id	sid	tid	token	lemma	pos
ejpam-4768	1	1	european	european	PROPN
ejpam-4768	1	2	journal	journal	PROPN
ejpam-4768	1	3	of	of	ADP
ejpam-4768	1	4	pure	pure	ADJ
ejpam-4768	1	5	and	and	CCONJ
ejpam-4768	1	6	applied	apply	VERB
ejpam-4768	1	7	mathematics	mathematic	NOUN
ejpam-4768	1	8	vol	vol	NOUN
ejpam-4768	1	9	.	.	PUNCT
ejpam-4768	2	1	16	16	NUM
ejpam-4768	2	2	,	,	PUNCT
ejpam-4768	2	3	no	no	INTJ
ejpam-4768	2	4	.	.	NOUN
ejpam-4768	2	5	3	3	NUM
ejpam-4768	2	6	,	,	PUNCT
ejpam-4768	2	7	2023	2023	NUM
ejpam-4768	2	8	,	,	PUNCT
ejpam-4768	2	9	1381	1381	NUM
ejpam-4768	2	10	-	-	SYM
ejpam-4768	2	11	1388	1388	NUM
ejpam-4768	2	12	issn	issn	PROPN
ejpam-4768	2	13	1307	1307	NUM
ejpam-4768	2	14	-	-	SYM
ejpam-4768	2	15	5543	5543	NUM
ejpam-4768	2	16	–	–	PUNCT
ejpam-4768	3	1	ejpam.com	ejpam.com	X
ejpam-4768	3	2	published	publish	VERB
ejpam-4768	3	3	by	by	ADP
ejpam-4768	3	4	new	new	PROPN
ejpam-4768	3	5	york	york	PROPN
ejpam-4768	3	6	business	business	PROPN
ejpam-4768	3	7	global	global	ADJ
ejpam-4768	3	8	hesitant	hesitant	ADJ
ejpam-4768	3	9	fuzzy	fuzzy	ADJ
ejpam-4768	3	10	compactness	compactness	NOUN
ejpam-4768	3	11	and	and	CCONJ
ejpam-4768	3	12	hesitant	hesitant	ADJ
ejpam-4768	3	13	fuzzy	fuzzy	ADJ
ejpam-4768	3	14	regularity	regularity	NOUN
ejpam-4768	3	15	in	in	ADP
ejpam-4768	3	16	hesitant	hesitant	ADJ
ejpam-4768	3	17	fuzzy	fuzzy	ADJ
ejpam-4768	3	18	topological	topological	ADJ
ejpam-4768	3	19	spaces	space	NOUN
ejpam-4768	3	20	a.	a.	NOUN
ejpam-4768	3	21	swaminathan1	swaminathan1	PROPN
ejpam-4768	3	22	,	,	PUNCT
ejpam-4768	3	23	cenap	cenap	VERB
ejpam-4768	3	24	ozel2	ozel2	PROPN
ejpam-4768	3	25	,	,	PUNCT
ejpam-4768	3	26	ibtesam	ibtesam	PROPN
ejpam-4768	3	27	alshammari3,∗	alshammari3,∗	ADJ
ejpam-4768	3	28	1	1	NUM
ejpam-4768	3	29	department	department	NOUN
ejpam-4768	3	30	of	of	ADP
ejpam-4768	3	31	mathematics	mathematic	NOUN
ejpam-4768	3	32	,	,	PUNCT
ejpam-4768	3	33	government	government	NOUN
ejpam-4768	3	34	arts	art	NOUN
ejpam-4768	3	35	college(a	college(a	PROPN
ejpam-4768	3	36	)	)	PUNCT
ejpam-4768	3	37	,	,	PUNCT
ejpam-4768	3	38	kumbakonam	kumbakonam	PROPN
ejpam-4768	3	39	,	,	PUNCT
ejpam-4768	3	40	tamil	tamil	PROPN
ejpam-4768	3	41	nadu612	nadu612	PROPN
ejpam-4768	3	42	002	002	NUM
ejpam-4768	3	43	,	,	PUNCT
ejpam-4768	3	44	india	india	PROPN
ejpam-4768	3	45	2	2	NUM
ejpam-4768	3	46	department	department	NOUN
ejpam-4768	3	47	of	of	ADP
ejpam-4768	3	48	mathematics	mathematic	NOUN
ejpam-4768	3	49	,	,	PUNCT
ejpam-4768	3	50	king	king	PROPN
ejpam-4768	3	51	abdulaziz	abdulaziz	PROPN
ejpam-4768	3	52	university	university	PROPN
ejpam-4768	3	53	,	,	PUNCT
ejpam-4768	3	54	jeddah-21589	jeddah-21589	NOUN
ejpam-4768	3	55	,	,	PUNCT
ejpam-4768	3	56	saudi	saudi	PROPN
ejpam-4768	3	57	arabia	arabia	PROPN
ejpam-4768	3	58	3	3	NUM
ejpam-4768	3	59	department	department	NOUN
ejpam-4768	3	60	of	of	ADP
ejpam-4768	3	61	mathematics	mathematics	PROPN
ejpam-4768	3	62	,	,	PUNCT
ejpam-4768	3	63	university	university	NOUN
ejpam-4768	3	64	of	of	ADP
ejpam-4768	3	65	hafr	hafr	PROPN
ejpam-4768	3	66	al	al	PROPN
ejpam-4768	3	67	-	-	PUNCT
ejpam-4768	3	68	batin	batin	PROPN
ejpam-4768	3	69	,	,	PUNCT
ejpam-4768	3	70	hafr	hafr	PROPN
ejpam-4768	3	71	al	al	PROPN
ejpam-4768	3	72	-	-	PUNCT
ejpam-4768	3	73	batin	batin	PROPN
ejpam-4768	3	74	,	,	PUNCT
ejpam-4768	3	75	saudi	saudi	PROPN
ejpam-4768	3	76	arabia	arabia	PROPN
ejpam-4768	3	77	abstract	abstract	NOUN
ejpam-4768	3	78	.	.	PUNCT
ejpam-4768	4	1	we	we	PRON
ejpam-4768	4	2	define	define	VERB
ejpam-4768	4	3	hesitant	hesitant	ADJ
ejpam-4768	4	4	fuzzy	fuzzy	ADJ
ejpam-4768	4	5	maximal	maximal	ADJ
ejpam-4768	4	6	open	open	ADJ
ejpam-4768	4	7	cover	cover	NOUN
ejpam-4768	4	8	to	to	PART
ejpam-4768	4	9	establish	establish	VERB
ejpam-4768	4	10	hesitant	hesitant	ADJ
ejpam-4768	4	11	fuzzy	fuzzy	ADJ
ejpam-4768	4	12	m	m	NOUN
ejpam-4768	4	13	-	-	NOUN
ejpam-4768	4	14	compactness	compactness	NOUN
ejpam-4768	4	15	and	and	CCONJ
ejpam-4768	4	16	discuss	discuss	VERB
ejpam-4768	4	17	its	its	PRON
ejpam-4768	4	18	properties	property	NOUN
ejpam-4768	4	19	.	.	PUNCT
ejpam-4768	5	1	further	far	ADV
ejpam-4768	5	2	we	we	PRON
ejpam-4768	5	3	obtain	obtain	VERB
ejpam-4768	5	4	few	few	ADJ
ejpam-4768	5	5	more	more	ADJ
ejpam-4768	5	6	results	result	NOUN
ejpam-4768	5	7	on	on	ADP
ejpam-4768	5	8	hesitant	hesitant	ADJ
ejpam-4768	5	9	fuzzy	fuzzy	ADJ
ejpam-4768	5	10	minimal	minimal	ADJ
ejpam-4768	5	11	c	c	NOUN
ejpam-4768	5	12	-	-	ADJ
ejpam-4768	5	13	regular	regular	ADJ
ejpam-4768	5	14	and	and	CCONJ
ejpam-4768	5	15	minimal	minimal	ADJ
ejpam-4768	5	16	c	c	X
ejpam-4768	5	17	-	-	ADJ
ejpam-4768	5	18	normal	normal	ADJ
ejpam-4768	5	19	spaces	space	NOUN
ejpam-4768	5	20	.	.	PUNCT
ejpam-4768	6	1	we	we	PRON
ejpam-4768	6	2	have	have	AUX
ejpam-4768	6	3	proved	prove	VERB
ejpam-4768	6	4	that	that	SCONJ
ejpam-4768	6	5	a	a	DET
ejpam-4768	6	6	hesitant	hesitant	ADJ
ejpam-4768	6	7	fuzzy	fuzzy	ADJ
ejpam-4768	6	8	haussdorff	haussdorff	PROPN
ejpam-4768	6	9	m	m	ADJ
ejpam-4768	6	10	-	-	ADJ
ejpam-4768	6	11	compact	compact	ADJ
ejpam-4768	6	12	space	space	NOUN
ejpam-4768	6	13	is	be	AUX
ejpam-4768	6	14	hesitant	hesitant	ADJ
ejpam-4768	6	15	fuzzy	fuzzy	ADJ
ejpam-4768	6	16	minimal	minimal	ADJ
ejpam-4768	6	17	c	c	NOUN
ejpam-4768	6	18	-	-	ADJ
ejpam-4768	6	19	normal	normal	ADJ
ejpam-4768	6	20	.	.	PUNCT
ejpam-4768	7	1	2020	2020	NUM
ejpam-4768	7	2	mathematics	mathematic	NOUN
ejpam-4768	7	3	subject	subject	NOUN
ejpam-4768	7	4	classifications	classification	NOUN
ejpam-4768	7	5	:	:	PUNCT
ejpam-4768	7	6	54a40	54a40	NUM
ejpam-4768	7	7	,	,	PUNCT
ejpam-4768	7	8	03e72	03e72	X
ejpam-4768	7	9	key	key	ADJ
ejpam-4768	7	10	words	word	NOUN
ejpam-4768	7	11	and	and	CCONJ
ejpam-4768	7	12	phrases	phrase	NOUN
ejpam-4768	7	13	:	:	PUNCT
ejpam-4768	7	14	hesitant	hesitant	ADJ
ejpam-4768	7	15	fuzzy	fuzzy	ADJ
ejpam-4768	7	16	minimal	minimal	ADJ
ejpam-4768	7	17	open	open	ADJ
ejpam-4768	7	18	,	,	PUNCT
ejpam-4768	7	19	hesitant	hesitant	ADJ
ejpam-4768	7	20	fuzzy	fuzzy	ADJ
ejpam-4768	7	21	maximal	maximal	ADJ
ejpam-4768	7	22	open	open	ADJ
ejpam-4768	7	23	cover	cover	NOUN
ejpam-4768	7	24	,	,	PUNCT
ejpam-4768	7	25	hesitant	hesitant	ADJ
ejpam-4768	7	26	fuzzy	fuzzy	ADJ
ejpam-4768	7	27	m	m	NOUN
ejpam-4768	7	28	-	-	ADJ
ejpam-4768	7	29	compact	compact	ADJ
ejpam-4768	7	30	,	,	PUNCT
ejpam-4768	7	31	hesitant	hesitant	ADJ
ejpam-4768	7	32	fuzzy	fuzzy	ADJ
ejpam-4768	7	33	minimal	minimal	ADJ
ejpam-4768	7	34	c	c	NOUN
ejpam-4768	7	35	-	-	ADJ
ejpam-4768	7	36	regular	regular	ADJ
ejpam-4768	7	37	1	1	NUM
ejpam-4768	7	38	.	.	PUNCT
ejpam-4768	7	39	introduction	introduction	NOUN
ejpam-4768	7	40	origination	origination	NOUN
ejpam-4768	7	41	of	of	ADP
ejpam-4768	7	42	fuzzy	fuzzy	ADJ
ejpam-4768	7	43	sets	set	NOUN
ejpam-4768	7	44	by	by	ADP
ejpam-4768	7	45	zadeh[11	zadeh[11	PROPN
ejpam-4768	7	46	]	]	PUNCT
ejpam-4768	7	47	emerged	emerge	VERB
ejpam-4768	7	48	many	many	ADJ
ejpam-4768	7	49	branches	branch	NOUN
ejpam-4768	7	50	of	of	ADP
ejpam-4768	7	51	mathematics	mathematic	NOUN
ejpam-4768	7	52	for	for	ADP
ejpam-4768	7	53	many	many	ADJ
ejpam-4768	7	54	decades	decade	NOUN
ejpam-4768	7	55	.	.	PUNCT
ejpam-4768	8	1	chang[1	chang[1	SYM
ejpam-4768	8	2	]	]	PUNCT
ejpam-4768	8	3	introduced	introduce	VERB
ejpam-4768	8	4	fuzzy	fuzzy	ADJ
ejpam-4768	8	5	topology	topology	NOUN
ejpam-4768	8	6	in	in	ADP
ejpam-4768	8	7	1968	1968	NUM
ejpam-4768	8	8	.	.	PUNCT
ejpam-4768	9	1	as	as	ADP
ejpam-4768	9	2	an	an	DET
ejpam-4768	9	3	addendum	addendum	NOUN
ejpam-4768	9	4	to	to	ADP
ejpam-4768	9	5	fuzzy	fuzzy	ADJ
ejpam-4768	9	6	sets	set	NOUN
ejpam-4768	9	7	,	,	PUNCT
ejpam-4768	9	8	the	the	DET
ejpam-4768	9	9	notion	notion	NOUN
ejpam-4768	9	10	hesitant	hesitant	ADJ
ejpam-4768	9	11	fuzzy	fuzzy	ADJ
ejpam-4768	9	12	set	set	NOUN
ejpam-4768	9	13	introduced	introduce	VERB
ejpam-4768	9	14	by	by	ADP
ejpam-4768	9	15	torra[4	torra[4	PROPN
ejpam-4768	9	16	]	]	X
ejpam-4768	9	17	in	in	ADP
ejpam-4768	9	18	2010	2010	NUM
ejpam-4768	9	19	.	.	PUNCT
ejpam-4768	10	1	deepak	deepak	PROPN
ejpam-4768	10	2	et	et	PROPN
ejpam-4768	10	3	.	.	PUNCT
ejpam-4768	11	1	al	al	PROPN
ejpam-4768	11	2	.	.	PUNCT
ejpam-4768	12	1	[	[	X
ejpam-4768	12	2	2	2	X
ejpam-4768	12	3	]	]	PUNCT
ejpam-4768	12	4	introduced	introduce	VERB
ejpam-4768	12	5	hesitant	hesitant	ADJ
ejpam-4768	12	6	fuzzy	fuzzy	ADJ
ejpam-4768	12	7	topological	topological	ADJ
ejpam-4768	12	8	space	space	NOUN
ejpam-4768	12	9	and	and	CCONJ
ejpam-4768	12	10	extended	extend	VERB
ejpam-4768	12	11	the	the	DET
ejpam-4768	12	12	study	study	NOUN
ejpam-4768	12	13	to	to	ADP
ejpam-4768	12	14	hesitant	hesitant	ADJ
ejpam-4768	12	15	connectedness	connectedness	NOUN
ejpam-4768	12	16	and	and	CCONJ
ejpam-4768	12	17	compactness	compactness	NOUN
ejpam-4768	12	18	in	in	ADP
ejpam-4768	12	19	hesitant	hesitant	ADJ
ejpam-4768	12	20	fuzzy	fuzzy	ADJ
ejpam-4768	12	21	topological	topological	ADJ
ejpam-4768	12	22	space	space	NOUN
ejpam-4768	12	23	.	.	PUNCT
ejpam-4768	13	1	the	the	DET
ejpam-4768	13	2	notions	notion	NOUN
ejpam-4768	13	3	of	of	ADP
ejpam-4768	13	4	hesitant	hesitant	ADJ
ejpam-4768	13	5	fuzzy	fuzzy	ADJ
ejpam-4768	13	6	minimal	minimal	ADJ
ejpam-4768	13	7	,	,	PUNCT
ejpam-4768	13	8	maximal	maximal	ADJ
ejpam-4768	13	9	open[9	open[9	NUM
ejpam-4768	13	10	]	]	PUNCT
ejpam-4768	13	11	and	and	CCONJ
ejpam-4768	13	12	hesitant	hesitant	ADJ
ejpam-4768	13	13	fuzzy	fuzzy	ADJ
ejpam-4768	13	14	minimal	minimal	ADJ
ejpam-4768	13	15	,	,	PUNCT
ejpam-4768	13	16	maximal	maximal	ADJ
ejpam-4768	13	17	clopen[7	clopen[7	NOUN
ejpam-4768	13	18	]	]	PUNCT
ejpam-4768	13	19	sets	set	NOUN
ejpam-4768	13	20	introduced	introduce	VERB
ejpam-4768	13	21	by	by	ADP
ejpam-4768	13	22	swaminathan	swaminathan	NOUN
ejpam-4768	13	23	and	and	CCONJ
ejpam-4768	13	24	sivaraja	sivaraja	ADJ
ejpam-4768	13	25	.	.	PUNCT
ejpam-4768	14	1	also	also	ADV
ejpam-4768	14	2	the	the	DET
ejpam-4768	14	3	idea	idea	NOUN
ejpam-4768	14	4	of	of	ADP
ejpam-4768	14	5	hesitant	hesitant	ADJ
ejpam-4768	14	6	fuzzy	fuzzy	ADJ
ejpam-4768	14	7	mean	mean	VERB
ejpam-4768	14	8	open	open	ADJ
ejpam-4768	14	9	and	and	CCONJ
ejpam-4768	14	10	closed	close	VERB
ejpam-4768	14	11	sets[8	sets[8	PROPN
ejpam-4768	14	12	]	]	PUNCT
ejpam-4768	14	13	investigated	investigate	VERB
ejpam-4768	14	14	by	by	ADP
ejpam-4768	14	15	swaminathan	swaminathan	ADV
ejpam-4768	14	16	and	and	CCONJ
ejpam-4768	14	17	sivaraja	sivaraja	ADJ
ejpam-4768	14	18	.	.	PUNCT
ejpam-4768	15	1	in	in	ADP
ejpam-4768	15	2	section	section	NOUN
ejpam-4768	15	3	2	2	NUM
ejpam-4768	15	4	,	,	PUNCT
ejpam-4768	15	5	we	we	PRON
ejpam-4768	15	6	define	define	VERB
ejpam-4768	15	7	a	a	DET
ejpam-4768	15	8	new	new	ADJ
ejpam-4768	15	9	notion	notion	NOUN
ejpam-4768	15	10	hesitant	hesitant	ADJ
ejpam-4768	15	11	fuzzy	fuzzy	ADJ
ejpam-4768	15	12	maximal	maximal	ADJ
ejpam-4768	15	13	open	open	ADJ
ejpam-4768	15	14	cover	cover	NOUN
ejpam-4768	15	15	in	in	ADP
ejpam-4768	15	16	hesitant	hesitant	ADJ
ejpam-4768	15	17	fuzzy	fuzzy	ADJ
ejpam-4768	15	18	topological	topological	ADJ
ejpam-4768	15	19	space	space	NOUN
ejpam-4768	15	20	.	.	PUNCT
ejpam-4768	16	1	section	section	NOUN
ejpam-4768	16	2	3	3	NUM
ejpam-4768	16	3	of	of	ADP
ejpam-4768	16	4	this	this	DET
ejpam-4768	16	5	paper	paper	NOUN
ejpam-4768	16	6	,	,	PUNCT
ejpam-4768	16	7	the	the	DET
ejpam-4768	16	8	concept	concept	NOUN
ejpam-4768	16	9	of	of	ADP
ejpam-4768	16	10	hesitant	hesitant	ADJ
ejpam-4768	16	11	fuzzy	fuzzy	ADJ
ejpam-4768	16	12	m	m	ADJ
ejpam-4768	16	13	-	-	ADJ
ejpam-4768	16	14	compact	compact	ADJ
ejpam-4768	16	15	space	space	NOUN
ejpam-4768	16	16	and	and	CCONJ
ejpam-4768	16	17	some	some	DET
ejpam-4768	16	18	properties	property	NOUN
ejpam-4768	16	19	are	be	AUX
ejpam-4768	16	20	discussed	discuss	VERB
ejpam-4768	16	21	.	.	PUNCT
ejpam-4768	17	1	in	in	ADP
ejpam-4768	17	2	section	section	NOUN
ejpam-4768	17	3	4	4	NUM
ejpam-4768	17	4	,	,	PUNCT
ejpam-4768	17	5	the	the	DET
ejpam-4768	17	6	notion	notion	NOUN
ejpam-4768	17	7	of	of	ADP
ejpam-4768	17	8	hesitant	hesitant	ADJ
ejpam-4768	17	9	fuzzy	fuzzy	ADJ
ejpam-4768	17	10	minimal	minimal	ADJ
ejpam-4768	17	11	c	c	NOUN
ejpam-4768	17	12	-	-	ADJ
ejpam-4768	17	13	regular	regular	ADJ
ejpam-4768	17	14	(	(	PUNCT
ejpam-4768	17	15	resp.c	resp.c	NOUN
ejpam-4768	17	16	-	-	PUNCT
ejpam-4768	17	17	normal	normal	ADJ
ejpam-4768	17	18	spaces	space	NOUN
ejpam-4768	17	19	)	)	PUNCT
ejpam-4768	17	20	are	be	AUX
ejpam-4768	17	21	extended	extend	VERB
ejpam-4768	17	22	from	from	ADP
ejpam-4768	17	23	which	which	PRON
ejpam-4768	17	24	it	it	PRON
ejpam-4768	17	25	is	be	AUX
ejpam-4768	17	26	showed	show	VERB
ejpam-4768	17	27	that	that	SCONJ
ejpam-4768	17	28	a	a	DET
ejpam-4768	17	29	hesitant	hesitant	ADJ
ejpam-4768	17	30	fuzzy	fuzzy	ADJ
ejpam-4768	17	31	haussdorff	haussdorff	PROPN
ejpam-4768	17	32	m	m	ADJ
ejpam-4768	17	33	-	-	ADJ
ejpam-4768	17	34	compact	compact	ADJ
ejpam-4768	17	35	space	space	NOUN
ejpam-4768	17	36	is	be	AUX
ejpam-4768	17	37	hesitant	hesitant	ADJ
ejpam-4768	17	38	fuzzy	fuzzy	ADJ
ejpam-4768	17	39	minimal	minimal	ADJ
ejpam-4768	17	40	c	c	NOUN
ejpam-4768	17	41	-	-	ADJ
ejpam-4768	17	42	normal	normal	ADJ
ejpam-4768	17	43	.	.	PUNCT
ejpam-4768	18	1	∗corresponding	∗corresponde	VERB
ejpam-4768	18	2	author	author	NOUN
ejpam-4768	18	3	.	.	PUNCT
ejpam-4768	19	1	doi	doi	NOUN
ejpam-4768	19	2	:	:	PUNCT
ejpam-4768	19	3	https://doi.org/10.29020/nybg.ejpam.v16i3.4768	https://doi.org/10.29020/nybg.ejpam.v16i3.4768	PROPN
ejpam-4768	19	4	email	email	NOUN
ejpam-4768	19	5	addresses	address	VERB
ejpam-4768	19	6	:	:	PUNCT
ejpam-4768	20	1	asnathanway@gmail.com	asnathanway@gmail.com	X
ejpam-4768	20	2	(	(	PUNCT
ejpam-4768	20	3	a.	a.	NOUN
ejpam-4768	20	4	swaminathan	swaminathan	PROPN
ejpam-4768	20	5	)	)	PUNCT
ejpam-4768	20	6	,	,	PUNCT
ejpam-4768	20	7	cenap.ozel@gmail.com	cenap.ozel@gmail.com	X
ejpam-4768	20	8	(	(	PUNCT
ejpam-4768	20	9	c.	c.	PROPN
ejpam-4768	20	10	ozel	ozel	PROPN
ejpam-4768	20	11	)	)	PUNCT
ejpam-4768	20	12	,	,	PUNCT
ejpam-4768	20	13	iealshamri@uhb.edu.sa	iealshamri@uhb.edu.sa	NOUN
ejpam-4768	20	14	,	,	PUNCT
ejpam-4768	20	15	iealshamri@hotmail.com	iealshamri@hotmail.com	X
ejpam-4768	20	16	(	(	PUNCT
ejpam-4768	20	17	i.	i.	PROPN
ejpam-4768	20	18	alshammari	alshammari	PROPN
ejpam-4768	20	19	)	)	PUNCT
ejpam-4768	20	20	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4768	20	21	1381	1381	NUM
ejpam-4768	20	22	©	©	PROPN
ejpam-4768	20	23	2023	2023	NUM
ejpam-4768	20	24	ejpam	ejpam	NOUN
ejpam-4768	20	25	all	all	DET
ejpam-4768	20	26	rights	right	NOUN
ejpam-4768	20	27	reserved	reserve	VERB
ejpam-4768	20	28	.	.	PUNCT
ejpam-4768	21	1	a.	a.	NOUN
ejpam-4768	21	2	swaminathan	swaminathan	PROPN
ejpam-4768	21	3	,	,	PUNCT
ejpam-4768	21	4	cenap	cenap	VERB
ejpam-4768	21	5	ozel	ozel	ADJ
ejpam-4768	21	6	,	,	PUNCT
ejpam-4768	21	7	ibtesam	ibtesam	PROPN
ejpam-4768	21	8	alshammari	alshammari	PROPN
ejpam-4768	21	9	/	/	SYM
ejpam-4768	21	10	eur	eur	PROPN
ejpam-4768	21	11	.	.	PUNCT
ejpam-4768	22	1	j.	j.	PROPN
ejpam-4768	22	2	pure	pure	PROPN
ejpam-4768	22	3	appl	appl	PROPN
ejpam-4768	22	4	.	.	PROPN
ejpam-4768	22	5	math	math	PROPN
ejpam-4768	22	6	,	,	PUNCT
ejpam-4768	22	7	16	16	NUM
ejpam-4768	22	8	(	(	PUNCT
ejpam-4768	22	9	3	3	NUM
ejpam-4768	22	10	)	)	PUNCT
ejpam-4768	22	11	(	(	PUNCT
ejpam-4768	22	12	2023	2023	NUM
ejpam-4768	22	13	)	)	PUNCT
ejpam-4768	22	14	,	,	PUNCT
ejpam-4768	22	15	1381	1381	NUM
ejpam-4768	22	16	-	-	SYM
ejpam-4768	22	17	1388	1388	NUM
ejpam-4768	22	18	1382	1382	NUM
ejpam-4768	22	19	the	the	DET
ejpam-4768	22	20	following	follow	VERB
ejpam-4768	22	21	terminologies	terminology	NOUN
ejpam-4768	22	22	,	,	PUNCT
ejpam-4768	22	23	“	"	PUNCT
ejpam-4768	22	24	hesitant	hesitant	ADJ
ejpam-4768	22	25	fuzzy	fuzzy	ADJ
ejpam-4768	22	26	minimal	minimal	ADJ
ejpam-4768	22	27	open	open	ADJ
ejpam-4768	22	28	set	set	NOUN
ejpam-4768	22	29	,	,	PUNCT
ejpam-4768	22	30	hesitant	hesitant	ADJ
ejpam-4768	22	31	fuzzy	fuzzy	ADJ
ejpam-4768	22	32	maximal	maximal	ADJ
ejpam-4768	22	33	open	open	ADJ
ejpam-4768	22	34	set	set	NOUN
ejpam-4768	22	35	,	,	PUNCT
ejpam-4768	22	36	hesitant	hesitant	ADJ
ejpam-4768	22	37	fuzzy	fuzzy	ADJ
ejpam-4768	22	38	mean	mean	VERB
ejpam-4768	22	39	open	open	ADJ
ejpam-4768	22	40	set	set	NOUN
ejpam-4768	22	41	,	,	PUNCT
ejpam-4768	22	42	hesitant	hesitant	ADJ
ejpam-4768	22	43	fuzzy	fuzzy	ADJ
ejpam-4768	22	44	clopen	clopen	ADJ
ejpam-4768	22	45	set	set	NOUN
ejpam-4768	22	46	,	,	PUNCT
ejpam-4768	22	47	hesitant	hesitant	ADJ
ejpam-4768	22	48	fuzzy	fuzzy	ADJ
ejpam-4768	22	49	cut	cut	NOUN
ejpam-4768	22	50	-	-	PUNCT
ejpam-4768	22	51	point	point	NOUN
ejpam-4768	22	52	space	space	NOUN
ejpam-4768	22	53	,	,	PUNCT
ejpam-4768	22	54	hesitant	hesitant	ADJ
ejpam-4768	22	55	fuzzy	fuzzy	ADJ
ejpam-4768	22	56	connected	connected	ADJ
ejpam-4768	22	57	topological	topological	ADJ
ejpam-4768	22	58	space	space	NOUN
ejpam-4768	22	59	,	,	PUNCT
ejpam-4768	22	60	hesitant	hesitant	ADJ
ejpam-4768	22	61	fuzzy	fuzzy	ADJ
ejpam-4768	22	62	disconnected	disconnected	ADJ
ejpam-4768	22	63	topological	topological	ADJ
ejpam-4768	22	64	space	space	NOUN
ejpam-4768	22	65	and	and	CCONJ
ejpam-4768	22	66	hesitant	hesitant	ADJ
ejpam-4768	22	67	fuzzy	fuzzy	ADJ
ejpam-4768	22	68	topological	topological	ADJ
ejpam-4768	22	69	space”are	space”are	PROPN
ejpam-4768	22	70	respectively	respectively	ADV
ejpam-4768	22	71	abbreviated	abbreviate	VERB
ejpam-4768	22	72	as	as	ADP
ejpam-4768	22	73	“	"	PUNCT
ejpam-4768	22	74	hfmio	hfmio	PROPN
ejpam-4768	22	75	,	,	PUNCT
ejpam-4768	22	76	hfmao	hfmao	PROPN
ejpam-4768	22	77	,	,	PUNCT
ejpam-4768	22	78	hfmeo	hfmeo	PROPN
ejpam-4768	22	79	,	,	PUNCT
ejpam-4768	22	80	hfclo	hfclo	NOUN
ejpam-4768	22	81	,	,	PUNCT
ejpam-4768	22	82	hfcs	hfc	NOUN
ejpam-4768	22	83	,	,	PUNCT
ejpam-4768	22	84	hfcts	hfct	NOUN
ejpam-4768	22	85	,	,	PUNCT
ejpam-4768	22	86	hfdts	hfdts	ADJ
ejpam-4768	22	87	and	and	CCONJ
ejpam-4768	22	88	hfts	hft	NOUN
ejpam-4768	22	89	.	.	PUNCT
ejpam-4768	22	90	”	"	PUNCT
ejpam-4768	23	1	2	2	NUM
ejpam-4768	23	2	.	.	PUNCT
ejpam-4768	23	3	preliminaries	preliminary	NOUN
ejpam-4768	23	4	definition	definition	NOUN
ejpam-4768	23	5	2.1	2.1	NUM
ejpam-4768	23	6	.	.	PUNCT
ejpam-4768	24	1	[	[	X
ejpam-4768	24	2	4	4	X
ejpam-4768	24	3	]	]	PUNCT
ejpam-4768	24	4	a	a	DET
ejpam-4768	24	5	hfs	hfs	ADJ
ejpam-4768	24	6	h	h	NOUN
ejpam-4768	24	7	in	in	ADP
ejpam-4768	24	8	x	x	PRON
ejpam-4768	24	9	is	be	AUX
ejpam-4768	24	10	a	a	DET
ejpam-4768	24	11	function	function	NOUN
ejpam-4768	24	12	h	h	NOUN
ejpam-4768	24	13	:	:	PUNCT
ejpam-4768	24	14	x	x	X
ejpam-4768	24	15	→	→	PUNCT
ejpam-4768	24	16	p	p	X
ejpam-4768	25	1	[	[	X
ejpam-4768	25	2	0	0	NUM
ejpam-4768	25	3	,	,	PUNCT
ejpam-4768	25	4	1	1	NUM
ejpam-4768	25	5	]	]	PUNCT
ejpam-4768	25	6	,	,	PUNCT
ejpam-4768	25	7	where	where	SCONJ
ejpam-4768	25	8	p	p	X
ejpam-4768	25	9	[	[	X
ejpam-4768	25	10	0	0	NUM
ejpam-4768	25	11	,	,	PUNCT
ejpam-4768	25	12	1	1	NUM
ejpam-4768	25	13	]	]	PUNCT
ejpam-4768	25	14	represents	represent	VERB
ejpam-4768	25	15	the	the	DET
ejpam-4768	25	16	power	power	NOUN
ejpam-4768	25	17	set	set	NOUN
ejpam-4768	25	18	of	of	ADP
ejpam-4768	25	19	[	[	X
ejpam-4768	25	20	0	0	NUM
ejpam-4768	25	21	,	,	PUNCT
ejpam-4768	25	22	1	1	NUM
ejpam-4768	25	23	]	]	PUNCT
ejpam-4768	25	24	.	.	PUNCT
ejpam-4768	26	1	we	we	PRON
ejpam-4768	26	2	define	define	VERB
ejpam-4768	26	3	the	the	DET
ejpam-4768	26	4	hesitant	hesitant	ADJ
ejpam-4768	26	5	fuzzy	fuzzy	ADJ
ejpam-4768	26	6	empty	empty	ADJ
ejpam-4768	26	7	set	set	VERB
ejpam-4768	26	8	h0(resp	h0(resp	PROPN
ejpam-4768	26	9	.	.	PUNCT
ejpam-4768	27	1	whole	whole	ADJ
ejpam-4768	27	2	set	set	VERB
ejpam-4768	27	3	h1	h1	NOUN
ejpam-4768	27	4	)	)	PUNCT
ejpam-4768	27	5	is	be	AUX
ejpam-4768	27	6	a	a	DET
ejpam-4768	27	7	hfs	hfs	NOUN
ejpam-4768	27	8	in	in	ADP
ejpam-4768	27	9	x	x	PUNCT
ejpam-4768	27	10	as	as	SCONJ
ejpam-4768	27	11	follows	follow	VERB
ejpam-4768	27	12	:	:	PUNCT
ejpam-4768	27	13	h0(x	h0(x	X
ejpam-4768	27	14	)	)	PUNCT
ejpam-4768	27	15	=	=	SYM
ejpam-4768	27	16	ϕ	ϕ	PROPN
ejpam-4768	27	17	(	(	PUNCT
ejpam-4768	27	18	resp	resp	NOUN
ejpam-4768	27	19	.	.	PUNCT
ejpam-4768	28	1	h1(x	h1(x	X
ejpam-4768	28	2	)	)	PUNCT
ejpam-4768	28	3	=	=	PUNCT
ejpam-4768	29	1	[	[	X
ejpam-4768	29	2	0	0	NUM
ejpam-4768	29	3	,	,	PUNCT
ejpam-4768	29	4	1]),∀x	1]),∀x	NUM
ejpam-4768	29	5	∈	∈	NOUN
ejpam-4768	29	6	x.	x.	NOUN
ejpam-4768	29	7	hs(x	hs(x	PROPN
ejpam-4768	29	8	)	)	PUNCT
ejpam-4768	29	9	stands	stand	VERB
ejpam-4768	29	10	for	for	ADP
ejpam-4768	29	11	collection	collection	NOUN
ejpam-4768	29	12	of	of	ADP
ejpam-4768	29	13	hfs	hfs	NOUN
ejpam-4768	29	14	in	in	ADP
ejpam-4768	29	15	x.	x.	NOUN
ejpam-4768	29	16	definition	definition	NOUN
ejpam-4768	29	17	2.2	2.2	NUM
ejpam-4768	29	18	.	.	PUNCT
ejpam-4768	30	1	[	[	X
ejpam-4768	30	2	5	5	X
ejpam-4768	30	3	]	]	PUNCT
ejpam-4768	30	4	let	let	VERB
ejpam-4768	30	5	x	x	PRON
ejpam-4768	30	6	be	be	AUX
ejpam-4768	30	7	a	a	DET
ejpam-4768	30	8	nonempty	nonempty	ADV
ejpam-4768	30	9	set	set	VERB
ejpam-4768	30	10	.	.	PUNCT
ejpam-4768	31	1	a	a	DET
ejpam-4768	31	2	hft	hft	PROPN
ejpam-4768	31	3	τ	τ	PROPN
ejpam-4768	31	4	of	of	ADP
ejpam-4768	31	5	subsets	subset	NOUN
ejpam-4768	31	6	x	x	VERB
ejpam-4768	31	7	is	be	AUX
ejpam-4768	31	8	said	say	VERB
ejpam-4768	31	9	to	to	PART
ejpam-4768	31	10	be	be	AUX
ejpam-4768	31	11	hft	hft	NOUN
ejpam-4768	31	12	on	on	ADP
ejpam-4768	31	13	x	x	SYM
ejpam-4768	31	14	if	if	SCONJ
ejpam-4768	31	15	(	(	PUNCT
ejpam-4768	31	16	i	i	NOUN
ejpam-4768	31	17	)	)	PUNCT
ejpam-4768	31	18	h0	h0	PROPN
ejpam-4768	31	19	,	,	PUNCT
ejpam-4768	31	20	h1	h1	PROPN
ejpam-4768	31	21	∈	∈	PROPN
ejpam-4768	31	22	τ	τ	X
ejpam-4768	31	23	.	.	PUNCT
ejpam-4768	32	1	(	(	PUNCT
ejpam-4768	32	2	ii	ii	NOUN
ejpam-4768	32	3	)	)	PUNCT
ejpam-4768	33	1	⋃	⋃	ADP
ejpam-4768	33	2	i∈j	i∈j	NOUN
ejpam-4768	33	3	hi	hi	INTJ
ejpam-4768	33	4	∈	∈	PROPN
ejpam-4768	33	5	τ	τ	X
ejpam-4768	33	6	for	for	ADP
ejpam-4768	33	7	each	each	PRON
ejpam-4768	33	8	(	(	PUNCT
ejpam-4768	33	9	hi)i∈j	hi)i∈j	X
ejpam-4768	33	10	⊂	⊂	X
ejpam-4768	33	11	τ	τ	X
ejpam-4768	33	12	.	.	PUNCT
ejpam-4768	34	1	(	(	PUNCT
ejpam-4768	34	2	iii	iii	X
ejpam-4768	34	3	)	)	PUNCT
ejpam-4768	34	4	h1	h1	NOUN
ejpam-4768	34	5	∩	∩	ADJ
ejpam-4768	34	6	h2	h2	PROPN
ejpam-4768	34	7	∈	∈	PROPN
ejpam-4768	34	8	τ	τ	X
ejpam-4768	34	9	for	for	ADP
ejpam-4768	34	10	any	any	DET
ejpam-4768	34	11	h1	h1	NOUN
ejpam-4768	34	12	,	,	PUNCT
ejpam-4768	34	13	h2	h2	PROPN
ejpam-4768	34	14	∈	∈	PROPN
ejpam-4768	34	15	τ	τ	X
ejpam-4768	34	16	.	.	PUNCT
ejpam-4768	35	1	“	"	PUNCT
ejpam-4768	35	2	the	the	DET
ejpam-4768	35	3	pair	pair	NOUN
ejpam-4768	35	4	(	(	PUNCT
ejpam-4768	35	5	x	x	X
ejpam-4768	35	6	,	,	PUNCT
ejpam-4768	35	7	τ	τ	X
ejpam-4768	35	8	)	)	PUNCT
ejpam-4768	35	9	is	be	AUX
ejpam-4768	35	10	called	call	VERB
ejpam-4768	35	11	hfts	hft	NOUN
ejpam-4768	35	12	.	.	PUNCT
ejpam-4768	36	1	the	the	DET
ejpam-4768	36	2	members	member	NOUN
ejpam-4768	36	3	of	of	ADP
ejpam-4768	36	4	τ	τ	PROPN
ejpam-4768	36	5	are	be	AUX
ejpam-4768	36	6	called	call	VERB
ejpam-4768	36	7	hfo	hfo	NOUN
ejpam-4768	36	8	sets	set	NOUN
ejpam-4768	36	9	in	in	ADP
ejpam-4768	36	10	x.	x.	NOUN
ejpam-4768	36	11	a	a	DET
ejpam-4768	36	12	hfs	hfs	ADJ
ejpam-4768	36	13	h	h	NOUN
ejpam-4768	36	14	in	in	ADP
ejpam-4768	36	15	x	x	PUNCT
ejpam-4768	36	16	is	be	AUX
ejpam-4768	36	17	hfc	hfc	ADJ
ejpam-4768	36	18	set	set	NOUN
ejpam-4768	36	19	(	(	PUNCT
ejpam-4768	36	20	in	in	ADP
ejpam-4768	36	21	short	short	ADJ
ejpam-4768	36	22	hfc	hfc	NOUN
ejpam-4768	36	23	)	)	PUNCT
ejpam-4768	36	24	in	in	ADP
ejpam-4768	36	25	(	(	PUNCT
ejpam-4768	36	26	x	x	NOUN
ejpam-4768	36	27	,	,	PUNCT
ejpam-4768	36	28	τ	τ	X
ejpam-4768	36	29	)	)	PUNCT
ejpam-4768	36	30	if	if	SCONJ
ejpam-4768	36	31	hc	hc	PROPN
ejpam-4768	36	32	∈	∈	PROPN
ejpam-4768	36	33	τ	τ	X
ejpam-4768	36	34	.	.	PUNCT
ejpam-4768	36	35	”	"	PUNCT
ejpam-4768	37	1	definition	definition	NOUN
ejpam-4768	37	2	2.3	2.3	NUM
ejpam-4768	37	3	.	.	PUNCT
ejpam-4768	38	1	[	[	X
ejpam-4768	38	2	3	3	X
ejpam-4768	38	3	]	]	PUNCT
ejpam-4768	38	4	two	two	NUM
ejpam-4768	38	5	hfs	hfs	ADJ
ejpam-4768	38	6	h1	h1	NOUN
ejpam-4768	38	7	and	and	CCONJ
ejpam-4768	38	8	h2	h2	PROPN
ejpam-4768	38	9	of	of	ADP
ejpam-4768	38	10	x	x	SYM
ejpam-4768	38	11	are	be	AUX
ejpam-4768	38	12	said	say	VERB
ejpam-4768	38	13	to	to	PART
ejpam-4768	38	14	be	be	AUX
ejpam-4768	38	15	equal	equal	ADJ
ejpam-4768	38	16	if	if	SCONJ
ejpam-4768	38	17	h1	h1	PROPN
ejpam-4768	38	18	⊂	⊂	PROPN
ejpam-4768	38	19	h2	h2	PROPN
ejpam-4768	38	20	and	and	CCONJ
ejpam-4768	38	21	h2	h2	PROPN
ejpam-4768	38	22	⊂	⊂	PROPN
ejpam-4768	38	23	h1	h1	PROPN
ejpam-4768	38	24	.	.	PUNCT
ejpam-4768	39	1	definition	definition	NOUN
ejpam-4768	39	2	2.4	2.4	NUM
ejpam-4768	39	3	.	.	PUNCT
ejpam-4768	40	1	[	[	X
ejpam-4768	40	2	4	4	X
ejpam-4768	40	3	]	]	PUNCT
ejpam-4768	40	4	let	let	VERB
ejpam-4768	40	5	h	h	PROPN
ejpam-4768	40	6	∈	∈	PROPN
ejpam-4768	40	7	hs(x	hs(x	NOUN
ejpam-4768	40	8	)	)	PUNCT
ejpam-4768	40	9	for	for	ADP
ejpam-4768	40	10	any	any	DET
ejpam-4768	40	11	nonempty	nonempty	ADV
ejpam-4768	40	12	set	set	VERB
ejpam-4768	40	13	x.	x.	NOUN
ejpam-4768	40	14	then	then	ADV
ejpam-4768	40	15	hc	hc	PROPN
ejpam-4768	40	16	is	be	AUX
ejpam-4768	40	17	the	the	DET
ejpam-4768	40	18	complement	complement	NOUN
ejpam-4768	40	19	of	of	ADP
ejpam-4768	40	20	h	h	PRON
ejpam-4768	40	21	which	which	PRON
ejpam-4768	40	22	is	be	AUX
ejpam-4768	40	23	hfs	hfs	ADJ
ejpam-4768	40	24	in	in	ADP
ejpam-4768	40	25	x	x	INTJ
ejpam-4768	40	26	such	such	ADJ
ejpam-4768	40	27	that	that	DET
ejpam-4768	40	28	hc(x	hc(x	NOUN
ejpam-4768	40	29	)	)	PUNCT
ejpam-4768	40	30	=	=	PUNCT
ejpam-4768	41	1	[	[	X
ejpam-4768	41	2	h(x)]c	h(x)]c	X
ejpam-4768	41	3	=	=	SYM
ejpam-4768	41	4	[	[	X
ejpam-4768	41	5	0	0	NUM
ejpam-4768	41	6	,	,	PUNCT
ejpam-4768	41	7	1]\h(x	1]\h(x	NUM
ejpam-4768	41	8	)	)	PUNCT
ejpam-4768	41	9	.	.	PUNCT
ejpam-4768	42	1	definition	definition	NOUN
ejpam-4768	42	2	2.5	2.5	NUM
ejpam-4768	42	3	.	.	PUNCT
ejpam-4768	43	1	[	[	X
ejpam-4768	43	2	5	5	X
ejpam-4768	43	3	]	]	PUNCT
ejpam-4768	43	4	suppose	suppose	VERB
ejpam-4768	43	5	that	that	SCONJ
ejpam-4768	43	6	(	(	PUNCT
ejpam-4768	43	7	x	x	X
ejpam-4768	43	8	,	,	PUNCT
ejpam-4768	43	9	τ	τ	X
ejpam-4768	43	10	)	)	PUNCT
ejpam-4768	43	11	is	be	AUX
ejpam-4768	43	12	a	a	DET
ejpam-4768	43	13	hfts	hft	NOUN
ejpam-4768	43	14	such	such	ADJ
ejpam-4768	43	15	that	that	SCONJ
ejpam-4768	43	16	xλ	xλ	PROPN
ejpam-4768	43	17	∈	∈	PROPN
ejpam-4768	43	18	hp(x	hp(x	PRON
ejpam-4768	43	19	)	)	PUNCT
ejpam-4768	43	20	and	and	CCONJ
ejpam-4768	43	21	n	n	PRON
ejpam-4768	43	22	∈	∈	NOUN
ejpam-4768	43	23	hs(η	hs(η	X
ejpam-4768	43	24	)	)	PUNCT
ejpam-4768	43	25	.	.	PUNCT
ejpam-4768	44	1	then	then	ADV
ejpam-4768	44	2	the	the	DET
ejpam-4768	44	3	hesitant	hesitant	ADJ
ejpam-4768	44	4	fuzzy	fuzzy	ADJ
ejpam-4768	44	5	neighbourhood	neighbourhood	NOUN
ejpam-4768	44	6	n	n	NOUN
ejpam-4768	44	7	of	of	ADP
ejpam-4768	44	8	xλ	xλ	PROPN
ejpam-4768	44	9	is	be	AUX
ejpam-4768	44	10	defined	define	VERB
ejpam-4768	44	11	as	as	SCONJ
ejpam-4768	44	12	if	if	SCONJ
ejpam-4768	44	13	for	for	ADP
ejpam-4768	44	14	an	an	DET
ejpam-4768	44	15	hesitant	hesitant	ADJ
ejpam-4768	44	16	fuzzy	fuzzy	ADJ
ejpam-4768	44	17	set	set	VERB
ejpam-4768	44	18	u	u	PRON
ejpam-4768	44	19	∈	∈	PROPN
ejpam-4768	44	20	τ	τ	X
ejpam-4768	44	21	such	such	ADJ
ejpam-4768	44	22	that	that	SCONJ
ejpam-4768	44	23	xλ	xλ	PROPN
ejpam-4768	44	24	∈	∈	PROPN
ejpam-4768	44	25	u	u	PROPN
ejpam-4768	44	26	⊂	⊂	PROPN
ejpam-4768	44	27	n	n	PROPN
ejpam-4768	44	28	.	.	PUNCT
ejpam-4768	45	1	definition	definition	NOUN
ejpam-4768	45	2	2.6	2.6	NUM
ejpam-4768	45	3	.	.	PUNCT
ejpam-4768	46	1	[	[	X
ejpam-4768	46	2	9]a	9]a	NUM
ejpam-4768	46	3	proper	proper	ADJ
ejpam-4768	46	4	nonzero	nonzero	PROPN
ejpam-4768	46	5	hfo	hfo	PROPN
ejpam-4768	46	6	set	set	VERB
ejpam-4768	46	7	ξ	ξ	PROPN
ejpam-4768	46	8	of	of	ADP
ejpam-4768	46	9	xis	xis	PROPN
ejpam-4768	46	10	said	say	VERB
ejpam-4768	46	11	to	to	PART
ejpam-4768	46	12	be	be	AUX
ejpam-4768	46	13	(	(	PUNCT
ejpam-4768	46	14	i)hfmio	i)hfmio	ADV
ejpam-4768	46	15	set	set	VERB
ejpam-4768	46	16	if	if	SCONJ
ejpam-4768	46	17	ξ	ξ	PROPN
ejpam-4768	46	18	and	and	CCONJ
ejpam-4768	46	19	h0	h0	NOUN
ejpam-4768	46	20	are	be	AUX
ejpam-4768	46	21	only	only	ADV
ejpam-4768	46	22	hfo	hfo	NOUN
ejpam-4768	46	23	sets	set	NOUN
ejpam-4768	46	24	contained	contain	VERB
ejpam-4768	46	25	in	in	ADP
ejpam-4768	46	26	ξ	ξ	PROPN
ejpam-4768	46	27	.	.	PUNCT
ejpam-4768	47	1	(	(	PUNCT
ejpam-4768	47	2	ii)hfmao	ii)hfmao	VERB
ejpam-4768	47	3	set	set	NOUN
ejpam-4768	47	4	if	if	SCONJ
ejpam-4768	47	5	h1	h1	PROPN
ejpam-4768	47	6	and	and	CCONJ
ejpam-4768	47	7	ξ	ξ	PROPN
ejpam-4768	47	8	are	be	AUX
ejpam-4768	47	9	only	only	ADV
ejpam-4768	47	10	hfo	hfo	NOUN
ejpam-4768	47	11	sets	set	NOUN
ejpam-4768	47	12	containing	contain	VERB
ejpam-4768	47	13	ξ	ξ	PROPN
ejpam-4768	47	14	.	.	PUNCT
ejpam-4768	48	1	definition	definition	NOUN
ejpam-4768	48	2	2.7	2.7	NUM
ejpam-4768	48	3	.	.	PUNCT
ejpam-4768	49	1	[	[	X
ejpam-4768	49	2	9]a	9]a	NUM
ejpam-4768	49	3	proper	proper	ADJ
ejpam-4768	49	4	nonzero	nonzero	PROPN
ejpam-4768	49	5	hfc	hfc	PROPN
ejpam-4768	49	6	set	set	PROPN
ejpam-4768	49	7	η	η	PROPN
ejpam-4768	49	8	of	of	ADP
ejpam-4768	49	9	xis	xis	PROPN
ejpam-4768	49	10	said	say	VERB
ejpam-4768	49	11	to	to	PART
ejpam-4768	49	12	be	be	AUX
ejpam-4768	49	13	(	(	PUNCT
ejpam-4768	49	14	i	i	NOUN
ejpam-4768	49	15	)	)	PUNCT
ejpam-4768	49	16	hfmac	hfmac	NOUN
ejpam-4768	49	17	set	set	VERB
ejpam-4768	49	18	if	if	SCONJ
ejpam-4768	49	19	any	any	DET
ejpam-4768	49	20	hfc	hfc	NOUN
ejpam-4768	49	21	set	set	NOUN
ejpam-4768	49	22	which	which	PRON
ejpam-4768	49	23	contains	contain	VERB
ejpam-4768	49	24	η	η	PROPN
ejpam-4768	49	25	is	be	AUX
ejpam-4768	49	26	h1	h1	ADJ
ejpam-4768	49	27	or	or	CCONJ
ejpam-4768	49	28	η	η	PROPN
ejpam-4768	49	29	.	.	PROPN
ejpam-4768	49	30	(	(	PUNCT
ejpam-4768	49	31	ii)hfmic	ii)hfmic	NOUN
ejpam-4768	49	32	set	set	VERB
ejpam-4768	49	33	if	if	SCONJ
ejpam-4768	49	34	any	any	DET
ejpam-4768	49	35	hfc	hfc	NOUN
ejpam-4768	49	36	set	set	NOUN
ejpam-4768	49	37	which	which	PRON
ejpam-4768	49	38	is	be	AUX
ejpam-4768	49	39	contained	contain	VERB
ejpam-4768	49	40	in	in	ADP
ejpam-4768	49	41	η	η	PROPN
ejpam-4768	49	42	is	be	AUX
ejpam-4768	49	43	h0	h0	ADJ
ejpam-4768	49	44	or	or	CCONJ
ejpam-4768	49	45	η	η	PROPN
ejpam-4768	49	46	.	.	PROPN
ejpam-4768	49	47	definition	definition	NOUN
ejpam-4768	49	48	2.8	2.8	NUM
ejpam-4768	49	49	.	.	PUNCT
ejpam-4768	50	1	[	[	X
ejpam-4768	50	2	7	7	X
ejpam-4768	50	3	]	]	X
ejpam-4768	50	4	a	a	DET
ejpam-4768	50	5	proper	proper	ADJ
ejpam-4768	50	6	hfclo	hfclo	NOUN
ejpam-4768	50	7	set	set	VERB
ejpam-4768	50	8	φ	φ	PROPN
ejpam-4768	50	9	of	of	ADP
ejpam-4768	50	10	x	x	PROPN
ejpam-4768	50	11	is	be	AUX
ejpam-4768	50	12	called	call	VERB
ejpam-4768	50	13	a	a	DET
ejpam-4768	50	14	hfmiclo	hfmiclo	NOUN
ejpam-4768	50	15	set	set	VERB
ejpam-4768	50	16	if	if	SCONJ
ejpam-4768	50	17	ϱ	ϱ	PROPN
ejpam-4768	50	18	is	be	AUX
ejpam-4768	50	19	a	a	DET
ejpam-4768	50	20	hfclo	hfclo	NOUN
ejpam-4768	50	21	set	set	VERB
ejpam-4768	50	22	such	such	ADJ
ejpam-4768	50	23	that	that	SCONJ
ejpam-4768	50	24	ϱ	ϱ	ADP
ejpam-4768	50	25	<	<	X
ejpam-4768	50	26	φ	φ	PROPN
ejpam-4768	50	27	,	,	PUNCT
ejpam-4768	50	28	then	then	ADV
ejpam-4768	50	29	ϱ	ϱ	X
ejpam-4768	50	30	=	=	SYM
ejpam-4768	50	31	φ	φ	PROPN
ejpam-4768	50	32	or	or	CCONJ
ejpam-4768	50	33	ϱ	ϱ	PROPN
ejpam-4768	50	34	=	=	PROPN
ejpam-4768	50	35	h0	h0	PROPN
ejpam-4768	50	36	.	.	PROPN
ejpam-4768	51	1	definition	definition	NOUN
ejpam-4768	51	2	2.9	2.9	NUM
ejpam-4768	51	3	.	.	PUNCT
ejpam-4768	52	1	[	[	X
ejpam-4768	52	2	7	7	X
ejpam-4768	52	3	]	]	X
ejpam-4768	52	4	a	a	DET
ejpam-4768	52	5	proper	proper	ADJ
ejpam-4768	52	6	hfclo	hfclo	NOUN
ejpam-4768	52	7	set	set	VERB
ejpam-4768	52	8	φ	φ	PROPN
ejpam-4768	52	9	of	of	ADP
ejpam-4768	52	10	x	x	PROPN
ejpam-4768	52	11	is	be	AUX
ejpam-4768	52	12	called	call	VERB
ejpam-4768	52	13	a	a	DET
ejpam-4768	52	14	hfmaclo	hfmaclo	NOUN
ejpam-4768	52	15	set	set	NOUN
ejpam-4768	52	16	if	if	SCONJ
ejpam-4768	52	17	ϱ	ϱ	PROPN
ejpam-4768	52	18	is	be	AUX
ejpam-4768	52	19	a	a	DET
ejpam-4768	52	20	hfclo	hfclo	NOUN
ejpam-4768	52	21	set	set	VERB
ejpam-4768	52	22	such	such	ADJ
ejpam-4768	52	23	that	that	SCONJ
ejpam-4768	52	24	φ	φ	PROPN
ejpam-4768	52	25	<	<	X
ejpam-4768	52	26	ϱ	ϱ	PROPN
ejpam-4768	52	27	,	,	PUNCT
ejpam-4768	52	28	then	then	ADV
ejpam-4768	52	29	φ	φ	PROPN
ejpam-4768	52	30	=	=	SYM
ejpam-4768	52	31	ϱ	ϱ	PROPN
ejpam-4768	52	32	and	and	CCONJ
ejpam-4768	52	33	ϱ	ϱ	NOUN
ejpam-4768	52	34	=	=	PROPN
ejpam-4768	52	35	h1	h1	PROPN
ejpam-4768	52	36	.	.	PUNCT
ejpam-4768	53	1	definition	definition	NOUN
ejpam-4768	53	2	2.10	2.10	NUM
ejpam-4768	53	3	.	.	PUNCT
ejpam-4768	54	1	[	[	X
ejpam-4768	54	2	8	8	NUM
ejpam-4768	54	3	]	]	PUNCT
ejpam-4768	54	4	in	in	ADP
ejpam-4768	54	5	a	a	DET
ejpam-4768	54	6	fts	fts	PROPN
ejpam-4768	54	7	x	x	X
ejpam-4768	54	8	,	,	PUNCT
ejpam-4768	54	9	ξ	ξ	PROPN
ejpam-4768	54	10	is	be	AUX
ejpam-4768	54	11	called	call	VERB
ejpam-4768	54	12	a	a	DET
ejpam-4768	54	13	hfmeo(resp.γ	hfmeo(resp.γ	PROPN
ejpam-4768	54	14	fmec	fmec	NOUN
ejpam-4768	54	15	)	)	PUNCT
ejpam-4768	54	16	if	if	SCONJ
ejpam-4768	54	17	∃	∃	PROPN
ejpam-4768	54	18	λ	λ	PROPN
ejpam-4768	54	19	,	,	PUNCT
ejpam-4768	54	20	µ(̸=	µ(̸=	PROPN
ejpam-4768	54	21	ξ	ξ	PROPN
ejpam-4768	54	22	)	)	PUNCT
ejpam-4768	54	23	two	two	NUM
ejpam-4768	54	24	distinct	distinct	ADJ
ejpam-4768	54	25	proper	proper	ADJ
ejpam-4768	54	26	hfo	hfo	NOUN
ejpam-4768	54	27	sets	set	NOUN
ejpam-4768	54	28	(	(	PUNCT
ejpam-4768	54	29	resp	resp	NOUN
ejpam-4768	54	30	.	.	PUNCT
ejpam-4768	55	1	two	two	NUM
ejpam-4768	55	2	distinct	distinct	ADJ
ejpam-4768	55	3	proper	proper	ADJ
ejpam-4768	55	4	hesitant	hesitant	ADJ
ejpam-4768	55	5	fuzzy	fuzzy	ADJ
ejpam-4768	55	6	closed	closed	ADJ
ejpam-4768	55	7	sets	set	NOUN
ejpam-4768	55	8	ζ	ζ	NOUN
ejpam-4768	55	9	,	,	PUNCT
ejpam-4768	55	10	φ(̸=	φ(̸=	PROPN
ejpam-4768	55	11	γ	γ	NOUN
ejpam-4768	55	12	)	)	PUNCT
ejpam-4768	55	13	)	)	PUNCT
ejpam-4768	55	14	such	such	ADJ
ejpam-4768	55	15	that	that	SCONJ
ejpam-4768	55	16	λ	λ	PROPN
ejpam-4768	55	17	<	<	X
ejpam-4768	55	18	ξ	ξ	X
ejpam-4768	55	19	<	<	X
ejpam-4768	55	20	µ(resp	µ(resp	X
ejpam-4768	55	21	.	.	PUNCT
ejpam-4768	56	1	ζ	ζ	NOUN
ejpam-4768	56	2	<	<	X
ejpam-4768	56	3	γ	γ	X
ejpam-4768	56	4	<	<	X
ejpam-4768	56	5	φ	φ	NUM
ejpam-4768	56	6	)	)	PUNCT
ejpam-4768	56	7	a.	a.	NOUN
ejpam-4768	56	8	swaminathan	swaminathan	PROPN
ejpam-4768	56	9	,	,	PUNCT
ejpam-4768	56	10	cenap	cenap	VERB
ejpam-4768	56	11	ozel	ozel	ADJ
ejpam-4768	56	12	,	,	PUNCT
ejpam-4768	56	13	ibtesam	ibtesam	PROPN
ejpam-4768	56	14	alshammari	alshammari	PROPN
ejpam-4768	56	15	/	/	SYM
ejpam-4768	56	16	eur	eur	PROPN
ejpam-4768	56	17	.	.	PUNCT
ejpam-4768	57	1	j.	j.	PROPN
ejpam-4768	57	2	pure	pure	PROPN
ejpam-4768	57	3	appl	appl	PROPN
ejpam-4768	57	4	.	.	PROPN
ejpam-4768	57	5	math	math	PROPN
ejpam-4768	57	6	,	,	PUNCT
ejpam-4768	57	7	16	16	NUM
ejpam-4768	57	8	(	(	PUNCT
ejpam-4768	57	9	3	3	NUM
ejpam-4768	57	10	)	)	PUNCT
ejpam-4768	57	11	(	(	PUNCT
ejpam-4768	57	12	2023	2023	NUM
ejpam-4768	57	13	)	)	PUNCT
ejpam-4768	57	14	,	,	PUNCT
ejpam-4768	57	15	1381	1381	NUM
ejpam-4768	57	16	-	-	SYM
ejpam-4768	57	17	1388	1388	NUM
ejpam-4768	57	18	1383	1383	NUM
ejpam-4768	57	19	lemma	lemma	PROPN
ejpam-4768	57	20	2.1	2.1	NUM
ejpam-4768	57	21	..	..	PUNCT
ejpam-4768	58	1	[	[	X
ejpam-4768	58	2	6	6	X
ejpam-4768	58	3	]	]	PUNCT
ejpam-4768	58	4	each	each	DET
ejpam-4768	58	5	nonzero	nonzero	PROPN
ejpam-4768	58	6	hfo	hfo	PROPN
ejpam-4768	58	7	set	set	VERB
ejpam-4768	58	8	γ	γ	NOUN
ejpam-4768	58	9	of	of	ADP
ejpam-4768	58	10	a	a	DET
ejpam-4768	58	11	t1	t1	NOUN
ejpam-4768	58	12	-	-	PUNCT
ejpam-4768	58	13	fcts	fct	NOUN
ejpam-4768	58	14	x	x	PUNCT
ejpam-4768	58	15	is	be	AUX
ejpam-4768	58	16	infinite	infinite	ADJ
ejpam-4768	58	17	and	and	CCONJ
ejpam-4768	58	18	is	be	AUX
ejpam-4768	58	19	not	not	PART
ejpam-4768	58	20	a	a	DET
ejpam-4768	58	21	hfmio	hfmio	NOUN
ejpam-4768	58	22	in	in	ADP
ejpam-4768	58	23	x.	x.	PROPN
ejpam-4768	58	24	theorem	theorem	VERB
ejpam-4768	58	25	2.2	2.2	NUM
ejpam-4768	58	26	..	..	PUNCT
ejpam-4768	59	1	[	[	X
ejpam-4768	59	2	6	6	NUM
ejpam-4768	59	3	]	]	PUNCT
ejpam-4768	59	4	a	a	DET
ejpam-4768	59	5	proper	proper	ADJ
ejpam-4768	59	6	hfo	hfo	NOUN
ejpam-4768	59	7	set	set	VERB
ejpam-4768	59	8	γ	γ	NOUN
ejpam-4768	59	9	of	of	ADP
ejpam-4768	59	10	a	a	DET
ejpam-4768	59	11	t1	t1	NOUN
ejpam-4768	59	12	-	-	PUNCT
ejpam-4768	59	13	fcts	fct	NOUN
ejpam-4768	59	14	x	x	PUNCT
ejpam-4768	59	15	is	be	AUX
ejpam-4768	59	16	a	a	DET
ejpam-4768	59	17	hfmeo	hfmeo	NOUN
ejpam-4768	59	18	set	set	VERB
ejpam-4768	59	19	in	in	ADP
ejpam-4768	59	20	x	x	PROPN
ejpam-4768	59	21	iff	iff	PROPN
ejpam-4768	59	22	γ	γ	PROPN
ejpam-4768	59	23	̸=	̸=	PROPN
ejpam-4768	59	24	h1	h1	VERB
ejpam-4768	59	25	−	−	PROPN
ejpam-4768	59	26	{	{	PUNCT
ejpam-4768	59	27	xα	xα	ADP
ejpam-4768	59	28	}	}	PUNCT
ejpam-4768	59	29	for	for	ADP
ejpam-4768	59	30	any	any	PRON
ejpam-4768	59	31	xα	xα	ADP
ejpam-4768	59	32	∈	∈	PROPN
ejpam-4768	59	33	x.	x.	NOUN
ejpam-4768	59	34	2.1	2.1	NUM
ejpam-4768	59	35	.	.	PUNCT
ejpam-4768	60	1	hesitant	hesitant	ADJ
ejpam-4768	60	2	fuzzy	fuzzy	ADJ
ejpam-4768	60	3	maximal	maximal	ADJ
ejpam-4768	60	4	open	open	ADJ
ejpam-4768	60	5	cover	cover	NOUN
ejpam-4768	60	6	and	and	CCONJ
ejpam-4768	60	7	hesitant	hesitant	ADJ
ejpam-4768	60	8	fuzzy	fuzzy	ADJ
ejpam-4768	60	9	m	m	ADJ
ejpam-4768	60	10	-	-	ADJ
ejpam-4768	60	11	compact	compact	ADJ
ejpam-4768	60	12	spaces	space	NOUN
ejpam-4768	60	13	we	we	PRON
ejpam-4768	60	14	now	now	ADV
ejpam-4768	60	15	introduce	introduce	VERB
ejpam-4768	60	16	hesitant	hesitant	ADJ
ejpam-4768	60	17	fuzzy	fuzzy	ADJ
ejpam-4768	60	18	maximal	maximal	ADJ
ejpam-4768	60	19	open	open	ADJ
ejpam-4768	60	20	covers	cover	NOUN
ejpam-4768	60	21	.	.	PUNCT
ejpam-4768	61	1	further	far	ADV
ejpam-4768	61	2	the	the	DET
ejpam-4768	61	3	idea	idea	NOUN
ejpam-4768	61	4	of	of	ADP
ejpam-4768	61	5	hesitant	hesitant	ADJ
ejpam-4768	61	6	fuzzy	fuzzy	ADJ
ejpam-4768	61	7	m	m	ADJ
ejpam-4768	61	8	-	-	ADJ
ejpam-4768	61	9	compact	compact	ADJ
ejpam-4768	61	10	space	space	NOUN
ejpam-4768	61	11	is	be	AUX
ejpam-4768	61	12	studied	study	VERB
ejpam-4768	61	13	by	by	ADP
ejpam-4768	61	14	means	mean	NOUN
ejpam-4768	61	15	of	of	ADP
ejpam-4768	61	16	hesitant	hesitant	ADJ
ejpam-4768	61	17	fuzzy	fuzzy	ADJ
ejpam-4768	61	18	maximal	maximal	ADJ
ejpam-4768	61	19	open	open	ADJ
ejpam-4768	61	20	covers	cover	NOUN
ejpam-4768	61	21	.	.	PUNCT
ejpam-4768	62	1	a	a	DET
ejpam-4768	62	2	hesitant	hesitant	ADJ
ejpam-4768	62	3	fuzzy	fuzzy	ADJ
ejpam-4768	62	4	cover	cover	NOUN
ejpam-4768	62	5	c	c	NOUN
ejpam-4768	62	6	of	of	ADP
ejpam-4768	62	7	x	x	PROPN
ejpam-4768	62	8	is	be	AUX
ejpam-4768	62	9	an	an	DET
ejpam-4768	62	10	hesitant	hesitant	ADJ
ejpam-4768	62	11	fuzzy	fuzzy	ADJ
ejpam-4768	62	12	refinement	refinement	NOUN
ejpam-4768	62	13	of	of	ADP
ejpam-4768	62	14	the	the	DET
ejpam-4768	62	15	hesitant	hesitant	ADJ
ejpam-4768	62	16	fuzzy	fuzzy	ADJ
ejpam-4768	62	17	cover	cover	NOUN
ejpam-4768	62	18	d	d	NOUN
ejpam-4768	62	19	of	of	ADP
ejpam-4768	62	20	x	x	PRON
ejpam-4768	63	1	if	if	SCONJ
ejpam-4768	63	2	∀	∀	NOUN
ejpam-4768	63	3	ξ	ξ	X
ejpam-4768	63	4	∈	∈	PROPN
ejpam-4768	63	5	c	c	NOUN
ejpam-4768	63	6	,	,	PUNCT
ejpam-4768	63	7	∃ζ	∃ζ	PROPN
ejpam-4768	63	8	∈	∈	PROPN
ejpam-4768	63	9	d	d	ADP
ejpam-4768	63	10	such	such	ADJ
ejpam-4768	63	11	that	that	SCONJ
ejpam-4768	63	12	ξ	ξ	X
ejpam-4768	63	13	<	<	X
ejpam-4768	63	14	ζ	ζ	X
ejpam-4768	63	15	.	.	PUNCT
ejpam-4768	63	16	definition	definition	NOUN
ejpam-4768	63	17	2.11	2.11	NUM
ejpam-4768	63	18	.	.	PUNCT
ejpam-4768	64	1	let	let	VERB
ejpam-4768	64	2	c	c	NOUN
ejpam-4768	64	3	and	and	CCONJ
ejpam-4768	64	4	d	d	NOUN
ejpam-4768	64	5	be	be	AUX
ejpam-4768	64	6	two	two	NUM
ejpam-4768	64	7	hesitant	hesitant	ADJ
ejpam-4768	64	8	fuzzy	fuzzy	ADJ
ejpam-4768	64	9	covers	cover	NOUN
ejpam-4768	64	10	of	of	ADP
ejpam-4768	64	11	a	a	DET
ejpam-4768	64	12	hfts	hft	NOUN
ejpam-4768	64	13	x.c	x.c	NOUN
ejpam-4768	64	14	is	be	AUX
ejpam-4768	64	15	an	an	DET
ejpam-4768	64	16	hesitant	hesitant	ADJ
ejpam-4768	64	17	fuzzy	fuzzy	ADJ
ejpam-4768	64	18	s	s	NOUN
ejpam-4768	64	19	-	-	NOUN
ejpam-4768	64	20	refinement	refinement	NOUN
ejpam-4768	64	21	of	of	ADP
ejpam-4768	64	22	d	d	PROPN
ejpam-4768	64	23	if	if	SCONJ
ejpam-4768	64	24	for	for	ADP
ejpam-4768	64	25	each	each	DET
ejpam-4768	64	26	ξ	ξ	PROPN
ejpam-4768	64	27	∈	∈	PROPN
ejpam-4768	64	28	c	c	PROPN
ejpam-4768	64	29	∃	∃	PROPN
ejpam-4768	64	30	ζ	ζ	PROPN
ejpam-4768	64	31	∈	∈	PROPN
ejpam-4768	65	1	d	d	ADP
ejpam-4768	65	2	such	such	ADJ
ejpam-4768	65	3	that	that	SCONJ
ejpam-4768	65	4	ξ	ξ	X
ejpam-4768	65	5	<	<	X
ejpam-4768	65	6	ζ	ζ	X
ejpam-4768	65	7	.	.	PUNCT
ejpam-4768	66	1	a	a	DET
ejpam-4768	66	2	hesitant	hesitant	ADJ
ejpam-4768	66	3	fuzzy	fuzzy	ADJ
ejpam-4768	66	4	srefinement	srefinement	NOUN
ejpam-4768	66	5	c	c	PROPN
ejpam-4768	66	6	of	of	ADP
ejpam-4768	66	7	d	d	PROPN
ejpam-4768	66	8	is	be	AUX
ejpam-4768	66	9	said	say	VERB
ejpam-4768	66	10	to	to	PART
ejpam-4768	66	11	be	be	AUX
ejpam-4768	66	12	a	a	DET
ejpam-4768	66	13	hfo	hfo	NOUN
ejpam-4768	66	14	s	s	NOUN
ejpam-4768	66	15	-	-	PUNCT
ejpam-4768	66	16	refinement	refinement	NOUN
ejpam-4768	66	17	of	of	ADP
ejpam-4768	66	18	d	d	PROPN
ejpam-4768	66	19	if	if	SCONJ
ejpam-4768	66	20	all	all	DET
ejpam-4768	66	21	members	member	NOUN
ejpam-4768	66	22	of	of	ADP
ejpam-4768	66	23	c	c	PROPN
ejpam-4768	66	24	and	and	CCONJ
ejpam-4768	66	25	d	d	PROPN
ejpam-4768	66	26	are	be	AUX
ejpam-4768	66	27	hfo	hfo	NOUN
ejpam-4768	66	28	.	.	PUNCT
ejpam-4768	67	1	it	it	PRON
ejpam-4768	67	2	is	be	AUX
ejpam-4768	67	3	clear	clear	ADJ
ejpam-4768	67	4	that	that	SCONJ
ejpam-4768	67	5	if	if	SCONJ
ejpam-4768	67	6	d	d	NOUN
ejpam-4768	67	7	=	=	PUNCT
ejpam-4768	67	8	{	{	PUNCT
ejpam-4768	67	9	h1	h1	PROPN
ejpam-4768	67	10	}	}	PUNCT
ejpam-4768	67	11	and	and	CCONJ
ejpam-4768	67	12	ξ	ξ	DET
ejpam-4768	67	13	̸=	̸=	PROPN
ejpam-4768	67	14	h1	h1	NOUN
ejpam-4768	67	15	for	for	ADP
ejpam-4768	67	16	each	each	DET
ejpam-4768	67	17	ξ	ξ	PROPN
ejpam-4768	67	18	∈	∈	PROPN
ejpam-4768	67	19	c	c	NOUN
ejpam-4768	67	20	,	,	PUNCT
ejpam-4768	67	21	then	then	ADV
ejpam-4768	67	22	c	c	PROPN
ejpam-4768	67	23	is	be	AUX
ejpam-4768	67	24	an	an	DET
ejpam-4768	67	25	hesitant	hesitant	ADJ
ejpam-4768	67	26	fuzzy	fuzzy	ADJ
ejpam-4768	67	27	s	s	NOUN
ejpam-4768	67	28	-	-	NOUN
ejpam-4768	67	29	refinement	refinement	NOUN
ejpam-4768	67	30	of	of	ADP
ejpam-4768	67	31	d	d	PROPN
ejpam-4768	67	32	.	.	PUNCT
ejpam-4768	68	1	if	if	SCONJ
ejpam-4768	68	2	c	c	PROPN
ejpam-4768	68	3	is	be	AUX
ejpam-4768	68	4	hesitant	hesitant	ADJ
ejpam-4768	68	5	fuzzy	fuzzy	ADJ
ejpam-4768	68	6	s	s	NOUN
ejpam-4768	68	7	-	-	NOUN
ejpam-4768	68	8	refinement	refinement	NOUN
ejpam-4768	68	9	of	of	ADP
ejpam-4768	68	10	d	d	NOUN
ejpam-4768	68	11	then	then	ADV
ejpam-4768	68	12	c	c	PROPN
ejpam-4768	68	13	is	be	AUX
ejpam-4768	68	14	an	an	DET
ejpam-4768	68	15	hesitant	hesitant	ADJ
ejpam-4768	68	16	fuzzy	fuzzy	ADJ
ejpam-4768	68	17	refinement	refinement	NOUN
ejpam-4768	68	18	of	of	ADP
ejpam-4768	68	19	d	d	PROPN
ejpam-4768	68	20	.	.	PUNCT
ejpam-4768	69	1	further	far	ADV
ejpam-4768	69	2	we	we	PRON
ejpam-4768	69	3	see	see	VERB
ejpam-4768	69	4	that	that	SCONJ
ejpam-4768	69	5	no	no	DET
ejpam-4768	69	6	element	element	NOUN
ejpam-4768	69	7	of	of	ADP
ejpam-4768	69	8	an	an	DET
ejpam-4768	69	9	s	s	NOUN
ejpam-4768	69	10	-	-	ADJ
ejpam-4768	69	11	hesitant	hesitant	ADJ
ejpam-4768	69	12	fuzzy	fuzzy	ADJ
ejpam-4768	69	13	refinement	refinement	NOUN
ejpam-4768	69	14	of	of	ADP
ejpam-4768	69	15	any	any	DET
ejpam-4768	69	16	hesitant	hesitant	ADJ
ejpam-4768	69	17	fuzzy	fuzzy	ADJ
ejpam-4768	69	18	cover	cover	NOUN
ejpam-4768	69	19	of	of	ADP
ejpam-4768	69	20	x	x	SYM
ejpam-4768	69	21	is	be	AUX
ejpam-4768	69	22	hfmao	hfmao	ADJ
ejpam-4768	69	23	.	.	PUNCT
ejpam-4768	70	1	definition	definition	NOUN
ejpam-4768	70	2	2.12	2.12	NUM
ejpam-4768	70	3	.	.	PUNCT
ejpam-4768	71	1	a	a	DET
ejpam-4768	71	2	hfo	hfo	PROPN
ejpam-4768	71	3	cover	cover	NOUN
ejpam-4768	71	4	c	c	PROPN
ejpam-4768	71	5	of	of	ADP
ejpam-4768	71	6	a	a	DET
ejpam-4768	71	7	hfts	hft	NOUN
ejpam-4768	71	8	x	x	PUNCT
ejpam-4768	71	9	is	be	AUX
ejpam-4768	71	10	called	call	VERB
ejpam-4768	71	11	a	a	DET
ejpam-4768	71	12	hfmao	hfmao	ADJ
ejpam-4768	71	13	cover	cover	NOUN
ejpam-4768	71	14	of	of	ADP
ejpam-4768	71	15	x	x	PRON
ejpam-4768	71	16	if	if	SCONJ
ejpam-4768	71	17	c	c	PROPN
ejpam-4768	71	18	is	be	AUX
ejpam-4768	71	19	not	not	PART
ejpam-4768	71	20	an	an	DET
ejpam-4768	71	21	hesitant	hesitant	ADJ
ejpam-4768	71	22	fuzzy	fuzzy	ADJ
ejpam-4768	71	23	s	s	NOUN
ejpam-4768	71	24	-	-	NOUN
ejpam-4768	71	25	refinement	refinement	NOUN
ejpam-4768	71	26	of	of	ADP
ejpam-4768	71	27	any	any	DET
ejpam-4768	71	28	other	other	ADJ
ejpam-4768	71	29	hfo	hfo	NOUN
ejpam-4768	71	30	cover	cover	NOUN
ejpam-4768	71	31	of	of	ADP
ejpam-4768	71	32	x.	x.	PROPN
ejpam-4768	71	33	lemma	lemma	PROPN
ejpam-4768	71	34	2.3	2.3	NUM
ejpam-4768	71	35	..	..	PUNCT
ejpam-4768	71	36	a	a	DET
ejpam-4768	71	37	hfo	hfo	PROPN
ejpam-4768	71	38	cover	cover	NOUN
ejpam-4768	71	39	containing	contain	VERB
ejpam-4768	71	40	a	a	DET
ejpam-4768	71	41	hfmao	hfmao	NOUN
ejpam-4768	71	42	set	set	NOUN
ejpam-4768	71	43	is	be	AUX
ejpam-4768	71	44	hesitant	hesitant	ADJ
ejpam-4768	71	45	fuzzy	fuzzy	ADJ
ejpam-4768	71	46	maximal	maximal	ADJ
ejpam-4768	71	47	.	.	PUNCT
ejpam-4768	72	1	proof	proof	NOUN
ejpam-4768	72	2	.	.	PUNCT
ejpam-4768	73	1	obvious	obvious	ADJ
ejpam-4768	73	2	.	.	PUNCT
ejpam-4768	74	1	theorem	theorem	VERB
ejpam-4768	74	2	2.4	2.4	NUM
ejpam-4768	74	3	.	.	PUNCT
ejpam-4768	75	1	(	(	PUNCT
ejpam-4768	75	2	existence	existence	NOUN
ejpam-4768	75	3	of	of	ADP
ejpam-4768	75	4	hfmao	hfmao	NOUN
ejpam-4768	75	5	covers	cover	NOUN
ejpam-4768	75	6	)	)	PUNCT
ejpam-4768	75	7	.	.	PUNCT
ejpam-4768	76	1	there	there	PRON
ejpam-4768	76	2	exists	exist	VERB
ejpam-4768	76	3	a	a	DET
ejpam-4768	76	4	hfmao	hfmao	NOUN
ejpam-4768	76	5	cover	cover	NOUN
ejpam-4768	76	6	in	in	ADP
ejpam-4768	76	7	an	an	DET
ejpam-4768	76	8	infinite	infinite	ADJ
ejpam-4768	76	9	t1	t1	NOUN
ejpam-4768	76	10	-	-	PUNCT
ejpam-4768	76	11	hfts	hft	NOUN
ejpam-4768	76	12	.	.	PUNCT
ejpam-4768	77	1	proof	proof	NOUN
ejpam-4768	77	2	.	.	PUNCT
ejpam-4768	78	1	letx	letx	PROPN
ejpam-4768	78	2	be	be	AUX
ejpam-4768	78	3	an	an	DET
ejpam-4768	78	4	infinite	infinite	ADJ
ejpam-4768	78	5	t1	t1	NOUN
ejpam-4768	78	6	-	-	PUNCT
ejpam-4768	78	7	hfts	hft	NOUN
ejpam-4768	78	8	.	.	PUNCT
ejpam-4768	79	1	then	then	ADV
ejpam-4768	79	2	for	for	SCONJ
ejpam-4768	79	3	each	each	PRON
ejpam-4768	79	4	xα	xα	PUNCT
ejpam-4768	79	5	∈	∈	PROPN
ejpam-4768	79	6	x	x	X
ejpam-4768	79	7	,	,	PUNCT
ejpam-4768	79	8	h1−{xα	h1−{xα	PROPN
ejpam-4768	79	9	}	}	PUNCT
ejpam-4768	79	10	is	be	AUX
ejpam-4768	79	11	hfmao	hfmao	ADV
ejpam-4768	79	12	set	set	VERB
ejpam-4768	79	13	in	in	ADP
ejpam-4768	79	14	x.	x.	NOUN
ejpam-4768	79	15	let	let	VERB
ejpam-4768	79	16	xβ	xβ	NOUN
ejpam-4768	79	17	∈	∈	PROPN
ejpam-4768	79	18	x.	x.	NOUN
ejpam-4768	79	19	consider	consider	VERB
ejpam-4768	79	20	a	a	DET
ejpam-4768	79	21	finite	finite	ADJ
ejpam-4768	79	22	hesitant	hesitant	ADJ
ejpam-4768	79	23	fuzzy	fuzzy	ADJ
ejpam-4768	79	24	subset	subset	VERB
ejpam-4768	79	25	m	m	VERB
ejpam-4768	79	26	=	=	SYM
ejpam-4768	79	27	{	{	PUNCT
ejpam-4768	79	28	xαi	xαi	PROPN
ejpam-4768	79	29	|xαi	|xαi	PROPN
ejpam-4768	79	30	̸=	̸=	PROPN
ejpam-4768	79	31	φ	φ	NUM
ejpam-4768	79	32	,	,	PUNCT
ejpam-4768	79	33	i	i	PROPN
ejpam-4768	79	34	∈	∈	PROPN
ejpam-4768	80	1	z	z	X
ejpam-4768	80	2	;	;	PUNCT
ejpam-4768	80	3	1	1	NUM
ejpam-4768	80	4	≤	≤	NUM
ejpam-4768	80	5	i	i	PRON
ejpam-4768	80	6	≤	≤	NOUN
ejpam-4768	80	7	n	n	CCONJ
ejpam-4768	80	8	}	}	PUNCT
ejpam-4768	80	9	.	.	PUNCT
ejpam-4768	81	1	also	also	ADV
ejpam-4768	81	2	ξ	ξ	X
ejpam-4768	81	3	in	in	ADP
ejpam-4768	81	4	x	x	SYM
ejpam-4768	81	5	is	be	AUX
ejpam-4768	81	6	hesitant	hesitant	ADJ
ejpam-4768	81	7	fuzzy	fuzzy	ADJ
ejpam-4768	81	8	closed	closed	ADJ
ejpam-4768	81	9	as	as	SCONJ
ejpam-4768	81	10	x	x	PROPN
ejpam-4768	81	11	is	be	AUX
ejpam-4768	81	12	t1	t1	NOUN
ejpam-4768	81	13	-	-	PUNCT
ejpam-4768	81	14	hfts	hft	NOUN
ejpam-4768	81	15	.	.	PUNCT
ejpam-4768	82	1	henceforth	henceforth	ADV
ejpam-4768	82	2	{	{	PUNCT
ejpam-4768	82	3	h1−{xβ	h1−{xβ	NOUN
ejpam-4768	82	4	}	}	PUNCT
ejpam-4768	82	5	,	,	PUNCT
ejpam-4768	82	6	h1−g	h1−g	PROPN
ejpam-4768	82	7	}	}	PUNCT
ejpam-4768	82	8	is	be	AUX
ejpam-4768	82	9	hfo	hfo	NOUN
ejpam-4768	82	10	cover	cover	NOUN
ejpam-4768	82	11	of	of	ADP
ejpam-4768	82	12	x	x	PUNCT
ejpam-4768	82	13	having	having	AUX
ejpam-4768	82	14	hfmao	hfmao	ADV
ejpam-4768	82	15	set	set	VERB
ejpam-4768	82	16	h1−{xβ	h1−{xβ	NOUN
ejpam-4768	82	17	}	}	PUNCT
ejpam-4768	82	18	.	.	PUNCT
ejpam-4768	83	1	hence	hence	ADV
ejpam-4768	83	2	by	by	ADP
ejpam-4768	83	3	lemma	lemma	PROPN
ejpam-4768	83	4	2.3.,{h1−{xβ	2.3.,{h1−{xβ	PROPN
ejpam-4768	83	5	}	}	PUNCT
ejpam-4768	83	6	,	,	PUNCT
ejpam-4768	83	7	h1−m	h1−m	PROPN
ejpam-4768	83	8	}	}	PUNCT
ejpam-4768	83	9	is	be	AUX
ejpam-4768	83	10	hfmao	hfmao	NOUN
ejpam-4768	83	11	cover	cover	NOUN
ejpam-4768	83	12	of	of	ADP
ejpam-4768	83	13	x.	x.	NOUN
ejpam-4768	83	14	theorem	theorem	VERB
ejpam-4768	83	15	2.5	2.5	NUM
ejpam-4768	83	16	..	..	PUNCT
ejpam-4768	84	1	any	any	DET
ejpam-4768	84	2	hfo	hfo	NOUN
ejpam-4768	84	3	cover	cover	VERB
ejpam-4768	84	4	m	m	PROPN
ejpam-4768	84	5	of	of	ADP
ejpam-4768	84	6	an	an	DET
ejpam-4768	84	7	infinite	infinite	ADJ
ejpam-4768	84	8	t1	t1	NOUN
ejpam-4768	84	9	-	-	PUNCT
ejpam-4768	84	10	hfts	hft	NOUN
ejpam-4768	84	11	is	be	AUX
ejpam-4768	84	12	a	a	DET
ejpam-4768	84	13	hfmao	hfmao	ADJ
ejpam-4768	84	14	cover	cover	NOUN
ejpam-4768	84	15	of	of	ADP
ejpam-4768	84	16	x	x	SYM
ejpam-4768	84	17	iff	iff	PROPN
ejpam-4768	84	18	m	m	PROPN
ejpam-4768	84	19	contains	contain	VERB
ejpam-4768	84	20	a	a	DET
ejpam-4768	84	21	hfmao	hfmao	NOUN
ejpam-4768	84	22	set	set	NOUN
ejpam-4768	84	23	.	.	PUNCT
ejpam-4768	85	1	proof	proof	NOUN
ejpam-4768	85	2	.	.	PUNCT
ejpam-4768	86	1	let	let	VERB
ejpam-4768	86	2	m	m	VERB
ejpam-4768	86	3	=	=	PRON
ejpam-4768	86	4	{	{	PUNCT
ejpam-4768	86	5	uk|k	uk|k	NOUN
ejpam-4768	86	6	∈	∈	NOUN
ejpam-4768	86	7	v	v	AUX
ejpam-4768	86	8	}	}	PUNCT
ejpam-4768	86	9	be	be	AUX
ejpam-4768	86	10	a	a	DET
ejpam-4768	86	11	hfmao	hfmao	ADJ
ejpam-4768	86	12	cover	cover	NOUN
ejpam-4768	86	13	of	of	ADP
ejpam-4768	86	14	x	x	SYM
ejpam-4768	86	15	such	such	ADJ
ejpam-4768	86	16	that	that	SCONJ
ejpam-4768	86	17	no	no	DET
ejpam-4768	86	18	uk	uk	PROPN
ejpam-4768	86	19	,	,	PUNCT
ejpam-4768	86	20	k	k	PROPN
ejpam-4768	86	21	∈	∈	PROPN
ejpam-4768	86	22	v	v	NOUN
ejpam-4768	86	23	is	be	AUX
ejpam-4768	86	24	hfmao	hfmao	ADJ
ejpam-4768	86	25	.	.	PUNCT
ejpam-4768	87	1	by	by	ADP
ejpam-4768	87	2	theorem	theorem	NOUN
ejpam-4768	87	3	2.2	2.2	NUM
ejpam-4768	87	4	.	.	NUM
ejpam-4768	87	5	,	,	PUNCT
ejpam-4768	87	6	uk	uk	PROPN
ejpam-4768	87	7	is	be	AUX
ejpam-4768	87	8	not	not	PART
ejpam-4768	87	9	also	also	ADV
ejpam-4768	87	10	hfmio	hfmio	VERB
ejpam-4768	87	11	for	for	ADP
ejpam-4768	87	12	each	each	DET
ejpam-4768	87	13	k	k	PROPN
ejpam-4768	87	14	∈	∈	PROPN
ejpam-4768	87	15	v	v	ADP
ejpam-4768	87	16	which	which	PRON
ejpam-4768	87	17	implies	imply	VERB
ejpam-4768	87	18	that	that	SCONJ
ejpam-4768	87	19	uk	uk	PROPN
ejpam-4768	87	20	,	,	PUNCT
ejpam-4768	87	21	k	k	PROPN
ejpam-4768	87	22	∈	∈	PROPN
ejpam-4768	87	23	v	v	NOUN
ejpam-4768	87	24	is	be	AUX
ejpam-4768	87	25	hfmeo	hfmeo	NOUN
ejpam-4768	87	26	.	.	PUNCT
ejpam-4768	88	1	so	so	ADV
ejpam-4768	88	2	∀	∀	PUNCT
ejpam-4768	88	3	k	k	X
ejpam-4768	88	4	∈	∈	PROPN
ejpam-4768	88	5	v	v	NOUN
ejpam-4768	88	6	,	,	PUNCT
ejpam-4768	88	7	∃vk	∃vk	VERB
ejpam-4768	88	8	a	a	DET
ejpam-4768	88	9	proper	proper	ADJ
ejpam-4768	88	10	hfo	hfo	NOUN
ejpam-4768	88	11	set	set	VERB
ejpam-4768	88	12	vksuch	vksuch	ADP
ejpam-4768	88	13	that	that	SCONJ
ejpam-4768	88	14	uk	uk	PROPN
ejpam-4768	88	15	<	<	X
ejpam-4768	88	16	̸	̸	PUNCT
ejpam-4768	88	17	=	=	SYM
ejpam-4768	88	18	vk	vk	PROPN
ejpam-4768	88	19	.	.	PUNCT
ejpam-4768	89	1	let	let	VERB
ejpam-4768	89	2	a.	a.	NOUN
ejpam-4768	89	3	swaminathan	swaminathan	PROPN
ejpam-4768	89	4	,	,	PUNCT
ejpam-4768	89	5	cenap	cenap	VERB
ejpam-4768	89	6	ozel	ozel	ADJ
ejpam-4768	89	7	,	,	PUNCT
ejpam-4768	89	8	ibtesam	ibtesam	PROPN
ejpam-4768	89	9	alshammari	alshammari	PROPN
ejpam-4768	89	10	/	/	SYM
ejpam-4768	89	11	eur	eur	PROPN
ejpam-4768	89	12	.	.	PUNCT
ejpam-4768	90	1	j.	j.	PROPN
ejpam-4768	90	2	pure	pure	PROPN
ejpam-4768	90	3	appl	appl	PROPN
ejpam-4768	90	4	.	.	PROPN
ejpam-4768	90	5	math	math	PROPN
ejpam-4768	90	6	,	,	PUNCT
ejpam-4768	90	7	16	16	NUM
ejpam-4768	90	8	(	(	PUNCT
ejpam-4768	90	9	3	3	NUM
ejpam-4768	90	10	)	)	PUNCT
ejpam-4768	90	11	(	(	PUNCT
ejpam-4768	90	12	2023	2023	NUM
ejpam-4768	90	13	)	)	PUNCT
ejpam-4768	90	14	,	,	PUNCT
ejpam-4768	90	15	1381	1381	NUM
ejpam-4768	90	16	-	-	SYM
ejpam-4768	90	17	1388	1388	NUM
ejpam-4768	90	18	1384	1384	NUM
ejpam-4768	90	19	n	n	NOUN
ejpam-4768	90	20	=	=	PRON
ejpam-4768	90	21	{	{	PUNCT
ejpam-4768	90	22	vk|uk	vk|uk	PROPN
ejpam-4768	90	23	⪇	⪇	X
ejpam-4768	90	24	vk	vk	PROPN
ejpam-4768	90	25	,	,	PUNCT
ejpam-4768	90	26	uk	uk	PROPN
ejpam-4768	90	27	∈	∈	PROPN
ejpam-4768	90	28	m	m	PROPN
ejpam-4768	90	29	}	}	PUNCT
ejpam-4768	90	30	.	.	PUNCT
ejpam-4768	91	1	clearly	clearly	ADV
ejpam-4768	91	2	n	n	PRON
ejpam-4768	91	3	is	be	AUX
ejpam-4768	91	4	hesitant	hesitant	ADJ
ejpam-4768	91	5	fuzzy	fuzzy	ADJ
ejpam-4768	91	6	cover	cover	NOUN
ejpam-4768	91	7	of	of	ADP
ejpam-4768	91	8	x.	x.	NOUN
ejpam-4768	91	9	therefore	therefore	ADV
ejpam-4768	91	10	m	m	PROPN
ejpam-4768	91	11	is	be	AUX
ejpam-4768	91	12	an	an	DET
ejpam-4768	91	13	hesitant	hesitant	ADJ
ejpam-4768	91	14	fuzzy	fuzzy	ADJ
ejpam-4768	91	15	s	s	NOUN
ejpam-4768	91	16	-	-	NOUN
ejpam-4768	91	17	refinement	refinement	NOUN
ejpam-4768	91	18	of	of	ADP
ejpam-4768	91	19	n	n	DET
ejpam-4768	91	20	a	a	DET
ejpam-4768	91	21	contradiction	contradiction	NOUN
ejpam-4768	91	22	to	to	ADP
ejpam-4768	91	23	tha	tha	ADJ
ejpam-4768	91	24	fact	fact	NOUN
ejpam-4768	91	25	that	that	SCONJ
ejpam-4768	91	26	m	m	NOUN
ejpam-4768	91	27	is	be	AUX
ejpam-4768	91	28	a	a	DET
ejpam-4768	91	29	hfmao	hfmao	ADJ
ejpam-4768	91	30	cover	cover	NOUN
ejpam-4768	91	31	of	of	ADP
ejpam-4768	91	32	x.	x.	NOUN
ejpam-4768	91	33	hence	hence	ADV
ejpam-4768	91	34	m	m	VERB
ejpam-4768	91	35	has	have	VERB
ejpam-4768	91	36	a	a	DET
ejpam-4768	91	37	hfmao	hfmao	NOUN
ejpam-4768	91	38	set	set	VERB
ejpam-4768	91	39	as	as	ADP
ejpam-4768	91	40	one	one	NUM
ejpam-4768	91	41	among	among	ADP
ejpam-4768	91	42	its	its	PRON
ejpam-4768	91	43	members	member	NOUN
ejpam-4768	91	44	.	.	PUNCT
ejpam-4768	92	1	the	the	DET
ejpam-4768	92	2	converse	converse	NOUN
ejpam-4768	92	3	part	part	NOUN
ejpam-4768	92	4	follows	follow	VERB
ejpam-4768	92	5	by	by	ADP
ejpam-4768	92	6	lemma	lemma	PROPN
ejpam-4768	92	7	2.3	2.3	NUM
ejpam-4768	92	8	..	..	PUNCT
ejpam-4768	92	9	definition	definition	NOUN
ejpam-4768	92	10	2.13	2.13	NUM
ejpam-4768	92	11	.	.	PUNCT
ejpam-4768	93	1	a	a	DET
ejpam-4768	93	2	hfts	hft	NOUN
ejpam-4768	93	3	x	x	PRON
ejpam-4768	93	4	is	be	AUX
ejpam-4768	93	5	said	say	VERB
ejpam-4768	93	6	to	to	PART
ejpam-4768	93	7	be	be	AUX
ejpam-4768	93	8	a	a	DET
ejpam-4768	93	9	hesitant	hesitant	ADJ
ejpam-4768	93	10	fuzzy	fuzzy	ADJ
ejpam-4768	93	11	m	m	NOUN
ejpam-4768	93	12	-	-	ADJ
ejpam-4768	93	13	compact	compact	ADJ
ejpam-4768	93	14	if	if	SCONJ
ejpam-4768	93	15	each	each	DET
ejpam-4768	93	16	hfmo	hfmo	NOUN
ejpam-4768	93	17	cover	cover	VERB
ejpam-4768	93	18	of	of	ADP
ejpam-4768	93	19	x	x	PUNCT
ejpam-4768	93	20	has	have	VERB
ejpam-4768	93	21	a	a	DET
ejpam-4768	93	22	finite	finite	ADJ
ejpam-4768	93	23	hfo	hfo	PROPN
ejpam-4768	93	24	s	s	PROPN
ejpam-4768	93	25	-	-	PUNCT
ejpam-4768	93	26	refinement	refinement	NOUN
ejpam-4768	93	27	.	.	PUNCT
ejpam-4768	94	1	theorem	theorem	VERB
ejpam-4768	94	2	2.6	2.6	NUM
ejpam-4768	94	3	..	..	PUNCT
ejpam-4768	94	4	every	every	DET
ejpam-4768	94	5	infinite	infinite	ADJ
ejpam-4768	94	6	t1	t1	NOUN
ejpam-4768	94	7	-	-	PUNCT
ejpam-4768	94	8	hfcts	hfct	NOUN
ejpam-4768	94	9	is	be	AUX
ejpam-4768	94	10	hesitant	hesitant	ADJ
ejpam-4768	94	11	fuzzy	fuzzy	ADJ
ejpam-4768	94	12	m	m	NOUN
ejpam-4768	94	13	-	-	ADJ
ejpam-4768	94	14	compact	compact	ADJ
ejpam-4768	94	15	.	.	PUNCT
ejpam-4768	95	1	proof	proof	NOUN
ejpam-4768	95	2	.	.	PUNCT
ejpam-4768	96	1	let	let	VERB
ejpam-4768	96	2	m	m	PRON
ejpam-4768	96	3	be	be	AUX
ejpam-4768	96	4	hfmao	hfmao	ADJ
ejpam-4768	96	5	cover	cover	NOUN
ejpam-4768	96	6	of	of	ADP
ejpam-4768	96	7	an	an	DET
ejpam-4768	96	8	infinite	infinite	ADJ
ejpam-4768	96	9	t1	t1	NOUN
ejpam-4768	96	10	-	-	PUNCT
ejpam-4768	96	11	hfcts	hfct	NOUN
ejpam-4768	96	12	x.	x.	NOUN
ejpam-4768	96	13	by	by	ADP
ejpam-4768	96	14	theorem	theorem	NOUN
ejpam-4768	96	15	2.5	2.5	NUM
ejpam-4768	96	16	.	.	PUNCT
ejpam-4768	96	17	,	,	PUNCT
ejpam-4768	96	18	m	m	VERB
ejpam-4768	96	19	contains	contain	VERB
ejpam-4768	96	20	a	a	DET
ejpam-4768	96	21	hfmao	hfmao	NOUN
ejpam-4768	96	22	set	set	NOUN
ejpam-4768	96	23	u	u	NOUN
ejpam-4768	96	24	.	.	PUNCT
ejpam-4768	97	1	by	by	ADP
ejpam-4768	97	2	theorem	theorem	NOUN
ejpam-4768	97	3	2.5	2.5	NUM
ejpam-4768	97	4	.	.	PUNCT
ejpam-4768	97	5	,	,	PUNCT
ejpam-4768	97	6	take	take	VERB
ejpam-4768	97	7	u	u	NOUN
ejpam-4768	97	8	=	=	SYM
ejpam-4768	97	9	h1−{xα	h1−{xα	NOUN
ejpam-4768	97	10	}	}	PUNCT
ejpam-4768	97	11	for	for	ADP
ejpam-4768	97	12	some	some	PRON
ejpam-4768	97	13	xα	xα	PUNCT
ejpam-4768	97	14	∈	∈	PROPN
ejpam-4768	97	15	x.	x.	NOUN
ejpam-4768	97	16	there	there	PRON
ejpam-4768	97	17	is	be	VERB
ejpam-4768	97	18	an	an	DET
ejpam-4768	97	19	v	v	NUM
ejpam-4768	97	20	∈	∈	NOUN
ejpam-4768	97	21	m	m	VERB
ejpam-4768	97	22	such	such	ADJ
ejpam-4768	97	23	that	that	SCONJ
ejpam-4768	97	24	xα	xα	PUNCT
ejpam-4768	97	25	∈	∈	PROPN
ejpam-4768	97	26	v	v	NOUN
ejpam-4768	97	27	.	.	PUNCT
ejpam-4768	98	1	by	by	ADP
ejpam-4768	98	2	lemma	lemma	PROPN
ejpam-4768	98	3	2.1	2.1	NUM
ejpam-4768	98	4	.	.	PUNCT
ejpam-4768	98	5	,	,	PUNCT
ejpam-4768	98	6	for	for	ADP
ejpam-4768	98	7	hesitant	hesitant	ADJ
ejpam-4768	98	8	fuzzy	fuzzy	ADJ
ejpam-4768	98	9	points	point	NOUN
ejpam-4768	98	10	xα	xα	ADJ
ejpam-4768	98	11	,	,	PUNCT
ejpam-4768	98	12	xβ	xβ	PROPN
ejpam-4768	98	13	∈	∈	PROPN
ejpam-4768	98	14	v	v	NOUN
ejpam-4768	98	15	with	with	ADP
ejpam-4768	98	16	xα	xα	CCONJ
ejpam-4768	99	1	̸=	̸=	PROPN
ejpam-4768	99	2	xβ	xβ	ADV
ejpam-4768	99	3	there	there	PRON
ejpam-4768	99	4	are	be	VERB
ejpam-4768	99	5	hfo	hfo	PROPN
ejpam-4768	99	6	sets	set	NOUN
ejpam-4768	99	7	v1	v1	NOUN
ejpam-4768	99	8	=	=	PUNCT
ejpam-4768	99	9	h1	h1	PROPN
ejpam-4768	99	10	−	−	PROPN
ejpam-4768	99	11	{	{	PUNCT
ejpam-4768	99	12	xα	xα	PROPN
ejpam-4768	99	13	,	,	PUNCT
ejpam-4768	99	14	xβ},v2	xβ},v2	PROPN
ejpam-4768	99	15	=	=	SYM
ejpam-4768	100	1	v	v	PROPN
ejpam-4768	100	2	−	−	PROPN
ejpam-4768	100	3	{	{	PUNCT
ejpam-4768	100	4	xα},v3	xα},v3	PROPN
ejpam-4768	100	5	=	=	PROPN
ejpam-4768	100	6	v	v	PROPN
ejpam-4768	100	7	−	−	PROPN
ejpam-4768	100	8	{	{	PUNCT
ejpam-4768	100	9	xβ	xβ	NOUN
ejpam-4768	100	10	}	}	PUNCT
ejpam-4768	100	11	of	of	ADP
ejpam-4768	100	12	x.	x.	NOUN
ejpam-4768	100	13	then	then	ADV
ejpam-4768	100	14	{	{	PUNCT
ejpam-4768	100	15	v1	v1	PROPN
ejpam-4768	100	16	,	,	PUNCT
ejpam-4768	100	17	v2	v2	PROPN
ejpam-4768	100	18	,	,	PUNCT
ejpam-4768	100	19	v3	v3	PROPN
ejpam-4768	100	20	}	}	PUNCT
ejpam-4768	100	21	is	be	AUX
ejpam-4768	100	22	an	an	DET
ejpam-4768	100	23	hesitant	hesitant	ADJ
ejpam-4768	100	24	fuzzy	fuzzy	ADJ
ejpam-4768	100	25	s	s	NOUN
ejpam-4768	100	26	-	-	NOUN
ejpam-4768	100	27	refinement	refinement	NOUN
ejpam-4768	100	28	of	of	ADP
ejpam-4768	100	29	m	m	PROPN
ejpam-4768	100	30	.	.	PUNCT
ejpam-4768	101	1	example	example	NOUN
ejpam-4768	101	2	2.7	2.7	NUM
ejpam-4768	101	3	..	..	PUNCT
ejpam-4768	102	1	let	let	VERB
ejpam-4768	102	2	τ	τ	PROPN
ejpam-4768	102	3	=	=	SYM
ejpam-4768	102	4	{	{	PUNCT
ejpam-4768	102	5	h0	h0	PROPN
ejpam-4768	102	6	,	,	PUNCT
ejpam-4768	102	7	h1	h1	PROPN
ejpam-4768	102	8	,	,	PUNCT
ejpam-4768	102	9	h1	h1	PROPN
ejpam-4768	102	10	,	,	PUNCT
ejpam-4768	102	11	h2	h2	PROPN
ejpam-4768	102	12	,	,	PUNCT
ejpam-4768	102	13	h3	h3	NOUN
ejpam-4768	102	14	,	,	PUNCT
ejpam-4768	102	15	h4	h4	NOUN
ejpam-4768	102	16	}	}	PUNCT
ejpam-4768	102	17	and	and	CCONJ
ejpam-4768	102	18	(	(	PUNCT
ejpam-4768	102	19	x	x	X
ejpam-4768	102	20	,	,	PUNCT
ejpam-4768	102	21	τ	τ	X
ejpam-4768	102	22	)	)	PUNCT
ejpam-4768	102	23	be	be	VERB
ejpam-4768	102	24	a	a	DET
ejpam-4768	102	25	hesitant	hesitant	ADJ
ejpam-4768	102	26	fuzzy	fuzzy	ADJ
ejpam-4768	102	27	topological	topological	ADJ
ejpam-4768	102	28	space	space	NOUN
ejpam-4768	102	29	where	where	SCONJ
ejpam-4768	102	30	h1	h1	NOUN
ejpam-4768	102	31	=	=	PRON
ejpam-4768	102	32	{	{	PUNCT
ejpam-4768	102	33	[	[	X
ejpam-4768	102	34	0	0	NUM
ejpam-4768	102	35	,	,	PUNCT
ejpam-4768	102	36	1	1	NUM
ejpam-4768	102	37	]	]	PUNCT
ejpam-4768	102	38	if	if	SCONJ
ejpam-4768	102	39	x	x	PROPN
ejpam-4768	102	40	̸=	̸=	NOUN
ejpam-4768	102	41	1	1	NUM
ejpam-4768	102	42	4	4	NUM
ejpam-4768	102	43	0	0	NUM
ejpam-4768	102	44	if	if	SCONJ
ejpam-4768	102	45	x	x	SYM
ejpam-4768	102	46	=	=	SYM
ejpam-4768	102	47	1	1	NUM
ejpam-4768	102	48	4	4	NUM
ejpam-4768	102	49	;	;	PUNCT
ejpam-4768	102	50	h2	h2	NOUN
ejpam-4768	102	51	=	=	PUNCT
ejpam-4768	102	52	{	{	PUNCT
ejpam-4768	102	53	0	0	NUM
ejpam-4768	102	54	if	if	SCONJ
ejpam-4768	102	55	x	x	NUM
ejpam-4768	102	56	̸=	̸=	NOUN
ejpam-4768	102	57	1	1	NUM
ejpam-4768	102	58	4	4	NUM
ejpam-4768	102	59	[	[	X
ejpam-4768	102	60	0	0	NUM
ejpam-4768	102	61	,	,	PUNCT
ejpam-4768	102	62	1	1	NUM
ejpam-4768	102	63	]	]	PUNCT
ejpam-4768	102	64	if	if	SCONJ
ejpam-4768	102	65	x	x	SYM
ejpam-4768	102	66	=	=	SYM
ejpam-4768	102	67	1	1	NUM
ejpam-4768	102	68	4	4	NUM
ejpam-4768	102	69	;	;	PUNCT
ejpam-4768	102	70	h3	h3	NOUN
ejpam-4768	102	71	=	=	SYM
ejpam-4768	102	72	{	{	PUNCT
ejpam-4768	102	73	[	[	X
ejpam-4768	102	74	0	0	NUM
ejpam-4768	102	75	,	,	PUNCT
ejpam-4768	102	76	14	14	NUM
ejpam-4768	102	77	]	]	PUNCT
ejpam-4768	102	78	if	if	SCONJ
ejpam-4768	102	79	x	x	PROPN
ejpam-4768	102	80	̸=	̸=	NOUN
ejpam-4768	102	81	1	1	NUM
ejpam-4768	102	82	4	4	NUM
ejpam-4768	102	83	[	[	X
ejpam-4768	102	84	0	0	NUM
ejpam-4768	102	85	,	,	PUNCT
ejpam-4768	102	86	1	1	NUM
ejpam-4768	102	87	]	]	PUNCT
ejpam-4768	102	88	if	if	SCONJ
ejpam-4768	102	89	x	x	SYM
ejpam-4768	102	90	=	=	SYM
ejpam-4768	102	91	1	1	NUM
ejpam-4768	102	92	4	4	NUM
ejpam-4768	102	93	;	;	PUNCT
ejpam-4768	102	94	h4	h4	PROPN
ejpam-4768	102	95	=	=	NUM
ejpam-4768	102	96	{	{	PUNCT
ejpam-4768	102	97	[	[	X
ejpam-4768	102	98	0	0	NUM
ejpam-4768	102	99	,	,	PUNCT
ejpam-4768	102	100	14	14	NUM
ejpam-4768	102	101	]	]	PUNCT
ejpam-4768	102	102	if	if	SCONJ
ejpam-4768	102	103	x	x	PROPN
ejpam-4768	102	104	̸=	̸=	NOUN
ejpam-4768	102	105	1	1	NUM
ejpam-4768	102	106	4	4	NUM
ejpam-4768	102	107	0	0	NUM
ejpam-4768	102	108	if	if	SCONJ
ejpam-4768	102	109	x	x	NOUN
ejpam-4768	102	110	=	=	SYM
ejpam-4768	102	111	1	1	NUM
ejpam-4768	102	112	4	4	NUM
ejpam-4768	102	113	.	.	PUNCT
ejpam-4768	103	1	clearly	clearly	ADV
ejpam-4768	103	2	(	(	PUNCT
ejpam-4768	103	3	x	x	X
ejpam-4768	103	4	,	,	PUNCT
ejpam-4768	103	5	τ	τ	X
ejpam-4768	103	6	)	)	PUNCT
ejpam-4768	103	7	is	be	AUX
ejpam-4768	103	8	hesitant	hesitant	ADJ
ejpam-4768	103	9	fuzzy	fuzzy	ADJ
ejpam-4768	103	10	compact	compact	ADJ
ejpam-4768	103	11	but	but	CCONJ
ejpam-4768	103	12	not	not	PART
ejpam-4768	103	13	hesitant	hesitant	ADJ
ejpam-4768	103	14	fuzzy	fuzzy	ADJ
ejpam-4768	103	15	m	m	NOUN
ejpam-4768	103	16	-	-	ADJ
ejpam-4768	103	17	compact	compact	ADJ
ejpam-4768	103	18	.	.	PUNCT
ejpam-4768	104	1	remark	remark	NOUN
ejpam-4768	104	2	2.8	2.8	NUM
ejpam-4768	104	3	..	..	PUNCT
ejpam-4768	104	4	by	by	ADP
ejpam-4768	104	5	theorem	theorem	NOUN
ejpam-4768	104	6	3.4	3.4	NUM
ejpam-4768	104	7	,	,	PUNCT
ejpam-4768	105	1	the	the	DET
ejpam-4768	105	2	real	real	ADJ
ejpam-4768	105	3	number	number	NOUN
ejpam-4768	105	4	space	space	NOUN
ejpam-4768	105	5	with	with	ADP
ejpam-4768	105	6	the	the	DET
ejpam-4768	105	7	usual	usual	ADJ
ejpam-4768	105	8	hesitant	hesitant	ADJ
ejpam-4768	105	9	fuzzy	fuzzy	ADJ
ejpam-4768	105	10	topology	topology	NOUN
ejpam-4768	105	11	is	be	AUX
ejpam-4768	105	12	hesitant	hesitant	ADJ
ejpam-4768	105	13	fuzzy	fuzzy	ADJ
ejpam-4768	105	14	m	m	ADJ
ejpam-4768	105	15	-	-	ADJ
ejpam-4768	105	16	compact	compact	ADJ
ejpam-4768	106	1	but	but	CCONJ
ejpam-4768	106	2	generally	generally	ADV
ejpam-4768	106	3	it	it	PRON
ejpam-4768	106	4	is	be	AUX
ejpam-4768	106	5	not	not	PART
ejpam-4768	106	6	hesitant	hesitant	ADJ
ejpam-4768	106	7	fuzzy	fuzzy	ADJ
ejpam-4768	106	8	compact	compact	ADJ
ejpam-4768	106	9	.	.	PUNCT
ejpam-4768	107	1	since	since	SCONJ
ejpam-4768	107	2	by	by	ADP
ejpam-4768	107	3	theorem	theorem	NOUN
ejpam-4768	107	4	2.6	2.6	NUM
ejpam-4768	107	5	.	.	PUNCT
ejpam-4768	108	1	along	along	ADP
ejpam-4768	108	2	with	with	ADP
ejpam-4768	108	3	example	example	NOUN
ejpam-4768	108	4	2.7	2.7	NUM
ejpam-4768	108	5	.	.	PUNCT
ejpam-4768	108	6	,	,	PUNCT
ejpam-4768	108	7	we	we	PRON
ejpam-4768	108	8	conclude	conclude	VERB
ejpam-4768	108	9	that	that	SCONJ
ejpam-4768	108	10	both	both	CCONJ
ejpam-4768	108	11	hesitant	hesitant	ADJ
ejpam-4768	108	12	fuzzy	fuzzy	ADJ
ejpam-4768	108	13	compactness	compactness	NOUN
ejpam-4768	108	14	and	and	CCONJ
ejpam-4768	108	15	hesitant	hesitant	ADJ
ejpam-4768	108	16	fuzzy	fuzzy	ADJ
ejpam-4768	108	17	m	m	NOUN
ejpam-4768	108	18	-	-	PUNCT
ejpam-4768	108	19	compactness	compactness	NOUN
ejpam-4768	108	20	are	be	AUX
ejpam-4768	108	21	independent	independent	ADJ
ejpam-4768	108	22	.	.	PUNCT
ejpam-4768	109	1	definition	definition	NOUN
ejpam-4768	109	2	2.14	2.14	NUM
ejpam-4768	109	3	.	.	PUNCT
ejpam-4768	110	1	a	a	DET
ejpam-4768	110	2	function	function	NOUN
ejpam-4768	110	3	f	f	NOUN
ejpam-4768	110	4	:	:	PUNCT
ejpam-4768	110	5	x	x	X
ejpam-4768	110	6	→	→	SYM
ejpam-4768	110	7	y	y	PROPN
ejpam-4768	110	8	is	be	AUX
ejpam-4768	110	9	said	say	VERB
ejpam-4768	110	10	to	to	PART
ejpam-4768	110	11	be	be	AUX
ejpam-4768	110	12	hesitant	hesitant	ADJ
ejpam-4768	110	13	fuzzy	fuzzy	ADJ
ejpam-4768	110	14	m	m	NOUN
ejpam-4768	110	15	-	-	ADJ
ejpam-4768	110	16	continuous	continuous	ADJ
ejpam-4768	110	17	if	if	SCONJ
ejpam-4768	110	18	inverse	inverse	ADJ
ejpam-4768	110	19	image	image	NOUN
ejpam-4768	110	20	of	of	ADP
ejpam-4768	110	21	each	each	DET
ejpam-4768	110	22	proper	proper	ADJ
ejpam-4768	110	23	hfo	hfo	NOUN
ejpam-4768	110	24	set	set	VERB
ejpam-4768	110	25	in	in	ADP
ejpam-4768	110	26	y	y	PROPN
ejpam-4768	110	27	is	be	AUX
ejpam-4768	110	28	hfmao	hfmao	ADV
ejpam-4768	110	29	in	in	ADP
ejpam-4768	110	30	x.	x.	PROPN
ejpam-4768	110	31	theorem	theorem	VERB
ejpam-4768	110	32	2.9	2.9	NUM
ejpam-4768	110	33	..	..	PUNCT
ejpam-4768	110	34	let	let	VERB
ejpam-4768	110	35	x	x	PRON
ejpam-4768	110	36	be	be	AUX
ejpam-4768	110	37	a	a	DET
ejpam-4768	110	38	hesitant	hesitant	ADJ
ejpam-4768	110	39	fuzzy	fuzzy	ADJ
ejpam-4768	110	40	m	m	ADJ
ejpam-4768	110	41	-	-	ADJ
ejpam-4768	110	42	compact	compact	ADJ
ejpam-4768	110	43	topological	topological	ADJ
ejpam-4768	110	44	space	space	NOUN
ejpam-4768	110	45	and	and	CCONJ
ejpam-4768	110	46	f	f	NOUN
ejpam-4768	110	47	:	:	PUNCT
ejpam-4768	110	48	x	x	X
ejpam-4768	110	49	→	→	SYM
ejpam-4768	110	50	y	y	X
ejpam-4768	110	51	be	be	AUX
ejpam-4768	110	52	a	a	DET
ejpam-4768	110	53	bijective	bijective	ADJ
ejpam-4768	110	54	hesitant	hesitant	ADJ
ejpam-4768	110	55	fuzzy	fuzzy	ADJ
ejpam-4768	110	56	m	m	ADJ
ejpam-4768	110	57	-	-	ADJ
ejpam-4768	110	58	continuous	continuous	ADJ
ejpam-4768	110	59	function	function	NOUN
ejpam-4768	110	60	.	.	PUNCT
ejpam-4768	111	1	then	then	ADV
ejpam-4768	111	2	y	y	PROPN
ejpam-4768	111	3	is	be	AUX
ejpam-4768	111	4	hesitant	hesitant	ADJ
ejpam-4768	111	5	fuzzy	fuzzy	ADJ
ejpam-4768	111	6	m	m	NOUN
ejpam-4768	111	7	-	-	ADJ
ejpam-4768	111	8	compact	compact	ADJ
ejpam-4768	111	9	.	.	PUNCT
ejpam-4768	112	1	proof	proof	NOUN
ejpam-4768	112	2	.	.	PUNCT
ejpam-4768	113	1	let	let	VERB
ejpam-4768	113	2	s(y	s(y	PROPN
ejpam-4768	113	3	)	)	PUNCT
ejpam-4768	113	4	be	be	AUX
ejpam-4768	113	5	a	a	DET
ejpam-4768	113	6	hesitant	hesitant	ADJ
ejpam-4768	113	7	fuzzy	fuzzy	ADJ
ejpam-4768	113	8	cover	cover	NOUN
ejpam-4768	113	9	of	of	ADP
ejpam-4768	113	10	y	y	PROPN
ejpam-4768	113	11	.	.	PUNCT
ejpam-4768	114	1	then	then	ADV
ejpam-4768	114	2	s	s	X
ejpam-4768	114	3	(	(	PUNCT
ejpam-4768	114	4	x	x	NOUN
ejpam-4768	114	5	)	)	PUNCT
ejpam-4768	114	6	=	=	SYM
ejpam-4768	114	7	{	{	PUNCT
ejpam-4768	114	8	f−1(uk)|uk	f−1(uk)|uk	PROPN
ejpam-4768	114	9	∈	∈	PROPN
ejpam-4768	114	10	s	s	PART
ejpam-4768	114	11	(	(	PUNCT
ejpam-4768	114	12	y	y	PROPN
ejpam-4768	114	13	)	)	PUNCT
ejpam-4768	114	14	}	}	PUNCT
ejpam-4768	114	15	is	be	AUX
ejpam-4768	114	16	a	a	DET
ejpam-4768	114	17	hfmao	hfmao	ADJ
ejpam-4768	114	18	cover	cover	NOUN
ejpam-4768	114	19	of	of	ADP
ejpam-4768	114	20	x	x	X
ejpam-4768	114	21	.	.	PUNCT
ejpam-4768	115	1	by	by	ADP
ejpam-4768	115	2	hesitant	hesitant	ADJ
ejpam-4768	115	3	fuzzy	fuzzy	ADJ
ejpam-4768	115	4	m	m	NOUN
ejpam-4768	115	5	-	-	NOUN
ejpam-4768	115	6	compactness	compactness	NOUN
ejpam-4768	115	7	of	of	ADP
ejpam-4768	115	8	x	x	X
ejpam-4768	115	9	,	,	PUNCT
ejpam-4768	115	10	s	s	PART
ejpam-4768	115	11	(	(	PUNCT
ejpam-4768	115	12	x	x	X
ejpam-4768	115	13	)	)	PUNCT
ejpam-4768	115	14	has	have	VERB
ejpam-4768	115	15	a	a	DET
ejpam-4768	115	16	finite	finite	ADJ
ejpam-4768	115	17	hesitant	hesitant	ADJ
ejpam-4768	115	18	fuzzy	fuzzy	ADJ
ejpam-4768	115	19	s	s	NOUN
ejpam-4768	115	20	-	-	PUNCT
ejpam-4768	115	21	refinement	refinement	NOUN
ejpam-4768	115	22	s1	s1	NOUN
ejpam-4768	115	23	(	(	PUNCT
ejpam-4768	115	24	x	x	NOUN
ejpam-4768	115	25	)	)	PUNCT
ejpam-4768	115	26	=	=	SYM
ejpam-4768	115	27	{	{	PUNCT
ejpam-4768	115	28	f−1(uk)|uk	f−1(uk)|uk	PROPN
ejpam-4768	115	29	∈	∈	PROPN
ejpam-4768	115	30	s	s	PART
ejpam-4768	115	31	(	(	PUNCT
ejpam-4768	115	32	y	y	PROPN
ejpam-4768	115	33	)	)	PUNCT
ejpam-4768	115	34	,	,	PUNCT
ejpam-4768	115	35	k	k	PROPN
ejpam-4768	115	36	∈	∈	PROPN
ejpam-4768	115	37	z+	z+	X
ejpam-4768	115	38	}	}	PUNCT
ejpam-4768	115	39	which	which	PRON
ejpam-4768	115	40	gives	give	VERB
ejpam-4768	115	41	s1	s1	PROPN
ejpam-4768	115	42	(	(	PUNCT
ejpam-4768	115	43	y	y	PROPN
ejpam-4768	115	44	)	)	PUNCT
ejpam-4768	115	45	=	=	PRON
ejpam-4768	116	1	{	{	PUNCT
ejpam-4768	116	2	f(f−1(uk))|uk	f(f−1(uk))|uk	PROPN
ejpam-4768	116	3	∈	∈	X
ejpam-4768	116	4	s	s	X
ejpam-4768	116	5	(	(	PUNCT
ejpam-4768	116	6	y	y	PROPN
ejpam-4768	116	7	)	)	PUNCT
ejpam-4768	116	8	,	,	PUNCT
ejpam-4768	116	9	k	k	PROPN
ejpam-4768	116	10	∈	∈	PROPN
ejpam-4768	116	11	z+	z+	PRON
ejpam-4768	116	12	}	}	PUNCT
ejpam-4768	116	13	=	=	PUNCT
ejpam-4768	116	14	{	{	PUNCT
ejpam-4768	116	15	uk|uk	uk|uk	PROPN
ejpam-4768	116	16	∈	∈	PROPN
ejpam-4768	116	17	s	s	X
ejpam-4768	116	18	(	(	PUNCT
ejpam-4768	116	19	y	y	PROPN
ejpam-4768	116	20	)	)	PUNCT
ejpam-4768	116	21	,	,	PUNCT
ejpam-4768	116	22	k	k	PROPN
ejpam-4768	116	23	∈	∈	PROPN
ejpam-4768	116	24	z+	z+	PRON
ejpam-4768	116	25	}	}	PUNCT
ejpam-4768	116	26	.	.	PUNCT
ejpam-4768	117	1	for	for	ADP
ejpam-4768	117	2	each	each	DET
ejpam-4768	117	3	k	k	PROPN
ejpam-4768	117	4	∈	∈	PROPN
ejpam-4768	117	5	z+	z+	X
ejpam-4768	117	6	,	,	PUNCT
ejpam-4768	117	7	there	there	PRON
ejpam-4768	117	8	exists	exist	VERB
ejpam-4768	117	9	u	u	PROPN
ejpam-4768	117	10	∈	∈	PROPN
ejpam-4768	117	11	s	s	PART
ejpam-4768	117	12	(	(	PUNCT
ejpam-4768	117	13	y	y	PROPN
ejpam-4768	117	14	)	)	PUNCT
ejpam-4768	117	15	such	such	ADJ
ejpam-4768	117	16	that	that	SCONJ
ejpam-4768	117	17	f−1(uk	f−1(uk	PROPN
ejpam-4768	117	18	)	)	PUNCT
ejpam-4768	117	19	⪇	⪇	PUNCT
ejpam-4768	118	1	f−1(u	f−1(u	PROPN
ejpam-4768	118	2	)	)	PUNCT
ejpam-4768	118	3	gives	give	VERB
ejpam-4768	118	4	uk	uk	PROPN
ejpam-4768	118	5	⪇	⪇	PROPN
ejpam-4768	118	6	u	u	PROPN
ejpam-4768	118	7	.	.	PUNCT
ejpam-4768	119	1	hence	hence	ADV
ejpam-4768	119	2	s1	s1	PROPN
ejpam-4768	119	3	(	(	PUNCT
ejpam-4768	119	4	y	y	PROPN
ejpam-4768	119	5	)	)	PUNCT
ejpam-4768	119	6	is	be	AUX
ejpam-4768	119	7	a	a	DET
ejpam-4768	119	8	hesitant	hesitant	ADJ
ejpam-4768	119	9	fuzzy	fuzzy	ADJ
ejpam-4768	119	10	finite	finite	NOUN
ejpam-4768	119	11	s	s	NOUN
ejpam-4768	119	12	-	-	NOUN
ejpam-4768	119	13	refinement	refinement	NOUN
ejpam-4768	119	14	of	of	ADP
ejpam-4768	119	15	s	s	PROPN
ejpam-4768	119	16	(	(	PUNCT
ejpam-4768	119	17	y	y	PROPN
ejpam-4768	119	18	)	)	PUNCT
ejpam-4768	119	19	.	.	PUNCT
ejpam-4768	120	1	definition	definition	NOUN
ejpam-4768	120	2	2.15	2.15	NUM
ejpam-4768	120	3	.	.	PUNCT
ejpam-4768	121	1	a	a	DET
ejpam-4768	121	2	hesitant	hesitant	ADJ
ejpam-4768	121	3	fuzzy	fuzzy	ADJ
ejpam-4768	121	4	point	point	NOUN
ejpam-4768	121	5	xα	xα	ADP
ejpam-4768	121	6	of	of	ADP
ejpam-4768	121	7	a	a	DET
ejpam-4768	121	8	hfts	hft	NOUN
ejpam-4768	121	9	x	x	PUNCT
ejpam-4768	121	10	is	be	AUX
ejpam-4768	121	11	hesitant	hesitant	ADJ
ejpam-4768	121	12	fuzzy	fuzzy	ADJ
ejpam-4768	121	13	m	m	ADJ
ejpam-4768	121	14	-	-	ADJ
ejpam-4768	121	15	complete	complete	ADJ
ejpam-4768	121	16	accumulation	accumulation	NOUN
ejpam-4768	121	17	point	point	NOUN
ejpam-4768	121	18	of	of	ADP
ejpam-4768	121	19	any	any	DET
ejpam-4768	121	20	hesitant	hesitant	ADJ
ejpam-4768	121	21	fuzzy	fuzzy	ADJ
ejpam-4768	121	22	subset	subset	NOUN
ejpam-4768	121	23	m	m	NOUN
ejpam-4768	121	24	of	of	ADP
ejpam-4768	121	25	x	x	PRON
ejpam-4768	121	26	if	if	SCONJ
ejpam-4768	121	27	|u∧m	|u∧m	NOUN
ejpam-4768	121	28	|	|	ADV
ejpam-4768	121	29	=	=	SYM
ejpam-4768	121	30	|m	|m	NOUN
ejpam-4768	121	31	|	|	ADV
ejpam-4768	121	32	for	for	SCONJ
ejpam-4768	121	33	each	each	DET
ejpam-4768	121	34	hfmao	hfmao	NOUN
ejpam-4768	121	35	set	set	VERB
ejpam-4768	121	36	u	u	NOUN
ejpam-4768	121	37	containing	contain	VERB
ejpam-4768	121	38	xα	xα	PROPN
ejpam-4768	121	39	.	.	PUNCT
ejpam-4768	122	1	a.	a.	NOUN
ejpam-4768	122	2	swaminathan	swaminathan	PROPN
ejpam-4768	122	3	,	,	PUNCT
ejpam-4768	122	4	cenap	cenap	VERB
ejpam-4768	122	5	ozel	ozel	ADJ
ejpam-4768	122	6	,	,	PUNCT
ejpam-4768	122	7	ibtesam	ibtesam	PROPN
ejpam-4768	122	8	alshammari	alshammari	PROPN
ejpam-4768	122	9	/	/	SYM
ejpam-4768	122	10	eur	eur	PROPN
ejpam-4768	122	11	.	.	PUNCT
ejpam-4768	123	1	j.	j.	PROPN
ejpam-4768	123	2	pure	pure	PROPN
ejpam-4768	123	3	appl	appl	PROPN
ejpam-4768	123	4	.	.	PROPN
ejpam-4768	123	5	math	math	PROPN
ejpam-4768	123	6	,	,	PUNCT
ejpam-4768	123	7	16	16	NUM
ejpam-4768	123	8	(	(	PUNCT
ejpam-4768	123	9	3	3	NUM
ejpam-4768	123	10	)	)	PUNCT
ejpam-4768	123	11	(	(	PUNCT
ejpam-4768	123	12	2023	2023	NUM
ejpam-4768	123	13	)	)	PUNCT
ejpam-4768	123	14	,	,	PUNCT
ejpam-4768	123	15	1381	1381	NUM
ejpam-4768	123	16	-	-	SYM
ejpam-4768	123	17	1388	1388	NUM
ejpam-4768	123	18	1385	1385	NUM
ejpam-4768	123	19	theorem	theorem	VERB
ejpam-4768	123	20	2.10	2.10	NUM
ejpam-4768	123	21	..	..	PUNCT
ejpam-4768	123	22	each	each	DET
ejpam-4768	123	23	infinite	infinite	ADJ
ejpam-4768	123	24	hesitant	hesitant	ADJ
ejpam-4768	123	25	fuzzy	fuzzy	ADJ
ejpam-4768	123	26	subset	subset	NOUN
ejpam-4768	123	27	of	of	ADP
ejpam-4768	123	28	a	a	DET
ejpam-4768	123	29	hesitant	hesitant	ADJ
ejpam-4768	123	30	fuzzy	fuzzy	ADJ
ejpam-4768	123	31	m	m	ADJ
ejpam-4768	123	32	-	-	ADJ
ejpam-4768	123	33	compact	compact	ADJ
ejpam-4768	123	34	space	space	NOUN
ejpam-4768	123	35	has	have	VERB
ejpam-4768	123	36	an	an	DET
ejpam-4768	123	37	hesitant	hesitant	ADJ
ejpam-4768	123	38	fuzzy	fuzzy	ADJ
ejpam-4768	123	39	m	m	ADJ
ejpam-4768	123	40	-	-	ADJ
ejpam-4768	123	41	complete	complete	ADJ
ejpam-4768	123	42	accumulation	accumulation	NOUN
ejpam-4768	123	43	point	point	NOUN
ejpam-4768	123	44	.	.	PUNCT
ejpam-4768	124	1	proof	proof	NOUN
ejpam-4768	124	2	.	.	PUNCT
ejpam-4768	125	1	let	let	VERB
ejpam-4768	125	2	g	g	PRON
ejpam-4768	125	3	be	be	AUX
ejpam-4768	125	4	an	an	DET
ejpam-4768	125	5	infinite	infinite	ADJ
ejpam-4768	125	6	hesitant	hesitant	ADJ
ejpam-4768	125	7	fuzzy	fuzzy	ADJ
ejpam-4768	125	8	subset	subset	NOUN
ejpam-4768	125	9	of	of	ADP
ejpam-4768	125	10	a	a	DET
ejpam-4768	125	11	hesitant	hesitant	ADJ
ejpam-4768	125	12	fuzzy	fuzzy	ADJ
ejpam-4768	125	13	m	m	ADJ
ejpam-4768	125	14	-	-	ADJ
ejpam-4768	125	15	compact	compact	ADJ
ejpam-4768	125	16	hfts	hft	NOUN
ejpam-4768	125	17	x.	x.	NOUN
ejpam-4768	125	18	assume	assume	VERB
ejpam-4768	125	19	for	for	ADP
ejpam-4768	125	20	each	each	PRON
ejpam-4768	125	21	xα	xα	PUNCT
ejpam-4768	125	22	∈	∈	PROPN
ejpam-4768	126	1	x	x	PRON
ejpam-4768	126	2	,	,	PUNCT
ejpam-4768	126	3	there	there	PRON
ejpam-4768	126	4	is	be	VERB
ejpam-4768	126	5	a	a	DET
ejpam-4768	126	6	hfmao	hfmao	NOUN
ejpam-4768	126	7	set	set	NOUN
ejpam-4768	126	8	wxα	wxα	PROPN
ejpam-4768	126	9	containing	contain	VERB
ejpam-4768	126	10	xα	xα	X
ejpam-4768	126	11	and	and	CCONJ
ejpam-4768	126	12	satisfying	satisfy	VERB
ejpam-4768	126	13	|wxα	|wxα	PROPN
ejpam-4768	126	14	∧	∧	PROPN
ejpam-4768	126	15	ϱ|	ϱ|	PROPN
ejpam-4768	126	16	<	<	X
ejpam-4768	126	17	|ϱ|	|ϱ|	PROPN
ejpam-4768	126	18	.	.	PROPN
ejpam-4768	127	1	since	since	SCONJ
ejpam-4768	127	2	{	{	PUNCT
ejpam-4768	127	3	wxα	wxα	PROPN
ejpam-4768	127	4	|xα	|xα	PROPN
ejpam-4768	127	5	∈	∈	PROPN
ejpam-4768	127	6	x	x	PRON
ejpam-4768	127	7	}	}	PUNCT
ejpam-4768	127	8	is	be	AUX
ejpam-4768	127	9	an	an	DET
ejpam-4768	127	10	hfo	hfo	NOUN
ejpam-4768	127	11	cover	cover	NOUN
ejpam-4768	127	12	of	of	ADP
ejpam-4768	127	13	x	x	X
ejpam-4768	127	14	consists	consist	NOUN
ejpam-4768	127	15	of	of	ADP
ejpam-4768	127	16	hfmao	hfmao	NOUN
ejpam-4768	127	17	sets	set	NOUN
ejpam-4768	127	18	,	,	PUNCT
ejpam-4768	127	19	by	by	ADP
ejpam-4768	127	20	lemma	lemma	PROPN
ejpam-4768	127	21	2.3	2.3	NUM
ejpam-4768	127	22	.	.	PUNCT
ejpam-4768	127	23	,	,	PUNCT
ejpam-4768	127	24	{	{	PUNCT
ejpam-4768	127	25	wxα	wxα	NOUN
ejpam-4768	127	26	|xα	|xα	PROPN
ejpam-4768	127	27	∈	∈	PROPN
ejpam-4768	127	28	x	x	PRON
ejpam-4768	127	29	}	}	PUNCT
ejpam-4768	127	30	is	be	AUX
ejpam-4768	127	31	a	a	DET
ejpam-4768	127	32	hfmao	hfmao	ADJ
ejpam-4768	127	33	cover	cover	NOUN
ejpam-4768	127	34	of	of	ADP
ejpam-4768	127	35	x.	x.	NOUN
ejpam-4768	127	36	therefore	therefore	ADV
ejpam-4768	127	37	a	a	DET
ejpam-4768	127	38	finite	finite	ADJ
ejpam-4768	127	39	hesitant	hesitant	ADJ
ejpam-4768	127	40	fuzzy	fuzzy	ADJ
ejpam-4768	127	41	s	s	NOUN
ejpam-4768	127	42	-	-	NOUN
ejpam-4768	127	43	refinement	refinement	NOUN
ejpam-4768	127	44	{	{	PUNCT
ejpam-4768	127	45	wxα	wxα	NOUN
ejpam-4768	127	46	|xαi	|xαi	PROPN
ejpam-4768	127	47	∈	∈	PROPN
ejpam-4768	127	48	x	x	NOUN
ejpam-4768	127	49	,	,	PUNCT
ejpam-4768	127	50	i	i	PRON
ejpam-4768	127	51	∈	∈	PROPN
ejpam-4768	127	52	z+	z+	PRON
ejpam-4768	127	53	}	}	PUNCT
ejpam-4768	127	54	of	of	ADP
ejpam-4768	127	55	{	{	PUNCT
ejpam-4768	127	56	wxα	wxα	PROPN
ejpam-4768	127	57	|xα	|xα	PROPN
ejpam-4768	127	58	∈	∈	PROPN
ejpam-4768	127	59	x	x	X
ejpam-4768	127	60	}	}	PUNCT
ejpam-4768	127	61	.	.	PUNCT
ejpam-4768	128	1	now	now	ADV
ejpam-4768	128	2	|ϱ|	|ϱ|	PROPN
ejpam-4768	129	1	=	=	SYM
ejpam-4768	130	1	|	|	ADV
ejpam-4768	130	2	n	n	NOUN
ejpam-4768	130	3	∨	∨	NOUN
ejpam-4768	130	4	i=1	i=1	PROPN
ejpam-4768	130	5	(	(	PUNCT
ejpam-4768	130	6	wxα	wxα	PROPN
ejpam-4768	130	7	∧	∧	PROPN
ejpam-4768	130	8	ϱ)|	ϱ)|	PROPN
ejpam-4768	130	9	<	<	X
ejpam-4768	130	10	|ϱ|	|ϱ|	PROPN
ejpam-4768	130	11	,	,	PUNCT
ejpam-4768	130	12	a	a	DET
ejpam-4768	130	13	contradiction	contradiction	NOUN
ejpam-4768	130	14	.	.	PUNCT
ejpam-4768	131	1	2.2	2.2	NUM
ejpam-4768	131	2	.	.	PUNCT
ejpam-4768	132	1	hesitant	hesitant	ADJ
ejpam-4768	132	2	fuzzy	fuzzy	ADJ
ejpam-4768	132	3	minimal	minimal	ADJ
ejpam-4768	132	4	c	c	NOUN
ejpam-4768	132	5	-	-	ADJ
ejpam-4768	132	6	regular	regular	ADJ
ejpam-4768	132	7	and	and	CCONJ
ejpam-4768	132	8	hesitant	hesitant	ADJ
ejpam-4768	132	9	fuzzy	fuzzy	ADJ
ejpam-4768	132	10	c	c	NOUN
ejpam-4768	132	11	-	-	ADJ
ejpam-4768	132	12	normal	normal	ADJ
ejpam-4768	132	13	spaces	space	NOUN
ejpam-4768	132	14	definition	definition	NOUN
ejpam-4768	132	15	2.16	2.16	NUM
ejpam-4768	132	16	.	.	PUNCT
ejpam-4768	133	1	a	a	DET
ejpam-4768	133	2	hfts	hft	NOUN
ejpam-4768	133	3	x	x	PUNCT
ejpam-4768	133	4	is	be	AUX
ejpam-4768	133	5	called	call	VERB
ejpam-4768	133	6	a	a	DET
ejpam-4768	133	7	hesitant	hesitant	ADJ
ejpam-4768	133	8	fuzzy	fuzzy	ADJ
ejpam-4768	133	9	minimal	minimal	ADJ
ejpam-4768	133	10	c	c	NOUN
ejpam-4768	133	11	-	-	NOUN
ejpam-4768	133	12	regular	regular	ADJ
ejpam-4768	133	13	if	if	SCONJ
ejpam-4768	133	14	for	for	ADP
ejpam-4768	133	15	each	each	PRON
ejpam-4768	133	16	xα	xα	NOUN
ejpam-4768	134	1	∈	∈	PROPN
ejpam-4768	134	2	x	x	X
ejpam-4768	134	3	and	and	CCONJ
ejpam-4768	134	4	each	each	DET
ejpam-4768	134	5	hfmic	hfmic	ADJ
ejpam-4768	134	6	set	set	NOUN
ejpam-4768	134	7	γ	γ	X
ejpam-4768	134	8	with	with	ADP
ejpam-4768	134	9	xα	xα	PROPN
ejpam-4768	134	10	/∈	/∈	PUNCT
ejpam-4768	135	1	γ	γ	NOUN
ejpam-4768	135	2	,	,	PUNCT
ejpam-4768	135	3	there	there	PRON
ejpam-4768	135	4	exists	exist	VERB
ejpam-4768	135	5	disjoint	disjoint	PROPN
ejpam-4768	135	6	hfo	hfo	PROPN
ejpam-4768	135	7	sets	set	NOUN
ejpam-4768	135	8	λ,µ	λ,µ	VERB
ejpam-4768	135	9	such	such	ADJ
ejpam-4768	135	10	that	that	SCONJ
ejpam-4768	135	11	xα	xα	PUNCT
ejpam-4768	135	12	∈	∈	PROPN
ejpam-4768	135	13	λ	λ	PROPN
ejpam-4768	135	14	and	and	CCONJ
ejpam-4768	135	15	λ	λ	X
ejpam-4768	135	16	<	<	X
ejpam-4768	135	17	µ.	µ.	PROPN
ejpam-4768	135	18	theorem	theorem	VERB
ejpam-4768	135	19	2.11	2.11	NUM
ejpam-4768	135	20	..	..	PUNCT
ejpam-4768	135	21	let	let	VERB
ejpam-4768	135	22	x	x	PRON
ejpam-4768	135	23	be	be	AUX
ejpam-4768	135	24	a	a	DET
ejpam-4768	135	25	hfts	hft	NOUN
ejpam-4768	135	26	.	.	PUNCT
ejpam-4768	136	1	then	then	ADV
ejpam-4768	136	2	the	the	DET
ejpam-4768	136	3	following	follow	VERB
ejpam-4768	136	4	are	be	AUX
ejpam-4768	136	5	equivalent	equivalent	ADJ
ejpam-4768	136	6	:	:	PUNCT
ejpam-4768	136	7	(	(	PUNCT
ejpam-4768	136	8	i	i	NOUN
ejpam-4768	136	9	)	)	PUNCT
ejpam-4768	136	10	x	x	X
ejpam-4768	136	11	is	be	AUX
ejpam-4768	136	12	hesitant	hesitant	ADJ
ejpam-4768	136	13	fuzzy	fuzzy	ADJ
ejpam-4768	136	14	minimal	minimal	ADJ
ejpam-4768	136	15	c	c	NOUN
ejpam-4768	136	16	-	-	NOUN
ejpam-4768	136	17	regular	regular	ADJ
ejpam-4768	136	18	.	.	PUNCT
ejpam-4768	137	1	(	(	PUNCT
ejpam-4768	137	2	ii	ii	NOUN
ejpam-4768	137	3	)	)	PUNCT
ejpam-4768	137	4	given	give	VERB
ejpam-4768	137	5	a	a	DET
ejpam-4768	137	6	hesitant	hesitant	ADJ
ejpam-4768	137	7	fuzzy	fuzzy	ADJ
ejpam-4768	137	8	point	point	NOUN
ejpam-4768	137	9	xα	xα	PUNCT
ejpam-4768	138	1	∈	∈	PROPN
ejpam-4768	138	2	x	x	X
ejpam-4768	138	3	and	and	CCONJ
ejpam-4768	138	4	a	a	DET
ejpam-4768	138	5	hfmao	hfmao	NOUN
ejpam-4768	138	6	set	set	VERB
ejpam-4768	138	7	ω	ω	NUM
ejpam-4768	138	8	containing	contain	VERB
ejpam-4768	138	9	xα	xα	ADV
ejpam-4768	138	10	,	,	PUNCT
ejpam-4768	138	11	there	there	PRON
ejpam-4768	138	12	is	be	VERB
ejpam-4768	138	13	an	an	DET
ejpam-4768	138	14	hfo	hfo	NOUN
ejpam-4768	138	15	set	set	VERB
ejpam-4768	138	16	ϱ	ϱ	ADP
ejpam-4768	138	17	such	such	ADJ
ejpam-4768	138	18	that	that	PRON
ejpam-4768	138	19	xα	xα	PUNCT
ejpam-4768	138	20	∈	∈	PROPN
ejpam-4768	138	21	ϱ	ϱ	ADP
ejpam-4768	138	22	<	<	X
ejpam-4768	138	23	cl(ϱ	cl(ϱ	X
ejpam-4768	138	24	)	)	PUNCT
ejpam-4768	138	25	<	<	X
ejpam-4768	138	26	ω	ω	X
ejpam-4768	138	27	.	.	PUNCT
ejpam-4768	138	28	(	(	PUNCT
ejpam-4768	138	29	iii	iii	NOUN
ejpam-4768	138	30	)	)	PUNCT
ejpam-4768	138	31	for	for	ADP
ejpam-4768	138	32	a	a	DET
ejpam-4768	138	33	hesitant	hesitant	ADJ
ejpam-4768	138	34	fuzzy	fuzzy	ADJ
ejpam-4768	138	35	point	point	NOUN
ejpam-4768	138	36	xα	xα	PUNCT
ejpam-4768	139	1	∈	∈	PROPN
ejpam-4768	139	2	x	x	X
ejpam-4768	139	3	and	and	CCONJ
ejpam-4768	139	4	a	a	DET
ejpam-4768	139	5	hfmic	hfmic	ADJ
ejpam-4768	139	6	set	set	NOUN
ejpam-4768	139	7	γ	γ	X
ejpam-4768	139	8	with	with	ADP
ejpam-4768	139	9	xα	xα	PROPN
ejpam-4768	139	10	/∈	/∈	PUNCT
ejpam-4768	140	1	γ	γ	NOUN
ejpam-4768	140	2	,	,	PUNCT
ejpam-4768	140	3	there	there	PRON
ejpam-4768	140	4	exists	exist	VERB
ejpam-4768	140	5	hfo	hfo	PROPN
ejpam-4768	140	6	set	set	VERB
ejpam-4768	140	7	ω	ω	PROPN
ejpam-4768	140	8	containing	contain	VERB
ejpam-4768	140	9	xα	xα	INTJ
ejpam-4768	140	10	such	such	ADJ
ejpam-4768	140	11	that	that	SCONJ
ejpam-4768	140	12	cl(ω	cl(ω	X
ejpam-4768	140	13	)	)	PUNCT
ejpam-4768	140	14	∧	∧	PROPN
ejpam-4768	140	15	γ	γ	X
ejpam-4768	140	16	=	=	SYM
ejpam-4768	140	17	h0	h0	PROPN
ejpam-4768	140	18	.	.	PUNCT
ejpam-4768	141	1	proof	proof	NOUN
ejpam-4768	141	2	.	.	PUNCT
ejpam-4768	142	1	(	(	PUNCT
ejpam-4768	142	2	i	i	NOUN
ejpam-4768	142	3	)	)	PUNCT
ejpam-4768	142	4	⇒	⇒	PROPN
ejpam-4768	142	5	(	(	PUNCT
ejpam-4768	142	6	ii	ii	NOUN
ejpam-4768	142	7	)	)	PUNCT
ejpam-4768	142	8	,	,	PUNCT
ejpam-4768	142	9	(	(	PUNCT
ejpam-4768	142	10	ii	ii	NOUN
ejpam-4768	142	11	)	)	PUNCT
ejpam-4768	142	12	⇒	⇒	NOUN
ejpam-4768	142	13	(	(	PUNCT
ejpam-4768	142	14	iii	iii	NOUN
ejpam-4768	142	15	)	)	PUNCT
ejpam-4768	142	16	,	,	PUNCT
ejpam-4768	142	17	(	(	PUNCT
ejpam-4768	142	18	iii	iii	X
ejpam-4768	142	19	)	)	PUNCT
ejpam-4768	142	20	⇒	⇒	NOUN
ejpam-4768	142	21	(	(	PUNCT
ejpam-4768	142	22	i	i	NOUN
ejpam-4768	142	23	)	)	PUNCT
ejpam-4768	142	24	:	:	PUNCT
ejpam-4768	142	25	proof	proof	NOUN
ejpam-4768	142	26	follows	follow	VERB
ejpam-4768	142	27	.	.	PUNCT
ejpam-4768	143	1	definition	definition	NOUN
ejpam-4768	143	2	2.17	2.17	NUM
ejpam-4768	143	3	.	.	PUNCT
ejpam-4768	144	1	a	a	DET
ejpam-4768	144	2	hfts	hft	NOUN
ejpam-4768	144	3	x	x	PUNCT
ejpam-4768	144	4	is	be	AUX
ejpam-4768	144	5	called	call	VERB
ejpam-4768	144	6	a	a	DET
ejpam-4768	144	7	hesitant	hesitant	ADJ
ejpam-4768	144	8	fuzzy	fuzzy	ADJ
ejpam-4768	144	9	minimal	minimal	ADJ
ejpam-4768	144	10	c	c	NOUN
ejpam-4768	144	11	-	-	ADJ
ejpam-4768	144	12	normal	normal	ADJ
ejpam-4768	144	13	if	if	SCONJ
ejpam-4768	144	14	for	for	ADP
ejpam-4768	144	15	each	each	DET
ejpam-4768	144	16	pair	pair	NOUN
ejpam-4768	144	17	of	of	ADP
ejpam-4768	144	18	distinct	distinct	ADJ
ejpam-4768	144	19	hfmic	hfmic	ADJ
ejpam-4768	144	20	sets	set	NOUN
ejpam-4768	144	21	η	η	PROPN
ejpam-4768	144	22	,	,	PUNCT
ejpam-4768	144	23	γ	γ	NOUN
ejpam-4768	144	24	there	there	PRON
ejpam-4768	144	25	exists	exist	VERB
ejpam-4768	144	26	disjoint	disjoint	PROPN
ejpam-4768	144	27	hfo	hfo	PROPN
ejpam-4768	144	28	sets	set	NOUN
ejpam-4768	144	29	λ,µ	λ,µ	VERB
ejpam-4768	144	30	such	such	ADJ
ejpam-4768	144	31	that	that	SCONJ
ejpam-4768	144	32	η	η	PROPN
ejpam-4768	144	33	<	<	X
ejpam-4768	144	34	λ	λ	PROPN
ejpam-4768	144	35	and	and	CCONJ
ejpam-4768	144	36	γ	γ	X
ejpam-4768	144	37	<	<	X
ejpam-4768	144	38	µ.	µ.	PROPN
ejpam-4768	144	39	theorem	theorem	VERB
ejpam-4768	144	40	2.12	2.12	NUM
ejpam-4768	144	41	..	..	PUNCT
ejpam-4768	144	42	let	let	VERB
ejpam-4768	144	43	x	x	PRON
ejpam-4768	144	44	be	be	AUX
ejpam-4768	144	45	a	a	DET
ejpam-4768	144	46	hfts	hft	NOUN
ejpam-4768	144	47	.	.	PUNCT
ejpam-4768	145	1	then	then	ADV
ejpam-4768	145	2	the	the	DET
ejpam-4768	145	3	following	follow	VERB
ejpam-4768	145	4	are	be	AUX
ejpam-4768	145	5	equivalent	equivalent	ADJ
ejpam-4768	145	6	:	:	PUNCT
ejpam-4768	145	7	(	(	PUNCT
ejpam-4768	145	8	i	i	NOUN
ejpam-4768	145	9	)	)	PUNCT
ejpam-4768	145	10	x	x	X
ejpam-4768	145	11	is	be	AUX
ejpam-4768	145	12	hesitant	hesitant	ADJ
ejpam-4768	145	13	fuzzy	fuzzy	ADJ
ejpam-4768	145	14	minimal	minimal	ADJ
ejpam-4768	145	15	c	c	NOUN
ejpam-4768	145	16	-	-	ADJ
ejpam-4768	145	17	normal	normal	ADJ
ejpam-4768	145	18	.	.	PUNCT
ejpam-4768	146	1	(	(	PUNCT
ejpam-4768	146	2	ii	ii	NOUN
ejpam-4768	146	3	)	)	PUNCT
ejpam-4768	146	4	for	for	ADP
ejpam-4768	146	5	each	each	DET
ejpam-4768	146	6	hfmic	hfmic	ADJ
ejpam-4768	146	7	set	set	NOUN
ejpam-4768	146	8	ξ	ξ	PROPN
ejpam-4768	146	9	and	and	CCONJ
ejpam-4768	146	10	each	each	DET
ejpam-4768	146	11	hfmao	hfmao	NOUN
ejpam-4768	146	12	set	set	VERB
ejpam-4768	146	13	ω	ω	PROPN
ejpam-4768	146	14	with	with	ADP
ejpam-4768	146	15	ξ	ξ	PROPN
ejpam-4768	146	16	<	<	X
ejpam-4768	146	17	ω	ω	X
ejpam-4768	146	18	,	,	PUNCT
ejpam-4768	146	19	there	there	PRON
ejpam-4768	146	20	is	be	VERB
ejpam-4768	146	21	a	a	DET
ejpam-4768	146	22	hfo	hfo	NOUN
ejpam-4768	146	23	set	set	VERB
ejpam-4768	146	24	ϱ	ϱ	ADP
ejpam-4768	146	25	such	such	ADJ
ejpam-4768	146	26	that	that	SCONJ
ejpam-4768	146	27	ξ	ξ	X
ejpam-4768	146	28	<	<	X
ejpam-4768	146	29	ϱ	ϱ	ADP
ejpam-4768	146	30	<	<	X
ejpam-4768	146	31	cl(ϱ	cl(ϱ	X
ejpam-4768	146	32	)	)	PUNCT
ejpam-4768	146	33	<	<	X
ejpam-4768	146	34	ω	ω	X
ejpam-4768	146	35	.	.	PUNCT
ejpam-4768	147	1	(	(	PUNCT
ejpam-4768	147	2	iii	iii	NOUN
ejpam-4768	147	3	)	)	PUNCT
ejpam-4768	147	4	for	for	ADP
ejpam-4768	147	5	each	each	DET
ejpam-4768	147	6	pair	pair	NOUN
ejpam-4768	147	7	of	of	ADP
ejpam-4768	147	8	distinct	distinct	ADJ
ejpam-4768	147	9	hfmic	hfmic	ADJ
ejpam-4768	147	10	sets	set	NOUN
ejpam-4768	147	11	ξ	ξ	PROPN
ejpam-4768	147	12	,	,	PUNCT
ejpam-4768	147	13	ζ	ζ	NOUN
ejpam-4768	147	14	,	,	PUNCT
ejpam-4768	147	15	there	there	PRON
ejpam-4768	147	16	exists	exist	VERB
ejpam-4768	147	17	disjoint	disjoint	PROPN
ejpam-4768	147	18	hfo	hfo	PROPN
ejpam-4768	147	19	sets	set	VERB
ejpam-4768	147	20	ω	ω	PROPN
ejpam-4768	147	21	,	,	PUNCT
ejpam-4768	147	22	ϱ	ϱ	AUX
ejpam-4768	147	23	disjoint	disjoint	NOUN
ejpam-4768	147	24	hfo	hfo	NOUN
ejpam-4768	147	25	sets	set	VERB
ejpam-4768	147	26	such	such	ADJ
ejpam-4768	147	27	that	that	SCONJ
ejpam-4768	147	28	ξ	ξ	PROPN
ejpam-4768	147	29	<	<	X
ejpam-4768	147	30	ω	ω	PROPN
ejpam-4768	147	31	,	,	PUNCT
ejpam-4768	147	32	cl(ω	cl(ω	X
ejpam-4768	147	33	)	)	PUNCT
ejpam-4768	147	34	∧	∧	NOUN
ejpam-4768	147	35	ζ	ζ	NOUN
ejpam-4768	147	36	=	=	SYM
ejpam-4768	147	37	h0	h0	NOUN
ejpam-4768	147	38	and	and	CCONJ
ejpam-4768	147	39	ζ	ζ	NOUN
ejpam-4768	147	40	<	<	X
ejpam-4768	147	41	ϱ	ϱ	PROPN
ejpam-4768	147	42	,	,	PUNCT
ejpam-4768	147	43	cl(ϱ	cl(ϱ	NOUN
ejpam-4768	147	44	)	)	PUNCT
ejpam-4768	147	45	∧	∧	PROPN
ejpam-4768	147	46	ξ	ξ	PROPN
ejpam-4768	147	47	=	=	SYM
ejpam-4768	147	48	h0	h0	PROPN
ejpam-4768	147	49	.	.	PUNCT
ejpam-4768	148	1	(	(	PUNCT
ejpam-4768	148	2	iv	iv	X
ejpam-4768	148	3	)	)	PUNCT
ejpam-4768	148	4	for	for	ADP
ejpam-4768	148	5	each	each	DET
ejpam-4768	148	6	pair	pair	NOUN
ejpam-4768	148	7	of	of	ADP
ejpam-4768	148	8	distinct	distinct	ADJ
ejpam-4768	148	9	hfmic	hfmic	ADJ
ejpam-4768	148	10	sets	set	NOUN
ejpam-4768	148	11	ξ	ξ	PROPN
ejpam-4768	148	12	,	,	PUNCT
ejpam-4768	148	13	ζ	ζ	NOUN
ejpam-4768	148	14	,	,	PUNCT
ejpam-4768	148	15	there	there	PRON
ejpam-4768	148	16	exists	exist	VERB
ejpam-4768	148	17	a	a	DET
ejpam-4768	148	18	pair	pair	NOUN
ejpam-4768	148	19	of	of	ADP
ejpam-4768	148	20	disjoint	disjoint	NOUN
ejpam-4768	148	21	hfo	hfo	PROPN
ejpam-4768	148	22	sets	set	VERB
ejpam-4768	148	23	ω	ω	PROPN
ejpam-4768	148	24	,	,	PUNCT
ejpam-4768	148	25	ϱ	ϱ	ADP
ejpam-4768	148	26	such	such	ADJ
ejpam-4768	148	27	that	that	SCONJ
ejpam-4768	148	28	ξ	ξ	PRON
ejpam-4768	148	29	<	<	X
ejpam-4768	148	30	ω	ω	PROPN
ejpam-4768	148	31	,	,	PUNCT
ejpam-4768	148	32	ζ	ζ	NOUN
ejpam-4768	148	33	<	<	X
ejpam-4768	148	34	ϱ	ϱ	NOUN
ejpam-4768	148	35	and	and	CCONJ
ejpam-4768	148	36	cl(ω	cl(ω	X
ejpam-4768	148	37	)	)	PUNCT
ejpam-4768	148	38	∧	∧	PROPN
ejpam-4768	148	39	cl(ϱ	cl(ϱ	NOUN
ejpam-4768	148	40	)	)	PUNCT
ejpam-4768	148	41	=	=	SYM
ejpam-4768	148	42	h0	h0	PROPN
ejpam-4768	148	43	.	.	PROPN
ejpam-4768	148	44	proof	proof	NOUN
ejpam-4768	148	45	.	.	PUNCT
ejpam-4768	149	1	(	(	PUNCT
ejpam-4768	149	2	i	i	NOUN
ejpam-4768	149	3	)	)	PUNCT
ejpam-4768	149	4	⇒	⇒	PROPN
ejpam-4768	149	5	(	(	PUNCT
ejpam-4768	149	6	ii	ii	NOUN
ejpam-4768	149	7	):	):	PUNCT
ejpam-4768	149	8	obvious	obvious	ADJ
ejpam-4768	149	9	.	.	PUNCT
ejpam-4768	150	1	(	(	PUNCT
ejpam-4768	150	2	ii	ii	NOUN
ejpam-4768	150	3	)	)	PUNCT
ejpam-4768	150	4	⇒	⇒	NOUN
ejpam-4768	150	5	(	(	PUNCT
ejpam-4768	150	6	iii):suppose	iii):suppose	X
ejpam-4768	150	7	that	that	DET
ejpam-4768	150	8	ξ	ξ	X
ejpam-4768	150	9	<	<	X
ejpam-4768	150	10	h1	h1	PROPN
ejpam-4768	150	11	−	−	PROPN
ejpam-4768	150	12	ζ	ζ	NOUN
ejpam-4768	150	13	for	for	ADP
ejpam-4768	150	14	any	any	DET
ejpam-4768	150	15	hfmao	hfmao	NOUN
ejpam-4768	150	16	set	set	VERB
ejpam-4768	150	17	h1	h1	PROPN
ejpam-4768	150	18	−	−	PROPN
ejpam-4768	150	19	ζ.by	ζ.by	PROPN
ejpam-4768	150	20	(	(	PUNCT
ejpam-4768	150	21	ii	ii	PROPN
ejpam-4768	150	22	)	)	PUNCT
ejpam-4768	150	23	there	there	PRON
ejpam-4768	150	24	exists	exist	VERB
ejpam-4768	150	25	hfo	hfo	PROPN
ejpam-4768	150	26	set	set	VERB
ejpam-4768	150	27	ω	ω	NUM
ejpam-4768	150	28	such	such	ADJ
ejpam-4768	150	29	that	that	SCONJ
ejpam-4768	150	30	ξ	ξ	X
ejpam-4768	150	31	<	<	X
ejpam-4768	150	32	ω	ω	X
ejpam-4768	150	33	<	<	X
ejpam-4768	150	34	cl(ω	cl(ω	X
ejpam-4768	150	35	)	)	PUNCT
ejpam-4768	150	36	<	<	X
ejpam-4768	150	37	h1	h1	PROPN
ejpam-4768	150	38	−	−	PROPN
ejpam-4768	150	39	ζ.clearly	ζ.clearly	ADV
ejpam-4768	150	40	cl(ω	cl(ω	ADV
ejpam-4768	150	41	)	)	PUNCT
ejpam-4768	150	42	∧	∧	NOUN
ejpam-4768	150	43	ζ	ζ	NOUN
ejpam-4768	150	44	=	=	SYM
ejpam-4768	150	45	h0	h0	NOUN
ejpam-4768	150	46	as	as	ADP
ejpam-4768	150	47	cl(ω	cl(ω	ADV
ejpam-4768	150	48	)	)	PUNCT
ejpam-4768	150	49	<	<	X
ejpam-4768	150	50	h1	h1	PROPN
ejpam-4768	150	51	−	−	PROPN
ejpam-4768	150	52	ζ	ζ	NOUN
ejpam-4768	150	53	.	.	PUNCT
ejpam-4768	150	54	by	by	ADP
ejpam-4768	150	55	assuming	assume	VERB
ejpam-4768	150	56	ϱ	ϱ	ADP
ejpam-4768	150	57	=	=	PUNCT
ejpam-4768	150	58	h1	h1	PROPN
ejpam-4768	150	59	−	−	PROPN
ejpam-4768	150	60	cl(ω),we	cl(ω),we	NOUN
ejpam-4768	150	61	get	get	VERB
ejpam-4768	150	62	ζ	ζ	NOUN
ejpam-4768	150	63	<	<	X
ejpam-4768	150	64	ϱ	ϱ	ADP
ejpam-4768	150	65	<	<	X
ejpam-4768	150	66	h1	h1	PROPN
ejpam-4768	150	67	−	−	PROPN
ejpam-4768	150	68	ω	ω	PROPN
ejpam-4768	150	69	<	<	X
ejpam-4768	150	70	h1	h1	PROPN
ejpam-4768	150	71	−	−	PROPN
ejpam-4768	150	72	ξ	ξ	PROPN
ejpam-4768	150	73	.	.	PUNCT
ejpam-4768	151	1	since	since	SCONJ
ejpam-4768	151	2	h1	h1	PROPN
ejpam-4768	151	3	−	−	PROPN
ejpam-4768	151	4	ω	ω	PROPN
ejpam-4768	151	5	is	be	AUX
ejpam-4768	151	6	hfc	hfc	ADJ
ejpam-4768	151	7	set	set	NOUN
ejpam-4768	151	8	ζ	ζ	NOUN
ejpam-4768	151	9	<	<	X
ejpam-4768	151	10	cl(ϱ	cl(ϱ	NOUN
ejpam-4768	151	11	)	)	PUNCT
ejpam-4768	151	12	<	<	X
ejpam-4768	151	13	h1	h1	PROPN
ejpam-4768	151	14	−	−	PROPN
ejpam-4768	151	15	ω	ω	PROPN
ejpam-4768	151	16	<	<	X
ejpam-4768	151	17	h1	h1	PROPN
ejpam-4768	151	18	−	−	NOUN
ejpam-4768	151	19	ξ.clearly	ξ.clearly	ADV
ejpam-4768	151	20	,	,	PUNCT
ejpam-4768	151	21	cl(ϱ	cl(ϱ	NOUN
ejpam-4768	151	22	)	)	PUNCT
ejpam-4768	152	1	∧	∧	NOUN
ejpam-4768	152	2	ξ	ξ	X
ejpam-4768	152	3	=	=	SYM
ejpam-4768	152	4	h0	h0	NOUN
ejpam-4768	152	5	as	as	ADP
ejpam-4768	152	6	cl(ϱ	cl(ϱ	NOUN
ejpam-4768	152	7	)	)	PUNCT
ejpam-4768	152	8	<	<	X
ejpam-4768	152	9	h1	h1	PROPN
ejpam-4768	152	10	−	−	PROPN
ejpam-4768	152	11	ξ	ξ	PROPN
ejpam-4768	152	12	.	.	PUNCT
ejpam-4768	153	1	it	it	PRON
ejpam-4768	153	2	is	be	AUX
ejpam-4768	153	3	evident	evident	ADJ
ejpam-4768	153	4	that	that	SCONJ
ejpam-4768	153	5	ω	ω	PROPN
ejpam-4768	153	6	∨	∨	NUM
ejpam-4768	153	7	ϱ	ϱ	PROPN
ejpam-4768	153	8	=	=	PROPN
ejpam-4768	153	9	h0	h0	PROPN
ejpam-4768	153	10	.	.	PUNCT
ejpam-4768	154	1	(	(	PUNCT
ejpam-4768	154	2	iii	iii	X
ejpam-4768	154	3	)	)	PUNCT
ejpam-4768	154	4	⇒	⇒	NOUN
ejpam-4768	154	5	(	(	PUNCT
ejpam-4768	154	6	iv	iv	NUM
ejpam-4768	154	7	):	):	PUNCT
ejpam-4768	154	8	by	by	ADP
ejpam-4768	154	9	(	(	PUNCT
ejpam-4768	154	10	iii	iii	NOUN
ejpam-4768	154	11	)	)	PUNCT
ejpam-4768	154	12	for	for	ADP
ejpam-4768	154	13	any	any	DET
ejpam-4768	154	14	distinct	distinct	ADJ
ejpam-4768	154	15	hfo	hfo	NOUN
ejpam-4768	154	16	sets	set	VERB
ejpam-4768	154	17	ω,ϱ	ω,ϱ	ADP
ejpam-4768	154	18	such	such	ADJ
ejpam-4768	154	19	that	that	SCONJ
ejpam-4768	154	20	ξ	ξ	PRON
ejpam-4768	154	21	<	<	X
ejpam-4768	154	22	ω	ω	PROPN
ejpam-4768	154	23	,	,	PUNCT
ejpam-4768	154	24	cl(ω)∧ζ	cl(ω)∧ζ	ADJ
ejpam-4768	154	25	=	=	SYM
ejpam-4768	154	26	h0	h0	NOUN
ejpam-4768	154	27	and	and	CCONJ
ejpam-4768	154	28	ζ	ζ	NOUN
ejpam-4768	154	29	<	<	X
ejpam-4768	154	30	ϱ,cl(ϱ	ϱ,cl(ϱ	NOUN
ejpam-4768	154	31	)	)	PUNCT
ejpam-4768	154	32	∧	∧	PROPN
ejpam-4768	154	33	ξ	ξ	PROPN
ejpam-4768	154	34	=	=	SYM
ejpam-4768	154	35	h0	h0	PROPN
ejpam-4768	154	36	.	.	PUNCT
ejpam-4768	155	1	as	as	ADP
ejpam-4768	155	2	cl(ω	cl(ω	X
ejpam-4768	155	3	)	)	PUNCT
ejpam-4768	155	4	∧	∧	NOUN
ejpam-4768	155	5	ζ	ζ	NOUN
ejpam-4768	155	6	=	=	SYM
ejpam-4768	155	7	h0	h0	NOUN
ejpam-4768	155	8	,	,	PUNCT
ejpam-4768	155	9	cl(ϱ	cl(ϱ	NOUN
ejpam-4768	155	10	)	)	PUNCT
ejpam-4768	155	11	∧	∧	NOUN
ejpam-4768	155	12	ξ	ξ	X
ejpam-4768	155	13	=	=	SYM
ejpam-4768	155	14	h0	h0	NOUN
ejpam-4768	155	15	imply	imply	VERB
ejpam-4768	155	16	that	that	SCONJ
ejpam-4768	155	17	cl(ω	cl(ω	X
ejpam-4768	155	18	)	)	PUNCT
ejpam-4768	155	19	∧	∧	PROPN
ejpam-4768	155	20	cl(ϱ	cl(ϱ	NOUN
ejpam-4768	155	21	)	)	PUNCT
ejpam-4768	155	22	=	=	SYM
ejpam-4768	155	23	h0	h0	PROPN
ejpam-4768	155	24	.	.	PUNCT
ejpam-4768	155	25	a.	a.	PROPN
ejpam-4768	155	26	swaminathan	swaminathan	PROPN
ejpam-4768	155	27	,	,	PUNCT
ejpam-4768	155	28	cenap	cenap	VERB
ejpam-4768	155	29	ozel	ozel	ADJ
ejpam-4768	155	30	,	,	PUNCT
ejpam-4768	155	31	ibtesam	ibtesam	PROPN
ejpam-4768	155	32	alshammari	alshammari	PROPN
ejpam-4768	155	33	/	/	SYM
ejpam-4768	155	34	eur	eur	PROPN
ejpam-4768	155	35	.	.	PUNCT
ejpam-4768	156	1	j.	j.	PROPN
ejpam-4768	156	2	pure	pure	PROPN
ejpam-4768	156	3	appl	appl	PROPN
ejpam-4768	156	4	.	.	PROPN
ejpam-4768	156	5	math	math	PROPN
ejpam-4768	156	6	,	,	PUNCT
ejpam-4768	156	7	16	16	NUM
ejpam-4768	156	8	(	(	PUNCT
ejpam-4768	156	9	3	3	NUM
ejpam-4768	156	10	)	)	PUNCT
ejpam-4768	156	11	(	(	PUNCT
ejpam-4768	156	12	2023	2023	NUM
ejpam-4768	156	13	)	)	PUNCT
ejpam-4768	156	14	,	,	PUNCT
ejpam-4768	156	15	1381	1381	NUM
ejpam-4768	156	16	-	-	SYM
ejpam-4768	156	17	1388	1388	NUM
ejpam-4768	156	18	1386	1386	NUM
ejpam-4768	156	19	(	(	PUNCT
ejpam-4768	156	20	iv	iv	X
ejpam-4768	156	21	)	)	PUNCT
ejpam-4768	156	22	⇒	⇒	NOUN
ejpam-4768	156	23	(	(	PUNCT
ejpam-4768	156	24	i	i	NOUN
ejpam-4768	156	25	):	):	PUNCT
ejpam-4768	156	26	proof	proof	NOUN
ejpam-4768	156	27	is	be	AUX
ejpam-4768	156	28	easy	easy	ADJ
ejpam-4768	156	29	and	and	CCONJ
ejpam-4768	156	30	hence	hence	ADV
ejpam-4768	156	31	omitted	omit	VERB
ejpam-4768	156	32	.	.	PUNCT
ejpam-4768	157	1	theorem	theorem	VERB
ejpam-4768	157	2	2.13	2.13	NUM
ejpam-4768	157	3	..	..	PUNCT
ejpam-4768	157	4	every	every	DET
ejpam-4768	157	5	hesitant	hesitant	ADJ
ejpam-4768	157	6	fuzzy	fuzzy	ADJ
ejpam-4768	157	7	hausdorff	hausdorff	PROPN
ejpam-4768	157	8	m	m	PROPN
ejpam-4768	157	9	-	-	ADJ
ejpam-4768	157	10	compact	compact	ADJ
ejpam-4768	157	11	space	space	NOUN
ejpam-4768	157	12	is	be	AUX
ejpam-4768	157	13	hesitant	hesitant	ADJ
ejpam-4768	157	14	fuzzy	fuzzy	ADJ
ejpam-4768	157	15	minimal	minimal	ADJ
ejpam-4768	157	16	hesitant	hesitant	ADJ
ejpam-4768	157	17	fuzzy	fuzzy	ADJ
ejpam-4768	157	18	c	c	NOUN
ejpam-4768	157	19	-	-	NOUN
ejpam-4768	157	20	regular	regular	ADJ
ejpam-4768	157	21	.	.	PUNCT
ejpam-4768	158	1	proof	proof	NOUN
ejpam-4768	158	2	.	.	PUNCT
ejpam-4768	159	1	let	let	VERB
ejpam-4768	159	2	x	x	PRON
ejpam-4768	159	3	be	be	AUX
ejpam-4768	159	4	a	a	DET
ejpam-4768	159	5	hesitant	hesitant	ADJ
ejpam-4768	159	6	fuzzy	fuzzy	ADJ
ejpam-4768	159	7	hausdorff	hausdorff	NOUN
ejpam-4768	159	8	m	m	NOUN
ejpam-4768	159	9	-	-	ADJ
ejpam-4768	159	10	compact	compact	ADJ
ejpam-4768	159	11	.	.	PUNCT
ejpam-4768	160	1	suppose	suppose	VERB
ejpam-4768	160	2	γ	γ	X
ejpam-4768	160	3	∈	∈	PROPN
ejpam-4768	160	4	x	x	PUNCT
ejpam-4768	160	5	is	be	AUX
ejpam-4768	160	6	hfmic	hfmic	ADJ
ejpam-4768	160	7	set	set	NOUN
ejpam-4768	160	8	and	and	CCONJ
ejpam-4768	160	9	xα	xα	ADP
ejpam-4768	160	10	∈	∈	PROPN
ejpam-4768	160	11	x	x	PUNCT
ejpam-4768	160	12	such	such	ADJ
ejpam-4768	160	13	that	that	PRON
ejpam-4768	160	14	xα	xα	PUNCT
ejpam-4768	160	15	/∈	/∈	PUNCT
ejpam-4768	161	1	λ	λ	INTJ
ejpam-4768	161	2	.	.	PUNCT
ejpam-4768	162	1	since	since	SCONJ
ejpam-4768	162	2	x	x	PRON
ejpam-4768	162	3	is	be	AUX
ejpam-4768	162	4	hesitant	hesitant	ADJ
ejpam-4768	162	5	fuzzy	fuzzy	ADJ
ejpam-4768	162	6	hausdorff	hausdorff	NOUN
ejpam-4768	162	7	,	,	PUNCT
ejpam-4768	162	8	for	for	ADP
ejpam-4768	162	9	each	each	DET
ejpam-4768	162	10	xβ	xβ	PROPN
ejpam-4768	162	11	∈	∈	PROPN
ejpam-4768	162	12	g	g	PROPN
ejpam-4768	162	13	,	,	PUNCT
ejpam-4768	162	14	we	we	PRON
ejpam-4768	162	15	have	have	VERB
ejpam-4768	162	16	gxβ	gxβ	NOUN
ejpam-4768	162	17	,	,	PUNCT
ejpam-4768	162	18	hxβ	hxβ	VERB
ejpam-4768	162	19	disjoint	disjoint	NOUN
ejpam-4768	162	20	hfo	hfo	PROPN
ejpam-4768	162	21	sets	set	VERB
ejpam-4768	162	22	such	such	ADJ
ejpam-4768	162	23	that	that	DET
ejpam-4768	162	24	xα	xα	PROPN
ejpam-4768	162	25	∈	∈	PROPN
ejpam-4768	162	26	gxβ	gxβ	NOUN
ejpam-4768	162	27	,	,	PUNCT
ejpam-4768	162	28	xβ	xβ	PROPN
ejpam-4768	162	29	∈	∈	PROPN
ejpam-4768	162	30	hxβ	hxβ	NOUN
ejpam-4768	162	31	.	.	PUNCT
ejpam-4768	163	1	let	let	VERB
ejpam-4768	163	2	g	g	NOUN
ejpam-4768	163	3	=	=	PUNCT
ejpam-4768	163	4	{	{	PUNCT
ejpam-4768	163	5	hxβ	hxβ	X
ejpam-4768	163	6	|xβ	|xβ	PUNCT
ejpam-4768	163	7	∈	∈	PROPN
ejpam-4768	163	8	λ	λ	PROPN
ejpam-4768	163	9	}	}	PUNCT
ejpam-4768	163	10	∨	∨	NUM
ejpam-4768	163	11	{	{	PUNCT
ejpam-4768	163	12	h1	h1	PROPN
ejpam-4768	163	13	−	−	PROPN
ejpam-4768	163	14	λ	λ	NOUN
ejpam-4768	163	15	}	}	PUNCT
ejpam-4768	163	16	.	.	PUNCT
ejpam-4768	164	1	then	then	ADV
ejpam-4768	164	2	g	g	PROPN
ejpam-4768	164	3	is	be	AUX
ejpam-4768	164	4	hfmao	hfmao	NOUN
ejpam-4768	164	5	cover	cover	NOUN
ejpam-4768	164	6	of	of	ADP
ejpam-4768	164	7	x	x	PUNCT
ejpam-4768	164	8	by	by	ADP
ejpam-4768	164	9	lemma	lemma	PROPN
ejpam-4768	164	10	2.3	2.3	NUM
ejpam-4768	164	11	..	..	PUNCT
ejpam-4768	164	12	by	by	ADP
ejpam-4768	164	13	hesitant	hesitant	ADJ
ejpam-4768	164	14	fuzzy	fuzzy	ADJ
ejpam-4768	164	15	mcompactness	mcompactness	NOUN
ejpam-4768	164	16	of	of	ADP
ejpam-4768	164	17	x	x	PRON
ejpam-4768	164	18	,	,	PUNCT
ejpam-4768	164	19	then	then	ADV
ejpam-4768	164	20	we	we	PRON
ejpam-4768	164	21	have	have	VERB
ejpam-4768	164	22	a	a	DET
ejpam-4768	164	23	finite	finite	ADJ
ejpam-4768	164	24	hesitant	hesitant	ADJ
ejpam-4768	164	25	fuzzy	fuzzy	ADJ
ejpam-4768	164	26	s	s	NOUN
ejpam-4768	164	27	-	-	PUNCT
ejpam-4768	164	28	refinement	refinement	ADJ
ejpam-4768	164	29	h	h	NOUN
ejpam-4768	164	30	of	of	ADP
ejpam-4768	164	31	g	g	PROPN
ejpam-4768	164	32	.	.	PUNCT
ejpam-4768	165	1	let	let	VERB
ejpam-4768	165	2	m	m	VERB
ejpam-4768	165	3	=	=	SYM
ejpam-4768	165	4	∨{λ	∨{λ	PROPN
ejpam-4768	165	5	∈	∈	PROPN
ejpam-4768	165	6	h	h	NOUN
ejpam-4768	165	7	|λ∧λ	|λ∧λ	NOUN
ejpam-4768	165	8	̸=	̸=	PROPN
ejpam-4768	165	9	h0	h0	PROPN
ejpam-4768	165	10	}	}	PUNCT
ejpam-4768	165	11	.	.	PUNCT
ejpam-4768	166	1	so	so	ADV
ejpam-4768	166	2	m	m	PROPN
ejpam-4768	166	3	is	be	AUX
ejpam-4768	166	4	an	an	DET
ejpam-4768	166	5	hfo	hfo	NOUN
ejpam-4768	166	6	set	set	NOUN
ejpam-4768	166	7	which	which	PRON
ejpam-4768	166	8	contains	contain	VERB
ejpam-4768	166	9	λ	λ	X
ejpam-4768	166	10	.	.	PUNCT
ejpam-4768	167	1	let	let	AUX
ejpam-4768	167	2	λ1,λ2	λ1,λ2	PROPN
ejpam-4768	167	3	...	...	PUNCT
ejpam-4768	167	4	λn	λn	PROPN
ejpam-4768	167	5	be	be	AUX
ejpam-4768	167	6	the	the	DET
ejpam-4768	167	7	only	only	ADV
ejpam-4768	167	8	hesitant	hesitant	ADJ
ejpam-4768	167	9	fuzzy	fuzzy	ADJ
ejpam-4768	167	10	members	member	NOUN
ejpam-4768	167	11	of	of	ADP
ejpam-4768	167	12	h	h	NOUN
ejpam-4768	167	13	such	such	ADJ
ejpam-4768	167	14	that	that	SCONJ
ejpam-4768	167	15	λk	λk	ADP
ejpam-4768	167	16	∧	∧	PROPN
ejpam-4768	167	17	λ	λ	PROPN
ejpam-4768	167	18	̸=	̸=	PROPN
ejpam-4768	167	19	h0,k	h0,k	PROPN
ejpam-4768	167	20	∈	∈	PROPN
ejpam-4768	167	21	z+	z+	NUM
ejpam-4768	167	22	.	.	PUNCT
ejpam-4768	168	1	for	for	ADP
ejpam-4768	168	2	each	each	DET
ejpam-4768	168	3	k	k	PROPN
ejpam-4768	168	4	∈	∈	PROPN
ejpam-4768	168	5	z+,∃	z+,∃	PUNCT
ejpam-4768	168	6	xγ	xγ	NOUN
ejpam-4768	168	7	∈	∈	PROPN
ejpam-4768	168	8	λ	λ	NOUN
ejpam-4768	168	9	such	such	ADJ
ejpam-4768	168	10	that	that	SCONJ
ejpam-4768	168	11	λk	λk	X
ejpam-4768	168	12	<	<	X
ejpam-4768	168	13	̸	̸	PUNCT
ejpam-4768	168	14	=	=	SYM
ejpam-4768	168	15	hxβγ	hxβγ	NOUN
ejpam-4768	168	16	,	,	PUNCT
ejpam-4768	168	17	k	k	PROPN
ejpam-4768	168	18	∈	∈	PROPN
ejpam-4768	168	19	z+	z+	PUNCT
ejpam-4768	168	20	.	.	PUNCT
ejpam-4768	169	1	we	we	PRON
ejpam-4768	169	2	put	put	VERB
ejpam-4768	169	3	h	h	NOUN
ejpam-4768	169	4	=	=	PUNCT
ejpam-4768	169	5	n	n	PRON
ejpam-4768	169	6	∧	∧	PROPN
ejpam-4768	169	7	k=1	k=1	PROPN
ejpam-4768	169	8	gxβγ	gxβγ	PROPN
ejpam-4768	169	9	.	.	PUNCT
ejpam-4768	170	1	then	then	ADV
ejpam-4768	170	2	xα	xα	INTJ
ejpam-4768	170	3	∈	∈	PROPN
ejpam-4768	170	4	µ.	µ.	NOUN
ejpam-4768	170	5	it	it	PRON
ejpam-4768	170	6	is	be	AUX
ejpam-4768	170	7	easy	easy	ADJ
ejpam-4768	170	8	to	to	PART
ejpam-4768	170	9	show	show	VERB
ejpam-4768	170	10	that	that	SCONJ
ejpam-4768	170	11	g	g	PROPN
ejpam-4768	170	12	∧h	∧h	PROPN
ejpam-4768	170	13	=	=	SYM
ejpam-4768	170	14	h0	h0	PROPN
ejpam-4768	170	15	.	.	PROPN
ejpam-4768	170	16	corollary	corollary	ADJ
ejpam-4768	170	17	2.14	2.14	NUM
ejpam-4768	170	18	..	..	PUNCT
ejpam-4768	170	19	a	a	DET
ejpam-4768	170	20	hesitant	hesitant	ADJ
ejpam-4768	170	21	fuzzy	fuzzy	ADJ
ejpam-4768	170	22	hausdorff	hausdorff	PROPN
ejpam-4768	170	23	m	m	PROPN
ejpam-4768	170	24	-	-	ADJ
ejpam-4768	170	25	compact	compact	ADJ
ejpam-4768	170	26	space	space	NOUN
ejpam-4768	170	27	is	be	AUX
ejpam-4768	170	28	hesitant	hesitant	ADJ
ejpam-4768	170	29	fuzzy	fuzzy	ADJ
ejpam-4768	170	30	minimal	minimal	ADJ
ejpam-4768	170	31	c	c	NOUN
ejpam-4768	170	32	-	-	ADJ
ejpam-4768	170	33	normal	normal	ADJ
ejpam-4768	170	34	.	.	PUNCT
ejpam-4768	171	1	proof	proof	NOUN
ejpam-4768	171	2	.	.	PUNCT
ejpam-4768	172	1	let	let	VERB
ejpam-4768	172	2	ξ	ξ	X
ejpam-4768	172	3	,	,	PUNCT
ejpam-4768	172	4	ζ	ζ	NOUN
ejpam-4768	172	5	be	be	AUX
ejpam-4768	172	6	distinct	distinct	ADJ
ejpam-4768	172	7	hfmic	hfmic	ADJ
ejpam-4768	172	8	sets	set	NOUN
ejpam-4768	172	9	in	in	ADP
ejpam-4768	172	10	hesitant	hesitant	ADJ
ejpam-4768	172	11	fuzzy	fuzzy	ADJ
ejpam-4768	172	12	hausdorff	hausdorff	PROPN
ejpam-4768	172	13	m	m	PROPN
ejpam-4768	172	14	-	-	ADJ
ejpam-4768	172	15	compact	compact	ADJ
ejpam-4768	172	16	space	space	NOUN
ejpam-4768	172	17	x.	x.	NOUN
ejpam-4768	172	18	by	by	ADP
ejpam-4768	172	19	theorem	theorem	NOUN
ejpam-4768	172	20	2.13	2.13	NUM
ejpam-4768	172	21	.	.	PUNCT
ejpam-4768	172	22	,	,	PUNCT
ejpam-4768	172	23	x	x	X
ejpam-4768	172	24	is	be	AUX
ejpam-4768	172	25	hesitant	hesitant	ADJ
ejpam-4768	172	26	fuzzy	fuzzy	ADJ
ejpam-4768	172	27	minimal	minimal	ADJ
ejpam-4768	172	28	c	c	NOUN
ejpam-4768	172	29	-	-	NOUN
ejpam-4768	172	30	regular	regular	ADJ
ejpam-4768	172	31	.	.	PUNCT
ejpam-4768	173	1	hence	hence	ADV
ejpam-4768	173	2	for	for	ADP
ejpam-4768	173	3	each	each	DET
ejpam-4768	173	4	xφ	xφ	PROPN
ejpam-4768	173	5	∈	∈	PROPN
ejpam-4768	173	6	ξ	ξ	PROPN
ejpam-4768	173	7	,	,	PUNCT
ejpam-4768	173	8	∃	∃	PROPN
ejpam-4768	173	9	g	g	PROPN
ejpam-4768	173	10	,	,	PUNCT
ejpam-4768	173	11	h	h	PROPN
ejpam-4768	173	12	hfo	hfo	PROPN
ejpam-4768	173	13	sets	set	VERB
ejpam-4768	173	14	such	such	ADJ
ejpam-4768	173	15	that	that	SCONJ
ejpam-4768	173	16	xφ	xφ	PROPN
ejpam-4768	173	17	∈	∈	PROPN
ejpam-4768	173	18	g	g	PROPN
ejpam-4768	173	19	,	,	PUNCT
ejpam-4768	173	20	ζ	ζ	NOUN
ejpam-4768	173	21	<	<	X
ejpam-4768	173	22	h	h	NOUN
ejpam-4768	173	23	and	and	CCONJ
ejpam-4768	173	24	g	g	PROPN
ejpam-4768	173	25	∧h	∧h	PROPN
ejpam-4768	173	26	=	=	SYM
ejpam-4768	173	27	h0	h0	PROPN
ejpam-4768	173	28	.	.	PUNCT
ejpam-4768	174	1	the	the	DET
ejpam-4768	174	2	collection	collection	NOUN
ejpam-4768	174	3	g	g	NOUN
ejpam-4768	174	4	=	=	PUNCT
ejpam-4768	174	5	{	{	PUNCT
ejpam-4768	174	6	gxφ	gxφ	NOUN
ejpam-4768	174	7	|xφ	|xφ	X
ejpam-4768	174	8	∈	∈	PROPN
ejpam-4768	174	9	ξ	ξ	PROPN
ejpam-4768	174	10	}	}	PUNCT
ejpam-4768	174	11	∨	∨	NUM
ejpam-4768	174	12	{	{	PUNCT
ejpam-4768	174	13	h1	h1	PROPN
ejpam-4768	174	14	−	−	PART
ejpam-4768	174	15	ξ	ξ	NUM
ejpam-4768	174	16	}	}	PUNCT
ejpam-4768	174	17	is	be	AUX
ejpam-4768	174	18	a	a	DET
ejpam-4768	174	19	hfmao	hfmao	ADJ
ejpam-4768	174	20	cover	cover	NOUN
ejpam-4768	174	21	of	of	ADP
ejpam-4768	174	22	x	x	PUNCT
ejpam-4768	174	23	by	by	ADP
ejpam-4768	174	24	lemma	lemma	PROPN
ejpam-4768	174	25	2.3	2.3	NUM
ejpam-4768	174	26	..	..	PUNCT
ejpam-4768	174	27	now	now	ADV
ejpam-4768	174	28	proceeding	proceed	VERB
ejpam-4768	174	29	like	like	ADP
ejpam-4768	174	30	the	the	DET
ejpam-4768	174	31	proof	proof	NOUN
ejpam-4768	174	32	of	of	ADP
ejpam-4768	174	33	theorem	theorem	NOUN
ejpam-4768	174	34	4.3	4.3	NUM
ejpam-4768	174	35	,	,	PUNCT
ejpam-4768	174	36	we	we	PRON
ejpam-4768	174	37	get	get	VERB
ejpam-4768	174	38	two	two	NUM
ejpam-4768	174	39	hfo	hfo	PROPN
ejpam-4768	174	40	sets	set	NOUN
ejpam-4768	174	41	η	η	PROPN
ejpam-4768	174	42	and	and	CCONJ
ejpam-4768	174	43	µ	µ	PRON
ejpam-4768	174	44	such	such	ADJ
ejpam-4768	174	45	that	that	SCONJ
ejpam-4768	174	46	ξ	ξ	X
ejpam-4768	174	47	<	<	X
ejpam-4768	174	48	λ	λ	PROPN
ejpam-4768	174	49	,	,	PUNCT
ejpam-4768	174	50	ζ	ζ	X
ejpam-4768	174	51	<	<	X
ejpam-4768	174	52	µ	µ	NOUN
ejpam-4768	174	53	and	and	CCONJ
ejpam-4768	174	54	g	g	PROPN
ejpam-4768	174	55	∧h	∧h	PROPN
ejpam-4768	174	56	=	=	SYM
ejpam-4768	174	57	h0	h0	PROPN
ejpam-4768	174	58	.	.	PUNCT
ejpam-4768	175	1	lemma	lemma	PROPN
ejpam-4768	175	2	2.15	2.15	NUM
ejpam-4768	175	3	..	..	PUNCT
ejpam-4768	175	4	if	if	SCONJ
ejpam-4768	175	5	y	y	PROPN
ejpam-4768	175	6	is	be	AUX
ejpam-4768	175	7	a	a	DET
ejpam-4768	175	8	hfc(resp.hfo	hfc(resp.hfo	NOUN
ejpam-4768	175	9	)	)	PUNCT
ejpam-4768	175	10	subset	subset	NOUN
ejpam-4768	175	11	of	of	ADP
ejpam-4768	175	12	a	a	DET
ejpam-4768	175	13	hfts	hft	NOUN
ejpam-4768	175	14	x	x	NOUN
ejpam-4768	175	15	,	,	PUNCT
ejpam-4768	175	16	then	then	ADV
ejpam-4768	175	17	hfmic	hfmic	ADJ
ejpam-4768	175	18	(	(	PUNCT
ejpam-4768	175	19	resp.hfmio	resp.hfmio	NUM
ejpam-4768	175	20	)	)	PUNCT
ejpam-4768	175	21	sets	set	NOUN
ejpam-4768	175	22	in	in	ADP
ejpam-4768	175	23	the	the	DET
ejpam-4768	175	24	subspace	subspace	NOUN
ejpam-4768	175	25	y	y	PROPN
ejpam-4768	175	26	of	of	ADP
ejpam-4768	175	27	x	x	SYM
ejpam-4768	175	28	are	be	AUX
ejpam-4768	175	29	hfmic	hfmic	ADJ
ejpam-4768	175	30	(	(	PUNCT
ejpam-4768	175	31	resp.hfmio	resp.hfmio	NUM
ejpam-4768	175	32	)	)	PUNCT
ejpam-4768	175	33	sets	set	NOUN
ejpam-4768	175	34	in	in	ADP
ejpam-4768	175	35	x.	x.	NOUN
ejpam-4768	175	36	proof	proof	NOUN
ejpam-4768	175	37	.	.	PUNCT
ejpam-4768	176	1	let	let	VERB
ejpam-4768	176	2	ξ	ξ	X
ejpam-4768	176	3	be	be	AUX
ejpam-4768	176	4	a	a	DET
ejpam-4768	176	5	hfmic	hfmic	ADJ
ejpam-4768	176	6	set	set	NOUN
ejpam-4768	176	7	in	in	ADP
ejpam-4768	176	8	y	y	PROPN
ejpam-4768	176	9	,	,	PUNCT
ejpam-4768	176	10	a	a	DET
ejpam-4768	176	11	hfc	hfc	ADJ
ejpam-4768	176	12	subset	subset	NOUN
ejpam-4768	176	13	of	of	ADP
ejpam-4768	176	14	a	a	DET
ejpam-4768	176	15	hfts	hft	NOUN
ejpam-4768	176	16	x.	x.	NOUN
ejpam-4768	176	17	evidently	evidently	ADV
ejpam-4768	176	18	ξ	ξ	X
ejpam-4768	176	19	is	be	AUX
ejpam-4768	176	20	also	also	ADV
ejpam-4768	176	21	hfc	hfc	ADJ
ejpam-4768	176	22	in	in	ADP
ejpam-4768	176	23	x	x	X
ejpam-4768	176	24	as	as	ADP
ejpam-4768	176	25	ξ	ξ	X
ejpam-4768	176	26	=	=	SYM
ejpam-4768	176	27	η	η	PROPN
ejpam-4768	176	28	∧	∧	PROPN
ejpam-4768	176	29	y	y	PROPN
ejpam-4768	176	30	for	for	ADP
ejpam-4768	176	31	any	any	DET
ejpam-4768	176	32	hfc	hfc	NOUN
ejpam-4768	176	33	set	set	NOUN
ejpam-4768	176	34	η	η	PROPN
ejpam-4768	176	35	in	in	ADP
ejpam-4768	176	36	x	x	X
ejpam-4768	176	37	.	.	PUNCT
ejpam-4768	177	1	if	if	SCONJ
ejpam-4768	177	2	possible	possible	ADJ
ejpam-4768	177	3	,	,	PUNCT
ejpam-4768	177	4	suppose	suppose	VERB
ejpam-4768	177	5	we	we	PRON
ejpam-4768	177	6	have	have	VERB
ejpam-4768	177	7	a	a	DET
ejpam-4768	177	8	hfc	hfc	ADJ
ejpam-4768	177	9	set	set	NOUN
ejpam-4768	177	10	β	β	NOUN
ejpam-4768	177	11	in	in	ADP
ejpam-4768	177	12	x	x	X
ejpam-4768	177	13	such	such	ADJ
ejpam-4768	177	14	that	that	SCONJ
ejpam-4768	177	15	β	β	X
ejpam-4768	177	16	<	<	X
ejpam-4768	177	17	ξ	ξ	X
ejpam-4768	177	18	.	.	PUNCT
ejpam-4768	177	19	clearly	clearly	ADV
ejpam-4768	177	20	β	β	X
ejpam-4768	177	21	∧	∧	PROPN
ejpam-4768	177	22	y	y	PROPN
ejpam-4768	177	23	is	be	AUX
ejpam-4768	177	24	hfc	hfc	ADJ
ejpam-4768	177	25	in	in	ADP
ejpam-4768	177	26	y	y	PROPN
ejpam-4768	177	27	such	such	ADJ
ejpam-4768	177	28	that	that	SCONJ
ejpam-4768	177	29	β	β	X
ejpam-4768	177	30	∧	∧	PROPN
ejpam-4768	177	31	y	y	PROPN
ejpam-4768	177	32	<	<	X
ejpam-4768	177	33	β	β	X
ejpam-4768	177	34	<	<	X
ejpam-4768	177	35	ξ	ξ	PROPN
ejpam-4768	177	36	;	;	PUNCT
ejpam-4768	177	37	either	either	CCONJ
ejpam-4768	177	38	β	β	X
ejpam-4768	177	39	∧	∧	PROPN
ejpam-4768	177	40	y	y	PROPN
ejpam-4768	177	41	=	=	SYM
ejpam-4768	177	42	ξ	ξ	PROPN
ejpam-4768	177	43	or	or	CCONJ
ejpam-4768	177	44	β	β	X
ejpam-4768	177	45	∧	∧	PROPN
ejpam-4768	177	46	y	y	PROPN
ejpam-4768	177	47	=	=	PROPN
ejpam-4768	177	48	h0	h0	PROPN
ejpam-4768	177	49	as	as	SCONJ
ejpam-4768	177	50	ξ	ξ	PROPN
ejpam-4768	177	51	is	be	AUX
ejpam-4768	177	52	hfmic	hfmic	ADJ
ejpam-4768	177	53	in	in	ADP
ejpam-4768	177	54	y	y	PROPN
ejpam-4768	177	55	.	.	PUNCT
ejpam-4768	178	1	β	β	X
ejpam-4768	178	2	∧	∧	NOUN
ejpam-4768	178	3	y	y	PROPN
ejpam-4768	178	4	=	=	SYM
ejpam-4768	178	5	ξ	ξ	PROPN
ejpam-4768	178	6	implies	imply	VERB
ejpam-4768	178	7	that	that	SCONJ
ejpam-4768	178	8	β	β	PROPN
ejpam-4768	178	9	∧	∧	NOUN
ejpam-4768	178	10	y	y	PROPN
ejpam-4768	178	11	=	=	PUNCT
ejpam-4768	178	12	β	β	X
ejpam-4768	178	13	=	=	SYM
ejpam-4768	178	14	ξ	ξ	X
ejpam-4768	178	15	.	.	PUNCT
ejpam-4768	179	1	now	now	ADV
ejpam-4768	179	2	it	it	PRON
ejpam-4768	179	3	is	be	AUX
ejpam-4768	179	4	enough	enough	ADJ
ejpam-4768	179	5	to	to	PART
ejpam-4768	179	6	prove	prove	VERB
ejpam-4768	179	7	that	that	SCONJ
ejpam-4768	179	8	β	β	NOUN
ejpam-4768	179	9	=	=	SYM
ejpam-4768	179	10	h0	h0	PROPN
ejpam-4768	179	11	for	for	ADP
ejpam-4768	179	12	β	β	X
ejpam-4768	179	13	∧	∧	PROPN
ejpam-4768	179	14	y	y	PROPN
ejpam-4768	179	15	=	=	PROPN
ejpam-4768	179	16	h0	h0	PROPN
ejpam-4768	179	17	.	.	PUNCT
ejpam-4768	180	1	we	we	PRON
ejpam-4768	180	2	see	see	VERB
ejpam-4768	180	3	that	that	SCONJ
ejpam-4768	180	4	β	β	X
ejpam-4768	180	5	<	<	X
ejpam-4768	180	6	ξ	ξ	X
ejpam-4768	180	7	<	<	X
ejpam-4768	180	8	y	y	PROPN
ejpam-4768	180	9	as	as	SCONJ
ejpam-4768	180	10	ξ	ξ	PROPN
ejpam-4768	180	11	is	be	AUX
ejpam-4768	180	12	a	a	DET
ejpam-4768	180	13	hesitant	hesitant	ADJ
ejpam-4768	180	14	fuzzy	fuzzy	ADJ
ejpam-4768	180	15	subset	subset	NOUN
ejpam-4768	180	16	of	of	ADP
ejpam-4768	180	17	y	y	PROPN
ejpam-4768	180	18	.	.	PUNCT
ejpam-4768	181	1	so	so	ADV
ejpam-4768	181	2	we	we	PRON
ejpam-4768	181	3	have	have	VERB
ejpam-4768	181	4	β	β	X
ejpam-4768	181	5	∧	∧	PROPN
ejpam-4768	181	6	y	y	NOUN
ejpam-4768	181	7	=	=	PUNCT
ejpam-4768	181	8	β	β	PROPN
ejpam-4768	181	9	̸=	̸=	PROPN
ejpam-4768	181	10	h0	h0	NOUN
ejpam-4768	181	11	if	if	SCONJ
ejpam-4768	181	12	ξ	ξ	PRON
ejpam-4768	181	13	̸=	̸=	PROPN
ejpam-4768	181	14	h0	h0	NOUN
ejpam-4768	181	15	.	.	PUNCT
ejpam-4768	182	1	hence	hence	ADV
ejpam-4768	182	2	β	β	PROPN
ejpam-4768	182	3	=	=	SYM
ejpam-4768	182	4	h0	h0	PROPN
ejpam-4768	182	5	.	.	PROPN
ejpam-4768	183	1	similarly	similarly	ADV
ejpam-4768	183	2	we	we	PRON
ejpam-4768	183	3	can	can	AUX
ejpam-4768	183	4	prove	prove	VERB
ejpam-4768	183	5	for	for	ADP
ejpam-4768	183	6	hfo	hfo	NOUN
ejpam-4768	183	7	sets	set	NOUN
ejpam-4768	183	8	.	.	PUNCT
ejpam-4768	184	1	definition	definition	NOUN
ejpam-4768	184	2	2.18	2.18	NUM
ejpam-4768	184	3	.	.	PUNCT
ejpam-4768	185	1	a	a	DET
ejpam-4768	185	2	hesitant	hesitant	ADJ
ejpam-4768	185	3	fuzzy	fuzzy	ADJ
ejpam-4768	185	4	subspace	subspace	NOUN
ejpam-4768	185	5	y	y	PROPN
ejpam-4768	185	6	of	of	ADP
ejpam-4768	185	7	a	a	DET
ejpam-4768	185	8	hfts	hft	NOUN
ejpam-4768	185	9	x	x	PUNCT
ejpam-4768	185	10	is	be	AUX
ejpam-4768	185	11	said	say	VERB
ejpam-4768	185	12	to	to	PART
ejpam-4768	185	13	be	be	AUX
ejpam-4768	185	14	hesitant	hesitant	ADJ
ejpam-4768	185	15	fuzzy	fuzzy	ADJ
ejpam-4768	185	16	minimally	minimally	ADV
ejpam-4768	185	17	closed(resp	closed(resp	PROPN
ejpam-4768	185	18	.	.	PUNCT
ejpam-4768	186	1	hesitant	hesitant	ADJ
ejpam-4768	186	2	fuzzy	fuzzy	ADJ
ejpam-4768	186	3	minimally	minimally	ADV
ejpam-4768	186	4	open	open	ADJ
ejpam-4768	186	5	)	)	PUNCT
ejpam-4768	186	6	invariant	invariant	ADJ
ejpam-4768	186	7	if	if	SCONJ
ejpam-4768	186	8	hfmic(resp.hfmio	hfmic(resp.hfmio	NOUN
ejpam-4768	186	9	)	)	PUNCT
ejpam-4768	186	10	sets	set	NOUN
ejpam-4768	186	11	of	of	ADP
ejpam-4768	186	12	y	y	PROPN
ejpam-4768	186	13	are	be	AUX
ejpam-4768	186	14	also	also	ADV
ejpam-4768	186	15	hfmic	hfmic	ADJ
ejpam-4768	186	16	(	(	PUNCT
ejpam-4768	186	17	resp.hfmio	resp.hfmio	NUM
ejpam-4768	186	18	)	)	PUNCT
ejpam-4768	186	19	sets	set	NOUN
ejpam-4768	186	20	of	of	ADP
ejpam-4768	186	21	x.	x.	PROPN
ejpam-4768	186	22	theorem	theorem	VERB
ejpam-4768	186	23	2.16	2.16	NUM
ejpam-4768	186	24	..	..	PUNCT
ejpam-4768	187	1	hesitant	hesitant	ADJ
ejpam-4768	187	2	fuzzy	fuzzy	ADJ
ejpam-4768	187	3	minimally	minimally	ADV
ejpam-4768	187	4	closed	close	VERB
ejpam-4768	187	5	invariant	invariant	ADJ
ejpam-4768	187	6	subspaces	subspace	NOUN
ejpam-4768	187	7	of	of	ADP
ejpam-4768	187	8	hesitant	hesitant	ADJ
ejpam-4768	187	9	fuzzy	fuzzy	ADJ
ejpam-4768	187	10	minimal	minimal	ADJ
ejpam-4768	187	11	c	c	NOUN
ejpam-4768	187	12	-	-	ADJ
ejpam-4768	187	13	normal	normal	ADJ
ejpam-4768	187	14	spaces	space	NOUN
ejpam-4768	187	15	are	be	AUX
ejpam-4768	187	16	hesitant	hesitant	ADJ
ejpam-4768	187	17	fuzzy	fuzzy	ADJ
ejpam-4768	187	18	minimal	minimal	ADJ
ejpam-4768	187	19	c	c	NOUN
ejpam-4768	187	20	-	-	ADJ
ejpam-4768	187	21	normal	normal	ADJ
ejpam-4768	187	22	.	.	PUNCT
ejpam-4768	188	1	proof	proof	NOUN
ejpam-4768	188	2	.	.	PUNCT
ejpam-4768	189	1	let	let	VERB
ejpam-4768	189	2	ξ	ξ	X
ejpam-4768	189	3	,	,	PUNCT
ejpam-4768	189	4	ζ	ζ	NOUN
ejpam-4768	189	5	be	be	AUX
ejpam-4768	189	6	two	two	NUM
ejpam-4768	189	7	distinct	distinct	ADJ
ejpam-4768	189	8	hfmic	hfmic	ADJ
ejpam-4768	189	9	sets	set	NOUN
ejpam-4768	189	10	in	in	ADP
ejpam-4768	189	11	y	y	PROPN
ejpam-4768	189	12	,	,	PUNCT
ejpam-4768	189	13	where	where	SCONJ
ejpam-4768	189	14	y	y	PROPN
ejpam-4768	189	15	is	be	AUX
ejpam-4768	189	16	hesitant	hesitant	ADJ
ejpam-4768	189	17	fuzzy	fuzzy	ADJ
ejpam-4768	189	18	minimally	minimally	ADV
ejpam-4768	189	19	invariant	invariant	ADJ
ejpam-4768	189	20	subspace	subspace	NOUN
ejpam-4768	189	21	of	of	ADP
ejpam-4768	189	22	a	a	DET
ejpam-4768	189	23	hesitant	hesitant	ADJ
ejpam-4768	189	24	fuzzy	fuzzy	ADJ
ejpam-4768	189	25	minimal	minimal	ADJ
ejpam-4768	189	26	c	c	NOUN
ejpam-4768	189	27	-	-	ADJ
ejpam-4768	189	28	normal	normal	ADJ
ejpam-4768	189	29	space	space	NOUN
ejpam-4768	189	30	x.	x.	NOUN
ejpam-4768	189	31	hence	hence	ADV
ejpam-4768	189	32	ξ	ξ	PROPN
ejpam-4768	189	33	,	,	PUNCT
ejpam-4768	189	34	ζ	ζ	NOUN
ejpam-4768	189	35	are	be	AUX
ejpam-4768	189	36	hfmic	hfmic	ADJ
ejpam-4768	189	37	references	reference	NOUN
ejpam-4768	189	38	1387	1387	NUM
ejpam-4768	189	39	sets	set	NOUN
ejpam-4768	189	40	in	in	ADP
ejpam-4768	189	41	x.	x.	NOUN
ejpam-4768	189	42	as	as	SCONJ
ejpam-4768	189	43	x	x	PRON
ejpam-4768	189	44	is	be	AUX
ejpam-4768	189	45	hesitant	hesitant	ADJ
ejpam-4768	189	46	fuzzy	fuzzy	ADJ
ejpam-4768	189	47	minimal	minimal	ADJ
ejpam-4768	189	48	c	c	NOUN
ejpam-4768	189	49	-	-	ADJ
ejpam-4768	189	50	normal	normal	ADJ
ejpam-4768	189	51	space	space	NOUN
ejpam-4768	189	52	,	,	PUNCT
ejpam-4768	189	53	∃	∃	PROPN
ejpam-4768	189	54	η,µ	η,µ	VERB
ejpam-4768	189	55	distinct	distinct	ADJ
ejpam-4768	189	56	hfo	hfo	NOUN
ejpam-4768	189	57	sets	set	NOUN
ejpam-4768	189	58	in	in	ADP
ejpam-4768	189	59	x	x	SYM
ejpam-4768	189	60	such	such	ADJ
ejpam-4768	189	61	that	that	SCONJ
ejpam-4768	189	62	ξ	ξ	X
ejpam-4768	189	63	<	<	X
ejpam-4768	189	64	η	η	PROPN
ejpam-4768	189	65	,	,	PUNCT
ejpam-4768	189	66	ζ	ζ	X
ejpam-4768	189	67	<	<	X
ejpam-4768	189	68	µ	µ	X
ejpam-4768	189	69	and	and	CCONJ
ejpam-4768	189	70	(	(	PUNCT
ejpam-4768	189	71	y	y	PROPN
ejpam-4768	189	72	∧	∧	PROPN
ejpam-4768	189	73	η	η	PROPN
ejpam-4768	189	74	)	)	PUNCT
ejpam-4768	189	75	∧	∧	PROPN
ejpam-4768	189	76	(	(	PUNCT
ejpam-4768	189	77	y	y	PROPN
ejpam-4768	189	78	∧	∧	PROPN
ejpam-4768	189	79	µ	µ	X
ejpam-4768	189	80	)	)	PUNCT
ejpam-4768	189	81	=	=	PUNCT
ejpam-4768	190	1	h0.that	h0.that	PRON
ejpam-4768	190	2	is	be	AUX
ejpam-4768	190	3	y	y	PROPN
ejpam-4768	190	4	∧	∧	PROPN
ejpam-4768	190	5	η	η	PROPN
ejpam-4768	190	6	;	;	PUNCT
ejpam-4768	190	7	y	y	PROPN
ejpam-4768	190	8	∧	∧	PROPN
ejpam-4768	190	9	µ	µ	X
ejpam-4768	190	10	are	be	AUX
ejpam-4768	190	11	distinct	distinct	ADJ
ejpam-4768	190	12	hfo	hfo	NOUN
ejpam-4768	190	13	sets	set	NOUN
ejpam-4768	190	14	in	in	ADP
ejpam-4768	190	15	y	y	PRON
ejpam-4768	190	16	such	such	ADJ
ejpam-4768	190	17	that	that	SCONJ
ejpam-4768	190	18	ξ	ξ	X
ejpam-4768	190	19	<	<	X
ejpam-4768	190	20	(	(	PUNCT
ejpam-4768	190	21	y	y	PROPN
ejpam-4768	190	22	∧	∧	PROPN
ejpam-4768	190	23	η	η	PROPN
ejpam-4768	190	24	)	)	PUNCT
ejpam-4768	190	25	and	and	CCONJ
ejpam-4768	190	26	ζ	ζ	NOUN
ejpam-4768	190	27	<	<	X
ejpam-4768	190	28	(	(	PUNCT
ejpam-4768	190	29	y	y	PROPN
ejpam-4768	190	30	∧	∧	PROPN
ejpam-4768	190	31	µ	µ	PROPN
ejpam-4768	190	32	)	)	PUNCT
ejpam-4768	190	33	.	.	PUNCT
ejpam-4768	191	1	corollary	corollary	ADJ
ejpam-4768	191	2	2.17	2.17	NUM
ejpam-4768	191	3	..	..	PUNCT
ejpam-4768	191	4	each	each	DET
ejpam-4768	191	5	hfc	hfc	ADJ
ejpam-4768	191	6	subspace	subspace	NOUN
ejpam-4768	191	7	of	of	ADP
ejpam-4768	191	8	a	a	DET
ejpam-4768	191	9	hesitant	hesitant	ADJ
ejpam-4768	191	10	fuzzy	fuzzy	ADJ
ejpam-4768	191	11	minimal	minimal	ADJ
ejpam-4768	191	12	c	c	NOUN
ejpam-4768	191	13	-	-	ADJ
ejpam-4768	191	14	normal	normal	ADJ
ejpam-4768	191	15	space	space	NOUN
ejpam-4768	191	16	is	be	AUX
ejpam-4768	191	17	hesitant	hesitant	ADJ
ejpam-4768	191	18	fuzzy	fuzzy	ADJ
ejpam-4768	191	19	minimal	minimal	ADJ
ejpam-4768	191	20	c	c	NOUN
ejpam-4768	191	21	-	-	ADJ
ejpam-4768	191	22	normal	normal	ADJ
ejpam-4768	191	23	.	.	PUNCT
ejpam-4768	192	1	proof	proof	NOUN
ejpam-4768	192	2	.	.	PUNCT
ejpam-4768	193	1	using	use	VERB
ejpam-4768	193	2	lemma	lemma	PROPN
ejpam-4768	193	3	2.15	2.15	NUM
ejpam-4768	193	4	.	.	PROPN
ejpam-4768	193	5	,	,	PUNCT
ejpam-4768	193	6	we	we	PRON
ejpam-4768	193	7	have	have	VERB
ejpam-4768	193	8	to	to	PART
ejpam-4768	193	9	proceed	proceed	VERB
ejpam-4768	193	10	like	like	ADP
ejpam-4768	193	11	that	that	PRON
ejpam-4768	193	12	of	of	ADP
ejpam-4768	193	13	theorem	theorem	ADJ
ejpam-4768	193	14	2.16	2.16	NUM
ejpam-4768	193	15	..	..	PUNCT
ejpam-4768	194	1	3	3	X
ejpam-4768	194	2	.	.	X
ejpam-4768	194	3	conclusion	conclusion	NOUN
ejpam-4768	194	4	in	in	ADP
ejpam-4768	194	5	recent	recent	ADJ
ejpam-4768	194	6	times	time	NOUN
ejpam-4768	194	7	the	the	DET
ejpam-4768	194	8	notion	notion	NOUN
ejpam-4768	194	9	of	of	ADP
ejpam-4768	194	10	hesitant	hesitant	ADJ
ejpam-4768	194	11	fuzzy	fuzzy	ADJ
ejpam-4768	194	12	minimal	minimal	ADJ
ejpam-4768	194	13	and	and	CCONJ
ejpam-4768	194	14	maximal	maximal	ADJ
ejpam-4768	194	15	open	open	ADJ
ejpam-4768	194	16	sets	set	NOUN
ejpam-4768	194	17	have	have	AUX
ejpam-4768	194	18	been	be	AUX
ejpam-4768	194	19	important	important	ADJ
ejpam-4768	194	20	concepts	concept	NOUN
ejpam-4768	194	21	in	in	ADP
ejpam-4768	194	22	the	the	DET
ejpam-4768	194	23	literature	literature	NOUN
ejpam-4768	194	24	.	.	PUNCT
ejpam-4768	195	1	there	there	PRON
ejpam-4768	195	2	are	be	VERB
ejpam-4768	195	3	some	some	DET
ejpam-4768	195	4	family	family	NOUN
ejpam-4768	195	5	between	between	ADP
ejpam-4768	195	6	hesitant	hesitant	ADJ
ejpam-4768	195	7	fuzzy	fuzzy	ADJ
ejpam-4768	195	8	maximal	maximal	ADJ
ejpam-4768	195	9	and	and	CCONJ
ejpam-4768	195	10	hesitant	hesitant	ADJ
ejpam-4768	195	11	fuzzy	fuzzy	ADJ
ejpam-4768	195	12	minimal	minimal	ADJ
ejpam-4768	195	13	sets	set	NOUN
ejpam-4768	195	14	which	which	PRON
ejpam-4768	195	15	is	be	AUX
ejpam-4768	195	16	called	call	VERB
ejpam-4768	195	17	as	as	ADV
ejpam-4768	195	18	hesitant	hesitant	ADJ
ejpam-4768	195	19	fuzzy	fuzzy	ADJ
ejpam-4768	195	20	mean	mean	VERB
ejpam-4768	195	21	open	open	ADJ
ejpam-4768	195	22	sets	set	NOUN
ejpam-4768	195	23	.	.	PUNCT
ejpam-4768	196	1	when	when	SCONJ
ejpam-4768	196	2	we	we	PRON
ejpam-4768	196	3	are	be	AUX
ejpam-4768	196	4	dealing	deal	VERB
ejpam-4768	196	5	with	with	ADP
ejpam-4768	196	6	hesitant	hesitant	ADJ
ejpam-4768	196	7	fuzzy	fuzzy	ADJ
ejpam-4768	196	8	compactness	compactness	NOUN
ejpam-4768	196	9	,	,	PUNCT
ejpam-4768	196	10	we	we	PRON
ejpam-4768	196	11	may	may	AUX
ejpam-4768	196	12	have	have	VERB
ejpam-4768	196	13	various	various	ADJ
ejpam-4768	196	14	covers	cover	NOUN
ejpam-4768	196	15	to	to	PART
ejpam-4768	196	16	h1	h1	VERB
ejpam-4768	196	17	.	.	PUNCT
ejpam-4768	197	1	in	in	ADP
ejpam-4768	197	2	this	this	DET
ejpam-4768	197	3	paper	paper	NOUN
ejpam-4768	197	4	,	,	PUNCT
ejpam-4768	197	5	we	we	PRON
ejpam-4768	197	6	have	have	AUX
ejpam-4768	197	7	used	use	VERB
ejpam-4768	197	8	particularly	particularly	ADV
ejpam-4768	197	9	hesitant	hesitant	ADJ
ejpam-4768	197	10	fuzzy	fuzzy	ADJ
ejpam-4768	197	11	maximal	maximal	ADJ
ejpam-4768	197	12	open	open	ADJ
ejpam-4768	197	13	cover	cover	NOUN
ejpam-4768	197	14	for	for	ADP
ejpam-4768	197	15	compactness	compactness	NOUN
ejpam-4768	197	16	.	.	PUNCT
ejpam-4768	198	1	further	far	ADV
ejpam-4768	198	2	another	another	DET
ejpam-4768	198	3	new	new	ADJ
ejpam-4768	198	4	ideas	idea	NOUN
ejpam-4768	198	5	namely	namely	ADV
ejpam-4768	198	6	hesitant	hesitant	ADJ
ejpam-4768	198	7	fuzzy	fuzzy	ADJ
ejpam-4768	198	8	minimal	minimal	ADJ
ejpam-4768	198	9	c	c	NOUN
ejpam-4768	198	10	-	-	ADJ
ejpam-4768	198	11	regular	regular	ADJ
ejpam-4768	198	12	and	and	CCONJ
ejpam-4768	198	13	hesitant	hesitant	ADJ
ejpam-4768	198	14	fuzzy	fuzzy	ADJ
ejpam-4768	198	15	minimal	minimal	ADJ
ejpam-4768	198	16	c	c	NOUN
ejpam-4768	198	17	-	-	ADJ
ejpam-4768	198	18	normal	normal	ADJ
ejpam-4768	198	19	are	be	AUX
ejpam-4768	198	20	extended	extend	VERB
ejpam-4768	198	21	with	with	ADP
ejpam-4768	198	22	various	various	ADJ
ejpam-4768	198	23	properties	property	NOUN
ejpam-4768	198	24	.	.	PUNCT
ejpam-4768	199	1	in	in	ADP
ejpam-4768	199	2	future	future	ADJ
ejpam-4768	199	3	one	one	PRON
ejpam-4768	199	4	can	can	AUX
ejpam-4768	199	5	conclude	conclude	VERB
ejpam-4768	199	6	and	and	CCONJ
ejpam-4768	199	7	study	study	VERB
ejpam-4768	199	8	numerous	numerous	ADJ
ejpam-4768	199	9	properties	property	NOUN
ejpam-4768	199	10	of	of	ADP
ejpam-4768	199	11	connectedness	connectedness	NOUN
ejpam-4768	199	12	and	and	CCONJ
ejpam-4768	199	13	compactness	compactness	NOUN
ejpam-4768	199	14	in	in	ADP
ejpam-4768	199	15	hesitant	hesitant	ADJ
ejpam-4768	199	16	fuzzy	fuzzy	ADJ
ejpam-4768	199	17	topology	topology	NOUN
ejpam-4768	199	18	.	.	PUNCT
ejpam-4768	200	1	therefore	therefore	ADV
ejpam-4768	200	2	the	the	DET
ejpam-4768	200	3	hesitant	hesitant	ADJ
ejpam-4768	200	4	fuzzy	fuzzy	ADJ
ejpam-4768	200	5	minimal	minimal	ADJ
ejpam-4768	200	6	,	,	PUNCT
ejpam-4768	200	7	maximal	maximal	ADJ
ejpam-4768	200	8	and	and	CCONJ
ejpam-4768	200	9	mean	mean	VERB
ejpam-4768	200	10	open	open	ADJ
ejpam-4768	200	11	sets	set	NOUN
ejpam-4768	200	12	play	play	VERB
ejpam-4768	200	13	dominant	dominant	ADJ
ejpam-4768	200	14	role	role	NOUN
ejpam-4768	200	15	and	and	CCONJ
ejpam-4768	200	16	in	in	ADP
ejpam-4768	200	17	further	further	ADJ
ejpam-4768	200	18	study	study	NOUN
ejpam-4768	200	19	these	these	DET
ejpam-4768	200	20	notions	notion	NOUN
ejpam-4768	200	21	can	can	AUX
ejpam-4768	200	22	be	be	AUX
ejpam-4768	200	23	investigated	investigate	VERB
ejpam-4768	200	24	via	via	ADP
ejpam-4768	200	25	various	various	ADJ
ejpam-4768	200	26	kinds	kind	NOUN
ejpam-4768	200	27	of	of	ADP
ejpam-4768	200	28	hesitant	hesitant	ADJ
ejpam-4768	200	29	open	open	ADJ
ejpam-4768	200	30	sets	set	NOUN
ejpam-4768	200	31	.	.	PUNCT
ejpam-4768	201	1	references	reference	NOUN
ejpam-4768	201	2	[	[	X
ejpam-4768	201	3	1	1	NUM
ejpam-4768	201	4	]	]	PUNCT
ejpam-4768	201	5	c.	c.	PROPN
ejpam-4768	201	6	l.	l.	PROPN
ejpam-4768	201	7	chang	chang	PROPN
ejpam-4768	201	8	,	,	PUNCT
ejpam-4768	201	9	fuzzy	fuzzy	ADJ
ejpam-4768	201	10	topological	topological	ADJ
ejpam-4768	201	11	spaces	space	NOUN
ejpam-4768	201	12	,	,	PUNCT
ejpam-4768	201	13	j.math	j.math	NOUN
ejpam-4768	201	14	.	.	PUNCT
ejpam-4768	202	1	anal	anal	PROPN
ejpam-4768	202	2	.	.	PUNCT
ejpam-4768	202	3	appl	appl	PROPN
ejpam-4768	202	4	.	.	PROPN
ejpam-4768	202	5	,	,	PUNCT
ejpam-4768	202	6	24(1968),182	24(1968),182	NUM
ejpam-4768	202	7	-	-	SYM
ejpam-4768	202	8	190	190	NUM
ejpam-4768	202	9	.	.	PUNCT
ejpam-4768	203	1	[	[	X
ejpam-4768	203	2	2	2	X
ejpam-4768	203	3	]	]	X
ejpam-4768	203	4	d.	d.	PROPN
ejpam-4768	203	5	deepak	deepak	PROPN
ejpam-4768	203	6	,	,	PUNCT
ejpam-4768	203	7	b.	b.	PROPN
ejpam-4768	203	8	mathew	mathew	PROPN
ejpam-4768	203	9	,	,	PUNCT
ejpam-4768	203	10	s.mohn	s.mohn	PROPN
ejpam-4768	203	11	and	and	CCONJ
ejpam-4768	203	12	h.a	h.a	PROPN
ejpam-4768	203	13	.	.	PROPN
ejpam-4768	203	14	garg	garg	PROPN
ejpam-4768	203	15	,	,	PUNCT
ejpam-4768	203	16	topological	topological	ADJ
ejpam-4768	203	17	structure	structure	NOUN
ejpam-4768	203	18	involving	involve	VERB
ejpam-4768	203	19	hesitant	hesitant	ADJ
ejpam-4768	203	20	fuzzy	fuzzy	ADJ
ejpam-4768	203	21	sets	set	NOUN
ejpam-4768	203	22	,	,	PUNCT
ejpam-4768	203	23	j.	j.	PROPN
ejpam-4768	203	24	intell.fuzzy	intell.fuzzy	PROPN
ejpam-4768	203	25	syst	syst	PROPN
ejpam-4768	203	26	.	.	PUNCT
ejpam-4768	203	27	,2019,36,6401	,2019,36,6401	PUNCT
ejpam-4768	203	28	-	-	PUNCT
ejpam-4768	203	29	6412	6412	NUM
ejpam-4768	203	30	.	.	PUNCT
ejpam-4768	204	1	[	[	X
ejpam-4768	204	2	3	3	X
ejpam-4768	204	3	]	]	X
ejpam-4768	204	4	d.	d.	NOUN
ejpam-4768	204	5	divakaran	divakaran	PROPN
ejpam-4768	204	6	and	and	CCONJ
ejpam-4768	204	7	s.	s.	PROPN
ejpam-4768	204	8	j.	j.	PROPN
ejpam-4768	204	9	john	john	PROPN
ejpam-4768	204	10	,	,	PUNCT
ejpam-4768	204	11	hesitant	hesitant	ADJ
ejpam-4768	204	12	fuzzy	fuzzy	ADJ
ejpam-4768	204	13	rough	rough	ADJ
ejpam-4768	204	14	sets	set	NOUN
ejpam-4768	204	15	through	through	ADP
ejpam-4768	204	16	hesitant	hesitant	ADJ
ejpam-4768	204	17	fuzzy	fuzzy	ADJ
ejpam-4768	204	18	relations	relation	NOUN
ejpam-4768	204	19	,	,	PUNCT
ejpam-4768	204	20	ann	ann	PROPN
ejpam-4768	204	21	.	.	PROPN
ejpam-4768	204	22	fuzzy	fuzzy	ADJ
ejpam-4768	204	23	math	math	NOUN
ejpam-4768	204	24	.	.	PUNCT
ejpam-4768	205	1	inform	inform	NOUN
ejpam-4768	205	2	.	.	PUNCT
ejpam-4768	205	3	,2014,8,33	,2014,8,33	PUNCT
ejpam-4768	205	4	-	-	PUNCT
ejpam-4768	205	5	46	46	NUM
ejpam-4768	205	6	.	.	PUNCT
ejpam-4768	206	1	[	[	X
ejpam-4768	206	2	4	4	X
ejpam-4768	206	3	]	]	PUNCT
ejpam-4768	206	4	j.	j.	PROPN
ejpam-4768	206	5	kim	kim	PROPN
ejpam-4768	206	6	,	,	PUNCT
ejpam-4768	206	7	y.	y.	PROPN
ejpam-4768	206	8	b.	b.	PROPN
ejpam-4768	206	9	jun	jun	PROPN
ejpam-4768	206	10	,	,	PUNCT
ejpam-4768	206	11	p.	p.	PROPN
ejpam-4768	206	12	k.	k.	PROPN
ejpam-4768	207	1	lim	lim	PROPN
ejpam-4768	207	2	,	,	PUNCT
ejpam-4768	207	3	j.	j.	PROPN
ejpam-4768	207	4	g	g	PROPN
ejpam-4768	207	5	.	.	PUNCT
ejpam-4768	208	1	lee	lee	PROPN
ejpam-4768	208	2	and	and	CCONJ
ejpam-4768	208	3	k.	k.	PROPN
ejpam-4768	208	4	hur	hur	PROPN
ejpam-4768	208	5	,	,	PUNCT
ejpam-4768	208	6	the	the	DET
ejpam-4768	208	7	category	category	NOUN
ejpam-4768	208	8	of	of	ADP
ejpam-4768	208	9	hesitant	hesitant	ADJ
ejpam-4768	208	10	h	h	NOUN
ejpam-4768	208	11	-	-	PUNCT
ejpam-4768	208	12	fuzzy	fuzzy	ADJ
ejpam-4768	208	13	sets	set	NOUN
ejpam-4768	208	14	.	.	PUNCT
ejpam-4768	209	1	,ann.fuzzy	,ann.fuzzy	PUNCT
ejpam-4768	209	2	math.inform	math.inform	INTJ
ejpam-4768	209	3	.	.	PUNCT
ejpam-4768	209	4	,2019,18,57	,2019,18,57	PUNCT
ejpam-4768	209	5	-	-	PUNCT
ejpam-4768	209	6	74	74	NUM
ejpam-4768	209	7	.	.	PUNCT
ejpam-4768	210	1	[	[	X
ejpam-4768	210	2	5	5	X
ejpam-4768	210	3	]	]	PUNCT
ejpam-4768	210	4	j.	j.	PROPN
ejpam-4768	210	5	g.	g.	PROPN
ejpam-4768	210	6	lee	lee	PROPN
ejpam-4768	210	7	and	and	CCONJ
ejpam-4768	210	8	k.	k.	PROPN
ejpam-4768	210	9	hur	hur	PROPN
ejpam-4768	210	10	,	,	PUNCT
ejpam-4768	210	11	hesitant	hesitant	ADJ
ejpam-4768	210	12	fuzzy	fuzzy	ADJ
ejpam-4768	210	13	topological	topological	ADJ
ejpam-4768	210	14	spaces	space	NOUN
ejpam-4768	210	15	,	,	PUNCT
ejpam-4768	210	16	mathematics,2020,8,188	mathematics,2020,8,188	NOUN
ejpam-4768	210	17	.	.	PUNCT
ejpam-4768	211	1	[	[	X
ejpam-4768	211	2	6	6	NUM
ejpam-4768	211	3	]	]	PUNCT
ejpam-4768	211	4	m.	m.	NOUN
ejpam-4768	211	5	sankari	sankari	PROPN
ejpam-4768	211	6	and	and	CCONJ
ejpam-4768	211	7	c.	c.	PROPN
ejpam-4768	211	8	murugesan	murugesan	PROPN
ejpam-4768	211	9	,	,	PUNCT
ejpam-4768	211	10	hesitant	hesitant	ADJ
ejpam-4768	211	11	fuzzy	fuzzy	ADJ
ejpam-4768	211	12	cut	cut	NOUN
ejpam-4768	211	13	-	-	PUNCT
ejpam-4768	211	14	point	point	NOUN
ejpam-4768	211	15	spaces(submitted	spaces(submitte	VERB
ejpam-4768	211	16	)	)	PUNCT
ejpam-4768	211	17	.	.	PUNCT
ejpam-4768	212	1	[	[	X
ejpam-4768	212	2	7	7	X
ejpam-4768	212	3	]	]	PUNCT
ejpam-4768	212	4	a.	a.	NOUN
ejpam-4768	212	5	swaminathan	swaminathan	NOUN
ejpam-4768	212	6	and	and	CCONJ
ejpam-4768	212	7	s.	s.	PROPN
ejpam-4768	212	8	sivaraja	sivaraja	PROPN
ejpam-4768	212	9	,	,	PUNCT
ejpam-4768	212	10	hesitant	hesitant	ADJ
ejpam-4768	212	11	fuzzy	fuzzy	ADJ
ejpam-4768	212	12	maximal	maximal	ADJ
ejpam-4768	212	13	and	and	CCONJ
ejpam-4768	212	14	minimal	minimal	ADJ
ejpam-4768	212	15	clopen	clopen	ADJ
ejpam-4768	212	16	sets	set	NOUN
ejpam-4768	212	17	,	,	PUNCT
ejpam-4768	212	18	creative	creative	ADJ
ejpam-4768	212	19	mathematics	mathematic	NOUN
ejpam-4768	212	20	and	and	CCONJ
ejpam-4768	212	21	informatics	informatic	NOUN
ejpam-4768	212	22	,	,	PUNCT
ejpam-4768	212	23	vol.31,no.2(2022	vol.31,no.2(2022	NOUN
ejpam-4768	212	24	)	)	PUNCT
ejpam-4768	212	25	.	.	PUNCT
ejpam-4768	213	1	[	[	X
ejpam-4768	213	2	8	8	NUM
ejpam-4768	213	3	]	]	PUNCT
ejpam-4768	213	4	a.	a.	NOUN
ejpam-4768	213	5	swaminathan	swaminathan	NOUN
ejpam-4768	213	6	and	and	CCONJ
ejpam-4768	213	7	s.	s.	PROPN
ejpam-4768	213	8	sivaraja	sivaraja	PROPN
ejpam-4768	213	9	,	,	PUNCT
ejpam-4768	213	10	hesitant	hesitant	ADJ
ejpam-4768	213	11	fuzzy	fuzzy	ADJ
ejpam-4768	213	12	paraopen	paraopen	NOUN
ejpam-4768	213	13	and	and	CCONJ
ejpam-4768	213	14	hesitant	hesitant	ADJ
ejpam-4768	213	15	fuzzy	fuzzy	ADJ
ejpam-4768	213	16	mean	mean	VERB
ejpam-4768	213	17	open	open	ADJ
ejpam-4768	213	18	sets	set	NOUN
ejpam-4768	213	19	,	,	PUNCT
ejpam-4768	213	20	j.	j.	PROPN
ejpam-4768	213	21	appl	appl	PROPN
ejpam-4768	213	22	.	.	PROPN
ejpam-4768	214	1	and	and	CCONJ
ejpam-4768	214	2	pure	pure	ADJ
ejpam-4768	214	3	math	math	NOUN
ejpam-4768	214	4	.	.	PUNCT
ejpam-4768	215	1	,	,	PUNCT
ejpam-4768	215	2	vol	vol	NOUN
ejpam-4768	215	3	.	.	PUNCT
ejpam-4768	216	1	4(2022	4(2022	NOUN
ejpam-4768	216	2	)	)	PUNCT
ejpam-4768	216	3	,	,	PUNCT
ejpam-4768	216	4	no.3	no.3	NOUN
ejpam-4768	216	5	-	-	SYM
ejpam-4768	216	6	4	4	NUM
ejpam-4768	216	7	,	,	PUNCT
ejpam-4768	216	8	pp	pp	ADJ
ejpam-4768	216	9	.	.	PUNCT
ejpam-4768	217	1	141	141	NUM
ejpam-4768	217	2	-	-	SYM
ejpam-4768	217	3	150	150	NUM
ejpam-4768	217	4	.	.	PUNCT
ejpam-4768	217	5	references	reference	NOUN
ejpam-4768	217	6	1388	1388	NUM
ejpam-4768	217	7	[	[	X
ejpam-4768	217	8	9	9	NUM
ejpam-4768	217	9	]	]	PUNCT
ejpam-4768	217	10	a.	a.	NOUN
ejpam-4768	217	11	swaminathan	swaminathan	NOUN
ejpam-4768	217	12	and	and	CCONJ
ejpam-4768	217	13	s.sivaraja	s.sivaraja	NOUN
ejpam-4768	217	14	,	,	PUNCT
ejpam-4768	217	15	hesitant	hesitant	ADJ
ejpam-4768	217	16	fuzzy	fuzzy	ADJ
ejpam-4768	217	17	minimal	minimal	ADJ
ejpam-4768	217	18	and	and	CCONJ
ejpam-4768	217	19	maximal	maximal	ADJ
ejpam-4768	217	20	open	open	ADJ
ejpam-4768	217	21	sets	set	NOUN
ejpam-4768	217	22	,	,	PUNCT
ejpam-4768	217	23	j.	j.	PROPN
ejpam-4768	217	24	appl	appl	PROPN
ejpam-4768	217	25	.	.	PROPN
ejpam-4768	218	1	and	and	CCONJ
ejpam-4768	218	2	pure	pure	ADJ
ejpam-4768	218	3	math	math	NOUN
ejpam-4768	218	4	.	.	PUNCT
ejpam-4768	219	1	,	,	PUNCT
ejpam-4768	219	2	vol	vol	NOUN
ejpam-4768	219	3	.	.	NOUN
ejpam-4768	219	4	5(2023),1	5(2023),1	NOUN
ejpam-4768	219	5	-	-	SYM
ejpam-4768	219	6	2	2	NUM
ejpam-4768	219	7	,	,	PUNCT
ejpam-4768	219	8	121	121	NUM
ejpam-4768	219	9	-	-	SYM
ejpam-4768	219	10	128	128	NUM
ejpam-4768	219	11	..	..	PUNCT
ejpam-4768	220	1	[	[	X
ejpam-4768	220	2	10	10	NUM
ejpam-4768	220	3	]	]	X
ejpam-4768	220	4	v.	v.	CCONJ
ejpam-4768	220	5	torra	torra	ADJ
ejpam-4768	220	6	,	,	PUNCT
ejpam-4768	220	7	hesitant	hesitant	ADJ
ejpam-4768	220	8	fuzzy	fuzzy	ADJ
ejpam-4768	220	9	sets	set	NOUN
ejpam-4768	220	10	.	.	PUNCT
ejpam-4768	221	1	int	int	NOUN
ejpam-4768	221	2	.	.	PUNCT
ejpam-4768	222	1	j.	j.	PROPN
ejpam-4768	222	2	intel	intel	PROPN
ejpam-4768	222	3	.	.	PUNCT
ejpam-4768	223	1	sys	sys	PROPN
ejpam-4768	223	2	.	.	PROPN
ejpam-4768	223	3	,	,	PUNCT
ejpam-4768	223	4	2010,25,529	2010,25,529	NOUN
ejpam-4768	223	5	-	-	SYM
ejpam-4768	223	6	539	539	NUM
ejpam-4768	223	7	.	.	PUNCT
ejpam-4768	224	1	[	[	X
ejpam-4768	224	2	11	11	NUM
ejpam-4768	224	3	]	]	PUNCT
ejpam-4768	224	4	l.	l.	PROPN
ejpam-4768	224	5	a.	a.	PROPN
ejpam-4768	224	6	zadeh	zadeh	PROPN
ejpam-4768	224	7	,	,	PUNCT
ejpam-4768	224	8	fuzzy	fuzzy	ADJ
ejpam-4768	224	9	sets	set	NOUN
ejpam-4768	224	10	,	,	PUNCT
ejpam-4768	224	11	information	information	NOUN
ejpam-4768	224	12	and	and	CCONJ
ejpam-4768	224	13	control,8	control,8	PROPN
ejpam-4768	224	14	(	(	PUNCT
ejpam-4768	224	15	1965	1965	NUM
ejpam-4768	224	16	)	)	PUNCT
ejpam-4768	224	17	,	,	PUNCT
ejpam-4768	224	18	338	338	NUM
ejpam-4768	224	19	-	-	SYM
ejpam-4768	224	20	353	353	NUM
ejpam-4768	224	21	.	.	PUNCT