id	sid	tid	token	lemma	pos
ejpam-5856	1	1	european	european	PROPN
ejpam-5856	1	2	journal	journal	PROPN
ejpam-5856	1	3	of	of	ADP
ejpam-5856	1	4	pure	pure	ADJ
ejpam-5856	1	5	and	and	CCONJ
ejpam-5856	1	6	applied	applied	ADJ
ejpam-5856	1	7	mathematics	mathematic	NOUN
ejpam-5856	1	8	2025	2025	NUM
ejpam-5856	1	9	,	,	PUNCT
ejpam-5856	1	10	vol	vol	NOUN
ejpam-5856	1	11	.	.	PROPN
ejpam-5856	1	12	18	18	NUM
ejpam-5856	1	13	,	,	PUNCT
ejpam-5856	1	14	issue	issue	NOUN
ejpam-5856	1	15	1	1	NUM
ejpam-5856	1	16	,	,	PUNCT
ejpam-5856	1	17	article	article	NOUN
ejpam-5856	1	18	number	number	NOUN
ejpam-5856	1	19	5856	5856	NUM
ejpam-5856	1	20	issn	issn	VERB
ejpam-5856	1	21	1307	1307	NUM
ejpam-5856	1	22	-	-	SYM
ejpam-5856	1	23	5543	5543	NUM
ejpam-5856	1	24	–	–	PUNCT
ejpam-5856	1	25	ejpam.com	ejpam.com	X
ejpam-5856	1	26	published	publish	VERB
ejpam-5856	1	27	by	by	ADP
ejpam-5856	1	28	new	new	PROPN
ejpam-5856	1	29	york	york	PROPN
ejpam-5856	1	30	business	business	PROPN
ejpam-5856	1	31	global	global	ADJ
ejpam-5856	1	32	novel	novel	NOUN
ejpam-5856	1	33	categories	category	NOUN
ejpam-5856	1	34	of	of	ADP
ejpam-5856	1	35	spaces	space	NOUN
ejpam-5856	1	36	in	in	ADP
ejpam-5856	1	37	the	the	DET
ejpam-5856	1	38	frame	frame	NOUN
ejpam-5856	1	39	of	of	ADP
ejpam-5856	1	40	generalized	generalized	ADJ
ejpam-5856	1	41	fuzzy	fuzzy	ADJ
ejpam-5856	1	42	topologies	topology	NOUN
ejpam-5856	1	43	via	via	ADP
ejpam-5856	1	44	fuzzy	fuzzy	ADJ
ejpam-5856	1	45	gµ-closed	gµ-close	VERB
ejpam-5856	1	46	sets	set	NOUN
ejpam-5856	1	47	salem	salem	PROPN
ejpam-5856	1	48	saleh1,2	saleh1,2	PROPN
ejpam-5856	1	49	,	,	PUNCT
ejpam-5856	1	50	fathea	fathea	PROPN
ejpam-5856	1	51	m.	m.	PROPN
ejpam-5856	1	52	osman	osman	PROPN
ejpam-5856	1	53	birkea3∗	birkea3∗	PROPN
ejpam-5856	1	54	,	,	PUNCT
ejpam-5856	1	55	tareq	tareq	PROPN
ejpam-5856	1	56	m.	m.	PROPN
ejpam-5856	1	57	al	al	PROPN
ejpam-5856	1	58	-	-	PUNCT
ejpam-5856	1	59	shami4,5	shami4,5	PROPN
ejpam-5856	1	60	,	,	PUNCT
ejpam-5856	1	61	murad	murad	NOUN
ejpam-5856	1	62	arar6	arar6	PROPN
ejpam-5856	1	63	,	,	PUNCT
ejpam-5856	1	64	m.	m.	NOUN
ejpam-5856	1	65	omran7	omran7	AUX
ejpam-5856	1	66	1	1	NUM
ejpam-5856	1	67	department	department	NOUN
ejpam-5856	1	68	of	of	ADP
ejpam-5856	1	69	mathematics	mathematic	NOUN
ejpam-5856	1	70	,	,	PUNCT
ejpam-5856	1	71	hodeidah	hodeidah	PROPN
ejpam-5856	1	72	university	university	NOUN
ejpam-5856	1	73	,	,	PUNCT
ejpam-5856	1	74	hodeidah	hodeidah	PROPN
ejpam-5856	1	75	,	,	PUNCT
ejpam-5856	1	76	yemen	yemen	PROPN
ejpam-5856	1	77	2	2	NUM
ejpam-5856	1	78	department	department	NOUN
ejpam-5856	1	79	of	of	ADP
ejpam-5856	1	80	computer	computer	NOUN
ejpam-5856	1	81	science	science	NOUN
ejpam-5856	1	82	,	,	PUNCT
ejpam-5856	1	83	cihan	cihan	VERB
ejpam-5856	1	84	university	university	NOUN
ejpam-5856	1	85	-	-	PUNCT
ejpam-5856	1	86	erbil	erbil	PROPN
ejpam-5856	1	87	,	,	PUNCT
ejpam-5856	1	88	erbil	erbil	PROPN
ejpam-5856	1	89	,	,	PUNCT
ejpam-5856	1	90	iraq	iraq	PROPN
ejpam-5856	1	91	3	3	NUM
ejpam-5856	1	92	department	department	NOUN
ejpam-5856	1	93	of	of	ADP
ejpam-5856	1	94	mathematics	mathematic	NOUN
ejpam-5856	1	95	,	,	PUNCT
ejpam-5856	1	96	faculty	faculty	NOUN
ejpam-5856	1	97	of	of	ADP
ejpam-5856	1	98	science	science	NOUN
ejpam-5856	1	99	,	,	PUNCT
ejpam-5856	1	100	northern	northern	ADJ
ejpam-5856	1	101	border	border	NOUN
ejpam-5856	1	102	university	university	PROPN
ejpam-5856	1	103	,	,	PUNCT
ejpam-5856	1	104	arar	arar	PROPN
ejpam-5856	1	105	,	,	PUNCT
ejpam-5856	1	106	saudi	saudi	PROPN
ejpam-5856	1	107	arabia	arabia	PROPN
ejpam-5856	1	108	4	4	NUM
ejpam-5856	1	109	department	department	NOUN
ejpam-5856	1	110	of	of	ADP
ejpam-5856	1	111	mathematics	mathematic	NOUN
ejpam-5856	1	112	,	,	PUNCT
ejpam-5856	1	113	sana’a	sana’a	NOUN
ejpam-5856	1	114	university	university	NOUN
ejpam-5856	1	115	,	,	PUNCT
ejpam-5856	1	116	p.o.box	p.o.box	PROPN
ejpam-5856	1	117	1247	1247	NUM
ejpam-5856	1	118	sana’a	sana’a	NOUN
ejpam-5856	1	119	,	,	PUNCT
ejpam-5856	1	120	yemen	yemen	PROPN
ejpam-5856	1	121	5	5	NUM
ejpam-5856	1	122	jadara	jadara	PROPN
ejpam-5856	1	123	university	university	PROPN
ejpam-5856	1	124	research	research	NOUN
ejpam-5856	1	125	center	center	NOUN
ejpam-5856	1	126	,	,	PUNCT
ejpam-5856	1	127	jadara	jadara	PROPN
ejpam-5856	1	128	university	university	PROPN
ejpam-5856	1	129	,	,	PUNCT
ejpam-5856	1	130	irbid	irbid	PROPN
ejpam-5856	1	131	,	,	PUNCT
ejpam-5856	1	132	jordan	jordan	PROPN
ejpam-5856	1	133	6	6	NUM
ejpam-5856	1	134	department	department	NOUN
ejpam-5856	1	135	of	of	ADP
ejpam-5856	1	136	mathematics	mathematic	NOUN
ejpam-5856	1	137	,	,	PUNCT
ejpam-5856	1	138	college	college	NOUN
ejpam-5856	1	139	of	of	ADP
ejpam-5856	1	140	sciences	science	NOUN
ejpam-5856	1	141	and	and	CCONJ
ejpam-5856	1	142	humanities	humanity	NOUN
ejpam-5856	1	143	in	in	ADP
ejpam-5856	1	144	aflaj	aflaj	NOUN
ejpam-5856	1	145	,	,	PUNCT
ejpam-5856	1	146	prince	prince	PROPN
ejpam-5856	1	147	sattam	sattam	PROPN
ejpam-5856	1	148	bin	bin	PROPN
ejpam-5856	1	149	abdulaziz	abdulaziz	PROPN
ejpam-5856	1	150	university	university	PROPN
ejpam-5856	1	151	,	,	PUNCT
ejpam-5856	1	152	riyadh	riyadh	PROPN
ejpam-5856	1	153	,	,	PUNCT
ejpam-5856	1	154	saudi	saudi	PROPN
ejpam-5856	1	155	arabia	arabia	PROPN
ejpam-5856	1	156	7	7	NUM
ejpam-5856	1	157	department	department	PROPN
ejpam-5856	1	158	of	of	ADP
ejpam-5856	1	159	physics	physics	PROPN
ejpam-5856	1	160	and	and	CCONJ
ejpam-5856	1	161	engineering	engineering	NOUN
ejpam-5856	1	162	mathematics	mathematic	NOUN
ejpam-5856	1	163	,	,	PUNCT
ejpam-5856	1	164	faculty	faculty	NOUN
ejpam-5856	1	165	of	of	ADP
ejpam-5856	1	166	engineering	engineering	PROPN
ejpam-5856	1	167	,	,	PUNCT
ejpam-5856	1	168	tanta	tanta	PROPN
ejpam-5856	1	169	university	university	PROPN
ejpam-5856	1	170	,	,	PUNCT
ejpam-5856	1	171	egypt	egypt	PROPN
ejpam-5856	1	172	abstract	abstract	PROPN
ejpam-5856	1	173	.	.	PUNCT
ejpam-5856	2	1	one	one	NUM
ejpam-5856	2	2	of	of	ADP
ejpam-5856	2	3	the	the	DET
ejpam-5856	2	4	known	know	VERB
ejpam-5856	2	5	approaches	approach	NOUN
ejpam-5856	2	6	to	to	ADP
ejpam-5856	2	7	studying	study	VERB
ejpam-5856	2	8	topological	topological	ADJ
ejpam-5856	2	9	concepts	concept	NOUN
ejpam-5856	2	10	is	be	AUX
ejpam-5856	2	11	to	to	PART
ejpam-5856	2	12	utilize	utilize	VERB
ejpam-5856	2	13	subclasses	subclass	NOUN
ejpam-5856	2	14	of	of	ADP
ejpam-5856	2	15	topology	topology	NOUN
ejpam-5856	2	16	,	,	PUNCT
ejpam-5856	2	17	such	such	ADJ
ejpam-5856	2	18	as	as	ADP
ejpam-5856	2	19	clopen	clopen	ADJ
ejpam-5856	2	20	sets	set	NOUN
ejpam-5856	2	21	and	and	CCONJ
ejpam-5856	2	22	generalized	generalize	VERB
ejpam-5856	2	23	closed	closed	ADJ
ejpam-5856	2	24	sets	set	NOUN
ejpam-5856	2	25	.	.	PUNCT
ejpam-5856	3	1	in	in	ADP
ejpam-5856	3	2	this	this	DET
ejpam-5856	3	3	study	study	NOUN
ejpam-5856	3	4	,	,	PUNCT
ejpam-5856	3	5	we	we	PRON
ejpam-5856	3	6	apply	apply	VERB
ejpam-5856	3	7	the	the	DET
ejpam-5856	3	8	notion	notion	NOUN
ejpam-5856	3	9	of	of	ADP
ejpam-5856	3	10	fuzzy	fuzzy	ADJ
ejpam-5856	3	11	generalized	generalize	VERB
ejpam-5856	3	12	µ-closed	µ-close	VERB
ejpam-5856	3	13	sets	set	NOUN
ejpam-5856	3	14	(	(	PUNCT
ejpam-5856	3	15	fgµ-closed	fgµ-closed	ADJ
ejpam-5856	3	16	sets	set	NOUN
ejpam-5856	3	17	)	)	PUNCT
ejpam-5856	3	18	to	to	PART
ejpam-5856	3	19	establish	establish	VERB
ejpam-5856	3	20	and	and	CCONJ
ejpam-5856	3	21	analyze	analyze	VERB
ejpam-5856	3	22	novel	novel	ADJ
ejpam-5856	3	23	categories	category	NOUN
ejpam-5856	3	24	of	of	ADP
ejpam-5856	3	25	spaces	space	NOUN
ejpam-5856	3	26	,	,	PUNCT
ejpam-5856	3	27	namely	namely	ADV
ejpam-5856	3	28	fgµ-regular	fgµ-regular	ADJ
ejpam-5856	3	29	,	,	PUNCT
ejpam-5856	3	30	fgµ-normal	fgµ-normal	ADJ
ejpam-5856	3	31	,	,	PUNCT
ejpam-5856	3	32	and	and	CCONJ
ejpam-5856	3	33	fµ-symmetric	fµ-symmetric	ADJ
ejpam-5856	3	34	spaces	space	NOUN
ejpam-5856	3	35	in	in	ADP
ejpam-5856	3	36	the	the	DET
ejpam-5856	3	37	frame	frame	NOUN
ejpam-5856	3	38	of	of	ADP
ejpam-5856	3	39	generalized	generalized	ADJ
ejpam-5856	3	40	fuzzy	fuzzy	ADJ
ejpam-5856	3	41	topology	topology	NOUN
ejpam-5856	3	42	(	(	PUNCT
ejpam-5856	3	43	gft	gft	PROPN
ejpam-5856	3	44	)	)	PUNCT
ejpam-5856	3	45	.	.	PUNCT
ejpam-5856	4	1	we	we	PRON
ejpam-5856	4	2	investigate	investigate	VERB
ejpam-5856	4	3	the	the	DET
ejpam-5856	4	4	fundamental	fundamental	ADJ
ejpam-5856	4	5	properties	property	NOUN
ejpam-5856	4	6	of	of	ADP
ejpam-5856	4	7	these	these	DET
ejpam-5856	4	8	classes	class	NOUN
ejpam-5856	4	9	,	,	PUNCT
ejpam-5856	4	10	exploring	explore	VERB
ejpam-5856	4	11	their	their	PRON
ejpam-5856	4	12	unique	unique	ADJ
ejpam-5856	4	13	characteristics	characteristic	NOUN
ejpam-5856	4	14	and	and	CCONJ
ejpam-5856	4	15	preservation	preservation	NOUN
ejpam-5856	4	16	theorems	theorem	NOUN
ejpam-5856	4	17	under	under	ADP
ejpam-5856	4	18	fgµ-continuous	fgµ-continuous	ADJ
ejpam-5856	4	19	maps	map	NOUN
ejpam-5856	4	20	.	.	PUNCT
ejpam-5856	5	1	we	we	PRON
ejpam-5856	5	2	establish	establish	VERB
ejpam-5856	5	3	the	the	DET
ejpam-5856	5	4	interrelationships	interrelationship	NOUN
ejpam-5856	5	5	between	between	ADP
ejpam-5856	5	6	these	these	DET
ejpam-5856	5	7	classes	class	NOUN
ejpam-5856	5	8	and	and	CCONJ
ejpam-5856	5	9	the	the	DET
ejpam-5856	5	10	other	other	ADJ
ejpam-5856	5	11	separation	separation	NOUN
ejpam-5856	5	12	axioms	axiom	NOUN
ejpam-5856	5	13	in	in	ADP
ejpam-5856	5	14	this	this	DET
ejpam-5856	5	15	setting	setting	NOUN
ejpam-5856	5	16	,	,	PUNCT
ejpam-5856	5	17	and	and	CCONJ
ejpam-5856	5	18	we	we	PRON
ejpam-5856	5	19	demonstrate	demonstrate	VERB
ejpam-5856	5	20	that	that	SCONJ
ejpam-5856	5	21	fµ-regular	fµ-regular	ADJ
ejpam-5856	5	22	,	,	PUNCT
ejpam-5856	5	23	fµ-normal	fµ-normal	ADJ
ejpam-5856	5	24	,	,	PUNCT
ejpam-5856	5	25	and	and	CCONJ
ejpam-5856	5	26	fµ-symmetric	fµ-symmetric	ADJ
ejpam-5856	5	27	spaces	space	NOUN
ejpam-5856	5	28	are	be	AUX
ejpam-5856	5	29	special	special	ADJ
ejpam-5856	5	30	cases	case	NOUN
ejpam-5856	5	31	of	of	ADP
ejpam-5856	5	32	fgµ-regular	fgµ-regular	ADJ
ejpam-5856	5	33	,	,	PUNCT
ejpam-5856	5	34	fgµ-normal	fgµ-normal	ADJ
ejpam-5856	5	35	,	,	PUNCT
ejpam-5856	5	36	and	and	CCONJ
ejpam-5856	5	37	fµ-t1	fµ-t1	NOUN
ejpam-5856	5	38	spaces	space	NOUN
ejpam-5856	5	39	,	,	PUNCT
ejpam-5856	5	40	respectively	respectively	ADV
ejpam-5856	5	41	.	.	PUNCT
ejpam-5856	6	1	additionally	additionally	ADV
ejpam-5856	6	2	,	,	PUNCT
ejpam-5856	6	3	we	we	PRON
ejpam-5856	6	4	show	show	VERB
ejpam-5856	6	5	that	that	SCONJ
ejpam-5856	6	6	the	the	DET
ejpam-5856	6	7	equivalence	equivalence	NOUN
ejpam-5856	6	8	for	for	ADP
ejpam-5856	6	9	these	these	DET
ejpam-5856	6	10	cases	case	NOUN
ejpam-5856	6	11	hold	hold	VERB
ejpam-5856	6	12	when	when	SCONJ
ejpam-5856	6	13	the	the	DET
ejpam-5856	6	14	gft	gft	PROPN
ejpam-5856	6	15	is	be	AUX
ejpam-5856	6	16	fµ-t	fµ-t	PROPN
ejpam-5856	6	17	1	1	NUM
ejpam-5856	6	18	2	2	NUM
ejpam-5856	6	19	.	.	PUNCT
ejpam-5856	7	1	the	the	DET
ejpam-5856	7	2	connections	connection	NOUN
ejpam-5856	7	3	between	between	ADP
ejpam-5856	7	4	these	these	DET
ejpam-5856	7	5	classes	class	NOUN
ejpam-5856	7	6	and	and	CCONJ
ejpam-5856	7	7	their	their	PRON
ejpam-5856	7	8	counterparts	counterpart	NOUN
ejpam-5856	7	9	in	in	ADP
ejpam-5856	7	10	the	the	DET
ejpam-5856	7	11	crisp	crisp	ADJ
ejpam-5856	7	12	gt	gt	PROPN
ejpam-5856	7	13	are	be	AUX
ejpam-5856	7	14	studied	study	VERB
ejpam-5856	7	15	.	.	PUNCT
ejpam-5856	8	1	finally	finally	ADV
ejpam-5856	8	2	,	,	PUNCT
ejpam-5856	8	3	we	we	PRON
ejpam-5856	8	4	discuss	discuss	VERB
ejpam-5856	8	5	these	these	DET
ejpam-5856	8	6	classes	class	NOUN
ejpam-5856	8	7	’	'	PUNCT
ejpam-5856	8	8	hereditary	hereditary	ADJ
ejpam-5856	8	9	and	and	CCONJ
ejpam-5856	8	10	topological	topological	ADJ
ejpam-5856	8	11	properties	property	NOUN
ejpam-5856	8	12	,	,	PUNCT
ejpam-5856	8	13	further	far	ADV
ejpam-5856	8	14	enhancing	enhance	VERB
ejpam-5856	8	15	our	our	PRON
ejpam-5856	8	16	comprehension	comprehension	NOUN
ejpam-5856	8	17	of	of	ADP
ejpam-5856	8	18	their	their	PRON
ejpam-5856	8	19	behavior	behavior	NOUN
ejpam-5856	8	20	and	and	CCONJ
ejpam-5856	8	21	implications	implication	NOUN
ejpam-5856	8	22	.	.	PUNCT
ejpam-5856	9	1	2020	2020	NUM
ejpam-5856	9	2	mathematics	mathematic	NOUN
ejpam-5856	9	3	subject	subject	NOUN
ejpam-5856	9	4	classifications	classification	NOUN
ejpam-5856	9	5	:	:	PUNCT
ejpam-5856	9	6	54a40	54a40	NUM
ejpam-5856	9	7	,	,	PUNCT
ejpam-5856	9	8	54c08	54c08	NUM
ejpam-5856	9	9	,	,	PUNCT
ejpam-5856	9	10	54d10	54d10	NUM
ejpam-5856	9	11	,	,	PUNCT
ejpam-5856	9	12	54d15	54d15	PRON
ejpam-5856	9	13	key	key	ADJ
ejpam-5856	9	14	words	word	NOUN
ejpam-5856	9	15	and	and	CCONJ
ejpam-5856	9	16	phrases	phrase	NOUN
ejpam-5856	9	17	:	:	PUNCT
ejpam-5856	9	18	fuzzy	fuzzy	ADJ
ejpam-5856	9	19	µ-closed	µ-close	VERB
ejpam-5856	9	20	set	set	VERB
ejpam-5856	9	21	;	;	PUNCT
ejpam-5856	9	22	fuzzy	fuzzy	ADJ
ejpam-5856	9	23	gµ-closed	gµ-close	VERB
ejpam-5856	9	24	set	set	NOUN
ejpam-5856	9	25	;	;	PUNCT
ejpam-5856	9	26	generalized	generalize	VERB
ejpam-5856	9	27	fuzzy	fuzzy	ADJ
ejpam-5856	9	28	topology	topology	NOUN
ejpam-5856	9	29	;	;	PUNCT
ejpam-5856	9	30	fuzzy	fuzzy	ADJ
ejpam-5856	9	31	gµ-continuous	gµ-continuous	ADJ
ejpam-5856	9	32	map	map	NOUN
ejpam-5856	9	33	;	;	PUNCT
ejpam-5856	9	34	fuzzy	fuzzy	ADJ
ejpam-5856	9	35	gµ-regular	gµ-regular	NOUN
ejpam-5856	9	36	;	;	PUNCT
ejpam-5856	9	37	fuzzy	fuzzy	ADJ
ejpam-5856	9	38	gµ-normal	gµ-normal	ADJ
ejpam-5856	9	39	space	space	NOUN
ejpam-5856	9	40	∗corresponding	∗corresponde	VERB
ejpam-5856	9	41	author	author	NOUN
ejpam-5856	9	42	.	.	PUNCT
ejpam-5856	10	1	doi	doi	NOUN
ejpam-5856	10	2	:	:	PUNCT
ejpam-5856	10	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5856	https://doi.org/10.29020/nybg.ejpam.v18i1.5856	DET
ejpam-5856	10	4	email	email	NOUN
ejpam-5856	10	5	addresses	address	VERB
ejpam-5856	10	6	:	:	PUNCT
ejpam-5856	10	7	s	s	VERB
ejpam-5856	10	8	wosabi@yahoo.com	wosabi@yahoo.com	X
ejpam-5856	10	9	(	(	PUNCT
ejpam-5856	10	10	s.	s.	PROPN
ejpam-5856	10	11	saleh	saleh	PROPN
ejpam-5856	10	12	)	)	PUNCT
ejpam-5856	10	13	,	,	PUNCT
ejpam-5856	10	14	fathia.birkia@nbu.edu.sa	fathia.birkia@nbu.edu.sa	PROPN
ejpam-5856	10	15	(	(	PUNCT
ejpam-5856	10	16	f.m.o	f.m.o	NOUN
ejpam-5856	10	17	.	.	PUNCT
ejpam-5856	10	18	birkea	birkea	PROPN
ejpam-5856	10	19	)	)	PUNCT
ejpam-5856	10	20	,	,	PUNCT
ejpam-5856	10	21	tareqalshami83@gmail.com	tareqalshami83@gmail.com	X
ejpam-5856	10	22	(	(	PUNCT
ejpam-5856	10	23	t.m	t.m	PROPN
ejpam-5856	10	24	.	.	PROPN
ejpam-5856	10	25	al	al	PROPN
ejpam-5856	10	26	-	-	PUNCT
ejpam-5856	10	27	shami	shami	PROPN
ejpam-5856	10	28	)	)	PUNCT
ejpam-5856	10	29	,	,	PUNCT
ejpam-5856	10	30	muradshhada@gmail.com	muradshhada@gmail.com	PROPN
ejpam-5856	10	31	(	(	PUNCT
ejpam-5856	10	32	m.	m.	NOUN
ejpam-5856	10	33	arar	arar	PROPN
ejpam-5856	10	34	)	)	PUNCT
ejpam-5856	10	35	,	,	PUNCT
ejpam-5856	10	36	manar.omran@f-eng.tanta.edu.eg	manar.omran@f-eng.tanta.edu.eg	X
ejpam-5856	10	37	(	(	PUNCT
ejpam-5856	10	38	m.	m.	NOUN
ejpam-5856	10	39	omran	omran	PROPN
ejpam-5856	10	40	)	)	PUNCT
ejpam-5856	10	41	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5856	11	1	1	1	NUM
ejpam-5856	11	2	copyright	copyright	NOUN
ejpam-5856	11	3	:	:	PUNCT
ejpam-5856	11	4	©	©	PROPN
ejpam-5856	11	5	2025	2025	NUM
ejpam-5856	11	6	the	the	DET
ejpam-5856	11	7	author(s	author(s	NOUN
ejpam-5856	11	8	)	)	PUNCT
ejpam-5856	11	9	.	.	PUNCT
ejpam-5856	12	1	(	(	PUNCT
ejpam-5856	12	2	cc	cc	NOUN
ejpam-5856	12	3	by	by	ADP
ejpam-5856	12	4	-	-	PUNCT
ejpam-5856	12	5	nc	nc	PROPN
ejpam-5856	12	6	4.0	4.0	NUM
ejpam-5856	12	7	)	)	PUNCT
ejpam-5856	12	8	s.	s.	PROPN
ejpam-5856	12	9	saleh	saleh	PROPN
ejpam-5856	12	10	et	et	PROPN
ejpam-5856	12	11	al	al	PROPN
ejpam-5856	12	12	.	.	PUNCT
ejpam-5856	12	13	/	/	SYM
ejpam-5856	12	14	eur	eur	PROPN
ejpam-5856	12	15	.	.	PUNCT
ejpam-5856	13	1	j.	j.	PROPN
ejpam-5856	13	2	pure	pure	PROPN
ejpam-5856	13	3	appl	appl	PROPN
ejpam-5856	13	4	.	.	PROPN
ejpam-5856	13	5	math	math	PROPN
ejpam-5856	13	6	,	,	PUNCT
ejpam-5856	13	7	18	18	NUM
ejpam-5856	13	8	(	(	PUNCT
ejpam-5856	13	9	1	1	NUM
ejpam-5856	13	10	)	)	PUNCT
ejpam-5856	13	11	(	(	PUNCT
ejpam-5856	13	12	2025	2025	NUM
ejpam-5856	13	13	)	)	PUNCT
ejpam-5856	13	14	,	,	PUNCT
ejpam-5856	13	15	5856	5856	NUM
ejpam-5856	13	16	2	2	NUM
ejpam-5856	13	17	of	of	ADP
ejpam-5856	13	18	15	15	NUM
ejpam-5856	13	19	1	1	NUM
ejpam-5856	13	20	.	.	PUNCT
ejpam-5856	14	1	introduction	introduction	NOUN
ejpam-5856	14	2	fuzzy	fuzzy	ADJ
ejpam-5856	14	3	sets	set	NOUN
ejpam-5856	14	4	(	(	PUNCT
ejpam-5856	14	5	f	f	NOUN
ejpam-5856	14	6	-sets	-set	NOUN
ejpam-5856	14	7	)	)	PUNCT
ejpam-5856	14	8	were	be	AUX
ejpam-5856	14	9	proposed	propose	VERB
ejpam-5856	14	10	by	by	ADP
ejpam-5856	14	11	zadeh	zadeh	PROPN
ejpam-5856	15	1	[	[	X
ejpam-5856	15	2	49	49	NUM
ejpam-5856	15	3	]	]	PUNCT
ejpam-5856	15	4	in	in	ADP
ejpam-5856	15	5	1965	1965	NUM
ejpam-5856	15	6	as	as	ADP
ejpam-5856	15	7	a	a	DET
ejpam-5856	15	8	suitable	suitable	ADJ
ejpam-5856	15	9	approach	approach	NOUN
ejpam-5856	15	10	to	to	PART
ejpam-5856	15	11	address	address	VERB
ejpam-5856	15	12	with	with	ADP
ejpam-5856	15	13	uncertainty	uncertainty	NOUN
ejpam-5856	15	14	cases	case	NOUN
ejpam-5856	15	15	that	that	SCONJ
ejpam-5856	15	16	we	we	PRON
ejpam-5856	15	17	can	can	AUX
ejpam-5856	15	18	not	not	PART
ejpam-5856	15	19	be	be	AUX
ejpam-5856	15	20	efficiently	efficiently	ADV
ejpam-5856	15	21	managed	manage	VERB
ejpam-5856	15	22	using	use	VERB
ejpam-5856	15	23	classical	classical	ADJ
ejpam-5856	15	24	techniques	technique	NOUN
ejpam-5856	15	25	.	.	PUNCT
ejpam-5856	16	1	over	over	ADP
ejpam-5856	16	2	the	the	DET
ejpam-5856	16	3	last	last	ADJ
ejpam-5856	16	4	decades	decade	NOUN
ejpam-5856	16	5	,	,	PUNCT
ejpam-5856	16	6	the	the	DET
ejpam-5856	16	7	researches	research	NOUN
ejpam-5856	16	8	of	of	ADP
ejpam-5856	16	9	f	f	PROPN
ejpam-5856	16	10	-sets	-set	NOUN
ejpam-5856	16	11	have	have	VERB
ejpam-5856	16	12	a	a	DET
ejpam-5856	16	13	vital	vital	ADJ
ejpam-5856	16	14	role	role	NOUN
ejpam-5856	16	15	in	in	ADP
ejpam-5856	16	16	mathematics	mathematic	NOUN
ejpam-5856	16	17	and	and	CCONJ
ejpam-5856	16	18	applied	apply	VERB
ejpam-5856	16	19	sciences	science	NOUN
ejpam-5856	16	20	and	and	CCONJ
ejpam-5856	16	21	garnered	garner	VERB
ejpam-5856	16	22	significant	significant	ADJ
ejpam-5856	16	23	attention	attention	NOUN
ejpam-5856	16	24	due	due	ADP
ejpam-5856	16	25	to	to	ADP
ejpam-5856	16	26	its	its	PRON
ejpam-5856	16	27	ability	ability	NOUN
ejpam-5856	16	28	to	to	PART
ejpam-5856	16	29	handle	handle	VERB
ejpam-5856	16	30	uncertain	uncertain	ADJ
ejpam-5856	16	31	and	and	CCONJ
ejpam-5856	16	32	vague	vague	ADJ
ejpam-5856	16	33	information	information	NOUN
ejpam-5856	16	34	in	in	ADP
ejpam-5856	16	35	various	various	ADJ
ejpam-5856	16	36	real	real	ADJ
ejpam-5856	16	37	-	-	PUNCT
ejpam-5856	16	38	life	life	NOUN
ejpam-5856	16	39	applications	application	NOUN
ejpam-5856	16	40	such	such	ADJ
ejpam-5856	16	41	as	as	ADP
ejpam-5856	16	42	artificial	artificial	ADJ
ejpam-5856	16	43	intelligence	intelligence	NOUN
ejpam-5856	17	1	[	[	X
ejpam-5856	17	2	47	47	NUM
ejpam-5856	17	3	,	,	PUNCT
ejpam-5856	17	4	50	50	NUM
ejpam-5856	17	5	]	]	PUNCT
ejpam-5856	17	6	,	,	PUNCT
ejpam-5856	17	7	control	control	NOUN
ejpam-5856	17	8	systems	system	NOUN
ejpam-5856	17	9	[	[	X
ejpam-5856	17	10	8	8	NUM
ejpam-5856	17	11	,	,	PUNCT
ejpam-5856	17	12	28	28	NUM
ejpam-5856	17	13	]	]	PUNCT
ejpam-5856	17	14	,	,	PUNCT
ejpam-5856	17	15	decision	decision	NOUN
ejpam-5856	17	16	-	-	PUNCT
ejpam-5856	17	17	making	making	NOUN
ejpam-5856	17	18	[	[	X
ejpam-5856	17	19	17	17	NUM
ejpam-5856	17	20	,	,	PUNCT
ejpam-5856	17	21	23	23	NUM
ejpam-5856	17	22	]	]	PUNCT
ejpam-5856	17	23	,	,	PUNCT
ejpam-5856	17	24	image	image	NOUN
ejpam-5856	17	25	processing	processing	NOUN
ejpam-5856	17	26	[	[	X
ejpam-5856	17	27	1	1	NUM
ejpam-5856	17	28	,	,	PUNCT
ejpam-5856	17	29	46	46	NUM
ejpam-5856	17	30	]	]	PUNCT
ejpam-5856	17	31	,	,	PUNCT
ejpam-5856	17	32	classifications	classification	NOUN
ejpam-5856	17	33	[	[	X
ejpam-5856	17	34	22	22	NUM
ejpam-5856	17	35	,	,	PUNCT
ejpam-5856	17	36	24	24	NUM
ejpam-5856	17	37	]	]	PUNCT
ejpam-5856	17	38	,	,	PUNCT
ejpam-5856	17	39	etc	etc	X
ejpam-5856	17	40	.	.	X
ejpam-5856	18	1	chang	chang	PROPN
ejpam-5856	19	1	[	[	X
ejpam-5856	19	2	16	16	NUM
ejpam-5856	19	3	]	]	X
ejpam-5856	19	4	,	,	PUNCT
ejpam-5856	19	5	in	in	ADP
ejpam-5856	19	6	1968	1968	NUM
ejpam-5856	19	7	,	,	PUNCT
ejpam-5856	19	8	defined	define	VERB
ejpam-5856	19	9	the	the	DET
ejpam-5856	19	10	fuzzy	fuzzy	ADJ
ejpam-5856	19	11	topology	topology	NOUN
ejpam-5856	19	12	(	(	PUNCT
ejpam-5856	19	13	ft	ft	NOUN
ejpam-5856	19	14	)	)	PUNCT
ejpam-5856	19	15	,	,	PUNCT
ejpam-5856	19	16	allowing	allow	VERB
ejpam-5856	19	17	the	the	DET
ejpam-5856	19	18	study	study	NOUN
ejpam-5856	19	19	of	of	ADP
ejpam-5856	19	20	topological	topological	ADJ
ejpam-5856	19	21	properties	property	NOUN
ejpam-5856	19	22	within	within	ADP
ejpam-5856	19	23	the	the	DET
ejpam-5856	19	24	frame	frame	NOUN
ejpam-5856	19	25	of	of	ADP
ejpam-5856	19	26	f	f	PROPN
ejpam-5856	19	27	-sets	-set	NOUN
ejpam-5856	19	28	.	.	PUNCT
ejpam-5856	20	1	this	this	DET
ejpam-5856	20	2	development	development	NOUN
ejpam-5856	20	3	has	have	AUX
ejpam-5856	20	4	led	lead	VERB
ejpam-5856	20	5	to	to	ADP
ejpam-5856	20	6	the	the	DET
ejpam-5856	20	7	expansion	expansion	NOUN
ejpam-5856	20	8	and	and	CCONJ
ejpam-5856	20	9	investigation	investigation	NOUN
ejpam-5856	20	10	of	of	ADP
ejpam-5856	20	11	many	many	ADJ
ejpam-5856	20	12	classical	classical	ADJ
ejpam-5856	20	13	topological	topological	ADJ
ejpam-5856	20	14	notions	notion	NOUN
ejpam-5856	20	15	in	in	ADP
ejpam-5856	20	16	the	the	DET
ejpam-5856	20	17	context	context	NOUN
ejpam-5856	20	18	of	of	ADP
ejpam-5856	20	19	ft	ft	NOUN
ejpam-5856	21	1	[	[	X
ejpam-5856	21	2	2	2	NUM
ejpam-5856	21	3	,	,	PUNCT
ejpam-5856	21	4	7	7	NUM
ejpam-5856	21	5	,	,	PUNCT
ejpam-5856	21	6	9	9	NUM
ejpam-5856	21	7	,	,	PUNCT
ejpam-5856	21	8	10	10	NUM
ejpam-5856	21	9	,	,	PUNCT
ejpam-5856	21	10	42	42	NUM
ejpam-5856	21	11	]	]	PUNCT
ejpam-5856	21	12	,	,	PUNCT
ejpam-5856	21	13	providing	provide	VERB
ejpam-5856	21	14	more	more	ADV
ejpam-5856	21	15	accurate	accurate	ADJ
ejpam-5856	21	16	and	and	CCONJ
ejpam-5856	21	17	flexible	flexible	ADJ
ejpam-5856	21	18	models	model	NOUN
ejpam-5856	21	19	to	to	PART
ejpam-5856	21	20	address	address	VERB
ejpam-5856	21	21	problems	problem	NOUN
ejpam-5856	21	22	of	of	ADP
ejpam-5856	21	23	uncertainty	uncertainty	NOUN
ejpam-5856	21	24	in	in	ADP
ejpam-5856	21	25	various	various	ADJ
ejpam-5856	21	26	real	real	ADJ
ejpam-5856	21	27	life	life	NOUN
ejpam-5856	21	28	ears	ear	NOUN
ejpam-5856	21	29	.	.	PUNCT
ejpam-5856	22	1	moreover	moreover	ADV
ejpam-5856	22	2	,	,	PUNCT
ejpam-5856	22	3	the	the	DET
ejpam-5856	22	4	hybridization	hybridization	NOUN
ejpam-5856	22	5	of	of	ADP
ejpam-5856	22	6	fuzzy	fuzzy	ADJ
ejpam-5856	22	7	topology	topology	NOUN
ejpam-5856	22	8	with	with	ADP
ejpam-5856	22	9	soft	soft	ADJ
ejpam-5856	22	10	topology	topology	NOUN
ejpam-5856	22	11	was	be	AUX
ejpam-5856	22	12	introduced	introduce	VERB
ejpam-5856	22	13	and	and	CCONJ
ejpam-5856	22	14	studied	study	VERB
ejpam-5856	22	15	by	by	ADP
ejpam-5856	22	16	several	several	ADJ
ejpam-5856	22	17	authors	author	NOUN
ejpam-5856	22	18	[	[	X
ejpam-5856	22	19	41	41	NUM
ejpam-5856	22	20	,	,	PUNCT
ejpam-5856	22	21	43	43	NUM
ejpam-5856	22	22	,	,	PUNCT
ejpam-5856	22	23	44	44	NUM
ejpam-5856	22	24	]	]	PUNCT
ejpam-5856	22	25	.	.	PUNCT
ejpam-5856	23	1	generalized	generalize	VERB
ejpam-5856	23	2	closed	close	VERB
ejpam-5856	23	3	sets	set	NOUN
ejpam-5856	23	4	,	,	PUNCT
ejpam-5856	23	5	abbreviated	abbreviate	VERB
ejpam-5856	23	6	as	as	ADP
ejpam-5856	23	7	g	g	NOUN
ejpam-5856	23	8	-	-	PUNCT
ejpam-5856	23	9	closed	close	VERB
ejpam-5856	23	10	sets	set	NOUN
ejpam-5856	23	11	,	,	PUNCT
ejpam-5856	23	12	is	be	AUX
ejpam-5856	23	13	a	a	DET
ejpam-5856	23	14	fundamental	fundamental	ADJ
ejpam-5856	23	15	notion	notion	NOUN
ejpam-5856	23	16	in	in	ADP
ejpam-5856	23	17	both	both	DET
ejpam-5856	23	18	topology	topology	NOUN
ejpam-5856	23	19	and	and	CCONJ
ejpam-5856	23	20	ft	ft	NOUN
ejpam-5856	23	21	.	.	PUNCT
ejpam-5856	24	1	it	it	PRON
ejpam-5856	24	2	was	be	AUX
ejpam-5856	24	3	proposed	propose	VERB
ejpam-5856	24	4	in	in	ADP
ejpam-5856	24	5	general	general	ADJ
ejpam-5856	24	6	topology	topology	NOUN
ejpam-5856	24	7	by	by	ADP
ejpam-5856	24	8	levine	levine	PROPN
ejpam-5856	24	9	[	[	X
ejpam-5856	24	10	29	29	NUM
ejpam-5856	24	11	]	]	PUNCT
ejpam-5856	24	12	in	in	ADP
ejpam-5856	24	13	1970	1970	NUM
ejpam-5856	24	14	.	.	PUNCT
ejpam-5856	25	1	this	this	DET
ejpam-5856	25	2	notion	notion	NOUN
ejpam-5856	25	3	has	have	AUX
ejpam-5856	25	4	undergone	undergo	VERB
ejpam-5856	25	5	extensive	extensive	ADJ
ejpam-5856	25	6	study	study	NOUN
ejpam-5856	25	7	in	in	ADP
ejpam-5856	25	8	the	the	DET
ejpam-5856	25	9	fields	field	NOUN
ejpam-5856	25	10	of	of	ADP
ejpam-5856	25	11	topology	topology	NOUN
ejpam-5856	25	12	and	and	CCONJ
ejpam-5856	25	13	ft	ft	NOUN
ejpam-5856	25	14	by	by	ADP
ejpam-5856	25	15	numerous	numerous	ADJ
ejpam-5856	25	16	authors	author	NOUN
ejpam-5856	25	17	,	,	PUNCT
ejpam-5856	25	18	as	as	ADP
ejpam-5856	25	19	in	in	ADP
ejpam-5856	25	20	[	[	X
ejpam-5856	25	21	15	15	NUM
ejpam-5856	25	22	,	,	PUNCT
ejpam-5856	25	23	19	19	NUM
ejpam-5856	25	24	,	,	PUNCT
ejpam-5856	25	25	30	30	NUM
ejpam-5856	25	26	,	,	PUNCT
ejpam-5856	25	27	33	33	NUM
ejpam-5856	25	28	,	,	PUNCT
ejpam-5856	25	29	36	36	NUM
ejpam-5856	25	30	,	,	PUNCT
ejpam-5856	25	31	40	40	NUM
ejpam-5856	25	32	,	,	PUNCT
ejpam-5856	25	33	48	48	NUM
ejpam-5856	25	34	]	]	PUNCT
ejpam-5856	25	35	.	.	PUNCT
ejpam-5856	26	1	since	since	SCONJ
ejpam-5856	26	2	then	then	ADV
ejpam-5856	26	3	,	,	PUNCT
ejpam-5856	26	4	it	it	PRON
ejpam-5856	26	5	has	have	AUX
ejpam-5856	26	6	been	be	AUX
ejpam-5856	26	7	widely	widely	ADV
ejpam-5856	26	8	used	use	VERB
ejpam-5856	26	9	as	as	ADP
ejpam-5856	26	10	a	a	DET
ejpam-5856	26	11	powerful	powerful	ADJ
ejpam-5856	26	12	tool	tool	NOUN
ejpam-5856	26	13	to	to	PART
ejpam-5856	26	14	explore	explore	VERB
ejpam-5856	26	15	various	various	ADJ
ejpam-5856	26	16	concepts	concept	NOUN
ejpam-5856	26	17	,	,	PUNCT
ejpam-5856	26	18	including	include	VERB
ejpam-5856	26	19	g	g	NOUN
ejpam-5856	26	20	-	-	PUNCT
ejpam-5856	26	21	regular	regular	ADJ
ejpam-5856	26	22	and	and	CCONJ
ejpam-5856	26	23	g	g	NOUN
ejpam-5856	26	24	-	-	PUNCT
ejpam-5856	26	25	normal	normal	ADJ
ejpam-5856	26	26	spaces	space	NOUN
ejpam-5856	26	27	,	,	PUNCT
ejpam-5856	26	28	which	which	PRON
ejpam-5856	26	29	have	have	AUX
ejpam-5856	26	30	been	be	AUX
ejpam-5856	26	31	further	far	ADV
ejpam-5856	26	32	generalized	generalize	VERB
ejpam-5856	26	33	and	and	CCONJ
ejpam-5856	26	34	investigated	investigate	VERB
ejpam-5856	26	35	as	as	ADP
ejpam-5856	26	36	in	in	ADP
ejpam-5856	26	37	[	[	PUNCT
ejpam-5856	26	38	11	11	NUM
ejpam-5856	26	39	,	,	PUNCT
ejpam-5856	26	40	21	21	NUM
ejpam-5856	26	41	,	,	PUNCT
ejpam-5856	26	42	25	25	NUM
ejpam-5856	26	43	,	,	PUNCT
ejpam-5856	26	44	34	34	NUM
ejpam-5856	26	45	,	,	PUNCT
ejpam-5856	26	46	35	35	NUM
ejpam-5856	26	47	,	,	PUNCT
ejpam-5856	26	48	38	38	NUM
ejpam-5856	26	49	]	]	PUNCT
ejpam-5856	26	50	,	,	PUNCT
ejpam-5856	26	51	and	and	CCONJ
ejpam-5856	26	52	others	other	NOUN
ejpam-5856	26	53	.	.	PUNCT
ejpam-5856	27	1	these	these	DET
ejpam-5856	27	2	studies	study	NOUN
ejpam-5856	27	3	have	have	AUX
ejpam-5856	27	4	also	also	ADV
ejpam-5856	27	5	led	lead	VERB
ejpam-5856	27	6	to	to	ADP
ejpam-5856	27	7	the	the	DET
ejpam-5856	27	8	introduction	introduction	NOUN
ejpam-5856	27	9	of	of	ADP
ejpam-5856	27	10	new	new	ADJ
ejpam-5856	27	11	separation	separation	NOUN
ejpam-5856	27	12	axioms	axiom	NOUN
ejpam-5856	27	13	that	that	PRON
ejpam-5856	27	14	are	be	AUX
ejpam-5856	27	15	weaker	weak	ADJ
ejpam-5856	27	16	than	than	ADP
ejpam-5856	27	17	t1	t1	NOUN
ejpam-5856	27	18	.	.	PUNCT
ejpam-5856	28	1	in	in	ADP
ejpam-5856	28	2	the	the	DET
ejpam-5856	28	3	fuzzy	fuzzy	ADJ
ejpam-5856	28	4	context	context	NOUN
ejpam-5856	28	5	,	,	PUNCT
ejpam-5856	28	6	balasubramanian	balasubramanian	PROPN
ejpam-5856	28	7	et	et	PROPN
ejpam-5856	28	8	al	al	PROPN
ejpam-5856	28	9	[	[	X
ejpam-5856	28	10	12	12	NUM
ejpam-5856	28	11	]	]	PUNCT
ejpam-5856	28	12	proposed	propose	VERB
ejpam-5856	28	13	the	the	DET
ejpam-5856	28	14	notion	notion	NOUN
ejpam-5856	28	15	of	of	ADP
ejpam-5856	28	16	generalized	generalized	ADJ
ejpam-5856	28	17	fuzzy	fuzzy	ADJ
ejpam-5856	28	18	closed	close	VERB
ejpam-5856	28	19	sets	set	NOUN
ejpam-5856	28	20	in	in	ADP
ejpam-5856	28	21	1997	1997	NUM
ejpam-5856	28	22	,	,	PUNCT
ejpam-5856	28	23	sparking	spark	VERB
ejpam-5856	28	24	further	further	ADJ
ejpam-5856	28	25	research	research	NOUN
ejpam-5856	28	26	by	by	ADP
ejpam-5856	28	27	authors	author	NOUN
ejpam-5856	28	28	like	like	ADP
ejpam-5856	28	29	saraf	saraf	PROPN
ejpam-5856	28	30	et	et	PROPN
ejpam-5856	28	31	al	al	PROPN
ejpam-5856	28	32	.	.	PUNCT
ejpam-5856	29	1	[	[	X
ejpam-5856	29	2	45	45	NUM
ejpam-5856	29	3	]	]	PUNCT
ejpam-5856	29	4	and	and	CCONJ
ejpam-5856	29	5	park	park	NOUN
ejpam-5856	29	6	et	et	PROPN
ejpam-5856	29	7	al	al	PROPN
ejpam-5856	29	8	.	.	PUNCT
ejpam-5856	30	1	[	[	X
ejpam-5856	30	2	37	37	NUM
ejpam-5856	30	3	]	]	PUNCT
ejpam-5856	30	4	who	who	PRON
ejpam-5856	30	5	extensively	extensively	ADV
ejpam-5856	30	6	studied	study	VERB
ejpam-5856	30	7	different	different	ADJ
ejpam-5856	30	8	forms	form	NOUN
ejpam-5856	30	9	of	of	ADP
ejpam-5856	30	10	generalized	generalized	ADJ
ejpam-5856	30	11	fuzzy	fuzzy	ADJ
ejpam-5856	30	12	closed	close	VERB
ejpam-5856	30	13	sets	set	NOUN
ejpam-5856	30	14	.	.	PUNCT
ejpam-5856	31	1	on	on	ADP
ejpam-5856	31	2	the	the	DET
ejpam-5856	31	3	other	other	ADJ
ejpam-5856	31	4	hand	hand	NOUN
ejpam-5856	31	5	,	,	PUNCT
ejpam-5856	31	6	császár	császár	PROPN
ejpam-5856	32	1	[	[	X
ejpam-5856	32	2	20	20	NUM
ejpam-5856	32	3	]	]	PUNCT
ejpam-5856	32	4	introduced	introduce	VERB
ejpam-5856	32	5	the	the	DET
ejpam-5856	32	6	concept	concept	NOUN
ejpam-5856	32	7	of	of	ADP
ejpam-5856	32	8	generalized	generalized	ADJ
ejpam-5856	32	9	topology	topology	NOUN
ejpam-5856	32	10	(	(	PUNCT
ejpam-5856	32	11	or	or	CCONJ
ejpam-5856	32	12	gt	gt	PROPN
ejpam-5856	32	13	)	)	PUNCT
ejpam-5856	32	14	,	,	PUNCT
ejpam-5856	32	15	expanding	expand	VERB
ejpam-5856	32	16	the	the	DET
ejpam-5856	32	17	scope	scope	NOUN
ejpam-5856	32	18	of	of	ADP
ejpam-5856	32	19	general	general	ADJ
ejpam-5856	32	20	topology	topology	NOUN
ejpam-5856	32	21	.	.	PUNCT
ejpam-5856	33	1	over	over	ADP
ejpam-5856	33	2	time	time	NOUN
ejpam-5856	33	3	,	,	PUNCT
ejpam-5856	33	4	many	many	ADJ
ejpam-5856	33	5	researchers	researcher	NOUN
ejpam-5856	33	6	have	have	AUX
ejpam-5856	33	7	endeavored	endeavor	VERB
ejpam-5856	33	8	to	to	PART
ejpam-5856	33	9	extend	extend	VERB
ejpam-5856	33	10	the	the	DET
ejpam-5856	33	11	notion	notion	NOUN
ejpam-5856	33	12	of	of	ADP
ejpam-5856	33	13	g	g	NOUN
ejpam-5856	33	14	-	-	PUNCT
ejpam-5856	33	15	closed	close	VERB
ejpam-5856	33	16	sets	set	NOUN
ejpam-5856	33	17	to	to	ADP
ejpam-5856	33	18	the	the	DET
ejpam-5856	33	19	broader	broad	ADJ
ejpam-5856	33	20	framework	framework	NOUN
ejpam-5856	33	21	of	of	ADP
ejpam-5856	33	22	gt	gt	PROPN
ejpam-5856	33	23	.	.	PUNCT
ejpam-5856	34	1	maragathavalli	maragathavalli	PROPN
ejpam-5856	34	2	et	et	PROPN
ejpam-5856	34	3	al	al	PROPN
ejpam-5856	35	1	[	[	X
ejpam-5856	35	2	16	16	NUM
ejpam-5856	35	3	]	]	PUNCT
ejpam-5856	35	4	notably	notably	ADV
ejpam-5856	35	5	explored	explore	VERB
ejpam-5856	35	6	g	g	NOUN
ejpam-5856	35	7	-	-	PUNCT
ejpam-5856	35	8	closed	close	VERB
ejpam-5856	35	9	sets	set	NOUN
ejpam-5856	35	10	and	and	CCONJ
ejpam-5856	35	11	their	their	PRON
ejpam-5856	35	12	fundamental	fundamental	ADJ
ejpam-5856	35	13	properties	property	NOUN
ejpam-5856	35	14	within	within	ADP
ejpam-5856	35	15	gts	gts	NOUN
ejpam-5856	35	16	.	.	PUNCT
ejpam-5856	36	1	prior	prior	ADV
ejpam-5856	36	2	to	to	ADP
ejpam-5856	36	3	that	that	PRON
ejpam-5856	36	4	,	,	PUNCT
ejpam-5856	36	5	chetty	chetty	VERB
ejpam-5856	36	6	[	[	X
ejpam-5856	36	7	18	18	NUM
ejpam-5856	36	8	]	]	PUNCT
ejpam-5856	36	9	extended	extend	VERB
ejpam-5856	36	10	the	the	DET
ejpam-5856	36	11	concept	concept	NOUN
ejpam-5856	36	12	of	of	ADP
ejpam-5856	36	13	gt	gt	PROPN
ejpam-5856	36	14	into	into	ADP
ejpam-5856	36	15	a	a	DET
ejpam-5856	36	16	fuzzy	fuzzy	ADJ
ejpam-5856	36	17	environment	environment	NOUN
ejpam-5856	36	18	,	,	PUNCT
ejpam-5856	36	19	leading	lead	VERB
ejpam-5856	36	20	to	to	ADP
ejpam-5856	36	21	the	the	DET
ejpam-5856	36	22	development	development	NOUN
ejpam-5856	36	23	of	of	ADP
ejpam-5856	36	24	gft	gft	PROPN
ejpam-5856	36	25	.	.	PUNCT
ejpam-5856	37	1	mandal	mandal	PROPN
ejpam-5856	37	2	et	et	PROPN
ejpam-5856	37	3	al	al	PROPN
ejpam-5856	38	1	[	[	X
ejpam-5856	38	2	31	31	NUM
ejpam-5856	38	3	]	]	PUNCT
ejpam-5856	38	4	defined	define	VERB
ejpam-5856	38	5	the	the	DET
ejpam-5856	38	6	notion	notion	NOUN
ejpam-5856	38	7	of	of	ADP
ejpam-5856	38	8	fgµ-closed	fgµ-closed	ADJ
ejpam-5856	38	9	sets	set	NOUN
ejpam-5856	38	10	in	in	ADP
ejpam-5856	38	11	gfts	gft	NOUN
ejpam-5856	38	12	and	and	CCONJ
ejpam-5856	38	13	study	study	VERB
ejpam-5856	38	14	the	the	DET
ejpam-5856	38	15	concepts	concept	NOUN
ejpam-5856	38	16	of	of	ADP
ejpam-5856	38	17	fµ-regular	fµ-regular	ADJ
ejpam-5856	38	18	and	and	CCONJ
ejpam-5856	38	19	fµ-normal	fµ-normal	ADJ
ejpam-5856	38	20	in	in	ADP
ejpam-5856	38	21	gfts	gft	NOUN
ejpam-5856	38	22	.	.	PUNCT
ejpam-5856	39	1	furthermore	furthermore	ADV
ejpam-5856	39	2	,	,	PUNCT
ejpam-5856	39	3	chakraborty	chakraborty	PROPN
ejpam-5856	39	4	et	et	PROPN
ejpam-5856	39	5	al	al	PROPN
ejpam-5856	39	6	[	[	X
ejpam-5856	39	7	15	15	NUM
ejpam-5856	39	8	]	]	PUNCT
ejpam-5856	39	9	study	study	VERB
ejpam-5856	39	10	some	some	DET
ejpam-5856	39	11	properties	property	NOUN
ejpam-5856	39	12	of	of	ADP
ejpam-5856	39	13	fgµ-closed	fgµ-closed	ADJ
ejpam-5856	39	14	sets	set	NOUN
ejpam-5856	39	15	in	in	ADP
ejpam-5856	39	16	gfts	gft	NOUN
ejpam-5856	39	17	.	.	PUNCT
ejpam-5856	40	1	they	they	PRON
ejpam-5856	40	2	also	also	ADV
ejpam-5856	40	3	,	,	PUNCT
ejpam-5856	40	4	investigated	investigate	VERB
ejpam-5856	40	5	various	various	ADJ
ejpam-5856	40	6	concepts	concept	NOUN
ejpam-5856	40	7	within	within	ADP
ejpam-5856	40	8	gfts	gft	NOUN
ejpam-5856	40	9	as	as	ADP
ejpam-5856	40	10	in	in	ADP
ejpam-5856	40	11	[	[	X
ejpam-5856	40	12	13	13	NUM
ejpam-5856	40	13	,	,	PUNCT
ejpam-5856	40	14	14	14	NUM
ejpam-5856	40	15	]	]	PUNCT
ejpam-5856	40	16	.	.	PUNCT
ejpam-5856	41	1	however	however	ADV
ejpam-5856	41	2	,	,	PUNCT
ejpam-5856	41	3	there	there	PRON
ejpam-5856	41	4	are	be	VERB
ejpam-5856	41	5	many	many	ADJ
ejpam-5856	41	6	research	research	NOUN
ejpam-5856	41	7	gaps	gap	NOUN
ejpam-5856	41	8	and	and	CCONJ
ejpam-5856	41	9	further	further	ADJ
ejpam-5856	41	10	developments	development	NOUN
ejpam-5856	41	11	that	that	PRON
ejpam-5856	41	12	have	have	AUX
ejpam-5856	41	13	not	not	PART
ejpam-5856	41	14	yet	yet	ADV
ejpam-5856	41	15	been	be	AUX
ejpam-5856	41	16	achieved	achieve	VERB
ejpam-5856	41	17	in	in	ADP
ejpam-5856	41	18	the	the	DET
ejpam-5856	41	19	context	context	NOUN
ejpam-5856	41	20	of	of	ADP
ejpam-5856	41	21	gft	gft	PROPN
ejpam-5856	41	22	.	.	PUNCT
ejpam-5856	42	1	this	this	DET
ejpam-5856	42	2	article	article	NOUN
ejpam-5856	42	3	aims	aim	VERB
ejpam-5856	42	4	to	to	PART
ejpam-5856	42	5	contribute	contribute	VERB
ejpam-5856	42	6	to	to	ADP
ejpam-5856	42	7	developing	develop	VERB
ejpam-5856	42	8	the	the	DET
ejpam-5856	42	9	theoretical	theoretical	ADJ
ejpam-5856	42	10	foundation	foundation	NOUN
ejpam-5856	42	11	for	for	ADP
ejpam-5856	42	12	gft	gft	PROPN
ejpam-5856	42	13	by	by	ADP
ejpam-5856	42	14	introducing	introduce	VERB
ejpam-5856	42	15	and	and	CCONJ
ejpam-5856	42	16	analyzing	analyze	VERB
ejpam-5856	42	17	novel	novel	ADJ
ejpam-5856	42	18	categories	category	NOUN
ejpam-5856	42	19	of	of	ADP
ejpam-5856	42	20	spaces	space	NOUN
ejpam-5856	42	21	within	within	ADP
ejpam-5856	42	22	the	the	DET
ejpam-5856	42	23	framework	framework	NOUN
ejpam-5856	42	24	of	of	ADP
ejpam-5856	42	25	gft	gft	PROPN
ejpam-5856	42	26	via	via	ADP
ejpam-5856	42	27	fgµ-closed	fgµ-closed	ADJ
ejpam-5856	42	28	sets	set	NOUN
ejpam-5856	42	29	.	.	PUNCT
ejpam-5856	43	1	after	after	ADP
ejpam-5856	43	2	introductory	introductory	ADJ
ejpam-5856	43	3	section	section	NOUN
ejpam-5856	43	4	,	,	PUNCT
ejpam-5856	43	5	the	the	DET
ejpam-5856	43	6	rest	rest	NOUN
ejpam-5856	43	7	of	of	ADP
ejpam-5856	43	8	the	the	DET
ejpam-5856	43	9	article	article	NOUN
ejpam-5856	43	10	is	be	AUX
ejpam-5856	43	11	systematized	systematize	VERB
ejpam-5856	43	12	as	as	SCONJ
ejpam-5856	43	13	follows	follow	VERB
ejpam-5856	43	14	:	:	PUNCT
ejpam-5856	43	15	•	•	NOUN
ejpam-5856	43	16	in	in	ADP
ejpam-5856	43	17	section	section	NOUN
ejpam-5856	43	18	2	2	NUM
ejpam-5856	43	19	.	.	PUNCT
ejpam-5856	44	1	we	we	PRON
ejpam-5856	44	2	have	have	AUX
ejpam-5856	44	3	review	review	VERB
ejpam-5856	44	4	some	some	DET
ejpam-5856	44	5	fundamental	fundamental	ADJ
ejpam-5856	44	6	definitions	definition	NOUN
ejpam-5856	44	7	and	and	CCONJ
ejpam-5856	44	8	findings	finding	NOUN
ejpam-5856	44	9	that	that	PRON
ejpam-5856	44	10	will	will	AUX
ejpam-5856	44	11	be	be	AUX
ejpam-5856	44	12	utilized	utilize	VERB
ejpam-5856	44	13	throughout	throughout	ADP
ejpam-5856	44	14	this	this	DET
ejpam-5856	44	15	article	article	NOUN
ejpam-5856	44	16	.	.	PUNCT
ejpam-5856	45	1	•	•	NUM
ejpam-5856	45	2	in	in	ADP
ejpam-5856	45	3	section	section	NOUN
ejpam-5856	45	4	3	3	NUM
ejpam-5856	45	5	.	.	PUNCT
ejpam-5856	46	1	we	we	PRON
ejpam-5856	46	2	apply	apply	VERB
ejpam-5856	46	3	the	the	DET
ejpam-5856	46	4	notion	notion	NOUN
ejpam-5856	46	5	of	of	ADP
ejpam-5856	46	6	fgµ-closed	fgµ-closed	ADJ
ejpam-5856	46	7	sets	set	NOUN
ejpam-5856	46	8	to	to	PART
ejpam-5856	46	9	introduce	introduce	VERB
ejpam-5856	46	10	and	and	CCONJ
ejpam-5856	46	11	discuss	discuss	VERB
ejpam-5856	46	12	novel	novel	ADJ
ejpam-5856	46	13	categories	category	NOUN
ejpam-5856	46	14	of	of	ADP
ejpam-5856	46	15	spaces	space	NOUN
ejpam-5856	46	16	such	such	ADJ
ejpam-5856	46	17	as	as	ADP
ejpam-5856	46	18	fgµ-regular	fgµ-regular	ADJ
ejpam-5856	46	19	,	,	PUNCT
ejpam-5856	46	20	fµ-g3	fµ-g3	NOUN
ejpam-5856	46	21	,	,	PUNCT
ejpam-5856	46	22	fµ-t	fµ-t	PROPN
ejpam-5856	46	23	1	1	NUM
ejpam-5856	46	24	2	2	NUM
ejpam-5856	46	25	,	,	PUNCT
ejpam-5856	46	26	fµ-t2	fµ-t2	NOUN
ejpam-5856	46	27	1	1	NUM
ejpam-5856	46	28	2	2	NUM
ejpam-5856	46	29	,	,	PUNCT
ejpam-5856	46	30	and	and	CCONJ
ejpam-5856	46	31	fµ-symmetric	fµ-symmetric	ADJ
ejpam-5856	46	32	s.	s.	PROPN
ejpam-5856	46	33	saleh	saleh	PROPN
ejpam-5856	46	34	et	et	PROPN
ejpam-5856	47	1	al	al	PROPN
ejpam-5856	47	2	.	.	PUNCT
ejpam-5856	47	3	/	/	SYM
ejpam-5856	47	4	eur	eur	PROPN
ejpam-5856	47	5	.	.	PUNCT
ejpam-5856	48	1	j.	j.	PROPN
ejpam-5856	48	2	pure	pure	PROPN
ejpam-5856	48	3	appl	appl	PROPN
ejpam-5856	48	4	.	.	PROPN
ejpam-5856	48	5	math	math	PROPN
ejpam-5856	48	6	,	,	PUNCT
ejpam-5856	48	7	18	18	NUM
ejpam-5856	48	8	(	(	PUNCT
ejpam-5856	48	9	1	1	NUM
ejpam-5856	48	10	)	)	PUNCT
ejpam-5856	48	11	(	(	PUNCT
ejpam-5856	48	12	2025	2025	NUM
ejpam-5856	48	13	)	)	PUNCT
ejpam-5856	48	14	,	,	PUNCT
ejpam-5856	48	15	5856	5856	NUM
ejpam-5856	48	16	3	3	NUM
ejpam-5856	48	17	of	of	ADP
ejpam-5856	48	18	15	15	NUM
ejpam-5856	48	19	spaces	space	NOUN
ejpam-5856	48	20	in	in	ADP
ejpam-5856	48	21	the	the	DET
ejpam-5856	48	22	context	context	NOUN
ejpam-5856	48	23	of	of	ADP
ejpam-5856	48	24	gft	gft	PROPN
ejpam-5856	48	25	.	.	PUNCT
ejpam-5856	49	1	we	we	PRON
ejpam-5856	49	2	analyze	analyze	VERB
ejpam-5856	49	3	their	their	PRON
ejpam-5856	49	4	basic	basic	ADJ
ejpam-5856	49	5	characteristics	characteristic	NOUN
ejpam-5856	49	6	and	and	CCONJ
ejpam-5856	49	7	properties	property	NOUN
ejpam-5856	49	8	.	.	PUNCT
ejpam-5856	50	1	some	some	DET
ejpam-5856	50	2	related	relate	VERB
ejpam-5856	50	3	theorems	theorem	NOUN
ejpam-5856	50	4	,	,	PUNCT
ejpam-5856	50	5	relations	relation	NOUN
ejpam-5856	50	6	,	,	PUNCT
ejpam-5856	50	7	and	and	CCONJ
ejpam-5856	50	8	implications	implication	NOUN
ejpam-5856	50	9	are	be	AUX
ejpam-5856	50	10	discussed	discuss	VERB
ejpam-5856	50	11	.	.	PUNCT
ejpam-5856	51	1	•	•	NUM
ejpam-5856	51	2	in	in	ADP
ejpam-5856	51	3	section	section	NOUN
ejpam-5856	51	4	4	4	NUM
ejpam-5856	51	5	.	.	PUNCT
ejpam-5856	52	1	we	we	PRON
ejpam-5856	52	2	introduce	introduce	VERB
ejpam-5856	52	3	new	new	ADJ
ejpam-5856	52	4	classes	class	NOUN
ejpam-5856	52	5	of	of	ADP
ejpam-5856	52	6	spaces	space	NOUN
ejpam-5856	52	7	named	name	VERB
ejpam-5856	52	8	,	,	PUNCT
ejpam-5856	52	9	fgµ-normal	fgµ-normal	ADJ
ejpam-5856	52	10	and	and	CCONJ
ejpam-5856	52	11	fµ-g4	fµ-g4	NOUN
ejpam-5856	52	12	spaces	space	NOUN
ejpam-5856	52	13	in	in	ADP
ejpam-5856	52	14	gft	gft	PROPN
ejpam-5856	52	15	via	via	ADP
ejpam-5856	52	16	fgµ-closed	fgµ-closed	ADJ
ejpam-5856	52	17	sets	set	NOUN
ejpam-5856	52	18	.	.	PUNCT
ejpam-5856	53	1	we	we	PRON
ejpam-5856	53	2	investigate	investigate	VERB
ejpam-5856	53	3	some	some	DET
ejpam-5856	53	4	properties	property	NOUN
ejpam-5856	53	5	,	,	PUNCT
ejpam-5856	53	6	related	related	ADJ
ejpam-5856	53	7	theorems	theorem	NOUN
ejpam-5856	53	8	,	,	PUNCT
ejpam-5856	53	9	implications	implication	NOUN
ejpam-5856	53	10	,	,	PUNCT
ejpam-5856	53	11	and	and	CCONJ
ejpam-5856	53	12	results	result	NOUN
ejpam-5856	53	13	in	in	ADP
ejpam-5856	53	14	this	this	DET
ejpam-5856	53	15	sequel	sequel	NOUN
ejpam-5856	53	16	.	.	PUNCT
ejpam-5856	54	1	we	we	PRON
ejpam-5856	54	2	explore	explore	VERB
ejpam-5856	54	3	the	the	DET
ejpam-5856	54	4	interrelationships	interrelationship	NOUN
ejpam-5856	54	5	between	between	ADP
ejpam-5856	54	6	these	these	DET
ejpam-5856	54	7	classes	class	NOUN
ejpam-5856	54	8	and	and	CCONJ
ejpam-5856	54	9	the	the	DET
ejpam-5856	54	10	other	other	ADJ
ejpam-5856	54	11	separation	separation	NOUN
ejpam-5856	54	12	axioms	axiom	VERB
ejpam-5856	54	13	with	with	ADP
ejpam-5856	54	14	some	some	DET
ejpam-5856	54	15	supporting	support	VERB
ejpam-5856	54	16	examples	example	NOUN
ejpam-5856	54	17	.	.	PUNCT
ejpam-5856	55	1	•	•	NOUN
ejpam-5856	55	2	in	in	ADP
ejpam-5856	55	3	section	section	NOUN
ejpam-5856	55	4	5	5	NUM
ejpam-5856	55	5	.	.	PUNCT
ejpam-5856	56	1	the	the	DET
ejpam-5856	56	2	connections	connection	NOUN
ejpam-5856	56	3	of	of	ADP
ejpam-5856	56	4	fgµ-regular	fgµ-regular	ADJ
ejpam-5856	56	5	(	(	PUNCT
ejpam-5856	56	6	fgµ-normal	fgµ-normal	ADJ
ejpam-5856	56	7	)	)	PUNCT
ejpam-5856	56	8	spaces	space	NOUN
ejpam-5856	56	9	and	and	CCONJ
ejpam-5856	56	10	that	that	SCONJ
ejpam-5856	56	11	in	in	ADP
ejpam-5856	56	12	the	the	DET
ejpam-5856	56	13	crisp	crisp	ADJ
ejpam-5856	56	14	gt	gt	PROPN
ejpam-5856	56	15	are	be	AUX
ejpam-5856	56	16	presented	present	VERB
ejpam-5856	56	17	.	.	PUNCT
ejpam-5856	57	1	moreover	moreover	ADV
ejpam-5856	57	2	,	,	PUNCT
ejpam-5856	57	3	we	we	PRON
ejpam-5856	57	4	have	have	AUX
ejpam-5856	57	5	explore	explore	VERB
ejpam-5856	57	6	the	the	DET
ejpam-5856	57	7	basic	basic	ADJ
ejpam-5856	57	8	preservation	preservation	NOUN
ejpam-5856	57	9	theorems	theorem	NOUN
ejpam-5856	57	10	and	and	CCONJ
ejpam-5856	57	11	discuss	discuss	VERB
ejpam-5856	57	12	the	the	DET
ejpam-5856	57	13	hereditary	hereditary	ADJ
ejpam-5856	57	14	and	and	CCONJ
ejpam-5856	57	15	topological	topological	ADJ
ejpam-5856	57	16	property	property	NOUN
ejpam-5856	57	17	of	of	ADP
ejpam-5856	57	18	these	these	DET
ejpam-5856	57	19	classes	class	NOUN
ejpam-5856	57	20	.	.	PUNCT
ejpam-5856	58	1	•	•	NUM
ejpam-5856	58	2	in	in	ADP
ejpam-5856	58	3	section	section	NOUN
ejpam-5856	58	4	6	6	NUM
ejpam-5856	58	5	.	.	PUNCT
ejpam-5856	59	1	conclusion	conclusion	NOUN
ejpam-5856	59	2	and	and	CCONJ
ejpam-5856	59	3	future	future	ADJ
ejpam-5856	59	4	works	work	NOUN
ejpam-5856	60	1	,	,	PUNCT
ejpam-5856	60	2	we	we	PRON
ejpam-5856	60	3	outline	outline	VERB
ejpam-5856	60	4	the	the	DET
ejpam-5856	60	5	article	article	NOUN
ejpam-5856	60	6	’s	’s	PART
ejpam-5856	60	7	contributions	contribution	NOUN
ejpam-5856	60	8	and	and	CCONJ
ejpam-5856	60	9	suggest	suggest	VERB
ejpam-5856	60	10	some	some	DET
ejpam-5856	60	11	points	point	NOUN
ejpam-5856	60	12	to	to	PART
ejpam-5856	60	13	open	open	VERB
ejpam-5856	60	14	up	up	ADP
ejpam-5856	60	15	new	new	ADJ
ejpam-5856	60	16	avenues	avenue	NOUN
ejpam-5856	60	17	for	for	ADP
ejpam-5856	60	18	further	further	ADJ
ejpam-5856	60	19	research	research	NOUN
ejpam-5856	60	20	in	in	ADP
ejpam-5856	60	21	this	this	DET
ejpam-5856	60	22	area	area	NOUN
ejpam-5856	60	23	.	.	PUNCT
ejpam-5856	61	1	2	2	X
ejpam-5856	61	2	.	.	X
ejpam-5856	61	3	basic	basic	ADJ
ejpam-5856	61	4	definitions	definition	NOUN
ejpam-5856	61	5	and	and	CCONJ
ejpam-5856	61	6	results	result	NOUN
ejpam-5856	61	7	in	in	ADP
ejpam-5856	61	8	this	this	DET
ejpam-5856	61	9	document	document	NOUN
ejpam-5856	61	10	,	,	PUNCT
ejpam-5856	61	11	u	u	NOUN
ejpam-5856	61	12	refers	refer	VERB
ejpam-5856	61	13	to	to	ADP
ejpam-5856	61	14	a	a	DET
ejpam-5856	61	15	universe	universe	NOUN
ejpam-5856	61	16	set	set	NOUN
ejpam-5856	61	17	,	,	PUNCT
ejpam-5856	61	18	iu	iu	ADP
ejpam-5856	61	19	(	(	PUNCT
ejpam-5856	61	20	i	i	NOUN
ejpam-5856	61	21	=	=	PUNCT
ejpam-5856	62	1	[	[	X
ejpam-5856	62	2	0	0	NUM
ejpam-5856	62	3	,	,	PUNCT
ejpam-5856	62	4	1	1	NUM
ejpam-5856	62	5	]	]	PUNCT
ejpam-5856	62	6	)	)	PUNCT
ejpam-5856	62	7	is	be	AUX
ejpam-5856	62	8	the	the	DET
ejpam-5856	62	9	class	class	NOUN
ejpam-5856	62	10	of	of	ADP
ejpam-5856	62	11	all	all	DET
ejpam-5856	62	12	f	f	PROPN
ejpam-5856	62	13	-sets	-set	NOUN
ejpam-5856	62	14	on	on	ADP
ejpam-5856	62	15	u	u	NOUN
ejpam-5856	62	16	,	,	PUNCT
ejpam-5856	62	17	(	(	PUNCT
ejpam-5856	62	18	u	u	NOUN
ejpam-5856	62	19	,	,	PUNCT
ejpam-5856	62	20	τ	τ	PROPN
ejpam-5856	62	21	)	)	PUNCT
ejpam-5856	62	22	means	mean	VERB
ejpam-5856	62	23	fts	fts	PROPN
ejpam-5856	62	24	,	,	PUNCT
ejpam-5856	62	25	and	and	CCONJ
ejpam-5856	62	26	(	(	PUNCT
ejpam-5856	62	27	u	u	NOUN
ejpam-5856	62	28	,	,	PUNCT
ejpam-5856	62	29	µ	µ	NOUN
ejpam-5856	62	30	)	)	PUNCT
ejpam-5856	62	31	means	mean	VERB
ejpam-5856	62	32	gfts	gft	NOUN
ejpam-5856	62	33	.	.	PUNCT
ejpam-5856	63	1	in	in	ADP
ejpam-5856	63	2	the	the	DET
ejpam-5856	63	3	following	following	NOUN
ejpam-5856	63	4	,	,	PUNCT
ejpam-5856	63	5	let	let	VERB
ejpam-5856	63	6	’s	’s	PRON
ejpam-5856	63	7	review	review	VERB
ejpam-5856	63	8	a	a	DET
ejpam-5856	63	9	few	few	ADJ
ejpam-5856	63	10	fundamental	fundamental	ADJ
ejpam-5856	63	11	definitions	definition	NOUN
ejpam-5856	63	12	and	and	CCONJ
ejpam-5856	63	13	findings	finding	NOUN
ejpam-5856	63	14	that	that	PRON
ejpam-5856	63	15	will	will	AUX
ejpam-5856	63	16	be	be	AUX
ejpam-5856	63	17	utilized	utilize	VERB
ejpam-5856	63	18	throughout	throughout	ADP
ejpam-5856	63	19	the	the	DET
ejpam-5856	63	20	rest	rest	NOUN
ejpam-5856	63	21	of	of	ADP
ejpam-5856	63	22	this	this	DET
ejpam-5856	63	23	study	study	NOUN
ejpam-5856	63	24	.	.	PUNCT
ejpam-5856	64	1	definition	definition	NOUN
ejpam-5856	64	2	1	1	NUM
ejpam-5856	64	3	.	.	PUNCT
ejpam-5856	65	1	[	[	X
ejpam-5856	65	2	49	49	NUM
ejpam-5856	65	3	]	]	PUNCT
ejpam-5856	65	4	a	a	DET
ejpam-5856	65	5	fuzzy	fuzzy	ADJ
ejpam-5856	65	6	set	set	NOUN
ejpam-5856	65	7	(	(	PUNCT
ejpam-5856	65	8	or	or	CCONJ
ejpam-5856	65	9	f	f	PROPN
ejpam-5856	65	10	-set	-set	NUM
ejpam-5856	65	11	)	)	PUNCT
ejpam-5856	65	12	h	h	NOUN
ejpam-5856	65	13	in	in	ADP
ejpam-5856	65	14	u	u	PROPN
ejpam-5856	65	15	is	be	AUX
ejpam-5856	65	16	a	a	DET
ejpam-5856	65	17	map	map	NOUN
ejpam-5856	65	18	h	h	NOUN
ejpam-5856	65	19	:	:	PUNCT
ejpam-5856	65	20	u	u	NOUN
ejpam-5856	65	21	−→	−→	ADJ
ejpam-5856	65	22	i.	i.	NOUN
ejpam-5856	66	1	it	it	PRON
ejpam-5856	66	2	can	can	AUX
ejpam-5856	66	3	be	be	AUX
ejpam-5856	66	4	written	write	VERB
ejpam-5856	66	5	as	as	ADP
ejpam-5856	66	6	h	h	NOUN
ejpam-5856	66	7	=	=	PRON
ejpam-5856	66	8	{	{	PUNCT
ejpam-5856	66	9	(	(	PUNCT
ejpam-5856	66	10	u	u	NOUN
ejpam-5856	66	11	,	,	PUNCT
ejpam-5856	66	12	h(u	h(u	PROPN
ejpam-5856	66	13	)	)	PUNCT
ejpam-5856	66	14	)	)	PUNCT
ejpam-5856	66	15	:	:	PUNCT
ejpam-5856	67	1	u	u	PROPN
ejpam-5856	67	2	∈	∈	PROPN
ejpam-5856	67	3	u	u	PROPN
ejpam-5856	67	4	,	,	PUNCT
ejpam-5856	67	5	h(u	h(u	PROPN
ejpam-5856	67	6	)	)	PUNCT
ejpam-5856	67	7	∈	∈	PROPN
ejpam-5856	67	8	i	i	PRON
ejpam-5856	67	9	}	}	PUNCT
ejpam-5856	67	10	.	.	PUNCT
ejpam-5856	68	1	the	the	DET
ejpam-5856	68	2	fuzzy	fuzzy	ADJ
ejpam-5856	68	3	point	point	NOUN
ejpam-5856	68	4	(	(	PUNCT
ejpam-5856	68	5	or	or	CCONJ
ejpam-5856	68	6	f	f	PROPN
ejpam-5856	68	7	-point	-point	PROPN
ejpam-5856	68	8	)	)	PUNCT
ejpam-5856	68	9	uα	uα	PROPN
ejpam-5856	68	10	is	be	AUX
ejpam-5856	68	11	an	an	DET
ejpam-5856	68	12	f	f	X
ejpam-5856	68	13	-set	-set	PUNCT
ejpam-5856	68	14	such	such	ADJ
ejpam-5856	68	15	that	that	SCONJ
ejpam-5856	68	16	uα	uα	PROPN
ejpam-5856	68	17	(	(	PUNCT
ejpam-5856	68	18	v	v	NOUN
ejpam-5856	68	19	)	)	PUNCT
ejpam-5856	68	20	=	=	PUNCT
ejpam-5856	68	21	α	α	PROPN
ejpam-5856	68	22	>	>	X
ejpam-5856	68	23	0	0	PUNCT
ejpam-5856	69	1	if	if	SCONJ
ejpam-5856	69	2	u	u	PROPN
ejpam-5856	69	3	=	=	SYM
ejpam-5856	69	4	v	v	PROPN
ejpam-5856	69	5	and	and	CCONJ
ejpam-5856	69	6	uα	uα	PROPN
ejpam-5856	69	7	(	(	PUNCT
ejpam-5856	69	8	v	v	NOUN
ejpam-5856	69	9	)	)	PUNCT
ejpam-5856	69	10	=	=	SYM
ejpam-5856	69	11	0	0	PUNCT
ejpam-5856	69	12	if	if	SCONJ
ejpam-5856	69	13	u	u	PROPN
ejpam-5856	69	14	̸=	̸=	PROPN
ejpam-5856	69	15	v	v	NOUN
ejpam-5856	69	16	for	for	ADP
ejpam-5856	69	17	all	all	DET
ejpam-5856	69	18	v	v	ADP
ejpam-5856	69	19	∈	∈	PROPN
ejpam-5856	69	20	u	u	NOUN
ejpam-5856	69	21	.	.	PUNCT
ejpam-5856	70	1	uα	uα	PROPN
ejpam-5856	70	2	∈	∈	PROPN
ejpam-5856	70	3	h	h	NOUN
ejpam-5856	70	4	if	if	SCONJ
ejpam-5856	70	5	α	α	NOUN
ejpam-5856	70	6	≤	≤	PROPN
ejpam-5856	70	7	h(u	h(u	PROPN
ejpam-5856	70	8	)	)	PUNCT
ejpam-5856	70	9	.	.	PUNCT
ejpam-5856	71	1	fp	fp	X
ejpam-5856	71	2	(	(	PUNCT
ejpam-5856	71	3	u	u	NOUN
ejpam-5856	71	4	)	)	PUNCT
ejpam-5856	71	5	refers	refer	VERB
ejpam-5856	71	6	to	to	ADP
ejpam-5856	71	7	the	the	DET
ejpam-5856	71	8	family	family	NOUN
ejpam-5856	71	9	of	of	ADP
ejpam-5856	71	10	all	all	DET
ejpam-5856	71	11	f	f	PROPN
ejpam-5856	71	12	-points	-point	NOUN
ejpam-5856	71	13	in	in	ADP
ejpam-5856	71	14	u	u	NOUN
ejpam-5856	71	15	.	.	PUNCT
ejpam-5856	72	1	the	the	DET
ejpam-5856	72	2	constant	constant	ADJ
ejpam-5856	72	3	f	f	PROPN
ejpam-5856	72	4	-sets	-set	NOUN
ejpam-5856	72	5	0	0	NUM
ejpam-5856	72	6	and	and	CCONJ
ejpam-5856	72	7	1	1	NUM
ejpam-5856	72	8	are	be	AUX
ejpam-5856	72	9	given	give	VERB
ejpam-5856	72	10	by	by	ADP
ejpam-5856	72	11	0(u	0(u	NUM
ejpam-5856	72	12	)	)	PUNCT
ejpam-5856	73	1	=	=	SYM
ejpam-5856	73	2	0	0	NUM
ejpam-5856	73	3	and	and	CCONJ
ejpam-5856	73	4	1	1	NUM
ejpam-5856	73	5	(	(	PUNCT
ejpam-5856	73	6	u	u	NOUN
ejpam-5856	73	7	)	)	PUNCT
ejpam-5856	73	8	=	=	SYM
ejpam-5856	73	9	1	1	NUM
ejpam-5856	73	10	for	for	ADP
ejpam-5856	73	11	any	any	DET
ejpam-5856	73	12	u	u	PROPN
ejpam-5856	73	13	∈	∈	PROPN
ejpam-5856	73	14	u	u	NOUN
ejpam-5856	73	15	.	.	PUNCT
ejpam-5856	74	1	for	for	ADP
ejpam-5856	74	2	h	h	NOUN
ejpam-5856	74	3	,	,	PUNCT
ejpam-5856	74	4	g	g	PROPN
ejpam-5856	74	5	∈	∈	PROPN
ejpam-5856	74	6	iu	iu	ADV
ejpam-5856	74	7	,	,	PUNCT
ejpam-5856	74	8	we	we	PRON
ejpam-5856	74	9	have	have	VERB
ejpam-5856	74	10	the	the	DET
ejpam-5856	74	11	following	follow	VERB
ejpam-5856	74	12	properties	property	NOUN
ejpam-5856	74	13	of	of	ADP
ejpam-5856	74	14	f	f	PROPN
ejpam-5856	74	15	-sets	-set	NOUN
ejpam-5856	74	16	(	(	PUNCT
ejpam-5856	74	17	see	see	VERB
ejpam-5856	74	18	[	[	X
ejpam-5856	74	19	16	16	NUM
ejpam-5856	74	20	,	,	PUNCT
ejpam-5856	74	21	39	39	NUM
ejpam-5856	74	22	,	,	PUNCT
ejpam-5856	74	23	49	49	NUM
ejpam-5856	74	24	]	]	PUNCT
ejpam-5856	74	25	):	):	PUNCT
ejpam-5856	74	26	(	(	PUNCT
ejpam-5856	74	27	i	i	NOUN
ejpam-5856	74	28	)	)	PUNCT
ejpam-5856	74	29	h	h	NOUN
ejpam-5856	74	30	∪g	∪g	PROPN
ejpam-5856	74	31	∈	∈	NOUN
ejpam-5856	74	32	iu	iu	SCONJ
ejpam-5856	74	33	given	give	VERB
ejpam-5856	74	34	by	by	ADP
ejpam-5856	74	35	(	(	PUNCT
ejpam-5856	74	36	h	h	NOUN
ejpam-5856	74	37	∨g)(u	∨g)(u	PROPN
ejpam-5856	74	38	)	)	PUNCT
ejpam-5856	74	39	=	=	SYM
ejpam-5856	74	40	max{h(u	max{h(u	PROPN
ejpam-5856	74	41	)	)	PUNCT
ejpam-5856	74	42	,	,	PUNCT
ejpam-5856	74	43	g(u	g(u	PROPN
ejpam-5856	74	44	)	)	PUNCT
ejpam-5856	74	45	}	}	PUNCT
ejpam-5856	74	46	for	for	ADP
ejpam-5856	74	47	every	every	DET
ejpam-5856	74	48	u	u	PROPN
ejpam-5856	74	49	∈	∈	PROPN
ejpam-5856	74	50	u	u	NOUN
ejpam-5856	74	51	.	.	PUNCT
ejpam-5856	75	1	(	(	PUNCT
ejpam-5856	75	2	ii	ii	NOUN
ejpam-5856	75	3	)	)	PUNCT
ejpam-5856	75	4	h	h	NOUN
ejpam-5856	75	5	∩g	∩g	PROPN
ejpam-5856	75	6	∈	∈	PROPN
ejpam-5856	75	7	iu	iu	SCONJ
ejpam-5856	75	8	given	give	VERB
ejpam-5856	75	9	by	by	ADP
ejpam-5856	75	10	(	(	PUNCT
ejpam-5856	75	11	h	h	NOUN
ejpam-5856	75	12	∧g)(u	∧g)(u	X
ejpam-5856	75	13	)	)	PUNCT
ejpam-5856	75	14	=	=	SYM
ejpam-5856	75	15	min{h(u	min{h(u	PROPN
ejpam-5856	75	16	)	)	PUNCT
ejpam-5856	75	17	,	,	PUNCT
ejpam-5856	75	18	g(u	g(u	PROPN
ejpam-5856	75	19	)	)	PUNCT
ejpam-5856	75	20	}	}	PUNCT
ejpam-5856	75	21	for	for	ADP
ejpam-5856	75	22	every	every	DET
ejpam-5856	75	23	u	u	PROPN
ejpam-5856	75	24	∈	∈	PROPN
ejpam-5856	75	25	u	u	NOUN
ejpam-5856	75	26	.	.	PUNCT
ejpam-5856	76	1	(	(	PUNCT
ejpam-5856	76	2	iii	iii	X
ejpam-5856	76	3	)	)	PUNCT
ejpam-5856	76	4	hc	hc	PROPN
ejpam-5856	76	5	∈	∈	NOUN
ejpam-5856	76	6	iu	iu	SCONJ
ejpam-5856	76	7	given	give	VERB
ejpam-5856	76	8	by	by	ADP
ejpam-5856	76	9	hc(u	hc(u	PROPN
ejpam-5856	76	10	)	)	PUNCT
ejpam-5856	76	11	=	=	SYM
ejpam-5856	77	1	1−h(u	1−h(u	NUM
ejpam-5856	77	2	)	)	PUNCT
ejpam-5856	77	3	for	for	ADP
ejpam-5856	77	4	all	all	PRON
ejpam-5856	77	5	u	u	PRON
ejpam-5856	77	6	∈	∈	PROPN
ejpam-5856	77	7	u	u	NOUN
ejpam-5856	77	8	.	.	PUNCT
ejpam-5856	78	1	(	(	PUNCT
ejpam-5856	78	2	iv	iv	X
ejpam-5856	78	3	)	)	PUNCT
ejpam-5856	78	4	for	for	ADP
ejpam-5856	78	5	a	a	DET
ejpam-5856	78	6	⊂	⊂	PROPN
ejpam-5856	78	7	u	u	PROPN
ejpam-5856	78	8	,	,	PUNCT
ejpam-5856	78	9	the	the	DET
ejpam-5856	78	10	characteristic	characteristic	ADJ
ejpam-5856	78	11	function	function	NOUN
ejpam-5856	78	12	χa	χa	PROPN
ejpam-5856	78	13	is	be	AUX
ejpam-5856	78	14	an	an	DET
ejpam-5856	78	15	f	f	X
ejpam-5856	78	16	-set	-set	PUNCT
ejpam-5856	78	17	on	on	ADP
ejpam-5856	78	18	u	u	PROPN
ejpam-5856	78	19	.	.	PUNCT
ejpam-5856	79	1	(	(	PUNCT
ejpam-5856	79	2	v	v	NOUN
ejpam-5856	79	3	)	)	PUNCT
ejpam-5856	79	4	the	the	DET
ejpam-5856	79	5	support	support	NOUN
ejpam-5856	79	6	of	of	ADP
ejpam-5856	79	7	h	h	NOUN
ejpam-5856	79	8	∈	∈	PROPN
ejpam-5856	79	9	iu	iu	ADV
ejpam-5856	79	10	is	be	AUX
ejpam-5856	79	11	denoted	denote	VERB
ejpam-5856	79	12	by	by	ADP
ejpam-5856	79	13	s(h	s(h	PROPN
ejpam-5856	79	14	)	)	PUNCT
ejpam-5856	79	15	and	and	CCONJ
ejpam-5856	79	16	given	give	VERB
ejpam-5856	79	17	by	by	ADP
ejpam-5856	79	18	s	s	PROPN
ejpam-5856	79	19	(	(	PUNCT
ejpam-5856	79	20	h	h	NOUN
ejpam-5856	79	21	)	)	PUNCT
ejpam-5856	79	22	=	=	PRON
ejpam-5856	80	1	{	{	PUNCT
ejpam-5856	80	2	u	u	NOUN
ejpam-5856	80	3	∈	∈	PROPN
ejpam-5856	80	4	u	u	NOUN
ejpam-5856	80	5	:	:	PUNCT
ejpam-5856	80	6	h	h	PROPN
ejpam-5856	80	7	(	(	PUNCT
ejpam-5856	80	8	u	u	NOUN
ejpam-5856	80	9	)	)	PUNCT
ejpam-5856	80	10	>	>	X
ejpam-5856	80	11	0	0	NUM
ejpam-5856	80	12	}	}	PUNCT
ejpam-5856	80	13	.	.	PUNCT
ejpam-5856	81	1	(	(	PUNCT
ejpam-5856	81	2	vi	vi	X
ejpam-5856	81	3	)	)	PUNCT
ejpam-5856	81	4	for	for	ADP
ejpam-5856	81	5	a	a	DET
ejpam-5856	81	6	map	map	NOUN
ejpam-5856	82	1	f	f	NOUN
ejpam-5856	82	2	:	:	PUNCT
ejpam-5856	82	3	u	u	NOUN
ejpam-5856	82	4	−→	−→	NOUN
ejpam-5856	82	5	w	w	NOUN
ejpam-5856	83	1	and	and	CCONJ
ejpam-5856	83	2	h	h	NOUN
ejpam-5856	83	3	∈	∈	PROPN
ejpam-5856	83	4	iu	iu	ADV
ejpam-5856	83	5	,	,	PUNCT
ejpam-5856	83	6	g	g	PROPN
ejpam-5856	83	7	∈	∈	PROPN
ejpam-5856	83	8	iw	iw	INTJ
ejpam-5856	83	9	,	,	PUNCT
ejpam-5856	83	10	we	we	PRON
ejpam-5856	83	11	have	have	AUX
ejpam-5856	83	12	:	:	PUNCT
ejpam-5856	83	13	(	(	PUNCT
ejpam-5856	83	14	a	a	X
ejpam-5856	83	15	)	)	PUNCT
ejpam-5856	83	16	f(h	f(h	PROPN
ejpam-5856	83	17	)	)	PUNCT
ejpam-5856	83	18	is	be	AUX
ejpam-5856	83	19	an	an	DET
ejpam-5856	83	20	f	f	NOUN
ejpam-5856	83	21	-set	-set	PUNCT
ejpam-5856	83	22	on	on	ADP
ejpam-5856	83	23	w	w	NOUN
ejpam-5856	83	24	given	give	VERB
ejpam-5856	83	25	as	as	ADP
ejpam-5856	83	26	f(h)(w	f(h)(w	NOUN
ejpam-5856	83	27	)	)	PUNCT
ejpam-5856	83	28	=	=	SYM
ejpam-5856	83	29	sup{h(u	sup{h(u	PROPN
ejpam-5856	83	30	)	)	PUNCT
ejpam-5856	83	31	:	:	PUNCT
ejpam-5856	84	1	u	u	PROPN
ejpam-5856	84	2	∈	∈	PROPN
ejpam-5856	84	3	f−1(w	f−1(w	PROPN
ejpam-5856	84	4	)	)	PUNCT
ejpam-5856	84	5	}	}	PUNCT
ejpam-5856	84	6	if	if	SCONJ
ejpam-5856	84	7	f−1(w	f−1(w	PROPN
ejpam-5856	84	8	)	)	PUNCT
ejpam-5856	84	9	̸=	̸=	PROPN
ejpam-5856	84	10	∅	∅	NOUN
ejpam-5856	84	11	and	and	CCONJ
ejpam-5856	84	12	f(h)(w	f(h)(w	NOUN
ejpam-5856	84	13	)	)	PUNCT
ejpam-5856	84	14	=	=	SYM
ejpam-5856	84	15	0	0	PUNCT
ejpam-5856	84	16	if	if	SCONJ
ejpam-5856	84	17	f−1(w	f−1(w	PROPN
ejpam-5856	84	18	)	)	PUNCT
ejpam-5856	84	19	=	=	SYM
ejpam-5856	84	20	∅.	∅.	X
ejpam-5856	84	21	(	(	PUNCT
ejpam-5856	84	22	b	b	NOUN
ejpam-5856	84	23	)	)	PUNCT
ejpam-5856	84	24	f−1(g	f−1(g	PROPN
ejpam-5856	84	25	)	)	PUNCT
ejpam-5856	84	26	is	be	AUX
ejpam-5856	84	27	an	an	DET
ejpam-5856	84	28	f	f	X
ejpam-5856	84	29	-set	-set	PUNCT
ejpam-5856	84	30	on	on	ADP
ejpam-5856	84	31	u	u	NOUN
ejpam-5856	84	32	given	give	VERB
ejpam-5856	84	33	as	as	ADP
ejpam-5856	84	34	f−1(g)(u	f−1(g)(u	PROPN
ejpam-5856	84	35	)	)	PUNCT
ejpam-5856	84	36	=	=	SYM
ejpam-5856	84	37	g(f(u	g(f(u	NOUN
ejpam-5856	84	38	)	)	PUNCT
ejpam-5856	84	39	)	)	PUNCT
ejpam-5856	84	40	for	for	ADP
ejpam-5856	84	41	every	every	DET
ejpam-5856	84	42	u	u	PROPN
ejpam-5856	84	43	∈	∈	PROPN
ejpam-5856	84	44	u	u	NOUN
ejpam-5856	84	45	.	.	PUNCT
ejpam-5856	85	1	definition	definition	NOUN
ejpam-5856	85	2	2	2	NUM
ejpam-5856	85	3	.	.	PUNCT
ejpam-5856	86	1	[	[	X
ejpam-5856	86	2	16	16	NUM
ejpam-5856	86	3	]	]	X
ejpam-5856	86	4	an	an	DET
ejpam-5856	86	5	fts	fts	PROPN
ejpam-5856	86	6	is	be	AUX
ejpam-5856	86	7	the	the	DET
ejpam-5856	86	8	pair	pair	NOUN
ejpam-5856	86	9	(	(	PUNCT
ejpam-5856	86	10	u	u	NOUN
ejpam-5856	86	11	,	,	PUNCT
ejpam-5856	86	12	τ	τ	PROPN
ejpam-5856	86	13	)	)	PUNCT
ejpam-5856	86	14	,	,	PUNCT
ejpam-5856	86	15	where	where	SCONJ
ejpam-5856	86	16	τ	τ	PROPN
ejpam-5856	86	17	⊆	⊆	NUM
ejpam-5856	86	18	iu	iu	ADP
ejpam-5856	86	19	which	which	PRON
ejpam-5856	86	20	is	be	AUX
ejpam-5856	86	21	closed	close	VERB
ejpam-5856	86	22	under	under	ADP
ejpam-5856	86	23	finite	finite	ADJ
ejpam-5856	86	24	intersections	intersection	NOUN
ejpam-5856	86	25	,	,	PUNCT
ejpam-5856	86	26	arbitrary	arbitrary	ADJ
ejpam-5856	86	27	union	union	NOUN
ejpam-5856	86	28	,	,	PUNCT
ejpam-5856	86	29	and	and	CCONJ
ejpam-5856	86	30	0	0	NUM
ejpam-5856	86	31	,	,	PUNCT
ejpam-5856	86	32	1	1	NUM
ejpam-5856	86	33	in	in	ADP
ejpam-5856	86	34	τ	τ	PROPN
ejpam-5856	86	35	.	.	PUNCT
ejpam-5856	87	1	an	an	DET
ejpam-5856	87	2	f	f	PROPN
ejpam-5856	87	3	-set	-set	PROPN
ejpam-5856	87	4	h	h	NOUN
ejpam-5856	87	5	is	be	AUX
ejpam-5856	87	6	called	call	VERB
ejpam-5856	87	7	f	f	PROPN
ejpam-5856	87	8	-open	-open	NOUN
ejpam-5856	87	9	set	set	VERB
ejpam-5856	87	10	if	if	SCONJ
ejpam-5856	87	11	h	h	NOUN
ejpam-5856	87	12	∈	∈	PROPN
ejpam-5856	87	13	τ	τ	X
ejpam-5856	87	14	and	and	CCONJ
ejpam-5856	87	15	the	the	DET
ejpam-5856	87	16	complement	complement	NOUN
ejpam-5856	87	17	of	of	ADP
ejpam-5856	87	18	h	h	NOUN
ejpam-5856	87	19	is	be	AUX
ejpam-5856	87	20	called	call	VERB
ejpam-5856	87	21	f	f	PROPN
ejpam-5856	87	22	-closed	-close	VERB
ejpam-5856	87	23	set	set	NOUN
ejpam-5856	87	24	.	.	PUNCT
ejpam-5856	88	1	for	for	ADP
ejpam-5856	88	2	an	an	DET
ejpam-5856	88	3	f	f	PROPN
ejpam-5856	88	4	-set	-set	NOUN
ejpam-5856	88	5	h	h	NOUN
ejpam-5856	88	6	in	in	ADP
ejpam-5856	88	7	(	(	PUNCT
ejpam-5856	88	8	u	u	NOUN
ejpam-5856	88	9	,	,	PUNCT
ejpam-5856	88	10	τ	τ	PROPN
ejpam-5856	88	11	)	)	PUNCT
ejpam-5856	88	12	,	,	PUNCT
ejpam-5856	88	13	the	the	DET
ejpam-5856	88	14	f	f	PROPN
ejpam-5856	88	15	-complement	-complement	PROPN
ejpam-5856	88	16	,	,	PUNCT
ejpam-5856	88	17	f	f	PROPN
ejpam-5856	88	18	-interior	-interior	NOUN
ejpam-5856	88	19	,	,	PUNCT
ejpam-5856	88	20	and	and	CCONJ
ejpam-5856	88	21	f	f	PROPN
ejpam-5856	88	22	-closure	-closure	NOUN
ejpam-5856	88	23	of	of	ADP
ejpam-5856	88	24	h	h	NOUN
ejpam-5856	88	25	are	be	AUX
ejpam-5856	88	26	written	write	VERB
ejpam-5856	88	27	as	as	ADP
ejpam-5856	88	28	hc	hc	PROPN
ejpam-5856	88	29	,	,	PUNCT
ejpam-5856	88	30	int	int	NOUN
ejpam-5856	88	31	(	(	PUNCT
ejpam-5856	88	32	h	h	NOUN
ejpam-5856	88	33	)	)	PUNCT
ejpam-5856	88	34	,	,	PUNCT
ejpam-5856	88	35	and	and	CCONJ
ejpam-5856	88	36	cl(h	cl(h	NUM
ejpam-5856	88	37	)	)	PUNCT
ejpam-5856	88	38	respectively	respectively	ADV
ejpam-5856	88	39	.	.	PUNCT
ejpam-5856	89	1	s.	s.	PROPN
ejpam-5856	89	2	saleh	saleh	PROPN
ejpam-5856	89	3	et	et	PROPN
ejpam-5856	89	4	al	al	PROPN
ejpam-5856	89	5	.	.	PUNCT
ejpam-5856	89	6	/	/	SYM
ejpam-5856	89	7	eur	eur	PROPN
ejpam-5856	89	8	.	.	PUNCT
ejpam-5856	90	1	j.	j.	PROPN
ejpam-5856	90	2	pure	pure	PROPN
ejpam-5856	90	3	appl	appl	PROPN
ejpam-5856	90	4	.	.	PROPN
ejpam-5856	90	5	math	math	PROPN
ejpam-5856	90	6	,	,	PUNCT
ejpam-5856	90	7	18	18	NUM
ejpam-5856	90	8	(	(	PUNCT
ejpam-5856	90	9	1	1	NUM
ejpam-5856	90	10	)	)	PUNCT
ejpam-5856	90	11	(	(	PUNCT
ejpam-5856	90	12	2025	2025	NUM
ejpam-5856	90	13	)	)	PUNCT
ejpam-5856	90	14	,	,	PUNCT
ejpam-5856	90	15	5856	5856	NUM
ejpam-5856	90	16	4	4	NUM
ejpam-5856	90	17	of	of	ADP
ejpam-5856	90	18	15	15	NUM
ejpam-5856	90	19	definition	definition	NOUN
ejpam-5856	90	20	3	3	NUM
ejpam-5856	90	21	.	.	PUNCT
ejpam-5856	91	1	[	[	X
ejpam-5856	91	2	39	39	NUM
ejpam-5856	91	3	]	]	PUNCT
ejpam-5856	91	4	an	an	DET
ejpam-5856	91	5	f	f	PROPN
ejpam-5856	91	6	-point	-point	PROPN
ejpam-5856	91	7	uα	uα	PROPN
ejpam-5856	91	8	is	be	AUX
ejpam-5856	91	9	called	call	VERB
ejpam-5856	91	10	quasi	quasi	ADJ
ejpam-5856	91	11	-	-	NOUN
ejpam-5856	91	12	coincident	coincident	ADJ
ejpam-5856	91	13	with	with	ADP
ejpam-5856	91	14	a	a	DET
ejpam-5856	91	15	f	f	PROPN
ejpam-5856	91	16	-set	-set	NOUN
ejpam-5856	91	17	h	h	NOUN
ejpam-5856	91	18	in	in	ADP
ejpam-5856	91	19	u	u	PROPN
ejpam-5856	91	20	,	,	PUNCT
ejpam-5856	91	21	symbolized	symbolize	VERB
ejpam-5856	91	22	by	by	ADP
ejpam-5856	91	23	uαqh	uαqh	ADJ
ejpam-5856	91	24	,	,	PUNCT
ejpam-5856	91	25	if	if	SCONJ
ejpam-5856	91	26	there	there	PRON
ejpam-5856	91	27	is	be	VERB
ejpam-5856	91	28	u	u	PROPN
ejpam-5856	91	29	∈	∈	NOUN
ejpam-5856	91	30	u	u	NOUN
ejpam-5856	91	31	such	such	ADJ
ejpam-5856	91	32	that	that	PRON
ejpam-5856	91	33	α+h(u	α+h(u	NUM
ejpam-5856	91	34	)	)	PUNCT
ejpam-5856	91	35	>	>	X
ejpam-5856	91	36	1	1	X
ejpam-5856	91	37	.	.	PUNCT
ejpam-5856	92	1	in	in	ADP
ejpam-5856	92	2	general	general	ADJ
ejpam-5856	92	3	,	,	PUNCT
ejpam-5856	92	4	hqg	hqg	PROPN
ejpam-5856	92	5	if	if	SCONJ
ejpam-5856	92	6	h(u)+g(u	h(u)+g(u	PROPN
ejpam-5856	92	7	)	)	PUNCT
ejpam-5856	92	8	>	>	X
ejpam-5856	92	9	1	1	NUM
ejpam-5856	92	10	for	for	ADP
ejpam-5856	92	11	some	some	DET
ejpam-5856	92	12	u	u	NOUN
ejpam-5856	92	13	∈	∈	PROPN
ejpam-5856	92	14	u	u	NOUN
ejpam-5856	92	15	.	.	PUNCT
ejpam-5856	93	1	if	if	SCONJ
ejpam-5856	93	2	h	h	NOUN
ejpam-5856	93	3	is	be	AUX
ejpam-5856	93	4	not	not	PART
ejpam-5856	93	5	quasi	quasi	ADJ
ejpam-5856	93	6	-	-	NOUN
ejpam-5856	93	7	coincident	coincident	ADJ
ejpam-5856	93	8	with	with	ADP
ejpam-5856	93	9	g	g	NOUN
ejpam-5856	93	10	,	,	PUNCT
ejpam-5856	93	11	then	then	ADV
ejpam-5856	93	12	we	we	PRON
ejpam-5856	93	13	write	write	VERB
ejpam-5856	93	14	hq̃g	hq̃g	PROPN
ejpam-5856	93	15	.	.	PUNCT
ejpam-5856	94	1	definition	definition	NOUN
ejpam-5856	94	2	4	4	NUM
ejpam-5856	94	3	.	.	PUNCT
ejpam-5856	95	1	[	[	X
ejpam-5856	95	2	16	16	NUM
ejpam-5856	95	3	,	,	PUNCT
ejpam-5856	95	4	27	27	NUM
ejpam-5856	95	5	,	,	PUNCT
ejpam-5856	95	6	32	32	NUM
ejpam-5856	95	7	,	,	PUNCT
ejpam-5856	95	8	39	39	NUM
ejpam-5856	95	9	]	]	PUNCT
ejpam-5856	95	10	for	for	ADP
ejpam-5856	95	11	any	any	DET
ejpam-5856	95	12	two	two	NUM
ejpam-5856	95	13	f	f	PROPN
ejpam-5856	95	14	-sets	-set	NOUN
ejpam-5856	95	15	h	h	NOUN
ejpam-5856	95	16	,	,	PUNCT
ejpam-5856	95	17	g	g	NOUN
ejpam-5856	95	18	in	in	ADP
ejpam-5856	95	19	(	(	PUNCT
ejpam-5856	95	20	u	u	NOUN
ejpam-5856	95	21	,	,	PUNCT
ejpam-5856	95	22	τ	τ	PROPN
ejpam-5856	95	23	)	)	PUNCT
ejpam-5856	95	24	and	and	CCONJ
ejpam-5856	95	25	uα	uα	PROPN
ejpam-5856	95	26	∈	∈	PROPN
ejpam-5856	95	27	fp	fp	PROPN
ejpam-5856	95	28	(	(	PUNCT
ejpam-5856	95	29	u	u	NOUN
ejpam-5856	95	30	)	)	PUNCT
ejpam-5856	95	31	,	,	PUNCT
ejpam-5856	95	32	we	we	PRON
ejpam-5856	95	33	have	have	VERB
ejpam-5856	95	34	:	:	PUNCT
ejpam-5856	95	35	(	(	PUNCT
ejpam-5856	95	36	1	1	X
ejpam-5856	95	37	)	)	PUNCT
ejpam-5856	95	38	uαq̃h	uαq̃h	PROPN
ejpam-5856	95	39	⇐	⇐	ADJ
ejpam-5856	95	40	⇒	⇒	NOUN
ejpam-5856	95	41	uα	uα	PROPN
ejpam-5856	95	42	∈	∈	PROPN
ejpam-5856	95	43	hc	hc	PROPN
ejpam-5856	95	44	,	,	PUNCT
ejpam-5856	95	45	in	in	ADP
ejpam-5856	95	46	general	general	ADJ
ejpam-5856	95	47	hq̃g	hq̃g	PROPN
ejpam-5856	95	48	⇐	⇐	ADJ
ejpam-5856	95	49	⇒	⇒	PROPN
ejpam-5856	95	50	h	h	PROPN
ejpam-5856	95	51	⊆	⊆	NUM
ejpam-5856	95	52	gc	gc	PROPN
ejpam-5856	95	53	(	(	PUNCT
ejpam-5856	95	54	2	2	NUM
ejpam-5856	95	55	)	)	PUNCT
ejpam-5856	95	56	h	h	NOUN
ejpam-5856	95	57	∩g	∩g	NOUN
ejpam-5856	96	1	=	=	SYM
ejpam-5856	96	2	0	0	PUNCT
ejpam-5856	97	1	=	=	NOUN
ejpam-5856	97	2	⇒	⇒	X
ejpam-5856	97	3	hq̃g	hq̃g	PROPN
ejpam-5856	97	4	(	(	PUNCT
ejpam-5856	97	5	3	3	NUM
ejpam-5856	97	6	)	)	PUNCT
ejpam-5856	97	7	hq̃g	hq̃g	PROPN
ejpam-5856	97	8	,	,	PUNCT
ejpam-5856	97	9	f	f	PROPN
ejpam-5856	97	10	⊆	⊆	NUM
ejpam-5856	97	11	g	g	NOUN
ejpam-5856	97	12	=	=	NOUN
ejpam-5856	97	13	⇒	⇒	NOUN
ejpam-5856	97	14	hq̃f	hq̃f	PROPN
ejpam-5856	98	1	(	(	PUNCT
ejpam-5856	98	2	4	4	NUM
ejpam-5856	98	3	)	)	PUNCT
ejpam-5856	98	4	h	h	NOUN
ejpam-5856	98	5	⊆	⊆	NUM
ejpam-5856	98	6	g	g	ADP
ejpam-5856	98	7	⇐	⇐	ADJ
ejpam-5856	98	8	⇒	⇒	NOUN
ejpam-5856	98	9	(	(	PUNCT
ejpam-5856	98	10	uαqh	uαqh	ADJ
ejpam-5856	98	11	=	=	PRON
ejpam-5856	98	12	⇒	⇒	X
ejpam-5856	98	13	uαqg	uαqg	PROPN
ejpam-5856	98	14	)	)	PUNCT
ejpam-5856	98	15	for	for	ADP
ejpam-5856	98	16	all	all	DET
ejpam-5856	98	17	uα	uα	PROPN
ejpam-5856	98	18	∈	∈	PROPN
ejpam-5856	98	19	fp	fp	X
ejpam-5856	98	20	(	(	PUNCT
ejpam-5856	98	21	u	u	NOUN
ejpam-5856	98	22	)	)	PUNCT
ejpam-5856	98	23	(	(	PUNCT
ejpam-5856	98	24	5	5	X
ejpam-5856	98	25	)	)	PUNCT
ejpam-5856	98	26	uαq̃vβ	uαq̃vβ	PROPN
ejpam-5856	98	27	⇐	⇐	ADJ
ejpam-5856	98	28	⇒	⇒	NOUN
ejpam-5856	98	29	u	u	NOUN
ejpam-5856	98	30	̸=	̸=	PROPN
ejpam-5856	98	31	v	v	NOUN
ejpam-5856	98	32	or	or	CCONJ
ejpam-5856	98	33	(	(	PUNCT
ejpam-5856	98	34	u	u	NOUN
ejpam-5856	98	35	=	=	PROPN
ejpam-5856	98	36	v	v	PROPN
ejpam-5856	98	37	and	and	CCONJ
ejpam-5856	98	38	α+	α+	X
ejpam-5856	98	39	β	β	X
ejpam-5856	98	40	>	>	X
ejpam-5856	98	41	1	1	NUM
ejpam-5856	98	42	)	)	PUNCT
ejpam-5856	98	43	.	.	PUNCT
ejpam-5856	99	1	for	for	ADP
ejpam-5856	99	2	a	a	DET
ejpam-5856	99	3	map	map	NOUN
ejpam-5856	99	4	f	f	NOUN
ejpam-5856	99	5	:	:	PUNCT
ejpam-5856	99	6	u	u	VERB
ejpam-5856	99	7	−→	−→	NOUN
ejpam-5856	99	8	v	v	NOUN
ejpam-5856	99	9	,	,	PUNCT
ejpam-5856	99	10	h	h	NOUN
ejpam-5856	99	11	∈	∈	PROPN
ejpam-5856	100	1	iu	iu	ADV
ejpam-5856	100	2	,	,	PUNCT
ejpam-5856	100	3	g	g	PROPN
ejpam-5856	100	4	∈	∈	PROPN
ejpam-5856	100	5	iv	iv	X
ejpam-5856	100	6	,	,	PUNCT
ejpam-5856	100	7	and	and	CCONJ
ejpam-5856	100	8	uα	uα	PROPN
ejpam-5856	100	9	∈	∈	PROPN
ejpam-5856	100	10	fp	fp	PROPN
ejpam-5856	100	11	(	(	PUNCT
ejpam-5856	100	12	u	u	NOUN
ejpam-5856	100	13	)	)	PUNCT
ejpam-5856	100	14	,	,	PUNCT
ejpam-5856	100	15	we	we	PRON
ejpam-5856	100	16	have	have	VERB
ejpam-5856	100	17	:	:	PUNCT
ejpam-5856	100	18	(	(	PUNCT
ejpam-5856	100	19	i	i	NOUN
ejpam-5856	100	20	)	)	PUNCT
ejpam-5856	100	21	f(uα)qg	f(uα)qg	NOUN
ejpam-5856	100	22	=	=	NOUN
ejpam-5856	100	23	⇒	⇒	X
ejpam-5856	100	24	uαqf	uαqf	PRON
ejpam-5856	100	25	−1	−1	NOUN
ejpam-5856	100	26	(	(	PUNCT
ejpam-5856	100	27	g	g	NOUN
ejpam-5856	100	28	)	)	PUNCT
ejpam-5856	100	29	,	,	PUNCT
ejpam-5856	100	30	and	and	CCONJ
ejpam-5856	100	31	uαqh	uαqh	ADJ
ejpam-5856	101	1	=	=	NOUN
ejpam-5856	101	2	⇒	⇒	VERB
ejpam-5856	101	3	f(uα)qf	f(uα)qf	NOUN
ejpam-5856	101	4	(	(	PUNCT
ejpam-5856	101	5	h	h	NOUN
ejpam-5856	101	6	)	)	PUNCT
ejpam-5856	101	7	.	.	PUNCT
ejpam-5856	102	1	(	(	PUNCT
ejpam-5856	102	2	ii	ii	NOUN
ejpam-5856	102	3	)	)	PUNCT
ejpam-5856	102	4	uαqf	uαqf	PROPN
ejpam-5856	102	5	−1(g	−1(g	NOUN
ejpam-5856	102	6	)	)	PUNCT
ejpam-5856	102	7	if	if	SCONJ
ejpam-5856	102	8	f(uα	f(uα	NOUN
ejpam-5856	102	9	)	)	PUNCT
ejpam-5856	102	10	∈	∈	PROPN
ejpam-5856	102	11	g	g	NOUN
ejpam-5856	102	12	,	,	PUNCT
ejpam-5856	102	13	and	and	CCONJ
ejpam-5856	102	14	f(uα	f(uα	NOUN
ejpam-5856	102	15	)	)	PUNCT
ejpam-5856	102	16	∈	∈	PROPN
ejpam-5856	102	17	f(h	f(h	PROPN
ejpam-5856	102	18	)	)	PUNCT
ejpam-5856	103	1	if	if	SCONJ
ejpam-5856	103	2	uα	uα	PROPN
ejpam-5856	103	3	∈	∈	PROPN
ejpam-5856	103	4	h.	h.	PROPN
ejpam-5856	103	5	definition	definition	NOUN
ejpam-5856	103	6	5	5	NUM
ejpam-5856	104	1	.	.	PUNCT
ejpam-5856	105	1	[	[	X
ejpam-5856	105	2	18	18	NUM
ejpam-5856	105	3	]	]	PUNCT
ejpam-5856	105	4	a	a	DET
ejpam-5856	105	5	collection	collection	NOUN
ejpam-5856	105	6	µ	µ	PROPN
ejpam-5856	105	7	⊆	⊆	NUM
ejpam-5856	105	8	iu	iu	NOUN
ejpam-5856	105	9	is	be	AUX
ejpam-5856	105	10	called	call	VERB
ejpam-5856	105	11	gft	gft	PROPN
ejpam-5856	105	12	on	on	ADP
ejpam-5856	105	13	u	u	PROPN
ejpam-5856	105	14	iff	iff	PROPN
ejpam-5856	105	15	0	0	NUM
ejpam-5856	105	16	∈	∈	PROPN
ejpam-5856	105	17	µ	µ	X
ejpam-5856	105	18	and	and	CCONJ
ejpam-5856	105	19	∨	∨	NUM
ejpam-5856	105	20	i∈j	i∈j	NOUN
ejpam-5856	105	21	hi	hi	PROPN
ejpam-5856	105	22	∈	∈	PROPN
ejpam-5856	105	23	µ	µ	PROPN
ejpam-5856	105	24	for	for	ADP
ejpam-5856	105	25	any	any	DET
ejpam-5856	105	26	class	class	NOUN
ejpam-5856	105	27	{	{	PUNCT
ejpam-5856	105	28	hi	hi	INTJ
ejpam-5856	105	29	:	:	PUNCT
ejpam-5856	106	1	i	i	PROPN
ejpam-5856	106	2	∈	∈	PROPN
ejpam-5856	106	3	j	j	X
ejpam-5856	106	4	}	}	PUNCT
ejpam-5856	106	5	⊂	⊂	PRON
ejpam-5856	106	6	µ.	µ.	VERB
ejpam-5856	106	7	the	the	DET
ejpam-5856	106	8	structure	structure	NOUN
ejpam-5856	106	9	(	(	PUNCT
ejpam-5856	106	10	u	u	NOUN
ejpam-5856	106	11	,	,	PUNCT
ejpam-5856	106	12	µ	µ	NOUN
ejpam-5856	106	13	)	)	PUNCT
ejpam-5856	106	14	is	be	AUX
ejpam-5856	106	15	called	call	VERB
ejpam-5856	106	16	an	an	DET
ejpam-5856	106	17	gfts	gft	NOUN
ejpam-5856	106	18	.	.	PUNCT
ejpam-5856	107	1	every	every	DET
ejpam-5856	107	2	member	member	NOUN
ejpam-5856	107	3	of	of	ADP
ejpam-5856	107	4	µ	µ	PROPN
ejpam-5856	107	5	is	be	AUX
ejpam-5856	107	6	called	call	VERB
ejpam-5856	107	7	a	a	DET
ejpam-5856	107	8	fuzzy	fuzzy	ADJ
ejpam-5856	107	9	µ-open	µ-open	NOUN
ejpam-5856	107	10	set	set	NOUN
ejpam-5856	107	11	(	(	PUNCT
ejpam-5856	107	12	in	in	ADP
ejpam-5856	107	13	short	short	ADJ
ejpam-5856	107	14	,	,	PUNCT
ejpam-5856	107	15	fµ-open	fµ-open	ADJ
ejpam-5856	107	16	set	set	NOUN
ejpam-5856	107	17	)	)	PUNCT
ejpam-5856	107	18	and	and	CCONJ
ejpam-5856	107	19	the	the	DET
ejpam-5856	107	20	complement	complement	NOUN
ejpam-5856	107	21	of	of	ADP
ejpam-5856	107	22	a	a	DET
ejpam-5856	107	23	fµ-open	fµ-open	ADJ
ejpam-5856	107	24	set	set	NOUN
ejpam-5856	107	25	is	be	AUX
ejpam-5856	107	26	called	call	VERB
ejpam-5856	107	27	fµ-closed	fµ-close	VERB
ejpam-5856	107	28	set	set	NOUN
ejpam-5856	107	29	.	.	PUNCT
ejpam-5856	108	1	the	the	DET
ejpam-5856	108	2	family	family	NOUN
ejpam-5856	108	3	fµo(u	fµo(u	PROPN
ejpam-5856	108	4	)	)	PUNCT
ejpam-5856	108	5	(	(	PUNCT
ejpam-5856	108	6	resp	resp	NOUN
ejpam-5856	108	7	.	.	PUNCT
ejpam-5856	109	1	fµc(u	fµc(u	PROPN
ejpam-5856	109	2	)	)	PUNCT
ejpam-5856	109	3	denotes	denote	NOUN
ejpam-5856	109	4	to	to	ADP
ejpam-5856	109	5	the	the	DET
ejpam-5856	109	6	class	class	NOUN
ejpam-5856	109	7	of	of	ADP
ejpam-5856	109	8	all	all	DET
ejpam-5856	109	9	fµ-open	fµ-open	ADJ
ejpam-5856	109	10	(	(	PUNCT
ejpam-5856	109	11	resp	resp	NOUN
ejpam-5856	109	12	.	.	PUNCT
ejpam-5856	110	1	fµ-closed	fµ-close	VERB
ejpam-5856	110	2	)	)	PUNCT
ejpam-5856	110	3	sets	set	NOUN
ejpam-5856	110	4	on	on	ADP
ejpam-5856	110	5	u	u	PROPN
ejpam-5856	110	6	.	.	PUNCT
ejpam-5856	111	1	for	for	ADP
ejpam-5856	111	2	an	an	DET
ejpam-5856	111	3	gfts	gft	NOUN
ejpam-5856	111	4	(	(	PUNCT
ejpam-5856	111	5	u	u	NOUN
ejpam-5856	111	6	,	,	PUNCT
ejpam-5856	111	7	µ	µ	NOUN
ejpam-5856	111	8	)	)	PUNCT
ejpam-5856	111	9	and	and	CCONJ
ejpam-5856	111	10	h∈iu	h∈iu	NOUN
ejpam-5856	111	11	.	.	PUNCT
ejpam-5856	112	1	the	the	DET
ejpam-5856	112	2	fµ-closure	fµ-closure	NOUN
ejpam-5856	112	3	of	of	ADP
ejpam-5856	112	4	h	h	NOUN
ejpam-5856	112	5	is	be	AUX
ejpam-5856	112	6	the	the	DET
ejpam-5856	112	7	smallest	small	ADJ
ejpam-5856	112	8	fµ-closed	fµ-close	VERB
ejpam-5856	112	9	set	set	NOUN
ejpam-5856	112	10	containing	contain	VERB
ejpam-5856	112	11	h	h	NOUN
ejpam-5856	112	12	,	,	PUNCT
ejpam-5856	112	13	it	it	PRON
ejpam-5856	112	14	is	be	AUX
ejpam-5856	112	15	symbolized	symbolize	VERB
ejpam-5856	112	16	by	by	ADP
ejpam-5856	112	17	clµ(h	clµ(h	NOUN
ejpam-5856	112	18	)	)	PUNCT
ejpam-5856	112	19	and	and	CCONJ
ejpam-5856	112	20	the	the	DET
ejpam-5856	112	21	fµ-interior	fµ-interior	NOUN
ejpam-5856	112	22	of	of	ADP
ejpam-5856	112	23	h	h	NOUN
ejpam-5856	112	24	,	,	PUNCT
ejpam-5856	112	25	symbolized	symbolize	VERB
ejpam-5856	112	26	by	by	ADP
ejpam-5856	112	27	intµ(h	intµ(h	NOUN
ejpam-5856	112	28	)	)	PUNCT
ejpam-5856	112	29	is	be	AUX
ejpam-5856	112	30	the	the	DET
ejpam-5856	112	31	largest	large	ADJ
ejpam-5856	112	32	fµ-open	fµ-open	ADJ
ejpam-5856	112	33	set	set	NOUN
ejpam-5856	112	34	contained	contain	VERB
ejpam-5856	112	35	in	in	ADP
ejpam-5856	112	36	h.	h.	PROPN
ejpam-5856	112	37	evidently	evidently	ADV
ejpam-5856	112	38	,	,	PUNCT
ejpam-5856	112	39	h	h	PROPN
ejpam-5856	112	40	∈	∈	PROPN
ejpam-5856	112	41	iu	iu	ADV
ejpam-5856	112	42	is	be	AUX
ejpam-5856	112	43	fµ-open	fµ-open	ADJ
ejpam-5856	112	44	(	(	PUNCT
ejpam-5856	112	45	resp	resp	NOUN
ejpam-5856	112	46	.	.	PUNCT
ejpam-5856	113	1	fµ-closed	fµ-close	VERB
ejpam-5856	113	2	)	)	PUNCT
ejpam-5856	114	1	if	if	SCONJ
ejpam-5856	114	2	and	and	CCONJ
ejpam-5856	114	3	only	only	ADV
ejpam-5856	114	4	if	if	SCONJ
ejpam-5856	114	5	h	h	NOUN
ejpam-5856	114	6	=	=	NOUN
ejpam-5856	114	7	intµ(h	intµ(h	PROPN
ejpam-5856	114	8	)	)	PUNCT
ejpam-5856	114	9	(	(	PUNCT
ejpam-5856	114	10	resp	resp	NOUN
ejpam-5856	114	11	.	.	PUNCT
ejpam-5856	115	1	h	h	NOUN
ejpam-5856	115	2	=	=	SYM
ejpam-5856	115	3	clµ(h	clµ(h	PROPN
ejpam-5856	115	4	)	)	PUNCT
ejpam-5856	115	5	)	)	PUNCT
ejpam-5856	116	1	it	it	PRON
ejpam-5856	116	2	is	be	AUX
ejpam-5856	116	3	clear	clear	ADJ
ejpam-5856	116	4	that	that	SCONJ
ejpam-5856	116	5	intµ	intµ	NOUN
ejpam-5856	116	6	and	and	CCONJ
ejpam-5856	116	7	clµboth	clµboth	NOUN
ejpam-5856	116	8	are	be	AUX
ejpam-5856	116	9	monotonic	monotonic	ADJ
ejpam-5856	116	10	and	and	CCONJ
ejpam-5856	116	11	idempotent	idempotent	ADJ
ejpam-5856	116	12	operators	operator	NOUN
ejpam-5856	116	13	.	.	PUNCT
ejpam-5856	117	1	notation	notation	NOUN
ejpam-5856	117	2	.	.	PUNCT
ejpam-5856	118	1	for	for	ADP
ejpam-5856	118	2	an	an	DET
ejpam-5856	118	3	gfts	gft	NOUN
ejpam-5856	118	4	(	(	PUNCT
ejpam-5856	118	5	u	u	NOUN
ejpam-5856	118	6	,	,	PUNCT
ejpam-5856	118	7	µ	µ	NOUN
ejpam-5856	118	8	)	)	PUNCT
ejpam-5856	118	9	and	and	CCONJ
ejpam-5856	118	10	uα	uα	PROPN
ejpam-5856	118	11	∈	∈	PROPN
ejpam-5856	118	12	fp	fp	PROPN
ejpam-5856	118	13	(	(	PUNCT
ejpam-5856	118	14	u	u	NOUN
ejpam-5856	118	15	)	)	PUNCT
ejpam-5856	118	16	.	.	PUNCT
ejpam-5856	119	1	ouα	ouα	NOUN
ejpam-5856	119	2	refers	refer	VERB
ejpam-5856	119	3	to	to	ADP
ejpam-5856	119	4	an	an	DET
ejpam-5856	119	5	fµ-open	fµ-open	ADJ
ejpam-5856	119	6	set	set	NOUN
ejpam-5856	119	7	containing	contain	VERB
ejpam-5856	119	8	uα	uα	NOUN
ejpam-5856	120	1	and	and	CCONJ
ejpam-5856	120	2	it	it	PRON
ejpam-5856	120	3	is	be	AUX
ejpam-5856	120	4	called	call	VERB
ejpam-5856	120	5	an	an	DET
ejpam-5856	120	6	fµ-open	fµ-open	ADJ
ejpam-5856	120	7	neighborhood	neighborhood	NOUN
ejpam-5856	120	8	(	(	PUNCT
ejpam-5856	120	9	or	or	CCONJ
ejpam-5856	120	10	fµ-open	fµ-open	ADJ
ejpam-5856	120	11	nbd	nbd	PROPN
ejpam-5856	120	12	)	)	PUNCT
ejpam-5856	120	13	of	of	ADP
ejpam-5856	120	14	uα	uα	PROPN
ejpam-5856	120	15	.	.	PUNCT
ejpam-5856	121	1	in	in	ADP
ejpam-5856	121	2	general	general	ADJ
ejpam-5856	121	3	,	,	PUNCT
ejpam-5856	121	4	oh	oh	INTJ
ejpam-5856	121	5	refers	refer	VERB
ejpam-5856	121	6	to	to	ADP
ejpam-5856	121	7	an	an	DET
ejpam-5856	121	8	fµ-open	fµ-open	ADJ
ejpam-5856	121	9	set	set	NOUN
ejpam-5856	121	10	containing	contain	VERB
ejpam-5856	121	11	h.	h.	PROPN
ejpam-5856	121	12	definition	definition	NOUN
ejpam-5856	121	13	6	6	NUM
ejpam-5856	121	14	.	.	PUNCT
ejpam-5856	122	1	let	let	VERB
ejpam-5856	122	2	(	(	PUNCT
ejpam-5856	122	3	u	u	NOUN
ejpam-5856	122	4	,	,	PUNCT
ejpam-5856	122	5	µ	µ	NOUN
ejpam-5856	122	6	)	)	PUNCT
ejpam-5856	122	7	be	be	VERB
ejpam-5856	122	8	an	an	DET
ejpam-5856	122	9	gfts	gft	NOUN
ejpam-5856	122	10	and	and	CCONJ
ejpam-5856	122	11	v	v	ADP
ejpam-5856	122	12	⊆	⊆	NUM
ejpam-5856	122	13	u	u	NOUN
ejpam-5856	122	14	.	.	PUNCT
ejpam-5856	123	1	the	the	DET
ejpam-5856	123	2	family	family	NOUN
ejpam-5856	123	3	µv	µv	PROPN
ejpam-5856	123	4	=	=	PUNCT
ejpam-5856	123	5	{	{	PUNCT
ejpam-5856	123	6	χv	χv	PRON
ejpam-5856	123	7	∩h	∩h	NOUN
ejpam-5856	123	8	:	:	PUNCT
ejpam-5856	124	1	h	h	PROPN
ejpam-5856	124	2	∈	∈	PROPN
ejpam-5856	124	3	µ	µ	PROPN
ejpam-5856	124	4	}	}	PUNCT
ejpam-5856	124	5	is	be	AUX
ejpam-5856	124	6	an	an	DET
ejpam-5856	124	7	gft	gft	NOUN
ejpam-5856	124	8	on	on	ADP
ejpam-5856	124	9	v	v	NOUN
ejpam-5856	124	10	.	.	PUNCT
ejpam-5856	125	1	the	the	DET
ejpam-5856	125	2	pair	pair	NOUN
ejpam-5856	125	3	(	(	PUNCT
ejpam-5856	125	4	v	v	NOUN
ejpam-5856	125	5	,	,	PUNCT
ejpam-5856	125	6	µv	µv	PROPN
ejpam-5856	125	7	)	)	PUNCT
ejpam-5856	125	8	is	be	AUX
ejpam-5856	125	9	called	call	VERB
ejpam-5856	125	10	an	an	DET
ejpam-5856	125	11	gft	gft	NOUN
ejpam-5856	125	12	-subspace	-subspace	NOUN
ejpam-5856	125	13	(	(	PUNCT
ejpam-5856	125	14	or	or	CCONJ
ejpam-5856	125	15	gftss	gftss	ADJ
ejpam-5856	125	16	)	)	PUNCT
ejpam-5856	125	17	of	of	ADP
ejpam-5856	125	18	(	(	PUNCT
ejpam-5856	125	19	u	u	NOUN
ejpam-5856	125	20	,	,	PUNCT
ejpam-5856	125	21	µ	µ	NOUN
ejpam-5856	125	22	)	)	PUNCT
ejpam-5856	125	23	.	.	PUNCT
ejpam-5856	126	1	lemma	lemma	PROPN
ejpam-5856	126	2	1	1	NUM
ejpam-5856	126	3	.	.	PUNCT
ejpam-5856	127	1	[	[	X
ejpam-5856	127	2	27	27	NUM
ejpam-5856	127	3	]	]	X
ejpam-5856	127	4	let	let	AUX
ejpam-5856	127	5	(	(	PUNCT
ejpam-5856	127	6	u	u	NOUN
ejpam-5856	127	7	,	,	PUNCT
ejpam-5856	127	8	µ	µ	NOUN
ejpam-5856	127	9	)	)	PUNCT
ejpam-5856	127	10	be	be	AUX
ejpam-5856	127	11	an	an	DET
ejpam-5856	127	12	gfts	gft	NOUN
ejpam-5856	127	13	,	,	PUNCT
ejpam-5856	127	14	h	h	NOUN
ejpam-5856	127	15	∈	∈	PROPN
ejpam-5856	127	16	iu	iu	ADV
ejpam-5856	127	17	and	and	CCONJ
ejpam-5856	127	18	uα	uα	PROPN
ejpam-5856	127	19	∈	∈	PROPN
ejpam-5856	127	20	fp	fp	PROPN
ejpam-5856	127	21	(	(	PUNCT
ejpam-5856	127	22	u	u	NOUN
ejpam-5856	127	23	)	)	PUNCT
ejpam-5856	127	24	,	,	PUNCT
ejpam-5856	127	25	we	we	PRON
ejpam-5856	127	26	have	have	VERB
ejpam-5856	127	27	:	:	PUNCT
ejpam-5856	127	28	(	(	PUNCT
ejpam-5856	127	29	i	i	NOUN
ejpam-5856	127	30	)	)	PUNCT
ejpam-5856	127	31	for	for	ADP
ejpam-5856	127	32	any	any	DET
ejpam-5856	127	33	two	two	NUM
ejpam-5856	127	34	fµ-open	fµ-open	ADJ
ejpam-5856	127	35	sets	set	NOUN
ejpam-5856	127	36	f	f	PROPN
ejpam-5856	127	37	and	and	CCONJ
ejpam-5856	127	38	g	g	NOUN
ejpam-5856	127	39	,	,	PUNCT
ejpam-5856	127	40	if	if	SCONJ
ejpam-5856	127	41	f	f	PROPN
ejpam-5856	127	42	q̃g	q̃g	VERB
ejpam-5856	127	43	,	,	PUNCT
ejpam-5856	127	44	then	then	ADV
ejpam-5856	127	45	clµ(f	clµ(f	PROPN
ejpam-5856	127	46	)	)	PUNCT
ejpam-5856	127	47	q̃g	q̃g	PROPN
ejpam-5856	127	48	and	and	CCONJ
ejpam-5856	127	49	f	f	PROPN
ejpam-5856	127	50	q̃clµ(g	q̃clµ(g	PROPN
ejpam-5856	127	51	)	)	PUNCT
ejpam-5856	127	52	.	.	PUNCT
ejpam-5856	128	1	(	(	PUNCT
ejpam-5856	128	2	ii	ii	X
ejpam-5856	128	3	)	)	PUNCT
ejpam-5856	128	4	uαqclµ(h	uαqclµ(h	NOUN
ejpam-5856	128	5	)	)	PUNCT
ejpam-5856	129	1	if	if	SCONJ
ejpam-5856	129	2	and	and	CCONJ
ejpam-5856	129	3	only	only	ADV
ejpam-5856	129	4	if	if	SCONJ
ejpam-5856	129	5	ouαqh	ouαqh	ADJ
ejpam-5856	129	6	for	for	ADP
ejpam-5856	129	7	all	all	DET
ejpam-5856	129	8	ouα	ouα	NOUN
ejpam-5856	129	9	∈	∈	PROPN
ejpam-5856	129	10	µ.	µ.	NOUN
ejpam-5856	129	11	definition	definition	NOUN
ejpam-5856	129	12	7	7	NUM
ejpam-5856	129	13	.	.	PUNCT
ejpam-5856	130	1	[	[	X
ejpam-5856	130	2	14	14	NUM
ejpam-5856	130	3	]	]	X
ejpam-5856	130	4	an	an	DET
ejpam-5856	130	5	f	f	PROPN
ejpam-5856	130	6	-set	-set	X
ejpam-5856	130	7	h	h	NOUN
ejpam-5856	130	8	in	in	ADP
ejpam-5856	130	9	gfts	gft	NOUN
ejpam-5856	130	10	(	(	PUNCT
ejpam-5856	130	11	u	u	NOUN
ejpam-5856	130	12	,	,	PUNCT
ejpam-5856	130	13	µ	µ	NOUN
ejpam-5856	130	14	)	)	PUNCT
ejpam-5856	130	15	is	be	AUX
ejpam-5856	130	16	called	call	VERB
ejpam-5856	130	17	:	:	PUNCT
ejpam-5856	130	18	(	(	PUNCT
ejpam-5856	130	19	i	i	NOUN
ejpam-5856	130	20	)	)	PUNCT
ejpam-5856	130	21	fµ-regular	fµ-regular	PROPN
ejpam-5856	130	22	closed	close	VERB
ejpam-5856	130	23	(	(	PUNCT
ejpam-5856	130	24	resp	resp	NOUN
ejpam-5856	130	25	.	.	PUNCT
ejpam-5856	130	26	,	,	PUNCT
ejpam-5856	130	27	fµ-regular	fµ-regular	ADJ
ejpam-5856	130	28	open	open	VERB
ejpam-5856	130	29	)	)	PUNCT
ejpam-5856	130	30	if	if	SCONJ
ejpam-5856	130	31	h	h	NOUN
ejpam-5856	130	32	=	=	PUNCT
ejpam-5856	131	1	clµ(intµ(h))(resp	clµ(intµ(h))(resp	PROPN
ejpam-5856	131	2	.	.	PUNCT
ejpam-5856	131	3	,h	,h	PUNCT
ejpam-5856	132	1	=	=	PUNCT
ejpam-5856	132	2	intµ(clµ(h	intµ(clµ(h	NOUN
ejpam-5856	132	3	)	)	PUNCT
ejpam-5856	132	4	)	)	PUNCT
ejpam-5856	132	5	.	.	PUNCT
ejpam-5856	133	1	(	(	PUNCT
ejpam-5856	133	2	ii	ii	NOUN
ejpam-5856	133	3	)	)	PUNCT
ejpam-5856	133	4	fµ-locally	fµ-locally	ADV
ejpam-5856	133	5	closed	close	VERB
ejpam-5856	133	6	if	if	SCONJ
ejpam-5856	133	7	there	there	PRON
ejpam-5856	133	8	is	be	VERB
ejpam-5856	133	9	f	f	PROPN
ejpam-5856	133	10	∈	∈	PROPN
ejpam-5856	133	11	µ	µ	X
ejpam-5856	133	12	and	and	CCONJ
ejpam-5856	133	13	g	g	PROPN
ejpam-5856	133	14	∈	∈	PROPN
ejpam-5856	133	15	fµc(u	fµc(u	PROPN
ejpam-5856	133	16	)	)	PUNCT
ejpam-5856	133	17	such	such	ADJ
ejpam-5856	133	18	that	that	SCONJ
ejpam-5856	133	19	h	h	NOUN
ejpam-5856	134	1	=	=	NOUN
ejpam-5856	134	2	f	f	PROPN
ejpam-5856	134	3	∩g	∩g	PROPN
ejpam-5856	134	4	.	.	PUNCT
ejpam-5856	135	1	definition	definition	NOUN
ejpam-5856	135	2	8	8	NUM
ejpam-5856	135	3	.	.	PUNCT
ejpam-5856	136	1	[	[	X
ejpam-5856	136	2	31	31	NUM
ejpam-5856	136	3	]	]	PUNCT
ejpam-5856	136	4	an	an	DET
ejpam-5856	136	5	f	f	PROPN
ejpam-5856	136	6	-set	-set	X
ejpam-5856	136	7	h	h	NOUN
ejpam-5856	136	8	in	in	ADP
ejpam-5856	136	9	gfts	gft	NOUN
ejpam-5856	136	10	(	(	PUNCT
ejpam-5856	136	11	u	u	NOUN
ejpam-5856	136	12	,	,	PUNCT
ejpam-5856	136	13	µ	µ	NOUN
ejpam-5856	136	14	)	)	PUNCT
ejpam-5856	136	15	is	be	AUX
ejpam-5856	136	16	called	call	VERB
ejpam-5856	136	17	fuzzy	fuzzy	ADJ
ejpam-5856	136	18	generalized	generalized	ADJ
ejpam-5856	136	19	µ-closed	µ-close	VERB
ejpam-5856	136	20	(	(	PUNCT
ejpam-5856	136	21	or	or	CCONJ
ejpam-5856	136	22	fgµ-closed	fgµ-closed	ADJ
ejpam-5856	136	23	)	)	PUNCT
ejpam-5856	136	24	if	if	SCONJ
ejpam-5856	136	25	clµ(h	clµ(h	NOUN
ejpam-5856	136	26	)	)	PUNCT
ejpam-5856	136	27	⊆	⊆	NUM
ejpam-5856	136	28	g	g	NOUN
ejpam-5856	136	29	whenever	whenever	SCONJ
ejpam-5856	136	30	h	h	NOUN
ejpam-5856	136	31	⊆	⊆	NUM
ejpam-5856	136	32	g	g	NOUN
ejpam-5856	136	33	and	and	CCONJ
ejpam-5856	136	34	g	g	PROPN
ejpam-5856	136	35	∈	∈	PROPN
ejpam-5856	136	36	fµo(u	fµo(u	PROPN
ejpam-5856	136	37	)	)	PUNCT
ejpam-5856	136	38	.	.	PUNCT
ejpam-5856	137	1	the	the	DET
ejpam-5856	137	2	class	class	NOUN
ejpam-5856	137	3	of	of	ADP
ejpam-5856	137	4	all	all	DET
ejpam-5856	137	5	fµgclosed	fµgclosed	ADJ
ejpam-5856	137	6	sets	set	NOUN
ejpam-5856	137	7	in	in	ADP
ejpam-5856	137	8	(	(	PUNCT
ejpam-5856	137	9	u	u	NOUN
ejpam-5856	137	10	,	,	PUNCT
ejpam-5856	137	11	µ	µ	NOUN
ejpam-5856	137	12	)	)	PUNCT
ejpam-5856	137	13	is	be	AUX
ejpam-5856	137	14	symbolized	symbolize	VERB
ejpam-5856	137	15	by	by	ADP
ejpam-5856	137	16	fgµc(u	fgµc(u	NOUN
ejpam-5856	137	17	)	)	PUNCT
ejpam-5856	137	18	.	.	PUNCT
ejpam-5856	138	1	the	the	DET
ejpam-5856	138	2	complement	complement	NOUN
ejpam-5856	138	3	of	of	ADP
ejpam-5856	138	4	fgµ-closed	fgµ-closed	ADJ
ejpam-5856	138	5	set	set	NOUN
ejpam-5856	138	6	is	be	AUX
ejpam-5856	138	7	called	call	VERB
ejpam-5856	138	8	an	an	DET
ejpam-5856	138	9	fgµ-open	fgµ-open	ADJ
ejpam-5856	138	10	set	set	NOUN
ejpam-5856	138	11	.	.	PUNCT
ejpam-5856	139	1	s.	s.	PROPN
ejpam-5856	139	2	saleh	saleh	PROPN
ejpam-5856	139	3	et	et	PROPN
ejpam-5856	139	4	al	al	PROPN
ejpam-5856	139	5	.	.	PUNCT
ejpam-5856	139	6	/	/	SYM
ejpam-5856	139	7	eur	eur	PROPN
ejpam-5856	139	8	.	.	PUNCT
ejpam-5856	140	1	j.	j.	PROPN
ejpam-5856	140	2	pure	pure	PROPN
ejpam-5856	140	3	appl	appl	PROPN
ejpam-5856	140	4	.	.	PROPN
ejpam-5856	140	5	math	math	PROPN
ejpam-5856	140	6	,	,	PUNCT
ejpam-5856	140	7	18	18	NUM
ejpam-5856	140	8	(	(	PUNCT
ejpam-5856	140	9	1	1	NUM
ejpam-5856	140	10	)	)	PUNCT
ejpam-5856	140	11	(	(	PUNCT
ejpam-5856	140	12	2025	2025	NUM
ejpam-5856	140	13	)	)	PUNCT
ejpam-5856	140	14	,	,	PUNCT
ejpam-5856	140	15	5856	5856	NUM
ejpam-5856	140	16	5	5	NUM
ejpam-5856	140	17	of	of	ADP
ejpam-5856	140	18	15	15	NUM
ejpam-5856	140	19	remark	remark	NOUN
ejpam-5856	140	20	1	1	NUM
ejpam-5856	140	21	.	.	PUNCT
ejpam-5856	141	1	[	[	X
ejpam-5856	141	2	15	15	NUM
ejpam-5856	141	3	]	]	PUNCT
ejpam-5856	141	4	in	in	ADP
ejpam-5856	141	5	gfts	gft	NOUN
ejpam-5856	141	6	(	(	PUNCT
ejpam-5856	141	7	u	u	NOUN
ejpam-5856	141	8	,	,	PUNCT
ejpam-5856	141	9	µ	µ	NOUN
ejpam-5856	141	10	)	)	PUNCT
ejpam-5856	141	11	,	,	PUNCT
ejpam-5856	141	12	we	we	PRON
ejpam-5856	141	13	have	have	VERB
ejpam-5856	141	14	:	:	PUNCT
ejpam-5856	141	15	(	(	PUNCT
ejpam-5856	141	16	i	i	NOUN
ejpam-5856	141	17	)	)	PUNCT
ejpam-5856	141	18	every	every	PRON
ejpam-5856	141	19	fµ-closed	fµ-close	VERB
ejpam-5856	141	20	(	(	PUNCT
ejpam-5856	141	21	resp	resp	NOUN
ejpam-5856	141	22	.	.	PUNCT
ejpam-5856	141	23	,	,	PUNCT
ejpam-5856	141	24	fµ-open	fµ-open	NOUN
ejpam-5856	141	25	)	)	PUNCT
ejpam-5856	141	26	set	set	NOUN
ejpam-5856	141	27	is	be	AUX
ejpam-5856	141	28	an	an	DET
ejpam-5856	141	29	fgµ-closed	fgµ-closed	ADJ
ejpam-5856	141	30	(	(	PUNCT
ejpam-5856	141	31	resp	resp	NOUN
ejpam-5856	141	32	.	.	PUNCT
ejpam-5856	141	33	,	,	PUNCT
ejpam-5856	141	34	fgµ-open	fgµ-open	NOUN
ejpam-5856	141	35	)	)	PUNCT
ejpam-5856	141	36	set	set	NOUN
ejpam-5856	141	37	,	,	PUNCT
ejpam-5856	141	38	(	(	PUNCT
ejpam-5856	141	39	ii	ii	NOUN
ejpam-5856	141	40	)	)	PUNCT
ejpam-5856	141	41	every	every	PRON
ejpam-5856	141	42	fµ-closed	fµ-close	VERB
ejpam-5856	141	43	(	(	PUNCT
ejpam-5856	141	44	fµ-open	fµ-open	NOUN
ejpam-5856	141	45	)	)	PUNCT
ejpam-5856	141	46	set	set	NOUN
ejpam-5856	141	47	is	be	AUX
ejpam-5856	141	48	an	an	DET
ejpam-5856	141	49	fµ-locally	fµ-locally	ADV
ejpam-5856	141	50	closed	close	VERB
ejpam-5856	141	51	set	set	NOUN
ejpam-5856	141	52	,	,	PUNCT
ejpam-5856	141	53	but	but	CCONJ
ejpam-5856	141	54	not	not	PART
ejpam-5856	141	55	conversely	conversely	ADV
ejpam-5856	141	56	.	.	PUNCT
ejpam-5856	142	1	remark	remark	NOUN
ejpam-5856	142	2	2	2	NUM
ejpam-5856	142	3	.	.	PUNCT
ejpam-5856	143	1	the	the	DET
ejpam-5856	143	2	concepts	concept	NOUN
ejpam-5856	143	3	of	of	ADP
ejpam-5856	143	4	fgµ-closed	fgµ-closed	ADJ
ejpam-5856	143	5	sets	set	NOUN
ejpam-5856	143	6	and	and	CCONJ
ejpam-5856	143	7	fµ-locally	fµ-locally	ADV
ejpam-5856	143	8	closed	closed	ADJ
ejpam-5856	143	9	sets	set	NOUN
ejpam-5856	143	10	are	be	AUX
ejpam-5856	143	11	generalizations	generalization	NOUN
ejpam-5856	143	12	of	of	ADP
ejpam-5856	143	13	fµ-closed	fµ-close	VERB
ejpam-5856	143	14	sets	set	NOUN
ejpam-5856	143	15	but	but	CCONJ
ejpam-5856	143	16	both	both	PRON
ejpam-5856	143	17	are	be	AUX
ejpam-5856	143	18	independent	independent	ADJ
ejpam-5856	143	19	to	to	ADP
ejpam-5856	143	20	each	each	DET
ejpam-5856	143	21	other	other	ADJ
ejpam-5856	143	22	.	.	PUNCT
ejpam-5856	144	1	for	for	ADP
ejpam-5856	144	2	examples	example	NOUN
ejpam-5856	144	3	see	see	VERB
ejpam-5856	144	4	[	[	X
ejpam-5856	144	5	15	15	NUM
ejpam-5856	144	6	]	]	PUNCT
ejpam-5856	144	7	.	.	PUNCT
ejpam-5856	145	1	proposition	proposition	NOUN
ejpam-5856	145	2	1	1	NUM
ejpam-5856	145	3	.	.	PUNCT
ejpam-5856	146	1	[	[	X
ejpam-5856	146	2	15	15	NUM
ejpam-5856	146	3	]	]	X
ejpam-5856	146	4	an	an	DET
ejpam-5856	146	5	fgµ-closed	fgµ-closed	ADJ
ejpam-5856	146	6	set	set	NOUN
ejpam-5856	146	7	in	in	ADP
ejpam-5856	146	8	an	an	DET
ejpam-5856	146	9	gfts	gft	NOUN
ejpam-5856	146	10	(	(	PUNCT
ejpam-5856	146	11	u	u	NOUN
ejpam-5856	146	12	,	,	PUNCT
ejpam-5856	146	13	µ	µ	NOUN
ejpam-5856	146	14	)	)	PUNCT
ejpam-5856	146	15	is	be	AUX
ejpam-5856	146	16	an	an	DET
ejpam-5856	146	17	fµ-closed	fµ-close	VERB
ejpam-5856	146	18	set	set	NOUN
ejpam-5856	146	19	if	if	SCONJ
ejpam-5856	146	20	and	and	CCONJ
ejpam-5856	146	21	only	only	ADV
ejpam-5856	146	22	if	if	SCONJ
ejpam-5856	146	23	it	it	PRON
ejpam-5856	146	24	is	be	AUX
ejpam-5856	146	25	fµ-locally	fµ-locally	ADV
ejpam-5856	146	26	closed	close	VERB
ejpam-5856	146	27	.	.	PUNCT
ejpam-5856	147	1	according	accord	VERB
ejpam-5856	147	2	to	to	ADP
ejpam-5856	147	3	definition	definition	NOUN
ejpam-5856	147	4	provided	provide	VERB
ejpam-5856	147	5	by	by	ADP
ejpam-5856	147	6	kandil	kandil	PROPN
ejpam-5856	147	7	et	et	PROPN
ejpam-5856	147	8	al	al	PROPN
ejpam-5856	147	9	.	.	PUNCT
ejpam-5856	148	1	[	[	X
ejpam-5856	148	2	26	26	NUM
ejpam-5856	148	3	]	]	PUNCT
ejpam-5856	148	4	,	,	PUNCT
ejpam-5856	148	5	the	the	DET
ejpam-5856	148	6	next	next	ADJ
ejpam-5856	148	7	definition	definition	NOUN
ejpam-5856	148	8	is	be	AUX
ejpam-5856	148	9	obtained	obtain	VERB
ejpam-5856	148	10	by	by	ADP
ejpam-5856	148	11	taking	take	VERB
ejpam-5856	148	12	µ	µ	PRON
ejpam-5856	148	13	=	=	SYM
ejpam-5856	148	14	δ	δ	PROPN
ejpam-5856	148	15	and	and	CCONJ
ejpam-5856	148	16	replacing	replace	VERB
ejpam-5856	148	17	f	f	X
ejpam-5856	148	18	-open	-open	ADJ
ejpam-5856	148	19	sets	set	NOUN
ejpam-5856	148	20	with	with	ADP
ejpam-5856	148	21	fµ-open	fµ-open	ADJ
ejpam-5856	148	22	sets	set	NOUN
ejpam-5856	148	23	.	.	PUNCT
ejpam-5856	149	1	definition	definition	NOUN
ejpam-5856	149	2	9	9	NUM
ejpam-5856	149	3	.	.	PUNCT
ejpam-5856	150	1	an	an	DET
ejpam-5856	150	2	gfts	gft	NOUN
ejpam-5856	150	3	(	(	PUNCT
ejpam-5856	150	4	u	u	NOUN
ejpam-5856	150	5	,	,	PUNCT
ejpam-5856	150	6	µ	µ	NOUN
ejpam-5856	150	7	)	)	PUNCT
ejpam-5856	150	8	is	be	AUX
ejpam-5856	150	9	said	say	VERB
ejpam-5856	150	10	to	to	PART
ejpam-5856	150	11	be	be	AUX
ejpam-5856	150	12	:	:	PUNCT
ejpam-5856	150	13	(	(	PUNCT
ejpam-5856	150	14	i	i	NOUN
ejpam-5856	150	15	)	)	PUNCT
ejpam-5856	150	16	fµ-t0	fµ-t0	NOUN
ejpam-5856	150	17	iff	iff	VERB
ejpam-5856	150	18	for	for	ADP
ejpam-5856	150	19	any	any	DET
ejpam-5856	150	20	uα	uα	PROPN
ejpam-5856	150	21	,	,	PUNCT
ejpam-5856	150	22	vβ	vβ	ADP
ejpam-5856	150	23	∈	∈	PROPN
ejpam-5856	150	24	fp	fp	X
ejpam-5856	150	25	(	(	PUNCT
ejpam-5856	150	26	u	u	NOUN
ejpam-5856	150	27	)	)	PUNCT
ejpam-5856	150	28	with	with	ADP
ejpam-5856	150	29	uαq̃vβ	uαq̃vβ	PROPN
ejpam-5856	150	30	implies	imply	VERB
ejpam-5856	150	31	uαq̃clµ(vβ	uαq̃clµ(vβ	PROPN
ejpam-5856	150	32	)	)	PUNCT
ejpam-5856	150	33	or	or	CCONJ
ejpam-5856	150	34	clµ(uα)q̃vβ	clµ(uα)q̃vβ	PROPN
ejpam-5856	150	35	.	.	PUNCT
ejpam-5856	151	1	(	(	PUNCT
ejpam-5856	151	2	ii	ii	NOUN
ejpam-5856	151	3	)	)	PUNCT
ejpam-5856	151	4	fµ-t1	fµ-t1	VERB
ejpam-5856	152	1	iff	iff	VERB
ejpam-5856	152	2	for	for	ADP
ejpam-5856	152	3	any	any	DET
ejpam-5856	152	4	uα	uα	PROPN
ejpam-5856	152	5	,	,	PUNCT
ejpam-5856	152	6	vβ	vβ	ADP
ejpam-5856	152	7	∈	∈	PROPN
ejpam-5856	152	8	fp	fp	X
ejpam-5856	152	9	(	(	PUNCT
ejpam-5856	152	10	u	u	NOUN
ejpam-5856	152	11	)	)	PUNCT
ejpam-5856	152	12	with	with	ADP
ejpam-5856	152	13	uαq̃vβ	uαq̃vβ	PROPN
ejpam-5856	152	14	implies	imply	VERB
ejpam-5856	152	15	uαq̃clµ(vβ	uαq̃clµ(vβ	PROPN
ejpam-5856	152	16	)	)	PUNCT
ejpam-5856	152	17	and	and	CCONJ
ejpam-5856	152	18	clµ(uα)q̃vβ	clµ(uα)q̃vβ	PROPN
ejpam-5856	152	19	.	.	PUNCT
ejpam-5856	153	1	(	(	PUNCT
ejpam-5856	153	2	iii	iii	X
ejpam-5856	153	3	)	)	PUNCT
ejpam-5856	153	4	fµ-t2	fµ-t2	PROPN
ejpam-5856	153	5	iff	iff	PROPN
ejpam-5856	153	6	for	for	ADP
ejpam-5856	153	7	any	any	DET
ejpam-5856	153	8	uα	uα	PROPN
ejpam-5856	153	9	,	,	PUNCT
ejpam-5856	153	10	vβ	vβ	ADP
ejpam-5856	153	11	∈	∈	PROPN
ejpam-5856	153	12	fp	fp	X
ejpam-5856	153	13	(	(	PUNCT
ejpam-5856	153	14	u	u	NOUN
ejpam-5856	153	15	)	)	PUNCT
ejpam-5856	153	16	with	with	ADP
ejpam-5856	153	17	uαq̃vβ	uαq̃vβ	PROPN
ejpam-5856	153	18	,	,	PUNCT
ejpam-5856	153	19	there	there	PRON
ejpam-5856	153	20	are	be	VERB
ejpam-5856	153	21	g	g	NOUN
ejpam-5856	153	22	,	,	PUNCT
ejpam-5856	153	23	h	h	PROPN
ejpam-5856	153	24	∈	∈	PROPN
ejpam-5856	153	25	µ	µ	PRON
ejpam-5856	153	26	such	such	ADJ
ejpam-5856	153	27	that	that	SCONJ
ejpam-5856	153	28	uα	uα	PROPN
ejpam-5856	153	29	∈	∈	PROPN
ejpam-5856	153	30	g	g	PROPN
ejpam-5856	153	31	,	,	PUNCT
ejpam-5856	153	32	vβ	vβ	DET
ejpam-5856	153	33	∈	∈	PROPN
ejpam-5856	153	34	h	h	NOUN
ejpam-5856	153	35	and	and	CCONJ
ejpam-5856	153	36	gq̃h	gq̃h	PROPN
ejpam-5856	153	37	.	.	PUNCT
ejpam-5856	154	1	(	(	PUNCT
ejpam-5856	154	2	iv	iv	X
ejpam-5856	154	3	)	)	PUNCT
ejpam-5856	154	4	fµ-regular	fµ-regular	NOUN
ejpam-5856	154	5	(	(	PUNCT
ejpam-5856	154	6	or	or	CCONJ
ejpam-5856	154	7	fµ-r2	fµ-r2	PROPN
ejpam-5856	154	8	)	)	PUNCT
ejpam-5856	154	9	iff	iff	PROPN
ejpam-5856	154	10	for	for	ADP
ejpam-5856	154	11	any	any	DET
ejpam-5856	154	12	uα	uα	PROPN
ejpam-5856	154	13	∈	∈	PROPN
ejpam-5856	154	14	fp	fp	X
ejpam-5856	154	15	(	(	PUNCT
ejpam-5856	154	16	u	u	NOUN
ejpam-5856	154	17	)	)	PUNCT
ejpam-5856	154	18	and	and	CCONJ
ejpam-5856	154	19	any	any	DET
ejpam-5856	154	20	h	h	NOUN
ejpam-5856	154	21	∈	∈	PROPN
ejpam-5856	154	22	fµc(u	fµc(u	PROPN
ejpam-5856	154	23	)	)	PUNCT
ejpam-5856	154	24	with	with	ADP
ejpam-5856	154	25	uαq̃h	uαq̃h	PROPN
ejpam-5856	154	26	,	,	PUNCT
ejpam-5856	154	27	there	there	PRON
ejpam-5856	154	28	are	be	VERB
ejpam-5856	154	29	f	f	X
ejpam-5856	154	30	,	,	PUNCT
ejpam-5856	154	31	g	g	PROPN
ejpam-5856	154	32	∈	∈	PROPN
ejpam-5856	154	33	µ	µ	PRON
ejpam-5856	154	34	such	such	ADJ
ejpam-5856	154	35	that	that	SCONJ
ejpam-5856	154	36	uα	uα	PROPN
ejpam-5856	154	37	∈	∈	PROPN
ejpam-5856	154	38	f	f	PROPN
ejpam-5856	154	39	,	,	PUNCT
ejpam-5856	154	40	h	h	NOUN
ejpam-5856	154	41	⊆	⊆	NUM
ejpam-5856	154	42	g	g	NOUN
ejpam-5856	154	43	and	and	CCONJ
ejpam-5856	154	44	f	f	PROPN
ejpam-5856	154	45	q̃g	q̃g	PROPN
ejpam-5856	154	46	.	.	PUNCT
ejpam-5856	155	1	(	(	PUNCT
ejpam-5856	155	2	v	v	NOUN
ejpam-5856	155	3	)	)	PUNCT
ejpam-5856	155	4	fµ-normal	fµ-normal	NOUN
ejpam-5856	155	5	(	(	PUNCT
ejpam-5856	155	6	or	or	CCONJ
ejpam-5856	155	7	fµ-r3	fµ-r3	PRON
ejpam-5856	155	8	)	)	PUNCT
ejpam-5856	155	9	iff	iff	NOUN
ejpam-5856	155	10	for	for	ADP
ejpam-5856	155	11	any	any	DET
ejpam-5856	155	12	fµ-closed	fµ-close	VERB
ejpam-5856	155	13	sets	set	NOUN
ejpam-5856	155	14	f1	f1	NOUN
ejpam-5856	155	15	,	,	PUNCT
ejpam-5856	155	16	f2	f2	PROPN
ejpam-5856	155	17	with	with	ADP
ejpam-5856	155	18	f1q̃f2	f1q̃f2	PROPN
ejpam-5856	155	19	,	,	PUNCT
ejpam-5856	155	20	there	there	PRON
ejpam-5856	155	21	are	be	VERB
ejpam-5856	155	22	h	h	NOUN
ejpam-5856	155	23	,	,	PUNCT
ejpam-5856	155	24	g	g	PROPN
ejpam-5856	155	25	∈	∈	PROPN
ejpam-5856	155	26	µ	µ	PRON
ejpam-5856	155	27	such	such	ADJ
ejpam-5856	155	28	that	that	DET
ejpam-5856	155	29	f1	f1	PROPN
ejpam-5856	155	30	⊆	⊆	NUM
ejpam-5856	155	31	h	h	NOUN
ejpam-5856	155	32	,	,	PUNCT
ejpam-5856	155	33	f2	f2	ADV
ejpam-5856	155	34	⊆	⊆	NUM
ejpam-5856	155	35	g	g	NOUN
ejpam-5856	155	36	and	and	CCONJ
ejpam-5856	155	37	hq̃g	hq̃g	PROPN
ejpam-5856	155	38	.	.	PUNCT
ejpam-5856	156	1	(	(	PUNCT
ejpam-5856	156	2	vi	vi	NOUN
ejpam-5856	156	3	)	)	PUNCT
ejpam-5856	156	4	fµ-t3	fµ-t3	NOUN
ejpam-5856	156	5	(	(	PUNCT
ejpam-5856	156	6	resp	resp	NOUN
ejpam-5856	156	7	.	.	PUNCT
ejpam-5856	157	1	fµ-t4	fµ-t4	PROPN
ejpam-5856	157	2	)	)	PUNCT
ejpam-5856	158	1	iff	iff	VERB
ejpam-5856	158	2	it	it	PRON
ejpam-5856	158	3	is	be	AUX
ejpam-5856	158	4	both	both	PRON
ejpam-5856	158	5	fµ-r2	fµ-r2	PROPN
ejpam-5856	159	1	(	(	PUNCT
ejpam-5856	159	2	resp	resp	NOUN
ejpam-5856	159	3	.	.	PUNCT
ejpam-5856	160	1	fµ-r3	fµ-r3	CCONJ
ejpam-5856	160	2	)	)	PUNCT
ejpam-5856	161	1	and	and	CCONJ
ejpam-5856	161	2	fµ-t1	fµ-t1	AUX
ejpam-5856	161	3	.	.	PUNCT
ejpam-5856	161	4	note	note	NOUN
ejpam-5856	161	5	.	.	PUNCT
ejpam-5856	162	1	evidently	evidently	ADV
ejpam-5856	162	2	,	,	PUNCT
ejpam-5856	162	3	fµ-t4	fµ-t4	X
ejpam-5856	163	1	=	=	NOUN
ejpam-5856	163	2	⇒	⇒	NOUN
ejpam-5856	163	3	fµ-t3	fµ-t3	PUNCT
ejpam-5856	164	1	=	=	AUX
ejpam-5856	164	2	⇒	⇒	VERB
ejpam-5856	164	3	fµ-t2	fµ-t2	X
ejpam-5856	165	1	=	=	VERB
ejpam-5856	165	2	⇒	⇒	NOUN
ejpam-5856	165	3	fµ-t1	fµ-t1	PUNCT
ejpam-5856	165	4	.	.	PUNCT
ejpam-5856	166	1	definition	definition	NOUN
ejpam-5856	166	2	10	10	NUM
ejpam-5856	166	3	.	.	PUNCT
ejpam-5856	167	1	a	a	DET
ejpam-5856	167	2	map	map	NOUN
ejpam-5856	167	3	f	f	X
ejpam-5856	167	4	:	:	PUNCT
ejpam-5856	167	5	(	(	PUNCT
ejpam-5856	167	6	u	u	NOUN
ejpam-5856	167	7	,	,	PUNCT
ejpam-5856	167	8	µ1	µ1	PROPN
ejpam-5856	167	9	)	)	PUNCT
ejpam-5856	167	10	−→	−→	NOUN
ejpam-5856	167	11	(	(	PUNCT
ejpam-5856	167	12	v	v	NOUN
ejpam-5856	167	13	,	,	PUNCT
ejpam-5856	167	14	µ2	µ2	PROPN
ejpam-5856	167	15	)	)	PUNCT
ejpam-5856	167	16	is	be	AUX
ejpam-5856	167	17	called	call	VERB
ejpam-5856	167	18	:	:	PUNCT
ejpam-5856	167	19	(	(	PUNCT
ejpam-5856	167	20	i	i	NOUN
ejpam-5856	167	21	)	)	PUNCT
ejpam-5856	167	22	fµ-continuous	fµ-continuous	PROPN
ejpam-5856	167	23	iff	iff	PROPN
ejpam-5856	167	24	f−1(h	f−1(h	PROPN
ejpam-5856	167	25	)	)	PUNCT
ejpam-5856	167	26	∈	∈	PROPN
ejpam-5856	167	27	fµc(u	fµc(u	PROPN
ejpam-5856	167	28	)	)	PUNCT
ejpam-5856	167	29	for	for	ADP
ejpam-5856	167	30	each	each	DET
ejpam-5856	167	31	h	h	NOUN
ejpam-5856	167	32	∈	∈	PROPN
ejpam-5856	167	33	fµc(v)[31	fµc(v)[31	PROPN
ejpam-5856	167	34	]	]	X
ejpam-5856	167	35	.	.	PUNCT
ejpam-5856	168	1	(	(	PUNCT
ejpam-5856	168	2	ii	ii	NOUN
ejpam-5856	168	3	)	)	PUNCT
ejpam-5856	168	4	fgµ-continuous	fgµ-continuous	ADJ
ejpam-5856	168	5	iff	iff	PROPN
ejpam-5856	168	6	f−1(h	f−1(h	PROPN
ejpam-5856	168	7	)	)	PUNCT
ejpam-5856	168	8	∈	∈	PROPN
ejpam-5856	168	9	fgµc(u	fgµc(u	PROPN
ejpam-5856	168	10	)	)	PUNCT
ejpam-5856	168	11	for	for	ADP
ejpam-5856	168	12	each	each	DET
ejpam-5856	168	13	h	h	NOUN
ejpam-5856	168	14	∈	∈	NOUN
ejpam-5856	168	15	fµc(v)[15	fµc(v)[15	PROPN
ejpam-5856	168	16	]	]	X
ejpam-5856	168	17	.	.	PUNCT
ejpam-5856	169	1	(	(	PUNCT
ejpam-5856	169	2	iii	iii	X
ejpam-5856	169	3	)	)	PUNCT
ejpam-5856	169	4	fgµ-closed(fgµ-open	fgµ-closed(fgµ-open	PROPN
ejpam-5856	169	5	)	)	PUNCT
ejpam-5856	169	6	iff	iff	PROPN
ejpam-5856	169	7	f(h	f(h	PROPN
ejpam-5856	169	8	)	)	PUNCT
ejpam-5856	169	9	is	be	AUX
ejpam-5856	169	10	fgµ-closed(fgµ-open	fgµ-closed(fgµ-open	NOUN
ejpam-5856	169	11	)	)	PUNCT
ejpam-5856	169	12	set	set	VERB
ejpam-5856	169	13	in	in	ADP
ejpam-5856	169	14	(	(	PUNCT
ejpam-5856	169	15	v	v	NOUN
ejpam-5856	169	16	,	,	PUNCT
ejpam-5856	169	17	µ2	µ2	PROPN
ejpam-5856	169	18	)	)	PUNCT
ejpam-5856	169	19	for	for	ADP
ejpam-5856	169	20	every	every	DET
ejpam-5856	169	21	fµ-closed(fµ-open	fµ-closed(fµ-open	NOUN
ejpam-5856	169	22	)	)	PUNCT
ejpam-5856	169	23	set	set	NOUN
ejpam-5856	169	24	h	h	NOUN
ejpam-5856	169	25	in	in	ADP
ejpam-5856	169	26	(	(	PUNCT
ejpam-5856	169	27	u	u	NOUN
ejpam-5856	169	28	,	,	PUNCT
ejpam-5856	169	29	µ1	µ1	PROPN
ejpam-5856	169	30	)	)	PUNCT
ejpam-5856	170	1	[	[	X
ejpam-5856	170	2	14	14	NUM
ejpam-5856	170	3	]	]	PUNCT
ejpam-5856	170	4	.	.	PUNCT
ejpam-5856	171	1	note	note	VERB
ejpam-5856	171	2	.	.	PUNCT
ejpam-5856	172	1	evidently	evidently	ADV
ejpam-5856	172	2	,	,	PUNCT
ejpam-5856	172	3	every	every	DET
ejpam-5856	172	4	fµ-continuous	fµ-continuous	ADJ
ejpam-5856	172	5	is	be	AUX
ejpam-5856	172	6	fgµ-continuous	fgµ-continuous	ADJ
ejpam-5856	172	7	.	.	PUNCT
ejpam-5856	173	1	3	3	X
ejpam-5856	173	2	.	.	X
ejpam-5856	173	3	fuzzy	fuzzy	ADJ
ejpam-5856	173	4	gµ-regular	gµ-regular	ADJ
ejpam-5856	173	5	spaces	space	NOUN
ejpam-5856	173	6	in	in	ADP
ejpam-5856	173	7	this	this	DET
ejpam-5856	173	8	part	part	NOUN
ejpam-5856	173	9	,	,	PUNCT
ejpam-5856	173	10	we	we	PRON
ejpam-5856	173	11	introduce	introduce	VERB
ejpam-5856	173	12	and	and	CCONJ
ejpam-5856	173	13	discuss	discuss	VERB
ejpam-5856	173	14	some	some	DET
ejpam-5856	173	15	characteristics	characteristic	NOUN
ejpam-5856	173	16	and	and	CCONJ
ejpam-5856	173	17	properties	property	NOUN
ejpam-5856	173	18	of	of	ADP
ejpam-5856	173	19	a	a	DET
ejpam-5856	173	20	new	new	ADJ
ejpam-5856	173	21	class	class	NOUN
ejpam-5856	173	22	of	of	ADP
ejpam-5856	173	23	spaces	space	NOUN
ejpam-5856	173	24	named	name	VERB
ejpam-5856	173	25	,	,	PUNCT
ejpam-5856	173	26	fgµ-regular	fgµ-regular	ADJ
ejpam-5856	173	27	spaces	space	NOUN
ejpam-5856	173	28	in	in	ADP
ejpam-5856	173	29	gfts	gft	NOUN
ejpam-5856	173	30	.	.	PUNCT
ejpam-5856	174	1	first	first	ADV
ejpam-5856	174	2	let	let	VERB
ejpam-5856	174	3	’s	’s	NOUN
ejpam-5856	174	4	give	give	VERB
ejpam-5856	174	5	the	the	DET
ejpam-5856	174	6	next	next	ADJ
ejpam-5856	174	7	definition	definition	NOUN
ejpam-5856	174	8	.	.	PUNCT
ejpam-5856	175	1	definition	definition	NOUN
ejpam-5856	175	2	11	11	NUM
ejpam-5856	175	3	.	.	PUNCT
ejpam-5856	176	1	an	an	DET
ejpam-5856	176	2	gfts	gft	NOUN
ejpam-5856	176	3	(	(	PUNCT
ejpam-5856	176	4	u	u	NOUN
ejpam-5856	176	5	,	,	PUNCT
ejpam-5856	176	6	µ	µ	NOUN
ejpam-5856	176	7	)	)	PUNCT
ejpam-5856	176	8	is	be	AUX
ejpam-5856	176	9	named	name	VERB
ejpam-5856	176	10	:	:	PUNCT
ejpam-5856	176	11	(	(	PUNCT
ejpam-5856	176	12	i	i	NOUN
ejpam-5856	176	13	)	)	PUNCT
ejpam-5856	176	14	fµ-t	fµ-t	PROPN
ejpam-5856	176	15	1	1	NUM
ejpam-5856	176	16	2	2	NUM
ejpam-5856	176	17	iff	iff	NOUN
ejpam-5856	176	18	every	every	DET
ejpam-5856	176	19	fgµ-closed	fgµ-closed	ADJ
ejpam-5856	176	20	set	set	NOUN
ejpam-5856	176	21	in	in	ADP
ejpam-5856	176	22	(	(	PUNCT
ejpam-5856	176	23	u	u	INTJ
ejpam-5856	176	24	,	,	PUNCT
ejpam-5856	176	25	µ	µ	NOUN
ejpam-5856	176	26	)	)	PUNCT
ejpam-5856	176	27	is	be	AUX
ejpam-5856	176	28	an	an	DET
ejpam-5856	176	29	fµ-closed	fµ-close	VERB
ejpam-5856	176	30	set	set	NOUN
ejpam-5856	176	31	.	.	PUNCT
ejpam-5856	177	1	s.	s.	PROPN
ejpam-5856	177	2	saleh	saleh	PROPN
ejpam-5856	177	3	et	et	PROPN
ejpam-5856	177	4	al	al	PROPN
ejpam-5856	177	5	.	.	PUNCT
ejpam-5856	177	6	/	/	SYM
ejpam-5856	177	7	eur	eur	PROPN
ejpam-5856	177	8	.	.	PUNCT
ejpam-5856	178	1	j.	j.	PROPN
ejpam-5856	178	2	pure	pure	PROPN
ejpam-5856	178	3	appl	appl	PROPN
ejpam-5856	178	4	.	.	PROPN
ejpam-5856	178	5	math	math	PROPN
ejpam-5856	178	6	,	,	PUNCT
ejpam-5856	178	7	18	18	NUM
ejpam-5856	178	8	(	(	PUNCT
ejpam-5856	178	9	1	1	NUM
ejpam-5856	178	10	)	)	PUNCT
ejpam-5856	178	11	(	(	PUNCT
ejpam-5856	178	12	2025	2025	NUM
ejpam-5856	178	13	)	)	PUNCT
ejpam-5856	178	14	,	,	PUNCT
ejpam-5856	178	15	5856	5856	NUM
ejpam-5856	178	16	6	6	NUM
ejpam-5856	178	17	of	of	ADP
ejpam-5856	178	18	15	15	NUM
ejpam-5856	178	19	(	(	PUNCT
ejpam-5856	178	20	ii	ii	NOUN
ejpam-5856	178	21	)	)	PUNCT
ejpam-5856	178	22	fµ-t2	fµ-t2	NOUN
ejpam-5856	179	1	1	1	NUM
ejpam-5856	179	2	2	2	NUM
ejpam-5856	179	3	iff	iff	NOUN
ejpam-5856	179	4	for	for	ADP
ejpam-5856	179	5	each	each	DET
ejpam-5856	179	6	uα	uα	PROPN
ejpam-5856	179	7	,	,	PUNCT
ejpam-5856	179	8	vβ	vβ	PRON
ejpam-5856	179	9	∈	∈	PROPN
ejpam-5856	179	10	fp	fp	X
ejpam-5856	179	11	(	(	PUNCT
ejpam-5856	179	12	u	u	NOUN
ejpam-5856	179	13	)	)	PUNCT
ejpam-5856	179	14	with	with	ADP
ejpam-5856	179	15	uαq̃vβ	uαq̃vβ	PROPN
ejpam-5856	179	16	,	,	PUNCT
ejpam-5856	179	17	there	there	PRON
ejpam-5856	179	18	are	be	VERB
ejpam-5856	179	19	g	g	NOUN
ejpam-5856	179	20	,	,	PUNCT
ejpam-5856	179	21	h	h	PROPN
ejpam-5856	179	22	∈	∈	PROPN
ejpam-5856	179	23	µ	µ	PRON
ejpam-5856	179	24	such	such	ADJ
ejpam-5856	179	25	uα	uα	PROPN
ejpam-5856	179	26	∈	∈	PROPN
ejpam-5856	179	27	g	g	PROPN
ejpam-5856	179	28	,	,	PUNCT
ejpam-5856	179	29	vβ	vβ	DET
ejpam-5856	179	30	∈	∈	PROPN
ejpam-5856	179	31	h	h	NOUN
ejpam-5856	179	32	and	and	CCONJ
ejpam-5856	179	33	clµ(g)q̃clµ(h	clµ(g)q̃clµ(h	NOUN
ejpam-5856	179	34	)	)	PUNCT
ejpam-5856	179	35	.	.	PUNCT
ejpam-5856	180	1	proposition	proposition	NOUN
ejpam-5856	180	2	2	2	NUM
ejpam-5856	180	3	.	.	X
ejpam-5856	180	4	for	for	ADP
ejpam-5856	180	5	an	an	DET
ejpam-5856	180	6	gfts	gft	NOUN
ejpam-5856	180	7	(	(	PUNCT
ejpam-5856	180	8	u	u	NOUN
ejpam-5856	180	9	,	,	PUNCT
ejpam-5856	180	10	µ	µ	NOUN
ejpam-5856	180	11	)	)	PUNCT
ejpam-5856	180	12	,	,	PUNCT
ejpam-5856	180	13	the	the	DET
ejpam-5856	180	14	next	next	ADJ
ejpam-5856	180	15	items	item	NOUN
ejpam-5856	180	16	are	be	AUX
ejpam-5856	180	17	equivalent	equivalent	ADJ
ejpam-5856	180	18	:	:	PUNCT
ejpam-5856	180	19	(	(	PUNCT
ejpam-5856	180	20	1	1	X
ejpam-5856	180	21	)	)	PUNCT
ejpam-5856	180	22	(	(	PUNCT
ejpam-5856	180	23	u	u	NOUN
ejpam-5856	180	24	,	,	PUNCT
ejpam-5856	180	25	µ	µ	NOUN
ejpam-5856	180	26	)	)	PUNCT
ejpam-5856	180	27	is	be	AUX
ejpam-5856	180	28	fµ-t	fµ-t	PROPN
ejpam-5856	180	29	1	1	NUM
ejpam-5856	180	30	2	2	NUM
ejpam-5856	180	31	.	.	PUNCT
ejpam-5856	181	1	(	(	PUNCT
ejpam-5856	181	2	2	2	X
ejpam-5856	181	3	)	)	PUNCT
ejpam-5856	181	4	every	every	DET
ejpam-5856	181	5	fgµ-closed	fgµ-closed	ADJ
ejpam-5856	181	6	set	set	NOUN
ejpam-5856	181	7	is	be	AUX
ejpam-5856	181	8	an	an	DET
ejpam-5856	181	9	fµ-locally	fµ-locally	ADV
ejpam-5856	181	10	closed	close	VERB
ejpam-5856	181	11	set	set	NOUN
ejpam-5856	181	12	.	.	PUNCT
ejpam-5856	182	1	proof	proof	NOUN
ejpam-5856	182	2	.	.	PUNCT
ejpam-5856	183	1	(	(	PUNCT
ejpam-5856	183	2	1	1	X
ejpam-5856	183	3	)	)	PUNCT
ejpam-5856	183	4	=	=	NOUN
ejpam-5856	183	5	⇒	⇒	NOUN
ejpam-5856	183	6	(	(	PUNCT
ejpam-5856	183	7	2	2	NUM
ejpam-5856	183	8	)	)	PUNCT
ejpam-5856	183	9	.	.	PUNCT
ejpam-5856	184	1	let	let	VERB
ejpam-5856	184	2	(	(	PUNCT
ejpam-5856	184	3	u	u	NOUN
ejpam-5856	184	4	,	,	PUNCT
ejpam-5856	184	5	µ	µ	NOUN
ejpam-5856	184	6	)	)	PUNCT
ejpam-5856	184	7	be	be	VERB
ejpam-5856	184	8	an	an	DET
ejpam-5856	184	9	fµ-t	fµ-t	PROPN
ejpam-5856	184	10	1	1	NUM
ejpam-5856	184	11	2	2	NUM
ejpam-5856	184	12	space	space	NOUN
ejpam-5856	184	13	,	,	PUNCT
ejpam-5856	184	14	then	then	ADV
ejpam-5856	184	15	every	every	DET
ejpam-5856	184	16	fgµ-closed	fgµ-closed	ADJ
ejpam-5856	184	17	set	set	NOUN
ejpam-5856	184	18	is	be	AUX
ejpam-5856	184	19	fµclosed	fµclose	VERB
ejpam-5856	184	20	set	set	VERB
ejpam-5856	184	21	.	.	PUNCT
ejpam-5856	185	1	by	by	ADP
ejpam-5856	185	2	remark	remark	NOUN
ejpam-5856	185	3	1	1	NUM
ejpam-5856	185	4	,	,	PUNCT
ejpam-5856	185	5	every	every	DET
ejpam-5856	185	6	fµ-closed	fµ-close	VERB
ejpam-5856	185	7	set	set	NOUN
ejpam-5856	185	8	is	be	AUX
ejpam-5856	185	9	fµ-locally	fµ-locally	ADV
ejpam-5856	185	10	closed	close	VERB
ejpam-5856	185	11	set	set	VERB
ejpam-5856	185	12	.	.	PUNCT
ejpam-5856	186	1	the	the	DET
ejpam-5856	186	2	result	result	NOUN
ejpam-5856	186	3	holds	hold	VERB
ejpam-5856	186	4	.	.	PUNCT
ejpam-5856	187	1	(	(	PUNCT
ejpam-5856	187	2	2	2	X
ejpam-5856	187	3	)	)	PUNCT
ejpam-5856	187	4	=	=	NOUN
ejpam-5856	187	5	⇒	⇒	NOUN
ejpam-5856	187	6	(	(	PUNCT
ejpam-5856	187	7	1	1	NUM
ejpam-5856	187	8	)	)	PUNCT
ejpam-5856	187	9	.	.	PUNCT
ejpam-5856	188	1	it	it	PRON
ejpam-5856	188	2	follows	follow	VERB
ejpam-5856	188	3	directly	directly	ADV
ejpam-5856	188	4	from	from	ADP
ejpam-5856	188	5	proposition	proposition	NOUN
ejpam-5856	188	6	1	1	NUM
ejpam-5856	188	7	.	.	PUNCT
ejpam-5856	188	8	definition	definition	NOUN
ejpam-5856	188	9	12	12	NUM
ejpam-5856	188	10	.	.	PUNCT
ejpam-5856	189	1	an	an	DET
ejpam-5856	189	2	gfts	gft	NOUN
ejpam-5856	189	3	(	(	PUNCT
ejpam-5856	189	4	u	u	NOUN
ejpam-5856	189	5	,	,	PUNCT
ejpam-5856	189	6	µ	µ	NOUN
ejpam-5856	189	7	)	)	PUNCT
ejpam-5856	189	8	is	be	AUX
ejpam-5856	189	9	called	call	VERB
ejpam-5856	189	10	fgµ-regular	fgµ-regular	ADJ
ejpam-5856	189	11	(	(	PUNCT
ejpam-5856	189	12	or	or	CCONJ
ejpam-5856	189	13	fg-µr2	fg-µr2	NOUN
ejpam-5856	189	14	)	)	PUNCT
ejpam-5856	189	15	iff	iff	NOUN
ejpam-5856	189	16	for	for	ADP
ejpam-5856	189	17	every	every	DET
ejpam-5856	189	18	fgµclosed	fgµclose	VERB
ejpam-5856	189	19	set	set	VERB
ejpam-5856	189	20	h	h	NOUN
ejpam-5856	189	21	with	with	ADP
ejpam-5856	189	22	uαq̃h	uαq̃h	PROPN
ejpam-5856	189	23	for	for	ADP
ejpam-5856	189	24	each	each	DET
ejpam-5856	189	25	f	f	PROPN
ejpam-5856	189	26	-point	-point	PROPN
ejpam-5856	189	27	uα	uα	PROPN
ejpam-5856	189	28	,	,	PUNCT
ejpam-5856	189	29	there	there	PRON
ejpam-5856	189	30	are	be	VERB
ejpam-5856	189	31	fµ-open	fµ-open	ADJ
ejpam-5856	189	32	sets	set	NOUN
ejpam-5856	189	33	f	f	X
ejpam-5856	189	34	,	,	PUNCT
ejpam-5856	189	35	g	g	PROPN
ejpam-5856	189	36	containing	contain	VERB
ejpam-5856	189	37	uα	uα	PROPN
ejpam-5856	189	38	,	,	PUNCT
ejpam-5856	189	39	h	h	NOUN
ejpam-5856	189	40	respectively	respectively	ADV
ejpam-5856	189	41	,	,	PUNCT
ejpam-5856	190	1	such	such	ADJ
ejpam-5856	190	2	that	that	SCONJ
ejpam-5856	190	3	f	f	PROPN
ejpam-5856	190	4	q̃g	q̃g	PROPN
ejpam-5856	190	5	.	.	PUNCT
ejpam-5856	190	6	remark	remark	PROPN
ejpam-5856	190	7	3	3	NUM
ejpam-5856	190	8	.	.	PUNCT
ejpam-5856	191	1	evidently	evidently	ADV
ejpam-5856	191	2	,	,	PUNCT
ejpam-5856	191	3	any	any	DET
ejpam-5856	191	4	fg-µr2	fg-µr2	NOUN
ejpam-5856	191	5	space	space	NOUN
ejpam-5856	191	6	is	be	AUX
ejpam-5856	191	7	fµ-r2	fµ-r2	NOUN
ejpam-5856	191	8	but	but	CCONJ
ejpam-5856	191	9	not	not	PART
ejpam-5856	191	10	conversely	conversely	ADV
ejpam-5856	191	11	.	.	PUNCT
ejpam-5856	192	1	example	example	NOUN
ejpam-5856	193	1	1	1	NUM
ejpam-5856	193	2	.	.	PUNCT
ejpam-5856	193	3	let	let	VERB
ejpam-5856	193	4	u	u	PRON
ejpam-5856	193	5	=	=	PUNCT
ejpam-5856	193	6	{	{	PUNCT
ejpam-5856	193	7	u	u	NOUN
ejpam-5856	193	8	,	,	PUNCT
ejpam-5856	193	9	v	v	NOUN
ejpam-5856	193	10	}	}	PUNCT
ejpam-5856	193	11	and	and	CCONJ
ejpam-5856	193	12	µ	µ	X
ejpam-5856	193	13	=	=	SYM
ejpam-5856	193	14	{	{	PUNCT
ejpam-5856	193	15	0	0	NUM
ejpam-5856	193	16	,	,	PUNCT
ejpam-5856	193	17	1	1	NUM
ejpam-5856	193	18	,	,	PUNCT
ejpam-5856	193	19	h	h	NOUN
ejpam-5856	193	20	,	,	PUNCT
ejpam-5856	193	21	g	g	NOUN
ejpam-5856	193	22	}	}	PUNCT
ejpam-5856	193	23	,	,	PUNCT
ejpam-5856	193	24	where	where	SCONJ
ejpam-5856	193	25	h	h	NOUN
ejpam-5856	193	26	=	=	SYM
ejpam-5856	193	27	(	(	PUNCT
ejpam-5856	193	28	u0.3	u0.3	PROPN
ejpam-5856	193	29	,	,	PUNCT
ejpam-5856	193	30	v0.5	v0.5	NOUN
ejpam-5856	193	31	)	)	PUNCT
ejpam-5856	193	32	,	,	PUNCT
ejpam-5856	193	33	g	g	NOUN
ejpam-5856	193	34	=	=	SYM
ejpam-5856	193	35	(	(	PUNCT
ejpam-5856	193	36	u0.7	u0.7	PROPN
ejpam-5856	193	37	,	,	PUNCT
ejpam-5856	193	38	v0.5	v0.5	NOUN
ejpam-5856	193	39	)	)	PUNCT
ejpam-5856	193	40	,	,	PUNCT
ejpam-5856	193	41	then	then	ADV
ejpam-5856	193	42	µ	µ	NOUN
ejpam-5856	193	43	is	be	AUX
ejpam-5856	193	44	an	an	DET
ejpam-5856	193	45	gft	gft	PROPN
ejpam-5856	193	46	on	on	ADP
ejpam-5856	193	47	u	u	PROPN
ejpam-5856	193	48	.	.	PUNCT
ejpam-5856	194	1	one	one	PRON
ejpam-5856	194	2	can	can	AUX
ejpam-5856	194	3	check	check	VERB
ejpam-5856	194	4	that	that	PRON
ejpam-5856	194	5	(	(	PUNCT
ejpam-5856	194	6	u	u	NOUN
ejpam-5856	194	7	,	,	PUNCT
ejpam-5856	194	8	µ	µ	NOUN
ejpam-5856	194	9	)	)	PUNCT
ejpam-5856	194	10	is	be	AUX
ejpam-5856	194	11	fµ-r2	fµ-r2	PROPN
ejpam-5856	194	12	but	but	CCONJ
ejpam-5856	194	13	not	not	PART
ejpam-5856	194	14	fg-µr2	fg-µr2	NOUN
ejpam-5856	194	15	.	.	PUNCT
ejpam-5856	195	1	indeed	indeed	ADV
ejpam-5856	195	2	,	,	PUNCT
ejpam-5856	195	3	for	for	ADP
ejpam-5856	195	4	u0.5	u0.5	PRON
ejpam-5856	195	5	∈	∈	PROPN
ejpam-5856	195	6	fp	fp	X
ejpam-5856	195	7	(	(	PUNCT
ejpam-5856	195	8	u	u	NOUN
ejpam-5856	195	9	)	)	PUNCT
ejpam-5856	195	10	and	and	CCONJ
ejpam-5856	195	11	fgµ-closed	fgµ-close	VERB
ejpam-5856	195	12	set	set	VERB
ejpam-5856	195	13	f	f	PROPN
ejpam-5856	195	14	=	=	SYM
ejpam-5856	195	15	(	(	PUNCT
ejpam-5856	195	16	u0.4	u0.4	PROPN
ejpam-5856	195	17	,	,	PUNCT
ejpam-5856	195	18	v0.7	v0.7	NOUN
ejpam-5856	195	19	)	)	PUNCT
ejpam-5856	195	20	with	with	ADP
ejpam-5856	195	21	u0.5q̃f	u0.5q̃f	PRON
ejpam-5856	195	22	,	,	PUNCT
ejpam-5856	195	23	there	there	PRON
ejpam-5856	195	24	are	be	VERB
ejpam-5856	195	25	ou0.5	ou0.5	NOUN
ejpam-5856	195	26	=	=	SYM
ejpam-5856	195	27	g	g	PROPN
ejpam-5856	195	28	∈	∈	PROPN
ejpam-5856	195	29	µ	µ	X
ejpam-5856	195	30	and	and	CCONJ
ejpam-5856	195	31	of	of	ADP
ejpam-5856	195	32	=	=	SYM
ejpam-5856	195	33	1	1	NUM
ejpam-5856	195	34	∈	∈	PROPN
ejpam-5856	195	35	µ	µ	NOUN
ejpam-5856	195	36	but	but	CCONJ
ejpam-5856	195	37	ou0.5qof	ou0.5qof	NOUN
ejpam-5856	195	38	.	.	PUNCT
ejpam-5856	196	1	hence	hence	ADV
ejpam-5856	196	2	(	(	PUNCT
ejpam-5856	196	3	u	u	NOUN
ejpam-5856	196	4	,	,	PUNCT
ejpam-5856	196	5	µ	µ	NOUN
ejpam-5856	196	6	)	)	PUNCT
ejpam-5856	196	7	is	be	AUX
ejpam-5856	196	8	not	not	PART
ejpam-5856	196	9	fg-µr2	fg-µr2	NOUN
ejpam-5856	196	10	.	.	PUNCT
ejpam-5856	197	1	theorem	theorem	NOUN
ejpam-5856	197	2	1	1	NUM
ejpam-5856	197	3	.	.	PUNCT
ejpam-5856	198	1	an	an	DET
ejpam-5856	198	2	gfts	gft	NOUN
ejpam-5856	198	3	(	(	PUNCT
ejpam-5856	198	4	u	u	NOUN
ejpam-5856	198	5	,	,	PUNCT
ejpam-5856	198	6	µ	µ	NOUN
ejpam-5856	198	7	)	)	PUNCT
ejpam-5856	198	8	is	be	AUX
ejpam-5856	198	9	fg-µr2	fg-µr2	NOUN
ejpam-5856	198	10	if	if	SCONJ
ejpam-5856	198	11	and	and	CCONJ
ejpam-5856	198	12	only	only	ADV
ejpam-5856	198	13	if	if	SCONJ
ejpam-5856	198	14	is	be	AUX
ejpam-5856	198	15	both	both	DET
ejpam-5856	198	16	fµ-r2	fµ-r2	PROPN
ejpam-5856	198	17	and	and	CCONJ
ejpam-5856	198	18	fµ-t	fµ-t	PROPN
ejpam-5856	198	19	1	1	NUM
ejpam-5856	198	20	2	2	NUM
ejpam-5856	198	21	.	.	PUNCT
ejpam-5856	199	1	proof	proof	NOUN
ejpam-5856	199	2	.	.	PUNCT
ejpam-5856	200	1	assume	assume	VERB
ejpam-5856	200	2	that	that	SCONJ
ejpam-5856	200	3	(	(	PUNCT
ejpam-5856	200	4	u	u	NOUN
ejpam-5856	200	5	,	,	PUNCT
ejpam-5856	200	6	µ	µ	NOUN
ejpam-5856	200	7	)	)	PUNCT
ejpam-5856	200	8	is	be	AUX
ejpam-5856	200	9	fg-µr2	fg-µr2	NOUN
ejpam-5856	200	10	.	.	PUNCT
ejpam-5856	201	1	by	by	ADP
ejpam-5856	201	2	remark	remark	NOUN
ejpam-5856	201	3	3	3	NUM
ejpam-5856	201	4	,	,	PUNCT
ejpam-5856	201	5	it	it	PRON
ejpam-5856	201	6	is	be	AUX
ejpam-5856	201	7	fµ-r2	fµ-r2	PROPN
ejpam-5856	201	8	.	.	PUNCT
ejpam-5856	202	1	let	let	VERB
ejpam-5856	202	2	h	h	NOUN
ejpam-5856	202	3	be	be	AUX
ejpam-5856	202	4	any	any	DET
ejpam-5856	202	5	fgµ-closed	fgµ-closed	ADJ
ejpam-5856	202	6	set	set	NOUN
ejpam-5856	202	7	with	with	ADP
ejpam-5856	202	8	uαq̃h	uαq̃h	PROPN
ejpam-5856	202	9	for	for	ADP
ejpam-5856	202	10	each	each	DET
ejpam-5856	202	11	uα	uα	PROPN
ejpam-5856	202	12	∈	∈	PROPN
ejpam-5856	202	13	fp	fp	X
ejpam-5856	202	14	(	(	PUNCT
ejpam-5856	202	15	u	u	NOUN
ejpam-5856	202	16	)	)	PUNCT
ejpam-5856	202	17	that	that	PRON
ejpam-5856	202	18	is	be	AUX
ejpam-5856	202	19	,	,	PUNCT
ejpam-5856	202	20	uα	uα	PROPN
ejpam-5856	202	21	∈	∈	PROPN
ejpam-5856	202	22	hc	hc	PROPN
ejpam-5856	202	23	,	,	PUNCT
ejpam-5856	202	24	there	there	PRON
ejpam-5856	202	25	are	be	VERB
ejpam-5856	202	26	f	f	X
ejpam-5856	202	27	,	,	PUNCT
ejpam-5856	202	28	g	g	PROPN
ejpam-5856	202	29	∈	∈	PROPN
ejpam-5856	202	30	µ	µ	PRON
ejpam-5856	202	31	such	such	ADJ
ejpam-5856	202	32	that	that	DET
ejpam-5856	202	33	ouα	ouα	NOUN
ejpam-5856	202	34	∈	∈	PROPN
ejpam-5856	202	35	f	f	PROPN
ejpam-5856	202	36	,	,	PUNCT
ejpam-5856	202	37	h	h	NOUN
ejpam-5856	202	38	⊆	⊆	NUM
ejpam-5856	202	39	g	g	NOUN
ejpam-5856	202	40	and	and	CCONJ
ejpam-5856	202	41	f	f	PROPN
ejpam-5856	202	42	q̃g	q̃g	NOUN
ejpam-5856	202	43	implies	imply	VERB
ejpam-5856	202	44	that	that	SCONJ
ejpam-5856	202	45	f	f	PROPN
ejpam-5856	202	46	q̃h	q̃h	PROPN
ejpam-5856	202	47	.	.	PROPN
ejpam-5856	203	1	from	from	ADP
ejpam-5856	203	2	lemma	lemma	PROPN
ejpam-5856	203	3	1	1	NUM
ejpam-5856	203	4	,	,	PUNCT
ejpam-5856	203	5	we	we	PRON
ejpam-5856	203	6	have	have	VERB
ejpam-5856	203	7	uαq̃clµ(h	uαq̃clµ(h	NOUN
ejpam-5856	203	8	)	)	PUNCT
ejpam-5856	203	9	that	that	PRON
ejpam-5856	203	10	is	be	AUX
ejpam-5856	203	11	,	,	PUNCT
ejpam-5856	204	1	uα∈(clµ(h))c	uα∈(clµ(h))c	PROPN
ejpam-5856	204	2	.	.	PUNCT
ejpam-5856	205	1	therefore	therefore	ADV
ejpam-5856	205	2	,	,	PUNCT
ejpam-5856	205	3	hc⊆(clµ	hc⊆(clµ	PROPN
ejpam-5856	205	4	(	(	PUNCT
ejpam-5856	205	5	h))c	h))c	PROPN
ejpam-5856	205	6	implies	imply	VERB
ejpam-5856	205	7	clµ(h)⊆h	clµ(h)⊆h	PROPN
ejpam-5856	205	8	and	and	CCONJ
ejpam-5856	205	9	so	so	ADV
ejpam-5856	205	10	,	,	PUNCT
ejpam-5856	205	11	h	h	NOUN
ejpam-5856	205	12	=	=	SYM
ejpam-5856	205	13	clµ(h	clµ(h	X
ejpam-5856	205	14	)	)	PUNCT
ejpam-5856	205	15	this	this	PRON
ejpam-5856	205	16	means	mean	VERB
ejpam-5856	205	17	that	that	SCONJ
ejpam-5856	205	18	,	,	PUNCT
ejpam-5856	205	19	any	any	DET
ejpam-5856	205	20	fgµ-closed	fgµ-closed	ADJ
ejpam-5856	205	21	set	set	NOUN
ejpam-5856	205	22	in	in	ADP
ejpam-5856	205	23	(	(	PUNCT
ejpam-5856	205	24	u	u	INTJ
ejpam-5856	205	25	,	,	PUNCT
ejpam-5856	205	26	µ	µ	NOUN
ejpam-5856	205	27	)	)	PUNCT
ejpam-5856	205	28	is	be	AUX
ejpam-5856	205	29	an	an	DET
ejpam-5856	205	30	fµ-closed	fµ-close	VERB
ejpam-5856	205	31	set	set	NOUN
ejpam-5856	205	32	.	.	PUNCT
ejpam-5856	206	1	hence	hence	ADV
ejpam-5856	206	2	(	(	PUNCT
ejpam-5856	206	3	u	u	NOUN
ejpam-5856	206	4	,	,	PUNCT
ejpam-5856	206	5	µ	µ	NOUN
ejpam-5856	206	6	)	)	PUNCT
ejpam-5856	206	7	is	be	AUX
ejpam-5856	206	8	fµ-t	fµ-t	PROPN
ejpam-5856	206	9	1	1	NUM
ejpam-5856	206	10	2	2	NUM
ejpam-5856	206	11	.	.	PUNCT
ejpam-5856	207	1	conversely	conversely	ADV
ejpam-5856	207	2	,	,	PUNCT
ejpam-5856	207	3	it	it	PRON
ejpam-5856	207	4	is	be	AUX
ejpam-5856	207	5	obvious	obvious	ADJ
ejpam-5856	207	6	.	.	PUNCT
ejpam-5856	208	1	theorem	theorem	NOUN
ejpam-5856	208	2	2	2	NUM
ejpam-5856	208	3	.	.	X
ejpam-5856	209	1	let	let	VERB
ejpam-5856	209	2	(	(	PUNCT
ejpam-5856	209	3	u	u	NOUN
ejpam-5856	209	4	,	,	PUNCT
ejpam-5856	209	5	µ	µ	NOUN
ejpam-5856	209	6	)	)	PUNCT
ejpam-5856	209	7	be	be	VERB
ejpam-5856	209	8	gfts	gft	NOUN
ejpam-5856	209	9	and	and	CCONJ
ejpam-5856	209	10	uα	uα	PROPN
ejpam-5856	209	11	∈	∈	PROPN
ejpam-5856	209	12	fp	fp	PROPN
ejpam-5856	209	13	(	(	PUNCT
ejpam-5856	209	14	u	u	NOUN
ejpam-5856	209	15	)	)	PUNCT
ejpam-5856	209	16	.	.	PUNCT
ejpam-5856	210	1	the	the	DET
ejpam-5856	210	2	next	next	ADJ
ejpam-5856	210	3	items	item	NOUN
ejpam-5856	210	4	are	be	AUX
ejpam-5856	210	5	equivalent	equivalent	ADJ
ejpam-5856	210	6	:	:	PUNCT
ejpam-5856	210	7	(	(	PUNCT
ejpam-5856	210	8	1	1	X
ejpam-5856	210	9	)	)	PUNCT
ejpam-5856	210	10	(	(	PUNCT
ejpam-5856	210	11	u	u	NOUN
ejpam-5856	210	12	,	,	PUNCT
ejpam-5856	210	13	µ	µ	NOUN
ejpam-5856	210	14	)	)	PUNCT
ejpam-5856	210	15	is	be	AUX
ejpam-5856	210	16	fg-µr2	fg-µr2	NOUN
ejpam-5856	210	17	,	,	PUNCT
ejpam-5856	210	18	(	(	PUNCT
ejpam-5856	210	19	2	2	X
ejpam-5856	210	20	)	)	PUNCT
ejpam-5856	210	21	for	for	ADP
ejpam-5856	210	22	any	any	DET
ejpam-5856	210	23	fgµ-open	fgµ-open	ADJ
ejpam-5856	210	24	set	set	VERB
ejpam-5856	210	25	ouα	ouα	NOUN
ejpam-5856	210	26	containing	contain	VERB
ejpam-5856	210	27	uα	uα	NOUN
ejpam-5856	210	28	,	,	PUNCT
ejpam-5856	210	29	there	there	PRON
ejpam-5856	210	30	is	be	VERB
ejpam-5856	210	31	o∗	o∗	PROPN
ejpam-5856	210	32	uα	uα	PROPN
ejpam-5856	210	33	∈	∈	PROPN
ejpam-5856	210	34	µ	µ	PRON
ejpam-5856	210	35	such	such	ADJ
ejpam-5856	211	1	that	that	SCONJ
ejpam-5856	211	2	clµ(o	clµ(o	PROPN
ejpam-5856	211	3	∗	∗	NOUN
ejpam-5856	211	4	uα	uα	PROPN
ejpam-5856	211	5	)	)	PUNCT
ejpam-5856	211	6	⊆	⊆	NUM
ejpam-5856	211	7	ouα	ouα	NOUN
ejpam-5856	211	8	.	.	PUNCT
ejpam-5856	212	1	proof	proof	NOUN
ejpam-5856	212	2	.	.	PUNCT
ejpam-5856	213	1	(	(	PUNCT
ejpam-5856	213	2	1	1	X
ejpam-5856	213	3	)	)	PUNCT
ejpam-5856	213	4	=	=	NOUN
ejpam-5856	213	5	⇒	⇒	NOUN
ejpam-5856	213	6	(	(	PUNCT
ejpam-5856	213	7	2	2	NUM
ejpam-5856	213	8	)	)	PUNCT
ejpam-5856	213	9	.	.	PUNCT
ejpam-5856	214	1	suppose	suppose	VERB
ejpam-5856	214	2	that	that	SCONJ
ejpam-5856	214	3	(	(	PUNCT
ejpam-5856	214	4	u	u	NOUN
ejpam-5856	214	5	,	,	PUNCT
ejpam-5856	214	6	µ	µ	NOUN
ejpam-5856	214	7	)	)	PUNCT
ejpam-5856	214	8	is	be	AUX
ejpam-5856	214	9	fg-µr2	fg-µr2	NOUN
ejpam-5856	214	10	and	and	CCONJ
ejpam-5856	214	11	ouα	ouα	NOUN
ejpam-5856	214	12	is	be	AUX
ejpam-5856	214	13	an	an	DET
ejpam-5856	214	14	fgµ-open	fgµ-open	ADJ
ejpam-5856	214	15	set	set	NOUN
ejpam-5856	214	16	containing	contain	VERB
ejpam-5856	214	17	uα	uα	PROPN
ejpam-5856	214	18	,	,	PUNCT
ejpam-5856	214	19	we	we	PRON
ejpam-5856	214	20	have	have	VERB
ejpam-5856	214	21	o	o	PROPN
ejpam-5856	214	22	c	c	NOUN
ejpam-5856	215	1	uα	uα	NOUN
ejpam-5856	215	2	=	=	PUNCT
ejpam-5856	215	3	h	h	PROPN
ejpam-5856	215	4	∈	∈	PROPN
ejpam-5856	215	5	fgµc(u	fgµc(u	PROPN
ejpam-5856	215	6	)	)	PUNCT
ejpam-5856	215	7	.	.	PUNCT
ejpam-5856	216	1	clearly	clearly	ADV
ejpam-5856	216	2	,	,	PUNCT
ejpam-5856	216	3	ouα	ouα	NOUN
ejpam-5856	216	4	q̃h	q̃h	PROPN
ejpam-5856	216	5	that	that	PRON
ejpam-5856	216	6	is	be	AUX
ejpam-5856	216	7	,	,	PUNCT
ejpam-5856	216	8	uαq̃h	uαq̃h	PROPN
ejpam-5856	216	9	.	.	PUNCT
ejpam-5856	217	1	since	since	SCONJ
ejpam-5856	217	2	(	(	PUNCT
ejpam-5856	217	3	u	u	INTJ
ejpam-5856	217	4	,	,	PUNCT
ejpam-5856	217	5	µ	µ	NOUN
ejpam-5856	217	6	)	)	PUNCT
ejpam-5856	217	7	is	be	AUX
ejpam-5856	217	8	fg-µr2	fg-µr2	NOUN
ejpam-5856	217	9	,	,	PUNCT
ejpam-5856	217	10	there	there	PRON
ejpam-5856	217	11	are	be	VERB
ejpam-5856	217	12	o∗	o∗	PROPN
ejpam-5856	217	13	uα	uα	PROPN
ejpam-5856	217	14	,	,	PUNCT
ejpam-5856	218	1	oh	oh	INTJ
ejpam-5856	218	2	∈	∈	PROPN
ejpam-5856	218	3	µ	µ	PRON
ejpam-5856	218	4	such	such	ADJ
ejpam-5856	218	5	that	that	PRON
ejpam-5856	218	6	o∗	o∗	PROPN
ejpam-5856	218	7	uα	uα	PROPN
ejpam-5856	218	8	q̃oh	q̃oh	PROPN
ejpam-5856	218	9	implies	imply	VERB
ejpam-5856	218	10	that	that	SCONJ
ejpam-5856	218	11	o∗	o∗	PROPN
ejpam-5856	218	12	uα	uα	PROPN
ejpam-5856	218	13	⊆oc	⊆oc	PRON
ejpam-5856	218	14	h	h	NOUN
ejpam-5856	219	1	so	so	SCONJ
ejpam-5856	219	2	that	that	SCONJ
ejpam-5856	219	3	,	,	PUNCT
ejpam-5856	219	4	clµ(o	clµ(o	PROPN
ejpam-5856	219	5	∗	∗	NOUN
ejpam-5856	219	6	uα	uα	PROPN
ejpam-5856	219	7	)	)	PUNCT
ejpam-5856	219	8	⊆oc	⊆oc	PROPN
ejpam-5856	220	1	h	h	NOUN
ejpam-5856	220	2	.	.	PUNCT
ejpam-5856	221	1	since	since	SCONJ
ejpam-5856	221	2	h	h	NOUN
ejpam-5856	221	3	⊆	⊆	NUM
ejpam-5856	221	4	oh	oh	INTJ
ejpam-5856	221	5	,	,	PUNCT
ejpam-5856	221	6	we	we	PRON
ejpam-5856	221	7	have	have	VERB
ejpam-5856	221	8	oc	oc	ADP
ejpam-5856	221	9	h	h	NOUN
ejpam-5856	221	10	⊆	⊆	NUM
ejpam-5856	221	11	hc	hc	NOUN
ejpam-5856	221	12	=	=	PUNCT
ejpam-5856	221	13	ouα	ouα	NOUN
ejpam-5856	221	14	.	.	PUNCT
ejpam-5856	222	1	therefore	therefore	ADV
ejpam-5856	222	2	clµ(o	clµ(o	VERB
ejpam-5856	222	3	∗	∗	NOUN
ejpam-5856	222	4	uα	uα	PROPN
ejpam-5856	222	5	)	)	PUNCT
ejpam-5856	222	6	⊆ouα	⊆ouα	VERB
ejpam-5856	222	7	.	.	PUNCT
ejpam-5856	223	1	(	(	PUNCT
ejpam-5856	223	2	2	2	X
ejpam-5856	223	3	)	)	PUNCT
ejpam-5856	223	4	=	=	NOUN
ejpam-5856	223	5	⇒	⇒	NOUN
ejpam-5856	223	6	(	(	PUNCT
ejpam-5856	223	7	1	1	NUM
ejpam-5856	223	8	)	)	PUNCT
ejpam-5856	223	9	.	.	PUNCT
ejpam-5856	224	1	let	let	VERB
ejpam-5856	224	2	g	g	PROPN
ejpam-5856	224	3	∈	∈	PROPN
ejpam-5856	224	4	fgµc(u	fgµc(u	NOUN
ejpam-5856	224	5	)	)	PUNCT
ejpam-5856	224	6	with	with	ADP
ejpam-5856	224	7	uαq̃g	uαq̃g	PROPN
ejpam-5856	224	8	,	,	PUNCT
ejpam-5856	224	9	then	then	ADV
ejpam-5856	224	10	uα	uα	PROPN
ejpam-5856	224	11	∈	∈	PROPN
ejpam-5856	224	12	gc	gc	PROPN
ejpam-5856	224	13	=	=	SYM
ejpam-5856	224	14	ouα	ouα	NOUN
ejpam-5856	224	15	which	which	PRON
ejpam-5856	224	16	is	be	AUX
ejpam-5856	224	17	fgµ-open	fgµ-open	ADJ
ejpam-5856	224	18	set	set	NOUN
ejpam-5856	224	19	containing	contain	VERB
ejpam-5856	224	20	uα	uα	NOUN
ejpam-5856	224	21	.	.	PUNCT
ejpam-5856	225	1	by	by	ADP
ejpam-5856	225	2	given	give	VERB
ejpam-5856	225	3	,	,	PUNCT
ejpam-5856	225	4	there	there	PRON
ejpam-5856	225	5	is	be	VERB
ejpam-5856	225	6	fµ-open	fµ-open	ADJ
ejpam-5856	225	7	set	set	VERB
ejpam-5856	225	8	o∗	o∗	PROPN
ejpam-5856	225	9	uα	uα	PROPN
ejpam-5856	225	10	such	such	ADJ
ejpam-5856	226	1	that	that	SCONJ
ejpam-5856	226	2	clµ(o	clµ(o	PROPN
ejpam-5856	226	3	∗	∗	NOUN
ejpam-5856	226	4	uα	uα	PROPN
ejpam-5856	226	5	)	)	PUNCT
ejpam-5856	226	6	⊆	⊆	NUM
ejpam-5856	226	7	ouα	ouα	NOUN
ejpam-5856	226	8	=	=	SYM
ejpam-5856	226	9	gc	gc	PROPN
ejpam-5856	226	10	that	that	PRON
ejpam-5856	226	11	is	be	AUX
ejpam-5856	226	12	,	,	PUNCT
ejpam-5856	226	13	g	g	PROPN
ejpam-5856	226	14	⊆	⊆	NUM
ejpam-5856	226	15	(	(	PUNCT
ejpam-5856	226	16	clµ(o	clµ(o	PROPN
ejpam-5856	226	17	∗	∗	NOUN
ejpam-5856	226	18	uα	uα	PROPN
ejpam-5856	226	19	)	)	PUNCT
ejpam-5856	226	20	)	)	PUNCT
ejpam-5856	227	1	c	c	X
ejpam-5856	227	2	=	=	SYM
ejpam-5856	227	3	og	og	PROPN
ejpam-5856	227	4	and	and	CCONJ
ejpam-5856	227	5	clµ(o	clµ(o	PROPN
ejpam-5856	227	6	∗	∗	NOUN
ejpam-5856	227	7	uα	uα	PROPN
ejpam-5856	227	8	)	)	PUNCT
ejpam-5856	228	1	q̃	q̃	PROPN
ejpam-5856	228	2	(	(	PUNCT
ejpam-5856	228	3	clµ(o	clµ(o	PROPN
ejpam-5856	228	4	∗	∗	NOUN
ejpam-5856	228	5	uα	uα	PROPN
ejpam-5856	228	6	)	)	PUNCT
ejpam-5856	228	7	)	)	PUNCT
ejpam-5856	229	1	c	c	X
ejpam-5856	229	2	=	=	SYM
ejpam-5856	229	3	og	og	PROPN
ejpam-5856	229	4	.	.	PUNCT
ejpam-5856	230	1	therefore	therefore	ADV
ejpam-5856	230	2	o∗	o∗	PROPN
ejpam-5856	230	3	uα	uα	PROPN
ejpam-5856	230	4	q̃o	q̃o	PROPN
ejpam-5856	230	5	g	g	PROPN
ejpam-5856	230	6	.	.	PUNCT
ejpam-5856	231	1	this	this	PRON
ejpam-5856	231	2	completes	complete	VERB
ejpam-5856	231	3	the	the	DET
ejpam-5856	231	4	proof	proof	NOUN
ejpam-5856	231	5	.	.	PUNCT
ejpam-5856	232	1	s.	s.	PROPN
ejpam-5856	232	2	saleh	saleh	PROPN
ejpam-5856	232	3	et	et	PROPN
ejpam-5856	232	4	al	al	PROPN
ejpam-5856	232	5	.	.	PUNCT
ejpam-5856	232	6	/	/	SYM
ejpam-5856	232	7	eur	eur	PROPN
ejpam-5856	232	8	.	.	PUNCT
ejpam-5856	233	1	j.	j.	PROPN
ejpam-5856	233	2	pure	pure	PROPN
ejpam-5856	233	3	appl	appl	PROPN
ejpam-5856	233	4	.	.	PROPN
ejpam-5856	233	5	math	math	PROPN
ejpam-5856	233	6	,	,	PUNCT
ejpam-5856	233	7	18	18	NUM
ejpam-5856	233	8	(	(	PUNCT
ejpam-5856	233	9	1	1	NUM
ejpam-5856	233	10	)	)	PUNCT
ejpam-5856	233	11	(	(	PUNCT
ejpam-5856	233	12	2025	2025	NUM
ejpam-5856	233	13	)	)	PUNCT
ejpam-5856	233	14	,	,	PUNCT
ejpam-5856	233	15	5856	5856	NUM
ejpam-5856	233	16	7	7	NUM
ejpam-5856	233	17	of	of	ADP
ejpam-5856	233	18	15	15	NUM
ejpam-5856	233	19	theorem	theorem	NOUN
ejpam-5856	233	20	3	3	NUM
ejpam-5856	233	21	.	.	X
ejpam-5856	233	22	for	for	ADP
ejpam-5856	233	23	an	an	DET
ejpam-5856	233	24	gfts	gft	NOUN
ejpam-5856	233	25	(	(	PUNCT
ejpam-5856	233	26	u	u	NOUN
ejpam-5856	233	27	,	,	PUNCT
ejpam-5856	233	28	µ	µ	NOUN
ejpam-5856	233	29	)	)	PUNCT
ejpam-5856	233	30	and	and	CCONJ
ejpam-5856	233	31	uα	uα	PROPN
ejpam-5856	233	32	∈	∈	PROPN
ejpam-5856	233	33	fp	fp	PROPN
ejpam-5856	233	34	(	(	PUNCT
ejpam-5856	233	35	u	u	NOUN
ejpam-5856	233	36	)	)	PUNCT
ejpam-5856	233	37	.	.	PUNCT
ejpam-5856	234	1	the	the	DET
ejpam-5856	234	2	next	next	ADJ
ejpam-5856	234	3	items	item	NOUN
ejpam-5856	234	4	are	be	AUX
ejpam-5856	234	5	equivalent	equivalent	ADJ
ejpam-5856	234	6	:	:	PUNCT
ejpam-5856	234	7	(	(	PUNCT
ejpam-5856	234	8	1	1	X
ejpam-5856	234	9	)	)	PUNCT
ejpam-5856	234	10	(	(	PUNCT
ejpam-5856	234	11	u	u	NOUN
ejpam-5856	234	12	,	,	PUNCT
ejpam-5856	234	13	µ	µ	NOUN
ejpam-5856	234	14	)	)	PUNCT
ejpam-5856	234	15	is	be	AUX
ejpam-5856	234	16	fs	fs	PROPN
ejpam-5856	234	17	-	-	PUNCT
ejpam-5856	234	18	gr2	gr2	NOUN
ejpam-5856	234	19	,	,	PUNCT
ejpam-5856	234	20	(	(	PUNCT
ejpam-5856	234	21	2	2	X
ejpam-5856	234	22	)	)	PUNCT
ejpam-5856	234	23	for	for	ADP
ejpam-5856	234	24	any	any	DET
ejpam-5856	234	25	fgµ-closed	fgµ-closed	ADJ
ejpam-5856	234	26	set	set	NOUN
ejpam-5856	234	27	g	g	NOUN
ejpam-5856	234	28	with	with	ADP
ejpam-5856	234	29	uαq̃g	uαq̃g	PROPN
ejpam-5856	234	30	,	,	PUNCT
ejpam-5856	234	31	there	there	PRON
ejpam-5856	234	32	are	be	VERB
ejpam-5856	234	33	ouα	ouα	NOUN
ejpam-5856	234	34	,	,	PUNCT
ejpam-5856	234	35	og	og	PROPN
ejpam-5856	234	36	∈	∈	PROPN
ejpam-5856	234	37	µ	µ	PRON
ejpam-5856	234	38	such	such	ADJ
ejpam-5856	234	39	that	that	DET
ejpam-5856	234	40	clµ(ouα)q̃clµ(og	clµ(ouα)q̃clµ(og	NOUN
ejpam-5856	234	41	)	)	PUNCT
ejpam-5856	234	42	.	.	PUNCT
ejpam-5856	235	1	proof	proof	NOUN
ejpam-5856	235	2	.	.	PUNCT
ejpam-5856	236	1	necessity	necessity	NOUN
ejpam-5856	236	2	.	.	PUNCT
ejpam-5856	237	1	let	let	VERB
ejpam-5856	237	2	(	(	PUNCT
ejpam-5856	237	3	u	u	NOUN
ejpam-5856	237	4	,	,	PUNCT
ejpam-5856	237	5	µ	µ	NOUN
ejpam-5856	237	6	)	)	PUNCT
ejpam-5856	237	7	be	be	AUX
ejpam-5856	237	8	fg-µr2	fg-µr2	NOUN
ejpam-5856	237	9	and	and	CCONJ
ejpam-5856	237	10	g	g	PROPN
ejpam-5856	237	11	∈	∈	PROPN
ejpam-5856	237	12	fgµc(u	fgµc(u	PROPN
ejpam-5856	237	13	)	)	PUNCT
ejpam-5856	237	14	with	with	ADP
ejpam-5856	237	15	uαq̃g	uαq̃g	PROPN
ejpam-5856	237	16	,	,	PUNCT
ejpam-5856	237	17	there	there	PRON
ejpam-5856	237	18	are	be	VERB
ejpam-5856	237	19	o∗	o∗	PROPN
ejpam-5856	237	20	uα	uα	PROPN
ejpam-5856	237	21	and	and	CCONJ
ejpam-5856	237	22	og	og	PROPN
ejpam-5856	237	23	∈	∈	PROPN
ejpam-5856	237	24	µ	µ	PRON
ejpam-5856	237	25	such	such	ADJ
ejpam-5856	237	26	that	that	SCONJ
ejpam-5856	237	27	ogq̃o	ogq̃o	PROPN
ejpam-5856	237	28	∗	∗	VERB
ejpam-5856	237	29	uα	uα	PROPN
ejpam-5856	237	30	.	.	PUNCT
ejpam-5856	238	1	by	by	ADP
ejpam-5856	238	2	lemma	lemma	PROPN
ejpam-5856	238	3	1	1	NUM
ejpam-5856	238	4	,	,	PUNCT
ejpam-5856	238	5	we	we	PRON
ejpam-5856	238	6	have	have	AUX
ejpam-5856	238	7	clµ(og)q̃o	clµ(og)q̃o	VERB
ejpam-5856	238	8	∗	∗	NOUN
ejpam-5856	238	9	uα	uα	PROPN
ejpam-5856	238	10	implies	imply	VERB
ejpam-5856	238	11	clµ(og)q̃uα	clµ(og)q̃uα	NOUN
ejpam-5856	238	12	.	.	PUNCT
ejpam-5856	239	1	in	in	ADP
ejpam-5856	239	2	similar	similar	ADJ
ejpam-5856	239	3	,	,	PUNCT
ejpam-5856	239	4	since	since	SCONJ
ejpam-5856	239	5	(	(	PUNCT
ejpam-5856	239	6	u	u	INTJ
ejpam-5856	239	7	,	,	PUNCT
ejpam-5856	239	8	µ	µ	NOUN
ejpam-5856	239	9	)	)	PUNCT
ejpam-5856	239	10	is	be	AUX
ejpam-5856	239	11	fg-µr2	fg-µr2	NOUN
ejpam-5856	239	12	,	,	PUNCT
ejpam-5856	239	13	there	there	PRON
ejpam-5856	239	14	are	be	VERB
ejpam-5856	239	15	o	o	NOUN
ejpam-5856	239	16	∗∗	∗∗	X
ejpam-5856	239	17	uα	uα	X
ejpam-5856	239	18	and	and	CCONJ
ejpam-5856	239	19	oclµ(og	oclµ(og	ADJ
ejpam-5856	239	20	)	)	PUNCT
ejpam-5856	239	21	∈	∈	PROPN
ejpam-5856	239	22	µ	µ	NOUN
ejpam-5856	239	23	such	such	ADJ
ejpam-5856	239	24	that	that	DET
ejpam-5856	239	25	o∗∗	o∗∗	NOUN
ejpam-5856	239	26	uα	uα	X
ejpam-5856	239	27	q̃oclµ(og	q̃oclµ(og	PROPN
ejpam-5856	239	28	)	)	PUNCT
ejpam-5856	239	29	.	.	PUNCT
ejpam-5856	240	1	by	by	ADP
ejpam-5856	240	2	lemma	lemma	PROPN
ejpam-5856	240	3	1	1	NUM
ejpam-5856	240	4	,	,	PUNCT
ejpam-5856	240	5	we	we	PRON
ejpam-5856	240	6	get	get	VERB
ejpam-5856	240	7	clµ(o	clµ(o	PROPN
ejpam-5856	240	8	∗∗	∗∗	PROPN
ejpam-5856	240	9	uα	uα	X
ejpam-5856	240	10	)	)	PUNCT
ejpam-5856	240	11	q̃oclµ(og	q̃oclµ(og	PROPN
ejpam-5856	240	12	)	)	PUNCT
ejpam-5856	240	13	.	.	PUNCT
ejpam-5856	241	1	takeouα	takeouα	NOUN
ejpam-5856	241	2	=	=	PUNCT
ejpam-5856	241	3	o∗	o∗	PROPN
ejpam-5856	241	4	uα	uα	X
ejpam-5856	241	5	∪o∗∗	∪o∗∗	NOUN
ejpam-5856	241	6	uα	uα	PROPN
ejpam-5856	241	7	∈	∈	PROPN
ejpam-5856	241	8	µ.	µ.	NOUN
ejpam-5856	241	9	by	by	ADP
ejpam-5856	241	10	the	the	DET
ejpam-5856	241	11	above	above	ADJ
ejpam-5856	241	12	theorem	theorem	NOUN
ejpam-5856	241	13	,	,	PUNCT
ejpam-5856	241	14	there	there	PRON
ejpam-5856	241	15	is	be	VERB
ejpam-5856	241	16	ouα	ouα	NOUN
ejpam-5856	241	17	∈	∈	PROPN
ejpam-5856	241	18	µ	µ	PRON
ejpam-5856	241	19	such	such	ADJ
ejpam-5856	241	20	that	that	SCONJ
ejpam-5856	241	21	clµ(ouα)⊆o∗	clµ(ouα)⊆o∗	PROPN
ejpam-5856	241	22	uα	uα	PROPN
ejpam-5856	241	23	.	.	PUNCT
ejpam-5856	242	1	since	since	SCONJ
ejpam-5856	242	2	clµ(og)q̃o	clµ(og)q̃o	PROPN
ejpam-5856	242	3	∗	∗	NOUN
ejpam-5856	242	4	uα	uα	PROPN
ejpam-5856	242	5	,	,	PUNCT
ejpam-5856	242	6	we	we	PRON
ejpam-5856	242	7	have	have	VERB
ejpam-5856	242	8	clµ(og)q̃clµ(ouα	clµ(og)q̃clµ(ouα	NOUN
ejpam-5856	242	9	)	)	PUNCT
ejpam-5856	242	10	.	.	PUNCT
ejpam-5856	243	1	conversely	conversely	ADV
ejpam-5856	243	2	,	,	PUNCT
ejpam-5856	243	3	it	it	PRON
ejpam-5856	243	4	follows	follow	VERB
ejpam-5856	243	5	by	by	ADP
ejpam-5856	243	6	the	the	DET
ejpam-5856	243	7	hypothesis	hypothesis	NOUN
ejpam-5856	243	8	.	.	PUNCT
ejpam-5856	244	1	corollary	corollary	ADJ
ejpam-5856	244	2	1	1	NUM
ejpam-5856	244	3	.	.	PUNCT
ejpam-5856	245	1	an	an	DET
ejpam-5856	245	2	gfts	gft	NOUN
ejpam-5856	245	3	(	(	PUNCT
ejpam-5856	245	4	u	u	NOUN
ejpam-5856	245	5	,	,	PUNCT
ejpam-5856	245	6	µ	µ	NOUN
ejpam-5856	245	7	)	)	PUNCT
ejpam-5856	245	8	is	be	AUX
ejpam-5856	245	9	fs	fs	PROPN
ejpam-5856	245	10	-	-	PUNCT
ejpam-5856	245	11	gr2	gr2	NOUN
ejpam-5856	245	12	if	if	SCONJ
ejpam-5856	246	1	and	and	CCONJ
ejpam-5856	246	2	only	only	ADV
ejpam-5856	246	3	if	if	SCONJ
ejpam-5856	246	4	for	for	ADP
ejpam-5856	246	5	any	any	DET
ejpam-5856	246	6	h	h	NOUN
ejpam-5856	246	7	∈	∈	PROPN
ejpam-5856	246	8	iuand	iuand	NOUN
ejpam-5856	246	9	any	any	DET
ejpam-5856	246	10	fgµclosed	fgµclose	VERB
ejpam-5856	246	11	set	set	VERB
ejpam-5856	246	12	g	g	NOUN
ejpam-5856	246	13	with	with	ADP
ejpam-5856	246	14	hq̃g	hq̃g	PROPN
ejpam-5856	246	15	,	,	PUNCT
ejpam-5856	246	16	there	there	PRON
ejpam-5856	246	17	are	be	VERB
ejpam-5856	246	18	oh	oh	INTJ
ejpam-5856	246	19	,	,	PUNCT
ejpam-5856	246	20	og	og	PROPN
ejpam-5856	246	21	∈	∈	PROPN
ejpam-5856	246	22	fgµo(u	fgµo(u	PROPN
ejpam-5856	246	23	)	)	PUNCT
ejpam-5856	246	24	such	such	ADJ
ejpam-5856	246	25	that	that	SCONJ
ejpam-5856	246	26	oh	oh	INTJ
ejpam-5856	246	27	q̃og	q̃og	PROPN
ejpam-5856	246	28	.	.	PROPN
ejpam-5856	246	29	proof	proof	NOUN
ejpam-5856	246	30	.	.	PUNCT
ejpam-5856	247	1	it	it	PRON
ejpam-5856	247	2	can	can	AUX
ejpam-5856	247	3	be	be	AUX
ejpam-5856	247	4	obtained	obtain	VERB
ejpam-5856	247	5	from	from	ADP
ejpam-5856	247	6	definition	definition	NOUN
ejpam-5856	247	7	12	12	NUM
ejpam-5856	247	8	and	and	CCONJ
ejpam-5856	247	9	remark	remark	NOUN
ejpam-5856	247	10	1	1	NUM
ejpam-5856	247	11	.	.	PUNCT
ejpam-5856	248	1	definition	definition	NOUN
ejpam-5856	248	2	13	13	NUM
ejpam-5856	248	3	.	.	PUNCT
ejpam-5856	249	1	an	an	DET
ejpam-5856	249	2	gfts	gft	NOUN
ejpam-5856	249	3	(	(	PUNCT
ejpam-5856	249	4	u	u	NOUN
ejpam-5856	249	5	,	,	PUNCT
ejpam-5856	249	6	µ	µ	NOUN
ejpam-5856	249	7	)	)	PUNCT
ejpam-5856	249	8	is	be	AUX
ejpam-5856	249	9	said	say	VERB
ejpam-5856	249	10	to	to	PART
ejpam-5856	249	11	be	be	AUX
ejpam-5856	249	12	fµ-symmetric	fµ-symmetric	ADJ
ejpam-5856	249	13	iff	iff	PROPN
ejpam-5856	249	14	uαq̃clµ(vβ	uαq̃clµ(vβ	PROPN
ejpam-5856	249	15	)	)	PUNCT
ejpam-5856	249	16	implies	imply	VERB
ejpam-5856	249	17	vβ	vβ	DET
ejpam-5856	249	18	q̃clµ(uα	q̃clµ(uα	NOUN
ejpam-5856	249	19	)	)	PUNCT
ejpam-5856	249	20	for	for	ADP
ejpam-5856	249	21	any	any	DET
ejpam-5856	249	22	uα	uα	PROPN
ejpam-5856	249	23	,	,	PUNCT
ejpam-5856	249	24	vβ	vβ	ADP
ejpam-5856	249	25	∈	∈	PROPN
ejpam-5856	249	26	fp	fp	X
ejpam-5856	249	27	(	(	PUNCT
ejpam-5856	249	28	u	u	NOUN
ejpam-5856	249	29	)	)	PUNCT
ejpam-5856	249	30	.	.	PUNCT
ejpam-5856	250	1	theorem	theorem	ADJ
ejpam-5856	250	2	4	4	NUM
ejpam-5856	250	3	.	.	X
ejpam-5856	250	4	for	for	ADP
ejpam-5856	250	5	an	an	DET
ejpam-5856	250	6	gfts	gft	NOUN
ejpam-5856	250	7	(	(	PUNCT
ejpam-5856	250	8	u	u	NOUN
ejpam-5856	250	9	,	,	PUNCT
ejpam-5856	250	10	µ	µ	NOUN
ejpam-5856	250	11	)	)	PUNCT
ejpam-5856	250	12	.	.	PUNCT
ejpam-5856	251	1	the	the	DET
ejpam-5856	251	2	next	next	ADJ
ejpam-5856	251	3	items	item	NOUN
ejpam-5856	251	4	are	be	AUX
ejpam-5856	251	5	equivalent	equivalent	ADJ
ejpam-5856	251	6	:	:	PUNCT
ejpam-5856	251	7	(	(	PUNCT
ejpam-5856	251	8	1	1	X
ejpam-5856	251	9	)	)	PUNCT
ejpam-5856	251	10	(	(	PUNCT
ejpam-5856	251	11	u	u	NOUN
ejpam-5856	251	12	,	,	PUNCT
ejpam-5856	251	13	µ	µ	NOUN
ejpam-5856	251	14	)	)	PUNCT
ejpam-5856	251	15	is	be	AUX
ejpam-5856	251	16	fµ-symmetric	fµ-symmetric	ADJ
ejpam-5856	251	17	,	,	PUNCT
ejpam-5856	251	18	(	(	PUNCT
ejpam-5856	251	19	2	2	X
ejpam-5856	251	20	)	)	PUNCT
ejpam-5856	251	21	clµ(uα)q̃g	clµ(uα)q̃g	PROPN
ejpam-5856	251	22	for	for	ADP
ejpam-5856	251	23	any	any	DET
ejpam-5856	251	24	g	g	PROPN
ejpam-5856	251	25	∈	∈	PROPN
ejpam-5856	251	26	fµc(u	fµc(u	PROPN
ejpam-5856	251	27	)	)	PUNCT
ejpam-5856	251	28	with	with	ADP
ejpam-5856	251	29	uαq̃g	uαq̃g	PROPN
ejpam-5856	251	30	.	.	PUNCT
ejpam-5856	251	31	proof	proof	NOUN
ejpam-5856	251	32	.	.	PUNCT
ejpam-5856	252	1	necessity	necessity	NOUN
ejpam-5856	252	2	.	.	PUNCT
ejpam-5856	253	1	let	let	VERB
ejpam-5856	253	2	g	g	PROPN
ejpam-5856	253	3	∈	∈	PROPN
ejpam-5856	253	4	fµc(u	fµc(u	PROPN
ejpam-5856	253	5	)	)	PUNCT
ejpam-5856	253	6	such	such	ADJ
ejpam-5856	253	7	that	that	SCONJ
ejpam-5856	253	8	uαq̃g	uαq̃g	PROPN
ejpam-5856	253	9	,	,	PUNCT
ejpam-5856	253	10	then	then	ADV
ejpam-5856	253	11	clµ(vβ	clµ(vβ	NOUN
ejpam-5856	253	12	)	)	PUNCT
ejpam-5856	253	13	⊆	⊆	NUM
ejpam-5856	253	14	g	g	NOUN
ejpam-5856	253	15	for	for	ADP
ejpam-5856	253	16	any	any	DET
ejpam-5856	253	17	vβ	vβ	ADP
ejpam-5856	253	18	∈	∈	PROPN
ejpam-5856	253	19	g.	g.	NOUN
ejpam-5856	253	20	this	this	PRON
ejpam-5856	253	21	implies	imply	VERB
ejpam-5856	253	22	that	that	SCONJ
ejpam-5856	253	23	uαq̃clµ(vβ	uαq̃clµ(vβ	PROPN
ejpam-5856	253	24	)	)	PUNCT
ejpam-5856	253	25	.	.	PUNCT
ejpam-5856	254	1	since	since	SCONJ
ejpam-5856	254	2	(	(	PUNCT
ejpam-5856	254	3	u	u	INTJ
ejpam-5856	254	4	,	,	PUNCT
ejpam-5856	254	5	µ	µ	NOUN
ejpam-5856	254	6	)	)	PUNCT
ejpam-5856	254	7	is	be	AUX
ejpam-5856	254	8	fµ-symmetric	fµ-symmetric	ADJ
ejpam-5856	254	9	,	,	PUNCT
ejpam-5856	254	10	we	we	PRON
ejpam-5856	254	11	have	have	VERB
ejpam-5856	254	12	vβ	vβ	DET
ejpam-5856	254	13	q̃clµ(uα	q̃clµ(uα	NOUN
ejpam-5856	254	14	)	)	PUNCT
ejpam-5856	254	15	for	for	ADP
ejpam-5856	254	16	any	any	DET
ejpam-5856	254	17	vβ	vβ	ADP
ejpam-5856	254	18	∈	∈	PROPN
ejpam-5856	254	19	g	g	NOUN
ejpam-5856	254	20	and	and	CCONJ
ejpam-5856	254	21	so	so	ADV
ejpam-5856	254	22	,	,	PUNCT
ejpam-5856	254	23	there	there	PRON
ejpam-5856	254	24	is	be	VERB
ejpam-5856	254	25	ovβ	ovβ	NOUN
ejpam-5856	254	26	∈	∈	PROPN
ejpam-5856	254	27	µ	µ	NOUN
ejpam-5856	254	28	,	,	PUNCT
ejpam-5856	254	29	vβ	vβ	DET
ejpam-5856	254	30	∈	∈	NOUN
ejpam-5856	254	31	ovβ	ovβ	NOUN
ejpam-5856	254	32	with	with	ADP
ejpam-5856	254	33	uαq̃ovβ	uαq̃ovβ	NOUN
ejpam-5856	254	34	.	.	PUNCT
ejpam-5856	255	1	now	now	ADV
ejpam-5856	255	2	take	take	VERB
ejpam-5856	255	3	h	h	NOUN
ejpam-5856	255	4	=	=	PUNCT
ejpam-5856	255	5	∪{ovβ	∪{ovβ	NOUN
ejpam-5856	255	6	:	:	PUNCT
ejpam-5856	255	7	vβ	vβ	ADP
ejpam-5856	255	8	∈	∈	PROPN
ejpam-5856	255	9	g	g	NOUN
ejpam-5856	255	10	and	and	CCONJ
ejpam-5856	255	11	uαq̃ovβ	uαq̃ovβ	NOUN
ejpam-5856	255	12	}	}	PUNCT
ejpam-5856	255	13	,	,	PUNCT
ejpam-5856	255	14	then	then	ADV
ejpam-5856	255	15	h	h	NOUN
ejpam-5856	255	16	=	=	PUNCT
ejpam-5856	255	17	og	og	PROPN
ejpam-5856	255	18	and	and	CCONJ
ejpam-5856	255	19	uαq̃h	uαq̃h	PROPN
ejpam-5856	255	20	implies	imply	VERB
ejpam-5856	255	21	uα	uα	PROPN
ejpam-5856	255	22	∈	∈	PROPN
ejpam-5856	255	23	hc	hc	PROPN
ejpam-5856	255	24	and	and	CCONJ
ejpam-5856	255	25	so	so	ADV
ejpam-5856	255	26	,	,	PUNCT
ejpam-5856	255	27	clµ(uα	clµ(uα	NOUN
ejpam-5856	255	28	)	)	PUNCT
ejpam-5856	255	29	⊆	⊆	NUM
ejpam-5856	255	30	hc	hc	NOUN
ejpam-5856	255	31	that	that	PRON
ejpam-5856	255	32	is	be	AUX
ejpam-5856	255	33	,	,	PUNCT
ejpam-5856	255	34	clµ(uα)q̃h	clµ(uα)q̃h	PROPN
ejpam-5856	255	35	.	.	PUNCT
ejpam-5856	256	1	therefore	therefore	ADV
ejpam-5856	256	2	clµ(uα)q̃g	clµ(uα)q̃g	PROPN
ejpam-5856	256	3	.	.	PUNCT
ejpam-5856	257	1	conversely	conversely	ADV
ejpam-5856	257	2	.	.	PUNCT
ejpam-5856	258	1	it	it	PRON
ejpam-5856	258	2	is	be	AUX
ejpam-5856	258	3	obvious	obvious	ADJ
ejpam-5856	258	4	.	.	PUNCT
ejpam-5856	259	1	corollary	corollary	ADJ
ejpam-5856	259	2	2	2	NUM
ejpam-5856	259	3	.	.	PUNCT
ejpam-5856	260	1	an	an	DET
ejpam-5856	260	2	gfts	gft	NOUN
ejpam-5856	260	3	(	(	PUNCT
ejpam-5856	260	4	u	u	NOUN
ejpam-5856	260	5	,	,	PUNCT
ejpam-5856	260	6	µ	µ	NOUN
ejpam-5856	260	7	)	)	PUNCT
ejpam-5856	260	8	is	be	AUX
ejpam-5856	260	9	fµ-symmetric	fµ-symmetric	ADJ
ejpam-5856	260	10	iff	iff	PROPN
ejpam-5856	260	11	uα	uα	PROPN
ejpam-5856	260	12	is	be	AUX
ejpam-5856	260	13	an	an	DET
ejpam-5856	260	14	fgµ-closed	fgµ-closed	ADJ
ejpam-5856	260	15	set	set	NOUN
ejpam-5856	260	16	for	for	ADP
ejpam-5856	260	17	any	any	DET
ejpam-5856	260	18	uα	uα	PROPN
ejpam-5856	260	19	∈	∈	PROPN
ejpam-5856	260	20	fp	fp	X
ejpam-5856	260	21	(	(	PUNCT
ejpam-5856	260	22	u	u	NOUN
ejpam-5856	260	23	)	)	PUNCT
ejpam-5856	260	24	.	.	PUNCT
ejpam-5856	261	1	remark	remark	PROPN
ejpam-5856	261	2	4	4	NUM
ejpam-5856	261	3	.	.	PUNCT
ejpam-5856	262	1	evidently	evidently	ADV
ejpam-5856	262	2	,	,	PUNCT
ejpam-5856	262	3	every	every	DET
ejpam-5856	262	4	fµ-t1	fµ-t1	NOUN
ejpam-5856	262	5	space	space	NOUN
ejpam-5856	262	6	is	be	AUX
ejpam-5856	262	7	fµ-symmetric	fµ-symmetric	ADJ
ejpam-5856	262	8	but	but	CCONJ
ejpam-5856	262	9	not	not	PART
ejpam-5856	262	10	conversely	conversely	ADV
ejpam-5856	262	11	.	.	PUNCT
ejpam-5856	263	1	example	example	NOUN
ejpam-5856	263	2	2	2	NUM
ejpam-5856	263	3	.	.	X
ejpam-5856	264	1	consider	consider	VERB
ejpam-5856	264	2	u	u	PRON
ejpam-5856	264	3	=	=	X
ejpam-5856	264	4	{	{	PUNCT
ejpam-5856	264	5	u	u	NOUN
ejpam-5856	264	6	}	}	PUNCT
ejpam-5856	264	7	and	and	CCONJ
ejpam-5856	264	8	µ	µ	X
ejpam-5856	264	9	=	=	SYM
ejpam-5856	264	10	{	{	PUNCT
ejpam-5856	264	11	0	0	NUM
ejpam-5856	264	12	,	,	PUNCT
ejpam-5856	264	13	1	1	NUM
ejpam-5856	264	14	,	,	PUNCT
ejpam-5856	264	15	u0.5	u0.5	X
ejpam-5856	264	16	}	}	PUNCT
ejpam-5856	264	17	,	,	PUNCT
ejpam-5856	264	18	then	then	ADV
ejpam-5856	264	19	µ	µ	X
ejpam-5856	264	20	is	be	AUX
ejpam-5856	264	21	an	an	DET
ejpam-5856	264	22	gft	gft	PROPN
ejpam-5856	264	23	on	on	ADP
ejpam-5856	264	24	u	u	PROPN
ejpam-5856	264	25	.	.	PUNCT
ejpam-5856	265	1	one	one	PRON
ejpam-5856	265	2	can	can	AUX
ejpam-5856	265	3	check	check	VERB
ejpam-5856	265	4	that	that	SCONJ
ejpam-5856	265	5	µ	µ	NOUN
ejpam-5856	265	6	is	be	AUX
ejpam-5856	265	7	fµ-symmetric	fµ-symmetric	ADJ
ejpam-5856	265	8	but	but	CCONJ
ejpam-5856	265	9	not	not	PART
ejpam-5856	265	10	fµ-t1	fµ-t1	NOUN
ejpam-5856	265	11	.	.	PUNCT
ejpam-5856	266	1	further	far	ADV
ejpam-5856	266	2	,	,	PUNCT
ejpam-5856	266	3	µ	µ	X
ejpam-5856	266	4	is	be	AUX
ejpam-5856	266	5	not	not	PART
ejpam-5856	266	6	fµ-t	fµ-t	PROPN
ejpam-5856	266	7	1	1	NUM
ejpam-5856	266	8	2	2	NUM
ejpam-5856	266	9	.	.	PUNCT
ejpam-5856	267	1	proposition	proposition	NOUN
ejpam-5856	267	2	3	3	NUM
ejpam-5856	267	3	.	.	PUNCT
ejpam-5856	268	1	an	an	DET
ejpam-5856	268	2	gfts	gft	NOUN
ejpam-5856	268	3	(	(	PUNCT
ejpam-5856	268	4	u	u	NOUN
ejpam-5856	268	5	,	,	PUNCT
ejpam-5856	268	6	µ	µ	NOUN
ejpam-5856	268	7	)	)	PUNCT
ejpam-5856	268	8	is	be	AUX
ejpam-5856	268	9	fµ-t1	fµ-t1	NOUN
ejpam-5856	269	1	iff	iff	PROPN
ejpam-5856	269	2	is	be	AUX
ejpam-5856	269	3	both	both	PRON
ejpam-5856	269	4	fµ-symmetric	fµ-symmetric	ADJ
ejpam-5856	269	5	and	and	CCONJ
ejpam-5856	269	6	fµ-t0	fµ-t0	NOUN
ejpam-5856	269	7	.	.	PUNCT
ejpam-5856	270	1	proof	proof	NOUN
ejpam-5856	270	2	.	.	PUNCT
ejpam-5856	271	1	evidently	evidently	ADV
ejpam-5856	271	2	,	,	PUNCT
ejpam-5856	271	3	if	if	SCONJ
ejpam-5856	271	4	(	(	PUNCT
ejpam-5856	271	5	u	u	NOUN
ejpam-5856	271	6	,	,	PUNCT
ejpam-5856	271	7	µ	µ	NOUN
ejpam-5856	271	8	)	)	PUNCT
ejpam-5856	271	9	is	be	AUX
ejpam-5856	271	10	fµ-t1	fµ-t1	NOUN
ejpam-5856	271	11	,	,	PUNCT
ejpam-5856	271	12	then	then	ADV
ejpam-5856	271	13	it	it	PRON
ejpam-5856	271	14	is	be	AUX
ejpam-5856	271	15	fµ-symmetric	fµ-symmetric	ADJ
ejpam-5856	271	16	and	and	CCONJ
ejpam-5856	271	17	fµ-t0	fµ-t0	NOUN
ejpam-5856	271	18	.	.	PUNCT
ejpam-5856	272	1	conversely	conversely	ADV
ejpam-5856	272	2	,	,	PUNCT
ejpam-5856	272	3	let	let	VERB
ejpam-5856	272	4	(	(	PUNCT
ejpam-5856	272	5	u	u	NOUN
ejpam-5856	272	6	,	,	PUNCT
ejpam-5856	272	7	µ	µ	NOUN
ejpam-5856	272	8	)	)	PUNCT
ejpam-5856	272	9	be	be	AUX
ejpam-5856	272	10	fµ-symmetric	fµ-symmetric	ADJ
ejpam-5856	272	11	and	and	CCONJ
ejpam-5856	272	12	fµ-t0	fµ-t0	PROPN
ejpam-5856	272	13	.	.	PUNCT
ejpam-5856	272	14	suppose	suppose	VERB
ejpam-5856	272	15	uαq̃vβ	uαq̃vβ	PROPN
ejpam-5856	272	16	,	,	PUNCT
ejpam-5856	272	17	we	we	PRON
ejpam-5856	272	18	have	have	VERB
ejpam-5856	272	19	either	either	CCONJ
ejpam-5856	272	20	uαq̃clµ(vβ	uαq̃clµ(vβ	PROPN
ejpam-5856	272	21	)	)	PUNCT
ejpam-5856	272	22	or	or	CCONJ
ejpam-5856	272	23	vβ	vβ	DET
ejpam-5856	272	24	q̃clµ(uα	q̃clµ(uα	NOUN
ejpam-5856	272	25	)	)	PUNCT
ejpam-5856	272	26	.	.	PUNCT
ejpam-5856	273	1	by	by	ADP
ejpam-5856	273	2	fµ-symmetric	fµ-symmetric	ADJ
ejpam-5856	273	3	,	,	PUNCT
ejpam-5856	273	4	we	we	PRON
ejpam-5856	273	5	get	get	VERB
ejpam-5856	273	6	uαq̃clµ(vβ	uαq̃clµ(vβ	PROPN
ejpam-5856	273	7	)	)	PUNCT
ejpam-5856	273	8	and	and	CCONJ
ejpam-5856	273	9	vβ	vβ	DET
ejpam-5856	273	10	q̃clµ(uα	q̃clµ(uα	NOUN
ejpam-5856	273	11	)	)	PUNCT
ejpam-5856	273	12	for	for	ADP
ejpam-5856	273	13	any	any	DET
ejpam-5856	273	14	uα	uα	PROPN
ejpam-5856	273	15	,	,	PUNCT
ejpam-5856	273	16	vβ	vβ	ADP
ejpam-5856	273	17	∈	∈	PROPN
ejpam-5856	273	18	fp	fp	X
ejpam-5856	273	19	(	(	PUNCT
ejpam-5856	273	20	u	u	NOUN
ejpam-5856	273	21	)	)	PUNCT
ejpam-5856	273	22	.	.	PUNCT
ejpam-5856	274	1	this	this	PRON
ejpam-5856	274	2	completes	complete	VERB
ejpam-5856	274	3	the	the	DET
ejpam-5856	274	4	proof	proof	NOUN
ejpam-5856	274	5	.	.	PUNCT
ejpam-5856	275	1	from	from	ADP
ejpam-5856	275	2	the	the	DET
ejpam-5856	275	3	pervious	pervious	ADJ
ejpam-5856	275	4	results	result	NOUN
ejpam-5856	275	5	,	,	PUNCT
ejpam-5856	275	6	one	one	PRON
ejpam-5856	275	7	can	can	AUX
ejpam-5856	275	8	verify	verify	VERB
ejpam-5856	275	9	the	the	DET
ejpam-5856	275	10	following	follow	VERB
ejpam-5856	275	11	proposition	proposition	NOUN
ejpam-5856	275	12	.	.	PUNCT
ejpam-5856	276	1	s.	s.	PROPN
ejpam-5856	276	2	saleh	saleh	PROPN
ejpam-5856	276	3	et	et	PROPN
ejpam-5856	276	4	al	al	PROPN
ejpam-5856	276	5	.	.	PUNCT
ejpam-5856	276	6	/	/	SYM
ejpam-5856	276	7	eur	eur	PROPN
ejpam-5856	276	8	.	.	PUNCT
ejpam-5856	277	1	j.	j.	PROPN
ejpam-5856	277	2	pure	pure	PROPN
ejpam-5856	277	3	appl	appl	PROPN
ejpam-5856	277	4	.	.	PROPN
ejpam-5856	277	5	math	math	PROPN
ejpam-5856	277	6	,	,	PUNCT
ejpam-5856	277	7	18	18	NUM
ejpam-5856	277	8	(	(	PUNCT
ejpam-5856	277	9	1	1	NUM
ejpam-5856	277	10	)	)	PUNCT
ejpam-5856	277	11	(	(	PUNCT
ejpam-5856	277	12	2025	2025	NUM
ejpam-5856	277	13	)	)	PUNCT
ejpam-5856	277	14	,	,	PUNCT
ejpam-5856	277	15	5856	5856	NUM
ejpam-5856	277	16	8	8	NUM
ejpam-5856	277	17	of	of	ADP
ejpam-5856	277	18	15	15	NUM
ejpam-5856	277	19	proposition	proposition	NOUN
ejpam-5856	277	20	4	4	NUM
ejpam-5856	277	21	.	.	X
ejpam-5856	278	1	for	for	ADP
ejpam-5856	278	2	an	an	DET
ejpam-5856	278	3	fµ-symmetric	fµ-symmetric	ADJ
ejpam-5856	278	4	space	space	NOUN
ejpam-5856	278	5	(	(	PUNCT
ejpam-5856	278	6	u	u	NOUN
ejpam-5856	278	7	,	,	PUNCT
ejpam-5856	278	8	µ	µ	NOUN
ejpam-5856	278	9	)	)	PUNCT
ejpam-5856	278	10	.	.	PUNCT
ejpam-5856	279	1	the	the	DET
ejpam-5856	279	2	next	next	ADJ
ejpam-5856	279	3	items	item	NOUN
ejpam-5856	279	4	are	be	AUX
ejpam-5856	279	5	equivalent	equivalent	ADJ
ejpam-5856	279	6	:	:	PUNCT
ejpam-5856	279	7	(	(	PUNCT
ejpam-5856	279	8	1	1	X
ejpam-5856	279	9	)	)	PUNCT
ejpam-5856	279	10	(	(	PUNCT
ejpam-5856	279	11	u	u	NOUN
ejpam-5856	279	12	,	,	PUNCT
ejpam-5856	279	13	µ	µ	NOUN
ejpam-5856	279	14	)	)	PUNCT
ejpam-5856	279	15	is	be	AUX
ejpam-5856	279	16	fµ-t0	fµ-t0	NOUN
ejpam-5856	279	17	,	,	PUNCT
ejpam-5856	279	18	(	(	PUNCT
ejpam-5856	279	19	2	2	NUM
ejpam-5856	279	20	)	)	PUNCT
ejpam-5856	279	21	(	(	PUNCT
ejpam-5856	279	22	u	u	NOUN
ejpam-5856	279	23	,	,	PUNCT
ejpam-5856	279	24	µ	µ	NOUN
ejpam-5856	279	25	)	)	PUNCT
ejpam-5856	279	26	is	be	AUX
ejpam-5856	279	27	fµ-t	fµ-t	PROPN
ejpam-5856	279	28	1	1	NUM
ejpam-5856	279	29	2	2	NUM
ejpam-5856	279	30	,	,	PUNCT
ejpam-5856	279	31	(	(	PUNCT
ejpam-5856	279	32	3	3	NUM
ejpam-5856	279	33	)	)	PUNCT
ejpam-5856	279	34	(	(	PUNCT
ejpam-5856	279	35	u	u	NOUN
ejpam-5856	279	36	,	,	PUNCT
ejpam-5856	279	37	µ	µ	NOUN
ejpam-5856	279	38	)	)	PUNCT
ejpam-5856	279	39	is	be	AUX
ejpam-5856	279	40	fµ-t1	fµ-t1	NOUN
ejpam-5856	279	41	.	.	PUNCT
ejpam-5856	280	1	definition	definition	NOUN
ejpam-5856	280	2	14	14	NUM
ejpam-5856	280	3	.	.	PUNCT
ejpam-5856	281	1	an	an	DET
ejpam-5856	281	2	gfts	gft	NOUN
ejpam-5856	281	3	(	(	PUNCT
ejpam-5856	281	4	u	u	NOUN
ejpam-5856	281	5	,	,	PUNCT
ejpam-5856	281	6	µ	µ	NOUN
ejpam-5856	281	7	)	)	PUNCT
ejpam-5856	281	8	is	be	AUX
ejpam-5856	281	9	called	call	VERB
ejpam-5856	281	10	fµ-g3	fµ-g3	NOUN
ejpam-5856	281	11	iff	iff	PROPN
ejpam-5856	281	12	it	it	PRON
ejpam-5856	281	13	is	be	AUX
ejpam-5856	281	14	fg-µr2	fg-µr2	NOUN
ejpam-5856	281	15	and	and	CCONJ
ejpam-5856	281	16	fµ-symmetric	fµ-symmetric	ADJ
ejpam-5856	281	17	.	.	PUNCT
ejpam-5856	282	1	theorem	theorem	VERB
ejpam-5856	282	2	5	5	NUM
ejpam-5856	282	3	.	.	PUNCT
ejpam-5856	283	1	every	every	DET
ejpam-5856	283	2	fµ-g3	fµ-g3	NOUN
ejpam-5856	283	3	space	space	NOUN
ejpam-5856	283	4	is	be	AUX
ejpam-5856	283	5	fµ-t2	fµ-t2	PROPN
ejpam-5856	283	6	1	1	NUM
ejpam-5856	283	7	2	2	NUM
ejpam-5856	283	8	.	.	PUNCT
ejpam-5856	284	1	proof	proof	NOUN
ejpam-5856	284	2	.	.	PUNCT
ejpam-5856	285	1	let	let	VERB
ejpam-5856	285	2	(	(	PUNCT
ejpam-5856	285	3	u	u	NOUN
ejpam-5856	285	4	,	,	PUNCT
ejpam-5856	285	5	µ	µ	NOUN
ejpam-5856	285	6	)	)	PUNCT
ejpam-5856	285	7	be	be	AUX
ejpam-5856	285	8	fµ-g3	fµ-g3	NOUN
ejpam-5856	285	9	and	and	CCONJ
ejpam-5856	285	10	uα	uα	PROPN
ejpam-5856	285	11	,	,	PUNCT
ejpam-5856	285	12	vβ	vβ	PRON
ejpam-5856	285	13	∈	∈	PROPN
ejpam-5856	285	14	fp	fp	X
ejpam-5856	285	15	(	(	PUNCT
ejpam-5856	285	16	u	u	NOUN
ejpam-5856	285	17	)	)	PUNCT
ejpam-5856	285	18	with	with	ADP
ejpam-5856	285	19	uαq̃vβ	uαq̃vβ	PROPN
ejpam-5856	285	20	.	.	PUNCT
ejpam-5856	286	1	since	since	SCONJ
ejpam-5856	286	2	(	(	PUNCT
ejpam-5856	286	3	u	u	INTJ
ejpam-5856	286	4	,	,	PUNCT
ejpam-5856	286	5	µ	µ	NOUN
ejpam-5856	286	6	)	)	PUNCT
ejpam-5856	286	7	is	be	AUX
ejpam-5856	286	8	fµsymmetric	fµsymmetric	ADJ
ejpam-5856	286	9	and	and	CCONJ
ejpam-5856	286	10	so	so	ADV
ejpam-5856	286	11	,	,	PUNCT
ejpam-5856	286	12	uα	uα	PROPN
ejpam-5856	286	13	is	be	AUX
ejpam-5856	286	14	a	a	DET
ejpam-5856	286	15	fgµ-closed	fgµ-closed	ADJ
ejpam-5856	286	16	set	set	NOUN
ejpam-5856	286	17	for	for	ADP
ejpam-5856	286	18	any	any	DET
ejpam-5856	286	19	uα	uα	PROPN
ejpam-5856	286	20	∈	∈	PROPN
ejpam-5856	286	21	fp	fp	X
ejpam-5856	286	22	(	(	PUNCT
ejpam-5856	286	23	u	u	NOUN
ejpam-5856	286	24	)	)	PUNCT
ejpam-5856	286	25	.	.	PUNCT
ejpam-5856	287	1	by	by	ADP
ejpam-5856	287	2	theorem	theorem	NOUN
ejpam-5856	287	3	3	3	NUM
ejpam-5856	287	4	,	,	PUNCT
ejpam-5856	287	5	there	there	PRON
ejpam-5856	287	6	are	be	VERB
ejpam-5856	287	7	ouα	ouα	NOUN
ejpam-5856	287	8	,	,	PUNCT
ejpam-5856	287	9	ovβ	ovβ	NOUN
ejpam-5856	287	10	∈	∈	PROPN
ejpam-5856	287	11	µ	µ	PRON
ejpam-5856	287	12	such	such	ADJ
ejpam-5856	287	13	that	that	DET
ejpam-5856	287	14	cl(ouα)q̃cl(ovβ	cl(ouα)q̃cl(ovβ	NOUN
ejpam-5856	287	15	)	)	PUNCT
ejpam-5856	287	16	.	.	PUNCT
ejpam-5856	288	1	therefore	therefore	ADV
ejpam-5856	288	2	(	(	PUNCT
ejpam-5856	288	3	u	u	NOUN
ejpam-5856	288	4	,	,	PUNCT
ejpam-5856	288	5	µ	µ	NOUN
ejpam-5856	288	6	)	)	PUNCT
ejpam-5856	288	7	is	be	AUX
ejpam-5856	288	8	fµ-t2	fµ-t2	PROPN
ejpam-5856	288	9	1	1	NUM
ejpam-5856	288	10	2	2	NUM
ejpam-5856	288	11	.	.	PUNCT
ejpam-5856	289	1	corollary	corollary	ADJ
ejpam-5856	289	2	3	3	X
ejpam-5856	289	3	.	.	PUNCT
ejpam-5856	290	1	clearly	clearly	ADV
ejpam-5856	290	2	,	,	PUNCT
ejpam-5856	290	3	every	every	DET
ejpam-5856	290	4	fµ-g3	fµ-g3	NOUN
ejpam-5856	290	5	space	space	NOUN
ejpam-5856	290	6	is	be	AUX
ejpam-5856	290	7	fµ-t2	fµ-t2	NOUN
ejpam-5856	290	8	but	but	CCONJ
ejpam-5856	290	9	not	not	PART
ejpam-5856	290	10	conversely	conversely	ADV
ejpam-5856	290	11	.	.	PUNCT
ejpam-5856	291	1	example	example	NOUN
ejpam-5856	292	1	3	3	X
ejpam-5856	292	2	.	.	PUNCT
ejpam-5856	292	3	let	let	VERB
ejpam-5856	292	4	u	u	PRON
ejpam-5856	292	5	be	be	AUX
ejpam-5856	292	6	an	an	DET
ejpam-5856	292	7	infinite	infinite	ADJ
ejpam-5856	292	8	set	set	NOUN
ejpam-5856	292	9	.	.	PUNCT
ejpam-5856	293	1	for	for	ADP
ejpam-5856	293	2	u	u	NOUN
ejpam-5856	293	3	,	,	PUNCT
ejpam-5856	293	4	v	v	PROPN
ejpam-5856	293	5	∈	∈	PROPN
ejpam-5856	293	6	u	u	NOUN
ejpam-5856	293	7	,	,	PUNCT
ejpam-5856	293	8	u	u	PROPN
ejpam-5856	293	9	̸=	̸=	PROPN
ejpam-5856	293	10	v	v	NOUN
ejpam-5856	293	11	,	,	PUNCT
ejpam-5856	293	12	let	let	VERB
ejpam-5856	293	13	hu	hu	PROPN
ejpam-5856	293	14	,	,	PUNCT
ejpam-5856	293	15	v	v	ADP
ejpam-5856	293	16	∈	∈	PROPN
ejpam-5856	293	17	iu	iu	ADV
ejpam-5856	293	18	defined	define	VERB
ejpam-5856	293	19	as	as	ADP
ejpam-5856	293	20	:	:	PUNCT
ejpam-5856	293	21	hu	hu	PROPN
ejpam-5856	293	22	,	,	PUNCT
ejpam-5856	293	23	v(w	v(w	X
ejpam-5856	293	24	)	)	PUNCT
ejpam-5856	293	25	=	=	SYM
ejpam-5856	294	1			NOUN
ejpam-5856	294	2	1	1	NUM
ejpam-5856	294	3	,	,	PUNCT
ejpam-5856	294	4	if	if	SCONJ
ejpam-5856	294	5	w	w	PROPN
ejpam-5856	294	6	=	=	SYM
ejpam-5856	294	7	u	u	NOUN
ejpam-5856	294	8	0	0	NUM
ejpam-5856	294	9	,	,	PUNCT
ejpam-5856	294	10	if	if	SCONJ
ejpam-5856	294	11	w	w	PROPN
ejpam-5856	294	12	=	=	SYM
ejpam-5856	294	13	v	v	ADP
ejpam-5856	294	14	0.5	0.5	NUM
ejpam-5856	294	15	,	,	PUNCT
ejpam-5856	294	16	if	if	SCONJ
ejpam-5856	294	17	w	w	PROPN
ejpam-5856	294	18	̸=	̸=	PROPN
ejpam-5856	294	19	u	u	NOUN
ejpam-5856	294	20	and	and	CCONJ
ejpam-5856	294	21	w	w	PROPN
ejpam-5856	294	22	̸=	̸=	PROPN
ejpam-5856	294	23	v	v	NOUN
ejpam-5856	294	24	for	for	ADP
ejpam-5856	294	25	all	all	DET
ejpam-5856	294	26	w	w	PROPN
ejpam-5856	294	27	∈	∈	PROPN
ejpam-5856	294	28	u	u	NOUN
ejpam-5856	294	29	.	.	PUNCT
ejpam-5856	295	1	consider	consider	VERB
ejpam-5856	295	2	the	the	DET
ejpam-5856	295	3	gft	gft	PROPN
ejpam-5856	295	4	µ	µ	X
ejpam-5856	295	5	on	on	ADP
ejpam-5856	295	6	u	u	PRON
ejpam-5856	295	7	which	which	PRON
ejpam-5856	295	8	is	be	AUX
ejpam-5856	295	9	induced	induce	VERB
ejpam-5856	295	10	by	by	ADP
ejpam-5856	295	11	the	the	DET
ejpam-5856	295	12	class	class	NOUN
ejpam-5856	295	13	{	{	PUNCT
ejpam-5856	295	14	hu	hu	PROPN
ejpam-5856	295	15	,	,	PUNCT
ejpam-5856	295	16	v	v	NOUN
ejpam-5856	295	17	:	:	PUNCT
ejpam-5856	295	18	u	u	NOUN
ejpam-5856	295	19	,	,	PUNCT
ejpam-5856	295	20	v	v	PROPN
ejpam-5856	295	21	∈	∈	PROPN
ejpam-5856	295	22	u	u	NOUN
ejpam-5856	295	23	,	,	PUNCT
ejpam-5856	295	24	u	u	PROPN
ejpam-5856	295	25	̸=	̸=	PROPN
ejpam-5856	295	26	v	v	NOUN
ejpam-5856	295	27	}	}	PUNCT
ejpam-5856	295	28	.	.	PUNCT
ejpam-5856	296	1	one	one	PRON
ejpam-5856	296	2	can	can	AUX
ejpam-5856	296	3	verify	verify	VERB
ejpam-5856	296	4	that	that	SCONJ
ejpam-5856	296	5	µ	µ	NOUN
ejpam-5856	296	6	is	be	AUX
ejpam-5856	296	7	fµ-t2	fµ-t2	NOUN
ejpam-5856	296	8	but	but	CCONJ
ejpam-5856	296	9	not	not	PART
ejpam-5856	296	10	fg-µr2	fg-µr2	NOUN
ejpam-5856	296	11	and	and	CCONJ
ejpam-5856	296	12	so	so	ADV
ejpam-5856	296	13	,	,	PUNCT
ejpam-5856	296	14	is	be	AUX
ejpam-5856	296	15	not	not	PART
ejpam-5856	296	16	fµ-g3	fµ-g3	NOUN
ejpam-5856	296	17	.	.	PUNCT
ejpam-5856	297	1	theorem	theorem	VERB
ejpam-5856	297	2	6	6	NUM
ejpam-5856	297	3	.	.	PUNCT
ejpam-5856	297	4	for	for	ADP
ejpam-5856	297	5	an	an	DET
ejpam-5856	297	6	gfts	gft	NOUN
ejpam-5856	297	7	(	(	PUNCT
ejpam-5856	297	8	u	u	NOUN
ejpam-5856	297	9	,	,	PUNCT
ejpam-5856	297	10	µ	µ	NOUN
ejpam-5856	297	11	)	)	PUNCT
ejpam-5856	297	12	.	.	PUNCT
ejpam-5856	298	1	the	the	DET
ejpam-5856	298	2	next	next	ADJ
ejpam-5856	298	3	items	item	NOUN
ejpam-5856	298	4	are	be	AUX
ejpam-5856	298	5	equivalent	equivalent	ADJ
ejpam-5856	298	6	:	:	PUNCT
ejpam-5856	298	7	(	(	PUNCT
ejpam-5856	298	8	1	1	X
ejpam-5856	298	9	)	)	PUNCT
ejpam-5856	298	10	(	(	PUNCT
ejpam-5856	298	11	u	u	NOUN
ejpam-5856	298	12	,	,	PUNCT
ejpam-5856	298	13	µ	µ	NOUN
ejpam-5856	298	14	)	)	PUNCT
ejpam-5856	298	15	is	be	AUX
ejpam-5856	298	16	fµ-g3	fµ-g3	NOUN
ejpam-5856	298	17	,	,	PUNCT
ejpam-5856	298	18	(	(	PUNCT
ejpam-5856	298	19	2	2	NUM
ejpam-5856	298	20	)	)	PUNCT
ejpam-5856	298	21	(	(	PUNCT
ejpam-5856	298	22	u	u	NOUN
ejpam-5856	298	23	,	,	PUNCT
ejpam-5856	298	24	µ	µ	NOUN
ejpam-5856	298	25	)	)	PUNCT
ejpam-5856	298	26	is	be	AUX
ejpam-5856	298	27	fµ-t3	fµ-t3	NOUN
ejpam-5856	298	28	.	.	PUNCT
ejpam-5856	299	1	proof	proof	NOUN
ejpam-5856	299	2	.	.	PUNCT
ejpam-5856	300	1	(	(	PUNCT
ejpam-5856	300	2	1	1	X
ejpam-5856	300	3	)	)	PUNCT
ejpam-5856	300	4	=	=	NOUN
ejpam-5856	300	5	⇒	⇒	NOUN
ejpam-5856	300	6	(	(	PUNCT
ejpam-5856	300	7	2	2	NUM
ejpam-5856	300	8	)	)	PUNCT
ejpam-5856	300	9	.	.	PUNCT
ejpam-5856	301	1	assume	assume	VERB
ejpam-5856	301	2	that	that	SCONJ
ejpam-5856	301	3	(	(	PUNCT
ejpam-5856	301	4	u	u	NOUN
ejpam-5856	301	5	,	,	PUNCT
ejpam-5856	301	6	µ	µ	NOUN
ejpam-5856	301	7	)	)	PUNCT
ejpam-5856	301	8	is	be	AUX
ejpam-5856	301	9	fµ-g3	fµ-g3	NOUN
ejpam-5856	301	10	,	,	PUNCT
ejpam-5856	301	11	we	we	PRON
ejpam-5856	301	12	have	have	VERB
ejpam-5856	301	13	it	it	PRON
ejpam-5856	301	14	is	be	AUX
ejpam-5856	301	15	both	both	PRON
ejpam-5856	301	16	fg-µr2	fg-µr2	NOUN
ejpam-5856	301	17	and	and	CCONJ
ejpam-5856	301	18	fµsymmetric	fµsymmetric	NOUN
ejpam-5856	301	19	.	.	PUNCT
ejpam-5856	302	1	clearly	clearly	ADV
ejpam-5856	302	2	,	,	PUNCT
ejpam-5856	302	3	every	every	DET
ejpam-5856	302	4	fg-µr2	fg-µr2	NOUN
ejpam-5856	302	5	is	be	AUX
ejpam-5856	302	6	fµ-r2	fµ-r2	VERB
ejpam-5856	302	7	also	also	ADV
ejpam-5856	302	8	,	,	PUNCT
ejpam-5856	302	9	every	every	DET
ejpam-5856	302	10	fµ-g3	fµ-g3	NOUN
ejpam-5856	302	11	is	be	AUX
ejpam-5856	302	12	fµ-t2	fµ-t2	PRON
ejpam-5856	302	13	.	.	PUNCT
ejpam-5856	303	1	hence	hence	ADV
ejpam-5856	303	2	(	(	PUNCT
ejpam-5856	303	3	u	u	NOUN
ejpam-5856	303	4	,	,	PUNCT
ejpam-5856	303	5	µ	µ	NOUN
ejpam-5856	303	6	)	)	PUNCT
ejpam-5856	303	7	is	be	AUX
ejpam-5856	303	8	fµ-r2	fµ-r2	PROPN
ejpam-5856	303	9	and	and	CCONJ
ejpam-5856	303	10	fµ-t1	fµ-t1	VERB
ejpam-5856	303	11	that	that	PRON
ejpam-5856	303	12	is	be	AUX
ejpam-5856	303	13	,	,	PUNCT
ejpam-5856	303	14	(	(	PUNCT
ejpam-5856	303	15	u	u	NOUN
ejpam-5856	303	16	,	,	PUNCT
ejpam-5856	303	17	µ	µ	NOUN
ejpam-5856	303	18	)	)	PUNCT
ejpam-5856	303	19	is	be	AUX
ejpam-5856	303	20	fµ-t3	fµ-t3	NOUN
ejpam-5856	303	21	.	.	PUNCT
ejpam-5856	304	1	(	(	PUNCT
ejpam-5856	304	2	2	2	X
ejpam-5856	304	3	)	)	PUNCT
ejpam-5856	304	4	=	=	NOUN
ejpam-5856	304	5	⇒(1	⇒(1	PROPN
ejpam-5856	304	6	)	)	PUNCT
ejpam-5856	304	7	.	.	PUNCT
ejpam-5856	305	1	let	let	VERB
ejpam-5856	305	2	(	(	PUNCT
ejpam-5856	305	3	u	u	NOUN
ejpam-5856	305	4	,	,	PUNCT
ejpam-5856	305	5	µ	µ	NOUN
ejpam-5856	305	6	)	)	PUNCT
ejpam-5856	305	7	be	be	AUX
ejpam-5856	305	8	fµ-t3	fµ-t3	NOUN
ejpam-5856	305	9	,	,	PUNCT
ejpam-5856	305	10	then	then	ADV
ejpam-5856	305	11	it	it	PRON
ejpam-5856	305	12	is	be	AUX
ejpam-5856	305	13	both	both	PRON
ejpam-5856	305	14	fµ-r2	fµ-r2	PROPN
ejpam-5856	305	15	and	and	CCONJ
ejpam-5856	305	16	fµ-t1	fµ-t1	PROPN
ejpam-5856	305	17	.	.	PUNCT
ejpam-5856	306	1	this	this	PRON
ejpam-5856	306	2	implies	imply	VERB
ejpam-5856	306	3	that	that	SCONJ
ejpam-5856	306	4	(	(	PUNCT
ejpam-5856	306	5	u	u	NOUN
ejpam-5856	306	6	,	,	PUNCT
ejpam-5856	306	7	µ	µ	NOUN
ejpam-5856	306	8	)	)	PUNCT
ejpam-5856	306	9	is	be	AUX
ejpam-5856	306	10	fµ-t	fµ-t	PROPN
ejpam-5856	306	11	1	1	NUM
ejpam-5856	306	12	2	2	NUM
ejpam-5856	306	13	and	and	CCONJ
ejpam-5856	306	14	fµ-symmetric	fµ-symmetric	ADJ
ejpam-5856	306	15	.	.	PUNCT
ejpam-5856	307	1	thus	thus	ADV
ejpam-5856	307	2	,	,	PUNCT
ejpam-5856	307	3	(	(	PUNCT
ejpam-5856	307	4	u	u	NOUN
ejpam-5856	307	5	,	,	PUNCT
ejpam-5856	307	6	µ	µ	NOUN
ejpam-5856	307	7	)	)	PUNCT
ejpam-5856	307	8	is	be	AUX
ejpam-5856	307	9	fµ-r2	fµ-r2	PROPN
ejpam-5856	307	10	and	and	CCONJ
ejpam-5856	307	11	fµ-t	fµ-t	PROPN
ejpam-5856	307	12	1	1	NUM
ejpam-5856	307	13	2	2	NUM
ejpam-5856	307	14	implies	imply	VERB
ejpam-5856	307	15	that	that	SCONJ
ejpam-5856	307	16	(	(	PUNCT
ejpam-5856	307	17	u	u	NOUN
ejpam-5856	307	18	,	,	PUNCT
ejpam-5856	307	19	µ	µ	NOUN
ejpam-5856	307	20	)	)	PUNCT
ejpam-5856	307	21	is	be	AUX
ejpam-5856	307	22	fg-µr2	fg-µr2	NOUN
ejpam-5856	307	23	as	as	ADV
ejpam-5856	307	24	well	well	ADV
ejpam-5856	307	25	as	as	ADP
ejpam-5856	307	26	,	,	PUNCT
ejpam-5856	307	27	it	it	PRON
ejpam-5856	307	28	is	be	AUX
ejpam-5856	307	29	fµ-symmetric	fµ-symmetric	ADJ
ejpam-5856	307	30	.	.	PUNCT
ejpam-5856	308	1	therefore	therefore	ADV
ejpam-5856	308	2	(	(	PUNCT
ejpam-5856	308	3	u	u	NOUN
ejpam-5856	308	4	,	,	PUNCT
ejpam-5856	308	5	µ	µ	NOUN
ejpam-5856	308	6	)	)	PUNCT
ejpam-5856	308	7	is	be	AUX
ejpam-5856	308	8	fµ-g3	fµ-g3	NOUN
ejpam-5856	308	9	.	.	PUNCT
ejpam-5856	309	1	4	4	X
ejpam-5856	309	2	.	.	X
ejpam-5856	309	3	fuzzy	fuzzy	ADJ
ejpam-5856	309	4	gµ-normal	gµ-normal	ADJ
ejpam-5856	309	5	spaces	space	NOUN
ejpam-5856	309	6	in	in	ADP
ejpam-5856	309	7	this	this	DET
ejpam-5856	309	8	part	part	NOUN
ejpam-5856	309	9	,	,	PUNCT
ejpam-5856	309	10	we	we	PRON
ejpam-5856	309	11	introduce	introduce	VERB
ejpam-5856	309	12	a	a	DET
ejpam-5856	309	13	new	new	ADJ
ejpam-5856	309	14	class	class	NOUN
ejpam-5856	309	15	of	of	ADP
ejpam-5856	309	16	spaces	space	NOUN
ejpam-5856	309	17	called	call	VERB
ejpam-5856	309	18	,	,	PUNCT
ejpam-5856	309	19	fgµ-normal	fgµ-normal	ADJ
ejpam-5856	309	20	spaces	space	NOUN
ejpam-5856	309	21	in	in	ADP
ejpam-5856	309	22	the	the	DET
ejpam-5856	309	23	frame	frame	NOUN
ejpam-5856	309	24	of	of	ADP
ejpam-5856	309	25	gfts	gft	NOUN
ejpam-5856	309	26	via	via	ADP
ejpam-5856	309	27	fgµ-closed	fgµ-closed	ADJ
ejpam-5856	309	28	sets	set	NOUN
ejpam-5856	309	29	and	and	CCONJ
ejpam-5856	309	30	discuss	discuss	VERB
ejpam-5856	309	31	some	some	DET
ejpam-5856	309	32	properties	property	NOUN
ejpam-5856	309	33	and	and	CCONJ
ejpam-5856	309	34	related	relate	VERB
ejpam-5856	309	35	theorems	theorem	NOUN
ejpam-5856	309	36	in	in	ADP
ejpam-5856	309	37	this	this	DET
ejpam-5856	309	38	sequel	sequel	NOUN
ejpam-5856	309	39	.	.	PUNCT
ejpam-5856	310	1	definition	definition	NOUN
ejpam-5856	310	2	15	15	NUM
ejpam-5856	310	3	.	.	PUNCT
ejpam-5856	311	1	an	an	DET
ejpam-5856	311	2	gfts	gft	NOUN
ejpam-5856	311	3	(	(	PUNCT
ejpam-5856	311	4	u	u	NOUN
ejpam-5856	311	5	,	,	PUNCT
ejpam-5856	311	6	µ	µ	NOUN
ejpam-5856	311	7	)	)	PUNCT
ejpam-5856	311	8	is	be	AUX
ejpam-5856	311	9	called	call	VERB
ejpam-5856	311	10	fgµ-normal	fgµ-normal	ADJ
ejpam-5856	311	11	(	(	PUNCT
ejpam-5856	311	12	or	or	CCONJ
ejpam-5856	311	13	fg-µr3	fg-µr3	PROPN
ejpam-5856	311	14	)	)	PUNCT
ejpam-5856	311	15	iff	iff	NOUN
ejpam-5856	311	16	for	for	ADP
ejpam-5856	311	17	any	any	DET
ejpam-5856	311	18	g	g	NOUN
ejpam-5856	311	19	,	,	PUNCT
ejpam-5856	311	20	h	h	NOUN
ejpam-5856	311	21	∈	∈	PROPN
ejpam-5856	311	22	fgµc(u	fgµc(u	PROPN
ejpam-5856	311	23	)	)	PUNCT
ejpam-5856	311	24	with	with	ADP
ejpam-5856	311	25	gq̃h	gq̃h	PROPN
ejpam-5856	311	26	,	,	PUNCT
ejpam-5856	311	27	there	there	PRON
ejpam-5856	311	28	are	be	VERB
ejpam-5856	311	29	og	og	PROPN
ejpam-5856	311	30	,	,	PUNCT
ejpam-5856	311	31	oh	oh	INTJ
ejpam-5856	311	32	∈	∈	PROPN
ejpam-5856	311	33	µ	µ	X
ejpam-5856	311	34	containing	contain	VERB
ejpam-5856	311	35	g	g	NOUN
ejpam-5856	311	36	,	,	PUNCT
ejpam-5856	311	37	h	h	NOUN
ejpam-5856	311	38	respectively	respectively	ADV
ejpam-5856	311	39	,	,	PUNCT
ejpam-5856	311	40	such	such	ADJ
ejpam-5856	311	41	that	that	DET
ejpam-5856	311	42	ogq̃oh	ogq̃oh	PROPN
ejpam-5856	311	43	.	.	PUNCT
ejpam-5856	312	1	s.	s.	PROPN
ejpam-5856	312	2	saleh	saleh	PROPN
ejpam-5856	312	3	et	et	PROPN
ejpam-5856	312	4	al	al	PROPN
ejpam-5856	312	5	.	.	PUNCT
ejpam-5856	312	6	/	/	SYM
ejpam-5856	312	7	eur	eur	PROPN
ejpam-5856	312	8	.	.	PUNCT
ejpam-5856	313	1	j.	j.	PROPN
ejpam-5856	313	2	pure	pure	PROPN
ejpam-5856	313	3	appl	appl	PROPN
ejpam-5856	313	4	.	.	PROPN
ejpam-5856	313	5	math	math	PROPN
ejpam-5856	313	6	,	,	PUNCT
ejpam-5856	313	7	18	18	NUM
ejpam-5856	313	8	(	(	PUNCT
ejpam-5856	313	9	1	1	NUM
ejpam-5856	313	10	)	)	PUNCT
ejpam-5856	313	11	(	(	PUNCT
ejpam-5856	313	12	2025	2025	NUM
ejpam-5856	313	13	)	)	PUNCT
ejpam-5856	313	14	,	,	PUNCT
ejpam-5856	313	15	5856	5856	NUM
ejpam-5856	313	16	9	9	NUM
ejpam-5856	313	17	of	of	ADP
ejpam-5856	313	18	15	15	NUM
ejpam-5856	313	19	remark	remark	NOUN
ejpam-5856	313	20	5	5	NUM
ejpam-5856	313	21	.	.	PUNCT
ejpam-5856	314	1	evidently	evidently	ADV
ejpam-5856	314	2	,	,	PUNCT
ejpam-5856	314	3	every	every	DET
ejpam-5856	314	4	fg-µr3	fg-µr3	NOUN
ejpam-5856	314	5	space	space	NOUN
ejpam-5856	314	6	is	be	AUX
ejpam-5856	314	7	fµ-r3	fµ-r3	NOUN
ejpam-5856	314	8	.	.	PUNCT
ejpam-5856	315	1	corollary	corollary	ADJ
ejpam-5856	315	2	4	4	NUM
ejpam-5856	315	3	.	.	PUNCT
ejpam-5856	316	1	an	an	DET
ejpam-5856	316	2	gfts	gft	NOUN
ejpam-5856	316	3	(	(	PUNCT
ejpam-5856	316	4	u	u	NOUN
ejpam-5856	316	5	,	,	PUNCT
ejpam-5856	316	6	µ	µ	NOUN
ejpam-5856	316	7	)	)	PUNCT
ejpam-5856	316	8	is	be	AUX
ejpam-5856	316	9	fg-µr3	fg-µr3	NOUN
ejpam-5856	316	10	if	if	SCONJ
ejpam-5856	316	11	and	and	CCONJ
ejpam-5856	316	12	only	only	ADV
ejpam-5856	316	13	if	if	SCONJ
ejpam-5856	316	14	for	for	ADP
ejpam-5856	316	15	any	any	DET
ejpam-5856	316	16	two	two	NUM
ejpam-5856	316	17	fgµ-closed	fgµ-closed	ADJ
ejpam-5856	316	18	sets	set	NOUN
ejpam-5856	316	19	g	g	ADP
ejpam-5856	316	20	,	,	PUNCT
ejpam-5856	316	21	h	h	NOUN
ejpam-5856	316	22	with	with	ADP
ejpam-5856	316	23	gq̃h	gq̃h	PROPN
ejpam-5856	316	24	,	,	PUNCT
ejpam-5856	316	25	there	there	PRON
ejpam-5856	316	26	are	be	VERB
ejpam-5856	316	27	og	og	PROPN
ejpam-5856	316	28	,	,	PUNCT
ejpam-5856	316	29	oh	oh	INTJ
ejpam-5856	316	30	∈	∈	PROPN
ejpam-5856	316	31	fgµo(u	fgµo(u	NOUN
ejpam-5856	316	32	)	)	PUNCT
ejpam-5856	316	33	such	such	ADJ
ejpam-5856	316	34	that	that	PRON
ejpam-5856	316	35	ogq̃	ogq̃	NOUN
ejpam-5856	317	1	oh	oh	INTJ
ejpam-5856	317	2	.	.	PUNCT
ejpam-5856	318	1	proof	proof	NOUN
ejpam-5856	318	2	.	.	PUNCT
ejpam-5856	319	1	it	it	PRON
ejpam-5856	319	2	can	can	AUX
ejpam-5856	319	3	be	be	AUX
ejpam-5856	319	4	obtained	obtain	VERB
ejpam-5856	319	5	from	from	ADP
ejpam-5856	319	6	definition	definition	NOUN
ejpam-5856	319	7	15	15	NUM
ejpam-5856	319	8	and	and	CCONJ
ejpam-5856	319	9	remark	remark	NOUN
ejpam-5856	319	10	1	1	NUM
ejpam-5856	319	11	.	.	PUNCT
ejpam-5856	319	12	theorem	theorem	VERB
ejpam-5856	319	13	7	7	NUM
ejpam-5856	319	14	.	.	X
ejpam-5856	319	15	for	for	ADP
ejpam-5856	319	16	an	an	DET
ejpam-5856	319	17	gfts	gft	NOUN
ejpam-5856	319	18	(	(	PUNCT
ejpam-5856	319	19	u	u	NOUN
ejpam-5856	319	20	,	,	PUNCT
ejpam-5856	319	21	µ	µ	NOUN
ejpam-5856	319	22	)	)	PUNCT
ejpam-5856	319	23	.	.	PUNCT
ejpam-5856	320	1	the	the	DET
ejpam-5856	320	2	next	next	ADJ
ejpam-5856	320	3	items	item	NOUN
ejpam-5856	320	4	are	be	AUX
ejpam-5856	320	5	equivalent	equivalent	ADJ
ejpam-5856	320	6	:	:	PUNCT
ejpam-5856	320	7	(	(	PUNCT
ejpam-5856	320	8	1	1	X
ejpam-5856	320	9	)	)	PUNCT
ejpam-5856	320	10	(	(	PUNCT
ejpam-5856	320	11	u	u	NOUN
ejpam-5856	320	12	,	,	PUNCT
ejpam-5856	320	13	µ	µ	NOUN
ejpam-5856	320	14	)	)	PUNCT
ejpam-5856	320	15	is	be	AUX
ejpam-5856	320	16	fg-µr3	fg-µr3	NOUN
ejpam-5856	320	17	,	,	PUNCT
ejpam-5856	320	18	(	(	PUNCT
ejpam-5856	320	19	2	2	NUM
ejpam-5856	320	20	)	)	PUNCT
ejpam-5856	320	21	for	for	ADP
ejpam-5856	320	22	any	any	DET
ejpam-5856	320	23	h	h	NOUN
ejpam-5856	320	24	∈	∈	PROPN
ejpam-5856	320	25	fgµc(u	fgµc(u	PROPN
ejpam-5856	320	26	)	)	PUNCT
ejpam-5856	320	27	and	and	CCONJ
ejpam-5856	320	28	any	any	DET
ejpam-5856	320	29	oh	oh	NOUN
ejpam-5856	320	30	∈	∈	PROPN
ejpam-5856	320	31	µ	µ	NOUN
ejpam-5856	320	32	containing	contain	VERB
ejpam-5856	320	33	h	h	NOUN
ejpam-5856	320	34	,	,	PUNCT
ejpam-5856	320	35	there	there	PRON
ejpam-5856	320	36	is	be	VERB
ejpam-5856	320	37	o∗	o∗	PROPN
ejpam-5856	320	38	h	h	PROPN
ejpam-5856	320	39	∈	∈	PROPN
ejpam-5856	320	40	µ	µ	PRON
ejpam-5856	320	41	such	such	ADJ
ejpam-5856	320	42	that	that	DET
ejpam-5856	320	43	clµ	clµ	NOUN
ejpam-5856	320	44	(	(	PUNCT
ejpam-5856	320	45	o	o	PROPN
ejpam-5856	320	46	∗	∗	PROPN
ejpam-5856	320	47	h	h	NOUN
ejpam-5856	320	48	)	)	PUNCT
ejpam-5856	320	49	⊆	⊆	NUM
ejpam-5856	320	50	oh	oh	INTJ
ejpam-5856	320	51	.	.	PUNCT
ejpam-5856	321	1	proof	proof	NOUN
ejpam-5856	321	2	.	.	PUNCT
ejpam-5856	322	1	necessity	necessity	NOUN
ejpam-5856	322	2	.	.	PUNCT
ejpam-5856	323	1	assume	assume	VERB
ejpam-5856	323	2	that	that	SCONJ
ejpam-5856	323	3	(	(	PUNCT
ejpam-5856	323	4	u	u	NOUN
ejpam-5856	323	5	,	,	PUNCT
ejpam-5856	323	6	µ	µ	NOUN
ejpam-5856	323	7	)	)	PUNCT
ejpam-5856	323	8	be	be	VERB
ejpam-5856	323	9	fg-µr3	fg-µr3	NOUN
ejpam-5856	323	10	,	,	PUNCT
ejpam-5856	323	11	h	h	NOUN
ejpam-5856	323	12	∈	∈	PROPN
ejpam-5856	323	13	fgµc(u	fgµc(u	PROPN
ejpam-5856	323	14	)	)	PUNCT
ejpam-5856	323	15	,	,	PUNCT
ejpam-5856	323	16	and	and	CCONJ
ejpam-5856	323	17	oh	oh	INTJ
ejpam-5856	323	18	∈	∈	PROPN
ejpam-5856	323	19	fµo(u	fµo(u	PROPN
ejpam-5856	323	20	)	)	PUNCT
ejpam-5856	323	21	containingh	containingh	NOUN
ejpam-5856	323	22	,	,	PUNCT
ejpam-5856	323	23	we	we	PRON
ejpam-5856	323	24	have	have	VERB
ejpam-5856	323	25	oc	oc	ADP
ejpam-5856	323	26	h	h	PROPN
ejpam-5856	323	27	∈	∈	PROPN
ejpam-5856	323	28	fµc(u	fµc(u	PROPN
ejpam-5856	323	29	)	)	PUNCT
ejpam-5856	323	30	.	.	PUNCT
ejpam-5856	324	1	clearly	clearly	ADV
ejpam-5856	324	2	,	,	PUNCT
ejpam-5856	324	3	oh	oh	INTJ
ejpam-5856	324	4	q̃oc	q̃oc	PROPN
ejpam-5856	324	5	h	h	NOUN
ejpam-5856	324	6	that	that	DET
ejpam-5856	324	7	implieshq̃oc	implieshq̃oc	PROPN
ejpam-5856	324	8	h	h	NOUN
ejpam-5856	324	9	.	.	PUNCT
ejpam-5856	325	1	since	since	SCONJ
ejpam-5856	325	2	(	(	PUNCT
ejpam-5856	325	3	u	u	INTJ
ejpam-5856	325	4	,	,	PUNCT
ejpam-5856	325	5	µ	µ	NOUN
ejpam-5856	325	6	)	)	PUNCT
ejpam-5856	325	7	is	be	AUX
ejpam-5856	325	8	fg-µr3	fg-µr3	NOUN
ejpam-5856	325	9	,	,	PUNCT
ejpam-5856	325	10	there	there	PRON
ejpam-5856	325	11	areo	areo	PROPN
ejpam-5856	325	12	∗	∗	NOUN
ejpam-5856	325	13	h	h	NOUN
ejpam-5856	325	14	,	,	PUNCT
ejpam-5856	325	15	ooc	ooc	PRON
ejpam-5856	325	16	h	h	NOUN
ejpam-5856	325	17	∈	∈	PROPN
ejpam-5856	325	18	µ	µ	PRON
ejpam-5856	325	19	such	such	ADJ
ejpam-5856	325	20	thato∗	thato∗	NOUN
ejpam-5856	325	21	h	h	NOUN
ejpam-5856	325	22	q̃ooc	q̃ooc	ADV
ejpam-5856	325	23	h	h	NOUN
ejpam-5856	325	24	implies	imply	VERB
ejpam-5856	325	25	thato∗	thato∗	X
ejpam-5856	325	26	h⊆(ooc	h⊆(ooc	PROPN
ejpam-5856	325	27	h	h	NOUN
ejpam-5856	325	28	)	)	PUNCT
ejpam-5856	325	29	c	c	NOUN
ejpam-5856	326	1	and	and	CCONJ
ejpam-5856	326	2	so	so	ADV
ejpam-5856	326	3	,	,	PUNCT
ejpam-5856	326	4	clµ(o	clµ(o	PROPN
ejpam-5856	326	5	∗	∗	NOUN
ejpam-5856	326	6	h)⊆(ooc	h)⊆(ooc	NOUN
ejpam-5856	326	7	h	h	NOUN
ejpam-5856	326	8	)	)	PUNCT
ejpam-5856	326	9	c.	c.	NOUN
ejpam-5856	326	10	since	since	SCONJ
ejpam-5856	326	11	oc	oc	ADP
ejpam-5856	326	12	h⊆ooc	h⊆ooc	PROPN
ejpam-5856	326	13	h	h	NOUN
ejpam-5856	326	14	,	,	PUNCT
ejpam-5856	326	15	we	we	PRON
ejpam-5856	326	16	have	have	VERB
ejpam-5856	326	17	(	(	PUNCT
ejpam-5856	326	18	ooc	ooc	NOUN
ejpam-5856	326	19	h	h	NOUN
ejpam-5856	326	20	)	)	PUNCT
ejpam-5856	326	21	c⊆oh	c⊆oh	PROPN
ejpam-5856	326	22	and	and	CCONJ
ejpam-5856	326	23	clµ(o	clµ(o	PROPN
ejpam-5856	326	24	∗	∗	NOUN
ejpam-5856	327	1	h)⊆(ooc	h)⊆(ooc	NOUN
ejpam-5856	327	2	h	h	NOUN
ejpam-5856	327	3	)	)	PUNCT
ejpam-5856	327	4	c⊆oh	c⊆oh	PROPN
ejpam-5856	327	5	.	.	PUNCT
ejpam-5856	328	1	the	the	DET
ejpam-5856	328	2	result	result	NOUN
ejpam-5856	328	3	holds	hold	VERB
ejpam-5856	328	4	.	.	PUNCT
ejpam-5856	329	1	conversely	conversely	ADV
ejpam-5856	329	2	,	,	PUNCT
ejpam-5856	329	3	it	it	PRON
ejpam-5856	329	4	follows	follow	VERB
ejpam-5856	329	5	directly	directly	ADV
ejpam-5856	329	6	by	by	ADP
ejpam-5856	329	7	the	the	DET
ejpam-5856	329	8	hypothesis	hypothesis	NOUN
ejpam-5856	329	9	.	.	PUNCT
ejpam-5856	330	1	theorem	theorem	ADJ
ejpam-5856	330	2	8	8	NUM
ejpam-5856	330	3	.	.	PUNCT
ejpam-5856	331	1	for	for	ADP
ejpam-5856	331	2	an	an	DET
ejpam-5856	331	3	gfts	gft	NOUN
ejpam-5856	331	4	(	(	PUNCT
ejpam-5856	331	5	u	u	NOUN
ejpam-5856	331	6	,	,	PUNCT
ejpam-5856	331	7	µ	µ	NOUN
ejpam-5856	331	8	)	)	PUNCT
ejpam-5856	331	9	.	.	PUNCT
ejpam-5856	332	1	the	the	DET
ejpam-5856	332	2	following	follow	VERB
ejpam-5856	332	3	items	item	NOUN
ejpam-5856	332	4	are	be	AUX
ejpam-5856	332	5	equivalent	equivalent	ADJ
ejpam-5856	332	6	:	:	PUNCT
ejpam-5856	332	7	(	(	PUNCT
ejpam-5856	332	8	1	1	X
ejpam-5856	332	9	)	)	PUNCT
ejpam-5856	332	10	(	(	PUNCT
ejpam-5856	332	11	u	u	NOUN
ejpam-5856	332	12	,	,	PUNCT
ejpam-5856	332	13	µ	µ	NOUN
ejpam-5856	332	14	)	)	PUNCT
ejpam-5856	332	15	is	be	AUX
ejpam-5856	332	16	fg-µr3	fg-µr3	NOUN
ejpam-5856	332	17	,	,	PUNCT
ejpam-5856	332	18	(	(	PUNCT
ejpam-5856	332	19	2	2	NUM
ejpam-5856	332	20	)	)	PUNCT
ejpam-5856	332	21	for	for	ADP
ejpam-5856	332	22	any	any	DET
ejpam-5856	332	23	f	f	NOUN
ejpam-5856	332	24	,	,	PUNCT
ejpam-5856	332	25	g	g	PROPN
ejpam-5856	332	26	∈	∈	PROPN
ejpam-5856	332	27	fgµc(u	fgµc(u	NOUN
ejpam-5856	332	28	)	)	PUNCT
ejpam-5856	332	29	with	with	ADP
ejpam-5856	332	30	f	f	PROPN
ejpam-5856	332	31	q̃g	q̃g	PROPN
ejpam-5856	332	32	,	,	PUNCT
ejpam-5856	332	33	there	there	PRON
ejpam-5856	332	34	are	be	VERB
ejpam-5856	332	35	of	of	ADP
ejpam-5856	332	36	,	,	PUNCT
ejpam-5856	332	37	og	og	PROPN
ejpam-5856	332	38	∈	∈	PROPN
ejpam-5856	332	39	µ	µ	X
ejpam-5856	332	40	containing	contain	VERB
ejpam-5856	332	41	f	f	PROPN
ejpam-5856	332	42	,	,	PUNCT
ejpam-5856	332	43	g	g	PROPN
ejpam-5856	332	44	respectively	respectively	ADV
ejpam-5856	332	45	,	,	PUNCT
ejpam-5856	332	46	such	such	ADJ
ejpam-5856	332	47	that	that	DET
ejpam-5856	332	48	clµ(of	clµ(of	NOUN
ejpam-5856	332	49	)	)	PUNCT
ejpam-5856	332	50	q̃clµ(og	q̃clµ(og	VERB
ejpam-5856	332	51	)	)	PUNCT
ejpam-5856	332	52	.	.	PUNCT
ejpam-5856	333	1	proof	proof	NOUN
ejpam-5856	333	2	.	.	PUNCT
ejpam-5856	334	1	necessity	necessity	NOUN
ejpam-5856	334	2	.	.	PUNCT
ejpam-5856	335	1	assume	assume	VERB
ejpam-5856	335	2	that	that	SCONJ
ejpam-5856	335	3	(	(	PUNCT
ejpam-5856	335	4	u	u	NOUN
ejpam-5856	335	5	,	,	PUNCT
ejpam-5856	335	6	µ	µ	NOUN
ejpam-5856	335	7	)	)	PUNCT
ejpam-5856	335	8	is	be	AUX
ejpam-5856	335	9	fg-µr3	fg-µr3	NOUN
ejpam-5856	335	10	and	and	CCONJ
ejpam-5856	335	11	f	f	X
ejpam-5856	335	12	,	,	PUNCT
ejpam-5856	335	13	g	g	PROPN
ejpam-5856	335	14	∈	∈	PROPN
ejpam-5856	335	15	fgµc(u	fgµc(u	NOUN
ejpam-5856	335	16	)	)	PUNCT
ejpam-5856	335	17	with	with	ADP
ejpam-5856	335	18	f	f	PROPN
ejpam-5856	335	19	q̃g	q̃g	PROPN
ejpam-5856	335	20	,	,	PUNCT
ejpam-5856	335	21	there	there	PRON
ejpam-5856	335	22	are	be	VERB
ejpam-5856	335	23	o∗	o∗	PROPN
ejpam-5856	335	24	f	f	PROPN
ejpam-5856	335	25	,	,	PUNCT
ejpam-5856	335	26	og	og	PROPN
ejpam-5856	335	27	∈	∈	PROPN
ejpam-5856	335	28	µ	µ	PRON
ejpam-5856	335	29	such	such	ADJ
ejpam-5856	335	30	that	that	SCONJ
ejpam-5856	335	31	o∗	o∗	PROPN
ejpam-5856	335	32	f	f	PROPN
ejpam-5856	335	33	q̃og	q̃og	PROPN
ejpam-5856	335	34	implies	imply	VERB
ejpam-5856	335	35	that	that	SCONJ
ejpam-5856	335	36	o∗	o∗	PROPN
ejpam-5856	335	37	f	f	PROPN
ejpam-5856	335	38	q̃clµ(og	q̃clµ(og	X
ejpam-5856	335	39	)	)	PUNCT
ejpam-5856	335	40	(	(	PUNCT
ejpam-5856	335	41	by	by	ADP
ejpam-5856	335	42	lemma	lemma	PROPN
ejpam-5856	335	43	1	1	NUM
ejpam-5856	335	44	)	)	PUNCT
ejpam-5856	335	45	.	.	PUNCT
ejpam-5856	336	1	again	again	ADV
ejpam-5856	336	2	,	,	PUNCT
ejpam-5856	336	3	(	(	PUNCT
ejpam-5856	336	4	u	u	NOUN
ejpam-5856	336	5	,	,	PUNCT
ejpam-5856	336	6	µ	µ	NOUN
ejpam-5856	336	7	)	)	PUNCT
ejpam-5856	336	8	is	be	AUX
ejpam-5856	336	9	fg-µr3	fg-µr3	NOUN
ejpam-5856	336	10	,	,	PUNCT
ejpam-5856	336	11	there	there	PRON
ejpam-5856	336	12	are	be	VERB
ejpam-5856	336	13	o∗∗	o∗∗	PROPN
ejpam-5856	336	14	f	f	X
ejpam-5856	336	15	,	,	PUNCT
ejpam-5856	336	16	oclµ(og	oclµ(og	ADJ
ejpam-5856	336	17	)	)	PUNCT
ejpam-5856	336	18	∈	∈	PROPN
ejpam-5856	336	19	µ	µ	NOUN
ejpam-5856	336	20	such	such	ADJ
ejpam-5856	336	21	that	that	DET
ejpam-5856	336	22	o∗∗	o∗∗	PROPN
ejpam-5856	336	23	f	f	X
ejpam-5856	336	24	q̃oclµ(og	q̃oclµ(og	PROPN
ejpam-5856	336	25	)	)	PUNCT
ejpam-5856	336	26	.	.	PUNCT
ejpam-5856	337	1	this	this	PRON
ejpam-5856	337	2	implies	imply	VERB
ejpam-5856	337	3	that	that	PRON
ejpam-5856	337	4	clµ(o	clµ(o	VERB
ejpam-5856	337	5	∗∗	∗∗	PROPN
ejpam-5856	337	6	f	f	X
ejpam-5856	337	7	)	)	PUNCT
ejpam-5856	337	8	q̃oclµ(og	q̃oclµ(og	PROPN
ejpam-5856	337	9	)	)	PUNCT
ejpam-5856	337	10	(	(	PUNCT
ejpam-5856	337	11	by	by	ADP
ejpam-5856	337	12	lemma	lemma	PROPN
ejpam-5856	337	13	1	1	NUM
ejpam-5856	337	14	)	)	PUNCT
ejpam-5856	337	15	.	.	PUNCT
ejpam-5856	338	1	take	take	VERB
ejpam-5856	338	2	of	of	ADP
ejpam-5856	338	3	=	=	PUNCT
ejpam-5856	338	4	o∗	o∗	PROPN
ejpam-5856	338	5	f	f	PROPN
ejpam-5856	338	6	∪	∪	ADP
ejpam-5856	338	7	o∗∗	o∗∗	PROPN
ejpam-5856	338	8	f	f	PROPN
ejpam-5856	338	9	∈	∈	PROPN
ejpam-5856	338	10	µ.	µ.	NOUN
ejpam-5856	338	11	since	since	SCONJ
ejpam-5856	338	12	(	(	PUNCT
ejpam-5856	338	13	u	u	INTJ
ejpam-5856	338	14	,	,	PUNCT
ejpam-5856	338	15	µ	µ	NOUN
ejpam-5856	338	16	)	)	PUNCT
ejpam-5856	338	17	is	be	AUX
ejpam-5856	338	18	fg-µr3	fg-µr3	PROPN
ejpam-5856	338	19	and	and	CCONJ
ejpam-5856	338	20	o∗	o∗	PROPN
ejpam-5856	338	21	f	f	PROPN
ejpam-5856	338	22	∈	∈	PROPN
ejpam-5856	338	23	µ.	µ.	NOUN
ejpam-5856	338	24	so	so	ADV
ejpam-5856	338	25	by	by	ADP
ejpam-5856	338	26	the	the	DET
ejpam-5856	338	27	above	above	ADJ
ejpam-5856	338	28	theorem	theorem	NOUN
ejpam-5856	338	29	,	,	PUNCT
ejpam-5856	338	30	there	there	PRON
ejpam-5856	338	31	is	be	VERB
ejpam-5856	338	32	of	of	ADP
ejpam-5856	338	33	∈	∈	PROPN
ejpam-5856	338	34	µ	µ	NOUN
ejpam-5856	338	35	such	such	ADJ
ejpam-5856	338	36	that	that	DET
ejpam-5856	338	37	clµ(of	clµ(of	NOUN
ejpam-5856	338	38	)	)	PUNCT
ejpam-5856	338	39	⊆	⊆	NUM
ejpam-5856	338	40	o∗	o∗	PROPN
ejpam-5856	338	41	f	f	PROPN
ejpam-5856	338	42	.	.	PUNCT
ejpam-5856	339	1	since	since	SCONJ
ejpam-5856	339	2	o∗	o∗	PROPN
ejpam-5856	339	3	f	f	PROPN
ejpam-5856	339	4	q̃clµ(og	q̃clµ(og	VERB
ejpam-5856	339	5	)	)	PUNCT
ejpam-5856	339	6	,	,	PUNCT
ejpam-5856	339	7	we	we	PRON
ejpam-5856	339	8	have	have	VERB
ejpam-5856	339	9	clµ(of	clµ(of	NOUN
ejpam-5856	339	10	)	)	PUNCT
ejpam-5856	339	11	q̃clµ(og	q̃clµ(og	VERB
ejpam-5856	339	12	)	)	PUNCT
ejpam-5856	339	13	.	.	PUNCT
ejpam-5856	340	1	conversely	conversely	ADV
ejpam-5856	340	2	,	,	PUNCT
ejpam-5856	340	3	it	it	PRON
ejpam-5856	340	4	follows	follow	VERB
ejpam-5856	340	5	directly	directly	ADV
ejpam-5856	340	6	from	from	ADP
ejpam-5856	340	7	the	the	DET
ejpam-5856	340	8	hypothesis	hypothesis	NOUN
ejpam-5856	340	9	.	.	PUNCT
ejpam-5856	341	1	definition	definition	NOUN
ejpam-5856	341	2	16	16	NUM
ejpam-5856	341	3	.	.	PUNCT
ejpam-5856	342	1	an	an	DET
ejpam-5856	342	2	gfts	gft	NOUN
ejpam-5856	342	3	(	(	PUNCT
ejpam-5856	342	4	u	u	NOUN
ejpam-5856	342	5	,	,	PUNCT
ejpam-5856	342	6	µ	µ	NOUN
ejpam-5856	342	7	)	)	PUNCT
ejpam-5856	342	8	is	be	AUX
ejpam-5856	342	9	called	call	VERB
ejpam-5856	342	10	fµ-g4	fµ-g4	PUNCT
ejpam-5856	343	1	iff	iff	PROPN
ejpam-5856	343	2	it	it	PRON
ejpam-5856	343	3	is	be	AUX
ejpam-5856	343	4	fg-µr3	fg-µr3	NOUN
ejpam-5856	343	5	and	and	CCONJ
ejpam-5856	343	6	fµ-symmetric	fµ-symmetric	ADJ
ejpam-5856	343	7	.	.	PUNCT
ejpam-5856	344	1	theorem	theorem	VERB
ejpam-5856	344	2	9	9	NUM
ejpam-5856	344	3	.	.	PUNCT
ejpam-5856	345	1	every	every	DET
ejpam-5856	345	2	fµ-g4	fµ-g4	NOUN
ejpam-5856	345	3	space	space	NOUN
ejpam-5856	345	4	is	be	AUX
ejpam-5856	345	5	fµ-g3	fµ-g3	NOUN
ejpam-5856	345	6	.	.	PUNCT
ejpam-5856	346	1	proof	proof	NOUN
ejpam-5856	346	2	.	.	PUNCT
ejpam-5856	347	1	suppose	suppose	VERB
ejpam-5856	347	2	that	that	SCONJ
ejpam-5856	347	3	(	(	PUNCT
ejpam-5856	347	4	u	u	NOUN
ejpam-5856	347	5	,	,	PUNCT
ejpam-5856	347	6	µ	µ	NOUN
ejpam-5856	347	7	)	)	PUNCT
ejpam-5856	347	8	is	be	AUX
ejpam-5856	347	9	fµ-g4	fµ-g4	NOUN
ejpam-5856	347	10	,	,	PUNCT
ejpam-5856	347	11	then	then	ADV
ejpam-5856	347	12	it	it	PRON
ejpam-5856	347	13	is	be	AUX
ejpam-5856	347	14	fg-µr3	fg-µr3	NOUN
ejpam-5856	347	15	and	and	CCONJ
ejpam-5856	347	16	fµ-symmetric	fµ-symmetric	ADJ
ejpam-5856	347	17	.	.	PUNCT
ejpam-5856	348	1	consider	consider	VERB
ejpam-5856	348	2	h	h	NOUN
ejpam-5856	348	3	is	be	AUX
ejpam-5856	348	4	fgµ-closed	fgµ-close	VERB
ejpam-5856	348	5	set	set	VERB
ejpam-5856	348	6	with	with	ADP
ejpam-5856	348	7	uαq̃h	uαq̃h	PROPN
ejpam-5856	348	8	,	,	PUNCT
ejpam-5856	348	9	then	then	ADV
ejpam-5856	348	10	uα	uα	PROPN
ejpam-5856	348	11	is	be	AUX
ejpam-5856	348	12	an	an	DET
ejpam-5856	348	13	fgµ-closed	fgµ-closed	ADJ
ejpam-5856	348	14	set	set	NOUN
ejpam-5856	348	15	(	(	PUNCT
ejpam-5856	348	16	as	as	ADP
ejpam-5856	348	17	(	(	PUNCT
ejpam-5856	348	18	u	u	NOUN
ejpam-5856	348	19	,	,	PUNCT
ejpam-5856	348	20	µ	µ	NOUN
ejpam-5856	348	21	)	)	PUNCT
ejpam-5856	348	22	is	be	AUX
ejpam-5856	348	23	fµ-symmetric	fµ-symmetric	ADJ
ejpam-5856	348	24	)	)	PUNCT
ejpam-5856	348	25	.	.	PUNCT
ejpam-5856	349	1	since	since	SCONJ
ejpam-5856	349	2	(	(	PUNCT
ejpam-5856	349	3	u	u	INTJ
ejpam-5856	349	4	,	,	PUNCT
ejpam-5856	349	5	µ	µ	NOUN
ejpam-5856	349	6	)	)	PUNCT
ejpam-5856	349	7	is	be	AUX
ejpam-5856	349	8	fg-µr3	fg-µr3	NOUN
ejpam-5856	349	9	,	,	PUNCT
ejpam-5856	349	10	there	there	PRON
ejpam-5856	349	11	are	be	VERB
ejpam-5856	349	12	ouα	ouα	NOUN
ejpam-5856	349	13	,	,	PUNCT
ejpam-5856	349	14	oh	oh	INTJ
ejpam-5856	349	15	∈	∈	PROPN
ejpam-5856	349	16	µ	µ	PRON
ejpam-5856	349	17	such	such	ADJ
ejpam-5856	349	18	that	that	DET
ejpam-5856	349	19	ouα	ouα	NOUN
ejpam-5856	349	20	q̃oh	q̃oh	PROPN
ejpam-5856	349	21	.	.	PUNCT
ejpam-5856	350	1	hence	hence	ADV
ejpam-5856	350	2	(	(	PUNCT
ejpam-5856	350	3	u	u	NOUN
ejpam-5856	350	4	,	,	PUNCT
ejpam-5856	350	5	µ	µ	NOUN
ejpam-5856	350	6	)	)	PUNCT
ejpam-5856	350	7	is	be	AUX
ejpam-5856	350	8	fg-µr2	fg-µr2	NOUN
ejpam-5856	350	9	.	.	PUNCT
ejpam-5856	351	1	therefore	therefore	ADV
ejpam-5856	351	2	(	(	PUNCT
ejpam-5856	351	3	u	u	NOUN
ejpam-5856	351	4	,	,	PUNCT
ejpam-5856	351	5	µ	µ	NOUN
ejpam-5856	351	6	)	)	PUNCT
ejpam-5856	351	7	is	be	AUX
ejpam-5856	351	8	fµ-g3	fµ-g3	NOUN
ejpam-5856	351	9	.	.	PUNCT
ejpam-5856	352	1	corollary	corollary	ADJ
ejpam-5856	352	2	5	5	NUM
ejpam-5856	352	3	.	.	PUNCT
ejpam-5856	353	1	if	if	SCONJ
ejpam-5856	353	2	(	(	PUNCT
ejpam-5856	353	3	u	u	NOUN
ejpam-5856	353	4	,	,	PUNCT
ejpam-5856	353	5	µ	µ	NOUN
ejpam-5856	353	6	)	)	PUNCT
ejpam-5856	353	7	is	be	AUX
ejpam-5856	353	8	fg-µr3	fg-µr3	PROPN
ejpam-5856	353	9	and	and	CCONJ
ejpam-5856	353	10	fµ-symmetric	fµ-symmetric	ADJ
ejpam-5856	353	11	space	space	NOUN
ejpam-5856	353	12	,	,	PUNCT
ejpam-5856	353	13	then	then	ADV
ejpam-5856	353	14	(	(	PUNCT
ejpam-5856	353	15	u	u	NOUN
ejpam-5856	353	16	,	,	PUNCT
ejpam-5856	353	17	µ	µ	NOUN
ejpam-5856	353	18	)	)	PUNCT
ejpam-5856	353	19	is	be	AUX
ejpam-5856	353	20	fg-µr2	fg-µr2	NOUN
ejpam-5856	353	21	.	.	PUNCT
ejpam-5856	354	1	proposition	proposition	NOUN
ejpam-5856	354	2	5	5	NUM
ejpam-5856	354	3	.	.	PUNCT
ejpam-5856	355	1	an	an	DET
ejpam-5856	355	2	gfts	gft	NOUN
ejpam-5856	355	3	(	(	PUNCT
ejpam-5856	355	4	u	u	NOUN
ejpam-5856	355	5	,	,	PUNCT
ejpam-5856	355	6	µ	µ	NOUN
ejpam-5856	355	7	)	)	PUNCT
ejpam-5856	355	8	is	be	AUX
ejpam-5856	355	9	fg-µr3	fg-µr3	NOUN
ejpam-5856	355	10	iff	iff	VERB
ejpam-5856	355	11	it	it	PRON
ejpam-5856	355	12	is	be	AUX
ejpam-5856	355	13	both	both	PRON
ejpam-5856	355	14	fµ-r3	fµ-r3	NOUN
ejpam-5856	355	15	and	and	CCONJ
ejpam-5856	355	16	fµ-t	fµ-t	PROPN
ejpam-5856	355	17	1	1	NUM
ejpam-5856	355	18	2	2	NUM
ejpam-5856	355	19	.	.	PUNCT
ejpam-5856	356	1	s.	s.	PROPN
ejpam-5856	356	2	saleh	saleh	PROPN
ejpam-5856	356	3	et	et	PROPN
ejpam-5856	356	4	al	al	PROPN
ejpam-5856	356	5	.	.	PUNCT
ejpam-5856	356	6	/	/	SYM
ejpam-5856	356	7	eur	eur	PROPN
ejpam-5856	356	8	.	.	PUNCT
ejpam-5856	357	1	j.	j.	PROPN
ejpam-5856	357	2	pure	pure	PROPN
ejpam-5856	357	3	appl	appl	PROPN
ejpam-5856	357	4	.	.	PROPN
ejpam-5856	357	5	math	math	PROPN
ejpam-5856	357	6	,	,	PUNCT
ejpam-5856	357	7	18	18	NUM
ejpam-5856	357	8	(	(	PUNCT
ejpam-5856	357	9	1	1	NUM
ejpam-5856	357	10	)	)	PUNCT
ejpam-5856	357	11	(	(	PUNCT
ejpam-5856	357	12	2025	2025	NUM
ejpam-5856	357	13	)	)	PUNCT
ejpam-5856	357	14	,	,	PUNCT
ejpam-5856	357	15	5856	5856	NUM
ejpam-5856	357	16	10	10	NUM
ejpam-5856	357	17	of	of	ADP
ejpam-5856	357	18	15	15	NUM
ejpam-5856	357	19	proof	proof	NOUN
ejpam-5856	357	20	.	.	PUNCT
ejpam-5856	358	1	it	it	PRON
ejpam-5856	358	2	is	be	AUX
ejpam-5856	358	3	analogues	analogue	NOUN
ejpam-5856	358	4	to	to	ADP
ejpam-5856	358	5	that	that	PRON
ejpam-5856	358	6	of	of	ADP
ejpam-5856	358	7	theorem	theorem	ADJ
ejpam-5856	358	8	1	1	NUM
ejpam-5856	358	9	.	.	PUNCT
ejpam-5856	358	10	theorem	theorem	VERB
ejpam-5856	358	11	10	10	NUM
ejpam-5856	358	12	.	.	PUNCT
ejpam-5856	359	1	an	an	DET
ejpam-5856	359	2	gfts	gft	NOUN
ejpam-5856	359	3	(	(	PUNCT
ejpam-5856	359	4	u	u	NOUN
ejpam-5856	359	5	,	,	PUNCT
ejpam-5856	359	6	µ	µ	NOUN
ejpam-5856	359	7	)	)	PUNCT
ejpam-5856	359	8	is	be	AUX
ejpam-5856	359	9	fµ-g4	fµ-g4	NOUN
ejpam-5856	359	10	if	if	SCONJ
ejpam-5856	360	1	and	and	CCONJ
ejpam-5856	360	2	only	only	ADV
ejpam-5856	360	3	if	if	SCONJ
ejpam-5856	360	4	it	it	PRON
ejpam-5856	360	5	is	be	AUX
ejpam-5856	360	6	fµ-t4	fµ-t4	NOUN
ejpam-5856	360	7	.	.	PUNCT
ejpam-5856	361	1	proof	proof	NOUN
ejpam-5856	361	2	.	.	PUNCT
ejpam-5856	362	1	it	it	PRON
ejpam-5856	362	2	is	be	AUX
ejpam-5856	362	3	analogues	analogue	NOUN
ejpam-5856	362	4	to	to	ADP
ejpam-5856	362	5	that	that	PRON
ejpam-5856	362	6	of	of	ADP
ejpam-5856	362	7	theorem	theorem	NOUN
ejpam-5856	362	8	6	6	NUM
ejpam-5856	362	9	.	.	PUNCT
ejpam-5856	362	10	from	from	ADP
ejpam-5856	362	11	the	the	DET
ejpam-5856	362	12	definitions	definition	NOUN
ejpam-5856	362	13	and	and	CCONJ
ejpam-5856	362	14	discussions	discussion	NOUN
ejpam-5856	362	15	in	in	ADP
ejpam-5856	362	16	section	section	NOUN
ejpam-5856	362	17	3	3	NUM
ejpam-5856	362	18	and	and	CCONJ
ejpam-5856	362	19	4	4	NUM
ejpam-5856	362	20	.	.	PUNCT
ejpam-5856	363	1	the	the	DET
ejpam-5856	363	2	following	follow	VERB
ejpam-5856	363	3	implications	implication	NOUN
ejpam-5856	363	4	hold	hold	VERB
ejpam-5856	363	5	.	.	PUNCT
ejpam-5856	364	1	corollary	corollary	ADJ
ejpam-5856	364	2	6	6	NUM
ejpam-5856	364	3	.	.	PUNCT
ejpam-5856	365	1	the	the	DET
ejpam-5856	365	2	following	follow	VERB
ejpam-5856	365	3	implications	implication	NOUN
ejpam-5856	365	4	hold	hold	VERB
ejpam-5856	365	5	.	.	PUNCT
ejpam-5856	366	1	fµ−	fµ−	X
ejpam-5856	367	1	t4	t4	PROPN
ejpam-5856	367	2	=	=	PROPN
ejpam-5856	367	3	⇒	⇒	NOUN
ejpam-5856	367	4	fµ−	fµ−	PUNCT
ejpam-5856	367	5	t3	t3	NOUN
ejpam-5856	367	6	=	=	NOUN
ejpam-5856	367	7	⇒	⇒	NOUN
ejpam-5856	367	8	fµ−	fµ−	PUNCT
ejpam-5856	367	9	t2	t2	NOUN
ejpam-5856	367	10	1	1	NUM
ejpam-5856	367	11	2	2	NUM
ejpam-5856	367	12	=	=	NOUN
ejpam-5856	367	13	⇒	⇒	NOUN
ejpam-5856	367	14	fµ−	fµ−	PUNCT
ejpam-5856	367	15	t2	t2	NOUN
ejpam-5856	367	16	=	=	SYM
ejpam-5856	367	17	⇒	⇒	NOUN
ejpam-5856	367	18	fµ−	fµ−	PUNCT
ejpam-5856	367	19	t1	t1	NOUN
ejpam-5856	367	20	=	=	NOUN
ejpam-5856	367	21	⇒	⇒	NOUN
ejpam-5856	367	22	fµ−	fµ−	PUNCT
ejpam-5856	367	23	t0	t0	PROPN
ejpam-5856	367	24	⇕	⇕	NOUN
ejpam-5856	367	25	⇕	⇕	NOUN
ejpam-5856	367	26	fµ−g4	fµ−g4	NOUN
ejpam-5856	367	27	=	=	NOUN
ejpam-5856	367	28	⇒	⇒	VERB
ejpam-5856	367	29	fµ−g3	fµ−g3	X
ejpam-5856	367	30	⇐	⇐	ADJ
ejpam-5856	367	31	⇒	⇒	NOUN
ejpam-5856	367	32	fg−	fg−	NUM
ejpam-5856	367	33	µr2	µr2	NOUN
ejpam-5856	367	34	∧	∧	NOUN
ejpam-5856	367	35	fµ−	fµ−	PUNCT
ejpam-5856	367	36	symmetric	symmetric	ADJ
ejpam-5856	367	37	⇕	⇕	NOUN
ejpam-5856	367	38	fg−	fg−	NUM
ejpam-5856	367	39	µr3	µr3	ADP
ejpam-5856	367	40	∧	∧	NOUN
ejpam-5856	367	41	fµ−	fµ−	PUNCT
ejpam-5856	367	42	symmetric	symmetric	ADJ
ejpam-5856	367	43	=	=	NOUN
ejpam-5856	367	44	⇒	⇒	NOUN
ejpam-5856	367	45	fg−	fg−	NUM
ejpam-5856	367	46	µr2	µr2	NOUN
ejpam-5856	367	47	=	=	NOUN
ejpam-5856	367	48	⇒	⇒	NOUN
ejpam-5856	367	49	fµ−r2	fµ−r2	PROPN
ejpam-5856	367	50	5	5	NUM
ejpam-5856	367	51	.	.	PUNCT
ejpam-5856	367	52	further	further	ADJ
ejpam-5856	367	53	applications	application	NOUN
ejpam-5856	367	54	and	and	CCONJ
ejpam-5856	367	55	relations	relation	NOUN
ejpam-5856	367	56	in	in	ADP
ejpam-5856	367	57	the	the	DET
ejpam-5856	367	58	following	follow	VERB
ejpam-5856	367	59	discussion	discussion	NOUN
ejpam-5856	367	60	,	,	PUNCT
ejpam-5856	367	61	we	we	PRON
ejpam-5856	367	62	will	will	AUX
ejpam-5856	367	63	explore	explore	VERB
ejpam-5856	367	64	the	the	DET
ejpam-5856	367	65	basic	basic	ADJ
ejpam-5856	367	66	preservation	preservation	NOUN
ejpam-5856	367	67	theorems	theorem	NOUN
ejpam-5856	367	68	and	and	CCONJ
ejpam-5856	367	69	some	some	DET
ejpam-5856	367	70	relations	relation	NOUN
ejpam-5856	367	71	of	of	ADP
ejpam-5856	367	72	fg-µr2	fg-µr2	NOUN
ejpam-5856	367	73	and	and	CCONJ
ejpam-5856	367	74	fg-µr3	fg-µr3	PROPN
ejpam-5856	367	75	.	.	PUNCT
ejpam-5856	368	1	definition	definition	NOUN
ejpam-5856	368	2	17	17	NUM
ejpam-5856	368	3	.	.	PUNCT
ejpam-5856	369	1	for	for	ADP
ejpam-5856	369	2	an	an	DET
ejpam-5856	369	3	gts	gts	NOUN
ejpam-5856	369	4	(	(	PUNCT
ejpam-5856	369	5	u	u	NOUN
ejpam-5856	369	6	,	,	PUNCT
ejpam-5856	369	7	θ	θ	PROPN
ejpam-5856	369	8	)	)	PUNCT
ejpam-5856	369	9	.	.	PUNCT
ejpam-5856	370	1	the	the	DET
ejpam-5856	370	2	class	class	NOUN
ejpam-5856	370	3	µθ	µθ	ADP
ejpam-5856	370	4	=	=	PUNCT
ejpam-5856	370	5	{	{	PUNCT
ejpam-5856	370	6	χh	χh	NOUN
ejpam-5856	370	7	:	:	PUNCT
ejpam-5856	370	8	h	h	PROPN
ejpam-5856	370	9	∈	∈	PROPN
ejpam-5856	370	10	θ	θ	PROPN
ejpam-5856	370	11	}	}	PUNCT
ejpam-5856	370	12	forms	form	VERB
ejpam-5856	370	13	an	an	DET
ejpam-5856	370	14	gft	gft	PROPN
ejpam-5856	370	15	on	on	ADP
ejpam-5856	370	16	u	u	NOUN
ejpam-5856	370	17	generated	generate	VERB
ejpam-5856	370	18	by	by	ADP
ejpam-5856	370	19	θ	θ	PROPN
ejpam-5856	370	20	.	.	PUNCT
ejpam-5856	370	21	theorem	theorem	VERB
ejpam-5856	370	22	11	11	NUM
ejpam-5856	370	23	.	.	PUNCT
ejpam-5856	371	1	(	(	PUNCT
ejpam-5856	371	2	u	u	NOUN
ejpam-5856	371	3	,	,	PUNCT
ejpam-5856	371	4	µθ	µθ	PROPN
ejpam-5856	371	5	)	)	PUNCT
ejpam-5856	371	6	is	be	AUX
ejpam-5856	371	7	fg-µr2	fg-µr2	NOUN
ejpam-5856	371	8	⇐	⇐	ADJ
ejpam-5856	371	9	⇒	⇒	NOUN
ejpam-5856	371	10	(	(	PUNCT
ejpam-5856	371	11	u	u	NOUN
ejpam-5856	371	12	,	,	PUNCT
ejpam-5856	371	13	θ	θ	PROPN
ejpam-5856	371	14	)	)	PUNCT
ejpam-5856	371	15	is	be	AUX
ejpam-5856	371	16	µ-regular	µ-regular	ADJ
ejpam-5856	371	17	.	.	PUNCT
ejpam-5856	372	1	proof	proof	NOUN
ejpam-5856	372	2	.	.	PUNCT
ejpam-5856	373	1	necessity	necessity	NOUN
ejpam-5856	373	2	.	.	PUNCT
ejpam-5856	374	1	suppose	suppose	VERB
ejpam-5856	374	2	that	that	SCONJ
ejpam-5856	374	3	(	(	PUNCT
ejpam-5856	374	4	u	u	NOUN
ejpam-5856	374	5	,	,	PUNCT
ejpam-5856	374	6	µθ	µθ	PROPN
ejpam-5856	374	7	)	)	PUNCT
ejpam-5856	374	8	is	be	AUX
ejpam-5856	374	9	fg-µr2	fg-µr2	NOUN
ejpam-5856	374	10	and	and	CCONJ
ejpam-5856	374	11	g	g	NOUN
ejpam-5856	374	12	is	be	AUX
ejpam-5856	374	13	any	any	DET
ejpam-5856	374	14	µ-closed	µ-close	VERB
ejpam-5856	374	15	set	set	VERB
ejpam-5856	374	16	in	in	ADP
ejpam-5856	374	17	(	(	PUNCT
ejpam-5856	374	18	u	u	NOUN
ejpam-5856	374	19	,	,	PUNCT
ejpam-5856	374	20	θ	θ	PROPN
ejpam-5856	374	21	)	)	PUNCT
ejpam-5856	375	1	such	such	ADJ
ejpam-5856	375	2	that	that	SCONJ
ejpam-5856	375	3	u	u	NOUN
ejpam-5856	375	4	/∈	/∈	PUNCT
ejpam-5856	376	1	g	g	NOUN
ejpam-5856	376	2	,	,	PUNCT
ejpam-5856	376	3	then	then	ADV
ejpam-5856	376	4	χg	χg	NOUN
ejpam-5856	376	5	=	=	SYM
ejpam-5856	376	6	h	h	NOUN
ejpam-5856	376	7	∈	∈	PROPN
ejpam-5856	376	8	fµc(u	fµc(u	PROPN
ejpam-5856	376	9	)	)	PUNCT
ejpam-5856	376	10	which	which	PRON
ejpam-5856	376	11	is	be	AUX
ejpam-5856	376	12	also	also	ADV
ejpam-5856	376	13	,	,	PUNCT
ejpam-5856	376	14	fgµ-closed	fgµ-closed	ADJ
ejpam-5856	376	15	set	set	NOUN
ejpam-5856	376	16	in	in	ADP
ejpam-5856	376	17	(	(	PUNCT
ejpam-5856	376	18	u	u	NOUN
ejpam-5856	376	19	,	,	PUNCT
ejpam-5856	376	20	µθ	µθ	PROPN
ejpam-5856	376	21	)	)	PUNCT
ejpam-5856	376	22	with	with	ADP
ejpam-5856	376	23	u1q̃h	u1q̃h	PROPN
ejpam-5856	376	24	.	.	PROPN
ejpam-5856	377	1	since	since	SCONJ
ejpam-5856	377	2	(	(	PUNCT
ejpam-5856	377	3	u	u	INTJ
ejpam-5856	377	4	,	,	PUNCT
ejpam-5856	377	5	µθ	µθ	PROPN
ejpam-5856	377	6	)	)	PUNCT
ejpam-5856	377	7	is	be	AUX
ejpam-5856	377	8	fg-µr2	fg-µr2	NOUN
ejpam-5856	377	9	,	,	PUNCT
ejpam-5856	377	10	there	there	PRON
ejpam-5856	377	11	are	be	VERB
ejpam-5856	377	12	ou1	ou1	NOUN
ejpam-5856	377	13	,	,	PUNCT
ejpam-5856	377	14	oh	oh	INTJ
ejpam-5856	377	15	∈	∈	PROPN
ejpam-5856	377	16	µθ	µθ	ADP
ejpam-5856	377	17	such	such	ADJ
ejpam-5856	377	18	that	that	SCONJ
ejpam-5856	377	19	ou1	ou1	PROPN
ejpam-5856	377	20	q̃oh	q̃oh	PROPN
ejpam-5856	377	21	.	.	PUNCT
ejpam-5856	378	1	thus	thus	ADV
ejpam-5856	378	2	,	,	PUNCT
ejpam-5856	378	3	there	there	PRON
ejpam-5856	378	4	are	be	VERB
ejpam-5856	378	5	ou	ou	ADP
ejpam-5856	378	6	,	,	PUNCT
ejpam-5856	378	7	og	og	PROPN
ejpam-5856	378	8	∈	∈	PROPN
ejpam-5856	378	9	θ	θ	NOUN
ejpam-5856	378	10	such	such	ADJ
ejpam-5856	378	11	that	that	DET
ejpam-5856	378	12	ou1	ou1	NOUN
ejpam-5856	378	13	=	=	X
ejpam-5856	378	14	χou	χou	NOUN
ejpam-5856	378	15	,	,	PUNCT
ejpam-5856	379	1	oh	oh	INTJ
ejpam-5856	379	2	=	=	PUNCT
ejpam-5856	379	3	χog	χog	PROPN
ejpam-5856	379	4	and	and	CCONJ
ejpam-5856	379	5	ou	ou	X
ejpam-5856	379	6	∩	∩	NOUN
ejpam-5856	379	7	og	og	X
ejpam-5856	379	8	=	=	PROPN
ejpam-5856	379	9	∅.	∅.	VERB
ejpam-5856	379	10	hence	hence	ADV
ejpam-5856	379	11	(	(	PUNCT
ejpam-5856	379	12	u	u	NOUN
ejpam-5856	379	13	,	,	PUNCT
ejpam-5856	379	14	θ	θ	PROPN
ejpam-5856	379	15	)	)	PUNCT
ejpam-5856	379	16	is	be	AUX
ejpam-5856	379	17	µ-regular	µ-regular	PROPN
ejpam-5856	379	18	.	.	PUNCT
ejpam-5856	380	1	conversely	conversely	ADV
ejpam-5856	380	2	,	,	PUNCT
ejpam-5856	380	3	let	let	VERB
ejpam-5856	380	4	(	(	PUNCT
ejpam-5856	380	5	u	u	NOUN
ejpam-5856	380	6	,	,	PUNCT
ejpam-5856	380	7	θ	θ	PROPN
ejpam-5856	380	8	)	)	PUNCT
ejpam-5856	380	9	be	be	VERB
ejpam-5856	380	10	µ-regular	µ-regular	ADJ
ejpam-5856	380	11	and	and	CCONJ
ejpam-5856	380	12	h	h	NOUN
ejpam-5856	380	13	any	any	DET
ejpam-5856	380	14	fgµ-closed	fgµ-closed	ADJ
ejpam-5856	380	15	set	set	NOUN
ejpam-5856	380	16	in	in	ADP
ejpam-5856	380	17	(	(	PUNCT
ejpam-5856	380	18	u	u	NOUN
ejpam-5856	380	19	,	,	PUNCT
ejpam-5856	380	20	µθ	µθ	PROPN
ejpam-5856	380	21	)	)	PUNCT
ejpam-5856	380	22	such	such	ADJ
ejpam-5856	380	23	that	that	SCONJ
ejpam-5856	380	24	uαq̃h	uαq̃h	NOUN
ejpam-5856	380	25	,	,	PUNCT
ejpam-5856	380	26	there	there	PRON
ejpam-5856	380	27	is	be	VERB
ejpam-5856	380	28	µ-closed	µ-close	VERB
ejpam-5856	380	29	set	set	VERB
ejpam-5856	380	30	b	b	PROPN
ejpam-5856	380	31	in	in	ADP
ejpam-5856	380	32	(	(	PUNCT
ejpam-5856	380	33	u	u	NOUN
ejpam-5856	380	34	,	,	PUNCT
ejpam-5856	380	35	θ	θ	PROPN
ejpam-5856	380	36	)	)	PUNCT
ejpam-5856	380	37	such	such	ADJ
ejpam-5856	380	38	that	that	DET
ejpam-5856	380	39	h	h	NOUN
ejpam-5856	380	40	=	=	PUNCT
ejpam-5856	380	41	χob	χob	ADJ
ejpam-5856	380	42	and	and	CCONJ
ejpam-5856	380	43	u	u	PROPN
ejpam-5856	380	44	/∈	/∈	PROPN
ejpam-5856	380	45	b.	b.	PROPN
ejpam-5856	381	1	since	since	SCONJ
ejpam-5856	381	2	(	(	PUNCT
ejpam-5856	381	3	u	u	INTJ
ejpam-5856	381	4	,	,	PUNCT
ejpam-5856	381	5	θ	θ	PROPN
ejpam-5856	381	6	)	)	PUNCT
ejpam-5856	381	7	is	be	AUX
ejpam-5856	381	8	µ-regular	µ-regular	ADJ
ejpam-5856	381	9	,	,	PUNCT
ejpam-5856	381	10	there	there	PRON
ejpam-5856	381	11	are	be	VERB
ejpam-5856	381	12	ou	ou	ADP
ejpam-5856	381	13	,	,	PUNCT
ejpam-5856	381	14	ob	ob	NOUN
ejpam-5856	381	15	∈	∈	NOUN
ejpam-5856	381	16	θ	θ	NOUN
ejpam-5856	381	17	such	such	ADJ
ejpam-5856	381	18	that	that	DET
ejpam-5856	381	19	ou∩ob	ou∩ob	NOUN
ejpam-5856	381	20	=	=	NOUN
ejpam-5856	381	21	∅	∅	NOUN
ejpam-5856	381	22	and	and	CCONJ
ejpam-5856	381	23	so	so	ADV
ejpam-5856	381	24	,	,	PUNCT
ejpam-5856	381	25	there	there	PRON
ejpam-5856	381	26	are	be	VERB
ejpam-5856	381	27	ouα	ouα	NOUN
ejpam-5856	382	1	and	and	CCONJ
ejpam-5856	382	2	oh	oh	INTJ
ejpam-5856	382	3	∈	∈	PROPN
ejpam-5856	382	4	µθ	µθ	ADP
ejpam-5856	382	5	such	such	ADJ
ejpam-5856	382	6	that	that	DET
ejpam-5856	382	7	ouα	ouα	NOUN
ejpam-5856	382	8	=	=	SYM
ejpam-5856	382	9	χou	χou	NOUN
ejpam-5856	382	10	,	,	PUNCT
ejpam-5856	383	1	oh	oh	INTJ
ejpam-5856	383	2	=	=	NOUN
ejpam-5856	383	3	χob	χob	ADJ
ejpam-5856	383	4	with	with	ADP
ejpam-5856	383	5	ouα	ouα	NOUN
ejpam-5856	383	6	q̃oh	q̃oh	PROPN
ejpam-5856	383	7	.	.	PUNCT
ejpam-5856	384	1	therefore	therefore	ADV
ejpam-5856	384	2	(	(	PUNCT
ejpam-5856	384	3	u	u	NOUN
ejpam-5856	384	4	,	,	PUNCT
ejpam-5856	384	5	µθ	µθ	PROPN
ejpam-5856	384	6	)	)	PUNCT
ejpam-5856	384	7	is	be	AUX
ejpam-5856	384	8	fg-µr2	fg-µr2	NOUN
ejpam-5856	384	9	.	.	PUNCT
ejpam-5856	385	1	theorem	theorem	PROPN
ejpam-5856	385	2	12	12	NUM
ejpam-5856	385	3	.	.	PUNCT
ejpam-5856	386	1	(	(	PUNCT
ejpam-5856	386	2	u	u	NOUN
ejpam-5856	386	3	,	,	PUNCT
ejpam-5856	386	4	µθ	µθ	PROPN
ejpam-5856	386	5	)	)	PUNCT
ejpam-5856	386	6	is	be	AUX
ejpam-5856	386	7	fg-µr3	fg-µr3	NOUN
ejpam-5856	386	8	⇐	⇐	ADJ
ejpam-5856	386	9	⇒	⇒	NOUN
ejpam-5856	386	10	(	(	PUNCT
ejpam-5856	386	11	u	u	NOUN
ejpam-5856	386	12	,	,	PUNCT
ejpam-5856	386	13	θ	θ	PROPN
ejpam-5856	386	14	)	)	PUNCT
ejpam-5856	386	15	is	be	AUX
ejpam-5856	386	16	µ-normal	µ-normal	ADJ
ejpam-5856	386	17	.	.	PUNCT
ejpam-5856	387	1	proof	proof	NOUN
ejpam-5856	387	2	.	.	PUNCT
ejpam-5856	388	1	it	it	PRON
ejpam-5856	388	2	can	can	AUX
ejpam-5856	388	3	be	be	AUX
ejpam-5856	388	4	obtained	obtain	VERB
ejpam-5856	388	5	by	by	ADP
ejpam-5856	388	6	a	a	DET
ejpam-5856	388	7	similar	similar	ADJ
ejpam-5856	388	8	way	way	NOUN
ejpam-5856	388	9	of	of	ADP
ejpam-5856	388	10	that	that	PRON
ejpam-5856	388	11	in	in	ADP
ejpam-5856	388	12	theorem	theorem	NOUN
ejpam-5856	388	13	11	11	NUM
ejpam-5856	388	14	.	.	PUNCT
ejpam-5856	389	1	definition	definition	NOUN
ejpam-5856	389	2	18	18	NUM
ejpam-5856	389	3	.	.	PUNCT
ejpam-5856	390	1	for	for	ADP
ejpam-5856	390	2	two	two	NUM
ejpam-5856	390	3	gftss	gftss	ADJ
ejpam-5856	390	4	(	(	PUNCT
ejpam-5856	390	5	u	u	NOUN
ejpam-5856	390	6	,	,	PUNCT
ejpam-5856	390	7	µ1	µ1	PROPN
ejpam-5856	390	8	)	)	PUNCT
ejpam-5856	390	9	,	,	PUNCT
ejpam-5856	390	10	(	(	PUNCT
ejpam-5856	390	11	v	v	NOUN
ejpam-5856	390	12	,	,	PUNCT
ejpam-5856	390	13	µ2	µ2	PROPN
ejpam-5856	390	14	)	)	PUNCT
ejpam-5856	390	15	.	.	PUNCT
ejpam-5856	391	1	a	a	DET
ejpam-5856	391	2	map	map	NOUN
ejpam-5856	391	3	f	f	NOUN
ejpam-5856	391	4	:(	:(	PROPN
ejpam-5856	391	5	u	u	NOUN
ejpam-5856	391	6	,	,	PUNCT
ejpam-5856	391	7	µ1)−→(v	µ1)−→(v	NOUN
ejpam-5856	391	8	,	,	PUNCT
ejpam-5856	391	9	µ2	µ2	PROPN
ejpam-5856	391	10	)	)	PUNCT
ejpam-5856	391	11	is	be	AUX
ejpam-5856	391	12	called	call	VERB
ejpam-5856	391	13	fgµc	fgµc	PROPN
ejpam-5856	391	14	-	-	PUNCT
ejpam-5856	391	15	irresolute	irresolute	ADJ
ejpam-5856	391	16	iff	iff	PROPN
ejpam-5856	391	17	f−1(g	f−1(g	PROPN
ejpam-5856	391	18	)	)	PUNCT
ejpam-5856	391	19	∈	∈	PROPN
ejpam-5856	391	20	fgµc(u	fgµc(u	PROPN
ejpam-5856	391	21	)	)	PUNCT
ejpam-5856	391	22	for	for	ADP
ejpam-5856	391	23	any	any	DET
ejpam-5856	391	24	g	g	PROPN
ejpam-5856	391	25	∈	∈	PROPN
ejpam-5856	391	26	fgµc(v	fgµc(v	PROPN
ejpam-5856	391	27	)	)	PUNCT
ejpam-5856	391	28	.	.	PUNCT
ejpam-5856	392	1	note	note	VERB
ejpam-5856	392	2	.	.	PUNCT
ejpam-5856	393	1	evidently	evidently	ADV
ejpam-5856	393	2	,	,	PUNCT
ejpam-5856	393	3	every	every	DET
ejpam-5856	393	4	fgµc	fgµc	NOUN
ejpam-5856	393	5	-	-	PUNCT
ejpam-5856	393	6	irresolute	irresolute	ADJ
ejpam-5856	393	7	map	map	NOUN
ejpam-5856	393	8	is	be	AUX
ejpam-5856	393	9	fgµ-continuous	fgµ-continuous	ADJ
ejpam-5856	393	10	.	.	PUNCT
ejpam-5856	394	1	theorem	theorem	NOUN
ejpam-5856	394	2	13	13	NUM
ejpam-5856	394	3	.	.	PUNCT
ejpam-5856	395	1	let	let	VERB
ejpam-5856	395	2	f	f	NOUN
ejpam-5856	395	3	:	:	PUNCT
ejpam-5856	395	4	(	(	PUNCT
ejpam-5856	395	5	u	u	NOUN
ejpam-5856	395	6	,	,	PUNCT
ejpam-5856	395	7	µ1)−→(v	µ1)−→(v	NOUN
ejpam-5856	395	8	,	,	PUNCT
ejpam-5856	395	9	µ2	µ2	PROPN
ejpam-5856	395	10	)	)	PUNCT
ejpam-5856	395	11	be	be	VERB
ejpam-5856	395	12	an	an	DET
ejpam-5856	395	13	fµ-open	fµ-open	ADJ
ejpam-5856	395	14	and	and	CCONJ
ejpam-5856	395	15	fgµ-continuous	fgµ-continuous	ADJ
ejpam-5856	395	16	bijection	bijection	NOUN
ejpam-5856	395	17	map	map	NOUN
ejpam-5856	395	18	.	.	PUNCT
ejpam-5856	396	1	if	if	SCONJ
ejpam-5856	396	2	h	h	NOUN
ejpam-5856	396	3	is	be	AUX
ejpam-5856	396	4	fgµ-closed	fgµ-close	VERB
ejpam-5856	396	5	set	set	VERB
ejpam-5856	396	6	in	in	ADP
ejpam-5856	396	7	(	(	PUNCT
ejpam-5856	396	8	v	v	NOUN
ejpam-5856	396	9	,	,	PUNCT
ejpam-5856	396	10	µ2	µ2	PROPN
ejpam-5856	396	11	)	)	PUNCT
ejpam-5856	396	12	,	,	PUNCT
ejpam-5856	396	13	then	then	ADV
ejpam-5856	396	14	f−1(h	f−1(h	PROPN
ejpam-5856	396	15	)	)	PUNCT
ejpam-5856	396	16	is	be	AUX
ejpam-5856	396	17	fgµ-closed	fgµ-close	VERB
ejpam-5856	396	18	set	set	VERB
ejpam-5856	396	19	in	in	ADP
ejpam-5856	396	20	(	(	PUNCT
ejpam-5856	396	21	u	u	NOUN
ejpam-5856	396	22	,	,	PUNCT
ejpam-5856	396	23	µ1	µ1	PROPN
ejpam-5856	396	24	)	)	PUNCT
ejpam-5856	396	25	.	.	PUNCT
ejpam-5856	397	1	s.	s.	PROPN
ejpam-5856	397	2	saleh	saleh	PROPN
ejpam-5856	397	3	et	et	PROPN
ejpam-5856	397	4	al	al	PROPN
ejpam-5856	397	5	.	.	PUNCT
ejpam-5856	397	6	/	/	SYM
ejpam-5856	397	7	eur	eur	PROPN
ejpam-5856	397	8	.	.	PUNCT
ejpam-5856	398	1	j.	j.	PROPN
ejpam-5856	398	2	pure	pure	PROPN
ejpam-5856	398	3	appl	appl	PROPN
ejpam-5856	398	4	.	.	PROPN
ejpam-5856	398	5	math	math	PROPN
ejpam-5856	398	6	,	,	PUNCT
ejpam-5856	398	7	18	18	NUM
ejpam-5856	398	8	(	(	PUNCT
ejpam-5856	398	9	1	1	NUM
ejpam-5856	398	10	)	)	PUNCT
ejpam-5856	398	11	(	(	PUNCT
ejpam-5856	398	12	2025	2025	NUM
ejpam-5856	398	13	)	)	PUNCT
ejpam-5856	398	14	,	,	PUNCT
ejpam-5856	398	15	5856	5856	NUM
ejpam-5856	398	16	11	11	NUM
ejpam-5856	398	17	of	of	ADP
ejpam-5856	398	18	15	15	NUM
ejpam-5856	398	19	proof	proof	NOUN
ejpam-5856	398	20	.	.	PUNCT
ejpam-5856	399	1	consider	consider	VERB
ejpam-5856	399	2	h	h	PROPN
ejpam-5856	399	3	∈	∈	PROPN
ejpam-5856	399	4	fgµc(v	fgµc(v	PROPN
ejpam-5856	399	5	)	)	PUNCT
ejpam-5856	399	6	and	and	CCONJ
ejpam-5856	399	7	f−1(h	f−1(h	PROPN
ejpam-5856	399	8	)	)	PUNCT
ejpam-5856	400	1	⊆	⊆	NUM
ejpam-5856	400	2	g	g	NOUN
ejpam-5856	400	3	where	where	SCONJ
ejpam-5856	400	4	g	g	PROPN
ejpam-5856	400	5	∈	∈	PROPN
ejpam-5856	400	6	µ1	µ1	PROPN
ejpam-5856	400	7	,	,	PUNCT
ejpam-5856	400	8	then	then	ADV
ejpam-5856	400	9	h	h	NOUN
ejpam-5856	400	10	⊆	⊆	NUM
ejpam-5856	400	11	f(g	f(g	NOUN
ejpam-5856	400	12	)	)	PUNCT
ejpam-5856	400	13	.	.	PUNCT
ejpam-5856	401	1	since	since	SCONJ
ejpam-5856	401	2	f	f	PROPN
ejpam-5856	401	3	is	be	AUX
ejpam-5856	401	4	fµ-open	fµ-open	ADJ
ejpam-5856	401	5	,	,	PUNCT
ejpam-5856	401	6	we	we	PRON
ejpam-5856	401	7	have	have	VERB
ejpam-5856	401	8	f(g	f(g	NOUN
ejpam-5856	401	9	)	)	PUNCT
ejpam-5856	401	10	∈	∈	PROPN
ejpam-5856	401	11	µ2	µ2	NOUN
ejpam-5856	401	12	.	.	PUNCT
ejpam-5856	402	1	by	by	ADP
ejpam-5856	402	2	given	give	VERB
ejpam-5856	402	3	,	,	PUNCT
ejpam-5856	402	4	h	h	NOUN
ejpam-5856	402	5	is	be	AUX
ejpam-5856	402	6	a	a	DET
ejpam-5856	402	7	fgµ-closed	fgµ-closed	ADJ
ejpam-5856	402	8	set	set	NOUN
ejpam-5856	402	9	in	in	ADP
ejpam-5856	402	10	(	(	PUNCT
ejpam-5856	402	11	v	v	NOUN
ejpam-5856	402	12	,	,	PUNCT
ejpam-5856	402	13	µ2	µ2	PROPN
ejpam-5856	402	14	)	)	PUNCT
ejpam-5856	402	15	,	,	PUNCT
ejpam-5856	402	16	then	then	ADV
ejpam-5856	402	17	clµ(h	clµ(h	NOUN
ejpam-5856	402	18	)	)	PUNCT
ejpam-5856	402	19	⊆	⊆	NUM
ejpam-5856	402	20	f(g	f(g	NOUN
ejpam-5856	402	21	)	)	PUNCT
ejpam-5856	402	22	.	.	PUNCT
ejpam-5856	403	1	so	so	ADV
ejpam-5856	403	2	that	that	DET
ejpam-5856	403	3	f−1(clµ(h	f−1(clµ(h	NOUN
ejpam-5856	403	4	)	)	PUNCT
ejpam-5856	403	5	)	)	PUNCT
ejpam-5856	404	1	⊆	⊆	NUM
ejpam-5856	404	2	g	g	NOUN
ejpam-5856	404	3	(	(	PUNCT
ejpam-5856	404	4	as	as	SCONJ
ejpam-5856	404	5	f	f	PROPN
ejpam-5856	404	6	is	be	AUX
ejpam-5856	404	7	injective	injective	ADJ
ejpam-5856	404	8	)	)	PUNCT
ejpam-5856	404	9	.	.	PUNCT
ejpam-5856	405	1	evidently	evidently	ADV
ejpam-5856	405	2	,	,	PUNCT
ejpam-5856	405	3	f	f	PROPN
ejpam-5856	405	4	is	be	AUX
ejpam-5856	405	5	fgµ-continuous	fgµ-continuous	ADJ
ejpam-5856	405	6	,	,	PUNCT
ejpam-5856	405	7	then	then	ADV
ejpam-5856	405	8	f−1(clµ(h	f−1(clµ(h	NOUN
ejpam-5856	405	9	)	)	PUNCT
ejpam-5856	405	10	)	)	PUNCT
ejpam-5856	405	11	is	be	AUX
ejpam-5856	405	12	fgµ-closed	fgµ-close	VERB
ejpam-5856	405	13	set	set	VERB
ejpam-5856	405	14	in	in	ADP
ejpam-5856	405	15	(	(	PUNCT
ejpam-5856	405	16	u	u	NOUN
ejpam-5856	405	17	,	,	PUNCT
ejpam-5856	405	18	µ1	µ1	PROPN
ejpam-5856	405	19	)	)	PUNCT
ejpam-5856	405	20	.	.	PUNCT
ejpam-5856	406	1	hence	hence	ADV
ejpam-5856	406	2	f−1(clµ(h	f−1(clµ(h	NOUN
ejpam-5856	406	3	)	)	PUNCT
ejpam-5856	406	4	)	)	PUNCT
ejpam-5856	407	1	⊆	⊆	NUM
ejpam-5856	407	2	clµ(f	clµ(f	PROPN
ejpam-5856	407	3	−1(clµ(h	−1(clµ(h	NOUN
ejpam-5856	407	4	)	)	PUNCT
ejpam-5856	407	5	)	)	PUNCT
ejpam-5856	407	6	)	)	PUNCT
ejpam-5856	408	1	=	=	SYM
ejpam-5856	408	2	f−1(clµ(h	f−1(clµ(h	NOUN
ejpam-5856	408	3	)	)	PUNCT
ejpam-5856	408	4	)	)	PUNCT
ejpam-5856	409	1	⊆	⊆	NUM
ejpam-5856	409	2	g.	g.	PROPN
ejpam-5856	409	3	therefore	therefore	ADV
ejpam-5856	409	4	,	,	PUNCT
ejpam-5856	409	5	f−1(h	f−1(h	PROPN
ejpam-5856	409	6	)	)	PUNCT
ejpam-5856	409	7	is	be	AUX
ejpam-5856	409	8	an	an	DET
ejpam-5856	409	9	fgµ-closed	fgµ-closed	ADJ
ejpam-5856	409	10	set	set	NOUN
ejpam-5856	409	11	in	in	ADP
ejpam-5856	409	12	(	(	PUNCT
ejpam-5856	409	13	u	u	NOUN
ejpam-5856	409	14	,	,	PUNCT
ejpam-5856	409	15	µ1	µ1	PROPN
ejpam-5856	409	16	)	)	PUNCT
ejpam-5856	409	17	.	.	PUNCT
ejpam-5856	410	1	corollary	corollary	ADJ
ejpam-5856	410	2	7	7	NUM
ejpam-5856	410	3	.	.	PUNCT
ejpam-5856	411	1	for	for	ADP
ejpam-5856	411	2	two	two	NUM
ejpam-5856	411	3	gftss	gftss	ADJ
ejpam-5856	411	4	(	(	PUNCT
ejpam-5856	411	5	u	u	NOUN
ejpam-5856	411	6	,	,	PUNCT
ejpam-5856	411	7	µ1	µ1	PROPN
ejpam-5856	411	8	)	)	PUNCT
ejpam-5856	411	9	,	,	PUNCT
ejpam-5856	411	10	(	(	PUNCT
ejpam-5856	411	11	v	v	NOUN
ejpam-5856	411	12	,	,	PUNCT
ejpam-5856	411	13	µ2	µ2	PROPN
ejpam-5856	411	14	)	)	PUNCT
ejpam-5856	411	15	.	.	PUNCT
ejpam-5856	412	1	if	if	SCONJ
ejpam-5856	412	2	f	f	PROPN
ejpam-5856	412	3	:	:	PUNCT
ejpam-5856	412	4	(	(	PUNCT
ejpam-5856	412	5	u	u	NOUN
ejpam-5856	412	6	,	,	PUNCT
ejpam-5856	412	7	µ1	µ1	PROPN
ejpam-5856	412	8	)	)	PUNCT
ejpam-5856	412	9	−→	−→	NOUN
ejpam-5856	412	10	(	(	PUNCT
ejpam-5856	412	11	v	v	NOUN
ejpam-5856	412	12	,	,	PUNCT
ejpam-5856	412	13	µ2	µ2	PROPN
ejpam-5856	412	14	)	)	PUNCT
ejpam-5856	412	15	is	be	AUX
ejpam-5856	412	16	an	an	DET
ejpam-5856	412	17	fµ-open	fµ-open	ADJ
ejpam-5856	412	18	and	and	CCONJ
ejpam-5856	412	19	fgµ-continuous	fgµ-continuous	ADJ
ejpam-5856	412	20	bijection	bijection	NOUN
ejpam-5856	412	21	map	map	NOUN
ejpam-5856	412	22	,	,	PUNCT
ejpam-5856	412	23	then	then	ADV
ejpam-5856	412	24	f	f	PROPN
ejpam-5856	412	25	is	be	AUX
ejpam-5856	412	26	fgµc	fgµc	NOUN
ejpam-5856	412	27	-	-	PUNCT
ejpam-5856	412	28	irresolute	irresolute	ADJ
ejpam-5856	412	29	.	.	PUNCT
ejpam-5856	413	1	theorem	theorem	NOUN
ejpam-5856	413	2	14	14	NUM
ejpam-5856	413	3	.	.	PUNCT
ejpam-5856	414	1	let	let	VERB
ejpam-5856	414	2	f	f	NOUN
ejpam-5856	414	3	:	:	PUNCT
ejpam-5856	414	4	(	(	PUNCT
ejpam-5856	414	5	u	u	NOUN
ejpam-5856	414	6	,	,	PUNCT
ejpam-5856	414	7	µ1)−→(v	µ1)−→(v	NOUN
ejpam-5856	414	8	,	,	PUNCT
ejpam-5856	414	9	µ2	µ2	PROPN
ejpam-5856	414	10	)	)	PUNCT
ejpam-5856	414	11	be	be	AUX
ejpam-5856	414	12	a	a	DET
ejpam-5856	414	13	fµ-open	fµ-open	ADJ
ejpam-5856	414	14	and	and	CCONJ
ejpam-5856	414	15	fgµ-continuous	fgµ-continuous	ADJ
ejpam-5856	414	16	bijection	bijection	NOUN
ejpam-5856	414	17	map	map	NOUN
ejpam-5856	414	18	.	.	PUNCT
ejpam-5856	415	1	if	if	SCONJ
ejpam-5856	415	2	(	(	PUNCT
ejpam-5856	415	3	u	u	NOUN
ejpam-5856	415	4	,	,	PUNCT
ejpam-5856	415	5	µ1	µ1	PROPN
ejpam-5856	415	6	)	)	PUNCT
ejpam-5856	415	7	is	be	AUX
ejpam-5856	415	8	fg-µr2	fg-µr2	NOUN
ejpam-5856	415	9	,	,	PUNCT
ejpam-5856	415	10	then	then	ADV
ejpam-5856	415	11	(	(	PUNCT
ejpam-5856	415	12	v	v	NOUN
ejpam-5856	415	13	,	,	PUNCT
ejpam-5856	415	14	µ2	µ2	PROPN
ejpam-5856	415	15	)	)	PUNCT
ejpam-5856	415	16	also	also	ADV
ejpam-5856	415	17	,	,	PUNCT
ejpam-5856	415	18	is	be	AUX
ejpam-5856	415	19	fg-µr2	fg-µr2	NOUN
ejpam-5856	415	20	.	.	PUNCT
ejpam-5856	416	1	proof	proof	NOUN
ejpam-5856	416	2	.	.	PUNCT
ejpam-5856	417	1	leth	leth	PROPN
ejpam-5856	417	2	∈	∈	PROPN
ejpam-5856	417	3	fgµc(v	fgµc(v	PROPN
ejpam-5856	417	4	)	)	PUNCT
ejpam-5856	417	5	and	and	CCONJ
ejpam-5856	417	6	vαq̃h	vαq̃h	NOUN
ejpam-5856	417	7	.	.	PUNCT
ejpam-5856	418	1	since	since	SCONJ
ejpam-5856	418	2	f	f	PROPN
ejpam-5856	418	3	is	be	AUX
ejpam-5856	418	4	fµ-open	fµ-open	ADJ
ejpam-5856	418	5	and	and	CCONJ
ejpam-5856	418	6	fgµ-continuous	fgµ-continuous	ADJ
ejpam-5856	418	7	bijective	bijective	NOUN
ejpam-5856	418	8	,	,	PUNCT
ejpam-5856	418	9	we	we	PRON
ejpam-5856	418	10	have	have	VERB
ejpam-5856	418	11	by	by	ADP
ejpam-5856	418	12	theorem	theorem	ADJ
ejpam-5856	418	13	13	13	NUM
ejpam-5856	418	14	,	,	PUNCT
ejpam-5856	418	15	f−1(h	f−1(h	PROPN
ejpam-5856	418	16	)	)	PUNCT
ejpam-5856	418	17	is	be	AUX
ejpam-5856	418	18	fgµ-closed	fgµ-close	VERB
ejpam-5856	418	19	.	.	PUNCT
ejpam-5856	419	1	put	put	VERB
ejpam-5856	419	2	f	f	PROPN
ejpam-5856	419	3	(	(	PUNCT
ejpam-5856	419	4	uα	uα	PROPN
ejpam-5856	419	5	)	)	PUNCT
ejpam-5856	419	6	=	=	SYM
ejpam-5856	420	1	vα	vα	PROPN
ejpam-5856	420	2	,	,	PUNCT
ejpam-5856	420	3	then	then	ADV
ejpam-5856	420	4	uαq̃f	uαq̃f	PROPN
ejpam-5856	420	5	−1(h	−1(h	NOUN
ejpam-5856	420	6	)	)	PUNCT
ejpam-5856	420	7	.	.	PUNCT
ejpam-5856	421	1	since	since	SCONJ
ejpam-5856	421	2	(	(	PUNCT
ejpam-5856	421	3	u	u	NOUN
ejpam-5856	421	4	,	,	PUNCT
ejpam-5856	421	5	µ1	µ1	PROPN
ejpam-5856	421	6	)	)	PUNCT
ejpam-5856	421	7	is	be	AUX
ejpam-5856	421	8	fg-µr2	fg-µr2	NOUN
ejpam-5856	421	9	,	,	PUNCT
ejpam-5856	421	10	there	there	PRON
ejpam-5856	421	11	are	be	VERB
ejpam-5856	421	12	ouα	ouα	NOUN
ejpam-5856	421	13	,	,	PUNCT
ejpam-5856	421	14	of−1(h	of−1(h	PROPN
ejpam-5856	421	15	)	)	PUNCT
ejpam-5856	421	16	∈	∈	PROPN
ejpam-5856	421	17	µ1	µ1	NOUN
ejpam-5856	421	18	such	such	ADJ
ejpam-5856	421	19	that	that	DET
ejpam-5856	421	20	ouα	ouα	NOUN
ejpam-5856	421	21	q̃of−1(h	q̃of−1(h	NOUN
ejpam-5856	421	22	)	)	PUNCT
ejpam-5856	421	23	.	.	PUNCT
ejpam-5856	422	1	since	since	SCONJ
ejpam-5856	422	2	fup	fup	PROPN
ejpam-5856	422	3	is	be	AUX
ejpam-5856	422	4	fµ-open	fµ-open	ADJ
ejpam-5856	422	5	and	and	CCONJ
ejpam-5856	422	6	bijective	bijective	ADJ
ejpam-5856	422	7	,	,	PUNCT
ejpam-5856	422	8	we	we	PRON
ejpam-5856	422	9	get	get	VERB
ejpam-5856	422	10	f(ouα	f(ouα	NOUN
ejpam-5856	422	11	)	)	PUNCT
ejpam-5856	422	12	,	,	PUNCT
ejpam-5856	422	13	f(of−1(h	f(of−1(h	PROPN
ejpam-5856	422	14	)	)	PUNCT
ejpam-5856	422	15	)	)	PUNCT
ejpam-5856	423	1	∈	∈	PROPN
ejpam-5856	423	2	µ2	µ2	NOUN
ejpam-5856	423	3	such	such	ADJ
ejpam-5856	423	4	that	that	SCONJ
ejpam-5856	423	5	vα	vα	PROPN
ejpam-5856	423	6	∈	∈	PROPN
ejpam-5856	423	7	f(ouα	f(ouα	NOUN
ejpam-5856	423	8	)	)	PUNCT
ejpam-5856	423	9	,	,	PUNCT
ejpam-5856	423	10	h	h	PROPN
ejpam-5856	423	11	⊆	⊆	NUM
ejpam-5856	423	12	f(of−1(h	f(of−1(h	PROPN
ejpam-5856	423	13	)	)	PUNCT
ejpam-5856	423	14	)	)	PUNCT
ejpam-5856	423	15	and	and	CCONJ
ejpam-5856	423	16	f(ouα)q̃f(of−1(h	f(ouα)q̃f(of−1(h	NOUN
ejpam-5856	423	17	)	)	PUNCT
ejpam-5856	423	18	)	)	PUNCT
ejpam-5856	423	19	.	.	PUNCT
ejpam-5856	424	1	therefore	therefore	ADV
ejpam-5856	424	2	,	,	PUNCT
ejpam-5856	424	3	(	(	PUNCT
ejpam-5856	424	4	v	v	NOUN
ejpam-5856	424	5	,	,	PUNCT
ejpam-5856	424	6	µ2	µ2	PROPN
ejpam-5856	424	7	)	)	PUNCT
ejpam-5856	424	8	is	be	AUX
ejpam-5856	424	9	fg-µr2	fg-µr2	NOUN
ejpam-5856	424	10	.	.	PUNCT
ejpam-5856	425	1	theorem	theorem	NOUN
ejpam-5856	425	2	15	15	NUM
ejpam-5856	425	3	.	.	PUNCT
ejpam-5856	426	1	consider	consider	VERB
ejpam-5856	426	2	f	f	NOUN
ejpam-5856	426	3	:	:	PUNCT
ejpam-5856	426	4	(	(	PUNCT
ejpam-5856	426	5	u	u	NOUN
ejpam-5856	426	6	,	,	PUNCT
ejpam-5856	426	7	µ1)−→(v	µ1)−→(v	NOUN
ejpam-5856	426	8	,	,	PUNCT
ejpam-5856	426	9	µ2	µ2	PROPN
ejpam-5856	426	10	)	)	PUNCT
ejpam-5856	426	11	is	be	AUX
ejpam-5856	426	12	fµ-open	fµ-open	ADJ
ejpam-5856	426	13	and	and	CCONJ
ejpam-5856	426	14	fgµ-continuous	fgµ-continuous	ADJ
ejpam-5856	426	15	bijection	bijection	NOUN
ejpam-5856	426	16	.	.	PUNCT
ejpam-5856	427	1	if	if	SCONJ
ejpam-5856	427	2	(	(	PUNCT
ejpam-5856	427	3	u	u	NOUN
ejpam-5856	427	4	,	,	PUNCT
ejpam-5856	427	5	µ1	µ1	PROPN
ejpam-5856	427	6	)	)	PUNCT
ejpam-5856	427	7	is	be	AUX
ejpam-5856	427	8	fg-µr3	fg-µr3	NOUN
ejpam-5856	427	9	,	,	PUNCT
ejpam-5856	427	10	then	then	ADV
ejpam-5856	427	11	(	(	PUNCT
ejpam-5856	427	12	v	v	NOUN
ejpam-5856	427	13	,	,	PUNCT
ejpam-5856	427	14	µ2	µ2	PROPN
ejpam-5856	427	15	)	)	PUNCT
ejpam-5856	427	16	also	also	ADV
ejpam-5856	427	17	,	,	PUNCT
ejpam-5856	427	18	is	be	AUX
ejpam-5856	427	19	fg-µr3	fg-µr3	NOUN
ejpam-5856	427	20	.	.	PUNCT
ejpam-5856	428	1	proof	proof	NOUN
ejpam-5856	428	2	.	.	PUNCT
ejpam-5856	429	1	it	it	PRON
ejpam-5856	429	2	can	can	AUX
ejpam-5856	429	3	be	be	AUX
ejpam-5856	429	4	obtained	obtain	VERB
ejpam-5856	429	5	by	by	ADP
ejpam-5856	429	6	a	a	DET
ejpam-5856	429	7	similar	similar	ADJ
ejpam-5856	429	8	way	way	NOUN
ejpam-5856	429	9	of	of	ADP
ejpam-5856	429	10	that	that	PRON
ejpam-5856	429	11	in	in	ADP
ejpam-5856	429	12	theorem	theorem	NOUN
ejpam-5856	429	13	14	14	NUM
ejpam-5856	429	14	.	.	PUNCT
ejpam-5856	430	1	theorem	theorem	VERB
ejpam-5856	430	2	16	16	NUM
ejpam-5856	430	3	.	.	PUNCT
ejpam-5856	431	1	for	for	ADP
ejpam-5856	431	2	an	an	DET
ejpam-5856	431	3	fµ-continuous	fµ-continuous	ADJ
ejpam-5856	431	4	and	and	CCONJ
ejpam-5856	431	5	fgµ-closed	fgµ-closed	ADJ
ejpam-5856	431	6	injective	injective	ADJ
ejpam-5856	431	7	map	map	NOUN
ejpam-5856	431	8	f	f	X
ejpam-5856	431	9	:	:	PUNCT
ejpam-5856	431	10	(	(	PUNCT
ejpam-5856	431	11	u	u	NOUN
ejpam-5856	431	12	,	,	PUNCT
ejpam-5856	431	13	µ1)−→(v	µ1)−→(v	NOUN
ejpam-5856	431	14	,	,	PUNCT
ejpam-5856	431	15	µ2	µ2	PROPN
ejpam-5856	431	16	)	)	PUNCT
ejpam-5856	431	17	.	.	PUNCT
ejpam-5856	432	1	if	if	SCONJ
ejpam-5856	432	2	(	(	PUNCT
ejpam-5856	432	3	v	v	NOUN
ejpam-5856	432	4	,	,	PUNCT
ejpam-5856	432	5	µ2	µ2	PROPN
ejpam-5856	432	6	)	)	PUNCT
ejpam-5856	432	7	is	be	AUX
ejpam-5856	432	8	fg-µr2	fg-µr2	NOUN
ejpam-5856	432	9	,	,	PUNCT
ejpam-5856	432	10	then	then	ADV
ejpam-5856	432	11	(	(	PUNCT
ejpam-5856	432	12	u	u	NOUN
ejpam-5856	432	13	,	,	PUNCT
ejpam-5856	432	14	µ1	µ1	PROPN
ejpam-5856	432	15	)	)	PUNCT
ejpam-5856	432	16	also	also	ADV
ejpam-5856	432	17	,	,	PUNCT
ejpam-5856	432	18	is	be	AUX
ejpam-5856	432	19	fg-µr2	fg-µr2	NOUN
ejpam-5856	432	20	.	.	PUNCT
ejpam-5856	433	1	proof	proof	NOUN
ejpam-5856	433	2	.	.	PUNCT
ejpam-5856	434	1	let	let	VERB
ejpam-5856	434	2	h	h	PROPN
ejpam-5856	434	3	∈	∈	PROPN
ejpam-5856	434	4	fgµc(u	fgµc(u	PROPN
ejpam-5856	434	5	)	)	PUNCT
ejpam-5856	434	6	with	with	ADP
ejpam-5856	434	7	uαq̃h	uαq̃h	PROPN
ejpam-5856	434	8	.	.	PUNCT
ejpam-5856	434	9	by	by	ADP
ejpam-5856	434	10	fµ-continuity	fµ-continuity	NOUN
ejpam-5856	434	11	and	and	CCONJ
ejpam-5856	434	12	fgµ-closedness	fgµ-closedness	NOUN
ejpam-5856	434	13	,	,	PUNCT
ejpam-5856	434	14	we	we	PRON
ejpam-5856	434	15	have	have	VERB
ejpam-5856	434	16	f(h	f(h	PROPN
ejpam-5856	434	17	)	)	PUNCT
ejpam-5856	434	18	∈	∈	PROPN
ejpam-5856	434	19	fgµc(v	fgµc(v	PROPN
ejpam-5856	434	20	)	)	PUNCT
ejpam-5856	434	21	.	.	PUNCT
ejpam-5856	435	1	in	in	ADP
ejpam-5856	435	2	fact	fact	NOUN
ejpam-5856	435	3	,	,	PUNCT
ejpam-5856	435	4	if	if	SCONJ
ejpam-5856	435	5	f(h	f(h	PROPN
ejpam-5856	435	6	)	)	PUNCT
ejpam-5856	435	7	⊆	⊆	NUM
ejpam-5856	435	8	g	g	NOUN
ejpam-5856	435	9	and	and	CCONJ
ejpam-5856	435	10	g	g	PROPN
ejpam-5856	435	11	∈	∈	PROPN
ejpam-5856	435	12	µ2	µ2	PROPN
ejpam-5856	435	13	,	,	PUNCT
ejpam-5856	435	14	then	then	ADV
ejpam-5856	435	15	h	h	PROPN
ejpam-5856	435	16	⊆	⊆	NUM
ejpam-5856	435	17	f−1(g	f−1(g	PROPN
ejpam-5856	435	18	)	)	PUNCT
ejpam-5856	435	19	and	and	CCONJ
ejpam-5856	435	20	so	so	ADV
ejpam-5856	435	21	,	,	PUNCT
ejpam-5856	435	22	clµ(h	clµ(h	PROPN
ejpam-5856	435	23	)	)	PUNCT
ejpam-5856	435	24	⊆	⊆	NUM
ejpam-5856	435	25	f−1(g	f−1(g	PROPN
ejpam-5856	435	26	)	)	PUNCT
ejpam-5856	435	27	implies	imply	VERB
ejpam-5856	435	28	that	that	SCONJ
ejpam-5856	435	29	f(h	f(h	PROPN
ejpam-5856	435	30	)	)	PUNCT
ejpam-5856	435	31	⊆	⊆	NUM
ejpam-5856	435	32	f(clµ(h	f(clµ(h	NOUN
ejpam-5856	435	33	)	)	PUNCT
ejpam-5856	435	34	)	)	PUNCT
ejpam-5856	435	35	⊆	⊆	NUM
ejpam-5856	435	36	ff−1(g	ff−1(g	NOUN
ejpam-5856	435	37	)	)	PUNCT
ejpam-5856	435	38	⊆	⊆	NUM
ejpam-5856	435	39	g	g	NOUN
ejpam-5856	435	40	that	that	PRON
ejpam-5856	435	41	is	be	AUX
ejpam-5856	435	42	,	,	PUNCT
ejpam-5856	435	43	f(h	f(h	PROPN
ejpam-5856	435	44	)	)	PUNCT
ejpam-5856	435	45	⊆	⊆	NUM
ejpam-5856	435	46	g.	g.	NOUN
ejpam-5856	435	47	hence	hence	ADV
ejpam-5856	435	48	f(h	f(h	PROPN
ejpam-5856	435	49	)	)	PUNCT
ejpam-5856	435	50	is	be	AUX
ejpam-5856	435	51	fgµ-closed	fgµ-close	VERB
ejpam-5856	435	52	.	.	PUNCT
ejpam-5856	436	1	since	since	SCONJ
ejpam-5856	436	2	f	f	PROPN
ejpam-5856	436	3	is	be	AUX
ejpam-5856	436	4	injective	injective	ADJ
ejpam-5856	436	5	,	,	PUNCT
ejpam-5856	436	6	we	we	PRON
ejpam-5856	436	7	have	have	VERB
ejpam-5856	436	8	f	f	PROPN
ejpam-5856	436	9	(	(	PUNCT
ejpam-5856	436	10	uα	uα	PROPN
ejpam-5856	436	11	)	)	PUNCT
ejpam-5856	436	12	q̃f(h	q̃f(h	NOUN
ejpam-5856	436	13	)	)	PUNCT
ejpam-5856	436	14	.	.	PUNCT
ejpam-5856	437	1	given	give	VERB
ejpam-5856	437	2	that	that	SCONJ
ejpam-5856	437	3	(	(	PUNCT
ejpam-5856	437	4	v	v	NOUN
ejpam-5856	437	5	,	,	PUNCT
ejpam-5856	437	6	µ2	µ2	PROPN
ejpam-5856	437	7	)	)	PUNCT
ejpam-5856	437	8	is	be	AUX
ejpam-5856	437	9	fg-µr2	fg-µr2	NOUN
ejpam-5856	437	10	,	,	PUNCT
ejpam-5856	437	11	there	there	PRON
ejpam-5856	437	12	areof(uα	areof(uα	VERB
ejpam-5856	437	13	)	)	PUNCT
ejpam-5856	437	14	,	,	PUNCT
ejpam-5856	437	15	of(h	of(h	ADJ
ejpam-5856	437	16	)	)	PUNCT
ejpam-5856	438	1	∈	∈	PROPN
ejpam-5856	438	2	µ2	µ2	VERB
ejpam-5856	438	3	such	such	ADJ
ejpam-5856	438	4	thatof(uα)q̃of(h	thatof(uα)q̃of(h	PROPN
ejpam-5856	438	5	)	)	PUNCT
ejpam-5856	438	6	.	.	PUNCT
ejpam-5856	439	1	since	since	SCONJ
ejpam-5856	439	2	f	f	PROPN
ejpam-5856	439	3	is	be	AUX
ejpam-5856	439	4	fµ-continuous	fµ-continuous	ADJ
ejpam-5856	439	5	,	,	PUNCT
ejpam-5856	439	6	we	we	PRON
ejpam-5856	439	7	have	have	VERB
ejpam-5856	439	8	f−1(of(uα	f−1(of(uα	NOUN
ejpam-5856	439	9	)	)	PUNCT
ejpam-5856	439	10	)	)	PUNCT
ejpam-5856	439	11	,	,	PUNCT
ejpam-5856	439	12	f	f	PROPN
ejpam-5856	439	13	−1(of(h	−1(of(h	PROPN
ejpam-5856	439	14	)	)	PUNCT
ejpam-5856	439	15	)	)	PUNCT
ejpam-5856	440	1	∈	∈	PROPN
ejpam-5856	440	2	µ1	µ1	VERB
ejpam-5856	440	3	such	such	ADJ
ejpam-5856	440	4	that	that	SCONJ
ejpam-5856	440	5	uα	uα	PROPN
ejpam-5856	440	6	∈	∈	PROPN
ejpam-5856	440	7	f−1(of(uα	f−1(of(uα	PROPN
ejpam-5856	440	8	)	)	PUNCT
ejpam-5856	440	9	)	)	PUNCT
ejpam-5856	440	10	,	,	PUNCT
ejpam-5856	440	11	h	h	NOUN
ejpam-5856	440	12	⊆	⊆	NUM
ejpam-5856	440	13	f−1(of(h	f−1(of(h	NOUN
ejpam-5856	440	14	)	)	PUNCT
ejpam-5856	440	15	)	)	PUNCT
ejpam-5856	440	16	,	,	PUNCT
ejpam-5856	440	17	and	and	CCONJ
ejpam-5856	440	18	f−1(of(uα))q̃f	f−1(of(uα))q̃f	NOUN
ejpam-5856	440	19	−1(of(h	−1(of(h	PROPN
ejpam-5856	440	20	)	)	PUNCT
ejpam-5856	440	21	)	)	PUNCT
ejpam-5856	440	22	.	.	PUNCT
ejpam-5856	441	1	therefore	therefore	ADV
ejpam-5856	441	2	,	,	PUNCT
ejpam-5856	441	3	(	(	PUNCT
ejpam-5856	441	4	u	u	NOUN
ejpam-5856	441	5	,	,	PUNCT
ejpam-5856	441	6	µ1	µ1	PROPN
ejpam-5856	441	7	)	)	PUNCT
ejpam-5856	441	8	is	be	AUX
ejpam-5856	441	9	fg-µr2	fg-µr2	NOUN
ejpam-5856	441	10	.	.	PUNCT
ejpam-5856	442	1	theorem	theorem	NOUN
ejpam-5856	442	2	17	17	NUM
ejpam-5856	442	3	.	.	PUNCT
ejpam-5856	443	1	let	let	VERB
ejpam-5856	443	2	f	f	NOUN
ejpam-5856	443	3	:	:	PUNCT
ejpam-5856	443	4	(	(	PUNCT
ejpam-5856	443	5	u	u	NOUN
ejpam-5856	443	6	,	,	PUNCT
ejpam-5856	443	7	µ1)−→(v	µ1)−→(v	NOUN
ejpam-5856	443	8	,	,	PUNCT
ejpam-5856	443	9	µ2	µ2	PROPN
ejpam-5856	443	10	)	)	PUNCT
ejpam-5856	443	11	be	be	AUX
ejpam-5856	443	12	fµ-continuous	fµ-continuous	ADJ
ejpam-5856	443	13	,	,	PUNCT
ejpam-5856	443	14	fgµ-closed	fgµ-closed	ADJ
ejpam-5856	443	15	injective	injective	NOUN
ejpam-5856	443	16	.	.	PUNCT
ejpam-5856	444	1	if	if	SCONJ
ejpam-5856	444	2	(	(	PUNCT
ejpam-5856	444	3	v	v	NOUN
ejpam-5856	444	4	,	,	PUNCT
ejpam-5856	444	5	µ2	µ2	PROPN
ejpam-5856	444	6	)	)	PUNCT
ejpam-5856	444	7	is	be	AUX
ejpam-5856	444	8	fg-µr3	fg-µr3	NOUN
ejpam-5856	444	9	,	,	PUNCT
ejpam-5856	444	10	then	then	ADV
ejpam-5856	444	11	(	(	PUNCT
ejpam-5856	444	12	u	u	NOUN
ejpam-5856	444	13	,	,	PUNCT
ejpam-5856	444	14	µ1	µ1	PROPN
ejpam-5856	444	15	)	)	PUNCT
ejpam-5856	444	16	is	be	AUX
ejpam-5856	444	17	fg-µr3	fg-µr3	NOUN
ejpam-5856	444	18	.	.	PUNCT
ejpam-5856	445	1	proof	proof	NOUN
ejpam-5856	445	2	.	.	PUNCT
ejpam-5856	446	1	suppose	suppose	VERB
ejpam-5856	446	2	thath	thath	PROPN
ejpam-5856	446	3	,	,	PUNCT
ejpam-5856	446	4	g	g	PROPN
ejpam-5856	446	5	∈	∈	PROPN
ejpam-5856	446	6	fgµc(u	fgµc(u	NOUN
ejpam-5856	446	7	)	)	PUNCT
ejpam-5856	446	8	)	)	PUNCT
ejpam-5856	446	9	withhq̃g	withhq̃g	X
ejpam-5856	446	10	.	.	PUNCT
ejpam-5856	447	1	as	as	ADP
ejpam-5856	447	2	in	in	ADP
ejpam-5856	447	3	the	the	DET
ejpam-5856	447	4	above	above	ADJ
ejpam-5856	447	5	theorem	theorem	ADJ
ejpam-5856	447	6	f	f	PROPN
ejpam-5856	447	7	(	(	PUNCT
ejpam-5856	447	8	h	h	NOUN
ejpam-5856	447	9	)	)	PUNCT
ejpam-5856	447	10	,	,	PUNCT
ejpam-5856	447	11	f(g	f(g	NOUN
ejpam-5856	447	12	)	)	PUNCT
ejpam-5856	447	13	∈	∈	PROPN
ejpam-5856	447	14	fgµc	fgµc	NOUN
ejpam-5856	447	15	(	(	PUNCT
ejpam-5856	447	16	v	v	NOUN
ejpam-5856	447	17	)	)	PUNCT
ejpam-5856	447	18	.	.	PUNCT
ejpam-5856	448	1	since	since	SCONJ
ejpam-5856	448	2	fup	fup	PROPN
ejpam-5856	448	3	is	be	AUX
ejpam-5856	448	4	injective	injective	ADJ
ejpam-5856	448	5	,	,	PUNCT
ejpam-5856	448	6	then	then	ADV
ejpam-5856	448	7	f(h)q̃f	f(h)q̃f	NOUN
ejpam-5856	448	8	(	(	PUNCT
ejpam-5856	448	9	g	g	NOUN
ejpam-5856	448	10	)	)	PUNCT
ejpam-5856	448	11	.	.	PUNCT
ejpam-5856	449	1	by	by	ADP
ejpam-5856	449	2	given	give	VERB
ejpam-5856	449	3	(	(	PUNCT
ejpam-5856	449	4	v	v	NOUN
ejpam-5856	449	5	,	,	PUNCT
ejpam-5856	449	6	µ2	µ2	PROPN
ejpam-5856	449	7	)	)	PUNCT
ejpam-5856	449	8	is	be	AUX
ejpam-5856	449	9	fg-µr3	fg-µr3	NOUN
ejpam-5856	449	10	,	,	PUNCT
ejpam-5856	449	11	there	there	PRON
ejpam-5856	449	12	are	be	VERB
ejpam-5856	449	13	of(h	of(h	ADJ
ejpam-5856	449	14	)	)	PUNCT
ejpam-5856	449	15	,	,	PUNCT
ejpam-5856	449	16	of(g	of(g	NUM
ejpam-5856	449	17	)	)	PUNCT
ejpam-5856	449	18	∈	∈	PROPN
ejpam-5856	449	19	µ2	µ2	PROPN
ejpam-5856	449	20	withof(h)q̃of(g	withof(h)q̃of(g	PROPN
ejpam-5856	449	21	)	)	PUNCT
ejpam-5856	449	22	.	.	PUNCT
ejpam-5856	450	1	since	since	SCONJ
ejpam-5856	450	2	f	f	PROPN
ejpam-5856	450	3	is	be	AUX
ejpam-5856	450	4	fµ-continuous	fµ-continuous	ADJ
ejpam-5856	450	5	,	,	PUNCT
ejpam-5856	450	6	we	we	PRON
ejpam-5856	450	7	have	have	VERB
ejpam-5856	450	8	f−1(of(h	f−1(of(h	NOUN
ejpam-5856	450	9	)	)	PUNCT
ejpam-5856	450	10	)	)	PUNCT
ejpam-5856	450	11	,	,	PUNCT
ejpam-5856	450	12	f	f	PROPN
ejpam-5856	450	13	−1(of(g	−1(of(g	PROPN
ejpam-5856	450	14	)	)	PUNCT
ejpam-5856	450	15	)	)	PUNCT
ejpam-5856	451	1	∈	∈	PROPN
ejpam-5856	451	2	µ1	µ1	NOUN
ejpam-5856	451	3	andh	andh	NOUN
ejpam-5856	451	4	⊆	⊆	NUM
ejpam-5856	451	5	f−1(of(h	f−1(of(h	NOUN
ejpam-5856	451	6	)	)	PUNCT
ejpam-5856	451	7	)	)	PUNCT
ejpam-5856	451	8	,	,	PUNCT
ejpam-5856	451	9	g	g	ADP
ejpam-5856	451	10	⊆	⊆	NUM
ejpam-5856	451	11	f−1(of(g	f−1(of(g	NOUN
ejpam-5856	451	12	)	)	PUNCT
ejpam-5856	451	13	)	)	PUNCT
ejpam-5856	451	14	with	with	ADP
ejpam-5856	451	15	f−1(of(h))q̃f	f−1(of(h))q̃f	PROPN
ejpam-5856	451	16	−1(of(g	−1(of(g	PROPN
ejpam-5856	451	17	)	)	PUNCT
ejpam-5856	451	18	)	)	PUNCT
ejpam-5856	451	19	.	.	PUNCT
ejpam-5856	452	1	therefore	therefore	ADV
ejpam-5856	452	2	,	,	PUNCT
ejpam-5856	452	3	(	(	PUNCT
ejpam-5856	452	4	u	u	NOUN
ejpam-5856	452	5	,	,	PUNCT
ejpam-5856	452	6	µ1	µ1	PROPN
ejpam-5856	452	7	)	)	PUNCT
ejpam-5856	452	8	is	be	AUX
ejpam-5856	452	9	fg-µr2	fg-µr2	NOUN
ejpam-5856	452	10	.	.	PUNCT
ejpam-5856	453	1	theorem	theorem	NOUN
ejpam-5856	453	2	18	18	NUM
ejpam-5856	453	3	.	.	PUNCT
ejpam-5856	454	1	let	let	VERB
ejpam-5856	454	2	f	f	NOUN
ejpam-5856	454	3	:	:	PUNCT
ejpam-5856	454	4	(	(	PUNCT
ejpam-5856	454	5	u	u	NOUN
ejpam-5856	454	6	,	,	PUNCT
ejpam-5856	454	7	µ1)−→(v	µ1)−→(v	NOUN
ejpam-5856	454	8	,	,	PUNCT
ejpam-5856	454	9	µ2	µ2	PROPN
ejpam-5856	454	10	)	)	PUNCT
ejpam-5856	454	11	be	be	AUX
ejpam-5856	454	12	fgµc	fgµc	NOUN
ejpam-5856	454	13	-	-	PUNCT
ejpam-5856	454	14	irresolute	irresolute	ADJ
ejpam-5856	454	15	and	and	CCONJ
ejpam-5856	454	16	fµ-open	fµ-open	ADJ
ejpam-5856	454	17	surjective	surjective	NOUN
ejpam-5856	454	18	.	.	PUNCT
ejpam-5856	455	1	if	if	SCONJ
ejpam-5856	455	2	(	(	PUNCT
ejpam-5856	455	3	u	u	NOUN
ejpam-5856	455	4	,	,	PUNCT
ejpam-5856	455	5	µ1	µ1	PROPN
ejpam-5856	455	6	)	)	PUNCT
ejpam-5856	455	7	is	be	AUX
ejpam-5856	455	8	fg-µr3	fg-µr3	NOUN
ejpam-5856	455	9	,	,	PUNCT
ejpam-5856	455	10	then	then	ADV
ejpam-5856	455	11	(	(	PUNCT
ejpam-5856	455	12	v	v	NOUN
ejpam-5856	455	13	,	,	PUNCT
ejpam-5856	455	14	µ2	µ2	PROPN
ejpam-5856	455	15	)	)	PUNCT
ejpam-5856	455	16	is	be	AUX
ejpam-5856	455	17	fg-µr3	fg-µr3	NOUN
ejpam-5856	455	18	.	.	PUNCT
ejpam-5856	456	1	s.	s.	PROPN
ejpam-5856	456	2	saleh	saleh	PROPN
ejpam-5856	456	3	et	et	PROPN
ejpam-5856	456	4	al	al	PROPN
ejpam-5856	456	5	.	.	PUNCT
ejpam-5856	456	6	/	/	SYM
ejpam-5856	456	7	eur	eur	PROPN
ejpam-5856	456	8	.	.	PUNCT
ejpam-5856	457	1	j.	j.	PROPN
ejpam-5856	457	2	pure	pure	PROPN
ejpam-5856	457	3	appl	appl	PROPN
ejpam-5856	457	4	.	.	PROPN
ejpam-5856	457	5	math	math	PROPN
ejpam-5856	457	6	,	,	PUNCT
ejpam-5856	457	7	18	18	NUM
ejpam-5856	457	8	(	(	PUNCT
ejpam-5856	457	9	1	1	NUM
ejpam-5856	457	10	)	)	PUNCT
ejpam-5856	457	11	(	(	PUNCT
ejpam-5856	457	12	2025	2025	NUM
ejpam-5856	457	13	)	)	PUNCT
ejpam-5856	457	14	,	,	PUNCT
ejpam-5856	457	15	5856	5856	NUM
ejpam-5856	457	16	12	12	NUM
ejpam-5856	457	17	of	of	ADP
ejpam-5856	457	18	15	15	NUM
ejpam-5856	457	19	proof	proof	NOUN
ejpam-5856	457	20	.	.	PUNCT
ejpam-5856	458	1	letg	letg	PROPN
ejpam-5856	458	2	,	,	PUNCT
ejpam-5856	458	3	h	h	PROPN
ejpam-5856	458	4	∈	∈	PROPN
ejpam-5856	458	5	fgµc(v	fgµc(v	PROPN
ejpam-5856	458	6	)	)	PUNCT
ejpam-5856	458	7	such	such	ADJ
ejpam-5856	458	8	thatgq̃h	thatgq̃h	PROPN
ejpam-5856	458	9	,	,	PUNCT
ejpam-5856	458	10	then	then	ADV
ejpam-5856	458	11	f−1	f−1	PROPN
ejpam-5856	458	12	(	(	PUNCT
ejpam-5856	458	13	g	g	NOUN
ejpam-5856	458	14	)	)	PUNCT
ejpam-5856	458	15	,	,	PUNCT
ejpam-5856	458	16	f−1(h	f−1(h	PROPN
ejpam-5856	458	17	)	)	PUNCT
ejpam-5856	458	18	are	be	AUX
ejpam-5856	458	19	fgµ-closed	fgµ-closed	ADJ
ejpam-5856	458	20	sets	set	NOUN
ejpam-5856	458	21	in	in	ADP
ejpam-5856	458	22	(	(	PUNCT
ejpam-5856	458	23	u	u	NOUN
ejpam-5856	458	24	,	,	PUNCT
ejpam-5856	458	25	µ1	µ1	PROPN
ejpam-5856	458	26	)	)	PUNCT
ejpam-5856	458	27	with	with	ADP
ejpam-5856	458	28	f−1	f−1	PROPN
ejpam-5856	458	29	(	(	PUNCT
ejpam-5856	458	30	g	g	NOUN
ejpam-5856	458	31	)	)	PUNCT
ejpam-5856	458	32	q̃f−1(h	q̃f−1(h	PROPN
ejpam-5856	458	33	)	)	PUNCT
ejpam-5856	458	34	.	.	PUNCT
ejpam-5856	459	1	since	since	SCONJ
ejpam-5856	459	2	(	(	PUNCT
ejpam-5856	459	3	u	u	NOUN
ejpam-5856	459	4	,	,	PUNCT
ejpam-5856	459	5	µ1	µ1	PROPN
ejpam-5856	459	6	)	)	PUNCT
ejpam-5856	459	7	is	be	AUX
ejpam-5856	459	8	fg-µr3	fg-µr3	NOUN
ejpam-5856	459	9	,	,	PUNCT
ejpam-5856	459	10	there	there	PRON
ejpam-5856	459	11	are	be	VERB
ejpam-5856	459	12	of−1(g	of−1(g	NOUN
ejpam-5856	459	13	)	)	PUNCT
ejpam-5856	459	14	,	,	PUNCT
ejpam-5856	459	15	of−1(h	of−1(h	PROPN
ejpam-5856	459	16	)	)	PUNCT
ejpam-5856	459	17	∈	∈	PROPN
ejpam-5856	459	18	µ1	µ1	NOUN
ejpam-5856	459	19	containing	contain	VERB
ejpam-5856	459	20	f−1	f−1	PROPN
ejpam-5856	459	21	(	(	PUNCT
ejpam-5856	459	22	g	g	NOUN
ejpam-5856	459	23	)	)	PUNCT
ejpam-5856	459	24	,	,	PUNCT
ejpam-5856	459	25	f−1	f−1	PROPN
ejpam-5856	459	26	(	(	PUNCT
ejpam-5856	459	27	h	h	NOUN
ejpam-5856	459	28	)	)	PUNCT
ejpam-5856	459	29	,	,	PUNCT
ejpam-5856	459	30	respectively	respectively	ADV
ejpam-5856	459	31	with	with	ADP
ejpam-5856	459	32	of−1(g)q̃of−1(h	of−1(g)q̃of−1(h	NOUN
ejpam-5856	459	33	)	)	PUNCT
ejpam-5856	459	34	.	.	PUNCT
ejpam-5856	460	1	since	since	SCONJ
ejpam-5856	460	2	f	f	PROPN
ejpam-5856	460	3	is	be	AUX
ejpam-5856	460	4	surjective	surjective	ADJ
ejpam-5856	460	5	,	,	PUNCT
ejpam-5856	460	6	we	we	PRON
ejpam-5856	460	7	have	have	VERB
ejpam-5856	460	8	g	g	PROPN
ejpam-5856	460	9	⊆	⊆	NUM
ejpam-5856	460	10	f(of−1(g	f(of−1(g	PROPN
ejpam-5856	460	11	)	)	PUNCT
ejpam-5856	460	12	)	)	PUNCT
ejpam-5856	460	13	,	,	PUNCT
ejpam-5856	460	14	h	h	PROPN
ejpam-5856	460	15	⊆	⊆	NUM
ejpam-5856	460	16	f(of−1(h	f(of−1(h	PROPN
ejpam-5856	460	17	)	)	PUNCT
ejpam-5856	460	18	)	)	PUNCT
ejpam-5856	460	19	and	and	CCONJ
ejpam-5856	460	20	f(of−1(g	f(of−1(g	PROPN
ejpam-5856	460	21	)	)	PUNCT
ejpam-5856	460	22	)	)	PUNCT
ejpam-5856	460	23	,	,	PUNCT
ejpam-5856	460	24	f(of−1(h	f(of−1(h	PROPN
ejpam-5856	460	25	)	)	PUNCT
ejpam-5856	460	26	)	)	PUNCT
ejpam-5856	461	1	∈	∈	PROPN
ejpam-5856	462	1	µ2(as	µ2(as	PROPN
ejpam-5856	462	2	f	f	PROPN
ejpam-5856	462	3	is	be	AUX
ejpam-5856	462	4	fµ-open	fµ-open	ADJ
ejpam-5856	462	5	)	)	PUNCT
ejpam-5856	462	6	with	with	ADP
ejpam-5856	462	7	(	(	PUNCT
ejpam-5856	462	8	of−1(g))q̃f(of−1(h	of−1(g))q̃f(of−1(h	PROPN
ejpam-5856	462	9	)	)	PUNCT
ejpam-5856	462	10	)	)	PUNCT
ejpam-5856	462	11	.	.	PUNCT
ejpam-5856	463	1	hence	hence	ADV
ejpam-5856	463	2	(	(	PUNCT
ejpam-5856	463	3	v	v	NOUN
ejpam-5856	463	4	,	,	PUNCT
ejpam-5856	463	5	µ2	µ2	PROPN
ejpam-5856	463	6	)	)	PUNCT
ejpam-5856	463	7	is	be	AUX
ejpam-5856	463	8	fg-µr3	fg-µr3	NOUN
ejpam-5856	463	9	.	.	PUNCT
ejpam-5856	464	1	from	from	ADP
ejpam-5856	464	2	theorems	theorem	NOUN
ejpam-5856	464	3	14	14	NUM
ejpam-5856	464	4	and	and	CCONJ
ejpam-5856	464	5	15	15	NUM
ejpam-5856	464	6	,	,	PUNCT
ejpam-5856	464	7	one	one	PRON
ejpam-5856	464	8	can	can	AUX
ejpam-5856	464	9	verify	verify	VERB
ejpam-5856	464	10	the	the	DET
ejpam-5856	464	11	next	next	ADJ
ejpam-5856	464	12	theorem	theorem	PROPN
ejpam-5856	464	13	.	.	PUNCT
ejpam-5856	464	14	theorem	theorem	PROPN
ejpam-5856	464	15	19	19	NUM
ejpam-5856	464	16	.	.	PUNCT
ejpam-5856	465	1	the	the	DET
ejpam-5856	465	2	property	property	NOUN
ejpam-5856	465	3	of	of	ADP
ejpam-5856	465	4	being	be	AUX
ejpam-5856	465	5	fg-µr2	fg-µr2	NOUN
ejpam-5856	465	6	(	(	PUNCT
ejpam-5856	465	7	fg-µr3	fg-µr3	NOUN
ejpam-5856	465	8	)	)	PUNCT
ejpam-5856	465	9	is	be	AUX
ejpam-5856	465	10	a	a	DET
ejpam-5856	465	11	fgµ-topological	fgµ-topological	ADJ
ejpam-5856	465	12	property	property	NOUN
ejpam-5856	465	13	.	.	PUNCT
ejpam-5856	466	1	in	in	ADP
ejpam-5856	466	2	the	the	DET
ejpam-5856	466	3	following	following	NOUN
ejpam-5856	466	4	,	,	PUNCT
ejpam-5856	466	5	we	we	PRON
ejpam-5856	466	6	show	show	VERB
ejpam-5856	466	7	that	that	SCONJ
ejpam-5856	466	8	the	the	DET
ejpam-5856	466	9	being	be	AUX
ejpam-5856	466	10	fg-µr2	fg-µr2	NOUN
ejpam-5856	466	11	(	(	PUNCT
ejpam-5856	466	12	fg-µr3	fg-µr3	NOUN
ejpam-5856	466	13	)	)	PUNCT
ejpam-5856	466	14	are	be	AUX
ejpam-5856	466	15	hereditary	hereditary	ADJ
ejpam-5856	466	16	property	property	NOUN
ejpam-5856	466	17	.	.	PUNCT
ejpam-5856	467	1	theorem	theorem	ADJ
ejpam-5856	467	2	20	20	NUM
ejpam-5856	467	3	.	.	PUNCT
ejpam-5856	468	1	every	every	DET
ejpam-5856	468	2	fµ-subspace	fµ-subspace	NOUN
ejpam-5856	468	3	(	(	PUNCT
ejpam-5856	468	4	v	v	NOUN
ejpam-5856	468	5	,	,	PUNCT
ejpam-5856	468	6	µv	µv	NOUN
ejpam-5856	468	7	)	)	PUNCT
ejpam-5856	468	8	of	of	ADP
ejpam-5856	468	9	fg-µr2	fg-µr2	NOUN
ejpam-5856	468	10	is	be	AUX
ejpam-5856	468	11	fg-µr2	fg-µr2	NOUN
ejpam-5856	468	12	.	.	PUNCT
ejpam-5856	469	1	proof	proof	NOUN
ejpam-5856	469	2	.	.	PUNCT
ejpam-5856	470	1	let	let	VERB
ejpam-5856	470	2	(	(	PUNCT
ejpam-5856	470	3	u	u	NOUN
ejpam-5856	470	4	,	,	PUNCT
ejpam-5856	470	5	µ	µ	NOUN
ejpam-5856	470	6	)	)	PUNCT
ejpam-5856	470	7	be	be	VERB
ejpam-5856	470	8	fg-µr2	fg-µr2	NOUN
ejpam-5856	470	9	,	,	PUNCT
ejpam-5856	470	10	uα	uα	PROPN
ejpam-5856	470	11	∈	∈	PROPN
ejpam-5856	470	12	fp	fp	X
ejpam-5856	470	13	(	(	PUNCT
ejpam-5856	470	14	v	v	NOUN
ejpam-5856	470	15	)	)	PUNCT
ejpam-5856	470	16	and	and	CCONJ
ejpam-5856	470	17	h	h	NOUN
ejpam-5856	470	18	∈	∈	PROPN
ejpam-5856	470	19	fgµc(v	fgµc(v	PROPN
ejpam-5856	470	20	)	)	PUNCT
ejpam-5856	470	21	with	with	ADP
ejpam-5856	470	22	uαq̃h	uαq̃h	PROPN
ejpam-5856	470	23	,	,	PUNCT
ejpam-5856	470	24	there	there	PRON
ejpam-5856	470	25	is	be	VERB
ejpam-5856	470	26	an	an	DET
ejpam-5856	470	27	fgµ-closed	fgµ-closed	ADJ
ejpam-5856	470	28	set	set	NOUN
ejpam-5856	470	29	g	g	NOUN
ejpam-5856	470	30	in	in	ADP
ejpam-5856	470	31	(	(	PUNCT
ejpam-5856	470	32	u	u	NOUN
ejpam-5856	470	33	,	,	PUNCT
ejpam-5856	470	34	µ	µ	NOUN
ejpam-5856	470	35	)	)	PUNCT
ejpam-5856	470	36	such	such	ADJ
ejpam-5856	470	37	that	that	SCONJ
ejpam-5856	470	38	h	h	NOUN
ejpam-5856	471	1	=	=	NOUN
ejpam-5856	471	2	χv	χv	ADP
ejpam-5856	471	3	∩g	∩g	NOUN
ejpam-5856	471	4	and	and	CCONJ
ejpam-5856	471	5	uαq̃g	uαq̃g	PROPN
ejpam-5856	471	6	.	.	PUNCT
ejpam-5856	472	1	since	since	SCONJ
ejpam-5856	472	2	(	(	PUNCT
ejpam-5856	472	3	u	u	INTJ
ejpam-5856	472	4	,	,	PUNCT
ejpam-5856	472	5	µ	µ	NOUN
ejpam-5856	472	6	)	)	PUNCT
ejpam-5856	472	7	is	be	AUX
ejpam-5856	472	8	fg-µr2	fg-µr2	NOUN
ejpam-5856	472	9	,	,	PUNCT
ejpam-5856	472	10	we	we	PRON
ejpam-5856	472	11	have	have	VERB
ejpam-5856	472	12	ouα	ouα	NOUN
ejpam-5856	472	13	,	,	PUNCT
ejpam-5856	472	14	og	og	PROPN
ejpam-5856	472	15	∈	∈	PROPN
ejpam-5856	472	16	µ	µ	PRON
ejpam-5856	472	17	such	such	ADJ
ejpam-5856	472	18	that	that	DET
ejpam-5856	472	19	ouα	ouα	NOUN
ejpam-5856	472	20	q̃og	q̃og	PROPN
ejpam-5856	472	21	.	.	PROPN
ejpam-5856	473	1	put	put	VERB
ejpam-5856	473	2	o	o	NOUN
ejpam-5856	473	3	∗	∗	NOUN
ejpam-5856	473	4	uα	uα	NOUN
ejpam-5856	474	1	=	=	PUNCT
ejpam-5856	474	2	χv	χv	ADP
ejpam-5856	474	3	∩ouα	∩ouα	PROPN
ejpam-5856	474	4	∈	∈	PROPN
ejpam-5856	474	5	µv	µv	NOUN
ejpam-5856	474	6	and	and	CCONJ
ejpam-5856	474	7	o∗	o∗	PROPN
ejpam-5856	474	8	g	g	PROPN
ejpam-5856	474	9	=	=	PUNCT
ejpam-5856	474	10	χv	χv	ADP
ejpam-5856	474	11	∩og	∩og	NOUN
ejpam-5856	474	12	∈	∈	PROPN
ejpam-5856	474	13	µv	µv	PRON
ejpam-5856	474	14	which	which	PRON
ejpam-5856	474	15	are	be	AUX
ejpam-5856	474	16	containing	contain	VERB
ejpam-5856	474	17	uα	uα	PRON
ejpam-5856	474	18	and	and	CCONJ
ejpam-5856	474	19	g	g	NOUN
ejpam-5856	474	20	respectively	respectively	ADV
ejpam-5856	474	21	,	,	PUNCT
ejpam-5856	474	22	and	and	CCONJ
ejpam-5856	474	23	o∗	o∗	PROPN
ejpam-5856	474	24	uα	uα	PROPN
ejpam-5856	474	25	q̃o∗	q̃o∗	ADJ
ejpam-5856	474	26	g.	g.	PROPN
ejpam-5856	475	1	this	this	PRON
ejpam-5856	475	2	completes	complete	VERB
ejpam-5856	475	3	the	the	DET
ejpam-5856	475	4	proof	proof	NOUN
ejpam-5856	475	5	.	.	PUNCT
ejpam-5856	476	1	theorem	theorem	NOUN
ejpam-5856	476	2	21	21	NUM
ejpam-5856	476	3	.	.	PUNCT
ejpam-5856	477	1	every	every	DET
ejpam-5856	477	2	fµ-closed	fµ-close	VERB
ejpam-5856	477	3	subspace	subspace	NOUN
ejpam-5856	477	4	(	(	PUNCT
ejpam-5856	477	5	v	v	NOUN
ejpam-5856	477	6	,	,	PUNCT
ejpam-5856	477	7	µv	µv	PROPN
ejpam-5856	477	8	)	)	PUNCT
ejpam-5856	477	9	of	of	ADP
ejpam-5856	477	10	fg-µr3	fg-µr3	PROPN
ejpam-5856	477	11	is	be	AUX
ejpam-5856	477	12	fg-µr3	fg-µr3	NOUN
ejpam-5856	477	13	.	.	PUNCT
ejpam-5856	478	1	proof	proof	NOUN
ejpam-5856	478	2	.	.	PUNCT
ejpam-5856	479	1	it	it	PRON
ejpam-5856	479	2	follows	follow	VERB
ejpam-5856	479	3	by	by	ADP
ejpam-5856	479	4	a	a	DET
ejpam-5856	479	5	similar	similar	ADJ
ejpam-5856	479	6	way	way	NOUN
ejpam-5856	479	7	of	of	ADP
ejpam-5856	479	8	that	that	PRON
ejpam-5856	479	9	in	in	ADP
ejpam-5856	479	10	theorem	theorem	NOUN
ejpam-5856	479	11	20	20	NUM
ejpam-5856	479	12	.	.	NOUN
ejpam-5856	480	1	6	6	NUM
ejpam-5856	480	2	.	.	X
ejpam-5856	480	3	conclusion	conclusion	NOUN
ejpam-5856	480	4	and	and	CCONJ
ejpam-5856	480	5	future	future	ADJ
ejpam-5856	480	6	work	work	NOUN
ejpam-5856	480	7	topology	topology	NOUN
ejpam-5856	480	8	is	be	AUX
ejpam-5856	480	9	a	a	DET
ejpam-5856	480	10	branch	branch	NOUN
ejpam-5856	480	11	of	of	ADP
ejpam-5856	480	12	mathematics	mathematic	NOUN
ejpam-5856	480	13	that	that	PRON
ejpam-5856	480	14	studies	study	VERB
ejpam-5856	480	15	the	the	DET
ejpam-5856	480	16	properties	property	NOUN
ejpam-5856	480	17	of	of	ADP
ejpam-5856	480	18	space	space	NOUN
ejpam-5856	480	19	preserved	preserve	VERB
ejpam-5856	480	20	under	under	ADP
ejpam-5856	480	21	continuous	continuous	ADJ
ejpam-5856	480	22	transformations	transformation	NOUN
ejpam-5856	480	23	.	.	PUNCT
ejpam-5856	481	1	it	it	PRON
ejpam-5856	481	2	allows	allow	VERB
ejpam-5856	481	3	mathematicians	mathematician	NOUN
ejpam-5856	481	4	to	to	PART
ejpam-5856	481	5	analyze	analyze	VERB
ejpam-5856	481	6	and	and	CCONJ
ejpam-5856	481	7	classify	classify	VERB
ejpam-5856	481	8	spaces	space	NOUN
ejpam-5856	481	9	,	,	PUNCT
ejpam-5856	481	10	leading	lead	VERB
ejpam-5856	481	11	to	to	ADP
ejpam-5856	481	12	applications	application	NOUN
ejpam-5856	481	13	in	in	ADP
ejpam-5856	481	14	various	various	ADJ
ejpam-5856	481	15	fields	field	NOUN
ejpam-5856	481	16	,	,	PUNCT
ejpam-5856	481	17	where	where	SCONJ
ejpam-5856	481	18	understanding	understand	VERB
ejpam-5856	481	19	the	the	DET
ejpam-5856	481	20	fundamental	fundamental	ADJ
ejpam-5856	481	21	structure	structure	NOUN
ejpam-5856	481	22	of	of	ADP
ejpam-5856	481	23	spaces	space	NOUN
ejpam-5856	481	24	is	be	AUX
ejpam-5856	481	25	of	of	ADP
ejpam-5856	481	26	great	great	ADJ
ejpam-5856	481	27	importance	importance	NOUN
ejpam-5856	481	28	.	.	PUNCT
ejpam-5856	482	1	this	this	DET
ejpam-5856	482	2	study	study	NOUN
ejpam-5856	482	3	focuses	focus	VERB
ejpam-5856	482	4	on	on	ADP
ejpam-5856	482	5	the	the	DET
ejpam-5856	482	6	applications	application	NOUN
ejpam-5856	482	7	of	of	ADP
ejpam-5856	482	8	fgµ-closed	fgµ-closed	ADJ
ejpam-5856	482	9	sets	set	NOUN
ejpam-5856	482	10	in	in	ADP
ejpam-5856	482	11	generalized	generalized	ADJ
ejpam-5856	482	12	fuzzy	fuzzy	ADJ
ejpam-5856	482	13	topology	topology	NOUN
ejpam-5856	482	14	.	.	PUNCT
ejpam-5856	483	1	some	some	DET
ejpam-5856	483	2	classes	class	NOUN
ejpam-5856	483	3	,	,	PUNCT
ejpam-5856	483	4	namely	namely	ADV
ejpam-5856	483	5	fgµ-regular	fgµ-regular	ADJ
ejpam-5856	483	6	,	,	PUNCT
ejpam-5856	483	7	fgµ-normal	fgµ-normal	ADJ
ejpam-5856	483	8	,	,	PUNCT
ejpam-5856	483	9	fµ-symmetric	fµ-symmetric	ADJ
ejpam-5856	483	10	,	,	PUNCT
ejpam-5856	483	11	have	have	AUX
ejpam-5856	483	12	been	be	AUX
ejpam-5856	483	13	introduced	introduce	VERB
ejpam-5856	483	14	and	and	CCONJ
ejpam-5856	483	15	analyzed	analyze	VERB
ejpam-5856	483	16	.	.	PUNCT
ejpam-5856	484	1	the	the	DET
ejpam-5856	484	2	paper	paper	NOUN
ejpam-5856	484	3	thoroughly	thoroughly	ADV
ejpam-5856	484	4	have	have	AUX
ejpam-5856	484	5	investigated	investigate	VERB
ejpam-5856	484	6	the	the	DET
ejpam-5856	484	7	fundamental	fundamental	ADJ
ejpam-5856	484	8	properties	property	NOUN
ejpam-5856	484	9	and	and	CCONJ
ejpam-5856	484	10	unique	unique	ADJ
ejpam-5856	484	11	characteristics	characteristic	NOUN
ejpam-5856	484	12	of	of	ADP
ejpam-5856	484	13	these	these	DET
ejpam-5856	484	14	classes	class	NOUN
ejpam-5856	484	15	.	.	PUNCT
ejpam-5856	485	1	a	a	DET
ejpam-5856	485	2	comprehensive	comprehensive	ADJ
ejpam-5856	485	3	is	be	AUX
ejpam-5856	485	4	framework	framework	NOUN
ejpam-5856	485	5	has	have	AUX
ejpam-5856	485	6	been	be	AUX
ejpam-5856	485	7	established	establish	VERB
ejpam-5856	485	8	through	through	ADP
ejpam-5856	485	9	the	the	DET
ejpam-5856	485	10	presentation	presentation	NOUN
ejpam-5856	485	11	of	of	ADP
ejpam-5856	485	12	related	related	ADJ
ejpam-5856	485	13	theorems	theorem	NOUN
ejpam-5856	485	14	and	and	CCONJ
ejpam-5856	485	15	relations	relation	NOUN
ejpam-5856	485	16	,	,	PUNCT
ejpam-5856	485	17	demonstrating	demonstrate	VERB
ejpam-5856	485	18	their	their	PRON
ejpam-5856	485	19	interrelationships	interrelationship	NOUN
ejpam-5856	485	20	with	with	ADP
ejpam-5856	485	21	other	other	ADJ
ejpam-5856	485	22	separation	separation	NOUN
ejpam-5856	485	23	axioms	axiom	NOUN
ejpam-5856	485	24	in	in	ADP
ejpam-5856	485	25	this	this	DET
ejpam-5856	485	26	context	context	NOUN
ejpam-5856	485	27	.	.	PUNCT
ejpam-5856	486	1	additionally	additionally	ADV
ejpam-5856	486	2	,	,	PUNCT
ejpam-5856	486	3	the	the	DET
ejpam-5856	486	4	hereditary	hereditary	ADJ
ejpam-5856	486	5	and	and	CCONJ
ejpam-5856	486	6	topological	topological	ADJ
ejpam-5856	486	7	properties	property	NOUN
ejpam-5856	486	8	of	of	ADP
ejpam-5856	486	9	these	these	DET
ejpam-5856	486	10	classes	class	NOUN
ejpam-5856	486	11	have	have	AUX
ejpam-5856	486	12	been	be	AUX
ejpam-5856	486	13	explored	explore	VERB
ejpam-5856	486	14	.	.	PUNCT
ejpam-5856	487	1	the	the	DET
ejpam-5856	487	2	present	present	ADJ
ejpam-5856	487	3	results	result	NOUN
ejpam-5856	487	4	in	in	ADP
ejpam-5856	487	5	this	this	DET
ejpam-5856	487	6	article	article	NOUN
ejpam-5856	487	7	are	be	AUX
ejpam-5856	487	8	very	very	ADV
ejpam-5856	487	9	useful	useful	ADJ
ejpam-5856	487	10	and	and	CCONJ
ejpam-5856	487	11	contribute	contribute	VERB
ejpam-5856	487	12	to	to	ADP
ejpam-5856	487	13	the	the	DET
ejpam-5856	487	14	development	development	NOUN
ejpam-5856	487	15	of	of	ADP
ejpam-5856	487	16	the	the	DET
ejpam-5856	487	17	theoretical	theoretical	ADJ
ejpam-5856	487	18	and	and	CCONJ
ejpam-5856	487	19	practical	practical	ADJ
ejpam-5856	487	20	foundations	foundation	NOUN
ejpam-5856	487	21	of	of	ADP
ejpam-5856	487	22	the	the	DET
ejpam-5856	487	23	gft	gft	PROPN
ejpam-5856	487	24	,	,	PUNCT
ejpam-5856	487	25	and	and	CCONJ
ejpam-5856	487	26	will	will	AUX
ejpam-5856	487	27	open	open	VERB
ejpam-5856	487	28	up	up	ADP
ejpam-5856	487	29	the	the	DET
ejpam-5856	487	30	door	door	NOUN
ejpam-5856	487	31	for	for	ADP
ejpam-5856	487	32	future	future	ADJ
ejpam-5856	487	33	works	work	NOUN
ejpam-5856	487	34	in	in	ADP
ejpam-5856	487	35	this	this	DET
ejpam-5856	487	36	area	area	NOUN
ejpam-5856	487	37	such	such	ADJ
ejpam-5856	487	38	as	as	ADP
ejpam-5856	487	39	:	:	PUNCT
ejpam-5856	487	40	•	•	NOUN
ejpam-5856	487	41	we	we	PRON
ejpam-5856	487	42	plan	plan	VERB
ejpam-5856	487	43	to	to	PART
ejpam-5856	487	44	further	far	ADV
ejpam-5856	487	45	study	study	VERB
ejpam-5856	487	46	for	for	ADP
ejpam-5856	487	47	fgµ-closed	fgµ-closed	ADJ
ejpam-5856	487	48	sets	set	NOUN
ejpam-5856	487	49	with	with	ADP
ejpam-5856	487	50	some	some	DET
ejpam-5856	487	51	separation	separation	NOUN
ejpam-5856	487	52	axioms	axiom	NOUN
ejpam-5856	487	53	in	in	ADP
ejpam-5856	487	54	this	this	DET
ejpam-5856	487	55	settings	setting	NOUN
ejpam-5856	487	56	.	.	PUNCT
ejpam-5856	488	1	•	•	INTJ
ejpam-5856	488	2	we	we	PRON
ejpam-5856	488	3	intend	intend	VERB
ejpam-5856	488	4	to	to	PART
ejpam-5856	488	5	discuss	discuss	VERB
ejpam-5856	488	6	some	some	DET
ejpam-5856	488	7	weaker	weak	ADJ
ejpam-5856	488	8	forms	form	NOUN
ejpam-5856	488	9	of	of	ADP
ejpam-5856	488	10	fgµ-closed	fgµ-closed	ADJ
ejpam-5856	488	11	sets	set	NOUN
ejpam-5856	488	12	with	with	ADP
ejpam-5856	488	13	some	some	DET
ejpam-5856	488	14	applications	application	NOUN
ejpam-5856	488	15	of	of	ADP
ejpam-5856	488	16	them	they	PRON
ejpam-5856	488	17	in	in	ADP
ejpam-5856	488	18	fgt	fgt	PROPN
ejpam-5856	488	19	-spaces	-space	NOUN
ejpam-5856	488	20	.	.	PUNCT
ejpam-5856	489	1	s.	s.	PROPN
ejpam-5856	489	2	saleh	saleh	PROPN
ejpam-5856	489	3	et	et	PROPN
ejpam-5856	489	4	al	al	PROPN
ejpam-5856	489	5	.	.	PUNCT
ejpam-5856	489	6	/	/	SYM
ejpam-5856	489	7	eur	eur	PROPN
ejpam-5856	489	8	.	.	PUNCT
ejpam-5856	490	1	j.	j.	PROPN
ejpam-5856	490	2	pure	pure	PROPN
ejpam-5856	490	3	appl	appl	PROPN
ejpam-5856	490	4	.	.	PROPN
ejpam-5856	490	5	math	math	PROPN
ejpam-5856	490	6	,	,	PUNCT
ejpam-5856	490	7	18	18	NUM
ejpam-5856	490	8	(	(	PUNCT
ejpam-5856	490	9	1	1	NUM
ejpam-5856	490	10	)	)	PUNCT
ejpam-5856	490	11	(	(	PUNCT
ejpam-5856	490	12	2025	2025	NUM
ejpam-5856	490	13	)	)	PUNCT
ejpam-5856	490	14	,	,	PUNCT
ejpam-5856	490	15	5856	5856	NUM
ejpam-5856	490	16	13	13	NUM
ejpam-5856	490	17	of	of	ADP
ejpam-5856	490	18	15	15	NUM
ejpam-5856	490	19	•	•	NOUN
ejpam-5856	490	20	we	we	PRON
ejpam-5856	490	21	plan	plan	VERB
ejpam-5856	490	22	to	to	PART
ejpam-5856	490	23	extend	extend	VERB
ejpam-5856	490	24	the	the	DET
ejpam-5856	490	25	characterizations	characterization	NOUN
ejpam-5856	490	26	of	of	ADP
ejpam-5856	490	27	these	these	DET
ejpam-5856	490	28	classes	class	NOUN
ejpam-5856	490	29	within	within	ADP
ejpam-5856	490	30	infra	infra	NOUN
ejpam-5856	490	31	soft	soft	ADJ
ejpam-5856	490	32	topological	topological	ADJ
ejpam-5856	490	33	spaces	space	NOUN
ejpam-5856	491	1	[	[	X
ejpam-5856	491	2	3	3	NUM
ejpam-5856	491	3	,	,	PUNCT
ejpam-5856	491	4	4	4	NUM
ejpam-5856	491	5	]	]	PUNCT
ejpam-5856	491	6	,	,	PUNCT
ejpam-5856	491	7	and	and	CCONJ
ejpam-5856	491	8	explore	explore	VERB
ejpam-5856	491	9	their	their	PRON
ejpam-5856	491	10	potential	potential	ADJ
ejpam-5856	491	11	applications	application	NOUN
ejpam-5856	491	12	.	.	PUNCT
ejpam-5856	492	1	•	•	PUNCT
ejpam-5856	492	2	exploring	explore	VERB
ejpam-5856	492	3	the	the	DET
ejpam-5856	492	4	proposed	propose	VERB
ejpam-5856	492	5	concepts	concept	NOUN
ejpam-5856	492	6	through	through	ADP
ejpam-5856	492	7	well	well	ADV
ejpam-5856	492	8	-	-	PUNCT
ejpam-5856	492	9	known	know	VERB
ejpam-5856	492	10	topological	topological	ADJ
ejpam-5856	492	11	structures	structure	NOUN
ejpam-5856	493	1	[	[	X
ejpam-5856	493	2	5	5	NUM
ejpam-5856	493	3	,	,	PUNCT
ejpam-5856	493	4	6	6	NUM
ejpam-5856	493	5	]	]	PUNCT
ejpam-5856	493	6	is	be	AUX
ejpam-5856	493	7	an	an	DET
ejpam-5856	493	8	interesting	interesting	ADJ
ejpam-5856	493	9	idea	idea	NOUN
ejpam-5856	493	10	for	for	ADP
ejpam-5856	493	11	researchers	researcher	NOUN
ejpam-5856	493	12	and	and	CCONJ
ejpam-5856	493	13	scholars	scholar	NOUN
ejpam-5856	493	14	interested	interested	ADJ
ejpam-5856	493	15	in	in	ADP
ejpam-5856	493	16	topological	topological	ADJ
ejpam-5856	493	17	studies	study	NOUN
ejpam-5856	493	18	,	,	PUNCT
ejpam-5856	493	19	which	which	PRON
ejpam-5856	493	20	we	we	PRON
ejpam-5856	493	21	have	have	AUX
ejpam-5856	493	22	left	leave	VERB
ejpam-5856	493	23	for	for	ADP
ejpam-5856	493	24	future	future	ADJ
ejpam-5856	493	25	investigations	investigation	NOUN
ejpam-5856	493	26	.	.	PUNCT
ejpam-5856	494	1	acknowledgments	acknowledgment	NOUN
ejpam-5856	494	2	the	the	DET
ejpam-5856	494	3	authors	author	NOUN
ejpam-5856	494	4	extend	extend	VERB
ejpam-5856	494	5	their	their	PRON
ejpam-5856	494	6	appreciation	appreciation	NOUN
ejpam-5856	494	7	to	to	ADP
ejpam-5856	494	8	the	the	DET
ejpam-5856	494	9	deanship	deanship	NOUN
ejpam-5856	494	10	of	of	ADP
ejpam-5856	494	11	scientific	scientific	ADJ
ejpam-5856	494	12	research	research	NOUN
ejpam-5856	494	13	at	at	ADP
ejpam-5856	494	14	northern	northern	ADJ
ejpam-5856	494	15	border	border	NOUN
ejpam-5856	494	16	university	university	PROPN
ejpam-5856	494	17	,	,	PUNCT
ejpam-5856	494	18	arar	arar	PROPN
ejpam-5856	494	19	,	,	PUNCT
ejpam-5856	494	20	ksa	ksa	PROPN
ejpam-5856	494	21	for	for	ADP
ejpam-5856	494	22	funding	fund	VERB
ejpam-5856	494	23	this	this	DET
ejpam-5856	494	24	research	research	NOUN
ejpam-5856	494	25	work	work	NOUN
ejpam-5856	494	26	through	through	ADP
ejpam-5856	494	27	the	the	DET
ejpam-5856	494	28	project	project	NOUN
ejpam-5856	494	29	number	number	NOUN
ejpam-5856	494	30	“	"	PUNCT
ejpam-5856	494	31	nbu	nbu	NOUN
ejpam-5856	494	32	-	-	PUNCT
ejpam-5856	494	33	ffr-2025	ffr-2025	NOUN
ejpam-5856	494	34	-	-	PUNCT
ejpam-5856	494	35	1166	1166	NUM
ejpam-5856	494	36	-	-	PUNCT
ejpam-5856	494	37	02	02	NUM
ejpam-5856	494	38	”	"	PUNCT
ejpam-5856	494	39	conflict	conflict	NOUN
ejpam-5856	494	40	of	of	ADP
ejpam-5856	494	41	interest	interest	NOUN
ejpam-5856	494	42	the	the	DET
ejpam-5856	494	43	authors	author	NOUN
ejpam-5856	494	44	declare	declare	VERB
ejpam-5856	494	45	that	that	SCONJ
ejpam-5856	494	46	there	there	PRON
ejpam-5856	494	47	is	be	VERB
ejpam-5856	494	48	no	no	DET
ejpam-5856	494	49	conflict	conflict	NOUN
ejpam-5856	494	50	of	of	ADP
ejpam-5856	494	51	interest	interest	NOUN
ejpam-5856	494	52	regarding	regard	VERB
ejpam-5856	494	53	the	the	DET
ejpam-5856	494	54	publication	publication	NOUN
ejpam-5856	494	55	of	of	ADP
ejpam-5856	494	56	this	this	DET
ejpam-5856	494	57	paper	paper	NOUN
ejpam-5856	494	58	.	.	PUNCT
ejpam-5856	495	1	references	reference	NOUN
ejpam-5856	495	2	[	[	X
ejpam-5856	495	3	1	1	NUM
ejpam-5856	495	4	]	]	X
ejpam-5856	495	5	n.	n.	PROPN
ejpam-5856	495	6	ahmed	ahmed	PROPN
ejpam-5856	495	7	and	and	CCONJ
ejpam-5856	495	8	p.	p.	PROPN
ejpam-5856	495	9	kumar	kumar	PROPN
ejpam-5856	495	10	.	.	PUNCT
ejpam-5856	496	1	fuzzy	fuzzy	ADJ
ejpam-5856	496	2	logic	logic	NOUN
ejpam-5856	496	3	in	in	ADP
ejpam-5856	496	4	image	image	NOUN
ejpam-5856	496	5	processing	processing	NOUN
ejpam-5856	496	6	:	:	PUNCT
ejpam-5856	496	7	a	a	DET
ejpam-5856	496	8	survey	survey	NOUN
ejpam-5856	496	9	of	of	ADP
ejpam-5856	496	10	methods	method	NOUN
ejpam-5856	496	11	and	and	CCONJ
ejpam-5856	496	12	applications	application	NOUN
ejpam-5856	496	13	.	.	PUNCT
ejpam-5856	497	1	image	image	NOUN
ejpam-5856	497	2	and	and	CCONJ
ejpam-5856	497	3	vision	vision	NOUN
ejpam-5856	497	4	computing	computing	NOUN
ejpam-5856	497	5	,	,	PUNCT
ejpam-5856	497	6	100:100–120	100:100–120	NUM
ejpam-5856	497	7	,	,	PUNCT
ejpam-5856	497	8	2022	2022	NUM
ejpam-5856	497	9	.	.	PUNCT
ejpam-5856	498	1	[	[	X
ejpam-5856	498	2	2	2	X
ejpam-5856	498	3	]	]	PUNCT
ejpam-5856	498	4	t.	t.	PROPN
ejpam-5856	498	5	m.	m.	PROPN
ejpam-5856	498	6	al	al	PROPN
ejpam-5856	498	7	-	-	PUNCT
ejpam-5856	498	8	shami	shami	PROPN
ejpam-5856	498	9	.	.	PUNCT
ejpam-5856	499	1	investigation	investigation	NOUN
ejpam-5856	499	2	and	and	CCONJ
ejpam-5856	499	3	corrigendum	corrigendum	VERB
ejpam-5856	499	4	to	to	ADP
ejpam-5856	499	5	some	some	DET
ejpam-5856	499	6	results	result	NOUN
ejpam-5856	499	7	related	relate	VERB
ejpam-5856	499	8	to	to	ADP
ejpam-5856	499	9	g	g	NOUN
ejpam-5856	499	10	-	-	PUNCT
ejpam-5856	499	11	soft	soft	ADJ
ejpam-5856	499	12	equality	equality	NOUN
ejpam-5856	499	13	and	and	CCONJ
ejpam-5856	499	14	gf	gf	NOUN
ejpam-5856	499	15	-soft	-soft	PROPN
ejpam-5856	499	16	equality	equality	NOUN
ejpam-5856	499	17	relations	relation	NOUN
ejpam-5856	499	18	.	.	PUNCT
ejpam-5856	500	1	filomat	filomat	PROPN
ejpam-5856	500	2	,	,	PUNCT
ejpam-5856	500	3	33(11):3375–3383	33(11):3375–3383	NUM
ejpam-5856	500	4	,	,	PUNCT
ejpam-5856	500	5	2019	2019	NUM
ejpam-5856	500	6	.	.	PUNCT
ejpam-5856	501	1	[	[	X
ejpam-5856	501	2	3	3	X
ejpam-5856	501	3	]	]	PUNCT
ejpam-5856	501	4	t.	t.	PROPN
ejpam-5856	501	5	m.	m.	PROPN
ejpam-5856	501	6	al	al	PROPN
ejpam-5856	501	7	-	-	PUNCT
ejpam-5856	501	8	shami	shami	PROPN
ejpam-5856	501	9	.	.	PUNCT
ejpam-5856	502	1	infra	infra	NOUN
ejpam-5856	502	2	soft	soft	ADJ
ejpam-5856	502	3	compact	compact	ADJ
ejpam-5856	502	4	spaces	space	NOUN
ejpam-5856	502	5	and	and	CCONJ
ejpam-5856	502	6	application	application	NOUN
ejpam-5856	502	7	to	to	ADP
ejpam-5856	502	8	fixed	fix	VERB
ejpam-5856	502	9	point	point	NOUN
ejpam-5856	502	10	theorem	theorem	VERB
ejpam-5856	502	11	.	.	PROPN
ejpam-5856	502	12	journal	journal	PROPN
ejpam-5856	502	13	of	of	ADP
ejpam-5856	502	14	function	function	NOUN
ejpam-5856	502	15	spaces	space	NOUN
ejpam-5856	502	16	,	,	PUNCT
ejpam-5856	502	17	2021:9	2021:9	NUM
ejpam-5856	502	18	pages	page	NOUN
ejpam-5856	502	19	,	,	PUNCT
ejpam-5856	502	20	2021	2021	NUM
ejpam-5856	502	21	.	.	PUNCT
ejpam-5856	503	1	[	[	X
ejpam-5856	503	2	4	4	X
ejpam-5856	503	3	]	]	PUNCT
ejpam-5856	503	4	t.	t.	PROPN
ejpam-5856	503	5	m.	m.	PROPN
ejpam-5856	503	6	al	al	PROPN
ejpam-5856	503	7	-	-	PUNCT
ejpam-5856	503	8	shami	shami	PROPN
ejpam-5856	503	9	.	.	PUNCT
ejpam-5856	504	1	new	new	ADJ
ejpam-5856	504	2	soft	soft	ADJ
ejpam-5856	504	3	structure	structure	NOUN
ejpam-5856	504	4	:	:	PUNCT
ejpam-5856	504	5	infra	infra	NOUN
ejpam-5856	504	6	soft	soft	ADJ
ejpam-5856	504	7	topological	topological	ADJ
ejpam-5856	504	8	spaces	space	NOUN
ejpam-5856	504	9	.	.	PUNCT
ejpam-5856	505	1	mathematical	mathematical	ADJ
ejpam-5856	505	2	problems	problem	NOUN
ejpam-5856	505	3	in	in	ADP
ejpam-5856	505	4	engineering	engineering	NOUN
ejpam-5856	505	5	,	,	PUNCT
ejpam-5856	505	6	2021:12	2021:12	NUM
ejpam-5856	505	7	pages	page	NOUN
ejpam-5856	505	8	,	,	PUNCT
ejpam-5856	505	9	2021	2021	NUM
ejpam-5856	505	10	.	.	PUNCT
ejpam-5856	506	1	[	[	X
ejpam-5856	506	2	5	5	X
ejpam-5856	506	3	]	]	PUNCT
ejpam-5856	506	4	t.	t.	PROPN
ejpam-5856	506	5	m.	m.	PROPN
ejpam-5856	506	6	al	al	PROPN
ejpam-5856	506	7	-	-	PUNCT
ejpam-5856	506	8	shami	shami	PROPN
ejpam-5856	506	9	and	and	CCONJ
ejpam-5856	506	10	m.	m.	PROPN
ejpam-5856	506	11	e.	e.	PROPN
ejpam-5856	506	12	el	el	PROPN
ejpam-5856	506	13	-	-	PROPN
ejpam-5856	506	14	shafei	shafei	PROPN
ejpam-5856	506	15	.	.	PUNCT
ejpam-5856	507	1	on	on	ADP
ejpam-5856	507	2	supra	supra	PROPN
ejpam-5856	507	3	soft	soft	ADJ
ejpam-5856	507	4	topological	topological	ADJ
ejpam-5856	507	5	ordered	order	VERB
ejpam-5856	507	6	spaces	space	NOUN
ejpam-5856	507	7	.	.	PUNCT
ejpam-5856	508	1	arab	arab	PROPN
ejpam-5856	508	2	journal	journal	PROPN
ejpam-5856	508	3	of	of	ADP
ejpam-5856	508	4	basic	basic	ADJ
ejpam-5856	508	5	and	and	CCONJ
ejpam-5856	508	6	applied	applied	ADJ
ejpam-5856	508	7	sciences	science	NOUN
ejpam-5856	508	8	,	,	PUNCT
ejpam-5856	508	9	26(1):433–445	26(1):433–445	NOUN
ejpam-5856	508	10	,	,	PUNCT
ejpam-5856	508	11	2019	2019	NUM
ejpam-5856	508	12	.	.	PUNCT
ejpam-5856	509	1	[	[	X
ejpam-5856	509	2	6	6	NUM
ejpam-5856	509	3	]	]	PUNCT
ejpam-5856	509	4	t.	t.	PROPN
ejpam-5856	509	5	m.	m.	PROPN
ejpam-5856	509	6	al	al	PROPN
ejpam-5856	509	7	-	-	PUNCT
ejpam-5856	509	8	shami	shami	PROPN
ejpam-5856	509	9	and	and	CCONJ
ejpam-5856	509	10	m.	m.	PROPN
ejpam-5856	509	11	e.	e.	PROPN
ejpam-5856	509	12	el	el	PROPN
ejpam-5856	509	13	-	-	PROPN
ejpam-5856	509	14	shafei	shafei	PROPN
ejpam-5856	509	15	.	.	PUNCT
ejpam-5856	510	1	two	two	NUM
ejpam-5856	510	2	types	type	NOUN
ejpam-5856	510	3	of	of	ADP
ejpam-5856	510	4	separation	separation	NOUN
ejpam-5856	510	5	axioms	axiom	NOUN
ejpam-5856	510	6	on	on	ADP
ejpam-5856	510	7	supra	supra	ADJ
ejpam-5856	510	8	soft	soft	ADJ
ejpam-5856	510	9	separation	separation	NOUN
ejpam-5856	510	10	spaces	space	NOUN
ejpam-5856	510	11	.	.	PUNCT
ejpam-5856	511	1	demonstratio	demonstratio	PROPN
ejpam-5856	511	2	mathematica	mathematica	PROPN
ejpam-5856	511	3	,	,	PUNCT
ejpam-5856	511	4	52(1):147–165	52(1):147–165	PROPN
ejpam-5856	511	5	,	,	PUNCT
ejpam-5856	511	6	2019	2019	NUM
ejpam-5856	511	7	.	.	PUNCT
ejpam-5856	512	1	[	[	X
ejpam-5856	512	2	7	7	X
ejpam-5856	512	3	]	]	PUNCT
ejpam-5856	512	4	t.	t.	PROPN
ejpam-5856	512	5	m.	m.	PROPN
ejpam-5856	512	6	al	al	PROPN
ejpam-5856	512	7	-	-	PUNCT
ejpam-5856	512	8	shami	shami	PROPN
ejpam-5856	512	9	,	,	PUNCT
ejpam-5856	512	10	h.	h.	PROPN
ejpam-5856	512	11	z.	z.	PROPN
ejpam-5856	512	12	ibrahim	ibrahim	PROPN
ejpam-5856	512	13	,	,	PUNCT
ejpam-5856	512	14	a.	a.	NOUN
ejpam-5856	512	15	mhemdi	mhemdi	PROPN
ejpam-5856	512	16	,	,	PUNCT
ejpam-5856	512	17	and	and	CCONJ
ejpam-5856	512	18	r.	r.	PROPN
ejpam-5856	512	19	abu	abu	PROPN
ejpam-5856	512	20	-	-	PUNCT
ejpam-5856	512	21	gdairi	gdairi	PROPN
ejpam-5856	512	22	.	.	PUNCT
ejpam-5856	513	1	nth	nth	PROPN
ejpam-5856	513	2	power	power	NOUN
ejpam-5856	513	3	root	root	NOUN
ejpam-5856	513	4	fuzzy	fuzzy	ADJ
ejpam-5856	513	5	sets	set	NOUN
ejpam-5856	513	6	and	and	CCONJ
ejpam-5856	513	7	its	its	PRON
ejpam-5856	513	8	topology	topology	NOUN
ejpam-5856	513	9	.	.	PUNCT
ejpam-5856	514	1	international	international	ADJ
ejpam-5856	514	2	journal	journal	PROPN
ejpam-5856	514	3	of	of	ADP
ejpam-5856	514	4	fuzzy	fuzzy	ADJ
ejpam-5856	514	5	logic	logic	NOUN
ejpam-5856	514	6	and	and	CCONJ
ejpam-5856	514	7	intelligent	intelligent	ADJ
ejpam-5856	514	8	systems	system	NOUN
ejpam-5856	514	9	,	,	PUNCT
ejpam-5856	514	10	22(4):350–365	22(4):350–365	NOUN
ejpam-5856	514	11	,	,	PUNCT
ejpam-5856	514	12	2022	2022	NUM
ejpam-5856	514	13	.	.	PUNCT
ejpam-5856	515	1	[	[	X
ejpam-5856	515	2	8	8	NUM
ejpam-5856	515	3	]	]	PUNCT
ejpam-5856	515	4	m.	m.	NOUN
ejpam-5856	515	5	ali	ali	PROPN
ejpam-5856	515	6	and	and	CCONJ
ejpam-5856	515	7	h.	h.	PROPN
ejpam-5856	515	8	wang	wang	PROPN
ejpam-5856	515	9	.	.	PUNCT
ejpam-5856	516	1	application	application	NOUN
ejpam-5856	516	2	of	of	ADP
ejpam-5856	516	3	fuzzy	fuzzy	ADJ
ejpam-5856	516	4	logic	logic	NOUN
ejpam-5856	516	5	in	in	ADP
ejpam-5856	516	6	control	control	NOUN
ejpam-5856	516	7	systems	system	NOUN
ejpam-5856	516	8	:	:	PUNCT
ejpam-5856	516	9	a	a	DET
ejpam-5856	516	10	comprehensive	comprehensive	ADJ
ejpam-5856	516	11	survey	survey	NOUN
ejpam-5856	516	12	.	.	PUNCT
ejpam-5856	517	1	journal	journal	PROPN
ejpam-5856	517	2	of	of	ADP
ejpam-5856	517	3	control	control	PROPN
ejpam-5856	517	4	engineering	engineering	NOUN
ejpam-5856	517	5	and	and	CCONJ
ejpam-5856	517	6	technology	technology	NOUN
ejpam-5856	517	7	,	,	PUNCT
ejpam-5856	517	8	18(1):23–45	18(1):23–45	NUM
ejpam-5856	517	9	,	,	PUNCT
ejpam-5856	517	10	2022	2022	NUM
ejpam-5856	517	11	.	.	PUNCT
ejpam-5856	518	1	[	[	X
ejpam-5856	518	2	9	9	NUM
ejpam-5856	518	3	]	]	PUNCT
ejpam-5856	518	4	z.	z.	PROPN
ejpam-5856	518	5	a.	a.	PROPN
ejpam-5856	518	6	ameen	ameen	PROPN
ejpam-5856	518	7	,	,	PUNCT
ejpam-5856	518	8	t.	t.	PROPN
ejpam-5856	518	9	m.	m.	PROPN
ejpam-5856	518	10	al	al	PROPN
ejpam-5856	518	11	-	-	PUNCT
ejpam-5856	518	12	shami	shami	PROPN
ejpam-5856	518	13	,	,	PUNCT
ejpam-5856	518	14	a.	a.	PROPN
ejpam-5856	518	15	a.	a.	NOUN
ejpam-5856	518	16	azzam	azzam	PROPN
ejpam-5856	518	17	,	,	PUNCT
ejpam-5856	518	18	and	and	CCONJ
ejpam-5856	518	19	a.	a.	NOUN
ejpam-5856	518	20	mhemdi	mhemdi	PROPN
ejpam-5856	518	21	.	.	PUNCT
ejpam-5856	519	1	a	a	DET
ejpam-5856	519	2	novel	novel	ADJ
ejpam-5856	519	3	fuzzy	fuzzy	ADJ
ejpam-5856	519	4	structure	structure	NOUN
ejpam-5856	519	5	:	:	PUNCT
ejpam-5856	519	6	infra	infra	NOUN
ejpam-5856	519	7	-	-	PUNCT
ejpam-5856	519	8	fuzzy	fuzzy	ADJ
ejpam-5856	519	9	topological	topological	ADJ
ejpam-5856	519	10	spaces	space	NOUN
ejpam-5856	519	11	.	.	PUNCT
ejpam-5856	520	1	journal	journal	NOUN
ejpam-5856	520	2	of	of	ADP
ejpam-5856	520	3	function	function	NOUN
ejpam-5856	520	4	spaces	space	NOUN
ejpam-5856	520	5	,	,	PUNCT
ejpam-5856	520	6	2022:11	2022:11	NUM
ejpam-5856	520	7	pages	page	NOUN
ejpam-5856	520	8	,	,	PUNCT
ejpam-5856	520	9	2022	2022	NUM
ejpam-5856	520	10	.	.	PUNCT
ejpam-5856	521	1	[	[	X
ejpam-5856	521	2	10	10	NUM
ejpam-5856	521	3	]	]	PUNCT
ejpam-5856	521	4	z.	z.	PROPN
ejpam-5856	521	5	a.	a.	PROPN
ejpam-5856	521	6	ameen	ameen	PROPN
ejpam-5856	521	7	,	,	PUNCT
ejpam-5856	521	8	r.	r.	PROPN
ejpam-5856	521	9	a.	a.	PROPN
ejpam-5856	521	10	mohammed	mohammed	PROPN
ejpam-5856	521	11	,	,	PUNCT
ejpam-5856	521	12	t.	t.	PROPN
ejpam-5856	521	13	m.	m.	PROPN
ejpam-5856	521	14	al	al	PROPN
ejpam-5856	521	15	-	-	PUNCT
ejpam-5856	521	16	shami	shami	PROPN
ejpam-5856	521	17	,	,	PUNCT
ejpam-5856	521	18	and	and	CCONJ
ejpam-5856	521	19	b.	b.	PROPN
ejpam-5856	521	20	a.	a.	PROPN
ejpam-5856	521	21	asaad	asaad	PROPN
ejpam-5856	521	22	.	.	PUNCT
ejpam-5856	522	1	novel	novel	ADJ
ejpam-5856	522	2	fuzzy	fuzzy	ADJ
ejpam-5856	522	3	topologies	topology	NOUN
ejpam-5856	522	4	formed	form	VERB
ejpam-5856	522	5	by	by	ADP
ejpam-5856	522	6	fuzzy	fuzzy	ADJ
ejpam-5856	522	7	primal	primal	ADJ
ejpam-5856	522	8	frameworks	framework	NOUN
ejpam-5856	522	9	.	.	PUNCT
ejpam-5856	523	1	journal	journal	NOUN
ejpam-5856	523	2	of	of	ADP
ejpam-5856	523	3	intelligent	intelligent	ADJ
ejpam-5856	523	4	&	&	CCONJ
ejpam-5856	523	5	fuzzy	fuzzy	ADJ
ejpam-5856	523	6	systems	system	NOUN
ejpam-5856	523	7	,	,	PUNCT
ejpam-5856	523	8	2024	2024	NUM
ejpam-5856	523	9	.	.	PUNCT
ejpam-5856	524	1	s.	s.	PROPN
ejpam-5856	524	2	saleh	saleh	PROPN
ejpam-5856	524	3	et	et	PROPN
ejpam-5856	524	4	al	al	PROPN
ejpam-5856	524	5	.	.	PUNCT
ejpam-5856	524	6	/	/	SYM
ejpam-5856	524	7	eur	eur	PROPN
ejpam-5856	524	8	.	.	PUNCT
ejpam-5856	525	1	j.	j.	PROPN
ejpam-5856	525	2	pure	pure	PROPN
ejpam-5856	525	3	appl	appl	PROPN
ejpam-5856	525	4	.	.	PROPN
ejpam-5856	525	5	math	math	PROPN
ejpam-5856	525	6	,	,	PUNCT
ejpam-5856	525	7	18	18	NUM
ejpam-5856	525	8	(	(	PUNCT
ejpam-5856	525	9	1	1	NUM
ejpam-5856	525	10	)	)	PUNCT
ejpam-5856	525	11	(	(	PUNCT
ejpam-5856	525	12	2025	2025	NUM
ejpam-5856	525	13	)	)	PUNCT
ejpam-5856	525	14	,	,	PUNCT
ejpam-5856	525	15	5856	5856	NUM
ejpam-5856	525	16	14	14	NUM
ejpam-5856	525	17	of	of	ADP
ejpam-5856	525	18	15	15	NUM
ejpam-5856	526	1	[	[	SYM
ejpam-5856	526	2	11	11	NUM
ejpam-5856	526	3	]	]	PUNCT
ejpam-5856	526	4	s.	s.	PROPN
ejpam-5856	526	5	p.	p.	PROPN
ejpam-5856	526	6	arya	arya	PROPN
ejpam-5856	526	7	and	and	CCONJ
ejpam-5856	526	8	m.	m.	PROPN
ejpam-5856	526	9	p.	p.	PROPN
ejpam-5856	526	10	bhamini	bhamini	PROPN
ejpam-5856	526	11	.	.	PUNCT
ejpam-5856	527	1	a	a	DET
ejpam-5856	527	2	generalization	generalization	NOUN
ejpam-5856	527	3	of	of	ADP
ejpam-5856	527	4	normal	normal	ADJ
ejpam-5856	527	5	spaces	space	NOUN
ejpam-5856	527	6	.	.	PUNCT
ejpam-5856	528	1	mat	mat	PROPN
ejpam-5856	528	2	.	.	PROPN
ejpam-5856	528	3	vesnik	vesnik	PROPN
ejpam-5856	528	4	,	,	PUNCT
ejpam-5856	528	5	35:1–10	35:1–10	NUM
ejpam-5856	528	6	,	,	PUNCT
ejpam-5856	528	7	1983	1983	NUM
ejpam-5856	528	8	.	.	PUNCT
ejpam-5856	529	1	[	[	X
ejpam-5856	529	2	12	12	NUM
ejpam-5856	529	3	]	]	X
ejpam-5856	529	4	g.	g.	PROPN
ejpam-5856	529	5	balasubramanian	balasubramanian	PROPN
ejpam-5856	529	6	and	and	CCONJ
ejpam-5856	529	7	p.	p.	PROPN
ejpam-5856	529	8	sundaram	sundaram	PROPN
ejpam-5856	529	9	.	.	PUNCT
ejpam-5856	530	1	on	on	ADP
ejpam-5856	530	2	some	some	DET
ejpam-5856	530	3	generalizations	generalization	NOUN
ejpam-5856	530	4	of	of	ADP
ejpam-5856	530	5	fuzzy	fuzzy	ADJ
ejpam-5856	530	6	continuous	continuous	ADJ
ejpam-5856	530	7	functions	function	NOUN
ejpam-5856	530	8	.	.	PUNCT
ejpam-5856	531	1	fuzzy	fuzzy	ADJ
ejpam-5856	531	2	sets	set	NOUN
ejpam-5856	531	3	and	and	CCONJ
ejpam-5856	531	4	systems	system	NOUN
ejpam-5856	531	5	,	,	PUNCT
ejpam-5856	531	6	86:93–100	86:93–100	NUM
ejpam-5856	531	7	,	,	PUNCT
ejpam-5856	531	8	1997	1997	NUM
ejpam-5856	531	9	.	.	PUNCT
ejpam-5856	532	1	[	[	X
ejpam-5856	532	2	13	13	NUM
ejpam-5856	532	3	]	]	PUNCT
ejpam-5856	532	4	j.	j.	PROPN
ejpam-5856	532	5	chakraborty	chakraborty	PROPN
ejpam-5856	532	6	,	,	PUNCT
ejpam-5856	532	7	b.	b.	PROPN
ejpam-5856	532	8	bhattacharya	bhattacharya	PROPN
ejpam-5856	532	9	,	,	PUNCT
ejpam-5856	532	10	and	and	CCONJ
ejpam-5856	532	11	a.	a.	NOUN
ejpam-5856	532	12	paul	paul	PROPN
ejpam-5856	532	13	.	.	PUNCT
ejpam-5856	533	1	some	some	DET
ejpam-5856	533	2	properties	property	NOUN
ejpam-5856	533	3	of	of	ADP
ejpam-5856	533	4	generalized	generalized	ADJ
ejpam-5856	533	5	fuzzy	fuzzy	ADJ
ejpam-5856	533	6	hyperconnected	hyperconnecte	VERB
ejpam-5856	533	7	spaces	space	NOUN
ejpam-5856	533	8	.	.	PUNCT
ejpam-5856	534	1	ann	ann	PROPN
ejpam-5856	534	2	.	.	PUNCT
ejpam-5856	534	3	fuzzy	fuzzy	ADJ
ejpam-5856	534	4	math	math	NOUN
ejpam-5856	534	5	.	.	PUNCT
ejpam-5856	535	1	inform	inform	NOUN
ejpam-5856	535	2	.	.	PUNCT
ejpam-5856	535	3	,	,	PUNCT
ejpam-5856	536	1	12(5):659–668	12(5):659–668	PROPN
ejpam-5856	536	2	,	,	PUNCT
ejpam-5856	536	3	2016	2016	NUM
ejpam-5856	536	4	.	.	PUNCT
ejpam-5856	537	1	[	[	X
ejpam-5856	537	2	14	14	NUM
ejpam-5856	537	3	]	]	PUNCT
ejpam-5856	537	4	j.	j.	PROPN
ejpam-5856	537	5	chakraborty	chakraborty	PROPN
ejpam-5856	537	6	,	,	PUNCT
ejpam-5856	537	7	b.	b.	PROPN
ejpam-5856	537	8	bhattacharya	bhattacharya	PROPN
ejpam-5856	537	9	,	,	PUNCT
ejpam-5856	537	10	and	and	CCONJ
ejpam-5856	537	11	a.	a.	NOUN
ejpam-5856	537	12	paul	paul	PROPN
ejpam-5856	537	13	.	.	PUNCT
ejpam-5856	538	1	fuzzy	fuzzy	ADJ
ejpam-5856	538	2	λgx	λgx	VERB
ejpam-5856	538	3	r	r	NOUN
ejpam-5856	538	4	-sets	-set	NOUN
ejpam-5856	538	5	and	and	CCONJ
ejpam-5856	538	6	generalization	generalization	NOUN
ejpam-5856	538	7	of	of	ADP
ejpam-5856	538	8	closed	closed	ADJ
ejpam-5856	538	9	sets	set	NOUN
ejpam-5856	538	10	in	in	ADP
ejpam-5856	538	11	generalized	generalized	ADJ
ejpam-5856	538	12	fuzzy	fuzzy	ADJ
ejpam-5856	538	13	topological	topological	ADJ
ejpam-5856	538	14	spaces	space	NOUN
ejpam-5856	538	15	.	.	PUNCT
ejpam-5856	539	1	songklanakarin	songklanakarin	PROPN
ejpam-5856	539	2	j.	j.	PROPN
ejpam-5856	539	3	sci	sci	PROPN
ejpam-5856	539	4	.	.	PUNCT
ejpam-5856	539	5	tech	tech	PROPN
ejpam-5856	539	6	.	.	PUNCT
ejpam-5856	539	7	,	,	PUNCT
ejpam-5856	540	1	39(3):275–291	39(3):275–291	PROPN
ejpam-5856	540	2	,	,	PUNCT
ejpam-5856	540	3	2017	2017	NUM
ejpam-5856	540	4	.	.	PUNCT
ejpam-5856	541	1	[	[	X
ejpam-5856	541	2	15	15	NUM
ejpam-5856	541	3	]	]	PUNCT
ejpam-5856	541	4	j.	j.	PROPN
ejpam-5856	541	5	chakraborty	chakraborty	PROPN
ejpam-5856	541	6	,	,	PUNCT
ejpam-5856	541	7	b.	b.	PROPN
ejpam-5856	541	8	bhattacharya	bhattacharya	PROPN
ejpam-5856	541	9	,	,	PUNCT
ejpam-5856	541	10	and	and	CCONJ
ejpam-5856	541	11	a.	a.	NOUN
ejpam-5856	541	12	paul	paul	PROPN
ejpam-5856	541	13	.	.	PUNCT
ejpam-5856	542	1	generalized	generalize	VERB
ejpam-5856	542	2	fuzzy	fuzzy	ADJ
ejpam-5856	542	3	closed	close	VERB
ejpam-5856	542	4	sets	set	NOUN
ejpam-5856	542	5	in	in	ADP
ejpam-5856	542	6	generalized	generalized	ADJ
ejpam-5856	542	7	fuzzy	fuzzy	ADJ
ejpam-5856	542	8	topological	topological	ADJ
ejpam-5856	542	9	spaces	space	NOUN
ejpam-5856	542	10	.	.	PUNCT
ejpam-5856	543	1	songklanakarin	songklanakarin	PROPN
ejpam-5856	543	2	j.	j.	PROPN
ejpam-5856	543	3	sci	sci	PROPN
ejpam-5856	543	4	.	.	PUNCT
ejpam-5856	543	5	tech	tech	PROPN
ejpam-5856	543	6	.	.	PUNCT
ejpam-5856	543	7	,	,	PUNCT
ejpam-5856	543	8	41(1):216–221	41(1):216–221	PROPN
ejpam-5856	543	9	,	,	PUNCT
ejpam-5856	543	10	2019	2019	NUM
ejpam-5856	543	11	.	.	PUNCT
ejpam-5856	544	1	[	[	X
ejpam-5856	544	2	16	16	NUM
ejpam-5856	544	3	]	]	X
ejpam-5856	544	4	c.	c.	PROPN
ejpam-5856	544	5	l.	l.	PROPN
ejpam-5856	544	6	chang	chang	PROPN
ejpam-5856	544	7	.	.	PUNCT
ejpam-5856	545	1	fuzzy	fuzzy	ADJ
ejpam-5856	545	2	topological	topological	ADJ
ejpam-5856	545	3	spaces	space	NOUN
ejpam-5856	545	4	.	.	PUNCT
ejpam-5856	546	1	j.	j.	PROPN
ejpam-5856	546	2	math	math	PROPN
ejpam-5856	546	3	.	.	PUNCT
ejpam-5856	547	1	anal	anal	PROPN
ejpam-5856	547	2	.	.	PUNCT
ejpam-5856	548	1	appl	appl	PROPN
ejpam-5856	548	2	.	.	PROPN
ejpam-5856	548	3	,	,	PUNCT
ejpam-5856	549	1	24:182–190	24:182–190	NUM
ejpam-5856	549	2	,	,	PUNCT
ejpam-5856	549	3	1968	1968	NUM
ejpam-5856	549	4	.	.	PUNCT
ejpam-5856	550	1	[	[	X
ejpam-5856	550	2	17	17	NUM
ejpam-5856	550	3	]	]	PUNCT
ejpam-5856	550	4	l.	l.	PROPN
ejpam-5856	550	5	chen	chen	PROPN
ejpam-5856	550	6	and	and	CCONJ
ejpam-5856	550	7	y.	y.	PROPN
ejpam-5856	550	8	zhao	zhao	PROPN
ejpam-5856	550	9	.	.	PUNCT
ejpam-5856	551	1	fuzzy	fuzzy	ADJ
ejpam-5856	551	2	decision	decision	NOUN
ejpam-5856	551	3	-	-	PUNCT
ejpam-5856	551	4	making	make	VERB
ejpam-5856	551	5	models	model	NOUN
ejpam-5856	551	6	:	:	PUNCT
ejpam-5856	551	7	a	a	DET
ejpam-5856	551	8	review	review	NOUN
ejpam-5856	551	9	of	of	ADP
ejpam-5856	551	10	trends	trend	NOUN
ejpam-5856	551	11	and	and	CCONJ
ejpam-5856	551	12	applications	application	NOUN
ejpam-5856	551	13	.	.	PUNCT
ejpam-5856	552	1	journal	journal	NOUN
ejpam-5856	552	2	of	of	ADP
ejpam-5856	552	3	decision	decision	NOUN
ejpam-5856	552	4	systems	system	NOUN
ejpam-5856	552	5	,	,	PUNCT
ejpam-5856	552	6	32:110–135	32:110–135	PROPN
ejpam-5856	552	7	,	,	PUNCT
ejpam-5856	552	8	2023	2023	NUM
ejpam-5856	552	9	.	.	PUNCT
ejpam-5856	553	1	[	[	X
ejpam-5856	553	2	18	18	NUM
ejpam-5856	553	3	]	]	PUNCT
ejpam-5856	553	4	p.	p.	NOUN
ejpam-5856	553	5	g.	g.	PROPN
ejpam-5856	553	6	chetty	chetty	PROPN
ejpam-5856	553	7	.	.	PUNCT
ejpam-5856	554	1	generalized	generalize	VERB
ejpam-5856	554	2	fuzzy	fuzzy	ADJ
ejpam-5856	554	3	topology	topology	NOUN
ejpam-5856	554	4	.	.	PUNCT
ejpam-5856	555	1	ital	ital	PROPN
ejpam-5856	555	2	.	.	PUNCT
ejpam-5856	556	1	j.	j.	PROPN
ejpam-5856	556	2	pure	pure	PROPN
ejpam-5856	556	3	appl	appl	PROPN
ejpam-5856	556	4	.	.	PUNCT
ejpam-5856	556	5	math	math	PROPN
ejpam-5856	556	6	.	.	PUNCT
ejpam-5856	556	7	,	,	PUNCT
ejpam-5856	557	1	24:91–96	24:91–96	NUM
ejpam-5856	557	2	,	,	PUNCT
ejpam-5856	557	3	2008	2008	NUM
ejpam-5856	557	4	.	.	PUNCT
ejpam-5856	558	1	[	[	X
ejpam-5856	558	2	19	19	NUM
ejpam-5856	558	3	]	]	PUNCT
ejpam-5856	558	4	a.	a.	NOUN
ejpam-5856	558	5	császár	császár	PROPN
ejpam-5856	558	6	.	.	PUNCT
ejpam-5856	559	1	generalized	generalize	VERB
ejpam-5856	559	2	open	open	ADJ
ejpam-5856	559	3	sets	set	NOUN
ejpam-5856	559	4	.	.	PUNCT
ejpam-5856	560	1	acta	acta	PROPN
ejpam-5856	560	2	math	math	PROPN
ejpam-5856	560	3	.	.	PUNCT
ejpam-5856	561	1	hungar	hungar	PROPN
ejpam-5856	561	2	.	.	PUNCT
ejpam-5856	561	3	,	,	PUNCT
ejpam-5856	562	1	75:65–87	75:65–87	NUM
ejpam-5856	562	2	,	,	PUNCT
ejpam-5856	562	3	1997	1997	NUM
ejpam-5856	562	4	.	.	PUNCT
ejpam-5856	563	1	[	[	X
ejpam-5856	563	2	20	20	NUM
ejpam-5856	563	3	]	]	PUNCT
ejpam-5856	563	4	a.	a.	NOUN
ejpam-5856	563	5	császár	császár	PROPN
ejpam-5856	563	6	.	.	PUNCT
ejpam-5856	564	1	generalized	generalize	VERB
ejpam-5856	564	2	topology	topology	NOUN
ejpam-5856	564	3	,	,	PUNCT
ejpam-5856	564	4	generalized	generalize	VERB
ejpam-5856	564	5	continuity	continuity	NOUN
ejpam-5856	564	6	.	.	PUNCT
ejpam-5856	565	1	acta	acta	PROPN
ejpam-5856	565	2	math	math	PROPN
ejpam-5856	565	3	.	.	PUNCT
ejpam-5856	566	1	hungar	hungar	PROPN
ejpam-5856	566	2	.	.	PUNCT
ejpam-5856	567	1	,	,	PUNCT
ejpam-5856	567	2	96(4):351–357	96(4):351–357	NOUN
ejpam-5856	567	3	,	,	PUNCT
ejpam-5856	567	4	2002	2002	NUM
ejpam-5856	567	5	.	.	PUNCT
ejpam-5856	568	1	[	[	X
ejpam-5856	568	2	21	21	NUM
ejpam-5856	568	3	]	]	PUNCT
ejpam-5856	568	4	a.	a.	NOUN
ejpam-5856	568	5	császár	császár	PROPN
ejpam-5856	568	6	.	.	PUNCT
ejpam-5856	569	1	normal	normal	ADJ
ejpam-5856	569	2	generalized	generalized	ADJ
ejpam-5856	569	3	topologies	topology	NOUN
ejpam-5856	569	4	.	.	PUNCT
ejpam-5856	570	1	acta	acta	PROPN
ejpam-5856	570	2	math	math	PROPN
ejpam-5856	570	3	.	.	PUNCT
ejpam-5856	571	1	hungar	hungar	PROPN
ejpam-5856	571	2	.	.	PUNCT
ejpam-5856	571	3	,	,	PUNCT
ejpam-5856	571	4	115:309–313	115:309–313	NUM
ejpam-5856	571	5	,	,	PUNCT
ejpam-5856	571	6	2007	2007	NUM
ejpam-5856	571	7	.	.	PUNCT
ejpam-5856	572	1	[	[	X
ejpam-5856	572	2	22	22	NUM
ejpam-5856	572	3	]	]	PUNCT
ejpam-5856	572	4	s.	s.	PROPN
ejpam-5856	572	5	demiralp	demiralp	PROPN
ejpam-5856	572	6	,	,	PUNCT
ejpam-5856	572	7	t.	t.	PROPN
ejpam-5856	572	8	m.	m.	PROPN
ejpam-5856	572	9	al	al	PROPN
ejpam-5856	572	10	-	-	PUNCT
ejpam-5856	572	11	shami	shami	PROPN
ejpam-5856	572	12	,	,	PUNCT
ejpam-5856	572	13	a.	a.	NOUN
ejpam-5856	572	14	m.	m.	PROPN
ejpam-5856	572	15	abd	abd	PROPN
ejpam-5856	572	16	el	el	PROPN
ejpam-5856	572	17	-	-	PROPN
ejpam-5856	572	18	latif	latif	PROPN
ejpam-5856	572	19	,	,	PUNCT
ejpam-5856	572	20	and	and	CCONJ
ejpam-5856	572	21	f.	f.	PROPN
ejpam-5856	572	22	a.	a.	PROPN
ejpam-5856	572	23	abu	abu	PROPN
ejpam-5856	572	24	shaheen	shaheen	PROPN
ejpam-5856	572	25	.	.	PUNCT
ejpam-5856	573	1	topologically	topologically	ADV
ejpam-5856	573	2	indistinguishable	indistinguishable	ADJ
ejpam-5856	573	3	relations	relation	NOUN
ejpam-5856	573	4	and	and	CCONJ
ejpam-5856	573	5	separation	separation	NOUN
ejpam-5856	573	6	axioms	axiom	NOUN
ejpam-5856	573	7	.	.	PUNCT
ejpam-5856	574	1	aims	aim	VERB
ejpam-5856	574	2	mathematics	mathematic	NOUN
ejpam-5856	574	3	,	,	PUNCT
ejpam-5856	574	4	9(6):1570115723	9(6):1570115723	NUM
ejpam-5856	574	5	,	,	PUNCT
ejpam-5856	574	6	2024	2024	NUM
ejpam-5856	574	7	.	.	PUNCT
ejpam-5856	575	1	[	[	X
ejpam-5856	575	2	23	23	NUM
ejpam-5856	575	3	]	]	X
ejpam-5856	575	4	d.	d.	PROPN
ejpam-5856	575	5	dubois	dubois	PROPN
ejpam-5856	575	6	.	.	PUNCT
ejpam-5856	575	7	fuzzy	fuzzy	ADJ
ejpam-5856	575	8	sets	set	NOUN
ejpam-5856	575	9	and	and	CCONJ
ejpam-5856	575	10	systems	system	NOUN
ejpam-5856	575	11	:	:	PUNCT
ejpam-5856	575	12	theory	theory	NOUN
ejpam-5856	575	13	and	and	CCONJ
ejpam-5856	575	14	applications	application	NOUN
ejpam-5856	575	15	,	,	PUNCT
ejpam-5856	575	16	volume	volume	NOUN
ejpam-5856	575	17	144	144	NUM
ejpam-5856	575	18	.	.	PUNCT
ejpam-5856	576	1	academic	academic	ADJ
ejpam-5856	576	2	press	press	NOUN
ejpam-5856	576	3	,	,	PUNCT
ejpam-5856	576	4	1980	1980	NUM
ejpam-5856	576	5	.	.	PUNCT
ejpam-5856	577	1	[	[	X
ejpam-5856	577	2	24	24	NUM
ejpam-5856	577	3	]	]	PUNCT
ejpam-5856	577	4	m.	m.	NOUN
ejpam-5856	577	5	hosny	hosny	PROPN
ejpam-5856	577	6	and	and	CCONJ
ejpam-5856	577	7	t.	t.	PROPN
ejpam-5856	577	8	m.	m.	PROPN
ejpam-5856	577	9	al	al	PROPN
ejpam-5856	577	10	-	-	PUNCT
ejpam-5856	577	11	shami	shami	PROPN
ejpam-5856	577	12	.	.	PUNCT
ejpam-5856	578	1	employing	employ	VERB
ejpam-5856	578	2	a	a	DET
ejpam-5856	578	3	generalization	generalization	NOUN
ejpam-5856	578	4	of	of	ADP
ejpam-5856	578	5	open	open	ADJ
ejpam-5856	578	6	sets	set	NOUN
ejpam-5856	578	7	defined	define	VERB
ejpam-5856	578	8	by	by	ADP
ejpam-5856	578	9	ideals	ideal	NOUN
ejpam-5856	578	10	to	to	PART
ejpam-5856	578	11	initiate	initiate	VERB
ejpam-5856	578	12	novel	novel	ADJ
ejpam-5856	578	13	rough	rough	ADJ
ejpam-5856	578	14	approximation	approximation	NOUN
ejpam-5856	578	15	spaces	space	NOUN
ejpam-5856	578	16	with	with	ADP
ejpam-5856	578	17	a	a	DET
ejpam-5856	578	18	chemical	chemical	NOUN
ejpam-5856	578	19	application	application	NOUN
ejpam-5856	578	20	.	.	PUNCT
ejpam-5856	579	1	european	european	ADJ
ejpam-5856	579	2	journal	journal	PROPN
ejpam-5856	579	3	of	of	ADP
ejpam-5856	579	4	pure	pure	ADJ
ejpam-5856	579	5	and	and	CCONJ
ejpam-5856	579	6	applied	applied	ADJ
ejpam-5856	579	7	mathematics	mathematic	NOUN
ejpam-5856	579	8	,	,	PUNCT
ejpam-5856	579	9	17(4):3436–3463	17(4):3436–3463	NUM
ejpam-5856	579	10	,	,	PUNCT
ejpam-5856	579	11	2024	2024	NUM
ejpam-5856	579	12	.	.	PUNCT
ejpam-5856	580	1	[	[	X
ejpam-5856	580	2	25	25	NUM
ejpam-5856	580	3	]	]	PUNCT
ejpam-5856	580	4	a.	a.	NOUN
ejpam-5856	580	5	l.	l.	PROPN
ejpam-5856	580	6	kalantan	kalantan	PROPN
ejpam-5856	580	7	.	.	PUNCT
ejpam-5856	581	1	results	result	VERB
ejpam-5856	581	2	about	about	ADP
ejpam-5856	581	3	normality	normality	NOUN
ejpam-5856	581	4	.	.	PUNCT
ejpam-5856	582	1	topology	topology	NOUN
ejpam-5856	582	2	appl	appl	PROPN
ejpam-5856	582	3	.	.	PROPN
ejpam-5856	582	4	,	,	PUNCT
ejpam-5856	582	5	125:47–62	125:47–62	NUM
ejpam-5856	582	6	,	,	PUNCT
ejpam-5856	582	7	2002	2002	NUM
ejpam-5856	582	8	.	.	PUNCT
ejpam-5856	583	1	[	[	X
ejpam-5856	583	2	26	26	NUM
ejpam-5856	583	3	]	]	PUNCT
ejpam-5856	583	4	a.	a.	NOUN
ejpam-5856	583	5	kandil	kandil	PROPN
ejpam-5856	583	6	and	and	CCONJ
ejpam-5856	583	7	m.	m.	PROPN
ejpam-5856	583	8	e.	e.	PROPN
ejpam-5856	583	9	el	el	PROPN
ejpam-5856	583	10	-	-	PROPN
ejpam-5856	583	11	shafei	shafei	PROPN
ejpam-5856	583	12	.	.	PUNCT
ejpam-5856	584	1	regularity	regularity	NOUN
ejpam-5856	584	2	axioms	axiom	NOUN
ejpam-5856	584	3	in	in	ADP
ejpam-5856	584	4	fuzzy	fuzzy	ADJ
ejpam-5856	584	5	topological	topological	ADJ
ejpam-5856	584	6	spaces	space	NOUN
ejpam-5856	584	7	and	and	CCONJ
ejpam-5856	584	8	fri	fri	NOUN
ejpam-5856	584	9	-	-	NOUN
ejpam-5856	584	10	proximities	proximity	NOUN
ejpam-5856	584	11	.	.	PUNCT
ejpam-5856	585	1	fuzzy	fuzzy	ADJ
ejpam-5856	585	2	sets	set	NOUN
ejpam-5856	585	3	and	and	CCONJ
ejpam-5856	585	4	systems	system	NOUN
ejpam-5856	585	5	,	,	PUNCT
ejpam-5856	585	6	27:217–231	27:217–231	NUM
ejpam-5856	585	7	,	,	PUNCT
ejpam-5856	585	8	1988	1988	NUM
ejpam-5856	585	9	.	.	PUNCT
ejpam-5856	586	1	[	[	X
ejpam-5856	586	2	27	27	NUM
ejpam-5856	586	3	]	]	PUNCT
ejpam-5856	586	4	a.	a.	NOUN
ejpam-5856	586	5	kandil	kandil	PROPN
ejpam-5856	586	6	,	,	PUNCT
ejpam-5856	586	7	s.	s.	PROPN
ejpam-5856	586	8	saleh	saleh	PROPN
ejpam-5856	586	9	,	,	PUNCT
ejpam-5856	586	10	and	and	CCONJ
ejpam-5856	586	11	m.	m.	NOUN
ejpam-5856	586	12	takout	takout	PROPN
ejpam-5856	586	13	.	.	PUNCT
ejpam-5856	587	1	fuzzy	fuzzy	ADJ
ejpam-5856	587	2	topology	topology	NOUN
ejpam-5856	587	3	on	on	ADP
ejpam-5856	587	4	fuzzy	fuzzy	ADJ
ejpam-5856	587	5	sets	set	NOUN
ejpam-5856	587	6	:	:	PUNCT
ejpam-5856	587	7	regularity	regularity	NOUN
ejpam-5856	587	8	and	and	CCONJ
ejpam-5856	587	9	separation	separation	NOUN
ejpam-5856	587	10	axioms	axiom	NOUN
ejpam-5856	587	11	.	.	PUNCT
ejpam-5856	588	1	american	american	PROPN
ejpam-5856	588	2	academic	academic	PROPN
ejpam-5856	588	3	&	&	CCONJ
ejpam-5856	588	4	scholarly	scholarly	ADJ
ejpam-5856	588	5	research	research	NOUN
ejpam-5856	588	6	journal	journal	NOUN
ejpam-5856	588	7	,	,	PUNCT
ejpam-5856	588	8	4(2	4(2	NUM
ejpam-5856	588	9	)	)	PUNCT
ejpam-5856	588	10	,	,	PUNCT
ejpam-5856	588	11	2012	2012	NUM
ejpam-5856	588	12	.	.	PUNCT
ejpam-5856	589	1	[	[	X
ejpam-5856	589	2	28	28	NUM
ejpam-5856	589	3	]	]	X
ejpam-5856	589	4	r.	r.	PROPN
ejpam-5856	589	5	kumar	kumar	PROPN
ejpam-5856	589	6	,	,	PUNCT
ejpam-5856	589	7	p.	p.	PROPN
ejpam-5856	589	8	singh	singh	PROPN
ejpam-5856	589	9	,	,	PUNCT
ejpam-5856	589	10	and	and	CCONJ
ejpam-5856	589	11	t.	t.	PROPN
ejpam-5856	589	12	zhang	zhang	PROPN
ejpam-5856	589	13	.	.	PUNCT
ejpam-5856	589	14	fuzzy	fuzzy	PROPN
ejpam-5856	589	15	control	control	PROPN
ejpam-5856	589	16	systems	system	NOUN
ejpam-5856	589	17	:	:	PUNCT
ejpam-5856	589	18	advances	advance	NOUN
ejpam-5856	589	19	and	and	CCONJ
ejpam-5856	589	20	applications	application	NOUN
ejpam-5856	589	21	.	.	PUNCT
ejpam-5856	590	1	control	control	NOUN
ejpam-5856	590	2	theory	theory	NOUN
ejpam-5856	590	3	and	and	CCONJ
ejpam-5856	590	4	technology	technology	NOUN
ejpam-5856	590	5	,	,	PUNCT
ejpam-5856	590	6	19:210–234	19:210–234	NUM
ejpam-5856	590	7	,	,	PUNCT
ejpam-5856	590	8	2021	2021	NUM
ejpam-5856	590	9	.	.	PUNCT
ejpam-5856	591	1	[	[	X
ejpam-5856	591	2	29	29	NUM
ejpam-5856	591	3	]	]	X
ejpam-5856	591	4	l.	l.	PROPN
ejpam-5856	591	5	levine	levine	PROPN
ejpam-5856	591	6	.	.	PUNCT
ejpam-5856	592	1	generalized	generalize	VERB
ejpam-5856	592	2	closed	closed	ADJ
ejpam-5856	592	3	sets	set	NOUN
ejpam-5856	592	4	in	in	ADP
ejpam-5856	592	5	topology	topology	NOUN
ejpam-5856	592	6	.	.	PUNCT
ejpam-5856	593	1	rend	rend	VERB
ejpam-5856	593	2	.	.	PUNCT
ejpam-5856	594	1	circ	circ	PROPN
ejpam-5856	594	2	.	.	PUNCT
ejpam-5856	595	1	mat	mat	PROPN
ejpam-5856	595	2	.	.	PUNCT
ejpam-5856	595	3	palermo	palermo	NOUN
ejpam-5856	595	4	,	,	PUNCT
ejpam-5856	595	5	19(2):89	19(2):89	NUM
ejpam-5856	595	6	–	–	PUNCT
ejpam-5856	595	7	96	96	NUM
ejpam-5856	595	8	,	,	PUNCT
ejpam-5856	595	9	1970	1970	NUM
ejpam-5856	595	10	.	.	PUNCT
ejpam-5856	596	1	[	[	X
ejpam-5856	596	2	30	30	NUM
ejpam-5856	596	3	]	]	X
ejpam-5856	596	4	n.	n.	PROPN
ejpam-5856	596	5	levine	levine	PROPN
ejpam-5856	596	6	.	.	PUNCT
ejpam-5856	597	1	semi	semi	ADJ
ejpam-5856	597	2	-	-	ADJ
ejpam-5856	597	3	open	open	ADJ
ejpam-5856	597	4	sets	set	NOUN
ejpam-5856	597	5	and	and	CCONJ
ejpam-5856	597	6	semi	semi	ADJ
ejpam-5856	597	7	-	-	NOUN
ejpam-5856	597	8	continuity	continuity	NOUN
ejpam-5856	597	9	in	in	ADP
ejpam-5856	597	10	topological	topological	ADJ
ejpam-5856	597	11	spaces	space	NOUN
ejpam-5856	597	12	.	.	PUNCT
ejpam-5856	598	1	amer	amer	PROPN
ejpam-5856	598	2	.	.	PUNCT
ejpam-5856	598	3	math	math	PROPN
ejpam-5856	598	4	.	.	PUNCT
ejpam-5856	599	1	monthly	monthly	ADJ
ejpam-5856	599	2	,	,	PUNCT
ejpam-5856	599	3	36:41–70	36:41–70	PROPN
ejpam-5856	599	4	,	,	PUNCT
ejpam-5856	599	5	1963	1963	NUM
ejpam-5856	599	6	.	.	PUNCT
ejpam-5856	600	1	[	[	X
ejpam-5856	600	2	31	31	NUM
ejpam-5856	600	3	]	]	X
ejpam-5856	600	4	d.	d.	PROPN
ejpam-5856	600	5	mandal	mandal	PROPN
ejpam-5856	600	6	and	and	CCONJ
ejpam-5856	600	7	m.	m.	PROPN
ejpam-5856	600	8	n.	n.	PROPN
ejpam-5856	600	9	mukherjee	mukherjee	PROPN
ejpam-5856	600	10	.	.	PUNCT
ejpam-5856	601	1	some	some	DET
ejpam-5856	601	2	classes	class	NOUN
ejpam-5856	601	3	of	of	ADP
ejpam-5856	601	4	fuzzy	fuzzy	ADJ
ejpam-5856	601	5	sets	set	NOUN
ejpam-5856	601	6	in	in	ADP
ejpam-5856	601	7	a	a	DET
ejpam-5856	601	8	generalized	generalized	ADJ
ejpam-5856	601	9	fuzzy	fuzzy	ADJ
ejpam-5856	601	10	topological	topological	ADJ
ejpam-5856	601	11	spaces	space	NOUN
ejpam-5856	601	12	and	and	CCONJ
ejpam-5856	601	13	certain	certain	ADJ
ejpam-5856	601	14	unifications	unification	NOUN
ejpam-5856	601	15	.	.	PUNCT
ejpam-5856	602	1	ann	ann	PROPN
ejpam-5856	602	2	.	.	PUNCT
ejpam-5856	602	3	fuzzy	fuzzy	ADJ
ejpam-5856	602	4	math	math	NOUN
ejpam-5856	602	5	.	.	PUNCT
ejpam-5856	603	1	inform	inform	NOUN
ejpam-5856	603	2	.	.	PUNCT
ejpam-5856	603	3	,	,	PUNCT
ejpam-5856	603	4	7(6):949–957	7(6):949–957	NOUN
ejpam-5856	603	5	,	,	PUNCT
ejpam-5856	603	6	2014	2014	NUM
ejpam-5856	603	7	.	.	PUNCT
ejpam-5856	604	1	[	[	X
ejpam-5856	604	2	32	32	NUM
ejpam-5856	604	3	]	]	PUNCT
ejpam-5856	604	4	m.	m.	NOUN
ejpam-5856	604	5	n.	n.	PROPN
ejpam-5856	604	6	mukherjee	mukherjee	PROPN
ejpam-5856	604	7	and	and	CCONJ
ejpam-5856	604	8	s.	s.	PROPN
ejpam-5856	604	9	p.	p.	PROPN
ejpam-5856	604	10	sinha	sinha	PROPN
ejpam-5856	604	11	.	.	PUNCT
ejpam-5856	605	1	on	on	ADP
ejpam-5856	605	2	some	some	DET
ejpam-5856	605	3	near	near	ADV
ejpam-5856	605	4	-	-	PUNCT
ejpam-5856	605	5	fuzzy	fuzzy	ADJ
ejpam-5856	605	6	continuous	continuous	ADJ
ejpam-5856	605	7	functions	function	NOUN
ejpam-5856	605	8	between	between	ADP
ejpam-5856	605	9	s.	s.	PROPN
ejpam-5856	605	10	saleh	saleh	PROPN
ejpam-5856	605	11	et	et	PROPN
ejpam-5856	605	12	al	al	PROPN
ejpam-5856	605	13	.	.	PUNCT
ejpam-5856	605	14	/	/	SYM
ejpam-5856	605	15	eur	eur	PROPN
ejpam-5856	605	16	.	.	PUNCT
ejpam-5856	606	1	j.	j.	PROPN
ejpam-5856	606	2	pure	pure	PROPN
ejpam-5856	606	3	appl	appl	PROPN
ejpam-5856	606	4	.	.	PROPN
ejpam-5856	606	5	math	math	PROPN
ejpam-5856	606	6	,	,	PUNCT
ejpam-5856	606	7	18	18	NUM
ejpam-5856	606	8	(	(	PUNCT
ejpam-5856	606	9	1	1	NUM
ejpam-5856	606	10	)	)	PUNCT
ejpam-5856	606	11	(	(	PUNCT
ejpam-5856	606	12	2025	2025	NUM
ejpam-5856	606	13	)	)	PUNCT
ejpam-5856	606	14	,	,	PUNCT
ejpam-5856	606	15	5856	5856	NUM
ejpam-5856	606	16	15	15	NUM
ejpam-5856	606	17	of	of	ADP
ejpam-5856	606	18	15	15	NUM
ejpam-5856	606	19	fuzzy	fuzzy	ADJ
ejpam-5856	606	20	topological	topological	ADJ
ejpam-5856	606	21	spaces	space	NOUN
ejpam-5856	606	22	.	.	PUNCT
ejpam-5856	607	1	fuzzy	fuzzy	ADJ
ejpam-5856	607	2	sets	set	NOUN
ejpam-5856	607	3	and	and	CCONJ
ejpam-5856	607	4	systems	system	NOUN
ejpam-5856	607	5	,	,	PUNCT
ejpam-5856	607	6	34:245–254	34:245–254	NUM
ejpam-5856	607	7	,	,	PUNCT
ejpam-5856	607	8	1990	1990	NUM
ejpam-5856	607	9	.	.	PUNCT
ejpam-5856	608	1	[	[	X
ejpam-5856	608	2	33	33	NUM
ejpam-5856	608	3	]	]	PUNCT
ejpam-5856	608	4	m.	m.	NOUN
ejpam-5856	608	5	navaneethakrishnan	navaneethakrishnan	NOUN
ejpam-5856	608	6	and	and	CCONJ
ejpam-5856	608	7	j.	j.	PROPN
ejpam-5856	608	8	p.	p.	PROPN
ejpam-5856	608	9	joseph	joseph	PROPN
ejpam-5856	608	10	.	.	PUNCT
ejpam-5856	609	1	g	g	NOUN
ejpam-5856	609	2	-	-	PUNCT
ejpam-5856	609	3	closed	close	VERB
ejpam-5856	609	4	sets	set	NOUN
ejpam-5856	609	5	in	in	ADP
ejpam-5856	609	6	ideal	ideal	ADJ
ejpam-5856	609	7	topological	topological	ADJ
ejpam-5856	609	8	spaces	space	NOUN
ejpam-5856	609	9	.	.	PUNCT
ejpam-5856	610	1	acta	acta	PROPN
ejpam-5856	610	2	math	math	PROPN
ejpam-5856	610	3	.	.	PUNCT
ejpam-5856	611	1	hungar	hungar	PROPN
ejpam-5856	611	2	.	.	PUNCT
ejpam-5856	611	3	,	,	PUNCT
ejpam-5856	611	4	119:365–371	119:365–371	NUM
ejpam-5856	611	5	,	,	PUNCT
ejpam-5856	611	6	2008	2008	NUM
ejpam-5856	611	7	.	.	PUNCT
ejpam-5856	612	1	[	[	X
ejpam-5856	612	2	34	34	NUM
ejpam-5856	612	3	]	]	X
ejpam-5856	612	4	m.	m.	NOUN
ejpam-5856	612	5	navaneethakrishnan	navaneethakrishnan	PROPN
ejpam-5856	612	6	,	,	PUNCT
ejpam-5856	612	7	j.	j.	PROPN
ejpam-5856	612	8	p.	p.	PROPN
ejpam-5856	612	9	joseph	joseph	PROPN
ejpam-5856	612	10	,	,	PUNCT
ejpam-5856	612	11	and	and	CCONJ
ejpam-5856	612	12	d.	d.	PROPN
ejpam-5856	612	13	sivaraj	sivaraj	PROPN
ejpam-5856	612	14	.	.	PUNCT
ejpam-5856	613	1	ig	ig	ADJ
ejpam-5856	613	2	-	-	ADJ
ejpam-5856	613	3	normal	normal	ADJ
ejpam-5856	613	4	and	and	CCONJ
ejpam-5856	613	5	ig	ig	ADJ
ejpam-5856	613	6	-	-	ADJ
ejpam-5856	613	7	regular	regular	ADJ
ejpam-5856	613	8	spaces	space	NOUN
ejpam-5856	613	9	.	.	PUNCT
ejpam-5856	614	1	acta	acta	PROPN
ejpam-5856	614	2	math	math	PROPN
ejpam-5856	614	3	.	.	PUNCT
ejpam-5856	615	1	hungar	hungar	PROPN
ejpam-5856	615	2	.	.	PUNCT
ejpam-5856	615	3	,	,	PUNCT
ejpam-5856	615	4	125:327–340	125:327–340	NUM
ejpam-5856	615	5	,	,	PUNCT
ejpam-5856	615	6	2009	2009	NUM
ejpam-5856	615	7	.	.	PUNCT
ejpam-5856	616	1	[	[	X
ejpam-5856	616	2	35	35	NUM
ejpam-5856	616	3	]	]	PUNCT
ejpam-5856	616	4	t.	t.	PROPN
ejpam-5856	616	5	noiri	noiri	PROPN
ejpam-5856	616	6	and	and	CCONJ
ejpam-5856	616	7	v.	v.	ADP
ejpam-5856	616	8	popa	popa	NOUN
ejpam-5856	616	9	.	.	PUNCT
ejpam-5856	617	1	on	on	ADP
ejpam-5856	617	2	g	g	NOUN
ejpam-5856	617	3	-	-	PUNCT
ejpam-5856	617	4	regular	regular	ADJ
ejpam-5856	617	5	spaces	space	NOUN
ejpam-5856	617	6	and	and	CCONJ
ejpam-5856	617	7	some	some	DET
ejpam-5856	617	8	functions	function	NOUN
ejpam-5856	617	9	.	.	PUNCT
ejpam-5856	618	1	mem	mem	PROPN
ejpam-5856	618	2	.	.	PUNCT
ejpam-5856	618	3	fac	fac	PROPN
ejpam-5856	618	4	.	.	PUNCT
ejpam-5856	619	1	sci	sci	PROPN
ejpam-5856	619	2	.	.	PROPN
ejpam-5856	619	3	kochi	kochi	PROPN
ejpam-5856	619	4	univ	univ	PROPN
ejpam-5856	619	5	.	.	PUNCT
ejpam-5856	620	1	(	(	PUNCT
ejpam-5856	620	2	math	math	NOUN
ejpam-5856	620	3	.	.	PUNCT
ejpam-5856	620	4	)	)	PUNCT
ejpam-5856	620	5	,	,	PUNCT
ejpam-5856	621	1	20:67	20:67	NUM
ejpam-5856	621	2	,	,	PUNCT
ejpam-5856	621	3	1999	1999	NUM
ejpam-5856	621	4	.	.	PUNCT
ejpam-5856	622	1	[	[	X
ejpam-5856	622	2	36	36	NUM
ejpam-5856	622	3	]	]	X
ejpam-5856	622	4	r.	r.	PROPN
ejpam-5856	622	5	parimelazhagan	parimelazhagan	PROPN
ejpam-5856	622	6	and	and	CCONJ
ejpam-5856	622	7	v.	v.	ADP
ejpam-5856	622	8	subramoniapillai	subramoniapillai	PROPN
ejpam-5856	622	9	.	.	PUNCT
ejpam-5856	623	1	strongly	strongly	ADV
ejpam-5856	623	2	g∗-closed	g∗-close	VERB
ejpam-5856	623	3	sets	set	NOUN
ejpam-5856	623	4	in	in	ADP
ejpam-5856	623	5	topological	topological	ADJ
ejpam-5856	623	6	spaces	space	NOUN
ejpam-5856	623	7	.	.	PUNCT
ejpam-5856	624	1	int	int	NOUN
ejpam-5856	624	2	.	.	PUNCT
ejpam-5856	625	1	j.	j.	PROPN
ejpam-5856	625	2	math	math	PROPN
ejpam-5856	625	3	.	.	PUNCT
ejpam-5856	626	1	anal	anal	PROPN
ejpam-5856	626	2	.	.	PROPN
ejpam-5856	626	3	,	,	PUNCT
ejpam-5856	626	4	6(30):1481–1489	6(30):1481–1489	NOUN
ejpam-5856	626	5	,	,	PUNCT
ejpam-5856	626	6	2012	2012	NUM
ejpam-5856	626	7	.	.	PUNCT
ejpam-5856	627	1	[	[	X
ejpam-5856	627	2	37	37	NUM
ejpam-5856	627	3	]	]	PUNCT
ejpam-5856	627	4	j.	j.	PROPN
ejpam-5856	627	5	h.	h.	PROPN
ejpam-5856	627	6	park	park	PROPN
ejpam-5856	627	7	and	and	CCONJ
ejpam-5856	627	8	j.	j.	PROPN
ejpam-5856	627	9	k.	k.	PROPN
ejpam-5856	627	10	park	park	PROPN
ejpam-5856	627	11	.	.	PUNCT
ejpam-5856	628	1	on	on	ADP
ejpam-5856	628	2	regular	regular	ADJ
ejpam-5856	628	3	generalized	generalize	VERB
ejpam-5856	628	4	fuzzy	fuzzy	ADJ
ejpam-5856	628	5	closed	close	VERB
ejpam-5856	628	6	sets	set	NOUN
ejpam-5856	628	7	and	and	CCONJ
ejpam-5856	628	8	generalizations	generalization	NOUN
ejpam-5856	628	9	of	of	ADP
ejpam-5856	628	10	fuzzy	fuzzy	ADJ
ejpam-5856	628	11	continuous	continuous	ADJ
ejpam-5856	628	12	functions	function	NOUN
ejpam-5856	628	13	.	.	PUNCT
ejpam-5856	629	1	ind	ind	NOUN
ejpam-5856	629	2	.	.	PUNCT
ejpam-5856	630	1	j.	j.	PROPN
ejpam-5856	630	2	pure	pure	PROPN
ejpam-5856	630	3	appl	appl	PROPN
ejpam-5856	630	4	.	.	PUNCT
ejpam-5856	630	5	math	math	PROPN
ejpam-5856	630	6	.	.	PUNCT
ejpam-5856	630	7	,	,	PUNCT
ejpam-5856	630	8	34(7):1013–1024	34(7):1013–1024	NUM
ejpam-5856	630	9	,	,	PUNCT
ejpam-5856	630	10	2003	2003	NUM
ejpam-5856	630	11	.	.	PUNCT
ejpam-5856	631	1	[	[	X
ejpam-5856	631	2	38	38	NUM
ejpam-5856	631	3	]	]	PUNCT
ejpam-5856	631	4	j.	j.	PROPN
ejpam-5856	631	5	k.	k.	PROPN
ejpam-5856	631	6	park	park	PROPN
ejpam-5856	631	7	and	and	CCONJ
ejpam-5856	631	8	j.	j.	PROPN
ejpam-5856	631	9	h.	h.	PROPN
ejpam-5856	631	10	park	park	PROPN
ejpam-5856	631	11	.	.	PUNCT
ejpam-5856	632	1	mildly	mildly	ADV
ejpam-5856	632	2	generalized	generalize	VERB
ejpam-5856	632	3	closed	closed	ADJ
ejpam-5856	632	4	sets	set	NOUN
ejpam-5856	632	5	,	,	PUNCT
ejpam-5856	632	6	almost	almost	ADV
ejpam-5856	632	7	normal	normal	ADJ
ejpam-5856	632	8	and	and	CCONJ
ejpam-5856	632	9	mildly	mildly	ADV
ejpam-5856	632	10	normal	normal	ADJ
ejpam-5856	632	11	spaces	space	NOUN
ejpam-5856	632	12	.	.	PUNCT
ejpam-5856	633	1	chaos	chaos	NOUN
ejpam-5856	633	2	,	,	PUNCT
ejpam-5856	633	3	solitons	soliton	NOUN
ejpam-5856	633	4	and	and	CCONJ
ejpam-5856	633	5	fractals	fractal	NOUN
ejpam-5856	633	6	,	,	PUNCT
ejpam-5856	633	7	20:1103–1111	20:1103–1111	NUM
ejpam-5856	633	8	,	,	PUNCT
ejpam-5856	633	9	2004	2004	NUM
ejpam-5856	633	10	.	.	PUNCT
ejpam-5856	634	1	[	[	X
ejpam-5856	634	2	39	39	NUM
ejpam-5856	634	3	]	]	PUNCT
ejpam-5856	634	4	pao	pao	PROPN
ejpam-5856	634	5	-	-	PROPN
ejpam-5856	634	6	ming	ming	PROPN
ejpam-5856	634	7	pu	pu	PROPN
ejpam-5856	634	8	and	and	CCONJ
ejpam-5856	634	9	ying	ying	PROPN
ejpam-5856	634	10	-	-	PUNCT
ejpam-5856	634	11	ming	ming	PROPN
ejpam-5856	634	12	liu	liu	PROPN
ejpam-5856	634	13	.	.	PUNCT
ejpam-5856	635	1	fuzzy	fuzzy	ADJ
ejpam-5856	635	2	topology	topology	PROPN
ejpam-5856	635	3	i.	i.	PROPN
ejpam-5856	635	4	neighborhood	neighborhood	PROPN
ejpam-5856	635	5	structure	structure	NOUN
ejpam-5856	635	6	of	of	ADP
ejpam-5856	635	7	a	a	DET
ejpam-5856	635	8	fuzzy	fuzzy	ADJ
ejpam-5856	635	9	point	point	NOUN
ejpam-5856	635	10	and	and	CCONJ
ejpam-5856	635	11	moore	moore	PROPN
ejpam-5856	635	12	-	-	PUNCT
ejpam-5856	635	13	smith	smith	PROPN
ejpam-5856	635	14	convergence	convergence	NOUN
ejpam-5856	635	15	.	.	PUNCT
ejpam-5856	636	1	j.	j.	PROPN
ejpam-5856	636	2	math	math	PROPN
ejpam-5856	636	3	.	.	PUNCT
ejpam-5856	637	1	anal	anal	PROPN
ejpam-5856	637	2	.	.	PUNCT
ejpam-5856	638	1	appl	appl	PROPN
ejpam-5856	638	2	.	.	PROPN
ejpam-5856	638	3	,	,	PUNCT
ejpam-5856	639	1	76:571–599	76:571–599	NUM
ejpam-5856	639	2	,	,	PUNCT
ejpam-5856	639	3	1980	1980	NUM
ejpam-5856	639	4	.	.	PUNCT
ejpam-5856	640	1	[	[	X
ejpam-5856	640	2	40	40	NUM
ejpam-5856	640	3	]	]	PUNCT
ejpam-5856	640	4	t.	t.	PROPN
ejpam-5856	640	5	rajendrakumar	rajendrakumar	PROPN
ejpam-5856	640	6	and	and	CCONJ
ejpam-5856	640	7	g.	g.	PROPN
ejpam-5856	640	8	anandajothi	anandajothi	PROPN
ejpam-5856	640	9	.	.	PUNCT
ejpam-5856	641	1	on	on	ADP
ejpam-5856	641	2	fuzzy	fuzzy	ADJ
ejpam-5856	641	3	strongly	strongly	ADV
ejpam-5856	641	4	g	g	NOUN
ejpam-5856	641	5	-	-	PUNCT
ejpam-5856	641	6	closed	close	VERB
ejpam-5856	641	7	sets	set	NOUN
ejpam-5856	641	8	in	in	ADP
ejpam-5856	641	9	fuzzy	fuzzy	ADJ
ejpam-5856	641	10	topological	topological	ADJ
ejpam-5856	641	11	spaces	space	NOUN
ejpam-5856	641	12	.	.	PUNCT
ejpam-5856	642	1	intern	intern	PROPN
ejpam-5856	642	2	.	.	PUNCT
ejpam-5856	643	1	j.	j.	PROPN
ejpam-5856	643	2	fuzzy	fuzzy	PROPN
ejpam-5856	643	3	mathematical	mathematical	PROPN
ejpam-5856	643	4	archive	archive	NOUN
ejpam-5856	643	5	,	,	PUNCT
ejpam-5856	643	6	3:68–75	3:68–75	NUM
ejpam-5856	643	7	,	,	PUNCT
ejpam-5856	643	8	2013	2013	NUM
ejpam-5856	643	9	.	.	PUNCT
ejpam-5856	644	1	[	[	X
ejpam-5856	644	2	41	41	NUM
ejpam-5856	644	3	]	]	X
ejpam-5856	644	4	s.	s.	PROPN
ejpam-5856	644	5	saleh	saleh	PROPN
ejpam-5856	644	6	,	,	PUNCT
ejpam-5856	644	7	r.	r.	PROPN
ejpam-5856	644	8	abu	abu	PROPN
ejpam-5856	644	9	-	-	PUNCT
ejpam-5856	644	10	gdairi	gdairi	PROPN
ejpam-5856	644	11	,	,	PUNCT
ejpam-5856	644	12	t.	t.	PROPN
ejpam-5856	644	13	m.	m.	PROPN
ejpam-5856	644	14	al	al	PROPN
ejpam-5856	644	15	-	-	PUNCT
ejpam-5856	644	16	shami	shami	PROPN
ejpam-5856	644	17	,	,	PUNCT
ejpam-5856	644	18	and	and	CCONJ
ejpam-5856	644	19	mohammed	mohammed	PROPN
ejpam-5856	644	20	s.	s.	PROPN
ejpam-5856	644	21	abdo	abdo	PROPN
ejpam-5856	644	22	.	.	PUNCT
ejpam-5856	645	1	on	on	ADP
ejpam-5856	645	2	categorical	categorical	ADJ
ejpam-5856	645	3	property	property	NOUN
ejpam-5856	645	4	of	of	ADP
ejpam-5856	645	5	fuzzy	fuzzy	ADJ
ejpam-5856	645	6	soft	soft	ADJ
ejpam-5856	645	7	topological	topological	ADJ
ejpam-5856	645	8	spaces	space	NOUN
ejpam-5856	645	9	.	.	PUNCT
ejpam-5856	646	1	applied	apply	VERB
ejpam-5856	646	2	mathematics	mathematics	PROPN
ejpam-5856	646	3	&	&	CCONJ
ejpam-5856	646	4	information	information	NOUN
ejpam-5856	646	5	sciences	sciences	PROPN
ejpam-5856	646	6	,	,	PUNCT
ejpam-5856	646	7	16(4):635–641	16(4):635–641	PROPN
ejpam-5856	646	8	,	,	PUNCT
ejpam-5856	646	9	2022	2022	NUM
ejpam-5856	646	10	.	.	PUNCT
ejpam-5856	647	1	[	[	X
ejpam-5856	647	2	42	42	NUM
ejpam-5856	647	3	]	]	PUNCT
ejpam-5856	647	4	s.	s.	PROPN
ejpam-5856	647	5	saleh	saleh	PROPN
ejpam-5856	647	6	,	,	PUNCT
ejpam-5856	647	7	t.	t.	PROPN
ejpam-5856	647	8	m.	m.	PROPN
ejpam-5856	647	9	al	al	PROPN
ejpam-5856	647	10	-	-	PUNCT
ejpam-5856	647	11	shami	shami	PROPN
ejpam-5856	647	12	,	,	PUNCT
ejpam-5856	647	13	a.	a.	PROPN
ejpam-5856	647	14	a.	a.	NOUN
ejpam-5856	647	15	azzam	azzam	PROPN
ejpam-5856	647	16	,	,	PUNCT
ejpam-5856	647	17	and	and	CCONJ
ejpam-5856	647	18	m.	m.	PROPN
ejpam-5856	647	19	hosny	hosny	PROPN
ejpam-5856	647	20	.	.	PUNCT
ejpam-5856	648	1	stronger	strong	ADJ
ejpam-5856	648	2	forms	form	NOUN
ejpam-5856	648	3	of	of	ADP
ejpam-5856	648	4	fuzzy	fuzzy	ADJ
ejpam-5856	648	5	pre	pre	NOUN
ejpam-5856	648	6	-	-	NOUN
ejpam-5856	648	7	separation	separation	NOUN
ejpam-5856	648	8	and	and	CCONJ
ejpam-5856	648	9	regularity	regularity	NOUN
ejpam-5856	648	10	axioms	axiom	NOUN
ejpam-5856	648	11	via	via	ADP
ejpam-5856	648	12	fuzzy	fuzzy	ADJ
ejpam-5856	648	13	topology	topology	NOUN
ejpam-5856	648	14	.	.	PUNCT
ejpam-5856	649	1	mathematics	mathematic	NOUN
ejpam-5856	649	2	,	,	PUNCT
ejpam-5856	649	3	11(23):4801	11(23):4801	NUM
ejpam-5856	649	4	,	,	PUNCT
ejpam-5856	649	5	2023	2023	NUM
ejpam-5856	649	6	.	.	PUNCT
ejpam-5856	650	1	[	[	X
ejpam-5856	650	2	43	43	NUM
ejpam-5856	650	3	]	]	X
ejpam-5856	650	4	s.	s.	PROPN
ejpam-5856	650	5	saleh	saleh	PROPN
ejpam-5856	650	6	,	,	PUNCT
ejpam-5856	650	7	t.	t.	PROPN
ejpam-5856	650	8	m.	m.	PROPN
ejpam-5856	650	9	al	al	PROPN
ejpam-5856	650	10	-	-	PUNCT
ejpam-5856	650	11	shami	shami	PROPN
ejpam-5856	650	12	,	,	PUNCT
ejpam-5856	650	13	l.	l.	PROPN
ejpam-5856	650	14	r.	r.	PROPN
ejpam-5856	650	15	flaih	flaih	PROPN
ejpam-5856	650	16	,	,	PUNCT
ejpam-5856	650	17	m.	m.	NOUN
ejpam-5856	650	18	arar	arar	PROPN
ejpam-5856	650	19	,	,	PUNCT
ejpam-5856	650	20	and	and	CCONJ
ejpam-5856	650	21	r.	r.	PROPN
ejpam-5856	650	22	abu	abu	PROPN
ejpam-5856	650	23	-	-	PUNCT
ejpam-5856	650	24	gdairi	gdairi	PROPN
ejpam-5856	650	25	.	.	PUNCT
ejpam-5856	651	1	ri	ri	NOUN
ejpam-5856	651	2	-	-	PUNCT
ejpam-5856	651	3	separation	separation	NOUN
ejpam-5856	651	4	axioms	axiom	NOUN
ejpam-5856	651	5	via	via	ADP
ejpam-5856	651	6	supra	supra	PROPN
ejpam-5856	651	7	soft	soft	ADJ
ejpam-5856	651	8	topological	topological	ADJ
ejpam-5856	651	9	spaces	space	NOUN
ejpam-5856	651	10	.	.	PUNCT
ejpam-5856	652	1	journal	journal	NOUN
ejpam-5856	652	2	of	of	ADP
ejpam-5856	652	3	mathematics	mathematic	NOUN
ejpam-5856	652	4	and	and	CCONJ
ejpam-5856	652	5	computer	computer	NOUN
ejpam-5856	652	6	science	science	NOUN
ejpam-5856	652	7	,	,	PUNCT
ejpam-5856	652	8	32(3):263–274	32(3):263–274	PROPN
ejpam-5856	652	9	,	,	PUNCT
ejpam-5856	652	10	2024	2024	NUM
ejpam-5856	652	11	.	.	PUNCT
ejpam-5856	653	1	[	[	X
ejpam-5856	653	2	44	44	NUM
ejpam-5856	653	3	]	]	PUNCT
ejpam-5856	653	4	s.	s.	PROPN
ejpam-5856	653	5	saleh	saleh	PROPN
ejpam-5856	653	6	,	,	PUNCT
ejpam-5856	653	7	t.	t.	PROPN
ejpam-5856	653	8	m.	m.	PROPN
ejpam-5856	653	9	al	al	PROPN
ejpam-5856	653	10	-	-	PUNCT
ejpam-5856	653	11	shami	shami	PROPN
ejpam-5856	653	12	,	,	PUNCT
ejpam-5856	653	13	and	and	CCONJ
ejpam-5856	653	14	a.	a.	NOUN
ejpam-5856	653	15	mhemdi	mhemdi	PROPN
ejpam-5856	653	16	.	.	PUNCT
ejpam-5856	654	1	on	on	ADP
ejpam-5856	654	2	some	some	DET
ejpam-5856	654	3	new	new	ADJ
ejpam-5856	654	4	types	type	NOUN
ejpam-5856	654	5	of	of	ADP
ejpam-5856	654	6	fuzzy	fuzzy	ADJ
ejpam-5856	654	7	soft	soft	ADJ
ejpam-5856	654	8	compact	compact	ADJ
ejpam-5856	654	9	spaces	space	NOUN
ejpam-5856	654	10	.	.	PUNCT
ejpam-5856	655	1	journal	journal	NOUN
ejpam-5856	655	2	of	of	ADP
ejpam-5856	655	3	mathematics	mathematic	NOUN
ejpam-5856	655	4	,	,	PUNCT
ejpam-5856	655	5	2023	2023	NUM
ejpam-5856	655	6	:	:	PUNCT
ejpam-5856	655	7	article	article	NOUN
ejpam-5856	655	8	i	i	PROPN
ejpam-5856	655	9	d	d	PROPN
ejpam-5856	655	10	5065592	5065592	NUM
ejpam-5856	655	11	,	,	PUNCT
ejpam-5856	655	12	8	8	NUM
ejpam-5856	655	13	pages	page	NOUN
ejpam-5856	655	14	,	,	PUNCT
ejpam-5856	655	15	2023	2023	NUM
ejpam-5856	655	16	.	.	PUNCT
ejpam-5856	656	1	[	[	X
ejpam-5856	656	2	45	45	NUM
ejpam-5856	656	3	]	]	PUNCT
ejpam-5856	656	4	r.	r.	PROPN
ejpam-5856	656	5	k.	k.	PROPN
ejpam-5856	656	6	saraf	saraf	PROPN
ejpam-5856	656	7	,	,	PUNCT
ejpam-5856	656	8	g.	g.	PROPN
ejpam-5856	656	9	navalagi	navalagi	PROPN
ejpam-5856	656	10	,	,	PUNCT
ejpam-5856	656	11	and	and	CCONJ
ejpam-5856	656	12	m.	m.	NOUN
ejpam-5856	656	13	khanna	khanna	PROPN
ejpam-5856	656	14	.	.	PUNCT
ejpam-5856	657	1	on	on	ADP
ejpam-5856	657	2	fuzzy	fuzzy	ADJ
ejpam-5856	657	3	semi	semi	ADJ
ejpam-5856	657	4	-	-	ADJ
ejpam-5856	657	5	pre	pre	ADJ
ejpam-5856	657	6	-	-	ADJ
ejpam-5856	657	7	generalized	generalized	ADJ
ejpam-5856	657	8	closed	closed	ADJ
ejpam-5856	657	9	sets	set	NOUN
ejpam-5856	657	10	.	.	PUNCT
ejpam-5856	658	1	bull	bull	NOUN
ejpam-5856	658	2	.	.	PUNCT
ejpam-5856	659	1	malays	malays	PROPN
ejpam-5856	659	2	.	.	PUNCT
ejpam-5856	660	1	math	math	NOUN
ejpam-5856	660	2	.	.	PUNCT
ejpam-5856	661	1	sci	sci	PROPN
ejpam-5856	661	2	.	.	PROPN
ejpam-5856	661	3	soc	soc	PROPN
ejpam-5856	661	4	.	.	PUNCT
ejpam-5856	661	5	,	,	PUNCT
ejpam-5856	661	6	28(1):19–30	28(1):19–30	NUM
ejpam-5856	661	7	,	,	PUNCT
ejpam-5856	661	8	2005	2005	NUM
ejpam-5856	661	9	.	.	PUNCT
ejpam-5856	662	1	[	[	X
ejpam-5856	662	2	46	46	NUM
ejpam-5856	662	3	]	]	X
ejpam-5856	662	4	v.	v.	CCONJ
ejpam-5856	662	5	sharma	sharma	PROPN
ejpam-5856	662	6	,	,	PUNCT
ejpam-5856	662	7	r.	r.	PROPN
ejpam-5856	662	8	kumar	kumar	PROPN
ejpam-5856	662	9	,	,	PUNCT
ejpam-5856	662	10	and	and	CCONJ
ejpam-5856	662	11	m.	m.	NOUN
ejpam-5856	662	12	patel	patel	PROPN
ejpam-5856	662	13	.	.	PUNCT
ejpam-5856	663	1	fuzzy	fuzzy	ADJ
ejpam-5856	663	2	image	image	NOUN
ejpam-5856	663	3	processing	processing	NOUN
ejpam-5856	663	4	:	:	PUNCT
ejpam-5856	663	5	techniques	technique	NOUN
ejpam-5856	663	6	and	and	CCONJ
ejpam-5856	663	7	applications	application	NOUN
ejpam-5856	663	8	.	.	PUNCT
ejpam-5856	664	1	pattern	pattern	NOUN
ejpam-5856	664	2	recognition	recognition	NOUN
ejpam-5856	664	3	letters	letter	NOUN
ejpam-5856	664	4	,	,	PUNCT
ejpam-5856	664	5	142:45–60	142:45–60	NUM
ejpam-5856	664	6	,	,	PUNCT
ejpam-5856	664	7	2023	2023	NUM
ejpam-5856	664	8	.	.	PUNCT
ejpam-5856	665	1	[	[	X
ejpam-5856	665	2	47	47	NUM
ejpam-5856	665	3	]	]	PUNCT
ejpam-5856	665	4	j.	j.	PROPN
ejpam-5856	665	5	smith	smith	PROPN
ejpam-5856	665	6	and	and	CCONJ
ejpam-5856	665	7	a.	a.	PROPN
ejpam-5856	665	8	gupta	gupta	PROPN
ejpam-5856	665	9	.	.	PUNCT
ejpam-5856	666	1	fuzzy	fuzzy	ADJ
ejpam-5856	666	2	logic	logic	NOUN
ejpam-5856	666	3	in	in	ADP
ejpam-5856	666	4	artificial	artificial	ADJ
ejpam-5856	666	5	intelligence	intelligence	NOUN
ejpam-5856	666	6	:	:	PUNCT
ejpam-5856	666	7	current	current	ADJ
ejpam-5856	666	8	trends	trend	NOUN
ejpam-5856	666	9	and	and	CCONJ
ejpam-5856	666	10	future	future	ADJ
ejpam-5856	666	11	directions	direction	NOUN
ejpam-5856	666	12	.	.	PUNCT
ejpam-5856	667	1	artificial	artificial	ADJ
ejpam-5856	667	2	intelligence	intelligence	NOUN
ejpam-5856	667	3	review	review	NOUN
ejpam-5856	667	4	,	,	PUNCT
ejpam-5856	667	5	55(2):345–367	55(2):345–367	NUM
ejpam-5856	667	6	,	,	PUNCT
ejpam-5856	667	7	2022	2022	NUM
ejpam-5856	667	8	.	.	PUNCT
ejpam-5856	668	1	[	[	X
ejpam-5856	668	2	48	48	NUM
ejpam-5856	668	3	]	]	PUNCT
ejpam-5856	668	4	m.	m.	NOUN
ejpam-5856	668	5	k.	k.	PROPN
ejpam-5856	668	6	r.	r.	PROPN
ejpam-5856	668	7	s.	s.	PROPN
ejpam-5856	668	8	veera	veera	PROPN
ejpam-5856	668	9	kumar	kumar	PROPN
ejpam-5856	668	10	.	.	PROPN
ejpam-5856	668	11	between	between	ADP
ejpam-5856	668	12	closed	close	VERB
ejpam-5856	668	13	sets	set	NOUN
ejpam-5856	668	14	and	and	CCONJ
ejpam-5856	668	15	g	g	NOUN
ejpam-5856	668	16	-	-	PUNCT
ejpam-5856	668	17	closed	close	VERB
ejpam-5856	668	18	sets	set	NOUN
ejpam-5856	668	19	.	.	PUNCT
ejpam-5856	669	1	mem	mem	PROPN
ejpam-5856	669	2	.	.	PUNCT
ejpam-5856	669	3	fac	fac	PROPN
ejpam-5856	669	4	.	.	PUNCT
ejpam-5856	670	1	sci	sci	PROPN
ejpam-5856	670	2	.	.	PROPN
ejpam-5856	670	3	kochi	kochi	PROPN
ejpam-5856	670	4	univ	univ	PROPN
ejpam-5856	670	5	.	.	PUNCT
ejpam-5856	671	1	(	(	PUNCT
ejpam-5856	671	2	math	math	NOUN
ejpam-5856	671	3	.	.	PUNCT
ejpam-5856	671	4	)	)	PUNCT
ejpam-5856	671	5	,	,	PUNCT
ejpam-5856	671	6	21:1–19	21:1–19	NUM
ejpam-5856	671	7	,	,	PUNCT
ejpam-5856	671	8	2000	2000	NUM
ejpam-5856	671	9	.	.	PUNCT
ejpam-5856	672	1	[	[	X
ejpam-5856	672	2	49	49	NUM
ejpam-5856	672	3	]	]	PUNCT
ejpam-5856	672	4	l.	l.	PROPN
ejpam-5856	672	5	a.	a.	PROPN
ejpam-5856	672	6	zadeh	zadeh	PROPN
ejpam-5856	672	7	.	.	PUNCT
ejpam-5856	672	8	fuzzy	fuzzy	ADJ
ejpam-5856	672	9	sets	set	NOUN
ejpam-5856	672	10	.	.	PUNCT
ejpam-5856	673	1	information	information	NOUN
ejpam-5856	673	2	and	and	CCONJ
ejpam-5856	673	3	control	control	NOUN
ejpam-5856	673	4	,	,	PUNCT
ejpam-5856	673	5	8(3):338–353	8(3):338–353	NUM
ejpam-5856	673	6	,	,	PUNCT
ejpam-5856	673	7	1965	1965	NUM
ejpam-5856	673	8	.	.	PUNCT
ejpam-5856	674	1	[	[	X
ejpam-5856	674	2	50	50	NUM
ejpam-5856	674	3	]	]	PUNCT
ejpam-5856	674	4	q.	q.	PROPN
ejpam-5856	674	5	zhang	zhang	PROPN
ejpam-5856	674	6	,	,	PUNCT
ejpam-5856	674	7	l.	l.	PROPN
ejpam-5856	674	8	li	li	PROPN
ejpam-5856	674	9	,	,	PUNCT
ejpam-5856	674	10	and	and	CCONJ
ejpam-5856	674	11	t.	t.	PROPN
ejpam-5856	674	12	zhang	zhang	PROPN
ejpam-5856	674	13	.	.	PUNCT
ejpam-5856	674	14	fuzzy	fuzzy	ADJ
ejpam-5856	674	15	sets	set	NOUN
ejpam-5856	674	16	and	and	CCONJ
ejpam-5856	674	17	their	their	PRON
ejpam-5856	674	18	applications	application	NOUN
ejpam-5856	674	19	in	in	ADP
ejpam-5856	674	20	artificial	artificial	ADJ
ejpam-5856	674	21	intelligence	intelligence	NOUN
ejpam-5856	674	22	:	:	PUNCT
ejpam-5856	674	23	a	a	DET
ejpam-5856	674	24	review	review	NOUN
ejpam-5856	674	25	.	.	PUNCT
ejpam-5856	675	1	ieee	ieee	NOUN
ejpam-5856	675	2	transactions	transaction	NOUN
ejpam-5856	675	3	on	on	ADP
ejpam-5856	675	4	fuzzy	fuzzy	ADJ
ejpam-5856	675	5	systems	system	NOUN
ejpam-5856	675	6	,	,	PUNCT
ejpam-5856	675	7	31(3):789–804	31(3):789–804	NOUN
ejpam-5856	675	8	,	,	PUNCT
ejpam-5856	675	9	2023	2023	NUM
ejpam-5856	675	10	.	.	PUNCT