id	sid	tid	token	lemma	pos
ejpam-4808	1	1	european	european	PROPN
ejpam-4808	1	2	journal	journal	PROPN
ejpam-4808	1	3	of	of	ADP
ejpam-4808	1	4	pure	pure	ADJ
ejpam-4808	1	5	and	and	CCONJ
ejpam-4808	1	6	applied	apply	VERB
ejpam-4808	1	7	mathematics	mathematic	NOUN
ejpam-4808	1	8	vol	vol	NOUN
ejpam-4808	1	9	.	.	PUNCT
ejpam-4808	2	1	16	16	NUM
ejpam-4808	2	2	,	,	PUNCT
ejpam-4808	2	3	no	no	INTJ
ejpam-4808	2	4	.	.	NOUN
ejpam-4808	2	5	3	3	NUM
ejpam-4808	2	6	,	,	PUNCT
ejpam-4808	2	7	2023	2023	NUM
ejpam-4808	2	8	,	,	PUNCT
ejpam-4808	2	9	1980	1980	NUM
ejpam-4808	2	10	-	-	SYM
ejpam-4808	2	11	1990	1990	NUM
ejpam-4808	2	12	issn	issn	PROPN
ejpam-4808	2	13	1307	1307	NUM
ejpam-4808	2	14	-	-	SYM
ejpam-4808	2	15	5543	5543	NUM
ejpam-4808	2	16	–	–	PUNCT
ejpam-4808	3	1	ejpam.com	ejpam.com	X
ejpam-4808	3	2	published	publish	VERB
ejpam-4808	3	3	by	by	ADP
ejpam-4808	3	4	new	new	PROPN
ejpam-4808	3	5	york	york	PROPN
ejpam-4808	3	6	business	business	PROPN
ejpam-4808	3	7	global	global	ADJ
ejpam-4808	3	8	note	note	NOUN
ejpam-4808	3	9	on	on	ADP
ejpam-4808	3	10	generalized	generalized	ADJ
ejpam-4808	3	11	neighborhoods	neighborhood	NOUN
ejpam-4808	3	12	structures	structure	NOUN
ejpam-4808	3	13	in	in	ADP
ejpam-4808	3	14	fuzzy	fuzzy	ADJ
ejpam-4808	3	15	bitopological	bitopological	ADJ
ejpam-4808	3	16	spaces	space	NOUN
ejpam-4808	3	17	ahlam	ahlam	PROPN
ejpam-4808	3	18	ahmed	ahme	VERB
ejpam-4808	3	19	alharbi1,2	alharbi1,2	PROPN
ejpam-4808	3	20	,	,	PUNCT
ejpam-4808	3	21	adem	adem	PROPN
ejpam-4808	3	22	kilicman2,∗	kilicman2,∗	PROPN
ejpam-4808	3	23	1	1	NUM
ejpam-4808	3	24	department	department	NOUN
ejpam-4808	3	25	of	of	ADP
ejpam-4808	3	26	mathematics	mathematic	NOUN
ejpam-4808	3	27	,	,	PUNCT
ejpam-4808	3	28	faculty	faculty	NOUN
ejpam-4808	3	29	of	of	ADP
ejpam-4808	3	30	science	science	NOUN
ejpam-4808	3	31	,	,	PUNCT
ejpam-4808	3	32	taibah	taibah	PROPN
ejpam-4808	3	33	university	university	PROPN
ejpam-4808	3	34	,	,	PUNCT
ejpam-4808	3	35	madinah	madinah	PROPN
ejpam-4808	3	36	42353	42353	NUM
ejpam-4808	3	37	,	,	PUNCT
ejpam-4808	3	38	kingdom	kingdom	NOUN
ejpam-4808	3	39	of	of	ADP
ejpam-4808	3	40	saudi	saudi	PROPN
ejpam-4808	3	41	arabia	arabia	PROPN
ejpam-4808	3	42	2	2	NUM
ejpam-4808	3	43	department	department	NOUN
ejpam-4808	3	44	of	of	ADP
ejpam-4808	3	45	mathematics	mathematic	NOUN
ejpam-4808	3	46	and	and	CCONJ
ejpam-4808	3	47	statistics	statistic	NOUN
ejpam-4808	3	48	,	,	PUNCT
ejpam-4808	3	49	faculty	faculty	NOUN
ejpam-4808	3	50	of	of	ADP
ejpam-4808	3	51	science	science	NOUN
ejpam-4808	3	52	,	,	PUNCT
ejpam-4808	3	53	universiti	universiti	PROPN
ejpam-4808	3	54	putra	putra	PROPN
ejpam-4808	3	55	malaysia	malaysia	PROPN
ejpam-4808	3	56	,	,	PUNCT
ejpam-4808	3	57	43400	43400	NUM
ejpam-4808	3	58	upm	upm	PROPN
ejpam-4808	3	59	serdang	serdang	PROPN
ejpam-4808	3	60	,	,	PUNCT
ejpam-4808	3	61	selangor	selangor	PROPN
ejpam-4808	3	62	,	,	PUNCT
ejpam-4808	3	63	malaysia	malaysia	PROPN
ejpam-4808	3	64	abstract	abstract	NOUN
ejpam-4808	3	65	.	.	PUNCT
ejpam-4808	4	1	this	this	DET
ejpam-4808	4	2	article	article	NOUN
ejpam-4808	4	3	’s	’s	PART
ejpam-4808	4	4	main	main	ADJ
ejpam-4808	4	5	aim	aim	NOUN
ejpam-4808	4	6	is	be	AUX
ejpam-4808	4	7	to	to	PART
ejpam-4808	4	8	study	study	VERB
ejpam-4808	4	9	the	the	DET
ejpam-4808	4	10	concepts	concept	NOUN
ejpam-4808	4	11	of	of	ADP
ejpam-4808	4	12	the	the	DET
ejpam-4808	4	13	generalized	generalized	ADJ
ejpam-4808	4	14	neighborhood	neighborhood	NOUN
ejpam-4808	4	15	and	and	CCONJ
ejpam-4808	4	16	generalized	generalized	ADJ
ejpam-4808	4	17	quasi	quasi	NOUN
ejpam-4808	4	18	-	-	NOUN
ejpam-4808	4	19	neighborhood	neighborhood	NOUN
ejpam-4808	4	20	in	in	ADP
ejpam-4808	4	21	fuzzy	fuzzy	ADJ
ejpam-4808	4	22	bitopological	bitopological	ADJ
ejpam-4808	4	23	spaces	space	NOUN
ejpam-4808	4	24	.	.	PUNCT
ejpam-4808	5	1	it	it	PRON
ejpam-4808	5	2	also	also	ADV
ejpam-4808	5	3	introduces	introduce	VERB
ejpam-4808	5	4	fundamental	fundamental	ADJ
ejpam-4808	5	5	theorems	theorem	NOUN
ejpam-4808	5	6	for	for	ADP
ejpam-4808	5	7	determining	determine	VERB
ejpam-4808	5	8	the	the	DET
ejpam-4808	5	9	relationships	relationship	NOUN
ejpam-4808	5	10	between	between	ADP
ejpam-4808	5	11	them	they	PRON
ejpam-4808	5	12	.	.	PUNCT
ejpam-4808	6	1	additionally	additionally	ADV
ejpam-4808	6	2	,	,	PUNCT
ejpam-4808	6	3	some	some	DET
ejpam-4808	6	4	significant	significant	ADJ
ejpam-4808	6	5	examples	example	NOUN
ejpam-4808	6	6	were	be	AUX
ejpam-4808	6	7	examined	examine	VERB
ejpam-4808	6	8	to	to	PART
ejpam-4808	6	9	demonstrate	demonstrate	VERB
ejpam-4808	6	10	the	the	DET
ejpam-4808	6	11	significance	significance	NOUN
ejpam-4808	6	12	of	of	ADP
ejpam-4808	6	13	the	the	DET
ejpam-4808	6	14	interconnections	interconnection	NOUN
ejpam-4808	6	15	,	,	PUNCT
ejpam-4808	6	16	some	some	DET
ejpam-4808	6	17	theorems	theorem	NOUN
ejpam-4808	6	18	were	be	AUX
ejpam-4808	6	19	also	also	ADV
ejpam-4808	6	20	introduced	introduce	VERB
ejpam-4808	6	21	to	to	PART
ejpam-4808	6	22	study	study	VERB
ejpam-4808	6	23	some	some	DET
ejpam-4808	6	24	main	main	ADJ
ejpam-4808	6	25	properties	property	NOUN
ejpam-4808	6	26	of	of	ADP
ejpam-4808	6	27	neighborhood	neighborhood	NOUN
ejpam-4808	6	28	structures	structure	NOUN
ejpam-4808	6	29	.	.	PUNCT
ejpam-4808	7	1	finally	finally	ADV
ejpam-4808	7	2	,	,	PUNCT
ejpam-4808	7	3	we	we	PRON
ejpam-4808	7	4	also	also	ADV
ejpam-4808	7	5	studied	study	VERB
ejpam-4808	7	6	the	the	DET
ejpam-4808	7	7	concepts	concept	NOUN
ejpam-4808	7	8	of	of	ADP
ejpam-4808	7	9	closure	closure	NOUN
ejpam-4808	7	10	,	,	PUNCT
ejpam-4808	7	11	interior	interior	NOUN
ejpam-4808	7	12	,	,	PUNCT
ejpam-4808	7	13	and	and	CCONJ
ejpam-4808	7	14	each	each	PRON
ejpam-4808	7	15	of	of	ADP
ejpam-4808	7	16	their	their	PRON
ejpam-4808	7	17	critical	critical	ADJ
ejpam-4808	7	18	theories	theory	NOUN
ejpam-4808	7	19	and	and	CCONJ
ejpam-4808	7	20	properties	property	NOUN
ejpam-4808	7	21	by	by	ADP
ejpam-4808	7	22	generalized	generalized	ADJ
ejpam-4808	7	23	neighborhood	neighborhood	NOUN
ejpam-4808	7	24	systems	system	NOUN
ejpam-4808	7	25	in	in	ADP
ejpam-4808	7	26	fuzzy	fuzzy	ADJ
ejpam-4808	7	27	bitopological	bitopological	ADJ
ejpam-4808	7	28	spaces	space	NOUN
ejpam-4808	7	29	.	.	PUNCT
ejpam-4808	8	1	2020	2020	NUM
ejpam-4808	8	2	mathematics	mathematic	NOUN
ejpam-4808	8	3	subject	subject	NOUN
ejpam-4808	8	4	classifications	classification	NOUN
ejpam-4808	8	5	:	:	PUNCT
ejpam-4808	8	6	03b52	03b52	NUM
ejpam-4808	8	7	,	,	PUNCT
ejpam-4808	8	8	03e72	03e72	NUM
ejpam-4808	8	9	,	,	PUNCT
ejpam-4808	8	10	54a40	54a40	NUM
ejpam-4808	8	11	,	,	PUNCT
ejpam-4808	8	12	54e55	54e55	NUM
ejpam-4808	8	13	,	,	PUNCT
ejpam-4808	8	14	57n40	57n40	NUM
ejpam-4808	8	15	,	,	PUNCT
ejpam-4808	8	16	94d05	94d05	NUM
ejpam-4808	8	17	key	key	ADJ
ejpam-4808	8	18	words	word	NOUN
ejpam-4808	8	19	and	and	CCONJ
ejpam-4808	8	20	phrases	phrase	NOUN
ejpam-4808	8	21	:	:	PUNCT
ejpam-4808	8	22	fuzzy	fuzzy	ADJ
ejpam-4808	8	23	bitopological	bitopological	ADJ
ejpam-4808	8	24	spaces	space	NOUN
ejpam-4808	8	25	(	(	PUNCT
ejpam-4808	8	26	fbts	fbt	NOUN
ejpam-4808	8	27	)	)	PUNCT
ejpam-4808	8	28	,	,	PUNCT
ejpam-4808	8	29	fuzzy	fuzzy	ADJ
ejpam-4808	8	30	generalized	generalize	VERB
ejpam-4808	8	31	closed	closed	ADJ
ejpam-4808	8	32	sets	set	NOUN
ejpam-4808	8	33	(	(	PUNCT
ejpam-4808	8	34	g	g	NOUN
ejpam-4808	8	35	−	−	PROPN
ejpam-4808	8	36	closed	closed	ADJ
ejpam-4808	8	37	)	)	PUNCT
ejpam-4808	8	38	,	,	PUNCT
ejpam-4808	8	39	fuzzy	fuzzy	ADJ
ejpam-4808	8	40	closure	closure	NOUN
ejpam-4808	8	41	operator	operator	NOUN
ejpam-4808	8	42	(	(	PUNCT
ejpam-4808	8	43	cl	cl	NOUN
ejpam-4808	8	44	)	)	PUNCT
ejpam-4808	8	45	,	,	PUNCT
ejpam-4808	8	46	fuzzy	fuzzy	ADJ
ejpam-4808	8	47	interior	interior	ADJ
ejpam-4808	8	48	operator	operator	NOUN
ejpam-4808	8	49	(	(	PUNCT
ejpam-4808	8	50	int	int	NOUN
ejpam-4808	8	51	)	)	PUNCT
ejpam-4808	8	52	,	,	PUNCT
ejpam-4808	8	53	fuzzy	fuzzy	ADJ
ejpam-4808	8	54	generalized	generalize	VERB
ejpam-4808	8	55	neigborhood	neigborhood	PROPN
ejpam-4808	8	56	(	(	PUNCT
ejpam-4808	8	57	ngφ	ngφ	ADJ
ejpam-4808	8	58	)	)	PUNCT
ejpam-4808	8	59	,	,	PUNCT
ejpam-4808	8	60	and	and	CCONJ
ejpam-4808	8	61	fuzzy	fuzzy	ADJ
ejpam-4808	8	62	generalized	generalize	VERB
ejpam-4808	8	63	quasi	quasi	X
ejpam-4808	8	64	neigborhood	neigborhood	PROPN
ejpam-4808	8	65	(	(	PUNCT
ejpam-4808	8	66	ngφq	ngφq	NOUN
ejpam-4808	8	67	)	)	PUNCT
ejpam-4808	8	68	1	1	NUM
ejpam-4808	8	69	.	.	X
ejpam-4808	8	70	introduction	introduction	NOUN
ejpam-4808	8	71	in	in	ADP
ejpam-4808	8	72	this	this	DET
ejpam-4808	8	73	project	project	NOUN
ejpam-4808	8	74	,	,	PUNCT
ejpam-4808	8	75	we	we	PRON
ejpam-4808	8	76	have	have	AUX
ejpam-4808	8	77	prioritized	prioritize	VERB
ejpam-4808	8	78	our	our	PRON
ejpam-4808	8	79	study	study	NOUN
ejpam-4808	8	80	on	on	ADP
ejpam-4808	8	81	fuzzy	fuzzy	ADJ
ejpam-4808	8	82	bitopology	bitopology	NOUN
ejpam-4808	8	83	,	,	PUNCT
ejpam-4808	8	84	which	which	PRON
ejpam-4808	8	85	derived	derive	VERB
ejpam-4808	8	86	from	from	ADP
ejpam-4808	8	87	fuzzy	fuzzy	ADJ
ejpam-4808	8	88	topology	topology	NOUN
ejpam-4808	8	89	that	that	PRON
ejpam-4808	8	90	was	be	AUX
ejpam-4808	8	91	first	first	ADV
ejpam-4808	8	92	introduced	introduce	VERB
ejpam-4808	8	93	in	in	ADP
ejpam-4808	8	94	1965	1965	NUM
ejpam-4808	8	95	by	by	ADP
ejpam-4808	8	96	the	the	DET
ejpam-4808	8	97	scientist	scientist	NOUN
ejpam-4808	8	98	zadeh	zadeh	PROPN
ejpam-4808	9	1	[	[	X
ejpam-4808	9	2	8	8	NUM
ejpam-4808	9	3	]	]	PUNCT
ejpam-4808	9	4	.	.	PUNCT
ejpam-4808	10	1	following	follow	VERB
ejpam-4808	10	2	this	this	PRON
ejpam-4808	10	3	,	,	PUNCT
ejpam-4808	10	4	many	many	ADJ
ejpam-4808	10	5	researchers	researcher	NOUN
ejpam-4808	10	6	applied	apply	VERB
ejpam-4808	10	7	fundamental	fundamental	ADJ
ejpam-4808	10	8	ideas	idea	NOUN
ejpam-4808	10	9	on	on	ADP
ejpam-4808	10	10	fuzzy	fuzzy	ADJ
ejpam-4808	10	11	settings	setting	NOUN
ejpam-4808	10	12	from	from	ADP
ejpam-4808	10	13	general	general	ADJ
ejpam-4808	10	14	topology	topology	NOUN
ejpam-4808	10	15	and	and	CCONJ
ejpam-4808	10	16	improved	improve	VERB
ejpam-4808	10	17	the	the	DET
ejpam-4808	10	18	concept	concept	NOUN
ejpam-4808	10	19	of	of	ADP
ejpam-4808	10	20	fuzzy	fuzzy	ADJ
ejpam-4808	10	21	topology	topology	NOUN
ejpam-4808	10	22	.	.	PUNCT
ejpam-4808	11	1	such	such	ADJ
ejpam-4808	11	2	as	as	ADP
ejpam-4808	11	3	chang	chang	PROPN
ejpam-4808	11	4	,	,	PUNCT
ejpam-4808	11	5	in	in	ADP
ejpam-4808	11	6	1968	1968	NUM
ejpam-4808	11	7	introduced	introduce	VERB
ejpam-4808	11	8	some	some	DET
ejpam-4808	11	9	fuzzy	fuzzy	ADJ
ejpam-4808	11	10	concepts	concept	NOUN
ejpam-4808	11	11	in	in	ADP
ejpam-4808	11	12	fuzzy	fuzzy	ADJ
ejpam-4808	11	13	topology	topology	NOUN
ejpam-4808	11	14	[	[	X
ejpam-4808	11	15	4	4	NUM
ejpam-4808	11	16	]	]	PUNCT
ejpam-4808	11	17	.	.	PUNCT
ejpam-4808	12	1	in	in	ADP
ejpam-4808	12	2	addition	addition	NOUN
ejpam-4808	12	3	,	,	PUNCT
ejpam-4808	12	4	in	in	ADP
ejpam-4808	12	5	1989	1989	NUM
ejpam-4808	12	6	kandil	kandil	NOUN
ejpam-4808	12	7	introduced	introduce	VERB
ejpam-4808	12	8	fuzzy	fuzzy	ADJ
ejpam-4808	12	9	bitopological	bitopological	ADJ
ejpam-4808	12	10	spaces	space	NOUN
ejpam-4808	12	11	[	[	X
ejpam-4808	12	12	1	1	NUM
ejpam-4808	12	13	]	]	PUNCT
ejpam-4808	12	14	.	.	PUNCT
ejpam-4808	13	1	also	also	ADV
ejpam-4808	13	2	,	,	PUNCT
ejpam-4808	13	3	generalized	generalize	VERB
ejpam-4808	13	4	fuzzy	fuzzy	ADJ
ejpam-4808	13	5	closed	closed	ADJ
ejpam-4808	13	6	groups	group	NOUN
ejpam-4808	13	7	were	be	AUX
ejpam-4808	13	8	established	establish	VERB
ejpam-4808	13	9	in	in	ADP
ejpam-4808	13	10	fuzzy	fuzzy	ADJ
ejpam-4808	13	11	topology	topology	NOUN
ejpam-4808	13	12	in	in	ADP
ejpam-4808	13	13	1997	1997	NUM
ejpam-4808	13	14	by	by	ADP
ejpam-4808	13	15	balasubramanian	balasubramanian	PROPN
ejpam-4808	13	16	and	and	CCONJ
ejpam-4808	13	17	sundaram	sundaram	PROPN
ejpam-4808	13	18	[	[	X
ejpam-4808	13	19	6	6	NUM
ejpam-4808	13	20	]	]	PUNCT
ejpam-4808	13	21	.	.	PUNCT
ejpam-4808	14	1	after	after	ADP
ejpam-4808	14	2	that	that	PRON
ejpam-4808	14	3	,	,	PUNCT
ejpam-4808	14	4	many	many	ADJ
ejpam-4808	14	5	scientists	scientist	NOUN
ejpam-4808	14	6	applied	apply	VERB
ejpam-4808	14	7	the	the	DET
ejpam-4808	14	8	notion	notion	NOUN
ejpam-4808	14	9	of	of	ADP
ejpam-4808	14	10	a	a	DET
ejpam-4808	14	11	generalized	generalize	VERB
ejpam-4808	14	12	closed	close	VERB
ejpam-4808	14	13	set	set	VERB
ejpam-4808	14	14	in	in	ADP
ejpam-4808	14	15	fuzzy	fuzzy	ADJ
ejpam-4808	14	16	space	space	NOUN
ejpam-4808	14	17	and	and	CCONJ
ejpam-4808	14	18	in	in	ADP
ejpam-4808	14	19	2005	2005	NUM
ejpam-4808	14	20	el	el	PROPN
ejpam-4808	14	21	-	-	PUNCT
ejpam-4808	14	22	shafei	shafei	PROPN
ejpam-4808	14	23	introduced	introduce	VERB
ejpam-4808	14	24	some	some	DET
ejpam-4808	14	25	applications	application	NOUN
ejpam-4808	14	26	of	of	ADP
ejpam-4808	14	27	it	it	PRON
ejpam-4808	15	1	[	[	X
ejpam-4808	15	2	9	9	NUM
ejpam-4808	15	3	]	]	PUNCT
ejpam-4808	15	4	.	.	PUNCT
ejpam-4808	16	1	also	also	ADV
ejpam-4808	16	2	,	,	PUNCT
ejpam-4808	16	3	in	in	ADP
ejpam-4808	16	4	2009	2009	NUM
ejpam-4808	16	5	xuzhu	xuzhu	NOUN
ejpam-4808	16	6	wang	wang	PROPN
ejpam-4808	16	7	et	et	PROPN
ejpam-4808	16	8	al	al	PROPN
ejpam-4808	16	9	presented	present	VERB
ejpam-4808	16	10	a	a	DET
ejpam-4808	16	11	book	book	NOUN
ejpam-4808	16	12	that	that	PRON
ejpam-4808	16	13	contains	contain	VERB
ejpam-4808	16	14	all	all	DET
ejpam-4808	16	15	the	the	DET
ejpam-4808	16	16	basic	basic	ADJ
ejpam-4808	16	17	operations	operation	NOUN
ejpam-4808	16	18	in	in	ADP
ejpam-4808	16	19	fuzzy	fuzzy	ADJ
ejpam-4808	16	20	science	science	NOUN
ejpam-4808	16	21	[	[	X
ejpam-4808	16	22	12	12	NUM
ejpam-4808	16	23	]	]	PUNCT
ejpam-4808	16	24	.	.	PUNCT
ejpam-4808	17	1	as	as	SCONJ
ejpam-4808	17	2	zahran	zahran	NOUN
ejpam-4808	17	3	and	and	CCONJ
ejpam-4808	17	4	el	el	NOUN
ejpam-4808	17	5	-	-	PUNCT
ejpam-4808	17	6	maghrabi	maghrabi	NOUN
ejpam-4808	17	7	studied	study	VERB
ejpam-4808	17	8	in	in	ADP
ejpam-4808	17	9	2011	2011	NUM
ejpam-4808	17	10	some	some	DET
ejpam-4808	17	11	operations	operation	NOUN
ejpam-4808	17	12	on	on	ADP
ejpam-4808	17	13	it	it	PRON
ejpam-4808	17	14	in	in	ADP
ejpam-4808	17	15	fuzzy	fuzzy	ADJ
ejpam-4808	17	16	space	space	NOUN
ejpam-4808	17	17	[	[	X
ejpam-4808	17	18	13	13	NUM
ejpam-4808	17	19	]	]	PUNCT
ejpam-4808	17	20	.	.	PUNCT
ejpam-4808	18	1	then	then	ADV
ejpam-4808	18	2	in	in	ADP
ejpam-4808	18	3	2017	2017	NUM
ejpam-4808	18	4	benchalli	benchalli	NOUN
ejpam-4808	18	5	et	et	PROPN
ejpam-4808	18	6	al	al	PROPN
ejpam-4808	18	7	studied	study	VERB
ejpam-4808	18	8	delta	delta	NOUN
ejpam-4808	18	9	∗corresponding	∗corresponde	VERB
ejpam-4808	18	10	author	author	NOUN
ejpam-4808	18	11	.	.	PUNCT
ejpam-4808	19	1	doi	doi	NOUN
ejpam-4808	19	2	:	:	PUNCT
ejpam-4808	19	3	https://doi.org/10.29020/nybg.ejpam.v16i3.4808	https://doi.org/10.29020/nybg.ejpam.v16i3.4808	NUM
ejpam-4808	19	4	email	email	NOUN
ejpam-4808	19	5	addresses	address	NOUN
ejpam-4808	19	6	:	:	PUNCT
ejpam-4808	19	7	aasehli@taibahu.edu.sa	aasehli@taibahu.edu.sa	NOUN
ejpam-4808	19	8	(	(	PUNCT
ejpam-4808	19	9	ahlam	ahlam	PROPN
ejpam-4808	19	10	ahmed	ahmed	PROPN
ejpam-4808	19	11	alharbi	alharbi	PROPN
ejpam-4808	19	12	)	)	PUNCT
ejpam-4808	19	13	,	,	PUNCT
ejpam-4808	19	14	akilic@upm.edu.my	akilic@upm.edu.my	PROPN
ejpam-4808	19	15	(	(	PUNCT
ejpam-4808	19	16	adem	adem	PROPN
ejpam-4808	19	17	kilicman	kilicman	PROPN
ejpam-4808	19	18	)	)	PUNCT
ejpam-4808	19	19	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4808	19	20	1980	1980	NUM
ejpam-4808	19	21	©	©	PROPN
ejpam-4808	19	22	2023	2023	NUM
ejpam-4808	19	23	ejpam	ejpam	NOUN
ejpam-4808	19	24	all	all	DET
ejpam-4808	19	25	rights	right	NOUN
ejpam-4808	19	26	reserved	reserve	VERB
ejpam-4808	19	27	.	.	PUNCT
ejpam-4808	20	1	a.	a.	NOUN
ejpam-4808	20	2	a.	a.	PROPN
ejpam-4808	20	3	alharbi	alharbi	PROPN
ejpam-4808	20	4	,	,	PUNCT
ejpam-4808	20	5	a.	a.	NOUN
ejpam-4808	20	6	kilicman	kilicman	PROPN
ejpam-4808	20	7	/	/	SYM
ejpam-4808	20	8	eur	eur	PROPN
ejpam-4808	20	9	.	.	PUNCT
ejpam-4808	21	1	j.	j.	PROPN
ejpam-4808	21	2	pure	pure	PROPN
ejpam-4808	21	3	appl	appl	PROPN
ejpam-4808	21	4	.	.	PROPN
ejpam-4808	21	5	math	math	PROPN
ejpam-4808	21	6	,	,	PUNCT
ejpam-4808	21	7	16	16	NUM
ejpam-4808	21	8	(	(	PUNCT
ejpam-4808	21	9	3	3	NUM
ejpam-4808	21	10	)	)	PUNCT
ejpam-4808	21	11	(	(	PUNCT
ejpam-4808	21	12	2023	2023	NUM
ejpam-4808	21	13	)	)	PUNCT
ejpam-4808	21	14	,	,	PUNCT
ejpam-4808	21	15	1980	1980	NUM
ejpam-4808	21	16	-	-	SYM
ejpam-4808	21	17	1990	1990	NUM
ejpam-4808	21	18	1981	1981	NUM
ejpam-4808	21	19	generalized	generalize	VERB
ejpam-4808	21	20	beta	beta	NOUN
ejpam-4808	21	21	closed	close	VERB
ejpam-4808	21	22	in	in	ADP
ejpam-4808	21	23	topological	topological	ADJ
ejpam-4808	21	24	spaces	space	NOUN
ejpam-4808	21	25	[	[	X
ejpam-4808	21	26	3	3	NUM
ejpam-4808	21	27	]	]	PUNCT
ejpam-4808	21	28	.	.	PUNCT
ejpam-4808	22	1	after	after	ADP
ejpam-4808	22	2	one	one	NUM
ejpam-4808	22	3	year	year	NOUN
ejpam-4808	22	4	,	,	PUNCT
ejpam-4808	22	5	kandil	kandil	PROPN
ejpam-4808	22	6	et	et	PROPN
ejpam-4808	22	7	al	al	PROPN
ejpam-4808	22	8	defined	define	VERB
ejpam-4808	22	9	the	the	DET
ejpam-4808	22	10	concept	concept	NOUN
ejpam-4808	22	11	of	of	ADP
ejpam-4808	22	12	locally	locally	ADV
ejpam-4808	22	13	pairwise	pairwise	NOUN
ejpam-4808	22	14	closed	close	VERB
ejpam-4808	22	15	sets	set	NOUN
ejpam-4808	22	16	and	and	CCONJ
ejpam-4808	22	17	studied	study	VERB
ejpam-4808	22	18	some	some	PRON
ejpam-4808	22	19	of	of	ADP
ejpam-4808	22	20	their	their	PRON
ejpam-4808	22	21	properties	property	NOUN
ejpam-4808	22	22	[	[	X
ejpam-4808	22	23	7	7	NUM
ejpam-4808	22	24	]	]	PUNCT
ejpam-4808	22	25	.	.	PUNCT
ejpam-4808	23	1	in	in	ADP
ejpam-4808	23	2	2019	2019	NUM
ejpam-4808	23	3	ramaboopathi	ramaboopathi	NOUN
ejpam-4808	23	4	and	and	CCONJ
ejpam-4808	23	5	dharmalingam	dharmalingam	PROPN
ejpam-4808	23	6	introduced	introduce	VERB
ejpam-4808	23	7	a	a	DET
ejpam-4808	23	8	new	new	ADJ
ejpam-4808	23	9	class	class	NOUN
ejpam-4808	23	10	of	of	ADP
ejpam-4808	23	11	generalized	generalized	ADJ
ejpam-4808	23	12	closed	closed	ADJ
ejpam-4808	23	13	sets	set	NOUN
ejpam-4808	23	14	in	in	ADP
ejpam-4808	23	15	bitopological	bitopological	ADJ
ejpam-4808	23	16	spaces	space	NOUN
ejpam-4808	23	17	[	[	X
ejpam-4808	23	18	11	11	NUM
ejpam-4808	23	19	]	]	PUNCT
ejpam-4808	23	20	,	,	PUNCT
ejpam-4808	23	21	as	as	SCONJ
ejpam-4808	23	22	in	in	ADP
ejpam-4808	23	23	the	the	DET
ejpam-4808	23	24	same	same	ADJ
ejpam-4808	23	25	year	year	NOUN
ejpam-4808	23	26	andal	andal	PROPN
ejpam-4808	23	27	and	and	CCONJ
ejpam-4808	23	28	thiripurasundari	thiripurasundari	PROPN
ejpam-4808	23	29	introduced	introduce	VERB
ejpam-4808	23	30	a	a	DET
ejpam-4808	23	31	new	new	ADJ
ejpam-4808	23	32	concept	concept	NOUN
ejpam-4808	23	33	of	of	ADP
ejpam-4808	23	34	fuzzy	fuzzy	ADJ
ejpam-4808	23	35	generalized	generalize	VERB
ejpam-4808	23	36	pi	pi	NOUN
ejpam-4808	23	37	closed	close	VERB
ejpam-4808	23	38	in	in	ADP
ejpam-4808	23	39	fuzzy	fuzzy	ADJ
ejpam-4808	23	40	bitopological	bitopological	ADJ
ejpam-4808	23	41	spaces	space	NOUN
ejpam-4808	23	42	[	[	X
ejpam-4808	23	43	2	2	NUM
ejpam-4808	23	44	]	]	PUNCT
ejpam-4808	23	45	.	.	PUNCT
ejpam-4808	24	1	finally	finally	ADV
ejpam-4808	24	2	,	,	PUNCT
ejpam-4808	24	3	in	in	ADP
ejpam-4808	24	4	2021	2021	NUM
ejpam-4808	24	5	das	das	PROPN
ejpam-4808	24	6	et	et	PROPN
ejpam-4808	24	7	al	al	PROPN
ejpam-4808	24	8	introduced	introduce	VERB
ejpam-4808	24	9	the	the	DET
ejpam-4808	24	10	idea	idea	NOUN
ejpam-4808	24	11	of	of	ADP
ejpam-4808	24	12	γ	γ	X
ejpam-4808	24	13	generalized	generalize	VERB
ejpam-4808	24	14	fuzzy	fuzzy	ADJ
ejpam-4808	24	15	quasi	quasi	ADJ
ejpam-4808	24	16	neighborhood	neighborhood	NOUN
ejpam-4808	24	17	of	of	ADP
ejpam-4808	24	18	a	a	DET
ejpam-4808	24	19	fuzzy	fuzzy	ADJ
ejpam-4808	24	20	point	point	NOUN
ejpam-4808	24	21	[	[	X
ejpam-4808	24	22	5	5	NUM
ejpam-4808	24	23	]	]	PUNCT
ejpam-4808	24	24	.	.	PUNCT
ejpam-4808	25	1	2	2	X
ejpam-4808	25	2	.	.	X
ejpam-4808	25	3	preliminaries	preliminary	NOUN
ejpam-4808	25	4	in	in	ADP
ejpam-4808	25	5	the	the	DET
ejpam-4808	25	6	following	following	ADJ
ejpam-4808	25	7	part	part	NOUN
ejpam-4808	25	8	,	,	PUNCT
ejpam-4808	25	9	we	we	PRON
ejpam-4808	25	10	go	go	VERB
ejpam-4808	25	11	over	over	ADP
ejpam-4808	25	12	important	important	ADJ
ejpam-4808	25	13	antecedent	antecedent	NOUN
ejpam-4808	25	14	notions	notion	NOUN
ejpam-4808	25	15	that	that	PRON
ejpam-4808	25	16	are	be	AUX
ejpam-4808	25	17	essential	essential	ADJ
ejpam-4808	25	18	to	to	ADP
ejpam-4808	25	19	the	the	DET
ejpam-4808	25	20	development	development	NOUN
ejpam-4808	25	21	of	of	ADP
ejpam-4808	25	22	this	this	DET
ejpam-4808	25	23	paper	paper	NOUN
ejpam-4808	25	24	.	.	PUNCT
ejpam-4808	26	1	definition	definition	NOUN
ejpam-4808	26	2	1	1	NUM
ejpam-4808	26	3	.	.	PUNCT
ejpam-4808	27	1	[	[	X
ejpam-4808	27	2	10	10	NUM
ejpam-4808	27	3	]	]	PUNCT
ejpam-4808	27	4	suppose	suppose	VERB
ejpam-4808	27	5	the	the	DET
ejpam-4808	27	6	set	set	NOUN
ejpam-4808	27	7	x	x	PUNCT
ejpam-4808	27	8	is	be	AUX
ejpam-4808	27	9	not	not	PART
ejpam-4808	27	10	empty	empty	ADJ
ejpam-4808	27	11	and	and	CCONJ
ejpam-4808	27	12	the	the	DET
ejpam-4808	27	13	i	i	PRON
ejpam-4808	27	14	sign	sign	NOUN
ejpam-4808	27	15	represents	represent	VERB
ejpam-4808	27	16	the	the	DET
ejpam-4808	27	17	unit	unit	NOUN
ejpam-4808	27	18	period	period	NOUN
ejpam-4808	28	1	[	[	X
ejpam-4808	28	2	0	0	NUM
ejpam-4808	28	3	,	,	PUNCT
ejpam-4808	28	4	1	1	NUM
ejpam-4808	28	5	]	]	PUNCT
ejpam-4808	28	6	,	,	PUNCT
ejpam-4808	28	7	then	then	ADV
ejpam-4808	28	8	the	the	DET
ejpam-4808	28	9	following	following	NOUN
ejpam-4808	28	10	defined	define	VERB
ejpam-4808	28	11	as	as	ADP
ejpam-4808	28	12	:	:	PUNCT
ejpam-4808	28	13	(	(	PUNCT
ejpam-4808	28	14	1	1	X
ejpam-4808	28	15	)	)	PUNCT
ejpam-4808	28	16	an	an	DET
ejpam-4808	28	17	operator	operator	NOUN
ejpam-4808	28	18	with	with	ADP
ejpam-4808	28	19	x	x	NOUN
ejpam-4808	28	20	domain	domain	NOUN
ejpam-4808	28	21	and	and	CCONJ
ejpam-4808	28	22	i	i	PRON
ejpam-4808	28	23	range	range	VERB
ejpam-4808	28	24	is	be	AUX
ejpam-4808	28	25	known	know	VERB
ejpam-4808	28	26	as	as	ADP
ejpam-4808	28	27	a	a	DET
ejpam-4808	28	28	fuzzy	fuzzy	ADJ
ejpam-4808	28	29	set	set	NOUN
ejpam-4808	28	30	e	e	NOUN
ejpam-4808	28	31	,	,	PUNCT
ejpam-4808	28	32	where	where	SCONJ
ejpam-4808	28	33	e(x	e(x	NUM
ejpam-4808	28	34	)	)	PUNCT
ejpam-4808	28	35	∈	∈	PROPN
ejpam-4808	28	36	(	(	PUNCT
ejpam-4808	28	37	0	0	NUM
ejpam-4808	28	38	,	,	PUNCT
ejpam-4808	28	39	1	1	NUM
ejpam-4808	28	40	]	]	PUNCT
ejpam-4808	28	41	when	when	SCONJ
ejpam-4808	28	42	x	x	SYM
ejpam-4808	28	43	∈	∈	PROPN
ejpam-4808	28	44	e	e	NOUN
ejpam-4808	28	45	,	,	PUNCT
ejpam-4808	28	46	and	and	CCONJ
ejpam-4808	28	47	e(x	e(x	NUM
ejpam-4808	28	48	)	)	PUNCT
ejpam-4808	28	49	=	=	SYM
ejpam-4808	28	50	0	0	NUM
ejpam-4808	29	1	in	in	ADP
ejpam-4808	29	2	case	case	NOUN
ejpam-4808	29	3	x	x	X
ejpam-4808	29	4	̸∈	̸∈	PROPN
ejpam-4808	29	5	e.	e.	PROPN
ejpam-4808	29	6	(	(	PUNCT
ejpam-4808	29	7	2	2	NUM
ejpam-4808	29	8	)	)	PUNCT
ejpam-4808	29	9	a	a	DET
ejpam-4808	29	10	set	set	NOUN
ejpam-4808	29	11	d	d	X
ejpam-4808	29	12	is	be	AUX
ejpam-4808	29	13	including	include	VERB
ejpam-4808	29	14	e	e	NOUN
ejpam-4808	29	15	indicated	indicate	VERB
ejpam-4808	29	16	via	via	ADP
ejpam-4808	29	17	e	e	PROPN
ejpam-4808	29	18	⊆	⊆	NUM
ejpam-4808	29	19	d	d	NOUN
ejpam-4808	29	20	if	if	SCONJ
ejpam-4808	29	21	e(x	e(x	NUM
ejpam-4808	29	22	)	)	PUNCT
ejpam-4808	29	23	≤	≤	NOUN
ejpam-4808	29	24	d(x	d(x	NOUN
ejpam-4808	29	25	)	)	PUNCT
ejpam-4808	29	26	,	,	PUNCT
ejpam-4808	29	27	whenever	whenever	SCONJ
ejpam-4808	29	28	x	x	SYM
ejpam-4808	29	29	∈	∈	PROPN
ejpam-4808	29	30	x	x	SYM
ejpam-4808	29	31	(	(	PUNCT
ejpam-4808	29	32	3	3	NUM
ejpam-4808	29	33	)	)	PUNCT
ejpam-4808	29	34	e	e	NOUN
ejpam-4808	29	35	and	and	CCONJ
ejpam-4808	29	36	d	d	PROPN
ejpam-4808	29	37	combination	combination	NOUN
ejpam-4808	29	38	indicated	indicate	VERB
ejpam-4808	29	39	by	by	ADP
ejpam-4808	29	40	e	e	NOUN
ejpam-4808	29	41	∨d	∨d	VERB
ejpam-4808	29	42	if	if	SCONJ
ejpam-4808	29	43	(	(	PUNCT
ejpam-4808	29	44	e	e	NOUN
ejpam-4808	29	45	∨d)(x	∨d)(x	PROPN
ejpam-4808	29	46	)	)	PUNCT
ejpam-4808	29	47	=	=	SYM
ejpam-4808	29	48	max{e(x	max{e(x	PROPN
ejpam-4808	29	49	)	)	PUNCT
ejpam-4808	29	50	,	,	PUNCT
ejpam-4808	29	51	d(x	d(x	PROPN
ejpam-4808	29	52	)	)	PUNCT
ejpam-4808	29	53	}	}	PUNCT
ejpam-4808	29	54	∀	∀	X
ejpam-4808	29	55	x	x	SYM
ejpam-4808	29	56	∈	∈	NOUN
ejpam-4808	29	57	x.	x.	NOUN
ejpam-4808	29	58	(	(	PUNCT
ejpam-4808	29	59	4	4	X
ejpam-4808	29	60	)	)	PUNCT
ejpam-4808	29	61	the	the	DET
ejpam-4808	29	62	intersection	intersection	NOUN
ejpam-4808	29	63	of	of	ADP
ejpam-4808	29	64	e	e	NOUN
ejpam-4808	29	65	,	,	PUNCT
ejpam-4808	29	66	d	d	PROPN
ejpam-4808	29	67	indicated	indicate	VERB
ejpam-4808	29	68	by	by	ADP
ejpam-4808	29	69	e∧d	e∧d	NOUN
ejpam-4808	29	70	if	if	SCONJ
ejpam-4808	29	71	(	(	PUNCT
ejpam-4808	29	72	e∧d)(x	e∧d)(x	PROPN
ejpam-4808	29	73	)	)	PUNCT
ejpam-4808	29	74	=	=	SYM
ejpam-4808	29	75	min{e(x	min{e(x	PROPN
ejpam-4808	29	76	)	)	PUNCT
ejpam-4808	29	77	,	,	PUNCT
ejpam-4808	29	78	d(x	d(x	PROPN
ejpam-4808	29	79	)	)	PUNCT
ejpam-4808	29	80	}	}	PUNCT
ejpam-4808	29	81	∀	∀	X
ejpam-4808	29	82	x	x	SYM
ejpam-4808	29	83	∈	∈	NOUN
ejpam-4808	29	84	x.	x.	NOUN
ejpam-4808	29	85	(	(	PUNCT
ejpam-4808	29	86	5	5	NUM
ejpam-4808	29	87	)	)	PUNCT
ejpam-4808	29	88	the	the	DET
ejpam-4808	29	89	completeness	completeness	NOUN
ejpam-4808	29	90	of	of	ADP
ejpam-4808	29	91	e	e	PROPN
ejpam-4808	29	92	denoted	denote	VERB
ejpam-4808	29	93	via	via	ADP
ejpam-4808	29	94	ec	ec	PROPN
ejpam-4808	29	95	as	as	ADP
ejpam-4808	29	96	(	(	PUNCT
ejpam-4808	29	97	e(x))c	e(x))c	PROPN
ejpam-4808	29	98	=	=	SYM
ejpam-4808	29	99	1−	1−	NUM
ejpam-4808	29	100	e(x	e(x	NUM
ejpam-4808	29	101	)	)	PUNCT
ejpam-4808	29	102	,	,	PUNCT
ejpam-4808	29	103	∀	∀	PUNCT
ejpam-4808	29	104	x	x	SYM
ejpam-4808	29	105	∈	∈	NOUN
ejpam-4808	29	106	x.	x.	NOUN
ejpam-4808	30	1	the	the	DET
ejpam-4808	30	2	following	follow	VERB
ejpam-4808	30	3	definitions	definition	NOUN
ejpam-4808	30	4	explain	explain	VERB
ejpam-4808	30	5	the	the	DET
ejpam-4808	30	6	meaning	meaning	NOUN
ejpam-4808	30	7	of	of	ADP
ejpam-4808	30	8	fuzzy	fuzzy	ADJ
ejpam-4808	30	9	topology	topology	NOUN
ejpam-4808	30	10	and	and	CCONJ
ejpam-4808	30	11	fuzzy	fuzzy	ADJ
ejpam-4808	30	12	bitopological	bitopological	ADJ
ejpam-4808	30	13	spaces	space	NOUN
ejpam-4808	30	14	.	.	PUNCT
ejpam-4808	31	1	definition	definition	NOUN
ejpam-4808	31	2	2	2	NUM
ejpam-4808	31	3	.	.	PUNCT
ejpam-4808	32	1	[	[	X
ejpam-4808	32	2	10	10	NUM
ejpam-4808	32	3	]	]	X
ejpam-4808	32	4	a	a	DET
ejpam-4808	32	5	fuzzy	fuzzy	ADJ
ejpam-4808	32	6	topology	topology	NOUN
ejpam-4808	32	7	of	of	ADP
ejpam-4808	32	8	x	x	PRON
ejpam-4808	32	9	is	be	AUX
ejpam-4808	32	10	a	a	DET
ejpam-4808	32	11	class	class	NOUN
ejpam-4808	32	12	of	of	ADP
ejpam-4808	32	13	fuzzy	fuzzy	ADJ
ejpam-4808	32	14	groups	group	NOUN
ejpam-4808	32	15	δ	δ	NOUN
ejpam-4808	32	16	∈	∈	PROPN
ejpam-4808	32	17	i	i	PRON
ejpam-4808	32	18	which	which	PRON
ejpam-4808	32	19	holds	hold	VERB
ejpam-4808	32	20	the	the	DET
ejpam-4808	32	21	coming	come	VERB
ejpam-4808	32	22	three	three	NUM
ejpam-4808	32	23	conditions	condition	NOUN
ejpam-4808	32	24	:	:	PUNCT
ejpam-4808	32	25	1	1	NUM
ejpam-4808	32	26	.	.	NUM
ejpam-4808	32	27	0	0	NUM
ejpam-4808	32	28	and	and	CCONJ
ejpam-4808	32	29	1	1	NUM
ejpam-4808	32	30	contained	contain	VERB
ejpam-4808	32	31	in	in	ADP
ejpam-4808	32	32	δ	δ	PROPN
ejpam-4808	32	33	,	,	PUNCT
ejpam-4808	32	34	where	where	SCONJ
ejpam-4808	32	35	0(x	0(x	NOUN
ejpam-4808	32	36	)	)	PUNCT
ejpam-4808	32	37	=	=	SYM
ejpam-4808	32	38	0	0	NUM
ejpam-4808	32	39	,	,	PUNCT
ejpam-4808	32	40	1(x	1(x	NUM
ejpam-4808	32	41	)	)	PUNCT
ejpam-4808	32	42	=	=	SYM
ejpam-4808	33	1	1	1	X
ejpam-4808	33	2	,	,	PUNCT
ejpam-4808	33	3	whenever	whenever	SCONJ
ejpam-4808	33	4	x	x	SYM
ejpam-4808	33	5	∈	∈	NOUN
ejpam-4808	33	6	x.	x.	NOUN
ejpam-4808	33	7	2	2	X
ejpam-4808	33	8	.	.	X
ejpam-4808	33	9	for	for	ADP
ejpam-4808	33	10	any	any	DET
ejpam-4808	33	11	e	e	NOUN
ejpam-4808	33	12	,	,	PUNCT
ejpam-4808	33	13	d	d	PROPN
ejpam-4808	33	14	∈	∈	PROPN
ejpam-4808	33	15	δ	δ	PROPN
ejpam-4808	33	16	,	,	PUNCT
ejpam-4808	33	17	e	e	PROPN
ejpam-4808	33	18	∧d	∧d	PROPN
ejpam-4808	33	19	∈	∈	PROPN
ejpam-4808	33	20	δ	δ	PROPN
ejpam-4808	33	21	.	.	PUNCT
ejpam-4808	34	1	3	3	X
ejpam-4808	34	2	.	.	X
ejpam-4808	35	1	for	for	ADP
ejpam-4808	35	2	any	any	DET
ejpam-4808	35	3	(	(	PUNCT
ejpam-4808	35	4	ei∈i	ei∈i	PROPN
ejpam-4808	35	5	)	)	PUNCT
ejpam-4808	35	6	∈	∈	PROPN
ejpam-4808	35	7	δ	δ	PROPN
ejpam-4808	35	8	,	,	PUNCT
ejpam-4808	35	9	∨i∈iei	∨i∈iei	PUNCT
ejpam-4808	35	10	∈	∈	PROPN
ejpam-4808	35	11	δ	δ	PROPN
ejpam-4808	35	12	.	.	PUNCT
ejpam-4808	36	1	the	the	DET
ejpam-4808	36	2	term	term	NOUN
ejpam-4808	36	3	”	"	PUNCT
ejpam-4808	36	4	fuzzy	fuzzy	ADJ
ejpam-4808	36	5	topological	topological	ADJ
ejpam-4808	36	6	space	space	NOUN
ejpam-4808	36	7	,	,	PUNCT
ejpam-4808	36	8	”	"	PUNCT
ejpam-4808	36	9	or	or	CCONJ
ejpam-4808	36	10	”	"	PUNCT
ejpam-4808	36	11	fts	fts	X
ejpam-4808	36	12	,	,	PUNCT
ejpam-4808	36	13	”	"	PUNCT
ejpam-4808	36	14	refers	refer	VERB
ejpam-4808	36	15	to	to	ADP
ejpam-4808	36	16	the	the	DET
ejpam-4808	36	17	pair	pair	NOUN
ejpam-4808	36	18	(	(	PUNCT
ejpam-4808	36	19	x	x	NOUN
ejpam-4808	36	20	,	,	PUNCT
ejpam-4808	36	21	δ	δ	PROPN
ejpam-4808	36	22	)	)	PUNCT
ejpam-4808	36	23	.	.	PUNCT
ejpam-4808	37	1	the	the	DET
ejpam-4808	37	2	components	component	NOUN
ejpam-4808	37	3	of	of	ADP
ejpam-4808	37	4	δ	δ	PROPN
ejpam-4808	37	5	are	be	AUX
ejpam-4808	37	6	named	name	VERB
ejpam-4808	37	7	fuzzy	fuzzy	ADJ
ejpam-4808	37	8	open	open	ADJ
ejpam-4808	37	9	sets	set	NOUN
ejpam-4808	37	10	.	.	PUNCT
ejpam-4808	38	1	if	if	SCONJ
ejpam-4808	38	2	f	f	PROPN
ejpam-4808	38	3	c	c	PROPN
ejpam-4808	38	4	∈	∈	PROPN
ejpam-4808	38	5	δ	δ	PROPN
ejpam-4808	38	6	,	,	PUNCT
ejpam-4808	38	7	then	then	ADV
ejpam-4808	38	8	f	f	PROPN
ejpam-4808	38	9	is	be	AUX
ejpam-4808	38	10	mean	mean	ADJ
ejpam-4808	38	11	as	as	ADP
ejpam-4808	38	12	fuzzy	fuzzy	ADJ
ejpam-4808	38	13	closed	closed	ADJ
ejpam-4808	38	14	.	.	PUNCT
ejpam-4808	39	1	the	the	DET
ejpam-4808	39	2	collection	collection	NOUN
ejpam-4808	39	3	including	include	VERB
ejpam-4808	39	4	whole	whole	ADJ
ejpam-4808	39	5	fuzzy	fuzzy	ADJ
ejpam-4808	39	6	closed	closed	ADJ
ejpam-4808	39	7	groups	group	NOUN
ejpam-4808	39	8	in	in	ADP
ejpam-4808	39	9	fuzzy	fuzzy	ADJ
ejpam-4808	39	10	topology	topology	NOUN
ejpam-4808	39	11	δ	δ	PROPN
ejpam-4808	39	12	denote	denote	VERB
ejpam-4808	39	13	by	by	ADP
ejpam-4808	39	14	fδ	fδ	NOUN
ejpam-4808	39	15	.	.	NOUN
ejpam-4808	39	16	definition	definition	NOUN
ejpam-4808	39	17	3	3	NUM
ejpam-4808	39	18	.	.	PUNCT
ejpam-4808	40	1	[	[	X
ejpam-4808	40	2	1	1	X
ejpam-4808	40	3	]	]	PUNCT
ejpam-4808	40	4	a	a	DET
ejpam-4808	40	5	fuzzy	fuzzy	ADJ
ejpam-4808	40	6	bitopological	bitopological	ADJ
ejpam-4808	40	7	spaces	space	NOUN
ejpam-4808	40	8	,	,	PUNCT
ejpam-4808	40	9	or	or	CCONJ
ejpam-4808	40	10	fbts	fbt	NOUN
ejpam-4808	40	11	for	for	ADP
ejpam-4808	40	12	short	short	ADJ
ejpam-4808	40	13	,	,	PUNCT
ejpam-4808	40	14	(	(	PUNCT
ejpam-4808	40	15	x	x	NOUN
ejpam-4808	40	16	,	,	PUNCT
ejpam-4808	40	17	δ1	δ1	NOUN
ejpam-4808	40	18	,	,	PUNCT
ejpam-4808	40	19	δ2	δ2	PROPN
ejpam-4808	40	20	)	)	PUNCT
ejpam-4808	40	21	since	since	SCONJ
ejpam-4808	40	22	x	x	PRON
ejpam-4808	40	23	is	be	AUX
ejpam-4808	40	24	not	not	PART
ejpam-4808	40	25	empty	empty	ADJ
ejpam-4808	40	26	,	,	PUNCT
ejpam-4808	40	27	δ1	δ1	NOUN
ejpam-4808	40	28	,	,	PUNCT
ejpam-4808	40	29	and	and	CCONJ
ejpam-4808	40	30	δ2	δ2	VERB
ejpam-4808	40	31	are	be	AUX
ejpam-4808	40	32	fuzzy	fuzzy	ADJ
ejpam-4808	40	33	topological	topological	ADJ
ejpam-4808	40	34	spaces	space	NOUN
ejpam-4808	40	35	on	on	ADP
ejpam-4808	40	36	x.	x.	NOUN
ejpam-4808	40	37	over	over	ADP
ejpam-4808	40	38	this	this	DET
ejpam-4808	40	39	dissertation	dissertation	NOUN
ejpam-4808	40	40	x	x	PUNCT
ejpam-4808	40	41	perform	perform	VERB
ejpam-4808	40	42	fuzzy	fuzzy	ADJ
ejpam-4808	40	43	bitopology	bitopology	NOUN
ejpam-4808	40	44	(	(	PUNCT
ejpam-4808	40	45	x	x	NOUN
ejpam-4808	40	46	,	,	PUNCT
ejpam-4808	40	47	δ1	δ1	NOUN
ejpam-4808	40	48	,	,	PUNCT
ejpam-4808	40	49	δ2	δ2	PROPN
ejpam-4808	40	50	)	)	PUNCT
ejpam-4808	40	51	,	,	PUNCT
ejpam-4808	40	52	and	and	CCONJ
ejpam-4808	40	53	y	y	PROPN
ejpam-4808	40	54	to	to	PART
ejpam-4808	40	55	(	(	PUNCT
ejpam-4808	40	56	y	y	PROPN
ejpam-4808	40	57	,	,	PUNCT
ejpam-4808	40	58	σ1	σ1	PROPN
ejpam-4808	40	59	,	,	PUNCT
ejpam-4808	40	60	σ2	σ2	NOUN
ejpam-4808	40	61	)	)	PUNCT
ejpam-4808	40	62	,	,	PUNCT
ejpam-4808	40	63	where	where	SCONJ
ejpam-4808	40	64	i	i	PRON
ejpam-4808	40	65	̸=	̸=	PROPN
ejpam-4808	40	66	j	j	PROPN
ejpam-4808	40	67	,	,	PUNCT
ejpam-4808	40	68	and	and	CCONJ
ejpam-4808	40	69	i	i	PRON
ejpam-4808	40	70	,	,	PUNCT
ejpam-4808	40	71	j	j	PROPN
ejpam-4808	40	72	∈	∈	PROPN
ejpam-4808	40	73	{	{	PUNCT
ejpam-4808	40	74	1	1	NUM
ejpam-4808	40	75	,	,	PUNCT
ejpam-4808	40	76	2	2	NUM
ejpam-4808	40	77	}	}	PUNCT
ejpam-4808	40	78	.	.	PUNCT
ejpam-4808	41	1	in	in	ADP
ejpam-4808	41	2	the	the	DET
ejpam-4808	41	3	section	section	NOUN
ejpam-4808	41	4	which	which	PRON
ejpam-4808	41	5	follows	follow	VERB
ejpam-4808	41	6	,	,	PUNCT
ejpam-4808	41	7	the	the	DET
ejpam-4808	41	8	definitions	definition	NOUN
ejpam-4808	41	9	of	of	ADP
ejpam-4808	41	10	fuzzy	fuzzy	ADJ
ejpam-4808	41	11	set	set	VERB
ejpam-4808	41	12	interiors	interior	NOUN
ejpam-4808	41	13	and	and	CCONJ
ejpam-4808	41	14	closings	closing	NOUN
ejpam-4808	41	15	are	be	AUX
ejpam-4808	41	16	covered	cover	VERB
ejpam-4808	41	17	.	.	PUNCT
ejpam-4808	42	1	a.	a.	NOUN
ejpam-4808	42	2	a.	a.	PROPN
ejpam-4808	42	3	alharbi	alharbi	PROPN
ejpam-4808	42	4	,	,	PUNCT
ejpam-4808	42	5	a.	a.	NOUN
ejpam-4808	42	6	kilicman	kilicman	PROPN
ejpam-4808	42	7	/	/	SYM
ejpam-4808	42	8	eur	eur	PROPN
ejpam-4808	42	9	.	.	PUNCT
ejpam-4808	43	1	j.	j.	PROPN
ejpam-4808	43	2	pure	pure	PROPN
ejpam-4808	43	3	appl	appl	PROPN
ejpam-4808	43	4	.	.	PROPN
ejpam-4808	43	5	math	math	PROPN
ejpam-4808	43	6	,	,	PUNCT
ejpam-4808	43	7	16	16	NUM
ejpam-4808	43	8	(	(	PUNCT
ejpam-4808	43	9	3	3	NUM
ejpam-4808	43	10	)	)	PUNCT
ejpam-4808	43	11	(	(	PUNCT
ejpam-4808	43	12	2023	2023	NUM
ejpam-4808	43	13	)	)	PUNCT
ejpam-4808	43	14	,	,	PUNCT
ejpam-4808	43	15	1980	1980	NUM
ejpam-4808	43	16	-	-	SYM
ejpam-4808	43	17	1990	1990	NUM
ejpam-4808	43	18	1982	1982	NUM
ejpam-4808	43	19	definition	definition	NOUN
ejpam-4808	43	20	4	4	NUM
ejpam-4808	43	21	.	.	PUNCT
ejpam-4808	44	1	[	[	X
ejpam-4808	44	2	10	10	NUM
ejpam-4808	44	3	]	]	X
ejpam-4808	44	4	closing	closing	NOUN
ejpam-4808	44	5	and	and	CCONJ
ejpam-4808	44	6	internal	internal	ADJ
ejpam-4808	44	7	of	of	ADP
ejpam-4808	44	8	any	any	DET
ejpam-4808	44	9	fuzzy	fuzzy	ADJ
ejpam-4808	44	10	set	set	NOUN
ejpam-4808	44	11	m	m	NOUN
ejpam-4808	44	12	of	of	ADP
ejpam-4808	44	13	(	(	PUNCT
ejpam-4808	44	14	x	x	NOUN
ejpam-4808	44	15	,	,	PUNCT
ejpam-4808	44	16	δ	δ	PROPN
ejpam-4808	44	17	)	)	PUNCT
ejpam-4808	44	18	are	be	AUX
ejpam-4808	44	19	indicated	indicate	VERB
ejpam-4808	44	20	also	also	ADV
ejpam-4808	44	21	defined	define	VERB
ejpam-4808	44	22	as	as	SCONJ
ejpam-4808	44	23	follows	follow	VERB
ejpam-4808	44	24	:	:	PUNCT
ejpam-4808	44	25	cl(m	cl(m	X
ejpam-4808	44	26	)	)	PUNCT
ejpam-4808	45	1	=	=	SYM
ejpam-4808	45	2	∧	∧	NOUN
ejpam-4808	45	3	{	{	PUNCT
ejpam-4808	45	4	f	f	NOUN
ejpam-4808	45	5	:	:	PUNCT
ejpam-4808	45	6	m	m	VERB
ejpam-4808	45	7	≤	≤	NUM
ejpam-4808	46	1	f	f	X
ejpam-4808	46	2	,	,	PUNCT
ejpam-4808	46	3	f	f	PROPN
ejpam-4808	46	4	c	c	PROPN
ejpam-4808	46	5	∈	∈	PROPN
ejpam-4808	46	6	δ	δ	PROPN
ejpam-4808	46	7	}	}	PUNCT
ejpam-4808	46	8	int(m	int(m	PROPN
ejpam-4808	46	9	)	)	PUNCT
ejpam-4808	46	10	=	=	PUNCT
ejpam-4808	46	11	∨	∨	X
ejpam-4808	46	12	{	{	PUNCT
ejpam-4808	46	13	o	o	NOUN
ejpam-4808	46	14	:	:	PUNCT
ejpam-4808	46	15	o	o	X
ejpam-4808	46	16	≤	≤	NUM
ejpam-4808	46	17	m	m	ADP
ejpam-4808	46	18	,	,	PUNCT
ejpam-4808	46	19	o	o	PROPN
ejpam-4808	46	20	∈	∈	PROPN
ejpam-4808	46	21	δ	δ	PROPN
ejpam-4808	46	22	}	}	PUNCT
ejpam-4808	46	23	,	,	PUNCT
ejpam-4808	46	24	respectively	respectively	ADV
ejpam-4808	46	25	.	.	PUNCT
ejpam-4808	47	1	the	the	DET
ejpam-4808	47	2	closing	closing	NOUN
ejpam-4808	47	3	,	,	PUNCT
ejpam-4808	47	4	internal	internal	ADJ
ejpam-4808	47	5	,	,	PUNCT
ejpam-4808	47	6	and	and	CCONJ
ejpam-4808	47	7	complements	complement	NOUN
ejpam-4808	47	8	of	of	ADP
ejpam-4808	47	9	m	m	NOUN
ejpam-4808	47	10	of	of	ADP
ejpam-4808	47	11	x	x	PRON
ejpam-4808	47	12	are	be	AUX
ejpam-4808	47	13	indicated	indicate	VERB
ejpam-4808	47	14	by	by	ADP
ejpam-4808	47	15	δi−cl(m	δi−cl(m	PROPN
ejpam-4808	47	16	)	)	PUNCT
ejpam-4808	47	17	,	,	PUNCT
ejpam-4808	47	18	δi−int(m	δi−int(m	PROPN
ejpam-4808	47	19	)	)	PUNCT
ejpam-4808	47	20	,	,	PUNCT
ejpam-4808	47	21	and	and	CCONJ
ejpam-4808	47	22	m	m	PROPN
ejpam-4808	47	23	c	c	NOUN
ejpam-4808	47	24	i	i	PRON
ejpam-4808	47	25	,	,	PUNCT
ejpam-4808	47	26	respectively	respectively	ADV
ejpam-4808	47	27	,	,	PUNCT
ejpam-4808	47	28	with	with	ADP
ejpam-4808	47	29	regard	regard	NOUN
ejpam-4808	47	30	to	to	ADP
ejpam-4808	47	31	fuzzy	fuzzy	ADJ
ejpam-4808	47	32	topology	topology	NOUN
ejpam-4808	47	33	δi	δi	NOUN
ejpam-4808	47	34	.	.	PUNCT
ejpam-4808	48	1	additionally	additionally	ADV
ejpam-4808	48	2	,	,	PUNCT
ejpam-4808	48	3	we	we	PRON
ejpam-4808	48	4	designate	designate	VERB
ejpam-4808	48	5	the	the	DET
ejpam-4808	48	6	class	class	NOUN
ejpam-4808	48	7	of	of	ADP
ejpam-4808	48	8	all	all	DET
ejpam-4808	48	9	fuzzy	fuzzy	ADJ
ejpam-4808	48	10	δj−closed	δj−close	VERB
ejpam-4808	48	11	by	by	ADP
ejpam-4808	48	12	the	the	DET
ejpam-4808	48	13	mathematical	mathematical	ADJ
ejpam-4808	48	14	symbol	symbol	NOUN
ejpam-4808	48	15	fδj	fδj	NOUN
ejpam-4808	48	16	.	.	PUNCT
ejpam-4808	49	1	one	one	NUM
ejpam-4808	49	2	of	of	ADP
ejpam-4808	49	3	the	the	DET
ejpam-4808	49	4	work	work	NOUN
ejpam-4808	49	5	’s	’s	PART
ejpam-4808	49	6	core	core	NOUN
ejpam-4808	49	7	tenets	tenet	NOUN
ejpam-4808	49	8	is	be	AUX
ejpam-4808	49	9	the	the	DET
ejpam-4808	49	10	definition	definition	NOUN
ejpam-4808	49	11	of	of	ADP
ejpam-4808	49	12	the	the	DET
ejpam-4808	49	13	fuzzy	fuzzy	ADJ
ejpam-4808	49	14	generalized	generalize	VERB
ejpam-4808	49	15	closed	close	VERB
ejpam-4808	49	16	set	set	NOUN
ejpam-4808	49	17	,	,	PUNCT
ejpam-4808	49	18	which	which	PRON
ejpam-4808	49	19	as	as	ADP
ejpam-4808	49	20	following	follow	VERB
ejpam-4808	49	21	:	:	PUNCT
ejpam-4808	49	22	definition	definition	NOUN
ejpam-4808	49	23	5	5	NUM
ejpam-4808	49	24	.	.	PUNCT
ejpam-4808	50	1	[	[	X
ejpam-4808	50	2	6	6	NUM
ejpam-4808	50	3	]	]	PUNCT
ejpam-4808	50	4	any	any	DET
ejpam-4808	50	5	fuzzy	fuzzy	ADJ
ejpam-4808	50	6	group	group	NOUN
ejpam-4808	50	7	e	e	NOUN
ejpam-4808	50	8	of	of	ADP
ejpam-4808	50	9	x	x	PROPN
ejpam-4808	50	10	is	be	AUX
ejpam-4808	50	11	termed	term	VERB
ejpam-4808	50	12	fuzzy	fuzzy	ADJ
ejpam-4808	50	13	generalised	generalise	VERB
ejpam-4808	50	14	closed	close	VERB
ejpam-4808	50	15	when	when	SCONJ
ejpam-4808	50	16	closure	closure	NOUN
ejpam-4808	50	17	e	e	NOUN
ejpam-4808	50	18	is	be	AUX
ejpam-4808	50	19	subset	subset	VERB
ejpam-4808	50	20	of	of	ADP
ejpam-4808	50	21	w	w	NOUN
ejpam-4808	50	22	,	,	PUNCT
ejpam-4808	50	23	wherever	wherever	SCONJ
ejpam-4808	50	24	e	e	PROPN
ejpam-4808	50	25	is	be	AUX
ejpam-4808	50	26	subset	subset	VERB
ejpam-4808	50	27	of	of	ADP
ejpam-4808	50	28	w	w	PROPN
ejpam-4808	50	29	,	,	PUNCT
ejpam-4808	50	30	w	w	NOUN
ejpam-4808	50	31	is	be	AUX
ejpam-4808	50	32	fuzzy	fuzzy	ADJ
ejpam-4808	50	33	open	open	ADJ
ejpam-4808	50	34	.	.	PUNCT
ejpam-4808	51	1	i.e.	i.e.	X
ejpam-4808	51	2	,	,	PUNCT
ejpam-4808	51	3	e	e	X
ejpam-4808	51	4	is	be	AUX
ejpam-4808	51	5	fuzzy	fuzzy	ADJ
ejpam-4808	51	6	generalised	generalise	VERB
ejpam-4808	51	7	closed	close	VERB
ejpam-4808	51	8	in	in	ADP
ejpam-4808	51	9	case	case	NOUN
ejpam-4808	51	10	of	of	ADP
ejpam-4808	51	11	cl(e	cl(e	NOUN
ejpam-4808	51	12	)	)	PUNCT
ejpam-4808	51	13	≤	≤	NOUN
ejpam-4808	52	1	w	w	ADP
ejpam-4808	52	2	,	,	PUNCT
ejpam-4808	52	3	wherever	wherever	SCONJ
ejpam-4808	52	4	e	e	ADP
ejpam-4808	52	5	≤	≤	PROPN
ejpam-4808	52	6	w	w	ADP
ejpam-4808	52	7	,	,	PUNCT
ejpam-4808	52	8	w	w	NOUN
ejpam-4808	52	9	is	be	AUX
ejpam-4808	52	10	fuzzy	fuzzy	ADJ
ejpam-4808	52	11	open	open	ADJ
ejpam-4808	52	12	.	.	PUNCT
ejpam-4808	53	1	definition	definition	NOUN
ejpam-4808	53	2	6	6	NUM
ejpam-4808	53	3	.	.	PUNCT
ejpam-4808	54	1	[	[	X
ejpam-4808	54	2	10	10	NUM
ejpam-4808	54	3	]	]	SYM
ejpam-4808	54	4	(	(	PUNCT
ejpam-4808	54	5	1	1	X
ejpam-4808	54	6	)	)	PUNCT
ejpam-4808	54	7	a	a	DET
ejpam-4808	54	8	fuzzy	fuzzy	ADJ
ejpam-4808	54	9	point	point	NOUN
ejpam-4808	54	10	xλ	xλ	PROPN
ejpam-4808	54	11	is	be	AUX
ejpam-4808	54	12	claimed	claim	VERB
ejpam-4808	54	13	that	that	SCONJ
ejpam-4808	54	14	quasi	quasi	NOUN
ejpam-4808	54	15	-	-	NOUN
ejpam-4808	54	16	coincident	coincident	ADJ
ejpam-4808	54	17	with	with	ADP
ejpam-4808	54	18	e	e	NOUN
ejpam-4808	54	19	,	,	PUNCT
ejpam-4808	54	20	shown	show	VERB
ejpam-4808	54	21	by	by	ADP
ejpam-4808	54	22	xλ	xλ	PROPN
ejpam-4808	54	23	q	q	X
ejpam-4808	54	24	e	e	NOUN
ejpam-4808	54	25	if	if	SCONJ
ejpam-4808	54	26	λ	λ	PROPN
ejpam-4808	54	27	>	>	X
ejpam-4808	54	28	ec(x	ec(x	NOUN
ejpam-4808	54	29	)	)	PUNCT
ejpam-4808	54	30	,	,	PUNCT
ejpam-4808	54	31	or	or	CCONJ
ejpam-4808	54	32	λ+e(x	λ+e(x	ADV
ejpam-4808	54	33	)	)	PUNCT
ejpam-4808	54	34	>	>	X
ejpam-4808	54	35	1	1	NUM
ejpam-4808	54	36	and	and	CCONJ
ejpam-4808	54	37	xλ	xλ	PROPN
ejpam-4808	54	38	is	be	AUX
ejpam-4808	54	39	claimed	claim	VERB
ejpam-4808	54	40	does	do	AUX
ejpam-4808	54	41	not	not	PART
ejpam-4808	54	42	quasi	quasi	VERB
ejpam-4808	54	43	-	-	VERB
ejpam-4808	54	44	coincident	coincident	ADJ
ejpam-4808	54	45	with	with	ADP
ejpam-4808	54	46	e	e	NOUN
ejpam-4808	54	47	if	if	SCONJ
ejpam-4808	54	48	λ+e(x	λ+e(x	ADV
ejpam-4808	54	49	)	)	PUNCT
ejpam-4808	54	50	≤	≤	NUM
ejpam-4808	54	51	1	1	NUM
ejpam-4808	55	1	and	and	CCONJ
ejpam-4808	55	2	we	we	PRON
ejpam-4808	55	3	write	write	VERB
ejpam-4808	55	4	e	e	PROPN
ejpam-4808	55	5	q	q	NOUN
ejpam-4808	55	6	xλ	xλ	PROPN
ejpam-4808	55	7	.	.	PUNCT
ejpam-4808	56	1	(	(	PUNCT
ejpam-4808	56	2	2	2	X
ejpam-4808	56	3	)	)	PUNCT
ejpam-4808	56	4	e	e	NOUN
ejpam-4808	56	5	is	be	AUX
ejpam-4808	56	6	claimed	claim	VERB
ejpam-4808	56	7	quasi	quasi	ADJ
ejpam-4808	56	8	-	-	NOUN
ejpam-4808	56	9	coincident	coincident	ADJ
ejpam-4808	56	10	with	with	ADP
ejpam-4808	56	11	c	c	NOUN
ejpam-4808	56	12	indicated	indicate	VERB
ejpam-4808	56	13	as	as	ADP
ejpam-4808	56	14	e	e	X
ejpam-4808	56	15	q	q	PROPN
ejpam-4808	56	16	c	c	NOUN
ejpam-4808	56	17	if	if	SCONJ
ejpam-4808	56	18	there	there	PRON
ejpam-4808	56	19	exists	exist	VERB
ejpam-4808	56	20	x	x	X
ejpam-4808	56	21	∈	∈	NOUN
ejpam-4808	56	22	x	x	PUNCT
ejpam-4808	56	23	so	so	SCONJ
ejpam-4808	56	24	that	that	SCONJ
ejpam-4808	56	25	e(x	e(x	NUM
ejpam-4808	56	26	)	)	PUNCT
ejpam-4808	56	27	>	>	X
ejpam-4808	56	28	cc(x	cc(x	NOUN
ejpam-4808	56	29	)	)	PUNCT
ejpam-4808	56	30	or	or	CCONJ
ejpam-4808	56	31	e(x	e(x	NUM
ejpam-4808	56	32	)	)	PUNCT
ejpam-4808	57	1	+	+	NOUN
ejpam-4808	57	2	c(x	c(x	NOUN
ejpam-4808	57	3	)	)	PUNCT
ejpam-4808	57	4	>	>	X
ejpam-4808	58	1	1	1	NUM
ejpam-4808	58	2	,	,	PUNCT
ejpam-4808	58	3	and	and	CCONJ
ejpam-4808	58	4	e	e	NOUN
ejpam-4808	58	5	is	be	AUX
ejpam-4808	58	6	claimed	claim	VERB
ejpam-4808	58	7	does	do	AUX
ejpam-4808	58	8	not	not	PART
ejpam-4808	58	9	quasi	quasi	VERB
ejpam-4808	58	10	-	-	VERB
ejpam-4808	58	11	coincident	coincident	ADJ
ejpam-4808	58	12	with	with	ADP
ejpam-4808	58	13	c	c	NOUN
ejpam-4808	58	14	if	if	SCONJ
ejpam-4808	58	15	there	there	PRON
ejpam-4808	58	16	exists	exist	VERB
ejpam-4808	58	17	x	x	X
ejpam-4808	58	18	∈	∈	NOUN
ejpam-4808	58	19	x	x	PUNCT
ejpam-4808	58	20	so	so	SCONJ
ejpam-4808	58	21	that	that	SCONJ
ejpam-4808	58	22	e(x	e(x	NUM
ejpam-4808	58	23	)	)	PUNCT
ejpam-4808	59	1	+	+	CCONJ
ejpam-4808	59	2	c(x	c(x	NOUN
ejpam-4808	59	3	)	)	PUNCT
ejpam-4808	59	4	≤	≤	NOUN
ejpam-4808	59	5	1	1	NUM
ejpam-4808	60	1	and	and	CCONJ
ejpam-4808	60	2	we	we	PRON
ejpam-4808	60	3	write	write	VERB
ejpam-4808	60	4	e	e	PROPN
ejpam-4808	60	5	q	q	PROPN
ejpam-4808	60	6	c.	c.	NOUN
ejpam-4808	60	7	if	if	SCONJ
ejpam-4808	60	8	e	e	PROPN
ejpam-4808	60	9	q	q	X
ejpam-4808	60	10	c	c	PROPN
ejpam-4808	60	11	(	(	PUNCT
ejpam-4808	60	12	resp	resp	PROPN
ejpam-4808	60	13	,	,	PUNCT
ejpam-4808	60	14	e	e	X
ejpam-4808	61	1	q	q	PROPN
ejpam-4808	61	2	c	c	X
ejpam-4808	61	3	)	)	PUNCT
ejpam-4808	61	4	is	be	AUX
ejpam-4808	61	5	true	true	ADJ
ejpam-4808	61	6	,	,	PUNCT
ejpam-4808	61	7	then	then	ADV
ejpam-4808	61	8	e	e	PROPN
ejpam-4808	61	9	and	and	CCONJ
ejpam-4808	61	10	c	c	PROPN
ejpam-4808	61	11	are	be	AUX
ejpam-4808	61	12	quasi	quasi	ADJ
ejpam-4808	61	13	-	-	ADJ
ejpam-4808	61	14	coincident	coincident	ADJ
ejpam-4808	61	15	(	(	PUNCT
ejpam-4808	61	16	resp	resp	NOUN
ejpam-4808	61	17	,	,	PUNCT
ejpam-4808	61	18	not	not	PART
ejpam-4808	61	19	quasicoincident)with	quasicoincident)with	ADP
ejpam-4808	61	20	each	each	DET
ejpam-4808	61	21	other	other	ADJ
ejpam-4808	61	22	at	at	ADP
ejpam-4808	61	23	x.	x.	NOUN
ejpam-4808	61	24	3	3	NUM
ejpam-4808	61	25	.	.	PUNCT
ejpam-4808	61	26	generalized	generalize	VERB
ejpam-4808	61	27	neighborhoods	neighborhood	NOUN
ejpam-4808	61	28	structures	structure	NOUN
ejpam-4808	61	29	at	at	ADP
ejpam-4808	61	30	fuzzy	fuzzy	ADJ
ejpam-4808	61	31	bitopological	bitopological	ADJ
ejpam-4808	61	32	spaces	space	NOUN
ejpam-4808	61	33	this	this	DET
ejpam-4808	61	34	section	section	NOUN
ejpam-4808	61	35	introduces	introduce	VERB
ejpam-4808	61	36	the	the	DET
ejpam-4808	61	37	idea	idea	NOUN
ejpam-4808	61	38	of	of	ADP
ejpam-4808	61	39	generalized	generalized	ADJ
ejpam-4808	61	40	neighborhoods	neighborhood	NOUN
ejpam-4808	61	41	concepts	concept	NOUN
ejpam-4808	61	42	by	by	ADP
ejpam-4808	61	43	using	use	VERB
ejpam-4808	61	44	(	(	PUNCT
ejpam-4808	61	45	∈	∈	PROPN
ejpam-4808	61	46	)	)	PUNCT
ejpam-4808	61	47	relationship	relationship	NOUN
ejpam-4808	61	48	and	and	CCONJ
ejpam-4808	61	49	quasi	quasi	VERB
ejpam-4808	61	50	coincident	coincident	ADJ
ejpam-4808	61	51	concept	concept	NOUN
ejpam-4808	61	52	(	(	PUNCT
ejpam-4808	61	53	q	q	X
ejpam-4808	61	54	)	)	PUNCT
ejpam-4808	61	55	in	in	ADP
ejpam-4808	61	56	fuzzy	fuzzy	ADJ
ejpam-4808	61	57	bitopological	bitopological	ADJ
ejpam-4808	61	58	spaces	space	NOUN
ejpam-4808	61	59	and	and	CCONJ
ejpam-4808	61	60	characterize	characterize	VERB
ejpam-4808	61	61	it	it	PRON
ejpam-4808	61	62	in	in	ADP
ejpam-4808	61	63	terms	term	NOUN
ejpam-4808	61	64	of	of	ADP
ejpam-4808	61	65	important	important	ADJ
ejpam-4808	61	66	theorems	theorem	NOUN
ejpam-4808	61	67	and	and	CCONJ
ejpam-4808	61	68	some	some	DET
ejpam-4808	61	69	properties	property	NOUN
ejpam-4808	61	70	.	.	PUNCT
ejpam-4808	62	1	definition	definition	NOUN
ejpam-4808	62	2	7	7	NUM
ejpam-4808	62	3	.	.	PUNCT
ejpam-4808	63	1	a	a	DET
ejpam-4808	63	2	fuzzy	fuzzy	ADJ
ejpam-4808	63	3	subgroup	subgroup	NOUN
ejpam-4808	63	4	e	e	PROPN
ejpam-4808	63	5	of	of	ADP
ejpam-4808	63	6	fbts	fbt	NOUN
ejpam-4808	63	7	(	(	PUNCT
ejpam-4808	63	8	x	x	NOUN
ejpam-4808	63	9	,	,	PUNCT
ejpam-4808	63	10	δ1	δ1	NOUN
ejpam-4808	63	11	,	,	PUNCT
ejpam-4808	63	12	δ2	δ2	PROPN
ejpam-4808	63	13	)	)	PUNCT
ejpam-4808	63	14	is	be	AUX
ejpam-4808	63	15	known	know	VERB
ejpam-4808	63	16	as	as	ADP
ejpam-4808	63	17	:	:	PUNCT
ejpam-4808	63	18	(	(	PUNCT
ejpam-4808	63	19	1	1	X
ejpam-4808	63	20	)	)	PUNCT
ejpam-4808	63	21	fuzzy	fuzzy	NOUN
ejpam-4808	63	22	(	(	PUNCT
ejpam-4808	63	23	i	i	NOUN
ejpam-4808	63	24	,	,	PUNCT
ejpam-4808	63	25	j)−generalized	j)−generalize	VERB
ejpam-4808	63	26	φ−closed	φ−closed	ADV
ejpam-4808	63	27	(	(	PUNCT
ejpam-4808	63	28	in	in	ADP
ejpam-4808	63	29	sum	sum	NOUN
ejpam-4808	63	30	,	,	PUNCT
ejpam-4808	63	31	(	(	PUNCT
ejpam-4808	63	32	i	i	PROPN
ejpam-4808	63	33	,	,	PUNCT
ejpam-4808	63	34	j)−	j)−	PROPN
ejpam-4808	63	35	gφ−	gφ−	PROPN
ejpam-4808	63	36	closed	close	VERB
ejpam-4808	63	37	)	)	PUNCT
ejpam-4808	63	38	if	if	SCONJ
ejpam-4808	63	39	δj	δj	ADJ
ejpam-4808	63	40	−φ−	−φ−	NOUN
ejpam-4808	63	41	cl(e	cl(e	NOUN
ejpam-4808	63	42	)	)	PUNCT
ejpam-4808	63	43	≤	≤	PUNCT
ejpam-4808	63	44	u	u	NOUN
ejpam-4808	63	45	where	where	SCONJ
ejpam-4808	63	46	e	e	NOUN
ejpam-4808	63	47	≤	≤	NOUN
ejpam-4808	63	48	u	u	NOUN
ejpam-4808	63	49	,	,	PUNCT
ejpam-4808	63	50	u	u	PROPN
ejpam-4808	63	51	∈	∈	PROPN
ejpam-4808	63	52	δi	δi	PROPN
ejpam-4808	63	53	,	,	PUNCT
ejpam-4808	63	54	and	and	CCONJ
ejpam-4808	63	55	φ	φ	X
ejpam-4808	63	56	including	include	VERB
ejpam-4808	63	57	the	the	DET
ejpam-4808	63	58	types	type	NOUN
ejpam-4808	63	59	(	(	PUNCT
ejpam-4808	63	60	alpha	alpha	NOUN
ejpam-4808	63	61	(	(	PUNCT
ejpam-4808	63	62	α	α	NOUN
ejpam-4808	63	63	)	)	PUNCT
ejpam-4808	63	64	,	,	PUNCT
ejpam-4808	63	65	semi	semi	ADV
ejpam-4808	63	66	(	(	PUNCT
ejpam-4808	63	67	s	s	NOUN
ejpam-4808	63	68	)	)	PUNCT
ejpam-4808	63	69	,	,	PUNCT
ejpam-4808	63	70	pre	pre	X
ejpam-4808	64	1	(	(	PUNCT
ejpam-4808	64	2	p	p	NOUN
ejpam-4808	64	3	)	)	PUNCT
ejpam-4808	64	4	,	,	PUNCT
ejpam-4808	64	5	and	and	CCONJ
ejpam-4808	64	6	beta	beta	NOUN
ejpam-4808	64	7	(	(	PUNCT
ejpam-4808	64	8	β	β	NOUN
ejpam-4808	64	9	)	)	PUNCT
ejpam-4808	64	10	)	)	PUNCT
ejpam-4808	64	11	.	.	PUNCT
ejpam-4808	65	1	(	(	PUNCT
ejpam-4808	65	2	2	2	X
ejpam-4808	65	3	)	)	PUNCT
ejpam-4808	65	4	the	the	DET
ejpam-4808	65	5	supplement	supplement	NOUN
ejpam-4808	65	6	of	of	ADP
ejpam-4808	65	7	the	the	DET
ejpam-4808	65	8	fuzzy	fuzzy	ADJ
ejpam-4808	65	9	(	(	PUNCT
ejpam-4808	65	10	i	i	PROPN
ejpam-4808	65	11	,	,	PUNCT
ejpam-4808	65	12	j	j	PROPN
ejpam-4808	65	13	)	)	PUNCT
ejpam-4808	65	14	−	−	PROPN
ejpam-4808	65	15	gφ	gφ	PROPN
ejpam-4808	65	16	−	−	PROPN
ejpam-4808	65	17	closed	closed	ADJ
ejpam-4808	65	18	set	set	NOUN
ejpam-4808	65	19	is	be	AUX
ejpam-4808	65	20	referred	refer	VERB
ejpam-4808	65	21	to	to	ADP
ejpam-4808	65	22	(	(	PUNCT
ejpam-4808	65	23	i	i	PROPN
ejpam-4808	65	24	,	,	PUNCT
ejpam-4808	65	25	j	j	PROPN
ejpam-4808	65	26	)	)	PUNCT
ejpam-4808	65	27	−	−	PROPN
ejpam-4808	65	28	gφ	gφ	NOUN
ejpam-4808	65	29	−	−	PROPN
ejpam-4808	65	30	open	open	ADJ
ejpam-4808	65	31	set	set	VERB
ejpam-4808	65	32	in	in	ADP
ejpam-4808	65	33	x.	x.	NOUN
ejpam-4808	65	34	remark	remark	PROPN
ejpam-4808	65	35	1	1	NUM
ejpam-4808	65	36	.	.	PUNCT
ejpam-4808	66	1	(	(	PUNCT
ejpam-4808	66	2	1	1	X
ejpam-4808	66	3	)	)	PUNCT
ejpam-4808	66	4	the	the	DET
ejpam-4808	66	5	universal	universal	ADJ
ejpam-4808	66	6	set	set	NOUN
ejpam-4808	66	7	of	of	ADP
ejpam-4808	66	8	all	all	DET
ejpam-4808	66	9	fuzzy	fuzzy	ADJ
ejpam-4808	66	10	(	(	PUNCT
ejpam-4808	66	11	i	i	PROPN
ejpam-4808	66	12	,	,	PUNCT
ejpam-4808	66	13	j	j	PROPN
ejpam-4808	66	14	)	)	PUNCT
ejpam-4808	66	15	−	−	PROPN
ejpam-4808	66	16	gφ−open	gφ−open	NOUN
ejpam-4808	66	17	,	,	PUNCT
ejpam-4808	66	18	and	and	CCONJ
ejpam-4808	66	19	(	(	PUNCT
ejpam-4808	66	20	i	i	PROPN
ejpam-4808	66	21	,	,	PUNCT
ejpam-4808	66	22	j	j	PROPN
ejpam-4808	66	23	)	)	PUNCT
ejpam-4808	67	1	−	−	PROPN
ejpam-4808	67	2	gφ−closed	gφ−close	VERB
ejpam-4808	67	3	sets	set	NOUN
ejpam-4808	67	4	of	of	ADP
ejpam-4808	67	5	fbts	fbt	NOUN
ejpam-4808	67	6	(	(	PUNCT
ejpam-4808	67	7	x	x	NOUN
ejpam-4808	67	8	,	,	PUNCT
ejpam-4808	67	9	δ1	δ1	NOUN
ejpam-4808	67	10	,	,	PUNCT
ejpam-4808	67	11	δ2	δ2	PROPN
ejpam-4808	67	12	)	)	PUNCT
ejpam-4808	67	13	is	be	AUX
ejpam-4808	67	14	represented	represent	VERB
ejpam-4808	67	15	by	by	ADP
ejpam-4808	67	16	ofgφ	ofgφ	NOUN
ejpam-4808	67	17	(	(	PUNCT
ejpam-4808	67	18	i	i	PROPN
ejpam-4808	67	19	,	,	PUNCT
ejpam-4808	67	20	j	j	PROPN
ejpam-4808	67	21	)	)	PUNCT
ejpam-4808	67	22	,	,	PUNCT
ejpam-4808	67	23	f	f	PROPN
ejpam-4808	67	24	fgφ	fgφ	PROPN
ejpam-4808	67	25	(	(	PUNCT
ejpam-4808	67	26	i	i	PROPN
ejpam-4808	67	27	,	,	PUNCT
ejpam-4808	67	28	j	j	PROPN
ejpam-4808	67	29	)	)	PUNCT
ejpam-4808	67	30	,	,	PUNCT
ejpam-4808	67	31	and	and	CCONJ
ejpam-4808	67	32	so	so	ADV
ejpam-4808	67	33	forth	forth	ADV
ejpam-4808	67	34	.	.	PUNCT
ejpam-4808	68	1	a.	a.	NOUN
ejpam-4808	68	2	a.	a.	PROPN
ejpam-4808	68	3	alharbi	alharbi	PROPN
ejpam-4808	68	4	,	,	PUNCT
ejpam-4808	68	5	a.	a.	NOUN
ejpam-4808	68	6	kilicman	kilicman	PROPN
ejpam-4808	68	7	/	/	SYM
ejpam-4808	68	8	eur	eur	PROPN
ejpam-4808	68	9	.	.	PUNCT
ejpam-4808	69	1	j.	j.	PROPN
ejpam-4808	69	2	pure	pure	PROPN
ejpam-4808	69	3	appl	appl	PROPN
ejpam-4808	69	4	.	.	PROPN
ejpam-4808	69	5	math	math	PROPN
ejpam-4808	69	6	,	,	PUNCT
ejpam-4808	69	7	16	16	NUM
ejpam-4808	69	8	(	(	PUNCT
ejpam-4808	69	9	3	3	NUM
ejpam-4808	69	10	)	)	PUNCT
ejpam-4808	69	11	(	(	PUNCT
ejpam-4808	69	12	2023	2023	NUM
ejpam-4808	69	13	)	)	PUNCT
ejpam-4808	69	14	,	,	PUNCT
ejpam-4808	69	15	1980	1980	NUM
ejpam-4808	69	16	-	-	SYM
ejpam-4808	69	17	1990	1990	NUM
ejpam-4808	69	18	1983	1983	NUM
ejpam-4808	69	19	(	(	PUNCT
ejpam-4808	69	20	2	2	NUM
ejpam-4808	69	21	)	)	PUNCT
ejpam-4808	69	22	also	also	ADV
ejpam-4808	69	23	,	,	PUNCT
ejpam-4808	69	24	the	the	DET
ejpam-4808	69	25	family	family	NOUN
ejpam-4808	69	26	of	of	ADP
ejpam-4808	69	27	all	all	DET
ejpam-4808	69	28	gφ−open	gφ−open	NOUN
ejpam-4808	69	29	,	,	PUNCT
ejpam-4808	69	30	and	and	CCONJ
ejpam-4808	69	31	gφ−closed	gφ−close	VERB
ejpam-4808	69	32	subsets	subset	NOUN
ejpam-4808	69	33	of	of	ADP
ejpam-4808	69	34	x	x	PUNCT
ejpam-4808	69	35	pertaining	pertain	VERB
ejpam-4808	69	36	to	to	ADP
ejpam-4808	69	37	the	the	DET
ejpam-4808	69	38	fuzzy	fuzzy	ADJ
ejpam-4808	69	39	topology	topology	NOUN
ejpam-4808	69	40	δi	δi	NOUN
ejpam-4808	69	41	is	be	AUX
ejpam-4808	69	42	indicated	indicate	VERB
ejpam-4808	69	43	ofgφ	ofgφ	ADJ
ejpam-4808	69	44	i	i	PRON
ejpam-4808	69	45	,	,	PUNCT
ejpam-4808	69	46	and	and	CCONJ
ejpam-4808	69	47	ffgφ	ffgφ	VERB
ejpam-4808	69	48	i	i	PRON
ejpam-4808	69	49	,	,	PUNCT
ejpam-4808	69	50	i	i	PRON
ejpam-4808	69	51	=	=	NOUN
ejpam-4808	69	52	1	1	NUM
ejpam-4808	69	53	,	,	PUNCT
ejpam-4808	69	54	2	2	NUM
ejpam-4808	69	55	.	.	X
ejpam-4808	69	56	proposition	proposition	NOUN
ejpam-4808	69	57	1	1	NUM
ejpam-4808	69	58	.	.	PUNCT
ejpam-4808	70	1	a	a	DET
ejpam-4808	70	2	fuzzy	fuzzy	ADJ
ejpam-4808	70	3	group	group	NOUN
ejpam-4808	70	4	e	e	NOUN
ejpam-4808	70	5	in	in	ADP
ejpam-4808	70	6	fbts	fbt	NOUN
ejpam-4808	70	7	(	(	PUNCT
ejpam-4808	70	8	x	x	NOUN
ejpam-4808	70	9	,	,	PUNCT
ejpam-4808	70	10	δ1	δ1	NOUN
ejpam-4808	70	11	,	,	PUNCT
ejpam-4808	70	12	δ2	δ2	PROPN
ejpam-4808	70	13	)	)	PUNCT
ejpam-4808	70	14	is	be	AUX
ejpam-4808	70	15	fuzzy	fuzzy	ADJ
ejpam-4808	70	16	(	(	PUNCT
ejpam-4808	70	17	i	i	PROPN
ejpam-4808	70	18	,	,	PUNCT
ejpam-4808	70	19	j	j	PROPN
ejpam-4808	70	20	)	)	PUNCT
ejpam-4808	70	21	−	−	PROPN
ejpam-4808	70	22	gφ	gφ	NOUN
ejpam-4808	70	23	-	-	PUNCT
ejpam-4808	70	24	open	open	ADJ
ejpam-4808	70	25	⇐	⇐	ADJ
ejpam-4808	70	26	⇒	⇒	NOUN
ejpam-4808	70	27	f	f	PROPN
ejpam-4808	70	28	≤	≤	NUM
ejpam-4808	70	29	δj	δj	ADP
ejpam-4808	70	30	−	−	PROPN
ejpam-4808	70	31	φ−	φ−	PROPN
ejpam-4808	70	32	int(e	int(e	PROPN
ejpam-4808	70	33	)	)	PUNCT
ejpam-4808	70	34	wherever	wherever	SCONJ
ejpam-4808	70	35	f	f	PROPN
ejpam-4808	70	36	c	c	PROPN
ejpam-4808	70	37	∈	∈	PROPN
ejpam-4808	70	38	δi	δi	PROPN
ejpam-4808	70	39	,	,	PUNCT
ejpam-4808	70	40	f	f	PROPN
ejpam-4808	70	41	≤	≤	PROPN
ejpam-4808	70	42	e.	e.	PROPN
ejpam-4808	70	43	proof	proof	PROPN
ejpam-4808	70	44	.	.	PUNCT
ejpam-4808	71	1	assume	assume	VERB
ejpam-4808	71	2	e	e	NOUN
ejpam-4808	71	3	is	be	AUX
ejpam-4808	71	4	fuzzy	fuzzy	ADJ
ejpam-4808	71	5	(	(	PUNCT
ejpam-4808	71	6	i	i	PROPN
ejpam-4808	71	7	,	,	PUNCT
ejpam-4808	71	8	j	j	PROPN
ejpam-4808	71	9	)	)	PUNCT
ejpam-4808	72	1	−	−	PROPN
ejpam-4808	72	2	gφ−open	gφ−open	NOUN
ejpam-4808	72	3	,	,	PUNCT
ejpam-4808	72	4	f	f	PROPN
ejpam-4808	72	5	c	c	NOUN
ejpam-4808	72	6	∈	∈	PROPN
ejpam-4808	72	7	δi	δi	PROPN
ejpam-4808	72	8	,	,	PUNCT
ejpam-4808	72	9	when	when	SCONJ
ejpam-4808	72	10	f	f	PROPN
ejpam-4808	72	11	≤	≤	PROPN
ejpam-4808	72	12	e.	e.	PROPN
ejpam-4808	72	13	then	then	ADV
ejpam-4808	72	14	ec	ec	PROPN
ejpam-4808	72	15	≤	≤	PROPN
ejpam-4808	72	16	f	f	PROPN
ejpam-4808	72	17	c.	c.	PROPN
ejpam-4808	72	18	as	as	SCONJ
ejpam-4808	72	19	ec	ec	PROPN
ejpam-4808	72	20	is	be	AUX
ejpam-4808	72	21	fuzzy	fuzzy	ADJ
ejpam-4808	72	22	(	(	PUNCT
ejpam-4808	72	23	i	i	PROPN
ejpam-4808	72	24	,	,	PUNCT
ejpam-4808	72	25	j	j	PROPN
ejpam-4808	72	26	)	)	PUNCT
ejpam-4808	72	27	−	−	PROPN
ejpam-4808	72	28	gφ−closed	gφ−close	VERB
ejpam-4808	72	29	,	,	PUNCT
ejpam-4808	72	30	thus	thus	ADV
ejpam-4808	72	31	δj	δj	ADP
ejpam-4808	72	32	−	−	PROPN
ejpam-4808	72	33	φ	φ	PROPN
ejpam-4808	72	34	−	−	PROPN
ejpam-4808	72	35	cl(ec	cl(ec	PROPN
ejpam-4808	72	36	)	)	PUNCT
ejpam-4808	73	1	=	=	PUNCT
ejpam-4808	73	2	(	(	PUNCT
ejpam-4808	73	3	δj	δj	ADP
ejpam-4808	73	4	−	−	PROPN
ejpam-4808	73	5	φ	φ	PROPN
ejpam-4808	73	6	−	−	PROPN
ejpam-4808	73	7	int(e))c	int(e))c	PROPN
ejpam-4808	73	8	≤	≤	PROPN
ejpam-4808	74	1	f	f	PROPN
ejpam-4808	74	2	c	c	NOUN
ejpam-4808	74	3	that	that	PRON
ejpam-4808	74	4	indicates	indicate	VERB
ejpam-4808	74	5	f	f	PROPN
ejpam-4808	74	6	≤	≤	PROPN
ejpam-4808	74	7	δj	δj	ADP
ejpam-4808	74	8	−	−	PROPN
ejpam-4808	74	9	φ−	φ−	PROPN
ejpam-4808	74	10	int(e	int(e	PROPN
ejpam-4808	74	11	)	)	PUNCT
ejpam-4808	74	12	.	.	PUNCT
ejpam-4808	75	1	conversely	conversely	ADV
ejpam-4808	75	2	,	,	PUNCT
ejpam-4808	75	3	assume	assume	VERB
ejpam-4808	75	4	e	e	NOUN
ejpam-4808	75	5	is	be	AUX
ejpam-4808	75	6	fuzzy	fuzzy	ADJ
ejpam-4808	75	7	set	set	NOUN
ejpam-4808	75	8	of	of	ADP
ejpam-4808	75	9	x	x	PROPN
ejpam-4808	75	10	,	,	PUNCT
ejpam-4808	75	11	f	f	PROPN
ejpam-4808	75	12	∈	∈	PROPN
ejpam-4808	75	13	fi	fi	NOUN
ejpam-4808	76	1	so	so	CCONJ
ejpam-4808	76	2	f	f	PROPN
ejpam-4808	76	3	≤	≤	PROPN
ejpam-4808	76	4	δj	δj	ADP
ejpam-4808	76	5	−	−	PROPN
ejpam-4808	76	6	φ	φ	PROPN
ejpam-4808	76	7	−	−	PROPN
ejpam-4808	76	8	int(e	int(e	PROPN
ejpam-4808	76	9	)	)	PUNCT
ejpam-4808	76	10	,	,	PUNCT
ejpam-4808	76	11	f	f	PROPN
ejpam-4808	76	12	≤	≤	PROPN
ejpam-4808	76	13	e.	e.	PROPN
ejpam-4808	76	14	after	after	ADP
ejpam-4808	76	15	adding	add	VERB
ejpam-4808	76	16	the	the	DET
ejpam-4808	76	17	supplement	supplement	NOUN
ejpam-4808	76	18	to	to	ADP
ejpam-4808	76	19	both	both	DET
ejpam-4808	76	20	sides	side	NOUN
ejpam-4808	76	21	,	,	PUNCT
ejpam-4808	76	22	we	we	PRON
ejpam-4808	76	23	find	find	VERB
ejpam-4808	76	24	(	(	PUNCT
ejpam-4808	76	25	δj	δj	ADP
ejpam-4808	76	26	−	−	PROPN
ejpam-4808	76	27	φ	φ	PROPN
ejpam-4808	76	28	−	−	PROPN
ejpam-4808	76	29	int(e))c	int(e))c	PROPN
ejpam-4808	76	30	≤	≤	PROPN
ejpam-4808	77	1	f	f	PROPN
ejpam-4808	77	2	c	c	NOUN
ejpam-4808	78	1	so	so	ADV
ejpam-4808	78	2	ec	ec	PROPN
ejpam-4808	78	3	≤	≤	PROPN
ejpam-4808	78	4	f	f	PROPN
ejpam-4808	78	5	c	c	PROPN
ejpam-4808	78	6	and	and	CCONJ
ejpam-4808	78	7	f	f	PROPN
ejpam-4808	78	8	c	c	NOUN
ejpam-4808	78	9	is	be	AUX
ejpam-4808	78	10	fuzzy	fuzzy	ADJ
ejpam-4808	78	11	open	open	ADJ
ejpam-4808	78	12	in	in	ADP
ejpam-4808	78	13	δi	δi	NOUN
ejpam-4808	78	14	,	,	PUNCT
ejpam-4808	78	15	thus	thus	ADV
ejpam-4808	78	16	e	e	X
ejpam-4808	78	17	c	c	PROPN
ejpam-4808	78	18	is	be	AUX
ejpam-4808	78	19	fuzzy	fuzzy	ADJ
ejpam-4808	78	20	(	(	PUNCT
ejpam-4808	78	21	i	i	PROPN
ejpam-4808	78	22	,	,	PUNCT
ejpam-4808	78	23	j)−	j)−	PROPN
ejpam-4808	78	24	gφ−closed	gφ−close	VERB
ejpam-4808	78	25	(	(	PUNCT
ejpam-4808	78	26	defention7	defention7	X
ejpam-4808	78	27	)	)	PUNCT
ejpam-4808	78	28	.	.	PUNCT
ejpam-4808	79	1	hence	hence	ADV
ejpam-4808	79	2	e	e	PROPN
ejpam-4808	79	3	is	be	AUX
ejpam-4808	79	4	fuzzy	fuzzy	ADJ
ejpam-4808	79	5	(	(	PUNCT
ejpam-4808	79	6	i	i	NOUN
ejpam-4808	79	7	,	,	PUNCT
ejpam-4808	79	8	j)−	j)−	PROPN
ejpam-4808	79	9	gφ−open	gφ−open	PROPN
ejpam-4808	79	10	.	.	PUNCT
ejpam-4808	80	1	definition	definition	NOUN
ejpam-4808	80	2	8	8	NUM
ejpam-4808	80	3	.	.	PUNCT
ejpam-4808	81	1	a	a	DET
ejpam-4808	81	2	fuzzy	fuzzy	ADJ
ejpam-4808	81	3	group	group	NOUN
ejpam-4808	81	4	e	e	NOUN
ejpam-4808	81	5	in	in	ADP
ejpam-4808	81	6	fbts	fbt	NOUN
ejpam-4808	81	7	(	(	PUNCT
ejpam-4808	81	8	x	x	NOUN
ejpam-4808	81	9	,	,	PUNCT
ejpam-4808	81	10	δ1	δ1	NOUN
ejpam-4808	81	11	,	,	PUNCT
ejpam-4808	81	12	δ2	δ2	PROPN
ejpam-4808	81	13	)	)	PUNCT
ejpam-4808	81	14	is	be	AUX
ejpam-4808	81	15	known	know	VERB
ejpam-4808	81	16	as	as	ADP
ejpam-4808	81	17	:	:	PUNCT
ejpam-4808	81	18	(	(	PUNCT
ejpam-4808	81	19	1	1	X
ejpam-4808	81	20	)	)	PUNCT
ejpam-4808	81	21	fuzzy	fuzzy	NOUN
ejpam-4808	81	22	(	(	PUNCT
ejpam-4808	81	23	i	i	NOUN
ejpam-4808	81	24	,	,	PUNCT
ejpam-4808	81	25	j)−generalizedφ−neighborhood	j)−generalizedφ−neighborhood	PROPN
ejpam-4808	81	26	(	(	PUNCT
ejpam-4808	81	27	shortly	shortly	ADV
ejpam-4808	81	28	,	,	PUNCT
ejpam-4808	81	29	(	(	PUNCT
ejpam-4808	81	30	i	i	X
ejpam-4808	81	31	,	,	PUNCT
ejpam-4808	81	32	j)−gφ−nbd	j)−gφ−nbd	PROPN
ejpam-4808	81	33	)	)	PUNCT
ejpam-4808	81	34	of	of	ADP
ejpam-4808	81	35	fuzzy	fuzzy	ADJ
ejpam-4808	81	36	singleton	singleton	PROPN
ejpam-4808	81	37	set	set	VERB
ejpam-4808	81	38	xr	xr	PROPN
ejpam-4808	81	39	if	if	SCONJ
ejpam-4808	81	40	∃	∃	PROPN
ejpam-4808	81	41	fuzzy	fuzzy	ADJ
ejpam-4808	81	42	(	(	PUNCT
ejpam-4808	81	43	i	i	PROPN
ejpam-4808	81	44	,	,	PUNCT
ejpam-4808	82	1	j)−	j)−	PROPN
ejpam-4808	82	2	gφ−	gφ−	PROPN
ejpam-4808	82	3	open	open	ADJ
ejpam-4808	82	4	set	set	NOUN
ejpam-4808	82	5	c	c	PROPN
ejpam-4808	83	1	so	so	ADV
ejpam-4808	83	2	xr	xr	PROPN
ejpam-4808	83	3	∈	∈	PROPN
ejpam-4808	83	4	c	c	PROPN
ejpam-4808	83	5	≤	≤	PROPN
ejpam-4808	83	6	e.	e.	PROPN
ejpam-4808	83	7	the	the	DET
ejpam-4808	83	8	family	family	NOUN
ejpam-4808	83	9	of	of	ADP
ejpam-4808	83	10	all	all	DET
ejpam-4808	83	11	fuzzy	fuzzy	ADJ
ejpam-4808	83	12	(	(	PUNCT
ejpam-4808	83	13	i	i	NOUN
ejpam-4808	83	14	,	,	PUNCT
ejpam-4808	83	15	j)−	j)−	PROPN
ejpam-4808	83	16	gφ−nbds	gφ−nbds	NOUN
ejpam-4808	83	17	of	of	ADP
ejpam-4808	83	18	fuzzy	fuzzy	ADJ
ejpam-4808	83	19	singleton	singleton	PROPN
ejpam-4808	83	20	set	set	PROPN
ejpam-4808	83	21	xr	xr	PROPN
ejpam-4808	83	22	,	,	PUNCT
ejpam-4808	83	23	will	will	AUX
ejpam-4808	83	24	be	be	AUX
ejpam-4808	83	25	denoted	denote	VERB
ejpam-4808	83	26	by	by	ADP
ejpam-4808	83	27	ngφ	ngφ	PROPN
ejpam-4808	83	28	(	(	PUNCT
ejpam-4808	83	29	i	i	NOUN
ejpam-4808	83	30	,	,	PUNCT
ejpam-4808	83	31	j)(xr	j)(xr	PROPN
ejpam-4808	83	32	)	)	PUNCT
ejpam-4808	83	33	.	.	PUNCT
ejpam-4808	84	1	(	(	PUNCT
ejpam-4808	84	2	2	2	X
ejpam-4808	84	3	)	)	PUNCT
ejpam-4808	84	4	fuzzy	fuzzy	NOUN
ejpam-4808	84	5	(	(	PUNCT
ejpam-4808	84	6	i	i	PROPN
ejpam-4808	84	7	,	,	PUNCT
ejpam-4808	84	8	j)−	j)−	PROPN
ejpam-4808	84	9	generalizedφ−q−	generalizedφ−q−	PROPN
ejpam-4808	84	10	neighborhood	neighborhood	NOUN
ejpam-4808	84	11	(	(	PUNCT
ejpam-4808	84	12	shortly	shortly	ADV
ejpam-4808	84	13	,	,	PUNCT
ejpam-4808	84	14	(	(	PUNCT
ejpam-4808	84	15	i	i	PRON
ejpam-4808	84	16	,	,	PUNCT
ejpam-4808	84	17	j)−	j)−	PROPN
ejpam-4808	84	18	gφq−	gφq−	PROPN
ejpam-4808	84	19	nbd	nbd	PROPN
ejpam-4808	84	20	)	)	PUNCT
ejpam-4808	84	21	of	of	ADP
ejpam-4808	84	22	fuzzy	fuzzy	ADJ
ejpam-4808	84	23	singleton	singleton	PROPN
ejpam-4808	84	24	xr	xr	PROPN
ejpam-4808	84	25	if	if	SCONJ
ejpam-4808	84	26	∃	∃	PROPN
ejpam-4808	84	27	fuzzy	fuzzy	ADJ
ejpam-4808	84	28	(	(	PUNCT
ejpam-4808	84	29	i	i	PROPN
ejpam-4808	84	30	,	,	PUNCT
ejpam-4808	85	1	j)−	j)−	PROPN
ejpam-4808	85	2	gφ−	gφ−	PROPN
ejpam-4808	85	3	open	open	ADJ
ejpam-4808	85	4	set	set	NOUN
ejpam-4808	85	5	c	c	PROPN
ejpam-4808	86	1	so	so	ADV
ejpam-4808	86	2	xr	xr	PROPN
ejpam-4808	86	3	q	q	PROPN
ejpam-4808	87	1	c	c	PROPN
ejpam-4808	87	2	≤	≤	PROPN
ejpam-4808	87	3	e.	e.	PROPN
ejpam-4808	87	4	the	the	DET
ejpam-4808	87	5	family	family	NOUN
ejpam-4808	87	6	of	of	ADP
ejpam-4808	87	7	all	all	DET
ejpam-4808	87	8	fuzzy	fuzzy	ADJ
ejpam-4808	87	9	(	(	PUNCT
ejpam-4808	87	10	i	i	PROPN
ejpam-4808	87	11	,	,	PUNCT
ejpam-4808	87	12	j)−	j)−	PROPN
ejpam-4808	87	13	gφq−	gφq−	PROPN
ejpam-4808	87	14	nbds	nbds	NOUN
ejpam-4808	87	15	of	of	ADP
ejpam-4808	87	16	fuzzy	fuzzy	ADJ
ejpam-4808	87	17	singleton	singleton	PROPN
ejpam-4808	87	18	xr	xr	PROPN
ejpam-4808	87	19	,	,	PUNCT
ejpam-4808	87	20	will	will	AUX
ejpam-4808	87	21	be	be	AUX
ejpam-4808	87	22	denoted	denote	VERB
ejpam-4808	87	23	by	by	ADP
ejpam-4808	87	24	ngφq	ngφq	NOUN
ejpam-4808	87	25	(	(	PUNCT
ejpam-4808	87	26	i	i	PROPN
ejpam-4808	87	27	,	,	PUNCT
ejpam-4808	87	28	j	j	PROPN
ejpam-4808	87	29	)	)	PUNCT
ejpam-4808	87	30	(	(	PUNCT
ejpam-4808	87	31	xr	xr	X
ejpam-4808	87	32	)	)	PUNCT
ejpam-4808	87	33	.	.	PUNCT
ejpam-4808	88	1	remark	remark	NOUN
ejpam-4808	88	2	2	2	NUM
ejpam-4808	88	3	.	.	PUNCT
ejpam-4808	89	1	in	in	ADP
ejpam-4808	89	2	general	general	ADJ
ejpam-4808	89	3	,	,	PUNCT
ejpam-4808	89	4	every	every	DET
ejpam-4808	89	5	fuzzy	fuzzy	ADJ
ejpam-4808	89	6	δ−q−neighborhood	δ−q−neighborhood	NOUN
ejpam-4808	89	7	of	of	ADP
ejpam-4808	89	8	a	a	DET
ejpam-4808	89	9	fuzzy	fuzzy	ADJ
ejpam-4808	89	10	point	point	NOUN
ejpam-4808	89	11	does	do	AUX
ejpam-4808	89	12	not	not	PART
ejpam-4808	89	13	include	include	VERB
ejpam-4808	89	14	the	the	DET
ejpam-4808	89	15	point	point	NOUN
ejpam-4808	89	16	itself	itself	PRON
ejpam-4808	89	17	.	.	PUNCT
ejpam-4808	90	1	the	the	DET
ejpam-4808	90	2	coming	come	VERB
ejpam-4808	90	3	example	example	NOUN
ejpam-4808	90	4	show	show	VERB
ejpam-4808	90	5	that	that	SCONJ
ejpam-4808	90	6	:	:	PUNCT
ejpam-4808	90	7	example	example	NOUN
ejpam-4808	90	8	1	1	X
ejpam-4808	90	9	.	.	X
ejpam-4808	91	1	assume	assume	VERB
ejpam-4808	91	2	x0.7	x0.7	PROPN
ejpam-4808	91	3	is	be	AUX
ejpam-4808	91	4	fuzzy	fuzzy	ADJ
ejpam-4808	91	5	point	point	NOUN
ejpam-4808	91	6	of	of	ADP
ejpam-4808	91	7	x	x	X
ejpam-4808	91	8	=	=	X
ejpam-4808	91	9	{	{	PUNCT
ejpam-4808	91	10	a	a	PRON
ejpam-4808	91	11	,	,	PUNCT
ejpam-4808	91	12	b	b	NOUN
ejpam-4808	91	13	,	,	PUNCT
ejpam-4808	91	14	c	c	NOUN
ejpam-4808	91	15	}	}	PUNCT
ejpam-4808	91	16	and	and	CCONJ
ejpam-4808	91	17	e	e	NOUN
ejpam-4808	91	18	is	be	AUX
ejpam-4808	91	19	fuzzy	fuzzy	ADJ
ejpam-4808	91	20	set	set	NOUN
ejpam-4808	91	21	of	of	ADP
ejpam-4808	91	22	x	x	PUNCT
ejpam-4808	91	23	defined	define	VERB
ejpam-4808	91	24	as	as	ADP
ejpam-4808	91	25	e(a	e(a	NOUN
ejpam-4808	91	26	)	)	PUNCT
ejpam-4808	91	27	=	=	SYM
ejpam-4808	91	28	0.4	0.4	NUM
ejpam-4808	91	29	,	,	PUNCT
ejpam-4808	91	30	e(b	e(b	X
ejpam-4808	91	31	)	)	PUNCT
ejpam-4808	91	32	=	=	SYM
ejpam-4808	91	33	0.5	0.5	NUM
ejpam-4808	91	34	,	,	PUNCT
ejpam-4808	91	35	e(c	e(c	NUM
ejpam-4808	91	36	)	)	PUNCT
ejpam-4808	91	37	=	=	PUNCT
ejpam-4808	92	1	0.3	0.3	NUM
ejpam-4808	92	2	.	.	PUNCT
ejpam-4808	93	1	let	let	VERB
ejpam-4808	93	2	δ	δ	PRON
ejpam-4808	93	3	=	=	PRON
ejpam-4808	93	4	{	{	PUNCT
ejpam-4808	93	5	0	0	NUM
ejpam-4808	93	6	,	,	PUNCT
ejpam-4808	93	7	1	1	NUM
ejpam-4808	93	8	,	,	PUNCT
ejpam-4808	93	9	e	e	NOUN
ejpam-4808	93	10	}	}	PUNCT
ejpam-4808	93	11	on	on	ADP
ejpam-4808	93	12	x.	x.	NOUN
ejpam-4808	93	13	then	then	ADV
ejpam-4808	93	14	e	e	PROPN
ejpam-4808	93	15	∈	∈	PROPN
ejpam-4808	93	16	nq	nq	PROPN
ejpam-4808	93	17	δ	δ	PROPN
ejpam-4808	93	18	(	(	PUNCT
ejpam-4808	93	19	x0.7	x0.7	PROPN
ejpam-4808	93	20	)	)	PUNCT
ejpam-4808	93	21	but	but	CCONJ
ejpam-4808	93	22	0.7	0.7	NUM
ejpam-4808	93	23	≰	≰	NOUN
ejpam-4808	93	24	e(x	e(x	NUM
ejpam-4808	93	25	)	)	PUNCT
ejpam-4808	93	26	,	,	PUNCT
ejpam-4808	93	27	and	and	CCONJ
ejpam-4808	93	28	hence	hence	ADV
ejpam-4808	93	29	x0.7	x0.7	X
ejpam-4808	93	30	̸∈	̸∈	PROPN
ejpam-4808	93	31	e	e	PROPN
ejpam-4808	93	32	but	but	CCONJ
ejpam-4808	93	33	x1−0.7=0.3	x1−0.7=0.3	PROPN
ejpam-4808	93	34	∈	∈	PROPN
ejpam-4808	93	35	e.	e.	PROPN
ejpam-4808	93	36	corollary	corollary	PROPN
ejpam-4808	93	37	1	1	PROPN
ejpam-4808	93	38	.	.	PUNCT
ejpam-4808	94	1	in	in	ADP
ejpam-4808	94	2	fbts	fbt	NOUN
ejpam-4808	94	3	(	(	PUNCT
ejpam-4808	94	4	x	x	NOUN
ejpam-4808	94	5	,	,	PUNCT
ejpam-4808	94	6	δ1	δ1	NOUN
ejpam-4808	94	7	,	,	PUNCT
ejpam-4808	94	8	δ2	δ2	VERB
ejpam-4808	94	9	)	)	PUNCT
ejpam-4808	94	10	every	every	DET
ejpam-4808	94	11	fuzzy	fuzzy	ADJ
ejpam-4808	94	12	(	(	PUNCT
ejpam-4808	94	13	i	i	PROPN
ejpam-4808	94	14	,	,	PUNCT
ejpam-4808	94	15	j	j	PROPN
ejpam-4808	94	16	)	)	PUNCT
ejpam-4808	94	17	−	−	PROPN
ejpam-4808	94	18	gφq	gφq	PROPN
ejpam-4808	94	19	−	−	PROPN
ejpam-4808	94	20	nbd	nbd	PROPN
ejpam-4808	94	21	of	of	ADP
ejpam-4808	94	22	fuzzy	fuzzy	ADJ
ejpam-4808	94	23	point	point	NOUN
ejpam-4808	94	24	xr	xr	PROPN
ejpam-4808	94	25	of	of	ADP
ejpam-4808	94	26	x	x	PROPN
ejpam-4808	94	27	is	be	AUX
ejpam-4808	94	28	equivlant	equivlant	ADJ
ejpam-4808	94	29	to	to	ADP
ejpam-4808	94	30	(	(	PUNCT
ejpam-4808	94	31	i	i	PROPN
ejpam-4808	94	32	,	,	PUNCT
ejpam-4808	94	33	j)−	j)−	PROPN
ejpam-4808	94	34	gφ−	gφ−	PROPN
ejpam-4808	94	35	nbd	nbd	PROPN
ejpam-4808	94	36	of	of	ADP
ejpam-4808	94	37	fuzzy	fuzzy	ADJ
ejpam-4808	94	38	point	point	NOUN
ejpam-4808	94	39	x1−r	x1−r	PROPN
ejpam-4808	94	40	.	.	PUNCT
ejpam-4808	95	1	theorem	theorem	NOUN
ejpam-4808	95	2	1	1	NUM
ejpam-4808	95	3	.	.	PUNCT
ejpam-4808	96	1	(	(	PUNCT
ejpam-4808	96	2	1	1	X
ejpam-4808	96	3	)	)	PUNCT
ejpam-4808	96	4	every	every	PRON
ejpam-4808	96	5	fuzzy	fuzzy	ADJ
ejpam-4808	96	6	δj	δj	ADP
ejpam-4808	96	7	−	−	PROPN
ejpam-4808	96	8	nbd	nbd	PROPN
ejpam-4808	96	9	of	of	ADP
ejpam-4808	96	10	fuzzy	fuzzy	ADJ
ejpam-4808	96	11	point	point	NOUN
ejpam-4808	96	12	xr	xr	PROPN
ejpam-4808	96	13	is	be	AUX
ejpam-4808	96	14	fuzzy	fuzzy	ADJ
ejpam-4808	96	15	(	(	PUNCT
ejpam-4808	96	16	i	i	NOUN
ejpam-4808	96	17	,	,	PUNCT
ejpam-4808	96	18	j)−	j)−	PROPN
ejpam-4808	96	19	g	g	PROPN
ejpam-4808	96	20	−	−	PROPN
ejpam-4808	96	21	nbd	nbd	PROPN
ejpam-4808	96	22	of	of	ADP
ejpam-4808	96	23	xr	xr	PROPN
ejpam-4808	96	24	.	.	PUNCT
ejpam-4808	97	1	(	(	PUNCT
ejpam-4808	97	2	2	2	X
ejpam-4808	97	3	)	)	PUNCT
ejpam-4808	97	4	every	every	PRON
ejpam-4808	97	5	fuzzy	fuzzy	ADJ
ejpam-4808	97	6	(	(	PUNCT
ejpam-4808	97	7	i	i	NOUN
ejpam-4808	97	8	,	,	PUNCT
ejpam-4808	97	9	j)−	j)−	PROPN
ejpam-4808	97	10	g	g	PROPN
ejpam-4808	97	11	−	−	PROPN
ejpam-4808	97	12	nbd	nbd	PROPN
ejpam-4808	97	13	of	of	ADP
ejpam-4808	97	14	fuzzy	fuzzy	ADJ
ejpam-4808	97	15	point	point	NOUN
ejpam-4808	97	16	xr	xr	PROPN
ejpam-4808	97	17	is	be	AUX
ejpam-4808	97	18	fuzzy	fuzzy	ADJ
ejpam-4808	97	19	(	(	PUNCT
ejpam-4808	97	20	i	i	NOUN
ejpam-4808	97	21	,	,	PUNCT
ejpam-4808	97	22	j)−	j)−	PROPN
ejpam-4808	97	23	gα−	gα−	SYM
ejpam-4808	97	24	nbd	nbd	PROPN
ejpam-4808	97	25	of	of	ADP
ejpam-4808	97	26	xr	xr	PROPN
ejpam-4808	97	27	.	.	PUNCT
ejpam-4808	98	1	(	(	PUNCT
ejpam-4808	98	2	3	3	X
ejpam-4808	98	3	)	)	PUNCT
ejpam-4808	98	4	every	every	PRON
ejpam-4808	98	5	fuzzy	fuzzy	ADJ
ejpam-4808	98	6	(	(	PUNCT
ejpam-4808	98	7	i	i	PROPN
ejpam-4808	98	8	,	,	PUNCT
ejpam-4808	98	9	j)−	j)−	PROPN
ejpam-4808	98	10	gα−nbd	gα−nbd	PROPN
ejpam-4808	98	11	of	of	ADP
ejpam-4808	98	12	xr	xr	PROPN
ejpam-4808	98	13	is	be	AUX
ejpam-4808	98	14	fuzzy	fuzzy	ADJ
ejpam-4808	98	15	(	(	PUNCT
ejpam-4808	98	16	i	i	NOUN
ejpam-4808	98	17	,	,	PUNCT
ejpam-4808	98	18	j)−	j)−	PROPN
ejpam-4808	98	19	gs−nbd	gs−nbd	PROPN
ejpam-4808	98	20	and	and	CCONJ
ejpam-4808	98	21	(	(	PUNCT
ejpam-4808	98	22	i	i	PROPN
ejpam-4808	98	23	,	,	PUNCT
ejpam-4808	98	24	j)−	j)−	PROPN
ejpam-4808	98	25	gp−nbd	gp−nbd	PROPN
ejpam-4808	98	26	of	of	ADP
ejpam-4808	98	27	xr	xr	PROPN
ejpam-4808	98	28	.	.	PUNCT
ejpam-4808	99	1	(	(	PUNCT
ejpam-4808	99	2	4	4	X
ejpam-4808	99	3	)	)	PUNCT
ejpam-4808	99	4	every	every	PRON
ejpam-4808	99	5	fuzzy	fuzzy	ADJ
ejpam-4808	99	6	(	(	PUNCT
ejpam-4808	99	7	i	i	PROPN
ejpam-4808	99	8	,	,	PUNCT
ejpam-4808	99	9	j)−	j)−	PROPN
ejpam-4808	99	10	gs−	gs−	PROPN
ejpam-4808	99	11	nb	nb	INTJ
ejpam-4808	99	12	or	or	CCONJ
ejpam-4808	99	13	(	(	PUNCT
ejpam-4808	99	14	i	i	PROPN
ejpam-4808	99	15	,	,	PUNCT
ejpam-4808	99	16	j)−	j)−	PROPN
ejpam-4808	99	17	gp−	gp−	PROPN
ejpam-4808	99	18	nbd	nbd	PROPN
ejpam-4808	99	19	of	of	ADP
ejpam-4808	99	20	xr	xr	PROPN
ejpam-4808	99	21	is	be	AUX
ejpam-4808	99	22	fuzzy	fuzzy	ADJ
ejpam-4808	99	23	(	(	PUNCT
ejpam-4808	100	1	i	i	NOUN
ejpam-4808	100	2	,	,	PUNCT
ejpam-4808	100	3	j)−	j)−	PROPN
ejpam-4808	100	4	gβ	gβ	PROPN
ejpam-4808	100	5	−	−	PROPN
ejpam-4808	100	6	nbd	nbd	PROPN
ejpam-4808	100	7	of	of	ADP
ejpam-4808	100	8	xr	xr	PROPN
ejpam-4808	100	9	.	.	PUNCT
ejpam-4808	101	1	proof	proof	NOUN
ejpam-4808	101	2	.	.	PUNCT
ejpam-4808	102	1	(	(	PUNCT
ejpam-4808	102	2	1	1	X
ejpam-4808	102	3	)	)	PUNCT
ejpam-4808	102	4	suppose	suppose	VERB
ejpam-4808	102	5	that	that	SCONJ
ejpam-4808	102	6	e	e	PROPN
ejpam-4808	102	7	∈	∈	PROPN
ejpam-4808	102	8	nj(xr	nj(xr	PROPN
ejpam-4808	102	9	)	)	PUNCT
ejpam-4808	102	10	,	,	PUNCT
ejpam-4808	102	11	thus	thus	ADV
ejpam-4808	102	12	∃c	∃c	PROPN
ejpam-4808	102	13	∈	∈	PROPN
ejpam-4808	102	14	δj	δj	NOUN
ejpam-4808	102	15	,	,	PUNCT
ejpam-4808	102	16	so	so	ADV
ejpam-4808	102	17	xr	xr	PROPN
ejpam-4808	102	18	∈	∈	PROPN
ejpam-4808	102	19	c	c	PROPN
ejpam-4808	102	20	≤	≤	PROPN
ejpam-4808	102	21	e.	e.	PROPN
ejpam-4808	102	22	as	as	SCONJ
ejpam-4808	102	23	every	every	DET
ejpam-4808	102	24	δj	δj	ADJ
ejpam-4808	102	25	−	−	PUNCT
ejpam-4808	102	26	open	open	ADJ
ejpam-4808	102	27	set	set	NOUN
ejpam-4808	102	28	is	be	AUX
ejpam-4808	102	29	(	(	PUNCT
ejpam-4808	102	30	i	i	PROPN
ejpam-4808	102	31	,	,	PUNCT
ejpam-4808	102	32	j)−g−open	j)−g−open	PROPN
ejpam-4808	102	33	set	set	NOUN
ejpam-4808	102	34	,	,	PUNCT
ejpam-4808	102	35	then	then	ADV
ejpam-4808	102	36	∃c	∃c	PROPN
ejpam-4808	102	37	is	be	AUX
ejpam-4808	102	38	fuzzy	fuzzy	ADJ
ejpam-4808	102	39	(	(	PUNCT
ejpam-4808	102	40	i	i	NOUN
ejpam-4808	102	41	,	,	PUNCT
ejpam-4808	102	42	j)−g−open	j)−g−open	PROPN
ejpam-4808	102	43	set	set	NOUN
ejpam-4808	102	44	,	,	PUNCT
ejpam-4808	102	45	so	so	ADV
ejpam-4808	102	46	xr	xr	PROPN
ejpam-4808	102	47	∈	∈	PROPN
ejpam-4808	102	48	c	c	NOUN
ejpam-4808	102	49	≤	≤	NOUN
ejpam-4808	102	50	e	e	NOUN
ejpam-4808	102	51	,	,	PUNCT
ejpam-4808	102	52	and	and	CCONJ
ejpam-4808	102	53	hence	hence	ADV
ejpam-4808	102	54	e	e	PROPN
ejpam-4808	102	55	∈	∈	PROPN
ejpam-4808	102	56	ng	ng	PROPN
ejpam-4808	102	57	(	(	PUNCT
ejpam-4808	102	58	i	i	NOUN
ejpam-4808	102	59	,	,	PUNCT
ejpam-4808	102	60	j)(xr	j)(xr	PROPN
ejpam-4808	102	61	)	)	PUNCT
ejpam-4808	102	62	.	.	PUNCT
ejpam-4808	103	1	a.	a.	NOUN
ejpam-4808	103	2	a.	a.	PROPN
ejpam-4808	103	3	alharbi	alharbi	PROPN
ejpam-4808	103	4	,	,	PUNCT
ejpam-4808	103	5	a.	a.	NOUN
ejpam-4808	103	6	kilicman	kilicman	PROPN
ejpam-4808	103	7	/	/	SYM
ejpam-4808	103	8	eur	eur	PROPN
ejpam-4808	103	9	.	.	PUNCT
ejpam-4808	104	1	j.	j.	PROPN
ejpam-4808	104	2	pure	pure	PROPN
ejpam-4808	104	3	appl	appl	PROPN
ejpam-4808	104	4	.	.	PROPN
ejpam-4808	104	5	math	math	PROPN
ejpam-4808	104	6	,	,	PUNCT
ejpam-4808	104	7	16	16	NUM
ejpam-4808	104	8	(	(	PUNCT
ejpam-4808	104	9	3	3	NUM
ejpam-4808	104	10	)	)	PUNCT
ejpam-4808	104	11	(	(	PUNCT
ejpam-4808	104	12	2023	2023	NUM
ejpam-4808	104	13	)	)	PUNCT
ejpam-4808	104	14	,	,	PUNCT
ejpam-4808	104	15	1980	1980	NUM
ejpam-4808	104	16	-	-	SYM
ejpam-4808	104	17	1990	1990	NUM
ejpam-4808	104	18	1984	1984	NUM
ejpam-4808	104	19	(	(	PUNCT
ejpam-4808	104	20	2	2	X
ejpam-4808	104	21	)	)	PUNCT
ejpam-4808	104	22	suppose	suppose	VERB
ejpam-4808	104	23	that	that	SCONJ
ejpam-4808	104	24	e	e	PROPN
ejpam-4808	104	25	∈	∈	PROPN
ejpam-4808	104	26	ng	ng	PROPN
ejpam-4808	104	27	(	(	PUNCT
ejpam-4808	104	28	i	i	NOUN
ejpam-4808	104	29	,	,	PUNCT
ejpam-4808	104	30	j)(xr	j)(xr	PROPN
ejpam-4808	104	31	)	)	PUNCT
ejpam-4808	104	32	,	,	PUNCT
ejpam-4808	104	33	thus	thus	ADV
ejpam-4808	104	34	∃c	∃c	PROPN
ejpam-4808	104	35	is	be	AUX
ejpam-4808	104	36	fuzzy	fuzzy	ADJ
ejpam-4808	104	37	(	(	PUNCT
ejpam-4808	104	38	i	i	PROPN
ejpam-4808	104	39	,	,	PUNCT
ejpam-4808	104	40	j	j	PROPN
ejpam-4808	104	41	)	)	PUNCT
ejpam-4808	104	42	−	−	PROPN
ejpam-4808	104	43	g	g	PROPN
ejpam-4808	104	44	−	−	PROPN
ejpam-4808	104	45	open	open	ADJ
ejpam-4808	104	46	set	set	NOUN
ejpam-4808	104	47	,	,	PUNCT
ejpam-4808	104	48	so	so	ADV
ejpam-4808	105	1	xr	xr	PROPN
ejpam-4808	105	2	∈	∈	PROPN
ejpam-4808	105	3	c	c	NOUN
ejpam-4808	105	4	≤	≤	NOUN
ejpam-4808	105	5	e	e	NOUN
ejpam-4808	105	6	,	,	PUNCT
ejpam-4808	105	7	and	and	CCONJ
ejpam-4808	105	8	since	since	SCONJ
ejpam-4808	105	9	every	every	DET
ejpam-4808	105	10	fuzzy	fuzzy	ADJ
ejpam-4808	105	11	(	(	PUNCT
ejpam-4808	105	12	i	i	NOUN
ejpam-4808	105	13	,	,	PUNCT
ejpam-4808	105	14	j)−	j)−	PROPN
ejpam-4808	105	15	g	g	PROPN
ejpam-4808	105	16	−	−	PROPN
ejpam-4808	105	17	open	open	ADJ
ejpam-4808	105	18	is	be	AUX
ejpam-4808	105	19	fuzzy	fuzzy	ADJ
ejpam-4808	105	20	(	(	PUNCT
ejpam-4808	105	21	i	i	NOUN
ejpam-4808	105	22	,	,	PUNCT
ejpam-4808	105	23	j)−	j)−	PROPN
ejpam-4808	105	24	gα−	gα−	PUNCT
ejpam-4808	105	25	open	open	ADJ
ejpam-4808	105	26	,	,	PUNCT
ejpam-4808	105	27	then	then	ADV
ejpam-4808	105	28	∃c	∃c	PROPN
ejpam-4808	105	29	is	be	AUX
ejpam-4808	105	30	fuzzy	fuzzy	ADJ
ejpam-4808	105	31	(	(	PUNCT
ejpam-4808	105	32	i	i	NOUN
ejpam-4808	105	33	,	,	PUNCT
ejpam-4808	105	34	j)−	j)−	PROPN
ejpam-4808	105	35	gα−	gα−	PUNCT
ejpam-4808	105	36	open	open	ADJ
ejpam-4808	105	37	set	set	NOUN
ejpam-4808	105	38	,	,	PUNCT
ejpam-4808	105	39	so	so	ADV
ejpam-4808	106	1	xr	xr	PROPN
ejpam-4808	106	2	∈	∈	PROPN
ejpam-4808	106	3	c	c	NOUN
ejpam-4808	106	4	≤	≤	NOUN
ejpam-4808	106	5	e	e	NOUN
ejpam-4808	106	6	,	,	PUNCT
ejpam-4808	106	7	and	and	CCONJ
ejpam-4808	106	8	hence	hence	ADV
ejpam-4808	106	9	e	e	X
ejpam-4808	106	10	∈	∈	PROPN
ejpam-4808	106	11	ngα	ngα	NOUN
ejpam-4808	106	12	(	(	PUNCT
ejpam-4808	106	13	i	i	NOUN
ejpam-4808	106	14	,	,	PUNCT
ejpam-4808	106	15	j)(xr	j)(xr	PROPN
ejpam-4808	106	16	)	)	PUNCT
ejpam-4808	106	17	.	.	PUNCT
ejpam-4808	107	1	(	(	PUNCT
ejpam-4808	107	2	3	3	X
ejpam-4808	107	3	)	)	PUNCT
ejpam-4808	107	4	suppose	suppose	VERB
ejpam-4808	107	5	that	that	SCONJ
ejpam-4808	107	6	e	e	PROPN
ejpam-4808	107	7	∈	∈	PROPN
ejpam-4808	107	8	ngα	ngα	NOUN
ejpam-4808	107	9	(	(	PUNCT
ejpam-4808	107	10	i	i	NOUN
ejpam-4808	107	11	,	,	PUNCT
ejpam-4808	107	12	j)(xr	j)(xr	PROPN
ejpam-4808	107	13	)	)	PUNCT
ejpam-4808	107	14	,	,	PUNCT
ejpam-4808	107	15	thus	thus	ADV
ejpam-4808	107	16	∃c	∃c	PROPN
ejpam-4808	107	17	is	be	AUX
ejpam-4808	107	18	fuzzy	fuzzy	ADJ
ejpam-4808	107	19	(	(	PUNCT
ejpam-4808	107	20	i	i	NOUN
ejpam-4808	107	21	,	,	PUNCT
ejpam-4808	107	22	j)−	j)−	PROPN
ejpam-4808	107	23	gα	gα	ADP
ejpam-4808	107	24	−	−	PUNCT
ejpam-4808	107	25	open	open	ADJ
ejpam-4808	107	26	set	set	NOUN
ejpam-4808	107	27	,	,	PUNCT
ejpam-4808	107	28	so	so	ADV
ejpam-4808	107	29	xr	xr	PROPN
ejpam-4808	107	30	∈	∈	PROPN
ejpam-4808	107	31	c	c	NOUN
ejpam-4808	107	32	≤	≤	NOUN
ejpam-4808	107	33	e	e	NOUN
ejpam-4808	107	34	,	,	PUNCT
ejpam-4808	107	35	and	and	CCONJ
ejpam-4808	107	36	since	since	SCONJ
ejpam-4808	107	37	every	every	DET
ejpam-4808	107	38	fuzzy	fuzzy	ADJ
ejpam-4808	107	39	(	(	PUNCT
ejpam-4808	107	40	i	i	PROPN
ejpam-4808	107	41	,	,	PUNCT
ejpam-4808	107	42	j)−gα−open	j)−gα−open	PROPN
ejpam-4808	107	43	is	be	AUX
ejpam-4808	107	44	fuzzy	fuzzy	ADJ
ejpam-4808	107	45	(	(	PUNCT
ejpam-4808	107	46	i	i	NOUN
ejpam-4808	107	47	,	,	PUNCT
ejpam-4808	107	48	j)−gs−open	j)−gs−open	VERB
ejpam-4808	107	49	and	and	CCONJ
ejpam-4808	107	50	(	(	PUNCT
ejpam-4808	107	51	i	i	PROPN
ejpam-4808	107	52	,	,	PUNCT
ejpam-4808	107	53	j)−gp−open	j)−gp−open	PROPN
ejpam-4808	107	54	,	,	PUNCT
ejpam-4808	107	55	then	then	ADV
ejpam-4808	107	56	∃c	∃c	PROPN
ejpam-4808	107	57	is	be	AUX
ejpam-4808	107	58	fuzzy	fuzzy	ADJ
ejpam-4808	108	1	(	(	PUNCT
ejpam-4808	108	2	i	i	PROPN
ejpam-4808	108	3	,	,	PUNCT
ejpam-4808	108	4	j	j	PROPN
ejpam-4808	108	5	)	)	PUNCT
ejpam-4808	108	6	−	−	PROPN
ejpam-4808	108	7	gs	gs	INTJ
ejpam-4808	109	1	−	−	ADV
ejpam-4808	109	2	open	open	ADJ
ejpam-4808	109	3	and	and	CCONJ
ejpam-4808	109	4	(	(	PUNCT
ejpam-4808	109	5	i	i	PROPN
ejpam-4808	109	6	,	,	PUNCT
ejpam-4808	109	7	j	j	PROPN
ejpam-4808	109	8	)	)	PUNCT
ejpam-4808	109	9	−	−	PROPN
ejpam-4808	109	10	gp	gp	NOUN
ejpam-4808	109	11	−	−	ADP
ejpam-4808	109	12	open	open	ADJ
ejpam-4808	109	13	set	set	NOUN
ejpam-4808	109	14	,	,	PUNCT
ejpam-4808	109	15	so	so	ADV
ejpam-4808	109	16	xr	xr	PROPN
ejpam-4808	109	17	∈	∈	PROPN
ejpam-4808	109	18	c	c	NOUN
ejpam-4808	109	19	≤	≤	NOUN
ejpam-4808	109	20	e	e	NOUN
ejpam-4808	109	21	,	,	PUNCT
ejpam-4808	109	22	and	and	CCONJ
ejpam-4808	109	23	hence	hence	ADV
ejpam-4808	109	24	e	e	X
ejpam-4808	109	25	∈	∈	PROPN
ejpam-4808	109	26	ngs	ng	NOUN
ejpam-4808	109	27	(	(	PUNCT
ejpam-4808	109	28	i	i	NOUN
ejpam-4808	109	29	,	,	PUNCT
ejpam-4808	109	30	j)(xr	j)(xr	PROPN
ejpam-4808	109	31	)	)	PUNCT
ejpam-4808	109	32	,	,	PUNCT
ejpam-4808	109	33	and	and	CCONJ
ejpam-4808	109	34	e	e	PROPN
ejpam-4808	109	35	∈	∈	PROPN
ejpam-4808	109	36	ngp	ngp	X
ejpam-4808	109	37	(	(	PUNCT
ejpam-4808	109	38	i	i	NOUN
ejpam-4808	109	39	,	,	PUNCT
ejpam-4808	109	40	j)(xr	j)(xr	PROPN
ejpam-4808	109	41	)	)	PUNCT
ejpam-4808	109	42	.	.	PUNCT
ejpam-4808	110	1	(	(	PUNCT
ejpam-4808	110	2	4	4	X
ejpam-4808	110	3	)	)	PUNCT
ejpam-4808	110	4	suppose	suppose	VERB
ejpam-4808	110	5	that	that	SCONJ
ejpam-4808	110	6	e	e	PROPN
ejpam-4808	110	7	∈	∈	PROPN
ejpam-4808	110	8	ngs	ng	NOUN
ejpam-4808	110	9	(	(	PUNCT
ejpam-4808	110	10	i	i	NOUN
ejpam-4808	110	11	,	,	PUNCT
ejpam-4808	110	12	j)(xr	j)(xr	PROPN
ejpam-4808	110	13	)	)	PUNCT
ejpam-4808	110	14	,	,	PUNCT
ejpam-4808	110	15	or	or	CCONJ
ejpam-4808	110	16	e	e	X
ejpam-4808	110	17	∈	∈	PROPN
ejpam-4808	110	18	ngp	ngp	X
ejpam-4808	110	19	(	(	PUNCT
ejpam-4808	110	20	i	i	NOUN
ejpam-4808	110	21	,	,	PUNCT
ejpam-4808	110	22	j)(xr	j)(xr	PROPN
ejpam-4808	110	23	)	)	PUNCT
ejpam-4808	110	24	,	,	PUNCT
ejpam-4808	110	25	thus	thus	ADV
ejpam-4808	110	26	∃c	∃c	PROPN
ejpam-4808	110	27	is	be	AUX
ejpam-4808	110	28	fuzzy	fuzzy	ADJ
ejpam-4808	110	29	(	(	PUNCT
ejpam-4808	110	30	i	i	NOUN
ejpam-4808	110	31	,	,	PUNCT
ejpam-4808	110	32	j)−	j)−	PROPN
ejpam-4808	110	33	gs−	gs−	PROPN
ejpam-4808	110	34	open	open	ADJ
ejpam-4808	110	35	or	or	CCONJ
ejpam-4808	110	36	(	(	PUNCT
ejpam-4808	110	37	i	i	PROPN
ejpam-4808	110	38	,	,	PUNCT
ejpam-4808	110	39	j	j	PROPN
ejpam-4808	110	40	)	)	PUNCT
ejpam-4808	110	41	−	−	PROPN
ejpam-4808	110	42	gp	gp	NOUN
ejpam-4808	110	43	−	−	ADP
ejpam-4808	110	44	open	open	ADJ
ejpam-4808	110	45	set	set	NOUN
ejpam-4808	110	46	,	,	PUNCT
ejpam-4808	110	47	so	so	ADV
ejpam-4808	110	48	xr	xr	PROPN
ejpam-4808	110	49	∈	∈	PROPN
ejpam-4808	110	50	c	c	NOUN
ejpam-4808	110	51	≤	≤	NOUN
ejpam-4808	110	52	e	e	NOUN
ejpam-4808	110	53	,	,	PUNCT
ejpam-4808	110	54	and	and	CCONJ
ejpam-4808	110	55	since	since	SCONJ
ejpam-4808	110	56	every	every	DET
ejpam-4808	110	57	fuzzy	fuzzy	ADJ
ejpam-4808	110	58	(	(	PUNCT
ejpam-4808	110	59	i	i	PROPN
ejpam-4808	110	60	,	,	PUNCT
ejpam-4808	110	61	j	j	PROPN
ejpam-4808	110	62	)	)	PUNCT
ejpam-4808	110	63	−	−	PROPN
ejpam-4808	110	64	gs	gs	INTJ
ejpam-4808	111	1	−	−	ADV
ejpam-4808	111	2	open	open	ADJ
ejpam-4808	111	3	or	or	CCONJ
ejpam-4808	111	4	(	(	PUNCT
ejpam-4808	111	5	i	i	PROPN
ejpam-4808	111	6	,	,	PUNCT
ejpam-4808	111	7	j)−	j)−	PROPN
ejpam-4808	111	8	gp−	gp−	PROPN
ejpam-4808	111	9	open	open	ADJ
ejpam-4808	111	10	is	be	AUX
ejpam-4808	111	11	fuzzy	fuzzy	ADJ
ejpam-4808	111	12	(	(	PUNCT
ejpam-4808	111	13	i	i	NOUN
ejpam-4808	111	14	,	,	PUNCT
ejpam-4808	111	15	j)−	j)−	PROPN
ejpam-4808	111	16	gβ	gβ	AUX
ejpam-4808	111	17	−	−	PROPN
ejpam-4808	111	18	open	open	ADJ
ejpam-4808	111	19	,	,	PUNCT
ejpam-4808	111	20	then	then	ADV
ejpam-4808	111	21	∃c	∃c	PROPN
ejpam-4808	111	22	is	be	AUX
ejpam-4808	111	23	fuzzy	fuzzy	ADJ
ejpam-4808	111	24	(	(	PUNCT
ejpam-4808	111	25	i	i	NOUN
ejpam-4808	111	26	,	,	PUNCT
ejpam-4808	111	27	j)−	j)−	PROPN
ejpam-4808	111	28	gβ	gβ	AUX
ejpam-4808	111	29	−	−	PUNCT
ejpam-4808	111	30	open	open	ADJ
ejpam-4808	111	31	set	set	NOUN
ejpam-4808	111	32	,	,	PUNCT
ejpam-4808	111	33	so	so	ADV
ejpam-4808	111	34	xr	xr	PROPN
ejpam-4808	111	35	∈	∈	PROPN
ejpam-4808	111	36	c	c	NOUN
ejpam-4808	111	37	≤	≤	NOUN
ejpam-4808	111	38	e	e	NOUN
ejpam-4808	111	39	,	,	PUNCT
ejpam-4808	111	40	and	and	CCONJ
ejpam-4808	111	41	hence	hence	ADV
ejpam-4808	111	42	e	e	X
ejpam-4808	111	43	∈	∈	PROPN
ejpam-4808	112	1	ngβ	ngβ	INTJ
ejpam-4808	112	2	(	(	PUNCT
ejpam-4808	112	3	i	i	NOUN
ejpam-4808	112	4	,	,	PUNCT
ejpam-4808	112	5	j)(xr	j)(xr	PROPN
ejpam-4808	112	6	)	)	PUNCT
ejpam-4808	112	7	.	.	PUNCT
ejpam-4808	113	1	remark	remark	NOUN
ejpam-4808	113	2	3	3	NUM
ejpam-4808	113	3	.	.	PUNCT
ejpam-4808	114	1	in	in	ADP
ejpam-4808	114	2	fbts	fbt	NOUN
ejpam-4808	114	3	(	(	PUNCT
ejpam-4808	114	4	x	x	NOUN
ejpam-4808	114	5	,	,	PUNCT
ejpam-4808	114	6	δ1	δ1	NOUN
ejpam-4808	114	7	,	,	PUNCT
ejpam-4808	114	8	δ2	δ2	VERB
ejpam-4808	114	9	)	)	PUNCT
ejpam-4808	114	10	every	every	DET
ejpam-4808	114	11	fuzzy	fuzzy	ADJ
ejpam-4808	114	12	ngs	ng	NOUN
ejpam-4808	114	13	(	(	PUNCT
ejpam-4808	114	14	i	i	NOUN
ejpam-4808	114	15	,	,	PUNCT
ejpam-4808	114	16	j)(xr	j)(xr	PROPN
ejpam-4808	114	17	)	)	PUNCT
ejpam-4808	114	18	,	,	PUNCT
ejpam-4808	114	19	and	and	CCONJ
ejpam-4808	114	20	ngp	ngp	NOUN
ejpam-4808	114	21	(	(	PUNCT
ejpam-4808	114	22	i	i	NOUN
ejpam-4808	114	23	,	,	PUNCT
ejpam-4808	114	24	j)(xr	j)(xr	PROPN
ejpam-4808	114	25	)	)	PUNCT
ejpam-4808	114	26	are	be	AUX
ejpam-4808	114	27	independents	independent	NOUN
ejpam-4808	114	28	.	.	PUNCT
ejpam-4808	115	1	the	the	DET
ejpam-4808	115	2	following	follow	VERB
ejpam-4808	115	3	example	example	NOUN
ejpam-4808	115	4	show	show	VERB
ejpam-4808	115	5	that	that	SCONJ
ejpam-4808	115	6	if	if	SCONJ
ejpam-4808	115	7	x	x	X
ejpam-4808	115	8	=	=	X
ejpam-4808	115	9	{	{	PUNCT
ejpam-4808	115	10	a	a	PRON
ejpam-4808	115	11	,	,	PUNCT
ejpam-4808	115	12	b	b	NOUN
ejpam-4808	115	13	,	,	PUNCT
ejpam-4808	115	14	c	c	NOUN
ejpam-4808	115	15	}	}	PUNCT
ejpam-4808	115	16	,	,	PUNCT
ejpam-4808	115	17	δ1	δ1	NOUN
ejpam-4808	115	18	=	=	SYM
ejpam-4808	115	19	{	{	PUNCT
ejpam-4808	115	20	0	0	NUM
ejpam-4808	115	21	,	,	PUNCT
ejpam-4808	115	22	1	1	NUM
ejpam-4808	115	23	,	,	PUNCT
ejpam-4808	115	24	e	e	NOUN
ejpam-4808	115	25	}	}	PUNCT
ejpam-4808	115	26	,	,	PUNCT
ejpam-4808	115	27	and	and	CCONJ
ejpam-4808	115	28	δ2	δ2	ADJ
ejpam-4808	115	29	=	=	SYM
ejpam-4808	115	30	{	{	PUNCT
ejpam-4808	115	31	0	0	NUM
ejpam-4808	115	32	,	,	PUNCT
ejpam-4808	115	33	1	1	NUM
ejpam-4808	115	34	,	,	PUNCT
ejpam-4808	115	35	c	c	X
ejpam-4808	115	36	,	,	PUNCT
ejpam-4808	115	37	d	d	NOUN
ejpam-4808	115	38	}	}	PUNCT
ejpam-4808	115	39	.	.	PUNCT
ejpam-4808	116	1	as	as	ADP
ejpam-4808	116	2	ea	ea	X
ejpam-4808	116	3	,	,	PUNCT
ejpam-4808	116	4	b	b	NOUN
ejpam-4808	116	5	,	,	PUNCT
ejpam-4808	116	6	c	c	NOUN
ejpam-4808	116	7	=	=	PUNCT
ejpam-4808	116	8	{	{	PUNCT
ejpam-4808	116	9	0.7	0.7	NUM
ejpam-4808	116	10	,	,	PUNCT
ejpam-4808	116	11	0.5	0.5	NUM
ejpam-4808	116	12	,	,	PUNCT
ejpam-4808	116	13	0.6	0.6	NUM
ejpam-4808	116	14	}	}	PUNCT
ejpam-4808	116	15	,	,	PUNCT
ejpam-4808	116	16	ca	ca	PROPN
ejpam-4808	116	17	,	,	PUNCT
ejpam-4808	116	18	b	b	NOUN
ejpam-4808	116	19	,	,	PUNCT
ejpam-4808	116	20	c	c	NOUN
ejpam-4808	116	21	=	=	SYM
ejpam-4808	116	22	{	{	PUNCT
ejpam-4808	116	23	0.5	0.5	NUM
ejpam-4808	116	24	,	,	PUNCT
ejpam-4808	116	25	0.4	0.4	NUM
ejpam-4808	116	26	,	,	PUNCT
ejpam-4808	116	27	0.3	0.3	NUM
ejpam-4808	116	28	}	}	PUNCT
ejpam-4808	116	29	,	,	PUNCT
ejpam-4808	116	30	and	and	CCONJ
ejpam-4808	116	31	da	da	PROPN
ejpam-4808	116	32	,	,	PUNCT
ejpam-4808	116	33	b	b	NOUN
ejpam-4808	116	34	,	,	PUNCT
ejpam-4808	116	35	c	c	NOUN
ejpam-4808	116	36	=	=	PUNCT
ejpam-4808	116	37	{	{	PUNCT
ejpam-4808	116	38	0.4	0.4	NUM
ejpam-4808	116	39	,	,	PUNCT
ejpam-4808	116	40	0.3	0.3	NUM
ejpam-4808	116	41	,	,	PUNCT
ejpam-4808	116	42	0.2	0.2	NUM
ejpam-4808	116	43	}	}	PUNCT
ejpam-4808	116	44	,	,	PUNCT
ejpam-4808	116	45	then	then	ADV
ejpam-4808	116	46	∃	∃	PROPN
ejpam-4808	116	47	sa	sa	PROPN
ejpam-4808	116	48	,	,	PUNCT
ejpam-4808	116	49	b	b	PROPN
ejpam-4808	116	50	,	,	PUNCT
ejpam-4808	116	51	c	c	NOUN
ejpam-4808	116	52	=	=	SYM
ejpam-4808	116	53	{	{	PUNCT
ejpam-4808	116	54	0.5	0.5	NUM
ejpam-4808	116	55	,	,	PUNCT
ejpam-4808	116	56	0.5	0.5	NUM
ejpam-4808	116	57	,	,	PUNCT
ejpam-4808	116	58	0.6	0.6	NUM
ejpam-4808	116	59	}	}	PUNCT
ejpam-4808	116	60	∈	∈	NOUN
ejpam-4808	116	61	ngs	ng	NOUN
ejpam-4808	116	62	(	(	PUNCT
ejpam-4808	116	63	i	i	NOUN
ejpam-4808	116	64	,	,	PUNCT
ejpam-4808	116	65	j)(xr	j)(xr	PROPN
ejpam-4808	116	66	)	)	PUNCT
ejpam-4808	116	67	,	,	PUNCT
ejpam-4808	116	68	but	but	CCONJ
ejpam-4808	116	69	s	s	X
ejpam-4808	116	70	/∈	/∈	INTJ
ejpam-4808	116	71	ngp	ngp	PROPN
ejpam-4808	116	72	(	(	PUNCT
ejpam-4808	116	73	i	i	NOUN
ejpam-4808	116	74	,	,	PUNCT
ejpam-4808	116	75	j)(xr	j)(xr	PROPN
ejpam-4808	116	76	)	)	PUNCT
ejpam-4808	116	77	,	,	PUNCT
ejpam-4808	116	78	as	as	SCONJ
ejpam-4808	116	79	ec	ec	PROPN
ejpam-4808	116	80	≤	≤	PROPN
ejpam-4808	116	81	s	s	PROPN
ejpam-4808	116	82	,	,	PUNCT
ejpam-4808	116	83	but	but	CCONJ
ejpam-4808	116	84	ec	ec	PROPN
ejpam-4808	116	85	≰	≰	PROPN
ejpam-4808	116	86	δ2	δ2	VERB
ejpam-4808	117	1	−	−	PROPN
ejpam-4808	117	2	p	p	NOUN
ejpam-4808	117	3	−	−	PROPN
ejpam-4808	117	4	int(s	int(s	PROPN
ejpam-4808	117	5	)	)	PUNCT
ejpam-4808	117	6	=	=	SYM
ejpam-4808	117	7	c.	c.	NOUN
ejpam-4808	117	8	on	on	ADP
ejpam-4808	117	9	other	other	ADJ
ejpam-4808	117	10	hand	hand	NOUN
ejpam-4808	117	11	for	for	ADP
ejpam-4808	117	12	the	the	DET
ejpam-4808	117	13	same	same	ADJ
ejpam-4808	117	14	topologies	topology	NOUN
ejpam-4808	117	15	above	above	ADP
ejpam-4808	117	16	if	if	SCONJ
ejpam-4808	117	17	ea	ea	PROPN
ejpam-4808	117	18	,	,	PUNCT
ejpam-4808	117	19	b	b	NOUN
ejpam-4808	117	20	,	,	PUNCT
ejpam-4808	117	21	c	c	NOUN
ejpam-4808	117	22	=	=	PUNCT
ejpam-4808	117	23	{	{	PUNCT
ejpam-4808	117	24	0.3	0.3	NUM
ejpam-4808	117	25	,	,	PUNCT
ejpam-4808	117	26	0.5	0.5	NUM
ejpam-4808	117	27	,	,	PUNCT
ejpam-4808	117	28	0.4	0.4	NUM
ejpam-4808	117	29	}	}	PUNCT
ejpam-4808	117	30	,	,	PUNCT
ejpam-4808	117	31	ca	ca	NOUN
ejpam-4808	117	32	,	,	PUNCT
ejpam-4808	117	33	b	b	NOUN
ejpam-4808	117	34	,	,	PUNCT
ejpam-4808	117	35	c	c	NOUN
ejpam-4808	117	36	=	=	SYM
ejpam-4808	117	37	{	{	PUNCT
ejpam-4808	117	38	0.6	0.6	NUM
ejpam-4808	117	39	,	,	PUNCT
ejpam-4808	117	40	0.8	0.8	NUM
ejpam-4808	117	41	,	,	PUNCT
ejpam-4808	117	42	0.9	0.9	NUM
ejpam-4808	117	43	}	}	PUNCT
ejpam-4808	117	44	,	,	PUNCT
ejpam-4808	117	45	and	and	CCONJ
ejpam-4808	117	46	da	da	PROPN
ejpam-4808	117	47	,	,	PUNCT
ejpam-4808	117	48	b	b	NOUN
ejpam-4808	117	49	,	,	PUNCT
ejpam-4808	117	50	c	c	NOUN
ejpam-4808	117	51	=	=	PUNCT
ejpam-4808	117	52	{	{	PUNCT
ejpam-4808	117	53	0.4	0.4	NUM
ejpam-4808	117	54	,	,	PUNCT
ejpam-4808	117	55	0.3	0.3	NUM
ejpam-4808	117	56	,	,	PUNCT
ejpam-4808	117	57	0.2	0.2	NUM
ejpam-4808	117	58	}	}	PUNCT
ejpam-4808	117	59	,	,	PUNCT
ejpam-4808	117	60	then	then	ADV
ejpam-4808	117	61	∃	∃	PROPN
ejpam-4808	117	62	sa	sa	PROPN
ejpam-4808	117	63	,	,	PUNCT
ejpam-4808	117	64	b	b	PROPN
ejpam-4808	117	65	,	,	PUNCT
ejpam-4808	117	66	c	c	NOUN
ejpam-4808	117	67	=	=	PUNCT
ejpam-4808	117	68	{	{	PUNCT
ejpam-4808	117	69	0.8	0.8	NUM
ejpam-4808	117	70	,	,	PUNCT
ejpam-4808	117	71	0.6	0.6	NUM
ejpam-4808	117	72	,	,	PUNCT
ejpam-4808	117	73	0.5	0.5	NUM
ejpam-4808	117	74	}	}	PUNCT
ejpam-4808	117	75	∈	∈	PROPN
ejpam-4808	117	76	ngp	ngp	NOUN
ejpam-4808	117	77	(	(	PUNCT
ejpam-4808	117	78	i	i	NOUN
ejpam-4808	117	79	,	,	PUNCT
ejpam-4808	117	80	j)(xr	j)(xr	PROPN
ejpam-4808	117	81	)	)	PUNCT
ejpam-4808	117	82	,	,	PUNCT
ejpam-4808	117	83	but	but	CCONJ
ejpam-4808	117	84	s	s	X
ejpam-4808	117	85	/∈	/∈	INTJ
ejpam-4808	117	86	ngs	ng	NOUN
ejpam-4808	117	87	(	(	PUNCT
ejpam-4808	117	88	i	i	NOUN
ejpam-4808	117	89	,	,	PUNCT
ejpam-4808	117	90	j)(xr	j)(xr	PROPN
ejpam-4808	117	91	)	)	PUNCT
ejpam-4808	117	92	,	,	PUNCT
ejpam-4808	117	93	as	as	ADP
ejpam-4808	117	94	ec	ec	PROPN
ejpam-4808	117	95	≤	≤	PROPN
ejpam-4808	117	96	s	s	PROPN
ejpam-4808	117	97	,	,	PUNCT
ejpam-4808	117	98	but	but	CCONJ
ejpam-4808	117	99	ec	ec	PROPN
ejpam-4808	117	100	≰	≰	PROPN
ejpam-4808	117	101	δ2	δ2	VERB
ejpam-4808	117	102	−	−	PROPN
ejpam-4808	117	103	s−	s−	PROPN
ejpam-4808	117	104	int(s	int(s	PROPN
ejpam-4808	117	105	)	)	PUNCT
ejpam-4808	117	106	=	=	SYM
ejpam-4808	117	107	cc	cc	PROPN
ejpam-4808	117	108	.	.	PUNCT
ejpam-4808	118	1	the	the	DET
ejpam-4808	118	2	following	follow	VERB
ejpam-4808	118	3	figure	figure	NOUN
ejpam-4808	118	4	explaining	explain	VERB
ejpam-4808	118	5	the	the	DET
ejpam-4808	118	6	relation	relation	NOUN
ejpam-4808	118	7	between	between	ADP
ejpam-4808	118	8	nbds	nbds	NOUN
ejpam-4808	118	9	structures	structure	NOUN
ejpam-4808	118	10	of	of	ADP
ejpam-4808	118	11	all	all	DET
ejpam-4808	118	12	cases	case	NOUN
ejpam-4808	118	13	.	.	PUNCT
ejpam-4808	119	1	figure	figure	NOUN
ejpam-4808	119	2	1	1	NUM
ejpam-4808	119	3	:	:	PUNCT
ejpam-4808	119	4	explain	explain	VERB
ejpam-4808	119	5	the	the	DET
ejpam-4808	119	6	relations	relation	NOUN
ejpam-4808	119	7	between	between	ADP
ejpam-4808	119	8	all	all	DET
ejpam-4808	119	9	types	type	NOUN
ejpam-4808	119	10	of	of	ADP
ejpam-4808	119	11	fuzzy	fuzzy	ADJ
ejpam-4808	119	12	ngφ	ngφ	ADJ
ejpam-4808	119	13	(	(	PUNCT
ejpam-4808	119	14	i	i	NOUN
ejpam-4808	119	15	,	,	PUNCT
ejpam-4808	119	16	j)(xr	j)(xr	PROPN
ejpam-4808	119	17	)	)	PUNCT
ejpam-4808	119	18	,	,	PUNCT
ejpam-4808	119	19	and	and	CCONJ
ejpam-4808	119	20	all	all	DET
ejpam-4808	119	21	types	type	NOUN
ejpam-4808	119	22	of	of	ADP
ejpam-4808	119	23	ngφq	ngφq	NOUN
ejpam-4808	119	24	(	(	PUNCT
ejpam-4808	119	25	i	i	PROPN
ejpam-4808	119	26	,	,	PUNCT
ejpam-4808	119	27	j	j	PROPN
ejpam-4808	119	28	)	)	PUNCT
ejpam-4808	119	29	(	(	PUNCT
ejpam-4808	119	30	xr	xr	X
ejpam-4808	119	31	)	)	PUNCT
ejpam-4808	119	32	.	.	PUNCT
ejpam-4808	120	1	the	the	DET
ejpam-4808	120	2	reversal	reversal	NOUN
ejpam-4808	120	3	of	of	ADP
ejpam-4808	120	4	the	the	DET
ejpam-4808	120	5	prior	prior	ADJ
ejpam-4808	120	6	relationships	relationship	NOUN
ejpam-4808	120	7	in	in	ADP
ejpam-4808	120	8	figure	figure	NOUN
ejpam-4808	120	9	(	(	PUNCT
ejpam-4808	120	10	1	1	NUM
ejpam-4808	120	11	)	)	PUNCT
ejpam-4808	120	12	is	be	AUX
ejpam-4808	120	13	wrong	wrong	ADJ
ejpam-4808	120	14	in	in	ADP
ejpam-4808	120	15	fbts	fbt	NOUN
ejpam-4808	120	16	(	(	PUNCT
ejpam-4808	120	17	x	x	NOUN
ejpam-4808	120	18	,	,	PUNCT
ejpam-4808	120	19	δ1	δ1	NOUN
ejpam-4808	120	20	,	,	PUNCT
ejpam-4808	120	21	δ2	δ2	PROPN
ejpam-4808	120	22	)	)	PUNCT
ejpam-4808	120	23	,	,	PUNCT
ejpam-4808	120	24	as	as	SCONJ
ejpam-4808	120	25	demonstrated	demonstrate	VERB
ejpam-4808	120	26	by	by	ADP
ejpam-4808	120	27	the	the	DET
ejpam-4808	120	28	instances	instance	NOUN
ejpam-4808	120	29	that	that	PRON
ejpam-4808	120	30	follow	follow	VERB
ejpam-4808	120	31	:	:	PUNCT
ejpam-4808	120	32	suppose	suppose	VERB
ejpam-4808	120	33	x	x	X
ejpam-4808	120	34	=	=	PRON
ejpam-4808	120	35	{	{	PUNCT
ejpam-4808	120	36	a	a	PRON
ejpam-4808	120	37	,	,	PUNCT
ejpam-4808	120	38	b	b	NOUN
ejpam-4808	120	39	,	,	PUNCT
ejpam-4808	120	40	c	c	NOUN
ejpam-4808	120	41	}	}	PUNCT
ejpam-4808	120	42	,	,	PUNCT
ejpam-4808	120	43	δ1	δ1	NOUN
ejpam-4808	120	44	=	=	SYM
ejpam-4808	120	45	{	{	PUNCT
ejpam-4808	120	46	0	0	NUM
ejpam-4808	120	47	,	,	PUNCT
ejpam-4808	120	48	1	1	NUM
ejpam-4808	120	49	,	,	PUNCT
ejpam-4808	120	50	e	e	NOUN
ejpam-4808	120	51	}	}	PUNCT
ejpam-4808	120	52	,	,	PUNCT
ejpam-4808	120	53	and	and	CCONJ
ejpam-4808	120	54	δ2	δ2	ADJ
ejpam-4808	120	55	=	=	SYM
ejpam-4808	120	56	{	{	PUNCT
ejpam-4808	120	57	0	0	NUM
ejpam-4808	120	58	,	,	PUNCT
ejpam-4808	120	59	1	1	NUM
ejpam-4808	120	60	,	,	PUNCT
ejpam-4808	120	61	h	h	NOUN
ejpam-4808	120	62	,	,	PUNCT
ejpam-4808	120	63	r	r	NOUN
ejpam-4808	120	64	}	}	PUNCT
ejpam-4808	120	65	.	.	PUNCT
ejpam-4808	121	1	example	example	NOUN
ejpam-4808	122	1	2	2	NUM
ejpam-4808	122	2	.	.	X
ejpam-4808	122	3	if	if	SCONJ
ejpam-4808	122	4	ea	ea	PROPN
ejpam-4808	122	5	,	,	PUNCT
ejpam-4808	122	6	b	b	NOUN
ejpam-4808	122	7	,	,	PUNCT
ejpam-4808	122	8	c	c	NOUN
ejpam-4808	122	9	=	=	PUNCT
ejpam-4808	122	10	{	{	PUNCT
ejpam-4808	122	11	0.7	0.7	NUM
ejpam-4808	122	12	,	,	PUNCT
ejpam-4808	122	13	0.5	0.5	NUM
ejpam-4808	122	14	,	,	PUNCT
ejpam-4808	122	15	0.4	0.4	NUM
ejpam-4808	122	16	}	}	PUNCT
ejpam-4808	122	17	,	,	PUNCT
ejpam-4808	122	18	ha	ha	INTJ
ejpam-4808	122	19	,	,	PUNCT
ejpam-4808	122	20	b	b	NOUN
ejpam-4808	122	21	,	,	PUNCT
ejpam-4808	122	22	c	c	NOUN
ejpam-4808	122	23	=	=	PUNCT
ejpam-4808	122	24	{	{	PUNCT
ejpam-4808	122	25	0.7	0.7	NUM
ejpam-4808	122	26	,	,	PUNCT
ejpam-4808	122	27	0.6	0.6	NUM
ejpam-4808	122	28	,	,	PUNCT
ejpam-4808	122	29	0.5	0.5	NUM
ejpam-4808	122	30	}	}	PUNCT
ejpam-4808	122	31	,	,	PUNCT
ejpam-4808	122	32	ra	ra	PROPN
ejpam-4808	122	33	,	,	PUNCT
ejpam-4808	122	34	b	b	NOUN
ejpam-4808	122	35	,	,	PUNCT
ejpam-4808	122	36	c	c	NOUN
ejpam-4808	122	37	=	=	PUNCT
ejpam-4808	122	38	{	{	PUNCT
ejpam-4808	122	39	0.2	0.2	NUM
ejpam-4808	122	40	,	,	PUNCT
ejpam-4808	122	41	0.4	0.4	NUM
ejpam-4808	122	42	,	,	PUNCT
ejpam-4808	122	43	0.3	0.3	NUM
ejpam-4808	122	44	}	}	PUNCT
ejpam-4808	122	45	,	,	PUNCT
ejpam-4808	122	46	sa	sa	PROPN
ejpam-4808	122	47	,	,	PUNCT
ejpam-4808	122	48	b	b	NOUN
ejpam-4808	122	49	,	,	PUNCT
ejpam-4808	122	50	c	c	NOUN
ejpam-4808	122	51	=	=	SYM
ejpam-4808	122	52	{	{	PUNCT
ejpam-4808	122	53	0.6	0.6	NUM
ejpam-4808	122	54	,	,	PUNCT
ejpam-4808	122	55	0.6	0.6	NUM
ejpam-4808	122	56	,	,	PUNCT
ejpam-4808	122	57	0.5	0.5	NUM
ejpam-4808	122	58	}	}	PUNCT
ejpam-4808	122	59	.	.	PUNCT
ejpam-4808	123	1	the	the	DET
ejpam-4808	123	2	conclusion	conclusion	NOUN
ejpam-4808	123	3	is	be	AUX
ejpam-4808	123	4	s	s	PROPN
ejpam-4808	123	5	∈	∈	PROPN
ejpam-4808	123	6	ng	ng	PROPN
ejpam-4808	123	7	(	(	PUNCT
ejpam-4808	123	8	1,2)(xr	1,2)(xr	ADV
ejpam-4808	123	9	)	)	PUNCT
ejpam-4808	123	10	,	,	PUNCT
ejpam-4808	123	11	but	but	CCONJ
ejpam-4808	123	12	never	never	ADV
ejpam-4808	123	13	s	s	VERB
ejpam-4808	123	14	/∈	/∈	PUNCT
ejpam-4808	123	15	n2(xr	n2(xr	PROPN
ejpam-4808	123	16	)	)	PUNCT
ejpam-4808	123	17	.	.	PUNCT
ejpam-4808	124	1	the	the	DET
ejpam-4808	124	2	next	next	ADJ
ejpam-4808	124	3	example	example	NOUN
ejpam-4808	124	4	clear	clear	ADJ
ejpam-4808	124	5	that	that	SCONJ
ejpam-4808	124	6	ngα	ngα	NOUN
ejpam-4808	124	7	(	(	PUNCT
ejpam-4808	124	8	1,2)(xr	1,2)(xr	ADV
ejpam-4808	124	9	)	)	PUNCT
ejpam-4808	124	10	⇏	⇏	ADJ
ejpam-4808	124	11	ng	ng	PROPN
ejpam-4808	124	12	(	(	PUNCT
ejpam-4808	124	13	1,2)(xr	1,2)(xr	ADV
ejpam-4808	124	14	)	)	PUNCT
ejpam-4808	124	15	.	.	PUNCT
ejpam-4808	125	1	example	example	NOUN
ejpam-4808	126	1	3	3	X
ejpam-4808	126	2	.	.	PUNCT
ejpam-4808	126	3	suppose	suppose	VERB
ejpam-4808	126	4	ea	ea	NOUN
ejpam-4808	126	5	,	,	PUNCT
ejpam-4808	126	6	b	b	NOUN
ejpam-4808	126	7	,	,	PUNCT
ejpam-4808	126	8	c	c	NOUN
ejpam-4808	126	9	=	=	SYM
ejpam-4808	126	10	{	{	PUNCT
ejpam-4808	126	11	0.5	0.5	NUM
ejpam-4808	126	12	,	,	PUNCT
ejpam-4808	126	13	0.4	0.4	NUM
ejpam-4808	126	14	,	,	PUNCT
ejpam-4808	126	15	0.3	0.3	NUM
ejpam-4808	126	16	}	}	PUNCT
ejpam-4808	126	17	,	,	PUNCT
ejpam-4808	126	18	ha	ha	INTJ
ejpam-4808	126	19	,	,	PUNCT
ejpam-4808	126	20	b	b	NOUN
ejpam-4808	126	21	,	,	PUNCT
ejpam-4808	126	22	c	c	NOUN
ejpam-4808	126	23	=	=	PUNCT
ejpam-4808	126	24	{	{	PUNCT
ejpam-4808	126	25	0.7	0.7	NUM
ejpam-4808	126	26	,	,	PUNCT
ejpam-4808	126	27	0.5	0.5	NUM
ejpam-4808	126	28	,	,	PUNCT
ejpam-4808	126	29	0.4	0.4	NUM
ejpam-4808	126	30	}	}	PUNCT
ejpam-4808	126	31	,	,	PUNCT
ejpam-4808	126	32	ra	ra	PROPN
ejpam-4808	126	33	,	,	PUNCT
ejpam-4808	126	34	b	b	NOUN
ejpam-4808	126	35	,	,	PUNCT
ejpam-4808	126	36	c	c	NOUN
ejpam-4808	126	37	=	=	PUNCT
ejpam-4808	126	38	{	{	PUNCT
ejpam-4808	126	39	0.4	0.4	NUM
ejpam-4808	126	40	,	,	PUNCT
ejpam-4808	126	41	0.3	0.3	NUM
ejpam-4808	126	42	,	,	PUNCT
ejpam-4808	126	43	0.2	0.2	NUM
ejpam-4808	126	44	}	}	PUNCT
ejpam-4808	126	45	,	,	PUNCT
ejpam-4808	126	46	sa	sa	PROPN
ejpam-4808	126	47	,	,	PUNCT
ejpam-4808	126	48	b	b	NOUN
ejpam-4808	126	49	,	,	PUNCT
ejpam-4808	126	50	c	c	NOUN
ejpam-4808	126	51	=	=	PUNCT
ejpam-4808	126	52	{	{	PUNCT
ejpam-4808	126	53	0.7	0.7	NUM
ejpam-4808	126	54	,	,	PUNCT
ejpam-4808	126	55	0.6	0.6	NUM
ejpam-4808	126	56	,	,	PUNCT
ejpam-4808	126	57	0.8	0.8	NUM
ejpam-4808	126	58	}	}	PUNCT
ejpam-4808	126	59	.	.	PUNCT
ejpam-4808	127	1	the	the	DET
ejpam-4808	127	2	conclusion	conclusion	NOUN
ejpam-4808	127	3	is	be	AUX
ejpam-4808	127	4	s	s	PROPN
ejpam-4808	127	5	∈	∈	NOUN
ejpam-4808	127	6	ngα	ngα	NOUN
ejpam-4808	127	7	(	(	PUNCT
ejpam-4808	127	8	1,2)(xr	1,2)(xr	ADV
ejpam-4808	127	9	)	)	PUNCT
ejpam-4808	127	10	,	,	PUNCT
ejpam-4808	127	11	but	but	CCONJ
ejpam-4808	127	12	never	never	ADV
ejpam-4808	127	13	s	s	VERB
ejpam-4808	127	14	/∈	/∈	PROPN
ejpam-4808	127	15	ng	ng	PROPN
ejpam-4808	127	16	(	(	PUNCT
ejpam-4808	127	17	1,2)(xr	1,2)(xr	ADV
ejpam-4808	127	18	)	)	PUNCT
ejpam-4808	127	19	.	.	PUNCT
ejpam-4808	128	1	a.	a.	NOUN
ejpam-4808	128	2	a.	a.	PROPN
ejpam-4808	128	3	alharbi	alharbi	PROPN
ejpam-4808	128	4	,	,	PUNCT
ejpam-4808	128	5	a.	a.	NOUN
ejpam-4808	128	6	kilicman	kilicman	PROPN
ejpam-4808	128	7	/	/	SYM
ejpam-4808	128	8	eur	eur	PROPN
ejpam-4808	128	9	.	.	PUNCT
ejpam-4808	129	1	j.	j.	PROPN
ejpam-4808	129	2	pure	pure	PROPN
ejpam-4808	129	3	appl	appl	PROPN
ejpam-4808	129	4	.	.	PROPN
ejpam-4808	129	5	math	math	PROPN
ejpam-4808	129	6	,	,	PUNCT
ejpam-4808	129	7	16	16	NUM
ejpam-4808	129	8	(	(	PUNCT
ejpam-4808	129	9	3	3	NUM
ejpam-4808	129	10	)	)	PUNCT
ejpam-4808	129	11	(	(	PUNCT
ejpam-4808	129	12	2023	2023	NUM
ejpam-4808	129	13	)	)	PUNCT
ejpam-4808	129	14	,	,	PUNCT
ejpam-4808	129	15	1980	1980	NUM
ejpam-4808	129	16	-	-	SYM
ejpam-4808	129	17	1990	1990	NUM
ejpam-4808	129	18	1985	1985	NUM
ejpam-4808	129	19	in	in	ADP
ejpam-4808	129	20	the	the	DET
ejpam-4808	129	21	coming	come	VERB
ejpam-4808	129	22	example	example	NOUN
ejpam-4808	129	23	we	we	PRON
ejpam-4808	129	24	show	show	VERB
ejpam-4808	129	25	that	that	SCONJ
ejpam-4808	129	26	ngs	ng	NOUN
ejpam-4808	129	27	(	(	PUNCT
ejpam-4808	129	28	1,2)(xr	1,2)(xr	ADV
ejpam-4808	129	29	)	)	PUNCT
ejpam-4808	129	30	⇏	⇏	ADJ
ejpam-4808	129	31	ngα	ngα	NOUN
ejpam-4808	129	32	(	(	PUNCT
ejpam-4808	129	33	1,2)(xr	1,2)(xr	ADV
ejpam-4808	129	34	)	)	PUNCT
ejpam-4808	129	35	.	.	PUNCT
ejpam-4808	130	1	example	example	NOUN
ejpam-4808	131	1	4	4	X
ejpam-4808	131	2	.	.	PUNCT
ejpam-4808	131	3	suppose	suppose	VERB
ejpam-4808	131	4	ea	ea	NOUN
ejpam-4808	131	5	,	,	PUNCT
ejpam-4808	131	6	b	b	NOUN
ejpam-4808	131	7	,	,	PUNCT
ejpam-4808	131	8	c	c	NOUN
ejpam-4808	131	9	=	=	PUNCT
ejpam-4808	131	10	{	{	PUNCT
ejpam-4808	131	11	0.7	0.7	NUM
ejpam-4808	131	12	,	,	PUNCT
ejpam-4808	131	13	0.5	0.5	NUM
ejpam-4808	131	14	,	,	PUNCT
ejpam-4808	131	15	0.5	0.5	NUM
ejpam-4808	131	16	}	}	PUNCT
ejpam-4808	131	17	,	,	PUNCT
ejpam-4808	131	18	ha	ha	INTJ
ejpam-4808	131	19	,	,	PUNCT
ejpam-4808	131	20	b	b	NOUN
ejpam-4808	131	21	,	,	PUNCT
ejpam-4808	131	22	c	c	NOUN
ejpam-4808	131	23	=	=	SYM
ejpam-4808	131	24	{	{	PUNCT
ejpam-4808	131	25	0.5	0.5	NUM
ejpam-4808	131	26	,	,	PUNCT
ejpam-4808	131	27	0.4	0.4	NUM
ejpam-4808	131	28	,	,	PUNCT
ejpam-4808	131	29	0.3	0.3	NUM
ejpam-4808	131	30	}	}	PUNCT
ejpam-4808	131	31	,	,	PUNCT
ejpam-4808	131	32	ra	ra	PROPN
ejpam-4808	131	33	,	,	PUNCT
ejpam-4808	131	34	b	b	NOUN
ejpam-4808	131	35	,	,	PUNCT
ejpam-4808	131	36	c	c	NOUN
ejpam-4808	131	37	=	=	PUNCT
ejpam-4808	131	38	{	{	PUNCT
ejpam-4808	131	39	0.4	0.4	NUM
ejpam-4808	131	40	,	,	PUNCT
ejpam-4808	131	41	0.3	0.3	NUM
ejpam-4808	131	42	,	,	PUNCT
ejpam-4808	131	43	0.2	0.2	NUM
ejpam-4808	131	44	}	}	PUNCT
ejpam-4808	131	45	,	,	PUNCT
ejpam-4808	131	46	sa	sa	PROPN
ejpam-4808	131	47	,	,	PUNCT
ejpam-4808	131	48	b	b	NOUN
ejpam-4808	131	49	,	,	PUNCT
ejpam-4808	131	50	c	c	NOUN
ejpam-4808	131	51	=	=	SYM
ejpam-4808	131	52	{	{	PUNCT
ejpam-4808	131	53	0.5	0.5	NUM
ejpam-4808	131	54	,	,	PUNCT
ejpam-4808	131	55	0.5	0.5	NUM
ejpam-4808	131	56	,	,	PUNCT
ejpam-4808	131	57	0.5	0.5	NUM
ejpam-4808	131	58	}	}	PUNCT
ejpam-4808	131	59	.	.	PUNCT
ejpam-4808	132	1	the	the	DET
ejpam-4808	132	2	conclusion	conclusion	NOUN
ejpam-4808	132	3	is	be	AUX
ejpam-4808	132	4	s	s	NOUN
ejpam-4808	132	5	∈	∈	NOUN
ejpam-4808	132	6	ngs	ng	NOUN
ejpam-4808	132	7	(	(	PUNCT
ejpam-4808	132	8	1,2)(xr	1,2)(xr	ADV
ejpam-4808	132	9	)	)	PUNCT
ejpam-4808	132	10	,	,	PUNCT
ejpam-4808	132	11	but	but	CCONJ
ejpam-4808	132	12	never	never	ADV
ejpam-4808	132	13	s	s	PART
ejpam-4808	132	14	/∈	/∈	NOUN
ejpam-4808	132	15	ngα	ngα	NOUN
ejpam-4808	132	16	(	(	PUNCT
ejpam-4808	132	17	1,2)(xr	1,2)(xr	ADV
ejpam-4808	132	18	)	)	PUNCT
ejpam-4808	132	19	.	.	PUNCT
ejpam-4808	133	1	the	the	DET
ejpam-4808	133	2	following	following	ADJ
ejpam-4808	133	3	example	example	NOUN
ejpam-4808	133	4	clear	clear	ADJ
ejpam-4808	133	5	that	that	SCONJ
ejpam-4808	133	6	ngp	ngp	NOUN
ejpam-4808	133	7	(	(	PUNCT
ejpam-4808	133	8	1,2)(xr	1,2)(xr	ADV
ejpam-4808	133	9	)	)	PUNCT
ejpam-4808	133	10	⇏	⇏	ADJ
ejpam-4808	133	11	ngα	ngα	NOUN
ejpam-4808	133	12	(	(	PUNCT
ejpam-4808	133	13	1,2)(xr	1,2)(xr	ADV
ejpam-4808	133	14	)	)	PUNCT
ejpam-4808	133	15	.	.	PUNCT
ejpam-4808	134	1	example	example	NOUN
ejpam-4808	134	2	5	5	NUM
ejpam-4808	134	3	.	.	PUNCT
ejpam-4808	134	4	suppose	suppose	VERB
ejpam-4808	135	1	ea	ea	NOUN
ejpam-4808	135	2	,	,	PUNCT
ejpam-4808	135	3	b	b	NOUN
ejpam-4808	135	4	,	,	PUNCT
ejpam-4808	135	5	c	c	NOUN
ejpam-4808	135	6	=	=	PUNCT
ejpam-4808	135	7	{	{	PUNCT
ejpam-4808	135	8	0.7	0.7	NUM
ejpam-4808	135	9	,	,	PUNCT
ejpam-4808	135	10	0.5	0.5	NUM
ejpam-4808	135	11	,	,	PUNCT
ejpam-4808	135	12	0.4	0.4	NUM
ejpam-4808	135	13	}	}	PUNCT
ejpam-4808	135	14	,	,	PUNCT
ejpam-4808	135	15	ha	ha	INTJ
ejpam-4808	135	16	,	,	PUNCT
ejpam-4808	135	17	b	b	NOUN
ejpam-4808	135	18	,	,	PUNCT
ejpam-4808	135	19	c	c	NOUN
ejpam-4808	135	20	=	=	SYM
ejpam-4808	135	21	{	{	PUNCT
ejpam-4808	135	22	0.6	0.6	NUM
ejpam-4808	135	23	,	,	PUNCT
ejpam-4808	135	24	0.8	0.8	NUM
ejpam-4808	135	25	,	,	PUNCT
ejpam-4808	135	26	0.8	0.8	NUM
ejpam-4808	135	27	}	}	PUNCT
ejpam-4808	135	28	,	,	PUNCT
ejpam-4808	135	29	ra	ra	PROPN
ejpam-4808	135	30	,	,	PUNCT
ejpam-4808	135	31	b	b	NOUN
ejpam-4808	135	32	,	,	PUNCT
ejpam-4808	135	33	c	c	NOUN
ejpam-4808	135	34	=	=	PUNCT
ejpam-4808	135	35	{	{	PUNCT
ejpam-4808	135	36	0.4	0.4	NUM
ejpam-4808	135	37	,	,	PUNCT
ejpam-4808	135	38	0.3	0.3	NUM
ejpam-4808	135	39	,	,	PUNCT
ejpam-4808	135	40	0.2	0.2	NUM
ejpam-4808	135	41	}	}	PUNCT
ejpam-4808	135	42	,	,	PUNCT
ejpam-4808	135	43	sa	sa	PROPN
ejpam-4808	135	44	,	,	PUNCT
ejpam-4808	135	45	b	b	NOUN
ejpam-4808	135	46	,	,	PUNCT
ejpam-4808	135	47	c	c	NOUN
ejpam-4808	135	48	=	=	PUNCT
ejpam-4808	135	49	{	{	PUNCT
ejpam-4808	135	50	0.8	0.8	NUM
ejpam-4808	135	51	,	,	PUNCT
ejpam-4808	135	52	0.6	0.6	NUM
ejpam-4808	135	53	,	,	PUNCT
ejpam-4808	135	54	0.7	0.7	NUM
ejpam-4808	135	55	}	}	PUNCT
ejpam-4808	135	56	.	.	PUNCT
ejpam-4808	136	1	the	the	DET
ejpam-4808	136	2	conclusion	conclusion	NOUN
ejpam-4808	136	3	is	be	AUX
ejpam-4808	136	4	s	s	PROPN
ejpam-4808	136	5	∈	∈	PROPN
ejpam-4808	136	6	ngp	ngp	X
ejpam-4808	136	7	(	(	PUNCT
ejpam-4808	136	8	1,2)(xr	1,2)(xr	ADV
ejpam-4808	136	9	)	)	PUNCT
ejpam-4808	136	10	,	,	PUNCT
ejpam-4808	136	11	but	but	CCONJ
ejpam-4808	136	12	never	never	ADV
ejpam-4808	136	13	s	s	PART
ejpam-4808	136	14	/∈	/∈	NOUN
ejpam-4808	136	15	ngα	ngα	NOUN
ejpam-4808	136	16	(	(	PUNCT
ejpam-4808	136	17	1,2)(xr	1,2)(xr	ADV
ejpam-4808	136	18	)	)	PUNCT
ejpam-4808	136	19	.	.	PUNCT
ejpam-4808	137	1	the	the	DET
ejpam-4808	137	2	example	example	NOUN
ejpam-4808	137	3	follow	follow	NOUN
ejpam-4808	137	4	indicates	indicate	VERB
ejpam-4808	137	5	that	that	SCONJ
ejpam-4808	137	6	ngβ	ngβ	INTJ
ejpam-4808	137	7	(	(	PUNCT
ejpam-4808	137	8	1,2	1,2	NUM
ejpam-4808	137	9	)	)	PUNCT
ejpam-4808	137	10	⇏	⇏	ADJ
ejpam-4808	137	11	ngs	ng	NOUN
ejpam-4808	137	12	(	(	PUNCT
ejpam-4808	137	13	1,2)(xr	1,2)(xr	ADV
ejpam-4808	137	14	)	)	PUNCT
ejpam-4808	137	15	.	.	PUNCT
ejpam-4808	138	1	example	example	NOUN
ejpam-4808	139	1	6	6	NUM
ejpam-4808	139	2	.	.	PUNCT
ejpam-4808	139	3	suppose	suppose	VERB
ejpam-4808	139	4	ea	ea	NOUN
ejpam-4808	139	5	,	,	PUNCT
ejpam-4808	139	6	b	b	NOUN
ejpam-4808	139	7	,	,	PUNCT
ejpam-4808	139	8	c	c	NOUN
ejpam-4808	139	9	=	=	SYM
ejpam-4808	139	10	{	{	PUNCT
ejpam-4808	139	11	0.5	0.5	NUM
ejpam-4808	139	12	,	,	PUNCT
ejpam-4808	139	13	0.7	0.7	NUM
ejpam-4808	139	14	,	,	PUNCT
ejpam-4808	139	15	0.6	0.6	NUM
ejpam-4808	139	16	}	}	PUNCT
ejpam-4808	139	17	,	,	PUNCT
ejpam-4808	139	18	ha	ha	INTJ
ejpam-4808	139	19	,	,	PUNCT
ejpam-4808	139	20	b	b	NOUN
ejpam-4808	139	21	,	,	PUNCT
ejpam-4808	139	22	c	c	NOUN
ejpam-4808	139	23	=	=	SYM
ejpam-4808	139	24	{	{	PUNCT
ejpam-4808	139	25	0.6	0.6	NUM
ejpam-4808	139	26	,	,	PUNCT
ejpam-4808	139	27	0.5	0.5	NUM
ejpam-4808	139	28	,	,	PUNCT
ejpam-4808	139	29	0.4	0.4	NUM
ejpam-4808	139	30	}	}	PUNCT
ejpam-4808	139	31	,	,	PUNCT
ejpam-4808	139	32	ra	ra	PROPN
ejpam-4808	139	33	,	,	PUNCT
ejpam-4808	139	34	b	b	NOUN
ejpam-4808	139	35	,	,	PUNCT
ejpam-4808	139	36	c	c	NOUN
ejpam-4808	139	37	=	=	PUNCT
ejpam-4808	139	38	{	{	PUNCT
ejpam-4808	139	39	0.4	0.4	NUM
ejpam-4808	139	40	,	,	PUNCT
ejpam-4808	139	41	0.3	0.3	NUM
ejpam-4808	139	42	,	,	PUNCT
ejpam-4808	139	43	0.2	0.2	NUM
ejpam-4808	139	44	}	}	PUNCT
ejpam-4808	139	45	,	,	PUNCT
ejpam-4808	139	46	sa	sa	PROPN
ejpam-4808	139	47	,	,	PUNCT
ejpam-4808	139	48	b	b	NOUN
ejpam-4808	139	49	,	,	PUNCT
ejpam-4808	139	50	c	c	NOUN
ejpam-4808	139	51	=	=	SYM
ejpam-4808	139	52	{	{	PUNCT
ejpam-4808	139	53	0.5	0.5	NUM
ejpam-4808	139	54	,	,	PUNCT
ejpam-4808	139	55	0.5	0.5	NUM
ejpam-4808	139	56	,	,	PUNCT
ejpam-4808	139	57	0.6	0.6	NUM
ejpam-4808	139	58	}	}	PUNCT
ejpam-4808	139	59	.	.	PUNCT
ejpam-4808	140	1	the	the	DET
ejpam-4808	140	2	conclusion	conclusion	NOUN
ejpam-4808	140	3	is	be	AUX
ejpam-4808	140	4	s	s	PROPN
ejpam-4808	140	5	∈	∈	ADJ
ejpam-4808	140	6	ngβ	ngβ	INTJ
ejpam-4808	140	7	(	(	PUNCT
ejpam-4808	140	8	1,2)(xr	1,2)(xr	ADV
ejpam-4808	140	9	)	)	PUNCT
ejpam-4808	140	10	,	,	PUNCT
ejpam-4808	140	11	but	but	CCONJ
ejpam-4808	140	12	never	never	ADV
ejpam-4808	140	13	s	s	VERB
ejpam-4808	140	14	/∈	/∈	PUNCT
ejpam-4808	140	15	ngs	ng	NOUN
ejpam-4808	140	16	(	(	PUNCT
ejpam-4808	140	17	1,2)(xr	1,2)(xr	ADV
ejpam-4808	140	18	)	)	PUNCT
ejpam-4808	140	19	.	.	PUNCT
ejpam-4808	141	1	as	as	ADV
ejpam-4808	141	2	well	well	ADV
ejpam-4808	141	3	,	,	PUNCT
ejpam-4808	141	4	the	the	DET
ejpam-4808	141	5	coming	come	VERB
ejpam-4808	141	6	example	example	NOUN
ejpam-4808	141	7	demonstrates	demonstrate	VERB
ejpam-4808	141	8	that	that	SCONJ
ejpam-4808	141	9	ngβ	ngβ	INTJ
ejpam-4808	141	10	(	(	PUNCT
ejpam-4808	141	11	1,2	1,2	NUM
ejpam-4808	141	12	)	)	PUNCT
ejpam-4808	141	13	⇏	⇏	ADJ
ejpam-4808	141	14	ngp	ngp	NOUN
ejpam-4808	141	15	(	(	PUNCT
ejpam-4808	141	16	1,2)(xr	1,2)(xr	ADV
ejpam-4808	141	17	)	)	PUNCT
ejpam-4808	141	18	.	.	PUNCT
ejpam-4808	142	1	example	example	NOUN
ejpam-4808	142	2	7	7	X
ejpam-4808	142	3	.	.	PUNCT
ejpam-4808	142	4	suppose	suppose	VERB
ejpam-4808	142	5	ea	ea	NOUN
ejpam-4808	142	6	,	,	PUNCT
ejpam-4808	142	7	b	b	NOUN
ejpam-4808	142	8	,	,	PUNCT
ejpam-4808	142	9	c	c	NOUN
ejpam-4808	142	10	=	=	SYM
ejpam-4808	142	11	{	{	PUNCT
ejpam-4808	142	12	0.5	0.5	NUM
ejpam-4808	142	13	,	,	PUNCT
ejpam-4808	142	14	0.7	0.7	NUM
ejpam-4808	142	15	,	,	PUNCT
ejpam-4808	142	16	0.6	0.6	NUM
ejpam-4808	142	17	}	}	PUNCT
ejpam-4808	142	18	,	,	PUNCT
ejpam-4808	142	19	ha	ha	INTJ
ejpam-4808	142	20	,	,	PUNCT
ejpam-4808	142	21	b	b	NOUN
ejpam-4808	142	22	,	,	PUNCT
ejpam-4808	142	23	c	c	NOUN
ejpam-4808	142	24	=	=	PUNCT
ejpam-4808	142	25	{	{	PUNCT
ejpam-4808	142	26	0.4	0.4	NUM
ejpam-4808	142	27	,	,	PUNCT
ejpam-4808	142	28	0.6	0.6	NUM
ejpam-4808	142	29	,	,	PUNCT
ejpam-4808	142	30	0.7	0.7	NUM
ejpam-4808	142	31	}	}	PUNCT
ejpam-4808	142	32	,	,	PUNCT
ejpam-4808	142	33	ra	ra	PROPN
ejpam-4808	142	34	,	,	PUNCT
ejpam-4808	142	35	b	b	NOUN
ejpam-4808	142	36	,	,	PUNCT
ejpam-4808	142	37	c	c	NOUN
ejpam-4808	142	38	=	=	PUNCT
ejpam-4808	142	39	{	{	PUNCT
ejpam-4808	142	40	0.3	0.3	NUM
ejpam-4808	142	41	,	,	PUNCT
ejpam-4808	142	42	0.4	0.4	NUM
ejpam-4808	142	43	,	,	PUNCT
ejpam-4808	142	44	0.5	0.5	NUM
ejpam-4808	142	45	}	}	PUNCT
ejpam-4808	142	46	,	,	PUNCT
ejpam-4808	142	47	sa	sa	PROPN
ejpam-4808	142	48	,	,	PUNCT
ejpam-4808	142	49	b	b	NOUN
ejpam-4808	142	50	,	,	PUNCT
ejpam-4808	142	51	c	c	NOUN
ejpam-4808	142	52	=	=	SYM
ejpam-4808	142	53	{	{	PUNCT
ejpam-4808	142	54	0.5	0.5	NUM
ejpam-4808	142	55	,	,	PUNCT
ejpam-4808	142	56	0.5	0.5	NUM
ejpam-4808	142	57	,	,	PUNCT
ejpam-4808	142	58	0.6	0.6	NUM
ejpam-4808	142	59	}	}	PUNCT
ejpam-4808	142	60	.	.	PUNCT
ejpam-4808	143	1	the	the	DET
ejpam-4808	143	2	conclusion	conclusion	NOUN
ejpam-4808	143	3	is	be	AUX
ejpam-4808	143	4	s	s	PROPN
ejpam-4808	143	5	∈	∈	ADJ
ejpam-4808	143	6	ngβ	ngβ	INTJ
ejpam-4808	143	7	(	(	PUNCT
ejpam-4808	143	8	1,2)(xr	1,2)(xr	ADV
ejpam-4808	143	9	)	)	PUNCT
ejpam-4808	143	10	,	,	PUNCT
ejpam-4808	143	11	but	but	CCONJ
ejpam-4808	143	12	never	never	ADV
ejpam-4808	143	13	s	s	VERB
ejpam-4808	143	14	/∈	/∈	X
ejpam-4808	143	15	ngp	ngp	NOUN
ejpam-4808	143	16	(	(	PUNCT
ejpam-4808	143	17	1,2)(xr	1,2)(xr	ADV
ejpam-4808	143	18	)	)	PUNCT
ejpam-4808	143	19	.	.	PUNCT
ejpam-4808	144	1	definition	definition	NOUN
ejpam-4808	144	2	9	9	NUM
ejpam-4808	144	3	.	.	PUNCT
ejpam-4808	145	1	a	a	DET
ejpam-4808	145	2	fuzzy	fuzzy	ADJ
ejpam-4808	145	3	singleton	singleton	NOUN
ejpam-4808	145	4	set	set	NOUN
ejpam-4808	145	5	xr	xr	PROPN
ejpam-4808	145	6	is	be	AUX
ejpam-4808	145	7	named	name	VERB
ejpam-4808	145	8	fuzzy	fuzzy	ADJ
ejpam-4808	145	9	(	(	PUNCT
ejpam-4808	145	10	i	i	PROPN
ejpam-4808	145	11	,	,	PUNCT
ejpam-4808	145	12	j	j	PROPN
ejpam-4808	145	13	)	)	PUNCT
ejpam-4808	145	14	−	−	PROPN
ejpam-4808	145	15	generalizedφ	generalizedφ	NOUN
ejpam-4808	145	16	−	−	NOUN
ejpam-4808	145	17	cluster	cluster	NOUN
ejpam-4808	145	18	point	point	NOUN
ejpam-4808	145	19	of	of	ADP
ejpam-4808	145	20	fuzzy	fuzzy	ADJ
ejpam-4808	145	21	subset	subset	NOUN
ejpam-4808	145	22	e	e	NOUN
ejpam-4808	145	23	in	in	ADP
ejpam-4808	145	24	fbts	fbt	NOUN
ejpam-4808	145	25	(	(	PUNCT
ejpam-4808	145	26	x	x	NOUN
ejpam-4808	145	27	,	,	PUNCT
ejpam-4808	145	28	δ1	δ1	NOUN
ejpam-4808	145	29	,	,	PUNCT
ejpam-4808	145	30	δ2	δ2	ADJ
ejpam-4808	145	31	)	)	PUNCT
ejpam-4808	145	32	if	if	SCONJ
ejpam-4808	145	33	and	and	CCONJ
ejpam-4808	145	34	only	only	ADV
ejpam-4808	145	35	if	if	SCONJ
ejpam-4808	145	36	all	all	DET
ejpam-4808	145	37	h	h	NOUN
ejpam-4808	145	38	∈	∈	PROPN
ejpam-4808	145	39	ngφq	ngφq	NOUN
ejpam-4808	145	40	(	(	PUNCT
ejpam-4808	145	41	i	i	PROPN
ejpam-4808	145	42	,	,	PUNCT
ejpam-4808	145	43	j	j	PROPN
ejpam-4808	145	44	)	)	PUNCT
ejpam-4808	145	45	of	of	ADP
ejpam-4808	145	46	xr	xr	PROPN
ejpam-4808	145	47	,	,	PUNCT
ejpam-4808	145	48	h	h	PROPN
ejpam-4808	145	49	q	q	PROPN
ejpam-4808	145	50	e.	e.	PROPN
ejpam-4808	146	1	the	the	DET
ejpam-4808	146	2	following	follow	VERB
ejpam-4808	146	3	theorem	theorem	ADJ
ejpam-4808	146	4	examines	examine	NOUN
ejpam-4808	146	5	some	some	PRON
ejpam-4808	146	6	of	of	ADP
ejpam-4808	146	7	the	the	DET
ejpam-4808	146	8	generalized	generalized	ADJ
ejpam-4808	146	9	neighborhood	neighborhood	NOUN
ejpam-4808	146	10	characteristics	characteristic	NOUN
ejpam-4808	146	11	.	.	PUNCT
ejpam-4808	147	1	theorem	theorem	NOUN
ejpam-4808	147	2	2	2	NUM
ejpam-4808	147	3	.	.	PUNCT
ejpam-4808	148	1	if	if	SCONJ
ejpam-4808	148	2	(	(	PUNCT
ejpam-4808	148	3	x	x	NOUN
ejpam-4808	148	4	,	,	PUNCT
ejpam-4808	148	5	δ1	δ1	NOUN
ejpam-4808	148	6	,	,	PUNCT
ejpam-4808	148	7	δ2	δ2	PROPN
ejpam-4808	148	8	)	)	PUNCT
ejpam-4808	148	9	is	be	AUX
ejpam-4808	148	10	fbts	fbt	NOUN
ejpam-4808	148	11	.	.	PUNCT
ejpam-4808	149	1	next	next	ADV
ejpam-4808	149	2	,	,	PUNCT
ejpam-4808	149	3	we	we	PRON
ejpam-4808	149	4	find	find	VERB
ejpam-4808	149	5	:	:	PUNCT
ejpam-4808	149	6	(	(	PUNCT
ejpam-4808	149	7	1	1	X
ejpam-4808	149	8	)	)	PUNCT
ejpam-4808	149	9	∀xr	∀xr	PROPN
ejpam-4808	149	10	∈	∈	PROPN
ejpam-4808	150	1	x	x	NOUN
ejpam-4808	150	2	,	,	PUNCT
ejpam-4808	150	3	ngφ	ngφ	X
ejpam-4808	150	4	(	(	PUNCT
ejpam-4808	150	5	i	i	NOUN
ejpam-4808	150	6	,	,	PUNCT
ejpam-4808	150	7	j)(xr	j)(xr	NOUN
ejpam-4808	150	8	)	)	PUNCT
ejpam-4808	150	9	̸=	̸=	PROPN
ejpam-4808	150	10	ϕ.	ϕ.	PROPN
ejpam-4808	150	11	(	(	PUNCT
ejpam-4808	150	12	2	2	NUM
ejpam-4808	150	13	)	)	PUNCT
ejpam-4808	150	14	∀h	∀h	PROPN
ejpam-4808	150	15	∈	∈	PROPN
ejpam-4808	150	16	ngφ	ngφ	NOUN
ejpam-4808	150	17	(	(	PUNCT
ejpam-4808	150	18	i	i	NOUN
ejpam-4808	150	19	,	,	PUNCT
ejpam-4808	150	20	j)(xr),xr	j)(xr),xr	PROPN
ejpam-4808	150	21	∈	∈	PROPN
ejpam-4808	150	22	h.	h.	PROPN
ejpam-4808	150	23	(	(	PUNCT
ejpam-4808	150	24	3	3	NUM
ejpam-4808	150	25	)	)	PUNCT
ejpam-4808	150	26	when	when	SCONJ
ejpam-4808	150	27	h	h	NOUN
ejpam-4808	150	28	,	,	PUNCT
ejpam-4808	150	29	r	r	NOUN
ejpam-4808	150	30	∈	∈	PROPN
ejpam-4808	150	31	ngφ	ngφ	NOUN
ejpam-4808	150	32	(	(	PUNCT
ejpam-4808	150	33	i	i	NOUN
ejpam-4808	150	34	,	,	PUNCT
ejpam-4808	150	35	j)(xr	j)(xr	PROPN
ejpam-4808	150	36	)	)	PUNCT
ejpam-4808	150	37	,	,	PUNCT
ejpam-4808	150	38	then	then	ADV
ejpam-4808	150	39	h	h	PROPN
ejpam-4808	150	40	∧r	∧r	NUM
ejpam-4808	150	41	∈	∈	PROPN
ejpam-4808	150	42	ngφ	ngφ	NOUN
ejpam-4808	150	43	(	(	PUNCT
ejpam-4808	150	44	i	i	NOUN
ejpam-4808	150	45	,	,	PUNCT
ejpam-4808	150	46	j)(xr	j)(xr	PROPN
ejpam-4808	150	47	)	)	PUNCT
ejpam-4808	150	48	.	.	PUNCT
ejpam-4808	151	1	(	(	PUNCT
ejpam-4808	151	2	4	4	X
ejpam-4808	151	3	)	)	PUNCT
ejpam-4808	151	4	when	when	SCONJ
ejpam-4808	151	5	h	h	PROPN
ejpam-4808	151	6	∈	∈	PROPN
ejpam-4808	151	7	ngφ	ngφ	INTJ
ejpam-4808	151	8	(	(	PUNCT
ejpam-4808	151	9	i	i	NOUN
ejpam-4808	151	10	,	,	PUNCT
ejpam-4808	151	11	j)(xr	j)(xr	PROPN
ejpam-4808	151	12	)	)	PUNCT
ejpam-4808	151	13	and	and	CCONJ
ejpam-4808	151	14	h	h	NOUN
ejpam-4808	151	15	≤	≤	NOUN
ejpam-4808	151	16	r	r	NOUN
ejpam-4808	151	17	,	,	PUNCT
ejpam-4808	151	18	then	then	ADV
ejpam-4808	151	19	r	r	NOUN
ejpam-4808	151	20	∈	∈	PROPN
ejpam-4808	152	1	ngφ	ngφ	ADV
ejpam-4808	152	2	(	(	PUNCT
ejpam-4808	152	3	i	i	NOUN
ejpam-4808	152	4	,	,	PUNCT
ejpam-4808	152	5	j)(xr	j)(xr	PROPN
ejpam-4808	152	6	)	)	PUNCT
ejpam-4808	152	7	.	.	PUNCT
ejpam-4808	153	1	(	(	PUNCT
ejpam-4808	153	2	5	5	X
ejpam-4808	153	3	)	)	PUNCT
ejpam-4808	153	4	when	when	SCONJ
ejpam-4808	153	5	h	h	PROPN
ejpam-4808	153	6	∈	∈	PROPN
ejpam-4808	153	7	ngφ	ngφ	INTJ
ejpam-4808	153	8	(	(	PUNCT
ejpam-4808	153	9	i	i	NOUN
ejpam-4808	153	10	,	,	PUNCT
ejpam-4808	153	11	j)(xr	j)(xr	PROPN
ejpam-4808	153	12	)	)	PUNCT
ejpam-4808	153	13	,	,	PUNCT
ejpam-4808	153	14	then	then	ADV
ejpam-4808	153	15	there	there	PRON
ejpam-4808	153	16	exists	exist	VERB
ejpam-4808	153	17	r	r	NOUN
ejpam-4808	153	18	∈	∈	PROPN
ejpam-4808	153	19	ngφ	ngφ	NOUN
ejpam-4808	153	20	(	(	PUNCT
ejpam-4808	153	21	i	i	NOUN
ejpam-4808	153	22	,	,	PUNCT
ejpam-4808	153	23	j)(xr	j)(xr	PROPN
ejpam-4808	153	24	)	)	PUNCT
ejpam-4808	153	25	such	such	ADJ
ejpam-4808	153	26	that	that	SCONJ
ejpam-4808	153	27	r	r	NOUN
ejpam-4808	153	28	≤	≤	NUM
ejpam-4808	153	29	h	h	NOUN
ejpam-4808	153	30	and	and	CCONJ
ejpam-4808	153	31	r	r	NOUN
ejpam-4808	153	32	∈	∈	PROPN
ejpam-4808	154	1	ngφ	ngφ	ADV
ejpam-4808	154	2	(	(	PUNCT
ejpam-4808	154	3	i	i	NOUN
ejpam-4808	154	4	,	,	PUNCT
ejpam-4808	154	5	j)(xh	j)(xh	PROPN
ejpam-4808	154	6	)	)	PUNCT
ejpam-4808	154	7	,	,	PUNCT
ejpam-4808	154	8	∀xh	∀xh	PROPN
ejpam-4808	154	9	∈	∈	PROPN
ejpam-4808	154	10	r.	r.	PROPN
ejpam-4808	154	11	proof	proof	NOUN
ejpam-4808	154	12	.	.	PUNCT
ejpam-4808	155	1	from	from	ADP
ejpam-4808	155	2	definition	definition	NOUN
ejpam-4808	155	3	8	8	NUM
ejpam-4808	155	4	we	we	PRON
ejpam-4808	155	5	conclude	conclude	VERB
ejpam-4808	155	6	the	the	DET
ejpam-4808	155	7	prove	prove	NOUN
ejpam-4808	155	8	of	of	ADP
ejpam-4808	155	9	(	(	PUNCT
ejpam-4808	155	10	1	1	NUM
ejpam-4808	155	11	)	)	PUNCT
ejpam-4808	155	12	and	and	CCONJ
ejpam-4808	155	13	(	(	PUNCT
ejpam-4808	155	14	2	2	NUM
ejpam-4808	155	15	)	)	PUNCT
ejpam-4808	155	16	.	.	PUNCT
ejpam-4808	156	1	(	(	PUNCT
ejpam-4808	156	2	3	3	X
ejpam-4808	156	3	)	)	PUNCT
ejpam-4808	156	4	assume	assume	VERB
ejpam-4808	156	5	h	h	NOUN
ejpam-4808	156	6	,	,	PUNCT
ejpam-4808	156	7	r	r	NOUN
ejpam-4808	156	8	∈	∈	PROPN
ejpam-4808	156	9	ngφ	ngφ	NOUN
ejpam-4808	156	10	(	(	PUNCT
ejpam-4808	156	11	i	i	NOUN
ejpam-4808	156	12	,	,	PUNCT
ejpam-4808	156	13	j)(xr	j)(xr	PROPN
ejpam-4808	156	14	)	)	PUNCT
ejpam-4808	156	15	.	.	PUNCT
ejpam-4808	157	1	thus	thus	ADV
ejpam-4808	157	2	∃s	∃s	PROPN
ejpam-4808	157	3	,	,	PUNCT
ejpam-4808	157	4	t	t	PROPN
ejpam-4808	157	5	are	be	AUX
ejpam-4808	157	6	fuzzy	fuzzy	ADJ
ejpam-4808	157	7	(	(	PUNCT
ejpam-4808	157	8	i	i	NOUN
ejpam-4808	157	9	,	,	PUNCT
ejpam-4808	157	10	j)−	j)−	PROPN
ejpam-4808	157	11	gφ−open	gφ−open	PROPN
ejpam-4808	157	12	,	,	PUNCT
ejpam-4808	157	13	so	so	SCONJ
ejpam-4808	157	14	xr	xr	PROPN
ejpam-4808	157	15	∈	∈	PROPN
ejpam-4808	157	16	s	s	PROPN
ejpam-4808	157	17	,	,	PUNCT
ejpam-4808	157	18	xr	xr	PROPN
ejpam-4808	157	19	∈	∈	PROPN
ejpam-4808	157	20	t	t	PROPN
ejpam-4808	157	21	,	,	PUNCT
ejpam-4808	157	22	then	then	ADV
ejpam-4808	157	23	xr	xr	PROPN
ejpam-4808	157	24	∈	∈	PROPN
ejpam-4808	157	25	s	s	PART
ejpam-4808	157	26	∧	∧	PROPN
ejpam-4808	157	27	t	t	PROPN
ejpam-4808	157	28	.	.	PUNCT
ejpam-4808	158	1	as	as	ADP
ejpam-4808	158	2	s	s	PROPN
ejpam-4808	158	3	,	,	PUNCT
ejpam-4808	158	4	t	t	PROPN
ejpam-4808	158	5	are	be	AUX
ejpam-4808	158	6	fuzzy	fuzzy	ADJ
ejpam-4808	158	7	(	(	PUNCT
ejpam-4808	158	8	i	i	NOUN
ejpam-4808	158	9	,	,	PUNCT
ejpam-4808	158	10	j)−	j)−	PROPN
ejpam-4808	158	11	gφ−open	gφ−open	PROPN
ejpam-4808	158	12	,	,	PUNCT
ejpam-4808	158	13	and	and	CCONJ
ejpam-4808	158	14	hence	hence	ADV
ejpam-4808	158	15	we	we	PRON
ejpam-4808	158	16	find	find	VERB
ejpam-4808	158	17	s	s	PRON
ejpam-4808	158	18	∧	∧	PROPN
ejpam-4808	158	19	t	t	PROPN
ejpam-4808	158	20	is	be	AUX
ejpam-4808	158	21	fuzzy	fuzzy	ADJ
ejpam-4808	158	22	(	(	PUNCT
ejpam-4808	158	23	i	i	NOUN
ejpam-4808	158	24	,	,	PUNCT
ejpam-4808	158	25	j)−	j)−	PROPN
ejpam-4808	158	26	gφ−open	gφ−open	PROPN
ejpam-4808	158	27	,	,	PUNCT
ejpam-4808	158	28	s	s	PART
ejpam-4808	158	29	∧	∧	PROPN
ejpam-4808	158	30	t	t	PROPN
ejpam-4808	158	31	≤	≤	NUM
ejpam-4808	158	32	h	h	NUM
ejpam-4808	158	33	∧r	∧r	PROPN
ejpam-4808	158	34	.	.	PUNCT
ejpam-4808	159	1	as	as	ADP
ejpam-4808	159	2	a	a	DET
ejpam-4808	159	3	result	result	NOUN
ejpam-4808	159	4	of	of	ADP
ejpam-4808	159	5	that	that	PRON
ejpam-4808	159	6	,	,	PUNCT
ejpam-4808	159	7	a	a	DET
ejpam-4808	159	8	∧b	∧b	NOUN
ejpam-4808	159	9	∈	∈	NOUN
ejpam-4808	159	10	ngφ	ngφ	NOUN
ejpam-4808	159	11	(	(	PUNCT
ejpam-4808	159	12	i	i	NOUN
ejpam-4808	159	13	,	,	PUNCT
ejpam-4808	159	14	j)(xr	j)(xr	PROPN
ejpam-4808	159	15	)	)	PUNCT
ejpam-4808	159	16	.	.	PUNCT
ejpam-4808	160	1	a.	a.	NOUN
ejpam-4808	160	2	a.	a.	PROPN
ejpam-4808	160	3	alharbi	alharbi	PROPN
ejpam-4808	160	4	,	,	PUNCT
ejpam-4808	160	5	a.	a.	NOUN
ejpam-4808	160	6	kilicman	kilicman	PROPN
ejpam-4808	160	7	/	/	SYM
ejpam-4808	160	8	eur	eur	PROPN
ejpam-4808	160	9	.	.	PUNCT
ejpam-4808	161	1	j.	j.	PROPN
ejpam-4808	161	2	pure	pure	PROPN
ejpam-4808	161	3	appl	appl	PROPN
ejpam-4808	161	4	.	.	PROPN
ejpam-4808	161	5	math	math	PROPN
ejpam-4808	161	6	,	,	PUNCT
ejpam-4808	161	7	16	16	NUM
ejpam-4808	161	8	(	(	PUNCT
ejpam-4808	161	9	3	3	NUM
ejpam-4808	161	10	)	)	PUNCT
ejpam-4808	161	11	(	(	PUNCT
ejpam-4808	161	12	2023	2023	NUM
ejpam-4808	161	13	)	)	PUNCT
ejpam-4808	161	14	,	,	PUNCT
ejpam-4808	161	15	1980	1980	NUM
ejpam-4808	161	16	-	-	SYM
ejpam-4808	161	17	1990	1990	NUM
ejpam-4808	161	18	1986	1986	NUM
ejpam-4808	161	19	(	(	PUNCT
ejpam-4808	161	20	4	4	X
ejpam-4808	161	21	)	)	PUNCT
ejpam-4808	161	22	assume	assume	VERB
ejpam-4808	161	23	h	h	PROPN
ejpam-4808	161	24	∈	∈	PROPN
ejpam-4808	162	1	ngφ	ngφ	INTJ
ejpam-4808	163	1	(	(	PUNCT
ejpam-4808	163	2	i	i	NOUN
ejpam-4808	163	3	,	,	PUNCT
ejpam-4808	163	4	j)(xr	j)(xr	PROPN
ejpam-4808	163	5	)	)	PUNCT
ejpam-4808	163	6	.	.	PUNCT
ejpam-4808	164	1	so	so	ADV
ejpam-4808	164	2	∃s	∃s	PROPN
ejpam-4808	164	3	is	be	AUX
ejpam-4808	164	4	fuzzy	fuzzy	ADJ
ejpam-4808	164	5	(	(	PUNCT
ejpam-4808	164	6	i	i	NOUN
ejpam-4808	164	7	,	,	PUNCT
ejpam-4808	164	8	j)−	j)−	PROPN
ejpam-4808	164	9	gφ−open	gφ−open	PROPN
ejpam-4808	164	10	and	and	CCONJ
ejpam-4808	164	11	xr	xr	PROPN
ejpam-4808	164	12	∈	∈	PROPN
ejpam-4808	164	13	s	s	PART
ejpam-4808	164	14	≤	≤	NUM
ejpam-4808	164	15	h	h	NOUN
ejpam-4808	164	16	but	but	CCONJ
ejpam-4808	164	17	h	h	NOUN
ejpam-4808	164	18	≤	≤	NOUN
ejpam-4808	164	19	r	r	NOUN
ejpam-4808	164	20	,	,	PUNCT
ejpam-4808	164	21	then	then	ADV
ejpam-4808	164	22	xr	xr	PROPN
ejpam-4808	164	23	∈	∈	PROPN
ejpam-4808	164	24	s	s	PART
ejpam-4808	164	25	≤	≤	NOUN
ejpam-4808	164	26	r.	r.	NOUN
ejpam-4808	164	27	as	as	ADP
ejpam-4808	164	28	a	a	DET
ejpam-4808	164	29	result	result	NOUN
ejpam-4808	164	30	of	of	ADP
ejpam-4808	164	31	that	that	PRON
ejpam-4808	164	32	,	,	PUNCT
ejpam-4808	164	33	r	r	NOUN
ejpam-4808	164	34	∈	∈	PROPN
ejpam-4808	164	35	ngφ	ngφ	ADV
ejpam-4808	164	36	(	(	PUNCT
ejpam-4808	164	37	i	i	NOUN
ejpam-4808	164	38	,	,	PUNCT
ejpam-4808	164	39	j)(xr	j)(xr	PROPN
ejpam-4808	164	40	)	)	PUNCT
ejpam-4808	164	41	.	.	PUNCT
ejpam-4808	165	1	(	(	PUNCT
ejpam-4808	165	2	5	5	X
ejpam-4808	165	3	)	)	PUNCT
ejpam-4808	165	4	assume	assume	VERB
ejpam-4808	165	5	h	h	PROPN
ejpam-4808	165	6	∈	∈	PROPN
ejpam-4808	166	1	ngφ	ngφ	INTJ
ejpam-4808	167	1	(	(	PUNCT
ejpam-4808	167	2	i	i	NOUN
ejpam-4808	167	3	,	,	PUNCT
ejpam-4808	167	4	j)(xr	j)(xr	PROPN
ejpam-4808	167	5	)	)	PUNCT
ejpam-4808	167	6	,	,	PUNCT
ejpam-4808	167	7	so	so	CCONJ
ejpam-4808	167	8	there	there	PRON
ejpam-4808	167	9	exists	exist	VERB
ejpam-4808	167	10	fuzzy	fuzzy	ADJ
ejpam-4808	167	11	(	(	PUNCT
ejpam-4808	167	12	i	i	NOUN
ejpam-4808	167	13	,	,	PUNCT
ejpam-4808	167	14	j)−	j)−	PROPN
ejpam-4808	167	15	gφ−open	gφ−open	PROPN
ejpam-4808	167	16	set	set	NOUN
ejpam-4808	167	17	r	r	NOUN
ejpam-4808	167	18	,	,	PUNCT
ejpam-4808	167	19	xr	xr	PROPN
ejpam-4808	167	20	∈	∈	PROPN
ejpam-4808	167	21	r	r	NOUN
ejpam-4808	167	22	≤	≤	NOUN
ejpam-4808	167	23	h.	h.	NOUN
ejpam-4808	167	24	as	as	SCONJ
ejpam-4808	167	25	r	r	NOUN
ejpam-4808	167	26	is	be	AUX
ejpam-4808	167	27	fuzzy	fuzzy	ADJ
ejpam-4808	167	28	(	(	PUNCT
ejpam-4808	167	29	i	i	PROPN
ejpam-4808	167	30	,	,	PUNCT
ejpam-4808	167	31	j	j	PROPN
ejpam-4808	167	32	)	)	PUNCT
ejpam-4808	168	1	−	−	PROPN
ejpam-4808	168	2	gφ−open	gφ−open	NOUN
ejpam-4808	168	3	,	,	PUNCT
ejpam-4808	168	4	then	then	ADV
ejpam-4808	168	5	r	r	NOUN
ejpam-4808	168	6	∈	∈	PROPN
ejpam-4808	168	7	ngφ	ngφ	ADV
ejpam-4808	168	8	(	(	PUNCT
ejpam-4808	168	9	i	i	NOUN
ejpam-4808	168	10	,	,	PUNCT
ejpam-4808	168	11	j)(xr	j)(xr	PROPN
ejpam-4808	168	12	)	)	PUNCT
ejpam-4808	168	13	.	.	PUNCT
ejpam-4808	169	1	since	since	SCONJ
ejpam-4808	169	2	it	it	PRON
ejpam-4808	169	3	is	be	AUX
ejpam-4808	169	4	an	an	DET
ejpam-4808	169	5	(	(	PUNCT
ejpam-4808	169	6	i	i	PROPN
ejpam-4808	169	7	,	,	PUNCT
ejpam-4808	169	8	j	j	PROPN
ejpam-4808	169	9	)	)	PUNCT
ejpam-4808	169	10	−	−	PROPN
ejpam-4808	169	11	gφ	gφ	PROPN
ejpam-4808	169	12	−	−	PROPN
ejpam-4808	169	13	nbd	nbd	PROPN
ejpam-4808	169	14	of	of	ADP
ejpam-4808	169	15	each	each	PRON
ejpam-4808	169	16	of	of	ADP
ejpam-4808	169	17	it	it	PRON
ejpam-4808	169	18	is	be	AUX
ejpam-4808	169	19	point	point	NOUN
ejpam-4808	169	20	.	.	PUNCT
ejpam-4808	170	1	as	as	ADP
ejpam-4808	170	2	a	a	DET
ejpam-4808	170	3	result	result	NOUN
ejpam-4808	170	4	of	of	ADP
ejpam-4808	170	5	that	that	PRON
ejpam-4808	170	6	,	,	PUNCT
ejpam-4808	170	7	b	b	PROPN
ejpam-4808	170	8	∈	∈	X
ejpam-4808	170	9	ngφ	ngφ	ADJ
ejpam-4808	170	10	(	(	PUNCT
ejpam-4808	170	11	i	i	PROPN
ejpam-4808	170	12	,	,	PUNCT
ejpam-4808	170	13	j)(xh),∀xh	j)(xh),∀xh	PROPN
ejpam-4808	170	14	∈	∈	PROPN
ejpam-4808	170	15	b.	b.	PROPN
ejpam-4808	171	1	the	the	DET
ejpam-4808	171	2	following	follow	VERB
ejpam-4808	171	3	theorem	theorem	ADJ
ejpam-4808	171	4	examines	examine	NOUN
ejpam-4808	171	5	some	some	PRON
ejpam-4808	171	6	of	of	ADP
ejpam-4808	171	7	the	the	DET
ejpam-4808	171	8	generalized	generalized	ADJ
ejpam-4808	171	9	q	q	ADJ
ejpam-4808	171	10	-	-	PUNCT
ejpam-4808	171	11	neighborhood	neighborhood	NOUN
ejpam-4808	171	12	properties	property	NOUN
ejpam-4808	171	13	.	.	PUNCT
ejpam-4808	172	1	theorem	theorem	NOUN
ejpam-4808	172	2	3	3	NUM
ejpam-4808	172	3	.	.	PUNCT
ejpam-4808	173	1	when	when	SCONJ
ejpam-4808	173	2	(	(	PUNCT
ejpam-4808	173	3	x	x	NOUN
ejpam-4808	173	4	,	,	PUNCT
ejpam-4808	173	5	δ1	δ1	NOUN
ejpam-4808	173	6	,	,	PUNCT
ejpam-4808	173	7	δ2	δ2	PROPN
ejpam-4808	173	8	)	)	PUNCT
ejpam-4808	173	9	is	be	AUX
ejpam-4808	173	10	fbts	fbt	NOUN
ejpam-4808	173	11	.	.	PUNCT
ejpam-4808	174	1	then	then	ADV
ejpam-4808	174	2	we	we	PRON
ejpam-4808	174	3	have	have	VERB
ejpam-4808	174	4	:	:	PUNCT
ejpam-4808	174	5	(	(	PUNCT
ejpam-4808	174	6	1	1	X
ejpam-4808	174	7	)	)	PUNCT
ejpam-4808	174	8	∀xr	∀xr	ADJ
ejpam-4808	174	9	q	q	NOUN
ejpam-4808	174	10	or	or	CCONJ
ejpam-4808	174	11	∈	∈	PROPN
ejpam-4808	174	12	x	x	SYM
ejpam-4808	174	13	,	,	PUNCT
ejpam-4808	174	14	ngφq	ngφq	NOUN
ejpam-4808	174	15	(	(	PUNCT
ejpam-4808	174	16	i	i	PROPN
ejpam-4808	174	17	,	,	PUNCT
ejpam-4808	174	18	j	j	PROPN
ejpam-4808	174	19	)	)	PUNCT
ejpam-4808	174	20	(	(	PUNCT
ejpam-4808	174	21	xr	xr	X
ejpam-4808	174	22	)	)	PUNCT
ejpam-4808	174	23	̸=	̸=	PROPN
ejpam-4808	174	24	ϕ.	ϕ.	PROPN
ejpam-4808	174	25	(	(	PUNCT
ejpam-4808	174	26	2	2	NUM
ejpam-4808	174	27	)	)	PUNCT
ejpam-4808	174	28	∀e	∀e	NOUN
ejpam-4808	174	29	∈	∈	PROPN
ejpam-4808	174	30	ngφq	ngφq	NOUN
ejpam-4808	174	31	(	(	PUNCT
ejpam-4808	174	32	i	i	PROPN
ejpam-4808	174	33	,	,	PUNCT
ejpam-4808	174	34	j	j	PROPN
ejpam-4808	174	35	)	)	PUNCT
ejpam-4808	174	36	(	(	PUNCT
ejpam-4808	174	37	xr),xr	xr),xr	PROPN
ejpam-4808	174	38	q	q	PROPN
ejpam-4808	174	39	e.	e.	PROPN
ejpam-4808	174	40	(	(	PUNCT
ejpam-4808	174	41	3	3	NUM
ejpam-4808	174	42	)	)	PUNCT
ejpam-4808	174	43	when	when	SCONJ
ejpam-4808	174	44	e	e	X
ejpam-4808	174	45	,	,	PUNCT
ejpam-4808	174	46	t	t	PROPN
ejpam-4808	174	47	∈	∈	PROPN
ejpam-4808	174	48	ngφq	ngφq	NOUN
ejpam-4808	174	49	(	(	PUNCT
ejpam-4808	174	50	i	i	PROPN
ejpam-4808	174	51	,	,	PUNCT
ejpam-4808	174	52	j	j	PROPN
ejpam-4808	174	53	)	)	PUNCT
ejpam-4808	174	54	(	(	PUNCT
ejpam-4808	174	55	xr	xr	X
ejpam-4808	174	56	)	)	PUNCT
ejpam-4808	174	57	,	,	PUNCT
ejpam-4808	174	58	then	then	ADV
ejpam-4808	174	59	e	e	PROPN
ejpam-4808	174	60	∧	∧	PROPN
ejpam-4808	174	61	t	t	PROPN
ejpam-4808	174	62	∈	∈	PROPN
ejpam-4808	174	63	ngφq	ngφq	NOUN
ejpam-4808	174	64	(	(	PUNCT
ejpam-4808	174	65	i	i	PROPN
ejpam-4808	174	66	,	,	PUNCT
ejpam-4808	174	67	j	j	PROPN
ejpam-4808	174	68	)	)	PUNCT
ejpam-4808	174	69	(	(	PUNCT
ejpam-4808	174	70	xr	xr	X
ejpam-4808	174	71	)	)	PUNCT
ejpam-4808	174	72	.	.	PUNCT
ejpam-4808	175	1	(	(	PUNCT
ejpam-4808	175	2	4	4	X
ejpam-4808	175	3	)	)	PUNCT
ejpam-4808	175	4	when	when	SCONJ
ejpam-4808	175	5	e	e	PROPN
ejpam-4808	175	6	∈	∈	PROPN
ejpam-4808	175	7	ngφq	ngφq	NOUN
ejpam-4808	175	8	(	(	PUNCT
ejpam-4808	175	9	i	i	PROPN
ejpam-4808	175	10	,	,	PUNCT
ejpam-4808	175	11	j	j	PROPN
ejpam-4808	175	12	)	)	PUNCT
ejpam-4808	175	13	(	(	PUNCT
ejpam-4808	175	14	xr	xr	X
ejpam-4808	175	15	)	)	PUNCT
ejpam-4808	175	16	,	,	PUNCT
ejpam-4808	175	17	and	and	CCONJ
ejpam-4808	175	18	e	e	X
ejpam-4808	175	19	≤	≤	PROPN
ejpam-4808	175	20	t	t	NOUN
ejpam-4808	175	21	,	,	PUNCT
ejpam-4808	175	22	then	then	ADV
ejpam-4808	175	23	t	t	PROPN
ejpam-4808	175	24	∈	∈	PROPN
ejpam-4808	175	25	ngφq	ngφq	NOUN
ejpam-4808	175	26	(	(	PUNCT
ejpam-4808	175	27	i	i	PROPN
ejpam-4808	175	28	,	,	PUNCT
ejpam-4808	175	29	j	j	PROPN
ejpam-4808	175	30	)	)	PUNCT
ejpam-4808	175	31	(	(	PUNCT
ejpam-4808	175	32	xr	xr	X
ejpam-4808	175	33	)	)	PUNCT
ejpam-4808	175	34	.	.	PUNCT
ejpam-4808	176	1	(	(	PUNCT
ejpam-4808	176	2	5	5	X
ejpam-4808	176	3	)	)	PUNCT
ejpam-4808	176	4	when	when	SCONJ
ejpam-4808	176	5	e	e	PROPN
ejpam-4808	176	6	∈	∈	PROPN
ejpam-4808	176	7	ngφq	ngφq	NOUN
ejpam-4808	176	8	(	(	PUNCT
ejpam-4808	176	9	i	i	PROPN
ejpam-4808	176	10	,	,	PUNCT
ejpam-4808	176	11	j	j	PROPN
ejpam-4808	176	12	)	)	PUNCT
ejpam-4808	176	13	(	(	PUNCT
ejpam-4808	176	14	xr	xr	X
ejpam-4808	176	15	)	)	PUNCT
ejpam-4808	176	16	,	,	PUNCT
ejpam-4808	176	17	then	then	ADV
ejpam-4808	176	18	∃	∃	PROPN
ejpam-4808	176	19	t	t	PROPN
ejpam-4808	176	20	∈	∈	PROPN
ejpam-4808	176	21	ngφq	ngφq	NOUN
ejpam-4808	176	22	(	(	PUNCT
ejpam-4808	176	23	i	i	PROPN
ejpam-4808	176	24	,	,	PUNCT
ejpam-4808	176	25	j	j	PROPN
ejpam-4808	176	26	)	)	PUNCT
ejpam-4808	176	27	(	(	PUNCT
ejpam-4808	176	28	xr	xr	X
ejpam-4808	176	29	)	)	PUNCT
ejpam-4808	176	30	so	so	SCONJ
ejpam-4808	176	31	t	t	X
ejpam-4808	176	32	≤	≤	ADJ
ejpam-4808	176	33	e	e	NOUN
ejpam-4808	176	34	,	,	PUNCT
ejpam-4808	176	35	and	and	CCONJ
ejpam-4808	176	36	t	t	PROPN
ejpam-4808	176	37	∈	∈	PROPN
ejpam-4808	176	38	ngφq	ngφq	NOUN
ejpam-4808	176	39	(	(	PUNCT
ejpam-4808	176	40	i	i	PROPN
ejpam-4808	176	41	,	,	PUNCT
ejpam-4808	176	42	j	j	PROPN
ejpam-4808	176	43	)	)	PUNCT
ejpam-4808	176	44	(	(	PUNCT
ejpam-4808	176	45	xh	xh	PROPN
ejpam-4808	176	46	)	)	PUNCT
ejpam-4808	176	47	∀xh	∀xh	PROPN
ejpam-4808	176	48	∈	∈	PROPN
ejpam-4808	176	49	t.	t.	NOUN
ejpam-4808	176	50	proof	proof	NOUN
ejpam-4808	176	51	.	.	PUNCT
ejpam-4808	177	1	it	it	PRON
ejpam-4808	177	2	resembles	resemble	VERB
ejpam-4808	177	3	the	the	DET
ejpam-4808	177	4	earlier	early	ADJ
ejpam-4808	177	5	theorem	theorem	ADJ
ejpam-4808	177	6	2	2	NUM
ejpam-4808	177	7	proof	proof	NOUN
ejpam-4808	177	8	.	.	PUNCT
ejpam-4808	178	1	using	use	VERB
ejpam-4808	178	2	the	the	DET
ejpam-4808	178	3	above	above	ADV
ejpam-4808	178	4	-	-	PUNCT
ejpam-4808	178	5	mentioned	mention	VERB
ejpam-4808	178	6	novel	novel	NOUN
ejpam-4808	178	7	notion	notion	NOUN
ejpam-4808	178	8	of	of	ADP
ejpam-4808	178	9	fuzzy	fuzzy	ADJ
ejpam-4808	178	10	neighbourhood	neighbourhood	NOUN
ejpam-4808	178	11	and	and	CCONJ
ejpam-4808	178	12	quasi	quasi	ADJ
ejpam-4808	178	13	-	-	ADJ
ejpam-4808	178	14	neighborhood	neighborhood	ADJ
ejpam-4808	178	15	structure	structure	NOUN
ejpam-4808	178	16	,	,	PUNCT
ejpam-4808	178	17	we	we	PRON
ejpam-4808	178	18	introduced	introduce	VERB
ejpam-4808	178	19	the	the	DET
ejpam-4808	178	20	study	study	NOUN
ejpam-4808	178	21	of	of	ADP
ejpam-4808	178	22	the	the	DET
ejpam-4808	178	23	degree	degree	NOUN
ejpam-4808	178	24	of	of	ADP
ejpam-4808	178	25	affiliation	affiliation	NOUN
ejpam-4808	178	26	of	of	ADP
ejpam-4808	178	27	a	a	DET
ejpam-4808	178	28	fuzzy	fuzzy	ADJ
ejpam-4808	178	29	element	element	NOUN
ejpam-4808	178	30	to	to	ADP
ejpam-4808	178	31	fuzzy	fuzzy	ADJ
ejpam-4808	178	32	generalised	generalised	ADJ
ejpam-4808	178	33	closure	closure	NOUN
ejpam-4808	178	34	in	in	ADP
ejpam-4808	178	35	the	the	DET
ejpam-4808	178	36	subsequent	subsequent	ADJ
ejpam-4808	178	37	theorem	theorem	NOUN
ejpam-4808	178	38	.	.	PUNCT
ejpam-4808	178	39	theorem	theorem	NOUN
ejpam-4808	178	40	4	4	NUM
ejpam-4808	178	41	.	.	PUNCT
ejpam-4808	179	1	if	if	SCONJ
ejpam-4808	179	2	e	e	NOUN
ejpam-4808	179	3	is	be	AUX
ejpam-4808	179	4	fuzzy	fuzzy	ADJ
ejpam-4808	179	5	set	set	VERB
ejpam-4808	179	6	and	and	CCONJ
ejpam-4808	179	7	xr	xr	PROPN
ejpam-4808	179	8	is	be	AUX
ejpam-4808	179	9	fuzzy	fuzzy	ADJ
ejpam-4808	179	10	point	point	NOUN
ejpam-4808	179	11	of	of	ADP
ejpam-4808	179	12	fbts	fbt	NOUN
ejpam-4808	179	13	(	(	PUNCT
ejpam-4808	179	14	x	x	NOUN
ejpam-4808	179	15	,	,	PUNCT
ejpam-4808	179	16	δ1	δ1	NOUN
ejpam-4808	179	17	,	,	PUNCT
ejpam-4808	179	18	δ2	δ2	PROPN
ejpam-4808	179	19	)	)	PUNCT
ejpam-4808	179	20	,	,	PUNCT
ejpam-4808	179	21	then	then	ADV
ejpam-4808	179	22	the	the	DET
ejpam-4808	179	23	following	follow	VERB
ejpam-4808	179	24	propositions	proposition	NOUN
ejpam-4808	179	25	are	be	AUX
ejpam-4808	179	26	correct	correct	ADJ
ejpam-4808	179	27	:	:	PUNCT
ejpam-4808	179	28	(	(	PUNCT
ejpam-4808	179	29	1	1	X
ejpam-4808	179	30	)	)	PUNCT
ejpam-4808	179	31	xr	xr	PROPN
ejpam-4808	179	32	∈	∈	PROPN
ejpam-4808	179	33	(	(	PUNCT
ejpam-4808	179	34	i	i	PROPN
ejpam-4808	179	35	,	,	PUNCT
ejpam-4808	179	36	j)−	j)−	PROPN
ejpam-4808	179	37	gφ−	gφ−	PROPN
ejpam-4808	179	38	cl(e	cl(e	X
ejpam-4808	179	39	)	)	PUNCT
ejpam-4808	179	40	⇐	⇐	ADJ
ejpam-4808	179	41	⇒	⇒	NOUN
ejpam-4808	179	42	∀t	∀t	PROPN
ejpam-4808	179	43	∈	∈	PROPN
ejpam-4808	179	44	ngφq	ngφq	NOUN
ejpam-4808	179	45	(	(	PUNCT
ejpam-4808	179	46	i	i	PROPN
ejpam-4808	179	47	,	,	PUNCT
ejpam-4808	179	48	j	j	PROPN
ejpam-4808	179	49	)	)	PUNCT
ejpam-4808	179	50	(	(	PUNCT
ejpam-4808	179	51	xr	xr	X
ejpam-4808	179	52	)	)	PUNCT
ejpam-4808	179	53	,	,	PUNCT
ejpam-4808	179	54	t	t	PROPN
ejpam-4808	180	1	q	q	PROPN
ejpam-4808	180	2	e.	e.	PROPN
ejpam-4808	180	3	(	(	PUNCT
ejpam-4808	180	4	2	2	NUM
ejpam-4808	180	5	)	)	PUNCT
ejpam-4808	180	6	xr	xr	PROPN
ejpam-4808	180	7	∈	∈	PROPN
ejpam-4808	180	8	(	(	PUNCT
ejpam-4808	180	9	i	i	PROPN
ejpam-4808	180	10	,	,	PUNCT
ejpam-4808	180	11	j)−	j)−	PROPN
ejpam-4808	180	12	gφ−	gφ−	PROPN
ejpam-4808	180	13	cl(e	cl(e	X
ejpam-4808	180	14	)	)	PUNCT
ejpam-4808	180	15	⇐	⇐	ADJ
ejpam-4808	180	16	⇒	⇒	NOUN
ejpam-4808	180	17	∀t	∀t	PROPN
ejpam-4808	180	18	∈	∈	PRON
ejpam-4808	180	19	ngφ	ngφ	NOUN
ejpam-4808	181	1	(	(	PUNCT
ejpam-4808	182	1	i	i	PROPN
ejpam-4808	182	2	,	,	PUNCT
ejpam-4808	182	3	j)(x1−r	j)(x1−r	PROPN
ejpam-4808	182	4	)	)	PUNCT
ejpam-4808	182	5	,	,	PUNCT
ejpam-4808	182	6	t	t	PROPN
ejpam-4808	182	7	q	q	PROPN
ejpam-4808	182	8	e.	e.	PROPN
ejpam-4808	182	9	(	(	PUNCT
ejpam-4808	182	10	3	3	NUM
ejpam-4808	182	11	)	)	PUNCT
ejpam-4808	183	1	if	if	SCONJ
ejpam-4808	183	2	e	e	NOUN
ejpam-4808	183	3	is	be	AUX
ejpam-4808	183	4	fuzzy	fuzzy	ADJ
ejpam-4808	183	5	(	(	PUNCT
ejpam-4808	183	6	i	i	PROPN
ejpam-4808	183	7	,	,	PUNCT
ejpam-4808	183	8	j)−	j)−	PROPN
ejpam-4808	183	9	gφ−closed	gφ−close	VERB
ejpam-4808	183	10	,	,	PUNCT
ejpam-4808	183	11	and	and	CCONJ
ejpam-4808	183	12	hence	hence	ADV
ejpam-4808	183	13	δi	δi	VERB
ejpam-4808	183	14	−	−	PROPN
ejpam-4808	183	15	cl(xr	cl(xr	NOUN
ejpam-4808	183	16	)	)	PUNCT
ejpam-4808	183	17	q	q	PUNCT
ejpam-4808	184	1	e	e	NOUN
ejpam-4808	184	2	holds	hold	VERB
ejpam-4808	184	3	∀xr	∀xr	ADJ
ejpam-4808	184	4	q	q	PUNCT
ejpam-4808	184	5	δj	δj	ADP
ejpam-4808	184	6	−	−	PROPN
ejpam-4808	184	7	φ−	φ−	PROPN
ejpam-4808	184	8	cl(e	cl(e	NOUN
ejpam-4808	184	9	)	)	PUNCT
ejpam-4808	184	10	.	.	PUNCT
ejpam-4808	185	1	proof	proof	NOUN
ejpam-4808	185	2	.	.	PUNCT
ejpam-4808	186	1	(	(	PUNCT
ejpam-4808	186	2	1	1	X
ejpam-4808	186	3	)	)	PUNCT
ejpam-4808	186	4	let	let	VERB
ejpam-4808	186	5	xr	xr	PROPN
ejpam-4808	186	6	∈	∈	PROPN
ejpam-4808	186	7	(	(	PUNCT
ejpam-4808	186	8	i	i	PROPN
ejpam-4808	186	9	,	,	PUNCT
ejpam-4808	186	10	j)−	j)−	PROPN
ejpam-4808	186	11	gφ−	gφ−	PROPN
ejpam-4808	186	12	cl(e	cl(e	NUM
ejpam-4808	186	13	)	)	PUNCT
ejpam-4808	186	14	⇔	⇔	X
ejpam-4808	186	15	∀f	∀f	PROPN
ejpam-4808	186	16	is	be	AUX
ejpam-4808	186	17	fuzzy	fuzzy	ADJ
ejpam-4808	186	18	(	(	PUNCT
ejpam-4808	186	19	i	i	NOUN
ejpam-4808	186	20	,	,	PUNCT
ejpam-4808	186	21	j)−	j)−	PROPN
ejpam-4808	186	22	gφ−	gφ−	PROPN
ejpam-4808	186	23	closed	close	VERB
ejpam-4808	186	24	,	,	PUNCT
ejpam-4808	187	1	e	e	NOUN
ejpam-4808	187	2	≤	≤	NOUN
ejpam-4808	187	3	f	f	X
ejpam-4808	187	4	,	,	PUNCT
ejpam-4808	187	5	r	r	NOUN
ejpam-4808	187	6	≤	≤	NUM
ejpam-4808	187	7	f	f	X
ejpam-4808	187	8	(	(	PUNCT
ejpam-4808	187	9	x	x	X
ejpam-4808	187	10	)	)	PUNCT
ejpam-4808	187	11	⇔	⇔	X
ejpam-4808	187	12	∀f	∀f	PROPN
ejpam-4808	187	13	c	c	NOUN
ejpam-4808	187	14	is	be	AUX
ejpam-4808	187	15	fuzzy	fuzzy	ADJ
ejpam-4808	187	16	(	(	PUNCT
ejpam-4808	187	17	i	i	NOUN
ejpam-4808	187	18	,	,	PUNCT
ejpam-4808	187	19	j)−	j)−	PROPN
ejpam-4808	187	20	gφ−	gφ−	PUNCT
ejpam-4808	187	21	open	open	ADJ
ejpam-4808	187	22	,	,	PUNCT
ejpam-4808	187	23	f	f	PROPN
ejpam-4808	187	24	c	c	PROPN
ejpam-4808	187	25	≤	≤	PROPN
ejpam-4808	187	26	ec	ec	PROPN
ejpam-4808	187	27	,	,	PUNCT
ejpam-4808	187	28	f	f	PROPN
ejpam-4808	187	29	c(x	c(x	NOUN
ejpam-4808	187	30	)	)	PUNCT
ejpam-4808	187	31	≤	≤	NOUN
ejpam-4808	187	32	1−	1−	NUM
ejpam-4808	187	33	r	r	NOUN
ejpam-4808	187	34	⇔	⇔	PROPN
ejpam-4808	187	35	∀t	∀t	PROPN
ejpam-4808	187	36	is	be	AUX
ejpam-4808	187	37	fuzzy	fuzzy	ADJ
ejpam-4808	187	38	(	(	PUNCT
ejpam-4808	187	39	i	i	NOUN
ejpam-4808	187	40	,	,	PUNCT
ejpam-4808	187	41	j)−	j)−	PROPN
ejpam-4808	187	42	gφ−	gφ−	PROPN
ejpam-4808	187	43	open	open	ADJ
ejpam-4808	187	44	,	,	PUNCT
ejpam-4808	187	45	t	t	PROPN
ejpam-4808	187	46	≤	≤	PROPN
ejpam-4808	187	47	ec	ec	PROPN
ejpam-4808	187	48	,	,	PUNCT
ejpam-4808	187	49	t	t	PROPN
ejpam-4808	187	50	(	(	PUNCT
ejpam-4808	187	51	x	x	NOUN
ejpam-4808	187	52	)	)	PUNCT
ejpam-4808	187	53	≤	≤	NOUN
ejpam-4808	187	54	1−	1−	NUM
ejpam-4808	187	55	r	r	NOUN
ejpam-4808	187	56	⇔	⇔	PROPN
ejpam-4808	187	57	∀t	∀t	PROPN
ejpam-4808	187	58	is	be	AUX
ejpam-4808	187	59	fuzzy	fuzzy	ADJ
ejpam-4808	187	60	(	(	PUNCT
ejpam-4808	187	61	i	i	NOUN
ejpam-4808	187	62	,	,	PUNCT
ejpam-4808	187	63	j)−	j)−	PROPN
ejpam-4808	187	64	gφ−	gφ−	PUNCT
ejpam-4808	187	65	open	open	ADJ
ejpam-4808	187	66	,	,	PUNCT
ejpam-4808	187	67	1−	1−	NUM
ejpam-4808	187	68	r	r	NOUN
ejpam-4808	187	69	<	<	X
ejpam-4808	187	70	t	t	PROPN
ejpam-4808	187	71	(	(	PUNCT
ejpam-4808	187	72	x	x	NOUN
ejpam-4808	187	73	)	)	PUNCT
ejpam-4808	187	74	⇒	⇒	PROPN
ejpam-4808	187	75	t	t	PROPN
ejpam-4808	187	76	̸≤	̸≤	VERB
ejpam-4808	187	77	ec	ec	PROPN
ejpam-4808	187	78	⇔	⇔	PROPN
ejpam-4808	187	79	∀t	∀t	PROPN
ejpam-4808	187	80	is	be	AUX
ejpam-4808	187	81	fuzzy	fuzzy	ADJ
ejpam-4808	187	82	(	(	PUNCT
ejpam-4808	187	83	i	i	NOUN
ejpam-4808	187	84	,	,	PUNCT
ejpam-4808	187	85	j)−	j)−	PROPN
ejpam-4808	187	86	gφ−	gφ−	PROPN
ejpam-4808	187	87	open	open	ADJ
ejpam-4808	187	88	,	,	PUNCT
ejpam-4808	187	89	xr	xr	PROPN
ejpam-4808	187	90	q	q	PROPN
ejpam-4808	187	91	t	t	PROPN
ejpam-4808	187	92	,	,	PUNCT
ejpam-4808	187	93	t	t	PROPN
ejpam-4808	187	94	q	q	PROPN
ejpam-4808	187	95	e	e	X
ejpam-4808	187	96	⇔	⇔	X
ejpam-4808	187	97	∀t	∀t	PROPN
ejpam-4808	187	98	∈	∈	PROPN
ejpam-4808	187	99	ngφq	ngφq	NOUN
ejpam-4808	187	100	(	(	PUNCT
ejpam-4808	187	101	i	i	PROPN
ejpam-4808	187	102	,	,	PUNCT
ejpam-4808	187	103	j	j	PROPN
ejpam-4808	187	104	)	)	PUNCT
ejpam-4808	187	105	(	(	PUNCT
ejpam-4808	187	106	xr	xr	X
ejpam-4808	187	107	)	)	PUNCT
ejpam-4808	187	108	,	,	PUNCT
ejpam-4808	187	109	t	t	PROPN
ejpam-4808	187	110	q	q	PROPN
ejpam-4808	187	111	e.	e.	PROPN
ejpam-4808	187	112	a.	a.	PROPN
ejpam-4808	187	113	a.	a.	PROPN
ejpam-4808	187	114	alharbi	alharbi	PROPN
ejpam-4808	187	115	,	,	PUNCT
ejpam-4808	187	116	a.	a.	NOUN
ejpam-4808	187	117	kilicman	kilicman	PROPN
ejpam-4808	187	118	/	/	SYM
ejpam-4808	187	119	eur	eur	PROPN
ejpam-4808	187	120	.	.	PUNCT
ejpam-4808	188	1	j.	j.	PROPN
ejpam-4808	188	2	pure	pure	PROPN
ejpam-4808	188	3	appl	appl	PROPN
ejpam-4808	188	4	.	.	PROPN
ejpam-4808	188	5	math	math	PROPN
ejpam-4808	188	6	,	,	PUNCT
ejpam-4808	188	7	16	16	NUM
ejpam-4808	188	8	(	(	PUNCT
ejpam-4808	188	9	3	3	NUM
ejpam-4808	188	10	)	)	PUNCT
ejpam-4808	188	11	(	(	PUNCT
ejpam-4808	188	12	2023	2023	NUM
ejpam-4808	188	13	)	)	PUNCT
ejpam-4808	188	14	,	,	PUNCT
ejpam-4808	188	15	1980	1980	NUM
ejpam-4808	188	16	-	-	SYM
ejpam-4808	188	17	1990	1990	NUM
ejpam-4808	188	18	1987	1987	NUM
ejpam-4808	188	19	(	(	PUNCT
ejpam-4808	188	20	2	2	NUM
ejpam-4808	188	21	)	)	PUNCT
ejpam-4808	188	22	from	from	ADP
ejpam-4808	188	23	(	(	PUNCT
ejpam-4808	188	24	1	1	X
ejpam-4808	188	25	)	)	PUNCT
ejpam-4808	188	26	we	we	PRON
ejpam-4808	188	27	have	have	VERB
ejpam-4808	188	28	xr	xr	PROPN
ejpam-4808	188	29	∈	∈	PROPN
ejpam-4808	188	30	(	(	PUNCT
ejpam-4808	188	31	i	i	PROPN
ejpam-4808	188	32	,	,	PUNCT
ejpam-4808	188	33	j	j	PROPN
ejpam-4808	188	34	)	)	PUNCT
ejpam-4808	188	35	−	−	PROPN
ejpam-4808	188	36	gφ	gφ	PROPN
ejpam-4808	188	37	−	−	PROPN
ejpam-4808	188	38	cl(e	cl(e	NOUN
ejpam-4808	188	39	)	)	PUNCT
ejpam-4808	188	40	⇔	⇔	NOUN
ejpam-4808	188	41	∀t	∀t	PROPN
ejpam-4808	188	42	∈	∈	PROPN
ejpam-4808	188	43	ngφq	ngφq	NOUN
ejpam-4808	188	44	(	(	PUNCT
ejpam-4808	188	45	i	i	PROPN
ejpam-4808	188	46	,	,	PUNCT
ejpam-4808	188	47	j	j	PROPN
ejpam-4808	188	48	)	)	PUNCT
ejpam-4808	188	49	(	(	PUNCT
ejpam-4808	188	50	xr	xr	X
ejpam-4808	188	51	)	)	PUNCT
ejpam-4808	188	52	,	,	PUNCT
ejpam-4808	188	53	t	t	PROPN
ejpam-4808	188	54	q	q	PROPN
ejpam-4808	188	55	e.	e.	PROPN
ejpam-4808	189	1	so	so	ADV
ejpam-4808	189	2	,	,	PUNCT
ejpam-4808	189	3	we	we	PRON
ejpam-4808	189	4	need	need	VERB
ejpam-4808	189	5	to	to	PART
ejpam-4808	189	6	show	show	VERB
ejpam-4808	189	7	that	that	SCONJ
ejpam-4808	189	8	t	t	PROPN
ejpam-4808	189	9	∈	∈	PROPN
ejpam-4808	189	10	ngφ	ngφ	ADV
ejpam-4808	189	11	(	(	PUNCT
ejpam-4808	189	12	i	i	PROPN
ejpam-4808	189	13	,	,	PUNCT
ejpam-4808	189	14	j)(x1−r	j)(x1−r	PROPN
ejpam-4808	189	15	)	)	PUNCT
ejpam-4808	189	16	⇔	⇔	PROPN
ejpam-4808	189	17	t	t	PROPN
ejpam-4808	189	18	∈	∈	PROPN
ejpam-4808	189	19	ngφq	ngφq	NOUN
ejpam-4808	189	20	(	(	PUNCT
ejpam-4808	189	21	i	i	PROPN
ejpam-4808	189	22	,	,	PUNCT
ejpam-4808	189	23	j	j	PROPN
ejpam-4808	189	24	)	)	PUNCT
ejpam-4808	189	25	(	(	PUNCT
ejpam-4808	189	26	xr	xr	X
ejpam-4808	189	27	)	)	PUNCT
ejpam-4808	189	28	.	.	PUNCT
ejpam-4808	190	1	assume	assume	VERB
ejpam-4808	190	2	t	t	PROPN
ejpam-4808	190	3	∈	∈	PROPN
ejpam-4808	191	1	ngφ	ngφ	INTJ
ejpam-4808	192	1	(	(	PUNCT
ejpam-4808	192	2	i	i	PROPN
ejpam-4808	192	3	,	,	PUNCT
ejpam-4808	192	4	j)(x1−r	j)(x1−r	PROPN
ejpam-4808	192	5	)	)	PUNCT
ejpam-4808	192	6	.	.	PUNCT
ejpam-4808	193	1	after	after	ADP
ejpam-4808	193	2	that	that	PRON
ejpam-4808	193	3	,	,	PUNCT
ejpam-4808	193	4	∃	∃	PROPN
ejpam-4808	193	5	fuzzy	fuzzy	ADJ
ejpam-4808	193	6	(	(	PUNCT
ejpam-4808	193	7	i	i	PROPN
ejpam-4808	193	8	,	,	PUNCT
ejpam-4808	193	9	j	j	PROPN
ejpam-4808	193	10	)	)	PUNCT
ejpam-4808	193	11	−	−	PROPN
ejpam-4808	193	12	gφ	gφ	NOUN
ejpam-4808	193	13	−	−	PROPN
ejpam-4808	193	14	open	open	ADJ
ejpam-4808	193	15	set	set	VERB
ejpam-4808	193	16	v	v	ADP
ejpam-4808	193	17	so	so	ADV
ejpam-4808	193	18	x1−r	x1−r	PROPN
ejpam-4808	193	19	∈	∈	PROPN
ejpam-4808	193	20	v	v	ADP
ejpam-4808	193	21	≤	≤	X
ejpam-4808	193	22	t	t	NOUN
ejpam-4808	193	23	,	,	PUNCT
ejpam-4808	193	24	then	then	ADV
ejpam-4808	193	25	xr	xr	PROPN
ejpam-4808	193	26	q	q	PROPN
ejpam-4808	193	27	v	v	PROPN
ejpam-4808	193	28	≤	≤	PROPN
ejpam-4808	193	29	t	t	NOUN
ejpam-4808	193	30	.	.	PUNCT
ejpam-4808	194	1	as	as	ADP
ejpam-4808	194	2	a	a	DET
ejpam-4808	194	3	result	result	NOUN
ejpam-4808	194	4	of	of	ADP
ejpam-4808	194	5	that	that	PRON
ejpam-4808	194	6	,	,	PUNCT
ejpam-4808	194	7	t	t	PROPN
ejpam-4808	194	8	∈	∈	PROPN
ejpam-4808	194	9	ngφq	ngφq	NOUN
ejpam-4808	194	10	(	(	PUNCT
ejpam-4808	194	11	i	i	PROPN
ejpam-4808	194	12	,	,	PUNCT
ejpam-4808	194	13	j	j	PROPN
ejpam-4808	194	14	)	)	PUNCT
ejpam-4808	194	15	(	(	PUNCT
ejpam-4808	194	16	xr	xr	X
ejpam-4808	194	17	)	)	PUNCT
ejpam-4808	194	18	.	.	PUNCT
ejpam-4808	195	1	in	in	ADP
ejpam-4808	195	2	the	the	DET
ejpam-4808	195	3	opposite	opposite	ADJ
ejpam-4808	195	4	direction	direction	NOUN
ejpam-4808	195	5	,	,	PUNCT
ejpam-4808	195	6	assume	assume	VERB
ejpam-4808	195	7	t	t	PROPN
ejpam-4808	195	8	∈	∈	PROPN
ejpam-4808	195	9	ngφq	ngφq	NOUN
ejpam-4808	195	10	(	(	PUNCT
ejpam-4808	195	11	i	i	PROPN
ejpam-4808	195	12	,	,	PUNCT
ejpam-4808	195	13	j	j	PROPN
ejpam-4808	195	14	)	)	PUNCT
ejpam-4808	195	15	(	(	PUNCT
ejpam-4808	195	16	xr	xr	X
ejpam-4808	195	17	)	)	PUNCT
ejpam-4808	195	18	.	.	PUNCT
ejpam-4808	196	1	thus	thus	ADV
ejpam-4808	196	2	∃	∃	NUM
ejpam-4808	196	3	fuzzy	fuzzy	ADJ
ejpam-4808	196	4	(	(	PUNCT
ejpam-4808	196	5	i	i	PROPN
ejpam-4808	196	6	,	,	PUNCT
ejpam-4808	196	7	j)−	j)−	PROPN
ejpam-4808	196	8	gφ−	gφ−	PROPN
ejpam-4808	196	9	open	open	ADJ
ejpam-4808	196	10	set	set	VERB
ejpam-4808	196	11	v	v	NUM
ejpam-4808	196	12	so	so	ADV
ejpam-4808	196	13	xr	xr	PROPN
ejpam-4808	196	14	q	q	PROPN
ejpam-4808	196	15	v	v	PROPN
ejpam-4808	196	16	≤	≤	X
ejpam-4808	196	17	t	t	NOUN
ejpam-4808	196	18	,	,	PUNCT
ejpam-4808	196	19	and	and	CCONJ
ejpam-4808	196	20	hence	hence	ADV
ejpam-4808	196	21	x1−r	x1−r	PROPN
ejpam-4808	196	22	∈	∈	PROPN
ejpam-4808	196	23	v	v	ADP
ejpam-4808	196	24	≤	≤	X
ejpam-4808	196	25	t	t	NOUN
ejpam-4808	196	26	.	.	PUNCT
ejpam-4808	197	1	as	as	ADP
ejpam-4808	197	2	a	a	DET
ejpam-4808	197	3	result	result	NOUN
ejpam-4808	197	4	of	of	ADP
ejpam-4808	197	5	that	that	PRON
ejpam-4808	197	6	,	,	PUNCT
ejpam-4808	197	7	t	t	PROPN
ejpam-4808	197	8	∈	∈	PROPN
ejpam-4808	197	9	ngφ	ngφ	ADV
ejpam-4808	197	10	(	(	PUNCT
ejpam-4808	197	11	i	i	PROPN
ejpam-4808	197	12	,	,	PUNCT
ejpam-4808	197	13	j)(x1−r	j)(x1−r	PROPN
ejpam-4808	197	14	)	)	PUNCT
ejpam-4808	197	15	.	.	PUNCT
ejpam-4808	198	1	(	(	PUNCT
ejpam-4808	198	2	3	3	X
ejpam-4808	198	3	)	)	PUNCT
ejpam-4808	198	4	assume	assume	VERB
ejpam-4808	198	5	e	e	PRON
ejpam-4808	198	6	be	be	AUX
ejpam-4808	198	7	fuzzy	fuzzy	ADJ
ejpam-4808	198	8	(	(	PUNCT
ejpam-4808	198	9	i	i	PROPN
ejpam-4808	198	10	,	,	PUNCT
ejpam-4808	198	11	j)−	j)−	PROPN
ejpam-4808	198	12	gφ−closed	gφ−close	VERB
ejpam-4808	198	13	.	.	PUNCT
ejpam-4808	199	1	suppose	suppose	VERB
ejpam-4808	199	2	there	there	PRON
ejpam-4808	199	3	∃	∃	PROPN
ejpam-4808	199	4	fuzzy	fuzzy	ADJ
ejpam-4808	199	5	point	point	NOUN
ejpam-4808	199	6	xr	xr	PROPN
ejpam-4808	200	1	so	so	ADV
ejpam-4808	200	2	xr	xr	PROPN
ejpam-4808	200	3	q	q	PROPN
ejpam-4808	200	4	δj	δj	ADJ
ejpam-4808	200	5	−φ−	−φ−	NOUN
ejpam-4808	200	6	cl(e	cl(e	NUM
ejpam-4808	200	7	)	)	PUNCT
ejpam-4808	200	8	,	,	PUNCT
ejpam-4808	200	9	but	but	CCONJ
ejpam-4808	200	10	δi−	δi−	PROPN
ejpam-4808	200	11	cl(xr	cl(xr	NOUN
ejpam-4808	200	12	)	)	PUNCT
ejpam-4808	200	13	q	q	PROPN
ejpam-4808	201	1	e.	e.	PROPN
ejpam-4808	201	2	thus	thus	ADV
ejpam-4808	201	3	e	e	X
ejpam-4808	201	4	≤	≤	X
ejpam-4808	201	5	(	(	PUNCT
ejpam-4808	201	6	δi	δi	ADP
ejpam-4808	201	7	−	−	NOUN
ejpam-4808	201	8	cl(xr	cl(xr	NOUN
ejpam-4808	201	9	)	)	PUNCT
ejpam-4808	201	10	)	)	PUNCT
ejpam-4808	201	11	c.	c.	NOUN
ejpam-4808	201	12	as	as	SCONJ
ejpam-4808	201	13	e	e	PROPN
ejpam-4808	201	14	is	be	AUX
ejpam-4808	201	15	fuzzy	fuzzy	ADJ
ejpam-4808	201	16	(	(	PUNCT
ejpam-4808	201	17	i	i	PROPN
ejpam-4808	201	18	,	,	PUNCT
ejpam-4808	201	19	j)−	j)−	PROPN
ejpam-4808	201	20	gφ−closed	gφ−close	VERB
ejpam-4808	201	21	,	,	PUNCT
ejpam-4808	201	22	thus	thus	ADV
ejpam-4808	201	23	δj	δj	ADJ
ejpam-4808	201	24	−φ−	−φ−	ADJ
ejpam-4808	201	25	cl(e	cl(e	NOUN
ejpam-4808	201	26	)	)	PUNCT
ejpam-4808	201	27	≤	≤	NOUN
ejpam-4808	201	28	(	(	PUNCT
ejpam-4808	201	29	δi	δi	ADP
ejpam-4808	201	30	−	−	NOUN
ejpam-4808	201	31	cl(xr	cl(xr	NOUN
ejpam-4808	201	32	)	)	PUNCT
ejpam-4808	201	33	)	)	PUNCT
ejpam-4808	202	1	c	c	X
ejpam-4808	202	2	,	,	PUNCT
ejpam-4808	202	3	hence	hence	ADV
ejpam-4808	202	4	δj	δj	ADJ
ejpam-4808	202	5	−φ−	−φ−	ADJ
ejpam-4808	202	6	cl(e	cl(e	NOUN
ejpam-4808	202	7	)	)	PUNCT
ejpam-4808	202	8	q	q	NOUN
ejpam-4808	202	9	δi−	δi−	NOUN
ejpam-4808	202	10	cl(xr	cl(xr	NOUN
ejpam-4808	202	11	)	)	PUNCT
ejpam-4808	202	12	.	.	PUNCT
ejpam-4808	203	1	as	as	ADP
ejpam-4808	203	2	xr	xr	PROPN
ejpam-4808	203	3	∈	∈	PROPN
ejpam-4808	203	4	δi−	δi−	PROPN
ejpam-4808	203	5	cl(xr	cl(xr	NOUN
ejpam-4808	203	6	)	)	PUNCT
ejpam-4808	203	7	,	,	PUNCT
ejpam-4808	203	8	thus	thus	ADV
ejpam-4808	203	9	xr	xr	PROPN
ejpam-4808	203	10	q	q	PROPN
ejpam-4808	203	11	δj	δj	ADP
ejpam-4808	203	12	−	−	PROPN
ejpam-4808	203	13	φ	φ	NUM
ejpam-4808	203	14	−	−	PROPN
ejpam-4808	203	15	cl(e	cl(e	NOUN
ejpam-4808	203	16	)	)	PUNCT
ejpam-4808	203	17	that	that	PRON
ejpam-4808	203	18	is	be	AUX
ejpam-4808	203	19	a	a	DET
ejpam-4808	203	20	contradiction	contradiction	NOUN
ejpam-4808	203	21	.	.	PUNCT
ejpam-4808	204	1	as	as	ADP
ejpam-4808	204	2	a	a	DET
ejpam-4808	204	3	result	result	NOUN
ejpam-4808	204	4	of	of	ADP
ejpam-4808	204	5	that	that	PRON
ejpam-4808	204	6	,	,	PUNCT
ejpam-4808	204	7	δi	δi	ADP
ejpam-4808	204	8	−	−	PROPN
ejpam-4808	204	9	cl(xr	cl(xr	NOUN
ejpam-4808	204	10	)	)	PUNCT
ejpam-4808	204	11	q	q	PUNCT
ejpam-4808	205	1	e	e	NOUN
ejpam-4808	205	2	holds	hold	VERB
ejpam-4808	205	3	∀xr	∀xr	ADJ
ejpam-4808	205	4	q	q	PUNCT
ejpam-4808	205	5	δj	δj	ADP
ejpam-4808	205	6	−	−	PROPN
ejpam-4808	205	7	φ−	φ−	PROPN
ejpam-4808	205	8	cl(e	cl(e	NOUN
ejpam-4808	205	9	)	)	PUNCT
ejpam-4808	205	10	.	.	PUNCT
ejpam-4808	206	1	corollary	corollary	ADJ
ejpam-4808	206	2	2	2	NUM
ejpam-4808	206	3	.	.	PUNCT
ejpam-4808	207	1	if	if	SCONJ
ejpam-4808	207	2	e	e	NOUN
ejpam-4808	207	3	is	be	AUX
ejpam-4808	207	4	fuzzy	fuzzy	ADJ
ejpam-4808	207	5	(	(	PUNCT
ejpam-4808	207	6	i	i	NOUN
ejpam-4808	207	7	,	,	PUNCT
ejpam-4808	207	8	j)−gφ−closed	j)−gφ−close	VERB
ejpam-4808	207	9	,	,	PUNCT
ejpam-4808	207	10	and	and	CCONJ
ejpam-4808	207	11	xr	xr	PROPN
ejpam-4808	207	12	is	be	AUX
ejpam-4808	207	13	fuzzy	fuzzy	ADJ
ejpam-4808	207	14	point	point	NOUN
ejpam-4808	207	15	in	in	ADP
ejpam-4808	207	16	fbts	fbt	NOUN
ejpam-4808	207	17	(	(	PUNCT
ejpam-4808	207	18	x	x	NOUN
ejpam-4808	207	19	,	,	PUNCT
ejpam-4808	207	20	δ1	δ1	NOUN
ejpam-4808	207	21	,	,	PUNCT
ejpam-4808	207	22	δ2	δ2	PROPN
ejpam-4808	207	23	)	)	PUNCT
ejpam-4808	207	24	,	,	PUNCT
ejpam-4808	207	25	then	then	ADV
ejpam-4808	207	26	δi	δi	VERB
ejpam-4808	207	27	−	−	PROPN
ejpam-4808	207	28	cl(xr	cl(xr	NOUN
ejpam-4808	207	29	)	)	PUNCT
ejpam-4808	207	30	q	q	PUNCT
ejpam-4808	208	1	e	e	NOUN
ejpam-4808	208	2	holds	hold	VERB
ejpam-4808	208	3	∀xr	∀xr	ADJ
ejpam-4808	208	4	q	q	PUNCT
ejpam-4808	208	5	δj	δj	ADP
ejpam-4808	208	6	−	−	PROPN
ejpam-4808	208	7	β	β	X
ejpam-4808	208	8	−	−	NOUN
ejpam-4808	208	9	cl(e	cl(e	NUM
ejpam-4808	208	10	)	)	PUNCT
ejpam-4808	208	11	.	.	PUNCT
ejpam-4808	209	1	in	in	ADP
ejpam-4808	209	2	the	the	DET
ejpam-4808	209	3	theory	theory	NOUN
ejpam-4808	209	4	that	that	PRON
ejpam-4808	209	5	follows	follow	VERB
ejpam-4808	209	6	,	,	PUNCT
ejpam-4808	209	7	we	we	PRON
ejpam-4808	209	8	studied	study	VERB
ejpam-4808	209	9	the	the	DET
ejpam-4808	209	10	most	most	ADV
ejpam-4808	209	11	fundamental	fundamental	ADJ
ejpam-4808	209	12	generalized	generalized	ADJ
ejpam-4808	209	13	closure	closure	NOUN
ejpam-4808	209	14	characteristics	characteristic	NOUN
ejpam-4808	209	15	and	and	CCONJ
ejpam-4808	209	16	demonstrated	demonstrate	VERB
ejpam-4808	209	17	them	they	PRON
ejpam-4808	209	18	using	use	VERB
ejpam-4808	209	19	new	new	ADJ
ejpam-4808	209	20	neighborhood	neighborhood	NOUN
ejpam-4808	209	21	structure	structure	NOUN
ejpam-4808	209	22	notions	notion	NOUN
ejpam-4808	209	23	.	.	PUNCT
ejpam-4808	210	1	theorem	theorem	NOUN
ejpam-4808	210	2	5	5	NUM
ejpam-4808	210	3	.	.	PUNCT
ejpam-4808	211	1	if	if	SCONJ
ejpam-4808	211	2	e	e	NOUN
ejpam-4808	211	3	,	,	PUNCT
ejpam-4808	211	4	and	and	CCONJ
ejpam-4808	211	5	t	t	PROPN
ejpam-4808	211	6	are	be	AUX
ejpam-4808	211	7	fuzzy	fuzzy	ADJ
ejpam-4808	211	8	subsets	subset	NOUN
ejpam-4808	211	9	of	of	ADP
ejpam-4808	211	10	fbts	fbt	NOUN
ejpam-4808	211	11	(	(	PUNCT
ejpam-4808	211	12	x	x	NOUN
ejpam-4808	211	13	,	,	PUNCT
ejpam-4808	211	14	δ1	δ1	NOUN
ejpam-4808	211	15	,	,	PUNCT
ejpam-4808	211	16	δ2	δ2	PROPN
ejpam-4808	211	17	)	)	PUNCT
ejpam-4808	211	18	,	,	PUNCT
ejpam-4808	211	19	thus	thus	ADV
ejpam-4808	211	20	the	the	DET
ejpam-4808	211	21	following	follow	VERB
ejpam-4808	211	22	arguments	argument	NOUN
ejpam-4808	211	23	are	be	AUX
ejpam-4808	211	24	correct	correct	ADJ
ejpam-4808	211	25	:	:	PUNCT
ejpam-4808	211	26	(	(	PUNCT
ejpam-4808	211	27	1	1	NUM
ejpam-4808	211	28	)	)	PUNCT
ejpam-4808	211	29	0	0	NUM
ejpam-4808	211	30	,	,	PUNCT
ejpam-4808	211	31	and	and	CCONJ
ejpam-4808	211	32	1	1	NUM
ejpam-4808	211	33	are	be	AUX
ejpam-4808	211	34	fuzzy	fuzzy	ADJ
ejpam-4808	211	35	(	(	PUNCT
ejpam-4808	211	36	i	i	NOUN
ejpam-4808	211	37	,	,	PUNCT
ejpam-4808	211	38	j)−	j)−	PROPN
ejpam-4808	211	39	gφ−	gφ−	PROPN
ejpam-4808	211	40	closed	close	VERB
ejpam-4808	211	41	.	.	PUNCT
ejpam-4808	212	1	(	(	PUNCT
ejpam-4808	212	2	2	2	X
ejpam-4808	212	3	)	)	PUNCT
ejpam-4808	212	4	when	when	SCONJ
ejpam-4808	212	5	e	e	X
ejpam-4808	212	6	≤	≤	PROPN
ejpam-4808	212	7	t	t	NOUN
ejpam-4808	212	8	,	,	PUNCT
ejpam-4808	212	9	then	then	ADV
ejpam-4808	212	10	(	(	PUNCT
ejpam-4808	212	11	i	i	NOUN
ejpam-4808	212	12	,	,	PUNCT
ejpam-4808	212	13	j)−	j)−	PROPN
ejpam-4808	212	14	gφ−	gφ−	PROPN
ejpam-4808	212	15	cl(e	cl(e	NOUN
ejpam-4808	212	16	)	)	PUNCT
ejpam-4808	212	17	≤	≤	NOUN
ejpam-4808	212	18	(	(	PUNCT
ejpam-4808	212	19	i	i	NOUN
ejpam-4808	212	20	,	,	PUNCT
ejpam-4808	212	21	j)−	j)−	PROPN
ejpam-4808	212	22	gφ−	gφ−	PROPN
ejpam-4808	212	23	cl(t	cl(t	X
ejpam-4808	212	24	)	)	PUNCT
ejpam-4808	212	25	.	.	PUNCT
ejpam-4808	213	1	(	(	PUNCT
ejpam-4808	213	2	3	3	X
ejpam-4808	213	3	)	)	PUNCT
ejpam-4808	213	4	e	e	NOUN
ejpam-4808	213	5	≤	≤	NOUN
ejpam-4808	213	6	(	(	PUNCT
ejpam-4808	213	7	i	i	NOUN
ejpam-4808	213	8	,	,	PUNCT
ejpam-4808	213	9	j)−	j)−	PROPN
ejpam-4808	213	10	gφ−	gφ−	PROPN
ejpam-4808	213	11	cl(e	cl(e	NUM
ejpam-4808	213	12	)	)	PUNCT
ejpam-4808	213	13	,	,	PUNCT
ejpam-4808	213	14	∀	∀	X
ejpam-4808	213	15	fuzzy	fuzzy	ADJ
ejpam-4808	213	16	set	set	VERB
ejpam-4808	213	17	e	e	X
ejpam-4808	213	18	∈	∈	PROPN
ejpam-4808	213	19	ix	ix	X
ejpam-4808	213	20	.	.	PUNCT
ejpam-4808	214	1	(	(	PUNCT
ejpam-4808	214	2	4	4	X
ejpam-4808	214	3	)	)	PUNCT
ejpam-4808	214	4	when	when	SCONJ
ejpam-4808	214	5	e	e	NOUN
ejpam-4808	214	6	is	be	AUX
ejpam-4808	214	7	fuzzy	fuzzy	ADJ
ejpam-4808	214	8	(	(	PUNCT
ejpam-4808	214	9	i	i	NOUN
ejpam-4808	214	10	,	,	PUNCT
ejpam-4808	214	11	j)−gφ−closed	j)−gφ−closed	PROPN
ejpam-4808	214	12	,	,	PUNCT
ejpam-4808	214	13	then	then	ADV
ejpam-4808	214	14	(	(	PUNCT
ejpam-4808	214	15	i	i	NOUN
ejpam-4808	214	16	,	,	PUNCT
ejpam-4808	214	17	j)−gφ−cl(e	j)−gφ−cl(e	PROPN
ejpam-4808	214	18	)	)	PUNCT
ejpam-4808	214	19	=	=	VERB
ejpam-4808	215	1	e.	e.	PROPN
ejpam-4808	216	1	the	the	DET
ejpam-4808	216	2	converse	converse	NOUN
ejpam-4808	216	3	is	be	AUX
ejpam-4808	216	4	false	false	ADJ
ejpam-4808	216	5	,	,	PUNCT
ejpam-4808	216	6	as	as	SCONJ
ejpam-4808	216	7	the	the	DET
ejpam-4808	216	8	intersection	intersection	NOUN
ejpam-4808	216	9	of	of	ADP
ejpam-4808	216	10	fuzzy	fuzzy	ADJ
ejpam-4808	216	11	(	(	PUNCT
ejpam-4808	216	12	i	i	NOUN
ejpam-4808	216	13	,	,	PUNCT
ejpam-4808	216	14	j)−gφ−closed	j)−gφ−close	VERB
ejpam-4808	216	15	sets	set	NOUN
ejpam-4808	216	16	need	need	AUX
ejpam-4808	216	17	not	not	PART
ejpam-4808	216	18	be	be	AUX
ejpam-4808	216	19	fuzzy	fuzzy	ADJ
ejpam-4808	216	20	(	(	PUNCT
ejpam-4808	216	21	i	i	NOUN
ejpam-4808	216	22	,	,	PUNCT
ejpam-4808	216	23	j)−gφ−closed	j)−gφ−closed	PROPN
ejpam-4808	216	24	.	.	PUNCT
ejpam-4808	217	1	(	(	PUNCT
ejpam-4808	217	2	5	5	NUM
ejpam-4808	217	3	)	)	PUNCT
ejpam-4808	217	4	(	(	PUNCT
ejpam-4808	217	5	i	i	NOUN
ejpam-4808	217	6	,	,	PUNCT
ejpam-4808	217	7	j)−	j)−	PROPN
ejpam-4808	217	8	gφ−	gφ−	PROPN
ejpam-4808	217	9	cl((i	cl((i	PROPN
ejpam-4808	217	10	,	,	PUNCT
ejpam-4808	217	11	j)−	j)−	PROPN
ejpam-4808	217	12	gφ−	gφ−	PROPN
ejpam-4808	217	13	cl(e	cl(e	NUM
ejpam-4808	217	14	)	)	PUNCT
ejpam-4808	217	15	)	)	PUNCT
ejpam-4808	218	1	=	=	PUNCT
ejpam-4808	218	2	(	(	PUNCT
ejpam-4808	218	3	i	i	PROPN
ejpam-4808	218	4	,	,	PUNCT
ejpam-4808	218	5	j)−	j)−	PROPN
ejpam-4808	218	6	gφ−	gφ−	PROPN
ejpam-4808	218	7	cl(e	cl(e	NUM
ejpam-4808	218	8	)	)	PUNCT
ejpam-4808	218	9	.	.	PUNCT
ejpam-4808	219	1	(	(	PUNCT
ejpam-4808	219	2	6	6	NUM
ejpam-4808	219	3	)	)	PUNCT
ejpam-4808	219	4	when	when	SCONJ
ejpam-4808	219	5	v	v	NOUN
ejpam-4808	219	6	is	be	AUX
ejpam-4808	219	7	(	(	PUNCT
ejpam-4808	219	8	i	i	PROPN
ejpam-4808	219	9	,	,	PUNCT
ejpam-4808	219	10	j)−	j)−	PROPN
ejpam-4808	219	11	gφ−	gφ−	PROPN
ejpam-4808	219	12	open	open	ADJ
ejpam-4808	219	13	,	,	PUNCT
ejpam-4808	219	14	then	then	ADV
ejpam-4808	219	15	v	v	ADP
ejpam-4808	219	16	q	q	X
ejpam-4808	219	17	e	e	NOUN
ejpam-4808	219	18	⇐	⇐	ADJ
ejpam-4808	219	19	⇒	⇒	NOUN
ejpam-4808	219	20	v	v	X
ejpam-4808	219	21	q	q	X
ejpam-4808	219	22	(	(	PUNCT
ejpam-4808	219	23	i	i	NOUN
ejpam-4808	219	24	,	,	PUNCT
ejpam-4808	219	25	j)−	j)−	PROPN
ejpam-4808	219	26	gφ−	gφ−	PROPN
ejpam-4808	219	27	cl(e	cl(e	NUM
ejpam-4808	219	28	)	)	PUNCT
ejpam-4808	219	29	.	.	PUNCT
ejpam-4808	220	1	(	(	PUNCT
ejpam-4808	220	2	7	7	X
ejpam-4808	220	3	)	)	PUNCT
ejpam-4808	220	4	(	(	PUNCT
ejpam-4808	220	5	i	i	NOUN
ejpam-4808	220	6	,	,	PUNCT
ejpam-4808	220	7	j)−	j)−	PROPN
ejpam-4808	220	8	gφ−	gφ−	PROPN
ejpam-4808	220	9	cl(e	cl(e	NUM
ejpam-4808	220	10	)	)	PUNCT
ejpam-4808	220	11	∨	∨	NUM
ejpam-4808	220	12	(	(	PUNCT
ejpam-4808	220	13	i	i	PROPN
ejpam-4808	220	14	,	,	PUNCT
ejpam-4808	220	15	j)−	j)−	PROPN
ejpam-4808	220	16	gφ−	gφ−	PROPN
ejpam-4808	220	17	cl(t	cl(t	X
ejpam-4808	220	18	)	)	PUNCT
ejpam-4808	220	19	≤	≤	NOUN
ejpam-4808	220	20	(	(	PUNCT
ejpam-4808	220	21	i	i	NOUN
ejpam-4808	220	22	,	,	PUNCT
ejpam-4808	220	23	j)−	j)−	PROPN
ejpam-4808	220	24	gφ−	gφ−	PROPN
ejpam-4808	220	25	cl(e	cl(e	NOUN
ejpam-4808	220	26	∨	∨	NUM
ejpam-4808	220	27	t	t	PROPN
ejpam-4808	220	28	)	)	PUNCT
ejpam-4808	220	29	.	.	PUNCT
ejpam-4808	221	1	proof	proof	NOUN
ejpam-4808	221	2	.	.	PUNCT
ejpam-4808	222	1	by	by	ADP
ejpam-4808	222	2	using	use	VERB
ejpam-4808	222	3	definition	definition	NOUN
ejpam-4808	222	4	7	7	NUM
ejpam-4808	222	5	and	and	CCONJ
ejpam-4808	222	6	theorem4	theorem4	NOUN
ejpam-4808	222	7	we	we	PRON
ejpam-4808	222	8	can	can	AUX
ejpam-4808	222	9	easily	easily	ADV
ejpam-4808	222	10	proved	prove	VERB
ejpam-4808	222	11	(	(	PUNCT
ejpam-4808	222	12	1	1	NUM
ejpam-4808	222	13	)	)	PUNCT
ejpam-4808	222	14	,	,	PUNCT
ejpam-4808	222	15	(	(	PUNCT
ejpam-4808	222	16	2	2	NUM
ejpam-4808	222	17	)	)	PUNCT
ejpam-4808	222	18	,	,	PUNCT
ejpam-4808	222	19	(	(	PUNCT
ejpam-4808	222	20	3	3	NUM
ejpam-4808	222	21	)	)	PUNCT
ejpam-4808	222	22	,	,	PUNCT
ejpam-4808	222	23	and	and	CCONJ
ejpam-4808	222	24	(	(	PUNCT
ejpam-4808	222	25	4	4	NUM
ejpam-4808	222	26	)	)	PUNCT
ejpam-4808	222	27	.	.	PUNCT
ejpam-4808	223	1	(	(	PUNCT
ejpam-4808	223	2	5	5	X
ejpam-4808	223	3	)	)	PUNCT
ejpam-4808	223	4	assume	assume	VERB
ejpam-4808	223	5	xr	xr	PROPN
ejpam-4808	223	6	is	be	AUX
ejpam-4808	223	7	fuzzy	fuzzy	ADJ
ejpam-4808	223	8	point	point	NOUN
ejpam-4808	223	9	with	with	ADP
ejpam-4808	223	10	xr	xr	PROPN
ejpam-4808	223	11	̸∈	̸∈	PROPN
ejpam-4808	223	12	(	(	PUNCT
ejpam-4808	223	13	i	i	PROPN
ejpam-4808	223	14	,	,	PUNCT
ejpam-4808	223	15	j	j	PROPN
ejpam-4808	223	16	)	)	PUNCT
ejpam-4808	223	17	−	−	PROPN
ejpam-4808	223	18	gφ	gφ	NOUN
ejpam-4808	223	19	−	−	PROPN
ejpam-4808	223	20	cl(e	cl(e	NUM
ejpam-4808	223	21	)	)	PUNCT
ejpam-4808	223	22	.	.	PUNCT
ejpam-4808	224	1	after	after	ADP
ejpam-4808	224	2	that	that	PRON
ejpam-4808	224	3	,	,	PUNCT
ejpam-4808	224	4	∃v	∃v	PROPN
ejpam-4808	224	5	∈	∈	PROPN
ejpam-4808	224	6	ngφq	ngφq	NOUN
ejpam-4808	224	7	(	(	PUNCT
ejpam-4808	224	8	i	i	PROPN
ejpam-4808	224	9	,	,	PUNCT
ejpam-4808	224	10	j	j	PROPN
ejpam-4808	224	11	)	)	PUNCT
ejpam-4808	224	12	(	(	PUNCT
ejpam-4808	224	13	xr	xr	X
ejpam-4808	224	14	)	)	PUNCT
ejpam-4808	224	15	so	so	ADV
ejpam-4808	224	16	xr	xr	PROPN
ejpam-4808	224	17	q	q	PROPN
ejpam-4808	224	18	v	v	PROPN
ejpam-4808	224	19	,	,	PUNCT
ejpam-4808	224	20	v	v	NOUN
ejpam-4808	224	21	q	q	NOUN
ejpam-4808	224	22	e	e	NOUN
ejpam-4808	224	23	,	,	PUNCT
ejpam-4808	224	24	then	then	ADV
ejpam-4808	224	25	∃u	∃u	PROPN
ejpam-4808	224	26	is	be	AUX
ejpam-4808	224	27	fuzzy	fuzzy	ADJ
ejpam-4808	224	28	(	(	PUNCT
ejpam-4808	224	29	i	i	NOUN
ejpam-4808	224	30	,	,	PUNCT
ejpam-4808	224	31	j)−	j)−	PROPN
ejpam-4808	224	32	gφ−	gφ−	PUNCT
ejpam-4808	224	33	open	open	ADJ
ejpam-4808	224	34	so	so	SCONJ
ejpam-4808	224	35	xr	xr	PROPN
ejpam-4808	224	36	q	q	PROPN
ejpam-4808	224	37	u	u	PROPN
ejpam-4808	224	38	≤	≤	X
ejpam-4808	224	39	v	v	NOUN
ejpam-4808	224	40	and	and	CCONJ
ejpam-4808	224	41	u	u	NOUN
ejpam-4808	224	42	q	q	PROPN
ejpam-4808	224	43	e.	e.	PROPN
ejpam-4808	224	44	thus	thus	ADV
ejpam-4808	224	45	from	from	ADP
ejpam-4808	224	46	(	(	PUNCT
ejpam-4808	224	47	6)u	6)u	NOUN
ejpam-4808	224	48	q	q	X
ejpam-4808	224	49	(	(	PUNCT
ejpam-4808	224	50	i	i	NOUN
ejpam-4808	224	51	,	,	PUNCT
ejpam-4808	224	52	j)−	j)−	PROPN
ejpam-4808	224	53	gφ−	gφ−	PROPN
ejpam-4808	224	54	cl(e	cl(e	NUM
ejpam-4808	224	55	)	)	PUNCT
ejpam-4808	224	56	.	.	PUNCT
ejpam-4808	225	1	as	as	SCONJ
ejpam-4808	225	2	∃u	∃u	PROPN
ejpam-4808	225	3	is	be	AUX
ejpam-4808	225	4	fuzzy	fuzzy	ADJ
ejpam-4808	225	5	(	(	PUNCT
ejpam-4808	225	6	i	i	NOUN
ejpam-4808	225	7	,	,	PUNCT
ejpam-4808	225	8	j)−	j)−	PROPN
ejpam-4808	225	9	gφ−	gφ−	PUNCT
ejpam-4808	225	10	open	open	ADJ
ejpam-4808	226	1	so	so	SCONJ
ejpam-4808	226	2	xr	xr	PROPN
ejpam-4808	226	3	q	q	PROPN
ejpam-4808	226	4	u	u	PROPN
ejpam-4808	226	5	and	and	CCONJ
ejpam-4808	226	6	u	u	NOUN
ejpam-4808	226	7	q	q	PROPN
ejpam-4808	226	8	(	(	PUNCT
ejpam-4808	226	9	i	i	PROPN
ejpam-4808	226	10	,	,	PUNCT
ejpam-4808	226	11	j)−	j)−	PROPN
ejpam-4808	226	12	gφ−	gφ−	PROPN
ejpam-4808	226	13	cl(e	cl(e	NUM
ejpam-4808	226	14	)	)	PUNCT
ejpam-4808	226	15	.	.	PUNCT
ejpam-4808	227	1	then	then	ADV
ejpam-4808	227	2	xr	xr	PROPN
ejpam-4808	227	3	̸∈	̸∈	PROPN
ejpam-4808	227	4	(	(	PUNCT
ejpam-4808	227	5	i	i	PROPN
ejpam-4808	227	6	,	,	PUNCT
ejpam-4808	227	7	j)−	j)−	PROPN
ejpam-4808	227	8	gφ−	gφ−	PROPN
ejpam-4808	227	9	cl((i	cl((i	PROPN
ejpam-4808	227	10	,	,	PUNCT
ejpam-4808	227	11	j)−	j)−	PROPN
ejpam-4808	227	12	gφ−	gφ−	PROPN
ejpam-4808	227	13	cl(e	cl(e	NUM
ejpam-4808	227	14	)	)	PUNCT
ejpam-4808	227	15	)	)	PUNCT
ejpam-4808	227	16	,	,	PUNCT
ejpam-4808	227	17	after	after	ADP
ejpam-4808	227	18	that	that	PRON
ejpam-4808	227	19	(	(	PUNCT
ejpam-4808	227	20	i	i	NOUN
ejpam-4808	227	21	,	,	PUNCT
ejpam-4808	227	22	j)−	j)−	PROPN
ejpam-4808	227	23	gφ−	gφ−	PROPN
ejpam-4808	227	24	cl((i	cl((i	PROPN
ejpam-4808	227	25	,	,	PUNCT
ejpam-4808	227	26	j)−	j)−	PROPN
ejpam-4808	227	27	gφ−	gφ−	PROPN
ejpam-4808	227	28	cl(e	cl(e	NUM
ejpam-4808	227	29	)	)	PUNCT
ejpam-4808	227	30	)	)	PUNCT
ejpam-4808	227	31	≤	≤	NOUN
ejpam-4808	227	32	(	(	PUNCT
ejpam-4808	227	33	i	i	NOUN
ejpam-4808	227	34	,	,	PUNCT
ejpam-4808	227	35	j)−	j)−	PROPN
ejpam-4808	227	36	gφ−	gφ−	PROPN
ejpam-4808	227	37	cl(e	cl(e	NUM
ejpam-4808	227	38	)	)	PUNCT
ejpam-4808	227	39	.	.	PUNCT
ejpam-4808	228	1	but	but	CCONJ
ejpam-4808	228	2	(	(	PUNCT
ejpam-4808	228	3	i	i	NOUN
ejpam-4808	228	4	,	,	PUNCT
ejpam-4808	228	5	j)−	j)−	PROPN
ejpam-4808	228	6	gφ−	gφ−	PROPN
ejpam-4808	228	7	cl(e	cl(e	NOUN
ejpam-4808	228	8	)	)	PUNCT
ejpam-4808	228	9	≤	≤	NOUN
ejpam-4808	228	10	(	(	PUNCT
ejpam-4808	228	11	i	i	NOUN
ejpam-4808	228	12	,	,	PUNCT
ejpam-4808	228	13	j)−	j)−	PROPN
ejpam-4808	228	14	gφ−	gφ−	PROPN
ejpam-4808	228	15	cl((i	cl((i	PROPN
ejpam-4808	228	16	,	,	PUNCT
ejpam-4808	228	17	j)−	j)−	PROPN
ejpam-4808	228	18	gφ−	gφ−	PROPN
ejpam-4808	228	19	cl(e	cl(e	NUM
ejpam-4808	228	20	)	)	PUNCT
ejpam-4808	228	21	)	)	PUNCT
ejpam-4808	228	22	.	.	PUNCT
ejpam-4808	229	1	as	as	ADP
ejpam-4808	229	2	a	a	DET
ejpam-4808	229	3	result	result	NOUN
ejpam-4808	229	4	of	of	ADP
ejpam-4808	229	5	that	that	PRON
ejpam-4808	229	6	,	,	PUNCT
ejpam-4808	229	7	(	(	PUNCT
ejpam-4808	229	8	i	i	PROPN
ejpam-4808	229	9	,	,	PUNCT
ejpam-4808	229	10	j)−	j)−	PROPN
ejpam-4808	229	11	gφ−	gφ−	PROPN
ejpam-4808	229	12	cl(e	cl(e	NUM
ejpam-4808	229	13	)	)	PUNCT
ejpam-4808	229	14	=	=	PUNCT
ejpam-4808	229	15	(	(	PUNCT
ejpam-4808	229	16	i	i	PROPN
ejpam-4808	229	17	,	,	PUNCT
ejpam-4808	229	18	j)−	j)−	PROPN
ejpam-4808	229	19	gφ−	gφ−	PROPN
ejpam-4808	229	20	cl((i	cl((i	PROPN
ejpam-4808	229	21	,	,	PUNCT
ejpam-4808	229	22	j)−	j)−	PROPN
ejpam-4808	229	23	gφ−	gφ−	PROPN
ejpam-4808	229	24	cl(e	cl(e	NUM
ejpam-4808	229	25	)	)	PUNCT
ejpam-4808	229	26	)	)	PUNCT
ejpam-4808	229	27	.	.	PUNCT
ejpam-4808	230	1	a.	a.	NOUN
ejpam-4808	230	2	a.	a.	PROPN
ejpam-4808	230	3	alharbi	alharbi	PROPN
ejpam-4808	230	4	,	,	PUNCT
ejpam-4808	230	5	a.	a.	NOUN
ejpam-4808	230	6	kilicman	kilicman	PROPN
ejpam-4808	230	7	/	/	SYM
ejpam-4808	230	8	eur	eur	PROPN
ejpam-4808	230	9	.	.	PUNCT
ejpam-4808	231	1	j.	j.	PROPN
ejpam-4808	231	2	pure	pure	PROPN
ejpam-4808	231	3	appl	appl	PROPN
ejpam-4808	231	4	.	.	PROPN
ejpam-4808	231	5	math	math	PROPN
ejpam-4808	231	6	,	,	PUNCT
ejpam-4808	231	7	16	16	NUM
ejpam-4808	231	8	(	(	PUNCT
ejpam-4808	231	9	3	3	NUM
ejpam-4808	231	10	)	)	PUNCT
ejpam-4808	231	11	(	(	PUNCT
ejpam-4808	231	12	2023	2023	NUM
ejpam-4808	231	13	)	)	PUNCT
ejpam-4808	231	14	,	,	PUNCT
ejpam-4808	231	15	1980	1980	NUM
ejpam-4808	231	16	-	-	SYM
ejpam-4808	231	17	1990	1990	NUM
ejpam-4808	231	18	1988	1988	NUM
ejpam-4808	231	19	(	(	PUNCT
ejpam-4808	231	20	6	6	NUM
ejpam-4808	231	21	)	)	PUNCT
ejpam-4808	231	22	sufficiency	sufficiency	NOUN
ejpam-4808	231	23	,	,	PUNCT
ejpam-4808	231	24	assume	assume	VERB
ejpam-4808	231	25	v	v	ADP
ejpam-4808	231	26	q	q	PROPN
ejpam-4808	231	27	e.	e.	PROPN
ejpam-4808	231	28	after	after	ADP
ejpam-4808	231	29	that	that	PRON
ejpam-4808	231	30	,	,	PUNCT
ejpam-4808	231	31	e	e	PROPN
ejpam-4808	231	32	≤	≤	PROPN
ejpam-4808	231	33	v	v	ADP
ejpam-4808	231	34	c	c	NOUN
ejpam-4808	231	35	,	,	PUNCT
ejpam-4808	231	36	v	v	NOUN
ejpam-4808	231	37	c	c	NOUN
ejpam-4808	231	38	is	be	AUX
ejpam-4808	231	39	fuzzy	fuzzy	ADJ
ejpam-4808	231	40	(	(	PUNCT
ejpam-4808	231	41	i	i	NOUN
ejpam-4808	231	42	,	,	PUNCT
ejpam-4808	231	43	j)−gφ−closed	j)−gφ−closed	PROPN
ejpam-4808	231	44	,	,	PUNCT
ejpam-4808	231	45	then	then	ADV
ejpam-4808	231	46	by	by	ADP
ejpam-4808	231	47	applying	apply	VERB
ejpam-4808	231	48	(	(	PUNCT
ejpam-4808	231	49	i	i	PROPN
ejpam-4808	231	50	,	,	PUNCT
ejpam-4808	231	51	j)−gφ−clouser	j)−gφ−clouser	NOUN
ejpam-4808	231	52	for	for	ADP
ejpam-4808	231	53	all	all	DET
ejpam-4808	231	54	sides	side	NOUN
ejpam-4808	231	55	and	and	CCONJ
ejpam-4808	231	56	from	from	ADP
ejpam-4808	231	57	(	(	PUNCT
ejpam-4808	231	58	5	5	X
ejpam-4808	231	59	)	)	PUNCT
ejpam-4808	231	60	we	we	PRON
ejpam-4808	231	61	find	find	VERB
ejpam-4808	231	62	v	v	ADP
ejpam-4808	231	63	q	q	NOUN
ejpam-4808	232	1	(	(	PUNCT
ejpam-4808	232	2	i	i	NOUN
ejpam-4808	232	3	,	,	PUNCT
ejpam-4808	232	4	j)−gφ−cl(e	j)−gφ−cl(e	PROPN
ejpam-4808	232	5	)	)	PUNCT
ejpam-4808	232	6	.	.	PUNCT
ejpam-4808	233	1	as	as	ADP
ejpam-4808	233	2	a	a	DET
ejpam-4808	233	3	result	result	NOUN
ejpam-4808	233	4	of	of	ADP
ejpam-4808	233	5	that	that	PRON
ejpam-4808	233	6	,	,	PUNCT
ejpam-4808	233	7	v	v	X
ejpam-4808	233	8	q	q	X
ejpam-4808	233	9	e	e	NOUN
ejpam-4808	233	10	⇐	⇐	ADJ
ejpam-4808	233	11	⇒	⇒	NOUN
ejpam-4808	233	12	v	v	X
ejpam-4808	233	13	q	q	X
ejpam-4808	233	14	(	(	PUNCT
ejpam-4808	233	15	i	i	NOUN
ejpam-4808	233	16	,	,	PUNCT
ejpam-4808	233	17	j)−	j)−	PROPN
ejpam-4808	233	18	gφ−	gφ−	PROPN
ejpam-4808	233	19	cl(e	cl(e	NUM
ejpam-4808	233	20	)	)	PUNCT
ejpam-4808	233	21	.	.	PUNCT
ejpam-4808	234	1	(	(	PUNCT
ejpam-4808	234	2	7	7	X
ejpam-4808	234	3	)	)	PUNCT
ejpam-4808	234	4	as	as	ADP
ejpam-4808	234	5	e	e	X
ejpam-4808	234	6	≤	≤	X
ejpam-4808	234	7	(	(	PUNCT
ejpam-4808	234	8	e	e	X
ejpam-4808	234	9	∨	∨	PROPN
ejpam-4808	234	10	t	t	PROPN
ejpam-4808	234	11	)	)	PUNCT
ejpam-4808	234	12	,	,	PUNCT
ejpam-4808	234	13	and	and	CCONJ
ejpam-4808	234	14	t	t	X
ejpam-4808	234	15	≤	≤	NUM
ejpam-4808	234	16	(	(	PUNCT
ejpam-4808	234	17	e	e	X
ejpam-4808	234	18	∨	∨	PROPN
ejpam-4808	234	19	t	t	PROPN
ejpam-4808	234	20	)	)	PUNCT
ejpam-4808	234	21	,	,	PUNCT
ejpam-4808	234	22	then	then	ADV
ejpam-4808	234	23	(	(	PUNCT
ejpam-4808	234	24	i	i	NOUN
ejpam-4808	234	25	,	,	PUNCT
ejpam-4808	234	26	j)−	j)−	PROPN
ejpam-4808	234	27	gφ−	gφ−	PROPN
ejpam-4808	234	28	cl(e	cl(e	NUM
ejpam-4808	234	29	)	)	PUNCT
ejpam-4808	234	30	∨	∨	NUM
ejpam-4808	234	31	(	(	PUNCT
ejpam-4808	234	32	i	i	PROPN
ejpam-4808	234	33	,	,	PUNCT
ejpam-4808	234	34	j)−	j)−	PROPN
ejpam-4808	234	35	gφ−	gφ−	PROPN
ejpam-4808	234	36	cl(t	cl(t	X
ejpam-4808	234	37	)	)	PUNCT
ejpam-4808	234	38	≤	≤	NOUN
ejpam-4808	234	39	(	(	PUNCT
ejpam-4808	234	40	i	i	NOUN
ejpam-4808	234	41	,	,	PUNCT
ejpam-4808	234	42	j)−	j)−	PROPN
ejpam-4808	234	43	gφ−	gφ−	PROPN
ejpam-4808	234	44	cl(e	cl(e	NOUN
ejpam-4808	234	45	∨	∨	NUM
ejpam-4808	234	46	t	t	PROPN
ejpam-4808	234	47	)	)	PUNCT
ejpam-4808	234	48	.	.	PUNCT
ejpam-4808	235	1	from	from	ADP
ejpam-4808	235	2	the	the	DET
ejpam-4808	235	3	relationship	relationship	NOUN
ejpam-4808	235	4	between	between	ADP
ejpam-4808	235	5	closure	closure	NOUN
ejpam-4808	235	6	,	,	PUNCT
ejpam-4808	235	7	interior	interior	NOUN
ejpam-4808	235	8	,	,	PUNCT
ejpam-4808	235	9	complement	complement	NOUN
ejpam-4808	235	10	,	,	PUNCT
ejpam-4808	235	11	and	and	CCONJ
ejpam-4808	235	12	theorem5	theorem5	NOUN
ejpam-4808	235	13	we	we	PRON
ejpam-4808	235	14	conclude	conclude	VERB
ejpam-4808	235	15	the	the	DET
ejpam-4808	235	16	following	following	NOUN
ejpam-4808	235	17	:	:	PUNCT
ejpam-4808	235	18	theorem	theorem	VERB
ejpam-4808	235	19	6	6	NUM
ejpam-4808	235	20	.	.	PUNCT
ejpam-4808	236	1	if	if	SCONJ
ejpam-4808	236	2	e	e	PROPN
ejpam-4808	236	3	and	and	CCONJ
ejpam-4808	236	4	t	t	PROPN
ejpam-4808	236	5	are	be	AUX
ejpam-4808	236	6	fuzzy	fuzzy	ADJ
ejpam-4808	236	7	subsets	subset	NOUN
ejpam-4808	236	8	of	of	ADP
ejpam-4808	236	9	fbts	fbt	NOUN
ejpam-4808	236	10	(	(	PUNCT
ejpam-4808	236	11	x	x	NOUN
ejpam-4808	236	12	,	,	PUNCT
ejpam-4808	236	13	δ1	δ1	NOUN
ejpam-4808	236	14	,	,	PUNCT
ejpam-4808	236	15	δ2	δ2	PROPN
ejpam-4808	236	16	)	)	PUNCT
ejpam-4808	236	17	,	,	PUNCT
ejpam-4808	236	18	then	then	ADV
ejpam-4808	236	19	the	the	DET
ejpam-4808	236	20	coming	coming	ADJ
ejpam-4808	236	21	statements	statement	NOUN
ejpam-4808	236	22	are	be	AUX
ejpam-4808	236	23	correct	correct	ADJ
ejpam-4808	236	24	:	:	PUNCT
ejpam-4808	236	25	(	(	PUNCT
ejpam-4808	236	26	1	1	NUM
ejpam-4808	236	27	)	)	PUNCT
ejpam-4808	236	28	0	0	NUM
ejpam-4808	236	29	,	,	PUNCT
ejpam-4808	236	30	and	and	CCONJ
ejpam-4808	236	31	1	1	NUM
ejpam-4808	236	32	are	be	AUX
ejpam-4808	236	33	fuzzy	fuzzy	ADJ
ejpam-4808	236	34	(	(	PUNCT
ejpam-4808	236	35	i	i	NOUN
ejpam-4808	236	36	,	,	PUNCT
ejpam-4808	236	37	j)−	j)−	PROPN
ejpam-4808	236	38	gφ−	gφ−	PROPN
ejpam-4808	236	39	open	open	ADJ
ejpam-4808	236	40	.	.	PUNCT
ejpam-4808	237	1	(	(	PUNCT
ejpam-4808	237	2	2	2	X
ejpam-4808	237	3	)	)	PUNCT
ejpam-4808	237	4	when	when	SCONJ
ejpam-4808	237	5	e	e	X
ejpam-4808	237	6	≤	≤	PROPN
ejpam-4808	237	7	t	t	NOUN
ejpam-4808	237	8	,	,	PUNCT
ejpam-4808	237	9	then	then	ADV
ejpam-4808	237	10	(	(	PUNCT
ejpam-4808	237	11	i	i	NOUN
ejpam-4808	237	12	,	,	PUNCT
ejpam-4808	237	13	j)−	j)−	PROPN
ejpam-4808	237	14	gφ−	gφ−	PROPN
ejpam-4808	237	15	int(e	int(e	PROPN
ejpam-4808	237	16	)	)	PUNCT
ejpam-4808	237	17	≤	≤	NOUN
ejpam-4808	237	18	(	(	PUNCT
ejpam-4808	237	19	i	i	NOUN
ejpam-4808	237	20	,	,	PUNCT
ejpam-4808	237	21	j)−	j)−	PROPN
ejpam-4808	237	22	gφ−	gφ−	PROPN
ejpam-4808	237	23	int(t	int(t	PROPN
ejpam-4808	237	24	)	)	PUNCT
ejpam-4808	237	25	.	.	PUNCT
ejpam-4808	238	1	(	(	PUNCT
ejpam-4808	238	2	3	3	X
ejpam-4808	238	3	)	)	PUNCT
ejpam-4808	238	4	(	(	PUNCT
ejpam-4808	238	5	i	i	NOUN
ejpam-4808	238	6	,	,	PUNCT
ejpam-4808	238	7	j)−	j)−	PROPN
ejpam-4808	238	8	gφ−	gφ−	PROPN
ejpam-4808	238	9	int(e	int(e	PROPN
ejpam-4808	238	10	)	)	PUNCT
ejpam-4808	238	11	≤	≤	NOUN
ejpam-4808	238	12	e	e	NOUN
ejpam-4808	238	13	,	,	PUNCT
ejpam-4808	238	14	∀	∀	X
ejpam-4808	238	15	fuzzy	fuzzy	ADJ
ejpam-4808	238	16	set	set	VERB
ejpam-4808	238	17	e	e	X
ejpam-4808	238	18	∈	∈	PROPN
ejpam-4808	238	19	ix	ix	X
ejpam-4808	238	20	.	.	PUNCT
ejpam-4808	239	1	(	(	PUNCT
ejpam-4808	239	2	4	4	X
ejpam-4808	239	3	)	)	PUNCT
ejpam-4808	239	4	when	when	SCONJ
ejpam-4808	239	5	e	e	NOUN
ejpam-4808	239	6	is	be	AUX
ejpam-4808	239	7	fuzzy	fuzzy	ADJ
ejpam-4808	239	8	(	(	PUNCT
ejpam-4808	239	9	i	i	PROPN
ejpam-4808	239	10	,	,	PUNCT
ejpam-4808	239	11	j	j	PROPN
ejpam-4808	239	12	)	)	PUNCT
ejpam-4808	239	13	−	−	PROPN
ejpam-4808	239	14	gφ	gφ	NOUN
ejpam-4808	239	15	−	−	PROPN
ejpam-4808	239	16	open	open	ADJ
ejpam-4808	239	17	,	,	PUNCT
ejpam-4808	239	18	then	then	ADV
ejpam-4808	239	19	(	(	PUNCT
ejpam-4808	239	20	i	i	PROPN
ejpam-4808	239	21	,	,	PUNCT
ejpam-4808	239	22	j	j	PROPN
ejpam-4808	239	23	)	)	PUNCT
ejpam-4808	240	1	−	−	PROPN
ejpam-4808	240	2	gφ	gφ	INTJ
ejpam-4808	240	3	−	−	PROPN
ejpam-4808	240	4	int(e	int(e	PROPN
ejpam-4808	240	5	)	)	PUNCT
ejpam-4808	241	1	=	=	VERB
ejpam-4808	241	2	e.	e.	PROPN
ejpam-4808	242	1	the	the	DET
ejpam-4808	242	2	converse	converse	NOUN
ejpam-4808	242	3	is	be	AUX
ejpam-4808	242	4	false	false	ADJ
ejpam-4808	242	5	,	,	PUNCT
ejpam-4808	242	6	as	as	SCONJ
ejpam-4808	242	7	the	the	DET
ejpam-4808	242	8	combination	combination	NOUN
ejpam-4808	242	9	of	of	ADP
ejpam-4808	242	10	fuzzy	fuzzy	ADJ
ejpam-4808	242	11	(	(	PUNCT
ejpam-4808	242	12	i	i	PROPN
ejpam-4808	242	13	,	,	PUNCT
ejpam-4808	242	14	j	j	PROPN
ejpam-4808	242	15	)	)	PUNCT
ejpam-4808	242	16	−	−	PROPN
ejpam-4808	242	17	gφ	gφ	NOUN
ejpam-4808	242	18	−	−	PROPN
ejpam-4808	242	19	open	open	ADJ
ejpam-4808	242	20	sets	set	NOUN
ejpam-4808	242	21	not	not	PART
ejpam-4808	242	22	necessary	necessary	ADJ
ejpam-4808	242	23	to	to	PART
ejpam-4808	242	24	be	be	AUX
ejpam-4808	242	25	fuzzy	fuzzy	ADJ
ejpam-4808	242	26	(	(	PUNCT
ejpam-4808	242	27	i	i	NOUN
ejpam-4808	242	28	,	,	PUNCT
ejpam-4808	242	29	j)−	j)−	PROPN
ejpam-4808	242	30	gφ−	gφ−	PROPN
ejpam-4808	242	31	open	open	ADJ
ejpam-4808	242	32	.	.	PUNCT
ejpam-4808	243	1	(	(	PUNCT
ejpam-4808	243	2	5	5	NUM
ejpam-4808	243	3	)	)	PUNCT
ejpam-4808	243	4	(	(	PUNCT
ejpam-4808	243	5	i	i	NOUN
ejpam-4808	243	6	,	,	PUNCT
ejpam-4808	243	7	j)−	j)−	PROPN
ejpam-4808	243	8	gφ−	gφ−	PROPN
ejpam-4808	243	9	int((i	int((i	PROPN
ejpam-4808	243	10	,	,	PUNCT
ejpam-4808	243	11	j)−	j)−	PROPN
ejpam-4808	243	12	gφ−	gφ−	PROPN
ejpam-4808	243	13	int(e	int(e	PROPN
ejpam-4808	243	14	)	)	PUNCT
ejpam-4808	243	15	)	)	PUNCT
ejpam-4808	244	1	=	=	PUNCT
ejpam-4808	244	2	(	(	PUNCT
ejpam-4808	244	3	i	i	PROPN
ejpam-4808	244	4	,	,	PUNCT
ejpam-4808	244	5	j)−	j)−	PROPN
ejpam-4808	244	6	gφ−	gφ−	PROPN
ejpam-4808	244	7	int(e	int(e	PROPN
ejpam-4808	244	8	)	)	PUNCT
ejpam-4808	244	9	.	.	PUNCT
ejpam-4808	245	1	(	(	PUNCT
ejpam-4808	245	2	6	6	NUM
ejpam-4808	245	3	)	)	PUNCT
ejpam-4808	245	4	when	when	SCONJ
ejpam-4808	245	5	v	v	NOUN
ejpam-4808	245	6	is	be	AUX
ejpam-4808	245	7	(	(	PUNCT
ejpam-4808	245	8	i	i	PROPN
ejpam-4808	245	9	,	,	PUNCT
ejpam-4808	245	10	j)−	j)−	PROPN
ejpam-4808	245	11	gφ−	gφ−	PROPN
ejpam-4808	245	12	closed	close	VERB
ejpam-4808	245	13	,	,	PUNCT
ejpam-4808	245	14	then	then	ADV
ejpam-4808	245	15	v	v	ADP
ejpam-4808	245	16	q	q	X
ejpam-4808	245	17	e	e	NOUN
ejpam-4808	245	18	⇐	⇐	ADJ
ejpam-4808	245	19	⇒	⇒	NOUN
ejpam-4808	245	20	v	v	X
ejpam-4808	245	21	q	q	X
ejpam-4808	245	22	(	(	PUNCT
ejpam-4808	245	23	i	i	PROPN
ejpam-4808	245	24	,	,	PUNCT
ejpam-4808	245	25	j)−	j)−	PROPN
ejpam-4808	245	26	gφ−	gφ−	PROPN
ejpam-4808	245	27	int(e	int(e	PROPN
ejpam-4808	245	28	)	)	PUNCT
ejpam-4808	245	29	.	.	PUNCT
ejpam-4808	246	1	(	(	PUNCT
ejpam-4808	246	2	7	7	X
ejpam-4808	246	3	)	)	PUNCT
ejpam-4808	246	4	(	(	PUNCT
ejpam-4808	246	5	i	i	NOUN
ejpam-4808	246	6	,	,	PUNCT
ejpam-4808	246	7	j)−	j)−	PROPN
ejpam-4808	246	8	gφ−	gφ−	PROPN
ejpam-4808	247	1	int(e	int(e	PROPN
ejpam-4808	247	2	∧	∧	PROPN
ejpam-4808	247	3	t	t	PROPN
ejpam-4808	247	4	)	)	PUNCT
ejpam-4808	247	5	≤	≤	NOUN
ejpam-4808	247	6	(	(	PUNCT
ejpam-4808	247	7	i	i	NOUN
ejpam-4808	247	8	,	,	PUNCT
ejpam-4808	247	9	j)−	j)−	PROPN
ejpam-4808	247	10	gφ−	gφ−	PROPN
ejpam-4808	247	11	int(e	int(e	PROPN
ejpam-4808	247	12	)	)	PUNCT
ejpam-4808	247	13	∧	∧	PROPN
ejpam-4808	247	14	(	(	PUNCT
ejpam-4808	247	15	i	i	PROPN
ejpam-4808	247	16	,	,	PUNCT
ejpam-4808	247	17	j)−	j)−	PROPN
ejpam-4808	247	18	gφ−	gφ−	PROPN
ejpam-4808	247	19	int(t	int(t	PROPN
ejpam-4808	247	20	)	)	PUNCT
ejpam-4808	247	21	.	.	PUNCT
ejpam-4808	248	1	theorem	theorem	VERB
ejpam-4808	248	2	7	7	NUM
ejpam-4808	248	3	.	.	PUNCT
ejpam-4808	249	1	if	if	SCONJ
ejpam-4808	249	2	xr	xr	PROPN
ejpam-4808	249	3	is	be	AUX
ejpam-4808	249	4	fuzzy	fuzzy	ADJ
ejpam-4808	249	5	point	point	NOUN
ejpam-4808	249	6	,	,	PUNCT
ejpam-4808	249	7	and	and	CCONJ
ejpam-4808	249	8	e	e	NOUN
ejpam-4808	249	9	is	be	AUX
ejpam-4808	249	10	fuzzy	fuzzy	ADJ
ejpam-4808	249	11	subset	subset	NOUN
ejpam-4808	249	12	of	of	ADP
ejpam-4808	249	13	fbts	fbt	NOUN
ejpam-4808	249	14	(	(	PUNCT
ejpam-4808	249	15	x	x	NOUN
ejpam-4808	249	16	,	,	PUNCT
ejpam-4808	249	17	δ1	δ1	NOUN
ejpam-4808	249	18	,	,	PUNCT
ejpam-4808	249	19	δ2	δ2	PROPN
ejpam-4808	249	20	)	)	PUNCT
ejpam-4808	249	21	,	,	PUNCT
ejpam-4808	249	22	then	then	ADV
ejpam-4808	249	23	xr	xr	PROPN
ejpam-4808	249	24	∈	∈	PROPN
ejpam-4808	249	25	(	(	PUNCT
ejpam-4808	249	26	i	i	PROPN
ejpam-4808	249	27	,	,	PUNCT
ejpam-4808	249	28	j)−	j)−	PROPN
ejpam-4808	249	29	gφ−	gφ−	PROPN
ejpam-4808	249	30	int(e	int(e	PROPN
ejpam-4808	249	31	)	)	PUNCT
ejpam-4808	249	32	⇐	⇐	ADJ
ejpam-4808	249	33	⇒	⇒	PROPN
ejpam-4808	249	34	∃	∃	PROPN
ejpam-4808	249	35	fuzzy	fuzzy	ADJ
ejpam-4808	249	36	(	(	PUNCT
ejpam-4808	249	37	i	i	PROPN
ejpam-4808	249	38	,	,	PUNCT
ejpam-4808	249	39	j)−	j)−	PROPN
ejpam-4808	249	40	gφ−	gφ−	PROPN
ejpam-4808	249	41	open	open	ADJ
ejpam-4808	249	42	set	set	VERB
ejpam-4808	249	43	g	g	NOUN
ejpam-4808	249	44	,	,	PUNCT
ejpam-4808	249	45	so	so	ADV
ejpam-4808	249	46	xr	xr	PROPN
ejpam-4808	249	47	∈	∈	PROPN
ejpam-4808	249	48	g	g	PROPN
ejpam-4808	249	49	≤	≤	PROPN
ejpam-4808	249	50	e.	e.	PROPN
ejpam-4808	249	51	theorem	theorem	PROPN
ejpam-4808	249	52	8	8	PROPN
ejpam-4808	249	53	.	.	PUNCT
ejpam-4808	249	54	suppose	suppose	VERB
ejpam-4808	249	55	e	e	NOUN
ejpam-4808	249	56	is	be	AUX
ejpam-4808	249	57	fuzzy	fuzzy	ADJ
ejpam-4808	249	58	set	set	VERB
ejpam-4808	249	59	in	in	ADP
ejpam-4808	249	60	fbts	fbt	NOUN
ejpam-4808	249	61	(	(	PUNCT
ejpam-4808	249	62	x	x	NOUN
ejpam-4808	249	63	,	,	PUNCT
ejpam-4808	249	64	δ1	δ1	NOUN
ejpam-4808	249	65	,	,	PUNCT
ejpam-4808	249	66	δ2	δ2	PROPN
ejpam-4808	249	67	)	)	PUNCT
ejpam-4808	249	68	.	.	PUNCT
ejpam-4808	250	1	if	if	SCONJ
ejpam-4808	250	2	e	e	NOUN
ejpam-4808	250	3	is	be	AUX
ejpam-4808	250	4	fuzzy	fuzzy	ADJ
ejpam-4808	250	5	(	(	PUNCT
ejpam-4808	250	6	i	i	PROPN
ejpam-4808	250	7	,	,	PUNCT
ejpam-4808	250	8	j	j	PROPN
ejpam-4808	250	9	)	)	PUNCT
ejpam-4808	250	10	−	−	PROPN
ejpam-4808	250	11	gφ	gφ	NOUN
ejpam-4808	250	12	−	−	PROPN
ejpam-4808	250	13	open	open	ADJ
ejpam-4808	250	14	,	,	PUNCT
ejpam-4808	250	15	then	then	ADV
ejpam-4808	250	16	e	e	PROPN
ejpam-4808	250	17	∈	∈	PROPN
ejpam-4808	250	18	ngφ	ngφ	ADJ
ejpam-4808	250	19	(	(	PUNCT
ejpam-4808	250	20	i	i	NOUN
ejpam-4808	250	21	,	,	PUNCT
ejpam-4808	250	22	j)(xr	j)(xr	PROPN
ejpam-4808	250	23	)	)	PUNCT
ejpam-4808	250	24	for	for	ADP
ejpam-4808	250	25	each	each	DET
ejpam-4808	250	26	xr	xr	PROPN
ejpam-4808	250	27	∈	∈	PROPN
ejpam-4808	250	28	e.	e.	PROPN
ejpam-4808	250	29	theorem	theorem	VERB
ejpam-4808	250	30	9	9	NUM
ejpam-4808	250	31	.	.	PUNCT
ejpam-4808	251	1	if	if	SCONJ
ejpam-4808	251	2	(	(	PUNCT
ejpam-4808	251	3	x	x	NOUN
ejpam-4808	251	4	,	,	PUNCT
ejpam-4808	251	5	δ1	δ1	NOUN
ejpam-4808	251	6	,	,	PUNCT
ejpam-4808	251	7	δ2	δ2	PROPN
ejpam-4808	251	8	)	)	PUNCT
ejpam-4808	251	9	is	be	AUX
ejpam-4808	251	10	fbts	fbt	NOUN
ejpam-4808	251	11	,	,	PUNCT
ejpam-4808	251	12	e	e	NOUN
ejpam-4808	251	13	is	be	AUX
ejpam-4808	251	14	fuzzy	fuzzy	ADJ
ejpam-4808	251	15	(	(	PUNCT
ejpam-4808	251	16	i	i	NOUN
ejpam-4808	251	17	,	,	PUNCT
ejpam-4808	251	18	j)−gφ−closed	j)−gφ−close	VERB
ejpam-4808	251	19	,	,	PUNCT
ejpam-4808	251	20	and	and	CCONJ
ejpam-4808	251	21	e	e	X
ejpam-4808	251	22	≤	≤	PROPN
ejpam-4808	251	23	t	t	X
ejpam-4808	251	24	≤	≤	NUM
ejpam-4808	251	25	δj−φ−cl(e	δj−φ−cl(e	NOUN
ejpam-4808	251	26	)	)	PUNCT
ejpam-4808	251	27	,	,	PUNCT
ejpam-4808	251	28	then	then	ADV
ejpam-4808	251	29	t	t	PROPN
ejpam-4808	251	30	is	be	AUX
ejpam-4808	251	31	fuzzy	fuzzy	ADJ
ejpam-4808	251	32	(	(	PUNCT
ejpam-4808	251	33	i	i	NOUN
ejpam-4808	251	34	,	,	PUNCT
ejpam-4808	251	35	j)−	j)−	PROPN
ejpam-4808	251	36	gφ−	gφ−	PROPN
ejpam-4808	251	37	closed	close	VERB
ejpam-4808	251	38	.	.	PUNCT
ejpam-4808	252	1	proof	proof	NOUN
ejpam-4808	252	2	.	.	PUNCT
ejpam-4808	253	1	assume	assume	VERB
ejpam-4808	253	2	t	t	PROPN
ejpam-4808	253	3	≤	≤	NUM
ejpam-4808	253	4	u	u	PROPN
ejpam-4808	253	5	,	,	PUNCT
ejpam-4808	253	6	and	and	CCONJ
ejpam-4808	253	7	u	u	NOUN
ejpam-4808	253	8	is	be	AUX
ejpam-4808	253	9	fuzzy	fuzzy	ADJ
ejpam-4808	253	10	open	open	ADJ
ejpam-4808	253	11	of	of	ADP
ejpam-4808	253	12	δi	δi	NOUN
ejpam-4808	253	13	.	.	PUNCT
ejpam-4808	254	1	as	as	ADP
ejpam-4808	254	2	e	e	PROPN
ejpam-4808	254	3	≤	≤	NOUN
ejpam-4808	254	4	t	t	NOUN
ejpam-4808	254	5	,	,	PUNCT
ejpam-4808	254	6	thus	thus	ADV
ejpam-4808	254	7	e	e	X
ejpam-4808	254	8	≤	≤	NOUN
ejpam-4808	254	9	u	u	NOUN
ejpam-4808	254	10	,	,	PUNCT
ejpam-4808	254	11	after	after	ADP
ejpam-4808	254	12	that	that	PRON
ejpam-4808	254	13	δj	δj	ADP
ejpam-4808	254	14	−	−	PROPN
ejpam-4808	254	15	φ−	φ−	PROPN
ejpam-4808	254	16	cl(e	cl(e	NOUN
ejpam-4808	254	17	)	)	PUNCT
ejpam-4808	254	18	=	=	NOUN
ejpam-4808	254	19	δj	δj	ADP
ejpam-4808	254	20	−	−	PROPN
ejpam-4808	254	21	φ−	φ−	PROPN
ejpam-4808	254	22	cl(t	cl(t	X
ejpam-4808	254	23	)	)	PUNCT
ejpam-4808	254	24	,	,	PUNCT
ejpam-4808	254	25	which	which	PRON
ejpam-4808	254	26	implies	imply	VERB
ejpam-4808	254	27	δj	δj	ADP
ejpam-4808	254	28	−	−	PROPN
ejpam-4808	254	29	φ−	φ−	PROPN
ejpam-4808	254	30	cl(t	cl(t	X
ejpam-4808	254	31	)	)	PUNCT
ejpam-4808	254	32	≤	≤	NUM
ejpam-4808	254	33	u	u	NOUN
ejpam-4808	254	34	.	.	PUNCT
ejpam-4808	255	1	as	as	ADP
ejpam-4808	255	2	a	a	DET
ejpam-4808	255	3	result	result	NOUN
ejpam-4808	255	4	of	of	ADP
ejpam-4808	255	5	that	that	PRON
ejpam-4808	255	6	,	,	PUNCT
ejpam-4808	255	7	t	t	PROPN
ejpam-4808	255	8	is	be	AUX
ejpam-4808	255	9	fuzzy	fuzzy	ADJ
ejpam-4808	255	10	(	(	PUNCT
ejpam-4808	255	11	i	i	NOUN
ejpam-4808	255	12	,	,	PUNCT
ejpam-4808	255	13	j)−	j)−	PROPN
ejpam-4808	255	14	gφ−	gφ−	PROPN
ejpam-4808	255	15	closed	close	VERB
ejpam-4808	255	16	.	.	PUNCT
ejpam-4808	256	1	from	from	ADP
ejpam-4808	256	2	the	the	DET
ejpam-4808	256	3	above	above	ADV
ejpam-4808	256	4	we	we	PRON
ejpam-4808	256	5	conclude	conclude	VERB
ejpam-4808	256	6	the	the	DET
ejpam-4808	256	7	following	follow	VERB
ejpam-4808	256	8	:	:	PUNCT
ejpam-4808	256	9	corollary	corollary	ADJ
ejpam-4808	256	10	3	3	X
ejpam-4808	256	11	.	.	PUNCT
ejpam-4808	257	1	assume	assume	VERB
ejpam-4808	257	2	(	(	PUNCT
ejpam-4808	257	3	x	x	NOUN
ejpam-4808	257	4	,	,	PUNCT
ejpam-4808	257	5	δ1	δ1	NOUN
ejpam-4808	257	6	,	,	PUNCT
ejpam-4808	257	7	δ2	δ2	PROPN
ejpam-4808	257	8	)	)	PUNCT
ejpam-4808	257	9	is	be	AUX
ejpam-4808	257	10	fbts	fbt	NOUN
ejpam-4808	257	11	,	,	PUNCT
ejpam-4808	257	12	e	e	NOUN
ejpam-4808	257	13	is	be	AUX
ejpam-4808	257	14	fuzzy	fuzzy	ADJ
ejpam-4808	257	15	(	(	PUNCT
ejpam-4808	257	16	i	i	NOUN
ejpam-4808	257	17	,	,	PUNCT
ejpam-4808	257	18	j)−	j)−	PROPN
ejpam-4808	257	19	gφ−	gφ−	PROPN
ejpam-4808	257	20	closed	close	VERB
ejpam-4808	257	21	,	,	PUNCT
ejpam-4808	257	22	and	and	CCONJ
ejpam-4808	257	23	e	e	X
ejpam-4808	257	24	≤	≤	PROPN
ejpam-4808	257	25	t	t	X
ejpam-4808	257	26	≤	≤	NOUN
ejpam-4808	257	27	δj	δj	ADP
ejpam-4808	257	28	−	−	PROPN
ejpam-4808	257	29	β	β	NOUN
ejpam-4808	257	30	−	−	NOUN
ejpam-4808	257	31	cl(e	cl(e	NUM
ejpam-4808	257	32	)	)	PUNCT
ejpam-4808	257	33	.	.	PUNCT
ejpam-4808	258	1	then	then	ADV
ejpam-4808	258	2	t	t	PROPN
ejpam-4808	258	3	is	be	AUX
ejpam-4808	258	4	fuzzy	fuzzy	ADJ
ejpam-4808	258	5	(	(	PUNCT
ejpam-4808	258	6	i	i	NOUN
ejpam-4808	258	7	,	,	PUNCT
ejpam-4808	258	8	j)−	j)−	PROPN
ejpam-4808	258	9	gφ−	gφ−	PROPN
ejpam-4808	258	10	closed	close	VERB
ejpam-4808	258	11	.	.	PUNCT
ejpam-4808	259	1	corollary	corollary	ADJ
ejpam-4808	259	2	4	4	NUM
ejpam-4808	259	3	.	.	PUNCT
ejpam-4808	260	1	assume	assume	VERB
ejpam-4808	260	2	(	(	PUNCT
ejpam-4808	260	3	x	x	NOUN
ejpam-4808	260	4	,	,	PUNCT
ejpam-4808	260	5	δ1	δ1	NOUN
ejpam-4808	260	6	,	,	PUNCT
ejpam-4808	260	7	δ2	δ2	PROPN
ejpam-4808	260	8	)	)	PUNCT
ejpam-4808	260	9	is	be	AUX
ejpam-4808	260	10	fbts	fbt	NOUN
ejpam-4808	260	11	,	,	PUNCT
ejpam-4808	260	12	e	e	NOUN
ejpam-4808	260	13	is	be	AUX
ejpam-4808	260	14	fuzzy	fuzzy	ADJ
ejpam-4808	260	15	(	(	PUNCT
ejpam-4808	260	16	i	i	NOUN
ejpam-4808	260	17	,	,	PUNCT
ejpam-4808	260	18	j)−	j)−	PROPN
ejpam-4808	260	19	gφ−	gφ−	PROPN
ejpam-4808	260	20	open	open	ADJ
ejpam-4808	260	21	,	,	PUNCT
ejpam-4808	260	22	and	and	CCONJ
ejpam-4808	260	23	δj	δj	ADP
ejpam-4808	260	24	−	−	PROPN
ejpam-4808	260	25	φ−	φ−	PROPN
ejpam-4808	260	26	int(e	int(e	PROPN
ejpam-4808	260	27	)	)	PUNCT
ejpam-4808	260	28	≤	≤	NUM
ejpam-4808	260	29	t	t	PROPN
ejpam-4808	260	30	≤	≤	PROPN
ejpam-4808	261	1	e.	e.	PROPN
ejpam-4808	262	1	then	then	ADV
ejpam-4808	262	2	t	t	PROPN
ejpam-4808	262	3	is	be	AUX
ejpam-4808	262	4	fuzzy	fuzzy	ADJ
ejpam-4808	262	5	(	(	PUNCT
ejpam-4808	262	6	i	i	NOUN
ejpam-4808	262	7	,	,	PUNCT
ejpam-4808	262	8	j)−	j)−	PROPN
ejpam-4808	262	9	gφ−	gφ−	PUNCT
ejpam-4808	262	10	open	open	ADJ
ejpam-4808	262	11	.	.	PUNCT
ejpam-4808	263	1	a.	a.	NOUN
ejpam-4808	263	2	a.	a.	PROPN
ejpam-4808	263	3	alharbi	alharbi	PROPN
ejpam-4808	263	4	,	,	PUNCT
ejpam-4808	263	5	a.	a.	NOUN
ejpam-4808	263	6	kilicman	kilicman	PROPN
ejpam-4808	263	7	/	/	SYM
ejpam-4808	263	8	eur	eur	PROPN
ejpam-4808	263	9	.	.	PUNCT
ejpam-4808	264	1	j.	j.	PROPN
ejpam-4808	264	2	pure	pure	PROPN
ejpam-4808	264	3	appl	appl	PROPN
ejpam-4808	264	4	.	.	PROPN
ejpam-4808	264	5	math	math	PROPN
ejpam-4808	264	6	,	,	PUNCT
ejpam-4808	264	7	16	16	NUM
ejpam-4808	264	8	(	(	PUNCT
ejpam-4808	264	9	3	3	NUM
ejpam-4808	264	10	)	)	PUNCT
ejpam-4808	264	11	(	(	PUNCT
ejpam-4808	264	12	2023	2023	NUM
ejpam-4808	264	13	)	)	PUNCT
ejpam-4808	264	14	,	,	PUNCT
ejpam-4808	264	15	1980	1980	NUM
ejpam-4808	264	16	-	-	SYM
ejpam-4808	264	17	1990	1990	NUM
ejpam-4808	264	18	1989	1989	NUM
ejpam-4808	264	19	corollary	corollary	NOUN
ejpam-4808	264	20	5	5	NUM
ejpam-4808	264	21	.	.	PUNCT
ejpam-4808	265	1	assume	assume	VERB
ejpam-4808	265	2	(	(	PUNCT
ejpam-4808	265	3	x	x	NOUN
ejpam-4808	265	4	,	,	PUNCT
ejpam-4808	265	5	δ1	δ1	NOUN
ejpam-4808	265	6	,	,	PUNCT
ejpam-4808	265	7	δ2	δ2	PROPN
ejpam-4808	265	8	)	)	PUNCT
ejpam-4808	265	9	is	be	AUX
ejpam-4808	265	10	fbts	fbt	NOUN
ejpam-4808	265	11	,	,	PUNCT
ejpam-4808	265	12	e	e	NOUN
ejpam-4808	265	13	is	be	AUX
ejpam-4808	265	14	fuzzy	fuzzy	ADJ
ejpam-4808	265	15	(	(	PUNCT
ejpam-4808	265	16	i	i	NOUN
ejpam-4808	265	17	,	,	PUNCT
ejpam-4808	265	18	j)−	j)−	PROPN
ejpam-4808	265	19	gφ−	gφ−	PROPN
ejpam-4808	265	20	open	open	ADJ
ejpam-4808	265	21	,	,	PUNCT
ejpam-4808	265	22	and	and	CCONJ
ejpam-4808	265	23	δj	δj	ADP
ejpam-4808	265	24	−	−	PROPN
ejpam-4808	265	25	β	β	NOUN
ejpam-4808	265	26	−	−	PROPN
ejpam-4808	265	27	int(e	int(e	PROPN
ejpam-4808	265	28	)	)	PUNCT
ejpam-4808	265	29	≤	≤	NUM
ejpam-4808	265	30	t	t	PROPN
ejpam-4808	265	31	≤	≤	PROPN
ejpam-4808	265	32	e.	e.	PROPN
ejpam-4808	266	1	then	then	ADV
ejpam-4808	266	2	t	t	PROPN
ejpam-4808	266	3	is	be	AUX
ejpam-4808	266	4	fuzzy	fuzzy	ADJ
ejpam-4808	266	5	(	(	PUNCT
ejpam-4808	266	6	i	i	NOUN
ejpam-4808	266	7	,	,	PUNCT
ejpam-4808	266	8	j)−	j)−	PROPN
ejpam-4808	266	9	gφ−	gφ−	PUNCT
ejpam-4808	266	10	open	open	ADJ
ejpam-4808	266	11	.	.	PUNCT
ejpam-4808	267	1	the	the	DET
ejpam-4808	267	2	following	follow	VERB
ejpam-4808	267	3	important	important	ADJ
ejpam-4808	267	4	study	study	NOUN
ejpam-4808	267	5	demonstrates	demonstrate	VERB
ejpam-4808	267	6	when	when	SCONJ
ejpam-4808	267	7	equivalence	equivalence	NOUN
ejpam-4808	267	8	between	between	ADP
ejpam-4808	267	9	the	the	DET
ejpam-4808	267	10	types	type	NOUN
ejpam-4808	267	11	of	of	ADP
ejpam-4808	267	12	generalized	generalized	ADJ
ejpam-4808	267	13	closed	closed	ADJ
ejpam-4808	267	14	sets	set	NOUN
ejpam-4808	267	15	in	in	ADP
ejpam-4808	267	16	fuzzy	fuzzy	ADJ
ejpam-4808	267	17	bitopology	bitopology	NOUN
ejpam-4808	267	18	and	and	CCONJ
ejpam-4808	267	19	types	type	NOUN
ejpam-4808	267	20	of	of	ADP
ejpam-4808	267	21	fuzzy	fuzzy	ADJ
ejpam-4808	267	22	sets	set	NOUN
ejpam-4808	267	23	from	from	ADP
ejpam-4808	267	24	one	one	NUM
ejpam-4808	267	25	topology	topology	NOUN
ejpam-4808	267	26	is	be	AUX
ejpam-4808	267	27	attained	attain	VERB
ejpam-4808	267	28	.	.	PUNCT
ejpam-4808	268	1	theorem	theorem	ADJ
ejpam-4808	268	2	10	10	NUM
ejpam-4808	268	3	.	.	PUNCT
ejpam-4808	269	1	in	in	ADP
ejpam-4808	269	2	fbts	fbt	NOUN
ejpam-4808	269	3	(	(	PUNCT
ejpam-4808	269	4	x	x	NOUN
ejpam-4808	269	5	,	,	PUNCT
ejpam-4808	269	6	δ1	δ1	NOUN
ejpam-4808	269	7	,	,	PUNCT
ejpam-4808	269	8	δ2	δ2	PROPN
ejpam-4808	269	9	)	)	PUNCT
ejpam-4808	269	10	the	the	DET
ejpam-4808	269	11	following	follow	VERB
ejpam-4808	269	12	statements	statement	NOUN
ejpam-4808	269	13	are	be	AUX
ejpam-4808	269	14	equivalents	equivalent	NOUN
ejpam-4808	269	15	:	:	PUNCT
ejpam-4808	269	16	(	(	PUNCT
ejpam-4808	269	17	i	i	NOUN
ejpam-4808	269	18	)	)	PUNCT
ejpam-4808	269	19	δi	δi	ADP
ejpam-4808	269	20	⊆	⊆	NUM
ejpam-4808	269	21	ffφ	ffφ	NOUN
ejpam-4808	269	22	(	(	PUNCT
ejpam-4808	269	23	x	x	NOUN
ejpam-4808	269	24	,	,	PUNCT
ejpam-4808	269	25	δj	δj	NOUN
ejpam-4808	269	26	)	)	PUNCT
ejpam-4808	269	27	(	(	PUNCT
ejpam-4808	269	28	ii	ii	NOUN
ejpam-4808	269	29	)	)	PUNCT
ejpam-4808	269	30	all	all	DET
ejpam-4808	269	31	fuzzy	fuzzy	ADJ
ejpam-4808	269	32	groups	group	NOUN
ejpam-4808	269	33	of	of	ADP
ejpam-4808	269	34	x	x	SYM
ejpam-4808	269	35	are	be	AUX
ejpam-4808	269	36	fuzzy	fuzzy	ADJ
ejpam-4808	269	37	(	(	PUNCT
ejpam-4808	269	38	i	i	NOUN
ejpam-4808	269	39	,	,	PUNCT
ejpam-4808	269	40	j)−	j)−	PROPN
ejpam-4808	269	41	gφ−	gφ−	PROPN
ejpam-4808	269	42	closed	close	VERB
ejpam-4808	269	43	.	.	PUNCT
ejpam-4808	270	1	proof	proof	NOUN
ejpam-4808	270	2	.	.	PUNCT
ejpam-4808	271	1	(	(	PUNCT
ejpam-4808	271	2	i	i	NOUN
ejpam-4808	271	3	)	)	PUNCT
ejpam-4808	271	4	→	→	SYM
ejpam-4808	271	5	(	(	PUNCT
ejpam-4808	271	6	ii	ii	NOUN
ejpam-4808	271	7	)	)	PUNCT
ejpam-4808	271	8	assume	assume	VERB
ejpam-4808	271	9	e	e	NOUN
ejpam-4808	271	10	is	be	AUX
ejpam-4808	271	11	fuzzy	fuzzy	ADJ
ejpam-4808	271	12	subset	subset	NOUN
ejpam-4808	271	13	of	of	ADP
ejpam-4808	271	14	x	x	PRON
ejpam-4808	271	15	,	,	PUNCT
ejpam-4808	271	16	so	so	SCONJ
ejpam-4808	271	17	e	e	NOUN
ejpam-4808	271	18	≤	≤	NUM
ejpam-4808	271	19	u	u	NOUN
ejpam-4808	271	20	∈	∈	PROPN
ejpam-4808	271	21	δi	δi	NOUN
ejpam-4808	271	22	.	.	PUNCT
ejpam-4808	272	1	then	then	ADV
ejpam-4808	272	2	from	from	ADP
ejpam-4808	272	3	(	(	PUNCT
ejpam-4808	272	4	i	i	NOUN
ejpam-4808	272	5	)	)	PUNCT
ejpam-4808	272	6	we	we	PRON
ejpam-4808	272	7	find	find	VERB
ejpam-4808	272	8	u	u	PRON
ejpam-4808	272	9	∈	∈	PROPN
ejpam-4808	272	10	ffφ	ffφ	NOUN
ejpam-4808	272	11	(	(	PUNCT
ejpam-4808	272	12	x	x	NOUN
ejpam-4808	272	13	,	,	PUNCT
ejpam-4808	272	14	δj	δj	NOUN
ejpam-4808	272	15	)	)	PUNCT
ejpam-4808	272	16	,	,	PUNCT
ejpam-4808	272	17	after	after	ADP
ejpam-4808	272	18	that	that	PRON
ejpam-4808	272	19	δj	δj	ADP
ejpam-4808	272	20	−	−	PROPN
ejpam-4808	272	21	φ−	φ−	PROPN
ejpam-4808	272	22	cl(e	cl(e	NOUN
ejpam-4808	272	23	)	)	PUNCT
ejpam-4808	272	24	≤	≤	NUM
ejpam-4808	272	25	u	u	NOUN
ejpam-4808	272	26	.	.	PUNCT
ejpam-4808	273	1	as	as	ADP
ejpam-4808	273	2	a	a	DET
ejpam-4808	273	3	result	result	NOUN
ejpam-4808	273	4	of	of	ADP
ejpam-4808	273	5	that	that	PRON
ejpam-4808	273	6	,	,	PUNCT
ejpam-4808	273	7	e	e	NOUN
ejpam-4808	273	8	is	be	AUX
ejpam-4808	273	9	fuzzy	fuzzy	ADJ
ejpam-4808	273	10	(	(	PUNCT
ejpam-4808	273	11	i	i	NOUN
ejpam-4808	273	12	,	,	PUNCT
ejpam-4808	273	13	j)−	j)−	PROPN
ejpam-4808	273	14	gφ−	gφ−	PROPN
ejpam-4808	273	15	closed	close	VERB
ejpam-4808	273	16	.	.	PUNCT
ejpam-4808	274	1	(	(	PUNCT
ejpam-4808	274	2	ii	ii	NOUN
ejpam-4808	274	3	)	)	PUNCT
ejpam-4808	274	4	→	→	SYM
ejpam-4808	274	5	(	(	PUNCT
ejpam-4808	274	6	i	i	NOUN
ejpam-4808	274	7	)	)	PUNCT
ejpam-4808	274	8	let	let	VERB
ejpam-4808	274	9	e	e	PRON
ejpam-4808	274	10	be	be	AUX
ejpam-4808	274	11	fuzzy	fuzzy	ADJ
ejpam-4808	274	12	(	(	PUNCT
ejpam-4808	274	13	i	i	NOUN
ejpam-4808	274	14	,	,	PUNCT
ejpam-4808	274	15	j)−gφ−closed	j)−gφ−close	VERB
ejpam-4808	274	16	,	,	PUNCT
ejpam-4808	274	17	e	e	PROPN
ejpam-4808	274	18	∈	∈	PROPN
ejpam-4808	274	19	δi	δi	ADV
ejpam-4808	274	20	.	.	PUNCT
ejpam-4808	275	1	since	since	SCONJ
ejpam-4808	275	2	e	e	NOUN
ejpam-4808	275	3	≤	≤	X
ejpam-4808	275	4	e	e	NOUN
ejpam-4808	275	5	,	,	PUNCT
ejpam-4808	275	6	then	then	ADV
ejpam-4808	275	7	δj−φ−cl(e	δj−φ−cl(e	NOUN
ejpam-4808	275	8	)	)	PUNCT
ejpam-4808	275	9	≤	≤	NOUN
ejpam-4808	275	10	e	e	NOUN
ejpam-4808	275	11	,	,	PUNCT
ejpam-4808	275	12	thus	thus	ADV
ejpam-4808	275	13	e	e	NOUN
ejpam-4808	275	14	is	be	AUX
ejpam-4808	275	15	fuzzy	fuzzy	ADJ
ejpam-4808	275	16	δj	δj	ADP
ejpam-4808	275	17	−	−	PROPN
ejpam-4808	275	18	φ−	φ−	PROPN
ejpam-4808	275	19	closed	close	VERB
ejpam-4808	275	20	.	.	PUNCT
ejpam-4808	276	1	therefore	therefore	ADV
ejpam-4808	276	2	δi	δi	VERB
ejpam-4808	276	3	⊆	⊆	NUM
ejpam-4808	276	4	ffφ	ffφ	NOUN
ejpam-4808	276	5	(	(	PUNCT
ejpam-4808	276	6	x	x	NOUN
ejpam-4808	276	7	,	,	PUNCT
ejpam-4808	276	8	δj	δj	NOUN
ejpam-4808	276	9	)	)	PUNCT
ejpam-4808	276	10	.	.	PUNCT
ejpam-4808	277	1	from	from	ADP
ejpam-4808	277	2	the	the	DET
ejpam-4808	277	3	above	above	NOUN
ejpam-4808	277	4	and	and	CCONJ
ejpam-4808	277	5	the	the	DET
ejpam-4808	277	6	complenent	complenent	NOUN
ejpam-4808	277	7	relation	relation	NOUN
ejpam-4808	277	8	we	we	PRON
ejpam-4808	277	9	conclude	conclude	VERB
ejpam-4808	277	10	the	the	DET
ejpam-4808	277	11	following	follow	VERB
ejpam-4808	277	12	:	:	PUNCT
ejpam-4808	277	13	corollary	corollary	ADJ
ejpam-4808	277	14	6	6	NUM
ejpam-4808	277	15	.	.	PUNCT
ejpam-4808	278	1	in	in	ADP
ejpam-4808	278	2	fbts	fbt	NOUN
ejpam-4808	278	3	(	(	PUNCT
ejpam-4808	278	4	x	x	NOUN
ejpam-4808	278	5	,	,	PUNCT
ejpam-4808	278	6	δ1	δ1	NOUN
ejpam-4808	278	7	,	,	PUNCT
ejpam-4808	278	8	δ2	δ2	PROPN
ejpam-4808	278	9	)	)	PUNCT
ejpam-4808	278	10	the	the	DET
ejpam-4808	278	11	following	follow	VERB
ejpam-4808	278	12	statements	statement	NOUN
ejpam-4808	278	13	are	be	AUX
ejpam-4808	278	14	equivalents	equivalent	NOUN
ejpam-4808	278	15	:	:	PUNCT
ejpam-4808	278	16	(	(	PUNCT
ejpam-4808	278	17	1	1	X
ejpam-4808	278	18	)	)	PUNCT
ejpam-4808	278	19	fδi	fδi	NOUN
ejpam-4808	278	20	⊆	⊆	NUM
ejpam-4808	278	21	ofφ	ofφ	NOUN
ejpam-4808	278	22	(	(	PUNCT
ejpam-4808	278	23	x	x	NOUN
ejpam-4808	278	24	,	,	PUNCT
ejpam-4808	278	25	δj	δj	NOUN
ejpam-4808	278	26	)	)	PUNCT
ejpam-4808	278	27	(	(	PUNCT
ejpam-4808	278	28	2	2	X
ejpam-4808	278	29	)	)	PUNCT
ejpam-4808	278	30	all	all	DET
ejpam-4808	278	31	fuzzy	fuzzy	ADJ
ejpam-4808	278	32	subset	subset	NOUN
ejpam-4808	278	33	of	of	ADP
ejpam-4808	278	34	x	x	PUNCT
ejpam-4808	278	35	is	be	AUX
ejpam-4808	278	36	fuzzy	fuzzy	ADJ
ejpam-4808	278	37	(	(	PUNCT
ejpam-4808	278	38	i	i	NOUN
ejpam-4808	278	39	,	,	PUNCT
ejpam-4808	278	40	j)−	j)−	PROPN
ejpam-4808	278	41	gφ−	gφ−	PUNCT
ejpam-4808	278	42	open	open	ADJ
ejpam-4808	278	43	.	.	PUNCT
ejpam-4808	279	1	corollary	corollary	ADJ
ejpam-4808	279	2	7	7	PROPN
ejpam-4808	279	3	.	.	PUNCT
ejpam-4808	279	4	assume	assume	VERB
ejpam-4808	279	5	e	e	NOUN
ejpam-4808	279	6	,	,	PUNCT
ejpam-4808	279	7	and	and	CCONJ
ejpam-4808	279	8	t	t	PROPN
ejpam-4808	279	9	are	be	AUX
ejpam-4808	279	10	fuzzy	fuzzy	ADJ
ejpam-4808	279	11	(	(	PUNCT
ejpam-4808	279	12	i	i	NOUN
ejpam-4808	279	13	,	,	PUNCT
ejpam-4808	279	14	j)−	j)−	PROPN
ejpam-4808	279	15	gφ−	gφ−	NUM
ejpam-4808	279	16	closed	close	VERB
ejpam-4808	279	17	sets	set	NOUN
ejpam-4808	279	18	in	in	ADP
ejpam-4808	279	19	fbts	fbt	NOUN
ejpam-4808	279	20	(	(	PUNCT
ejpam-4808	279	21	x	x	NOUN
ejpam-4808	279	22	,	,	PUNCT
ejpam-4808	279	23	δ1	δ1	NOUN
ejpam-4808	279	24	,	,	PUNCT
ejpam-4808	279	25	δ2	δ2	PROPN
ejpam-4808	279	26	)	)	PUNCT
ejpam-4808	279	27	with	with	ADP
ejpam-4808	279	28	e	e	NOUN
ejpam-4808	279	29	∨	∨	NUM
ejpam-4808	279	30	δi	δi	ADP
ejpam-4808	279	31	−	−	PROPN
ejpam-4808	279	32	int(t	int(t	PROPN
ejpam-4808	279	33	)	)	PUNCT
ejpam-4808	280	1	=	=	SYM
ejpam-4808	280	2	t	t	PROPN
ejpam-4808	280	3	∨	∨	NUM
ejpam-4808	280	4	δi	δi	ADP
ejpam-4808	280	5	−	−	PROPN
ejpam-4808	280	6	int(e	int(e	PROPN
ejpam-4808	280	7	)	)	PUNCT
ejpam-4808	280	8	=	=	SYM
ejpam-4808	280	9	1	1	NUM
ejpam-4808	280	10	,	,	PUNCT
ejpam-4808	280	11	then	then	ADV
ejpam-4808	280	12	e	e	PROPN
ejpam-4808	280	13	∧	∧	PROPN
ejpam-4808	280	14	t	t	PROPN
ejpam-4808	280	15	is	be	AUX
ejpam-4808	280	16	fuzzy	fuzzy	ADJ
ejpam-4808	280	17	(	(	PUNCT
ejpam-4808	280	18	i	i	NOUN
ejpam-4808	280	19	,	,	PUNCT
ejpam-4808	280	20	j)−	j)−	PROPN
ejpam-4808	280	21	gφ−	gφ−	PROPN
ejpam-4808	280	22	closed	close	VERB
ejpam-4808	280	23	.	.	PUNCT
ejpam-4808	281	1	4	4	X
ejpam-4808	281	2	.	.	X
ejpam-4808	281	3	conclusion	conclusion	NOUN
ejpam-4808	281	4	in	in	ADP
ejpam-4808	281	5	this	this	DET
ejpam-4808	281	6	study	study	NOUN
ejpam-4808	281	7	,	,	PUNCT
ejpam-4808	281	8	we	we	PRON
ejpam-4808	281	9	introduced	introduce	VERB
ejpam-4808	281	10	and	and	CCONJ
ejpam-4808	281	11	studied	study	VERB
ejpam-4808	281	12	the	the	DET
ejpam-4808	281	13	definition	definition	NOUN
ejpam-4808	281	14	of	of	ADP
ejpam-4808	281	15	some	some	DET
ejpam-4808	281	16	types	type	NOUN
ejpam-4808	281	17	of	of	ADP
ejpam-4808	281	18	generalized	generalized	ADJ
ejpam-4808	281	19	neighborhood	neighborhood	NOUN
ejpam-4808	281	20	and	and	CCONJ
ejpam-4808	281	21	generalized	generalized	ADJ
ejpam-4808	281	22	quasi	quasi	ADJ
ejpam-4808	281	23	-	-	ADJ
ejpam-4808	281	24	neighborhood	neighborhood	ADJ
ejpam-4808	281	25	ideas	idea	NOUN
ejpam-4808	281	26	fuzzy	fuzzy	ADJ
ejpam-4808	281	27	bitopology	bitopology	NOUN
ejpam-4808	281	28	space	space	NOUN
ejpam-4808	281	29	,	,	PUNCT
ejpam-4808	281	30	and	and	CCONJ
ejpam-4808	281	31	we	we	PRON
ejpam-4808	281	32	prove	prove	VERB
ejpam-4808	281	33	some	some	DET
ejpam-4808	281	34	relations	relation	NOUN
ejpam-4808	281	35	and	and	CCONJ
ejpam-4808	281	36	inclusion	inclusion	NOUN
ejpam-4808	281	37	relation	relation	NOUN
ejpam-4808	281	38	between	between	ADP
ejpam-4808	281	39	them	they	PRON
ejpam-4808	281	40	by	by	ADP
ejpam-4808	281	41	listing	list	VERB
ejpam-4808	281	42	some	some	DET
ejpam-4808	281	43	examples	example	NOUN
ejpam-4808	281	44	,	,	PUNCT
ejpam-4808	281	45	then	then	ADV
ejpam-4808	281	46	applied	apply	VERB
ejpam-4808	281	47	them	they	PRON
ejpam-4808	281	48	to	to	ADP
ejpam-4808	281	49	,	,	PUNCT
ejpam-4808	281	50	closure	closure	NOUN
ejpam-4808	281	51	,	,	PUNCT
ejpam-4808	281	52	interior	interior	NOUN
ejpam-4808	281	53	,	,	PUNCT
ejpam-4808	281	54	and	and	CCONJ
ejpam-4808	281	55	studied	study	VERB
ejpam-4808	281	56	some	some	DET
ejpam-4808	281	57	key	key	ADJ
ejpam-4808	281	58	properties	property	NOUN
ejpam-4808	281	59	of	of	ADP
ejpam-4808	281	60	them	they	PRON
ejpam-4808	281	61	.	.	PUNCT
ejpam-4808	282	1	acknowledgements	acknowledgement	VERB
ejpam-4808	282	2	the	the	DET
ejpam-4808	282	3	authors	author	NOUN
ejpam-4808	282	4	would	would	AUX
ejpam-4808	282	5	like	like	VERB
ejpam-4808	282	6	to	to	PART
ejpam-4808	282	7	thank	thank	VERB
ejpam-4808	282	8	the	the	DET
ejpam-4808	282	9	referee(s	referee(s	NOUN
ejpam-4808	282	10	)	)	PUNCT
ejpam-4808	282	11	for	for	ADP
ejpam-4808	282	12	their	their	PRON
ejpam-4808	282	13	valuable	valuable	ADJ
ejpam-4808	282	14	comments	comment	NOUN
ejpam-4808	282	15	.	.	PUNCT
ejpam-4808	283	1	references	reference	NOUN
ejpam-4808	283	2	1990	1990	NUM
ejpam-4808	283	3	references	reference	NOUN
ejpam-4808	283	4	[	[	X
ejpam-4808	283	5	1	1	NUM
ejpam-4808	283	6	]	]	PUNCT
ejpam-4808	283	7	a.	a.	NOUN
ejpam-4808	283	8	kandil	kandil	PROPN
ejpam-4808	283	9	,	,	PUNCT
ejpam-4808	283	10	biproximities	biproximitie	NOUN
ejpam-4808	283	11	and	and	CCONJ
ejpam-4808	283	12	fuzzy	fuzzy	ADJ
ejpam-4808	283	13	bitopological	bitopological	ADJ
ejpam-4808	283	14	spaces	space	NOUN
ejpam-4808	283	15	.	.	PUNCT
ejpam-4808	284	1	simon	simon	PROPN
ejpam-4808	284	2	stevin	stevin	PROPN
ejpam-4808	284	3	,	,	PUNCT
ejpam-4808	284	4	(	(	PUNCT
ejpam-4808	284	5	1989	1989	NUM
ejpam-4808	284	6	)	)	PUNCT
ejpam-4808	284	7	,	,	PUNCT
ejpam-4808	284	8	pp	pp	PROPN
ejpam-4808	284	9	.	.	PUNCT
ejpam-4808	285	1	45	45	NUM
ejpam-4808	285	2	-	-	SYM
ejpam-4808	285	3	66	66	NUM
ejpam-4808	285	4	.	.	PUNCT
ejpam-4808	286	1	[	[	X
ejpam-4808	286	2	2	2	NUM
ejpam-4808	286	3	]	]	X
ejpam-4808	286	4	andal	andal	PROPN
ejpam-4808	286	5	,	,	PUNCT
ejpam-4808	286	6	m.	m.	NOUN
ejpam-4808	286	7	,	,	PUNCT
ejpam-4808	286	8	and	and	CCONJ
ejpam-4808	286	9	thiripurasundari	thiripurasundari	ADV
ejpam-4808	286	10	,	,	PUNCT
ejpam-4808	286	11	v.	v.	ADP
ejpam-4808	286	12	fuzzy	fuzzy	ADJ
ejpam-4808	286	13	generalized	generalize	VERB
ejpam-4808	286	14	π	π	NOUN
ejpam-4808	286	15	closed	close	VERB
ejpam-4808	286	16	set	set	VERB
ejpam-4808	286	17	in	in	ADP
ejpam-4808	286	18	fuzzy	fuzzy	ADJ
ejpam-4808	286	19	topological	topological	ADJ
ejpam-4808	286	20	spaces	space	NOUN
ejpam-4808	286	21	.	.	PUNCT
ejpam-4808	287	1	journal	journal	NOUN
ejpam-4808	287	2	of	of	ADP
ejpam-4808	287	3	information	information	NOUN
ejpam-4808	287	4	and	and	CCONJ
ejpam-4808	287	5	computational	computational	ADJ
ejpam-4808	287	6	science	science	NOUN
ejpam-4808	287	7	,	,	PUNCT
ejpam-4808	287	8	(	(	PUNCT
ejpam-4808	287	9	2019	2019	NUM
ejpam-4808	287	10	)	)	PUNCT
ejpam-4808	287	11	,	,	PUNCT
ejpam-4808	287	12	pp	pp	ADP
ejpam-4808	287	13	.	.	PUNCT
ejpam-4808	287	14	1548	1548	NUM
ejpam-4808	287	15	–	–	PUNCT
ejpam-4808	287	16	7741	7741	NUM
ejpam-4808	287	17	.	.	PUNCT
ejpam-4808	288	1	[	[	X
ejpam-4808	288	2	3	3	NUM
ejpam-4808	288	3	]	]	X
ejpam-4808	288	4	benchalli	benchalli	NOUN
ejpam-4808	288	5	,	,	PUNCT
ejpam-4808	288	6	s.	s.	PROPN
ejpam-4808	288	7	s.	s.	PROPN
ejpam-4808	288	8	,	,	PUNCT
ejpam-4808	288	9	patil	patil	PROPN
ejpam-4808	288	10	,	,	PUNCT
ejpam-4808	288	11	p.	p.	PROPN
ejpam-4808	288	12	g.	g.	PROPN
ejpam-4808	288	13	,	,	PUNCT
ejpam-4808	288	14	toranagatti	toranagatti	VERB
ejpam-4808	288	15	,	,	PUNCT
ejpam-4808	288	16	j.	j.	PROPN
ejpam-4808	288	17	b.	b.	PROPN
ejpam-4808	288	18	,	,	PUNCT
ejpam-4808	288	19	and	and	CCONJ
ejpam-4808	288	20	vighneshi	vighneshi	NOUN
ejpam-4808	288	21	,	,	PUNCT
ejpam-4808	288	22	s.	s.	PROPN
ejpam-4808	288	23	r.	r.	PROPN
ejpam-4808	288	24	a	a	DET
ejpam-4808	288	25	new	new	ADJ
ejpam-4808	288	26	class	class	NOUN
ejpam-4808	288	27	of	of	ADP
ejpam-4808	288	28	generalized	generalized	ADJ
ejpam-4808	288	29	closed	closed	ADJ
ejpam-4808	288	30	sets	set	NOUN
ejpam-4808	288	31	in	in	ADP
ejpam-4808	288	32	topological	topological	ADJ
ejpam-4808	288	33	spaces	space	NOUN
ejpam-4808	288	34	.	.	PUNCT
ejpam-4808	289	1	global	global	ADJ
ejpam-4808	289	2	journal	journal	PROPN
ejpam-4808	289	3	of	of	ADP
ejpam-4808	289	4	pure	pure	ADJ
ejpam-4808	289	5	and	and	CCONJ
ejpam-4808	289	6	applied	applied	ADJ
ejpam-4808	289	7	mathematics	mathematic	NOUN
ejpam-4808	289	8	,	,	PUNCT
ejpam-4808	289	9	(	(	PUNCT
ejpam-4808	289	10	2017	2017	NUM
ejpam-4808	289	11	)	)	PUNCT
ejpam-4808	289	12	,	,	PUNCT
ejpam-4808	289	13	pp	pp	ADP
ejpam-4808	289	14	.	.	PUNCT
ejpam-4808	290	1	331–345	331–345	NUM
ejpam-4808	290	2	.	.	PUNCT
ejpam-4808	291	1	[	[	X
ejpam-4808	291	2	4	4	NUM
ejpam-4808	291	3	]	]	X
ejpam-4808	291	4	c.	c.	PROPN
ejpam-4808	291	5	chang	chang	PROPN
ejpam-4808	291	6	,	,	PUNCT
ejpam-4808	291	7	fuzzy	fuzzy	ADJ
ejpam-4808	291	8	topological	topological	ADJ
ejpam-4808	291	9	spaces	space	NOUN
ejpam-4808	291	10	.	.	PUNCT
ejpam-4808	292	1	j.	j.	PROPN
ejpam-4808	292	2	math	math	PROPN
ejpam-4808	292	3	.	.	PUNCT
ejpam-4808	293	1	anal	anal	ADJ
ejpam-4808	293	2	appl	appl	PROPN
ejpam-4808	293	3	,	,	PUNCT
ejpam-4808	293	4	(	(	PUNCT
ejpam-4808	293	5	1968	1968	NUM
ejpam-4808	293	6	)	)	PUNCT
ejpam-4808	293	7	,	,	PUNCT
ejpam-4808	293	8	pp	pp	ADP
ejpam-4808	293	9	.	.	PUNCT
ejpam-4808	294	1	182–190	182–190	NUM
ejpam-4808	294	2	.	.	PUNCT
ejpam-4808	295	1	[	[	X
ejpam-4808	295	2	5	5	NUM
ejpam-4808	295	3	]	]	X
ejpam-4808	295	4	das	das	PROPN
ejpam-4808	295	5	,	,	PUNCT
ejpam-4808	295	6	b.	b.	PROPN
ejpam-4808	295	7	,	,	PUNCT
ejpam-4808	295	8	bhattacharya	bhattacharya	PROPN
ejpam-4808	295	9	,	,	PUNCT
ejpam-4808	295	10	b.	b.	PROPN
ejpam-4808	295	11	,	,	PUNCT
ejpam-4808	295	12	chakraborty	chakraborty	PROPN
ejpam-4808	295	13	,	,	PUNCT
ejpam-4808	295	14	j.	j.	PROPN
ejpam-4808	295	15	,	,	PUNCT
ejpam-4808	295	16	and	and	CCONJ
ejpam-4808	295	17	tripathy	tripathy	PROPN
ejpam-4808	295	18	,	,	PUNCT
ejpam-4808	295	19	b.	b.	PROPN
ejpam-4808	295	20	c.	c.	PROPN
ejpam-4808	295	21	generalized	generalize	VERB
ejpam-4808	295	22	fuzzy	fuzzy	ADJ
ejpam-4808	295	23	closed	close	VERB
ejpam-4808	295	24	sets	set	NOUN
ejpam-4808	295	25	in	in	ADP
ejpam-4808	295	26	a	a	DET
ejpam-4808	295	27	fuzzy	fuzzy	ADJ
ejpam-4808	295	28	bitopological	bitopological	ADJ
ejpam-4808	295	29	space	space	NOUN
ejpam-4808	295	30	via	via	ADP
ejpam-4808	295	31	γ	γ	ADJ
ejpam-4808	295	32	-	-	ADJ
ejpam-4808	295	33	open	open	ADJ
ejpam-4808	295	34	sets	set	NOUN
ejpam-4808	295	35	.	.	PUNCT
ejpam-4808	296	1	afrika	afrika	ADJ
ejpam-4808	296	2	matematika	matematika	PROPN
ejpam-4808	296	3	,	,	PUNCT
ejpam-4808	296	4	(	(	PUNCT
ejpam-4808	296	5	2021	2021	NUM
ejpam-4808	296	6	)	)	PUNCT
ejpam-4808	296	7	,	,	PUNCT
ejpam-4808	296	8	pp	pp	ADP
ejpam-4808	296	9	.	.	PUNCT
ejpam-4808	297	1	333–345	333–345	NUM
ejpam-4808	297	2	.	.	PUNCT
ejpam-4808	298	1	[	[	X
ejpam-4808	298	2	6	6	NUM
ejpam-4808	298	3	]	]	PUNCT
ejpam-4808	298	4	g.	g.	PROPN
ejpam-4808	298	5	balasubramanian	balasubramanian	PROPN
ejpam-4808	298	6	and	and	CCONJ
ejpam-4808	298	7	p.	p.	PROPN
ejpam-4808	298	8	sundaram	sundaram	PROPN
ejpam-4808	298	9	,	,	PUNCT
ejpam-4808	298	10	on	on	ADP
ejpam-4808	298	11	some	some	DET
ejpam-4808	298	12	generalizations	generalization	NOUN
ejpam-4808	298	13	of	of	ADP
ejpam-4808	298	14	fuzzy	fuzzy	ADJ
ejpam-4808	298	15	continuous	continuous	ADJ
ejpam-4808	298	16	functions	function	NOUN
ejpam-4808	298	17	.	.	PUNCT
ejpam-4808	299	1	fuzzy	fuzzy	ADJ
ejpam-4808	299	2	sets	set	NOUN
ejpam-4808	299	3	and	and	CCONJ
ejpam-4808	299	4	systems	system	NOUN
ejpam-4808	299	5	,	,	PUNCT
ejpam-4808	299	6	(	(	PUNCT
ejpam-4808	299	7	1997	1997	NUM
ejpam-4808	299	8	)	)	PUNCT
ejpam-4808	299	9	,	,	PUNCT
ejpam-4808	299	10	pp	pp	ADP
ejpam-4808	299	11	.	.	PUNCT
ejpam-4808	300	1	93–100	93–100	X
ejpam-4808	300	2	.	.	PUNCT
ejpam-4808	301	1	[	[	X
ejpam-4808	301	2	7	7	NUM
ejpam-4808	301	3	]	]	SYM
ejpam-4808	301	4	kandil	kandil	NOUN
ejpam-4808	301	5	,	,	PUNCT
ejpam-4808	301	6	a.	a.	NOUN
ejpam-4808	301	7	,	,	PUNCT
ejpam-4808	301	8	tantawy	tantawy	NOUN
ejpam-4808	301	9	,	,	PUNCT
ejpam-4808	301	10	o.	o.	PROPN
ejpam-4808	301	11	,	,	PUNCT
ejpam-4808	301	12	el	el	PROPN
ejpam-4808	301	13	-	-	PUNCT
ejpam-4808	301	14	sheikh	sheikh	PROPN
ejpam-4808	301	15	,	,	PUNCT
ejpam-4808	301	16	s.	s.	PROPN
ejpam-4808	301	17	,	,	PUNCT
ejpam-4808	301	18	and	and	CCONJ
ejpam-4808	301	19	shalaby	shalaby	PROPN
ejpam-4808	301	20	,	,	PUNCT
ejpam-4808	301	21	e.	e.	PROPN
ejpam-4808	301	22	generalized	generalize	VERB
ejpam-4808	301	23	locally	locally	ADV
ejpam-4808	301	24	pairwise	pairwise	NOUN
ejpam-4808	301	25	closed	close	VERB
ejpam-4808	301	26	sets	set	NOUN
ejpam-4808	301	27	on	on	ADP
ejpam-4808	301	28	bitopological	bitopological	ADJ
ejpam-4808	301	29	spaces	space	NOUN
ejpam-4808	301	30	and	and	CCONJ
ejpam-4808	301	31	some	some	PRON
ejpam-4808	301	32	of	of	ADP
ejpam-4808	301	33	its	its	PRON
ejpam-4808	301	34	properties	property	NOUN
ejpam-4808	301	35	.	.	PUNCT
ejpam-4808	302	1	journal	journal	NOUN
ejpam-4808	302	2	of	of	ADP
ejpam-4808	302	3	the	the	DET
ejpam-4808	302	4	egyptian	egyptian	PROPN
ejpam-4808	302	5	mathematical	mathematical	PROPN
ejpam-4808	302	6	society	society	NOUN
ejpam-4808	302	7	,	,	PUNCT
ejpam-4808	302	8	(	(	PUNCT
ejpam-4808	302	9	2018	2018	NUM
ejpam-4808	302	10	)	)	PUNCT
ejpam-4808	302	11	,	,	PUNCT
ejpam-4808	302	12	116–126	116–126	NUM
ejpam-4808	302	13	.	.	PUNCT
ejpam-4808	303	1	[	[	X
ejpam-4808	303	2	8	8	NUM
ejpam-4808	303	3	]	]	X
ejpam-4808	303	4	l.	l.	PROPN
ejpam-4808	303	5	zadeh	zadeh	PROPN
ejpam-4808	303	6	,	,	PUNCT
ejpam-4808	303	7	fuzzy	fuzzy	ADJ
ejpam-4808	303	8	sets	set	NOUN
ejpam-4808	303	9	,	,	PUNCT
ejpam-4808	303	10	information	information	NOUN
ejpam-4808	303	11	and	and	CCONJ
ejpam-4808	303	12	control	control	NOUN
ejpam-4808	303	13	,	,	PUNCT
ejpam-4808	303	14	(	(	PUNCT
ejpam-4808	303	15	1965	1965	NUM
ejpam-4808	303	16	)	)	PUNCT
ejpam-4808	303	17	,	,	PUNCT
ejpam-4808	303	18	pp	pp	ADJ
ejpam-4808	303	19	.	.	PUNCT
ejpam-4808	304	1	338–353	338–353	NUM
ejpam-4808	304	2	.	.	PUNCT
ejpam-4808	305	1	[	[	X
ejpam-4808	305	2	9	9	NUM
ejpam-4808	305	3	]	]	PUNCT
ejpam-4808	305	4	m.	m.	NOUN
ejpam-4808	305	5	el	el	PROPN
ejpam-4808	305	6	-	-	PUNCT
ejpam-4808	305	7	shafei	shafei	PROPN
ejpam-4808	305	8	,	,	PUNCT
ejpam-4808	305	9	some	some	DET
ejpam-4808	305	10	applications	application	NOUN
ejpam-4808	305	11	of	of	ADP
ejpam-4808	305	12	generalized	generalized	ADJ
ejpam-4808	305	13	closed	closed	ADJ
ejpam-4808	305	14	sets	set	NOUN
ejpam-4808	305	15	in	in	ADP
ejpam-4808	305	16	fuzzy	fuzzy	ADJ
ejpam-4808	305	17	topological	topological	ADJ
ejpam-4808	305	18	space	space	NOUN
ejpam-4808	305	19	.	.	PUNCT
ejpam-4808	306	1	kyngpook	kyngpook	NOUN
ejpam-4808	306	2	math	math	NOUN
ejpam-4808	306	3	,	,	PUNCT
ejpam-4808	306	4	(	(	PUNCT
ejpam-4808	306	5	2005	2005	NUM
ejpam-4808	306	6	)	)	PUNCT
ejpam-4808	306	7	,	,	PUNCT
ejpam-4808	306	8	pp	pp	ADJ
ejpam-4808	306	9	.	.	PUNCT
ejpam-4808	307	1	13–19	13–19	NUM
ejpam-4808	307	2	.	.	PUNCT
ejpam-4808	308	1	[	[	X
ejpam-4808	308	2	10	10	NUM
ejpam-4808	308	3	]	]	X
ejpam-4808	308	4	n.	n.	NOUN
ejpam-4808	308	5	palaniappan	palaniappan	PROPN
ejpam-4808	308	6	,	,	PUNCT
ejpam-4808	308	7	fuzzy	fuzzy	ADJ
ejpam-4808	308	8	topology	topology	NOUN
ejpam-4808	308	9	.	.	PUNCT
ejpam-4808	309	1	alpha	alpha	PROPN
ejpam-4808	309	2	science	science	PROPN
ejpam-4808	309	3	international	international	PROPN
ejpam-4808	309	4	ltd	ltd	PROPN
ejpam-4808	309	5	,	,	PUNCT
ejpam-4808	309	6	(	(	PUNCT
ejpam-4808	309	7	2002	2002	NUM
ejpam-4808	309	8	)	)	PUNCT
ejpam-4808	309	9	,	,	PUNCT
ejpam-4808	309	10	pp	pp	ADP
ejpam-4808	309	11	.	.	PUNCT
ejpam-4808	310	1	1–177	1–177	X
ejpam-4808	310	2	.	.	PUNCT
ejpam-4808	311	1	[	[	X
ejpam-4808	311	2	11	11	NUM
ejpam-4808	311	3	]	]	PUNCT
ejpam-4808	311	4	ramaboopathi	ramaboopathi	NOUN
ejpam-4808	311	5	,	,	PUNCT
ejpam-4808	311	6	m.	m.	NOUN
ejpam-4808	311	7	,	,	PUNCT
ejpam-4808	311	8	and	and	CCONJ
ejpam-4808	311	9	dharmalingam	dharmalingam	ADV
ejpam-4808	311	10	,	,	PUNCT
ejpam-4808	311	11	k.	k.	PROPN
ejpam-4808	311	12	m.	m.	PROPN
ejpam-4808	311	13	on	on	ADP
ejpam-4808	311	14	(	(	PUNCT
ejpam-4808	311	15	1	1	NUM
ejpam-4808	311	16	,	,	PUNCT
ejpam-4808	311	17	2)∗-ˇg	2)∗-ˇg	NOUN
ejpam-4808	311	18	-	-	PUNCT
ejpam-4808	311	19	closed	close	VERB
ejpam-4808	311	20	sets	set	NOUN
ejpam-4808	311	21	in	in	ADP
ejpam-4808	311	22	bitopological	bitopological	ADJ
ejpam-4808	311	23	spaces	space	NOUN
ejpam-4808	311	24	.	.	PUNCT
ejpam-4808	312	1	malaya	malaya	PROPN
ejpam-4808	312	2	journal	journal	PROPN
ejpam-4808	312	3	of	of	ADP
ejpam-4808	312	4	matematik	matematik	PROPN
ejpam-4808	312	5	,	,	PUNCT
ejpam-4808	312	6	(	(	PUNCT
ejpam-4808	312	7	2019	2019	NUM
ejpam-4808	312	8	)	)	PUNCT
ejpam-4808	312	9	,	,	PUNCT
ejpam-4808	312	10	pp	pp	ADJ
ejpam-4808	312	11	.	.	PUNCT
ejpam-4808	313	1	463–467	463–467	NUM
ejpam-4808	313	2	.	.	PUNCT
ejpam-4808	314	1	[	[	X
ejpam-4808	314	2	12	12	NUM
ejpam-4808	314	3	]	]	PUNCT
ejpam-4808	314	4	xuzhu	xuzhu	PROPN
ejpam-4808	314	5	wang	wang	PROPN
ejpam-4808	314	6	,	,	PUNCT
ejpam-4808	314	7	da	da	PROPN
ejpam-4808	314	8	ruan	ruan	PROPN
ejpam-4808	314	9	,	,	PUNCT
ejpam-4808	314	10	and	and	CCONJ
ejpam-4808	314	11	etienn	etienn	PROPN
ejpam-4808	314	12	e.	e.	PROPN
ejpam-4808	314	13	kerre	kerre	PROPN
ejpam-4808	314	14	.	.	PUNCT
ejpam-4808	315	1	mathematics	mathematic	NOUN
ejpam-4808	315	2	of	of	ADP
ejpam-4808	315	3	fuzziness	fuzziness	NOUN
ejpam-4808	315	4	-	-	PUNCT
ejpam-4808	315	5	basic	basic	ADJ
ejpam-4808	315	6	issues	issue	NOUN
ejpam-4808	315	7	.	.	PUNCT
ejpam-4808	316	1	springer	springer	NOUN
ejpam-4808	316	2	nature	nature	NOUN
ejpam-4808	316	3	,	,	PUNCT
ejpam-4808	316	4	(	(	PUNCT
ejpam-4808	316	5	2009	2009	NUM
ejpam-4808	316	6	)	)	PUNCT
ejpam-4808	316	7	.	.	PUNCT
ejpam-4808	317	1	[	[	X
ejpam-4808	317	2	13	13	NUM
ejpam-4808	317	3	]	]	PUNCT
ejpam-4808	317	4	zahran	zahran	NOUN
ejpam-4808	317	5	,	,	PUNCT
ejpam-4808	317	6	a.	a.	NOUN
ejpam-4808	317	7	m	m	PROPN
ejpam-4808	317	8	and	and	CCONJ
ejpam-4808	317	9	el	el	PROPN
ejpam-4808	317	10	-	-	PUNCT
ejpam-4808	317	11	maghrabi	maghrabi	PROPN
ejpam-4808	317	12	,	,	PUNCT
ejpam-4808	317	13	a.	a.	PROPN
ejpam-4808	317	14	i.	i.	PROPN
ejpam-4808	317	15	generalized	generalize	VERB
ejpam-4808	317	16	-	-	PUNCT
ejpam-4808	317	17	operations	operation	NOUN
ejpam-4808	317	18	on	on	ADP
ejpam-4808	317	19	fuzzy	fuzzy	ADJ
ejpam-4808	317	20	topological	topological	ADJ
ejpam-4808	317	21	spaces	space	NOUN
ejpam-4808	317	22	.	.	PUNCT
ejpam-4808	318	1	abstract	abstract	ADJ
ejpam-4808	318	2	and	and	CCONJ
ejpam-4808	318	3	applied	apply	VERB
ejpam-4808	318	4	analysis	analysis	NOUN
ejpam-4808	318	5	,	,	PUNCT
ejpam-4808	318	6	hindawi	hindawi	ADJ
ejpam-4808	318	7	,	,	PUNCT
ejpam-4808	318	8	(	(	PUNCT
ejpam-4808	318	9	2011	2011	NUM
ejpam-4808	318	10	)	)	PUNCT
ejpam-4808	318	11	,	,	PUNCT
ejpam-4808	318	12	pp	pp	PROPN
ejpam-4808	318	13	.	.	PUNCT
ejpam-4808	319	1	1–12	1–12	NOUN
ejpam-4808	319	2	.	.	PUNCT