id	sid	tid	token	lemma	pos
ejpam-5027	1	1	european	european	PROPN
ejpam-5027	1	2	journal	journal	PROPN
ejpam-5027	1	3	of	of	ADP
ejpam-5027	1	4	pure	pure	ADJ
ejpam-5027	1	5	and	and	CCONJ
ejpam-5027	1	6	applied	apply	VERB
ejpam-5027	1	7	mathematics	mathematic	NOUN
ejpam-5027	1	8	vol	vol	NOUN
ejpam-5027	1	9	.	.	PROPN
ejpam-5027	2	1	17	17	NUM
ejpam-5027	2	2	,	,	PUNCT
ejpam-5027	2	3	no	no	INTJ
ejpam-5027	2	4	.	.	NOUN
ejpam-5027	2	5	1	1	NUM
ejpam-5027	2	6	,	,	PUNCT
ejpam-5027	2	7	2024	2024	NUM
ejpam-5027	2	8	,	,	PUNCT
ejpam-5027	2	9	30	30	NUM
ejpam-5027	2	10	-	-	SYM
ejpam-5027	2	11	41	41	NUM
ejpam-5027	2	12	issn	issn	PROPN
ejpam-5027	2	13	1307	1307	NUM
ejpam-5027	2	14	-	-	SYM
ejpam-5027	2	15	5543	5543	NUM
ejpam-5027	2	16	–	–	PUNCT
ejpam-5027	3	1	ejpam.com	ejpam.com	X
ejpam-5027	3	2	published	publish	VERB
ejpam-5027	3	3	by	by	ADP
ejpam-5027	3	4	new	new	PROPN
ejpam-5027	3	5	york	york	PROPN
ejpam-5027	3	6	business	business	PROPN
ejpam-5027	3	7	global	global	ADJ
ejpam-5027	3	8	generalized	generalized	ADJ
ejpam-5027	3	9	compactness	compactness	NOUN
ejpam-5027	3	10	in	in	ADP
ejpam-5027	3	11	fuzzy	fuzzy	ADJ
ejpam-5027	3	12	bitopological	bitopological	ADJ
ejpam-5027	3	13	spaces	space	NOUN
ejpam-5027	3	14	ahlam	ahlam	PROPN
ejpam-5027	3	15	ahmed	ahme	VERB
ejpam-5027	3	16	alharbi1,2	alharbi1,2	PROPN
ejpam-5027	3	17	,	,	PUNCT
ejpam-5027	3	18	adem	adem	PROPN
ejpam-5027	3	19	kilicman2,∗	kilicman2,∗	PROPN
ejpam-5027	3	20	1	1	NUM
ejpam-5027	3	21	department	department	NOUN
ejpam-5027	3	22	of	of	ADP
ejpam-5027	3	23	mathematics	mathematic	NOUN
ejpam-5027	3	24	,	,	PUNCT
ejpam-5027	3	25	faculty	faculty	NOUN
ejpam-5027	3	26	of	of	ADP
ejpam-5027	3	27	science	science	NOUN
ejpam-5027	3	28	,	,	PUNCT
ejpam-5027	3	29	taibah	taibah	PROPN
ejpam-5027	3	30	university	university	PROPN
ejpam-5027	3	31	,	,	PUNCT
ejpam-5027	3	32	madinah	madinah	PROPN
ejpam-5027	3	33	42353	42353	NUM
ejpam-5027	3	34	,	,	PUNCT
ejpam-5027	3	35	kingdom	kingdom	NOUN
ejpam-5027	3	36	of	of	ADP
ejpam-5027	3	37	saudi	saudi	PROPN
ejpam-5027	3	38	arabia	arabia	PROPN
ejpam-5027	3	39	2	2	NUM
ejpam-5027	3	40	department	department	NOUN
ejpam-5027	3	41	of	of	ADP
ejpam-5027	3	42	mathematics	mathematic	NOUN
ejpam-5027	3	43	and	and	CCONJ
ejpam-5027	3	44	statistics	statistic	NOUN
ejpam-5027	3	45	,	,	PUNCT
ejpam-5027	3	46	faculty	faculty	NOUN
ejpam-5027	3	47	of	of	ADP
ejpam-5027	3	48	science	science	PROPN
ejpam-5027	3	49	university	university	PROPN
ejpam-5027	3	50	putra	putra	PROPN
ejpam-5027	3	51	malaysia	malaysia	PROPN
ejpam-5027	3	52	,	,	PUNCT
ejpam-5027	3	53	43400	43400	NUM
ejpam-5027	3	54	upm	upm	PROPN
ejpam-5027	3	55	serdang	serdang	PROPN
ejpam-5027	3	56	,	,	PUNCT
ejpam-5027	3	57	selangor	selangor	PROPN
ejpam-5027	3	58	,	,	PUNCT
ejpam-5027	3	59	malaysia	malaysia	PROPN
ejpam-5027	3	60	abstract	abstract	NOUN
ejpam-5027	3	61	.	.	PUNCT
ejpam-5027	4	1	the	the	DET
ejpam-5027	4	2	main	main	ADJ
ejpam-5027	4	3	objective	objective	NOUN
ejpam-5027	4	4	of	of	ADP
ejpam-5027	4	5	this	this	DET
ejpam-5027	4	6	research	research	NOUN
ejpam-5027	4	7	is	be	AUX
ejpam-5027	4	8	to	to	PART
ejpam-5027	4	9	study	study	VERB
ejpam-5027	4	10	some	some	DET
ejpam-5027	4	11	types	type	NOUN
ejpam-5027	4	12	of	of	ADP
ejpam-5027	4	13	generalized	generalized	ADJ
ejpam-5027	4	14	closed	closed	ADJ
ejpam-5027	4	15	sets	set	NOUN
ejpam-5027	4	16	in	in	ADP
ejpam-5027	4	17	fuzzy	fuzzy	ADJ
ejpam-5027	4	18	bitopology	bitopology	NOUN
ejpam-5027	4	19	including	include	VERB
ejpam-5027	4	20	(	(	PUNCT
ejpam-5027	4	21	i	i	PROPN
ejpam-5027	4	22	,	,	PUNCT
ejpam-5027	4	23	j)−gα−cld	j)−gα−cld	PROPN
ejpam-5027	4	24	,	,	PUNCT
ejpam-5027	4	25	(	(	PUNCT
ejpam-5027	4	26	i	i	PROPN
ejpam-5027	4	27	,	,	PUNCT
ejpam-5027	4	28	j)−gs−cld	j)−gs−cld	PROPN
ejpam-5027	4	29	,	,	PUNCT
ejpam-5027	4	30	(	(	PUNCT
ejpam-5027	4	31	i	i	PROPN
ejpam-5027	4	32	,	,	PUNCT
ejpam-5027	4	33	j)−gp−cld	j)−gp−cld	PROPN
ejpam-5027	4	34	,	,	PUNCT
ejpam-5027	4	35	and	and	CCONJ
ejpam-5027	4	36	(	(	PUNCT
ejpam-5027	4	37	i	i	INTJ
ejpam-5027	4	38	,	,	PUNCT
ejpam-5027	4	39	j)−gβ−cld	j)−gβ−cld	PROPN
ejpam-5027	4	40	.	.	PUNCT
ejpam-5027	5	1	we	we	PRON
ejpam-5027	5	2	then	then	ADV
ejpam-5027	5	3	present	present	VERB
ejpam-5027	5	4	basic	basic	ADJ
ejpam-5027	5	5	theorems	theorem	NOUN
ejpam-5027	5	6	for	for	ADP
ejpam-5027	5	7	determining	determine	VERB
ejpam-5027	5	8	their	their	PRON
ejpam-5027	5	9	relationships	relationship	NOUN
ejpam-5027	5	10	and	and	CCONJ
ejpam-5027	5	11	explain	explain	VERB
ejpam-5027	5	12	their	their	PRON
ejpam-5027	5	13	properties	property	NOUN
ejpam-5027	5	14	,	,	PUNCT
ejpam-5027	5	15	such	such	ADJ
ejpam-5027	5	16	as	as	ADP
ejpam-5027	5	17	closure	closure	NOUN
ejpam-5027	5	18	and	and	CCONJ
ejpam-5027	5	19	interior	interior	NOUN
ejpam-5027	5	20	.	.	PUNCT
ejpam-5027	6	1	in	in	ADP
ejpam-5027	6	2	addition	addition	NOUN
ejpam-5027	6	3	,	,	PUNCT
ejpam-5027	6	4	there	there	PRON
ejpam-5027	6	5	are	be	VERB
ejpam-5027	6	6	many	many	ADJ
ejpam-5027	6	7	interesting	interesting	ADJ
ejpam-5027	6	8	counterexamples	counterexample	NOUN
ejpam-5027	6	9	.	.	PUNCT
ejpam-5027	7	1	the	the	DET
ejpam-5027	7	2	last	last	ADJ
ejpam-5027	7	3	part	part	NOUN
ejpam-5027	7	4	of	of	ADP
ejpam-5027	7	5	the	the	DET
ejpam-5027	7	6	research	research	NOUN
ejpam-5027	7	7	focuses	focus	VERB
ejpam-5027	7	8	on	on	ADP
ejpam-5027	7	9	compactness	compactness	NOUN
ejpam-5027	7	10	as	as	ADP
ejpam-5027	7	11	an	an	DET
ejpam-5027	7	12	application	application	NOUN
ejpam-5027	7	13	of	of	ADP
ejpam-5027	7	14	the	the	DET
ejpam-5027	7	15	types	type	NOUN
ejpam-5027	7	16	of	of	ADP
ejpam-5027	7	17	fuzzy	fuzzy	ADJ
ejpam-5027	7	18	generalized	generalize	VERB
ejpam-5027	7	19	closed	close	VERB
ejpam-5027	7	20	sets	set	NOUN
ejpam-5027	7	21	in	in	ADP
ejpam-5027	7	22	fuzzy	fuzzy	ADJ
ejpam-5027	7	23	bitopological	bitopological	ADJ
ejpam-5027	7	24	spaces	space	NOUN
ejpam-5027	7	25	and	and	CCONJ
ejpam-5027	7	26	their	their	PRON
ejpam-5027	7	27	types	type	NOUN
ejpam-5027	7	28	and	and	CCONJ
ejpam-5027	7	29	explores	explore	VERB
ejpam-5027	7	30	the	the	DET
ejpam-5027	7	31	relationships	relationship	NOUN
ejpam-5027	7	32	between	between	ADP
ejpam-5027	7	33	these	these	DET
ejpam-5027	7	34	concepts	concept	NOUN
ejpam-5027	7	35	,	,	PUNCT
ejpam-5027	7	36	their	their	PRON
ejpam-5027	7	37	important	important	ADJ
ejpam-5027	7	38	theories	theory	NOUN
ejpam-5027	7	39	,	,	PUNCT
ejpam-5027	7	40	and	and	CCONJ
ejpam-5027	7	41	some	some	DET
ejpam-5027	7	42	relevant	relevant	ADJ
ejpam-5027	7	43	counterexamples	counterexample	NOUN
ejpam-5027	7	44	.	.	PUNCT
ejpam-5027	8	1	this	this	DET
ejpam-5027	8	2	approach	approach	NOUN
ejpam-5027	8	3	provides	provide	VERB
ejpam-5027	8	4	a	a	DET
ejpam-5027	8	5	better	well	ADJ
ejpam-5027	8	6	characterization	characterization	NOUN
ejpam-5027	8	7	of	of	ADP
ejpam-5027	8	8	fuzzy	fuzzy	ADJ
ejpam-5027	8	9	compactness	compactness	NOUN
ejpam-5027	8	10	and	and	CCONJ
ejpam-5027	8	11	allows	allow	VERB
ejpam-5027	8	12	for	for	ADP
ejpam-5027	8	13	more	more	ADV
ejpam-5027	8	14	precise	precise	ADJ
ejpam-5027	8	15	characterization	characterization	NOUN
ejpam-5027	8	16	in	in	ADP
ejpam-5027	8	17	fuzzy	fuzzy	ADJ
ejpam-5027	8	18	bitopology	bitopology	NOUN
ejpam-5027	8	19	.	.	PUNCT
ejpam-5027	9	1	the	the	DET
ejpam-5027	9	2	results	result	NOUN
ejpam-5027	9	3	of	of	ADP
ejpam-5027	9	4	this	this	DET
ejpam-5027	9	5	study	study	NOUN
ejpam-5027	9	6	are	be	AUX
ejpam-5027	9	7	new	new	ADJ
ejpam-5027	9	8	to	to	ADP
ejpam-5027	9	9	the	the	DET
ejpam-5027	9	10	domain	domain	NOUN
ejpam-5027	9	11	of	of	ADP
ejpam-5027	9	12	fuzzy	fuzzy	ADJ
ejpam-5027	9	13	bitopology	bitopology	NOUN
ejpam-5027	9	14	.	.	PUNCT
ejpam-5027	10	1	2020	2020	NUM
ejpam-5027	10	2	mathematics	mathematic	NOUN
ejpam-5027	10	3	subject	subject	NOUN
ejpam-5027	10	4	classifications	classification	NOUN
ejpam-5027	10	5	:	:	PUNCT
ejpam-5027	10	6	54a40	54a40	NUM
ejpam-5027	10	7	,	,	PUNCT
ejpam-5027	10	8	57s40	57s40	NUM
ejpam-5027	10	9	,	,	PUNCT
ejpam-5027	10	10	03b52	03b52	NUM
ejpam-5027	10	11	,	,	PUNCT
ejpam-5027	10	12	03e72	03e72	NUM
ejpam-5027	10	13	,	,	PUNCT
ejpam-5027	10	14	47s40	47s40	NUM
ejpam-5027	10	15	key	key	ADJ
ejpam-5027	10	16	words	word	NOUN
ejpam-5027	10	17	and	and	CCONJ
ejpam-5027	10	18	phrases	phrase	NOUN
ejpam-5027	10	19	:	:	PUNCT
ejpam-5027	10	20	fuzzy	fuzzy	ADJ
ejpam-5027	10	21	bitopological	bitopological	ADJ
ejpam-5027	10	22	spaces	space	NOUN
ejpam-5027	10	23	(	(	PUNCT
ejpam-5027	10	24	fbts	fbt	NOUN
ejpam-5027	10	25	)	)	PUNCT
ejpam-5027	10	26	,	,	PUNCT
ejpam-5027	10	27	fuzzy	fuzzy	ADJ
ejpam-5027	10	28	generalized	generalize	VERB
ejpam-5027	10	29	closed	closed	ADJ
ejpam-5027	10	30	sets	set	NOUN
ejpam-5027	10	31	(	(	PUNCT
ejpam-5027	10	32	(	(	PUNCT
ejpam-5027	10	33	i	i	NOUN
ejpam-5027	10	34	,	,	PUNCT
ejpam-5027	10	35	j)−	j)−	PROPN
ejpam-5027	10	36	g	g	PROPN
ejpam-5027	10	37	−	−	PROPN
ejpam-5027	10	38	cld	cld	PROPN
ejpam-5027	10	39	)	)	PUNCT
ejpam-5027	10	40	,	,	PUNCT
ejpam-5027	10	41	fuzzy	fuzzy	ADJ
ejpam-5027	10	42	generalized	generalize	VERB
ejpam-5027	10	43	closure	closure	NOUN
ejpam-5027	10	44	operator	operator	NOUN
ejpam-5027	10	45	(	(	PUNCT
ejpam-5027	10	46	(	(	PUNCT
ejpam-5027	10	47	i	i	PROPN
ejpam-5027	10	48	,	,	PUNCT
ejpam-5027	10	49	j	j	PROPN
ejpam-5027	10	50	)	)	PUNCT
ejpam-5027	10	51	−	−	PROPN
ejpam-5027	10	52	g	g	PROPN
ejpam-5027	10	53	−	−	PROPN
ejpam-5027	10	54	cl	cl	NOUN
ejpam-5027	10	55	)	)	PUNCT
ejpam-5027	10	56	,	,	PUNCT
ejpam-5027	10	57	fuzzy	fuzzy	ADJ
ejpam-5027	10	58	generalized	generalized	ADJ
ejpam-5027	10	59	interior	interior	ADJ
ejpam-5027	10	60	operator	operator	NOUN
ejpam-5027	10	61	(	(	PUNCT
ejpam-5027	10	62	(	(	PUNCT
ejpam-5027	10	63	i	i	PROPN
ejpam-5027	10	64	,	,	PUNCT
ejpam-5027	10	65	j	j	PROPN
ejpam-5027	10	66	)	)	PUNCT
ejpam-5027	11	1	−	−	PROPN
ejpam-5027	11	2	g	g	NOUN
ejpam-5027	11	3	−	−	PROPN
ejpam-5027	11	4	int	int	NOUN
ejpam-5027	11	5	)	)	PUNCT
ejpam-5027	11	6	,	,	PUNCT
ejpam-5027	11	7	fuzzy	fuzzy	ADJ
ejpam-5027	11	8	generalized	generalize	VERB
ejpam-5027	11	9	continuous	continuous	ADJ
ejpam-5027	11	10	(	(	PUNCT
ejpam-5027	11	11	(	(	PUNCT
ejpam-5027	11	12	i	i	PROPN
ejpam-5027	11	13	,	,	PUNCT
ejpam-5027	11	14	j	j	PROPN
ejpam-5027	11	15	)	)	PUNCT
ejpam-5027	11	16	−	−	PROPN
ejpam-5027	11	17	g	g	PROPN
ejpam-5027	11	18	−	−	PROPN
ejpam-5027	11	19	conts	cont	NOUN
ejpam-5027	11	20	)	)	PUNCT
ejpam-5027	11	21	,	,	PUNCT
ejpam-5027	11	22	fuzzy	fuzzy	ADJ
ejpam-5027	11	23	generalized	generalize	VERB
ejpam-5027	11	24	irresolute	irresolute	NOUN
ejpam-5027	11	25	(	(	PUNCT
ejpam-5027	11	26	(	(	PUNCT
ejpam-5027	11	27	i	i	NOUN
ejpam-5027	11	28	,	,	PUNCT
ejpam-5027	11	29	j)−	j)−	PROPN
ejpam-5027	11	30	g	g	PROPN
ejpam-5027	11	31	−	−	PROPN
ejpam-5027	11	32	irres	irre	NOUN
ejpam-5027	11	33	)	)	PUNCT
ejpam-5027	11	34	,	,	PUNCT
ejpam-5027	11	35	and	and	CCONJ
ejpam-5027	11	36	fuzzy	fuzzy	ADJ
ejpam-5027	11	37	generalized	generalized	ADJ
ejpam-5027	11	38	compact	compact	NOUN
ejpam-5027	11	39	(	(	PUNCT
ejpam-5027	11	40	(	(	PUNCT
ejpam-5027	11	41	i	i	NOUN
ejpam-5027	11	42	,	,	PUNCT
ejpam-5027	11	43	j)−	j)−	PROPN
ejpam-5027	11	44	g	g	PROPN
ejpam-5027	11	45	−	−	PROPN
ejpam-5027	11	46	compact	compact	ADJ
ejpam-5027	11	47	)	)	PUNCT
ejpam-5027	11	48	1	1	NUM
ejpam-5027	11	49	.	.	X
ejpam-5027	11	50	introduction	introduction	NOUN
ejpam-5027	11	51	in	in	ADP
ejpam-5027	11	52	this	this	DET
ejpam-5027	11	53	project	project	NOUN
ejpam-5027	11	54	,	,	PUNCT
ejpam-5027	11	55	we	we	PRON
ejpam-5027	11	56	prioritized	prioritize	VERB
ejpam-5027	11	57	our	our	PRON
ejpam-5027	11	58	study	study	NOUN
ejpam-5027	11	59	on	on	ADP
ejpam-5027	11	60	fuzzy	fuzzy	ADJ
ejpam-5027	11	61	bitopology	bitopology	NOUN
ejpam-5027	11	62	,	,	PUNCT
ejpam-5027	11	63	which	which	PRON
ejpam-5027	11	64	was	be	AUX
ejpam-5027	11	65	derived	derive	VERB
ejpam-5027	11	66	from	from	ADP
ejpam-5027	11	67	a	a	DET
ejpam-5027	11	68	fuzzy	fuzzy	ADJ
ejpam-5027	11	69	topology	topology	NOUN
ejpam-5027	11	70	first	first	ADV
ejpam-5027	11	71	introduced	introduce	VERB
ejpam-5027	11	72	in	in	ADP
ejpam-5027	11	73	1965	1965	NUM
ejpam-5027	11	74	by	by	ADP
ejpam-5027	11	75	zadeh	zadeh	PROPN
ejpam-5027	11	76	[	[	X
ejpam-5027	11	77	23	23	NUM
ejpam-5027	11	78	]	]	PUNCT
ejpam-5027	11	79	.	.	PUNCT
ejpam-5027	12	1	following	follow	VERB
ejpam-5027	12	2	this	this	PRON
ejpam-5027	12	3	,	,	PUNCT
ejpam-5027	12	4	many	many	ADJ
ejpam-5027	12	5	researchers	researcher	NOUN
ejpam-5027	12	6	have	have	AUX
ejpam-5027	12	7	applied	apply	VERB
ejpam-5027	12	8	fundamental	fundamental	ADJ
ejpam-5027	12	9	ideas	idea	NOUN
ejpam-5027	12	10	on	on	ADP
ejpam-5027	12	11	fuzzy	fuzzy	ADJ
ejpam-5027	12	12	settings	setting	NOUN
ejpam-5027	12	13	from	from	ADP
ejpam-5027	12	14	a	a	DET
ejpam-5027	12	15	general	general	ADJ
ejpam-5027	12	16	topology	topology	NOUN
ejpam-5027	12	17	and	and	CCONJ
ejpam-5027	12	18	improved	improve	VERB
ejpam-5027	12	19	the	the	DET
ejpam-5027	12	20	concept	concept	NOUN
ejpam-5027	12	21	of	of	ADP
ejpam-5027	12	22	fuzzy	fuzzy	ADJ
ejpam-5027	12	23	topology	topology	NOUN
ejpam-5027	12	24	.	.	PUNCT
ejpam-5027	13	1	chang	chang	PROPN
ejpam-5027	13	2	(	(	PUNCT
ejpam-5027	13	3	1968	1968	NUM
ejpam-5027	13	4	)	)	PUNCT
ejpam-5027	13	5	introduced	introduce	VERB
ejpam-5027	13	6	fuzzy	fuzzy	ADJ
ejpam-5027	13	7	concepts	concept	NOUN
ejpam-5027	13	8	into	into	ADP
ejpam-5027	13	9	fuzzy	fuzzy	ADJ
ejpam-5027	13	10	topology	topology	NOUN
ejpam-5027	13	11	[	[	X
ejpam-5027	13	12	9	9	NUM
ejpam-5027	13	13	]	]	PUNCT
ejpam-5027	13	14	.	.	PUNCT
ejpam-5027	14	1	kandil	kandil	PROPN
ejpam-5027	14	2	(	(	PUNCT
ejpam-5027	14	3	1989	1989	NUM
ejpam-5027	14	4	)	)	PUNCT
ejpam-5027	14	5	introduced	introduce	VERB
ejpam-5027	14	6	fuzzy	fuzzy	ADJ
ejpam-5027	14	7	bitopological	bitopological	ADJ
ejpam-5027	14	8	spaces	space	NOUN
ejpam-5027	14	9	[	[	X
ejpam-5027	14	10	11	11	NUM
ejpam-5027	14	11	]	]	PUNCT
ejpam-5027	14	12	.	.	PUNCT
ejpam-5027	15	1	in	in	ADP
ejpam-5027	15	2	addition	addition	NOUN
ejpam-5027	15	3	,	,	PUNCT
ejpam-5027	15	4	generalized	generalize	VERB
ejpam-5027	15	5	fuzzy	fuzzy	ADJ
ejpam-5027	15	6	closed	closed	ADJ
ejpam-5027	15	7	sets	set	NOUN
ejpam-5027	15	8	were	be	AUX
ejpam-5027	15	9	established	establish	VERB
ejpam-5027	15	10	in	in	ADP
ejpam-5027	15	11	a	a	DET
ejpam-5027	15	12	fuzzy	fuzzy	ADJ
ejpam-5027	15	13	topology	topology	NOUN
ejpam-5027	15	14	by	by	ADP
ejpam-5027	15	15	balasubramanian	balasubramanian	PROPN
ejpam-5027	15	16	and	and	CCONJ
ejpam-5027	15	17	sundaram	sundaram	PROPN
ejpam-5027	15	18	in	in	ADP
ejpam-5027	15	19	1997	1997	NUM
ejpam-5027	15	20	[	[	X
ejpam-5027	15	21	7	7	NUM
ejpam-5027	15	22	]	]	PUNCT
ejpam-5027	15	23	.	.	PUNCT
ejpam-5027	16	1	some	some	DET
ejpam-5027	16	2	scholars	scholar	NOUN
ejpam-5027	16	3	have	have	AUX
ejpam-5027	16	4	presented	present	VERB
ejpam-5027	16	5	many	many	ADJ
ejpam-5027	16	6	important	important	ADJ
ejpam-5027	16	7	papers	paper	NOUN
ejpam-5027	16	8	on	on	ADP
ejpam-5027	16	9	the	the	DET
ejpam-5027	16	10	development	development	NOUN
ejpam-5027	16	11	types	type	NOUN
ejpam-5027	16	12	of	of	ADP
ejpam-5027	16	13	fuzzy	fuzzy	ADJ
ejpam-5027	16	14	sets	set	NOUN
ejpam-5027	16	15	;	;	PUNCT
ejpam-5027	16	16	for	for	ADP
ejpam-5027	16	17	example	example	NOUN
ejpam-5027	16	18	,	,	PUNCT
ejpam-5027	16	19	singal	singal	PROPN
ejpam-5027	16	20	and	and	CCONJ
ejpam-5027	16	21	prakash	prakash	PROPN
ejpam-5027	16	22	presented	present	VERB
ejpam-5027	16	23	a	a	DET
ejpam-5027	16	24	study	study	NOUN
ejpam-5027	16	25	of	of	ADP
ejpam-5027	16	26	a	a	DET
ejpam-5027	16	27	fuzzy	fuzzy	ADJ
ejpam-5027	16	28	pre	pre	ADJ
ejpam-5027	16	29	-	-	ADJ
ejpam-5027	16	30	open	open	ADJ
ejpam-5027	16	31	set	set	NOUN
ejpam-5027	16	32	[	[	X
ejpam-5027	16	33	20	20	NUM
ejpam-5027	16	34	]	]	PUNCT
ejpam-5027	16	35	.	.	PUNCT
ejpam-5027	17	1	balasubramanian	balasubramanian	PROPN
ejpam-5027	17	2	developed	develop	VERB
ejpam-5027	17	3	a	a	DET
ejpam-5027	17	4	theory	theory	NOUN
ejpam-5027	17	5	of	of	ADP
ejpam-5027	17	6	fuzzy	fuzzy	ADJ
ejpam-5027	17	7	β	β	X
ejpam-5027	17	8	open	open	ADJ
ejpam-5027	17	9	set	set	NOUN
ejpam-5027	17	10	[	[	X
ejpam-5027	17	11	6	6	NUM
ejpam-5027	17	12	]	]	PUNCT
ejpam-5027	17	13	.	.	PUNCT
ejpam-5027	18	1	ahmad	ahmad	PROPN
ejpam-5027	18	2	and	and	CCONJ
ejpam-5027	18	3	athar	athar	ADJ
ejpam-5027	18	4	∗corresponding	∗corresponde	VERB
ejpam-5027	18	5	author	author	NOUN
ejpam-5027	18	6	.	.	PUNCT
ejpam-5027	19	1	doi	doi	NOUN
ejpam-5027	19	2	:	:	PUNCT
ejpam-5027	19	3	https://doi.org/10.29020/nybg.ejpam.v17i1.5027	https://doi.org/10.29020/nybg.ejpam.v17i1.5027	PROPN
ejpam-5027	19	4	email	email	NOUN
ejpam-5027	19	5	addresses	address	NOUN
ejpam-5027	19	6	:	:	PUNCT
ejpam-5027	19	7	aasehli@taibahu.edu.sa	aasehli@taibahu.edu.sa	NOUN
ejpam-5027	19	8	(	(	PUNCT
ejpam-5027	19	9	a.	a.	NOUN
ejpam-5027	19	10	a.	a.	NOUN
ejpam-5027	19	11	alharbi	alharbi	PROPN
ejpam-5027	19	12	)	)	PUNCT
ejpam-5027	19	13	,	,	PUNCT
ejpam-5027	19	14	akilic@upm.edu.my	akilic@upm.edu.my	PROPN
ejpam-5027	19	15	(	(	PUNCT
ejpam-5027	19	16	a.	a.	NOUN
ejpam-5027	19	17	kilicman	kilicman	PROPN
ejpam-5027	19	18	)	)	PUNCT
ejpam-5027	19	19	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5027	19	20	30	30	NUM
ejpam-5027	19	21	©	©	ADP
ejpam-5027	19	22	2024	2024	NUM
ejpam-5027	19	23	ejpam	ejpam	NOUN
ejpam-5027	19	24	all	all	DET
ejpam-5027	19	25	rights	right	NOUN
ejpam-5027	19	26	reserved	reserve	VERB
ejpam-5027	19	27	.	.	PUNCT
ejpam-5027	20	1	ahlam	ahlam	PROPN
ejpam-5027	20	2	ahmed	ahmed	PROPN
ejpam-5027	20	3	alharbi	alharbi	PROPN
ejpam-5027	20	4	,	,	PUNCT
ejpam-5027	20	5	adem	adem	PROPN
ejpam-5027	20	6	kilicman	kilicman	PROPN
ejpam-5027	20	7	/	/	SYM
ejpam-5027	20	8	eur	eur	PROPN
ejpam-5027	20	9	.	.	PUNCT
ejpam-5027	21	1	j.	j.	PROPN
ejpam-5027	21	2	pure	pure	PROPN
ejpam-5027	21	3	appl	appl	PROPN
ejpam-5027	21	4	.	.	PROPN
ejpam-5027	21	5	math	math	PROPN
ejpam-5027	21	6	,	,	PUNCT
ejpam-5027	21	7	17	17	NUM
ejpam-5027	21	8	(	(	PUNCT
ejpam-5027	21	9	1	1	NUM
ejpam-5027	21	10	)	)	PUNCT
ejpam-5027	21	11	(	(	PUNCT
ejpam-5027	21	12	2024	2024	NUM
ejpam-5027	21	13	)	)	PUNCT
ejpam-5027	21	14	,	,	PUNCT
ejpam-5027	21	15	30	30	NUM
ejpam-5027	21	16	-	-	SYM
ejpam-5027	21	17	41	41	NUM
ejpam-5027	21	18	31	31	NUM
ejpam-5027	21	19	found	find	VERB
ejpam-5027	21	20	important	important	ADJ
ejpam-5027	21	21	results	result	NOUN
ejpam-5027	21	22	on	on	ADP
ejpam-5027	21	23	fuzzy	fuzzy	ADJ
ejpam-5027	21	24	semi	semi	ADJ
ejpam-5027	21	25	open	open	ADJ
ejpam-5027	21	26	sets	set	NOUN
ejpam-5027	21	27	[	[	X
ejpam-5027	21	28	2	2	NUM
ejpam-5027	21	29	]	]	PUNCT
ejpam-5027	21	30	.	.	PUNCT
ejpam-5027	22	1	in	in	ADP
ejpam-5027	22	2	addition	addition	NOUN
ejpam-5027	22	3	,	,	PUNCT
ejpam-5027	22	4	hakeem	hakeem	PROPN
ejpam-5027	22	5	and	and	CCONJ
ejpam-5027	22	6	latha	latha	PROPN
ejpam-5027	22	7	introduced	introduce	VERB
ejpam-5027	22	8	new	new	ADJ
ejpam-5027	22	9	results	result	NOUN
ejpam-5027	22	10	for	for	ADP
ejpam-5027	22	11	fuzzy	fuzzy	ADJ
ejpam-5027	22	12	α	α	PROPN
ejpam-5027	22	13	open	open	ADJ
ejpam-5027	22	14	set	set	NOUN
ejpam-5027	22	15	[	[	X
ejpam-5027	22	16	15	15	NUM
ejpam-5027	22	17	]	]	PUNCT
ejpam-5027	22	18	.	.	PUNCT
ejpam-5027	23	1	furthermore	furthermore	ADV
ejpam-5027	23	2	,	,	PUNCT
ejpam-5027	23	3	extensive	extensive	ADJ
ejpam-5027	23	4	research	research	NOUN
ejpam-5027	23	5	has	have	AUX
ejpam-5027	23	6	been	be	AUX
ejpam-5027	23	7	conducted	conduct	VERB
ejpam-5027	23	8	on	on	ADP
ejpam-5027	23	9	the	the	DET
ejpam-5027	23	10	concept	concept	NOUN
ejpam-5027	23	11	of	of	ADP
ejpam-5027	23	12	generalized	generalized	ADJ
ejpam-5027	23	13	closed	closed	ADJ
ejpam-5027	23	14	sets	set	NOUN
ejpam-5027	23	15	in	in	ADP
ejpam-5027	23	16	fuzzy	fuzzy	ADJ
ejpam-5027	23	17	space	space	NOUN
ejpam-5027	23	18	[	[	X
ejpam-5027	23	19	14	14	NUM
ejpam-5027	23	20	,	,	PUNCT
ejpam-5027	23	21	24	24	NUM
ejpam-5027	23	22	]	]	PUNCT
ejpam-5027	23	23	.	.	PUNCT
ejpam-5027	24	1	subsequently	subsequently	ADV
ejpam-5027	24	2	,	,	PUNCT
ejpam-5027	24	3	many	many	ADJ
ejpam-5027	24	4	studies	study	NOUN
ejpam-5027	24	5	have	have	AUX
ejpam-5027	24	6	introduced	introduce	VERB
ejpam-5027	24	7	the	the	DET
ejpam-5027	24	8	use	use	NOUN
ejpam-5027	24	9	of	of	ADP
ejpam-5027	24	10	generalized	generalized	ADJ
ejpam-5027	24	11	closed	closed	ADJ
ejpam-5027	24	12	sets	set	NOUN
ejpam-5027	24	13	in	in	ADP
ejpam-5027	24	14	fuzzy	fuzzy	ADJ
ejpam-5027	24	15	topologies	topology	NOUN
ejpam-5027	24	16	,	,	PUNCT
ejpam-5027	24	17	such	such	ADJ
ejpam-5027	24	18	as	as	ADP
ejpam-5027	24	19	el	el	PROPN
ejpam-5027	24	20	-	-	NOUN
ejpam-5027	24	21	shafei	shafei	NOUN
ejpam-5027	24	22	[	[	X
ejpam-5027	24	23	10	10	NUM
ejpam-5027	24	24	]	]	PUNCT
ejpam-5027	24	25	.	.	PUNCT
ejpam-5027	25	1	some	some	DET
ejpam-5027	25	2	studies	study	NOUN
ejpam-5027	25	3	have	have	AUX
ejpam-5027	25	4	applied	apply	VERB
ejpam-5027	25	5	these	these	PRON
ejpam-5027	25	6	to	to	ADP
ejpam-5027	25	7	the	the	DET
ejpam-5027	25	8	concept	concept	NOUN
ejpam-5027	25	9	of	of	ADP
ejpam-5027	25	10	functions	function	NOUN
ejpam-5027	25	11	that	that	PRON
ejpam-5027	25	12	contribute	contribute	VERB
ejpam-5027	25	13	to	to	ADP
ejpam-5027	25	14	enriching	enrich	VERB
ejpam-5027	25	15	this	this	DET
ejpam-5027	25	16	research	research	NOUN
ejpam-5027	25	17	area	area	NOUN
ejpam-5027	25	18	too	too	ADV
ejpam-5027	26	1	[	[	X
ejpam-5027	26	2	13	13	NUM
ejpam-5027	26	3	,	,	PUNCT
ejpam-5027	26	4	18	18	NUM
ejpam-5027	26	5	,	,	PUNCT
ejpam-5027	26	6	19	19	NUM
ejpam-5027	26	7	]	]	PUNCT
ejpam-5027	26	8	.	.	PUNCT
ejpam-5027	27	1	on	on	ADP
ejpam-5027	27	2	the	the	DET
ejpam-5027	27	3	other	other	ADJ
ejpam-5027	27	4	hand	hand	NOUN
ejpam-5027	27	5	,	,	PUNCT
ejpam-5027	27	6	earlier	early	ADJ
ejpam-5027	27	7	research	research	NOUN
ejpam-5027	27	8	on	on	ADP
ejpam-5027	27	9	compactness	compactness	NOUN
ejpam-5027	27	10	informed	inform	VERB
ejpam-5027	27	11	our	our	PRON
ejpam-5027	27	12	study	study	NOUN
ejpam-5027	27	13	of	of	ADP
ejpam-5027	27	14	this	this	DET
ejpam-5027	27	15	topic	topic	NOUN
ejpam-5027	27	16	[	[	X
ejpam-5027	27	17	1	1	NUM
ejpam-5027	27	18	,	,	PUNCT
ejpam-5027	27	19	21	21	NUM
ejpam-5027	27	20	]	]	PUNCT
ejpam-5027	27	21	.	.	PUNCT
ejpam-5027	28	1	a	a	DET
ejpam-5027	28	2	recent	recent	ADJ
ejpam-5027	28	3	study	study	NOUN
ejpam-5027	28	4	discussed	discuss	VERB
ejpam-5027	28	5	the	the	DET
ejpam-5027	28	6	properties	property	NOUN
ejpam-5027	28	7	of	of	ADP
ejpam-5027	28	8	compactness	compactness	NOUN
ejpam-5027	28	9	,	,	PUNCT
ejpam-5027	28	10	but	but	CCONJ
ejpam-5027	28	11	in	in	ADP
ejpam-5027	28	12	another	another	DET
ejpam-5027	28	13	field	field	NOUN
ejpam-5027	28	14	,	,	PUNCT
ejpam-5027	28	15	as	as	ADP
ejpam-5027	28	16	g	g	NOUN
ejpam-5027	28	17	-	-	PUNCT
ejpam-5027	28	18	metric	metric	ADJ
ejpam-5027	28	19	spaces	space	NOUN
ejpam-5027	28	20	[	[	X
ejpam-5027	28	21	12	12	NUM
ejpam-5027	28	22	]	]	PUNCT
ejpam-5027	28	23	and	and	CCONJ
ejpam-5027	28	24	fuzzy	fuzzy	ADJ
ejpam-5027	28	25	soft	soft	ADJ
ejpam-5027	28	26	space	space	NOUN
ejpam-5027	28	27	as	as	ADP
ejpam-5027	28	28	[	[	X
ejpam-5027	28	29	22	22	NUM
ejpam-5027	28	30	]	]	PUNCT
ejpam-5027	28	31	.	.	PUNCT
ejpam-5027	29	1	in	in	ADP
ejpam-5027	29	2	addition	addition	NOUN
ejpam-5027	29	3	,	,	PUNCT
ejpam-5027	29	4	jamal	jamal	PROPN
ejpam-5027	29	5	et	et	PROPN
ejpam-5027	29	6	al	al	PROPN
ejpam-5027	29	7	.	.	PROPN
ejpam-5027	29	8	studied	study	VERB
ejpam-5027	29	9	several	several	ADJ
ejpam-5027	29	10	properties	property	NOUN
ejpam-5027	29	11	of	of	ADP
ejpam-5027	29	12	compact	compact	ADJ
ejpam-5027	29	13	space	space	NOUN
ejpam-5027	29	14	using	use	VERB
ejpam-5027	29	15	regular	regular	ADJ
ejpam-5027	29	16	open	open	ADJ
ejpam-5027	29	17	sets	set	NOUN
ejpam-5027	29	18	[	[	X
ejpam-5027	29	19	16	16	NUM
ejpam-5027	29	20	]	]	PUNCT
ejpam-5027	29	21	.	.	PUNCT
ejpam-5027	30	1	the	the	DET
ejpam-5027	30	2	study	study	NOUN
ejpam-5027	30	3	explores	explore	VERB
ejpam-5027	30	4	the	the	DET
ejpam-5027	30	5	concept	concept	NOUN
ejpam-5027	30	6	of	of	ADP
ejpam-5027	30	7	generalized	generalized	ADJ
ejpam-5027	30	8	closed	closed	ADJ
ejpam-5027	30	9	sets	set	NOUN
ejpam-5027	30	10	in	in	ADP
ejpam-5027	30	11	fuzzy	fuzzy	ADJ
ejpam-5027	30	12	bitopological	bitopological	ADJ
ejpam-5027	30	13	spaces	space	NOUN
ejpam-5027	30	14	,	,	PUNCT
ejpam-5027	30	15	a	a	DET
ejpam-5027	30	16	flexible	flexible	ADJ
ejpam-5027	30	17	framework	framework	NOUN
ejpam-5027	30	18	for	for	ADP
ejpam-5027	30	19	studying	study	VERB
ejpam-5027	30	20	topological	topological	ADJ
ejpam-5027	30	21	properties	property	NOUN
ejpam-5027	30	22	and	and	CCONJ
ejpam-5027	30	23	partial	partial	ADJ
ejpam-5027	30	24	membership	membership	NOUN
ejpam-5027	30	25	.	.	PUNCT
ejpam-5027	31	1	it	it	PRON
ejpam-5027	31	2	provides	provide	VERB
ejpam-5027	31	3	a	a	DET
ejpam-5027	31	4	smooth	smooth	ADJ
ejpam-5027	31	5	transition	transition	NOUN
ejpam-5027	31	6	between	between	ADP
ejpam-5027	31	7	open	open	ADJ
ejpam-5027	31	8	and	and	CCONJ
ejpam-5027	31	9	closed	closed	ADJ
ejpam-5027	31	10	sets	set	NOUN
ejpam-5027	31	11	,	,	PUNCT
ejpam-5027	31	12	offering	offer	VERB
ejpam-5027	31	13	a	a	DET
ejpam-5027	31	14	more	more	ADV
ejpam-5027	31	15	flexible	flexible	ADJ
ejpam-5027	31	16	definition	definition	NOUN
ejpam-5027	31	17	of	of	ADP
ejpam-5027	31	18	closure	closure	NOUN
ejpam-5027	31	19	than	than	ADP
ejpam-5027	31	20	traditional	traditional	ADJ
ejpam-5027	31	21	closed	closed	ADJ
ejpam-5027	31	22	sets	set	NOUN
ejpam-5027	31	23	.	.	PUNCT
ejpam-5027	32	1	also	also	ADV
ejpam-5027	32	2	,	,	PUNCT
ejpam-5027	32	3	delves	delve	VERB
ejpam-5027	32	4	into	into	ADP
ejpam-5027	32	5	their	their	PRON
ejpam-5027	32	6	interrelationships	interrelationship	NOUN
ejpam-5027	32	7	and	and	CCONJ
ejpam-5027	32	8	highlights	highlight	VERB
ejpam-5027	32	9	important	important	ADJ
ejpam-5027	32	10	theories	theory	NOUN
ejpam-5027	32	11	and	and	CCONJ
ejpam-5027	32	12	counterexamples	counterexample	NOUN
ejpam-5027	32	13	.	.	PUNCT
ejpam-5027	33	1	moreover	moreover	ADV
ejpam-5027	33	2	,	,	PUNCT
ejpam-5027	33	3	because	because	SCONJ
ejpam-5027	33	4	the	the	DET
ejpam-5027	33	5	generalized	generalize	VERB
ejpam-5027	33	6	closed	closed	ADJ
ejpam-5027	33	7	sets	set	NOUN
ejpam-5027	33	8	have	have	VERB
ejpam-5027	33	9	many	many	ADJ
ejpam-5027	33	10	applications	application	NOUN
ejpam-5027	33	11	in	in	ADP
ejpam-5027	33	12	a	a	DET
ejpam-5027	33	13	range	range	NOUN
ejpam-5027	33	14	of	of	ADP
ejpam-5027	33	15	topological	topological	ADJ
ejpam-5027	33	16	concepts	concept	NOUN
ejpam-5027	33	17	,	,	PUNCT
ejpam-5027	33	18	such	such	ADJ
ejpam-5027	33	19	as	as	ADP
ejpam-5027	33	20	neighborhoods	neighborhood	NOUN
ejpam-5027	33	21	,	,	PUNCT
ejpam-5027	33	22	which	which	PRON
ejpam-5027	33	23	are	be	AUX
ejpam-5027	33	24	discussed	discuss	VERB
ejpam-5027	33	25	and	and	CCONJ
ejpam-5027	33	26	explained	explain	VERB
ejpam-5027	33	27	in	in	ADP
ejpam-5027	33	28	detail	detail	NOUN
ejpam-5027	33	29	in	in	ADP
ejpam-5027	33	30	reference	reference	NOUN
ejpam-5027	33	31	[	[	X
ejpam-5027	33	32	4	4	NUM
ejpam-5027	33	33	]	]	PUNCT
ejpam-5027	33	34	,	,	PUNCT
ejpam-5027	33	35	they	they	PRON
ejpam-5027	33	36	were	be	AUX
ejpam-5027	33	37	applied	apply	VERB
ejpam-5027	33	38	to	to	ADP
ejpam-5027	33	39	connectedness	connectedness	NOUN
ejpam-5027	33	40	as	as	ADP
ejpam-5027	33	41	in	in	ADP
ejpam-5027	33	42	[	[	X
ejpam-5027	33	43	3	3	NUM
ejpam-5027	33	44	]	]	PUNCT
ejpam-5027	33	45	,	,	PUNCT
ejpam-5027	33	46	also	also	ADV
ejpam-5027	33	47	to	to	PART
ejpam-5027	33	48	functions	function	NOUN
ejpam-5027	33	49	as	as	ADP
ejpam-5027	33	50	in	in	ADP
ejpam-5027	33	51	[	[	X
ejpam-5027	33	52	5	5	NUM
ejpam-5027	33	53	]	]	PUNCT
ejpam-5027	33	54	,	,	PUNCT
ejpam-5027	33	55	but	but	CCONJ
ejpam-5027	33	56	we	we	PRON
ejpam-5027	33	57	aim	aim	VERB
ejpam-5027	33	58	to	to	PART
ejpam-5027	33	59	apply	apply	VERB
ejpam-5027	33	60	them	they	PRON
ejpam-5027	33	61	to	to	ADP
ejpam-5027	33	62	another	another	DET
ejpam-5027	33	63	topological	topological	ADJ
ejpam-5027	33	64	topic	topic	NOUN
ejpam-5027	33	65	,	,	PUNCT
ejpam-5027	33	66	that	that	PRON
ejpam-5027	33	67	is	be	AUX
ejpam-5027	33	68	compactness	compactness	NOUN
ejpam-5027	33	69	.	.	PUNCT
ejpam-5027	34	1	it	it	PRON
ejpam-5027	34	2	provides	provide	VERB
ejpam-5027	34	3	better	well	ADJ
ejpam-5027	34	4	characterizations	characterization	NOUN
ejpam-5027	34	5	of	of	ADP
ejpam-5027	34	6	fuzzy	fuzzy	ADJ
ejpam-5027	34	7	openness	openness	NOUN
ejpam-5027	34	8	and	and	CCONJ
ejpam-5027	34	9	fuzzy	fuzzy	ADJ
ejpam-5027	34	10	compactness	compactness	NOUN
ejpam-5027	34	11	and	and	CCONJ
ejpam-5027	34	12	allows	allow	VERB
ejpam-5027	34	13	for	for	ADP
ejpam-5027	34	14	more	more	ADV
ejpam-5027	34	15	precise	precise	ADJ
ejpam-5027	34	16	characterizations	characterization	NOUN
ejpam-5027	34	17	,	,	PUNCT
ejpam-5027	34	18	which	which	PRON
ejpam-5027	34	19	are	be	AUX
ejpam-5027	34	20	important	important	ADJ
ejpam-5027	34	21	properties	property	NOUN
ejpam-5027	34	22	in	in	ADP
ejpam-5027	34	23	fuzzy	fuzzy	ADJ
ejpam-5027	34	24	bitopology	bitopology	NOUN
ejpam-5027	34	25	.	.	PUNCT
ejpam-5027	35	1	finally	finally	ADV
ejpam-5027	35	2	,	,	PUNCT
ejpam-5027	35	3	the	the	DET
ejpam-5027	35	4	research	research	NOUN
ejpam-5027	35	5	is	be	AUX
ejpam-5027	35	6	organized	organize	VERB
ejpam-5027	35	7	as	as	SCONJ
ejpam-5027	35	8	follows	follow	VERB
ejpam-5027	35	9	.	.	PUNCT
ejpam-5027	36	1	the	the	DET
ejpam-5027	36	2	first	first	ADJ
ejpam-5027	36	3	section	section	NOUN
ejpam-5027	36	4	(	(	PUNCT
ejpam-5027	36	5	introduction	introduction	NOUN
ejpam-5027	36	6	)	)	PUNCT
ejpam-5027	36	7	looks	look	VERB
ejpam-5027	36	8	at	at	ADP
ejpam-5027	36	9	the	the	DET
ejpam-5027	36	10	subject	subject	NOUN
ejpam-5027	36	11	’s	’s	PART
ejpam-5027	36	12	background	background	NOUN
ejpam-5027	36	13	and	and	CCONJ
ejpam-5027	36	14	related	related	ADJ
ejpam-5027	36	15	studies	study	NOUN
ejpam-5027	36	16	.	.	PUNCT
ejpam-5027	37	1	in	in	ADP
ejpam-5027	37	2	section	section	NOUN
ejpam-5027	37	3	2	2	NUM
ejpam-5027	37	4	(	(	PUNCT
ejpam-5027	37	5	preliminaries	preliminary	NOUN
ejpam-5027	37	6	)	)	PUNCT
ejpam-5027	37	7	,	,	PUNCT
ejpam-5027	37	8	we	we	PRON
ejpam-5027	37	9	briefly	briefly	ADV
ejpam-5027	37	10	discuss	discuss	VERB
ejpam-5027	37	11	several	several	ADJ
ejpam-5027	37	12	important	important	ADJ
ejpam-5027	37	13	concepts	concept	NOUN
ejpam-5027	37	14	pertinent	pertinent	ADJ
ejpam-5027	37	15	to	to	ADP
ejpam-5027	37	16	our	our	PRON
ejpam-5027	37	17	investigation	investigation	NOUN
ejpam-5027	37	18	.	.	PUNCT
ejpam-5027	38	1	the	the	DET
ejpam-5027	38	2	concept	concept	NOUN
ejpam-5027	38	3	of	of	ADP
ejpam-5027	38	4	generalized	generalized	ADJ
ejpam-5027	38	5	closed	closed	ADJ
ejpam-5027	38	6	sets	set	NOUN
ejpam-5027	38	7	is	be	AUX
ejpam-5027	38	8	presented	present	VERB
ejpam-5027	38	9	in	in	ADP
ejpam-5027	38	10	section	section	NOUN
ejpam-5027	38	11	3	3	NUM
ejpam-5027	38	12	(	(	PUNCT
ejpam-5027	38	13	types	type	NOUN
ejpam-5027	38	14	of	of	ADP
ejpam-5027	38	15	fuzzy	fuzzy	ADJ
ejpam-5027	38	16	generalized	generalize	VERB
ejpam-5027	38	17	closed	closed	ADJ
ejpam-5027	38	18	groups	group	NOUN
ejpam-5027	38	19	in	in	ADP
ejpam-5027	38	20	fuzzy	fuzzy	ADJ
ejpam-5027	38	21	bitopology	bitopology	NOUN
ejpam-5027	38	22	space	space	NOUN
ejpam-5027	38	23	)	)	PUNCT
ejpam-5027	38	24	,	,	PUNCT
ejpam-5027	38	25	important	important	ADJ
ejpam-5027	38	26	theorems	theorem	NOUN
ejpam-5027	38	27	and	and	CCONJ
ejpam-5027	38	28	distinctive	distinctive	ADJ
ejpam-5027	38	29	properties	property	NOUN
ejpam-5027	38	30	are	be	AUX
ejpam-5027	38	31	discussed	discuss	VERB
ejpam-5027	38	32	,	,	PUNCT
ejpam-5027	38	33	and	and	CCONJ
ejpam-5027	38	34	some	some	DET
ejpam-5027	38	35	interesting	interesting	ADJ
ejpam-5027	38	36	counterexamples	counterexample	NOUN
ejpam-5027	38	37	are	be	AUX
ejpam-5027	38	38	introduced	introduce	VERB
ejpam-5027	38	39	.	.	PUNCT
ejpam-5027	39	1	then	then	ADV
ejpam-5027	39	2	,	,	PUNCT
ejpam-5027	39	3	we	we	PRON
ejpam-5027	39	4	provide	provide	VERB
ejpam-5027	39	5	crucial	crucial	ADJ
ejpam-5027	39	6	definitions	definition	NOUN
ejpam-5027	39	7	of	of	ADP
ejpam-5027	39	8	fuzzy	fuzzy	ADJ
ejpam-5027	39	9	generalized	generalized	ADJ
ejpam-5027	39	10	compactness	compactness	NOUN
ejpam-5027	39	11	in	in	ADP
ejpam-5027	39	12	section	section	NOUN
ejpam-5027	39	13	4	4	NUM
ejpam-5027	39	14	(	(	PUNCT
ejpam-5027	39	15	types	type	NOUN
ejpam-5027	39	16	of	of	ADP
ejpam-5027	39	17	fuzzy	fuzzy	ADJ
ejpam-5027	39	18	generalized	generalized	ADJ
ejpam-5027	39	19	compactness	compactness	NOUN
ejpam-5027	39	20	in	in	ADP
ejpam-5027	39	21	fuzzy	fuzzy	ADJ
ejpam-5027	39	22	bitopological	bitopological	ADJ
ejpam-5027	39	23	spaces	space	NOUN
ejpam-5027	39	24	)	)	PUNCT
ejpam-5027	39	25	.	.	PUNCT
ejpam-5027	40	1	in	in	ADP
ejpam-5027	40	2	section	section	NOUN
ejpam-5027	40	3	5	5	NUM
ejpam-5027	40	4	(	(	PUNCT
ejpam-5027	40	5	conclusion	conclusion	NOUN
ejpam-5027	40	6	)	)	PUNCT
ejpam-5027	40	7	,	,	PUNCT
ejpam-5027	40	8	we	we	PRON
ejpam-5027	40	9	summarize	summarize	VERB
ejpam-5027	40	10	our	our	PRON
ejpam-5027	40	11	results	result	NOUN
ejpam-5027	40	12	.	.	PUNCT
ejpam-5027	41	1	2	2	X
ejpam-5027	41	2	.	.	X
ejpam-5027	41	3	preliminaries	preliminary	NOUN
ejpam-5027	41	4	in	in	ADP
ejpam-5027	41	5	the	the	DET
ejpam-5027	41	6	following	following	ADJ
ejpam-5027	41	7	part	part	NOUN
ejpam-5027	41	8	,	,	PUNCT
ejpam-5027	41	9	we	we	PRON
ejpam-5027	41	10	go	go	VERB
ejpam-5027	41	11	over	over	ADP
ejpam-5027	41	12	important	important	ADJ
ejpam-5027	41	13	antecedent	antecedent	NOUN
ejpam-5027	41	14	notions	notion	NOUN
ejpam-5027	41	15	that	that	PRON
ejpam-5027	41	16	are	be	AUX
ejpam-5027	41	17	essential	essential	ADJ
ejpam-5027	41	18	to	to	ADP
ejpam-5027	41	19	the	the	DET
ejpam-5027	41	20	development	development	NOUN
ejpam-5027	41	21	of	of	ADP
ejpam-5027	41	22	this	this	DET
ejpam-5027	41	23	paper	paper	NOUN
ejpam-5027	41	24	.	.	PUNCT
ejpam-5027	42	1	definition	definition	NOUN
ejpam-5027	42	2	1	1	NUM
ejpam-5027	42	3	.	.	PUNCT
ejpam-5027	43	1	[	[	X
ejpam-5027	43	2	17	17	NUM
ejpam-5027	43	3	]	]	PUNCT
ejpam-5027	43	4	suppose	suppose	VERB
ejpam-5027	43	5	the	the	DET
ejpam-5027	43	6	set	set	NOUN
ejpam-5027	43	7	x	x	PUNCT
ejpam-5027	43	8	is	be	AUX
ejpam-5027	43	9	not	not	PART
ejpam-5027	43	10	empty	empty	ADJ
ejpam-5027	43	11	and	and	CCONJ
ejpam-5027	43	12	the	the	DET
ejpam-5027	43	13	i	i	PRON
ejpam-5027	43	14	sign	sign	NOUN
ejpam-5027	43	15	represents	represent	VERB
ejpam-5027	43	16	the	the	DET
ejpam-5027	43	17	unit	unit	NOUN
ejpam-5027	43	18	period	period	NOUN
ejpam-5027	44	1	[	[	X
ejpam-5027	44	2	0	0	NUM
ejpam-5027	44	3	,	,	PUNCT
ejpam-5027	44	4	1	1	NUM
ejpam-5027	44	5	]	]	PUNCT
ejpam-5027	44	6	,	,	PUNCT
ejpam-5027	44	7	then	then	ADV
ejpam-5027	44	8	the	the	DET
ejpam-5027	44	9	following	following	NOUN
ejpam-5027	44	10	defined	define	VERB
ejpam-5027	44	11	as	as	ADP
ejpam-5027	44	12	:	:	PUNCT
ejpam-5027	44	13	(	(	PUNCT
ejpam-5027	44	14	1	1	X
ejpam-5027	44	15	)	)	PUNCT
ejpam-5027	44	16	an	an	DET
ejpam-5027	44	17	operator	operator	NOUN
ejpam-5027	44	18	with	with	ADP
ejpam-5027	44	19	x	x	NOUN
ejpam-5027	44	20	domain	domain	NOUN
ejpam-5027	44	21	and	and	CCONJ
ejpam-5027	44	22	i	i	PRON
ejpam-5027	44	23	range	range	VERB
ejpam-5027	44	24	is	be	AUX
ejpam-5027	44	25	known	know	VERB
ejpam-5027	44	26	as	as	ADP
ejpam-5027	44	27	a	a	DET
ejpam-5027	44	28	fuzzy	fuzzy	ADJ
ejpam-5027	44	29	set	set	NOUN
ejpam-5027	44	30	e	e	NOUN
ejpam-5027	44	31	,	,	PUNCT
ejpam-5027	44	32	where	where	SCONJ
ejpam-5027	44	33	e(x	e(x	NUM
ejpam-5027	44	34	)	)	PUNCT
ejpam-5027	44	35	∈	∈	PROPN
ejpam-5027	44	36	(	(	PUNCT
ejpam-5027	44	37	0	0	NUM
ejpam-5027	44	38	,	,	PUNCT
ejpam-5027	44	39	1	1	NUM
ejpam-5027	44	40	]	]	PUNCT
ejpam-5027	44	41	when	when	SCONJ
ejpam-5027	44	42	x	x	SYM
ejpam-5027	44	43	∈	∈	PROPN
ejpam-5027	44	44	e	e	NOUN
ejpam-5027	44	45	,	,	PUNCT
ejpam-5027	44	46	and	and	CCONJ
ejpam-5027	44	47	e(x	e(x	NUM
ejpam-5027	44	48	)	)	PUNCT
ejpam-5027	44	49	=	=	SYM
ejpam-5027	44	50	0	0	NUM
ejpam-5027	45	1	in	in	ADP
ejpam-5027	45	2	case	case	NOUN
ejpam-5027	45	3	x	x	X
ejpam-5027	45	4	̸∈	̸∈	PROPN
ejpam-5027	45	5	e.	e.	PROPN
ejpam-5027	45	6	(	(	PUNCT
ejpam-5027	45	7	2	2	NUM
ejpam-5027	45	8	)	)	PUNCT
ejpam-5027	45	9	a	a	DET
ejpam-5027	45	10	set	set	NOUN
ejpam-5027	45	11	d	d	X
ejpam-5027	45	12	is	be	AUX
ejpam-5027	45	13	including	include	VERB
ejpam-5027	45	14	e	e	NOUN
ejpam-5027	45	15	indicated	indicate	VERB
ejpam-5027	45	16	via	via	ADP
ejpam-5027	45	17	e	e	PROPN
ejpam-5027	45	18	⊆	⊆	NUM
ejpam-5027	45	19	d	d	NOUN
ejpam-5027	45	20	if	if	SCONJ
ejpam-5027	45	21	e(x	e(x	NUM
ejpam-5027	45	22	)	)	PUNCT
ejpam-5027	45	23	≤	≤	NOUN
ejpam-5027	45	24	d(x	d(x	NOUN
ejpam-5027	45	25	)	)	PUNCT
ejpam-5027	45	26	,	,	PUNCT
ejpam-5027	45	27	whenever	whenever	SCONJ
ejpam-5027	45	28	x	x	SYM
ejpam-5027	45	29	∈	∈	PROPN
ejpam-5027	45	30	x	x	SYM
ejpam-5027	45	31	(	(	PUNCT
ejpam-5027	45	32	3	3	NUM
ejpam-5027	45	33	)	)	PUNCT
ejpam-5027	45	34	e	e	NOUN
ejpam-5027	45	35	and	and	CCONJ
ejpam-5027	45	36	d	d	PROPN
ejpam-5027	45	37	combination	combination	NOUN
ejpam-5027	45	38	indicated	indicate	VERB
ejpam-5027	45	39	by	by	ADP
ejpam-5027	45	40	e	e	NOUN
ejpam-5027	45	41	∨d	∨d	VERB
ejpam-5027	45	42	if	if	SCONJ
ejpam-5027	45	43	(	(	PUNCT
ejpam-5027	45	44	e	e	NOUN
ejpam-5027	45	45	∨d)(x	∨d)(x	PROPN
ejpam-5027	45	46	)	)	PUNCT
ejpam-5027	45	47	=	=	SYM
ejpam-5027	45	48	max{e(x	max{e(x	PROPN
ejpam-5027	45	49	)	)	PUNCT
ejpam-5027	45	50	,	,	PUNCT
ejpam-5027	45	51	d(x	d(x	PROPN
ejpam-5027	45	52	)	)	PUNCT
ejpam-5027	45	53	}	}	PUNCT
ejpam-5027	45	54	∀	∀	X
ejpam-5027	46	1	x	x	SYM
ejpam-5027	46	2	∈	∈	NOUN
ejpam-5027	46	3	x.	x.	NOUN
ejpam-5027	46	4	ahlam	ahlam	PROPN
ejpam-5027	46	5	ahmed	ahmed	PROPN
ejpam-5027	46	6	alharbi	alharbi	PROPN
ejpam-5027	46	7	,	,	PUNCT
ejpam-5027	46	8	adem	adem	PROPN
ejpam-5027	46	9	kilicman	kilicman	PROPN
ejpam-5027	46	10	/	/	SYM
ejpam-5027	46	11	eur	eur	PROPN
ejpam-5027	46	12	.	.	PUNCT
ejpam-5027	47	1	j.	j.	PROPN
ejpam-5027	47	2	pure	pure	PROPN
ejpam-5027	47	3	appl	appl	PROPN
ejpam-5027	47	4	.	.	PROPN
ejpam-5027	47	5	math	math	PROPN
ejpam-5027	47	6	,	,	PUNCT
ejpam-5027	47	7	17	17	NUM
ejpam-5027	47	8	(	(	PUNCT
ejpam-5027	47	9	1	1	NUM
ejpam-5027	47	10	)	)	PUNCT
ejpam-5027	47	11	(	(	PUNCT
ejpam-5027	47	12	2024	2024	NUM
ejpam-5027	47	13	)	)	PUNCT
ejpam-5027	47	14	,	,	PUNCT
ejpam-5027	47	15	30	30	NUM
ejpam-5027	47	16	-	-	SYM
ejpam-5027	47	17	41	41	NUM
ejpam-5027	47	18	32	32	NUM
ejpam-5027	47	19	(	(	PUNCT
ejpam-5027	47	20	4	4	NUM
ejpam-5027	47	21	)	)	PUNCT
ejpam-5027	47	22	the	the	DET
ejpam-5027	47	23	intersection	intersection	NOUN
ejpam-5027	47	24	of	of	ADP
ejpam-5027	47	25	e	e	NOUN
ejpam-5027	47	26	,	,	PUNCT
ejpam-5027	47	27	d	d	PROPN
ejpam-5027	47	28	indicated	indicate	VERB
ejpam-5027	47	29	by	by	ADP
ejpam-5027	47	30	e∧d	e∧d	NOUN
ejpam-5027	47	31	if	if	SCONJ
ejpam-5027	47	32	(	(	PUNCT
ejpam-5027	47	33	e∧d)(x	e∧d)(x	PROPN
ejpam-5027	47	34	)	)	PUNCT
ejpam-5027	47	35	=	=	SYM
ejpam-5027	47	36	min{e(x	min{e(x	PROPN
ejpam-5027	47	37	)	)	PUNCT
ejpam-5027	47	38	,	,	PUNCT
ejpam-5027	47	39	d(x	d(x	PROPN
ejpam-5027	47	40	)	)	PUNCT
ejpam-5027	47	41	}	}	PUNCT
ejpam-5027	47	42	∀	∀	X
ejpam-5027	48	1	x	x	SYM
ejpam-5027	48	2	∈	∈	NOUN
ejpam-5027	48	3	x.	x.	NOUN
ejpam-5027	48	4	(	(	PUNCT
ejpam-5027	48	5	5	5	NUM
ejpam-5027	48	6	)	)	PUNCT
ejpam-5027	48	7	the	the	DET
ejpam-5027	48	8	completeness	completeness	NOUN
ejpam-5027	48	9	of	of	ADP
ejpam-5027	48	10	e	e	PROPN
ejpam-5027	48	11	denoted	denote	VERB
ejpam-5027	48	12	via	via	ADP
ejpam-5027	48	13	ec	ec	PROPN
ejpam-5027	48	14	such	such	ADJ
ejpam-5027	48	15	that	that	PRON
ejpam-5027	48	16	(	(	PUNCT
ejpam-5027	48	17	e(x))c	e(x))c	PROPN
ejpam-5027	48	18	=	=	SYM
ejpam-5027	48	19	1−	1−	NUM
ejpam-5027	48	20	e(x	e(x	NUM
ejpam-5027	48	21	)	)	PUNCT
ejpam-5027	48	22	,	,	PUNCT
ejpam-5027	48	23	∀	∀	PUNCT
ejpam-5027	48	24	x	x	SYM
ejpam-5027	48	25	∈	∈	NOUN
ejpam-5027	48	26	x.	x.	NOUN
ejpam-5027	49	1	the	the	DET
ejpam-5027	49	2	following	follow	VERB
ejpam-5027	49	3	definitions	definition	NOUN
ejpam-5027	49	4	explain	explain	VERB
ejpam-5027	49	5	the	the	DET
ejpam-5027	49	6	meaning	meaning	NOUN
ejpam-5027	49	7	of	of	ADP
ejpam-5027	49	8	fuzzy	fuzzy	ADJ
ejpam-5027	49	9	topology	topology	NOUN
ejpam-5027	49	10	and	and	CCONJ
ejpam-5027	49	11	fuzzy	fuzzy	ADJ
ejpam-5027	49	12	bitopological	bitopological	ADJ
ejpam-5027	49	13	spaces	space	NOUN
ejpam-5027	49	14	.	.	PUNCT
ejpam-5027	50	1	definition	definition	NOUN
ejpam-5027	50	2	2	2	NUM
ejpam-5027	50	3	.	.	PUNCT
ejpam-5027	51	1	[	[	X
ejpam-5027	51	2	17	17	NUM
ejpam-5027	51	3	]	]	PUNCT
ejpam-5027	51	4	a	a	DET
ejpam-5027	51	5	fuzzy	fuzzy	ADJ
ejpam-5027	51	6	topology	topology	NOUN
ejpam-5027	51	7	of	of	ADP
ejpam-5027	51	8	x	x	PRON
ejpam-5027	51	9	is	be	AUX
ejpam-5027	51	10	a	a	DET
ejpam-5027	51	11	class	class	NOUN
ejpam-5027	51	12	of	of	ADP
ejpam-5027	51	13	fuzzy	fuzzy	ADJ
ejpam-5027	51	14	groups	group	NOUN
ejpam-5027	51	15	δ	δ	NOUN
ejpam-5027	51	16	∈	∈	PROPN
ejpam-5027	52	1	i	i	PRON
ejpam-5027	52	2	that	that	PRON
ejpam-5027	52	3	holds	hold	VERB
ejpam-5027	52	4	the	the	DET
ejpam-5027	52	5	coming	come	VERB
ejpam-5027	52	6	three	three	NUM
ejpam-5027	52	7	conditions	condition	NOUN
ejpam-5027	52	8	:	:	PUNCT
ejpam-5027	52	9	1	1	NUM
ejpam-5027	52	10	.	.	NUM
ejpam-5027	52	11	0	0	NUM
ejpam-5027	52	12	and	and	CCONJ
ejpam-5027	52	13	1	1	NUM
ejpam-5027	52	14	contained	contain	VERB
ejpam-5027	52	15	in	in	ADP
ejpam-5027	52	16	δ	δ	PROPN
ejpam-5027	52	17	,	,	PUNCT
ejpam-5027	52	18	where	where	SCONJ
ejpam-5027	52	19	0(x	0(x	NOUN
ejpam-5027	52	20	)	)	PUNCT
ejpam-5027	53	1	=	=	SYM
ejpam-5027	53	2	0	0	NUM
ejpam-5027	53	3	,	,	PUNCT
ejpam-5027	53	4	1(x	1(x	NUM
ejpam-5027	53	5	)	)	PUNCT
ejpam-5027	53	6	=	=	SYM
ejpam-5027	53	7	1	1	X
ejpam-5027	53	8	,	,	PUNCT
ejpam-5027	53	9	whenever	whenever	SCONJ
ejpam-5027	53	10	x	x	SYM
ejpam-5027	53	11	∈	∈	NOUN
ejpam-5027	53	12	x.	x.	NOUN
ejpam-5027	53	13	2	2	X
ejpam-5027	53	14	.	.	X
ejpam-5027	54	1	for	for	ADP
ejpam-5027	54	2	any	any	DET
ejpam-5027	54	3	e	e	NOUN
ejpam-5027	54	4	,	,	PUNCT
ejpam-5027	54	5	d	d	PROPN
ejpam-5027	54	6	∈	∈	PROPN
ejpam-5027	54	7	δ	δ	PROPN
ejpam-5027	54	8	,	,	PUNCT
ejpam-5027	54	9	e	e	PROPN
ejpam-5027	54	10	∧d	∧d	PROPN
ejpam-5027	54	11	∈	∈	PROPN
ejpam-5027	54	12	δ	δ	PROPN
ejpam-5027	54	13	.	.	PUNCT
ejpam-5027	55	1	3	3	X
ejpam-5027	55	2	.	.	X
ejpam-5027	56	1	for	for	ADP
ejpam-5027	56	2	any	any	DET
ejpam-5027	56	3	(	(	PUNCT
ejpam-5027	56	4	ei∈i	ei∈i	PROPN
ejpam-5027	56	5	)	)	PUNCT
ejpam-5027	56	6	∈	∈	PROPN
ejpam-5027	56	7	δ	δ	PROPN
ejpam-5027	56	8	,	,	PUNCT
ejpam-5027	56	9	∨i∈iei	∨i∈iei	PUNCT
ejpam-5027	56	10	∈	∈	PROPN
ejpam-5027	56	11	δ	δ	PROPN
ejpam-5027	56	12	.	.	PUNCT
ejpam-5027	57	1	the	the	DET
ejpam-5027	57	2	term	term	NOUN
ejpam-5027	57	3	”	"	PUNCT
ejpam-5027	57	4	fuzzy	fuzzy	ADJ
ejpam-5027	57	5	topological	topological	ADJ
ejpam-5027	57	6	space	space	NOUN
ejpam-5027	57	7	,	,	PUNCT
ejpam-5027	57	8	”	"	PUNCT
ejpam-5027	57	9	or	or	CCONJ
ejpam-5027	57	10	”	"	PUNCT
ejpam-5027	57	11	fts	fts	X
ejpam-5027	57	12	,	,	PUNCT
ejpam-5027	57	13	”	"	PUNCT
ejpam-5027	57	14	refers	refer	VERB
ejpam-5027	57	15	to	to	ADP
ejpam-5027	57	16	the	the	DET
ejpam-5027	57	17	pair	pair	NOUN
ejpam-5027	57	18	(	(	PUNCT
ejpam-5027	57	19	x	x	NOUN
ejpam-5027	57	20	,	,	PUNCT
ejpam-5027	57	21	δ	δ	PROPN
ejpam-5027	57	22	)	)	PUNCT
ejpam-5027	57	23	.	.	PUNCT
ejpam-5027	58	1	the	the	DET
ejpam-5027	58	2	components	component	NOUN
ejpam-5027	58	3	of	of	ADP
ejpam-5027	58	4	δ	δ	PROPN
ejpam-5027	58	5	are	be	AUX
ejpam-5027	58	6	named	name	VERB
ejpam-5027	58	7	fuzzy	fuzzy	ADJ
ejpam-5027	58	8	open	open	ADJ
ejpam-5027	58	9	sets	set	NOUN
ejpam-5027	58	10	.	.	PUNCT
ejpam-5027	59	1	if	if	SCONJ
ejpam-5027	59	2	f	f	PROPN
ejpam-5027	59	3	c	c	PROPN
ejpam-5027	59	4	∈	∈	PROPN
ejpam-5027	59	5	δ	δ	PROPN
ejpam-5027	59	6	,	,	PUNCT
ejpam-5027	59	7	a	a	DET
ejpam-5027	59	8	fuzzy	fuzzy	ADJ
ejpam-5027	59	9	set	set	NOUN
ejpam-5027	59	10	f	f	X
ejpam-5027	59	11	is	be	AUX
ejpam-5027	59	12	mean	mean	ADJ
ejpam-5027	59	13	as	as	ADP
ejpam-5027	59	14	fuzzy	fuzzy	ADJ
ejpam-5027	59	15	closed	closed	ADJ
ejpam-5027	59	16	.	.	PUNCT
ejpam-5027	60	1	the	the	DET
ejpam-5027	60	2	collection	collection	NOUN
ejpam-5027	60	3	including	include	VERB
ejpam-5027	60	4	all	all	DET
ejpam-5027	60	5	fuzzy	fuzzy	ADJ
ejpam-5027	60	6	closed	close	VERB
ejpam-5027	60	7	sets	set	NOUN
ejpam-5027	60	8	in	in	ADP
ejpam-5027	60	9	fuzzy	fuzzy	ADJ
ejpam-5027	60	10	topology	topology	NOUN
ejpam-5027	60	11	δ	δ	PROPN
ejpam-5027	60	12	denote	denote	VERB
ejpam-5027	60	13	by	by	ADP
ejpam-5027	60	14	fδ	fδ	NOUN
ejpam-5027	60	15	.	.	NOUN
ejpam-5027	60	16	definition	definition	NOUN
ejpam-5027	60	17	3	3	NUM
ejpam-5027	60	18	.	.	PUNCT
ejpam-5027	61	1	[	[	X
ejpam-5027	61	2	11	11	NUM
ejpam-5027	61	3	]	]	PUNCT
ejpam-5027	61	4	a	a	DET
ejpam-5027	61	5	fuzzy	fuzzy	ADJ
ejpam-5027	61	6	bitopological	bitopological	ADJ
ejpam-5027	61	7	spaces	space	NOUN
ejpam-5027	61	8	,	,	PUNCT
ejpam-5027	61	9	or	or	CCONJ
ejpam-5027	61	10	fbts	fbt	NOUN
ejpam-5027	61	11	for	for	ADP
ejpam-5027	61	12	short	short	ADJ
ejpam-5027	61	13	,	,	PUNCT
ejpam-5027	61	14	(	(	PUNCT
ejpam-5027	61	15	x	x	NOUN
ejpam-5027	61	16	,	,	PUNCT
ejpam-5027	61	17	δ1	δ1	NOUN
ejpam-5027	61	18	,	,	PUNCT
ejpam-5027	61	19	δ2	δ2	PROPN
ejpam-5027	61	20	)	)	PUNCT
ejpam-5027	61	21	since	since	SCONJ
ejpam-5027	61	22	x	x	PRON
ejpam-5027	61	23	is	be	AUX
ejpam-5027	61	24	not	not	PART
ejpam-5027	61	25	empty	empty	ADJ
ejpam-5027	61	26	,	,	PUNCT
ejpam-5027	61	27	δ1	δ1	NOUN
ejpam-5027	61	28	,	,	PUNCT
ejpam-5027	61	29	and	and	CCONJ
ejpam-5027	61	30	δ2	δ2	VERB
ejpam-5027	61	31	are	be	AUX
ejpam-5027	61	32	fuzzy	fuzzy	ADJ
ejpam-5027	61	33	topological	topological	ADJ
ejpam-5027	61	34	spaces	space	NOUN
ejpam-5027	61	35	on	on	ADP
ejpam-5027	61	36	x.	x.	NOUN
ejpam-5027	61	37	over	over	ADP
ejpam-5027	61	38	this	this	DET
ejpam-5027	61	39	dissertation	dissertation	NOUN
ejpam-5027	61	40	x	x	PUNCT
ejpam-5027	61	41	perform	perform	VERB
ejpam-5027	61	42	fuzzy	fuzzy	ADJ
ejpam-5027	61	43	bitopology	bitopology	NOUN
ejpam-5027	61	44	(	(	PUNCT
ejpam-5027	61	45	x	x	NOUN
ejpam-5027	61	46	,	,	PUNCT
ejpam-5027	61	47	δ1	δ1	NOUN
ejpam-5027	61	48	,	,	PUNCT
ejpam-5027	61	49	δ2	δ2	PROPN
ejpam-5027	61	50	)	)	PUNCT
ejpam-5027	61	51	,	,	PUNCT
ejpam-5027	61	52	and	and	CCONJ
ejpam-5027	61	53	y	y	PROPN
ejpam-5027	61	54	to	to	PART
ejpam-5027	61	55	(	(	PUNCT
ejpam-5027	61	56	y	y	PROPN
ejpam-5027	61	57	,	,	PUNCT
ejpam-5027	61	58	σ1	σ1	PROPN
ejpam-5027	61	59	,	,	PUNCT
ejpam-5027	61	60	σ2	σ2	NOUN
ejpam-5027	61	61	)	)	PUNCT
ejpam-5027	61	62	,	,	PUNCT
ejpam-5027	61	63	where	where	SCONJ
ejpam-5027	61	64	i	i	PRON
ejpam-5027	61	65	̸=	̸=	PROPN
ejpam-5027	61	66	j	j	PROPN
ejpam-5027	61	67	,	,	PUNCT
ejpam-5027	61	68	and	and	CCONJ
ejpam-5027	61	69	i	i	PRON
ejpam-5027	61	70	,	,	PUNCT
ejpam-5027	61	71	j	j	PROPN
ejpam-5027	61	72	∈	∈	PROPN
ejpam-5027	61	73	{	{	PUNCT
ejpam-5027	61	74	1	1	NUM
ejpam-5027	61	75	,	,	PUNCT
ejpam-5027	61	76	2	2	NUM
ejpam-5027	61	77	}	}	PUNCT
ejpam-5027	61	78	.	.	PUNCT
ejpam-5027	62	1	in	in	ADP
ejpam-5027	62	2	the	the	DET
ejpam-5027	62	3	section	section	NOUN
ejpam-5027	62	4	that	that	PRON
ejpam-5027	62	5	follows	follow	VERB
ejpam-5027	62	6	,	,	PUNCT
ejpam-5027	62	7	the	the	DET
ejpam-5027	62	8	definitions	definition	NOUN
ejpam-5027	62	9	of	of	ADP
ejpam-5027	62	10	fuzzy	fuzzy	ADJ
ejpam-5027	62	11	set	set	VERB
ejpam-5027	62	12	interiors	interior	NOUN
ejpam-5027	62	13	and	and	CCONJ
ejpam-5027	62	14	closings	closing	NOUN
ejpam-5027	62	15	are	be	AUX
ejpam-5027	62	16	covered	cover	VERB
ejpam-5027	62	17	.	.	PUNCT
ejpam-5027	63	1	definition	definition	NOUN
ejpam-5027	63	2	4	4	NUM
ejpam-5027	63	3	.	.	PUNCT
ejpam-5027	64	1	[	[	X
ejpam-5027	64	2	17	17	NUM
ejpam-5027	64	3	]	]	PUNCT
ejpam-5027	64	4	closing	closing	NOUN
ejpam-5027	64	5	and	and	CCONJ
ejpam-5027	64	6	internal	internal	ADJ
ejpam-5027	64	7	of	of	ADP
ejpam-5027	64	8	any	any	DET
ejpam-5027	64	9	fuzzy	fuzzy	ADJ
ejpam-5027	64	10	set	set	NOUN
ejpam-5027	64	11	m	m	NOUN
ejpam-5027	64	12	of	of	ADP
ejpam-5027	64	13	(	(	PUNCT
ejpam-5027	64	14	x	x	NOUN
ejpam-5027	64	15	,	,	PUNCT
ejpam-5027	64	16	δ	δ	PROPN
ejpam-5027	64	17	)	)	PUNCT
ejpam-5027	64	18	are	be	AUX
ejpam-5027	64	19	indicated	indicate	VERB
ejpam-5027	64	20	also	also	ADV
ejpam-5027	64	21	defined	define	VERB
ejpam-5027	64	22	as	as	SCONJ
ejpam-5027	64	23	follows	follow	VERB
ejpam-5027	64	24	:	:	PUNCT
ejpam-5027	64	25	cl(m	cl(m	X
ejpam-5027	64	26	)	)	PUNCT
ejpam-5027	65	1	=	=	SYM
ejpam-5027	65	2	∧	∧	NOUN
ejpam-5027	65	3	{	{	PUNCT
ejpam-5027	65	4	f	f	NOUN
ejpam-5027	65	5	:	:	PUNCT
ejpam-5027	65	6	m	m	VERB
ejpam-5027	65	7	≤	≤	NUM
ejpam-5027	66	1	f	f	X
ejpam-5027	66	2	,	,	PUNCT
ejpam-5027	66	3	f	f	PROPN
ejpam-5027	66	4	c	c	PROPN
ejpam-5027	66	5	∈	∈	PROPN
ejpam-5027	66	6	δ	δ	PROPN
ejpam-5027	66	7	}	}	PUNCT
ejpam-5027	66	8	int(m	int(m	PROPN
ejpam-5027	66	9	)	)	PUNCT
ejpam-5027	66	10	=	=	PUNCT
ejpam-5027	66	11	∨	∨	X
ejpam-5027	66	12	{	{	PUNCT
ejpam-5027	66	13	o	o	NOUN
ejpam-5027	66	14	:	:	PUNCT
ejpam-5027	66	15	o	o	X
ejpam-5027	66	16	≤m	≤m	PROPN
ejpam-5027	66	17	,	,	PUNCT
ejpam-5027	66	18	o	o	PROPN
ejpam-5027	66	19	∈	∈	PROPN
ejpam-5027	66	20	δ	δ	PROPN
ejpam-5027	66	21	}	}	PUNCT
ejpam-5027	66	22	,	,	PUNCT
ejpam-5027	66	23	respectively	respectively	ADV
ejpam-5027	66	24	.	.	PUNCT
ejpam-5027	67	1	the	the	DET
ejpam-5027	67	2	closing	closing	NOUN
ejpam-5027	67	3	,	,	PUNCT
ejpam-5027	67	4	internal	internal	ADJ
ejpam-5027	67	5	,	,	PUNCT
ejpam-5027	67	6	and	and	CCONJ
ejpam-5027	67	7	complements	complement	VERB
ejpam-5027	67	8	ofm	ofm	PROPN
ejpam-5027	67	9	of	of	ADP
ejpam-5027	67	10	x	x	PRON
ejpam-5027	67	11	are	be	AUX
ejpam-5027	67	12	indicated	indicate	VERB
ejpam-5027	67	13	by	by	ADP
ejpam-5027	67	14	δi−cl(m	δi−cl(m	PROPN
ejpam-5027	67	15	)	)	PUNCT
ejpam-5027	67	16	,	,	PUNCT
ejpam-5027	67	17	δi−int(m	δi−int(m	PROPN
ejpam-5027	67	18	)	)	PUNCT
ejpam-5027	67	19	,	,	PUNCT
ejpam-5027	67	20	and	and	CCONJ
ejpam-5027	67	21	m	m	PROPN
ejpam-5027	67	22	c	c	NOUN
ejpam-5027	67	23	i	i	PRON
ejpam-5027	67	24	,	,	PUNCT
ejpam-5027	67	25	respectively	respectively	ADV
ejpam-5027	67	26	,	,	PUNCT
ejpam-5027	67	27	with	with	ADP
ejpam-5027	67	28	regard	regard	NOUN
ejpam-5027	67	29	to	to	ADP
ejpam-5027	67	30	fuzzy	fuzzy	ADJ
ejpam-5027	67	31	topology	topology	NOUN
ejpam-5027	67	32	δi	δi	NOUN
ejpam-5027	67	33	.	.	PUNCT
ejpam-5027	68	1	additionally	additionally	ADV
ejpam-5027	68	2	,	,	PUNCT
ejpam-5027	68	3	we	we	PRON
ejpam-5027	68	4	designate	designate	VERB
ejpam-5027	68	5	the	the	DET
ejpam-5027	68	6	class	class	NOUN
ejpam-5027	68	7	of	of	ADP
ejpam-5027	68	8	all	all	PRON
ejpam-5027	68	9	fuzzy	fuzzy	ADJ
ejpam-5027	68	10	δj	δj	NOUN
ejpam-5027	68	11	-	-	PUNCT
ejpam-5027	68	12	closed	close	VERB
ejpam-5027	68	13	by	by	ADP
ejpam-5027	68	14	the	the	DET
ejpam-5027	68	15	mathematical	mathematical	ADJ
ejpam-5027	68	16	symbol	symbol	NOUN
ejpam-5027	68	17	fδj	fδj	NOUN
ejpam-5027	68	18	.	.	PUNCT
ejpam-5027	69	1	one	one	NUM
ejpam-5027	69	2	of	of	ADP
ejpam-5027	69	3	the	the	DET
ejpam-5027	69	4	work	work	NOUN
ejpam-5027	69	5	’s	’s	PART
ejpam-5027	69	6	core	core	NOUN
ejpam-5027	69	7	tenets	tenet	NOUN
ejpam-5027	69	8	is	be	AUX
ejpam-5027	69	9	the	the	DET
ejpam-5027	69	10	definition	definition	NOUN
ejpam-5027	69	11	of	of	ADP
ejpam-5027	69	12	the	the	DET
ejpam-5027	69	13	fuzzy	fuzzy	ADJ
ejpam-5027	69	14	generalized	generalize	VERB
ejpam-5027	69	15	closed	close	VERB
ejpam-5027	69	16	set	set	NOUN
ejpam-5027	69	17	,	,	PUNCT
ejpam-5027	69	18	which	which	PRON
ejpam-5027	69	19	as	as	ADP
ejpam-5027	69	20	following	follow	VERB
ejpam-5027	69	21	:	:	PUNCT
ejpam-5027	69	22	definition	definition	NOUN
ejpam-5027	69	23	5	5	NUM
ejpam-5027	69	24	.	.	PUNCT
ejpam-5027	70	1	[	[	X
ejpam-5027	70	2	7	7	X
ejpam-5027	70	3	]	]	PUNCT
ejpam-5027	70	4	any	any	DET
ejpam-5027	70	5	fuzzy	fuzzy	ADJ
ejpam-5027	70	6	set	set	VERB
ejpam-5027	70	7	n	n	PROPN
ejpam-5027	70	8	of	of	ADP
ejpam-5027	70	9	x	x	VERB
ejpam-5027	70	10	is	be	AUX
ejpam-5027	70	11	termed	term	VERB
ejpam-5027	70	12	fuzzy	fuzzy	ADJ
ejpam-5027	70	13	generalized	generalize	VERB
ejpam-5027	70	14	closed	close	VERB
ejpam-5027	70	15	when	when	SCONJ
ejpam-5027	70	16	closure	closure	NOUN
ejpam-5027	70	17	n	n	NOUN
ejpam-5027	70	18	is	be	AUX
ejpam-5027	70	19	subset	subset	VERB
ejpam-5027	70	20	of	of	ADP
ejpam-5027	70	21	u	u	NOUN
ejpam-5027	70	22	,	,	PUNCT
ejpam-5027	70	23	wherever	wherever	SCONJ
ejpam-5027	70	24	n	n	X
ejpam-5027	70	25	is	be	AUX
ejpam-5027	70	26	subset	subset	VERB
ejpam-5027	70	27	of	of	ADP
ejpam-5027	70	28	u	u	NOUN
ejpam-5027	70	29	and	and	CCONJ
ejpam-5027	70	30	u	u	NOUN
ejpam-5027	70	31	is	be	AUX
ejpam-5027	70	32	fuzzy	fuzzy	ADJ
ejpam-5027	70	33	open	open	ADJ
ejpam-5027	70	34	.	.	PUNCT
ejpam-5027	71	1	i.e.	i.e.	X
ejpam-5027	71	2	,	,	PUNCT
ejpam-5027	71	3	n	n	PRON
ejpam-5027	71	4	is	be	AUX
ejpam-5027	71	5	fuzzy	fuzzy	ADJ
ejpam-5027	71	6	generalized	generalized	ADJ
ejpam-5027	71	7	closed	close	VERB
ejpam-5027	71	8	if	if	SCONJ
ejpam-5027	71	9	cl(n	cl(n	NUM
ejpam-5027	71	10	)	)	PUNCT
ejpam-5027	71	11	≤	≤	NUM
ejpam-5027	71	12	u	u	NOUN
ejpam-5027	71	13	,	,	PUNCT
ejpam-5027	71	14	wherever	wherever	SCONJ
ejpam-5027	71	15	n	n	DET
ejpam-5027	71	16	≤	≤	NOUN
ejpam-5027	71	17	u	u	NOUN
ejpam-5027	71	18	,	,	PUNCT
ejpam-5027	71	19	u	u	NOUN
ejpam-5027	71	20	is	be	AUX
ejpam-5027	71	21	fuzzy	fuzzy	ADJ
ejpam-5027	71	22	open	open	ADJ
ejpam-5027	71	23	.	.	PUNCT
ejpam-5027	72	1	one	one	NUM
ejpam-5027	72	2	of	of	ADP
ejpam-5027	72	3	the	the	DET
ejpam-5027	72	4	fundamental	fundamental	ADJ
ejpam-5027	72	5	ideas	idea	NOUN
ejpam-5027	72	6	in	in	ADP
ejpam-5027	72	7	this	this	DET
ejpam-5027	72	8	research	research	NOUN
ejpam-5027	72	9	is	be	AUX
ejpam-5027	72	10	continuous	continuous	ADJ
ejpam-5027	72	11	and	and	CCONJ
ejpam-5027	72	12	irresolute	irresolute	ADJ
ejpam-5027	72	13	mapping	mapping	NOUN
ejpam-5027	72	14	,	,	PUNCT
ejpam-5027	72	15	in	in	ADP
ejpam-5027	72	16	addition	addition	NOUN
ejpam-5027	72	17	to	to	ADP
ejpam-5027	72	18	compactness	compactness	NOUN
ejpam-5027	72	19	,	,	PUNCT
ejpam-5027	72	20	they	they	PRON
ejpam-5027	72	21	are	be	AUX
ejpam-5027	72	22	defined	define	VERB
ejpam-5027	72	23	as	as	SCONJ
ejpam-5027	72	24	follows	follow	VERB
ejpam-5027	72	25	:	:	PUNCT
ejpam-5027	72	26	definition	definition	NOUN
ejpam-5027	72	27	6	6	NUM
ejpam-5027	72	28	.	.	PUNCT
ejpam-5027	73	1	[	[	X
ejpam-5027	73	2	17	17	NUM
ejpam-5027	73	3	]	]	X
ejpam-5027	73	4	let	let	AUX
ejpam-5027	73	5	(	(	PUNCT
ejpam-5027	73	6	x	x	NOUN
ejpam-5027	73	7	,	,	PUNCT
ejpam-5027	73	8	δ	δ	PROPN
ejpam-5027	73	9	)	)	PUNCT
ejpam-5027	73	10	and	and	CCONJ
ejpam-5027	73	11	(	(	PUNCT
ejpam-5027	73	12	y	y	PROPN
ejpam-5027	73	13	,	,	PUNCT
ejpam-5027	73	14	σ	σ	PROPN
ejpam-5027	73	15	)	)	PUNCT
ejpam-5027	73	16	be	be	VERB
ejpam-5027	73	17	an	an	DET
ejpam-5027	73	18	fts	fts	PROPN
ejpam-5027	73	19	and	and	CCONJ
ejpam-5027	73	20	f	f	PROPN
ejpam-5027	73	21	a	a	DET
ejpam-5027	73	22	function	function	NOUN
ejpam-5027	73	23	from	from	ADP
ejpam-5027	73	24	x	x	PUNCT
ejpam-5027	73	25	to	to	ADP
ejpam-5027	73	26	y	y	PROPN
ejpam-5027	73	27	.	.	PUNCT
ejpam-5027	74	1	then	then	ADV
ejpam-5027	74	2	f	f	PROPN
ejpam-5027	74	3	is	be	AUX
ejpam-5027	74	4	fuzzy	fuzzy	ADJ
ejpam-5027	74	5	δ−continuous	δ−continuous	ADJ
ejpam-5027	74	6	if	if	SCONJ
ejpam-5027	74	7	and	and	CCONJ
ejpam-5027	74	8	only	only	ADV
ejpam-5027	74	9	if	if	SCONJ
ejpam-5027	74	10	f−1(v	f−1(v	PROPN
ejpam-5027	74	11	)	)	PUNCT
ejpam-5027	74	12	∈	∈	PROPN
ejpam-5027	74	13	δ	δ	PROPN
ejpam-5027	74	14	,	,	PUNCT
ejpam-5027	74	15	∀v	∀v	PROPN
ejpam-5027	74	16	∈	∈	PROPN
ejpam-5027	74	17	σ	σ	PROPN
ejpam-5027	74	18	.	.	PUNCT
ejpam-5027	75	1	ahlam	ahlam	PROPN
ejpam-5027	75	2	ahmed	ahmed	PROPN
ejpam-5027	75	3	alharbi	alharbi	PROPN
ejpam-5027	75	4	,	,	PUNCT
ejpam-5027	75	5	adem	adem	PROPN
ejpam-5027	75	6	kilicman	kilicman	PROPN
ejpam-5027	75	7	/	/	SYM
ejpam-5027	75	8	eur	eur	PROPN
ejpam-5027	75	9	.	.	PUNCT
ejpam-5027	76	1	j.	j.	PROPN
ejpam-5027	76	2	pure	pure	PROPN
ejpam-5027	76	3	appl	appl	PROPN
ejpam-5027	76	4	.	.	PROPN
ejpam-5027	76	5	math	math	PROPN
ejpam-5027	76	6	,	,	PUNCT
ejpam-5027	76	7	17	17	NUM
ejpam-5027	76	8	(	(	PUNCT
ejpam-5027	76	9	1	1	NUM
ejpam-5027	76	10	)	)	PUNCT
ejpam-5027	76	11	(	(	PUNCT
ejpam-5027	76	12	2024	2024	NUM
ejpam-5027	76	13	)	)	PUNCT
ejpam-5027	76	14	,	,	PUNCT
ejpam-5027	76	15	30	30	NUM
ejpam-5027	76	16	-	-	SYM
ejpam-5027	76	17	41	41	NUM
ejpam-5027	76	18	33	33	NUM
ejpam-5027	76	19	definition	definition	NOUN
ejpam-5027	76	20	7	7	NUM
ejpam-5027	76	21	.	.	PUNCT
ejpam-5027	77	1	[	[	X
ejpam-5027	77	2	8	8	NUM
ejpam-5027	77	3	]	]	PUNCT
ejpam-5027	77	4	a	a	DET
ejpam-5027	77	5	mapping	mapping	NOUN
ejpam-5027	77	6	f	f	NOUN
ejpam-5027	77	7	:	:	PUNCT
ejpam-5027	77	8	(	(	PUNCT
ejpam-5027	77	9	x	x	NOUN
ejpam-5027	77	10	,	,	PUNCT
ejpam-5027	77	11	δ	δ	PROPN
ejpam-5027	77	12	)	)	PUNCT
ejpam-5027	77	13	−→	−→	NOUN
ejpam-5027	77	14	(	(	PUNCT
ejpam-5027	77	15	y	y	PROPN
ejpam-5027	77	16	,	,	PUNCT
ejpam-5027	77	17	σ	σ	PROPN
ejpam-5027	77	18	)	)	PUNCT
ejpam-5027	77	19	is	be	AUX
ejpam-5027	77	20	said	say	VERB
ejpam-5027	77	21	to	to	PART
ejpam-5027	77	22	be	be	AUX
ejpam-5027	77	23	fuzzy	fuzzy	ADJ
ejpam-5027	77	24	δ	δ	NOUN
ejpam-5027	77	25	−	−	NOUN
ejpam-5027	77	26	α	α	PRON
ejpam-5027	77	27	−	−	PROPN
ejpam-5027	77	28	irresolute	irresolute	ADJ
ejpam-5027	77	29	if	if	SCONJ
ejpam-5027	77	30	f−1(v	f−1(v	PROPN
ejpam-5027	77	31	)	)	PUNCT
ejpam-5027	77	32	is	be	AUX
ejpam-5027	77	33	fuzzy	fuzzy	ADJ
ejpam-5027	77	34	α−open	α−open	VERB
ejpam-5027	77	35	set	set	VERB
ejpam-5027	77	36	in	in	ADP
ejpam-5027	77	37	x	x	PUNCT
ejpam-5027	77	38	for	for	ADP
ejpam-5027	77	39	each	each	DET
ejpam-5027	77	40	fuzzy	fuzzy	ADJ
ejpam-5027	77	41	α−open	α−open	NOUN
ejpam-5027	77	42	set	set	VERB
ejpam-5027	77	43	v	v	NOUN
ejpam-5027	77	44	in	in	ADP
ejpam-5027	77	45	y	y	PROPN
ejpam-5027	77	46	.	.	PUNCT
ejpam-5027	78	1	definition	definition	NOUN
ejpam-5027	78	2	8	8	NUM
ejpam-5027	78	3	.	.	PUNCT
ejpam-5027	79	1	[	[	X
ejpam-5027	79	2	9	9	NUM
ejpam-5027	79	3	]	]	SYM
ejpam-5027	79	4	(	(	PUNCT
ejpam-5027	79	5	1	1	X
ejpam-5027	79	6	)	)	PUNCT
ejpam-5027	79	7	any	any	DET
ejpam-5027	79	8	fuzzy	fuzzy	ADJ
ejpam-5027	79	9	topology	topology	NOUN
ejpam-5027	79	10	(	(	PUNCT
ejpam-5027	79	11	x	x	X
ejpam-5027	79	12	,	,	PUNCT
ejpam-5027	79	13	τ	τ	X
ejpam-5027	79	14	)	)	PUNCT
ejpam-5027	79	15	is	be	AUX
ejpam-5027	79	16	named	name	VERB
ejpam-5027	79	17	fuzzy	fuzzy	ADJ
ejpam-5027	79	18	compact	compact	ADJ
ejpam-5027	79	19	when	when	SCONJ
ejpam-5027	79	20	every	every	DET
ejpam-5027	79	21	fuzzy	fuzzy	ADJ
ejpam-5027	79	22	open	open	ADJ
ejpam-5027	79	23	covering	covering	NOUN
ejpam-5027	79	24	x	x	VERB
ejpam-5027	79	25	has	have	VERB
ejpam-5027	79	26	a	a	DET
ejpam-5027	79	27	limited	limited	ADJ
ejpam-5027	79	28	subcover	subcover	PROPN
ejpam-5027	79	29	.	.	PUNCT
ejpam-5027	80	1	(	(	PUNCT
ejpam-5027	80	2	2	2	X
ejpam-5027	80	3	)	)	PUNCT
ejpam-5027	80	4	any	any	PRON
ejpam-5027	80	5	fuzzy	fuzzy	ADJ
ejpam-5027	80	6	set	set	NOUN
ejpam-5027	80	7	b	b	PROPN
ejpam-5027	80	8	of	of	ADP
ejpam-5027	80	9	(	(	PUNCT
ejpam-5027	80	10	x	x	PROPN
ejpam-5027	80	11	,	,	PUNCT
ejpam-5027	80	12	τ	τ	X
ejpam-5027	80	13	)	)	PUNCT
ejpam-5027	80	14	is	be	AUX
ejpam-5027	80	15	named	name	VERB
ejpam-5027	80	16	a	a	DET
ejpam-5027	80	17	fuzzy	fuzzy	ADJ
ejpam-5027	80	18	compact	compact	ADJ
ejpam-5027	80	19	subset	subset	NOUN
ejpam-5027	80	20	of	of	ADP
ejpam-5027	80	21	x	x	PRON
ejpam-5027	80	22	when	when	SCONJ
ejpam-5027	80	23	every	every	DET
ejpam-5027	80	24	fuzzy	fuzzy	ADJ
ejpam-5027	80	25	open	open	ADJ
ejpam-5027	80	26	covering	cover	VERB
ejpam-5027	80	27	b	b	NOUN
ejpam-5027	80	28	has	have	AUX
ejpam-5027	80	29	a	a	DET
ejpam-5027	80	30	limited	limited	ADJ
ejpam-5027	80	31	subcover	subcover	PROPN
ejpam-5027	80	32	.	.	PUNCT
ejpam-5027	81	1	an	an	DET
ejpam-5027	81	2	important	important	ADJ
ejpam-5027	81	3	property	property	NOUN
ejpam-5027	81	4	in	in	ADP
ejpam-5027	81	5	the	the	DET
ejpam-5027	81	6	study	study	NOUN
ejpam-5027	81	7	of	of	ADP
ejpam-5027	81	8	compactness	compactness	NOUN
ejpam-5027	81	9	is	be	AUX
ejpam-5027	81	10	the	the	DET
ejpam-5027	81	11	finite	finite	ADJ
ejpam-5027	81	12	intersection	intersection	NOUN
ejpam-5027	81	13	property	property	NOUN
ejpam-5027	81	14	,	,	PUNCT
ejpam-5027	81	15	which	which	PRON
ejpam-5027	81	16	was	be	AUX
ejpam-5027	81	17	define	define	VERB
ejpam-5027	81	18	as	as	ADP
ejpam-5027	81	19	:	:	PUNCT
ejpam-5027	81	20	definition	definition	NOUN
ejpam-5027	81	21	9	9	NUM
ejpam-5027	81	22	.	.	PUNCT
ejpam-5027	82	1	[	[	X
ejpam-5027	82	2	9	9	NUM
ejpam-5027	82	3	]	]	PUNCT
ejpam-5027	82	4	a	a	DET
ejpam-5027	82	5	class	class	NOUN
ejpam-5027	82	6	{	{	PUNCT
ejpam-5027	82	7	ai	ai	VERB
ejpam-5027	82	8	}	}	PUNCT
ejpam-5027	82	9	of	of	ADP
ejpam-5027	82	10	fuzzy	fuzzy	ADJ
ejpam-5027	82	11	groups	group	NOUN
ejpam-5027	82	12	of	of	ADP
ejpam-5027	82	13	x	x	PUNCT
ejpam-5027	82	14	is	be	AUX
ejpam-5027	82	15	entitled	entitle	VERB
ejpam-5027	82	16	having	have	VERB
ejpam-5027	82	17	finite	finite	ADJ
ejpam-5027	82	18	intersection	intersection	NOUN
ejpam-5027	82	19	characteristic	characteristic	ADJ
ejpam-5027	82	20	(	(	PUNCT
ejpam-5027	82	21	in	in	ADP
ejpam-5027	82	22	sum	sum	NOUN
ejpam-5027	82	23	,	,	PUNCT
ejpam-5027	82	24	f.i.p	f.i.p	ADV
ejpam-5027	82	25	)	)	PUNCT
ejpam-5027	82	26	when	when	SCONJ
ejpam-5027	82	27	all	all	DET
ejpam-5027	82	28	finite	finite	VERB
ejpam-5027	82	29	subclass	subclass	NOUN
ejpam-5027	82	30	{	{	PUNCT
ejpam-5027	82	31	ai1	ai1	PROPN
ejpam-5027	82	32	,	,	PUNCT
ejpam-5027	82	33	ai2	ai2	INTJ
ejpam-5027	82	34	,	,	PUNCT
ejpam-5027	82	35	...	...	PUNCT
ejpam-5027	82	36	,	,	PUNCT
ejpam-5027	82	37	ain	ain	PROPN
ejpam-5027	82	38	}	}	PUNCT
ejpam-5027	82	39	has	have	VERB
ejpam-5027	82	40	a	a	DET
ejpam-5027	82	41	non	non	ADJ
ejpam-5027	82	42	empty	empty	ADJ
ejpam-5027	82	43	intersection	intersection	NOUN
ejpam-5027	82	44	ai1	ai1	X
ejpam-5027	82	45	∩ai2	∩ai2	PROPN
ejpam-5027	82	46	∩	∩	NOUN
ejpam-5027	82	47	...	...	PUNCT
ejpam-5027	82	48	∩ain	∩ain	VERB
ejpam-5027	82	49	̸=	̸=	PROPN
ejpam-5027	82	50	ϕ	ϕ	PROPN
ejpam-5027	82	51	3	3	NUM
ejpam-5027	82	52	.	.	NOUN
ejpam-5027	82	53	types	type	NOUN
ejpam-5027	82	54	of	of	ADP
ejpam-5027	82	55	fuzzy	fuzzy	ADJ
ejpam-5027	82	56	generalized	generalize	VERB
ejpam-5027	82	57	closed	close	VERB
ejpam-5027	82	58	classes	class	NOUN
ejpam-5027	82	59	in	in	ADP
ejpam-5027	82	60	fuzzy	fuzzy	ADJ
ejpam-5027	82	61	bitopology	bitopology	NOUN
ejpam-5027	82	62	space	space	NOUN
ejpam-5027	82	63	in	in	ADP
ejpam-5027	82	64	the	the	DET
ejpam-5027	82	65	following	follow	VERB
ejpam-5027	82	66	section	section	NOUN
ejpam-5027	82	67	,	,	PUNCT
ejpam-5027	82	68	we	we	PRON
ejpam-5027	82	69	discuss	discuss	VERB
ejpam-5027	82	70	some	some	DET
ejpam-5027	82	71	types	type	NOUN
ejpam-5027	82	72	of	of	ADP
ejpam-5027	82	73	fuzzy	fuzzy	ADJ
ejpam-5027	82	74	generalized	generalize	VERB
ejpam-5027	82	75	closed	closed	ADJ
ejpam-5027	82	76	groups	group	NOUN
ejpam-5027	82	77	,	,	PUNCT
ejpam-5027	82	78	theorems	theorem	NOUN
ejpam-5027	82	79	,	,	PUNCT
ejpam-5027	82	80	and	and	CCONJ
ejpam-5027	82	81	relationships	relationship	NOUN
ejpam-5027	82	82	,	,	PUNCT
ejpam-5027	82	83	and	and	CCONJ
ejpam-5027	82	84	examine	examine	VERB
ejpam-5027	82	85	their	their	PRON
ejpam-5027	82	86	closure	closure	NOUN
ejpam-5027	82	87	and	and	CCONJ
ejpam-5027	82	88	interiors	interior	NOUN
ejpam-5027	82	89	in	in	ADP
ejpam-5027	82	90	an	an	DET
ejpam-5027	82	91	fbts	fbt	NOUN
ejpam-5027	82	92	.	.	PUNCT
ejpam-5027	83	1	definition	definition	NOUN
ejpam-5027	83	2	10	10	NUM
ejpam-5027	83	3	.	.	PUNCT
ejpam-5027	84	1	any	any	DET
ejpam-5027	84	2	fuzzy	fuzzy	ADJ
ejpam-5027	84	3	set	set	VERB
ejpam-5027	84	4	h	h	NOUN
ejpam-5027	84	5	of	of	ADP
ejpam-5027	84	6	fbts	fbt	NOUN
ejpam-5027	84	7	(	(	PUNCT
ejpam-5027	84	8	x	x	NOUN
ejpam-5027	84	9	,	,	PUNCT
ejpam-5027	84	10	τ1	τ1	NOUN
ejpam-5027	84	11	,	,	PUNCT
ejpam-5027	84	12	τ2	τ2	NOUN
ejpam-5027	84	13	)	)	PUNCT
ejpam-5027	84	14	,	,	PUNCT
ejpam-5027	84	15	where	where	SCONJ
ejpam-5027	84	16	i	i	PRON
ejpam-5027	84	17	,	,	PUNCT
ejpam-5027	84	18	j	j	PROPN
ejpam-5027	84	19	∈	∈	PROPN
ejpam-5027	84	20	{	{	PUNCT
ejpam-5027	84	21	0	0	NUM
ejpam-5027	84	22	,	,	PUNCT
ejpam-5027	84	23	1	1	NUM
ejpam-5027	84	24	}	}	PUNCT
ejpam-5027	84	25	,	,	PUNCT
ejpam-5027	84	26	i	i	PRON
ejpam-5027	84	27	̸=	̸=	PROPN
ejpam-5027	84	28	j	j	PROPN
ejpam-5027	84	29	is	be	AUX
ejpam-5027	84	30	called	call	VERB
ejpam-5027	84	31	:	:	PUNCT
ejpam-5027	84	32	(	(	PUNCT
ejpam-5027	84	33	1	1	X
ejpam-5027	84	34	)	)	PUNCT
ejpam-5027	84	35	fuzzy	fuzzy	NOUN
ejpam-5027	84	36	(	(	PUNCT
ejpam-5027	84	37	i	i	NOUN
ejpam-5027	84	38	,	,	PUNCT
ejpam-5027	84	39	j)−generalized	j)−generalized	PROPN
ejpam-5027	84	40	α−closed	α−close	VERB
ejpam-5027	84	41	(	(	PUNCT
ejpam-5027	84	42	in	in	ADP
ejpam-5027	84	43	sum	sum	NOUN
ejpam-5027	84	44	,	,	PUNCT
ejpam-5027	84	45	(	(	PUNCT
ejpam-5027	84	46	i	i	PROPN
ejpam-5027	84	47	,	,	PUNCT
ejpam-5027	84	48	j	j	PROPN
ejpam-5027	84	49	)	)	PUNCT
ejpam-5027	84	50	−	−	PROPN
ejpam-5027	84	51	gα	gα	ADP
ejpam-5027	84	52	−	−	PROPN
ejpam-5027	84	53	cld	cld	NOUN
ejpam-5027	84	54	)	)	PUNCT
ejpam-5027	84	55	if	if	SCONJ
ejpam-5027	84	56	τj	τj	ADP
ejpam-5027	84	57	−	−	PROPN
ejpam-5027	84	58	αcl(h	αcl(h	PROPN
ejpam-5027	84	59	)	)	PUNCT
ejpam-5027	84	60	≤	≤	NOUN
ejpam-5027	84	61	w	w	ADP
ejpam-5027	84	62	,	,	PUNCT
ejpam-5027	84	63	wherever	wherever	SCONJ
ejpam-5027	84	64	h	h	NOUN
ejpam-5027	84	65	≤w	≤w	NOUN
ejpam-5027	84	66	,	,	PUNCT
ejpam-5027	84	67	w	w	PROPN
ejpam-5027	84	68	∈	∈	PROPN
ejpam-5027	84	69	τi	τi	NOUN
ejpam-5027	84	70	.	.	PUNCT
ejpam-5027	85	1	(	(	PUNCT
ejpam-5027	85	2	2	2	X
ejpam-5027	85	3	)	)	PUNCT
ejpam-5027	85	4	fuzzy	fuzzy	NOUN
ejpam-5027	85	5	(	(	PUNCT
ejpam-5027	85	6	i	i	NOUN
ejpam-5027	85	7	,	,	PUNCT
ejpam-5027	85	8	j)−generalized	j)−generalized	PROPN
ejpam-5027	85	9	semi−closed	semi−close	VERB
ejpam-5027	85	10	(	(	PUNCT
ejpam-5027	85	11	in	in	ADP
ejpam-5027	85	12	sum	sum	NOUN
ejpam-5027	85	13	,	,	PUNCT
ejpam-5027	85	14	(	(	PUNCT
ejpam-5027	85	15	i	i	PROPN
ejpam-5027	85	16	,	,	PUNCT
ejpam-5027	85	17	j	j	PROPN
ejpam-5027	85	18	)	)	PUNCT
ejpam-5027	86	1	−	−	PROPN
ejpam-5027	87	1	gs	gs	INTJ
ejpam-5027	88	1	−	−	PROPN
ejpam-5027	88	2	cld	cld	NOUN
ejpam-5027	88	3	)	)	PUNCT
ejpam-5027	88	4	if	if	SCONJ
ejpam-5027	88	5	τj	τj	ADP
ejpam-5027	88	6	−	−	PROPN
ejpam-5027	88	7	scl(h	scl(h	PROPN
ejpam-5027	88	8	)	)	PUNCT
ejpam-5027	88	9	≤	≤	NOUN
ejpam-5027	88	10	w	w	ADP
ejpam-5027	88	11	,	,	PUNCT
ejpam-5027	88	12	wherever	wherever	SCONJ
ejpam-5027	88	13	h	h	NOUN
ejpam-5027	88	14	≤w	≤w	NOUN
ejpam-5027	88	15	,	,	PUNCT
ejpam-5027	88	16	w	w	PROPN
ejpam-5027	88	17	∈	∈	PROPN
ejpam-5027	88	18	τi	τi	NOUN
ejpam-5027	88	19	.	.	PUNCT
ejpam-5027	89	1	(	(	PUNCT
ejpam-5027	89	2	3	3	X
ejpam-5027	89	3	)	)	PUNCT
ejpam-5027	89	4	fuzzy	fuzzy	NOUN
ejpam-5027	89	5	(	(	PUNCT
ejpam-5027	89	6	i	i	NOUN
ejpam-5027	89	7	,	,	PUNCT
ejpam-5027	89	8	j)−generalized	j)−generalize	VERB
ejpam-5027	89	9	pre−closed	pre−close	VERB
ejpam-5027	89	10	(	(	PUNCT
ejpam-5027	89	11	in	in	ADP
ejpam-5027	89	12	sum	sum	NOUN
ejpam-5027	89	13	,	,	PUNCT
ejpam-5027	89	14	(	(	PUNCT
ejpam-5027	89	15	i	i	PROPN
ejpam-5027	89	16	,	,	PUNCT
ejpam-5027	89	17	j	j	PROPN
ejpam-5027	89	18	)	)	PUNCT
ejpam-5027	89	19	−	−	PROPN
ejpam-5027	89	20	gp	gp	NOUN
ejpam-5027	89	21	−	−	PROPN
ejpam-5027	89	22	cld	cld	NOUN
ejpam-5027	89	23	)	)	PUNCT
ejpam-5027	90	1	if	if	SCONJ
ejpam-5027	90	2	τj	τj	ADP
ejpam-5027	90	3	−	−	PROPN
ejpam-5027	90	4	pcl(h	pcl(h	NOUN
ejpam-5027	90	5	)	)	PUNCT
ejpam-5027	90	6	≤	≤	NOUN
ejpam-5027	91	1	w	w	ADP
ejpam-5027	91	2	,	,	PUNCT
ejpam-5027	91	3	wherever	wherever	SCONJ
ejpam-5027	91	4	h	h	NOUN
ejpam-5027	91	5	≤w	≤w	NOUN
ejpam-5027	91	6	,	,	PUNCT
ejpam-5027	91	7	w	w	PROPN
ejpam-5027	91	8	∈	∈	PROPN
ejpam-5027	91	9	τi	τi	X
ejpam-5027	91	10	(	(	PUNCT
ejpam-5027	91	11	4	4	X
ejpam-5027	91	12	)	)	PUNCT
ejpam-5027	91	13	fuzzy	fuzzy	ADJ
ejpam-5027	91	14	(	(	PUNCT
ejpam-5027	91	15	i	i	NOUN
ejpam-5027	91	16	,	,	PUNCT
ejpam-5027	91	17	j)−generalized	j)−generalized	PROPN
ejpam-5027	91	18	β−closed	β−close	VERB
ejpam-5027	91	19	(	(	PUNCT
ejpam-5027	91	20	in	in	ADP
ejpam-5027	91	21	sum	sum	NOUN
ejpam-5027	91	22	,	,	PUNCT
ejpam-5027	91	23	(	(	PUNCT
ejpam-5027	91	24	i	i	PROPN
ejpam-5027	91	25	,	,	PUNCT
ejpam-5027	91	26	j	j	PROPN
ejpam-5027	91	27	)	)	PUNCT
ejpam-5027	91	28	−	−	PROPN
ejpam-5027	92	1	gβ	gβ	NOUN
ejpam-5027	92	2	−	−	PROPN
ejpam-5027	92	3	cld	cld	NOUN
ejpam-5027	92	4	)	)	PUNCT
ejpam-5027	92	5	if	if	SCONJ
ejpam-5027	92	6	τj	τj	ADP
ejpam-5027	92	7	−	−	PROPN
ejpam-5027	92	8	βcl(h	βcl(h	PROPN
ejpam-5027	92	9	)	)	PUNCT
ejpam-5027	92	10	≤	≤	NOUN
ejpam-5027	93	1	w	w	ADP
ejpam-5027	93	2	,	,	PUNCT
ejpam-5027	93	3	wherever	wherever	SCONJ
ejpam-5027	93	4	h	h	NOUN
ejpam-5027	93	5	≤w	≤w	NOUN
ejpam-5027	93	6	,	,	PUNCT
ejpam-5027	93	7	w	w	PROPN
ejpam-5027	93	8	∈	∈	PROPN
ejpam-5027	93	9	τi	τi	NOUN
ejpam-5027	93	10	.	.	PUNCT
ejpam-5027	94	1	(	(	PUNCT
ejpam-5027	94	2	5	5	X
ejpam-5027	94	3	)	)	PUNCT
ejpam-5027	94	4	the	the	DET
ejpam-5027	94	5	complement	complement	NOUN
ejpam-5027	94	6	of	of	ADP
ejpam-5027	94	7	the	the	DET
ejpam-5027	94	8	above	above	ADJ
ejpam-5027	94	9	sets	set	NOUN
ejpam-5027	94	10	are	be	AUX
ejpam-5027	94	11	called	call	VERB
ejpam-5027	94	12	fuzzy	fuzzy	ADJ
ejpam-5027	94	13	(	(	PUNCT
ejpam-5027	94	14	i	i	PROPN
ejpam-5027	94	15	,	,	PUNCT
ejpam-5027	94	16	j	j	PROPN
ejpam-5027	94	17	)	)	PUNCT
ejpam-5027	95	1	−	−	PROPN
ejpam-5027	95	2	gα	gα	ADP
ejpam-5027	95	3	−	−	PROPN
ejpam-5027	95	4	open	open	ADJ
ejpam-5027	95	5	,	,	PUNCT
ejpam-5027	95	6	(	(	PUNCT
ejpam-5027	95	7	i	i	PROPN
ejpam-5027	95	8	,	,	PUNCT
ejpam-5027	95	9	j	j	PROPN
ejpam-5027	95	10	)	)	PUNCT
ejpam-5027	95	11	−	−	PROPN
ejpam-5027	96	1	gs	gs	INTJ
ejpam-5027	97	1	−	−	PROPN
ejpam-5027	97	2	open	open	ADJ
ejpam-5027	97	3	,	,	PUNCT
ejpam-5027	97	4	(	(	PUNCT
ejpam-5027	97	5	i	i	PROPN
ejpam-5027	97	6	,	,	PUNCT
ejpam-5027	97	7	j)−	j)−	PROPN
ejpam-5027	97	8	gp−	gp−	PROPN
ejpam-5027	97	9	open	open	ADJ
ejpam-5027	97	10	,	,	PUNCT
ejpam-5027	97	11	and	and	CCONJ
ejpam-5027	97	12	(	(	PUNCT
ejpam-5027	97	13	i	i	NOUN
ejpam-5027	97	14	,	,	PUNCT
ejpam-5027	97	15	j)−	j)−	PROPN
ejpam-5027	97	16	gβ	gβ	AUX
ejpam-5027	97	17	−	−	PUNCT
ejpam-5027	97	18	open	open	ADJ
ejpam-5027	97	19	.	.	PUNCT
ejpam-5027	98	1	remark	remark	PROPN
ejpam-5027	98	2	1	1	NUM
ejpam-5027	98	3	.	.	PUNCT
ejpam-5027	99	1	(	(	PUNCT
ejpam-5027	99	2	1	1	X
ejpam-5027	99	3	)	)	PUNCT
ejpam-5027	99	4	we	we	PRON
ejpam-5027	99	5	denote	denote	VERB
ejpam-5027	99	6	the	the	DET
ejpam-5027	99	7	class	class	NOUN
ejpam-5027	99	8	for	for	ADP
ejpam-5027	99	9	every	every	DET
ejpam-5027	99	10	fuzzy	fuzzy	ADJ
ejpam-5027	99	11	(	(	PUNCT
ejpam-5027	99	12	i	i	PROPN
ejpam-5027	99	13	,	,	PUNCT
ejpam-5027	99	14	j)−	j)−	PROPN
ejpam-5027	99	15	gα−open	gα−open	PROPN
ejpam-5027	99	16	,	,	PUNCT
ejpam-5027	99	17	(	(	PUNCT
ejpam-5027	99	18	i	i	PROPN
ejpam-5027	99	19	,	,	PUNCT
ejpam-5027	99	20	j)−	j)−	PROPN
ejpam-5027	99	21	gs−open	gs−open	PROPN
ejpam-5027	99	22	,	,	PUNCT
ejpam-5027	99	23	(	(	PUNCT
ejpam-5027	99	24	i	i	PROPN
ejpam-5027	99	25	,	,	PUNCT
ejpam-5027	99	26	j	j	PROPN
ejpam-5027	99	27	)	)	PUNCT
ejpam-5027	99	28	−	−	PROPN
ejpam-5027	99	29	gp−open	gp−open	INTJ
ejpam-5027	100	1	and	and	CCONJ
ejpam-5027	100	2	(	(	PUNCT
ejpam-5027	100	3	i	i	PROPN
ejpam-5027	100	4	,	,	PUNCT
ejpam-5027	100	5	j	j	PROPN
ejpam-5027	100	6	)	)	PUNCT
ejpam-5027	100	7	−	−	PROPN
ejpam-5027	101	1	gβ−open	gβ−open	ADJ
ejpam-5027	101	2	(	(	PUNCT
ejpam-5027	101	3	resp	resp	NOUN
ejpam-5027	101	4	,	,	PUNCT
ejpam-5027	101	5	fuzzy	fuzzy	ADJ
ejpam-5027	101	6	(	(	PUNCT
ejpam-5027	101	7	i	i	PROPN
ejpam-5027	101	8	,	,	PUNCT
ejpam-5027	101	9	j	j	PROPN
ejpam-5027	101	10	)	)	PUNCT
ejpam-5027	101	11	−	−	PROPN
ejpam-5027	102	1	gα−cld	gα−cld	PROPN
ejpam-5027	102	2	,	,	PUNCT
ejpam-5027	102	3	(	(	PUNCT
ejpam-5027	102	4	i	i	PROPN
ejpam-5027	102	5	,	,	PUNCT
ejpam-5027	102	6	j	j	PROPN
ejpam-5027	102	7	)	)	PUNCT
ejpam-5027	102	8	−	−	PROPN
ejpam-5027	103	1	gs−cld	gs−cld	PROPN
ejpam-5027	103	2	,	,	PUNCT
ejpam-5027	103	3	(	(	PUNCT
ejpam-5027	103	4	i	i	PRON
ejpam-5027	103	5	,	,	PUNCT
ejpam-5027	103	6	j)−	j)−	PROPN
ejpam-5027	103	7	gp−cld	gp−cld	PROPN
ejpam-5027	103	8	,	,	PUNCT
ejpam-5027	103	9	and	and	CCONJ
ejpam-5027	103	10	(	(	PUNCT
ejpam-5027	103	11	i	i	NOUN
ejpam-5027	103	12	,	,	PUNCT
ejpam-5027	103	13	j)−	j)−	PROPN
ejpam-5027	103	14	gβ−cld	gβ−cld	PROPN
ejpam-5027	103	15	)	)	PUNCT
ejpam-5027	103	16	sets	set	NOUN
ejpam-5027	103	17	in	in	ADP
ejpam-5027	103	18	(	(	PUNCT
ejpam-5027	103	19	x	x	NOUN
ejpam-5027	103	20	,	,	PUNCT
ejpam-5027	103	21	τi	τi	ADJ
ejpam-5027	103	22	,	,	PUNCT
ejpam-5027	103	23	τj	τj	ADP
ejpam-5027	103	24	)	)	PUNCT
ejpam-5027	103	25	by	by	ADP
ejpam-5027	103	26	ofgφ	ofgφ	NOUN
ejpam-5027	103	27	(	(	PUNCT
ejpam-5027	103	28	i	i	PROPN
ejpam-5027	103	29	,	,	PUNCT
ejpam-5027	103	30	j	j	PROPN
ejpam-5027	103	31	)	)	PUNCT
ejpam-5027	103	32	and	and	CCONJ
ejpam-5027	103	33	ffgφ	ffgφ	NOUN
ejpam-5027	103	34	(	(	PUNCT
ejpam-5027	103	35	i	i	PROPN
ejpam-5027	103	36	,	,	PUNCT
ejpam-5027	103	37	j	j	PROPN
ejpam-5027	103	38	)	)	PUNCT
ejpam-5027	103	39	resp	resp	NOUN
ejpam-5027	103	40	.	.	PUNCT
ejpam-5027	104	1	also	also	ADV
ejpam-5027	104	2	,	,	PUNCT
ejpam-5027	104	3	we	we	PRON
ejpam-5027	104	4	gave	give	VERB
ejpam-5027	104	5	the	the	DET
ejpam-5027	104	6	names	name	NOUN
ejpam-5027	104	7	(	(	PUNCT
ejpam-5027	104	8	i	i	PROPN
ejpam-5027	104	9	,	,	PUNCT
ejpam-5027	104	10	j)−gφ−cld	j)−gφ−cld	PROPN
ejpam-5027	104	11	and	and	CCONJ
ejpam-5027	104	12	(	(	PUNCT
ejpam-5027	104	13	i	i	NOUN
ejpam-5027	104	14	,	,	PUNCT
ejpam-5027	104	15	j)−gφ−open	j)−gφ−open	ADJ
ejpam-5027	104	16	to	to	ADP
ejpam-5027	104	17	all	all	DET
ejpam-5027	104	18	fuzzy	fuzzy	ADJ
ejpam-5027	104	19	types	type	NOUN
ejpam-5027	104	20	of	of	ADP
ejpam-5027	104	21	generalized	generalized	ADJ
ejpam-5027	104	22	closed	closed	ADJ
ejpam-5027	104	23	and	and	CCONJ
ejpam-5027	104	24	open	open	ADJ
ejpam-5027	104	25	groups	group	NOUN
ejpam-5027	104	26	,	,	PUNCT
ejpam-5027	104	27	respectively	respectively	ADV
ejpam-5027	104	28	.	.	PUNCT
ejpam-5027	105	1	(	(	PUNCT
ejpam-5027	105	2	2	2	X
ejpam-5027	105	3	)	)	PUNCT
ejpam-5027	105	4	in	in	ADP
ejpam-5027	105	5	all	all	DET
ejpam-5027	105	6	sections	section	NOUN
ejpam-5027	105	7	of	of	ADP
ejpam-5027	105	8	this	this	DET
ejpam-5027	105	9	research	research	NOUN
ejpam-5027	105	10	i	i	PRON
ejpam-5027	105	11	,	,	PUNCT
ejpam-5027	105	12	j	j	PROPN
ejpam-5027	105	13	∈	∈	PROPN
ejpam-5027	105	14	{	{	PUNCT
ejpam-5027	105	15	0	0	NUM
ejpam-5027	105	16	,	,	PUNCT
ejpam-5027	105	17	1	1	NUM
ejpam-5027	105	18	}	}	PUNCT
ejpam-5027	105	19	,	,	PUNCT
ejpam-5027	105	20	i	i	PRON
ejpam-5027	105	21	̸=	̸=	PROPN
ejpam-5027	105	22	j	j	PROPN
ejpam-5027	105	23	ahlam	ahlam	PROPN
ejpam-5027	105	24	ahmed	ahmed	PROPN
ejpam-5027	105	25	alharbi	alharbi	PROPN
ejpam-5027	105	26	,	,	PUNCT
ejpam-5027	105	27	adem	adem	PROPN
ejpam-5027	105	28	kilicman	kilicman	PROPN
ejpam-5027	105	29	/	/	SYM
ejpam-5027	105	30	eur	eur	PROPN
ejpam-5027	105	31	.	.	PUNCT
ejpam-5027	106	1	j.	j.	PROPN
ejpam-5027	106	2	pure	pure	PROPN
ejpam-5027	106	3	appl	appl	PROPN
ejpam-5027	106	4	.	.	PROPN
ejpam-5027	106	5	math	math	PROPN
ejpam-5027	106	6	,	,	PUNCT
ejpam-5027	106	7	17	17	NUM
ejpam-5027	106	8	(	(	PUNCT
ejpam-5027	106	9	1	1	NUM
ejpam-5027	106	10	)	)	PUNCT
ejpam-5027	106	11	(	(	PUNCT
ejpam-5027	106	12	2024	2024	NUM
ejpam-5027	106	13	)	)	PUNCT
ejpam-5027	106	14	,	,	PUNCT
ejpam-5027	106	15	30	30	NUM
ejpam-5027	106	16	-	-	SYM
ejpam-5027	106	17	41	41	NUM
ejpam-5027	106	18	34	34	NUM
ejpam-5027	106	19	from	from	ADP
ejpam-5027	106	20	the	the	DET
ejpam-5027	106	21	above	above	ADJ
ejpam-5027	106	22	definition10	definition10	NOUN
ejpam-5027	106	23	we	we	PRON
ejpam-5027	106	24	conclude	conclude	VERB
ejpam-5027	106	25	the	the	DET
ejpam-5027	106	26	following	following	NOUN
ejpam-5027	106	27	:	:	PUNCT
ejpam-5027	106	28	proposition	proposition	NOUN
ejpam-5027	106	29	1	1	NUM
ejpam-5027	106	30	.	.	PUNCT
ejpam-5027	107	1	any	any	DET
ejpam-5027	107	2	fuzzy	fuzzy	ADJ
ejpam-5027	107	3	subset	subset	NOUN
ejpam-5027	107	4	e	e	X
ejpam-5027	107	5	of	of	ADP
ejpam-5027	107	6	(	(	PUNCT
ejpam-5027	107	7	x	x	NOUN
ejpam-5027	107	8	,	,	PUNCT
ejpam-5027	107	9	τ1	τ1	NOUN
ejpam-5027	107	10	,	,	PUNCT
ejpam-5027	107	11	τ2	τ2	NOUN
ejpam-5027	107	12	)	)	PUNCT
ejpam-5027	107	13	considered	consider	VERB
ejpam-5027	107	14	fuzzy	fuzzy	ADJ
ejpam-5027	107	15	(	(	PUNCT
ejpam-5027	107	16	i	i	PROPN
ejpam-5027	107	17	,	,	PUNCT
ejpam-5027	107	18	j	j	PROPN
ejpam-5027	107	19	)	)	PUNCT
ejpam-5027	107	20	−	−	PROPN
ejpam-5027	107	21	gφ−open	gφ−open	PROPN
ejpam-5027	107	22	⇔	⇔	PROPN
ejpam-5027	107	23	f	f	PROPN
ejpam-5027	107	24	≤	≤	PROPN
ejpam-5027	107	25	τj	τj	ADP
ejpam-5027	107	26	−	−	PROPN
ejpam-5027	107	27	φ−	φ−	PROPN
ejpam-5027	107	28	int(e	int(e	PROPN
ejpam-5027	107	29	)	)	PUNCT
ejpam-5027	107	30	,	,	PUNCT
ejpam-5027	107	31	wherever	wherever	SCONJ
ejpam-5027	107	32	f	f	PROPN
ejpam-5027	107	33	∈	∈	PROPN
ejpam-5027	107	34	fτi	fτi	NOUN
ejpam-5027	107	35	,	,	PUNCT
ejpam-5027	107	36	and	and	CCONJ
ejpam-5027	107	37	f	f	PROPN
ejpam-5027	107	38	≤	≤	NUM
ejpam-5027	107	39	e	e	NOUN
ejpam-5027	107	40	,	,	PUNCT
ejpam-5027	107	41	where	where	SCONJ
ejpam-5027	107	42	i	i	PRON
ejpam-5027	107	43	,	,	PUNCT
ejpam-5027	107	44	j	j	PROPN
ejpam-5027	107	45	∈	∈	PROPN
ejpam-5027	107	46	{	{	PUNCT
ejpam-5027	107	47	0	0	NUM
ejpam-5027	107	48	,	,	PUNCT
ejpam-5027	107	49	1	1	NUM
ejpam-5027	107	50	}	}	PUNCT
ejpam-5027	107	51	,	,	PUNCT
ejpam-5027	107	52	i	i	PRON
ejpam-5027	107	53	̸=	̸=	PROPN
ejpam-5027	107	54	j.	j.	PROPN
ejpam-5027	107	55	proof	proof	PROPN
ejpam-5027	107	56	.	.	PUNCT
ejpam-5027	108	1	assume	assume	VERB
ejpam-5027	108	2	e	e	NOUN
ejpam-5027	108	3	is	be	AUX
ejpam-5027	108	4	fuzzy	fuzzy	ADJ
ejpam-5027	108	5	(	(	PUNCT
ejpam-5027	108	6	i	i	PROPN
ejpam-5027	108	7	,	,	PUNCT
ejpam-5027	108	8	j	j	PROPN
ejpam-5027	108	9	)	)	PUNCT
ejpam-5027	109	1	−	−	PROPN
ejpam-5027	109	2	gφ−open	gφ−open	NOUN
ejpam-5027	109	3	.	.	PUNCT
ejpam-5027	110	1	then	then	ADV
ejpam-5027	110	2	ec	ec	PROPN
ejpam-5027	110	3	is	be	AUX
ejpam-5027	110	4	(	(	PUNCT
ejpam-5027	110	5	i	i	PROPN
ejpam-5027	110	6	,	,	PUNCT
ejpam-5027	110	7	j	j	PROPN
ejpam-5027	110	8	)	)	PUNCT
ejpam-5027	110	9	−	−	PROPN
ejpam-5027	111	1	gφ−cld	gφ−cld	NOUN
ejpam-5027	111	2	,	,	PUNCT
ejpam-5027	111	3	thus	thus	ADV
ejpam-5027	111	4	the	the	DET
ejpam-5027	111	5	condition	condition	NOUN
ejpam-5027	111	6	relation	relation	NOUN
ejpam-5027	111	7	is	be	AUX
ejpam-5027	111	8	hold	hold	NOUN
ejpam-5027	111	9	for	for	ADP
ejpam-5027	111	10	ec	ec	PROPN
ejpam-5027	111	11	.	.	PUNCT
ejpam-5027	112	1	therefore	therefore	ADV
ejpam-5027	112	2	,	,	PUNCT
ejpam-5027	112	3	by	by	ADP
ejpam-5027	112	4	using	use	VERB
ejpam-5027	112	5	the	the	DET
ejpam-5027	112	6	complent	complent	NOUN
ejpam-5027	112	7	we	we	PRON
ejpam-5027	112	8	find	find	VERB
ejpam-5027	112	9	τj	τj	ADP
ejpam-5027	112	10	−	−	PROPN
ejpam-5027	112	11	φ−	φ−	PROPN
ejpam-5027	112	12	cl(ec	cl(ec	PROPN
ejpam-5027	112	13	)	)	PUNCT
ejpam-5027	113	1	=	=	PUNCT
ejpam-5027	113	2	(	(	PUNCT
ejpam-5027	113	3	τj	τj	ADP
ejpam-5027	113	4	−	−	PROPN
ejpam-5027	113	5	φ−	φ−	PROPN
ejpam-5027	113	6	int(e))c	int(e))c	PROPN
ejpam-5027	113	7	≤	≤	PROPN
ejpam-5027	114	1	f	f	PROPN
ejpam-5027	114	2	c	c	NOUN
ejpam-5027	114	3	which	which	PRON
ejpam-5027	114	4	implies	imply	VERB
ejpam-5027	114	5	f	f	PROPN
ejpam-5027	114	6	≤	≤	NOUN
ejpam-5027	114	7	τj	τj	ADP
ejpam-5027	114	8	−	−	PROPN
ejpam-5027	114	9	φ−	φ−	PROPN
ejpam-5027	114	10	int(e	int(e	PROPN
ejpam-5027	114	11	)	)	PUNCT
ejpam-5027	114	12	.	.	PUNCT
ejpam-5027	115	1	conversely	conversely	ADV
ejpam-5027	115	2	,	,	PUNCT
ejpam-5027	115	3	by	by	ADP
ejpam-5027	115	4	using	use	VERB
ejpam-5027	115	5	definition	definition	NOUN
ejpam-5027	115	6	10	10	NUM
ejpam-5027	115	7	and	and	CCONJ
ejpam-5027	115	8	taking	take	VERB
ejpam-5027	115	9	the	the	DET
ejpam-5027	115	10	complement	complement	NOUN
ejpam-5027	115	11	for	for	ADP
ejpam-5027	115	12	both	both	DET
ejpam-5027	115	13	sides	side	NOUN
ejpam-5027	115	14	in	in	ADP
ejpam-5027	115	15	condition	condition	NOUN
ejpam-5027	115	16	we	we	PRON
ejpam-5027	115	17	find	find	VERB
ejpam-5027	115	18	ec	ec	PROPN
ejpam-5027	115	19	is	be	AUX
ejpam-5027	115	20	fuzzy	fuzzy	ADJ
ejpam-5027	115	21	(	(	PUNCT
ejpam-5027	115	22	i	i	NOUN
ejpam-5027	115	23	,	,	PUNCT
ejpam-5027	115	24	j)−	j)−	PROPN
ejpam-5027	115	25	gφ−cld	gφ−cld	PROPN
ejpam-5027	115	26	.	.	PUNCT
ejpam-5027	116	1	for	for	ADP
ejpam-5027	116	2	that	that	PRON
ejpam-5027	116	3	e	e	NOUN
ejpam-5027	116	4	is	be	AUX
ejpam-5027	116	5	fuzzy	fuzzy	ADJ
ejpam-5027	116	6	(	(	PUNCT
ejpam-5027	116	7	i	i	NOUN
ejpam-5027	116	8	,	,	PUNCT
ejpam-5027	116	9	j)−	j)−	PROPN
ejpam-5027	116	10	gφ−open	gφ−open	PROPN
ejpam-5027	116	11	.	.	PUNCT
ejpam-5027	117	1	in	in	ADP
ejpam-5027	117	2	the	the	DET
ejpam-5027	117	3	section	section	NOUN
ejpam-5027	117	4	that	that	PRON
ejpam-5027	117	5	follows	follow	VERB
ejpam-5027	117	6	,	,	PUNCT
ejpam-5027	117	7	we	we	PRON
ejpam-5027	117	8	define	define	VERB
ejpam-5027	117	9	the	the	DET
ejpam-5027	117	10	terms	term	NOUN
ejpam-5027	117	11	”	"	PUNCT
ejpam-5027	117	12	closure	closure	NOUN
ejpam-5027	117	13	”	"	PUNCT
ejpam-5027	117	14	and	and	CCONJ
ejpam-5027	117	15	”	"	PUNCT
ejpam-5027	117	16	interior	interior	NOUN
ejpam-5027	117	17	”	"	PUNCT
ejpam-5027	117	18	of	of	ADP
ejpam-5027	117	19	fuzzy	fuzzy	ADJ
ejpam-5027	117	20	generalized	generalize	VERB
ejpam-5027	117	21	closed	close	VERB
ejpam-5027	117	22	sets	set	NOUN
ejpam-5027	117	23	in	in	ADP
ejpam-5027	117	24	fbts	fbt	NOUN
ejpam-5027	117	25	field	field	NOUN
ejpam-5027	117	26	,	,	PUNCT
ejpam-5027	117	27	as	as	ADV
ejpam-5027	117	28	well	well	ADV
ejpam-5027	117	29	as	as	ADP
ejpam-5027	117	30	the	the	DET
ejpam-5027	117	31	key	key	ADJ
ejpam-5027	117	32	theories	theory	NOUN
ejpam-5027	117	33	,	,	PUNCT
ejpam-5027	117	34	connections	connection	NOUN
ejpam-5027	117	35	between	between	ADP
ejpam-5027	117	36	these	these	DET
ejpam-5027	117	37	notions	notion	NOUN
ejpam-5027	117	38	,	,	PUNCT
ejpam-5027	117	39	and	and	CCONJ
ejpam-5027	117	40	their	their	PRON
ejpam-5027	117	41	complement	complement	NOUN
ejpam-5027	117	42	.	.	PUNCT
ejpam-5027	118	1	definition	definition	NOUN
ejpam-5027	118	2	11	11	NUM
ejpam-5027	118	3	.	.	PUNCT
ejpam-5027	119	1	for	for	ADP
ejpam-5027	119	2	all	all	DET
ejpam-5027	119	3	fbts	fbt	NOUN
ejpam-5027	119	4	(	(	PUNCT
ejpam-5027	119	5	x	x	NOUN
ejpam-5027	119	6	,	,	PUNCT
ejpam-5027	119	7	τ1	τ1	NOUN
ejpam-5027	119	8	,	,	PUNCT
ejpam-5027	119	9	τ2	τ2	NOUN
ejpam-5027	119	10	)	)	PUNCT
ejpam-5027	119	11	,	,	PUNCT
ejpam-5027	119	12	e	e	PROPN
ejpam-5027	119	13	∈	∈	PROPN
ejpam-5027	119	14	ix	ix	X
ejpam-5027	119	15	,	,	PUNCT
ejpam-5027	119	16	(	(	PUNCT
ejpam-5027	119	17	i	i	PROPN
ejpam-5027	119	18	,	,	PUNCT
ejpam-5027	119	19	j	j	PROPN
ejpam-5027	119	20	)	)	PUNCT
ejpam-5027	119	21	−	−	PROPN
ejpam-5027	119	22	gφ	gφ	NOUN
ejpam-5027	119	23	−	−	PROPN
ejpam-5027	119	24	closure	closure	NOUN
ejpam-5027	119	25	and	and	CCONJ
ejpam-5027	119	26	(	(	PUNCT
ejpam-5027	119	27	i	i	PROPN
ejpam-5027	119	28	,	,	PUNCT
ejpam-5027	119	29	j	j	PROPN
ejpam-5027	119	30	)	)	PUNCT
ejpam-5027	119	31	−	−	PROPN
ejpam-5027	119	32	gφ	gφ	PROPN
ejpam-5027	119	33	−	−	PROPN
ejpam-5027	119	34	interior	interior	PROPN
ejpam-5027	119	35	in	in	ADP
ejpam-5027	119	36	regard	regard	NOUN
ejpam-5027	119	37	to	to	ADP
ejpam-5027	119	38	e	e	PROPN
ejpam-5027	119	39	are	be	AUX
ejpam-5027	119	40	indicated	indicate	VERB
ejpam-5027	119	41	and	and	CCONJ
ejpam-5027	119	42	defined	define	VERB
ejpam-5027	119	43	as	as	SCONJ
ejpam-5027	119	44	shown	show	VERB
ejpam-5027	119	45	:	:	PUNCT
ejpam-5027	119	46	(	(	PUNCT
ejpam-5027	119	47	i	i	NOUN
ejpam-5027	119	48	)	)	PUNCT
ejpam-5027	119	49	(	(	PUNCT
ejpam-5027	119	50	i	i	PROPN
ejpam-5027	119	51	,	,	PUNCT
ejpam-5027	119	52	j)−	j)−	PROPN
ejpam-5027	119	53	gφ−	gφ−	PROPN
ejpam-5027	119	54	cl(e	cl(e	NUM
ejpam-5027	119	55	)	)	PUNCT
ejpam-5027	119	56	=	=	SYM
ejpam-5027	120	1	∧	∧	NOUN
ejpam-5027	120	2	{	{	PUNCT
ejpam-5027	120	3	f	f	NOUN
ejpam-5027	120	4	:	:	PUNCT
ejpam-5027	120	5	e	e	X
ejpam-5027	120	6	≤	≤	PROPN
ejpam-5027	120	7	f	f	X
ejpam-5027	120	8	,	,	PUNCT
ejpam-5027	120	9	f	f	PROPN
ejpam-5027	120	10	is	be	AUX
ejpam-5027	120	11	(	(	PUNCT
ejpam-5027	120	12	i	i	PROPN
ejpam-5027	120	13	,	,	PUNCT
ejpam-5027	120	14	j)−	j)−	PROPN
ejpam-5027	120	15	gφ−	gφ−	PUNCT
ejpam-5027	120	16	cld	cld	PROPN
ejpam-5027	120	17	}	}	PUNCT
ejpam-5027	120	18	(	(	PUNCT
ejpam-5027	120	19	ii	ii	NOUN
ejpam-5027	120	20	)	)	PUNCT
ejpam-5027	120	21	(	(	PUNCT
ejpam-5027	120	22	i	i	PROPN
ejpam-5027	120	23	,	,	PUNCT
ejpam-5027	120	24	j)−	j)−	PROPN
ejpam-5027	120	25	gφ−	gφ−	PROPN
ejpam-5027	120	26	int(e	int(e	PROPN
ejpam-5027	120	27	)	)	PUNCT
ejpam-5027	120	28	=	=	SYM
ejpam-5027	121	1	∨	∨	X
ejpam-5027	121	2	{	{	PUNCT
ejpam-5027	121	3	o	o	NOUN
ejpam-5027	121	4	:	:	PUNCT
ejpam-5027	122	1	o	o	X
ejpam-5027	122	2	≤	≤	X
ejpam-5027	122	3	e	e	X
ejpam-5027	122	4	,	,	PUNCT
ejpam-5027	122	5	o	o	PROPN
ejpam-5027	122	6	is	be	AUX
ejpam-5027	122	7	(	(	PUNCT
ejpam-5027	122	8	i	i	PROPN
ejpam-5027	122	9	,	,	PUNCT
ejpam-5027	122	10	j)−	j)−	PROPN
ejpam-5027	122	11	gφ−	gφ−	PUNCT
ejpam-5027	122	12	open	open	ADJ
ejpam-5027	122	13	}	}	PUNCT
ejpam-5027	122	14	.	.	PUNCT
ejpam-5027	123	1	theorem	theorem	NOUN
ejpam-5027	123	2	1	1	NUM
ejpam-5027	123	3	.	.	PUNCT
ejpam-5027	124	1	if	if	SCONJ
ejpam-5027	124	2	e	e	PROPN
ejpam-5027	124	3	is	be	AUX
ejpam-5027	124	4	a	a	DET
ejpam-5027	124	5	fuzzy	fuzzy	ADJ
ejpam-5027	124	6	subset	subset	NOUN
ejpam-5027	124	7	of	of	ADP
ejpam-5027	124	8	(	(	PUNCT
ejpam-5027	124	9	x	x	NOUN
ejpam-5027	124	10	,	,	PUNCT
ejpam-5027	124	11	τ1	τ1	NOUN
ejpam-5027	124	12	,	,	PUNCT
ejpam-5027	124	13	τ2	τ2	NOUN
ejpam-5027	124	14	)	)	PUNCT
ejpam-5027	124	15	.	.	PUNCT
ejpam-5027	125	1	then	then	ADV
ejpam-5027	125	2	the	the	DET
ejpam-5027	125	3	coming	coming	ADJ
ejpam-5027	125	4	conditions	condition	NOUN
ejpam-5027	125	5	are	be	AUX
ejpam-5027	125	6	met	meet	VERB
ejpam-5027	125	7	:	:	PUNCT
ejpam-5027	125	8	(	(	PUNCT
ejpam-5027	125	9	1	1	X
ejpam-5027	125	10	)	)	PUNCT
ejpam-5027	125	11	(	(	PUNCT
ejpam-5027	125	12	(	(	PUNCT
ejpam-5027	125	13	i	i	INTJ
ejpam-5027	125	14	,	,	PUNCT
ejpam-5027	125	15	j)−	j)−	PROPN
ejpam-5027	125	16	gφ−	gφ−	PROPN
ejpam-5027	125	17	int(e	int(e	PROPN
ejpam-5027	125	18	)	)	PUNCT
ejpam-5027	125	19	)	)	PUNCT
ejpam-5027	126	1	c	c	X
ejpam-5027	126	2	=	=	SYM
ejpam-5027	126	3	(	(	PUNCT
ejpam-5027	126	4	i	i	PROPN
ejpam-5027	126	5	,	,	PUNCT
ejpam-5027	126	6	j)−	j)−	PROPN
ejpam-5027	126	7	gφ−	gφ−	PROPN
ejpam-5027	126	8	cl(ec	cl(ec	PROPN
ejpam-5027	126	9	)	)	PUNCT
ejpam-5027	126	10	(	(	PUNCT
ejpam-5027	126	11	2	2	X
ejpam-5027	126	12	)	)	PUNCT
ejpam-5027	126	13	(	(	PUNCT
ejpam-5027	126	14	(	(	PUNCT
ejpam-5027	126	15	i	i	NOUN
ejpam-5027	126	16	,	,	PUNCT
ejpam-5027	126	17	j)−	j)−	PROPN
ejpam-5027	126	18	gφ−	gφ−	PROPN
ejpam-5027	126	19	cl(e	cl(e	NUM
ejpam-5027	126	20	)	)	PUNCT
ejpam-5027	126	21	)	)	PUNCT
ejpam-5027	127	1	c	c	X
ejpam-5027	127	2	=	=	SYM
ejpam-5027	127	3	(	(	PUNCT
ejpam-5027	127	4	i	i	PROPN
ejpam-5027	127	5	,	,	PUNCT
ejpam-5027	127	6	j)−	j)−	PROPN
ejpam-5027	127	7	gφ−	gφ−	PROPN
ejpam-5027	127	8	int(ec	int(ec	PROPN
ejpam-5027	127	9	)	)	PUNCT
ejpam-5027	127	10	.	.	PUNCT
ejpam-5027	128	1	proof	proof	NOUN
ejpam-5027	128	2	.	.	PUNCT
ejpam-5027	129	1	it	it	PRON
ejpam-5027	129	2	is	be	AUX
ejpam-5027	129	3	clear	clear	ADJ
ejpam-5027	129	4	from	from	ADP
ejpam-5027	129	5	the	the	DET
ejpam-5027	129	6	complement	complement	NOUN
ejpam-5027	129	7	low	low	ADJ
ejpam-5027	129	8	and	and	CCONJ
ejpam-5027	129	9	de	de	PROPN
ejpam-5027	129	10	morgan	morgan	PROPN
ejpam-5027	129	11	theorem	theorem	PROPN
ejpam-5027	129	12	.	.	PUNCT
ejpam-5027	129	13	theorem	theorem	NOUN
ejpam-5027	129	14	2	2	NUM
ejpam-5027	129	15	.	.	PUNCT
ejpam-5027	130	1	if	if	SCONJ
ejpam-5027	130	2	(	(	PUNCT
ejpam-5027	130	3	x	x	NOUN
ejpam-5027	130	4	,	,	PUNCT
ejpam-5027	130	5	τ1	τ1	NOUN
ejpam-5027	130	6	,	,	PUNCT
ejpam-5027	130	7	τ2	τ2	NOUN
ejpam-5027	130	8	)	)	PUNCT
ejpam-5027	130	9	is	be	AUX
ejpam-5027	130	10	fbts	fbt	NOUN
ejpam-5027	130	11	.	.	PUNCT
ejpam-5027	131	1	then	then	ADV
ejpam-5027	131	2	the	the	DET
ejpam-5027	131	3	next	next	ADJ
ejpam-5027	131	4	statements	statement	NOUN
ejpam-5027	131	5	are	be	AUX
ejpam-5027	131	6	satisfied	satisfied	ADJ
ejpam-5027	131	7	:	:	PUNCT
ejpam-5027	131	8	(	(	PUNCT
ejpam-5027	131	9	1	1	X
ejpam-5027	131	10	)	)	PUNCT
ejpam-5027	131	11	every	every	PRON
ejpam-5027	131	12	fuzzy	fuzzy	ADJ
ejpam-5027	131	13	(	(	PUNCT
ejpam-5027	131	14	i	i	NOUN
ejpam-5027	131	15	,	,	PUNCT
ejpam-5027	131	16	j)−	j)−	PROPN
ejpam-5027	131	17	g	g	PROPN
ejpam-5027	131	18	−	−	PROPN
ejpam-5027	131	19	cld	cld	PROPN
ejpam-5027	131	20	is	be	AUX
ejpam-5027	131	21	fuzzy	fuzzy	ADJ
ejpam-5027	131	22	(	(	PUNCT
ejpam-5027	131	23	i	i	NOUN
ejpam-5027	131	24	,	,	PUNCT
ejpam-5027	131	25	j)−	j)−	PROPN
ejpam-5027	131	26	gα−	gα−	PUNCT
ejpam-5027	131	27	cld	cld	PROPN
ejpam-5027	131	28	.	.	PUNCT
ejpam-5027	132	1	(	(	PUNCT
ejpam-5027	132	2	2	2	X
ejpam-5027	132	3	)	)	PUNCT
ejpam-5027	132	4	every	every	PRON
ejpam-5027	132	5	fuzzy	fuzzy	ADJ
ejpam-5027	132	6	(	(	PUNCT
ejpam-5027	132	7	i	i	NOUN
ejpam-5027	132	8	,	,	PUNCT
ejpam-5027	132	9	j)−	j)−	PROPN
ejpam-5027	132	10	gα−	gα−	PUNCT
ejpam-5027	132	11	cld	cld	PROPN
ejpam-5027	132	12	is	be	AUX
ejpam-5027	132	13	fuzzy	fuzzy	ADJ
ejpam-5027	132	14	(	(	PUNCT
ejpam-5027	132	15	i	i	NOUN
ejpam-5027	132	16	,	,	PUNCT
ejpam-5027	132	17	j)−	j)−	PROPN
ejpam-5027	132	18	gp−	gp−	PROPN
ejpam-5027	132	19	cld	cld	NOUN
ejpam-5027	132	20	and	and	CCONJ
ejpam-5027	132	21	fuzzy	fuzzy	ADJ
ejpam-5027	132	22	(	(	PUNCT
ejpam-5027	132	23	i	i	NOUN
ejpam-5027	132	24	,	,	PUNCT
ejpam-5027	132	25	j)−	j)−	PROPN
ejpam-5027	132	26	gs−	gs−	NUM
ejpam-5027	132	27	cld	cld	PROPN
ejpam-5027	132	28	.	.	PUNCT
ejpam-5027	133	1	(	(	PUNCT
ejpam-5027	133	2	3	3	X
ejpam-5027	133	3	)	)	PUNCT
ejpam-5027	133	4	every	every	PRON
ejpam-5027	133	5	fuzzy	fuzzy	ADJ
ejpam-5027	133	6	(	(	PUNCT
ejpam-5027	133	7	i	i	NOUN
ejpam-5027	133	8	,	,	PUNCT
ejpam-5027	133	9	j)−	j)−	PROPN
ejpam-5027	133	10	gp−	gp−	PROPN
ejpam-5027	133	11	cld	cld	NOUN
ejpam-5027	133	12	or	or	CCONJ
ejpam-5027	133	13	fuzzy	fuzzy	ADJ
ejpam-5027	133	14	(	(	PUNCT
ejpam-5027	133	15	i	i	NOUN
ejpam-5027	133	16	,	,	PUNCT
ejpam-5027	133	17	j)−	j)−	PROPN
ejpam-5027	133	18	gs−	gs−	NUM
ejpam-5027	133	19	cld	cld	PROPN
ejpam-5027	133	20	is	be	AUX
ejpam-5027	133	21	fuzzy	fuzzy	ADJ
ejpam-5027	133	22	(	(	PUNCT
ejpam-5027	133	23	i	i	NOUN
ejpam-5027	133	24	,	,	PUNCT
ejpam-5027	133	25	j)−	j)−	PROPN
ejpam-5027	133	26	gβ	gβ	PROPN
ejpam-5027	133	27	−	−	PROPN
ejpam-5027	133	28	cld	cld	PROPN
ejpam-5027	133	29	.	.	PUNCT
ejpam-5027	134	1	proof	proof	NOUN
ejpam-5027	134	2	.	.	PUNCT
ejpam-5027	135	1	it	it	PRON
ejpam-5027	135	2	is	be	AUX
ejpam-5027	135	3	clear	clear	ADJ
ejpam-5027	135	4	from	from	ADP
ejpam-5027	135	5	definition	definition	NOUN
ejpam-5027	135	6	10	10	NUM
ejpam-5027	135	7	and	and	CCONJ
ejpam-5027	135	8	the	the	DET
ejpam-5027	135	9	relations	relation	NOUN
ejpam-5027	135	10	between	between	ADP
ejpam-5027	135	11	types	type	NOUN
ejpam-5027	135	12	of	of	ADP
ejpam-5027	135	13	fuzzy	fuzzy	ADJ
ejpam-5027	135	14	sets	set	NOUN
ejpam-5027	135	15	where	where	SCONJ
ejpam-5027	135	16	remark	remark	NOUN
ejpam-5027	135	17	2	2	NUM
ejpam-5027	135	18	.	.	PUNCT
ejpam-5027	136	1	the	the	DET
ejpam-5027	136	2	following	follow	VERB
ejpam-5027	136	3	diagram	diagram	NOUN
ejpam-5027	136	4	explaining	explain	VERB
ejpam-5027	136	5	the	the	DET
ejpam-5027	136	6	relations	relation	NOUN
ejpam-5027	136	7	between	between	ADP
ejpam-5027	136	8	all	all	DET
ejpam-5027	136	9	types	type	NOUN
ejpam-5027	136	10	generalized	generalize	VERB
ejpam-5027	136	11	closed	closed	ADJ
ejpam-5027	136	12	sets	set	NOUN
ejpam-5027	136	13	in	in	ADP
ejpam-5027	136	14	(	(	PUNCT
ejpam-5027	136	15	x	x	NOUN
ejpam-5027	136	16	,	,	PUNCT
ejpam-5027	136	17	τi	τi	ADP
ejpam-5027	136	18	,	,	PUNCT
ejpam-5027	136	19	τj	τj	ADP
ejpam-5027	136	20	)	)	PUNCT
ejpam-5027	136	21	,	,	PUNCT
ejpam-5027	136	22	i	i	PRON
ejpam-5027	136	23	,	,	PUNCT
ejpam-5027	136	24	j	j	PROPN
ejpam-5027	136	25	∈	∈	PROPN
ejpam-5027	136	26	{	{	PUNCT
ejpam-5027	136	27	0	0	NUM
ejpam-5027	136	28	,	,	PUNCT
ejpam-5027	136	29	1	1	NUM
ejpam-5027	136	30	}	}	PUNCT
ejpam-5027	136	31	,	,	PUNCT
ejpam-5027	136	32	i	i	PROPN
ejpam-5027	136	33	̸=	̸=	PROPN
ejpam-5027	136	34	j	j	PROPN
ejpam-5027	136	35	:	:	PUNCT
ejpam-5027	136	36	ahlam	ahlam	PROPN
ejpam-5027	136	37	ahmed	ahmed	PROPN
ejpam-5027	136	38	alharbi	alharbi	PROPN
ejpam-5027	136	39	,	,	PUNCT
ejpam-5027	136	40	adem	adem	PROPN
ejpam-5027	136	41	kilicman	kilicman	PROPN
ejpam-5027	136	42	/	/	SYM
ejpam-5027	136	43	eur	eur	PROPN
ejpam-5027	136	44	.	.	PUNCT
ejpam-5027	137	1	j.	j.	PROPN
ejpam-5027	137	2	pure	pure	PROPN
ejpam-5027	137	3	appl	appl	PROPN
ejpam-5027	137	4	.	.	PROPN
ejpam-5027	137	5	math	math	PROPN
ejpam-5027	137	6	,	,	PUNCT
ejpam-5027	137	7	17	17	NUM
ejpam-5027	137	8	(	(	PUNCT
ejpam-5027	137	9	1	1	NUM
ejpam-5027	137	10	)	)	PUNCT
ejpam-5027	137	11	(	(	PUNCT
ejpam-5027	137	12	2024	2024	NUM
ejpam-5027	137	13	)	)	PUNCT
ejpam-5027	137	14	,	,	PUNCT
ejpam-5027	137	15	30	30	NUM
ejpam-5027	137	16	-	-	SYM
ejpam-5027	137	17	41	41	NUM
ejpam-5027	137	18	35	35	NUM
ejpam-5027	137	19	figure	figure	NOUN
ejpam-5027	137	20	1	1	NUM
ejpam-5027	137	21	:	:	PUNCT
ejpam-5027	137	22	explain	explain	VERB
ejpam-5027	137	23	the	the	DET
ejpam-5027	137	24	relations	relation	NOUN
ejpam-5027	137	25	between	between	ADP
ejpam-5027	137	26	(	(	PUNCT
ejpam-5027	137	27	i	i	PROPN
ejpam-5027	137	28	,	,	PUNCT
ejpam-5027	137	29	j)−	j)−	PROPN
ejpam-5027	137	30	gφ−cld	gφ−cld	NOUN
ejpam-5027	137	31	sets	set	VERB
ejpam-5027	137	32	.	.	PUNCT
ejpam-5027	138	1	the	the	DET
ejpam-5027	138	2	examples	example	NOUN
ejpam-5027	138	3	that	that	PRON
ejpam-5027	138	4	follow	follow	VERB
ejpam-5027	138	5	demonstrate	demonstrate	NOUN
ejpam-5027	138	6	that	that	SCONJ
ejpam-5027	138	7	the	the	DET
ejpam-5027	138	8	above	above	ADJ
ejpam-5027	138	9	diagram	diagram	NOUN
ejpam-5027	138	10	’s	’s	PART
ejpam-5027	138	11	opposite	opposite	NOUN
ejpam-5027	138	12	is	be	AUX
ejpam-5027	138	13	not	not	PART
ejpam-5027	138	14	typically	typically	ADV
ejpam-5027	138	15	true	true	ADJ
ejpam-5027	138	16	.	.	PUNCT
ejpam-5027	139	1	example	example	NOUN
ejpam-5027	140	1	1	1	NUM
ejpam-5027	140	2	.	.	PUNCT
ejpam-5027	140	3	suppose	suppose	VERB
ejpam-5027	140	4	e	e	NOUN
ejpam-5027	140	5	,	,	PUNCT
ejpam-5027	140	6	h	h	NOUN
ejpam-5027	140	7	,	,	PUNCT
ejpam-5027	140	8	r	r	NOUN
ejpam-5027	140	9	,	,	PUNCT
ejpam-5027	140	10	and	and	CCONJ
ejpam-5027	140	11	s	s	VERB
ejpam-5027	140	12	fuzzy	fuzzy	ADJ
ejpam-5027	140	13	subsets	subset	NOUN
ejpam-5027	140	14	of	of	ADP
ejpam-5027	140	15	x	x	X
ejpam-5027	140	16	=	=	X
ejpam-5027	140	17	{	{	PUNCT
ejpam-5027	140	18	a	a	DET
ejpam-5027	140	19	,	,	PUNCT
ejpam-5027	140	20	b	b	NOUN
ejpam-5027	140	21	}	}	PUNCT
ejpam-5027	140	22	as	as	SCONJ
ejpam-5027	140	23	follows	follow	VERB
ejpam-5027	140	24	:	:	PUNCT
ejpam-5027	140	25	e(a	e(a	NOUN
ejpam-5027	140	26	,	,	PUNCT
ejpam-5027	140	27	b	b	X
ejpam-5027	140	28	)	)	PUNCT
ejpam-5027	140	29	=	=	NOUN
ejpam-5027	140	30	{	{	PUNCT
ejpam-5027	140	31	0.7	0.7	NUM
ejpam-5027	140	32	,	,	PUNCT
ejpam-5027	140	33	0.5	0.5	NUM
ejpam-5027	140	34	}	}	PUNCT
ejpam-5027	140	35	,	,	PUNCT
ejpam-5027	140	36	h(a	h(a	PROPN
ejpam-5027	140	37	,	,	PUNCT
ejpam-5027	140	38	b	b	NOUN
ejpam-5027	140	39	)	)	PUNCT
ejpam-5027	140	40	=	=	PUNCT
ejpam-5027	140	41	{	{	PUNCT
ejpam-5027	140	42	0.7	0.7	NUM
ejpam-5027	140	43	,	,	PUNCT
ejpam-5027	140	44	0.6	0.6	NUM
ejpam-5027	140	45	}	}	PUNCT
ejpam-5027	140	46	,	,	PUNCT
ejpam-5027	140	47	r(a	r(a	PROPN
ejpam-5027	140	48	,	,	PUNCT
ejpam-5027	140	49	b	b	X
ejpam-5027	140	50	)	)	PUNCT
ejpam-5027	140	51	=	=	NOUN
ejpam-5027	140	52	{	{	PUNCT
ejpam-5027	140	53	0.2	0.2	NUM
ejpam-5027	140	54	,	,	PUNCT
ejpam-5027	140	55	0.4	0.4	NUM
ejpam-5027	140	56	}	}	PUNCT
ejpam-5027	140	57	,	,	PUNCT
ejpam-5027	140	58	s(a	s(a	PROPN
ejpam-5027	140	59	,	,	PUNCT
ejpam-5027	140	60	b	b	NOUN
ejpam-5027	140	61	)	)	PUNCT
ejpam-5027	140	62	=	=	NOUN
ejpam-5027	140	63	{	{	PUNCT
ejpam-5027	140	64	0.6	0.6	NUM
ejpam-5027	140	65	,	,	PUNCT
ejpam-5027	140	66	0.6	0.6	NUM
ejpam-5027	140	67	}	}	PUNCT
ejpam-5027	140	68	.	.	PUNCT
ejpam-5027	141	1	assume	assume	VERB
ejpam-5027	141	2	τ1	τ1	PROPN
ejpam-5027	141	3	=	=	SYM
ejpam-5027	141	4	{	{	PUNCT
ejpam-5027	141	5	0	0	NUM
ejpam-5027	141	6	,	,	PUNCT
ejpam-5027	141	7	1	1	NUM
ejpam-5027	141	8	,	,	PUNCT
ejpam-5027	141	9	e	e	NOUN
ejpam-5027	141	10	}	}	PUNCT
ejpam-5027	141	11	,	,	PUNCT
ejpam-5027	141	12	and	and	CCONJ
ejpam-5027	141	13	τ2	τ2	NOUN
ejpam-5027	141	14	=	=	SYM
ejpam-5027	141	15	{	{	PUNCT
ejpam-5027	141	16	0	0	NUM
ejpam-5027	141	17	,	,	PUNCT
ejpam-5027	141	18	1	1	NUM
ejpam-5027	141	19	,	,	PUNCT
ejpam-5027	141	20	h	h	NOUN
ejpam-5027	141	21	,	,	PUNCT
ejpam-5027	141	22	r	r	NOUN
ejpam-5027	141	23	}	}	PUNCT
ejpam-5027	141	24	.	.	PUNCT
ejpam-5027	142	1	then	then	ADV
ejpam-5027	142	2	we	we	PRON
ejpam-5027	142	3	can	can	AUX
ejpam-5027	142	4	see	see	VERB
ejpam-5027	142	5	that	that	PRON
ejpam-5027	142	6	s	s	VERB
ejpam-5027	142	7	is	be	AUX
ejpam-5027	142	8	fuzzy	fuzzy	ADJ
ejpam-5027	142	9	(	(	PUNCT
ejpam-5027	142	10	1	1	NUM
ejpam-5027	142	11	,	,	PUNCT
ejpam-5027	142	12	2)−g−cld	2)−g−cld	NUM
ejpam-5027	142	13	never	never	ADV
ejpam-5027	142	14	fuzzy	fuzzy	ADJ
ejpam-5027	142	15	τ2	τ2	PROPN
ejpam-5027	142	16	−	−	PROPN
ejpam-5027	142	17	g−cld	g−cld	NOUN
ejpam-5027	142	18	,	,	PUNCT
ejpam-5027	142	19	since	since	SCONJ
ejpam-5027	142	20	s	s	NOUN
ejpam-5027	142	21	≤	≤	NUM
ejpam-5027	142	22	h	h	NOUN
ejpam-5027	142	23	∈	∈	PROPN
ejpam-5027	142	24	τ2	τ2	PROPN
ejpam-5027	142	25	and	and	CCONJ
ejpam-5027	142	26	cl2(s	cl2(s	NOUN
ejpam-5027	142	27	)	)	PUNCT
ejpam-5027	142	28	̸≤	̸≤	NOUN
ejpam-5027	142	29	h	h	NOUN
ejpam-5027	142	30	.	.	PUNCT
ejpam-5027	143	1	the	the	DET
ejpam-5027	143	2	coming	come	VERB
ejpam-5027	143	3	example	example	NOUN
ejpam-5027	143	4	show	show	VERB
ejpam-5027	143	5	that	that	SCONJ
ejpam-5027	143	6	fuzzy	fuzzy	ADJ
ejpam-5027	143	7	(	(	PUNCT
ejpam-5027	143	8	1	1	NUM
ejpam-5027	143	9	,	,	PUNCT
ejpam-5027	143	10	2)−	2)−	PROPN
ejpam-5027	143	11	gα−	gα−	PUNCT
ejpam-5027	143	12	cld	cld	NOUN
ejpam-5027	143	13	⇏	⇏	VERB
ejpam-5027	143	14	fuzzy	fuzzy	ADJ
ejpam-5027	143	15	(	(	PUNCT
ejpam-5027	143	16	1	1	NUM
ejpam-5027	143	17	,	,	PUNCT
ejpam-5027	143	18	2)−	2)−	NUM
ejpam-5027	143	19	g	g	NOUN
ejpam-5027	143	20	−	−	PROPN
ejpam-5027	143	21	cld	cld	PROPN
ejpam-5027	143	22	.	.	PUNCT
ejpam-5027	143	23	example	example	NOUN
ejpam-5027	144	1	2	2	NUM
ejpam-5027	144	2	.	.	PUNCT
ejpam-5027	144	3	suppose	suppose	VERB
ejpam-5027	144	4	e	e	NOUN
ejpam-5027	144	5	,	,	PUNCT
ejpam-5027	144	6	h	h	NOUN
ejpam-5027	144	7	,	,	PUNCT
ejpam-5027	144	8	r	r	NOUN
ejpam-5027	144	9	,	,	PUNCT
ejpam-5027	144	10	and	and	CCONJ
ejpam-5027	144	11	s	s	VERB
ejpam-5027	144	12	fuzzy	fuzzy	ADJ
ejpam-5027	144	13	subsets	subset	NOUN
ejpam-5027	144	14	of	of	ADP
ejpam-5027	144	15	x	x	X
ejpam-5027	144	16	=	=	X
ejpam-5027	144	17	{	{	PUNCT
ejpam-5027	144	18	a	a	DET
ejpam-5027	144	19	,	,	PUNCT
ejpam-5027	144	20	b	b	NOUN
ejpam-5027	144	21	}	}	PUNCT
ejpam-5027	144	22	as	as	SCONJ
ejpam-5027	144	23	follows	follow	VERB
ejpam-5027	144	24	:	:	PUNCT
ejpam-5027	144	25	e(a	e(a	NOUN
ejpam-5027	144	26	,	,	PUNCT
ejpam-5027	144	27	b	b	X
ejpam-5027	144	28	)	)	PUNCT
ejpam-5027	144	29	=	=	SYM
ejpam-5027	144	30	{	{	PUNCT
ejpam-5027	144	31	0.5	0.5	NUM
ejpam-5027	144	32	,	,	PUNCT
ejpam-5027	144	33	0.4	0.4	NUM
ejpam-5027	144	34	}	}	PUNCT
ejpam-5027	144	35	,	,	PUNCT
ejpam-5027	144	36	h(a	h(a	PROPN
ejpam-5027	144	37	,	,	PUNCT
ejpam-5027	144	38	b	b	NOUN
ejpam-5027	144	39	)	)	PUNCT
ejpam-5027	144	40	=	=	NOUN
ejpam-5027	144	41	{	{	PUNCT
ejpam-5027	144	42	0.7	0.7	NUM
ejpam-5027	144	43	,	,	PUNCT
ejpam-5027	144	44	0.5	0.5	NUM
ejpam-5027	144	45	}	}	PUNCT
ejpam-5027	144	46	,	,	PUNCT
ejpam-5027	144	47	r(a	r(a	PROPN
ejpam-5027	144	48	,	,	PUNCT
ejpam-5027	144	49	b	b	X
ejpam-5027	144	50	)	)	PUNCT
ejpam-5027	144	51	=	=	SYM
ejpam-5027	144	52	{	{	PUNCT
ejpam-5027	144	53	0.4	0.4	NUM
ejpam-5027	144	54	,	,	PUNCT
ejpam-5027	144	55	0.3	0.3	NUM
ejpam-5027	144	56	}	}	PUNCT
ejpam-5027	144	57	,	,	PUNCT
ejpam-5027	144	58	s(a	s(a	PROPN
ejpam-5027	144	59	,	,	PUNCT
ejpam-5027	144	60	b	b	NOUN
ejpam-5027	144	61	)	)	PUNCT
ejpam-5027	144	62	=	=	PUNCT
ejpam-5027	144	63	{	{	PUNCT
ejpam-5027	144	64	0.3	0.3	NUM
ejpam-5027	144	65	,	,	PUNCT
ejpam-5027	144	66	0.4	0.4	NUM
ejpam-5027	144	67	}	}	PUNCT
ejpam-5027	144	68	.	.	PUNCT
ejpam-5027	145	1	assume	assume	VERB
ejpam-5027	145	2	τ1	τ1	PROPN
ejpam-5027	145	3	=	=	SYM
ejpam-5027	145	4	{	{	PUNCT
ejpam-5027	145	5	0	0	NUM
ejpam-5027	145	6	,	,	PUNCT
ejpam-5027	145	7	1	1	NUM
ejpam-5027	145	8	,	,	PUNCT
ejpam-5027	145	9	e	e	NOUN
ejpam-5027	145	10	}	}	PUNCT
ejpam-5027	145	11	,	,	PUNCT
ejpam-5027	145	12	and	and	CCONJ
ejpam-5027	145	13	τ2	τ2	NOUN
ejpam-5027	145	14	=	=	SYM
ejpam-5027	145	15	{	{	PUNCT
ejpam-5027	145	16	0	0	NUM
ejpam-5027	145	17	,	,	PUNCT
ejpam-5027	145	18	1	1	NUM
ejpam-5027	145	19	,	,	PUNCT
ejpam-5027	145	20	h	h	NOUN
ejpam-5027	145	21	,	,	PUNCT
ejpam-5027	145	22	r	r	NOUN
ejpam-5027	145	23	}	}	PUNCT
ejpam-5027	145	24	.	.	PUNCT
ejpam-5027	146	1	then	then	ADV
ejpam-5027	146	2	we	we	PRON
ejpam-5027	146	3	can	can	AUX
ejpam-5027	146	4	see	see	VERB
ejpam-5027	146	5	that	that	PRON
ejpam-5027	146	6	s	s	VERB
ejpam-5027	146	7	is	be	AUX
ejpam-5027	146	8	fuzzy	fuzzy	ADJ
ejpam-5027	146	9	(	(	PUNCT
ejpam-5027	146	10	1	1	NUM
ejpam-5027	146	11	,	,	PUNCT
ejpam-5027	146	12	2	2	NUM
ejpam-5027	146	13	)	)	PUNCT
ejpam-5027	146	14	−	−	PROPN
ejpam-5027	147	1	gα−cld	gα−cld	NOUN
ejpam-5027	147	2	never	never	ADV
ejpam-5027	147	3	fuzzy	fuzzy	ADJ
ejpam-5027	147	4	(	(	PUNCT
ejpam-5027	147	5	1	1	NUM
ejpam-5027	147	6	,	,	PUNCT
ejpam-5027	147	7	2)−	2)−	NUM
ejpam-5027	147	8	g−cld	g−cld	NOUN
ejpam-5027	147	9	,	,	PUNCT
ejpam-5027	147	10	since	since	SCONJ
ejpam-5027	147	11	s	s	NOUN
ejpam-5027	147	12	≤	≤	NUM
ejpam-5027	147	13	e	e	NOUN
ejpam-5027	147	14	∈	∈	PROPN
ejpam-5027	147	15	τ1	τ1	NOUN
ejpam-5027	147	16	,	,	PUNCT
ejpam-5027	147	17	and	and	CCONJ
ejpam-5027	147	18	cl2(s	cl2(s	NOUN
ejpam-5027	147	19	)	)	PUNCT
ejpam-5027	148	1	=	=	PUNCT
ejpam-5027	148	2	hc	hc	PROPN
ejpam-5027	148	3	̸≤	̸≤	PROPN
ejpam-5027	148	4	e.	e.	PROPN
ejpam-5027	148	5	in	in	ADP
ejpam-5027	148	6	the	the	DET
ejpam-5027	148	7	following	following	ADJ
ejpam-5027	148	8	example	example	NOUN
ejpam-5027	148	9	we	we	PRON
ejpam-5027	148	10	explain	explain	VERB
ejpam-5027	148	11	that	that	SCONJ
ejpam-5027	148	12	fuzzy	fuzzy	ADJ
ejpam-5027	148	13	(	(	PUNCT
ejpam-5027	148	14	1	1	NUM
ejpam-5027	148	15	,	,	PUNCT
ejpam-5027	148	16	2)−gs−cld⇏	2)−gs−cld⇏	NUM
ejpam-5027	148	17	fuzzy	fuzzy	ADJ
ejpam-5027	148	18	(	(	PUNCT
ejpam-5027	148	19	1	1	NUM
ejpam-5027	148	20	,	,	PUNCT
ejpam-5027	148	21	2)−gα−cld	2)−gα−cld	NUM
ejpam-5027	148	22	.	.	PUNCT
ejpam-5027	148	23	example	example	NOUN
ejpam-5027	149	1	3	3	X
ejpam-5027	149	2	.	.	PUNCT
ejpam-5027	149	3	suppose	suppose	VERB
ejpam-5027	149	4	e	e	NOUN
ejpam-5027	149	5	,	,	PUNCT
ejpam-5027	149	6	h	h	NOUN
ejpam-5027	149	7	,	,	PUNCT
ejpam-5027	149	8	r	r	NOUN
ejpam-5027	149	9	,	,	PUNCT
ejpam-5027	149	10	and	and	CCONJ
ejpam-5027	149	11	s	s	VERB
ejpam-5027	149	12	fuzzy	fuzzy	ADJ
ejpam-5027	149	13	subsets	subset	NOUN
ejpam-5027	149	14	of	of	ADP
ejpam-5027	149	15	x	x	X
ejpam-5027	149	16	=	=	X
ejpam-5027	149	17	{	{	PUNCT
ejpam-5027	149	18	a	a	DET
ejpam-5027	149	19	,	,	PUNCT
ejpam-5027	149	20	b	b	NOUN
ejpam-5027	149	21	}	}	PUNCT
ejpam-5027	149	22	as	as	SCONJ
ejpam-5027	149	23	follows	follow	VERB
ejpam-5027	149	24	:	:	PUNCT
ejpam-5027	149	25	e(a	e(a	NOUN
ejpam-5027	149	26	,	,	PUNCT
ejpam-5027	149	27	b	b	X
ejpam-5027	149	28	)	)	PUNCT
ejpam-5027	149	29	=	=	NOUN
ejpam-5027	149	30	{	{	PUNCT
ejpam-5027	149	31	0.7	0.7	NUM
ejpam-5027	149	32	,	,	PUNCT
ejpam-5027	149	33	0.5	0.5	NUM
ejpam-5027	149	34	}	}	PUNCT
ejpam-5027	149	35	,	,	PUNCT
ejpam-5027	149	36	h(a	h(a	PROPN
ejpam-5027	149	37	,	,	PUNCT
ejpam-5027	149	38	b	b	NOUN
ejpam-5027	149	39	)	)	PUNCT
ejpam-5027	149	40	=	=	SYM
ejpam-5027	149	41	{	{	PUNCT
ejpam-5027	149	42	0.5	0.5	NUM
ejpam-5027	149	43	,	,	PUNCT
ejpam-5027	149	44	0.4	0.4	NUM
ejpam-5027	149	45	}	}	PUNCT
ejpam-5027	149	46	,	,	PUNCT
ejpam-5027	149	47	r(a	r(a	PROPN
ejpam-5027	149	48	,	,	PUNCT
ejpam-5027	149	49	b	b	X
ejpam-5027	149	50	)	)	PUNCT
ejpam-5027	149	51	=	=	SYM
ejpam-5027	149	52	{	{	PUNCT
ejpam-5027	149	53	0.4	0.4	NUM
ejpam-5027	149	54	,	,	PUNCT
ejpam-5027	149	55	0.3	0.3	NUM
ejpam-5027	149	56	}	}	PUNCT
ejpam-5027	149	57	,	,	PUNCT
ejpam-5027	149	58	s(a	s(a	PROPN
ejpam-5027	149	59	,	,	PUNCT
ejpam-5027	149	60	b	b	NOUN
ejpam-5027	149	61	)	)	PUNCT
ejpam-5027	149	62	=	=	SYM
ejpam-5027	149	63	{	{	PUNCT
ejpam-5027	149	64	0.5	0.5	NUM
ejpam-5027	149	65	,	,	PUNCT
ejpam-5027	149	66	0.5	0.5	NUM
ejpam-5027	149	67	}	}	PUNCT
ejpam-5027	149	68	.	.	PUNCT
ejpam-5027	150	1	assume	assume	VERB
ejpam-5027	150	2	τ1	τ1	PROPN
ejpam-5027	150	3	=	=	SYM
ejpam-5027	150	4	{	{	PUNCT
ejpam-5027	150	5	0	0	NUM
ejpam-5027	150	6	,	,	PUNCT
ejpam-5027	150	7	1	1	NUM
ejpam-5027	150	8	,	,	PUNCT
ejpam-5027	150	9	e	e	NOUN
ejpam-5027	150	10	}	}	PUNCT
ejpam-5027	150	11	,	,	PUNCT
ejpam-5027	150	12	and	and	CCONJ
ejpam-5027	150	13	τ2	τ2	NOUN
ejpam-5027	150	14	=	=	SYM
ejpam-5027	150	15	{	{	PUNCT
ejpam-5027	150	16	0	0	NUM
ejpam-5027	150	17	,	,	PUNCT
ejpam-5027	150	18	1	1	NUM
ejpam-5027	150	19	,	,	PUNCT
ejpam-5027	150	20	h	h	NOUN
ejpam-5027	150	21	,	,	PUNCT
ejpam-5027	150	22	r	r	NOUN
ejpam-5027	150	23	}	}	PUNCT
ejpam-5027	150	24	.	.	PUNCT
ejpam-5027	151	1	then	then	ADV
ejpam-5027	151	2	we	we	PRON
ejpam-5027	151	3	can	can	AUX
ejpam-5027	151	4	see	see	VERB
ejpam-5027	151	5	that	that	PRON
ejpam-5027	151	6	s	s	VERB
ejpam-5027	151	7	is	be	AUX
ejpam-5027	151	8	fuzzy	fuzzy	ADJ
ejpam-5027	151	9	(	(	PUNCT
ejpam-5027	151	10	1	1	NUM
ejpam-5027	151	11	,	,	PUNCT
ejpam-5027	151	12	2	2	NUM
ejpam-5027	151	13	)	)	PUNCT
ejpam-5027	151	14	−	−	NOUN
ejpam-5027	151	15	gs−cld	gs−cld	NOUN
ejpam-5027	151	16	never	never	ADV
ejpam-5027	151	17	fuzzy	fuzzy	ADJ
ejpam-5027	151	18	(	(	PUNCT
ejpam-5027	151	19	1	1	NUM
ejpam-5027	151	20	,	,	PUNCT
ejpam-5027	151	21	2)−	2)−	NUM
ejpam-5027	151	22	gα−cld	gα−cld	NOUN
ejpam-5027	151	23	,	,	PUNCT
ejpam-5027	151	24	since	since	SCONJ
ejpam-5027	151	25	s	s	NOUN
ejpam-5027	151	26	≤	≤	NUM
ejpam-5027	151	27	e	e	NOUN
ejpam-5027	151	28	∈	∈	PROPN
ejpam-5027	151	29	τ1	τ1	NOUN
ejpam-5027	151	30	,	,	PUNCT
ejpam-5027	151	31	and	and	CCONJ
ejpam-5027	151	32	α−	α−	ADP
ejpam-5027	151	33	cl2(s	cl2(s	NOUN
ejpam-5027	151	34	)	)	PUNCT
ejpam-5027	152	1	=	=	PUNCT
ejpam-5027	152	2	hc	hc	PROPN
ejpam-5027	152	3	̸≤	̸≤	PROPN
ejpam-5027	152	4	e.	e.	PROPN
ejpam-5027	152	5	the	the	DET
ejpam-5027	152	6	next	next	ADJ
ejpam-5027	152	7	example	example	NOUN
ejpam-5027	152	8	shows	show	VERB
ejpam-5027	152	9	that	that	SCONJ
ejpam-5027	152	10	fuzzy	fuzzy	ADJ
ejpam-5027	152	11	(	(	PUNCT
ejpam-5027	152	12	1	1	NUM
ejpam-5027	152	13	,	,	PUNCT
ejpam-5027	152	14	2)−	2)−	PROPN
ejpam-5027	152	15	gp−	gp−	PUNCT
ejpam-5027	152	16	cld	cld	NOUN
ejpam-5027	152	17	⇏	⇏	VERB
ejpam-5027	152	18	fuzzy	fuzzy	ADJ
ejpam-5027	152	19	(	(	PUNCT
ejpam-5027	152	20	1	1	NUM
ejpam-5027	152	21	,	,	PUNCT
ejpam-5027	152	22	2)−	2)−	PROPN
ejpam-5027	152	23	gα−	gα−	SYM
ejpam-5027	152	24	cld	cld	PROPN
ejpam-5027	152	25	.	.	PUNCT
ejpam-5027	152	26	example	example	NOUN
ejpam-5027	152	27	4	4	NUM
ejpam-5027	152	28	.	.	PUNCT
ejpam-5027	152	29	suppose	suppose	VERB
ejpam-5027	152	30	e	e	NOUN
ejpam-5027	152	31	,	,	PUNCT
ejpam-5027	152	32	h	h	NOUN
ejpam-5027	152	33	,	,	PUNCT
ejpam-5027	152	34	r	r	NOUN
ejpam-5027	152	35	,	,	PUNCT
ejpam-5027	152	36	and	and	CCONJ
ejpam-5027	152	37	s	s	VERB
ejpam-5027	152	38	fuzzy	fuzzy	ADJ
ejpam-5027	152	39	subsets	subset	NOUN
ejpam-5027	152	40	of	of	ADP
ejpam-5027	152	41	x	x	X
ejpam-5027	152	42	=	=	X
ejpam-5027	152	43	{	{	PUNCT
ejpam-5027	152	44	a	a	DET
ejpam-5027	152	45	,	,	PUNCT
ejpam-5027	152	46	b	b	NOUN
ejpam-5027	152	47	}	}	PUNCT
ejpam-5027	152	48	as	as	SCONJ
ejpam-5027	152	49	follows	follow	VERB
ejpam-5027	152	50	:	:	PUNCT
ejpam-5027	152	51	e(a	e(a	NOUN
ejpam-5027	152	52	,	,	PUNCT
ejpam-5027	152	53	b	b	X
ejpam-5027	152	54	)	)	PUNCT
ejpam-5027	152	55	=	=	NOUN
ejpam-5027	152	56	{	{	PUNCT
ejpam-5027	152	57	0.7	0.7	NUM
ejpam-5027	152	58	,	,	PUNCT
ejpam-5027	152	59	0.5	0.5	NUM
ejpam-5027	152	60	}	}	PUNCT
ejpam-5027	152	61	,	,	PUNCT
ejpam-5027	152	62	h(a	h(a	PROPN
ejpam-5027	152	63	,	,	PUNCT
ejpam-5027	152	64	b	b	NOUN
ejpam-5027	152	65	)	)	PUNCT
ejpam-5027	152	66	=	=	NOUN
ejpam-5027	152	67	{	{	PUNCT
ejpam-5027	152	68	0.6	0.6	NUM
ejpam-5027	152	69	,	,	PUNCT
ejpam-5027	152	70	0.8	0.8	NUM
ejpam-5027	152	71	}	}	PUNCT
ejpam-5027	152	72	,	,	PUNCT
ejpam-5027	152	73	r(a	r(a	PROPN
ejpam-5027	152	74	,	,	PUNCT
ejpam-5027	152	75	b	b	X
ejpam-5027	152	76	)	)	PUNCT
ejpam-5027	152	77	=	=	SYM
ejpam-5027	152	78	{	{	PUNCT
ejpam-5027	152	79	0.4	0.4	NUM
ejpam-5027	152	80	,	,	PUNCT
ejpam-5027	152	81	0.3	0.3	NUM
ejpam-5027	152	82	}	}	PUNCT
ejpam-5027	152	83	,	,	PUNCT
ejpam-5027	152	84	s(a	s(a	PROPN
ejpam-5027	152	85	,	,	PUNCT
ejpam-5027	152	86	b	b	NOUN
ejpam-5027	152	87	)	)	PUNCT
ejpam-5027	152	88	=	=	NOUN
ejpam-5027	152	89	{	{	PUNCT
ejpam-5027	152	90	0.2	0.2	NUM
ejpam-5027	152	91	,	,	PUNCT
ejpam-5027	152	92	0.4	0.4	NUM
ejpam-5027	152	93	}	}	PUNCT
ejpam-5027	152	94	.	.	PUNCT
ejpam-5027	153	1	assume	assume	VERB
ejpam-5027	153	2	τ1	τ1	PROPN
ejpam-5027	153	3	=	=	SYM
ejpam-5027	153	4	{	{	PUNCT
ejpam-5027	153	5	0	0	NUM
ejpam-5027	153	6	,	,	PUNCT
ejpam-5027	153	7	1	1	NUM
ejpam-5027	153	8	,	,	PUNCT
ejpam-5027	153	9	e	e	NOUN
ejpam-5027	153	10	}	}	PUNCT
ejpam-5027	153	11	,	,	PUNCT
ejpam-5027	153	12	and	and	CCONJ
ejpam-5027	153	13	τ2	τ2	NOUN
ejpam-5027	153	14	=	=	SYM
ejpam-5027	153	15	{	{	PUNCT
ejpam-5027	153	16	0	0	NUM
ejpam-5027	153	17	,	,	PUNCT
ejpam-5027	153	18	1	1	NUM
ejpam-5027	153	19	,	,	PUNCT
ejpam-5027	153	20	h	h	NOUN
ejpam-5027	153	21	,	,	PUNCT
ejpam-5027	153	22	r	r	NOUN
ejpam-5027	153	23	}	}	PUNCT
ejpam-5027	153	24	.	.	PUNCT
ejpam-5027	154	1	then	then	ADV
ejpam-5027	154	2	we	we	PRON
ejpam-5027	154	3	can	can	AUX
ejpam-5027	154	4	see	see	VERB
ejpam-5027	154	5	that	that	PRON
ejpam-5027	154	6	s	s	VERB
ejpam-5027	154	7	is	be	AUX
ejpam-5027	154	8	fuzzy	fuzzy	ADJ
ejpam-5027	154	9	(	(	PUNCT
ejpam-5027	154	10	1	1	NUM
ejpam-5027	154	11	,	,	PUNCT
ejpam-5027	154	12	2	2	NUM
ejpam-5027	154	13	)	)	PUNCT
ejpam-5027	154	14	−	−	NOUN
ejpam-5027	154	15	gp−cld	gp−cld	NOUN
ejpam-5027	154	16	never	never	ADV
ejpam-5027	154	17	fuzzy	fuzzy	ADJ
ejpam-5027	154	18	(	(	PUNCT
ejpam-5027	154	19	1	1	NUM
ejpam-5027	154	20	,	,	PUNCT
ejpam-5027	154	21	2)−	2)−	NUM
ejpam-5027	154	22	gα−cld	gα−cld	NOUN
ejpam-5027	154	23	,	,	PUNCT
ejpam-5027	154	24	since	since	SCONJ
ejpam-5027	154	25	s	s	NOUN
ejpam-5027	154	26	≤	≤	NUM
ejpam-5027	154	27	e	e	NOUN
ejpam-5027	154	28	∈	∈	PROPN
ejpam-5027	154	29	τ1	τ1	NOUN
ejpam-5027	154	30	,	,	PUNCT
ejpam-5027	154	31	and	and	CCONJ
ejpam-5027	154	32	α−	α−	ADP
ejpam-5027	154	33	cl2(s	cl2(s	NOUN
ejpam-5027	154	34	)	)	PUNCT
ejpam-5027	155	1	=	=	SYM
ejpam-5027	155	2	rc	rc	PROPN
ejpam-5027	155	3	̸≤	̸≤	PROPN
ejpam-5027	155	4	e.	e.	PROPN
ejpam-5027	155	5	the	the	DET
ejpam-5027	155	6	example	example	NOUN
ejpam-5027	155	7	below	below	ADV
ejpam-5027	155	8	indicates	indicate	VERB
ejpam-5027	155	9	that	that	SCONJ
ejpam-5027	155	10	fuzzy	fuzzy	ADJ
ejpam-5027	155	11	(	(	PUNCT
ejpam-5027	155	12	1	1	NUM
ejpam-5027	155	13	,	,	PUNCT
ejpam-5027	155	14	2)−	2)−	NUM
ejpam-5027	155	15	gβ	gβ	ADP
ejpam-5027	155	16	−	−	PUNCT
ejpam-5027	155	17	cld	cld	NOUN
ejpam-5027	155	18	⇏	⇏	VERB
ejpam-5027	155	19	fuzzy	fuzzy	ADJ
ejpam-5027	155	20	(	(	PUNCT
ejpam-5027	155	21	1	1	NUM
ejpam-5027	155	22	,	,	PUNCT
ejpam-5027	155	23	2)−	2)−	NUM
ejpam-5027	155	24	gs−	gs−	NUM
ejpam-5027	155	25	cld	cld	PROPN
ejpam-5027	155	26	.	.	PUNCT
ejpam-5027	155	27	example	example	NOUN
ejpam-5027	155	28	5	5	NUM
ejpam-5027	155	29	.	.	PUNCT
ejpam-5027	155	30	suppose	suppose	VERB
ejpam-5027	155	31	e	e	NOUN
ejpam-5027	155	32	,	,	PUNCT
ejpam-5027	155	33	h	h	NOUN
ejpam-5027	155	34	,	,	PUNCT
ejpam-5027	155	35	r	r	NOUN
ejpam-5027	155	36	,	,	PUNCT
ejpam-5027	155	37	and	and	CCONJ
ejpam-5027	155	38	s	s	VERB
ejpam-5027	155	39	fuzzy	fuzzy	ADJ
ejpam-5027	155	40	subsets	subset	NOUN
ejpam-5027	155	41	of	of	ADP
ejpam-5027	155	42	x	x	X
ejpam-5027	155	43	=	=	X
ejpam-5027	155	44	{	{	PUNCT
ejpam-5027	155	45	a	a	DET
ejpam-5027	155	46	,	,	PUNCT
ejpam-5027	155	47	b	b	NOUN
ejpam-5027	155	48	}	}	PUNCT
ejpam-5027	155	49	as	as	SCONJ
ejpam-5027	155	50	follows	follow	VERB
ejpam-5027	155	51	:	:	PUNCT
ejpam-5027	155	52	e(a	e(a	NOUN
ejpam-5027	155	53	,	,	PUNCT
ejpam-5027	155	54	b	b	X
ejpam-5027	155	55	)	)	PUNCT
ejpam-5027	155	56	=	=	SYM
ejpam-5027	155	57	{	{	PUNCT
ejpam-5027	155	58	0.5	0.5	NUM
ejpam-5027	155	59	,	,	PUNCT
ejpam-5027	155	60	0.7	0.7	NUM
ejpam-5027	155	61	}	}	PUNCT
ejpam-5027	155	62	,	,	PUNCT
ejpam-5027	155	63	h(a	h(a	PROPN
ejpam-5027	155	64	,	,	PUNCT
ejpam-5027	155	65	b	b	NOUN
ejpam-5027	155	66	)	)	PUNCT
ejpam-5027	155	67	=	=	SYM
ejpam-5027	155	68	{	{	PUNCT
ejpam-5027	155	69	0.6	0.6	NUM
ejpam-5027	155	70	,	,	PUNCT
ejpam-5027	155	71	0.5	0.5	NUM
ejpam-5027	155	72	}	}	PUNCT
ejpam-5027	155	73	,	,	PUNCT
ejpam-5027	155	74	r(a	r(a	PROPN
ejpam-5027	155	75	,	,	PUNCT
ejpam-5027	155	76	b	b	X
ejpam-5027	155	77	)	)	PUNCT
ejpam-5027	155	78	=	=	SYM
ejpam-5027	155	79	{	{	PUNCT
ejpam-5027	155	80	0.4	0.4	NUM
ejpam-5027	155	81	,	,	PUNCT
ejpam-5027	155	82	0.3	0.3	NUM
ejpam-5027	155	83	}	}	PUNCT
ejpam-5027	155	84	,	,	PUNCT
ejpam-5027	155	85	s(a	s(a	PROPN
ejpam-5027	155	86	,	,	PUNCT
ejpam-5027	155	87	b	b	NOUN
ejpam-5027	155	88	)	)	PUNCT
ejpam-5027	155	89	=	=	SYM
ejpam-5027	155	90	{	{	PUNCT
ejpam-5027	155	91	0.5	0.5	NUM
ejpam-5027	155	92	,	,	PUNCT
ejpam-5027	155	93	0.5	0.5	NUM
ejpam-5027	155	94	}	}	PUNCT
ejpam-5027	155	95	.	.	PUNCT
ejpam-5027	156	1	assume	assume	VERB
ejpam-5027	156	2	τ1	τ1	PROPN
ejpam-5027	156	3	=	=	SYM
ejpam-5027	156	4	{	{	PUNCT
ejpam-5027	156	5	0	0	NUM
ejpam-5027	156	6	,	,	PUNCT
ejpam-5027	156	7	1	1	NUM
ejpam-5027	156	8	,	,	PUNCT
ejpam-5027	156	9	e	e	NOUN
ejpam-5027	156	10	}	}	PUNCT
ejpam-5027	156	11	,	,	PUNCT
ejpam-5027	156	12	and	and	CCONJ
ejpam-5027	156	13	τ2	τ2	NOUN
ejpam-5027	156	14	=	=	SYM
ejpam-5027	156	15	{	{	PUNCT
ejpam-5027	156	16	0	0	NUM
ejpam-5027	156	17	,	,	PUNCT
ejpam-5027	156	18	1	1	NUM
ejpam-5027	156	19	,	,	PUNCT
ejpam-5027	156	20	h	h	NOUN
ejpam-5027	156	21	,	,	PUNCT
ejpam-5027	156	22	r	r	NOUN
ejpam-5027	156	23	}	}	PUNCT
ejpam-5027	156	24	.	.	PUNCT
ejpam-5027	157	1	then	then	ADV
ejpam-5027	157	2	we	we	PRON
ejpam-5027	157	3	can	can	AUX
ejpam-5027	157	4	see	see	VERB
ejpam-5027	157	5	that	that	PRON
ejpam-5027	157	6	s	s	VERB
ejpam-5027	157	7	is	be	AUX
ejpam-5027	157	8	fuzzy	fuzzy	ADJ
ejpam-5027	157	9	(	(	PUNCT
ejpam-5027	157	10	1	1	NUM
ejpam-5027	157	11	,	,	PUNCT
ejpam-5027	157	12	2	2	NUM
ejpam-5027	157	13	)	)	PUNCT
ejpam-5027	157	14	−	−	PROPN
ejpam-5027	158	1	gβ−cld	gβ−cld	ADP
ejpam-5027	158	2	never	never	ADV
ejpam-5027	158	3	fuzzy	fuzzy	ADJ
ejpam-5027	158	4	(	(	PUNCT
ejpam-5027	158	5	1	1	NUM
ejpam-5027	158	6	,	,	PUNCT
ejpam-5027	158	7	2	2	NUM
ejpam-5027	158	8	)	)	PUNCT
ejpam-5027	158	9	−	−	NOUN
ejpam-5027	159	1	gs−cld	gs−cld	NOUN
ejpam-5027	159	2	,	,	PUNCT
ejpam-5027	159	3	since	since	SCONJ
ejpam-5027	159	4	s	s	NOUN
ejpam-5027	159	5	≤	≤	NUM
ejpam-5027	159	6	e	e	NOUN
ejpam-5027	159	7	∈	∈	PROPN
ejpam-5027	159	8	τ1	τ1	NOUN
ejpam-5027	159	9	,	,	PUNCT
ejpam-5027	159	10	and	and	CCONJ
ejpam-5027	159	11	s	s	VERB
ejpam-5027	159	12	−	−	PROPN
ejpam-5027	159	13	cl2(s	cl2(s	NOUN
ejpam-5027	159	14	)	)	PUNCT
ejpam-5027	160	1	=	=	SYM
ejpam-5027	160	2	f	f	X
ejpam-5027	160	3	(	(	PUNCT
ejpam-5027	160	4	a	a	DET
ejpam-5027	160	5	,	,	PUNCT
ejpam-5027	160	6	b	b	NOUN
ejpam-5027	160	7	)	)	PUNCT
ejpam-5027	160	8	=	=	SYM
ejpam-5027	160	9	{	{	PUNCT
ejpam-5027	160	10	0.6	0.6	NUM
ejpam-5027	160	11	,	,	PUNCT
ejpam-5027	160	12	0.5	0.5	NUM
ejpam-5027	160	13	}	}	PUNCT
ejpam-5027	160	14	̸≤	̸≤	PROPN
ejpam-5027	160	15	e.	e.	PROPN
ejpam-5027	160	16	ahlam	ahlam	PROPN
ejpam-5027	160	17	ahmed	ahmed	PROPN
ejpam-5027	160	18	alharbi	alharbi	PROPN
ejpam-5027	160	19	,	,	PUNCT
ejpam-5027	160	20	adem	adem	PROPN
ejpam-5027	160	21	kilicman	kilicman	PROPN
ejpam-5027	160	22	/	/	SYM
ejpam-5027	160	23	eur	eur	PROPN
ejpam-5027	160	24	.	.	PUNCT
ejpam-5027	161	1	j.	j.	PROPN
ejpam-5027	161	2	pure	pure	PROPN
ejpam-5027	161	3	appl	appl	PROPN
ejpam-5027	161	4	.	.	PROPN
ejpam-5027	161	5	math	math	PROPN
ejpam-5027	161	6	,	,	PUNCT
ejpam-5027	161	7	17	17	NUM
ejpam-5027	161	8	(	(	PUNCT
ejpam-5027	161	9	1	1	NUM
ejpam-5027	161	10	)	)	PUNCT
ejpam-5027	161	11	(	(	PUNCT
ejpam-5027	161	12	2024	2024	NUM
ejpam-5027	161	13	)	)	PUNCT
ejpam-5027	161	14	,	,	PUNCT
ejpam-5027	161	15	30	30	NUM
ejpam-5027	161	16	-	-	SYM
ejpam-5027	161	17	41	41	NUM
ejpam-5027	161	18	36	36	NUM
ejpam-5027	161	19	likewise	likewise	ADV
ejpam-5027	161	20	,	,	PUNCT
ejpam-5027	161	21	the	the	DET
ejpam-5027	161	22	following	follow	VERB
ejpam-5027	161	23	example	example	NOUN
ejpam-5027	161	24	shows	show	VERB
ejpam-5027	161	25	that	that	SCONJ
ejpam-5027	161	26	fuzzy	fuzzy	ADJ
ejpam-5027	161	27	(	(	PUNCT
ejpam-5027	161	28	1	1	NUM
ejpam-5027	161	29	,	,	PUNCT
ejpam-5027	161	30	2)−gβ−cld⇏	2)−gβ−cld⇏	NUM
ejpam-5027	161	31	fuzzy	fuzzy	ADJ
ejpam-5027	161	32	(	(	PUNCT
ejpam-5027	161	33	1	1	NUM
ejpam-5027	161	34	,	,	PUNCT
ejpam-5027	161	35	2)−gp−	2)−gp−	NUM
ejpam-5027	161	36	cld	cld	PROPN
ejpam-5027	161	37	.	.	PUNCT
ejpam-5027	161	38	example	example	NOUN
ejpam-5027	161	39	6	6	NUM
ejpam-5027	161	40	.	.	PUNCT
ejpam-5027	161	41	suppose	suppose	VERB
ejpam-5027	161	42	e	e	NOUN
ejpam-5027	161	43	,	,	PUNCT
ejpam-5027	161	44	h	h	NOUN
ejpam-5027	161	45	,	,	PUNCT
ejpam-5027	161	46	r	r	NOUN
ejpam-5027	161	47	,	,	PUNCT
ejpam-5027	161	48	and	and	CCONJ
ejpam-5027	161	49	s	s	VERB
ejpam-5027	161	50	fuzzy	fuzzy	ADJ
ejpam-5027	161	51	subsets	subset	NOUN
ejpam-5027	161	52	of	of	ADP
ejpam-5027	161	53	x	x	X
ejpam-5027	161	54	=	=	X
ejpam-5027	161	55	{	{	PUNCT
ejpam-5027	161	56	a	a	DET
ejpam-5027	161	57	,	,	PUNCT
ejpam-5027	161	58	b	b	NOUN
ejpam-5027	161	59	}	}	PUNCT
ejpam-5027	161	60	as	as	SCONJ
ejpam-5027	161	61	follows	follow	VERB
ejpam-5027	161	62	:	:	PUNCT
ejpam-5027	161	63	e(a	e(a	NOUN
ejpam-5027	161	64	,	,	PUNCT
ejpam-5027	161	65	b	b	X
ejpam-5027	161	66	)	)	PUNCT
ejpam-5027	161	67	=	=	SYM
ejpam-5027	161	68	{	{	PUNCT
ejpam-5027	161	69	0.5	0.5	NUM
ejpam-5027	161	70	,	,	PUNCT
ejpam-5027	161	71	0.7	0.7	NUM
ejpam-5027	161	72	}	}	PUNCT
ejpam-5027	161	73	,	,	PUNCT
ejpam-5027	161	74	h(a	h(a	PROPN
ejpam-5027	161	75	,	,	PUNCT
ejpam-5027	161	76	b	b	NOUN
ejpam-5027	161	77	)	)	PUNCT
ejpam-5027	161	78	=	=	SYM
ejpam-5027	161	79	{	{	PUNCT
ejpam-5027	161	80	0.4	0.4	NUM
ejpam-5027	161	81	,	,	PUNCT
ejpam-5027	161	82	0.6	0.6	NUM
ejpam-5027	161	83	}	}	PUNCT
ejpam-5027	161	84	,	,	PUNCT
ejpam-5027	161	85	r(a	r(a	PROPN
ejpam-5027	161	86	,	,	PUNCT
ejpam-5027	161	87	b	b	X
ejpam-5027	161	88	)	)	PUNCT
ejpam-5027	161	89	=	=	PUNCT
ejpam-5027	161	90	{	{	PUNCT
ejpam-5027	161	91	0.3	0.3	NUM
ejpam-5027	161	92	,	,	PUNCT
ejpam-5027	161	93	0.4	0.4	NUM
ejpam-5027	161	94	}	}	PUNCT
ejpam-5027	161	95	,	,	PUNCT
ejpam-5027	161	96	s(a	s(a	PROPN
ejpam-5027	161	97	,	,	PUNCT
ejpam-5027	161	98	b	b	NOUN
ejpam-5027	161	99	)	)	PUNCT
ejpam-5027	161	100	=	=	SYM
ejpam-5027	161	101	{	{	PUNCT
ejpam-5027	161	102	0.5	0.5	NUM
ejpam-5027	161	103	,	,	PUNCT
ejpam-5027	161	104	0.5	0.5	NUM
ejpam-5027	161	105	}	}	PUNCT
ejpam-5027	161	106	.	.	PUNCT
ejpam-5027	162	1	assume	assume	VERB
ejpam-5027	162	2	τ1	τ1	PROPN
ejpam-5027	162	3	=	=	SYM
ejpam-5027	162	4	{	{	PUNCT
ejpam-5027	162	5	0	0	NUM
ejpam-5027	162	6	,	,	PUNCT
ejpam-5027	162	7	1	1	NUM
ejpam-5027	162	8	,	,	PUNCT
ejpam-5027	162	9	e	e	NOUN
ejpam-5027	162	10	}	}	PUNCT
ejpam-5027	162	11	,	,	PUNCT
ejpam-5027	162	12	and	and	CCONJ
ejpam-5027	162	13	τ2	τ2	NOUN
ejpam-5027	162	14	=	=	SYM
ejpam-5027	162	15	{	{	PUNCT
ejpam-5027	162	16	0	0	NUM
ejpam-5027	162	17	,	,	PUNCT
ejpam-5027	162	18	1	1	NUM
ejpam-5027	162	19	,	,	PUNCT
ejpam-5027	162	20	h	h	NOUN
ejpam-5027	162	21	,	,	PUNCT
ejpam-5027	162	22	r	r	NOUN
ejpam-5027	162	23	}	}	PUNCT
ejpam-5027	162	24	.	.	PUNCT
ejpam-5027	163	1	then	then	ADV
ejpam-5027	163	2	we	we	PRON
ejpam-5027	163	3	can	can	AUX
ejpam-5027	163	4	see	see	VERB
ejpam-5027	163	5	that	that	PRON
ejpam-5027	163	6	s	s	VERB
ejpam-5027	163	7	is	be	AUX
ejpam-5027	163	8	fuzzy	fuzzy	ADJ
ejpam-5027	163	9	(	(	PUNCT
ejpam-5027	163	10	1	1	NUM
ejpam-5027	163	11	,	,	PUNCT
ejpam-5027	163	12	2	2	NUM
ejpam-5027	163	13	)	)	PUNCT
ejpam-5027	163	14	−	−	PROPN
ejpam-5027	164	1	gβ−cld	gβ−cld	ADP
ejpam-5027	164	2	never	never	ADV
ejpam-5027	164	3	fuzzy	fuzzy	ADJ
ejpam-5027	164	4	(	(	PUNCT
ejpam-5027	164	5	1	1	NUM
ejpam-5027	164	6	,	,	PUNCT
ejpam-5027	164	7	2	2	NUM
ejpam-5027	164	8	)	)	PUNCT
ejpam-5027	164	9	−	−	NOUN
ejpam-5027	165	1	gp−cld	gp−cld	NOUN
ejpam-5027	165	2	,	,	PUNCT
ejpam-5027	165	3	since	since	SCONJ
ejpam-5027	165	4	s	s	NOUN
ejpam-5027	165	5	≤	≤	NUM
ejpam-5027	165	6	e	e	NOUN
ejpam-5027	165	7	∈	∈	PROPN
ejpam-5027	165	8	τ1	τ1	NOUN
ejpam-5027	165	9	,	,	PUNCT
ejpam-5027	165	10	and	and	CCONJ
ejpam-5027	165	11	p	p	PRON
ejpam-5027	165	12	−	−	PROPN
ejpam-5027	165	13	cl2(s	cl2(s	NOUN
ejpam-5027	165	14	)	)	PUNCT
ejpam-5027	166	1	=	=	SYM
ejpam-5027	166	2	f	f	X
ejpam-5027	166	3	(	(	PUNCT
ejpam-5027	166	4	a	a	DET
ejpam-5027	166	5	,	,	PUNCT
ejpam-5027	166	6	b	b	NOUN
ejpam-5027	166	7	)	)	PUNCT
ejpam-5027	166	8	=	=	SYM
ejpam-5027	166	9	{	{	PUNCT
ejpam-5027	166	10	0.6	0.6	NUM
ejpam-5027	166	11	,	,	PUNCT
ejpam-5027	166	12	0.5	0.5	NUM
ejpam-5027	166	13	}	}	PUNCT
ejpam-5027	166	14	̸≤	̸≤	PROPN
ejpam-5027	166	15	e.	e.	PROPN
ejpam-5027	166	16	theorem	theorem	PROPN
ejpam-5027	166	17	3	3	X
ejpam-5027	166	18	.	.	X
ejpam-5027	166	19	assume	assume	VERB
ejpam-5027	166	20	(	(	PUNCT
ejpam-5027	166	21	x	x	NOUN
ejpam-5027	166	22	,	,	PUNCT
ejpam-5027	166	23	τ1	τ1	NOUN
ejpam-5027	166	24	,	,	PUNCT
ejpam-5027	166	25	τ2	τ2	NOUN
ejpam-5027	166	26	)	)	PUNCT
ejpam-5027	166	27	is	be	AUX
ejpam-5027	166	28	fbts	fbt	NOUN
ejpam-5027	166	29	and	and	CCONJ
ejpam-5027	166	30	e	e	NOUN
ejpam-5027	166	31	is	be	AUX
ejpam-5027	166	32	fuzzy	fuzzy	ADJ
ejpam-5027	166	33	τi−open	τi−open	INTJ
ejpam-5027	166	34	(	(	PUNCT
ejpam-5027	166	35	resp	resp	NOUN
ejpam-5027	166	36	,	,	PUNCT
ejpam-5027	166	37	τi	τi	ADP
ejpam-5027	166	38	−	−	PROPN
ejpam-5027	166	39	cld	cld	PROPN
ejpam-5027	166	40	)	)	PUNCT
ejpam-5027	166	41	.	.	PUNCT
ejpam-5027	167	1	then	then	ADV
ejpam-5027	167	2	,	,	PUNCT
ejpam-5027	167	3	the	the	DET
ejpam-5027	167	4	statements	statement	NOUN
ejpam-5027	167	5	below	below	ADV
ejpam-5027	167	6	are	be	AUX
ejpam-5027	167	7	equal	equal	ADJ
ejpam-5027	167	8	:	:	PUNCT
ejpam-5027	167	9	(	(	PUNCT
ejpam-5027	167	10	1	1	X
ejpam-5027	167	11	)	)	PUNCT
ejpam-5027	167	12	e	e	NOUN
ejpam-5027	167	13	is	be	AUX
ejpam-5027	167	14	fuzzy	fuzzy	ADJ
ejpam-5027	167	15	(	(	PUNCT
ejpam-5027	167	16	i	i	NOUN
ejpam-5027	167	17	,	,	PUNCT
ejpam-5027	167	18	j)−	j)−	PROPN
ejpam-5027	167	19	gφ−	gφ−	PUNCT
ejpam-5027	167	20	cld	cld	PROPN
ejpam-5027	167	21	(	(	PUNCT
ejpam-5027	167	22	resp	resp	NOUN
ejpam-5027	167	23	,	,	PUNCT
ejpam-5027	167	24	fuzzy	fuzzy	ADJ
ejpam-5027	167	25	(	(	PUNCT
ejpam-5027	167	26	i	i	PROPN
ejpam-5027	167	27	,	,	PUNCT
ejpam-5027	167	28	j)−	j)−	PROPN
ejpam-5027	167	29	gφ−	gφ−	PROPN
ejpam-5027	167	30	open	open	ADJ
ejpam-5027	167	31	)	)	PUNCT
ejpam-5027	167	32	.	.	PUNCT
ejpam-5027	168	1	(	(	PUNCT
ejpam-5027	168	2	2	2	X
ejpam-5027	168	3	)	)	PUNCT
ejpam-5027	168	4	e	e	NOUN
ejpam-5027	168	5	is	be	AUX
ejpam-5027	168	6	fuzzy	fuzzy	ADJ
ejpam-5027	168	7	τj	τj	ADP
ejpam-5027	168	8	−	−	PROPN
ejpam-5027	168	9	φ−	φ−	PROPN
ejpam-5027	168	10	cld	cld	PROPN
ejpam-5027	168	11	(	(	PUNCT
ejpam-5027	168	12	resp	resp	NOUN
ejpam-5027	168	13	,	,	PUNCT
ejpam-5027	168	14	fuzzy	fuzzy	ADJ
ejpam-5027	168	15	τj	τj	ADP
ejpam-5027	168	16	−	−	PROPN
ejpam-5027	168	17	φ−	φ−	PROPN
ejpam-5027	168	18	open	open	ADJ
ejpam-5027	168	19	)	)	PUNCT
ejpam-5027	168	20	.	.	PUNCT
ejpam-5027	169	1	proof	proof	NOUN
ejpam-5027	169	2	.	.	PUNCT
ejpam-5027	170	1	suppose	suppose	VERB
ejpam-5027	170	2	e	e	X
ejpam-5027	170	3	∈	∈	PROPN
ejpam-5027	170	4	τi	τi	VERB
ejpam-5027	170	5	,	,	PUNCT
ejpam-5027	170	6	and	and	CCONJ
ejpam-5027	170	7	fuzzy	fuzzy	ADJ
ejpam-5027	170	8	(	(	PUNCT
ejpam-5027	170	9	i	i	NOUN
ejpam-5027	170	10	,	,	PUNCT
ejpam-5027	170	11	j)−	j)−	PROPN
ejpam-5027	170	12	gφ−cld	gφ−cld	PROPN
ejpam-5027	170	13	.	.	PUNCT
ejpam-5027	171	1	then	then	ADV
ejpam-5027	171	2	τj	τj	ADP
ejpam-5027	171	3	−φ−	−φ−	ADJ
ejpam-5027	171	4	cl(e	cl(e	NOUN
ejpam-5027	171	5	)	)	PUNCT
ejpam-5027	171	6	≤	≤	NOUN
ejpam-5027	171	7	e	e	NOUN
ejpam-5027	171	8	,	,	PUNCT
ejpam-5027	171	9	and	and	CCONJ
ejpam-5027	171	10	hence	hence	ADV
ejpam-5027	171	11	e	e	NOUN
ejpam-5027	171	12	is	be	AUX
ejpam-5027	171	13	fuzzy	fuzzy	ADJ
ejpam-5027	171	14	τj	τj	ADP
ejpam-5027	171	15	−	−	PROPN
ejpam-5027	171	16	φ−cld	φ−cld	NOUN
ejpam-5027	171	17	.	.	PUNCT
ejpam-5027	172	1	conversely	conversely	ADV
ejpam-5027	172	2	,	,	PUNCT
ejpam-5027	172	3	it	it	PRON
ejpam-5027	172	4	is	be	AUX
ejpam-5027	172	5	obvious	obvious	ADJ
ejpam-5027	172	6	in	in	ADP
ejpam-5027	172	7	theorem	theorem	NOUN
ejpam-5027	172	8	2	2	NUM
ejpam-5027	172	9	,	,	PUNCT
ejpam-5027	172	10	also	also	ADV
ejpam-5027	172	11	from	from	ADP
ejpam-5027	172	12	figure	figure	NOUN
ejpam-5027	172	13	(	(	PUNCT
ejpam-5027	172	14	1	1	NUM
ejpam-5027	172	15	)	)	PUNCT
ejpam-5027	172	16	.	.	PUNCT
ejpam-5027	173	1	theorem	theorem	ADJ
ejpam-5027	173	2	4	4	NUM
ejpam-5027	173	3	.	.	PUNCT
ejpam-5027	174	1	let	let	VERB
ejpam-5027	174	2	e	e	X
ejpam-5027	174	3	∈	∈	PROPN
ejpam-5027	174	4	τi	τi	VERB
ejpam-5027	174	5	and	and	CCONJ
ejpam-5027	174	6	be	be	AUX
ejpam-5027	174	7	fuzzy	fuzzy	ADJ
ejpam-5027	174	8	(	(	PUNCT
ejpam-5027	174	9	i	i	NOUN
ejpam-5027	174	10	,	,	PUNCT
ejpam-5027	174	11	j)−gα−cld	j)−gα−cld	PROPN
ejpam-5027	174	12	.	.	PUNCT
ejpam-5027	175	1	then	then	ADV
ejpam-5027	175	2	e∧f	e∧f	PROPN
ejpam-5027	175	3	is	be	AUX
ejpam-5027	175	4	fuzzy	fuzzy	ADJ
ejpam-5027	175	5	(	(	PUNCT
ejpam-5027	175	6	i	i	NOUN
ejpam-5027	175	7	,	,	PUNCT
ejpam-5027	175	8	j)−gφ−cld	j)−gφ−cld	NOUN
ejpam-5027	175	9	,	,	PUNCT
ejpam-5027	175	10	wherever	wherever	SCONJ
ejpam-5027	175	11	f	f	PROPN
ejpam-5027	175	12	∈	∈	PROPN
ejpam-5027	175	13	fτj	fτj	NOUN
ejpam-5027	175	14	.	.	PUNCT
ejpam-5027	176	1	proof	proof	NOUN
ejpam-5027	176	2	.	.	PUNCT
ejpam-5027	177	1	as	as	SCONJ
ejpam-5027	177	2	e	e	PROPN
ejpam-5027	177	3	∈	∈	PROPN
ejpam-5027	177	4	τi	τi	NOUN
ejpam-5027	177	5	,	,	PUNCT
ejpam-5027	177	6	and	and	CCONJ
ejpam-5027	177	7	fuzzy	fuzzy	ADJ
ejpam-5027	177	8	(	(	PUNCT
ejpam-5027	177	9	i	i	NOUN
ejpam-5027	177	10	,	,	PUNCT
ejpam-5027	177	11	j)−	j)−	PROPN
ejpam-5027	177	12	gα−cld	gα−cld	PROPN
ejpam-5027	177	13	,	,	PUNCT
ejpam-5027	177	14	then	then	ADV
ejpam-5027	177	15	by	by	ADP
ejpam-5027	177	16	theorem	theorem	NOUN
ejpam-5027	177	17	3	3	NUM
ejpam-5027	177	18	e	e	NOUN
ejpam-5027	177	19	is	be	AUX
ejpam-5027	177	20	fuzzy	fuzzy	ADJ
ejpam-5027	177	21	τj	τj	ADP
ejpam-5027	177	22	−α−cld	−α−cld	PROPN
ejpam-5027	177	23	.	.	PUNCT
ejpam-5027	178	1	after	after	ADP
ejpam-5027	178	2	that	that	PRON
ejpam-5027	178	3	,	,	PUNCT
ejpam-5027	178	4	e	e	PROPN
ejpam-5027	178	5	∧	∧	PROPN
ejpam-5027	178	6	f	f	PROPN
ejpam-5027	178	7	is	be	AUX
ejpam-5027	178	8	fuzzy	fuzzy	ADJ
ejpam-5027	178	9	τj	τj	ADP
ejpam-5027	178	10	−	−	PROPN
ejpam-5027	178	11	α−cld	α−cld	NOUN
ejpam-5027	178	12	,	,	PUNCT
ejpam-5027	178	13	which	which	PRON
ejpam-5027	178	14	implies	imply	VERB
ejpam-5027	178	15	that	that	SCONJ
ejpam-5027	178	16	it	it	PRON
ejpam-5027	178	17	is	be	AUX
ejpam-5027	178	18	fuzzy	fuzzy	ADJ
ejpam-5027	178	19	(	(	PUNCT
ejpam-5027	178	20	i	i	NOUN
ejpam-5027	178	21	,	,	PUNCT
ejpam-5027	178	22	j)−	j)−	PROPN
ejpam-5027	178	23	gα−cld	gα−cld	PROPN
ejpam-5027	178	24	.	.	PUNCT
ejpam-5027	179	1	therefore	therefore	ADV
ejpam-5027	179	2	by	by	ADP
ejpam-5027	179	3	figure	figure	NOUN
ejpam-5027	179	4	(	(	PUNCT
ejpam-5027	179	5	1	1	X
ejpam-5027	179	6	)	)	PUNCT
ejpam-5027	179	7	we	we	PRON
ejpam-5027	179	8	conclude	conclude	VERB
ejpam-5027	179	9	e	e	X
ejpam-5027	179	10	∧	∧	PROPN
ejpam-5027	179	11	f	f	PROPN
ejpam-5027	179	12	is	be	AUX
ejpam-5027	179	13	fuzzy	fuzzy	ADJ
ejpam-5027	179	14	(	(	PUNCT
ejpam-5027	179	15	i	i	NOUN
ejpam-5027	179	16	,	,	PUNCT
ejpam-5027	179	17	j)−	j)−	PROPN
ejpam-5027	179	18	gφ−cld	gφ−cld	PROPN
ejpam-5027	179	19	.	.	PUNCT
ejpam-5027	180	1	corollary	corollary	ADJ
ejpam-5027	180	2	1	1	PROPN
ejpam-5027	180	3	.	.	PUNCT
ejpam-5027	180	4	suppose	suppose	VERB
ejpam-5027	180	5	a	a	DET
ejpam-5027	180	6	∈	∈	PROPN
ejpam-5027	180	7	fi	fi	NOUN
ejpam-5027	180	8	,	,	PUNCT
ejpam-5027	180	9	and	and	CCONJ
ejpam-5027	180	10	fuzzy	fuzzy	ADJ
ejpam-5027	180	11	(	(	PUNCT
ejpam-5027	180	12	i	i	NOUN
ejpam-5027	180	13	,	,	PUNCT
ejpam-5027	180	14	j)−	j)−	PROPN
ejpam-5027	180	15	gα−	gα−	PUNCT
ejpam-5027	180	16	open	open	ADJ
ejpam-5027	180	17	.	.	PUNCT
ejpam-5027	181	1	thereafter	thereafter	ADV
ejpam-5027	181	2	a	a	DET
ejpam-5027	181	3	∨	∨	NOUN
ejpam-5027	181	4	f	f	PROPN
ejpam-5027	181	5	is	be	AUX
ejpam-5027	181	6	fuzzy	fuzzy	ADJ
ejpam-5027	181	7	(	(	PUNCT
ejpam-5027	181	8	i	i	PROPN
ejpam-5027	181	9	,	,	PUNCT
ejpam-5027	181	10	j)−	j)−	PROPN
ejpam-5027	181	11	gφ−open	gφ−open	PROPN
ejpam-5027	181	12	,	,	PUNCT
ejpam-5027	181	13	whenever	whenever	SCONJ
ejpam-5027	181	14	f	f	PROPN
ejpam-5027	181	15	∈	∈	PROPN
ejpam-5027	181	16	τj	τj	ADP
ejpam-5027	181	17	.	.	PUNCT
ejpam-5027	182	1	theorem	theorem	ADJ
ejpam-5027	182	2	5	5	NUM
ejpam-5027	182	3	.	.	PUNCT
ejpam-5027	182	4	finite	finite	PROPN
ejpam-5027	182	5	union	union	NOUN
ejpam-5027	182	6	of	of	ADP
ejpam-5027	182	7	fuzzy	fuzzy	ADJ
ejpam-5027	182	8	(	(	PUNCT
ejpam-5027	182	9	i	i	NOUN
ejpam-5027	182	10	,	,	PUNCT
ejpam-5027	182	11	j)−	j)−	PROPN
ejpam-5027	182	12	gφ−cld	gφ−cld	PROPN
ejpam-5027	182	13	of	of	ADP
ejpam-5027	182	14	(	(	PUNCT
ejpam-5027	182	15	x	x	NOUN
ejpam-5027	182	16	,	,	PUNCT
ejpam-5027	182	17	τ1	τ1	NOUN
ejpam-5027	182	18	,	,	PUNCT
ejpam-5027	182	19	τ2	τ2	NOUN
ejpam-5027	182	20	)	)	PUNCT
ejpam-5027	182	21	is	be	AUX
ejpam-5027	182	22	fuzzy	fuzzy	ADJ
ejpam-5027	182	23	(	(	PUNCT
ejpam-5027	182	24	i	i	NOUN
ejpam-5027	182	25	,	,	PUNCT
ejpam-5027	182	26	j)−	j)−	PROPN
ejpam-5027	182	27	gφ−cld	gφ−cld	PROPN
ejpam-5027	182	28	.	.	PUNCT
ejpam-5027	183	1	proof	proof	NOUN
ejpam-5027	183	2	.	.	PUNCT
ejpam-5027	184	1	assume	assume	VERB
ejpam-5027	184	2	e	e	X
ejpam-5027	184	3	,	,	PUNCT
ejpam-5027	184	4	andd	andd	PROPN
ejpam-5027	184	5	are	be	AUX
ejpam-5027	184	6	fuzzy	fuzzy	ADJ
ejpam-5027	184	7	(	(	PUNCT
ejpam-5027	184	8	i	i	PROPN
ejpam-5027	184	9	,	,	PUNCT
ejpam-5027	184	10	j)−gφ−cld	j)−gφ−cld	PROPN
ejpam-5027	184	11	in	in	ADP
ejpam-5027	184	12	fbts	fbt	NOUN
ejpam-5027	184	13	(	(	PUNCT
ejpam-5027	184	14	x	x	NOUN
ejpam-5027	184	15	,	,	PUNCT
ejpam-5027	184	16	τ1	τ1	NOUN
ejpam-5027	184	17	,	,	PUNCT
ejpam-5027	184	18	τ2	τ2	NOUN
ejpam-5027	184	19	)	)	PUNCT
ejpam-5027	184	20	.	.	PUNCT
ejpam-5027	185	1	then	then	ADV
ejpam-5027	185	2	e∨d	e∨d	NOUN
ejpam-5027	185	3	is	be	AUX
ejpam-5027	185	4	fuzzy	fuzzy	ADJ
ejpam-5027	185	5	(	(	PUNCT
ejpam-5027	185	6	i	i	NOUN
ejpam-5027	185	7	,	,	PUNCT
ejpam-5027	185	8	j)−gφ−cld	j)−gφ−cld	PROPN
ejpam-5027	185	9	.	.	PUNCT
ejpam-5027	186	1	it	it	PRON
ejpam-5027	186	2	follows	follow	VERB
ejpam-5027	186	3	from	from	ADP
ejpam-5027	186	4	the	the	DET
ejpam-5027	186	5	fact	fact	NOUN
ejpam-5027	186	6	τj−φ−cl(e∨d	τj−φ−cl(e∨d	NOUN
ejpam-5027	186	7	)	)	PUNCT
ejpam-5027	186	8	=	=	PUNCT
ejpam-5027	186	9	τj−φ−cl(e)∨τj−φ−cl(d	τj−φ−cl(e)∨τj−φ−cl(d	NUM
ejpam-5027	186	10	)	)	PUNCT
ejpam-5027	186	11	.	.	PUNCT
ejpam-5027	187	1	corollary	corollary	ADJ
ejpam-5027	187	2	2	2	NUM
ejpam-5027	187	3	.	.	PUNCT
ejpam-5027	188	1	if	if	SCONJ
ejpam-5027	188	2	e	e	NOUN
ejpam-5027	188	3	,	,	PUNCT
ejpam-5027	188	4	and	and	CCONJ
ejpam-5027	188	5	d	d	NOUN
ejpam-5027	188	6	are	be	AUX
ejpam-5027	188	7	fuzzy	fuzzy	ADJ
ejpam-5027	188	8	(	(	PUNCT
ejpam-5027	188	9	i	i	NOUN
ejpam-5027	188	10	,	,	PUNCT
ejpam-5027	188	11	j)−	j)−	PROPN
ejpam-5027	188	12	gφ−open	gφ−open	PROPN
ejpam-5027	188	13	.	.	PUNCT
ejpam-5027	189	1	thereafter	thereafter	ADV
ejpam-5027	189	2	e	e	X
ejpam-5027	189	3	∧d	∧d	PRON
ejpam-5027	189	4	is	be	AUX
ejpam-5027	189	5	fuzzy	fuzzy	ADJ
ejpam-5027	189	6	(	(	PUNCT
ejpam-5027	189	7	i	i	NOUN
ejpam-5027	189	8	,	,	PUNCT
ejpam-5027	189	9	j)−	j)−	PROPN
ejpam-5027	189	10	gφ−open	gφ−open	PROPN
ejpam-5027	189	11	.	.	PUNCT
ejpam-5027	190	1	remark	remark	PROPN
ejpam-5027	190	2	3	3	NUM
ejpam-5027	190	3	.	.	PUNCT
ejpam-5027	191	1	the	the	DET
ejpam-5027	191	2	finite	finite	ADJ
ejpam-5027	191	3	intersection	intersection	NOUN
ejpam-5027	191	4	of	of	ADP
ejpam-5027	191	5	fuzzy	fuzzy	ADJ
ejpam-5027	191	6	(	(	PUNCT
ejpam-5027	191	7	i	i	NOUN
ejpam-5027	191	8	,	,	PUNCT
ejpam-5027	191	9	j)−	j)−	PROPN
ejpam-5027	191	10	gφ−cld	gφ−cld	NOUN
ejpam-5027	191	11	in	in	ADP
ejpam-5027	191	12	fbts	fbt	NOUN
ejpam-5027	191	13	(	(	PUNCT
ejpam-5027	191	14	x	x	NOUN
ejpam-5027	191	15	,	,	PUNCT
ejpam-5027	191	16	τ1	τ1	NOUN
ejpam-5027	191	17	,	,	PUNCT
ejpam-5027	191	18	τ2	τ2	NOUN
ejpam-5027	191	19	)	)	PUNCT
ejpam-5027	191	20	is	be	AUX
ejpam-5027	191	21	not	not	PART
ejpam-5027	191	22	fuzzy	fuzzy	ADJ
ejpam-5027	191	23	(	(	PUNCT
ejpam-5027	191	24	i	i	NOUN
ejpam-5027	191	25	,	,	PUNCT
ejpam-5027	191	26	j)−	j)−	PROPN
ejpam-5027	191	27	gφ−cld	gφ−cld	NOUN
ejpam-5027	191	28	in	in	ADP
ejpam-5027	191	29	general	general	ADJ
ejpam-5027	191	30	.	.	PUNCT
ejpam-5027	192	1	we	we	PRON
ejpam-5027	192	2	show	show	VERB
ejpam-5027	192	3	that	that	SCONJ
ejpam-5027	192	4	by	by	ADP
ejpam-5027	192	5	the	the	DET
ejpam-5027	192	6	following	following	ADJ
ejpam-5027	192	7	example	example	NOUN
ejpam-5027	192	8	for	for	ADP
ejpam-5027	192	9	the	the	DET
ejpam-5027	192	10	specific	specific	ADJ
ejpam-5027	192	11	type	type	NOUN
ejpam-5027	192	12	that	that	PRON
ejpam-5027	192	13	is	be	AUX
ejpam-5027	192	14	fuzzy	fuzzy	ADJ
ejpam-5027	192	15	(	(	PUNCT
ejpam-5027	192	16	i	i	NOUN
ejpam-5027	192	17	,	,	PUNCT
ejpam-5027	192	18	j)−	j)−	PROPN
ejpam-5027	192	19	gα−cld	gα−cld	PROPN
ejpam-5027	192	20	.	.	PUNCT
ejpam-5027	193	1	suppose	suppose	VERB
ejpam-5027	193	2	e	e	NOUN
ejpam-5027	193	3	,	,	PUNCT
ejpam-5027	193	4	h	h	NOUN
ejpam-5027	193	5	,	,	PUNCT
ejpam-5027	193	6	r	r	NOUN
ejpam-5027	193	7	,	,	PUNCT
ejpam-5027	193	8	d1	d1	NOUN
ejpam-5027	193	9	,	,	PUNCT
ejpam-5027	193	10	and	and	CCONJ
ejpam-5027	193	11	d2	d2	PROPN
ejpam-5027	193	12	are	be	AUX
ejpam-5027	193	13	fuzzy	fuzzy	ADJ
ejpam-5027	193	14	subsets	subset	NOUN
ejpam-5027	193	15	of	of	ADP
ejpam-5027	193	16	x	x	X
ejpam-5027	193	17	=	=	X
ejpam-5027	193	18	{	{	PUNCT
ejpam-5027	193	19	a	a	PRON
ejpam-5027	193	20	,	,	PUNCT
ejpam-5027	193	21	b	b	NOUN
ejpam-5027	193	22	}	}	PUNCT
ejpam-5027	193	23	as	as	ADP
ejpam-5027	193	24	below	below	ADV
ejpam-5027	193	25	:	:	PUNCT
ejpam-5027	193	26	e(a	e(a	NOUN
ejpam-5027	193	27	,	,	PUNCT
ejpam-5027	193	28	b	b	X
ejpam-5027	193	29	)	)	PUNCT
ejpam-5027	193	30	=	=	NOUN
ejpam-5027	193	31	{	{	PUNCT
ejpam-5027	193	32	0.6	0.6	NUM
ejpam-5027	193	33	,	,	PUNCT
ejpam-5027	193	34	0.6	0.6	NUM
ejpam-5027	193	35	}	}	PUNCT
ejpam-5027	193	36	,	,	PUNCT
ejpam-5027	193	37	h(a	h(a	PROPN
ejpam-5027	193	38	,	,	PUNCT
ejpam-5027	193	39	b	b	NOUN
ejpam-5027	193	40	)	)	PUNCT
ejpam-5027	193	41	=	=	NOUN
ejpam-5027	193	42	{	{	PUNCT
ejpam-5027	193	43	0.7	0.7	NUM
ejpam-5027	193	44	,	,	PUNCT
ejpam-5027	193	45	0.8	0.8	NUM
ejpam-5027	193	46	}	}	PUNCT
ejpam-5027	193	47	,	,	PUNCT
ejpam-5027	193	48	r(a	r(a	PROPN
ejpam-5027	193	49	,	,	PUNCT
ejpam-5027	193	50	b	b	X
ejpam-5027	193	51	)	)	PUNCT
ejpam-5027	194	1	=	=	NOUN
ejpam-5027	194	2	{	{	PUNCT
ejpam-5027	194	3	0.6	0.6	NUM
ejpam-5027	194	4	,	,	PUNCT
ejpam-5027	194	5	0.7	0.7	NUM
ejpam-5027	194	6	}	}	PUNCT
ejpam-5027	194	7	,	,	PUNCT
ejpam-5027	194	8	d1(a	d1(a	PROPN
ejpam-5027	194	9	,	,	PUNCT
ejpam-5027	194	10	b	b	NOUN
ejpam-5027	194	11	)	)	PUNCT
ejpam-5027	194	12	=	=	SYM
ejpam-5027	194	13	{	{	PUNCT
ejpam-5027	194	14	0.5	0.5	NUM
ejpam-5027	194	15	,	,	PUNCT
ejpam-5027	194	16	0.7	0.7	NUM
ejpam-5027	194	17	}	}	PUNCT
ejpam-5027	194	18	,	,	PUNCT
ejpam-5027	194	19	d2(a	d2(a	PROPN
ejpam-5027	194	20	,	,	PUNCT
ejpam-5027	194	21	b	b	NOUN
ejpam-5027	194	22	)	)	PUNCT
ejpam-5027	194	23	=	=	NOUN
ejpam-5027	194	24	{	{	PUNCT
ejpam-5027	194	25	0.8	0.8	NUM
ejpam-5027	194	26	,	,	PUNCT
ejpam-5027	194	27	0.5	0.5	NUM
ejpam-5027	194	28	}	}	PUNCT
ejpam-5027	194	29	.	.	PUNCT
ejpam-5027	195	1	assume	assume	VERB
ejpam-5027	195	2	τ1	τ1	PROPN
ejpam-5027	195	3	=	=	SYM
ejpam-5027	195	4	{	{	PUNCT
ejpam-5027	195	5	0	0	NUM
ejpam-5027	195	6	,	,	PUNCT
ejpam-5027	195	7	1	1	NUM
ejpam-5027	195	8	,	,	PUNCT
ejpam-5027	195	9	e	e	NOUN
ejpam-5027	195	10	}	}	PUNCT
ejpam-5027	195	11	,	,	PUNCT
ejpam-5027	195	12	and	and	CCONJ
ejpam-5027	195	13	τ2	τ2	NOUN
ejpam-5027	195	14	=	=	SYM
ejpam-5027	195	15	{	{	PUNCT
ejpam-5027	195	16	0	0	NUM
ejpam-5027	195	17	,	,	PUNCT
ejpam-5027	195	18	1	1	NUM
ejpam-5027	195	19	,	,	PUNCT
ejpam-5027	195	20	h	h	NOUN
ejpam-5027	195	21	,	,	PUNCT
ejpam-5027	195	22	r	r	NOUN
ejpam-5027	195	23	}	}	PUNCT
ejpam-5027	195	24	.	.	PUNCT
ejpam-5027	196	1	then	then	ADV
ejpam-5027	196	2	d1	d1	PROPN
ejpam-5027	196	3	and	and	CCONJ
ejpam-5027	196	4	d2	d2	PROPN
ejpam-5027	196	5	are	be	AUX
ejpam-5027	196	6	fuzzy	fuzzy	ADJ
ejpam-5027	196	7	(	(	PUNCT
ejpam-5027	196	8	1	1	NUM
ejpam-5027	196	9	,	,	PUNCT
ejpam-5027	196	10	2)−	2)−	PROPN
ejpam-5027	196	11	gα−	gα−	SYM
ejpam-5027	196	12	cld	cld	PROPN
ejpam-5027	196	13	,	,	PUNCT
ejpam-5027	196	14	but	but	CCONJ
ejpam-5027	196	15	d1	d1	PROPN
ejpam-5027	196	16	∧d2	∧d2	VERB
ejpam-5027	196	17	is	be	AUX
ejpam-5027	196	18	not	not	PART
ejpam-5027	196	19	fuzzy	fuzzy	ADJ
ejpam-5027	196	20	(	(	PUNCT
ejpam-5027	196	21	1	1	NUM
ejpam-5027	196	22	,	,	PUNCT
ejpam-5027	196	23	2)−	2)−	PROPN
ejpam-5027	196	24	gα−	gα−	SYM
ejpam-5027	196	25	cld	cld	PROPN
ejpam-5027	196	26	.	.	PUNCT
ejpam-5027	196	27	corollary	corollary	ADJ
ejpam-5027	196	28	3	3	NUM
ejpam-5027	196	29	.	.	PUNCT
ejpam-5027	197	1	(	(	PUNCT
ejpam-5027	197	2	1	1	X
ejpam-5027	197	3	)	)	PUNCT
ejpam-5027	197	4	the	the	DET
ejpam-5027	197	5	finite	finite	ADJ
ejpam-5027	197	6	itersection	itersection	NOUN
ejpam-5027	197	7	of	of	ADP
ejpam-5027	197	8	fuzzy	fuzzy	ADJ
ejpam-5027	197	9	(	(	PUNCT
ejpam-5027	197	10	i	i	NOUN
ejpam-5027	197	11	,	,	PUNCT
ejpam-5027	197	12	j)−gφ−open	j)−gφ−open	ADJ
ejpam-5027	197	13	in	in	ADP
ejpam-5027	197	14	fbts	fbt	NOUN
ejpam-5027	197	15	(	(	PUNCT
ejpam-5027	197	16	x	x	NOUN
ejpam-5027	197	17	,	,	PUNCT
ejpam-5027	197	18	τ1	τ1	NOUN
ejpam-5027	197	19	,	,	PUNCT
ejpam-5027	197	20	τ2	τ2	NOUN
ejpam-5027	197	21	)	)	PUNCT
ejpam-5027	197	22	is	be	AUX
ejpam-5027	197	23	fuzzy	fuzzy	ADJ
ejpam-5027	197	24	(	(	PUNCT
ejpam-5027	197	25	i	i	NOUN
ejpam-5027	197	26	,	,	PUNCT
ejpam-5027	197	27	j)−	j)−	PROPN
ejpam-5027	197	28	gφ−open	gφ−open	PROPN
ejpam-5027	197	29	.	.	PUNCT
ejpam-5027	198	1	(	(	PUNCT
ejpam-5027	198	2	2	2	X
ejpam-5027	198	3	)	)	PUNCT
ejpam-5027	198	4	the	the	DET
ejpam-5027	198	5	finite	finite	PROPN
ejpam-5027	198	6	union	union	NOUN
ejpam-5027	198	7	of	of	ADP
ejpam-5027	198	8	fuzzy	fuzzy	ADJ
ejpam-5027	198	9	(	(	PUNCT
ejpam-5027	198	10	i	i	NOUN
ejpam-5027	198	11	,	,	PUNCT
ejpam-5027	198	12	j)−gφ−open	j)−gφ−open	ADJ
ejpam-5027	198	13	in	in	ADP
ejpam-5027	198	14	fbts	fbt	NOUN
ejpam-5027	198	15	(	(	PUNCT
ejpam-5027	198	16	x	x	NOUN
ejpam-5027	198	17	,	,	PUNCT
ejpam-5027	198	18	τ1	τ1	NOUN
ejpam-5027	198	19	,	,	PUNCT
ejpam-5027	198	20	τ2	τ2	NOUN
ejpam-5027	198	21	)	)	PUNCT
ejpam-5027	198	22	is	be	AUX
ejpam-5027	198	23	not	not	PART
ejpam-5027	198	24	fuzzy	fuzzy	ADJ
ejpam-5027	198	25	(	(	PUNCT
ejpam-5027	198	26	i	i	NOUN
ejpam-5027	198	27	,	,	PUNCT
ejpam-5027	198	28	j)−gφ−open	j)−gφ−open	PROPN
ejpam-5027	198	29	in	in	ADP
ejpam-5027	198	30	general	general	ADJ
ejpam-5027	198	31	.	.	PUNCT
ejpam-5027	199	1	ahlam	ahlam	PROPN
ejpam-5027	199	2	ahmed	ahmed	PROPN
ejpam-5027	199	3	alharbi	alharbi	PROPN
ejpam-5027	199	4	,	,	PUNCT
ejpam-5027	199	5	adem	adem	PROPN
ejpam-5027	199	6	kilicman	kilicman	PROPN
ejpam-5027	199	7	/	/	SYM
ejpam-5027	199	8	eur	eur	PROPN
ejpam-5027	199	9	.	.	PUNCT
ejpam-5027	200	1	j.	j.	PROPN
ejpam-5027	200	2	pure	pure	PROPN
ejpam-5027	200	3	appl	appl	PROPN
ejpam-5027	200	4	.	.	PROPN
ejpam-5027	200	5	math	math	PROPN
ejpam-5027	200	6	,	,	PUNCT
ejpam-5027	200	7	17	17	NUM
ejpam-5027	200	8	(	(	PUNCT
ejpam-5027	200	9	1	1	NUM
ejpam-5027	200	10	)	)	PUNCT
ejpam-5027	200	11	(	(	PUNCT
ejpam-5027	200	12	2024	2024	NUM
ejpam-5027	200	13	)	)	PUNCT
ejpam-5027	200	14	,	,	PUNCT
ejpam-5027	200	15	30	30	NUM
ejpam-5027	200	16	-	-	SYM
ejpam-5027	200	17	41	41	NUM
ejpam-5027	200	18	37	37	NUM
ejpam-5027	200	19	4	4	NUM
ejpam-5027	200	20	.	.	PUNCT
ejpam-5027	200	21	types	type	NOUN
ejpam-5027	200	22	of	of	ADP
ejpam-5027	200	23	fuzzy	fuzzy	ADJ
ejpam-5027	200	24	generalized	generalized	ADJ
ejpam-5027	200	25	compactness	compactness	NOUN
ejpam-5027	200	26	in	in	ADP
ejpam-5027	200	27	fuzzy	fuzzy	ADJ
ejpam-5027	200	28	bitopological	bitopological	ADJ
ejpam-5027	200	29	spaces	space	NOUN
ejpam-5027	200	30	this	this	DET
ejpam-5027	200	31	section	section	NOUN
ejpam-5027	200	32	introduces	introduce	VERB
ejpam-5027	200	33	the	the	DET
ejpam-5027	200	34	idea	idea	NOUN
ejpam-5027	200	35	of	of	ADP
ejpam-5027	200	36	generalized	generalized	ADJ
ejpam-5027	200	37	compactness	compactness	NOUN
ejpam-5027	200	38	in	in	ADP
ejpam-5027	200	39	fuzzy	fuzzy	ADJ
ejpam-5027	200	40	bitoplogy	bitoplogy	NOUN
ejpam-5027	200	41	and	and	CCONJ
ejpam-5027	200	42	characterize	characterize	VERB
ejpam-5027	200	43	it	it	PRON
ejpam-5027	200	44	in	in	ADP
ejpam-5027	200	45	terms	term	NOUN
ejpam-5027	200	46	of	of	ADP
ejpam-5027	200	47	important	important	ADJ
ejpam-5027	200	48	theorems	theorem	NOUN
ejpam-5027	200	49	and	and	CCONJ
ejpam-5027	200	50	some	some	DET
ejpam-5027	200	51	properties	property	NOUN
ejpam-5027	200	52	.	.	PUNCT
ejpam-5027	201	1	definition	definition	NOUN
ejpam-5027	201	2	12	12	NUM
ejpam-5027	201	3	.	.	PUNCT
ejpam-5027	202	1	the	the	DET
ejpam-5027	202	2	space	space	NOUN
ejpam-5027	202	3	x	x	X
ejpam-5027	202	4	of	of	ADP
ejpam-5027	202	5	fbts	fbt	NOUN
ejpam-5027	202	6	(	(	PUNCT
ejpam-5027	202	7	x	x	NOUN
ejpam-5027	202	8	,	,	PUNCT
ejpam-5027	202	9	δ1	δ1	NOUN
ejpam-5027	202	10	,	,	PUNCT
ejpam-5027	202	11	δ2	δ2	PROPN
ejpam-5027	202	12	)	)	PUNCT
ejpam-5027	202	13	is	be	AUX
ejpam-5027	202	14	named	name	VERB
ejpam-5027	202	15	fuzzy	fuzzy	ADJ
ejpam-5027	202	16	(	(	PUNCT
ejpam-5027	202	17	i	i	PROPN
ejpam-5027	202	18	,	,	PUNCT
ejpam-5027	202	19	j)−	j)−	PROPN
ejpam-5027	202	20	gφ−compact	gφ−compact	PROPN
ejpam-5027	202	21	when	when	SCONJ
ejpam-5027	202	22	all	all	DET
ejpam-5027	202	23	fuzzy	fuzzy	ADJ
ejpam-5027	202	24	(	(	PUNCT
ejpam-5027	202	25	i	i	PROPN
ejpam-5027	202	26	,	,	PUNCT
ejpam-5027	202	27	j)−	j)−	PROPN
ejpam-5027	202	28	gφ−open	gφ−open	NOUN
ejpam-5027	202	29	cover	cover	NOUN
ejpam-5027	202	30	for	for	ADP
ejpam-5027	202	31	x	x	PUNCT
ejpam-5027	202	32	has	have	VERB
ejpam-5027	202	33	a	a	DET
ejpam-5027	202	34	finite	finite	ADJ
ejpam-5027	202	35	subcover	subcover	PROPN
ejpam-5027	202	36	.	.	PUNCT
ejpam-5027	203	1	in	in	ADP
ejpam-5027	203	2	addition	addition	NOUN
ejpam-5027	203	3	,	,	PUNCT
ejpam-5027	203	4	a	a	DET
ejpam-5027	203	5	fuzzy	fuzzy	NOUN
ejpam-5027	203	6	subset	subset	VERB
ejpam-5027	203	7	a	a	PRON
ejpam-5027	203	8	of	of	ADP
ejpam-5027	203	9	fbts	fbt	NOUN
ejpam-5027	203	10	(	(	PUNCT
ejpam-5027	203	11	x	x	NOUN
ejpam-5027	203	12	,	,	PUNCT
ejpam-5027	203	13	δ1	δ1	NOUN
ejpam-5027	203	14	,	,	PUNCT
ejpam-5027	203	15	δ2	δ2	PROPN
ejpam-5027	203	16	)	)	PUNCT
ejpam-5027	203	17	is	be	AUX
ejpam-5027	203	18	called	call	VERB
ejpam-5027	203	19	fuzzy	fuzzy	ADJ
ejpam-5027	203	20	(	(	PUNCT
ejpam-5027	203	21	i	i	PROPN
ejpam-5027	203	22	,	,	PUNCT
ejpam-5027	203	23	j)−	j)−	PROPN
ejpam-5027	203	24	gφ−compact	gφ−compact	PROPN
ejpam-5027	203	25	subset	subset	VERB
ejpam-5027	203	26	of	of	ADP
ejpam-5027	203	27	x	x	PRON
ejpam-5027	203	28	when	when	SCONJ
ejpam-5027	203	29	all	all	DET
ejpam-5027	203	30	fuzzy	fuzzy	ADJ
ejpam-5027	203	31	(	(	PUNCT
ejpam-5027	203	32	i	i	PROPN
ejpam-5027	203	33	,	,	PUNCT
ejpam-5027	203	34	j)−	j)−	PROPN
ejpam-5027	203	35	gφ−open	gφ−open	NOUN
ejpam-5027	203	36	cover	cover	NOUN
ejpam-5027	203	37	for	for	ADP
ejpam-5027	203	38	a	a	PRON
ejpam-5027	203	39	has	have	AUX
ejpam-5027	203	40	a	a	DET
ejpam-5027	203	41	finite	finite	ADJ
ejpam-5027	203	42	subcover	subcover	PROPN
ejpam-5027	203	43	.	.	PUNCT
ejpam-5027	203	44	example	example	NOUN
ejpam-5027	204	1	7	7	NUM
ejpam-5027	204	2	.	.	PUNCT
ejpam-5027	204	3	suppose	suppose	VERB
ejpam-5027	204	4	a(a	a(a	PROPN
ejpam-5027	204	5	,	,	PUNCT
ejpam-5027	204	6	b	b	X
ejpam-5027	204	7	)	)	PUNCT
ejpam-5027	204	8	=	=	SYM
ejpam-5027	204	9	{	{	PUNCT
ejpam-5027	204	10	0.5	0.5	NUM
ejpam-5027	204	11	,	,	PUNCT
ejpam-5027	204	12	0.5	0.5	NUM
ejpam-5027	204	13	}	}	PUNCT
ejpam-5027	204	14	is	be	AUX
ejpam-5027	204	15	fuzzy	fuzzy	ADJ
ejpam-5027	204	16	subset	subset	NOUN
ejpam-5027	204	17	of	of	ADP
ejpam-5027	204	18	x	x	X
ejpam-5027	204	19	=	=	X
ejpam-5027	204	20	{	{	PUNCT
ejpam-5027	204	21	a	a	PRON
ejpam-5027	204	22	,	,	PUNCT
ejpam-5027	204	23	b	b	NOUN
ejpam-5027	204	24	}	}	PUNCT
ejpam-5027	204	25	,	,	PUNCT
ejpam-5027	204	26	and	and	CCONJ
ejpam-5027	204	27	the	the	DET
ejpam-5027	204	28	fuzzy	fuzzy	ADJ
ejpam-5027	204	29	topologies	topology	NOUN
ejpam-5027	204	30	δ1	δ1	NOUN
ejpam-5027	204	31	=	=	PUNCT
ejpam-5027	204	32	{	{	PUNCT
ejpam-5027	204	33	0	0	NUM
ejpam-5027	204	34	,	,	PUNCT
ejpam-5027	204	35	1	1	NUM
ejpam-5027	204	36	}	}	PUNCT
ejpam-5027	204	37	,	,	PUNCT
ejpam-5027	204	38	δ2	δ2	VERB
ejpam-5027	204	39	=	=	SYM
ejpam-5027	204	40	{	{	PUNCT
ejpam-5027	204	41	0	0	NUM
ejpam-5027	204	42	,	,	PUNCT
ejpam-5027	204	43	1	1	NUM
ejpam-5027	204	44	,	,	PUNCT
ejpam-5027	204	45	a	a	PRON
ejpam-5027	204	46	}	}	PUNCT
ejpam-5027	204	47	.	.	PUNCT
ejpam-5027	205	1	then	then	ADV
ejpam-5027	205	2	x	x	X
ejpam-5027	205	3	is	be	AUX
ejpam-5027	205	4	fuzzy	fuzzy	ADJ
ejpam-5027	205	5	(	(	PUNCT
ejpam-5027	205	6	1	1	NUM
ejpam-5027	205	7	,	,	PUNCT
ejpam-5027	205	8	2	2	NUM
ejpam-5027	205	9	)	)	PUNCT
ejpam-5027	205	10	−	−	PROPN
ejpam-5027	205	11	gφ−compact	gφ−compact	PROPN
ejpam-5027	205	12	space	space	NOUN
ejpam-5027	205	13	.	.	PUNCT
ejpam-5027	206	1	furthermore	furthermore	ADV
ejpam-5027	206	2	,	,	PUNCT
ejpam-5027	206	3	a	a	PRON
ejpam-5027	206	4	is	be	AUX
ejpam-5027	206	5	fuzzy	fuzzy	ADJ
ejpam-5027	206	6	(	(	PUNCT
ejpam-5027	206	7	1	1	NUM
ejpam-5027	206	8	,	,	PUNCT
ejpam-5027	206	9	2)−	2)−	NUM
ejpam-5027	206	10	gφ−compact	gφ−compact	PROPN
ejpam-5027	206	11	subset	subset	VERB
ejpam-5027	206	12	of	of	ADP
ejpam-5027	206	13	x.	x.	PROPN
ejpam-5027	206	14	corollary	corollary	PROPN
ejpam-5027	206	15	4	4	NUM
ejpam-5027	206	16	.	.	PUNCT
ejpam-5027	207	1	in	in	ADP
ejpam-5027	207	2	any	any	DET
ejpam-5027	207	3	fbts	fbt	NOUN
ejpam-5027	207	4	(	(	PUNCT
ejpam-5027	207	5	x	x	NOUN
ejpam-5027	207	6	,	,	PUNCT
ejpam-5027	207	7	δ1	δ1	NOUN
ejpam-5027	207	8	,	,	PUNCT
ejpam-5027	207	9	δ2	δ2	ADJ
ejpam-5027	207	10	)	)	PUNCT
ejpam-5027	207	11	if	if	SCONJ
ejpam-5027	207	12	δi	δi	PROPN
ejpam-5027	207	13	is	be	AUX
ejpam-5027	207	14	a	a	DET
ejpam-5027	207	15	fuzzy	fuzzy	ADJ
ejpam-5027	207	16	indiscrete	indiscrete	ADJ
ejpam-5027	207	17	topology	topology	NOUN
ejpam-5027	207	18	,	,	PUNCT
ejpam-5027	207	19	then	then	ADV
ejpam-5027	207	20	(	(	PUNCT
ejpam-5027	207	21	x	x	NOUN
ejpam-5027	207	22	,	,	PUNCT
ejpam-5027	207	23	δ1	δ1	NOUN
ejpam-5027	207	24	,	,	PUNCT
ejpam-5027	207	25	δ2	δ2	PROPN
ejpam-5027	207	26	)	)	PUNCT
ejpam-5027	207	27	is	be	AUX
ejpam-5027	207	28	fuzzy	fuzzy	ADJ
ejpam-5027	207	29	(	(	PUNCT
ejpam-5027	207	30	i	i	PROPN
ejpam-5027	207	31	,	,	PUNCT
ejpam-5027	207	32	j)−	j)−	PROPN
ejpam-5027	207	33	gφ−compact	gφ−compact	PROPN
ejpam-5027	207	34	,	,	PUNCT
ejpam-5027	207	35	and	and	CCONJ
ejpam-5027	207	36	any	any	DET
ejpam-5027	207	37	subset	subset	NOUN
ejpam-5027	207	38	of	of	ADP
ejpam-5027	207	39	it	it	PRON
ejpam-5027	207	40	is	be	AUX
ejpam-5027	207	41	fuzzy	fuzzy	ADJ
ejpam-5027	207	42	(	(	PUNCT
ejpam-5027	207	43	i	i	NOUN
ejpam-5027	207	44	,	,	PUNCT
ejpam-5027	207	45	j)−	j)−	PROPN
ejpam-5027	207	46	gφ−compact	gφ−compact	PROPN
ejpam-5027	207	47	.	.	PUNCT
ejpam-5027	208	1	theorem	theorem	VERB
ejpam-5027	208	2	6	6	NUM
ejpam-5027	208	3	.	.	PUNCT
ejpam-5027	209	1	all	all	PRON
ejpam-5027	209	2	fuzzy	fuzzy	ADJ
ejpam-5027	209	3	(	(	PUNCT
ejpam-5027	209	4	i	i	NOUN
ejpam-5027	209	5	,	,	PUNCT
ejpam-5027	209	6	j)−	j)−	PROPN
ejpam-5027	209	7	gφ−cld	gφ−cld	PROPN
ejpam-5027	209	8	subset	subset	VERB
ejpam-5027	209	9	of	of	ADP
ejpam-5027	209	10	fuzzy	fuzzy	ADJ
ejpam-5027	209	11	(	(	PUNCT
ejpam-5027	209	12	i	i	PROPN
ejpam-5027	209	13	,	,	PUNCT
ejpam-5027	209	14	j)−	j)−	PROPN
ejpam-5027	209	15	gφ−compact	gφ−compact	PROPN
ejpam-5027	209	16	space	space	NOUN
ejpam-5027	209	17	is	be	AUX
ejpam-5027	209	18	(	(	PUNCT
ejpam-5027	209	19	i	i	PROPN
ejpam-5027	209	20	,	,	PUNCT
ejpam-5027	209	21	j)−	j)−	PROPN
ejpam-5027	209	22	gφ−compact	gφ−compact	PROPN
ejpam-5027	209	23	.	.	PUNCT
ejpam-5027	210	1	proof	proof	NOUN
ejpam-5027	210	2	.	.	PUNCT
ejpam-5027	211	1	assume	assume	VERB
ejpam-5027	211	2	e	e	NOUN
ejpam-5027	211	3	is	be	AUX
ejpam-5027	211	4	fuzzy	fuzzy	ADJ
ejpam-5027	211	5	(	(	PUNCT
ejpam-5027	211	6	i	i	NOUN
ejpam-5027	211	7	,	,	PUNCT
ejpam-5027	211	8	j)−gφ−cld	j)−gφ−cld	NOUN
ejpam-5027	211	9	,	,	PUNCT
ejpam-5027	211	10	and	and	CCONJ
ejpam-5027	211	11	{	{	PUNCT
ejpam-5027	211	12	gi	gi	X
ejpam-5027	211	13	:	:	PUNCT
ejpam-5027	211	14	i	i	PRON
ejpam-5027	211	15	∈	∈	VERB
ejpam-5027	212	1	i	i	PRON
ejpam-5027	212	2	}	}	PUNCT
ejpam-5027	212	3	is	be	AUX
ejpam-5027	212	4	fuzzy	fuzzy	ADJ
ejpam-5027	212	5	(	(	PUNCT
ejpam-5027	212	6	i	i	NOUN
ejpam-5027	212	7	,	,	PUNCT
ejpam-5027	212	8	j)−gφ−open	j)−gφ−open	ADJ
ejpam-5027	212	9	cover	cover	NOUN
ejpam-5027	212	10	for	for	ADP
ejpam-5027	212	11	e.	e.	PROPN
ejpam-5027	212	12	then	then	ADV
ejpam-5027	212	13	,	,	PUNCT
ejpam-5027	212	14	ec	ec	PROPN
ejpam-5027	212	15	is	be	AUX
ejpam-5027	212	16	fuzzy	fuzzy	ADJ
ejpam-5027	212	17	(	(	PUNCT
ejpam-5027	212	18	i	i	NOUN
ejpam-5027	212	19	,	,	PUNCT
ejpam-5027	212	20	j)−	j)−	PROPN
ejpam-5027	212	21	gφ−open	gφ−open	PROPN
ejpam-5027	212	22	,	,	PUNCT
ejpam-5027	212	23	and	and	CCONJ
ejpam-5027	212	24	hence	hence	ADV
ejpam-5027	212	25	{	{	PUNCT
ejpam-5027	212	26	gi	gi	INTJ
ejpam-5027	212	27	,	,	PUNCT
ejpam-5027	212	28	e	e	PROPN
ejpam-5027	212	29	c	c	NOUN
ejpam-5027	212	30	:	:	PUNCT
ejpam-5027	213	1	i	i	PRON
ejpam-5027	213	2	∈	∈	PROPN
ejpam-5027	213	3	i	i	PRON
ejpam-5027	213	4	}	}	PUNCT
ejpam-5027	213	5	is	be	AUX
ejpam-5027	213	6	(	(	PUNCT
ejpam-5027	213	7	i	i	PROPN
ejpam-5027	213	8	,	,	PUNCT
ejpam-5027	213	9	j)−	j)−	PROPN
ejpam-5027	213	10	gφ−open	gφ−open	NOUN
ejpam-5027	213	11	cover	cover	NOUN
ejpam-5027	213	12	for	for	ADP
ejpam-5027	213	13	x.	x.	PROPN
ejpam-5027	213	14	then	then	ADV
ejpam-5027	213	15	∃	∃	PROPN
ejpam-5027	213	16	finite	finite	PROPN
ejpam-5027	213	17	subcover	subcover	PROPN
ejpam-5027	213	18	to	to	ADP
ejpam-5027	213	19	x	x	PRON
ejpam-5027	213	20	,	,	PUNCT
ejpam-5027	213	21	which	which	PRON
ejpam-5027	213	22	is	be	AUX
ejpam-5027	213	23	{	{	PUNCT
ejpam-5027	213	24	gij	gij	INTJ
ejpam-5027	213	25	,	,	PUNCT
ejpam-5027	213	26	e	e	PROPN
ejpam-5027	213	27	c	c	NOUN
ejpam-5027	213	28	:	:	PUNCT
ejpam-5027	213	29	j	j	PROPN
ejpam-5027	213	30	=	=	SYM
ejpam-5027	213	31	1	1	NUM
ejpam-5027	213	32	,	,	PUNCT
ejpam-5027	213	33	2	2	NUM
ejpam-5027	213	34	,	,	PUNCT
ejpam-5027	213	35	...	...	PUNCT
ejpam-5027	213	36	,	,	PUNCT
ejpam-5027	213	37	n	n	CCONJ
ejpam-5027	213	38	}	}	PUNCT
ejpam-5027	213	39	,	,	PUNCT
ejpam-5027	213	40	and	and	CCONJ
ejpam-5027	213	41	hence	hence	ADV
ejpam-5027	213	42	∃	∃	PROPN
ejpam-5027	213	43	finite	finite	PROPN
ejpam-5027	213	44	subcover	subcover	PROPN
ejpam-5027	213	45	of	of	ADP
ejpam-5027	213	46	e	e	PROPN
ejpam-5027	213	47	,	,	PUNCT
ejpam-5027	213	48	which	which	PRON
ejpam-5027	213	49	is	be	AUX
ejpam-5027	213	50	{	{	PUNCT
ejpam-5027	213	51	gij	gij	NOUN
ejpam-5027	213	52	:	:	PUNCT
ejpam-5027	214	1	i	i	PRON
ejpam-5027	214	2	∈	∈	VERB
ejpam-5027	215	1	i	i	PRON
ejpam-5027	215	2	,	,	PUNCT
ejpam-5027	215	3	j	j	PROPN
ejpam-5027	215	4	=	=	SYM
ejpam-5027	215	5	1	1	NUM
ejpam-5027	215	6	,	,	PUNCT
ejpam-5027	215	7	2	2	NUM
ejpam-5027	215	8	,	,	PUNCT
ejpam-5027	215	9	...	...	PUNCT
ejpam-5027	215	10	,	,	PUNCT
ejpam-5027	215	11	n	n	CCONJ
ejpam-5027	215	12	}	}	PUNCT
ejpam-5027	215	13	.	.	PUNCT
ejpam-5027	216	1	therefore	therefore	ADV
ejpam-5027	216	2	,	,	PUNCT
ejpam-5027	216	3	e	e	NOUN
ejpam-5027	216	4	is	be	AUX
ejpam-5027	216	5	fuzzy	fuzzy	ADJ
ejpam-5027	216	6	(	(	PUNCT
ejpam-5027	216	7	i	i	NOUN
ejpam-5027	216	8	,	,	PUNCT
ejpam-5027	216	9	j)−	j)−	PROPN
ejpam-5027	216	10	gφ−compact	gφ−compact	PROPN
ejpam-5027	216	11	.	.	PUNCT
ejpam-5027	217	1	corollary	corollary	ADJ
ejpam-5027	217	2	5	5	NUM
ejpam-5027	217	3	.	.	PUNCT
ejpam-5027	218	1	all	all	DET
ejpam-5027	218	2	fuzzy	fuzzy	ADJ
ejpam-5027	218	3	δj−cld	δj−cld	NOUN
ejpam-5027	218	4	subset	subset	NOUN
ejpam-5027	218	5	of	of	ADP
ejpam-5027	218	6	fuzzy	fuzzy	ADJ
ejpam-5027	218	7	(	(	PUNCT
ejpam-5027	218	8	i	i	PROPN
ejpam-5027	218	9	,	,	PUNCT
ejpam-5027	218	10	j)−	j)−	PROPN
ejpam-5027	218	11	gφ−compact	gφ−compact	PROPN
ejpam-5027	218	12	space	space	NOUN
ejpam-5027	218	13	is	be	AUX
ejpam-5027	218	14	fuzzy	fuzzy	ADJ
ejpam-5027	218	15	(	(	PUNCT
ejpam-5027	218	16	i	i	PROPN
ejpam-5027	218	17	,	,	PUNCT
ejpam-5027	218	18	j)−	j)−	PROPN
ejpam-5027	218	19	gφ−compact	gφ−compact	PROPN
ejpam-5027	218	20	too	too	ADV
ejpam-5027	218	21	.	.	PUNCT
ejpam-5027	219	1	theorem	theorem	VERB
ejpam-5027	219	2	7	7	NUM
ejpam-5027	219	3	.	.	PUNCT
ejpam-5027	220	1	if	if	SCONJ
ejpam-5027	220	2	(	(	PUNCT
ejpam-5027	220	3	x	x	NOUN
ejpam-5027	220	4	,	,	PUNCT
ejpam-5027	220	5	δ1	δ1	NOUN
ejpam-5027	220	6	,	,	PUNCT
ejpam-5027	220	7	δ2	δ2	PROPN
ejpam-5027	220	8	)	)	PUNCT
ejpam-5027	220	9	is	be	AUX
ejpam-5027	220	10	fuzzy	fuzzy	ADJ
ejpam-5027	220	11	(	(	PUNCT
ejpam-5027	220	12	i	i	PROPN
ejpam-5027	220	13	,	,	PUNCT
ejpam-5027	220	14	j)−	j)−	PROPN
ejpam-5027	220	15	gφ−compact	gφ−compact	PROPN
ejpam-5027	220	16	space	space	NOUN
ejpam-5027	220	17	,	,	PUNCT
ejpam-5027	220	18	thus	thus	ADV
ejpam-5027	220	19	it	it	PRON
ejpam-5027	220	20	is	be	AUX
ejpam-5027	220	21	fuzzy	fuzzy	ADJ
ejpam-5027	220	22	δj−compact	δj−compact	NOUN
ejpam-5027	220	23	space	space	NOUN
ejpam-5027	220	24	.	.	PUNCT
ejpam-5027	221	1	proof	proof	NOUN
ejpam-5027	221	2	.	.	PUNCT
ejpam-5027	222	1	suppose	suppose	VERB
ejpam-5027	222	2	{	{	PUNCT
ejpam-5027	222	3	gj	gj	NOUN
ejpam-5027	222	4	:	:	PUNCT
ejpam-5027	222	5	j	j	PROPN
ejpam-5027	222	6	∈	∈	PROPN
ejpam-5027	223	1	i	i	PRON
ejpam-5027	223	2	}	}	PUNCT
ejpam-5027	223	3	is	be	AUX
ejpam-5027	223	4	an	an	DET
ejpam-5027	223	5	open	open	ADJ
ejpam-5027	223	6	cover	cover	NOUN
ejpam-5027	223	7	of	of	ADP
ejpam-5027	223	8	(	(	PUNCT
ejpam-5027	223	9	x	x	NOUN
ejpam-5027	223	10	,	,	PUNCT
ejpam-5027	223	11	δj	δj	ADJ
ejpam-5027	223	12	)	)	PUNCT
ejpam-5027	223	13	.	.	PUNCT
ejpam-5027	224	1	then	then	ADV
ejpam-5027	224	2	from	from	ADP
ejpam-5027	224	3	figure(1	figure(1	ADJ
ejpam-5027	224	4	)	)	PUNCT
ejpam-5027	224	5	and	and	CCONJ
ejpam-5027	224	6	theorm	theorm	NOUN
ejpam-5027	224	7	2	2	NUM
ejpam-5027	224	8	,	,	PUNCT
ejpam-5027	224	9	{	{	PUNCT
ejpam-5027	224	10	gi	gi	X
ejpam-5027	224	11	:	:	PUNCT
ejpam-5027	224	12	i	i	PRON
ejpam-5027	224	13	∈	∈	VERB
ejpam-5027	224	14	i	i	PRON
ejpam-5027	224	15	}	}	PUNCT
ejpam-5027	224	16	is	be	AUX
ejpam-5027	224	17	consider	consider	VERB
ejpam-5027	224	18	fuzzy	fuzzy	ADJ
ejpam-5027	224	19	(	(	PUNCT
ejpam-5027	224	20	i	i	PROPN
ejpam-5027	224	21	,	,	PUNCT
ejpam-5027	224	22	j)−	j)−	PROPN
ejpam-5027	224	23	gφ−open	gφ−open	PROPN
ejpam-5027	224	24	cover	cover	NOUN
ejpam-5027	224	25	to	to	ADP
ejpam-5027	224	26	x	x	PRON
ejpam-5027	224	27	,	,	PUNCT
ejpam-5027	224	28	after	after	ADP
ejpam-5027	224	29	that	that	PRON
ejpam-5027	224	30	{	{	PUNCT
ejpam-5027	224	31	gi	gi	INTJ
ejpam-5027	224	32	}	}	PUNCT
ejpam-5027	224	33	has	have	VERB
ejpam-5027	224	34	finite	finite	PROPN
ejpam-5027	224	35	subcover	subcover	PROPN
ejpam-5027	224	36	.	.	PUNCT
ejpam-5027	225	1	therefore	therefore	ADV
ejpam-5027	225	2	,	,	PUNCT
ejpam-5027	225	3	x	x	X
ejpam-5027	225	4	is	be	AUX
ejpam-5027	225	5	fuzzy	fuzzy	ADJ
ejpam-5027	225	6	δj−compact	δj−compact	NOUN
ejpam-5027	225	7	space	space	NOUN
ejpam-5027	225	8	.	.	PUNCT
ejpam-5027	226	1	theorem	theorem	VERB
ejpam-5027	226	2	8	8	NUM
ejpam-5027	226	3	.	.	PUNCT
ejpam-5027	227	1	if	if	SCONJ
ejpam-5027	227	2	(	(	PUNCT
ejpam-5027	227	3	x	x	NOUN
ejpam-5027	227	4	,	,	PUNCT
ejpam-5027	227	5	δ1	δ1	NOUN
ejpam-5027	227	6	,	,	PUNCT
ejpam-5027	227	7	δ2	δ2	PROPN
ejpam-5027	227	8	)	)	PUNCT
ejpam-5027	227	9	is	be	AUX
ejpam-5027	227	10	fuzzy	fuzzy	ADJ
ejpam-5027	227	11	δi−cld	δi−cld	NOUN
ejpam-5027	227	12	and	and	CCONJ
ejpam-5027	227	13	δj−compact	δj−compact	VERB
ejpam-5027	227	14	space	space	NOUN
ejpam-5027	227	15	.	.	PUNCT
ejpam-5027	228	1	after	after	ADP
ejpam-5027	228	2	that	that	PRON
ejpam-5027	228	3	,	,	PUNCT
ejpam-5027	228	4	it	it	PRON
ejpam-5027	228	5	is	be	AUX
ejpam-5027	228	6	fuzzy	fuzzy	ADJ
ejpam-5027	228	7	(	(	PUNCT
ejpam-5027	228	8	i	i	NOUN
ejpam-5027	228	9	,	,	PUNCT
ejpam-5027	228	10	j)−	j)−	PROPN
ejpam-5027	228	11	gφ−compact	gφ−compact	PROPN
ejpam-5027	228	12	.	.	PUNCT
ejpam-5027	229	1	proof	proof	NOUN
ejpam-5027	229	2	.	.	PUNCT
ejpam-5027	230	1	assume	assume	VERB
ejpam-5027	230	2	{	{	PUNCT
ejpam-5027	230	3	gi	gi	X
ejpam-5027	230	4	:	:	PUNCT
ejpam-5027	230	5	i	i	PRON
ejpam-5027	230	6	∈	∈	VERB
ejpam-5027	231	1	i	i	PRON
ejpam-5027	231	2	}	}	PUNCT
ejpam-5027	231	3	is	be	AUX
ejpam-5027	231	4	fuzzy	fuzzy	ADJ
ejpam-5027	231	5	(	(	PUNCT
ejpam-5027	231	6	i	i	PROPN
ejpam-5027	231	7	,	,	PUNCT
ejpam-5027	231	8	j	j	PROPN
ejpam-5027	231	9	)	)	PUNCT
ejpam-5027	232	1	−	−	PROPN
ejpam-5027	232	2	gφ−open	gφ−open	NOUN
ejpam-5027	232	3	cover	cover	NOUN
ejpam-5027	232	4	for	for	ADP
ejpam-5027	232	5	x.	x.	NOUN
ejpam-5027	232	6	as	as	SCONJ
ejpam-5027	232	7	x	x	PROPN
ejpam-5027	232	8	is	be	AUX
ejpam-5027	232	9	δi−cld	δi−cld	NOUN
ejpam-5027	232	10	,	,	PUNCT
ejpam-5027	232	11	then	then	ADV
ejpam-5027	232	12	by	by	ADP
ejpam-5027	232	13	theorem	theorem	NOUN
ejpam-5027	232	14	3	3	NUM
ejpam-5027	232	15	{	{	PUNCT
ejpam-5027	232	16	gi	gi	X
ejpam-5027	232	17	:	:	PUNCT
ejpam-5027	232	18	i	i	PRON
ejpam-5027	232	19	∈	∈	VERB
ejpam-5027	233	1	i	i	PRON
ejpam-5027	233	2	}	}	PUNCT
ejpam-5027	233	3	is	be	AUX
ejpam-5027	233	4	fuzzy	fuzzy	ADJ
ejpam-5027	233	5	δj−open	δj−open	NOUN
ejpam-5027	233	6	cover	cover	NOUN
ejpam-5027	233	7	to	to	ADP
ejpam-5027	233	8	x	x	PRON
ejpam-5027	233	9	,	,	PUNCT
ejpam-5027	233	10	but	but	CCONJ
ejpam-5027	233	11	x	x	PRON
ejpam-5027	233	12	is	be	AUX
ejpam-5027	233	13	δj−compact	δj−compact	ADJ
ejpam-5027	233	14	,	,	PUNCT
ejpam-5027	233	15	after	after	ADP
ejpam-5027	233	16	that	that	DET
ejpam-5027	233	17	∃	∃	PROPN
ejpam-5027	233	18	finite	finite	PROPN
ejpam-5027	233	19	subcover	subcover	PROPN
ejpam-5027	233	20	.	.	PUNCT
ejpam-5027	234	1	therefore	therefore	ADV
ejpam-5027	234	2	x	x	X
ejpam-5027	234	3	is	be	AUX
ejpam-5027	234	4	fuzzy	fuzzy	ADJ
ejpam-5027	234	5	(	(	PUNCT
ejpam-5027	234	6	i	i	PROPN
ejpam-5027	234	7	,	,	PUNCT
ejpam-5027	234	8	j)−	j)−	PROPN
ejpam-5027	234	9	gφ−compact	gφ−compact	PROPN
ejpam-5027	234	10	space	space	NOUN
ejpam-5027	234	11	.	.	PUNCT
ejpam-5027	235	1	theorem	theorem	VERB
ejpam-5027	235	2	9	9	NUM
ejpam-5027	235	3	.	.	PUNCT
ejpam-5027	236	1	in	in	ADP
ejpam-5027	236	2	fbts	fbt	NOUN
ejpam-5027	236	3	(	(	PUNCT
ejpam-5027	236	4	x	x	NOUN
ejpam-5027	236	5	,	,	PUNCT
ejpam-5027	236	6	δ1	δ1	NOUN
ejpam-5027	236	7	,	,	PUNCT
ejpam-5027	236	8	δ2	δ2	PROPN
ejpam-5027	236	9	)	)	PUNCT
ejpam-5027	236	10	.	.	PUNCT
ejpam-5027	237	1	the	the	DET
ejpam-5027	237	2	next	next	ADJ
ejpam-5027	237	3	explanations	explanation	NOUN
ejpam-5027	237	4	are	be	AUX
ejpam-5027	237	5	true	true	ADJ
ejpam-5027	237	6	:	:	PUNCT
ejpam-5027	237	7	(	(	PUNCT
ejpam-5027	237	8	1	1	X
ejpam-5027	237	9	)	)	PUNCT
ejpam-5027	237	10	∀	∀	NOUN
ejpam-5027	237	11	fuzzy	fuzzy	ADJ
ejpam-5027	237	12	(	(	PUNCT
ejpam-5027	237	13	i	i	PRON
ejpam-5027	237	14	,	,	PUNCT
ejpam-5027	237	15	j)−gβ−compact	j)−gβ−compact	PROPN
ejpam-5027	237	16	is	be	AUX
ejpam-5027	237	17	fuzzy	fuzzy	ADJ
ejpam-5027	237	18	(	(	PUNCT
ejpam-5027	237	19	i	i	NOUN
ejpam-5027	237	20	,	,	PUNCT
ejpam-5027	237	21	j)−gp−compact	j)−gp−compact	PROPN
ejpam-5027	237	22	and	and	CCONJ
ejpam-5027	237	23	fuzzy	fuzzy	ADJ
ejpam-5027	237	24	(	(	PUNCT
ejpam-5027	237	25	i	i	NOUN
ejpam-5027	237	26	,	,	PUNCT
ejpam-5027	237	27	j)−gs−compact	j)−gs−compact	PROPN
ejpam-5027	237	28	.	.	PUNCT
ejpam-5027	238	1	ahlam	ahlam	PROPN
ejpam-5027	238	2	ahmed	ahmed	PROPN
ejpam-5027	238	3	alharbi	alharbi	PROPN
ejpam-5027	238	4	,	,	PUNCT
ejpam-5027	238	5	adem	adem	PROPN
ejpam-5027	238	6	kilicman	kilicman	PROPN
ejpam-5027	238	7	/	/	SYM
ejpam-5027	238	8	eur	eur	PROPN
ejpam-5027	238	9	.	.	PUNCT
ejpam-5027	239	1	j.	j.	PROPN
ejpam-5027	239	2	pure	pure	PROPN
ejpam-5027	239	3	appl	appl	PROPN
ejpam-5027	239	4	.	.	PROPN
ejpam-5027	239	5	math	math	PROPN
ejpam-5027	239	6	,	,	PUNCT
ejpam-5027	239	7	17	17	NUM
ejpam-5027	239	8	(	(	PUNCT
ejpam-5027	239	9	1	1	NUM
ejpam-5027	239	10	)	)	PUNCT
ejpam-5027	239	11	(	(	PUNCT
ejpam-5027	239	12	2024	2024	NUM
ejpam-5027	239	13	)	)	PUNCT
ejpam-5027	239	14	,	,	PUNCT
ejpam-5027	239	15	30	30	NUM
ejpam-5027	239	16	-	-	SYM
ejpam-5027	239	17	41	41	NUM
ejpam-5027	239	18	38	38	NUM
ejpam-5027	239	19	(	(	PUNCT
ejpam-5027	239	20	2	2	NUM
ejpam-5027	239	21	)	)	PUNCT
ejpam-5027	239	22	∀	∀	NOUN
ejpam-5027	239	23	fuzzy	fuzzy	ADJ
ejpam-5027	239	24	(	(	PUNCT
ejpam-5027	239	25	i	i	NOUN
ejpam-5027	239	26	,	,	PUNCT
ejpam-5027	239	27	j)−gp−compact	j)−gp−compact	PROPN
ejpam-5027	239	28	or	or	CCONJ
ejpam-5027	239	29	fuzzy	fuzzy	ADJ
ejpam-5027	239	30	(	(	PUNCT
ejpam-5027	239	31	i	i	NOUN
ejpam-5027	239	32	,	,	PUNCT
ejpam-5027	239	33	j)−gs−compact	j)−gs−compact	PROPN
ejpam-5027	239	34	is	be	AUX
ejpam-5027	239	35	fuzzy	fuzzy	ADJ
ejpam-5027	239	36	(	(	PUNCT
ejpam-5027	239	37	i	i	NOUN
ejpam-5027	239	38	,	,	PUNCT
ejpam-5027	239	39	j)−gα−compact	j)−gα−compact	PROPN
ejpam-5027	239	40	.	.	PUNCT
ejpam-5027	240	1	(	(	PUNCT
ejpam-5027	240	2	3	3	X
ejpam-5027	240	3	)	)	PUNCT
ejpam-5027	240	4	∀	∀	NOUN
ejpam-5027	240	5	fuzzy	fuzzy	ADJ
ejpam-5027	240	6	(	(	PUNCT
ejpam-5027	240	7	i	i	NOUN
ejpam-5027	240	8	,	,	PUNCT
ejpam-5027	240	9	j)−	j)−	PROPN
ejpam-5027	240	10	gα−	gα−	PUNCT
ejpam-5027	240	11	compact	compact	ADJ
ejpam-5027	240	12	is	be	AUX
ejpam-5027	240	13	fuzzy	fuzzy	ADJ
ejpam-5027	240	14	δj−compact	δj−compact	NOUN
ejpam-5027	240	15	.	.	PUNCT
ejpam-5027	241	1	proof	proof	NOUN
ejpam-5027	241	2	.	.	PUNCT
ejpam-5027	242	1	obviously	obviously	ADV
ejpam-5027	242	2	from	from	ADP
ejpam-5027	242	3	definition	definition	NOUN
ejpam-5027	242	4	12	12	NUM
ejpam-5027	242	5	and	and	CCONJ
ejpam-5027	242	6	the	the	DET
ejpam-5027	242	7	relations	relation	NOUN
ejpam-5027	242	8	between	between	ADP
ejpam-5027	242	9	types	type	NOUN
ejpam-5027	242	10	of	of	ADP
ejpam-5027	242	11	(	(	PUNCT
ejpam-5027	242	12	i	i	PROPN
ejpam-5027	242	13	,	,	PUNCT
ejpam-5027	242	14	j)−gφ−cld	j)−gφ−cld	PROPN
ejpam-5027	242	15	sets	set	VERB
ejpam-5027	242	16	in	in	ADP
ejpam-5027	242	17	theorem	theorem	ADJ
ejpam-5027	242	18	2	2	NUM
ejpam-5027	242	19	and	and	CCONJ
ejpam-5027	242	20	figure	figure	NOUN
ejpam-5027	242	21	(	(	PUNCT
ejpam-5027	242	22	1	1	NUM
ejpam-5027	242	23	)	)	PUNCT
ejpam-5027	242	24	.	.	PUNCT
ejpam-5027	243	1	the	the	DET
ejpam-5027	243	2	diagram	diagram	NOUN
ejpam-5027	243	3	below	below	ADV
ejpam-5027	243	4	explains	explain	VERB
ejpam-5027	243	5	the	the	DET
ejpam-5027	243	6	relationships	relationship	NOUN
ejpam-5027	243	7	between	between	ADP
ejpam-5027	243	8	all	all	DET
ejpam-5027	243	9	types	type	NOUN
ejpam-5027	243	10	of	of	ADP
ejpam-5027	243	11	fuzzy	fuzzy	ADJ
ejpam-5027	243	12	(	(	PUNCT
ejpam-5027	243	13	i	i	NOUN
ejpam-5027	243	14	,	,	PUNCT
ejpam-5027	243	15	j)−gφ−compact	j)−gφ−compact	PROPN
ejpam-5027	243	16	:	:	PUNCT
ejpam-5027	243	17	figure	figure	NOUN
ejpam-5027	243	18	2	2	NUM
ejpam-5027	243	19	:	:	PUNCT
ejpam-5027	243	20	explain	explain	VERB
ejpam-5027	243	21	the	the	DET
ejpam-5027	243	22	relations	relation	NOUN
ejpam-5027	243	23	between	between	ADP
ejpam-5027	243	24	(	(	PUNCT
ejpam-5027	243	25	i	i	PROPN
ejpam-5027	243	26	,	,	PUNCT
ejpam-5027	243	27	j)−	j)−	PROPN
ejpam-5027	243	28	gφ−compact	gφ−compact	PROPN
ejpam-5027	243	29	.	.	PUNCT
ejpam-5027	244	1	remark	remark	PROPN
ejpam-5027	244	2	4	4	NUM
ejpam-5027	244	3	.	.	PUNCT
ejpam-5027	245	1	in	in	ADP
ejpam-5027	245	2	general	general	ADJ
ejpam-5027	245	3	,	,	PUNCT
ejpam-5027	245	4	the	the	DET
ejpam-5027	245	5	opposite	opposite	NOUN
ejpam-5027	245	6	of	of	ADP
ejpam-5027	245	7	the	the	DET
ejpam-5027	245	8	aforementioned	aforementioned	ADJ
ejpam-5027	245	9	graph	graph	NOUN
ejpam-5027	245	10	is	be	AUX
ejpam-5027	245	11	not	not	PART
ejpam-5027	245	12	true	true	ADJ
ejpam-5027	245	13	,	,	PUNCT
ejpam-5027	245	14	and	and	CCONJ
ejpam-5027	245	15	this	this	PRON
ejpam-5027	245	16	is	be	AUX
ejpam-5027	245	17	clear	clear	ADJ
ejpam-5027	245	18	from	from	ADP
ejpam-5027	245	19	definition	definition	NOUN
ejpam-5027	245	20	12	12	NUM
ejpam-5027	245	21	and	and	CCONJ
ejpam-5027	245	22	the	the	DET
ejpam-5027	245	23	relations	relation	NOUN
ejpam-5027	245	24	between	between	ADP
ejpam-5027	245	25	(	(	PUNCT
ejpam-5027	245	26	i	i	PROPN
ejpam-5027	245	27	,	,	PUNCT
ejpam-5027	245	28	j	j	PROPN
ejpam-5027	245	29	)	)	PUNCT
ejpam-5027	245	30	−	−	PROPN
ejpam-5027	245	31	gφ−cld	gφ−cld	PROPN
ejpam-5027	245	32	sets	set	VERB
ejpam-5027	245	33	in	in	ADP
ejpam-5027	245	34	theory	theory	NOUN
ejpam-5027	245	35	2	2	NUM
ejpam-5027	245	36	and	and	CCONJ
ejpam-5027	245	37	examples	example	NOUN
ejpam-5027	245	38	2	2	NUM
ejpam-5027	245	39	through	through	ADP
ejpam-5027	245	40	1	1	NUM
ejpam-5027	245	41	.	.	PUNCT
ejpam-5027	246	1	in	in	ADP
ejpam-5027	246	2	addition	addition	NOUN
ejpam-5027	246	3	,	,	PUNCT
ejpam-5027	246	4	we	we	PRON
ejpam-5027	246	5	can	can	AUX
ejpam-5027	246	6	see	see	VERB
ejpam-5027	246	7	that	that	SCONJ
ejpam-5027	246	8	the	the	DET
ejpam-5027	246	9	concepts	concept	NOUN
ejpam-5027	246	10	of	of	ADP
ejpam-5027	246	11	the	the	DET
ejpam-5027	246	12	fuzzy	fuzzy	ADJ
ejpam-5027	246	13	(	(	PUNCT
ejpam-5027	246	14	i	i	PROPN
ejpam-5027	246	15	,	,	PUNCT
ejpam-5027	246	16	j	j	PROPN
ejpam-5027	246	17	)	)	PUNCT
ejpam-5027	246	18	−	−	ADP
ejpam-5027	246	19	gp−compact	gp−compact	NOUN
ejpam-5027	246	20	space	space	NOUN
ejpam-5027	246	21	and	and	CCONJ
ejpam-5027	246	22	(	(	PUNCT
ejpam-5027	246	23	i	i	PROPN
ejpam-5027	246	24	,	,	PUNCT
ejpam-5027	246	25	j)−	j)−	PROPN
ejpam-5027	246	26	gs−compact	gs−compact	PROPN
ejpam-5027	246	27	space	space	NOUN
ejpam-5027	246	28	are	be	AUX
ejpam-5027	246	29	independent	independent	ADJ
ejpam-5027	246	30	.	.	PUNCT
ejpam-5027	247	1	theorem	theorem	ADJ
ejpam-5027	247	2	10	10	NUM
ejpam-5027	247	3	.	.	PUNCT
ejpam-5027	248	1	if	if	SCONJ
ejpam-5027	248	2	e	e	X
ejpam-5027	248	3	,	,	PUNCT
ejpam-5027	248	4	d	d	X
ejpam-5027	248	5	are	be	AUX
ejpam-5027	248	6	fuzzy	fuzzy	ADJ
ejpam-5027	248	7	(	(	PUNCT
ejpam-5027	248	8	i	i	PROPN
ejpam-5027	248	9	,	,	PUNCT
ejpam-5027	248	10	j)−	j)−	PROPN
ejpam-5027	248	11	gφ−compact	gφ−compact	PROPN
ejpam-5027	248	12	subsets	subset	NOUN
ejpam-5027	248	13	of	of	ADP
ejpam-5027	248	14	(	(	PUNCT
ejpam-5027	248	15	x	x	NOUN
ejpam-5027	248	16	,	,	PUNCT
ejpam-5027	248	17	δ1	δ1	NOUN
ejpam-5027	248	18	,	,	PUNCT
ejpam-5027	248	19	δ2	δ2	PROPN
ejpam-5027	248	20	)	)	PUNCT
ejpam-5027	248	21	.	.	PUNCT
ejpam-5027	249	1	then	then	ADV
ejpam-5027	249	2	e	e	X
ejpam-5027	249	3	∧d	∧d	PRON
ejpam-5027	249	4	is	be	AUX
ejpam-5027	249	5	fuzzy	fuzzy	ADJ
ejpam-5027	249	6	(	(	PUNCT
ejpam-5027	249	7	i	i	NOUN
ejpam-5027	249	8	,	,	PUNCT
ejpam-5027	249	9	j)−	j)−	PROPN
ejpam-5027	249	10	gφ−compact	gφ−compact	PROPN
ejpam-5027	249	11	.	.	PUNCT
ejpam-5027	250	1	proof	proof	NOUN
ejpam-5027	250	2	.	.	PUNCT
ejpam-5027	251	1	suppose	suppose	VERB
ejpam-5027	251	2	{	{	PUNCT
ejpam-5027	251	3	gi	gi	X
ejpam-5027	251	4	:	:	PUNCT
ejpam-5027	251	5	i	i	PRON
ejpam-5027	251	6	∈	∈	VERB
ejpam-5027	251	7	i	i	PRON
ejpam-5027	251	8	}	}	PUNCT
ejpam-5027	251	9	is	be	AUX
ejpam-5027	251	10	fuzzy	fuzzy	ADJ
ejpam-5027	251	11	(	(	PUNCT
ejpam-5027	251	12	i	i	NOUN
ejpam-5027	251	13	,	,	PUNCT
ejpam-5027	251	14	j)−gφ−open	j)−gφ−open	ADJ
ejpam-5027	251	15	cover	cover	NOUN
ejpam-5027	251	16	of	of	ADP
ejpam-5027	251	17	e∧d	e∧d	PROPN
ejpam-5027	251	18	.	.	PUNCT
ejpam-5027	252	1	since	since	SCONJ
ejpam-5027	252	2	e∧d	e∧d	VERB
ejpam-5027	252	3	≤	≤	NUM
ejpam-5027	252	4	e	e	NOUN
ejpam-5027	252	5	,	,	PUNCT
ejpam-5027	252	6	and	and	CCONJ
ejpam-5027	252	7	e	e	X
ejpam-5027	252	8	∧	∧	PROPN
ejpam-5027	252	9	d	d	PROPN
ejpam-5027	252	10	≤	≤	PROPN
ejpam-5027	252	11	d	d	NOUN
ejpam-5027	252	12	,	,	PUNCT
ejpam-5027	252	13	then	then	ADV
ejpam-5027	252	14	{	{	PUNCT
ejpam-5027	252	15	gi	gi	INTJ
ejpam-5027	252	16	:	:	PUNCT
ejpam-5027	252	17	i	i	PRON
ejpam-5027	252	18	∈	∈	VERB
ejpam-5027	252	19	i	i	X
ejpam-5027	252	20	}	}	PUNCT
ejpam-5027	252	21	≤	≤	NOUN
ejpam-5027	252	22	{	{	PUNCT
ejpam-5027	252	23	ui	ui	NOUN
ejpam-5027	252	24	:	:	PUNCT
ejpam-5027	252	25	i	i	PRON
ejpam-5027	252	26	∈	∈	VERB
ejpam-5027	253	1	i	i	PRON
ejpam-5027	253	2	,	,	PUNCT
ejpam-5027	253	3	such	such	ADJ
ejpam-5027	253	4	that	that	SCONJ
ejpam-5027	253	5	e	e	NOUN
ejpam-5027	253	6	≤	≤	PUNCT
ejpam-5027	253	7	∪i=1ui	∪i=1ui	PROPN
ejpam-5027	253	8	}	}	PUNCT
ejpam-5027	253	9	∧	∧	PROPN
ejpam-5027	253	10	{	{	PUNCT
ejpam-5027	253	11	vi	vi	NOUN
ejpam-5027	253	12	:	:	PUNCT
ejpam-5027	253	13	i	i	PRON
ejpam-5027	253	14	∈	∈	PROPN
ejpam-5027	254	1	i	i	PRON
ejpam-5027	254	2	,	,	PUNCT
ejpam-5027	254	3	such	such	ADJ
ejpam-5027	254	4	that	that	SCONJ
ejpam-5027	254	5	d	d	PROPN
ejpam-5027	254	6	≤	≤	NUM
ejpam-5027	254	7	∪i=1vi	∪i=1vi	NOUN
ejpam-5027	254	8	}	}	PUNCT
ejpam-5027	254	9	.	.	PUNCT
ejpam-5027	255	1	then	then	ADV
ejpam-5027	255	2	by	by	ADP
ejpam-5027	255	3	corollary	corollary	ADJ
ejpam-5027	255	4	2	2	NUM
ejpam-5027	255	5	,	,	PUNCT
ejpam-5027	255	6	and	and	CCONJ
ejpam-5027	255	7	as	as	ADP
ejpam-5027	255	8	e	e	PROPN
ejpam-5027	255	9	,	,	PUNCT
ejpam-5027	255	10	d	d	NOUN
ejpam-5027	255	11	are	be	AUX
ejpam-5027	255	12	fuzzy	fuzzy	ADJ
ejpam-5027	255	13	(	(	PUNCT
ejpam-5027	255	14	i	i	PROPN
ejpam-5027	255	15	,	,	PUNCT
ejpam-5027	255	16	j	j	PROPN
ejpam-5027	255	17	)	)	PUNCT
ejpam-5027	255	18	−	−	PROPN
ejpam-5027	255	19	gφ−compact	gφ−compact	PROPN
ejpam-5027	255	20	,	,	PUNCT
ejpam-5027	255	21	then	then	ADV
ejpam-5027	255	22	{	{	PUNCT
ejpam-5027	255	23	gi	gi	INTJ
ejpam-5027	255	24	}	}	PUNCT
ejpam-5027	255	25	has	have	VERB
ejpam-5027	255	26	a	a	DET
ejpam-5027	255	27	finite	finite	ADJ
ejpam-5027	255	28	subcover	subcover	PROPN
ejpam-5027	255	29	{	{	PUNCT
ejpam-5027	255	30	gij	gij	PROPN
ejpam-5027	255	31	:	:	PUNCT
ejpam-5027	256	1	j	j	PROPN
ejpam-5027	256	2	=	=	SYM
ejpam-5027	256	3	1	1	NUM
ejpam-5027	256	4	,	,	PUNCT
ejpam-5027	256	5	2	2	NUM
ejpam-5027	256	6	,	,	PUNCT
ejpam-5027	256	7	...	...	PUNCT
ejpam-5027	256	8	,	,	PUNCT
ejpam-5027	256	9	n	n	CCONJ
ejpam-5027	256	10	}	}	PUNCT
ejpam-5027	256	11	.	.	PUNCT
ejpam-5027	257	1	therefore	therefore	ADV
ejpam-5027	257	2	e	e	X
ejpam-5027	257	3	∧	∧	PROPN
ejpam-5027	257	4	d	d	PROPN
ejpam-5027	257	5	is	be	AUX
ejpam-5027	257	6	fuzzy	fuzzy	ADJ
ejpam-5027	257	7	(	(	PUNCT
ejpam-5027	257	8	i	i	NOUN
ejpam-5027	257	9	,	,	PUNCT
ejpam-5027	257	10	j)−	j)−	PROPN
ejpam-5027	257	11	gφ−compact	gφ−compact	PROPN
ejpam-5027	257	12	.	.	PUNCT
ejpam-5027	258	1	definition	definition	NOUN
ejpam-5027	258	2	13	13	NUM
ejpam-5027	258	3	.	.	PUNCT
ejpam-5027	259	1	a	a	DET
ejpam-5027	259	2	mapping	mapping	NOUN
ejpam-5027	259	3	f	f	NOUN
ejpam-5027	259	4	:	:	PUNCT
ejpam-5027	259	5	(	(	PUNCT
ejpam-5027	259	6	x	x	X
ejpam-5027	259	7	,	,	PUNCT
ejpam-5027	259	8	δ1	δ1	NOUN
ejpam-5027	259	9	,	,	PUNCT
ejpam-5027	259	10	δ2	δ2	ADJ
ejpam-5027	259	11	)	)	PUNCT
ejpam-5027	259	12	→	→	SYM
ejpam-5027	259	13	(	(	PUNCT
ejpam-5027	259	14	y	y	PROPN
ejpam-5027	259	15	,	,	PUNCT
ejpam-5027	259	16	σ1	σ1	PROPN
ejpam-5027	259	17	,	,	PUNCT
ejpam-5027	259	18	σ2	σ2	PROPN
ejpam-5027	259	19	)	)	PUNCT
ejpam-5027	259	20	is	be	AUX
ejpam-5027	259	21	named	name	VERB
ejpam-5027	259	22	fuzzy	fuzzy	ADJ
ejpam-5027	259	23	(	(	PUNCT
ejpam-5027	259	24	i	i	PRON
ejpam-5027	259	25	,	,	PUNCT
ejpam-5027	259	26	j)−generalized	j)−generalize	VERB
ejpam-5027	259	27	φ−	φ−	PROPN
ejpam-5027	259	28	continuous	continuous	ADJ
ejpam-5027	259	29	(	(	PUNCT
ejpam-5027	259	30	shortly	shortly	ADV
ejpam-5027	259	31	,	,	PUNCT
ejpam-5027	259	32	(	(	PUNCT
ejpam-5027	259	33	i	i	PROPN
ejpam-5027	259	34	,	,	PUNCT
ejpam-5027	259	35	j	j	PROPN
ejpam-5027	259	36	)	)	PUNCT
ejpam-5027	259	37	−	−	PROPN
ejpam-5027	259	38	gφ	gφ	NOUN
ejpam-5027	259	39	−	−	PROPN
ejpam-5027	259	40	conts	cont	NOUN
ejpam-5027	259	41	)	)	PUNCT
ejpam-5027	259	42	when	when	SCONJ
ejpam-5027	259	43	the	the	DET
ejpam-5027	259	44	opposite	opposite	ADJ
ejpam-5027	259	45	image	image	NOUN
ejpam-5027	259	46	of	of	ADP
ejpam-5027	259	47	each	each	DET
ejpam-5027	259	48	fuzzy	fuzzy	ADJ
ejpam-5027	259	49	open	open	NOUN
ejpam-5027	259	50	of	of	ADP
ejpam-5027	259	51	(	(	PUNCT
ejpam-5027	259	52	y	y	PROPN
ejpam-5027	259	53	,	,	PUNCT
ejpam-5027	259	54	σj	σj	VERB
ejpam-5027	259	55	)	)	PUNCT
ejpam-5027	259	56	is	be	AUX
ejpam-5027	259	57	fuzzy	fuzzy	ADJ
ejpam-5027	259	58	(	(	PUNCT
ejpam-5027	259	59	i	i	NOUN
ejpam-5027	259	60	,	,	PUNCT
ejpam-5027	259	61	j)−	j)−	PROPN
ejpam-5027	259	62	gφ−	gφ−	PROPN
ejpam-5027	259	63	open	open	ADJ
ejpam-5027	259	64	of	of	ADP
ejpam-5027	259	65	x.	x.	NOUN
ejpam-5027	259	66	by	by	ADP
ejpam-5027	259	67	using	use	VERB
ejpam-5027	259	68	the	the	DET
ejpam-5027	259	69	complement	complement	NOUN
ejpam-5027	259	70	,	,	PUNCT
ejpam-5027	259	71	we	we	PRON
ejpam-5027	259	72	find	find	VERB
ejpam-5027	259	73	:	:	PUNCT
ejpam-5027	259	74	theorem	theorem	NOUN
ejpam-5027	259	75	11	11	NUM
ejpam-5027	259	76	.	.	PUNCT
ejpam-5027	260	1	suppose	suppose	VERB
ejpam-5027	260	2	f	f	X
ejpam-5027	260	3	:	:	PUNCT
ejpam-5027	260	4	(	(	PUNCT
ejpam-5027	260	5	x	x	NOUN
ejpam-5027	260	6	,	,	PUNCT
ejpam-5027	260	7	δ1	δ1	NOUN
ejpam-5027	260	8	,	,	PUNCT
ejpam-5027	260	9	δ2	δ2	ADJ
ejpam-5027	260	10	)	)	PUNCT
ejpam-5027	260	11	→	→	SYM
ejpam-5027	260	12	(	(	PUNCT
ejpam-5027	260	13	y	y	PROPN
ejpam-5027	260	14	,	,	PUNCT
ejpam-5027	260	15	σ1	σ1	PROPN
ejpam-5027	260	16	,	,	PUNCT
ejpam-5027	260	17	σ2	σ2	NOUN
ejpam-5027	260	18	)	)	PUNCT
ejpam-5027	260	19	.	.	PUNCT
ejpam-5027	261	1	then	then	ADV
ejpam-5027	261	2	f	f	PROPN
ejpam-5027	261	3	is	be	AUX
ejpam-5027	261	4	fuzzy	fuzzy	ADJ
ejpam-5027	261	5	(	(	PUNCT
ejpam-5027	261	6	i	i	NOUN
ejpam-5027	261	7	,	,	PUNCT
ejpam-5027	261	8	j)−	j)−	PROPN
ejpam-5027	261	9	gφ−	gφ−	PROPN
ejpam-5027	261	10	conts	conts	PROPN
ejpam-5027	261	11	⇔	⇔	X
ejpam-5027	261	12	∀	∀	X
ejpam-5027	261	13	fuzzy	fuzzy	ADJ
ejpam-5027	261	14	closed	close	VERB
ejpam-5027	261	15	set	set	VERB
ejpam-5027	261	16	v	v	NOUN
ejpam-5027	261	17	at	at	ADP
ejpam-5027	261	18	(	(	PUNCT
ejpam-5027	261	19	y	y	NOUN
ejpam-5027	261	20	,	,	PUNCT
ejpam-5027	261	21	σj	σj	NOUN
ejpam-5027	261	22	)	)	PUNCT
ejpam-5027	261	23	,	,	PUNCT
ejpam-5027	261	24	f	f	PROPN
ejpam-5027	261	25	−1(v	−1(v	PROPN
ejpam-5027	261	26	)	)	PUNCT
ejpam-5027	261	27	is	be	AUX
ejpam-5027	261	28	fuzzy	fuzzy	ADJ
ejpam-5027	261	29	(	(	PUNCT
ejpam-5027	261	30	i	i	NOUN
ejpam-5027	261	31	,	,	PUNCT
ejpam-5027	261	32	j)−	j)−	PROPN
ejpam-5027	261	33	gφ−	gφ−	PUNCT
ejpam-5027	261	34	cld	cld	PROPN
ejpam-5027	261	35	set	set	VERB
ejpam-5027	261	36	at	at	ADP
ejpam-5027	261	37	x.	x.	PROPN
ejpam-5027	261	38	theorem	theorem	VERB
ejpam-5027	261	39	12	12	NUM
ejpam-5027	261	40	.	.	PUNCT
ejpam-5027	262	1	the	the	DET
ejpam-5027	262	2	portrait	portrait	NOUN
ejpam-5027	262	3	(	(	PUNCT
ejpam-5027	262	4	i	i	PROPN
ejpam-5027	262	5	,	,	PUNCT
ejpam-5027	262	6	j)−gφ−conts	j)−gφ−cont	NOUN
ejpam-5027	262	7	of	of	ADP
ejpam-5027	262	8	fuzzy	fuzzy	ADJ
ejpam-5027	262	9	(	(	PUNCT
ejpam-5027	262	10	i	i	PROPN
ejpam-5027	262	11	,	,	PUNCT
ejpam-5027	262	12	j)−gφ−compact	j)−gφ−compact	PROPN
ejpam-5027	262	13	is	be	AUX
ejpam-5027	262	14	fuzzy	fuzzy	ADJ
ejpam-5027	262	15	δj−compact	δj−compact	NOUN
ejpam-5027	262	16	.	.	PUNCT
ejpam-5027	263	1	proof	proof	NOUN
ejpam-5027	263	2	.	.	PUNCT
ejpam-5027	264	1	suppose	suppose	VERB
ejpam-5027	264	2	f	f	X
ejpam-5027	264	3	:	:	PUNCT
ejpam-5027	264	4	(	(	PUNCT
ejpam-5027	264	5	x	x	NOUN
ejpam-5027	264	6	,	,	PUNCT
ejpam-5027	264	7	δ1	δ1	NOUN
ejpam-5027	264	8	,	,	PUNCT
ejpam-5027	264	9	δ2	δ2	ADJ
ejpam-5027	264	10	)	)	PUNCT
ejpam-5027	264	11	→	→	SYM
ejpam-5027	264	12	(	(	PUNCT
ejpam-5027	264	13	y	y	PROPN
ejpam-5027	264	14	,	,	PUNCT
ejpam-5027	264	15	σ1	σ1	PROPN
ejpam-5027	264	16	,	,	PUNCT
ejpam-5027	264	17	σ2	σ2	NOUN
ejpam-5027	264	18	)	)	PUNCT
ejpam-5027	264	19	is	be	AUX
ejpam-5027	264	20	fuzzy	fuzzy	ADJ
ejpam-5027	264	21	(	(	PUNCT
ejpam-5027	264	22	i	i	PROPN
ejpam-5027	264	23	,	,	PUNCT
ejpam-5027	264	24	j	j	PROPN
ejpam-5027	264	25	)	)	PUNCT
ejpam-5027	264	26	−	−	PROPN
ejpam-5027	264	27	gφ	gφ	NOUN
ejpam-5027	264	28	−	−	PROPN
ejpam-5027	264	29	conts	cont	NOUN
ejpam-5027	264	30	,	,	PUNCT
ejpam-5027	264	31	surjective	surjective	ADJ
ejpam-5027	264	32	mapping	mapping	NOUN
ejpam-5027	264	33	,	,	PUNCT
ejpam-5027	264	34	and	and	CCONJ
ejpam-5027	264	35	(	(	PUNCT
ejpam-5027	264	36	x	x	NOUN
ejpam-5027	264	37	,	,	PUNCT
ejpam-5027	264	38	δ1	δ1	NOUN
ejpam-5027	264	39	,	,	PUNCT
ejpam-5027	264	40	δ2	δ2	PROPN
ejpam-5027	264	41	)	)	PUNCT
ejpam-5027	264	42	is	be	AUX
ejpam-5027	264	43	fuzzy	fuzzy	ADJ
ejpam-5027	264	44	(	(	PUNCT
ejpam-5027	264	45	i	i	PROPN
ejpam-5027	264	46	,	,	PUNCT
ejpam-5027	264	47	j)−	j)−	PROPN
ejpam-5027	264	48	gφ−compact	gφ−compact	PROPN
ejpam-5027	264	49	space	space	NOUN
ejpam-5027	264	50	.	.	PUNCT
ejpam-5027	265	1	assume	assume	VERB
ejpam-5027	265	2	that	that	SCONJ
ejpam-5027	265	3	{	{	PUNCT
ejpam-5027	265	4	bj	bj	NOUN
ejpam-5027	265	5	:	:	PUNCT
ejpam-5027	265	6	j	j	PROPN
ejpam-5027	265	7	∈	∈	PROPN
ejpam-5027	265	8	i	i	PRON
ejpam-5027	265	9	}	}	PUNCT
ejpam-5027	265	10	is	be	AUX
ejpam-5027	265	11	ahlam	ahlam	PROPN
ejpam-5027	265	12	ahmed	ahmed	PROPN
ejpam-5027	265	13	alharbi	alharbi	PROPN
ejpam-5027	265	14	,	,	PUNCT
ejpam-5027	265	15	adem	adem	PROPN
ejpam-5027	265	16	kilicman	kilicman	PROPN
ejpam-5027	265	17	/	/	SYM
ejpam-5027	265	18	eur	eur	PROPN
ejpam-5027	265	19	.	.	PUNCT
ejpam-5027	266	1	j.	j.	PROPN
ejpam-5027	266	2	pure	pure	PROPN
ejpam-5027	266	3	appl	appl	PROPN
ejpam-5027	266	4	.	.	PROPN
ejpam-5027	266	5	math	math	PROPN
ejpam-5027	266	6	,	,	PUNCT
ejpam-5027	266	7	17	17	NUM
ejpam-5027	266	8	(	(	PUNCT
ejpam-5027	266	9	1	1	NUM
ejpam-5027	266	10	)	)	PUNCT
ejpam-5027	266	11	(	(	PUNCT
ejpam-5027	266	12	2024	2024	NUM
ejpam-5027	266	13	)	)	PUNCT
ejpam-5027	266	14	,	,	PUNCT
ejpam-5027	266	15	30	30	NUM
ejpam-5027	266	16	-	-	SYM
ejpam-5027	266	17	41	41	NUM
ejpam-5027	266	18	39	39	NUM
ejpam-5027	266	19	δj−open	δj−open	NOUN
ejpam-5027	266	20	cover	cover	NOUN
ejpam-5027	266	21	for	for	ADP
ejpam-5027	266	22	y	y	PROPN
ejpam-5027	266	23	,	,	PUNCT
ejpam-5027	266	24	thus	thus	ADV
ejpam-5027	266	25	{	{	PUNCT
ejpam-5027	266	26	f−1(bj	f−1(bj	NOUN
ejpam-5027	266	27	)	)	PUNCT
ejpam-5027	266	28	:	:	PUNCT
ejpam-5027	267	1	j	j	PROPN
ejpam-5027	267	2	∈	∈	PROPN
ejpam-5027	267	3	i	i	PRON
ejpam-5027	267	4	}	}	PUNCT
ejpam-5027	267	5	is	be	AUX
ejpam-5027	267	6	fuzzy	fuzzy	ADJ
ejpam-5027	267	7	(	(	PUNCT
ejpam-5027	267	8	i	i	PROPN
ejpam-5027	267	9	,	,	PUNCT
ejpam-5027	267	10	j	j	PROPN
ejpam-5027	267	11	)	)	PUNCT
ejpam-5027	268	1	−	−	PROPN
ejpam-5027	268	2	gφ−open	gφ−open	NOUN
ejpam-5027	268	3	cover	cover	NOUN
ejpam-5027	268	4	for	for	ADP
ejpam-5027	268	5	x	x	X
ejpam-5027	268	6	,	,	PUNCT
ejpam-5027	268	7	then	then	ADV
ejpam-5027	268	8	it	it	PRON
ejpam-5027	268	9	has	have	VERB
ejpam-5027	268	10	finite	finite	PROPN
ejpam-5027	268	11	subcover	subcover	PROPN
ejpam-5027	268	12	for	for	ADP
ejpam-5027	268	13	x	x	X
ejpam-5027	268	14	,	,	PUNCT
ejpam-5027	268	15	and	and	CCONJ
ejpam-5027	268	16	since	since	SCONJ
ejpam-5027	268	17	f	f	PROPN
ejpam-5027	268	18	is	be	AUX
ejpam-5027	268	19	surjective	surjective	ADJ
ejpam-5027	268	20	mapping	mapping	NOUN
ejpam-5027	268	21	,	,	PUNCT
ejpam-5027	268	22	so	so	ADV
ejpam-5027	268	23	∃	∃	PROPN
ejpam-5027	268	24	{	{	PUNCT
ejpam-5027	268	25	b1	b1	PROPN
ejpam-5027	268	26	,	,	PUNCT
ejpam-5027	268	27	b2	b2	NOUN
ejpam-5027	268	28	,	,	PUNCT
ejpam-5027	268	29	...	...	PUNCT
ejpam-5027	268	30	,	,	PUNCT
ejpam-5027	268	31	bn	bn	CCONJ
ejpam-5027	268	32	}	}	PUNCT
ejpam-5027	268	33	finite	finite	VERB
ejpam-5027	268	34	subcover	subcover	PROPN
ejpam-5027	268	35	for	for	ADP
ejpam-5027	268	36	y	y	PROPN
ejpam-5027	268	37	.	.	PUNCT
ejpam-5027	269	1	therefore	therefore	ADV
ejpam-5027	269	2	y	y	PROPN
ejpam-5027	269	3	is	be	AUX
ejpam-5027	269	4	fuzzy	fuzzy	ADJ
ejpam-5027	269	5	δj−compact	δj−compact	NOUN
ejpam-5027	269	6	.	.	PUNCT
ejpam-5027	270	1	corollary	corollary	ADJ
ejpam-5027	270	2	6	6	NUM
ejpam-5027	270	3	.	.	PUNCT
ejpam-5027	271	1	the	the	DET
ejpam-5027	271	2	δj−continuous	δj−continuous	ADJ
ejpam-5027	271	3	image	image	NOUN
ejpam-5027	271	4	of	of	ADP
ejpam-5027	271	5	(	(	PUNCT
ejpam-5027	271	6	i	i	PROPN
ejpam-5027	271	7	,	,	PUNCT
ejpam-5027	271	8	j)−	j)−	PROPN
ejpam-5027	271	9	gφ−compact	gφ−compact	PROPN
ejpam-5027	271	10	is	be	AUX
ejpam-5027	271	11	δj−compact	δj−compact	ADJ
ejpam-5027	271	12	.	.	PUNCT
ejpam-5027	272	1	definition	definition	NOUN
ejpam-5027	272	2	14	14	NUM
ejpam-5027	272	3	.	.	PUNCT
ejpam-5027	273	1	a	a	DET
ejpam-5027	273	2	mapping	mapping	NOUN
ejpam-5027	273	3	f	f	NOUN
ejpam-5027	273	4	:	:	PUNCT
ejpam-5027	273	5	(	(	PUNCT
ejpam-5027	273	6	x	x	X
ejpam-5027	273	7	,	,	PUNCT
ejpam-5027	273	8	δ1	δ1	NOUN
ejpam-5027	273	9	,	,	PUNCT
ejpam-5027	273	10	δ2	δ2	ADJ
ejpam-5027	273	11	)	)	PUNCT
ejpam-5027	273	12	→	→	SYM
ejpam-5027	273	13	(	(	PUNCT
ejpam-5027	273	14	y	y	PROPN
ejpam-5027	273	15	,	,	PUNCT
ejpam-5027	273	16	σ1	σ1	PROPN
ejpam-5027	273	17	,	,	PUNCT
ejpam-5027	273	18	σ2	σ2	PROPN
ejpam-5027	273	19	)	)	PUNCT
ejpam-5027	273	20	is	be	AUX
ejpam-5027	273	21	named	name	VERB
ejpam-5027	273	22	fuzzy	fuzzy	ADJ
ejpam-5027	273	23	(	(	PUNCT
ejpam-5027	273	24	i	i	PROPN
ejpam-5027	273	25	,	,	PUNCT
ejpam-5027	273	26	j)−generalizedφ−	j)−generalizedφ−	PROPN
ejpam-5027	273	27	irresolute	irresolute	VERB
ejpam-5027	273	28	mapping	mapping	NOUN
ejpam-5027	273	29	(	(	PUNCT
ejpam-5027	273	30	shortly	shortly	ADV
ejpam-5027	273	31	,	,	PUNCT
ejpam-5027	273	32	(	(	PUNCT
ejpam-5027	273	33	i	i	PROPN
ejpam-5027	273	34	,	,	PUNCT
ejpam-5027	273	35	j)−	j)−	PROPN
ejpam-5027	273	36	gφ−	gφ−	PROPN
ejpam-5027	273	37	irres	irre	NOUN
ejpam-5027	273	38	)	)	PUNCT
ejpam-5027	273	39	when	when	SCONJ
ejpam-5027	273	40	the	the	DET
ejpam-5027	273	41	opposite	opposite	ADJ
ejpam-5027	273	42	image	image	NOUN
ejpam-5027	273	43	of	of	ADP
ejpam-5027	273	44	all	all	PRON
ejpam-5027	273	45	fuzzy	fuzzy	ADJ
ejpam-5027	273	46	(	(	PUNCT
ejpam-5027	273	47	i	i	NOUN
ejpam-5027	273	48	,	,	PUNCT
ejpam-5027	273	49	j)−	j)−	PROPN
ejpam-5027	273	50	gφ−	gφ−	PROPN
ejpam-5027	273	51	open	open	ADJ
ejpam-5027	273	52	set	set	NOUN
ejpam-5027	273	53	of	of	ADP
ejpam-5027	273	54	x	x	PUNCT
ejpam-5027	273	55	is	be	AUX
ejpam-5027	273	56	fuzzy	fuzzy	ADJ
ejpam-5027	273	57	(	(	PUNCT
ejpam-5027	273	58	i	i	NOUN
ejpam-5027	273	59	,	,	PUNCT
ejpam-5027	273	60	j)−	j)−	PROPN
ejpam-5027	273	61	gφ−	gφ−	PROPN
ejpam-5027	273	62	open	open	ADJ
ejpam-5027	273	63	of	of	ADP
ejpam-5027	273	64	y	y	PROPN
ejpam-5027	273	65	.	.	PUNCT
ejpam-5027	274	1	by	by	ADP
ejpam-5027	274	2	using	use	VERB
ejpam-5027	274	3	the	the	DET
ejpam-5027	274	4	complement	complement	NOUN
ejpam-5027	274	5	we	we	PRON
ejpam-5027	274	6	find	find	VERB
ejpam-5027	274	7	:	:	PUNCT
ejpam-5027	274	8	theorem	theorem	NOUN
ejpam-5027	274	9	13	13	NUM
ejpam-5027	274	10	.	.	PUNCT
ejpam-5027	275	1	suppose	suppose	VERB
ejpam-5027	275	2	f	f	X
ejpam-5027	275	3	:	:	PUNCT
ejpam-5027	275	4	(	(	PUNCT
ejpam-5027	275	5	x	x	NOUN
ejpam-5027	275	6	,	,	PUNCT
ejpam-5027	275	7	δ1	δ1	NOUN
ejpam-5027	275	8	,	,	PUNCT
ejpam-5027	275	9	δ2	δ2	ADJ
ejpam-5027	275	10	)	)	PUNCT
ejpam-5027	275	11	→	→	SYM
ejpam-5027	275	12	(	(	PUNCT
ejpam-5027	275	13	y	y	PROPN
ejpam-5027	275	14	,	,	PUNCT
ejpam-5027	275	15	σ1	σ1	PROPN
ejpam-5027	275	16	,	,	PUNCT
ejpam-5027	275	17	σ2	σ2	NOUN
ejpam-5027	275	18	)	)	PUNCT
ejpam-5027	275	19	.	.	PUNCT
ejpam-5027	276	1	then	then	ADV
ejpam-5027	276	2	f	f	PROPN
ejpam-5027	276	3	is	be	AUX
ejpam-5027	276	4	fuzzy	fuzzy	ADJ
ejpam-5027	276	5	(	(	PUNCT
ejpam-5027	276	6	i	i	NOUN
ejpam-5027	276	7	,	,	PUNCT
ejpam-5027	276	8	j)−	j)−	PROPN
ejpam-5027	276	9	gφ−	gφ−	PROPN
ejpam-5027	276	10	irres	irres	PROPN
ejpam-5027	276	11	⇔	⇔	NOUN
ejpam-5027	276	12	for	for	ADP
ejpam-5027	276	13	all	all	DET
ejpam-5027	276	14	fuzzy	fuzzy	ADJ
ejpam-5027	276	15	(	(	PUNCT
ejpam-5027	276	16	i	i	NOUN
ejpam-5027	276	17	,	,	PUNCT
ejpam-5027	276	18	j)−	j)−	PROPN
ejpam-5027	276	19	gφ−cld	gφ−cld	NOUN
ejpam-5027	276	20	v	v	NOUN
ejpam-5027	276	21	at	at	ADP
ejpam-5027	276	22	y	y	PROPN
ejpam-5027	276	23	,	,	PUNCT
ejpam-5027	276	24	f−1(v	f−1(v	PROPN
ejpam-5027	276	25	)	)	PUNCT
ejpam-5027	276	26	is	be	AUX
ejpam-5027	276	27	fuzzy	fuzzy	ADJ
ejpam-5027	276	28	(	(	PUNCT
ejpam-5027	276	29	i	i	NOUN
ejpam-5027	276	30	,	,	PUNCT
ejpam-5027	276	31	j)−	j)−	PROPN
ejpam-5027	276	32	gφ−	gφ−	PUNCT
ejpam-5027	276	33	cld	cld	PROPN
ejpam-5027	276	34	at	at	ADP
ejpam-5027	276	35	x.	x.	PROPN
ejpam-5027	276	36	theorem	theorem	VERB
ejpam-5027	276	37	14	14	NUM
ejpam-5027	276	38	.	.	PUNCT
ejpam-5027	277	1	if	if	SCONJ
ejpam-5027	277	2	f	f	PROPN
ejpam-5027	277	3	:	:	PUNCT
ejpam-5027	277	4	(	(	PUNCT
ejpam-5027	277	5	x	x	NOUN
ejpam-5027	277	6	,	,	PUNCT
ejpam-5027	277	7	δ1	δ1	NOUN
ejpam-5027	277	8	,	,	PUNCT
ejpam-5027	277	9	δ2	δ2	ADJ
ejpam-5027	277	10	)	)	PUNCT
ejpam-5027	277	11	→	→	SYM
ejpam-5027	277	12	(	(	PUNCT
ejpam-5027	277	13	y	y	PROPN
ejpam-5027	277	14	,	,	PUNCT
ejpam-5027	277	15	σ1	σ1	PROPN
ejpam-5027	277	16	,	,	PUNCT
ejpam-5027	277	17	σ2	σ2	NOUN
ejpam-5027	277	18	)	)	PUNCT
ejpam-5027	277	19	is	be	AUX
ejpam-5027	277	20	fuzzy	fuzzy	ADJ
ejpam-5027	277	21	(	(	PUNCT
ejpam-5027	277	22	i	i	NOUN
ejpam-5027	277	23	,	,	PUNCT
ejpam-5027	277	24	j)−	j)−	PROPN
ejpam-5027	277	25	gφ−	gφ−	PROPN
ejpam-5027	277	26	irres	irre	VERB
ejpam-5027	277	27	mapping	mapping	NOUN
ejpam-5027	277	28	,	,	PUNCT
ejpam-5027	277	29	and	and	CCONJ
ejpam-5027	277	30	e	e	NOUN
ejpam-5027	277	31	is	be	AUX
ejpam-5027	277	32	fuzzy	fuzzy	ADJ
ejpam-5027	277	33	(	(	PUNCT
ejpam-5027	277	34	i	i	PROPN
ejpam-5027	277	35	,	,	PUNCT
ejpam-5027	277	36	j)−	j)−	PROPN
ejpam-5027	277	37	gφ−compact	gφ−compact	PROPN
ejpam-5027	277	38	set	set	PROPN
ejpam-5027	277	39	of	of	ADP
ejpam-5027	277	40	x.	x.	NOUN
ejpam-5027	277	41	thus	thus	ADV
ejpam-5027	277	42	f(e	f(e	VERB
ejpam-5027	277	43	)	)	PUNCT
ejpam-5027	277	44	is	be	AUX
ejpam-5027	277	45	fuzzy	fuzzy	ADJ
ejpam-5027	277	46	(	(	PUNCT
ejpam-5027	277	47	i	i	PROPN
ejpam-5027	277	48	,	,	PUNCT
ejpam-5027	277	49	j)−	j)−	PROPN
ejpam-5027	277	50	gφ−compact	gφ−compact	PROPN
ejpam-5027	277	51	of	of	ADP
ejpam-5027	277	52	y	y	PROPN
ejpam-5027	277	53	.	.	PUNCT
ejpam-5027	278	1	proof	proof	NOUN
ejpam-5027	278	2	.	.	PUNCT
ejpam-5027	279	1	suppose	suppose	VERB
ejpam-5027	279	2	f	f	X
ejpam-5027	279	3	:	:	PUNCT
ejpam-5027	279	4	(	(	PUNCT
ejpam-5027	279	5	x	x	NOUN
ejpam-5027	279	6	,	,	PUNCT
ejpam-5027	279	7	δ1	δ1	NOUN
ejpam-5027	279	8	,	,	PUNCT
ejpam-5027	279	9	δ2	δ2	ADJ
ejpam-5027	279	10	)	)	PUNCT
ejpam-5027	279	11	→	→	SYM
ejpam-5027	279	12	(	(	PUNCT
ejpam-5027	279	13	y	y	PROPN
ejpam-5027	279	14	,	,	PUNCT
ejpam-5027	279	15	σ1	σ1	PROPN
ejpam-5027	279	16	,	,	PUNCT
ejpam-5027	279	17	σ2	σ2	NOUN
ejpam-5027	279	18	)	)	PUNCT
ejpam-5027	279	19	is	be	AUX
ejpam-5027	279	20	fuzzy	fuzzy	ADJ
ejpam-5027	279	21	(	(	PUNCT
ejpam-5027	279	22	i	i	NOUN
ejpam-5027	279	23	,	,	PUNCT
ejpam-5027	279	24	j)−	j)−	PROPN
ejpam-5027	279	25	gφ−	gφ−	PROPN
ejpam-5027	279	26	irres	irre	NOUN
ejpam-5027	279	27	,	,	PUNCT
ejpam-5027	279	28	onto	onto	ADP
ejpam-5027	279	29	mapping	mapping	NOUN
ejpam-5027	279	30	,	,	PUNCT
ejpam-5027	279	31	also	also	ADV
ejpam-5027	279	32	{	{	PUNCT
ejpam-5027	279	33	vi	vi	X
ejpam-5027	279	34	:	:	PUNCT
ejpam-5027	280	1	i	i	PRON
ejpam-5027	280	2	∈	∈	PROPN
ejpam-5027	280	3	i	i	PRON
ejpam-5027	280	4	}	}	PUNCT
ejpam-5027	280	5	is	be	AUX
ejpam-5027	280	6	fuzzy	fuzzy	ADJ
ejpam-5027	280	7	(	(	PUNCT
ejpam-5027	280	8	i	i	PROPN
ejpam-5027	280	9	,	,	PUNCT
ejpam-5027	280	10	j)−	j)−	PROPN
ejpam-5027	280	11	gφ−open	gφ−open	PROPN
ejpam-5027	280	12	cover	cover	NOUN
ejpam-5027	280	13	of	of	ADP
ejpam-5027	280	14	f(e	f(e	NOUN
ejpam-5027	280	15	)	)	PUNCT
ejpam-5027	280	16	.	.	PUNCT
ejpam-5027	281	1	as	as	SCONJ
ejpam-5027	281	2	f	f	PROPN
ejpam-5027	281	3	is	be	AUX
ejpam-5027	281	4	onto	onto	ADP
ejpam-5027	281	5	,	,	PUNCT
ejpam-5027	281	6	then	then	ADV
ejpam-5027	281	7	f(e	f(e	NOUN
ejpam-5027	281	8	)	)	PUNCT
ejpam-5027	281	9	≤	≤	PROPN
ejpam-5027	281	10	f(∪n	f(∪n	PROPN
ejpam-5027	281	11	j=1f	j=1f	NOUN
ejpam-5027	281	12	−1(vij	−1(vij	PROPN
ejpam-5027	281	13	)	)	PUNCT
ejpam-5027	281	14	)	)	PUNCT
ejpam-5027	282	1	≤	≤	NOUN
ejpam-5027	282	2	∪n	∪n	X
ejpam-5027	283	1	j=1vij	j=1vij	PROPN
ejpam-5027	283	2	.	.	PUNCT
ejpam-5027	284	1	so	so	ADV
ejpam-5027	284	2	,	,	PUNCT
ejpam-5027	284	3	f(e	f(e	NOUN
ejpam-5027	284	4	)	)	PUNCT
ejpam-5027	284	5	is	be	AUX
ejpam-5027	284	6	fuzzy	fuzzy	ADJ
ejpam-5027	284	7	(	(	PUNCT
ejpam-5027	284	8	i	i	PROPN
ejpam-5027	284	9	,	,	PUNCT
ejpam-5027	284	10	j)−	j)−	PROPN
ejpam-5027	284	11	gφ−compact	gφ−compact	PROPN
ejpam-5027	284	12	at	at	ADP
ejpam-5027	284	13	y	y	PROPN
ejpam-5027	284	14	.	.	PUNCT
ejpam-5027	285	1	corollary	corollary	ADJ
ejpam-5027	285	2	7	7	NUM
ejpam-5027	285	3	.	.	PUNCT
ejpam-5027	286	1	when	when	SCONJ
ejpam-5027	286	2	f	f	X
ejpam-5027	286	3	:	:	PUNCT
ejpam-5027	286	4	(	(	PUNCT
ejpam-5027	286	5	x	x	NOUN
ejpam-5027	286	6	,	,	PUNCT
ejpam-5027	286	7	δ1	δ1	NOUN
ejpam-5027	286	8	,	,	PUNCT
ejpam-5027	286	9	δ2	δ2	ADJ
ejpam-5027	286	10	)	)	PUNCT
ejpam-5027	286	11	→	→	SYM
ejpam-5027	286	12	(	(	PUNCT
ejpam-5027	286	13	y	y	PROPN
ejpam-5027	286	14	,	,	PUNCT
ejpam-5027	286	15	σ1	σ1	PROPN
ejpam-5027	286	16	,	,	PUNCT
ejpam-5027	286	17	σ2	σ2	NOUN
ejpam-5027	286	18	)	)	PUNCT
ejpam-5027	286	19	is	be	AUX
ejpam-5027	286	20	fuzzy	fuzzy	ADJ
ejpam-5027	286	21	(	(	PUNCT
ejpam-5027	286	22	i	i	PROPN
ejpam-5027	286	23	,	,	PUNCT
ejpam-5027	286	24	j)−gφ−	j)−gφ−	PROPN
ejpam-5027	286	25	irres	irre	NOUN
ejpam-5027	286	26	,	,	PUNCT
ejpam-5027	286	27	onto	onto	ADP
ejpam-5027	286	28	mapping	mapping	NOUN
ejpam-5027	286	29	,	,	PUNCT
ejpam-5027	286	30	and	and	CCONJ
ejpam-5027	286	31	x	x	X
ejpam-5027	286	32	is	be	AUX
ejpam-5027	286	33	fuzzy	fuzzy	ADJ
ejpam-5027	286	34	(	(	PUNCT
ejpam-5027	286	35	i	i	NOUN
ejpam-5027	286	36	,	,	PUNCT
ejpam-5027	286	37	j)−	j)−	PROPN
ejpam-5027	286	38	gφ−compact	gφ−compact	PROPN
ejpam-5027	286	39	.	.	PUNCT
ejpam-5027	287	1	after	after	ADP
ejpam-5027	287	2	that	that	PRON
ejpam-5027	287	3	,	,	PUNCT
ejpam-5027	287	4	y	y	PROPN
ejpam-5027	287	5	is	be	AUX
ejpam-5027	287	6	fuzzy	fuzzy	ADJ
ejpam-5027	287	7	(	(	PUNCT
ejpam-5027	287	8	i	i	NOUN
ejpam-5027	287	9	,	,	PUNCT
ejpam-5027	287	10	j)−	j)−	PROPN
ejpam-5027	287	11	gφ−compact	gφ−compact	PROPN
ejpam-5027	287	12	.	.	PUNCT
ejpam-5027	288	1	theorem	theorem	VERB
ejpam-5027	288	2	15	15	NUM
ejpam-5027	288	3	.	.	PUNCT
ejpam-5027	289	1	if	if	SCONJ
ejpam-5027	289	2	(	(	PUNCT
ejpam-5027	289	3	x	x	NOUN
ejpam-5027	289	4	,	,	PUNCT
ejpam-5027	289	5	δ1	δ1	NOUN
ejpam-5027	289	6	,	,	PUNCT
ejpam-5027	289	7	δ2	δ2	PROPN
ejpam-5027	289	8	)	)	PUNCT
ejpam-5027	289	9	is	be	AUX
ejpam-5027	289	10	fbts	fbt	NOUN
ejpam-5027	289	11	.	.	PUNCT
ejpam-5027	290	1	so	so	ADV
ejpam-5027	290	2	x	x	X
ejpam-5027	290	3	is	be	AUX
ejpam-5027	290	4	fuzzy	fuzzy	ADJ
ejpam-5027	290	5	(	(	PUNCT
ejpam-5027	290	6	i	i	PROPN
ejpam-5027	290	7	,	,	PUNCT
ejpam-5027	290	8	j	j	PROPN
ejpam-5027	290	9	)	)	PUNCT
ejpam-5027	290	10	−	−	PROPN
ejpam-5027	291	1	gφ−compact	gφ−compact	PROPN
ejpam-5027	291	2	⇔	⇔	X
ejpam-5027	291	3	∀	∀	X
ejpam-5027	291	4	{	{	PUNCT
ejpam-5027	291	5	fi	fi	NOUN
ejpam-5027	291	6	}	}	PUNCT
ejpam-5027	291	7	of	of	ADP
ejpam-5027	291	8	fuzzy	fuzzy	ADJ
ejpam-5027	291	9	(	(	PUNCT
ejpam-5027	291	10	i	i	PROPN
ejpam-5027	291	11	,	,	PUNCT
ejpam-5027	291	12	j	j	PROPN
ejpam-5027	291	13	)	)	PUNCT
ejpam-5027	291	14	−	−	PROPN
ejpam-5027	292	1	gφ−cld	gφ−cld	NOUN
ejpam-5027	292	2	sets	set	VERB
ejpam-5027	292	3	of	of	ADP
ejpam-5027	292	4	x	x	PUNCT
ejpam-5027	292	5	satisfying	satisfy	VERB
ejpam-5027	292	6	f.i.p	f.i.p	ADJ
ejpam-5027	292	7	(	(	PUNCT
ejpam-5027	292	8	definition	definition	NOUN
ejpam-5027	292	9	9	9	NUM
ejpam-5027	292	10	)	)	PUNCT
ejpam-5027	292	11	has	have	VERB
ejpam-5027	292	12	itself	itself	PRON
ejpam-5027	292	13	a	a	DET
ejpam-5027	292	14	non	non	X
ejpam-5027	292	15	empty	empty	ADJ
ejpam-5027	292	16	intersection	intersection	NOUN
ejpam-5027	292	17	.	.	PUNCT
ejpam-5027	293	1	proof	proof	NOUN
ejpam-5027	293	2	.	.	PUNCT
ejpam-5027	294	1	suppose	suppose	VERB
ejpam-5027	294	2	(	(	PUNCT
ejpam-5027	294	3	x	x	NOUN
ejpam-5027	294	4	,	,	PUNCT
ejpam-5027	294	5	δ1	δ1	NOUN
ejpam-5027	294	6	,	,	PUNCT
ejpam-5027	294	7	δ2	δ2	PROPN
ejpam-5027	294	8	)	)	PUNCT
ejpam-5027	294	9	is	be	AUX
ejpam-5027	294	10	fuzzy	fuzzy	ADJ
ejpam-5027	294	11	(	(	PUNCT
ejpam-5027	294	12	i	i	PROPN
ejpam-5027	294	13	,	,	PUNCT
ejpam-5027	294	14	j	j	PROPN
ejpam-5027	294	15	)	)	PUNCT
ejpam-5027	295	1	−	−	PROPN
ejpam-5027	295	2	gφ−compact	gφ−compact	PROPN
ejpam-5027	295	3	,	,	PUNCT
ejpam-5027	295	4	{	{	PUNCT
ejpam-5027	295	5	fi	fi	NOUN
ejpam-5027	295	6	:	:	PUNCT
ejpam-5027	295	7	i	i	PRON
ejpam-5027	295	8	∈	∈	VERB
ejpam-5027	296	1	i	i	PRON
ejpam-5027	296	2	}	}	PUNCT
ejpam-5027	296	3	is	be	AUX
ejpam-5027	296	4	fuzzy	fuzzy	ADJ
ejpam-5027	296	5	(	(	PUNCT
ejpam-5027	296	6	i	i	PROPN
ejpam-5027	296	7	,	,	PUNCT
ejpam-5027	296	8	j	j	PROPN
ejpam-5027	296	9	)	)	PUNCT
ejpam-5027	296	10	−	−	PROPN
ejpam-5027	297	1	gφ−cld	gφ−cld	NOUN
ejpam-5027	297	2	sets	set	VERB
ejpam-5027	297	3	of	of	ADP
ejpam-5027	297	4	x	x	PUNCT
ejpam-5027	297	5	satisfying	satisfy	VERB
ejpam-5027	297	6	f.i.p	f.i.p	ADV
ejpam-5027	297	7	,	,	PUNCT
ejpam-5027	297	8	and	and	CCONJ
ejpam-5027	297	9	∩{fi	∩{fi	PROPN
ejpam-5027	297	10	:	:	PUNCT
ejpam-5027	298	1	i	i	PRON
ejpam-5027	298	2	∈	∈	VERB
ejpam-5027	298	3	i	i	PRON
ejpam-5027	298	4	}	}	PUNCT
ejpam-5027	298	5	=	=	PUNCT
ejpam-5027	298	6	ϕ.	ϕ.	NOUN
ejpam-5027	298	7	then	then	ADV
ejpam-5027	298	8	x	x	X
ejpam-5027	298	9	=	=	PUNCT
ejpam-5027	299	1	∪{fi	∪{fi	NOUN
ejpam-5027	299	2	c	c	NOUN
ejpam-5027	299	3	:	:	PUNCT
ejpam-5027	299	4	i	i	PRON
ejpam-5027	299	5	∈	∈	VERB
ejpam-5027	299	6	i	i	PRON
ejpam-5027	299	7	}	}	PUNCT
ejpam-5027	299	8	.	.	PUNCT
ejpam-5027	300	1	let	let	VERB
ejpam-5027	300	2	u	u	PRON
ejpam-5027	300	3	=	=	PUNCT
ejpam-5027	300	4	(	(	PUNCT
ejpam-5027	300	5	fi	fi	NOUN
ejpam-5027	300	6	c	c	X
ejpam-5027	300	7	)	)	PUNCT
ejpam-5027	300	8	is	be	AUX
ejpam-5027	300	9	fuzzy	fuzzy	ADJ
ejpam-5027	300	10	(	(	PUNCT
ejpam-5027	300	11	i	i	PROPN
ejpam-5027	300	12	,	,	PUNCT
ejpam-5027	300	13	j)−	j)−	PROPN
ejpam-5027	300	14	gφ−open	gφ−open	NOUN
ejpam-5027	300	15	cover	cover	NOUN
ejpam-5027	300	16	for	for	ADP
ejpam-5027	300	17	x.	x.	NOUN
ejpam-5027	300	18	as	as	SCONJ
ejpam-5027	300	19	x	x	PRON
ejpam-5027	300	20	is	be	AUX
ejpam-5027	300	21	fuzzy	fuzzy	ADJ
ejpam-5027	300	22	(	(	PUNCT
ejpam-5027	300	23	i	i	PROPN
ejpam-5027	300	24	,	,	PUNCT
ejpam-5027	300	25	j)−	j)−	PROPN
ejpam-5027	300	26	gφ−compact	gφ−compact	PROPN
ejpam-5027	300	27	,	,	PUNCT
ejpam-5027	300	28	then	then	ADV
ejpam-5027	300	29	u	u	NOUN
ejpam-5027	300	30	most	most	ADV
ejpam-5027	300	31	contain	contain	VERB
ejpam-5027	300	32	finite	finite	PROPN
ejpam-5027	300	33	subcover	subcover	PROPN
ejpam-5027	300	34	of	of	ADP
ejpam-5027	300	35	x	x	PROPN
ejpam-5027	300	36	and	and	CCONJ
ejpam-5027	300	37	x	x	SYM
ejpam-5027	300	38	=	=	SYM
ejpam-5027	300	39	(	(	PUNCT
ejpam-5027	300	40	∩n	∩n	NOUN
ejpam-5027	300	41	j=1fij	j=1fij	PROPN
ejpam-5027	300	42	)	)	PUNCT
ejpam-5027	301	1	c	c	X
ejpam-5027	301	2	,	,	PUNCT
ejpam-5027	301	3	which	which	PRON
ejpam-5027	301	4	implies	imply	VERB
ejpam-5027	301	5	∩n	∩n	PROPN
ejpam-5027	301	6	j=1fij	j=1fij	PROPN
ejpam-5027	301	7	=	=	PUNCT
ejpam-5027	301	8	ϕ.	ϕ.	NOUN
ejpam-5027	301	9	this	this	PRON
ejpam-5027	301	10	runs	run	VERB
ejpam-5027	301	11	counter	counter	ADV
ejpam-5027	301	12	to	to	ADP
ejpam-5027	301	13	the	the	DET
ejpam-5027	301	14	hypothesis	hypothesis	NOUN
ejpam-5027	301	15	that	that	DET
ejpam-5027	301	16	fi	fi	NOUN
ejpam-5027	301	17	has	have	VERB
ejpam-5027	301	18	f.i.p	f.i.p	ADV
ejpam-5027	301	19	.	.	PUNCT
ejpam-5027	302	1	conversely	conversely	ADV
ejpam-5027	302	2	,	,	PUNCT
ejpam-5027	302	3	assume	assume	VERB
ejpam-5027	302	4	x	x	PRON
ejpam-5027	302	5	is	be	AUX
ejpam-5027	302	6	not	not	PART
ejpam-5027	302	7	compact	compact	ADJ
ejpam-5027	302	8	and	and	CCONJ
ejpam-5027	302	9	∩	∩	ADJ
ejpam-5027	302	10	{	{	PUNCT
ejpam-5027	302	11	fi	fi	NOUN
ejpam-5027	302	12	:	:	PUNCT
ejpam-5027	302	13	i	i	PRON
ejpam-5027	302	14	∈	∈	VERB
ejpam-5027	302	15	i	i	PRON
ejpam-5027	302	16	}	}	PUNCT
ejpam-5027	302	17	=	=	PROPN
ejpam-5027	302	18	̸	̸	NUM
ejpam-5027	303	1	ϕ	ϕ	NOUN
ejpam-5027	303	2	,	,	PUNCT
ejpam-5027	303	3	where	where	SCONJ
ejpam-5027	303	4	{	{	PUNCT
ejpam-5027	303	5	fi	fi	NOUN
ejpam-5027	303	6	}	}	PUNCT
ejpam-5027	303	7	is	be	AUX
ejpam-5027	303	8	collection	collection	NOUN
ejpam-5027	303	9	of	of	ADP
ejpam-5027	303	10	fuzzy	fuzzy	ADJ
ejpam-5027	303	11	(	(	PUNCT
ejpam-5027	303	12	i	i	NOUN
ejpam-5027	303	13	,	,	PUNCT
ejpam-5027	303	14	j)−	j)−	PROPN
ejpam-5027	303	15	gφ−cld	gφ−cld	PROPN
ejpam-5027	303	16	subsets	subset	NOUN
ejpam-5027	303	17	at	at	ADP
ejpam-5027	303	18	x	x	PROPN
ejpam-5027	303	19	has	have	VERB
ejpam-5027	303	20	f.i.p	f.i.p	ADJ
ejpam-5027	303	21	.	.	PUNCT
ejpam-5027	304	1	then	then	ADV
ejpam-5027	304	2	∃	∃	PROPN
ejpam-5027	304	3	u	u	PROPN
ejpam-5027	304	4	=	=	PUNCT
ejpam-5027	304	5	{	{	PUNCT
ejpam-5027	304	6	gi	gi	INTJ
ejpam-5027	304	7	:	:	PUNCT
ejpam-5027	304	8	i	i	PRON
ejpam-5027	304	9	∈	∈	VERB
ejpam-5027	305	1	i	i	PRON
ejpam-5027	305	2	}	}	PUNCT
ejpam-5027	305	3	is	be	AUX
ejpam-5027	305	4	(	(	PUNCT
ejpam-5027	305	5	i	i	PROPN
ejpam-5027	305	6	,	,	PUNCT
ejpam-5027	305	7	j)−	j)−	PROPN
ejpam-5027	305	8	gφ−open	gφ−open	NOUN
ejpam-5027	305	9	cover	cover	NOUN
ejpam-5027	305	10	for	for	ADP
ejpam-5027	305	11	x	x	X
ejpam-5027	305	12	,	,	PUNCT
ejpam-5027	305	13	that	that	PRON
ejpam-5027	305	14	is	be	AUX
ejpam-5027	305	15	lacking	lack	VERB
ejpam-5027	305	16	finite	finite	PROPN
ejpam-5027	305	17	subcover	subcover	PROPN
ejpam-5027	305	18	of	of	ADP
ejpam-5027	305	19	x	x	PRON
ejpam-5027	305	20	,	,	PUNCT
ejpam-5027	305	21	then	then	ADV
ejpam-5027	305	22	{	{	PUNCT
ejpam-5027	305	23	x	x	PROPN
ejpam-5027	305	24	−gi1	−gi1	PROPN
ejpam-5027	305	25	,	,	PUNCT
ejpam-5027	305	26	x	x	PROPN
ejpam-5027	305	27	−gi2	−gi2	NOUN
ejpam-5027	305	28	,	,	PUNCT
ejpam-5027	305	29	...	...	PUNCT
ejpam-5027	305	30	,	,	PUNCT
ejpam-5027	305	31	x	x	PRON
ejpam-5027	305	32	−gin	−gin	ADV
ejpam-5027	305	33	}	}	PUNCT
ejpam-5027	305	34	is	be	AUX
ejpam-5027	305	35	a	a	DET
ejpam-5027	305	36	class	class	NOUN
ejpam-5027	305	37	of	of	ADP
ejpam-5027	305	38	(	(	PUNCT
ejpam-5027	305	39	i	i	PROPN
ejpam-5027	305	40	,	,	PUNCT
ejpam-5027	305	41	j	j	PROPN
ejpam-5027	305	42	)	)	PUNCT
ejpam-5027	305	43	−	−	PROPN
ejpam-5027	305	44	gφ−cld	gφ−cld	NOUN
ejpam-5027	305	45	sets	set	NOUN
ejpam-5027	305	46	has	have	VERB
ejpam-5027	305	47	f.i.p	f.i.p	ADV
ejpam-5027	305	48	,	,	PUNCT
ejpam-5027	305	49	and	and	CCONJ
ejpam-5027	305	50	hence	hence	ADV
ejpam-5027	305	51	∩	∩	X
ejpam-5027	305	52	{	{	PUNCT
ejpam-5027	305	53	x	x	X
ejpam-5027	305	54	−	−	PROPN
ejpam-5027	305	55	gi	gi	NOUN
ejpam-5027	305	56	}	}	PUNCT
ejpam-5027	305	57	=	=	PUNCT
ejpam-5027	305	58	x	x	ADP
ejpam-5027	305	59	−	−	NOUN
ejpam-5027	305	60	∪	∪	NOUN
ejpam-5027	305	61	gi	gi	VERB
ejpam-5027	305	62	̸=	̸=	PROPN
ejpam-5027	305	63	ϕ	ϕ	NOUN
ejpam-5027	305	64	,	,	PUNCT
ejpam-5027	305	65	then	then	ADV
ejpam-5027	305	66	x	x	PART
ejpam-5027	305	67	̸=	̸=	PROPN
ejpam-5027	305	68	∪i=1gi	∪i=1gi	PROPN
ejpam-5027	305	69	.	.	PUNCT
ejpam-5027	306	1	the	the	DET
ejpam-5027	306	2	reality	reality	NOUN
ejpam-5027	306	3	that	that	SCONJ
ejpam-5027	306	4	u	u	NOUN
ejpam-5027	306	5	is	be	AUX
ejpam-5027	306	6	a	a	DET
ejpam-5027	306	7	fuzzy	fuzzy	ADJ
ejpam-5027	306	8	(	(	PUNCT
ejpam-5027	306	9	i	i	PROPN
ejpam-5027	306	10	,	,	PUNCT
ejpam-5027	306	11	j)−	j)−	PROPN
ejpam-5027	306	12	gφ−open	gφ−open	NOUN
ejpam-5027	306	13	cover	cover	NOUN
ejpam-5027	306	14	for	for	ADP
ejpam-5027	306	15	x	x	SYM
ejpam-5027	306	16	is	be	AUX
ejpam-5027	306	17	in	in	ADP
ejpam-5027	306	18	conflict	conflict	NOUN
ejpam-5027	306	19	with	with	ADP
ejpam-5027	306	20	this	this	PRON
ejpam-5027	306	21	.	.	PUNCT
ejpam-5027	307	1	references	reference	NOUN
ejpam-5027	307	2	40	40	NUM
ejpam-5027	307	3	5	5	NUM
ejpam-5027	307	4	.	.	PUNCT
ejpam-5027	307	5	conclusion	conclusion	NOUN
ejpam-5027	307	6	and	and	CCONJ
ejpam-5027	307	7	future	future	ADJ
ejpam-5027	307	8	studies	study	NOUN
ejpam-5027	307	9	in	in	ADP
ejpam-5027	307	10	this	this	DET
ejpam-5027	307	11	research	research	NOUN
ejpam-5027	307	12	,	,	PUNCT
ejpam-5027	307	13	we	we	PRON
ejpam-5027	307	14	explore	explore	VERB
ejpam-5027	307	15	the	the	DET
ejpam-5027	307	16	relationships	relationship	NOUN
ejpam-5027	307	17	between	between	ADP
ejpam-5027	307	18	different	different	ADJ
ejpam-5027	307	19	types	type	NOUN
ejpam-5027	307	20	of	of	ADP
ejpam-5027	307	21	generalized	generalized	ADJ
ejpam-5027	307	22	closed	closed	ADJ
ejpam-5027	307	23	sets	set	NOUN
ejpam-5027	307	24	in	in	ADP
ejpam-5027	307	25	a	a	DET
ejpam-5027	307	26	new	new	ADJ
ejpam-5027	307	27	domain	domain	NOUN
ejpam-5027	307	28	,	,	PUNCT
ejpam-5027	307	29	which	which	PRON
ejpam-5027	307	30	is	be	AUX
ejpam-5027	307	31	a	a	DET
ejpam-5027	307	32	fuzzy	fuzzy	ADJ
ejpam-5027	307	33	bitopological	bitopological	ADJ
ejpam-5027	307	34	space	space	NOUN
ejpam-5027	307	35	.	.	PUNCT
ejpam-5027	308	1	in	in	ADP
ejpam-5027	308	2	addition	addition	NOUN
ejpam-5027	308	3	,	,	PUNCT
ejpam-5027	308	4	we	we	PRON
ejpam-5027	308	5	explored	explore	VERB
ejpam-5027	308	6	the	the	DET
ejpam-5027	308	7	interconnections	interconnection	NOUN
ejpam-5027	308	8	between	between	ADP
ejpam-5027	308	9	these	these	DET
ejpam-5027	308	10	sets	set	NOUN
ejpam-5027	308	11	by	by	ADP
ejpam-5027	308	12	some	some	DET
ejpam-5027	308	13	counterexamples	counterexample	NOUN
ejpam-5027	308	14	.	.	PUNCT
ejpam-5027	309	1	after	after	ADP
ejpam-5027	309	2	that	that	PRON
ejpam-5027	309	3	,	,	PUNCT
ejpam-5027	309	4	we	we	PRON
ejpam-5027	309	5	scrutinize	scrutinize	VERB
ejpam-5027	309	6	the	the	DET
ejpam-5027	309	7	fundamental	fundamental	ADJ
ejpam-5027	309	8	theorems	theorem	NOUN
ejpam-5027	309	9	and	and	CCONJ
ejpam-5027	309	10	distinctive	distinctive	ADJ
ejpam-5027	309	11	characteristics	characteristic	NOUN
ejpam-5027	309	12	associated	associate	VERB
ejpam-5027	309	13	with	with	ADP
ejpam-5027	309	14	these	these	DET
ejpam-5027	309	15	concepts	concept	NOUN
ejpam-5027	309	16	.	.	PUNCT
ejpam-5027	310	1	also	also	ADV
ejpam-5027	310	2	,	,	PUNCT
ejpam-5027	310	3	we	we	PRON
ejpam-5027	310	4	applied	apply	VERB
ejpam-5027	310	5	them	they	PRON
ejpam-5027	310	6	to	to	ADP
ejpam-5027	310	7	fuzzy	fuzzy	ADJ
ejpam-5027	310	8	compactness	compactness	NOUN
ejpam-5027	310	9	and	and	CCONJ
ejpam-5027	310	10	studied	study	VERB
ejpam-5027	310	11	their	their	PRON
ejpam-5027	310	12	theorems	theorem	NOUN
ejpam-5027	310	13	,	,	PUNCT
ejpam-5027	310	14	properties	property	NOUN
ejpam-5027	310	15	,	,	PUNCT
ejpam-5027	310	16	and	and	CCONJ
ejpam-5027	310	17	relationships	relationship	NOUN
ejpam-5027	310	18	.	.	PUNCT
ejpam-5027	311	1	through	through	ADP
ejpam-5027	311	2	this	this	DET
ejpam-5027	311	3	in	in	ADP
ejpam-5027	311	4	-	-	PUNCT
ejpam-5027	311	5	depth	depth	NOUN
ejpam-5027	311	6	analysis	analysis	NOUN
ejpam-5027	311	7	,	,	PUNCT
ejpam-5027	311	8	we	we	PRON
ejpam-5027	311	9	contribute	contribute	VERB
ejpam-5027	311	10	to	to	ADP
ejpam-5027	311	11	a	a	DET
ejpam-5027	311	12	better	well	ADJ
ejpam-5027	311	13	comprehension	comprehension	NOUN
ejpam-5027	311	14	of	of	ADP
ejpam-5027	311	15	these	these	DET
ejpam-5027	311	16	key	key	ADJ
ejpam-5027	311	17	ideas	idea	NOUN
ejpam-5027	311	18	in	in	ADP
ejpam-5027	311	19	the	the	DET
ejpam-5027	311	20	context	context	NOUN
ejpam-5027	311	21	of	of	ADP
ejpam-5027	311	22	fuzzy	fuzzy	ADJ
ejpam-5027	311	23	bitopological	bitopological	ADJ
ejpam-5027	311	24	spaces	space	NOUN
ejpam-5027	311	25	.	.	PUNCT
ejpam-5027	312	1	this	this	DET
ejpam-5027	312	2	work	work	NOUN
ejpam-5027	312	3	also	also	ADV
ejpam-5027	312	4	opens	open	VERB
ejpam-5027	312	5	up	up	ADP
ejpam-5027	312	6	new	new	ADJ
ejpam-5027	312	7	horizons	horizon	NOUN
ejpam-5027	312	8	for	for	ADP
ejpam-5027	312	9	the	the	DET
ejpam-5027	312	10	future	future	ADJ
ejpam-5027	312	11	study	study	NOUN
ejpam-5027	312	12	of	of	ADP
ejpam-5027	312	13	these	these	DET
ejpam-5027	312	14	sets	set	NOUN
ejpam-5027	312	15	in	in	ADP
ejpam-5027	312	16	other	other	ADJ
ejpam-5027	312	17	fields	field	NOUN
ejpam-5027	312	18	of	of	ADP
ejpam-5027	312	19	fuzzy	fuzzy	ADJ
ejpam-5027	312	20	sets	set	NOUN
ejpam-5027	312	21	,	,	PUNCT
ejpam-5027	312	22	such	such	ADJ
ejpam-5027	312	23	as	as	ADP
ejpam-5027	312	24	regular	regular	ADJ
ejpam-5027	312	25	sets	set	NOUN
ejpam-5027	312	26	,	,	PUNCT
ejpam-5027	312	27	study	study	VERB
ejpam-5027	312	28	them	they	PRON
ejpam-5027	312	29	in	in	ADP
ejpam-5027	312	30	more	more	ADJ
ejpam-5027	312	31	than	than	ADP
ejpam-5027	312	32	two	two	NUM
ejpam-5027	312	33	topologies	topology	NOUN
ejpam-5027	312	34	,	,	PUNCT
ejpam-5027	312	35	or	or	CCONJ
ejpam-5027	312	36	in	in	ADP
ejpam-5027	312	37	another	another	DET
ejpam-5027	312	38	domain	domain	NOUN
ejpam-5027	312	39	,	,	PUNCT
ejpam-5027	312	40	such	such	ADJ
ejpam-5027	312	41	as	as	ADP
ejpam-5027	312	42	fuzzy	fuzzy	ADJ
ejpam-5027	312	43	soft	soft	ADJ
ejpam-5027	312	44	spaces	space	NOUN
ejpam-5027	312	45	.	.	PUNCT
ejpam-5027	313	1	references	reference	NOUN
ejpam-5027	313	2	[	[	X
ejpam-5027	313	3	1	1	NUM
ejpam-5027	313	4	]	]	PUNCT
ejpam-5027	313	5	a.	a.	NOUN
ejpam-5027	313	6	abu	abu	PROPN
ejpam-5027	313	7	safiya	safiya	PROPN
ejpam-5027	313	8	,	,	PUNCT
ejpam-5027	313	9	a.	a.	NOUN
ejpam-5027	313	10	fora	fora	NOUN
ejpam-5027	313	11	and	and	CCONJ
ejpam-5027	313	12	m.	m.	PROPN
ejpam-5027	313	13	warner	warner	PROPN
ejpam-5027	313	14	.	.	PUNCT
ejpam-5027	314	1	compactness	compactness	NOUN
ejpam-5027	314	2	and	and	CCONJ
ejpam-5027	314	3	weakly	weakly	ADV
ejpam-5027	314	4	induced	induced	ADJ
ejpam-5027	314	5	bifuzzy	bifuzzy	ADJ
ejpam-5027	314	6	topological	topological	ADJ
ejpam-5027	314	7	spaces	space	NOUN
ejpam-5027	314	8	.	.	PUNCT
ejpam-5027	315	1	fuzzy	fuzzy	ADJ
ejpam-5027	315	2	sets	set	NOUN
ejpam-5027	315	3	and	and	CCONJ
ejpam-5027	315	4	systems	system	NOUN
ejpam-5027	315	5	,	,	PUNCT
ejpam-5027	315	6	pp	pp	X
ejpam-5027	315	7	.	.	PUNCT
ejpam-5027	316	1	89–96	89–96	NUM
ejpam-5027	316	2	,	,	PUNCT
ejpam-5027	316	3	1994	1994	NUM
ejpam-5027	316	4	.	.	PUNCT
ejpam-5027	317	1	[	[	X
ejpam-5027	317	2	2	2	NUM
ejpam-5027	317	3	]	]	X
ejpam-5027	317	4	b.	b.	PROPN
ejpam-5027	317	5	ahmad	ahmad	PROPN
ejpam-5027	317	6	and	and	CCONJ
ejpam-5027	317	7	athar	athar	PROPN
ejpam-5027	317	8	kharal	kharal	PROPN
ejpam-5027	317	9	.	.	PUNCT
ejpam-5027	318	1	fuzzy	fuzzy	ADJ
ejpam-5027	318	2	sets	set	NOUN
ejpam-5027	318	3	,	,	PUNCT
ejpam-5027	318	4	fuzzy	fuzzy	ADJ
ejpam-5027	318	5	s	s	NOUN
ejpam-5027	318	6	-	-	PUNCT
ejpam-5027	318	7	open	open	ADJ
ejpam-5027	318	8	and	and	CCONJ
ejpam-5027	318	9	s	s	NOUN
ejpam-5027	318	10	-	-	PUNCT
ejpam-5027	318	11	closed	closed	ADJ
ejpam-5027	318	12	mappings	mapping	NOUN
ejpam-5027	318	13	.	.	PUNCT
ejpam-5027	319	1	advances	advance	NOUN
ejpam-5027	319	2	in	in	ADP
ejpam-5027	319	3	fuzzy	fuzzy	ADJ
ejpam-5027	319	4	systems	system	NOUN
ejpam-5027	319	5	,	,	PUNCT
ejpam-5027	319	6	article	article	NOUN
ejpam-5027	319	7	i	i	PROPN
ejpam-5027	319	8	d	d	PROPN
ejpam-5027	319	9	303042	303042	NUM
ejpam-5027	319	10	,	,	PUNCT
ejpam-5027	319	11	5	5	NUM
ejpam-5027	319	12	pages	page	NOUN
ejpam-5027	319	13	,	,	PUNCT
ejpam-5027	319	14	2009	2009	NUM
ejpam-5027	319	15	.	.	PUNCT
ejpam-5027	320	1	[	[	X
ejpam-5027	320	2	3	3	NUM
ejpam-5027	320	3	]	]	PUNCT
ejpam-5027	320	4	a.	a.	NOUN
ejpam-5027	320	5	alharbi	alharbi	PROPN
ejpam-5027	320	6	and	and	CCONJ
ejpam-5027	320	7	a.	a.	NOUN
ejpam-5027	320	8	kilicman	kilicman	PROPN
ejpam-5027	320	9	.	.	PUNCT
ejpam-5027	321	1	generalized	generalized	ADJ
ejpam-5027	321	2	connectedness	connectedness	NOUN
ejpam-5027	321	3	in	in	ADP
ejpam-5027	321	4	fuzzy	fuzzy	ADJ
ejpam-5027	321	5	bitopological	bitopological	ADJ
ejpam-5027	321	6	spaces.applied	spaces.applie	VERB
ejpam-5027	321	7	mathematics	mathematic	NOUN
ejpam-5027	321	8	and	and	CCONJ
ejpam-5027	321	9	information	information	NOUN
ejpam-5027	321	10	sciences	science	NOUN
ejpam-5027	321	11	,	,	PUNCT
ejpam-5027	321	12	pp	pp	ADP
ejpam-5027	321	13	.	.	PUNCT
ejpam-5027	321	14	1019–1023	1019–1023	NUM
ejpam-5027	321	15	,	,	PUNCT
ejpam-5027	321	16	2023	2023	NUM
ejpam-5027	321	17	.	.	PUNCT
ejpam-5027	322	1	[	[	X
ejpam-5027	322	2	4	4	NUM
ejpam-5027	322	3	]	]	PUNCT
ejpam-5027	322	4	a.	a.	NOUN
ejpam-5027	322	5	alharbi	alharbi	PROPN
ejpam-5027	322	6	and	and	CCONJ
ejpam-5027	322	7	a.	a.	NOUN
ejpam-5027	322	8	kilicman	kilicman	PROPN
ejpam-5027	322	9	.	.	PUNCT
ejpam-5027	323	1	note	note	NOUN
ejpam-5027	323	2	on	on	ADP
ejpam-5027	323	3	generalized	generalized	ADJ
ejpam-5027	323	4	neighborhoods	neighborhood	NOUN
ejpam-5027	323	5	structures	structure	NOUN
ejpam-5027	323	6	in	in	ADP
ejpam-5027	323	7	fuzzy	fuzzy	ADJ
ejpam-5027	323	8	bitopological	bitopological	ADJ
ejpam-5027	323	9	spaces	space	NOUN
ejpam-5027	323	10	.	.	PUNCT
ejpam-5027	324	1	european	european	ADJ
ejpam-5027	324	2	journal	journal	PROPN
ejpam-5027	324	3	of	of	ADP
ejpam-5027	324	4	pure	pure	ADJ
ejpam-5027	324	5	and	and	CCONJ
ejpam-5027	324	6	applied	applied	ADJ
ejpam-5027	324	7	mathematics	mathematic	NOUN
ejpam-5027	324	8	,	,	PUNCT
ejpam-5027	324	9	pp	pp	ADJ
ejpam-5027	324	10	.	.	PUNCT
ejpam-5027	324	11	1980	1980	NUM
ejpam-5027	324	12	–	–	PUNCT
ejpam-5027	324	13	1990	1990	NUM
ejpam-5027	324	14	,	,	PUNCT
ejpam-5027	324	15	2023	2023	NUM
ejpam-5027	324	16	.	.	PUNCT
ejpam-5027	325	1	[	[	X
ejpam-5027	325	2	5	5	NUM
ejpam-5027	325	3	]	]	PUNCT
ejpam-5027	325	4	a.	a.	NOUN
ejpam-5027	325	5	alharbi	alharbi	PROPN
ejpam-5027	325	6	and	and	CCONJ
ejpam-5027	325	7	a.	a.	NOUN
ejpam-5027	325	8	kilicman	kilicman	PROPN
ejpam-5027	325	9	.	.	PUNCT
ejpam-5027	326	1	generalized	generalize	VERB
ejpam-5027	326	2	different	different	ADJ
ejpam-5027	326	3	types	type	NOUN
ejpam-5027	326	4	of	of	ADP
ejpam-5027	326	5	mappings	mapping	NOUN
ejpam-5027	326	6	in	in	ADP
ejpam-5027	326	7	fuzzy	fuzzy	ADJ
ejpam-5027	326	8	bitopological	bitopological	ADJ
ejpam-5027	326	9	spaces	space	NOUN
ejpam-5027	326	10	.	.	PUNCT
ejpam-5027	327	1	european	european	ADJ
ejpam-5027	327	2	journal	journal	PROPN
ejpam-5027	327	3	of	of	ADP
ejpam-5027	327	4	pure	pure	ADJ
ejpam-5027	327	5	and	and	CCONJ
ejpam-5027	327	6	applied	applied	ADJ
ejpam-5027	327	7	mathematics	mathematic	NOUN
ejpam-5027	327	8	,	,	PUNCT
ejpam-5027	327	9	pp	pp	ADJ
ejpam-5027	327	10	.	.	PUNCT
ejpam-5027	327	11	26132631	26132631	NUM
ejpam-5027	327	12	,	,	PUNCT
ejpam-5027	327	13	2023	2023	NUM
ejpam-5027	327	14	.	.	PUNCT
ejpam-5027	328	1	[	[	X
ejpam-5027	328	2	6	6	NUM
ejpam-5027	328	3	]	]	X
ejpam-5027	328	4	g.	g.	PROPN
ejpam-5027	328	5	balasubramanian	balasubramanian	PROPN
ejpam-5027	328	6	.	.	PUNCT
ejpam-5027	329	1	fuzzy	fuzzy	ADJ
ejpam-5027	329	2	β−open	β−open	PUNCT
ejpam-5027	329	3	sets	set	NOUN
ejpam-5027	329	4	and	and	CCONJ
ejpam-5027	329	5	fuzzy	fuzzy	ADJ
ejpam-5027	329	6	β−separation	β−separation	NOUN
ejpam-5027	329	7	axioms	axiom	NOUN
ejpam-5027	329	8	.	.	PUNCT
ejpam-5027	330	1	kybernetika	kybernetika	NOUN
ejpam-5027	330	2	,	,	PUNCT
ejpam-5027	330	3	vol	vol	NOUN
ejpam-5027	330	4	.	.	PROPN
ejpam-5027	330	5	35	35	NUM
ejpam-5027	330	6	,	,	PUNCT
ejpam-5027	330	7	pp	pp	ADJ
ejpam-5027	330	8	.	.	PUNCT
ejpam-5027	331	1	215–223	215–223	NUM
ejpam-5027	331	2	,	,	PUNCT
ejpam-5027	331	3	1999	1999	NUM
ejpam-5027	331	4	.	.	PUNCT
ejpam-5027	332	1	[	[	X
ejpam-5027	332	2	7	7	X
ejpam-5027	332	3	]	]	X
ejpam-5027	332	4	g.	g.	PROPN
ejpam-5027	332	5	balasubramanian	balasubramanian	PROPN
ejpam-5027	332	6	and	and	CCONJ
ejpam-5027	332	7	p.	p.	PROPN
ejpam-5027	332	8	sundaram	sundaram	PROPN
ejpam-5027	332	9	.	.	PUNCT
ejpam-5027	333	1	on	on	ADP
ejpam-5027	333	2	some	some	DET
ejpam-5027	333	3	generalizations	generalization	NOUN
ejpam-5027	333	4	of	of	ADP
ejpam-5027	333	5	fuzzy	fuzzy	ADJ
ejpam-5027	333	6	continuous	continuous	ADJ
ejpam-5027	333	7	functions	function	NOUN
ejpam-5027	333	8	.	.	PUNCT
ejpam-5027	334	1	fuzzy	fuzzy	ADJ
ejpam-5027	334	2	sets	set	NOUN
ejpam-5027	334	3	and	and	CCONJ
ejpam-5027	334	4	systems	system	NOUN
ejpam-5027	334	5	,	,	PUNCT
ejpam-5027	334	6	pp	pp	ADV
ejpam-5027	334	7	.	.	PUNCT
ejpam-5027	335	1	93–100	93–100	NUM
ejpam-5027	335	2	,	,	PUNCT
ejpam-5027	335	3	1997	1997	NUM
ejpam-5027	335	4	.	.	PUNCT
ejpam-5027	336	1	[	[	X
ejpam-5027	336	2	8	8	NUM
ejpam-5027	336	3	]	]	X
ejpam-5027	336	4	y.	y.	NOUN
ejpam-5027	336	5	beceren	beceren	PROPN
ejpam-5027	336	6	and	and	CCONJ
ejpam-5027	336	7	t.	t.	PROPN
ejpam-5027	336	8	noiri	noiri	PROPN
ejpam-5027	336	9	.	.	PUNCT
ejpam-5027	337	1	some	some	DET
ejpam-5027	337	2	functions	function	NOUN
ejpam-5027	337	3	defined	define	VERB
ejpam-5027	337	4	by	by	ADP
ejpam-5027	337	5	semi−open	semi−open	ADJ
ejpam-5027	337	6	and	and	CCONJ
ejpam-5027	337	7	β−open	β−open	PUNCT
ejpam-5027	337	8	sets	set	NOUN
ejpam-5027	337	9	.	.	PUNCT
ejpam-5027	338	1	chaos	chaos	NOUN
ejpam-5027	338	2	,	,	PUNCT
ejpam-5027	338	3	solitons	soliton	NOUN
ejpam-5027	338	4	and	and	CCONJ
ejpam-5027	338	5	fractals	fractal	NOUN
ejpam-5027	338	6	,	,	PUNCT
ejpam-5027	338	7	pp	pp	NUM
ejpam-5027	338	8	.	.	PUNCT
ejpam-5027	338	9	1225–1231	1225–1231	NUM
ejpam-5027	338	10	,	,	PUNCT
ejpam-5027	338	11	2008	2008	NUM
ejpam-5027	338	12	.	.	PUNCT
ejpam-5027	339	1	[	[	X
ejpam-5027	339	2	9	9	NUM
ejpam-5027	339	3	]	]	PUNCT
ejpam-5027	339	4	c.	c.	PROPN
ejpam-5027	339	5	chang	chang	PROPN
ejpam-5027	339	6	.	.	PUNCT
ejpam-5027	340	1	fuzzy	fuzzy	ADJ
ejpam-5027	340	2	topological	topological	ADJ
ejpam-5027	340	3	spaces	space	NOUN
ejpam-5027	340	4	.	.	PUNCT
ejpam-5027	341	1	j.	j.	PROPN
ejpam-5027	341	2	math	math	PROPN
ejpam-5027	341	3	.	.	PUNCT
ejpam-5027	342	1	anal	anal	ADJ
ejpam-5027	342	2	appl	appl	PROPN
ejpam-5027	342	3	,	,	PUNCT
ejpam-5027	342	4	pp	pp	X
ejpam-5027	342	5	.	.	PUNCT
ejpam-5027	343	1	182–190	182–190	NUM
ejpam-5027	343	2	,	,	PUNCT
ejpam-5027	343	3	1968	1968	NUM
ejpam-5027	343	4	.	.	PUNCT
ejpam-5027	344	1	[	[	X
ejpam-5027	344	2	10	10	NUM
ejpam-5027	344	3	]	]	PUNCT
ejpam-5027	344	4	m.	m.	NOUN
ejpam-5027	344	5	el	el	PROPN
ejpam-5027	344	6	-	-	PUNCT
ejpam-5027	344	7	shafei	shafei	NOUN
ejpam-5027	344	8	.	.	PUNCT
ejpam-5027	345	1	some	some	DET
ejpam-5027	345	2	applications	application	NOUN
ejpam-5027	345	3	of	of	ADP
ejpam-5027	345	4	generalized	generalized	ADJ
ejpam-5027	345	5	closed	closed	ADJ
ejpam-5027	345	6	sets	set	NOUN
ejpam-5027	345	7	in	in	ADP
ejpam-5027	345	8	fuzzy	fuzzy	ADJ
ejpam-5027	345	9	topological	topological	ADJ
ejpam-5027	345	10	spaces	space	NOUN
ejpam-5027	345	11	.	.	PUNCT
ejpam-5027	346	1	kyngpook	kyngpook	NOUN
ejpam-5027	346	2	math	math	NOUN
ejpam-5027	346	3	,	,	PUNCT
ejpam-5027	346	4	pp	pp	ADJ
ejpam-5027	346	5	.	.	PUNCT
ejpam-5027	347	1	13–19	13–19	NUM
ejpam-5027	347	2	,	,	PUNCT
ejpam-5027	347	3	2005	2005	NUM
ejpam-5027	347	4	.	.	PUNCT
ejpam-5027	348	1	[	[	X
ejpam-5027	348	2	11	11	NUM
ejpam-5027	348	3	]	]	PUNCT
ejpam-5027	348	4	a.	a.	NOUN
ejpam-5027	348	5	kandil	kandil	PROPN
ejpam-5027	348	6	.	.	PUNCT
ejpam-5027	349	1	biproximities	biproximitie	NOUN
ejpam-5027	349	2	and	and	CCONJ
ejpam-5027	349	3	fuzzy	fuzzy	ADJ
ejpam-5027	349	4	bitopological	bitopological	ADJ
ejpam-5027	349	5	spaces	space	NOUN
ejpam-5027	349	6	.	.	PUNCT
ejpam-5027	350	1	simon	simon	PROPN
ejpam-5027	350	2	stevin	stevin	PROPN
ejpam-5027	350	3	,	,	PUNCT
ejpam-5027	350	4	pp	pp	PROPN
ejpam-5027	350	5	.	.	PUNCT
ejpam-5027	351	1	45	45	NUM
ejpam-5027	351	2	-	-	SYM
ejpam-5027	351	3	66	66	NUM
ejpam-5027	351	4	,	,	PUNCT
ejpam-5027	351	5	1989	1989	NUM
ejpam-5027	351	6	.	.	PUNCT
ejpam-5027	352	1	references	reference	NOUN
ejpam-5027	352	2	41	41	NUM
ejpam-5027	353	1	[	[	X
ejpam-5027	353	2	12	12	NUM
ejpam-5027	353	3	]	]	PUNCT
ejpam-5027	353	4	a.	a.	PROPN
ejpam-5027	353	5	d.	d.	PROPN
ejpam-5027	353	6	kusumaningati	kusumaningati	PROPN
ejpam-5027	353	7	,	,	PUNCT
ejpam-5027	353	8	and	and	CCONJ
ejpam-5027	353	9	m.	m.	NOUN
ejpam-5027	353	10	jakfar	jakfar	PROPN
ejpam-5027	353	11	,	,	PUNCT
ejpam-5027	353	12	properties	property	NOUN
ejpam-5027	353	13	of	of	ADP
ejpam-5027	353	14	compact	compact	ADJ
ejpam-5027	353	15	set	set	NOUN
ejpam-5027	353	16	in	in	ADP
ejpam-5027	353	17	g	g	NOUN
ejpam-5027	353	18	-	-	PUNCT
ejpam-5027	353	19	metric	metric	ADJ
ejpam-5027	353	20	space	space	NOUN
ejpam-5027	353	21	.	.	PUNCT
ejpam-5027	354	1	international	international	ADJ
ejpam-5027	354	2	journal	journal	PROPN
ejpam-5027	354	3	of	of	ADP
ejpam-5027	354	4	research	research	NOUN
ejpam-5027	354	5	in	in	ADP
ejpam-5027	354	6	engineering	engineering	NOUN
ejpam-5027	354	7	,	,	PUNCT
ejpam-5027	354	8	science	science	NOUN
ejpam-5027	354	9	and	and	CCONJ
ejpam-5027	354	10	management	management	NOUN
ejpam-5027	354	11	,	,	PUNCT
ejpam-5027	354	12	6(9	6(9	NUM
ejpam-5027	354	13	)	)	PUNCT
ejpam-5027	354	14	,	,	PUNCT
ejpam-5027	354	15	pp	pp	ADP
ejpam-5027	354	16	.	.	PUNCT
ejpam-5027	355	1	1–8	1–8	NUM
ejpam-5027	355	2	,	,	PUNCT
ejpam-5027	355	3	2023	2023	NUM
ejpam-5027	355	4	.	.	PUNCT
ejpam-5027	356	1	[	[	X
ejpam-5027	356	2	13	13	NUM
ejpam-5027	356	3	]	]	PUNCT
ejpam-5027	356	4	a.	a.	NOUN
ejpam-5027	356	5	mashhour	mashhour	PROPN
ejpam-5027	356	6	,	,	PUNCT
ejpam-5027	356	7	a.	a.	PROPN
ejpam-5027	356	8	allam	allam	PROPN
ejpam-5027	356	9	and	and	CCONJ
ejpam-5027	356	10	a.	a.	NOUN
ejpam-5027	356	11	zahran	zahran	NOUN
ejpam-5027	356	12	.	.	PUNCT
ejpam-5027	357	1	fuzzy	fuzzy	ADJ
ejpam-5027	357	2	g−continuous	g−continuous	ADJ
ejpam-5027	357	3	and	and	CCONJ
ejpam-5027	357	4	fuzzy	fuzzy	ADJ
ejpam-5027	357	5	g−open	g−open	NOUN
ejpam-5027	357	6	mapping	mapping	NOUN
ejpam-5027	357	7	.	.	PUNCT
ejpam-5027	358	1	bulletin	bulletin	NOUN
ejpam-5027	358	2	.	.	PUNCT
ejpam-5027	359	1	assiut	assiut	PROPN
ejpam-5027	359	2	university	university	PROPN
ejpam-5027	359	3	,	,	PUNCT
ejpam-5027	359	4	pp	pp	ADV
ejpam-5027	359	5	.	.	PUNCT
ejpam-5027	360	1	93–106	93–106	NUM
ejpam-5027	360	2	,	,	PUNCT
ejpam-5027	360	3	1985	1985	NUM
ejpam-5027	360	4	.	.	PUNCT
ejpam-5027	361	1	[	[	X
ejpam-5027	361	2	14	14	NUM
ejpam-5027	361	3	]	]	X
ejpam-5027	361	4	n.	n.	PROPN
ejpam-5027	361	5	nakajima	nakajima	PROPN
ejpam-5027	361	6	.	.	PROPN
ejpam-5027	361	7	generalized	generalize	VERB
ejpam-5027	361	8	fuzzy	fuzzy	ADJ
ejpam-5027	361	9	sets	set	NOUN
ejpam-5027	361	10	.	.	PUNCT
ejpam-5027	362	1	fuzzy	fuzzy	ADJ
ejpam-5027	362	2	sets	set	NOUN
ejpam-5027	362	3	and	and	CCONJ
ejpam-5027	362	4	systems	system	NOUN
ejpam-5027	362	5	,	,	PUNCT
ejpam-5027	362	6	pp	pp	ADP
ejpam-5027	362	7	.	.	PUNCT
ejpam-5027	363	1	307–314	307–314	NUM
ejpam-5027	363	2	,	,	PUNCT
ejpam-5027	363	3	1989	1989	NUM
ejpam-5027	363	4	.	.	PUNCT
ejpam-5027	364	1	[	[	X
ejpam-5027	364	2	15	15	NUM
ejpam-5027	364	3	]	]	X
ejpam-5027	364	4	hakeem	hakeem	PROPN
ejpam-5027	364	5	.	.	PUNCT
ejpam-5027	365	1	othman	othman	PROPN
ejpam-5027	365	2	and	and	CCONJ
ejpam-5027	365	3	s.	s.	PROPN
ejpam-5027	365	4	latha	latha	PROPN
ejpam-5027	365	5	.	.	PUNCT
ejpam-5027	366	1	new	new	ADJ
ejpam-5027	366	2	results	result	NOUN
ejpam-5027	366	3	of	of	ADP
ejpam-5027	366	4	fuzzy	fuzzy	ADJ
ejpam-5027	366	5	alpha	alpha	NOUN
ejpam-5027	366	6	-	-	PUNCT
ejpam-5027	366	7	open	open	ADJ
ejpam-5027	366	8	sets	set	VERB
ejpam-5027	366	9	fuzzy	fuzzy	ADJ
ejpam-5027	366	10	alphacontinuous	alphacontinuous	ADJ
ejpam-5027	366	11	mappings	mapping	NOUN
ejpam-5027	366	12	.	.	PUNCT
ejpam-5027	367	1	int	int	NOUN
ejpam-5027	367	2	.	.	PUNCT
ejpam-5027	368	1	j.	j.	PROPN
ejpam-5027	368	2	contemp	contemp	PROPN
ejpam-5027	368	3	.	.	PUNCT
ejpam-5027	369	1	math	math	NOUN
ejpam-5027	369	2	.	.	PUNCT
ejpam-5027	370	1	sciences	science	NOUN
ejpam-5027	370	2	,	,	PUNCT
ejpam-5027	370	3	pp	pp	ADV
ejpam-5027	370	4	.	.	PUNCT
ejpam-5027	370	5	1415–1422	1415–1422	NUM
ejpam-5027	370	6	,	,	PUNCT
ejpam-5027	370	7	2009	2009	NUM
ejpam-5027	370	8	.	.	PUNCT
ejpam-5027	371	1	[	[	X
ejpam-5027	371	2	16	16	NUM
ejpam-5027	371	3	]	]	X
ejpam-5027	371	4	j.	j.	PROPN
ejpam-5027	371	5	oudetallah	oudetallah	PROPN
ejpam-5027	371	6	,	,	PUNCT
ejpam-5027	371	7	r.	r.	PROPN
ejpam-5027	371	8	alharbi	alharbi	PROPN
ejpam-5027	371	9	,	,	PUNCT
ejpam-5027	371	10	and	and	CCONJ
ejpam-5027	371	11	i.	i.	PROPN
ejpam-5027	371	12	m.	m.	PROPN
ejpam-5027	371	13	batiha	batiha	PROPN
ejpam-5027	371	14	.	.	PUNCT
ejpam-5027	372	1	on	on	ADP
ejpam-5027	372	2	r−compactness	r−compactness	PROPN
ejpam-5027	372	3	in	in	ADP
ejpam-5027	372	4	topological	topological	ADJ
ejpam-5027	372	5	and	and	CCONJ
ejpam-5027	372	6	bitopological	bitopological	ADJ
ejpam-5027	372	7	spaces	space	NOUN
ejpam-5027	372	8	.	.	PUNCT
ejpam-5027	373	1	axioms	axiom	NOUN
ejpam-5027	373	2	,	,	PUNCT
ejpam-5027	373	3	12(2	12(2	NUM
ejpam-5027	373	4	)	)	PUNCT
ejpam-5027	373	5	,	,	PUNCT
ejpam-5027	374	1	pp	pp	ADP
ejpam-5027	374	2	.	.	PUNCT
ejpam-5027	375	1	210	210	NUM
ejpam-5027	375	2	,	,	PUNCT
ejpam-5027	375	3	2023	2023	NUM
ejpam-5027	375	4	.	.	PUNCT
ejpam-5027	376	1	[	[	X
ejpam-5027	376	2	17	17	NUM
ejpam-5027	376	3	]	]	X
ejpam-5027	376	4	n.	n.	PROPN
ejpam-5027	376	5	palaniappan	palaniappan	PROPN
ejpam-5027	376	6	.	.	PUNCT
ejpam-5027	376	7	fuzzy	fuzzy	ADJ
ejpam-5027	376	8	topology	topology	NOUN
ejpam-5027	376	9	.	.	PUNCT
ejpam-5027	377	1	alpha	alpha	PROPN
ejpam-5027	377	2	science	science	PROPN
ejpam-5027	377	3	international	international	PROPN
ejpam-5027	377	4	ltd	ltd	PROPN
ejpam-5027	377	5	,	,	PUNCT
ejpam-5027	377	6	pp	pp	X
ejpam-5027	377	7	.	.	PUNCT
ejpam-5027	378	1	1–177	1–177	NUM
ejpam-5027	378	2	,	,	PUNCT
ejpam-5027	378	3	2002	2002	NUM
ejpam-5027	378	4	.	.	PUNCT
ejpam-5027	379	1	[	[	X
ejpam-5027	379	2	18	18	NUM
ejpam-5027	379	3	]	]	X
ejpam-5027	379	4	s.	s.	PROPN
ejpam-5027	379	5	parimala	parimala	PROPN
ejpam-5027	379	6	,	,	PUNCT
ejpam-5027	379	7	b.	b.	PROPN
ejpam-5027	379	8	vijayalakshmi	vijayalakshmi	NOUN
ejpam-5027	379	9	,	,	PUNCT
ejpam-5027	379	10	and	and	CCONJ
ejpam-5027	379	11	v.	v.	ADP
ejpam-5027	379	12	chandrasekar	chandrasekar	NOUN
ejpam-5027	379	13	.	.	PUNCT
ejpam-5027	380	1	on	on	ADP
ejpam-5027	380	2	fuzzy	fuzzy	ADJ
ejpam-5027	380	3	almost	almost	ADV
ejpam-5027	380	4	generalized	generalize	VERB
ejpam-5027	380	5	b	b	X
ejpam-5027	380	6	-	-	PUNCT
ejpam-5027	380	7	continuous	continuous	ADJ
ejpam-5027	380	8	mappings	mapping	NOUN
ejpam-5027	380	9	in	in	ADP
ejpam-5027	380	10	šostak	šostak	NOUN
ejpam-5027	380	11	’s	’s	PART
ejpam-5027	380	12	sense	sense	NOUN
ejpam-5027	380	13	.	.	PUNCT
ejpam-5027	381	1	in	in	ADP
ejpam-5027	381	2	aip	aip	PROPN
ejpam-5027	381	3	conference	conference	NOUN
ejpam-5027	381	4	proceedings	proceeding	NOUN
ejpam-5027	381	5	,	,	PUNCT
ejpam-5027	381	6	vol	vol	NOUN
ejpam-5027	381	7	.	.	PROPN
ejpam-5027	381	8	2177	2177	NUM
ejpam-5027	381	9	,	,	PUNCT
ejpam-5027	381	10	no.1	no.1	NUM
ejpam-5027	381	11	,	,	PUNCT
ejpam-5027	381	12	pp	pp	ADJ
ejpam-5027	381	13	.	.	PUNCT
ejpam-5027	381	14	020106	020106	NUM
ejpam-5027	381	15	,	,	PUNCT
ejpam-5027	381	16	2019	2019	NUM
ejpam-5027	381	17	.	.	PUNCT
ejpam-5027	382	1	[	[	X
ejpam-5027	382	2	19	19	NUM
ejpam-5027	382	3	]	]	SYM
ejpam-5027	382	4	sadanand	sadanand	PROPN
ejpam-5027	382	5	.	.	PROPN
ejpam-5027	382	6	potil	potil	PROPN
ejpam-5027	382	7	,	,	PUNCT
ejpam-5027	382	8	a.	a.	NOUN
ejpam-5027	382	9	madabhavi	madabhavi	PROPN
ejpam-5027	382	10	,	,	PUNCT
ejpam-5027	382	11	s.	s.	PROPN
ejpam-5027	382	12	sadugol	sadugol	PROPN
ejpam-5027	382	13	and	and	CCONJ
ejpam-5027	382	14	g.	g.	PROPN
ejpam-5027	382	15	madagi	madagi	PROPN
ejpam-5027	382	16	.	.	PUNCT
ejpam-5027	383	1	on	on	ADP
ejpam-5027	383	2	fuzzy	fuzzy	ADJ
ejpam-5027	383	3	gµ−closed	gµ−close	VERB
ejpam-5027	383	4	map	map	NOUN
ejpam-5027	383	5	,	,	PUNCT
ejpam-5027	383	6	fuzzy	fuzzy	ADJ
ejpam-5027	383	7	gµ−continuous	gµ−continuous	ADJ
ejpam-5027	383	8	maps	map	NOUN
ejpam-5027	383	9	and	and	CCONJ
ejpam-5027	383	10	fuzzy	fuzzy	ADJ
ejpam-5027	383	11	gµ−irresolute	gµ−irresolute	NOUN
ejpam-5027	383	12	mapgings	mapging	NOUN
ejpam-5027	383	13	in	in	ADP
ejpam-5027	383	14	fuzzy	fuzzy	ADJ
ejpam-5027	383	15	topological	topological	ADJ
ejpam-5027	383	16	spaces	space	NOUN
ejpam-5027	383	17	.	.	PUNCT
ejpam-5027	384	1	conference	conference	NOUN
ejpam-5027	384	2	on	on	ADP
ejpam-5027	384	3	mathematics	mathematic	NOUN
ejpam-5027	384	4	,	,	PUNCT
ejpam-5027	384	5	statistics	statistic	NOUN
ejpam-5027	384	6	and	and	CCONJ
ejpam-5027	384	7	its	its	PRON
ejpam-5027	384	8	application	application	NOUN
ejpam-5027	384	9	,	,	PUNCT
ejpam-5027	384	10	pp	pp	ADJ
ejpam-5027	384	11	.	.	PUNCT
ejpam-5027	385	1	214–227	214–227	NUM
ejpam-5027	385	2	,	,	PUNCT
ejpam-5027	385	3	2010	2010	NUM
ejpam-5027	385	4	.	.	PUNCT
ejpam-5027	386	1	[	[	X
ejpam-5027	386	2	20	20	NUM
ejpam-5027	386	3	]	]	PUNCT
ejpam-5027	386	4	m.	m.	NOUN
ejpam-5027	386	5	k.	k.	PROPN
ejpam-5027	386	6	singal	singal	PROPN
ejpam-5027	386	7	and	and	CCONJ
ejpam-5027	386	8	niti	niti	NOUN
ejpam-5027	386	9	.	.	PUNCT
ejpam-5027	387	1	prakash	prakash	PROPN
ejpam-5027	387	2	.	.	PROPN
ejpam-5027	387	3	fuzzy	fuzzy	ADJ
ejpam-5027	387	4	preopen	preopen	ADJ
ejpam-5027	387	5	sets	set	NOUN
ejpam-5027	387	6	and	and	CCONJ
ejpam-5027	387	7	fuzzy	fuzzy	ADJ
ejpam-5027	387	8	preseparation	preseparation	NOUN
ejpam-5027	387	9	axioms	axiom	NOUN
ejpam-5027	387	10	.	.	PUNCT
ejpam-5027	388	1	fuzzy	fuzzy	ADJ
ejpam-5027	388	2	sets	set	NOUN
ejpam-5027	388	3	and	and	CCONJ
ejpam-5027	388	4	systems	system	NOUN
ejpam-5027	388	5	,	,	PUNCT
ejpam-5027	388	6	pp	pp	ADJ
ejpam-5027	388	7	.	.	PUNCT
ejpam-5027	389	1	273–281	273–281	NUM
ejpam-5027	389	2	,	,	PUNCT
ejpam-5027	389	3	1991	1991	NUM
ejpam-5027	389	4	.	.	PUNCT
ejpam-5027	390	1	[	[	X
ejpam-5027	390	2	21	21	NUM
ejpam-5027	390	3	]	]	X
ejpam-5027	390	4	r.	r.	PROPN
ejpam-5027	390	5	srivastava	srivastava	PROPN
ejpam-5027	390	6	and	and	CCONJ
ejpam-5027	390	7	m.	m.	PROPN
ejpam-5027	390	8	srivastava	srivastava	PROPN
ejpam-5027	390	9	.	.	PUNCT
ejpam-5027	391	1	on	on	ADP
ejpam-5027	391	2	compactness	compactness	NOUN
ejpam-5027	391	3	in	in	ADP
ejpam-5027	391	4	bifuzzy	bifuzzy	PROPN
ejpam-5027	391	5	topological	topological	ADJ
ejpam-5027	391	6	spaces	space	NOUN
ejpam-5027	391	7	.	.	PUNCT
ejpam-5027	392	1	fuzzy	fuzzy	ADJ
ejpam-5027	392	2	sets	set	NOUN
ejpam-5027	392	3	and	and	CCONJ
ejpam-5027	392	4	systems	system	NOUN
ejpam-5027	392	5	,	,	PUNCT
ejpam-5027	392	6	pp	pp	ADV
ejpam-5027	392	7	.	.	PUNCT
ejpam-5027	393	1	285–292	285–292	NUM
ejpam-5027	393	2	,	,	PUNCT
ejpam-5027	393	3	(	(	PUNCT
ejpam-5027	393	4	2001	2001	NUM
ejpam-5027	393	5	)	)	PUNCT
ejpam-5027	393	6	.	.	PUNCT
ejpam-5027	394	1	[	[	X
ejpam-5027	394	2	22	22	NUM
ejpam-5027	394	3	]	]	X
ejpam-5027	394	4	i.	i.	PROPN
ejpam-5027	394	5	taha	taha	PROPN
ejpam-5027	394	6	.	.	PUNCT
ejpam-5027	395	1	compactness	compactness	NOUN
ejpam-5027	395	2	on	on	ADP
ejpam-5027	395	3	fuzzy	fuzzy	ADJ
ejpam-5027	395	4	soft	soft	ADJ
ejpam-5027	395	5	r	r	NOUN
ejpam-5027	395	6	-	-	PUNCT
ejpam-5027	395	7	minimal	minimal	ADJ
ejpam-5027	395	8	spaces	space	NOUN
ejpam-5027	395	9	.	.	PUNCT
ejpam-5027	396	1	international	international	ADJ
ejpam-5027	396	2	journal	journal	NOUN
ejpam-5027	396	3	of	of	ADP
ejpam-5027	396	4	fuzzy	fuzzy	ADJ
ejpam-5027	396	5	logic	logic	NOUN
ejpam-5027	396	6	and	and	CCONJ
ejpam-5027	396	7	intelligent	intelligent	ADJ
ejpam-5027	396	8	systems	system	NOUN
ejpam-5027	396	9	,	,	PUNCT
ejpam-5027	396	10	21(3	21(3	NUM
ejpam-5027	396	11	)	)	PUNCT
ejpam-5027	396	12	,	,	PUNCT
ejpam-5027	396	13	251	251	NUM
ejpam-5027	396	14	-	-	SYM
ejpam-5027	396	15	258	258	NUM
ejpam-5027	396	16	,	,	PUNCT
ejpam-5027	396	17	2021	2021	NUM
ejpam-5027	396	18	.	.	PUNCT
ejpam-5027	397	1	[	[	X
ejpam-5027	397	2	23	23	NUM
ejpam-5027	397	3	]	]	PUNCT
ejpam-5027	397	4	l.	l.	PROPN
ejpam-5027	397	5	zadeh	zadeh	PROPN
ejpam-5027	397	6	.	.	PUNCT
ejpam-5027	397	7	fuzzy	fuzzy	ADJ
ejpam-5027	397	8	sets	set	NOUN
ejpam-5027	397	9	,	,	PUNCT
ejpam-5027	397	10	information	information	NOUN
ejpam-5027	397	11	and	and	CCONJ
ejpam-5027	397	12	control	control	NOUN
ejpam-5027	397	13	,	,	PUNCT
ejpam-5027	397	14	pp	pp	ADV
ejpam-5027	397	15	.	.	PUNCT
ejpam-5027	398	1	338–353	338–353	NUM
ejpam-5027	398	2	,	,	PUNCT
ejpam-5027	398	3	1965	1965	NUM
ejpam-5027	398	4	.	.	PUNCT
ejpam-5027	399	1	[	[	X
ejpam-5027	399	2	24	24	NUM
ejpam-5027	399	3	]	]	PUNCT
ejpam-5027	399	4	a.	a.	NOUN
ejpam-5027	399	5	zahran	zahran	NOUN
ejpam-5027	399	6	and	and	CCONJ
ejpam-5027	399	7	a.	a.	NOUN
ejpam-5027	399	8	almograbi	almograbi	PROPN
ejpam-5027	399	9	.	.	PUNCT
ejpam-5027	400	1	generalized	generalized	ADJ
ejpam-5027	400	2	ψρ−operations	ψρ−operation	NOUN
ejpam-5027	400	3	on	on	ADP
ejpam-5027	400	4	fuzzy	fuzzy	ADJ
ejpam-5027	400	5	topological	topological	PROPN
ejpam-5027	400	6	.	.	PUNCT
ejpam-5027	401	1	journal	journal	PROPN
ejpam-5027	401	2	of	of	ADP
ejpam-5027	401	3	abstract	abstract	ADJ
ejpam-5027	401	4	and	and	CCONJ
ejpam-5027	401	5	applied	apply	VERB
ejpam-5027	401	6	analysis	analysis	NOUN
ejpam-5027	401	7	,	,	PUNCT
ejpam-5027	401	8	12	12	NUM
ejpam-5027	401	9	pages	page	NOUN
ejpam-5027	401	10	,	,	PUNCT
ejpam-5027	401	11	2011	2011	NUM
ejpam-5027	401	12	.	.	PUNCT