,	PUNCT
ejpam-5839	712	87	5	5	NUM
ejpam-5839	712	88	10⟩	10⟩	NUM
ejpam-5839	712	89	]	]	PUNCT
ejpam-5839	712	90	theorem	theorem	VERB
ejpam-5839	712	91	9	9	NUM
ejpam-5839	712	92	.	.	PUNCT
ejpam-5839	713	1	let	let	AUX
ejpam-5839	713	2	(	(	PUNCT
ejpam-5839	713	3	x	x	NOUN
ejpam-5839	713	4	,	,	PUNCT
ejpam-5839	713	5	τ1	τ1	NOUN
ejpam-5839	713	6	,	,	PUNCT
ejpam-5839	713	7	τ2,ω	τ2,ω	PUNCT
ejpam-5839	713	8	)	)	PUNCT
ejpam-5839	713	9	be	be	VERB
ejpam-5839	713	10	a	a	DET
ejpam-5839	713	11	qpnsbts	qpnsbt	NOUN
ejpam-5839	713	12	.	.	PUNCT
ejpam-5839	714	1	then	then	ADV
ejpam-5839	714	2	τ1	τ1	ADP
ejpam-5839	714	3	∩	∩	ADJ
ejpam-5839	714	4	τ2	τ2	NOUN
ejpam-5839	714	5	is	be	AUX
ejpam-5839	714	6	a	a	DET
ejpam-5839	714	7	qpnsbts	qpnsbt	NOUN
ejpam-5839	714	8	on	on	ADP
ejpam-5839	714	9	x.	x.	NOUN
ejpam-5839	714	10	proof	proof	NOUN
ejpam-5839	714	11	.	.	PUNCT
ejpam-5839	715	1	the	the	DET
ejpam-5839	715	2	first	first	ADJ
ejpam-5839	715	3	and	and	CCONJ
ejpam-5839	715	4	third	third	ADJ
ejpam-5839	715	5	requirements	requirement	NOUN
ejpam-5839	715	6	are	be	AUX
ejpam-5839	715	7	clear	clear	ADJ
ejpam-5839	715	8	,	,	PUNCT
ejpam-5839	715	9	and	and	CCONJ
ejpam-5839	715	10	we	we	PRON
ejpam-5839	715	11	move	move	VERB
ejpam-5839	715	12	forward	forward	ADV
ejpam-5839	715	13	as	as	SCONJ
ejpam-5839	715	14	follows	follow	VERB
ejpam-5839	715	15	for	for	ADP
ejpam-5839	715	16	the	the	DET
ejpam-5839	715	17	second	second	ADJ
ejpam-5839	715	18	condition	condition	NOUN
ejpam-5839	715	19	.	.	PUNCT
ejpam-5839	716	1	let	let	VERB
ejpam-5839	716	2	{	{	PUNCT
ejpam-5839	716	3	(	(	PUNCT
ejpam-5839	716	4	f̃i	f̃i	NOUN
ejpam-5839	716	5	,	,	PUNCT
ejpam-5839	716	6	ω	ω	NOUN
ejpam-5839	716	7	)	)	PUNCT
ejpam-5839	716	8	;	;	PUNCT
ejpam-5839	716	9	i	i	PRON
ejpam-5839	716	10	∈	∈	VERB
ejpam-5839	716	11	i	i	PRON
ejpam-5839	716	12	}	}	PUNCT
ejpam-5839	716	13	∈	∈	PROPN
ejpam-5839	716	14	τ1	τ1	NOUN
ejpam-5839	716	15	∩	∩	ADJ
ejpam-5839	716	16	τ2	τ2	NOUN
ejpam-5839	716	17	,	,	PUNCT
ejpam-5839	716	18	then	then	ADV
ejpam-5839	716	19	(	(	PUNCT
ejpam-5839	716	20	f̃i	f̃i	NOUN
ejpam-5839	716	21	,	,	PUNCT
ejpam-5839	716	22	ω	ω	NOUN
ejpam-5839	716	23	)	)	PUNCT
ejpam-5839	716	24	∈	∈	PROPN
ejpam-5839	716	25	τ1	τ1	NOUN
ejpam-5839	716	26	and	and	CCONJ
ejpam-5839	716	27	(	(	PUNCT
ejpam-5839	716	28	f̃i	f̃i	NOUN
ejpam-5839	716	29	,	,	PUNCT
ejpam-5839	716	30	ω	ω	NOUN
ejpam-5839	716	31	)	)	PUNCT
ejpam-5839	716	32	∈	∈	PROPN
ejpam-5839	716	33	τ2	τ2	NOUN
ejpam-5839	716	34	.	.	PUNCT
ejpam-5839	717	1	as	as	ADP
ejpam-5839	717	2	τ1	τ1	NOUN
ejpam-5839	717	3	and	and	CCONJ
ejpam-5839	717	4	τ2	τ2	NOUN
ejpam-5839	717	5	are	be	AUX
ejpam-5839	717	6	qpnsbtss	qpnsbtss	ADJ
ejpam-5839	717	7	on	on	ADP
ejpam-5839	717	8	x	x	NOUN
ejpam-5839	717	9	,	,	PUNCT
ejpam-5839	717	10	then	then	ADV
ejpam-5839	717	11	⋃	⋃	NOUN
ejpam-5839	717	12	i(f̃i	i(f̃i	NOUN
ejpam-5839	717	13	,	,	PUNCT
ejpam-5839	717	14	ω	ω	NOUN
ejpam-5839	717	15	)	)	PUNCT
ejpam-5839	717	16	∈	∈	PROPN
ejpam-5839	717	17	τ1	τ1	NOUN
ejpam-5839	717	18	and	and	CCONJ
ejpam-5839	717	19	⋃	⋃	PROPN
ejpam-5839	717	20	i(f̃i	i(f̃i	NOUN
ejpam-5839	717	21	,	,	PUNCT
ejpam-5839	717	22	ω	ω	NOUN
ejpam-5839	717	23	)	)	PUNCT
ejpam-5839	717	24	∈	∈	PROPN
ejpam-5839	717	25	τ2	τ2	NOUN
ejpam-5839	717	26	.	.	PUNCT
ejpam-5839	718	1	so	so	ADV
ejpam-5839	718	2	,	,	PUNCT
ejpam-5839	718	3	⋃	⋃	NOUN
ejpam-5839	718	4	i(f̃i	i(f̃i	NOUN
ejpam-5839	718	5	,	,	PUNCT
ejpam-5839	718	6	ω	ω	NOUN
ejpam-5839	718	7	)	)	PUNCT
ejpam-5839	718	8	∈	∈	PROPN
ejpam-5839	718	9	τ1	τ1	NOUN
ejpam-5839	718	10	∩	∩	ADJ
ejpam-5839	718	11	τ2	τ2	NOUN
ejpam-5839	718	12	.	.	PUNCT
ejpam-5839	719	1	definition	definition	NOUN
ejpam-5839	719	2	27	27	NUM
ejpam-5839	719	3	.	.	PUNCT
ejpam-5839	720	1	let	let	VERB
ejpam-5839	720	2	(	(	PUNCT
ejpam-5839	720	3	x	x	NOUN
ejpam-5839	720	4	,	,	PUNCT
ejpam-5839	720	5	τ1	τ1	NOUN
ejpam-5839	720	6	,	,	PUNCT
ejpam-5839	720	7	τ2,ω	τ2,ω	PUNCT
ejpam-5839	720	8	)	)	PUNCT
ejpam-5839	720	9	be	be	AUX
ejpam-5839	720	10	a	a	DET
ejpam-5839	720	11	qpnsbts	qpnsbt	NOUN
ejpam-5839	720	12	over	over	ADP
ejpam-5839	720	13	x	x	NOUN
ejpam-5839	720	14	,	,	PUNCT
ejpam-5839	720	15	and	and	CCONJ
ejpam-5839	720	16	let	let	VERB
ejpam-5839	720	17	(	(	PUNCT
ejpam-5839	720	18	˜̈υ	˜̈υ	PROPN
ejpam-5839	720	19	,	,	PUNCT
ejpam-5839	720	20	ω	ω	NOUN
ejpam-5839	720	21	)	)	PUNCT
ejpam-5839	720	22	be	be	AUX
ejpam-5839	720	23	a	a	DET
ejpam-5839	720	24	qpnss	qpnss	NOUN
ejpam-5839	720	25	.	.	PUNCT
ejpam-5839	721	1	then	then	ADV
ejpam-5839	721	2	,	,	PUNCT
ejpam-5839	721	3	(	(	PUNCT
ejpam-5839	721	4	i	i	NOUN
ejpam-5839	721	5	)	)	PUNCT
ejpam-5839	721	6	(	(	PUNCT
ejpam-5839	721	7	˜̈υ	˜̈υ	PROPN
ejpam-5839	721	8	,	,	PUNCT
ejpam-5839	721	9	ω	ω	NOUN
ejpam-5839	721	10	)	)	PUNCT
ejpam-5839	721	11	is	be	AUX
ejpam-5839	721	12	qpns	qpns	NOUN
ejpam-5839	721	13	semi	semi	ADJ
ejpam-5839	721	14	-	-	ADJ
ejpam-5839	721	15	open	open	ADJ
ejpam-5839	721	16	if	if	SCONJ
ejpam-5839	721	17	(	(	PUNCT
ejpam-5839	721	18	˜̈υ	˜̈υ	PROPN
ejpam-5839	721	19	,	,	PUNCT
ejpam-5839	721	20	ω	ω	NOUN
ejpam-5839	721	21	)	)	PUNCT
ejpam-5839	721	22	⊆	⊆	NUM
ejpam-5839	721	23	nscl(nsint	nscl(nsint	PROPN
ejpam-5839	721	24	(	(	PUNCT
ejpam-5839	721	25	˜̈υ	˜̈υ	PROPN
ejpam-5839	721	26	,	,	PUNCT
ejpam-5839	721	27	ω	ω	NOUN
ejpam-5839	721	28	)	)	PUNCT
ejpam-5839	721	29	)	)	PUNCT
ejpam-5839	721	30	(	(	PUNCT
ejpam-5839	721	31	ii	ii	NOUN
ejpam-5839	721	32	)	)	PUNCT
ejpam-5839	721	33	(	(	PUNCT
ejpam-5839	721	34	˜̈υ	˜̈υ	PROPN
ejpam-5839	721	35	,	,	PUNCT
ejpam-5839	721	36	ω	ω	NOUN
ejpam-5839	721	37	)	)	PUNCT
ejpam-5839	721	38	is	be	AUX
ejpam-5839	721	39	qpns	qpns	NOUN
ejpam-5839	721	40	pre	pre	ADJ
ejpam-5839	721	41	-	-	ADJ
ejpam-5839	721	42	open	open	ADJ
ejpam-5839	721	43	(	(	PUNCT
ejpam-5839	721	44	p	p	NOUN
ejpam-5839	721	45	-	-	PUNCT
ejpam-5839	721	46	open	open	ADJ
ejpam-5839	721	47	)	)	PUNCT
ejpam-5839	721	48	if	if	SCONJ
ejpam-5839	721	49	(	(	PUNCT
ejpam-5839	721	50	˜̈υ	˜̈υ	PROPN
ejpam-5839	721	51	,	,	PUNCT
ejpam-5839	721	52	ω	ω	NOUN
ejpam-5839	721	53	)	)	PUNCT
ejpam-5839	721	54	⊆	⊆	NUM
ejpam-5839	721	55	nsint(nscl	nsint(nscl	PROPN
ejpam-5839	721	56	(	(	PUNCT
ejpam-5839	721	57	˜̈υ	˜̈υ	PROPN
ejpam-5839	721	58	,	,	PUNCT
ejpam-5839	721	59	ω	ω	NOUN
ejpam-5839	721	60	)	)	PUNCT
ejpam-5839	721	61	)	)	PUNCT
ejpam-5839	721	62	(	(	PUNCT
ejpam-5839	721	63	iii	iii	NOUN
ejpam-5839	721	64	)	)	PUNCT
ejpam-5839	721	65	(	(	PUNCT
ejpam-5839	721	66	˜̈υ	˜̈υ	PROPN
ejpam-5839	721	67	,	,	PUNCT
ejpam-5839	721	68	ω	ω	NOUN
ejpam-5839	721	69	)	)	PUNCT
ejpam-5839	721	70	is	be	AUX
ejpam-5839	721	71	qpns	qpns	NOUN
ejpam-5839	721	72	∗b	∗b	NOUN
ejpam-5839	721	73	-	-	PUNCT
ejpam-5839	721	74	open	open	ADJ
ejpam-5839	721	75	if	if	SCONJ
ejpam-5839	721	76	(	(	PUNCT
ejpam-5839	721	77	˜̈υ	˜̈υ	PROPN
ejpam-5839	721	78	,	,	PUNCT
ejpam-5839	721	79	ω	ω	NOUN
ejpam-5839	721	80	)	)	PUNCT
ejpam-5839	721	81	⊆	⊆	NUM
ejpam-5839	721	82	nscl(nsint	nscl(nsint	PROPN
ejpam-5839	721	83	(	(	PUNCT
ejpam-5839	721	84	˜̈υ	˜̈υ	PROPN
ejpam-5839	721	85	,	,	PUNCT
ejpam-5839	721	86	ω	ω	NOUN
ejpam-5839	721	87	)	)	PUNCT
ejpam-5839	721	88	)	)	PUNCT
ejpam-5839	722	1	∪nsint(nscl	∪nsint(nscl	PROPN
ejpam-5839	722	2	(	(	PUNCT
ejpam-5839	722	3	˜̈υ	˜̈υ	PROPN
ejpam-5839	722	4	,	,	PUNCT
ejpam-5839	722	5	ω	ω	NOUN
ejpam-5839	722	6	)	)	PUNCT
ejpam-5839	722	7	)	)	PUNCT
ejpam-5839	722	8	(	(	PUNCT
ejpam-5839	722	9	iv	iv	X
ejpam-5839	722	10	)	)	PUNCT
ejpam-5839	722	11	(	(	PUNCT
ejpam-5839	722	12	˜̈υ	˜̈υ	PROPN
ejpam-5839	722	13	,	,	PUNCT
ejpam-5839	722	14	ω	ω	NOUN
ejpam-5839	722	15	)	)	PUNCT
ejpam-5839	722	16	is	be	AUX
ejpam-5839	722	17	qpns	qpns	NOUN
ejpam-5839	722	18	∗b	∗b	NOUN
ejpam-5839	722	19	-	-	PUNCT
ejpam-5839	722	20	close	close	NOUN
ejpam-5839	722	21	if	if	SCONJ
ejpam-5839	722	22	(	(	PUNCT
ejpam-5839	722	23	˜̈υ	˜̈υ	PROPN
ejpam-5839	722	24	,	,	PUNCT
ejpam-5839	722	25	ω	ω	NOUN
ejpam-5839	722	26	)	)	PUNCT
ejpam-5839	722	27	⊇	⊇	PROPN
ejpam-5839	722	28	nscl(nsint	nscl(nsint	PROPN
ejpam-5839	722	29	(	(	PUNCT
ejpam-5839	722	30	˜̈υ	˜̈υ	PROPN
ejpam-5839	722	31	,	,	PUNCT
ejpam-5839	722	32	ω	ω	NOUN
ejpam-5839	722	33	)	)	PUNCT
ejpam-5839	722	34	)	)	PUNCT
ejpam-5839	723	1	∩nsint(nscl	∩nsint(nscl	PROPN
ejpam-5839	723	2	(	(	PUNCT
ejpam-5839	723	3	˜̈υ	˜̈υ	PROPN
ejpam-5839	723	4	,	,	PUNCT
ejpam-5839	723	5	ω	ω	NOUN
ejpam-5839	723	6	)	)	PUNCT
ejpam-5839	723	7	)	)	PUNCT
ejpam-5839	723	8	definition	definition	NOUN
ejpam-5839	723	9	28	28	NUM
ejpam-5839	723	10	.	.	PUNCT
ejpam-5839	724	1	let	let	AUX
ejpam-5839	724	2	(	(	PUNCT
ejpam-5839	724	3	x	x	X
ejpam-5839	724	4	,	,	PUNCT
ejpam-5839	724	5	τ	τ	PROPN
ejpam-5839	724	6	,	,	PUNCT
ejpam-5839	724	7	ω	ω	NOUN
ejpam-5839	724	8	)	)	PUNCT
ejpam-5839	724	9	be	be	VERB
ejpam-5839	724	10	a	a	DET
ejpam-5839	724	11	quadripartitioned	quadripartitione	VERB
ejpam-5839	724	12	neutrosophic	neutrosophic	ADJ
ejpam-5839	724	13	soft	soft	ADJ
ejpam-5839	724	14	topological	topological	ADJ
ejpam-5839	724	15	space	space	NOUN
ejpam-5839	724	16	over	over	ADP
ejpam-5839	724	17	x	x	PUNCT
ejpam-5839	724	18	and	and	CCONJ
ejpam-5839	724	19	(	(	PUNCT
ejpam-5839	724	20	f̃	f̃	PROPN
ejpam-5839	724	21	,	,	PUNCT
ejpam-5839	724	22	ω	ω	NUM
ejpam-5839	724	23	)	)	PUNCT
ejpam-5839	724	24	∈	∈	PROPN
ejpam-5839	724	25	qpnss(x	qpnss(x	PROPN
ejpam-5839	724	26	,	,	PUNCT
ejpam-5839	724	27	ω	ω	NOUN
ejpam-5839	724	28	)	)	PUNCT
ejpam-5839	724	29	.	.	PUNCT
ejpam-5839	725	1	then	then	ADV
ejpam-5839	725	2	,	,	PUNCT
ejpam-5839	725	3	the	the	DET
ejpam-5839	725	4	collection	collection	NOUN
ejpam-5839	725	5	τ(f̃	τ(f̃	PROPN
ejpam-5839	725	6	,	,	PUNCT
ejpam-5839	725	7	ω	ω	NOUN
ejpam-5839	725	8	)	)	PUNCT
ejpam-5839	725	9	=	=	PRON
ejpam-5839	725	10	{	{	PUNCT
ejpam-5839	725	11	(	(	PUNCT
ejpam-5839	725	12	f̃	f̃	PROPN
ejpam-5839	725	13	,	,	PUNCT
ejpam-5839	725	14	ω	ω	NOUN
ejpam-5839	725	15	)	)	PUNCT
ejpam-5839	725	16	∩	∩	NOUN
ejpam-5839	725	17	(	(	PUNCT
ejpam-5839	725	18	g̃,ω	g̃,ω	PROPN
ejpam-5839	725	19	)	)	PUNCT
ejpam-5839	725	20	:	:	PUNCT
ejpam-5839	725	21	(	(	PUNCT
ejpam-5839	725	22	g̃,ω	g̃,ω	NOUN
ejpam-5839	725	23	)	)	PUNCT
ejpam-5839	725	24	∈	∈	PROPN
ejpam-5839	725	25	τ	τ	X
ejpam-5839	725	26	for	for	ADP
ejpam-5839	725	27	i	i	PRON
ejpam-5839	725	28	∈	∈	PROPN
ejpam-5839	726	1	i	i	PRON
ejpam-5839	726	2	}	}	PUNCT
ejpam-5839	726	3	is	be	AUX
ejpam-5839	726	4	called	call	VERB
ejpam-5839	726	5	a	a	DET
ejpam-5839	726	6	quadripartitioned	quadripartitione	VERB
ejpam-5839	726	7	neutrosophic	neutrosophic	ADJ
ejpam-5839	726	8	soft	soft	ADJ
ejpam-5839	726	9	subspace	subspace	NOUN
ejpam-5839	726	10	topology	topology	NOUN
ejpam-5839	726	11	on	on	ADP
ejpam-5839	726	12	(	(	PUNCT
ejpam-5839	726	13	f̃	f̃	PROPN
ejpam-5839	726	14	,	,	PUNCT
ejpam-5839	726	15	ω	ω	PROPN
ejpam-5839	726	16	)	)	PUNCT
ejpam-5839	726	17	,	,	PUNCT
ejpam-5839	726	18	and	and	CCONJ
ejpam-5839	726	19	(	(	PUNCT
ejpam-5839	726	20	τ(f	τ(f	PROPN
ejpam-5839	726	21	,	,	PUNCT
ejpam-5839	726	22	ω	ω	NOUN
ejpam-5839	726	23	)	)	PUNCT
ejpam-5839	726	24	,	,	PUNCT
ejpam-5839	726	25	τ(f̃	τ(f̃	PRON
ejpam-5839	726	26	,	,	PUNCT
ejpam-5839	726	27	ω),ω	ω),ω	PROPN
ejpam-5839	726	28	)	)	PUNCT
ejpam-5839	726	29	is	be	AUX
ejpam-5839	726	30	called	call	VERB
ejpam-5839	726	31	a	a	DET
ejpam-5839	726	32	quadripartitioned	quadripartitione	VERB
ejpam-5839	726	33	neutrosophic	neutrosophic	ADJ
ejpam-5839	726	34	soft	soft	ADJ
ejpam-5839	726	35	topological	topological	ADJ
ejpam-5839	726	36	subspace	subspace	NOUN
ejpam-5839	726	37	of	of	ADP
ejpam-5839	726	38	(	(	PUNCT
ejpam-5839	726	39	x	x	PROPN
ejpam-5839	726	40	,	,	PUNCT
ejpam-5839	726	41	τ	τ	PROPN
ejpam-5839	726	42	,	,	PUNCT
ejpam-5839	726	43	ω	ω	NOUN
ejpam-5839	726	44	)	)	PUNCT
ejpam-5839	726	45	.	.	PUNCT
ejpam-5839	727	1	in	in	ADP
ejpam-5839	727	2	order	order	NOUN
ejpam-5839	727	3	for	for	SCONJ
ejpam-5839	727	4	the	the	DET
ejpam-5839	727	5	above	above	ADJ
ejpam-5839	727	6	definition	definition	NOUN
ejpam-5839	727	7	to	to	PART
ejpam-5839	727	8	be	be	AUX
ejpam-5839	727	9	consistent	consistent	ADJ
ejpam-5839	727	10	,	,	PUNCT
ejpam-5839	727	11	we	we	PRON
ejpam-5839	727	12	must	must	AUX
ejpam-5839	727	13	prove	prove	VERB
ejpam-5839	727	14	that	that	SCONJ
ejpam-5839	727	15	(	(	PUNCT
ejpam-5839	727	16	τ(f	τ(f	PROPN
ejpam-5839	727	17	,	,	PUNCT
ejpam-5839	727	18	ω	ω	NOUN
ejpam-5839	727	19	)	)	PUNCT
ejpam-5839	727	20	,	,	PUNCT
ejpam-5839	727	21	τ(f̃	τ(f̃	PRON
ejpam-5839	727	22	,	,	PUNCT
ejpam-5839	727	23	ω),ω	ω),ω	PROPN
ejpam-5839	727	24	)	)	PUNCT
ejpam-5839	727	25	is	be	AUX
ejpam-5839	727	26	actually	actually	ADV
ejpam-5839	727	27	a	a	DET
ejpam-5839	727	28	quadripartitioned	quadripartitione	VERB
ejpam-5839	727	29	neutrosophic	neutrosophic	ADJ
ejpam-5839	727	30	soft	soft	ADJ
ejpam-5839	727	31	topology	topology	NOUN
ejpam-5839	727	32	for	for	ADP
ejpam-5839	727	33	(	(	PUNCT
ejpam-5839	727	34	f̃	f̃	PROPN
ejpam-5839	727	35	,	,	PUNCT
ejpam-5839	727	36	ω	ω	PROPN
ejpam-5839	727	37	)	)	PUNCT
ejpam-5839	727	38	.	.	PUNCT
ejpam-5839	728	1	theorem	theorem	ADJ
ejpam-5839	728	2	10	10	NUM
ejpam-5839	728	3	.	.	PUNCT
ejpam-5839	729	1	let	let	VERB
ejpam-5839	729	2	(	(	PUNCT
ejpam-5839	729	3	x	x	X
ejpam-5839	729	4	,	,	PUNCT
ejpam-5839	729	5	τ	τ	PROPN
ejpam-5839	729	6	,	,	PUNCT
ejpam-5839	729	7	ω	ω	NOUN
ejpam-5839	729	8	)	)	PUNCT
ejpam-5839	729	9	be	be	VERB
ejpam-5839	729	10	a	a	DET
ejpam-5839	729	11	quadripartitioned	quadripartitione	VERB
ejpam-5839	729	12	neutrosophic	neutrosophic	ADJ
ejpam-5839	729	13	soft	soft	ADJ
ejpam-5839	729	14	topological	topological	ADJ
ejpam-5839	729	15	space	space	NOUN
ejpam-5839	729	16	over	over	ADP
ejpam-5839	729	17	x	x	PUNCT
ejpam-5839	729	18	and	and	CCONJ
ejpam-5839	729	19	(	(	PUNCT
ejpam-5839	729	20	f̃	f̃	PROPN
ejpam-5839	729	21	,	,	PUNCT
ejpam-5839	729	22	ω	ω	NUM
ejpam-5839	729	23	)	)	PUNCT
ejpam-5839	729	24	∈	∈	PROPN
ejpam-5839	729	25	qpnss(x	qpnss(x	PROPN
ejpam-5839	729	26	,	,	PUNCT
ejpam-5839	729	27	ω	ω	NOUN
ejpam-5839	729	28	)	)	PUNCT
ejpam-5839	729	29	.	.	PUNCT
ejpam-5839	730	1	then	then	ADV
ejpam-5839	730	2	,	,	PUNCT
ejpam-5839	730	3	the	the	DET
ejpam-5839	730	4	collection	collection	NOUN
ejpam-5839	730	5	τ(f̃	τ(f̃	PROPN
ejpam-5839	730	6	,	,	PUNCT
ejpam-5839	730	7	ω	ω	NOUN
ejpam-5839	730	8	)	)	PUNCT
ejpam-5839	730	9	=	=	PRON
ejpam-5839	730	10	{	{	PUNCT
ejpam-5839	730	11	(	(	PUNCT
ejpam-5839	730	12	f̃	f̃	PROPN
ejpam-5839	730	13	,	,	PUNCT
ejpam-5839	730	14	ω	ω	NOUN
ejpam-5839	730	15	)	)	PUNCT
ejpam-5839	730	16	∩	∩	NOUN
ejpam-5839	730	17	(	(	PUNCT
ejpam-5839	730	18	g̃,ω	g̃,ω	PROPN
ejpam-5839	730	19	)	)	PUNCT
ejpam-5839	730	20	:	:	PUNCT
ejpam-5839	730	21	(	(	PUNCT
ejpam-5839	730	22	g̃,ω	g̃,ω	NOUN
ejpam-5839	730	23	)	)	PUNCT
ejpam-5839	730	24	∈	∈	PROPN
ejpam-5839	730	25	τ	τ	PROPN
ejpam-5839	730	26	}	}	PUNCT
ejpam-5839	730	27	is	be	AUX
ejpam-5839	730	28	a	a	DET
ejpam-5839	730	29	quadripartitioned	quadripartitione	VERB
ejpam-5839	730	30	neutrosophic	neutrosophic	ADJ
ejpam-5839	730	31	soft	soft	ADJ
ejpam-5839	730	32	topology	topology	NOUN
ejpam-5839	730	33	on	on	ADP
ejpam-5839	730	34	(	(	PUNCT
ejpam-5839	730	35	f̃	f̃	PROPN
ejpam-5839	730	36	,	,	PUNCT
ejpam-5839	730	37	ω	ω	PROPN
ejpam-5839	730	38	)	)	PUNCT
ejpam-5839	730	39	,	,	PUNCT
ejpam-5839	730	40	and	and	CCONJ
ejpam-5839	730	41	(	(	PUNCT
ejpam-5839	730	42	x(f	x(f	PROPN
ejpam-5839	730	43	,	,	PUNCT
ejpam-5839	730	44	ω	ω	NOUN
ejpam-5839	730	45	)	)	PUNCT
ejpam-5839	730	46	,	,	PUNCT
ejpam-5839	730	47	τ(f̃	τ(f̃	PRON
ejpam-5839	730	48	,	,	PUNCT
ejpam-5839	730	49	ω),ω	ω),ω	PROPN
ejpam-5839	730	50	)	)	PUNCT
ejpam-5839	730	51	is	be	AUX
ejpam-5839	730	52	a	a	DET
ejpam-5839	730	53	quadripartitioned	quadripartitione	VERB
ejpam-5839	730	54	neutrosophic	neutrosophic	ADJ
ejpam-5839	730	55	soft	soft	ADJ
ejpam-5839	730	56	topological	topological	ADJ
ejpam-5839	730	57	space	space	NOUN
ejpam-5839	730	58	of	of	ADP
ejpam-5839	730	59	(	(	PUNCT
ejpam-5839	730	60	x	x	PROPN
ejpam-5839	730	61	,	,	PUNCT
ejpam-5839	730	62	τ	τ	PROPN
ejpam-5839	730	63	,	,	PUNCT
ejpam-5839	730	64	ω	ω	NOUN
ejpam-5839	730	65	)	)	PUNCT
ejpam-5839	730	66	.	.	PUNCT
ejpam-5839	731	1	a.	a.	PROPN
ejpam-5839	731	2	shihadeh	shihadeh	VERB
ejpam-5839	731	3	et	et	PROPN
ejpam-5839	731	4	al	al	PROPN
ejpam-5839	731	5	.	.	PUNCT
ejpam-5839	731	6	/	/	SYM
ejpam-5839	731	7	eur	eur	PROPN
ejpam-5839	731	8	.	.	PUNCT
ejpam-5839	732	1	j.	j.	PROPN
ejpam-5839	732	2	pure	pure	PROPN
ejpam-5839	732	3	appl	appl	PROPN
ejpam-5839	732	4	.	.	PROPN
ejpam-5839	732	5	math	math	PROPN
ejpam-5839	732	6	,	,	PUNCT
ejpam-5839	732	7	18	18	NUM
ejpam-5839	732	8	(	(	PUNCT
ejpam-5839	732	9	2	2	NUM
ejpam-5839	732	10	)	)	PUNCT
ejpam-5839	732	11	(	(	PUNCT
ejpam-5839	732	12	2025	2025	NUM
ejpam-5839	732	13	)	)	PUNCT
ejpam-5839	732	14	,	,	PUNCT
ejpam-5839	732	15	5839	5839	NUM
ejpam-5839	732	16	32	32	NUM
ejpam-5839	732	17	of	of	ADP
ejpam-5839	732	18	54	54	NUM
ejpam-5839	732	19	proof	proof	NOUN
ejpam-5839	732	20	.	.	PUNCT
ejpam-5839	733	1	(	(	PUNCT
ejpam-5839	733	2	1	1	X
ejpam-5839	733	3	)	)	PUNCT
ejpam-5839	733	4	since	since	SCONJ
ejpam-5839	733	5	0(f̃	0(f̃	NUM
ejpam-5839	733	6	,	,	PUNCT
ejpam-5839	733	7	ω	ω	PROPN
ejpam-5839	733	8	)	)	PUNCT
ejpam-5839	733	9	,	,	PUNCT
ejpam-5839	733	10	1(f̃	1(f̃	NUM
ejpam-5839	733	11	,	,	PUNCT
ejpam-5839	733	12	ω	ω	NUM
ejpam-5839	733	13	)	)	PUNCT
ejpam-5839	733	14	∈	∈	PROPN
ejpam-5839	733	15	(	(	PUNCT
ejpam-5839	733	16	x	x	X
ejpam-5839	733	17	,	,	PUNCT
ejpam-5839	733	18	τ	τ	PROPN
ejpam-5839	733	19	,	,	PUNCT
ejpam-5839	733	20	ω	ω	NOUN
ejpam-5839	733	21	)	)	PUNCT
ejpam-5839	733	22	,	,	PUNCT
ejpam-5839	733	23	so	so	CCONJ
ejpam-5839	733	24	by	by	ADP
ejpam-5839	733	25	definition	definition	NOUN
ejpam-5839	733	26	:	:	PUNCT
ejpam-5839	733	27	0(f̃	0(f̃	NUM
ejpam-5839	733	28	,	,	PUNCT
ejpam-5839	733	29	ω	ω	NUM
ejpam-5839	733	30	)	)	PUNCT
ejpam-5839	733	31	∩	∩	NOUN
ejpam-5839	733	32	(	(	PUNCT
ejpam-5839	733	33	f̃	f̃	PROPN
ejpam-5839	733	34	,	,	PUNCT
ejpam-5839	733	35	ω	ω	NUM
ejpam-5839	733	36	)	)	PUNCT
ejpam-5839	733	37	=	=	SYM
ejpam-5839	733	38	0(f̃	0(f̃	PROPN
ejpam-5839	733	39	,	,	PUNCT
ejpam-5839	733	40	ω	ω	PROPN
ejpam-5839	733	41	)	)	PUNCT
ejpam-5839	733	42	,	,	PUNCT
ejpam-5839	733	43	1(f̃	1(f̃	NUM
ejpam-5839	733	44	,	,	PUNCT
ejpam-5839	733	45	ω	ω	NUM
ejpam-5839	733	46	)	)	PUNCT
ejpam-5839	733	47	∩	∩	NOUN
ejpam-5839	733	48	(	(	PUNCT
ejpam-5839	733	49	f̃	f̃	PROPN
ejpam-5839	733	50	,	,	PUNCT
ejpam-5839	733	51	ω	ω	NOUN
ejpam-5839	733	52	)	)	PUNCT
ejpam-5839	733	53	=	=	SYM
ejpam-5839	733	54	(	(	PUNCT
ejpam-5839	733	55	f̃	f̃	PROPN
ejpam-5839	733	56	,	,	PUNCT
ejpam-5839	733	57	ω	ω	PROPN
ejpam-5839	733	58	)	)	PUNCT
ejpam-5839	733	59	.	.	PUNCT
ejpam-5839	734	1	thus	thus	ADV
ejpam-5839	734	2	,	,	PUNCT
ejpam-5839	734	3	0(f̃	0(f̃	NUM
ejpam-5839	734	4	,	,	PUNCT
ejpam-5839	734	5	ω	ω	PROPN
ejpam-5839	734	6	)	)	PUNCT
ejpam-5839	734	7	,	,	PUNCT
ejpam-5839	734	8	(	(	PUNCT
ejpam-5839	734	9	f̃	f̃	PROPN
ejpam-5839	734	10	,	,	PUNCT
ejpam-5839	734	11	ω	ω	NUM
ejpam-5839	734	12	)	)	PUNCT
ejpam-5839	734	13	∈	∈	PROPN
ejpam-5839	734	14	τ(f̃	τ(f̃	NOUN
ejpam-5839	734	15	,	,	PUNCT
ejpam-5839	734	16	ω	ω	NOUN
ejpam-5839	734	17	)	)	PUNCT
ejpam-5839	734	18	.	.	PUNCT
ejpam-5839	735	1	(	(	PUNCT
ejpam-5839	735	2	2	2	X
ejpam-5839	735	3	)	)	PUNCT
ejpam-5839	735	4	let	let	VERB
ejpam-5839	735	5	{	{	PUNCT
ejpam-5839	735	6	(	(	PUNCT
ejpam-5839	735	7	h̃i	h̃i	PROPN
ejpam-5839	735	8	,	,	PUNCT
ejpam-5839	735	9	ω	ω	NOUN
ejpam-5839	735	10	)	)	PUNCT
ejpam-5839	735	11	:	:	PUNCT
ejpam-5839	736	1	i	i	PRON
ejpam-5839	736	2	∈	∈	VERB
ejpam-5839	736	3	i	i	PRON
ejpam-5839	736	4	}	}	PUNCT
ejpam-5839	736	5	be	be	VERB
ejpam-5839	736	6	a	a	DET
ejpam-5839	736	7	quadripartitioned	quadripartitione	VERB
ejpam-5839	736	8	neutrosophic	neutrosophic	ADJ
ejpam-5839	736	9	soft	soft	ADJ
ejpam-5839	736	10	sub	sub	NOUN
ejpam-5839	736	11	-	-	NOUN
ejpam-5839	736	12	collection	collection	NOUN
ejpam-5839	736	13	of	of	ADP
ejpam-5839	736	14	τ(f̃	τ(f̃	PROPN
ejpam-5839	736	15	,	,	PUNCT
ejpam-5839	736	16	ω	ω	NOUN
ejpam-5839	736	17	)	)	PUNCT
ejpam-5839	736	18	.	.	PUNCT
ejpam-5839	737	1	then	then	ADV
ejpam-5839	737	2	(	(	PUNCT
ejpam-5839	737	3	h̃i	h̃i	PROPN
ejpam-5839	737	4	,	,	PUNCT
ejpam-5839	737	5	ω	ω	NOUN
ejpam-5839	737	6	)	)	PUNCT
ejpam-5839	737	7	∈	∈	PROPN
ejpam-5839	737	8	τ(f̃	τ(f̃	NOUN
ejpam-5839	737	9	,	,	PUNCT
ejpam-5839	737	10	ω	ω	NOUN
ejpam-5839	737	11	)	)	PUNCT
ejpam-5839	737	12	for	for	ADP
ejpam-5839	737	13	all	all	PRON
ejpam-5839	737	14	i	i	PRON
ejpam-5839	737	15	∈	∈	PROPN
ejpam-5839	738	1	i	i	PRON
ejpam-5839	738	2	,	,	PUNCT
ejpam-5839	738	3	so	so	ADV
ejpam-5839	738	4	by	by	ADP
ejpam-5839	738	5	definition	definition	NOUN
ejpam-5839	738	6	,	,	PUNCT
ejpam-5839	738	7	this	this	PRON
ejpam-5839	738	8	implies	imply	VERB
ejpam-5839	738	9	that	that	SCONJ
ejpam-5839	738	10	:	:	PUNCT
ejpam-5839	738	11	(	(	PUNCT
ejpam-5839	738	12	h̃i	h̃i	PROPN
ejpam-5839	738	13	,	,	PUNCT
ejpam-5839	738	14	ω	ω	NOUN
ejpam-5839	738	15	)	)	PUNCT
ejpam-5839	738	16	=	=	SYM
ejpam-5839	738	17	(	(	PUNCT
ejpam-5839	738	18	f̃	f̃	PROPN
ejpam-5839	738	19	,	,	PUNCT
ejpam-5839	738	20	ω	ω	NOUN
ejpam-5839	738	21	)	)	PUNCT
ejpam-5839	738	22	∩	∩	NOUN
ejpam-5839	738	23	(	(	PUNCT
ejpam-5839	738	24	g̃i	g̃i	NOUN
ejpam-5839	738	25	,	,	PUNCT
ejpam-5839	738	26	ω	ω	NOUN
ejpam-5839	738	27	)	)	PUNCT
ejpam-5839	738	28	for	for	ADP
ejpam-5839	738	29	some	some	DET
ejpam-5839	738	30	(	(	PUNCT
ejpam-5839	738	31	g̃i	g̃i	PROPN
ejpam-5839	738	32	,	,	PUNCT
ejpam-5839	738	33	ω	ω	NOUN
ejpam-5839	738	34	)	)	PUNCT
ejpam-5839	738	35	∈	∈	PROPN
ejpam-5839	738	36	τ	τ	PROPN
ejpam-5839	738	37	.	.	PUNCT
ejpam-5839	739	1	taking	take	VERB
ejpam-5839	739	2	the	the	DET
ejpam-5839	739	3	union	union	NOUN
ejpam-5839	739	4	,	,	PUNCT
ejpam-5839	739	5	we	we	PRON
ejpam-5839	739	6	obtain:⋃	obtain:⋃	VERB
ejpam-5839	739	7	i∈i	i∈i	ADV
ejpam-5839	739	8	(	(	PUNCT
ejpam-5839	739	9	h̃i	h̃i	PROPN
ejpam-5839	739	10	,	,	PUNCT
ejpam-5839	739	11	ω	ω	NOUN
ejpam-5839	739	12	)	)	PUNCT
ejpam-5839	740	1	=	=	SYM
ejpam-5839	740	2	⋃	⋃	NOUN
ejpam-5839	740	3	i∈i	i∈i	ADJ
ejpam-5839	740	4	(	(	PUNCT
ejpam-5839	740	5	(	(	PUNCT
ejpam-5839	740	6	f̃	f̃	PROPN
ejpam-5839	740	7	,	,	PUNCT
ejpam-5839	740	8	ω	ω	NOUN
ejpam-5839	740	9	)	)	PUNCT
ejpam-5839	740	10	∩	∩	NOUN
ejpam-5839	740	11	(	(	PUNCT
ejpam-5839	740	12	g̃i	g̃i	NOUN
ejpam-5839	740	13	,	,	PUNCT
ejpam-5839	740	14	ω	ω	NOUN
ejpam-5839	740	15	)	)	PUNCT
ejpam-5839	740	16	)	)	PUNCT
ejpam-5839	741	1	=	=	SYM
ejpam-5839	742	1	(	(	PUNCT
ejpam-5839	742	2	f̃	f̃	PROPN
ejpam-5839	742	3	,	,	PUNCT
ejpam-5839	742	4	ω	ω	NOUN
ejpam-5839	742	5	)	)	PUNCT
ejpam-5839	742	6	∩	∩	NOUN
ejpam-5839	742	7	(	(	PUNCT
ejpam-5839	742	8	⋃	⋃	PROPN
ejpam-5839	742	9	i∈i	i∈i	ADJ
ejpam-5839	742	10	(	(	PUNCT
ejpam-5839	742	11	g̃i	g̃i	NOUN
ejpam-5839	742	12	,	,	PUNCT
ejpam-5839	742	13	ω	ω	NOUN
ejpam-5839	742	14	)	)	PUNCT
ejpam-5839	742	15	)	)	PUNCT
ejpam-5839	742	16	.	.	PUNCT
ejpam-5839	743	1	since	since	SCONJ
ejpam-5839	743	2	(	(	PUNCT
ejpam-5839	743	3	g̃i	g̃i	NOUN
ejpam-5839	743	4	,	,	PUNCT
ejpam-5839	743	5	ω	ω	NOUN
ejpam-5839	743	6	)	)	PUNCT
ejpam-5839	743	7	∈	∈	PROPN
ejpam-5839	743	8	τ	τ	PROPN
ejpam-5839	743	9	for	for	ADP
ejpam-5839	743	10	all	all	PRON
ejpam-5839	743	11	i	i	PRON
ejpam-5839	743	12	∈	∈	VERB
ejpam-5839	744	1	i	i	PRON
ejpam-5839	744	2	and	and	CCONJ
ejpam-5839	744	3	τ	τ	PROPN
ejpam-5839	744	4	is	be	AUX
ejpam-5839	744	5	a	a	DET
ejpam-5839	744	6	quadripartitioned	quadripartitione	VERB
ejpam-5839	744	7	neutrosophic	neutrosophic	ADJ
ejpam-5839	744	8	soft	soft	ADJ
ejpam-5839	744	9	topological	topological	ADJ
ejpam-5839	744	10	space	space	NOUN
ejpam-5839	744	11	,	,	PUNCT
ejpam-5839	744	12	we	we	PRON
ejpam-5839	744	13	conclude	conclude	VERB
ejpam-5839	744	14	that	that	PRON
ejpam-5839	744	15	:	:	PUNCT
ejpam-5839	744	16	⋃	⋃	PUNCT
ejpam-5839	744	17	i∈i	i∈i	ADJ
ejpam-5839	744	18	(	(	PUNCT
ejpam-5839	744	19	g̃i	g̃i	NOUN
ejpam-5839	744	20	,	,	PUNCT
ejpam-5839	744	21	ω	ω	NOUN
ejpam-5839	744	22	)	)	PUNCT
ejpam-5839	744	23	∈	∈	PROPN
ejpam-5839	744	24	τ	τ	PROPN
ejpam-5839	744	25	.	.	PUNCT
ejpam-5839	745	1	thus	thus	ADV
ejpam-5839	745	2	,	,	PUNCT
ejpam-5839	745	3	(	(	PUNCT
ejpam-5839	745	4	f̃	f̃	PROPN
ejpam-5839	745	5	,	,	PUNCT
ejpam-5839	745	6	ω	ω	NOUN
ejpam-5839	745	7	)	)	PUNCT
ejpam-5839	745	8	∩	∩	NOUN
ejpam-5839	745	9	(	(	PUNCT
ejpam-5839	745	10	⋃	⋃	PROPN
ejpam-5839	745	11	i∈i	i∈i	ADJ
ejpam-5839	745	12	(	(	PUNCT
ejpam-5839	745	13	g̃i	g̃i	NOUN
ejpam-5839	745	14	,	,	PUNCT
ejpam-5839	745	15	ω	ω	NOUN
ejpam-5839	745	16	)	)	PUNCT
ejpam-5839	745	17	)	)	PUNCT
ejpam-5839	745	18	∈	∈	PROPN
ejpam-5839	745	19	τ(f̃	τ(f̃	NOUN
ejpam-5839	745	20	,	,	PUNCT
ejpam-5839	745	21	ω	ω	NOUN
ejpam-5839	745	22	)	)	PUNCT
ejpam-5839	745	23	,	,	PUNCT
ejpam-5839	745	24	implying	imply	VERB
ejpam-5839	745	25	that	that	SCONJ
ejpam-5839	745	26	⋃	⋃	PROPN
ejpam-5839	745	27	i∈i(h̃i	i∈i(h̃i	PROPN
ejpam-5839	745	28	,	,	PUNCT
ejpam-5839	745	29	ω	ω	NOUN
ejpam-5839	745	30	)	)	PUNCT
ejpam-5839	745	31	∈	∈	PROPN
ejpam-5839	745	32	τ(f̃	τ(f̃	NOUN
ejpam-5839	745	33	,	,	PUNCT
ejpam-5839	745	34	ω	ω	NOUN
ejpam-5839	745	35	)	)	PUNCT
ejpam-5839	745	36	.	.	PUNCT
ejpam-5839	746	1	(	(	PUNCT
ejpam-5839	746	2	3	3	X
ejpam-5839	746	3	)	)	PUNCT
ejpam-5839	746	4	now	now	ADV
ejpam-5839	746	5	,	,	PUNCT
ejpam-5839	746	6	let	let	VERB
ejpam-5839	746	7	(	(	PUNCT
ejpam-5839	746	8	h̃1,ω	h̃1,ω	PROPN
ejpam-5839	746	9	)	)	PUNCT
ejpam-5839	746	10	,	,	PUNCT
ejpam-5839	746	11	(	(	PUNCT
ejpam-5839	746	12	h̃2,ω	h̃2,ω	NOUN
ejpam-5839	746	13	)	)	PUNCT
ejpam-5839	746	14	,	,	PUNCT
ejpam-5839	746	15	.	.	PUNCT
ejpam-5839	746	16	.	.	PUNCT
ejpam-5839	747	1	.	.	PUNCT
ejpam-5839	748	1	,	,	PUNCT
ejpam-5839	748	2	(	(	PUNCT
ejpam-5839	748	3	h̃n	h̃n	NOUN
ejpam-5839	748	4	,	,	PUNCT
ejpam-5839	748	5	ω	ω	NOUN
ejpam-5839	748	6	)	)	PUNCT
ejpam-5839	748	7	∈	∈	PROPN
ejpam-5839	748	8	τ(f̃	τ(f̃	NOUN
ejpam-5839	748	9	,	,	PUNCT
ejpam-5839	748	10	ω	ω	NOUN
ejpam-5839	748	11	)	)	PUNCT
ejpam-5839	748	12	.	.	PUNCT
ejpam-5839	749	1	then	then	ADV
ejpam-5839	749	2	,	,	PUNCT
ejpam-5839	749	3	for	for	ADP
ejpam-5839	749	4	all	all	DET
ejpam-5839	749	5	i	i	PRON
ejpam-5839	749	6	=	=	NOUN
ejpam-5839	749	7	1	1	NUM
ejpam-5839	749	8	,	,	PUNCT
ejpam-5839	749	9	2	2	NUM
ejpam-5839	749	10	,	,	PUNCT
ejpam-5839	749	11	.	.	PUNCT
ejpam-5839	749	12	.	.	PUNCT
ejpam-5839	749	13	.	.	PUNCT
ejpam-5839	750	1	,	,	PUNCT
ejpam-5839	750	2	n	n	CCONJ
ejpam-5839	750	3	,	,	PUNCT
ejpam-5839	750	4	we	we	PRON
ejpam-5839	750	5	have	have	VERB
ejpam-5839	750	6	:	:	PUNCT
ejpam-5839	750	7	(	(	PUNCT
ejpam-5839	750	8	h̃i	h̃i	PROPN
ejpam-5839	750	9	,	,	PUNCT
ejpam-5839	750	10	ω	ω	NOUN
ejpam-5839	750	11	)	)	PUNCT
ejpam-5839	750	12	=	=	SYM
ejpam-5839	750	13	(	(	PUNCT
ejpam-5839	750	14	f̃	f̃	PROPN
ejpam-5839	750	15	,	,	PUNCT
ejpam-5839	750	16	ω	ω	NOUN
ejpam-5839	750	17	)	)	PUNCT
ejpam-5839	751	1	∩	∩	NOUN
ejpam-5839	751	2	(	(	PUNCT
ejpam-5839	751	3	g̃i	g̃i	NOUN
ejpam-5839	751	4	,	,	PUNCT
ejpam-5839	751	5	ω	ω	NOUN
ejpam-5839	751	6	)	)	PUNCT
ejpam-5839	751	7	for	for	ADP
ejpam-5839	751	8	some	some	DET
ejpam-5839	751	9	(	(	PUNCT
ejpam-5839	751	10	g̃i	g̃i	PROPN
ejpam-5839	751	11	,	,	PUNCT
ejpam-5839	751	12	ω	ω	NOUN
ejpam-5839	751	13	)	)	PUNCT
ejpam-5839	751	14	∈	∈	PROPN
ejpam-5839	751	15	τ	τ	PROPN
ejpam-5839	751	16	.	.	PUNCT
ejpam-5839	752	1	taking	take	VERB
ejpam-5839	752	2	the	the	DET
ejpam-5839	752	3	intersection	intersection	NOUN
ejpam-5839	752	4	,	,	PUNCT
ejpam-5839	752	5	we	we	PRON
ejpam-5839	752	6	obtain	obtain	VERB
ejpam-5839	752	7	:	:	PUNCT
ejpam-5839	752	8	n⋂	n⋂	NOUN
ejpam-5839	752	9	i=1	i=1	PROPN
ejpam-5839	752	10	(	(	PUNCT
ejpam-5839	752	11	h̃i	h̃i	PROPN
ejpam-5839	752	12	,	,	PUNCT
ejpam-5839	752	13	ω	ω	NOUN
ejpam-5839	752	14	)	)	PUNCT
ejpam-5839	752	15	=	=	SYM
ejpam-5839	753	1	n⋂	n⋂	NOUN
ejpam-5839	753	2	i=1	i=1	X
ejpam-5839	754	1	(	(	PUNCT
ejpam-5839	754	2	(	(	PUNCT
ejpam-5839	754	3	f̃	f̃	PROPN
ejpam-5839	754	4	,	,	PUNCT
ejpam-5839	754	5	ω	ω	NOUN
ejpam-5839	754	6	)	)	PUNCT
ejpam-5839	754	7	∩	∩	NOUN
ejpam-5839	754	8	(	(	PUNCT
ejpam-5839	754	9	g̃i	g̃i	NOUN
ejpam-5839	754	10	,	,	PUNCT
ejpam-5839	754	11	ω	ω	NOUN
ejpam-5839	754	12	)	)	PUNCT
ejpam-5839	754	13	)	)	PUNCT
ejpam-5839	755	1	=	=	SYM
ejpam-5839	755	2	(	(	PUNCT
ejpam-5839	755	3	f̃	f̃	PROPN
ejpam-5839	755	4	,	,	PUNCT
ejpam-5839	755	5	ω	ω	NOUN
ejpam-5839	755	6	)	)	PUNCT
ejpam-5839	755	7	∩	∩	NOUN
ejpam-5839	755	8	(	(	PUNCT
ejpam-5839	755	9	n⋂	n⋂	NOUN
ejpam-5839	755	10	i=1	i=1	PROPN
ejpam-5839	755	11	(	(	PUNCT
ejpam-5839	755	12	g̃i	g̃i	PROPN
ejpam-5839	755	13	,	,	PUNCT
ejpam-5839	755	14	ω	ω	NOUN
ejpam-5839	755	15	)	)	PUNCT
ejpam-5839	755	16	)	)	PUNCT
ejpam-5839	755	17	.	.	PUNCT
ejpam-5839	756	1	since	since	SCONJ
ejpam-5839	756	2	(	(	PUNCT
ejpam-5839	756	3	g̃i	g̃i	NOUN
ejpam-5839	756	4	,	,	PUNCT
ejpam-5839	756	5	ω	ω	NOUN
ejpam-5839	756	6	)	)	PUNCT
ejpam-5839	756	7	∈	∈	PROPN
ejpam-5839	756	8	τ	τ	PROPN
ejpam-5839	756	9	for	for	ADP
ejpam-5839	756	10	all	all	DET
ejpam-5839	756	11	i	i	PRON
ejpam-5839	756	12	=	=	NOUN
ejpam-5839	756	13	1	1	NUM
ejpam-5839	756	14	,	,	PUNCT
ejpam-5839	756	15	2	2	NUM
ejpam-5839	756	16	,	,	PUNCT
ejpam-5839	756	17	.	.	PUNCT
ejpam-5839	756	18	.	.	PUNCT
ejpam-5839	756	19	.	.	PUNCT
ejpam-5839	757	1	,	,	PUNCT
ejpam-5839	757	2	n	n	PROPN
ejpam-5839	757	3	and	and	CCONJ
ejpam-5839	757	4	τ	τ	PROPN
ejpam-5839	757	5	is	be	AUX
ejpam-5839	757	6	a	a	DET
ejpam-5839	757	7	quadripartitioned	quadripartitione	VERB
ejpam-5839	757	8	neutrosophic	neutrosophic	ADJ
ejpam-5839	757	9	soft	soft	ADJ
ejpam-5839	757	10	topology	topology	NOUN
ejpam-5839	757	11	,	,	PUNCT
ejpam-5839	757	12	we	we	PRON
ejpam-5839	757	13	conclude	conclude	VERB
ejpam-5839	757	14	that	that	PRON
ejpam-5839	757	15	:	:	PUNCT
ejpam-5839	757	16	n⋂	n⋂	VERB
ejpam-5839	757	17	i=1	i=1	PROPN
ejpam-5839	758	1	(	(	PUNCT
ejpam-5839	758	2	g̃i	g̃i	PROPN
ejpam-5839	758	3	,	,	PUNCT
ejpam-5839	758	4	ω	ω	NOUN
ejpam-5839	758	5	)	)	PUNCT
ejpam-5839	758	6	∈	∈	PROPN
ejpam-5839	758	7	τ	τ	PROPN
ejpam-5839	758	8	.	.	PUNCT
ejpam-5839	759	1	therefore	therefore	ADV
ejpam-5839	759	2	,	,	PUNCT
ejpam-5839	759	3	(	(	PUNCT
ejpam-5839	759	4	f̃	f̃	PROPN
ejpam-5839	759	5	,	,	PUNCT
ejpam-5839	759	6	ω	ω	NOUN
ejpam-5839	759	7	)	)	PUNCT
ejpam-5839	759	8	∩	∩	NOUN
ejpam-5839	759	9	(	(	PUNCT
ejpam-5839	759	10	n⋂	n⋂	NOUN
ejpam-5839	759	11	i=1	i=1	PROPN
ejpam-5839	759	12	(	(	PUNCT
ejpam-5839	759	13	g̃i	g̃i	PROPN
ejpam-5839	759	14	,	,	PUNCT
ejpam-5839	759	15	ω	ω	NOUN
ejpam-5839	759	16	)	)	PUNCT
ejpam-5839	759	17	)	)	PUNCT
ejpam-5839	760	1	∈	∈	PROPN
ejpam-5839	760	2	τ(f̃	τ(f̃	NOUN
ejpam-5839	760	3	,	,	PUNCT
ejpam-5839	760	4	ω	ω	NOUN
ejpam-5839	760	5	)	)	PUNCT
ejpam-5839	760	6	,	,	PUNCT
ejpam-5839	760	7	implying	imply	VERB
ejpam-5839	760	8	that	that	SCONJ
ejpam-5839	760	9	⋂n	⋂n	PROPN
ejpam-5839	760	10	i=1(h̃i	i=1(h̃i	PROPN
ejpam-5839	760	11	,	,	PUNCT
ejpam-5839	760	12	ω	ω	NOUN
ejpam-5839	760	13	)	)	PUNCT
ejpam-5839	760	14	∈	∈	PROPN
ejpam-5839	760	15	τ(f̃	τ(f̃	NOUN
ejpam-5839	760	16	,	,	PUNCT
ejpam-5839	760	17	ω	ω	NOUN
ejpam-5839	760	18	)	)	PUNCT
ejpam-5839	760	19	.	.	PUNCT
ejpam-5839	761	1	thus	thus	ADV
ejpam-5839	761	2	,	,	PUNCT
ejpam-5839	761	3	τ(f̃	τ(f̃	ADJ
ejpam-5839	761	4	,	,	PUNCT
ejpam-5839	761	5	ω	ω	NOUN
ejpam-5839	761	6	)	)	PUNCT
ejpam-5839	761	7	=	=	PRON
ejpam-5839	761	8	{	{	PUNCT
ejpam-5839	761	9	(	(	PUNCT
ejpam-5839	761	10	f̃	f̃	PROPN
ejpam-5839	761	11	,	,	PUNCT
ejpam-5839	761	12	ω	ω	NOUN
ejpam-5839	761	13	)	)	PUNCT
ejpam-5839	761	14	∩	∩	NOUN
ejpam-5839	761	15	(	(	PUNCT
ejpam-5839	761	16	g̃,ω	g̃,ω	PROPN
ejpam-5839	761	17	)	)	PUNCT
ejpam-5839	761	18	:	:	PUNCT
ejpam-5839	761	19	(	(	PUNCT
ejpam-5839	761	20	g̃,ω	g̃,ω	NOUN
ejpam-5839	761	21	)	)	PUNCT
ejpam-5839	761	22	∈	∈	PROPN
ejpam-5839	761	23	τ	τ	PROPN
ejpam-5839	761	24	}	}	PUNCT
ejpam-5839	761	25	is	be	AUX
ejpam-5839	761	26	a	a	DET
ejpam-5839	761	27	quadripartitioned	quadripartitione	VERB
ejpam-5839	761	28	neutrosophic	neutrosophic	ADJ
ejpam-5839	761	29	soft	soft	ADJ
ejpam-5839	761	30	topology	topology	NOUN
ejpam-5839	761	31	on	on	ADP
ejpam-5839	761	32	(	(	PUNCT
ejpam-5839	761	33	f̃	f̃	PROPN
ejpam-5839	761	34	,	,	PUNCT
ejpam-5839	761	35	ω	ω	PROPN
ejpam-5839	761	36	)	)	PUNCT
ejpam-5839	761	37	.	.	PUNCT
ejpam-5839	762	1	a.	a.	PROPN
ejpam-5839	762	2	shihadeh	shihadeh	VERB
ejpam-5839	762	3	et	et	PROPN
ejpam-5839	762	4	al	al	PROPN
ejpam-5839	762	5	.	.	PUNCT
ejpam-5839	762	6	/	/	SYM
ejpam-5839	762	7	eur	eur	PROPN
ejpam-5839	762	8	.	.	PUNCT
ejpam-5839	763	1	j.	j.	PROPN
ejpam-5839	763	2	pure	pure	PROPN
ejpam-5839	763	3	appl	appl	PROPN
ejpam-5839	763	4	.	.	PROPN
ejpam-5839	763	5	math	math	PROPN
ejpam-5839	763	6	,	,	PUNCT
ejpam-5839	763	7	18	18	NUM
ejpam-5839	763	8	(	(	PUNCT
ejpam-5839	763	9	2	2	NUM
ejpam-5839	763	10	)	)	PUNCT
ejpam-5839	763	11	(	(	PUNCT
ejpam-5839	763	12	2025	2025	NUM
ejpam-5839	763	13	)	)	PUNCT
ejpam-5839	763	14	,	,	PUNCT
ejpam-5839	763	15	5839	5839	NUM
ejpam-5839	763	16	33	33	NUM
ejpam-5839	763	17	of	of	ADP
ejpam-5839	763	18	54	54	NUM
ejpam-5839	763	19	definition	definition	NOUN
ejpam-5839	763	20	29	29	NUM
ejpam-5839	763	21	.	.	PUNCT
ejpam-5839	764	1	let	let	VERB
ejpam-5839	764	2	(	(	PUNCT
ejpam-5839	764	3	x	x	NOUN
ejpam-5839	764	4	,	,	PUNCT
ejpam-5839	764	5	τ1	τ1	NOUN
ejpam-5839	764	6	,	,	PUNCT
ejpam-5839	764	7	τ2,ω	τ2,ω	PUNCT
ejpam-5839	764	8	)	)	PUNCT
ejpam-5839	764	9	be	be	AUX
ejpam-5839	764	10	a	a	DET
ejpam-5839	764	11	qpnsbts	qpnsbts	NOUN
ejpam-5839	764	12	over	over	ADP
ejpam-5839	764	13	x	x	PUNCT
ejpam-5839	764	14	and	and	CCONJ
ejpam-5839	764	15	(	(	PUNCT
ejpam-5839	764	16	˜̈υ	˜̈υ	PROPN
ejpam-5839	764	17	,	,	PUNCT
ejpam-5839	764	18	ω	ω	NOUN
ejpam-5839	764	19	)	)	PUNCT
ejpam-5839	764	20	be	be	AUX
ejpam-5839	764	21	a	a	DET
ejpam-5839	764	22	qpns	qpns	NOUN
ejpam-5839	764	23	.	.	PUNCT
ejpam-5839	765	1	then	then	ADV
ejpam-5839	765	2	the	the	DET
ejpam-5839	765	3	interior	interior	NOUN
ejpam-5839	765	4	of	of	ADP
ejpam-5839	765	5	(	(	PUNCT
ejpam-5839	765	6	˜̈υ	˜̈υ	PROPN
ejpam-5839	765	7	,	,	PUNCT
ejpam-5839	765	8	ω	ω	NOUN
ejpam-5839	765	9	)	)	PUNCT
ejpam-5839	765	10	,	,	PUNCT
ejpam-5839	765	11	designated	designate	VERB
ejpam-5839	765	12	by	by	ADP
ejpam-5839	765	13	(	(	PUNCT
ejpam-5839	765	14	˜̈υ	˜̈υ	PROPN
ejpam-5839	765	15	,	,	PUNCT
ejpam-5839	765	16	ω	ω	NOUN
ejpam-5839	765	17	)	)	PUNCT
ejpam-5839	765	18	◦	◦	NOUN
ejpam-5839	765	19	,	,	PUNCT
ejpam-5839	765	20	is	be	AUX
ejpam-5839	765	21	the	the	DET
ejpam-5839	765	22	union	union	NOUN
ejpam-5839	765	23	of	of	ADP
ejpam-5839	765	24	all	all	DET
ejpam-5839	765	25	qpns	qpns	NOUN
ejpam-5839	765	26	s	s	NOUN
ejpam-5839	765	27	-	-	ADJ
ejpam-5839	765	28	open	open	ADJ
ejpam-5839	765	29	sets	set	NOUN
ejpam-5839	765	30	of	of	ADP
ejpam-5839	765	31	(	(	PUNCT
ejpam-5839	765	32	˜̈υ	˜̈υ	PROPN
ejpam-5839	765	33	,	,	PUNCT
ejpam-5839	765	34	ω	ω	NOUN
ejpam-5839	765	35	)	)	PUNCT
ejpam-5839	765	36	.	.	PUNCT
ejpam-5839	766	1	clearly	clearly	ADV
ejpam-5839	766	2	,	,	PUNCT
ejpam-5839	766	3	(	(	PUNCT
ejpam-5839	766	4	˜̈υ	˜̈υ	PROPN
ejpam-5839	766	5	,	,	PUNCT
ejpam-5839	766	6	ω	ω	NOUN
ejpam-5839	766	7	)	)	PUNCT
ejpam-5839	766	8	◦	◦	NOUN
ejpam-5839	766	9	is	be	AUX
ejpam-5839	766	10	the	the	DET
ejpam-5839	766	11	largest	large	ADJ
ejpam-5839	766	12	qpns	qpns	NOUN
ejpam-5839	766	13	s	s	NOUN
ejpam-5839	766	14	-	-	NOUN
ejpam-5839	766	15	os	os	NOUN
ejpam-5839	766	16	that	that	PRON
ejpam-5839	766	17	is	be	AUX
ejpam-5839	766	18	contained	contain	VERB
ejpam-5839	766	19	in	in	ADP
ejpam-5839	766	20	(	(	PUNCT
ejpam-5839	766	21	˜̈υ	˜̈υ	PROPN
ejpam-5839	766	22	,	,	PUNCT
ejpam-5839	766	23	ω	ω	NOUN
ejpam-5839	766	24	)	)	PUNCT
ejpam-5839	766	25	.	.	PUNCT
ejpam-5839	767	1	definition	definition	NOUN
ejpam-5839	767	2	30	30	NUM
ejpam-5839	767	3	.	.	PUNCT
ejpam-5839	768	1	let	let	AUX
ejpam-5839	768	2	(	(	PUNCT
ejpam-5839	768	3	x	x	NOUN
ejpam-5839	768	4	,	,	PUNCT
ejpam-5839	768	5	τ1	τ1	NOUN
ejpam-5839	768	6	,	,	PUNCT
ejpam-5839	768	7	τ2,ω	τ2,ω	PUNCT
ejpam-5839	768	8	)	)	PUNCT
ejpam-5839	768	9	be	be	VERB
ejpam-5839	768	10	a	a	DET
ejpam-5839	768	11	qpnsbts	qpnsbt	NOUN
ejpam-5839	768	12	,	,	PUNCT
ejpam-5839	768	13	and	and	CCONJ
ejpam-5839	768	14	let	let	VERB
ejpam-5839	768	15	(	(	PUNCT
ejpam-5839	768	16	˜̈υ	˜̈υ	PROPN
ejpam-5839	768	17	,	,	PUNCT
ejpam-5839	768	18	ω	ω	NOUN
ejpam-5839	768	19	)	)	PUNCT
ejpam-5839	768	20	be	be	AUX
ejpam-5839	768	21	a	a	DET
ejpam-5839	768	22	qpns	qpns	NOUN
ejpam-5839	768	23	.	.	PUNCT
ejpam-5839	769	1	the	the	DET
ejpam-5839	769	2	frontier	frontier	NOUN
ejpam-5839	769	3	of	of	ADP
ejpam-5839	769	4	(	(	PUNCT
ejpam-5839	769	5	˜̈υ	˜̈υ	PROPN
ejpam-5839	769	6	,	,	PUNCT
ejpam-5839	769	7	ω	ω	NOUN
ejpam-5839	769	8	)	)	PUNCT
ejpam-5839	769	9	,	,	PUNCT
ejpam-5839	769	10	denoted	denote	VERB
ejpam-5839	769	11	as	as	ADP
ejpam-5839	769	12	fr	fr	PROPN
ejpam-5839	769	13	(	(	PUNCT
ejpam-5839	769	14	(	(	PUNCT
ejpam-5839	769	15	˜̈υ	˜̈υ	PROPN
ejpam-5839	769	16	,	,	PUNCT
ejpam-5839	769	17	ω	ω	NOUN
ejpam-5839	769	18	)	)	PUNCT
ejpam-5839	769	19	)	)	PUNCT
ejpam-5839	769	20	,	,	PUNCT
ejpam-5839	769	21	is	be	AUX
ejpam-5839	769	22	a	a	DET
ejpam-5839	769	23	qpns	qpns	NOUN
ejpam-5839	769	24	point	point	NOUN
ejpam-5839	769	25	x1	x1	PROPN
ejpam-5839	769	26	λ	λ	PROPN
ejpam-5839	769	27	⟨r1,r2,r3,r4⟩.	⟨r1,r2,r3,r4⟩.	NOUN
ejpam-5839	769	28	a	a	DET
ejpam-5839	769	29	point	point	NOUN
ejpam-5839	769	30	x1λ⟨r1,r2,r3,r4⟩	x1λ⟨r1,r2,r3,r4⟩	ADV
ejpam-5839	769	31	is	be	AUX
ejpam-5839	769	32	in	in	ADP
ejpam-5839	769	33	the	the	DET
ejpam-5839	769	34	frontier	frontier	NOUN
ejpam-5839	769	35	of	of	ADP
ejpam-5839	769	36	(	(	PUNCT
ejpam-5839	769	37	˜̈υ	˜̈υ	PROPN
ejpam-5839	769	38	,	,	PUNCT
ejpam-5839	769	39	ω	ω	NOUN
ejpam-5839	769	40	)	)	PUNCT
ejpam-5839	769	41	if	if	SCONJ
ejpam-5839	769	42	every	every	DET
ejpam-5839	769	43	qpns	qpns	NOUN
ejpam-5839	769	44	s	s	VERB
ejpam-5839	769	45	-	-	ADJ
ejpam-5839	769	46	open	open	ADJ
ejpam-5839	769	47	set	set	NOUN
ejpam-5839	769	48	containing	contain	VERB
ejpam-5839	769	49	x1λ⟨r1,r2,r3,r4⟩	x1λ⟨r1,r2,r3,r4⟩	PROPN
ejpam-5839	769	50	contains	contain	VERB
ejpam-5839	769	51	at	at	ADV
ejpam-5839	769	52	least	least	ADV
ejpam-5839	769	53	one	one	NUM
ejpam-5839	769	54	point	point	NOUN
ejpam-5839	769	55	of	of	ADP
ejpam-5839	769	56	(	(	PUNCT
ejpam-5839	769	57	˜̈υ	˜̈υ	PROPN
ejpam-5839	769	58	,	,	PUNCT
ejpam-5839	769	59	ω	ω	NOUN
ejpam-5839	769	60	)	)	PUNCT
ejpam-5839	769	61	and	and	CCONJ
ejpam-5839	769	62	at	at	ADV
ejpam-5839	769	63	least	least	ADV
ejpam-5839	769	64	one	one	NUM
ejpam-5839	769	65	qpns	qpns	NOUN
ejpam-5839	769	66	point	point	NOUN
ejpam-5839	769	67	of	of	ADP
ejpam-5839	769	68	(	(	PUNCT
ejpam-5839	769	69	˜̈υ	˜̈υ	PROPN
ejpam-5839	769	70	,	,	PUNCT
ejpam-5839	769	71	ω)c	ω)c	NOUN
ejpam-5839	769	72	.	.	PUNCT
ejpam-5839	770	1	definition	definition	NOUN
ejpam-5839	770	2	31	31	NUM
ejpam-5839	770	3	.	.	PUNCT
ejpam-5839	771	1	if	if	SCONJ
ejpam-5839	771	2	(	(	PUNCT
ejpam-5839	771	3	x	x	NOUN
ejpam-5839	771	4	,	,	PUNCT
ejpam-5839	771	5	τ1	τ1	NOUN
ejpam-5839	771	6	,	,	PUNCT
ejpam-5839	771	7	τ2,ω	τ2,ω	PROPN
ejpam-5839	771	8	)	)	PUNCT
ejpam-5839	771	9	is	be	AUX
ejpam-5839	771	10	a	a	DET
ejpam-5839	771	11	qpnsbts	qpnsbt	NOUN
ejpam-5839	771	12	and	and	CCONJ
ejpam-5839	771	13	(	(	PUNCT
ejpam-5839	771	14	˜̈υ	˜̈υ	PROPN
ejpam-5839	771	15	,	,	PUNCT
ejpam-5839	771	16	ω	ω	NOUN
ejpam-5839	771	17	)	)	PUNCT
ejpam-5839	771	18	is	be	AUX
ejpam-5839	771	19	a	a	DET
ejpam-5839	771	20	qpns	qpns	NOUN
ejpam-5839	771	21	,	,	PUNCT
ejpam-5839	771	22	then	then	ADV
ejpam-5839	771	23	the	the	DET
ejpam-5839	771	24	exterior	exterior	NOUN
ejpam-5839	771	25	of	of	ADP
ejpam-5839	771	26	(	(	PUNCT
ejpam-5839	771	27	˜̈υ	˜̈υ	PROPN
ejpam-5839	771	28	,	,	PUNCT
ejpam-5839	771	29	ω	ω	NOUN
ejpam-5839	771	30	)	)	PUNCT
ejpam-5839	771	31	,	,	PUNCT
ejpam-5839	771	32	denoted	denote	VERB
ejpam-5839	771	33	by	by	ADP
ejpam-5839	771	34	ext	ext	PROPN
ejpam-5839	771	35	(	(	PUNCT
ejpam-5839	771	36	(	(	PUNCT
ejpam-5839	771	37	˜̈υ	˜̈υ	PROPN
ejpam-5839	771	38	,	,	PUNCT
ejpam-5839	771	39	ω	ω	NOUN
ejpam-5839	771	40	)	)	PUNCT
ejpam-5839	771	41	)	)	PUNCT
ejpam-5839	771	42	,	,	PUNCT
ejpam-5839	771	43	is	be	AUX
ejpam-5839	771	44	a	a	DET
ejpam-5839	771	45	qpns	qpns	NOUN
ejpam-5839	771	46	point	point	NOUN
ejpam-5839	771	47	x1	x1	PROPN
ejpam-5839	771	48	λ	λ	PROPN
ejpam-5839	771	49	⟨r1,r2,r3,r4⟩.	⟨r1,r2,r3,r4⟩.	X
ejpam-5839	771	50	a	a	DET
ejpam-5839	771	51	qpns	qpns	NOUN
ejpam-5839	771	52	point	point	NOUN
ejpam-5839	771	53	x1	x1	PROPN
ejpam-5839	772	1	λ	λ	PROPN
ejpam-5839	772	2	⟨r1,r2,r3,r4⟩	⟨r1,r2,r3,r4⟩	PROPN
ejpam-5839	772	3	is	be	AUX
ejpam-5839	772	4	in	in	ADP
ejpam-5839	772	5	the	the	DET
ejpam-5839	772	6	exterior	exterior	NOUN
ejpam-5839	772	7	of	of	ADP
ejpam-5839	772	8	(	(	PUNCT
ejpam-5839	772	9	˜̈υ	˜̈υ	PROPN
ejpam-5839	772	10	,	,	PUNCT
ejpam-5839	772	11	ω	ω	NOUN
ejpam-5839	772	12	)	)	PUNCT
ejpam-5839	772	13	if	if	SCONJ
ejpam-5839	772	14	and	and	CCONJ
ejpam-5839	772	15	only	only	ADV
ejpam-5839	772	16	if	if	SCONJ
ejpam-5839	772	17	it	it	PRON
ejpam-5839	772	18	is	be	AUX
ejpam-5839	772	19	in	in	ADP
ejpam-5839	772	20	the	the	DET
ejpam-5839	772	21	interior	interior	NOUN
ejpam-5839	772	22	of	of	ADP
ejpam-5839	772	23	(	(	PUNCT
ejpam-5839	772	24	˜̈υ	˜̈υ	PROPN
ejpam-5839	772	25	,	,	PUNCT
ejpam-5839	772	26	ω)c	ω)c	NOUN
ejpam-5839	772	27	,	,	PUNCT
ejpam-5839	772	28	meaning	mean	VERB
ejpam-5839	772	29	there	there	PRON
ejpam-5839	772	30	exists	exist	VERB
ejpam-5839	772	31	a	a	DET
ejpam-5839	772	32	qpns	qpns	NOUN
ejpam-5839	772	33	s	s	NOUN
ejpam-5839	772	34	-	-	ADJ
ejpam-5839	772	35	open	open	ADJ
ejpam-5839	772	36	set	set	NOUN
ejpam-5839	772	37	(	(	PUNCT
ejpam-5839	772	38	g̃,ω	g̃,ω	PROPN
ejpam-5839	772	39	)	)	PUNCT
ejpam-5839	773	1	such	such	ADJ
ejpam-5839	773	2	that	that	AUX
ejpam-5839	773	3	x1	x1	PROPN
ejpam-5839	773	4	λ	λ	PROPN
ejpam-5839	773	5	⟨r1,r2,r3,r4⟩	⟨r1,r2,r3,r4⟩	PROPN
ejpam-5839	773	6	∈	∈	PROPN
ejpam-5839	773	7	(	(	PUNCT
ejpam-5839	773	8	g̃,ω	g̃,ω	PROPN
ejpam-5839	773	9	)	)	PUNCT
ejpam-5839	773	10	⊆	⊆	NUM
ejpam-5839	773	11	(	(	PUNCT
ejpam-5839	773	12	˜̈υ	˜̈υ	PROPN
ejpam-5839	773	13	,	,	PUNCT
ejpam-5839	773	14	ω)c	ω)c	NOUN
ejpam-5839	773	15	.	.	PUNCT
ejpam-5839	774	1	definition	definition	NOUN
ejpam-5839	774	2	32	32	NUM
ejpam-5839	774	3	.	.	PUNCT
ejpam-5839	775	1	if	if	SCONJ
ejpam-5839	775	2	(	(	PUNCT
ejpam-5839	775	3	x̃	x̃	PROPN
ejpam-5839	775	4	,	,	PUNCT
ejpam-5839	775	5	τ1	τ1	NOUN
ejpam-5839	775	6	,	,	PUNCT
ejpam-5839	775	7	τ2,ω	τ2,ω	PROPN
ejpam-5839	775	8	)	)	PUNCT
ejpam-5839	775	9	and	and	CCONJ
ejpam-5839	775	10	(	(	PUNCT
ejpam-5839	775	11	⟨ỹ	⟨ỹ	NOUN
ejpam-5839	775	12	⟩,f1,f2,ω	⟩,f1,f2,ω	NOUN
ejpam-5839	775	13	)	)	PUNCT
ejpam-5839	775	14	are	be	AUX
ejpam-5839	775	15	qpnsbtss	qpnsbtss	ADJ
ejpam-5839	775	16	,	,	PUNCT
ejpam-5839	775	17	and	and	CCONJ
ejpam-5839	775	18	(	(	PUNCT
ejpam-5839	775	19	{	{	PUNCT
ejpam-5839	775	20	,	,	PUNCT
ejpam-5839	775	21	φ	φ	NUM
ejpam-5839	775	22	)	)	PUNCT
ejpam-5839	775	23	:	:	PUNCT
ejpam-5839	775	24	(	(	PUNCT
ejpam-5839	775	25	x̃	x̃	PROPN
ejpam-5839	775	26	,	,	PUNCT
ejpam-5839	775	27	τ1	τ1	NOUN
ejpam-5839	775	28	,	,	PUNCT
ejpam-5839	775	29	τ2,ω	τ2,ω	PROPN
ejpam-5839	775	30	)	)	PUNCT
ejpam-5839	775	31	→	→	SYM
ejpam-5839	775	32	(	(	PUNCT
ejpam-5839	775	33	⟨ỹ	⟨ỹ	NOUN
ejpam-5839	775	34	⟩,f1,f2,ω	⟩,f1,f2,ω	NOUN
ejpam-5839	775	35	)	)	PUNCT
ejpam-5839	775	36	is	be	AUX
ejpam-5839	775	37	a	a	DET
ejpam-5839	775	38	qpns	qpns	NOUN
ejpam-5839	775	39	mapping	mapping	NOUN
ejpam-5839	775	40	,	,	PUNCT
ejpam-5839	775	41	then	then	ADV
ejpam-5839	775	42	if	if	SCONJ
ejpam-5839	775	43	the	the	DET
ejpam-5839	775	44	image	image	NOUN
ejpam-5839	775	45	(	(	PUNCT
ejpam-5839	775	46	{	{	PUNCT
ejpam-5839	775	47	,	,	PUNCT
ejpam-5839	775	48	φ	φ	NUM
ejpam-5839	775	49	)	)	PUNCT
ejpam-5839	775	50	(	(	PUNCT
ejpam-5839	775	51	˜̈υ	˜̈υ	PROPN
ejpam-5839	775	52	,	,	PUNCT
ejpam-5839	775	53	ω	ω	NOUN
ejpam-5839	775	54	)	)	PUNCT
ejpam-5839	775	55	of	of	ADP
ejpam-5839	775	56	each	each	DET
ejpam-5839	775	57	qpns	qpns	NOUN
ejpam-5839	775	58	s	s	NOUN
ejpam-5839	775	59	-	-	PUNCT
ejpam-5839	775	60	closed	closed	ADJ
ejpam-5839	775	61	set	set	NOUN
ejpam-5839	775	62	(	(	PUNCT
ejpam-5839	775	63	˜̈υ	˜̈υ	PROPN
ejpam-5839	775	64	,	,	PUNCT
ejpam-5839	775	65	ω	ω	NOUN
ejpam-5839	775	66	)	)	PUNCT
ejpam-5839	775	67	over	over	ADP
ejpam-5839	775	68	x̃	x̃	PROPN
ejpam-5839	775	69	is	be	AUX
ejpam-5839	775	70	a	a	DET
ejpam-5839	775	71	qpns	qpns	NOUN
ejpam-5839	775	72	s	s	NOUN
ejpam-5839	775	73	-	-	PUNCT
ejpam-5839	775	74	closed	closed	ADJ
ejpam-5839	775	75	set	set	VERB
ejpam-5839	775	76	in	in	ADP
ejpam-5839	775	77	⟨ỹ	⟨ỹ	NOUN
ejpam-5839	775	78	⟩	⟩	NOUN
ejpam-5839	775	79	,	,	PUNCT
ejpam-5839	775	80	the	the	DET
ejpam-5839	775	81	mapping	mapping	NOUN
ejpam-5839	775	82	(	(	PUNCT
ejpam-5839	775	83	{	{	PUNCT
ejpam-5839	775	84	,	,	PUNCT
ejpam-5839	775	85	φ	φ	NUM
ejpam-5839	775	86	)	)	PUNCT
ejpam-5839	775	87	is	be	AUX
ejpam-5839	775	88	said	say	VERB
ejpam-5839	775	89	to	to	PART
ejpam-5839	775	90	be	be	AUX
ejpam-5839	775	91	a	a	DET
ejpam-5839	775	92	qpns	qpns	NOUN
ejpam-5839	775	93	s	s	NOUN
ejpam-5839	775	94	-	-	PUNCT
ejpam-5839	775	95	closed	closed	ADJ
ejpam-5839	775	96	mapping	mapping	NOUN
ejpam-5839	775	97	.	.	PUNCT
ejpam-5839	776	1	theorem	theorem	VERB
ejpam-5839	776	2	11	11	NUM
ejpam-5839	776	3	.	.	PUNCT
ejpam-5839	777	1	let	let	VERB
ejpam-5839	777	2	(	(	PUNCT
ejpam-5839	777	3	x	x	NOUN
ejpam-5839	777	4	,	,	PUNCT
ejpam-5839	777	5	τ1	τ1	NOUN
ejpam-5839	777	6	,	,	PUNCT
ejpam-5839	777	7	τ2,ω	τ2,ω	PUNCT
ejpam-5839	777	8	)	)	PUNCT
ejpam-5839	777	9	be	be	AUX
ejpam-5839	777	10	a	a	DET
ejpam-5839	777	11	qpnsbts	qpnsbts	NOUN
ejpam-5839	777	12	over	over	ADP
ejpam-5839	777	13	x	x	PUNCT
ejpam-5839	777	14	and	and	CCONJ
ejpam-5839	777	15	(	(	PUNCT
ejpam-5839	777	16	˜̈υ	˜̈υ	PROPN
ejpam-5839	777	17	,	,	PUNCT
ejpam-5839	777	18	ω	ω	NOUN
ejpam-5839	777	19	)	)	PUNCT
ejpam-5839	777	20	be	be	AUX
ejpam-5839	777	21	a	a	DET
ejpam-5839	777	22	qpns	qpns	NOUN
ejpam-5839	777	23	subset	subset	VERB
ejpam-5839	777	24	.	.	PUNCT
ejpam-5839	778	1	then	then	ADV
ejpam-5839	778	2	,	,	PUNCT
ejpam-5839	778	3	(	(	PUNCT
ejpam-5839	778	4	˜̈υ	˜̈υ	PROPN
ejpam-5839	778	5	,	,	PUNCT
ejpam-5839	778	6	ω	ω	NOUN
ejpam-5839	778	7	)	)	PUNCT
ejpam-5839	778	8	is	be	AUX
ejpam-5839	778	9	a	a	DET
ejpam-5839	778	10	qpns	qpns	NOUN
ejpam-5839	778	11	s	s	NOUN
ejpam-5839	778	12	-	-	ADJ
ejpam-5839	778	13	open	open	ADJ
ejpam-5839	778	14	set	set	NOUN
ejpam-5839	778	15	if	if	SCONJ
ejpam-5839	778	16	and	and	CCONJ
ejpam-5839	778	17	only	only	ADV
ejpam-5839	778	18	if	if	SCONJ
ejpam-5839	778	19	(	(	PUNCT
ejpam-5839	778	20	˜̈υ	˜̈υ	PROPN
ejpam-5839	778	21	,	,	PUNCT
ejpam-5839	778	22	ω	ω	NOUN
ejpam-5839	778	23	)	)	PUNCT
ejpam-5839	778	24	=	=	SYM
ejpam-5839	778	25	(	(	PUNCT
ejpam-5839	778	26	˜̈υ	˜̈υ	PROPN
ejpam-5839	778	27	,	,	PUNCT
ejpam-5839	778	28	ω)	ω)	NUM
ejpam-5839	778	29	◦	◦	NOUN
ejpam-5839	778	30	.	.	NOUN
ejpam-5839	778	31	proof	proof	NOUN
ejpam-5839	778	32	.	.	PUNCT
ejpam-5839	779	1	let	let	VERB
ejpam-5839	779	2	(	(	PUNCT
ejpam-5839	779	3	˜̈υ	˜̈υ	PROPN
ejpam-5839	779	4	,	,	PUNCT
ejpam-5839	779	5	ω	ω	NOUN
ejpam-5839	779	6	)	)	PUNCT
ejpam-5839	779	7	be	be	VERB
ejpam-5839	779	8	a	a	DET
ejpam-5839	779	9	hqpns	hqpns	ADJ
ejpam-5839	779	10	s	s	NOUN
ejpam-5839	779	11	-	-	ADJ
ejpam-5839	779	12	open	open	ADJ
ejpam-5839	779	13	set	set	NOUN
ejpam-5839	779	14	.	.	PUNCT
ejpam-5839	780	1	then	then	ADV
ejpam-5839	780	2	,	,	PUNCT
ejpam-5839	780	3	the	the	DET
ejpam-5839	780	4	largest	large	ADJ
ejpam-5839	780	5	qpns	qpns	NOUN
ejpam-5839	780	6	s	s	NOUN
ejpam-5839	780	7	-	-	ADJ
ejpam-5839	780	8	open	open	ADJ
ejpam-5839	780	9	set	set	NOUN
ejpam-5839	780	10	that	that	PRON
ejpam-5839	780	11	is	be	AUX
ejpam-5839	780	12	contained	contain	VERB
ejpam-5839	780	13	within	within	ADP
ejpam-5839	780	14	(	(	PUNCT
ejpam-5839	780	15	˜̈υ	˜̈υ	PROPN
ejpam-5839	780	16	,	,	PUNCT
ejpam-5839	780	17	ω	ω	NOUN
ejpam-5839	780	18	)	)	PUNCT
ejpam-5839	780	19	is	be	AUX
ejpam-5839	780	20	equal	equal	ADJ
ejpam-5839	780	21	to	to	ADP
ejpam-5839	780	22	(	(	PUNCT
ejpam-5839	780	23	˜̈υ	˜̈υ	PROPN
ejpam-5839	780	24	,	,	PUNCT
ejpam-5839	780	25	ω	ω	NOUN
ejpam-5839	780	26	)	)	PUNCT
ejpam-5839	780	27	.	.	PUNCT
ejpam-5839	781	1	hence	hence	ADV
ejpam-5839	781	2	,	,	PUNCT
ejpam-5839	781	3	(	(	PUNCT
ejpam-5839	781	4	˜̈υ	˜̈υ	PROPN
ejpam-5839	781	5	,	,	PUNCT
ejpam-5839	781	6	ω	ω	NOUN
ejpam-5839	781	7	)	)	PUNCT
ejpam-5839	781	8	=	=	SYM
ejpam-5839	781	9	(	(	PUNCT
ejpam-5839	781	10	˜̈υ	˜̈υ	PROPN
ejpam-5839	781	11	,	,	PUNCT
ejpam-5839	781	12	ω)	ω)	NUM
ejpam-5839	781	13	◦	◦	NOUN
ejpam-5839	781	14	.	.	PUNCT
ejpam-5839	781	15	conversely	conversely	ADV
ejpam-5839	781	16	,	,	PUNCT
ejpam-5839	781	17	it	it	PRON
ejpam-5839	781	18	is	be	AUX
ejpam-5839	781	19	known	know	VERB
ejpam-5839	781	20	that	that	SCONJ
ejpam-5839	781	21	(	(	PUNCT
ejpam-5839	781	22	˜̈υ	˜̈υ	PROPN
ejpam-5839	781	23	,	,	PUNCT
ejpam-5839	781	24	ω	ω	NOUN
ejpam-5839	781	25	)	)	PUNCT
ejpam-5839	781	26	◦	◦	NOUN
ejpam-5839	781	27	is	be	AUX
ejpam-5839	781	28	a	a	DET
ejpam-5839	781	29	qpns	qpns	NOUN
ejpam-5839	781	30	s	s	NOUN
ejpam-5839	781	31	-	-	ADJ
ejpam-5839	781	32	open	open	ADJ
ejpam-5839	781	33	set	set	NOUN
ejpam-5839	781	34	,	,	PUNCT
ejpam-5839	781	35	and	and	CCONJ
ejpam-5839	781	36	if	if	SCONJ
ejpam-5839	781	37	(	(	PUNCT
ejpam-5839	781	38	˜̈υ	˜̈υ	PROPN
ejpam-5839	781	39	,	,	PUNCT
ejpam-5839	781	40	ω	ω	NOUN
ejpam-5839	781	41	)	)	PUNCT
ejpam-5839	781	42	=	=	PRON
ejpam-5839	781	43	(	(	PUNCT
ejpam-5839	781	44	˜̈υ	˜̈υ	PROPN
ejpam-5839	781	45	,	,	PUNCT
ejpam-5839	781	46	ω	ω	NOUN
ejpam-5839	781	47	)	)	PUNCT
ejpam-5839	781	48	◦	◦	NOUN
ejpam-5839	781	49	,	,	PUNCT
ejpam-5839	781	50	then	then	ADV
ejpam-5839	781	51	(	(	PUNCT
ejpam-5839	781	52	˜̈υ	˜̈υ	PROPN
ejpam-5839	781	53	,	,	PUNCT
ejpam-5839	781	54	ω	ω	NOUN
ejpam-5839	781	55	)	)	PUNCT
ejpam-5839	781	56	is	be	AUX
ejpam-5839	781	57	a	a	DET
ejpam-5839	781	58	qpns	qpns	NOUN
ejpam-5839	781	59	p	p	NOUN
ejpam-5839	781	60	-	-	PUNCT
ejpam-5839	781	61	open	open	ADJ
ejpam-5839	781	62	set	set	NOUN
ejpam-5839	781	63	.	.	PUNCT
ejpam-5839	782	1	theorem	theorem	PROPN
ejpam-5839	782	2	12	12	NUM
ejpam-5839	782	3	.	.	PUNCT
ejpam-5839	783	1	let	let	VERB
ejpam-5839	783	2	(	(	PUNCT
ejpam-5839	783	3	x	x	NOUN
ejpam-5839	783	4	,	,	PUNCT
ejpam-5839	783	5	τ1	τ1	NOUN
ejpam-5839	783	6	,	,	PUNCT
ejpam-5839	783	7	τ2,ω	τ2,ω	PUNCT
ejpam-5839	783	8	)	)	PUNCT
ejpam-5839	783	9	be	be	AUX
ejpam-5839	783	10	a	a	DET
ejpam-5839	783	11	qpnsbts	qpnsbt	NOUN
ejpam-5839	783	12	over	over	ADP
ejpam-5839	783	13	x	x	NOUN
ejpam-5839	783	14	,	,	PUNCT
ejpam-5839	783	15	and	and	CCONJ
ejpam-5839	783	16	let	let	VERB
ejpam-5839	783	17	(	(	PUNCT
ejpam-5839	783	18	f̃	f̃	PROPN
ejpam-5839	783	19	,	,	PUNCT
ejpam-5839	783	20	ω	ω	PROPN
ejpam-5839	783	21	)	)	PUNCT
ejpam-5839	783	22	,	,	PUNCT
ejpam-5839	783	23	(	(	PUNCT
ejpam-5839	783	24	g̃,ω	g̃,ω	PROPN
ejpam-5839	783	25	)	)	PUNCT
ejpam-5839	783	26	be	be	AUX
ejpam-5839	783	27	qpns	qpns	NOUN
ejpam-5839	783	28	subsets	subset	NOUN
ejpam-5839	783	29	.	.	PUNCT
ejpam-5839	784	1	then	then	ADV
ejpam-5839	784	2	,	,	PUNCT
ejpam-5839	784	3	1	1	X
ejpam-5839	784	4	.	.	PUNCT
ejpam-5839	785	1	[	[	PUNCT
ejpam-5839	785	2	(	(	PUNCT
ejpam-5839	785	3	f̃	f̃	PROPN
ejpam-5839	785	4	,	,	PUNCT
ejpam-5839	785	5	ω	ω	NOUN
ejpam-5839	785	6	)	)	PUNCT
ejpam-5839	785	7	◦	◦	NOUN
ejpam-5839	785	8	]	]	X
ejpam-5839	785	9	◦	◦	NOUN
ejpam-5839	785	10	=	=	SYM
ejpam-5839	785	11	(	(	PUNCT
ejpam-5839	785	12	f̃	f̃	PROPN
ejpam-5839	785	13	,	,	PUNCT
ejpam-5839	785	14	ω	ω	NOUN
ejpam-5839	785	15	)	)	PUNCT
ejpam-5839	785	16	◦	◦	NOUN
ejpam-5839	785	17	,	,	PUNCT
ejpam-5839	785	18	2	2	NUM
ejpam-5839	785	19	.	.	PUNCT
ejpam-5839	785	20	(	(	PUNCT
ejpam-5839	785	21	0(⟨x⟩,ω	0(⟨x⟩,ω	NUM
ejpam-5839	785	22	)	)	PUNCT
ejpam-5839	785	23	)	)	PUNCT
ejpam-5839	786	1	◦	◦	NOUN
ejpam-5839	786	2	=	=	SYM
ejpam-5839	786	3	0(⟨x⟩,ω	0(⟨x⟩,ω	NUM
ejpam-5839	786	4	)	)	PUNCT
ejpam-5839	786	5	and	and	CCONJ
ejpam-5839	786	6	(	(	PUNCT
ejpam-5839	786	7	1(⟨x⟩,ω	1(⟨x⟩,ω	NUM
ejpam-5839	786	8	)	)	PUNCT
ejpam-5839	786	9	)	)	PUNCT
ejpam-5839	787	1	◦	◦	NOUN
ejpam-5839	787	2	=	=	SYM
ejpam-5839	787	3	1(⟨x⟩,ω	1(⟨x⟩,ω	NUM
ejpam-5839	787	4	)	)	PUNCT
ejpam-5839	787	5	,	,	PUNCT
ejpam-5839	787	6	3	3	X
ejpam-5839	787	7	.	.	PUNCT
ejpam-5839	787	8	(	(	PUNCT
ejpam-5839	787	9	f̃	f̃	PROPN
ejpam-5839	787	10	,	,	PUNCT
ejpam-5839	787	11	ω	ω	PROPN
ejpam-5839	787	12	)	)	PUNCT
ejpam-5839	787	13	⊆	⊆	NUM
ejpam-5839	787	14	(	(	PUNCT
ejpam-5839	787	15	g̃,ω	g̃,ω	NOUN
ejpam-5839	787	16	)	)	PUNCT
ejpam-5839	787	17	⇒	⇒	NOUN
ejpam-5839	787	18	(	(	PUNCT
ejpam-5839	787	19	f̃	f̃	PROPN
ejpam-5839	787	20	,	,	PUNCT
ejpam-5839	787	21	ω	ω	NOUN
ejpam-5839	787	22	)	)	PUNCT
ejpam-5839	787	23	◦	◦	NOUN
ejpam-5839	787	24	⊆	⊆	NUM
ejpam-5839	787	25	(	(	PUNCT
ejpam-5839	787	26	g̃,ω	g̃,ω	NOUN
ejpam-5839	787	27	)	)	PUNCT
ejpam-5839	787	28	◦	◦	NOUN
ejpam-5839	787	29	,	,	PUNCT
ejpam-5839	787	30	4	4	NUM
ejpam-5839	787	31	.	.	PUNCT
ejpam-5839	788	1	[	[	PUNCT
ejpam-5839	788	2	(	(	PUNCT
ejpam-5839	788	3	f̃	f̃	PROPN
ejpam-5839	788	4	,	,	PUNCT
ejpam-5839	788	5	ω	ω	NOUN
ejpam-5839	788	6	)	)	PUNCT
ejpam-5839	788	7	∩	∩	NOUN
ejpam-5839	788	8	(	(	PUNCT
ejpam-5839	788	9	g̃,ω	g̃,ω	PROPN
ejpam-5839	788	10	)	)	PUNCT
ejpam-5839	788	11	]	]	PUNCT
ejpam-5839	788	12	◦	◦	NOUN
ejpam-5839	788	13	=	=	SYM
ejpam-5839	788	14	(	(	PUNCT
ejpam-5839	788	15	f̃	f̃	PROPN
ejpam-5839	788	16	,	,	PUNCT
ejpam-5839	788	17	ω	ω	NOUN
ejpam-5839	788	18	)	)	PUNCT
ejpam-5839	788	19	◦	◦	NOUN
ejpam-5839	788	20	∩	∩	NOUN
ejpam-5839	788	21	(	(	PUNCT
ejpam-5839	788	22	g̃,ω	g̃,ω	NOUN
ejpam-5839	788	23	)	)	PUNCT
ejpam-5839	788	24	◦	◦	NOUN
ejpam-5839	788	25	,	,	PUNCT
ejpam-5839	788	26	5	5	NUM
ejpam-5839	788	27	.	.	PUNCT
ejpam-5839	788	28	(	(	PUNCT
ejpam-5839	788	29	f̃	f̃	PROPN
ejpam-5839	788	30	,	,	PUNCT
ejpam-5839	788	31	ω	ω	NOUN
ejpam-5839	788	32	)	)	PUNCT
ejpam-5839	788	33	◦	◦	NOUN
ejpam-5839	788	34	∪	∪	ADP
ejpam-5839	788	35	(	(	PUNCT
ejpam-5839	788	36	g̃,ω	g̃,ω	NOUN
ejpam-5839	788	37	)	)	PUNCT
ejpam-5839	788	38	◦	◦	NOUN
ejpam-5839	788	39	⊆	⊆	NUM
ejpam-5839	788	40	[	[	PUNCT
ejpam-5839	788	41	(	(	PUNCT
ejpam-5839	788	42	f̃	f̃	PROPN
ejpam-5839	788	43	,	,	PUNCT
ejpam-5839	788	44	ω	ω	NOUN
ejpam-5839	788	45	)	)	PUNCT
ejpam-5839	788	46	∪	∪	NOUN
ejpam-5839	788	47	(	(	PUNCT
ejpam-5839	788	48	g̃,ω	g̃,ω	PROPN
ejpam-5839	788	49	)	)	PUNCT
ejpam-5839	788	50	]	]	PUNCT
ejpam-5839	788	51	◦	◦	NOUN
ejpam-5839	788	52	.	.	PUNCT
ejpam-5839	789	1	proof	proof	NOUN
ejpam-5839	789	2	.	.	PUNCT
ejpam-5839	790	1	let	let	VERB
ejpam-5839	790	2	(	(	PUNCT
ejpam-5839	790	3	x	x	NOUN
ejpam-5839	790	4	,	,	PUNCT
ejpam-5839	790	5	τ1	τ1	NOUN
ejpam-5839	790	6	,	,	PUNCT
ejpam-5839	790	7	τ2,ω	τ2,ω	PUNCT
ejpam-5839	790	8	)	)	PUNCT
ejpam-5839	790	9	be	be	AUX
ejpam-5839	790	10	a	a	DET
ejpam-5839	790	11	qpnsbts	qpnsbt	NOUN
ejpam-5839	790	12	over	over	ADP
ejpam-5839	790	13	x	x	NOUN
ejpam-5839	790	14	,	,	PUNCT
ejpam-5839	790	15	and	and	CCONJ
ejpam-5839	790	16	let	let	VERB
ejpam-5839	790	17	(	(	PUNCT
ejpam-5839	790	18	f̃	f̃	PROPN
ejpam-5839	790	19	,	,	PUNCT
ejpam-5839	790	20	ω	ω	PROPN
ejpam-5839	790	21	)	)	PUNCT
ejpam-5839	790	22	,	,	PUNCT
ejpam-5839	790	23	(	(	PUNCT
ejpam-5839	790	24	g̃,ω	g̃,ω	PROPN
ejpam-5839	790	25	)	)	PUNCT
ejpam-5839	790	26	be	be	AUX
ejpam-5839	790	27	qpns	qpns	NOUN
ejpam-5839	790	28	subsets	subset	NOUN
ejpam-5839	790	29	.	.	PUNCT
ejpam-5839	791	1	then	then	ADV
ejpam-5839	791	2	,	,	PUNCT
ejpam-5839	791	3	1	1	X
ejpam-5839	791	4	.	.	PUNCT
ejpam-5839	792	1	if	if	SCONJ
ejpam-5839	792	2	(	(	PUNCT
ejpam-5839	792	3	f̃	f̃	PROPN
ejpam-5839	792	4	,	,	PUNCT
ejpam-5839	792	5	ω	ω	NOUN
ejpam-5839	792	6	)	)	PUNCT
ejpam-5839	792	7	◦	◦	NOUN
ejpam-5839	792	8	=	=	SYM
ejpam-5839	792	9	(	(	PUNCT
ejpam-5839	792	10	g̃,ω	g̃,ω	PROPN
ejpam-5839	792	11	)	)	PUNCT
ejpam-5839	792	12	,	,	PUNCT
ejpam-5839	792	13	then	then	ADV
ejpam-5839	792	14	(	(	PUNCT
ejpam-5839	792	15	g̃,ω	g̃,ω	NOUN
ejpam-5839	792	16	)	)	PUNCT
ejpam-5839	792	17	∈	∈	PROPN
ejpam-5839	792	18	τ	τ	X
ejpam-5839	792	19	if	if	SCONJ
ejpam-5839	792	20	and	and	CCONJ
ejpam-5839	792	21	only	only	ADV
ejpam-5839	792	22	if	if	SCONJ
ejpam-5839	792	23	(	(	PUNCT
ejpam-5839	792	24	g̃,ω	g̃,ω	NOUN
ejpam-5839	792	25	)	)	PUNCT
ejpam-5839	792	26	=	=	PUNCT
ejpam-5839	792	27	(	(	PUNCT
ejpam-5839	792	28	f̃	f̃	PROPN
ejpam-5839	792	29	,	,	PUNCT
ejpam-5839	792	30	ω)	ω)	NUM
ejpam-5839	792	31	◦	◦	NOUN
ejpam-5839	792	32	.	.	PUNCT
ejpam-5839	793	1	thus	thus	ADV
ejpam-5839	793	2	,	,	PUNCT
ejpam-5839	793	3	[	[	PUNCT
ejpam-5839	793	4	(	(	PUNCT
ejpam-5839	793	5	f̃	f̃	PROPN
ejpam-5839	793	6	,	,	PUNCT
ejpam-5839	793	7	ω	ω	NOUN
ejpam-5839	793	8	)	)	PUNCT
ejpam-5839	793	9	◦	◦	NOUN
ejpam-5839	793	10	]	]	X
ejpam-5839	793	11	◦	◦	NOUN
ejpam-5839	793	12	=	=	SYM
ejpam-5839	793	13	(	(	PUNCT
ejpam-5839	793	14	f̃	f̃	PROPN
ejpam-5839	793	15	,	,	PUNCT
ejpam-5839	793	16	ω)	ω)	NUM
ejpam-5839	793	17	◦	◦	NOUN
ejpam-5839	793	18	.	.	NOUN
ejpam-5839	793	19	2	2	X
ejpam-5839	793	20	.	.	PUNCT
ejpam-5839	793	21	since	since	SCONJ
ejpam-5839	793	22	0(⟨x⟩,ω	0(⟨x⟩,ω	NUM
ejpam-5839	793	23	)	)	PUNCT
ejpam-5839	793	24	and	and	CCONJ
ejpam-5839	793	25	1(⟨x⟩,ω	1(⟨x⟩,ω	NUM
ejpam-5839	793	26	)	)	PUNCT
ejpam-5839	793	27	are	be	AUX
ejpam-5839	793	28	always	always	ADV
ejpam-5839	793	29	qpns	qpns	NOUN
ejpam-5839	793	30	s	s	NOUN
ejpam-5839	793	31	-	-	PUNCT
ejpam-5839	793	32	open	open	ADJ
ejpam-5839	793	33	sets	set	NOUN
ejpam-5839	793	34	,	,	PUNCT
ejpam-5839	793	35	we	we	PRON
ejpam-5839	793	36	have	have	VERB
ejpam-5839	793	37	(	(	PUNCT
ejpam-5839	793	38	0(⟨x⟩,ω	0(⟨x⟩,ω	NUM
ejpam-5839	793	39	)	)	PUNCT
ejpam-5839	793	40	)	)	PUNCT
ejpam-5839	794	1	◦	◦	NOUN
ejpam-5839	794	2	=	=	SYM
ejpam-5839	794	3	0(⟨x⟩,ω	0(⟨x⟩,ω	NUM
ejpam-5839	794	4	)	)	PUNCT
ejpam-5839	794	5	and	and	CCONJ
ejpam-5839	794	6	(	(	PUNCT
ejpam-5839	794	7	1(⟨x⟩,ω	1(⟨x⟩,ω	NUM
ejpam-5839	794	8	)	)	PUNCT
ejpam-5839	794	9	)	)	PUNCT
ejpam-5839	795	1	◦	◦	NOUN
ejpam-5839	795	2	=	=	SYM
ejpam-5839	795	3	1(⟨x⟩,ω	1(⟨x⟩,ω	NUM
ejpam-5839	795	4	)	)	PUNCT
ejpam-5839	795	5	.	.	PUNCT
ejpam-5839	796	1	3	3	X
ejpam-5839	796	2	.	.	X
ejpam-5839	797	1	it	it	PRON
ejpam-5839	797	2	is	be	AUX
ejpam-5839	797	3	known	know	VERB
ejpam-5839	797	4	that	that	SCONJ
ejpam-5839	797	5	(	(	PUNCT
ejpam-5839	797	6	f̃	f̃	PROPN
ejpam-5839	797	7	,	,	PUNCT
ejpam-5839	797	8	ω	ω	NOUN
ejpam-5839	797	9	)	)	PUNCT
ejpam-5839	797	10	◦	◦	NOUN
ejpam-5839	797	11	⊆	⊆	NUM
ejpam-5839	797	12	(	(	PUNCT
ejpam-5839	797	13	f̃	f̃	PROPN
ejpam-5839	797	14	,	,	PUNCT
ejpam-5839	797	15	ω	ω	NUM
ejpam-5839	797	16	)	)	PUNCT
ejpam-5839	797	17	⊆	⊆	NUM
ejpam-5839	797	18	(	(	PUNCT
ejpam-5839	797	19	g̃,ω	g̃,ω	NOUN
ejpam-5839	797	20	)	)	PUNCT
ejpam-5839	797	21	and	and	CCONJ
ejpam-5839	797	22	(	(	PUNCT
ejpam-5839	797	23	g̃,ω	g̃,ω	NOUN
ejpam-5839	797	24	)	)	PUNCT
ejpam-5839	797	25	◦	◦	NOUN
ejpam-5839	797	26	⊆	⊆	NUM
ejpam-5839	797	27	(	(	PUNCT
ejpam-5839	797	28	g̃,ω	g̃,ω	NOUN
ejpam-5839	797	29	)	)	PUNCT
ejpam-5839	797	30	.	.	PUNCT
ejpam-5839	798	1	since	since	SCONJ
ejpam-5839	798	2	(	(	PUNCT
ejpam-5839	798	3	g̃,ω	g̃,ω	NOUN
ejpam-5839	798	4	)	)	PUNCT
ejpam-5839	798	5	◦	◦	NOUN
ejpam-5839	798	6	is	be	AUX
ejpam-5839	798	7	the	the	DET
ejpam-5839	798	8	largest	large	ADJ
ejpam-5839	798	9	qpns	qpns	NOUN
ejpam-5839	798	10	s	s	NOUN
ejpam-5839	798	11	-	-	ADJ
ejpam-5839	798	12	open	open	ADJ
ejpam-5839	798	13	set	set	NOUN
ejpam-5839	798	14	contained	contain	VERB
ejpam-5839	798	15	in	in	ADP
ejpam-5839	798	16	(	(	PUNCT
ejpam-5839	798	17	g̃,ω	g̃,ω	PROPN
ejpam-5839	798	18	)	)	PUNCT
ejpam-5839	798	19	,	,	PUNCT
ejpam-5839	798	20	it	it	PRON
ejpam-5839	798	21	follows	follow	VERB
ejpam-5839	798	22	that	that	SCONJ
ejpam-5839	798	23	(	(	PUNCT
ejpam-5839	798	24	f̃	f̃	PROPN
ejpam-5839	798	25	,	,	PUNCT
ejpam-5839	798	26	ω	ω	NOUN
ejpam-5839	798	27	)	)	PUNCT
ejpam-5839	798	28	◦	◦	NOUN
ejpam-5839	798	29	⊆	⊆	NUM
ejpam-5839	798	30	(	(	PUNCT
ejpam-5839	798	31	g̃,ω)	g̃,ω)	NOUN
ejpam-5839	798	32	◦	◦	NOUN
ejpam-5839	798	33	.	.	PUNCT
ejpam-5839	799	1	a.	a.	NOUN
ejpam-5839	799	2	shihadeh	shihadeh	PROPN
ejpam-5839	799	3	et	et	PROPN
ejpam-5839	799	4	al	al	PROPN
ejpam-5839	799	5	.	.	PUNCT
ejpam-5839	799	6	/	/	SYM
ejpam-5839	799	7	eur	eur	PROPN
ejpam-5839	799	8	.	.	PUNCT
ejpam-5839	800	1	j.	j.	PROPN
ejpam-5839	800	2	pure	pure	PROPN
ejpam-5839	800	3	appl	appl	PROPN
ejpam-5839	800	4	.	.	PROPN
ejpam-5839	800	5	math	math	PROPN
ejpam-5839	800	6	,	,	PUNCT
ejpam-5839	800	7	18	18	NUM
ejpam-5839	800	8	(	(	PUNCT
ejpam-5839	800	9	2	2	NUM
ejpam-5839	800	10	)	)	PUNCT
ejpam-5839	800	11	(	(	PUNCT
ejpam-5839	800	12	2025	2025	NUM
ejpam-5839	800	13	)	)	PUNCT
ejpam-5839	800	14	,	,	PUNCT
ejpam-5839	800	15	5839	5839	NUM
ejpam-5839	800	16	34	34	NUM
ejpam-5839	800	17	of	of	ADP
ejpam-5839	800	18	54	54	NUM
ejpam-5839	800	19	4	4	NUM
ejpam-5839	800	20	.	.	PUNCT
ejpam-5839	801	1	since	since	SCONJ
ejpam-5839	801	2	(	(	PUNCT
ejpam-5839	801	3	f̃	f̃	PROPN
ejpam-5839	801	4	,	,	PUNCT
ejpam-5839	801	5	ω	ω	NOUN
ejpam-5839	801	6	)	)	PUNCT
ejpam-5839	801	7	∩	∩	NOUN
ejpam-5839	801	8	(	(	PUNCT
ejpam-5839	801	9	g̃,ω	g̃,ω	PROPN
ejpam-5839	801	10	)	)	PUNCT
ejpam-5839	801	11	⊆	⊆	NUM
ejpam-5839	801	12	(	(	PUNCT
ejpam-5839	801	13	f̃	f̃	PROPN
ejpam-5839	801	14	,	,	PUNCT
ejpam-5839	801	15	ω	ω	PROPN
ejpam-5839	801	16	)	)	PUNCT
ejpam-5839	801	17	and	and	CCONJ
ejpam-5839	801	18	(	(	PUNCT
ejpam-5839	801	19	f̃	f̃	PROPN
ejpam-5839	801	20	,	,	PUNCT
ejpam-5839	801	21	ω	ω	NOUN
ejpam-5839	801	22	)	)	PUNCT
ejpam-5839	801	23	∩	∩	NOUN
ejpam-5839	801	24	(	(	PUNCT
ejpam-5839	801	25	g̃,ω	g̃,ω	PROPN
ejpam-5839	801	26	)	)	PUNCT
ejpam-5839	801	27	⊆	⊆	NUM
ejpam-5839	801	28	(	(	PUNCT
ejpam-5839	801	29	g̃,ω	g̃,ω	PROPN
ejpam-5839	801	30	)	)	PUNCT
ejpam-5839	801	31	,	,	PUNCT
ejpam-5839	801	32	we	we	PRON
ejpam-5839	801	33	have	have	VERB
ejpam-5839	801	34	[	[	PUNCT
ejpam-5839	801	35	(	(	PUNCT
ejpam-5839	801	36	f̃	f̃	PROPN
ejpam-5839	801	37	,	,	PUNCT
ejpam-5839	801	38	ω	ω	NOUN
ejpam-5839	801	39	)	)	PUNCT
ejpam-5839	801	40	∩	∩	NOUN
ejpam-5839	801	41	(	(	PUNCT
ejpam-5839	801	42	g̃,ω	g̃,ω	PROPN
ejpam-5839	801	43	)	)	PUNCT
ejpam-5839	801	44	]	]	PUNCT
ejpam-5839	801	45	◦	◦	NOUN
ejpam-5839	801	46	⊆	⊆	NUM
ejpam-5839	801	47	(	(	PUNCT
ejpam-5839	801	48	f̃	f̃	PROPN
ejpam-5839	801	49	,	,	PUNCT
ejpam-5839	801	50	ω	ω	NOUN
ejpam-5839	801	51	)	)	PUNCT
ejpam-5839	801	52	◦	◦	NOUN
ejpam-5839	801	53	and	and	CCONJ
ejpam-5839	801	54	[	[	PUNCT
ejpam-5839	801	55	(	(	PUNCT
ejpam-5839	801	56	f̃	f̃	PROPN
ejpam-5839	801	57	,	,	PUNCT
ejpam-5839	801	58	ω	ω	NOUN
ejpam-5839	801	59	)	)	PUNCT
ejpam-5839	801	60	∩	∩	NOUN
ejpam-5839	801	61	(	(	PUNCT
ejpam-5839	801	62	g̃,ω	g̃,ω	PROPN
ejpam-5839	801	63	)	)	PUNCT
ejpam-5839	801	64	]	]	PUNCT
ejpam-5839	801	65	◦	◦	NOUN
ejpam-5839	801	66	⊆	⊆	NUM
ejpam-5839	801	67	(	(	PUNCT
ejpam-5839	801	68	g̃,ω)	g̃,ω)	NOUN
ejpam-5839	801	69	◦	◦	NOUN
ejpam-5839	801	70	.	.	PUNCT
ejpam-5839	802	1	therefore	therefore	ADV
ejpam-5839	802	2	,	,	PUNCT
ejpam-5839	802	3	[	[	PUNCT
ejpam-5839	802	4	(	(	PUNCT
ejpam-5839	802	5	f̃	f̃	PROPN
ejpam-5839	802	6	,	,	PUNCT
ejpam-5839	802	7	ω	ω	NOUN
ejpam-5839	802	8	)	)	PUNCT
ejpam-5839	802	9	∩	∩	NOUN
ejpam-5839	802	10	(	(	PUNCT
ejpam-5839	802	11	g̃,ω	g̃,ω	PROPN
ejpam-5839	802	12	)	)	PUNCT
ejpam-5839	802	13	]	]	PUNCT
ejpam-5839	802	14	◦	◦	NOUN
ejpam-5839	802	15	⊆	⊆	NUM
ejpam-5839	802	16	(	(	PUNCT
ejpam-5839	802	17	f̃	f̃	PROPN
ejpam-5839	802	18	,	,	PUNCT
ejpam-5839	802	19	ω	ω	NOUN
ejpam-5839	802	20	)	)	PUNCT
ejpam-5839	802	21	◦	◦	NOUN
ejpam-5839	802	22	∩	∩	NOUN
ejpam-5839	802	23	(	(	PUNCT
ejpam-5839	802	24	g̃,ω)	g̃,ω)	NOUN
ejpam-5839	802	25	◦	◦	NOUN
ejpam-5839	802	26	.	.	PUNCT
ejpam-5839	803	1	conversely	conversely	ADV
ejpam-5839	803	2	,	,	PUNCT
ejpam-5839	803	3	since	since	SCONJ
ejpam-5839	803	4	(	(	PUNCT
ejpam-5839	803	5	f̃	f̃	PROPN
ejpam-5839	803	6	,	,	PUNCT
ejpam-5839	803	7	ω	ω	NOUN
ejpam-5839	803	8	)	)	PUNCT
ejpam-5839	803	9	◦	◦	NOUN
ejpam-5839	803	10	⊆	⊆	NUM
ejpam-5839	803	11	(	(	PUNCT
ejpam-5839	803	12	f̃	f̃	PROPN
ejpam-5839	803	13	,	,	PUNCT
ejpam-5839	803	14	ω	ω	PROPN
ejpam-5839	803	15	)	)	PUNCT
ejpam-5839	803	16	and	and	CCONJ
ejpam-5839	803	17	(	(	PUNCT
ejpam-5839	803	18	g̃,ω	g̃,ω	NOUN
ejpam-5839	803	19	)	)	PUNCT
ejpam-5839	803	20	◦	◦	NOUN
ejpam-5839	803	21	⊆	⊆	NUM
ejpam-5839	803	22	(	(	PUNCT
ejpam-5839	803	23	g̃,ω	g̃,ω	NOUN
ejpam-5839	803	24	)	)	PUNCT
ejpam-5839	803	25	,	,	PUNCT
ejpam-5839	803	26	we	we	PRON
ejpam-5839	803	27	obtain	obtain	VERB
ejpam-5839	803	28	(	(	PUNCT
ejpam-5839	803	29	f̃	f̃	PROPN
ejpam-5839	803	30	,	,	PUNCT
ejpam-5839	803	31	ω	ω	NOUN
ejpam-5839	803	32	)	)	PUNCT
ejpam-5839	803	33	◦	◦	NOUN
ejpam-5839	803	34	∩	∩	NOUN
ejpam-5839	803	35	(	(	PUNCT
ejpam-5839	803	36	g̃,ω	g̃,ω	NOUN
ejpam-5839	803	37	)	)	PUNCT
ejpam-5839	803	38	◦	◦	NOUN
ejpam-5839	803	39	⊆	⊆	NUM
ejpam-5839	803	40	(	(	PUNCT
ejpam-5839	803	41	f̃	f̃	PROPN
ejpam-5839	803	42	,	,	PUNCT
ejpam-5839	803	43	ω	ω	NOUN
ejpam-5839	803	44	)	)	PUNCT
ejpam-5839	803	45	∩	∩	NOUN
ejpam-5839	803	46	(	(	PUNCT
ejpam-5839	803	47	g̃,ω	g̃,ω	PROPN
ejpam-5839	803	48	)	)	PUNCT
ejpam-5839	803	49	.	.	PUNCT
ejpam-5839	804	1	since	since	SCONJ
ejpam-5839	804	2	[	[	PUNCT
ejpam-5839	804	3	(	(	PUNCT
ejpam-5839	804	4	f̃	f̃	PROPN
ejpam-5839	804	5	,	,	PUNCT
ejpam-5839	804	6	ω	ω	NOUN
ejpam-5839	804	7	)	)	PUNCT
ejpam-5839	804	8	∩	∩	NOUN
ejpam-5839	804	9	(	(	PUNCT
ejpam-5839	804	10	g̃,ω	g̃,ω	PROPN
ejpam-5839	804	11	)	)	PUNCT
ejpam-5839	804	12	]	]	PUNCT
ejpam-5839	804	13	◦	◦	NOUN
ejpam-5839	804	14	is	be	AUX
ejpam-5839	804	15	the	the	DET
ejpam-5839	804	16	largest	large	ADJ
ejpam-5839	804	17	qpns	qpns	NOUN
ejpam-5839	804	18	s	s	NOUN
ejpam-5839	804	19	-	-	ADJ
ejpam-5839	804	20	open	open	ADJ
ejpam-5839	804	21	set	set	NOUN
ejpam-5839	804	22	contained	contain	VERB
ejpam-5839	804	23	in	in	ADP
ejpam-5839	804	24	(	(	PUNCT
ejpam-5839	804	25	f̃	f̃	PROPN
ejpam-5839	804	26	,	,	PUNCT
ejpam-5839	804	27	ω)∩	ω)∩	NUM
ejpam-5839	804	28	(	(	PUNCT
ejpam-5839	804	29	g̃,ω	g̃,ω	PROPN
ejpam-5839	804	30	)	)	PUNCT
ejpam-5839	804	31	,	,	PUNCT
ejpam-5839	804	32	it	it	PRON
ejpam-5839	804	33	follows	follow	VERB
ejpam-5839	804	34	that	that	SCONJ
ejpam-5839	804	35	(	(	PUNCT
ejpam-5839	804	36	f̃	f̃	PROPN
ejpam-5839	804	37	,	,	PUNCT
ejpam-5839	804	38	ω	ω	NOUN
ejpam-5839	804	39	)	)	PUNCT
ejpam-5839	804	40	◦	◦	NOUN
ejpam-5839	804	41	∩	∩	NOUN
ejpam-5839	804	42	(	(	PUNCT
ejpam-5839	804	43	g̃,ω	g̃,ω	NOUN
ejpam-5839	804	44	)	)	PUNCT
ejpam-5839	804	45	◦	◦	NOUN
ejpam-5839	804	46	⊆	⊆	NUM
ejpam-5839	804	47	[	[	PUNCT
ejpam-5839	804	48	(	(	PUNCT
ejpam-5839	804	49	f̃	f̃	PROPN
ejpam-5839	804	50	,	,	PUNCT
ejpam-5839	804	51	ω	ω	NOUN
ejpam-5839	804	52	)	)	PUNCT
ejpam-5839	804	53	∩	∩	NOUN
ejpam-5839	804	54	(	(	PUNCT
ejpam-5839	804	55	g̃,ω	g̃,ω	PROPN
ejpam-5839	804	56	)	)	PUNCT
ejpam-5839	804	57	]	]	PUNCT
ejpam-5839	804	58	◦	◦	NOUN
ejpam-5839	804	59	.	.	PUNCT
ejpam-5839	805	1	thus	thus	ADV
ejpam-5839	805	2	,	,	PUNCT
ejpam-5839	805	3	[	[	PUNCT
ejpam-5839	805	4	(	(	PUNCT
ejpam-5839	805	5	f̃	f̃	PROPN
ejpam-5839	805	6	,	,	PUNCT
ejpam-5839	805	7	ω	ω	NOUN
ejpam-5839	805	8	)	)	PUNCT
ejpam-5839	805	9	∩	∩	NOUN
ejpam-5839	805	10	(	(	PUNCT
ejpam-5839	805	11	g̃,ω	g̃,ω	PROPN
ejpam-5839	805	12	)	)	PUNCT
ejpam-5839	805	13	]	]	PUNCT
ejpam-5839	805	14	◦	◦	NOUN
ejpam-5839	805	15	=	=	SYM
ejpam-5839	805	16	(	(	PUNCT
ejpam-5839	805	17	f̃	f̃	PROPN
ejpam-5839	805	18	,	,	PUNCT
ejpam-5839	805	19	ω	ω	NOUN
ejpam-5839	805	20	)	)	PUNCT
ejpam-5839	805	21	◦	◦	NOUN
ejpam-5839	805	22	∩	∩	NOUN
ejpam-5839	805	23	(	(	PUNCT
ejpam-5839	805	24	g̃,ω)	g̃,ω)	NOUN
ejpam-5839	805	25	◦	◦	NOUN
ejpam-5839	805	26	.	.	PROPN
ejpam-5839	805	27	5	5	NUM
ejpam-5839	805	28	.	.	PUNCT
ejpam-5839	806	1	since	since	SCONJ
ejpam-5839	806	2	(	(	PUNCT
ejpam-5839	806	3	f̃	f̃	PROPN
ejpam-5839	806	4	,	,	PUNCT
ejpam-5839	806	5	ω	ω	NUM
ejpam-5839	806	6	)	)	PUNCT
ejpam-5839	806	7	⊆	⊆	NUM
ejpam-5839	806	8	(	(	PUNCT
ejpam-5839	806	9	f̃	f̃	PROPN
ejpam-5839	806	10	,	,	PUNCT
ejpam-5839	806	11	ω	ω	NUM
ejpam-5839	806	12	)	)	PUNCT
ejpam-5839	806	13	∪	∪	NOUN
ejpam-5839	806	14	(	(	PUNCT
ejpam-5839	806	15	g̃,ω	g̃,ω	NOUN
ejpam-5839	806	16	)	)	PUNCT
ejpam-5839	806	17	and	and	CCONJ
ejpam-5839	806	18	(	(	PUNCT
ejpam-5839	806	19	g̃,ω	g̃,ω	PROPN
ejpam-5839	806	20	)	)	PUNCT
ejpam-5839	806	21	⊆	⊆	NUM
ejpam-5839	806	22	(	(	PUNCT
ejpam-5839	806	23	f̃	f̃	PROPN
ejpam-5839	806	24	,	,	PUNCT
ejpam-5839	806	25	ω	ω	NUM
ejpam-5839	806	26	)	)	PUNCT
ejpam-5839	806	27	∪	∪	NOUN
ejpam-5839	806	28	(	(	PUNCT
ejpam-5839	806	29	g̃,ω	g̃,ω	PROPN
ejpam-5839	806	30	)	)	PUNCT
ejpam-5839	806	31	,	,	PUNCT
ejpam-5839	806	32	we	we	PRON
ejpam-5839	806	33	have	have	VERB
ejpam-5839	806	34	(	(	PUNCT
ejpam-5839	806	35	f̃	f̃	PROPN
ejpam-5839	806	36	,	,	PUNCT
ejpam-5839	806	37	ω	ω	NOUN
ejpam-5839	806	38	)	)	PUNCT
ejpam-5839	806	39	◦	◦	NOUN
ejpam-5839	806	40	⊆	⊆	NUM
ejpam-5839	806	41	[	[	PUNCT
ejpam-5839	806	42	(	(	PUNCT
ejpam-5839	806	43	f̃	f̃	PROPN
ejpam-5839	806	44	,	,	PUNCT
ejpam-5839	806	45	ω	ω	NOUN
ejpam-5839	806	46	)	)	PUNCT
ejpam-5839	806	47	∪	∪	NOUN
ejpam-5839	806	48	(	(	PUNCT
ejpam-5839	806	49	g̃,ω	g̃,ω	PROPN
ejpam-5839	806	50	)	)	PUNCT
ejpam-5839	806	51	]	]	PUNCT
ejpam-5839	806	52	◦	◦	NOUN
ejpam-5839	806	53	and	and	CCONJ
ejpam-5839	806	54	(	(	PUNCT
ejpam-5839	806	55	g̃,ω	g̃,ω	NOUN
ejpam-5839	806	56	)	)	PUNCT
ejpam-5839	806	57	◦	◦	NOUN
ejpam-5839	806	58	⊆	⊆	NUM
ejpam-5839	806	59	[	[	PUNCT
ejpam-5839	806	60	(	(	PUNCT
ejpam-5839	806	61	f̃	f̃	PROPN
ejpam-5839	806	62	,	,	PUNCT
ejpam-5839	806	63	ω	ω	NOUN
ejpam-5839	806	64	)	)	PUNCT
ejpam-5839	806	65	∪	∪	NOUN
ejpam-5839	806	66	(	(	PUNCT
ejpam-5839	806	67	g̃,ω	g̃,ω	PROPN
ejpam-5839	806	68	)	)	PUNCT
ejpam-5839	806	69	]	]	PUNCT
ejpam-5839	806	70	◦	◦	NOUN
ejpam-5839	806	71	.	.	PUNCT
ejpam-5839	807	1	thus	thus	ADV
ejpam-5839	807	2	,	,	PUNCT
ejpam-5839	807	3	(	(	PUNCT
ejpam-5839	807	4	f̃	f̃	PROPN
ejpam-5839	807	5	,	,	PUNCT
ejpam-5839	807	6	ω	ω	NOUN
ejpam-5839	807	7	)	)	PUNCT
ejpam-5839	807	8	◦	◦	NOUN
ejpam-5839	807	9	∪	∪	ADP
ejpam-5839	807	10	(	(	PUNCT
ejpam-5839	807	11	g̃,ω	g̃,ω	NOUN
ejpam-5839	807	12	)	)	PUNCT
ejpam-5839	807	13	◦	◦	NOUN
ejpam-5839	807	14	⊆	⊆	NUM
ejpam-5839	807	15	[	[	PUNCT
ejpam-5839	807	16	(	(	PUNCT
ejpam-5839	807	17	f̃	f̃	PROPN
ejpam-5839	807	18	,	,	PUNCT
ejpam-5839	807	19	ω	ω	NOUN
ejpam-5839	807	20	)	)	PUNCT
ejpam-5839	807	21	∪	∪	NOUN
ejpam-5839	807	22	(	(	PUNCT
ejpam-5839	807	23	g̃,ω	g̃,ω	PROPN
ejpam-5839	807	24	)	)	PUNCT
ejpam-5839	807	25	]	]	PUNCT
ejpam-5839	807	26	◦	◦	NOUN
ejpam-5839	807	27	.	.	PUNCT
ejpam-5839	808	1	theorem	theorem	VERB
ejpam-5839	808	2	13	13	NUM
ejpam-5839	808	3	.	.	PUNCT
ejpam-5839	809	1	let	let	AUX
ejpam-5839	809	2	(	(	PUNCT
ejpam-5839	809	3	x	x	NOUN
ejpam-5839	809	4	,	,	PUNCT
ejpam-5839	809	5	τ1	τ1	NOUN
ejpam-5839	809	6	,	,	PUNCT
ejpam-5839	809	7	τ2,ω	τ2,ω	PUNCT
ejpam-5839	809	8	)	)	PUNCT
ejpam-5839	809	9	be	be	VERB
ejpam-5839	809	10	a	a	DET
ejpam-5839	809	11	qpnsbts	qpnsbt	NOUN
ejpam-5839	809	12	over	over	ADP
ejpam-5839	809	13	x	x	NOUN
ejpam-5839	809	14	,	,	PUNCT
ejpam-5839	809	15	and	and	CCONJ
ejpam-5839	809	16	let	let	VERB
ejpam-5839	809	17	(	(	PUNCT
ejpam-5839	809	18	f̃	f̃	PROPN
ejpam-5839	809	19	,	,	PUNCT
ejpam-5839	809	20	ω	ω	PROPN
ejpam-5839	809	21	)	)	PUNCT
ejpam-5839	809	22	be	be	VERB
ejpam-5839	809	23	a	a	DET
ejpam-5839	809	24	qpns	qpns	NOUN
ejpam-5839	809	25	subset	subset	VERB
ejpam-5839	809	26	.	.	PUNCT
ejpam-5839	810	1	then	then	ADV
ejpam-5839	810	2	,	,	PUNCT
ejpam-5839	810	3	(	(	PUNCT
ejpam-5839	810	4	f̃	f̃	PROPN
ejpam-5839	810	5	,	,	PUNCT
ejpam-5839	810	6	ω	ω	PROPN
ejpam-5839	810	7	)	)	PUNCT
ejpam-5839	810	8	is	be	AUX
ejpam-5839	810	9	a	a	DET
ejpam-5839	810	10	qpns	qpns	NOUN
ejpam-5839	810	11	p	p	NOUN
ejpam-5839	810	12	-	-	PUNCT
ejpam-5839	810	13	closer	close	ADJ
ejpam-5839	810	14	set	set	NOUN
ejpam-5839	810	15	if	if	SCONJ
ejpam-5839	810	16	and	and	CCONJ
ejpam-5839	810	17	only	only	ADV
ejpam-5839	810	18	if	if	SCONJ
ejpam-5839	810	19	(	(	PUNCT
ejpam-5839	810	20	f̃	f̃	PROPN
ejpam-5839	810	21	,	,	PUNCT
ejpam-5839	810	22	ω	ω	NOUN
ejpam-5839	810	23	)	)	PUNCT
ejpam-5839	810	24	=	=	SYM
ejpam-5839	810	25	(	(	PUNCT
ejpam-5839	810	26	f̃	f̃	PROPN
ejpam-5839	810	27	,	,	PUNCT
ejpam-5839	810	28	ω	ω	PROPN
ejpam-5839	810	29	)	)	PUNCT
ejpam-5839	810	30	.	.	PUNCT
ejpam-5839	811	1	proof	proof	NOUN
ejpam-5839	811	2	.	.	PUNCT
ejpam-5839	812	1	let	let	VERB
ejpam-5839	812	2	(	(	PUNCT
ejpam-5839	812	3	f̃	f̃	PROPN
ejpam-5839	812	4	,	,	PUNCT
ejpam-5839	812	5	ω	ω	PROPN
ejpam-5839	812	6	)	)	PUNCT
ejpam-5839	812	7	be	be	AUX
ejpam-5839	812	8	a	a	DET
ejpam-5839	812	9	qpns	qpns	NOUN
ejpam-5839	812	10	p	p	NOUN
ejpam-5839	812	11	-	-	PUNCT
ejpam-5839	812	12	closer	close	ADJ
ejpam-5839	812	13	set	set	NOUN
ejpam-5839	812	14	.	.	PUNCT
ejpam-5839	813	1	then	then	ADV
ejpam-5839	813	2	,	,	PUNCT
ejpam-5839	813	3	(	(	PUNCT
ejpam-5839	813	4	f̃	f̃	PROPN
ejpam-5839	813	5	,	,	PUNCT
ejpam-5839	813	6	ω)d	ω)d	NOUN
ejpam-5839	813	7	=	=	SYM
ejpam-5839	813	8	(	(	PUNCT
ejpam-5839	813	9	f̃	f̃	PROPN
ejpam-5839	813	10	,	,	PUNCT
ejpam-5839	813	11	ω	ω	PROPN
ejpam-5839	813	12	)	)	PUNCT
ejpam-5839	813	13	which	which	PRON
ejpam-5839	813	14	implies	imply	VERB
ejpam-5839	813	15	(	(	PUNCT
ejpam-5839	813	16	f̃	f̃	PROPN
ejpam-5839	813	17	,	,	PUNCT
ejpam-5839	813	18	ω)∪̃(f̃	ω)∪̃(f̃	PROPN
ejpam-5839	813	19	,	,	PUNCT
ejpam-5839	813	20	ω)d	ω)d	X
ejpam-5839	813	21	∼=	∼=	PROPN
ejpam-5839	813	22	(	(	PUNCT
ejpam-5839	813	23	f̃	f̃	PROPN
ejpam-5839	813	24	,	,	PUNCT
ejpam-5839	813	25	ω	ω	NOUN
ejpam-5839	813	26	)	)	PUNCT
ejpam-5839	813	27	⇒	⇒	NOUN
ejpam-5839	813	28	(	(	PUNCT
ejpam-5839	813	29	f̃	f̃	PROPN
ejpam-5839	813	30	,	,	PUNCT
ejpam-5839	813	31	ω	ω	NOUN
ejpam-5839	813	32	)	)	PUNCT
ejpam-5839	813	33	∼=	∼=	PROPN
ejpam-5839	813	34	(	(	PUNCT
ejpam-5839	813	35	f̃	f̃	PROPN
ejpam-5839	813	36	,	,	PUNCT
ejpam-5839	813	37	ω	ω	NOUN
ejpam-5839	813	38	)	)	PUNCT
ejpam-5839	813	39	conversely	conversely	ADV
ejpam-5839	813	40	,	,	PUNCT
ejpam-5839	813	41	let	let	VERB
ejpam-5839	813	42	(	(	PUNCT
ejpam-5839	813	43	f̃	f̃	PROPN
ejpam-5839	813	44	,	,	PUNCT
ejpam-5839	813	45	ω	ω	NOUN
ejpam-5839	813	46	)	)	PUNCT
ejpam-5839	813	47	∼=	∼=	PROPN
ejpam-5839	813	48	(	(	PUNCT
ejpam-5839	813	49	f̃	f̃	PROPN
ejpam-5839	813	50	,	,	PUNCT
ejpam-5839	813	51	ω	ω	NUM
ejpam-5839	813	52	)	)	PUNCT
ejpam-5839	813	53	this	this	PRON
ejpam-5839	813	54	implies	imply	VERB
ejpam-5839	813	55	(	(	PUNCT
ejpam-5839	813	56	f̃	f̃	PROPN
ejpam-5839	813	57	,	,	PUNCT
ejpam-5839	813	58	ω)∪̃(f̃	ω)∪̃(f̃	PROPN
ejpam-5839	813	59	,	,	PUNCT
ejpam-5839	813	60	ω)d	ω)d	X
ejpam-5839	813	61	∼=	∼=	PROPN
ejpam-5839	813	62	(	(	PUNCT
ejpam-5839	813	63	f̃	f̃	PROPN
ejpam-5839	813	64	,	,	PUNCT
ejpam-5839	813	65	ω	ω	NOUN
ejpam-5839	813	66	)	)	PUNCT
ejpam-5839	813	67	⇒	⇒	NOUN
ejpam-5839	813	68	(	(	PUNCT
ejpam-5839	813	69	f̃	f̃	PROPN
ejpam-5839	813	70	,	,	PUNCT
ejpam-5839	813	71	ω)d	ω)d	X
ejpam-5839	813	72	∼=	∼=	PROPN
ejpam-5839	813	73	(	(	PUNCT
ejpam-5839	813	74	f̃	f̃	PROPN
ejpam-5839	813	75	,	,	PUNCT
ejpam-5839	813	76	ω	ω	PROPN
ejpam-5839	813	77	)	)	PUNCT
ejpam-5839	813	78	which	which	PRON
ejpam-5839	813	79	implies	imply	VERB
ejpam-5839	813	80	that	that	SCONJ
ejpam-5839	813	81	(	(	PUNCT
ejpam-5839	813	82	f̃	f̃	PROPN
ejpam-5839	813	83	,	,	PUNCT
ejpam-5839	813	84	ω	ω	PROPN
ejpam-5839	813	85	)	)	PUNCT
ejpam-5839	813	86	is	be	AUX
ejpam-5839	813	87	a	a	DET
ejpam-5839	813	88	qpns	qpns	NOUN
ejpam-5839	813	89	p	p	NOUN
ejpam-5839	813	90	-	-	PUNCT
ejpam-5839	813	91	closer	close	ADJ
ejpam-5839	813	92	set	set	NOUN
ejpam-5839	813	93	.	.	PUNCT
ejpam-5839	814	1	theorem	theorem	VERB
ejpam-5839	814	2	14	14	NUM
ejpam-5839	814	3	.	.	PUNCT
ejpam-5839	815	1	let	let	VERB
ejpam-5839	815	2	(	(	PUNCT
ejpam-5839	815	3	x	x	NOUN
ejpam-5839	815	4	,	,	PUNCT
ejpam-5839	815	5	τ1	τ1	NOUN
ejpam-5839	815	6	,	,	PUNCT
ejpam-5839	815	7	τ2,ω	τ2,ω	PUNCT
ejpam-5839	815	8	)	)	PUNCT
ejpam-5839	815	9	be	be	AUX
ejpam-5839	815	10	a	a	DET
ejpam-5839	815	11	qpnsbts	qpnsbt	NOUN
ejpam-5839	815	12	over	over	ADP
ejpam-5839	815	13	x	x	NOUN
ejpam-5839	815	14	,	,	PUNCT
ejpam-5839	815	15	and	and	CCONJ
ejpam-5839	815	16	let	let	VERB
ejpam-5839	815	17	(	(	PUNCT
ejpam-5839	815	18	f̃	f̃	PROPN
ejpam-5839	815	19	,	,	PUNCT
ejpam-5839	815	20	ω	ω	PROPN
ejpam-5839	815	21	)	)	PUNCT
ejpam-5839	815	22	and	and	CCONJ
ejpam-5839	815	23	(	(	PUNCT
ejpam-5839	815	24	g̃,ω	g̃,ω	PROPN
ejpam-5839	815	25	)	)	PUNCT
ejpam-5839	815	26	be	be	AUX
ejpam-5839	815	27	qpns	qpns	NOUN
ejpam-5839	815	28	subsets	subset	NOUN
ejpam-5839	815	29	.	.	PUNCT
ejpam-5839	816	1	then	then	ADV
ejpam-5839	816	2	:	:	PUNCT
ejpam-5839	816	3	(	(	PUNCT
ejpam-5839	816	4	i	i	NOUN
ejpam-5839	816	5	)	)	PUNCT
ejpam-5839	816	6	(	(	PUNCT
ejpam-5839	816	7	f̃	f̃	PROPN
ejpam-5839	816	8	,	,	PUNCT
ejpam-5839	816	9	ω	ω	NOUN
ejpam-5839	816	10	)	)	PUNCT
ejpam-5839	816	11	=	=	SYM
ejpam-5839	816	12	(	(	PUNCT
ejpam-5839	816	13	f̃	f̃	PROPN
ejpam-5839	816	14	,	,	PUNCT
ejpam-5839	816	15	ω	ω	PROPN
ejpam-5839	816	16	)	)	PUNCT
ejpam-5839	816	17	,	,	PUNCT
ejpam-5839	816	18	a.	a.	NOUN
ejpam-5839	816	19	shihadeh	shihadeh	VERB
ejpam-5839	816	20	et	et	PROPN
ejpam-5839	816	21	al	al	PROPN
ejpam-5839	816	22	.	.	PUNCT
ejpam-5839	816	23	/	/	SYM
ejpam-5839	816	24	eur	eur	PROPN
ejpam-5839	816	25	.	.	PUNCT
ejpam-5839	817	1	j.	j.	PROPN
ejpam-5839	817	2	pure	pure	PROPN
ejpam-5839	817	3	appl	appl	PROPN
ejpam-5839	817	4	.	.	PROPN
ejpam-5839	817	5	math	math	PROPN
ejpam-5839	817	6	,	,	PUNCT
ejpam-5839	817	7	18	18	NUM
ejpam-5839	817	8	(	(	PUNCT
ejpam-5839	817	9	2	2	NUM
ejpam-5839	817	10	)	)	PUNCT
ejpam-5839	817	11	(	(	PUNCT
ejpam-5839	817	12	2025	2025	NUM
ejpam-5839	817	13	)	)	PUNCT
ejpam-5839	817	14	,	,	PUNCT
ejpam-5839	817	15	5839	5839	NUM
ejpam-5839	817	16	35	35	NUM
ejpam-5839	817	17	of	of	ADP
ejpam-5839	817	18	54	54	NUM
ejpam-5839	817	19	(	(	PUNCT
ejpam-5839	817	20	ii	ii	NOUN
ejpam-5839	817	21	)	)	PUNCT
ejpam-5839	817	22	0(⟨x̃,ω⟩	0(⟨x̃,ω⟩	NUM
ejpam-5839	817	23	)	)	PUNCT
ejpam-5839	817	24	=	=	SYM
ejpam-5839	817	25	0(⟨x̃,ω⟩	0(⟨x̃,ω⟩	NUM
ejpam-5839	817	26	)	)	PUNCT
ejpam-5839	817	27	and	and	CCONJ
ejpam-5839	817	28	1(⟨x̃,ω⟩	1(⟨x̃,ω⟩	NUM
ejpam-5839	817	29	)	)	PUNCT
ejpam-5839	817	30	=	=	SYM
ejpam-5839	817	31	1(⟨x̃,ω⟩	1(⟨x̃,ω⟩	NUM
ejpam-5839	817	32	)	)	PUNCT
ejpam-5839	817	33	,	,	PUNCT
ejpam-5839	817	34	(	(	PUNCT
ejpam-5839	817	35	iii	iii	X
ejpam-5839	817	36	)	)	PUNCT
ejpam-5839	817	37	(	(	PUNCT
ejpam-5839	817	38	f̃	f̃	PROPN
ejpam-5839	817	39	,	,	PUNCT
ejpam-5839	817	40	ω	ω	NUM
ejpam-5839	817	41	)	)	PUNCT
ejpam-5839	818	1	⊆	⊆	NUM
ejpam-5839	818	2	⟨(g̃,ω)⟩	⟨(g̃,ω)⟩	SYM
ejpam-5839	818	3	⇒	⇒	NOUN
ejpam-5839	818	4	(	(	PUNCT
ejpam-5839	818	5	f̃	f̃	PROPN
ejpam-5839	818	6	,	,	PUNCT
ejpam-5839	818	7	ω	ω	PROPN
ejpam-5839	818	8	)	)	PUNCT
ejpam-5839	818	9	⊆	⊆	NUM
ejpam-5839	818	10	(	(	PUNCT
ejpam-5839	818	11	g̃,ω	g̃,ω	NOUN
ejpam-5839	818	12	)	)	PUNCT
ejpam-5839	818	13	,	,	PUNCT
ejpam-5839	818	14	(	(	PUNCT
ejpam-5839	818	15	iv	iv	X
ejpam-5839	818	16	)	)	PUNCT
ejpam-5839	818	17	(	(	PUNCT
ejpam-5839	818	18	f̃	f̃	PROPN
ejpam-5839	818	19	,	,	PUNCT
ejpam-5839	818	20	ω	ω	NUM
ejpam-5839	818	21	)	)	PUNCT
ejpam-5839	818	22	∪	∪	NOUN
ejpam-5839	818	23	(	(	PUNCT
ejpam-5839	818	24	g̃,ω	g̃,ω	NOUN
ejpam-5839	818	25	)	)	PUNCT
ejpam-5839	818	26	=	=	PUNCT
ejpam-5839	818	27	(	(	PUNCT
ejpam-5839	818	28	f̃	f̃	PROPN
ejpam-5839	818	29	,	,	PUNCT
ejpam-5839	818	30	ω	ω	NUM
ejpam-5839	818	31	)	)	PUNCT
ejpam-5839	818	32	∪	∪	NOUN
ejpam-5839	818	33	(	(	PUNCT
ejpam-5839	818	34	g̃,ω	g̃,ω	PROPN
ejpam-5839	818	35	)	)	PUNCT
ejpam-5839	818	36	,	,	PUNCT
ejpam-5839	818	37	(	(	PUNCT
ejpam-5839	818	38	v	v	NOUN
ejpam-5839	818	39	)	)	PUNCT
ejpam-5839	818	40	(	(	PUNCT
ejpam-5839	818	41	f̃	f̃	PROPN
ejpam-5839	818	42	,	,	PUNCT
ejpam-5839	818	43	ω	ω	NOUN
ejpam-5839	818	44	)	)	PUNCT
ejpam-5839	818	45	∩	∩	NOUN
ejpam-5839	818	46	(	(	PUNCT
ejpam-5839	818	47	g̃,ω	g̃,ω	PROPN
ejpam-5839	818	48	)	)	PUNCT
ejpam-5839	818	49	⊆	⊆	NUM
ejpam-5839	818	50	(	(	PUNCT
ejpam-5839	818	51	f̃	f̃	PROPN
ejpam-5839	818	52	,	,	PUNCT
ejpam-5839	818	53	ω	ω	NOUN
ejpam-5839	818	54	)	)	PUNCT
ejpam-5839	818	55	∩	∩	NOUN
ejpam-5839	818	56	(	(	PUNCT
ejpam-5839	818	57	g̃,ω	g̃,ω	PROPN
ejpam-5839	818	58	)	)	PUNCT
ejpam-5839	818	59	.	.	PUNCT
ejpam-5839	819	1	proof	proof	NOUN
ejpam-5839	819	2	.	.	PUNCT
ejpam-5839	820	1	let	let	VERB
ejpam-5839	820	2	(	(	PUNCT
ejpam-5839	820	3	x	x	NOUN
ejpam-5839	820	4	,	,	PUNCT
ejpam-5839	820	5	τ1	τ1	NOUN
ejpam-5839	820	6	,	,	PUNCT
ejpam-5839	820	7	τ2,ω	τ2,ω	PUNCT
ejpam-5839	820	8	)	)	PUNCT
ejpam-5839	820	9	be	be	AUX
ejpam-5839	820	10	a	a	DET
ejpam-5839	820	11	qpnsbts	qpnsbt	NOUN
ejpam-5839	820	12	over	over	ADP
ejpam-5839	820	13	x	x	NOUN
ejpam-5839	820	14	,	,	PUNCT
ejpam-5839	820	15	and	and	CCONJ
ejpam-5839	820	16	let	let	VERB
ejpam-5839	820	17	(	(	PUNCT
ejpam-5839	820	18	f̃	f̃	PROPN
ejpam-5839	820	19	,	,	PUNCT
ejpam-5839	820	20	ω	ω	PROPN
ejpam-5839	820	21	)	)	PUNCT
ejpam-5839	820	22	and	and	CCONJ
ejpam-5839	820	23	(	(	PUNCT
ejpam-5839	820	24	g̃,ω	g̃,ω	PROPN
ejpam-5839	820	25	)	)	PUNCT
ejpam-5839	820	26	be	be	AUX
ejpam-5839	820	27	qpns	qpns	NOUN
ejpam-5839	820	28	subsets	subset	NOUN
ejpam-5839	820	29	.	.	PUNCT
ejpam-5839	821	1	then	then	ADV
ejpam-5839	821	2	:	:	PUNCT
ejpam-5839	821	3	(	(	PUNCT
ejpam-5839	821	4	i	i	NOUN
ejpam-5839	821	5	)	)	PUNCT
ejpam-5839	821	6	if	if	SCONJ
ejpam-5839	821	7	(	(	PUNCT
ejpam-5839	821	8	f̃	f̃	PROPN
ejpam-5839	821	9	,	,	PUNCT
ejpam-5839	821	10	ω	ω	NOUN
ejpam-5839	821	11	)	)	PUNCT
ejpam-5839	821	12	=	=	SYM
ejpam-5839	821	13	(	(	PUNCT
ejpam-5839	821	14	g̃,ω	g̃,ω	PROPN
ejpam-5839	821	15	)	)	PUNCT
ejpam-5839	821	16	,	,	PUNCT
ejpam-5839	821	17	then	then	ADV
ejpam-5839	821	18	(	(	PUNCT
ejpam-5839	821	19	g̃,ω	g̃,ω	PROPN
ejpam-5839	821	20	)	)	PUNCT
ejpam-5839	821	21	is	be	AUX
ejpam-5839	821	22	a	a	DET
ejpam-5839	821	23	qpns	qpns	NOUN
ejpam-5839	821	24	s	s	NOUN
ejpam-5839	821	25	-	-	PUNCT
ejpam-5839	821	26	cs	cs	PROPN
ejpam-5839	821	27	.	.	PROPN
ejpam-5839	822	1	hence	hence	ADV
ejpam-5839	822	2	,	,	PUNCT
ejpam-5839	822	3	if	if	SCONJ
ejpam-5839	822	4	(	(	PUNCT
ejpam-5839	822	5	g̃,ω	g̃,ω	NOUN
ejpam-5839	822	6	)	)	PUNCT
ejpam-5839	822	7	and	and	CCONJ
ejpam-5839	822	8	(	(	PUNCT
ejpam-5839	822	9	g̃,ω	g̃,ω	PROPN
ejpam-5839	822	10	)	)	PUNCT
ejpam-5839	822	11	are	be	AUX
ejpam-5839	822	12	equal	equal	ADJ
ejpam-5839	822	13	,	,	PUNCT
ejpam-5839	822	14	then	then	ADV
ejpam-5839	822	15	:	:	PUNCT
ejpam-5839	822	16	(	(	PUNCT
ejpam-5839	822	17	f̃	f̃	PROPN
ejpam-5839	822	18	,	,	PUNCT
ejpam-5839	822	19	ω	ω	NOUN
ejpam-5839	822	20	)	)	PUNCT
ejpam-5839	822	21	=	=	SYM
ejpam-5839	822	22	(	(	PUNCT
ejpam-5839	822	23	f̃	f̃	PROPN
ejpam-5839	822	24	,	,	PUNCT
ejpam-5839	822	25	ω	ω	PROPN
ejpam-5839	822	26	)	)	PUNCT
ejpam-5839	822	27	(	(	PUNCT
ejpam-5839	822	28	ii	ii	NOUN
ejpam-5839	822	29	)	)	PUNCT
ejpam-5839	822	30	since	since	SCONJ
ejpam-5839	822	31	0(⟨x̃,ω⟩	0(⟨x̃,ω⟩	NUM
ejpam-5839	822	32	)	)	PUNCT
ejpam-5839	822	33	and	and	CCONJ
ejpam-5839	822	34	1(⟨x̃,ω⟩	1(⟨x̃,ω⟩	NUM
ejpam-5839	822	35	)	)	PUNCT
ejpam-5839	822	36	are	be	AUX
ejpam-5839	822	37	always	always	ADV
ejpam-5839	822	38	qpns	qpns	NOUN
ejpam-5839	822	39	s	s	NOUN
ejpam-5839	822	40	-	-	PUNCT
ejpam-5839	822	41	cs	cs	ADJ
ejpam-5839	822	42	,	,	PUNCT
ejpam-5839	822	43	by	by	ADP
ejpam-5839	822	44	the	the	DET
ejpam-5839	822	45	above	above	ADJ
ejpam-5839	822	46	result	result	NOUN
ejpam-5839	822	47	(	(	PUNCT
ejpam-5839	822	48	1	1	NUM
ejpam-5839	822	49	)	)	PUNCT
ejpam-5839	822	50	,	,	PUNCT
ejpam-5839	822	51	we	we	PRON
ejpam-5839	822	52	get	get	VERB
ejpam-5839	822	53	:	:	PUNCT
ejpam-5839	822	54	0(⟨x̃,ω⟩	0(⟨x̃,ω⟩	NUM
ejpam-5839	822	55	)	)	PUNCT
ejpam-5839	822	56	=	=	SYM
ejpam-5839	822	57	0(⟨x̃,ω⟩	0(⟨x̃,ω⟩	NUM
ejpam-5839	822	58	)	)	PUNCT
ejpam-5839	822	59	and	and	CCONJ
ejpam-5839	822	60	1(⟨x̃,ω⟩	1(⟨x̃,ω⟩	NUM
ejpam-5839	822	61	)	)	PUNCT
ejpam-5839	822	62	=	=	SYM
ejpam-5839	822	63	1(⟨x̃,ω⟩	1(⟨x̃,ω⟩	NUM
ejpam-5839	822	64	)	)	PUNCT
ejpam-5839	822	65	.	.	PUNCT
ejpam-5839	823	1	(	(	PUNCT
ejpam-5839	823	2	iii	iii	NOUN
ejpam-5839	823	3	)	)	PUNCT
ejpam-5839	823	4	since	since	SCONJ
ejpam-5839	823	5	(	(	PUNCT
ejpam-5839	823	6	f̃	f̃	PROPN
ejpam-5839	823	7	,	,	PUNCT
ejpam-5839	823	8	ω	ω	NUM
ejpam-5839	823	9	)	)	PUNCT
ejpam-5839	823	10	⊆	⊆	NUM
ejpam-5839	823	11	(	(	PUNCT
ejpam-5839	823	12	f̃	f̃	PROPN
ejpam-5839	823	13	,	,	PUNCT
ejpam-5839	823	14	ω	ω	PROPN
ejpam-5839	823	15	)	)	PUNCT
ejpam-5839	823	16	and	and	CCONJ
ejpam-5839	823	17	(	(	PUNCT
ejpam-5839	823	18	g̃,ω	g̃,ω	PROPN
ejpam-5839	823	19	)	)	PUNCT
ejpam-5839	823	20	⊆	⊆	NUM
ejpam-5839	823	21	(	(	PUNCT
ejpam-5839	823	22	g̃,ω	g̃,ω	NOUN
ejpam-5839	823	23	)	)	PUNCT
ejpam-5839	823	24	,	,	PUNCT
ejpam-5839	823	25	it	it	PRON
ejpam-5839	823	26	follows	follow	VERB
ejpam-5839	823	27	that	that	SCONJ
ejpam-5839	823	28	:	:	PUNCT
ejpam-5839	823	29	(	(	PUNCT
ejpam-5839	823	30	f̃	f̃	PROPN
ejpam-5839	823	31	,	,	PUNCT
ejpam-5839	823	32	ω	ω	PROPN
ejpam-5839	823	33	)	)	PUNCT
ejpam-5839	823	34	⊆	⊆	NUM
ejpam-5839	823	35	(	(	PUNCT
ejpam-5839	823	36	g̃,ω	g̃,ω	PROPN
ejpam-5839	823	37	)	)	PUNCT
ejpam-5839	823	38	⊆	⊆	NUM
ejpam-5839	823	39	(	(	PUNCT
ejpam-5839	823	40	g̃,ω	g̃,ω	NOUN
ejpam-5839	823	41	)	)	PUNCT
ejpam-5839	823	42	.	.	PUNCT
ejpam-5839	824	1	since	since	SCONJ
ejpam-5839	824	2	(	(	PUNCT
ejpam-5839	824	3	f̃	f̃	PROPN
ejpam-5839	824	4	,	,	PUNCT
ejpam-5839	824	5	ω	ω	PROPN
ejpam-5839	824	6	)	)	PUNCT
ejpam-5839	824	7	is	be	AUX
ejpam-5839	824	8	the	the	DET
ejpam-5839	824	9	smallest	small	ADJ
ejpam-5839	824	10	qpns	qpns	NOUN
ejpam-5839	824	11	p	p	PROPN
ejpam-5839	824	12	-	-	PUNCT
ejpam-5839	824	13	cs	cs	ADJ
ejpam-5839	824	14	covering	covering	NOUN
ejpam-5839	824	15	(	(	PUNCT
ejpam-5839	824	16	f̃	f̃	PROPN
ejpam-5839	824	17	,	,	PUNCT
ejpam-5839	824	18	ω	ω	PROPN
ejpam-5839	824	19	)	)	PUNCT
ejpam-5839	824	20	,	,	PUNCT
ejpam-5839	824	21	we	we	PRON
ejpam-5839	824	22	obtain	obtain	VERB
ejpam-5839	824	23	:	:	PUNCT
ejpam-5839	824	24	(	(	PUNCT
ejpam-5839	824	25	f̃	f̃	PROPN
ejpam-5839	824	26	,	,	PUNCT
ejpam-5839	824	27	ω	ω	PROPN
ejpam-5839	824	28	)	)	PUNCT
ejpam-5839	824	29	⊆	⊆	NUM
ejpam-5839	824	30	(	(	PUNCT
ejpam-5839	824	31	g̃,ω	g̃,ω	NOUN
ejpam-5839	824	32	)	)	PUNCT
ejpam-5839	824	33	.	.	PUNCT
ejpam-5839	825	1	(	(	PUNCT
ejpam-5839	825	2	iv	iv	X
ejpam-5839	825	3	)	)	PUNCT
ejpam-5839	825	4	since	since	SCONJ
ejpam-5839	825	5	(	(	PUNCT
ejpam-5839	825	6	f̃	f̃	PROPN
ejpam-5839	825	7	,	,	PUNCT
ejpam-5839	825	8	ω	ω	NUM
ejpam-5839	825	9	)	)	PUNCT
ejpam-5839	825	10	⊆	⊆	NUM
ejpam-5839	825	11	(	(	PUNCT
ejpam-5839	825	12	f̃	f̃	PROPN
ejpam-5839	825	13	,	,	PUNCT
ejpam-5839	825	14	ω	ω	NUM
ejpam-5839	825	15	)	)	PUNCT
ejpam-5839	825	16	∪	∪	NOUN
ejpam-5839	825	17	(	(	PUNCT
ejpam-5839	825	18	g̃,ω	g̃,ω	NOUN
ejpam-5839	825	19	)	)	PUNCT
ejpam-5839	825	20	and	and	CCONJ
ejpam-5839	825	21	(	(	PUNCT
ejpam-5839	825	22	g̃,ω	g̃,ω	PROPN
ejpam-5839	825	23	)	)	PUNCT
ejpam-5839	825	24	⊆	⊆	NUM
ejpam-5839	825	25	(	(	PUNCT
ejpam-5839	825	26	f̃	f̃	PROPN
ejpam-5839	825	27	,	,	PUNCT
ejpam-5839	825	28	ω	ω	NUM
ejpam-5839	825	29	)	)	PUNCT
ejpam-5839	825	30	∪	∪	NOUN
ejpam-5839	825	31	(	(	PUNCT
ejpam-5839	825	32	g̃,ω	g̃,ω	PROPN
ejpam-5839	825	33	)	)	PUNCT
ejpam-5839	825	34	,	,	PUNCT
ejpam-5839	825	35	we	we	PRON
ejpam-5839	825	36	have	have	VERB
ejpam-5839	825	37	:	:	PUNCT
ejpam-5839	825	38	(	(	PUNCT
ejpam-5839	825	39	f̃	f̃	PROPN
ejpam-5839	825	40	,	,	PUNCT
ejpam-5839	825	41	ω	ω	PROPN
ejpam-5839	825	42	)	)	PUNCT
ejpam-5839	825	43	⊆	⊆	NUM
ejpam-5839	825	44	(	(	PUNCT
ejpam-5839	825	45	f̃	f̃	PROPN
ejpam-5839	825	46	,	,	PUNCT
ejpam-5839	825	47	ω	ω	NUM
ejpam-5839	825	48	)	)	PUNCT
ejpam-5839	825	49	∪	∪	NOUN
ejpam-5839	825	50	(	(	PUNCT
ejpam-5839	825	51	g̃,ω	g̃,ω	NOUN
ejpam-5839	825	52	)	)	PUNCT
ejpam-5839	825	53	and	and	CCONJ
ejpam-5839	825	54	(	(	PUNCT
ejpam-5839	825	55	g̃,ω	g̃,ω	PROPN
ejpam-5839	825	56	)	)	PUNCT
ejpam-5839	825	57	⊆	⊆	NUM
ejpam-5839	825	58	(	(	PUNCT
ejpam-5839	825	59	f̃	f̃	PROPN
ejpam-5839	825	60	,	,	PUNCT
ejpam-5839	825	61	ω	ω	NUM
ejpam-5839	825	62	)	)	PUNCT
ejpam-5839	825	63	∪	∪	NOUN
ejpam-5839	825	64	(	(	PUNCT
ejpam-5839	825	65	g̃,ω	g̃,ω	NOUN
ejpam-5839	825	66	)	)	PUNCT
ejpam-5839	825	67	.	.	PUNCT
ejpam-5839	826	1	thus	thus	ADV
ejpam-5839	826	2	,	,	PUNCT
ejpam-5839	826	3	(	(	PUNCT
ejpam-5839	826	4	f̃	f̃	PROPN
ejpam-5839	826	5	,	,	PUNCT
ejpam-5839	826	6	ω	ω	NOUN
ejpam-5839	826	7	)	)	PUNCT
ejpam-5839	826	8	∪	∪	NOUN
ejpam-5839	826	9	(	(	PUNCT
ejpam-5839	826	10	g̃,ω	g̃,ω	PROPN
ejpam-5839	826	11	)	)	PUNCT
ejpam-5839	826	12	⊆	⊆	NUM
ejpam-5839	826	13	(	(	PUNCT
ejpam-5839	826	14	f̃	f̃	PROPN
ejpam-5839	826	15	,	,	PUNCT
ejpam-5839	826	16	ω	ω	NUM
ejpam-5839	826	17	)	)	PUNCT
ejpam-5839	826	18	∪	∪	NOUN
ejpam-5839	826	19	(	(	PUNCT
ejpam-5839	826	20	g̃,ω	g̃,ω	NOUN
ejpam-5839	826	21	)	)	PUNCT
ejpam-5839	826	22	.	.	PUNCT
ejpam-5839	827	1	conversely	conversely	ADV
ejpam-5839	827	2	,	,	PUNCT
ejpam-5839	827	3	since	since	SCONJ
ejpam-5839	827	4	(	(	PUNCT
ejpam-5839	827	5	f̃	f̃	PROPN
ejpam-5839	827	6	,	,	PUNCT
ejpam-5839	827	7	ω	ω	NUM
ejpam-5839	827	8	)	)	PUNCT
ejpam-5839	827	9	⊆	⊆	NUM
ejpam-5839	827	10	(	(	PUNCT
ejpam-5839	827	11	f̃	f̃	PROPN
ejpam-5839	827	12	,	,	PUNCT
ejpam-5839	827	13	ω	ω	PROPN
ejpam-5839	827	14	)	)	PUNCT
ejpam-5839	827	15	and	and	CCONJ
ejpam-5839	827	16	(	(	PUNCT
ejpam-5839	827	17	g̃,ω	g̃,ω	PROPN
ejpam-5839	827	18	)	)	PUNCT
ejpam-5839	827	19	⊆	⊆	NUM
ejpam-5839	827	20	(	(	PUNCT
ejpam-5839	827	21	g̃,ω	g̃,ω	PROPN
ejpam-5839	827	22	)	)	PUNCT
ejpam-5839	827	23	,	,	PUNCT
ejpam-5839	827	24	we	we	PRON
ejpam-5839	827	25	have	have	VERB
ejpam-5839	827	26	:	:	PUNCT
ejpam-5839	827	27	(	(	PUNCT
ejpam-5839	827	28	f̃	f̃	PROPN
ejpam-5839	827	29	,	,	PUNCT
ejpam-5839	827	30	ω	ω	NOUN
ejpam-5839	827	31	)	)	PUNCT
ejpam-5839	827	32	∪	∪	NOUN
ejpam-5839	827	33	(	(	PUNCT
ejpam-5839	827	34	g̃,ω	g̃,ω	PROPN
ejpam-5839	827	35	)	)	PUNCT
ejpam-5839	827	36	⊆	⊆	NUM
ejpam-5839	827	37	(	(	PUNCT
ejpam-5839	827	38	f̃	f̃	PROPN
ejpam-5839	827	39	,	,	PUNCT
ejpam-5839	827	40	ω	ω	NUM
ejpam-5839	827	41	)	)	PUNCT
ejpam-5839	827	42	∪	∪	NOUN
ejpam-5839	827	43	(	(	PUNCT
ejpam-5839	827	44	g̃,ω	g̃,ω	NOUN
ejpam-5839	827	45	)	)	PUNCT
ejpam-5839	827	46	.	.	PUNCT
ejpam-5839	828	1	since	since	SCONJ
ejpam-5839	828	2	(	(	PUNCT
ejpam-5839	828	3	f̃	f̃	PROPN
ejpam-5839	828	4	,	,	PUNCT
ejpam-5839	828	5	ω	ω	NOUN
ejpam-5839	828	6	)	)	PUNCT
ejpam-5839	828	7	∪	∪	NOUN
ejpam-5839	828	8	(	(	PUNCT
ejpam-5839	828	9	g̃,ω	g̃,ω	PROPN
ejpam-5839	828	10	)	)	PUNCT
ejpam-5839	828	11	is	be	AUX
ejpam-5839	828	12	the	the	DET
ejpam-5839	828	13	smallest	small	ADJ
ejpam-5839	828	14	qpns	qpns	NOUN
ejpam-5839	828	15	p	p	NOUN
ejpam-5839	828	16	-	-	PUNCT
ejpam-5839	828	17	closed	close	VERB
ejpam-5839	828	18	set	set	NOUN
ejpam-5839	828	19	enclosing	enclosing	NOUN
ejpam-5839	828	20	(	(	PUNCT
ejpam-5839	828	21	f̃	f̃	PROPN
ejpam-5839	828	22	,	,	PUNCT
ejpam-5839	828	23	ω	ω	NOUN
ejpam-5839	828	24	)	)	PUNCT
ejpam-5839	828	25	∪	∪	NOUN
ejpam-5839	828	26	(	(	PUNCT
ejpam-5839	828	27	g̃,ω	g̃,ω	PROPN
ejpam-5839	828	28	)	)	PUNCT
ejpam-5839	828	29	,	,	PUNCT
ejpam-5839	828	30	we	we	PRON
ejpam-5839	828	31	obtain	obtain	VERB
ejpam-5839	828	32	:	:	PUNCT
ejpam-5839	828	33	(	(	PUNCT
ejpam-5839	828	34	f̃	f̃	PROPN
ejpam-5839	828	35	,	,	PUNCT
ejpam-5839	828	36	ω	ω	NOUN
ejpam-5839	828	37	)	)	PUNCT
ejpam-5839	828	38	∪	∪	NOUN
ejpam-5839	828	39	(	(	PUNCT
ejpam-5839	828	40	g̃,ω	g̃,ω	PROPN
ejpam-5839	828	41	)	)	PUNCT
ejpam-5839	828	42	⊆	⊆	NUM
ejpam-5839	828	43	(	(	PUNCT
ejpam-5839	828	44	f̃	f̃	PROPN
ejpam-5839	828	45	,	,	PUNCT
ejpam-5839	828	46	ω	ω	NUM
ejpam-5839	828	47	)	)	PUNCT
ejpam-5839	828	48	∪	∪	NOUN
ejpam-5839	828	49	(	(	PUNCT
ejpam-5839	828	50	g̃,ω	g̃,ω	NOUN
ejpam-5839	828	51	)	)	PUNCT
ejpam-5839	828	52	.	.	PUNCT
ejpam-5839	829	1	hence	hence	ADV
ejpam-5839	829	2	,	,	PUNCT
ejpam-5839	829	3	(	(	PUNCT
ejpam-5839	829	4	f̃	f̃	PROPN
ejpam-5839	829	5	,	,	PUNCT
ejpam-5839	829	6	ω	ω	NOUN
ejpam-5839	829	7	)	)	PUNCT
ejpam-5839	829	8	∪	∪	NOUN
ejpam-5839	829	9	(	(	PUNCT
ejpam-5839	829	10	g̃,ω	g̃,ω	NOUN
ejpam-5839	829	11	)	)	PUNCT
ejpam-5839	829	12	=	=	PUNCT
ejpam-5839	829	13	(	(	PUNCT
ejpam-5839	829	14	f̃	f̃	PROPN
ejpam-5839	829	15	,	,	PUNCT
ejpam-5839	829	16	ω	ω	NUM
ejpam-5839	829	17	)	)	PUNCT
ejpam-5839	829	18	∪	∪	NOUN
ejpam-5839	829	19	(	(	PUNCT
ejpam-5839	829	20	g̃,ω	g̃,ω	NOUN
ejpam-5839	829	21	)	)	PUNCT
ejpam-5839	829	22	.	.	PUNCT
ejpam-5839	830	1	(	(	PUNCT
ejpam-5839	830	2	v	v	NOUN
ejpam-5839	830	3	)	)	PUNCT
ejpam-5839	830	4	since	since	SCONJ
ejpam-5839	830	5	⟨0(⟨x̃,ω⟩)⟩	⟨0(⟨x̃,ω⟩)⟩	NOUN
ejpam-5839	830	6	∩	∩	PROPN
ejpam-5839	830	7	(	(	PUNCT
ejpam-5839	830	8	g̃,ω	g̃,ω	PROPN
ejpam-5839	830	9	)	)	PUNCT
ejpam-5839	830	10	⊆	⊆	NUM
ejpam-5839	830	11	(	(	PUNCT
ejpam-5839	830	12	f̃	f̃	PROPN
ejpam-5839	830	13	,	,	PUNCT
ejpam-5839	830	14	ω	ω	NOUN
ejpam-5839	830	15	)	)	PUNCT
ejpam-5839	830	16	∩	∩	NOUN
ejpam-5839	830	17	(	(	PUNCT
ejpam-5839	830	18	g̃,ω	g̃,ω	PROPN
ejpam-5839	830	19	)	)	PUNCT
ejpam-5839	830	20	and	and	CCONJ
ejpam-5839	830	21	(	(	PUNCT
ejpam-5839	830	22	f̃	f̃	PROPN
ejpam-5839	830	23	,	,	PUNCT
ejpam-5839	830	24	ω	ω	NOUN
ejpam-5839	830	25	)	)	PUNCT
ejpam-5839	830	26	∩	∩	NOUN
ejpam-5839	830	27	(	(	PUNCT
ejpam-5839	830	28	g̃,ω	g̃,ω	PROPN
ejpam-5839	830	29	)	)	PUNCT
ejpam-5839	830	30	is	be	AUX
ejpam-5839	830	31	the	the	DET
ejpam-5839	830	32	smallest	small	ADJ
ejpam-5839	830	33	qpns	qpns	NOUN
ejpam-5839	830	34	pclosed	pclose	VERB
ejpam-5839	830	35	set	set	ADJ
ejpam-5839	830	36	enclosing	enclosing	NOUN
ejpam-5839	830	37	(	(	PUNCT
ejpam-5839	830	38	f̃	f̃	PROPN
ejpam-5839	830	39	,	,	PUNCT
ejpam-5839	830	40	ω	ω	NOUN
ejpam-5839	830	41	)	)	PUNCT
ejpam-5839	830	42	∩	∩	NOUN
ejpam-5839	830	43	(	(	PUNCT
ejpam-5839	830	44	g̃,ω	g̃,ω	PROPN
ejpam-5839	830	45	)	)	PUNCT
ejpam-5839	830	46	,	,	PUNCT
ejpam-5839	830	47	we	we	PRON
ejpam-5839	830	48	conclude	conclude	VERB
ejpam-5839	830	49	:	:	PUNCT
ejpam-5839	830	50	(	(	PUNCT
ejpam-5839	830	51	f̃	f̃	PROPN
ejpam-5839	830	52	,	,	PUNCT
ejpam-5839	830	53	ω	ω	NOUN
ejpam-5839	830	54	)	)	PUNCT
ejpam-5839	830	55	∩	∩	NOUN
ejpam-5839	830	56	(	(	PUNCT
ejpam-5839	830	57	g̃,ω	g̃,ω	PROPN
ejpam-5839	830	58	)	)	PUNCT
ejpam-5839	830	59	⊆	⊆	NUM
ejpam-5839	830	60	(	(	PUNCT
ejpam-5839	830	61	f̃	f̃	PROPN
ejpam-5839	830	62	,	,	PUNCT
ejpam-5839	830	63	ω	ω	NOUN
ejpam-5839	830	64	)	)	PUNCT
ejpam-5839	830	65	∩	∩	NOUN
ejpam-5839	830	66	(	(	PUNCT
ejpam-5839	830	67	g̃,ω	g̃,ω	PROPN
ejpam-5839	830	68	)	)	PUNCT
ejpam-5839	830	69	.	.	PUNCT
ejpam-5839	831	1	a.	a.	PROPN
ejpam-5839	831	2	shihadeh	shihadeh	VERB
ejpam-5839	831	3	et	et	PROPN
ejpam-5839	831	4	al	al	PROPN
ejpam-5839	831	5	.	.	PUNCT
ejpam-5839	831	6	/	/	SYM
ejpam-5839	831	7	eur	eur	PROPN
ejpam-5839	831	8	.	.	PUNCT
ejpam-5839	832	1	j.	j.	PROPN
ejpam-5839	832	2	pure	pure	PROPN
ejpam-5839	832	3	appl	appl	PROPN
ejpam-5839	832	4	.	.	PROPN
ejpam-5839	832	5	math	math	PROPN
ejpam-5839	832	6	,	,	PUNCT
ejpam-5839	832	7	18	18	NUM
ejpam-5839	832	8	(	(	PUNCT
ejpam-5839	832	9	2	2	NUM
ejpam-5839	832	10	)	)	PUNCT
ejpam-5839	832	11	(	(	PUNCT
ejpam-5839	832	12	2025	2025	NUM
ejpam-5839	832	13	)	)	PUNCT
ejpam-5839	832	14	,	,	PUNCT
ejpam-5839	832	15	5839	5839	NUM
ejpam-5839	832	16	36	36	NUM
ejpam-5839	832	17	of	of	ADP
ejpam-5839	832	18	54	54	NUM
ejpam-5839	832	19	9	9	NUM
ejpam-5839	832	20	.	.	PUNCT
ejpam-5839	833	1	characterization	characterization	NOUN
ejpam-5839	833	2	of	of	ADP
ejpam-5839	833	3	few	few	ADJ
ejpam-5839	833	4	more	more	ADJ
ejpam-5839	833	5	results	result	NOUN
ejpam-5839	833	6	in	in	ADP
ejpam-5839	833	7	terms	term	NOUN
ejpam-5839	833	8	of	of	ADP
ejpam-5839	833	9	basis	basis	NOUN
ejpam-5839	833	10	concerning	concern	VERB
ejpam-5839	833	11	p	p	NOUN
ejpam-5839	833	12	-	-	PUNCT
ejpam-5839	833	13	open	open	ADJ
ejpam-5839	833	14	sets	set	NOUN
ejpam-5839	833	15	definition	definition	NOUN
ejpam-5839	833	16	33	33	NUM
ejpam-5839	833	17	.	.	PUNCT
ejpam-5839	834	1	let	let	AUX
ejpam-5839	834	2	(	(	PUNCT
ejpam-5839	834	3	x	x	NOUN
ejpam-5839	834	4	,	,	PUNCT
ejpam-5839	834	5	τqpnss	τqpnss	PROPN
ejpam-5839	834	6	,	,	PUNCT
ejpam-5839	834	7	ω	ω	PROPN
ejpam-5839	834	8	)	)	PUNCT
ejpam-5839	834	9	be	be	VERB
ejpam-5839	834	10	a	a	DET
ejpam-5839	834	11	quadripartitioned	quadripartitione	VERB
ejpam-5839	834	12	neutrosophic	neutrosophic	ADJ
ejpam-5839	834	13	soft	soft	ADJ
ejpam-5839	834	14	topological	topological	ADJ
ejpam-5839	834	15	space	space	NOUN
ejpam-5839	834	16	over	over	ADP
ejpam-5839	834	17	x	x	NOUN
ejpam-5839	834	18	,	,	PUNCT
ejpam-5839	834	19	and	and	CCONJ
ejpam-5839	834	20	let	let	VERB
ejpam-5839	834	21	bnss	bns	NOUN
ejpam-5839	834	22	be	be	AUX
ejpam-5839	834	23	a	a	DET
ejpam-5839	834	24	sub	sub	NOUN
ejpam-5839	834	25	-	-	NOUN
ejpam-5839	834	26	family	family	NOUN
ejpam-5839	834	27	of	of	ADP
ejpam-5839	834	28	τqpnss	τqpnss	PROPN
ejpam-5839	834	29	.	.	PUNCT
ejpam-5839	835	1	bnss	bnss	PROPN
ejpam-5839	835	2	is	be	AUX
ejpam-5839	835	3	said	say	VERB
ejpam-5839	835	4	to	to	PART
ejpam-5839	835	5	be	be	AUX
ejpam-5839	835	6	a	a	DET
ejpam-5839	835	7	quadripartitioned	quadripartitione	VERB
ejpam-5839	835	8	neutrosophic	neutrosophic	ADJ
ejpam-5839	835	9	soft	soft	ADJ
ejpam-5839	835	10	base	base	NOUN
ejpam-5839	835	11	(	(	PUNCT
ejpam-5839	835	12	or	or	CCONJ
ejpam-5839	835	13	p	p	ADJ
ejpam-5839	835	14	-	-	PUNCT
ejpam-5839	835	15	open	open	ADJ
ejpam-5839	835	16	base	base	NOUN
ejpam-5839	835	17	or	or	CCONJ
ejpam-5839	835	18	basis	basis	NOUN
ejpam-5839	835	19	)	)	PUNCT
ejpam-5839	835	20	for	for	ADP
ejpam-5839	835	21	the	the	DET
ejpam-5839	835	22	quadripartitioned	quadripartitione	VERB
ejpam-5839	835	23	neutrosophic	neutrosophic	ADJ
ejpam-5839	835	24	soft	soft	ADJ
ejpam-5839	835	25	topology	topology	NOUN
ejpam-5839	835	26	τqpnss	τqpnss	NOUN
ejpam-5839	835	27	if	if	SCONJ
ejpam-5839	835	28	for	for	ADP
ejpam-5839	835	29	any	any	DET
ejpam-5839	835	30	non	non	ADJ
ejpam-5839	835	31	-	-	ADJ
ejpam-5839	835	32	empty	empty	ADJ
ejpam-5839	835	33	quadripartitioned	quadripartitione	VERB
ejpam-5839	835	34	neutrosophic	neutrosophic	ADJ
ejpam-5839	835	35	soft	soft	ADJ
ejpam-5839	835	36	set	set	NOUN
ejpam-5839	835	37	(	(	PUNCT
ejpam-5839	835	38	g̃,ω	g̃,ω	NOUN
ejpam-5839	835	39	)	)	PUNCT
ejpam-5839	835	40	∈	∈	PROPN
ejpam-5839	835	41	τqpnss	τqpns	NOUN
ejpam-5839	835	42	,	,	PUNCT
ejpam-5839	835	43	there	there	PRON
ejpam-5839	835	44	exists	exist	VERB
ejpam-5839	835	45	b1	b1	NOUN
ejpam-5839	835	46	⊆	⊆	NUM
ejpam-5839	835	47	bnss	bns	NOUN
ejpam-5839	835	48	such	such	ADJ
ejpam-5839	835	49	that	that	PRON
ejpam-5839	835	50	:	:	PUNCT
ejpam-5839	835	51	(	(	PUNCT
ejpam-5839	835	52	g̃,ω	g̃,ω	NOUN
ejpam-5839	835	53	)	)	PUNCT
ejpam-5839	835	54	=	=	PUNCT
ejpam-5839	835	55	⋃	⋃	NOUN
ejpam-5839	835	56	{	{	PUNCT
ejpam-5839	835	57	b	b	NOUN
ejpam-5839	835	58	:	:	PUNCT
ejpam-5839	835	59	b	b	PROPN
ejpam-5839	835	60	∈	∈	PROPN
ejpam-5839	835	61	b1	b1	NOUN
ejpam-5839	835	62	}	}	PUNCT
ejpam-5839	835	63	.	.	PUNCT
ejpam-5839	836	1	in	in	ADP
ejpam-5839	836	2	other	other	ADJ
ejpam-5839	836	3	words	word	NOUN
ejpam-5839	836	4	,	,	PUNCT
ejpam-5839	836	5	bnss	bns	NOUN
ejpam-5839	836	6	is	be	AUX
ejpam-5839	836	7	said	say	VERB
ejpam-5839	836	8	to	to	PART
ejpam-5839	836	9	be	be	AUX
ejpam-5839	836	10	a	a	DET
ejpam-5839	836	11	base	base	NOUN
ejpam-5839	836	12	for	for	ADP
ejpam-5839	836	13	the	the	DET
ejpam-5839	836	14	quadripartitioned	quadripartitione	VERB
ejpam-5839	836	15	neutrosophic	neutrosophic	ADJ
ejpam-5839	836	16	soft	soft	ADJ
ejpam-5839	836	17	topology	topology	NOUN
ejpam-5839	836	18	if	if	SCONJ
ejpam-5839	836	19	for	for	ADP
ejpam-5839	836	20	every	every	DET
ejpam-5839	836	21	x(r1,r2,r3,r4	x(r1,r2,r3,r4	NUM
ejpam-5839	836	22	)	)	PUNCT
ejpam-5839	836	23	∈	∈	PROPN
ejpam-5839	836	24	(	(	PUNCT
ejpam-5839	836	25	g	g	PROPN
ejpam-5839	836	26	,	,	PUNCT
ejpam-5839	836	27	ω	ω	NOUN
ejpam-5839	836	28	)	)	PUNCT
ejpam-5839	836	29	,	,	PUNCT
ejpam-5839	836	30	there	there	PRON
ejpam-5839	836	31	exists	exist	VERB
ejpam-5839	836	32	b	b	PROPN
ejpam-5839	836	33	∈	∈	PROPN
ejpam-5839	836	34	b	b	NOUN
ejpam-5839	836	35	such	such	ADJ
ejpam-5839	836	36	that	that	PRON
ejpam-5839	836	37	:	:	PUNCT
ejpam-5839	836	38	x(r1,r2,r3,r4	x(r1,r2,r3,r4	X
ejpam-5839	836	39	)	)	PUNCT
ejpam-5839	837	1	∈	∈	PROPN
ejpam-5839	837	2	b	b	X
ejpam-5839	837	3	⊆	⊆	NUM
ejpam-5839	837	4	(	(	PUNCT
ejpam-5839	837	5	g̃,ω	g̃,ω	NOUN
ejpam-5839	837	6	)	)	PUNCT
ejpam-5839	837	7	.	.	PUNCT
ejpam-5839	838	1	moreover	moreover	ADV
ejpam-5839	838	2	,	,	PUNCT
ejpam-5839	838	3	if	if	SCONJ
ejpam-5839	838	4	(	(	PUNCT
ejpam-5839	838	5	g̃,ω	g̃,ω	NOUN
ejpam-5839	838	6	)	)	PUNCT
ejpam-5839	838	7	∈	∈	PROPN
ejpam-5839	838	8	τqpnss	τqpns	NOUN
ejpam-5839	838	9	,	,	PUNCT
ejpam-5839	838	10	then	then	ADV
ejpam-5839	838	11	there	there	PRON
ejpam-5839	838	12	must	must	AUX
ejpam-5839	838	13	exist	exist	VERB
ejpam-5839	838	14	some	some	DET
ejpam-5839	838	15	base	base	NOUN
ejpam-5839	838	16	element	element	NOUN
ejpam-5839	838	17	b	b	PROPN
ejpam-5839	838	18	∈	∈	PROPN
ejpam-5839	838	19	bnss	bns	NOUN
ejpam-5839	838	20	satisfying	satisfying	ADJ
ejpam-5839	838	21	:	:	PUNCT
ejpam-5839	838	22	x(r1,r2,r3,r4	x(r1,r2,r3,r4	X
ejpam-5839	838	23	)	)	PUNCT
ejpam-5839	839	1	∈	∈	PROPN
ejpam-5839	839	2	b	b	X
ejpam-5839	839	3	⊆	⊆	NUM
ejpam-5839	839	4	(	(	PUNCT
ejpam-5839	839	5	g̃,ω	g̃,ω	NOUN
ejpam-5839	839	6	)	)	PUNCT
ejpam-5839	839	7	.	.	PUNCT
ejpam-5839	840	1	definition	definition	NOUN
ejpam-5839	840	2	34	34	NUM
ejpam-5839	840	3	.	.	PUNCT
ejpam-5839	841	1	let	let	AUX
ejpam-5839	841	2	(	(	PUNCT
ejpam-5839	841	3	x	x	NOUN
ejpam-5839	841	4	,	,	PUNCT
ejpam-5839	841	5	τqpnss	τqpnss	PROPN
ejpam-5839	841	6	,	,	PUNCT
ejpam-5839	841	7	ω	ω	PROPN
ejpam-5839	841	8	)	)	PUNCT
ejpam-5839	841	9	be	be	VERB
ejpam-5839	841	10	a	a	DET
ejpam-5839	841	11	quadripartitioned	quadripartitione	VERB
ejpam-5839	841	12	neutrosophic	neutrosophic	ADJ
ejpam-5839	841	13	soft	soft	ADJ
ejpam-5839	841	14	topological	topological	ADJ
ejpam-5839	841	15	space	space	NOUN
ejpam-5839	841	16	over	over	ADP
ejpam-5839	841	17	x	x	NOUN
ejpam-5839	841	18	,	,	PUNCT
ejpam-5839	841	19	and	and	CCONJ
ejpam-5839	841	20	let	let	VERB
ejpam-5839	841	21	snss	sns	NOUN
ejpam-5839	841	22	be	be	AUX
ejpam-5839	841	23	a	a	DET
ejpam-5839	841	24	sub	sub	NOUN
ejpam-5839	841	25	-	-	NOUN
ejpam-5839	841	26	family	family	NOUN
ejpam-5839	841	27	of	of	ADP
ejpam-5839	841	28	τqpnss	τqpnss	PROPN
ejpam-5839	841	29	.	.	PUNCT
ejpam-5839	842	1	snss	sns	NOUN
ejpam-5839	842	2	is	be	AUX
ejpam-5839	842	3	said	say	VERB
ejpam-5839	842	4	to	to	PART
ejpam-5839	842	5	be	be	AUX
ejpam-5839	842	6	a	a	DET
ejpam-5839	842	7	quadripartitioned	quadripartitione	VERB
ejpam-5839	842	8	neutrosophic	neutrosophic	ADJ
ejpam-5839	842	9	soft	soft	ADJ
ejpam-5839	842	10	sub	sub	NOUN
ejpam-5839	842	11	-	-	NOUN
ejpam-5839	842	12	base	base	ADJ
ejpam-5839	842	13	(	(	PUNCT
ejpam-5839	842	14	or	or	CCONJ
ejpam-5839	842	15	p	p	X
ejpam-5839	842	16	-	-	PUNCT
ejpam-5839	842	17	open	open	ADJ
ejpam-5839	842	18	sub	sub	NOUN
ejpam-5839	842	19	-	-	ADJ
ejpam-5839	842	20	base	base	ADJ
ejpam-5839	842	21	or	or	CCONJ
ejpam-5839	842	22	subbasis	subbasis	NOUN
ejpam-5839	842	23	)	)	PUNCT
ejpam-5839	842	24	for	for	ADP
ejpam-5839	842	25	the	the	DET
ejpam-5839	842	26	quadripartitioned	quadripartitione	VERB
ejpam-5839	842	27	neutrosophic	neutrosophic	ADJ
ejpam-5839	842	28	soft	soft	ADJ
ejpam-5839	842	29	topology	topology	NOUN
ejpam-5839	842	30	τqpnss	τqpns	NOUN
ejpam-5839	842	31	on	on	ADP
ejpam-5839	842	32	x	x	SYM
ejpam-5839	842	33	if	if	SCONJ
ejpam-5839	842	34	finite	finite	ADJ
ejpam-5839	842	35	intersections	intersection	NOUN
ejpam-5839	842	36	of	of	ADP
ejpam-5839	842	37	the	the	DET
ejpam-5839	842	38	members	member	NOUN
ejpam-5839	842	39	of	of	ADP
ejpam-5839	842	40	snss	sns	NOUN
ejpam-5839	842	41	form	form	VERB
ejpam-5839	842	42	a	a	DET
ejpam-5839	842	43	base	base	NOUN
ejpam-5839	842	44	for	for	ADP
ejpam-5839	842	45	the	the	DET
ejpam-5839	842	46	quadripartitioned	quadripartitione	VERB
ejpam-5839	842	47	neutrosophic	neutrosophic	ADJ
ejpam-5839	842	48	soft	soft	ADJ
ejpam-5839	842	49	topology	topology	NOUN
ejpam-5839	842	50	τqpnss	τqpns	NOUN
ejpam-5839	842	51	on	on	ADP
ejpam-5839	842	52	x.	x.	NOUN
ejpam-5839	842	53	that	that	PRON
ejpam-5839	842	54	is	is	ADV
ejpam-5839	842	55	,	,	PUNCT
ejpam-5839	842	56	the	the	DET
ejpam-5839	842	57	union	union	NOUN
ejpam-5839	842	58	of	of	ADP
ejpam-5839	842	59	the	the	DET
ejpam-5839	842	60	members	member	NOUN
ejpam-5839	842	61	of	of	ADP
ejpam-5839	842	62	snss	sns	NOUN
ejpam-5839	842	63	generates	generate	VERB
ejpam-5839	842	64	all	all	DET
ejpam-5839	842	65	the	the	DET
ejpam-5839	842	66	members	member	NOUN
ejpam-5839	842	67	of	of	ADP
ejpam-5839	842	68	τqpnss	τqpnss	PROPN
ejpam-5839	842	69	.	.	PUNCT
ejpam-5839	843	1	the	the	DET
ejpam-5839	843	2	elements	element	NOUN
ejpam-5839	843	3	of	of	ADP
ejpam-5839	843	4	snss	sns	NOUN
ejpam-5839	843	5	are	be	AUX
ejpam-5839	843	6	referred	refer	VERB
ejpam-5839	843	7	to	to	ADP
ejpam-5839	843	8	as	as	ADP
ejpam-5839	843	9	sub	sub	ADJ
ejpam-5839	843	10	-	-	ADJ
ejpam-5839	843	11	basic	basic	ADJ
ejpam-5839	843	12	quadripartitioned	quadripartitione	VERB
ejpam-5839	843	13	neutrosophic	neutrosophic	ADJ
ejpam-5839	843	14	soft	soft	ADJ
ejpam-5839	843	15	p	p	NOUN
ejpam-5839	843	16	-	-	PUNCT
ejpam-5839	843	17	open	open	ADJ
ejpam-5839	843	18	sets	set	NOUN
ejpam-5839	843	19	.	.	PUNCT
ejpam-5839	844	1	if	if	SCONJ
ejpam-5839	844	2	,	,	PUNCT
ejpam-5839	844	3	for	for	ADP
ejpam-5839	844	4	any	any	DET
ejpam-5839	844	5	non	non	ADJ
ejpam-5839	844	6	-	-	ADJ
ejpam-5839	844	7	empty	empty	ADJ
ejpam-5839	844	8	quadripartitioned	quadripartitione	VERB
ejpam-5839	844	9	neutrosophic	neutrosophic	ADJ
ejpam-5839	844	10	soft	soft	ADJ
ejpam-5839	844	11	set	set	NOUN
ejpam-5839	844	12	(	(	PUNCT
ejpam-5839	844	13	g̃,ω	g̃,ω	NOUN
ejpam-5839	844	14	)	)	PUNCT
ejpam-5839	844	15	∈	∈	PROPN
ejpam-5839	844	16	τqpnss	τqpns	NOUN
ejpam-5839	844	17	,	,	PUNCT
ejpam-5839	844	18	there	there	PRON
ejpam-5839	844	19	exists	exist	VERB
ejpam-5839	844	20	b1	b1	NOUN
ejpam-5839	844	21	⊆	⊆	NUM
ejpam-5839	844	22	bnss	bns	NOUN
ejpam-5839	844	23	such	such	ADJ
ejpam-5839	844	24	that	that	PRON
ejpam-5839	844	25	:	:	PUNCT
ejpam-5839	844	26	(	(	PUNCT
ejpam-5839	844	27	g̃,ω	g̃,ω	NOUN
ejpam-5839	844	28	)	)	PUNCT
ejpam-5839	844	29	=	=	PUNCT
ejpam-5839	844	30	⋃	⋃	NOUN
ejpam-5839	844	31	{	{	PUNCT
ejpam-5839	844	32	b	b	NOUN
ejpam-5839	844	33	:	:	PUNCT
ejpam-5839	844	34	b	b	PROPN
ejpam-5839	844	35	∈	∈	PROPN
ejpam-5839	844	36	b1	b1	NOUN
ejpam-5839	844	37	}	}	PUNCT
ejpam-5839	844	38	,	,	PUNCT
ejpam-5839	844	39	then	then	ADV
ejpam-5839	844	40	bnss	bns	NOUN
ejpam-5839	844	41	is	be	AUX
ejpam-5839	844	42	said	say	VERB
ejpam-5839	844	43	to	to	PART
ejpam-5839	844	44	be	be	AUX
ejpam-5839	844	45	a	a	DET
ejpam-5839	844	46	base	base	NOUN
ejpam-5839	844	47	for	for	ADP
ejpam-5839	844	48	the	the	DET
ejpam-5839	844	49	quadripartitioned	quadripartitione	VERB
ejpam-5839	844	50	neutrosophic	neutrosophic	ADJ
ejpam-5839	844	51	soft	soft	ADJ
ejpam-5839	844	52	topology	topology	NOUN
ejpam-5839	844	53	.	.	PUNCT
ejpam-5839	845	1	in	in	ADP
ejpam-5839	845	2	other	other	ADJ
ejpam-5839	845	3	words	word	NOUN
ejpam-5839	845	4	,	,	PUNCT
ejpam-5839	845	5	bnss	bns	NOUN
ejpam-5839	845	6	is	be	AUX
ejpam-5839	845	7	a	a	DET
ejpam-5839	845	8	base	base	NOUN
ejpam-5839	845	9	for	for	ADP
ejpam-5839	845	10	the	the	DET
ejpam-5839	845	11	quadripartitioned	quadripartitione	VERB
ejpam-5839	845	12	neutrosophic	neutrosophic	ADJ
ejpam-5839	845	13	soft	soft	ADJ
ejpam-5839	845	14	topology	topology	NOUN
ejpam-5839	845	15	if	if	SCONJ
ejpam-5839	845	16	,	,	PUNCT
ejpam-5839	845	17	for	for	ADP
ejpam-5839	845	18	every	every	DET
ejpam-5839	845	19	point	point	NOUN
ejpam-5839	845	20	x(r1,r2,r3,r4	x(r1,r2,r3,r4	X
ejpam-5839	845	21	)	)	PUNCT
ejpam-5839	845	22	∈	∈	PROPN
ejpam-5839	845	23	(	(	PUNCT
ejpam-5839	845	24	g̃,ω	g̃,ω	PROPN
ejpam-5839	845	25	)	)	PUNCT
ejpam-5839	845	26	,	,	PUNCT
ejpam-5839	845	27	there	there	PRON
ejpam-5839	845	28	exists	exist	VERB
ejpam-5839	845	29	b	b	PROPN
ejpam-5839	845	30	∈	∈	PROPN
ejpam-5839	845	31	bnss	bns	NOUN
ejpam-5839	845	32	such	such	ADJ
ejpam-5839	845	33	that	that	PRON
ejpam-5839	845	34	:	:	PUNCT
ejpam-5839	845	35	x(r1,r2,r3,r4	x(r1,r2,r3,r4	X
ejpam-5839	845	36	)	)	PUNCT
ejpam-5839	846	1	∈	∈	PROPN
ejpam-5839	846	2	b	b	X
ejpam-5839	846	3	⊆	⊆	NUM
ejpam-5839	846	4	(	(	PUNCT
ejpam-5839	846	5	g̃,ω	g̃,ω	NOUN
ejpam-5839	846	6	)	)	PUNCT
ejpam-5839	846	7	.	.	PUNCT
ejpam-5839	847	1	definition	definition	NOUN
ejpam-5839	847	2	35	35	NUM
ejpam-5839	847	3	.	.	PUNCT
ejpam-5839	848	1	let	let	VERB
ejpam-5839	848	2	(	(	PUNCT
ejpam-5839	848	3	x	x	NOUN
ejpam-5839	848	4	,	,	PUNCT
ejpam-5839	848	5	τqpnss	τqpnss	PROPN
ejpam-5839	848	6	,	,	PUNCT
ejpam-5839	848	7	ω	ω	PROPN
ejpam-5839	848	8	)	)	PUNCT
ejpam-5839	848	9	be	be	VERB
ejpam-5839	848	10	a	a	DET
ejpam-5839	848	11	quadripartitioned	quadripartitione	VERB
ejpam-5839	848	12	neutrosophic	neutrosophic	ADJ
ejpam-5839	848	13	soft	soft	ADJ
ejpam-5839	848	14	topological	topological	ADJ
ejpam-5839	848	15	space	space	NOUN
ejpam-5839	848	16	over	over	ADP
ejpam-5839	848	17	x.	x.	NOUN
ejpam-5839	848	18	a	a	DET
ejpam-5839	848	19	family	family	NOUN
ejpam-5839	848	20	bα	bα	PROPN
ejpam-5839	848	21	of	of	ADP
ejpam-5839	848	22	quadripartitioned	quadripartitione	VERB
ejpam-5839	848	23	neutrosophic	neutrosophic	ADJ
ejpam-5839	848	24	soft	soft	ADJ
ejpam-5839	848	25	p	p	NOUN
ejpam-5839	848	26	-	-	PUNCT
ejpam-5839	848	27	open	open	ADJ
ejpam-5839	848	28	subsets	subset	NOUN
ejpam-5839	848	29	of	of	ADP
ejpam-5839	848	30	x	x	SYM
ejpam-5839	848	31	is	be	AUX
ejpam-5839	848	32	said	say	VERB
ejpam-5839	848	33	to	to	PART
ejpam-5839	848	34	be	be	AUX
ejpam-5839	848	35	a	a	DET
ejpam-5839	848	36	quadripartitioned	quadripartitione	VERB
ejpam-5839	848	37	neutrosophic	neutrosophic	ADJ
ejpam-5839	848	38	soft	soft	ADJ
ejpam-5839	848	39	local	local	ADJ
ejpam-5839	848	40	base	base	NOUN
ejpam-5839	848	41	at	at	ADP
ejpam-5839	848	42	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	848	43	)	)	PUNCT
ejpam-5839	848	44	in	in	ADP
ejpam-5839	848	45	the	the	DET
ejpam-5839	848	46	neutrosophic	neutrosophic	ADJ
ejpam-5839	848	47	soft	soft	ADJ
ejpam-5839	848	48	topology	topology	NOUN
ejpam-5839	848	49	on	on	ADP
ejpam-5839	848	50	x	x	SYM
ejpam-5839	848	51	if	if	SCONJ
ejpam-5839	848	52	:	:	PUNCT
ejpam-5839	848	53	(	(	PUNCT
ejpam-5839	848	54	i	i	NOUN
ejpam-5839	848	55	)	)	PUNCT
ejpam-5839	848	56	for	for	ADP
ejpam-5839	848	57	any	any	DET
ejpam-5839	848	58	b	b	PROPN
ejpam-5839	848	59	∈	∈	PROPN
ejpam-5839	848	60	bxθ	bxθ	NOUN
ejpam-5839	848	61	(	(	PUNCT
ejpam-5839	848	62	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	848	63	)	)	PUNCT
ejpam-5839	848	64	,	,	PUNCT
ejpam-5839	848	65	we	we	PRON
ejpam-5839	848	66	have	have	VERB
ejpam-5839	848	67	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	848	68	)	)	PUNCT
ejpam-5839	849	1	∈	∈	PROPN
ejpam-5839	849	2	b.	b.	PROPN
ejpam-5839	849	3	(	(	PUNCT
ejpam-5839	849	4	ii	ii	PROPN
ejpam-5839	849	5	)	)	PUNCT
ejpam-5839	849	6	for	for	ADP
ejpam-5839	849	7	any	any	DET
ejpam-5839	849	8	(	(	PUNCT
ejpam-5839	849	9	g̃,ω	g̃,ω	NOUN
ejpam-5839	849	10	)	)	PUNCT
ejpam-5839	849	11	∈	∈	PROPN
ejpam-5839	849	12	τqpnss	τqpns	NOUN
ejpam-5839	849	13	with	with	ADP
ejpam-5839	849	14	yθ	yθ	NOUN
ejpam-5839	849	15	′	′	NUM
ejpam-5839	849	16	(	(	PUNCT
ejpam-5839	849	17	r′1,r	r′1,r	VERB
ejpam-5839	849	18	′	′	NUM
ejpam-5839	849	19	2,r	2,r	NUM
ejpam-5839	849	20	′	′	NUM
ejpam-5839	850	1	3,r	3,r	NUM
ejpam-5839	850	2	′	′	NUM
ejpam-5839	850	3	4	4	NUM
ejpam-5839	850	4	)	)	PUNCT
ejpam-5839	850	5	∈	∈	PROPN
ejpam-5839	850	6	b	b	ADP
ejpam-5839	850	7	⊆	⊆	NUM
ejpam-5839	850	8	(	(	PUNCT
ejpam-5839	850	9	g̃,ω	g̃,ω	PROPN
ejpam-5839	850	10	)	)	PUNCT
ejpam-5839	850	11	,	,	PUNCT
ejpam-5839	850	12	there	there	PRON
ejpam-5839	850	13	exists	exist	VERB
ejpam-5839	850	14	b	b	PROPN
ejpam-5839	850	15	∈	∈	PROPN
ejpam-5839	850	16	bxθ	bxθ	NOUN
ejpam-5839	850	17	(	(	PUNCT
ejpam-5839	850	18	r1,r2,r3,r4	r1,r2,r3,r4	NOUN
ejpam-5839	850	19	)	)	PUNCT
ejpam-5839	850	20	such	such	ADJ
ejpam-5839	850	21	that	that	PRON
ejpam-5839	850	22	:	:	PUNCT
ejpam-5839	850	23	yθ	yθ	NOUN
ejpam-5839	850	24	′	′	NUM
ejpam-5839	850	25	(	(	PUNCT
ejpam-5839	850	26	r′1,r	r′1,r	VERB
ejpam-5839	850	27	′	′	NUM
ejpam-5839	850	28	2,r	2,r	NUM
ejpam-5839	850	29	′	′	NUM
ejpam-5839	850	30	3,r	3,r	NUM
ejpam-5839	850	31	′	′	NUM
ejpam-5839	850	32	4	4	NUM
ejpam-5839	850	33	)	)	PUNCT
ejpam-5839	850	34	∈	∈	PROPN
ejpam-5839	850	35	b	b	ADP
ejpam-5839	850	36	⊆	⊆	NUM
ejpam-5839	850	37	(	(	PUNCT
ejpam-5839	850	38	g̃,ω	g̃,ω	NOUN
ejpam-5839	850	39	)	)	PUNCT
ejpam-5839	850	40	.	.	PUNCT
ejpam-5839	851	1	definition	definition	NOUN
ejpam-5839	851	2	36	36	NUM
ejpam-5839	851	3	.	.	PUNCT
ejpam-5839	852	1	let	let	AUX
ejpam-5839	852	2	(	(	PUNCT
ejpam-5839	852	3	x	x	NOUN
ejpam-5839	852	4	,	,	PUNCT
ejpam-5839	852	5	τqpnss	τqpnss	PROPN
ejpam-5839	852	6	,	,	PUNCT
ejpam-5839	852	7	ω	ω	PROPN
ejpam-5839	852	8	)	)	PUNCT
ejpam-5839	852	9	be	be	VERB
ejpam-5839	852	10	a	a	DET
ejpam-5839	852	11	quadripartitioned	quadripartitione	VERB
ejpam-5839	852	12	neutrosophic	neutrosophic	ADJ
ejpam-5839	852	13	soft	soft	ADJ
ejpam-5839	852	14	topological	topological	ADJ
ejpam-5839	852	15	space	space	NOUN
ejpam-5839	852	16	over	over	ADP
ejpam-5839	852	17	x.	x.	NOUN
ejpam-5839	852	18	the	the	DET
ejpam-5839	852	19	space	space	NOUN
ejpam-5839	852	20	x	x	NOUN
ejpam-5839	852	21	satisfies	satisfy	VERB
ejpam-5839	852	22	the	the	DET
ejpam-5839	852	23	first	first	ADJ
ejpam-5839	852	24	axiom	axiom	NOUN
ejpam-5839	852	25	of	of	ADP
ejpam-5839	852	26	quadripartitioned	quadripartitione	VERB
ejpam-5839	852	27	neutrosophic	neutrosophic	ADJ
ejpam-5839	852	28	soft	soft	ADJ
ejpam-5839	852	29	countability	countability	NOUN
ejpam-5839	852	30	if	if	SCONJ
ejpam-5839	852	31	x	x	PRON
ejpam-5839	852	32	has	have	VERB
ejpam-5839	852	33	a	a	DET
ejpam-5839	852	34	quadripartitioned	quadripartitione	VERB
ejpam-5839	852	35	neutrosophic	neutrosophic	ADJ
ejpam-5839	852	36	soft	soft	ADJ
ejpam-5839	852	37	countable	countable	ADJ
ejpam-5839	852	38	local	local	ADJ
ejpam-5839	852	39	base	base	NOUN
ejpam-5839	852	40	at	at	ADP
ejpam-5839	852	41	each	each	DET
ejpam-5839	852	42	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	852	43	)	)	PUNCT
ejpam-5839	853	1	∈	∈	PROPN
ejpam-5839	853	2	x.	x.	NOUN
ejpam-5839	853	3	a	a	DET
ejpam-5839	853	4	quadripartitioned	quadripartitione	VERB
ejpam-5839	853	5	neutrosophic	neutrosophic	ADJ
ejpam-5839	853	6	soft	soft	ADJ
ejpam-5839	853	7	space	space	NOUN
ejpam-5839	853	8	x	x	PUNCT
ejpam-5839	853	9	satisfying	satisfy	VERB
ejpam-5839	853	10	this	this	DET
ejpam-5839	853	11	condition	condition	NOUN
ejpam-5839	853	12	is	be	AUX
ejpam-5839	853	13	called	call	VERB
ejpam-5839	853	14	a	a	DET
ejpam-5839	853	15	first	first	ADJ
ejpam-5839	853	16	quadripartitioned	quadripartitione	VERB
ejpam-5839	853	17	neutrosophic	neutrosophic	ADJ
ejpam-5839	853	18	soft	soft	ADJ
ejpam-5839	853	19	countable	countable	ADJ
ejpam-5839	853	20	space	space	NOUN
ejpam-5839	853	21	.	.	PUNCT
ejpam-5839	854	1	a.	a.	NOUN
ejpam-5839	854	2	shihadeh	shihadeh	VERB
ejpam-5839	854	3	et	et	PROPN
ejpam-5839	854	4	al	al	PROPN
ejpam-5839	854	5	.	.	PUNCT
ejpam-5839	854	6	/	/	SYM
ejpam-5839	854	7	eur	eur	PROPN
ejpam-5839	854	8	.	.	PUNCT
ejpam-5839	855	1	j.	j.	PROPN
ejpam-5839	855	2	pure	pure	PROPN
ejpam-5839	855	3	appl	appl	PROPN
ejpam-5839	855	4	.	.	PROPN
ejpam-5839	855	5	math	math	PROPN
ejpam-5839	855	6	,	,	PUNCT
ejpam-5839	855	7	18	18	NUM
ejpam-5839	855	8	(	(	PUNCT
ejpam-5839	855	9	2	2	NUM
ejpam-5839	855	10	)	)	PUNCT
ejpam-5839	855	11	(	(	PUNCT
ejpam-5839	855	12	2025	2025	NUM
ejpam-5839	855	13	)	)	PUNCT
ejpam-5839	855	14	,	,	PUNCT
ejpam-5839	855	15	5839	5839	NUM
ejpam-5839	855	16	37	37	NUM
ejpam-5839	855	17	of	of	ADP
ejpam-5839	855	18	54	54	NUM
ejpam-5839	855	19	definition	definition	NOUN
ejpam-5839	855	20	37	37	NUM
ejpam-5839	855	21	.	.	PUNCT
ejpam-5839	856	1	let	let	AUX
ejpam-5839	856	2	(	(	PUNCT
ejpam-5839	856	3	x	x	NOUN
ejpam-5839	856	4	,	,	PUNCT
ejpam-5839	856	5	τqpnss	τqpnss	PROPN
ejpam-5839	856	6	,	,	PUNCT
ejpam-5839	856	7	ω	ω	PROPN
ejpam-5839	856	8	)	)	PUNCT
ejpam-5839	856	9	be	be	VERB
ejpam-5839	856	10	a	a	DET
ejpam-5839	856	11	quadripartitioned	quadripartitione	VERB
ejpam-5839	856	12	neutrosophic	neutrosophic	ADJ
ejpam-5839	856	13	soft	soft	ADJ
ejpam-5839	856	14	topological	topological	ADJ
ejpam-5839	856	15	space	space	NOUN
ejpam-5839	856	16	over	over	ADP
ejpam-5839	856	17	x.	x.	NOUN
ejpam-5839	856	18	the	the	DET
ejpam-5839	856	19	space	space	NOUN
ejpam-5839	856	20	x	x	NOUN
ejpam-5839	856	21	satisfies	satisfy	VERB
ejpam-5839	856	22	the	the	DET
ejpam-5839	856	23	second	second	ADJ
ejpam-5839	856	24	axiom	axiom	NOUN
ejpam-5839	856	25	of	of	ADP
ejpam-5839	856	26	quadripartitioned	quadripartitione	VERB
ejpam-5839	856	27	neutrosophic	neutrosophic	ADJ
ejpam-5839	856	28	soft	soft	ADJ
ejpam-5839	856	29	countability	countability	NOUN
ejpam-5839	856	30	if	if	SCONJ
ejpam-5839	856	31	there	there	PRON
ejpam-5839	856	32	exists	exist	VERB
ejpam-5839	856	33	a	a	DET
ejpam-5839	856	34	quadripartitioned	quadripartitioned	ADJ
ejpam-5839	856	35	neutrosophic	neutrosophic	ADJ
ejpam-5839	856	36	soft	soft	ADJ
ejpam-5839	856	37	countable	countable	ADJ
ejpam-5839	856	38	base	base	NOUN
ejpam-5839	856	39	for	for	ADP
ejpam-5839	856	40	τqpnss	τqpns	NOUN
ejpam-5839	856	41	on	on	ADP
ejpam-5839	856	42	x.	x.	PROPN
ejpam-5839	856	43	a	a	DET
ejpam-5839	856	44	quadripartitioned	quadripartitione	VERB
ejpam-5839	856	45	neutrosophic	neutrosophic	ADJ
ejpam-5839	856	46	soft	soft	ADJ
ejpam-5839	856	47	space	space	NOUN
ejpam-5839	856	48	x	x	PUNCT
ejpam-5839	856	49	satisfying	satisfy	VERB
ejpam-5839	856	50	this	this	DET
ejpam-5839	856	51	condition	condition	NOUN
ejpam-5839	856	52	is	be	AUX
ejpam-5839	856	53	called	call	VERB
ejpam-5839	856	54	a	a	DET
ejpam-5839	856	55	second	second	ADJ
ejpam-5839	856	56	quadripartitioned	quadripartitione	VERB
ejpam-5839	856	57	neutrosophic	neutrosophic	ADJ
ejpam-5839	856	58	soft	soft	ADJ
ejpam-5839	856	59	countable	countable	ADJ
ejpam-5839	856	60	space	space	NOUN
ejpam-5839	856	61	.	.	PUNCT
ejpam-5839	857	1	a	a	DET
ejpam-5839	857	2	second	second	ADJ
ejpam-5839	857	3	quadripartitioned	quadripartitione	VERB
ejpam-5839	857	4	neutrosophic	neutrosophic	ADJ
ejpam-5839	857	5	soft	soft	ADJ
ejpam-5839	857	6	countable	countable	ADJ
ejpam-5839	857	7	space	space	NOUN
ejpam-5839	857	8	is	be	AUX
ejpam-5839	857	9	also	also	ADV
ejpam-5839	857	10	called	call	VERB
ejpam-5839	857	11	a	a	DET
ejpam-5839	857	12	quadripartitioned	quadripartitione	VERB
ejpam-5839	857	13	neutrosophic	neutrosophic	ADJ
ejpam-5839	857	14	soft	soft	ADJ
ejpam-5839	857	15	completely	completely	ADV
ejpam-5839	857	16	separable	separable	ADJ
ejpam-5839	857	17	space	space	NOUN
ejpam-5839	857	18	.	.	PUNCT
ejpam-5839	858	1	definition	definition	NOUN
ejpam-5839	858	2	38	38	NUM
ejpam-5839	858	3	.	.	PUNCT
ejpam-5839	859	1	let	let	AUX
ejpam-5839	859	2	(	(	PUNCT
ejpam-5839	859	3	x	x	NOUN
ejpam-5839	859	4	,	,	PUNCT
ejpam-5839	859	5	τqpnss	τqpnss	PROPN
ejpam-5839	859	6	,	,	PUNCT
ejpam-5839	859	7	ω	ω	PROPN
ejpam-5839	859	8	)	)	PUNCT
ejpam-5839	859	9	be	be	VERB
ejpam-5839	859	10	a	a	DET
ejpam-5839	859	11	quadripartitioned	quadripartitione	VERB
ejpam-5839	859	12	neutrosophic	neutrosophic	ADJ
ejpam-5839	859	13	soft	soft	ADJ
ejpam-5839	859	14	topological	topological	ADJ
ejpam-5839	859	15	space	space	NOUN
ejpam-5839	859	16	over	over	ADP
ejpam-5839	859	17	x.	x.	NOUN
ejpam-5839	859	18	a	a	DET
ejpam-5839	859	19	property	property	NOUN
ejpam-5839	859	20	pqpnss	pqpns	NOUN
ejpam-5839	859	21	of	of	ADP
ejpam-5839	859	22	x	x	VERB
ejpam-5839	859	23	is	be	AUX
ejpam-5839	859	24	said	say	VERB
ejpam-5839	859	25	to	to	PART
ejpam-5839	859	26	be	be	AUX
ejpam-5839	859	27	hereditary	hereditary	ADJ
ejpam-5839	859	28	if	if	SCONJ
ejpam-5839	859	29	the	the	DET
ejpam-5839	859	30	property	property	NOUN
ejpam-5839	859	31	is	be	AUX
ejpam-5839	859	32	possessed	possess	VERB
ejpam-5839	859	33	by	by	ADP
ejpam-5839	859	34	every	every	DET
ejpam-5839	859	35	subspace	subspace	NOUN
ejpam-5839	859	36	of	of	ADP
ejpam-5839	859	37	x.	x.	NOUN
ejpam-5839	859	38	for	for	ADP
ejpam-5839	859	39	example	example	NOUN
ejpam-5839	859	40	,	,	PUNCT
ejpam-5839	859	41	quadripartitioned	quadripartitione	VERB
ejpam-5839	859	42	neutrosophic	neutrosophic	ADJ
ejpam-5839	859	43	soft	soft	ADJ
ejpam-5839	859	44	first	first	ADJ
ejpam-5839	859	45	countability	countability	NOUN
ejpam-5839	859	46	and	and	CCONJ
ejpam-5839	859	47	quadripartitioned	quadripartitione	VERB
ejpam-5839	859	48	neutrosophic	neutrosophic	ADJ
ejpam-5839	859	49	soft	soft	ADJ
ejpam-5839	859	50	second	second	ADJ
ejpam-5839	859	51	countability	countability	NOUN
ejpam-5839	859	52	are	be	AUX
ejpam-5839	859	53	hereditary	hereditary	ADJ
ejpam-5839	859	54	properties	property	NOUN
ejpam-5839	859	55	.	.	PUNCT
ejpam-5839	860	1	however	however	ADV
ejpam-5839	860	2	,	,	PUNCT
ejpam-5839	860	3	quadripartitioned	quadripartitione	VERB
ejpam-5839	860	4	neutrosophic	neutrosophic	ADJ
ejpam-5839	860	5	soft	soft	ADJ
ejpam-5839	860	6	p	p	NOUN
ejpam-5839	860	7	-	-	PUNCT
ejpam-5839	860	8	closed	close	VERB
ejpam-5839	860	9	sets	set	NOUN
ejpam-5839	860	10	and	and	CCONJ
ejpam-5839	860	11	quadripartitioned	quadripartitione	VERB
ejpam-5839	860	12	neutrosophic	neutrosophic	ADJ
ejpam-5839	860	13	soft	soft	ADJ
ejpam-5839	860	14	p	p	NOUN
ejpam-5839	860	15	-	-	PUNCT
ejpam-5839	860	16	open	open	ADJ
ejpam-5839	860	17	sets	set	NOUN
ejpam-5839	860	18	are	be	AUX
ejpam-5839	860	19	not	not	PART
ejpam-5839	860	20	hereditary	hereditary	ADJ
ejpam-5839	860	21	properties	property	NOUN
ejpam-5839	860	22	.	.	PUNCT
ejpam-5839	861	1	definition	definition	NOUN
ejpam-5839	861	2	39	39	NUM
ejpam-5839	861	3	.	.	PUNCT
ejpam-5839	862	1	let	let	VERB
ejpam-5839	862	2	(	(	PUNCT
ejpam-5839	862	3	x	x	NOUN
ejpam-5839	862	4	,	,	PUNCT
ejpam-5839	862	5	τqpnss	τqpnss	PROPN
ejpam-5839	862	6	,	,	PUNCT
ejpam-5839	862	7	ω	ω	PROPN
ejpam-5839	862	8	)	)	PUNCT
ejpam-5839	862	9	be	be	VERB
ejpam-5839	862	10	a	a	DET
ejpam-5839	862	11	quadripartitioned	quadripartitione	VERB
ejpam-5839	862	12	neutrosophic	neutrosophic	ADJ
ejpam-5839	862	13	soft	soft	ADJ
ejpam-5839	862	14	topological	topological	ADJ
ejpam-5839	862	15	space	space	NOUN
ejpam-5839	862	16	over	over	ADP
ejpam-5839	862	17	x.	x.	NOUN
ejpam-5839	862	18	this	this	DET
ejpam-5839	862	19	space	space	NOUN
ejpam-5839	862	20	is	be	AUX
ejpam-5839	862	21	said	say	VERB
ejpam-5839	862	22	to	to	PART
ejpam-5839	862	23	be	be	AUX
ejpam-5839	862	24	quadripartitioned	quadripartitione	VERB
ejpam-5839	862	25	neutrosophic	neutrosophic	ADJ
ejpam-5839	862	26	soft	soft	ADJ
ejpam-5839	862	27	separable	separable	NOUN
ejpam-5839	862	28	if	if	SCONJ
ejpam-5839	862	29	and	and	CCONJ
ejpam-5839	862	30	only	only	ADV
ejpam-5839	862	31	if	if	SCONJ
ejpam-5839	862	32	x	x	PRON
ejpam-5839	862	33	contains	contain	VERB
ejpam-5839	862	34	a	a	DET
ejpam-5839	862	35	quadripartitioned	quadripartitione	VERB
ejpam-5839	862	36	neutrosophic	neutrosophic	ADJ
ejpam-5839	862	37	soft	soft	ADJ
ejpam-5839	862	38	countable	countable	ADJ
ejpam-5839	862	39	dense	dense	ADJ
ejpam-5839	862	40	subset	subset	NOUN
ejpam-5839	862	41	.	.	PUNCT
ejpam-5839	863	1	that	that	PRON
ejpam-5839	863	2	is	be	AUX
ejpam-5839	863	3	,	,	PUNCT
ejpam-5839	863	4	there	there	PRON
ejpam-5839	863	5	exists	exist	VERB
ejpam-5839	863	6	a	a	DET
ejpam-5839	863	7	quadripartitioned	quadripartitioned	ADJ
ejpam-5839	863	8	neutrosophic	neutrosophic	ADJ
ejpam-5839	863	9	soft	soft	ADJ
ejpam-5839	863	10	countable	countable	ADJ
ejpam-5839	863	11	subset	subset	NOUN
ejpam-5839	863	12	(	(	PUNCT
ejpam-5839	863	13	k̃,ω	k̃,ω	NOUN
ejpam-5839	863	14	)	)	PUNCT
ejpam-5839	863	15	of	of	ADP
ejpam-5839	863	16	x	x	SYM
ejpam-5839	863	17	such	such	ADJ
ejpam-5839	863	18	that	that	PRON
ejpam-5839	863	19	(	(	PUNCT
ejpam-5839	863	20	k̃,ω	k̃,ω	NOUN
ejpam-5839	863	21	)	)	PUNCT
ejpam-5839	863	22	=	=	SYM
ejpam-5839	863	23	x.	x.	NOUN
ejpam-5839	863	24	theorem	theorem	VERB
ejpam-5839	863	25	15	15	NUM
ejpam-5839	863	26	.	.	PUNCT
ejpam-5839	864	1	let	let	AUX
ejpam-5839	864	2	(	(	PUNCT
ejpam-5839	864	3	x	x	NOUN
ejpam-5839	864	4	,	,	PUNCT
ejpam-5839	864	5	τqpnss	τqpnss	PROPN
ejpam-5839	864	6	,	,	PUNCT
ejpam-5839	864	7	ω	ω	PROPN
ejpam-5839	864	8	)	)	PUNCT
ejpam-5839	864	9	be	be	VERB
ejpam-5839	864	10	a	a	DET
ejpam-5839	864	11	quadripartitioned	quadripartitione	VERB
ejpam-5839	864	12	neutrosophic	neutrosophic	ADJ
ejpam-5839	864	13	soft	soft	ADJ
ejpam-5839	864	14	topological	topological	ADJ
ejpam-5839	864	15	space	space	NOUN
ejpam-5839	864	16	over	over	ADP
ejpam-5839	864	17	x	x	NOUN
ejpam-5839	864	18	,	,	PUNCT
ejpam-5839	864	19	and	and	CCONJ
ejpam-5839	864	20	let	let	VERB
ejpam-5839	864	21	bqpnss	bqpns	NOUN
ejpam-5839	864	22	be	be	AUX
ejpam-5839	864	23	a	a	DET
ejpam-5839	864	24	quadripartitioned	quadripartitioned	ADJ
ejpam-5839	864	25	neutrosophic	neutrosophic	ADJ
ejpam-5839	864	26	soft	soft	ADJ
ejpam-5839	864	27	basis	basis	NOUN
ejpam-5839	864	28	for	for	ADP
ejpam-5839	864	29	τqpnss	τqpns	NOUN
ejpam-5839	864	30	.	.	PUNCT
ejpam-5839	865	1	then	then	ADV
ejpam-5839	865	2	,	,	PUNCT
ejpam-5839	865	3	the	the	DET
ejpam-5839	865	4	topology	topology	NOUN
ejpam-5839	865	5	τqpnss	τqpnss	NOUN
ejpam-5839	865	6	is	be	AUX
ejpam-5839	865	7	given	give	VERB
ejpam-5839	865	8	by	by	ADP
ejpam-5839	865	9	the	the	DET
ejpam-5839	865	10	collection	collection	NOUN
ejpam-5839	865	11	of	of	ADP
ejpam-5839	865	12	all	all	DET
ejpam-5839	865	13	quadripartitioned	quadripartitione	VERB
ejpam-5839	865	14	neutrosophic	neutrosophic	ADJ
ejpam-5839	865	15	soft	soft	ADJ
ejpam-5839	865	16	unions	union	NOUN
ejpam-5839	865	17	of	of	ADP
ejpam-5839	865	18	elements	element	NOUN
ejpam-5839	865	19	of	of	ADP
ejpam-5839	865	20	bqpnss	bqpns	NOUN
ejpam-5839	865	21	,	,	PUNCT
ejpam-5839	865	22	that	that	ADV
ejpam-5839	865	23	is	be	AUX
ejpam-5839	865	24	,	,	PUNCT
ejpam-5839	865	25	τqpnss	τqpns	NOUN
ejpam-5839	865	26	=	=	SYM
ejpam-5839	865	27	{	{	PUNCT
ejpam-5839	865	28	⋃	⋃	NOUN
ejpam-5839	865	29	α∈i	α∈i	NUM
ejpam-5839	865	30	bα	bα	NOUN
ejpam-5839	865	31	|	|	ADV
ejpam-5839	865	32	bα	bα	NOUN
ejpam-5839	865	33	∈	∈	NOUN
ejpam-5839	865	34	bqpnss	bqpns	NOUN
ejpam-5839	865	35	,	,	PUNCT
ejpam-5839	865	36	i	i	PRON
ejpam-5839	865	37	is	be	AUX
ejpam-5839	865	38	an	an	DET
ejpam-5839	865	39	index	index	NOUN
ejpam-5839	865	40	set	set	VERB
ejpam-5839	865	41	}	}	PUNCT
ejpam-5839	865	42	.	.	PUNCT
ejpam-5839	866	1	proof	proof	NOUN
ejpam-5839	866	2	.	.	PUNCT
ejpam-5839	867	1	this	this	PRON
ejpam-5839	867	2	is	be	AUX
ejpam-5839	867	3	easily	easily	ADV
ejpam-5839	867	4	seen	see	VERB
ejpam-5839	867	5	from	from	ADP
ejpam-5839	867	6	the	the	DET
ejpam-5839	867	7	definition	definition	NOUN
ejpam-5839	867	8	of	of	ADP
ejpam-5839	867	9	quadripartitioned	quadripartitione	VERB
ejpam-5839	867	10	neutrosophic	neutrosophic	ADJ
ejpam-5839	867	11	soft	soft	ADJ
ejpam-5839	867	12	basis	basis	NOUN
ejpam-5839	867	13	.	.	PUNCT
ejpam-5839	868	1	theorem	theorem	NOUN
ejpam-5839	868	2	16	16	NUM
ejpam-5839	868	3	.	.	PUNCT
ejpam-5839	869	1	let	let	AUX
ejpam-5839	869	2	(	(	PUNCT
ejpam-5839	869	3	x	x	NOUN
ejpam-5839	869	4	,	,	PUNCT
ejpam-5839	869	5	τqpnss	τqpnss	PROPN
ejpam-5839	869	6	,	,	PUNCT
ejpam-5839	869	7	ω	ω	PROPN
ejpam-5839	869	8	)	)	PUNCT
ejpam-5839	869	9	be	be	VERB
ejpam-5839	869	10	a	a	DET
ejpam-5839	869	11	quadripartitioned	quadripartitione	VERB
ejpam-5839	869	12	neutrosophic	neutrosophic	ADJ
ejpam-5839	869	13	soft	soft	ADJ
ejpam-5839	869	14	topological	topological	ADJ
ejpam-5839	869	15	space	space	NOUN
ejpam-5839	869	16	over	over	ADP
ejpam-5839	869	17	x.	x.	NOUN
ejpam-5839	869	18	a	a	DET
ejpam-5839	869	19	sub	sub	ADJ
ejpam-5839	869	20	-	-	ADJ
ejpam-5839	869	21	collection	collection	ADJ
ejpam-5839	869	22	bqpnss	bqpns	NOUN
ejpam-5839	869	23	of	of	ADP
ejpam-5839	869	24	τqpnss	τqpnss	PROPN
ejpam-5839	869	25	is	be	AUX
ejpam-5839	869	26	a	a	DET
ejpam-5839	869	27	basis	basis	NOUN
ejpam-5839	869	28	for	for	ADP
ejpam-5839	869	29	τqpnss	τqpns	NOUN
ejpam-5839	869	30	if	if	SCONJ
ejpam-5839	869	31	and	and	CCONJ
ejpam-5839	869	32	only	only	ADV
ejpam-5839	869	33	if	if	SCONJ
ejpam-5839	869	34	,	,	PUNCT
ejpam-5839	869	35	for	for	ADP
ejpam-5839	869	36	each	each	DET
ejpam-5839	869	37	quadripartitioned	quadripartitione	VERB
ejpam-5839	869	38	neutrosophic	neutrosophic	ADJ
ejpam-5839	869	39	soft	soft	ADJ
ejpam-5839	869	40	p	p	NOUN
ejpam-5839	869	41	-	-	PUNCT
ejpam-5839	869	42	open	open	ADJ
ejpam-5839	869	43	set	set	NOUN
ejpam-5839	869	44	(	(	PUNCT
ejpam-5839	869	45	g̃,ω	g̃,ω	NOUN
ejpam-5839	869	46	)	)	PUNCT
ejpam-5839	869	47	∈	∈	PROPN
ejpam-5839	869	48	τqpnss	τqpns	NOUN
ejpam-5839	869	49	and	and	CCONJ
ejpam-5839	869	50	for	for	ADP
ejpam-5839	869	51	each	each	DET
ejpam-5839	869	52	quadripartitioned	quadripartitione	VERB
ejpam-5839	869	53	neutrosophic	neutrosophic	ADJ
ejpam-5839	869	54	soft	soft	ADJ
ejpam-5839	869	55	point	point	NOUN
ejpam-5839	869	56	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	869	57	)	)	PUNCT
ejpam-5839	869	58	∈	∈	PROPN
ejpam-5839	869	59	(	(	PUNCT
ejpam-5839	869	60	g̃,ω	g̃,ω	PROPN
ejpam-5839	869	61	)	)	PUNCT
ejpam-5839	869	62	,	,	PUNCT
ejpam-5839	869	63	there	there	PRON
ejpam-5839	869	64	exists	exist	VERB
ejpam-5839	869	65	a	a	DET
ejpam-5839	869	66	basis	basis	NOUN
ejpam-5839	869	67	element	element	NOUN
ejpam-5839	869	68	bxθ	bxθ	NOUN
ejpam-5839	869	69	(	(	PUNCT
ejpam-5839	869	70	r1,r2,r3,r4	r1,r2,r3,r4	NOUN
ejpam-5839	869	71	)	)	PUNCT
ejpam-5839	869	72	∈	∈	NOUN
ejpam-5839	869	73	bqpnss	bqpns	NOUN
ejpam-5839	869	74	such	such	ADJ
ejpam-5839	869	75	that	that	DET
ejpam-5839	869	76	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	869	77	)	)	PUNCT
ejpam-5839	869	78	∈	∈	PROPN
ejpam-5839	869	79	bxθ	bxθ	NOUN
ejpam-5839	869	80	(	(	PUNCT
ejpam-5839	869	81	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	869	82	)	)	PUNCT
ejpam-5839	869	83	⊆	⊆	NUM
ejpam-5839	869	84	(	(	PUNCT
ejpam-5839	869	85	g̃,ω	g̃,ω	NOUN
ejpam-5839	869	86	)	)	PUNCT
ejpam-5839	869	87	.	.	PUNCT
ejpam-5839	870	1	proof	proof	NOUN
ejpam-5839	870	2	.	.	PUNCT
ejpam-5839	871	1	let	let	VERB
ejpam-5839	871	2	(	(	PUNCT
ejpam-5839	871	3	x	x	NOUN
ejpam-5839	871	4	,	,	PUNCT
ejpam-5839	871	5	τqpnss	τqpnss	PROPN
ejpam-5839	871	6	,	,	PUNCT
ejpam-5839	871	7	ω	ω	PROPN
ejpam-5839	871	8	)	)	PUNCT
ejpam-5839	871	9	be	be	VERB
ejpam-5839	871	10	a	a	DET
ejpam-5839	871	11	quadripartitioned	quadripartitione	VERB
ejpam-5839	871	12	neutrosophic	neutrosophic	ADJ
ejpam-5839	871	13	soft	soft	ADJ
ejpam-5839	871	14	topological	topological	ADJ
ejpam-5839	871	15	space	space	NOUN
ejpam-5839	871	16	,	,	PUNCT
ejpam-5839	871	17	and	and	CCONJ
ejpam-5839	871	18	let	let	VERB
ejpam-5839	871	19	bqpnss	bqpns	NOUN
ejpam-5839	871	20	be	be	AUX
ejpam-5839	871	21	a	a	DET
ejpam-5839	871	22	collection	collection	NOUN
ejpam-5839	871	23	of	of	ADP
ejpam-5839	871	24	quadripartitioned	quadripartitione	VERB
ejpam-5839	871	25	neutrosophic	neutrosophic	ADJ
ejpam-5839	871	26	soft	soft	ADJ
ejpam-5839	871	27	p	p	NOUN
ejpam-5839	871	28	-	-	PUNCT
ejpam-5839	871	29	open	open	ADJ
ejpam-5839	871	30	sets	set	NOUN
ejpam-5839	871	31	.	.	PUNCT
ejpam-5839	872	1	suppose	suppose	VERB
ejpam-5839	872	2	that	that	SCONJ
ejpam-5839	872	3	bqpnss	bqpns	NOUN
ejpam-5839	872	4	forms	form	VERB
ejpam-5839	872	5	a	a	DET
ejpam-5839	872	6	basis	basis	NOUN
ejpam-5839	872	7	for	for	ADP
ejpam-5839	872	8	the	the	DET
ejpam-5839	872	9	quadripartitioned	quadripartitione	VERB
ejpam-5839	872	10	neutrosophic	neutrosophic	ADJ
ejpam-5839	872	11	soft	soft	ADJ
ejpam-5839	872	12	topology	topology	NOUN
ejpam-5839	872	13	τqpnss	τqpns	NOUN
ejpam-5839	872	14	.	.	PUNCT
ejpam-5839	873	1	then	then	ADV
ejpam-5839	873	2	,	,	PUNCT
ejpam-5839	873	3	for	for	ADP
ejpam-5839	873	4	every	every	DET
ejpam-5839	873	5	quadripartitioned	quadripartitione	VERB
ejpam-5839	873	6	neutrosophic	neutrosophic	ADJ
ejpam-5839	873	7	soft	soft	ADJ
ejpam-5839	873	8	p	p	NOUN
ejpam-5839	873	9	-	-	PUNCT
ejpam-5839	873	10	open	open	ADJ
ejpam-5839	873	11	set	set	NOUN
ejpam-5839	873	12	(	(	PUNCT
ejpam-5839	873	13	g̃,ω	g̃,ω	NOUN
ejpam-5839	873	14	)	)	PUNCT
ejpam-5839	873	15	∈	∈	PROPN
ejpam-5839	873	16	τqpnss	τqpns	NOUN
ejpam-5839	873	17	and	and	CCONJ
ejpam-5839	873	18	for	for	ADP
ejpam-5839	873	19	every	every	DET
ejpam-5839	873	20	quadripartitioned	quadripartitione	VERB
ejpam-5839	873	21	neutrosophic	neutrosophic	ADJ
ejpam-5839	873	22	soft	soft	ADJ
ejpam-5839	873	23	point	point	NOUN
ejpam-5839	873	24	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	873	25	)	)	PUNCT
ejpam-5839	873	26	∈	∈	PROPN
ejpam-5839	873	27	(	(	PUNCT
ejpam-5839	873	28	g̃,ω	g̃,ω	PROPN
ejpam-5839	873	29	)	)	PUNCT
ejpam-5839	873	30	,	,	PUNCT
ejpam-5839	873	31	there	there	PRON
ejpam-5839	873	32	exists	exist	VERB
ejpam-5839	873	33	a	a	DET
ejpam-5839	873	34	basis	basis	NOUN
ejpam-5839	873	35	element	element	NOUN
ejpam-5839	873	36	bxθ	bxθ	NOUN
ejpam-5839	873	37	(	(	PUNCT
ejpam-5839	873	38	r1,r2,r3,r4	r1,r2,r3,r4	NOUN
ejpam-5839	873	39	)	)	PUNCT
ejpam-5839	873	40	∈	∈	NOUN
ejpam-5839	873	41	bqpnss	bqpns	NOUN
ejpam-5839	873	42	such	such	ADJ
ejpam-5839	873	43	that	that	DET
ejpam-5839	873	44	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	873	45	)	)	PUNCT
ejpam-5839	873	46	∈	∈	PROPN
ejpam-5839	873	47	bxθ	bxθ	NOUN
ejpam-5839	873	48	(	(	PUNCT
ejpam-5839	873	49	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	873	50	)	)	PUNCT
ejpam-5839	873	51	⊆	⊆	NUM
ejpam-5839	873	52	(	(	PUNCT
ejpam-5839	873	53	g̃,ω	g̃,ω	NOUN
ejpam-5839	873	54	)	)	PUNCT
ejpam-5839	873	55	.	.	PUNCT
ejpam-5839	874	1	given	give	VERB
ejpam-5839	874	2	that	that	SCONJ
ejpam-5839	874	3	(	(	PUNCT
ejpam-5839	874	4	x	x	X
ejpam-5839	874	5	,	,	PUNCT
ejpam-5839	874	6	τqpnss	τqpnss	PROPN
ejpam-5839	874	7	,	,	PUNCT
ejpam-5839	874	8	ω	ω	PROPN
ejpam-5839	874	9	)	)	PUNCT
ejpam-5839	874	10	be	be	VERB
ejpam-5839	874	11	a	a	DET
ejpam-5839	874	12	quadripartitioned	quadripartitione	VERB
ejpam-5839	874	13	neutrosophic	neutrosophic	ADJ
ejpam-5839	874	14	soft	soft	ADJ
ejpam-5839	874	15	topological	topological	ADJ
ejpam-5839	874	16	space	space	NOUN
ejpam-5839	874	17	and	and	CCONJ
ejpam-5839	874	18	bqpnss	bqpns	NOUN
ejpam-5839	874	19	is	be	AUX
ejpam-5839	874	20	a	a	DET
ejpam-5839	874	21	collection	collection	NOUN
ejpam-5839	874	22	of	of	ADP
ejpam-5839	874	23	quadripartitioned	quadripartitione	VERB
ejpam-5839	874	24	neutrosophic	neutrosophic	ADJ
ejpam-5839	874	25	soft	soft	ADJ
ejpam-5839	874	26	p	p	NOUN
ejpam-5839	874	27	-	-	PUNCT
ejpam-5839	874	28	open	open	ADJ
ejpam-5839	874	29	sets	set	NOUN
ejpam-5839	874	30	.	.	PUNCT
ejpam-5839	875	1	let	let	VERB
ejpam-5839	875	2	bqpnss	bqpns	NOUN
ejpam-5839	875	3	be	be	AUX
ejpam-5839	875	4	a	a	DET
ejpam-5839	875	5	base	base	NOUN
ejpam-5839	875	6	for	for	ADP
ejpam-5839	875	7	a	a	DET
ejpam-5839	875	8	quadripartitioned	quadripartitione	VERB
ejpam-5839	875	9	neutrosophic	neutrosophic	ADJ
ejpam-5839	875	10	soft	soft	ADJ
ejpam-5839	875	11	topology	topology	NOUN
ejpam-5839	875	12	τqpnss	τqpns	NOUN
ejpam-5839	875	13	,	,	PUNCT
ejpam-5839	875	14	then	then	ADV
ejpam-5839	875	15	by	by	ADP
ejpam-5839	875	16	definition	definition	NOUN
ejpam-5839	875	17	every	every	DET
ejpam-5839	875	18	a.	a.	NOUN
ejpam-5839	875	19	shihadeh	shihadeh	NOUN
ejpam-5839	875	20	et	et	PROPN
ejpam-5839	875	21	al	al	PROPN
ejpam-5839	875	22	.	.	PUNCT
ejpam-5839	875	23	/	/	SYM
ejpam-5839	875	24	eur	eur	PROPN
ejpam-5839	875	25	.	.	PUNCT
ejpam-5839	876	1	j.	j.	PROPN
ejpam-5839	876	2	pure	pure	PROPN
ejpam-5839	876	3	appl	appl	PROPN
ejpam-5839	876	4	.	.	PROPN
ejpam-5839	876	5	math	math	PROPN
ejpam-5839	876	6	,	,	PUNCT
ejpam-5839	876	7	18	18	NUM
ejpam-5839	876	8	(	(	PUNCT
ejpam-5839	876	9	2	2	NUM
ejpam-5839	876	10	)	)	PUNCT
ejpam-5839	876	11	(	(	PUNCT
ejpam-5839	876	12	2025	2025	NUM
ejpam-5839	876	13	)	)	PUNCT
ejpam-5839	876	14	,	,	PUNCT
ejpam-5839	876	15	5839	5839	NUM
ejpam-5839	876	16	38	38	NUM
ejpam-5839	876	17	of	of	ADP
ejpam-5839	876	18	54	54	NUM
ejpam-5839	876	19	quadripartitioned	quadripartitione	VERB
ejpam-5839	876	20	neutrosophic	neutrosophic	ADJ
ejpam-5839	876	21	soft	soft	ADJ
ejpam-5839	876	22	p	p	NOUN
ejpam-5839	876	23	-	-	PUNCT
ejpam-5839	876	24	open	open	ADJ
ejpam-5839	876	25	set	set	NOUN
ejpam-5839	876	26	(	(	PUNCT
ejpam-5839	876	27	g̃,ω	g̃,ω	PROPN
ejpam-5839	876	28	)	)	PUNCT
ejpam-5839	876	29	is	be	AUX
ejpam-5839	876	30	the	the	DET
ejpam-5839	876	31	union	union	NOUN
ejpam-5839	876	32	of	of	ADP
ejpam-5839	876	33	some	some	DET
ejpam-5839	876	34	members	member	NOUN
ejpam-5839	876	35	of	of	ADP
ejpam-5839	876	36	bqpnss	bqpns	NOUN
ejpam-5839	876	37	,	,	PUNCT
ejpam-5839	876	38	i.e.	i.e.	X
ejpam-5839	876	39	,	,	PUNCT
ejpam-5839	876	40	(	(	PUNCT
ejpam-5839	876	41	g̃,ω	g̃,ω	NOUN
ejpam-5839	876	42	)	)	PUNCT
ejpam-5839	876	43	=	=	PUNCT
ejpam-5839	877	1	⋃	⋃	ADP
ejpam-5839	877	2	i∈i	i∈i	ADJ
ejpam-5839	877	3	bi	bi	NOUN
ejpam-5839	877	4	,	,	PUNCT
ejpam-5839	877	5	wherebi	wherebi	NOUN
ejpam-5839	877	6	∈	∈	PROPN
ejpam-5839	877	7	bqpnss	bqpns	NOUN
ejpam-5839	877	8	for	for	ADP
ejpam-5839	877	9	all	all	PRON
ejpam-5839	877	10	i	i	PRON
ejpam-5839	877	11	∈	∈	PROPN
ejpam-5839	877	12	i.	i.	NOUN
ejpam-5839	877	13	let	let	AUX
ejpam-5839	877	14	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	877	15	)	)	PUNCT
ejpam-5839	877	16	be	be	AUX
ejpam-5839	877	17	an	an	DET
ejpam-5839	877	18	arbitrary	arbitrary	ADJ
ejpam-5839	877	19	quadripartitioned	quadripartitione	VERB
ejpam-5839	877	20	neutrosophic	neutrosophic	ADJ
ejpam-5839	877	21	soft	soft	ADJ
ejpam-5839	877	22	point	point	NOUN
ejpam-5839	877	23	of	of	ADP
ejpam-5839	877	24	(	(	PUNCT
ejpam-5839	877	25	g̃,ω	g̃,ω	PROPN
ejpam-5839	877	26	)	)	PUNCT
ejpam-5839	877	27	.	.	PUNCT
ejpam-5839	878	1	we	we	PRON
ejpam-5839	878	2	are	be	AUX
ejpam-5839	878	3	to	to	PART
ejpam-5839	878	4	prove	prove	VERB
ejpam-5839	878	5	that	that	SCONJ
ejpam-5839	878	6	there	there	PRON
ejpam-5839	878	7	exists	exist	VERB
ejpam-5839	878	8	a	a	DET
ejpam-5839	878	9	quadripartitioned	quadripartitioned	ADJ
ejpam-5839	878	10	neutrosophic	neutrosophic	ADJ
ejpam-5839	878	11	soft	soft	ADJ
ejpam-5839	878	12	basis	basis	NOUN
ejpam-5839	878	13	element	element	NOUN
ejpam-5839	878	14	bxθ	bxθ	NOUN
ejpam-5839	878	15	(	(	PUNCT
ejpam-5839	878	16	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	878	17	)	)	PUNCT
ejpam-5839	878	18	containing	contain	VERB
ejpam-5839	878	19	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	878	20	)	)	PUNCT
ejpam-5839	878	21	such	such	ADJ
ejpam-5839	878	22	that	that	DET
ejpam-5839	878	23	bxθ	bxθ	NOUN
ejpam-5839	878	24	(	(	PUNCT
ejpam-5839	878	25	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	878	26	)	)	PUNCT
ejpam-5839	878	27	⊆	⊆	NUM
ejpam-5839	878	28	(	(	PUNCT
ejpam-5839	878	29	g̃,ω	g̃,ω	NOUN
ejpam-5839	878	30	)	)	PUNCT
ejpam-5839	878	31	.	.	PUNCT
ejpam-5839	879	1	since	since	SCONJ
ejpam-5839	879	2	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	879	3	)	)	PUNCT
ejpam-5839	879	4	∈	∈	PROPN
ejpam-5839	879	5	(	(	PUNCT
ejpam-5839	879	6	g̃,ω	g̃,ω	PROPN
ejpam-5839	879	7	)	)	PUNCT
ejpam-5839	879	8	but	but	CCONJ
ejpam-5839	879	9	(	(	PUNCT
ejpam-5839	879	10	g̃,ω	g̃,ω	NOUN
ejpam-5839	879	11	)	)	PUNCT
ejpam-5839	879	12	=	=	SYM
ejpam-5839	880	1	⋃	⋃	ADP
ejpam-5839	880	2	i∈i	i∈i	ADJ
ejpam-5839	880	3	bi	bi	NOUN
ejpam-5839	880	4	,	,	PUNCT
ejpam-5839	880	5	it	it	PRON
ejpam-5839	880	6	follows	follow	VERB
ejpam-5839	881	1	that	that	SCONJ
ejpam-5839	881	2	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	881	3	)	)	PUNCT
ejpam-5839	881	4	∈	∈	PROPN
ejpam-5839	881	5	⋃	⋃	ADP
ejpam-5839	881	6	i∈i	i∈i	ADJ
ejpam-5839	881	7	bi	bi	NOUN
ejpam-5839	881	8	,	,	PUNCT
ejpam-5839	881	9	which	which	PRON
ejpam-5839	881	10	implies	imply	VERB
ejpam-5839	881	11	that	that	SCONJ
ejpam-5839	881	12	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	881	13	)	)	PUNCT
ejpam-5839	881	14	∈	∈	PROPN
ejpam-5839	881	15	bi	bi	NOUN
ejpam-5839	881	16	for	for	ADP
ejpam-5839	881	17	some	some	PRON
ejpam-5839	881	18	i	i	PRON
ejpam-5839	881	19	∈	∈	PROPN
ejpam-5839	881	20	i.	i.	NOUN
ejpam-5839	881	21	let	let	VERB
ejpam-5839	882	1	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	882	2	)	)	PUNCT
ejpam-5839	882	3	∈	∈	PROPN
ejpam-5839	882	4	bi	bi	NOUN
ejpam-5839	882	5	for	for	ADP
ejpam-5839	882	6	i	i	PRON
ejpam-5839	882	7	=	=	PUNCT
ejpam-5839	882	8	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	882	9	)	)	PUNCT
ejpam-5839	882	10	,	,	PUNCT
ejpam-5839	882	11	then	then	ADV
ejpam-5839	882	12	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	882	13	)	)	PUNCT
ejpam-5839	882	14	∈	∈	PROPN
ejpam-5839	882	15	bxθ	bxθ	NOUN
ejpam-5839	882	16	(	(	PUNCT
ejpam-5839	882	17	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	882	18	)	)	PUNCT
ejpam-5839	883	1	⊆	⊆	NUM
ejpam-5839	883	2	⋃	⋃	NOUN
ejpam-5839	883	3	bi	bi	NOUN
ejpam-5839	883	4	,	,	PUNCT
ejpam-5839	883	5	i	i	PROPN
ejpam-5839	883	6	∈	∈	PROPN
ejpam-5839	883	7	i.	i.	NOUN
ejpam-5839	883	8	since	since	SCONJ
ejpam-5839	883	9	bi	bi	NOUN
ejpam-5839	883	10	⊆	⊆	NUM
ejpam-5839	883	11	⋃	⋃	PROPN
ejpam-5839	883	12	bi	bi	NOUN
ejpam-5839	883	13	for	for	ADP
ejpam-5839	883	14	all	all	DET
ejpam-5839	883	15	i	i	PRON
ejpam-5839	883	16	,	,	PUNCT
ejpam-5839	883	17	it	it	PRON
ejpam-5839	883	18	implies	imply	VERB
ejpam-5839	883	19	that	that	SCONJ
ejpam-5839	883	20	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	883	21	)	)	PUNCT
ejpam-5839	883	22	∈	∈	PROPN
ejpam-5839	883	23	bxθ	bxθ	NOUN
ejpam-5839	883	24	(	(	PUNCT
ejpam-5839	883	25	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	883	26	)	)	PUNCT
ejpam-5839	883	27	⊆	⊆	NUM
ejpam-5839	883	28	⋃	⋃	NOUN
ejpam-5839	883	29	bi	bi	NOUN
ejpam-5839	883	30	,	,	PUNCT
ejpam-5839	883	31	i	i	PRON
ejpam-5839	883	32	∈	∈	PROPN
ejpam-5839	883	33	i.	i.	NOUN
ejpam-5839	883	34	this	this	PRON
ejpam-5839	883	35	further	far	ADV
ejpam-5839	883	36	implies	imply	VERB
ejpam-5839	883	37	that	that	SCONJ
ejpam-5839	883	38	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	883	39	)	)	PUNCT
ejpam-5839	883	40	∈	∈	PROPN
ejpam-5839	883	41	bxθ	bxθ	NOUN
ejpam-5839	883	42	(	(	PUNCT
ejpam-5839	883	43	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	883	44	)	)	PUNCT
ejpam-5839	883	45	⊆	⊆	NUM
ejpam-5839	883	46	(	(	PUNCT
ejpam-5839	883	47	g̃,ω	g̃,ω	NOUN
ejpam-5839	883	48	)	)	PUNCT
ejpam-5839	883	49	,	,	PUNCT
ejpam-5839	883	50	where	where	SCONJ
ejpam-5839	883	51	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	883	52	)	)	PUNCT
ejpam-5839	883	53	∈	∈	PROPN
ejpam-5839	883	54	bqpnss	bqpns	NOUN
ejpam-5839	883	55	.	.	PUNCT
ejpam-5839	884	1	conversely	conversely	ADV
ejpam-5839	884	2	,	,	PUNCT
ejpam-5839	884	3	suppose	suppose	VERB
ejpam-5839	884	4	for	for	ADP
ejpam-5839	884	5	each	each	DET
ejpam-5839	884	6	quadripartitioned	quadripartitione	VERB
ejpam-5839	884	7	neutrosophic	neutrosophic	ADJ
ejpam-5839	884	8	soft	soft	ADJ
ejpam-5839	884	9	point	point	NOUN
ejpam-5839	884	10	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	884	11	)	)	PUNCT
ejpam-5839	884	12	of	of	ADP
ejpam-5839	884	13	a	a	DET
ejpam-5839	884	14	quadripartitioned	quadripartitione	VERB
ejpam-5839	884	15	neutrosophic	neutrosophic	ADJ
ejpam-5839	884	16	soft	soft	ADJ
ejpam-5839	884	17	p	p	NOUN
ejpam-5839	884	18	-	-	PUNCT
ejpam-5839	884	19	open	open	ADJ
ejpam-5839	884	20	set	set	NOUN
ejpam-5839	884	21	(	(	PUNCT
ejpam-5839	884	22	g̃,ω	g̃,ω	PROPN
ejpam-5839	884	23	)	)	PUNCT
ejpam-5839	884	24	,	,	PUNCT
ejpam-5839	884	25	there	there	PRON
ejpam-5839	884	26	exists	exist	VERB
ejpam-5839	884	27	a	a	DET
ejpam-5839	884	28	quadripartitioned	quadripartitioned	ADJ
ejpam-5839	884	29	neutrosophic	neutrosophic	ADJ
ejpam-5839	884	30	soft	soft	ADJ
ejpam-5839	884	31	set	set	NOUN
ejpam-5839	884	32	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	NOUN
ejpam-5839	884	33	)	)	PUNCT
ejpam-5839	884	34	∈	∈	NOUN
ejpam-5839	884	35	bqpnss	bqpns	NOUN
ejpam-5839	884	36	such	such	ADJ
ejpam-5839	884	37	that	that	DET
ejpam-5839	884	38	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	884	39	)	)	PUNCT
ejpam-5839	884	40	∈	∈	PROPN
ejpam-5839	884	41	bxθ	bxθ	NOUN
ejpam-5839	884	42	(	(	PUNCT
ejpam-5839	884	43	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	884	44	)	)	PUNCT
ejpam-5839	884	45	⊆	⊆	NUM
ejpam-5839	884	46	(	(	PUNCT
ejpam-5839	884	47	g̃,ω	g̃,ω	NOUN
ejpam-5839	884	48	)	)	PUNCT
ejpam-5839	884	49	.	.	PUNCT
ejpam-5839	885	1	we	we	PRON
ejpam-5839	885	2	are	be	AUX
ejpam-5839	885	3	to	to	PART
ejpam-5839	885	4	prove	prove	VERB
ejpam-5839	885	5	that	that	SCONJ
ejpam-5839	885	6	bqpnss	bqpns	NOUN
ejpam-5839	885	7	is	be	AUX
ejpam-5839	885	8	a	a	DET
ejpam-5839	885	9	quadripartitioned	quadripartitione	VERB
ejpam-5839	885	10	neutrosophic	neutrosophic	ADJ
ejpam-5839	885	11	soft	soft	ADJ
ejpam-5839	885	12	basis	basis	NOUN
ejpam-5839	885	13	for	for	ADP
ejpam-5839	885	14	the	the	DET
ejpam-5839	885	15	quadripartitioned	quadripartitione	VERB
ejpam-5839	885	16	neutrosophic	neutrosophic	ADJ
ejpam-5839	885	17	soft	soft	ADJ
ejpam-5839	885	18	topology	topology	NOUN
ejpam-5839	885	19	τqpnss	τqpns	NOUN
ejpam-5839	885	20	.	.	PUNCT
ejpam-5839	886	1	for	for	ADP
ejpam-5839	886	2	this	this	PRON
ejpam-5839	886	3	,	,	PUNCT
ejpam-5839	886	4	we	we	PRON
ejpam-5839	886	5	will	will	AUX
ejpam-5839	886	6	prove	prove	VERB
ejpam-5839	886	7	that	that	SCONJ
ejpam-5839	886	8	every	every	DET
ejpam-5839	886	9	quadripartitioned	quadripartitione	VERB
ejpam-5839	886	10	neutrosophic	neutrosophic	ADJ
ejpam-5839	886	11	soft	soft	ADJ
ejpam-5839	886	12	p	p	NOUN
ejpam-5839	886	13	-	-	PUNCT
ejpam-5839	886	14	open	open	ADJ
ejpam-5839	886	15	set	set	NOUN
ejpam-5839	886	16	(	(	PUNCT
ejpam-5839	886	17	g̃,ω	g̃,ω	PROPN
ejpam-5839	886	18	)	)	PUNCT
ejpam-5839	886	19	can	can	AUX
ejpam-5839	886	20	be	be	AUX
ejpam-5839	886	21	written	write	VERB
ejpam-5839	886	22	as	as	ADP
ejpam-5839	886	23	a	a	DET
ejpam-5839	886	24	union	union	NOUN
ejpam-5839	886	25	of	of	ADP
ejpam-5839	886	26	some	some	DET
ejpam-5839	886	27	members	member	NOUN
ejpam-5839	886	28	of	of	ADP
ejpam-5839	886	29	bqpnss	bqpns	NOUN
ejpam-5839	886	30	.	.	PUNCT
ejpam-5839	887	1	since	since	SCONJ
ejpam-5839	887	2	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	887	3	)	)	PUNCT
ejpam-5839	887	4	∈	∈	PROPN
ejpam-5839	887	5	bxe	bxe	X
ejpam-5839	887	6	(	(	PUNCT
ejpam-5839	887	7	r1,r2,r3,r4	r1,r2,r3,r4	NOUN
ejpam-5839	887	8	)	)	PUNCT
ejpam-5839	887	9	⊆	⊆	NUM
ejpam-5839	887	10	(	(	PUNCT
ejpam-5839	887	11	g̃,ω	g̃,ω	NOUN
ejpam-5839	887	12	)	)	PUNCT
ejpam-5839	887	13	,	,	PUNCT
ejpam-5839	887	14	it	it	PRON
ejpam-5839	887	15	follows	follow	VERB
ejpam-5839	887	16	that	that	SCONJ
ejpam-5839	887	17	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	887	18	)	)	PUNCT
ejpam-5839	887	19	∈	∈	PROPN
ejpam-5839	887	20	bxθ	bxθ	NOUN
ejpam-5839	887	21	(	(	PUNCT
ejpam-5839	887	22	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	887	23	)	)	PUNCT
ejpam-5839	887	24	,	,	PUNCT
ejpam-5839	887	25	and	and	CCONJ
ejpam-5839	887	26	bxθ	bxθ	NOUN
ejpam-5839	887	27	(	(	PUNCT
ejpam-5839	887	28	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	887	29	)	)	PUNCT
ejpam-5839	888	1	⊆	⊆	NUM
ejpam-5839	888	2	(	(	PUNCT
ejpam-5839	888	3	g̃,ω	g̃,ω	NOUN
ejpam-5839	888	4	)	)	PUNCT
ejpam-5839	888	5	.	.	PUNCT
ejpam-5839	889	1	thus	thus	ADV
ejpam-5839	889	2	,	,	PUNCT
ejpam-5839	889	3	we	we	PRON
ejpam-5839	889	4	have⋃	have⋃	VERB
ejpam-5839	889	5	{	{	PUNCT
ejpam-5839	889	6	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	889	7	)	)	PUNCT
ejpam-5839	889	8	}	}	PUNCT
ejpam-5839	890	1	⊆	⊆	NUM
ejpam-5839	890	2	⋃	⋃	PROPN
ejpam-5839	890	3	xθ	xθ	PROPN
ejpam-5839	890	4	(	(	PUNCT
ejpam-5839	890	5	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	890	6	)	)	PUNCT
ejpam-5839	890	7	∈(g̃,ω	∈(g̃,ω	PROPN
ejpam-5839	890	8	)	)	PUNCT
ejpam-5839	890	9	bxθ	bxθ	NOUN
ejpam-5839	890	10	(	(	PUNCT
ejpam-5839	890	11	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	890	12	)	)	PUNCT
ejpam-5839	891	1	⊆	⊆	NUM
ejpam-5839	891	2	⋃	⋃	PROPN
ejpam-5839	891	3	xθ	xθ	PROPN
ejpam-5839	891	4	(	(	PUNCT
ejpam-5839	891	5	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	891	6	)	)	PUNCT
ejpam-5839	891	7	∈(g̃,ω	∈(g̃,ω	PROPN
ejpam-5839	891	8	)	)	PUNCT
ejpam-5839	891	9	(	(	PUNCT
ejpam-5839	891	10	g̃,ω	g̃,ω	PROPN
ejpam-5839	891	11	)	)	PUNCT
ejpam-5839	891	12	.	.	PUNCT
ejpam-5839	892	1	this	this	PRON
ejpam-5839	892	2	implies	imply	VERB
ejpam-5839	892	3	that	that	SCONJ
ejpam-5839	892	4	(	(	PUNCT
ejpam-5839	892	5	g̃,ω	g̃,ω	PROPN
ejpam-5839	892	6	)	)	PUNCT
ejpam-5839	892	7	⊆	⊆	NUM
ejpam-5839	892	8	⋃	⋃	PROPN
ejpam-5839	892	9	xθ	xθ	PROPN
ejpam-5839	892	10	(	(	PUNCT
ejpam-5839	892	11	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	892	12	)	)	PUNCT
ejpam-5839	892	13	∈(g̃,ω	∈(g̃,ω	PROPN
ejpam-5839	892	14	)	)	PUNCT
ejpam-5839	892	15	bxθ	bxθ	NOUN
ejpam-5839	892	16	(	(	PUNCT
ejpam-5839	892	17	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	892	18	)	)	PUNCT
ejpam-5839	892	19	,	,	PUNCT
ejpam-5839	892	20	a.	a.	NOUN
ejpam-5839	892	21	shihadeh	shihadeh	VERB
ejpam-5839	892	22	et	et	PROPN
ejpam-5839	892	23	al	al	PROPN
ejpam-5839	892	24	.	.	PUNCT
ejpam-5839	892	25	/	/	SYM
ejpam-5839	892	26	eur	eur	PROPN
ejpam-5839	892	27	.	.	PUNCT
ejpam-5839	893	1	j.	j.	PROPN
ejpam-5839	893	2	pure	pure	PROPN
ejpam-5839	893	3	appl	appl	PROPN
ejpam-5839	893	4	.	.	PROPN
ejpam-5839	893	5	math	math	PROPN
ejpam-5839	893	6	,	,	PUNCT
ejpam-5839	893	7	18	18	NUM
ejpam-5839	893	8	(	(	PUNCT
ejpam-5839	893	9	2	2	NUM
ejpam-5839	893	10	)	)	PUNCT
ejpam-5839	893	11	(	(	PUNCT
ejpam-5839	893	12	2025	2025	NUM
ejpam-5839	893	13	)	)	PUNCT
ejpam-5839	893	14	,	,	PUNCT
ejpam-5839	893	15	5839	5839	NUM
ejpam-5839	893	16	39	39	NUM
ejpam-5839	893	17	of	of	ADP
ejpam-5839	893	18	54	54	NUM
ejpam-5839	893	19	and	and	CCONJ
ejpam-5839	893	20	⋃	⋃	PROPN
ejpam-5839	893	21	xθ	xθ	PROPN
ejpam-5839	893	22	(	(	PUNCT
ejpam-5839	893	23	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	893	24	)	)	PUNCT
ejpam-5839	893	25	∈(g̃,ω	∈(g̃,ω	PROPN
ejpam-5839	893	26	)	)	PUNCT
ejpam-5839	893	27	bxθ	bxθ	NOUN
ejpam-5839	893	28	(	(	PUNCT
ejpam-5839	893	29	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	893	30	)	)	PUNCT
ejpam-5839	894	1	⊆	⊆	NUM
ejpam-5839	894	2	(	(	PUNCT
ejpam-5839	894	3	g̃,ω	g̃,ω	NOUN
ejpam-5839	894	4	)	)	PUNCT
ejpam-5839	894	5	.	.	PUNCT
ejpam-5839	895	1	therefore	therefore	ADV
ejpam-5839	895	2	,	,	PUNCT
ejpam-5839	895	3	(	(	PUNCT
ejpam-5839	895	4	g̃,ω	g̃,ω	NOUN
ejpam-5839	895	5	)	)	PUNCT
ejpam-5839	895	6	=	=	PUNCT
ejpam-5839	895	7	⋃	⋃	PROPN
ejpam-5839	895	8	xθ	xθ	PROPN
ejpam-5839	895	9	(	(	PUNCT
ejpam-5839	895	10	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	895	11	)	)	PUNCT
ejpam-5839	895	12	∈(g̃,ω	∈(g̃,ω	PROPN
ejpam-5839	895	13	)	)	PUNCT
ejpam-5839	895	14	bxθ	bxθ	NOUN
ejpam-5839	895	15	(	(	PUNCT
ejpam-5839	895	16	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	895	17	)	)	PUNCT
ejpam-5839	895	18	.	.	PUNCT
ejpam-5839	896	1	since	since	SCONJ
ejpam-5839	896	2	each	each	DET
ejpam-5839	896	3	bxθ	bxθ	NOUN
ejpam-5839	896	4	(	(	PUNCT
ejpam-5839	896	5	r1,r2,r3,r4	r1,r2,r3,r4	NOUN
ejpam-5839	896	6	)	)	PUNCT
ejpam-5839	896	7	∈	∈	PROPN
ejpam-5839	896	8	bqpnss	bqpns	NOUN
ejpam-5839	896	9	,	,	PUNCT
ejpam-5839	896	10	it	it	PRON
ejpam-5839	896	11	follows	follow	VERB
ejpam-5839	896	12	that	that	SCONJ
ejpam-5839	896	13	(	(	PUNCT
ejpam-5839	896	14	g̃,ω	g̃,ω	PROPN
ejpam-5839	896	15	)	)	PUNCT
ejpam-5839	896	16	is	be	AUX
ejpam-5839	896	17	the	the	DET
ejpam-5839	896	18	union	union	NOUN
ejpam-5839	896	19	of	of	ADP
ejpam-5839	896	20	some	some	DET
ejpam-5839	896	21	members	member	NOUN
ejpam-5839	896	22	of	of	ADP
ejpam-5839	896	23	bqpnss	bqpns	NOUN
ejpam-5839	896	24	.	.	PUNCT
ejpam-5839	897	1	since	since	SCONJ
ejpam-5839	897	2	(	(	PUNCT
ejpam-5839	897	3	g̃,ω	g̃,ω	PROPN
ejpam-5839	897	4	)	)	PUNCT
ejpam-5839	897	5	is	be	AUX
ejpam-5839	897	6	an	an	DET
ejpam-5839	897	7	arbitrary	arbitrary	ADJ
ejpam-5839	897	8	quadripartitioned	quadripartitione	VERB
ejpam-5839	897	9	neutrosophic	neutrosophic	ADJ
ejpam-5839	897	10	soft	soft	ADJ
ejpam-5839	897	11	p	p	NOUN
ejpam-5839	897	12	-	-	PUNCT
ejpam-5839	897	13	open	open	ADJ
ejpam-5839	897	14	set	set	NOUN
ejpam-5839	897	15	,	,	PUNCT
ejpam-5839	897	16	we	we	PRON
ejpam-5839	897	17	conclude	conclude	VERB
ejpam-5839	897	18	that	that	SCONJ
ejpam-5839	897	19	every	every	DET
ejpam-5839	897	20	quadripartitioned	quadripartitione	VERB
ejpam-5839	897	21	neutrosophic	neutrosophic	ADJ
ejpam-5839	897	22	soft	soft	ADJ
ejpam-5839	897	23	p	p	NOUN
ejpam-5839	897	24	-	-	PUNCT
ejpam-5839	897	25	open	open	ADJ
ejpam-5839	897	26	set	set	NOUN
ejpam-5839	897	27	is	be	AUX
ejpam-5839	897	28	the	the	DET
ejpam-5839	897	29	union	union	NOUN
ejpam-5839	897	30	of	of	ADP
ejpam-5839	897	31	some	some	DET
ejpam-5839	897	32	members	member	NOUN
ejpam-5839	897	33	of	of	ADP
ejpam-5839	897	34	bqpnss	bqpns	NOUN
ejpam-5839	897	35	.	.	PUNCT
ejpam-5839	898	1	thus	thus	ADV
ejpam-5839	898	2	,	,	PUNCT
ejpam-5839	898	3	bqpnss	bqpns	NOUN
ejpam-5839	898	4	is	be	AUX
ejpam-5839	898	5	a	a	DET
ejpam-5839	898	6	quadripartitioned	quadripartitione	VERB
ejpam-5839	898	7	neutrosophic	neutrosophic	ADJ
ejpam-5839	898	8	soft	soft	ADJ
ejpam-5839	898	9	basis	basis	NOUN
ejpam-5839	898	10	for	for	ADP
ejpam-5839	898	11	the	the	DET
ejpam-5839	898	12	quadripartitioned	quadripartitione	VERB
ejpam-5839	898	13	neutrosophic	neutrosophic	ADJ
ejpam-5839	898	14	soft	soft	ADJ
ejpam-5839	898	15	topology	topology	NOUN
ejpam-5839	898	16	τqpnss	τqpns	NOUN
ejpam-5839	898	17	.	.	PUNCT
ejpam-5839	899	1	theorem	theorem	VERB
ejpam-5839	899	2	17	17	NUM
ejpam-5839	899	3	.	.	PUNCT
ejpam-5839	900	1	let	let	AUX
ejpam-5839	900	2	(	(	PUNCT
ejpam-5839	900	3	x	x	NOUN
ejpam-5839	900	4	,	,	PUNCT
ejpam-5839	900	5	τqpnss	τqpnss	PROPN
ejpam-5839	900	6	,	,	PUNCT
ejpam-5839	900	7	ω	ω	PROPN
ejpam-5839	900	8	)	)	PUNCT
ejpam-5839	900	9	be	be	VERB
ejpam-5839	900	10	a	a	DET
ejpam-5839	900	11	quadripartitioned	quadripartitione	VERB
ejpam-5839	900	12	neutrosophic	neutrosophic	ADJ
ejpam-5839	900	13	soft	soft	ADJ
ejpam-5839	900	14	topological	topological	ADJ
ejpam-5839	900	15	space	space	NOUN
ejpam-5839	900	16	over	over	ADP
ejpam-5839	900	17	x.	x.	NOUN
ejpam-5839	900	18	a	a	DET
ejpam-5839	900	19	sub	sub	ADJ
ejpam-5839	900	20	-	-	ADJ
ejpam-5839	900	21	collection	collection	ADJ
ejpam-5839	900	22	bqpnss	bqpns	NOUN
ejpam-5839	900	23	of	of	ADP
ejpam-5839	900	24	τqpnss	τqpnss	PROPN
ejpam-5839	900	25	is	be	AUX
ejpam-5839	900	26	a	a	DET
ejpam-5839	900	27	base	base	NOUN
ejpam-5839	900	28	for	for	ADP
ejpam-5839	900	29	τqpnss	τqpns	NOUN
ejpam-5839	900	30	if	if	SCONJ
ejpam-5839	900	31	and	and	CCONJ
ejpam-5839	900	32	only	only	ADV
ejpam-5839	900	33	if	if	SCONJ
ejpam-5839	900	34	:	:	PUNCT
ejpam-5839	900	35	(	(	PUNCT
ejpam-5839	900	36	i	i	NOUN
ejpam-5839	900	37	)	)	PUNCT
ejpam-5839	900	38	every	every	DET
ejpam-5839	900	39	quadripartitioned	quadripartitione	VERB
ejpam-5839	900	40	neutrosophic	neutrosophic	ADJ
ejpam-5839	900	41	soft	soft	ADJ
ejpam-5839	900	42	point	point	NOUN
ejpam-5839	900	43	of	of	ADP
ejpam-5839	900	44	x	x	NOUN
ejpam-5839	900	45	is	be	AUX
ejpam-5839	900	46	in	in	ADP
ejpam-5839	900	47	some	some	DET
ejpam-5839	900	48	b	b	NOUN
ejpam-5839	900	49	∈	∈	PROPN
ejpam-5839	900	50	bqpnss	bqpns	NOUN
ejpam-5839	900	51	.	.	PUNCT
ejpam-5839	901	1	(	(	PUNCT
ejpam-5839	901	2	ii	ii	NOUN
ejpam-5839	901	3	)	)	PUNCT
ejpam-5839	901	4	for	for	ADP
ejpam-5839	901	5	b1	b1	NOUN
ejpam-5839	901	6	,	,	PUNCT
ejpam-5839	901	7	b2	b2	NOUN
ejpam-5839	901	8	∈	∈	NOUN
ejpam-5839	901	9	bqpnss	bqpns	NOUN
ejpam-5839	901	10	and	and	CCONJ
ejpam-5839	901	11	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	NUM
ejpam-5839	901	12	)	)	PUNCT
ejpam-5839	901	13	∈	∈	PROPN
ejpam-5839	901	14	b1	b1	NOUN
ejpam-5839	901	15	∩	∩	ADJ
ejpam-5839	901	16	b2	b2	NOUN
ejpam-5839	901	17	,	,	PUNCT
ejpam-5839	901	18	there	there	PRON
ejpam-5839	901	19	is	be	VERB
ejpam-5839	901	20	a	a	DET
ejpam-5839	901	21	b	b	PROPN
ejpam-5839	901	22	∈	∈	NOUN
ejpam-5839	901	23	bqpnss	bqpns	NOUN
ejpam-5839	902	1	such	such	ADJ
ejpam-5839	902	2	that	that	PRON
ejpam-5839	902	3	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	902	4	)	)	PUNCT
ejpam-5839	903	1	∈	∈	PROPN
ejpam-5839	903	2	b	b	X
ejpam-5839	903	3	⊆	⊆	NUM
ejpam-5839	903	4	b1	b1	PROPN
ejpam-5839	903	5	∩b2	∩b2	NOUN
ejpam-5839	903	6	.	.	PUNCT
ejpam-5839	903	7	proof	proof	NOUN
ejpam-5839	903	8	.	.	PUNCT
ejpam-5839	904	1	let	let	VERB
ejpam-5839	904	2	bqpnss	bqpns	NOUN
ejpam-5839	904	3	be	be	AUX
ejpam-5839	904	4	a	a	DET
ejpam-5839	904	5	base	base	NOUN
ejpam-5839	904	6	for	for	ADP
ejpam-5839	904	7	τqpnss	τqpns	NOUN
ejpam-5839	904	8	.	.	PUNCT
ejpam-5839	905	1	1	1	X
ejpam-5839	905	2	.	.	X
ejpam-5839	905	3	let	let	AUX
ejpam-5839	905	4	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	905	5	)	)	PUNCT
ejpam-5839	905	6	be	be	AUX
ejpam-5839	905	7	an	an	DET
ejpam-5839	905	8	arbitrary	arbitrary	ADJ
ejpam-5839	905	9	quadripartitioned	quadripartitione	VERB
ejpam-5839	905	10	neutrosophic	neutrosophic	ADJ
ejpam-5839	905	11	soft	soft	ADJ
ejpam-5839	905	12	point	point	NOUN
ejpam-5839	905	13	of	of	ADP
ejpam-5839	905	14	x.	x.	NOUN
ejpam-5839	905	15	2	2	NUM
ejpam-5839	905	16	.	.	PUNCT
ejpam-5839	906	1	since	since	SCONJ
ejpam-5839	906	2	x	x	PRON
ejpam-5839	906	3	is	be	AUX
ejpam-5839	906	4	a	a	DET
ejpam-5839	906	5	quadripartitioned	quadripartitione	VERB
ejpam-5839	906	6	neutrosophic	neutrosophic	ADJ
ejpam-5839	906	7	soft	soft	ADJ
ejpam-5839	906	8	p	p	NOUN
ejpam-5839	906	9	-	-	PUNCT
ejpam-5839	906	10	open	open	ADJ
ejpam-5839	906	11	set	set	NOUN
ejpam-5839	906	12	,	,	PUNCT
ejpam-5839	906	13	there	there	PRON
ejpam-5839	906	14	exists	exist	VERB
ejpam-5839	906	15	bxθ	bxθ	NOUN
ejpam-5839	906	16	(	(	PUNCT
ejpam-5839	906	17	r1,r2,r3,r4	r1,r2,r3,r4	NOUN
ejpam-5839	906	18	)	)	PUNCT
ejpam-5839	906	19	∈	∈	NOUN
ejpam-5839	906	20	bqpnss	bqpns	NOUN
ejpam-5839	906	21	such	such	ADJ
ejpam-5839	906	22	that	that	DET
ejpam-5839	906	23	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	906	24	)	)	PUNCT
ejpam-5839	906	25	∈	∈	PROPN
ejpam-5839	906	26	bxθ	bxθ	NOUN
ejpam-5839	906	27	(	(	PUNCT
ejpam-5839	906	28	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	906	29	)	)	PUNCT
ejpam-5839	906	30	⊆	⊆	NUM
ejpam-5839	906	31	x.	x.	NOUN
ejpam-5839	906	32	3	3	NUM
ejpam-5839	906	33	.	.	PUNCT
ejpam-5839	907	1	this	this	PRON
ejpam-5839	907	2	implies	imply	VERB
ejpam-5839	907	3	that	that	SCONJ
ejpam-5839	907	4	:	:	PUNCT
ejpam-5839	907	5	⋃	⋃	PROPN
ejpam-5839	907	6	{	{	PUNCT
ejpam-5839	907	7	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	907	8	)	)	PUNCT
ejpam-5839	908	1	|	|	ADV
ejpam-5839	908	2	x	x	SYM
ejpam-5839	908	3	θ	θ	NOUN
ejpam-5839	908	4	(	(	PUNCT
ejpam-5839	908	5	r1,r2,r3,r4	r1,r2,r3,r4	NOUN
ejpam-5839	908	6	)	)	PUNCT
ejpam-5839	908	7	∈	∈	PROPN
ejpam-5839	908	8	x	x	SYM
ejpam-5839	908	9	}	}	PUNCT
ejpam-5839	908	10	⊆	⊆	NUM
ejpam-5839	908	11	x.	x.	NOUN
ejpam-5839	908	12	4	4	NUM
ejpam-5839	908	13	.	.	PUNCT
ejpam-5839	909	1	furthermore	furthermore	ADV
ejpam-5839	909	2	,	,	PUNCT
ejpam-5839	909	3	since	since	SCONJ
ejpam-5839	909	4	bxθ	bxθ	NOUN
ejpam-5839	909	5	(	(	PUNCT
ejpam-5839	909	6	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	909	7	)	)	PUNCT
ejpam-5839	909	8	is	be	AUX
ejpam-5839	909	9	a	a	DET
ejpam-5839	909	10	base	base	NOUN
ejpam-5839	909	11	element	element	NOUN
ejpam-5839	909	12	,	,	PUNCT
ejpam-5839	909	13	we	we	PRON
ejpam-5839	909	14	get:⋃	get:⋃	VERB
ejpam-5839	909	15	x(α	x(α	PROPN
ejpam-5839	909	16	,	,	PUNCT
ejpam-5839	909	17	β	β	X
ejpam-5839	909	18	,	,	PUNCT
ejpam-5839	909	19	γ)∈x	γ)∈x	SYM
ejpam-5839	909	20	bxθ	bxθ	NOUN
ejpam-5839	909	21	(	(	PUNCT
ejpam-5839	909	22	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	909	23	)	)	PUNCT
ejpam-5839	909	24	⊆	⊆	NUM
ejpam-5839	909	25	x.	x.	NOUN
ejpam-5839	909	26	5	5	NUM
ejpam-5839	909	27	.	.	PUNCT
ejpam-5839	910	1	therefore	therefore	ADV
ejpam-5839	910	2	,	,	PUNCT
ejpam-5839	910	3	x	x	PUNCT
ejpam-5839	910	4	=	=	PUNCT
ejpam-5839	910	5	⋃	⋃	VERB
ejpam-5839	910	6	xθ	xθ	PROPN
ejpam-5839	910	7	(	(	PUNCT
ejpam-5839	910	8	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	910	9	)	)	PUNCT
ejpam-5839	910	10	∈x	∈x	NOUN
ejpam-5839	910	11	bxθ	bxθ	NOUN
ejpam-5839	910	12	(	(	PUNCT
ejpam-5839	910	13	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	910	14	)	)	PUNCT
ejpam-5839	910	15	.	.	PUNCT
ejpam-5839	911	1	this	this	PRON
ejpam-5839	911	2	shows	show	VERB
ejpam-5839	911	3	that	that	SCONJ
ejpam-5839	911	4	each	each	DET
ejpam-5839	911	5	quadripartitioned	quadripartitione	VERB
ejpam-5839	911	6	neutrosophic	neutrosophic	ADJ
ejpam-5839	911	7	soft	soft	ADJ
ejpam-5839	911	8	point	point	NOUN
ejpam-5839	911	9	of	of	ADP
ejpam-5839	911	10	x	x	PUNCT
ejpam-5839	911	11	belongs	belong	VERB
ejpam-5839	911	12	to	to	ADP
ejpam-5839	911	13	some	some	DET
ejpam-5839	911	14	b	b	NOUN
ejpam-5839	911	15	∈	∈	PROPN
ejpam-5839	911	16	bqpnss	bqpns	NOUN
ejpam-5839	911	17	.	.	PUNCT
ejpam-5839	912	1	2	2	X
ejpam-5839	912	2	.	.	X
ejpam-5839	912	3	let	let	VERB
ejpam-5839	912	4	b1	b1	NOUN
ejpam-5839	912	5	,	,	PUNCT
ejpam-5839	912	6	b2	b2	NOUN
ejpam-5839	912	7	∈	∈	NOUN
ejpam-5839	912	8	bqpnss	bqpns	NOUN
ejpam-5839	912	9	and	and	CCONJ
ejpam-5839	913	1	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	NUM
ejpam-5839	913	2	)	)	PUNCT
ejpam-5839	913	3	∈	∈	PROPN
ejpam-5839	913	4	b1	b1	PROPN
ejpam-5839	913	5	∩b2	∩b2	PROPN
ejpam-5839	913	6	.	.	PUNCT
ejpam-5839	914	1	since	since	SCONJ
ejpam-5839	914	2	b1	b1	NOUN
ejpam-5839	914	3	and	and	CCONJ
ejpam-5839	914	4	b2	b2	NOUN
ejpam-5839	914	5	are	be	AUX
ejpam-5839	914	6	quadripartitioned	quadripartitione	VERB
ejpam-5839	914	7	neutrosophic	neutrosophic	ADJ
ejpam-5839	914	8	p	p	ADJ
ejpam-5839	914	9	-	-	PUNCT
ejpam-5839	914	10	open	open	ADJ
ejpam-5839	914	11	sets	set	NOUN
ejpam-5839	914	12	,	,	PUNCT
ejpam-5839	914	13	it	it	PRON
ejpam-5839	914	14	follows	follow	VERB
ejpam-5839	914	15	that	that	SCONJ
ejpam-5839	914	16	b1	b1	NOUN
ejpam-5839	914	17	∩	∩	ADJ
ejpam-5839	914	18	b2	b2	NOUN
ejpam-5839	914	19	is	be	AUX
ejpam-5839	914	20	also	also	ADV
ejpam-5839	914	21	a	a	DET
ejpam-5839	914	22	quadripartitioned	quadripartitione	VERB
ejpam-5839	914	23	neutrosophic	neutrosophic	ADJ
ejpam-5839	914	24	p	p	NOUN
ejpam-5839	914	25	-	-	PUNCT
ejpam-5839	914	26	open	open	ADJ
ejpam-5839	914	27	set	set	NOUN
ejpam-5839	914	28	.	.	PUNCT
ejpam-5839	915	1	therefore	therefore	ADV
ejpam-5839	915	2	,	,	PUNCT
ejpam-5839	915	3	there	there	PRON
ejpam-5839	915	4	exists	exist	VERB
ejpam-5839	915	5	b	b	PROPN
ejpam-5839	915	6	∈	∈	PROPN
ejpam-5839	915	7	bqpnss	bqpns	NOUN
ejpam-5839	916	1	such	such	ADJ
ejpam-5839	916	2	that	that	PRON
ejpam-5839	916	3	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	916	4	)	)	PUNCT
ejpam-5839	917	1	∈	∈	PROPN
ejpam-5839	917	2	b	b	X
ejpam-5839	917	3	⊆	⊆	NUM
ejpam-5839	917	4	b1	b1	PROPN
ejpam-5839	917	5	∩b2	∩b2	NOUN
ejpam-5839	917	6	.	.	PUNCT
ejpam-5839	918	1	conversely	conversely	ADV
ejpam-5839	918	2	,	,	PUNCT
ejpam-5839	918	3	suppose	suppose	VERB
ejpam-5839	918	4	that	that	SCONJ
ejpam-5839	918	5	(	(	PUNCT
ejpam-5839	918	6	1	1	X
ejpam-5839	918	7	)	)	PUNCT
ejpam-5839	918	8	and	and	CCONJ
ejpam-5839	918	9	(	(	PUNCT
ejpam-5839	918	10	2	2	X
ejpam-5839	918	11	)	)	PUNCT
ejpam-5839	918	12	hold	hold	NOUN
ejpam-5839	918	13	.	.	PUNCT
ejpam-5839	919	1	we	we	PRON
ejpam-5839	919	2	now	now	ADV
ejpam-5839	919	3	prove	prove	VERB
ejpam-5839	919	4	that	that	SCONJ
ejpam-5839	919	5	a	a	DET
ejpam-5839	919	6	sub	sub	ADJ
ejpam-5839	919	7	-	-	ADJ
ejpam-5839	919	8	collection	collection	ADJ
ejpam-5839	919	9	bqpnss	bqpns	NOUN
ejpam-5839	919	10	of	of	ADP
ejpam-5839	919	11	τqpnss	τqpnss	PROPN
ejpam-5839	919	12	forms	form	VERB
ejpam-5839	919	13	a	a	DET
ejpam-5839	919	14	base	base	NOUN
ejpam-5839	919	15	for	for	ADP
ejpam-5839	919	16	τqpnss	τqpns	NOUN
ejpam-5839	919	17	.	.	PUNCT
ejpam-5839	920	1	a.	a.	PROPN
ejpam-5839	920	2	shihadeh	shihadeh	VERB
ejpam-5839	920	3	et	et	PROPN
ejpam-5839	920	4	al	al	PROPN
ejpam-5839	920	5	.	.	PUNCT
ejpam-5839	920	6	/	/	SYM
ejpam-5839	920	7	eur	eur	PROPN
ejpam-5839	920	8	.	.	PUNCT
ejpam-5839	921	1	j.	j.	PROPN
ejpam-5839	921	2	pure	pure	PROPN
ejpam-5839	921	3	appl	appl	PROPN
ejpam-5839	921	4	.	.	PROPN
ejpam-5839	921	5	math	math	PROPN
ejpam-5839	921	6	,	,	PUNCT
ejpam-5839	921	7	18	18	NUM
ejpam-5839	921	8	(	(	PUNCT
ejpam-5839	921	9	2	2	NUM
ejpam-5839	921	10	)	)	PUNCT
ejpam-5839	921	11	(	(	PUNCT
ejpam-5839	921	12	2025	2025	NUM
ejpam-5839	921	13	)	)	PUNCT
ejpam-5839	921	14	,	,	PUNCT
ejpam-5839	921	15	5839	5839	NUM
ejpam-5839	921	16	40	40	NUM
ejpam-5839	921	17	of	of	ADP
ejpam-5839	921	18	54	54	NUM
ejpam-5839	921	19	to	to	PART
ejpam-5839	921	20	establish	establish	VERB
ejpam-5839	921	21	this	this	PRON
ejpam-5839	922	1	,	,	PUNCT
ejpam-5839	922	2	we	we	PRON
ejpam-5839	922	3	show	show	VERB
ejpam-5839	922	4	that	that	SCONJ
ejpam-5839	922	5	the	the	DET
ejpam-5839	922	6	sub	sub	ADJ
ejpam-5839	922	7	-	-	ADJ
ejpam-5839	922	8	collection	collection	ADJ
ejpam-5839	922	9	bqpnss	bqpns	NOUN
ejpam-5839	922	10	of	of	ADP
ejpam-5839	922	11	τqpnss	τqpnss	PROPN
ejpam-5839	922	12	satisfies	satisfy	VERB
ejpam-5839	922	13	the	the	DET
ejpam-5839	922	14	three	three	NUM
ejpam-5839	922	15	conditions	condition	NOUN
ejpam-5839	922	16	of	of	ADP
ejpam-5839	922	17	quadripartitioned	quadripartitione	VERB
ejpam-5839	922	18	neutrosophic	neutrosophic	ADJ
ejpam-5839	922	19	soft	soft	ADJ
ejpam-5839	922	20	topology	topology	NOUN
ejpam-5839	922	21	.	.	PUNCT
ejpam-5839	923	1	we	we	PRON
ejpam-5839	923	2	proceed	proceed	VERB
ejpam-5839	923	3	as	as	SCONJ
ejpam-5839	923	4	follows	follow	VERB
ejpam-5839	923	5	:	:	PUNCT
ejpam-5839	923	6	the	the	DET
ejpam-5839	923	7	quadripartitioned	quadripartitione	VERB
ejpam-5839	923	8	neutrosophic	neutrosophic	ADJ
ejpam-5839	923	9	soft	soft	ADJ
ejpam-5839	923	10	null	null	ADJ
ejpam-5839	923	11	set	set	NOUN
ejpam-5839	923	12	0(x	0(x	NOUN
ejpam-5839	923	13	,	,	PUNCT
ejpam-5839	923	14	ω	ω	NOUN
ejpam-5839	923	15	)	)	PUNCT
ejpam-5839	923	16	,	,	PUNCT
ejpam-5839	923	17	being	be	AUX
ejpam-5839	923	18	the	the	DET
ejpam-5839	923	19	union	union	NOUN
ejpam-5839	923	20	of	of	ADP
ejpam-5839	923	21	a	a	DET
ejpam-5839	923	22	quadripartitioned	quadripartitione	VERB
ejpam-5839	923	23	neutrosophic	neutrosophic	ADJ
ejpam-5839	923	24	soft	soft	ADJ
ejpam-5839	923	25	null	null	ADJ
ejpam-5839	923	26	collection	collection	NOUN
ejpam-5839	923	27	of	of	ADP
ejpam-5839	923	28	quadripartitioned	quadripartitione	VERB
ejpam-5839	923	29	neutrosophic	neutrosophic	ADJ
ejpam-5839	923	30	soft	soft	ADJ
ejpam-5839	923	31	subsets	subset	NOUN
ejpam-5839	923	32	in	in	ADP
ejpam-5839	923	33	bqpnss	bqpns	NOUN
ejpam-5839	923	34	,	,	PUNCT
ejpam-5839	923	35	belongs	belong	VERB
ejpam-5839	923	36	to	to	ADP
ejpam-5839	923	37	τqpnss	τqpns	NOUN
ejpam-5839	923	38	.	.	PUNCT
ejpam-5839	924	1	since	since	SCONJ
ejpam-5839	924	2	x	x	PRON
ejpam-5839	924	3	is	be	AUX
ejpam-5839	924	4	quadripartitioned	quadripartitione	VERB
ejpam-5839	924	5	neutrosophic	neutrosophic	ADJ
ejpam-5839	924	6	soft	soft	ADJ
ejpam-5839	924	7	p	p	NOUN
ejpam-5839	924	8	-	-	PUNCT
ejpam-5839	924	9	open	open	ADJ
ejpam-5839	924	10	,	,	PUNCT
ejpam-5839	924	11	for	for	ADP
ejpam-5839	924	12	any	any	DET
ejpam-5839	924	13	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	NOUN
ejpam-5839	924	14	)	)	PUNCT
ejpam-5839	924	15	∈	∈	PROPN
ejpam-5839	924	16	x	x	PUNCT
ejpam-5839	924	17	the	the	DET
ejpam-5839	924	18	condition	condition	NOUN
ejpam-5839	924	19	(	(	PUNCT
ejpam-5839	924	20	1	1	X
ejpam-5839	924	21	)	)	PUNCT
ejpam-5839	924	22	provides	provide	VERB
ejpam-5839	924	23	a	a	DET
ejpam-5839	924	24	bxθ	bxθ	NOUN
ejpam-5839	924	25	(	(	PUNCT
ejpam-5839	924	26	r1,r2,r3,r4	r1,r2,r3,r4	NOUN
ejpam-5839	924	27	)	)	PUNCT
ejpam-5839	924	28	∈	∈	NOUN
ejpam-5839	924	29	bqpnss	bqpns	NOUN
ejpam-5839	924	30	such	such	ADJ
ejpam-5839	924	31	that	that	DET
ejpam-5839	924	32	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	924	33	)	)	PUNCT
ejpam-5839	924	34	∈	∈	PROPN
ejpam-5839	924	35	bxθ	bxθ	NOUN
ejpam-5839	924	36	(	(	PUNCT
ejpam-5839	924	37	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	924	38	)	)	PUNCT
ejpam-5839	924	39	⊆	⊆	NUM
ejpam-5839	924	40	x.	x.	NOUN
ejpam-5839	924	41	this	this	PRON
ejpam-5839	924	42	implies	imply	VERB
ejpam-5839	924	43	:	:	PUNCT
ejpam-5839	924	44	⋃	⋃	PROPN
ejpam-5839	924	45	xθ	xθ	PROPN
ejpam-5839	924	46	(	(	PUNCT
ejpam-5839	924	47	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	924	48	)	)	PUNCT
ejpam-5839	924	49	∈x	∈x	NOUN
ejpam-5839	924	50	bxθ	bxθ	NOUN
ejpam-5839	924	51	(	(	PUNCT
ejpam-5839	924	52	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	924	53	)	)	PUNCT
ejpam-5839	925	1	⊆	⊆	NUM
ejpam-5839	925	2	x.	x.	NOUN
ejpam-5839	925	3	since	since	SCONJ
ejpam-5839	925	4	x	x	PROPN
ejpam-5839	925	5	⊆	⊆	NUM
ejpam-5839	925	6	⋃	⋃	PROPN
ejpam-5839	925	7	xθ	xθ	PROPN
ejpam-5839	925	8	(	(	PUNCT
ejpam-5839	925	9	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	925	10	)	)	PUNCT
ejpam-5839	925	11	∈x	∈x	NOUN
ejpam-5839	925	12	bxθ	bxθ	NOUN
ejpam-5839	925	13	(	(	PUNCT
ejpam-5839	925	14	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	925	15	)	)	PUNCT
ejpam-5839	925	16	⊆	⊆	NUM
ejpam-5839	925	17	x	x	X
ejpam-5839	925	18	,	,	PUNCT
ejpam-5839	925	19	it	it	PRON
ejpam-5839	925	20	follows	follow	VERB
ejpam-5839	925	21	that	that	SCONJ
ejpam-5839	925	22	:	:	PUNCT
ejpam-5839	925	23	x	x	X
ejpam-5839	925	24	=	=	PUNCT
ejpam-5839	926	1	⋃	⋃	PROPN
ejpam-5839	926	2	xθ	xθ	PROPN
ejpam-5839	926	3	(	(	PUNCT
ejpam-5839	926	4	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	926	5	)	)	PUNCT
ejpam-5839	926	6	∈x	∈x	NOUN
ejpam-5839	926	7	bxθ	bxθ	NOUN
ejpam-5839	926	8	(	(	PUNCT
ejpam-5839	926	9	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	926	10	)	)	PUNCT
ejpam-5839	926	11	.	.	PUNCT
ejpam-5839	927	1	this	this	PRON
ejpam-5839	927	2	implies	imply	VERB
ejpam-5839	927	3	that	that	SCONJ
ejpam-5839	927	4	x	x	X
ejpam-5839	927	5	=	=	PUNCT
ejpam-5839	927	6	⋃	⋃	PROPN
ejpam-5839	927	7	xθ	xθ	PROPN
ejpam-5839	927	8	(	(	PUNCT
ejpam-5839	927	9	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	927	10	)	)	PUNCT
ejpam-5839	927	11	∈x	∈x	NOUN
ejpam-5839	927	12	bxe	bxe	X
ejpam-5839	927	13	(	(	PUNCT
ejpam-5839	927	14	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	927	15	)	)	PUNCT
ejpam-5839	927	16	.	.	PUNCT
ejpam-5839	928	1	this	this	PRON
ejpam-5839	928	2	shows	show	VERB
ejpam-5839	928	3	that	that	SCONJ
ejpam-5839	928	4	x	x	X
ejpam-5839	928	5	,	,	PUNCT
ejpam-5839	928	6	being	be	AUX
ejpam-5839	928	7	the	the	DET
ejpam-5839	928	8	union	union	NOUN
ejpam-5839	928	9	of	of	ADP
ejpam-5839	928	10	members	member	NOUN
ejpam-5839	928	11	of	of	ADP
ejpam-5839	928	12	bqpnss	bqpns	NOUN
ejpam-5839	928	13	,	,	PUNCT
ejpam-5839	928	14	is	be	AUX
ejpam-5839	928	15	in	in	ADP
ejpam-5839	928	16	τqpnss	τqpns	NOUN
ejpam-5839	928	17	.	.	PUNCT
ejpam-5839	929	1	next	next	ADV
ejpam-5839	929	2	,	,	PUNCT
ejpam-5839	929	3	we	we	PRON
ejpam-5839	929	4	proceed	proceed	VERB
ejpam-5839	929	5	with	with	ADP
ejpam-5839	929	6	the	the	DET
ejpam-5839	929	7	second	second	ADJ
ejpam-5839	929	8	condition	condition	NOUN
ejpam-5839	929	9	as	as	SCONJ
ejpam-5839	929	10	follows	follow	VERB
ejpam-5839	929	11	:	:	PUNCT
ejpam-5839	929	12	the	the	DET
ejpam-5839	929	13	union	union	NOUN
ejpam-5839	929	14	of	of	ADP
ejpam-5839	929	15	any	any	DET
ejpam-5839	929	16	number	number	NOUN
ejpam-5839	929	17	of	of	ADP
ejpam-5839	929	18	members	member	NOUN
ejpam-5839	929	19	of	of	ADP
ejpam-5839	929	20	τqpnss	τqpns	NOUN
ejpam-5839	929	21	,	,	PUNCT
ejpam-5839	929	22	being	be	AUX
ejpam-5839	929	23	the	the	DET
ejpam-5839	929	24	union	union	NOUN
ejpam-5839	929	25	of	of	ADP
ejpam-5839	929	26	members	member	NOUN
ejpam-5839	929	27	of	of	ADP
ejpam-5839	929	28	bqpnss	bqpns	NOUN
ejpam-5839	929	29	,	,	PUNCT
ejpam-5839	929	30	is	be	AUX
ejpam-5839	929	31	in	in	ADP
ejpam-5839	929	32	τqpnss	τqpns	NOUN
ejpam-5839	929	33	.	.	PUNCT
ejpam-5839	930	1	now	now	ADV
ejpam-5839	930	2	,	,	PUNCT
ejpam-5839	930	3	we	we	PRON
ejpam-5839	930	4	proceed	proceed	VERB
ejpam-5839	930	5	with	with	ADP
ejpam-5839	930	6	the	the	DET
ejpam-5839	930	7	third	third	ADJ
ejpam-5839	930	8	condition	condition	NOUN
ejpam-5839	930	9	as	as	SCONJ
ejpam-5839	930	10	follows	follow	VERB
ejpam-5839	930	11	:	:	PUNCT
ejpam-5839	930	12	let	let	VERB
ejpam-5839	930	13	(	(	PUNCT
ejpam-5839	930	14	g	g	NOUN
ejpam-5839	930	15	,	,	PUNCT
ejpam-5839	930	16	ω)1	ω)1	PROPN
ejpam-5839	930	17	,	,	PUNCT
ejpam-5839	930	18	(	(	PUNCT
ejpam-5839	930	19	g	g	NOUN
ejpam-5839	930	20	,	,	PUNCT
ejpam-5839	930	21	ω)2	ω)2	NOUN
ejpam-5839	930	22	,	,	PUNCT
ejpam-5839	930	23	(	(	PUNCT
ejpam-5839	930	24	g	g	PROPN
ejpam-5839	930	25	,	,	PUNCT
ejpam-5839	930	26	ω)3	ω)3	PROPN
ejpam-5839	930	27	,	,	PUNCT
ejpam-5839	930	28	(	(	PUNCT
ejpam-5839	930	29	g	g	NOUN
ejpam-5839	930	30	,	,	PUNCT
ejpam-5839	930	31	ω)4	ω)4	PROPN
ejpam-5839	930	32	∈	∈	PROPN
ejpam-5839	930	33	τqpnss	τqpns	NOUN
ejpam-5839	930	34	.	.	PUNCT
ejpam-5839	931	1	by	by	ADP
ejpam-5839	931	2	the	the	DET
ejpam-5839	931	3	definition	definition	NOUN
ejpam-5839	931	4	of	of	ADP
ejpam-5839	931	5	τqpnss	τqpns	NOUN
ejpam-5839	931	6	,	,	PUNCT
ejpam-5839	931	7	we	we	PRON
ejpam-5839	931	8	have	have	VERB
ejpam-5839	931	9	(	(	PUNCT
ejpam-5839	931	10	g	g	NOUN
ejpam-5839	931	11	,	,	PUNCT
ejpam-5839	931	12	ω)1	ω)1	PROPN
ejpam-5839	931	13	=	=	PUNCT
ejpam-5839	931	14	⋃	⋃	PROPN
ejpam-5839	931	15	br1	br1	PROPN
ejpam-5839	931	16	,	,	PUNCT
ejpam-5839	931	17	(	(	PUNCT
ejpam-5839	931	18	g	g	NOUN
ejpam-5839	931	19	,	,	PUNCT
ejpam-5839	931	20	ω)2	ω)2	NOUN
ejpam-5839	931	21	=	=	PUNCT
ejpam-5839	931	22	⋃	⋃	ADP
ejpam-5839	931	23	br2	br2	NOUN
ejpam-5839	931	24	,	,	PUNCT
ejpam-5839	931	25	(	(	PUNCT
ejpam-5839	931	26	g	g	NOUN
ejpam-5839	931	27	,	,	PUNCT
ejpam-5839	931	28	ω)3	ω)3	PROPN
ejpam-5839	931	29	=	=	PUNCT
ejpam-5839	931	30	⋃	⋃	PROPN
ejpam-5839	931	31	br3	br3	PROPN
ejpam-5839	931	32	,	,	PUNCT
ejpam-5839	931	33	(	(	PUNCT
ejpam-5839	931	34	g	g	NOUN
ejpam-5839	931	35	,	,	PUNCT
ejpam-5839	931	36	ω)4	ω)4	NOUN
ejpam-5839	931	37	=	=	SYM
ejpam-5839	931	38	⋃	⋃	NOUN
ejpam-5839	931	39	br4	br4	NOUN
ejpam-5839	931	40	for	for	ADP
ejpam-5839	931	41	some	some	DET
ejpam-5839	931	42	α	α	NOUN
ejpam-5839	931	43	,	,	PUNCT
ejpam-5839	931	44	γ	γ	X
ejpam-5839	931	45	ranging	range	VERB
ejpam-5839	931	46	over	over	ADP
ejpam-5839	931	47	a	a	DET
ejpam-5839	931	48	sub	sub	NOUN
ejpam-5839	931	49	-	-	NOUN
ejpam-5839	931	50	collection	collection	NOUN
ejpam-5839	931	51	of	of	ADP
ejpam-5839	931	52	bqpnss	bqpns	NOUN
ejpam-5839	931	53	.	.	PUNCT
ejpam-5839	932	1	therefore	therefore	ADV
ejpam-5839	932	2	,	,	PUNCT
ejpam-5839	932	3	(	(	PUNCT
ejpam-5839	932	4	g	g	NOUN
ejpam-5839	932	5	,	,	PUNCT
ejpam-5839	932	6	ω)1	ω)1	PROPN
ejpam-5839	932	7	∩	∩	X
ejpam-5839	932	8	(	(	PUNCT
ejpam-5839	932	9	g	g	PROPN
ejpam-5839	932	10	,	,	PUNCT
ejpam-5839	932	11	ω)2	ω)2	NOUN
ejpam-5839	932	12	∩	∩	NOUN
ejpam-5839	932	13	(	(	PUNCT
ejpam-5839	932	14	g	g	NOUN
ejpam-5839	932	15	,	,	PUNCT
ejpam-5839	932	16	ω)3	ω)3	PROPN
ejpam-5839	932	17	∩	∩	NOUN
ejpam-5839	932	18	(	(	PUNCT
ejpam-5839	932	19	g	g	NOUN
ejpam-5839	932	20	,	,	PUNCT
ejpam-5839	932	21	ω)4	ω)4	NOUN
ejpam-5839	932	22	=	=	SYM
ejpam-5839	932	23	⋃	⋃	PROPN
ejpam-5839	932	24	(	(	PUNCT
ejpam-5839	932	25	br1	br1	PROPN
ejpam-5839	932	26	∩br2	∩br2	PROPN
ejpam-5839	932	27	∩br3	∩br3	PROPN
ejpam-5839	932	28	∩br4	∩br4	NOUN
ejpam-5839	932	29	)	)	PUNCT
ejpam-5839	932	30	.	.	PUNCT
ejpam-5839	933	1	(	(	PUNCT
ejpam-5839	933	2	i	i	NOUN
ejpam-5839	933	3	)	)	PUNCT
ejpam-5839	933	4	by	by	ADP
ejpam-5839	933	5	condition	condition	NOUN
ejpam-5839	933	6	(	(	PUNCT
ejpam-5839	933	7	2	2	NUM
ejpam-5839	933	8	)	)	PUNCT
ejpam-5839	933	9	,	,	PUNCT
ejpam-5839	933	10	for	for	ADP
ejpam-5839	933	11	any	any	DET
ejpam-5839	933	12	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	NOUN
ejpam-5839	933	13	)	)	PUNCT
ejpam-5839	933	14	∈	∈	PROPN
ejpam-5839	933	15	b1	b1	PROPN
ejpam-5839	933	16	∩b2	∩b2	PROPN
ejpam-5839	933	17	,	,	PUNCT
ejpam-5839	933	18	there	there	PRON
ejpam-5839	933	19	exists	exist	VERB
ejpam-5839	933	20	bxe	bxe	NOUN
ejpam-5839	933	21	(	(	PUNCT
ejpam-5839	933	22	r1,r2,r3,r4	r1,r2,r3,r4	NOUN
ejpam-5839	933	23	)	)	PUNCT
ejpam-5839	933	24	∈	∈	NOUN
ejpam-5839	933	25	bqpnss	bqpns	NOUN
ejpam-5839	933	26	such	such	ADJ
ejpam-5839	933	27	that	that	DET
ejpam-5839	933	28	bxθ	bxθ	NOUN
ejpam-5839	933	29	(	(	PUNCT
ejpam-5839	933	30	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	933	31	)	)	PUNCT
ejpam-5839	933	32	⊆	⊆	NUM
ejpam-5839	933	33	br1	br1	PROPN
ejpam-5839	933	34	∩br2	∩br2	PROPN
ejpam-5839	933	35	∩br3	∩br3	PROPN
ejpam-5839	933	36	∩br4	∩br4	PROPN
ejpam-5839	933	37	.	.	PUNCT
ejpam-5839	934	1	this	this	PRON
ejpam-5839	934	2	implies	imply	VERB
ejpam-5839	934	3	that	that	SCONJ
ejpam-5839	934	4	⋃	⋃	PROPN
ejpam-5839	934	5	{	{	PUNCT
ejpam-5839	934	6	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	934	7	)	)	PUNCT
ejpam-5839	934	8	}	}	PUNCT
ejpam-5839	934	9	⊆	⊆	NUM
ejpam-5839	934	10	⋃	⋃	PROPN
ejpam-5839	934	11	xθ	xθ	PROPN
ejpam-5839	934	12	(	(	PUNCT
ejpam-5839	934	13	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	934	14	)	)	PUNCT
ejpam-5839	935	1	∈bα∩bγ	∈bα∩bγ	ADJ
ejpam-5839	935	2	bxθ	bxθ	NOUN
ejpam-5839	935	3	(	(	PUNCT
ejpam-5839	935	4	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	935	5	)	)	PUNCT
ejpam-5839	935	6	.	.	PUNCT
ejpam-5839	936	1	a.	a.	NOUN
ejpam-5839	936	2	shihadeh	shihadeh	VERB
ejpam-5839	936	3	et	et	PROPN
ejpam-5839	936	4	al	al	PROPN
ejpam-5839	936	5	.	.	PUNCT
ejpam-5839	936	6	/	/	SYM
ejpam-5839	936	7	eur	eur	PROPN
ejpam-5839	936	8	.	.	PUNCT
ejpam-5839	937	1	j.	j.	PROPN
ejpam-5839	937	2	pure	pure	PROPN
ejpam-5839	937	3	appl	appl	PROPN
ejpam-5839	937	4	.	.	PROPN
ejpam-5839	937	5	math	math	PROPN
ejpam-5839	937	6	,	,	PUNCT
ejpam-5839	937	7	18	18	NUM
ejpam-5839	937	8	(	(	PUNCT
ejpam-5839	937	9	2	2	NUM
ejpam-5839	937	10	)	)	PUNCT
ejpam-5839	937	11	(	(	PUNCT
ejpam-5839	937	12	2025	2025	NUM
ejpam-5839	937	13	)	)	PUNCT
ejpam-5839	937	14	,	,	PUNCT
ejpam-5839	937	15	5839	5839	NUM
ejpam-5839	937	16	41	41	NUM
ejpam-5839	937	17	of	of	ADP
ejpam-5839	937	18	54	54	NUM
ejpam-5839	937	19	since	since	SCONJ
ejpam-5839	937	20	⋃	⋃	PROPN
ejpam-5839	937	21	xθ	xθ	PROPN
ejpam-5839	937	22	(	(	PUNCT
ejpam-5839	937	23	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	937	24	)	)	PUNCT
ejpam-5839	937	25	∈(br1∩br2∩br3∩br4	∈(br1∩br2∩br3∩br4	PROPN
ejpam-5839	937	26	)	)	PUNCT
ejpam-5839	937	27	bxθ	bxθ	NOUN
ejpam-5839	937	28	(	(	PUNCT
ejpam-5839	937	29	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	937	30	)	)	PUNCT
ejpam-5839	937	31	⊆	⊆	NUM
ejpam-5839	937	32	br1	br1	PROPN
ejpam-5839	937	33	∩br2	∩br2	PROPN
ejpam-5839	937	34	∩br3	∩br3	PROPN
ejpam-5839	937	35	∩br4	∩br4	PROPN
ejpam-5839	937	36	,	,	PUNCT
ejpam-5839	937	37	it	it	PRON
ejpam-5839	937	38	follows	follow	VERB
ejpam-5839	937	39	that	that	SCONJ
ejpam-5839	937	40	br1	br1	PROPN
ejpam-5839	937	41	∩br2	∩br2	PROPN
ejpam-5839	937	42	∩br3	∩br3	PROPN
ejpam-5839	937	43	∩br4	∩br4	ADP
ejpam-5839	937	44	⊆	⊆	NUM
ejpam-5839	937	45	⋃	⋃	PROPN
ejpam-5839	938	1	xθ	xθ	PROPN
ejpam-5839	939	1	(	(	PUNCT
ejpam-5839	939	2	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	939	3	)	)	PUNCT
ejpam-5839	940	1	∈bα∩bγ	∈bα∩bγ	ADJ
ejpam-5839	940	2	bxθ	bxθ	NOUN
ejpam-5839	940	3	(	(	PUNCT
ejpam-5839	940	4	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	940	5	)	)	PUNCT
ejpam-5839	940	6	⊆	⊆	NUM
ejpam-5839	940	7	br1	br1	PROPN
ejpam-5839	940	8	∩br2	∩br2	PROPN
ejpam-5839	940	9	∩br3	∩br3	PROPN
ejpam-5839	940	10	∩br4	∩br4	PROPN
ejpam-5839	940	11	.	.	PUNCT
ejpam-5839	941	1	thus	thus	ADV
ejpam-5839	941	2	,	,	PUNCT
ejpam-5839	941	3	we	we	PRON
ejpam-5839	941	4	conclude	conclude	VERB
ejpam-5839	941	5	that	that	PRON
ejpam-5839	941	6	br1	br1	PROPN
ejpam-5839	941	7	∩br2	∩br2	PROPN
ejpam-5839	941	8	∩br3	∩br3	PROPN
ejpam-5839	941	9	∩br4	∩br4	ADP
ejpam-5839	941	10	=	=	SYM
ejpam-5839	941	11	⋃	⋃	PROPN
ejpam-5839	941	12	xθ	xθ	PROPN
ejpam-5839	941	13	(	(	PUNCT
ejpam-5839	941	14	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	941	15	)	)	PUNCT
ejpam-5839	942	1	∈bα∩bγ	∈bα∩bγ	ADJ
ejpam-5839	942	2	bxθ	bxθ	NOUN
ejpam-5839	942	3	(	(	PUNCT
ejpam-5839	942	4	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	942	5	)	)	PUNCT
ejpam-5839	942	6	.	.	PUNCT
ejpam-5839	943	1	substituting	substitute	VERB
ejpam-5839	943	2	this	this	DET
ejpam-5839	943	3	value	value	NOUN
ejpam-5839	943	4	in	in	ADP
ejpam-5839	943	5	equation	equation	NOUN
ejpam-5839	943	6	(	(	PUNCT
ejpam-5839	943	7	i	i	NOUN
ejpam-5839	943	8	)	)	PUNCT
ejpam-5839	943	9	,	,	PUNCT
ejpam-5839	943	10	we	we	PRON
ejpam-5839	943	11	obtain	obtain	VERB
ejpam-5839	943	12	:	:	PUNCT
ejpam-5839	943	13	(	(	PUNCT
ejpam-5839	943	14	g	g	NOUN
ejpam-5839	943	15	,	,	PUNCT
ejpam-5839	943	16	ω)1	ω)1	PROPN
ejpam-5839	943	17	∩	∩	X
ejpam-5839	943	18	(	(	PUNCT
ejpam-5839	943	19	g	g	PROPN
ejpam-5839	943	20	,	,	PUNCT
ejpam-5839	943	21	ω)2	ω)2	NOUN
ejpam-5839	943	22	∩	∩	NOUN
ejpam-5839	943	23	(	(	PUNCT
ejpam-5839	943	24	g	g	NOUN
ejpam-5839	943	25	,	,	PUNCT
ejpam-5839	943	26	ω)3	ω)3	PROPN
ejpam-5839	943	27	∩	∩	NOUN
ejpam-5839	943	28	(	(	PUNCT
ejpam-5839	943	29	g	g	NOUN
ejpam-5839	943	30	,	,	PUNCT
ejpam-5839	943	31	ω)4	ω)4	NOUN
ejpam-5839	943	32	=	=	SYM
ejpam-5839	943	33	⋃	⋃	PROPN
ejpam-5839	943	34	(	(	PUNCT
ejpam-5839	943	35	br1	br1	PROPN
ejpam-5839	943	36	∩br2	∩br2	PROPN
ejpam-5839	943	37	∩br3	∩br3	PROPN
ejpam-5839	943	38	∩br4	∩br4	NOUN
ejpam-5839	943	39	)	)	PUNCT
ejpam-5839	943	40	.	.	PUNCT
ejpam-5839	944	1	since	since	SCONJ
ejpam-5839	944	2	br1	br1	PROPN
ejpam-5839	944	3	∩br2	∩br2	PROPN
ejpam-5839	944	4	∩br3	∩br3	PROPN
ejpam-5839	944	5	∩br4	∩br4	ADP
ejpam-5839	944	6	=	=	SYM
ejpam-5839	944	7	⋃	⋃	PROPN
ejpam-5839	944	8	xθ	xθ	PROPN
ejpam-5839	944	9	(	(	PUNCT
ejpam-5839	944	10	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	944	11	)	)	PUNCT
ejpam-5839	944	12	∈br1∩br2∩br3∩br4	∈br1∩br2∩br3∩br4	NOUN
ejpam-5839	944	13	bxθ	bxθ	NOUN
ejpam-5839	944	14	(	(	PUNCT
ejpam-5839	944	15	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	944	16	)	)	PUNCT
ejpam-5839	944	17	we	we	PRON
ejpam-5839	944	18	conclude	conclude	VERB
ejpam-5839	944	19	that	that	PRON
ejpam-5839	944	20	(	(	PUNCT
ejpam-5839	944	21	g	g	NOUN
ejpam-5839	944	22	,	,	PUNCT
ejpam-5839	944	23	ω)1	ω)1	PROPN
ejpam-5839	944	24	∩	∩	X
ejpam-5839	944	25	(	(	PUNCT
ejpam-5839	944	26	g	g	PROPN
ejpam-5839	944	27	,	,	PUNCT
ejpam-5839	944	28	ω)2	ω)2	NOUN
ejpam-5839	944	29	∩	∩	NOUN
ejpam-5839	944	30	(	(	PUNCT
ejpam-5839	944	31	g	g	NOUN
ejpam-5839	944	32	,	,	PUNCT
ejpam-5839	944	33	ω)3	ω)3	PROPN
ejpam-5839	944	34	∩	∩	NOUN
ejpam-5839	944	35	(	(	PUNCT
ejpam-5839	944	36	g	g	NOUN
ejpam-5839	944	37	,	,	PUNCT
ejpam-5839	944	38	ω)4	ω)4	NOUN
ejpam-5839	944	39	=	=	PUNCT
ejpam-5839	944	40	⋃	⋃	PROPN
ejpam-5839	944	41	xθ	xθ	PROPN
ejpam-5839	944	42	(	(	PUNCT
ejpam-5839	944	43	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	944	44	)	)	PUNCT
ejpam-5839	944	45	∈br1∩br2∩br3∩br4	∈br1∩br2∩br3∩br4	NOUN
ejpam-5839	944	46	bxθ	bxθ	NOUN
ejpam-5839	944	47	(	(	PUNCT
ejpam-5839	944	48	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	944	49	)	)	PUNCT
ejpam-5839	944	50	.	.	PUNCT
ejpam-5839	945	1	this	this	PRON
ejpam-5839	945	2	shows	show	VERB
ejpam-5839	945	3	that	that	SCONJ
ejpam-5839	945	4	(	(	PUNCT
ejpam-5839	945	5	g	g	NOUN
ejpam-5839	945	6	,	,	PUNCT
ejpam-5839	945	7	ω)1	ω)1	PROPN
ejpam-5839	945	8	∩	∩	X
ejpam-5839	945	9	(	(	PUNCT
ejpam-5839	945	10	g	g	PROPN
ejpam-5839	945	11	,	,	PUNCT
ejpam-5839	945	12	ω)2	ω)2	NOUN
ejpam-5839	945	13	∩	∩	NOUN
ejpam-5839	945	14	(	(	PUNCT
ejpam-5839	945	15	g	g	NOUN
ejpam-5839	945	16	,	,	PUNCT
ejpam-5839	945	17	ω)3	ω)3	PROPN
ejpam-5839	945	18	∩	∩	NOUN
ejpam-5839	945	19	(	(	PUNCT
ejpam-5839	945	20	g	g	NOUN
ejpam-5839	945	21	,	,	PUNCT
ejpam-5839	945	22	ω)4	ω)4	PROPN
ejpam-5839	945	23	is	be	AUX
ejpam-5839	945	24	the	the	DET
ejpam-5839	945	25	union	union	NOUN
ejpam-5839	945	26	of	of	ADP
ejpam-5839	945	27	members	member	NOUN
ejpam-5839	945	28	of	of	ADP
ejpam-5839	945	29	bqpnss	bqpns	NOUN
ejpam-5839	945	30	,	,	PUNCT
ejpam-5839	945	31	which	which	PRON
ejpam-5839	945	32	implies	imply	VERB
ejpam-5839	945	33	it	it	PRON
ejpam-5839	945	34	is	be	AUX
ejpam-5839	945	35	in	in	ADP
ejpam-5839	945	36	τqpnss	τqpns	NOUN
ejpam-5839	945	37	.	.	PUNCT
ejpam-5839	946	1	similarly	similarly	ADV
ejpam-5839	946	2	,	,	PUNCT
ejpam-5839	946	3	we	we	PRON
ejpam-5839	946	4	can	can	AUX
ejpam-5839	946	5	prove	prove	VERB
ejpam-5839	946	6	that	that	SCONJ
ejpam-5839	946	7	the	the	DET
ejpam-5839	946	8	intersection	intersection	NOUN
ejpam-5839	946	9	of	of	ADP
ejpam-5839	946	10	any	any	DET
ejpam-5839	946	11	finite	finite	ADJ
ejpam-5839	946	12	number	number	NOUN
ejpam-5839	946	13	of	of	ADP
ejpam-5839	946	14	members	member	NOUN
ejpam-5839	946	15	of	of	ADP
ejpam-5839	946	16	bqpnss	bqpns	NOUN
ejpam-5839	946	17	is	be	AUX
ejpam-5839	946	18	in	in	ADP
ejpam-5839	946	19	τqpnss	τqpns	NOUN
ejpam-5839	946	20	.	.	PUNCT
ejpam-5839	947	1	since	since	SCONJ
ejpam-5839	947	2	all	all	DET
ejpam-5839	947	3	the	the	DET
ejpam-5839	947	4	conditions	condition	NOUN
ejpam-5839	947	5	of	of	ADP
ejpam-5839	947	6	quadripartitioned	quadripartitione	VERB
ejpam-5839	947	7	neutrosophic	neutrosophic	ADJ
ejpam-5839	947	8	soft	soft	ADJ
ejpam-5839	947	9	topology	topology	NOUN
ejpam-5839	947	10	are	be	AUX
ejpam-5839	947	11	satisfied	satisfied	ADJ
ejpam-5839	947	12	,	,	PUNCT
ejpam-5839	947	13	we	we	PRON
ejpam-5839	947	14	conclude	conclude	VERB
ejpam-5839	947	15	that	that	SCONJ
ejpam-5839	947	16	τqpnss	τqpnss	PROPN
ejpam-5839	947	17	is	be	AUX
ejpam-5839	947	18	a	a	DET
ejpam-5839	947	19	quadripartitioned	quadripartitione	VERB
ejpam-5839	947	20	neutrosophic	neutrosophic	ADJ
ejpam-5839	947	21	soft	soft	ADJ
ejpam-5839	947	22	topology	topology	NOUN
ejpam-5839	947	23	on	on	ADP
ejpam-5839	947	24	x.	x.	NOUN
ejpam-5839	947	25	consequently	consequently	ADV
ejpam-5839	947	26	,	,	PUNCT
ejpam-5839	947	27	bqpnss	bqpns	NOUN
ejpam-5839	947	28	is	be	AUX
ejpam-5839	947	29	a	a	DET
ejpam-5839	947	30	quadripartitioned	quadripartitione	VERB
ejpam-5839	947	31	neutrosophic	neutrosophic	ADJ
ejpam-5839	947	32	soft	soft	ADJ
ejpam-5839	947	33	base	base	NOUN
ejpam-5839	947	34	for	for	ADP
ejpam-5839	947	35	τqpnss	τqpns	NOUN
ejpam-5839	947	36	.	.	PUNCT
ejpam-5839	948	1	theorem	theorem	VERB
ejpam-5839	948	2	18	18	NUM
ejpam-5839	948	3	.	.	PUNCT
ejpam-5839	949	1	let	let	AUX
ejpam-5839	949	2	(	(	PUNCT
ejpam-5839	949	3	x	x	NOUN
ejpam-5839	949	4	,	,	PUNCT
ejpam-5839	949	5	τqpnss	τqpnss	PROPN
ejpam-5839	949	6	,	,	PUNCT
ejpam-5839	949	7	ω	ω	PROPN
ejpam-5839	949	8	)	)	PUNCT
ejpam-5839	949	9	be	be	VERB
ejpam-5839	949	10	a	a	DET
ejpam-5839	949	11	quadripartitioned	quadripartitione	VERB
ejpam-5839	949	12	neutrosophic	neutrosophic	ADJ
ejpam-5839	949	13	soft	soft	ADJ
ejpam-5839	949	14	topological	topological	ADJ
ejpam-5839	949	15	space	space	NOUN
ejpam-5839	949	16	over	over	ADP
ejpam-5839	949	17	x.	x.	PROPN
ejpam-5839	950	1	a	a	DET
ejpam-5839	950	2	quadripartitioned	quadripartitione	VERB
ejpam-5839	950	3	neutrosophic	neutrosophic	ADJ
ejpam-5839	950	4	soft	soft	ADJ
ejpam-5839	950	5	point	point	NOUN
ejpam-5839	950	6	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	950	7	)	)	PUNCT
ejpam-5839	950	8	in	in	ADP
ejpam-5839	950	9	a	a	DET
ejpam-5839	950	10	quadripartitioned	quadripartitione	VERB
ejpam-5839	950	11	neutrosophic	neutrosophic	ADJ
ejpam-5839	950	12	soft	soft	ADJ
ejpam-5839	950	13	topological	topological	ADJ
ejpam-5839	950	14	space	space	NOUN
ejpam-5839	950	15	is	be	AUX
ejpam-5839	950	16	a	a	DET
ejpam-5839	950	17	quadripartitioned	quadripartitione	VERB
ejpam-5839	950	18	neutrosophic	neutrosophic	ADJ
ejpam-5839	950	19	soft	soft	ADJ
ejpam-5839	950	20	limit	limit	NOUN
ejpam-5839	950	21	point	point	NOUN
ejpam-5839	950	22	of	of	ADP
ejpam-5839	950	23	(	(	PUNCT
ejpam-5839	950	24	f̃	f̃	PROPN
ejpam-5839	950	25	,	,	PUNCT
ejpam-5839	950	26	ω	ω	NUM
ejpam-5839	950	27	)	)	PUNCT
ejpam-5839	950	28	⊆	⊆	NUM
ejpam-5839	950	29	x	x	SYM
ejpam-5839	950	30	if	if	SCONJ
ejpam-5839	951	1	and	and	CCONJ
ejpam-5839	951	2	only	only	ADV
ejpam-5839	951	3	if	if	SCONJ
ejpam-5839	951	4	every	every	DET
ejpam-5839	951	5	member	member	NOUN
ejpam-5839	951	6	of	of	ADP
ejpam-5839	951	7	any	any	DET
ejpam-5839	951	8	quadripartitioned	quadripartitione	VERB
ejpam-5839	951	9	neutrosophic	neutrosophic	ADJ
ejpam-5839	951	10	soft	soft	ADJ
ejpam-5839	951	11	local	local	ADJ
ejpam-5839	951	12	base	base	NOUN
ejpam-5839	951	13	bxθ	bxθ	NOUN
ejpam-5839	951	14	(	(	PUNCT
ejpam-5839	951	15	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	951	16	)	)	PUNCT
ejpam-5839	951	17	at	at	ADP
ejpam-5839	951	18	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	951	19	)	)	PUNCT
ejpam-5839	951	20	contains	contain	VERB
ejpam-5839	951	21	a	a	DET
ejpam-5839	951	22	point	point	NOUN
ejpam-5839	951	23	of	of	ADP
ejpam-5839	951	24	(	(	PUNCT
ejpam-5839	951	25	f̃	f̃	PROPN
ejpam-5839	951	26	,	,	PUNCT
ejpam-5839	951	27	ω	ω	NOUN
ejpam-5839	951	28	)	)	PUNCT
ejpam-5839	951	29	different	different	ADJ
ejpam-5839	951	30	from	from	ADP
ejpam-5839	951	31	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	951	32	)	)	PUNCT
ejpam-5839	951	33	.	.	PUNCT
ejpam-5839	952	1	proof	proof	NOUN
ejpam-5839	952	2	.	.	PUNCT
ejpam-5839	953	1	let	let	VERB
ejpam-5839	953	2	(	(	PUNCT
ejpam-5839	953	3	x	x	NOUN
ejpam-5839	953	4	,	,	PUNCT
ejpam-5839	953	5	τqpnss	τqpnss	PROPN
ejpam-5839	953	6	,	,	PUNCT
ejpam-5839	953	7	ω	ω	PROPN
ejpam-5839	953	8	)	)	PUNCT
ejpam-5839	953	9	be	be	VERB
ejpam-5839	953	10	a	a	DET
ejpam-5839	953	11	quadripartitioned	quadripartitione	VERB
ejpam-5839	953	12	neutrosophic	neutrosophic	ADJ
ejpam-5839	953	13	soft	soft	ADJ
ejpam-5839	953	14	topological	topological	ADJ
ejpam-5839	953	15	space	space	NOUN
ejpam-5839	953	16	over	over	ADP
ejpam-5839	953	17	x	x	NOUN
ejpam-5839	953	18	,	,	PUNCT
ejpam-5839	953	19	and	and	CCONJ
ejpam-5839	953	20	let	let	VERB
ejpam-5839	953	21	(	(	PUNCT
ejpam-5839	953	22	f̃	f̃	PROPN
ejpam-5839	953	23	,	,	PUNCT
ejpam-5839	953	24	ω	ω	NUM
ejpam-5839	953	25	)	)	PUNCT
ejpam-5839	954	1	⊆	⊆	NUM
ejpam-5839	954	2	x.	x.	NOUN
ejpam-5839	954	3	let	let	VERB
ejpam-5839	955	1	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	955	2	)	)	PUNCT
ejpam-5839	955	3	∈	∈	PROPN
ejpam-5839	955	4	x	x	VERB
ejpam-5839	955	5	be	be	AUX
ejpam-5839	955	6	a	a	DET
ejpam-5839	955	7	quadripartitioned	quadripartitione	VERB
ejpam-5839	955	8	neutrosophic	neutrosophic	ADJ
ejpam-5839	955	9	soft	soft	ADJ
ejpam-5839	955	10	limit	limit	NOUN
ejpam-5839	955	11	point	point	NOUN
ejpam-5839	955	12	of	of	ADP
ejpam-5839	955	13	(	(	PUNCT
ejpam-5839	955	14	f̃	f̃	PROPN
ejpam-5839	955	15	,	,	PUNCT
ejpam-5839	955	16	ω	ω	PROPN
ejpam-5839	955	17	)	)	PUNCT
ejpam-5839	955	18	.	.	PUNCT
ejpam-5839	956	1	let	let	VERB
ejpam-5839	956	2	bxθ	bxθ	NOUN
ejpam-5839	956	3	(	(	PUNCT
ejpam-5839	956	4	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	956	5	)	)	PUNCT
ejpam-5839	956	6	be	be	AUX
ejpam-5839	956	7	a	a	DET
ejpam-5839	956	8	local	local	ADJ
ejpam-5839	956	9	base	base	NOUN
ejpam-5839	956	10	at	at	ADP
ejpam-5839	956	11	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	956	12	)	)	PUNCT
ejpam-5839	956	13	.	.	PUNCT
ejpam-5839	957	1	we	we	PRON
ejpam-5839	957	2	need	need	VERB
ejpam-5839	957	3	to	to	PART
ejpam-5839	957	4	prove	prove	VERB
ejpam-5839	957	5	that	that	SCONJ
ejpam-5839	957	6	:	:	PUNCT
ejpam-5839	957	7	(	(	PUNCT
ejpam-5839	957	8	b	b	X
ejpam-5839	957	9	−	−	NOUN
ejpam-5839	957	10	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	NUM
ejpam-5839	957	11	)	)	PUNCT
ejpam-5839	957	12	)	)	PUNCT
ejpam-5839	957	13	∩	∩	NOUN
ejpam-5839	957	14	(	(	PUNCT
ejpam-5839	957	15	f̃	f̃	PROPN
ejpam-5839	957	16	,	,	PUNCT
ejpam-5839	957	17	ω	ω	NUM
ejpam-5839	957	18	)	)	PUNCT
ejpam-5839	957	19	̸=	̸=	PROPN
ejpam-5839	957	20	∅	∅	CCONJ
ejpam-5839	957	21	∀b	∀b	NOUN
ejpam-5839	957	22	∈	∈	NOUN
ejpam-5839	957	23	bxθ	bxθ	NOUN
ejpam-5839	957	24	(	(	PUNCT
ejpam-5839	957	25	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	957	26	)	)	PUNCT
ejpam-5839	957	27	since	since	SCONJ
ejpam-5839	957	28	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	957	29	)	)	PUNCT
ejpam-5839	957	30	is	be	AUX
ejpam-5839	957	31	a	a	DET
ejpam-5839	957	32	quadripartitioned	quadripartitione	VERB
ejpam-5839	957	33	neutrosophic	neutrosophic	ADJ
ejpam-5839	957	34	soft	soft	ADJ
ejpam-5839	957	35	limit	limit	NOUN
ejpam-5839	957	36	point	point	NOUN
ejpam-5839	957	37	of	of	ADP
ejpam-5839	957	38	(	(	PUNCT
ejpam-5839	957	39	f̃	f̃	PROPN
ejpam-5839	957	40	,	,	PUNCT
ejpam-5839	957	41	ω	ω	PROPN
ejpam-5839	957	42	)	)	PUNCT
ejpam-5839	957	43	,	,	PUNCT
ejpam-5839	957	44	we	we	PRON
ejpam-5839	957	45	have	have	VERB
ejpam-5839	957	46	:	:	PUNCT
ejpam-5839	957	47	(	(	PUNCT
ejpam-5839	957	48	(	(	PUNCT
ejpam-5839	957	49	g̃,ω)−	g̃,ω)−	PROPN
ejpam-5839	957	50	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	957	51	)	)	PUNCT
ejpam-5839	957	52	)	)	PUNCT
ejpam-5839	958	1	∩	∩	NOUN
ejpam-5839	958	2	(	(	PUNCT
ejpam-5839	958	3	f̃	f̃	PROPN
ejpam-5839	958	4	,	,	PUNCT
ejpam-5839	958	5	ω	ω	NUM
ejpam-5839	958	6	)	)	PUNCT
ejpam-5839	958	7	̸=	̸=	PROPN
ejpam-5839	958	8	∅	∅	NOUN
ejpam-5839	958	9	∀(g̃,ω	∀(g̃,ω	PROPN
ejpam-5839	958	10	)	)	PUNCT
ejpam-5839	958	11	∈	∈	PROPN
ejpam-5839	958	12	τqpnss	τqpns	NOUN
ejpam-5839	958	13	.	.	PUNCT
ejpam-5839	959	1	by	by	ADP
ejpam-5839	959	2	the	the	DET
ejpam-5839	959	3	definition	definition	NOUN
ejpam-5839	959	4	of	of	ADP
ejpam-5839	959	5	a	a	DET
ejpam-5839	959	6	quadripartitioned	quadripartitione	VERB
ejpam-5839	959	7	neutrosophic	neutrosophic	ADJ
ejpam-5839	959	8	soft	soft	ADJ
ejpam-5839	959	9	local	local	ADJ
ejpam-5839	959	10	base	base	NOUN
ejpam-5839	959	11	,	,	PUNCT
ejpam-5839	959	12	we	we	PRON
ejpam-5839	959	13	know	know	VERB
ejpam-5839	959	14	that	that	PRON
ejpam-5839	959	15	:	:	PUNCT
ejpam-5839	959	16	a.	a.	NOUN
ejpam-5839	959	17	shihadeh	shihadeh	VERB
ejpam-5839	959	18	et	et	PROPN
ejpam-5839	959	19	al	al	PROPN
ejpam-5839	959	20	.	.	PUNCT
ejpam-5839	959	21	/	/	SYM
ejpam-5839	959	22	eur	eur	PROPN
ejpam-5839	959	23	.	.	PUNCT
ejpam-5839	960	1	j.	j.	PROPN
ejpam-5839	960	2	pure	pure	PROPN
ejpam-5839	960	3	appl	appl	PROPN
ejpam-5839	960	4	.	.	PROPN
ejpam-5839	960	5	math	math	PROPN
ejpam-5839	960	6	,	,	PUNCT
ejpam-5839	960	7	18	18	NUM
ejpam-5839	960	8	(	(	PUNCT
ejpam-5839	960	9	2	2	NUM
ejpam-5839	960	10	)	)	PUNCT
ejpam-5839	960	11	(	(	PUNCT
ejpam-5839	960	12	2025	2025	NUM
ejpam-5839	960	13	)	)	PUNCT
ejpam-5839	960	14	,	,	PUNCT
ejpam-5839	960	15	5839	5839	NUM
ejpam-5839	960	16	42	42	NUM
ejpam-5839	960	17	of	of	ADP
ejpam-5839	960	18	54	54	NUM
ejpam-5839	960	19	(	(	PUNCT
ejpam-5839	960	20	g̃,ω	g̃,ω	NOUN
ejpam-5839	960	21	)	)	PUNCT
ejpam-5839	960	22	∈	∈	PROPN
ejpam-5839	960	23	bxθ	bxθ	NOUN
ejpam-5839	960	24	(	(	PUNCT
ejpam-5839	960	25	r1,r2,r3,r4	r1,r2,r3,r4	NOUN
ejpam-5839	960	26	)	)	PUNCT
ejpam-5839	961	1	=	=	NOUN
ejpam-5839	961	2	⇒	⇒	NOUN
ejpam-5839	961	3	(	(	PUNCT
ejpam-5839	961	4	g̃,ω	g̃,ω	NOUN
ejpam-5839	961	5	)	)	PUNCT
ejpam-5839	961	6	∈	∈	PROPN
ejpam-5839	961	7	τqpnss	τqpns	NOUN
ejpam-5839	961	8	.	.	PUNCT
ejpam-5839	962	1	thus	thus	ADV
ejpam-5839	962	2	,	,	PUNCT
ejpam-5839	962	3	since	since	SCONJ
ejpam-5839	962	4	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	962	5	)	)	PUNCT
ejpam-5839	962	6	∈	∈	PROPN
ejpam-5839	962	7	(	(	PUNCT
ejpam-5839	962	8	g̃,ω	g̃,ω	PROPN
ejpam-5839	962	9	)	)	PUNCT
ejpam-5839	962	10	,	,	PUNCT
ejpam-5839	962	11	it	it	PRON
ejpam-5839	962	12	follows	follow	VERB
ejpam-5839	962	13	that	that	SCONJ
ejpam-5839	962	14	:	:	PUNCT
ejpam-5839	962	15	(	(	PUNCT
ejpam-5839	962	16	(	(	PUNCT
ejpam-5839	962	17	g̃,ω)−	g̃,ω)−	PROPN
ejpam-5839	962	18	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	962	19	)	)	PUNCT
ejpam-5839	962	20	)	)	PUNCT
ejpam-5839	962	21	∩	∩	NOUN
ejpam-5839	962	22	(	(	PUNCT
ejpam-5839	962	23	f̃	f̃	PROPN
ejpam-5839	962	24	,	,	PUNCT
ejpam-5839	962	25	ω	ω	NUM
ejpam-5839	962	26	)	)	PUNCT
ejpam-5839	962	27	̸=	̸=	PROPN
ejpam-5839	962	28	∅.	∅.	NOUN
ejpam-5839	962	29	since	since	SCONJ
ejpam-5839	962	30	bxθ	bxθ	NOUN
ejpam-5839	962	31	(	(	PUNCT
ejpam-5839	962	32	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	962	33	)	)	PUNCT
ejpam-5839	962	34	consists	consist	VERB
ejpam-5839	962	35	of	of	ADP
ejpam-5839	962	36	members	member	NOUN
ejpam-5839	962	37	of	of	ADP
ejpam-5839	962	38	τqpnss	τqpns	NOUN
ejpam-5839	962	39	,	,	PUNCT
ejpam-5839	962	40	we	we	PRON
ejpam-5839	962	41	conclude	conclude	VERB
ejpam-5839	962	42	:	:	PUNCT
ejpam-5839	962	43	(	(	PUNCT
ejpam-5839	962	44	b	b	X
ejpam-5839	962	45	−	−	NOUN
ejpam-5839	962	46	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	NUM
ejpam-5839	962	47	)	)	PUNCT
ejpam-5839	962	48	)	)	PUNCT
ejpam-5839	962	49	∩	∩	NOUN
ejpam-5839	962	50	(	(	PUNCT
ejpam-5839	962	51	f̃	f̃	PROPN
ejpam-5839	962	52	,	,	PUNCT
ejpam-5839	962	53	ω	ω	NUM
ejpam-5839	962	54	)	)	PUNCT
ejpam-5839	963	1	̸=	̸=	PROPN
ejpam-5839	963	2	∅	∅	CCONJ
ejpam-5839	963	3	∀b	∀b	NOUN
ejpam-5839	963	4	∈	∈	NOUN
ejpam-5839	963	5	bxθ	bxθ	NOUN
ejpam-5839	963	6	(	(	PUNCT
ejpam-5839	963	7	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	963	8	)	)	PUNCT
ejpam-5839	963	9	.	.	PUNCT
ejpam-5839	964	1	conversely	conversely	ADV
ejpam-5839	964	2	,	,	PUNCT
ejpam-5839	964	3	suppose	suppose	VERB
ejpam-5839	964	4	that	that	SCONJ
ejpam-5839	964	5	for	for	ADP
ejpam-5839	964	6	some	some	DET
ejpam-5839	964	7	quadripartitioned	quadripartitione	VERB
ejpam-5839	964	8	neutrosophic	neutrosophic	ADJ
ejpam-5839	964	9	soft	soft	ADJ
ejpam-5839	964	10	topology	topology	NOUN
ejpam-5839	964	11	τqpnss	τqpns	NOUN
ejpam-5839	964	12	on	on	ADP
ejpam-5839	964	13	x	x	SYM
ejpam-5839	964	14	,	,	PUNCT
ejpam-5839	964	15	we	we	PRON
ejpam-5839	964	16	have	have	VERB
ejpam-5839	964	17	:	:	PUNCT
ejpam-5839	964	18	(	(	PUNCT
ejpam-5839	964	19	b	b	X
ejpam-5839	964	20	−	−	NOUN
ejpam-5839	964	21	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	NUM
ejpam-5839	964	22	)	)	PUNCT
ejpam-5839	964	23	)	)	PUNCT
ejpam-5839	964	24	∩	∩	NOUN
ejpam-5839	964	25	(	(	PUNCT
ejpam-5839	964	26	f̃	f̃	PROPN
ejpam-5839	964	27	,	,	PUNCT
ejpam-5839	964	28	ω	ω	NUM
ejpam-5839	964	29	)	)	PUNCT
ejpam-5839	964	30	̸=	̸=	PROPN
ejpam-5839	964	31	∅	∅	CCONJ
ejpam-5839	964	32	∀b	∀b	NOUN
ejpam-5839	964	33	∈	∈	NOUN
ejpam-5839	964	34	bxθ	bxθ	NOUN
ejpam-5839	964	35	(	(	PUNCT
ejpam-5839	964	36	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	964	37	)	)	PUNCT
ejpam-5839	964	38	.	.	PUNCT
ejpam-5839	965	1	let	let	VERB
ejpam-5839	965	2	(	(	PUNCT
ejpam-5839	965	3	g̃,ω	g̃,ω	NOUN
ejpam-5839	965	4	)	)	PUNCT
ejpam-5839	965	5	∈	∈	PROPN
ejpam-5839	965	6	τqpnss	τqpns	NOUN
ejpam-5839	965	7	be	be	VERB
ejpam-5839	965	8	an	an	DET
ejpam-5839	965	9	arbitrary	arbitrary	ADJ
ejpam-5839	965	10	set	set	NOUN
ejpam-5839	966	1	such	such	ADJ
ejpam-5839	966	2	that	that	DET
ejpam-5839	966	3	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	966	4	)	)	PUNCT
ejpam-5839	966	5	∈	∈	PROPN
ejpam-5839	966	6	(	(	PUNCT
ejpam-5839	966	7	g̃,ω	g̃,ω	PROPN
ejpam-5839	966	8	)	)	PUNCT
ejpam-5839	966	9	.	.	PUNCT
ejpam-5839	967	1	by	by	ADP
ejpam-5839	967	2	the	the	DET
ejpam-5839	967	3	definition	definition	NOUN
ejpam-5839	967	4	of	of	ADP
ejpam-5839	967	5	a	a	DET
ejpam-5839	967	6	quadripartitioned	quadripartitione	VERB
ejpam-5839	967	7	neutrosophic	neutrosophic	ADJ
ejpam-5839	967	8	soft	soft	ADJ
ejpam-5839	967	9	local	local	ADJ
ejpam-5839	967	10	base	base	NOUN
ejpam-5839	967	11	,	,	PUNCT
ejpam-5839	967	12	there	there	PRON
ejpam-5839	967	13	exists	exist	VERB
ejpam-5839	967	14	b	b	PROPN
ejpam-5839	967	15	∈	∈	PROPN
ejpam-5839	967	16	bxθ	bxθ	NOUN
ejpam-5839	967	17	(	(	PUNCT
ejpam-5839	967	18	r1,r2,r3,r4	r1,r2,r3,r4	NOUN
ejpam-5839	967	19	)	)	PUNCT
ejpam-5839	967	20	such	such	ADJ
ejpam-5839	967	21	that	that	SCONJ
ejpam-5839	967	22	:	:	PUNCT
ejpam-5839	967	23	b	b	X
ejpam-5839	967	24	⊆	⊆	NUM
ejpam-5839	967	25	(	(	PUNCT
ejpam-5839	967	26	g̃,ω	g̃,ω	NOUN
ejpam-5839	967	27	)	)	PUNCT
ejpam-5839	967	28	.	.	PUNCT
ejpam-5839	968	1	consequently	consequently	ADV
ejpam-5839	968	2	,	,	PUNCT
ejpam-5839	968	3	we	we	PRON
ejpam-5839	968	4	have	have	VERB
ejpam-5839	968	5	:	:	PUNCT
ejpam-5839	968	6	(	(	PUNCT
ejpam-5839	968	7	(	(	PUNCT
ejpam-5839	968	8	g̃,ω)−	g̃,ω)−	PROPN
ejpam-5839	968	9	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	968	10	)	)	PUNCT
ejpam-5839	968	11	)	)	PUNCT
ejpam-5839	969	1	∩	∩	NOUN
ejpam-5839	969	2	(	(	PUNCT
ejpam-5839	969	3	f̃	f̃	PROPN
ejpam-5839	969	4	,	,	PUNCT
ejpam-5839	969	5	ω	ω	NUM
ejpam-5839	969	6	)	)	PUNCT
ejpam-5839	969	7	̸=	̸=	PROPN
ejpam-5839	969	8	∅.	∅.	ADP
ejpam-5839	969	9	thus	thus	ADV
ejpam-5839	969	10	,	,	PUNCT
ejpam-5839	969	11	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	969	12	)	)	PUNCT
ejpam-5839	969	13	is	be	AUX
ejpam-5839	969	14	a	a	DET
ejpam-5839	969	15	quadripartitioned	quadripartitione	VERB
ejpam-5839	969	16	neutrosophic	neutrosophic	ADJ
ejpam-5839	969	17	soft	soft	ADJ
ejpam-5839	969	18	limit	limit	NOUN
ejpam-5839	969	19	point	point	NOUN
ejpam-5839	969	20	of	of	ADP
ejpam-5839	969	21	(	(	PUNCT
ejpam-5839	969	22	f̃	f̃	PROPN
ejpam-5839	969	23	,	,	PUNCT
ejpam-5839	969	24	ω	ω	PROPN
ejpam-5839	969	25	)	)	PUNCT
ejpam-5839	969	26	,	,	PUNCT
ejpam-5839	969	27	completing	complete	VERB
ejpam-5839	969	28	the	the	DET
ejpam-5839	969	29	proof	proof	NOUN
ejpam-5839	969	30	.	.	PUNCT
ejpam-5839	970	1	theorem	theorem	NOUN
ejpam-5839	970	2	19	19	NUM
ejpam-5839	970	3	.	.	PUNCT
ejpam-5839	971	1	let	let	VERB
ejpam-5839	971	2	τqpnss	τqpnss	PROPN
ejpam-5839	971	3	1	1	NUM
ejpam-5839	971	4	and	and	CCONJ
ejpam-5839	971	5	τqpnss	τqpns	NOUN
ejpam-5839	971	6	2	2	NUM
ejpam-5839	971	7	be	be	VERB
ejpam-5839	971	8	two	two	NUM
ejpam-5839	971	9	quadripartitioned	quadripartitione	VERB
ejpam-5839	971	10	neutrosophic	neutrosophic	ADJ
ejpam-5839	971	11	soft	soft	ADJ
ejpam-5839	971	12	topologies	topology	NOUN
ejpam-5839	971	13	over	over	ADP
ejpam-5839	971	14	x	x	PUNCT
ejpam-5839	971	15	generated	generate	VERB
ejpam-5839	971	16	by	by	ADP
ejpam-5839	971	17	the	the	DET
ejpam-5839	971	18	quadripartitioned	quadripartitioned	ADJ
ejpam-5839	971	19	neutrosophic	neutrosophic	ADJ
ejpam-5839	971	20	soft	soft	ADJ
ejpam-5839	971	21	bases	basis	NOUN
ejpam-5839	971	22	bqpnss	bqpns	NOUN
ejpam-5839	971	23	1	1	NUM
ejpam-5839	971	24	and	and	CCONJ
ejpam-5839	971	25	bqpnss	bqpns	NOUN
ejpam-5839	971	26	2	2	NUM
ejpam-5839	971	27	,	,	PUNCT
ejpam-5839	971	28	respectively	respectively	ADV
ejpam-5839	971	29	.	.	PUNCT
ejpam-5839	972	1	then	then	ADV
ejpam-5839	972	2	τqpnss	τqpns	VERB
ejpam-5839	972	3	1	1	NUM
ejpam-5839	972	4	⊆	⊆	NUM
ejpam-5839	972	5	τqpnss	τqpns	NOUN
ejpam-5839	972	6	2	2	NUM
ejpam-5839	972	7	if	if	SCONJ
ejpam-5839	972	8	and	and	CCONJ
ejpam-5839	972	9	only	only	ADV
ejpam-5839	972	10	if	if	SCONJ
ejpam-5839	972	11	for	for	ADP
ejpam-5839	972	12	each	each	DET
ejpam-5839	972	13	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	972	14	)	)	PUNCT
ejpam-5839	972	15	∈	∈	PROPN
ejpam-5839	972	16	qpnss(x	qpnss(x	PROPN
ejpam-5839	972	17	,	,	PUNCT
ejpam-5839	972	18	ω	ω	NOUN
ejpam-5839	972	19	)	)	PUNCT
ejpam-5839	972	20	and	and	CCONJ
ejpam-5839	972	21	for	for	ADP
ejpam-5839	972	22	each	each	DET
ejpam-5839	972	23	(	(	PUNCT
ejpam-5839	972	24	b̃1,ω	b̃1,ω	NOUN
ejpam-5839	972	25	)	)	PUNCT
ejpam-5839	972	26	∈	∈	PROPN
ejpam-5839	972	27	bqpnss	bqpns	NOUN
ejpam-5839	972	28	1	1	NUM
ejpam-5839	972	29	containing	contain	VERB
ejpam-5839	972	30	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	972	31	)	)	PUNCT
ejpam-5839	972	32	,	,	PUNCT
ejpam-5839	972	33	there	there	PRON
ejpam-5839	972	34	exists	exist	VERB
ejpam-5839	972	35	(	(	PUNCT
ejpam-5839	972	36	b̃2,ω	b̃2,ω	NOUN
ejpam-5839	972	37	)	)	PUNCT
ejpam-5839	972	38	∈	∈	PROPN
ejpam-5839	972	39	bqpnss	bqpns	NOUN
ejpam-5839	972	40	2	2	NUM
ejpam-5839	973	1	such	such	ADJ
ejpam-5839	973	2	that	that	DET
ejpam-5839	973	3	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	973	4	)	)	PUNCT
ejpam-5839	973	5	∈	∈	PROPN
ejpam-5839	973	6	(	(	PUNCT
ejpam-5839	973	7	b̃2,ω	b̃2,ω	NOUN
ejpam-5839	973	8	)	)	PUNCT
ejpam-5839	973	9	⊆	⊆	NUM
ejpam-5839	973	10	(	(	PUNCT
ejpam-5839	973	11	b̃1,ω	b̃1,ω	NOUN
ejpam-5839	973	12	)	)	PUNCT
ejpam-5839	973	13	.	.	PUNCT
ejpam-5839	974	1	proof	proof	NOUN
ejpam-5839	974	2	.	.	PUNCT
ejpam-5839	975	1	suppose	suppose	VERB
ejpam-5839	975	2	that	that	SCONJ
ejpam-5839	975	3	τqpnss	τqpns	NOUN
ejpam-5839	975	4	1	1	NUM
ejpam-5839	975	5	⊆	⊆	NUM
ejpam-5839	975	6	τqpnss	τqpns	NOUN
ejpam-5839	975	7	2	2	NUM
ejpam-5839	975	8	and	and	CCONJ
ejpam-5839	975	9	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	NUM
ejpam-5839	975	10	)	)	PUNCT
ejpam-5839	975	11	∈	∈	PROPN
ejpam-5839	975	12	qpnss(x	qpnss(x	PROPN
ejpam-5839	975	13	,	,	PUNCT
ejpam-5839	975	14	ω	ω	NOUN
ejpam-5839	975	15	)	)	PUNCT
ejpam-5839	975	16	,	,	PUNCT
ejpam-5839	975	17	(	(	PUNCT
ejpam-5839	975	18	b̃1,ω	b̃1,ω	NOUN
ejpam-5839	975	19	)	)	PUNCT
ejpam-5839	975	20	∈	∈	PROPN
ejpam-5839	975	21	bqpnss	bqpns	NOUN
ejpam-5839	975	22	1	1	NUM
ejpam-5839	975	23	such	such	ADJ
ejpam-5839	975	24	that	that	DET
ejpam-5839	975	25	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	975	26	)	)	PUNCT
ejpam-5839	975	27	∈	∈	PROPN
ejpam-5839	975	28	(	(	PUNCT
ejpam-5839	975	29	b̃1,ω	b̃1,ω	NOUN
ejpam-5839	975	30	)	)	PUNCT
ejpam-5839	975	31	.	.	PUNCT
ejpam-5839	976	1	since	since	SCONJ
ejpam-5839	976	2	bqpnss	bqpns	NOUN
ejpam-5839	976	3	1	1	NUM
ejpam-5839	976	4	is	be	AUX
ejpam-5839	976	5	a	a	DET
ejpam-5839	976	6	quadripartitioned	quadripartitione	VERB
ejpam-5839	976	7	neutrosophic	neutrosophic	ADJ
ejpam-5839	976	8	soft	soft	ADJ
ejpam-5839	976	9	basis	basis	NOUN
ejpam-5839	976	10	for	for	ADP
ejpam-5839	976	11	quadripartitioned	quadripartitione	VERB
ejpam-5839	976	12	neutrosophic	neutrosophic	ADJ
ejpam-5839	976	13	soft	soft	ADJ
ejpam-5839	976	14	topology	topology	NOUN
ejpam-5839	976	15	τqpnss	τqpns	NOUN
ejpam-5839	976	16	1	1	NUM
ejpam-5839	976	17	over	over	ADP
ejpam-5839	976	18	x	x	NOUN
ejpam-5839	976	19	,	,	PUNCT
ejpam-5839	976	20	then	then	ADV
ejpam-5839	976	21	bqpnss	bqpns	VERB
ejpam-5839	976	22	1	1	NUM
ejpam-5839	976	23	⊆	⊆	NUM
ejpam-5839	976	24	τqpnss	τqpnss	NOUN
ejpam-5839	976	25	1	1	NUM
ejpam-5839	976	26	.	.	PUNCT
ejpam-5839	977	1	thus	thus	ADV
ejpam-5839	977	2	,	,	PUNCT
ejpam-5839	977	3	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	977	4	)	)	PUNCT
ejpam-5839	977	5	∈	∈	PROPN
ejpam-5839	977	6	(	(	PUNCT
ejpam-5839	977	7	b̃1,ω	b̃1,ω	NOUN
ejpam-5839	977	8	)	)	PUNCT
ejpam-5839	977	9	∈	∈	PROPN
ejpam-5839	977	10	bqpnss	bqpns	NOUN
ejpam-5839	977	11	2	2	NUM
ejpam-5839	977	12	⊆	⊆	NUM
ejpam-5839	977	13	τqpnss	τqpnss	NOUN
ejpam-5839	977	14	1	1	NUM
ejpam-5839	977	15	,	,	PUNCT
ejpam-5839	977	16	i.e.	i.e.	X
ejpam-5839	977	17	,	,	PUNCT
ejpam-5839	977	18	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	ADJ
ejpam-5839	977	19	)	)	PUNCT
ejpam-5839	977	20	∈	∈	PROPN
ejpam-5839	977	21	(	(	PUNCT
ejpam-5839	977	22	b̃1,ω	b̃1,ω	NOUN
ejpam-5839	977	23	)	)	PUNCT
ejpam-5839	977	24	∈	∈	PROPN
ejpam-5839	977	25	τqpnss	τqpns	NOUN
ejpam-5839	977	26	2	2	NUM
ejpam-5839	977	27	.	.	PUNCT
ejpam-5839	978	1	since	since	SCONJ
ejpam-5839	978	2	bqpnss	bqpns	NOUN
ejpam-5839	978	3	2	2	NUM
ejpam-5839	978	4	is	be	AUX
ejpam-5839	978	5	a	a	DET
ejpam-5839	978	6	quadripartitioned	quadripartitione	VERB
ejpam-5839	978	7	neutrosophic	neutrosophic	ADJ
ejpam-5839	978	8	soft	soft	ADJ
ejpam-5839	978	9	basis	basis	NOUN
ejpam-5839	978	10	for	for	ADP
ejpam-5839	978	11	τqpnss	τqpnss	NOUN
ejpam-5839	978	12	2	2	NUM
ejpam-5839	978	13	,	,	PUNCT
ejpam-5839	978	14	there	there	PRON
ejpam-5839	978	15	exists	exist	VERB
ejpam-5839	978	16	(	(	PUNCT
ejpam-5839	978	17	b̃2,ω	b̃2,ω	NOUN
ejpam-5839	978	18	)	)	PUNCT
ejpam-5839	978	19	∈	∈	PROPN
ejpam-5839	978	20	bqpnss	bqpns	NOUN
ejpam-5839	978	21	2	2	NUM
ejpam-5839	979	1	such	such	ADJ
ejpam-5839	979	2	that	that	DET
ejpam-5839	979	3	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	979	4	)	)	PUNCT
ejpam-5839	979	5	∈	∈	PROPN
ejpam-5839	979	6	(	(	PUNCT
ejpam-5839	979	7	b̃2,ω	b̃2,ω	NOUN
ejpam-5839	979	8	)	)	PUNCT
ejpam-5839	979	9	⊆	⊆	NUM
ejpam-5839	979	10	(	(	PUNCT
ejpam-5839	979	11	b̃1,ω	b̃1,ω	NOUN
ejpam-5839	979	12	)	)	PUNCT
ejpam-5839	979	13	.	.	PUNCT
ejpam-5839	980	1	conversely	conversely	ADV
ejpam-5839	980	2	,	,	PUNCT
ejpam-5839	980	3	assume	assume	VERB
ejpam-5839	980	4	that	that	SCONJ
ejpam-5839	980	5	the	the	DET
ejpam-5839	980	6	hypothesis	hypothesis	NOUN
ejpam-5839	980	7	holds	hold	VERB
ejpam-5839	980	8	.	.	PUNCT
ejpam-5839	981	1	let	let	VERB
ejpam-5839	981	2	(	(	PUNCT
ejpam-5839	981	3	f̃	f̃	PROPN
ejpam-5839	981	4	,	,	PUNCT
ejpam-5839	981	5	ω	ω	NUM
ejpam-5839	981	6	)	)	PUNCT
ejpam-5839	981	7	∈	∈	PROPN
ejpam-5839	981	8	τqpnss	τqpns	NOUN
ejpam-5839	981	9	1	1	NUM
ejpam-5839	981	10	.	.	PUNCT
ejpam-5839	982	1	since	since	SCONJ
ejpam-5839	982	2	bqpnss	bqpns	NOUN
ejpam-5839	982	3	1	1	NUM
ejpam-5839	982	4	is	be	AUX
ejpam-5839	982	5	a	a	DET
ejpam-5839	982	6	quadripartitioned	quadripartitione	VERB
ejpam-5839	982	7	neutrosophic	neutrosophic	ADJ
ejpam-5839	982	8	soft	soft	ADJ
ejpam-5839	982	9	basis	basis	NOUN
ejpam-5839	982	10	for	for	ADP
ejpam-5839	982	11	quadripartitioned	quadripartitione	VERB
ejpam-5839	982	12	neutrosophic	neutrosophic	ADJ
ejpam-5839	982	13	soft	soft	ADJ
ejpam-5839	982	14	topology	topology	NOUN
ejpam-5839	982	15	τqpnss	τqpns	NOUN
ejpam-5839	982	16	1	1	NUM
ejpam-5839	982	17	,	,	PUNCT
ejpam-5839	982	18	then	then	ADV
ejpam-5839	982	19	for	for	ADP
ejpam-5839	982	20	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	982	21	)	)	PUNCT
ejpam-5839	982	22	∈	∈	PROPN
ejpam-5839	982	23	(	(	PUNCT
ejpam-5839	982	24	f̃	f̃	PROPN
ejpam-5839	982	25	,	,	PUNCT
ejpam-5839	982	26	ω	ω	PROPN
ejpam-5839	982	27	)	)	PUNCT
ejpam-5839	982	28	,	,	PUNCT
ejpam-5839	982	29	there	there	PRON
ejpam-5839	982	30	exists	exist	VERB
ejpam-5839	982	31	(	(	PUNCT
ejpam-5839	982	32	b̃1,ω	b̃1,ω	NOUN
ejpam-5839	982	33	)	)	PUNCT
ejpam-5839	982	34	∈	∈	PROPN
ejpam-5839	982	35	bqpnss	bqpns	NOUN
ejpam-5839	982	36	1	1	NUM
ejpam-5839	982	37	such	such	ADJ
ejpam-5839	982	38	that	that	DET
ejpam-5839	982	39	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	982	40	)	)	PUNCT
ejpam-5839	982	41	∈	∈	PROPN
ejpam-5839	982	42	(	(	PUNCT
ejpam-5839	982	43	b̃1,ω	b̃1,ω	NOUN
ejpam-5839	982	44	)	)	PUNCT
ejpam-5839	982	45	⊆	⊆	NUM
ejpam-5839	982	46	(	(	PUNCT
ejpam-5839	982	47	f̃	f̃	PROPN
ejpam-5839	982	48	,	,	PUNCT
ejpam-5839	982	49	ω	ω	PROPN
ejpam-5839	982	50	)	)	PUNCT
ejpam-5839	982	51	.	.	PUNCT
ejpam-5839	983	1	by	by	ADP
ejpam-5839	983	2	hypothesis	hypothesis	NOUN
ejpam-5839	983	3	,	,	PUNCT
ejpam-5839	983	4	there	there	PRON
ejpam-5839	983	5	exists	exist	VERB
ejpam-5839	983	6	(	(	PUNCT
ejpam-5839	983	7	b̃2,ω	b̃2,ω	NOUN
ejpam-5839	983	8	)	)	PUNCT
ejpam-5839	983	9	∈	∈	PROPN
ejpam-5839	983	10	bqpnss	bqpns	NOUN
ejpam-5839	983	11	2	2	NUM
ejpam-5839	983	12	such	such	ADJ
ejpam-5839	983	13	that	that	PRON
ejpam-5839	983	14	(	(	PUNCT
ejpam-5839	983	15	b̃2,ω	b̃2,ω	NOUN
ejpam-5839	983	16	)	)	PUNCT
ejpam-5839	983	17	⊆	⊆	NUM
ejpam-5839	983	18	(	(	PUNCT
ejpam-5839	983	19	b̃1,ω	b̃1,ω	NOUN
ejpam-5839	983	20	)	)	PUNCT
ejpam-5839	983	21	⊆	⊆	NUM
ejpam-5839	983	22	(	(	PUNCT
ejpam-5839	983	23	f̃	f̃	PROPN
ejpam-5839	983	24	,	,	PUNCT
ejpam-5839	983	25	ω	ω	PROPN
ejpam-5839	983	26	)	)	PUNCT
ejpam-5839	983	27	.	.	PUNCT
ejpam-5839	984	1	this	this	PRON
ejpam-5839	984	2	implies	imply	VERB
ejpam-5839	984	3	(	(	PUNCT
ejpam-5839	984	4	b̃2,ω	b̃2,ω	NOUN
ejpam-5839	984	5	)	)	PUNCT
ejpam-5839	984	6	⊆	⊆	NUM
ejpam-5839	984	7	(	(	PUNCT
ejpam-5839	984	8	f̃	f̃	PROPN
ejpam-5839	984	9	,	,	PUNCT
ejpam-5839	984	10	ω	ω	PROPN
ejpam-5839	984	11	)	)	PUNCT
ejpam-5839	984	12	,	,	PUNCT
ejpam-5839	984	13	which	which	PRON
ejpam-5839	984	14	means	mean	VERB
ejpam-5839	984	15	(	(	PUNCT
ejpam-5839	984	16	f̃	f̃	PROPN
ejpam-5839	984	17	,	,	PUNCT
ejpam-5839	984	18	ω	ω	NUM
ejpam-5839	984	19	)	)	PUNCT
ejpam-5839	984	20	∈	∈	PROPN
ejpam-5839	984	21	τqpnss	τqpns	NOUN
ejpam-5839	984	22	2	2	NUM
ejpam-5839	984	23	.	.	PUNCT
ejpam-5839	985	1	thus	thus	ADV
ejpam-5839	985	2	,	,	PUNCT
ejpam-5839	985	3	we	we	PRON
ejpam-5839	985	4	conclude	conclude	VERB
ejpam-5839	985	5	that	that	SCONJ
ejpam-5839	985	6	τqpnss	τqpns	NOUN
ejpam-5839	985	7	1	1	NUM
ejpam-5839	985	8	⊆	⊆	NUM
ejpam-5839	985	9	τqpnss	τqpnss	NOUN
ejpam-5839	985	10	2	2	NUM
ejpam-5839	985	11	.	.	PUNCT
ejpam-5839	986	1	theorem	theorem	NOUN
ejpam-5839	986	2	20	20	NUM
ejpam-5839	986	3	.	.	PUNCT
ejpam-5839	987	1	let	let	AUX
ejpam-5839	987	2	(	(	PUNCT
ejpam-5839	987	3	x	x	NOUN
ejpam-5839	987	4	,	,	PUNCT
ejpam-5839	987	5	τqpnss	τqpns	NOUN
ejpam-5839	987	6	,	,	PUNCT
ejpam-5839	987	7	e	e	X
ejpam-5839	987	8	)	)	PUNCT
ejpam-5839	987	9	be	be	VERB
ejpam-5839	987	10	a	a	DET
ejpam-5839	987	11	quadripartitioned	quadripartitione	VERB
ejpam-5839	987	12	neutrosophic	neutrosophic	ADJ
ejpam-5839	987	13	soft	soft	ADJ
ejpam-5839	987	14	topological	topological	ADJ
ejpam-5839	987	15	space	space	NOUN
ejpam-5839	987	16	over	over	ADP
ejpam-5839	987	17	(	(	PUNCT
ejpam-5839	987	18	f̃	f̃	PROPN
ejpam-5839	987	19	,	,	PUNCT
ejpam-5839	987	20	ω	ω	PROPN
ejpam-5839	987	21	)	)	PUNCT
ejpam-5839	987	22	,	,	PUNCT
ejpam-5839	987	23	(	(	PUNCT
ejpam-5839	987	24	k̃,ω	k̃,ω	NOUN
ejpam-5839	987	25	)	)	PUNCT
ejpam-5839	987	26	∈	∈	PROPN
ejpam-5839	987	27	qpnss(x	qpnss(x	PROPN
ejpam-5839	987	28	,	,	PUNCT
ejpam-5839	987	29	ω	ω	NOUN
ejpam-5839	987	30	)	)	PUNCT
ejpam-5839	987	31	.	.	PUNCT
ejpam-5839	988	1	a.	a.	PROPN
ejpam-5839	988	2	shihadeh	shihadeh	VERB
ejpam-5839	988	3	et	et	PROPN
ejpam-5839	988	4	al	al	PROPN
ejpam-5839	988	5	.	.	PUNCT
ejpam-5839	988	6	/	/	SYM
ejpam-5839	988	7	eur	eur	PROPN
ejpam-5839	988	8	.	.	PUNCT
ejpam-5839	989	1	j.	j.	PROPN
ejpam-5839	989	2	pure	pure	PROPN
ejpam-5839	989	3	appl	appl	PROPN
ejpam-5839	989	4	.	.	PROPN
ejpam-5839	989	5	math	math	PROPN
ejpam-5839	989	6	,	,	PUNCT
ejpam-5839	989	7	18	18	NUM
ejpam-5839	989	8	(	(	PUNCT
ejpam-5839	989	9	2	2	NUM
ejpam-5839	989	10	)	)	PUNCT
ejpam-5839	989	11	(	(	PUNCT
ejpam-5839	989	12	2025	2025	NUM
ejpam-5839	989	13	)	)	PUNCT
ejpam-5839	989	14	,	,	PUNCT
ejpam-5839	989	15	5839	5839	NUM
ejpam-5839	989	16	43	43	NUM
ejpam-5839	989	17	of	of	ADP
ejpam-5839	989	18	54	54	NUM
ejpam-5839	989	19	(	(	PUNCT
ejpam-5839	989	20	i	i	NOUN
ejpam-5839	989	21	)	)	PUNCT
ejpam-5839	989	22	if	if	SCONJ
ejpam-5839	989	23	bqpnss	bqpns	NOUN
ejpam-5839	989	24	is	be	AUX
ejpam-5839	989	25	a	a	DET
ejpam-5839	989	26	quadripartitioned	quadripartitione	VERB
ejpam-5839	989	27	neutrosophic	neutrosophic	ADJ
ejpam-5839	989	28	soft	soft	ADJ
ejpam-5839	989	29	base	base	NOUN
ejpam-5839	989	30	for	for	ADP
ejpam-5839	989	31	τqpnss	τqpns	NOUN
ejpam-5839	989	32	,	,	PUNCT
ejpam-5839	989	33	then	then	ADV
ejpam-5839	989	34	b(f̃	b(f̃	PROPN
ejpam-5839	989	35	,	,	PUNCT
ejpam-5839	989	36	e)qpnss	e)qpnss	PROPN
ejpam-5839	989	37	=	=	PRON
ejpam-5839	989	38	{	{	PUNCT
ejpam-5839	989	39	(	(	PUNCT
ejpam-5839	989	40	b̃,ω	b̃,ω	NOUN
ejpam-5839	989	41	)	)	PUNCT
ejpam-5839	989	42	∩	∩	NOUN
ejpam-5839	989	43	(	(	PUNCT
ejpam-5839	989	44	f̃	f̃	PROPN
ejpam-5839	989	45	,	,	PUNCT
ejpam-5839	989	46	ω	ω	PROPN
ejpam-5839	989	47	)	)	PUNCT
ejpam-5839	989	48	:	:	PUNCT
ejpam-5839	989	49	(	(	PUNCT
ejpam-5839	989	50	b̃,ω	b̃,ω	NOUN
ejpam-5839	989	51	)	)	PUNCT
ejpam-5839	989	52	∈	∈	PROPN
ejpam-5839	989	53	bqpnss	bqpns	NOUN
ejpam-5839	989	54	}	}	PUNCT
ejpam-5839	989	55	is	be	AUX
ejpam-5839	989	56	a	a	DET
ejpam-5839	989	57	quadripartitioned	quadripartitione	VERB
ejpam-5839	989	58	neutrosophic	neutrosophic	ADJ
ejpam-5839	989	59	soft	soft	ADJ
ejpam-5839	989	60	base	base	NOUN
ejpam-5839	989	61	for	for	ADP
ejpam-5839	989	62	the	the	DET
ejpam-5839	989	63	quadripartitioned	quadripartitione	VERB
ejpam-5839	989	64	neutrosophic	neutrosophic	ADJ
ejpam-5839	989	65	soft	soft	ADJ
ejpam-5839	989	66	sub	sub	ADJ
ejpam-5839	989	67	-	-	ADJ
ejpam-5839	989	68	topology	topology	ADJ
ejpam-5839	989	69	τqpnss	τqpns	NOUN
ejpam-5839	989	70	(	(	PUNCT
ejpam-5839	989	71	f̃	f̃	PROPN
ejpam-5839	989	72	,	,	PUNCT
ejpam-5839	989	73	e	e	NOUN
ejpam-5839	989	74	)	)	PUNCT
ejpam-5839	989	75	.	.	PUNCT
ejpam-5839	990	1	(	(	PUNCT
ejpam-5839	990	2	ii	ii	NOUN
ejpam-5839	990	3	)	)	PUNCT
ejpam-5839	990	4	if	if	SCONJ
ejpam-5839	990	5	(	(	PUNCT
ejpam-5839	990	6	g̃,ω	g̃,ω	NOUN
ejpam-5839	990	7	)	)	PUNCT
ejpam-5839	990	8	is	be	AUX
ejpam-5839	990	9	a	a	DET
ejpam-5839	990	10	quadripartitioned	quadripartitione	VERB
ejpam-5839	990	11	neutrosophic	neutrosophic	ADJ
ejpam-5839	990	12	soft	soft	ADJ
ejpam-5839	990	13	p	p	NOUN
ejpam-5839	990	14	-	-	PUNCT
ejpam-5839	990	15	closed	close	VERB
ejpam-5839	990	16	set	set	NOUN
ejpam-5839	990	17	in	in	ADP
ejpam-5839	990	18	τqpnss	τqpns	NOUN
ejpam-5839	990	19	(	(	PUNCT
ejpam-5839	990	20	f̃	f̃	PROPN
ejpam-5839	990	21	,	,	PUNCT
ejpam-5839	990	22	e	e	NOUN
ejpam-5839	990	23	)	)	PUNCT
ejpam-5839	990	24	and	and	CCONJ
ejpam-5839	990	25	(	(	PUNCT
ejpam-5839	990	26	f̃	f̃	PROPN
ejpam-5839	990	27	,	,	PUNCT
ejpam-5839	990	28	ω	ω	PROPN
ejpam-5839	990	29	)	)	PUNCT
ejpam-5839	990	30	is	be	AUX
ejpam-5839	990	31	a	a	DET
ejpam-5839	990	32	quadripartitioned	quadripartitione	VERB
ejpam-5839	990	33	neutrosophic	neutrosophic	ADJ
ejpam-5839	990	34	soft	soft	ADJ
ejpam-5839	990	35	p	p	NOUN
ejpam-5839	990	36	-	-	PUNCT
ejpam-5839	990	37	closed	close	VERB
ejpam-5839	990	38	set	set	NOUN
ejpam-5839	990	39	in	in	ADP
ejpam-5839	990	40	τqpnss	τqpns	NOUN
ejpam-5839	990	41	(	(	PUNCT
ejpam-5839	990	42	f̃	f̃	PROPN
ejpam-5839	990	43	,	,	PUNCT
ejpam-5839	990	44	e	e	NOUN
ejpam-5839	990	45	)	)	PUNCT
ejpam-5839	990	46	,	,	PUNCT
ejpam-5839	990	47	then	then	ADV
ejpam-5839	990	48	(	(	PUNCT
ejpam-5839	990	49	f̃	f̃	PROPN
ejpam-5839	990	50	,	,	PUNCT
ejpam-5839	990	51	ω	ω	PROPN
ejpam-5839	990	52	)	)	PUNCT
ejpam-5839	990	53	is	be	AUX
ejpam-5839	990	54	a	a	DET
ejpam-5839	990	55	quadripartitioned	quadripartitione	VERB
ejpam-5839	990	56	neutrosophic	neutrosophic	ADJ
ejpam-5839	990	57	soft	soft	ADJ
ejpam-5839	990	58	p	p	NOUN
ejpam-5839	990	59	-	-	PUNCT
ejpam-5839	990	60	closed	close	VERB
ejpam-5839	990	61	set	set	NOUN
ejpam-5839	990	62	in	in	ADP
ejpam-5839	990	63	τqpnss	τqpns	NOUN
ejpam-5839	990	64	(	(	PUNCT
ejpam-5839	990	65	f̃	f̃	PROPN
ejpam-5839	990	66	,	,	PUNCT
ejpam-5839	990	67	e	e	NOUN
ejpam-5839	990	68	)	)	PUNCT
ejpam-5839	990	69	.	.	PUNCT
ejpam-5839	991	1	(	(	PUNCT
ejpam-5839	991	2	iii	iii	X
ejpam-5839	991	3	)	)	PUNCT
ejpam-5839	991	4	let	let	NOUN
ejpam-5839	991	5	(	(	PUNCT
ejpam-5839	991	6	f̃	f̃	PROPN
ejpam-5839	991	7	,	,	PUNCT
ejpam-5839	991	8	ω	ω	NUM
ejpam-5839	991	9	)	)	PUNCT
ejpam-5839	991	10	⊆	⊆	NUM
ejpam-5839	991	11	(	(	PUNCT
ejpam-5839	991	12	k̃,ω	k̃,ω	NOUN
ejpam-5839	991	13	)	)	PUNCT
ejpam-5839	991	14	.	.	PUNCT
ejpam-5839	992	1	if	if	SCONJ
ejpam-5839	992	2	(	(	PUNCT
ejpam-5839	992	3	g̃,ω	g̃,ω	NOUN
ejpam-5839	992	4	)	)	PUNCT
ejpam-5839	992	5	∈	∈	PROPN
ejpam-5839	992	6	τqpnss	τqpns	NOUN
ejpam-5839	992	7	,	,	PUNCT
ejpam-5839	992	8	then	then	ADV
ejpam-5839	992	9	(	(	PUNCT
ejpam-5839	992	10	g̃,ω	g̃,ω	NOUN
ejpam-5839	992	11	)	)	PUNCT
ejpam-5839	992	12	∩	∩	NOUN
ejpam-5839	992	13	(	(	PUNCT
ejpam-5839	992	14	f̃	f̃	PROPN
ejpam-5839	992	15	,	,	PUNCT
ejpam-5839	992	16	ω	ω	PROPN
ejpam-5839	992	17	)	)	PUNCT
ejpam-5839	992	18	is	be	AUX
ejpam-5839	992	19	the	the	DET
ejpam-5839	992	20	quadripartitioned	quadripartitione	VERB
ejpam-5839	992	21	neutrosophic	neutrosophic	ADJ
ejpam-5839	992	22	soft	soft	ADJ
ejpam-5839	992	23	closure	closure	NOUN
ejpam-5839	992	24	in	in	ADP
ejpam-5839	992	25	(	(	PUNCT
ejpam-5839	992	26	x(f̃	x(f̃	X
ejpam-5839	992	27	,	,	PUNCT
ejpam-5839	992	28	e	e	NOUN
ejpam-5839	992	29	)	)	PUNCT
ejpam-5839	992	30	,	,	PUNCT
ejpam-5839	992	31	τ	τ	PROPN
ejpam-5839	992	32	qpnss	qpnss	NOUN
ejpam-5839	992	33	(	(	PUNCT
ejpam-5839	992	34	f̃	f̃	PROPN
ejpam-5839	992	35	,	,	PUNCT
ejpam-5839	992	36	e	e	NOUN
ejpam-5839	992	37	)	)	PUNCT
ejpam-5839	992	38	,	,	PUNCT
ejpam-5839	992	39	ω	ω	NOUN
ejpam-5839	992	40	)	)	PUNCT
ejpam-5839	992	41	.	.	PUNCT
ejpam-5839	993	1	proof	proof	NOUN
ejpam-5839	993	2	.	.	PUNCT
ejpam-5839	994	1	1	1	X
ejpam-5839	994	2	.	.	X
ejpam-5839	994	3	since	since	SCONJ
ejpam-5839	994	4	bqpnss	bqpns	NOUN
ejpam-5839	994	5	is	be	AUX
ejpam-5839	994	6	a	a	DET
ejpam-5839	994	7	quadripartitioned	quadripartitione	VERB
ejpam-5839	994	8	neutrosophic	neutrosophic	ADJ
ejpam-5839	994	9	soft	soft	ADJ
ejpam-5839	994	10	base	base	NOUN
ejpam-5839	994	11	for	for	ADP
ejpam-5839	994	12	τqpnss	τqpns	NOUN
ejpam-5839	994	13	,	,	PUNCT
ejpam-5839	994	14	for	for	ADP
ejpam-5839	994	15	arbitrary	arbitrary	ADJ
ejpam-5839	994	16	(	(	PUNCT
ejpam-5839	994	17	ũ	ũ	PROPN
ejpam-5839	994	18	,	,	PUNCT
ejpam-5839	994	19	ω	ω	NOUN
ejpam-5839	994	20	)	)	PUNCT
ejpam-5839	994	21	∈	∈	PROPN
ejpam-5839	994	22	τqpnss	τqpns	NOUN
ejpam-5839	994	23	,	,	PUNCT
ejpam-5839	994	24	we	we	PRON
ejpam-5839	994	25	have	have	VERB
ejpam-5839	994	26	:	:	PUNCT
ejpam-5839	994	27	(	(	PUNCT
ejpam-5839	994	28	ũ	ũ	PROPN
ejpam-5839	994	29	,	,	PUNCT
ejpam-5839	994	30	ω	ω	NOUN
ejpam-5839	994	31	)	)	PUNCT
ejpam-5839	994	32	=	=	SYM
ejpam-5839	994	33	⋃	⋃	NOUN
ejpam-5839	994	34	(	(	PUNCT
ejpam-5839	994	35	b̃,ω)∈bqpnss	b̃,ω)∈bqpnss	X
ejpam-5839	994	36	(	(	PUNCT
ejpam-5839	994	37	b̃,ω	b̃,ω	NOUN
ejpam-5839	994	38	)	)	PUNCT
ejpam-5839	994	39	.	.	PUNCT
ejpam-5839	995	1	thus	thus	ADV
ejpam-5839	995	2	,	,	PUNCT
ejpam-5839	995	3	(	(	PUNCT
ejpam-5839	995	4	ũ	ũ	PROPN
ejpam-5839	995	5	,	,	PUNCT
ejpam-5839	995	6	ω	ω	NOUN
ejpam-5839	995	7	)	)	PUNCT
ejpam-5839	995	8	∩	∩	NOUN
ejpam-5839	995	9	(	(	PUNCT
ejpam-5839	995	10	f̃	f̃	PROPN
ejpam-5839	995	11	,	,	PUNCT
ejpam-5839	995	12	ω	ω	NOUN
ejpam-5839	995	13	)	)	PUNCT
ejpam-5839	995	14	=	=	SYM
ejpam-5839	995	15	⋃	⋃	NOUN
ejpam-5839	995	16	(	(	PUNCT
ejpam-5839	995	17	b̃,ω)∈bqpnss	b̃,ω)∈bqpnss	X
ejpam-5839	995	18	(	(	PUNCT
ejpam-5839	995	19	b̃,ω	b̃,ω	NOUN
ejpam-5839	995	20	)	)	PUNCT
ejpam-5839	995	21	∩	∩	NOUN
ejpam-5839	995	22	(	(	PUNCT
ejpam-5839	995	23	f̃	f̃	PROPN
ejpam-5839	995	24	,	,	PUNCT
ejpam-5839	995	25	ω	ω	PROPN
ejpam-5839	995	26	)	)	PUNCT
ejpam-5839	995	27	.	.	PUNCT
ejpam-5839	996	1	since	since	SCONJ
ejpam-5839	996	2	(	(	PUNCT
ejpam-5839	996	3	ũ	ũ	PROPN
ejpam-5839	996	4	,	,	PUNCT
ejpam-5839	996	5	ω	ω	NOUN
ejpam-5839	996	6	)	)	PUNCT
ejpam-5839	996	7	∩	∩	NOUN
ejpam-5839	996	8	(	(	PUNCT
ejpam-5839	996	9	f̃	f̃	PROPN
ejpam-5839	996	10	,	,	PUNCT
ejpam-5839	996	11	ω	ω	NUM
ejpam-5839	996	12	)	)	PUNCT
ejpam-5839	996	13	∈	∈	PROPN
ejpam-5839	996	14	τqpnss	τqpns	NOUN
ejpam-5839	996	15	(	(	PUNCT
ejpam-5839	996	16	f̃	f̃	PROPN
ejpam-5839	996	17	,	,	PUNCT
ejpam-5839	996	18	e	e	NOUN
ejpam-5839	996	19	)	)	PUNCT
ejpam-5839	996	20	,	,	PUNCT
ejpam-5839	996	21	it	it	PRON
ejpam-5839	996	22	follows	follow	VERB
ejpam-5839	996	23	that⋃	that⋃	PROPN
ejpam-5839	996	24	(	(	PUNCT
ejpam-5839	996	25	b̃,ω)∈bqpnss	b̃,ω)∈bqpnss	X
ejpam-5839	996	26	(	(	PUNCT
ejpam-5839	996	27	(	(	PUNCT
ejpam-5839	996	28	b̃,ω	b̃,ω	NOUN
ejpam-5839	996	29	)	)	PUNCT
ejpam-5839	996	30	∩	∩	NOUN
ejpam-5839	996	31	(	(	PUNCT
ejpam-5839	996	32	f̃	f̃	PROPN
ejpam-5839	996	33	,	,	PUNCT
ejpam-5839	996	34	ω	ω	NOUN
ejpam-5839	996	35	)	)	PUNCT
ejpam-5839	996	36	)	)	PUNCT
ejpam-5839	997	1	∈	∈	PROPN
ejpam-5839	997	2	τqpnss	τqpns	NOUN
ejpam-5839	997	3	(	(	PUNCT
ejpam-5839	997	4	f̃	f̃	PROPN
ejpam-5839	997	5	,	,	PUNCT
ejpam-5839	997	6	e	e	NOUN
ejpam-5839	997	7	)	)	PUNCT
ejpam-5839	997	8	.	.	PUNCT
ejpam-5839	998	1	since	since	SCONJ
ejpam-5839	998	2	an	an	DET
ejpam-5839	998	3	arbitrary	arbitrary	ADJ
ejpam-5839	998	4	member	member	NOUN
ejpam-5839	998	5	of	of	ADP
ejpam-5839	998	6	τqpnss	τqpnss	PROPN
ejpam-5839	998	7	(	(	PUNCT
ejpam-5839	998	8	f̃	f̃	PROPN
ejpam-5839	998	9	,	,	PUNCT
ejpam-5839	998	10	e	e	NOUN
ejpam-5839	998	11	)	)	PUNCT
ejpam-5839	998	12	can	can	AUX
ejpam-5839	998	13	be	be	AUX
ejpam-5839	998	14	expressed	express	VERB
ejpam-5839	998	15	as	as	ADP
ejpam-5839	998	16	the	the	DET
ejpam-5839	998	17	union	union	NOUN
ejpam-5839	998	18	of	of	ADP
ejpam-5839	998	19	members	member	NOUN
ejpam-5839	998	20	of	of	ADP
ejpam-5839	998	21	bqpnss	bqpns	NOUN
ejpam-5839	998	22	(	(	PUNCT
ejpam-5839	998	23	f̃	f̃	PROPN
ejpam-5839	998	24	,	,	PUNCT
ejpam-5839	998	25	e	e	NOUN
ejpam-5839	998	26	)	)	PUNCT
ejpam-5839	998	27	,	,	PUNCT
ejpam-5839	998	28	it	it	PRON
ejpam-5839	998	29	follows	follow	VERB
ejpam-5839	998	30	that	that	SCONJ
ejpam-5839	998	31	bqpnss	bqpns	NOUN
ejpam-5839	998	32	(	(	PUNCT
ejpam-5839	998	33	f̃	f̃	PROPN
ejpam-5839	998	34	,	,	PUNCT
ejpam-5839	998	35	e	e	NOUN
ejpam-5839	998	36	)	)	PUNCT
ejpam-5839	998	37	is	be	AUX
ejpam-5839	998	38	a	a	DET
ejpam-5839	998	39	quadripartitioned	quadripartitione	VERB
ejpam-5839	998	40	neutrosophic	neutrosophic	ADJ
ejpam-5839	998	41	soft	soft	ADJ
ejpam-5839	998	42	base	base	NOUN
ejpam-5839	998	43	for	for	ADP
ejpam-5839	998	44	τqpnss	τqpns	NOUN
ejpam-5839	998	45	(	(	PUNCT
ejpam-5839	998	46	f̃	f̃	PROPN
ejpam-5839	998	47	,	,	PUNCT
ejpam-5839	998	48	e	e	NOUN
ejpam-5839	998	49	)	)	PUNCT
ejpam-5839	998	50	.	.	PUNCT
ejpam-5839	999	1	2	2	X
ejpam-5839	999	2	.	.	X
ejpam-5839	999	3	we	we	PRON
ejpam-5839	999	4	first	first	ADV
ejpam-5839	999	5	show	show	VERB
ejpam-5839	999	6	that	that	SCONJ
ejpam-5839	999	7	if	if	SCONJ
ejpam-5839	999	8	(	(	PUNCT
ejpam-5839	999	9	g̃,ω	g̃,ω	NOUN
ejpam-5839	999	10	)	)	PUNCT
ejpam-5839	999	11	is	be	AUX
ejpam-5839	999	12	a	a	DET
ejpam-5839	999	13	quadripartitioned	quadripartitione	VERB
ejpam-5839	999	14	neutrosophic	neutrosophic	ADJ
ejpam-5839	999	15	soft	soft	ADJ
ejpam-5839	999	16	p	p	NOUN
ejpam-5839	999	17	-	-	PUNCT
ejpam-5839	999	18	closed	close	VERB
ejpam-5839	999	19	set	set	NOUN
ejpam-5839	999	20	in	in	ADP
ejpam-5839	999	21	τqpnss	τqpns	NOUN
ejpam-5839	999	22	(	(	PUNCT
ejpam-5839	999	23	f̃	f̃	PROPN
ejpam-5839	999	24	,	,	PUNCT
ejpam-5839	999	25	e	e	NOUN
ejpam-5839	999	26	)	)	PUNCT
ejpam-5839	999	27	then	then	ADV
ejpam-5839	999	28	there	there	PRON
ejpam-5839	999	29	exists	exist	VERB
ejpam-5839	999	30	a	a	DET
ejpam-5839	999	31	p	p	NOUN
ejpam-5839	999	32	-	-	PUNCT
ejpam-5839	999	33	closed	closed	ADJ
ejpam-5839	999	34	set	set	NOUN
ejpam-5839	999	35	(	(	PUNCT
ejpam-5839	999	36	ṽ	ṽ	PROPN
ejpam-5839	999	37	,	,	PUNCT
ejpam-5839	999	38	ω	ω	NUM
ejpam-5839	999	39	)	)	PUNCT
ejpam-5839	999	40	⊆	⊆	NUM
ejpam-5839	999	41	(	(	PUNCT
ejpam-5839	999	42	k̃,ω	k̃,ω	NOUN
ejpam-5839	999	43	)	)	PUNCT
ejpam-5839	999	44	i.e.	i.e.	X
ejpam-5839	999	45	,	,	PUNCT
ejpam-5839	999	46	(	(	PUNCT
ejpam-5839	999	47	ṽ	ṽ	PROPN
ejpam-5839	999	48	,	,	PUNCT
ejpam-5839	999	49	ω	ω	PROPN
ejpam-5839	999	50	)	)	PUNCT
ejpam-5839	999	51	/∈	/∈	PUNCT
ejpam-5839	1000	1	τqpnss	τqpns	NOUN
ejpam-5839	1000	2	such	such	ADJ
ejpam-5839	1000	3	that	that	SCONJ
ejpam-5839	1000	4	(	(	PUNCT
ejpam-5839	1000	5	g̃,ω	g̃,ω	NOUN
ejpam-5839	1000	6	)	)	PUNCT
ejpam-5839	1000	7	=	=	SYM
ejpam-5839	1001	1	(	(	PUNCT
ejpam-5839	1001	2	ṽ	ṽ	PROPN
ejpam-5839	1001	3	,	,	PUNCT
ejpam-5839	1001	4	ω	ω	NOUN
ejpam-5839	1001	5	)	)	PUNCT
ejpam-5839	1001	6	∩	∩	NOUN
ejpam-5839	1001	7	(	(	PUNCT
ejpam-5839	1001	8	f̃	f̃	PROPN
ejpam-5839	1001	9	,	,	PUNCT
ejpam-5839	1001	10	ω	ω	PROPN
ejpam-5839	1001	11	)	)	PUNCT
ejpam-5839	1001	12	.	.	PUNCT
ejpam-5839	1002	1	let	let	VERB
ejpam-5839	1002	2	(	(	PUNCT
ejpam-5839	1002	3	g̃,ω	g̃,ω	PROPN
ejpam-5839	1002	4	)	)	PUNCT
ejpam-5839	1002	5	be	be	AUX
ejpam-5839	1002	6	p	p	NOUN
ejpam-5839	1002	7	-	-	PUNCT
ejpam-5839	1002	8	closed	closed	ADJ
ejpam-5839	1002	9	in	in	ADP
ejpam-5839	1002	10	τqpnss	τqpns	NOUN
ejpam-5839	1002	11	(	(	PUNCT
ejpam-5839	1002	12	f̃	f̃	PROPN
ejpam-5839	1002	13	,	,	PUNCT
ejpam-5839	1002	14	e	e	NOUN
ejpam-5839	1002	15	)	)	PUNCT
ejpam-5839	1002	16	.	.	PUNCT
ejpam-5839	1003	1	then	then	ADV
ejpam-5839	1003	2	(	(	PUNCT
ejpam-5839	1003	3	g̃i	g̃i	NOUN
ejpam-5839	1003	4	,	,	PUNCT
ejpam-5839	1003	5	ω	ω	NOUN
ejpam-5839	1003	6	)	)	PUNCT
ejpam-5839	1003	7	c	c	PROPN
ejpam-5839	1003	8	is	be	AUX
ejpam-5839	1003	9	a	a	DET
ejpam-5839	1003	10	quadripartitioned	quadripartitione	VERB
ejpam-5839	1003	11	neutrosophic	neutrosophic	ADJ
ejpam-5839	1003	12	soft	soft	ADJ
ejpam-5839	1003	13	p	p	NOUN
ejpam-5839	1003	14	-	-	PUNCT
ejpam-5839	1003	15	open	open	ADJ
ejpam-5839	1004	1	set	set	NOUN
ejpam-5839	1005	1	in	in	ADP
ejpam-5839	1005	2	τqpnss	τqpns	NOUN
ejpam-5839	1005	3	(	(	PUNCT
ejpam-5839	1005	4	f̃	f̃	PROPN
ejpam-5839	1005	5	,	,	PUNCT
ejpam-5839	1005	6	e	e	NOUN
ejpam-5839	1005	7	)	)	PUNCT
ejpam-5839	1005	8	,	,	PUNCT
ejpam-5839	1006	1	i.e.	i.e.	X
ejpam-5839	1006	2	,	,	PUNCT
ejpam-5839	1006	3	(	(	PUNCT
ejpam-5839	1006	4	g̃i	g̃i	NOUN
ejpam-5839	1006	5	,	,	PUNCT
ejpam-5839	1006	6	ω	ω	NOUN
ejpam-5839	1006	7	)	)	PUNCT
ejpam-5839	1006	8	c	c	NOUN
ejpam-5839	1006	9	can	can	AUX
ejpam-5839	1006	10	be	be	AUX
ejpam-5839	1006	11	written	write	VERB
ejpam-5839	1006	12	as	as	ADP
ejpam-5839	1006	13	(	(	PUNCT
ejpam-5839	1006	14	g̃′,ω)c	g̃′,ω)c	NOUN
ejpam-5839	1006	15	=	=	SYM
ejpam-5839	1006	16	(	(	PUNCT
ejpam-5839	1006	17	ũ	ũ	PROPN
ejpam-5839	1006	18	,	,	PUNCT
ejpam-5839	1006	19	ω	ω	NOUN
ejpam-5839	1006	20	)	)	PUNCT
ejpam-5839	1006	21	∩	∩	NOUN
ejpam-5839	1006	22	(	(	PUNCT
ejpam-5839	1006	23	f̃	f̃	PROPN
ejpam-5839	1006	24	,	,	PUNCT
ejpam-5839	1006	25	ω	ω	PROPN
ejpam-5839	1006	26	)	)	PUNCT
ejpam-5839	1006	27	,	,	PUNCT
ejpam-5839	1006	28	where	where	SCONJ
ejpam-5839	1006	29	(	(	PUNCT
ejpam-5839	1006	30	ũ	ũ	PROPN
ejpam-5839	1006	31	,	,	PUNCT
ejpam-5839	1006	32	ω	ω	NOUN
ejpam-5839	1006	33	)	)	PUNCT
ejpam-5839	1006	34	∈	∈	PROPN
ejpam-5839	1006	35	τqpnss	τqpns	NOUN
ejpam-5839	1006	36	.	.	PUNCT
ejpam-5839	1007	1	thus	thus	ADV
ejpam-5839	1007	2	,	,	PUNCT
ejpam-5839	1007	3	(	(	PUNCT
ejpam-5839	1007	4	(	(	PUNCT
ejpam-5839	1007	5	g̃′,ω)c)c	g̃′,ω)c)c	X
ejpam-5839	1007	6	=	=	SYM
ejpam-5839	1007	7	(	(	PUNCT
ejpam-5839	1007	8	f̃	f̃	PROPN
ejpam-5839	1007	9	,	,	PUNCT
ejpam-5839	1007	10	ω	ω	NOUN
ejpam-5839	1007	11	)	)	PUNCT
ejpam-5839	1007	12	∩	∩	NOUN
ejpam-5839	1007	13	(	(	PUNCT
ejpam-5839	1007	14	(	(	PUNCT
ejpam-5839	1007	15	ũ	ũ	PROPN
ejpam-5839	1007	16	,	,	PUNCT
ejpam-5839	1007	17	ω	ω	NOUN
ejpam-5839	1007	18	)	)	PUNCT
ejpam-5839	1007	19	∩	∩	NOUN
ejpam-5839	1007	20	(	(	PUNCT
ejpam-5839	1007	21	f̃	f̃	PROPN
ejpam-5839	1007	22	,	,	PUNCT
ejpam-5839	1007	23	ω))c	ω))c	NOUN
ejpam-5839	1007	24	=	=	SYM
ejpam-5839	1007	25	(	(	PUNCT
ejpam-5839	1007	26	ũ	ũ	PROPN
ejpam-5839	1007	27	′,ω)c	′,ω)c	PROPN
ejpam-5839	1007	28	∩	∩	NOUN
ejpam-5839	1007	29	(	(	PUNCT
ejpam-5839	1007	30	f̃	f̃	PROPN
ejpam-5839	1007	31	,	,	PUNCT
ejpam-5839	1007	32	ω	ω	PROPN
ejpam-5839	1007	33	)	)	PUNCT
ejpam-5839	1007	34	.	.	PUNCT
ejpam-5839	1008	1	here	here	ADV
ejpam-5839	1008	2	,	,	PUNCT
ejpam-5839	1008	3	(	(	PUNCT
ejpam-5839	1008	4	ũ	ũ	PROPN
ejpam-5839	1008	5	,	,	PUNCT
ejpam-5839	1008	6	ω)c	ω)c	NOUN
ejpam-5839	1008	7	is	be	AUX
ejpam-5839	1008	8	p	p	NOUN
ejpam-5839	1008	9	-	-	PUNCT
ejpam-5839	1008	10	closed	closed	ADJ
ejpam-5839	1008	11	in	in	ADP
ejpam-5839	1008	12	τqpnss	τqpns	NOUN
ejpam-5839	1008	13	.	.	PUNCT
ejpam-5839	1009	1	so	so	ADV
ejpam-5839	1009	2	,	,	PUNCT
ejpam-5839	1009	3	it	it	PRON
ejpam-5839	1009	4	acts	act	VERB
ejpam-5839	1009	5	as	as	ADP
ejpam-5839	1009	6	(	(	PUNCT
ejpam-5839	1009	7	ṽ	ṽ	PROPN
ejpam-5839	1009	8	,	,	PUNCT
ejpam-5839	1009	9	ω	ω	NUM
ejpam-5839	1009	10	)	)	PUNCT
ejpam-5839	1009	11	⊆	⊆	NUM
ejpam-5839	1009	12	(	(	PUNCT
ejpam-5839	1009	13	k̃,ω	k̃,ω	NOUN
ejpam-5839	1009	14	)	)	PUNCT
ejpam-5839	1009	15	.	.	PUNCT
ejpam-5839	1010	1	conversely	conversely	ADV
ejpam-5839	1010	2	,	,	PUNCT
ejpam-5839	1010	3	suppose	suppose	VERB
ejpam-5839	1010	4	that	that	SCONJ
ejpam-5839	1010	5	(	(	PUNCT
ejpam-5839	1010	6	g̃,ω	g̃,ω	NOUN
ejpam-5839	1010	7	)	)	PUNCT
ejpam-5839	1010	8	=	=	SYM
ejpam-5839	1010	9	(	(	PUNCT
ejpam-5839	1010	10	ṽ	ṽ	PROPN
ejpam-5839	1010	11	,	,	PUNCT
ejpam-5839	1010	12	ω	ω	NOUN
ejpam-5839	1010	13	)	)	PUNCT
ejpam-5839	1010	14	∩	∩	NOUN
ejpam-5839	1010	15	(	(	PUNCT
ejpam-5839	1010	16	f̃	f̃	PROPN
ejpam-5839	1010	17	,	,	PUNCT
ejpam-5839	1010	18	ω	ω	PROPN
ejpam-5839	1010	19	)	)	PUNCT
ejpam-5839	1010	20	,	,	PUNCT
ejpam-5839	1010	21	where	where	SCONJ
ejpam-5839	1010	22	(	(	PUNCT
ejpam-5839	1010	23	f̃	f̃	PROPN
ejpam-5839	1010	24	,	,	PUNCT
ejpam-5839	1010	25	ω	ω	NUM
ejpam-5839	1010	26	)	)	PUNCT
ejpam-5839	1010	27	⊆	⊆	NUM
ejpam-5839	1010	28	(	(	PUNCT
ejpam-5839	1010	29	k̃,ω	k̃,ω	NOUN
ejpam-5839	1010	30	)	)	PUNCT
ejpam-5839	1010	31	and	and	CCONJ
ejpam-5839	1010	32	(	(	PUNCT
ejpam-5839	1010	33	ṽ	ṽ	PROPN
ejpam-5839	1010	34	,	,	PUNCT
ejpam-5839	1010	35	ω	ω	PROPN
ejpam-5839	1010	36	)	)	PUNCT
ejpam-5839	1010	37	is	be	AUX
ejpam-5839	1010	38	p	p	NOUN
ejpam-5839	1010	39	-	-	PUNCT
ejpam-5839	1010	40	closed	closed	ADJ
ejpam-5839	1010	41	in	in	ADP
ejpam-5839	1010	42	τqpnss	τqpnss	PROPN
ejpam-5839	1010	43	(	(	PUNCT
ejpam-5839	1010	44	k̃,e	k̃,e	PROPN
ejpam-5839	1010	45	)	)	PUNCT
ejpam-5839	1010	46	.	.	PUNCT
ejpam-5839	1011	1	clearly	clearly	ADV
ejpam-5839	1011	2	,	,	PUNCT
ejpam-5839	1011	3	(	(	PUNCT
ejpam-5839	1011	4	ṽ	ṽ	PROPN
ejpam-5839	1011	5	,	,	PUNCT
ejpam-5839	1011	6	ω)c	ω)c	NOUN
ejpam-5839	1011	7	∈	∈	PROPN
ejpam-5839	1011	8	τqpnss	τqpns	NOUN
ejpam-5839	1011	9	,	,	PUNCT
ejpam-5839	1011	10	so	so	SCONJ
ejpam-5839	1011	11	that	that	SCONJ
ejpam-5839	1011	12	(	(	PUNCT
ejpam-5839	1011	13	ṽ	ṽ	NOUN
ejpam-5839	1011	14	,	,	PUNCT
ejpam-5839	1011	15	ω)c	ω)c	ADJ
ejpam-5839	1011	16	∩	∩	NOUN
ejpam-5839	1011	17	(	(	PUNCT
ejpam-5839	1011	18	f̃	f̃	PROPN
ejpam-5839	1011	19	,	,	PUNCT
ejpam-5839	1011	20	ω	ω	NUM
ejpam-5839	1011	21	)	)	PUNCT
ejpam-5839	1011	22	∈	∈	PROPN
ejpam-5839	1011	23	τqpnss(k̃	τqpnss(k̃	NOUN
ejpam-5839	1011	24	,	,	PUNCT
ejpam-5839	1011	25	e	e	NOUN
ejpam-5839	1011	26	)	)	PUNCT
ejpam-5839	1011	27	.	.	PUNCT
ejpam-5839	1012	1	a.	a.	PROPN
ejpam-5839	1012	2	shihadeh	shihadeh	VERB
ejpam-5839	1012	3	et	et	PROPN
ejpam-5839	1012	4	al	al	PROPN
ejpam-5839	1012	5	.	.	PUNCT
ejpam-5839	1012	6	/	/	SYM
ejpam-5839	1012	7	eur	eur	PROPN
ejpam-5839	1012	8	.	.	PUNCT
ejpam-5839	1013	1	j.	j.	PROPN
ejpam-5839	1013	2	pure	pure	PROPN
ejpam-5839	1013	3	appl	appl	PROPN
ejpam-5839	1013	4	.	.	PROPN
ejpam-5839	1013	5	math	math	PROPN
ejpam-5839	1013	6	,	,	PUNCT
ejpam-5839	1013	7	18	18	NUM
ejpam-5839	1013	8	(	(	PUNCT
ejpam-5839	1013	9	2	2	NUM
ejpam-5839	1013	10	)	)	PUNCT
ejpam-5839	1013	11	(	(	PUNCT
ejpam-5839	1013	12	2025	2025	NUM
ejpam-5839	1013	13	)	)	PUNCT
ejpam-5839	1013	14	,	,	PUNCT
ejpam-5839	1013	15	5839	5839	NUM
ejpam-5839	1013	16	44	44	NUM
ejpam-5839	1013	17	of	of	ADP
ejpam-5839	1013	18	54	54	NUM
ejpam-5839	1013	19	now	now	ADV
ejpam-5839	1013	20	,	,	PUNCT
ejpam-5839	1013	21	(	(	PUNCT
ejpam-5839	1013	22	ṽ	ṽ	PROPN
ejpam-5839	1013	23	,	,	PUNCT
ejpam-5839	1013	24	ω)c	ω)c	ADJ
ejpam-5839	1013	25	∩	∩	NOUN
ejpam-5839	1013	26	(	(	PUNCT
ejpam-5839	1013	27	f̃	f̃	PROPN
ejpam-5839	1013	28	,	,	PUNCT
ejpam-5839	1013	29	ω	ω	NOUN
ejpam-5839	1013	30	)	)	PUNCT
ejpam-5839	1013	31	=	=	SYM
ejpam-5839	1013	32	(	(	PUNCT
ejpam-5839	1013	33	(	(	PUNCT
ejpam-5839	1013	34	k̃,ω	k̃,ω	NOUN
ejpam-5839	1013	35	)	)	PUNCT
ejpam-5839	1013	36	\	\	PUNCT
ejpam-5839	1014	1	(	(	PUNCT
ejpam-5839	1014	2	ṽ	ṽ	PROPN
ejpam-5839	1014	3	,	,	PUNCT
ejpam-5839	1014	4	ω	ω	NOUN
ejpam-5839	1014	5	)	)	PUNCT
ejpam-5839	1014	6	)	)	PUNCT
ejpam-5839	1014	7	∩	∩	NOUN
ejpam-5839	1014	8	(	(	PUNCT
ejpam-5839	1014	9	f̃	f̃	PROPN
ejpam-5839	1014	10	,	,	PUNCT
ejpam-5839	1014	11	ω	ω	NOUN
ejpam-5839	1014	12	)	)	PUNCT
ejpam-5839	1014	13	=	=	SYM
ejpam-5839	1014	14	(	(	PUNCT
ejpam-5839	1014	15	(	(	PUNCT
ejpam-5839	1014	16	k̃,ω	k̃,ω	NOUN
ejpam-5839	1014	17	)	)	PUNCT
ejpam-5839	1014	18	∩	∩	NOUN
ejpam-5839	1014	19	(	(	PUNCT
ejpam-5839	1014	20	f̃	f̃	PROPN
ejpam-5839	1014	21	,	,	PUNCT
ejpam-5839	1014	22	ω	ω	NOUN
ejpam-5839	1014	23	)	)	PUNCT
ejpam-5839	1014	24	)	)	PUNCT
ejpam-5839	1014	25	\	\	PUNCT
ejpam-5839	1015	1	(	(	PUNCT
ejpam-5839	1015	2	(	(	PUNCT
ejpam-5839	1015	3	ṽ	ṽ	PROPN
ejpam-5839	1015	4	,	,	PUNCT
ejpam-5839	1015	5	ω	ω	NOUN
ejpam-5839	1015	6	)	)	PUNCT
ejpam-5839	1015	7	∩	∩	NOUN
ejpam-5839	1015	8	(	(	PUNCT
ejpam-5839	1015	9	f̃	f̃	PROPN
ejpam-5839	1015	10	,	,	PUNCT
ejpam-5839	1015	11	ω	ω	NOUN
ejpam-5839	1015	12	)	)	PUNCT
ejpam-5839	1015	13	)	)	PUNCT
ejpam-5839	1016	1	=	=	SYM
ejpam-5839	1016	2	(	(	PUNCT
ejpam-5839	1016	3	f̃	f̃	PROPN
ejpam-5839	1016	4	,	,	PUNCT
ejpam-5839	1016	5	ω	ω	NUM
ejpam-5839	1016	6	)	)	PUNCT
ejpam-5839	1016	7	\	\	PUNCT
ejpam-5839	1016	8	(	(	PUNCT
ejpam-5839	1016	9	g̃,ω	g̃,ω	PROPN
ejpam-5839	1016	10	)	)	PUNCT
ejpam-5839	1016	11	.	.	PUNCT
ejpam-5839	1017	1	this	this	PRON
ejpam-5839	1017	2	implies	imply	VERB
ejpam-5839	1017	3	that	that	SCONJ
ejpam-5839	1017	4	(	(	PUNCT
ejpam-5839	1017	5	f̃	f̃	PROPN
ejpam-5839	1017	6	,	,	PUNCT
ejpam-5839	1017	7	ω	ω	NUM
ejpam-5839	1017	8	)	)	PUNCT
ejpam-5839	1017	9	\	\	PUNCT
ejpam-5839	1017	10	(	(	PUNCT
ejpam-5839	1017	11	g̃,ω	g̃,ω	PROPN
ejpam-5839	1017	12	)	)	PUNCT
ejpam-5839	1017	13	is	be	AUX
ejpam-5839	1017	14	a	a	DET
ejpam-5839	1017	15	quadripartitioned	quadripartitione	VERB
ejpam-5839	1017	16	neutrosophic	neutrosophic	ADJ
ejpam-5839	1017	17	soft	soft	ADJ
ejpam-5839	1017	18	set	set	NOUN
ejpam-5839	1017	19	in	in	ADP
ejpam-5839	1017	20	(	(	PUNCT
ejpam-5839	1017	21	f̃	f̃	PROPN
ejpam-5839	1017	22	,	,	PUNCT
ejpam-5839	1017	23	ω	ω	PROPN
ejpam-5839	1017	24	)	)	PUNCT
ejpam-5839	1017	25	,	,	PUNCT
ejpam-5839	1017	26	i.e.	i.e.	X
ejpam-5839	1017	27	,	,	PUNCT
ejpam-5839	1017	28	(	(	PUNCT
ejpam-5839	1017	29	g̃,ω	g̃,ω	PROPN
ejpam-5839	1017	30	)	)	PUNCT
ejpam-5839	1017	31	is	be	AUX
ejpam-5839	1017	32	a	a	DET
ejpam-5839	1017	33	neutrosophic	neutrosophic	ADJ
ejpam-5839	1017	34	soft	soft	ADJ
ejpam-5839	1017	35	p	p	NOUN
ejpam-5839	1017	36	-	-	PUNCT
ejpam-5839	1017	37	closed	close	VERB
ejpam-5839	1017	38	set	set	NOUN
ejpam-5839	1017	39	in	in	ADP
ejpam-5839	1017	40	τqpnss	τqpnss	PROPN
ejpam-5839	1017	41	(	(	PUNCT
ejpam-5839	1017	42	k̃,e	k̃,e	PROPN
ejpam-5839	1017	43	)	)	PUNCT
ejpam-5839	1017	44	.	.	PUNCT
ejpam-5839	1018	1	⋂	⋂	PROPN
ejpam-5839	1018	2	{	{	PUNCT
ejpam-5839	1018	3	(	(	PUNCT
ejpam-5839	1018	4	g̃i	g̃i	PROPN
ejpam-5839	1018	5	,	,	PUNCT
ejpam-5839	1018	6	ω	ω	NOUN
ejpam-5839	1018	7	)	)	PUNCT
ejpam-5839	1019	1	|	|	CCONJ
ejpam-5839	1019	2	(	(	PUNCT
ejpam-5839	1019	3	g̃i	g̃i	NOUN
ejpam-5839	1019	4	,	,	PUNCT
ejpam-5839	1019	5	ω	ω	NOUN
ejpam-5839	1019	6	)	)	PUNCT
ejpam-5839	1019	7	is	be	AUX
ejpam-5839	1019	8	closed	close	VERB
ejpam-5839	1019	9	and	and	CCONJ
ejpam-5839	1019	10	(	(	PUNCT
ejpam-5839	1019	11	g̃i	g̃i	PROPN
ejpam-5839	1019	12	,	,	PUNCT
ejpam-5839	1019	13	ω	ω	NOUN
ejpam-5839	1019	14	)	)	PUNCT
ejpam-5839	1019	15	⊇	⊇	NOUN
ejpam-5839	1019	16	(	(	PUNCT
ejpam-5839	1019	17	g̃,ω	g̃,ω	PROPN
ejpam-5839	1019	18	)	)	PUNCT
ejpam-5839	1019	19	}	}	PUNCT
ejpam-5839	1019	20	is	be	AUX
ejpam-5839	1019	21	the	the	DET
ejpam-5839	1019	22	quadripartitioned	quadripartitione	VERB
ejpam-5839	1019	23	neutrosophic	neutrosophic	ADJ
ejpam-5839	1019	24	soft	soft	ADJ
ejpam-5839	1019	25	closure	closure	NOUN
ejpam-5839	1019	26	of	of	ADP
ejpam-5839	1019	27	(	(	PUNCT
ejpam-5839	1019	28	g̃,ω	g̃,ω	NOUN
ejpam-5839	1019	29	)	)	PUNCT
ejpam-5839	1019	30	and	and	CCONJ
ejpam-5839	1019	31	so	so	ADV
ejpam-5839	1019	32	(	(	PUNCT
ejpam-5839	1019	33	g̃,ω	g̃,ω	PROPN
ejpam-5839	1019	34	)	)	PUNCT
ejpam-5839	1019	35	is	be	AUX
ejpam-5839	1019	36	a	a	DET
ejpam-5839	1019	37	quadripartitioned	quadripartitione	VERB
ejpam-5839	1019	38	neutrosophic	neutrosophic	ADJ
ejpam-5839	1019	39	soft	soft	ADJ
ejpam-5839	1019	40	p	p	NOUN
ejpam-5839	1019	41	-	-	PUNCT
ejpam-5839	1019	42	closed	close	VERB
ejpam-5839	1019	43	set	set	NOUN
ejpam-5839	1019	44	.	.	PUNCT
ejpam-5839	1020	1	now	now	ADV
ejpam-5839	1020	2	,	,	PUNCT
ejpam-5839	1020	3	(	(	PUNCT
ejpam-5839	1020	4	g̃,ω	g̃,ω	NOUN
ejpam-5839	1020	5	)	)	PUNCT
ejpam-5839	1020	6	∩	∩	NOUN
ejpam-5839	1020	7	(	(	PUNCT
ejpam-5839	1020	8	f̃	f̃	PROPN
ejpam-5839	1020	9	,	,	PUNCT
ejpam-5839	1020	10	ω	ω	NUM
ejpam-5839	1020	11	)	)	PUNCT
ejpam-5839	1020	12	=	=	SYM
ejpam-5839	1020	13	⋂	⋂	PROPN
ejpam-5839	1020	14	{	{	PUNCT
ejpam-5839	1020	15	(	(	PUNCT
ejpam-5839	1020	16	g̃i	g̃i	PROPN
ejpam-5839	1020	17	,	,	PUNCT
ejpam-5839	1020	18	ω	ω	NOUN
ejpam-5839	1020	19	)	)	PUNCT
ejpam-5839	1021	1	|	|	CCONJ
ejpam-5839	1021	2	(	(	PUNCT
ejpam-5839	1021	3	g̃i	g̃i	NOUN
ejpam-5839	1021	4	,	,	PUNCT
ejpam-5839	1021	5	ω	ω	NOUN
ejpam-5839	1021	6	)	)	PUNCT
ejpam-5839	1021	7	is	be	AUX
ejpam-5839	1021	8	closed	close	VERB
ejpam-5839	1021	9	and	and	CCONJ
ejpam-5839	1021	10	(	(	PUNCT
ejpam-5839	1021	11	g̃i	g̃i	PROPN
ejpam-5839	1021	12	,	,	PUNCT
ejpam-5839	1021	13	ω	ω	NOUN
ejpam-5839	1021	14	)	)	PUNCT
ejpam-5839	1021	15	⊇	⊇	NOUN
ejpam-5839	1021	16	(	(	PUNCT
ejpam-5839	1021	17	g̃,ω	g̃,ω	PROPN
ejpam-5839	1021	18	)	)	PUNCT
ejpam-5839	1021	19	}	}	PUNCT
ejpam-5839	1021	20	∩	∩	NOUN
ejpam-5839	1021	21	(	(	PUNCT
ejpam-5839	1021	22	f̃	f̃	PROPN
ejpam-5839	1021	23	,	,	PUNCT
ejpam-5839	1021	24	ω	ω	NUM
ejpam-5839	1021	25	)	)	PUNCT
ejpam-5839	1021	26	=	=	SYM
ejpam-5839	1021	27	⋂	⋂	PROPN
ejpam-5839	1021	28	(	(	PUNCT
ejpam-5839	1021	29	(	(	PUNCT
ejpam-5839	1021	30	g̃i	g̃i	NOUN
ejpam-5839	1021	31	,	,	PUNCT
ejpam-5839	1021	32	ω	ω	NOUN
ejpam-5839	1021	33	)	)	PUNCT
ejpam-5839	1021	34	∩	∩	NOUN
ejpam-5839	1021	35	(	(	PUNCT
ejpam-5839	1021	36	f̃	f̃	PROPN
ejpam-5839	1021	37	,	,	PUNCT
ejpam-5839	1021	38	ω	ω	NOUN
ejpam-5839	1021	39	)	)	PUNCT
ejpam-5839	1021	40	)	)	PUNCT
ejpam-5839	1021	41	.	.	PUNCT
ejpam-5839	1022	1	since	since	SCONJ
ejpam-5839	1022	2	each	each	PRON
ejpam-5839	1022	3	(	(	PUNCT
ejpam-5839	1022	4	g̃i	g̃i	PROPN
ejpam-5839	1022	5	,	,	PUNCT
ejpam-5839	1022	6	ω	ω	NOUN
ejpam-5839	1022	7	)	)	PUNCT
ejpam-5839	1022	8	is	be	AUX
ejpam-5839	1022	9	p	p	NOUN
ejpam-5839	1022	10	-	-	PUNCT
ejpam-5839	1022	11	closed	closed	ADJ
ejpam-5839	1022	12	,	,	PUNCT
ejpam-5839	1022	13	then	then	ADV
ejpam-5839	1022	14	each	each	DET
ejpam-5839	1022	15	(	(	PUNCT
ejpam-5839	1022	16	g̃i	g̃i	PROPN
ejpam-5839	1022	17	,	,	PUNCT
ejpam-5839	1022	18	ω	ω	NOUN
ejpam-5839	1022	19	)	)	PUNCT
ejpam-5839	1022	20	∩	∩	NOUN
ejpam-5839	1022	21	(	(	PUNCT
ejpam-5839	1022	22	f̃	f̃	PROPN
ejpam-5839	1022	23	,	,	PUNCT
ejpam-5839	1022	24	ω	ω	NUM
ejpam-5839	1022	25	)	)	PUNCT
ejpam-5839	1022	26	is	be	AUX
ejpam-5839	1022	27	p	p	NOUN
ejpam-5839	1022	28	-	-	PUNCT
ejpam-5839	1022	29	closed	closed	ADJ
ejpam-5839	1022	30	in	in	ADP
ejpam-5839	1022	31	τqpnss	τqpns	NOUN
ejpam-5839	1022	32	(	(	PUNCT
ejpam-5839	1022	33	f̃	f̃	PROPN
ejpam-5839	1022	34	,	,	PUNCT
ejpam-5839	1022	35	e	e	NOUN
ejpam-5839	1022	36	)	)	PUNCT
ejpam-5839	1022	37	.	.	PUNCT
ejpam-5839	1023	1	now	now	ADV
ejpam-5839	1023	2	,	,	PUNCT
ejpam-5839	1023	3	(	(	PUNCT
ejpam-5839	1023	4	g	g	NOUN
ejpam-5839	1023	5	,	,	PUNCT
ejpam-5839	1023	6	ω	ω	NOUN
ejpam-5839	1023	7	)	)	PUNCT
ejpam-5839	1023	8	⊆	⊆	NUM
ejpam-5839	1023	9	(	(	PUNCT
ejpam-5839	1023	10	g̃i	g̃i	NOUN
ejpam-5839	1023	11	,	,	PUNCT
ejpam-5839	1023	12	ω	ω	NOUN
ejpam-5839	1023	13	)	)	PUNCT
ejpam-5839	1023	14	and	and	CCONJ
ejpam-5839	1023	15	(	(	PUNCT
ejpam-5839	1023	16	g	g	PROPN
ejpam-5839	1023	17	,	,	PUNCT
ejpam-5839	1023	18	ω	ω	NOUN
ejpam-5839	1023	19	)	)	PUNCT
ejpam-5839	1023	20	⊆	⊆	NUM
ejpam-5839	1023	21	(	(	PUNCT
ejpam-5839	1023	22	f̃	f̃	PROPN
ejpam-5839	1023	23	,	,	PUNCT
ejpam-5839	1023	24	ω	ω	PROPN
ejpam-5839	1023	25	)	)	PUNCT
ejpam-5839	1023	26	.	.	PUNCT
ejpam-5839	1024	1	so	so	ADV
ejpam-5839	1024	2	,	,	PUNCT
ejpam-5839	1024	3	(	(	PUNCT
ejpam-5839	1024	4	g̃,ω	g̃,ω	NOUN
ejpam-5839	1024	5	)	)	PUNCT
ejpam-5839	1024	6	∩	∩	NOUN
ejpam-5839	1024	7	(	(	PUNCT
ejpam-5839	1024	8	f̃	f̃	PROPN
ejpam-5839	1024	9	,	,	PUNCT
ejpam-5839	1024	10	ω	ω	NUM
ejpam-5839	1024	11	)	)	PUNCT
ejpam-5839	1024	12	⊆	⊆	NUM
ejpam-5839	1024	13	(	(	PUNCT
ejpam-5839	1024	14	g̃i	g̃i	NOUN
ejpam-5839	1024	15	,	,	PUNCT
ejpam-5839	1024	16	ω	ω	NOUN
ejpam-5839	1024	17	)	)	PUNCT
ejpam-5839	1024	18	∩	∩	NOUN
ejpam-5839	1024	19	(	(	PUNCT
ejpam-5839	1024	20	f̃	f̃	PROPN
ejpam-5839	1024	21	,	,	PUNCT
ejpam-5839	1024	22	ω	ω	NOUN
ejpam-5839	1024	23	)	)	PUNCT
ejpam-5839	1024	24	⇒	⇒	NOUN
ejpam-5839	1024	25	(	(	PUNCT
ejpam-5839	1024	26	g̃,ω	g̃,ω	PROPN
ejpam-5839	1024	27	)	)	PUNCT
ejpam-5839	1024	28	⊆	⊆	NUM
ejpam-5839	1024	29	(	(	PUNCT
ejpam-5839	1024	30	g̃i	g̃i	NOUN
ejpam-5839	1024	31	,	,	PUNCT
ejpam-5839	1024	32	ω	ω	NOUN
ejpam-5839	1024	33	)	)	PUNCT
ejpam-5839	1024	34	∩	∩	NOUN
ejpam-5839	1024	35	(	(	PUNCT
ejpam-5839	1024	36	f̃	f̃	PROPN
ejpam-5839	1024	37	,	,	PUNCT
ejpam-5839	1024	38	ω	ω	PROPN
ejpam-5839	1024	39	)	)	PUNCT
ejpam-5839	1024	40	.	.	PUNCT
ejpam-5839	1025	1	therefore	therefore	ADV
ejpam-5839	1025	2	,	,	PUNCT
ejpam-5839	1025	3	(	(	PUNCT
ejpam-5839	1025	4	g̃,ω)∩(f̃	g̃,ω)∩(f̃	PROPN
ejpam-5839	1025	5	,	,	PUNCT
ejpam-5839	1025	6	ω	ω	NOUN
ejpam-5839	1025	7	)	)	PUNCT
ejpam-5839	1025	8	=	=	SYM
ejpam-5839	1025	9	⋂	⋂	PROPN
ejpam-5839	1025	10	{	{	PUNCT
ejpam-5839	1025	11	(	(	PUNCT
ejpam-5839	1025	12	g̃i	g̃i	NOUN
ejpam-5839	1025	13	,	,	PUNCT
ejpam-5839	1025	14	ω)∩(f̃	ω)∩(f̃	PROPN
ejpam-5839	1025	15	,	,	PUNCT
ejpam-5839	1025	16	ω	ω	NUM
ejpam-5839	1025	17	)	)	PUNCT
ejpam-5839	1025	18	|	|	CCONJ
ejpam-5839	1025	19	(	(	PUNCT
ejpam-5839	1025	20	g̃i	g̃i	NOUN
ejpam-5839	1025	21	,	,	PUNCT
ejpam-5839	1025	22	ω)∩(f̃	ω)∩(f̃	PROPN
ejpam-5839	1025	23	,	,	PUNCT
ejpam-5839	1025	24	ω	ω	NUM
ejpam-5839	1025	25	)	)	PUNCT
ejpam-5839	1025	26	is	be	AUX
ejpam-5839	1025	27	p	p	NOUN
ejpam-5839	1025	28	-	-	PUNCT
ejpam-5839	1025	29	closed	close	VERB
ejpam-5839	1025	30	and	and	CCONJ
ejpam-5839	1025	31	(	(	PUNCT
ejpam-5839	1025	32	g̃i	g̃i	NOUN
ejpam-5839	1025	33	,	,	PUNCT
ejpam-5839	1025	34	ω)∩(f̃	ω)∩(f̃	PROPN
ejpam-5839	1025	35	,	,	PUNCT
ejpam-5839	1025	36	ω	ω	NUM
ejpam-5839	1025	37	)	)	PUNCT
ejpam-5839	1025	38	⊇	⊇	NOUN
ejpam-5839	1025	39	(	(	PUNCT
ejpam-5839	1025	40	g̃i	g̃i	NOUN
ejpam-5839	1025	41	,	,	PUNCT
ejpam-5839	1025	42	ω	ω	NOUN
ejpam-5839	1025	43	)	)	PUNCT
ejpam-5839	1025	44	}	}	PUNCT
ejpam-5839	1025	45	.	.	PUNCT
ejpam-5839	1026	1	thus	thus	ADV
ejpam-5839	1026	2	,	,	PUNCT
ejpam-5839	1026	3	(	(	PUNCT
ejpam-5839	1026	4	g̃,ω	g̃,ω	NOUN
ejpam-5839	1026	5	)	)	PUNCT
ejpam-5839	1026	6	∩	∩	NOUN
ejpam-5839	1026	7	(	(	PUNCT
ejpam-5839	1026	8	f̃	f̃	PROPN
ejpam-5839	1026	9	,	,	PUNCT
ejpam-5839	1026	10	ω	ω	PROPN
ejpam-5839	1026	11	)	)	PUNCT
ejpam-5839	1026	12	is	be	AUX
ejpam-5839	1026	13	a	a	DET
ejpam-5839	1026	14	quadripartitioned	quadripartitione	VERB
ejpam-5839	1026	15	neutrosophic	neutrosophic	ADJ
ejpam-5839	1026	16	soft	soft	ADJ
ejpam-5839	1026	17	closure	closure	NOUN
ejpam-5839	1026	18	of	of	ADP
ejpam-5839	1026	19	(	(	PUNCT
ejpam-5839	1026	20	g̃,ω	g̃,ω	PROPN
ejpam-5839	1026	21	)	)	PUNCT
ejpam-5839	1026	22	in	in	ADP
ejpam-5839	1026	23	τqpnss	τqpnss	PROPN
ejpam-5839	1026	24	(	(	PUNCT
ejpam-5839	1026	25	f̃	f̃	PROPN
ejpam-5839	1026	26	,	,	PUNCT
ejpam-5839	1026	27	e	e	NOUN
ejpam-5839	1026	28	)	)	PUNCT
ejpam-5839	1026	29	.	.	PUNCT
ejpam-5839	1027	1	theorem	theorem	NOUN
ejpam-5839	1027	2	21	21	NUM
ejpam-5839	1027	3	.	.	PUNCT
ejpam-5839	1028	1	let	let	AUX
ejpam-5839	1028	2	(	(	PUNCT
ejpam-5839	1028	3	x(f̃	x(f̃	X
ejpam-5839	1028	4	,	,	PUNCT
ejpam-5839	1028	5	e	e	NOUN
ejpam-5839	1028	6	)	)	PUNCT
ejpam-5839	1028	7	,	,	PUNCT
ejpam-5839	1028	8	τqpnss	τqpnss	PROPN
ejpam-5839	1028	9	,	,	PUNCT
ejpam-5839	1028	10	ω	ω	PROPN
ejpam-5839	1028	11	)	)	PUNCT
ejpam-5839	1028	12	be	be	VERB
ejpam-5839	1028	13	a	a	DET
ejpam-5839	1028	14	quadripartitioned	quadripartitione	VERB
ejpam-5839	1028	15	neutrosophic	neutrosophic	ADJ
ejpam-5839	1028	16	soft	soft	ADJ
ejpam-5839	1028	17	subspace	subspace	NOUN
ejpam-5839	1028	18	of	of	ADP
ejpam-5839	1028	19	a	a	DET
ejpam-5839	1028	20	quadripartitioned	quadripartitione	VERB
ejpam-5839	1028	21	neutrosophic	neutrosophic	ADJ
ejpam-5839	1028	22	soft	soft	ADJ
ejpam-5839	1028	23	topological	topological	ADJ
ejpam-5839	1028	24	space	space	NOUN
ejpam-5839	1028	25	(	(	PUNCT
ejpam-5839	1028	26	x	x	NOUN
ejpam-5839	1028	27	,	,	PUNCT
ejpam-5839	1028	28	τqpnss	τqpns	NOUN
ejpam-5839	1028	29	,	,	PUNCT
ejpam-5839	1028	30	e	e	NOUN
ejpam-5839	1028	31	)	)	PUNCT
ejpam-5839	1028	32	over	over	ADP
ejpam-5839	1028	33	x.	x.	NOUN
ejpam-5839	1029	1	if	if	SCONJ
ejpam-5839	1029	2	(	(	PUNCT
ejpam-5839	1029	3	f̃	f̃	PROPN
ejpam-5839	1029	4	,	,	PUNCT
ejpam-5839	1029	5	ω	ω	PROPN
ejpam-5839	1029	6	)	)	PUNCT
ejpam-5839	1029	7	is	be	AUX
ejpam-5839	1029	8	a	a	DET
ejpam-5839	1029	9	quadripartitioned	quadripartitione	VERB
ejpam-5839	1029	10	neutrosophic	neutrosophic	ADJ
ejpam-5839	1029	11	soft	soft	ADJ
ejpam-5839	1029	12	p	p	NOUN
ejpam-5839	1029	13	-	-	PUNCT
ejpam-5839	1029	14	open	open	ADJ
ejpam-5839	1030	1	set	set	NOUN
ejpam-5839	1031	1	in	in	ADP
ejpam-5839	1031	2	(	(	PUNCT
ejpam-5839	1031	3	x	x	NOUN
ejpam-5839	1031	4	,	,	PUNCT
ejpam-5839	1031	5	τqpnss	τqpns	NOUN
ejpam-5839	1031	6	,	,	PUNCT
ejpam-5839	1031	7	e	e	NOUN
ejpam-5839	1031	8	)	)	PUNCT
ejpam-5839	1031	9	if	if	SCONJ
ejpam-5839	1031	10	and	and	CCONJ
ejpam-5839	1031	11	only	only	ADV
ejpam-5839	1031	12	if	if	SCONJ
ejpam-5839	1031	13	(	(	PUNCT
ejpam-5839	1031	14	f̃1,ω	f̃1,ω	NOUN
ejpam-5839	1031	15	)	)	PUNCT
ejpam-5839	1031	16	is	be	AUX
ejpam-5839	1031	17	a	a	DET
ejpam-5839	1031	18	quadripartitioned	quadripartitione	VERB
ejpam-5839	1031	19	neutrosophic	neutrosophic	ADJ
ejpam-5839	1031	20	soft	soft	ADJ
ejpam-5839	1031	21	p	p	NOUN
ejpam-5839	1031	22	-	-	PUNCT
ejpam-5839	1031	23	open	open	ADJ
ejpam-5839	1032	1	set	set	NOUN
ejpam-5839	1033	1	in	in	ADP
ejpam-5839	1033	2	(	(	PUNCT
ejpam-5839	1033	3	x	x	NOUN
ejpam-5839	1033	4	,	,	PUNCT
ejpam-5839	1033	5	τqpnss	τqpnss	PROPN
ejpam-5839	1033	6	,	,	PUNCT
ejpam-5839	1033	7	ω	ω	PROPN
ejpam-5839	1033	8	)	)	PUNCT
ejpam-5839	1033	9	.	.	PUNCT
ejpam-5839	1034	1	proof	proof	NOUN
ejpam-5839	1034	2	.	.	PUNCT
ejpam-5839	1035	1	suppose	suppose	VERB
ejpam-5839	1035	2	that	that	SCONJ
ejpam-5839	1035	3	(	(	PUNCT
ejpam-5839	1035	4	f̃	f̃	PROPN
ejpam-5839	1035	5	,	,	PUNCT
ejpam-5839	1035	6	ω	ω	PROPN
ejpam-5839	1035	7	)	)	PUNCT
ejpam-5839	1035	8	is	be	AUX
ejpam-5839	1035	9	a	a	DET
ejpam-5839	1035	10	quadripartitioned	quadripartitione	VERB
ejpam-5839	1035	11	neutrosophic	neutrosophic	ADJ
ejpam-5839	1035	12	soft	soft	ADJ
ejpam-5839	1035	13	p	p	NOUN
ejpam-5839	1035	14	-	-	PUNCT
ejpam-5839	1035	15	open	open	ADJ
ejpam-5839	1036	1	set	set	NOUN
ejpam-5839	1037	1	in	in	ADP
ejpam-5839	1037	2	(	(	PUNCT
ejpam-5839	1037	3	x	x	NOUN
ejpam-5839	1037	4	,	,	PUNCT
ejpam-5839	1037	5	τqpnss	τqpns	NOUN
ejpam-5839	1037	6	,	,	PUNCT
ejpam-5839	1037	7	e	e	X
ejpam-5839	1037	8	)	)	PUNCT
ejpam-5839	1037	9	such	such	ADJ
ejpam-5839	1037	10	that	that	SCONJ
ejpam-5839	1037	11	a	a	DET
ejpam-5839	1037	12	quadripartitioned	quadripartitione	VERB
ejpam-5839	1037	13	neutrosophic	neutrosophic	ADJ
ejpam-5839	1037	14	soft	soft	ADJ
ejpam-5839	1037	15	subset	subset	NOUN
ejpam-5839	1037	16	(	(	PUNCT
ejpam-5839	1037	17	f̃1,ω	f̃1,ω	NOUN
ejpam-5839	1037	18	)	)	PUNCT
ejpam-5839	1037	19	of	of	ADP
ejpam-5839	1037	20	(	(	PUNCT
ejpam-5839	1037	21	f̃	f̃	PROPN
ejpam-5839	1037	22	,	,	PUNCT
ejpam-5839	1037	23	ω	ω	PROPN
ejpam-5839	1037	24	)	)	PUNCT
ejpam-5839	1037	25	is	be	AUX
ejpam-5839	1037	26	a	a	DET
ejpam-5839	1037	27	p	p	NOUN
ejpam-5839	1037	28	-	-	PUNCT
ejpam-5839	1037	29	open	open	ADJ
ejpam-5839	1037	30	set	set	NOUN
ejpam-5839	1037	31	in	in	ADP
ejpam-5839	1037	32	(	(	PUNCT
ejpam-5839	1037	33	x(f̃	x(f̃	X
ejpam-5839	1037	34	,	,	PUNCT
ejpam-5839	1037	35	e	e	NOUN
ejpam-5839	1037	36	)	)	PUNCT
ejpam-5839	1037	37	,	,	PUNCT
ejpam-5839	1037	38	τ	τ	PROPN
ejpam-5839	1037	39	qpnss	qpnss	NOUN
ejpam-5839	1037	40	(	(	PUNCT
ejpam-5839	1037	41	f̃	f̃	PROPN
ejpam-5839	1037	42	,	,	PUNCT
ejpam-5839	1037	43	e	e	NOUN
ejpam-5839	1037	44	)	)	PUNCT
ejpam-5839	1037	45	,	,	PUNCT
ejpam-5839	1037	46	ω	ω	NOUN
ejpam-5839	1037	47	)	)	PUNCT
ejpam-5839	1037	48	.	.	PUNCT
ejpam-5839	1038	1	then	then	ADV
ejpam-5839	1038	2	(	(	PUNCT
ejpam-5839	1038	3	f̃1,ω	f̃1,ω	NOUN
ejpam-5839	1038	4	)	)	PUNCT
ejpam-5839	1038	5	∈	∈	PROPN
ejpam-5839	1038	6	τqpnss	τqpns	NOUN
ejpam-5839	1038	7	(	(	PUNCT
ejpam-5839	1038	8	f̃	f̃	PROPN
ejpam-5839	1038	9	,	,	PUNCT
ejpam-5839	1038	10	e	e	NOUN
ejpam-5839	1038	11	)	)	PUNCT
ejpam-5839	1038	12	and	and	CCONJ
ejpam-5839	1038	13	so	so	ADV
ejpam-5839	1038	14	(	(	PUNCT
ejpam-5839	1038	15	f̃1,ω	f̃1,ω	NOUN
ejpam-5839	1038	16	)	)	PUNCT
ejpam-5839	1038	17	=	=	PUNCT
ejpam-5839	1038	18	(	(	PUNCT
ejpam-5839	1038	19	ũ	ũ	PROPN
ejpam-5839	1038	20	,	,	PUNCT
ejpam-5839	1038	21	ω	ω	NOUN
ejpam-5839	1038	22	)	)	PUNCT
ejpam-5839	1038	23	∩	∩	NOUN
ejpam-5839	1038	24	(	(	PUNCT
ejpam-5839	1038	25	f̃	f̃	PROPN
ejpam-5839	1038	26	,	,	PUNCT
ejpam-5839	1038	27	ω	ω	PROPN
ejpam-5839	1038	28	)	)	PUNCT
ejpam-5839	1038	29	for	for	ADP
ejpam-5839	1038	30	some	some	DET
ejpam-5839	1038	31	(	(	PUNCT
ejpam-5839	1038	32	ũ	ũ	PROPN
ejpam-5839	1038	33	,	,	PUNCT
ejpam-5839	1038	34	ω	ω	NOUN
ejpam-5839	1038	35	)	)	PUNCT
ejpam-5839	1038	36	∈	∈	PROPN
ejpam-5839	1038	37	τqpnss	τqpns	NOUN
ejpam-5839	1038	38	.	.	PUNCT
ejpam-5839	1039	1	but	but	CCONJ
ejpam-5839	1039	2	(	(	PUNCT
ejpam-5839	1039	3	f̃1,ω	f̃1,ω	NOUN
ejpam-5839	1039	4	)	)	PUNCT
ejpam-5839	1039	5	is	be	AUX
ejpam-5839	1039	6	a	a	DET
ejpam-5839	1039	7	quadripartitioned	quadripartitione	VERB
ejpam-5839	1039	8	neutrosophic	neutrosophic	ADJ
ejpam-5839	1039	9	soft	soft	ADJ
ejpam-5839	1039	10	p	p	NOUN
ejpam-5839	1039	11	-	-	PUNCT
ejpam-5839	1039	12	open	open	ADJ
ejpam-5839	1040	1	set	set	NOUN
ejpam-5839	1041	1	in	in	ADP
ejpam-5839	1041	2	(	(	PUNCT
ejpam-5839	1041	3	x	x	NOUN
ejpam-5839	1041	4	,	,	PUNCT
ejpam-5839	1041	5	τqpnss	τqpns	NOUN
ejpam-5839	1041	6	,	,	PUNCT
ejpam-5839	1041	7	e	e	NOUN
ejpam-5839	1041	8	)	)	PUNCT
ejpam-5839	1041	9	as	as	ADP
ejpam-5839	1041	10	(	(	PUNCT
ejpam-5839	1041	11	ũ	ũ	PROPN
ejpam-5839	1041	12	,	,	PUNCT
ejpam-5839	1041	13	ω	ω	PROPN
ejpam-5839	1041	14	)	)	PUNCT
ejpam-5839	1041	15	and	and	CCONJ
ejpam-5839	1041	16	(	(	PUNCT
ejpam-5839	1041	17	f̃	f̃	PROPN
ejpam-5839	1041	18	,	,	PUNCT
ejpam-5839	1041	19	ω	ω	NUM
ejpam-5839	1041	20	)	)	PUNCT
ejpam-5839	1041	21	are	be	AUX
ejpam-5839	1041	22	both	both	PRON
ejpam-5839	1041	23	quadripartitioned	quadripartitione	VERB
ejpam-5839	1041	24	neutrosophic	neutrosophic	ADJ
ejpam-5839	1041	25	soft	soft	ADJ
ejpam-5839	1041	26	p	p	NOUN
ejpam-5839	1041	27	-	-	PUNCT
ejpam-5839	1041	28	open	open	ADJ
ejpam-5839	1041	29	sets	set	NOUN
ejpam-5839	1041	30	in	in	ADP
ejpam-5839	1041	31	(	(	PUNCT
ejpam-5839	1041	32	x	x	NOUN
ejpam-5839	1041	33	,	,	PUNCT
ejpam-5839	1041	34	τqpnss	τqpns	NOUN
ejpam-5839	1041	35	,	,	PUNCT
ejpam-5839	1041	36	e	e	NOUN
ejpam-5839	1041	37	)	)	PUNCT
ejpam-5839	1041	38	.	.	PUNCT
ejpam-5839	1042	1	conversely	conversely	ADV
ejpam-5839	1042	2	,	,	PUNCT
ejpam-5839	1042	3	assume	assume	VERB
ejpam-5839	1042	4	that	that	SCONJ
ejpam-5839	1042	5	(	(	PUNCT
ejpam-5839	1042	6	f̃1,ω	f̃1,ω	NOUN
ejpam-5839	1042	7	)	)	PUNCT
ejpam-5839	1042	8	is	be	AUX
ejpam-5839	1042	9	a	a	DET
ejpam-5839	1042	10	quadripartitioned	quadripartitione	VERB
ejpam-5839	1042	11	neutrosophic	neutrosophic	ADJ
ejpam-5839	1042	12	soft	soft	ADJ
ejpam-5839	1042	13	p	p	NOUN
ejpam-5839	1042	14	-	-	PUNCT
ejpam-5839	1042	15	open	open	ADJ
ejpam-5839	1043	1	set	set	NOUN
ejpam-5839	1044	1	in	in	ADP
ejpam-5839	1044	2	(	(	PUNCT
ejpam-5839	1044	3	x	x	NOUN
ejpam-5839	1044	4	,	,	PUNCT
ejpam-5839	1044	5	τqpnss	τqpns	NOUN
ejpam-5839	1044	6	,	,	PUNCT
ejpam-5839	1044	7	e	e	NOUN
ejpam-5839	1044	8	)	)	PUNCT
ejpam-5839	1044	9	when	when	SCONJ
ejpam-5839	1044	10	(	(	PUNCT
ejpam-5839	1044	11	f̃	f̃	PROPN
ejpam-5839	1044	12	,	,	PUNCT
ejpam-5839	1044	13	ω	ω	PROPN
ejpam-5839	1044	14	)	)	PUNCT
ejpam-5839	1044	15	is	be	AUX
ejpam-5839	1044	16	a	a	DET
ejpam-5839	1044	17	quadripartitioned	quadripartitione	VERB
ejpam-5839	1044	18	neutrosophic	neutrosophic	ADJ
ejpam-5839	1044	19	soft	soft	ADJ
ejpam-5839	1044	20	p	p	NOUN
ejpam-5839	1044	21	-	-	PUNCT
ejpam-5839	1044	22	open	open	ADJ
ejpam-5839	1045	1	set	set	NOUN
ejpam-5839	1045	2	in	in	ADP
ejpam-5839	1045	3	(	(	PUNCT
ejpam-5839	1045	4	x	x	NOUN
ejpam-5839	1045	5	,	,	PUNCT
ejpam-5839	1045	6	τqpnss	τqpns	NOUN
ejpam-5839	1045	7	,	,	PUNCT
ejpam-5839	1045	8	e	e	NOUN
ejpam-5839	1045	9	)	)	PUNCT
ejpam-5839	1045	10	and	and	CCONJ
ejpam-5839	1045	11	(	(	PUNCT
ejpam-5839	1045	12	f̃1,ω	f̃1,ω	NOUN
ejpam-5839	1045	13	)	)	PUNCT
ejpam-5839	1045	14	⊆	⊆	NUM
ejpam-5839	1045	15	(	(	PUNCT
ejpam-5839	1045	16	f̃	f̃	PROPN
ejpam-5839	1045	17	,	,	PUNCT
ejpam-5839	1045	18	ω	ω	PROPN
ejpam-5839	1045	19	)	)	PUNCT
ejpam-5839	1045	20	.	.	PUNCT
ejpam-5839	1046	1	then	then	ADV
ejpam-5839	1046	2	(	(	PUNCT
ejpam-5839	1046	3	f̃1,ω	f̃1,ω	NOUN
ejpam-5839	1046	4	)	)	PUNCT
ejpam-5839	1046	5	∈	∈	PROPN
ejpam-5839	1046	6	τqpnss	τqpns	NOUN
ejpam-5839	1046	7	.	.	PUNCT
ejpam-5839	1047	1	but	but	CCONJ
ejpam-5839	1047	2	(	(	PUNCT
ejpam-5839	1047	3	f̃1,ω)∩(f̃	f̃1,ω)∩(f̃	NOUN
ejpam-5839	1047	4	,	,	PUNCT
ejpam-5839	1047	5	ω	ω	NOUN
ejpam-5839	1047	6	)	)	PUNCT
ejpam-5839	1047	7	=	=	SYM
ejpam-5839	1047	8	(	(	PUNCT
ejpam-5839	1047	9	f̃1,ω	f̃1,ω	NOUN
ejpam-5839	1047	10	)	)	PUNCT
ejpam-5839	1047	11	,	,	PUNCT
ejpam-5839	1047	12	and	and	CCONJ
ejpam-5839	1047	13	so	so	ADV
ejpam-5839	1047	14	(	(	PUNCT
ejpam-5839	1047	15	f̃1,ω	f̃1,ω	NOUN
ejpam-5839	1047	16	)	)	PUNCT
ejpam-5839	1047	17	is	be	AUX
ejpam-5839	1047	18	a	a	DET
ejpam-5839	1047	19	quadripartitioned	quadripartitione	VERB
ejpam-5839	1047	20	neutrosophic	neutrosophic	ADJ
ejpam-5839	1047	21	soft	soft	ADJ
ejpam-5839	1047	22	set	set	NOUN
ejpam-5839	1047	23	in	in	ADP
ejpam-5839	1047	24	(	(	PUNCT
ejpam-5839	1047	25	x	x	NOUN
ejpam-5839	1047	26	,	,	PUNCT
ejpam-5839	1047	27	τqpnss	τqpns	NOUN
ejpam-5839	1047	28	,	,	PUNCT
ejpam-5839	1047	29	e	e	NOUN
ejpam-5839	1047	30	)	)	PUNCT
ejpam-5839	1047	31	.	.	PUNCT
ejpam-5839	1048	1	therefore	therefore	ADV
ejpam-5839	1048	2	,	,	PUNCT
ejpam-5839	1048	3	the	the	DET
ejpam-5839	1048	4	first	first	ADJ
ejpam-5839	1048	5	part	part	NOUN
ejpam-5839	1048	6	is	be	AUX
ejpam-5839	1048	7	proved	prove	VERB
ejpam-5839	1048	8	.	.	PUNCT
ejpam-5839	1049	1	a.	a.	PROPN
ejpam-5839	1049	2	shihadeh	shihadeh	VERB
ejpam-5839	1049	3	et	et	PROPN
ejpam-5839	1049	4	al	al	PROPN
ejpam-5839	1049	5	.	.	PUNCT
ejpam-5839	1049	6	/	/	SYM
ejpam-5839	1049	7	eur	eur	PROPN
ejpam-5839	1049	8	.	.	PUNCT
ejpam-5839	1050	1	j.	j.	PROPN
ejpam-5839	1050	2	pure	pure	PROPN
ejpam-5839	1050	3	appl	appl	PROPN
ejpam-5839	1050	4	.	.	PROPN
ejpam-5839	1050	5	math	math	PROPN
ejpam-5839	1050	6	,	,	PUNCT
ejpam-5839	1050	7	18	18	NUM
ejpam-5839	1050	8	(	(	PUNCT
ejpam-5839	1050	9	2	2	NUM
ejpam-5839	1050	10	)	)	PUNCT
ejpam-5839	1050	11	(	(	PUNCT
ejpam-5839	1050	12	2025	2025	NUM
ejpam-5839	1050	13	)	)	PUNCT
ejpam-5839	1050	14	,	,	PUNCT
ejpam-5839	1050	15	5839	5839	NUM
ejpam-5839	1050	16	45	45	NUM
ejpam-5839	1050	17	of	of	ADP
ejpam-5839	1050	18	54	54	NUM
ejpam-5839	1050	19	theorem	theorem	NOUN
ejpam-5839	1050	20	22	22	NUM
ejpam-5839	1050	21	.	.	PUNCT
ejpam-5839	1051	1	let	let	VERB
ejpam-5839	1051	2	(	(	PUNCT
ejpam-5839	1051	3	x(k̃,e	x(k̃,e	PROPN
ejpam-5839	1051	4	)	)	PUNCT
ejpam-5839	1051	5	,	,	PUNCT
ejpam-5839	1051	6	τ	τ	PROPN
ejpam-5839	1051	7	qpnss	qpnss	NOUN
ejpam-5839	1051	8	,	,	PUNCT
ejpam-5839	1051	9	ω	ω	NOUN
ejpam-5839	1051	10	)	)	PUNCT
ejpam-5839	1051	11	be	be	VERB
ejpam-5839	1051	12	a	a	DET
ejpam-5839	1051	13	quadripartitioned	quadripartitione	VERB
ejpam-5839	1051	14	neutrosophic	neutrosophic	ADJ
ejpam-5839	1051	15	soft	soft	ADJ
ejpam-5839	1051	16	subspace	subspace	NOUN
ejpam-5839	1051	17	of	of	ADP
ejpam-5839	1051	18	a	a	DET
ejpam-5839	1051	19	quadripartitioned	quadripartitione	VERB
ejpam-5839	1051	20	neutrosophic	neutrosophic	ADJ
ejpam-5839	1051	21	soft	soft	ADJ
ejpam-5839	1051	22	topological	topological	ADJ
ejpam-5839	1051	23	space	space	NOUN
ejpam-5839	1051	24	(	(	PUNCT
ejpam-5839	1051	25	x	x	NOUN
ejpam-5839	1051	26	,	,	PUNCT
ejpam-5839	1051	27	τqpnss	τqpns	NOUN
ejpam-5839	1051	28	,	,	PUNCT
ejpam-5839	1051	29	e	e	NOUN
ejpam-5839	1051	30	)	)	PUNCT
ejpam-5839	1051	31	over	over	ADP
ejpam-5839	1051	32	x.	x.	NOUN
ejpam-5839	1052	1	if	if	SCONJ
ejpam-5839	1052	2	(	(	PUNCT
ejpam-5839	1052	3	k̃,ω	k̃,ω	NOUN
ejpam-5839	1052	4	)	)	PUNCT
ejpam-5839	1052	5	is	be	AUX
ejpam-5839	1052	6	a	a	DET
ejpam-5839	1052	7	quadripartitioned	quadripartitione	VERB
ejpam-5839	1052	8	neutrosophic	neutrosophic	ADJ
ejpam-5839	1052	9	soft	soft	ADJ
ejpam-5839	1052	10	p	p	NOUN
ejpam-5839	1052	11	-	-	PUNCT
ejpam-5839	1052	12	closed	close	VERB
ejpam-5839	1052	13	set	set	NOUN
ejpam-5839	1052	14	in	in	ADP
ejpam-5839	1052	15	(	(	PUNCT
ejpam-5839	1052	16	x	x	NOUN
ejpam-5839	1052	17	,	,	PUNCT
ejpam-5839	1052	18	τqpnss	τqpns	NOUN
ejpam-5839	1052	19	,	,	PUNCT
ejpam-5839	1052	20	e	e	NOUN
ejpam-5839	1052	21	)	)	PUNCT
ejpam-5839	1052	22	,	,	PUNCT
ejpam-5839	1052	23	then	then	ADV
ejpam-5839	1052	24	a	a	DET
ejpam-5839	1052	25	quadripartitioned	quadripartitione	VERB
ejpam-5839	1052	26	neutrosophic	neutrosophic	ADJ
ejpam-5839	1052	27	soft	soft	ADJ
ejpam-5839	1052	28	set	set	NOUN
ejpam-5839	1052	29	(	(	PUNCT
ejpam-5839	1052	30	k̃1,ω	k̃1,ω	NOUN
ejpam-5839	1052	31	)	)	PUNCT
ejpam-5839	1052	32	⊆	⊆	NUM
ejpam-5839	1052	33	(	(	PUNCT
ejpam-5839	1052	34	k̃,ω	k̃,ω	NOUN
ejpam-5839	1052	35	)	)	PUNCT
ejpam-5839	1052	36	is	be	AUX
ejpam-5839	1052	37	a	a	DET
ejpam-5839	1052	38	quadripartitioned	quadripartitione	VERB
ejpam-5839	1052	39	neutrosophic	neutrosophic	ADJ
ejpam-5839	1052	40	soft	soft	ADJ
ejpam-5839	1052	41	p	p	NOUN
ejpam-5839	1052	42	-	-	PUNCT
ejpam-5839	1052	43	closed	close	VERB
ejpam-5839	1052	44	set	set	NOUN
ejpam-5839	1052	45	in	in	ADP
ejpam-5839	1052	46	(	(	PUNCT
ejpam-5839	1052	47	x(k̃,e	x(k̃,e	PROPN
ejpam-5839	1052	48	)	)	PUNCT
ejpam-5839	1052	49	,	,	PUNCT
ejpam-5839	1052	50	τ	τ	PROPN
ejpam-5839	1052	51	qpnss	qpnss	NOUN
ejpam-5839	1052	52	(	(	PUNCT
ejpam-5839	1052	53	k̃,e	k̃,e	PROPN
ejpam-5839	1052	54	)	)	PUNCT
ejpam-5839	1052	55	,	,	PUNCT
ejpam-5839	1052	56	ω	ω	X
ejpam-5839	1052	57	)	)	PUNCT
ejpam-5839	1053	1	if	if	SCONJ
ejpam-5839	1053	2	and	and	CCONJ
ejpam-5839	1053	3	only	only	ADV
ejpam-5839	1053	4	if	if	SCONJ
ejpam-5839	1053	5	(	(	PUNCT
ejpam-5839	1053	6	k̃1,ω	k̃1,ω	NOUN
ejpam-5839	1053	7	)	)	PUNCT
ejpam-5839	1053	8	is	be	AUX
ejpam-5839	1053	9	a	a	DET
ejpam-5839	1053	10	quadripartitioned	quadripartitione	VERB
ejpam-5839	1053	11	neutrosophic	neutrosophic	ADJ
ejpam-5839	1053	12	soft	soft	ADJ
ejpam-5839	1053	13	p	p	NOUN
ejpam-5839	1053	14	-	-	PUNCT
ejpam-5839	1053	15	closed	close	VERB
ejpam-5839	1053	16	set	set	NOUN
ejpam-5839	1053	17	in	in	ADP
ejpam-5839	1053	18	(	(	PUNCT
ejpam-5839	1053	19	x	x	NOUN
ejpam-5839	1053	20	,	,	PUNCT
ejpam-5839	1053	21	τqpnss	τqpns	NOUN
ejpam-5839	1053	22	,	,	PUNCT
ejpam-5839	1053	23	e	e	NOUN
ejpam-5839	1053	24	)	)	PUNCT
ejpam-5839	1053	25	.	.	PUNCT
ejpam-5839	1054	1	proof	proof	NOUN
ejpam-5839	1054	2	.	.	PUNCT
ejpam-5839	1055	1	suppose	suppose	VERB
ejpam-5839	1055	2	that	that	SCONJ
ejpam-5839	1055	3	(	(	PUNCT
ejpam-5839	1055	4	k̃,ω	k̃,ω	NOUN
ejpam-5839	1055	5	)	)	PUNCT
ejpam-5839	1055	6	is	be	AUX
ejpam-5839	1055	7	a	a	DET
ejpam-5839	1055	8	quadripartitioned	quadripartitione	VERB
ejpam-5839	1055	9	neutrosophic	neutrosophic	ADJ
ejpam-5839	1055	10	soft	soft	ADJ
ejpam-5839	1055	11	p	p	NOUN
ejpam-5839	1055	12	-	-	PUNCT
ejpam-5839	1055	13	closed	close	VERB
ejpam-5839	1055	14	set	set	NOUN
ejpam-5839	1055	15	in	in	ADP
ejpam-5839	1055	16	(	(	PUNCT
ejpam-5839	1055	17	x	x	NOUN
ejpam-5839	1055	18	,	,	PUNCT
ejpam-5839	1055	19	τqpnss	τqpns	NOUN
ejpam-5839	1055	20	,	,	PUNCT
ejpam-5839	1055	21	e	e	X
ejpam-5839	1055	22	)	)	PUNCT
ejpam-5839	1055	23	such	such	ADJ
ejpam-5839	1055	24	that	that	SCONJ
ejpam-5839	1055	25	a	a	DET
ejpam-5839	1055	26	quadripartitioned	quadripartitione	VERB
ejpam-5839	1055	27	neutrosophic	neutrosophic	ADJ
ejpam-5839	1055	28	soft	soft	ADJ
ejpam-5839	1055	29	subset	subset	NOUN
ejpam-5839	1055	30	(	(	PUNCT
ejpam-5839	1055	31	k̃1,ω	k̃1,ω	NOUN
ejpam-5839	1055	32	)	)	PUNCT
ejpam-5839	1055	33	or	or	CCONJ
ejpam-5839	1055	34	(	(	PUNCT
ejpam-5839	1055	35	k̃,ω	k̃,ω	NOUN
ejpam-5839	1055	36	)	)	PUNCT
ejpam-5839	1055	37	is	be	AUX
ejpam-5839	1055	38	a	a	DET
ejpam-5839	1055	39	quadripartitioned	quadripartitione	VERB
ejpam-5839	1055	40	neutrosophic	neutrosophic	ADJ
ejpam-5839	1055	41	soft	soft	ADJ
ejpam-5839	1055	42	p	p	NOUN
ejpam-5839	1055	43	-	-	PUNCT
ejpam-5839	1055	44	closed	close	VERB
ejpam-5839	1055	45	set	set	NOUN
ejpam-5839	1055	46	in	in	ADP
ejpam-5839	1055	47	(	(	PUNCT
ejpam-5839	1055	48	x(k̃,e	x(k̃,e	PROPN
ejpam-5839	1055	49	)	)	PUNCT
ejpam-5839	1055	50	,	,	PUNCT
ejpam-5839	1055	51	τ	τ	PROPN
ejpam-5839	1055	52	qpnss	qpnss	NOUN
ejpam-5839	1055	53	(	(	PUNCT
ejpam-5839	1055	54	k̃,e	k̃,e	PROPN
ejpam-5839	1055	55	)	)	PUNCT
ejpam-5839	1055	56	,	,	PUNCT
ejpam-5839	1055	57	ω	ω	NOUN
ejpam-5839	1055	58	)	)	PUNCT
ejpam-5839	1055	59	.	.	PUNCT
ejpam-5839	1056	1	since	since	SCONJ
ejpam-5839	1056	2	(	(	PUNCT
ejpam-5839	1056	3	k̃1,ω	k̃1,ω	NOUN
ejpam-5839	1056	4	)	)	PUNCT
ejpam-5839	1056	5	is	be	AUX
ejpam-5839	1056	6	p	p	NOUN
ejpam-5839	1056	7	-	-	PUNCT
ejpam-5839	1056	8	closed	closed	ADJ
ejpam-5839	1056	9	in	in	ADP
ejpam-5839	1056	10	(	(	PUNCT
ejpam-5839	1056	11	x(k̃,e),τ	x(k̃,e),τ	NOUN
ejpam-5839	1056	12	qpnss	qpnss	PROPN
ejpam-5839	1056	13	(	(	PUNCT
ejpam-5839	1056	14	k̃,e	k̃,e	PROPN
ejpam-5839	1056	15	)	)	PUNCT
ejpam-5839	1056	16	,	,	PUNCT
ejpam-5839	1056	17	ω	ω	PROPN
ejpam-5839	1056	18	)	)	PUNCT
ejpam-5839	1056	19	,	,	PUNCT
ejpam-5839	1056	20	it	it	PRON
ejpam-5839	1056	21	follows	follow	VERB
ejpam-5839	1056	22	that	that	SCONJ
ejpam-5839	1056	23	(	(	PUNCT
ejpam-5839	1056	24	k̃1,ω	k̃1,ω	NOUN
ejpam-5839	1056	25	)	)	PUNCT
ejpam-5839	1056	26	=	=	PUNCT
ejpam-5839	1057	1	(	(	PUNCT
ejpam-5839	1057	2	ṽ	ṽ	PROPN
ejpam-5839	1057	3	,	,	PUNCT
ejpam-5839	1057	4	ω	ω	NOUN
ejpam-5839	1057	5	)	)	PUNCT
ejpam-5839	1057	6	∩	∩	NOUN
ejpam-5839	1057	7	(	(	PUNCT
ejpam-5839	1057	8	k̃,ω	k̃,ω	NOUN
ejpam-5839	1057	9	)	)	PUNCT
ejpam-5839	1057	10	for	for	ADP
ejpam-5839	1057	11	some	some	PRON
ejpam-5839	1057	12	(	(	PUNCT
ejpam-5839	1057	13	ṽ	ṽ	PROPN
ejpam-5839	1057	14	,	,	PUNCT
ejpam-5839	1057	15	ω	ω	PROPN
ejpam-5839	1057	16	)	)	PUNCT
ejpam-5839	1057	17	,	,	PUNCT
ejpam-5839	1057	18	which	which	PRON
ejpam-5839	1057	19	is	be	AUX
ejpam-5839	1057	20	a	a	DET
ejpam-5839	1057	21	quadripartitioned	quadripartitione	VERB
ejpam-5839	1057	22	neutrosophic	neutrosophic	ADJ
ejpam-5839	1057	23	soft	soft	ADJ
ejpam-5839	1057	24	p	p	NOUN
ejpam-5839	1057	25	-	-	PUNCT
ejpam-5839	1057	26	closed	close	VERB
ejpam-5839	1057	27	set	set	NOUN
ejpam-5839	1057	28	in	in	ADP
ejpam-5839	1057	29	(	(	PUNCT
ejpam-5839	1057	30	x	x	NOUN
ejpam-5839	1057	31	,	,	PUNCT
ejpam-5839	1057	32	τqpnss	τqpns	NOUN
ejpam-5839	1057	33	,	,	PUNCT
ejpam-5839	1057	34	e	e	NOUN
ejpam-5839	1057	35	)	)	PUNCT
ejpam-5839	1057	36	.	.	PUNCT
ejpam-5839	1058	1	but	but	CCONJ
ejpam-5839	1058	2	(	(	PUNCT
ejpam-5839	1058	3	k̃1,ω	k̃1,ω	NOUN
ejpam-5839	1058	4	)	)	PUNCT
ejpam-5839	1058	5	is	be	AUX
ejpam-5839	1058	6	also	also	ADV
ejpam-5839	1058	7	a	a	DET
ejpam-5839	1058	8	quadripartitioned	quadripartitione	VERB
ejpam-5839	1058	9	neutrosophic	neutrosophic	ADJ
ejpam-5839	1058	10	soft	soft	ADJ
ejpam-5839	1058	11	p	p	NOUN
ejpam-5839	1058	12	-	-	PUNCT
ejpam-5839	1058	13	closed	close	VERB
ejpam-5839	1058	14	set	set	NOUN
ejpam-5839	1058	15	in	in	ADP
ejpam-5839	1058	16	(	(	PUNCT
ejpam-5839	1058	17	x	x	NOUN
ejpam-5839	1058	18	,	,	PUNCT
ejpam-5839	1058	19	τqpnss	τqpns	NOUN
ejpam-5839	1058	20	,	,	PUNCT
ejpam-5839	1058	21	e	e	NOUN
ejpam-5839	1058	22	)	)	PUNCT
ejpam-5839	1058	23	because	because	SCONJ
ejpam-5839	1058	24	both	both	PRON
ejpam-5839	1058	25	(	(	PUNCT
ejpam-5839	1058	26	ṽ	ṽ	PROPN
ejpam-5839	1058	27	,	,	PUNCT
ejpam-5839	1058	28	ω	ω	PROPN
ejpam-5839	1058	29	)	)	PUNCT
ejpam-5839	1058	30	and	and	CCONJ
ejpam-5839	1058	31	(	(	PUNCT
ejpam-5839	1058	32	k̃,ω	k̃,ω	NOUN
ejpam-5839	1058	33	)	)	PUNCT
ejpam-5839	1058	34	are	be	AUX
ejpam-5839	1058	35	quadripartitioned	quadripartitione	VERB
ejpam-5839	1058	36	neutrosophic	neutrosophic	ADJ
ejpam-5839	1058	37	soft	soft	ADJ
ejpam-5839	1058	38	p	p	NOUN
ejpam-5839	1058	39	-	-	PUNCT
ejpam-5839	1058	40	closed	close	VERB
ejpam-5839	1058	41	sets	set	NOUN
ejpam-5839	1058	42	in	in	ADP
ejpam-5839	1058	43	(	(	PUNCT
ejpam-5839	1058	44	x	x	NOUN
ejpam-5839	1058	45	,	,	PUNCT
ejpam-5839	1058	46	τqpnss	τqpns	NOUN
ejpam-5839	1058	47	,	,	PUNCT
ejpam-5839	1058	48	e	e	NOUN
ejpam-5839	1058	49	)	)	PUNCT
ejpam-5839	1058	50	.	.	PUNCT
ejpam-5839	1059	1	conversely	conversely	ADV
ejpam-5839	1059	2	,	,	PUNCT
ejpam-5839	1059	3	assume	assume	VERB
ejpam-5839	1059	4	that	that	SCONJ
ejpam-5839	1059	5	(	(	PUNCT
ejpam-5839	1059	6	f̃1,ω	f̃1,ω	NOUN
ejpam-5839	1059	7	)	)	PUNCT
ejpam-5839	1059	8	is	be	AUX
ejpam-5839	1059	9	a	a	DET
ejpam-5839	1059	10	quadripartitioned	quadripartitione	VERB
ejpam-5839	1059	11	neutrosophic	neutrosophic	ADJ
ejpam-5839	1059	12	soft	soft	ADJ
ejpam-5839	1059	13	p	p	NOUN
ejpam-5839	1059	14	-	-	PUNCT
ejpam-5839	1059	15	open	open	ADJ
ejpam-5839	1060	1	set	set	NOUN
ejpam-5839	1061	1	in	in	ADP
ejpam-5839	1061	2	(	(	PUNCT
ejpam-5839	1061	3	x	x	NOUN
ejpam-5839	1061	4	,	,	PUNCT
ejpam-5839	1061	5	τqpnss	τqpns	NOUN
ejpam-5839	1061	6	,	,	PUNCT
ejpam-5839	1061	7	e	e	NOUN
ejpam-5839	1061	8	)	)	PUNCT
ejpam-5839	1061	9	,	,	PUNCT
ejpam-5839	1061	10	where	where	SCONJ
ejpam-5839	1061	11	(	(	PUNCT
ejpam-5839	1061	12	k̃,ω	k̃,ω	NOUN
ejpam-5839	1061	13	)	)	PUNCT
ejpam-5839	1061	14	is	be	AUX
ejpam-5839	1061	15	a	a	DET
ejpam-5839	1061	16	quadripartitioned	quadripartitione	VERB
ejpam-5839	1061	17	neutrosophic	neutrosophic	ADJ
ejpam-5839	1061	18	soft	soft	ADJ
ejpam-5839	1061	19	p	p	NOUN
ejpam-5839	1061	20	-	-	PUNCT
ejpam-5839	1061	21	closed	close	VERB
ejpam-5839	1061	22	set	set	NOUN
ejpam-5839	1061	23	in	in	ADP
ejpam-5839	1061	24	(	(	PUNCT
ejpam-5839	1061	25	x	x	NOUN
ejpam-5839	1061	26	,	,	PUNCT
ejpam-5839	1061	27	τqpnss	τqpns	NOUN
ejpam-5839	1061	28	,	,	PUNCT
ejpam-5839	1061	29	e	e	NOUN
ejpam-5839	1061	30	)	)	PUNCT
ejpam-5839	1061	31	and	and	CCONJ
ejpam-5839	1061	32	(	(	PUNCT
ejpam-5839	1061	33	k̃1,ω	k̃1,ω	PROPN
ejpam-5839	1061	34	)	)	PUNCT
ejpam-5839	1061	35	⊆	⊆	NUM
ejpam-5839	1061	36	(	(	PUNCT
ejpam-5839	1061	37	k̃,ω	k̃,ω	NOUN
ejpam-5839	1061	38	)	)	PUNCT
ejpam-5839	1061	39	.	.	PUNCT
ejpam-5839	1062	1	then	then	ADV
ejpam-5839	1062	2	(	(	PUNCT
ejpam-5839	1062	3	k̃1,ω	k̃1,ω	NOUN
ejpam-5839	1062	4	)	)	PUNCT
ejpam-5839	1062	5	∩	∩	NOUN
ejpam-5839	1062	6	(	(	PUNCT
ejpam-5839	1062	7	k̃,ω	k̃,ω	NOUN
ejpam-5839	1062	8	)	)	PUNCT
ejpam-5839	1062	9	=	=	PRON
ejpam-5839	1062	10	(	(	PUNCT
ejpam-5839	1062	11	k̃1,ω	k̃1,ω	PROPN
ejpam-5839	1062	12	)	)	PUNCT
ejpam-5839	1062	13	which	which	PRON
ejpam-5839	1062	14	implies	imply	VERB
ejpam-5839	1062	15	that	that	SCONJ
ejpam-5839	1062	16	(	(	PUNCT
ejpam-5839	1062	17	k̃1,ω	k̃1,ω	NOUN
ejpam-5839	1062	18	)	)	PUNCT
ejpam-5839	1062	19	is	be	AUX
ejpam-5839	1062	20	a	a	DET
ejpam-5839	1062	21	quadripartitioned	quadripartitione	VERB
ejpam-5839	1062	22	neutrosophic	neutrosophic	ADJ
ejpam-5839	1062	23	soft	soft	ADJ
ejpam-5839	1062	24	p	p	NOUN
ejpam-5839	1062	25	-	-	PUNCT
ejpam-5839	1062	26	closed	close	VERB
ejpam-5839	1062	27	set	set	NOUN
ejpam-5839	1062	28	in	in	ADP
ejpam-5839	1062	29	(	(	PUNCT
ejpam-5839	1062	30	x(k̃,e	x(k̃,e	PROPN
ejpam-5839	1062	31	)	)	PUNCT
ejpam-5839	1062	32	,	,	PUNCT
ejpam-5839	1062	33	τ	τ	PROPN
ejpam-5839	1062	34	qpnss	qpnss	NOUN
ejpam-5839	1062	35	(	(	PUNCT
ejpam-5839	1062	36	k̃,e	k̃,e	PROPN
ejpam-5839	1062	37	)	)	PUNCT
ejpam-5839	1062	38	,	,	PUNCT
ejpam-5839	1062	39	ω	ω	NOUN
ejpam-5839	1062	40	)	)	PUNCT
ejpam-5839	1062	41	.	.	PUNCT
ejpam-5839	1063	1	hence	hence	ADV
ejpam-5839	1063	2	,	,	PUNCT
ejpam-5839	1063	3	the	the	DET
ejpam-5839	1063	4	first	first	ADJ
ejpam-5839	1063	5	part	part	NOUN
ejpam-5839	1063	6	is	be	AUX
ejpam-5839	1063	7	proved	prove	VERB
ejpam-5839	1063	8	.	.	PUNCT
ejpam-5839	1064	1	theorem	theorem	VERB
ejpam-5839	1064	2	23	23	NUM
ejpam-5839	1064	3	.	.	PUNCT
ejpam-5839	1065	1	every	every	DET
ejpam-5839	1065	2	quadripartitioned	quadripartitione	VERB
ejpam-5839	1065	3	neutrosophic	neutrosophic	ADJ
ejpam-5839	1065	4	soft	soft	ADJ
ejpam-5839	1065	5	second	second	ADJ
ejpam-5839	1065	6	countable	countable	ADJ
ejpam-5839	1065	7	space	space	NOUN
ejpam-5839	1065	8	is	be	AUX
ejpam-5839	1065	9	always	always	ADV
ejpam-5839	1065	10	quadripartitioned	quadripartitione	VERB
ejpam-5839	1065	11	neutrosophic	neutrosophic	ADJ
ejpam-5839	1065	12	soft	soft	ADJ
ejpam-5839	1065	13	first	first	ADJ
ejpam-5839	1065	14	countable	countable	ADJ
ejpam-5839	1065	15	space	space	NOUN
ejpam-5839	1065	16	.	.	PUNCT
ejpam-5839	1066	1	proof	proof	NOUN
ejpam-5839	1066	2	.	.	PUNCT
ejpam-5839	1067	1	let	let	VERB
ejpam-5839	1067	2	(	(	PUNCT
ejpam-5839	1067	3	x	x	NOUN
ejpam-5839	1067	4	,	,	PUNCT
ejpam-5839	1067	5	τqpnss	τqpnss	PROPN
ejpam-5839	1067	6	,	,	PUNCT
ejpam-5839	1067	7	ω	ω	PROPN
ejpam-5839	1067	8	)	)	PUNCT
ejpam-5839	1067	9	be	be	VERB
ejpam-5839	1067	10	a	a	DET
ejpam-5839	1067	11	quadripartitioned	quadripartitione	VERB
ejpam-5839	1067	12	neutrosophic	neutrosophic	ADJ
ejpam-5839	1067	13	soft	soft	ADJ
ejpam-5839	1067	14	topological	topological	ADJ
ejpam-5839	1067	15	space	space	NOUN
ejpam-5839	1067	16	over	over	ADP
ejpam-5839	1067	17	x	x	ADP
ejpam-5839	1067	18	which	which	PRON
ejpam-5839	1067	19	satisfies	satisfy	VERB
ejpam-5839	1067	20	the	the	DET
ejpam-5839	1067	21	second	second	ADJ
ejpam-5839	1067	22	axiom	axiom	NOUN
ejpam-5839	1067	23	of	of	ADP
ejpam-5839	1067	24	quadripartitioned	quadripartitione	VERB
ejpam-5839	1067	25	neutrosophic	neutrosophic	ADJ
ejpam-5839	1067	26	soft	soft	ADJ
ejpam-5839	1067	27	countability	countability	NOUN
ejpam-5839	1067	28	.	.	PUNCT
ejpam-5839	1068	1	that	that	PRON
ejpam-5839	1068	2	is	is	ADV
ejpam-5839	1068	3	,	,	PUNCT
ejpam-5839	1068	4	(	(	PUNCT
ejpam-5839	1068	5	x	x	X
ejpam-5839	1068	6	,	,	PUNCT
ejpam-5839	1068	7	τqpnss	τqpnss	PROPN
ejpam-5839	1068	8	,	,	PUNCT
ejpam-5839	1068	9	ω	ω	PROPN
ejpam-5839	1068	10	)	)	PUNCT
ejpam-5839	1068	11	is	be	AUX
ejpam-5839	1068	12	quadripartitioned	quadripartitione	VERB
ejpam-5839	1068	13	neutrosophic	neutrosophic	ADJ
ejpam-5839	1068	14	soft	soft	ADJ
ejpam-5839	1068	15	second	second	ADJ
ejpam-5839	1068	16	countable	countable	ADJ
ejpam-5839	1068	17	.	.	PUNCT
ejpam-5839	1069	1	to	to	PART
ejpam-5839	1069	2	prove	prove	VERB
ejpam-5839	1069	3	that	that	SCONJ
ejpam-5839	1069	4	(	(	PUNCT
ejpam-5839	1069	5	x	x	X
ejpam-5839	1069	6	,	,	PUNCT
ejpam-5839	1069	7	τqpnss	τqpnss	PROPN
ejpam-5839	1069	8	,	,	PUNCT
ejpam-5839	1069	9	ω	ω	PROPN
ejpam-5839	1069	10	)	)	PUNCT
ejpam-5839	1069	11	is	be	AUX
ejpam-5839	1069	12	quadripartitioned	quadripartitione	VERB
ejpam-5839	1069	13	neutrosophic	neutrosophic	ADJ
ejpam-5839	1069	14	soft	soft	ADJ
ejpam-5839	1069	15	first	first	ADJ
ejpam-5839	1069	16	countable	countable	ADJ
ejpam-5839	1069	17	,	,	PUNCT
ejpam-5839	1069	18	we	we	PRON
ejpam-5839	1069	19	proceed	proceed	VERB
ejpam-5839	1069	20	as	as	SCONJ
ejpam-5839	1069	21	follows	follow	VERB
ejpam-5839	1069	22	.	.	PUNCT
ejpam-5839	1070	1	by	by	ADP
ejpam-5839	1070	2	hypothesis	hypothesis	NOUN
ejpam-5839	1070	3	,	,	PUNCT
ejpam-5839	1070	4	there	there	PRON
ejpam-5839	1070	5	exists	exist	VERB
ejpam-5839	1070	6	a	a	DET
ejpam-5839	1070	7	quadripartitioned	quadripartitioned	ADJ
ejpam-5839	1070	8	neutrosophic	neutrosophic	ADJ
ejpam-5839	1070	9	soft	soft	ADJ
ejpam-5839	1070	10	countable	countable	ADJ
ejpam-5839	1070	11	base	base	NOUN
ejpam-5839	1070	12	bqpnss	bqpns	NOUN
ejpam-5839	1070	13	for	for	ADP
ejpam-5839	1070	14	the	the	DET
ejpam-5839	1070	15	quadripartitioned	quadripartitioned	ADJ
ejpam-5839	1070	16	neutrosophic	neutrosophic	ADJ
ejpam-5839	1070	17	soft	soft	ADJ
ejpam-5839	1070	18	topology	topology	NOUN
ejpam-5839	1070	19	τqpnss	τqpns	NOUN
ejpam-5839	1070	20	on	on	ADP
ejpam-5839	1070	21	x.	x.	NOUN
ejpam-5839	1070	22	the	the	DET
ejpam-5839	1070	23	countability	countability	NOUN
ejpam-5839	1070	24	of	of	ADP
ejpam-5839	1070	25	bqpnss	bqpns	NOUN
ejpam-5839	1070	26	implies	imply	VERB
ejpam-5839	1070	27	that	that	SCONJ
ejpam-5839	1070	28	bqpnss	bqpns	NOUN
ejpam-5839	1070	29	can	can	AUX
ejpam-5839	1070	30	be	be	AUX
ejpam-5839	1070	31	expressed	express	VERB
ejpam-5839	1070	32	as	as	ADP
ejpam-5839	1070	33	bqpnss	bqpns	NOUN
ejpam-5839	1070	34	=	=	PUNCT
ejpam-5839	1070	35	{	{	PUNCT
ejpam-5839	1070	36	bn	bn	X
ejpam-5839	1070	37	:	:	PUNCT
ejpam-5839	1070	38	n	n	CCONJ
ejpam-5839	1070	39	∈	∈	PROPN
ejpam-5839	1070	40	n	n	CCONJ
ejpam-5839	1070	41	}	}	PUNCT
ejpam-5839	1070	42	.	.	PUNCT
ejpam-5839	1071	1	let	let	AUX
ejpam-5839	1071	2	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	NOUN
ejpam-5839	1071	3	)	)	PUNCT
ejpam-5839	1071	4	∈	∈	PROPN
ejpam-5839	1071	5	x	x	PUNCT
ejpam-5839	1071	6	be	be	AUX
ejpam-5839	1071	7	arbitrary	arbitrary	ADJ
ejpam-5839	1071	8	.	.	PUNCT
ejpam-5839	1072	1	define	define	VERB
ejpam-5839	1072	2	the	the	DET
ejpam-5839	1072	3	set	set	ADJ
ejpam-5839	1072	4	lxθ	lxθ	NOUN
ejpam-5839	1072	5	(	(	PUNCT
ejpam-5839	1072	6	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	1072	7	)	)	PUNCT
ejpam-5839	1072	8	=	=	PRON
ejpam-5839	1072	9	{	{	PUNCT
ejpam-5839	1072	10	bn	bn	NUM
ejpam-5839	1072	11	∈	∈	PROPN
ejpam-5839	1072	12	bqpnss	bqpns	NOUN
ejpam-5839	1072	13	:	:	PUNCT
ejpam-5839	1072	14	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	X
ejpam-5839	1072	15	)	)	PUNCT
ejpam-5839	1072	16	∈	∈	PROPN
ejpam-5839	1072	17	bn	bn	NOUN
ejpam-5839	1072	18	}	}	PUNCT
ejpam-5839	1072	19	.	.	PUNCT
ejpam-5839	1073	1	(	(	PUNCT
ejpam-5839	1073	2	i	i	NOUN
ejpam-5839	1073	3	)	)	PUNCT
ejpam-5839	1073	4	since	since	SCONJ
ejpam-5839	1073	5	lxθ	lxθ	NOUN
ejpam-5839	1073	6	(	(	PUNCT
ejpam-5839	1073	7	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	1073	8	)	)	PUNCT
ejpam-5839	1073	9	is	be	AUX
ejpam-5839	1073	10	a	a	DET
ejpam-5839	1073	11	quadripartitioned	quadripartitione	VERB
ejpam-5839	1073	12	neutrosophic	neutrosophic	ADJ
ejpam-5839	1073	13	soft	soft	ADJ
ejpam-5839	1073	14	subset	subset	NOUN
ejpam-5839	1073	15	of	of	ADP
ejpam-5839	1073	16	the	the	DET
ejpam-5839	1073	17	countable	countable	ADJ
ejpam-5839	1073	18	set	set	NOUN
ejpam-5839	1073	19	bqpnss	bqpns	NOUN
ejpam-5839	1073	20	,	,	PUNCT
ejpam-5839	1073	21	it	it	PRON
ejpam-5839	1073	22	follows	follow	VERB
ejpam-5839	1073	23	that	that	PRON
ejpam-5839	1073	24	lxθ	lxθ	NOUN
ejpam-5839	1073	25	(	(	PUNCT
ejpam-5839	1073	26	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	1073	27	)	)	PUNCT
ejpam-5839	1073	28	is	be	AUX
ejpam-5839	1073	29	also	also	ADV
ejpam-5839	1073	30	countable	countable	ADJ
ejpam-5839	1073	31	.	.	PUNCT
ejpam-5839	1074	1	(	(	PUNCT
ejpam-5839	1074	2	ii	ii	NOUN
ejpam-5839	1074	3	)	)	PUNCT
ejpam-5839	1074	4	since	since	SCONJ
ejpam-5839	1074	5	members	member	NOUN
ejpam-5839	1074	6	of	of	ADP
ejpam-5839	1074	7	bqpnss	bqpns	NOUN
ejpam-5839	1074	8	are	be	AUX
ejpam-5839	1074	9	τqpnss	τqpnss	NOUN
ejpam-5839	1074	10	-	-	PUNCT
ejpam-5839	1074	11	open	open	ADJ
ejpam-5839	1074	12	sets	set	NOUN
ejpam-5839	1074	13	,	,	PUNCT
ejpam-5839	1074	14	the	the	DET
ejpam-5839	1074	15	members	member	NOUN
ejpam-5839	1074	16	of	of	ADP
ejpam-5839	1074	17	lxθ	lxθ	PROPN
ejpam-5839	1074	18	(	(	PUNCT
ejpam-5839	1074	19	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	1074	20	)	)	PUNCT
ejpam-5839	1074	21	are	be	AUX
ejpam-5839	1074	22	also	also	ADV
ejpam-5839	1074	23	contained	contain	VERB
ejpam-5839	1074	24	in	in	ADP
ejpam-5839	1074	25	τqpnss	τqpns	NOUN
ejpam-5839	1074	26	,	,	PUNCT
ejpam-5839	1074	27	i.e.	i.e.	X
ejpam-5839	1074	28	,	,	PUNCT
ejpam-5839	1074	29	lxθ	lxθ	NOUN
ejpam-5839	1074	30	(	(	PUNCT
ejpam-5839	1074	31	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	1074	32	)	)	PUNCT
ejpam-5839	1074	33	⊆	⊆	NUM
ejpam-5839	1074	34	τqpnss	τqpns	NOUN
ejpam-5839	1074	35	.	.	PUNCT
ejpam-5839	1075	1	(	(	PUNCT
ejpam-5839	1075	2	iii	iii	X
ejpam-5839	1075	3	)	)	PUNCT
ejpam-5839	1075	4	any	any	DET
ejpam-5839	1075	5	(	(	PUNCT
ejpam-5839	1075	6	g̃,ω	g̃,ω	NOUN
ejpam-5839	1075	7	)	)	PUNCT
ejpam-5839	1075	8	∈	∈	PROPN
ejpam-5839	1075	9	lxθ	lxθ	NOUN
ejpam-5839	1075	10	(	(	PUNCT
ejpam-5839	1075	11	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	1075	12	)	)	PUNCT
ejpam-5839	1075	13	implies	imply	VERB
ejpam-5839	1075	14	that	that	SCONJ
ejpam-5839	1075	15	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	1075	16	)	)	PUNCT
ejpam-5839	1075	17	∈	∈	PROPN
ejpam-5839	1075	18	(	(	PUNCT
ejpam-5839	1075	19	g̃,ω	g̃,ω	PROPN
ejpam-5839	1075	20	)	)	PUNCT
ejpam-5839	1075	21	.	.	PUNCT
ejpam-5839	1076	1	a.	a.	PROPN
ejpam-5839	1076	2	shihadeh	shihadeh	VERB
ejpam-5839	1076	3	et	et	PROPN
ejpam-5839	1076	4	al	al	PROPN
ejpam-5839	1076	5	.	.	PUNCT
ejpam-5839	1076	6	/	/	SYM
ejpam-5839	1076	7	eur	eur	PROPN
ejpam-5839	1076	8	.	.	PUNCT
ejpam-5839	1077	1	j.	j.	PROPN
ejpam-5839	1077	2	pure	pure	PROPN
ejpam-5839	1077	3	appl	appl	PROPN
ejpam-5839	1077	4	.	.	PROPN
ejpam-5839	1077	5	math	math	PROPN
ejpam-5839	1077	6	,	,	PUNCT
ejpam-5839	1077	7	18	18	NUM
ejpam-5839	1077	8	(	(	PUNCT
ejpam-5839	1077	9	2	2	NUM
ejpam-5839	1077	10	)	)	PUNCT
ejpam-5839	1077	11	(	(	PUNCT
ejpam-5839	1077	12	2025	2025	NUM
ejpam-5839	1077	13	)	)	PUNCT
ejpam-5839	1077	14	,	,	PUNCT
ejpam-5839	1077	15	5839	5839	NUM
ejpam-5839	1077	16	46	46	NUM
ejpam-5839	1077	17	of	of	ADP
ejpam-5839	1077	18	54	54	NUM
ejpam-5839	1077	19	(	(	PUNCT
ejpam-5839	1077	20	iv	iv	X
ejpam-5839	1077	21	)	)	PUNCT
ejpam-5839	1077	22	let	let	VERB
ejpam-5839	1077	23	(	(	PUNCT
ejpam-5839	1077	24	g̃,ω	g̃,ω	NOUN
ejpam-5839	1077	25	)	)	PUNCT
ejpam-5839	1077	26	∈	∈	PROPN
ejpam-5839	1077	27	τqpnss	τqpns	NOUN
ejpam-5839	1077	28	be	be	VERB
ejpam-5839	1077	29	arbitrary	arbitrary	ADJ
ejpam-5839	1077	30	such	such	ADJ
ejpam-5839	1077	31	that	that	DET
ejpam-5839	1077	32	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	1077	33	)	)	PUNCT
ejpam-5839	1077	34	∈	∈	PROPN
ejpam-5839	1077	35	(	(	PUNCT
ejpam-5839	1077	36	g̃,ω	g̃,ω	PROPN
ejpam-5839	1077	37	)	)	PUNCT
ejpam-5839	1077	38	.	.	PUNCT
ejpam-5839	1078	1	then	then	ADV
ejpam-5839	1078	2	,	,	PUNCT
ejpam-5839	1078	3	by	by	ADP
ejpam-5839	1078	4	the	the	DET
ejpam-5839	1078	5	definition	definition	NOUN
ejpam-5839	1078	6	of	of	ADP
ejpam-5839	1078	7	a	a	DET
ejpam-5839	1078	8	quadripartitioned	quadripartitione	VERB
ejpam-5839	1078	9	neutrosophic	neutrosophic	ADJ
ejpam-5839	1078	10	soft	soft	ADJ
ejpam-5839	1078	11	base	base	NOUN
ejpam-5839	1078	12	,	,	PUNCT
ejpam-5839	1078	13	there	there	PRON
ejpam-5839	1078	14	exists	exist	VERB
ejpam-5839	1078	15	some	some	DET
ejpam-5839	1078	16	br	br	NOUN
ejpam-5839	1078	17	∈	∈	PROPN
ejpam-5839	1078	18	bqpnss	bqpns	NOUN
ejpam-5839	1079	1	such	such	ADJ
ejpam-5839	1079	2	that	that	PRON
ejpam-5839	1079	3	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	1079	4	)	)	PUNCT
ejpam-5839	1079	5	∈	∈	PROPN
ejpam-5839	1079	6	br	br	NOUN
ejpam-5839	1079	7	⊆	⊆	NUM
ejpam-5839	1079	8	(	(	PUNCT
ejpam-5839	1079	9	g̃,ω	g̃,ω	NOUN
ejpam-5839	1079	10	)	)	PUNCT
ejpam-5839	1079	11	.	.	PUNCT
ejpam-5839	1080	1	since	since	SCONJ
ejpam-5839	1080	2	br	br	PROPN
ejpam-5839	1080	3	∈	∈	PROPN
ejpam-5839	1080	4	bqpnss	bqpns	NOUN
ejpam-5839	1080	5	and	and	CCONJ
ejpam-5839	1080	6	contains	contain	VERB
ejpam-5839	1080	7	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	1080	8	)	)	PUNCT
ejpam-5839	1080	9	,	,	PUNCT
ejpam-5839	1080	10	it	it	PRON
ejpam-5839	1080	11	follows	follow	VERB
ejpam-5839	1080	12	that	that	SCONJ
ejpam-5839	1080	13	br	br	PROPN
ejpam-5839	1080	14	∈	∈	PROPN
ejpam-5839	1080	15	lxθ	lxθ	NOUN
ejpam-5839	1080	16	(	(	PUNCT
ejpam-5839	1080	17	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	1080	18	)	)	PUNCT
ejpam-5839	1080	19	.	.	PUNCT
ejpam-5839	1081	1	thus	thus	ADV
ejpam-5839	1081	2	,	,	PUNCT
ejpam-5839	1081	3	lxθ	lxθ	INTJ
ejpam-5839	1081	4	(	(	PUNCT
ejpam-5839	1081	5	r1,r2,r3,r4	r1,r2,r3,r4	PROPN
ejpam-5839	1081	6	)	)	PUNCT
ejpam-5839	1081	7	forms	form	VERB
ejpam-5839	1081	8	a	a	DET
ejpam-5839	1081	9	quadripartitioned	quadripartitione	VERB
ejpam-5839	1081	10	neutrosophic	neutrosophic	ADJ
ejpam-5839	1081	11	soft	soft	ADJ
ejpam-5839	1081	12	countable	countable	ADJ
ejpam-5839	1081	13	local	local	ADJ
ejpam-5839	1081	14	base	base	NOUN
ejpam-5839	1081	15	at	at	ADP
ejpam-5839	1081	16	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	1081	17	)	)	PUNCT
ejpam-5839	1081	18	∈	∈	PROPN
ejpam-5839	1081	19	x.	x.	NOUN
ejpam-5839	1081	20	hence	hence	ADV
ejpam-5839	1081	21	,	,	PUNCT
ejpam-5839	1081	22	by	by	ADP
ejpam-5839	1081	23	definition	definition	NOUN
ejpam-5839	1081	24	,	,	PUNCT
ejpam-5839	1081	25	(	(	PUNCT
ejpam-5839	1081	26	x	x	X
ejpam-5839	1081	27	,	,	PUNCT
ejpam-5839	1081	28	τqpnss	τqpnss	PROPN
ejpam-5839	1081	29	,	,	PUNCT
ejpam-5839	1081	30	ω	ω	PROPN
ejpam-5839	1081	31	)	)	PUNCT
ejpam-5839	1081	32	is	be	AUX
ejpam-5839	1081	33	quadripartitioned	quadripartitione	VERB
ejpam-5839	1081	34	neutrosophic	neutrosophic	ADJ
ejpam-5839	1081	35	soft	soft	ADJ
ejpam-5839	1081	36	first	first	ADJ
ejpam-5839	1081	37	countable	countable	ADJ
ejpam-5839	1081	38	.	.	PUNCT
ejpam-5839	1082	1	theorem	theorem	NOUN
ejpam-5839	1082	2	24	24	NUM
ejpam-5839	1082	3	.	.	PUNCT
ejpam-5839	1083	1	let	let	AUX
ejpam-5839	1083	2	(	(	PUNCT
ejpam-5839	1083	3	x	x	NOUN
ejpam-5839	1083	4	,	,	PUNCT
ejpam-5839	1083	5	τqpnss	τqpnss	PROPN
ejpam-5839	1083	6	,	,	PUNCT
ejpam-5839	1083	7	ω	ω	PROPN
ejpam-5839	1083	8	)	)	PUNCT
ejpam-5839	1083	9	be	be	VERB
ejpam-5839	1083	10	a	a	DET
ejpam-5839	1083	11	quadripartitioned	quadripartitione	VERB
ejpam-5839	1083	12	neutrosophic	neutrosophic	ADJ
ejpam-5839	1083	13	soft	soft	ADJ
ejpam-5839	1083	14	topological	topological	ADJ
ejpam-5839	1083	15	space	space	NOUN
ejpam-5839	1083	16	over	over	ADP
ejpam-5839	1083	17	x	x	ADP
ejpam-5839	1083	18	such	such	ADJ
ejpam-5839	1083	19	that	that	SCONJ
ejpam-5839	1083	20	it	it	PRON
ejpam-5839	1083	21	is	be	AUX
ejpam-5839	1083	22	quadripartitioned	quadripartitione	VERB
ejpam-5839	1083	23	neutrosophic	neutrosophic	ADJ
ejpam-5839	1083	24	soft	soft	ADJ
ejpam-5839	1083	25	first	first	ADJ
ejpam-5839	1083	26	countable	countable	ADJ
ejpam-5839	1083	27	,	,	PUNCT
ejpam-5839	1083	28	and	and	CCONJ
ejpam-5839	1083	29	let	let	VERB
ejpam-5839	1083	30	(	(	PUNCT
ejpam-5839	1083	31	y	y	NOUN
ejpam-5839	1083	32	,	,	PUNCT
ejpam-5839	1083	33	j	j	PROPN
ejpam-5839	1083	34	qpnss	qpnss	NOUN
ejpam-5839	1083	35	,	,	PUNCT
ejpam-5839	1083	36	ω	ω	NOUN
ejpam-5839	1083	37	)	)	PUNCT
ejpam-5839	1083	38	be	be	VERB
ejpam-5839	1083	39	a	a	DET
ejpam-5839	1083	40	quadripartitioned	quadripartitione	VERB
ejpam-5839	1083	41	neutrosophic	neutrosophic	ADJ
ejpam-5839	1083	42	soft	soft	ADJ
ejpam-5839	1083	43	subspace	subspace	NOUN
ejpam-5839	1083	44	of	of	ADP
ejpam-5839	1083	45	(	(	PUNCT
ejpam-5839	1083	46	x	x	NOUN
ejpam-5839	1083	47	,	,	PUNCT
ejpam-5839	1083	48	τqpnss	τqpnss	PROPN
ejpam-5839	1083	49	,	,	PUNCT
ejpam-5839	1083	50	ω	ω	PROPN
ejpam-5839	1083	51	)	)	PUNCT
ejpam-5839	1083	52	.	.	PUNCT
ejpam-5839	1084	1	then	then	ADV
ejpam-5839	1084	2	(	(	PUNCT
ejpam-5839	1084	3	y	y	PROPN
ejpam-5839	1084	4	,	,	PUNCT
ejpam-5839	1084	5	j	j	PROPN
ejpam-5839	1084	6	qpnss	qpnss	NOUN
ejpam-5839	1084	7	,	,	PUNCT
ejpam-5839	1084	8	ω	ω	NOUN
ejpam-5839	1084	9	)	)	PUNCT
ejpam-5839	1084	10	is	be	AUX
ejpam-5839	1084	11	quadripartitioned	quadripartitione	VERB
ejpam-5839	1084	12	neutrosophic	neutrosophic	ADJ
ejpam-5839	1084	13	soft	soft	ADJ
ejpam-5839	1084	14	first	first	ADJ
ejpam-5839	1084	15	countable	countable	ADJ
ejpam-5839	1084	16	.	.	PUNCT
ejpam-5839	1085	1	proof	proof	NOUN
ejpam-5839	1085	2	.	.	PUNCT
ejpam-5839	1086	1	let	let	VERB
ejpam-5839	1086	2	yθ	yθ	PRON
ejpam-5839	1086	3	′	′	VERB
ejpam-5839	1086	4	(	(	PUNCT
ejpam-5839	1086	5	r′1,r	r′1,r	VERB
ejpam-5839	1086	6	′	′	NUM
ejpam-5839	1086	7	2,r	2,r	NUM
ejpam-5839	1087	1	′	′	NUM
ejpam-5839	1088	1	3,r	3,r	NUM
ejpam-5839	1088	2	′	′	NUM
ejpam-5839	1088	3	4	4	NUM
ejpam-5839	1088	4	)	)	PUNCT
ejpam-5839	1088	5	∈	∈	PROPN
ejpam-5839	1088	6	y	y	PROPN
ejpam-5839	1088	7	be	be	AUX
ejpam-5839	1088	8	arbitrary	arbitrary	ADJ
ejpam-5839	1088	9	,	,	PUNCT
ejpam-5839	1088	10	then	then	ADV
ejpam-5839	1088	11	yθ	yθ	NOUN
ejpam-5839	1088	12	′	′	NUM
ejpam-5839	1088	13	(	(	PUNCT
ejpam-5839	1088	14	r′1,r	r′1,r	VERB
ejpam-5839	1088	15	′	′	NUM
ejpam-5839	1088	16	2,r	2,r	NUM
ejpam-5839	1088	17	′	′	NUM
ejpam-5839	1089	1	3,r	3,r	NUM
ejpam-5839	1089	2	′	′	NUM
ejpam-5839	1089	3	4	4	NUM
ejpam-5839	1089	4	)	)	PUNCT
ejpam-5839	1089	5	∈	∈	PROPN
ejpam-5839	1089	6	y	y	PROPN
ejpam-5839	1089	7	as	as	ADP
ejpam-5839	1089	8	y	y	PROPN
ejpam-5839	1089	9	⊆	⊆	NUM
ejpam-5839	1089	10	x.	x.	NOUN
ejpam-5839	1089	11	since	since	SCONJ
ejpam-5839	1089	12	x	x	PROPN
ejpam-5839	1089	13	is	be	AUX
ejpam-5839	1089	14	quadripartitioned	quadripartitione	VERB
ejpam-5839	1089	15	neutrosophic	neutrosophic	ADJ
ejpam-5839	1089	16	soft	soft	ADJ
ejpam-5839	1089	17	first	first	ADJ
ejpam-5839	1089	18	countable	countable	ADJ
ejpam-5839	1089	19	,	,	PUNCT
ejpam-5839	1089	20	it	it	PRON
ejpam-5839	1089	21	guarantees	guarantee	VERB
ejpam-5839	1089	22	that	that	SCONJ
ejpam-5839	1089	23	there	there	PRON
ejpam-5839	1089	24	exists	exist	VERB
ejpam-5839	1089	25	a	a	DET
ejpam-5839	1089	26	quadripartitioned	quadripartitioned	ADJ
ejpam-5839	1089	27	neutrosophic	neutrosophic	ADJ
ejpam-5839	1089	28	soft	soft	ADJ
ejpam-5839	1089	29	countable	countable	ADJ
ejpam-5839	1089	30	local	local	ADJ
ejpam-5839	1089	31	base	base	NOUN
ejpam-5839	1089	32	at	at	ADP
ejpam-5839	1089	33	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	1089	34	)	)	PUNCT
ejpam-5839	1089	35	∈	∈	PROPN
ejpam-5839	1089	36	x	x	X
ejpam-5839	1089	37	and	and	CCONJ
ejpam-5839	1089	38	hence	hence	ADV
ejpam-5839	1089	39	,	,	PUNCT
ejpam-5839	1089	40	in	in	ADP
ejpam-5839	1089	41	particular	particular	ADJ
ejpam-5839	1089	42	,	,	PUNCT
ejpam-5839	1089	43	there	there	PRON
ejpam-5839	1089	44	exists	exist	VERB
ejpam-5839	1089	45	a	a	DET
ejpam-5839	1089	46	quadripartitioned	quadripartitioned	ADJ
ejpam-5839	1089	47	neutrosophic	neutrosophic	ADJ
ejpam-5839	1089	48	soft	soft	ADJ
ejpam-5839	1089	49	countable	countable	ADJ
ejpam-5839	1089	50	local	local	ADJ
ejpam-5839	1089	51	base	base	NOUN
ejpam-5839	1089	52	bqpnss	bqpns	NOUN
ejpam-5839	1089	53	at	at	ADP
ejpam-5839	1089	54	yθ	yθ	NOUN
ejpam-5839	1089	55	′	′	NUM
ejpam-5839	1089	56	(	(	PUNCT
ejpam-5839	1089	57	r′1,r	r′1,r	VERB
ejpam-5839	1089	58	′	′	NUM
ejpam-5839	1089	59	2,r	2,r	NUM
ejpam-5839	1089	60	′	′	NUM
ejpam-5839	1090	1	3,r	3,r	NUM
ejpam-5839	1090	2	′	′	NUM
ejpam-5839	1090	3	4	4	NUM
ejpam-5839	1090	4	)	)	PUNCT
ejpam-5839	1090	5	.	.	PUNCT
ejpam-5839	1091	1	members	member	NOUN
ejpam-5839	1091	2	of	of	ADP
ejpam-5839	1091	3	bqpnss	bqpns	NOUN
ejpam-5839	1091	4	can	can	AUX
ejpam-5839	1091	5	be	be	AUX
ejpam-5839	1091	6	enumerated	enumerate	VERB
ejpam-5839	1091	7	as	as	ADP
ejpam-5839	1091	8	b1	b1	NOUN
ejpam-5839	1091	9	,	,	PUNCT
ejpam-5839	1091	10	b2	b2	NOUN
ejpam-5839	1091	11	,	,	PUNCT
ejpam-5839	1091	12	b3	b3	PROPN
ejpam-5839	1091	13	,	,	PUNCT
ejpam-5839	1091	14	b4	b4	NOUN
ejpam-5839	1091	15	,	,	PUNCT
ejpam-5839	1091	16	b5	b5	PROPN
ejpam-5839	1091	17	,	,	PUNCT
ejpam-5839	1091	18	.	.	PUNCT
ejpam-5839	1091	19	.	.	PUNCT
ejpam-5839	1092	1	.	.	PUNCT
ejpam-5839	1093	1	,	,	PUNCT
ejpam-5839	1093	2	that	that	ADV
ejpam-5839	1093	3	is	is	ADV
ejpam-5839	1093	4	,	,	PUNCT
ejpam-5839	1093	5	bqpnss	bqpns	NOUN
ejpam-5839	1093	6	=	=	PUNCT
ejpam-5839	1093	7	{	{	PUNCT
ejpam-5839	1093	8	bn	bn	X
ejpam-5839	1093	9	:	:	PUNCT
ejpam-5839	1093	10	n	n	CCONJ
ejpam-5839	1093	11	∈	∈	PROPN
ejpam-5839	1093	12	n	n	CCONJ
ejpam-5839	1093	13	}	}	PUNCT
ejpam-5839	1093	14	.	.	PUNCT
ejpam-5839	1094	1	evidently	evidently	ADV
ejpam-5839	1094	2	,	,	PUNCT
ejpam-5839	1094	3	yθ	yθ	PROPN
ejpam-5839	1094	4	′	′	NUM
ejpam-5839	1094	5	(	(	PUNCT
ejpam-5839	1094	6	r′1,r	r′1,r	VERB
ejpam-5839	1094	7	′	′	NUM
ejpam-5839	1094	8	2,r	2,r	NUM
ejpam-5839	1094	9	′	′	NUM
ejpam-5839	1095	1	3,r	3,r	NUM
ejpam-5839	1095	2	′	′	NUM
ejpam-5839	1095	3	4	4	NUM
ejpam-5839	1095	4	)	)	PUNCT
ejpam-5839	1095	5	∈	∈	PROPN
ejpam-5839	1095	6	x.	x.	NOUN
ejpam-5839	1095	7	since	since	SCONJ
ejpam-5839	1095	8	yθ	yθ	PROPN
ejpam-5839	1095	9	′	′	NUM
ejpam-5839	1095	10	(	(	PUNCT
ejpam-5839	1095	11	r′1,r	r′1,r	VERB
ejpam-5839	1095	12	′	′	NUM
ejpam-5839	1095	13	2,r	2,r	NUM
ejpam-5839	1095	14	′	′	NUM
ejpam-5839	1095	15	3,r	3,r	NUM
ejpam-5839	1095	16	′	′	NUM
ejpam-5839	1095	17	4	4	NUM
ejpam-5839	1095	18	)	)	PUNCT
ejpam-5839	1095	19	∈	∈	PROPN
ejpam-5839	1095	20	bn	bn	NOUN
ejpam-5839	1095	21	for	for	ADP
ejpam-5839	1095	22	all	all	PRON
ejpam-5839	1095	23	n	n	PRON
ejpam-5839	1095	24	∈	∈	PROPN
ejpam-5839	1095	25	n	n	CCONJ
ejpam-5839	1095	26	,	,	PUNCT
ejpam-5839	1095	27	we	we	PRON
ejpam-5839	1095	28	write	write	VERB
ejpam-5839	1095	29	b1	b1	NOUN
ejpam-5839	1095	30	=	=	SYM
ejpam-5839	1095	31	{	{	PUNCT
ejpam-5839	1095	32	y	y	PROPN
ejpam-5839	1095	33	∩bn	∩bn	VERB
ejpam-5839	1095	34	:	:	PUNCT
ejpam-5839	1095	35	n	n	CCONJ
ejpam-5839	1095	36	∈	∈	PROPN
ejpam-5839	1095	37	ν	ν	NOUN
ejpam-5839	1095	38	/	/	SYM
ejpam-5839	1095	39	n	n	CCONJ
ejpam-5839	1095	40	}	}	PUNCT
ejpam-5839	1095	41	(	(	PUNCT
ejpam-5839	1095	42	1	1	NUM
ejpam-5839	1095	43	)	)	PUNCT
ejpam-5839	1095	44	.	.	PUNCT
ejpam-5839	1096	1	since	since	SCONJ
ejpam-5839	1096	2	yθ	yθ	PROPN
ejpam-5839	1096	3	′	′	NUM
ejpam-5839	1096	4	(	(	PUNCT
ejpam-5839	1096	5	r′1,r	r′1,r	VERB
ejpam-5839	1096	6	′	′	NUM
ejpam-5839	1096	7	2,r	2,r	NUM
ejpam-5839	1096	8	′	′	NUM
ejpam-5839	1097	1	3,r	3,r	NUM
ejpam-5839	1097	2	′	′	NUM
ejpam-5839	1097	3	4	4	NUM
ejpam-5839	1097	4	)	)	PUNCT
ejpam-5839	1097	5	∈	∈	PROPN
ejpam-5839	1097	6	y	y	PROPN
ejpam-5839	1097	7	and	and	CCONJ
ejpam-5839	1097	8	yθ	yθ	PROPN
ejpam-5839	1097	9	′	′	NUM
ejpam-5839	1097	10	(	(	PUNCT
ejpam-5839	1097	11	r′1,r	r′1,r	VERB
ejpam-5839	1097	12	′	′	NUM
ejpam-5839	1097	13	2,r	2,r	NUM
ejpam-5839	1097	14	′	′	NUM
ejpam-5839	1098	1	3,r	3,r	NUM
ejpam-5839	1098	2	′	′	NUM
ejpam-5839	1098	3	4	4	NUM
ejpam-5839	1098	4	)	)	PUNCT
ejpam-5839	1098	5	∈	∈	PROPN
ejpam-5839	1098	6	bn	bn	NOUN
ejpam-5839	1098	7	for	for	ADP
ejpam-5839	1098	8	all	all	PRON
ejpam-5839	1098	9	n	n	PRON
ejpam-5839	1098	10	∈	∈	PROPN
ejpam-5839	1098	11	n	n	CCONJ
ejpam-5839	1098	12	,	,	PUNCT
ejpam-5839	1098	13	it	it	PRON
ejpam-5839	1098	14	follows	follow	VERB
ejpam-5839	1098	15	that	that	PRON
ejpam-5839	1098	16	yθ	yθ	NOUN
ejpam-5839	1098	17	′	′	NUM
ejpam-5839	1098	18	(	(	PUNCT
ejpam-5839	1098	19	r′1,r	r′1,r	VERB
ejpam-5839	1098	20	′	′	NUM
ejpam-5839	1098	21	2,r	2,r	NUM
ejpam-5839	1098	22	′	′	NUM
ejpam-5839	1099	1	3,r	3,r	NUM
ejpam-5839	1099	2	′	′	NUM
ejpam-5839	1099	3	4	4	NUM
ejpam-5839	1099	4	)	)	PUNCT
ejpam-5839	1099	5	∈	∈	PROPN
ejpam-5839	1099	6	bn	bn	NOUN
ejpam-5839	1099	7	for	for	ADP
ejpam-5839	1099	8	all	all	PRON
ejpam-5839	1099	9	n	n	PRON
ejpam-5839	1099	10	∈	∈	PROPN
ejpam-5839	1099	11	n	n	CCONJ
ejpam-5839	1099	12	(	(	PUNCT
ejpam-5839	1099	13	2	2	NUM
ejpam-5839	1099	14	)	)	PUNCT
ejpam-5839	1099	15	.	.	PUNCT
ejpam-5839	1100	1	since	since	SCONJ
ejpam-5839	1100	2	bn	bn	NOUN
ejpam-5839	1100	3	∈	∈	PROPN
ejpam-5839	1100	4	bqpnss	bqpns	NOUN
ejpam-5839	1100	5	for	for	ADP
ejpam-5839	1100	6	all	all	DET
ejpam-5839	1100	7	n	n	PRON
ejpam-5839	1100	8	∈	∈	PROPN
ejpam-5839	1100	9	n	n	CCONJ
ejpam-5839	1100	10	,	,	PUNCT
ejpam-5839	1100	11	we	we	PRON
ejpam-5839	1100	12	have	have	VERB
ejpam-5839	1100	13	bn	bn	NUM
ejpam-5839	1100	14	∈	∈	PROPN
ejpam-5839	1100	15	τqpnss	τqpns	NOUN
ejpam-5839	1100	16	,	,	PUNCT
ejpam-5839	1100	17	which	which	PRON
ejpam-5839	1100	18	implies	imply	VERB
ejpam-5839	1100	19	that	that	SCONJ
ejpam-5839	1100	20	y	y	PROPN
ejpam-5839	1100	21	∩bn	∩bn	PROPN
ejpam-5839	1100	22	∈	∈	PROPN
ejpam-5839	1100	23	j	j	PROPN
ejpam-5839	1100	24	qpnss	qpnss	NOUN
ejpam-5839	1100	25	.	.	PUNCT
ejpam-5839	1101	1	theorem	theorem	VERB
ejpam-5839	1101	2	25	25	NUM
ejpam-5839	1101	3	.	.	PUNCT
ejpam-5839	1102	1	let	let	AUX
ejpam-5839	1102	2	(	(	PUNCT
ejpam-5839	1102	3	x	x	NOUN
ejpam-5839	1102	4	,	,	PUNCT
ejpam-5839	1102	5	τqpnss	τqpnss	PROPN
ejpam-5839	1102	6	,	,	PUNCT
ejpam-5839	1102	7	ω	ω	PROPN
ejpam-5839	1102	8	)	)	PUNCT
ejpam-5839	1102	9	be	be	VERB
ejpam-5839	1102	10	a	a	DET
ejpam-5839	1102	11	quadripartitioned	quadripartitione	VERB
ejpam-5839	1102	12	neutrosophic	neutrosophic	ADJ
ejpam-5839	1102	13	soft	soft	ADJ
ejpam-5839	1102	14	topological	topological	ADJ
ejpam-5839	1102	15	space	space	NOUN
ejpam-5839	1102	16	over	over	ADP
ejpam-5839	1102	17	x	x	ADP
ejpam-5839	1102	18	such	such	ADJ
ejpam-5839	1102	19	that	that	SCONJ
ejpam-5839	1102	20	it	it	PRON
ejpam-5839	1102	21	is	be	AUX
ejpam-5839	1102	22	quadripartitioned	quadripartitione	VERB
ejpam-5839	1102	23	neutrosophic	neutrosophic	ADJ
ejpam-5839	1102	24	soft	soft	ADJ
ejpam-5839	1102	25	second	second	ADJ
ejpam-5839	1102	26	countable	countable	ADJ
ejpam-5839	1102	27	,	,	PUNCT
ejpam-5839	1102	28	and	and	CCONJ
ejpam-5839	1102	29	let	let	VERB
ejpam-5839	1102	30	(	(	PUNCT
ejpam-5839	1102	31	y	y	NOUN
ejpam-5839	1102	32	,	,	PUNCT
ejpam-5839	1102	33	j	j	PROPN
ejpam-5839	1102	34	qpnss	qpnss	NOUN
ejpam-5839	1102	35	,	,	PUNCT
ejpam-5839	1102	36	ω	ω	NOUN
ejpam-5839	1102	37	)	)	PUNCT
ejpam-5839	1102	38	be	be	VERB
ejpam-5839	1102	39	a	a	DET
ejpam-5839	1102	40	quadripartitioned	quadripartitione	VERB
ejpam-5839	1102	41	neutrosophic	neutrosophic	ADJ
ejpam-5839	1102	42	soft	soft	ADJ
ejpam-5839	1102	43	subspace	subspace	NOUN
ejpam-5839	1102	44	of	of	ADP
ejpam-5839	1102	45	(	(	PUNCT
ejpam-5839	1102	46	x	x	NOUN
ejpam-5839	1102	47	,	,	PUNCT
ejpam-5839	1102	48	τqpnss	τqpnss	PROPN
ejpam-5839	1102	49	,	,	PUNCT
ejpam-5839	1102	50	ω	ω	PROPN
ejpam-5839	1102	51	)	)	PUNCT
ejpam-5839	1102	52	.	.	PUNCT
ejpam-5839	1103	1	then	then	ADV
ejpam-5839	1103	2	(	(	PUNCT
ejpam-5839	1103	3	y	y	PROPN
ejpam-5839	1103	4	,	,	PUNCT
ejpam-5839	1103	5	j	j	PROPN
ejpam-5839	1103	6	qpnss	qpnss	NOUN
ejpam-5839	1103	7	,	,	PUNCT
ejpam-5839	1103	8	ω	ω	NOUN
ejpam-5839	1103	9	)	)	PUNCT
ejpam-5839	1103	10	is	be	AUX
ejpam-5839	1103	11	quadripartitioned	quadripartitione	VERB
ejpam-5839	1103	12	neutrosophic	neutrosophic	ADJ
ejpam-5839	1103	13	soft	soft	ADJ
ejpam-5839	1103	14	second	second	ADJ
ejpam-5839	1103	15	countable	countable	ADJ
ejpam-5839	1103	16	.	.	PUNCT
ejpam-5839	1104	1	proof	proof	NOUN
ejpam-5839	1104	2	.	.	PUNCT
ejpam-5839	1105	1	let	let	VERB
ejpam-5839	1105	2	(	(	PUNCT
ejpam-5839	1105	3	y	y	NOUN
ejpam-5839	1105	4	,	,	PUNCT
ejpam-5839	1105	5	j	j	PROPN
ejpam-5839	1105	6	qpnss	qpnss	NOUN
ejpam-5839	1105	7	,	,	PUNCT
ejpam-5839	1105	8	ω	ω	NOUN
ejpam-5839	1105	9	)	)	PUNCT
ejpam-5839	1105	10	be	be	VERB
ejpam-5839	1105	11	a	a	DET
ejpam-5839	1105	12	quadripartitioned	quadripartitione	VERB
ejpam-5839	1105	13	neutrosophic	neutrosophic	ADJ
ejpam-5839	1105	14	soft	soft	ADJ
ejpam-5839	1105	15	subspace	subspace	NOUN
ejpam-5839	1105	16	of	of	ADP
ejpam-5839	1105	17	(	(	PUNCT
ejpam-5839	1105	18	x	x	NOUN
ejpam-5839	1105	19	,	,	PUNCT
ejpam-5839	1105	20	τqpnss	τqpnss	PROPN
ejpam-5839	1105	21	,	,	PUNCT
ejpam-5839	1105	22	ω	ω	PROPN
ejpam-5839	1105	23	)	)	PUNCT
ejpam-5839	1105	24	,	,	PUNCT
ejpam-5839	1105	25	a	a	DET
ejpam-5839	1105	26	quadripartitioned	quadripartitione	VERB
ejpam-5839	1105	27	neutrosophic	neutrosophic	ADJ
ejpam-5839	1105	28	soft	soft	ADJ
ejpam-5839	1105	29	topological	topological	ADJ
ejpam-5839	1105	30	space	space	NOUN
ejpam-5839	1105	31	over	over	ADP
ejpam-5839	1105	32	x	x	ADP
ejpam-5839	1105	33	which	which	PRON
ejpam-5839	1105	34	is	be	AUX
ejpam-5839	1105	35	quadripartitioned	quadripartitione	VERB
ejpam-5839	1105	36	neutrosophic	neutrosophic	ADJ
ejpam-5839	1105	37	soft	soft	ADJ
ejpam-5839	1105	38	second	second	ADJ
ejpam-5839	1105	39	countable	countable	ADJ
ejpam-5839	1105	40	.	.	PUNCT
ejpam-5839	1106	1	this	this	PRON
ejpam-5839	1106	2	implies	imply	VERB
ejpam-5839	1106	3	that	that	SCONJ
ejpam-5839	1106	4	there	there	PRON
ejpam-5839	1106	5	exists	exist	VERB
ejpam-5839	1106	6	a	a	DET
ejpam-5839	1106	7	quadripartitioned	quadripartitioned	ADJ
ejpam-5839	1106	8	neutrosophic	neutrosophic	ADJ
ejpam-5839	1106	9	soft	soft	ADJ
ejpam-5839	1106	10	countable	countable	ADJ
ejpam-5839	1106	11	base	base	NOUN
ejpam-5839	1106	12	bqpnss	bqpns	NOUN
ejpam-5839	1106	13	for	for	ADP
ejpam-5839	1106	14	τqpnss	τqpns	NOUN
ejpam-5839	1106	15	.	.	PUNCT
ejpam-5839	1107	1	if	if	SCONJ
ejpam-5839	1107	2	we	we	PRON
ejpam-5839	1107	3	prove	prove	VERB
ejpam-5839	1107	4	that	that	SCONJ
ejpam-5839	1107	5	(	(	PUNCT
ejpam-5839	1107	6	y	y	NOUN
ejpam-5839	1107	7	,	,	PUNCT
ejpam-5839	1107	8	j	j	PROPN
ejpam-5839	1107	9	qpnss	qpnss	NOUN
ejpam-5839	1107	10	,	,	PUNCT
ejpam-5839	1107	11	ω	ω	NOUN
ejpam-5839	1107	12	)	)	PUNCT
ejpam-5839	1107	13	is	be	AUX
ejpam-5839	1107	14	quadripartitioned	quadripartitione	VERB
ejpam-5839	1107	15	neutrosophic	neutrosophic	ADJ
ejpam-5839	1107	16	soft	soft	ADJ
ejpam-5839	1107	17	countable	countable	ADJ
ejpam-5839	1107	18	,	,	PUNCT
ejpam-5839	1107	19	the	the	DET
ejpam-5839	1107	20	result	result	NOUN
ejpam-5839	1107	21	will	will	AUX
ejpam-5839	1107	22	automatically	automatically	ADV
ejpam-5839	1107	23	follow	follow	VERB
ejpam-5839	1107	24	.	.	PUNCT
ejpam-5839	1108	1	since	since	SCONJ
ejpam-5839	1108	2	bqpnss	bqpns	NOUN
ejpam-5839	1108	3	is	be	AUX
ejpam-5839	1108	4	quadripartitioned	quadripartitione	VERB
ejpam-5839	1108	5	neutrosophic	neutrosophic	ADJ
ejpam-5839	1108	6	soft	soft	ADJ
ejpam-5839	1108	7	countable	countable	ADJ
ejpam-5839	1108	8	,	,	PUNCT
ejpam-5839	1108	9	it	it	PRON
ejpam-5839	1108	10	follows	follow	VERB
ejpam-5839	1108	11	that	that	SCONJ
ejpam-5839	1108	12	bqpnss	bqpns	NOUN
ejpam-5839	1108	13	∼	∼	NOUN
ejpam-5839	1108	14	n	n	CCONJ
ejpam-5839	1108	15	,	,	PUNCT
ejpam-5839	1108	16	which	which	PRON
ejpam-5839	1108	17	implies	imply	VERB
ejpam-5839	1108	18	that	that	SCONJ
ejpam-5839	1108	19	bqpnss	bqpns	NOUN
ejpam-5839	1108	20	can	can	AUX
ejpam-5839	1108	21	be	be	AUX
ejpam-5839	1108	22	expressed	express	VERB
ejpam-5839	1108	23	as	as	ADP
ejpam-5839	1108	24	bqpnss	bqpns	NOUN
ejpam-5839	1108	25	=	=	PUNCT
ejpam-5839	1108	26	{	{	PUNCT
ejpam-5839	1108	27	bn	bn	X
ejpam-5839	1108	28	:	:	PUNCT
ejpam-5839	1108	29	n	n	CCONJ
ejpam-5839	1108	30	∈	∈	PROPN
ejpam-5839	1108	31	n	n	CCONJ
ejpam-5839	1108	32	}	}	PUNCT
ejpam-5839	1108	33	.	.	PUNCT
ejpam-5839	1109	1	define	define	VERB
ejpam-5839	1109	2	b1	b1	NOUN
ejpam-5839	1109	3	=	=	SYM
ejpam-5839	1109	4	{	{	PUNCT
ejpam-5839	1109	5	y	y	PROPN
ejpam-5839	1109	6	∩bn	∩bn	VERB
ejpam-5839	1109	7	:	:	PUNCT
ejpam-5839	1109	8	n	n	CCONJ
ejpam-5839	1109	9	∈	∈	PROPN
ejpam-5839	1109	10	n	n	CCONJ
ejpam-5839	1109	11	}	}	PUNCT
ejpam-5839	1109	12	(	(	PUNCT
ejpam-5839	1109	13	i	i	NOUN
ejpam-5839	1109	14	)	)	PUNCT
ejpam-5839	1109	15	.	.	PUNCT
ejpam-5839	1110	1	a.	a.	PROPN
ejpam-5839	1110	2	shihadeh	shihadeh	VERB
ejpam-5839	1110	3	et	et	PROPN
ejpam-5839	1110	4	al	al	PROPN
ejpam-5839	1110	5	.	.	PUNCT
ejpam-5839	1110	6	/	/	SYM
ejpam-5839	1110	7	eur	eur	PROPN
ejpam-5839	1110	8	.	.	PUNCT
ejpam-5839	1111	1	j.	j.	PROPN
ejpam-5839	1111	2	pure	pure	PROPN
ejpam-5839	1111	3	appl	appl	PROPN
ejpam-5839	1111	4	.	.	PROPN
ejpam-5839	1111	5	math	math	PROPN
ejpam-5839	1111	6	,	,	PUNCT
ejpam-5839	1111	7	18	18	NUM
ejpam-5839	1111	8	(	(	PUNCT
ejpam-5839	1111	9	2	2	NUM
ejpam-5839	1111	10	)	)	PUNCT
ejpam-5839	1111	11	(	(	PUNCT
ejpam-5839	1111	12	2025	2025	NUM
ejpam-5839	1111	13	)	)	PUNCT
ejpam-5839	1111	14	,	,	PUNCT
ejpam-5839	1111	15	5839	5839	NUM
ejpam-5839	1111	16	47	47	NUM
ejpam-5839	1111	17	of	of	ADP
ejpam-5839	1111	18	54	54	NUM
ejpam-5839	1111	19	evidently	evidently	ADV
ejpam-5839	1111	20	,	,	PUNCT
ejpam-5839	1111	21	b1	b1	VERB
ejpam-5839	1111	22	∼	∼	NOUN
ejpam-5839	1111	23	n	n	CCONJ
ejpam-5839	1111	24	under	under	ADP
ejpam-5839	1111	25	the	the	DET
ejpam-5839	1111	26	quadripartitioned	quadripartitione	VERB
ejpam-5839	1111	27	neutrosophic	neutrosophic	ADJ
ejpam-5839	1111	28	soft	soft	ADJ
ejpam-5839	1111	29	map	map	NOUN
ejpam-5839	1111	30	y	y	PROPN
ejpam-5839	1111	31	∩bn	∩bn	PROPN
ejpam-5839	1111	32	→	→	PROPN
ejpam-5839	1111	33	n.	n.	PROPN
ejpam-5839	1111	34	therefore	therefore	ADV
ejpam-5839	1111	35	,	,	PUNCT
ejpam-5839	1111	36	b1	b1	PROPN
ejpam-5839	1111	37	is	be	AUX
ejpam-5839	1111	38	quadripartitioned	quadripartitione	VERB
ejpam-5839	1111	39	neutrosophic	neutrosophic	ADJ
ejpam-5839	1111	40	soft	soft	ADJ
ejpam-5839	1111	41	countable	countable	ADJ
ejpam-5839	1111	42	.	.	PUNCT
ejpam-5839	1112	1	(	(	PUNCT
ejpam-5839	1112	2	ii	ii	NOUN
ejpam-5839	1112	3	)	)	PUNCT
ejpam-5839	1112	4	b1	b1	NOUN
ejpam-5839	1112	5	is	be	AUX
ejpam-5839	1112	6	a	a	DET
ejpam-5839	1112	7	quadripartitioned	quadripartitione	VERB
ejpam-5839	1112	8	neutrosophic	neutrosophic	ADJ
ejpam-5839	1112	9	soft	soft	ADJ
ejpam-5839	1112	10	family	family	NOUN
ejpam-5839	1112	11	of	of	ADP
ejpam-5839	1112	12	all	all	DET
ejpam-5839	1112	13	j	j	PROPN
ejpam-5839	1112	14	qpnss	qpnss	NOUN
ejpam-5839	1112	15	-	-	PUNCT
ejpam-5839	1112	16	quadripartitioned	quadripartitione	VERB
ejpam-5839	1112	17	neutrosophic	neutrosophic	ADJ
ejpam-5839	1112	18	soft	soft	ADJ
ejpam-5839	1112	19	p	p	NOUN
ejpam-5839	1112	20	-	-	PUNCT
ejpam-5839	1112	21	open	open	ADJ
ejpam-5839	1112	22	sets	set	NOUN
ejpam-5839	1112	23	.	.	PUNCT
ejpam-5839	1113	1	since	since	SCONJ
ejpam-5839	1113	2	bn	bn	NOUN
ejpam-5839	1113	3	∈	∈	NOUN
ejpam-5839	1113	4	bqpnss	bqpns	NOUN
ejpam-5839	1113	5	implies	imply	VERB
ejpam-5839	1113	6	bn	bn	NOUN
ejpam-5839	1113	7	∈	∈	PROPN
ejpam-5839	1113	8	τqpnss	τqpns	NOUN
ejpam-5839	1113	9	,	,	PUNCT
ejpam-5839	1113	10	it	it	PRON
ejpam-5839	1113	11	follows	follow	VERB
ejpam-5839	1113	12	that	that	SCONJ
ejpam-5839	1113	13	b	b	PROPN
ejpam-5839	1113	14	⊆	⊆	NUM
ejpam-5839	1113	15	τqpnss	τqpns	NOUN
ejpam-5839	1113	16	,	,	PUNCT
ejpam-5839	1113	17	implying	imply	VERB
ejpam-5839	1113	18	that	that	SCONJ
ejpam-5839	1113	19	y	y	PROPN
ejpam-5839	1113	20	∩bn	∩bn	PROPN
ejpam-5839	1113	21	∈	∈	PROPN
ejpam-5839	1113	22	j	j	PROPN
ejpam-5839	1113	23	qpnss	qpnss	NOUN
ejpam-5839	1113	24	.	.	PUNCT
ejpam-5839	1114	1	(	(	PUNCT
ejpam-5839	1114	2	iii	iii	X
ejpam-5839	1114	3	)	)	PUNCT
ejpam-5839	1114	4	for	for	ADP
ejpam-5839	1114	5	any	any	DET
ejpam-5839	1114	6	yθ	yθ	NOUN
ejpam-5839	1114	7	′	′	NUM
ejpam-5839	1114	8	(	(	PUNCT
ejpam-5839	1114	9	r′1,r	r′1,r	VERB
ejpam-5839	1114	10	′	′	NUM
ejpam-5839	1114	11	2,r	2,r	NUM
ejpam-5839	1114	12	′	′	NUM
ejpam-5839	1115	1	3,r	3,r	NUM
ejpam-5839	1115	2	′	′	NUM
ejpam-5839	1115	3	4	4	NUM
ejpam-5839	1115	4	)	)	PUNCT
ejpam-5839	1115	5	∈	∈	PROPN
ejpam-5839	1115	6	(	(	PUNCT
ejpam-5839	1115	7	g̃,ω	g̃,ω	NOUN
ejpam-5839	1115	8	)	)	PUNCT
ejpam-5839	1115	9	∈	∈	PROPN
ejpam-5839	1115	10	j	j	PROPN
ejpam-5839	1115	11	qpnss	qpnss	NOUN
ejpam-5839	1115	12	,	,	PUNCT
ejpam-5839	1115	13	there	there	ADV
ejpam-5839	1115	14	existsbr∩y	existsbr∩y	NOUN
ejpam-5839	1115	15	∈	∈	NOUN
ejpam-5839	1115	16	b1	b1	VERB
ejpam-5839	1115	17	such	such	DET
ejpam-5839	1115	18	that	that	DET
ejpam-5839	1115	19	yθ	yθ	NOUN
ejpam-5839	1116	1	′	′	NUM
ejpam-5839	1116	2	(	(	PUNCT
ejpam-5839	1116	3	r′1,r	r′1,r	VERB
ejpam-5839	1116	4	′	′	NUM
ejpam-5839	1116	5	2,r	2,r	NUM
ejpam-5839	1116	6	′	′	NUM
ejpam-5839	1117	1	3,r	3,r	NUM
ejpam-5839	1117	2	′	′	NUM
ejpam-5839	1117	3	4	4	NUM
ejpam-5839	1117	4	)	)	PUNCT
ejpam-5839	1117	5	∈	∈	PROPN
ejpam-5839	1117	6	br	br	NOUN
ejpam-5839	1117	7	∩	∩	NOUN
ejpam-5839	1117	8	y	y	PROPN
ejpam-5839	1117	9	⊆	⊆	NUM
ejpam-5839	1117	10	(	(	PUNCT
ejpam-5839	1117	11	g̃,ω	g̃,ω	PROPN
ejpam-5839	1117	12	)	)	PUNCT
ejpam-5839	1117	13	.	.	PUNCT
ejpam-5839	1118	1	to	to	PART
ejpam-5839	1118	2	prove	prove	VERB
ejpam-5839	1118	3	this	this	PRON
ejpam-5839	1118	4	,	,	PUNCT
ejpam-5839	1118	5	let	let	VERB
ejpam-5839	1118	6	(	(	PUNCT
ejpam-5839	1118	7	g̃,ω	g̃,ω	NOUN
ejpam-5839	1118	8	)	)	PUNCT
ejpam-5839	1118	9	∈	∈	PROPN
ejpam-5839	1118	10	j	j	NOUN
ejpam-5839	1118	11	qpnss	qpnss	NOUN
ejpam-5839	1118	12	such	such	ADJ
ejpam-5839	1118	13	that	that	DET
ejpam-5839	1118	14	yθ	yθ	NOUN
ejpam-5839	1119	1	′	′	NUM
ejpam-5839	1119	2	(	(	PUNCT
ejpam-5839	1119	3	r′1,r	r′1,r	VERB
ejpam-5839	1119	4	′	′	NUM
ejpam-5839	1119	5	2,r	2,r	NUM
ejpam-5839	1119	6	′	′	NUM
ejpam-5839	1120	1	3,r	3,r	NUM
ejpam-5839	1120	2	′	′	NUM
ejpam-5839	1120	3	4	4	NUM
ejpam-5839	1120	4	)	)	PUNCT
ejpam-5839	1120	5	∈	∈	PROPN
ejpam-5839	1120	6	(	(	PUNCT
ejpam-5839	1120	7	g̃,ω	g̃,ω	PROPN
ejpam-5839	1120	8	)	)	PUNCT
ejpam-5839	1120	9	.	.	PUNCT
ejpam-5839	1121	1	then	then	ADV
ejpam-5839	1121	2	there	there	PRON
ejpam-5839	1121	3	exists	exist	VERB
ejpam-5839	1121	4	(	(	PUNCT
ejpam-5839	1121	5	h̃,ω	h̃,ω	NOUN
ejpam-5839	1121	6	)	)	PUNCT
ejpam-5839	1121	7	∈	∈	PROPN
ejpam-5839	1121	8	τqpnss	τqpns	NOUN
ejpam-5839	1121	9	such	such	ADJ
ejpam-5839	1121	10	that	that	SCONJ
ejpam-5839	1121	11	(	(	PUNCT
ejpam-5839	1121	12	g̃,ω	g̃,ω	NOUN
ejpam-5839	1121	13	)	)	PUNCT
ejpam-5839	1121	14	=	=	PUNCT
ejpam-5839	1121	15	(	(	PUNCT
ejpam-5839	1121	16	h̃,ω	h̃,ω	NOUN
ejpam-5839	1121	17	)	)	PUNCT
ejpam-5839	1121	18	∩	∩	PROPN
ejpam-5839	1121	19	y	y	PROPN
ejpam-5839	1121	20	.	.	PUNCT
ejpam-5839	1122	1	since	since	SCONJ
ejpam-5839	1122	2	yθ	yθ	PROPN
ejpam-5839	1122	3	′	′	NUM
ejpam-5839	1122	4	(	(	PUNCT
ejpam-5839	1122	5	r′1,r	r′1,r	VERB
ejpam-5839	1122	6	′	′	NUM
ejpam-5839	1122	7	2,r	2,r	NUM
ejpam-5839	1122	8	′	′	NUM
ejpam-5839	1123	1	3,r	3,r	NUM
ejpam-5839	1123	2	′	′	NUM
ejpam-5839	1123	3	4	4	NUM
ejpam-5839	1123	4	)	)	PUNCT
ejpam-5839	1123	5	∈	∈	PROPN
ejpam-5839	1123	6	(	(	PUNCT
ejpam-5839	1123	7	h̃,ω	h̃,ω	NOUN
ejpam-5839	1123	8	)	)	PUNCT
ejpam-5839	1123	9	∩	∩	PROPN
ejpam-5839	1123	10	y	y	PROPN
ejpam-5839	1123	11	,	,	PUNCT
ejpam-5839	1123	12	we	we	PRON
ejpam-5839	1123	13	have	have	AUX
ejpam-5839	1123	14	yθ	yθ	NOUN
ejpam-5839	1123	15	′	′	NUM
ejpam-5839	1123	16	(	(	PUNCT
ejpam-5839	1123	17	r′1,r	r′1,r	VERB
ejpam-5839	1123	18	′	′	NUM
ejpam-5839	1123	19	2,r	2,r	NUM
ejpam-5839	1124	1	′	′	NUM
ejpam-5839	1125	1	3,r	3,r	NUM
ejpam-5839	1125	2	′	′	NUM
ejpam-5839	1125	3	4	4	NUM
ejpam-5839	1125	4	)	)	PUNCT
ejpam-5839	1125	5	∈	∈	PROPN
ejpam-5839	1125	6	(	(	PUNCT
ejpam-5839	1125	7	g̃,ω	g̃,ω	PROPN
ejpam-5839	1125	8	)	)	PUNCT
ejpam-5839	1125	9	.	.	PUNCT
ejpam-5839	1126	1	by	by	ADP
ejpam-5839	1126	2	the	the	DET
ejpam-5839	1126	3	definition	definition	NOUN
ejpam-5839	1126	4	of	of	ADP
ejpam-5839	1126	5	the	the	DET
ejpam-5839	1126	6	quadripartitioned	quadripartitione	VERB
ejpam-5839	1126	7	neutrosophic	neutrosophic	ADJ
ejpam-5839	1126	8	soft	soft	ADJ
ejpam-5839	1126	9	base	base	NOUN
ejpam-5839	1126	10	,	,	PUNCT
ejpam-5839	1126	11	any	any	DET
ejpam-5839	1126	12	yθ	yθ	NOUN
ejpam-5839	1126	13	′	′	NUM
ejpam-5839	1126	14	(	(	PUNCT
ejpam-5839	1126	15	r′1,r	r′1,r	VERB
ejpam-5839	1126	16	′	′	NUM
ejpam-5839	1126	17	2,r	2,r	NUM
ejpam-5839	1126	18	′	′	NUM
ejpam-5839	1127	1	3,r	3,r	NUM
ejpam-5839	1127	2	′	′	NUM
ejpam-5839	1127	3	4	4	NUM
ejpam-5839	1127	4	)	)	PUNCT
ejpam-5839	1127	5	∈	∈	NOUN
ejpam-5839	1127	6	y	y	NOUN
ejpam-5839	1127	7	belonging	belong	VERB
ejpam-5839	1127	8	to	to	ADP
ejpam-5839	1127	9	j	j	PROPN
ejpam-5839	1127	10	qpnss	qpnss	NOUN
ejpam-5839	1127	11	implies	imply	VERB
ejpam-5839	1127	12	that	that	SCONJ
ejpam-5839	1127	13	there	there	PRON
ejpam-5839	1127	14	exists	exist	VERB
ejpam-5839	1127	15	br	br	PROPN
ejpam-5839	1127	16	∈	∈	PROPN
ejpam-5839	1127	17	bqpnss	bqpns	NOUN
ejpam-5839	1127	18	such	such	ADJ
ejpam-5839	1127	19	that	that	DET
ejpam-5839	1127	20	yθ	yθ	NOUN
ejpam-5839	1128	1	′	′	NUM
ejpam-5839	1128	2	(	(	PUNCT
ejpam-5839	1128	3	r′1,r	r′1,r	VERB
ejpam-5839	1128	4	′	′	NUM
ejpam-5839	1128	5	2,r	2,r	NUM
ejpam-5839	1128	6	′	′	NUM
ejpam-5839	1129	1	3,r	3,r	NUM
ejpam-5839	1129	2	′	′	NUM
ejpam-5839	1129	3	4	4	NUM
ejpam-5839	1129	4	)	)	PUNCT
ejpam-5839	1129	5	∈	∈	NOUN
ejpam-5839	1129	6	br	br	NOUN
ejpam-5839	1130	1	⊆	⊆	NUM
ejpam-5839	1130	2	(	(	PUNCT
ejpam-5839	1130	3	h̃,ω	h̃,ω	NOUN
ejpam-5839	1130	4	)	)	PUNCT
ejpam-5839	1130	5	.	.	PUNCT
ejpam-5839	1131	1	from	from	ADP
ejpam-5839	1131	2	the	the	DET
ejpam-5839	1131	3	above	above	NOUN
ejpam-5839	1131	4	,	,	PUNCT
ejpam-5839	1131	5	it	it	PRON
ejpam-5839	1131	6	follows	follow	VERB
ejpam-5839	1131	7	that	that	SCONJ
ejpam-5839	1131	8	b1	b1	PROPN
ejpam-5839	1131	9	is	be	AUX
ejpam-5839	1131	10	a	a	DET
ejpam-5839	1131	11	quadripartitioned	quadripartitione	VERB
ejpam-5839	1131	12	neutrosophic	neutrosophic	ADJ
ejpam-5839	1131	13	soft	soft	ADJ
ejpam-5839	1131	14	countable	countable	ADJ
ejpam-5839	1131	15	base	base	NOUN
ejpam-5839	1131	16	for	for	ADP
ejpam-5839	1131	17	the	the	DET
ejpam-5839	1131	18	quadripartitioned	quadripartitione	VERB
ejpam-5839	1131	19	neutrosophic	neutrosophic	PROPN
ejpam-5839	1131	20	soft	soft	ADJ
ejpam-5839	1131	21	topology	topology	NOUN
ejpam-5839	1131	22	j	j	PROPN
ejpam-5839	1131	23	qpnss	qpnss	NOUN
ejpam-5839	1131	24	on	on	ADP
ejpam-5839	1131	25	y	y	PROPN
ejpam-5839	1131	26	.	.	PUNCT
ejpam-5839	1132	1	consequently	consequently	ADV
ejpam-5839	1132	2	,	,	PUNCT
ejpam-5839	1132	3	(	(	PUNCT
ejpam-5839	1132	4	y	y	PROPN
ejpam-5839	1132	5	,	,	PUNCT
ejpam-5839	1132	6	j	j	PROPN
ejpam-5839	1132	7	qpnss	qpnss	NOUN
ejpam-5839	1132	8	,	,	PUNCT
ejpam-5839	1132	9	ω	ω	NOUN
ejpam-5839	1132	10	)	)	PUNCT
ejpam-5839	1132	11	is	be	AUX
ejpam-5839	1132	12	quadripartitioned	quadripartitione	VERB
ejpam-5839	1132	13	neutrosophic	neutrosophic	ADJ
ejpam-5839	1132	14	soft	soft	ADJ
ejpam-5839	1132	15	second	second	ADJ
ejpam-5839	1132	16	countable	countable	ADJ
ejpam-5839	1132	17	.	.	PUNCT
ejpam-5839	1133	1	theorem	theorem	NOUN
ejpam-5839	1133	2	26	26	NUM
ejpam-5839	1133	3	.	.	PUNCT
ejpam-5839	1134	1	let	let	AUX
ejpam-5839	1134	2	(	(	PUNCT
ejpam-5839	1134	3	x	x	NOUN
ejpam-5839	1134	4	,	,	PUNCT
ejpam-5839	1134	5	τqpnss	τqpnss	PROPN
ejpam-5839	1134	6	,	,	PUNCT
ejpam-5839	1134	7	ω	ω	PROPN
ejpam-5839	1134	8	)	)	PUNCT
ejpam-5839	1134	9	be	be	VERB
ejpam-5839	1134	10	a	a	DET
ejpam-5839	1134	11	quadripartitioned	quadripartitione	VERB
ejpam-5839	1134	12	neutrosophic	neutrosophic	ADJ
ejpam-5839	1134	13	soft	soft	ADJ
ejpam-5839	1134	14	topological	topological	ADJ
ejpam-5839	1134	15	space	space	NOUN
ejpam-5839	1134	16	over	over	ADP
ejpam-5839	1134	17	x	x	ADP
ejpam-5839	1134	18	such	such	ADJ
ejpam-5839	1134	19	that	that	SCONJ
ejpam-5839	1134	20	it	it	PRON
ejpam-5839	1134	21	is	be	AUX
ejpam-5839	1134	22	a	a	DET
ejpam-5839	1134	23	quadripartitioned	quadripartitione	VERB
ejpam-5839	1134	24	neutrosophic	neutrosophic	ADJ
ejpam-5839	1134	25	soft	soft	ADJ
ejpam-5839	1134	26	second	second	ADJ
ejpam-5839	1134	27	countable	countable	ADJ
ejpam-5839	1134	28	space	space	NOUN
ejpam-5839	1134	29	.	.	PUNCT
ejpam-5839	1135	1	then	then	ADV
ejpam-5839	1135	2	it	it	PRON
ejpam-5839	1135	3	also	also	ADV
ejpam-5839	1135	4	has	have	VERB
ejpam-5839	1135	5	the	the	DET
ejpam-5839	1135	6	characteristics	characteristic	NOUN
ejpam-5839	1135	7	of	of	ADP
ejpam-5839	1135	8	another	another	DET
ejpam-5839	1135	9	quadripartitioned	quadripartitione	VERB
ejpam-5839	1135	10	neutrosophic	neutrosophic	ADJ
ejpam-5839	1135	11	soft	soft	ADJ
ejpam-5839	1135	12	space	space	NOUN
ejpam-5839	1135	13	known	know	VERB
ejpam-5839	1135	14	as	as	ADP
ejpam-5839	1135	15	a	a	DET
ejpam-5839	1135	16	quadripartitioned	quadripartitione	VERB
ejpam-5839	1135	17	neutrosophic	neutrosophic	ADJ
ejpam-5839	1135	18	soft	soft	ADJ
ejpam-5839	1135	19	separable	separable	ADJ
ejpam-5839	1135	20	space	space	NOUN
ejpam-5839	1135	21	.	.	PUNCT
ejpam-5839	1136	1	interestingly	interestingly	ADV
ejpam-5839	1136	2	,	,	PUNCT
ejpam-5839	1136	3	the	the	DET
ejpam-5839	1136	4	converse	converse	NOUN
ejpam-5839	1136	5	is	be	AUX
ejpam-5839	1136	6	not	not	PART
ejpam-5839	1136	7	always	always	ADV
ejpam-5839	1136	8	true	true	ADJ
ejpam-5839	1136	9	.	.	PUNCT
ejpam-5839	1137	1	proof	proof	NOUN
ejpam-5839	1137	2	.	.	PUNCT
ejpam-5839	1138	1	let	let	VERB
ejpam-5839	1138	2	(	(	PUNCT
ejpam-5839	1138	3	x	x	NOUN
ejpam-5839	1138	4	,	,	PUNCT
ejpam-5839	1138	5	τqpnss	τqpnss	PROPN
ejpam-5839	1138	6	,	,	PUNCT
ejpam-5839	1138	7	ω	ω	PROPN
ejpam-5839	1138	8	)	)	PUNCT
ejpam-5839	1138	9	be	be	VERB
ejpam-5839	1138	10	a	a	DET
ejpam-5839	1138	11	quadripartitioned	quadripartitione	VERB
ejpam-5839	1138	12	neutrosophic	neutrosophic	ADJ
ejpam-5839	1138	13	soft	soft	ADJ
ejpam-5839	1138	14	topological	topological	ADJ
ejpam-5839	1138	15	space	space	NOUN
ejpam-5839	1138	16	over	over	ADP
ejpam-5839	1138	17	x	x	ADP
ejpam-5839	1138	18	such	such	ADJ
ejpam-5839	1138	19	that	that	SCONJ
ejpam-5839	1138	20	it	it	PRON
ejpam-5839	1138	21	is	be	AUX
ejpam-5839	1138	22	a	a	DET
ejpam-5839	1138	23	quadripartitioned	quadripartitione	VERB
ejpam-5839	1138	24	neutrosophic	neutrosophic	ADJ
ejpam-5839	1138	25	soft	soft	ADJ
ejpam-5839	1138	26	second	second	ADJ
ejpam-5839	1138	27	countable	countable	ADJ
ejpam-5839	1138	28	space	space	NOUN
ejpam-5839	1138	29	.	.	PUNCT
ejpam-5839	1139	1	since	since	SCONJ
ejpam-5839	1139	2	x	x	PRON
ejpam-5839	1139	3	is	be	AUX
ejpam-5839	1139	4	a	a	DET
ejpam-5839	1139	5	quadripartitioned	quadripartitione	VERB
ejpam-5839	1139	6	neutrosophic	neutrosophic	ADJ
ejpam-5839	1139	7	soft	soft	ADJ
ejpam-5839	1139	8	second	second	ADJ
ejpam-5839	1139	9	countable	countable	ADJ
ejpam-5839	1139	10	space	space	NOUN
ejpam-5839	1139	11	,	,	PUNCT
ejpam-5839	1139	12	there	there	PRON
ejpam-5839	1139	13	exists	exist	VERB
ejpam-5839	1139	14	a	a	DET
ejpam-5839	1139	15	quadripartitioned	quadripartitioned	ADJ
ejpam-5839	1139	16	neutrosophic	neutrosophic	ADJ
ejpam-5839	1139	17	soft	soft	ADJ
ejpam-5839	1139	18	countable	countable	ADJ
ejpam-5839	1139	19	base	base	NOUN
ejpam-5839	1139	20	bqpnss	bqpns	NOUN
ejpam-5839	1139	21	for	for	ADP
ejpam-5839	1139	22	the	the	DET
ejpam-5839	1139	23	quadripartitioned	quadripartitioned	ADJ
ejpam-5839	1139	24	neutrosophic	neutrosophic	ADJ
ejpam-5839	1139	25	soft	soft	ADJ
ejpam-5839	1139	26	topology	topology	NOUN
ejpam-5839	1139	27	τqpnss	τqpns	NOUN
ejpam-5839	1139	28	.	.	PUNCT
ejpam-5839	1140	1	members	member	NOUN
ejpam-5839	1140	2	of	of	ADP
ejpam-5839	1140	3	bqpnss	bqpns	NOUN
ejpam-5839	1140	4	may	may	AUX
ejpam-5839	1140	5	be	be	AUX
ejpam-5839	1140	6	enumerated	enumerate	VERB
ejpam-5839	1140	7	as	as	ADP
ejpam-5839	1140	8	b1	b1	NOUN
ejpam-5839	1140	9	,	,	PUNCT
ejpam-5839	1140	10	b2	b2	NOUN
ejpam-5839	1140	11	,	,	PUNCT
ejpam-5839	1140	12	b3	b3	NOUN
ejpam-5839	1140	13	,	,	PUNCT
ejpam-5839	1140	14	b4	b4	NOUN
ejpam-5839	1140	15	,	,	PUNCT
ejpam-5839	1140	16	.	.	PUNCT
ejpam-5839	1140	17	.	.	PUNCT
ejpam-5839	1140	18	.	.	PUNCT
ejpam-5839	1141	1	choose	choose	VERB
ejpam-5839	1141	2	any	any	DET
ejpam-5839	1141	3	quadripartitioned	quadripartitioned	ADJ
ejpam-5839	1141	4	neutrosophic	neutrosophic	ADJ
ejpam-5839	1141	5	soft	soft	ADJ
ejpam-5839	1141	6	point	point	NOUN
ejpam-5839	1141	7	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	1141	8	)	)	PUNCT
ejpam-5839	1141	9	from	from	ADP
ejpam-5839	1141	10	each	each	DET
ejpam-5839	1141	11	bi	bi	NOUN
ejpam-5839	1141	12	and	and	CCONJ
ejpam-5839	1141	13	take	take	VERB
ejpam-5839	1141	14	y	y	PROPN
ejpam-5839	1141	15	as	as	ADP
ejpam-5839	1141	16	a	a	DET
ejpam-5839	1141	17	collection	collection	NOUN
ejpam-5839	1141	18	of	of	ADP
ejpam-5839	1141	19	all	all	DET
ejpam-5839	1141	20	these	these	DET
ejpam-5839	1141	21	quadripartitioned	quadripartitione	VERB
ejpam-5839	1141	22	neutrosophic	neutrosophic	ADJ
ejpam-5839	1141	23	soft	soft	ADJ
ejpam-5839	1141	24	points	point	NOUN
ejpam-5839	1141	25	:	:	PUNCT
ejpam-5839	1142	1	y	y	PROPN
ejpam-5839	1142	2	=	=	PRON
ejpam-5839	1142	3	{	{	PUNCT
ejpam-5839	1142	4	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	1142	5	)	)	PUNCT
ejpam-5839	1143	1	|	|	CCONJ
ejpam-5839	1143	2	∀i	∀i	NOUN
ejpam-5839	1143	3	∈	∈	NOUN
ejpam-5839	1143	4	n	n	CCONJ
ejpam-5839	1143	5	}	}	PUNCT
ejpam-5839	1143	6	.	.	PUNCT
ejpam-5839	1144	1	(	(	PUNCT
ejpam-5839	1144	2	1	1	X
ejpam-5839	1144	3	)	)	PUNCT
ejpam-5839	1144	4	that	that	PRON
ejpam-5839	1144	5	is	be	AUX
ejpam-5839	1144	6	to	to	PART
ejpam-5839	1144	7	say	say	VERB
ejpam-5839	1145	1	,	,	PUNCT
ejpam-5839	1145	2	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	1145	3	)	)	PUNCT
ejpam-5839	1145	4	∈	∈	PROPN
ejpam-5839	1145	5	bi	bi	NOUN
ejpam-5839	1145	6	∈	∈	PROPN
ejpam-5839	1145	7	bqpnss	bqpns	NOUN
ejpam-5839	1145	8	,	,	PUNCT
ejpam-5839	1145	9	∀i	∀i	X
ejpam-5839	1145	10	∈	∈	PROPN
ejpam-5839	1145	11	n.	n.	NOUN
ejpam-5839	1145	12	(	(	PUNCT
ejpam-5839	1145	13	2	2	NUM
ejpam-5839	1145	14	)	)	PUNCT
ejpam-5839	1145	15	evidently	evidently	ADV
ejpam-5839	1145	16	,	,	PUNCT
ejpam-5839	1145	17	n	n	PRON
ejpam-5839	1145	18	∼	∼	NOUN
ejpam-5839	1145	19	y	y	NOUN
ejpam-5839	1145	20	under	under	ADP
ejpam-5839	1145	21	the	the	DET
ejpam-5839	1145	22	quadripartitioned	quadripartitione	VERB
ejpam-5839	1145	23	neutrosophic	neutrosophic	ADJ
ejpam-5839	1145	24	soft	soft	ADJ
ejpam-5839	1145	25	map	map	NOUN
ejpam-5839	1145	26	i	i	PRON
ejpam-5839	1145	27	→	→	PUNCT
ejpam-5839	1145	28	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	1145	29	)	)	PUNCT
ejpam-5839	1145	30	,	,	PUNCT
ejpam-5839	1145	31	therefore	therefore	ADV
ejpam-5839	1145	32	y	y	PROPN
ejpam-5839	1145	33	is	be	AUX
ejpam-5839	1145	34	enumerable	enumerable	ADJ
ejpam-5839	1145	35	.	.	PUNCT
ejpam-5839	1146	1	clearly	clearly	ADV
ejpam-5839	1146	2	,	,	PUNCT
ejpam-5839	1146	3	y	y	PROPN
ejpam-5839	1146	4	⊆	⊆	NUM
ejpam-5839	1146	5	x.	x.	NOUN
ejpam-5839	1146	6	we	we	PRON
ejpam-5839	1146	7	claim	claim	VERB
ejpam-5839	1146	8	that	that	SCONJ
ejpam-5839	1146	9	y	y	PROPN
ejpam-5839	1146	10	=	=	PUNCT
ejpam-5839	1146	11	x.	x.	NOUN
ejpam-5839	1146	12	suppose	suppose	VERB
ejpam-5839	1146	13	not	not	PART
ejpam-5839	1146	14	.	.	PUNCT
ejpam-5839	1147	1	then	then	ADV
ejpam-5839	1147	2	x	x	PRON
ejpam-5839	1147	3	−y	−y	VERB
ejpam-5839	1147	4	̸=	̸=	PROPN
ejpam-5839	1147	5	∅	∅	NOUN
ejpam-5839	1147	6	:	:	PUNCT
ejpam-5839	1147	7	x	x	X
ejpam-5839	1147	8	−y	−y	VERB
ejpam-5839	1147	9	̸=	̸=	PROPN
ejpam-5839	1147	10	∅.	∅.	ADV
ejpam-5839	1147	11	(	(	PUNCT
ejpam-5839	1147	12	3	3	X
ejpam-5839	1147	13	)	)	PUNCT
ejpam-5839	1147	14	let	let	VERB
ejpam-5839	1147	15	yθ	yθ	PRON
ejpam-5839	1147	16	′	′	NUM
ejpam-5839	1147	17	(	(	PUNCT
ejpam-5839	1147	18	r′1,r	r′1,r	VERB
ejpam-5839	1147	19	′	′	NUM
ejpam-5839	1147	20	2,r	2,r	NUM
ejpam-5839	1148	1	′	′	NUM
ejpam-5839	1149	1	3,r	3,r	NUM
ejpam-5839	1149	2	′	′	NUM
ejpam-5839	1149	3	4	4	NUM
ejpam-5839	1149	4	)	)	PUNCT
ejpam-5839	1149	5	∈	∈	NOUN
ejpam-5839	1149	6	x	x	AUX
ejpam-5839	1149	7	−y	−y	NOUN
ejpam-5839	1149	8	be	be	AUX
ejpam-5839	1149	9	arbitrary	arbitrary	ADJ
ejpam-5839	1149	10	.	.	PUNCT
ejpam-5839	1150	1	since	since	SCONJ
ejpam-5839	1150	2	y	y	PROPN
ejpam-5839	1150	3	is	be	AUX
ejpam-5839	1150	4	quadripartitioned	quadripartitione	VERB
ejpam-5839	1150	5	neutrosophic	neutrosophic	ADJ
ejpam-5839	1150	6	soft	soft	ADJ
ejpam-5839	1150	7	p	p	NOUN
ejpam-5839	1150	8	-	-	PUNCT
ejpam-5839	1150	9	closed	closed	ADJ
ejpam-5839	1150	10	,	,	PUNCT
ejpam-5839	1150	11	x	x	PRON
ejpam-5839	1150	12	−y	−y	PROPN
ejpam-5839	1150	13	is	be	AUX
ejpam-5839	1150	14	quadripartitioned	quadripartitione	VERB
ejpam-5839	1150	15	neutrosophic	neutrosophic	ADJ
ejpam-5839	1150	16	soft	soft	ADJ
ejpam-5839	1150	17	p	p	NOUN
ejpam-5839	1150	18	-	-	PUNCT
ejpam-5839	1150	19	open	open	ADJ
ejpam-5839	1150	20	.	.	PUNCT
ejpam-5839	1151	1	that	that	PRON
ejpam-5839	1151	2	is	be	AUX
ejpam-5839	1151	3	,	,	PUNCT
ejpam-5839	1151	4	yθ	yθ	NOUN
ejpam-5839	1151	5	′	′	NUM
ejpam-5839	1151	6	(	(	PUNCT
ejpam-5839	1151	7	r′1,r	r′1,r	VERB
ejpam-5839	1151	8	′	′	NUM
ejpam-5839	1151	9	2,r	2,r	NUM
ejpam-5839	1151	10	′	′	NUM
ejpam-5839	1152	1	3,r	3,r	NUM
ejpam-5839	1152	2	′	′	NUM
ejpam-5839	1152	3	4	4	NUM
ejpam-5839	1152	4	)	)	PUNCT
ejpam-5839	1152	5	∈	∈	NOUN
ejpam-5839	1152	6	x	x	PUNCT
ejpam-5839	1152	7	−y	−y	NOUN
ejpam-5839	1152	8	∈	∈	PROPN
ejpam-5839	1152	9	τqpnss	τqpns	NOUN
ejpam-5839	1152	10	.	.	PUNCT
ejpam-5839	1153	1	(	(	PUNCT
ejpam-5839	1153	2	4	4	NUM
ejpam-5839	1153	3	)	)	PUNCT
ejpam-5839	1153	4	by	by	ADP
ejpam-5839	1153	5	the	the	DET
ejpam-5839	1153	6	definition	definition	NOUN
ejpam-5839	1153	7	of	of	ADP
ejpam-5839	1153	8	the	the	DET
ejpam-5839	1153	9	quadripartitioned	quadripartitione	VERB
ejpam-5839	1153	10	neutrosophic	neutrosophic	ADJ
ejpam-5839	1153	11	soft	soft	ADJ
ejpam-5839	1153	12	base	base	NOUN
ejpam-5839	1153	13	,	,	PUNCT
ejpam-5839	1153	14	there	there	PRON
ejpam-5839	1153	15	exists	exist	VERB
ejpam-5839	1153	16	bn0	bn0	PROPN
ejpam-5839	1153	17	∈	∈	PROPN
ejpam-5839	1153	18	bqpnss	bqpns	NOUN
ejpam-5839	1154	1	such	such	ADJ
ejpam-5839	1154	2	that	that	DET
ejpam-5839	1154	3	yθ	yθ	NOUN
ejpam-5839	1154	4	′	′	NUM
ejpam-5839	1154	5	(	(	PUNCT
ejpam-5839	1154	6	r′1,r	r′1,r	VERB
ejpam-5839	1154	7	′	′	NUM
ejpam-5839	1154	8	2,r	2,r	NUM
ejpam-5839	1154	9	′	′	NUM
ejpam-5839	1155	1	3,r	3,r	NUM
ejpam-5839	1155	2	′	′	NUM
ejpam-5839	1155	3	4)n0	4)n0	NUM
ejpam-5839	1155	4	⊆	⊆	NUM
ejpam-5839	1155	5	x	x	SYM
ejpam-5839	1155	6	−y	−y	VERB
ejpam-5839	1155	7	.	.	PUNCT
ejpam-5839	1156	1	(	(	PUNCT
ejpam-5839	1156	2	5	5	NUM
ejpam-5839	1156	3	)	)	PUNCT
ejpam-5839	1156	4	but	but	CCONJ
ejpam-5839	1156	5	xθ(r1,r2,r3,r4)n0	xθ(r1,r2,r3,r4)n0	PROPN
ejpam-5839	1156	6	∈	∈	PROPN
ejpam-5839	1156	7	y	y	PROPN
ejpam-5839	1156	8	according	accord	VERB
ejpam-5839	1156	9	to	to	ADP
ejpam-5839	1156	10	(	(	PUNCT
ejpam-5839	1156	11	1	1	NUM
ejpam-5839	1156	12	)	)	PUNCT
ejpam-5839	1156	13	and	and	CCONJ
ejpam-5839	1156	14	(	(	PUNCT
ejpam-5839	1156	15	2	2	NUM
ejpam-5839	1156	16	)	)	PUNCT
ejpam-5839	1156	17	,	,	PUNCT
ejpam-5839	1156	18	contradicting	contradict	VERB
ejpam-5839	1156	19	(	(	PUNCT
ejpam-5839	1156	20	4	4	NUM
ejpam-5839	1156	21	)	)	PUNCT
ejpam-5839	1156	22	.	.	PUNCT
ejpam-5839	1157	1	thus	thus	ADV
ejpam-5839	1157	2	,	,	PUNCT
ejpam-5839	1157	3	our	our	PRON
ejpam-5839	1157	4	assumption	assumption	NOUN
ejpam-5839	1157	5	x	x	X
ejpam-5839	1157	6	−y	−y	NOUN
ejpam-5839	1157	7	̸=	̸=	NOUN
ejpam-5839	1157	8	∅	∅	NOUN
ejpam-5839	1157	9	was	be	AUX
ejpam-5839	1157	10	incorrect	incorrect	ADJ
ejpam-5839	1157	11	.	.	PUNCT
ejpam-5839	1158	1	consequently	consequently	ADV
ejpam-5839	1158	2	,	,	PUNCT
ejpam-5839	1158	3	x	x	PRON
ejpam-5839	1158	4	−y	−y	NOUN
ejpam-5839	1158	5	=	=	SYM
ejpam-5839	1158	6	∅	∅	NOUN
ejpam-5839	1158	7	⇒	⇒	NOUN
ejpam-5839	1158	8	x	x	PUNCT
ejpam-5839	1159	1	=	=	PUNCT
ejpam-5839	1159	2	y.	y.	NOUN
ejpam-5839	1159	3	(	(	PUNCT
ejpam-5839	1159	4	6	6	NUM
ejpam-5839	1159	5	)	)	PUNCT
ejpam-5839	1159	6	a.	a.	NOUN
ejpam-5839	1159	7	shihadeh	shihadeh	VERB
ejpam-5839	1159	8	et	et	PROPN
ejpam-5839	1159	9	al	al	PROPN
ejpam-5839	1159	10	.	.	PUNCT
ejpam-5839	1159	11	/	/	SYM
ejpam-5839	1159	12	eur	eur	PROPN
ejpam-5839	1159	13	.	.	PUNCT
ejpam-5839	1160	1	j.	j.	PROPN
ejpam-5839	1160	2	pure	pure	PROPN
ejpam-5839	1160	3	appl	appl	PROPN
ejpam-5839	1160	4	.	.	PROPN
ejpam-5839	1160	5	math	math	PROPN
ejpam-5839	1160	6	,	,	PUNCT
ejpam-5839	1160	7	18	18	NUM
ejpam-5839	1160	8	(	(	PUNCT
ejpam-5839	1160	9	2	2	NUM
ejpam-5839	1160	10	)	)	PUNCT
ejpam-5839	1160	11	(	(	PUNCT
ejpam-5839	1160	12	2025	2025	NUM
ejpam-5839	1160	13	)	)	PUNCT
ejpam-5839	1160	14	,	,	PUNCT
ejpam-5839	1160	15	5839	5839	NUM
ejpam-5839	1160	16	48	48	NUM
ejpam-5839	1160	17	of	of	ADP
ejpam-5839	1160	18	54	54	NUM
ejpam-5839	1160	19	thus	thus	ADV
ejpam-5839	1160	20	,	,	PUNCT
ejpam-5839	1160	21	we	we	PRON
ejpam-5839	1160	22	have	have	AUX
ejpam-5839	1160	23	proved	prove	VERB
ejpam-5839	1160	24	that	that	SCONJ
ejpam-5839	1160	25	there	there	PRON
ejpam-5839	1160	26	exists	exist	VERB
ejpam-5839	1160	27	y	y	PROPN
ejpam-5839	1160	28	⊆	⊆	NUM
ejpam-5839	1160	29	x	x	PUNCT
ejpam-5839	1160	30	such	such	ADJ
ejpam-5839	1160	31	that	that	SCONJ
ejpam-5839	1160	32	x	x	X
ejpam-5839	1160	33	=	=	SYM
ejpam-5839	1160	34	y	y	PROPN
ejpam-5839	1160	35	and	and	CCONJ
ejpam-5839	1160	36	y	y	PROPN
ejpam-5839	1160	37	is	be	AUX
ejpam-5839	1160	38	quadripartitioned	quadripartitione	VERB
ejpam-5839	1160	39	neutrosophic	neutrosophic	ADJ
ejpam-5839	1160	40	soft	soft	ADJ
ejpam-5839	1160	41	enumerable	enumerable	ADJ
ejpam-5839	1160	42	.	.	PUNCT
ejpam-5839	1161	1	by	by	ADP
ejpam-5839	1161	2	definition	definition	NOUN
ejpam-5839	1161	3	,	,	PUNCT
ejpam-5839	1161	4	this	this	PRON
ejpam-5839	1161	5	proves	prove	VERB
ejpam-5839	1161	6	that	that	SCONJ
ejpam-5839	1161	7	x	x	PRON
ejpam-5839	1161	8	is	be	AUX
ejpam-5839	1161	9	quadripartitioned	quadripartitione	VERB
ejpam-5839	1161	10	neutrosophic	neutrosophic	ADJ
ejpam-5839	1161	11	soft	soft	ADJ
ejpam-5839	1161	12	separable	separable	NOUN
ejpam-5839	1161	13	.	.	PUNCT
ejpam-5839	1162	1	let	let	VERB
ejpam-5839	1162	2	us	we	PRON
ejpam-5839	1162	3	now	now	ADV
ejpam-5839	1162	4	discuss	discuss	VERB
ejpam-5839	1162	5	the	the	DET
ejpam-5839	1162	6	converse	converse	NOUN
ejpam-5839	1162	7	.	.	PUNCT
ejpam-5839	1163	1	suppose	suppose	VERB
ejpam-5839	1163	2	x	x	PRON
ejpam-5839	1163	3	be	be	AUX
ejpam-5839	1163	4	an	an	DET
ejpam-5839	1163	5	infinite	infinite	ADJ
ejpam-5839	1163	6	quadripartitioned	quadripartitione	VERB
ejpam-5839	1163	7	neutrosophic	neutrosophic	ADJ
ejpam-5839	1163	8	soft	soft	ADJ
ejpam-5839	1163	9	set	set	NOUN
ejpam-5839	1163	10	.	.	PUNCT
ejpam-5839	1164	1	let	let	VERB
ejpam-5839	1164	2	τqpnss	τqpns	NOUN
ejpam-5839	1164	3	be	be	AUX
ejpam-5839	1164	4	a	a	DET
ejpam-5839	1164	5	family	family	NOUN
ejpam-5839	1164	6	consisting	consist	VERB
ejpam-5839	1164	7	of	of	ADP
ejpam-5839	1164	8	0(x	0(x	NOUN
ejpam-5839	1164	9	,	,	PUNCT
ejpam-5839	1164	10	ω	ω	NOUN
ejpam-5839	1164	11	)	)	PUNCT
ejpam-5839	1164	12	and	and	CCONJ
ejpam-5839	1164	13	all	all	DET
ejpam-5839	1164	14	those	those	DET
ejpam-5839	1164	15	quadripartitioned	quadripartitione	VERB
ejpam-5839	1164	16	neutrosophic	neutrosophic	ADJ
ejpam-5839	1164	17	soft	soft	ADJ
ejpam-5839	1164	18	subsets	subset	NOUN
ejpam-5839	1164	19	y	y	PROPN
ejpam-5839	1164	20	of	of	ADP
ejpam-5839	1164	21	x	x	INTJ
ejpam-5839	1164	22	such	such	ADJ
ejpam-5839	1164	23	that	that	SCONJ
ejpam-5839	1164	24	yc	yc	PROPN
ejpam-5839	1164	25	is	be	AUX
ejpam-5839	1164	26	quadripartitioned	quadripartitione	VERB
ejpam-5839	1164	27	neutrosophic	neutrosophic	ADJ
ejpam-5839	1164	28	soft	soft	ADJ
ejpam-5839	1164	29	finite	finite	NOUN
ejpam-5839	1164	30	.	.	PUNCT
ejpam-5839	1165	1	then	then	ADV
ejpam-5839	1165	2	τqpnss	τqpnss	PROPN
ejpam-5839	1165	3	is	be	AUX
ejpam-5839	1165	4	a	a	DET
ejpam-5839	1165	5	quadripartitioned	quadripartitione	VERB
ejpam-5839	1165	6	neutrosophic	neutrosophic	ADJ
ejpam-5839	1165	7	soft	soft	ADJ
ejpam-5839	1165	8	topology	topology	NOUN
ejpam-5839	1165	9	.	.	PUNCT
ejpam-5839	1166	1	we	we	PRON
ejpam-5839	1166	2	claim	claim	VERB
ejpam-5839	1166	3	that	that	SCONJ
ejpam-5839	1166	4	τqpnss	τqpnss	PROPN
ejpam-5839	1166	5	is	be	AUX
ejpam-5839	1166	6	quadripartitioned	quadripartitione	VERB
ejpam-5839	1166	7	neutrosophic	neutrosophic	ADJ
ejpam-5839	1166	8	soft	soft	ADJ
ejpam-5839	1166	9	separable	separable	NOUN
ejpam-5839	1166	10	.	.	PUNCT
ejpam-5839	1167	1	since	since	SCONJ
ejpam-5839	1167	2	x	x	PRON
ejpam-5839	1167	3	is	be	AUX
ejpam-5839	1167	4	an	an	DET
ejpam-5839	1167	5	infinite	infinite	ADJ
ejpam-5839	1167	6	quadripartitioned	quadripartitione	VERB
ejpam-5839	1167	7	neutrosophic	neutrosophic	ADJ
ejpam-5839	1167	8	soft	soft	ADJ
ejpam-5839	1167	9	set	set	NOUN
ejpam-5839	1167	10	,	,	PUNCT
ejpam-5839	1167	11	there	there	PRON
ejpam-5839	1167	12	existsy	existsy	VERB
ejpam-5839	1167	13	⊆	⊆	NUM
ejpam-5839	1167	14	x	x	X
ejpam-5839	1167	15	such	such	ADJ
ejpam-5839	1167	16	thaty	thaty	NOUN
ejpam-5839	1167	17	is	be	AUX
ejpam-5839	1167	18	quadripartitioned	quadripartitione	VERB
ejpam-5839	1167	19	neutrosophic	neutrosophic	ADJ
ejpam-5839	1167	20	soft	soft	ADJ
ejpam-5839	1167	21	enumerable	enumerable	ADJ
ejpam-5839	1167	22	.	.	PUNCT
ejpam-5839	1168	1	to	to	PART
ejpam-5839	1168	2	prove	prove	VERB
ejpam-5839	1168	3	thatx	thatx	NOUN
ejpam-5839	1168	4	=	=	SYM
ejpam-5839	1168	5	y	y	PROPN
ejpam-5839	1168	6	,	,	PUNCT
ejpam-5839	1168	7	we	we	PRON
ejpam-5839	1168	8	note	note	VERB
ejpam-5839	1168	9	thaty	thaty	VERB
ejpam-5839	1168	10	⊆	⊆	NUM
ejpam-5839	1168	11	x	x	NOUN
ejpam-5839	1168	12	,	,	PUNCT
ejpam-5839	1168	13	and	and	CCONJ
ejpam-5839	1168	14	hence	hence	ADV
ejpam-5839	1168	15	all	all	DET
ejpam-5839	1168	16	the	the	DET
ejpam-5839	1168	17	quadripartitioned	quadripartitioned	ADJ
ejpam-5839	1168	18	neutrosophic	neutrosophic	ADJ
ejpam-5839	1168	19	soft	soft	ADJ
ejpam-5839	1168	20	closure	closure	NOUN
ejpam-5839	1168	21	points	point	NOUN
ejpam-5839	1168	22	of	of	ADP
ejpam-5839	1168	23	y	y	PROPN
ejpam-5839	1168	24	will	will	AUX
ejpam-5839	1168	25	reside	reside	VERB
ejpam-5839	1168	26	in	in	ADP
ejpam-5839	1168	27	x	x	PROPN
ejpam-5839	1168	28	,	,	PUNCT
ejpam-5839	1168	29	which	which	PRON
ejpam-5839	1168	30	implies	imply	VERB
ejpam-5839	1168	31	that	that	SCONJ
ejpam-5839	1168	32	y	y	PROPN
ejpam-5839	1168	33	⊆	⊆	NUM
ejpam-5839	1168	34	x.	x.	NOUN
ejpam-5839	1169	1	if	if	SCONJ
ejpam-5839	1169	2	(	(	PUNCT
ejpam-5839	1169	3	g̃,ω	g̃,ω	NOUN
ejpam-5839	1169	4	)	)	PUNCT
ejpam-5839	1169	5	∈	∈	PROPN
ejpam-5839	1169	6	τqpnss	τqpns	NOUN
ejpam-5839	1169	7	,	,	PUNCT
ejpam-5839	1169	8	then	then	ADV
ejpam-5839	1169	9	(	(	PUNCT
ejpam-5839	1169	10	g̃,ω)c	g̃,ω)c	PROPN
ejpam-5839	1169	11	is	be	AUX
ejpam-5839	1169	12	quadripartitioned	quadripartitione	VERB
ejpam-5839	1169	13	neutrosophic	neutrosophic	ADJ
ejpam-5839	1169	14	soft	soft	ADJ
ejpam-5839	1169	15	p	p	NOUN
ejpam-5839	1169	16	-	-	PUNCT
ejpam-5839	1169	17	closed	closed	ADJ
ejpam-5839	1169	18	.	.	PUNCT
ejpam-5839	1170	1	thus	thus	ADV
ejpam-5839	1170	2	,	,	PUNCT
ejpam-5839	1170	3	(	(	PUNCT
ejpam-5839	1170	4	g̃,ω	g̃,ω	NOUN
ejpam-5839	1170	5	)	)	PUNCT
ejpam-5839	1170	6	∈	∈	PROPN
ejpam-5839	1170	7	τqpnss	τqpns	NOUN
ejpam-5839	1170	8	implies	imply	VERB
ejpam-5839	1170	9	that	that	SCONJ
ejpam-5839	1170	10	(	(	PUNCT
ejpam-5839	1170	11	g̃,ω)c	g̃,ω)c	PROPN
ejpam-5839	1170	12	is	be	AUX
ejpam-5839	1170	13	quadripartitioned	quadripartitione	VERB
ejpam-5839	1170	14	neutrosophic	neutrosophic	ADJ
ejpam-5839	1170	15	soft	soft	ADJ
ejpam-5839	1170	16	finite	finite	NOUN
ejpam-5839	1170	17	and	and	CCONJ
ejpam-5839	1170	18	quadripartitioned	quadripartitione	VERB
ejpam-5839	1170	19	neutrosophic	neutrosophic	ADJ
ejpam-5839	1170	20	soft	soft	ADJ
ejpam-5839	1170	21	p	p	NOUN
ejpam-5839	1170	22	-	-	PUNCT
ejpam-5839	1170	23	closed	closed	ADJ
ejpam-5839	1170	24	.	.	PUNCT
ejpam-5839	1171	1	this	this	PRON
ejpam-5839	1171	2	means	mean	VERB
ejpam-5839	1171	3	that	that	SCONJ
ejpam-5839	1171	4	all	all	DET
ejpam-5839	1171	5	the	the	DET
ejpam-5839	1171	6	quadripartitioned	quadripartitioned	ADJ
ejpam-5839	1171	7	neutrosophic	neutrosophic	ADJ
ejpam-5839	1171	8	soft	soft	ADJ
ejpam-5839	1171	9	p	p	NOUN
ejpam-5839	1171	10	-	-	PUNCT
ejpam-5839	1171	11	closed	closed	ADJ
ejpam-5839	1171	12	subsets	subset	NOUN
ejpam-5839	1171	13	of	of	ADP
ejpam-5839	1171	14	x	x	SYM
ejpam-5839	1171	15	are	be	AUX
ejpam-5839	1171	16	finite	finite	PROPN
ejpam-5839	1171	17	quadripartitioned	quadripartitione	VERB
ejpam-5839	1171	18	neutrosophic	neutrosophic	ADJ
ejpam-5839	1171	19	subsets	subset	NOUN
ejpam-5839	1171	20	of	of	ADP
ejpam-5839	1171	21	x	x	PUNCT
ejpam-5839	1171	22	and	and	CCONJ
ejpam-5839	1171	23	x	x	X
ejpam-5839	1171	24	itself	itself	PRON
ejpam-5839	1171	25	.	.	PUNCT
ejpam-5839	1172	1	thus	thus	ADV
ejpam-5839	1172	2	,	,	PUNCT
ejpam-5839	1172	3	the	the	DET
ejpam-5839	1172	4	only	only	ADJ
ejpam-5839	1172	5	infinite	infinite	ADJ
ejpam-5839	1172	6	quadripartitioned	quadripartitione	VERB
ejpam-5839	1172	7	neutrosophic	neutrosophic	ADJ
ejpam-5839	1172	8	soft	soft	ADJ
ejpam-5839	1172	9	p	p	NOUN
ejpam-5839	1172	10	-	-	PUNCT
ejpam-5839	1172	11	closed	close	VERB
ejpam-5839	1172	12	subset	subset	NOUN
ejpam-5839	1172	13	of	of	ADP
ejpam-5839	1172	14	x	x	PUNCT
ejpam-5839	1172	15	is	be	AUX
ejpam-5839	1172	16	x	x	X
ejpam-5839	1172	17	,	,	PUNCT
ejpam-5839	1172	18	which	which	PRON
ejpam-5839	1172	19	contains	contain	VERB
ejpam-5839	1172	20	y.	y.	PROPN
ejpam-5839	1172	21	therefore	therefore	ADV
ejpam-5839	1172	22	,	,	PUNCT
ejpam-5839	1172	23	x	x	PUNCT
ejpam-5839	1172	24	=	=	PUNCT
ejpam-5839	1172	25	y.	y.	NOUN
ejpam-5839	1172	26	since	since	SCONJ
ejpam-5839	1172	27	y	y	PROPN
ejpam-5839	1172	28	is	be	AUX
ejpam-5839	1172	29	the	the	DET
ejpam-5839	1172	30	smallest	small	ADJ
ejpam-5839	1172	31	quadripartitioned	quadripartitione	VERB
ejpam-5839	1172	32	neutrosophic	neutrosophic	ADJ
ejpam-5839	1172	33	soft	soft	ADJ
ejpam-5839	1172	34	p	p	NOUN
ejpam-5839	1172	35	-	-	PUNCT
ejpam-5839	1172	36	closed	close	VERB
ejpam-5839	1172	37	set	set	NOUN
ejpam-5839	1172	38	containing	contain	VERB
ejpam-5839	1172	39	y	y	PROPN
ejpam-5839	1172	40	and	and	CCONJ
ejpam-5839	1172	41	x	x	X
ejpam-5839	1172	42	is	be	AUX
ejpam-5839	1172	43	the	the	DET
ejpam-5839	1172	44	only	only	ADJ
ejpam-5839	1172	45	such	such	ADJ
ejpam-5839	1172	46	set	set	NOUN
ejpam-5839	1172	47	,	,	PUNCT
ejpam-5839	1172	48	we	we	PRON
ejpam-5839	1172	49	conclude	conclude	VERB
ejpam-5839	1172	50	that	that	PRON
ejpam-5839	1172	51	:	:	PUNCT
ejpam-5839	1172	52	x	x	X
ejpam-5839	1172	53	=	=	PUNCT
ejpam-5839	1172	54	y.	y.	NOUN
ejpam-5839	1172	55	to	to	PART
ejpam-5839	1172	56	prove	prove	VERB
ejpam-5839	1172	57	that	that	SCONJ
ejpam-5839	1172	58	(	(	PUNCT
ejpam-5839	1172	59	x	x	X
ejpam-5839	1172	60	,	,	PUNCT
ejpam-5839	1172	61	τqpnss	τqpnss	PROPN
ejpam-5839	1172	62	,	,	PUNCT
ejpam-5839	1172	63	ω	ω	PROPN
ejpam-5839	1172	64	)	)	PUNCT
ejpam-5839	1172	65	is	be	AUX
ejpam-5839	1172	66	not	not	PART
ejpam-5839	1172	67	quadripartitioned	quadripartitione	VERB
ejpam-5839	1172	68	neutrosophic	neutrosophic	ADJ
ejpam-5839	1172	69	soft	soft	ADJ
ejpam-5839	1172	70	second	second	ADJ
ejpam-5839	1172	71	countable	countable	ADJ
ejpam-5839	1172	72	,	,	PUNCT
ejpam-5839	1172	73	suppose	suppose	VERB
ejpam-5839	1172	74	the	the	DET
ejpam-5839	1172	75	contrary	contrary	NOUN
ejpam-5839	1172	76	.	.	PUNCT
ejpam-5839	1173	1	then	then	ADV
ejpam-5839	1173	2	x	x	X
ejpam-5839	1173	3	is	be	AUX
ejpam-5839	1173	4	quadripartitioned	quadripartitione	VERB
ejpam-5839	1173	5	neutrosophic	neutrosophic	ADJ
ejpam-5839	1173	6	soft	soft	ADJ
ejpam-5839	1173	7	second	second	ADJ
ejpam-5839	1173	8	countable	countable	ADJ
ejpam-5839	1173	9	,	,	PUNCT
ejpam-5839	1173	10	so	so	SCONJ
ejpam-5839	1173	11	there	there	PRON
ejpam-5839	1173	12	exists	exist	VERB
ejpam-5839	1173	13	a	a	DET
ejpam-5839	1173	14	quadripartitioned	quadripartitioned	ADJ
ejpam-5839	1173	15	neutrosophic	neutrosophic	ADJ
ejpam-5839	1173	16	soft	soft	ADJ
ejpam-5839	1173	17	countable	countable	ADJ
ejpam-5839	1173	18	base	base	NOUN
ejpam-5839	1173	19	bqpnss	bqpns	NOUN
ejpam-5839	1173	20	for	for	ADP
ejpam-5839	1173	21	the	the	DET
ejpam-5839	1173	22	quadripartitioned	quadripartitioned	ADJ
ejpam-5839	1173	23	neutrosophic	neutrosophic	ADJ
ejpam-5839	1173	24	soft	soft	ADJ
ejpam-5839	1173	25	topology	topology	NOUN
ejpam-5839	1173	26	on	on	ADP
ejpam-5839	1173	27	x.	x.	NOUN
ejpam-5839	1174	1	the	the	DET
ejpam-5839	1174	2	members	member	NOUN
ejpam-5839	1174	3	of	of	ADP
ejpam-5839	1174	4	bqpnss	bqpns	NOUN
ejpam-5839	1174	5	may	may	AUX
ejpam-5839	1174	6	be	be	AUX
ejpam-5839	1174	7	enumerated	enumerate	VERB
ejpam-5839	1174	8	as	as	ADP
ejpam-5839	1174	9	b1	b1	NOUN
ejpam-5839	1174	10	,	,	PUNCT
ejpam-5839	1174	11	b2	b2	NOUN
ejpam-5839	1174	12	,	,	PUNCT
ejpam-5839	1174	13	b3	b3	NOUN
ejpam-5839	1174	14	,	,	PUNCT
ejpam-5839	1174	15	b4	b4	NOUN
ejpam-5839	1174	16	,	,	PUNCT
ejpam-5839	1174	17	.	.	PUNCT
ejpam-5839	1174	18	.	.	PUNCT
ejpam-5839	1175	1	..	..	PUNCT
ejpam-5839	1175	2	let	let	VERB
ejpam-5839	1176	1	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	NOUN
ejpam-5839	1176	2	)	)	PUNCT
ejpam-5839	1176	3	∈	∈	PROPN
ejpam-5839	1176	4	x	x	PUNCT
ejpam-5839	1176	5	be	be	AUX
ejpam-5839	1176	6	arbitrary	arbitrary	ADJ
ejpam-5839	1176	7	but	but	CCONJ
ejpam-5839	1176	8	fixed	fix	VERB
ejpam-5839	1176	9	.	.	PUNCT
ejpam-5839	1177	1	define	define	NOUN
ejpam-5839	1177	2	:	:	PUNCT
ejpam-5839	1177	3	bqpnss	bqpns	NOUN
ejpam-5839	1177	4	0	0	PUNCT
ejpam-5839	1178	1	=	=	SYM
ejpam-5839	1178	2	{	{	PUNCT
ejpam-5839	1178	3	br	br	NOUN
ejpam-5839	1178	4	∈	∈	PROPN
ejpam-5839	1178	5	bqpnss	bqpns	NOUN
ejpam-5839	1178	6	|	|	ADV
ejpam-5839	1178	7	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	NOUN
ejpam-5839	1178	8	)	)	PUNCT
ejpam-5839	1178	9	∈	∈	PROPN
ejpam-5839	1178	10	br	br	PROPN
ejpam-5839	1178	11	}	}	PUNCT
ejpam-5839	1178	12	(	(	PUNCT
ejpam-5839	1178	13	1	1	X
ejpam-5839	1178	14	)	)	PUNCT
ejpam-5839	1178	15	y	y	PROPN
ejpam-5839	1178	16	=	=	SYM
ejpam-5839	1178	17	⋂	⋂	PROPN
ejpam-5839	1178	18	{	{	PUNCT
ejpam-5839	1178	19	br	br	INTJ
ejpam-5839	1179	1	|	|	ADV
ejpam-5839	1179	2	br	br	NOUN
ejpam-5839	1179	3	∈	∈	PROPN
ejpam-5839	1179	4	bqpnss	bqpns	NOUN
ejpam-5839	1179	5	0	0	NUM
ejpam-5839	1179	6	}	}	PUNCT
ejpam-5839	1179	7	(	(	PUNCT
ejpam-5839	1179	8	2	2	NUM
ejpam-5839	1179	9	)	)	PUNCT
ejpam-5839	1179	10	from	from	ADP
ejpam-5839	1179	11	(	(	PUNCT
ejpam-5839	1179	12	2	2	NUM
ejpam-5839	1179	13	)	)	PUNCT
ejpam-5839	1179	14	,	,	PUNCT
ejpam-5839	1179	15	it	it	PRON
ejpam-5839	1179	16	is	be	AUX
ejpam-5839	1179	17	clear	clear	ADJ
ejpam-5839	1179	18	that	that	SCONJ
ejpam-5839	1179	19	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	1179	20	)	)	PUNCT
ejpam-5839	1179	21	is	be	AUX
ejpam-5839	1179	22	common	common	ADJ
ejpam-5839	1179	23	in	in	ADP
ejpam-5839	1179	24	all	all	DET
ejpam-5839	1179	25	the	the	DET
ejpam-5839	1179	26	members	member	NOUN
ejpam-5839	1179	27	of	of	ADP
ejpam-5839	1179	28	bqpnss	bqpns	NOUN
ejpam-5839	1179	29	0	0	PUNCT
ejpam-5839	1179	30	and	and	CCONJ
ejpam-5839	1179	31	hence	hence	ADV
ejpam-5839	1179	32	:	:	PUNCT
ejpam-5839	1179	33	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	1179	34	)	)	PUNCT
ejpam-5839	1180	1	∈	∈	PROPN
ejpam-5839	1180	2	y.	y.	NOUN
ejpam-5839	1180	3	we	we	PRON
ejpam-5839	1180	4	claim	claim	VERB
ejpam-5839	1180	5	that	that	SCONJ
ejpam-5839	1180	6	:	:	PUNCT
ejpam-5839	1180	7	y	y	X
ejpam-5839	1180	8	=	=	PRON
ejpam-5839	1180	9	{	{	PUNCT
ejpam-5839	1180	10	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	1180	11	)	)	PUNCT
ejpam-5839	1180	12	}	}	PUNCT
ejpam-5839	1180	13	(	(	PUNCT
ejpam-5839	1180	14	3	3	NUM
ejpam-5839	1180	15	)	)	PUNCT
ejpam-5839	1180	16	.	.	PUNCT
ejpam-5839	1181	1	let	let	VERB
ejpam-5839	1181	2	yθ	yθ	PRON
ejpam-5839	1181	3	′	′	VERB
ejpam-5839	1181	4	(	(	PUNCT
ejpam-5839	1181	5	r′1,r	r′1,r	VERB
ejpam-5839	1181	6	′	′	NUM
ejpam-5839	1181	7	2,r	2,r	NUM
ejpam-5839	1182	1	′	′	NUM
ejpam-5839	1183	1	3,r	3,r	NUM
ejpam-5839	1183	2	′	′	NUM
ejpam-5839	1183	3	4	4	NUM
ejpam-5839	1183	4	)	)	PUNCT
ejpam-5839	1183	5	∈	∈	NOUN
ejpam-5839	1183	6	x	x	AUX
ejpam-5839	1183	7	be	be	AUX
ejpam-5839	1183	8	arbitrary	arbitrary	ADJ
ejpam-5839	1183	9	such	such	ADJ
ejpam-5839	1183	10	that	that	PRON
ejpam-5839	1183	11	:	:	PUNCT
ejpam-5839	1183	12	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	1183	13	)	)	PUNCT
ejpam-5839	1184	1	̸=	̸=	PROPN
ejpam-5839	1184	2	yθ	yθ	NOUN
ejpam-5839	1184	3	′	′	NUM
ejpam-5839	1184	4	(	(	PUNCT
ejpam-5839	1184	5	r′1,r	r′1,r	VERB
ejpam-5839	1184	6	′	′	NUM
ejpam-5839	1184	7	2,r	2,r	NUM
ejpam-5839	1184	8	′	′	NUM
ejpam-5839	1185	1	3,r	3,r	NUM
ejpam-5839	1185	2	′	′	NUM
ejpam-5839	1185	3	4	4	NUM
ejpam-5839	1185	4	)	)	PUNCT
ejpam-5839	1185	5	.	.	PUNCT
ejpam-5839	1186	1	since	since	SCONJ
ejpam-5839	1186	2	{	{	PUNCT
ejpam-5839	1186	3	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	1186	4	)	)	PUNCT
ejpam-5839	1186	5	}	}	PUNCT
ejpam-5839	1186	6	is	be	AUX
ejpam-5839	1186	7	a	a	DET
ejpam-5839	1186	8	quadripartitioned	quadripartitione	VERB
ejpam-5839	1186	9	neutrosophic	neutrosophic	ADJ
ejpam-5839	1186	10	soft	soft	ADJ
ejpam-5839	1186	11	finite	finite	NOUN
ejpam-5839	1186	12	set	set	NOUN
ejpam-5839	1186	13	,	,	PUNCT
ejpam-5839	1186	14	its	its	PRON
ejpam-5839	1186	15	complement	complement	NOUN
ejpam-5839	1186	16	is	be	AUX
ejpam-5839	1186	17	in	in	ADP
ejpam-5839	1186	18	τqpnss	τqpns	NOUN
ejpam-5839	1186	19	,	,	PUNCT
ejpam-5839	1186	20	i.e.	i.e.	X
ejpam-5839	1186	21	,	,	PUNCT
ejpam-5839	1186	22	{	{	PUNCT
ejpam-5839	1186	23	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	1186	24	)	)	PUNCT
ejpam-5839	1186	25	}	}	PUNCT
ejpam-5839	1186	26	c	c	PROPN
ejpam-5839	1186	27	∈	∈	PROPN
ejpam-5839	1186	28	τqpnss	τqpns	NOUN
ejpam-5839	1186	29	.	.	PUNCT
ejpam-5839	1187	1	clearly	clearly	ADV
ejpam-5839	1187	2	,	,	PUNCT
ejpam-5839	1187	3	yθ	yθ	NOUN
ejpam-5839	1187	4	′	′	NUM
ejpam-5839	1187	5	(	(	PUNCT
ejpam-5839	1187	6	r′1,r	r′1,r	VERB
ejpam-5839	1187	7	′	′	NUM
ejpam-5839	1187	8	2,r	2,r	NUM
ejpam-5839	1187	9	′	′	NUM
ejpam-5839	1188	1	3,r	3,r	NUM
ejpam-5839	1188	2	′	′	NUM
ejpam-5839	1188	3	4	4	NUM
ejpam-5839	1188	4	)	)	PUNCT
ejpam-5839	1188	5	∈	∈	PROPN
ejpam-5839	1188	6	{	{	PUNCT
ejpam-5839	1188	7	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	1188	8	)	)	PUNCT
ejpam-5839	1188	9	}	}	PUNCT
ejpam-5839	1188	10	c.	c.	NOUN
ejpam-5839	1188	11	by	by	ADP
ejpam-5839	1188	12	the	the	DET
ejpam-5839	1188	13	definition	definition	NOUN
ejpam-5839	1188	14	of	of	ADP
ejpam-5839	1188	15	the	the	DET
ejpam-5839	1188	16	quadripartitioned	quadripartitione	VERB
ejpam-5839	1188	17	neutrosophic	neutrosophic	ADJ
ejpam-5839	1188	18	soft	soft	ADJ
ejpam-5839	1188	19	base	base	NOUN
ejpam-5839	1188	20	,	,	PUNCT
ejpam-5839	1188	21	there	there	PRON
ejpam-5839	1188	22	exists	exist	VERB
ejpam-5839	1188	23	b	b	NOUN
ejpam-5839	1188	24	yθ	yθ	NOUN
ejpam-5839	1188	25	′	′	NUM
ejpam-5839	1188	26	(	(	PUNCT
ejpam-5839	1188	27	r′1,r	r′1,r	VERB
ejpam-5839	1188	28	′	′	NUM
ejpam-5839	1188	29	2,r	2,r	NUM
ejpam-5839	1188	30	′	′	NUM
ejpam-5839	1188	31	3,r	3,r	NUM
ejpam-5839	1188	32	′	′	NUM
ejpam-5839	1188	33	4	4	NUM
ejpam-5839	1188	34	)	)	PUNCT
ejpam-5839	1188	35	∈	∈	NOUN
ejpam-5839	1188	36	bqpnss	bqpns	NOUN
ejpam-5839	1188	37	such	such	ADJ
ejpam-5839	1188	38	that	that	PRON
ejpam-5839	1188	39	:	:	PUNCT
ejpam-5839	1188	40	yθ	yθ	NOUN
ejpam-5839	1188	41	′	′	NUM
ejpam-5839	1188	42	(	(	PUNCT
ejpam-5839	1188	43	r′1,r	r′1,r	VERB
ejpam-5839	1188	44	′	′	NUM
ejpam-5839	1188	45	2,r	2,r	NUM
ejpam-5839	1188	46	′	′	NUM
ejpam-5839	1189	1	3,r	3,r	NUM
ejpam-5839	1189	2	′	′	NUM
ejpam-5839	1189	3	4	4	NUM
ejpam-5839	1189	4	)	)	PUNCT
ejpam-5839	1189	5	∈	∈	PROPN
ejpam-5839	1189	6	b	b	NOUN
ejpam-5839	1189	7	yθ	yθ	NOUN
ejpam-5839	1190	1	′	′	NUM
ejpam-5839	1190	2	(	(	PUNCT
ejpam-5839	1190	3	r′1,r	r′1,r	VERB
ejpam-5839	1190	4	′	′	NUM
ejpam-5839	1190	5	2,r	2,r	NUM
ejpam-5839	1190	6	′	′	NUM
ejpam-5839	1191	1	3,r	3,r	NUM
ejpam-5839	1191	2	′	′	NUM
ejpam-5839	1191	3	4	4	NUM
ejpam-5839	1191	4	)	)	PUNCT
ejpam-5839	1191	5	⊆	⊆	NUM
ejpam-5839	1191	6	{	{	PUNCT
ejpam-5839	1191	7	xθ(r1,r2,r3,r4	xθ(r1,r2,r3,r4	PROPN
ejpam-5839	1191	8	)	)	PUNCT
ejpam-5839	1191	9	}	}	PUNCT
ejpam-5839	1191	10	c.	c.	PROPN
ejpam-5839	1191	11	a.	a.	NOUN
ejpam-5839	1191	12	shihadeh	shihadeh	VERB
ejpam-5839	1191	13	et	et	PROPN
ejpam-5839	1191	14	al	al	PROPN
ejpam-5839	1191	15	.	.	PUNCT
ejpam-5839	1191	16	/	/	SYM
ejpam-5839	1191	17	eur	eur	PROPN
ejpam-5839	1191	18	.	.	PUNCT
ejpam-5839	1192	1	j.	j.	PROPN
ejpam-5839	1192	2	pure	pure	PROPN
ejpam-5839	1192	3	appl	appl	PROPN
ejpam-5839	1192	4	.	.	PROPN
ejpam-5839	1192	5	math	math	PROPN
ejpam-5839	1192	6	,	,	PUNCT
ejpam-5839	1192	7	18	18	NUM
ejpam-5839	1192	8	(	(	PUNCT
ejpam-5839	1192	9	2	2	NUM
ejpam-5839	1192	10	)	)	PUNCT
ejpam-5839	1192	11	(	(	PUNCT
ejpam-5839	1192	12	2025	2025	NUM
ejpam-5839	1192	13	)	)	PUNCT
ejpam-5839	1192	14	,	,	PUNCT
ejpam-5839	1192	15	5839	5839	NUM
ejpam-5839	1192	16	49	49	NUM
ejpam-5839	1192	17	of	of	ADP
ejpam-5839	1192	18	54	54	NUM
ejpam-5839	1192	19	this	this	PRON
ejpam-5839	1192	20	implies	imply	VERB
ejpam-5839	1192	21	that	that	PRON
ejpam-5839	1192	22	:	:	PUNCT
ejpam-5839	1192	23	yθ	yθ	NOUN
ejpam-5839	1192	24	′	′	NUM
ejpam-5839	1192	25	(	(	PUNCT
ejpam-5839	1192	26	r′1,r	r′1,r	VERB
ejpam-5839	1192	27	′	′	NUM
ejpam-5839	1192	28	2,r	2,r	NUM
ejpam-5839	1192	29	′	′	NUM
ejpam-5839	1193	1	3,r	3,r	NUM
ejpam-5839	1193	2	′	′	NUM
ejpam-5839	1193	3	4	4	NUM
ejpam-5839	1193	4	)	)	PUNCT
ejpam-5839	1193	5	/∈	/∈	PUNCT
ejpam-5839	1194	1	bqpnss	bqpns	NOUN
ejpam-5839	1194	2	0	0	NUM
ejpam-5839	1194	3	.	.	PUNCT
ejpam-5839	1195	1	from	from	ADP
ejpam-5839	1195	2	(	(	PUNCT
ejpam-5839	1195	3	2	2	NUM
ejpam-5839	1195	4	)	)	PUNCT
ejpam-5839	1195	5	,	,	PUNCT
ejpam-5839	1195	6	this	this	PRON
ejpam-5839	1195	7	means	mean	VERB
ejpam-5839	1195	8	:	:	PUNCT
ejpam-5839	1195	9	yθ	yθ	NOUN
ejpam-5839	1196	1	′	′	NUM
ejpam-5839	1196	2	(	(	PUNCT
ejpam-5839	1196	3	r′1,r	r′1,r	VERB
ejpam-5839	1196	4	′	′	NUM
ejpam-5839	1196	5	2,r	2,r	NUM
ejpam-5839	1196	6	′	′	NUM
ejpam-5839	1197	1	3,r	3,r	NUM
ejpam-5839	1197	2	′	′	NUM
ejpam-5839	1197	3	4	4	NUM
ejpam-5839	1197	4	)	)	PUNCT
ejpam-5839	1197	5	/∈	/∈	PUNCT
ejpam-5839	1198	1	y.	y.	PROPN
ejpam-5839	1198	2	thus	thus	ADV
ejpam-5839	1198	3	,	,	PUNCT
ejpam-5839	1198	4	we	we	PRON
ejpam-5839	1198	5	have	have	AUX
ejpam-5839	1198	6	shown	show	VERB
ejpam-5839	1198	7	that	that	SCONJ
ejpam-5839	1198	8	:	:	PUNCT
ejpam-5839	1198	9	yθ	yθ	NOUN
ejpam-5839	1198	10	′	′	NUM
ejpam-5839	1198	11	(	(	PUNCT
ejpam-5839	1198	12	r′1,r	r′1,r	VERB
ejpam-5839	1198	13	′	′	NUM
ejpam-5839	1198	14	2,r	2,r	NUM
ejpam-5839	1198	15	′	′	NUM
ejpam-5839	1199	1	3,r	3,r	NUM
ejpam-5839	1199	2	′	′	NUM
ejpam-5839	1199	3	4	4	NUM
ejpam-5839	1199	4	)	)	PUNCT
ejpam-5839	1199	5	∈	∈	PROPN
ejpam-5839	1200	1	x	x	NOUN
ejpam-5839	1200	2	,	,	PUNCT
ejpam-5839	1200	3	yθ	yθ	NOUN
ejpam-5839	1200	4	′	′	NUM
ejpam-5839	1200	5	(	(	PUNCT
ejpam-5839	1200	6	r′1,r	r′1,r	VERB
ejpam-5839	1200	7	′	′	NUM
ejpam-5839	1200	8	2,r	2,r	NUM
ejpam-5839	1200	9	′	′	NUM
ejpam-5839	1201	1	3,r	3,r	NUM
ejpam-5839	1201	2	′	′	NUM
ejpam-5839	1201	3	4	4	NUM
ejpam-5839	1201	4	)	)	PUNCT
ejpam-5839	1201	5	/∈	/∈	PUNCT
ejpam-5839	1202	1	y.	y.	NOUN
ejpam-5839	1202	2	this	this	PRON
ejpam-5839	1202	3	proves	prove	VERB
ejpam-5839	1202	4	(	(	PUNCT
ejpam-5839	1202	5	3	3	NUM
ejpam-5839	1202	6	)	)	PUNCT
ejpam-5839	1202	7	,	,	PUNCT
ejpam-5839	1202	8	and	and	CCONJ
ejpam-5839	1202	9	consequently	consequently	ADV
ejpam-5839	1202	10	:	:	PUNCT
ejpam-5839	1202	11	yc	yc	PROPN
ejpam-5839	1202	12	is	be	AUX
ejpam-5839	1202	13	quadripartitioned	quadripartitione	VERB
ejpam-5839	1202	14	neutrosophic	neutrosophic	ADJ
ejpam-5839	1202	15	soft	soft	ADJ
ejpam-5839	1202	16	countable	countable	ADJ
ejpam-5839	1202	17	.	.	PUNCT
ejpam-5839	1203	1	(	(	PUNCT
ejpam-5839	1203	2	4	4	NUM
ejpam-5839	1203	3	)	)	PUNCT
ejpam-5839	1203	4	since	since	SCONJ
ejpam-5839	1203	5	x	x	PRON
ejpam-5839	1203	6	is	be	AUX
ejpam-5839	1203	7	quadripartitioned	quadripartitione	VERB
ejpam-5839	1203	8	neutrosophic	neutrosophic	ADJ
ejpam-5839	1203	9	soft	soft	ADJ
ejpam-5839	1203	10	uncountable	uncountable	ADJ
ejpam-5839	1203	11	and	and	CCONJ
ejpam-5839	1203	12	y	y	PROPN
ejpam-5839	1203	13	is	be	AUX
ejpam-5839	1203	14	a	a	DET
ejpam-5839	1203	15	quadripartitioned	quadripartitione	VERB
ejpam-5839	1203	16	neutrosophic	neutrosophic	ADJ
ejpam-5839	1203	17	soft	soft	ADJ
ejpam-5839	1203	18	singleton	singleton	NOUN
ejpam-5839	1203	19	set	set	NOUN
ejpam-5839	1203	20	,	,	PUNCT
ejpam-5839	1203	21	we	we	PRON
ejpam-5839	1203	22	get	get	VERB
ejpam-5839	1203	23	:	:	PUNCT
ejpam-5839	1203	24	yc	yc	X
ejpam-5839	1203	25	=	=	PUNCT
ejpam-5839	1204	1	x	x	PROPN
ejpam-5839	1204	2	−	−	PROPN
ejpam-5839	1204	3	⋂	⋂	PROPN
ejpam-5839	1204	4	{	{	PUNCT
ejpam-5839	1204	5	br	br	INTJ
ejpam-5839	1204	6	|	|	ADV
ejpam-5839	1204	7	br	br	NOUN
ejpam-5839	1204	8	∈	∈	PROPN
ejpam-5839	1204	9	bqpnss	bqpns	NOUN
ejpam-5839	1204	10	0	0	PUNCT
ejpam-5839	1204	11	}	}	PUNCT
ejpam-5839	1204	12	=	=	SYM
ejpam-5839	1204	13	⋃	⋃	NOUN
ejpam-5839	1204	14	{	{	PUNCT
ejpam-5839	1204	15	bc	bc	NOUN
ejpam-5839	1204	16	r	r	NOUN
ejpam-5839	1204	17	|	|	ADV
ejpam-5839	1204	18	br	br	NOUN
ejpam-5839	1204	19	∈	∈	PROPN
ejpam-5839	1204	20	bqpnss	bqpns	NOUN
ejpam-5839	1204	21	0	0	NUM
ejpam-5839	1204	22	}	}	PUNCT
ejpam-5839	1204	23	(	(	PUNCT
ejpam-5839	1204	24	5	5	NUM
ejpam-5839	1204	25	)	)	PUNCT
ejpam-5839	1204	26	.	.	PUNCT
ejpam-5839	1205	1	since	since	SCONJ
ejpam-5839	1205	2	br	br	PROPN
ejpam-5839	1205	3	∈	∈	PROPN
ejpam-5839	1205	4	bqpnss	bqpns	NOUN
ejpam-5839	1205	5	0	0	NUM
ejpam-5839	1205	6	,	,	PUNCT
ejpam-5839	1205	7	it	it	PRON
ejpam-5839	1205	8	follows	follow	VERB
ejpam-5839	1205	9	that	that	SCONJ
ejpam-5839	1205	10	br	br	PROPN
ejpam-5839	1205	11	∈	∈	PROPN
ejpam-5839	1205	12	bqpnss	bqpns	NOUN
ejpam-5839	1205	13	,	,	PUNCT
ejpam-5839	1205	14	so	so	ADV
ejpam-5839	1205	15	:	:	PUNCT
ejpam-5839	1205	16	bqpnss	bqpns	NOUN
ejpam-5839	1205	17	0	0	NUM
ejpam-5839	1205	18	⊆	⊆	NUM
ejpam-5839	1205	19	bqpnss	bqpns	NOUN
ejpam-5839	1205	20	⊆	⊆	NUM
ejpam-5839	1205	21	τqpnss	τqpns	NOUN
ejpam-5839	1205	22	.	.	PUNCT
ejpam-5839	1206	1	thus	thus	ADV
ejpam-5839	1206	2	,	,	PUNCT
ejpam-5839	1206	3	br	br	PROPN
ejpam-5839	1206	4	∈	∈	PROPN
ejpam-5839	1206	5	τqpnss	τqpns	NOUN
ejpam-5839	1206	6	implies	imply	VERB
ejpam-5839	1206	7	that	that	SCONJ
ejpam-5839	1206	8	bc	bc	PROPN
ejpam-5839	1206	9	r	r	PROPN
ejpam-5839	1206	10	is	be	AUX
ejpam-5839	1206	11	a	a	DET
ejpam-5839	1206	12	quadripartitioned	quadripartitione	VERB
ejpam-5839	1206	13	neutrosophic	neutrosophic	ADJ
ejpam-5839	1206	14	soft	soft	ADJ
ejpam-5839	1206	15	finite	finite	NOUN
ejpam-5839	1206	16	set	set	NOUN
ejpam-5839	1206	17	.	.	PUNCT
ejpam-5839	1207	1	being	be	AUX
ejpam-5839	1207	2	a	a	DET
ejpam-5839	1207	3	quadripartitioned	quadripartitione	VERB
ejpam-5839	1207	4	neutrosophic	neutrosophic	ADJ
ejpam-5839	1207	5	soft	soft	ADJ
ejpam-5839	1207	6	countable	countable	ADJ
ejpam-5839	1207	7	union	union	NOUN
ejpam-5839	1207	8	of	of	ADP
ejpam-5839	1207	9	finite	finite	PROPN
ejpam-5839	1207	10	quadripartitioned	quadripartitione	VERB
ejpam-5839	1207	11	neutrosophic	neutrosophic	ADJ
ejpam-5839	1207	12	soft	soft	ADJ
ejpam-5839	1207	13	sets	set	NOUN
ejpam-5839	1207	14	,	,	PUNCT
ejpam-5839	1207	15	⋃	⋃	PROPN
ejpam-5839	1207	16	{	{	PUNCT
ejpam-5839	1207	17	bc	bc	PROPN
ejpam-5839	1207	18	r	r	NOUN
ejpam-5839	1207	19	|	|	ADV
ejpam-5839	1207	20	br	br	NOUN
ejpam-5839	1207	21	∈	∈	PROPN
ejpam-5839	1207	22	bqpnss	bqpns	NOUN
ejpam-5839	1207	23	0	0	NUM
ejpam-5839	1207	24	}	}	PUNCT
ejpam-5839	1207	25	is	be	AUX
ejpam-5839	1207	26	quadripartitioned	quadripartitione	VERB
ejpam-5839	1207	27	neutrosophic	neutrosophic	ADJ
ejpam-5839	1207	28	soft	soft	ADJ
ejpam-5839	1207	29	countable	countable	ADJ
ejpam-5839	1207	30	,	,	PUNCT
ejpam-5839	1207	31	which	which	PRON
ejpam-5839	1207	32	means	mean	VERB
ejpam-5839	1207	33	:	:	PUNCT
ejpam-5839	1207	34	yc	yc	PRON
ejpam-5839	1207	35	is	be	AUX
ejpam-5839	1207	36	quadripartitioned	quadripartitione	VERB
ejpam-5839	1207	37	neutrosophic	neutrosophic	ADJ
ejpam-5839	1207	38	soft	soft	ADJ
ejpam-5839	1207	39	countable	countable	ADJ
ejpam-5839	1207	40	,	,	PUNCT
ejpam-5839	1207	41	in	in	ADP
ejpam-5839	1207	42	accordance	accordance	NOUN
ejpam-5839	1207	43	with	with	ADP
ejpam-5839	1207	44	(	(	PUNCT
ejpam-5839	1207	45	5	5	NUM
ejpam-5839	1207	46	)	)	PUNCT
ejpam-5839	1207	47	.	.	PUNCT
ejpam-5839	1208	1	this	this	PRON
ejpam-5839	1208	2	contradicts	contradict	VERB
ejpam-5839	1208	3	(	(	PUNCT
ejpam-5839	1208	4	4	4	NUM
ejpam-5839	1208	5	)	)	PUNCT
ejpam-5839	1208	6	.	.	PUNCT
ejpam-5839	1209	1	hence	hence	ADV
ejpam-5839	1209	2	,	,	PUNCT
ejpam-5839	1209	3	our	our	PRON
ejpam-5839	1209	4	supposition	supposition	NOUN
ejpam-5839	1209	5	was	be	AUX
ejpam-5839	1209	6	wrong	wrong	ADJ
ejpam-5839	1209	7	,	,	PUNCT
ejpam-5839	1209	8	and	and	CCONJ
ejpam-5839	1209	9	we	we	PRON
ejpam-5839	1209	10	conclude	conclude	VERB
ejpam-5839	1209	11	that	that	PRON
ejpam-5839	1209	12	:	:	PUNCT
ejpam-5839	1209	13	(	(	PUNCT
ejpam-5839	1209	14	x	x	X
ejpam-5839	1209	15	,	,	PUNCT
ejpam-5839	1209	16	τqpnss	τqpnss	PROPN
ejpam-5839	1209	17	,	,	PUNCT
ejpam-5839	1209	18	ω	ω	PROPN
ejpam-5839	1209	19	)	)	PUNCT
ejpam-5839	1209	20	is	be	AUX
ejpam-5839	1209	21	not	not	PART
ejpam-5839	1209	22	quadripartitioned	quadripartitione	VERB
ejpam-5839	1209	23	neutrosophic	neutrosophic	ADJ
ejpam-5839	1209	24	soft	soft	ADJ
ejpam-5839	1209	25	second	second	ADJ
ejpam-5839	1209	26	countable	countable	ADJ
ejpam-5839	1209	27	.	.	PUNCT
ejpam-5839	1210	1	10	10	NUM
ejpam-5839	1210	2	.	.	PUNCT
ejpam-5839	1210	3	advantages	advantage	NOUN
ejpam-5839	1210	4	of	of	ADP
ejpam-5839	1210	5	quadri	quadri	NOUN
ejpam-5839	1210	6	-	-	PUNCT
ejpam-5839	1210	7	partitioned	partition	VERB
ejpam-5839	1210	8	neutrosophic	neutrosophic	ADJ
ejpam-5839	1210	9	set	set	NOUN
ejpam-5839	1210	10	theory	theory	NOUN
ejpam-5839	1210	11	(	(	PUNCT
ejpam-5839	1210	12	i	i	NOUN
ejpam-5839	1210	13	)	)	PUNCT
ejpam-5839	1210	14	more	more	ADV
ejpam-5839	1210	15	complex	complex	ADJ
ejpam-5839	1210	16	and	and	CCONJ
ejpam-5839	1210	17	comprehensive	comprehensive	ADJ
ejpam-5839	1210	18	framework	framework	NOUN
ejpam-5839	1210	19	:	:	PUNCT
ejpam-5839	1210	20	by	by	ADP
ejpam-5839	1210	21	adding	add	VERB
ejpam-5839	1210	22	a	a	DET
ejpam-5839	1210	23	fourth	fourth	ADJ
ejpam-5839	1210	24	partition	partition	NOUN
ejpam-5839	1210	25	,	,	PUNCT
ejpam-5839	1210	26	qpnst	qpnst	ADJ
ejpam-5839	1210	27	provides	provide	VERB
ejpam-5839	1210	28	a	a	DET
ejpam-5839	1210	29	more	more	ADV
ejpam-5839	1210	30	detailed	detailed	ADJ
ejpam-5839	1210	31	structure	structure	NOUN
ejpam-5839	1210	32	for	for	ADP
ejpam-5839	1210	33	handling	handling	NOUN
ejpam-5839	1210	34	sets	set	NOUN
ejpam-5839	1210	35	,	,	PUNCT
ejpam-5839	1210	36	capturing	capture	VERB
ejpam-5839	1210	37	more	more	ADJ
ejpam-5839	1210	38	possibilities	possibility	NOUN
ejpam-5839	1210	39	and	and	CCONJ
ejpam-5839	1210	40	allowing	allow	VERB
ejpam-5839	1210	41	for	for	ADP
ejpam-5839	1210	42	a	a	DET
ejpam-5839	1210	43	more	more	ADV
ejpam-5839	1210	44	comprehensive	comprehensive	ADJ
ejpam-5839	1210	45	exploration	exploration	NOUN
ejpam-5839	1210	46	of	of	ADP
ejpam-5839	1210	47	complex	complex	ADJ
ejpam-5839	1210	48	systems	system	NOUN
ejpam-5839	1210	49	.	.	PUNCT
ejpam-5839	1211	1	this	this	DET
ejpam-5839	1211	2	expanded	expand	VERB
ejpam-5839	1211	3	framework	framework	NOUN
ejpam-5839	1211	4	is	be	AUX
ejpam-5839	1211	5	particularly	particularly	ADV
ejpam-5839	1211	6	useful	useful	ADJ
ejpam-5839	1211	7	in	in	ADP
ejpam-5839	1211	8	situations	situation	NOUN
ejpam-5839	1211	9	where	where	SCONJ
ejpam-5839	1211	10	traditional	traditional	ADJ
ejpam-5839	1211	11	fuzzy	fuzzy	ADJ
ejpam-5839	1211	12	logic	logic	NOUN
ejpam-5839	1211	13	or	or	CCONJ
ejpam-5839	1211	14	intuitionistic	intuitionistic	ADJ
ejpam-5839	1211	15	sets	set	NOUN
ejpam-5839	1211	16	may	may	AUX
ejpam-5839	1211	17	fall	fall	VERB
ejpam-5839	1211	18	short	short	ADJ
ejpam-5839	1211	19	.	.	PUNCT
ejpam-5839	1212	1	(	(	PUNCT
ejpam-5839	1212	2	ii	ii	NOUN
ejpam-5839	1212	3	)	)	PUNCT
ejpam-5839	1212	4	improved	improve	VERB
ejpam-5839	1212	5	mathematical	mathematical	ADJ
ejpam-5839	1212	6	tools	tool	NOUN
ejpam-5839	1212	7	:	:	PUNCT
ejpam-5839	1212	8	the	the	DET
ejpam-5839	1212	9	introduction	introduction	NOUN
ejpam-5839	1212	10	of	of	ADP
ejpam-5839	1212	11	quadri	quadri	NOUN
ejpam-5839	1212	12	-	-	PUNCT
ejpam-5839	1212	13	partitioned	partition	VERB
ejpam-5839	1212	14	neutrosophic	neutrosophic	ADJ
ejpam-5839	1212	15	riemann	riemann	PROPN
ejpam-5839	1212	16	integral	integral	ADJ
ejpam-5839	1212	17	theory	theory	NOUN
ejpam-5839	1212	18	(	(	PUNCT
ejpam-5839	1212	19	qpnrit	qpnrit	NOUN
ejpam-5839	1212	20	)	)	PUNCT
ejpam-5839	1212	21	offers	offer	VERB
ejpam-5839	1212	22	new	new	ADJ
ejpam-5839	1212	23	insights	insight	NOUN
ejpam-5839	1212	24	into	into	ADP
ejpam-5839	1212	25	the	the	DET
ejpam-5839	1212	26	riemann	riemann	PROPN
ejpam-5839	1212	27	integral	integral	PROPN
ejpam-5839	1212	28	,	,	PUNCT
ejpam-5839	1212	29	an	an	DET
ejpam-5839	1212	30	essential	essential	ADJ
ejpam-5839	1212	31	concept	concept	NOUN
ejpam-5839	1212	32	in	in	ADP
ejpam-5839	1212	33	analysis	analysis	NOUN
ejpam-5839	1212	34	.	.	PUNCT
ejpam-5839	1213	1	by	by	ADP
ejpam-5839	1213	2	extending	extend	VERB
ejpam-5839	1213	3	the	the	DET
ejpam-5839	1213	4	theory	theory	NOUN
ejpam-5839	1213	5	into	into	ADP
ejpam-5839	1213	6	the	the	DET
ejpam-5839	1213	7	qpnst	qpnst	ADJ
ejpam-5839	1213	8	context	context	NOUN
ejpam-5839	1213	9	,	,	PUNCT
ejpam-5839	1213	10	this	this	DET
ejpam-5839	1213	11	work	work	NOUN
ejpam-5839	1213	12	opens	open	VERB
ejpam-5839	1213	13	new	new	ADJ
ejpam-5839	1213	14	avenues	avenue	NOUN
ejpam-5839	1213	15	for	for	ADP
ejpam-5839	1213	16	the	the	DET
ejpam-5839	1213	17	study	study	NOUN
ejpam-5839	1213	18	of	of	ADP
ejpam-5839	1213	19	integration	integration	NOUN
ejpam-5839	1213	20	and	and	CCONJ
ejpam-5839	1213	21	its	its	PRON
ejpam-5839	1213	22	properties	property	NOUN
ejpam-5839	1213	23	under	under	ADP
ejpam-5839	1213	24	uncertainty	uncertainty	NOUN
ejpam-5839	1213	25	,	,	PUNCT
ejpam-5839	1213	26	helping	help	VERB
ejpam-5839	1213	27	to	to	PART
ejpam-5839	1213	28	reveal	reveal	VERB
ejpam-5839	1213	29	behaviors	behavior	NOUN
ejpam-5839	1213	30	and	and	CCONJ
ejpam-5839	1213	31	characteristics	characteristic	NOUN
ejpam-5839	1213	32	not	not	PART
ejpam-5839	1213	33	previously	previously	ADV
ejpam-5839	1213	34	observable	observable	ADJ
ejpam-5839	1213	35	.	.	PUNCT
ejpam-5839	1214	1	(	(	PUNCT
ejpam-5839	1214	2	iii	iii	NOUN
ejpam-5839	1214	3	)	)	PUNCT
ejpam-5839	1214	4	level	level	NOUN
ejpam-5839	1214	5	cut	cut	NOUN
ejpam-5839	1214	6	(	(	PUNCT
ejpam-5839	1214	7	four	four	NUM
ejpam-5839	1214	8	-	-	PUNCT
ejpam-5839	1214	9	tuple	tuple	NOUN
ejpam-5839	1214	10	representation	representation	NOUN
ejpam-5839	1214	11	):	):	PUNCT
ejpam-5839	1214	12	the	the	DET
ejpam-5839	1214	13	definition	definition	NOUN
ejpam-5839	1214	14	of	of	ADP
ejpam-5839	1214	15	the	the	DET
ejpam-5839	1214	16	level	level	NOUN
ejpam-5839	1214	17	cut	cut	NOUN
ejpam-5839	1214	18	as	as	ADP
ejpam-5839	1214	19	a	a	DET
ejpam-5839	1214	20	fourtuple	fourtuple	NOUN
ejpam-5839	1214	21	(	(	PUNCT
ejpam-5839	1214	22	i	i	PROPN
ejpam-5839	1214	23	,	,	PUNCT
ejpam-5839	1214	24	j	j	PROPN
ejpam-5839	1214	25	,	,	PUNCT
ejpam-5839	1214	26	k	k	PROPN
ejpam-5839	1214	27	,	,	PUNCT
ejpam-5839	1214	28	l	l	NOUN
ejpam-5839	1214	29	)	)	PUNCT
ejpam-5839	1214	30	captures	capture	VERB
ejpam-5839	1214	31	the	the	DET
ejpam-5839	1214	32	multiple	multiple	ADJ
ejpam-5839	1214	33	possibilities	possibility	NOUN
ejpam-5839	1214	34	inherent	inherent	ADJ
ejpam-5839	1214	35	in	in	ADP
ejpam-5839	1214	36	qpnst	qpnst	ADJ
ejpam-5839	1214	37	.	.	PUNCT
ejpam-5839	1215	1	this	this	PRON
ejpam-5839	1215	2	enables	enable	VERB
ejpam-5839	1215	3	more	more	ADV
ejpam-5839	1215	4	precise	precise	ADJ
ejpam-5839	1215	5	modeling	modeling	NOUN
ejpam-5839	1215	6	and	and	CCONJ
ejpam-5839	1215	7	analysis	analysis	NOUN
ejpam-5839	1215	8	,	,	PUNCT
ejpam-5839	1215	9	reflecting	reflect	VERB
ejpam-5839	1215	10	the	the	DET
ejpam-5839	1215	11	different	different	ADJ
ejpam-5839	1215	12	dimensions	dimension	NOUN
ejpam-5839	1215	13	of	of	ADP
ejpam-5839	1215	14	truth	truth	NOUN
ejpam-5839	1215	15	,	,	PUNCT
ejpam-5839	1215	16	indeterminacy	indeterminacy	NOUN
ejpam-5839	1215	17	,	,	PUNCT
ejpam-5839	1215	18	and	and	CCONJ
ejpam-5839	1215	19	falsity	falsity	NOUN
ejpam-5839	1215	20	in	in	ADP
ejpam-5839	1215	21	set	set	ADJ
ejpam-5839	1215	22	membership	membership	NOUN
ejpam-5839	1215	23	more	more	ADV
ejpam-5839	1215	24	clearly	clearly	ADV
ejpam-5839	1215	25	.	.	PUNCT
ejpam-5839	1216	1	this	this	DET
ejpam-5839	1216	2	richer	rich	ADJ
ejpam-5839	1216	3	structure	structure	NOUN
ejpam-5839	1216	4	supports	support	VERB
ejpam-5839	1216	5	more	more	ADV
ejpam-5839	1216	6	accurate	accurate	ADJ
ejpam-5839	1216	7	decision	decision	NOUN
ejpam-5839	1216	8	-	-	PUNCT
ejpam-5839	1216	9	making	making	NOUN
ejpam-5839	1216	10	and	and	CCONJ
ejpam-5839	1216	11	problem	problem	NOUN
ejpam-5839	1216	12	-	-	PUNCT
ejpam-5839	1216	13	solving	solving	NOUN
ejpam-5839	1216	14	in	in	ADP
ejpam-5839	1216	15	uncertain	uncertain	ADJ
ejpam-5839	1216	16	contexts	contexts	NOUN
ejpam-5839	1216	17	.	.	PUNCT
ejpam-5839	1217	1	a.	a.	NOUN
ejpam-5839	1217	2	shihadeh	shihadeh	VERB
ejpam-5839	1217	3	et	et	PROPN
ejpam-5839	1217	4	al	al	PROPN
ejpam-5839	1217	5	.	.	PUNCT
ejpam-5839	1217	6	/	/	SYM
ejpam-5839	1217	7	eur	eur	PROPN
ejpam-5839	1217	8	.	.	PUNCT
ejpam-5839	1218	1	j.	j.	PROPN
ejpam-5839	1218	2	pure	pure	PROPN
ejpam-5839	1218	3	appl	appl	PROPN
ejpam-5839	1218	4	.	.	PROPN
ejpam-5839	1218	5	math	math	PROPN
ejpam-5839	1218	6	,	,	PUNCT
ejpam-5839	1218	7	18	18	NUM
ejpam-5839	1218	8	(	(	PUNCT
ejpam-5839	1218	9	2	2	NUM
ejpam-5839	1218	10	)	)	PUNCT
ejpam-5839	1218	11	(	(	PUNCT
ejpam-5839	1218	12	2025	2025	NUM
ejpam-5839	1218	13	)	)	PUNCT
ejpam-5839	1218	14	,	,	PUNCT
ejpam-5839	1218	15	5839	5839	NUM
ejpam-5839	1218	16	50	50	NUM
ejpam-5839	1218	17	of	of	ADP
ejpam-5839	1218	18	54	54	NUM
ejpam-5839	1218	19	(	(	PUNCT
ejpam-5839	1218	20	iv	iv	X
ejpam-5839	1218	21	)	)	PUNCT
ejpam-5839	1218	22	numerical	numerical	ADJ
ejpam-5839	1218	23	study	study	NOUN
ejpam-5839	1218	24	and	and	CCONJ
ejpam-5839	1218	25	practical	practical	ADJ
ejpam-5839	1218	26	insights	insight	NOUN
ejpam-5839	1218	27	:	:	PUNCT
ejpam-5839	1218	28	the	the	DET
ejpam-5839	1218	29	numerical	numerical	PROPN
ejpam-5839	1218	30	study	study	NOUN
ejpam-5839	1218	31	conducted	conduct	VERB
ejpam-5839	1218	32	within	within	ADP
ejpam-5839	1218	33	the	the	DET
ejpam-5839	1218	34	qpnst	qpnst	ADJ
ejpam-5839	1218	35	framework	framework	NOUN
ejpam-5839	1218	36	provides	provide	VERB
ejpam-5839	1218	37	a	a	DET
ejpam-5839	1218	38	concrete	concrete	ADJ
ejpam-5839	1218	39	understanding	understanding	NOUN
ejpam-5839	1218	40	of	of	ADP
ejpam-5839	1218	41	the	the	DET
ejpam-5839	1218	42	behavior	behavior	NOUN
ejpam-5839	1218	43	of	of	ADP
ejpam-5839	1218	44	the	the	DET
ejpam-5839	1218	45	riemann	riemann	PROPN
ejpam-5839	1218	46	integral	integral	NOUN
ejpam-5839	1218	47	in	in	ADP
ejpam-5839	1218	48	this	this	DET
ejpam-5839	1218	49	extended	extended	ADJ
ejpam-5839	1218	50	context	context	NOUN
ejpam-5839	1218	51	.	.	PUNCT
ejpam-5839	1219	1	organizing	organize	VERB
ejpam-5839	1219	2	the	the	DET
ejpam-5839	1219	3	findings	finding	NOUN
ejpam-5839	1219	4	in	in	ADP
ejpam-5839	1219	5	tabular	tabular	NOUN
ejpam-5839	1219	6	form	form	NOUN
ejpam-5839	1219	7	makes	make	VERB
ejpam-5839	1219	8	it	it	PRON
ejpam-5839	1219	9	easier	easy	ADJ
ejpam-5839	1219	10	for	for	SCONJ
ejpam-5839	1219	11	researchers	researcher	NOUN
ejpam-5839	1219	12	and	and	CCONJ
ejpam-5839	1219	13	practitioners	practitioner	NOUN
ejpam-5839	1219	14	to	to	PART
ejpam-5839	1219	15	grasp	grasp	VERB
ejpam-5839	1219	16	the	the	DET
ejpam-5839	1219	17	implications	implication	NOUN
ejpam-5839	1219	18	and	and	CCONJ
ejpam-5839	1219	19	applications	application	NOUN
ejpam-5839	1219	20	of	of	ADP
ejpam-5839	1219	21	the	the	DET
ejpam-5839	1219	22	new	new	ADJ
ejpam-5839	1219	23	theory	theory	NOUN
ejpam-5839	1219	24	.	.	PUNCT
ejpam-5839	1220	1	11	11	NUM
ejpam-5839	1220	2	.	.	PUNCT
ejpam-5839	1220	3	limitations	limitation	NOUN
ejpam-5839	1220	4	of	of	ADP
ejpam-5839	1220	5	quadri	quadri	NOUN
ejpam-5839	1220	6	-	-	PUNCT
ejpam-5839	1220	7	partitioned	partition	VERB
ejpam-5839	1220	8	neutrosophic	neutrosophic	ADJ
ejpam-5839	1220	9	set	set	NOUN
ejpam-5839	1220	10	theory	theory	NOUN
ejpam-5839	1220	11	(	(	PUNCT
ejpam-5839	1220	12	i	i	NOUN
ejpam-5839	1220	13	)	)	PUNCT
ejpam-5839	1220	14	increased	increase	VERB
ejpam-5839	1220	15	complexity	complexity	NOUN
ejpam-5839	1220	16	:	:	PUNCT
ejpam-5839	1220	17	while	while	SCONJ
ejpam-5839	1220	18	the	the	DET
ejpam-5839	1220	19	added	add	VERB
ejpam-5839	1220	20	complexity	complexity	NOUN
ejpam-5839	1220	21	of	of	ADP
ejpam-5839	1220	22	qpnst	qpnst	ADJ
ejpam-5839	1220	23	allows	allow	NOUN
ejpam-5839	1220	24	for	for	ADP
ejpam-5839	1220	25	more	more	ADV
ejpam-5839	1220	26	detailed	detailed	ADJ
ejpam-5839	1220	27	and	and	CCONJ
ejpam-5839	1220	28	accurate	accurate	ADJ
ejpam-5839	1220	29	representations	representation	NOUN
ejpam-5839	1220	30	of	of	ADP
ejpam-5839	1220	31	uncertainty	uncertainty	NOUN
ejpam-5839	1220	32	,	,	PUNCT
ejpam-5839	1220	33	it	it	PRON
ejpam-5839	1220	34	also	also	ADV
ejpam-5839	1220	35	makes	make	VERB
ejpam-5839	1220	36	the	the	DET
ejpam-5839	1220	37	theory	theory	NOUN
ejpam-5839	1220	38	more	more	ADV
ejpam-5839	1220	39	challenging	challenging	ADJ
ejpam-5839	1220	40	to	to	PART
ejpam-5839	1220	41	apply	apply	VERB
ejpam-5839	1220	42	.	.	PUNCT
ejpam-5839	1221	1	researchers	researcher	NOUN
ejpam-5839	1221	2	may	may	AUX
ejpam-5839	1221	3	find	find	VERB
ejpam-5839	1221	4	it	it	PRON
ejpam-5839	1221	5	difficult	difficult	ADJ
ejpam-5839	1221	6	to	to	PART
ejpam-5839	1221	7	work	work	VERB
ejpam-5839	1221	8	with	with	ADP
ejpam-5839	1221	9	the	the	DET
ejpam-5839	1221	10	four	four	NUM
ejpam-5839	1221	11	-	-	PUNCT
ejpam-5839	1221	12	part	part	NOUN
ejpam-5839	1221	13	structure	structure	NOUN
ejpam-5839	1221	14	,	,	PUNCT
ejpam-5839	1221	15	especially	especially	ADV
ejpam-5839	1221	16	in	in	ADP
ejpam-5839	1221	17	cases	case	NOUN
ejpam-5839	1221	18	where	where	SCONJ
ejpam-5839	1221	19	the	the	DET
ejpam-5839	1221	20	additional	additional	ADJ
ejpam-5839	1221	21	partitions	partition	NOUN
ejpam-5839	1221	22	add	add	VERB
ejpam-5839	1221	23	little	little	ADJ
ejpam-5839	1221	24	value	value	NOUN
ejpam-5839	1221	25	in	in	ADP
ejpam-5839	1221	26	practical	practical	ADJ
ejpam-5839	1221	27	applications	application	NOUN
ejpam-5839	1221	28	.	.	PUNCT
ejpam-5839	1222	1	(	(	PUNCT
ejpam-5839	1222	2	ii	ii	NOUN
ejpam-5839	1222	3	)	)	PUNCT
ejpam-5839	1222	4	computational	computational	ADJ
ejpam-5839	1222	5	challenges	challenge	NOUN
ejpam-5839	1222	6	:	:	PUNCT
ejpam-5839	1222	7	with	with	ADP
ejpam-5839	1222	8	the	the	DET
ejpam-5839	1222	9	introduction	introduction	NOUN
ejpam-5839	1222	10	of	of	ADP
ejpam-5839	1222	11	additional	additional	ADJ
ejpam-5839	1222	12	partitions	partition	NOUN
ejpam-5839	1222	13	and	and	CCONJ
ejpam-5839	1222	14	the	the	DET
ejpam-5839	1222	15	need	need	NOUN
ejpam-5839	1222	16	to	to	PART
ejpam-5839	1222	17	calculate	calculate	VERB
ejpam-5839	1222	18	more	more	ADV
ejpam-5839	1222	19	complex	complex	ADJ
ejpam-5839	1222	20	level	level	NOUN
ejpam-5839	1222	21	cuts	cut	NOUN
ejpam-5839	1222	22	,	,	PUNCT
ejpam-5839	1222	23	the	the	DET
ejpam-5839	1222	24	computational	computational	ADJ
ejpam-5839	1222	25	effort	effort	NOUN
ejpam-5839	1222	26	required	require	VERB
ejpam-5839	1222	27	to	to	PART
ejpam-5839	1222	28	implement	implement	VERB
ejpam-5839	1222	29	qpnst	qpnst	NOUN
ejpam-5839	1222	30	and	and	CCONJ
ejpam-5839	1222	31	qpnrit	qpnrit	NOUN
ejpam-5839	1222	32	could	could	AUX
ejpam-5839	1222	33	be	be	AUX
ejpam-5839	1222	34	significantly	significantly	ADV
ejpam-5839	1222	35	higher	high	ADJ
ejpam-5839	1222	36	.	.	PUNCT
ejpam-5839	1223	1	this	this	PRON
ejpam-5839	1223	2	might	might	AUX
ejpam-5839	1223	3	limit	limit	VERB
ejpam-5839	1223	4	its	its	PRON
ejpam-5839	1223	5	use	use	NOUN
ejpam-5839	1223	6	in	in	ADP
ejpam-5839	1223	7	large	large	ADJ
ejpam-5839	1223	8	-	-	PUNCT
ejpam-5839	1223	9	scale	scale	NOUN
ejpam-5839	1223	10	or	or	CCONJ
ejpam-5839	1223	11	real	real	ADJ
ejpam-5839	1223	12	-	-	PUNCT
ejpam-5839	1223	13	time	time	NOUN
ejpam-5839	1223	14	applications	application	NOUN
ejpam-5839	1223	15	where	where	SCONJ
ejpam-5839	1223	16	computational	computational	ADJ
ejpam-5839	1223	17	efficiency	efficiency	NOUN
ejpam-5839	1223	18	is	be	AUX
ejpam-5839	1223	19	critical	critical	ADJ
ejpam-5839	1223	20	.	.	PUNCT
ejpam-5839	1224	1	(	(	PUNCT
ejpam-5839	1224	2	iii	iii	X
ejpam-5839	1224	3	)	)	PUNCT
ejpam-5839	1224	4	interpretation	interpretation	NOUN
ejpam-5839	1224	5	and	and	CCONJ
ejpam-5839	1224	6	practical	practical	ADJ
ejpam-5839	1224	7	implementation	implementation	NOUN
ejpam-5839	1224	8	:	:	PUNCT
ejpam-5839	1224	9	the	the	DET
ejpam-5839	1224	10	four	four	NUM
ejpam-5839	1224	11	-	-	PUNCT
ejpam-5839	1224	12	dimensional	dimensional	ADJ
ejpam-5839	1224	13	nature	nature	NOUN
ejpam-5839	1224	14	of	of	ADP
ejpam-5839	1224	15	the	the	DET
ejpam-5839	1224	16	model	model	NOUN
ejpam-5839	1224	17	may	may	AUX
ejpam-5839	1224	18	pose	pose	VERB
ejpam-5839	1224	19	interpretative	interpretative	ADJ
ejpam-5839	1224	20	challenges	challenge	NOUN
ejpam-5839	1224	21	.	.	PUNCT
ejpam-5839	1225	1	while	while	SCONJ
ejpam-5839	1225	2	it	it	PRON
ejpam-5839	1225	3	provides	provide	VERB
ejpam-5839	1225	4	a	a	DET
ejpam-5839	1225	5	richer	rich	ADJ
ejpam-5839	1225	6	model	model	NOUN
ejpam-5839	1225	7	for	for	ADP
ejpam-5839	1225	8	uncertainty	uncertainty	NOUN
ejpam-5839	1225	9	,	,	PUNCT
ejpam-5839	1225	10	translating	translate	VERB
ejpam-5839	1225	11	the	the	DET
ejpam-5839	1225	12	abstract	abstract	ADJ
ejpam-5839	1225	13	concepts	concept	NOUN
ejpam-5839	1225	14	into	into	ADP
ejpam-5839	1225	15	real	real	ADJ
ejpam-5839	1225	16	-	-	PUNCT
ejpam-5839	1225	17	world	world	NOUN
ejpam-5839	1225	18	decision	decision	NOUN
ejpam-5839	1225	19	-	-	PUNCT
ejpam-5839	1225	20	making	make	VERB
ejpam-5839	1225	21	processes	process	NOUN
ejpam-5839	1225	22	can	can	AUX
ejpam-5839	1225	23	be	be	AUX
ejpam-5839	1225	24	difficult	difficult	ADJ
ejpam-5839	1225	25	.	.	PUNCT
ejpam-5839	1226	1	practitioners	practitioner	NOUN
ejpam-5839	1226	2	may	may	AUX
ejpam-5839	1226	3	struggle	struggle	VERB
ejpam-5839	1226	4	to	to	PART
ejpam-5839	1226	5	interpret	interpret	VERB
ejpam-5839	1226	6	the	the	DET
ejpam-5839	1226	7	results	result	NOUN
ejpam-5839	1226	8	or	or	CCONJ
ejpam-5839	1226	9	apply	apply	VERB
ejpam-5839	1226	10	the	the	DET
ejpam-5839	1226	11	theory	theory	NOUN
ejpam-5839	1226	12	in	in	ADP
ejpam-5839	1226	13	practical	practical	ADJ
ejpam-5839	1226	14	situations	situation	NOUN
ejpam-5839	1226	15	,	,	PUNCT
ejpam-5839	1226	16	especially	especially	ADV
ejpam-5839	1226	17	in	in	ADP
ejpam-5839	1226	18	industries	industry	NOUN
ejpam-5839	1226	19	not	not	PART
ejpam-5839	1226	20	traditionally	traditionally	ADV
ejpam-5839	1226	21	familiar	familiar	ADJ
ejpam-5839	1226	22	with	with	ADP
ejpam-5839	1226	23	higher	high	ADJ
ejpam-5839	1226	24	-	-	PUNCT
ejpam-5839	1226	25	order	order	NOUN
ejpam-5839	1226	26	logic	logic	NOUN
ejpam-5839	1226	27	systems	system	NOUN
ejpam-5839	1226	28	.	.	PUNCT
ejpam-5839	1227	1	(	(	PUNCT
ejpam-5839	1227	2	iv	iv	X
ejpam-5839	1227	3	)	)	PUNCT
ejpam-5839	1227	4	limited	limited	ADJ
ejpam-5839	1227	5	existing	exist	VERB
ejpam-5839	1227	6	tools	tool	NOUN
ejpam-5839	1227	7	and	and	CCONJ
ejpam-5839	1227	8	resources	resource	NOUN
ejpam-5839	1227	9	:	:	PUNCT
ejpam-5839	1227	10	the	the	DET
ejpam-5839	1227	11	extension	extension	NOUN
ejpam-5839	1227	12	of	of	ADP
ejpam-5839	1227	13	riemann	riemann	PROPN
ejpam-5839	1227	14	integral	integral	ADJ
ejpam-5839	1227	15	theory	theory	NOUN
ejpam-5839	1227	16	into	into	ADP
ejpam-5839	1227	17	the	the	DET
ejpam-5839	1227	18	qpnst	qpnst	ADJ
ejpam-5839	1227	19	context	context	NOUN
ejpam-5839	1227	20	is	be	AUX
ejpam-5839	1227	21	a	a	DET
ejpam-5839	1227	22	relatively	relatively	ADV
ejpam-5839	1227	23	new	new	ADJ
ejpam-5839	1227	24	development	development	NOUN
ejpam-5839	1227	25	,	,	PUNCT
ejpam-5839	1227	26	and	and	CCONJ
ejpam-5839	1227	27	as	as	ADP
ejpam-5839	1227	28	such	such	ADJ
ejpam-5839	1227	29	,	,	PUNCT
ejpam-5839	1227	30	there	there	PRON
ejpam-5839	1227	31	may	may	AUX
ejpam-5839	1227	32	be	be	AUX
ejpam-5839	1227	33	limited	limited	ADJ
ejpam-5839	1227	34	resources	resource	NOUN
ejpam-5839	1227	35	,	,	PUNCT
ejpam-5839	1227	36	tools	tool	NOUN
ejpam-5839	1227	37	,	,	PUNCT
ejpam-5839	1227	38	and	and	CCONJ
ejpam-5839	1227	39	research	research	NOUN
ejpam-5839	1227	40	available	available	ADJ
ejpam-5839	1227	41	to	to	PART
ejpam-5839	1227	42	fully	fully	ADV
ejpam-5839	1227	43	support	support	VERB
ejpam-5839	1227	44	its	its	PRON
ejpam-5839	1227	45	application	application	NOUN
ejpam-5839	1227	46	.	.	PUNCT
ejpam-5839	1228	1	this	this	PRON
ejpam-5839	1228	2	could	could	AUX
ejpam-5839	1228	3	slow	slow	VERB
ejpam-5839	1228	4	down	down	ADP
ejpam-5839	1228	5	its	its	PRON
ejpam-5839	1228	6	adoption	adoption	NOUN
ejpam-5839	1228	7	and	and	CCONJ
ejpam-5839	1228	8	the	the	DET
ejpam-5839	1228	9	development	development	NOUN
ejpam-5839	1228	10	of	of	ADP
ejpam-5839	1228	11	practical	practical	ADJ
ejpam-5839	1228	12	applications	application	NOUN
ejpam-5839	1228	13	based	base	VERB
ejpam-5839	1228	14	on	on	ADP
ejpam-5839	1228	15	qpnrit	qpnrit	NOUN
ejpam-5839	1228	16	.	.	PUNCT
ejpam-5839	1229	1	(	(	PUNCT
ejpam-5839	1229	2	v	v	NOUN
ejpam-5839	1229	3	)	)	PUNCT
ejpam-5839	1229	4	need	need	NOUN
ejpam-5839	1229	5	for	for	ADP
ejpam-5839	1229	6	further	further	ADJ
ejpam-5839	1229	7	theoretical	theoretical	ADJ
ejpam-5839	1229	8	validation	validation	NOUN
ejpam-5839	1229	9	:	:	PUNCT
ejpam-5839	1229	10	although	although	SCONJ
ejpam-5839	1229	11	the	the	DET
ejpam-5839	1229	12	framework	framework	NOUN
ejpam-5839	1229	13	holds	hold	VERB
ejpam-5839	1229	14	promise	promise	NOUN
ejpam-5839	1229	15	,	,	PUNCT
ejpam-5839	1229	16	the	the	DET
ejpam-5839	1229	17	full	full	ADJ
ejpam-5839	1229	18	range	range	NOUN
ejpam-5839	1229	19	of	of	ADP
ejpam-5839	1229	20	theoretical	theoretical	ADJ
ejpam-5839	1229	21	properties	property	NOUN
ejpam-5839	1229	22	of	of	ADP
ejpam-5839	1229	23	qpnst	qpnst	NOUN
ejpam-5839	1229	24	and	and	CCONJ
ejpam-5839	1229	25	qpnrit	qpnrit	NOUN
ejpam-5839	1229	26	needs	need	VERB
ejpam-5839	1229	27	to	to	PART
ejpam-5839	1229	28	be	be	AUX
ejpam-5839	1229	29	further	far	ADV
ejpam-5839	1229	30	explored	explore	VERB
ejpam-5839	1229	31	.	.	PUNCT
ejpam-5839	1230	1	many	many	ADJ
ejpam-5839	1230	2	questions	question	NOUN
ejpam-5839	1230	3	regarding	regard	VERB
ejpam-5839	1230	4	the	the	DET
ejpam-5839	1230	5	consistency	consistency	NOUN
ejpam-5839	1230	6	,	,	PUNCT
ejpam-5839	1230	7	stability	stability	NOUN
ejpam-5839	1230	8	,	,	PUNCT
ejpam-5839	1230	9	and	and	CCONJ
ejpam-5839	1230	10	broader	broad	ADJ
ejpam-5839	1230	11	applicability	applicability	NOUN
ejpam-5839	1230	12	of	of	ADP
ejpam-5839	1230	13	these	these	DET
ejpam-5839	1230	14	theories	theory	NOUN
ejpam-5839	1230	15	remain	remain	VERB
ejpam-5839	1230	16	unanswered	unanswered	ADJ
ejpam-5839	1230	17	,	,	PUNCT
ejpam-5839	1230	18	requiring	require	VERB
ejpam-5839	1230	19	further	further	ADJ
ejpam-5839	1230	20	research	research	NOUN
ejpam-5839	1230	21	and	and	CCONJ
ejpam-5839	1230	22	validation	validation	NOUN
ejpam-5839	1230	23	.	.	PUNCT
ejpam-5839	1231	1	12	12	NUM
ejpam-5839	1231	2	.	.	PUNCT
ejpam-5839	1231	3	conclusion	conclusion	NOUN
ejpam-5839	1231	4	and	and	CCONJ
ejpam-5839	1231	5	future	future	ADJ
ejpam-5839	1231	6	work	work	NOUN
ejpam-5839	1231	7	finally	finally	ADV
ejpam-5839	1231	8	,	,	PUNCT
ejpam-5839	1231	9	by	by	ADP
ejpam-5839	1231	10	adding	add	VERB
ejpam-5839	1231	11	a	a	DET
ejpam-5839	1231	12	third	third	ADJ
ejpam-5839	1231	13	option	option	NOUN
ejpam-5839	1231	14	for	for	ADP
ejpam-5839	1231	15	set	set	ADJ
ejpam-5839	1231	16	representation	representation	NOUN
ejpam-5839	1231	17	,	,	PUNCT
ejpam-5839	1231	18	neutrosophic	neutrosophic	ADJ
ejpam-5839	1231	19	set	set	NOUN
ejpam-5839	1231	20	theory	theory	NOUN
ejpam-5839	1231	21	(	(	PUNCT
ejpam-5839	1231	22	nst	nst	NOUN
ejpam-5839	1231	23	)	)	PUNCT
ejpam-5839	1231	24	expands	expand	VERB
ejpam-5839	1231	25	on	on	ADP
ejpam-5839	1231	26	intuitionistic	intuitionistic	ADJ
ejpam-5839	1231	27	fuzzy	fuzzy	ADJ
ejpam-5839	1231	28	set	set	NOUN
ejpam-5839	1231	29	theory	theory	NOUN
ejpam-5839	1231	30	(	(	PUNCT
ejpam-5839	1231	31	ifst	ifst	NOUN
ejpam-5839	1231	32	)	)	PUNCT
ejpam-5839	1231	33	and	and	CCONJ
ejpam-5839	1231	34	improves	improve	VERB
ejpam-5839	1231	35	the	the	DET
ejpam-5839	1231	36	theory	theory	NOUN
ejpam-5839	1231	37	’s	’s	PART
ejpam-5839	1231	38	ability	ability	NOUN
ejpam-5839	1231	39	to	to	PART
ejpam-5839	1231	40	handle	handle	VERB
ejpam-5839	1231	41	uncertainty	uncertainty	NOUN
ejpam-5839	1231	42	.	.	PUNCT
ejpam-5839	1232	1	by	by	ADP
ejpam-5839	1232	2	introducing	introduce	VERB
ejpam-5839	1232	3	quadri	quadri	NOUN
ejpam-5839	1232	4	-	-	PUNCT
ejpam-5839	1232	5	partitioned	partition	VERB
ejpam-5839	1232	6	neutrosophic	neutrosophic	ADJ
ejpam-5839	1232	7	set	set	NOUN
ejpam-5839	1232	8	theory	theory	NOUN
ejpam-5839	1232	9	(	(	PUNCT
ejpam-5839	1232	10	qpnst	qpnst	ADJ
ejpam-5839	1232	11	)	)	PUNCT
ejpam-5839	1232	12	,	,	PUNCT
ejpam-5839	1232	13	which	which	PRON
ejpam-5839	1232	14	adds	add	VERB
ejpam-5839	1232	15	a	a	DET
ejpam-5839	1232	16	fourth	fourth	ADJ
ejpam-5839	1232	17	alternative	alternative	NOUN
ejpam-5839	1232	18	and	and	CCONJ
ejpam-5839	1232	19	offers	offer	VERB
ejpam-5839	1232	20	a	a	DET
ejpam-5839	1232	21	more	more	ADV
ejpam-5839	1232	22	complex	complex	ADJ
ejpam-5839	1232	23	and	and	CCONJ
ejpam-5839	1232	24	all	all	ADV
ejpam-5839	1232	25	-	-	PUNCT
ejpam-5839	1232	26	encompassing	encompass	VERB
ejpam-5839	1232	27	framework	framework	NOUN
ejpam-5839	1232	28	for	for	ADP
ejpam-5839	1232	29	set	set	ADJ
ejpam-5839	1232	30	representation	representation	NOUN
ejpam-5839	1232	31	,	,	PUNCT
ejpam-5839	1232	32	this	this	DET
ejpam-5839	1232	33	work	work	NOUN
ejpam-5839	1232	34	significantly	significantly	ADV
ejpam-5839	1232	35	develops	develop	VERB
ejpam-5839	1232	36	nst	nst	PROPN
ejpam-5839	1232	37	.	.	PUNCT
ejpam-5839	1233	1	within	within	ADP
ejpam-5839	1233	2	this	this	DET
ejpam-5839	1233	3	framework	framework	NOUN
ejpam-5839	1233	4	,	,	PUNCT
ejpam-5839	1233	5	we	we	PRON
ejpam-5839	1233	6	define	define	VERB
ejpam-5839	1233	7	the	the	DET
ejpam-5839	1233	8	riemann	riemann	PROPN
ejpam-5839	1233	9	integral	integral	ADJ
ejpam-5839	1233	10	theory	theory	NOUN
ejpam-5839	1233	11	(	(	PUNCT
ejpam-5839	1233	12	rit	rit	NOUN
ejpam-5839	1233	13	)	)	PUNCT
ejpam-5839	1233	14	,	,	PUNCT
ejpam-5839	1233	15	opening	open	VERB
ejpam-5839	1233	16	new	new	ADJ
ejpam-5839	1233	17	avenues	avenue	NOUN
ejpam-5839	1233	18	for	for	ADP
ejpam-5839	1233	19	exploring	explore	VERB
ejpam-5839	1233	20	the	the	DET
ejpam-5839	1233	21	properties	property	NOUN
ejpam-5839	1233	22	and	and	CCONJ
ejpam-5839	1233	23	characteristics	characteristic	NOUN
ejpam-5839	1233	24	of	of	ADP
ejpam-5839	1233	25	the	the	DET
ejpam-5839	1233	26	riemann	riemann	PROPN
ejpam-5839	1233	27	integral	integral	PROPN
ejpam-5839	1233	28	in	in	ADP
ejpam-5839	1233	29	an	an	DET
ejpam-5839	1233	30	extended	extended	ADJ
ejpam-5839	1233	31	context	context	NOUN
ejpam-5839	1233	32	.	.	PUNCT
ejpam-5839	1234	1	a	a	DET
ejpam-5839	1234	2	central	central	ADJ
ejpam-5839	1234	3	concept	concept	NOUN
ejpam-5839	1234	4	in	in	ADP
ejpam-5839	1234	5	this	this	DET
ejpam-5839	1234	6	work	work	NOUN
ejpam-5839	1234	7	is	be	AUX
ejpam-5839	1234	8	the	the	DET
ejpam-5839	1234	9	level	level	NOUN
ejpam-5839	1234	10	cut	cut	NOUN
ejpam-5839	1234	11	,	,	PUNCT
ejpam-5839	1234	12	defined	define	VERB
ejpam-5839	1234	13	as	as	ADP
ejpam-5839	1234	14	a	a	DET
ejpam-5839	1234	15	four	four	NUM
ejpam-5839	1234	16	-	-	PUNCT
ejpam-5839	1234	17	tuple	tuple	NOUN
ejpam-5839	1234	18	(	(	PUNCT
ejpam-5839	1234	19	i	i	PROPN
ejpam-5839	1234	20	,	,	PUNCT
ejpam-5839	1234	21	j	j	PROPN
ejpam-5839	1234	22	,	,	PUNCT
ejpam-5839	1234	23	k	k	PROPN
ejpam-5839	1234	24	,	,	PUNCT
ejpam-5839	1234	25	l	l	NOUN
ejpam-5839	1234	26	)	)	PUNCT
ejpam-5839	1234	27	,	,	PUNCT
ejpam-5839	1234	28	which	which	PRON
ejpam-5839	1234	29	captures	capture	VERB
ejpam-5839	1234	30	the	the	DET
ejpam-5839	1234	31	multiple	multiple	ADJ
ejpam-5839	1234	32	possibilities	possibility	NOUN
ejpam-5839	1234	33	inherent	inherent	ADJ
ejpam-5839	1234	34	in	in	ADP
ejpam-5839	1234	35	qpnst	qpnst	ADJ
ejpam-5839	1234	36	.	.	PUNCT
ejpam-5839	1235	1	furthermore	furthermore	ADV
ejpam-5839	1235	2	,	,	PUNCT
ejpam-5839	1235	3	we	we	PRON
ejpam-5839	1235	4	conduct	conduct	VERB
ejpam-5839	1235	5	a	a	DET
ejpam-5839	1235	6	numerical	numerical	ADJ
ejpam-5839	1235	7	study	study	NOUN
ejpam-5839	1235	8	of	of	ADP
ejpam-5839	1235	9	the	the	DET
ejpam-5839	1235	10	quadri	quadri	NOUN
ejpam-5839	1235	11	-	-	PUNCT
ejpam-5839	1235	12	partitioned	partition	VERB
ejpam-5839	1235	13	neutrosophic	neutrosophic	ADJ
ejpam-5839	1235	14	riemann	riemann	PROPN
ejpam-5839	1235	15	integral	integral	ADJ
ejpam-5839	1235	16	theory	theory	NOUN
ejpam-5839	1235	17	(	(	PUNCT
ejpam-5839	1235	18	qpnrit	qpnrit	NOUN
ejpam-5839	1235	19	)	)	PUNCT
ejpam-5839	1235	20	and	and	CCONJ
ejpam-5839	1235	21	provide	provide	VERB
ejpam-5839	1235	22	the	the	DET
ejpam-5839	1235	23	findings	finding	NOUN
ejpam-5839	1235	24	in	in	ADP
ejpam-5839	1235	25	an	an	DET
ejpam-5839	1235	26	organized	organize	VERB
ejpam-5839	1235	27	tabular	tabular	NOUN
ejpam-5839	1235	28	manner	manner	NOUN
ejpam-5839	1235	29	.	.	PUNCT
ejpam-5839	1236	1	this	this	DET
ejpam-5839	1236	2	numerical	numerical	ADJ
ejpam-5839	1236	3	study	study	NOUN
ejpam-5839	1236	4	enhances	enhance	VERB
ejpam-5839	1236	5	our	our	PRON
ejpam-5839	1236	6	comprehension	comprehension	NOUN
ejpam-5839	1236	7	of	of	ADP
ejpam-5839	1236	8	the	the	DET
ejpam-5839	1236	9	integral	integral	ADJ
ejpam-5839	1236	10	’s	’s	PART
ejpam-5839	1236	11	behavior	behavior	NOUN
ejpam-5839	1236	12	within	within	ADP
ejpam-5839	1236	13	the	the	DET
ejpam-5839	1236	14	qpnst	qpnst	ADJ
ejpam-5839	1236	15	framework	framework	NOUN
ejpam-5839	1236	16	and	and	CCONJ
ejpam-5839	1236	17	offers	offer	VERB
ejpam-5839	1236	18	insightful	insightful	ADJ
ejpam-5839	1236	19	information	information	NOUN
ejpam-5839	1236	20	about	about	ADP
ejpam-5839	1236	21	its	its	PRON
ejpam-5839	1236	22	characteristics	characteristic	NOUN
ejpam-5839	1236	23	.	.	PUNCT
ejpam-5839	1237	1	this	this	DET
ejpam-5839	1237	2	study	study	NOUN
ejpam-5839	1237	3	explores	explore	NOUN
ejpam-5839	1237	4	quadripartitioned	quadripartitione	VERB
ejpam-5839	1237	5	neutrosophic	neutrosophic	ADJ
ejpam-5839	1237	6	soft	soft	ADJ
ejpam-5839	1237	7	topological	topological	ADJ
ejpam-5839	1237	8	spaces	space	NOUN
ejpam-5839	1237	9	,	,	PUNCT
ejpam-5839	1237	10	extending	extend	VERB
ejpam-5839	1237	11	neutrosophic	neutrosophic	ADJ
ejpam-5839	1237	12	set	set	NOUN
ejpam-5839	1237	13	theory	theory	NOUN
ejpam-5839	1237	14	(	(	PUNCT
ejpam-5839	1237	15	nst	nst	PROPN
ejpam-5839	1237	16	)	)	PUNCT
ejpam-5839	1237	17	,	,	PUNCT
ejpam-5839	1237	18	which	which	PRON
ejpam-5839	1237	19	incorporates	incorporate	VERB
ejpam-5839	1237	20	three	three	NUM
ejpam-5839	1237	21	membership	membership	NOUN
ejpam-5839	1237	22	values	value	NOUN
ejpam-5839	1237	23	:	:	PUNCT
ejpam-5839	1237	24	true	true	ADJ
ejpam-5839	1237	25	,	,	PUNCT
ejpam-5839	1237	26	false	false	ADJ
ejpam-5839	1237	27	,	,	PUNCT
ejpam-5839	1237	28	and	and	CCONJ
ejpam-5839	1237	29	indeterminacy	indeterminacy	NOUN
ejpam-5839	1237	30	.	.	PUNCT
ejpam-5839	1238	1	the	the	DET
ejpam-5839	1238	2	study	study	NOUN
ejpam-5839	1238	3	introduces	introduce	VERB
ejpam-5839	1238	4	new	new	ADJ
ejpam-5839	1238	5	concepts	concept	NOUN
ejpam-5839	1238	6	such	such	ADJ
ejpam-5839	1238	7	as	as	ADP
ejpam-5839	1238	8	qpns	qpns	NOUN
ejpam-5839	1238	9	semi	semi	ADJ
ejpam-5839	1238	10	-	-	ADJ
ejpam-5839	1238	11	open	open	ADJ
ejpam-5839	1238	12	,	,	PUNCT
ejpam-5839	1238	13	qpns	qpns	NOUN
ejpam-5839	1238	14	pre	pre	ADJ
ejpam-5839	1238	15	-	-	ADJ
ejpam-5839	1238	16	open	open	ADJ
ejpam-5839	1238	17	,	,	PUNCT
ejpam-5839	1238	18	and	and	CCONJ
ejpam-5839	1238	19	qpns	qpns	NOUN
ejpam-5839	1238	20	∗b	∗b	PROPN
ejpam-5839	1238	21	open	open	ADJ
ejpam-5839	1238	22	sets	set	NOUN
ejpam-5839	1238	23	,	,	PUNCT
ejpam-5839	1238	24	and	and	CCONJ
ejpam-5839	1238	25	builds	build	VERB
ejpam-5839	1238	26	on	on	ADP
ejpam-5839	1238	27	these	these	PRON
ejpam-5839	1238	28	to	to	PART
ejpam-5839	1238	29	define	define	VERB
ejpam-5839	1238	30	qpns	qpns	NOUN
ejpam-5839	1238	31	closure	closure	NOUN
ejpam-5839	1238	32	,	,	PUNCT
ejpam-5839	1238	33	exterior	exterior	ADJ
ejpam-5839	1238	34	,	,	PUNCT
ejpam-5839	1238	35	boundary	boundary	ADJ
ejpam-5839	1238	36	,	,	PUNCT
ejpam-5839	1238	37	and	and	CCONJ
ejpam-5839	1238	38	interior	interior	NOUN
ejpam-5839	1238	39	.	.	PUNCT
ejpam-5839	1239	1	a	a	DET
ejpam-5839	1239	2	key	key	ADJ
ejpam-5839	1239	3	development	development	NOUN
ejpam-5839	1239	4	is	be	AUX
ejpam-5839	1239	5	a.	a.	NOUN
ejpam-5839	1239	6	shihadeh	shihadeh	NOUN
ejpam-5839	1239	7	et	et	PROPN
ejpam-5839	1239	8	al	al	PROPN
ejpam-5839	1239	9	.	.	PUNCT
ejpam-5839	1239	10	/	/	SYM
ejpam-5839	1239	11	eur	eur	PROPN
ejpam-5839	1239	12	.	.	PUNCT
ejpam-5839	1240	1	j.	j.	PROPN
ejpam-5839	1240	2	pure	pure	PROPN
ejpam-5839	1240	3	appl	appl	PROPN
ejpam-5839	1240	4	.	.	PROPN
ejpam-5839	1240	5	math	math	PROPN
ejpam-5839	1240	6	,	,	PUNCT
ejpam-5839	1240	7	18	18	NUM
ejpam-5839	1240	8	(	(	PUNCT
ejpam-5839	1240	9	2	2	NUM
ejpam-5839	1240	10	)	)	PUNCT
ejpam-5839	1240	11	(	(	PUNCT
ejpam-5839	1240	12	2025	2025	NUM
ejpam-5839	1240	13	)	)	PUNCT
ejpam-5839	1240	14	,	,	PUNCT
ejpam-5839	1240	15	5839	5839	NUM
ejpam-5839	1240	16	51	51	NUM
ejpam-5839	1240	17	of	of	ADP
ejpam-5839	1240	18	54	54	NUM
ejpam-5839	1240	19	the	the	DET
ejpam-5839	1240	20	definition	definition	NOUN
ejpam-5839	1240	21	of	of	ADP
ejpam-5839	1240	22	a	a	DET
ejpam-5839	1240	23	quadripartitioned	quadripartitione	VERB
ejpam-5839	1240	24	neutrosophic	neutrosophic	ADJ
ejpam-5839	1240	25	soft	soft	ADJ
ejpam-5839	1240	26	base	base	NOUN
ejpam-5839	1240	27	,	,	PUNCT
ejpam-5839	1240	28	which	which	PRON
ejpam-5839	1240	29	plays	play	VERB
ejpam-5839	1240	30	a	a	DET
ejpam-5839	1240	31	central	central	ADJ
ejpam-5839	1240	32	role	role	NOUN
ejpam-5839	1240	33	in	in	ADP
ejpam-5839	1240	34	these	these	DET
ejpam-5839	1240	35	topological	topological	ADJ
ejpam-5839	1240	36	structures	structure	NOUN
ejpam-5839	1240	37	.	.	PUNCT
ejpam-5839	1241	1	the	the	DET
ejpam-5839	1241	2	paper	paper	NOUN
ejpam-5839	1241	3	also	also	ADV
ejpam-5839	1241	4	explores	explore	VERB
ejpam-5839	1241	5	the	the	DET
ejpam-5839	1241	6	concept	concept	NOUN
ejpam-5839	1241	7	of	of	ADP
ejpam-5839	1241	8	a	a	DET
ejpam-5839	1241	9	quadripartitioned	quadripartitione	VERB
ejpam-5839	1241	10	neutrosophic	neutrosophic	ADJ
ejpam-5839	1241	11	soft	soft	ADJ
ejpam-5839	1241	12	sub	sub	NOUN
ejpam-5839	1241	13	-	-	NOUN
ejpam-5839	1241	14	base	base	NOUN
ejpam-5839	1241	15	and	and	CCONJ
ejpam-5839	1241	16	discusses	discuss	VERB
ejpam-5839	1241	17	local	local	ADJ
ejpam-5839	1241	18	bases	basis	NOUN
ejpam-5839	1241	19	,	,	PUNCT
ejpam-5839	1241	20	as	as	ADV
ejpam-5839	1241	21	well	well	ADV
ejpam-5839	1241	22	as	as	ADP
ejpam-5839	1241	23	the	the	DET
ejpam-5839	1241	24	firstand	firstand	NOUN
ejpam-5839	1241	25	second	second	ADJ
ejpam-5839	1241	26	-	-	PUNCT
ejpam-5839	1241	27	countability	countability	NOUN
ejpam-5839	1241	28	axioms	axiom	NOUN
ejpam-5839	1241	29	.	.	PUNCT
ejpam-5839	1242	1	the	the	DET
ejpam-5839	1242	2	study	study	NOUN
ejpam-5839	1242	3	further	far	ADV
ejpam-5839	1242	4	examines	examine	VERB
ejpam-5839	1242	5	hereditary	hereditary	ADJ
ejpam-5839	1242	6	properties	property	NOUN
ejpam-5839	1242	7	of	of	ADP
ejpam-5839	1242	8	these	these	DET
ejpam-5839	1242	9	spaces	space	NOUN
ejpam-5839	1242	10	,	,	PUNCT
ejpam-5839	1242	11	distinguishing	distinguish	VERB
ejpam-5839	1242	12	between	between	ADP
ejpam-5839	1242	13	inherited	inherit	VERB
ejpam-5839	1242	14	and	and	CCONJ
ejpam-5839	1242	15	non	non	ADJ
ejpam-5839	1242	16	-	-	ADJ
ejpam-5839	1242	17	inherited	inherited	ADJ
ejpam-5839	1242	18	properties	property	NOUN
ejpam-5839	1242	19	.	.	PUNCT
ejpam-5839	1243	1	key	key	ADJ
ejpam-5839	1243	2	results	result	NOUN
ejpam-5839	1243	3	include	include	VERB
ejpam-5839	1243	4	that	that	SCONJ
ejpam-5839	1243	5	a	a	DET
ejpam-5839	1243	6	quadripartitioned	quadripartitione	VERB
ejpam-5839	1243	7	neutrosophic	neutrosophic	ADJ
ejpam-5839	1243	8	soft	soft	ADJ
ejpam-5839	1243	9	subspace	subspace	NOUN
ejpam-5839	1243	10	of	of	ADP
ejpam-5839	1243	11	a	a	DET
ejpam-5839	1243	12	first	first	ADJ
ejpam-5839	1243	13	-	-	PUNCT
ejpam-5839	1243	14	countable	countable	ADJ
ejpam-5839	1243	15	space	space	NOUN
ejpam-5839	1243	16	is	be	AUX
ejpam-5839	1243	17	also	also	ADV
ejpam-5839	1243	18	first	first	ADV
ejpam-5839	1243	19	-	-	PUNCT
ejpam-5839	1243	20	countable	countable	ADJ
ejpam-5839	1243	21	,	,	PUNCT
ejpam-5839	1243	22	and	and	CCONJ
ejpam-5839	1243	23	a	a	DET
ejpam-5839	1243	24	second	second	ADJ
ejpam-5839	1243	25	countable	countable	ADJ
ejpam-5839	1243	26	subspace	subspace	NOUN
ejpam-5839	1243	27	of	of	ADP
ejpam-5839	1243	28	a	a	DET
ejpam-5839	1243	29	second	second	ADJ
ejpam-5839	1243	30	-	-	PUNCT
ejpam-5839	1243	31	countable	countable	ADJ
ejpam-5839	1243	32	space	space	NOUN
ejpam-5839	1243	33	remains	remain	VERB
ejpam-5839	1243	34	second	second	ADV
ejpam-5839	1243	35	-	-	PUNCT
ejpam-5839	1243	36	countable	countable	ADJ
ejpam-5839	1243	37	.	.	PUNCT
ejpam-5839	1244	1	it	it	PRON
ejpam-5839	1244	2	also	also	ADV
ejpam-5839	1244	3	highlights	highlight	VERB
ejpam-5839	1244	4	the	the	DET
ejpam-5839	1244	5	relationship	relationship	NOUN
ejpam-5839	1244	6	between	between	ADP
ejpam-5839	1244	7	second	second	ADJ
ejpam-5839	1244	8	countability	countability	NOUN
ejpam-5839	1244	9	and	and	CCONJ
ejpam-5839	1244	10	separability	separability	NOUN
ejpam-5839	1244	11	in	in	ADP
ejpam-5839	1244	12	these	these	DET
ejpam-5839	1244	13	spaces	space	NOUN
ejpam-5839	1244	14	,	,	PUNCT
ejpam-5839	1244	15	asserting	assert	VERB
ejpam-5839	1244	16	that	that	SCONJ
ejpam-5839	1244	17	a	a	DET
ejpam-5839	1244	18	second	second	ADV
ejpam-5839	1244	19	-	-	PUNCT
ejpam-5839	1244	20	countable	countable	ADJ
ejpam-5839	1244	21	quadripartitioned	quadripartitione	VERB
ejpam-5839	1244	22	neutrosophic	neutrosophic	ADJ
ejpam-5839	1244	23	soft	soft	ADJ
ejpam-5839	1244	24	space	space	NOUN
ejpam-5839	1244	25	is	be	AUX
ejpam-5839	1244	26	separable	separable	ADJ
ejpam-5839	1244	27	,	,	PUNCT
ejpam-5839	1244	28	though	though	SCONJ
ejpam-5839	1244	29	the	the	DET
ejpam-5839	1244	30	converse	converse	NOUN
ejpam-5839	1244	31	is	be	AUX
ejpam-5839	1244	32	not	not	PART
ejpam-5839	1244	33	always	always	ADV
ejpam-5839	1244	34	true	true	ADJ
ejpam-5839	1244	35	.	.	PUNCT
ejpam-5839	1245	1	this	this	DET
ejpam-5839	1245	2	work	work	NOUN
ejpam-5839	1245	3	lays	lay	VERB
ejpam-5839	1245	4	the	the	DET
ejpam-5839	1245	5	foundation	foundation	NOUN
ejpam-5839	1245	6	for	for	ADP
ejpam-5839	1245	7	further	further	ADJ
ejpam-5839	1245	8	research	research	NOUN
ejpam-5839	1245	9	in	in	ADP
ejpam-5839	1245	10	neutrosophic	neutrosophic	ADJ
ejpam-5839	1245	11	soft	soft	ADJ
ejpam-5839	1245	12	topologies	topology	NOUN
ejpam-5839	1245	13	.	.	PUNCT
ejpam-5839	1246	1	with	with	ADP
ejpam-5839	1246	2	the	the	DET
ejpam-5839	1246	3	possibility	possibility	NOUN
ejpam-5839	1246	4	of	of	ADP
ejpam-5839	1246	5	incorporating	incorporate	VERB
ejpam-5839	1246	6	it	it	PRON
ejpam-5839	1246	7	into	into	ADP
ejpam-5839	1246	8	other	other	ADJ
ejpam-5839	1246	9	sophisticated	sophisticated	ADJ
ejpam-5839	1246	10	theoretical	theoretical	ADJ
ejpam-5839	1246	11	frameworks	framework	NOUN
ejpam-5839	1246	12	,	,	PUNCT
ejpam-5839	1246	13	future	future	ADJ
ejpam-5839	1246	14	studies	study	NOUN
ejpam-5839	1246	15	will	will	AUX
ejpam-5839	1246	16	seek	seek	VERB
ejpam-5839	1246	17	to	to	PART
ejpam-5839	1246	18	broaden	broaden	VERB
ejpam-5839	1246	19	the	the	DET
ejpam-5839	1246	20	use	use	NOUN
ejpam-5839	1246	21	of	of	ADP
ejpam-5839	1246	22	quadri	quadri	NOUN
ejpam-5839	1246	23	-	-	PUNCT
ejpam-5839	1246	24	partitioned	partition	VERB
ejpam-5839	1246	25	neutrosophic	neutrosophic	ADJ
ejpam-5839	1246	26	set	set	NOUN
ejpam-5839	1246	27	theory	theory	NOUN
ejpam-5839	1246	28	(	(	PUNCT
ejpam-5839	1246	29	qpnst	qpnst	ADJ
ejpam-5839	1246	30	)	)	PUNCT
ejpam-5839	1246	31	in	in	ADP
ejpam-5839	1246	32	a	a	DET
ejpam-5839	1246	33	variety	variety	NOUN
ejpam-5839	1246	34	of	of	ADP
ejpam-5839	1246	35	mathematical	mathematical	ADJ
ejpam-5839	1246	36	fields	field	NOUN
ejpam-5839	1246	37	.	.	PUNCT
ejpam-5839	1247	1	investigating	investigate	VERB
ejpam-5839	1247	2	a	a	DET
ejpam-5839	1247	3	generalized	generalized	ADJ
ejpam-5839	1247	4	riemann	riemann	PROPN
ejpam-5839	1247	5	integral	integral	ADJ
ejpam-5839	1247	6	theory	theory	NOUN
ejpam-5839	1247	7	(	(	PUNCT
ejpam-5839	1247	8	rit	rit	NOUN
ejpam-5839	1247	9	)	)	PUNCT
ejpam-5839	1247	10	employing	employ	VERB
ejpam-5839	1247	11	qpnst	qpnst	NOUN
ejpam-5839	1247	12	in	in	ADP
ejpam-5839	1247	13	more	more	ADV
ejpam-5839	1247	14	intricate	intricate	ADJ
ejpam-5839	1247	15	contexts	context	NOUN
ejpam-5839	1247	16	,	,	PUNCT
ejpam-5839	1247	17	like	like	ADP
ejpam-5839	1247	18	multi	multi	ADJ
ejpam-5839	1247	19	-	-	ADJ
ejpam-5839	1247	20	dimensional	dimensional	ADJ
ejpam-5839	1247	21	spaces	space	NOUN
ejpam-5839	1247	22	and	and	CCONJ
ejpam-5839	1247	23	dynamic	dynamic	ADJ
ejpam-5839	1247	24	systems	system	NOUN
ejpam-5839	1247	25	,	,	PUNCT
ejpam-5839	1247	26	is	be	AUX
ejpam-5839	1247	27	one	one	NUM
ejpam-5839	1247	28	exciting	exciting	ADJ
ejpam-5839	1247	29	avenue	avenue	NOUN
ejpam-5839	1247	30	.	.	PUNCT
ejpam-5839	1248	1	in	in	ADP
ejpam-5839	1248	2	order	order	NOUN
ejpam-5839	1248	3	to	to	PART
ejpam-5839	1248	4	increase	increase	VERB
ejpam-5839	1248	5	computational	computational	ADJ
ejpam-5839	1248	6	accuracy	accuracy	NOUN
ejpam-5839	1248	7	and	and	CCONJ
ejpam-5839	1248	8	efficiency	efficiency	NOUN
ejpam-5839	1248	9	,	,	PUNCT
ejpam-5839	1248	10	more	more	ADJ
ejpam-5839	1248	11	effort	effort	NOUN
ejpam-5839	1248	12	will	will	AUX
ejpam-5839	1248	13	be	be	AUX
ejpam-5839	1248	14	done	do	VERB
ejpam-5839	1248	15	to	to	PART
ejpam-5839	1248	16	enhance	enhance	VERB
ejpam-5839	1248	17	numerical	numerical	ADJ
ejpam-5839	1248	18	methods	method	NOUN
ejpam-5839	1248	19	for	for	ADP
ejpam-5839	1248	20	computing	compute	VERB
ejpam-5839	1248	21	quadri	quadri	PROPN
ejpam-5839	1248	22	-	-	PUNCT
ejpam-5839	1248	23	partitioned	partition	VERB
ejpam-5839	1248	24	neutrosophic	neutrosophic	ADJ
ejpam-5839	1248	25	riemann	riemann	PROPN
ejpam-5839	1248	26	integrals	integral	NOUN
ejpam-5839	1248	27	(	(	PUNCT
ejpam-5839	1248	28	qpnrit	qpnrit	NOUN
ejpam-5839	1248	29	)	)	PUNCT
ejpam-5839	1248	30	.	.	PUNCT
ejpam-5839	1249	1	the	the	DET
ejpam-5839	1249	2	creation	creation	NOUN
ejpam-5839	1249	3	of	of	ADP
ejpam-5839	1249	4	decision	decision	NOUN
ejpam-5839	1249	5	-	-	PUNCT
ejpam-5839	1249	6	making	make	VERB
ejpam-5839	1249	7	models	model	NOUN
ejpam-5839	1249	8	that	that	PRON
ejpam-5839	1249	9	incorporate	incorporate	VERB
ejpam-5839	1249	10	qpnst	qpnst	ADJ
ejpam-5839	1249	11	will	will	AUX
ejpam-5839	1249	12	be	be	AUX
ejpam-5839	1249	13	another	another	DET
ejpam-5839	1249	14	crucial	crucial	ADJ
ejpam-5839	1249	15	topic	topic	NOUN
ejpam-5839	1249	16	.	.	PUNCT
ejpam-5839	1250	1	these	these	DET
ejpam-5839	1250	2	models	model	NOUN
ejpam-5839	1250	3	could	could	AUX
ejpam-5839	1250	4	provide	provide	VERB
ejpam-5839	1250	5	more	more	ADV
ejpam-5839	1250	6	reliable	reliable	ADJ
ejpam-5839	1250	7	frameworks	framework	NOUN
ejpam-5839	1250	8	for	for	ADP
ejpam-5839	1250	9	dealing	deal	VERB
ejpam-5839	1250	10	with	with	ADP
ejpam-5839	1250	11	uncertainty	uncertainty	NOUN
ejpam-5839	1250	12	in	in	ADP
ejpam-5839	1250	13	real	real	ADJ
ejpam-5839	1250	14	-	-	PUNCT
ejpam-5839	1250	15	world	world	NOUN
ejpam-5839	1250	16	applications	application	NOUN
ejpam-5839	1250	17	including	include	VERB
ejpam-5839	1250	18	artificial	artificial	ADJ
ejpam-5839	1250	19	intelligence	intelligence	NOUN
ejpam-5839	1250	20	,	,	PUNCT
ejpam-5839	1250	21	engineering	engineering	NOUN
ejpam-5839	1250	22	,	,	PUNCT
ejpam-5839	1250	23	and	and	CCONJ
ejpam-5839	1250	24	economics	economic	NOUN
ejpam-5839	1250	25	.	.	PUNCT
ejpam-5839	1251	1	furthermore	furthermore	ADV
ejpam-5839	1251	2	,	,	PUNCT
ejpam-5839	1251	3	it	it	PRON
ejpam-5839	1251	4	is	be	AUX
ejpam-5839	1251	5	crucial	crucial	ADJ
ejpam-5839	1251	6	to	to	PART
ejpam-5839	1251	7	conduct	conduct	VERB
ejpam-5839	1251	8	additional	additional	ADJ
ejpam-5839	1251	9	research	research	NOUN
ejpam-5839	1251	10	on	on	ADP
ejpam-5839	1251	11	the	the	DET
ejpam-5839	1251	12	theoretical	theoretical	ADJ
ejpam-5839	1251	13	characteristics	characteristic	NOUN
ejpam-5839	1251	14	of	of	ADP
ejpam-5839	1251	15	qpnst	qpnst	ADJ
ejpam-5839	1251	16	,	,	PUNCT
ejpam-5839	1251	17	such	such	ADJ
ejpam-5839	1251	18	as	as	ADP
ejpam-5839	1251	19	its	its	PRON
ejpam-5839	1251	20	algebraic	algebraic	ADJ
ejpam-5839	1251	21	and	and	CCONJ
ejpam-5839	1251	22	topological	topological	ADJ
ejpam-5839	1251	23	features	feature	NOUN
ejpam-5839	1251	24	.	.	PUNCT
ejpam-5839	1252	1	these	these	DET
ejpam-5839	1252	2	studies	study	NOUN
ejpam-5839	1252	3	could	could	AUX
ejpam-5839	1252	4	provide	provide	VERB
ejpam-5839	1252	5	deeper	deep	ADJ
ejpam-5839	1252	6	insights	insight	NOUN
ejpam-5839	1252	7	into	into	ADP
ejpam-5839	1252	8	the	the	DET
ejpam-5839	1252	9	behavior	behavior	NOUN
ejpam-5839	1252	10	of	of	ADP
ejpam-5839	1252	11	neutrosophic	neutrosophic	ADJ
ejpam-5839	1252	12	sets	set	NOUN
ejpam-5839	1252	13	in	in	ADP
ejpam-5839	1252	14	various	various	ADJ
ejpam-5839	1252	15	contexts	contexts	NOUN
ejpam-5839	1252	16	,	,	PUNCT
ejpam-5839	1252	17	enriching	enrich	VERB
ejpam-5839	1252	18	the	the	DET
ejpam-5839	1252	19	overall	overall	ADJ
ejpam-5839	1252	20	understanding	understanding	NOUN
ejpam-5839	1252	21	of	of	ADP
ejpam-5839	1252	22	this	this	DET
ejpam-5839	1252	23	extended	extend	VERB
ejpam-5839	1252	24	theory	theory	NOUN
ejpam-5839	1252	25	.	.	PUNCT
ejpam-5839	1253	1	acknowledgements	acknowledgement	NOUN
ejpam-5839	1253	2	the	the	DET
ejpam-5839	1253	3	authors	author	NOUN
ejpam-5839	1253	4	extend	extend	VERB
ejpam-5839	1253	5	their	their	PRON
ejpam-5839	1253	6	appreciation	appreciation	NOUN
ejpam-5839	1253	7	to	to	ADP
ejpam-5839	1253	8	the	the	DET
ejpam-5839	1253	9	deanship	deanship	NOUN
ejpam-5839	1253	10	of	of	ADP
ejpam-5839	1253	11	scientific	scientific	ADJ
ejpam-5839	1253	12	research	research	NOUN
ejpam-5839	1253	13	at	at	ADP
ejpam-5839	1253	14	northern	northern	ADJ
ejpam-5839	1253	15	border	border	NOUN
ejpam-5839	1253	16	university	university	PROPN
ejpam-5839	1253	17	,	,	PUNCT
ejpam-5839	1253	18	arar	arar	PROPN
ejpam-5839	1253	19	,	,	PUNCT
ejpam-5839	1253	20	ksa	ksa	PROPN
ejpam-5839	1253	21	for	for	ADP
ejpam-5839	1253	22	funding	fund	VERB
ejpam-5839	1253	23	this	this	DET
ejpam-5839	1253	24	research	research	NOUN
ejpam-5839	1253	25	work	work	NOUN
ejpam-5839	1253	26	through	through	ADP
ejpam-5839	1253	27	the	the	DET
ejpam-5839	1253	28	project	project	NOUN
ejpam-5839	1253	29	number	number	NOUN
ejpam-5839	1253	30	“	"	PUNCT
ejpam-5839	1253	31	nbuffr-2025	nbuffr-2025	ADJ
ejpam-5839	1253	32	-	-	PUNCT
ejpam-5839	1253	33	2727	2727	NUM
ejpam-5839	1253	34	-	-	SYM
ejpam-5839	1253	35	03	03	NUM
ejpam-5839	1253	36	”	"	PUNCT
ejpam-5839	1253	37	..	..	PUNCT
ejpam-5839	1254	1	authors	author	NOUN
ejpam-5839	1254	2	contributions	contribution	VERB
ejpam-5839	1254	3	:	:	PUNCT
ejpam-5839	1254	4	all	all	DET
ejpam-5839	1254	5	authors	author	NOUN
ejpam-5839	1254	6	contributed	contribute	VERB
ejpam-5839	1254	7	equally	equally	ADV
ejpam-5839	1254	8	.	.	PUNCT
ejpam-5839	1255	1	conflicts	conflict	NOUN
ejpam-5839	1255	2	of	of	ADP
ejpam-5839	1255	3	interests	interest	NOUN
ejpam-5839	1255	4	:	:	PUNCT
ejpam-5839	1255	5	the	the	DET
ejpam-5839	1255	6	authors	author	NOUN
ejpam-5839	1255	7	have	have	VERB
ejpam-5839	1255	8	no	no	DET
ejpam-5839	1255	9	conflicts	conflict	NOUN
ejpam-5839	1255	10	of	of	ADP
ejpam-5839	1255	11	interest	interest	NOUN
ejpam-5839	1255	12	.	.	PUNCT
ejpam-5839	1256	1	references	reference	NOUN
ejpam-5839	1256	2	[	[	X
ejpam-5839	1256	3	1	1	NUM
ejpam-5839	1256	4	]	]	PUNCT
ejpam-5839	1256	5	l.	l.	PROPN
ejpam-5839	1256	6	a.	a.	PROPN
ejpam-5839	1256	7	zadeh	zadeh	PROPN
ejpam-5839	1256	8	.	.	PUNCT
ejpam-5839	1257	1	fuzzy	fuzzy	ADJ
ejpam-5839	1257	2	sets	set	NOUN
ejpam-5839	1257	3	.	.	PUNCT
ejpam-5839	1258	1	information	information	NOUN
ejpam-5839	1258	2	and	and	CCONJ
ejpam-5839	1258	3	control	control	NOUN
ejpam-5839	1258	4	,	,	PUNCT
ejpam-5839	1258	5	8(3):338–353	8(3):338–353	NUM
ejpam-5839	1258	6	,	,	PUNCT
ejpam-5839	1258	7	1965	1965	NUM
ejpam-5839	1258	8	.	.	PUNCT
ejpam-5839	1259	1	[	[	X
ejpam-5839	1259	2	2	2	NUM
ejpam-5839	1259	3	]	]	PUNCT
ejpam-5839	1259	4	l.	l.	PROPN
ejpam-5839	1259	5	a.	a.	PROPN
ejpam-5839	1259	6	zadeh	zadeh	PROPN
ejpam-5839	1259	7	.	.	PUNCT
ejpam-5839	1260	1	the	the	DET
ejpam-5839	1260	2	concept	concept	NOUN
ejpam-5839	1260	3	of	of	ADP
ejpam-5839	1260	4	a	a	DET
ejpam-5839	1260	5	linguistic	linguistic	ADJ
ejpam-5839	1260	6	variable	variable	NOUN
ejpam-5839	1260	7	and	and	CCONJ
ejpam-5839	1260	8	its	its	PRON
ejpam-5839	1260	9	application	application	NOUN
ejpam-5839	1260	10	to	to	PART
ejpam-5839	1260	11	approximate	approximate	ADJ
ejpam-5839	1260	12	reasoning	reasoning	NOUN
ejpam-5839	1260	13	(	(	PUNCT
ejpam-5839	1260	14	i	i	NOUN
ejpam-5839	1260	15	)	)	PUNCT
ejpam-5839	1260	16	.	.	PUNCT
ejpam-5839	1261	1	information	information	NOUN
ejpam-5839	1261	2	sciences	sciences	PROPN
ejpam-5839	1261	3	,	,	PUNCT
ejpam-5839	1261	4	8(3):199–249	8(3):199–249	NUM
ejpam-5839	1261	5	,	,	PUNCT
ejpam-5839	1261	6	1975	1975	NUM
ejpam-5839	1261	7	.	.	PUNCT
ejpam-5839	1262	1	[	[	X
ejpam-5839	1262	2	3	3	X
ejpam-5839	1262	3	]	]	X
ejpam-5839	1262	4	l.	l.	PROPN
ejpam-5839	1262	5	a.	a.	PROPN
ejpam-5839	1262	6	zadeh	zadeh	PROPN
ejpam-5839	1262	7	.	.	PUNCT
ejpam-5839	1263	1	the	the	DET
ejpam-5839	1263	2	concept	concept	NOUN
ejpam-5839	1263	3	of	of	ADP
ejpam-5839	1263	4	a	a	DET
ejpam-5839	1263	5	linguistic	linguistic	ADJ
ejpam-5839	1263	6	variable	variable	NOUN
ejpam-5839	1263	7	and	and	CCONJ
ejpam-5839	1263	8	its	its	PRON
ejpam-5839	1263	9	application	application	NOUN
ejpam-5839	1263	10	to	to	PART
ejpam-5839	1263	11	approximate	approximate	ADJ
ejpam-5839	1263	12	reasoning	reasoning	NOUN
ejpam-5839	1263	13	(	(	PUNCT
ejpam-5839	1263	14	ii	ii	NOUN
ejpam-5839	1263	15	)	)	PUNCT
ejpam-5839	1263	16	.	.	PUNCT
ejpam-5839	1264	1	information	information	NOUN
ejpam-5839	1264	2	sciences	sciences	PROPN
ejpam-5839	1264	3	,	,	PUNCT
ejpam-5839	1264	4	8(4):301–357	8(4):301–357	NUM
ejpam-5839	1264	5	,	,	PUNCT
ejpam-5839	1264	6	1975	1975	NUM
ejpam-5839	1264	7	.	.	PUNCT
ejpam-5839	1265	1	[	[	X
ejpam-5839	1265	2	4	4	X
ejpam-5839	1265	3	]	]	PUNCT
ejpam-5839	1265	4	l.	l.	PROPN
ejpam-5839	1265	5	a.	a.	PROPN
ejpam-5839	1265	6	zadeh	zadeh	PROPN
ejpam-5839	1265	7	.	.	PUNCT
ejpam-5839	1266	1	the	the	DET
ejpam-5839	1266	2	concept	concept	NOUN
ejpam-5839	1266	3	of	of	ADP
ejpam-5839	1266	4	a	a	DET
ejpam-5839	1266	5	linguistic	linguistic	ADJ
ejpam-5839	1266	6	variable	variable	NOUN
ejpam-5839	1266	7	and	and	CCONJ
ejpam-5839	1266	8	its	its	PRON
ejpam-5839	1266	9	application	application	NOUN
ejpam-5839	1266	10	to	to	PART
ejpam-5839	1266	11	approximate	approximate	ADJ
ejpam-5839	1266	12	reasoning	reasoning	NOUN
ejpam-5839	1266	13	(	(	PUNCT
ejpam-5839	1266	14	iii	iii	NOUN
ejpam-5839	1266	15	)	)	PUNCT
ejpam-5839	1266	16	.	.	PUNCT
ejpam-5839	1267	1	information	information	NOUN
ejpam-5839	1267	2	sciences	sciences	PROPN
ejpam-5839	1267	3	,	,	PUNCT
ejpam-5839	1267	4	9(1):43–80	9(1):43–80	NUM
ejpam-5839	1267	5	,	,	PUNCT
ejpam-5839	1267	6	1975	1975	NUM
ejpam-5839	1267	7	.	.	PUNCT
ejpam-5839	1268	1	[	[	X
ejpam-5839	1268	2	5	5	X
ejpam-5839	1268	3	]	]	PUNCT
ejpam-5839	1268	4	l.	l.	PROPN
ejpam-5839	1268	5	a.	a.	PROPN
ejpam-5839	1268	6	zadeh	zadeh	PROPN
ejpam-5839	1268	7	.	.	PUNCT
ejpam-5839	1269	1	toward	toward	ADP
ejpam-5839	1269	2	a	a	DET
ejpam-5839	1269	3	generalized	generalized	ADJ
ejpam-5839	1269	4	theory	theory	NOUN
ejpam-5839	1269	5	of	of	ADP
ejpam-5839	1269	6	uncertainty	uncertainty	NOUN
ejpam-5839	1269	7	(	(	PUNCT
ejpam-5839	1269	8	gtu	gtu	NOUN
ejpam-5839	1269	9	):	):	PUNCT
ejpam-5839	1269	10	an	an	DET
ejpam-5839	1269	11	outline	outline	NOUN
ejpam-5839	1269	12	.	.	PUNCT
ejpam-5839	1270	1	information	information	NOUN
ejpam-5839	1270	2	sciences	sciences	PROPN
ejpam-5839	1270	3	,	,	PUNCT
ejpam-5839	1270	4	172(1–2):1–40	172(1–2):1–40	NUM
ejpam-5839	1270	5	,	,	PUNCT
ejpam-5839	1270	6	2005	2005	NUM
ejpam-5839	1270	7	.	.	PUNCT
ejpam-5839	1271	1	[	[	X
ejpam-5839	1271	2	6	6	NUM
ejpam-5839	1271	3	]	]	PUNCT
ejpam-5839	1271	4	j.	j.	PROPN
ejpam-5839	1271	5	ye	ye	PROPN
ejpam-5839	1271	6	.	.	PUNCT
ejpam-5839	1272	1	a	a	DET
ejpam-5839	1272	2	multicriteria	multicriteria	PROPN
ejpam-5839	1272	3	decision	decision	NOUN
ejpam-5839	1272	4	-	-	PUNCT
ejpam-5839	1272	5	making	make	VERB
ejpam-5839	1272	6	method	method	NOUN
ejpam-5839	1272	7	using	use	VERB
ejpam-5839	1272	8	aggregation	aggregation	NOUN
ejpam-5839	1272	9	operators	operator	NOUN
ejpam-5839	1272	10	for	for	ADP
ejpam-5839	1272	11	simplified	simplified	ADJ
ejpam-5839	1272	12	neutrosophic	neutrosophic	ADJ
ejpam-5839	1272	13	set	set	NOUN
ejpam-5839	1272	14	.	.	PUNCT
ejpam-5839	1273	1	journal	journal	NOUN
ejpam-5839	1273	2	of	of	ADP
ejpam-5839	1273	3	intelligent	intelligent	ADJ
ejpam-5839	1273	4	and	and	CCONJ
ejpam-5839	1273	5	fuzzy	fuzzy	ADJ
ejpam-5839	1273	6	systems	system	NOUN
ejpam-5839	1273	7	,	,	PUNCT
ejpam-5839	1273	8	26(5):2459–2466	26(5):2459–2466	NUM
ejpam-5839	1273	9	,	,	PUNCT
ejpam-5839	1273	10	2014	2014	NUM
ejpam-5839	1273	11	.	.	PUNCT
ejpam-5839	1274	1	[	[	X
ejpam-5839	1274	2	7	7	X
ejpam-5839	1274	3	]	]	X
ejpam-5839	1274	4	c.	c.	PROPN
ejpam-5839	1274	5	liu	liu	PROPN
ejpam-5839	1274	6	and	and	CCONJ
ejpam-5839	1274	7	y.	y.	PROPN
ejpam-5839	1274	8	luo	luo	PROPN
ejpam-5839	1274	9	.	.	PUNCT
ejpam-5839	1275	1	correlated	correlate	VERB
ejpam-5839	1275	2	aggregation	aggregation	NOUN
ejpam-5839	1275	3	operators	operator	NOUN
ejpam-5839	1275	4	for	for	ADP
ejpam-5839	1275	5	simplified	simplified	ADJ
ejpam-5839	1275	6	neutrosophic	neutrosophic	ADJ
ejpam-5839	1275	7	set	set	NOUN
ejpam-5839	1275	8	and	and	CCONJ
ejpam-5839	1275	9	their	their	PRON
ejpam-5839	1275	10	application	application	NOUN
ejpam-5839	1275	11	in	in	ADP
ejpam-5839	1275	12	multi	multi	ADJ
ejpam-5839	1275	13	-	-	ADJ
ejpam-5839	1275	14	attribute	attribute	NOUN
ejpam-5839	1275	15	group	group	NOUN
ejpam-5839	1275	16	decision	decision	NOUN
ejpam-5839	1275	17	making	making	NOUN
ejpam-5839	1275	18	.	.	PUNCT
ejpam-5839	1276	1	journal	journal	NOUN
ejpam-5839	1276	2	of	of	ADP
ejpam-5839	1276	3	intelligent	intelligent	ADJ
ejpam-5839	1276	4	and	and	CCONJ
ejpam-5839	1276	5	fuzzy	fuzzy	ADJ
ejpam-5839	1276	6	systems	system	NOUN
ejpam-5839	1276	7	,	,	PUNCT
ejpam-5839	1276	8	30(3):1755–1761	30(3):1755–1761	NUM
ejpam-5839	1276	9	,	,	PUNCT
ejpam-5839	1276	10	2016	2016	NUM
ejpam-5839	1276	11	.	.	PUNCT
ejpam-5839	1277	1	[	[	X
ejpam-5839	1277	2	8	8	NUM
ejpam-5839	1277	3	]	]	PUNCT
ejpam-5839	1277	4	k.	k.	PROPN
ejpam-5839	1277	5	atanassov	atanassov	PROPN
ejpam-5839	1277	6	.	.	PUNCT
ejpam-5839	1278	1	intuitionistic	intuitionistic	ADJ
ejpam-5839	1278	2	fuzzy	fuzzy	ADJ
ejpam-5839	1278	3	sets	set	NOUN
ejpam-5839	1278	4	.	.	PUNCT
ejpam-5839	1279	1	fuzzy	fuzzy	ADJ
ejpam-5839	1279	2	sets	set	NOUN
ejpam-5839	1279	3	and	and	CCONJ
ejpam-5839	1279	4	systems	system	NOUN
ejpam-5839	1279	5	,	,	PUNCT
ejpam-5839	1279	6	20(1):87–96	20(1):87–96	NUM
ejpam-5839	1279	7	,	,	PUNCT
ejpam-5839	1279	8	1986	1986	NUM
ejpam-5839	1279	9	.	.	PUNCT
ejpam-5839	1280	1	a.	a.	NOUN
ejpam-5839	1280	2	shihadeh	shihadeh	VERB
ejpam-5839	1280	3	et	et	PROPN
ejpam-5839	1280	4	al	al	PROPN
ejpam-5839	1280	5	.	.	PUNCT
ejpam-5839	1280	6	/	/	SYM
ejpam-5839	1280	7	eur	eur	PROPN
ejpam-5839	1280	8	.	.	PUNCT
ejpam-5839	1281	1	j.	j.	PROPN
ejpam-5839	1281	2	pure	pure	PROPN
ejpam-5839	1281	3	appl	appl	PROPN
ejpam-5839	1281	4	.	.	PROPN
ejpam-5839	1281	5	math	math	PROPN
ejpam-5839	1281	6	,	,	PUNCT
ejpam-5839	1281	7	18	18	NUM
ejpam-5839	1281	8	(	(	PUNCT
ejpam-5839	1281	9	2	2	NUM
ejpam-5839	1281	10	)	)	PUNCT
ejpam-5839	1281	11	(	(	PUNCT
ejpam-5839	1281	12	2025	2025	NUM
ejpam-5839	1281	13	)	)	PUNCT
ejpam-5839	1281	14	,	,	PUNCT
ejpam-5839	1281	15	5839	5839	NUM
ejpam-5839	1281	16	52	52	NUM
ejpam-5839	1281	17	of	of	ADP
ejpam-5839	1281	18	54	54	NUM
ejpam-5839	1281	19	[	[	SYM
ejpam-5839	1281	20	9	9	NUM
ejpam-5839	1281	21	]	]	PUNCT
ejpam-5839	1281	22	k.	k.	PROPN
ejpam-5839	1281	23	t.	t.	PROPN
ejpam-5839	1281	24	atanassov	atanassov	PROPN
ejpam-5839	1281	25	and	and	CCONJ
ejpam-5839	1281	26	g.	g.	PROPN
ejpam-5839	1281	27	gargov	gargov	PROPN
ejpam-5839	1281	28	.	.	PUNCT
ejpam-5839	1282	1	interval	interval	NOUN
ejpam-5839	1282	2	valued	value	VERB
ejpam-5839	1282	3	intuitionistic	intuitionistic	ADJ
ejpam-5839	1282	4	fuzzy	fuzzy	ADJ
ejpam-5839	1282	5	sets	set	NOUN
ejpam-5839	1282	6	.	.	PUNCT
ejpam-5839	1283	1	fuzzy	fuzzy	ADJ
ejpam-5839	1283	2	sets	set	NOUN
ejpam-5839	1283	3	and	and	CCONJ
ejpam-5839	1283	4	systems	system	NOUN
ejpam-5839	1283	5	,	,	PUNCT
ejpam-5839	1283	6	31(3):343–349	31(3):343–349	NUM
ejpam-5839	1283	7	,	,	PUNCT
ejpam-5839	1283	8	1989	1989	NUM
ejpam-5839	1283	9	.	.	PUNCT
ejpam-5839	1284	1	[	[	X
ejpam-5839	1284	2	10	10	NUM
ejpam-5839	1284	3	]	]	X
ejpam-5839	1284	4	f.	f.	PROPN
ejpam-5839	1284	5	smarandache	smarandache	PROPN
ejpam-5839	1284	6	.	.	PUNCT
ejpam-5839	1285	1	neutrosophy	neutrosophy	NOUN
ejpam-5839	1285	2	:	:	PUNCT
ejpam-5839	1285	3	neutrosophic	neutrosophic	ADJ
ejpam-5839	1285	4	probability	probability	NOUN
ejpam-5839	1285	5	,	,	PUNCT
ejpam-5839	1285	6	set	set	NOUN
ejpam-5839	1285	7	and	and	CCONJ
ejpam-5839	1285	8	logic	logic	NOUN
ejpam-5839	1285	9	.	.	PUNCT
ejpam-5839	1286	1	american	american	ADJ
ejpam-5839	1286	2	research	research	PROPN
ejpam-5839	1286	3	press	press	PROPN
ejpam-5839	1286	4	,	,	PUNCT
ejpam-5839	1286	5	rehoboth	rehoboth	PROPN
ejpam-5839	1286	6	,	,	PUNCT
ejpam-5839	1286	7	de	de	PROPN
ejpam-5839	1286	8	,	,	PUNCT
ejpam-5839	1286	9	1999	1999	NUM
ejpam-5839	1286	10	.	.	PUNCT
ejpam-5839	1287	1	[	[	X
ejpam-5839	1287	2	11	11	NUM
ejpam-5839	1287	3	]	]	X
ejpam-5839	1287	4	f.	f.	PROPN
ejpam-5839	1287	5	smarandache	smarandache	PROPN
ejpam-5839	1287	6	.	.	PUNCT
ejpam-5839	1288	1	a	a	DET
ejpam-5839	1288	2	unifying	unifying	ADJ
ejpam-5839	1288	3	field	field	NOUN
ejpam-5839	1288	4	in	in	ADP
ejpam-5839	1288	5	logics	logic	NOUN
ejpam-5839	1288	6	:	:	PUNCT
ejpam-5839	1288	7	neutrosophic	neutrosophic	ADJ
ejpam-5839	1288	8	logic	logic	NOUN
ejpam-5839	1288	9	:	:	PUNCT
ejpam-5839	1288	10	neutrosophy	neutrosophy	NOUN
ejpam-5839	1288	11	,	,	PUNCT
ejpam-5839	1288	12	neutrosophic	neutrosophic	ADJ
ejpam-5839	1288	13	set	set	NOUN
ejpam-5839	1288	14	and	and	CCONJ
ejpam-5839	1288	15	neutrosophic	neutrosophic	ADJ
ejpam-5839	1288	16	probability	probability	NOUN
ejpam-5839	1288	17	.	.	PUNCT
ejpam-5839	1289	1	american	american	PROPN
ejpam-5839	1289	2	research	research	PROPN
ejpam-5839	1289	3	press	press	PROPN
ejpam-5839	1289	4	,	,	PUNCT
ejpam-5839	1289	5	rehoboth	rehoboth	PROPN
ejpam-5839	1289	6	,	,	PUNCT
ejpam-5839	1289	7	de	de	PROPN
ejpam-5839	1289	8	,	,	PUNCT
ejpam-5839	1289	9	2003	2003	NUM
ejpam-5839	1289	10	.	.	PUNCT
ejpam-5839	1290	1	[	[	X
ejpam-5839	1290	2	12	12	NUM
ejpam-5839	1290	3	]	]	PUNCT
ejpam-5839	1290	4	h.	h.	PROPN
ejpam-5839	1290	5	wang	wang	PROPN
ejpam-5839	1290	6	,	,	PUNCT
ejpam-5839	1290	7	f.	f.	PROPN
ejpam-5839	1290	8	smarandache	smarandache	PROPN
ejpam-5839	1290	9	,	,	PUNCT
ejpam-5839	1290	10	y.	y.	PROPN
ejpam-5839	1290	11	zhang	zhang	PROPN
ejpam-5839	1290	12	,	,	PUNCT
ejpam-5839	1290	13	and	and	CCONJ
ejpam-5839	1290	14	r.	r.	PROPN
ejpam-5839	1290	15	sunderraman	sunderraman	PROPN
ejpam-5839	1290	16	.	.	PUNCT
ejpam-5839	1291	1	single	single	ADJ
ejpam-5839	1291	2	valued	value	VERB
ejpam-5839	1291	3	neutrosophic	neutrosophic	ADJ
ejpam-5839	1291	4	sets	set	NOUN
ejpam-5839	1291	5	.	.	PUNCT
ejpam-5839	1292	1	multi	multi	ADJ
ejpam-5839	1292	2	space	space	NOUN
ejpam-5839	1292	3	multistruction	multistruction	NOUN
ejpam-5839	1292	4	,	,	PUNCT
ejpam-5839	1292	5	(	(	PUNCT
ejpam-5839	1292	6	4):410–413	4):410–413	PROPN
ejpam-5839	1292	7	,	,	PUNCT
ejpam-5839	1292	8	2010	2010	NUM
ejpam-5839	1292	9	.	.	PUNCT
ejpam-5839	1293	1	[	[	X
ejpam-5839	1293	2	13	13	NUM
ejpam-5839	1293	3	]	]	X
ejpam-5839	1293	4	h.	h.	PROPN
ejpam-5839	1293	5	wang	wang	PROPN
ejpam-5839	1293	6	,	,	PUNCT
ejpam-5839	1293	7	f.	f.	PROPN
ejpam-5839	1293	8	smarandache	smarandache	PROPN
ejpam-5839	1293	9	,	,	PUNCT
ejpam-5839	1293	10	y.	y.	PROPN
ejpam-5839	1293	11	zhang	zhang	PROPN
ejpam-5839	1293	12	,	,	PUNCT
ejpam-5839	1293	13	and	and	CCONJ
ejpam-5839	1293	14	r.	r.	PROPN
ejpam-5839	1293	15	sunderraman	sunderraman	PROPN
ejpam-5839	1293	16	.	.	PUNCT
ejpam-5839	1294	1	interval	interval	NOUN
ejpam-5839	1294	2	neutrosophic	neutrosophic	ADJ
ejpam-5839	1294	3	sets	set	NOUN
ejpam-5839	1294	4	and	and	CCONJ
ejpam-5839	1294	5	logic	logic	NOUN
ejpam-5839	1294	6	:	:	PUNCT
ejpam-5839	1294	7	theory	theory	NOUN
ejpam-5839	1294	8	and	and	CCONJ
ejpam-5839	1294	9	applications	application	NOUN
ejpam-5839	1294	10	in	in	ADP
ejpam-5839	1294	11	computing	computing	NOUN
ejpam-5839	1294	12	.	.	PUNCT
ejpam-5839	1295	1	hexis	hexis	PROPN
ejpam-5839	1295	2	,	,	PUNCT
ejpam-5839	1295	3	phoenix	phoenix	PROPN
ejpam-5839	1295	4	,	,	PUNCT
ejpam-5839	1295	5	az	az	PROPN
ejpam-5839	1295	6	,	,	PUNCT
ejpam-5839	1295	7	2005	2005	NUM
ejpam-5839	1295	8	.	.	PUNCT
ejpam-5839	1296	1	[	[	X
ejpam-5839	1296	2	14	14	NUM
ejpam-5839	1296	3	]	]	X
ejpam-5839	1296	4	j.	j.	PROPN
ejpam-5839	1296	5	ye	ye	PROPN
ejpam-5839	1296	6	.	.	PROPN
ejpam-5839	1296	7	vector	vector	NOUN
ejpam-5839	1296	8	similarity	similarity	NOUN
ejpam-5839	1296	9	measures	measure	NOUN
ejpam-5839	1296	10	of	of	ADP
ejpam-5839	1296	11	simplified	simplified	ADJ
ejpam-5839	1296	12	neutrosophic	neutrosophic	ADJ
ejpam-5839	1296	13	sets	set	NOUN
ejpam-5839	1296	14	and	and	CCONJ
ejpam-5839	1296	15	their	their	PRON
ejpam-5839	1296	16	application	application	NOUN
ejpam-5839	1296	17	in	in	ADP
ejpam-5839	1296	18	multicriteria	multicriteria	PROPN
ejpam-5839	1296	19	decision	decision	NOUN
ejpam-5839	1296	20	making	making	NOUN
ejpam-5839	1296	21	.	.	PUNCT
ejpam-5839	1297	1	international	international	ADJ
ejpam-5839	1297	2	journal	journal	NOUN
ejpam-5839	1297	3	of	of	ADP
ejpam-5839	1297	4	fuzzy	fuzzy	ADJ
ejpam-5839	1297	5	systems	system	NOUN
ejpam-5839	1297	6	,	,	PUNCT
ejpam-5839	1297	7	16(2):204–211	16(2):204–211	NUM
ejpam-5839	1297	8	,	,	PUNCT
ejpam-5839	1297	9	2014	2014	NUM
ejpam-5839	1297	10	.	.	PUNCT
ejpam-5839	1298	1	[	[	X
ejpam-5839	1298	2	15	15	NUM
ejpam-5839	1298	3	]	]	X
ejpam-5839	1298	4	c.	c.	PROPN
ejpam-5839	1298	5	li	li	PROPN
ejpam-5839	1298	6	and	and	CCONJ
ejpam-5839	1298	7	s.	s.	PROPN
ejpam-5839	1298	8	luo	luo	PROPN
ejpam-5839	1298	9	.	.	PUNCT
ejpam-5839	1299	1	the	the	DET
ejpam-5839	1299	2	weighted	weight	VERB
ejpam-5839	1299	3	distance	distance	NOUN
ejpam-5839	1299	4	measure	measure	NOUN
ejpam-5839	1299	5	based	base	VERB
ejpam-5839	1299	6	method	method	NOUN
ejpam-5839	1299	7	to	to	ADP
ejpam-5839	1299	8	neutrosophic	neutrosophic	ADJ
ejpam-5839	1299	9	multiattribute	multiattribute	NOUN
ejpam-5839	1299	10	group	group	NOUN
ejpam-5839	1299	11	decision	decision	NOUN
ejpam-5839	1299	12	making	making	NOUN
ejpam-5839	1299	13	.	.	PUNCT
ejpam-5839	1300	1	mathematical	mathematical	ADJ
ejpam-5839	1300	2	problems	problem	NOUN
ejpam-5839	1300	3	in	in	ADP
ejpam-5839	1300	4	engineering	engineering	NOUN
ejpam-5839	1300	5	,	,	PUNCT
ejpam-5839	1300	6	2016:3145341	2016:3145341	NUM
ejpam-5839	1300	7	,	,	PUNCT
ejpam-5839	1300	8	2016	2016	NUM
ejpam-5839	1300	9	.	.	PUNCT
ejpam-5839	1301	1	[	[	X
ejpam-5839	1301	2	16	16	NUM
ejpam-5839	1301	3	]	]	PUNCT
ejpam-5839	1301	4	p.	p.	PROPN
ejpam-5839	1301	5	liu	liu	PROPN
ejpam-5839	1301	6	and	and	CCONJ
ejpam-5839	1301	7	l.	l.	PROPN
ejpam-5839	1301	8	shi	shi	PROPN
ejpam-5839	1301	9	.	.	PUNCT
ejpam-5839	1302	1	the	the	DET
ejpam-5839	1302	2	generalized	generalize	VERB
ejpam-5839	1302	3	hybrid	hybrid	NOUN
ejpam-5839	1302	4	weighted	weight	VERB
ejpam-5839	1302	5	average	average	ADJ
ejpam-5839	1302	6	operator	operator	NOUN
ejpam-5839	1302	7	based	base	VERB
ejpam-5839	1302	8	on	on	ADP
ejpam-5839	1302	9	interval	interval	NOUN
ejpam-5839	1302	10	neutrosophic	neutrosophic	ADJ
ejpam-5839	1302	11	hesitant	hesitant	ADJ
ejpam-5839	1302	12	set	set	NOUN
ejpam-5839	1302	13	and	and	CCONJ
ejpam-5839	1302	14	its	its	PRON
ejpam-5839	1302	15	application	application	NOUN
ejpam-5839	1302	16	to	to	ADP
ejpam-5839	1302	17	multiple	multiple	ADJ
ejpam-5839	1302	18	attribute	attribute	NOUN
ejpam-5839	1302	19	decision	decision	NOUN
ejpam-5839	1302	20	making	making	NOUN
ejpam-5839	1302	21	.	.	PUNCT
ejpam-5839	1303	1	neural	neural	ADJ
ejpam-5839	1303	2	computing	computing	NOUN
ejpam-5839	1303	3	and	and	CCONJ
ejpam-5839	1303	4	applications	application	NOUN
ejpam-5839	1303	5	,	,	PUNCT
ejpam-5839	1303	6	26(2):457–471	26(2):457–471	PROPN
ejpam-5839	1303	7	,	,	PUNCT
ejpam-5839	1303	8	2015	2015	NUM
ejpam-5839	1303	9	.	.	PUNCT
ejpam-5839	1304	1	[	[	X
ejpam-5839	1304	2	17	17	NUM
ejpam-5839	1304	3	]	]	X
ejpam-5839	1304	4	d.	d.	PROPN
ejpam-5839	1304	5	molodtsov	molodtsov	PROPN
ejpam-5839	1304	6	.	.	PUNCT
ejpam-5839	1305	1	soft	soft	ADJ
ejpam-5839	1305	2	set	set	ADJ
ejpam-5839	1305	3	theory	theory	NOUN
ejpam-5839	1305	4	first	first	ADJ
ejpam-5839	1305	5	results	result	NOUN
ejpam-5839	1305	6	.	.	PUNCT
ejpam-5839	1306	1	computers	computer	NOUN
ejpam-5839	1306	2	and	and	CCONJ
ejpam-5839	1306	3	mathematics	mathematic	NOUN
ejpam-5839	1306	4	with	with	ADP
ejpam-5839	1306	5	applications	application	NOUN
ejpam-5839	1306	6	,	,	PUNCT
ejpam-5839	1306	7	37(4–5):19–31	37(4–5):19–31	NUM
ejpam-5839	1306	8	,	,	PUNCT
ejpam-5839	1306	9	1999	1999	NUM
ejpam-5839	1306	10	.	.	PUNCT
ejpam-5839	1307	1	[	[	X
ejpam-5839	1307	2	18	18	NUM
ejpam-5839	1307	3	]	]	PUNCT
ejpam-5839	1307	4	p.	p.	PROPN
ejpam-5839	1307	5	k.	k.	PROPN
ejpam-5839	1308	1	maji	maji	PROPN
ejpam-5839	1308	2	,	,	PUNCT
ejpam-5839	1308	3	r.	r.	PROPN
ejpam-5839	1308	4	biswas	biswas	PROPN
ejpam-5839	1308	5	,	,	PUNCT
ejpam-5839	1308	6	and	and	CCONJ
ejpam-5839	1308	7	a.	a.	PROPN
ejpam-5839	1308	8	r.	r.	PROPN
ejpam-5839	1308	9	roy	roy	PROPN
ejpam-5839	1308	10	.	.	PROPN
ejpam-5839	1308	11	soft	soft	ADJ
ejpam-5839	1308	12	set	set	NOUN
ejpam-5839	1308	13	theory	theory	NOUN
ejpam-5839	1308	14	.	.	PUNCT
ejpam-5839	1309	1	computers	computer	NOUN
ejpam-5839	1309	2	and	and	CCONJ
ejpam-5839	1309	3	mathematics	mathematic	NOUN
ejpam-5839	1309	4	with	with	ADP
ejpam-5839	1309	5	applications	application	NOUN
ejpam-5839	1309	6	,	,	PUNCT
ejpam-5839	1309	7	45(4–5):555–562	45(4–5):555–562	NUM
ejpam-5839	1309	8	,	,	PUNCT
ejpam-5839	1309	9	2003	2003	NUM
ejpam-5839	1309	10	.	.	PUNCT
ejpam-5839	1310	1	[	[	X
ejpam-5839	1310	2	19	19	NUM
ejpam-5839	1310	3	]	]	PUNCT
ejpam-5839	1310	4	p.	p.	PROPN
ejpam-5839	1310	5	k.	k.	PROPN
ejpam-5839	1311	1	maji	maji	PROPN
ejpam-5839	1311	2	,	,	PUNCT
ejpam-5839	1311	3	r.	r.	PROPN
ejpam-5839	1311	4	biswas	biswas	PROPN
ejpam-5839	1311	5	,	,	PUNCT
ejpam-5839	1311	6	and	and	CCONJ
ejpam-5839	1312	1	a.	a.	PROPN
ejpam-5839	1312	2	r.	r.	PROPN
ejpam-5839	1312	3	roy	roy	PROPN
ejpam-5839	1312	4	.	.	PROPN
ejpam-5839	1312	5	fuzzy	fuzzy	ADJ
ejpam-5839	1312	6	soft	soft	ADJ
ejpam-5839	1312	7	sets	set	NOUN
ejpam-5839	1312	8	.	.	PUNCT
ejpam-5839	1313	1	journal	journal	NOUN
ejpam-5839	1313	2	of	of	ADP
ejpam-5839	1313	3	fuzzy	fuzzy	ADJ
ejpam-5839	1313	4	mathematics	mathematic	NOUN
ejpam-5839	1313	5	,	,	PUNCT
ejpam-5839	1313	6	9(3):589–602	9(3):589–602	NOUN
ejpam-5839	1313	7	,	,	PUNCT
ejpam-5839	1313	8	2001	2001	NUM
ejpam-5839	1313	9	.	.	PUNCT
ejpam-5839	1314	1	[	[	X
ejpam-5839	1314	2	20	20	NUM
ejpam-5839	1314	3	]	]	PUNCT
ejpam-5839	1314	4	f.	f.	PROPN
ejpam-5839	1314	5	wang	wang	PROPN
ejpam-5839	1314	6	,	,	PUNCT
ejpam-5839	1314	7	x.	x.	PROPN
ejpam-5839	1314	8	li	li	PROPN
ejpam-5839	1314	9	,	,	PUNCT
ejpam-5839	1314	10	and	and	CCONJ
ejpam-5839	1314	11	x.	x.	PROPN
ejpam-5839	1314	12	chen	chen	PROPN
ejpam-5839	1314	13	.	.	PUNCT
ejpam-5839	1315	1	hesitant	hesitant	ADJ
ejpam-5839	1315	2	fuzzy	fuzzy	ADJ
ejpam-5839	1315	3	soft	soft	ADJ
ejpam-5839	1315	4	set	set	NOUN
ejpam-5839	1315	5	and	and	CCONJ
ejpam-5839	1315	6	its	its	PRON
ejpam-5839	1315	7	applications	application	NOUN
ejpam-5839	1315	8	in	in	ADP
ejpam-5839	1315	9	multicriteria	multicriteria	PROPN
ejpam-5839	1315	10	decision	decision	NOUN
ejpam-5839	1315	11	making	making	NOUN
ejpam-5839	1315	12	.	.	PUNCT
ejpam-5839	1316	1	journal	journal	PROPN
ejpam-5839	1316	2	of	of	ADP
ejpam-5839	1316	3	applied	apply	VERB
ejpam-5839	1316	4	mathematics	mathematic	NOUN
ejpam-5839	1316	5	,	,	PUNCT
ejpam-5839	1316	6	2014:643785	2014:643785	NUM
ejpam-5839	1316	7	,	,	PUNCT
ejpam-5839	1316	8	2014	2014	NUM
ejpam-5839	1316	9	.	.	PUNCT
ejpam-5839	1317	1	[	[	X
ejpam-5839	1317	2	21	21	NUM
ejpam-5839	1317	3	]	]	X
ejpam-5839	1317	4	d.	d.	PROPN
ejpam-5839	1317	5	pei	pei	PROPN
ejpam-5839	1317	6	and	and	CCONJ
ejpam-5839	1317	7	d.	d.	PROPN
ejpam-5839	1317	8	miao	miao	PROPN
ejpam-5839	1317	9	.	.	PROPN
ejpam-5839	1318	1	from	from	ADP
ejpam-5839	1318	2	soft	soft	ADJ
ejpam-5839	1318	3	sets	set	NOUN
ejpam-5839	1318	4	to	to	ADP
ejpam-5839	1318	5	information	information	NOUN
ejpam-5839	1318	6	systems	system	NOUN
ejpam-5839	1318	7	.	.	PUNCT
ejpam-5839	1319	1	in	in	ADP
ejpam-5839	1319	2	proceedings	proceeding	NOUN
ejpam-5839	1319	3	of	of	ADP
ejpam-5839	1319	4	the	the	DET
ejpam-5839	1319	5	ieee	ieee	NOUN
ejpam-5839	1319	6	international	international	PROPN
ejpam-5839	1319	7	conference	conference	NOUN
ejpam-5839	1319	8	on	on	ADP
ejpam-5839	1319	9	granular	granular	ADJ
ejpam-5839	1319	10	computing	computing	NOUN
ejpam-5839	1319	11	,	,	PUNCT
ejpam-5839	1319	12	volume	volume	NOUN
ejpam-5839	1319	13	2	2	NUM
ejpam-5839	1319	14	,	,	PUNCT
ejpam-5839	1319	15	pages	page	NOUN
ejpam-5839	1319	16	617–621	617–621	NUM
ejpam-5839	1319	17	,	,	PUNCT
ejpam-5839	1319	18	2005	2005	NUM
ejpam-5839	1319	19	.	.	PUNCT
ejpam-5839	1320	1	[	[	X
ejpam-5839	1320	2	22	22	NUM
ejpam-5839	1320	3	]	]	PUNCT
ejpam-5839	1320	4	s.	s.	PROPN
ejpam-5839	1320	5	j.	j.	PROPN
ejpam-5839	1320	6	john	john	PROPN
ejpam-5839	1320	7	.	.	PROPN
ejpam-5839	1320	8	soft	soft	ADJ
ejpam-5839	1320	9	sets	set	NOUN
ejpam-5839	1320	10	,	,	PUNCT
ejpam-5839	1320	11	volume	volume	NOUN
ejpam-5839	1320	12	400	400	NUM
ejpam-5839	1320	13	of	of	ADP
ejpam-5839	1320	14	studies	study	NOUN
ejpam-5839	1320	15	in	in	ADP
ejpam-5839	1320	16	fuzziness	fuzziness	NOUN
ejpam-5839	1320	17	and	and	CCONJ
ejpam-5839	1320	18	soft	soft	ADJ
ejpam-5839	1320	19	computing	computing	NOUN
ejpam-5839	1320	20	.	.	PUNCT
ejpam-5839	1321	1	springer	springer	NOUN
ejpam-5839	1321	2	,	,	PUNCT
ejpam-5839	1321	3	cham	cham	NOUN
ejpam-5839	1321	4	,	,	PUNCT
ejpam-5839	1321	5	2021	2021	NUM
ejpam-5839	1321	6	.	.	PUNCT
ejpam-5839	1322	1	[	[	X
ejpam-5839	1322	2	23	23	NUM
ejpam-5839	1322	3	]	]	PUNCT
ejpam-5839	1322	4	s.	s.	PROPN
ejpam-5839	1322	5	j.	j.	PROPN
ejpam-5839	1322	6	john	john	PROPN
ejpam-5839	1322	7	.	.	PUNCT
ejpam-5839	1323	1	topological	topological	ADJ
ejpam-5839	1323	2	structures	structure	NOUN
ejpam-5839	1323	3	of	of	ADP
ejpam-5839	1323	4	soft	soft	ADJ
ejpam-5839	1323	5	sets	set	NOUN
ejpam-5839	1323	6	,	,	PUNCT
ejpam-5839	1323	7	volume	volume	NOUN
ejpam-5839	1323	8	400	400	NUM
ejpam-5839	1323	9	of	of	ADP
ejpam-5839	1323	10	studies	study	NOUN
ejpam-5839	1323	11	in	in	ADP
ejpam-5839	1323	12	fuzziness	fuzziness	NOUN
ejpam-5839	1323	13	and	and	CCONJ
ejpam-5839	1323	14	soft	soft	ADJ
ejpam-5839	1323	15	computing	computing	NOUN
ejpam-5839	1323	16	.	.	PUNCT
ejpam-5839	1324	1	springer	springer	NOUN
ejpam-5839	1324	2	,	,	PUNCT
ejpam-5839	1324	3	cham	cham	NOUN
ejpam-5839	1324	4	,	,	PUNCT
ejpam-5839	1324	5	2021	2021	NUM
ejpam-5839	1324	6	.	.	PUNCT
ejpam-5839	1325	1	[	[	X
ejpam-5839	1325	2	24	24	NUM
ejpam-5839	1325	3	]	]	PUNCT
ejpam-5839	1326	1	s.	s.	PROPN
ejpam-5839	1326	2	j.	j.	PROPN
ejpam-5839	1326	3	john	john	PROPN
ejpam-5839	1326	4	.	.	PUNCT
ejpam-5839	1326	5	hybrid	hybrid	ADJ
ejpam-5839	1326	6	structures	structure	NOUN
ejpam-5839	1326	7	involving	involve	VERB
ejpam-5839	1326	8	soft	soft	ADJ
ejpam-5839	1326	9	sets	set	NOUN
ejpam-5839	1326	10	,	,	PUNCT
ejpam-5839	1326	11	volume	volume	NOUN
ejpam-5839	1326	12	400	400	NUM
ejpam-5839	1326	13	of	of	ADP
ejpam-5839	1326	14	studies	study	NOUN
ejpam-5839	1326	15	in	in	ADP
ejpam-5839	1326	16	fuzziness	fuzziness	NOUN
ejpam-5839	1326	17	and	and	CCONJ
ejpam-5839	1326	18	soft	soft	ADJ
ejpam-5839	1326	19	computing	computing	NOUN
ejpam-5839	1326	20	.	.	PUNCT
ejpam-5839	1327	1	springer	springer	NOUN
ejpam-5839	1327	2	,	,	PUNCT
ejpam-5839	1327	3	cham	cham	NOUN
ejpam-5839	1327	4	,	,	PUNCT
ejpam-5839	1327	5	2021	2021	NUM
ejpam-5839	1327	6	.	.	PUNCT
ejpam-5839	1328	1	[	[	X
ejpam-5839	1328	2	25	25	NUM
ejpam-5839	1328	3	]	]	PUNCT
ejpam-5839	1328	4	t.	t.	PROPN
ejpam-5839	1328	5	m.	m.	PROPN
ejpam-5839	1328	6	al	al	PROPN
ejpam-5839	1328	7	-	-	PUNCT
ejpam-5839	1328	8	shami	shami	PROPN
ejpam-5839	1328	9	,	,	PUNCT
ejpam-5839	1328	10	d.	d.	PROPN
ejpam-5839	1328	11	ljubisa	ljubisa	PROPN
ejpam-5839	1328	12	,	,	PUNCT
ejpam-5839	1328	13	and	and	CCONJ
ejpam-5839	1328	14	r.	r.	PROPN
ejpam-5839	1328	15	kocinac	kocinac	PROPN
ejpam-5839	1328	16	.	.	PUNCT
ejpam-5839	1329	1	nearly	nearly	ADV
ejpam-5839	1329	2	soft	soft	ADJ
ejpam-5839	1329	3	menger	menger	NOUN
ejpam-5839	1329	4	spaces	space	NOUN
ejpam-5839	1329	5	.	.	PUNCT
ejpam-5839	1330	1	journal	journal	NOUN
ejpam-5839	1330	2	of	of	ADP
ejpam-5839	1330	3	mathematics	mathematic	NOUN
ejpam-5839	1330	4	,	,	PUNCT
ejpam-5839	1330	5	pages	page	NOUN
ejpam-5839	1330	6	1–9	1–9	NUM
ejpam-5839	1330	7	,	,	PUNCT
ejpam-5839	1330	8	2020	2020	NUM
ejpam-5839	1330	9	.	.	PUNCT
ejpam-5839	1331	1	[	[	X
ejpam-5839	1331	2	26	26	NUM
ejpam-5839	1331	3	]	]	PUNCT
ejpam-5839	1331	4	t.	t.	PROPN
ejpam-5839	1331	5	m.	m.	PROPN
ejpam-5839	1331	6	al	al	PROPN
ejpam-5839	1331	7	-	-	PUNCT
ejpam-5839	1331	8	shami	shami	PROPN
ejpam-5839	1331	9	.	.	PUNCT
ejpam-5839	1332	1	new	new	ADJ
ejpam-5839	1332	2	soft	soft	ADJ
ejpam-5839	1332	3	structure	structure	NOUN
ejpam-5839	1332	4	:	:	PUNCT
ejpam-5839	1332	5	infra	infra	NOUN
ejpam-5839	1332	6	soft	soft	ADJ
ejpam-5839	1332	7	topological	topological	ADJ
ejpam-5839	1332	8	spaces	space	NOUN
ejpam-5839	1332	9	.	.	PUNCT
ejpam-5839	1333	1	mathematical	mathematical	ADJ
ejpam-5839	1333	2	problems	problem	NOUN
ejpam-5839	1333	3	in	in	ADP
ejpam-5839	1333	4	engineering	engineering	NOUN
ejpam-5839	1333	5	,	,	PUNCT
ejpam-5839	1333	6	pages	page	NOUN
ejpam-5839	1333	7	1–12	1–12	PROPN
ejpam-5839	1333	8	,	,	PUNCT
ejpam-5839	1333	9	2021	2021	NUM
ejpam-5839	1333	10	.	.	PUNCT
ejpam-5839	1334	1	[	[	X
ejpam-5839	1334	2	27	27	NUM
ejpam-5839	1334	3	]	]	PUNCT
ejpam-5839	1334	4	t.	t.	PROPN
ejpam-5839	1334	5	m.	m.	PROPN
ejpam-5839	1334	6	al	al	PROPN
ejpam-5839	1334	7	-	-	PUNCT
ejpam-5839	1334	8	shami	shami	PROPN
ejpam-5839	1334	9	,	,	PUNCT
ejpam-5839	1334	10	e.	e.	PROPN
ejpam-5839	1334	11	a.	a.	PROPN
ejpam-5839	1334	12	tabl	tabl	PROPN
ejpam-5839	1334	13	,	,	PUNCT
ejpam-5839	1334	14	and	and	CCONJ
ejpam-5839	1334	15	b.	b.	PROPN
ejpam-5839	1334	16	a.	a.	PROPN
ejpam-5839	1334	17	asaad	asaad	PROPN
ejpam-5839	1334	18	.	.	PUNCT
ejpam-5839	1335	1	weak	weak	ADJ
ejpam-5839	1335	2	forms	form	NOUN
ejpam-5839	1335	3	of	of	ADP
ejpam-5839	1335	4	soft	soft	ADJ
ejpam-5839	1335	5	separation	separation	NOUN
ejpam-5839	1335	6	axioms	axiom	NOUN
ejpam-5839	1335	7	and	and	CCONJ
ejpam-5839	1335	8	fixed	fix	VERB
ejpam-5839	1335	9	soft	soft	ADJ
ejpam-5839	1335	10	points	point	NOUN
ejpam-5839	1335	11	.	.	PUNCT
ejpam-5839	1336	1	fuzzy	fuzzy	ADJ
ejpam-5839	1336	2	information	information	NOUN
ejpam-5839	1336	3	and	and	CCONJ
ejpam-5839	1336	4	engineering	engineering	NOUN
ejpam-5839	1336	5	,	,	PUNCT
ejpam-5839	1336	6	12(4):509–528	12(4):509–528	NUM
ejpam-5839	1336	7	,	,	PUNCT
ejpam-5839	1336	8	2020	2020	NUM
ejpam-5839	1336	9	.	.	PUNCT
ejpam-5839	1337	1	[	[	X
ejpam-5839	1337	2	28	28	NUM
ejpam-5839	1337	3	]	]	X
ejpam-5839	1337	4	t.	t.	PROPN
ejpam-5839	1337	5	m.	m.	PROPN
ejpam-5839	1337	6	al	al	PROPN
ejpam-5839	1337	7	-	-	PUNCT
ejpam-5839	1337	8	shami	shami	PROPN
ejpam-5839	1337	9	,	,	PUNCT
ejpam-5839	1337	10	a.	a.	PROPN
ejpam-5839	1337	11	el	el	PROPN
ejpam-5839	1337	12	-	-	PUNCT
ejpam-5839	1337	13	sayed	say	VERB
ejpam-5839	1337	14	,	,	PUNCT
ejpam-5839	1337	15	and	and	CCONJ
ejpam-5839	1337	16	a.	a.	NOUN
ejpam-5839	1337	17	tabi	tabi	PROPN
ejpam-5839	1337	18	.	.	PUNCT
ejpam-5839	1338	1	connectedness	connectedness	NOUN
ejpam-5839	1338	2	and	and	CCONJ
ejpam-5839	1338	3	local	local	ADJ
ejpam-5839	1338	4	connectedness	connectedness	NOUN
ejpam-5839	1338	5	on	on	ADP
ejpam-5839	1338	6	infra	infra	NOUN
ejpam-5839	1338	7	soft	soft	ADJ
ejpam-5839	1338	8	topological	topological	ADJ
ejpam-5839	1338	9	spaces	space	NOUN
ejpam-5839	1338	10	.	.	PUNCT
ejpam-5839	1339	1	mathematics	mathematic	NOUN
ejpam-5839	1339	2	,	,	PUNCT
ejpam-5839	1339	3	9:1–15	9:1–15	NUM
ejpam-5839	1339	4	,	,	PUNCT
ejpam-5839	1339	5	2021	2021	NUM
ejpam-5839	1339	6	.	.	PUNCT
ejpam-5839	1340	1	[	[	X
ejpam-5839	1340	2	29	29	NUM
ejpam-5839	1340	3	]	]	PUNCT
ejpam-5839	1340	4	t.	t.	PROPN
ejpam-5839	1340	5	m.	m.	PROPN
ejpam-5839	1340	6	al	al	PROPN
ejpam-5839	1340	7	-	-	PUNCT
ejpam-5839	1340	8	shami	shami	PROPN
ejpam-5839	1340	9	.	.	PUNCT
ejpam-5839	1341	1	homeomorphism	homeomorphism	PROPN
ejpam-5839	1341	2	and	and	CCONJ
ejpam-5839	1341	3	quotient	quotient	NOUN
ejpam-5839	1341	4	mappings	mapping	NOUN
ejpam-5839	1341	5	in	in	ADP
ejpam-5839	1341	6	infra	infra	NOUN
ejpam-5839	1341	7	soft	soft	ADJ
ejpam-5839	1341	8	topological	topological	ADJ
ejpam-5839	1341	9	spaces	space	NOUN
ejpam-5839	1341	10	.	.	PUNCT
ejpam-5839	1342	1	journal	journal	NOUN
ejpam-5839	1342	2	of	of	ADP
ejpam-5839	1342	3	mathematics	mathematic	NOUN
ejpam-5839	1342	4	,	,	PUNCT
ejpam-5839	1342	5	pages	page	NOUN
ejpam-5839	1342	6	1–10	1–10	NOUN
ejpam-5839	1342	7	,	,	PUNCT
ejpam-5839	1342	8	2021	2021	NUM
ejpam-5839	1342	9	.	.	PUNCT
ejpam-5839	1343	1	[	[	X
ejpam-5839	1343	2	30	30	NUM
ejpam-5839	1343	3	]	]	PUNCT
ejpam-5839	1343	4	t.	t.	PROPN
ejpam-5839	1343	5	m.	m.	PROPN
ejpam-5839	1343	6	al	al	PROPN
ejpam-5839	1343	7	-	-	PUNCT
ejpam-5839	1343	8	shami	shami	PROPN
ejpam-5839	1343	9	.	.	PUNCT
ejpam-5839	1344	1	infra	infra	NOUN
ejpam-5839	1344	2	soft	soft	ADJ
ejpam-5839	1344	3	compact	compact	ADJ
ejpam-5839	1344	4	spaces	space	NOUN
ejpam-5839	1344	5	and	and	CCONJ
ejpam-5839	1344	6	application	application	NOUN
ejpam-5839	1344	7	to	to	ADP
ejpam-5839	1344	8	fixed	fix	VERB
ejpam-5839	1344	9	point	point	NOUN
ejpam-5839	1344	10	theorem	theorem	VERB
ejpam-5839	1344	11	.	.	PROPN
ejpam-5839	1344	12	journal	journal	PROPN
ejpam-5839	1344	13	of	of	ADP
ejpam-5839	1344	14	function	function	NOUN
ejpam-5839	1344	15	spaces	space	NOUN
ejpam-5839	1344	16	,	,	PUNCT
ejpam-5839	1344	17	pages	page	NOUN
ejpam-5839	1344	18	1–9	1–9	NUM
ejpam-5839	1344	19	,	,	PUNCT
ejpam-5839	1344	20	2021	2021	NUM
ejpam-5839	1344	21	.	.	PUNCT
ejpam-5839	1345	1	[	[	X
ejpam-5839	1345	2	31	31	NUM
ejpam-5839	1345	3	]	]	PUNCT
ejpam-5839	1345	4	a.	a.	NOUN
ejpam-5839	1345	5	ahmad	ahmad	PROPN
ejpam-5839	1345	6	,	,	PUNCT
ejpam-5839	1345	7	r.	r.	PROPN
ejpam-5839	1345	8	hatamleh	hatamleh	PROPN
ejpam-5839	1345	9	,	,	PUNCT
ejpam-5839	1345	10	k.	k.	PROPN
ejpam-5839	1345	11	matarneh	matarneh	PROPN
ejpam-5839	1345	12	,	,	PUNCT
ejpam-5839	1345	13	and	and	CCONJ
ejpam-5839	1345	14	a.	a.	PROPN
ejpam-5839	1345	15	al	al	PROPN
ejpam-5839	1345	16	-	-	PUNCT
ejpam-5839	1345	17	husban	husban	PROPN
ejpam-5839	1345	18	.	.	PUNCT
ejpam-5839	1346	1	on	on	ADP
ejpam-5839	1346	2	the	the	DET
ejpam-5839	1346	3	irreversible	irreversible	ADJ
ejpam-5839	1346	4	k	k	ADJ
ejpam-5839	1346	5	-	-	PUNCT
ejpam-5839	1346	6	threshold	threshold	NOUN
ejpam-5839	1346	7	conversion	conversion	NOUN
ejpam-5839	1346	8	number	number	NOUN
ejpam-5839	1346	9	for	for	ADP
ejpam-5839	1346	10	some	some	DET
ejpam-5839	1346	11	graph	graph	NOUN
ejpam-5839	1346	12	products	product	NOUN
ejpam-5839	1346	13	and	and	CCONJ
ejpam-5839	1346	14	neutrosophic	neutrosophic	ADJ
ejpam-5839	1346	15	graphs	graph	NOUN
ejpam-5839	1346	16	.	.	PUNCT
ejpam-5839	1347	1	international	international	ADJ
ejpam-5839	1347	2	journal	journal	PROPN
ejpam-5839	1347	3	of	of	ADP
ejpam-5839	1347	4	neutrosophic	neutrosophic	ADJ
ejpam-5839	1347	5	science	science	NOUN
ejpam-5839	1347	6	,	,	PUNCT
ejpam-5839	1347	7	25(2):183–196	25(2):183–196	NUM
ejpam-5839	1347	8	,	,	PUNCT
ejpam-5839	1347	9	2025	2025	NUM
ejpam-5839	1347	10	.	.	PUNCT
ejpam-5839	1348	1	[	[	X
ejpam-5839	1348	2	32	32	NUM
ejpam-5839	1348	3	]	]	PUNCT
ejpam-5839	1348	4	r.	r.	PROPN
ejpam-5839	1348	5	hatamleh	hatamleh	PROPN
ejpam-5839	1348	6	,	,	PUNCT
ejpam-5839	1348	7	a.	a.	PROPN
ejpam-5839	1348	8	al	al	PROPN
ejpam-5839	1348	9	-	-	PUNCT
ejpam-5839	1348	10	husban	husban	PROPN
ejpam-5839	1348	11	,	,	PUNCT
ejpam-5839	1348	12	k.	k.	PROPN
ejpam-5839	1348	13	sundareswari	sundareswari	PROPN
ejpam-5839	1348	14	,	,	PUNCT
ejpam-5839	1348	15	g.	g.	PROPN
ejpam-5839	1348	16	balaj	balaj	PROPN
ejpam-5839	1348	17	,	,	PUNCT
ejpam-5839	1348	18	and	and	CCONJ
ejpam-5839	1348	19	m.	m.	NOUN
ejpam-5839	1348	20	palanikumar	palanikumar	PROPN
ejpam-5839	1348	21	.	.	PUNCT
ejpam-5839	1349	1	complex	complex	ADJ
ejpam-5839	1349	2	a.	a.	NOUN
ejpam-5839	1349	3	shihadeh	shihadeh	NOUN
ejpam-5839	1349	4	et	et	PROPN
ejpam-5839	1349	5	al	al	PROPN
ejpam-5839	1349	6	.	.	PUNCT
ejpam-5839	1349	7	/	/	SYM
ejpam-5839	1349	8	eur	eur	PROPN
ejpam-5839	1349	9	.	.	PUNCT
ejpam-5839	1350	1	j.	j.	PROPN
ejpam-5839	1350	2	pure	pure	PROPN
ejpam-5839	1350	3	appl	appl	PROPN
ejpam-5839	1350	4	.	.	PROPN
ejpam-5839	1350	5	math	math	PROPN
ejpam-5839	1350	6	,	,	PUNCT
ejpam-5839	1350	7	18	18	NUM
ejpam-5839	1350	8	(	(	PUNCT
ejpam-5839	1350	9	2	2	NUM
ejpam-5839	1350	10	)	)	PUNCT
ejpam-5839	1350	11	(	(	PUNCT
ejpam-5839	1350	12	2025	2025	NUM
ejpam-5839	1350	13	)	)	PUNCT
ejpam-5839	1350	14	,	,	PUNCT
ejpam-5839	1350	15	5839	5839	NUM
ejpam-5839	1350	16	53	53	NUM
ejpam-5839	1350	17	of	of	ADP
ejpam-5839	1350	18	54	54	NUM
ejpam-5839	1350	19	tangent	tangent	NOUN
ejpam-5839	1350	20	trigonometric	trigonometric	ADJ
ejpam-5839	1350	21	approach	approach	NOUN
ejpam-5839	1350	22	applied	apply	VERB
ejpam-5839	1350	23	to	to	ADP
ejpam-5839	1350	24	(	(	PUNCT
ejpam-5839	1350	25	?	?	PUNCT
ejpam-5839	1350	26	,	,	PUNCT
ejpam-5839	1350	27	t)-rung	t)-rung	ADJ
ejpam-5839	1350	28	fuzzy	fuzzy	ADJ
ejpam-5839	1350	29	set	set	VERB
ejpam-5839	1350	30	using	use	VERB
ejpam-5839	1350	31	weighted	weight	VERB
ejpam-5839	1350	32	averaging	averaging	NOUN
ejpam-5839	1350	33	,	,	PUNCT
ejpam-5839	1350	34	geometric	geometric	ADJ
ejpam-5839	1350	35	operators	operator	NOUN
ejpam-5839	1350	36	and	and	CCONJ
ejpam-5839	1350	37	its	its	PRON
ejpam-5839	1350	38	extension	extension	NOUN
ejpam-5839	1350	39	.	.	PUNCT
ejpam-5839	1351	1	communications	communication	NOUN
ejpam-5839	1351	2	on	on	ADP
ejpam-5839	1351	3	applied	apply	VERB
ejpam-5839	1351	4	nonlinear	nonlinear	ADJ
ejpam-5839	1351	5	analysis	analysis	NOUN
ejpam-5839	1351	6	,	,	PUNCT
ejpam-5839	1351	7	32(5):133–144	32(5):133–144	NUM
ejpam-5839	1351	8	,	,	PUNCT
ejpam-5839	1351	9	2025	2025	NUM
ejpam-5839	1351	10	.	.	PUNCT
ejpam-5839	1352	1	[	[	X
ejpam-5839	1352	2	33	33	NUM
ejpam-5839	1352	3	]	]	X
ejpam-5839	1352	4	r.	r.	PROPN
ejpam-5839	1352	5	hatamleh	hatamleh	PROPN
ejpam-5839	1352	6	,	,	PUNCT
ejpam-5839	1352	7	a.	a.	PROPN
ejpam-5839	1352	8	al	al	PROPN
ejpam-5839	1352	9	-	-	PUNCT
ejpam-5839	1352	10	husban	husban	PROPN
ejpam-5839	1352	11	,	,	PUNCT
ejpam-5839	1352	12	m.	m.	NOUN
ejpam-5839	1352	13	palanikumar	palanikumar	PROPN
ejpam-5839	1352	14	,	,	PUNCT
ejpam-5839	1352	15	and	and	CCONJ
ejpam-5839	1352	16	k.	k.	PROPN
ejpam-5839	1352	17	sundareswari	sundareswari	PROPN
ejpam-5839	1352	18	.	.	PUNCT
ejpam-5839	1353	1	different	different	ADJ
ejpam-5839	1353	2	weighted	weight	VERB
ejpam-5839	1353	3	operators	operator	NOUN
ejpam-5839	1353	4	such	such	ADJ
ejpam-5839	1353	5	as	as	ADP
ejpam-5839	1353	6	generalized	generalized	ADJ
ejpam-5839	1353	7	averaging	averaging	NOUN
ejpam-5839	1353	8	and	and	CCONJ
ejpam-5839	1353	9	generalized	generalized	ADJ
ejpam-5839	1353	10	geometric	geometric	NOUN
ejpam-5839	1353	11	based	base	VERB
ejpam-5839	1353	12	on	on	ADP
ejpam-5839	1353	13	trigonometric	trigonometric	ADJ
ejpam-5839	1353	14	prung	prung	VERB
ejpam-5839	1353	15	interval	interval	NOUN
ejpam-5839	1353	16	-	-	PUNCT
ejpam-5839	1353	17	valued	value	VERB
ejpam-5839	1353	18	approach	approach	NOUN
ejpam-5839	1353	19	.	.	PUNCT
ejpam-5839	1354	1	communications	communication	NOUN
ejpam-5839	1354	2	on	on	ADP
ejpam-5839	1354	3	applied	apply	VERB
ejpam-5839	1354	4	nonlinear	nonlinear	ADJ
ejpam-5839	1354	5	analysis	analysis	NOUN
ejpam-5839	1354	6	,	,	PUNCT
ejpam-5839	1354	7	32(5):91	32(5):91	NUM
ejpam-5839	1354	8	–	–	PUNCT
ejpam-5839	1354	9	101	101	NUM
ejpam-5839	1354	10	,	,	PUNCT
ejpam-5839	1354	11	2025	2025	NUM
ejpam-5839	1354	12	.	.	PUNCT
ejpam-5839	1355	1	[	[	X
ejpam-5839	1355	2	34	34	NUM
ejpam-5839	1355	3	]	]	PUNCT
ejpam-5839	1355	4	a.	a.	NOUN
ejpam-5839	1355	5	shihadeh	shihadeh	PROPN
ejpam-5839	1355	6	,	,	PUNCT
ejpam-5839	1355	7	r.	r.	PROPN
ejpam-5839	1355	8	hatamleh	hatamleh	PROPN
ejpam-5839	1355	9	,	,	PUNCT
ejpam-5839	1355	10	m.	m.	NOUN
ejpam-5839	1355	11	palanikumar	palanikumar	PROPN
ejpam-5839	1355	12	,	,	PUNCT
ejpam-5839	1355	13	and	and	CCONJ
ejpam-5839	1355	14	a.	a.	PROPN
ejpam-5839	1355	15	al	al	PROPN
ejpam-5839	1355	16	-	-	PUNCT
ejpam-5839	1355	17	husban	husban	PROPN
ejpam-5839	1355	18	.	.	PUNCT
ejpam-5839	1356	1	new	new	ADJ
ejpam-5839	1356	2	algebraic	algebraic	ADJ
ejpam-5839	1356	3	structures	structure	NOUN
ejpam-5839	1356	4	towards	towards	ADP
ejpam-5839	1356	5	different	different	ADJ
ejpam-5839	1356	6	(	(	PUNCT
ejpam-5839	1356	7	α	α	NOUN
ejpam-5839	1356	8	,	,	PUNCT
ejpam-5839	1356	9	β)intuitionistic	β)intuitionistic	ADJ
ejpam-5839	1356	10	fuzzy	fuzzy	ADJ
ejpam-5839	1356	11	ideals	ideal	NOUN
ejpam-5839	1356	12	and	and	CCONJ
ejpam-5839	1356	13	its	its	PRON
ejpam-5839	1356	14	characterization	characterization	NOUN
ejpam-5839	1356	15	of	of	ADP
ejpam-5839	1356	16	an	an	DET
ejpam-5839	1356	17	ordered	order	VERB
ejpam-5839	1356	18	ternary	ternary	ADJ
ejpam-5839	1356	19	semigroups	semigroup	NOUN
ejpam-5839	1356	20	.	.	PUNCT
ejpam-5839	1357	1	communications	communication	NOUN
ejpam-5839	1357	2	on	on	ADP
ejpam-5839	1357	3	applied	apply	VERB
ejpam-5839	1357	4	nonlinear	nonlinear	ADJ
ejpam-5839	1357	5	analysis	analysis	NOUN
ejpam-5839	1357	6	,	,	PUNCT
ejpam-5839	1357	7	32(6):568–578	32(6):568–578	PROPN
ejpam-5839	1357	8	,	,	PUNCT
ejpam-5839	1357	9	2025	2025	NUM
ejpam-5839	1357	10	.	.	PUNCT
ejpam-5839	1358	1	[	[	X
ejpam-5839	1358	2	35	35	NUM
ejpam-5839	1358	3	]	]	X
ejpam-5839	1358	4	r.	r.	PROPN
ejpam-5839	1358	5	hatamleh	hatamleh	PROPN
ejpam-5839	1358	6	,	,	PUNCT
ejpam-5839	1358	7	a.	a.	PROPN
ejpam-5839	1358	8	s.	s.	PROPN
ejpam-5839	1358	9	heilat	heilat	PROPN
ejpam-5839	1358	10	,	,	PUNCT
ejpam-5839	1358	11	m.	m.	NOUN
ejpam-5839	1358	12	palanikumar	palanikumar	PROPN
ejpam-5839	1358	13	,	,	PUNCT
ejpam-5839	1358	14	and	and	CCONJ
ejpam-5839	1358	15	a.	a.	PROPN
ejpam-5839	1358	16	al	al	PROPN
ejpam-5839	1358	17	-	-	PUNCT
ejpam-5839	1358	18	husban	husban	PROPN
ejpam-5839	1358	19	.	.	PUNCT
ejpam-5839	1359	1	different	different	ADJ
ejpam-5839	1359	2	operators	operator	NOUN
ejpam-5839	1359	3	via	via	ADP
ejpam-5839	1359	4	weighted	weighted	ADJ
ejpam-5839	1359	5	averaging	averaging	NOUN
ejpam-5839	1359	6	and	and	CCONJ
ejpam-5839	1359	7	geometric	geometric	ADJ
ejpam-5839	1359	8	approach	approach	NOUN
ejpam-5839	1359	9	using	use	VERB
ejpam-5839	1359	10	trigonometric	trigonometric	PROPN
ejpam-5839	1359	11	neutrosophic	neutrosophic	PROPN
ejpam-5839	1359	12	intervalvalued	intervalvalue	VERB
ejpam-5839	1359	13	set	set	VERB
ejpam-5839	1359	14	and	and	CCONJ
ejpam-5839	1359	15	its	its	PRON
ejpam-5839	1359	16	extension	extension	NOUN
ejpam-5839	1359	17	.	.	PUNCT
ejpam-5839	1360	1	neutrosophic	neutrosophic	ADJ
ejpam-5839	1360	2	sets	set	NOUN
ejpam-5839	1360	3	and	and	CCONJ
ejpam-5839	1360	4	systems	system	NOUN
ejpam-5839	1360	5	,	,	PUNCT
ejpam-5839	1360	6	80:194–213	80:194–213	NUM
ejpam-5839	1360	7	,	,	PUNCT
ejpam-5839	1360	8	2025	2025	NUM
ejpam-5839	1360	9	.	.	PUNCT
ejpam-5839	1361	1	[	[	X
ejpam-5839	1361	2	36	36	NUM
ejpam-5839	1361	3	]	]	X
ejpam-5839	1361	4	r.	r.	PROPN
ejpam-5839	1361	5	hatamleh	hatamleh	PROPN
ejpam-5839	1361	6	,	,	PUNCT
ejpam-5839	1361	7	a.	a.	PROPN
ejpam-5839	1361	8	s.	s.	PROPN
ejpam-5839	1361	9	heilat	heilat	PROPN
ejpam-5839	1361	10	,	,	PUNCT
ejpam-5839	1361	11	m.	m.	NOUN
ejpam-5839	1361	12	palanikumar	palanikumar	PROPN
ejpam-5839	1361	13	,	,	PUNCT
ejpam-5839	1361	14	and	and	CCONJ
ejpam-5839	1361	15	a.	a.	PROPN
ejpam-5839	1361	16	al	al	PROPN
ejpam-5839	1361	17	-	-	PUNCT
ejpam-5839	1361	18	husban	husban	PROPN
ejpam-5839	1361	19	.	.	PUNCT
ejpam-5839	1362	1	characterization	characterization	NOUN
ejpam-5839	1362	2	of	of	ADP
ejpam-5839	1362	3	interaction	interaction	NOUN
ejpam-5839	1362	4	aggregating	aggregate	VERB
ejpam-5839	1362	5	operators	operator	NOUN
ejpam-5839	1362	6	setting	set	VERB
ejpam-5839	1362	7	interval	interval	NOUN
ejpam-5839	1362	8	-	-	PUNCT
ejpam-5839	1362	9	valued	value	VERB
ejpam-5839	1362	10	pythagorean	pythagorean	PROPN
ejpam-5839	1362	11	neutrosophic	neutrosophic	PROPN
ejpam-5839	1362	12	set	set	PROPN
ejpam-5839	1362	13	.	.	PUNCT
ejpam-5839	1363	1	neutrosophic	neutrosophic	ADJ
ejpam-5839	1363	2	sets	set	NOUN
ejpam-5839	1363	3	and	and	CCONJ
ejpam-5839	1363	4	systems	system	NOUN
ejpam-5839	1363	5	,	,	PUNCT
ejpam-5839	1363	6	81:285–305	81:285–305	PROPN
ejpam-5839	1363	7	,	,	PUNCT
ejpam-5839	1363	8	2025	2025	NUM
ejpam-5839	1363	9	.	.	PUNCT
ejpam-5839	1364	1	[	[	X
ejpam-5839	1364	2	37	37	NUM
ejpam-5839	1364	3	]	]	X
ejpam-5839	1364	4	r.	r.	PROPN
ejpam-5839	1364	5	hatamleh	hatamleh	PROPN
ejpam-5839	1364	6	,	,	PUNCT
ejpam-5839	1364	7	a.	a.	PROPN
ejpam-5839	1364	8	al	al	PROPN
ejpam-5839	1364	9	-	-	PUNCT
ejpam-5839	1364	10	husban	husban	PROPN
ejpam-5839	1364	11	,	,	PUNCT
ejpam-5839	1364	12	s.	s.	PROPN
ejpam-5839	1364	13	a.	a.	PROPN
ejpam-5839	1364	14	m.	m.	PROPN
ejpam-5839	1364	15	zubair	zubair	PROPN
ejpam-5839	1364	16	,	,	PUNCT
ejpam-5839	1364	17	m.	m.	NOUN
ejpam-5839	1364	18	elamin	elamin	NOUN
ejpam-5839	1364	19	,	,	PUNCT
ejpam-5839	1364	20	m.	m.	NOUN
ejpam-5839	1364	21	m.	m.	PROPN
ejpam-5839	1364	22	saeed	saeed	PROPN
ejpam-5839	1364	23	,	,	PUNCT
ejpam-5839	1364	24	e.	e.	PROPN
ejpam-5839	1364	25	abdolmaleki	abdolmaleki	PROPN
ejpam-5839	1364	26	,	,	PUNCT
ejpam-5839	1364	27	and	and	CCONJ
ejpam-5839	1364	28	a.	a.	PROPN
ejpam-5839	1364	29	m.	m.	PROPN
ejpam-5839	1364	30	khattak	khattak	PROPN
ejpam-5839	1364	31	.	.	PUNCT
ejpam-5839	1365	1	ai	ai	AUX
ejpam-5839	1365	2	-	-	PUNCT
ejpam-5839	1365	3	assisted	assist	VERB
ejpam-5839	1365	4	wearable	wearable	ADJ
ejpam-5839	1365	5	devices	device	NOUN
ejpam-5839	1365	6	for	for	ADP
ejpam-5839	1365	7	promoting	promote	VERB
ejpam-5839	1365	8	human	human	ADJ
ejpam-5839	1365	9	health	health	NOUN
ejpam-5839	1365	10	and	and	CCONJ
ejpam-5839	1365	11	strength	strength	NOUN
ejpam-5839	1365	12	using	use	VERB
ejpam-5839	1365	13	complex	complex	ADJ
ejpam-5839	1365	14	interval	interval	NOUN
ejpam-5839	1365	15	-	-	PUNCT
ejpam-5839	1365	16	valued	value	VERB
ejpam-5839	1365	17	picture	picture	NOUN
ejpam-5839	1365	18	fuzzy	fuzzy	ADJ
ejpam-5839	1365	19	soft	soft	ADJ
ejpam-5839	1365	20	relations	relation	NOUN
ejpam-5839	1365	21	.	.	PUNCT
ejpam-5839	1366	1	european	european	PROPN
ejpam-5839	1366	2	journal	journal	PROPN
ejpam-5839	1366	3	of	of	ADP
ejpam-5839	1366	4	pure	pure	ADJ
ejpam-5839	1366	5	and	and	CCONJ
ejpam-5839	1366	6	applied	applied	ADJ
ejpam-5839	1366	7	mathematics	mathematic	NOUN
ejpam-5839	1366	8	,	,	PUNCT
ejpam-5839	1366	9	18(1):5523–5523	18(1):5523–5523	NUM
ejpam-5839	1366	10	,	,	PUNCT
ejpam-5839	1366	11	2025	2025	NUM
ejpam-5839	1366	12	.	.	PUNCT
ejpam-5839	1367	1	[	[	X
ejpam-5839	1367	2	38	38	NUM
ejpam-5839	1367	3	]	]	PUNCT
ejpam-5839	1367	4	s.	s.	PROPN
ejpam-5839	1367	5	a.	a.	PROPN
ejpam-5839	1367	6	el	el	PROPN
ejpam-5839	1367	7	-	-	PUNCT
ejpam-5839	1367	8	sheikh	sheikh	PROPN
ejpam-5839	1367	9	and	and	CCONJ
ejpam-5839	1367	10	a.	a.	NOUN
ejpam-5839	1367	11	m.	m.	NOUN
ejpam-5839	1367	12	abd	abd	PROPN
ejpam-5839	1367	13	el	el	PROPN
ejpam-5839	1367	14	-	-	PROPN
ejpam-5839	1367	15	latif	latif	PROPN
ejpam-5839	1367	16	.	.	PUNCT
ejpam-5839	1368	1	decompositions	decomposition	NOUN
ejpam-5839	1368	2	of	of	ADP
ejpam-5839	1368	3	some	some	DET
ejpam-5839	1368	4	types	type	NOUN
ejpam-5839	1368	5	of	of	ADP
ejpam-5839	1368	6	supra	supra	ADJ
ejpam-5839	1368	7	soft	soft	ADJ
ejpam-5839	1368	8	sets	set	NOUN
ejpam-5839	1368	9	and	and	CCONJ
ejpam-5839	1368	10	soft	soft	ADJ
ejpam-5839	1368	11	continuity	continuity	NOUN
ejpam-5839	1368	12	.	.	PUNCT
ejpam-5839	1369	1	international	international	ADJ
ejpam-5839	1369	2	journal	journal	PROPN
ejpam-5839	1369	3	of	of	ADP
ejpam-5839	1369	4	mathematical	mathematical	ADJ
ejpam-5839	1369	5	trends	trend	NOUN
ejpam-5839	1369	6	and	and	CCONJ
ejpam-5839	1369	7	technology	technology	NOUN
ejpam-5839	1369	8	,	,	PUNCT
ejpam-5839	1369	9	9(1):37–56	9(1):37–56	NUM
ejpam-5839	1369	10	,	,	PUNCT
ejpam-5839	1369	11	2014	2014	NUM
ejpam-5839	1369	12	.	.	PUNCT
ejpam-5839	1370	1	[	[	X
ejpam-5839	1370	2	39	39	NUM
ejpam-5839	1370	3	]	]	PUNCT
ejpam-5839	1370	4	a.	a.	NOUN
ejpam-5839	1370	5	m.	m.	PROPN
ejpam-5839	1370	6	abd	abd	PROPN
ejpam-5839	1370	7	el	el	PROPN
ejpam-5839	1370	8	-	-	PROPN
ejpam-5839	1370	9	latif	latif	PROPN
ejpam-5839	1370	10	.	.	PUNCT
ejpam-5839	1371	1	on	on	ADP
ejpam-5839	1371	2	soft	soft	ADJ
ejpam-5839	1371	3	supra	supra	ADJ
ejpam-5839	1371	4	compactness	compactness	NOUN
ejpam-5839	1371	5	in	in	ADP
ejpam-5839	1371	6	supra	supra	PROPN
ejpam-5839	1371	7	soft	soft	ADJ
ejpam-5839	1371	8	topological	topological	ADJ
ejpam-5839	1371	9	spaces	space	NOUN
ejpam-5839	1371	10	.	.	PUNCT
ejpam-5839	1372	1	tbilisi	tbilisi	PROPN
ejpam-5839	1372	2	mathematical	mathematical	PROPN
ejpam-5839	1372	3	journal	journal	PROPN
ejpam-5839	1372	4	,	,	PUNCT
ejpam-5839	1372	5	11(1):169–178	11(1):169–178	PROPN
ejpam-5839	1372	6	,	,	PUNCT
ejpam-5839	1372	7	2018	2018	NUM
ejpam-5839	1372	8	.	.	PUNCT
ejpam-5839	1373	1	[	[	X
ejpam-5839	1373	2	40	40	NUM
ejpam-5839	1373	3	]	]	PUNCT
ejpam-5839	1373	4	a.	a.	NOUN
ejpam-5839	1373	5	m.	m.	PROPN
ejpam-5839	1373	6	abd	abd	PROPN
ejpam-5839	1373	7	el	el	PROPN
ejpam-5839	1373	8	-	-	PROPN
ejpam-5839	1373	9	latif	latif	PROPN
ejpam-5839	1373	10	and	and	CCONJ
ejpam-5839	1373	11	r.	r.	PROPN
ejpam-5839	1373	12	a.	a.	PROPN
ejpam-5839	1373	13	hosny	hosny	PROPN
ejpam-5839	1373	14	.	.	PUNCT
ejpam-5839	1374	1	supra	supra	PROPN
ejpam-5839	1374	2	open	open	VERB
ejpam-5839	1374	3	soft	soft	ADJ
ejpam-5839	1374	4	sets	set	NOUN
ejpam-5839	1374	5	and	and	CCONJ
ejpam-5839	1374	6	associated	associate	VERB
ejpam-5839	1374	7	soft	soft	ADJ
ejpam-5839	1374	8	separation	separation	NOUN
ejpam-5839	1374	9	axioms	axiom	NOUN
ejpam-5839	1374	10	.	.	PUNCT
ejpam-5839	1375	1	international	international	ADJ
ejpam-5839	1375	2	journal	journal	NOUN
ejpam-5839	1375	3	of	of	ADP
ejpam-5839	1375	4	advances	advance	NOUN
ejpam-5839	1375	5	in	in	ADP
ejpam-5839	1375	6	mathematics	mathematic	NOUN
ejpam-5839	1375	7	,	,	PUNCT
ejpam-5839	1375	8	6:68–81	6:68–81	VERB
ejpam-5839	1375	9	,	,	PUNCT
ejpam-5839	1375	10	2017	2017	NUM
ejpam-5839	1375	11	.	.	PUNCT
ejpam-5839	1376	1	[	[	X
ejpam-5839	1376	2	41	41	NUM
ejpam-5839	1376	3	]	]	PUNCT
ejpam-5839	1376	4	a.	a.	NOUN
ejpam-5839	1376	5	m.	m.	PROPN
ejpam-5839	1376	6	abd	abd	PROPN
ejpam-5839	1376	7	el	el	PROPN
ejpam-5839	1376	8	-	-	PROPN
ejpam-5839	1376	9	latif	latif	PROPN
ejpam-5839	1376	10	and	and	CCONJ
ejpam-5839	1376	11	r.	r.	PROPN
ejpam-5839	1376	12	a.	a.	PROPN
ejpam-5839	1376	13	hosny	hosny	PROPN
ejpam-5839	1376	14	.	.	PUNCT
ejpam-5839	1376	15	soft	soft	ADJ
ejpam-5839	1376	16	supra	supra	PROPN
ejpam-5839	1376	17	extra	extra	ADJ
ejpam-5839	1376	18	strongly	strongly	ADV
ejpam-5839	1376	19	generalized	generalize	VERB
ejpam-5839	1376	20	closed	closed	ADJ
ejpam-5839	1376	21	.	.	PUNCT
ejpam-5839	1377	1	analele	analele	PROPN
ejpam-5839	1377	2	university	university	PROPN
ejpam-5839	1377	3	of	of	ADP
ejpam-5839	1377	4	oradea	oradea	PROPN
ejpam-5839	1377	5	,	,	PUNCT
ejpam-5839	1377	6	fascicula	fascicula	PROPN
ejpam-5839	1377	7	matematica	matematica	PROPN
ejpam-5839	1377	8	,	,	PUNCT
ejpam-5839	1377	9	24(1):103–112	24(1):103–112	PROPN
ejpam-5839	1377	10	,	,	PUNCT
ejpam-5839	1377	11	2017	2017	NUM
ejpam-5839	1377	12	.	.	PUNCT
ejpam-5839	1378	1	[	[	X
ejpam-5839	1378	2	42	42	NUM
ejpam-5839	1378	3	]	]	PUNCT
ejpam-5839	1378	4	a.	a.	NOUN
ejpam-5839	1378	5	m.	m.	PROPN
ejpam-5839	1378	6	abd	abd	PROPN
ejpam-5839	1378	7	el	el	PROPN
ejpam-5839	1378	8	-	-	PROPN
ejpam-5839	1378	9	latif	latif	PROPN
ejpam-5839	1378	10	and	and	CCONJ
ejpam-5839	1378	11	r.	r.	PROPN
ejpam-5839	1378	12	a.	a.	PROPN
ejpam-5839	1378	13	hosny	hosny	PROPN
ejpam-5839	1378	14	.	.	PUNCT
ejpam-5839	1379	1	supra	supra	PROPN
ejpam-5839	1379	2	soft	soft	ADJ
ejpam-5839	1379	3	separation	separation	NOUN
ejpam-5839	1379	4	axioms	axiom	NOUN
ejpam-5839	1379	5	and	and	CCONJ
ejpam-5839	1379	6	supra	supra	PROPN
ejpam-5839	1379	7	irresoluteness	irresoluteness	NOUN
ejpam-5839	1379	8	based	base	VERB
ejpam-5839	1379	9	on	on	ADP
ejpam-5839	1379	10	supra	supra	PROPN
ejpam-5839	1379	11	b	b	PROPN
ejpam-5839	1379	12	-	-	PUNCT
ejpam-5839	1379	13	soft	soft	ADJ
ejpam-5839	1379	14	sets	set	NOUN
ejpam-5839	1379	15	.	.	PUNCT
ejpam-5839	1380	1	gazi	gazi	PROPN
ejpam-5839	1380	2	university	university	PROPN
ejpam-5839	1380	3	journal	journal	PROPN
ejpam-5839	1380	4	of	of	ADP
ejpam-5839	1380	5	science	science	PROPN
ejpam-5839	1380	6	,	,	PUNCT
ejpam-5839	1380	7	29(4):845–854	29(4):845–854	PROPN
ejpam-5839	1380	8	,	,	PUNCT
ejpam-5839	1380	9	2016	2016	NUM
ejpam-5839	1380	10	.	.	PUNCT
ejpam-5839	1381	1	[	[	X
ejpam-5839	1381	2	43	43	NUM
ejpam-5839	1381	3	]	]	PUNCT
ejpam-5839	1381	4	s.	s.	PROPN
ejpam-5839	1381	5	bera	bera	PROPN
ejpam-5839	1381	6	,	,	PUNCT
ejpam-5839	1381	7	s.	s.	PROPN
ejpam-5839	1381	8	m.	m.	PROPN
ejpam-5839	1381	9	,	,	PUNCT
ejpam-5839	1381	10	and	and	CCONJ
ejpam-5839	1381	11	s.	s.	PROPN
ejpam-5839	1381	12	p.	p.	PROPN
ejpam-5839	1381	13	s.	s.	PROPN
ejpam-5839	1381	14	neutrosophic	neutrosophic	PROPN
ejpam-5839	1381	15	riemann	riemann	PROPN
ejpam-5839	1381	16	integration	integration	NOUN
ejpam-5839	1381	17	and	and	CCONJ
ejpam-5839	1381	18	its	its	PRON
ejpam-5839	1381	19	properties	property	NOUN
ejpam-5839	1381	20	.	.	PUNCT
ejpam-5839	1382	1	soft	soft	ADJ
ejpam-5839	1382	2	computing	computing	NOUN
ejpam-5839	1382	3	,	,	PUNCT
ejpam-5839	1382	4	2021	2021	NUM
ejpam-5839	1382	5	.	.	PUNCT
ejpam-5839	1383	1	[	[	X
ejpam-5839	1383	2	44	44	NUM
ejpam-5839	1383	3	]	]	PUNCT
ejpam-5839	1383	4	b.	b.	PROPN
ejpam-5839	1383	5	a.	a.	PROPN
ejpam-5839	1383	6	asaad	asaad	PROPN
ejpam-5839	1383	7	,	,	PUNCT
ejpam-5839	1383	8	t.	t.	PROPN
ejpam-5839	1383	9	m.	m.	PROPN
ejpam-5839	1383	10	al	al	PROPN
ejpam-5839	1383	11	-	-	PUNCT
ejpam-5839	1383	12	shami	shami	PROPN
ejpam-5839	1383	13	,	,	PUNCT
ejpam-5839	1383	14	and	and	CCONJ
ejpam-5839	1383	15	a.	a.	NOUN
ejpam-5839	1383	16	mhemdi	mhemdi	PROPN
ejpam-5839	1383	17	.	.	PUNCT
ejpam-5839	1384	1	bioperators	bioperator	NOUN
ejpam-5839	1384	2	on	on	ADP
ejpam-5839	1384	3	tiktok	tiktok	ADJ
ejpam-5839	1384	4	video	video	NOUN
ejpam-5839	1384	5	player	player	NOUN
ejpam-5839	1384	6	bioperators	bioperator	NOUN
ejpam-5839	1384	7	on	on	ADP
ejpam-5839	1384	8	soft	soft	ADJ
ejpam-5839	1384	9	topological	topological	ADJ
ejpam-5839	1384	10	spaces	space	NOUN
ejpam-5839	1384	11	.	.	PUNCT
ejpam-5839	1385	1	aims	aim	VERB
ejpam-5839	1385	2	mathematics	mathematic	NOUN
ejpam-5839	1385	3	,	,	PUNCT
ejpam-5839	1385	4	6(11):12471–12490	6(11):12471–12490	NUM
ejpam-5839	1385	5	,	,	PUNCT
ejpam-5839	1385	6	2021	2021	NUM
ejpam-5839	1385	7	.	.	PUNCT
ejpam-5839	1386	1	[	[	X
ejpam-5839	1386	2	45	45	NUM
ejpam-5839	1386	3	]	]	PUNCT
ejpam-5839	1386	4	t.	t.	PROPN
ejpam-5839	1386	5	y.	y.	PROPN
ejpam-5839	1386	6	ozturk	ozturk	PROPN
ejpam-5839	1386	7	,	,	PUNCT
ejpam-5839	1386	8	c.	c.	PROPN
ejpam-5839	1386	9	g.	g.	PROPN
ejpam-5839	1386	10	aras	aras	PROPN
ejpam-5839	1386	11	,	,	PUNCT
ejpam-5839	1386	12	and	and	CCONJ
ejpam-5839	1386	13	s.	s.	PROPN
ejpam-5839	1386	14	bayramov	bayramov	PROPN
ejpam-5839	1386	15	.	.	PUNCT
ejpam-5839	1387	1	a	a	DET
ejpam-5839	1387	2	new	new	ADJ
ejpam-5839	1387	3	approach	approach	NOUN
ejpam-5839	1387	4	to	to	ADP
ejpam-5839	1387	5	operations	operation	NOUN
ejpam-5839	1387	6	on	on	ADP
ejpam-5839	1387	7	neutrosophic	neutrosophic	ADJ
ejpam-5839	1387	8	soft	soft	ADJ
ejpam-5839	1387	9	sets	set	NOUN
ejpam-5839	1387	10	and	and	CCONJ
ejpam-5839	1387	11	to	to	ADP
ejpam-5839	1387	12	neutrosophic	neutrosophic	ADJ
ejpam-5839	1387	13	soft	soft	ADJ
ejpam-5839	1387	14	topological	topological	ADJ
ejpam-5839	1387	15	spaces	space	NOUN
ejpam-5839	1387	16	.	.	PUNCT
ejpam-5839	1388	1	communications	communication	NOUN
ejpam-5839	1388	2	in	in	ADP
ejpam-5839	1388	3	mathematics	mathematic	NOUN
ejpam-5839	1388	4	and	and	CCONJ
ejpam-5839	1388	5	applications	application	NOUN
ejpam-5839	1388	6	,	,	PUNCT
ejpam-5839	1388	7	10(3):481–493	10(3):481–493	NUM
ejpam-5839	1388	8	,	,	PUNCT
ejpam-5839	1388	9	2019	2019	NUM
ejpam-5839	1388	10	.	.	PUNCT
ejpam-5839	1389	1	[	[	X
ejpam-5839	1389	2	46	46	NUM
ejpam-5839	1389	3	]	]	PUNCT
ejpam-5839	1389	4	t.	t.	PROPN
ejpam-5839	1389	5	y.	y.	PROPN
ejpam-5839	1389	6	ozturk	ozturk	PROPN
ejpam-5839	1389	7	,	,	PUNCT
ejpam-5839	1389	8	e.	e.	PROPN
ejpam-5839	1389	9	karatas	karatas	PROPN
ejpam-5839	1389	10	,	,	PUNCT
ejpam-5839	1389	11	and	and	CCONJ
ejpam-5839	1389	12	a.	a.	NOUN
ejpam-5839	1389	13	yolcu	yolcu	PROPN
ejpam-5839	1389	14	.	.	PUNCT
ejpam-5839	1390	1	on	on	ADP
ejpam-5839	1390	2	neutrosophic	neutrosophic	ADJ
ejpam-5839	1390	3	soft	soft	ADJ
ejpam-5839	1390	4	continuous	continuous	ADJ
ejpam-5839	1390	5	mappings	mapping	NOUN
ejpam-5839	1390	6	.	.	PUNCT
ejpam-5839	1391	1	turkish	turkish	ADJ
ejpam-5839	1391	2	journal	journal	NOUN
ejpam-5839	1391	3	of	of	ADP
ejpam-5839	1391	4	mathematics	mathematic	NOUN
ejpam-5839	1391	5	,	,	PUNCT
ejpam-5839	1391	6	45(1):81–95	45(1):81–95	NUM
ejpam-5839	1391	7	,	,	PUNCT
ejpam-5839	1391	8	2021	2021	NUM
ejpam-5839	1391	9	.	.	PUNCT
ejpam-5839	1392	1	[	[	X
ejpam-5839	1392	2	47	47	NUM
ejpam-5839	1392	3	]	]	X
ejpam-5839	1392	4	c.	c.	NOUN
ejpam-5839	1392	5	gunduz	gunduz	PROPN
ejpam-5839	1392	6	,	,	PUNCT
ejpam-5839	1392	7	t.	t.	PROPN
ejpam-5839	1392	8	y.	y.	PROPN
ejpam-5839	1392	9	ozturk	ozturk	PROPN
ejpam-5839	1392	10	,	,	PUNCT
ejpam-5839	1392	11	and	and	CCONJ
ejpam-5839	1392	12	s.	s.	PROPN
ejpam-5839	1392	13	bayramov	bayramov	PROPN
ejpam-5839	1392	14	.	.	PUNCT
ejpam-5839	1393	1	separation	separation	NOUN
ejpam-5839	1393	2	axioms	axiom	NOUN
ejpam-5839	1393	3	on	on	ADP
ejpam-5839	1393	4	neutrosophic	neutrosophic	ADJ
ejpam-5839	1393	5	soft	soft	ADJ
ejpam-5839	1393	6	topological	topological	ADJ
ejpam-5839	1393	7	spaces	space	NOUN
ejpam-5839	1393	8	.	.	PUNCT
ejpam-5839	1394	1	turkish	turkish	ADJ
ejpam-5839	1394	2	journal	journal	NOUN
ejpam-5839	1394	3	of	of	ADP
ejpam-5839	1394	4	mathematics	mathematic	NOUN
ejpam-5839	1394	5	,	,	PUNCT
ejpam-5839	1394	6	43(1):498–510	43(1):498–510	NUM
ejpam-5839	1394	7	,	,	PUNCT
ejpam-5839	1394	8	2019	2019	NUM
ejpam-5839	1394	9	.	.	PUNCT
ejpam-5839	1395	1	[	[	X
ejpam-5839	1395	2	48	48	NUM
ejpam-5839	1395	3	]	]	PUNCT
ejpam-5839	1395	4	t.	t.	PROPN
ejpam-5839	1395	5	y.	y.	PROPN
ejpam-5839	1395	6	ozturk	ozturk	PROPN
ejpam-5839	1395	7	.	.	PUNCT
ejpam-5839	1396	1	some	some	DET
ejpam-5839	1396	2	structures	structure	NOUN
ejpam-5839	1396	3	on	on	ADP
ejpam-5839	1396	4	neutrosophic	neutrosophic	ADJ
ejpam-5839	1396	5	topological	topological	ADJ
ejpam-5839	1396	6	spaces	space	NOUN
ejpam-5839	1396	7	.	.	PUNCT
ejpam-5839	1397	1	applied	apply	VERB
ejpam-5839	1397	2	mathematics	mathematic	NOUN
ejpam-5839	1397	3	and	and	CCONJ
ejpam-5839	1397	4	nonlinear	nonlinear	ADJ
ejpam-5839	1397	5	sciences	sciences	PROPN
ejpam-5839	1397	6	,	,	PUNCT
ejpam-5839	1397	7	6(1):467–478	6(1):467–478	NUM
ejpam-5839	1397	8	,	,	PUNCT
ejpam-5839	1397	9	2021	2021	NUM
ejpam-5839	1397	10	.	.	PUNCT
ejpam-5839	1398	1	[	[	X
ejpam-5839	1398	2	49	49	NUM
ejpam-5839	1398	3	]	]	PUNCT
ejpam-5839	1398	4	a.	a.	NOUN
ejpam-5839	1398	5	mehmood	mehmood	PROPN
ejpam-5839	1398	6	,	,	PUNCT
ejpam-5839	1398	7	m.	m.	NOUN
ejpam-5839	1398	8	aslam	aslam	PROPN
ejpam-5839	1398	9	,	,	PUNCT
ejpam-5839	1398	10	m.	m.	PROPN
ejpam-5839	1398	11	i.	i.	PROPN
ejpam-5839	1398	12	khan	khan	PROPN
ejpam-5839	1398	13	,	,	PUNCT
ejpam-5839	1398	14	h.	h.	PROPN
ejpam-5839	1398	15	qureshi	qureshi	PROPN
ejpam-5839	1398	16	,	,	PUNCT
ejpam-5839	1398	17	and	and	CCONJ
ejpam-5839	1398	18	c.	c.	PROPN
ejpam-5839	1398	19	park	park	PROPN
ejpam-5839	1398	20	.	.	PUNCT
ejpam-5839	1399	1	a	a	DET
ejpam-5839	1399	2	new	new	ADJ
ejpam-5839	1399	3	attempt	attempt	NOUN
ejpam-5839	1399	4	to	to	PART
ejpam-5839	1399	5	neutrosophic	neutrosophic	ADJ
ejpam-5839	1399	6	soft	soft	ADJ
ejpam-5839	1399	7	bi	bi	ADJ
ejpam-5839	1399	8	-	-	ADJ
ejpam-5839	1399	9	topological	topological	ADJ
ejpam-5839	1399	10	spaces	space	NOUN
ejpam-5839	1399	11	.	.	PUNCT
ejpam-5839	1400	1	computer	computer	NOUN
ejpam-5839	1400	2	modeling	modeling	NOUN
ejpam-5839	1400	3	in	in	ADP
ejpam-5839	1400	4	engineering	engineering	NOUN
ejpam-5839	1400	5	and	and	CCONJ
ejpam-5839	1400	6	sciences	science	NOUN
ejpam-5839	1400	7	,	,	PUNCT
ejpam-5839	1400	8	10(3):1565–1585	10(3):1565–1585	NUM
ejpam-5839	1400	9	,	,	PUNCT
ejpam-5839	1400	10	2022	2022	NUM
ejpam-5839	1400	11	.	.	PUNCT
ejpam-5839	1401	1	[	[	X
ejpam-5839	1401	2	50	50	NUM
ejpam-5839	1401	3	]	]	PUNCT
ejpam-5839	1401	4	i.	i.	NOUN
ejpam-5839	1401	5	deli	deli	PROPN
ejpam-5839	1401	6	and	and	CCONJ
ejpam-5839	1401	7	s.	s.	PROPN
ejpam-5839	1401	8	broumi	broumi	PROPN
ejpam-5839	1401	9	.	.	PUNCT
ejpam-5839	1402	1	neutrosophic	neutrosophic	ADJ
ejpam-5839	1402	2	soft	soft	ADJ
ejpam-5839	1402	3	relations	relation	NOUN
ejpam-5839	1402	4	and	and	CCONJ
ejpam-5839	1402	5	some	some	DET
ejpam-5839	1402	6	properties	property	NOUN
ejpam-5839	1402	7	.	.	PUNCT
ejpam-5839	1403	1	annals	annal	NOUN
ejpam-5839	1403	2	of	of	ADP
ejpam-5839	1403	3	fuzzy	fuzzy	ADJ
ejpam-5839	1403	4	mathematics	mathematic	NOUN
ejpam-5839	1403	5	and	and	CCONJ
ejpam-5839	1403	6	informatics	informatic	NOUN
ejpam-5839	1403	7	,	,	PUNCT
ejpam-5839	1403	8	9(1):169–182	9(1):169–182	NUM
ejpam-5839	1403	9	,	,	PUNCT
ejpam-5839	1403	10	2015	2015	NUM
ejpam-5839	1403	11	.	.	PUNCT
ejpam-5839	1404	1	[	[	X
ejpam-5839	1404	2	51	51	NUM
ejpam-5839	1404	3	]	]	PUNCT
ejpam-5839	1404	4	t.	t.	NOUN
ejpam-5839	1404	5	bera	bera	NOUN
ejpam-5839	1404	6	and	and	CCONJ
ejpam-5839	1404	7	n.	n.	PROPN
ejpam-5839	1404	8	k.	k.	PROPN
ejpam-5839	1404	9	mahapatra	mahapatra	PROPN
ejpam-5839	1404	10	.	.	PUNCT
ejpam-5839	1405	1	introduction	introduction	NOUN
ejpam-5839	1405	2	to	to	ADP
ejpam-5839	1405	3	neutrosophic	neutrosophic	ADJ
ejpam-5839	1405	4	soft	soft	ADJ
ejpam-5839	1405	5	topological	topological	ADJ
ejpam-5839	1405	6	space	space	NOUN
ejpam-5839	1405	7	.	.	PUNCT
ejpam-5839	1406	1	opsearch	opsearch	PROPN
ejpam-5839	1406	2	,	,	PUNCT
ejpam-5839	1406	3	54(4):841–867	54(4):841–867	PROPN
ejpam-5839	1406	4	,	,	PUNCT
ejpam-5839	1406	5	2017	2017	NUM
ejpam-5839	1406	6	.	.	PUNCT
ejpam-5839	1407	1	a.	a.	NOUN
ejpam-5839	1407	2	shihadeh	shihadeh	VERB
ejpam-5839	1407	3	et	et	PROPN
ejpam-5839	1407	4	al	al	PROPN
ejpam-5839	1407	5	.	.	PUNCT
ejpam-5839	1407	6	/	/	SYM
ejpam-5839	1407	7	eur	eur	PROPN
ejpam-5839	1407	8	.	.	PUNCT
ejpam-5839	1408	1	j.	j.	PROPN
ejpam-5839	1408	2	pure	pure	PROPN
ejpam-5839	1408	3	appl	appl	PROPN
ejpam-5839	1408	4	.	.	PROPN
ejpam-5839	1408	5	math	math	PROPN
ejpam-5839	1408	6	,	,	PUNCT
ejpam-5839	1408	7	18	18	NUM
ejpam-5839	1408	8	(	(	PUNCT
ejpam-5839	1408	9	2	2	NUM
ejpam-5839	1408	10	)	)	PUNCT
ejpam-5839	1408	11	(	(	PUNCT
ejpam-5839	1408	12	2025	2025	NUM
ejpam-5839	1408	13	)	)	PUNCT
ejpam-5839	1408	14	,	,	PUNCT
ejpam-5839	1408	15	5839	5839	NUM
ejpam-5839	1408	16	54	54	NUM
ejpam-5839	1408	17	of	of	ADP
ejpam-5839	1408	18	54	54	NUM
ejpam-5839	1408	19	[	[	X
ejpam-5839	1408	20	52	52	NUM
ejpam-5839	1408	21	]	]	PUNCT
ejpam-5839	1408	22	t.	t.	PROPN
ejpam-5839	1408	23	h.	h.	PROPN
ejpam-5839	1408	24	s.	s.	PROPN
ejpam-5839	1408	25	nguyen	nguyen	PROPN
ejpam-5839	1408	26	,	,	PUNCT
ejpam-5839	1408	27	n.	n.	PROPN
ejpam-5839	1408	28	p.	p.	PROPN
ejpam-5839	1408	29	dong	dong	PROPN
ejpam-5839	1408	30	,	,	PUNCT
ejpam-5839	1408	31	and	and	CCONJ
ejpam-5839	1408	32	a.	a.	PROPN
ejpam-5839	1408	33	l.	l.	PROPN
ejpam-5839	1408	34	h.	h.	PROPN
ejpam-5839	1408	35	alireza	alireza	PROPN
ejpam-5839	1408	36	.	.	PUNCT
ejpam-5839	1409	1	linear	linear	ADJ
ejpam-5839	1409	2	quadratic	quadratic	ADJ
ejpam-5839	1409	3	regulator	regulator	NOUN
ejpam-5839	1409	4	problem	problem	NOUN
ejpam-5839	1409	5	governed	govern	VERB
ejpam-5839	1409	6	by	by	ADP
ejpam-5839	1409	7	granular	granular	ADJ
ejpam-5839	1409	8	neutrosophic	neutrosophic	ADJ
ejpam-5839	1409	9	fractional	fractional	ADJ
ejpam-5839	1409	10	differential	differential	ADJ
ejpam-5839	1409	11	equations	equation	NOUN
ejpam-5839	1409	12	.	.	PUNCT
ejpam-5839	1410	1	isa	isa	NOUN
ejpam-5839	1410	2	transactions	transaction	NOUN
ejpam-5839	1410	3	,	,	PUNCT
ejpam-5839	1410	4	97:296–316	97:296–316	NUM
ejpam-5839	1410	5	,	,	PUNCT
ejpam-5839	1410	6	2020	2020	NUM
ejpam-5839	1410	7	.	.	PUNCT
ejpam-5839	1411	1	[	[	X
ejpam-5839	1411	2	53	53	NUM
ejpam-5839	1411	3	]	]	PUNCT
ejpam-5839	1411	4	s.	s.	PROPN
ejpam-5839	1411	5	moi	moi	PROPN
ejpam-5839	1411	6	,	,	PUNCT
ejpam-5839	1411	7	s.	s.	PROPN
ejpam-5839	1411	8	biswas	biswas	PROPN
ejpam-5839	1411	9	,	,	PUNCT
ejpam-5839	1411	10	and	and	CCONJ
ejpam-5839	1411	11	s.	s.	PROPN
ejpam-5839	1411	12	pal	pal	PROPN
ejpam-5839	1411	13	.	.	PUNCT
ejpam-5839	1412	1	second	second	ADJ
ejpam-5839	1412	2	-	-	PUNCT
ejpam-5839	1412	3	order	order	NOUN
ejpam-5839	1412	4	neutrosophic	neutrosophic	ADJ
ejpam-5839	1412	5	boundary	boundary	ADJ
ejpam-5839	1412	6	-	-	PUNCT
ejpam-5839	1412	7	value	value	NOUN
ejpam-5839	1412	8	problem	problem	NOUN
ejpam-5839	1412	9	.	.	PUNCT
ejpam-5839	1413	1	complex	complex	ADJ
ejpam-5839	1413	2	and	and	CCONJ
ejpam-5839	1413	3	intelligent	intelligent	ADJ
ejpam-5839	1413	4	systems	system	NOUN
ejpam-5839	1413	5	,	,	PUNCT
ejpam-5839	1413	6	7(2):1079–1098	7(2):1079–1098	NUM
ejpam-5839	1413	7	,	,	PUNCT
ejpam-5839	1413	8	2021	2021	NUM
ejpam-5839	1413	9	.	.	PUNCT
ejpam-5839	1414	1	[	[	X
ejpam-5839	1414	2	54	54	NUM
ejpam-5839	1414	3	]	]	PUNCT
ejpam-5839	1414	4	t.	t.	PROPN
ejpam-5839	1414	5	m.	m.	PROPN
ejpam-5839	1414	6	al	al	PROPN
ejpam-5839	1414	7	-	-	PUNCT
ejpam-5839	1414	8	shami	shami	PROPN
ejpam-5839	1414	9	and	and	CCONJ
ejpam-5839	1414	10	m.	m.	PROPN
ejpam-5839	1414	11	e.	e.	PROPN
ejpam-5839	1414	12	el	el	PROPN
ejpam-5839	1414	13	-	-	PROPN
ejpam-5839	1414	14	shafei	shafei	PROPN
ejpam-5839	1414	15	.	.	PUNCT
ejpam-5839	1415	1	on	on	ADP
ejpam-5839	1415	2	supra	supra	PROPN
ejpam-5839	1415	3	soft	soft	ADJ
ejpam-5839	1415	4	topological	topological	ADJ
ejpam-5839	1415	5	ordered	order	VERB
ejpam-5839	1415	6	spaces	space	NOUN
ejpam-5839	1415	7	.	.	PUNCT
ejpam-5839	1416	1	arab	arab	PROPN
ejpam-5839	1416	2	journal	journal	PROPN
ejpam-5839	1416	3	of	of	ADP
ejpam-5839	1416	4	basic	basic	ADJ
ejpam-5839	1416	5	and	and	CCONJ
ejpam-5839	1416	6	applied	applied	ADJ
ejpam-5839	1416	7	sciences	science	NOUN
ejpam-5839	1416	8	,	,	PUNCT
ejpam-5839	1416	9	2021	2021	NUM
ejpam-5839	1416	10	.	.	PUNCT
ejpam-5839	1417	1	[	[	X
ejpam-5839	1417	2	55	55	NUM
ejpam-5839	1417	3	]	]	PUNCT
ejpam-5839	1417	4	t.	t.	PROPN
ejpam-5839	1417	5	m.	m.	PROPN
ejpam-5839	1417	6	al	al	PROPN
ejpam-5839	1417	7	-	-	PUNCT
ejpam-5839	1417	8	shami	shami	PROPN
ejpam-5839	1417	9	and	and	CCONJ
ejpam-5839	1417	10	m.	m.	PROPN
ejpam-5839	1417	11	e.	e.	PROPN
ejpam-5839	1417	12	el	el	PROPN
ejpam-5839	1417	13	-	-	PROPN
ejpam-5839	1417	14	shafei	shafei	PROPN
ejpam-5839	1417	15	.	.	PUNCT
ejpam-5839	1418	1	two	two	NUM
ejpam-5839	1418	2	types	type	NOUN
ejpam-5839	1418	3	of	of	ADP
ejpam-5839	1418	4	separation	separation	NOUN
ejpam-5839	1418	5	axioms	axiom	NOUN
ejpam-5839	1418	6	on	on	ADP
ejpam-5839	1418	7	supra	supra	PROPN
ejpam-5839	1418	8	soft	soft	ADJ
ejpam-5839	1418	9	topological	topological	ADJ
ejpam-5839	1418	10	spaces	space	NOUN
ejpam-5839	1418	11	.	.	PUNCT
ejpam-5839	1419	1	unknown	unknown	ADJ
ejpam-5839	1419	2	journal	journal	NOUN
ejpam-5839	1419	3	,	,	PUNCT
ejpam-5839	1419	4	2021	2021	NUM
ejpam-5839	1419	5	.	.	PUNCT
ejpam-5839	1420	1	[	[	X
ejpam-5839	1420	2	56	56	NUM
ejpam-5839	1420	3	]	]	X
ejpam-5839	1420	4	h.	h.	PROPN
ejpam-5839	1420	5	l.	l.	PROPN
ejpam-5839	1420	6	royden	royden	PROPN
ejpam-5839	1420	7	and	and	CCONJ
ejpam-5839	1420	8	p.	p.	PROPN
ejpam-5839	1420	9	fitzpatrick	fitzpatrick	PROPN
ejpam-5839	1420	10	.	.	PUNCT
ejpam-5839	1421	1	real	real	ADJ
ejpam-5839	1421	2	analysis	analysis	NOUN
ejpam-5839	1421	3	.	.	PUNCT
ejpam-5839	1422	1	macmillan	macmillan	PROPN
ejpam-5839	1422	2	,	,	PUNCT
ejpam-5839	1422	3	new	new	PROPN
ejpam-5839	1422	4	york	york	PROPN
ejpam-5839	1422	5	,	,	PUNCT
ejpam-5839	1422	6	32	32	NUM
ejpam-5839	1422	7	edition	edition	NOUN
ejpam-5839	1422	8	,	,	PUNCT
ejpam-5839	1422	9	1988	1988	NUM
ejpam-5839	1422	10	.	.	PUNCT