id	sid	tid	token	lemma	pos
ejpam-5062	1	1	european	european	PROPN
ejpam-5062	1	2	journal	journal	PROPN
ejpam-5062	1	3	of	of	ADP
ejpam-5062	1	4	pure	pure	ADJ
ejpam-5062	1	5	and	and	CCONJ
ejpam-5062	1	6	applied	apply	VERB
ejpam-5062	1	7	mathematics	mathematic	NOUN
ejpam-5062	1	8	vol	vol	NOUN
ejpam-5062	1	9	.	.	PROPN
ejpam-5062	2	1	17	17	NUM
ejpam-5062	2	2	,	,	PUNCT
ejpam-5062	2	3	no	no	INTJ
ejpam-5062	2	4	.	.	NOUN
ejpam-5062	2	5	2	2	NUM
ejpam-5062	2	6	,	,	PUNCT
ejpam-5062	2	7	2024	2024	NUM
ejpam-5062	2	8	,	,	PUNCT
ejpam-5062	2	9	638	638	NUM
ejpam-5062	2	10	-	-	SYM
ejpam-5062	2	11	662	662	NUM
ejpam-5062	2	12	issn	issn	PROPN
ejpam-5062	2	13	1307	1307	NUM
ejpam-5062	2	14	-	-	SYM
ejpam-5062	2	15	5543	5543	NUM
ejpam-5062	2	16	–	–	PUNCT
ejpam-5062	2	17	ejpam.com	ejpam.com	X
ejpam-5062	2	18	published	publish	VERB
ejpam-5062	2	19	by	by	ADP
ejpam-5062	2	20	new	new	PROPN
ejpam-5062	2	21	york	york	PROPN
ejpam-5062	2	22	business	business	PROPN
ejpam-5062	2	23	global	global	ADJ
ejpam-5062	2	24	fuzzy	fuzzy	ADJ
ejpam-5062	2	25	sspo	sspo	NOUN
ejpam-5062	2	26	-	-	PUNCT
ejpam-5062	2	27	separation	separation	NOUN
ejpam-5062	2	28	axioms	axiom	NOUN
ejpam-5062	2	29	and	and	CCONJ
ejpam-5062	2	30	fuzzy	fuzzy	ADJ
ejpam-5062	2	31	α	α	NOUN
ejpam-5062	2	32	-	-	PUNCT
ejpam-5062	2	33	sspo	sspo	NOUN
ejpam-5062	2	34	compactness	compactness	NOUN
ejpam-5062	2	35	shkumbin	shkumbin	PROPN
ejpam-5062	2	36	makolli1,∗	makolli1,∗	NOUN
ejpam-5062	2	37	,	,	PUNCT
ejpam-5062	2	38	biljana	biljana	ADJ
ejpam-5062	2	39	krsteska2	krsteska2	PROPN
ejpam-5062	2	40	1	1	NUM
ejpam-5062	2	41	department	department	NOUN
ejpam-5062	2	42	of	of	ADP
ejpam-5062	2	43	mathematics	mathematic	NOUN
ejpam-5062	2	44	,	,	PUNCT
ejpam-5062	2	45	faculty	faculty	NOUN
ejpam-5062	2	46	of	of	ADP
ejpam-5062	2	47	mathematics	mathematic	NOUN
ejpam-5062	2	48	and	and	CCONJ
ejpam-5062	2	49	natural	natural	ADJ
ejpam-5062	2	50	sciences	science	NOUN
ejpam-5062	2	51	,	,	PUNCT
ejpam-5062	2	52	university	university	PROPN
ejpam-5062	2	53	of	of	ADP
ejpam-5062	2	54	prishtina	prishtina	PROPN
ejpam-5062	2	55	,	,	PUNCT
ejpam-5062	2	56	prishtina	prishtina	PROPN
ejpam-5062	2	57	,	,	PUNCT
ejpam-5062	2	58	republic	republic	NOUN
ejpam-5062	2	59	of	of	ADP
ejpam-5062	2	60	kosovo	kosovo	PROPN
ejpam-5062	2	61	2	2	PROPN
ejpam-5062	2	62	department	department	NOUN
ejpam-5062	2	63	of	of	ADP
ejpam-5062	2	64	mathematics	mathematic	NOUN
ejpam-5062	2	65	,	,	PUNCT
ejpam-5062	2	66	faculty	faculty	NOUN
ejpam-5062	2	67	of	of	ADP
ejpam-5062	2	68	mathematics	mathematic	NOUN
ejpam-5062	2	69	and	and	CCONJ
ejpam-5062	2	70	natural	natural	ADJ
ejpam-5062	2	71	sciences	science	NOUN
ejpam-5062	2	72	,	,	PUNCT
ejpam-5062	2	73	university	university	NOUN
ejpam-5062	2	74	of	of	ADP
ejpam-5062	2	75	saint	saint	PROPN
ejpam-5062	2	76	cyril	cyril	PROPN
ejpam-5062	2	77	and	and	CCONJ
ejpam-5062	2	78	methodius	methodius	PROPN
ejpam-5062	2	79	,	,	PUNCT
ejpam-5062	2	80	skopje	skopje	PROPN
ejpam-5062	2	81	,	,	PUNCT
ejpam-5062	2	82	republic	republic	NOUN
ejpam-5062	2	83	of	of	ADP
ejpam-5062	2	84	north	north	PROPN
ejpam-5062	2	85	macedonia	macedonia	PROPN
ejpam-5062	2	86	abstract	abstract	NOUN
ejpam-5062	2	87	.	.	PUNCT
ejpam-5062	3	1	in	in	ADP
ejpam-5062	3	2	this	this	DET
ejpam-5062	3	3	paper	paper	NOUN
ejpam-5062	3	4	,	,	PUNCT
ejpam-5062	3	5	we	we	PRON
ejpam-5062	3	6	introduce	introduce	VERB
ejpam-5062	3	7	the	the	DET
ejpam-5062	3	8	concept	concept	NOUN
ejpam-5062	3	9	of	of	ADP
ejpam-5062	3	10	new	new	ADJ
ejpam-5062	3	11	separation	separation	NOUN
ejpam-5062	3	12	axioms	axiom	NOUN
ejpam-5062	3	13	named	name	VERB
ejpam-5062	3	14	fuzzy	fuzzy	ADJ
ejpam-5062	3	15	ssposeparation	ssposeparation	NOUN
ejpam-5062	3	16	axioms	axiom	NOUN
ejpam-5062	3	17	by	by	ADP
ejpam-5062	3	18	using	use	VERB
ejpam-5062	3	19	the	the	DET
ejpam-5062	3	20	fuzzy	fuzzy	ADJ
ejpam-5062	3	21	strong	strong	ADJ
ejpam-5062	3	22	semi	semi	ADJ
ejpam-5062	3	23	preo	preo	ADJ
ejpam-5062	3	24	-	-	PUNCT
ejpam-5062	3	25	pen	pen	NOUN
ejpam-5062	3	26	sets	set	NOUN
ejpam-5062	3	27	and	and	CCONJ
ejpam-5062	3	28	we	we	PRON
ejpam-5062	3	29	also	also	ADV
ejpam-5062	3	30	introduce	introduce	VERB
ejpam-5062	3	31	and	and	CCONJ
ejpam-5062	3	32	investigate	investigate	VERB
ejpam-5062	3	33	properties	property	NOUN
ejpam-5062	3	34	of	of	ADP
ejpam-5062	3	35	α	α	NOUN
ejpam-5062	3	36	-	-	PUNCT
ejpam-5062	3	37	sspo	sspo	NOUN
ejpam-5062	3	38	compactness	compactness	NOUN
ejpam-5062	3	39	.	.	PUNCT
ejpam-5062	4	1	we	we	PRON
ejpam-5062	4	2	define	define	VERB
ejpam-5062	4	3	and	and	CCONJ
ejpam-5062	4	4	investigate	investigate	VERB
ejpam-5062	4	5	the	the	DET
ejpam-5062	4	6	relation	relation	NOUN
ejpam-5062	4	7	between	between	ADP
ejpam-5062	4	8	fuzzy	fuzzy	ADJ
ejpam-5062	4	9	separation	separation	NOUN
ejpam-5062	4	10	axioms	axiom	NOUN
ejpam-5062	4	11	,	,	PUNCT
ejpam-5062	4	12	fuzzy	fuzzy	ADJ
ejpam-5062	4	13	pre	pre	ADJ
ejpam-5062	4	14	-	-	NOUN
ejpam-5062	4	15	separation	separation	NOUN
ejpam-5062	4	16	axioms	axiom	NOUN
ejpam-5062	4	17	,	,	PUNCT
ejpam-5062	4	18	and	and	CCONJ
ejpam-5062	4	19	different	different	ADJ
ejpam-5062	4	20	forms	form	NOUN
ejpam-5062	4	21	of	of	ADP
ejpam-5062	4	22	fuzzy	fuzzy	ADJ
ejpam-5062	4	23	continuous	continuous	ADJ
ejpam-5062	4	24	mappings	mapping	NOUN
ejpam-5062	4	25	.	.	PUNCT
ejpam-5062	5	1	we	we	PRON
ejpam-5062	5	2	also	also	ADV
ejpam-5062	5	3	investigate	investigate	VERB
ejpam-5062	5	4	the	the	DET
ejpam-5062	5	5	existence	existence	NOUN
ejpam-5062	5	6	of	of	ADP
ejpam-5062	5	7	a	a	DET
ejpam-5062	5	8	countable	countable	ADJ
ejpam-5062	5	9	base	base	NOUN
ejpam-5062	5	10	of	of	ADP
ejpam-5062	5	11	fuzzy	fuzzy	ADJ
ejpam-5062	5	12	strong	strong	ADJ
ejpam-5062	5	13	semi	semi	ADJ
ejpam-5062	5	14	pre	pre	ADJ
ejpam-5062	5	15	-	-	ADJ
ejpam-5062	5	16	open	open	ADJ
ejpam-5062	5	17	sets	set	NOUN
ejpam-5062	5	18	,	,	PUNCT
ejpam-5062	5	19	we	we	PRON
ejpam-5062	5	20	define	define	VERB
ejpam-5062	5	21	the	the	DET
ejpam-5062	5	22	concept	concept	NOUN
ejpam-5062	5	23	of	of	ADP
ejpam-5062	5	24	sspo	sspo	NOUN
ejpam-5062	5	25	separability	separability	NOUN
ejpam-5062	5	26	,	,	PUNCT
ejpam-5062	5	27	the	the	DET
ejpam-5062	5	28	concept	concept	NOUN
ejpam-5062	5	29	of	of	ADP
ejpam-5062	5	30	α−sspo	α−sspo	X
ejpam-5062	5	31	lindelof	lindelof	PROPN
ejpam-5062	5	32	sets	set	NOUN
ejpam-5062	5	33	and	and	CCONJ
ejpam-5062	5	34	examine	examine	VERB
ejpam-5062	5	35	their	their	PRON
ejpam-5062	5	36	properties	property	NOUN
ejpam-5062	5	37	.	.	PUNCT
ejpam-5062	6	1	with	with	ADP
ejpam-5062	6	2	the	the	DET
ejpam-5062	6	3	concepts	concept	NOUN
ejpam-5062	6	4	of	of	ADP
ejpam-5062	6	5	fuzzy	fuzzy	ADJ
ejpam-5062	6	6	strong	strong	ADJ
ejpam-5062	6	7	semi	semi	ADJ
ejpam-5062	6	8	pre	pre	ADJ
ejpam-5062	6	9	-	-	ADJ
ejpam-5062	6	10	continuity	continuity	ADJ
ejpam-5062	6	11	,	,	PUNCT
ejpam-5062	6	12	sspo	sspo	NOUN
ejpam-5062	6	13	-	-	PUNCT
ejpam-5062	6	14	irresolute	irresolute	ADJ
ejpam-5062	6	15	continuous	continuous	ADJ
ejpam-5062	6	16	mappings	mapping	NOUN
ejpam-5062	6	17	,	,	PUNCT
ejpam-5062	6	18	and	and	CCONJ
ejpam-5062	6	19	other	other	ADJ
ejpam-5062	6	20	forms	form	NOUN
ejpam-5062	6	21	of	of	ADP
ejpam-5062	6	22	fuzzy	fuzzy	ADJ
ejpam-5062	6	23	continuity	continuity	NOUN
ejpam-5062	6	24	,	,	PUNCT
ejpam-5062	6	25	we	we	PRON
ejpam-5062	6	26	investigate	investigate	VERB
ejpam-5062	6	27	the	the	DET
ejpam-5062	6	28	new	new	ADJ
ejpam-5062	6	29	concept	concept	NOUN
ejpam-5062	6	30	of	of	ADP
ejpam-5062	6	31	fuzzy	fuzzy	ADJ
ejpam-5062	6	32	compactness	compactness	NOUN
ejpam-5062	6	33	and	and	CCONJ
ejpam-5062	6	34	its	its	PRON
ejpam-5062	6	35	properties	property	NOUN
ejpam-5062	6	36	in	in	ADP
ejpam-5062	6	37	regard	regard	NOUN
ejpam-5062	6	38	to	to	ADP
ejpam-5062	6	39	the	the	DET
ejpam-5062	6	40	mentioned	mention	VERB
ejpam-5062	6	41	mappings	mapping	NOUN
ejpam-5062	6	42	.	.	PUNCT
ejpam-5062	7	1	2020	2020	NUM
ejpam-5062	7	2	mathematics	mathematic	NOUN
ejpam-5062	7	3	subject	subject	NOUN
ejpam-5062	7	4	classifications	classification	NOUN
ejpam-5062	7	5	:	:	PUNCT
ejpam-5062	7	6	54a40	54a40	NUM
ejpam-5062	7	7	,	,	PUNCT
ejpam-5062	7	8	03e72	03e72	X
ejpam-5062	7	9	key	key	ADJ
ejpam-5062	7	10	words	word	NOUN
ejpam-5062	7	11	and	and	CCONJ
ejpam-5062	7	12	phrases	phrase	NOUN
ejpam-5062	7	13	:	:	PUNCT
ejpam-5062	7	14	fuzzy	fuzzy	ADJ
ejpam-5062	7	15	separation	separation	NOUN
ejpam-5062	7	16	axioms	axiom	NOUN
ejpam-5062	7	17	,	,	PUNCT
ejpam-5062	7	18	fuzzy	fuzzy	ADJ
ejpam-5062	7	19	compactness	compactness	NOUN
ejpam-5062	7	20	,	,	PUNCT
ejpam-5062	7	21	fuzzy	fuzzy	ADJ
ejpam-5062	7	22	topological	topological	ADJ
ejpam-5062	7	23	space	space	NOUN
ejpam-5062	7	24	,	,	PUNCT
ejpam-5062	7	25	fuzzy	fuzzy	ADJ
ejpam-5062	7	26	strongly	strongly	ADV
ejpam-5062	7	27	semi	semi	ADV
ejpam-5062	7	28	pre	pre	ADJ
ejpam-5062	7	29	-	-	ADJ
ejpam-5062	7	30	open	open	ADJ
ejpam-5062	7	31	set	set	NOUN
ejpam-5062	7	32	,	,	PUNCT
ejpam-5062	7	33	fuzzy	fuzzy	ADJ
ejpam-5062	7	34	continuity	continuity	NOUN
ejpam-5062	7	35	,	,	PUNCT
ejpam-5062	7	36	fuzzy	fuzzy	ADJ
ejpam-5062	7	37	sspo	sspo	NOUN
ejpam-5062	7	38	-	-	PUNCT
ejpam-5062	7	39	irresolute	irresolute	ADJ
ejpam-5062	7	40	continuous	continuous	ADJ
ejpam-5062	7	41	mapping	mapping	NOUN
ejpam-5062	7	42	,	,	PUNCT
ejpam-5062	7	43	fuzzy	fuzzy	ADJ
ejpam-5062	7	44	sspo	sspo	NOUN
ejpam-5062	7	45	-	-	PUNCT
ejpam-5062	7	46	irresolute	irresolute	ADJ
ejpam-5062	7	47	open	open	ADJ
ejpam-5062	7	48	(	(	PUNCT
ejpam-5062	7	49	closed	closed	ADJ
ejpam-5062	7	50	)	)	PUNCT
ejpam-5062	7	51	mapping	mapping	NOUN
ejpam-5062	7	52	,	,	PUNCT
ejpam-5062	7	53	fuzzy	fuzzy	ADJ
ejpam-5062	7	54	sspo	sspo	NOUN
ejpam-5062	7	55	homeomorphism	homeomorphism	PROPN
ejpam-5062	7	56	1	1	X
ejpam-5062	7	57	.	.	PUNCT
ejpam-5062	7	58	introduction	introduction	NOUN
ejpam-5062	7	59	separation	separation	NOUN
ejpam-5062	7	60	axioms	axiom	NOUN
ejpam-5062	7	61	were	be	AUX
ejpam-5062	7	62	introduced	introduce	VERB
ejpam-5062	7	63	to	to	ADP
ejpam-5062	7	64	fuzzy	fuzzy	ADJ
ejpam-5062	7	65	topological	topological	ADJ
ejpam-5062	7	66	spaces	space	NOUN
ejpam-5062	7	67	in	in	ADP
ejpam-5062	7	68	[	[	X
ejpam-5062	7	69	9	9	NUM
ejpam-5062	7	70	]	]	PUNCT
ejpam-5062	7	71	,	,	PUNCT
ejpam-5062	7	72	[	[	X
ejpam-5062	7	73	10	10	NUM
ejpam-5062	7	74	]	]	PUNCT
ejpam-5062	7	75	,	,	PUNCT
ejpam-5062	8	1	[	[	X
ejpam-5062	8	2	11],[24],[32	11],[24],[32	X
ejpam-5062	8	3	]	]	PUNCT
ejpam-5062	8	4	,	,	PUNCT
ejpam-5062	8	5	and	and	CCONJ
ejpam-5062	8	6	in	in	ADP
ejpam-5062	8	7	some	some	DET
ejpam-5062	8	8	more	more	ADV
ejpam-5062	8	9	recent	recent	ADJ
ejpam-5062	8	10	works	work	NOUN
ejpam-5062	8	11	[	[	X
ejpam-5062	8	12	25	25	NUM
ejpam-5062	8	13	]	]	PUNCT
ejpam-5062	8	14	,	,	PUNCT
ejpam-5062	9	1	[	[	X
ejpam-5062	9	2	28	28	NUM
ejpam-5062	9	3	]	]	PUNCT
ejpam-5062	9	4	.	.	PUNCT
ejpam-5062	10	1	they	they	PRON
ejpam-5062	10	2	were	be	AUX
ejpam-5062	10	3	extensions	extension	NOUN
ejpam-5062	10	4	of	of	ADP
ejpam-5062	10	5	separation	separation	NOUN
ejpam-5062	10	6	axioms	axiom	NOUN
ejpam-5062	10	7	introduced	introduce	VERB
ejpam-5062	10	8	in	in	ADP
ejpam-5062	10	9	general	general	ADJ
ejpam-5062	10	10	topology	topology	NOUN
ejpam-5062	10	11	.	.	PUNCT
ejpam-5062	11	1	the	the	DET
ejpam-5062	11	2	separation	separation	NOUN
ejpam-5062	11	3	axioms	axiom	NOUN
ejpam-5062	11	4	are	be	AUX
ejpam-5062	11	5	more	more	ADV
ejpam-5062	11	6	restrictive	restrictive	ADJ
ejpam-5062	11	7	in	in	ADP
ejpam-5062	11	8	the	the	DET
ejpam-5062	11	9	fuzzy	fuzzy	ADJ
ejpam-5062	11	10	topologies	topology	NOUN
ejpam-5062	11	11	than	than	ADP
ejpam-5062	11	12	in	in	ADP
ejpam-5062	11	13	the	the	DET
ejpam-5062	11	14	general	general	ADJ
ejpam-5062	11	15	topologies	topology	NOUN
ejpam-5062	11	16	.	.	PUNCT
ejpam-5062	12	1	in	in	ADP
ejpam-5062	12	2	this	this	DET
ejpam-5062	12	3	sense	sense	NOUN
ejpam-5062	12	4	,	,	PUNCT
ejpam-5062	12	5	the	the	DET
ejpam-5062	12	6	separation	separation	NOUN
ejpam-5062	12	7	axioms	axiom	NOUN
ejpam-5062	12	8	are	be	AUX
ejpam-5062	12	9	modified	modify	VERB
ejpam-5062	12	10	,	,	PUNCT
ejpam-5062	12	11	and	and	CCONJ
ejpam-5062	12	12	in	in	ADP
ejpam-5062	12	13	many	many	ADJ
ejpam-5062	12	14	cases	case	NOUN
ejpam-5062	12	15	weaker	weak	ADJ
ejpam-5062	12	16	conditions	condition	NOUN
ejpam-5062	12	17	have	have	AUX
ejpam-5062	12	18	been	be	AUX
ejpam-5062	12	19	adapted	adapt	VERB
ejpam-5062	12	20	for	for	ADP
ejpam-5062	12	21	fuzzy	fuzzy	ADJ
ejpam-5062	12	22	topological	topological	ADJ
ejpam-5062	12	23	spaces	space	NOUN
ejpam-5062	12	24	.	.	PUNCT
ejpam-5062	13	1	with	with	ADP
ejpam-5062	13	2	the	the	DET
ejpam-5062	13	3	introduction	introduction	NOUN
ejpam-5062	13	4	of	of	ADP
ejpam-5062	13	5	fuzzy	fuzzy	ADJ
ejpam-5062	13	6	strongly	strongly	ADV
ejpam-5062	13	7	semi	semi	ADV
ejpam-5062	13	8	pre	pre	ADJ
ejpam-5062	13	9	-	-	ADJ
ejpam-5062	13	10	open	open	ADJ
ejpam-5062	13	11	(	(	PUNCT
ejpam-5062	13	12	short	short	ADJ
ejpam-5062	13	13	sspo	sspo	NOUN
ejpam-5062	13	14	)	)	PUNCT
ejpam-5062	13	15	sets	set	NOUN
ejpam-5062	13	16	,	,	PUNCT
ejpam-5062	13	17	we	we	PRON
ejpam-5062	13	18	introduce	introduce	VERB
ejpam-5062	13	19	the	the	DET
ejpam-5062	13	20	new	new	ADJ
ejpam-5062	13	21	separation	separation	NOUN
ejpam-5062	13	22	axioms	axiom	NOUN
ejpam-5062	13	23	and	and	CCONJ
ejpam-5062	13	24	investigate	investigate	VERB
ejpam-5062	13	25	their	their	PRON
ejpam-5062	13	26	relation	relation	NOUN
ejpam-5062	13	27	with	with	ADP
ejpam-5062	13	28	other	other	ADJ
ejpam-5062	13	29	forms	form	NOUN
ejpam-5062	13	30	of	of	ADP
ejpam-5062	13	31	fuzzy	fuzzy	ADJ
ejpam-5062	13	32	separation	separation	NOUN
ejpam-5062	13	33	axioms	axiom	NOUN
ejpam-5062	13	34	.	.	PUNCT
ejpam-5062	14	1	by	by	ADP
ejpam-5062	14	2	giving	give	VERB
ejpam-5062	14	3	several	several	ADJ
ejpam-5062	14	4	examples	example	NOUN
ejpam-5062	14	5	we	we	PRON
ejpam-5062	14	6	will	will	AUX
ejpam-5062	14	7	be	be	AUX
ejpam-5062	14	8	able	able	ADJ
ejpam-5062	14	9	to	to	PART
ejpam-5062	14	10	show	show	VERB
ejpam-5062	14	11	that	that	SCONJ
ejpam-5062	14	12	the	the	DET
ejpam-5062	14	13	newly	newly	ADV
ejpam-5062	14	14	introduced	introduce	VERB
ejpam-5062	14	15	∗corresponding	∗corresponde	VERB
ejpam-5062	14	16	author	author	NOUN
ejpam-5062	14	17	.	.	PUNCT
ejpam-5062	15	1	doi	doi	NOUN
ejpam-5062	15	2	:	:	PUNCT
ejpam-5062	15	3	https://doi.org/10.29020/nybg.ejpam.v17i2.5062	https://doi.org/10.29020/nybg.ejpam.v17i2.5062	X
ejpam-5062	15	4	email	email	NOUN
ejpam-5062	15	5	addresses	address	NOUN
ejpam-5062	15	6	:	:	PUNCT
ejpam-5062	15	7	shkumbin.makolli@uni-pr.edu	shkumbin.makolli@uni-pr.edu	PROPN
ejpam-5062	15	8	(	(	PUNCT
ejpam-5062	15	9	sh	sh	PROPN
ejpam-5062	15	10	.	.	PROPN
ejpam-5062	15	11	makolli	makolli	PROPN
ejpam-5062	15	12	)	)	PUNCT
ejpam-5062	15	13	,	,	PUNCT
ejpam-5062	15	14	madob2006@gmail.com	madob2006@gmail.com	X
ejpam-5062	16	1	(	(	PUNCT
ejpam-5062	16	2	b.	b.	PROPN
ejpam-5062	16	3	krsteska	krsteska	PROPN
ejpam-5062	16	4	)	)	PUNCT
ejpam-5062	16	5	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5062	17	1	638	638	NUM
ejpam-5062	17	2	©	©	ADP
ejpam-5062	17	3	2024	2024	NUM
ejpam-5062	17	4	ejpam	ejpam	NOUN
ejpam-5062	17	5	all	all	DET
ejpam-5062	17	6	rights	right	NOUN
ejpam-5062	17	7	reserved	reserve	VERB
ejpam-5062	17	8	.	.	PUNCT
ejpam-5062	18	1	sh	sh	PROPN
ejpam-5062	18	2	.	.	PROPN
ejpam-5062	18	3	makolli	makolli	PROPN
ejpam-5062	18	4	,	,	PUNCT
ejpam-5062	18	5	b.	b.	PROPN
ejpam-5062	18	6	krsteska	krsteska	PROPN
ejpam-5062	18	7	/	/	SYM
ejpam-5062	18	8	eur	eur	PROPN
ejpam-5062	18	9	.	.	PUNCT
ejpam-5062	19	1	j.	j.	PROPN
ejpam-5062	19	2	pure	pure	PROPN
ejpam-5062	19	3	appl	appl	PROPN
ejpam-5062	19	4	.	.	PROPN
ejpam-5062	19	5	math	math	PROPN
ejpam-5062	19	6	,	,	PUNCT
ejpam-5062	19	7	17	17	NUM
ejpam-5062	19	8	(	(	PUNCT
ejpam-5062	19	9	2	2	NUM
ejpam-5062	19	10	)	)	PUNCT
ejpam-5062	19	11	(	(	PUNCT
ejpam-5062	19	12	2024	2024	NUM
ejpam-5062	19	13	)	)	PUNCT
ejpam-5062	19	14	,	,	PUNCT
ejpam-5062	19	15	638	638	NUM
ejpam-5062	19	16	-	-	SYM
ejpam-5062	19	17	662	662	NUM
ejpam-5062	19	18	639	639	NUM
ejpam-5062	19	19	axioms	axiom	NOUN
ejpam-5062	19	20	are	be	AUX
ejpam-5062	19	21	different	different	ADJ
ejpam-5062	19	22	from	from	ADP
ejpam-5062	19	23	the	the	DET
ejpam-5062	19	24	other	other	ADJ
ejpam-5062	19	25	fuzzy	fuzzy	ADJ
ejpam-5062	19	26	separation	separation	NOUN
ejpam-5062	19	27	axioms	axiom	NOUN
ejpam-5062	19	28	introduced	introduce	VERB
ejpam-5062	19	29	by	by	ADP
ejpam-5062	19	30	other	other	ADJ
ejpam-5062	19	31	authors	author	NOUN
ejpam-5062	19	32	in	in	ADP
ejpam-5062	19	33	[	[	X
ejpam-5062	19	34	32	32	NUM
ejpam-5062	19	35	]	]	PUNCT
ejpam-5062	19	36	,	,	PUNCT
ejpam-5062	19	37	[	[	X
ejpam-5062	19	38	27	27	NUM
ejpam-5062	19	39	]	]	PUNCT
ejpam-5062	19	40	,	,	PUNCT
ejpam-5062	19	41	and	and	CCONJ
ejpam-5062	19	42	[	[	X
ejpam-5062	19	43	6	6	NUM
ejpam-5062	19	44	]	]	PUNCT
ejpam-5062	19	45	.	.	PUNCT
ejpam-5062	20	1	compactness	compactness	NOUN
ejpam-5062	20	2	is	be	AUX
ejpam-5062	20	3	another	another	DET
ejpam-5062	20	4	concept	concept	NOUN
ejpam-5062	20	5	that	that	PRON
ejpam-5062	20	6	was	be	AUX
ejpam-5062	20	7	also	also	ADV
ejpam-5062	20	8	introduced	introduce	VERB
ejpam-5062	20	9	to	to	ADP
ejpam-5062	20	10	fuzzy	fuzzy	ADJ
ejpam-5062	20	11	topological	topological	ADJ
ejpam-5062	20	12	spaces	space	NOUN
ejpam-5062	20	13	.	.	PUNCT
ejpam-5062	21	1	the	the	DET
ejpam-5062	21	2	first	first	ADJ
ejpam-5062	21	3	ideas	idea	NOUN
ejpam-5062	21	4	of	of	ADP
ejpam-5062	21	5	compactness	compactness	NOUN
ejpam-5062	21	6	in	in	ADP
ejpam-5062	21	7	fuzzy	fuzzy	ADJ
ejpam-5062	21	8	topological	topological	ADJ
ejpam-5062	21	9	spaces	space	NOUN
ejpam-5062	21	10	were	be	AUX
ejpam-5062	21	11	introduced	introduce	VERB
ejpam-5062	21	12	by	by	ADP
ejpam-5062	21	13	chang	chang	PROPN
ejpam-5062	21	14	in	in	ADP
ejpam-5062	21	15	[	[	X
ejpam-5062	21	16	4	4	NUM
ejpam-5062	21	17	]	]	PUNCT
ejpam-5062	21	18	.	.	PUNCT
ejpam-5062	22	1	some	some	DET
ejpam-5062	22	2	other	other	ADJ
ejpam-5062	22	3	results	result	NOUN
ejpam-5062	22	4	regarding	regard	VERB
ejpam-5062	22	5	compact	compact	ADJ
ejpam-5062	22	6	fuzzy	fuzzy	ADJ
ejpam-5062	22	7	spaces	space	NOUN
ejpam-5062	22	8	were	be	AUX
ejpam-5062	22	9	introduced	introduce	VERB
ejpam-5062	22	10	by	by	ADP
ejpam-5062	22	11	goguen	goguen	PROPN
ejpam-5062	22	12	[	[	X
ejpam-5062	22	13	7	7	NUM
ejpam-5062	22	14	]	]	PUNCT
ejpam-5062	22	15	.	.	PUNCT
ejpam-5062	23	1	other	other	ADJ
ejpam-5062	23	2	authors	author	NOUN
ejpam-5062	23	3	that	that	PRON
ejpam-5062	23	4	have	have	AUX
ejpam-5062	23	5	treated	treat	VERB
ejpam-5062	23	6	compactness	compactness	NOUN
ejpam-5062	23	7	in	in	ADP
ejpam-5062	23	8	fuzzy	fuzzy	ADJ
ejpam-5062	23	9	topological	topological	ADJ
ejpam-5062	23	10	spaces	space	NOUN
ejpam-5062	23	11	are	be	AUX
ejpam-5062	23	12	lowen	lowen	PROPN
ejpam-5062	23	13	in	in	ADP
ejpam-5062	23	14	[	[	X
ejpam-5062	23	15	15	15	NUM
ejpam-5062	23	16	]	]	PUNCT
ejpam-5062	23	17	and	and	CCONJ
ejpam-5062	23	18	[	[	X
ejpam-5062	23	19	16	16	NUM
ejpam-5062	23	20	]	]	PUNCT
ejpam-5062	23	21	,	,	PUNCT
ejpam-5062	23	22	wong	wong	PROPN
ejpam-5062	24	1	[	[	X
ejpam-5062	24	2	31	31	NUM
ejpam-5062	24	3	]	]	PUNCT
ejpam-5062	24	4	,	,	PUNCT
ejpam-5062	24	5	t.e	t.e	PROPN
ejpam-5062	24	6	.	.	PROPN
ejpam-5062	24	7	gantner	gantner	PROPN
ejpam-5062	24	8	et	et	PROPN
ejpam-5062	24	9	al	al	PROPN
ejpam-5062	25	1	[	[	X
ejpam-5062	25	2	5	5	NUM
ejpam-5062	25	3	]	]	PUNCT
ejpam-5062	25	4	,	,	PUNCT
ejpam-5062	25	5	and	and	CCONJ
ejpam-5062	25	6	more	more	ADV
ejpam-5062	25	7	recently	recently	ADV
ejpam-5062	25	8	saleh	saleh	PROPN
ejpam-5062	25	9	s.	s.	PROPN
ejpam-5062	25	10	et	et	PROPN
ejpam-5062	25	11	al	al	PROPN
ejpam-5062	25	12	in	in	ADP
ejpam-5062	25	13	[	[	X
ejpam-5062	25	14	26	26	NUM
ejpam-5062	25	15	]	]	PUNCT
ejpam-5062	25	16	.	.	PUNCT
ejpam-5062	26	1	the	the	DET
ejpam-5062	26	2	concept	concept	NOUN
ejpam-5062	26	3	of	of	ADP
ejpam-5062	26	4	α	α	NOUN
ejpam-5062	26	5	-	-	PUNCT
ejpam-5062	26	6	compactness	compactness	NOUN
ejpam-5062	26	7	was	be	AUX
ejpam-5062	26	8	introduced	introduce	VERB
ejpam-5062	26	9	by	by	ADP
ejpam-5062	26	10	t.e	t.e	PROPN
ejpam-5062	26	11	.	.	PROPN
ejpam-5062	26	12	gantner	gantner	PROPN
ejpam-5062	26	13	et	et	PROPN
ejpam-5062	26	14	al	al	PROPN
ejpam-5062	26	15	in	in	ADP
ejpam-5062	26	16	[	[	X
ejpam-5062	26	17	5	5	NUM
ejpam-5062	26	18	]	]	PUNCT
ejpam-5062	26	19	and	and	CCONJ
ejpam-5062	26	20	it	it	PRON
ejpam-5062	26	21	is	be	AUX
ejpam-5062	26	22	among	among	ADP
ejpam-5062	26	23	the	the	DET
ejpam-5062	26	24	most	most	ADV
ejpam-5062	26	25	acceptable	acceptable	ADJ
ejpam-5062	26	26	concepts	concept	NOUN
ejpam-5062	26	27	of	of	ADP
ejpam-5062	26	28	compactness	compactness	NOUN
ejpam-5062	26	29	in	in	ADP
ejpam-5062	26	30	fuzzy	fuzzy	ADJ
ejpam-5062	26	31	topological	topological	ADJ
ejpam-5062	26	32	spaces	space	NOUN
ejpam-5062	26	33	.	.	PUNCT
ejpam-5062	27	1	with	with	ADP
ejpam-5062	27	2	the	the	DET
ejpam-5062	27	3	definition	definition	NOUN
ejpam-5062	27	4	of	of	ADP
ejpam-5062	27	5	other	other	ADJ
ejpam-5062	27	6	forms	form	NOUN
ejpam-5062	27	7	of	of	ADP
ejpam-5062	27	8	generalized	generalized	ADJ
ejpam-5062	27	9	fuzzy	fuzzy	ADJ
ejpam-5062	27	10	open	open	ADJ
ejpam-5062	27	11	sets	set	NOUN
ejpam-5062	27	12	,	,	PUNCT
ejpam-5062	27	13	different	different	ADJ
ejpam-5062	27	14	authors	author	NOUN
ejpam-5062	27	15	,	,	PUNCT
ejpam-5062	27	16	[	[	X
ejpam-5062	27	17	13	13	NUM
ejpam-5062	27	18	]	]	PUNCT
ejpam-5062	27	19	,	,	PUNCT
ejpam-5062	27	20	[	[	X
ejpam-5062	27	21	29	29	NUM
ejpam-5062	27	22	]	]	PUNCT
ejpam-5062	27	23	,	,	PUNCT
ejpam-5062	27	24	[	[	X
ejpam-5062	27	25	8	8	NUM
ejpam-5062	27	26	]	]	PUNCT
ejpam-5062	27	27	,	,	PUNCT
ejpam-5062	27	28	have	have	AUX
ejpam-5062	27	29	defined	define	VERB
ejpam-5062	27	30	generalization	generalization	NOUN
ejpam-5062	27	31	of	of	ADP
ejpam-5062	27	32	the	the	DET
ejpam-5062	27	33	concept	concept	NOUN
ejpam-5062	27	34	of	of	ADP
ejpam-5062	27	35	fuzzy	fuzzy	ADJ
ejpam-5062	27	36	compactness	compactness	NOUN
ejpam-5062	27	37	.	.	PUNCT
ejpam-5062	28	1	in	in	ADP
ejpam-5062	28	2	our	our	PRON
ejpam-5062	28	3	work	work	NOUN
ejpam-5062	28	4	,	,	PUNCT
ejpam-5062	28	5	we	we	PRON
ejpam-5062	28	6	use	use	VERB
ejpam-5062	28	7	the	the	DET
ejpam-5062	28	8	same	same	ADJ
ejpam-5062	28	9	approach	approach	NOUN
ejpam-5062	28	10	as	as	ADP
ejpam-5062	28	11	gantner	gantner	NOUN
ejpam-5062	28	12	et	et	PROPN
ejpam-5062	28	13	al	al	PROPN
ejpam-5062	28	14	in	in	ADP
ejpam-5062	28	15	[	[	X
ejpam-5062	28	16	5	5	NUM
ejpam-5062	28	17	]	]	PUNCT
ejpam-5062	28	18	.	.	PUNCT
ejpam-5062	29	1	similarly	similarly	ADV
ejpam-5062	29	2	,	,	PUNCT
ejpam-5062	29	3	we	we	PRON
ejpam-5062	29	4	will	will	AUX
ejpam-5062	29	5	define	define	VERB
ejpam-5062	29	6	the	the	DET
ejpam-5062	29	7	concept	concept	NOUN
ejpam-5062	29	8	of	of	ADP
ejpam-5062	29	9	α	α	NOUN
ejpam-5062	29	10	-	-	PUNCT
ejpam-5062	29	11	sspo	sspo	NOUN
ejpam-5062	29	12	shading	shading	NOUN
ejpam-5062	29	13	and	and	CCONJ
ejpam-5062	29	14	α∗-sspo	α∗-sspo	ADV
ejpam-5062	29	15	shading	shading	NOUN
ejpam-5062	29	16	that	that	PRON
ejpam-5062	29	17	are	be	AUX
ejpam-5062	29	18	collections	collection	NOUN
ejpam-5062	29	19	of	of	ADP
ejpam-5062	29	20	fuzzy	fuzzy	ADJ
ejpam-5062	29	21	sets	set	NOUN
ejpam-5062	29	22	that	that	PRON
ejpam-5062	29	23	constitute	constitute	VERB
ejpam-5062	29	24	only	only	ADV
ejpam-5062	29	25	from	from	ADP
ejpam-5062	29	26	fuzzy	fuzzy	ADJ
ejpam-5062	29	27	strong	strong	ADJ
ejpam-5062	29	28	semi	semi	ADJ
ejpam-5062	29	29	pre	pre	ADJ
ejpam-5062	29	30	-	-	ADJ
ejpam-5062	29	31	open	open	ADJ
ejpam-5062	29	32	sets	set	NOUN
ejpam-5062	29	33	.	.	PUNCT
ejpam-5062	30	1	following	follow	VERB
ejpam-5062	30	2	the	the	DET
ejpam-5062	30	3	introduction	introduction	NOUN
ejpam-5062	30	4	of	of	ADP
ejpam-5062	30	5	α	α	NOUN
ejpam-5062	30	6	-	-	PUNCT
ejpam-5062	30	7	sspo	sspo	NOUN
ejpam-5062	30	8	shading	shade	VERB
ejpam-5062	30	9	(	(	PUNCT
ejpam-5062	30	10	α∗-sspo	α∗-sspo	NOUN
ejpam-5062	30	11	shading	shading	NOUN
ejpam-5062	30	12	)	)	PUNCT
ejpam-5062	30	13	we	we	PRON
ejpam-5062	30	14	introduce	introduce	VERB
ejpam-5062	30	15	the	the	DET
ejpam-5062	30	16	concepts	concept	NOUN
ejpam-5062	30	17	of	of	ADP
ejpam-5062	30	18	α	α	PROPN
ejpam-5062	30	19	-	-	PUNCT
ejpam-5062	30	20	sspo	sspo	NOUN
ejpam-5062	30	21	compact	compact	ADJ
ejpam-5062	30	22	(	(	PUNCT
ejpam-5062	30	23	α∗-sspo	α∗-sspo	ADP
ejpam-5062	30	24	compact	compact	ADJ
ejpam-5062	30	25	)	)	PUNCT
ejpam-5062	30	26	fuzzy	fuzzy	ADJ
ejpam-5062	30	27	sets	set	NOUN
ejpam-5062	30	28	and	and	CCONJ
ejpam-5062	30	29	fuzzy	fuzzy	ADJ
ejpam-5062	30	30	spaces	space	NOUN
ejpam-5062	30	31	.	.	PUNCT
ejpam-5062	31	1	the	the	DET
ejpam-5062	31	2	new	new	ADJ
ejpam-5062	31	3	concept	concept	NOUN
ejpam-5062	31	4	is	be	AUX
ejpam-5062	31	5	stronger	strong	ADJ
ejpam-5062	31	6	then	then	ADV
ejpam-5062	31	7	the	the	DET
ejpam-5062	31	8	concept	concept	NOUN
ejpam-5062	31	9	of	of	ADP
ejpam-5062	31	10	α	α	NOUN
ejpam-5062	31	11	-	-	PUNCT
ejpam-5062	31	12	compactness	compactness	NOUN
ejpam-5062	31	13	(	(	PUNCT
ejpam-5062	31	14	α∗compactness	α∗compactness	NOUN
ejpam-5062	31	15	)	)	PUNCT
ejpam-5062	31	16	.	.	PUNCT
ejpam-5062	32	1	we	we	PRON
ejpam-5062	32	2	also	also	ADV
ejpam-5062	32	3	investigate	investigate	VERB
ejpam-5062	32	4	the	the	DET
ejpam-5062	32	5	existence	existence	NOUN
ejpam-5062	32	6	of	of	ADP
ejpam-5062	32	7	a	a	DET
ejpam-5062	32	8	countable	countable	ADJ
ejpam-5062	32	9	base	base	NOUN
ejpam-5062	32	10	of	of	ADP
ejpam-5062	32	11	fuzzy	fuzzy	ADJ
ejpam-5062	32	12	strong	strong	ADJ
ejpam-5062	32	13	semi	semi	ADJ
ejpam-5062	32	14	pre	pre	ADJ
ejpam-5062	32	15	-	-	ADJ
ejpam-5062	32	16	open	open	ADJ
ejpam-5062	32	17	sets	set	NOUN
ejpam-5062	32	18	,	,	PUNCT
ejpam-5062	32	19	sspo	sspo	VERB
ejpam-5062	32	20	separability	separability	NOUN
ejpam-5062	32	21	and	and	CCONJ
ejpam-5062	32	22	define	define	VERB
ejpam-5062	32	23	the	the	DET
ejpam-5062	32	24	concept	concept	NOUN
ejpam-5062	32	25	of	of	ADP
ejpam-5062	32	26	α	α	NOUN
ejpam-5062	32	27	-	-	PUNCT
ejpam-5062	32	28	sspo	sspo	NOUN
ejpam-5062	32	29	lindelof	lindelof	NOUN
ejpam-5062	32	30	sets	set	NOUN
ejpam-5062	32	31	and	and	CCONJ
ejpam-5062	32	32	fuzzy	fuzzy	ADJ
ejpam-5062	32	33	topological	topological	ADJ
ejpam-5062	32	34	spaces	space	NOUN
ejpam-5062	32	35	as	as	ADV
ejpam-5062	32	36	well	well	ADV
ejpam-5062	32	37	as	as	ADP
ejpam-5062	32	38	examine	examine	VERB
ejpam-5062	32	39	their	their	PRON
ejpam-5062	32	40	properties	property	NOUN
ejpam-5062	32	41	.	.	PUNCT
ejpam-5062	33	1	with	with	ADP
ejpam-5062	33	2	the	the	DET
ejpam-5062	33	3	definition	definition	NOUN
ejpam-5062	33	4	of	of	ADP
ejpam-5062	33	5	fuzzy	fuzzy	ADJ
ejpam-5062	33	6	strong	strong	ADJ
ejpam-5062	33	7	semi	semi	ADJ
ejpam-5062	33	8	pre	pre	ADJ
ejpam-5062	33	9	-	-	ADJ
ejpam-5062	33	10	continuity	continuity	ADJ
ejpam-5062	33	11	and	and	CCONJ
ejpam-5062	33	12	sspo	sspo	NOUN
ejpam-5062	33	13	-	-	PUNCT
ejpam-5062	33	14	irresolute	irresolute	NOUN
ejpam-5062	33	15	mappings	mapping	NOUN
ejpam-5062	33	16	,	,	PUNCT
ejpam-5062	33	17	we	we	PRON
ejpam-5062	33	18	investigate	investigate	VERB
ejpam-5062	33	19	the	the	DET
ejpam-5062	33	20	new	new	ADJ
ejpam-5062	33	21	concept	concept	NOUN
ejpam-5062	33	22	of	of	ADP
ejpam-5062	33	23	fuzzy	fuzzy	ADJ
ejpam-5062	33	24	compactness	compactness	NOUN
ejpam-5062	33	25	and	and	CCONJ
ejpam-5062	33	26	its	its	PRON
ejpam-5062	33	27	properties	property	NOUN
ejpam-5062	33	28	in	in	ADP
ejpam-5062	33	29	relation	relation	NOUN
ejpam-5062	33	30	to	to	ADP
ejpam-5062	33	31	the	the	DET
ejpam-5062	33	32	mentioned	mention	VERB
ejpam-5062	33	33	mappings	mapping	NOUN
ejpam-5062	33	34	.	.	PUNCT
ejpam-5062	34	1	since	since	SCONJ
ejpam-5062	34	2	separation	separation	NOUN
ejpam-5062	34	3	axioms	axiom	NOUN
ejpam-5062	34	4	and	and	CCONJ
ejpam-5062	34	5	compactness	compactness	NOUN
ejpam-5062	34	6	are	be	AUX
ejpam-5062	34	7	among	among	ADP
ejpam-5062	34	8	the	the	DET
ejpam-5062	34	9	fundamental	fundamental	ADJ
ejpam-5062	34	10	principles	principle	NOUN
ejpam-5062	34	11	in	in	ADP
ejpam-5062	34	12	the	the	DET
ejpam-5062	34	13	field	field	NOUN
ejpam-5062	34	14	of	of	ADP
ejpam-5062	34	15	fuzzy	fuzzy	ADJ
ejpam-5062	34	16	topology	topology	NOUN
ejpam-5062	34	17	,	,	PUNCT
ejpam-5062	34	18	the	the	DET
ejpam-5062	34	19	aim	aim	NOUN
ejpam-5062	34	20	of	of	ADP
ejpam-5062	34	21	this	this	DET
ejpam-5062	34	22	research	research	NOUN
ejpam-5062	34	23	paper	paper	NOUN
ejpam-5062	34	24	is	be	AUX
ejpam-5062	34	25	to	to	PART
ejpam-5062	34	26	propose	propose	VERB
ejpam-5062	34	27	some	some	DET
ejpam-5062	34	28	novel	novel	ADJ
ejpam-5062	34	29	approaches	approach	NOUN
ejpam-5062	34	30	to	to	ADP
ejpam-5062	34	31	some	some	DET
ejpam-5062	34	32	theoretical	theoretical	ADJ
ejpam-5062	34	33	problems	problem	NOUN
ejpam-5062	34	34	in	in	ADP
ejpam-5062	34	35	light	light	NOUN
ejpam-5062	34	36	of	of	ADP
ejpam-5062	34	37	new	new	ADJ
ejpam-5062	34	38	generalized	generalized	ADJ
ejpam-5062	34	39	fuzzy	fuzzy	ADJ
ejpam-5062	34	40	opened	open	VERB
ejpam-5062	34	41	sets	set	NOUN
ejpam-5062	34	42	.	.	PUNCT
ejpam-5062	35	1	2	2	X
ejpam-5062	35	2	.	.	X
ejpam-5062	35	3	preliminaries	preliminary	NOUN
ejpam-5062	35	4	the	the	DET
ejpam-5062	35	5	concept	concept	NOUN
ejpam-5062	35	6	of	of	ADP
ejpam-5062	35	7	fuzzy	fuzzy	ADJ
ejpam-5062	35	8	set	set	NOUN
ejpam-5062	35	9	was	be	AUX
ejpam-5062	35	10	initially	initially	ADV
ejpam-5062	35	11	formulated	formulate	VERB
ejpam-5062	35	12	by	by	ADP
ejpam-5062	35	13	zadeh	zadeh	PROPN
ejpam-5062	35	14	in	in	ADP
ejpam-5062	35	15	[	[	X
ejpam-5062	35	16	33	33	NUM
ejpam-5062	35	17	]	]	PUNCT
ejpam-5062	35	18	.	.	PUNCT
ejpam-5062	36	1	chang	chang	PROPN
ejpam-5062	36	2	in	in	ADP
ejpam-5062	36	3	[	[	X
ejpam-5062	36	4	4	4	NUM
ejpam-5062	36	5	]	]	PUNCT
ejpam-5062	36	6	introduced	introduce	VERB
ejpam-5062	36	7	the	the	DET
ejpam-5062	36	8	concept	concept	NOUN
ejpam-5062	36	9	of	of	ADP
ejpam-5062	36	10	fuzzy	fuzzy	ADJ
ejpam-5062	36	11	topological	topological	ADJ
ejpam-5062	36	12	spaces	space	NOUN
ejpam-5062	36	13	(	(	PUNCT
ejpam-5062	36	14	short	short	ADJ
ejpam-5062	36	15	fts	fts	X
ejpam-5062	36	16	)	)	PUNCT
ejpam-5062	36	17	.	.	PUNCT
ejpam-5062	37	1	definition	definition	NOUN
ejpam-5062	37	2	1	1	NUM
ejpam-5062	37	3	.	.	PUNCT
ejpam-5062	38	1	[	[	X
ejpam-5062	38	2	33	33	NUM
ejpam-5062	38	3	]	]	PUNCT
ejpam-5062	38	4	let	let	VERB
ejpam-5062	38	5	x	x	PRON
ejpam-5062	38	6	be	be	AUX
ejpam-5062	38	7	a	a	DET
ejpam-5062	38	8	space	space	NOUN
ejpam-5062	38	9	of	of	ADP
ejpam-5062	38	10	points	point	NOUN
ejpam-5062	38	11	(	(	PUNCT
ejpam-5062	38	12	objects	object	NOUN
ejpam-5062	38	13	)	)	PUNCT
ejpam-5062	38	14	.	.	PUNCT
ejpam-5062	39	1	a	a	DET
ejpam-5062	39	2	fuzzy	fuzzy	ADJ
ejpam-5062	39	3	set	set	NOUN
ejpam-5062	39	4	(	(	PUNCT
ejpam-5062	39	5	class	class	NOUN
ejpam-5062	39	6	)	)	PUNCT
ejpam-5062	39	7	a	a	PRON
ejpam-5062	39	8	in	in	NOUN
ejpam-5062	39	9	x	x	SYM
ejpam-5062	39	10	is	be	AUX
ejpam-5062	39	11	characterized	characterize	VERB
ejpam-5062	39	12	by	by	ADP
ejpam-5062	39	13	a	a	DET
ejpam-5062	39	14	membership	membership	NOUN
ejpam-5062	39	15	(	(	PUNCT
ejpam-5062	39	16	characteristic	characteristic	ADJ
ejpam-5062	39	17	)	)	PUNCT
ejpam-5062	39	18	function	function	NOUN
ejpam-5062	39	19	a(x	a(x	NOUN
ejpam-5062	39	20	)	)	PUNCT
ejpam-5062	39	21	which	which	PRON
ejpam-5062	39	22	associates	associate	VERB
ejpam-5062	39	23	with	with	ADP
ejpam-5062	39	24	each	each	DET
ejpam-5062	39	25	point	point	NOUN
ejpam-5062	39	26	in	in	ADP
ejpam-5062	39	27	x	x	PUNCT
ejpam-5062	39	28	a	a	DET
ejpam-5062	39	29	real	real	ADJ
ejpam-5062	39	30	number	number	NOUN
ejpam-5062	39	31	in	in	ADP
ejpam-5062	39	32	the	the	DET
ejpam-5062	39	33	interval	interval	NOUN
ejpam-5062	39	34	[	[	X
ejpam-5062	39	35	0	0	NUM
ejpam-5062	39	36	,	,	PUNCT
ejpam-5062	39	37	1	1	NUM
ejpam-5062	39	38	]	]	PUNCT
ejpam-5062	39	39	,	,	PUNCT
ejpam-5062	39	40	with	with	ADP
ejpam-5062	39	41	the	the	DET
ejpam-5062	39	42	value	value	NOUN
ejpam-5062	39	43	of	of	ADP
ejpam-5062	39	44	a(x	a(x	NOUN
ejpam-5062	39	45	)	)	PUNCT
ejpam-5062	39	46	representing	represent	VERB
ejpam-5062	39	47	the	the	DET
ejpam-5062	39	48	”	"	PUNCT
ejpam-5062	39	49	grade	grade	NOUN
ejpam-5062	39	50	of	of	ADP
ejpam-5062	39	51	membership	membership	NOUN
ejpam-5062	39	52	”	"	PUNCT
ejpam-5062	39	53	of	of	ADP
ejpam-5062	39	54	x	x	PUNCT
ejpam-5062	39	55	in	in	ADP
ejpam-5062	39	56	a.	a.	NOUN
ejpam-5062	39	57	in	in	ADP
ejpam-5062	39	58	other	other	ADJ
ejpam-5062	39	59	words	word	NOUN
ejpam-5062	39	60	,	,	PUNCT
ejpam-5062	39	61	the	the	DET
ejpam-5062	39	62	nearer	near	ADJ
ejpam-5062	39	63	the	the	DET
ejpam-5062	39	64	value	value	NOUN
ejpam-5062	39	65	of	of	ADP
ejpam-5062	39	66	a(x	a(x	NOUN
ejpam-5062	39	67	)	)	PUNCT
ejpam-5062	39	68	to	to	ADP
ejpam-5062	39	69	1	1	NUM
ejpam-5062	39	70	,	,	PUNCT
ejpam-5062	39	71	the	the	PRON
ejpam-5062	39	72	higher	high	ADJ
ejpam-5062	39	73	the	the	DET
ejpam-5062	39	74	grade	grade	NOUN
ejpam-5062	39	75	of	of	ADP
ejpam-5062	39	76	membership	membership	NOUN
ejpam-5062	39	77	of	of	ADP
ejpam-5062	39	78	x	x	PUNCT
ejpam-5062	39	79	in	in	ADP
ejpam-5062	39	80	a.	a.	NOUN
ejpam-5062	39	81	definition	definition	NOUN
ejpam-5062	39	82	2	2	NUM
ejpam-5062	39	83	.	.	PUNCT
ejpam-5062	40	1	[	[	X
ejpam-5062	40	2	20	20	NUM
ejpam-5062	40	3	]	]	PUNCT
ejpam-5062	40	4	given	give	VERB
ejpam-5062	40	5	a	a	DET
ejpam-5062	40	6	fuzzy	fuzzy	ADJ
ejpam-5062	40	7	set	set	NOUN
ejpam-5062	40	8	a	a	PRON
ejpam-5062	40	9	of	of	ADP
ejpam-5062	40	10	a	a	DET
ejpam-5062	40	11	fuzzy	fuzzy	ADJ
ejpam-5062	40	12	topological	topological	ADJ
ejpam-5062	40	13	space	space	NOUN
ejpam-5062	40	14	(	(	PUNCT
ejpam-5062	40	15	x	x	X
ejpam-5062	40	16	,	,	PUNCT
ejpam-5062	40	17	τ	τ	X
ejpam-5062	40	18	)	)	PUNCT
ejpam-5062	40	19	,	,	PUNCT
ejpam-5062	40	20	the	the	DET
ejpam-5062	40	21	support	support	NOUN
ejpam-5062	40	22	of	of	ADP
ejpam-5062	40	23	the	the	DET
ejpam-5062	40	24	set	set	NOUN
ejpam-5062	40	25	a	a	PRON
ejpam-5062	40	26	is	be	AUX
ejpam-5062	40	27	defined	define	VERB
ejpam-5062	40	28	as	as	ADP
ejpam-5062	40	29	the	the	DET
ejpam-5062	40	30	set	set	NOUN
ejpam-5062	40	31	suppa	suppa	NOUN
ejpam-5062	40	32	=	=	SYM
ejpam-5062	40	33	{	{	PUNCT
ejpam-5062	40	34	x	x	PUNCT
ejpam-5062	40	35	∈	∈	NOUN
ejpam-5062	40	36	x	x	X
ejpam-5062	40	37	:	:	PUNCT
ejpam-5062	40	38	a(x	a(x	NOUN
ejpam-5062	40	39	)	)	PUNCT
ejpam-5062	40	40	>	>	X
ejpam-5062	40	41	0	0	NUM
ejpam-5062	40	42	}	}	PUNCT
ejpam-5062	40	43	.	.	PUNCT
ejpam-5062	41	1	lemma	lemma	PROPN
ejpam-5062	41	2	1	1	NUM
ejpam-5062	41	3	.	.	PUNCT
ejpam-5062	42	1	(	(	PUNCT
ejpam-5062	42	2	[	[	X
ejpam-5062	42	3	1	1	NUM
ejpam-5062	42	4	]	]	PUNCT
ejpam-5062	42	5	,	,	PUNCT
ejpam-5062	42	6	[	[	X
ejpam-5062	42	7	22	22	NUM
ejpam-5062	42	8	]	]	PUNCT
ejpam-5062	42	9	,	,	PUNCT
ejpam-5062	42	10	[	[	X
ejpam-5062	42	11	12	12	NUM
ejpam-5062	42	12	]	]	PUNCT
ejpam-5062	42	13	,	,	PUNCT
ejpam-5062	42	14	[	[	X
ejpam-5062	42	15	13	13	NUM
ejpam-5062	42	16	]	]	PUNCT
ejpam-5062	42	17	)	)	PUNCT
ejpam-5062	42	18	let	let	VERB
ejpam-5062	42	19	f	f	PRON
ejpam-5062	42	20	:	:	PUNCT
ejpam-5062	42	21	x	x	X
ejpam-5062	42	22	→	→	SYM
ejpam-5062	42	23	y	y	X
ejpam-5062	42	24	be	be	AUX
ejpam-5062	42	25	a	a	DET
ejpam-5062	42	26	mapping	mapping	NOUN
ejpam-5062	42	27	.	.	PUNCT
ejpam-5062	43	1	the	the	DET
ejpam-5062	43	2	following	follow	VERB
ejpam-5062	43	3	statements	statement	NOUN
ejpam-5062	43	4	hold	hold	VERB
ejpam-5062	43	5	:	:	PUNCT
ejpam-5062	43	6	(	(	PUNCT
ejpam-5062	43	7	i	i	NOUN
ejpam-5062	43	8	)	)	PUNCT
ejpam-5062	43	9	ff−1(b	ff−1(b	ADJ
ejpam-5062	43	10	)	)	PUNCT
ejpam-5062	43	11	≤	≤	NUM
ejpam-5062	43	12	b	b	NOUN
ejpam-5062	43	13	,	,	PUNCT
ejpam-5062	43	14	for	for	ADP
ejpam-5062	43	15	every	every	DET
ejpam-5062	43	16	fuzzy	fuzzy	ADJ
ejpam-5062	43	17	set	set	VERB
ejpam-5062	43	18	b	b	PROPN
ejpam-5062	43	19	in	in	ADP
ejpam-5062	43	20	y	y	PROPN
ejpam-5062	43	21	;	;	PUNCT
ejpam-5062	43	22	(	(	PUNCT
ejpam-5062	43	23	ii	ii	NOUN
ejpam-5062	43	24	)	)	PUNCT
ejpam-5062	43	25	f−1f(a	f−1f(a	PROPN
ejpam-5062	43	26	)	)	PUNCT
ejpam-5062	43	27	≥	≥	NOUN
ejpam-5062	43	28	a	a	PRON
ejpam-5062	43	29	,	,	PUNCT
ejpam-5062	43	30	for	for	SCONJ
ejpam-5062	43	31	every	every	DET
ejpam-5062	43	32	fuzzy	fuzzy	NOUN
ejpam-5062	43	33	set	set	VERB
ejpam-5062	43	34	a	a	PRON
ejpam-5062	43	35	in	in	ADP
ejpam-5062	43	36	x	x	SYM
ejpam-5062	43	37	;	;	PUNCT
ejpam-5062	43	38	sh	sh	PROPN
ejpam-5062	43	39	.	.	PROPN
ejpam-5062	43	40	makolli	makolli	PROPN
ejpam-5062	43	41	,	,	PUNCT
ejpam-5062	43	42	b.	b.	PROPN
ejpam-5062	43	43	krsteska	krsteska	PROPN
ejpam-5062	43	44	/	/	SYM
ejpam-5062	43	45	eur	eur	PROPN
ejpam-5062	43	46	.	.	PUNCT
ejpam-5062	44	1	j.	j.	PROPN
ejpam-5062	44	2	pure	pure	PROPN
ejpam-5062	44	3	appl	appl	PROPN
ejpam-5062	44	4	.	.	PROPN
ejpam-5062	44	5	math	math	PROPN
ejpam-5062	44	6	,	,	PUNCT
ejpam-5062	44	7	17	17	NUM
ejpam-5062	44	8	(	(	PUNCT
ejpam-5062	44	9	2	2	NUM
ejpam-5062	44	10	)	)	PUNCT
ejpam-5062	44	11	(	(	PUNCT
ejpam-5062	44	12	2024	2024	NUM
ejpam-5062	44	13	)	)	PUNCT
ejpam-5062	44	14	,	,	PUNCT
ejpam-5062	44	15	638	638	NUM
ejpam-5062	44	16	-	-	SYM
ejpam-5062	44	17	662	662	NUM
ejpam-5062	44	18	640	640	NUM
ejpam-5062	44	19	(	(	PUNCT
ejpam-5062	44	20	iii	iii	X
ejpam-5062	44	21	)	)	PUNCT
ejpam-5062	44	22	f(ac	f(ac	PROPN
ejpam-5062	44	23	)	)	PUNCT
ejpam-5062	44	24	≤	≤	NOUN
ejpam-5062	44	25	(	(	PUNCT
ejpam-5062	44	26	f(a))c	f(a))c	PROPN
ejpam-5062	44	27	,	,	PUNCT
ejpam-5062	44	28	for	for	ADP
ejpam-5062	44	29	every	every	DET
ejpam-5062	44	30	fuzzy	fuzzy	NOUN
ejpam-5062	44	31	set	set	VERB
ejpam-5062	44	32	a	a	PRON
ejpam-5062	44	33	in	in	NOUN
ejpam-5062	44	34	x	x	SYM
ejpam-5062	44	35	;	;	PUNCT
ejpam-5062	44	36	(	(	PUNCT
ejpam-5062	44	37	iv	iv	X
ejpam-5062	44	38	)	)	PUNCT
ejpam-5062	44	39	f−1(bc	f−1(bc	PROPN
ejpam-5062	44	40	)	)	PUNCT
ejpam-5062	44	41	=	=	PRON
ejpam-5062	45	1	(	(	PUNCT
ejpam-5062	45	2	f−1(b))c	f−1(b))c	PROPN
ejpam-5062	45	3	,	,	PUNCT
ejpam-5062	45	4	for	for	ADP
ejpam-5062	45	5	every	every	DET
ejpam-5062	45	6	fuzzy	fuzzy	ADJ
ejpam-5062	45	7	set	set	VERB
ejpam-5062	45	8	b	b	PROPN
ejpam-5062	45	9	in	in	ADP
ejpam-5062	45	10	y	y	PROPN
ejpam-5062	45	11	;	;	PUNCT
ejpam-5062	45	12	(	(	PUNCT
ejpam-5062	45	13	v	v	NOUN
ejpam-5062	45	14	)	)	PUNCT
ejpam-5062	45	15	if	if	SCONJ
ejpam-5062	45	16	a1	a1	PROPN
ejpam-5062	45	17	,	,	PUNCT
ejpam-5062	45	18	a2	a2	PROPN
ejpam-5062	45	19	are	be	AUX
ejpam-5062	45	20	fuzzy	fuzzy	ADJ
ejpam-5062	45	21	sets	set	NOUN
ejpam-5062	45	22	in	in	ADP
ejpam-5062	45	23	x	x	SYM
ejpam-5062	45	24	such	such	ADJ
ejpam-5062	45	25	that	that	DET
ejpam-5062	45	26	a1	a1	NOUN
ejpam-5062	45	27	≤	≤	NOUN
ejpam-5062	45	28	a2	a2	PROPN
ejpam-5062	45	29	,	,	PUNCT
ejpam-5062	45	30	then	then	ADV
ejpam-5062	45	31	f(a)1	f(a)1	PROPN
ejpam-5062	45	32	≤	≤	PROPN
ejpam-5062	45	33	f(a)2	f(a)2	PROPN
ejpam-5062	45	34	;	;	PUNCT
ejpam-5062	45	35	(	(	PUNCT
ejpam-5062	45	36	vi	vi	X
ejpam-5062	45	37	)	)	PUNCT
ejpam-5062	45	38	if	if	SCONJ
ejpam-5062	45	39	b1	b1	NOUN
ejpam-5062	45	40	,	,	PUNCT
ejpam-5062	45	41	b2	b2	NOUN
ejpam-5062	45	42	are	be	AUX
ejpam-5062	45	43	fuzzy	fuzzy	ADJ
ejpam-5062	45	44	sets	set	NOUN
ejpam-5062	45	45	in	in	ADP
ejpam-5062	45	46	y	y	PRON
ejpam-5062	45	47	such	such	ADJ
ejpam-5062	45	48	that	that	DET
ejpam-5062	45	49	b1	b1	PROPN
ejpam-5062	45	50	≤	≤	NUM
ejpam-5062	45	51	b2	b2	NOUN
ejpam-5062	45	52	,	,	PUNCT
ejpam-5062	45	53	then	then	ADV
ejpam-5062	45	54	f−1(b1	f−1(b1	VERB
ejpam-5062	45	55	)	)	PUNCT
ejpam-5062	45	56	≤	≤	NUM
ejpam-5062	45	57	f−1(b2	f−1(b2	NOUN
ejpam-5062	45	58	)	)	PUNCT
ejpam-5062	45	59	;	;	PUNCT
ejpam-5062	45	60	(	(	PUNCT
ejpam-5062	45	61	vii	vii	PROPN
ejpam-5062	45	62	)	)	PUNCT
ejpam-5062	45	63	if	if	SCONJ
ejpam-5062	45	64	f	f	PROPN
ejpam-5062	45	65	is	be	AUX
ejpam-5062	45	66	an	an	DET
ejpam-5062	45	67	injective	injective	ADJ
ejpam-5062	45	68	mapping	mapping	NOUN
ejpam-5062	45	69	,	,	PUNCT
ejpam-5062	45	70	then	then	ADV
ejpam-5062	45	71	f−1f(a	f−1f(a	PROPN
ejpam-5062	45	72	)	)	PUNCT
ejpam-5062	46	1	=	=	PUNCT
ejpam-5062	46	2	a	a	PRON
ejpam-5062	46	3	for	for	ADP
ejpam-5062	46	4	every	every	DET
ejpam-5062	46	5	fuzzy	fuzzy	ADJ
ejpam-5062	46	6	set	set	VERB
ejpam-5062	46	7	a	a	DET
ejpam-5062	46	8	inx	inx	NOUN
ejpam-5062	46	9	;	;	PUNCT
ejpam-5062	46	10	(	(	PUNCT
ejpam-5062	46	11	viii	viii	NOUN
ejpam-5062	46	12	)	)	PUNCT
ejpam-5062	46	13	if	if	SCONJ
ejpam-5062	46	14	f	f	PROPN
ejpam-5062	46	15	is	be	AUX
ejpam-5062	46	16	a	a	DET
ejpam-5062	46	17	surjective	surjective	ADJ
ejpam-5062	46	18	mapping	mapping	NOUN
ejpam-5062	46	19	,	,	PUNCT
ejpam-5062	46	20	then	then	ADV
ejpam-5062	46	21	ff−1(b	ff−1(b	ADJ
ejpam-5062	46	22	)	)	PUNCT
ejpam-5062	46	23	=	=	SYM
ejpam-5062	46	24	b	b	NOUN
ejpam-5062	46	25	for	for	ADP
ejpam-5062	46	26	every	every	DET
ejpam-5062	46	27	fuzzy	fuzzy	ADJ
ejpam-5062	46	28	set	set	VERB
ejpam-5062	46	29	b	b	PROPN
ejpam-5062	46	30	in	in	ADP
ejpam-5062	46	31	y	y	PROPN
ejpam-5062	46	32	;	;	PUNCT
ejpam-5062	46	33	(	(	PUNCT
ejpam-5062	46	34	ix	ix	INTJ
ejpam-5062	46	35	)	)	PUNCT
ejpam-5062	46	36	if	if	SCONJ
ejpam-5062	46	37	f	f	PROPN
ejpam-5062	46	38	is	be	AUX
ejpam-5062	46	39	a	a	DET
ejpam-5062	46	40	bijective	bijective	ADJ
ejpam-5062	46	41	mapping	mapping	NOUN
ejpam-5062	46	42	,	,	PUNCT
ejpam-5062	46	43	then	then	ADV
ejpam-5062	46	44	f(ac	f(ac	PROPN
ejpam-5062	46	45	)	)	PUNCT
ejpam-5062	46	46	=	=	SYM
ejpam-5062	46	47	(	(	PUNCT
ejpam-5062	46	48	f(a))c	f(a))c	PROPN
ejpam-5062	46	49	,	,	PUNCT
ejpam-5062	46	50	for	for	SCONJ
ejpam-5062	46	51	every	every	DET
ejpam-5062	46	52	fuzzy	fuzzy	NOUN
ejpam-5062	46	53	set	set	VERB
ejpam-5062	46	54	a	a	PRON
ejpam-5062	46	55	in	in	ADP
ejpam-5062	46	56	x	x	PRON
ejpam-5062	46	57	;	;	PUNCT
ejpam-5062	46	58	(	(	PUNCT
ejpam-5062	46	59	x	x	X
ejpam-5062	46	60	)	)	PUNCT
ejpam-5062	46	61	f	f	X
ejpam-5062	46	62	(	(	PUNCT
ejpam-5062	46	63	∧	∧	PROPN
ejpam-5062	46	64	i∈i	i∈i	ADJ
ejpam-5062	46	65	ai	ai	VERB
ejpam-5062	46	66	)	)	PUNCT
ejpam-5062	46	67	≤	≤	NOUN
ejpam-5062	46	68	∧	∧	PROPN
ejpam-5062	46	69	i∈i	i∈i	ADJ
ejpam-5062	46	70	f(ai	f(ai	PROPN
ejpam-5062	46	71	)	)	PUNCT
ejpam-5062	46	72	,	,	PUNCT
ejpam-5062	46	73	for	for	SCONJ
ejpam-5062	46	74	every	every	DET
ejpam-5062	46	75	family	family	NOUN
ejpam-5062	46	76	{	{	PUNCT
ejpam-5062	46	77	ai	ai	VERB
ejpam-5062	46	78	,	,	PUNCT
ejpam-5062	46	79	i	i	PROPN
ejpam-5062	46	80	∈	∈	VERB
ejpam-5062	46	81	i	i	PRON
ejpam-5062	46	82	}	}	PUNCT
ejpam-5062	46	83	of	of	ADP
ejpam-5062	46	84	fuzzy	fuzzy	ADJ
ejpam-5062	46	85	sets	set	NOUN
ejpam-5062	46	86	from	from	ADP
ejpam-5062	46	87	x	x	PUNCT
ejpam-5062	47	1	and	and	CCONJ
ejpam-5062	47	2	i	i	PRON
ejpam-5062	47	3	representing	represent	VERB
ejpam-5062	47	4	a	a	DET
ejpam-5062	47	5	set	set	NOUN
ejpam-5062	47	6	of	of	ADP
ejpam-5062	47	7	indexes	index	NOUN
ejpam-5062	47	8	;	;	PUNCT
ejpam-5062	47	9	(	(	PUNCT
ejpam-5062	47	10	xi	xi	X
ejpam-5062	47	11	)	)	PUNCT
ejpam-5062	47	12	f	f	PROPN
ejpam-5062	47	13	(	(	PUNCT
ejpam-5062	47	14	∨	∨	PROPN
ejpam-5062	47	15	i∈i	i∈i	ADJ
ejpam-5062	47	16	ai	ai	NOUN
ejpam-5062	47	17	)	)	PUNCT
ejpam-5062	47	18	=	=	PUNCT
ejpam-5062	47	19	∨	∨	NUM
ejpam-5062	47	20	i∈i	i∈i	ADJ
ejpam-5062	47	21	f(ai	f(ai	PROPN
ejpam-5062	47	22	)	)	PUNCT
ejpam-5062	47	23	,	,	PUNCT
ejpam-5062	47	24	for	for	SCONJ
ejpam-5062	47	25	every	every	DET
ejpam-5062	47	26	family	family	NOUN
ejpam-5062	47	27	{	{	PUNCT
ejpam-5062	47	28	ai	ai	VERB
ejpam-5062	47	29	,	,	PUNCT
ejpam-5062	47	30	i	i	PROPN
ejpam-5062	47	31	∈	∈	VERB
ejpam-5062	47	32	i	i	PRON
ejpam-5062	47	33	}	}	PUNCT
ejpam-5062	47	34	of	of	ADP
ejpam-5062	47	35	fuzzy	fuzzy	ADJ
ejpam-5062	47	36	sets	set	NOUN
ejpam-5062	47	37	from	from	ADP
ejpam-5062	47	38	x	x	PRON
ejpam-5062	47	39	;	;	PUNCT
ejpam-5062	48	1	(	(	PUNCT
ejpam-5062	48	2	xii	xii	NOUN
ejpam-5062	48	3	)	)	PUNCT
ejpam-5062	48	4	f−1	f−1	PROPN
ejpam-5062	48	5	(	(	PUNCT
ejpam-5062	48	6	∧	∧	PROPN
ejpam-5062	48	7	i∈i	i∈i	ADJ
ejpam-5062	48	8	bi	bi	NOUN
ejpam-5062	48	9	)	)	PUNCT
ejpam-5062	48	10	=	=	SYM
ejpam-5062	49	1	∧	∧	PROPN
ejpam-5062	49	2	i∈i	i∈i	ADJ
ejpam-5062	49	3	f	f	PROPN
ejpam-5062	49	4	−1(bi	−1(bi	PROPN
ejpam-5062	49	5	)	)	PUNCT
ejpam-5062	49	6	,	,	PUNCT
ejpam-5062	49	7	for	for	ADP
ejpam-5062	49	8	every	every	DET
ejpam-5062	49	9	family	family	NOUN
ejpam-5062	49	10	{	{	PUNCT
ejpam-5062	49	11	bi	bi	NOUN
ejpam-5062	49	12	,	,	PUNCT
ejpam-5062	49	13	i	i	PRON
ejpam-5062	49	14	∈	∈	VERB
ejpam-5062	50	1	i	i	PRON
ejpam-5062	50	2	}	}	PUNCT
ejpam-5062	50	3	of	of	ADP
ejpam-5062	50	4	fuzzy	fuzzy	ADJ
ejpam-5062	50	5	sets	set	NOUN
ejpam-5062	50	6	from	from	ADP
ejpam-5062	50	7	y	y	PROPN
ejpam-5062	51	1	and	and	CCONJ
ejpam-5062	51	2	i	i	PRON
ejpam-5062	51	3	representing	represent	VERB
ejpam-5062	51	4	a	a	DET
ejpam-5062	51	5	set	set	NOUN
ejpam-5062	51	6	of	of	ADP
ejpam-5062	51	7	indexes	index	NOUN
ejpam-5062	51	8	;	;	PUNCT
ejpam-5062	52	1	(	(	PUNCT
ejpam-5062	52	2	xiii	xiii	X
ejpam-5062	52	3	)	)	PUNCT
ejpam-5062	52	4	f−1	f−1	PROPN
ejpam-5062	52	5	(	(	PUNCT
ejpam-5062	52	6	∨	∨	NUM
ejpam-5062	52	7	i∈i	i∈i	ADJ
ejpam-5062	52	8	bi	bi	NOUN
ejpam-5062	52	9	)	)	PUNCT
ejpam-5062	52	10	=	=	PUNCT
ejpam-5062	53	1	∨	∨	NUM
ejpam-5062	53	2	i∈i	i∈i	PROPN
ejpam-5062	53	3	f	f	PROPN
ejpam-5062	53	4	−1(bi	−1(bi	PROPN
ejpam-5062	53	5	)	)	PUNCT
ejpam-5062	53	6	,	,	PUNCT
ejpam-5062	53	7	for	for	ADP
ejpam-5062	53	8	every	every	DET
ejpam-5062	53	9	family	family	NOUN
ejpam-5062	53	10	{	{	PUNCT
ejpam-5062	53	11	bi	bi	NOUN
ejpam-5062	53	12	,	,	PUNCT
ejpam-5062	53	13	i	i	PRON
ejpam-5062	53	14	∈	∈	VERB
ejpam-5062	53	15	i	i	PRON
ejpam-5062	53	16	}	}	PUNCT
ejpam-5062	53	17	of	of	ADP
ejpam-5062	53	18	fuzzy	fuzzy	ADJ
ejpam-5062	53	19	sets	set	NOUN
ejpam-5062	53	20	from	from	ADP
ejpam-5062	53	21	y	y	PROPN
ejpam-5062	53	22	;	;	PUNCT
ejpam-5062	53	23	definition	definition	NOUN
ejpam-5062	53	24	3	3	NUM
ejpam-5062	53	25	.	.	PUNCT
ejpam-5062	54	1	(	(	PUNCT
ejpam-5062	54	2	[	[	X
ejpam-5062	54	3	22	22	NUM
ejpam-5062	54	4	]	]	PUNCT
ejpam-5062	54	5	,	,	PUNCT
ejpam-5062	54	6	[	[	X
ejpam-5062	54	7	23	23	NUM
ejpam-5062	54	8	]	]	PUNCT
ejpam-5062	54	9	)	)	PUNCT
ejpam-5062	54	10	a	a	DET
ejpam-5062	54	11	fuzzy	fuzzy	ADJ
ejpam-5062	54	12	point	point	NOUN
ejpam-5062	54	13	xα	xα	INTJ
ejpam-5062	54	14	of	of	ADP
ejpam-5062	54	15	a	a	DET
ejpam-5062	54	16	fuzzy	fuzzy	ADJ
ejpam-5062	54	17	topological	topological	ADJ
ejpam-5062	54	18	space	space	NOUN
ejpam-5062	54	19	x	x	PUNCT
ejpam-5062	54	20	is	be	AUX
ejpam-5062	54	21	a	a	DET
ejpam-5062	54	22	fuzzy	fuzzy	ADJ
ejpam-5062	54	23	set	set	NOUN
ejpam-5062	54	24	defined	define	VERB
ejpam-5062	54	25	as	as	ADP
ejpam-5062	54	26	:	:	PUNCT
ejpam-5062	54	27	xα(z	xα(z	NUM
ejpam-5062	54	28	)	)	PUNCT
ejpam-5062	55	1	=	=	PRON
ejpam-5062	55	2	{	{	PUNCT
ejpam-5062	55	3	α	α	NOUN
ejpam-5062	55	4	if	if	SCONJ
ejpam-5062	55	5	z	z	NOUN
ejpam-5062	55	6	=	=	SYM
ejpam-5062	55	7	x	x	SYM
ejpam-5062	55	8	0	0	PUNCT
ejpam-5062	55	9	if	if	SCONJ
ejpam-5062	55	10	otherwise	otherwise	ADV
ejpam-5062	55	11	the	the	DET
ejpam-5062	55	12	support	support	NOUN
ejpam-5062	55	13	of	of	ADP
ejpam-5062	55	14	the	the	DET
ejpam-5062	55	15	fuzzy	fuzzy	ADJ
ejpam-5062	55	16	point	point	NOUN
ejpam-5062	55	17	xα	xα	INTJ
ejpam-5062	55	18	is	be	AUX
ejpam-5062	55	19	only	only	ADV
ejpam-5062	55	20	the	the	DET
ejpam-5062	55	21	element	element	NOUN
ejpam-5062	55	22	x	x	PUNCT
ejpam-5062	55	23	with	with	ADP
ejpam-5062	55	24	the	the	DET
ejpam-5062	55	25	value	value	NOUN
ejpam-5062	55	26	of	of	ADP
ejpam-5062	55	27	membership	membership	NOUN
ejpam-5062	55	28	α	α	NOUN
ejpam-5062	55	29	.	.	PUNCT
ejpam-5062	56	1	if	if	SCONJ
ejpam-5062	56	2	α	α	PRON
ejpam-5062	56	3	=	=	NOUN
ejpam-5062	56	4	1	1	NUM
ejpam-5062	56	5	then	then	ADV
ejpam-5062	56	6	xα	xα	INTJ
ejpam-5062	56	7	is	be	AUX
ejpam-5062	56	8	called	call	VERB
ejpam-5062	56	9	a	a	DET
ejpam-5062	56	10	singleton	singleton	NOUN
ejpam-5062	56	11	.	.	PUNCT
ejpam-5062	57	1	definition	definition	NOUN
ejpam-5062	57	2	4	4	NUM
ejpam-5062	57	3	.	.	PUNCT
ejpam-5062	58	1	a	a	DET
ejpam-5062	58	2	fuzzy	fuzzy	ADJ
ejpam-5062	58	3	set	set	VERB
ejpam-5062	58	4	a	a	PRON
ejpam-5062	58	5	of	of	ADP
ejpam-5062	58	6	the	the	DET
ejpam-5062	58	7	fuzzy	fuzzy	ADJ
ejpam-5062	58	8	topological	topological	ADJ
ejpam-5062	58	9	space	space	NOUN
ejpam-5062	58	10	x	x	PUNCT
ejpam-5062	58	11	is	be	AUX
ejpam-5062	58	12	called	call	VERB
ejpam-5062	58	13	:	:	PUNCT
ejpam-5062	58	14	(	(	PUNCT
ejpam-5062	58	15	i	i	NOUN
ejpam-5062	58	16	)	)	PUNCT
ejpam-5062	58	17	fuzzy	fuzzy	ADJ
ejpam-5062	58	18	preopen	preopen	NOUN
ejpam-5062	58	19	if	if	SCONJ
ejpam-5062	58	20	and	and	CCONJ
ejpam-5062	58	21	only	only	ADV
ejpam-5062	58	22	if	if	SCONJ
ejpam-5062	58	23	a	a	DET
ejpam-5062	58	24	≤	≤	NUM
ejpam-5062	58	25	int(cla	int(cla	NOUN
ejpam-5062	58	26	)	)	PUNCT
ejpam-5062	59	1	(	(	PUNCT
ejpam-5062	59	2	[	[	X
ejpam-5062	59	3	3	3	NUM
ejpam-5062	59	4	]	]	PUNCT
ejpam-5062	59	5	,	,	PUNCT
ejpam-5062	59	6	[	[	X
ejpam-5062	59	7	27	27	NUM
ejpam-5062	59	8	]	]	NUM
ejpam-5062	59	9	)	)	PUNCT
ejpam-5062	59	10	;	;	PUNCT
ejpam-5062	59	11	(	(	PUNCT
ejpam-5062	59	12	ii	ii	NOUN
ejpam-5062	59	13	)	)	PUNCT
ejpam-5062	59	14	fuzzy	fuzzy	NOUN
ejpam-5062	59	15	preclosed	preclose	VERB
ejpam-5062	59	16	if	if	SCONJ
ejpam-5062	59	17	and	and	CCONJ
ejpam-5062	59	18	only	only	ADV
ejpam-5062	59	19	if	if	SCONJ
ejpam-5062	59	20	ac	ac	PROPN
ejpam-5062	59	21	is	be	AUX
ejpam-5062	59	22	a	a	DET
ejpam-5062	59	23	fuzzy	fuzzy	ADJ
ejpam-5062	59	24	preopen	preopen	ADJ
ejpam-5062	59	25	set	set	NOUN
ejpam-5062	59	26	of	of	ADP
ejpam-5062	59	27	a	a	DET
ejpam-5062	59	28	fts	fts	PROPN
ejpam-5062	59	29	x	x	X
ejpam-5062	59	30	(	(	PUNCT
ejpam-5062	59	31	[	[	X
ejpam-5062	59	32	3	3	NUM
ejpam-5062	59	33	]	]	PUNCT
ejpam-5062	59	34	,	,	PUNCT
ejpam-5062	59	35	[	[	X
ejpam-5062	59	36	14	14	NUM
ejpam-5062	59	37	]	]	PUNCT
ejpam-5062	59	38	,	,	PUNCT
ejpam-5062	59	39	[	[	X
ejpam-5062	59	40	27	27	NUM
ejpam-5062	59	41	]	]	PUNCT
ejpam-5062	59	42	)	)	PUNCT
ejpam-5062	59	43	.	.	PUNCT
ejpam-5062	60	1	given	give	VERB
ejpam-5062	60	2	any	any	DET
ejpam-5062	60	3	fuzzy	fuzzy	ADJ
ejpam-5062	60	4	topological	topological	ADJ
ejpam-5062	60	5	space	space	NOUN
ejpam-5062	60	6	(	(	PUNCT
ejpam-5062	60	7	x	x	X
ejpam-5062	60	8	,	,	PUNCT
ejpam-5062	60	9	τ	τ	X
ejpam-5062	60	10	)	)	PUNCT
ejpam-5062	60	11	the	the	DET
ejpam-5062	60	12	family	family	NOUN
ejpam-5062	60	13	of	of	ADP
ejpam-5062	60	14	all	all	DET
ejpam-5062	60	15	fuzzy	fuzzy	ADJ
ejpam-5062	60	16	preopen	preopen	NOUN
ejpam-5062	60	17	(	(	PUNCT
ejpam-5062	60	18	preclosed	preclose	VERB
ejpam-5062	60	19	)	)	PUNCT
ejpam-5062	60	20	sets	set	NOUN
ejpam-5062	60	21	is	be	AUX
ejpam-5062	60	22	denoted	denote	VERB
ejpam-5062	60	23	fpo(τ	fpo(τ	PROPN
ejpam-5062	60	24	)	)	PUNCT
ejpam-5062	60	25	(	(	PUNCT
ejpam-5062	60	26	fpc(τ	fpc(τ	NOUN
ejpam-5062	60	27	)	)	PUNCT
ejpam-5062	60	28	)	)	PUNCT
ejpam-5062	60	29	.	.	PUNCT
ejpam-5062	61	1	definition	definition	NOUN
ejpam-5062	61	2	5	5	NUM
ejpam-5062	61	3	.	.	PUNCT
ejpam-5062	62	1	let	let	VERB
ejpam-5062	62	2	a	a	DET
ejpam-5062	62	3	be	be	AUX
ejpam-5062	62	4	a	a	DET
ejpam-5062	62	5	fuzzy	fuzzy	ADJ
ejpam-5062	62	6	set	set	NOUN
ejpam-5062	62	7	of	of	ADP
ejpam-5062	62	8	a	a	DET
ejpam-5062	62	9	fts	fts	X
ejpam-5062	62	10	(	(	PUNCT
ejpam-5062	62	11	x	x	X
ejpam-5062	62	12	,	,	PUNCT
ejpam-5062	62	13	τ	τ	PROPN
ejpam-5062	62	14	)	)	PUNCT
ejpam-5062	62	15	.	.	PUNCT
ejpam-5062	63	1	then	then	ADV
ejpam-5062	63	2	:	:	PUNCT
ejpam-5062	63	3	(	(	PUNCT
ejpam-5062	63	4	i	i	NOUN
ejpam-5062	63	5	)	)	PUNCT
ejpam-5062	63	6	pinta	pinta	NOUN
ejpam-5062	63	7	=	=	PUNCT
ejpam-5062	63	8	∧{b	∧{b	PROPN
ejpam-5062	63	9	≤	≤	NOUN
ejpam-5062	63	10	a;b	a;b	PROPN
ejpam-5062	63	11	∈	∈	PROPN
ejpam-5062	63	12	fpo(τ	fpo(τ	PROPN
ejpam-5062	63	13	)	)	PUNCT
ejpam-5062	63	14	}	}	PUNCT
ejpam-5062	63	15	,	,	PUNCT
ejpam-5062	63	16	is	be	AUX
ejpam-5062	63	17	called	call	VERB
ejpam-5062	63	18	the	the	DET
ejpam-5062	63	19	fuzzy	fuzzy	ADJ
ejpam-5062	63	20	preinterior	preinterior	NOUN
ejpam-5062	63	21	of	of	ADP
ejpam-5062	63	22	the	the	DET
ejpam-5062	63	23	set	set	NOUN
ejpam-5062	63	24	a	a	DET
ejpam-5062	63	25	(	(	PUNCT
ejpam-5062	63	26	[	[	X
ejpam-5062	63	27	27	27	NUM
ejpam-5062	63	28	]	]	NUM
ejpam-5062	63	29	)	)	PUNCT
ejpam-5062	63	30	;	;	PUNCT
ejpam-5062	63	31	(	(	PUNCT
ejpam-5062	63	32	ii	ii	NOUN
ejpam-5062	63	33	)	)	PUNCT
ejpam-5062	63	34	pcla	pcla	NOUN
ejpam-5062	63	35	=	=	SYM
ejpam-5062	63	36	∨{b	∨{b	NOUN
ejpam-5062	63	37	≥	≥	NOUN
ejpam-5062	63	38	a;b	a;b	NOUN
ejpam-5062	63	39	∈	∈	PROPN
ejpam-5062	63	40	fpc(τ	fpc(τ	NOUN
ejpam-5062	63	41	)	)	PUNCT
ejpam-5062	63	42	}	}	PUNCT
ejpam-5062	63	43	,	,	PUNCT
ejpam-5062	63	44	is	be	AUX
ejpam-5062	63	45	called	call	VERB
ejpam-5062	63	46	the	the	DET
ejpam-5062	63	47	fuzzy	fuzzy	ADJ
ejpam-5062	63	48	preclosure	preclosure	NOUN
ejpam-5062	63	49	of	of	ADP
ejpam-5062	63	50	the	the	DET
ejpam-5062	63	51	set	set	NOUN
ejpam-5062	63	52	a	a	DET
ejpam-5062	63	53	(	(	PUNCT
ejpam-5062	63	54	[	[	X
ejpam-5062	63	55	27	27	NUM
ejpam-5062	63	56	]	]	NUM
ejpam-5062	63	57	)	)	PUNCT
ejpam-5062	63	58	.	.	PUNCT
ejpam-5062	64	1	sh	sh	PROPN
ejpam-5062	64	2	.	.	PROPN
ejpam-5062	64	3	makolli	makolli	PROPN
ejpam-5062	64	4	,	,	PUNCT
ejpam-5062	64	5	b.	b.	PROPN
ejpam-5062	64	6	krsteska	krsteska	PROPN
ejpam-5062	64	7	/	/	SYM
ejpam-5062	64	8	eur	eur	PROPN
ejpam-5062	64	9	.	.	PUNCT
ejpam-5062	65	1	j.	j.	PROPN
ejpam-5062	65	2	pure	pure	PROPN
ejpam-5062	65	3	appl	appl	PROPN
ejpam-5062	65	4	.	.	PROPN
ejpam-5062	65	5	math	math	PROPN
ejpam-5062	65	6	,	,	PUNCT
ejpam-5062	65	7	17	17	NUM
ejpam-5062	65	8	(	(	PUNCT
ejpam-5062	65	9	2	2	NUM
ejpam-5062	65	10	)	)	PUNCT
ejpam-5062	65	11	(	(	PUNCT
ejpam-5062	65	12	2024	2024	NUM
ejpam-5062	65	13	)	)	PUNCT
ejpam-5062	65	14	,	,	PUNCT
ejpam-5062	65	15	638	638	NUM
ejpam-5062	65	16	-	-	SYM
ejpam-5062	65	17	662	662	NUM
ejpam-5062	65	18	641	641	NUM
ejpam-5062	65	19	definition	definition	NOUN
ejpam-5062	65	20	6	6	NUM
ejpam-5062	65	21	.	.	PUNCT
ejpam-5062	66	1	a	a	DET
ejpam-5062	66	2	fuzzy	fuzzy	ADJ
ejpam-5062	66	3	set	set	VERB
ejpam-5062	66	4	a	a	PRON
ejpam-5062	66	5	of	of	ADP
ejpam-5062	66	6	a	a	DET
ejpam-5062	66	7	fts	fts	PROPN
ejpam-5062	66	8	x	x	PUNCT
ejpam-5062	66	9	is	be	AUX
ejpam-5062	66	10	called	call	VERB
ejpam-5062	66	11	:	:	PUNCT
ejpam-5062	66	12	•	•	X
ejpam-5062	66	13	fuzzy	fuzzy	ADJ
ejpam-5062	66	14	strongly	strongly	ADV
ejpam-5062	66	15	preopen	preopen	ADJ
ejpam-5062	66	16	(	(	PUNCT
ejpam-5062	66	17	strongly	strongly	ADV
ejpam-5062	66	18	preclosed	preclose	VERB
ejpam-5062	66	19	)	)	PUNCT
ejpam-5062	66	20	if	if	SCONJ
ejpam-5062	67	1	and	and	CCONJ
ejpam-5062	67	2	only	only	ADV
ejpam-5062	67	3	if	if	SCONJ
ejpam-5062	67	4	a	a	DET
ejpam-5062	67	5	≤	≤	NUM
ejpam-5062	67	6	int(pcla	int(pcla	NOUN
ejpam-5062	67	7	)	)	PUNCT
ejpam-5062	67	8	(	(	PUNCT
ejpam-5062	67	9	a	a	DET
ejpam-5062	67	10	≥	≥	NOUN
ejpam-5062	67	11	cl(pinta	cl(pinta	NOUN
ejpam-5062	67	12	)	)	PUNCT
ejpam-5062	67	13	)	)	PUNCT
ejpam-5062	68	1	(	(	PUNCT
ejpam-5062	68	2	[	[	X
ejpam-5062	68	3	12	12	NUM
ejpam-5062	68	4	]	]	PUNCT
ejpam-5062	68	5	)	)	PUNCT
ejpam-5062	68	6	;	;	PUNCT
ejpam-5062	68	7	•	•	X
ejpam-5062	68	8	fuzzy	fuzzy	ADJ
ejpam-5062	68	9	strongly	strongly	ADV
ejpam-5062	68	10	semi	semi	ADV
ejpam-5062	68	11	pre	pre	ADJ
ejpam-5062	68	12	-	-	ADJ
ejpam-5062	68	13	open	open	ADJ
ejpam-5062	68	14	(	(	PUNCT
ejpam-5062	68	15	strongly	strongly	ADV
ejpam-5062	68	16	semi	semi	ADJ
ejpam-5062	68	17	pre	pre	ADJ
ejpam-5062	68	18	-	-	ADJ
ejpam-5062	68	19	closed	closed	ADJ
ejpam-5062	68	20	)	)	PUNCT
ejpam-5062	68	21	if	if	SCONJ
ejpam-5062	68	22	and	and	CCONJ
ejpam-5062	68	23	only	only	ADV
ejpam-5062	68	24	if	if	SCONJ
ejpam-5062	68	25	a	a	DET
ejpam-5062	68	26	≤	≤	NUM
ejpam-5062	68	27	int(pcla	int(pcla	NOUN
ejpam-5062	68	28	)	)	PUNCT
ejpam-5062	68	29	∨	∨	NUM
ejpam-5062	68	30	pcl(inta	pcl(inta	NUM
ejpam-5062	68	31	)	)	PUNCT
ejpam-5062	68	32	(	(	PUNCT
ejpam-5062	68	33	a	a	DET
ejpam-5062	68	34	≥	≥	NOUN
ejpam-5062	68	35	cl(pinta	cl(pinta	NOUN
ejpam-5062	68	36	)	)	PUNCT
ejpam-5062	68	37	∧	∧	NOUN
ejpam-5062	68	38	pint(cla	pint(cla	NOUN
ejpam-5062	68	39	)	)	PUNCT
ejpam-5062	68	40	)	)	PUNCT
ejpam-5062	69	1	(	(	PUNCT
ejpam-5062	69	2	[	[	X
ejpam-5062	69	3	17	17	NUM
ejpam-5062	69	4	]	]	NUM
ejpam-5062	69	5	)	)	PUNCT
ejpam-5062	69	6	.	.	PUNCT
ejpam-5062	70	1	the	the	DET
ejpam-5062	70	2	family	family	NOUN
ejpam-5062	70	3	of	of	ADP
ejpam-5062	70	4	all	all	PRON
ejpam-5062	70	5	fuzzy	fuzzy	ADJ
ejpam-5062	70	6	strongly	strongly	ADV
ejpam-5062	70	7	preopen	preopen	ADJ
ejpam-5062	70	8	(	(	PUNCT
ejpam-5062	70	9	strongly	strongly	ADV
ejpam-5062	70	10	preclosed	preclose	VERB
ejpam-5062	70	11	)	)	PUNCT
ejpam-5062	70	12	sets	set	NOUN
ejpam-5062	70	13	in	in	ADP
ejpam-5062	70	14	(	(	PUNCT
ejpam-5062	70	15	x	x	NOUN
ejpam-5062	70	16	,	,	PUNCT
ejpam-5062	70	17	τ	τ	X
ejpam-5062	70	18	)	)	PUNCT
ejpam-5062	70	19	is	be	AUX
ejpam-5062	70	20	denoted	denote	VERB
ejpam-5062	70	21	by	by	ADP
ejpam-5062	70	22	fspo(τ	fspo(τ	NOUN
ejpam-5062	70	23	)	)	PUNCT
ejpam-5062	70	24	(	(	PUNCT
ejpam-5062	70	25	fspc(τ	fspc(τ	NOUN
ejpam-5062	70	26	)	)	PUNCT
ejpam-5062	70	27	)	)	PUNCT
ejpam-5062	70	28	;	;	PUNCT
ejpam-5062	70	29	the	the	DET
ejpam-5062	70	30	family	family	NOUN
ejpam-5062	70	31	of	of	ADP
ejpam-5062	70	32	all	all	PRON
ejpam-5062	70	33	fuzzy	fuzzy	ADJ
ejpam-5062	70	34	strongly	strongly	ADV
ejpam-5062	70	35	semi	semi	ADV
ejpam-5062	70	36	pre	pre	ADJ
ejpam-5062	70	37	-	-	ADJ
ejpam-5062	70	38	open	open	ADJ
ejpam-5062	70	39	(	(	PUNCT
ejpam-5062	70	40	strongly	strongly	ADV
ejpam-5062	70	41	semi	semi	ADJ
ejpam-5062	70	42	pre	pre	ADJ
ejpam-5062	70	43	-	-	ADJ
ejpam-5062	70	44	closed	closed	ADJ
ejpam-5062	70	45	)	)	PUNCT
ejpam-5062	70	46	sets	set	NOUN
ejpam-5062	70	47	is	be	AUX
ejpam-5062	70	48	denoted	denote	VERB
ejpam-5062	70	49	fsspo(τ	fsspo(τ	PROPN
ejpam-5062	70	50	)	)	PUNCT
ejpam-5062	70	51	(	(	PUNCT
ejpam-5062	70	52	fsspc(τ	fsspc(τ	NOUN
ejpam-5062	70	53	)	)	PUNCT
ejpam-5062	70	54	)	)	PUNCT
ejpam-5062	70	55	.	.	PUNCT
ejpam-5062	71	1	definition	definition	NOUN
ejpam-5062	71	2	7	7	NUM
ejpam-5062	71	3	.	.	PUNCT
ejpam-5062	72	1	[	[	X
ejpam-5062	72	2	17	17	NUM
ejpam-5062	72	3	]	]	X
ejpam-5062	72	4	if	if	SCONJ
ejpam-5062	72	5	a	a	PRON
ejpam-5062	72	6	is	be	AUX
ejpam-5062	72	7	a	a	DET
ejpam-5062	72	8	fuzzy	fuzzy	ADJ
ejpam-5062	72	9	set	set	NOUN
ejpam-5062	72	10	of	of	ADP
ejpam-5062	72	11	a	a	DET
ejpam-5062	72	12	fts	fts	PROPN
ejpam-5062	72	13	x	x	NOUN
ejpam-5062	72	14	,	,	PUNCT
ejpam-5062	72	15	then	then	ADV
ejpam-5062	72	16	:	:	PUNCT
ejpam-5062	72	17	(	(	PUNCT
ejpam-5062	72	18	i	i	NOUN
ejpam-5062	72	19	)	)	PUNCT
ejpam-5062	72	20	the	the	DET
ejpam-5062	72	21	set	set	NOUN
ejpam-5062	72	22	:	:	PUNCT
ejpam-5062	72	23	sspinta	sspinta	NOUN
ejpam-5062	72	24	=	=	SYM
ejpam-5062	72	25	∨{b	∨{b	NOUN
ejpam-5062	72	26	≤	≤	NOUN
ejpam-5062	72	27	a;b	a;b	PROPN
ejpam-5062	72	28	∈	∈	PROPN
ejpam-5062	72	29	fsspo(τ	fsspo(τ	PROPN
ejpam-5062	72	30	)	)	PUNCT
ejpam-5062	72	31	}	}	PUNCT
ejpam-5062	72	32	,	,	PUNCT
ejpam-5062	72	33	is	be	AUX
ejpam-5062	72	34	called	call	VERB
ejpam-5062	72	35	the	the	DET
ejpam-5062	72	36	fuzzy	fuzzy	ADJ
ejpam-5062	72	37	strong	strong	ADJ
ejpam-5062	72	38	semi	semi	ADJ
ejpam-5062	72	39	preinterior	preinterior	NOUN
ejpam-5062	72	40	of	of	ADP
ejpam-5062	72	41	set	set	ADJ
ejpam-5062	72	42	a.	a.	NOUN
ejpam-5062	72	43	(	(	PUNCT
ejpam-5062	72	44	ii	ii	PROPN
ejpam-5062	72	45	)	)	PUNCT
ejpam-5062	72	46	the	the	DET
ejpam-5062	72	47	set	set	NOUN
ejpam-5062	72	48	:	:	PUNCT
ejpam-5062	72	49	sspcla	sspcla	X
ejpam-5062	72	50	=	=	PUNCT
ejpam-5062	72	51	∧{b	∧{b	PROPN
ejpam-5062	72	52	≥	≥	NOUN
ejpam-5062	72	53	a;b	a;b	PROPN
ejpam-5062	72	54	∈	∈	PROPN
ejpam-5062	72	55	fsspc(τ	fsspc(τ	NOUN
ejpam-5062	72	56	)	)	PUNCT
ejpam-5062	72	57	}	}	PUNCT
ejpam-5062	72	58	,	,	PUNCT
ejpam-5062	72	59	is	be	AUX
ejpam-5062	72	60	called	call	VERB
ejpam-5062	72	61	the	the	DET
ejpam-5062	72	62	fuzzy	fuzzy	ADJ
ejpam-5062	72	63	strong	strong	ADJ
ejpam-5062	72	64	semi	semi	ADV
ejpam-5062	72	65	preclosure	preclosure	ADJ
ejpam-5062	72	66	of	of	ADP
ejpam-5062	72	67	set	set	PROPN
ejpam-5062	72	68	a.	a.	PROPN
ejpam-5062	72	69	lemma	lemma	PROPN
ejpam-5062	72	70	2	2	X
ejpam-5062	72	71	.	.	PUNCT
ejpam-5062	73	1	[	[	X
ejpam-5062	73	2	17	17	NUM
ejpam-5062	73	3	]	]	X
ejpam-5062	73	4	if	if	SCONJ
ejpam-5062	73	5	a	a	PRON
ejpam-5062	73	6	is	be	AUX
ejpam-5062	73	7	a	a	DET
ejpam-5062	73	8	fuzzy	fuzzy	ADJ
ejpam-5062	73	9	set	set	NOUN
ejpam-5062	73	10	of	of	ADP
ejpam-5062	73	11	a	a	DET
ejpam-5062	73	12	fuzzy	fuzzy	ADJ
ejpam-5062	73	13	topological	topological	ADJ
ejpam-5062	73	14	space	space	NOUN
ejpam-5062	73	15	(	(	PUNCT
ejpam-5062	73	16	x	x	X
ejpam-5062	73	17	,	,	PUNCT
ejpam-5062	73	18	τ	τ	PROPN
ejpam-5062	73	19	)	)	PUNCT
ejpam-5062	73	20	,	,	PUNCT
ejpam-5062	73	21	then	then	ADV
ejpam-5062	73	22	:	:	PUNCT
ejpam-5062	73	23	•	•	NUM
ejpam-5062	73	24	sspclac	sspclac	PROPN
ejpam-5062	73	25	=	=	SYM
ejpam-5062	73	26	(	(	PUNCT
ejpam-5062	73	27	sspinta)c	sspinta)c	PROPN
ejpam-5062	73	28	;	;	PUNCT
ejpam-5062	73	29	•	•	NUM
ejpam-5062	73	30	sspintac	sspintac	NOUN
ejpam-5062	73	31	=	=	SYM
ejpam-5062	73	32	(	(	PUNCT
ejpam-5062	73	33	sspcla)c	sspcla)c	PROPN
ejpam-5062	73	34	.	.	PUNCT
ejpam-5062	74	1	definition	definition	NOUN
ejpam-5062	74	2	8	8	NUM
ejpam-5062	74	3	.	.	PUNCT
ejpam-5062	75	1	let	let	VERB
ejpam-5062	75	2	f	f	NOUN
ejpam-5062	75	3	:	:	PUNCT
ejpam-5062	75	4	(	(	PUNCT
ejpam-5062	75	5	x	x	X
ejpam-5062	75	6	,	,	PUNCT
ejpam-5062	75	7	τ	τ	X
ejpam-5062	75	8	)	)	PUNCT
ejpam-5062	75	9	→	→	SYM
ejpam-5062	75	10	(	(	PUNCT
ejpam-5062	75	11	y	y	PROPN
ejpam-5062	75	12	,	,	PUNCT
ejpam-5062	75	13	δ	δ	PROPN
ejpam-5062	75	14	)	)	PUNCT
ejpam-5062	75	15	be	be	VERB
ejpam-5062	75	16	a	a	DET
ejpam-5062	75	17	mapping	mapping	NOUN
ejpam-5062	75	18	from	from	ADP
ejpam-5062	75	19	a	a	DET
ejpam-5062	75	20	fts	fts	PROPN
ejpam-5062	75	21	(	(	PUNCT
ejpam-5062	75	22	x	x	X
ejpam-5062	75	23	,	,	PUNCT
ejpam-5062	75	24	τ	τ	X
ejpam-5062	75	25	)	)	PUNCT
ejpam-5062	75	26	to	to	ADP
ejpam-5062	75	27	a	a	DET
ejpam-5062	75	28	fts	fts	PROPN
ejpam-5062	75	29	(	(	PUNCT
ejpam-5062	75	30	y	y	PROPN
ejpam-5062	75	31	,	,	PUNCT
ejpam-5062	75	32	δ	δ	PROPN
ejpam-5062	75	33	)	)	PUNCT
ejpam-5062	75	34	.	.	PUNCT
ejpam-5062	76	1	the	the	DET
ejpam-5062	76	2	mapping	mapping	NOUN
ejpam-5062	76	3	f	f	PROPN
ejpam-5062	76	4	is	be	AUX
ejpam-5062	76	5	called	call	VERB
ejpam-5062	76	6	:	:	PUNCT
ejpam-5062	76	7	(	(	PUNCT
ejpam-5062	76	8	i	i	NOUN
ejpam-5062	76	9	)	)	PUNCT
ejpam-5062	76	10	fuzzy	fuzzy	ADJ
ejpam-5062	76	11	continuous	continuous	ADJ
ejpam-5062	76	12	if	if	SCONJ
ejpam-5062	76	13	f−1(b	f−1(b	PROPN
ejpam-5062	76	14	)	)	PUNCT
ejpam-5062	76	15	is	be	AUX
ejpam-5062	76	16	a	a	DET
ejpam-5062	76	17	fuzzy	fuzzy	ADJ
ejpam-5062	76	18	open	open	ADJ
ejpam-5062	76	19	set	set	NOUN
ejpam-5062	76	20	of	of	ADP
ejpam-5062	76	21	x	x	PRON
ejpam-5062	76	22	,	,	PUNCT
ejpam-5062	76	23	for	for	ADP
ejpam-5062	76	24	each	each	DET
ejpam-5062	76	25	b	b	PROPN
ejpam-5062	76	26	∈	∈	PROPN
ejpam-5062	76	27	δ	δ	PROPN
ejpam-5062	76	28	(	(	PUNCT
ejpam-5062	76	29	[	[	X
ejpam-5062	76	30	2	2	NUM
ejpam-5062	76	31	]	]	PUNCT
ejpam-5062	76	32	,	,	PUNCT
ejpam-5062	76	33	[	[	X
ejpam-5062	76	34	4	4	NUM
ejpam-5062	76	35	]	]	PUNCT
ejpam-5062	76	36	,	,	PUNCT
ejpam-5062	76	37	[	[	X
ejpam-5062	76	38	20	20	NUM
ejpam-5062	76	39	]	]	PUNCT
ejpam-5062	76	40	,	,	PUNCT
ejpam-5062	76	41	[	[	X
ejpam-5062	76	42	21	21	NUM
ejpam-5062	76	43	]	]	PUNCT
ejpam-5062	76	44	)	)	PUNCT
ejpam-5062	76	45	;	;	PUNCT
ejpam-5062	76	46	(	(	PUNCT
ejpam-5062	76	47	ii	ii	NOUN
ejpam-5062	76	48	)	)	PUNCT
ejpam-5062	76	49	fuzzy	fuzzy	ADJ
ejpam-5062	76	50	open	open	ADJ
ejpam-5062	76	51	(	(	PUNCT
ejpam-5062	76	52	closed	closed	ADJ
ejpam-5062	76	53	)	)	PUNCT
ejpam-5062	76	54	if	if	SCONJ
ejpam-5062	76	55	f(a	f(a	PROPN
ejpam-5062	76	56	)	)	PUNCT
ejpam-5062	76	57	is	be	AUX
ejpam-5062	76	58	a	a	DET
ejpam-5062	76	59	fuzzy	fuzzy	ADJ
ejpam-5062	76	60	open	open	ADJ
ejpam-5062	76	61	(	(	PUNCT
ejpam-5062	76	62	closed	closed	ADJ
ejpam-5062	76	63	)	)	PUNCT
ejpam-5062	76	64	set	set	NOUN
ejpam-5062	76	65	of	of	ADP
ejpam-5062	76	66	y	y	PROPN
ejpam-5062	76	67	,	,	PUNCT
ejpam-5062	76	68	for	for	ADP
ejpam-5062	76	69	each	each	DET
ejpam-5062	76	70	a	a	DET
ejpam-5062	76	71	∈	∈	NOUN
ejpam-5062	76	72	τ	τ	X
ejpam-5062	76	73	(	(	PUNCT
ejpam-5062	76	74	[	[	X
ejpam-5062	76	75	2	2	NUM
ejpam-5062	76	76	]	]	PUNCT
ejpam-5062	76	77	,	,	PUNCT
ejpam-5062	76	78	[	[	X
ejpam-5062	76	79	4	4	NUM
ejpam-5062	76	80	]	]	PUNCT
ejpam-5062	76	81	,	,	PUNCT
ejpam-5062	76	82	[	[	X
ejpam-5062	76	83	20	20	NUM
ejpam-5062	76	84	]	]	PUNCT
ejpam-5062	76	85	,	,	PUNCT
ejpam-5062	76	86	[	[	X
ejpam-5062	76	87	21	21	NUM
ejpam-5062	76	88	]	]	PUNCT
ejpam-5062	76	89	)	)	PUNCT
ejpam-5062	76	90	;	;	PUNCT
ejpam-5062	76	91	(	(	PUNCT
ejpam-5062	76	92	iii	iii	X
ejpam-5062	76	93	)	)	PUNCT
ejpam-5062	76	94	fuzzy	fuzzy	ADJ
ejpam-5062	76	95	strong	strong	ADJ
ejpam-5062	76	96	semi	semi	ADJ
ejpam-5062	76	97	pre	pre	ADJ
ejpam-5062	76	98	-	-	ADJ
ejpam-5062	76	99	continuous	continuous	ADJ
ejpam-5062	76	100	if	if	SCONJ
ejpam-5062	76	101	f−1(b	f−1(b	PROPN
ejpam-5062	76	102	)	)	PUNCT
ejpam-5062	76	103	∈	∈	PROPN
ejpam-5062	76	104	fsspo(τ	fsspo(τ	PROPN
ejpam-5062	76	105	)	)	PUNCT
ejpam-5062	76	106	for	for	ADP
ejpam-5062	76	107	every	every	DET
ejpam-5062	76	108	b	b	PROPN
ejpam-5062	76	109	∈	∈	PROPN
ejpam-5062	76	110	δ	δ	PROPN
ejpam-5062	76	111	(	(	PUNCT
ejpam-5062	76	112	[	[	X
ejpam-5062	76	113	17	17	NUM
ejpam-5062	76	114	]	]	NUM
ejpam-5062	76	115	)	)	PUNCT
ejpam-5062	76	116	;	;	PUNCT
ejpam-5062	76	117	(	(	PUNCT
ejpam-5062	76	118	iv	iv	X
ejpam-5062	76	119	)	)	PUNCT
ejpam-5062	76	120	fuzzy	fuzzy	ADJ
ejpam-5062	76	121	sspo	sspo	NOUN
ejpam-5062	76	122	-	-	PUNCT
ejpam-5062	76	123	irresolute	irresolute	ADJ
ejpam-5062	76	124	continuous	continuous	ADJ
ejpam-5062	76	125	if	if	SCONJ
ejpam-5062	76	126	f−1(b	f−1(b	PROPN
ejpam-5062	76	127	)	)	PUNCT
ejpam-5062	76	128	∈	∈	PROPN
ejpam-5062	76	129	fsspo(τ	fsspo(τ	PROPN
ejpam-5062	76	130	)	)	PUNCT
ejpam-5062	76	131	for	for	ADP
ejpam-5062	76	132	each	each	DET
ejpam-5062	76	133	b	b	PROPN
ejpam-5062	76	134	∈	∈	PROPN
ejpam-5062	76	135	fsspo(δ	fsspo(δ	PROPN
ejpam-5062	76	136	)	)	PUNCT
ejpam-5062	76	137	(	(	PUNCT
ejpam-5062	76	138	[	[	X
ejpam-5062	76	139	17	17	NUM
ejpam-5062	76	140	]	]	PUNCT
ejpam-5062	76	141	,	,	PUNCT
ejpam-5062	76	142	[	[	X
ejpam-5062	76	143	18	18	NUM
ejpam-5062	76	144	]	]	PUNCT
ejpam-5062	76	145	)	)	PUNCT
ejpam-5062	76	146	;	;	PUNCT
ejpam-5062	76	147	(	(	PUNCT
ejpam-5062	76	148	v	v	NOUN
ejpam-5062	76	149	)	)	PUNCT
ejpam-5062	76	150	fuzzy	fuzzy	ADJ
ejpam-5062	76	151	sspo	sspo	NOUN
ejpam-5062	76	152	homeomorphism	homeomorphism	PROPN
ejpam-5062	76	153	if	if	SCONJ
ejpam-5062	76	154	it	it	PRON
ejpam-5062	76	155	is	be	AUX
ejpam-5062	76	156	a	a	DET
ejpam-5062	76	157	bijective	bijective	ADJ
ejpam-5062	76	158	mapping	mapping	NOUN
ejpam-5062	76	159	and	and	CCONJ
ejpam-5062	76	160	if	if	SCONJ
ejpam-5062	76	161	the	the	DET
ejpam-5062	76	162	mapping	mapping	NOUN
ejpam-5062	76	163	f	f	PROPN
ejpam-5062	76	164	and	and	CCONJ
ejpam-5062	76	165	its	its	PRON
ejpam-5062	76	166	inverse	inverse	NOUN
ejpam-5062	76	167	are	be	AUX
ejpam-5062	76	168	both	both	PRON
ejpam-5062	76	169	fuzzy	fuzzy	ADJ
ejpam-5062	76	170	sspo	sspo	NOUN
ejpam-5062	76	171	−	−	PROPN
ejpam-5062	76	172	irresolute	irresolute	ADJ
ejpam-5062	76	173	continuous	continuous	ADJ
ejpam-5062	76	174	.	.	PUNCT
ejpam-5062	77	1	(	(	PUNCT
ejpam-5062	77	2	[	[	X
ejpam-5062	77	3	18	18	NUM
ejpam-5062	77	4	]	]	NUM
ejpam-5062	77	5	)	)	PUNCT
ejpam-5062	77	6	.	.	PUNCT
ejpam-5062	78	1	the	the	DET
ejpam-5062	78	2	concepts	concept	NOUN
ejpam-5062	78	3	of	of	ADP
ejpam-5062	78	4	fuzzy	fuzzy	ADJ
ejpam-5062	78	5	separation	separation	NOUN
ejpam-5062	78	6	axioms	axioms	ADJ
ejpam-5062	78	7	ft0	ft0	NOUN
ejpam-5062	78	8	(	(	PUNCT
ejpam-5062	78	9	ft1	ft1	PROPN
ejpam-5062	78	10	,	,	PUNCT
ejpam-5062	78	11	fts	fts	PROPN
ejpam-5062	78	12	,	,	PUNCT
ejpam-5062	78	13	ft2	ft2	PROPN
ejpam-5062	78	14	,	,	PUNCT
ejpam-5062	78	15	ft2	ft2	NOUN
ejpam-5062	78	16	1	1	NUM
ejpam-5062	78	17	2	2	NUM
ejpam-5062	78	18	,	,	PUNCT
ejpam-5062	78	19	fr	fr	PROPN
ejpam-5062	78	20	,	,	PUNCT
ejpam-5062	78	21	ft3	ft3	PROPN
ejpam-5062	78	22	,	,	PUNCT
ejpam-5062	78	23	fn	fn	PROPN
ejpam-5062	78	24	,	,	PUNCT
ejpam-5062	78	25	ft4	ft4	PROPN
ejpam-5062	78	26	)	)	PUNCT
ejpam-5062	78	27	will	will	AUX
ejpam-5062	78	28	be	be	AUX
ejpam-5062	78	29	based	base	VERB
ejpam-5062	78	30	on	on	ADP
ejpam-5062	78	31	definitions	definition	NOUN
ejpam-5062	78	32	given	give	VERB
ejpam-5062	78	33	in	in	ADP
ejpam-5062	78	34	[	[	X
ejpam-5062	78	35	6	6	NUM
ejpam-5062	78	36	]	]	PUNCT
ejpam-5062	78	37	.	.	PUNCT
ejpam-5062	79	1	the	the	DET
ejpam-5062	79	2	concepts	concept	NOUN
ejpam-5062	79	3	of	of	ADP
ejpam-5062	79	4	α	α	NOUN
ejpam-5062	79	5	−	−	NOUN
ejpam-5062	79	6	shading	shading	NOUN
ejpam-5062	79	7	(	(	PUNCT
ejpam-5062	79	8	α∗	α∗	NOUN
ejpam-5062	79	9	−	−	NOUN
ejpam-5062	79	10	shading	shading	NOUN
ejpam-5062	79	11	)	)	PUNCT
ejpam-5062	79	12	,	,	PUNCT
ejpam-5062	79	13	α	α	PROPN
ejpam-5062	79	14	−	−	NOUN
ejpam-5062	79	15	subshading	subshade	VERB
ejpam-5062	79	16	(	(	PUNCT
ejpam-5062	79	17	α∗	α∗	NOUN
ejpam-5062	79	18	−	−	NOUN
ejpam-5062	79	19	subshading	subshading	NOUN
ejpam-5062	79	20	)	)	PUNCT
ejpam-5062	79	21	and	and	CCONJ
ejpam-5062	79	22	α−	α−	ADP
ejpam-5062	79	23	compact	compact	ADJ
ejpam-5062	79	24	(	(	PUNCT
ejpam-5062	79	25	α∗	α∗	NOUN
ejpam-5062	79	26	−	−	NOUN
ejpam-5062	79	27	compact	compact	ADJ
ejpam-5062	79	28	)	)	PUNCT
ejpam-5062	79	29	will	will	AUX
ejpam-5062	79	30	be	be	AUX
ejpam-5062	79	31	based	base	VERB
ejpam-5062	79	32	on	on	ADP
ejpam-5062	79	33	the	the	DET
ejpam-5062	79	34	definitions	definition	NOUN
ejpam-5062	79	35	given	give	VERB
ejpam-5062	79	36	in	in	ADP
ejpam-5062	79	37	(	(	PUNCT
ejpam-5062	79	38	[	[	X
ejpam-5062	79	39	5	5	NUM
ejpam-5062	79	40	]	]	PUNCT
ejpam-5062	79	41	,	,	PUNCT
ejpam-5062	79	42	[	[	X
ejpam-5062	79	43	13	13	NUM
ejpam-5062	79	44	]	]	PUNCT
ejpam-5062	79	45	,	,	PUNCT
ejpam-5062	79	46	[	[	X
ejpam-5062	79	47	19	19	NUM
ejpam-5062	79	48	]	]	NUM
ejpam-5062	79	49	)	)	PUNCT
ejpam-5062	79	50	.	.	PUNCT
ejpam-5062	80	1	sh	sh	PROPN
ejpam-5062	80	2	.	.	PROPN
ejpam-5062	80	3	makolli	makolli	PROPN
ejpam-5062	80	4	,	,	PUNCT
ejpam-5062	80	5	b.	b.	PROPN
ejpam-5062	80	6	krsteska	krsteska	PROPN
ejpam-5062	80	7	/	/	SYM
ejpam-5062	80	8	eur	eur	PROPN
ejpam-5062	80	9	.	.	PUNCT
ejpam-5062	81	1	j.	j.	PROPN
ejpam-5062	81	2	pure	pure	PROPN
ejpam-5062	81	3	appl	appl	PROPN
ejpam-5062	81	4	.	.	PROPN
ejpam-5062	81	5	math	math	PROPN
ejpam-5062	81	6	,	,	PUNCT
ejpam-5062	81	7	17	17	NUM
ejpam-5062	81	8	(	(	PUNCT
ejpam-5062	81	9	2	2	NUM
ejpam-5062	81	10	)	)	PUNCT
ejpam-5062	81	11	(	(	PUNCT
ejpam-5062	81	12	2024	2024	NUM
ejpam-5062	81	13	)	)	PUNCT
ejpam-5062	81	14	,	,	PUNCT
ejpam-5062	81	15	638	638	NUM
ejpam-5062	81	16	-	-	SYM
ejpam-5062	81	17	662	662	NUM
ejpam-5062	81	18	642	642	NUM
ejpam-5062	81	19	definition	definition	NOUN
ejpam-5062	81	20	9	9	NUM
ejpam-5062	81	21	.	.	PUNCT
ejpam-5062	82	1	[	[	X
ejpam-5062	82	2	5	5	NUM
ejpam-5062	82	3	]	]	X
ejpam-5062	82	4	let	let	VERB
ejpam-5062	82	5	(	(	PUNCT
ejpam-5062	82	6	x	x	NOUN
ejpam-5062	82	7	,	,	PUNCT
ejpam-5062	82	8	τ	τ	X
ejpam-5062	82	9	)	)	PUNCT
ejpam-5062	82	10	be	be	VERB
ejpam-5062	82	11	a	a	DET
ejpam-5062	82	12	fuzzy	fuzzy	ADJ
ejpam-5062	82	13	topological	topological	ADJ
ejpam-5062	82	14	space	space	NOUN
ejpam-5062	82	15	and	and	CCONJ
ejpam-5062	82	16	let	let	VERB
ejpam-5062	82	17	α	α	PRON
ejpam-5062	82	18	∈	∈	PROPN
ejpam-5062	83	1	[	[	X
ejpam-5062	83	2	0	0	NUM
ejpam-5062	83	3	,	,	PUNCT
ejpam-5062	83	4	1	1	NUM
ejpam-5062	83	5	]	]	PUNCT
ejpam-5062	83	6	.	.	PUNCT
ejpam-5062	84	1	a	a	DET
ejpam-5062	84	2	collection	collection	NOUN
ejpam-5062	84	3	f	f	NOUN
ejpam-5062	84	4	of	of	ADP
ejpam-5062	84	5	fuzzy	fuzzy	ADJ
ejpam-5062	84	6	sets	set	NOUN
ejpam-5062	84	7	of	of	ADP
ejpam-5062	84	8	x	x	SYM
ejpam-5062	84	9	is	be	AUX
ejpam-5062	84	10	called	call	VERB
ejpam-5062	84	11	α	α	PRON
ejpam-5062	84	12	−	−	ADV
ejpam-5062	84	13	centered	center	VERB
ejpam-5062	84	14	(	(	PUNCT
ejpam-5062	84	15	α∗	α∗	NOUN
ejpam-5062	84	16	−	−	NOUN
ejpam-5062	84	17	centered	center	VERB
ejpam-5062	84	18	)	)	PUNCT
ejpam-5062	84	19	if	if	SCONJ
ejpam-5062	84	20	for	for	ADP
ejpam-5062	84	21	every	every	DET
ejpam-5062	84	22	finite	finite	ADJ
ejpam-5062	84	23	subcollection	subcollection	NOUN
ejpam-5062	84	24	u	u	PROPN
ejpam-5062	84	25	of	of	ADP
ejpam-5062	84	26	f	f	PROPN
ejpam-5062	84	27	,	,	PUNCT
ejpam-5062	84	28	there	there	PRON
ejpam-5062	84	29	exist	exist	VERB
ejpam-5062	84	30	x	x	X
ejpam-5062	84	31	∈	∈	PROPN
ejpam-5062	84	32	x	x	PUNCT
ejpam-5062	84	33	such	such	ADJ
ejpam-5062	84	34	that	that	SCONJ
ejpam-5062	84	35	u(x	u(x	PROPN
ejpam-5062	84	36	)	)	PUNCT
ejpam-5062	84	37	≥	≥	NOUN
ejpam-5062	84	38	1−	1−	NUM
ejpam-5062	84	39	α	α	NOUN
ejpam-5062	84	40	(	(	PUNCT
ejpam-5062	84	41	respectively	respectively	ADV
ejpam-5062	84	42	u(x	u(x	NOUN
ejpam-5062	84	43	)	)	PUNCT
ejpam-5062	84	44	>	>	X
ejpam-5062	85	1	1−	1−	NUM
ejpam-5062	85	2	α	α	NOUN
ejpam-5062	85	3	)	)	PUNCT
ejpam-5062	85	4	,	,	PUNCT
ejpam-5062	85	5	for	for	ADP
ejpam-5062	85	6	every	every	DET
ejpam-5062	85	7	u	u	PROPN
ejpam-5062	85	8	∈	∈	PROPN
ejpam-5062	85	9	u	u	NOUN
ejpam-5062	85	10	.	.	PUNCT
ejpam-5062	86	1	definition	definition	NOUN
ejpam-5062	86	2	10	10	NUM
ejpam-5062	86	3	.	.	PUNCT
ejpam-5062	87	1	[	[	X
ejpam-5062	87	2	30	30	NUM
ejpam-5062	87	3	]	]	X
ejpam-5062	87	4	a	a	DET
ejpam-5062	87	5	fuzzy	fuzzy	ADJ
ejpam-5062	87	6	topological	topological	ADJ
ejpam-5062	87	7	space	space	NOUN
ejpam-5062	87	8	x	x	PUNCT
ejpam-5062	87	9	is	be	AUX
ejpam-5062	87	10	called	call	VERB
ejpam-5062	87	11	fuzzy	fuzzy	ADJ
ejpam-5062	87	12	separable	separable	NOUN
ejpam-5062	87	13	if	if	SCONJ
ejpam-5062	87	14	there	there	PRON
ejpam-5062	87	15	exists	exist	VERB
ejpam-5062	87	16	a	a	DET
ejpam-5062	87	17	countable	countable	ADJ
ejpam-5062	87	18	sequence	sequence	NOUN
ejpam-5062	87	19	of	of	ADP
ejpam-5062	87	20	fuzzy	fuzzy	ADJ
ejpam-5062	87	21	points	point	NOUN
ejpam-5062	87	22	{	{	PUNCT
ejpam-5062	87	23	xi}i∈n	xi}i∈n	X
ejpam-5062	87	24	such	such	ADJ
ejpam-5062	87	25	that	that	PRON
ejpam-5062	87	26	for	for	ADP
ejpam-5062	87	27	each	each	DET
ejpam-5062	87	28	fuzzy	fuzzy	ADJ
ejpam-5062	87	29	open	open	NOUN
ejpam-5062	87	30	set	set	VERB
ejpam-5062	87	31	a	a	DET
ejpam-5062	87	32	̸=	̸=	PROPN
ejpam-5062	87	33	0x	0x	NOUN
ejpam-5062	87	34	,	,	PUNCT
ejpam-5062	87	35	there	there	PRON
ejpam-5062	87	36	exists	exist	VERB
ejpam-5062	87	37	xi	xi	X
ejpam-5062	87	38	∈	∈	PROPN
ejpam-5062	87	39	a.	a.	NOUN
ejpam-5062	87	40	3	3	NUM
ejpam-5062	87	41	.	.	PUNCT
ejpam-5062	88	1	axioms	axiom	NOUN
ejpam-5062	88	2	of	of	ADP
ejpam-5062	88	3	fuzzy	fuzzy	ADJ
ejpam-5062	88	4	strong	strong	ADJ
ejpam-5062	88	5	semi	semi	ADJ
ejpam-5062	88	6	pre	pre	NOUN
ejpam-5062	88	7	-	-	NOUN
ejpam-5062	88	8	separation	separation	NOUN
ejpam-5062	88	9	initially	initially	ADV
ejpam-5062	88	10	,	,	PUNCT
ejpam-5062	88	11	we	we	PRON
ejpam-5062	88	12	will	will	AUX
ejpam-5062	88	13	define	define	VERB
ejpam-5062	88	14	the	the	DET
ejpam-5062	88	15	axioms	axiom	NOUN
ejpam-5062	88	16	of	of	ADP
ejpam-5062	88	17	fuzzy	fuzzy	ADJ
ejpam-5062	88	18	strong	strong	ADJ
ejpam-5062	88	19	semi	semi	ADJ
ejpam-5062	88	20	pre	pre	NOUN
ejpam-5062	88	21	-	-	NOUN
ejpam-5062	88	22	separation	separation	NOUN
ejpam-5062	88	23	.	.	PUNCT
ejpam-5062	89	1	definition	definition	NOUN
ejpam-5062	89	2	11	11	NUM
ejpam-5062	89	3	.	.	PUNCT
ejpam-5062	90	1	a	a	DET
ejpam-5062	90	2	fuzzy	fuzzy	ADJ
ejpam-5062	90	3	topological	topological	ADJ
ejpam-5062	90	4	space	space	NOUN
ejpam-5062	90	5	x	x	PUNCT
ejpam-5062	90	6	is	be	AUX
ejpam-5062	90	7	a	a	DET
ejpam-5062	90	8	fuzzy	fuzzy	ADJ
ejpam-5062	90	9	strong	strong	ADJ
ejpam-5062	90	10	semi	semi	ADJ
ejpam-5062	90	11	pre	pre	ADJ
ejpam-5062	90	12	-	-	ADJ
ejpam-5062	90	13	t0	t0	NOUN
ejpam-5062	90	14	(	(	PUNCT
ejpam-5062	90	15	or	or	CCONJ
ejpam-5062	90	16	short	short	ADJ
ejpam-5062	90	17	fsspt0	fsspt0	NOUN
ejpam-5062	90	18	)	)	PUNCT
ejpam-5062	90	19	if	if	SCONJ
ejpam-5062	90	20	and	and	CCONJ
ejpam-5062	90	21	only	only	ADV
ejpam-5062	90	22	if	if	SCONJ
ejpam-5062	90	23	for	for	ADP
ejpam-5062	90	24	every	every	DET
ejpam-5062	90	25	pair	pair	NOUN
ejpam-5062	90	26	of	of	ADP
ejpam-5062	90	27	fuzzy	fuzzy	ADJ
ejpam-5062	90	28	points	point	NOUN
ejpam-5062	90	29	p1	p1	NOUN
ejpam-5062	90	30	and	and	CCONJ
ejpam-5062	90	31	p2	p2	NOUN
ejpam-5062	90	32	with	with	ADP
ejpam-5062	90	33	different	different	ADJ
ejpam-5062	90	34	supports	support	NOUN
ejpam-5062	90	35	,	,	PUNCT
ejpam-5062	90	36	there	there	PRON
ejpam-5062	90	37	exists	exist	VERB
ejpam-5062	90	38	a	a	DET
ejpam-5062	90	39	fuzzy	fuzzy	ADJ
ejpam-5062	90	40	strongly	strongly	ADV
ejpam-5062	90	41	semi	semi	ADV
ejpam-5062	90	42	pre	pre	ADJ
ejpam-5062	90	43	-	-	ADJ
ejpam-5062	90	44	open	open	ADJ
ejpam-5062	90	45	set	set	ADJ
ejpam-5062	90	46	o	o	NOUN
ejpam-5062	90	47	such	such	ADJ
ejpam-5062	90	48	that	that	DET
ejpam-5062	90	49	p1	p1	PROPN
ejpam-5062	90	50	≤	≤	X
ejpam-5062	90	51	o	o	NOUN
ejpam-5062	90	52	≤	≤	NOUN
ejpam-5062	90	53	pc2	pc2	NOUN
ejpam-5062	90	54	or	or	CCONJ
ejpam-5062	90	55	p2	p2	PROPN
ejpam-5062	90	56	≤	≤	NUM
ejpam-5062	90	57	o	o	NOUN
ejpam-5062	90	58	≤	≤	NUM
ejpam-5062	90	59	pc1	pc1	PROPN
ejpam-5062	90	60	.	.	PUNCT
ejpam-5062	91	1	it	it	PRON
ejpam-5062	91	2	follows	follow	VERB
ejpam-5062	91	3	directly	directly	ADV
ejpam-5062	91	4	from	from	ADP
ejpam-5062	91	5	the	the	DET
ejpam-5062	91	6	definition	definition	NOUN
ejpam-5062	91	7	11	11	NUM
ejpam-5062	91	8	and	and	CCONJ
ejpam-5062	91	9	[	[	X
ejpam-5062	91	10	6	6	NUM
ejpam-5062	91	11	]	]	PUNCT
ejpam-5062	91	12	that	that	SCONJ
ejpam-5062	91	13	every	every	DET
ejpam-5062	91	14	ft0	ft0	NOUN
ejpam-5062	91	15	space	space	NOUN
ejpam-5062	91	16	is	be	AUX
ejpam-5062	91	17	also	also	ADV
ejpam-5062	91	18	an	an	DET
ejpam-5062	91	19	fsspt0	fsspt0	NOUN
ejpam-5062	91	20	while	while	SCONJ
ejpam-5062	91	21	the	the	DET
ejpam-5062	91	22	converse	converse	NOUN
ejpam-5062	91	23	is	be	AUX
ejpam-5062	91	24	not	not	PART
ejpam-5062	91	25	true	true	ADJ
ejpam-5062	91	26	in	in	ADP
ejpam-5062	91	27	general	general	ADJ
ejpam-5062	91	28	.	.	PUNCT
ejpam-5062	92	1	we	we	PRON
ejpam-5062	92	2	will	will	AUX
ejpam-5062	92	3	give	give	VERB
ejpam-5062	92	4	the	the	DET
ejpam-5062	92	5	following	follow	VERB
ejpam-5062	92	6	example	example	NOUN
ejpam-5062	92	7	to	to	PART
ejpam-5062	92	8	illustrate	illustrate	VERB
ejpam-5062	92	9	this	this	DET
ejpam-5062	92	10	fact	fact	NOUN
ejpam-5062	92	11	.	.	PUNCT
ejpam-5062	93	1	example	example	NOUN
ejpam-5062	93	2	1	1	NUM
ejpam-5062	93	3	.	.	PUNCT
ejpam-5062	94	1	given	give	VERB
ejpam-5062	94	2	a	a	DET
ejpam-5062	94	3	set	set	NOUN
ejpam-5062	94	4	x	x	X
ejpam-5062	94	5	=	=	SYM
ejpam-5062	94	6	{	{	PUNCT
ejpam-5062	94	7	p1	p1	NOUN
ejpam-5062	94	8	,	,	PUNCT
ejpam-5062	94	9	p2	p2	NOUN
ejpam-5062	94	10	}	}	PUNCT
ejpam-5062	94	11	,	,	PUNCT
ejpam-5062	94	12	fuzzy	fuzzy	ADJ
ejpam-5062	94	13	set	set	VERB
ejpam-5062	94	14	u	u	NOUN
ejpam-5062	94	15	=	=	PRON
ejpam-5062	94	16	{	{	PUNCT
ejpam-5062	94	17	(	(	PUNCT
ejpam-5062	94	18	p1	p1	NOUN
ejpam-5062	94	19	,	,	PUNCT
ejpam-5062	94	20	0	0	NUM
ejpam-5062	94	21	)	)	PUNCT
ejpam-5062	94	22	,	,	PUNCT
ejpam-5062	94	23	(	(	PUNCT
ejpam-5062	94	24	p2	p2	X
ejpam-5062	94	25	,	,	PUNCT
ejpam-5062	94	26	0.6	0.6	NUM
ejpam-5062	94	27	)	)	PUNCT
ejpam-5062	94	28	}	}	PUNCT
ejpam-5062	94	29	and	and	CCONJ
ejpam-5062	94	30	fts	fts	PROPN
ejpam-5062	94	31	τ	τ	X
ejpam-5062	94	32	=	=	PUNCT
ejpam-5062	94	33	{	{	PUNCT
ejpam-5062	94	34	0	0	NUM
ejpam-5062	94	35	,	,	PUNCT
ejpam-5062	94	36	u	u	NOUN
ejpam-5062	94	37	,	,	PUNCT
ejpam-5062	94	38	1	1	NUM
ejpam-5062	94	39	}	}	PUNCT
ejpam-5062	94	40	.	.	PUNCT
ejpam-5062	95	1	it	it	PRON
ejpam-5062	95	2	is	be	AUX
ejpam-5062	95	3	obvious	obvious	ADJ
ejpam-5062	95	4	that	that	SCONJ
ejpam-5062	95	5	the	the	DET
ejpam-5062	95	6	fts	fts	PROPN
ejpam-5062	95	7	is	be	AUX
ejpam-5062	95	8	not	not	PART
ejpam-5062	95	9	ft0	ft0	NOUN
ejpam-5062	96	1	but	but	CCONJ
ejpam-5062	96	2	it	it	PRON
ejpam-5062	96	3	is	be	AUX
ejpam-5062	96	4	an	an	DET
ejpam-5062	96	5	fsspt0	fsspt0	NOUN
ejpam-5062	96	6	since	since	SCONJ
ejpam-5062	96	7	for	for	ADP
ejpam-5062	96	8	o	o	PROPN
ejpam-5062	96	9	=	=	SYM
ejpam-5062	96	10	{	{	PUNCT
ejpam-5062	96	11	(	(	PUNCT
ejpam-5062	96	12	p1	p1	NOUN
ejpam-5062	96	13	,	,	PUNCT
ejpam-5062	96	14	0	0	NUM
ejpam-5062	96	15	)	)	PUNCT
ejpam-5062	96	16	,	,	PUNCT
ejpam-5062	96	17	(	(	PUNCT
ejpam-5062	96	18	p2	p2	X
ejpam-5062	96	19	,	,	PUNCT
ejpam-5062	96	20	1	1	NUM
ejpam-5062	96	21	)	)	PUNCT
ejpam-5062	96	22	}	}	PUNCT
ejpam-5062	96	23	,	,	PUNCT
ejpam-5062	96	24	o	o	PROPN
ejpam-5062	96	25	∈	∈	PROPN
ejpam-5062	96	26	fsspo(τ	fsspo(τ	PROPN
ejpam-5062	96	27	)	)	PUNCT
ejpam-5062	96	28	it	it	PRON
ejpam-5062	96	29	follows	follow	VERB
ejpam-5062	96	30	that	that	SCONJ
ejpam-5062	96	31	p2	p2	VERB
ejpam-5062	96	32	≤	≤	NUM
ejpam-5062	96	33	o	o	NOUN
ejpam-5062	96	34	≤	≤	PROPN
ejpam-5062	96	35	pc1	pc1	PROPN
ejpam-5062	96	36	.	.	PUNCT
ejpam-5062	97	1	theorem	theorem	NOUN
ejpam-5062	97	2	1	1	NUM
ejpam-5062	97	3	.	.	PUNCT
ejpam-5062	98	1	if	if	SCONJ
ejpam-5062	98	2	the	the	DET
ejpam-5062	98	3	fuzzy	fuzzy	ADJ
ejpam-5062	98	4	topological	topological	ADJ
ejpam-5062	98	5	space	space	NOUN
ejpam-5062	98	6	x	x	PUNCT
ejpam-5062	98	7	is	be	AUX
ejpam-5062	98	8	an	an	DET
ejpam-5062	98	9	fsspt0	fsspt0	NOUN
ejpam-5062	98	10	,	,	PUNCT
ejpam-5062	98	11	and	and	CCONJ
ejpam-5062	98	12	given	give	VERB
ejpam-5062	98	13	any	any	DET
ejpam-5062	98	14	pair	pair	NOUN
ejpam-5062	98	15	of	of	ADP
ejpam-5062	98	16	fuzzy	fuzzy	ADJ
ejpam-5062	98	17	singletons	singleton	NOUN
ejpam-5062	98	18	p1	p1	NOUN
ejpam-5062	98	19	and	and	CCONJ
ejpam-5062	98	20	p2	p2	NOUN
ejpam-5062	98	21	with	with	ADP
ejpam-5062	98	22	different	different	ADJ
ejpam-5062	98	23	supports	support	NOUN
ejpam-5062	98	24	,	,	PUNCT
ejpam-5062	98	25	then	then	ADV
ejpam-5062	98	26	sspclp1	sspclp1	PROPN
ejpam-5062	98	27	̸=	̸=	PROPN
ejpam-5062	98	28	sspclp2	sspclp2	NOUN
ejpam-5062	98	29	.	.	PUNCT
ejpam-5062	99	1	proof	proof	NOUN
ejpam-5062	99	2	.	.	PUNCT
ejpam-5062	100	1	since	since	SCONJ
ejpam-5062	100	2	the	the	DET
ejpam-5062	100	3	fuzzy	fuzzy	ADJ
ejpam-5062	100	4	topological	topological	ADJ
ejpam-5062	100	5	space	space	NOUN
ejpam-5062	100	6	(	(	PUNCT
ejpam-5062	100	7	x	x	X
ejpam-5062	100	8	,	,	PUNCT
ejpam-5062	100	9	τ	τ	X
ejpam-5062	100	10	)	)	PUNCT
ejpam-5062	100	11	is	be	AUX
ejpam-5062	100	12	an	an	DET
ejpam-5062	100	13	fsspt0	fsspt0	NOUN
ejpam-5062	100	14	,	,	PUNCT
ejpam-5062	100	15	then	then	ADV
ejpam-5062	100	16	given	give	VERB
ejpam-5062	100	17	two	two	NUM
ejpam-5062	100	18	fuzzy	fuzzy	ADJ
ejpam-5062	100	19	singletons	singleton	NOUN
ejpam-5062	100	20	p1	p1	NOUN
ejpam-5062	100	21	and	and	CCONJ
ejpam-5062	100	22	p2	p2	NOUN
ejpam-5062	100	23	with	with	ADP
ejpam-5062	100	24	different	different	ADJ
ejpam-5062	100	25	support	support	NOUN
ejpam-5062	100	26	,	,	PUNCT
ejpam-5062	100	27	it	it	PRON
ejpam-5062	100	28	is	be	AUX
ejpam-5062	100	29	obvious	obvious	ADJ
ejpam-5062	100	30	that	that	SCONJ
ejpam-5062	100	31	there	there	PRON
ejpam-5062	100	32	exist	exist	VERB
ejpam-5062	100	33	a	a	DET
ejpam-5062	100	34	set	set	NOUN
ejpam-5062	100	35	o	o	X
ejpam-5062	100	36	∈	∈	PROPN
ejpam-5062	100	37	fsspo(τ	fsspo(τ	PROPN
ejpam-5062	100	38	)	)	PUNCT
ejpam-5062	100	39	,	,	PUNCT
ejpam-5062	100	40	such	such	ADJ
ejpam-5062	100	41	that	that	DET
ejpam-5062	100	42	p1	p1	PROPN
ejpam-5062	100	43	≤	≤	X
ejpam-5062	100	44	o	o	NOUN
ejpam-5062	100	45	≤	≤	NUM
ejpam-5062	100	46	pc2	pc2	NOUN
ejpam-5062	100	47	.	.	PUNCT
ejpam-5062	101	1	if	if	SCONJ
ejpam-5062	101	2	we	we	PRON
ejpam-5062	101	3	use	use	VERB
ejpam-5062	101	4	the	the	DET
ejpam-5062	101	5	fact	fact	NOUN
ejpam-5062	101	6	that	that	SCONJ
ejpam-5062	101	7	sspclp2	sspclp2	VERB
ejpam-5062	101	8	≤	≤	PUNCT
ejpam-5062	101	9	oc	oc	NOUN
ejpam-5062	101	10	and	and	CCONJ
ejpam-5062	101	11	since	since	SCONJ
ejpam-5062	101	12	p1	p1	PROPN
ejpam-5062	101	13	≰	≰	PROPN
ejpam-5062	101	14	oc	oc	VERB
ejpam-5062	101	15	,	,	PUNCT
ejpam-5062	101	16	it	it	PRON
ejpam-5062	101	17	follows	follow	VERB
ejpam-5062	101	18	that	that	SCONJ
ejpam-5062	101	19	sspclp1	sspclp1	PROPN
ejpam-5062	101	20	̸=	̸=	PROPN
ejpam-5062	101	21	sspclp2	sspclp2	NOUN
ejpam-5062	101	22	.	.	PUNCT
ejpam-5062	102	1	if	if	SCONJ
ejpam-5062	102	2	we	we	PRON
ejpam-5062	102	3	refer	refer	VERB
ejpam-5062	102	4	to	to	ADP
ejpam-5062	102	5	example	example	NOUN
ejpam-5062	102	6	1	1	NUM
ejpam-5062	102	7	,	,	PUNCT
ejpam-5062	102	8	it	it	PRON
ejpam-5062	102	9	is	be	AUX
ejpam-5062	102	10	obvious	obvious	ADJ
ejpam-5062	102	11	that	that	SCONJ
ejpam-5062	102	12	sspclp1	sspclp1	PROPN
ejpam-5062	102	13	≤	≤	X
ejpam-5062	102	14	{	{	PUNCT
ejpam-5062	102	15	(	(	PUNCT
ejpam-5062	102	16	p1	p1	NOUN
ejpam-5062	102	17	,	,	PUNCT
ejpam-5062	102	18	1	1	NUM
ejpam-5062	102	19	)	)	PUNCT
ejpam-5062	102	20	,	,	PUNCT
ejpam-5062	102	21	(	(	PUNCT
ejpam-5062	102	22	p2	p2	PROPN
ejpam-5062	102	23	,	,	PUNCT
ejpam-5062	102	24	0.4	0.4	NUM
ejpam-5062	102	25	)	)	PUNCT
ejpam-5062	102	26	}	}	PUNCT
ejpam-5062	102	27	while	while	SCONJ
ejpam-5062	102	28	sspclp2	sspclp2	NOUN
ejpam-5062	102	29	=	=	SYM
ejpam-5062	102	30	1x	1x	NUM
ejpam-5062	102	31	,	,	PUNCT
ejpam-5062	102	32	that	that	PRON
ejpam-5062	102	33	is	be	AUX
ejpam-5062	102	34	sspclp1	sspclp1	PROPN
ejpam-5062	102	35	̸=	̸=	PROPN
ejpam-5062	102	36	sspclp2	sspclp2	NOUN
ejpam-5062	102	37	.	.	PUNCT
ejpam-5062	103	1	definition	definition	NOUN
ejpam-5062	103	2	12	12	NUM
ejpam-5062	103	3	.	.	PUNCT
ejpam-5062	104	1	a	a	DET
ejpam-5062	104	2	fuzzy	fuzzy	ADJ
ejpam-5062	104	3	topological	topological	ADJ
ejpam-5062	104	4	space	space	NOUN
ejpam-5062	104	5	x	x	PUNCT
ejpam-5062	104	6	is	be	AUX
ejpam-5062	104	7	a	a	DET
ejpam-5062	104	8	fuzzy	fuzzy	ADJ
ejpam-5062	104	9	strong	strong	ADJ
ejpam-5062	104	10	semi	semi	ADJ
ejpam-5062	104	11	pre	pre	NOUN
ejpam-5062	104	12	-	-	NOUN
ejpam-5062	104	13	t1	t1	NOUN
ejpam-5062	104	14	(	(	PUNCT
ejpam-5062	104	15	or	or	CCONJ
ejpam-5062	104	16	short	short	ADJ
ejpam-5062	104	17	fsspt1	fsspt1	NOUN
ejpam-5062	104	18	)	)	PUNCT
ejpam-5062	104	19	if	if	SCONJ
ejpam-5062	104	20	and	and	CCONJ
ejpam-5062	104	21	only	only	ADV
ejpam-5062	104	22	if	if	SCONJ
ejpam-5062	104	23	for	for	ADP
ejpam-5062	104	24	any	any	DET
ejpam-5062	104	25	pair	pair	NOUN
ejpam-5062	104	26	of	of	ADP
ejpam-5062	104	27	fuzzy	fuzzy	ADJ
ejpam-5062	104	28	points	point	NOUN
ejpam-5062	104	29	p1	p1	NOUN
ejpam-5062	104	30	and	and	CCONJ
ejpam-5062	104	31	p2	p2	PROPN
ejpam-5062	104	32	which	which	PRON
ejpam-5062	104	33	have	have	VERB
ejpam-5062	104	34	different	different	ADJ
ejpam-5062	104	35	supports	support	NOUN
ejpam-5062	104	36	,	,	PUNCT
ejpam-5062	104	37	there	there	PRON
ejpam-5062	104	38	exist	exist	VERB
ejpam-5062	104	39	fuzzy	fuzzy	ADJ
ejpam-5062	104	40	strongly	strongly	ADV
ejpam-5062	104	41	semi	semi	ADV
ejpam-5062	104	42	pre	pre	ADJ
ejpam-5062	104	43	-	-	ADJ
ejpam-5062	104	44	open	open	ADJ
ejpam-5062	104	45	sets	set	NOUN
ejpam-5062	104	46	o1	o1	NOUN
ejpam-5062	104	47	,	,	PUNCT
ejpam-5062	104	48	o2	o2	PROPN
ejpam-5062	104	49	such	such	ADJ
ejpam-5062	104	50	that	that	DET
ejpam-5062	104	51	p1	p1	PROPN
ejpam-5062	104	52	≤	≤	NUM
ejpam-5062	104	53	o1	o1	NOUN
ejpam-5062	104	54	≤	≤	NOUN
ejpam-5062	104	55	pc2	pc2	NOUN
ejpam-5062	104	56	and	and	CCONJ
ejpam-5062	104	57	p2	p2	PROPN
ejpam-5062	104	58	≤	≤	NUM
ejpam-5062	104	59	o2	o2	PROPN
ejpam-5062	104	60	≤	≤	PROPN
ejpam-5062	104	61	pc1	pc1	PROPN
ejpam-5062	104	62	.	.	PUNCT
ejpam-5062	105	1	we	we	PRON
ejpam-5062	105	2	can	can	AUX
ejpam-5062	105	3	formulate	formulate	VERB
ejpam-5062	105	4	and	and	CCONJ
ejpam-5062	105	5	prove	prove	VERB
ejpam-5062	105	6	the	the	DET
ejpam-5062	105	7	following	follow	VERB
ejpam-5062	105	8	theorem	theorem	NOUN
ejpam-5062	105	9	which	which	PRON
ejpam-5062	105	10	gives	give	VERB
ejpam-5062	105	11	some	some	DET
ejpam-5062	105	12	characteristic	characteristic	ADJ
ejpam-5062	105	13	properties	property	NOUN
ejpam-5062	105	14	for	for	ADP
ejpam-5062	105	15	fsspt1	fsspt1	NOUN
ejpam-5062	105	16	spaces	space	NOUN
ejpam-5062	105	17	.	.	PUNCT
ejpam-5062	106	1	theorem	theorem	NOUN
ejpam-5062	106	2	2	2	NUM
ejpam-5062	106	3	.	.	PUNCT
ejpam-5062	107	1	the	the	DET
ejpam-5062	107	2	fuzzy	fuzzy	ADJ
ejpam-5062	107	3	topological	topological	ADJ
ejpam-5062	107	4	space	space	NOUN
ejpam-5062	107	5	x	x	PRON
ejpam-5062	107	6	is	be	AUX
ejpam-5062	107	7	an	an	DET
ejpam-5062	107	8	fsspt1	fsspt1	NOUN
ejpam-5062	107	9	space	space	NOUN
ejpam-5062	107	10	if	if	SCONJ
ejpam-5062	107	11	and	and	CCONJ
ejpam-5062	107	12	only	only	ADV
ejpam-5062	107	13	if	if	SCONJ
ejpam-5062	107	14	each	each	DET
ejpam-5062	107	15	fuzzy	fuzzy	ADJ
ejpam-5062	107	16	singleton	singleton	NOUN
ejpam-5062	107	17	is	be	AUX
ejpam-5062	107	18	a	a	DET
ejpam-5062	107	19	fuzzy	fuzzy	ADJ
ejpam-5062	107	20	strongly	strongly	ADV
ejpam-5062	107	21	semi	semi	ADV
ejpam-5062	107	22	pre	pre	ADJ
ejpam-5062	107	23	-	-	ADJ
ejpam-5062	107	24	closed	closed	ADJ
ejpam-5062	107	25	set	set	NOUN
ejpam-5062	107	26	.	.	PUNCT
ejpam-5062	108	1	sh	sh	PROPN
ejpam-5062	108	2	.	.	PROPN
ejpam-5062	108	3	makolli	makolli	PROPN
ejpam-5062	108	4	,	,	PUNCT
ejpam-5062	108	5	b.	b.	PROPN
ejpam-5062	108	6	krsteska	krsteska	PROPN
ejpam-5062	108	7	/	/	SYM
ejpam-5062	108	8	eur	eur	PROPN
ejpam-5062	108	9	.	.	PUNCT
ejpam-5062	109	1	j.	j.	PROPN
ejpam-5062	109	2	pure	pure	PROPN
ejpam-5062	109	3	appl	appl	PROPN
ejpam-5062	109	4	.	.	PROPN
ejpam-5062	109	5	math	math	PROPN
ejpam-5062	109	6	,	,	PUNCT
ejpam-5062	109	7	17	17	NUM
ejpam-5062	109	8	(	(	PUNCT
ejpam-5062	109	9	2	2	NUM
ejpam-5062	109	10	)	)	PUNCT
ejpam-5062	109	11	(	(	PUNCT
ejpam-5062	109	12	2024	2024	NUM
ejpam-5062	109	13	)	)	PUNCT
ejpam-5062	109	14	,	,	PUNCT
ejpam-5062	109	15	638	638	NUM
ejpam-5062	109	16	-	-	SYM
ejpam-5062	109	17	662	662	NUM
ejpam-5062	109	18	643	643	NUM
ejpam-5062	109	19	proof	proof	NOUN
ejpam-5062	109	20	.	.	PUNCT
ejpam-5062	110	1	let	let	VERB
ejpam-5062	110	2	us	we	PRON
ejpam-5062	110	3	suppose	suppose	VERB
ejpam-5062	110	4	that	that	SCONJ
ejpam-5062	110	5	the	the	DET
ejpam-5062	110	6	given	give	VERB
ejpam-5062	110	7	fuzzy	fuzzy	ADJ
ejpam-5062	110	8	topological	topological	ADJ
ejpam-5062	110	9	space	space	NOUN
ejpam-5062	110	10	x	x	PRON
ejpam-5062	110	11	is	be	AUX
ejpam-5062	110	12	an	an	DET
ejpam-5062	110	13	fsspt1	fsspt1	NOUN
ejpam-5062	110	14	space	space	NOUN
ejpam-5062	110	15	.	.	PUNCT
ejpam-5062	111	1	if	if	SCONJ
ejpam-5062	111	2	we	we	PRON
ejpam-5062	111	3	consider	consider	VERB
ejpam-5062	111	4	fuzzy	fuzzy	ADJ
ejpam-5062	111	5	singletons	singleton	NOUN
ejpam-5062	111	6	p	p	NOUN
ejpam-5062	111	7	and	and	CCONJ
ejpam-5062	111	8	x	x	PUNCT
ejpam-5062	111	9	with	with	ADP
ejpam-5062	111	10	different	different	ADJ
ejpam-5062	111	11	support	support	NOUN
ejpam-5062	111	12	,	,	PUNCT
ejpam-5062	111	13	it	it	PRON
ejpam-5062	111	14	is	be	AUX
ejpam-5062	111	15	obvious	obvious	ADJ
ejpam-5062	111	16	that	that	SCONJ
ejpam-5062	111	17	there	there	PRON
ejpam-5062	111	18	exist	exist	VERB
ejpam-5062	111	19	fuzzy	fuzzy	ADJ
ejpam-5062	111	20	strongly	strongly	ADV
ejpam-5062	111	21	semi	semi	ADV
ejpam-5062	111	22	pre	pre	ADJ
ejpam-5062	111	23	-	-	ADJ
ejpam-5062	111	24	open	open	ADJ
ejpam-5062	111	25	sets	set	VERB
ejpam-5062	111	26	op	op	NOUN
ejpam-5062	111	27	and	and	CCONJ
ejpam-5062	111	28	ox	ox	NOUN
ejpam-5062	111	29	such	such	ADJ
ejpam-5062	111	30	that	that	SCONJ
ejpam-5062	111	31	p	p	ADJ
ejpam-5062	111	32	≤	≤	NUM
ejpam-5062	111	33	op	op	NOUN
ejpam-5062	111	34	≤	≤	PUNCT
ejpam-5062	111	35	xc	xc	PROPN
ejpam-5062	112	1	and	and	CCONJ
ejpam-5062	112	2	x	x	SYM
ejpam-5062	112	3	≤	≤	ADJ
ejpam-5062	112	4	ox	ox	NOUN
ejpam-5062	112	5	≤	≤	ADJ
ejpam-5062	112	6	pc	pc	NOUN
ejpam-5062	112	7	.	.	PUNCT
ejpam-5062	113	1	now	now	ADV
ejpam-5062	113	2	,	,	PUNCT
ejpam-5062	113	3	if	if	SCONJ
ejpam-5062	113	4	we	we	PRON
ejpam-5062	113	5	consider	consider	VERB
ejpam-5062	113	6	the	the	DET
ejpam-5062	113	7	fuzzy	fuzzy	ADJ
ejpam-5062	113	8	set	set	VERB
ejpam-5062	113	9	pc	pc	NOUN
ejpam-5062	113	10	as	as	ADP
ejpam-5062	113	11	a	a	DET
ejpam-5062	113	12	fuzzy	fuzzy	ADJ
ejpam-5062	113	13	set	set	NOUN
ejpam-5062	113	14	that	that	PRON
ejpam-5062	113	15	contains	contain	VERB
ejpam-5062	113	16	all	all	PRON
ejpam-5062	113	17	of	of	ADP
ejpam-5062	113	18	its	its	PRON
ejpam-5062	113	19	fuzzy	fuzzy	ADJ
ejpam-5062	113	20	points	point	NOUN
ejpam-5062	113	21	,	,	PUNCT
ejpam-5062	113	22	we	we	PRON
ejpam-5062	113	23	can	can	AUX
ejpam-5062	113	24	write	write	VERB
ejpam-5062	113	25	that	that	PRON
ejpam-5062	113	26	as	as	ADP
ejpam-5062	113	27	pc	pc	NOUN
ejpam-5062	113	28	=	=	PUNCT
ejpam-5062	113	29	∨	∨	NUM
ejpam-5062	113	30	x≤pc	x≤pc	PROPN
ejpam-5062	113	31	x	x	SYM
ejpam-5062	113	32	≤	≤	ADV
ejpam-5062	113	33	∨	∨	NUM
ejpam-5062	113	34	x≤pc	x≤pc	PUNCT
ejpam-5062	113	35	ox	ox	NOUN
ejpam-5062	113	36	.	.	PUNCT
ejpam-5062	114	1	since	since	SCONJ
ejpam-5062	114	2	x	x	PRON
ejpam-5062	114	3	is	be	AUX
ejpam-5062	114	4	an	an	DET
ejpam-5062	114	5	fsspt1	fsspt1	NOUN
ejpam-5062	114	6	space	space	NOUN
ejpam-5062	114	7	,	,	PUNCT
ejpam-5062	114	8	we	we	PRON
ejpam-5062	114	9	also	also	ADV
ejpam-5062	114	10	have	have	VERB
ejpam-5062	114	11	that	that	PRON
ejpam-5062	114	12	:	:	PUNCT
ejpam-5062	115	1	ox	ox	ADJ
ejpam-5062	115	2	≤	≤	ADJ
ejpam-5062	115	3	pc	pc	NOUN
ejpam-5062	115	4	=	=	NOUN
ejpam-5062	115	5	⇒	⇒	NOUN
ejpam-5062	115	6	∨	∨	NUM
ejpam-5062	115	7	x≤pc	x≤pc	PROPN
ejpam-5062	115	8	ox	ox	ADJ
ejpam-5062	115	9	≤	≤	NUM
ejpam-5062	115	10	pc	pc	NOUN
ejpam-5062	115	11	from	from	ADP
ejpam-5062	115	12	the	the	DET
ejpam-5062	115	13	two	two	NUM
ejpam-5062	115	14	last	last	ADJ
ejpam-5062	115	15	inequalities	inequality	NOUN
ejpam-5062	115	16	,	,	PUNCT
ejpam-5062	115	17	we	we	PRON
ejpam-5062	115	18	have	have	VERB
ejpam-5062	115	19	pc	pc	NOUN
ejpam-5062	115	20	=	=	SYM
ejpam-5062	115	21	∨	∨	NUM
ejpam-5062	115	22	x≤pc	x≤pc	X
ejpam-5062	115	23	ox	ox	NOUN
ejpam-5062	115	24	.	.	PUNCT
ejpam-5062	116	1	in	in	ADP
ejpam-5062	116	2	other	other	ADJ
ejpam-5062	116	3	words	word	NOUN
ejpam-5062	116	4	,	,	PUNCT
ejpam-5062	116	5	the	the	DET
ejpam-5062	116	6	fuzzy	fuzzy	ADJ
ejpam-5062	116	7	set	set	VERB
ejpam-5062	116	8	pc	pc	NOUN
ejpam-5062	116	9	is	be	AUX
ejpam-5062	116	10	a	a	DET
ejpam-5062	116	11	fuzzy	fuzzy	ADJ
ejpam-5062	116	12	strongly	strongly	ADV
ejpam-5062	116	13	semi	semi	ADJ
ejpam-5062	116	14	pre	pre	ADJ
ejpam-5062	116	15	-	-	ADJ
ejpam-5062	116	16	open	open	ADJ
ejpam-5062	116	17	set	set	NOUN
ejpam-5062	116	18	as	as	ADP
ejpam-5062	116	19	a	a	DET
ejpam-5062	116	20	union	union	NOUN
ejpam-5062	116	21	of	of	ADP
ejpam-5062	116	22	such	such	ADJ
ejpam-5062	116	23	sets	set	NOUN
ejpam-5062	116	24	and	and	CCONJ
ejpam-5062	116	25	subsequently	subsequently	ADV
ejpam-5062	116	26	the	the	DET
ejpam-5062	116	27	singleton	singleton	PROPN
ejpam-5062	116	28	p	p	PROPN
ejpam-5062	116	29	is	be	AUX
ejpam-5062	116	30	a	a	DET
ejpam-5062	116	31	fuzzy	fuzzy	ADJ
ejpam-5062	116	32	strongly	strongly	ADV
ejpam-5062	116	33	semi	semi	ADV
ejpam-5062	116	34	pre	pre	ADJ
ejpam-5062	116	35	-	-	ADJ
ejpam-5062	116	36	closed	closed	ADJ
ejpam-5062	116	37	set	set	NOUN
ejpam-5062	116	38	.	.	PUNCT
ejpam-5062	117	1	conversely	conversely	ADV
ejpam-5062	117	2	,	,	PUNCT
ejpam-5062	117	3	if	if	SCONJ
ejpam-5062	117	4	each	each	DET
ejpam-5062	117	5	fuzzy	fuzzy	ADJ
ejpam-5062	117	6	singleton	singleton	NOUN
ejpam-5062	117	7	of	of	ADP
ejpam-5062	117	8	a	a	DET
ejpam-5062	117	9	fuzzy	fuzzy	ADJ
ejpam-5062	117	10	topological	topological	ADJ
ejpam-5062	117	11	space	space	NOUN
ejpam-5062	117	12	x	x	PUNCT
ejpam-5062	117	13	is	be	AUX
ejpam-5062	117	14	a	a	DET
ejpam-5062	117	15	fuzzy	fuzzy	ADJ
ejpam-5062	117	16	strongly	strongly	ADV
ejpam-5062	117	17	semi	semi	ADV
ejpam-5062	117	18	pre	pre	ADJ
ejpam-5062	117	19	-	-	ADJ
ejpam-5062	117	20	closed	closed	ADJ
ejpam-5062	117	21	set	set	NOUN
ejpam-5062	117	22	and	and	CCONJ
ejpam-5062	117	23	if	if	SCONJ
ejpam-5062	117	24	we	we	PRON
ejpam-5062	117	25	consider	consider	VERB
ejpam-5062	117	26	any	any	DET
ejpam-5062	117	27	pair	pair	NOUN
ejpam-5062	117	28	of	of	ADP
ejpam-5062	117	29	fuzzy	fuzzy	ADJ
ejpam-5062	117	30	singletons	singleton	NOUN
ejpam-5062	117	31	p	p	NOUN
ejpam-5062	117	32	and	and	CCONJ
ejpam-5062	117	33	x	x	PUNCT
ejpam-5062	117	34	with	with	ADP
ejpam-5062	117	35	different	different	ADJ
ejpam-5062	117	36	support	support	NOUN
ejpam-5062	117	37	,	,	PUNCT
ejpam-5062	117	38	it	it	PRON
ejpam-5062	117	39	is	be	AUX
ejpam-5062	117	40	obvious	obvious	ADJ
ejpam-5062	117	41	that	that	SCONJ
ejpam-5062	117	42	pc	pc	NOUN
ejpam-5062	117	43	and	and	CCONJ
ejpam-5062	117	44	xc	xc	PROPN
ejpam-5062	117	45	are	be	AUX
ejpam-5062	117	46	fuzzy	fuzzy	ADJ
ejpam-5062	117	47	strongly	strongly	ADV
ejpam-5062	117	48	semi	semi	ADJ
ejpam-5062	117	49	pre	pre	ADJ
ejpam-5062	117	50	-	-	ADJ
ejpam-5062	117	51	open	open	ADJ
ejpam-5062	117	52	sets	set	NOUN
ejpam-5062	117	53	such	such	ADJ
ejpam-5062	117	54	that	that	SCONJ
ejpam-5062	117	55	p	p	PROPN
ejpam-5062	117	56	≤	≤	X
ejpam-5062	117	57	xc	xc	PROPN
ejpam-5062	118	1	and	and	CCONJ
ejpam-5062	118	2	x	x	SYM
ejpam-5062	118	3	≤	≤	NUM
ejpam-5062	118	4	pc	pc	NOUN
ejpam-5062	118	5	.	.	PUNCT
ejpam-5062	119	1	if	if	SCONJ
ejpam-5062	119	2	we	we	PRON
ejpam-5062	119	3	write	write	VERB
ejpam-5062	119	4	xc	xc	X
ejpam-5062	120	1	=	=	PUNCT
ejpam-5062	120	2	op	op	NOUN
ejpam-5062	120	3	and	and	CCONJ
ejpam-5062	120	4	pc	pc	NOUN
ejpam-5062	120	5	=	=	SYM
ejpam-5062	120	6	ox	ox	NOUN
ejpam-5062	121	1	we	we	PRON
ejpam-5062	121	2	get	get	VERB
ejpam-5062	121	3	the	the	DET
ejpam-5062	121	4	following	follow	VERB
ejpam-5062	121	5	p	p	ADJ
ejpam-5062	121	6	≤	≤	ADJ
ejpam-5062	121	7	op	op	NOUN
ejpam-5062	121	8	≤	≤	NUM
ejpam-5062	121	9	xc	xc	PROPN
ejpam-5062	121	10	and	and	CCONJ
ejpam-5062	121	11	x	x	SYM
ejpam-5062	121	12	≤	≤	ADJ
ejpam-5062	121	13	ox	ox	NOUN
ejpam-5062	121	14	≤	≤	ADJ
ejpam-5062	121	15	pc	pc	NOUN
ejpam-5062	121	16	,	,	PUNCT
ejpam-5062	121	17	which	which	PRON
ejpam-5062	121	18	means	mean	VERB
ejpam-5062	121	19	that	that	SCONJ
ejpam-5062	121	20	fuzzy	fuzzy	ADJ
ejpam-5062	121	21	topological	topological	ADJ
ejpam-5062	121	22	space	space	NOUN
ejpam-5062	121	23	x	x	PUNCT
ejpam-5062	121	24	is	be	AUX
ejpam-5062	121	25	an	an	DET
ejpam-5062	121	26	fsspt1	fsspt1	NOUN
ejpam-5062	121	27	.	.	PUNCT
ejpam-5062	122	1	corollary	corollary	ADJ
ejpam-5062	122	2	1	1	NUM
ejpam-5062	122	3	.	.	PUNCT
ejpam-5062	123	1	a	a	DET
ejpam-5062	123	2	fuzzy	fuzzy	ADJ
ejpam-5062	123	3	topological	topological	ADJ
ejpam-5062	123	4	space	space	NOUN
ejpam-5062	123	5	is	be	AUX
ejpam-5062	123	6	an	an	DET
ejpam-5062	123	7	fsspt1	fsspt1	NOUN
ejpam-5062	123	8	space	space	NOUN
ejpam-5062	123	9	if	if	SCONJ
ejpam-5062	123	10	and	and	CCONJ
ejpam-5062	123	11	only	only	ADV
ejpam-5062	123	12	if	if	SCONJ
ejpam-5062	123	13	for	for	ADP
ejpam-5062	123	14	each	each	DET
ejpam-5062	123	15	pair	pair	NOUN
ejpam-5062	123	16	of	of	ADP
ejpam-5062	123	17	fuzzy	fuzzy	ADJ
ejpam-5062	123	18	singletons	singleton	NOUN
ejpam-5062	123	19	p1	p1	NOUN
ejpam-5062	123	20	and	and	CCONJ
ejpam-5062	123	21	p2	p2	PROPN
ejpam-5062	123	22	which	which	PRON
ejpam-5062	123	23	have	have	VERB
ejpam-5062	123	24	different	different	ADJ
ejpam-5062	123	25	supports	support	NOUN
ejpam-5062	123	26	,	,	PUNCT
ejpam-5062	123	27	there	there	PRON
ejpam-5062	123	28	exist	exist	VERB
ejpam-5062	123	29	fuzzy	fuzzy	ADJ
ejpam-5062	123	30	strongly	strongly	ADV
ejpam-5062	123	31	semi	semi	ADV
ejpam-5062	123	32	pre	pre	ADJ
ejpam-5062	123	33	-	-	ADJ
ejpam-5062	123	34	open	open	ADJ
ejpam-5062	123	35	sets	set	NOUN
ejpam-5062	123	36	o1	o1	NOUN
ejpam-5062	123	37	,	,	PUNCT
ejpam-5062	123	38	o2	o2	PROPN
ejpam-5062	123	39	such	such	ADJ
ejpam-5062	123	40	that	that	DET
ejpam-5062	123	41	o1(p1	o1(p1	NOUN
ejpam-5062	123	42	)	)	PUNCT
ejpam-5062	123	43	=	=	SYM
ejpam-5062	123	44	1	1	NUM
ejpam-5062	123	45	,	,	PUNCT
ejpam-5062	123	46	o1(p2	o1(p2	NOUN
ejpam-5062	123	47	)	)	PUNCT
ejpam-5062	123	48	=	=	SYM
ejpam-5062	123	49	0	0	NUM
ejpam-5062	123	50	and	and	CCONJ
ejpam-5062	123	51	o2(p1	o2(p1	NUM
ejpam-5062	123	52	)	)	PUNCT
ejpam-5062	124	1	=	=	SYM
ejpam-5062	124	2	0	0	NUM
ejpam-5062	124	3	,	,	PUNCT
ejpam-5062	124	4	o2(p2	o2(p2	NUM
ejpam-5062	124	5	)	)	PUNCT
ejpam-5062	124	6	=	=	SYM
ejpam-5062	124	7	1	1	X
ejpam-5062	124	8	.	.	PUNCT
ejpam-5062	124	9	proof	proof	NOUN
ejpam-5062	124	10	.	.	PUNCT
ejpam-5062	125	1	if	if	SCONJ
ejpam-5062	125	2	the	the	DET
ejpam-5062	125	3	fuzzy	fuzzy	ADJ
ejpam-5062	125	4	topological	topological	ADJ
ejpam-5062	125	5	space	space	NOUN
ejpam-5062	125	6	is	be	AUX
ejpam-5062	125	7	an	an	DET
ejpam-5062	125	8	fsspt1	fsspt1	NOUN
ejpam-5062	125	9	space	space	NOUN
ejpam-5062	125	10	,	,	PUNCT
ejpam-5062	125	11	then	then	ADV
ejpam-5062	125	12	according	accord	VERB
ejpam-5062	125	13	to	to	ADP
ejpam-5062	125	14	theorem	theorem	NOUN
ejpam-5062	125	15	2	2	NUM
ejpam-5062	125	16	,	,	PUNCT
ejpam-5062	125	17	the	the	DET
ejpam-5062	125	18	conditions	condition	NOUN
ejpam-5062	125	19	are	be	AUX
ejpam-5062	125	20	met	meet	VERB
ejpam-5062	125	21	if	if	SCONJ
ejpam-5062	125	22	we	we	PRON
ejpam-5062	125	23	put	put	VERB
ejpam-5062	125	24	pc2	pc2	NOUN
ejpam-5062	125	25	=	=	SYM
ejpam-5062	125	26	o1	o1	PROPN
ejpam-5062	125	27	and	and	CCONJ
ejpam-5062	125	28	pc1	pc1	NOUN
ejpam-5062	125	29	=	=	SYM
ejpam-5062	125	30	o2	o2	PROPN
ejpam-5062	125	31	.	.	PUNCT
ejpam-5062	126	1	conversely	conversely	ADV
ejpam-5062	126	2	,	,	PUNCT
ejpam-5062	126	3	if	if	SCONJ
ejpam-5062	126	4	for	for	ADP
ejpam-5062	126	5	any	any	DET
ejpam-5062	126	6	pair	pair	NOUN
ejpam-5062	126	7	of	of	ADP
ejpam-5062	126	8	fuzzy	fuzzy	ADJ
ejpam-5062	126	9	singletons	singleton	NOUN
ejpam-5062	126	10	p1	p1	NOUN
ejpam-5062	126	11	and	and	CCONJ
ejpam-5062	126	12	p2	p2	NOUN
ejpam-5062	126	13	,	,	PUNCT
ejpam-5062	126	14	with	with	ADP
ejpam-5062	126	15	different	different	ADJ
ejpam-5062	126	16	supports	support	NOUN
ejpam-5062	126	17	,	,	PUNCT
ejpam-5062	126	18	there	there	PRON
ejpam-5062	126	19	exist	exist	VERB
ejpam-5062	126	20	fuzzy	fuzzy	ADJ
ejpam-5062	126	21	strong	strong	ADJ
ejpam-5062	126	22	semi	semi	ADJ
ejpam-5062	126	23	pre	pre	ADJ
ejpam-5062	126	24	-	-	ADJ
ejpam-5062	126	25	open	open	ADJ
ejpam-5062	126	26	sets	set	NOUN
ejpam-5062	126	27	o1	o1	NOUN
ejpam-5062	126	28	,	,	PUNCT
ejpam-5062	126	29	o2	o2	PROPN
ejpam-5062	126	30	such	such	ADJ
ejpam-5062	126	31	that	that	DET
ejpam-5062	126	32	o1(p1	o1(p1	NOUN
ejpam-5062	126	33	)	)	PUNCT
ejpam-5062	126	34	=	=	SYM
ejpam-5062	127	1	1	1	NUM
ejpam-5062	127	2	,	,	PUNCT
ejpam-5062	127	3	o1(p2	o1(p2	NOUN
ejpam-5062	127	4	)	)	PUNCT
ejpam-5062	127	5	=	=	SYM
ejpam-5062	127	6	0	0	NUM
ejpam-5062	127	7	and	and	CCONJ
ejpam-5062	127	8	o2(p1	o2(p1	NUM
ejpam-5062	127	9	)	)	PUNCT
ejpam-5062	127	10	=	=	SYM
ejpam-5062	127	11	0	0	NUM
ejpam-5062	127	12	,	,	PUNCT
ejpam-5062	127	13	o2(p2	o2(p2	NUM
ejpam-5062	127	14	)	)	PUNCT
ejpam-5062	127	15	=	=	SYM
ejpam-5062	127	16	1	1	NUM
ejpam-5062	127	17	,	,	PUNCT
ejpam-5062	127	18	it	it	PRON
ejpam-5062	127	19	is	be	AUX
ejpam-5062	127	20	obvious	obvious	ADJ
ejpam-5062	127	21	that	that	SCONJ
ejpam-5062	127	22	p1	p1	PROPN
ejpam-5062	127	23	≤	≤	NUM
ejpam-5062	127	24	o1	o1	NOUN
ejpam-5062	127	25	≤	≤	NOUN
ejpam-5062	127	26	pc2	pc2	NOUN
ejpam-5062	127	27	and	and	CCONJ
ejpam-5062	127	28	p2	p2	PROPN
ejpam-5062	127	29	≤	≤	NUM
ejpam-5062	127	30	o2	o2	PROPN
ejpam-5062	127	31	≤	≤	PROPN
ejpam-5062	127	32	pc1	pc1	PROPN
ejpam-5062	127	33	,	,	PUNCT
ejpam-5062	127	34	which	which	PRON
ejpam-5062	127	35	means	mean	VERB
ejpam-5062	127	36	that	that	SCONJ
ejpam-5062	127	37	the	the	DET
ejpam-5062	127	38	fuzzy	fuzzy	ADJ
ejpam-5062	127	39	topological	topological	ADJ
ejpam-5062	127	40	space	space	NOUN
ejpam-5062	127	41	is	be	AUX
ejpam-5062	127	42	an	an	DET
ejpam-5062	127	43	fsspt1	fsspt1	NOUN
ejpam-5062	127	44	space	space	NOUN
ejpam-5062	127	45	.	.	PUNCT
ejpam-5062	128	1	we	we	PRON
ejpam-5062	128	2	can	can	AUX
ejpam-5062	128	3	easily	easily	ADV
ejpam-5062	128	4	conclude	conclude	VERB
ejpam-5062	128	5	that	that	SCONJ
ejpam-5062	128	6	any	any	DET
ejpam-5062	128	7	fsspt1	fsspt1	NOUN
ejpam-5062	128	8	space	space	NOUN
ejpam-5062	128	9	is	be	AUX
ejpam-5062	128	10	also	also	ADV
ejpam-5062	128	11	an	an	DET
ejpam-5062	128	12	fsspt0	fsspt0	NOUN
ejpam-5062	128	13	while	while	SCONJ
ejpam-5062	128	14	the	the	DET
ejpam-5062	128	15	converse	converse	NOUN
ejpam-5062	128	16	is	be	AUX
ejpam-5062	128	17	not	not	PART
ejpam-5062	128	18	always	always	ADV
ejpam-5062	128	19	true	true	ADJ
ejpam-5062	128	20	.	.	PUNCT
ejpam-5062	129	1	if	if	SCONJ
ejpam-5062	129	2	we	we	PRON
ejpam-5062	129	3	consider	consider	VERB
ejpam-5062	129	4	example	example	NOUN
ejpam-5062	129	5	1	1	NUM
ejpam-5062	129	6	,	,	PUNCT
ejpam-5062	129	7	it	it	PRON
ejpam-5062	129	8	is	be	AUX
ejpam-5062	129	9	obvious	obvious	ADJ
ejpam-5062	129	10	that	that	SCONJ
ejpam-5062	129	11	the	the	DET
ejpam-5062	129	12	fuzzy	fuzzy	ADJ
ejpam-5062	129	13	topological	topological	ADJ
ejpam-5062	129	14	space	space	NOUN
ejpam-5062	129	15	(	(	PUNCT
ejpam-5062	129	16	x	x	X
ejpam-5062	129	17	,	,	PUNCT
ejpam-5062	129	18	τ	τ	X
ejpam-5062	129	19	)	)	PUNCT
ejpam-5062	129	20	is	be	AUX
ejpam-5062	129	21	not	not	PART
ejpam-5062	129	22	an	an	DET
ejpam-5062	129	23	fsspt1	fsspt1	NOUN
ejpam-5062	129	24	space	space	NOUN
ejpam-5062	129	25	.	.	PUNCT
ejpam-5062	130	1	definition	definition	NOUN
ejpam-5062	130	2	13	13	NUM
ejpam-5062	130	3	.	.	PUNCT
ejpam-5062	131	1	a	a	DET
ejpam-5062	131	2	fuzzy	fuzzy	ADJ
ejpam-5062	131	3	topological	topological	ADJ
ejpam-5062	131	4	space	space	NOUN
ejpam-5062	131	5	x	x	PUNCT
ejpam-5062	131	6	is	be	AUX
ejpam-5062	131	7	a	a	DET
ejpam-5062	131	8	fuzzy	fuzzy	ADJ
ejpam-5062	131	9	strong	strong	ADJ
ejpam-5062	131	10	semi	semi	ADJ
ejpam-5062	131	11	pre	pre	ADJ
ejpam-5062	131	12	-	-	ADJ
ejpam-5062	131	13	ts	ts	ADJ
ejpam-5062	131	14	(	(	PUNCT
ejpam-5062	131	15	or	or	CCONJ
ejpam-5062	131	16	short	short	ADJ
ejpam-5062	131	17	fsspts	fsspt	NOUN
ejpam-5062	131	18	)	)	PUNCT
ejpam-5062	131	19	if	if	SCONJ
ejpam-5062	131	20	and	and	CCONJ
ejpam-5062	131	21	only	only	ADV
ejpam-5062	131	22	if	if	SCONJ
ejpam-5062	131	23	every	every	DET
ejpam-5062	131	24	fuzzy	fuzzy	ADJ
ejpam-5062	131	25	point	point	NOUN
ejpam-5062	131	26	is	be	AUX
ejpam-5062	131	27	a	a	DET
ejpam-5062	131	28	fuzzy	fuzzy	ADJ
ejpam-5062	131	29	strongly	strongly	ADV
ejpam-5062	131	30	semi	semi	ADV
ejpam-5062	131	31	pre	pre	ADJ
ejpam-5062	131	32	-	-	ADJ
ejpam-5062	131	33	closed	closed	ADJ
ejpam-5062	131	34	set	set	NOUN
ejpam-5062	131	35	.	.	PUNCT
ejpam-5062	132	1	by	by	ADP
ejpam-5062	132	2	theorem	theorem	NOUN
ejpam-5062	132	3	2	2	NUM
ejpam-5062	132	4	it	it	PRON
ejpam-5062	132	5	is	be	AUX
ejpam-5062	132	6	obvious	obvious	ADJ
ejpam-5062	132	7	that	that	SCONJ
ejpam-5062	132	8	any	any	DET
ejpam-5062	132	9	fsspts	fsspts	NOUN
ejpam-5062	132	10	space	space	NOUN
ejpam-5062	132	11	is	be	AUX
ejpam-5062	132	12	also	also	ADV
ejpam-5062	132	13	an	an	DET
ejpam-5062	132	14	fsspt1	fsspt1	NOUN
ejpam-5062	132	15	.	.	PUNCT
ejpam-5062	133	1	with	with	ADP
ejpam-5062	133	2	the	the	DET
ejpam-5062	133	3	following	follow	VERB
ejpam-5062	133	4	example	example	NOUN
ejpam-5062	133	5	,	,	PUNCT
ejpam-5062	133	6	we	we	PRON
ejpam-5062	133	7	will	will	AUX
ejpam-5062	133	8	show	show	VERB
ejpam-5062	133	9	that	that	SCONJ
ejpam-5062	133	10	the	the	DET
ejpam-5062	133	11	converse	converse	NOUN
ejpam-5062	133	12	is	be	AUX
ejpam-5062	133	13	not	not	PART
ejpam-5062	133	14	always	always	ADV
ejpam-5062	133	15	true	true	ADJ
ejpam-5062	133	16	.	.	PUNCT
ejpam-5062	134	1	example	example	NOUN
ejpam-5062	134	2	2	2	NUM
ejpam-5062	134	3	.	.	PUNCT
ejpam-5062	134	4	given	give	VERB
ejpam-5062	134	5	a	a	DET
ejpam-5062	134	6	set	set	NOUN
ejpam-5062	134	7	x	x	SYM
ejpam-5062	134	8	=	=	PUNCT
ejpam-5062	134	9	{	{	PUNCT
ejpam-5062	134	10	p	p	X
ejpam-5062	134	11	,	,	PUNCT
ejpam-5062	134	12	q	q	NOUN
ejpam-5062	134	13	}	}	PUNCT
ejpam-5062	134	14	,	,	PUNCT
ejpam-5062	134	15	and	and	CCONJ
ejpam-5062	134	16	fuzzy	fuzzy	ADJ
ejpam-5062	134	17	sets	set	VERB
ejpam-5062	134	18	u	u	NOUN
ejpam-5062	134	19	=	=	PRON
ejpam-5062	134	20	{	{	PUNCT
ejpam-5062	134	21	(	(	PUNCT
ejpam-5062	134	22	p	p	X
ejpam-5062	134	23	,	,	PUNCT
ejpam-5062	134	24	1	1	NUM
ejpam-5062	134	25	)	)	PUNCT
ejpam-5062	134	26	,	,	PUNCT
ejpam-5062	134	27	(	(	PUNCT
ejpam-5062	134	28	q	q	X
ejpam-5062	134	29	,	,	PUNCT
ejpam-5062	134	30	0	0	NUM
ejpam-5062	134	31	)	)	PUNCT
ejpam-5062	134	32	}	}	PUNCT
ejpam-5062	134	33	,	,	PUNCT
ejpam-5062	134	34	v	v	X
ejpam-5062	134	35	=	=	SYM
ejpam-5062	134	36	{	{	PUNCT
ejpam-5062	134	37	(	(	PUNCT
ejpam-5062	134	38	p	p	X
ejpam-5062	134	39	,	,	PUNCT
ejpam-5062	134	40	0	0	NUM
ejpam-5062	134	41	)	)	PUNCT
ejpam-5062	134	42	,	,	PUNCT
ejpam-5062	134	43	(	(	PUNCT
ejpam-5062	134	44	q	q	X
ejpam-5062	134	45	,	,	PUNCT
ejpam-5062	134	46	1	1	NUM
ejpam-5062	134	47	)	)	PUNCT
ejpam-5062	134	48	}	}	PUNCT
ejpam-5062	134	49	,	,	PUNCT
ejpam-5062	134	50	the	the	DET
ejpam-5062	134	51	fuzzy	fuzzy	ADJ
ejpam-5062	134	52	topological	topological	ADJ
ejpam-5062	134	53	space	space	NOUN
ejpam-5062	134	54	τ	τ	X
ejpam-5062	134	55	=	=	PUNCT
ejpam-5062	134	56	{	{	PUNCT
ejpam-5062	134	57	0	0	NUM
ejpam-5062	134	58	,	,	PUNCT
ejpam-5062	134	59	u	u	NOUN
ejpam-5062	134	60	,	,	PUNCT
ejpam-5062	134	61	v	v	NOUN
ejpam-5062	134	62	,	,	PUNCT
ejpam-5062	134	63	1	1	NUM
ejpam-5062	134	64	}	}	PUNCT
ejpam-5062	134	65	is	be	AUX
ejpam-5062	134	66	fsspt1	fsspt1	NOUN
ejpam-5062	135	1	but	but	CCONJ
ejpam-5062	135	2	it	it	PRON
ejpam-5062	135	3	is	be	AUX
ejpam-5062	135	4	not	not	PART
ejpam-5062	135	5	fsspts	fsspt	NOUN
ejpam-5062	135	6	.	.	PUNCT
ejpam-5062	136	1	it	it	PRON
ejpam-5062	136	2	is	be	AUX
ejpam-5062	136	3	obvious	obvious	ADJ
ejpam-5062	136	4	that	that	SCONJ
ejpam-5062	136	5	every	every	DET
ejpam-5062	136	6	singleton	singleton	NOUN
ejpam-5062	136	7	is	be	AUX
ejpam-5062	136	8	a	a	DET
ejpam-5062	136	9	fuzzy	fuzzy	ADJ
ejpam-5062	136	10	strongly	strongly	ADV
ejpam-5062	136	11	semi	semi	ADV
ejpam-5062	136	12	pre	pre	ADJ
ejpam-5062	136	13	-	-	ADJ
ejpam-5062	136	14	closed	closed	ADJ
ejpam-5062	136	15	set	set	NOUN
ejpam-5062	136	16	,	,	PUNCT
ejpam-5062	136	17	and	and	CCONJ
ejpam-5062	136	18	the	the	DET
ejpam-5062	136	19	conclusion	conclusion	NOUN
ejpam-5062	136	20	follows	follow	VERB
ejpam-5062	136	21	from	from	ADP
ejpam-5062	136	22	theorem	theorem	ADJ
ejpam-5062	136	23	2	2	NUM
ejpam-5062	136	24	.	.	NOUN
ejpam-5062	136	25	example	example	NOUN
ejpam-5062	136	26	3	3	NUM
ejpam-5062	136	27	.	.	PUNCT
ejpam-5062	136	28	given	give	VERB
ejpam-5062	136	29	a	a	DET
ejpam-5062	136	30	set	set	NOUN
ejpam-5062	136	31	x	x	X
ejpam-5062	136	32	=	=	SYM
ejpam-5062	136	33	{	{	PUNCT
ejpam-5062	136	34	p1	p1	NOUN
ejpam-5062	136	35	,	,	PUNCT
ejpam-5062	136	36	p2	p2	NOUN
ejpam-5062	136	37	}	}	PUNCT
ejpam-5062	136	38	,	,	PUNCT
ejpam-5062	136	39	and	and	CCONJ
ejpam-5062	136	40	fuzzy	fuzzy	ADJ
ejpam-5062	136	41	sets	set	VERB
ejpam-5062	136	42	u	u	NOUN
ejpam-5062	136	43	=	=	PRON
ejpam-5062	136	44	{	{	PUNCT
ejpam-5062	136	45	(	(	PUNCT
ejpam-5062	136	46	p1	p1	NOUN
ejpam-5062	136	47	,	,	PUNCT
ejpam-5062	136	48	0.6	0.6	NUM
ejpam-5062	136	49	)	)	PUNCT
ejpam-5062	136	50	,	,	PUNCT
ejpam-5062	136	51	(	(	PUNCT
ejpam-5062	136	52	p2	p2	X
ejpam-5062	136	53	,	,	PUNCT
ejpam-5062	136	54	0	0	NUM
ejpam-5062	136	55	)	)	PUNCT
ejpam-5062	136	56	}	}	PUNCT
ejpam-5062	136	57	,	,	PUNCT
ejpam-5062	136	58	v	v	X
ejpam-5062	136	59	=	=	SYM
ejpam-5062	136	60	{	{	PUNCT
ejpam-5062	136	61	(	(	PUNCT
ejpam-5062	136	62	p1	p1	NOUN
ejpam-5062	136	63	,	,	PUNCT
ejpam-5062	136	64	0.7	0.7	NUM
ejpam-5062	136	65	)	)	PUNCT
ejpam-5062	136	66	,	,	PUNCT
ejpam-5062	136	67	(	(	PUNCT
ejpam-5062	136	68	p2	p2	X
ejpam-5062	136	69	,	,	PUNCT
ejpam-5062	136	70	0	0	NUM
ejpam-5062	136	71	)	)	PUNCT
ejpam-5062	136	72	}	}	PUNCT
ejpam-5062	136	73	and	and	CCONJ
ejpam-5062	136	74	w	w	X
ejpam-5062	136	75	=	=	SYM
ejpam-5062	136	76	{	{	PUNCT
ejpam-5062	136	77	(	(	PUNCT
ejpam-5062	136	78	p1	p1	NOUN
ejpam-5062	136	79	,	,	PUNCT
ejpam-5062	136	80	0.8	0.8	NUM
ejpam-5062	136	81	)	)	PUNCT
ejpam-5062	136	82	,	,	PUNCT
ejpam-5062	136	83	(	(	PUNCT
ejpam-5062	136	84	p2	p2	X
ejpam-5062	136	85	,	,	PUNCT
ejpam-5062	136	86	0.7	0.7	NUM
ejpam-5062	136	87	)	)	PUNCT
ejpam-5062	136	88	}	}	PUNCT
ejpam-5062	136	89	.	.	PUNCT
ejpam-5062	137	1	if	if	SCONJ
ejpam-5062	137	2	τ	τ	PROPN
ejpam-5062	137	3	=	=	PUNCT
ejpam-5062	137	4	{	{	PUNCT
ejpam-5062	137	5	0	0	NUM
ejpam-5062	137	6	,	,	PUNCT
ejpam-5062	137	7	u	u	NOUN
ejpam-5062	137	8	,	,	PUNCT
ejpam-5062	137	9	v	v	NOUN
ejpam-5062	137	10	,	,	PUNCT
ejpam-5062	137	11	w	w	NOUN
ejpam-5062	137	12	,	,	PUNCT
ejpam-5062	137	13	1	1	NUM
ejpam-5062	137	14	}	}	PUNCT
ejpam-5062	137	15	.	.	PUNCT
ejpam-5062	138	1	it	it	PRON
ejpam-5062	138	2	can	can	AUX
ejpam-5062	138	3	be	be	AUX
ejpam-5062	138	4	shown	show	VERB
ejpam-5062	138	5	that	that	SCONJ
ejpam-5062	138	6	the	the	DET
ejpam-5062	138	7	fuzzy	fuzzy	ADJ
ejpam-5062	138	8	topological	topological	ADJ
ejpam-5062	138	9	space	space	NOUN
ejpam-5062	138	10	(	(	PUNCT
ejpam-5062	138	11	x	x	X
ejpam-5062	138	12	,	,	PUNCT
ejpam-5062	138	13	τ	τ	X
ejpam-5062	138	14	)	)	PUNCT
ejpam-5062	138	15	is	be	AUX
ejpam-5062	138	16	fsspt0	fsspt0	NOUN
ejpam-5062	139	1	but	but	CCONJ
ejpam-5062	139	2	it	it	PRON
ejpam-5062	139	3	is	be	AUX
ejpam-5062	139	4	not	not	PART
ejpam-5062	139	5	fsspt1	fsspt1	NOUN
ejpam-5062	139	6	and	and	CCONJ
ejpam-5062	139	7	fsspts	fsspt	NOUN
ejpam-5062	139	8	.	.	PUNCT
ejpam-5062	140	1	sh	sh	PROPN
ejpam-5062	140	2	.	.	PROPN
ejpam-5062	140	3	makolli	makolli	PROPN
ejpam-5062	140	4	,	,	PUNCT
ejpam-5062	140	5	b.	b.	PROPN
ejpam-5062	140	6	krsteska	krsteska	PROPN
ejpam-5062	140	7	/	/	SYM
ejpam-5062	140	8	eur	eur	PROPN
ejpam-5062	140	9	.	.	PUNCT
ejpam-5062	141	1	j.	j.	PROPN
ejpam-5062	141	2	pure	pure	PROPN
ejpam-5062	141	3	appl	appl	PROPN
ejpam-5062	141	4	.	.	PROPN
ejpam-5062	141	5	math	math	PROPN
ejpam-5062	141	6	,	,	PUNCT
ejpam-5062	141	7	17	17	NUM
ejpam-5062	141	8	(	(	PUNCT
ejpam-5062	141	9	2	2	NUM
ejpam-5062	141	10	)	)	PUNCT
ejpam-5062	141	11	(	(	PUNCT
ejpam-5062	141	12	2024	2024	NUM
ejpam-5062	141	13	)	)	PUNCT
ejpam-5062	141	14	,	,	PUNCT
ejpam-5062	141	15	638	638	NUM
ejpam-5062	141	16	-	-	SYM
ejpam-5062	141	17	662	662	NUM
ejpam-5062	141	18	644	644	NUM
ejpam-5062	141	19	definition	definition	NOUN
ejpam-5062	141	20	14	14	NUM
ejpam-5062	141	21	.	.	PUNCT
ejpam-5062	142	1	a	a	DET
ejpam-5062	142	2	fuzzy	fuzzy	ADJ
ejpam-5062	142	3	topological	topological	ADJ
ejpam-5062	142	4	space	space	NOUN
ejpam-5062	142	5	x	x	PUNCT
ejpam-5062	142	6	is	be	AUX
ejpam-5062	142	7	a	a	DET
ejpam-5062	142	8	fuzzy	fuzzy	ADJ
ejpam-5062	142	9	strong	strong	ADJ
ejpam-5062	142	10	semi	semi	ADJ
ejpam-5062	142	11	pre	pre	ADJ
ejpam-5062	142	12	-	-	ADJ
ejpam-5062	142	13	hausdorff	hausdorff	ADJ
ejpam-5062	142	14	(	(	PUNCT
ejpam-5062	142	15	or	or	CCONJ
ejpam-5062	142	16	short	short	ADJ
ejpam-5062	142	17	fsspt2	fsspt2	NOUN
ejpam-5062	142	18	)	)	PUNCT
ejpam-5062	142	19	if	if	SCONJ
ejpam-5062	142	20	and	and	CCONJ
ejpam-5062	142	21	only	only	ADV
ejpam-5062	142	22	if	if	SCONJ
ejpam-5062	142	23	for	for	ADP
ejpam-5062	142	24	any	any	DET
ejpam-5062	142	25	pair	pair	NOUN
ejpam-5062	142	26	of	of	ADP
ejpam-5062	142	27	fuzzy	fuzzy	ADJ
ejpam-5062	142	28	points	point	NOUN
ejpam-5062	142	29	p1	p1	NOUN
ejpam-5062	142	30	and	and	CCONJ
ejpam-5062	142	31	p2	p2	NOUN
ejpam-5062	142	32	,	,	PUNCT
ejpam-5062	142	33	which	which	PRON
ejpam-5062	142	34	have	have	VERB
ejpam-5062	142	35	different	different	ADJ
ejpam-5062	142	36	supports	support	NOUN
ejpam-5062	142	37	,	,	PUNCT
ejpam-5062	142	38	there	there	PRON
ejpam-5062	142	39	exist	exist	VERB
ejpam-5062	142	40	fuzzy	fuzzy	ADJ
ejpam-5062	142	41	strongly	strongly	ADV
ejpam-5062	142	42	semi	semi	ADJ
ejpam-5062	142	43	preo	preo	ADJ
ejpam-5062	142	44	-	-	PUNCT
ejpam-5062	142	45	pen	pen	NOUN
ejpam-5062	142	46	sets	set	NOUN
ejpam-5062	142	47	o1	o1	NOUN
ejpam-5062	142	48	,	,	PUNCT
ejpam-5062	142	49	o2	o2	PROPN
ejpam-5062	142	50	such	such	ADJ
ejpam-5062	142	51	that	that	DET
ejpam-5062	142	52	p1	p1	PROPN
ejpam-5062	142	53	≤	≤	NUM
ejpam-5062	142	54	o1	o1	NOUN
ejpam-5062	142	55	≤	≤	NUM
ejpam-5062	142	56	pc2	pc2	NOUN
ejpam-5062	142	57	,	,	PUNCT
ejpam-5062	142	58	p2	p2	PROPN
ejpam-5062	142	59	≤	≤	NUM
ejpam-5062	142	60	o2	o2	PROPN
ejpam-5062	142	61	≤	≤	PROPN
ejpam-5062	142	62	pc1	pc1	PROPN
ejpam-5062	142	63	and	and	CCONJ
ejpam-5062	142	64	o1	o1	NOUN
ejpam-5062	142	65	≤	≤	NOUN
ejpam-5062	142	66	oc	oc	ADP
ejpam-5062	142	67	2	2	NUM
ejpam-5062	142	68	.	.	PUNCT
ejpam-5062	142	69	theorem	theorem	NOUN
ejpam-5062	142	70	3	3	NUM
ejpam-5062	142	71	.	.	PUNCT
ejpam-5062	143	1	the	the	DET
ejpam-5062	143	2	fuzzy	fuzzy	ADJ
ejpam-5062	143	3	topological	topological	ADJ
ejpam-5062	143	4	space	space	NOUN
ejpam-5062	143	5	(	(	PUNCT
ejpam-5062	143	6	x	x	X
ejpam-5062	143	7	,	,	PUNCT
ejpam-5062	143	8	τ	τ	X
ejpam-5062	143	9	)	)	PUNCT
ejpam-5062	143	10	is	be	AUX
ejpam-5062	143	11	an	an	DET
ejpam-5062	143	12	fsspt2	fsspt2	NOUN
ejpam-5062	143	13	if	if	SCONJ
ejpam-5062	144	1	and	and	CCONJ
ejpam-5062	144	2	only	only	ADV
ejpam-5062	144	3	if	if	SCONJ
ejpam-5062	144	4	there	there	PRON
ejpam-5062	144	5	exists	exist	VERB
ejpam-5062	144	6	a	a	DET
ejpam-5062	144	7	fuzzy	fuzzy	ADJ
ejpam-5062	144	8	strongly	strongly	ADV
ejpam-5062	144	9	semi	semi	ADV
ejpam-5062	144	10	pre	pre	ADJ
ejpam-5062	144	11	-	-	ADJ
ejpam-5062	144	12	open	open	ADJ
ejpam-5062	144	13	set	set	ADJ
ejpam-5062	144	14	o	o	NOUN
ejpam-5062	145	1	such	such	ADJ
ejpam-5062	145	2	that	that	DET
ejpam-5062	145	3	p1	p1	PROPN
ejpam-5062	145	4	≤	≤	X
ejpam-5062	145	5	o	o	NOUN
ejpam-5062	145	6	≤	≤	X
ejpam-5062	145	7	sspclo	sspclo	NOUN
ejpam-5062	145	8	≤	≤	NUM
ejpam-5062	145	9	pc2	pc2	NOUN
ejpam-5062	145	10	,	,	PUNCT
ejpam-5062	145	11	where	where	SCONJ
ejpam-5062	145	12	p1	p1	NOUN
ejpam-5062	145	13	and	and	CCONJ
ejpam-5062	145	14	p2	p2	PROPN
ejpam-5062	145	15	are	be	AUX
ejpam-5062	145	16	any	any	DET
ejpam-5062	145	17	pair	pair	NOUN
ejpam-5062	145	18	of	of	ADP
ejpam-5062	145	19	fuzzy	fuzzy	ADJ
ejpam-5062	145	20	points	point	NOUN
ejpam-5062	145	21	from	from	ADP
ejpam-5062	145	22	x	x	SYM
ejpam-5062	145	23	that	that	PRON
ejpam-5062	145	24	have	have	VERB
ejpam-5062	145	25	different	different	ADJ
ejpam-5062	145	26	supports	support	NOUN
ejpam-5062	145	27	.	.	PUNCT
ejpam-5062	146	1	proof	proof	NOUN
ejpam-5062	146	2	.	.	PUNCT
ejpam-5062	147	1	if	if	SCONJ
ejpam-5062	147	2	the	the	DET
ejpam-5062	147	3	fuzzy	fuzzy	ADJ
ejpam-5062	147	4	topological	topological	ADJ
ejpam-5062	147	5	space	space	NOUN
ejpam-5062	147	6	(	(	PUNCT
ejpam-5062	147	7	x	x	X
ejpam-5062	147	8	,	,	PUNCT
ejpam-5062	147	9	τ	τ	X
ejpam-5062	147	10	)	)	PUNCT
ejpam-5062	147	11	is	be	AUX
ejpam-5062	147	12	an	an	DET
ejpam-5062	147	13	fsspt2	fsspt2	NOUN
ejpam-5062	147	14	then	then	ADV
ejpam-5062	147	15	it	it	PRON
ejpam-5062	147	16	is	be	AUX
ejpam-5062	147	17	obvious	obvious	ADJ
ejpam-5062	147	18	that	that	SCONJ
ejpam-5062	147	19	for	for	ADP
ejpam-5062	147	20	any	any	DET
ejpam-5062	147	21	pair	pair	NOUN
ejpam-5062	147	22	of	of	ADP
ejpam-5062	147	23	fuzzy	fuzzy	ADJ
ejpam-5062	147	24	points	point	NOUN
ejpam-5062	147	25	p1	p1	NOUN
ejpam-5062	147	26	,	,	PUNCT
ejpam-5062	147	27	p2	p2	NOUN
ejpam-5062	147	28	there	there	PRON
ejpam-5062	147	29	must	must	AUX
ejpam-5062	147	30	exist	exist	VERB
ejpam-5062	147	31	a	a	DET
ejpam-5062	147	32	set	set	NOUN
ejpam-5062	147	33	o	o	X
ejpam-5062	147	34	∈	∈	PROPN
ejpam-5062	147	35	fsspo(τ	fsspo(τ	PROPN
ejpam-5062	147	36	)	)	PUNCT
ejpam-5062	147	37	,	,	PUNCT
ejpam-5062	147	38	p1	p1	NOUN
ejpam-5062	147	39	≤	≤	NUM
ejpam-5062	147	40	o	o	NOUN
ejpam-5062	147	41	≤	≤	NUM
ejpam-5062	147	42	pc2	pc2	NOUN
ejpam-5062	147	43	,	,	PUNCT
ejpam-5062	147	44	and	and	CCONJ
ejpam-5062	147	45	a	a	DET
ejpam-5062	147	46	set	set	NOUN
ejpam-5062	147	47	w	w	PROPN
ejpam-5062	147	48	∈	∈	PROPN
ejpam-5062	147	49	fsspo(τ	fsspo(τ	PROPN
ejpam-5062	147	50	)	)	PUNCT
ejpam-5062	147	51	such	such	ADJ
ejpam-5062	147	52	that	that	SCONJ
ejpam-5062	147	53	p2	p2	PROPN
ejpam-5062	147	54	≤	≤	NUM
ejpam-5062	147	55	w	w	NOUN
ejpam-5062	147	56	≤	≤	NUM
ejpam-5062	147	57	pc1	pc1	NOUN
ejpam-5062	147	58	and	and	CCONJ
ejpam-5062	147	59	o	o	PROPN
ejpam-5062	147	60	≤	≤	PROPN
ejpam-5062	147	61	w	w	PROPN
ejpam-5062	147	62	c.	c.	PROPN
ejpam-5062	148	1	it	it	PRON
ejpam-5062	148	2	follows	follow	VERB
ejpam-5062	148	3	that	that	SCONJ
ejpam-5062	148	4	p1	p1	NOUN
ejpam-5062	148	5	≤	≤	ADJ
ejpam-5062	148	6	o	o	NOUN
ejpam-5062	148	7	≤	≤	PROPN
ejpam-5062	148	8	sspclo	sspclo	NOUN
ejpam-5062	148	9	≤	≤	NUM
ejpam-5062	148	10	sspclw	sspclw	NOUN
ejpam-5062	148	11	c	c	PROPN
ejpam-5062	149	1	=	=	PUNCT
ejpam-5062	149	2	w	w	PROPN
ejpam-5062	149	3	c	c	NOUN
ejpam-5062	149	4	≤	≤	NUM
ejpam-5062	149	5	pc2	pc2	NOUN
ejpam-5062	149	6	.	.	PUNCT
ejpam-5062	150	1	conversely	conversely	ADV
ejpam-5062	150	2	,	,	PUNCT
ejpam-5062	150	3	if	if	SCONJ
ejpam-5062	150	4	we	we	PRON
ejpam-5062	150	5	denote	denote	VERB
ejpam-5062	150	6	by	by	ADP
ejpam-5062	150	7	(	(	PUNCT
ejpam-5062	150	8	sspclo)c	sspclo)c	PROPN
ejpam-5062	150	9	=	=	SYM
ejpam-5062	150	10	w	w	PROPN
ejpam-5062	150	11	,	,	PUNCT
ejpam-5062	150	12	it	it	PRON
ejpam-5062	150	13	is	be	AUX
ejpam-5062	150	14	obvious	obvious	ADJ
ejpam-5062	150	15	that	that	SCONJ
ejpam-5062	150	16	p2	p2	VERB
ejpam-5062	150	17	≤	≤	PROPN
ejpam-5062	150	18	w	w	ADP
ejpam-5062	150	19	and	and	CCONJ
ejpam-5062	150	20	w	w	PROPN
ejpam-5062	150	21	∈	∈	PROPN
ejpam-5062	150	22	fsspo(τ	fsspo(τ	PROPN
ejpam-5062	150	23	)	)	PUNCT
ejpam-5062	150	24	.	.	PUNCT
ejpam-5062	151	1	now	now	ADV
ejpam-5062	151	2	we	we	PRON
ejpam-5062	151	3	have	have	VERB
ejpam-5062	151	4	a	a	DET
ejpam-5062	151	5	case	case	NOUN
ejpam-5062	151	6	where	where	SCONJ
ejpam-5062	151	7	p1	p1	PROPN
ejpam-5062	151	8	≤	≤	X
ejpam-5062	151	9	o	o	NOUN
ejpam-5062	151	10	≤	≤	NUM
ejpam-5062	151	11	pc2	pc2	NOUN
ejpam-5062	151	12	,	,	PUNCT
ejpam-5062	151	13	p2	p2	PROPN
ejpam-5062	151	14	≤	≤	NUM
ejpam-5062	151	15	w	w	NOUN
ejpam-5062	151	16	≤	≤	NUM
ejpam-5062	151	17	pc1	pc1	NOUN
ejpam-5062	151	18	and	and	CCONJ
ejpam-5062	151	19	also	also	ADV
ejpam-5062	151	20	o	o	X
ejpam-5062	151	21	≤	≤	NUM
ejpam-5062	151	22	w	w	PROPN
ejpam-5062	151	23	c	c	NOUN
ejpam-5062	151	24	,	,	PUNCT
ejpam-5062	151	25	meaning	mean	VERB
ejpam-5062	151	26	that	that	SCONJ
ejpam-5062	151	27	(	(	PUNCT
ejpam-5062	151	28	x	x	X
ejpam-5062	151	29	,	,	PUNCT
ejpam-5062	151	30	τ	τ	X
ejpam-5062	151	31	)	)	PUNCT
ejpam-5062	151	32	is	be	AUX
ejpam-5062	151	33	an	an	DET
ejpam-5062	151	34	fsspt2	fsspt2	PROPN
ejpam-5062	151	35	.	.	PUNCT
ejpam-5062	151	36	example	example	NOUN
ejpam-5062	152	1	4	4	NUM
ejpam-5062	152	2	.	.	PUNCT
ejpam-5062	152	3	given	give	VERB
ejpam-5062	152	4	a	a	DET
ejpam-5062	152	5	set	set	NOUN
ejpam-5062	152	6	x	x	X
ejpam-5062	152	7	=	=	SYM
ejpam-5062	152	8	{	{	PUNCT
ejpam-5062	152	9	p1	p1	NOUN
ejpam-5062	152	10	,	,	PUNCT
ejpam-5062	152	11	p2	p2	NOUN
ejpam-5062	152	12	}	}	PUNCT
ejpam-5062	152	13	,	,	PUNCT
ejpam-5062	152	14	and	and	CCONJ
ejpam-5062	152	15	fuzzy	fuzzy	ADJ
ejpam-5062	152	16	sets	set	VERB
ejpam-5062	152	17	u	u	NOUN
ejpam-5062	152	18	=	=	PRON
ejpam-5062	152	19	{	{	PUNCT
ejpam-5062	152	20	(	(	PUNCT
ejpam-5062	152	21	p1	p1	NOUN
ejpam-5062	152	22	,	,	PUNCT
ejpam-5062	152	23	0.6	0.6	NUM
ejpam-5062	152	24	)	)	PUNCT
ejpam-5062	152	25	,	,	PUNCT
ejpam-5062	152	26	(	(	PUNCT
ejpam-5062	152	27	p2	p2	X
ejpam-5062	152	28	,	,	PUNCT
ejpam-5062	152	29	0	0	NUM
ejpam-5062	152	30	)	)	PUNCT
ejpam-5062	152	31	}	}	PUNCT
ejpam-5062	152	32	,	,	PUNCT
ejpam-5062	152	33	v	v	X
ejpam-5062	152	34	=	=	SYM
ejpam-5062	152	35	{	{	PUNCT
ejpam-5062	152	36	(	(	PUNCT
ejpam-5062	152	37	p1	p1	NOUN
ejpam-5062	152	38	,	,	PUNCT
ejpam-5062	152	39	0	0	NUM
ejpam-5062	152	40	)	)	PUNCT
ejpam-5062	152	41	,	,	PUNCT
ejpam-5062	152	42	(	(	PUNCT
ejpam-5062	152	43	p2	p2	X
ejpam-5062	152	44	,	,	PUNCT
ejpam-5062	152	45	0.6	0.6	NUM
ejpam-5062	152	46	)	)	PUNCT
ejpam-5062	152	47	}	}	PUNCT
ejpam-5062	152	48	and	and	CCONJ
ejpam-5062	152	49	w	w	X
ejpam-5062	152	50	=	=	SYM
ejpam-5062	152	51	{	{	PUNCT
ejpam-5062	152	52	(	(	PUNCT
ejpam-5062	152	53	p1	p1	NOUN
ejpam-5062	152	54	,	,	PUNCT
ejpam-5062	152	55	0.6	0.6	NUM
ejpam-5062	152	56	)	)	PUNCT
ejpam-5062	152	57	,	,	PUNCT
ejpam-5062	152	58	(	(	PUNCT
ejpam-5062	152	59	p2	p2	PROPN
ejpam-5062	152	60	,	,	PUNCT
ejpam-5062	152	61	0.8	0.8	NUM
ejpam-5062	152	62	)	)	PUNCT
ejpam-5062	152	63	}	}	PUNCT
ejpam-5062	152	64	.	.	PUNCT
ejpam-5062	153	1	if	if	SCONJ
ejpam-5062	153	2	τ	τ	PROPN
ejpam-5062	153	3	=	=	PUNCT
ejpam-5062	153	4	{	{	PUNCT
ejpam-5062	153	5	0	0	NUM
ejpam-5062	153	6	,	,	PUNCT
ejpam-5062	153	7	u	u	NOUN
ejpam-5062	153	8	,	,	PUNCT
ejpam-5062	153	9	v	v	NOUN
ejpam-5062	153	10	,	,	PUNCT
ejpam-5062	153	11	u	u	NOUN
ejpam-5062	153	12	∨	∨	NUM
ejpam-5062	153	13	v	v	PROPN
ejpam-5062	153	14	,	,	PUNCT
ejpam-5062	153	15	w	w	NOUN
ejpam-5062	153	16	,	,	PUNCT
ejpam-5062	153	17	1	1	NUM
ejpam-5062	153	18	}	}	PUNCT
ejpam-5062	153	19	,	,	PUNCT
ejpam-5062	153	20	it	it	PRON
ejpam-5062	153	21	can	can	AUX
ejpam-5062	153	22	be	be	AUX
ejpam-5062	153	23	shown	show	VERB
ejpam-5062	153	24	that	that	SCONJ
ejpam-5062	153	25	the	the	DET
ejpam-5062	153	26	fuzzy	fuzzy	ADJ
ejpam-5062	153	27	topological	topological	ADJ
ejpam-5062	153	28	space	space	NOUN
ejpam-5062	153	29	(	(	PUNCT
ejpam-5062	153	30	x	x	X
ejpam-5062	153	31	,	,	PUNCT
ejpam-5062	153	32	τ	τ	X
ejpam-5062	153	33	)	)	PUNCT
ejpam-5062	153	34	is	be	AUX
ejpam-5062	153	35	an	an	DET
ejpam-5062	153	36	fsspt2	fsspt2	NOUN
ejpam-5062	153	37	and	and	CCONJ
ejpam-5062	153	38	it	it	PRON
ejpam-5062	153	39	is	be	AUX
ejpam-5062	153	40	not	not	PART
ejpam-5062	153	41	and	and	CCONJ
ejpam-5062	153	42	fsspts	fsspt	NOUN
ejpam-5062	153	43	.	.	PUNCT
ejpam-5062	154	1	it	it	PRON
ejpam-5062	154	2	is	be	AUX
ejpam-5062	154	3	also	also	ADV
ejpam-5062	154	4	obvious	obvious	ADJ
ejpam-5062	154	5	that	that	SCONJ
ejpam-5062	154	6	this	this	PRON
ejpam-5062	154	7	is	be	AUX
ejpam-5062	154	8	an	an	DET
ejpam-5062	154	9	example	example	NOUN
ejpam-5062	154	10	of	of	ADP
ejpam-5062	154	11	a	a	DET
ejpam-5062	154	12	fuzzy	fuzzy	ADJ
ejpam-5062	154	13	space	space	NOUN
ejpam-5062	154	14	that	that	PRON
ejpam-5062	154	15	is	be	AUX
ejpam-5062	154	16	not	not	PART
ejpam-5062	154	17	an	an	DET
ejpam-5062	154	18	ft2	ft2	NOUN
ejpam-5062	154	19	and	and	CCONJ
ejpam-5062	154	20	not	not	PART
ejpam-5062	154	21	an	an	DET
ejpam-5062	154	22	fspt2	fspt2	NOUN
ejpam-5062	154	23	(	(	PUNCT
ejpam-5062	154	24	[	[	X
ejpam-5062	154	25	13	13	NUM
ejpam-5062	154	26	]	]	NUM
ejpam-5062	154	27	)	)	PUNCT
ejpam-5062	154	28	.	.	PUNCT
ejpam-5062	155	1	example	example	NOUN
ejpam-5062	156	1	5	5	NUM
ejpam-5062	156	2	.	.	PUNCT
ejpam-5062	157	1	let	let	VERB
ejpam-5062	157	2	x	x	PRON
ejpam-5062	157	3	be	be	AUX
ejpam-5062	157	4	an	an	DET
ejpam-5062	157	5	infinite	infinite	NOUN
ejpam-5062	157	6	set	set	NOUN
ejpam-5062	157	7	and	and	CCONJ
ejpam-5062	157	8	let	let	VERB
ejpam-5062	157	9	the	the	DET
ejpam-5062	157	10	family	family	NOUN
ejpam-5062	157	11	of	of	ADP
ejpam-5062	157	12	fuzzy	fuzzy	ADJ
ejpam-5062	157	13	sets	set	NOUN
ejpam-5062	157	14	be	be	AUX
ejpam-5062	157	15	defined	define	VERB
ejpam-5062	157	16	as	as	ADP
ejpam-5062	157	17	:	:	PUNCT
ejpam-5062	157	18	τ	τ	X
ejpam-5062	157	19	=	=	PUNCT
ejpam-5062	157	20	{	{	PUNCT
ejpam-5062	157	21	g|suppgc	g|suppgc	NOUN
ejpam-5062	157	22	is	be	AUX
ejpam-5062	157	23	a	a	DET
ejpam-5062	157	24	finite	finite	ADJ
ejpam-5062	157	25	set	set	NOUN
ejpam-5062	157	26	}	}	PUNCT
ejpam-5062	157	27	.	.	PUNCT
ejpam-5062	158	1	it	it	PRON
ejpam-5062	158	2	is	be	AUX
ejpam-5062	158	3	clear	clear	ADJ
ejpam-5062	158	4	that	that	SCONJ
ejpam-5062	158	5	(	(	PUNCT
ejpam-5062	158	6	x	x	X
ejpam-5062	158	7	,	,	PUNCT
ejpam-5062	158	8	τ	τ	X
ejpam-5062	158	9	)	)	PUNCT
ejpam-5062	158	10	is	be	AUX
ejpam-5062	158	11	a	a	DET
ejpam-5062	158	12	fuzzy	fuzzy	ADJ
ejpam-5062	158	13	topological	topological	ADJ
ejpam-5062	158	14	space	space	NOUN
ejpam-5062	158	15	and	and	CCONJ
ejpam-5062	158	16	that	that	SCONJ
ejpam-5062	158	17	each	each	DET
ejpam-5062	158	18	fuzzy	fuzzy	ADJ
ejpam-5062	158	19	point	point	NOUN
ejpam-5062	158	20	in	in	ADP
ejpam-5062	158	21	τ	τ	PROPN
ejpam-5062	158	22	is	be	AUX
ejpam-5062	158	23	a	a	DET
ejpam-5062	158	24	fuzzy	fuzzy	ADJ
ejpam-5062	158	25	strongly	strongly	ADV
ejpam-5062	158	26	semi	semi	ADV
ejpam-5062	158	27	pre	pre	ADJ
ejpam-5062	158	28	-	-	ADJ
ejpam-5062	158	29	closed	closed	ADJ
ejpam-5062	158	30	set	set	NOUN
ejpam-5062	158	31	.	.	PUNCT
ejpam-5062	159	1	from	from	ADP
ejpam-5062	159	2	the	the	DET
ejpam-5062	159	3	other	other	ADJ
ejpam-5062	159	4	perspective	perspective	NOUN
ejpam-5062	159	5	,	,	PUNCT
ejpam-5062	159	6	it	it	PRON
ejpam-5062	159	7	is	be	AUX
ejpam-5062	159	8	impossible	impossible	ADJ
ejpam-5062	159	9	to	to	PART
ejpam-5062	159	10	find	find	VERB
ejpam-5062	159	11	any	any	DET
ejpam-5062	159	12	pair	pair	NOUN
ejpam-5062	159	13	of	of	ADP
ejpam-5062	159	14	fuzzy	fuzzy	ADJ
ejpam-5062	159	15	points	point	NOUN
ejpam-5062	159	16	p1	p1	NOUN
ejpam-5062	159	17	,	,	PUNCT
ejpam-5062	159	18	p2	p2	PROPN
ejpam-5062	159	19	and	and	CCONJ
ejpam-5062	159	20	fuzzy	fuzzy	ADJ
ejpam-5062	159	21	strongly	strongly	ADV
ejpam-5062	159	22	semi	semi	ADV
ejpam-5062	159	23	pre	pre	ADJ
ejpam-5062	159	24	-	-	ADJ
ejpam-5062	159	25	open	open	ADJ
ejpam-5062	159	26	sets	set	NOUN
ejpam-5062	159	27	o1	o1	NOUN
ejpam-5062	159	28	,	,	PUNCT
ejpam-5062	159	29	o2	o2	PROPN
ejpam-5062	159	30	such	such	ADJ
ejpam-5062	159	31	that	that	DET
ejpam-5062	159	32	p1	p1	PROPN
ejpam-5062	159	33	≤	≤	NUM
ejpam-5062	159	34	o1	o1	NOUN
ejpam-5062	159	35	≤	≤	NUM
ejpam-5062	159	36	pc2	pc2	NOUN
ejpam-5062	159	37	,	,	PUNCT
ejpam-5062	159	38	p2	p2	PROPN
ejpam-5062	159	39	≤	≤	NUM
ejpam-5062	159	40	o2	o2	PROPN
ejpam-5062	159	41	≤	≤	PROPN
ejpam-5062	159	42	pc1	pc1	PROPN
ejpam-5062	159	43	and	and	CCONJ
ejpam-5062	159	44	o1	o1	NOUN
ejpam-5062	159	45	≤	≤	NOUN
ejpam-5062	159	46	oc	oc	ADP
ejpam-5062	159	47	2	2	NUM
ejpam-5062	159	48	,	,	PUNCT
ejpam-5062	159	49	because	because	SCONJ
ejpam-5062	159	50	the	the	DET
ejpam-5062	159	51	last	last	ADJ
ejpam-5062	159	52	relation	relation	NOUN
ejpam-5062	159	53	would	would	AUX
ejpam-5062	159	54	imply	imply	VERB
ejpam-5062	159	55	that	that	SCONJ
ejpam-5062	159	56	an	an	DET
ejpam-5062	159	57	infinite	infinite	ADJ
ejpam-5062	159	58	fuzzy	fuzzy	ADJ
ejpam-5062	159	59	set	set	NOUN
ejpam-5062	159	60	is	be	AUX
ejpam-5062	159	61	the	the	DET
ejpam-5062	159	62	subset	subset	NOUN
ejpam-5062	159	63	of	of	ADP
ejpam-5062	159	64	a	a	DET
ejpam-5062	159	65	finite	finite	ADJ
ejpam-5062	159	66	fuzzy	fuzzy	ADJ
ejpam-5062	159	67	set	set	NOUN
ejpam-5062	159	68	.	.	PUNCT
ejpam-5062	160	1	the	the	DET
ejpam-5062	160	2	first	first	ADJ
ejpam-5062	160	3	argument	argument	NOUN
ejpam-5062	160	4	shows	show	VERB
ejpam-5062	160	5	that	that	SCONJ
ejpam-5062	160	6	the	the	DET
ejpam-5062	160	7	fuzzy	fuzzy	ADJ
ejpam-5062	160	8	topological	topological	ADJ
ejpam-5062	160	9	space	space	NOUN
ejpam-5062	160	10	(	(	PUNCT
ejpam-5062	160	11	x	x	X
ejpam-5062	160	12	,	,	PUNCT
ejpam-5062	160	13	τ	τ	X
ejpam-5062	160	14	)	)	PUNCT
ejpam-5062	160	15	is	be	AUX
ejpam-5062	160	16	an	an	DET
ejpam-5062	160	17	fsspts	fsspt	NOUN
ejpam-5062	160	18	while	while	SCONJ
ejpam-5062	160	19	the	the	DET
ejpam-5062	160	20	second	second	ADJ
ejpam-5062	160	21	arguments	argument	NOUN
ejpam-5062	160	22	tells	tell	VERB
ejpam-5062	160	23	us	we	PRON
ejpam-5062	160	24	that	that	SCONJ
ejpam-5062	160	25	it	it	PRON
ejpam-5062	160	26	is	be	AUX
ejpam-5062	160	27	not	not	PART
ejpam-5062	160	28	an	an	DET
ejpam-5062	160	29	fsspt2	fsspt2	NOUN
ejpam-5062	160	30	space	space	NOUN
ejpam-5062	160	31	.	.	PUNCT
ejpam-5062	161	1	in	in	ADP
ejpam-5062	161	2	other	other	ADJ
ejpam-5062	161	3	words	word	NOUN
ejpam-5062	161	4	,	,	PUNCT
ejpam-5062	161	5	we	we	PRON
ejpam-5062	161	6	have	have	AUX
ejpam-5062	161	7	illustrated	illustrate	VERB
ejpam-5062	161	8	with	with	ADP
ejpam-5062	161	9	two	two	NUM
ejpam-5062	161	10	last	last	ADJ
ejpam-5062	161	11	examples	example	NOUN
ejpam-5062	161	12	that	that	SCONJ
ejpam-5062	161	13	the	the	DET
ejpam-5062	161	14	classes	class	NOUN
ejpam-5062	161	15	of	of	ADP
ejpam-5062	161	16	fsspt2	fsspt2	NOUN
ejpam-5062	161	17	spaces	space	NOUN
ejpam-5062	161	18	and	and	CCONJ
ejpam-5062	161	19	fsspts	fsspt	NOUN
ejpam-5062	161	20	spaces	space	NOUN
ejpam-5062	161	21	are	be	AUX
ejpam-5062	161	22	independent	independent	ADJ
ejpam-5062	161	23	.	.	PUNCT
ejpam-5062	162	1	definition	definition	NOUN
ejpam-5062	162	2	15	15	NUM
ejpam-5062	162	3	.	.	PUNCT
ejpam-5062	163	1	a	a	DET
ejpam-5062	163	2	fuzzy	fuzzy	ADJ
ejpam-5062	163	3	topological	topological	ADJ
ejpam-5062	163	4	space	space	NOUN
ejpam-5062	163	5	x	x	PUNCT
ejpam-5062	163	6	is	be	AUX
ejpam-5062	163	7	a	a	DET
ejpam-5062	163	8	fuzzy	fuzzy	ADJ
ejpam-5062	163	9	strong	strong	ADJ
ejpam-5062	163	10	semi	semi	ADJ
ejpam-5062	163	11	pre	pre	ADJ
ejpam-5062	163	12	-	-	ADJ
ejpam-5062	163	13	urysohn	urysohn	ADJ
ejpam-5062	163	14	(	(	PUNCT
ejpam-5062	163	15	or	or	CCONJ
ejpam-5062	163	16	short	short	ADJ
ejpam-5062	163	17	fsspt2	fsspt2	NOUN
ejpam-5062	163	18	1	1	NUM
ejpam-5062	163	19	2	2	NUM
ejpam-5062	163	20	)	)	PUNCT
ejpam-5062	163	21	if	if	SCONJ
ejpam-5062	163	22	and	and	CCONJ
ejpam-5062	163	23	only	only	ADV
ejpam-5062	163	24	if	if	SCONJ
ejpam-5062	163	25	for	for	ADP
ejpam-5062	163	26	any	any	DET
ejpam-5062	163	27	pair	pair	NOUN
ejpam-5062	163	28	of	of	ADP
ejpam-5062	163	29	fuzzy	fuzzy	ADJ
ejpam-5062	163	30	points	point	NOUN
ejpam-5062	163	31	p1	p1	NOUN
ejpam-5062	163	32	and	and	CCONJ
ejpam-5062	163	33	p2	p2	NOUN
ejpam-5062	163	34	,	,	PUNCT
ejpam-5062	163	35	which	which	PRON
ejpam-5062	163	36	have	have	VERB
ejpam-5062	163	37	different	different	ADJ
ejpam-5062	163	38	supports	support	NOUN
ejpam-5062	163	39	,	,	PUNCT
ejpam-5062	163	40	there	there	PRON
ejpam-5062	163	41	exist	exist	VERB
ejpam-5062	163	42	fuzzy	fuzzy	ADJ
ejpam-5062	163	43	strongly	strongly	ADV
ejpam-5062	163	44	semi	semi	ADV
ejpam-5062	163	45	pre	pre	ADJ
ejpam-5062	163	46	-	-	ADJ
ejpam-5062	163	47	open	open	ADJ
ejpam-5062	163	48	set	set	VERB
ejpam-5062	163	49	o1	o1	NOUN
ejpam-5062	163	50	,	,	PUNCT
ejpam-5062	163	51	o2	o2	PROPN
ejpam-5062	163	52	such	such	ADJ
ejpam-5062	163	53	that	that	DET
ejpam-5062	163	54	p1	p1	PROPN
ejpam-5062	163	55	≤	≤	NUM
ejpam-5062	163	56	o1	o1	NOUN
ejpam-5062	163	57	≤	≤	NUM
ejpam-5062	163	58	pc2	pc2	NOUN
ejpam-5062	163	59	,	,	PUNCT
ejpam-5062	163	60	p2	p2	PROPN
ejpam-5062	163	61	≤	≤	NUM
ejpam-5062	163	62	o2	o2	PROPN
ejpam-5062	163	63	≤	≤	PROPN
ejpam-5062	163	64	pc1	pc1	PROPN
ejpam-5062	163	65	and	and	CCONJ
ejpam-5062	163	66	sspclo1	sspclo1	VERB
ejpam-5062	163	67	≤	≤	NUM
ejpam-5062	163	68	(	(	PUNCT
ejpam-5062	163	69	sspclo2	sspclo2	NOUN
ejpam-5062	163	70	)	)	PUNCT
ejpam-5062	163	71	c.	c.	NOUN
ejpam-5062	163	72	according	accord	VERB
ejpam-5062	163	73	to	to	ADP
ejpam-5062	163	74	the	the	DET
ejpam-5062	163	75	above	above	ADJ
ejpam-5062	163	76	definition	definition	NOUN
ejpam-5062	163	77	,	,	PUNCT
ejpam-5062	163	78	it	it	PRON
ejpam-5062	163	79	is	be	AUX
ejpam-5062	163	80	clear	clear	ADJ
ejpam-5062	163	81	that	that	SCONJ
ejpam-5062	163	82	any	any	DET
ejpam-5062	163	83	fuzzy	fuzzy	ADJ
ejpam-5062	163	84	strong	strong	ADJ
ejpam-5062	163	85	semi	semi	ADJ
ejpam-5062	163	86	pre	pre	ADJ
ejpam-5062	163	87	-	-	ADJ
ejpam-5062	163	88	urysohn	urysohn	ADJ
ejpam-5062	163	89	space	space	NOUN
ejpam-5062	163	90	is	be	AUX
ejpam-5062	163	91	also	also	ADV
ejpam-5062	163	92	a	a	DET
ejpam-5062	163	93	fuzzy	fuzzy	ADJ
ejpam-5062	163	94	strong	strong	ADJ
ejpam-5062	163	95	semi	semi	ADJ
ejpam-5062	163	96	pre	pre	ADJ
ejpam-5062	163	97	-	-	ADJ
ejpam-5062	163	98	hausdorff	hausdorff	ADJ
ejpam-5062	163	99	space	space	NOUN
ejpam-5062	163	100	.	.	PUNCT
ejpam-5062	164	1	with	with	ADP
ejpam-5062	164	2	the	the	DET
ejpam-5062	164	3	following	follow	VERB
ejpam-5062	164	4	example	example	NOUN
ejpam-5062	164	5	,	,	PUNCT
ejpam-5062	164	6	we	we	PRON
ejpam-5062	164	7	will	will	AUX
ejpam-5062	164	8	illustrate	illustrate	VERB
ejpam-5062	164	9	that	that	SCONJ
ejpam-5062	164	10	the	the	DET
ejpam-5062	164	11	converse	converse	NOUN
ejpam-5062	164	12	statement	statement	NOUN
ejpam-5062	164	13	does	do	AUX
ejpam-5062	164	14	not	not	PART
ejpam-5062	164	15	hold	hold	VERB
ejpam-5062	164	16	in	in	ADP
ejpam-5062	164	17	general	general	ADJ
ejpam-5062	164	18	case	case	NOUN
ejpam-5062	164	19	.	.	PUNCT
ejpam-5062	165	1	sh	sh	PROPN
ejpam-5062	165	2	.	.	PROPN
ejpam-5062	165	3	makolli	makolli	PROPN
ejpam-5062	165	4	,	,	PUNCT
ejpam-5062	165	5	b.	b.	PROPN
ejpam-5062	165	6	krsteska	krsteska	PROPN
ejpam-5062	165	7	/	/	SYM
ejpam-5062	165	8	eur	eur	PROPN
ejpam-5062	165	9	.	.	PUNCT
ejpam-5062	166	1	j.	j.	PROPN
ejpam-5062	166	2	pure	pure	PROPN
ejpam-5062	166	3	appl	appl	PROPN
ejpam-5062	166	4	.	.	PROPN
ejpam-5062	166	5	math	math	PROPN
ejpam-5062	166	6	,	,	PUNCT
ejpam-5062	166	7	17	17	NUM
ejpam-5062	166	8	(	(	PUNCT
ejpam-5062	166	9	2	2	NUM
ejpam-5062	166	10	)	)	PUNCT
ejpam-5062	166	11	(	(	PUNCT
ejpam-5062	166	12	2024	2024	NUM
ejpam-5062	166	13	)	)	PUNCT
ejpam-5062	166	14	,	,	PUNCT
ejpam-5062	166	15	638	638	NUM
ejpam-5062	166	16	-	-	SYM
ejpam-5062	166	17	662	662	NUM
ejpam-5062	166	18	645	645	NUM
ejpam-5062	166	19	example	example	NOUN
ejpam-5062	166	20	6	6	NUM
ejpam-5062	166	21	.	.	PUNCT
ejpam-5062	167	1	let	let	VERB
ejpam-5062	167	2	x	x	PRON
ejpam-5062	167	3	be	be	AUX
ejpam-5062	167	4	an	an	DET
ejpam-5062	167	5	infinite	infinite	NOUN
ejpam-5062	167	6	set	set	NOUN
ejpam-5062	167	7	and	and	CCONJ
ejpam-5062	167	8	let	let	VERB
ejpam-5062	167	9	there	there	PRON
ejpam-5062	167	10	p0	p0	NOUN
ejpam-5062	167	11	be	be	AUX
ejpam-5062	167	12	a	a	DET
ejpam-5062	167	13	fuzzy	fuzzy	ADJ
ejpam-5062	167	14	point	point	NOUN
ejpam-5062	167	15	with	with	ADP
ejpam-5062	167	16	x0	x0	PROPN
ejpam-5062	167	17	∈	∈	PROPN
ejpam-5062	167	18	x	x	PUNCT
ejpam-5062	167	19	as	as	ADP
ejpam-5062	167	20	its	its	PRON
ejpam-5062	167	21	support	support	NOUN
ejpam-5062	167	22	.	.	PUNCT
ejpam-5062	168	1	let	let	VERB
ejpam-5062	168	2	us	we	PRON
ejpam-5062	168	3	define	define	VERB
ejpam-5062	168	4	the	the	DET
ejpam-5062	168	5	family	family	NOUN
ejpam-5062	168	6	of	of	ADP
ejpam-5062	168	7	fuzzy	fuzzy	ADJ
ejpam-5062	168	8	sets	set	NOUN
ejpam-5062	168	9	as	as	SCONJ
ejpam-5062	168	10	follows	follow	VERB
ejpam-5062	168	11	:	:	PUNCT
ejpam-5062	168	12	a	a	DET
ejpam-5062	168	13	=	=	PUNCT
ejpam-5062	168	14	{	{	PUNCT
ejpam-5062	168	15	o|o(x0	o|o(x0	NOUN
ejpam-5062	168	16	)	)	PUNCT
ejpam-5062	168	17	≤	≤	NUM
ejpam-5062	168	18	p0(x0	p0(x0	NOUN
ejpam-5062	168	19	)	)	PUNCT
ejpam-5062	168	20	}	}	PUNCT
ejpam-5062	168	21	b	b	X
ejpam-5062	168	22	=	=	PRON
ejpam-5062	168	23	{	{	PUNCT
ejpam-5062	168	24	o|suppoc	o|suppoc	NOUN
ejpam-5062	168	25	is	be	AUX
ejpam-5062	168	26	a	a	DET
ejpam-5062	168	27	finite	finite	ADJ
ejpam-5062	168	28	set	set	NOUN
ejpam-5062	168	29	}	}	PUNCT
ejpam-5062	168	30	it	it	PRON
ejpam-5062	168	31	is	be	AUX
ejpam-5062	168	32	obvious	obvious	ADJ
ejpam-5062	168	33	that	that	SCONJ
ejpam-5062	168	34	τ	τ	PROPN
ejpam-5062	168	35	=	=	SYM
ejpam-5062	168	36	a∨b	a∨b	PROPN
ejpam-5062	168	37	is	be	AUX
ejpam-5062	168	38	a	a	DET
ejpam-5062	168	39	fuzzy	fuzzy	ADJ
ejpam-5062	168	40	topological	topological	ADJ
ejpam-5062	168	41	space	space	NOUN
ejpam-5062	168	42	that	that	PRON
ejpam-5062	168	43	is	be	AUX
ejpam-5062	168	44	a	a	DET
ejpam-5062	168	45	case	case	NOUN
ejpam-5062	168	46	of	of	ADP
ejpam-5062	168	47	an	an	DET
ejpam-5062	168	48	fsspt2	fsspt2	NOUN
ejpam-5062	168	49	space	space	NOUN
ejpam-5062	168	50	which	which	PRON
ejpam-5062	168	51	is	be	AUX
ejpam-5062	168	52	not	not	PART
ejpam-5062	168	53	an	an	DET
ejpam-5062	168	54	fsspt2	fsspt2	NOUN
ejpam-5062	168	55	1	1	NUM
ejpam-5062	168	56	2	2	NUM
ejpam-5062	168	57	.	.	PUNCT
ejpam-5062	169	1	definition	definition	NOUN
ejpam-5062	169	2	16	16	NUM
ejpam-5062	169	3	.	.	PUNCT
ejpam-5062	170	1	a	a	DET
ejpam-5062	170	2	fuzzy	fuzzy	ADJ
ejpam-5062	170	3	topological	topological	ADJ
ejpam-5062	170	4	space	space	NOUN
ejpam-5062	170	5	x	x	PUNCT
ejpam-5062	170	6	is	be	AUX
ejpam-5062	170	7	a	a	DET
ejpam-5062	170	8	fuzzy	fuzzy	ADJ
ejpam-5062	170	9	strong	strong	ADJ
ejpam-5062	170	10	semi	semi	ADJ
ejpam-5062	170	11	pre	pre	ADJ
ejpam-5062	170	12	-	-	ADJ
ejpam-5062	170	13	regular	regular	ADJ
ejpam-5062	170	14	(	(	PUNCT
ejpam-5062	170	15	or	or	CCONJ
ejpam-5062	170	16	short	short	ADJ
ejpam-5062	170	17	fsspr	fsspr	NOUN
ejpam-5062	170	18	)	)	PUNCT
ejpam-5062	171	1	if	if	SCONJ
ejpam-5062	171	2	and	and	CCONJ
ejpam-5062	171	3	only	only	ADV
ejpam-5062	171	4	if	if	SCONJ
ejpam-5062	171	5	for	for	ADP
ejpam-5062	171	6	every	every	DET
ejpam-5062	171	7	fuzzy	fuzzy	ADJ
ejpam-5062	171	8	points	point	NOUN
ejpam-5062	171	9	p	p	NOUN
ejpam-5062	171	10	and	and	CCONJ
ejpam-5062	171	11	every	every	DET
ejpam-5062	171	12	fuzzy	fuzzy	ADJ
ejpam-5062	171	13	strongly	strongly	ADV
ejpam-5062	171	14	semi	semi	ADV
ejpam-5062	171	15	pre	pre	ADJ
ejpam-5062	171	16	-	-	ADJ
ejpam-5062	171	17	closed	closed	ADJ
ejpam-5062	171	18	set	set	VERB
ejpam-5062	171	19	c	c	NOUN
ejpam-5062	171	20	in	in	ADP
ejpam-5062	171	21	x	x	PUNCT
ejpam-5062	171	22	such	such	ADJ
ejpam-5062	171	23	that	that	SCONJ
ejpam-5062	171	24	p	p	PROPN
ejpam-5062	171	25	≤	≤	NUM
ejpam-5062	171	26	cc	cc	NOUN
ejpam-5062	171	27	,	,	PUNCT
ejpam-5062	171	28	there	there	PRON
ejpam-5062	171	29	exist	exist	VERB
ejpam-5062	171	30	fuzzy	fuzzy	ADJ
ejpam-5062	171	31	strongly	strongly	ADV
ejpam-5062	171	32	semi	semi	ADV
ejpam-5062	171	33	pre	pre	ADJ
ejpam-5062	171	34	-	-	ADJ
ejpam-5062	171	35	open	open	ADJ
ejpam-5062	171	36	sets	set	NOUN
ejpam-5062	171	37	o1	o1	NOUN
ejpam-5062	171	38	,	,	PUNCT
ejpam-5062	171	39	o2	o2	PROPN
ejpam-5062	171	40	such	such	ADJ
ejpam-5062	171	41	that	that	SCONJ
ejpam-5062	171	42	p	p	PROPN
ejpam-5062	171	43	≤	≤	NUM
ejpam-5062	171	44	o1	o1	NOUN
ejpam-5062	171	45	,	,	PUNCT
ejpam-5062	171	46	c	c	PROPN
ejpam-5062	171	47	≤	≤	PUNCT
ejpam-5062	171	48	o2	o2	PROPN
ejpam-5062	171	49	and	and	CCONJ
ejpam-5062	171	50	o1	o1	NOUN
ejpam-5062	171	51	≤	≤	NOUN
ejpam-5062	171	52	oc	oc	ADP
ejpam-5062	171	53	2	2	NUM
ejpam-5062	171	54	.	.	PUNCT
ejpam-5062	172	1	the	the	DET
ejpam-5062	172	2	definition	definition	NOUN
ejpam-5062	172	3	of	of	ADP
ejpam-5062	172	4	fsspr	fsspr	NOUN
ejpam-5062	172	5	spaces	space	NOUN
ejpam-5062	172	6	can	can	AUX
ejpam-5062	172	7	also	also	ADV
ejpam-5062	172	8	be	be	AUX
ejpam-5062	172	9	given	give	VERB
ejpam-5062	172	10	in	in	ADP
ejpam-5062	172	11	the	the	DET
ejpam-5062	172	12	equivalent	equivalent	ADJ
ejpam-5062	172	13	form	form	NOUN
ejpam-5062	172	14	as	as	SCONJ
ejpam-5062	172	15	it	it	PRON
ejpam-5062	172	16	follows	follow	VERB
ejpam-5062	172	17	.	.	PUNCT
ejpam-5062	173	1	the	the	DET
ejpam-5062	173	2	fuzzy	fuzzy	ADJ
ejpam-5062	173	3	topological	topological	ADJ
ejpam-5062	173	4	space	space	NOUN
ejpam-5062	173	5	(	(	PUNCT
ejpam-5062	173	6	x	x	X
ejpam-5062	173	7	,	,	PUNCT
ejpam-5062	173	8	τ	τ	X
ejpam-5062	173	9	)	)	PUNCT
ejpam-5062	173	10	is	be	AUX
ejpam-5062	173	11	an	an	DET
ejpam-5062	173	12	fsspr	fsspr	ADJ
ejpam-5062	173	13	space	space	NOUN
ejpam-5062	173	14	if	if	SCONJ
ejpam-5062	173	15	and	and	CCONJ
ejpam-5062	173	16	only	only	ADV
ejpam-5062	173	17	if	if	SCONJ
ejpam-5062	173	18	for	for	ADP
ejpam-5062	173	19	every	every	DET
ejpam-5062	173	20	fuzzy	fuzzy	ADJ
ejpam-5062	173	21	point	point	NOUN
ejpam-5062	173	22	p	p	NOUN
ejpam-5062	173	23	and	and	CCONJ
ejpam-5062	173	24	every	every	DET
ejpam-5062	173	25	fuzzy	fuzzy	ADJ
ejpam-5062	173	26	strongly	strongly	ADV
ejpam-5062	173	27	semi	semi	ADV
ejpam-5062	173	28	pre	pre	ADJ
ejpam-5062	173	29	-	-	ADJ
ejpam-5062	173	30	open	open	ADJ
ejpam-5062	173	31	set	set	ADJ
ejpam-5062	173	32	o	o	NOUN
ejpam-5062	173	33	such	such	ADJ
ejpam-5062	173	34	that	that	SCONJ
ejpam-5062	173	35	p	p	PROPN
ejpam-5062	173	36	≤	≤	ADJ
ejpam-5062	173	37	o	o	NOUN
ejpam-5062	173	38	,	,	PUNCT
ejpam-5062	173	39	there	there	PRON
ejpam-5062	173	40	exists	exist	VERB
ejpam-5062	173	41	a	a	DET
ejpam-5062	173	42	fuzzy	fuzzy	ADJ
ejpam-5062	173	43	strongly	strongly	ADV
ejpam-5062	173	44	semi	semi	ADV
ejpam-5062	173	45	pre	pre	ADJ
ejpam-5062	173	46	-	-	ADJ
ejpam-5062	173	47	open	open	ADJ
ejpam-5062	173	48	set	set	ADJ
ejpam-5062	173	49	u	u	PRON
ejpam-5062	173	50	such	such	ADJ
ejpam-5062	173	51	that	that	SCONJ
ejpam-5062	173	52	p	p	PROPN
ejpam-5062	173	53	≤	≤	NUM
ejpam-5062	173	54	u	u	NOUN
ejpam-5062	173	55	≤	≤	NOUN
ejpam-5062	173	56	sspclu	sspclu	PROPN
ejpam-5062	173	57	≤	≤	ADJ
ejpam-5062	173	58	o.	o.	NOUN
ejpam-5062	173	59	definition	definition	NOUN
ejpam-5062	173	60	17	17	NUM
ejpam-5062	173	61	.	.	PUNCT
ejpam-5062	174	1	a	a	DET
ejpam-5062	174	2	fuzzy	fuzzy	ADJ
ejpam-5062	174	3	topological	topological	ADJ
ejpam-5062	174	4	space	space	NOUN
ejpam-5062	174	5	x	x	PUNCT
ejpam-5062	174	6	which	which	PRON
ejpam-5062	174	7	is	be	AUX
ejpam-5062	174	8	an	an	DET
ejpam-5062	174	9	fsspr	fsspr	NOUN
ejpam-5062	174	10	and	and	CCONJ
ejpam-5062	174	11	fsspts	fsspt	NOUN
ejpam-5062	174	12	is	be	AUX
ejpam-5062	174	13	called	call	VERB
ejpam-5062	174	14	fsspt3	fsspt3	NOUN
ejpam-5062	174	15	.	.	PUNCT
ejpam-5062	175	1	we	we	PRON
ejpam-5062	175	2	can	can	AUX
ejpam-5062	175	3	give	give	VERB
ejpam-5062	175	4	also	also	ADV
ejpam-5062	175	5	a	a	DET
ejpam-5062	175	6	different	different	ADJ
ejpam-5062	175	7	and	and	CCONJ
ejpam-5062	175	8	weaker	weak	ADJ
ejpam-5062	175	9	condition	condition	NOUN
ejpam-5062	175	10	of	of	ADP
ejpam-5062	175	11	fuzzy	fuzzy	ADJ
ejpam-5062	175	12	strong	strong	ADJ
ejpam-5062	175	13	semi	semi	ADJ
ejpam-5062	175	14	pre	pre	ADJ
ejpam-5062	175	15	-	-	NOUN
ejpam-5062	175	16	regularity	regularity	ADJ
ejpam-5062	175	17	with	with	ADP
ejpam-5062	175	18	the	the	DET
ejpam-5062	175	19	following	follow	VERB
ejpam-5062	175	20	definition	definition	NOUN
ejpam-5062	175	21	.	.	PUNCT
ejpam-5062	176	1	definition	definition	NOUN
ejpam-5062	176	2	18	18	NUM
ejpam-5062	176	3	.	.	PUNCT
ejpam-5062	177	1	a	a	DET
ejpam-5062	177	2	fuzzy	fuzzy	ADJ
ejpam-5062	177	3	topological	topological	ADJ
ejpam-5062	177	4	space	space	NOUN
ejpam-5062	177	5	x	x	PUNCT
ejpam-5062	177	6	is	be	AUX
ejpam-5062	177	7	a	a	DET
ejpam-5062	177	8	fuzzy	fuzzy	ADJ
ejpam-5062	177	9	strong	strong	ADJ
ejpam-5062	177	10	semi	semi	ADJ
ejpam-5062	177	11	pre	pre	ADJ
ejpam-5062	177	12	-	-	ADJ
ejpam-5062	177	13	weakly	weakly	ADJ
ejpam-5062	177	14	regular	regular	ADJ
ejpam-5062	177	15	(	(	PUNCT
ejpam-5062	177	16	or	or	CCONJ
ejpam-5062	177	17	short	short	ADJ
ejpam-5062	177	18	fsspwr	fsspwr	NOUN
ejpam-5062	177	19	)	)	PUNCT
ejpam-5062	177	20	if	if	SCONJ
ejpam-5062	177	21	and	and	CCONJ
ejpam-5062	177	22	only	only	ADV
ejpam-5062	177	23	if	if	SCONJ
ejpam-5062	177	24	for	for	ADP
ejpam-5062	177	25	every	every	DET
ejpam-5062	177	26	fuzzy	fuzzy	ADJ
ejpam-5062	177	27	points	point	NOUN
ejpam-5062	177	28	p	p	NOUN
ejpam-5062	177	29	and	and	CCONJ
ejpam-5062	177	30	every	every	DET
ejpam-5062	177	31	fuzzy	fuzzy	ADJ
ejpam-5062	177	32	closed	close	VERB
ejpam-5062	177	33	set	set	VERB
ejpam-5062	177	34	c	c	NOUN
ejpam-5062	177	35	in	in	ADP
ejpam-5062	177	36	x	x	PUNCT
ejpam-5062	177	37	such	such	ADJ
ejpam-5062	177	38	that	that	SCONJ
ejpam-5062	177	39	p	p	PROPN
ejpam-5062	177	40	≤	≤	NUM
ejpam-5062	177	41	cc	cc	NOUN
ejpam-5062	177	42	,	,	PUNCT
ejpam-5062	177	43	there	there	PRON
ejpam-5062	177	44	exist	exist	VERB
ejpam-5062	177	45	fuzzy	fuzzy	ADJ
ejpam-5062	177	46	strongly	strongly	ADV
ejpam-5062	177	47	semi	semi	ADV
ejpam-5062	177	48	pre	pre	ADJ
ejpam-5062	177	49	-	-	ADJ
ejpam-5062	177	50	open	open	ADJ
ejpam-5062	177	51	sets	set	NOUN
ejpam-5062	177	52	o1	o1	NOUN
ejpam-5062	177	53	,	,	PUNCT
ejpam-5062	177	54	o2	o2	PROPN
ejpam-5062	177	55	such	such	ADJ
ejpam-5062	177	56	that	that	SCONJ
ejpam-5062	177	57	p	p	PROPN
ejpam-5062	177	58	≤	≤	NUM
ejpam-5062	177	59	o1	o1	NOUN
ejpam-5062	177	60	,	,	PUNCT
ejpam-5062	177	61	c	c	PROPN
ejpam-5062	177	62	≤	≤	PUNCT
ejpam-5062	177	63	o2	o2	PROPN
ejpam-5062	177	64	and	and	CCONJ
ejpam-5062	177	65	o1	o1	NOUN
ejpam-5062	177	66	≤	≤	NOUN
ejpam-5062	177	67	oc	oc	ADP
ejpam-5062	177	68	2	2	NUM
ejpam-5062	177	69	.	.	PUNCT
ejpam-5062	177	70	theorem	theorem	NOUN
ejpam-5062	177	71	4	4	NUM
ejpam-5062	177	72	.	.	PUNCT
ejpam-5062	178	1	let	let	VERB
ejpam-5062	178	2	x	x	PRON
ejpam-5062	178	3	be	be	AUX
ejpam-5062	178	4	an	an	DET
ejpam-5062	178	5	fsspr	fsspr	NOUN
ejpam-5062	178	6	space	space	NOUN
ejpam-5062	178	7	,	,	PUNCT
ejpam-5062	178	8	then	then	ADV
ejpam-5062	178	9	for	for	ADP
ejpam-5062	178	10	every	every	DET
ejpam-5062	178	11	fuzzy	fuzzy	ADJ
ejpam-5062	178	12	strongly	strongly	ADV
ejpam-5062	178	13	semi	semi	ADV
ejpam-5062	178	14	pre	pre	ADJ
ejpam-5062	178	15	-	-	ADJ
ejpam-5062	178	16	closed	closed	ADJ
ejpam-5062	178	17	set	set	VERB
ejpam-5062	178	18	f	f	PROPN
ejpam-5062	178	19	in	in	ADP
ejpam-5062	178	20	x	x	PUNCT
ejpam-5062	178	21	and	and	CCONJ
ejpam-5062	178	22	any	any	DET
ejpam-5062	178	23	fuzzy	fuzzy	ADJ
ejpam-5062	178	24	point	point	NOUN
ejpam-5062	178	25	p	p	NOUN
ejpam-5062	179	1	≤	≤	NUM
ejpam-5062	179	2	f	f	NOUN
ejpam-5062	179	3	c	c	NOUN
ejpam-5062	179	4	,	,	PUNCT
ejpam-5062	179	5	there	there	PRON
ejpam-5062	179	6	exist	exist	VERB
ejpam-5062	179	7	fuzzy	fuzzy	ADJ
ejpam-5062	179	8	strongly	strongly	ADV
ejpam-5062	179	9	semi	semi	ADV
ejpam-5062	179	10	pre	pre	ADJ
ejpam-5062	179	11	-	-	ADJ
ejpam-5062	179	12	open	open	ADJ
ejpam-5062	179	13	sets	set	NOUN
ejpam-5062	179	14	u	u	PROPN
ejpam-5062	179	15	,	,	PUNCT
ejpam-5062	179	16	w	w	ADP
ejpam-5062	179	17	such	such	ADJ
ejpam-5062	179	18	that	that	SCONJ
ejpam-5062	179	19	p	p	PROPN
ejpam-5062	179	20	≤	≤	NUM
ejpam-5062	179	21	u	u	NOUN
ejpam-5062	179	22	,	,	PUNCT
ejpam-5062	179	23	f	f	PROPN
ejpam-5062	179	24	≤	≤	PROPN
ejpam-5062	179	25	w	w	PROPN
ejpam-5062	179	26	and	and	CCONJ
ejpam-5062	179	27	sspclu	sspclu	PROPN
ejpam-5062	179	28	≤	≤	PROPN
ejpam-5062	179	29	(	(	PUNCT
ejpam-5062	179	30	sspclw	sspclw	NOUN
ejpam-5062	179	31	)	)	PUNCT
ejpam-5062	179	32	c.	c.	NOUN
ejpam-5062	179	33	proof	proof	NOUN
ejpam-5062	179	34	.	.	PUNCT
ejpam-5062	180	1	according	accord	VERB
ejpam-5062	180	2	to	to	ADP
ejpam-5062	180	3	the	the	DET
ejpam-5062	180	4	statement	statement	NOUN
ejpam-5062	180	5	of	of	ADP
ejpam-5062	180	6	the	the	DET
ejpam-5062	180	7	theorem	theorem	NOUN
ejpam-5062	180	8	,	,	PUNCT
ejpam-5062	180	9	for	for	ADP
ejpam-5062	180	10	every	every	DET
ejpam-5062	180	11	fuzzy	fuzzy	ADJ
ejpam-5062	180	12	point	point	NOUN
ejpam-5062	180	13	p	p	NOUN
ejpam-5062	180	14	≤	≤	NUM
ejpam-5062	180	15	f	f	PROPN
ejpam-5062	180	16	c	c	NOUN
ejpam-5062	180	17	and	and	CCONJ
ejpam-5062	180	18	the	the	DET
ejpam-5062	180	19	fact	fact	NOUN
ejpam-5062	180	20	that	that	SCONJ
ejpam-5062	180	21	x	x	PRON
ejpam-5062	180	22	is	be	AUX
ejpam-5062	180	23	an	an	DET
ejpam-5062	180	24	fsspr	fsspr	NOUN
ejpam-5062	180	25	space	space	NOUN
ejpam-5062	180	26	,	,	PUNCT
ejpam-5062	180	27	there	there	PRON
ejpam-5062	180	28	exist	exist	VERB
ejpam-5062	180	29	fuzzy	fuzzy	ADJ
ejpam-5062	180	30	strongly	strongly	ADV
ejpam-5062	180	31	semi	semi	ADV
ejpam-5062	180	32	pre	pre	ADJ
ejpam-5062	180	33	-	-	ADJ
ejpam-5062	180	34	open	open	ADJ
ejpam-5062	180	35	sets	set	NOUN
ejpam-5062	180	36	o	o	NOUN
ejpam-5062	180	37	,	,	PUNCT
ejpam-5062	180	38	w	w	ADP
ejpam-5062	180	39	such	such	ADJ
ejpam-5062	180	40	that	that	SCONJ
ejpam-5062	180	41	p	p	PROPN
ejpam-5062	180	42	≤	≤	ADJ
ejpam-5062	180	43	o	o	NOUN
ejpam-5062	180	44	,	,	PUNCT
ejpam-5062	180	45	f	f	PROPN
ejpam-5062	180	46	≤	≤	PROPN
ejpam-5062	180	47	w	w	PROPN
ejpam-5062	180	48	and	and	CCONJ
ejpam-5062	180	49	o	o	PROPN
ejpam-5062	180	50	≤	≤	PROPN
ejpam-5062	180	51	w	w	PROPN
ejpam-5062	180	52	c.	c.	PROPN
ejpam-5062	180	53	also	also	ADV
ejpam-5062	180	54	from	from	ADP
ejpam-5062	180	55	the	the	DET
ejpam-5062	180	56	equivalent	equivalent	ADJ
ejpam-5062	180	57	definition	definition	NOUN
ejpam-5062	180	58	of	of	ADP
ejpam-5062	180	59	fsspr	fsspr	NOUN
ejpam-5062	180	60	spaces	space	NOUN
ejpam-5062	180	61	,	,	PUNCT
ejpam-5062	180	62	for	for	ADP
ejpam-5062	180	63	every	every	DET
ejpam-5062	180	64	fuzzy	fuzzy	ADJ
ejpam-5062	180	65	point	point	NOUN
ejpam-5062	180	66	p	p	NOUN
ejpam-5062	180	67	and	and	CCONJ
ejpam-5062	180	68	a	a	DET
ejpam-5062	180	69	fuzzy	fuzzy	ADJ
ejpam-5062	180	70	strongly	strongly	ADV
ejpam-5062	180	71	semi	semi	ADV
ejpam-5062	180	72	pre	pre	ADJ
ejpam-5062	180	73	-	-	ADJ
ejpam-5062	180	74	open	open	ADJ
ejpam-5062	180	75	set	set	ADJ
ejpam-5062	180	76	o	o	NOUN
ejpam-5062	180	77	such	such	ADJ
ejpam-5062	180	78	that	that	SCONJ
ejpam-5062	180	79	p	p	PROPN
ejpam-5062	180	80	≤	≤	ADJ
ejpam-5062	180	81	o	o	NOUN
ejpam-5062	180	82	,	,	PUNCT
ejpam-5062	180	83	there	there	PRON
ejpam-5062	180	84	exists	exist	VERB
ejpam-5062	180	85	a	a	DET
ejpam-5062	180	86	fuzzy	fuzzy	ADJ
ejpam-5062	180	87	strongly	strongly	ADV
ejpam-5062	180	88	semi	semi	ADV
ejpam-5062	180	89	pre	pre	ADJ
ejpam-5062	180	90	-	-	ADJ
ejpam-5062	180	91	open	open	ADJ
ejpam-5062	180	92	set	set	ADJ
ejpam-5062	180	93	u	u	PRON
ejpam-5062	180	94	such	such	ADJ
ejpam-5062	180	95	that	that	SCONJ
ejpam-5062	180	96	p	p	PROPN
ejpam-5062	180	97	≤	≤	NUM
ejpam-5062	180	98	u	u	NOUN
ejpam-5062	180	99	≤	≤	NOUN
ejpam-5062	180	100	sspclu	sspclu	PROPN
ejpam-5062	180	101	≤	≤	PROPN
ejpam-5062	181	1	o.	o.	NOUN
ejpam-5062	181	2	now	now	ADV
ejpam-5062	181	3	the	the	DET
ejpam-5062	181	4	conclusion	conclusion	NOUN
ejpam-5062	181	5	of	of	ADP
ejpam-5062	181	6	the	the	DET
ejpam-5062	181	7	theorem	theorem	NOUN
ejpam-5062	181	8	is	be	AUX
ejpam-5062	181	9	obvious	obvious	ADJ
ejpam-5062	181	10	.	.	PUNCT
ejpam-5062	182	1	corollary	corollary	ADJ
ejpam-5062	182	2	2	2	NUM
ejpam-5062	182	3	.	.	PUNCT
ejpam-5062	183	1	every	every	DET
ejpam-5062	183	2	fsspt3	fsspt3	NOUN
ejpam-5062	183	3	space	space	NOUN
ejpam-5062	183	4	is	be	AUX
ejpam-5062	183	5	an	an	DET
ejpam-5062	183	6	fsspt2	fsspt2	NOUN
ejpam-5062	183	7	1	1	NUM
ejpam-5062	183	8	2	2	NUM
ejpam-5062	183	9	space	space	NOUN
ejpam-5062	183	10	.	.	PUNCT
ejpam-5062	184	1	proof	proof	NOUN
ejpam-5062	184	2	.	.	PUNCT
ejpam-5062	185	1	it	it	PRON
ejpam-5062	185	2	follows	follow	VERB
ejpam-5062	185	3	directly	directly	ADV
ejpam-5062	185	4	from	from	ADP
ejpam-5062	185	5	the	the	DET
ejpam-5062	185	6	previous	previous	ADJ
ejpam-5062	185	7	theorem	theorem	NOUN
ejpam-5062	185	8	and	and	CCONJ
ejpam-5062	185	9	from	from	ADP
ejpam-5062	185	10	the	the	DET
ejpam-5062	185	11	fact	fact	NOUN
ejpam-5062	185	12	that	that	SCONJ
ejpam-5062	185	13	an	an	DET
ejpam-5062	185	14	fsspt3	fsspt3	NOUN
ejpam-5062	185	15	space	space	NOUN
ejpam-5062	185	16	is	be	AUX
ejpam-5062	185	17	an	an	DET
ejpam-5062	185	18	fsspr	fsspr	NOUN
ejpam-5062	185	19	and	and	CCONJ
ejpam-5062	185	20	fsspts	fsspt	VERB
ejpam-5062	185	21	space	space	NOUN
ejpam-5062	185	22	.	.	PUNCT
ejpam-5062	186	1	sh	sh	PROPN
ejpam-5062	186	2	.	.	PROPN
ejpam-5062	186	3	makolli	makolli	PROPN
ejpam-5062	186	4	,	,	PUNCT
ejpam-5062	186	5	b.	b.	PROPN
ejpam-5062	186	6	krsteska	krsteska	PROPN
ejpam-5062	186	7	/	/	SYM
ejpam-5062	186	8	eur	eur	PROPN
ejpam-5062	186	9	.	.	PUNCT
ejpam-5062	187	1	j.	j.	PROPN
ejpam-5062	187	2	pure	pure	PROPN
ejpam-5062	187	3	appl	appl	PROPN
ejpam-5062	187	4	.	.	PROPN
ejpam-5062	187	5	math	math	PROPN
ejpam-5062	187	6	,	,	PUNCT
ejpam-5062	187	7	17	17	NUM
ejpam-5062	187	8	(	(	PUNCT
ejpam-5062	187	9	2	2	NUM
ejpam-5062	187	10	)	)	PUNCT
ejpam-5062	187	11	(	(	PUNCT
ejpam-5062	187	12	2024	2024	NUM
ejpam-5062	187	13	)	)	PUNCT
ejpam-5062	187	14	,	,	PUNCT
ejpam-5062	187	15	638	638	NUM
ejpam-5062	187	16	-	-	SYM
ejpam-5062	187	17	662	662	NUM
ejpam-5062	187	18	646	646	NUM
ejpam-5062	187	19	theorem	theorem	NOUN
ejpam-5062	187	20	5	5	NUM
ejpam-5062	187	21	.	.	PUNCT
ejpam-5062	188	1	any	any	DET
ejpam-5062	188	2	fuzzy	fuzzy	ADJ
ejpam-5062	188	3	topological	topological	ADJ
ejpam-5062	188	4	space	space	NOUN
ejpam-5062	188	5	(	(	PUNCT
ejpam-5062	188	6	x	x	X
ejpam-5062	188	7	,	,	PUNCT
ejpam-5062	188	8	τ	τ	X
ejpam-5062	188	9	)	)	PUNCT
ejpam-5062	188	10	which	which	PRON
ejpam-5062	188	11	is	be	AUX
ejpam-5062	188	12	an	an	DET
ejpam-5062	188	13	fsspr	fsspr	NOUN
ejpam-5062	188	14	and	and	CCONJ
ejpam-5062	188	15	fsspt0	fsspt0	NOUN
ejpam-5062	188	16	space	space	NOUN
ejpam-5062	188	17	is	be	AUX
ejpam-5062	188	18	also	also	ADV
ejpam-5062	188	19	an	an	DET
ejpam-5062	188	20	fsspt2	fsspt2	NOUN
ejpam-5062	188	21	1	1	NUM
ejpam-5062	188	22	2	2	NUM
ejpam-5062	188	23	space	space	NOUN
ejpam-5062	188	24	.	.	PUNCT
ejpam-5062	189	1	proof	proof	NOUN
ejpam-5062	189	2	.	.	PUNCT
ejpam-5062	190	1	we	we	PRON
ejpam-5062	190	2	are	be	AUX
ejpam-5062	190	3	going	go	VERB
ejpam-5062	190	4	to	to	PART
ejpam-5062	190	5	take	take	VERB
ejpam-5062	190	6	into	into	ADP
ejpam-5062	190	7	consideration	consideration	NOUN
ejpam-5062	190	8	two	two	NUM
ejpam-5062	190	9	fuzzy	fuzzy	ADJ
ejpam-5062	190	10	points	point	NOUN
ejpam-5062	190	11	p1	p1	NOUN
ejpam-5062	190	12	and	and	CCONJ
ejpam-5062	190	13	p2	p2	NOUN
ejpam-5062	190	14	with	with	ADP
ejpam-5062	190	15	different	different	ADJ
ejpam-5062	190	16	support	support	NOUN
ejpam-5062	190	17	.	.	PUNCT
ejpam-5062	191	1	based	base	VERB
ejpam-5062	191	2	on	on	ADP
ejpam-5062	191	3	the	the	DET
ejpam-5062	191	4	assumption	assumption	NOUN
ejpam-5062	191	5	that	that	SCONJ
ejpam-5062	191	6	(	(	PUNCT
ejpam-5062	191	7	x	x	X
ejpam-5062	191	8	,	,	PUNCT
ejpam-5062	191	9	τ	τ	X
ejpam-5062	191	10	)	)	PUNCT
ejpam-5062	191	11	is	be	AUX
ejpam-5062	191	12	an	an	DET
ejpam-5062	191	13	fsspt0	fsspt0	NOUN
ejpam-5062	191	14	space	space	NOUN
ejpam-5062	191	15	,	,	PUNCT
ejpam-5062	191	16	it	it	PRON
ejpam-5062	191	17	follows	follow	VERB
ejpam-5062	191	18	that	that	SCONJ
ejpam-5062	191	19	there	there	PRON
ejpam-5062	191	20	exists	exist	VERB
ejpam-5062	191	21	a	a	DET
ejpam-5062	191	22	set	set	NOUN
ejpam-5062	191	23	u	u	PROPN
ejpam-5062	191	24	∈	∈	PROPN
ejpam-5062	191	25	fsspo(τ	fsspo(τ	PROPN
ejpam-5062	191	26	)	)	PUNCT
ejpam-5062	191	27	such	such	ADJ
ejpam-5062	191	28	that	that	SCONJ
ejpam-5062	191	29	p1	p1	PROPN
ejpam-5062	191	30	≤	≤	X
ejpam-5062	191	31	u	u	NOUN
ejpam-5062	191	32	≤	≤	NOUN
ejpam-5062	191	33	pc2	pc2	NOUN
ejpam-5062	191	34	.	.	PUNCT
ejpam-5062	192	1	if	if	SCONJ
ejpam-5062	192	2	we	we	PRON
ejpam-5062	192	3	denote	denote	VERB
ejpam-5062	192	4	by	by	ADP
ejpam-5062	192	5	f	f	PROPN
ejpam-5062	192	6	=	=	SYM
ejpam-5062	192	7	u	u	PROPN
ejpam-5062	192	8	c	c	NOUN
ejpam-5062	192	9	,	,	PUNCT
ejpam-5062	192	10	f	f	PROPN
ejpam-5062	192	11	∈	∈	PROPN
ejpam-5062	192	12	fsspc(τ	fsspc(τ	PROPN
ejpam-5062	192	13	)	)	PUNCT
ejpam-5062	192	14	,	,	PUNCT
ejpam-5062	192	15	it	it	PRON
ejpam-5062	192	16	is	be	AUX
ejpam-5062	192	17	obvious	obvious	ADJ
ejpam-5062	192	18	that	that	SCONJ
ejpam-5062	192	19	p1	p1	NOUN
ejpam-5062	192	20	≤	≤	NUM
ejpam-5062	192	21	f	f	PROPN
ejpam-5062	192	22	c	c	PROPN
ejpam-5062	192	23	and	and	CCONJ
ejpam-5062	192	24	since	since	SCONJ
ejpam-5062	192	25	(	(	PUNCT
ejpam-5062	192	26	x	x	NOUN
ejpam-5062	192	27	,	,	PUNCT
ejpam-5062	192	28	τ	τ	X
ejpam-5062	192	29	)	)	PUNCT
ejpam-5062	192	30	is	be	AUX
ejpam-5062	192	31	an	an	DET
ejpam-5062	192	32	fsspr	fsspr	NOUN
ejpam-5062	192	33	space	space	NOUN
ejpam-5062	192	34	,	,	PUNCT
ejpam-5062	192	35	it	it	PRON
ejpam-5062	192	36	implies	imply	VERB
ejpam-5062	192	37	the	the	DET
ejpam-5062	192	38	existence	existence	NOUN
ejpam-5062	192	39	of	of	ADP
ejpam-5062	192	40	fuzzy	fuzzy	ADJ
ejpam-5062	192	41	sets	set	NOUN
ejpam-5062	192	42	v	v	ADP
ejpam-5062	192	43	,	,	PUNCT
ejpam-5062	192	44	w	w	PROPN
ejpam-5062	192	45	∈	∈	PROPN
ejpam-5062	192	46	fsspo(τ	fsspo(τ	PROPN
ejpam-5062	192	47	)	)	PUNCT
ejpam-5062	192	48	such	such	ADJ
ejpam-5062	192	49	that	that	DET
ejpam-5062	192	50	p1	p1	PROPN
ejpam-5062	192	51	≤	≤	NOUN
ejpam-5062	192	52	v	v	NOUN
ejpam-5062	192	53	,	,	PUNCT
ejpam-5062	192	54	f	f	PROPN
ejpam-5062	192	55	≤	≤	PROPN
ejpam-5062	192	56	w	w	ADP
ejpam-5062	192	57	,	,	PUNCT
ejpam-5062	192	58	and	and	CCONJ
ejpam-5062	192	59	v	v	ADP
ejpam-5062	192	60	≤	≤	NUM
ejpam-5062	192	61	w	w	PROPN
ejpam-5062	192	62	c.	c.	PROPN
ejpam-5062	192	63	now	now	ADV
ejpam-5062	192	64	,	,	PUNCT
ejpam-5062	192	65	from	from	ADP
ejpam-5062	192	66	the	the	DET
ejpam-5062	192	67	theorem	theorem	NOUN
ejpam-5062	192	68	4	4	NUM
ejpam-5062	192	69	we	we	PRON
ejpam-5062	192	70	also	also	ADV
ejpam-5062	192	71	have	have	VERB
ejpam-5062	192	72	that	that	DET
ejpam-5062	192	73	sspclv	sspclv	PROPN
ejpam-5062	192	74	≤	≤	PROPN
ejpam-5062	192	75	(	(	PUNCT
ejpam-5062	192	76	sspclw	sspclw	PROPN
ejpam-5062	192	77	)	)	PUNCT
ejpam-5062	192	78	c	c	PROPN
ejpam-5062	192	79	and	and	CCONJ
ejpam-5062	192	80	combining	combine	VERB
ejpam-5062	192	81	it	it	PRON
ejpam-5062	192	82	with	with	ADP
ejpam-5062	192	83	the	the	DET
ejpam-5062	192	84	fact	fact	NOUN
ejpam-5062	192	85	that	that	SCONJ
ejpam-5062	192	86	p2	p2	VERB
ejpam-5062	192	87	≤	≤	NOUN
ejpam-5062	192	88	u	u	NOUN
ejpam-5062	192	89	c	c	NOUN
ejpam-5062	192	90	=	=	SYM
ejpam-5062	192	91	f	f	PROPN
ejpam-5062	192	92	≤	≤	NUM
ejpam-5062	192	93	w	w	PROPN
ejpam-5062	192	94	and	and	CCONJ
ejpam-5062	192	95	as	as	ADV
ejpam-5062	192	96	well	well	ADV
ejpam-5062	192	97	as	as	ADP
ejpam-5062	192	98	p1	p1	PROPN
ejpam-5062	192	99	≤	≤	NOUN
ejpam-5062	192	100	v	v	NOUN
ejpam-5062	192	101	,	,	PUNCT
ejpam-5062	192	102	we	we	PRON
ejpam-5062	192	103	reach	reach	VERB
ejpam-5062	192	104	the	the	DET
ejpam-5062	192	105	desired	desire	VERB
ejpam-5062	192	106	result	result	NOUN
ejpam-5062	192	107	.	.	PUNCT
ejpam-5062	193	1	the	the	DET
ejpam-5062	193	2	latest	late	ADJ
ejpam-5062	193	3	conditions	condition	NOUN
ejpam-5062	193	4	imply	imply	VERB
ejpam-5062	193	5	that	that	SCONJ
ejpam-5062	193	6	for	for	ADP
ejpam-5062	193	7	any	any	DET
ejpam-5062	193	8	given	give	VERB
ejpam-5062	193	9	pair	pair	NOUN
ejpam-5062	193	10	of	of	ADP
ejpam-5062	193	11	fuzzy	fuzzy	ADJ
ejpam-5062	193	12	points	point	NOUN
ejpam-5062	193	13	p1	p1	NOUN
ejpam-5062	193	14	and	and	CCONJ
ejpam-5062	193	15	p2	p2	NOUN
ejpam-5062	193	16	with	with	ADP
ejpam-5062	193	17	different	different	ADJ
ejpam-5062	193	18	support	support	NOUN
ejpam-5062	193	19	,	,	PUNCT
ejpam-5062	193	20	there	there	PRON
ejpam-5062	193	21	exist	exist	VERB
ejpam-5062	193	22	fuzzy	fuzzy	ADJ
ejpam-5062	193	23	sets	set	NOUN
ejpam-5062	193	24	v	v	ADP
ejpam-5062	193	25	,	,	PUNCT
ejpam-5062	193	26	w	w	PROPN
ejpam-5062	193	27	∈	∈	PROPN
ejpam-5062	193	28	fsspo(τ	fsspo(τ	PROPN
ejpam-5062	193	29	)	)	PUNCT
ejpam-5062	193	30	such	such	ADJ
ejpam-5062	193	31	that	that	SCONJ
ejpam-5062	193	32	p1	p1	PROPN
ejpam-5062	193	33	≤	≤	X
ejpam-5062	193	34	v	v	ADJ
ejpam-5062	193	35	≤	≤	NUM
ejpam-5062	193	36	pc2	pc2	NOUN
ejpam-5062	193	37	,	,	PUNCT
ejpam-5062	193	38	p2	p2	PROPN
ejpam-5062	193	39	≤	≤	NUM
ejpam-5062	193	40	w	w	NOUN
ejpam-5062	193	41	≤	≤	NUM
ejpam-5062	193	42	pc1	pc1	PROPN
ejpam-5062	193	43	and	and	CCONJ
ejpam-5062	193	44	sspclv	sspclv	PROPN
ejpam-5062	193	45	≤	≤	PROPN
ejpam-5062	193	46	(	(	PUNCT
ejpam-5062	194	1	sspclw	sspclw	NOUN
ejpam-5062	194	2	)	)	PUNCT
ejpam-5062	194	3	c	c	NOUN
ejpam-5062	194	4	,	,	PUNCT
ejpam-5062	194	5	hence	hence	ADV
ejpam-5062	194	6	the	the	DET
ejpam-5062	194	7	fuzzy	fuzzy	ADJ
ejpam-5062	194	8	topological	topological	ADJ
ejpam-5062	194	9	space	space	NOUN
ejpam-5062	194	10	(	(	PUNCT
ejpam-5062	194	11	x	x	X
ejpam-5062	194	12	,	,	PUNCT
ejpam-5062	194	13	τ	τ	X
ejpam-5062	194	14	)	)	PUNCT
ejpam-5062	194	15	is	be	AUX
ejpam-5062	194	16	fsspt2	fsspt2	NOUN
ejpam-5062	194	17	1	1	NUM
ejpam-5062	194	18	2	2	NUM
ejpam-5062	194	19	.	.	PUNCT
ejpam-5062	195	1	definition	definition	NOUN
ejpam-5062	195	2	19	19	NUM
ejpam-5062	195	3	.	.	PUNCT
ejpam-5062	196	1	a	a	DET
ejpam-5062	196	2	fuzzy	fuzzy	ADJ
ejpam-5062	196	3	topological	topological	ADJ
ejpam-5062	196	4	space	space	NOUN
ejpam-5062	196	5	x	x	PUNCT
ejpam-5062	196	6	is	be	AUX
ejpam-5062	196	7	a	a	DET
ejpam-5062	196	8	fuzzy	fuzzy	ADJ
ejpam-5062	196	9	strong	strong	ADJ
ejpam-5062	196	10	semi	semi	ADJ
ejpam-5062	196	11	pre	pre	ADJ
ejpam-5062	196	12	-	-	ADJ
ejpam-5062	196	13	normal	normal	ADJ
ejpam-5062	196	14	(	(	PUNCT
ejpam-5062	196	15	or	or	CCONJ
ejpam-5062	196	16	short	short	ADJ
ejpam-5062	196	17	fsspn	fsspn	NOUN
ejpam-5062	196	18	)	)	PUNCT
ejpam-5062	197	1	if	if	SCONJ
ejpam-5062	197	2	and	and	CCONJ
ejpam-5062	197	3	only	only	ADV
ejpam-5062	197	4	if	if	SCONJ
ejpam-5062	197	5	for	for	SCONJ
ejpam-5062	197	6	every	every	DET
ejpam-5062	197	7	pair	pair	NOUN
ejpam-5062	197	8	of	of	ADP
ejpam-5062	197	9	fuzzy	fuzzy	ADJ
ejpam-5062	197	10	strongly	strongly	ADV
ejpam-5062	197	11	semi	semi	ADV
ejpam-5062	197	12	pre	pre	ADJ
ejpam-5062	197	13	-	-	ADJ
ejpam-5062	197	14	closed	closed	ADJ
ejpam-5062	197	15	sets	set	NOUN
ejpam-5062	197	16	c1	c1	PROPN
ejpam-5062	197	17	,	,	PUNCT
ejpam-5062	197	18	c2	c2	PROPN
ejpam-5062	197	19	,	,	PUNCT
ejpam-5062	197	20	such	such	ADJ
ejpam-5062	197	21	that	that	DET
ejpam-5062	197	22	c1	c1	PROPN
ejpam-5062	197	23	≤	≤	PROPN
ejpam-5062	197	24	cc	cc	PROPN
ejpam-5062	197	25	2	2	NUM
ejpam-5062	197	26	,	,	PUNCT
ejpam-5062	197	27	there	there	PRON
ejpam-5062	197	28	exist	exist	VERB
ejpam-5062	197	29	fuzzy	fuzzy	ADJ
ejpam-5062	197	30	strongly	strongly	ADV
ejpam-5062	197	31	semi	semi	ADV
ejpam-5062	197	32	pre	pre	ADJ
ejpam-5062	197	33	-	-	ADJ
ejpam-5062	197	34	open	open	ADJ
ejpam-5062	197	35	sets	set	NOUN
ejpam-5062	197	36	o1	o1	NOUN
ejpam-5062	197	37	,	,	PUNCT
ejpam-5062	197	38	o2	o2	PROPN
ejpam-5062	197	39	such	such	ADJ
ejpam-5062	197	40	that	that	DET
ejpam-5062	197	41	c1	c1	PROPN
ejpam-5062	197	42	≤	≤	PROPN
ejpam-5062	197	43	o1	o1	PROPN
ejpam-5062	197	44	,	,	PUNCT
ejpam-5062	197	45	c2	c2	PROPN
ejpam-5062	197	46	≤	≤	PUNCT
ejpam-5062	197	47	o2	o2	PROPN
ejpam-5062	197	48	and	and	CCONJ
ejpam-5062	197	49	o1	o1	NOUN
ejpam-5062	197	50	≤	≤	NOUN
ejpam-5062	197	51	oc	oc	ADP
ejpam-5062	197	52	2	2	NUM
ejpam-5062	197	53	.	.	PUNCT
ejpam-5062	197	54	a	a	DET
ejpam-5062	197	55	fuzzy	fuzzy	ADJ
ejpam-5062	197	56	topological	topological	ADJ
ejpam-5062	197	57	space	space	NOUN
ejpam-5062	197	58	with	with	ADP
ejpam-5062	197	59	fsspn	fsspn	ADJ
ejpam-5062	197	60	and	and	CCONJ
ejpam-5062	197	61	fsspts	fsspt	VERB
ejpam-5062	197	62	properties	property	NOUN
ejpam-5062	197	63	is	be	AUX
ejpam-5062	197	64	called	call	VERB
ejpam-5062	197	65	an	an	DET
ejpam-5062	197	66	fsspt4	fsspt4	NOUN
ejpam-5062	197	67	space	space	NOUN
ejpam-5062	197	68	.	.	PUNCT
ejpam-5062	198	1	clearly	clearly	ADV
ejpam-5062	198	2	,	,	PUNCT
ejpam-5062	198	3	any	any	DET
ejpam-5062	198	4	fsspt4	fsspt4	NOUN
ejpam-5062	198	5	space	space	NOUN
ejpam-5062	198	6	is	be	AUX
ejpam-5062	198	7	also	also	ADV
ejpam-5062	198	8	an	an	DET
ejpam-5062	198	9	fsspt3	fsspt3	NOUN
ejpam-5062	198	10	space	space	NOUN
ejpam-5062	198	11	.	.	PUNCT
ejpam-5062	199	1	we	we	PRON
ejpam-5062	199	2	can	can	AUX
ejpam-5062	199	3	formulate	formulate	VERB
ejpam-5062	199	4	the	the	DET
ejpam-5062	199	5	following	follow	VERB
ejpam-5062	199	6	theorem	theorem	NOUN
ejpam-5062	199	7	which	which	PRON
ejpam-5062	199	8	gives	give	VERB
ejpam-5062	199	9	a	a	DET
ejpam-5062	199	10	necessary	necessary	ADJ
ejpam-5062	199	11	and	and	CCONJ
ejpam-5062	199	12	sufficient	sufficient	ADJ
ejpam-5062	199	13	condition	condition	NOUN
ejpam-5062	199	14	for	for	ADP
ejpam-5062	199	15	the	the	DET
ejpam-5062	199	16	existence	existence	NOUN
ejpam-5062	199	17	of	of	ADP
ejpam-5062	199	18	fsspn	fsspn	ADJ
ejpam-5062	199	19	spaces	space	NOUN
ejpam-5062	199	20	.	.	PUNCT
ejpam-5062	200	1	theorem	theorem	ADJ
ejpam-5062	200	2	6	6	NUM
ejpam-5062	200	3	.	.	PUNCT
ejpam-5062	201	1	the	the	DET
ejpam-5062	201	2	fuzzy	fuzzy	ADJ
ejpam-5062	201	3	topological	topological	ADJ
ejpam-5062	201	4	space	space	NOUN
ejpam-5062	201	5	(	(	PUNCT
ejpam-5062	201	6	x	x	X
ejpam-5062	201	7	,	,	PUNCT
ejpam-5062	201	8	τ	τ	X
ejpam-5062	201	9	)	)	PUNCT
ejpam-5062	201	10	is	be	AUX
ejpam-5062	201	11	an	an	DET
ejpam-5062	201	12	fsspn	fsspn	ADJ
ejpam-5062	201	13	if	if	SCONJ
ejpam-5062	202	1	and	and	CCONJ
ejpam-5062	202	2	only	only	ADV
ejpam-5062	202	3	if	if	SCONJ
ejpam-5062	202	4	for	for	ADP
ejpam-5062	202	5	any	any	DET
ejpam-5062	202	6	f	f	PROPN
ejpam-5062	202	7	∈	∈	PROPN
ejpam-5062	202	8	fsspc(τ	fsspc(τ	NOUN
ejpam-5062	202	9	)	)	PUNCT
ejpam-5062	202	10	and	and	CCONJ
ejpam-5062	202	11	a	a	DET
ejpam-5062	202	12	fuzzy	fuzzy	ADJ
ejpam-5062	202	13	set	set	VERB
ejpam-5062	202	14	o	o	X
ejpam-5062	202	15	∈	∈	PROPN
ejpam-5062	202	16	fsspo(τ	fsspo(τ	PROPN
ejpam-5062	202	17	)	)	PUNCT
ejpam-5062	202	18	such	such	ADJ
ejpam-5062	202	19	that	that	SCONJ
ejpam-5062	202	20	f	f	PROPN
ejpam-5062	202	21	≤	≤	NUM
ejpam-5062	202	22	o	o	NOUN
ejpam-5062	202	23	,	,	PUNCT
ejpam-5062	202	24	there	there	PRON
ejpam-5062	202	25	exists	exist	VERB
ejpam-5062	202	26	a	a	DET
ejpam-5062	202	27	fuzzy	fuzzy	ADJ
ejpam-5062	202	28	set	set	VERB
ejpam-5062	202	29	w	w	PROPN
ejpam-5062	202	30	∈	∈	PROPN
ejpam-5062	202	31	fsspo(τ	fsspo(τ	PROPN
ejpam-5062	202	32	)	)	PUNCT
ejpam-5062	203	1	such	such	ADJ
ejpam-5062	203	2	that	that	SCONJ
ejpam-5062	203	3	f	f	PROPN
ejpam-5062	203	4	≤	≤	PROPN
ejpam-5062	203	5	w	w	PROPN
ejpam-5062	203	6	≤	≤	NUM
ejpam-5062	203	7	sspclw	sspclw	NOUN
ejpam-5062	203	8	≤	≤	ADJ
ejpam-5062	203	9	o.	o.	NOUN
ejpam-5062	203	10	proof	proof	NOUN
ejpam-5062	203	11	.	.	PUNCT
ejpam-5062	204	1	we	we	PRON
ejpam-5062	204	2	can	can	AUX
ejpam-5062	204	3	use	use	VERB
ejpam-5062	204	4	similar	similar	ADJ
ejpam-5062	204	5	argumentation	argumentation	NOUN
ejpam-5062	204	6	as	as	ADP
ejpam-5062	204	7	in	in	ADP
ejpam-5062	204	8	theorem	theorem	NOUN
ejpam-5062	204	9	4	4	NUM
ejpam-5062	204	10	.	.	PUNCT
ejpam-5062	204	11	definition	definition	NOUN
ejpam-5062	204	12	20	20	NUM
ejpam-5062	204	13	.	.	PUNCT
ejpam-5062	205	1	a	a	DET
ejpam-5062	205	2	fuzzy	fuzzy	ADJ
ejpam-5062	205	3	topological	topological	ADJ
ejpam-5062	205	4	space	space	NOUN
ejpam-5062	205	5	x	x	PUNCT
ejpam-5062	205	6	is	be	AUX
ejpam-5062	205	7	a	a	DET
ejpam-5062	205	8	fuzzy	fuzzy	ADJ
ejpam-5062	205	9	strong	strong	ADJ
ejpam-5062	205	10	semi	semi	ADJ
ejpam-5062	205	11	pre	pre	ADJ
ejpam-5062	205	12	-	-	ADJ
ejpam-5062	205	13	weakly	weakly	ADJ
ejpam-5062	205	14	normal	normal	ADJ
ejpam-5062	205	15	(	(	PUNCT
ejpam-5062	205	16	or	or	CCONJ
ejpam-5062	205	17	short	short	ADJ
ejpam-5062	205	18	fsspwn	fsspwn	NOUN
ejpam-5062	205	19	)	)	PUNCT
ejpam-5062	205	20	if	if	SCONJ
ejpam-5062	205	21	and	and	CCONJ
ejpam-5062	205	22	only	only	ADV
ejpam-5062	205	23	if	if	SCONJ
ejpam-5062	205	24	for	for	SCONJ
ejpam-5062	205	25	every	every	DET
ejpam-5062	205	26	pair	pair	NOUN
ejpam-5062	205	27	of	of	ADP
ejpam-5062	205	28	fuzzy	fuzzy	ADJ
ejpam-5062	205	29	strongly	strongly	ADV
ejpam-5062	205	30	semi	semi	ADV
ejpam-5062	205	31	pre	pre	ADJ
ejpam-5062	205	32	-	-	ADJ
ejpam-5062	205	33	closed	closed	ADJ
ejpam-5062	205	34	sets	set	NOUN
ejpam-5062	205	35	c1	c1	PROPN
ejpam-5062	205	36	,	,	PUNCT
ejpam-5062	205	37	c2	c2	PROPN
ejpam-5062	205	38	,	,	PUNCT
ejpam-5062	205	39	such	such	ADJ
ejpam-5062	205	40	that	that	SCONJ
ejpam-5062	205	41	c1	c1	PROPN
ejpam-5062	205	42	∧	∧	PROPN
ejpam-5062	205	43	c2	c2	PROPN
ejpam-5062	205	44	=	=	PUNCT
ejpam-5062	205	45	∅	∅	NOUN
ejpam-5062	205	46	,	,	PUNCT
ejpam-5062	205	47	there	there	PRON
ejpam-5062	205	48	exist	exist	VERB
ejpam-5062	205	49	fuzzy	fuzzy	ADJ
ejpam-5062	205	50	strongly	strongly	ADV
ejpam-5062	205	51	semi	semi	ADV
ejpam-5062	205	52	pre	pre	ADJ
ejpam-5062	205	53	-	-	ADJ
ejpam-5062	205	54	open	open	ADJ
ejpam-5062	205	55	sets	set	NOUN
ejpam-5062	205	56	o1	o1	NOUN
ejpam-5062	205	57	,	,	PUNCT
ejpam-5062	205	58	o2	o2	PROPN
ejpam-5062	205	59	such	such	ADJ
ejpam-5062	205	60	that	that	DET
ejpam-5062	205	61	c1	c1	PROPN
ejpam-5062	205	62	≤	≤	PROPN
ejpam-5062	205	63	o1	o1	PROPN
ejpam-5062	205	64	,	,	PUNCT
ejpam-5062	205	65	c2	c2	PROPN
ejpam-5062	205	66	≤	≤	PUNCT
ejpam-5062	205	67	o2	o2	PROPN
ejpam-5062	205	68	and	and	CCONJ
ejpam-5062	205	69	o1	o1	NOUN
ejpam-5062	205	70	≤	≤	NOUN
ejpam-5062	205	71	oc	oc	ADP
ejpam-5062	205	72	2	2	NUM
ejpam-5062	205	73	.	.	X
ejpam-5062	206	1	we	we	PRON
ejpam-5062	206	2	can	can	AUX
ejpam-5062	206	3	formulate	formulate	VERB
ejpam-5062	206	4	the	the	DET
ejpam-5062	206	5	following	follow	VERB
ejpam-5062	206	6	theorem	theorem	NOUN
ejpam-5062	206	7	in	in	ADP
ejpam-5062	206	8	regards	regard	NOUN
ejpam-5062	206	9	to	to	ADP
ejpam-5062	206	10	the	the	DET
ejpam-5062	206	11	fsspwn	fsspwn	NOUN
ejpam-5062	206	12	spaces	space	NOUN
ejpam-5062	206	13	.	.	PUNCT
ejpam-5062	207	1	theorem	theorem	ADJ
ejpam-5062	207	2	7	7	NUM
ejpam-5062	207	3	.	.	PUNCT
ejpam-5062	208	1	every	every	DET
ejpam-5062	208	2	fuzzy	fuzzy	ADJ
ejpam-5062	208	3	topological	topological	ADJ
ejpam-5062	208	4	space	space	NOUN
ejpam-5062	208	5	(	(	PUNCT
ejpam-5062	208	6	x	x	X
ejpam-5062	208	7	,	,	PUNCT
ejpam-5062	208	8	τ	τ	X
ejpam-5062	208	9	)	)	PUNCT
ejpam-5062	208	10	which	which	PRON
ejpam-5062	208	11	is	be	AUX
ejpam-5062	208	12	an	an	DET
ejpam-5062	208	13	fsspn	fsspn	ADJ
ejpam-5062	208	14	space	space	NOUN
ejpam-5062	208	15	is	be	AUX
ejpam-5062	208	16	also	also	ADV
ejpam-5062	208	17	an	an	DET
ejpam-5062	208	18	fsspwn	fsspwn	NOUN
ejpam-5062	208	19	space	space	NOUN
ejpam-5062	208	20	.	.	PUNCT
ejpam-5062	209	1	proof	proof	NOUN
ejpam-5062	209	2	.	.	PUNCT
ejpam-5062	210	1	in	in	ADP
ejpam-5062	210	2	fuzzy	fuzzy	ADJ
ejpam-5062	210	3	topological	topological	ADJ
ejpam-5062	210	4	spaces	space	NOUN
ejpam-5062	210	5	the	the	DET
ejpam-5062	210	6	following	follow	VERB
ejpam-5062	210	7	implication	implication	NOUN
ejpam-5062	210	8	is	be	AUX
ejpam-5062	210	9	always	always	ADV
ejpam-5062	210	10	true	true	ADJ
ejpam-5062	210	11	:	:	PUNCT
ejpam-5062	210	12	c1	c1	PROPN
ejpam-5062	210	13	∧	∧	PROPN
ejpam-5062	210	14	c2	c2	PROPN
ejpam-5062	210	15	=	=	PROPN
ejpam-5062	210	16	∅	∅	NOUN
ejpam-5062	210	17	=	=	NOUN
ejpam-5062	210	18	⇒	⇒	PROPN
ejpam-5062	210	19	c1	c1	PROPN
ejpam-5062	210	20	≤	≤	PROPN
ejpam-5062	210	21	cc	cc	ADP
ejpam-5062	210	22	2	2	NUM
ejpam-5062	210	23	in	in	ADP
ejpam-5062	210	24	general	general	ADJ
ejpam-5062	210	25	,	,	PUNCT
ejpam-5062	210	26	the	the	DET
ejpam-5062	210	27	equivalence	equivalence	NOUN
ejpam-5062	210	28	is	be	AUX
ejpam-5062	210	29	not	not	PART
ejpam-5062	210	30	always	always	ADV
ejpam-5062	210	31	valid	valid	ADJ
ejpam-5062	210	32	for	for	ADP
ejpam-5062	210	33	fuzzy	fuzzy	ADJ
ejpam-5062	210	34	sets	set	NOUN
ejpam-5062	210	35	,	,	PUNCT
ejpam-5062	210	36	this	this	PRON
ejpam-5062	210	37	means	mean	VERB
ejpam-5062	210	38	that	that	SCONJ
ejpam-5062	210	39	if	if	SCONJ
ejpam-5062	210	40	the	the	DET
ejpam-5062	210	41	fuzzy	fuzzy	ADJ
ejpam-5062	210	42	topological	topological	ADJ
ejpam-5062	210	43	space	space	NOUN
ejpam-5062	210	44	is	be	AUX
ejpam-5062	210	45	fsspn	fsspn	ADJ
ejpam-5062	210	46	then	then	ADV
ejpam-5062	210	47	it	it	PRON
ejpam-5062	210	48	is	be	AUX
ejpam-5062	210	49	also	also	ADV
ejpam-5062	210	50	an	an	DET
ejpam-5062	210	51	fsspwn	fsspwn	NOUN
ejpam-5062	210	52	.	.	PUNCT
ejpam-5062	211	1	sh	sh	PROPN
ejpam-5062	211	2	.	.	PROPN
ejpam-5062	211	3	makolli	makolli	PROPN
ejpam-5062	211	4	,	,	PUNCT
ejpam-5062	211	5	b.	b.	PROPN
ejpam-5062	211	6	krsteska	krsteska	PROPN
ejpam-5062	211	7	/	/	SYM
ejpam-5062	211	8	eur	eur	PROPN
ejpam-5062	211	9	.	.	PUNCT
ejpam-5062	212	1	j.	j.	PROPN
ejpam-5062	212	2	pure	pure	PROPN
ejpam-5062	212	3	appl	appl	PROPN
ejpam-5062	212	4	.	.	PROPN
ejpam-5062	212	5	math	math	PROPN
ejpam-5062	212	6	,	,	PUNCT
ejpam-5062	212	7	17	17	NUM
ejpam-5062	212	8	(	(	PUNCT
ejpam-5062	212	9	2	2	NUM
ejpam-5062	212	10	)	)	PUNCT
ejpam-5062	212	11	(	(	PUNCT
ejpam-5062	212	12	2024	2024	NUM
ejpam-5062	212	13	)	)	PUNCT
ejpam-5062	212	14	,	,	PUNCT
ejpam-5062	212	15	638	638	NUM
ejpam-5062	212	16	-	-	SYM
ejpam-5062	212	17	662	662	NUM
ejpam-5062	212	18	647	647	NUM
ejpam-5062	212	19	4	4	NUM
ejpam-5062	212	20	.	.	PUNCT
ejpam-5062	213	1	axioms	axiom	NOUN
ejpam-5062	213	2	of	of	ADP
ejpam-5062	213	3	fuzzy	fuzzy	ADJ
ejpam-5062	213	4	strong	strong	ADJ
ejpam-5062	213	5	semi	semi	ADJ
ejpam-5062	213	6	pre	pre	ADJ
ejpam-5062	213	7	-	-	NOUN
ejpam-5062	213	8	separation	separation	NOUN
ejpam-5062	213	9	and	and	CCONJ
ejpam-5062	213	10	fuzzy	fuzzy	ADJ
ejpam-5062	213	11	strong	strong	ADJ
ejpam-5062	213	12	semi	semi	ADJ
ejpam-5062	213	13	pre	pre	ADJ
ejpam-5062	213	14	-	-	ADJ
ejpam-5062	213	15	continuous	continuous	ADJ
ejpam-5062	213	16	mappings	mapping	NOUN
ejpam-5062	213	17	in	in	ADP
ejpam-5062	213	18	this	this	DET
ejpam-5062	213	19	section	section	NOUN
ejpam-5062	213	20	,	,	PUNCT
ejpam-5062	213	21	we	we	PRON
ejpam-5062	213	22	will	will	AUX
ejpam-5062	213	23	investigate	investigate	VERB
ejpam-5062	213	24	the	the	DET
ejpam-5062	213	25	relation	relation	NOUN
ejpam-5062	213	26	between	between	ADP
ejpam-5062	213	27	fuzzy	fuzzy	ADJ
ejpam-5062	213	28	separation	separation	NOUN
ejpam-5062	213	29	axioms	axiom	NOUN
ejpam-5062	213	30	,	,	PUNCT
ejpam-5062	213	31	fuzzy	fuzzy	ADJ
ejpam-5062	213	32	pre	pre	ADJ
ejpam-5062	213	33	-	-	NOUN
ejpam-5062	213	34	separation	separation	NOUN
ejpam-5062	213	35	axioms	axiom	NOUN
ejpam-5062	213	36	and	and	CCONJ
ejpam-5062	213	37	different	different	ADJ
ejpam-5062	213	38	forms	form	NOUN
ejpam-5062	213	39	of	of	ADP
ejpam-5062	213	40	fuzzy	fuzzy	ADJ
ejpam-5062	213	41	continuity	continuity	NOUN
ejpam-5062	213	42	.	.	PUNCT
ejpam-5062	214	1	theorem	theorem	ADJ
ejpam-5062	214	2	8	8	NUM
ejpam-5062	214	3	.	.	PUNCT
ejpam-5062	215	1	let	let	VERB
ejpam-5062	215	2	f	f	NOUN
ejpam-5062	215	3	:	:	PUNCT
ejpam-5062	215	4	x	x	X
ejpam-5062	215	5	→	→	SYM
ejpam-5062	215	6	y	y	X
ejpam-5062	215	7	be	be	AUX
ejpam-5062	215	8	a	a	DET
ejpam-5062	215	9	fuzzy	fuzzy	ADJ
ejpam-5062	215	10	strong	strong	ADJ
ejpam-5062	215	11	semi	semi	ADJ
ejpam-5062	215	12	pre	pre	ADJ
ejpam-5062	215	13	-	-	ADJ
ejpam-5062	215	14	continuous	continuous	ADJ
ejpam-5062	215	15	and	and	CCONJ
ejpam-5062	215	16	injective	injective	ADJ
ejpam-5062	215	17	mapping	mapping	NOUN
ejpam-5062	215	18	from	from	ADP
ejpam-5062	215	19	the	the	DET
ejpam-5062	215	20	fuzzy	fuzzy	ADJ
ejpam-5062	215	21	topological	topological	ADJ
ejpam-5062	215	22	space	space	NOUN
ejpam-5062	215	23	x	x	PUNCT
ejpam-5062	215	24	to	to	ADP
ejpam-5062	215	25	a	a	DET
ejpam-5062	215	26	fuzzy	fuzzy	ADJ
ejpam-5062	215	27	topological	topological	ADJ
ejpam-5062	215	28	space	space	NOUN
ejpam-5062	215	29	y	y	PROPN
ejpam-5062	215	30	.	.	PUNCT
ejpam-5062	216	1	if	if	SCONJ
ejpam-5062	216	2	the	the	DET
ejpam-5062	216	3	fuzzy	fuzzy	ADJ
ejpam-5062	216	4	topological	topological	ADJ
ejpam-5062	216	5	space	space	NOUN
ejpam-5062	216	6	y	y	PROPN
ejpam-5062	216	7	is	be	AUX
ejpam-5062	216	8	an	an	DET
ejpam-5062	216	9	ft2	ft2	PROPN
ejpam-5062	216	10	(	(	PUNCT
ejpam-5062	216	11	ft1	ft1	PROPN
ejpam-5062	216	12	,	,	PUNCT
ejpam-5062	216	13	ft0	ft0	NOUN
ejpam-5062	216	14	)	)	PUNCT
ejpam-5062	216	15	space	space	NOUN
ejpam-5062	216	16	then	then	ADV
ejpam-5062	216	17	x	x	PRON
ejpam-5062	216	18	is	be	AUX
ejpam-5062	216	19	an	an	DET
ejpam-5062	216	20	fsspt2	fsspt2	NOUN
ejpam-5062	216	21	(	(	PUNCT
ejpam-5062	216	22	fsspt1	fsspt1	NOUN
ejpam-5062	216	23	,	,	PUNCT
ejpam-5062	216	24	fsspt0	fsspt0	NOUN
ejpam-5062	216	25	)	)	PUNCT
ejpam-5062	216	26	space	space	NOUN
ejpam-5062	216	27	.	.	PUNCT
ejpam-5062	217	1	proof	proof	NOUN
ejpam-5062	217	2	.	.	PUNCT
ejpam-5062	218	1	let	let	VERB
ejpam-5062	218	2	us	we	PRON
ejpam-5062	218	3	suppose	suppose	VERB
ejpam-5062	218	4	that	that	SCONJ
ejpam-5062	218	5	fuzzy	fuzzy	ADJ
ejpam-5062	218	6	points	point	VERB
ejpam-5062	218	7	p	p	X
ejpam-5062	218	8	,	,	PUNCT
ejpam-5062	218	9	q	q	PROPN
ejpam-5062	218	10	≤	≤	NUM
ejpam-5062	218	11	x	x	PUNCT
ejpam-5062	218	12	represent	represent	VERB
ejpam-5062	218	13	any	any	DET
ejpam-5062	218	14	pair	pair	NOUN
ejpam-5062	218	15	of	of	ADP
ejpam-5062	218	16	fuzzy	fuzzy	ADJ
ejpam-5062	218	17	points	point	NOUN
ejpam-5062	218	18	with	with	ADP
ejpam-5062	218	19	different	different	ADJ
ejpam-5062	218	20	support	support	NOUN
ejpam-5062	218	21	.	.	PUNCT
ejpam-5062	219	1	according	accord	VERB
ejpam-5062	219	2	to	to	ADP
ejpam-5062	219	3	the	the	DET
ejpam-5062	219	4	assumption	assumption	NOUN
ejpam-5062	219	5	of	of	ADP
ejpam-5062	219	6	the	the	DET
ejpam-5062	219	7	theorem	theorem	NOUN
ejpam-5062	219	8	,	,	PUNCT
ejpam-5062	219	9	the	the	DET
ejpam-5062	219	10	mapping	mapping	NOUN
ejpam-5062	219	11	f	f	X
ejpam-5062	219	12	:	:	PUNCT
ejpam-5062	219	13	x	x	X
ejpam-5062	219	14	→	→	SYM
ejpam-5062	219	15	y	y	PROPN
ejpam-5062	219	16	is	be	AUX
ejpam-5062	219	17	an	an	DET
ejpam-5062	219	18	injective	injective	ADJ
ejpam-5062	219	19	mapping	mapping	NOUN
ejpam-5062	219	20	,	,	PUNCT
ejpam-5062	219	21	it	it	PRON
ejpam-5062	219	22	is	be	AUX
ejpam-5062	219	23	obvious	obvious	ADJ
ejpam-5062	219	24	that	that	SCONJ
ejpam-5062	219	25	f(p	f(p	PROPN
ejpam-5062	219	26	)	)	PUNCT
ejpam-5062	219	27	,	,	PUNCT
ejpam-5062	219	28	f(q	f(q	PROPN
ejpam-5062	219	29	)	)	PUNCT
ejpam-5062	219	30	are	be	AUX
ejpam-5062	219	31	two	two	NUM
ejpam-5062	219	32	fuzzy	fuzzy	ADJ
ejpam-5062	219	33	points	point	NOUN
ejpam-5062	219	34	in	in	ADP
ejpam-5062	219	35	y	y	PROPN
ejpam-5062	219	36	with	with	ADP
ejpam-5062	219	37	different	different	ADJ
ejpam-5062	219	38	support	support	NOUN
ejpam-5062	219	39	.	.	PUNCT
ejpam-5062	220	1	now	now	ADV
ejpam-5062	220	2	,	,	PUNCT
ejpam-5062	220	3	since	since	SCONJ
ejpam-5062	220	4	the	the	DET
ejpam-5062	220	5	fuzzy	fuzzy	ADJ
ejpam-5062	220	6	topological	topological	ADJ
ejpam-5062	220	7	space	space	NOUN
ejpam-5062	220	8	y	y	PROPN
ejpam-5062	220	9	is	be	AUX
ejpam-5062	220	10	an	an	DET
ejpam-5062	220	11	ft2	ft2	NOUN
ejpam-5062	220	12	,	,	PUNCT
ejpam-5062	220	13	there	there	PRON
ejpam-5062	220	14	exist	exist	VERB
ejpam-5062	220	15	fuzzy	fuzzy	ADJ
ejpam-5062	220	16	open	open	ADJ
ejpam-5062	220	17	sets	set	NOUN
ejpam-5062	220	18	u	u	NOUN
ejpam-5062	220	19	,	,	PUNCT
ejpam-5062	220	20	v	v	ADP
ejpam-5062	220	21	such	such	ADJ
ejpam-5062	220	22	that	that	SCONJ
ejpam-5062	220	23	:	:	PUNCT
ejpam-5062	220	24	f(p	f(p	X
ejpam-5062	220	25	)	)	PUNCT
ejpam-5062	220	26	≤	≤	NUM
ejpam-5062	220	27	u	u	NOUN
ejpam-5062	220	28	≤	≤	ADJ
ejpam-5062	220	29	f(q)c	f(q)c	PROPN
ejpam-5062	220	30	,	,	PUNCT
ejpam-5062	220	31	f(q	f(q	PROPN
ejpam-5062	220	32	)	)	PUNCT
ejpam-5062	220	33	≤	≤	NUM
ejpam-5062	220	34	v	v	PRON
ejpam-5062	220	35	≤	≤	NUM
ejpam-5062	220	36	f(p)c	f(p)c	PROPN
ejpam-5062	220	37	and	and	CCONJ
ejpam-5062	220	38	u	u	NOUN
ejpam-5062	220	39	≤	≤	X
ejpam-5062	220	40	v	v	ADP
ejpam-5062	220	41	c.	c.	NOUN
ejpam-5062	220	42	since	since	SCONJ
ejpam-5062	220	43	the	the	DET
ejpam-5062	220	44	mapping	mapping	NOUN
ejpam-5062	220	45	f	f	NOUN
ejpam-5062	220	46	is	be	AUX
ejpam-5062	220	47	a	a	DET
ejpam-5062	220	48	fuzzy	fuzzy	ADJ
ejpam-5062	220	49	strong	strong	ADJ
ejpam-5062	220	50	semi	semi	ADJ
ejpam-5062	220	51	pre	pre	ADJ
ejpam-5062	220	52	-	-	ADJ
ejpam-5062	220	53	continuous	continuous	ADJ
ejpam-5062	220	54	mapping	mapping	NOUN
ejpam-5062	220	55	then	then	ADV
ejpam-5062	220	56	f−1(u	f−1(u	PROPN
ejpam-5062	220	57	)	)	PUNCT
ejpam-5062	220	58	,	,	PUNCT
ejpam-5062	220	59	f−1(v	f−1(v	PROPN
ejpam-5062	220	60	)	)	PUNCT
ejpam-5062	220	61	are	be	AUX
ejpam-5062	220	62	two	two	NUM
ejpam-5062	220	63	fuzzy	fuzzy	ADJ
ejpam-5062	220	64	strongly	strongly	ADV
ejpam-5062	220	65	semi	semi	ADJ
ejpam-5062	220	66	pre	pre	ADJ
ejpam-5062	220	67	-	-	ADJ
ejpam-5062	220	68	open	open	ADJ
ejpam-5062	220	69	sets	set	NOUN
ejpam-5062	220	70	in	in	ADP
ejpam-5062	220	71	x	x	SYM
ejpam-5062	220	72	such	such	ADJ
ejpam-5062	220	73	that	that	SCONJ
ejpam-5062	220	74	:	:	PUNCT
ejpam-5062	220	75	p	p	X
ejpam-5062	220	76	≤	≤	NUM
ejpam-5062	220	77	f−1(u	f−1(u	PROPN
ejpam-5062	220	78	)	)	PUNCT
ejpam-5062	220	79	≤	≤	PROPN
ejpam-5062	220	80	qc	qc	PROPN
ejpam-5062	220	81	,	,	PUNCT
ejpam-5062	220	82	q	q	PROPN
ejpam-5062	220	83	≤	≤	PROPN
ejpam-5062	220	84	f−1(v	f−1(v	NOUN
ejpam-5062	220	85	)	)	PUNCT
ejpam-5062	220	86	≤	≤	NUM
ejpam-5062	220	87	pc	pc	NOUN
ejpam-5062	220	88	and	and	CCONJ
ejpam-5062	220	89	also	also	ADV
ejpam-5062	220	90	f−1(u	f−1(u	PROPN
ejpam-5062	220	91	)	)	PUNCT
ejpam-5062	220	92	≤	≤	ADJ
ejpam-5062	220	93	f−1(v	f−1(v	NOUN
ejpam-5062	220	94	)	)	PUNCT
ejpam-5062	221	1	c	c	X
ejpam-5062	221	2	,	,	PUNCT
ejpam-5062	221	3	that	that	ADV
ejpam-5062	221	4	is	is	ADV
ejpam-5062	221	5	,	,	PUNCT
ejpam-5062	221	6	the	the	DET
ejpam-5062	221	7	fuzzy	fuzzy	ADJ
ejpam-5062	221	8	topological	topological	ADJ
ejpam-5062	221	9	space	space	NOUN
ejpam-5062	221	10	x	x	PUNCT
ejpam-5062	221	11	is	be	AUX
ejpam-5062	221	12	an	an	DET
ejpam-5062	221	13	fsspt2	fsspt2	NOUN
ejpam-5062	221	14	space	space	NOUN
ejpam-5062	221	15	.	.	PUNCT
ejpam-5062	222	1	similarly	similarly	ADV
ejpam-5062	222	2	,	,	PUNCT
ejpam-5062	222	3	we	we	PRON
ejpam-5062	222	4	can	can	AUX
ejpam-5062	222	5	prove	prove	VERB
ejpam-5062	222	6	the	the	DET
ejpam-5062	222	7	cases	case	NOUN
ejpam-5062	222	8	when	when	SCONJ
ejpam-5062	222	9	y	y	PROPN
ejpam-5062	222	10	is	be	AUX
ejpam-5062	222	11	an	an	DET
ejpam-5062	222	12	ft1	ft1	NOUN
ejpam-5062	222	13	and	and	CCONJ
ejpam-5062	222	14	ft0	ft0	PROPN
ejpam-5062	222	15	space	space	NOUN
ejpam-5062	222	16	.	.	PUNCT
ejpam-5062	223	1	theorem	theorem	NOUN
ejpam-5062	223	2	9	9	NUM
ejpam-5062	223	3	.	.	PUNCT
ejpam-5062	224	1	let	let	VERB
ejpam-5062	224	2	f	f	NOUN
ejpam-5062	224	3	:	:	PUNCT
ejpam-5062	224	4	x	x	X
ejpam-5062	224	5	→	→	SYM
ejpam-5062	224	6	y	y	X
ejpam-5062	224	7	be	be	AUX
ejpam-5062	224	8	a	a	DET
ejpam-5062	224	9	fuzzy	fuzzy	ADJ
ejpam-5062	224	10	strong	strong	ADJ
ejpam-5062	224	11	semi	semi	ADJ
ejpam-5062	224	12	pre	pre	ADJ
ejpam-5062	224	13	-	-	ADJ
ejpam-5062	224	14	open	open	ADJ
ejpam-5062	224	15	and	and	CCONJ
ejpam-5062	224	16	bijective	bijective	ADJ
ejpam-5062	224	17	mapping	mapping	NOUN
ejpam-5062	224	18	from	from	ADP
ejpam-5062	224	19	the	the	DET
ejpam-5062	224	20	fuzzy	fuzzy	ADJ
ejpam-5062	224	21	topological	topological	ADJ
ejpam-5062	224	22	space	space	NOUN
ejpam-5062	224	23	x	x	PUNCT
ejpam-5062	224	24	to	to	ADP
ejpam-5062	224	25	a	a	DET
ejpam-5062	224	26	fuzzy	fuzzy	ADJ
ejpam-5062	224	27	topological	topological	ADJ
ejpam-5062	224	28	space	space	NOUN
ejpam-5062	224	29	y	y	PROPN
ejpam-5062	224	30	.	.	PUNCT
ejpam-5062	225	1	if	if	SCONJ
ejpam-5062	225	2	the	the	DET
ejpam-5062	225	3	fuzzy	fuzzy	ADJ
ejpam-5062	225	4	topological	topological	ADJ
ejpam-5062	225	5	space	space	NOUN
ejpam-5062	225	6	x	x	PUNCT
ejpam-5062	225	7	is	be	AUX
ejpam-5062	225	8	an	an	DET
ejpam-5062	225	9	ft2	ft2	PROPN
ejpam-5062	225	10	(	(	PUNCT
ejpam-5062	225	11	ft1	ft1	PROPN
ejpam-5062	225	12	,	,	PUNCT
ejpam-5062	225	13	ft0	ft0	NOUN
ejpam-5062	225	14	)	)	PUNCT
ejpam-5062	225	15	space	space	NOUN
ejpam-5062	225	16	then	then	ADV
ejpam-5062	225	17	y	y	PROPN
ejpam-5062	225	18	is	be	AUX
ejpam-5062	225	19	an	an	DET
ejpam-5062	225	20	fsspt2	fsspt2	NOUN
ejpam-5062	225	21	(	(	PUNCT
ejpam-5062	225	22	fsspt1	fsspt1	NOUN
ejpam-5062	225	23	,	,	PUNCT
ejpam-5062	225	24	fsspt0	fsspt0	NOUN
ejpam-5062	225	25	)	)	PUNCT
ejpam-5062	225	26	space	space	NOUN
ejpam-5062	225	27	.	.	PUNCT
ejpam-5062	226	1	proof	proof	NOUN
ejpam-5062	226	2	.	.	PUNCT
ejpam-5062	227	1	let	let	VERB
ejpam-5062	227	2	us	we	PRON
ejpam-5062	227	3	suppose	suppose	VERB
ejpam-5062	227	4	that	that	SCONJ
ejpam-5062	227	5	p	p	X
ejpam-5062	227	6	,	,	PUNCT
ejpam-5062	227	7	q	q	PROPN
ejpam-5062	227	8	≤	≤	NOUN
ejpam-5062	227	9	y	y	NOUN
ejpam-5062	227	10	are	be	AUX
ejpam-5062	227	11	two	two	NUM
ejpam-5062	227	12	fuzzy	fuzzy	ADJ
ejpam-5062	227	13	points	point	NOUN
ejpam-5062	227	14	with	with	ADP
ejpam-5062	227	15	different	different	ADJ
ejpam-5062	227	16	support	support	NOUN
ejpam-5062	227	17	.	.	PUNCT
ejpam-5062	228	1	it	it	PRON
ejpam-5062	228	2	is	be	AUX
ejpam-5062	228	3	obvious	obvious	ADJ
ejpam-5062	228	4	from	from	ADP
ejpam-5062	228	5	the	the	DET
ejpam-5062	228	6	conditions	condition	NOUN
ejpam-5062	228	7	of	of	ADP
ejpam-5062	228	8	the	the	DET
ejpam-5062	228	9	theorem	theorem	NOUN
ejpam-5062	228	10	that	that	SCONJ
ejpam-5062	228	11	f−1(p	f−1(p	PROPN
ejpam-5062	228	12	)	)	PUNCT
ejpam-5062	228	13	,	,	PUNCT
ejpam-5062	228	14	f−1(q	f−1(q	NUM
ejpam-5062	228	15	)	)	PUNCT
ejpam-5062	228	16	≤	≤	NUM
ejpam-5062	228	17	x	x	PUNCT
ejpam-5062	228	18	are	be	AUX
ejpam-5062	228	19	two	two	NUM
ejpam-5062	228	20	fuzzy	fuzzy	ADJ
ejpam-5062	228	21	points	point	NOUN
ejpam-5062	228	22	with	with	ADP
ejpam-5062	228	23	different	different	ADJ
ejpam-5062	228	24	support	support	NOUN
ejpam-5062	228	25	.	.	PUNCT
ejpam-5062	229	1	since	since	SCONJ
ejpam-5062	229	2	the	the	DET
ejpam-5062	229	3	fuzzy	fuzzy	ADJ
ejpam-5062	229	4	topological	topological	ADJ
ejpam-5062	229	5	space	space	NOUN
ejpam-5062	229	6	x	x	PUNCT
ejpam-5062	229	7	is	be	AUX
ejpam-5062	229	8	an	an	DET
ejpam-5062	229	9	ft2	ft2	NOUN
ejpam-5062	229	10	,	,	PUNCT
ejpam-5062	229	11	there	there	PRON
ejpam-5062	229	12	are	be	VERB
ejpam-5062	229	13	fuzzy	fuzzy	ADJ
ejpam-5062	229	14	open	open	ADJ
ejpam-5062	229	15	sets	set	NOUN
ejpam-5062	229	16	u	u	NOUN
ejpam-5062	229	17	,	,	PUNCT
ejpam-5062	229	18	v	v	ADP
ejpam-5062	229	19	such	such	ADJ
ejpam-5062	229	20	that	that	PRON
ejpam-5062	229	21	:	:	PUNCT
ejpam-5062	229	22	f−1(p	f−1(p	PROPN
ejpam-5062	229	23	)	)	PUNCT
ejpam-5062	229	24	≤	≤	NUM
ejpam-5062	229	25	u	u	NOUN
ejpam-5062	229	26	≤	≤	NOUN
ejpam-5062	229	27	f−1(q)c	f−1(q)c	NOUN
ejpam-5062	229	28	,	,	PUNCT
ejpam-5062	229	29	f−1(q	f−1(q	NUM
ejpam-5062	229	30	)	)	PUNCT
ejpam-5062	229	31	≤	≤	NUM
ejpam-5062	229	32	v	v	X
ejpam-5062	229	33	≤	≤	NUM
ejpam-5062	229	34	f−1(p)c	f−1(p)c	NOUN
ejpam-5062	230	1	and	and	CCONJ
ejpam-5062	230	2	u	u	NOUN
ejpam-5062	230	3	≤	≤	X
ejpam-5062	230	4	v	v	ADP
ejpam-5062	230	5	c.	c.	NOUN
ejpam-5062	230	6	based	base	VERB
ejpam-5062	230	7	on	on	ADP
ejpam-5062	230	8	the	the	DET
ejpam-5062	230	9	assumption	assumption	NOUN
ejpam-5062	230	10	of	of	ADP
ejpam-5062	230	11	the	the	DET
ejpam-5062	230	12	theorem	theorem	NOUN
ejpam-5062	230	13	,	,	PUNCT
ejpam-5062	230	14	the	the	DET
ejpam-5062	230	15	images	image	NOUN
ejpam-5062	230	16	f(u	f(u	PROPN
ejpam-5062	230	17	)	)	PUNCT
ejpam-5062	230	18	,	,	PUNCT
ejpam-5062	230	19	f(v	f(v	PROPN
ejpam-5062	230	20	)	)	PUNCT
ejpam-5062	230	21	of	of	ADP
ejpam-5062	230	22	u	u	PRON
ejpam-5062	230	23	and	and	CCONJ
ejpam-5062	230	24	v	v	NOUN
ejpam-5062	230	25	are	be	AUX
ejpam-5062	230	26	fuzzy	fuzzy	ADJ
ejpam-5062	230	27	strongly	strongly	ADV
ejpam-5062	230	28	semi	semi	ADJ
ejpam-5062	230	29	pre	pre	ADJ
ejpam-5062	230	30	-	-	ADJ
ejpam-5062	230	31	open	open	ADJ
ejpam-5062	230	32	sets	set	NOUN
ejpam-5062	230	33	in	in	ADP
ejpam-5062	230	34	y	y	PROPN
ejpam-5062	230	35	and	and	CCONJ
ejpam-5062	230	36	the	the	DET
ejpam-5062	230	37	following	follow	VERB
ejpam-5062	230	38	stands	stand	NOUN
ejpam-5062	230	39	:	:	PUNCT
ejpam-5062	230	40	p	p	PROPN
ejpam-5062	230	41	≤	≤	PROPN
ejpam-5062	230	42	f(u	f(u	PROPN
ejpam-5062	230	43	)	)	PUNCT
ejpam-5062	230	44	≤	≤	PROPN
ejpam-5062	230	45	qc	qc	PROPN
ejpam-5062	230	46	,	,	PUNCT
ejpam-5062	230	47	q	q	PROPN
ejpam-5062	230	48	≤	≤	NUM
ejpam-5062	230	49	f(v	f(v	PROPN
ejpam-5062	230	50	)	)	PUNCT
ejpam-5062	230	51	≤	≤	NUM
ejpam-5062	230	52	pc	pc	NOUN
ejpam-5062	230	53	and	and	CCONJ
ejpam-5062	230	54	f(u	f(u	PROPN
ejpam-5062	230	55	)	)	PUNCT
ejpam-5062	230	56	≤	≤	NUM
ejpam-5062	230	57	f(v	f(v	PROPN
ejpam-5062	230	58	)	)	PUNCT
ejpam-5062	231	1	c	c	X
ejpam-5062	231	2	,	,	PUNCT
ejpam-5062	231	3	which	which	PRON
ejpam-5062	231	4	means	mean	VERB
ejpam-5062	231	5	that	that	SCONJ
ejpam-5062	231	6	y	y	PROPN
ejpam-5062	231	7	is	be	AUX
ejpam-5062	231	8	an	an	DET
ejpam-5062	231	9	fsspt2	fsspt2	NOUN
ejpam-5062	231	10	space	space	NOUN
ejpam-5062	231	11	.	.	PUNCT
ejpam-5062	232	1	in	in	ADP
ejpam-5062	232	2	similar	similar	ADJ
ejpam-5062	232	3	manner	manner	NOUN
ejpam-5062	232	4	we	we	PRON
ejpam-5062	232	5	can	can	AUX
ejpam-5062	232	6	show	show	VERB
ejpam-5062	232	7	that	that	SCONJ
ejpam-5062	232	8	the	the	DET
ejpam-5062	232	9	same	same	ADJ
ejpam-5062	232	10	holds	hold	VERB
ejpam-5062	232	11	when	when	SCONJ
ejpam-5062	232	12	x	x	PRON
ejpam-5062	232	13	is	be	AUX
ejpam-5062	232	14	an	an	DET
ejpam-5062	232	15	ft1	ft1	NOUN
ejpam-5062	232	16	and	and	CCONJ
ejpam-5062	232	17	ft0	ft0	PROPN
ejpam-5062	232	18	space	space	NOUN
ejpam-5062	232	19	.	.	PUNCT
ejpam-5062	233	1	theorem	theorem	ADJ
ejpam-5062	233	2	10	10	NUM
ejpam-5062	233	3	.	.	PUNCT
ejpam-5062	234	1	let	let	VERB
ejpam-5062	234	2	f	f	NOUN
ejpam-5062	234	3	:	:	PUNCT
ejpam-5062	234	4	x	x	X
ejpam-5062	234	5	→	→	SYM
ejpam-5062	234	6	y	y	X
ejpam-5062	234	7	be	be	AUX
ejpam-5062	234	8	a	a	DET
ejpam-5062	234	9	fuzzy	fuzzy	ADJ
ejpam-5062	234	10	strong	strong	ADJ
ejpam-5062	234	11	semi	semi	ADJ
ejpam-5062	234	12	pre	pre	ADJ
ejpam-5062	234	13	-	-	ADJ
ejpam-5062	234	14	continuous	continuous	ADJ
ejpam-5062	234	15	and	and	CCONJ
ejpam-5062	234	16	injective	injective	ADJ
ejpam-5062	234	17	mapping	mapping	NOUN
ejpam-5062	234	18	from	from	ADP
ejpam-5062	234	19	the	the	DET
ejpam-5062	234	20	fuzzy	fuzzy	ADJ
ejpam-5062	234	21	topological	topological	ADJ
ejpam-5062	234	22	space	space	NOUN
ejpam-5062	234	23	x	x	PUNCT
ejpam-5062	234	24	to	to	ADP
ejpam-5062	234	25	a	a	DET
ejpam-5062	234	26	fuzzy	fuzzy	ADJ
ejpam-5062	234	27	topological	topological	ADJ
ejpam-5062	234	28	space	space	NOUN
ejpam-5062	234	29	y	y	PROPN
ejpam-5062	234	30	.	.	PUNCT
ejpam-5062	235	1	if	if	SCONJ
ejpam-5062	235	2	the	the	DET
ejpam-5062	235	3	fuzzy	fuzzy	ADJ
ejpam-5062	235	4	topological	topological	ADJ
ejpam-5062	235	5	space	space	NOUN
ejpam-5062	235	6	y	y	PROPN
ejpam-5062	235	7	is	be	AUX
ejpam-5062	235	8	an	an	DET
ejpam-5062	235	9	fts	fts	PROPN
ejpam-5062	235	10	space	space	NOUN
ejpam-5062	235	11	then	then	ADV
ejpam-5062	235	12	x	x	PUNCT
ejpam-5062	235	13	is	be	AUX
ejpam-5062	235	14	an	an	DET
ejpam-5062	235	15	fsspts	fsspt	NOUN
ejpam-5062	235	16	space	space	NOUN
ejpam-5062	235	17	.	.	PUNCT
ejpam-5062	236	1	sh	sh	PROPN
ejpam-5062	236	2	.	.	PROPN
ejpam-5062	236	3	makolli	makolli	PROPN
ejpam-5062	236	4	,	,	PUNCT
ejpam-5062	236	5	b.	b.	PROPN
ejpam-5062	236	6	krsteska	krsteska	PROPN
ejpam-5062	236	7	/	/	SYM
ejpam-5062	236	8	eur	eur	PROPN
ejpam-5062	236	9	.	.	PUNCT
ejpam-5062	237	1	j.	j.	PROPN
ejpam-5062	237	2	pure	pure	PROPN
ejpam-5062	237	3	appl	appl	PROPN
ejpam-5062	237	4	.	.	PROPN
ejpam-5062	237	5	math	math	PROPN
ejpam-5062	237	6	,	,	PUNCT
ejpam-5062	237	7	17	17	NUM
ejpam-5062	237	8	(	(	PUNCT
ejpam-5062	237	9	2	2	NUM
ejpam-5062	237	10	)	)	PUNCT
ejpam-5062	237	11	(	(	PUNCT
ejpam-5062	237	12	2024	2024	NUM
ejpam-5062	237	13	)	)	PUNCT
ejpam-5062	237	14	,	,	PUNCT
ejpam-5062	237	15	638	638	NUM
ejpam-5062	237	16	-	-	SYM
ejpam-5062	237	17	662	662	NUM
ejpam-5062	237	18	648	648	NUM
ejpam-5062	237	19	proof	proof	NOUN
ejpam-5062	237	20	.	.	PUNCT
ejpam-5062	238	1	let	let	VERB
ejpam-5062	238	2	p	p	PRON
ejpam-5062	238	3	be	be	AUX
ejpam-5062	238	4	any	any	DET
ejpam-5062	238	5	fuzzy	fuzzy	ADJ
ejpam-5062	238	6	point	point	NOUN
ejpam-5062	238	7	in	in	ADP
ejpam-5062	238	8	the	the	DET
ejpam-5062	238	9	fuzzy	fuzzy	ADJ
ejpam-5062	238	10	topological	topological	ADJ
ejpam-5062	238	11	space	space	NOUN
ejpam-5062	238	12	x	x	X
ejpam-5062	238	13	then	then	ADV
ejpam-5062	238	14	f(p	f(p	NOUN
ejpam-5062	238	15	)	)	PUNCT
ejpam-5062	238	16	is	be	AUX
ejpam-5062	238	17	a	a	DET
ejpam-5062	238	18	fuzzy	fuzzy	ADJ
ejpam-5062	238	19	point	point	NOUN
ejpam-5062	238	20	in	in	ADP
ejpam-5062	238	21	y	y	PROPN
ejpam-5062	238	22	.	.	PUNCT
ejpam-5062	239	1	since	since	SCONJ
ejpam-5062	239	2	y	y	PROPN
ejpam-5062	239	3	is	be	AUX
ejpam-5062	239	4	an	an	DET
ejpam-5062	239	5	fts	fts	PROPN
ejpam-5062	239	6	space	space	NOUN
ejpam-5062	239	7	,	,	PUNCT
ejpam-5062	239	8	it	it	PRON
ejpam-5062	239	9	means	mean	VERB
ejpam-5062	239	10	that	that	SCONJ
ejpam-5062	239	11	any	any	DET
ejpam-5062	239	12	fuzzy	fuzzy	ADJ
ejpam-5062	239	13	point	point	NOUN
ejpam-5062	239	14	is	be	AUX
ejpam-5062	239	15	a	a	DET
ejpam-5062	239	16	fuzzy	fuzzy	ADJ
ejpam-5062	239	17	closed	close	VERB
ejpam-5062	239	18	set	set	NOUN
ejpam-5062	239	19	,	,	PUNCT
ejpam-5062	239	20	that	that	ADV
ejpam-5062	239	21	is	is	ADV
ejpam-5062	239	22	f(p	f(p	NOUN
ejpam-5062	239	23	)	)	PUNCT
ejpam-5062	239	24	is	be	AUX
ejpam-5062	239	25	a	a	DET
ejpam-5062	239	26	fuzzy	fuzzy	ADJ
ejpam-5062	239	27	closed	close	VERB
ejpam-5062	239	28	set	set	VERB
ejpam-5062	239	29	in	in	ADP
ejpam-5062	239	30	y	y	PROPN
ejpam-5062	239	31	.	.	PUNCT
ejpam-5062	240	1	because	because	SCONJ
ejpam-5062	240	2	f	f	PROPN
ejpam-5062	240	3	is	be	AUX
ejpam-5062	240	4	a	a	DET
ejpam-5062	240	5	fuzzy	fuzzy	ADJ
ejpam-5062	240	6	strong	strong	ADJ
ejpam-5062	240	7	semi	semi	ADJ
ejpam-5062	240	8	pre	pre	ADJ
ejpam-5062	240	9	-	-	ADJ
ejpam-5062	240	10	continuous	continuous	ADJ
ejpam-5062	240	11	mapping	mapping	NOUN
ejpam-5062	240	12	and	and	CCONJ
ejpam-5062	240	13	it	it	PRON
ejpam-5062	240	14	is	be	AUX
ejpam-5062	240	15	an	an	DET
ejpam-5062	240	16	injective	injective	ADJ
ejpam-5062	240	17	mapping	mapping	NOUN
ejpam-5062	240	18	then	then	ADV
ejpam-5062	240	19	f−1(f(p	f−1(f(p	PROPN
ejpam-5062	240	20	)	)	PUNCT
ejpam-5062	240	21	)	)	PUNCT
ejpam-5062	241	1	=	=	PUNCT
ejpam-5062	241	2	p	p	X
ejpam-5062	241	3	,	,	PUNCT
ejpam-5062	241	4	and	and	CCONJ
ejpam-5062	241	5	p	p	NOUN
ejpam-5062	241	6	is	be	AUX
ejpam-5062	241	7	a	a	DET
ejpam-5062	241	8	fuzzy	fuzzy	ADJ
ejpam-5062	241	9	strongly	strongly	ADV
ejpam-5062	241	10	semi	semi	ADV
ejpam-5062	241	11	pre	pre	ADJ
ejpam-5062	241	12	-	-	ADJ
ejpam-5062	241	13	closed	closed	ADJ
ejpam-5062	241	14	set	set	NOUN
ejpam-5062	241	15	in	in	ADP
ejpam-5062	241	16	x.	x.	NOUN
ejpam-5062	241	17	since	since	SCONJ
ejpam-5062	241	18	p	p	NOUN
ejpam-5062	241	19	is	be	AUX
ejpam-5062	241	20	any	any	DET
ejpam-5062	241	21	fuzzy	fuzzy	ADJ
ejpam-5062	241	22	point	point	NOUN
ejpam-5062	241	23	of	of	ADP
ejpam-5062	241	24	x	x	PRON
ejpam-5062	241	25	,	,	PUNCT
ejpam-5062	241	26	that	that	PRON
ejpam-5062	241	27	means	mean	VERB
ejpam-5062	241	28	that	that	SCONJ
ejpam-5062	241	29	the	the	DET
ejpam-5062	241	30	fuzzy	fuzzy	ADJ
ejpam-5062	241	31	topological	topological	ADJ
ejpam-5062	241	32	space	space	NOUN
ejpam-5062	241	33	x	x	PUNCT
ejpam-5062	241	34	is	be	AUX
ejpam-5062	241	35	an	an	DET
ejpam-5062	241	36	fsspts	fsspt	NOUN
ejpam-5062	241	37	.	.	PUNCT
ejpam-5062	242	1	theorem	theorem	NOUN
ejpam-5062	242	2	11	11	NUM
ejpam-5062	242	3	.	.	PUNCT
ejpam-5062	243	1	let	let	VERB
ejpam-5062	243	2	f	f	NOUN
ejpam-5062	243	3	:	:	PUNCT
ejpam-5062	243	4	x	x	X
ejpam-5062	243	5	→	→	SYM
ejpam-5062	243	6	y	y	X
ejpam-5062	243	7	be	be	AUX
ejpam-5062	243	8	a	a	DET
ejpam-5062	243	9	fuzzy	fuzzy	ADJ
ejpam-5062	243	10	strongly	strongly	ADV
ejpam-5062	243	11	semi	semi	ADJ
ejpam-5062	243	12	pre	pre	ADJ
ejpam-5062	243	13	-	-	ADJ
ejpam-5062	243	14	open	open	ADJ
ejpam-5062	243	15	and	and	CCONJ
ejpam-5062	243	16	bijective	bijective	ADJ
ejpam-5062	243	17	mapping	mapping	NOUN
ejpam-5062	243	18	from	from	ADP
ejpam-5062	243	19	the	the	DET
ejpam-5062	243	20	fuzzy	fuzzy	ADJ
ejpam-5062	243	21	topological	topological	ADJ
ejpam-5062	243	22	space	space	NOUN
ejpam-5062	243	23	x	x	PUNCT
ejpam-5062	243	24	to	to	ADP
ejpam-5062	243	25	a	a	DET
ejpam-5062	243	26	fuzzy	fuzzy	ADJ
ejpam-5062	243	27	topological	topological	ADJ
ejpam-5062	243	28	space	space	NOUN
ejpam-5062	243	29	y	y	PROPN
ejpam-5062	243	30	.	.	PUNCT
ejpam-5062	244	1	if	if	SCONJ
ejpam-5062	244	2	the	the	DET
ejpam-5062	244	3	fuzzy	fuzzy	ADJ
ejpam-5062	244	4	topological	topological	ADJ
ejpam-5062	244	5	space	space	NOUN
ejpam-5062	244	6	x	x	PRON
ejpam-5062	244	7	is	be	AUX
ejpam-5062	244	8	an	an	DET
ejpam-5062	244	9	fts	fts	PROPN
ejpam-5062	244	10	space	space	NOUN
ejpam-5062	244	11	then	then	ADV
ejpam-5062	244	12	y	y	PROPN
ejpam-5062	244	13	is	be	AUX
ejpam-5062	244	14	an	an	DET
ejpam-5062	244	15	fsspts	fsspt	NOUN
ejpam-5062	244	16	space	space	NOUN
ejpam-5062	244	17	.	.	PUNCT
ejpam-5062	245	1	proof	proof	NOUN
ejpam-5062	245	2	.	.	PUNCT
ejpam-5062	246	1	similar	similar	ADJ
ejpam-5062	246	2	to	to	ADP
ejpam-5062	246	3	theorem	theorem	VERB
ejpam-5062	246	4	10	10	NUM
ejpam-5062	246	5	.	.	PUNCT
ejpam-5062	246	6	theorem	theorem	NOUN
ejpam-5062	246	7	12	12	NUM
ejpam-5062	246	8	.	.	PUNCT
ejpam-5062	247	1	let	let	VERB
ejpam-5062	247	2	f	f	NOUN
ejpam-5062	247	3	:	:	PUNCT
ejpam-5062	247	4	x	x	X
ejpam-5062	247	5	→	→	SYM
ejpam-5062	247	6	y	y	X
ejpam-5062	247	7	be	be	AUX
ejpam-5062	247	8	a	a	DET
ejpam-5062	247	9	fuzzy	fuzzy	ADJ
ejpam-5062	247	10	strong	strong	ADJ
ejpam-5062	247	11	semi	semi	ADJ
ejpam-5062	247	12	pre	pre	ADJ
ejpam-5062	247	13	-	-	ADJ
ejpam-5062	247	14	continuous	continuous	ADJ
ejpam-5062	247	15	and	and	CCONJ
ejpam-5062	247	16	injective	injective	ADJ
ejpam-5062	247	17	mapping	mapping	NOUN
ejpam-5062	247	18	from	from	ADP
ejpam-5062	247	19	the	the	DET
ejpam-5062	247	20	fuzzy	fuzzy	ADJ
ejpam-5062	247	21	topological	topological	ADJ
ejpam-5062	247	22	space	space	NOUN
ejpam-5062	247	23	x	x	PUNCT
ejpam-5062	247	24	to	to	ADP
ejpam-5062	247	25	a	a	DET
ejpam-5062	247	26	fuzzy	fuzzy	ADJ
ejpam-5062	247	27	topological	topological	ADJ
ejpam-5062	247	28	space	space	NOUN
ejpam-5062	247	29	y	y	PROPN
ejpam-5062	247	30	.	.	PUNCT
ejpam-5062	248	1	if	if	SCONJ
ejpam-5062	248	2	the	the	DET
ejpam-5062	248	3	fuzzy	fuzzy	ADJ
ejpam-5062	248	4	topological	topological	ADJ
ejpam-5062	248	5	space	space	NOUN
ejpam-5062	248	6	y	y	PROPN
ejpam-5062	248	7	is	be	AUX
ejpam-5062	248	8	an	an	DET
ejpam-5062	248	9	ft2	ft2	PROPN
ejpam-5062	248	10	1	1	NUM
ejpam-5062	248	11	2	2	NUM
ejpam-5062	248	12	space	space	NOUN
ejpam-5062	248	13	then	then	ADV
ejpam-5062	248	14	x	x	PUNCT
ejpam-5062	248	15	is	be	AUX
ejpam-5062	248	16	an	an	DET
ejpam-5062	248	17	fsspt2	fsspt2	NOUN
ejpam-5062	248	18	1	1	NUM
ejpam-5062	248	19	2	2	NUM
ejpam-5062	248	20	space	space	NOUN
ejpam-5062	248	21	.	.	PUNCT
ejpam-5062	249	1	proof	proof	NOUN
ejpam-5062	249	2	.	.	PUNCT
ejpam-5062	250	1	let	let	VERB
ejpam-5062	250	2	us	we	PRON
ejpam-5062	250	3	suppose	suppose	VERB
ejpam-5062	250	4	that	that	SCONJ
ejpam-5062	250	5	p	p	X
ejpam-5062	250	6	,	,	PUNCT
ejpam-5062	250	7	q	q	PROPN
ejpam-5062	250	8	≤	≤	NUM
ejpam-5062	250	9	x	x	PUNCT
ejpam-5062	250	10	are	be	AUX
ejpam-5062	250	11	two	two	NUM
ejpam-5062	250	12	fuzzy	fuzzy	ADJ
ejpam-5062	250	13	points	point	NOUN
ejpam-5062	250	14	with	with	ADP
ejpam-5062	250	15	different	different	ADJ
ejpam-5062	250	16	support	support	NOUN
ejpam-5062	250	17	.	.	PUNCT
ejpam-5062	251	1	since	since	SCONJ
ejpam-5062	251	2	f	f	PROPN
ejpam-5062	251	3	:	:	PUNCT
ejpam-5062	251	4	x	x	X
ejpam-5062	251	5	→	→	SYM
ejpam-5062	251	6	y	y	PROPN
ejpam-5062	251	7	is	be	AUX
ejpam-5062	251	8	a	a	DET
ejpam-5062	251	9	fuzzy	fuzzy	ADJ
ejpam-5062	251	10	strong	strong	ADJ
ejpam-5062	251	11	semi	semi	ADJ
ejpam-5062	251	12	pre	pre	ADJ
ejpam-5062	251	13	-	-	ADJ
ejpam-5062	251	14	continuous	continuous	ADJ
ejpam-5062	251	15	and	and	CCONJ
ejpam-5062	251	16	an	an	DET
ejpam-5062	251	17	injective	injective	ADJ
ejpam-5062	251	18	mapping	mapping	NOUN
ejpam-5062	251	19	,	,	PUNCT
ejpam-5062	251	20	it	it	PRON
ejpam-5062	251	21	follows	follow	VERB
ejpam-5062	251	22	that	that	SCONJ
ejpam-5062	251	23	f(p	f(p	PROPN
ejpam-5062	251	24	)	)	PUNCT
ejpam-5062	251	25	,	,	PUNCT
ejpam-5062	251	26	f(q	f(q	PROPN
ejpam-5062	251	27	)	)	PUNCT
ejpam-5062	251	28	≤	≤	PUNCT
ejpam-5062	252	1	y	y	PROPN
ejpam-5062	252	2	are	be	AUX
ejpam-5062	252	3	two	two	NUM
ejpam-5062	252	4	fuzzy	fuzzy	ADJ
ejpam-5062	252	5	points	point	NOUN
ejpam-5062	252	6	with	with	ADP
ejpam-5062	252	7	different	different	ADJ
ejpam-5062	252	8	support	support	NOUN
ejpam-5062	252	9	.	.	PUNCT
ejpam-5062	253	1	due	due	ADP
ejpam-5062	253	2	to	to	ADP
ejpam-5062	253	3	the	the	DET
ejpam-5062	253	4	fact	fact	NOUN
ejpam-5062	253	5	that	that	SCONJ
ejpam-5062	253	6	the	the	DET
ejpam-5062	253	7	fuzzy	fuzzy	ADJ
ejpam-5062	253	8	topological	topological	ADJ
ejpam-5062	253	9	space	space	NOUN
ejpam-5062	253	10	y	y	PROPN
ejpam-5062	253	11	is	be	AUX
ejpam-5062	253	12	an	an	DET
ejpam-5062	253	13	ft2	ft2	PROPN
ejpam-5062	253	14	1	1	NUM
ejpam-5062	253	15	2	2	NUM
ejpam-5062	253	16	,	,	PUNCT
ejpam-5062	253	17	there	there	PRON
ejpam-5062	253	18	are	be	VERB
ejpam-5062	253	19	fuzzy	fuzzy	ADJ
ejpam-5062	253	20	open	open	ADJ
ejpam-5062	253	21	sets	set	NOUN
ejpam-5062	253	22	u	u	NOUN
ejpam-5062	253	23	,	,	PUNCT
ejpam-5062	253	24	v	v	ADP
ejpam-5062	253	25	such	such	ADJ
ejpam-5062	253	26	that	that	SCONJ
ejpam-5062	253	27	f(p	f(p	NOUN
ejpam-5062	253	28	)	)	PUNCT
ejpam-5062	253	29	≤	≤	NUM
ejpam-5062	253	30	u	u	NOUN
ejpam-5062	253	31	≤	≤	ADJ
ejpam-5062	253	32	f(q)c	f(q)c	PROPN
ejpam-5062	253	33	,	,	PUNCT
ejpam-5062	253	34	f(q	f(q	PROPN
ejpam-5062	253	35	)	)	PUNCT
ejpam-5062	253	36	≤	≤	NUM
ejpam-5062	254	1	v	v	X
ejpam-5062	254	2	≤	≤	NUM
ejpam-5062	254	3	f(p)c	f(p)c	PROPN
ejpam-5062	254	4	and	and	CCONJ
ejpam-5062	254	5	clu	clu	PROPN
ejpam-5062	254	6	≤	≤	PROPN
ejpam-5062	254	7	(	(	PUNCT
ejpam-5062	254	8	clv	clv	PROPN
ejpam-5062	254	9	)	)	PUNCT
ejpam-5062	254	10	c.	c.	PROPN
ejpam-5062	254	11	based	base	VERB
ejpam-5062	254	12	on	on	ADP
ejpam-5062	254	13	the	the	DET
ejpam-5062	254	14	assumption	assumption	NOUN
ejpam-5062	254	15	of	of	ADP
ejpam-5062	254	16	the	the	DET
ejpam-5062	254	17	theorem	theorem	NOUN
ejpam-5062	254	18	,	,	PUNCT
ejpam-5062	254	19	the	the	DET
ejpam-5062	254	20	images	image	NOUN
ejpam-5062	254	21	f−1(u	f−1(u	NOUN
ejpam-5062	254	22	)	)	PUNCT
ejpam-5062	254	23	,	,	PUNCT
ejpam-5062	254	24	f−1(v	f−1(v	PROPN
ejpam-5062	254	25	)	)	PUNCT
ejpam-5062	254	26	,	,	PUNCT
ejpam-5062	254	27	of	of	ADP
ejpam-5062	254	28	u	u	NOUN
ejpam-5062	254	29	and	and	CCONJ
ejpam-5062	254	30	v	v	NOUN
ejpam-5062	254	31	are	be	AUX
ejpam-5062	254	32	fuzzy	fuzzy	ADJ
ejpam-5062	254	33	strongly	strongly	ADV
ejpam-5062	254	34	semi	semi	ADJ
ejpam-5062	254	35	pre	pre	ADJ
ejpam-5062	254	36	-	-	ADJ
ejpam-5062	254	37	open	open	ADJ
ejpam-5062	254	38	sets	set	NOUN
ejpam-5062	254	39	in	in	ADP
ejpam-5062	254	40	y	y	PROPN
ejpam-5062	254	41	and	and	CCONJ
ejpam-5062	254	42	p	p	NOUN
ejpam-5062	254	43	≤	≤	NUM
ejpam-5062	254	44	f−1(u	f−1(u	PROPN
ejpam-5062	254	45	)	)	PUNCT
ejpam-5062	254	46	≤	≤	PROPN
ejpam-5062	254	47	qc	qc	PROPN
ejpam-5062	254	48	,	,	PUNCT
ejpam-5062	254	49	q	q	PROPN
ejpam-5062	254	50	≤	≤	PROPN
ejpam-5062	254	51	f−1(v	f−1(v	NOUN
ejpam-5062	254	52	)	)	PUNCT
ejpam-5062	254	53	≤	≤	NUM
ejpam-5062	254	54	pc	pc	NOUN
ejpam-5062	254	55	.	.	PUNCT
ejpam-5062	255	1	according	accord	VERB
ejpam-5062	255	2	to	to	ADP
ejpam-5062	255	3	the	the	DET
ejpam-5062	255	4	theorem	theorem	NOUN
ejpam-5062	255	5	4.1	4.1	NUM
ejpam-5062	255	6	.	.	PUNCT
ejpam-5062	256	1	[	[	X
ejpam-5062	256	2	17][17	17][17	X
ejpam-5062	256	3	]	]	X
ejpam-5062	256	4	we	we	PRON
ejpam-5062	256	5	have	have	VERB
ejpam-5062	256	6	that	that	PRON
ejpam-5062	256	7	:	:	PUNCT
ejpam-5062	256	8	sspclf−1(u	sspclf−1(u	X
ejpam-5062	256	9	)	)	PUNCT
ejpam-5062	256	10	≤	≤	NUM
ejpam-5062	256	11	f−1(clu	f−1(clu	NOUN
ejpam-5062	256	12	)	)	PUNCT
ejpam-5062	256	13	≤	≤	NOUN
ejpam-5062	256	14	f−1(clv	f−1(clv	PUNCT
ejpam-5062	256	15	)	)	PUNCT
ejpam-5062	256	16	c	c	NOUN
ejpam-5062	256	17	≤	≤	NOUN
ejpam-5062	256	18	f−1(intv	f−1(intv	PUNCT
ejpam-5062	256	19	c	c	NOUN
ejpam-5062	256	20	)	)	PUNCT
ejpam-5062	256	21	≤	≤	NUM
ejpam-5062	256	22	sspintf−1(v	sspintf−1(v	NOUN
ejpam-5062	256	23	c	c	NOUN
ejpam-5062	256	24	)	)	PUNCT
ejpam-5062	256	25	≤	≤	NOUN
ejpam-5062	256	26	(	(	PUNCT
ejpam-5062	256	27	sspclf−1(v	sspclf−1(v	NOUN
ejpam-5062	256	28	)	)	PUNCT
ejpam-5062	256	29	)	)	PUNCT
ejpam-5062	257	1	c	c	NOUN
ejpam-5062	257	2	the	the	DET
ejpam-5062	257	3	last	last	ADJ
ejpam-5062	257	4	expression	expression	NOUN
ejpam-5062	257	5	can	can	AUX
ejpam-5062	257	6	also	also	ADV
ejpam-5062	257	7	be	be	AUX
ejpam-5062	257	8	summarized	summarize	VERB
ejpam-5062	257	9	as	as	ADP
ejpam-5062	257	10	sspclf−1(u	sspclf−1(u	NOUN
ejpam-5062	257	11	)	)	PUNCT
ejpam-5062	257	12	≤	≤	NOUN
ejpam-5062	257	13	(	(	PUNCT
ejpam-5062	257	14	sspclf−1(v	sspclf−1(v	NOUN
ejpam-5062	257	15	)	)	PUNCT
ejpam-5062	257	16	)	)	PUNCT
ejpam-5062	258	1	c	c	NOUN
ejpam-5062	258	2	which	which	PRON
ejpam-5062	258	3	means	mean	VERB
ejpam-5062	258	4	that	that	SCONJ
ejpam-5062	258	5	x	x	PRON
ejpam-5062	258	6	is	be	AUX
ejpam-5062	258	7	an	an	DET
ejpam-5062	258	8	fsspt2	fsspt2	NOUN
ejpam-5062	258	9	1	1	NUM
ejpam-5062	258	10	2	2	NUM
ejpam-5062	258	11	space	space	NOUN
ejpam-5062	258	12	.	.	PUNCT
ejpam-5062	259	1	theorem	theorem	NOUN
ejpam-5062	259	2	13	13	NUM
ejpam-5062	259	3	.	.	PUNCT
ejpam-5062	260	1	let	let	VERB
ejpam-5062	260	2	f	f	NOUN
ejpam-5062	260	3	:	:	PUNCT
ejpam-5062	260	4	x	x	X
ejpam-5062	260	5	→	→	SYM
ejpam-5062	260	6	y	y	X
ejpam-5062	260	7	be	be	AUX
ejpam-5062	260	8	a	a	DET
ejpam-5062	260	9	fuzzy	fuzzy	ADJ
ejpam-5062	260	10	strongly	strongly	ADV
ejpam-5062	260	11	semi	semi	ADJ
ejpam-5062	260	12	pre	pre	ADJ
ejpam-5062	260	13	-	-	ADJ
ejpam-5062	260	14	open	open	ADJ
ejpam-5062	260	15	and	and	CCONJ
ejpam-5062	260	16	bijective	bijective	ADJ
ejpam-5062	260	17	mapping	mapping	NOUN
ejpam-5062	260	18	from	from	ADP
ejpam-5062	260	19	the	the	DET
ejpam-5062	260	20	fuzzy	fuzzy	ADJ
ejpam-5062	260	21	topological	topological	ADJ
ejpam-5062	260	22	space	space	NOUN
ejpam-5062	260	23	x	x	PUNCT
ejpam-5062	260	24	to	to	ADP
ejpam-5062	260	25	a	a	DET
ejpam-5062	260	26	fuzzy	fuzzy	ADJ
ejpam-5062	260	27	topological	topological	ADJ
ejpam-5062	260	28	space	space	NOUN
ejpam-5062	260	29	y	y	PROPN
ejpam-5062	260	30	.	.	PUNCT
ejpam-5062	261	1	if	if	SCONJ
ejpam-5062	261	2	the	the	DET
ejpam-5062	261	3	fuzzy	fuzzy	ADJ
ejpam-5062	261	4	topological	topological	ADJ
ejpam-5062	261	5	space	space	NOUN
ejpam-5062	261	6	x	x	PUNCT
ejpam-5062	261	7	is	be	AUX
ejpam-5062	261	8	an	an	DET
ejpam-5062	261	9	ft2	ft2	PROPN
ejpam-5062	261	10	1	1	NUM
ejpam-5062	261	11	2	2	NUM
ejpam-5062	261	12	space	space	NOUN
ejpam-5062	261	13	then	then	ADV
ejpam-5062	261	14	y	y	PROPN
ejpam-5062	261	15	is	be	AUX
ejpam-5062	261	16	an	an	DET
ejpam-5062	261	17	fsspt2	fsspt2	NOUN
ejpam-5062	261	18	1	1	NUM
ejpam-5062	261	19	2	2	NUM
ejpam-5062	261	20	space	space	NOUN
ejpam-5062	261	21	.	.	PUNCT
ejpam-5062	262	1	proof	proof	NOUN
ejpam-5062	262	2	.	.	PUNCT
ejpam-5062	263	1	let	let	VERB
ejpam-5062	263	2	us	we	PRON
ejpam-5062	263	3	suppose	suppose	VERB
ejpam-5062	263	4	that	that	SCONJ
ejpam-5062	263	5	p	p	X
ejpam-5062	263	6	,	,	PUNCT
ejpam-5062	263	7	q	q	PROPN
ejpam-5062	263	8	≤	≤	NOUN
ejpam-5062	263	9	y	y	NOUN
ejpam-5062	263	10	are	be	AUX
ejpam-5062	263	11	two	two	NUM
ejpam-5062	263	12	fuzzy	fuzzy	ADJ
ejpam-5062	263	13	points	point	NOUN
ejpam-5062	263	14	with	with	ADP
ejpam-5062	263	15	different	different	ADJ
ejpam-5062	263	16	support	support	NOUN
ejpam-5062	263	17	.	.	PUNCT
ejpam-5062	264	1	it	it	PRON
ejpam-5062	264	2	is	be	AUX
ejpam-5062	264	3	obvious	obvious	ADJ
ejpam-5062	264	4	from	from	ADP
ejpam-5062	264	5	the	the	DET
ejpam-5062	264	6	conditions	condition	NOUN
ejpam-5062	264	7	of	of	ADP
ejpam-5062	264	8	the	the	DET
ejpam-5062	264	9	theorem	theorem	NOUN
ejpam-5062	264	10	that	that	SCONJ
ejpam-5062	264	11	f−1(p	f−1(p	PROPN
ejpam-5062	264	12	)	)	PUNCT
ejpam-5062	264	13	,	,	PUNCT
ejpam-5062	264	14	f−1(q	f−1(q	NUM
ejpam-5062	264	15	)	)	PUNCT
ejpam-5062	264	16	≤	≤	NUM
ejpam-5062	264	17	x	x	PUNCT
ejpam-5062	264	18	are	be	AUX
ejpam-5062	264	19	two	two	NUM
ejpam-5062	264	20	fuzzy	fuzzy	ADJ
ejpam-5062	264	21	points	point	NOUN
ejpam-5062	264	22	with	with	ADP
ejpam-5062	264	23	different	different	ADJ
ejpam-5062	264	24	support	support	NOUN
ejpam-5062	264	25	.	.	PUNCT
ejpam-5062	265	1	since	since	SCONJ
ejpam-5062	265	2	the	the	DET
ejpam-5062	265	3	fuzzy	fuzzy	ADJ
ejpam-5062	265	4	topological	topological	ADJ
ejpam-5062	265	5	space	space	NOUN
ejpam-5062	265	6	x	x	PUNCT
ejpam-5062	265	7	is	be	AUX
ejpam-5062	265	8	an	an	DET
ejpam-5062	265	9	ft2	ft2	PROPN
ejpam-5062	265	10	1	1	NUM
ejpam-5062	265	11	2	2	NUM
ejpam-5062	265	12	,	,	PUNCT
ejpam-5062	265	13	there	there	PRON
ejpam-5062	265	14	are	be	VERB
ejpam-5062	265	15	fuzzy	fuzzy	ADJ
ejpam-5062	265	16	open	open	ADJ
ejpam-5062	265	17	sets	set	NOUN
ejpam-5062	265	18	u	u	NOUN
ejpam-5062	265	19	,	,	PUNCT
ejpam-5062	265	20	v	v	ADP
ejpam-5062	265	21	such	such	ADJ
ejpam-5062	265	22	that	that	PRON
ejpam-5062	265	23	f−1(p	f−1(p	PROPN
ejpam-5062	265	24	)	)	PUNCT
ejpam-5062	265	25	≤	≤	NUM
ejpam-5062	265	26	u	u	NOUN
ejpam-5062	265	27	≤	≤	NOUN
ejpam-5062	265	28	f−1(q)c	f−1(q)c	NOUN
ejpam-5062	265	29	,	,	PUNCT
ejpam-5062	265	30	f−1(q	f−1(q	NUM
ejpam-5062	265	31	)	)	PUNCT
ejpam-5062	265	32	≤	≤	NUM
ejpam-5062	265	33	v	v	X
ejpam-5062	265	34	≤	≤	NUM
ejpam-5062	265	35	f−1(p)c	f−1(p)c	PROPN
ejpam-5062	265	36	and	and	CCONJ
ejpam-5062	265	37	also	also	ADV
ejpam-5062	265	38	clu	clu	PROPN
ejpam-5062	265	39	≤	≤	PROPN
ejpam-5062	265	40	(	(	PUNCT
ejpam-5062	265	41	clv	clv	PROPN
ejpam-5062	265	42	)	)	PUNCT
ejpam-5062	265	43	c.	c.	PROPN
ejpam-5062	265	44	based	base	VERB
ejpam-5062	265	45	on	on	ADP
ejpam-5062	265	46	the	the	DET
ejpam-5062	265	47	assumption	assumption	NOUN
ejpam-5062	265	48	of	of	ADP
ejpam-5062	265	49	the	the	DET
ejpam-5062	265	50	theorem	theorem	NOUN
ejpam-5062	265	51	,	,	PUNCT
ejpam-5062	265	52	the	the	DET
ejpam-5062	265	53	images	image	NOUN
ejpam-5062	265	54	f(u	f(u	PROPN
ejpam-5062	265	55	)	)	PUNCT
ejpam-5062	265	56	,	,	PUNCT
ejpam-5062	265	57	f(v	f(v	PROPN
ejpam-5062	265	58	)	)	PUNCT
ejpam-5062	265	59	of	of	ADP
ejpam-5062	265	60	u	u	PRON
ejpam-5062	265	61	and	and	CCONJ
ejpam-5062	265	62	v	v	NOUN
ejpam-5062	265	63	are	be	AUX
ejpam-5062	265	64	fuzzy	fuzzy	ADJ
ejpam-5062	265	65	strongly	strongly	ADV
ejpam-5062	265	66	semi	semi	ADJ
ejpam-5062	265	67	pre	pre	ADJ
ejpam-5062	265	68	-	-	ADJ
ejpam-5062	265	69	open	open	ADJ
ejpam-5062	265	70	sets	set	NOUN
ejpam-5062	265	71	in	in	ADP
ejpam-5062	265	72	y	y	PROPN
ejpam-5062	265	73	and	and	CCONJ
ejpam-5062	265	74	the	the	DET
ejpam-5062	265	75	following	follow	VERB
ejpam-5062	265	76	stands	stand	NOUN
ejpam-5062	265	77	:	:	PUNCT
ejpam-5062	265	78	p	p	PROPN
ejpam-5062	265	79	≤	≤	PROPN
ejpam-5062	265	80	f(u	f(u	PROPN
ejpam-5062	265	81	)	)	PUNCT
ejpam-5062	265	82	≤	≤	PROPN
ejpam-5062	265	83	qc	qc	PROPN
ejpam-5062	265	84	,	,	PUNCT
ejpam-5062	265	85	q	q	PROPN
ejpam-5062	265	86	≤	≤	NUM
ejpam-5062	265	87	f(v	f(v	PROPN
ejpam-5062	265	88	)	)	PUNCT
ejpam-5062	265	89	≤	≤	NUM
ejpam-5062	265	90	pc	pc	NOUN
ejpam-5062	265	91	and	and	CCONJ
ejpam-5062	265	92	sh	sh	PROPN
ejpam-5062	265	93	.	.	PROPN
ejpam-5062	265	94	makolli	makolli	PROPN
ejpam-5062	265	95	,	,	PUNCT
ejpam-5062	265	96	b.	b.	PROPN
ejpam-5062	265	97	krsteska	krsteska	PROPN
ejpam-5062	265	98	/	/	SYM
ejpam-5062	265	99	eur	eur	PROPN
ejpam-5062	265	100	.	.	PUNCT
ejpam-5062	266	1	j.	j.	PROPN
ejpam-5062	266	2	pure	pure	PROPN
ejpam-5062	266	3	appl	appl	PROPN
ejpam-5062	266	4	.	.	PROPN
ejpam-5062	266	5	math	math	PROPN
ejpam-5062	266	6	,	,	PUNCT
ejpam-5062	266	7	17	17	NUM
ejpam-5062	266	8	(	(	PUNCT
ejpam-5062	266	9	2	2	NUM
ejpam-5062	266	10	)	)	PUNCT
ejpam-5062	266	11	(	(	PUNCT
ejpam-5062	266	12	2024	2024	NUM
ejpam-5062	266	13	)	)	PUNCT
ejpam-5062	266	14	,	,	PUNCT
ejpam-5062	266	15	638	638	NUM
ejpam-5062	266	16	-	-	SYM
ejpam-5062	266	17	662	662	NUM
ejpam-5062	266	18	649	649	NUM
ejpam-5062	266	19	sspclf(u	sspclf(u	NOUN
ejpam-5062	266	20	)	)	PUNCT
ejpam-5062	266	21	≤	≤	NUM
ejpam-5062	266	22	f(clu	f(clu	PROPN
ejpam-5062	266	23	)	)	PUNCT
ejpam-5062	266	24	≤	≤	NOUN
ejpam-5062	266	25	f(clv	f(clv	PROPN
ejpam-5062	266	26	)	)	PUNCT
ejpam-5062	266	27	c	c	PROPN
ejpam-5062	266	28	≤	≤	NUM
ejpam-5062	266	29	(	(	PUNCT
ejpam-5062	266	30	sspclf(v	sspclf(v	PROPN
ejpam-5062	266	31	)	)	PUNCT
ejpam-5062	266	32	)	)	PUNCT
ejpam-5062	267	1	c	c	NOUN
ejpam-5062	267	2	which	which	PRON
ejpam-5062	267	3	means	mean	VERB
ejpam-5062	267	4	that	that	SCONJ
ejpam-5062	267	5	y	y	PROPN
ejpam-5062	267	6	is	be	AUX
ejpam-5062	267	7	an	an	DET
ejpam-5062	267	8	fsspt2	fsspt2	NOUN
ejpam-5062	267	9	1	1	NUM
ejpam-5062	267	10	2	2	NUM
ejpam-5062	267	11	space	space	NOUN
ejpam-5062	267	12	.	.	PUNCT
ejpam-5062	268	1	theorem	theorem	VERB
ejpam-5062	268	2	14	14	NUM
ejpam-5062	268	3	.	.	PUNCT
ejpam-5062	269	1	let	let	VERB
ejpam-5062	269	2	f	f	NOUN
ejpam-5062	269	3	:	:	PUNCT
ejpam-5062	269	4	x	x	X
ejpam-5062	269	5	→	→	SYM
ejpam-5062	269	6	y	y	X
ejpam-5062	269	7	be	be	AUX
ejpam-5062	269	8	a	a	DET
ejpam-5062	269	9	fuzzy	fuzzy	ADJ
ejpam-5062	269	10	closed	closed	ADJ
ejpam-5062	269	11	and	and	CCONJ
ejpam-5062	269	12	fuzzy	fuzzy	ADJ
ejpam-5062	269	13	strong	strong	ADJ
ejpam-5062	269	14	semi	semi	ADJ
ejpam-5062	269	15	pre	pre	ADJ
ejpam-5062	269	16	-	-	ADJ
ejpam-5062	269	17	continuous	continuous	ADJ
ejpam-5062	269	18	and	and	CCONJ
ejpam-5062	269	19	bijective	bijective	ADJ
ejpam-5062	269	20	mapping	mapping	NOUN
ejpam-5062	269	21	from	from	ADP
ejpam-5062	269	22	the	the	DET
ejpam-5062	269	23	fuzzy	fuzzy	ADJ
ejpam-5062	269	24	topological	topological	ADJ
ejpam-5062	269	25	space	space	NOUN
ejpam-5062	269	26	x	x	PUNCT
ejpam-5062	269	27	to	to	ADP
ejpam-5062	269	28	a	a	DET
ejpam-5062	269	29	fuzzy	fuzzy	ADJ
ejpam-5062	269	30	topological	topological	ADJ
ejpam-5062	269	31	space	space	NOUN
ejpam-5062	269	32	y	y	PROPN
ejpam-5062	269	33	.	.	PUNCT
ejpam-5062	270	1	if	if	SCONJ
ejpam-5062	270	2	the	the	DET
ejpam-5062	270	3	fuzzy	fuzzy	ADJ
ejpam-5062	270	4	topological	topological	ADJ
ejpam-5062	270	5	space	space	NOUN
ejpam-5062	270	6	y	y	PROPN
ejpam-5062	270	7	is	be	AUX
ejpam-5062	270	8	an	an	DET
ejpam-5062	270	9	fr	fr	ADJ
ejpam-5062	270	10	space	space	NOUN
ejpam-5062	270	11	then	then	ADV
ejpam-5062	270	12	x	x	PUNCT
ejpam-5062	270	13	is	be	AUX
ejpam-5062	270	14	an	an	DET
ejpam-5062	270	15	fsspwr	fsspwr	ADJ
ejpam-5062	270	16	space	space	NOUN
ejpam-5062	270	17	.	.	PUNCT
ejpam-5062	271	1	proof	proof	NOUN
ejpam-5062	271	2	.	.	PUNCT
ejpam-5062	272	1	proof	proof	NOUN
ejpam-5062	272	2	:	:	PUNCT
ejpam-5062	272	3	let	let	VERB
ejpam-5062	272	4	x	x	PRON
ejpam-5062	272	5	be	be	AUX
ejpam-5062	272	6	a	a	DET
ejpam-5062	272	7	fuzzy	fuzzy	ADJ
ejpam-5062	272	8	topological	topological	ADJ
ejpam-5062	272	9	space	space	NOUN
ejpam-5062	272	10	and	and	CCONJ
ejpam-5062	272	11	let	let	VERB
ejpam-5062	272	12	p	p	PRON
ejpam-5062	272	13	be	be	AUX
ejpam-5062	272	14	a	a	DET
ejpam-5062	272	15	fuzzy	fuzzy	ADJ
ejpam-5062	272	16	point	point	NOUN
ejpam-5062	272	17	,	,	PUNCT
ejpam-5062	272	18	let	let	VERB
ejpam-5062	272	19	f	f	PRON
ejpam-5062	272	20	be	be	AUX
ejpam-5062	272	21	any	any	DET
ejpam-5062	272	22	fuzzy	fuzzy	ADJ
ejpam-5062	272	23	closed	close	VERB
ejpam-5062	272	24	set	set	VERB
ejpam-5062	272	25	in	in	ADP
ejpam-5062	272	26	x	x	INTJ
ejpam-5062	272	27	such	such	ADJ
ejpam-5062	272	28	that	that	SCONJ
ejpam-5062	272	29	p	p	PROPN
ejpam-5062	272	30	≤	≤	PROPN
ejpam-5062	272	31	f	f	PROPN
ejpam-5062	272	32	c.	c.	PROPN
ejpam-5062	272	33	then	then	ADV
ejpam-5062	272	34	,	,	PUNCT
ejpam-5062	272	35	f(p	f(p	PROPN
ejpam-5062	272	36	)	)	PUNCT
ejpam-5062	272	37	is	be	AUX
ejpam-5062	272	38	a	a	DET
ejpam-5062	272	39	fuzzy	fuzzy	ADJ
ejpam-5062	272	40	point	point	NOUN
ejpam-5062	272	41	in	in	ADP
ejpam-5062	272	42	y	y	PROPN
ejpam-5062	272	43	and	and	CCONJ
ejpam-5062	272	44	according	accord	VERB
ejpam-5062	272	45	to	to	ADP
ejpam-5062	272	46	the	the	DET
ejpam-5062	272	47	conditions	condition	NOUN
ejpam-5062	272	48	of	of	ADP
ejpam-5062	272	49	the	the	DET
ejpam-5062	272	50	theorem	theorem	ADJ
ejpam-5062	272	51	f(p	f(p	PROPN
ejpam-5062	272	52	)	)	PUNCT
ejpam-5062	272	53	≤	≤	PUNCT
ejpam-5062	273	1	f(f	f(f	PROPN
ejpam-5062	273	2	)	)	PUNCT
ejpam-5062	273	3	c.	c.	PROPN
ejpam-5062	273	4	it	it	PRON
ejpam-5062	273	5	is	be	AUX
ejpam-5062	273	6	obvious	obvious	ADJ
ejpam-5062	273	7	that	that	SCONJ
ejpam-5062	273	8	the	the	DET
ejpam-5062	273	9	fuzzy	fuzzy	ADJ
ejpam-5062	273	10	set	set	VERB
ejpam-5062	273	11	f(f	f(f	PROPN
ejpam-5062	273	12	)	)	PUNCT
ejpam-5062	273	13	is	be	AUX
ejpam-5062	273	14	a	a	DET
ejpam-5062	273	15	fuzzy	fuzzy	ADJ
ejpam-5062	273	16	closed	close	VERB
ejpam-5062	273	17	set	set	VERB
ejpam-5062	273	18	in	in	ADP
ejpam-5062	273	19	y	y	PROPN
ejpam-5062	273	20	.	.	PUNCT
ejpam-5062	274	1	since	since	SCONJ
ejpam-5062	274	2	y	y	PROPN
ejpam-5062	274	3	is	be	AUX
ejpam-5062	274	4	an	an	DET
ejpam-5062	274	5	fr	fr	ADJ
ejpam-5062	274	6	space	space	NOUN
ejpam-5062	274	7	,	,	PUNCT
ejpam-5062	274	8	then	then	ADV
ejpam-5062	274	9	there	there	PRON
ejpam-5062	274	10	exist	exist	VERB
ejpam-5062	274	11	fuzzy	fuzzy	ADJ
ejpam-5062	274	12	open	open	ADJ
ejpam-5062	274	13	sets	set	NOUN
ejpam-5062	274	14	u	u	NOUN
ejpam-5062	274	15	,	,	PUNCT
ejpam-5062	274	16	v	v	ADP
ejpam-5062	274	17	such	such	ADJ
ejpam-5062	274	18	that	that	SCONJ
ejpam-5062	274	19	f(p	f(p	NOUN
ejpam-5062	274	20	)	)	PUNCT
ejpam-5062	274	21	≤	≤	NOUN
ejpam-5062	274	22	u	u	NOUN
ejpam-5062	274	23	,	,	PUNCT
ejpam-5062	274	24	f(f	f(f	PROPN
ejpam-5062	274	25	)	)	PUNCT
ejpam-5062	274	26	≤	≤	PROPN
ejpam-5062	274	27	v	v	NOUN
ejpam-5062	274	28	and	and	CCONJ
ejpam-5062	274	29	u	u	NOUN
ejpam-5062	274	30	≤	≤	X
ejpam-5062	274	31	v	v	ADP
ejpam-5062	274	32	c.	c.	NOUN
ejpam-5062	274	33	if	if	SCONJ
ejpam-5062	274	34	we	we	PRON
ejpam-5062	274	35	refer	refer	VERB
ejpam-5062	274	36	again	again	ADV
ejpam-5062	274	37	to	to	ADP
ejpam-5062	274	38	the	the	DET
ejpam-5062	274	39	conditions	condition	NOUN
ejpam-5062	274	40	of	of	ADP
ejpam-5062	274	41	the	the	DET
ejpam-5062	274	42	theorem	theorem	NOUN
ejpam-5062	274	43	,	,	PUNCT
ejpam-5062	274	44	then	then	ADV
ejpam-5062	274	45	we	we	PRON
ejpam-5062	274	46	have	have	VERB
ejpam-5062	274	47	:	:	PUNCT
ejpam-5062	274	48	p	p	X
ejpam-5062	274	49	≤	≤	NUM
ejpam-5062	274	50	f−1(u	f−1(u	NOUN
ejpam-5062	274	51	)	)	PUNCT
ejpam-5062	274	52	,	,	PUNCT
ejpam-5062	274	53	f	f	PROPN
ejpam-5062	274	54	≤	≤	PROPN
ejpam-5062	274	55	f−1(v	f−1(v	PROPN
ejpam-5062	274	56	)	)	PUNCT
ejpam-5062	274	57	and	and	CCONJ
ejpam-5062	274	58	f−1(u	f−1(u	PROPN
ejpam-5062	274	59	)	)	PUNCT
ejpam-5062	274	60	≤	≤	ADJ
ejpam-5062	274	61	f−1(v	f−1(v	NOUN
ejpam-5062	274	62	)	)	PUNCT
ejpam-5062	275	1	c.	c.	PROPN
ejpam-5062	275	2	it	it	PRON
ejpam-5062	275	3	is	be	AUX
ejpam-5062	275	4	obvious	obvious	ADJ
ejpam-5062	275	5	that	that	SCONJ
ejpam-5062	275	6	f−1(u	f−1(u	NOUN
ejpam-5062	275	7	)	)	PUNCT
ejpam-5062	275	8	and	and	CCONJ
ejpam-5062	275	9	f−1(v	f−1(v	PROPN
ejpam-5062	275	10	)	)	PUNCT
ejpam-5062	275	11	are	be	AUX
ejpam-5062	275	12	fuzzy	fuzzy	ADJ
ejpam-5062	275	13	strongly	strongly	ADV
ejpam-5062	275	14	semi	semi	ADJ
ejpam-5062	275	15	pre	pre	ADJ
ejpam-5062	275	16	-	-	ADJ
ejpam-5062	275	17	open	open	ADJ
ejpam-5062	275	18	sets	set	NOUN
ejpam-5062	275	19	in	in	ADP
ejpam-5062	275	20	x.	x.	NOUN
ejpam-5062	275	21	hence	hence	ADV
ejpam-5062	275	22	the	the	DET
ejpam-5062	275	23	fuzzy	fuzzy	ADJ
ejpam-5062	275	24	topological	topological	ADJ
ejpam-5062	275	25	space	space	NOUN
ejpam-5062	275	26	x	x	PUNCT
ejpam-5062	275	27	is	be	AUX
ejpam-5062	275	28	an	an	DET
ejpam-5062	275	29	fsspwr	fsspwr	ADJ
ejpam-5062	275	30	space	space	NOUN
ejpam-5062	275	31	.	.	PUNCT
ejpam-5062	276	1	theorem	theorem	ADJ
ejpam-5062	276	2	15	15	NUM
ejpam-5062	276	3	.	.	PUNCT
ejpam-5062	277	1	theorem	theorem	NOUN
ejpam-5062	277	2	let	let	VERB
ejpam-5062	277	3	f	f	NOUN
ejpam-5062	277	4	:	:	PUNCT
ejpam-5062	277	5	x	x	X
ejpam-5062	277	6	→	→	SYM
ejpam-5062	277	7	y	y	X
ejpam-5062	277	8	be	be	AUX
ejpam-5062	277	9	a	a	DET
ejpam-5062	277	10	fuzzy	fuzzy	ADJ
ejpam-5062	277	11	continuous	continuous	ADJ
ejpam-5062	277	12	and	and	CCONJ
ejpam-5062	277	13	fuzzy	fuzzy	ADJ
ejpam-5062	277	14	strongly	strongly	ADV
ejpam-5062	277	15	semi	semi	ADV
ejpam-5062	277	16	pre	pre	ADJ
ejpam-5062	277	17	-	-	ADJ
ejpam-5062	277	18	open	open	ADJ
ejpam-5062	277	19	and	and	CCONJ
ejpam-5062	277	20	bijective	bijective	ADJ
ejpam-5062	277	21	mapping	mapping	NOUN
ejpam-5062	277	22	from	from	ADP
ejpam-5062	277	23	the	the	DET
ejpam-5062	277	24	fuzzy	fuzzy	ADJ
ejpam-5062	277	25	topological	topological	ADJ
ejpam-5062	277	26	space	space	NOUN
ejpam-5062	277	27	x	x	PUNCT
ejpam-5062	277	28	to	to	ADP
ejpam-5062	277	29	a	a	DET
ejpam-5062	277	30	fuzzy	fuzzy	ADJ
ejpam-5062	277	31	topological	topological	ADJ
ejpam-5062	277	32	space	space	NOUN
ejpam-5062	277	33	y	y	PROPN
ejpam-5062	277	34	.	.	PUNCT
ejpam-5062	278	1	if	if	SCONJ
ejpam-5062	278	2	the	the	DET
ejpam-5062	278	3	fuzzy	fuzzy	ADJ
ejpam-5062	278	4	topological	topological	ADJ
ejpam-5062	278	5	space	space	NOUN
ejpam-5062	278	6	x	x	PUNCT
ejpam-5062	278	7	is	be	AUX
ejpam-5062	278	8	an	an	DET
ejpam-5062	278	9	fr	fr	ADJ
ejpam-5062	278	10	space	space	NOUN
ejpam-5062	278	11	then	then	ADV
ejpam-5062	278	12	y	y	PROPN
ejpam-5062	278	13	is	be	AUX
ejpam-5062	278	14	an	an	DET
ejpam-5062	278	15	fsspwr	fsspwr	ADJ
ejpam-5062	278	16	space	space	NOUN
ejpam-5062	278	17	.	.	PUNCT
ejpam-5062	279	1	proof	proof	NOUN
ejpam-5062	279	2	.	.	PUNCT
ejpam-5062	280	1	similar	similar	ADJ
ejpam-5062	280	2	to	to	ADP
ejpam-5062	280	3	theorem	theorem	ADJ
ejpam-5062	280	4	14	14	NUM
ejpam-5062	280	5	.	.	PUNCT
ejpam-5062	281	1	theorem	theorem	VERB
ejpam-5062	281	2	16	16	NUM
ejpam-5062	281	3	.	.	PUNCT
ejpam-5062	282	1	let	let	VERB
ejpam-5062	282	2	f	f	NOUN
ejpam-5062	282	3	:	:	PUNCT
ejpam-5062	282	4	x	x	X
ejpam-5062	282	5	→	→	SYM
ejpam-5062	282	6	y	y	X
ejpam-5062	282	7	be	be	AUX
ejpam-5062	282	8	a	a	DET
ejpam-5062	282	9	fuzzy	fuzzy	ADJ
ejpam-5062	282	10	sspo	sspo	NOUN
ejpam-5062	282	11	-	-	PUNCT
ejpam-5062	282	12	irresolute	irresolute	ADJ
ejpam-5062	282	13	and	and	CCONJ
ejpam-5062	282	14	injective	injective	ADJ
ejpam-5062	282	15	mapping	mapping	NOUN
ejpam-5062	282	16	from	from	ADP
ejpam-5062	282	17	the	the	DET
ejpam-5062	282	18	fuzzy	fuzzy	ADJ
ejpam-5062	282	19	topological	topological	ADJ
ejpam-5062	282	20	space	space	NOUN
ejpam-5062	282	21	x	x	PUNCT
ejpam-5062	282	22	to	to	ADP
ejpam-5062	282	23	a	a	DET
ejpam-5062	282	24	fuzzy	fuzzy	ADJ
ejpam-5062	282	25	topological	topological	ADJ
ejpam-5062	282	26	space	space	NOUN
ejpam-5062	282	27	y	y	PROPN
ejpam-5062	282	28	.	.	PUNCT
ejpam-5062	283	1	if	if	SCONJ
ejpam-5062	283	2	the	the	DET
ejpam-5062	283	3	fuzzy	fuzzy	ADJ
ejpam-5062	283	4	topological	topological	ADJ
ejpam-5062	283	5	space	space	NOUN
ejpam-5062	283	6	y	y	PROPN
ejpam-5062	283	7	is	be	AUX
ejpam-5062	283	8	an	an	DET
ejpam-5062	283	9	fsspt2	fsspt2	NOUN
ejpam-5062	283	10	1	1	NUM
ejpam-5062	283	11	2	2	NUM
ejpam-5062	283	12	(	(	PUNCT
ejpam-5062	283	13	fsspt2	fsspt2	PROPN
ejpam-5062	283	14	,	,	PUNCT
ejpam-5062	283	15	fsspts	fsspt	NOUN
ejpam-5062	283	16	,	,	PUNCT
ejpam-5062	283	17	fsspt1	fsspt1	NOUN
ejpam-5062	283	18	,	,	PUNCT
ejpam-5062	283	19	fsspt0	fsspt0	NOUN
ejpam-5062	283	20	)	)	PUNCT
ejpam-5062	283	21	space	space	NOUN
ejpam-5062	283	22	then	then	ADV
ejpam-5062	283	23	x	x	PUNCT
ejpam-5062	283	24	is	be	AUX
ejpam-5062	283	25	also	also	ADV
ejpam-5062	283	26	an	an	DET
ejpam-5062	283	27	fsspt2	fsspt2	NOUN
ejpam-5062	283	28	1	1	NUM
ejpam-5062	283	29	2	2	NUM
ejpam-5062	283	30	(	(	PUNCT
ejpam-5062	283	31	fsspt2	fsspt2	PROPN
ejpam-5062	283	32	,	,	PUNCT
ejpam-5062	283	33	fsspts	fsspt	NOUN
ejpam-5062	283	34	,	,	PUNCT
ejpam-5062	283	35	fsspt1	fsspt1	NOUN
ejpam-5062	283	36	,	,	PUNCT
ejpam-5062	283	37	fsspt0	fsspt0	NOUN
ejpam-5062	283	38	)	)	PUNCT
ejpam-5062	283	39	space	space	NOUN
ejpam-5062	283	40	.	.	PUNCT
ejpam-5062	284	1	proof	proof	NOUN
ejpam-5062	284	2	.	.	PUNCT
ejpam-5062	285	1	let	let	VERB
ejpam-5062	285	2	us	we	PRON
ejpam-5062	285	3	suppose	suppose	VERB
ejpam-5062	285	4	that	that	SCONJ
ejpam-5062	285	5	fuzzy	fuzzy	ADJ
ejpam-5062	285	6	points	point	VERB
ejpam-5062	285	7	p	p	X
ejpam-5062	285	8	,	,	PUNCT
ejpam-5062	285	9	q	q	PROPN
ejpam-5062	285	10	≤	≤	NUM
ejpam-5062	285	11	x	x	PUNCT
ejpam-5062	285	12	represent	represent	VERB
ejpam-5062	285	13	any	any	DET
ejpam-5062	285	14	pair	pair	NOUN
ejpam-5062	285	15	of	of	ADP
ejpam-5062	285	16	fuzzy	fuzzy	ADJ
ejpam-5062	285	17	points	point	NOUN
ejpam-5062	285	18	with	with	ADP
ejpam-5062	285	19	different	different	ADJ
ejpam-5062	285	20	support	support	NOUN
ejpam-5062	285	21	.	.	PUNCT
ejpam-5062	286	1	according	accord	VERB
ejpam-5062	286	2	to	to	ADP
ejpam-5062	286	3	the	the	DET
ejpam-5062	286	4	assumption	assumption	NOUN
ejpam-5062	286	5	of	of	ADP
ejpam-5062	286	6	the	the	DET
ejpam-5062	286	7	theorem	theorem	NOUN
ejpam-5062	286	8	,	,	PUNCT
ejpam-5062	286	9	the	the	DET
ejpam-5062	286	10	mapping	mapping	NOUN
ejpam-5062	286	11	f	f	X
ejpam-5062	286	12	:	:	PUNCT
ejpam-5062	286	13	x	x	X
ejpam-5062	286	14	→	→	SYM
ejpam-5062	286	15	y	y	PROPN
ejpam-5062	286	16	is	be	AUX
ejpam-5062	286	17	an	an	DET
ejpam-5062	286	18	injective	injective	ADJ
ejpam-5062	286	19	mapping	mapping	NOUN
ejpam-5062	286	20	,	,	PUNCT
ejpam-5062	286	21	it	it	PRON
ejpam-5062	286	22	is	be	AUX
ejpam-5062	286	23	obvious	obvious	ADJ
ejpam-5062	286	24	that	that	SCONJ
ejpam-5062	286	25	f(p	f(p	PROPN
ejpam-5062	286	26	)	)	PUNCT
ejpam-5062	286	27	,	,	PUNCT
ejpam-5062	286	28	f(q	f(q	PROPN
ejpam-5062	286	29	)	)	PUNCT
ejpam-5062	286	30	are	be	AUX
ejpam-5062	286	31	two	two	NUM
ejpam-5062	286	32	fuzzy	fuzzy	ADJ
ejpam-5062	286	33	points	point	NOUN
ejpam-5062	286	34	in	in	ADP
ejpam-5062	286	35	y	y	PROPN
ejpam-5062	286	36	with	with	ADP
ejpam-5062	286	37	different	different	ADJ
ejpam-5062	286	38	support	support	NOUN
ejpam-5062	286	39	.	.	PUNCT
ejpam-5062	287	1	now	now	ADV
ejpam-5062	287	2	,	,	PUNCT
ejpam-5062	287	3	since	since	SCONJ
ejpam-5062	287	4	the	the	DET
ejpam-5062	287	5	fuzzy	fuzzy	ADJ
ejpam-5062	287	6	topological	topological	ADJ
ejpam-5062	287	7	space	space	NOUN
ejpam-5062	287	8	y	y	PROPN
ejpam-5062	287	9	is	be	AUX
ejpam-5062	287	10	an	an	DET
ejpam-5062	287	11	fsspt2	fsspt2	NOUN
ejpam-5062	287	12	1	1	NUM
ejpam-5062	287	13	2	2	NUM
ejpam-5062	287	14	,	,	PUNCT
ejpam-5062	287	15	there	there	PRON
ejpam-5062	287	16	exist	exist	VERB
ejpam-5062	287	17	fuzzy	fuzzy	ADJ
ejpam-5062	287	18	strongly	strongly	ADV
ejpam-5062	287	19	semi	semi	ADV
ejpam-5062	287	20	pre	pre	ADJ
ejpam-5062	287	21	-	-	ADJ
ejpam-5062	287	22	open	open	ADJ
ejpam-5062	287	23	sets	set	NOUN
ejpam-5062	287	24	u	u	NOUN
ejpam-5062	287	25	,	,	PUNCT
ejpam-5062	287	26	v	v	ADP
ejpam-5062	287	27	such	such	ADJ
ejpam-5062	287	28	that	that	SCONJ
ejpam-5062	287	29	:	:	PUNCT
ejpam-5062	287	30	f(p	f(p	X
ejpam-5062	287	31	)	)	PUNCT
ejpam-5062	287	32	≤	≤	NUM
ejpam-5062	287	33	u	u	NOUN
ejpam-5062	287	34	≤	≤	ADJ
ejpam-5062	287	35	f(q)c	f(q)c	PROPN
ejpam-5062	287	36	,	,	PUNCT
ejpam-5062	287	37	f(q	f(q	PROPN
ejpam-5062	287	38	)	)	PUNCT
ejpam-5062	287	39	≤	≤	NUM
ejpam-5062	287	40	v	v	X
ejpam-5062	287	41	≤	≤	NUM
ejpam-5062	287	42	f(p)c	f(p)c	PROPN
ejpam-5062	287	43	and	and	CCONJ
ejpam-5062	287	44	sspclu	sspclu	PROPN
ejpam-5062	287	45	≤	≤	PROPN
ejpam-5062	287	46	(	(	PUNCT
ejpam-5062	287	47	sspclv	sspclv	PROPN
ejpam-5062	287	48	)	)	PUNCT
ejpam-5062	287	49	c.	c.	NOUN
ejpam-5062	287	50	since	since	SCONJ
ejpam-5062	287	51	the	the	DET
ejpam-5062	287	52	mapping	mapping	NOUN
ejpam-5062	287	53	f	f	NOUN
ejpam-5062	287	54	is	be	AUX
ejpam-5062	287	55	a	a	DET
ejpam-5062	287	56	fuzzy	fuzzy	ADJ
ejpam-5062	287	57	sspo	sspo	NOUN
ejpam-5062	287	58	-	-	PUNCT
ejpam-5062	287	59	irresolute	irresolute	ADJ
ejpam-5062	287	60	,	,	PUNCT
ejpam-5062	287	61	it	it	PRON
ejpam-5062	287	62	follows	follow	VERB
ejpam-5062	287	63	that	that	SCONJ
ejpam-5062	287	64	f−1(u	f−1(u	PROPN
ejpam-5062	287	65	)	)	PUNCT
ejpam-5062	287	66	,	,	PUNCT
ejpam-5062	287	67	f−1(v	f−1(v	PROPN
ejpam-5062	287	68	)	)	PUNCT
ejpam-5062	287	69	are	be	AUX
ejpam-5062	287	70	two	two	NUM
ejpam-5062	287	71	fuzzy	fuzzy	ADJ
ejpam-5062	287	72	strongly	strongly	ADV
ejpam-5062	287	73	semi	semi	ADJ
ejpam-5062	287	74	pre	pre	ADJ
ejpam-5062	287	75	-	-	ADJ
ejpam-5062	287	76	open	open	ADJ
ejpam-5062	287	77	sets	set	NOUN
ejpam-5062	287	78	in	in	ADP
ejpam-5062	287	79	x	x	SYM
ejpam-5062	287	80	such	such	ADJ
ejpam-5062	287	81	that	that	SCONJ
ejpam-5062	287	82	:	:	PUNCT
ejpam-5062	287	83	p	p	X
ejpam-5062	287	84	≤	≤	NUM
ejpam-5062	287	85	f−1(u	f−1(u	PROPN
ejpam-5062	287	86	)	)	PUNCT
ejpam-5062	287	87	≤	≤	PROPN
ejpam-5062	287	88	qc	qc	PROPN
ejpam-5062	287	89	,	,	PUNCT
ejpam-5062	287	90	q	q	PROPN
ejpam-5062	287	91	≤	≤	PROPN
ejpam-5062	287	92	f−1(v	f−1(v	NOUN
ejpam-5062	287	93	)	)	PUNCT
ejpam-5062	287	94	≤	≤	NUM
ejpam-5062	287	95	pc	pc	NOUN
ejpam-5062	287	96	.	.	PUNCT
ejpam-5062	288	1	from	from	ADP
ejpam-5062	288	2	the	the	DET
ejpam-5062	288	3	conditions	condition	NOUN
ejpam-5062	288	4	set	set	VERB
ejpam-5062	288	5	out	out	ADP
ejpam-5062	288	6	by	by	ADP
ejpam-5062	288	7	theorem	theorem	NOUN
ejpam-5062	288	8	1	1	NUM
ejpam-5062	288	9	in	in	ADP
ejpam-5062	288	10	[	[	X
ejpam-5062	288	11	18	18	NUM
ejpam-5062	288	12	]	]	PUNCT
ejpam-5062	288	13	,	,	PUNCT
ejpam-5062	288	14	we	we	PRON
ejpam-5062	288	15	can	can	AUX
ejpam-5062	288	16	prove	prove	VERB
ejpam-5062	288	17	that	that	SCONJ
ejpam-5062	288	18	:	:	PUNCT
ejpam-5062	288	19	sh	sh	PROPN
ejpam-5062	288	20	.	.	PROPN
ejpam-5062	288	21	makolli	makolli	PROPN
ejpam-5062	288	22	,	,	PUNCT
ejpam-5062	288	23	b.	b.	PROPN
ejpam-5062	288	24	krsteska	krsteska	PROPN
ejpam-5062	288	25	/	/	SYM
ejpam-5062	288	26	eur	eur	PROPN
ejpam-5062	288	27	.	.	PUNCT
ejpam-5062	289	1	j.	j.	PROPN
ejpam-5062	289	2	pure	pure	PROPN
ejpam-5062	289	3	appl	appl	PROPN
ejpam-5062	289	4	.	.	PROPN
ejpam-5062	289	5	math	math	PROPN
ejpam-5062	289	6	,	,	PUNCT
ejpam-5062	289	7	17	17	NUM
ejpam-5062	289	8	(	(	PUNCT
ejpam-5062	289	9	2	2	NUM
ejpam-5062	289	10	)	)	PUNCT
ejpam-5062	289	11	(	(	PUNCT
ejpam-5062	289	12	2024	2024	NUM
ejpam-5062	289	13	)	)	PUNCT
ejpam-5062	289	14	,	,	PUNCT
ejpam-5062	289	15	638	638	NUM
ejpam-5062	289	16	-	-	SYM
ejpam-5062	289	17	662	662	NUM
ejpam-5062	289	18	650	650	NUM
ejpam-5062	289	19	sspclf−1(u	sspclf−1(u	NOUN
ejpam-5062	289	20	)	)	PUNCT
ejpam-5062	289	21	≤	≤	NUM
ejpam-5062	289	22	f−1(sspclu	f−1(sspclu	NOUN
ejpam-5062	289	23	)	)	PUNCT
ejpam-5062	289	24	≤	≤	NUM
ejpam-5062	289	25	f−1((sspclv	f−1((sspclv	PROPN
ejpam-5062	289	26	)	)	PUNCT
ejpam-5062	290	1	c	c	X
ejpam-5062	290	2	)	)	PUNCT
ejpam-5062	290	3	=	=	SYM
ejpam-5062	290	4	f−1(sspintv	f−1(sspintv	ADP
ejpam-5062	290	5	c	c	X
ejpam-5062	290	6	)	)	PUNCT
ejpam-5062	290	7	≤	≤	NOUN
ejpam-5062	290	8	≤	≤	NUM
ejpam-5062	290	9	sspint(f−1(v	sspint(f−1(v	NOUN
ejpam-5062	290	10	c	c	NOUN
ejpam-5062	290	11	)	)	PUNCT
ejpam-5062	290	12	)	)	PUNCT
ejpam-5062	291	1	=	=	SYM
ejpam-5062	291	2	(	(	PUNCT
ejpam-5062	291	3	sspcl(f−1(v	sspcl(f−1(v	NOUN
ejpam-5062	291	4	)	)	PUNCT
ejpam-5062	291	5	)	)	PUNCT
ejpam-5062	292	1	c.	c.	NOUN
ejpam-5062	292	2	we	we	PRON
ejpam-5062	292	3	have	have	AUX
ejpam-5062	292	4	shown	show	VERB
ejpam-5062	292	5	that	that	SCONJ
ejpam-5062	292	6	for	for	ADP
ejpam-5062	292	7	the	the	DET
ejpam-5062	292	8	given	give	VERB
ejpam-5062	292	9	fuzzy	fuzzy	NOUN
ejpam-5062	292	10	strongly	strongly	ADV
ejpam-5062	292	11	semi	semi	ADJ
ejpam-5062	292	12	pre	pre	ADJ
ejpam-5062	292	13	-	-	ADJ
ejpam-5062	292	14	open	open	ADJ
ejpam-5062	292	15	sets	set	NOUN
ejpam-5062	292	16	f−1(u	f−1(u	NOUN
ejpam-5062	292	17	)	)	PUNCT
ejpam-5062	292	18	,	,	PUNCT
ejpam-5062	292	19	f−1(v	f−1(v	PROPN
ejpam-5062	292	20	)	)	PUNCT
ejpam-5062	293	1	it	it	PRON
ejpam-5062	293	2	follows	follow	VERB
ejpam-5062	293	3	that	that	SCONJ
ejpam-5062	293	4	sspclf−1(u	sspclf−1(u	NOUN
ejpam-5062	293	5	)	)	PUNCT
ejpam-5062	293	6	≤	≤	NOUN
ejpam-5062	293	7	(	(	PUNCT
ejpam-5062	293	8	sspcl(f−1(v	sspcl(f−1(v	NOUN
ejpam-5062	293	9	)	)	PUNCT
ejpam-5062	293	10	)	)	PUNCT
ejpam-5062	294	1	c	c	X
ejpam-5062	294	2	,	,	PUNCT
ejpam-5062	294	3	which	which	PRON
ejpam-5062	294	4	means	mean	VERB
ejpam-5062	294	5	that	that	SCONJ
ejpam-5062	294	6	the	the	DET
ejpam-5062	294	7	fuzzy	fuzzy	ADJ
ejpam-5062	294	8	topological	topological	ADJ
ejpam-5062	294	9	space	space	NOUN
ejpam-5062	294	10	x	x	PUNCT
ejpam-5062	294	11	is	be	AUX
ejpam-5062	294	12	an	an	DET
ejpam-5062	294	13	fsspt2	fsspt2	NOUN
ejpam-5062	294	14	1	1	NUM
ejpam-5062	294	15	2	2	NUM
ejpam-5062	294	16	space	space	NOUN
ejpam-5062	294	17	.	.	PUNCT
ejpam-5062	295	1	in	in	ADP
ejpam-5062	295	2	the	the	DET
ejpam-5062	295	3	similar	similar	ADJ
ejpam-5062	295	4	way	way	NOUN
ejpam-5062	295	5	we	we	PRON
ejpam-5062	295	6	can	can	AUX
ejpam-5062	295	7	prove	prove	VERB
ejpam-5062	295	8	the	the	DET
ejpam-5062	295	9	cases	case	NOUN
ejpam-5062	295	10	when	when	SCONJ
ejpam-5062	295	11	y	y	PROPN
ejpam-5062	295	12	is	be	AUX
ejpam-5062	295	13	an	an	DET
ejpam-5062	295	14	fsspt2	fsspt2	PROPN
ejpam-5062	295	15	,	,	PUNCT
ejpam-5062	295	16	fsspts	fsspt	NOUN
ejpam-5062	295	17	,	,	PUNCT
ejpam-5062	295	18	fsspt1	fsspt1	NOUN
ejpam-5062	295	19	,	,	PUNCT
ejpam-5062	295	20	fsspt0	fsspt0	NOUN
ejpam-5062	295	21	space	space	NOUN
ejpam-5062	295	22	.	.	PUNCT
ejpam-5062	296	1	theorem	theorem	NOUN
ejpam-5062	296	2	17	17	NUM
ejpam-5062	296	3	.	.	PUNCT
ejpam-5062	297	1	let	let	VERB
ejpam-5062	297	2	f	f	NOUN
ejpam-5062	297	3	:	:	PUNCT
ejpam-5062	297	4	x	x	X
ejpam-5062	297	5	→	→	SYM
ejpam-5062	297	6	y	y	X
ejpam-5062	297	7	be	be	AUX
ejpam-5062	297	8	a	a	DET
ejpam-5062	297	9	fuzzy	fuzzy	ADJ
ejpam-5062	297	10	sspo	sspo	NOUN
ejpam-5062	297	11	-	-	PUNCT
ejpam-5062	297	12	irresolute	irresolute	ADJ
ejpam-5062	297	13	open	open	ADJ
ejpam-5062	297	14	and	and	CCONJ
ejpam-5062	297	15	bijective	bijective	ADJ
ejpam-5062	297	16	mapping	mapping	NOUN
ejpam-5062	297	17	from	from	ADP
ejpam-5062	297	18	the	the	DET
ejpam-5062	297	19	fuzzy	fuzzy	ADJ
ejpam-5062	297	20	topological	topological	ADJ
ejpam-5062	297	21	space	space	NOUN
ejpam-5062	297	22	x	x	PUNCT
ejpam-5062	297	23	to	to	ADP
ejpam-5062	297	24	a	a	DET
ejpam-5062	297	25	fuzzy	fuzzy	ADJ
ejpam-5062	297	26	topological	topological	ADJ
ejpam-5062	297	27	space	space	NOUN
ejpam-5062	297	28	y	y	PROPN
ejpam-5062	297	29	.	.	PUNCT
ejpam-5062	298	1	if	if	SCONJ
ejpam-5062	298	2	the	the	DET
ejpam-5062	298	3	fuzzy	fuzzy	ADJ
ejpam-5062	298	4	topological	topological	ADJ
ejpam-5062	298	5	space	space	NOUN
ejpam-5062	298	6	x	x	PUNCT
ejpam-5062	298	7	is	be	AUX
ejpam-5062	298	8	an	an	DET
ejpam-5062	298	9	fsspt2	fsspt2	NOUN
ejpam-5062	298	10	1	1	NUM
ejpam-5062	298	11	2	2	NUM
ejpam-5062	298	12	(	(	PUNCT
ejpam-5062	298	13	fsspt2	fsspt2	PROPN
ejpam-5062	298	14	,	,	PUNCT
ejpam-5062	298	15	fsspts	fsspt	NOUN
ejpam-5062	298	16	,	,	PUNCT
ejpam-5062	298	17	fsspt1	fsspt1	NOUN
ejpam-5062	298	18	,	,	PUNCT
ejpam-5062	298	19	fsspt0	fsspt0	NOUN
ejpam-5062	298	20	)	)	PUNCT
ejpam-5062	298	21	space	space	NOUN
ejpam-5062	298	22	then	then	ADV
ejpam-5062	298	23	y	y	PROPN
ejpam-5062	298	24	is	be	AUX
ejpam-5062	298	25	also	also	ADV
ejpam-5062	298	26	an	an	DET
ejpam-5062	298	27	fsspt2	fsspt2	NOUN
ejpam-5062	298	28	1	1	NUM
ejpam-5062	298	29	2	2	NUM
ejpam-5062	298	30	(	(	PUNCT
ejpam-5062	298	31	fsspt2	fsspt2	PROPN
ejpam-5062	298	32	,	,	PUNCT
ejpam-5062	298	33	fsspts	fsspt	NOUN
ejpam-5062	298	34	,	,	PUNCT
ejpam-5062	298	35	fsspt1	fsspt1	NOUN
ejpam-5062	298	36	,	,	PUNCT
ejpam-5062	298	37	fsspt0	fsspt0	NOUN
ejpam-5062	298	38	)	)	PUNCT
ejpam-5062	298	39	space	space	NOUN
ejpam-5062	298	40	.	.	PUNCT
ejpam-5062	299	1	proof	proof	NOUN
ejpam-5062	299	2	.	.	PUNCT
ejpam-5062	300	1	let	let	VERB
ejpam-5062	300	2	us	we	PRON
ejpam-5062	300	3	show	show	VERB
ejpam-5062	300	4	only	only	ADV
ejpam-5062	300	5	the	the	DET
ejpam-5062	300	6	case	case	NOUN
ejpam-5062	300	7	when	when	SCONJ
ejpam-5062	300	8	the	the	DET
ejpam-5062	300	9	fuzzy	fuzzy	ADJ
ejpam-5062	300	10	topological	topological	ADJ
ejpam-5062	300	11	space	space	NOUN
ejpam-5062	300	12	x	x	PUNCT
ejpam-5062	300	13	is	be	AUX
ejpam-5062	300	14	an	an	DET
ejpam-5062	300	15	fsspts	fsspt	NOUN
ejpam-5062	300	16	space	space	NOUN
ejpam-5062	300	17	.	.	PUNCT
ejpam-5062	301	1	other	other	ADJ
ejpam-5062	301	2	cases	case	NOUN
ejpam-5062	301	3	are	be	AUX
ejpam-5062	301	4	proved	prove	VERB
ejpam-5062	301	5	in	in	ADP
ejpam-5062	301	6	similar	similar	ADJ
ejpam-5062	301	7	manner	manner	NOUN
ejpam-5062	301	8	(	(	PUNCT
ejpam-5062	301	9	similar	similar	ADJ
ejpam-5062	301	10	to	to	ADP
ejpam-5062	301	11	theorem	theorem	NOUN
ejpam-5062	301	12	16	16	NUM
ejpam-5062	301	13	)	)	PUNCT
ejpam-5062	301	14	.	.	PUNCT
ejpam-5062	302	1	let	let	VERB
ejpam-5062	302	2	q	q	PROPN
ejpam-5062	302	3	≤	≤	NOUN
ejpam-5062	302	4	y	y	NOUN
ejpam-5062	302	5	be	be	AUX
ejpam-5062	302	6	any	any	DET
ejpam-5062	302	7	fuzzy	fuzzy	ADJ
ejpam-5062	302	8	point	point	NOUN
ejpam-5062	302	9	of	of	ADP
ejpam-5062	302	10	y	y	PROPN
ejpam-5062	302	11	.	.	PUNCT
ejpam-5062	303	1	the	the	DET
ejpam-5062	303	2	preimage	preimage	NOUN
ejpam-5062	303	3	of	of	ADP
ejpam-5062	303	4	this	this	DET
ejpam-5062	303	5	point	point	NOUN
ejpam-5062	303	6	satisfies	satisfy	VERB
ejpam-5062	303	7	the	the	DET
ejpam-5062	303	8	following	follow	VERB
ejpam-5062	303	9	f−1(q	f−1(q	PROPN
ejpam-5062	303	10	)	)	PUNCT
ejpam-5062	303	11	≤	≤	NUM
ejpam-5062	303	12	x.	x.	NOUN
ejpam-5062	303	13	based	base	VERB
ejpam-5062	303	14	on	on	ADP
ejpam-5062	303	15	the	the	DET
ejpam-5062	303	16	conditions	condition	NOUN
ejpam-5062	303	17	of	of	ADP
ejpam-5062	303	18	the	the	DET
ejpam-5062	303	19	theorem	theorem	NOUN
ejpam-5062	303	20	and	and	CCONJ
ejpam-5062	303	21	from	from	ADP
ejpam-5062	303	22	the	the	DET
ejpam-5062	303	23	fact	fact	NOUN
ejpam-5062	303	24	that	that	SCONJ
ejpam-5062	303	25	x	x	PRON
ejpam-5062	303	26	is	be	AUX
ejpam-5062	303	27	an	an	DET
ejpam-5062	303	28	fsspts	fsspt	NOUN
ejpam-5062	303	29	space	space	NOUN
ejpam-5062	303	30	,	,	PUNCT
ejpam-5062	303	31	that	that	ADV
ejpam-5062	303	32	is	is	ADV
ejpam-5062	303	33	,	,	PUNCT
ejpam-5062	303	34	any	any	DET
ejpam-5062	303	35	fuzzy	fuzzy	ADJ
ejpam-5062	303	36	point	point	NOUN
ejpam-5062	303	37	f−1(q	f−1(q	NOUN
ejpam-5062	303	38	)	)	PUNCT
ejpam-5062	303	39	≤	≤	NUM
ejpam-5062	303	40	x	x	X
ejpam-5062	303	41	is	be	AUX
ejpam-5062	303	42	a	a	DET
ejpam-5062	303	43	fuzzy	fuzzy	ADJ
ejpam-5062	303	44	strongly	strongly	ADV
ejpam-5062	303	45	semi	semi	ADV
ejpam-5062	303	46	pre	pre	ADJ
ejpam-5062	303	47	-	-	ADJ
ejpam-5062	303	48	closed	closed	ADJ
ejpam-5062	303	49	set	set	NOUN
ejpam-5062	303	50	in	in	ADP
ejpam-5062	303	51	x.	x.	NOUN
ejpam-5062	303	52	it	it	PRON
ejpam-5062	303	53	follows	follow	VERB
ejpam-5062	303	54	that	that	SCONJ
ejpam-5062	303	55	the	the	DET
ejpam-5062	303	56	image	image	NOUN
ejpam-5062	303	57	f(f−1(q	f(f−1(q	PROPN
ejpam-5062	303	58	)	)	PUNCT
ejpam-5062	303	59	)	)	PUNCT
ejpam-5062	304	1	=	=	PUNCT
ejpam-5062	305	1	q	q	PROPN
ejpam-5062	305	2	≤	≤	NUM
ejpam-5062	305	3	y	y	NOUN
ejpam-5062	305	4	of	of	ADP
ejpam-5062	305	5	the	the	DET
ejpam-5062	305	6	fuzzy	fuzzy	ADJ
ejpam-5062	305	7	point	point	NOUN
ejpam-5062	305	8	f−1(q	f−1(q	PROPN
ejpam-5062	305	9	)	)	PUNCT
ejpam-5062	305	10	is	be	AUX
ejpam-5062	305	11	also	also	ADV
ejpam-5062	305	12	a	a	DET
ejpam-5062	305	13	fuzzy	fuzzy	ADJ
ejpam-5062	305	14	strongly	strongly	ADV
ejpam-5062	305	15	semi	semi	ADV
ejpam-5062	305	16	pre	pre	ADJ
ejpam-5062	305	17	-	-	ADJ
ejpam-5062	305	18	closed	closed	ADJ
ejpam-5062	305	19	set	set	NOUN
ejpam-5062	305	20	in	in	ADP
ejpam-5062	305	21	y	y	PROPN
ejpam-5062	305	22	.	.	PUNCT
ejpam-5062	306	1	in	in	ADP
ejpam-5062	306	2	other	other	ADJ
ejpam-5062	306	3	words	word	NOUN
ejpam-5062	306	4	any	any	DET
ejpam-5062	306	5	fuzzy	fuzzy	ADJ
ejpam-5062	306	6	point	point	NOUN
ejpam-5062	306	7	of	of	ADP
ejpam-5062	306	8	y	y	PROPN
ejpam-5062	306	9	is	be	AUX
ejpam-5062	306	10	also	also	ADV
ejpam-5062	306	11	a	a	DET
ejpam-5062	306	12	fuzzy	fuzzy	ADJ
ejpam-5062	306	13	strongly	strongly	ADV
ejpam-5062	306	14	semi	semi	ADV
ejpam-5062	306	15	pre	pre	ADJ
ejpam-5062	306	16	-	-	ADJ
ejpam-5062	306	17	closed	closed	ADJ
ejpam-5062	306	18	set	set	NOUN
ejpam-5062	306	19	and	and	CCONJ
ejpam-5062	306	20	therefore	therefore	ADV
ejpam-5062	306	21	y	y	PROPN
ejpam-5062	306	22	is	be	AUX
ejpam-5062	306	23	also	also	ADV
ejpam-5062	306	24	an	an	DET
ejpam-5062	306	25	fsspts	fsspt	NOUN
ejpam-5062	306	26	space	space	NOUN
ejpam-5062	306	27	.	.	PUNCT
ejpam-5062	307	1	theorem	theorem	NOUN
ejpam-5062	307	2	18	18	NUM
ejpam-5062	307	3	.	.	PUNCT
ejpam-5062	308	1	let	let	VERB
ejpam-5062	308	2	f	f	NOUN
ejpam-5062	308	3	:	:	PUNCT
ejpam-5062	308	4	x	x	X
ejpam-5062	308	5	→	→	SYM
ejpam-5062	308	6	y	y	X
ejpam-5062	308	7	be	be	AUX
ejpam-5062	308	8	a	a	DET
ejpam-5062	308	9	fuzzy	fuzzy	ADJ
ejpam-5062	308	10	sspo	sspo	NOUN
ejpam-5062	308	11	-	-	PUNCT
ejpam-5062	308	12	irresolute	irresolute	NOUN
ejpam-5062	309	1	closed	closed	ADJ
ejpam-5062	309	2	and	and	CCONJ
ejpam-5062	309	3	fuzzy	fuzzy	ADJ
ejpam-5062	309	4	strong	strong	ADJ
ejpam-5062	309	5	semi	semi	ADJ
ejpam-5062	309	6	pre	pre	ADJ
ejpam-5062	309	7	-	-	ADJ
ejpam-5062	309	8	continuous	continuous	ADJ
ejpam-5062	309	9	bijective	bijective	ADJ
ejpam-5062	309	10	mapping	mapping	NOUN
ejpam-5062	309	11	from	from	ADP
ejpam-5062	309	12	the	the	DET
ejpam-5062	309	13	fuzzy	fuzzy	ADJ
ejpam-5062	309	14	topological	topological	ADJ
ejpam-5062	309	15	space	space	NOUN
ejpam-5062	309	16	x	x	PUNCT
ejpam-5062	309	17	to	to	ADP
ejpam-5062	309	18	a	a	DET
ejpam-5062	309	19	fuzzy	fuzzy	ADJ
ejpam-5062	309	20	topological	topological	ADJ
ejpam-5062	309	21	space	space	NOUN
ejpam-5062	309	22	y	y	PROPN
ejpam-5062	309	23	.	.	PUNCT
ejpam-5062	310	1	if	if	SCONJ
ejpam-5062	310	2	the	the	DET
ejpam-5062	310	3	fuzzy	fuzzy	ADJ
ejpam-5062	310	4	topological	topological	ADJ
ejpam-5062	310	5	space	space	NOUN
ejpam-5062	310	6	y	y	PROPN
ejpam-5062	310	7	is	be	AUX
ejpam-5062	310	8	an	an	DET
ejpam-5062	310	9	fsspn	fsspn	ADJ
ejpam-5062	310	10	(	(	PUNCT
ejpam-5062	310	11	fsspwn	fsspwn	NOUN
ejpam-5062	310	12	,	,	PUNCT
ejpam-5062	310	13	fsspt3	fsspt3	NOUN
ejpam-5062	310	14	,	,	PUNCT
ejpam-5062	310	15	fsspr	fsspr	NOUN
ejpam-5062	310	16	)	)	PUNCT
ejpam-5062	310	17	space	space	NOUN
ejpam-5062	310	18	then	then	ADV
ejpam-5062	310	19	x	x	PUNCT
ejpam-5062	310	20	is	be	AUX
ejpam-5062	310	21	also	also	ADV
ejpam-5062	310	22	an	an	DET
ejpam-5062	310	23	fsspn	fsspn	ADJ
ejpam-5062	310	24	(	(	PUNCT
ejpam-5062	310	25	fsspwn	fsspwn	NOUN
ejpam-5062	310	26	,	,	PUNCT
ejpam-5062	310	27	fsspt3	fsspt3	NOUN
ejpam-5062	310	28	,	,	PUNCT
ejpam-5062	310	29	fsspr	fsspr	NOUN
ejpam-5062	310	30	)	)	PUNCT
ejpam-5062	310	31	space	space	NOUN
ejpam-5062	310	32	.	.	PUNCT
ejpam-5062	311	1	proof	proof	NOUN
ejpam-5062	311	2	.	.	PUNCT
ejpam-5062	312	1	let	let	VERB
ejpam-5062	312	2	f1	f1	NOUN
ejpam-5062	312	3	,	,	PUNCT
ejpam-5062	312	4	f2	f2	PROPN
ejpam-5062	312	5	be	be	VERB
ejpam-5062	312	6	two	two	NUM
ejpam-5062	312	7	fuzzy	fuzzy	ADJ
ejpam-5062	312	8	strongly	strongly	ADV
ejpam-5062	312	9	semi	semi	ADV
ejpam-5062	312	10	pre	pre	ADJ
ejpam-5062	312	11	-	-	ADJ
ejpam-5062	312	12	closed	closed	ADJ
ejpam-5062	312	13	sets	set	NOUN
ejpam-5062	312	14	in	in	ADP
ejpam-5062	312	15	x	x	SYM
ejpam-5062	312	16	such	such	ADJ
ejpam-5062	312	17	that	that	DET
ejpam-5062	312	18	f1	f1	PROPN
ejpam-5062	313	1	≤	≤	X
ejpam-5062	313	2	f	f	PROPN
ejpam-5062	313	3	c	c	NOUN
ejpam-5062	313	4	2	2	NUM
ejpam-5062	313	5	.	.	PUNCT
ejpam-5062	314	1	obviously	obviously	ADV
ejpam-5062	314	2	,	,	PUNCT
ejpam-5062	314	3	due	due	ADP
ejpam-5062	314	4	to	to	ADP
ejpam-5062	314	5	the	the	DET
ejpam-5062	314	6	conditions	condition	NOUN
ejpam-5062	314	7	of	of	ADP
ejpam-5062	314	8	the	the	DET
ejpam-5062	314	9	theorem	theorem	PROPN
ejpam-5062	314	10	,	,	PUNCT
ejpam-5062	314	11	f(f1	f(f1	NOUN
ejpam-5062	314	12	)	)	PUNCT
ejpam-5062	314	13	,	,	PUNCT
ejpam-5062	314	14	f(f2	f(f2	PROPN
ejpam-5062	314	15	)	)	PUNCT
ejpam-5062	314	16	are	be	AUX
ejpam-5062	314	17	two	two	NUM
ejpam-5062	314	18	fuzzy	fuzzy	ADJ
ejpam-5062	314	19	strongly	strongly	ADV
ejpam-5062	314	20	semi	semi	ADV
ejpam-5062	314	21	pre	pre	ADJ
ejpam-5062	314	22	-	-	ADJ
ejpam-5062	314	23	closed	closed	ADJ
ejpam-5062	314	24	sets	set	NOUN
ejpam-5062	314	25	in	in	ADP
ejpam-5062	314	26	y	y	PRON
ejpam-5062	314	27	such	such	ADJ
ejpam-5062	314	28	that	that	DET
ejpam-5062	314	29	f(f1	f(f1	NOUN
ejpam-5062	314	30	)	)	PUNCT
ejpam-5062	314	31	≤	≤	NOUN
ejpam-5062	314	32	(	(	PUNCT
ejpam-5062	314	33	f(f2	f(f2	NOUN
ejpam-5062	314	34	)	)	PUNCT
ejpam-5062	314	35	)	)	PUNCT
ejpam-5062	314	36	c.	c.	NOUN
ejpam-5062	314	37	since	since	SCONJ
ejpam-5062	314	38	y	y	PROPN
ejpam-5062	314	39	is	be	AUX
ejpam-5062	314	40	an	an	DET
ejpam-5062	314	41	fsspn	fsspn	ADJ
ejpam-5062	314	42	space	space	NOUN
ejpam-5062	314	43	,	,	PUNCT
ejpam-5062	314	44	there	there	PRON
ejpam-5062	314	45	are	be	VERB
ejpam-5062	314	46	fuzzy	fuzzy	ADJ
ejpam-5062	314	47	strongly	strongly	ADV
ejpam-5062	314	48	semi	semi	ADJ
ejpam-5062	314	49	pre	pre	ADJ
ejpam-5062	314	50	-	-	ADJ
ejpam-5062	314	51	open	open	ADJ
ejpam-5062	314	52	sets	set	NOUN
ejpam-5062	315	1	w1,w2	w1,w2	PROPN
ejpam-5062	315	2	such	such	ADJ
ejpam-5062	315	3	that	that	PRON
ejpam-5062	315	4	:	:	PUNCT
ejpam-5062	315	5	f(f1	f(f1	NOUN
ejpam-5062	315	6	)	)	PUNCT
ejpam-5062	315	7	≤	≤	NOUN
ejpam-5062	315	8	w1	w1	NOUN
ejpam-5062	315	9	,	,	PUNCT
ejpam-5062	315	10	f(f2	f(f2	NOUN
ejpam-5062	315	11	)	)	PUNCT
ejpam-5062	315	12	≤	≤	NOUN
ejpam-5062	315	13	w2	w2	NOUN
ejpam-5062	315	14	and	and	CCONJ
ejpam-5062	315	15	w1	w1	NOUN
ejpam-5062	315	16	≤	≤	PROPN
ejpam-5062	315	17	w	w	PROPN
ejpam-5062	315	18	c	c	NOUN
ejpam-5062	315	19	2	2	NUM
ejpam-5062	315	20	.	.	PUNCT
ejpam-5062	315	21	from	from	ADP
ejpam-5062	315	22	the	the	DET
ejpam-5062	315	23	assumption	assumption	NOUN
ejpam-5062	315	24	that	that	SCONJ
ejpam-5062	315	25	f	f	PROPN
ejpam-5062	315	26	is	be	AUX
ejpam-5062	315	27	a	a	DET
ejpam-5062	315	28	fuzzy	fuzzy	ADJ
ejpam-5062	315	29	strong	strong	ADJ
ejpam-5062	315	30	semi	semi	ADJ
ejpam-5062	315	31	pre	pre	ADJ
ejpam-5062	315	32	-	-	ADJ
ejpam-5062	315	33	continuous	continuous	ADJ
ejpam-5062	315	34	mapping	mapping	NOUN
ejpam-5062	315	35	,	,	PUNCT
ejpam-5062	315	36	it	it	PRON
ejpam-5062	315	37	follows	follow	VERB
ejpam-5062	315	38	that	that	SCONJ
ejpam-5062	315	39	f−1(w1	f−1(w1	PROPN
ejpam-5062	315	40	)	)	PUNCT
ejpam-5062	315	41	and	and	CCONJ
ejpam-5062	315	42	f−1(w2	f−1(w2	X
ejpam-5062	315	43	)	)	PUNCT
ejpam-5062	315	44	are	be	AUX
ejpam-5062	315	45	two	two	NUM
ejpam-5062	315	46	fuzzy	fuzzy	ADJ
ejpam-5062	315	47	strongly	strongly	ADV
ejpam-5062	315	48	semi	semi	ADJ
ejpam-5062	315	49	pre	pre	ADJ
ejpam-5062	315	50	-	-	ADJ
ejpam-5062	315	51	open	open	ADJ
ejpam-5062	315	52	sets	set	NOUN
ejpam-5062	315	53	in	in	ADP
ejpam-5062	315	54	x	x	PUNCT
ejpam-5062	315	55	and	and	CCONJ
ejpam-5062	315	56	the	the	DET
ejpam-5062	315	57	following	following	ADJ
ejpam-5062	315	58	stands	stand	NOUN
ejpam-5062	315	59	:	:	PUNCT
ejpam-5062	315	60	f1	f1	PROPN
ejpam-5062	315	61	≤	≤	PROPN
ejpam-5062	315	62	f−1(w1	f−1(w1	PROPN
ejpam-5062	315	63	)	)	PUNCT
ejpam-5062	315	64	,	,	PUNCT
ejpam-5062	315	65	f2	f2	PROPN
ejpam-5062	315	66	≤	≤	NUM
ejpam-5062	315	67	f−1(w2	f−1(w2	NOUN
ejpam-5062	315	68	)	)	PUNCT
ejpam-5062	315	69	and	and	CCONJ
ejpam-5062	315	70	f−1(w1	f−1(w1	PROPN
ejpam-5062	315	71	)	)	PUNCT
ejpam-5062	315	72	≤	≤	NOUN
ejpam-5062	315	73	(	(	PUNCT
ejpam-5062	315	74	f−1(w2	f−1(w2	NOUN
ejpam-5062	315	75	)	)	PUNCT
ejpam-5062	315	76	)	)	PUNCT
ejpam-5062	316	1	c	c	X
ejpam-5062	316	2	therefore	therefore	ADV
ejpam-5062	316	3	the	the	DET
ejpam-5062	316	4	fuzzy	fuzzy	ADJ
ejpam-5062	316	5	topological	topological	ADJ
ejpam-5062	316	6	space	space	NOUN
ejpam-5062	316	7	x	x	PUNCT
ejpam-5062	316	8	is	be	AUX
ejpam-5062	316	9	an	an	DET
ejpam-5062	316	10	fsspn	fsspn	ADJ
ejpam-5062	316	11	space	space	NOUN
ejpam-5062	316	12	.	.	PUNCT
ejpam-5062	317	1	similarly	similarly	ADV
ejpam-5062	317	2	,	,	PUNCT
ejpam-5062	317	3	we	we	PRON
ejpam-5062	317	4	can	can	AUX
ejpam-5062	317	5	prove	prove	VERB
ejpam-5062	317	6	the	the	DET
ejpam-5062	317	7	other	other	ADJ
ejpam-5062	317	8	cases	case	NOUN
ejpam-5062	317	9	when	when	SCONJ
ejpam-5062	317	10	y	y	PROPN
ejpam-5062	317	11	is	be	AUX
ejpam-5062	317	12	an	an	DET
ejpam-5062	317	13	fsspwn	fsspwn	NOUN
ejpam-5062	317	14	,	,	PUNCT
ejpam-5062	317	15	fsspt3	fsspt3	NOUN
ejpam-5062	317	16	and	and	CCONJ
ejpam-5062	317	17	fsspr	fsspr	ADJ
ejpam-5062	317	18	space	space	NOUN
ejpam-5062	317	19	.	.	PUNCT
ejpam-5062	318	1	sh	sh	PROPN
ejpam-5062	318	2	.	.	PROPN
ejpam-5062	318	3	makolli	makolli	PROPN
ejpam-5062	318	4	,	,	PUNCT
ejpam-5062	318	5	b.	b.	PROPN
ejpam-5062	318	6	krsteska	krsteska	PROPN
ejpam-5062	318	7	/	/	SYM
ejpam-5062	318	8	eur	eur	PROPN
ejpam-5062	318	9	.	.	PUNCT
ejpam-5062	319	1	j.	j.	PROPN
ejpam-5062	319	2	pure	pure	PROPN
ejpam-5062	319	3	appl	appl	PROPN
ejpam-5062	319	4	.	.	PROPN
ejpam-5062	319	5	math	math	PROPN
ejpam-5062	319	6	,	,	PUNCT
ejpam-5062	319	7	17	17	NUM
ejpam-5062	319	8	(	(	PUNCT
ejpam-5062	319	9	2	2	NUM
ejpam-5062	319	10	)	)	PUNCT
ejpam-5062	319	11	(	(	PUNCT
ejpam-5062	319	12	2024	2024	NUM
ejpam-5062	319	13	)	)	PUNCT
ejpam-5062	319	14	,	,	PUNCT
ejpam-5062	319	15	638	638	NUM
ejpam-5062	319	16	-	-	SYM
ejpam-5062	319	17	662	662	NUM
ejpam-5062	319	18	651	651	NUM
ejpam-5062	319	19	theorem	theorem	NOUN
ejpam-5062	319	20	19	19	NUM
ejpam-5062	319	21	.	.	PUNCT
ejpam-5062	320	1	let	let	VERB
ejpam-5062	320	2	f	f	NOUN
ejpam-5062	320	3	:	:	PUNCT
ejpam-5062	320	4	x	x	X
ejpam-5062	320	5	→	→	SYM
ejpam-5062	320	6	y	y	X
ejpam-5062	320	7	be	be	AUX
ejpam-5062	320	8	a	a	DET
ejpam-5062	320	9	fuzzy	fuzzy	ADJ
ejpam-5062	320	10	sspo	sspo	NOUN
ejpam-5062	320	11	-	-	PUNCT
ejpam-5062	320	12	irresolute	irresolute	ADJ
ejpam-5062	320	13	open	open	ADJ
ejpam-5062	320	14	and	and	CCONJ
ejpam-5062	320	15	fuzzy	fuzzy	ADJ
ejpam-5062	320	16	strong	strong	ADJ
ejpam-5062	320	17	semi	semi	ADJ
ejpam-5062	320	18	pre	pre	ADJ
ejpam-5062	320	19	-	-	ADJ
ejpam-5062	320	20	continuous	continuous	ADJ
ejpam-5062	320	21	bijective	bijective	ADJ
ejpam-5062	320	22	mapping	mapping	NOUN
ejpam-5062	320	23	from	from	ADP
ejpam-5062	320	24	the	the	DET
ejpam-5062	320	25	fuzzy	fuzzy	ADJ
ejpam-5062	320	26	topological	topological	ADJ
ejpam-5062	320	27	space	space	NOUN
ejpam-5062	320	28	x	x	PUNCT
ejpam-5062	320	29	to	to	ADP
ejpam-5062	320	30	a	a	DET
ejpam-5062	320	31	fuzzy	fuzzy	ADJ
ejpam-5062	320	32	topological	topological	ADJ
ejpam-5062	320	33	space	space	NOUN
ejpam-5062	320	34	y	y	PROPN
ejpam-5062	320	35	.	.	PUNCT
ejpam-5062	321	1	if	if	SCONJ
ejpam-5062	321	2	the	the	DET
ejpam-5062	321	3	fuzzy	fuzzy	ADJ
ejpam-5062	321	4	topological	topological	ADJ
ejpam-5062	321	5	space	space	NOUN
ejpam-5062	321	6	x	x	PUNCT
ejpam-5062	321	7	is	be	AUX
ejpam-5062	321	8	an	an	DET
ejpam-5062	321	9	fsspn	fsspn	ADJ
ejpam-5062	321	10	(	(	PUNCT
ejpam-5062	321	11	fsspwn	fsspwn	NOUN
ejpam-5062	321	12	,	,	PUNCT
ejpam-5062	321	13	fsspt3	fsspt3	NOUN
ejpam-5062	321	14	,	,	PUNCT
ejpam-5062	321	15	fsspr	fsspr	NOUN
ejpam-5062	321	16	)	)	PUNCT
ejpam-5062	321	17	space	space	NOUN
ejpam-5062	321	18	then	then	ADV
ejpam-5062	321	19	y	y	PROPN
ejpam-5062	321	20	is	be	AUX
ejpam-5062	321	21	also	also	ADV
ejpam-5062	321	22	an	an	DET
ejpam-5062	321	23	fsspn	fsspn	ADJ
ejpam-5062	321	24	(	(	PUNCT
ejpam-5062	321	25	fsspwn	fsspwn	NOUN
ejpam-5062	321	26	,	,	PUNCT
ejpam-5062	321	27	fsspt3	fsspt3	NOUN
ejpam-5062	321	28	,	,	PUNCT
ejpam-5062	321	29	fsspr	fsspr	NOUN
ejpam-5062	321	30	)	)	PUNCT
ejpam-5062	321	31	space	space	NOUN
ejpam-5062	321	32	.	.	PUNCT
ejpam-5062	322	1	proof	proof	NOUN
ejpam-5062	322	2	.	.	PUNCT
ejpam-5062	323	1	let	let	VERB
ejpam-5062	323	2	v1	v1	NOUN
ejpam-5062	323	3	,	,	PUNCT
ejpam-5062	323	4	v2	v2	PROPN
ejpam-5062	323	5	be	be	AUX
ejpam-5062	323	6	two	two	NUM
ejpam-5062	323	7	fuzzy	fuzzy	ADJ
ejpam-5062	323	8	strongly	strongly	ADV
ejpam-5062	323	9	semi	semi	ADV
ejpam-5062	323	10	pre	pre	ADJ
ejpam-5062	323	11	-	-	ADJ
ejpam-5062	323	12	closed	closed	ADJ
ejpam-5062	323	13	sets	set	NOUN
ejpam-5062	323	14	in	in	ADP
ejpam-5062	323	15	y	y	PRON
ejpam-5062	323	16	such	such	ADJ
ejpam-5062	323	17	that	that	DET
ejpam-5062	323	18	v1	v1	PROPN
ejpam-5062	323	19	≤	≤	NUM
ejpam-5062	323	20	v	v	NOUN
ejpam-5062	323	21	c	c	NOUN
ejpam-5062	323	22	2	2	NUM
ejpam-5062	323	23	.	.	PUNCT
ejpam-5062	324	1	from	from	ADP
ejpam-5062	324	2	the	the	DET
ejpam-5062	324	3	assumptions	assumption	NOUN
ejpam-5062	324	4	of	of	ADP
ejpam-5062	324	5	the	the	DET
ejpam-5062	324	6	theorem	theorem	NOUN
ejpam-5062	324	7	,	,	PUNCT
ejpam-5062	324	8	since	since	SCONJ
ejpam-5062	324	9	f	f	PROPN
ejpam-5062	324	10	is	be	AUX
ejpam-5062	324	11	a	a	DET
ejpam-5062	324	12	fuzzy	fuzzy	ADJ
ejpam-5062	324	13	strong	strong	ADJ
ejpam-5062	324	14	semi	semi	ADJ
ejpam-5062	324	15	pre	pre	ADJ
ejpam-5062	324	16	-	-	ADJ
ejpam-5062	324	17	continuous	continuous	ADJ
ejpam-5062	324	18	mapping	mapping	NOUN
ejpam-5062	324	19	,	,	PUNCT
ejpam-5062	324	20	it	it	PRON
ejpam-5062	324	21	follows	follow	VERB
ejpam-5062	324	22	that	that	SCONJ
ejpam-5062	324	23	f−1(v1	f−1(v1	NOUN
ejpam-5062	324	24	)	)	PUNCT
ejpam-5062	324	25	,	,	PUNCT
ejpam-5062	324	26	f	f	PROPN
ejpam-5062	324	27	−1(v2	−1(v2	NOUN
ejpam-5062	324	28	)	)	PUNCT
ejpam-5062	324	29	are	be	AUX
ejpam-5062	324	30	two	two	NUM
ejpam-5062	324	31	fuzzy	fuzzy	ADJ
ejpam-5062	324	32	strongly	strongly	ADV
ejpam-5062	324	33	semi	semi	ADV
ejpam-5062	324	34	pre	pre	ADJ
ejpam-5062	324	35	-	-	ADJ
ejpam-5062	324	36	closed	closed	ADJ
ejpam-5062	324	37	sets	set	NOUN
ejpam-5062	324	38	in	in	ADP
ejpam-5062	324	39	x	x	SYM
ejpam-5062	324	40	such	such	ADJ
ejpam-5062	324	41	that	that	DET
ejpam-5062	324	42	f−1(v1	f−1(v1	NOUN
ejpam-5062	324	43	)	)	PUNCT
ejpam-5062	324	44	≤	≤	NUM
ejpam-5062	324	45	f−1(v1	f−1(v1	NOUN
ejpam-5062	324	46	)	)	PUNCT
ejpam-5062	324	47	c.	c.	NOUN
ejpam-5062	324	48	now	now	ADV
ejpam-5062	324	49	,	,	PUNCT
ejpam-5062	324	50	since	since	SCONJ
ejpam-5062	324	51	x	x	PRON
ejpam-5062	324	52	is	be	AUX
ejpam-5062	324	53	an	an	DET
ejpam-5062	324	54	fsspn	fsspn	ADJ
ejpam-5062	324	55	space	space	NOUN
ejpam-5062	324	56	,	,	PUNCT
ejpam-5062	324	57	there	there	PRON
ejpam-5062	324	58	are	be	VERB
ejpam-5062	324	59	fuzzy	fuzzy	ADJ
ejpam-5062	324	60	strongly	strongly	ADV
ejpam-5062	324	61	semi	semi	ADJ
ejpam-5062	324	62	pre	pre	ADJ
ejpam-5062	324	63	-	-	ADJ
ejpam-5062	324	64	open	open	ADJ
ejpam-5062	324	65	sets	set	NOUN
ejpam-5062	324	66	u1	u1	NOUN
ejpam-5062	324	67	,	,	PUNCT
ejpam-5062	324	68	u2	u2	NOUN
ejpam-5062	324	69	such	such	ADJ
ejpam-5062	324	70	that	that	SCONJ
ejpam-5062	324	71	:	:	PUNCT
ejpam-5062	324	72	f−1(v1	f−1(v1	X
ejpam-5062	324	73	)	)	PUNCT
ejpam-5062	324	74	≤	≤	NUM
ejpam-5062	324	75	u1	u1	NOUN
ejpam-5062	324	76	,	,	PUNCT
ejpam-5062	324	77	f	f	PROPN
ejpam-5062	324	78	−1(v2	−1(v2	NOUN
ejpam-5062	324	79	)	)	PUNCT
ejpam-5062	324	80	≤	≤	NOUN
ejpam-5062	324	81	u2	u2	NOUN
ejpam-5062	324	82	and	and	CCONJ
ejpam-5062	324	83	u1	u1	NOUN
ejpam-5062	324	84	≤	≤	NUM
ejpam-5062	324	85	u	u	NOUN
ejpam-5062	324	86	c	c	PROPN
ejpam-5062	324	87	2	2	NUM
ejpam-5062	324	88	.	.	PUNCT
ejpam-5062	325	1	from	from	ADP
ejpam-5062	325	2	the	the	DET
ejpam-5062	325	3	assumption	assumption	NOUN
ejpam-5062	325	4	that	that	SCONJ
ejpam-5062	325	5	f	f	PROPN
ejpam-5062	325	6	is	be	AUX
ejpam-5062	325	7	a	a	DET
ejpam-5062	325	8	fuzzy	fuzzy	ADJ
ejpam-5062	325	9	sspo	sspo	NOUN
ejpam-5062	325	10	-	-	PUNCT
ejpam-5062	325	11	irresolute	irresolute	ADJ
ejpam-5062	325	12	open	open	ADJ
ejpam-5062	325	13	mapping	mapping	NOUN
ejpam-5062	325	14	,	,	PUNCT
ejpam-5062	325	15	it	it	PRON
ejpam-5062	325	16	follows	follow	VERB
ejpam-5062	325	17	that	that	PRON
ejpam-5062	325	18	f(u1	f(u1	NOUN
ejpam-5062	325	19	)	)	PUNCT
ejpam-5062	325	20	and	and	CCONJ
ejpam-5062	325	21	f(u2	f(u2	PROPN
ejpam-5062	325	22	)	)	PUNCT
ejpam-5062	325	23	are	be	AUX
ejpam-5062	325	24	fuzzy	fuzzy	ADJ
ejpam-5062	325	25	strongly	strongly	ADV
ejpam-5062	325	26	semi	semi	ADJ
ejpam-5062	325	27	pre	pre	ADJ
ejpam-5062	325	28	-	-	ADJ
ejpam-5062	325	29	open	open	ADJ
ejpam-5062	325	30	sets	set	NOUN
ejpam-5062	325	31	in	in	ADP
ejpam-5062	325	32	y	y	PROPN
ejpam-5062	325	33	and	and	CCONJ
ejpam-5062	325	34	the	the	DET
ejpam-5062	325	35	following	follow	VERB
ejpam-5062	325	36	conditions	condition	NOUN
ejpam-5062	325	37	are	be	AUX
ejpam-5062	325	38	fulfilled	fulfil	VERB
ejpam-5062	325	39	:	:	PUNCT
ejpam-5062	325	40	v1	v1	VERB
ejpam-5062	325	41	≤	≤	NUM
ejpam-5062	325	42	f(u1	f(u1	NOUN
ejpam-5062	325	43	)	)	PUNCT
ejpam-5062	325	44	,	,	PUNCT
ejpam-5062	325	45	v2	v2	PROPN
ejpam-5062	325	46	≤	≤	PROPN
ejpam-5062	325	47	f(u2	f(u2	PROPN
ejpam-5062	325	48	)	)	PUNCT
ejpam-5062	325	49	and	and	CCONJ
ejpam-5062	325	50	f(u1	f(u1	X
ejpam-5062	325	51	)	)	PUNCT
ejpam-5062	325	52	≤	≤	PROPN
ejpam-5062	325	53	f(u2	f(u2	PROPN
ejpam-5062	325	54	)	)	PUNCT
ejpam-5062	325	55	c.	c.	PROPN
ejpam-5062	325	56	hence	hence	ADV
ejpam-5062	325	57	the	the	DET
ejpam-5062	325	58	fuzzy	fuzzy	ADJ
ejpam-5062	325	59	topological	topological	ADJ
ejpam-5062	325	60	space	space	NOUN
ejpam-5062	325	61	y	y	PROPN
ejpam-5062	325	62	is	be	AUX
ejpam-5062	325	63	an	an	DET
ejpam-5062	325	64	fsspn	fsspn	ADJ
ejpam-5062	325	65	space	space	NOUN
ejpam-5062	325	66	.	.	PUNCT
ejpam-5062	326	1	in	in	ADP
ejpam-5062	326	2	similar	similar	ADJ
ejpam-5062	326	3	way	way	NOUN
ejpam-5062	326	4	we	we	PRON
ejpam-5062	326	5	can	can	AUX
ejpam-5062	326	6	prove	prove	VERB
ejpam-5062	326	7	the	the	DET
ejpam-5062	326	8	other	other	ADJ
ejpam-5062	326	9	cases	case	NOUN
ejpam-5062	326	10	when	when	SCONJ
ejpam-5062	326	11	the	the	DET
ejpam-5062	326	12	fuzzy	fuzzy	ADJ
ejpam-5062	326	13	topological	topological	ADJ
ejpam-5062	326	14	space	space	NOUN
ejpam-5062	326	15	x	x	PUNCT
ejpam-5062	326	16	is	be	AUX
ejpam-5062	326	17	an	an	DET
ejpam-5062	326	18	fsspwn	fsspwn	NOUN
ejpam-5062	326	19	,	,	PUNCT
ejpam-5062	326	20	fsspt3	fsspt3	NOUN
ejpam-5062	326	21	,	,	PUNCT
ejpam-5062	326	22	and	and	CCONJ
ejpam-5062	326	23	fsspr	fsspr	ADJ
ejpam-5062	326	24	space	space	NOUN
ejpam-5062	326	25	.	.	PUNCT
ejpam-5062	327	1	5	5	X
ejpam-5062	327	2	.	.	X
ejpam-5062	327	3	a	a	DET
ejpam-5062	327	4	novel	novel	ADJ
ejpam-5062	327	5	form	form	NOUN
ejpam-5062	327	6	of	of	ADP
ejpam-5062	327	7	fuzzy	fuzzy	ADJ
ejpam-5062	327	8	compactness	compactness	NOUN
ejpam-5062	327	9	in	in	ADP
ejpam-5062	327	10	this	this	DET
ejpam-5062	327	11	section	section	NOUN
ejpam-5062	327	12	,	,	PUNCT
ejpam-5062	327	13	we	we	PRON
ejpam-5062	327	14	will	will	AUX
ejpam-5062	327	15	introduce	introduce	VERB
ejpam-5062	327	16	a	a	DET
ejpam-5062	327	17	novel	novel	ADJ
ejpam-5062	327	18	form	form	NOUN
ejpam-5062	327	19	of	of	ADP
ejpam-5062	327	20	compactness	compactness	NOUN
ejpam-5062	327	21	in	in	ADP
ejpam-5062	327	22	fuzzy	fuzzy	ADJ
ejpam-5062	327	23	topological	topological	ADJ
ejpam-5062	327	24	spaces	space	NOUN
ejpam-5062	327	25	.	.	PUNCT
ejpam-5062	328	1	the	the	DET
ejpam-5062	328	2	properties	property	NOUN
ejpam-5062	328	3	of	of	ADP
ejpam-5062	328	4	this	this	DET
ejpam-5062	328	5	new	new	ADJ
ejpam-5062	328	6	form	form	NOUN
ejpam-5062	328	7	of	of	ADP
ejpam-5062	328	8	fuzzy	fuzzy	ADJ
ejpam-5062	328	9	compactness	compactness	NOUN
ejpam-5062	328	10	,	,	PUNCT
ejpam-5062	328	11	similarities	similarity	NOUN
ejpam-5062	328	12	,	,	PUNCT
ejpam-5062	328	13	and	and	CCONJ
ejpam-5062	328	14	differences	difference	NOUN
ejpam-5062	328	15	with	with	ADP
ejpam-5062	328	16	other	other	ADJ
ejpam-5062	328	17	forms	form	NOUN
ejpam-5062	328	18	of	of	ADP
ejpam-5062	328	19	fuzzy	fuzzy	ADJ
ejpam-5062	328	20	compactness	compactness	NOUN
ejpam-5062	328	21	will	will	AUX
ejpam-5062	328	22	also	also	ADV
ejpam-5062	328	23	be	be	AUX
ejpam-5062	328	24	investigated	investigate	VERB
ejpam-5062	328	25	.	.	PUNCT
ejpam-5062	329	1	we	we	PRON
ejpam-5062	329	2	will	will	AUX
ejpam-5062	329	3	initially	initially	ADV
ejpam-5062	329	4	give	give	VERB
ejpam-5062	329	5	the	the	DET
ejpam-5062	329	6	following	follow	VERB
ejpam-5062	329	7	definition	definition	NOUN
ejpam-5062	329	8	.	.	PUNCT
ejpam-5062	330	1	definition	definition	NOUN
ejpam-5062	330	2	21	21	NUM
ejpam-5062	330	3	.	.	PUNCT
ejpam-5062	331	1	let	let	VERB
ejpam-5062	331	2	(	(	PUNCT
ejpam-5062	331	3	x	x	NOUN
ejpam-5062	331	4	,	,	PUNCT
ejpam-5062	331	5	τ	τ	X
ejpam-5062	331	6	)	)	PUNCT
ejpam-5062	331	7	be	be	VERB
ejpam-5062	331	8	a	a	DET
ejpam-5062	331	9	fuzzy	fuzzy	ADJ
ejpam-5062	331	10	topological	topological	ADJ
ejpam-5062	331	11	space	space	NOUN
ejpam-5062	331	12	and	and	CCONJ
ejpam-5062	331	13	let	let	VERB
ejpam-5062	331	14	α	α	PRON
ejpam-5062	331	15	∈	∈	PROPN
ejpam-5062	332	1	[	[	X
ejpam-5062	332	2	0	0	NUM
ejpam-5062	332	3	,	,	PUNCT
ejpam-5062	332	4	1	1	NUM
ejpam-5062	332	5	]	]	PUNCT
ejpam-5062	332	6	.	.	PUNCT
ejpam-5062	333	1	a	a	DET
ejpam-5062	333	2	collection	collection	NOUN
ejpam-5062	333	3	s	s	X
ejpam-5062	333	4	of	of	ADP
ejpam-5062	333	5	fuzzy	fuzzy	ADJ
ejpam-5062	333	6	strongly	strongly	ADV
ejpam-5062	333	7	semi	semi	ADV
ejpam-5062	333	8	pre	pre	ADJ
ejpam-5062	333	9	-	-	ADJ
ejpam-5062	333	10	open	open	ADJ
ejpam-5062	333	11	sets	set	NOUN
ejpam-5062	333	12	of	of	ADP
ejpam-5062	333	13	(	(	PUNCT
ejpam-5062	333	14	x	x	NOUN
ejpam-5062	333	15	,	,	PUNCT
ejpam-5062	333	16	τ	τ	X
ejpam-5062	333	17	)	)	PUNCT
ejpam-5062	333	18	is	be	AUX
ejpam-5062	333	19	called	call	VERB
ejpam-5062	333	20	an	an	DET
ejpam-5062	333	21	α−	α−	ADP
ejpam-5062	333	22	sspo	sspo	NOUN
ejpam-5062	333	23	shading	shade	VERB
ejpam-5062	333	24	(	(	PUNCT
ejpam-5062	333	25	respectively	respectively	ADV
ejpam-5062	333	26	α∗−sspo	α∗−sspo	PROPN
ejpam-5062	333	27	shading	shading	NOUN
ejpam-5062	333	28	)	)	PUNCT
ejpam-5062	333	29	of	of	ADP
ejpam-5062	333	30	the	the	DET
ejpam-5062	333	31	fuzzy	fuzzy	ADJ
ejpam-5062	333	32	set	set	VERB
ejpam-5062	333	33	a	a	DET
ejpam-5062	333	34	if	if	NOUN
ejpam-5062	333	35	,	,	PUNCT
ejpam-5062	333	36	for	for	ADP
ejpam-5062	333	37	every	every	DET
ejpam-5062	333	38	a	a	DET
ejpam-5062	333	39	∈	∈	PROPN
ejpam-5062	333	40	suppa	suppa	NOUN
ejpam-5062	333	41	,	,	PUNCT
ejpam-5062	333	42	there	there	PRON
ejpam-5062	333	43	exist	exist	VERB
ejpam-5062	333	44	a	a	DET
ejpam-5062	333	45	set	set	NOUN
ejpam-5062	333	46	w	w	PROPN
ejpam-5062	333	47	∈	∈	NOUN
ejpam-5062	333	48	s	s	VERB
ejpam-5062	333	49	such	such	ADJ
ejpam-5062	333	50	that	that	PRON
ejpam-5062	333	51	w	w	NOUN
ejpam-5062	333	52	(	(	PUNCT
ejpam-5062	333	53	a	a	NOUN
ejpam-5062	333	54	)	)	PUNCT
ejpam-5062	333	55	>	>	X
ejpam-5062	334	1	α	α	PROPN
ejpam-5062	334	2	(	(	PUNCT
ejpam-5062	334	3	respectively	respectively	ADV
ejpam-5062	334	4	w	w	PROPN
ejpam-5062	334	5	(	(	PUNCT
ejpam-5062	334	6	a	a	PRON
ejpam-5062	334	7	)	)	PUNCT
ejpam-5062	334	8	≥	≥	NOUN
ejpam-5062	334	9	α	α	NOUN
ejpam-5062	334	10	)	)	PUNCT
ejpam-5062	334	11	.	.	PUNCT
ejpam-5062	335	1	a	a	DET
ejpam-5062	335	2	subcollection	subcollection	NOUN
ejpam-5062	335	3	c	c	NOUN
ejpam-5062	335	4	of	of	ADP
ejpam-5062	335	5	sets	set	NOUN
ejpam-5062	335	6	from	from	ADP
ejpam-5062	335	7	α−sspo	α−sspo	NOUN
ejpam-5062	335	8	shading	shade	VERB
ejpam-5062	335	9	(	(	PUNCT
ejpam-5062	335	10	respectively	respectively	ADV
ejpam-5062	335	11	α∗−sspo	α∗−sspo	PROPN
ejpam-5062	335	12	shading	shading	NOUN
ejpam-5062	335	13	)	)	PUNCT
ejpam-5062	335	14	s	s	VERB
ejpam-5062	335	15	which	which	PRON
ejpam-5062	335	16	is	be	AUX
ejpam-5062	335	17	also	also	ADV
ejpam-5062	335	18	an	an	DET
ejpam-5062	335	19	α−sspo	α−sspo	NOUN
ejpam-5062	335	20	shading	shade	VERB
ejpam-5062	335	21	(	(	PUNCT
ejpam-5062	335	22	respectively	respectively	ADV
ejpam-5062	335	23	α∗−	α∗−	PROPN
ejpam-5062	335	24	sspo	sspo	NOUN
ejpam-5062	335	25	shading	shading	NOUN
ejpam-5062	335	26	)	)	PUNCT
ejpam-5062	335	27	for	for	ADP
ejpam-5062	335	28	the	the	DET
ejpam-5062	335	29	given	give	VERB
ejpam-5062	335	30	fuzzy	fuzzy	ADJ
ejpam-5062	335	31	set	set	VERB
ejpam-5062	335	32	a	a	PRON
ejpam-5062	335	33	,	,	PUNCT
ejpam-5062	335	34	is	be	AUX
ejpam-5062	335	35	called	call	VERB
ejpam-5062	335	36	an	an	DET
ejpam-5062	335	37	α−sspo	α−sspo	NOUN
ejpam-5062	335	38	subshading	subshade	VERB
ejpam-5062	335	39	(	(	PUNCT
ejpam-5062	335	40	respectively	respectively	ADV
ejpam-5062	335	41	α∗	α∗	VERB
ejpam-5062	335	42	−	−	PROPN
ejpam-5062	335	43	sspo	sspo	NOUN
ejpam-5062	335	44	subshading	subshade	VERB
ejpam-5062	335	45	)	)	PUNCT
ejpam-5062	335	46	of	of	ADP
ejpam-5062	335	47	the	the	DET
ejpam-5062	335	48	collection	collection	NOUN
ejpam-5062	335	49	s.	s.	PROPN
ejpam-5062	335	50	with	with	ADP
ejpam-5062	335	51	the	the	DET
ejpam-5062	335	52	concept	concept	NOUN
ejpam-5062	335	53	of	of	ADP
ejpam-5062	335	54	α−sspo	α−sspo	NOUN
ejpam-5062	335	55	shading	shade	VERB
ejpam-5062	335	56	(	(	PUNCT
ejpam-5062	335	57	α∗−sspo	α∗−sspo	PROPN
ejpam-5062	335	58	shading	shade	VERB
ejpam-5062	335	59	)	)	PUNCT
ejpam-5062	335	60	,	,	PUNCT
ejpam-5062	335	61	which	which	PRON
ejpam-5062	335	62	are	be	AUX
ejpam-5062	335	63	analogous	analogous	ADJ
ejpam-5062	335	64	to	to	ADP
ejpam-5062	335	65	the	the	DET
ejpam-5062	335	66	concept	concept	NOUN
ejpam-5062	335	67	of	of	ADP
ejpam-5062	335	68	open	open	ADJ
ejpam-5062	335	69	covers	cover	NOUN
ejpam-5062	335	70	in	in	ADP
ejpam-5062	335	71	the	the	DET
ejpam-5062	335	72	ordinary	ordinary	ADJ
ejpam-5062	335	73	topology	topology	NOUN
ejpam-5062	335	74	,	,	PUNCT
ejpam-5062	335	75	we	we	PRON
ejpam-5062	335	76	can	can	AUX
ejpam-5062	335	77	define	define	VERB
ejpam-5062	335	78	the	the	DET
ejpam-5062	335	79	concept	concept	NOUN
ejpam-5062	335	80	of	of	ADP
ejpam-5062	335	81	α−sspo	α−sspo	NOUN
ejpam-5062	335	82	compactness	compactness	NOUN
ejpam-5062	335	83	.	.	PUNCT
ejpam-5062	336	1	definition	definition	NOUN
ejpam-5062	336	2	22	22	NUM
ejpam-5062	336	3	.	.	PUNCT
ejpam-5062	337	1	the	the	DET
ejpam-5062	337	2	fuzzy	fuzzy	ADJ
ejpam-5062	337	3	set	set	VERB
ejpam-5062	337	4	a	a	PRON
ejpam-5062	337	5	of	of	ADP
ejpam-5062	337	6	the	the	DET
ejpam-5062	337	7	fuzzy	fuzzy	ADJ
ejpam-5062	337	8	topological	topological	ADJ
ejpam-5062	337	9	space	space	NOUN
ejpam-5062	337	10	(	(	PUNCT
ejpam-5062	337	11	x	x	X
ejpam-5062	337	12	,	,	PUNCT
ejpam-5062	337	13	τ	τ	X
ejpam-5062	337	14	)	)	PUNCT
ejpam-5062	337	15	is	be	AUX
ejpam-5062	337	16	called	call	VERB
ejpam-5062	337	17	α−	α−	ADP
ejpam-5062	337	18	sspo	sspo	NOUN
ejpam-5062	337	19	compact	compact	ADJ
ejpam-5062	337	20	(	(	PUNCT
ejpam-5062	337	21	α∗−sspo	α∗−sspo	PROPN
ejpam-5062	337	22	compact	compact	ADJ
ejpam-5062	337	23	)	)	PUNCT
ejpam-5062	337	24	if	if	SCONJ
ejpam-5062	337	25	every	every	PRON
ejpam-5062	337	26	α−sspo	α−sspo	NOUN
ejpam-5062	337	27	shading	shade	VERB
ejpam-5062	337	28	(	(	PUNCT
ejpam-5062	337	29	respectively	respectively	ADV
ejpam-5062	337	30	α∗−sspo	α∗−sspo	PROPN
ejpam-5062	337	31	shading	shading	NOUN
ejpam-5062	337	32	)	)	PUNCT
ejpam-5062	337	33	of	of	ADP
ejpam-5062	337	34	the	the	DET
ejpam-5062	337	35	set	set	NOUN
ejpam-5062	337	36	a	a	PRON
ejpam-5062	337	37	has	have	VERB
ejpam-5062	337	38	a	a	DET
ejpam-5062	337	39	finite	finite	NOUN
ejpam-5062	337	40	α−sspo	α−sspo	NOUN
ejpam-5062	337	41	subshading	subshade	VERB
ejpam-5062	337	42	(	(	PUNCT
ejpam-5062	337	43	respectively	respectively	ADV
ejpam-5062	337	44	α∗−sspo	α∗−sspo	PROPN
ejpam-5062	337	45	subshading	subshade	VERB
ejpam-5062	337	46	)	)	PUNCT
ejpam-5062	337	47	.	.	PUNCT
ejpam-5062	338	1	if	if	SCONJ
ejpam-5062	338	2	instead	instead	ADV
ejpam-5062	338	3	of	of	ADP
ejpam-5062	338	4	any	any	DET
ejpam-5062	338	5	set	set	NOUN
ejpam-5062	338	6	a	a	PRON
ejpam-5062	338	7	we	we	PRON
ejpam-5062	338	8	consider	consider	VERB
ejpam-5062	338	9	the	the	DET
ejpam-5062	338	10	set	set	NOUN
ejpam-5062	338	11	x	x	INTJ
ejpam-5062	338	12	in	in	ADP
ejpam-5062	338	13	general	general	ADJ
ejpam-5062	338	14	,	,	PUNCT
ejpam-5062	338	15	then	then	ADV
ejpam-5062	338	16	we	we	PRON
ejpam-5062	338	17	can	can	AUX
ejpam-5062	338	18	state	state	VERB
ejpam-5062	338	19	that	that	DET
ejpam-5062	338	20	space	space	NOUN
ejpam-5062	338	21	(	(	PUNCT
ejpam-5062	338	22	x	x	X
ejpam-5062	338	23	,	,	PUNCT
ejpam-5062	338	24	τ	τ	X
ejpam-5062	338	25	)	)	PUNCT
ejpam-5062	338	26	is	be	AUX
ejpam-5062	338	27	α−	α−	ADP
ejpam-5062	338	28	sspo	sspo	NOUN
ejpam-5062	338	29	compact	compact	ADJ
ejpam-5062	338	30	(	(	PUNCT
ejpam-5062	338	31	α∗	α∗	VERB
ejpam-5062	338	32	−	−	NOUN
ejpam-5062	338	33	sspocompact	sspocompact	NOUN
ejpam-5062	338	34	)	)	PUNCT
ejpam-5062	338	35	.	.	PUNCT
ejpam-5062	339	1	sh	sh	PROPN
ejpam-5062	339	2	.	.	PROPN
ejpam-5062	339	3	makolli	makolli	PROPN
ejpam-5062	339	4	,	,	PUNCT
ejpam-5062	339	5	b.	b.	PROPN
ejpam-5062	339	6	krsteska	krsteska	PROPN
ejpam-5062	339	7	/	/	SYM
ejpam-5062	339	8	eur	eur	PROPN
ejpam-5062	339	9	.	.	PUNCT
ejpam-5062	340	1	j.	j.	PROPN
ejpam-5062	340	2	pure	pure	PROPN
ejpam-5062	340	3	appl	appl	PROPN
ejpam-5062	340	4	.	.	PROPN
ejpam-5062	340	5	math	math	PROPN
ejpam-5062	340	6	,	,	PUNCT
ejpam-5062	340	7	17	17	NUM
ejpam-5062	340	8	(	(	PUNCT
ejpam-5062	340	9	2	2	NUM
ejpam-5062	340	10	)	)	PUNCT
ejpam-5062	340	11	(	(	PUNCT
ejpam-5062	340	12	2024	2024	NUM
ejpam-5062	340	13	)	)	PUNCT
ejpam-5062	340	14	,	,	PUNCT
ejpam-5062	340	15	638	638	NUM
ejpam-5062	340	16	-	-	SYM
ejpam-5062	340	17	662	662	NUM
ejpam-5062	340	18	652	652	NUM
ejpam-5062	340	19	definition	definition	NOUN
ejpam-5062	340	20	23	23	NUM
ejpam-5062	340	21	.	.	PUNCT
ejpam-5062	341	1	the	the	DET
ejpam-5062	341	2	fuzzy	fuzzy	ADJ
ejpam-5062	341	3	set	set	VERB
ejpam-5062	341	4	a	a	PRON
ejpam-5062	341	5	of	of	ADP
ejpam-5062	341	6	the	the	DET
ejpam-5062	341	7	fuzzy	fuzzy	ADJ
ejpam-5062	341	8	topological	topological	ADJ
ejpam-5062	341	9	space	space	NOUN
ejpam-5062	341	10	(	(	PUNCT
ejpam-5062	341	11	x	x	X
ejpam-5062	341	12	,	,	PUNCT
ejpam-5062	341	13	τ	τ	X
ejpam-5062	341	14	)	)	PUNCT
ejpam-5062	341	15	is	be	AUX
ejpam-5062	341	16	called	call	VERB
ejpam-5062	341	17	countable	countable	ADJ
ejpam-5062	341	18	α	α	NOUN
ejpam-5062	341	19	−	−	PROPN
ejpam-5062	341	20	sspo	sspo	NOUN
ejpam-5062	341	21	compact	compact	ADJ
ejpam-5062	341	22	(	(	PUNCT
ejpam-5062	341	23	respectively	respectively	ADV
ejpam-5062	341	24	countable	countable	ADJ
ejpam-5062	341	25	α∗	α∗	NOUN
ejpam-5062	341	26	−	−	NOUN
ejpam-5062	341	27	sspo	sspo	NOUN
ejpam-5062	341	28	compact	compact	ADJ
ejpam-5062	341	29	)	)	PUNCT
ejpam-5062	341	30	if	if	SCONJ
ejpam-5062	341	31	every	every	DET
ejpam-5062	341	32	countable	countable	ADJ
ejpam-5062	341	33	α	α	NOUN
ejpam-5062	341	34	−	−	NOUN
ejpam-5062	341	35	sspo	sspo	NOUN
ejpam-5062	341	36	shading	shade	VERB
ejpam-5062	341	37	(	(	PUNCT
ejpam-5062	341	38	respectively	respectively	ADV
ejpam-5062	341	39	α∗	α∗	VERB
ejpam-5062	341	40	−	−	PROPN
ejpam-5062	341	41	sspo	sspo	NOUN
ejpam-5062	341	42	shading	shading	NOUN
ejpam-5062	341	43	)	)	PUNCT
ejpam-5062	341	44	of	of	ADP
ejpam-5062	341	45	the	the	DET
ejpam-5062	341	46	set	set	NOUN
ejpam-5062	341	47	a	a	PRON
ejpam-5062	341	48	has	have	VERB
ejpam-5062	341	49	a	a	DET
ejpam-5062	341	50	finite	finite	NOUN
ejpam-5062	341	51	α	α	NOUN
ejpam-5062	341	52	−	−	PROPN
ejpam-5062	341	53	sspo	sspo	NOUN
ejpam-5062	341	54	subshading	subshade	VERB
ejpam-5062	341	55	(	(	PUNCT
ejpam-5062	341	56	respectively	respectively	ADV
ejpam-5062	341	57	α∗	α∗	VERB
ejpam-5062	341	58	−	−	PROPN
ejpam-5062	341	59	sspo	sspo	NOUN
ejpam-5062	341	60	subshading	subshade	VERB
ejpam-5062	341	61	)	)	PUNCT
ejpam-5062	341	62	.	.	PUNCT
ejpam-5062	342	1	if	if	SCONJ
ejpam-5062	342	2	instead	instead	ADV
ejpam-5062	342	3	of	of	ADP
ejpam-5062	342	4	the	the	DET
ejpam-5062	342	5	fuzzy	fuzzy	ADJ
ejpam-5062	342	6	set	set	VERB
ejpam-5062	342	7	a	a	PRON
ejpam-5062	342	8	we	we	PRON
ejpam-5062	342	9	consider	consider	VERB
ejpam-5062	342	10	the	the	DET
ejpam-5062	342	11	space	space	NOUN
ejpam-5062	342	12	x	x	PUNCT
ejpam-5062	342	13	then	then	ADV
ejpam-5062	342	14	we	we	PRON
ejpam-5062	342	15	can	can	AUX
ejpam-5062	342	16	state	state	VERB
ejpam-5062	342	17	that	that	SCONJ
ejpam-5062	342	18	the	the	DET
ejpam-5062	342	19	fuzzy	fuzzy	ADJ
ejpam-5062	342	20	topological	topological	ADJ
ejpam-5062	342	21	space	space	NOUN
ejpam-5062	342	22	x	x	PUNCT
ejpam-5062	342	23	is	be	AUX
ejpam-5062	342	24	a	a	DET
ejpam-5062	342	25	countable	countable	ADJ
ejpam-5062	342	26	α−	α−	ADP
ejpam-5062	342	27	sspo	sspo	NOUN
ejpam-5062	342	28	compact	compact	ADJ
ejpam-5062	342	29	(	(	PUNCT
ejpam-5062	342	30	respectively	respectively	ADV
ejpam-5062	342	31	countable	countable	ADJ
ejpam-5062	342	32	α∗	α∗	NOUN
ejpam-5062	342	33	−	−	NOUN
ejpam-5062	342	34	sspo	sspo	NOUN
ejpam-5062	342	35	compact	compact	ADJ
ejpam-5062	342	36	)	)	PUNCT
ejpam-5062	342	37	.	.	PUNCT
ejpam-5062	343	1	from	from	ADP
ejpam-5062	343	2	definition	definition	NOUN
ejpam-5062	343	3	23	23	NUM
ejpam-5062	343	4	it	it	PRON
ejpam-5062	343	5	is	be	AUX
ejpam-5062	343	6	obvious	obvious	ADJ
ejpam-5062	343	7	that	that	SCONJ
ejpam-5062	343	8	if	if	SCONJ
ejpam-5062	343	9	the	the	DET
ejpam-5062	343	10	fuzzy	fuzzy	ADJ
ejpam-5062	343	11	topological	topological	ADJ
ejpam-5062	343	12	space	space	NOUN
ejpam-5062	343	13	x	x	PUNCT
ejpam-5062	343	14	is	be	AUX
ejpam-5062	343	15	α	α	DET
ejpam-5062	343	16	−	−	PROPN
ejpam-5062	343	17	sspo	sspo	NOUN
ejpam-5062	343	18	compact	compact	ADJ
ejpam-5062	343	19	(	(	PUNCT
ejpam-5062	343	20	α∗	α∗	NOUN
ejpam-5062	343	21	−	−	NOUN
ejpam-5062	343	22	sspo	sspo	NOUN
ejpam-5062	343	23	compact	compact	ADJ
ejpam-5062	343	24	)	)	PUNCT
ejpam-5062	343	25	then	then	ADV
ejpam-5062	343	26	it	it	PRON
ejpam-5062	343	27	is	be	AUX
ejpam-5062	343	28	also	also	ADV
ejpam-5062	343	29	countable	countable	ADJ
ejpam-5062	343	30	α−	α−	ADP
ejpam-5062	343	31	sspo	sspo	NOUN
ejpam-5062	343	32	compact	compact	ADJ
ejpam-5062	343	33	(	(	PUNCT
ejpam-5062	343	34	countable	countable	ADJ
ejpam-5062	343	35	α∗	α∗	NOUN
ejpam-5062	343	36	−	−	NOUN
ejpam-5062	343	37	sspo	sspo	NOUN
ejpam-5062	343	38	compact	compact	ADJ
ejpam-5062	343	39	)	)	PUNCT
ejpam-5062	343	40	.	.	PUNCT
ejpam-5062	344	1	directly	directly	ADV
ejpam-5062	344	2	from	from	ADP
ejpam-5062	344	3	the	the	DET
ejpam-5062	344	4	definition	definition	NOUN
ejpam-5062	344	5	,	,	PUNCT
ejpam-5062	344	6	we	we	PRON
ejpam-5062	344	7	can	can	AUX
ejpam-5062	344	8	conclude	conclude	VERB
ejpam-5062	344	9	that	that	SCONJ
ejpam-5062	344	10	any	any	DET
ejpam-5062	344	11	fuzzy	fuzzy	ADJ
ejpam-5062	344	12	point	point	NOUN
ejpam-5062	344	13	is	be	AUX
ejpam-5062	344	14	α−	α−	ADP
ejpam-5062	344	15	sspo	sspo	X
ejpam-5062	344	16	compact	compact	ADJ
ejpam-5062	344	17	set	set	NOUN
ejpam-5062	344	18	and	and	CCONJ
ejpam-5062	344	19	α∗	α∗	NOUN
ejpam-5062	344	20	−	−	PROPN
ejpam-5062	344	21	sspo	sspo	NOUN
ejpam-5062	344	22	compact	compact	ADJ
ejpam-5062	344	23	set	set	NOUN
ejpam-5062	344	24	.	.	PUNCT
ejpam-5062	345	1	it	it	PRON
ejpam-5062	345	2	is	be	AUX
ejpam-5062	345	3	also	also	ADV
ejpam-5062	345	4	obvious	obvious	ADJ
ejpam-5062	345	5	that	that	SCONJ
ejpam-5062	345	6	any	any	DET
ejpam-5062	345	7	fuzzy	fuzzy	ADJ
ejpam-5062	345	8	set	set	NOUN
ejpam-5062	345	9	in	in	ADP
ejpam-5062	345	10	x	x	PROPN
ejpam-5062	345	11	is	be	AUX
ejpam-5062	345	12	1−	1−	NUM
ejpam-5062	345	13	sspo	sspo	NOUN
ejpam-5062	345	14	compact	compact	ADJ
ejpam-5062	345	15	and	and	CCONJ
ejpam-5062	345	16	0∗−sspo	0∗−sspo	NOUN
ejpam-5062	345	17	compact	compact	ADJ
ejpam-5062	345	18	.	.	PUNCT
ejpam-5062	346	1	also	also	ADV
ejpam-5062	346	2	from	from	ADP
ejpam-5062	346	3	the	the	DET
ejpam-5062	346	4	definition	definition	NOUN
ejpam-5062	346	5	22	22	NUM
ejpam-5062	346	6	it	it	PRON
ejpam-5062	346	7	follows	follow	VERB
ejpam-5062	346	8	that	that	SCONJ
ejpam-5062	346	9	any	any	DET
ejpam-5062	346	10	α−sspo	α−sspo	X
ejpam-5062	346	11	compact	compact	ADJ
ejpam-5062	346	12	(	(	PUNCT
ejpam-5062	346	13	α∗	α∗	NOUN
ejpam-5062	346	14	−	−	NOUN
ejpam-5062	346	15	sspo	sspo	NOUN
ejpam-5062	346	16	compact	compact	ADJ
ejpam-5062	346	17	)	)	PUNCT
ejpam-5062	346	18	space	space	NOUN
ejpam-5062	346	19	is	be	AUX
ejpam-5062	346	20	also	also	ADV
ejpam-5062	346	21	an	an	DET
ejpam-5062	346	22	αcompact	αcompact	NOUN
ejpam-5062	346	23	(	(	PUNCT
ejpam-5062	346	24	α∗-compact	α∗-compact	NUM
ejpam-5062	346	25	)	)	PUNCT
ejpam-5062	346	26	space	space	NOUN
ejpam-5062	346	27	.	.	PUNCT
ejpam-5062	347	1	the	the	DET
ejpam-5062	347	2	converse	converse	NOUN
ejpam-5062	347	3	is	be	AUX
ejpam-5062	347	4	not	not	PART
ejpam-5062	347	5	always	always	ADV
ejpam-5062	347	6	true	true	ADJ
ejpam-5062	347	7	as	as	SCONJ
ejpam-5062	347	8	it	it	PRON
ejpam-5062	347	9	can	can	AUX
ejpam-5062	347	10	be	be	AUX
ejpam-5062	347	11	presented	present	VERB
ejpam-5062	347	12	with	with	ADP
ejpam-5062	347	13	the	the	DET
ejpam-5062	347	14	following	follow	VERB
ejpam-5062	347	15	example	example	NOUN
ejpam-5062	347	16	.	.	PUNCT
ejpam-5062	348	1	example	example	NOUN
ejpam-5062	349	1	7	7	NUM
ejpam-5062	349	2	.	.	PUNCT
ejpam-5062	350	1	if	if	SCONJ
ejpam-5062	350	2	x	x	PRON
ejpam-5062	350	3	is	be	AUX
ejpam-5062	350	4	any	any	DET
ejpam-5062	350	5	infinite	infinite	ADJ
ejpam-5062	350	6	set	set	NOUN
ejpam-5062	350	7	and	and	CCONJ
ejpam-5062	350	8	if	if	SCONJ
ejpam-5062	350	9	α	α	PRON
ejpam-5062	350	10	∈	∈	PROPN
ejpam-5062	351	1	[	[	X
ejpam-5062	351	2	0	0	NUM
ejpam-5062	351	3	,	,	PUNCT
ejpam-5062	351	4	1	1	NUM
ejpam-5062	351	5	]	]	PUNCT
ejpam-5062	351	6	,	,	PUNCT
ejpam-5062	351	7	for	for	ADP
ejpam-5062	351	8	any	any	DET
ejpam-5062	351	9	p	p	NOUN
ejpam-5062	351	10	∈	∈	PROPN
ejpam-5062	351	11	x	x	X
ejpam-5062	351	12	we	we	PRON
ejpam-5062	351	13	will	will	AUX
ejpam-5062	351	14	define	define	VERB
ejpam-5062	351	15	the	the	DET
ejpam-5062	351	16	following	follow	VERB
ejpam-5062	351	17	sets	set	NOUN
ejpam-5062	351	18	:	:	PUNCT
ejpam-5062	351	19	uα	uα	PROPN
ejpam-5062	351	20	p	p	X
ejpam-5062	351	21	(	(	PUNCT
ejpam-5062	351	22	x	x	NOUN
ejpam-5062	351	23	)	)	PUNCT
ejpam-5062	351	24	=	=	SYM
ejpam-5062	351	25	{	{	PUNCT
ejpam-5062	351	26	1	1	NUM
ejpam-5062	351	27	if	if	SCONJ
ejpam-5062	351	28	x	x	PRON
ejpam-5062	351	29	=	=	PUNCT
ejpam-5062	351	30	p	p	X
ejpam-5062	351	31	α	α	NOUN
ejpam-5062	351	32	if	if	SCONJ
ejpam-5062	351	33	x	x	PROPN
ejpam-5062	351	34	̸=	̸=	PROPN
ejpam-5062	351	35	p	p	NOUN
ejpam-5062	351	36	let	let	VERB
ejpam-5062	351	37	as	as	SCONJ
ejpam-5062	351	38	denote	denote	VERB
ejpam-5062	351	39	with	with	ADP
ejpam-5062	351	40	tα	tα	PROPN
ejpam-5062	351	41	the	the	DET
ejpam-5062	351	42	fuzzy	fuzzy	ADJ
ejpam-5062	351	43	topology	topology	NOUN
ejpam-5062	351	44	on	on	ADP
ejpam-5062	351	45	x	x	PUNCT
ejpam-5062	351	46	which	which	PRON
ejpam-5062	351	47	is	be	AUX
ejpam-5062	351	48	generated	generate	VERB
ejpam-5062	351	49	by	by	ADP
ejpam-5062	351	50	{	{	PUNCT
ejpam-5062	351	51	uα	uα	PROPN
ejpam-5062	351	52	p	p	X
ejpam-5062	351	53	(	(	PUNCT
ejpam-5062	351	54	x	x	NOUN
ejpam-5062	351	55	)	)	PUNCT
ejpam-5062	351	56	:	:	PUNCT
ejpam-5062	352	1	p	p	X
ejpam-5062	352	2	∈	∈	PROPN
ejpam-5062	352	3	x	x	X
ejpam-5062	352	4	}	}	PUNCT
ejpam-5062	352	5	.	.	PUNCT
ejpam-5062	353	1	in	in	ADP
ejpam-5062	353	2	[	[	X
ejpam-5062	353	3	5	5	X
ejpam-5062	353	4	]	]	PUNCT
ejpam-5062	353	5	it	it	PRON
ejpam-5062	353	6	was	be	AUX
ejpam-5062	353	7	shown	show	VERB
ejpam-5062	353	8	that	that	SCONJ
ejpam-5062	353	9	(	(	PUNCT
ejpam-5062	353	10	x	x	NOUN
ejpam-5062	353	11	,	,	PUNCT
ejpam-5062	353	12	tα	tα	PROPN
ejpam-5062	353	13	)	)	PUNCT
ejpam-5062	353	14	is	be	AUX
ejpam-5062	353	15	β	β	NOUN
ejpam-5062	353	16	-	-	ADJ
ejpam-5062	353	17	compact	compact	ADJ
ejpam-5062	353	18	for	for	ADP
ejpam-5062	353	19	β	β	X
ejpam-5062	353	20	=	=	SYM
ejpam-5062	353	21	1	1	NUM
ejpam-5062	353	22	or	or	CCONJ
ejpam-5062	353	23	0	0	NUM
ejpam-5062	353	24	≤	≤	NUM
ejpam-5062	353	25	β	β	X
ejpam-5062	353	26	<	<	X
ejpam-5062	353	27	α	α	PROPN
ejpam-5062	353	28	and	and	CCONJ
ejpam-5062	353	29	is	be	AUX
ejpam-5062	353	30	β∗-compact	β∗-compact	PROPN
ejpam-5062	353	31	for	for	ADP
ejpam-5062	353	32	0	0	NUM
ejpam-5062	353	33	≤	≤	NOUN
ejpam-5062	353	34	β	β	NOUN
ejpam-5062	353	35	≤	≤	NUM
ejpam-5062	353	36	α	α	X
ejpam-5062	353	37	.	.	PUNCT
ejpam-5062	354	1	it	it	PRON
ejpam-5062	354	2	is	be	AUX
ejpam-5062	354	3	obvious	obvious	ADJ
ejpam-5062	354	4	that	that	SCONJ
ejpam-5062	354	5	(	(	PUNCT
ejpam-5062	354	6	x	x	NOUN
ejpam-5062	354	7	,	,	PUNCT
ejpam-5062	354	8	tα	tα	PROPN
ejpam-5062	354	9	)	)	PUNCT
ejpam-5062	354	10	is	be	AUX
ejpam-5062	354	11	β	β	X
ejpam-5062	354	12	−	−	PROPN
ejpam-5062	354	13	sspo	sspo	NOUN
ejpam-5062	354	14	compact	compact	ADJ
ejpam-5062	354	15	only	only	ADV
ejpam-5062	354	16	for	for	ADP
ejpam-5062	354	17	β	β	X
ejpam-5062	354	18	=	=	SYM
ejpam-5062	354	19	1	1	NUM
ejpam-5062	354	20	or	or	CCONJ
ejpam-5062	354	21	0	0	NUM
ejpam-5062	354	22	≤	≤	NUM
ejpam-5062	354	23	β	β	X
ejpam-5062	354	24	<	<	X
ejpam-5062	354	25	α	α	PROPN
ejpam-5062	354	26	and	and	CCONJ
ejpam-5062	354	27	is	be	AUX
ejpam-5062	354	28	β∗−sspo	β∗−sspo	PUNCT
ejpam-5062	354	29	compact	compact	ADJ
ejpam-5062	354	30	for	for	ADP
ejpam-5062	354	31	0	0	NUM
ejpam-5062	354	32	≤	≤	NOUN
ejpam-5062	354	33	β	β	NOUN
ejpam-5062	354	34	≤	≤	NUM
ejpam-5062	355	1	α	α	X
ejpam-5062	355	2	.	.	PUNCT
ejpam-5062	356	1	moreover	moreover	ADV
ejpam-5062	356	2	,	,	PUNCT
ejpam-5062	356	3	if	if	SCONJ
ejpam-5062	356	4	γ	γ	X
ejpam-5062	356	5	<	<	X
ejpam-5062	356	6	α	α	PROPN
ejpam-5062	356	7	,	,	PUNCT
ejpam-5062	356	8	then	then	ADV
ejpam-5062	356	9	(	(	PUNCT
ejpam-5062	356	10	x	x	X
ejpam-5062	356	11	,	,	PUNCT
ejpam-5062	356	12	tγ	tγ	NOUN
ejpam-5062	356	13	)	)	PUNCT
ejpam-5062	356	14	is	be	AUX
ejpam-5062	356	15	α	α	PRON
ejpam-5062	356	16	-	-	ADJ
ejpam-5062	356	17	compact	compact	ADJ
ejpam-5062	356	18	and	and	CCONJ
ejpam-5062	356	19	α∗-compact	α∗-compact	NUM
ejpam-5062	356	20	,	,	PUNCT
ejpam-5062	356	21	see	see	VERB
ejpam-5062	356	22	[	[	X
ejpam-5062	356	23	5	5	NUM
ejpam-5062	356	24	]	]	PUNCT
ejpam-5062	356	25	,	,	PUNCT
ejpam-5062	356	26	but	but	CCONJ
ejpam-5062	356	27	it	it	PRON
ejpam-5062	356	28	is	be	AUX
ejpam-5062	356	29	neither	neither	CCONJ
ejpam-5062	356	30	α−	α−	ADP
ejpam-5062	356	31	sspo	sspo	NOUN
ejpam-5062	356	32	compact	compact	ADJ
ejpam-5062	356	33	nor	nor	CCONJ
ejpam-5062	356	34	α∗	α∗	NOUN
ejpam-5062	356	35	−	−	PROPN
ejpam-5062	356	36	sspo	sspo	NOUN
ejpam-5062	356	37	compact	compact	ADJ
ejpam-5062	356	38	.	.	PUNCT
ejpam-5062	357	1	theorem	theorem	VERB
ejpam-5062	357	2	20	20	NUM
ejpam-5062	357	3	.	.	PUNCT
ejpam-5062	358	1	the	the	DET
ejpam-5062	358	2	fuzzy	fuzzy	ADJ
ejpam-5062	358	3	topological	topological	ADJ
ejpam-5062	358	4	space	space	NOUN
ejpam-5062	358	5	(	(	PUNCT
ejpam-5062	358	6	x	x	X
ejpam-5062	358	7	,	,	PUNCT
ejpam-5062	358	8	τ	τ	X
ejpam-5062	358	9	)	)	PUNCT
ejpam-5062	358	10	is	be	AUX
ejpam-5062	358	11	α−sspo	α−sspo	X
ejpam-5062	358	12	compact	compact	ADJ
ejpam-5062	358	13	(	(	PUNCT
ejpam-5062	358	14	respectively	respectively	ADV
ejpam-5062	358	15	α∗−	α∗−	PROPN
ejpam-5062	358	16	sspo	sspo	NOUN
ejpam-5062	358	17	compact	compact	ADJ
ejpam-5062	358	18	)	)	PUNCT
ejpam-5062	359	1	if	if	SCONJ
ejpam-5062	359	2	and	and	CCONJ
ejpam-5062	359	3	only	only	ADV
ejpam-5062	359	4	if	if	SCONJ
ejpam-5062	359	5	for	for	ADP
ejpam-5062	359	6	every	every	DET
ejpam-5062	359	7	α	α	NOUN
ejpam-5062	359	8	-	-	PUNCT
ejpam-5062	359	9	centered	center	VERB
ejpam-5062	359	10	(	(	PUNCT
ejpam-5062	359	11	α∗-centered	α∗-centere	VERB
ejpam-5062	359	12	)	)	PUNCT
ejpam-5062	359	13	family	family	NOUN
ejpam-5062	359	14	f	f	PROPN
ejpam-5062	359	15	consisting	consist	VERB
ejpam-5062	359	16	of	of	ADP
ejpam-5062	359	17	fuzzy	fuzzy	ADJ
ejpam-5062	359	18	strongly	strongly	ADV
ejpam-5062	359	19	semi	semi	ADV
ejpam-5062	359	20	pre	pre	ADJ
ejpam-5062	359	21	-	-	ADJ
ejpam-5062	359	22	closed	closed	ADJ
ejpam-5062	359	23	sets	set	NOUN
ejpam-5062	359	24	in	in	ADP
ejpam-5062	359	25	(	(	PUNCT
ejpam-5062	359	26	x	x	NOUN
ejpam-5062	359	27	,	,	PUNCT
ejpam-5062	359	28	τ	τ	PROPN
ejpam-5062	359	29	)	)	PUNCT
ejpam-5062	359	30	,	,	PUNCT
ejpam-5062	359	31	there	there	PRON
ejpam-5062	359	32	exists	exist	VERB
ejpam-5062	359	33	x	x	X
ejpam-5062	359	34	∈	∈	PROPN
ejpam-5062	359	35	x	x	PUNCT
ejpam-5062	359	36	such	such	ADJ
ejpam-5062	359	37	that	that	SCONJ
ejpam-5062	359	38	f	f	PROPN
ejpam-5062	359	39	(	(	PUNCT
ejpam-5062	359	40	x	x	X
ejpam-5062	359	41	)	)	PUNCT
ejpam-5062	359	42	≥	≥	NOUN
ejpam-5062	359	43	1	1	NUM
ejpam-5062	359	44	−	−	NOUN
ejpam-5062	359	45	α	α	INTJ
ejpam-5062	359	46	(	(	PUNCT
ejpam-5062	359	47	f	f	PROPN
ejpam-5062	359	48	(	(	PUNCT
ejpam-5062	359	49	x	x	X
ejpam-5062	359	50	)	)	PUNCT
ejpam-5062	359	51	>	>	X
ejpam-5062	359	52	1−	1−	NUM
ejpam-5062	359	53	α	α	NOUN
ejpam-5062	359	54	)	)	PUNCT
ejpam-5062	359	55	,	,	PUNCT
ejpam-5062	359	56	for	for	ADP
ejpam-5062	359	57	every	every	DET
ejpam-5062	359	58	f	f	PROPN
ejpam-5062	359	59	∈	∈	PROPN
ejpam-5062	359	60	f	f	PROPN
ejpam-5062	359	61	.	.	PUNCT
ejpam-5062	360	1	proof	proof	NOUN
ejpam-5062	360	2	.	.	PUNCT
ejpam-5062	361	1	let	let	VERB
ejpam-5062	361	2	us	we	PRON
ejpam-5062	361	3	suppose	suppose	VERB
ejpam-5062	361	4	that	that	SCONJ
ejpam-5062	361	5	f	f	PROPN
ejpam-5062	361	6	is	be	AUX
ejpam-5062	361	7	an	an	DET
ejpam-5062	361	8	α	α	NOUN
ejpam-5062	361	9	-	-	PUNCT
ejpam-5062	361	10	centered	center	VERB
ejpam-5062	361	11	family	family	NOUN
ejpam-5062	361	12	consisting	consist	VERB
ejpam-5062	361	13	of	of	ADP
ejpam-5062	361	14	fuzzy	fuzzy	ADJ
ejpam-5062	361	15	strongly	strongly	ADV
ejpam-5062	361	16	semi	semi	ADV
ejpam-5062	361	17	pre	pre	ADJ
ejpam-5062	361	18	-	-	ADJ
ejpam-5062	361	19	closed	closed	ADJ
ejpam-5062	361	20	sets	set	NOUN
ejpam-5062	361	21	in	in	ADP
ejpam-5062	361	22	(	(	PUNCT
ejpam-5062	361	23	x	x	NOUN
ejpam-5062	361	24	,	,	PUNCT
ejpam-5062	361	25	τ	τ	X
ejpam-5062	361	26	)	)	PUNCT
ejpam-5062	361	27	such	such	ADJ
ejpam-5062	361	28	that	that	PRON
ejpam-5062	361	29	for	for	ADP
ejpam-5062	361	30	each	each	DET
ejpam-5062	361	31	x	x	SYM
ejpam-5062	361	32	∈	∈	PROPN
ejpam-5062	361	33	x	x	X
ejpam-5062	361	34	,	,	PUNCT
ejpam-5062	361	35	there	there	PRON
ejpam-5062	361	36	exists	exist	VERB
ejpam-5062	361	37	a	a	DET
ejpam-5062	361	38	set	set	NOUN
ejpam-5062	361	39	f	f	PROPN
ejpam-5062	361	40	∈	∈	PROPN
ejpam-5062	361	41	f	f	PROPN
ejpam-5062	361	42	such	such	ADJ
ejpam-5062	361	43	that	that	SCONJ
ejpam-5062	361	44	f	f	PROPN
ejpam-5062	361	45	(	(	PUNCT
ejpam-5062	361	46	x	x	X
ejpam-5062	361	47	)	)	PUNCT
ejpam-5062	361	48	<	<	X
ejpam-5062	361	49	1−α	1−α	NUM
ejpam-5062	361	50	.	.	PUNCT
ejpam-5062	362	1	then	then	ADV
ejpam-5062	362	2	the	the	DET
ejpam-5062	362	3	family	family	NOUN
ejpam-5062	362	4	of	of	ADP
ejpam-5062	362	5	sets	set	NOUN
ejpam-5062	362	6	w	w	NOUN
ejpam-5062	363	1	=	=	PUNCT
ejpam-5062	363	2	{	{	PUNCT
ejpam-5062	363	3	f	f	PROPN
ejpam-5062	363	4	c	c	PROPN
ejpam-5062	363	5	,	,	PUNCT
ejpam-5062	363	6	f	f	PROPN
ejpam-5062	363	7	∈	∈	PROPN
ejpam-5062	363	8	f	f	X
ejpam-5062	363	9	}	}	PUNCT
ejpam-5062	363	10	is	be	AUX
ejpam-5062	363	11	an	an	DET
ejpam-5062	363	12	α−sspo	α−sspo	NOUN
ejpam-5062	363	13	shading	shading	NOUN
ejpam-5062	363	14	of	of	ADP
ejpam-5062	363	15	(	(	PUNCT
ejpam-5062	363	16	x	x	X
ejpam-5062	363	17	,	,	PUNCT
ejpam-5062	363	18	τ	τ	X
ejpam-5062	363	19	)	)	PUNCT
ejpam-5062	363	20	and	and	CCONJ
ejpam-5062	363	21	it	it	PRON
ejpam-5062	363	22	is	be	AUX
ejpam-5062	363	23	evident	evident	ADJ
ejpam-5062	363	24	that	that	SCONJ
ejpam-5062	363	25	it	it	PRON
ejpam-5062	363	26	does	do	AUX
ejpam-5062	363	27	not	not	PART
ejpam-5062	363	28	have	have	VERB
ejpam-5062	363	29	a	a	DET
ejpam-5062	363	30	finite	finite	NOUN
ejpam-5062	363	31	α	α	NOUN
ejpam-5062	363	32	−	−	PROPN
ejpam-5062	363	33	sspo	sspo	NOUN
ejpam-5062	363	34	subshading	subshade	VERB
ejpam-5062	363	35	.	.	PUNCT
ejpam-5062	364	1	if	if	SCONJ
ejpam-5062	364	2	it	it	PRON
ejpam-5062	364	3	had	have	VERB
ejpam-5062	364	4	a	a	DET
ejpam-5062	364	5	finite	finite	NOUN
ejpam-5062	364	6	α	α	NOUN
ejpam-5062	364	7	−	−	PROPN
ejpam-5062	364	8	sspo	sspo	NOUN
ejpam-5062	364	9	subshading	subshade	VERB
ejpam-5062	364	10	f	f	PROPN
ejpam-5062	364	11	c	c	PROPN
ejpam-5062	364	12	1	1	NUM
ejpam-5062	364	13	,	,	PUNCT
ejpam-5062	364	14	f	f	PROPN
ejpam-5062	364	15	c	c	PROPN
ejpam-5062	364	16	2	2	NUM
ejpam-5062	364	17	,	,	PUNCT
ejpam-5062	364	18	.	.	PUNCT
ejpam-5062	364	19	.	.	PUNCT
ejpam-5062	365	1	.	.	PUNCT
ejpam-5062	366	1	,	,	PUNCT
ejpam-5062	366	2	f	f	PROPN
ejpam-5062	366	3	c	c	PROPN
ejpam-5062	366	4	k	k	X
ejpam-5062	366	5	,	,	PUNCT
ejpam-5062	366	6	then	then	ADV
ejpam-5062	366	7	due	due	ADP
ejpam-5062	366	8	to	to	ADP
ejpam-5062	366	9	the	the	DET
ejpam-5062	366	10	fact	fact	NOUN
ejpam-5062	366	11	that	that	SCONJ
ejpam-5062	366	12	f	f	PROPN
ejpam-5062	366	13	is	be	AUX
ejpam-5062	366	14	α	α	NOUN
ejpam-5062	366	15	-	-	PUNCT
ejpam-5062	366	16	centered	center	VERB
ejpam-5062	366	17	there	there	PRON
ejpam-5062	366	18	exists	exist	VERB
ejpam-5062	366	19	x	x	X
ejpam-5062	366	20	∈	∈	PROPN
ejpam-5062	366	21	x	x	NOUN
ejpam-5062	366	22	,	,	PUNCT
ejpam-5062	366	23	such	such	ADJ
ejpam-5062	366	24	that	that	SCONJ
ejpam-5062	366	25	fj(x	fj(x	NOUN
ejpam-5062	366	26	)	)	PUNCT
ejpam-5062	366	27	≥	≥	NOUN
ejpam-5062	366	28	1	1	NUM
ejpam-5062	366	29	−	−	NOUN
ejpam-5062	366	30	α	α	NOUN
ejpam-5062	366	31	for	for	ADP
ejpam-5062	366	32	all	all	DET
ejpam-5062	366	33	j	j	NOUN
ejpam-5062	366	34	=	=	SYM
ejpam-5062	366	35	1	1	NUM
ejpam-5062	366	36	,	,	PUNCT
ejpam-5062	366	37	2	2	NUM
ejpam-5062	366	38	,	,	PUNCT
ejpam-5062	366	39	.	.	PUNCT
ejpam-5062	366	40	.	.	PUNCT
ejpam-5062	367	1	.	.	PUNCT
ejpam-5062	368	1	,	,	PUNCT
ejpam-5062	368	2	k	k	PROPN
ejpam-5062	368	3	and	and	CCONJ
ejpam-5062	368	4	consequently	consequently	ADV
ejpam-5062	368	5	f	f	PROPN
ejpam-5062	369	1	c	c	PROPN
ejpam-5062	369	2	j	j	PROPN
ejpam-5062	369	3	(	(	PUNCT
ejpam-5062	369	4	x	x	NOUN
ejpam-5062	369	5	)	)	PUNCT
ejpam-5062	369	6	≤	≤	NOUN
ejpam-5062	369	7	α	α	NOUN
ejpam-5062	369	8	for	for	ADP
ejpam-5062	369	9	all	all	DET
ejpam-5062	369	10	j	j	NOUN
ejpam-5062	369	11	=	=	SYM
ejpam-5062	369	12	1	1	NUM
ejpam-5062	369	13	,	,	PUNCT
ejpam-5062	369	14	2	2	NUM
ejpam-5062	369	15	,	,	PUNCT
ejpam-5062	369	16	.	.	PUNCT
ejpam-5062	369	17	.	.	PUNCT
ejpam-5062	370	1	.	.	PUNCT
ejpam-5062	371	1	,	,	PUNCT
ejpam-5062	371	2	k.	k.	PROPN
ejpam-5062	371	3	conversely	conversely	ADV
ejpam-5062	371	4	,	,	PUNCT
ejpam-5062	371	5	let	let	VERB
ejpam-5062	371	6	us	we	PRON
ejpam-5062	371	7	suppose	suppose	VERB
ejpam-5062	371	8	that	that	SCONJ
ejpam-5062	371	9	family	family	NOUN
ejpam-5062	371	10	s	s	X
ejpam-5062	371	11	of	of	ADP
ejpam-5062	371	12	fuzzy	fuzzy	ADJ
ejpam-5062	371	13	strongly	strongly	ADV
ejpam-5062	371	14	semi	semi	ADV
ejpam-5062	371	15	pre	pre	ADJ
ejpam-5062	371	16	-	-	ADJ
ejpam-5062	371	17	open	open	ADJ
ejpam-5062	371	18	sets	set	NOUN
ejpam-5062	371	19	of	of	ADP
ejpam-5062	371	20	(	(	PUNCT
ejpam-5062	371	21	x	x	NOUN
ejpam-5062	371	22	,	,	PUNCT
ejpam-5062	371	23	τ	τ	X
ejpam-5062	371	24	)	)	PUNCT
ejpam-5062	371	25	is	be	AUX
ejpam-5062	371	26	an	an	DET
ejpam-5062	371	27	α	α	NOUN
ejpam-5062	371	28	-	-	PUNCT
ejpam-5062	371	29	sspo	sspo	NOUN
ejpam-5062	371	30	shading	shading	NOUN
ejpam-5062	371	31	of	of	ADP
ejpam-5062	371	32	x	x	PUNCT
ejpam-5062	371	33	and	and	CCONJ
ejpam-5062	371	34	that	that	SCONJ
ejpam-5062	371	35	it	it	PRON
ejpam-5062	371	36	has	have	VERB
ejpam-5062	371	37	no	no	DET
ejpam-5062	371	38	finite	finite	NOUN
ejpam-5062	371	39	α	α	NOUN
ejpam-5062	371	40	-	-	PUNCT
ejpam-5062	371	41	sspo	sspo	NOUN
ejpam-5062	371	42	subshading	subshading	NOUN
ejpam-5062	371	43	.	.	PUNCT
ejpam-5062	372	1	then	then	ADV
ejpam-5062	372	2	the	the	DET
ejpam-5062	372	3	collection	collection	NOUN
ejpam-5062	372	4	of	of	ADP
ejpam-5062	372	5	fuzzy	fuzzy	ADJ
ejpam-5062	372	6	strongly	strongly	ADV
ejpam-5062	372	7	semi	semi	ADV
ejpam-5062	372	8	pre	pre	ADJ
ejpam-5062	372	9	-	-	ADJ
ejpam-5062	372	10	closed	closed	ADJ
ejpam-5062	372	11	sets	set	NOUN
ejpam-5062	372	12	f	f	NOUN
ejpam-5062	372	13	=	=	SYM
ejpam-5062	372	14	{	{	PUNCT
ejpam-5062	372	15	sc	sc	PROPN
ejpam-5062	372	16	,	,	PUNCT
ejpam-5062	372	17	s	s	PART
ejpam-5062	372	18	∈	∈	PROPN
ejpam-5062	372	19	s	s	PART
ejpam-5062	372	20	}	}	PUNCT
ejpam-5062	372	21	is	be	AUX
ejpam-5062	372	22	α	α	NOUN
ejpam-5062	372	23	-	-	PUNCT
ejpam-5062	372	24	centered	center	VERB
ejpam-5062	372	25	because	because	SCONJ
ejpam-5062	372	26	for	for	ADP
ejpam-5062	372	27	sh	sh	PROPN
ejpam-5062	372	28	.	.	PROPN
ejpam-5062	372	29	makolli	makolli	PROPN
ejpam-5062	372	30	,	,	PUNCT
ejpam-5062	372	31	b.	b.	PROPN
ejpam-5062	372	32	krsteska	krsteska	PROPN
ejpam-5062	372	33	/	/	SYM
ejpam-5062	372	34	eur	eur	PROPN
ejpam-5062	372	35	.	.	PUNCT
ejpam-5062	373	1	j.	j.	PROPN
ejpam-5062	373	2	pure	pure	PROPN
ejpam-5062	373	3	appl	appl	PROPN
ejpam-5062	373	4	.	.	PROPN
ejpam-5062	373	5	math	math	PROPN
ejpam-5062	373	6	,	,	PUNCT
ejpam-5062	373	7	17	17	NUM
ejpam-5062	373	8	(	(	PUNCT
ejpam-5062	373	9	2	2	NUM
ejpam-5062	373	10	)	)	PUNCT
ejpam-5062	373	11	(	(	PUNCT
ejpam-5062	373	12	2024	2024	NUM
ejpam-5062	373	13	)	)	PUNCT
ejpam-5062	373	14	,	,	PUNCT
ejpam-5062	373	15	638	638	NUM
ejpam-5062	373	16	-	-	SYM
ejpam-5062	373	17	662	662	NUM
ejpam-5062	373	18	653	653	NUM
ejpam-5062	373	19	sc	sc	NOUN
ejpam-5062	373	20	1	1	NUM
ejpam-5062	373	21	,	,	PUNCT
ejpam-5062	373	22	s	s	NOUN
ejpam-5062	373	23	c	c	NOUN
ejpam-5062	373	24	2	2	NUM
ejpam-5062	373	25	,	,	PUNCT
ejpam-5062	373	26	.	.	PUNCT
ejpam-5062	373	27	.	.	PUNCT
ejpam-5062	374	1	.	.	PUNCT
ejpam-5062	375	1	,	,	PUNCT
ejpam-5062	375	2	s	s	AUX
ejpam-5062	375	3	c	c	NOUN
ejpam-5062	375	4	k	k	PROPN
ejpam-5062	375	5	∈	∈	PROPN
ejpam-5062	375	6	f	f	NOUN
ejpam-5062	375	7	there	there	PRON
ejpam-5062	375	8	must	must	AUX
ejpam-5062	375	9	exist	exist	VERB
ejpam-5062	375	10	x	x	X
ejpam-5062	375	11	∈	∈	PROPN
ejpam-5062	375	12	x	x	X
ejpam-5062	375	13	such	such	ADJ
ejpam-5062	375	14	that	that	PRON
ejpam-5062	375	15	sj(x	sj(x	PUNCT
ejpam-5062	375	16	)	)	PUNCT
ejpam-5062	375	17	≤	≤	NUM
ejpam-5062	375	18	α	α	NOUN
ejpam-5062	375	19	for	for	ADP
ejpam-5062	375	20	all	all	DET
ejpam-5062	375	21	j	j	NOUN
ejpam-5062	375	22	=	=	SYM
ejpam-5062	375	23	1	1	NUM
ejpam-5062	375	24	,	,	PUNCT
ejpam-5062	375	25	2	2	NUM
ejpam-5062	375	26	,	,	PUNCT
ejpam-5062	375	27	.	.	PUNCT
ejpam-5062	375	28	.	.	PUNCT
ejpam-5062	376	1	.	.	PUNCT
ejpam-5062	377	1	,	,	PUNCT
ejpam-5062	377	2	k	k	X
ejpam-5062	377	3	(	(	PUNCT
ejpam-5062	377	4	or	or	CCONJ
ejpam-5062	377	5	otherwise	otherwise	ADV
ejpam-5062	377	6	the	the	DET
ejpam-5062	377	7	family	family	NOUN
ejpam-5062	377	8	s	s	PART
ejpam-5062	377	9	has	have	VERB
ejpam-5062	377	10	a	a	DET
ejpam-5062	377	11	finite	finite	NOUN
ejpam-5062	377	12	α	α	NOUN
ejpam-5062	377	13	−	−	PROPN
ejpam-5062	377	14	sspo	sspo	NOUN
ejpam-5062	377	15	subshading	subshade	VERB
ejpam-5062	377	16	)	)	PUNCT
ejpam-5062	377	17	,	,	PUNCT
ejpam-5062	377	18	and	and	CCONJ
ejpam-5062	377	19	therefore	therefore	ADV
ejpam-5062	377	20	sc	sc	PROPN
ejpam-5062	377	21	j	j	PROPN
ejpam-5062	377	22	(	(	PUNCT
ejpam-5062	377	23	x	x	PROPN
ejpam-5062	377	24	)	)	PUNCT
ejpam-5062	377	25	≥	≥	NOUN
ejpam-5062	377	26	1	1	NUM
ejpam-5062	377	27	−	−	NOUN
ejpam-5062	377	28	α	α	NOUN
ejpam-5062	377	29	for	for	ADP
ejpam-5062	377	30	all	all	DET
ejpam-5062	377	31	j	j	NOUN
ejpam-5062	377	32	=	=	SYM
ejpam-5062	377	33	1	1	NUM
ejpam-5062	377	34	,	,	PUNCT
ejpam-5062	377	35	2	2	NUM
ejpam-5062	377	36	,	,	PUNCT
ejpam-5062	377	37	.	.	PUNCT
ejpam-5062	377	38	.	.	PUNCT
ejpam-5062	377	39	.	.	PUNCT
ejpam-5062	378	1	,	,	PUNCT
ejpam-5062	378	2	k.	k.	PROPN
ejpam-5062	378	3	on	on	ADP
ejpam-5062	378	4	the	the	DET
ejpam-5062	378	5	other	other	ADJ
ejpam-5062	378	6	side	side	NOUN
ejpam-5062	378	7	,	,	PUNCT
ejpam-5062	378	8	given	give	VERB
ejpam-5062	378	9	any	any	DET
ejpam-5062	378	10	x	x	SYM
ejpam-5062	378	11	∈	∈	PROPN
ejpam-5062	378	12	x	x	PUNCT
ejpam-5062	378	13	there	there	PRON
ejpam-5062	378	14	exists	exist	VERB
ejpam-5062	378	15	s	s	X
ejpam-5062	378	16	∈	∈	PROPN
ejpam-5062	378	17	s	s	VERB
ejpam-5062	378	18	such	such	ADJ
ejpam-5062	378	19	that	that	DET
ejpam-5062	378	20	s(x	s(x	NOUN
ejpam-5062	378	21	)	)	PUNCT
ejpam-5062	378	22	>	>	X
ejpam-5062	379	1	α	α	PROPN
ejpam-5062	379	2	and	and	CCONJ
ejpam-5062	379	3	consequently	consequently	ADV
ejpam-5062	379	4	sc	sc	PROPN
ejpam-5062	379	5	∈	∈	PROPN
ejpam-5062	379	6	f	f	PROPN
ejpam-5062	379	7	and	and	CCONJ
ejpam-5062	379	8	as	as	ADV
ejpam-5062	379	9	well	well	ADV
ejpam-5062	379	10	sc(x	sc(x	NUM
ejpam-5062	379	11	)	)	PUNCT
ejpam-5062	379	12	<	<	X
ejpam-5062	379	13	1−	1−	NUM
ejpam-5062	379	14	α	α	NOUN
ejpam-5062	379	15	.	.	PUNCT
ejpam-5062	380	1	in	in	ADP
ejpam-5062	380	2	the	the	DET
ejpam-5062	380	3	same	same	ADJ
ejpam-5062	380	4	manner	manner	NOUN
ejpam-5062	380	5	we	we	PRON
ejpam-5062	380	6	can	can	AUX
ejpam-5062	380	7	prove	prove	VERB
ejpam-5062	380	8	the	the	DET
ejpam-5062	380	9	case	case	NOUN
ejpam-5062	380	10	when	when	SCONJ
ejpam-5062	380	11	the	the	DET
ejpam-5062	380	12	fuzzy	fuzzy	ADJ
ejpam-5062	380	13	topological	topological	ADJ
ejpam-5062	380	14	space	space	NOUN
ejpam-5062	380	15	(	(	PUNCT
ejpam-5062	380	16	x	x	X
ejpam-5062	380	17	,	,	PUNCT
ejpam-5062	380	18	τ	τ	X
ejpam-5062	380	19	)	)	PUNCT
ejpam-5062	380	20	is	be	AUX
ejpam-5062	380	21	α∗	α∗	NOUN
ejpam-5062	380	22	−	−	PROPN
ejpam-5062	380	23	sspo	sspo	NOUN
ejpam-5062	380	24	compact	compact	ADJ
ejpam-5062	380	25	.	.	PUNCT
ejpam-5062	381	1	corollary	corollary	ADJ
ejpam-5062	381	2	3	3	NUM
ejpam-5062	381	3	.	.	PUNCT
ejpam-5062	382	1	the	the	DET
ejpam-5062	382	2	fuzzy	fuzzy	ADJ
ejpam-5062	382	3	topological	topological	ADJ
ejpam-5062	382	4	space	space	NOUN
ejpam-5062	382	5	(	(	PUNCT
ejpam-5062	382	6	x	x	X
ejpam-5062	382	7	,	,	PUNCT
ejpam-5062	382	8	τ	τ	X
ejpam-5062	382	9	)	)	PUNCT
ejpam-5062	382	10	is	be	AUX
ejpam-5062	382	11	α−	α−	ADP
ejpam-5062	382	12	sspo	sspo	NOUN
ejpam-5062	382	13	compact	compact	ADJ
ejpam-5062	382	14	(	(	PUNCT
ejpam-5062	382	15	respectively	respectively	ADV
ejpam-5062	382	16	α∗	α∗	VERB
ejpam-5062	382	17	−	−	PROPN
ejpam-5062	382	18	sspo	sspo	NOUN
ejpam-5062	382	19	compact	compact	ADJ
ejpam-5062	382	20	)	)	PUNCT
ejpam-5062	383	1	if	if	SCONJ
ejpam-5062	383	2	and	and	CCONJ
ejpam-5062	383	3	only	only	ADV
ejpam-5062	383	4	if	if	SCONJ
ejpam-5062	383	5	for	for	ADP
ejpam-5062	383	6	every	every	DET
ejpam-5062	383	7	α	α	NOUN
ejpam-5062	383	8	-	-	PUNCT
ejpam-5062	383	9	centered	center	VERB
ejpam-5062	383	10	(	(	PUNCT
ejpam-5062	383	11	α∗-centered	α∗-centere	VERB
ejpam-5062	383	12	)	)	PUNCT
ejpam-5062	383	13	family	family	NOUN
ejpam-5062	383	14	f	f	PROPN
ejpam-5062	383	15	consisting	consist	VERB
ejpam-5062	383	16	of	of	ADP
ejpam-5062	383	17	fuzzy	fuzzy	ADJ
ejpam-5062	383	18	sets	set	NOUN
ejpam-5062	383	19	in	in	ADP
ejpam-5062	383	20	(	(	PUNCT
ejpam-5062	383	21	x	x	NOUN
ejpam-5062	383	22	,	,	PUNCT
ejpam-5062	383	23	τ	τ	PROPN
ejpam-5062	383	24	)	)	PUNCT
ejpam-5062	383	25	,	,	PUNCT
ejpam-5062	383	26	there	there	PRON
ejpam-5062	383	27	exists	exist	VERB
ejpam-5062	383	28	x	x	X
ejpam-5062	383	29	∈	∈	PROPN
ejpam-5062	383	30	x	x	PUNCT
ejpam-5062	383	31	such	such	ADJ
ejpam-5062	383	32	that	that	DET
ejpam-5062	383	33	sspclf	sspclf	NOUN
ejpam-5062	383	34	(	(	PUNCT
ejpam-5062	383	35	x	x	X
ejpam-5062	383	36	)	)	PUNCT
ejpam-5062	383	37	≥	≥	NOUN
ejpam-5062	383	38	1−	1−	NUM
ejpam-5062	383	39	α	α	NOUN
ejpam-5062	383	40	(	(	PUNCT
ejpam-5062	383	41	sspclf	sspclf	X
ejpam-5062	383	42	(	(	PUNCT
ejpam-5062	383	43	x	x	X
ejpam-5062	383	44	)	)	PUNCT
ejpam-5062	383	45	>	>	X
ejpam-5062	383	46	1−	1−	NUM
ejpam-5062	383	47	α	α	NOUN
ejpam-5062	383	48	)	)	PUNCT
ejpam-5062	383	49	,	,	PUNCT
ejpam-5062	383	50	for	for	ADP
ejpam-5062	383	51	every	every	DET
ejpam-5062	383	52	f	f	PROPN
ejpam-5062	383	53	∈	∈	PROPN
ejpam-5062	383	54	f	f	PROPN
ejpam-5062	383	55	.	.	PUNCT
ejpam-5062	384	1	proof	proof	NOUN
ejpam-5062	384	2	.	.	PUNCT
ejpam-5062	385	1	follows	follow	VERB
ejpam-5062	385	2	directly	directly	ADV
ejpam-5062	385	3	from	from	ADP
ejpam-5062	385	4	theorem	theorem	ADJ
ejpam-5062	385	5	20	20	NUM
ejpam-5062	385	6	.	.	PUNCT
ejpam-5062	386	1	theorem	theorem	NOUN
ejpam-5062	386	2	21	21	NUM
ejpam-5062	386	3	.	.	PUNCT
ejpam-5062	387	1	the	the	DET
ejpam-5062	387	2	fuzzy	fuzzy	ADJ
ejpam-5062	387	3	topological	topological	ADJ
ejpam-5062	387	4	space	space	NOUN
ejpam-5062	387	5	(	(	PUNCT
ejpam-5062	387	6	x	x	X
ejpam-5062	387	7	,	,	PUNCT
ejpam-5062	387	8	τ	τ	X
ejpam-5062	387	9	)	)	PUNCT
ejpam-5062	387	10	is	be	AUX
ejpam-5062	387	11	countable	countable	ADJ
ejpam-5062	387	12	α−sspo	α−sspo	X
ejpam-5062	387	13	compact	compact	ADJ
ejpam-5062	387	14	(	(	PUNCT
ejpam-5062	387	15	respectively	respectively	ADV
ejpam-5062	387	16	countable	countable	ADJ
ejpam-5062	387	17	α∗−sspo	α∗−sspo	PROPN
ejpam-5062	387	18	compact	compact	ADJ
ejpam-5062	387	19	)	)	PUNCT
ejpam-5062	388	1	if	if	SCONJ
ejpam-5062	388	2	and	and	CCONJ
ejpam-5062	388	3	only	only	ADV
ejpam-5062	388	4	if	if	SCONJ
ejpam-5062	388	5	for	for	ADP
ejpam-5062	388	6	every	every	DET
ejpam-5062	388	7	countable	countable	ADJ
ejpam-5062	388	8	α	α	PRON
ejpam-5062	388	9	-	-	PUNCT
ejpam-5062	388	10	centered	center	VERB
ejpam-5062	388	11	(	(	PUNCT
ejpam-5062	388	12	countable	countable	ADJ
ejpam-5062	388	13	α∗-centered	α∗-centere	VERB
ejpam-5062	388	14	)	)	PUNCT
ejpam-5062	388	15	family	family	NOUN
ejpam-5062	388	16	f	f	PROPN
ejpam-5062	388	17	consisting	consist	VERB
ejpam-5062	388	18	of	of	ADP
ejpam-5062	388	19	fuzzy	fuzzy	ADJ
ejpam-5062	388	20	strongly	strongly	ADV
ejpam-5062	388	21	semi	semi	ADV
ejpam-5062	388	22	pre	pre	ADJ
ejpam-5062	388	23	-	-	ADJ
ejpam-5062	388	24	closed	closed	ADJ
ejpam-5062	388	25	sets	set	NOUN
ejpam-5062	388	26	in	in	ADP
ejpam-5062	388	27	(	(	PUNCT
ejpam-5062	388	28	x	x	NOUN
ejpam-5062	388	29	,	,	PUNCT
ejpam-5062	388	30	τ	τ	PROPN
ejpam-5062	388	31	)	)	PUNCT
ejpam-5062	388	32	,	,	PUNCT
ejpam-5062	388	33	there	there	PRON
ejpam-5062	388	34	exists	exist	VERB
ejpam-5062	388	35	x	x	X
ejpam-5062	388	36	∈	∈	PROPN
ejpam-5062	388	37	x	x	PUNCT
ejpam-5062	388	38	such	such	ADJ
ejpam-5062	388	39	that	that	SCONJ
ejpam-5062	388	40	f	f	PROPN
ejpam-5062	388	41	(	(	PUNCT
ejpam-5062	388	42	x	x	PROPN
ejpam-5062	388	43	)	)	PUNCT
ejpam-5062	388	44	≥	≥	NOUN
ejpam-5062	388	45	1−	1−	NUM
ejpam-5062	388	46	α	α	NOUN
ejpam-5062	388	47	(	(	PUNCT
ejpam-5062	388	48	f	f	PROPN
ejpam-5062	388	49	(	(	PUNCT
ejpam-5062	388	50	x	x	X
ejpam-5062	388	51	)	)	PUNCT
ejpam-5062	388	52	>	>	X
ejpam-5062	388	53	1−	1−	NUM
ejpam-5062	388	54	α	α	NOUN
ejpam-5062	388	55	)	)	PUNCT
ejpam-5062	388	56	,	,	PUNCT
ejpam-5062	388	57	for	for	ADP
ejpam-5062	388	58	every	every	DET
ejpam-5062	388	59	f	f	PROPN
ejpam-5062	388	60	∈	∈	PROPN
ejpam-5062	388	61	f	f	PROPN
ejpam-5062	388	62	.	.	PUNCT
ejpam-5062	389	1	proof	proof	NOUN
ejpam-5062	389	2	.	.	PUNCT
ejpam-5062	390	1	similar	similar	ADJ
ejpam-5062	390	2	to	to	ADP
ejpam-5062	390	3	theorem	theorem	VERB
ejpam-5062	390	4	20	20	NUM
ejpam-5062	390	5	theorem	theorem	NOUN
ejpam-5062	390	6	22	22	NUM
ejpam-5062	390	7	.	.	PUNCT
ejpam-5062	391	1	let	let	VERB
ejpam-5062	391	2	a	a	DET
ejpam-5062	391	3	be	be	AUX
ejpam-5062	391	4	an	an	DET
ejpam-5062	391	5	α−sspo	α−sspo	X
ejpam-5062	391	6	compact	compact	ADJ
ejpam-5062	391	7	(	(	PUNCT
ejpam-5062	391	8	α∗	α∗	NOUN
ejpam-5062	391	9	−sspo	−sspo	NOUN
ejpam-5062	391	10	compact	compact	ADJ
ejpam-5062	391	11	)	)	PUNCT
ejpam-5062	391	12	fuzzy	fuzzy	ADJ
ejpam-5062	391	13	set	set	VERB
ejpam-5062	391	14	in	in	ADP
ejpam-5062	391	15	(	(	PUNCT
ejpam-5062	391	16	x	x	NOUN
ejpam-5062	391	17	,	,	PUNCT
ejpam-5062	391	18	τ	τ	X
ejpam-5062	391	19	)	)	PUNCT
ejpam-5062	391	20	and	and	CCONJ
ejpam-5062	391	21	let	let	VERB
ejpam-5062	391	22	b	b	PROPN
ejpam-5062	391	23	∈	∈	PROPN
ejpam-5062	391	24	fsspc(τ	fsspc(τ	NOUN
ejpam-5062	391	25	)	)	PUNCT
ejpam-5062	391	26	,	,	PUNCT
ejpam-5062	391	27	then	then	ADV
ejpam-5062	391	28	the	the	DET
ejpam-5062	391	29	fuzzy	fuzzy	NOUN
ejpam-5062	391	30	set	set	VERB
ejpam-5062	391	31	a	a	DET
ejpam-5062	391	32	∧b	∧b	NOUN
ejpam-5062	391	33	is	be	AUX
ejpam-5062	391	34	an	an	DET
ejpam-5062	391	35	α−	α−	NOUN
ejpam-5062	391	36	sspo	sspo	NOUN
ejpam-5062	391	37	compact	compact	ADJ
ejpam-5062	391	38	(	(	PUNCT
ejpam-5062	391	39	α∗	α∗	NOUN
ejpam-5062	391	40	−	−	NOUN
ejpam-5062	391	41	sspo	sspo	NOUN
ejpam-5062	391	42	compact	compact	ADJ
ejpam-5062	391	43	)	)	PUNCT
ejpam-5062	391	44	fuzzy	fuzzy	ADJ
ejpam-5062	391	45	set	set	VERB
ejpam-5062	391	46	in	in	ADP
ejpam-5062	391	47	the	the	DET
ejpam-5062	391	48	fuzzy	fuzzy	ADJ
ejpam-5062	391	49	topological	topological	ADJ
ejpam-5062	391	50	space	space	NOUN
ejpam-5062	391	51	(	(	PUNCT
ejpam-5062	391	52	x	x	X
ejpam-5062	391	53	,	,	PUNCT
ejpam-5062	391	54	τ	τ	PROPN
ejpam-5062	391	55	)	)	PUNCT
ejpam-5062	391	56	.	.	PUNCT
ejpam-5062	392	1	proof	proof	NOUN
ejpam-5062	392	2	.	.	PUNCT
ejpam-5062	393	1	let	let	VERB
ejpam-5062	393	2	us	we	PRON
ejpam-5062	393	3	suppose	suppose	VERB
ejpam-5062	393	4	that	that	SCONJ
ejpam-5062	393	5	u	u	PRON
ejpam-5062	393	6	=	=	X
ejpam-5062	393	7	{	{	PUNCT
ejpam-5062	393	8	ui	ui	PROPN
ejpam-5062	393	9	,	,	PUNCT
ejpam-5062	393	10	i	i	PRON
ejpam-5062	393	11	∈	∈	VERB
ejpam-5062	393	12	i	i	PRON
ejpam-5062	393	13	}	}	PUNCT
ejpam-5062	393	14	is	be	AUX
ejpam-5062	393	15	an	an	DET
ejpam-5062	393	16	α	α	NOUN
ejpam-5062	393	17	−	−	NOUN
ejpam-5062	393	18	sspo	sspo	NOUN
ejpam-5062	393	19	shading	shading	NOUN
ejpam-5062	393	20	of	of	ADP
ejpam-5062	393	21	the	the	DET
ejpam-5062	393	22	fuzzy	fuzzy	ADJ
ejpam-5062	393	23	set	set	VERB
ejpam-5062	393	24	a∧b	a∧b	PROPN
ejpam-5062	393	25	.	.	PUNCT
ejpam-5062	394	1	it	it	PRON
ejpam-5062	394	2	follows	follow	VERB
ejpam-5062	394	3	that	that	SCONJ
ejpam-5062	394	4	the	the	DET
ejpam-5062	394	5	collection	collection	NOUN
ejpam-5062	394	6	of	of	ADP
ejpam-5062	394	7	sets	set	NOUN
ejpam-5062	394	8	{	{	PUNCT
ejpam-5062	394	9	ui	ui	NOUN
ejpam-5062	394	10	,	,	PUNCT
ejpam-5062	394	11	i	i	PRON
ejpam-5062	394	12	∈	∈	PROPN
ejpam-5062	394	13	i}∨bc	i}∨bc	PROPN
ejpam-5062	394	14	is	be	AUX
ejpam-5062	394	15	an	an	DET
ejpam-5062	394	16	α−sspo	α−sspo	NOUN
ejpam-5062	394	17	shading	shading	NOUN
ejpam-5062	394	18	of	of	ADP
ejpam-5062	394	19	the	the	DET
ejpam-5062	394	20	fuzzy	fuzzy	ADJ
ejpam-5062	394	21	set	set	NOUN
ejpam-5062	394	22	a.	a.	NOUN
ejpam-5062	394	23	the	the	DET
ejpam-5062	394	24	last	last	NOUN
ejpam-5062	394	25	is	be	AUX
ejpam-5062	394	26	true	true	ADJ
ejpam-5062	394	27	because	because	SCONJ
ejpam-5062	394	28	if	if	SCONJ
ejpam-5062	394	29	a	a	DET
ejpam-5062	394	30	∈	∈	PROPN
ejpam-5062	394	31	suppa	suppa	NOUN
ejpam-5062	394	32	then	then	ADV
ejpam-5062	394	33	a	a	DET
ejpam-5062	394	34	∈	∈	PROPN
ejpam-5062	394	35	supp(a	supp(a	NOUN
ejpam-5062	394	36	∧	∧	PROPN
ejpam-5062	394	37	b	b	PROPN
ejpam-5062	394	38	)	)	PUNCT
ejpam-5062	394	39	or	or	CCONJ
ejpam-5062	394	40	b(a	b(a	NOUN
ejpam-5062	394	41	)	)	PUNCT
ejpam-5062	394	42	=	=	SYM
ejpam-5062	395	1	0	0	X
ejpam-5062	395	2	.	.	PUNCT
ejpam-5062	396	1	if	if	SCONJ
ejpam-5062	396	2	a	a	DET
ejpam-5062	396	3	∈	∈	PROPN
ejpam-5062	396	4	supp(a∧b	supp(a∧b	NOUN
ejpam-5062	396	5	)	)	PUNCT
ejpam-5062	396	6	then	then	ADV
ejpam-5062	396	7	there	there	PRON
ejpam-5062	396	8	exists	exist	VERB
ejpam-5062	396	9	uj	uj	PROPN
ejpam-5062	396	10	∈	∈	PROPN
ejpam-5062	396	11	u	u	NOUN
ejpam-5062	396	12	such	such	ADJ
ejpam-5062	396	13	that	that	SCONJ
ejpam-5062	396	14	uj(a	uj(a	NOUN
ejpam-5062	396	15	)	)	PUNCT
ejpam-5062	396	16	>	>	X
ejpam-5062	397	1	α	α	X
ejpam-5062	397	2	,	,	PUNCT
ejpam-5062	397	3	otherwise	otherwise	ADV
ejpam-5062	397	4	,	,	PUNCT
ejpam-5062	397	5	if	if	SCONJ
ejpam-5062	397	6	b(a	b(a	NOUN
ejpam-5062	397	7	)	)	PUNCT
ejpam-5062	397	8	=	=	SYM
ejpam-5062	397	9	0	0	NUM
ejpam-5062	398	1	then	then	ADV
ejpam-5062	398	2	bc(a	bc(a	NUM
ejpam-5062	398	3	)	)	PUNCT
ejpam-5062	399	1	=	=	SYM
ejpam-5062	399	2	1	1	X
ejpam-5062	399	3	>	>	SYM
ejpam-5062	399	4	α	α	X
ejpam-5062	399	5	.	.	PUNCT
ejpam-5062	400	1	in	in	ADP
ejpam-5062	400	2	other	other	ADJ
ejpam-5062	400	3	words	word	NOUN
ejpam-5062	400	4	the	the	DET
ejpam-5062	400	5	collection	collection	NOUN
ejpam-5062	400	6	{	{	PUNCT
ejpam-5062	400	7	ui	ui	PROPN
ejpam-5062	400	8	,	,	PUNCT
ejpam-5062	400	9	i	i	PRON
ejpam-5062	400	10	∈	∈	VERB
ejpam-5062	400	11	i	i	PRON
ejpam-5062	400	12	}	}	PUNCT
ejpam-5062	400	13	∨	∨	PROPN
ejpam-5062	400	14	bc	bc	PROPN
ejpam-5062	400	15	is	be	AUX
ejpam-5062	400	16	an	an	DET
ejpam-5062	400	17	α	α	NOUN
ejpam-5062	400	18	−	−	NOUN
ejpam-5062	400	19	sspo	sspo	NOUN
ejpam-5062	400	20	-	-	PUNCT
ejpam-5062	400	21	shading	shading	NOUN
ejpam-5062	400	22	of	of	ADP
ejpam-5062	400	23	the	the	DET
ejpam-5062	400	24	fuzzy	fuzzy	ADJ
ejpam-5062	400	25	set	set	VERB
ejpam-5062	400	26	a	a	PRON
ejpam-5062	400	27	and	and	CCONJ
ejpam-5062	400	28	since	since	SCONJ
ejpam-5062	400	29	a	a	PRON
ejpam-5062	400	30	is	be	AUX
ejpam-5062	400	31	α	α	DET
ejpam-5062	400	32	−	−	PROPN
ejpam-5062	400	33	sspo	sspo	NOUN
ejpam-5062	400	34	compact	compact	ADJ
ejpam-5062	400	35	,	,	PUNCT
ejpam-5062	400	36	there	there	PRON
ejpam-5062	400	37	exists	exist	VERB
ejpam-5062	400	38	a	a	DET
ejpam-5062	400	39	finite	finite	NOUN
ejpam-5062	400	40	α	α	NOUN
ejpam-5062	400	41	−	−	PROPN
ejpam-5062	400	42	sspo	sspo	NOUN
ejpam-5062	400	43	subshading	subshade	VERB
ejpam-5062	400	44	{	{	PUNCT
ejpam-5062	400	45	ui	ui	PROPN
ejpam-5062	400	46	,	,	PUNCT
ejpam-5062	400	47	i	i	NOUN
ejpam-5062	400	48	=	=	NOUN
ejpam-5062	400	49	1	1	NUM
ejpam-5062	400	50	,	,	PUNCT
ejpam-5062	400	51	2	2	NUM
ejpam-5062	400	52	,	,	PUNCT
ejpam-5062	400	53	.	.	PUNCT
ejpam-5062	400	54	.	.	PUNCT
ejpam-5062	401	1	.	.	PUNCT
ejpam-5062	402	1	,	,	PUNCT
ejpam-5062	402	2	k	k	X
ejpam-5062	402	3	}	}	PUNCT
ejpam-5062	402	4	∨	∨	NUM
ejpam-5062	402	5	bc	bc	PROPN
ejpam-5062	402	6	.	.	PUNCT
ejpam-5062	403	1	it	it	PRON
ejpam-5062	403	2	is	be	AUX
ejpam-5062	403	3	evident	evident	ADJ
ejpam-5062	403	4	that	that	SCONJ
ejpam-5062	403	5	{	{	PUNCT
ejpam-5062	403	6	ui	ui	NOUN
ejpam-5062	403	7	,	,	PUNCT
ejpam-5062	403	8	i	i	NOUN
ejpam-5062	403	9	=	=	NOUN
ejpam-5062	403	10	1	1	NUM
ejpam-5062	403	11	,	,	PUNCT
ejpam-5062	403	12	2	2	NUM
ejpam-5062	403	13	,	,	PUNCT
ejpam-5062	403	14	.	.	PUNCT
ejpam-5062	403	15	.	.	PUNCT
ejpam-5062	403	16	.	.	PUNCT
ejpam-5062	404	1	,	,	PUNCT
ejpam-5062	404	2	k	k	X
ejpam-5062	404	3	}	}	PUNCT
ejpam-5062	404	4	is	be	AUX
ejpam-5062	404	5	a	a	DET
ejpam-5062	404	6	finite	finite	NOUN
ejpam-5062	404	7	α−	α−	ADP
ejpam-5062	404	8	sspo	sspo	NOUN
ejpam-5062	404	9	subshading	subshade	VERB
ejpam-5062	404	10	of	of	ADP
ejpam-5062	404	11	a	a	DET
ejpam-5062	404	12	∧b	∧b	NOUN
ejpam-5062	404	13	,	,	PUNCT
ejpam-5062	404	14	that	that	PRON
ejpam-5062	404	15	is	be	AUX
ejpam-5062	404	16	a	a	DET
ejpam-5062	404	17	∧b	∧b	NOUN
ejpam-5062	404	18	is	be	AUX
ejpam-5062	404	19	α−	α−	ADP
ejpam-5062	404	20	sspo	sspo	NOUN
ejpam-5062	404	21	compact	compact	ADJ
ejpam-5062	404	22	.	.	PUNCT
ejpam-5062	405	1	in	in	ADP
ejpam-5062	405	2	similar	similar	ADJ
ejpam-5062	405	3	way	way	NOUN
ejpam-5062	405	4	we	we	PRON
ejpam-5062	405	5	can	can	AUX
ejpam-5062	405	6	show	show	VERB
ejpam-5062	405	7	the	the	DET
ejpam-5062	405	8	case	case	NOUN
ejpam-5062	405	9	when	when	SCONJ
ejpam-5062	405	10	the	the	DET
ejpam-5062	405	11	fuzzy	fuzzy	NOUN
ejpam-5062	405	12	set	set	VERB
ejpam-5062	405	13	a	a	PRON
ejpam-5062	405	14	is	be	AUX
ejpam-5062	405	15	α∗	α∗	NOUN
ejpam-5062	405	16	−	−	NOUN
ejpam-5062	405	17	sspo	sspo	NOUN
ejpam-5062	405	18	compact	compact	ADJ
ejpam-5062	405	19	.	.	PUNCT
ejpam-5062	406	1	corollary	corollary	ADJ
ejpam-5062	406	2	4	4	NUM
ejpam-5062	406	3	.	.	PUNCT
ejpam-5062	407	1	let	let	VERB
ejpam-5062	407	2	x	x	PRON
ejpam-5062	407	3	be	be	AUX
ejpam-5062	407	4	an	an	DET
ejpam-5062	407	5	α	α	NOUN
ejpam-5062	407	6	−	−	NOUN
ejpam-5062	407	7	sspo	sspo	NOUN
ejpam-5062	407	8	-	-	PUNCT
ejpam-5062	407	9	compact	compact	ADJ
ejpam-5062	407	10	(	(	PUNCT
ejpam-5062	407	11	α∗	α∗	NOUN
ejpam-5062	407	12	−	−	NOUN
ejpam-5062	407	13	sspo	sspo	NOUN
ejpam-5062	407	14	compact	compact	ADJ
ejpam-5062	407	15	)	)	PUNCT
ejpam-5062	407	16	fuzzy	fuzzy	ADJ
ejpam-5062	407	17	topological	topological	ADJ
ejpam-5062	407	18	space	space	NOUN
ejpam-5062	407	19	,	,	PUNCT
ejpam-5062	407	20	then	then	ADV
ejpam-5062	407	21	any	any	DET
ejpam-5062	407	22	fuzzy	fuzzy	ADJ
ejpam-5062	407	23	set	set	VERB
ejpam-5062	407	24	b	b	PROPN
ejpam-5062	407	25	∈	∈	PROPN
ejpam-5062	407	26	fsspc(τ	fsspc(τ	NOUN
ejpam-5062	407	27	)	)	PUNCT
ejpam-5062	407	28	is	be	AUX
ejpam-5062	407	29	an	an	DET
ejpam-5062	407	30	α−sspo	α−sspo	NOUN
ejpam-5062	407	31	-	-	ADJ
ejpam-5062	407	32	compact	compact	ADJ
ejpam-5062	407	33	(	(	PUNCT
ejpam-5062	407	34	α∗−sspo	α∗−sspo	NOUN
ejpam-5062	407	35	-	-	PUNCT
ejpam-5062	407	36	compact	compact	ADJ
ejpam-5062	407	37	)	)	PUNCT
ejpam-5062	407	38	fuzzy	fuzzy	ADJ
ejpam-5062	407	39	set	set	VERB
ejpam-5062	407	40	in	in	ADP
ejpam-5062	407	41	the	the	DET
ejpam-5062	407	42	fuzzy	fuzzy	ADJ
ejpam-5062	407	43	topological	topological	ADJ
ejpam-5062	407	44	space	space	NOUN
ejpam-5062	407	45	(	(	PUNCT
ejpam-5062	407	46	x	x	X
ejpam-5062	407	47	,	,	PUNCT
ejpam-5062	407	48	τ	τ	PROPN
ejpam-5062	407	49	)	)	PUNCT
ejpam-5062	407	50	.	.	PUNCT
ejpam-5062	408	1	proof	proof	NOUN
ejpam-5062	408	2	.	.	PUNCT
ejpam-5062	409	1	it	it	PRON
ejpam-5062	409	2	is	be	AUX
ejpam-5062	409	3	obvious	obvious	ADJ
ejpam-5062	409	4	,	,	PUNCT
ejpam-5062	409	5	from	from	ADP
ejpam-5062	409	6	theorem	theorem	NOUN
ejpam-5062	409	7	22	22	NUM
ejpam-5062	409	8	,	,	PUNCT
ejpam-5062	409	9	if	if	SCONJ
ejpam-5062	409	10	we	we	PRON
ejpam-5062	409	11	substitute	substitute	VERB
ejpam-5062	409	12	the	the	DET
ejpam-5062	409	13	fuzzy	fuzzy	ADJ
ejpam-5062	409	14	α−	α−	ADP
ejpam-5062	409	15	sspo	sspo	NOUN
ejpam-5062	409	16	-	-	PUNCT
ejpam-5062	409	17	compact	compact	NOUN
ejpam-5062	409	18	set	set	NOUN
ejpam-5062	409	19	a	a	PRON
ejpam-5062	409	20	with	with	ADP
ejpam-5062	409	21	x.	x.	NOUN
ejpam-5062	409	22	theorem	theorem	VERB
ejpam-5062	409	23	23	23	NUM
ejpam-5062	409	24	.	.	PUNCT
ejpam-5062	410	1	let	let	VERB
ejpam-5062	410	2	a	a	DET
ejpam-5062	410	3	,	,	PUNCT
ejpam-5062	410	4	b	b	NOUN
ejpam-5062	410	5	be	be	AUX
ejpam-5062	410	6	α−sspo	α−sspo	NOUN
ejpam-5062	410	7	-	-	ADJ
ejpam-5062	410	8	compact	compact	ADJ
ejpam-5062	410	9	(	(	PUNCT
ejpam-5062	410	10	α∗−sspo	α∗−sspo	PROPN
ejpam-5062	410	11	compact	compact	ADJ
ejpam-5062	410	12	)	)	PUNCT
ejpam-5062	410	13	fuzzy	fuzzy	ADJ
ejpam-5062	410	14	sets	set	NOUN
ejpam-5062	410	15	in	in	ADP
ejpam-5062	410	16	(	(	PUNCT
ejpam-5062	410	17	x	x	NOUN
ejpam-5062	410	18	,	,	PUNCT
ejpam-5062	410	19	τ	τ	PROPN
ejpam-5062	410	20	)	)	PUNCT
ejpam-5062	410	21	,	,	PUNCT
ejpam-5062	410	22	then	then	ADV
ejpam-5062	410	23	the	the	DET
ejpam-5062	410	24	fuzzy	fuzzy	ADJ
ejpam-5062	410	25	set	set	VERB
ejpam-5062	410	26	a	a	DET
ejpam-5062	410	27	∨	∨	PROPN
ejpam-5062	410	28	b	b	PROPN
ejpam-5062	410	29	is	be	AUX
ejpam-5062	410	30	also	also	ADV
ejpam-5062	410	31	an	an	DET
ejpam-5062	410	32	α	α	NOUN
ejpam-5062	410	33	−	−	NOUN
ejpam-5062	410	34	sspo	sspo	NOUN
ejpam-5062	410	35	-	-	PUNCT
ejpam-5062	410	36	compact	compact	ADJ
ejpam-5062	410	37	(	(	PUNCT
ejpam-5062	410	38	α∗	α∗	NOUN
ejpam-5062	410	39	−	−	NOUN
ejpam-5062	410	40	sspo	sspo	NOUN
ejpam-5062	410	41	compact	compact	ADJ
ejpam-5062	410	42	)	)	PUNCT
ejpam-5062	410	43	fuzzy	fuzzy	ADJ
ejpam-5062	410	44	set	set	VERB
ejpam-5062	410	45	in	in	ADP
ejpam-5062	410	46	the	the	DET
ejpam-5062	410	47	fuzzy	fuzzy	ADJ
ejpam-5062	410	48	topological	topological	ADJ
ejpam-5062	410	49	space	space	NOUN
ejpam-5062	410	50	(	(	PUNCT
ejpam-5062	410	51	x	x	X
ejpam-5062	410	52	,	,	PUNCT
ejpam-5062	410	53	τ	τ	PROPN
ejpam-5062	410	54	)	)	PUNCT
ejpam-5062	410	55	.	.	PUNCT
ejpam-5062	411	1	sh	sh	PROPN
ejpam-5062	411	2	.	.	PROPN
ejpam-5062	411	3	makolli	makolli	PROPN
ejpam-5062	411	4	,	,	PUNCT
ejpam-5062	411	5	b.	b.	PROPN
ejpam-5062	411	6	krsteska	krsteska	PROPN
ejpam-5062	411	7	/	/	SYM
ejpam-5062	411	8	eur	eur	PROPN
ejpam-5062	411	9	.	.	PUNCT
ejpam-5062	412	1	j.	j.	PROPN
ejpam-5062	412	2	pure	pure	PROPN
ejpam-5062	412	3	appl	appl	PROPN
ejpam-5062	412	4	.	.	PROPN
ejpam-5062	412	5	math	math	PROPN
ejpam-5062	412	6	,	,	PUNCT
ejpam-5062	412	7	17	17	NUM
ejpam-5062	412	8	(	(	PUNCT
ejpam-5062	412	9	2	2	NUM
ejpam-5062	412	10	)	)	PUNCT
ejpam-5062	412	11	(	(	PUNCT
ejpam-5062	412	12	2024	2024	NUM
ejpam-5062	412	13	)	)	PUNCT
ejpam-5062	412	14	,	,	PUNCT
ejpam-5062	412	15	638	638	NUM
ejpam-5062	412	16	-	-	SYM
ejpam-5062	412	17	662	662	NUM
ejpam-5062	412	18	654	654	NUM
ejpam-5062	412	19	proof	proof	NOUN
ejpam-5062	412	20	.	.	PUNCT
ejpam-5062	413	1	let	let	VERB
ejpam-5062	413	2	us	we	PRON
ejpam-5062	413	3	suppose	suppose	VERB
ejpam-5062	413	4	that	that	SCONJ
ejpam-5062	413	5	{	{	PUNCT
ejpam-5062	413	6	wi	wi	PROPN
ejpam-5062	413	7	,	,	PUNCT
ejpam-5062	413	8	i	i	PRON
ejpam-5062	413	9	∈	∈	VERB
ejpam-5062	413	10	i	i	PRON
ejpam-5062	413	11	}	}	PUNCT
ejpam-5062	413	12	is	be	AUX
ejpam-5062	413	13	an	an	DET
ejpam-5062	413	14	α	α	NOUN
ejpam-5062	413	15	−	−	NOUN
ejpam-5062	413	16	sspo	sspo	NOUN
ejpam-5062	413	17	shading	shading	NOUN
ejpam-5062	413	18	of	of	ADP
ejpam-5062	413	19	the	the	DET
ejpam-5062	413	20	fuzzy	fuzzy	ADJ
ejpam-5062	413	21	set	set	NOUN
ejpam-5062	413	22	a∨b	a∨b	PROPN
ejpam-5062	413	23	.	.	PUNCT
ejpam-5062	414	1	it	it	PRON
ejpam-5062	414	2	follows	follow	VERB
ejpam-5062	414	3	that	that	SCONJ
ejpam-5062	414	4	{	{	PUNCT
ejpam-5062	414	5	wi	wi	PROPN
ejpam-5062	414	6	,	,	PUNCT
ejpam-5062	414	7	i	i	PRON
ejpam-5062	414	8	∈	∈	VERB
ejpam-5062	414	9	i	i	PRON
ejpam-5062	414	10	}	}	PUNCT
ejpam-5062	414	11	is	be	AUX
ejpam-5062	414	12	also	also	ADV
ejpam-5062	414	13	an	an	DET
ejpam-5062	414	14	α−sspo	α−sspo	NOUN
ejpam-5062	414	15	shading	shading	NOUN
ejpam-5062	414	16	of	of	ADP
ejpam-5062	414	17	the	the	DET
ejpam-5062	414	18	fuzzy	fuzzy	ADJ
ejpam-5062	414	19	sets	set	VERB
ejpam-5062	414	20	a	a	PRON
ejpam-5062	414	21	and	and	CCONJ
ejpam-5062	414	22	b.	b.	PROPN
ejpam-5062	414	23	according	accord	VERB
ejpam-5062	414	24	to	to	ADP
ejpam-5062	414	25	the	the	DET
ejpam-5062	414	26	assumption	assumption	NOUN
ejpam-5062	414	27	of	of	ADP
ejpam-5062	414	28	the	the	DET
ejpam-5062	414	29	theorem	theorem	NOUN
ejpam-5062	414	30	,	,	PUNCT
ejpam-5062	414	31	a	a	PRON
ejpam-5062	414	32	and	and	CCONJ
ejpam-5062	414	33	b	b	NOUN
ejpam-5062	414	34	are	be	AUX
ejpam-5062	414	35	two	two	NUM
ejpam-5062	414	36	α−	α−	ADP
ejpam-5062	414	37	sspo	sspo	ADJ
ejpam-5062	414	38	compact	compact	ADJ
ejpam-5062	414	39	fuzzy	fuzzy	ADJ
ejpam-5062	414	40	sets	set	NOUN
ejpam-5062	414	41	in	in	ADP
ejpam-5062	414	42	(	(	PUNCT
ejpam-5062	414	43	x	x	NOUN
ejpam-5062	414	44	,	,	PUNCT
ejpam-5062	414	45	τ	τ	PROPN
ejpam-5062	414	46	)	)	PUNCT
ejpam-5062	414	47	,	,	PUNCT
ejpam-5062	414	48	therefore	therefore	ADV
ejpam-5062	414	49	there	there	PRON
ejpam-5062	414	50	exists	exist	VERB
ejpam-5062	414	51	a	a	DET
ejpam-5062	414	52	finite	finite	NOUN
ejpam-5062	414	53	α−sspo	α−sspo	NOUN
ejpam-5062	414	54	subshading	subshade	VERB
ejpam-5062	414	55	wi1	wi1	PROPN
ejpam-5062	414	56	,	,	PUNCT
ejpam-5062	414	57	wi2	wi2	PROPN
ejpam-5062	414	58	,	,	PUNCT
ejpam-5062	414	59	...	...	PUNCT
ejpam-5062	414	60	,	,	PUNCT
ejpam-5062	414	61	wik	wik	PROPN
ejpam-5062	414	62	of	of	ADP
ejpam-5062	414	63	a	a	PRON
ejpam-5062	414	64	as	as	ADV
ejpam-5062	414	65	well	well	ADV
ejpam-5062	414	66	as	as	ADP
ejpam-5062	414	67	a	a	DET
ejpam-5062	414	68	finite	finite	NOUN
ejpam-5062	414	69	α−sspo	α−sspo	NOUN
ejpam-5062	414	70	subshading	subshade	VERB
ejpam-5062	414	71	wj1	wj1	PROPN
ejpam-5062	414	72	,	,	PUNCT
ejpam-5062	414	73	wj2	wj2	INTJ
ejpam-5062	414	74	,	,	PUNCT
ejpam-5062	414	75	...	...	PUNCT
ejpam-5062	414	76	,	,	PUNCT
ejpam-5062	414	77	wjm	wjm	NOUN
ejpam-5062	414	78	of	of	ADP
ejpam-5062	414	79	b.	b.	PROPN
ejpam-5062	414	80	now	now	ADV
ejpam-5062	414	81	if	if	SCONJ
ejpam-5062	414	82	we	we	PRON
ejpam-5062	414	83	consider	consider	VERB
ejpam-5062	414	84	the	the	DET
ejpam-5062	414	85	finite	finite	ADJ
ejpam-5062	414	86	collection	collection	NOUN
ejpam-5062	414	87	of	of	ADP
ejpam-5062	414	88	sets	set	NOUN
ejpam-5062	414	89	wi1	wi1	NOUN
ejpam-5062	414	90	,	,	PUNCT
ejpam-5062	414	91	wi2	wi2	PROPN
ejpam-5062	414	92	,	,	PUNCT
ejpam-5062	414	93	...	...	PUNCT
ejpam-5062	414	94	,	,	PUNCT
ejpam-5062	414	95	wik	wik	PROPN
ejpam-5062	414	96	,	,	PUNCT
ejpam-5062	414	97	wj1	wj1	PROPN
ejpam-5062	414	98	,	,	PUNCT
ejpam-5062	414	99	wj2	wj2	INTJ
ejpam-5062	414	100	,	,	PUNCT
ejpam-5062	414	101	...	...	PUNCT
ejpam-5062	414	102	,	,	PUNCT
ejpam-5062	414	103	wjm	wjm	VERB
ejpam-5062	414	104	it	it	PRON
ejpam-5062	414	105	is	be	AUX
ejpam-5062	414	106	obvious	obvious	ADJ
ejpam-5062	414	107	that	that	SCONJ
ejpam-5062	414	108	it	it	PRON
ejpam-5062	414	109	consists	consist	VERB
ejpam-5062	414	110	a	a	DET
ejpam-5062	414	111	finite	finite	NOUN
ejpam-5062	415	1	α−sspo	α−sspo	NOUN
ejpam-5062	415	2	subshading	subshade	VERB
ejpam-5062	415	3	of	of	ADP
ejpam-5062	415	4	{	{	PUNCT
ejpam-5062	415	5	wi	wi	PROPN
ejpam-5062	415	6	,	,	PUNCT
ejpam-5062	415	7	i	i	PRON
ejpam-5062	415	8	∈	∈	VERB
ejpam-5062	415	9	i	i	X
ejpam-5062	415	10	}	}	PUNCT
ejpam-5062	415	11	and	and	CCONJ
ejpam-5062	415	12	obviously	obviously	ADV
ejpam-5062	415	13	a∨b	a∨b	PROPN
ejpam-5062	415	14	is	be	AUX
ejpam-5062	415	15	an	an	DET
ejpam-5062	415	16	α−sspo	α−sspo	X
ejpam-5062	415	17	compact	compact	ADJ
ejpam-5062	415	18	fuzzy	fuzzy	ADJ
ejpam-5062	415	19	set	set	VERB
ejpam-5062	415	20	in	in	ADP
ejpam-5062	415	21	(	(	PUNCT
ejpam-5062	415	22	x	x	NOUN
ejpam-5062	415	23	,	,	PUNCT
ejpam-5062	415	24	τ	τ	PROPN
ejpam-5062	415	25	)	)	PUNCT
ejpam-5062	415	26	.	.	PUNCT
ejpam-5062	416	1	the	the	DET
ejpam-5062	416	2	latter	latter	ADJ
ejpam-5062	416	3	is	be	AUX
ejpam-5062	416	4	true	true	ADJ
ejpam-5062	416	5	since	since	SCONJ
ejpam-5062	416	6	for	for	ADP
ejpam-5062	416	7	any	any	DET
ejpam-5062	416	8	x	x	SYM
ejpam-5062	416	9	∈	∈	PROPN
ejpam-5062	416	10	supp(a	supp(a	PROPN
ejpam-5062	416	11	∨	∨	NUM
ejpam-5062	416	12	b	b	NOUN
ejpam-5062	416	13	)	)	PUNCT
ejpam-5062	416	14	=	=	PUNCT
ejpam-5062	416	15	x	x	SYM
ejpam-5062	416	16	∈	∈	PROPN
ejpam-5062	416	17	(	(	PUNCT
ejpam-5062	416	18	suppa	suppa	PROPN
ejpam-5062	416	19	∪	∪	ADJ
ejpam-5062	416	20	suppb	suppb	PROPN
ejpam-5062	416	21	)	)	PUNCT
ejpam-5062	416	22	,	,	PUNCT
ejpam-5062	416	23	there	there	PRON
ejpam-5062	416	24	exists	exist	VERB
ejpam-5062	416	25	wx	wx	PROPN
ejpam-5062	416	26	∈	∈	PROPN
ejpam-5062	416	27	{	{	PUNCT
ejpam-5062	416	28	wi1	wi1	NOUN
ejpam-5062	416	29	,	,	PUNCT
ejpam-5062	416	30	wi2	wi2	PROPN
ejpam-5062	416	31	,	,	PUNCT
ejpam-5062	416	32	...	...	PUNCT
ejpam-5062	416	33	,	,	PUNCT
ejpam-5062	416	34	wik	wik	PROPN
ejpam-5062	416	35	,	,	PUNCT
ejpam-5062	416	36	wj1	wj1	PROPN
ejpam-5062	416	37	,	,	PUNCT
ejpam-5062	416	38	wj2	wj2	INTJ
ejpam-5062	416	39	,	,	PUNCT
ejpam-5062	416	40	...	...	PUNCT
ejpam-5062	416	41	,	,	PUNCT
ejpam-5062	416	42	wjm	wjm	NOUN
ejpam-5062	416	43	}	}	PUNCT
ejpam-5062	416	44	such	such	ADJ
ejpam-5062	416	45	that	that	SCONJ
ejpam-5062	416	46	wx(x	wx(x	NUM
ejpam-5062	416	47	)	)	PUNCT
ejpam-5062	416	48	>	>	X
ejpam-5062	417	1	α	α	X
ejpam-5062	417	2	.	.	PUNCT
ejpam-5062	418	1	in	in	ADP
ejpam-5062	418	2	similar	similar	ADJ
ejpam-5062	418	3	way	way	NOUN
ejpam-5062	418	4	we	we	PRON
ejpam-5062	418	5	can	can	AUX
ejpam-5062	418	6	show	show	VERB
ejpam-5062	418	7	the	the	DET
ejpam-5062	418	8	case	case	NOUN
ejpam-5062	418	9	when	when	SCONJ
ejpam-5062	418	10	the	the	DET
ejpam-5062	418	11	fuzzy	fuzzy	ADJ
ejpam-5062	418	12	sets	set	VERB
ejpam-5062	418	13	a	a	DET
ejpam-5062	418	14	,	,	PUNCT
ejpam-5062	418	15	b	b	NOUN
ejpam-5062	418	16	are	be	AUX
ejpam-5062	418	17	α∗−sspo	α∗−sspo	PROPN
ejpam-5062	418	18	compact	compact	ADJ
ejpam-5062	418	19	.	.	PUNCT
ejpam-5062	419	1	corollary	corollary	ADJ
ejpam-5062	419	2	5	5	NUM
ejpam-5062	419	3	.	.	PUNCT
ejpam-5062	420	1	let	let	VERB
ejpam-5062	420	2	a	a	DET
ejpam-5062	420	3	be	be	AUX
ejpam-5062	420	4	a	a	DET
ejpam-5062	420	5	fuzzy	fuzzy	ADJ
ejpam-5062	420	6	set	set	NOUN
ejpam-5062	420	7	in	in	ADP
ejpam-5062	420	8	fuzzy	fuzzy	ADJ
ejpam-5062	420	9	topological	topological	ADJ
ejpam-5062	420	10	space	space	NOUN
ejpam-5062	420	11	(	(	PUNCT
ejpam-5062	420	12	x	x	X
ejpam-5062	420	13	,	,	PUNCT
ejpam-5062	420	14	τ	τ	PROPN
ejpam-5062	420	15	)	)	PUNCT
ejpam-5062	420	16	.	.	PUNCT
ejpam-5062	421	1	if	if	SCONJ
ejpam-5062	421	2	the	the	DET
ejpam-5062	421	3	fuzzy	fuzzy	NOUN
ejpam-5062	421	4	set	set	VERB
ejpam-5062	421	5	a	a	PRON
ejpam-5062	421	6	has	have	VERB
ejpam-5062	421	7	a	a	DET
ejpam-5062	421	8	finite	finite	ADJ
ejpam-5062	421	9	support	support	NOUN
ejpam-5062	421	10	then	then	ADV
ejpam-5062	421	11	a	a	PRON
ejpam-5062	421	12	is	be	AUX
ejpam-5062	421	13	an	an	DET
ejpam-5062	421	14	α	α	NOUN
ejpam-5062	421	15	−	−	NOUN
ejpam-5062	421	16	sspo	sspo	NOUN
ejpam-5062	421	17	compact	compact	ADJ
ejpam-5062	421	18	(	(	PUNCT
ejpam-5062	421	19	α∗	α∗	NOUN
ejpam-5062	421	20	−	−	NOUN
ejpam-5062	421	21	sspo	sspo	NOUN
ejpam-5062	421	22	compact	compact	ADJ
ejpam-5062	421	23	)	)	PUNCT
ejpam-5062	421	24	fuzzy	fuzzy	ADJ
ejpam-5062	421	25	set	set	VERB
ejpam-5062	421	26	in	in	ADP
ejpam-5062	421	27	(	(	PUNCT
ejpam-5062	421	28	x	x	NOUN
ejpam-5062	421	29	,	,	PUNCT
ejpam-5062	421	30	τ	τ	PROPN
ejpam-5062	421	31	)	)	PUNCT
ejpam-5062	421	32	.	.	PUNCT
ejpam-5062	422	1	corollary	corollary	ADJ
ejpam-5062	422	2	6	6	NUM
ejpam-5062	422	3	.	.	PUNCT
ejpam-5062	423	1	let	let	VERB
ejpam-5062	423	2	x	x	PRON
ejpam-5062	423	3	be	be	AUX
ejpam-5062	423	4	a	a	DET
ejpam-5062	423	5	finite	finite	ADJ
ejpam-5062	423	6	fuzzy	fuzzy	ADJ
ejpam-5062	423	7	topological	topological	ADJ
ejpam-5062	423	8	space	space	NOUN
ejpam-5062	423	9	,	,	PUNCT
ejpam-5062	423	10	then	then	ADV
ejpam-5062	423	11	x	x	PUNCT
ejpam-5062	423	12	is	be	AUX
ejpam-5062	423	13	an	an	DET
ejpam-5062	423	14	α−	α−	NOUN
ejpam-5062	423	15	sspo	sspo	NOUN
ejpam-5062	423	16	compact	compact	ADJ
ejpam-5062	423	17	(	(	PUNCT
ejpam-5062	423	18	α∗	α∗	NOUN
ejpam-5062	423	19	−	−	NOUN
ejpam-5062	423	20	sspo	sspo	NOUN
ejpam-5062	423	21	compact	compact	ADJ
ejpam-5062	423	22	)	)	PUNCT
ejpam-5062	423	23	fuzzy	fuzzy	ADJ
ejpam-5062	423	24	set	set	VERB
ejpam-5062	423	25	in	in	ADP
ejpam-5062	423	26	(	(	PUNCT
ejpam-5062	423	27	x	x	NOUN
ejpam-5062	423	28	,	,	PUNCT
ejpam-5062	423	29	τ	τ	PROPN
ejpam-5062	423	30	)	)	PUNCT
ejpam-5062	423	31	.	.	PUNCT
ejpam-5062	424	1	theorem	theorem	VERB
ejpam-5062	424	2	24	24	NUM
ejpam-5062	424	3	.	.	PUNCT
ejpam-5062	425	1	if	if	SCONJ
ejpam-5062	425	2	f	f	PROPN
ejpam-5062	425	3	:	:	PUNCT
ejpam-5062	425	4	x	x	X
ejpam-5062	425	5	→	→	SYM
ejpam-5062	425	6	y	y	PROPN
ejpam-5062	425	7	is	be	AUX
ejpam-5062	425	8	a	a	DET
ejpam-5062	425	9	fuzzy	fuzzy	ADJ
ejpam-5062	425	10	sspo	sspo	NOUN
ejpam-5062	425	11	-	-	PUNCT
ejpam-5062	425	12	irresolute	irresolute	ADJ
ejpam-5062	425	13	mapping	mapping	NOUN
ejpam-5062	425	14	from	from	ADP
ejpam-5062	425	15	the	the	DET
ejpam-5062	425	16	fuzzy	fuzzy	ADJ
ejpam-5062	425	17	topological	topological	ADJ
ejpam-5062	425	18	space	space	NOUN
ejpam-5062	425	19	x	x	PUNCT
ejpam-5062	425	20	to	to	ADP
ejpam-5062	425	21	a	a	DET
ejpam-5062	425	22	fuzzy	fuzzy	ADJ
ejpam-5062	425	23	topological	topological	ADJ
ejpam-5062	425	24	space	space	NOUN
ejpam-5062	425	25	y	y	PROPN
ejpam-5062	425	26	.	.	PUNCT
ejpam-5062	426	1	if	if	SCONJ
ejpam-5062	426	2	the	the	DET
ejpam-5062	426	3	fuzzy	fuzzy	NOUN
ejpam-5062	426	4	set	set	VERB
ejpam-5062	426	5	a	a	PRON
ejpam-5062	426	6	is	be	AUX
ejpam-5062	426	7	α−sspo	α−sspo	NOUN
ejpam-5062	426	8	compact	compact	ADJ
ejpam-5062	426	9	(	(	PUNCT
ejpam-5062	426	10	α∗−sspo	α∗−sspo	PROPN
ejpam-5062	426	11	compact	compact	ADJ
ejpam-5062	426	12	)	)	PUNCT
ejpam-5062	426	13	fuzzy	fuzzy	ADJ
ejpam-5062	426	14	set	set	VERB
ejpam-5062	426	15	in	in	ADP
ejpam-5062	426	16	x	x	SYM
ejpam-5062	426	17	then	then	ADV
ejpam-5062	426	18	f(a	f(a	PROPN
ejpam-5062	426	19	)	)	PUNCT
ejpam-5062	426	20	is	be	AUX
ejpam-5062	426	21	an	an	DET
ejpam-5062	426	22	α−sspo	α−sspo	X
ejpam-5062	426	23	compact	compact	ADJ
ejpam-5062	426	24	(	(	PUNCT
ejpam-5062	426	25	α∗	α∗	NOUN
ejpam-5062	426	26	−sspo	−sspo	NOUN
ejpam-5062	426	27	compact	compact	ADJ
ejpam-5062	426	28	)	)	PUNCT
ejpam-5062	426	29	fuzzy	fuzzy	ADJ
ejpam-5062	426	30	set	set	VERB
ejpam-5062	426	31	in	in	ADP
ejpam-5062	426	32	y	y	PROPN
ejpam-5062	426	33	.	.	PUNCT
ejpam-5062	427	1	proof	proof	NOUN
ejpam-5062	427	2	.	.	PUNCT
ejpam-5062	428	1	let	let	VERB
ejpam-5062	428	2	us	we	PRON
ejpam-5062	428	3	suppose	suppose	VERB
ejpam-5062	428	4	that	that	SCONJ
ejpam-5062	428	5	u	u	PRON
ejpam-5062	428	6	=	=	X
ejpam-5062	428	7	{	{	PUNCT
ejpam-5062	428	8	ui	ui	PROPN
ejpam-5062	428	9	,	,	PUNCT
ejpam-5062	428	10	i	i	PRON
ejpam-5062	428	11	∈	∈	VERB
ejpam-5062	428	12	i	i	PRON
ejpam-5062	428	13	}	}	PUNCT
ejpam-5062	428	14	is	be	AUX
ejpam-5062	428	15	an	an	DET
ejpam-5062	428	16	α	α	NOUN
ejpam-5062	428	17	−	−	NOUN
ejpam-5062	428	18	sspo	sspo	NOUN
ejpam-5062	428	19	shading	shading	NOUN
ejpam-5062	428	20	of	of	ADP
ejpam-5062	428	21	the	the	DET
ejpam-5062	428	22	fuzzy	fuzzy	ADJ
ejpam-5062	428	23	set	set	VERB
ejpam-5062	428	24	f(a	f(a	NOUN
ejpam-5062	428	25	)	)	PUNCT
ejpam-5062	428	26	in	in	ADP
ejpam-5062	428	27	y	y	PROPN
ejpam-5062	428	28	.	.	PUNCT
ejpam-5062	429	1	then	then	ADV
ejpam-5062	429	2	the	the	DET
ejpam-5062	429	3	family	family	NOUN
ejpam-5062	429	4	w	w	PROPN
ejpam-5062	429	5	=	=	SYM
ejpam-5062	429	6	{	{	PUNCT
ejpam-5062	429	7	f−1(ui	f−1(ui	PROPN
ejpam-5062	429	8	)	)	PUNCT
ejpam-5062	429	9	,	,	PUNCT
ejpam-5062	429	10	ui	ui	PROPN
ejpam-5062	429	11	∈	∈	PROPN
ejpam-5062	429	12	u	u	NOUN
ejpam-5062	429	13	}	}	PUNCT
ejpam-5062	429	14	is	be	AUX
ejpam-5062	429	15	a	a	DET
ejpam-5062	429	16	collection	collection	NOUN
ejpam-5062	429	17	of	of	ADP
ejpam-5062	429	18	fuzzy	fuzzy	ADJ
ejpam-5062	429	19	strongly	strongly	ADV
ejpam-5062	429	20	semi	semi	ADV
ejpam-5062	429	21	pre	pre	ADJ
ejpam-5062	429	22	-	-	ADJ
ejpam-5062	429	23	open	open	ADJ
ejpam-5062	429	24	sets	set	NOUN
ejpam-5062	429	25	of	of	ADP
ejpam-5062	429	26	x.	x.	NOUN
ejpam-5062	429	27	since	since	SCONJ
ejpam-5062	429	28	for	for	ADP
ejpam-5062	429	29	every	every	DET
ejpam-5062	429	30	x	x	PROPN
ejpam-5062	429	31	∈	∈	PROPN
ejpam-5062	429	32	suppa	suppa	NOUN
ejpam-5062	429	33	we	we	PRON
ejpam-5062	429	34	have	have	VERB
ejpam-5062	429	35	that	that	DET
ejpam-5062	429	36	f(x	f(x	PROPN
ejpam-5062	429	37	)	)	PUNCT
ejpam-5062	429	38	∈	∈	PROPN
ejpam-5062	429	39	f(suppa	f(suppa	NOUN
ejpam-5062	429	40	)	)	PUNCT
ejpam-5062	429	41	=	=	SYM
ejpam-5062	429	42	suppf(a	suppf(a	PROPN
ejpam-5062	429	43	)	)	PUNCT
ejpam-5062	429	44	and	and	CCONJ
ejpam-5062	429	45	since	since	SCONJ
ejpam-5062	429	46	{	{	PUNCT
ejpam-5062	429	47	ui	ui	PROPN
ejpam-5062	429	48	,	,	PUNCT
ejpam-5062	429	49	i	i	PRON
ejpam-5062	429	50	∈	∈	VERB
ejpam-5062	429	51	i	i	PRON
ejpam-5062	429	52	}	}	PUNCT
ejpam-5062	429	53	is	be	AUX
ejpam-5062	429	54	an	an	DET
ejpam-5062	429	55	α	α	NOUN
ejpam-5062	429	56	−	−	NOUN
ejpam-5062	429	57	sspo	sspo	NOUN
ejpam-5062	429	58	shading	shading	NOUN
ejpam-5062	429	59	of	of	ADP
ejpam-5062	429	60	f(a	f(a	PROPN
ejpam-5062	429	61	)	)	PUNCT
ejpam-5062	429	62	,	,	PUNCT
ejpam-5062	429	63	there	there	PRON
ejpam-5062	429	64	exists	exist	VERB
ejpam-5062	429	65	uj	uj	PROPN
ejpam-5062	429	66	∈	∈	PROPN
ejpam-5062	429	67	u	u	NOUN
ejpam-5062	429	68	such	such	ADJ
ejpam-5062	429	69	that	that	SCONJ
ejpam-5062	429	70	uj(f(x	uj(f(x	PROPN
ejpam-5062	429	71	)	)	PUNCT
ejpam-5062	429	72	)	)	PUNCT
ejpam-5062	429	73	>	>	X
ejpam-5062	429	74	α	α	PROPN
ejpam-5062	429	75	and	and	CCONJ
ejpam-5062	429	76	subsequently	subsequently	ADV
ejpam-5062	429	77	f−1(uj)(x	f−1(uj)(x	NUM
ejpam-5062	429	78	)	)	PUNCT
ejpam-5062	429	79	=	=	SYM
ejpam-5062	430	1	uj(f(x	uj(f(x	PROPN
ejpam-5062	430	2	)	)	PUNCT
ejpam-5062	430	3	)	)	PUNCT
ejpam-5062	431	1	>	>	X
ejpam-5062	431	2	α	α	X
ejpam-5062	431	3	,	,	PUNCT
ejpam-5062	431	4	which	which	PRON
ejpam-5062	431	5	means	mean	VERB
ejpam-5062	431	6	that	that	SCONJ
ejpam-5062	431	7	the	the	DET
ejpam-5062	431	8	family	family	NOUN
ejpam-5062	431	9	w	w	NOUN
ejpam-5062	431	10	is	be	AUX
ejpam-5062	431	11	an	an	DET
ejpam-5062	431	12	α	α	NOUN
ejpam-5062	431	13	−	−	NOUN
ejpam-5062	431	14	sspo	sspo	NOUN
ejpam-5062	431	15	shading	shading	NOUN
ejpam-5062	431	16	of	of	ADP
ejpam-5062	431	17	a.	a.	NOUN
ejpam-5062	431	18	since	since	SCONJ
ejpam-5062	431	19	a	a	PRON
ejpam-5062	431	20	is	be	AUX
ejpam-5062	431	21	α	α	DET
ejpam-5062	431	22	−	−	PROPN
ejpam-5062	431	23	sspo	sspo	NOUN
ejpam-5062	431	24	compact	compact	ADJ
ejpam-5062	431	25	it	it	PRON
ejpam-5062	431	26	follows	follow	VERB
ejpam-5062	431	27	that	that	SCONJ
ejpam-5062	431	28	w	w	NOUN
ejpam-5062	431	29	contains	contain	VERB
ejpam-5062	431	30	a	a	DET
ejpam-5062	431	31	finite	finite	NOUN
ejpam-5062	431	32	α	α	NOUN
ejpam-5062	431	33	−	−	PROPN
ejpam-5062	431	34	sspo	sspo	NOUN
ejpam-5062	431	35	subshading	subshade	VERB
ejpam-5062	431	36	,	,	PUNCT
ejpam-5062	431	37	{	{	PUNCT
ejpam-5062	431	38	f−1(ui	f−1(ui	PROPN
ejpam-5062	431	39	)	)	PUNCT
ejpam-5062	431	40	,	,	PUNCT
ejpam-5062	431	41	i	i	PROPN
ejpam-5062	431	42	∈	∈	PROPN
ejpam-5062	431	43	j	j	PROPN
ejpam-5062	431	44	}	}	PUNCT
ejpam-5062	431	45	,	,	PUNCT
ejpam-5062	431	46	where	where	SCONJ
ejpam-5062	431	47	j	j	PROPN
ejpam-5062	431	48	is	be	AUX
ejpam-5062	431	49	a	a	DET
ejpam-5062	431	50	finite	finite	ADJ
ejpam-5062	431	51	set	set	NOUN
ejpam-5062	431	52	of	of	ADP
ejpam-5062	431	53	indexes	index	NOUN
ejpam-5062	431	54	.	.	PUNCT
ejpam-5062	432	1	therefore	therefore	ADV
ejpam-5062	432	2	we	we	PRON
ejpam-5062	432	3	can	can	AUX
ejpam-5062	432	4	conclude	conclude	VERB
ejpam-5062	432	5	that	that	SCONJ
ejpam-5062	432	6	the	the	DET
ejpam-5062	432	7	finite	finite	ADJ
ejpam-5062	432	8	collection	collection	NOUN
ejpam-5062	432	9	{	{	PUNCT
ejpam-5062	432	10	ui	ui	PROPN
ejpam-5062	432	11	,	,	PUNCT
ejpam-5062	432	12	i	i	PROPN
ejpam-5062	432	13	∈	∈	PROPN
ejpam-5062	432	14	j	j	PROPN
ejpam-5062	432	15	}	}	PUNCT
ejpam-5062	432	16	is	be	AUX
ejpam-5062	432	17	an	an	DET
ejpam-5062	432	18	α−	α−	NOUN
ejpam-5062	432	19	sspo	sspo	NOUN
ejpam-5062	432	20	subshading	subshade	VERB
ejpam-5062	432	21	of	of	ADP
ejpam-5062	432	22	the	the	DET
ejpam-5062	432	23	α	α	NOUN
ejpam-5062	432	24	−	−	PROPN
ejpam-5062	432	25	sspo	sspo	NOUN
ejpam-5062	432	26	shading	shade	VERB
ejpam-5062	432	27	u	u	NOUN
ejpam-5062	432	28	.	.	PUNCT
ejpam-5062	433	1	this	this	PRON
ejpam-5062	433	2	is	be	AUX
ejpam-5062	433	3	true	true	ADJ
ejpam-5062	433	4	due	due	ADP
ejpam-5062	433	5	to	to	ADP
ejpam-5062	433	6	the	the	DET
ejpam-5062	433	7	fact	fact	NOUN
ejpam-5062	433	8	that	that	SCONJ
ejpam-5062	433	9	for	for	ADP
ejpam-5062	433	10	every	every	DET
ejpam-5062	433	11	y	y	PROPN
ejpam-5062	433	12	∈	∈	PROPN
ejpam-5062	433	13	suppf(a	suppf(a	PROPN
ejpam-5062	433	14	)	)	PUNCT
ejpam-5062	433	15	there	there	PRON
ejpam-5062	433	16	exists	exist	VERB
ejpam-5062	433	17	x	x	X
ejpam-5062	433	18	∈	∈	PROPN
ejpam-5062	433	19	suppa	suppa	NOUN
ejpam-5062	433	20	such	such	ADJ
ejpam-5062	433	21	that	that	SCONJ
ejpam-5062	433	22	f(x	f(x	NOUN
ejpam-5062	433	23	)	)	PUNCT
ejpam-5062	434	1	=	=	PUNCT
ejpam-5062	435	1	y.	y.	PROPN
ejpam-5062	435	2	now	now	ADV
ejpam-5062	435	3	,	,	PUNCT
ejpam-5062	435	4	since	since	SCONJ
ejpam-5062	435	5	{	{	PUNCT
ejpam-5062	435	6	f−1(ui	f−1(ui	PROPN
ejpam-5062	435	7	)	)	PUNCT
ejpam-5062	435	8	,	,	PUNCT
ejpam-5062	435	9	i	i	PROPN
ejpam-5062	435	10	∈	∈	PROPN
ejpam-5062	435	11	j	j	PROPN
ejpam-5062	435	12	}	}	PUNCT
ejpam-5062	435	13	is	be	AUX
ejpam-5062	435	14	a	a	DET
ejpam-5062	435	15	finite	finite	NOUN
ejpam-5062	435	16	α	α	NOUN
ejpam-5062	435	17	−	−	PROPN
ejpam-5062	435	18	sspo	sspo	NOUN
ejpam-5062	435	19	subshading	subshade	VERB
ejpam-5062	435	20	of	of	ADP
ejpam-5062	435	21	a	a	PRON
ejpam-5062	435	22	,	,	PUNCT
ejpam-5062	435	23	there	there	PRON
ejpam-5062	435	24	exists	exist	VERB
ejpam-5062	435	25	m	m	VERB
ejpam-5062	435	26	∈	∈	PROPN
ejpam-5062	435	27	j	j	NOUN
ejpam-5062	435	28	such	such	ADJ
ejpam-5062	435	29	that	that	DET
ejpam-5062	435	30	f−1(um)(x	f−1(um)(x	NOUN
ejpam-5062	435	31	)	)	PUNCT
ejpam-5062	435	32	>	>	PUNCT
ejpam-5062	436	1	α	α	PROPN
ejpam-5062	436	2	and	and	CCONJ
ejpam-5062	436	3	therefore	therefore	ADV
ejpam-5062	436	4	f−1(um)(x	f−1(um)(x	ADJ
ejpam-5062	436	5	)	)	PUNCT
ejpam-5062	436	6	=	=	SYM
ejpam-5062	436	7	um(f(x	um(f(x	NOUN
ejpam-5062	436	8	)	)	PUNCT
ejpam-5062	436	9	)	)	PUNCT
ejpam-5062	437	1	=	=	PUNCT
ejpam-5062	437	2	um(y	um(y	PROPN
ejpam-5062	437	3	)	)	PUNCT
ejpam-5062	437	4	>	>	X
ejpam-5062	438	1	α	α	X
ejpam-5062	438	2	.	.	PUNCT
ejpam-5062	439	1	we	we	PRON
ejpam-5062	439	2	showed	show	VERB
ejpam-5062	439	3	that	that	SCONJ
ejpam-5062	439	4	f(a	f(a	NOUN
ejpam-5062	439	5	)	)	PUNCT
ejpam-5062	439	6	is	be	AUX
ejpam-5062	439	7	an	an	DET
ejpam-5062	439	8	α	α	NOUN
ejpam-5062	439	9	−	−	NOUN
ejpam-5062	439	10	sspo	sspo	NOUN
ejpam-5062	439	11	compact	compact	ADJ
ejpam-5062	439	12	set	set	VERB
ejpam-5062	439	13	in	in	ADP
ejpam-5062	439	14	y	y	PROPN
ejpam-5062	439	15	.	.	PUNCT
ejpam-5062	440	1	the	the	DET
ejpam-5062	440	2	other	other	ADJ
ejpam-5062	440	3	case	case	NOUN
ejpam-5062	440	4	is	be	AUX
ejpam-5062	440	5	proven	prove	VERB
ejpam-5062	440	6	in	in	ADP
ejpam-5062	440	7	a	a	DET
ejpam-5062	440	8	similar	similar	ADJ
ejpam-5062	440	9	way	way	NOUN
ejpam-5062	440	10	.	.	PUNCT
ejpam-5062	441	1	corollary	corollary	ADJ
ejpam-5062	441	2	7	7	NUM
ejpam-5062	441	3	.	.	PUNCT
ejpam-5062	442	1	if	if	SCONJ
ejpam-5062	442	2	f	f	PROPN
ejpam-5062	442	3	:	:	PUNCT
ejpam-5062	442	4	x	x	X
ejpam-5062	442	5	→	→	SYM
ejpam-5062	442	6	y	y	PROPN
ejpam-5062	442	7	is	be	AUX
ejpam-5062	442	8	a	a	DET
ejpam-5062	442	9	fuzzy	fuzzy	ADJ
ejpam-5062	442	10	sspo	sspo	NOUN
ejpam-5062	442	11	-	-	PUNCT
ejpam-5062	442	12	irresolute	irresolute	ADJ
ejpam-5062	442	13	mapping	mapping	NOUN
ejpam-5062	442	14	from	from	ADP
ejpam-5062	442	15	the	the	DET
ejpam-5062	442	16	fuzzy	fuzzy	ADJ
ejpam-5062	442	17	topological	topological	ADJ
ejpam-5062	442	18	space	space	NOUN
ejpam-5062	442	19	x	x	PUNCT
ejpam-5062	442	20	to	to	ADP
ejpam-5062	442	21	a	a	DET
ejpam-5062	442	22	fuzzy	fuzzy	ADJ
ejpam-5062	442	23	topological	topological	ADJ
ejpam-5062	442	24	space	space	NOUN
ejpam-5062	442	25	y	y	PROPN
ejpam-5062	442	26	.	.	PUNCT
ejpam-5062	443	1	if	if	SCONJ
ejpam-5062	443	2	x	x	PRON
ejpam-5062	443	3	is	be	AUX
ejpam-5062	443	4	α−sspo	α−sspo	X
ejpam-5062	443	5	compact	compact	ADJ
ejpam-5062	443	6	(	(	PUNCT
ejpam-5062	443	7	α∗−sspo	α∗−sspo	PROPN
ejpam-5062	443	8	compact	compact	ADJ
ejpam-5062	443	9	)	)	PUNCT
ejpam-5062	443	10	then	then	ADV
ejpam-5062	443	11	f(x	f(x	PROPN
ejpam-5062	443	12	)	)	PUNCT
ejpam-5062	443	13	is	be	AUX
ejpam-5062	443	14	an	an	DET
ejpam-5062	443	15	α−	α−	X
ejpam-5062	443	16	sspo	sspo	NOUN
ejpam-5062	443	17	compact	compact	ADJ
ejpam-5062	443	18	(	(	PUNCT
ejpam-5062	443	19	α∗	α∗	NOUN
ejpam-5062	443	20	−	−	NOUN
ejpam-5062	443	21	sspo	sspo	NOUN
ejpam-5062	443	22	compact	compact	ADJ
ejpam-5062	443	23	)	)	PUNCT
ejpam-5062	443	24	fuzzy	fuzzy	ADJ
ejpam-5062	443	25	set	set	VERB
ejpam-5062	443	26	in	in	ADP
ejpam-5062	443	27	y	y	PROPN
ejpam-5062	443	28	.	.	PUNCT
ejpam-5062	444	1	proof	proof	NOUN
ejpam-5062	444	2	.	.	PUNCT
ejpam-5062	445	1	it	it	PRON
ejpam-5062	445	2	follows	follow	VERB
ejpam-5062	445	3	directly	directly	ADV
ejpam-5062	445	4	from	from	ADP
ejpam-5062	445	5	theorem	theorem	ADJ
ejpam-5062	445	6	24	24	NUM
ejpam-5062	445	7	.	.	PUNCT
ejpam-5062	446	1	sh	sh	PROPN
ejpam-5062	446	2	.	.	PROPN
ejpam-5062	446	3	makolli	makolli	PROPN
ejpam-5062	446	4	,	,	PUNCT
ejpam-5062	446	5	b.	b.	PROPN
ejpam-5062	446	6	krsteska	krsteska	PROPN
ejpam-5062	446	7	/	/	SYM
ejpam-5062	446	8	eur	eur	PROPN
ejpam-5062	446	9	.	.	PUNCT
ejpam-5062	447	1	j.	j.	PROPN
ejpam-5062	447	2	pure	pure	PROPN
ejpam-5062	447	3	appl	appl	PROPN
ejpam-5062	447	4	.	.	PROPN
ejpam-5062	447	5	math	math	PROPN
ejpam-5062	447	6	,	,	PUNCT
ejpam-5062	447	7	17	17	NUM
ejpam-5062	447	8	(	(	PUNCT
ejpam-5062	447	9	2	2	NUM
ejpam-5062	447	10	)	)	PUNCT
ejpam-5062	447	11	(	(	PUNCT
ejpam-5062	447	12	2024	2024	NUM
ejpam-5062	447	13	)	)	PUNCT
ejpam-5062	447	14	,	,	PUNCT
ejpam-5062	447	15	638	638	NUM
ejpam-5062	447	16	-	-	SYM
ejpam-5062	447	17	662	662	NUM
ejpam-5062	447	18	655	655	NUM
ejpam-5062	447	19	corollary	corollary	ADJ
ejpam-5062	447	20	8	8	NUM
ejpam-5062	447	21	.	.	PUNCT
ejpam-5062	448	1	let	let	VERB
ejpam-5062	448	2	f	f	NOUN
ejpam-5062	448	3	:	:	PUNCT
ejpam-5062	448	4	x	x	X
ejpam-5062	448	5	→	→	SYM
ejpam-5062	448	6	y	y	PROPN
ejpam-5062	448	7	is	be	AUX
ejpam-5062	448	8	a	a	DET
ejpam-5062	448	9	fuzzy	fuzzy	ADJ
ejpam-5062	448	10	sspo	sspo	NOUN
ejpam-5062	448	11	-	-	PUNCT
ejpam-5062	448	12	irresolute	irresolute	ADJ
ejpam-5062	448	13	and	and	CCONJ
ejpam-5062	448	14	surjective	surjective	ADJ
ejpam-5062	448	15	mapping	mapping	NOUN
ejpam-5062	448	16	from	from	ADP
ejpam-5062	448	17	the	the	DET
ejpam-5062	448	18	fuzzy	fuzzy	ADJ
ejpam-5062	448	19	topological	topological	ADJ
ejpam-5062	448	20	space	space	NOUN
ejpam-5062	448	21	x	x	PUNCT
ejpam-5062	448	22	to	to	ADP
ejpam-5062	448	23	a	a	DET
ejpam-5062	448	24	fuzzy	fuzzy	ADJ
ejpam-5062	448	25	topological	topological	ADJ
ejpam-5062	448	26	space	space	NOUN
ejpam-5062	448	27	y	y	PROPN
ejpam-5062	448	28	.	.	PUNCT
ejpam-5062	449	1	if	if	SCONJ
ejpam-5062	449	2	x	x	PRON
ejpam-5062	449	3	is	be	AUX
ejpam-5062	449	4	α	α	PRON
ejpam-5062	449	5	−	−	PROPN
ejpam-5062	449	6	sspo	sspo	NOUN
ejpam-5062	449	7	compact	compact	ADJ
ejpam-5062	449	8	(	(	PUNCT
ejpam-5062	449	9	α∗	α∗	NOUN
ejpam-5062	449	10	−	−	NOUN
ejpam-5062	449	11	sspo	sspo	NOUN
ejpam-5062	449	12	compact	compact	ADJ
ejpam-5062	449	13	)	)	PUNCT
ejpam-5062	449	14	then	then	ADV
ejpam-5062	449	15	y	y	PROPN
ejpam-5062	449	16	is	be	AUX
ejpam-5062	449	17	an	an	DET
ejpam-5062	449	18	α−	α−	X
ejpam-5062	449	19	sspo	sspo	NOUN
ejpam-5062	449	20	compact	compact	ADJ
ejpam-5062	449	21	(	(	PUNCT
ejpam-5062	449	22	α∗	α∗	NOUN
ejpam-5062	449	23	−	−	NOUN
ejpam-5062	449	24	sspo	sspo	NOUN
ejpam-5062	449	25	compact	compact	ADJ
ejpam-5062	449	26	)	)	PUNCT
ejpam-5062	449	27	fuzzy	fuzzy	ADJ
ejpam-5062	449	28	set	set	NOUN
ejpam-5062	449	29	.	.	PUNCT
ejpam-5062	450	1	proof	proof	NOUN
ejpam-5062	450	2	.	.	PUNCT
ejpam-5062	451	1	it	it	PRON
ejpam-5062	451	2	follows	follow	VERB
ejpam-5062	451	3	from	from	ADP
ejpam-5062	451	4	corollary	corollary	ADJ
ejpam-5062	451	5	7	7	NUM
ejpam-5062	451	6	and	and	CCONJ
ejpam-5062	451	7	since	since	SCONJ
ejpam-5062	451	8	f(x	f(x	PROPN
ejpam-5062	451	9	)	)	PUNCT
ejpam-5062	452	1	=	=	PUNCT
ejpam-5062	452	2	y	y	PROPN
ejpam-5062	452	3	when	when	SCONJ
ejpam-5062	452	4	f	f	PROPN
ejpam-5062	452	5	is	be	AUX
ejpam-5062	452	6	a	a	DET
ejpam-5062	452	7	surjective	surjective	ADJ
ejpam-5062	452	8	mapping	mapping	NOUN
ejpam-5062	452	9	.	.	PUNCT
ejpam-5062	453	1	theorem	theorem	VERB
ejpam-5062	453	2	25	25	NUM
ejpam-5062	453	3	.	.	PUNCT
ejpam-5062	454	1	let	let	VERB
ejpam-5062	454	2	f	f	NOUN
ejpam-5062	454	3	:	:	PUNCT
ejpam-5062	454	4	x	x	X
ejpam-5062	454	5	→	→	SYM
ejpam-5062	454	6	y	y	X
ejpam-5062	454	7	be	be	AUX
ejpam-5062	454	8	a	a	DET
ejpam-5062	454	9	fuzzy	fuzzy	ADJ
ejpam-5062	454	10	strong	strong	ADJ
ejpam-5062	454	11	semi	semi	ADJ
ejpam-5062	454	12	pre	pre	ADJ
ejpam-5062	454	13	-	-	ADJ
ejpam-5062	454	14	continuous	continuous	ADJ
ejpam-5062	454	15	and	and	CCONJ
ejpam-5062	454	16	surjective	surjective	ADJ
ejpam-5062	454	17	mapping	mapping	NOUN
ejpam-5062	454	18	from	from	ADP
ejpam-5062	454	19	the	the	DET
ejpam-5062	454	20	fuzzy	fuzzy	ADJ
ejpam-5062	454	21	topological	topological	ADJ
ejpam-5062	454	22	space	space	NOUN
ejpam-5062	454	23	x	x	PUNCT
ejpam-5062	454	24	to	to	ADP
ejpam-5062	454	25	a	a	DET
ejpam-5062	454	26	fuzzy	fuzzy	ADJ
ejpam-5062	454	27	topological	topological	ADJ
ejpam-5062	454	28	space	space	NOUN
ejpam-5062	454	29	y	y	PROPN
ejpam-5062	454	30	.	.	PUNCT
ejpam-5062	455	1	if	if	SCONJ
ejpam-5062	455	2	x	x	PRON
ejpam-5062	455	3	is	be	AUX
ejpam-5062	455	4	α	α	PRON
ejpam-5062	455	5	−	−	PROPN
ejpam-5062	455	6	sspo	sspo	NOUN
ejpam-5062	455	7	compact	compact	ADJ
ejpam-5062	455	8	(	(	PUNCT
ejpam-5062	455	9	α∗	α∗	NOUN
ejpam-5062	455	10	−	−	NOUN
ejpam-5062	455	11	sspo	sspo	NOUN
ejpam-5062	455	12	compact	compact	ADJ
ejpam-5062	455	13	)	)	PUNCT
ejpam-5062	455	14	then	then	ADV
ejpam-5062	455	15	y	y	PROPN
ejpam-5062	455	16	is	be	AUX
ejpam-5062	455	17	an	an	DET
ejpam-5062	455	18	α	α	NOUN
ejpam-5062	455	19	-	-	ADJ
ejpam-5062	455	20	compact	compact	ADJ
ejpam-5062	455	21	(	(	PUNCT
ejpam-5062	455	22	α∗-compact	α∗-compact	NUM
ejpam-5062	455	23	)	)	PUNCT
ejpam-5062	455	24	.	.	PUNCT
ejpam-5062	456	1	proof	proof	NOUN
ejpam-5062	456	2	.	.	PUNCT
ejpam-5062	457	1	let	let	VERB
ejpam-5062	457	2	us	we	PRON
ejpam-5062	457	3	suppose	suppose	VERB
ejpam-5062	457	4	that	that	SCONJ
ejpam-5062	457	5	u	u	PRON
ejpam-5062	457	6	=	=	X
ejpam-5062	457	7	{	{	PUNCT
ejpam-5062	457	8	ui	ui	PROPN
ejpam-5062	457	9	,	,	PUNCT
ejpam-5062	457	10	i	i	PRON
ejpam-5062	457	11	∈	∈	VERB
ejpam-5062	457	12	i	i	PRON
ejpam-5062	457	13	}	}	PUNCT
ejpam-5062	457	14	is	be	AUX
ejpam-5062	457	15	an	an	DET
ejpam-5062	457	16	α	α	NOUN
ejpam-5062	457	17	-	-	PUNCT
ejpam-5062	457	18	shading	shading	NOUN
ejpam-5062	457	19	of	of	ADP
ejpam-5062	457	20	y	y	PROPN
ejpam-5062	457	21	.	.	PUNCT
ejpam-5062	458	1	then	then	ADV
ejpam-5062	458	2	the	the	DET
ejpam-5062	458	3	family	family	NOUN
ejpam-5062	458	4	w	w	PROPN
ejpam-5062	458	5	=	=	SYM
ejpam-5062	458	6	{	{	PUNCT
ejpam-5062	458	7	f−1(ui	f−1(ui	PROPN
ejpam-5062	458	8	)	)	PUNCT
ejpam-5062	458	9	,	,	PUNCT
ejpam-5062	458	10	ui	ui	PROPN
ejpam-5062	458	11	∈	∈	PROPN
ejpam-5062	458	12	u	u	NOUN
ejpam-5062	458	13	}	}	PUNCT
ejpam-5062	458	14	is	be	AUX
ejpam-5062	458	15	a	a	DET
ejpam-5062	458	16	collection	collection	NOUN
ejpam-5062	458	17	of	of	ADP
ejpam-5062	458	18	fuzzy	fuzzy	ADJ
ejpam-5062	458	19	strongly	strongly	ADV
ejpam-5062	458	20	semi	semi	ADV
ejpam-5062	458	21	pre	pre	ADJ
ejpam-5062	458	22	-	-	ADJ
ejpam-5062	458	23	open	open	ADJ
ejpam-5062	458	24	sets	set	NOUN
ejpam-5062	458	25	of	of	ADP
ejpam-5062	458	26	x.	x.	NOUN
ejpam-5062	458	27	since	since	SCONJ
ejpam-5062	458	28	for	for	ADP
ejpam-5062	458	29	every	every	DET
ejpam-5062	458	30	x	x	SYM
ejpam-5062	458	31	∈	∈	PROPN
ejpam-5062	458	32	x	x	INTJ
ejpam-5062	458	33	we	we	PRON
ejpam-5062	458	34	have	have	VERB
ejpam-5062	458	35	that	that	DET
ejpam-5062	458	36	f(x	f(x	PROPN
ejpam-5062	458	37	)	)	PUNCT
ejpam-5062	458	38	∈	∈	PROPN
ejpam-5062	458	39	f(suppx	f(suppx	NOUN
ejpam-5062	458	40	)	)	PUNCT
ejpam-5062	459	1	=	=	SYM
ejpam-5062	459	2	suppy	suppy	NOUN
ejpam-5062	459	3	and	and	CCONJ
ejpam-5062	459	4	since	since	SCONJ
ejpam-5062	459	5	{	{	PUNCT
ejpam-5062	459	6	ui	ui	PROPN
ejpam-5062	459	7	,	,	PUNCT
ejpam-5062	459	8	i	i	PRON
ejpam-5062	459	9	∈	∈	VERB
ejpam-5062	460	1	i	i	PRON
ejpam-5062	460	2	}	}	PUNCT
ejpam-5062	460	3	is	be	AUX
ejpam-5062	460	4	an	an	DET
ejpam-5062	460	5	αshading	αshading	NOUN
ejpam-5062	460	6	of	of	ADP
ejpam-5062	460	7	y	y	PRON
ejpam-5062	460	8	there	there	PRON
ejpam-5062	460	9	exists	exist	VERB
ejpam-5062	460	10	a	a	DET
ejpam-5062	460	11	fuzzy	fuzzy	ADJ
ejpam-5062	460	12	open	open	NOUN
ejpam-5062	460	13	set	set	VERB
ejpam-5062	460	14	uj	uj	PROPN
ejpam-5062	460	15	∈	∈	PROPN
ejpam-5062	460	16	u	u	NOUN
ejpam-5062	460	17	such	such	ADJ
ejpam-5062	460	18	that	that	SCONJ
ejpam-5062	460	19	uj(f(x	uj(f(x	PROPN
ejpam-5062	460	20	)	)	PUNCT
ejpam-5062	460	21	)	)	PUNCT
ejpam-5062	460	22	>	>	X
ejpam-5062	460	23	α	α	PROPN
ejpam-5062	460	24	and	and	CCONJ
ejpam-5062	460	25	subsequently	subsequently	ADV
ejpam-5062	460	26	f−1(uj)(x	f−1(uj)(x	NUM
ejpam-5062	460	27	)	)	PUNCT
ejpam-5062	460	28	=	=	SYM
ejpam-5062	460	29	uj(f(x	uj(f(x	PROPN
ejpam-5062	460	30	)	)	PUNCT
ejpam-5062	460	31	)	)	PUNCT
ejpam-5062	461	1	>	>	X
ejpam-5062	461	2	α	α	X
ejpam-5062	461	3	,	,	PUNCT
ejpam-5062	461	4	which	which	PRON
ejpam-5062	461	5	means	mean	VERB
ejpam-5062	461	6	that	that	SCONJ
ejpam-5062	461	7	the	the	DET
ejpam-5062	461	8	familyw	familyw	NOUN
ejpam-5062	461	9	is	be	AUX
ejpam-5062	461	10	an	an	DET
ejpam-5062	461	11	α−sspo	α−sspo	NOUN
ejpam-5062	461	12	shading	shade	VERB
ejpam-5062	461	13	ofx	ofx	NOUN
ejpam-5062	461	14	.	.	PUNCT
ejpam-5062	462	1	since	since	SCONJ
ejpam-5062	462	2	x	x	PROPN
ejpam-5062	462	3	is	be	AUX
ejpam-5062	462	4	α−sspo	α−sspo	PRON
ejpam-5062	462	5	compact	compact	ADJ
ejpam-5062	462	6	it	it	PRON
ejpam-5062	462	7	follows	follow	VERB
ejpam-5062	462	8	that	that	SCONJ
ejpam-5062	462	9	w	w	NOUN
ejpam-5062	462	10	contains	contain	VERB
ejpam-5062	462	11	a	a	DET
ejpam-5062	462	12	finite	finite	NOUN
ejpam-5062	462	13	α−sspo	α−sspo	NOUN
ejpam-5062	462	14	subshading	subshade	VERB
ejpam-5062	462	15	,	,	PUNCT
ejpam-5062	462	16	{	{	PUNCT
ejpam-5062	462	17	f−1(ui	f−1(ui	PROPN
ejpam-5062	462	18	)	)	PUNCT
ejpam-5062	462	19	,	,	PUNCT
ejpam-5062	462	20	i	i	PRON
ejpam-5062	462	21	∈	∈	PROPN
ejpam-5062	462	22	k	k	X
ejpam-5062	462	23	}	}	PUNCT
ejpam-5062	462	24	,	,	PUNCT
ejpam-5062	462	25	where	where	SCONJ
ejpam-5062	462	26	k	k	PROPN
ejpam-5062	462	27	is	be	AUX
ejpam-5062	462	28	a	a	DET
ejpam-5062	462	29	finite	finite	ADJ
ejpam-5062	462	30	set	set	NOUN
ejpam-5062	462	31	of	of	ADP
ejpam-5062	462	32	indexes	index	NOUN
ejpam-5062	462	33	.	.	PUNCT
ejpam-5062	463	1	therefore	therefore	ADV
ejpam-5062	463	2	we	we	PRON
ejpam-5062	463	3	can	can	AUX
ejpam-5062	463	4	conclude	conclude	VERB
ejpam-5062	463	5	that	that	SCONJ
ejpam-5062	463	6	the	the	DET
ejpam-5062	463	7	finite	finite	ADJ
ejpam-5062	463	8	collection	collection	NOUN
ejpam-5062	463	9	{	{	PUNCT
ejpam-5062	463	10	f(f−1(ui	f(f−1(ui	NOUN
ejpam-5062	463	11	)	)	PUNCT
ejpam-5062	463	12	=	=	SYM
ejpam-5062	463	13	ui	ui	PROPN
ejpam-5062	463	14	,	,	PUNCT
ejpam-5062	463	15	i	i	PROPN
ejpam-5062	463	16	∈	∈	PROPN
ejpam-5062	463	17	k	k	AUX
ejpam-5062	463	18	}	}	PUNCT
ejpam-5062	463	19	is	be	AUX
ejpam-5062	463	20	an	an	DET
ejpam-5062	463	21	α	α	NOUN
ejpam-5062	463	22	-	-	PUNCT
ejpam-5062	463	23	subshading	subshading	NOUN
ejpam-5062	463	24	of	of	ADP
ejpam-5062	463	25	the	the	DET
ejpam-5062	463	26	α	α	NOUN
ejpam-5062	463	27	-	-	PUNCT
ejpam-5062	463	28	shading	shade	VERB
ejpam-5062	463	29	u	u	NOUN
ejpam-5062	463	30	.	.	PUNCT
ejpam-5062	464	1	the	the	DET
ejpam-5062	464	2	last	last	ADJ
ejpam-5062	464	3	stands	stand	VERB
ejpam-5062	464	4	because	because	SCONJ
ejpam-5062	464	5	f	f	PROPN
ejpam-5062	464	6	is	be	AUX
ejpam-5062	464	7	a	a	DET
ejpam-5062	464	8	surjective	surjective	ADJ
ejpam-5062	464	9	mapping	mapping	NOUN
ejpam-5062	464	10	and	and	CCONJ
ejpam-5062	464	11	due	due	ADP
ejpam-5062	464	12	to	to	ADP
ejpam-5062	464	13	the	the	DET
ejpam-5062	464	14	fact	fact	NOUN
ejpam-5062	464	15	that	that	SCONJ
ejpam-5062	464	16	for	for	ADP
ejpam-5062	464	17	every	every	DET
ejpam-5062	464	18	y	y	PROPN
ejpam-5062	464	19	∈	∈	PROPN
ejpam-5062	464	20	y	y	NOUN
ejpam-5062	464	21	there	there	PRON
ejpam-5062	464	22	exists	exist	VERB
ejpam-5062	464	23	x	x	X
ejpam-5062	464	24	∈	∈	PROPN
ejpam-5062	464	25	x	x	PUNCT
ejpam-5062	464	26	such	such	ADJ
ejpam-5062	464	27	that	that	SCONJ
ejpam-5062	464	28	f(x	f(x	NOUN
ejpam-5062	464	29	)	)	PUNCT
ejpam-5062	465	1	=	=	PUNCT
ejpam-5062	466	1	y.	y.	PROPN
ejpam-5062	466	2	now	now	ADV
ejpam-5062	466	3	,	,	PUNCT
ejpam-5062	466	4	since	since	SCONJ
ejpam-5062	466	5	{	{	PUNCT
ejpam-5062	466	6	f−1(ui	f−1(ui	PROPN
ejpam-5062	466	7	)	)	PUNCT
ejpam-5062	466	8	,	,	PUNCT
ejpam-5062	466	9	i	i	PRON
ejpam-5062	466	10	∈	∈	PROPN
ejpam-5062	466	11	k	k	AUX
ejpam-5062	466	12	}	}	PUNCT
ejpam-5062	466	13	is	be	AUX
ejpam-5062	466	14	a	a	DET
ejpam-5062	466	15	finite	finite	NOUN
ejpam-5062	466	16	α−sspo	α−sspo	NOUN
ejpam-5062	466	17	subshading	subshade	VERB
ejpam-5062	466	18	of	of	ADP
ejpam-5062	466	19	x	x	PRON
ejpam-5062	466	20	,	,	PUNCT
ejpam-5062	466	21	there	there	PRON
ejpam-5062	466	22	exists	exist	VERB
ejpam-5062	466	23	m	m	VERB
ejpam-5062	466	24	∈	∈	ADJ
ejpam-5062	466	25	k	k	ADJ
ejpam-5062	466	26	such	such	ADJ
ejpam-5062	466	27	that	that	DET
ejpam-5062	466	28	f−1(um)(x	f−1(um)(x	NOUN
ejpam-5062	466	29	)	)	PUNCT
ejpam-5062	466	30	>	>	PUNCT
ejpam-5062	467	1	α	α	PROPN
ejpam-5062	467	2	and	and	CCONJ
ejpam-5062	467	3	therefore	therefore	ADV
ejpam-5062	467	4	f−1(um)(x	f−1(um)(x	ADJ
ejpam-5062	467	5	)	)	PUNCT
ejpam-5062	467	6	=	=	SYM
ejpam-5062	467	7	um(f(x	um(f(x	NOUN
ejpam-5062	467	8	)	)	PUNCT
ejpam-5062	467	9	)	)	PUNCT
ejpam-5062	468	1	=	=	PUNCT
ejpam-5062	468	2	um(y	um(y	PROPN
ejpam-5062	468	3	)	)	PUNCT
ejpam-5062	468	4	>	>	X
ejpam-5062	469	1	α	α	X
ejpam-5062	469	2	.	.	PUNCT
ejpam-5062	470	1	we	we	PRON
ejpam-5062	470	2	showed	show	VERB
ejpam-5062	470	3	that	that	SCONJ
ejpam-5062	470	4	for	for	ADP
ejpam-5062	470	5	any	any	DET
ejpam-5062	470	6	α	α	PRON
ejpam-5062	470	7	-	-	PUNCT
ejpam-5062	470	8	shading	shade	VERB
ejpam-5062	470	9	u	u	NOUN
ejpam-5062	470	10	=	=	SYM
ejpam-5062	470	11	{	{	PUNCT
ejpam-5062	470	12	ui	ui	PROPN
ejpam-5062	470	13	,	,	PUNCT
ejpam-5062	470	14	i	i	PRON
ejpam-5062	470	15	∈	∈	VERB
ejpam-5062	471	1	i	i	X
ejpam-5062	471	2	}	}	PUNCT
ejpam-5062	471	3	of	of	ADP
ejpam-5062	471	4	y	y	PROPN
ejpam-5062	471	5	there	there	PRON
ejpam-5062	471	6	exists	exist	VERB
ejpam-5062	471	7	a	a	DET
ejpam-5062	471	8	finite	finite	NOUN
ejpam-5062	471	9	α	α	NOUN
ejpam-5062	471	10	-	-	ADJ
ejpam-5062	471	11	subshading	subshade	VERB
ejpam-5062	471	12	{	{	PUNCT
ejpam-5062	471	13	ui	ui	PROPN
ejpam-5062	471	14	,	,	PUNCT
ejpam-5062	471	15	i	i	PROPN
ejpam-5062	471	16	∈	∈	PROPN
ejpam-5062	471	17	k	k	X
ejpam-5062	471	18	}	}	PUNCT
ejpam-5062	471	19	and	and	CCONJ
ejpam-5062	471	20	hence	hence	ADV
ejpam-5062	471	21	y	y	PROPN
ejpam-5062	471	22	is	be	AUX
ejpam-5062	471	23	an	an	DET
ejpam-5062	471	24	α	α	NOUN
ejpam-5062	471	25	-	-	ADJ
ejpam-5062	471	26	compact	compact	ADJ
ejpam-5062	471	27	set	set	NOUN
ejpam-5062	471	28	.	.	PUNCT
ejpam-5062	472	1	the	the	DET
ejpam-5062	472	2	proof	proof	NOUN
ejpam-5062	472	3	of	of	ADP
ejpam-5062	472	4	the	the	DET
ejpam-5062	472	5	case	case	NOUN
ejpam-5062	472	6	when	when	SCONJ
ejpam-5062	472	7	x	x	PRON
ejpam-5062	472	8	is	be	AUX
ejpam-5062	472	9	α∗	α∗	NOUN
ejpam-5062	472	10	−	−	NOUN
ejpam-5062	472	11	sspo	sspo	NOUN
ejpam-5062	472	12	compact	compact	NOUN
ejpam-5062	472	13	is	be	AUX
ejpam-5062	472	14	similar	similar	ADJ
ejpam-5062	472	15	and	and	CCONJ
ejpam-5062	472	16	is	be	AUX
ejpam-5062	472	17	therefore	therefore	ADV
ejpam-5062	472	18	omitted	omit	VERB
ejpam-5062	472	19	.	.	PUNCT
ejpam-5062	473	1	theorem	theorem	VERB
ejpam-5062	473	2	26	26	NUM
ejpam-5062	473	3	.	.	PUNCT
ejpam-5062	474	1	let	let	VERB
ejpam-5062	474	2	the	the	DET
ejpam-5062	474	3	mapping	mapping	NOUN
ejpam-5062	474	4	f	f	X
ejpam-5062	474	5	:	:	PUNCT
ejpam-5062	474	6	x	x	X
ejpam-5062	474	7	→	→	SYM
ejpam-5062	474	8	y	y	X
ejpam-5062	474	9	be	be	AUX
ejpam-5062	474	10	a	a	DET
ejpam-5062	474	11	fuzzy	fuzzy	ADJ
ejpam-5062	474	12	sspo	sspo	NOUN
ejpam-5062	474	13	homeomorphism	homeomorphism	PROPN
ejpam-5062	474	14	from	from	ADP
ejpam-5062	474	15	the	the	DET
ejpam-5062	474	16	fuzzy	fuzzy	ADJ
ejpam-5062	474	17	topological	topological	ADJ
ejpam-5062	474	18	space	space	NOUN
ejpam-5062	474	19	x	x	PUNCT
ejpam-5062	474	20	to	to	ADP
ejpam-5062	474	21	a	a	DET
ejpam-5062	474	22	fuzzy	fuzzy	ADJ
ejpam-5062	474	23	topological	topological	ADJ
ejpam-5062	474	24	space	space	NOUN
ejpam-5062	474	25	y	y	PROPN
ejpam-5062	474	26	.	.	PUNCT
ejpam-5062	475	1	if	if	SCONJ
ejpam-5062	475	2	the	the	DET
ejpam-5062	475	3	fuzzy	fuzzy	NOUN
ejpam-5062	475	4	set	set	VERB
ejpam-5062	475	5	a	a	PRON
ejpam-5062	475	6	is	be	AUX
ejpam-5062	475	7	α	α	DET
ejpam-5062	475	8	−	−	NOUN
ejpam-5062	475	9	sspo	sspo	NOUN
ejpam-5062	475	10	compact	compact	ADJ
ejpam-5062	475	11	(	(	PUNCT
ejpam-5062	475	12	α∗−sspo	α∗−sspo	PROPN
ejpam-5062	475	13	compact	compact	ADJ
ejpam-5062	475	14	)	)	PUNCT
ejpam-5062	475	15	then	then	ADV
ejpam-5062	475	16	f(a	f(a	PROPN
ejpam-5062	475	17	)	)	PUNCT
ejpam-5062	475	18	is	be	AUX
ejpam-5062	475	19	an	an	DET
ejpam-5062	475	20	α−sspo	α−sspo	X
ejpam-5062	475	21	compact	compact	ADJ
ejpam-5062	475	22	(	(	PUNCT
ejpam-5062	475	23	α∗−sspo	α∗−sspo	PROPN
ejpam-5062	475	24	compact	compact	ADJ
ejpam-5062	475	25	)	)	PUNCT
ejpam-5062	475	26	.	.	PUNCT
ejpam-5062	476	1	proof	proof	NOUN
ejpam-5062	476	2	.	.	PUNCT
ejpam-5062	477	1	similar	similar	ADJ
ejpam-5062	477	2	to	to	ADP
ejpam-5062	477	3	theorem	theorem	VERB
ejpam-5062	477	4	25	25	NUM
ejpam-5062	477	5	.	.	PUNCT
ejpam-5062	477	6	corollary	corollary	ADJ
ejpam-5062	477	7	9	9	NUM
ejpam-5062	477	8	.	.	PUNCT
ejpam-5062	478	1	let	let	VERB
ejpam-5062	478	2	the	the	DET
ejpam-5062	478	3	mapping	mapping	NOUN
ejpam-5062	478	4	f	f	X
ejpam-5062	478	5	:	:	PUNCT
ejpam-5062	478	6	x	x	X
ejpam-5062	478	7	→	→	SYM
ejpam-5062	478	8	y	y	X
ejpam-5062	478	9	be	be	AUX
ejpam-5062	478	10	a	a	DET
ejpam-5062	478	11	fuzzy	fuzzy	ADJ
ejpam-5062	478	12	sspo	sspo	NOUN
ejpam-5062	478	13	homeomorphism	homeomorphism	PROPN
ejpam-5062	478	14	from	from	ADP
ejpam-5062	478	15	the	the	DET
ejpam-5062	478	16	fuzzy	fuzzy	ADJ
ejpam-5062	478	17	topological	topological	ADJ
ejpam-5062	478	18	space	space	NOUN
ejpam-5062	478	19	x	x	PUNCT
ejpam-5062	478	20	to	to	ADP
ejpam-5062	478	21	a	a	DET
ejpam-5062	478	22	fuzzy	fuzzy	ADJ
ejpam-5062	478	23	topological	topological	ADJ
ejpam-5062	478	24	space	space	NOUN
ejpam-5062	478	25	y	y	PROPN
ejpam-5062	478	26	.	.	PUNCT
ejpam-5062	479	1	if	if	SCONJ
ejpam-5062	479	2	x	x	PRON
ejpam-5062	479	3	is	be	AUX
ejpam-5062	479	4	α	α	PRON
ejpam-5062	479	5	−	−	PROPN
ejpam-5062	479	6	sspo	sspo	NOUN
ejpam-5062	479	7	compact	compact	ADJ
ejpam-5062	479	8	(	(	PUNCT
ejpam-5062	479	9	α∗	α∗	NOUN
ejpam-5062	479	10	−	−	NOUN
ejpam-5062	479	11	sspo	sspo	NOUN
ejpam-5062	479	12	compact	compact	ADJ
ejpam-5062	479	13	)	)	PUNCT
ejpam-5062	479	14	then	then	ADV
ejpam-5062	479	15	y	y	PROPN
ejpam-5062	479	16	is	be	AUX
ejpam-5062	479	17	an	an	DET
ejpam-5062	479	18	α−	α−	X
ejpam-5062	479	19	sspo	sspo	NOUN
ejpam-5062	479	20	compact	compact	ADJ
ejpam-5062	479	21	(	(	PUNCT
ejpam-5062	479	22	α∗	α∗	NOUN
ejpam-5062	479	23	−	−	NOUN
ejpam-5062	479	24	sspo	sspo	NOUN
ejpam-5062	479	25	compact	compact	ADJ
ejpam-5062	479	26	)	)	PUNCT
ejpam-5062	479	27	.	.	PUNCT
ejpam-5062	480	1	theorem	theorem	NOUN
ejpam-5062	480	2	27	27	NUM
ejpam-5062	480	3	.	.	PUNCT
ejpam-5062	481	1	let	let	VERB
ejpam-5062	481	2	the	the	DET
ejpam-5062	481	3	mapping	mapping	NOUN
ejpam-5062	481	4	f	f	X
ejpam-5062	481	5	:	:	PUNCT
ejpam-5062	481	6	x	x	X
ejpam-5062	481	7	→	→	SYM
ejpam-5062	481	8	y	y	X
ejpam-5062	481	9	be	be	AUX
ejpam-5062	481	10	a	a	DET
ejpam-5062	481	11	fuzzy	fuzzy	ADJ
ejpam-5062	481	12	sspo	sspo	NOUN
ejpam-5062	481	13	homeomorphism	homeomorphism	PROPN
ejpam-5062	481	14	from	from	ADP
ejpam-5062	481	15	the	the	DET
ejpam-5062	481	16	fuzzy	fuzzy	ADJ
ejpam-5062	481	17	topological	topological	ADJ
ejpam-5062	481	18	space	space	NOUN
ejpam-5062	481	19	x	x	PUNCT
ejpam-5062	481	20	to	to	ADP
ejpam-5062	481	21	a	a	DET
ejpam-5062	481	22	fuzzy	fuzzy	ADJ
ejpam-5062	481	23	topological	topological	ADJ
ejpam-5062	481	24	space	space	NOUN
ejpam-5062	481	25	y	y	PROPN
ejpam-5062	481	26	.	.	PUNCT
ejpam-5062	482	1	if	if	SCONJ
ejpam-5062	482	2	x	x	PRON
ejpam-5062	482	3	is	be	AUX
ejpam-5062	482	4	α	α	PRON
ejpam-5062	482	5	−	−	PROPN
ejpam-5062	482	6	sspo	sspo	NOUN
ejpam-5062	482	7	compact	compact	ADJ
ejpam-5062	482	8	(	(	PUNCT
ejpam-5062	482	9	α∗	α∗	NOUN
ejpam-5062	482	10	−	−	NOUN
ejpam-5062	482	11	sspo	sspo	NOUN
ejpam-5062	482	12	compact	compact	ADJ
ejpam-5062	482	13	)	)	PUNCT
ejpam-5062	482	14	then	then	ADV
ejpam-5062	482	15	y	y	PROPN
ejpam-5062	482	16	is	be	AUX
ejpam-5062	482	17	an	an	DET
ejpam-5062	482	18	α	α	NOUN
ejpam-5062	482	19	-	-	ADJ
ejpam-5062	482	20	compact	compact	ADJ
ejpam-5062	482	21	(	(	PUNCT
ejpam-5062	482	22	α∗-compact	α∗-compact	NUM
ejpam-5062	482	23	)	)	PUNCT
ejpam-5062	482	24	.	.	PUNCT
ejpam-5062	483	1	proof	proof	NOUN
ejpam-5062	483	2	.	.	PUNCT
ejpam-5062	484	1	it	it	PRON
ejpam-5062	484	2	follows	follow	VERB
ejpam-5062	484	3	immediately	immediately	ADV
ejpam-5062	484	4	from	from	ADP
ejpam-5062	484	5	theorem	theorem	ADJ
ejpam-5062	484	6	25	25	NUM
ejpam-5062	484	7	.	.	PUNCT
ejpam-5062	485	1	corollary	corollary	ADJ
ejpam-5062	485	2	10	10	NUM
ejpam-5062	485	3	.	.	PUNCT
ejpam-5062	486	1	let	let	VERB
ejpam-5062	486	2	the	the	DET
ejpam-5062	486	3	mapping	mapping	NOUN
ejpam-5062	486	4	f	f	X
ejpam-5062	486	5	:	:	PUNCT
ejpam-5062	486	6	x	x	X
ejpam-5062	486	7	→	→	SYM
ejpam-5062	486	8	y	y	X
ejpam-5062	486	9	be	be	AUX
ejpam-5062	486	10	a	a	DET
ejpam-5062	486	11	fuzzy	fuzzy	ADJ
ejpam-5062	486	12	sspo	sspo	NOUN
ejpam-5062	486	13	homeomorphism	homeomorphism	PROPN
ejpam-5062	486	14	from	from	ADP
ejpam-5062	486	15	the	the	DET
ejpam-5062	486	16	fuzzy	fuzzy	ADJ
ejpam-5062	486	17	topological	topological	ADJ
ejpam-5062	486	18	space	space	NOUN
ejpam-5062	486	19	x	x	PUNCT
ejpam-5062	486	20	to	to	ADP
ejpam-5062	486	21	a	a	DET
ejpam-5062	486	22	fuzzy	fuzzy	ADJ
ejpam-5062	486	23	topological	topological	ADJ
ejpam-5062	486	24	space	space	NOUN
ejpam-5062	486	25	y	y	PROPN
ejpam-5062	486	26	.	.	PUNCT
ejpam-5062	487	1	if	if	SCONJ
ejpam-5062	487	2	y	y	PROPN
ejpam-5062	487	3	is	be	AUX
ejpam-5062	487	4	α	α	PRON
ejpam-5062	487	5	−	−	PROPN
ejpam-5062	487	6	sspo	sspo	NOUN
ejpam-5062	487	7	compact	compact	ADJ
ejpam-5062	487	8	(	(	PUNCT
ejpam-5062	487	9	α∗	α∗	NOUN
ejpam-5062	487	10	−	−	NOUN
ejpam-5062	487	11	sspo	sspo	NOUN
ejpam-5062	487	12	compact	compact	ADJ
ejpam-5062	487	13	)	)	PUNCT
ejpam-5062	487	14	then	then	ADV
ejpam-5062	487	15	x	x	X
ejpam-5062	487	16	is	be	AUX
ejpam-5062	487	17	an	an	DET
ejpam-5062	487	18	α	α	NOUN
ejpam-5062	487	19	-	-	ADJ
ejpam-5062	487	20	compact	compact	ADJ
ejpam-5062	487	21	(	(	PUNCT
ejpam-5062	487	22	α∗-compact	α∗-compact	NUM
ejpam-5062	487	23	)	)	PUNCT
ejpam-5062	487	24	.	.	PUNCT
ejpam-5062	488	1	sh	sh	PROPN
ejpam-5062	488	2	.	.	PROPN
ejpam-5062	488	3	makolli	makolli	PROPN
ejpam-5062	488	4	,	,	PUNCT
ejpam-5062	488	5	b.	b.	PROPN
ejpam-5062	488	6	krsteska	krsteska	PROPN
ejpam-5062	488	7	/	/	SYM
ejpam-5062	488	8	eur	eur	PROPN
ejpam-5062	488	9	.	.	PUNCT
ejpam-5062	489	1	j.	j.	PROPN
ejpam-5062	489	2	pure	pure	PROPN
ejpam-5062	489	3	appl	appl	PROPN
ejpam-5062	489	4	.	.	PROPN
ejpam-5062	489	5	math	math	PROPN
ejpam-5062	489	6	,	,	PUNCT
ejpam-5062	489	7	17	17	NUM
ejpam-5062	489	8	(	(	PUNCT
ejpam-5062	489	9	2	2	NUM
ejpam-5062	489	10	)	)	PUNCT
ejpam-5062	489	11	(	(	PUNCT
ejpam-5062	489	12	2024	2024	NUM
ejpam-5062	489	13	)	)	PUNCT
ejpam-5062	489	14	,	,	PUNCT
ejpam-5062	489	15	638	638	NUM
ejpam-5062	489	16	-	-	SYM
ejpam-5062	489	17	662	662	NUM
ejpam-5062	489	18	656	656	NUM
ejpam-5062	489	19	proof	proof	NOUN
ejpam-5062	489	20	.	.	PUNCT
ejpam-5062	490	1	it	it	PRON
ejpam-5062	490	2	follows	follow	VERB
ejpam-5062	490	3	immediately	immediately	ADV
ejpam-5062	490	4	from	from	ADP
ejpam-5062	490	5	theorem	theorem	ADJ
ejpam-5062	490	6	27	27	NUM
ejpam-5062	490	7	.	.	PUNCT
ejpam-5062	491	1	and	and	CCONJ
ejpam-5062	491	2	from	from	ADP
ejpam-5062	491	3	the	the	DET
ejpam-5062	491	4	fact	fact	NOUN
ejpam-5062	491	5	that	that	SCONJ
ejpam-5062	491	6	f−1	f−1	PROPN
ejpam-5062	491	7	:	:	PUNCT
ejpam-5062	491	8	y	y	PROPN
ejpam-5062	491	9	→	→	PUNCT
ejpam-5062	491	10	x	x	X
ejpam-5062	491	11	is	be	AUX
ejpam-5062	491	12	also	also	ADV
ejpam-5062	491	13	a	a	DET
ejpam-5062	491	14	fuzzy	fuzzy	ADJ
ejpam-5062	491	15	sspo	sspo	NOUN
ejpam-5062	491	16	homeomorphism	homeomorphism	X
ejpam-5062	491	17	.	.	PUNCT
ejpam-5062	492	1	definition	definition	NOUN
ejpam-5062	492	2	24	24	NUM
ejpam-5062	492	3	.	.	PUNCT
ejpam-5062	493	1	the	the	DET
ejpam-5062	493	2	family	family	PROPN
ejpam-5062	493	3	b	b	PROPN
ejpam-5062	493	4	of	of	ADP
ejpam-5062	493	5	fuzzy	fuzzy	ADJ
ejpam-5062	493	6	strongly	strongly	ADV
ejpam-5062	493	7	semi	semi	ADV
ejpam-5062	493	8	pre	pre	ADJ
ejpam-5062	493	9	-	-	ADJ
ejpam-5062	493	10	open	open	ADJ
ejpam-5062	493	11	sets	set	NOUN
ejpam-5062	493	12	of	of	ADP
ejpam-5062	493	13	the	the	DET
ejpam-5062	493	14	fuzzy	fuzzy	ADJ
ejpam-5062	493	15	topological	topological	ADJ
ejpam-5062	493	16	space	space	NOUN
ejpam-5062	493	17	(	(	PUNCT
ejpam-5062	493	18	x	x	X
ejpam-5062	493	19	,	,	PUNCT
ejpam-5062	493	20	τ	τ	X
ejpam-5062	493	21	)	)	PUNCT
ejpam-5062	493	22	is	be	AUX
ejpam-5062	493	23	called	call	VERB
ejpam-5062	493	24	a	a	DET
ejpam-5062	493	25	base	base	NOUN
ejpam-5062	493	26	of	of	ADP
ejpam-5062	493	27	fuzzy	fuzzy	ADJ
ejpam-5062	493	28	strongly	strongly	ADV
ejpam-5062	493	29	semi	semi	ADV
ejpam-5062	493	30	pre	pre	ADJ
ejpam-5062	493	31	-	-	ADJ
ejpam-5062	493	32	open	open	ADJ
ejpam-5062	493	33	sets	set	NOUN
ejpam-5062	493	34	in	in	ADP
ejpam-5062	493	35	(	(	PUNCT
ejpam-5062	493	36	x	x	NOUN
ejpam-5062	493	37	,	,	PUNCT
ejpam-5062	493	38	τ	τ	X
ejpam-5062	493	39	)	)	PUNCT
ejpam-5062	493	40	if	if	SCONJ
ejpam-5062	493	41	every	every	DET
ejpam-5062	493	42	fuzzy	fuzzy	ADJ
ejpam-5062	493	43	strongly	strongly	ADV
ejpam-5062	493	44	semi	semi	ADV
ejpam-5062	493	45	pre	pre	ADJ
ejpam-5062	493	46	-	-	ADJ
ejpam-5062	493	47	open	open	ADJ
ejpam-5062	493	48	set	set	NOUN
ejpam-5062	493	49	of	of	ADP
ejpam-5062	493	50	(	(	PUNCT
ejpam-5062	493	51	x	x	PROPN
ejpam-5062	493	52	,	,	PUNCT
ejpam-5062	493	53	τ	τ	X
ejpam-5062	493	54	)	)	PUNCT
ejpam-5062	493	55	can	can	AUX
ejpam-5062	493	56	be	be	AUX
ejpam-5062	493	57	written	write	VERB
ejpam-5062	493	58	as	as	ADP
ejpam-5062	493	59	union	union	NOUN
ejpam-5062	493	60	of	of	ADP
ejpam-5062	493	61	members	member	NOUN
ejpam-5062	493	62	of	of	ADP
ejpam-5062	493	63	b.	b.	PROPN
ejpam-5062	493	64	theorem	theorem	PROPN
ejpam-5062	493	65	28	28	NUM
ejpam-5062	493	66	.	.	PUNCT
ejpam-5062	494	1	if	if	SCONJ
ejpam-5062	494	2	the	the	DET
ejpam-5062	494	3	fuzzy	fuzzy	ADJ
ejpam-5062	494	4	topological	topological	ADJ
ejpam-5062	494	5	space	space	NOUN
ejpam-5062	494	6	(	(	PUNCT
ejpam-5062	494	7	x	x	X
ejpam-5062	494	8	,	,	PUNCT
ejpam-5062	494	9	τ	τ	X
ejpam-5062	494	10	)	)	PUNCT
ejpam-5062	494	11	has	have	VERB
ejpam-5062	494	12	a	a	DET
ejpam-5062	494	13	countable	countable	ADJ
ejpam-5062	494	14	base	base	NOUN
ejpam-5062	494	15	of	of	ADP
ejpam-5062	494	16	fuzzy	fuzzy	ADJ
ejpam-5062	494	17	strongly	strongly	ADV
ejpam-5062	494	18	semi	semi	ADV
ejpam-5062	494	19	pre	pre	ADJ
ejpam-5062	494	20	-	-	ADJ
ejpam-5062	494	21	open	open	ADJ
ejpam-5062	494	22	sets	set	NOUN
ejpam-5062	494	23	then	then	ADV
ejpam-5062	494	24	any	any	DET
ejpam-5062	494	25	fuzzy	fuzzy	ADJ
ejpam-5062	494	26	set	set	VERB
ejpam-5062	494	27	a	a	PRON
ejpam-5062	494	28	in	in	ADP
ejpam-5062	494	29	(	(	PUNCT
ejpam-5062	494	30	x	x	NOUN
ejpam-5062	494	31	,	,	PUNCT
ejpam-5062	494	32	τ	τ	X
ejpam-5062	494	33	)	)	PUNCT
ejpam-5062	494	34	is	be	AUX
ejpam-5062	494	35	α	α	NUM
ejpam-5062	494	36	−	−	PROPN
ejpam-5062	494	37	sspo	sspo	NOUN
ejpam-5062	494	38	compact	compact	ADJ
ejpam-5062	494	39	(	(	PUNCT
ejpam-5062	494	40	α∗	α∗	NOUN
ejpam-5062	494	41	−	−	NOUN
ejpam-5062	494	42	sspo	sspo	NOUN
ejpam-5062	494	43	compact	compact	ADJ
ejpam-5062	494	44	)	)	PUNCT
ejpam-5062	494	45	if	if	SCONJ
ejpam-5062	494	46	and	and	CCONJ
ejpam-5062	494	47	only	only	ADV
ejpam-5062	494	48	if	if	SCONJ
ejpam-5062	494	49	it	it	PRON
ejpam-5062	494	50	is	be	AUX
ejpam-5062	494	51	countable	countable	ADJ
ejpam-5062	494	52	α−sspo	α−sspo	X
ejpam-5062	494	53	compact	compact	ADJ
ejpam-5062	494	54	(	(	PUNCT
ejpam-5062	494	55	countable	countable	ADJ
ejpam-5062	494	56	α∗−sspo	α∗−sspo	PROPN
ejpam-5062	494	57	compact	compact	ADJ
ejpam-5062	494	58	)	)	PUNCT
ejpam-5062	494	59	.	.	PUNCT
ejpam-5062	495	1	proof	proof	NOUN
ejpam-5062	495	2	.	.	PUNCT
ejpam-5062	496	1	it	it	PRON
ejpam-5062	496	2	is	be	AUX
ejpam-5062	496	3	certain	certain	ADJ
ejpam-5062	496	4	that	that	SCONJ
ejpam-5062	496	5	every	every	DET
ejpam-5062	496	6	α	α	NOUN
ejpam-5062	496	7	−	−	NOUN
ejpam-5062	496	8	sspo	sspo	NOUN
ejpam-5062	496	9	compact	compact	ADJ
ejpam-5062	496	10	set	set	VERB
ejpam-5062	496	11	in	in	ADP
ejpam-5062	496	12	the	the	DET
ejpam-5062	496	13	fuzzy	fuzzy	ADJ
ejpam-5062	496	14	topological	topological	ADJ
ejpam-5062	496	15	space	space	NOUN
ejpam-5062	496	16	(	(	PUNCT
ejpam-5062	496	17	x	x	X
ejpam-5062	496	18	,	,	PUNCT
ejpam-5062	496	19	τ	τ	X
ejpam-5062	496	20	)	)	PUNCT
ejpam-5062	496	21	is	be	AUX
ejpam-5062	496	22	also	also	ADV
ejpam-5062	496	23	a	a	DET
ejpam-5062	496	24	countable	countable	ADJ
ejpam-5062	496	25	α−	α−	ADP
ejpam-5062	496	26	sspo	sspo	NOUN
ejpam-5062	496	27	compact	compact	ADJ
ejpam-5062	496	28	fuzzy	fuzzy	ADJ
ejpam-5062	496	29	set	set	NOUN
ejpam-5062	496	30	.	.	PUNCT
ejpam-5062	497	1	conversely	conversely	ADV
ejpam-5062	497	2	,	,	PUNCT
ejpam-5062	497	3	let	let	VERB
ejpam-5062	497	4	us	we	PRON
ejpam-5062	497	5	suppose	suppose	VERB
ejpam-5062	497	6	that	that	SCONJ
ejpam-5062	497	7	the	the	DET
ejpam-5062	497	8	fuzzy	fuzzy	NOUN
ejpam-5062	497	9	set	set	VERB
ejpam-5062	497	10	a	a	DET
ejpam-5062	497	11	in	in	ADP
ejpam-5062	497	12	(	(	PUNCT
ejpam-5062	497	13	x	x	NOUN
ejpam-5062	497	14	,	,	PUNCT
ejpam-5062	497	15	τ	τ	X
ejpam-5062	497	16	)	)	PUNCT
ejpam-5062	497	17	is	be	AUX
ejpam-5062	497	18	countable	countable	ADJ
ejpam-5062	497	19	α−sspo	α−sspo	PUNCT
ejpam-5062	497	20	compact	compact	ADJ
ejpam-5062	497	21	.	.	PUNCT
ejpam-5062	498	1	let	let	VERB
ejpam-5062	498	2	us	we	PRON
ejpam-5062	498	3	suppose	suppose	VERB
ejpam-5062	498	4	that	that	SCONJ
ejpam-5062	498	5	the	the	DET
ejpam-5062	498	6	family	family	NOUN
ejpam-5062	498	7	of	of	ADP
ejpam-5062	498	8	fuzzy	fuzzy	ADJ
ejpam-5062	498	9	strongly	strongly	ADV
ejpam-5062	498	10	semi	semi	ADV
ejpam-5062	498	11	pre	pre	ADJ
ejpam-5062	498	12	-	-	ADJ
ejpam-5062	498	13	open	open	ADJ
ejpam-5062	498	14	sets	set	VERB
ejpam-5062	498	15	u	u	NOUN
ejpam-5062	498	16	=	=	SYM
ejpam-5062	498	17	{	{	PUNCT
ejpam-5062	498	18	ui	ui	PROPN
ejpam-5062	498	19	,	,	PUNCT
ejpam-5062	498	20	i	i	PRON
ejpam-5062	498	21	∈	∈	VERB
ejpam-5062	498	22	i	i	PRON
ejpam-5062	498	23	}	}	PUNCT
ejpam-5062	498	24	is	be	AUX
ejpam-5062	498	25	an	an	DET
ejpam-5062	498	26	α	α	NOUN
ejpam-5062	498	27	−	−	NOUN
ejpam-5062	498	28	sspo	sspo	NOUN
ejpam-5062	498	29	shading	shading	NOUN
ejpam-5062	498	30	of	of	ADP
ejpam-5062	498	31	a.	a.	NOUN
ejpam-5062	498	32	since	since	SCONJ
ejpam-5062	498	33	(	(	PUNCT
ejpam-5062	498	34	x	x	NOUN
ejpam-5062	498	35	,	,	PUNCT
ejpam-5062	498	36	τ	τ	X
ejpam-5062	498	37	)	)	PUNCT
ejpam-5062	498	38	has	have	VERB
ejpam-5062	498	39	a	a	DET
ejpam-5062	498	40	countable	countable	ADJ
ejpam-5062	498	41	base	base	NOUN
ejpam-5062	498	42	b	b	NOUN
ejpam-5062	498	43	=	=	SYM
ejpam-5062	498	44	{	{	PUNCT
ejpam-5062	498	45	wi	wi	PROPN
ejpam-5062	498	46	,	,	PUNCT
ejpam-5062	498	47	i	i	PROPN
ejpam-5062	498	48	∈	∈	PROPN
ejpam-5062	498	49	n	n	CCONJ
ejpam-5062	498	50	}	}	PUNCT
ejpam-5062	498	51	of	of	ADP
ejpam-5062	498	52	fuzzy	fuzzy	ADJ
ejpam-5062	498	53	strongly	strongly	ADV
ejpam-5062	498	54	semi	semi	ADV
ejpam-5062	498	55	pre	pre	ADJ
ejpam-5062	498	56	-	-	ADJ
ejpam-5062	498	57	open	open	ADJ
ejpam-5062	498	58	sets	set	NOUN
ejpam-5062	498	59	wi	wi	PROPN
ejpam-5062	498	60	,	,	PUNCT
ejpam-5062	498	61	then	then	ADV
ejpam-5062	498	62	any	any	DET
ejpam-5062	498	63	fuzzy	fuzzy	ADJ
ejpam-5062	498	64	strongly	strongly	ADV
ejpam-5062	498	65	semi	semi	ADV
ejpam-5062	498	66	pre	pre	ADJ
ejpam-5062	498	67	-	-	ADJ
ejpam-5062	498	68	open	open	ADJ
ejpam-5062	498	69	set	set	NOUN
ejpam-5062	498	70	can	can	AUX
ejpam-5062	498	71	be	be	AUX
ejpam-5062	498	72	represented	represent	VERB
ejpam-5062	498	73	as	as	ADP
ejpam-5062	498	74	union	union	NOUN
ejpam-5062	498	75	of	of	ADP
ejpam-5062	498	76	sets	set	NOUN
ejpam-5062	498	77	from	from	ADP
ejpam-5062	498	78	b.	b.	PROPN
ejpam-5062	498	79	now	now	ADV
ejpam-5062	498	80	let	let	VERB
ejpam-5062	498	81	a	a	DET
ejpam-5062	498	82	∈	∈	PROPN
ejpam-5062	498	83	suppa	suppa	NOUN
ejpam-5062	498	84	,	,	PUNCT
ejpam-5062	498	85	there	there	PRON
ejpam-5062	498	86	exists	exist	VERB
ejpam-5062	498	87	uj	uj	PROPN
ejpam-5062	498	88	∈	∈	PROPN
ejpam-5062	498	89	u	u	PROPN
ejpam-5062	498	90	,	,	PUNCT
ejpam-5062	498	91	for	for	ADP
ejpam-5062	498	92	some	some	PRON
ejpam-5062	498	93	j	j	PROPN
ejpam-5062	498	94	∈	∈	PROPN
ejpam-5062	499	1	i	i	PRON
ejpam-5062	499	2	,	,	PUNCT
ejpam-5062	499	3	such	such	ADJ
ejpam-5062	499	4	that	that	SCONJ
ejpam-5062	499	5	uj(a	uj(a	NOUN
ejpam-5062	499	6	)	)	PUNCT
ejpam-5062	499	7	>	>	X
ejpam-5062	500	1	α	α	X
ejpam-5062	500	2	.	.	PUNCT
ejpam-5062	501	1	there	there	PRON
ejpam-5062	501	2	are	be	VERB
ejpam-5062	501	3	fuzzy	fuzzy	ADJ
ejpam-5062	501	4	strongly	strongly	ADV
ejpam-5062	501	5	semi	semi	ADJ
ejpam-5062	501	6	pre	pre	ADJ
ejpam-5062	501	7	-	-	ADJ
ejpam-5062	501	8	open	open	ADJ
ejpam-5062	501	9	sets	set	NOUN
ejpam-5062	501	10	wik	wik	PROPN
ejpam-5062	501	11	)	)	PUNCT
ejpam-5062	501	12	,	,	PUNCT
ejpam-5062	501	13	k	k	PROPN
ejpam-5062	501	14	=	=	SYM
ejpam-5062	501	15	1	1	NUM
ejpam-5062	501	16	,	,	PUNCT
ejpam-5062	501	17	2	2	NUM
ejpam-5062	501	18	,	,	PUNCT
ejpam-5062	501	19	.	.	PUNCT
ejpam-5062	501	20	.	.	PUNCT
ejpam-5062	502	1	.	.	PUNCT
ejpam-5062	503	1	,	,	PUNCT
ejpam-5062	503	2	m	m	PROPN
ejpam-5062	503	3	(	(	PUNCT
ejpam-5062	503	4	note	note	VERB
ejpam-5062	503	5	that	that	SCONJ
ejpam-5062	503	6	m	m	NOUN
ejpam-5062	503	7	must	must	AUX
ejpam-5062	503	8	not	not	PART
ejpam-5062	503	9	be	be	AUX
ejpam-5062	503	10	a	a	DET
ejpam-5062	503	11	finite	finite	ADJ
ejpam-5062	503	12	number	number	NOUN
ejpam-5062	503	13	)	)	PUNCT
ejpam-5062	503	14	from	from	ADP
ejpam-5062	503	15	b	b	X
ejpam-5062	503	16	such	such	ADJ
ejpam-5062	503	17	that	that	DET
ejpam-5062	503	18	uj	uj	PROPN
ejpam-5062	503	19	=	=	NOUN
ejpam-5062	503	20	∨m	∨m	PROPN
ejpam-5062	503	21	k=1wik	k=1wik	PROPN
ejpam-5062	503	22	.	.	PUNCT
ejpam-5062	504	1	the	the	DET
ejpam-5062	504	2	fact	fact	NOUN
ejpam-5062	504	3	that	that	SCONJ
ejpam-5062	504	4	uj(a	uj(a	X
ejpam-5062	504	5	)	)	PUNCT
ejpam-5062	504	6	>	>	PUNCT
ejpam-5062	505	1	α	α	PROPN
ejpam-5062	505	2	implies	imply	VERB
ejpam-5062	505	3	the	the	DET
ejpam-5062	505	4	existence	existence	NOUN
ejpam-5062	505	5	of	of	ADP
ejpam-5062	505	6	wis	wis	PROPN
ejpam-5062	505	7	,	,	PUNCT
ejpam-5062	505	8	is	be	AUX
ejpam-5062	505	9	∈	∈	PROPN
ejpam-5062	505	10	{	{	PUNCT
ejpam-5062	505	11	1	1	NUM
ejpam-5062	505	12	,	,	PUNCT
ejpam-5062	505	13	2	2	NUM
ejpam-5062	505	14	,	,	PUNCT
ejpam-5062	505	15	.	.	PUNCT
ejpam-5062	505	16	.	.	PUNCT
ejpam-5062	506	1	.	.	PUNCT
ejpam-5062	507	1	,	,	PUNCT
ejpam-5062	507	2	m	m	VERB
ejpam-5062	507	3	}	}	PUNCT
ejpam-5062	507	4	such	such	ADJ
ejpam-5062	507	5	that	that	SCONJ
ejpam-5062	507	6	wis(a	wis(a	PROPN
ejpam-5062	507	7	)	)	PUNCT
ejpam-5062	507	8	>	>	X
ejpam-5062	508	1	α	α	X
ejpam-5062	508	2	.	.	PUNCT
ejpam-5062	509	1	we	we	PRON
ejpam-5062	509	2	can	can	AUX
ejpam-5062	509	3	now	now	ADV
ejpam-5062	509	4	claim	claim	VERB
ejpam-5062	509	5	that	that	SCONJ
ejpam-5062	509	6	the	the	DET
ejpam-5062	509	7	family	family	NOUN
ejpam-5062	509	8	of	of	ADP
ejpam-5062	509	9	fuzzy	fuzzy	ADJ
ejpam-5062	509	10	sets	set	NOUN
ejpam-5062	509	11	b0	b0	NOUN
ejpam-5062	509	12	=	=	SYM
ejpam-5062	509	13	{	{	PUNCT
ejpam-5062	509	14	wik	wik	PROPN
ejpam-5062	509	15	,	,	PUNCT
ejpam-5062	509	16	k	k	PROPN
ejpam-5062	509	17	=	=	SYM
ejpam-5062	509	18	1	1	NUM
ejpam-5062	509	19	,	,	PUNCT
ejpam-5062	509	20	2	2	NUM
ejpam-5062	509	21	,	,	PUNCT
ejpam-5062	509	22	.	.	PUNCT
ejpam-5062	509	23	.	.	PUNCT
ejpam-5062	509	24	.	.	PUNCT
ejpam-5062	510	1	,	,	PUNCT
ejpam-5062	510	2	m	m	AUX
ejpam-5062	510	3	}	}	PUNCT
ejpam-5062	510	4	is	be	AUX
ejpam-5062	510	5	a	a	DET
ejpam-5062	510	6	countable	countable	ADJ
ejpam-5062	510	7	α−sspo	α−sspo	NOUN
ejpam-5062	510	8	shading	shading	NOUN
ejpam-5062	510	9	of	of	ADP
ejpam-5062	510	10	a	a	DET
ejpam-5062	510	11	in	in	ADP
ejpam-5062	510	12	(	(	PUNCT
ejpam-5062	510	13	x	x	NOUN
ejpam-5062	510	14	,	,	PUNCT
ejpam-5062	510	15	τ	τ	PROPN
ejpam-5062	510	16	)	)	PUNCT
ejpam-5062	510	17	.	.	PUNCT
ejpam-5062	511	1	since	since	SCONJ
ejpam-5062	511	2	,	,	PUNCT
ejpam-5062	511	3	from	from	ADP
ejpam-5062	511	4	our	our	PRON
ejpam-5062	511	5	assumption	assumption	NOUN
ejpam-5062	511	6	,	,	PUNCT
ejpam-5062	511	7	a	a	PRON
ejpam-5062	511	8	is	be	AUX
ejpam-5062	511	9	countable	countable	ADJ
ejpam-5062	511	10	α−sspo	α−sspo	NOUN
ejpam-5062	511	11	compact	compact	ADJ
ejpam-5062	511	12	,	,	PUNCT
ejpam-5062	511	13	there	there	PRON
ejpam-5062	511	14	exist	exist	VERB
ejpam-5062	511	15	a	a	DET
ejpam-5062	511	16	finite	finite	NOUN
ejpam-5062	511	17	α	α	NOUN
ejpam-5062	511	18	−	−	PROPN
ejpam-5062	511	19	sspo	sspo	NOUN
ejpam-5062	511	20	subshading	subshade	VERB
ejpam-5062	511	21	b1	b1	NOUN
ejpam-5062	511	22	≤	≤	NUM
ejpam-5062	511	23	b0	b0	NOUN
ejpam-5062	511	24	.	.	PUNCT
ejpam-5062	512	1	if	if	SCONJ
ejpam-5062	512	2	we	we	PRON
ejpam-5062	512	3	consider	consider	VERB
ejpam-5062	512	4	the	the	DET
ejpam-5062	512	5	finite	finite	ADJ
ejpam-5062	512	6	collection	collection	NOUN
ejpam-5062	512	7	of	of	ADP
ejpam-5062	512	8	fuzzy	fuzzy	ADJ
ejpam-5062	512	9	strongly	strongly	ADV
ejpam-5062	512	10	semi	semi	ADV
ejpam-5062	512	11	pre	pre	ADJ
ejpam-5062	512	12	-	-	ADJ
ejpam-5062	512	13	open	open	ADJ
ejpam-5062	512	14	sets	set	NOUN
ejpam-5062	512	15	:	:	PUNCT
ejpam-5062	512	16	u0	u0	ADJ
ejpam-5062	512	17	=	=	PUNCT
ejpam-5062	512	18	{	{	PUNCT
ejpam-5062	512	19	ui	ui	NOUN
ejpam-5062	512	20	:	:	PUNCT
ejpam-5062	512	21	wis	wis	PROPN
ejpam-5062	512	22	≤	≤	PROPN
ejpam-5062	512	23	ui	ui	PROPN
ejpam-5062	512	24	,	,	PUNCT
ejpam-5062	512	25	wis	wis	PROPN
ejpam-5062	512	26	∈	∈	PROPN
ejpam-5062	512	27	b0	b0	NOUN
ejpam-5062	512	28	}	}	PUNCT
ejpam-5062	512	29	it	it	PRON
ejpam-5062	512	30	is	be	AUX
ejpam-5062	512	31	obvious	obvious	ADJ
ejpam-5062	512	32	that	that	SCONJ
ejpam-5062	512	33	u0	u0	PROPN
ejpam-5062	512	34	is	be	AUX
ejpam-5062	512	35	a	a	DET
ejpam-5062	512	36	finite	finite	NOUN
ejpam-5062	512	37	α	α	NOUN
ejpam-5062	512	38	−	−	PROPN
ejpam-5062	512	39	sspo	sspo	NOUN
ejpam-5062	512	40	subshading	subshading	NOUN
ejpam-5062	512	41	of	of	ADP
ejpam-5062	512	42	u	u	PROPN
ejpam-5062	512	43	and	and	CCONJ
ejpam-5062	512	44	as	as	SCONJ
ejpam-5062	512	45	consequence	consequence	NOUN
ejpam-5062	512	46	a	a	PRON
ejpam-5062	512	47	is	be	AUX
ejpam-5062	512	48	α−	α−	ADP
ejpam-5062	512	49	sspo	sspo	NOUN
ejpam-5062	512	50	compact	compact	ADJ
ejpam-5062	512	51	.	.	PUNCT
ejpam-5062	513	1	in	in	ADP
ejpam-5062	513	2	similar	similar	ADJ
ejpam-5062	513	3	way	way	NOUN
ejpam-5062	513	4	we	we	PRON
ejpam-5062	513	5	can	can	AUX
ejpam-5062	513	6	prove	prove	VERB
ejpam-5062	513	7	the	the	DET
ejpam-5062	513	8	case	case	NOUN
ejpam-5062	513	9	when	when	SCONJ
ejpam-5062	513	10	a	a	PRON
ejpam-5062	513	11	is	is	NOUN
ejpam-5062	513	12	α∗	α∗	NOUN
ejpam-5062	513	13	−	−	NOUN
ejpam-5062	513	14	sspo	sspo	NOUN
ejpam-5062	513	15	compact	compact	ADJ
ejpam-5062	513	16	.	.	PUNCT
ejpam-5062	514	1	theorem	theorem	NOUN
ejpam-5062	514	2	29	29	NUM
ejpam-5062	514	3	.	.	PUNCT
ejpam-5062	515	1	let	let	VERB
ejpam-5062	515	2	the	the	DET
ejpam-5062	515	3	mapping	mapping	NOUN
ejpam-5062	515	4	f	f	X
ejpam-5062	515	5	:	:	PUNCT
ejpam-5062	515	6	x	x	X
ejpam-5062	515	7	→	→	SYM
ejpam-5062	515	8	y	y	X
ejpam-5062	515	9	be	be	AUX
ejpam-5062	515	10	a	a	DET
ejpam-5062	515	11	fuzzy	fuzzy	ADJ
ejpam-5062	515	12	strong	strong	ADJ
ejpam-5062	515	13	semi	semi	ADJ
ejpam-5062	515	14	pre	pre	ADJ
ejpam-5062	515	15	-	-	ADJ
ejpam-5062	515	16	continuous	continuous	ADJ
ejpam-5062	515	17	and	and	CCONJ
ejpam-5062	515	18	surjective	surjective	ADJ
ejpam-5062	515	19	fuzzy	fuzzy	ADJ
ejpam-5062	515	20	sspo	sspo	NOUN
ejpam-5062	515	21	-	-	PUNCT
ejpam-5062	515	22	irresolute	irresolute	ADJ
ejpam-5062	515	23	open	open	ADJ
ejpam-5062	515	24	mapping	mapping	NOUN
ejpam-5062	515	25	from	from	ADP
ejpam-5062	515	26	the	the	DET
ejpam-5062	515	27	fuzzy	fuzzy	ADJ
ejpam-5062	515	28	topological	topological	ADJ
ejpam-5062	515	29	space	space	NOUN
ejpam-5062	515	30	x	x	PUNCT
ejpam-5062	515	31	to	to	ADP
ejpam-5062	515	32	a	a	DET
ejpam-5062	515	33	fuzzy	fuzzy	ADJ
ejpam-5062	515	34	topological	topological	ADJ
ejpam-5062	515	35	space	space	NOUN
ejpam-5062	515	36	y	y	PROPN
ejpam-5062	515	37	.	.	PUNCT
ejpam-5062	516	1	if	if	SCONJ
ejpam-5062	516	2	the	the	DET
ejpam-5062	516	3	space	space	NOUN
ejpam-5062	516	4	x	x	PUNCT
ejpam-5062	516	5	has	have	VERB
ejpam-5062	516	6	a	a	DET
ejpam-5062	516	7	countable	countable	ADJ
ejpam-5062	516	8	base	base	NOUN
ejpam-5062	516	9	consisting	consist	VERB
ejpam-5062	516	10	of	of	ADP
ejpam-5062	516	11	fuzzy	fuzzy	ADJ
ejpam-5062	516	12	strongly	strongly	ADV
ejpam-5062	516	13	semi	semi	ADV
ejpam-5062	516	14	pre	pre	ADJ
ejpam-5062	516	15	-	-	ADJ
ejpam-5062	516	16	open	open	ADJ
ejpam-5062	516	17	sets	set	NOUN
ejpam-5062	516	18	then	then	ADV
ejpam-5062	516	19	y	y	PROPN
ejpam-5062	516	20	also	also	ADV
ejpam-5062	516	21	has	have	VERB
ejpam-5062	516	22	a	a	DET
ejpam-5062	516	23	countable	countable	ADJ
ejpam-5062	516	24	base	base	NOUN
ejpam-5062	516	25	consisting	consist	VERB
ejpam-5062	516	26	of	of	ADP
ejpam-5062	516	27	fuzzy	fuzzy	ADJ
ejpam-5062	516	28	strongly	strongly	ADV
ejpam-5062	516	29	semi	semi	ADV
ejpam-5062	516	30	pre	pre	ADJ
ejpam-5062	516	31	-	-	ADJ
ejpam-5062	516	32	open	open	ADJ
ejpam-5062	516	33	sets	set	NOUN
ejpam-5062	516	34	.	.	PUNCT
ejpam-5062	517	1	proof	proof	NOUN
ejpam-5062	517	2	.	.	PUNCT
ejpam-5062	518	1	let	let	VERB
ejpam-5062	518	2	us	we	PRON
ejpam-5062	518	3	suppose	suppose	VERB
ejpam-5062	518	4	that	that	SCONJ
ejpam-5062	518	5	b	b	X
ejpam-5062	518	6	=	=	PRON
ejpam-5062	518	7	{	{	PUNCT
ejpam-5062	518	8	bi	bi	NOUN
ejpam-5062	518	9	,	,	PUNCT
ejpam-5062	518	10	i	i	PROPN
ejpam-5062	518	11	∈	∈	PROPN
ejpam-5062	518	12	n	n	CCONJ
ejpam-5062	518	13	}	}	PUNCT
ejpam-5062	518	14	is	be	AUX
ejpam-5062	518	15	a	a	DET
ejpam-5062	518	16	base	base	NOUN
ejpam-5062	518	17	for	for	ADP
ejpam-5062	518	18	fuzzy	fuzzy	ADJ
ejpam-5062	518	19	strongly	strongly	ADV
ejpam-5062	518	20	semi	semi	ADJ
ejpam-5062	518	21	preopen	preopen	ADJ
ejpam-5062	518	22	sets	set	NOUN
ejpam-5062	518	23	of	of	ADP
ejpam-5062	518	24	x.	x.	NOUN
ejpam-5062	518	25	based	base	VERB
ejpam-5062	518	26	on	on	ADP
ejpam-5062	518	27	the	the	DET
ejpam-5062	518	28	assumption	assumption	NOUN
ejpam-5062	518	29	of	of	ADP
ejpam-5062	518	30	the	the	DET
ejpam-5062	518	31	theorem	theorem	NOUN
ejpam-5062	518	32	it	it	PRON
ejpam-5062	518	33	follows	follow	VERB
ejpam-5062	518	34	that	that	SCONJ
ejpam-5062	518	35	f(bi),∀i	f(bi),∀i	PROPN
ejpam-5062	518	36	∈	∈	PROPN
ejpam-5062	518	37	n	n	CCONJ
ejpam-5062	518	38	,	,	PUNCT
ejpam-5062	518	39	are	be	AUX
ejpam-5062	518	40	fuzzy	fuzzy	ADJ
ejpam-5062	518	41	strongly	strongly	ADV
ejpam-5062	518	42	semi	semi	ADJ
ejpam-5062	518	43	pre	pre	ADJ
ejpam-5062	518	44	-	-	ADJ
ejpam-5062	518	45	open	open	ADJ
ejpam-5062	518	46	sets	set	NOUN
ejpam-5062	518	47	in	in	ADP
ejpam-5062	518	48	y	y	PROPN
ejpam-5062	518	49	.	.	PUNCT
ejpam-5062	519	1	if	if	SCONJ
ejpam-5062	519	2	we	we	PRON
ejpam-5062	519	3	consider	consider	VERB
ejpam-5062	519	4	the	the	DET
ejpam-5062	519	5	collection	collection	NOUN
ejpam-5062	519	6	of	of	ADP
ejpam-5062	519	7	fuzzy	fuzzy	ADJ
ejpam-5062	519	8	sets	set	NOUN
ejpam-5062	519	9	m	m	VERB
ejpam-5062	519	10	=	=	SYM
ejpam-5062	519	11	{	{	PUNCT
ejpam-5062	519	12	f(bi	f(bi	PROPN
ejpam-5062	519	13	)	)	PUNCT
ejpam-5062	519	14	,	,	PUNCT
ejpam-5062	519	15	i	i	PRON
ejpam-5062	519	16	∈	∈	PROPN
ejpam-5062	519	17	n	n	CCONJ
ejpam-5062	519	18	}	}	PUNCT
ejpam-5062	519	19	,	,	PUNCT
ejpam-5062	519	20	and	and	CCONJ
ejpam-5062	519	21	given	give	VERB
ejpam-5062	519	22	any	any	DET
ejpam-5062	519	23	fuzzy	fuzzy	ADJ
ejpam-5062	519	24	strongly	strongly	ADV
ejpam-5062	519	25	semi	semi	ADV
ejpam-5062	519	26	pre	pre	ADJ
ejpam-5062	519	27	-	-	ADJ
ejpam-5062	519	28	open	open	ADJ
ejpam-5062	519	29	set	set	NOUN
ejpam-5062	519	30	w	w	NOUN
ejpam-5062	519	31	in	in	ADP
ejpam-5062	519	32	y	y	PROPN
ejpam-5062	519	33	,	,	PUNCT
ejpam-5062	519	34	then	then	ADV
ejpam-5062	519	35	again	again	ADV
ejpam-5062	519	36	due	due	ADP
ejpam-5062	519	37	to	to	ADP
ejpam-5062	519	38	the	the	DET
ejpam-5062	519	39	conditions	condition	NOUN
ejpam-5062	519	40	of	of	ADP
ejpam-5062	519	41	the	the	DET
ejpam-5062	519	42	theorem	theorem	NOUN
ejpam-5062	519	43	,	,	PUNCT
ejpam-5062	519	44	f−1(w	f−1(w	PROPN
ejpam-5062	519	45	)	)	PUNCT
ejpam-5062	519	46	is	be	AUX
ejpam-5062	519	47	a	a	DET
ejpam-5062	519	48	fuzzy	fuzzy	ADJ
ejpam-5062	519	49	strongly	strongly	ADV
ejpam-5062	519	50	semi	semi	ADJ
ejpam-5062	519	51	pre	pre	ADJ
ejpam-5062	519	52	-	-	ADJ
ejpam-5062	519	53	open	open	ADJ
ejpam-5062	519	54	set	set	NOUN
ejpam-5062	519	55	in	in	ADP
ejpam-5062	519	56	x	x	PUNCT
ejpam-5062	520	1	and	and	CCONJ
ejpam-5062	520	2	it	it	PRON
ejpam-5062	520	3	can	can	AUX
ejpam-5062	520	4	be	be	AUX
ejpam-5062	520	5	written	write	VERB
ejpam-5062	520	6	in	in	ADP
ejpam-5062	520	7	the	the	DET
ejpam-5062	520	8	following	follow	VERB
ejpam-5062	520	9	manner	manner	NOUN
ejpam-5062	520	10	f−1(w	f−1(w	ADV
ejpam-5062	520	11	)	)	PUNCT
ejpam-5062	520	12	=	=	SYM
ejpam-5062	520	13	∨i∈nbi	∨i∈nbi	NOUN
ejpam-5062	520	14	.	.	PUNCT
ejpam-5062	521	1	from	from	ADP
ejpam-5062	521	2	the	the	DET
ejpam-5062	521	3	fact	fact	NOUN
ejpam-5062	521	4	that	that	SCONJ
ejpam-5062	521	5	mapping	mapping	NOUN
ejpam-5062	521	6	f	f	NOUN
ejpam-5062	521	7	is	be	AUX
ejpam-5062	521	8	surjective	surjective	ADJ
ejpam-5062	521	9	,	,	PUNCT
ejpam-5062	521	10	we	we	PRON
ejpam-5062	521	11	get	get	VERB
ejpam-5062	521	12	w	w	NOUN
ejpam-5062	521	13	=	=	SYM
ejpam-5062	521	14	f(f−1(w	f(f−1(w	NOUN
ejpam-5062	521	15	)	)	PUNCT
ejpam-5062	521	16	)	)	PUNCT
ejpam-5062	522	1	=	=	SYM
ejpam-5062	522	2	f(∨i∈nbi	f(∨i∈nbi	NOUN
ejpam-5062	522	3	)	)	PUNCT
ejpam-5062	522	4	=	=	SYM
ejpam-5062	522	5	∨i∈nf(bi	∨i∈nf(bi	PROPN
ejpam-5062	522	6	)	)	PUNCT
ejpam-5062	522	7	.	.	PUNCT
ejpam-5062	523	1	therefore	therefore	ADV
ejpam-5062	523	2	m	m	PROPN
ejpam-5062	523	3	is	be	AUX
ejpam-5062	523	4	a	a	DET
ejpam-5062	523	5	base	base	NOUN
ejpam-5062	523	6	of	of	ADP
ejpam-5062	523	7	fuzzy	fuzzy	ADJ
ejpam-5062	523	8	strongly	strongly	ADV
ejpam-5062	523	9	semi	semi	ADV
ejpam-5062	523	10	pre	pre	ADJ
ejpam-5062	523	11	-	-	ADJ
ejpam-5062	523	12	open	open	ADJ
ejpam-5062	523	13	sets	set	NOUN
ejpam-5062	523	14	in	in	ADP
ejpam-5062	523	15	y	y	PROPN
ejpam-5062	523	16	.	.	PUNCT
ejpam-5062	524	1	sh	sh	PROPN
ejpam-5062	524	2	.	.	PROPN
ejpam-5062	524	3	makolli	makolli	PROPN
ejpam-5062	524	4	,	,	PUNCT
ejpam-5062	524	5	b.	b.	PROPN
ejpam-5062	524	6	krsteska	krsteska	PROPN
ejpam-5062	524	7	/	/	SYM
ejpam-5062	524	8	eur	eur	PROPN
ejpam-5062	524	9	.	.	PUNCT
ejpam-5062	525	1	j.	j.	PROPN
ejpam-5062	525	2	pure	pure	PROPN
ejpam-5062	525	3	appl	appl	PROPN
ejpam-5062	525	4	.	.	PROPN
ejpam-5062	525	5	math	math	PROPN
ejpam-5062	525	6	,	,	PUNCT
ejpam-5062	525	7	17	17	NUM
ejpam-5062	525	8	(	(	PUNCT
ejpam-5062	525	9	2	2	NUM
ejpam-5062	525	10	)	)	PUNCT
ejpam-5062	525	11	(	(	PUNCT
ejpam-5062	525	12	2024	2024	NUM
ejpam-5062	525	13	)	)	PUNCT
ejpam-5062	525	14	,	,	PUNCT
ejpam-5062	525	15	638	638	NUM
ejpam-5062	525	16	-	-	SYM
ejpam-5062	525	17	662	662	NUM
ejpam-5062	525	18	657	657	NUM
ejpam-5062	525	19	definition	definition	NOUN
ejpam-5062	525	20	25	25	NUM
ejpam-5062	525	21	.	.	PUNCT
ejpam-5062	526	1	fuzzy	fuzzy	ADJ
ejpam-5062	526	2	topological	topological	ADJ
ejpam-5062	526	3	space	space	NOUN
ejpam-5062	526	4	(	(	PUNCT
ejpam-5062	526	5	x	x	X
ejpam-5062	526	6	,	,	PUNCT
ejpam-5062	526	7	τ	τ	X
ejpam-5062	526	8	)	)	PUNCT
ejpam-5062	526	9	is	be	AUX
ejpam-5062	526	10	fuzzy	fuzzy	ADJ
ejpam-5062	526	11	sspo	sspo	NOUN
ejpam-5062	526	12	-	-	PUNCT
ejpam-5062	526	13	separable	separable	NOUN
ejpam-5062	526	14	if	if	SCONJ
ejpam-5062	526	15	and	and	CCONJ
ejpam-5062	526	16	only	only	ADV
ejpam-5062	526	17	if	if	SCONJ
ejpam-5062	526	18	there	there	PRON
ejpam-5062	526	19	exists	exist	VERB
ejpam-5062	526	20	a	a	DET
ejpam-5062	526	21	countable	countable	ADJ
ejpam-5062	526	22	sequence	sequence	NOUN
ejpam-5062	526	23	of	of	ADP
ejpam-5062	526	24	fuzzy	fuzzy	ADJ
ejpam-5062	526	25	points	point	NOUN
ejpam-5062	526	26	{	{	PUNCT
ejpam-5062	526	27	pi}i∈n	pi}i∈n	ADJ
ejpam-5062	526	28	such	such	ADJ
ejpam-5062	526	29	that	that	PRON
ejpam-5062	526	30	for	for	ADP
ejpam-5062	526	31	each	each	DET
ejpam-5062	526	32	u	u	PROPN
ejpam-5062	526	33	∈	∈	PROPN
ejpam-5062	526	34	fsspo(τ	fsspo(τ	PROPN
ejpam-5062	526	35	)	)	PUNCT
ejpam-5062	526	36	,	,	PUNCT
ejpam-5062	526	37	u	u	PROPN
ejpam-5062	526	38	̸=	̸=	PROPN
ejpam-5062	526	39	0x	0x	NOUN
ejpam-5062	526	40	,	,	PUNCT
ejpam-5062	526	41	there	there	PRON
ejpam-5062	526	42	exists	exist	VERB
ejpam-5062	526	43	a	a	DET
ejpam-5062	526	44	fuzzy	fuzzy	ADJ
ejpam-5062	526	45	point	point	NOUN
ejpam-5062	526	46	pj	pj	PROPN
ejpam-5062	527	1	such	such	ADJ
ejpam-5062	527	2	that	that	SCONJ
ejpam-5062	527	3	pj	pj	PROPN
ejpam-5062	527	4	∈	∈	PROPN
ejpam-5062	527	5	u	u	PROPN
ejpam-5062	527	6	,	,	PUNCT
ejpam-5062	527	7	for	for	ADP
ejpam-5062	527	8	some	some	DET
ejpam-5062	527	9	j	j	PROPN
ejpam-5062	527	10	∈	∈	PROPN
ejpam-5062	527	11	n.	n.	NOUN
ejpam-5062	527	12	it	it	PRON
ejpam-5062	527	13	is	be	AUX
ejpam-5062	527	14	obvious	obvious	ADJ
ejpam-5062	527	15	that	that	SCONJ
ejpam-5062	527	16	the	the	DET
ejpam-5062	527	17	concept	concept	NOUN
ejpam-5062	527	18	of	of	ADP
ejpam-5062	527	19	fuzzy	fuzzy	ADJ
ejpam-5062	527	20	sspo	sspo	NOUN
ejpam-5062	527	21	-	-	PUNCT
ejpam-5062	527	22	separability	separability	NOUN
ejpam-5062	527	23	is	be	AUX
ejpam-5062	527	24	the	the	DET
ejpam-5062	527	25	generalization	generalization	NOUN
ejpam-5062	527	26	of	of	ADP
ejpam-5062	527	27	fuzzy	fuzzy	ADJ
ejpam-5062	527	28	separability	separability	NOUN
ejpam-5062	527	29	.	.	PUNCT
ejpam-5062	528	1	if	if	SCONJ
ejpam-5062	528	2	a	a	DET
ejpam-5062	528	3	fuzzy	fuzzy	ADJ
ejpam-5062	528	4	topological	topological	ADJ
ejpam-5062	528	5	space	space	NOUN
ejpam-5062	528	6	is	be	AUX
ejpam-5062	528	7	fuzzy	fuzzy	ADJ
ejpam-5062	528	8	sspo	sspo	NOUN
ejpam-5062	528	9	-	-	PUNCT
ejpam-5062	528	10	separable	separable	NOUN
ejpam-5062	528	11	then	then	ADV
ejpam-5062	528	12	it	it	PRON
ejpam-5062	528	13	is	be	AUX
ejpam-5062	528	14	also	also	ADV
ejpam-5062	528	15	fuzzy	fuzzy	ADJ
ejpam-5062	528	16	separable	separable	ADJ
ejpam-5062	528	17	.	.	PUNCT
ejpam-5062	529	1	theorem	theorem	NOUN
ejpam-5062	529	2	30	30	NUM
ejpam-5062	529	3	.	.	PUNCT
ejpam-5062	530	1	if	if	SCONJ
ejpam-5062	530	2	the	the	DET
ejpam-5062	530	3	fuzzy	fuzzy	ADJ
ejpam-5062	530	4	topological	topological	ADJ
ejpam-5062	530	5	space	space	NOUN
ejpam-5062	530	6	(	(	PUNCT
ejpam-5062	530	7	x	x	X
ejpam-5062	530	8	,	,	PUNCT
ejpam-5062	530	9	τ	τ	X
ejpam-5062	530	10	)	)	PUNCT
ejpam-5062	530	11	has	have	VERB
ejpam-5062	530	12	a	a	DET
ejpam-5062	530	13	countable	countable	ADJ
ejpam-5062	530	14	base	base	NOUN
ejpam-5062	530	15	b	b	PROPN
ejpam-5062	530	16	of	of	ADP
ejpam-5062	530	17	fuzzy	fuzzy	ADJ
ejpam-5062	530	18	strongly	strongly	ADV
ejpam-5062	530	19	semi	semi	ADV
ejpam-5062	530	20	pre	pre	ADJ
ejpam-5062	530	21	-	-	ADJ
ejpam-5062	530	22	open	open	ADJ
ejpam-5062	530	23	sets	set	NOUN
ejpam-5062	530	24	then	then	ADV
ejpam-5062	530	25	(	(	PUNCT
ejpam-5062	530	26	x	x	X
ejpam-5062	530	27	,	,	PUNCT
ejpam-5062	530	28	τ	τ	X
ejpam-5062	530	29	)	)	PUNCT
ejpam-5062	530	30	is	be	AUX
ejpam-5062	530	31	an	an	DET
ejpam-5062	530	32	sspo	sspo	NOUN
ejpam-5062	530	33	-	-	PUNCT
ejpam-5062	530	34	separable	separable	NOUN
ejpam-5062	530	35	space	space	NOUN
ejpam-5062	530	36	.	.	PUNCT
ejpam-5062	531	1	proof	proof	NOUN
ejpam-5062	531	2	.	.	PUNCT
ejpam-5062	532	1	let	let	VERB
ejpam-5062	532	2	us	we	PRON
ejpam-5062	532	3	suppose	suppose	VERB
ejpam-5062	532	4	that	that	SCONJ
ejpam-5062	532	5	b	b	X
ejpam-5062	532	6	=	=	PRON
ejpam-5062	532	7	{	{	PUNCT
ejpam-5062	532	8	bi	bi	NOUN
ejpam-5062	532	9	,	,	PUNCT
ejpam-5062	532	10	i	i	PROPN
ejpam-5062	532	11	∈	∈	PROPN
ejpam-5062	532	12	n	n	CCONJ
ejpam-5062	532	13	}	}	PUNCT
ejpam-5062	532	14	is	be	AUX
ejpam-5062	532	15	a	a	DET
ejpam-5062	532	16	countable	countable	ADJ
ejpam-5062	532	17	base	base	NOUN
ejpam-5062	532	18	for	for	ADP
ejpam-5062	532	19	fuzzy	fuzzy	ADJ
ejpam-5062	532	20	strongly	strongly	ADV
ejpam-5062	532	21	semi	semi	ADJ
ejpam-5062	532	22	pre	pre	ADJ
ejpam-5062	532	23	-	-	ADJ
ejpam-5062	532	24	open	open	ADJ
ejpam-5062	532	25	sets	set	NOUN
ejpam-5062	532	26	in	in	ADP
ejpam-5062	532	27	(	(	PUNCT
ejpam-5062	532	28	x	x	NOUN
ejpam-5062	532	29	,	,	PUNCT
ejpam-5062	532	30	τ	τ	PROPN
ejpam-5062	532	31	)	)	PUNCT
ejpam-5062	532	32	.	.	PUNCT
ejpam-5062	533	1	let	let	VERB
ejpam-5062	533	2	us	we	PRON
ejpam-5062	533	3	consider	consider	VERB
ejpam-5062	533	4	any	any	DET
ejpam-5062	533	5	member	member	NOUN
ejpam-5062	533	6	of	of	ADP
ejpam-5062	533	7	b	b	PROPN
ejpam-5062	533	8	,	,	PUNCT
ejpam-5062	533	9	let	let	VERB
ejpam-5062	533	10	it	it	PRON
ejpam-5062	533	11	be	be	AUX
ejpam-5062	533	12	denoted	denote	VERB
ejpam-5062	533	13	as	as	ADP
ejpam-5062	533	14	bj	bj	NOUN
ejpam-5062	533	15	,	,	PUNCT
ejpam-5062	533	16	such	such	ADJ
ejpam-5062	533	17	that	that	PRON
ejpam-5062	533	18	bj	bj	ADP
ejpam-5062	533	19	̸=	̸=	PROPN
ejpam-5062	533	20	0x	0x	NOUN
ejpam-5062	533	21	,	,	PUNCT
ejpam-5062	533	22	then	then	ADV
ejpam-5062	533	23	there	there	PRON
ejpam-5062	533	24	exists	exist	VERB
ejpam-5062	533	25	a	a	DET
ejpam-5062	533	26	fuzzy	fuzzy	ADJ
ejpam-5062	533	27	point	point	NOUN
ejpam-5062	533	28	xj	xj	PROPN
ejpam-5062	533	29	∈	∈	PROPN
ejpam-5062	533	30	x	x	PUNCT
ejpam-5062	533	31	such	such	ADJ
ejpam-5062	533	32	that	that	DET
ejpam-5062	533	33	bj(xj	bj(xj	NOUN
ejpam-5062	533	34	)	)	PUNCT
ejpam-5062	533	35	>	>	X
ejpam-5062	534	1	0	0	X
ejpam-5062	534	2	.	.	PUNCT
ejpam-5062	535	1	if	if	SCONJ
ejpam-5062	535	2	we	we	PRON
ejpam-5062	535	3	now	now	ADV
ejpam-5062	535	4	define	define	VERB
ejpam-5062	535	5	a	a	DET
ejpam-5062	535	6	fuzzy	fuzzy	ADJ
ejpam-5062	535	7	point	point	NOUN
ejpam-5062	535	8	as	as	SCONJ
ejpam-5062	535	9	follows	follow	VERB
ejpam-5062	535	10	:	:	PUNCT
ejpam-5062	535	11	{	{	PUNCT
ejpam-5062	535	12	pj(x	pj(x	NOUN
ejpam-5062	535	13	)	)	PUNCT
ejpam-5062	535	14	=	=	SYM
ejpam-5062	535	15	bj(xj	bj(xj	X
ejpam-5062	535	16	)	)	PUNCT
ejpam-5062	535	17	if	if	SCONJ
ejpam-5062	535	18	x	x	PROPN
ejpam-5062	535	19	=	=	VERB
ejpam-5062	535	20	xj	xj	PROPN
ejpam-5062	535	21	pj(x	pj(x	ADJ
ejpam-5062	535	22	)	)	PUNCT
ejpam-5062	536	1	=	=	SYM
ejpam-5062	536	2	0	0	PUNCT
ejpam-5062	537	1	if	if	SCONJ
ejpam-5062	537	2	x	x	PROPN
ejpam-5062	537	3	̸=	̸=	PROPN
ejpam-5062	537	4	xj	xj	NUM
ejpam-5062	537	5	we	we	PRON
ejpam-5062	537	6	can	can	AUX
ejpam-5062	537	7	conclude	conclude	VERB
ejpam-5062	537	8	that	that	SCONJ
ejpam-5062	537	9	pj	pj	PROPN
ejpam-5062	537	10	≤	≤	PROPN
ejpam-5062	537	11	bj	bj	VERB
ejpam-5062	537	12	.	.	PUNCT
ejpam-5062	538	1	let	let	VERB
ejpam-5062	538	2	us	we	PRON
ejpam-5062	538	3	consider	consider	VERB
ejpam-5062	538	4	the	the	DET
ejpam-5062	538	5	corresponding	corresponding	ADJ
ejpam-5062	538	6	countable	countable	ADJ
ejpam-5062	538	7	sequence	sequence	NOUN
ejpam-5062	538	8	of	of	ADP
ejpam-5062	538	9	fuzzy	fuzzy	ADJ
ejpam-5062	538	10	points	point	NOUN
ejpam-5062	538	11	{	{	PUNCT
ejpam-5062	538	12	pi}i∈n	pi}i∈n	X
ejpam-5062	538	13	.	.	VERB
ejpam-5062	539	1	given	give	VERB
ejpam-5062	539	2	any	any	DET
ejpam-5062	539	3	fuzzy	fuzzy	ADJ
ejpam-5062	539	4	strongly	strongly	ADV
ejpam-5062	539	5	semi	semi	ADV
ejpam-5062	539	6	pre	pre	ADJ
ejpam-5062	539	7	-	-	ADJ
ejpam-5062	539	8	open	open	ADJ
ejpam-5062	539	9	set	set	ADJ
ejpam-5062	539	10	u	u	NOUN
ejpam-5062	539	11	in	in	ADP
ejpam-5062	539	12	(	(	PUNCT
ejpam-5062	539	13	x	x	NOUN
ejpam-5062	539	14	,	,	PUNCT
ejpam-5062	539	15	τ	τ	PROPN
ejpam-5062	539	16	)	)	PUNCT
ejpam-5062	539	17	,	,	PUNCT
ejpam-5062	539	18	it	it	PRON
ejpam-5062	539	19	must	must	AUX
ejpam-5062	539	20	contain	contain	VERB
ejpam-5062	539	21	a	a	DET
ejpam-5062	539	22	certain	certain	ADJ
ejpam-5062	539	23	bs	bs	NOUN
ejpam-5062	539	24	∈	∈	PROPN
ejpam-5062	539	25	b	b	PROPN
ejpam-5062	539	26	and	and	CCONJ
ejpam-5062	539	27	therefore	therefore	ADV
ejpam-5062	539	28	there	there	PRON
ejpam-5062	539	29	exists	exist	VERB
ejpam-5062	539	30	a	a	DET
ejpam-5062	539	31	fuzzy	fuzzy	ADJ
ejpam-5062	539	32	point	point	NOUN
ejpam-5062	539	33	ps	ps	NOUN
ejpam-5062	539	34	≤	≤	NOUN
ejpam-5062	539	35	bs	bs	NOUN
ejpam-5062	539	36	such	such	ADJ
ejpam-5062	539	37	that	that	DET
ejpam-5062	539	38	ps	ps	PROPN
ejpam-5062	539	39	≤	≤	NUM
ejpam-5062	539	40	u	u	NOUN
ejpam-5062	539	41	.	.	PUNCT
ejpam-5062	540	1	in	in	ADP
ejpam-5062	540	2	other	other	ADJ
ejpam-5062	540	3	words	word	NOUN
ejpam-5062	540	4	x	x	PUNCT
ejpam-5062	540	5	is	be	AUX
ejpam-5062	540	6	sspo	sspo	NOUN
ejpam-5062	540	7	-	-	PUNCT
ejpam-5062	540	8	separable	separable	NOUN
ejpam-5062	540	9	space	space	NOUN
ejpam-5062	540	10	.	.	PUNCT
ejpam-5062	541	1	the	the	DET
ejpam-5062	541	2	converse	converse	NOUN
ejpam-5062	541	3	of	of	ADP
ejpam-5062	541	4	this	this	DET
ejpam-5062	541	5	theorem	theorem	NOUN
ejpam-5062	541	6	does	do	AUX
ejpam-5062	541	7	not	not	PART
ejpam-5062	541	8	stand	stand	VERB
ejpam-5062	541	9	.	.	PUNCT
ejpam-5062	542	1	let	let	VERB
ejpam-5062	542	2	x	x	PRON
ejpam-5062	542	3	be	be	AUX
ejpam-5062	542	4	an	an	DET
ejpam-5062	542	5	infinite	infinite	ADJ
ejpam-5062	542	6	set	set	NOUN
ejpam-5062	542	7	,	,	PUNCT
ejpam-5062	542	8	and	and	CCONJ
ejpam-5062	542	9	let	let	VERB
ejpam-5062	542	10	fts(x	fts(x	PROPN
ejpam-5062	542	11	,	,	PUNCT
ejpam-5062	542	12	τ	τ	X
ejpam-5062	542	13	)	)	PUNCT
ejpam-5062	542	14	be	be	VERB
ejpam-5062	542	15	such	such	ADJ
ejpam-5062	542	16	that	that	SCONJ
ejpam-5062	542	17	any	any	DET
ejpam-5062	542	18	fuzzy	fuzzy	ADJ
ejpam-5062	542	19	open	open	NOUN
ejpam-5062	542	20	set	set	NOUN
ejpam-5062	542	21	in	in	ADP
ejpam-5062	542	22	τ	τ	PROPN
ejpam-5062	542	23	contains	contain	VERB
ejpam-5062	542	24	a	a	DET
ejpam-5062	542	25	fuzzy	fuzzy	ADJ
ejpam-5062	542	26	singleton	singleton	NOUN
ejpam-5062	542	27	p	p	PROPN
ejpam-5062	542	28	∈	∈	PROPN
ejpam-5062	542	29	x	x	X
ejpam-5062	542	30	(	(	PUNCT
ejpam-5062	542	31	or	or	CCONJ
ejpam-5062	542	32	a	a	DET
ejpam-5062	542	33	countable	countable	ADJ
ejpam-5062	542	34	set	set	NOUN
ejpam-5062	542	35	of	of	ADP
ejpam-5062	542	36	singletons	singleton	NOUN
ejpam-5062	542	37	)	)	PUNCT
ejpam-5062	542	38	.	.	PUNCT
ejpam-5062	543	1	in	in	ADP
ejpam-5062	543	2	this	this	DET
ejpam-5062	543	3	case	case	NOUN
ejpam-5062	543	4	(	(	PUNCT
ejpam-5062	543	5	x	x	X
ejpam-5062	543	6	,	,	PUNCT
ejpam-5062	543	7	τ	τ	X
ejpam-5062	543	8	)	)	PUNCT
ejpam-5062	543	9	does	do	AUX
ejpam-5062	543	10	not	not	PART
ejpam-5062	543	11	contain	contain	VERB
ejpam-5062	543	12	a	a	DET
ejpam-5062	543	13	fuzzy	fuzzy	ADJ
ejpam-5062	543	14	countable	countable	ADJ
ejpam-5062	543	15	base	base	NOUN
ejpam-5062	543	16	consisting	consist	VERB
ejpam-5062	543	17	of	of	ADP
ejpam-5062	543	18	fuzzy	fuzzy	ADJ
ejpam-5062	543	19	open	open	ADJ
ejpam-5062	543	20	sets	set	NOUN
ejpam-5062	543	21	and	and	CCONJ
ejpam-5062	543	22	it	it	PRON
ejpam-5062	543	23	does	do	AUX
ejpam-5062	543	24	not	not	PART
ejpam-5062	543	25	contain	contain	VERB
ejpam-5062	543	26	a	a	DET
ejpam-5062	543	27	countable	countable	ADJ
ejpam-5062	543	28	base	base	NOUN
ejpam-5062	543	29	of	of	ADP
ejpam-5062	543	30	fuzzy	fuzzy	ADJ
ejpam-5062	543	31	strongly	strongly	ADV
ejpam-5062	543	32	semi	semi	ADV
ejpam-5062	543	33	pre	pre	ADJ
ejpam-5062	543	34	-	-	ADJ
ejpam-5062	543	35	open	open	ADJ
ejpam-5062	543	36	sets	set	NOUN
ejpam-5062	543	37	.	.	PUNCT
ejpam-5062	544	1	theorem	theorem	NOUN
ejpam-5062	544	2	31	31	NUM
ejpam-5062	544	3	.	.	PUNCT
ejpam-5062	545	1	let	let	VERB
ejpam-5062	545	2	the	the	DET
ejpam-5062	545	3	mapping	mapping	NOUN
ejpam-5062	545	4	f	f	X
ejpam-5062	545	5	:	:	PUNCT
ejpam-5062	545	6	x	x	X
ejpam-5062	545	7	→	→	SYM
ejpam-5062	545	8	y	y	X
ejpam-5062	545	9	be	be	AUX
ejpam-5062	545	10	a	a	DET
ejpam-5062	545	11	fuzzy	fuzzy	ADJ
ejpam-5062	545	12	sspo	sspo	NOUN
ejpam-5062	545	13	-	-	PUNCT
ejpam-5062	545	14	irresolute	irresolute	ADJ
ejpam-5062	545	15	and	and	CCONJ
ejpam-5062	545	16	surjective	surjective	ADJ
ejpam-5062	545	17	mapping	mapping	NOUN
ejpam-5062	545	18	from	from	ADP
ejpam-5062	545	19	the	the	DET
ejpam-5062	545	20	fuzzy	fuzzy	ADJ
ejpam-5062	545	21	topological	topological	ADJ
ejpam-5062	545	22	space	space	NOUN
ejpam-5062	545	23	x	x	PUNCT
ejpam-5062	545	24	to	to	ADP
ejpam-5062	545	25	a	a	DET
ejpam-5062	545	26	fuzzy	fuzzy	ADJ
ejpam-5062	545	27	topological	topological	ADJ
ejpam-5062	545	28	space	space	NOUN
ejpam-5062	545	29	y	y	PROPN
ejpam-5062	545	30	.	.	PUNCT
ejpam-5062	546	1	if	if	SCONJ
ejpam-5062	546	2	the	the	DET
ejpam-5062	546	3	space	space	NOUN
ejpam-5062	546	4	x	x	PUNCT
ejpam-5062	546	5	is	be	AUX
ejpam-5062	546	6	fuzzy	fuzzy	ADJ
ejpam-5062	546	7	sspo	sspo	NOUN
ejpam-5062	546	8	-	-	PUNCT
ejpam-5062	546	9	separable	separable	NOUN
ejpam-5062	546	10	then	then	ADV
ejpam-5062	546	11	y	y	PROPN
ejpam-5062	546	12	is	be	AUX
ejpam-5062	546	13	a	a	DET
ejpam-5062	546	14	fuzzy	fuzzy	ADJ
ejpam-5062	546	15	sspo	sspo	NOUN
ejpam-5062	546	16	-	-	PUNCT
ejpam-5062	546	17	separable	separable	NOUN
ejpam-5062	546	18	space	space	NOUN
ejpam-5062	546	19	.	.	PUNCT
ejpam-5062	547	1	proof	proof	NOUN
ejpam-5062	547	2	.	.	PUNCT
ejpam-5062	548	1	let	let	VERB
ejpam-5062	548	2	us	we	PRON
ejpam-5062	548	3	consider	consider	VERB
ejpam-5062	548	4	a	a	DET
ejpam-5062	548	5	countable	countable	ADJ
ejpam-5062	548	6	sequence	sequence	NOUN
ejpam-5062	548	7	of	of	ADP
ejpam-5062	548	8	fuzzy	fuzzy	ADJ
ejpam-5062	548	9	points	point	NOUN
ejpam-5062	548	10	{	{	PUNCT
ejpam-5062	548	11	pi}i∈n	pi}i∈n	ADV
ejpam-5062	548	12	from	from	ADP
ejpam-5062	548	13	x	x	PRON
ejpam-5062	548	14	such	such	ADJ
ejpam-5062	548	15	that	that	PRON
ejpam-5062	548	16	for	for	ADP
ejpam-5062	548	17	any	any	DET
ejpam-5062	548	18	fuzzy	fuzzy	ADJ
ejpam-5062	548	19	strongly	strongly	ADV
ejpam-5062	548	20	semi	semi	ADV
ejpam-5062	548	21	pre	pre	ADJ
ejpam-5062	548	22	-	-	ADJ
ejpam-5062	548	23	open	open	ADJ
ejpam-5062	548	24	set	set	NOUN
ejpam-5062	548	25	w	w	NOUN
ejpam-5062	548	26	in	in	ADP
ejpam-5062	548	27	x	x	PROPN
ejpam-5062	548	28	,	,	PUNCT
ejpam-5062	548	29	w	w	PROPN
ejpam-5062	548	30	̸=	̸=	PROPN
ejpam-5062	548	31	0x	0x	NOUN
ejpam-5062	548	32	,	,	PUNCT
ejpam-5062	548	33	there	there	PRON
ejpam-5062	548	34	exists	exist	VERB
ejpam-5062	548	35	a	a	DET
ejpam-5062	548	36	fuzzy	fuzzy	ADJ
ejpam-5062	548	37	point	point	NOUN
ejpam-5062	548	38	pi	pi	NOUN
ejpam-5062	549	1	such	such	ADJ
ejpam-5062	549	2	that	that	DET
ejpam-5062	549	3	pi	pi	PROPN
ejpam-5062	549	4	≤	≤	NUM
ejpam-5062	549	5	w	w	NOUN
ejpam-5062	549	6	.	.	PUNCT
ejpam-5062	550	1	the	the	DET
ejpam-5062	550	2	sequence	sequence	NOUN
ejpam-5062	550	3	{	{	PUNCT
ejpam-5062	550	4	f(pi)}i∈n	f(pi)}i∈n	PROPN
ejpam-5062	550	5	is	be	AUX
ejpam-5062	550	6	a	a	DET
ejpam-5062	550	7	countable	countable	ADJ
ejpam-5062	550	8	sequence	sequence	NOUN
ejpam-5062	550	9	of	of	ADP
ejpam-5062	550	10	fuzzy	fuzzy	ADJ
ejpam-5062	550	11	points	point	NOUN
ejpam-5062	550	12	in	in	ADP
ejpam-5062	550	13	y	y	PROPN
ejpam-5062	550	14	.	.	PUNCT
ejpam-5062	551	1	let	let	VERB
ejpam-5062	551	2	us	we	PRON
ejpam-5062	551	3	suppose	suppose	VERB
ejpam-5062	551	4	that	that	SCONJ
ejpam-5062	551	5	v	v	NOUN
ejpam-5062	551	6	is	be	AUX
ejpam-5062	551	7	a	a	DET
ejpam-5062	551	8	fuzzy	fuzzy	ADJ
ejpam-5062	551	9	strongly	strongly	ADV
ejpam-5062	551	10	semi	semi	ADJ
ejpam-5062	551	11	pre	pre	ADJ
ejpam-5062	551	12	-	-	ADJ
ejpam-5062	551	13	open	open	ADJ
ejpam-5062	551	14	set	set	NOUN
ejpam-5062	551	15	in	in	ADP
ejpam-5062	551	16	y	y	PROPN
ejpam-5062	551	17	such	such	ADJ
ejpam-5062	551	18	that	that	PRON
ejpam-5062	551	19	v	v	ADP
ejpam-5062	551	20	̸=	̸=	PROPN
ejpam-5062	551	21	0y	0y	NOUN
ejpam-5062	551	22	.	.	PUNCT
ejpam-5062	552	1	from	from	ADP
ejpam-5062	552	2	the	the	DET
ejpam-5062	552	3	assumption	assumption	NOUN
ejpam-5062	552	4	of	of	ADP
ejpam-5062	552	5	the	the	DET
ejpam-5062	552	6	theorem	theorem	ADJ
ejpam-5062	552	7	f−1(v	f−1(v	PROPN
ejpam-5062	552	8	)	)	PUNCT
ejpam-5062	552	9	is	be	AUX
ejpam-5062	552	10	a	a	DET
ejpam-5062	552	11	fuzzy	fuzzy	ADJ
ejpam-5062	552	12	strongly	strongly	ADV
ejpam-5062	552	13	semi	semi	ADJ
ejpam-5062	552	14	pre	pre	ADJ
ejpam-5062	552	15	-	-	ADJ
ejpam-5062	552	16	open	open	ADJ
ejpam-5062	552	17	set	set	NOUN
ejpam-5062	552	18	in	in	ADP
ejpam-5062	552	19	x	x	PUNCT
ejpam-5062	552	20	and	and	CCONJ
ejpam-5062	552	21	f−1(v	f−1(v	NOUN
ejpam-5062	552	22	)	)	PUNCT
ejpam-5062	553	1	̸=	̸=	PROPN
ejpam-5062	553	2	0x	0x	NOUN
ejpam-5062	553	3	.	.	PUNCT
ejpam-5062	554	1	because	because	SCONJ
ejpam-5062	554	2	the	the	DET
ejpam-5062	554	3	space	space	NOUN
ejpam-5062	554	4	x	x	PUNCT
ejpam-5062	554	5	is	be	AUX
ejpam-5062	554	6	fuzzy	fuzzy	ADJ
ejpam-5062	554	7	sspo	sspo	NOUN
ejpam-5062	554	8	-	-	PUNCT
ejpam-5062	554	9	separable	separable	NOUN
ejpam-5062	554	10	then	then	ADV
ejpam-5062	554	11	there	there	PRON
ejpam-5062	554	12	exists	exist	VERB
ejpam-5062	554	13	a	a	DET
ejpam-5062	554	14	fuzzy	fuzzy	ADJ
ejpam-5062	554	15	point	point	NOUN
ejpam-5062	554	16	ps	ps	INTJ
ejpam-5062	554	17	such	such	ADJ
ejpam-5062	554	18	that	that	DET
ejpam-5062	554	19	ps	ps	PROPN
ejpam-5062	554	20	≤	≤	PROPN
ejpam-5062	554	21	f−1(v	f−1(v	PROPN
ejpam-5062	554	22	)	)	PUNCT
ejpam-5062	554	23	.	.	PUNCT
ejpam-5062	555	1	now	now	ADV
ejpam-5062	555	2	f(ps	f(ps	NUM
ejpam-5062	555	3	)	)	PUNCT
ejpam-5062	555	4	≤	≤	NUM
ejpam-5062	555	5	f(f−1(v	f(f−1(v	PROPN
ejpam-5062	555	6	)	)	PUNCT
ejpam-5062	555	7	)	)	PUNCT
ejpam-5062	556	1	=	=	SYM
ejpam-5062	556	2	v	v	NOUN
ejpam-5062	556	3	,	,	PUNCT
ejpam-5062	556	4	and	and	CCONJ
ejpam-5062	556	5	we	we	PRON
ejpam-5062	556	6	have	have	AUX
ejpam-5062	556	7	shown	show	VERB
ejpam-5062	556	8	that	that	SCONJ
ejpam-5062	556	9	{	{	PUNCT
ejpam-5062	556	10	f(pi)}i∈n	f(pi)}i∈n	NOUN
ejpam-5062	556	11	is	be	AUX
ejpam-5062	556	12	a	a	DET
ejpam-5062	556	13	countable	countable	ADJ
ejpam-5062	556	14	sequence	sequence	NOUN
ejpam-5062	556	15	of	of	ADP
ejpam-5062	556	16	fuzzy	fuzzy	ADJ
ejpam-5062	556	17	points	point	NOUN
ejpam-5062	556	18	in	in	ADP
ejpam-5062	556	19	y	y	PRON
ejpam-5062	556	20	such	such	ADJ
ejpam-5062	556	21	that	that	PRON
ejpam-5062	556	22	for	for	ADP
ejpam-5062	556	23	any	any	DET
ejpam-5062	556	24	fuzzy	fuzzy	ADJ
ejpam-5062	556	25	strongly	strongly	ADV
ejpam-5062	556	26	semi	semi	ADV
ejpam-5062	556	27	pre	pre	ADJ
ejpam-5062	556	28	-	-	ADJ
ejpam-5062	556	29	open	open	ADJ
ejpam-5062	556	30	set	set	VERB
ejpam-5062	556	31	v	v	NOUN
ejpam-5062	556	32	in	in	ADP
ejpam-5062	556	33	y	y	PROPN
ejpam-5062	556	34	,	,	PUNCT
ejpam-5062	556	35	v	v	ADP
ejpam-5062	556	36	̸=	̸=	PROPN
ejpam-5062	556	37	0y	0y	NOUN
ejpam-5062	556	38	,	,	PUNCT
ejpam-5062	556	39	there	there	PRON
ejpam-5062	556	40	exists	exist	VERB
ejpam-5062	556	41	a	a	DET
ejpam-5062	556	42	fuzzy	fuzzy	ADJ
ejpam-5062	556	43	point	point	NOUN
ejpam-5062	556	44	f(ps	f(ps	PROPN
ejpam-5062	556	45	)	)	PUNCT
ejpam-5062	556	46	such	such	ADJ
ejpam-5062	556	47	that	that	DET
ejpam-5062	556	48	ps	ps	PROPN
ejpam-5062	556	49	≤	≤	NUM
ejpam-5062	556	50	v	v	NOUN
ejpam-5062	556	51	,	,	PUNCT
ejpam-5062	556	52	that	that	PRON
ejpam-5062	556	53	is	is	ADV
ejpam-5062	556	54	y	y	NOUN
ejpam-5062	556	55	is	be	AUX
ejpam-5062	556	56	a	a	DET
ejpam-5062	556	57	fuzzy	fuzzy	ADJ
ejpam-5062	556	58	sspo	sspo	NOUN
ejpam-5062	556	59	-	-	PUNCT
ejpam-5062	556	60	separable	separable	NOUN
ejpam-5062	556	61	space	space	NOUN
ejpam-5062	556	62	.	.	PUNCT
ejpam-5062	557	1	sh	sh	PROPN
ejpam-5062	557	2	.	.	PROPN
ejpam-5062	557	3	makolli	makolli	PROPN
ejpam-5062	557	4	,	,	PUNCT
ejpam-5062	557	5	b.	b.	PROPN
ejpam-5062	557	6	krsteska	krsteska	PROPN
ejpam-5062	557	7	/	/	SYM
ejpam-5062	557	8	eur	eur	PROPN
ejpam-5062	557	9	.	.	PUNCT
ejpam-5062	558	1	j.	j.	PROPN
ejpam-5062	558	2	pure	pure	PROPN
ejpam-5062	558	3	appl	appl	PROPN
ejpam-5062	558	4	.	.	PROPN
ejpam-5062	558	5	math	math	PROPN
ejpam-5062	558	6	,	,	PUNCT
ejpam-5062	558	7	17	17	NUM
ejpam-5062	558	8	(	(	PUNCT
ejpam-5062	558	9	2	2	NUM
ejpam-5062	558	10	)	)	PUNCT
ejpam-5062	558	11	(	(	PUNCT
ejpam-5062	558	12	2024	2024	NUM
ejpam-5062	558	13	)	)	PUNCT
ejpam-5062	558	14	,	,	PUNCT
ejpam-5062	558	15	638	638	NUM
ejpam-5062	558	16	-	-	SYM
ejpam-5062	558	17	662	662	NUM
ejpam-5062	558	18	658	658	NUM
ejpam-5062	558	19	theorem	theorem	VERB
ejpam-5062	558	20	32	32	NUM
ejpam-5062	558	21	.	.	PUNCT
ejpam-5062	559	1	let	let	VERB
ejpam-5062	559	2	the	the	DET
ejpam-5062	559	3	mapping	mapping	NOUN
ejpam-5062	559	4	f	f	X
ejpam-5062	559	5	:	:	PUNCT
ejpam-5062	559	6	x	x	X
ejpam-5062	559	7	→	→	SYM
ejpam-5062	559	8	y	y	X
ejpam-5062	559	9	be	be	AUX
ejpam-5062	559	10	a	a	DET
ejpam-5062	559	11	fuzzy	fuzzy	ADJ
ejpam-5062	559	12	strong	strong	ADJ
ejpam-5062	559	13	semi	semi	ADJ
ejpam-5062	559	14	pre	pre	ADJ
ejpam-5062	559	15	-	-	ADJ
ejpam-5062	559	16	continuous	continuous	ADJ
ejpam-5062	559	17	and	and	CCONJ
ejpam-5062	559	18	surjective	surjective	ADJ
ejpam-5062	559	19	mapping	mapping	NOUN
ejpam-5062	559	20	from	from	ADP
ejpam-5062	559	21	the	the	DET
ejpam-5062	559	22	fuzzy	fuzzy	ADJ
ejpam-5062	559	23	topological	topological	ADJ
ejpam-5062	559	24	space	space	NOUN
ejpam-5062	559	25	x	x	PUNCT
ejpam-5062	559	26	to	to	ADP
ejpam-5062	559	27	a	a	DET
ejpam-5062	559	28	fuzzy	fuzzy	ADJ
ejpam-5062	559	29	topological	topological	ADJ
ejpam-5062	559	30	space	space	NOUN
ejpam-5062	559	31	y	y	PROPN
ejpam-5062	559	32	.	.	PUNCT
ejpam-5062	560	1	if	if	SCONJ
ejpam-5062	560	2	the	the	DET
ejpam-5062	560	3	space	space	NOUN
ejpam-5062	560	4	x	x	PUNCT
ejpam-5062	560	5	is	be	AUX
ejpam-5062	560	6	fuzzy	fuzzy	ADJ
ejpam-5062	560	7	sspo	sspo	NOUN
ejpam-5062	560	8	-	-	PUNCT
ejpam-5062	560	9	separable	separable	NOUN
ejpam-5062	560	10	then	then	ADV
ejpam-5062	560	11	the	the	DET
ejpam-5062	560	12	space	space	NOUN
ejpam-5062	560	13	y	y	PROPN
ejpam-5062	560	14	is	be	AUX
ejpam-5062	560	15	fuzzy	fuzzy	ADJ
ejpam-5062	560	16	separable	separable	ADJ
ejpam-5062	560	17	space	space	NOUN
ejpam-5062	560	18	.	.	PUNCT
ejpam-5062	561	1	proof	proof	NOUN
ejpam-5062	561	2	.	.	PUNCT
ejpam-5062	562	1	similar	similar	ADJ
ejpam-5062	562	2	to	to	ADP
ejpam-5062	562	3	theorem	theorem	VERB
ejpam-5062	562	4	31	31	NUM
ejpam-5062	562	5	theorem	theorem	NOUN
ejpam-5062	562	6	33	33	NUM
ejpam-5062	562	7	.	.	PUNCT
ejpam-5062	563	1	let	let	VERB
ejpam-5062	563	2	the	the	DET
ejpam-5062	563	3	mapping	mapping	NOUN
ejpam-5062	563	4	f	f	X
ejpam-5062	563	5	:	:	PUNCT
ejpam-5062	563	6	x	x	X
ejpam-5062	563	7	→	→	SYM
ejpam-5062	563	8	y	y	X
ejpam-5062	563	9	be	be	AUX
ejpam-5062	563	10	a	a	DET
ejpam-5062	563	11	fuzzy	fuzzy	ADJ
ejpam-5062	563	12	sspo	sspo	NOUN
ejpam-5062	563	13	homeomorphism	homeomorphism	PROPN
ejpam-5062	563	14	from	from	ADP
ejpam-5062	563	15	the	the	DET
ejpam-5062	563	16	fuzzy	fuzzy	ADJ
ejpam-5062	563	17	topological	topological	ADJ
ejpam-5062	563	18	space	space	NOUN
ejpam-5062	563	19	x	x	PUNCT
ejpam-5062	563	20	to	to	ADP
ejpam-5062	563	21	a	a	DET
ejpam-5062	563	22	fuzzy	fuzzy	ADJ
ejpam-5062	563	23	topological	topological	ADJ
ejpam-5062	563	24	space	space	NOUN
ejpam-5062	563	25	y	y	PROPN
ejpam-5062	563	26	.	.	PUNCT
ejpam-5062	564	1	if	if	SCONJ
ejpam-5062	564	2	the	the	DET
ejpam-5062	564	3	space	space	NOUN
ejpam-5062	564	4	x	x	PUNCT
ejpam-5062	564	5	is	be	AUX
ejpam-5062	564	6	sspo	sspo	NOUN
ejpam-5062	564	7	-	-	PUNCT
ejpam-5062	564	8	separable	separable	NOUN
ejpam-5062	564	9	then	then	ADV
ejpam-5062	564	10	y	y	PROPN
ejpam-5062	564	11	will	will	AUX
ejpam-5062	564	12	also	also	ADV
ejpam-5062	564	13	be	be	AUX
ejpam-5062	564	14	sspo	sspo	NOUN
ejpam-5062	564	15	-	-	PUNCT
ejpam-5062	564	16	separable	separable	NOUN
ejpam-5062	564	17	space	space	NOUN
ejpam-5062	564	18	.	.	PUNCT
ejpam-5062	565	1	proof	proof	NOUN
ejpam-5062	565	2	.	.	PUNCT
ejpam-5062	566	1	let	let	VERB
ejpam-5062	566	2	us	we	PRON
ejpam-5062	566	3	consider	consider	VERB
ejpam-5062	566	4	a	a	DET
ejpam-5062	566	5	countable	countable	ADJ
ejpam-5062	566	6	sequence	sequence	NOUN
ejpam-5062	566	7	of	of	ADP
ejpam-5062	566	8	fuzzy	fuzzy	ADJ
ejpam-5062	566	9	points	point	NOUN
ejpam-5062	566	10	{	{	PUNCT
ejpam-5062	566	11	pi}i∈n	pi}i∈n	ADV
ejpam-5062	566	12	from	from	ADP
ejpam-5062	566	13	x	x	PRON
ejpam-5062	566	14	such	such	ADJ
ejpam-5062	566	15	that	that	PRON
ejpam-5062	566	16	for	for	ADP
ejpam-5062	566	17	any	any	DET
ejpam-5062	566	18	fuzzy	fuzzy	ADJ
ejpam-5062	566	19	strongly	strongly	ADV
ejpam-5062	566	20	semi	semi	ADV
ejpam-5062	566	21	pre	pre	ADJ
ejpam-5062	566	22	-	-	ADJ
ejpam-5062	566	23	open	open	ADJ
ejpam-5062	566	24	set	set	NOUN
ejpam-5062	566	25	w	w	NOUN
ejpam-5062	566	26	in	in	ADP
ejpam-5062	566	27	x	x	PROPN
ejpam-5062	566	28	,	,	PUNCT
ejpam-5062	566	29	w	w	PROPN
ejpam-5062	566	30	̸=	̸=	PROPN
ejpam-5062	566	31	0x	0x	NOUN
ejpam-5062	566	32	,	,	PUNCT
ejpam-5062	566	33	there	there	PRON
ejpam-5062	566	34	exists	exist	VERB
ejpam-5062	566	35	a	a	DET
ejpam-5062	566	36	fuzzy	fuzzy	ADJ
ejpam-5062	566	37	point	point	NOUN
ejpam-5062	566	38	pi	pi	NOUN
ejpam-5062	566	39	such	such	ADJ
ejpam-5062	566	40	that	that	DET
ejpam-5062	566	41	pi	pi	NOUN
ejpam-5062	567	1	≤	≤	X
ejpam-5062	567	2	w	w	NOUN
ejpam-5062	567	3	.	.	PUNCT
ejpam-5062	568	1	then	then	ADV
ejpam-5062	568	2	the	the	DET
ejpam-5062	568	3	sequence	sequence	NOUN
ejpam-5062	568	4	{	{	PUNCT
ejpam-5062	568	5	f(pi)}i∈n	f(pi)}i∈n	PROPN
ejpam-5062	568	6	is	be	AUX
ejpam-5062	568	7	a	a	DET
ejpam-5062	568	8	countable	countable	ADJ
ejpam-5062	568	9	sequence	sequence	NOUN
ejpam-5062	568	10	of	of	ADP
ejpam-5062	568	11	fuzzy	fuzzy	ADJ
ejpam-5062	568	12	points	point	NOUN
ejpam-5062	568	13	in	in	ADP
ejpam-5062	568	14	y	y	PROPN
ejpam-5062	568	15	.	.	PUNCT
ejpam-5062	569	1	let	let	VERB
ejpam-5062	569	2	us	we	PRON
ejpam-5062	569	3	suppose	suppose	VERB
ejpam-5062	569	4	that	that	SCONJ
ejpam-5062	569	5	v	v	NOUN
ejpam-5062	569	6	is	be	AUX
ejpam-5062	569	7	a	a	DET
ejpam-5062	569	8	fuzzy	fuzzy	ADJ
ejpam-5062	569	9	strongly	strongly	ADV
ejpam-5062	569	10	semi	semi	ADJ
ejpam-5062	569	11	pre	pre	ADJ
ejpam-5062	569	12	-	-	ADJ
ejpam-5062	569	13	open	open	ADJ
ejpam-5062	569	14	set	set	NOUN
ejpam-5062	569	15	in	in	ADP
ejpam-5062	569	16	y	y	PROPN
ejpam-5062	569	17	such	such	ADJ
ejpam-5062	569	18	that	that	PRON
ejpam-5062	569	19	v	v	ADP
ejpam-5062	569	20	̸=	̸=	PROPN
ejpam-5062	569	21	0y	0y	NOUN
ejpam-5062	569	22	.	.	PUNCT
ejpam-5062	570	1	from	from	ADP
ejpam-5062	570	2	the	the	DET
ejpam-5062	570	3	assumption	assumption	NOUN
ejpam-5062	570	4	of	of	ADP
ejpam-5062	570	5	the	the	DET
ejpam-5062	570	6	theorem	theorem	ADJ
ejpam-5062	570	7	f−1(v	f−1(v	PROPN
ejpam-5062	570	8	)	)	PUNCT
ejpam-5062	570	9	is	be	AUX
ejpam-5062	570	10	a	a	DET
ejpam-5062	570	11	fuzzy	fuzzy	ADJ
ejpam-5062	570	12	strongly	strongly	ADV
ejpam-5062	570	13	semi	semi	ADJ
ejpam-5062	570	14	pre	pre	ADJ
ejpam-5062	570	15	-	-	ADJ
ejpam-5062	570	16	open	open	ADJ
ejpam-5062	570	17	set	set	NOUN
ejpam-5062	570	18	in	in	ADP
ejpam-5062	570	19	x	x	PUNCT
ejpam-5062	570	20	and	and	CCONJ
ejpam-5062	570	21	f−1(v	f−1(v	NOUN
ejpam-5062	570	22	)	)	PUNCT
ejpam-5062	571	1	̸=	̸=	PROPN
ejpam-5062	571	2	0x	0x	NOUN
ejpam-5062	571	3	.	.	PUNCT
ejpam-5062	572	1	due	due	ADP
ejpam-5062	572	2	to	to	ADP
ejpam-5062	572	3	the	the	DET
ejpam-5062	572	4	fact	fact	NOUN
ejpam-5062	572	5	that	that	SCONJ
ejpam-5062	572	6	the	the	DET
ejpam-5062	572	7	space	space	NOUN
ejpam-5062	572	8	x	x	PUNCT
ejpam-5062	572	9	is	be	AUX
ejpam-5062	572	10	fuzzy	fuzzy	ADJ
ejpam-5062	572	11	sspo	sspo	NOUN
ejpam-5062	572	12	-	-	PUNCT
ejpam-5062	572	13	separable	separable	NOUN
ejpam-5062	572	14	then	then	ADV
ejpam-5062	572	15	there	there	PRON
ejpam-5062	572	16	exists	exist	VERB
ejpam-5062	572	17	a	a	DET
ejpam-5062	572	18	fuzzy	fuzzy	ADJ
ejpam-5062	572	19	point	point	NOUN
ejpam-5062	572	20	ps	ps	INTJ
ejpam-5062	572	21	such	such	ADJ
ejpam-5062	572	22	that	that	DET
ejpam-5062	572	23	ps	ps	PROPN
ejpam-5062	572	24	≤	≤	PROPN
ejpam-5062	572	25	f−1(v	f−1(v	PROPN
ejpam-5062	572	26	)	)	PUNCT
ejpam-5062	572	27	.	.	PUNCT
ejpam-5062	573	1	now	now	ADV
ejpam-5062	573	2	f(ps	f(ps	NUM
ejpam-5062	573	3	)	)	PUNCT
ejpam-5062	573	4	≤	≤	NUM
ejpam-5062	573	5	f(f−1(v	f(f−1(v	PROPN
ejpam-5062	573	6	)	)	PUNCT
ejpam-5062	573	7	)	)	PUNCT
ejpam-5062	574	1	=	=	SYM
ejpam-5062	574	2	v	v	NOUN
ejpam-5062	574	3	and	and	CCONJ
ejpam-5062	574	4	we	we	PRON
ejpam-5062	574	5	have	have	AUX
ejpam-5062	574	6	shown	show	VERB
ejpam-5062	574	7	that	that	SCONJ
ejpam-5062	574	8	{	{	PUNCT
ejpam-5062	574	9	f(pi)}i∈n	f(pi)}i∈n	NOUN
ejpam-5062	574	10	is	be	AUX
ejpam-5062	574	11	a	a	DET
ejpam-5062	574	12	countable	countable	ADJ
ejpam-5062	574	13	sequence	sequence	NOUN
ejpam-5062	574	14	satisfying	satisfy	VERB
ejpam-5062	574	15	the	the	DET
ejpam-5062	574	16	conditions	condition	NOUN
ejpam-5062	574	17	of	of	ADP
ejpam-5062	574	18	definition	definition	NOUN
ejpam-5062	574	19	25	25	NUM
ejpam-5062	574	20	,	,	PUNCT
ejpam-5062	574	21	therefore	therefore	ADV
ejpam-5062	574	22	y	y	PROPN
ejpam-5062	574	23	is	be	AUX
ejpam-5062	574	24	a	a	DET
ejpam-5062	574	25	fuzzy	fuzzy	ADJ
ejpam-5062	574	26	sspo	sspo	NOUN
ejpam-5062	574	27	-	-	PUNCT
ejpam-5062	574	28	separable	separable	NOUN
ejpam-5062	574	29	space	space	NOUN
ejpam-5062	574	30	.	.	PUNCT
ejpam-5062	575	1	definition	definition	NOUN
ejpam-5062	575	2	26	26	NUM
ejpam-5062	575	3	.	.	PUNCT
ejpam-5062	576	1	the	the	DET
ejpam-5062	576	2	fuzzy	fuzzy	ADJ
ejpam-5062	576	3	set	set	VERB
ejpam-5062	576	4	a	a	PRON
ejpam-5062	576	5	of	of	ADP
ejpam-5062	576	6	the	the	DET
ejpam-5062	576	7	fuzzy	fuzzy	ADJ
ejpam-5062	576	8	topological	topological	ADJ
ejpam-5062	576	9	space	space	NOUN
ejpam-5062	576	10	(	(	PUNCT
ejpam-5062	576	11	x	x	X
ejpam-5062	576	12	,	,	PUNCT
ejpam-5062	576	13	τ	τ	X
ejpam-5062	576	14	)	)	PUNCT
ejpam-5062	576	15	is	be	AUX
ejpam-5062	576	16	called	call	VERB
ejpam-5062	576	17	α−	α−	ADP
ejpam-5062	576	18	sspo	sspo	PROPN
ejpam-5062	576	19	lindelof	lindelof	PROPN
ejpam-5062	576	20	(	(	PUNCT
ejpam-5062	576	21	respectively	respectively	ADV
ejpam-5062	576	22	α∗	α∗	VERB
ejpam-5062	576	23	−	−	PROPN
ejpam-5062	576	24	sspo	sspo	NOUN
ejpam-5062	576	25	lindelof	lindelof	NOUN
ejpam-5062	576	26	)	)	PUNCT
ejpam-5062	576	27	if	if	SCONJ
ejpam-5062	576	28	every	every	DET
ejpam-5062	576	29	α	α	NOUN
ejpam-5062	576	30	−	−	NOUN
ejpam-5062	576	31	sspo	sspo	NOUN
ejpam-5062	576	32	shading	shading	NOUN
ejpam-5062	576	33	(	(	PUNCT
ejpam-5062	576	34	α∗	α∗	NOUN
ejpam-5062	576	35	−	−	NOUN
ejpam-5062	576	36	sspo	sspo	NOUN
ejpam-5062	576	37	shading	shading	NOUN
ejpam-5062	576	38	)	)	PUNCT
ejpam-5062	576	39	of	of	ADP
ejpam-5062	576	40	the	the	DET
ejpam-5062	576	41	set	set	NOUN
ejpam-5062	576	42	a	a	PRON
ejpam-5062	576	43	has	have	VERB
ejpam-5062	576	44	a	a	DET
ejpam-5062	576	45	countable	countable	ADJ
ejpam-5062	576	46	α−	α−	ADP
ejpam-5062	576	47	sspo	sspo	NOUN
ejpam-5062	576	48	subshading	subshade	VERB
ejpam-5062	576	49	(	(	PUNCT
ejpam-5062	576	50	countable	countable	ADJ
ejpam-5062	576	51	α∗	α∗	NOUN
ejpam-5062	576	52	−	−	NOUN
ejpam-5062	576	53	sspo	sspo	NOUN
ejpam-5062	576	54	subshading	subshade	VERB
ejpam-5062	576	55	)	)	PUNCT
ejpam-5062	576	56	.	.	PUNCT
ejpam-5062	577	1	if	if	SCONJ
ejpam-5062	577	2	instead	instead	ADV
ejpam-5062	577	3	of	of	ADP
ejpam-5062	577	4	the	the	DET
ejpam-5062	577	5	fuzzy	fuzzy	ADJ
ejpam-5062	577	6	set	set	VERB
ejpam-5062	577	7	a	a	PRON
ejpam-5062	577	8	we	we	PRON
ejpam-5062	577	9	consider	consider	VERB
ejpam-5062	577	10	space	space	NOUN
ejpam-5062	577	11	x	x	PUNCT
ejpam-5062	577	12	then	then	ADV
ejpam-5062	577	13	we	we	PRON
ejpam-5062	577	14	can	can	AUX
ejpam-5062	577	15	state	state	VERB
ejpam-5062	577	16	that	that	SCONJ
ejpam-5062	577	17	the	the	DET
ejpam-5062	577	18	fuzzy	fuzzy	ADJ
ejpam-5062	577	19	topological	topological	ADJ
ejpam-5062	577	20	space	space	NOUN
ejpam-5062	577	21	x	x	PUNCT
ejpam-5062	577	22	is	be	AUX
ejpam-5062	577	23	α−	α−	ADP
ejpam-5062	577	24	sspo	sspo	NOUN
ejpam-5062	577	25	lindelof	lindelof	PROPN
ejpam-5062	577	26	(	(	PUNCT
ejpam-5062	577	27	respectively	respectively	ADV
ejpam-5062	577	28	α∗	α∗	VERB
ejpam-5062	577	29	−	−	PROPN
ejpam-5062	577	30	sspo	sspo	NOUN
ejpam-5062	577	31	lindelof	lindelof	NOUN
ejpam-5062	577	32	)	)	PUNCT
ejpam-5062	577	33	.	.	PUNCT
ejpam-5062	578	1	it	it	PRON
ejpam-5062	578	2	is	be	AUX
ejpam-5062	578	3	certain	certain	ADJ
ejpam-5062	578	4	that	that	SCONJ
ejpam-5062	578	5	from	from	ADP
ejpam-5062	578	6	the	the	DET
ejpam-5062	578	7	above	above	ADJ
ejpam-5062	578	8	definition	definition	NOUN
ejpam-5062	578	9	we	we	PRON
ejpam-5062	578	10	can	can	AUX
ejpam-5062	578	11	conclude	conclude	VERB
ejpam-5062	578	12	that	that	SCONJ
ejpam-5062	578	13	every	every	DET
ejpam-5062	578	14	α	α	NOUN
ejpam-5062	578	15	−	−	NOUN
ejpam-5062	578	16	sspo	sspo	NOUN
ejpam-5062	578	17	compact	compact	ADJ
ejpam-5062	578	18	(	(	PUNCT
ejpam-5062	578	19	α∗−sspo	α∗−sspo	PROPN
ejpam-5062	578	20	compact	compact	ADJ
ejpam-5062	578	21	)	)	PUNCT
ejpam-5062	578	22	space	space	NOUN
ejpam-5062	578	23	is	be	AUX
ejpam-5062	578	24	also	also	ADV
ejpam-5062	578	25	an	an	DET
ejpam-5062	578	26	α−sspo	α−sspo	X
ejpam-5062	578	27	lindelof	lindelof	X
ejpam-5062	578	28	(	(	PUNCT
ejpam-5062	578	29	α∗−sspo	α∗−sspo	PROPN
ejpam-5062	578	30	lindelof	lindelof	PROPN
ejpam-5062	578	31	)	)	PUNCT
ejpam-5062	578	32	space	space	NOUN
ejpam-5062	578	33	.	.	PUNCT
ejpam-5062	579	1	every	every	DET
ejpam-5062	579	2	α	α	NOUN
ejpam-5062	579	3	−	−	PROPN
ejpam-5062	579	4	sspo	sspo	NOUN
ejpam-5062	579	5	lindelof	lindelof	PROPN
ejpam-5062	579	6	(	(	PUNCT
ejpam-5062	579	7	α∗	α∗	NOUN
ejpam-5062	579	8	−	−	PROPN
ejpam-5062	579	9	sspo	sspo	NOUN
ejpam-5062	579	10	lindelof	lindelof	NOUN
ejpam-5062	579	11	)	)	PUNCT
ejpam-5062	579	12	space	space	NOUN
ejpam-5062	579	13	is	be	AUX
ejpam-5062	579	14	an	an	DET
ejpam-5062	579	15	αlindelof	αlindelof	ADJ
ejpam-5062	579	16	(	(	PUNCT
ejpam-5062	579	17	α∗-lindelof	α∗-lindelof	ADJ
ejpam-5062	579	18	)	)	PUNCT
ejpam-5062	579	19	space	space	NOUN
ejpam-5062	579	20	.	.	PUNCT
ejpam-5062	580	1	theorem	theorem	VERB
ejpam-5062	580	2	34	34	NUM
ejpam-5062	580	3	.	.	PUNCT
ejpam-5062	581	1	if	if	SCONJ
ejpam-5062	581	2	the	the	DET
ejpam-5062	581	3	fuzzy	fuzzy	ADJ
ejpam-5062	581	4	topological	topological	ADJ
ejpam-5062	581	5	space	space	NOUN
ejpam-5062	581	6	(	(	PUNCT
ejpam-5062	581	7	x	x	X
ejpam-5062	581	8	,	,	PUNCT
ejpam-5062	581	9	τ	τ	X
ejpam-5062	581	10	)	)	PUNCT
ejpam-5062	581	11	has	have	VERB
ejpam-5062	581	12	a	a	DET
ejpam-5062	581	13	countable	countable	ADJ
ejpam-5062	581	14	base	base	NOUN
ejpam-5062	581	15	b	b	PROPN
ejpam-5062	581	16	of	of	ADP
ejpam-5062	581	17	fuzzy	fuzzy	ADJ
ejpam-5062	581	18	strongly	strongly	ADV
ejpam-5062	581	19	semi	semi	ADV
ejpam-5062	581	20	pre	pre	ADJ
ejpam-5062	581	21	-	-	ADJ
ejpam-5062	581	22	open	open	ADJ
ejpam-5062	581	23	sets	set	NOUN
ejpam-5062	581	24	then	then	ADV
ejpam-5062	581	25	(	(	PUNCT
ejpam-5062	581	26	x	x	X
ejpam-5062	581	27	,	,	PUNCT
ejpam-5062	581	28	τ	τ	X
ejpam-5062	581	29	)	)	PUNCT
ejpam-5062	581	30	is	be	AUX
ejpam-5062	581	31	an	an	DET
ejpam-5062	581	32	α−sspo	α−sspo	NOUN
ejpam-5062	581	33	lindelof	lindelof	X
ejpam-5062	581	34	(	(	PUNCT
ejpam-5062	581	35	respectively	respectively	ADV
ejpam-5062	581	36	α∗−sspo	α∗−sspo	PROPN
ejpam-5062	581	37	lindelof	lindelof	PROPN
ejpam-5062	581	38	)	)	PUNCT
ejpam-5062	581	39	space	space	NOUN
ejpam-5062	581	40	.	.	PUNCT
ejpam-5062	582	1	proof	proof	NOUN
ejpam-5062	582	2	.	.	PUNCT
ejpam-5062	583	1	similar	similar	ADJ
ejpam-5062	583	2	to	to	ADP
ejpam-5062	583	3	theorem	theorem	NOUN
ejpam-5062	583	4	28	28	NUM
ejpam-5062	583	5	.	.	PUNCT
ejpam-5062	584	1	theorem	theorem	VERB
ejpam-5062	584	2	35	35	NUM
ejpam-5062	584	3	.	.	PUNCT
ejpam-5062	585	1	let	let	VERB
ejpam-5062	585	2	the	the	DET
ejpam-5062	585	3	fuzzy	fuzzy	ADJ
ejpam-5062	585	4	set	set	VERB
ejpam-5062	585	5	a	a	PRON
ejpam-5062	585	6	of	of	ADP
ejpam-5062	585	7	the	the	DET
ejpam-5062	585	8	fuzzy	fuzzy	ADJ
ejpam-5062	585	9	topological	topological	ADJ
ejpam-5062	585	10	space	space	NOUN
ejpam-5062	585	11	(	(	PUNCT
ejpam-5062	585	12	x	x	X
ejpam-5062	585	13	,	,	PUNCT
ejpam-5062	585	14	τ	τ	X
ejpam-5062	585	15	)	)	PUNCT
ejpam-5062	585	16	be	be	VERB
ejpam-5062	585	17	an	an	DET
ejpam-5062	585	18	α	α	NOUN
ejpam-5062	585	19	−	−	NOUN
ejpam-5062	585	20	sspo	sspo	NOUN
ejpam-5062	585	21	lindelof	lindelof	PROPN
ejpam-5062	585	22	(	(	PUNCT
ejpam-5062	585	23	α∗	α∗	NOUN
ejpam-5062	585	24	−	−	PROPN
ejpam-5062	585	25	sspo	sspo	NOUN
ejpam-5062	585	26	lindelof	lindelof	NOUN
ejpam-5062	585	27	)	)	PUNCT
ejpam-5062	585	28	set	set	NOUN
ejpam-5062	585	29	.	.	PUNCT
ejpam-5062	586	1	the	the	DET
ejpam-5062	586	2	fuzzy	fuzzy	ADJ
ejpam-5062	586	3	set	set	VERB
ejpam-5062	586	4	a	a	PRON
ejpam-5062	586	5	is	be	AUX
ejpam-5062	586	6	countable	countable	ADJ
ejpam-5062	586	7	α	α	PRON
ejpam-5062	586	8	−	−	NOUN
ejpam-5062	586	9	sspo	sspo	NOUN
ejpam-5062	586	10	compact	compact	ADJ
ejpam-5062	586	11	(	(	PUNCT
ejpam-5062	586	12	countable	countable	ADJ
ejpam-5062	586	13	α∗	α∗	NOUN
ejpam-5062	586	14	−	−	NOUN
ejpam-5062	586	15	sspo	sspo	NOUN
ejpam-5062	586	16	compact	compact	ADJ
ejpam-5062	586	17	)	)	PUNCT
ejpam-5062	587	1	if	if	SCONJ
ejpam-5062	587	2	and	and	CCONJ
ejpam-5062	587	3	only	only	ADV
ejpam-5062	587	4	if	if	SCONJ
ejpam-5062	587	5	a	a	PRON
ejpam-5062	587	6	is	be	AUX
ejpam-5062	587	7	α	α	DET
ejpam-5062	587	8	−	−	PROPN
ejpam-5062	587	9	sspo	sspo	NOUN
ejpam-5062	587	10	compact	compact	ADJ
ejpam-5062	587	11	(	(	PUNCT
ejpam-5062	587	12	α∗	α∗	NOUN
ejpam-5062	587	13	−	−	NOUN
ejpam-5062	587	14	sspo	sspo	NOUN
ejpam-5062	587	15	compact	compact	ADJ
ejpam-5062	587	16	)	)	PUNCT
ejpam-5062	587	17	.	.	PUNCT
ejpam-5062	588	1	sh	sh	PROPN
ejpam-5062	588	2	.	.	PROPN
ejpam-5062	588	3	makolli	makolli	PROPN
ejpam-5062	588	4	,	,	PUNCT
ejpam-5062	588	5	b.	b.	PROPN
ejpam-5062	588	6	krsteska	krsteska	PROPN
ejpam-5062	588	7	/	/	SYM
ejpam-5062	588	8	eur	eur	PROPN
ejpam-5062	588	9	.	.	PUNCT
ejpam-5062	589	1	j.	j.	PROPN
ejpam-5062	589	2	pure	pure	PROPN
ejpam-5062	589	3	appl	appl	PROPN
ejpam-5062	589	4	.	.	PROPN
ejpam-5062	589	5	math	math	PROPN
ejpam-5062	589	6	,	,	PUNCT
ejpam-5062	589	7	17	17	NUM
ejpam-5062	589	8	(	(	PUNCT
ejpam-5062	589	9	2	2	NUM
ejpam-5062	589	10	)	)	PUNCT
ejpam-5062	589	11	(	(	PUNCT
ejpam-5062	589	12	2024	2024	NUM
ejpam-5062	589	13	)	)	PUNCT
ejpam-5062	589	14	,	,	PUNCT
ejpam-5062	589	15	638	638	NUM
ejpam-5062	589	16	-	-	SYM
ejpam-5062	589	17	662	662	NUM
ejpam-5062	589	18	659	659	NUM
ejpam-5062	589	19	proof	proof	NOUN
ejpam-5062	589	20	.	.	PUNCT
ejpam-5062	590	1	it	it	PRON
ejpam-5062	590	2	is	be	AUX
ejpam-5062	590	3	certain	certain	ADJ
ejpam-5062	590	4	that	that	SCONJ
ejpam-5062	590	5	every	every	DET
ejpam-5062	590	6	α	α	NOUN
ejpam-5062	590	7	−	−	NOUN
ejpam-5062	590	8	sspo	sspo	NOUN
ejpam-5062	590	9	compact	compact	ADJ
ejpam-5062	590	10	set	set	VERB
ejpam-5062	590	11	in	in	ADP
ejpam-5062	590	12	the	the	DET
ejpam-5062	590	13	fuzzy	fuzzy	ADJ
ejpam-5062	590	14	topological	topological	ADJ
ejpam-5062	590	15	space	space	NOUN
ejpam-5062	590	16	(	(	PUNCT
ejpam-5062	590	17	x	x	X
ejpam-5062	590	18	,	,	PUNCT
ejpam-5062	590	19	τ	τ	X
ejpam-5062	590	20	)	)	PUNCT
ejpam-5062	590	21	is	be	AUX
ejpam-5062	590	22	also	also	ADV
ejpam-5062	590	23	a	a	DET
ejpam-5062	590	24	countableα−	countableα−	PROPN
ejpam-5062	590	25	sspo	sspo	NOUN
ejpam-5062	590	26	compact	compact	ADJ
ejpam-5062	590	27	fuzzy	fuzzy	ADJ
ejpam-5062	590	28	set	set	NOUN
ejpam-5062	590	29	.	.	PUNCT
ejpam-5062	591	1	conversely	conversely	ADV
ejpam-5062	591	2	,	,	PUNCT
ejpam-5062	591	3	let	let	VERB
ejpam-5062	591	4	us	we	PRON
ejpam-5062	591	5	suppose	suppose	VERB
ejpam-5062	591	6	that	that	SCONJ
ejpam-5062	591	7	the	the	DET
ejpam-5062	591	8	fuzzy	fuzzy	NOUN
ejpam-5062	591	9	set	set	VERB
ejpam-5062	591	10	a	a	DET
ejpam-5062	591	11	in	in	ADP
ejpam-5062	591	12	(	(	PUNCT
ejpam-5062	591	13	x	x	NOUN
ejpam-5062	591	14	,	,	PUNCT
ejpam-5062	591	15	τ	τ	X
ejpam-5062	591	16	)	)	PUNCT
ejpam-5062	591	17	is	be	AUX
ejpam-5062	591	18	a	a	DET
ejpam-5062	591	19	countable	countable	ADJ
ejpam-5062	591	20	α−sspo	α−sspo	NOUN
ejpam-5062	591	21	compact	compact	ADJ
ejpam-5062	591	22	set	set	NOUN
ejpam-5062	591	23	.	.	PUNCT
ejpam-5062	592	1	let	let	VERB
ejpam-5062	592	2	us	we	PRON
ejpam-5062	592	3	suppose	suppose	VERB
ejpam-5062	592	4	that	that	SCONJ
ejpam-5062	592	5	the	the	DET
ejpam-5062	592	6	family	family	NOUN
ejpam-5062	592	7	of	of	ADP
ejpam-5062	592	8	fuzzy	fuzzy	ADJ
ejpam-5062	592	9	strongly	strongly	ADV
ejpam-5062	592	10	semi	semi	ADV
ejpam-5062	592	11	pre	pre	ADJ
ejpam-5062	592	12	-	-	ADJ
ejpam-5062	592	13	open	open	ADJ
ejpam-5062	592	14	sets	set	VERB
ejpam-5062	592	15	u	u	NOUN
ejpam-5062	592	16	=	=	SYM
ejpam-5062	592	17	{	{	PUNCT
ejpam-5062	592	18	ui	ui	PROPN
ejpam-5062	592	19	,	,	PUNCT
ejpam-5062	592	20	i	i	PRON
ejpam-5062	592	21	∈	∈	VERB
ejpam-5062	592	22	i	i	PRON
ejpam-5062	592	23	}	}	PUNCT
ejpam-5062	592	24	is	be	AUX
ejpam-5062	592	25	an	an	DET
ejpam-5062	592	26	α	α	NOUN
ejpam-5062	592	27	−	−	NOUN
ejpam-5062	592	28	sspo	sspo	NOUN
ejpam-5062	592	29	shading	shading	NOUN
ejpam-5062	592	30	of	of	ADP
ejpam-5062	592	31	a.	a.	NOUN
ejpam-5062	592	32	since	since	SCONJ
ejpam-5062	592	33	the	the	DET
ejpam-5062	592	34	fuzzy	fuzzy	NOUN
ejpam-5062	592	35	set	set	VERB
ejpam-5062	592	36	a	a	PRON
ejpam-5062	592	37	of	of	ADP
ejpam-5062	592	38	(	(	PUNCT
ejpam-5062	592	39	x	x	PROPN
ejpam-5062	592	40	,	,	PUNCT
ejpam-5062	592	41	τ	τ	X
ejpam-5062	592	42	)	)	PUNCT
ejpam-5062	592	43	is	be	AUX
ejpam-5062	592	44	an	an	DET
ejpam-5062	592	45	α	α	NOUN
ejpam-5062	592	46	−	−	NOUN
ejpam-5062	592	47	sspo	sspo	NOUN
ejpam-5062	592	48	lindelof	lindelof	PROPN
ejpam-5062	592	49	then	then	ADV
ejpam-5062	592	50	there	there	PRON
ejpam-5062	592	51	exists	exist	VERB
ejpam-5062	592	52	a	a	DET
ejpam-5062	592	53	countable	countable	ADJ
ejpam-5062	592	54	α	α	NOUN
ejpam-5062	592	55	−	−	NOUN
ejpam-5062	592	56	sspo	sspo	NOUN
ejpam-5062	592	57	subshading	subshade	VERB
ejpam-5062	592	58	v1	v1	NOUN
ejpam-5062	592	59	of	of	ADP
ejpam-5062	592	60	α	α	NOUN
ejpam-5062	592	61	−	−	PROPN
ejpam-5062	592	62	sspo	sspo	NOUN
ejpam-5062	592	63	shading	shade	VERB
ejpam-5062	592	64	u	u	NOUN
ejpam-5062	592	65	.	.	PUNCT
ejpam-5062	593	1	based	base	VERB
ejpam-5062	593	2	on	on	ADP
ejpam-5062	593	3	the	the	DET
ejpam-5062	593	4	assumption	assumption	NOUN
ejpam-5062	593	5	that	that	SCONJ
ejpam-5062	593	6	the	the	DET
ejpam-5062	593	7	fuzzy	fuzzy	NOUN
ejpam-5062	593	8	set	set	VERB
ejpam-5062	593	9	a	a	PRON
ejpam-5062	593	10	is	be	AUX
ejpam-5062	593	11	countable	countable	ADJ
ejpam-5062	593	12	α	α	PRON
ejpam-5062	593	13	−	−	NOUN
ejpam-5062	593	14	sspo	sspo	NOUN
ejpam-5062	593	15	compact	compact	ADJ
ejpam-5062	593	16	set	set	NOUN
ejpam-5062	593	17	,	,	PUNCT
ejpam-5062	593	18	then	then	ADV
ejpam-5062	593	19	there	there	PRON
ejpam-5062	593	20	exists	exist	VERB
ejpam-5062	593	21	a	a	DET
ejpam-5062	593	22	finite	finite	NOUN
ejpam-5062	593	23	α−sspo	α−sspo	NOUN
ejpam-5062	593	24	subshading	subshade	VERB
ejpam-5062	593	25	v2	v2	PROPN
ejpam-5062	593	26	of	of	ADP
ejpam-5062	593	27	α−sspo	α−sspo	NOUN
ejpam-5062	593	28	shading	shade	VERB
ejpam-5062	593	29	u	u	NOUN
ejpam-5062	593	30	.	.	PUNCT
ejpam-5062	594	1	it	it	PRON
ejpam-5062	594	2	is	be	AUX
ejpam-5062	594	3	clear	clear	ADJ
ejpam-5062	594	4	that	that	SCONJ
ejpam-5062	594	5	given	give	VERB
ejpam-5062	594	6	an	an	DET
ejpam-5062	594	7	α−	α−	NOUN
ejpam-5062	594	8	sspo	sspo	NOUN
ejpam-5062	594	9	shading	shade	VERB
ejpam-5062	594	10	u	u	NOUN
ejpam-5062	594	11	of	of	ADP
ejpam-5062	594	12	the	the	DET
ejpam-5062	594	13	fuzzy	fuzzy	ADJ
ejpam-5062	594	14	set	set	NOUN
ejpam-5062	594	15	a	a	PRON
ejpam-5062	594	16	there	there	PRON
ejpam-5062	594	17	exists	exist	VERB
ejpam-5062	594	18	a	a	DET
ejpam-5062	594	19	finite	finite	NOUN
ejpam-5062	594	20	α−	α−	ADP
ejpam-5062	594	21	sspo	sspo	NOUN
ejpam-5062	594	22	subshading	subshade	VERB
ejpam-5062	594	23	v2	v2	PROPN
ejpam-5062	594	24	of	of	ADP
ejpam-5062	594	25	u	u	NOUN
ejpam-5062	594	26	and	and	CCONJ
ejpam-5062	594	27	subsequently	subsequently	ADV
ejpam-5062	594	28	the	the	DET
ejpam-5062	594	29	fuzzy	fuzzy	ADJ
ejpam-5062	594	30	set	set	VERB
ejpam-5062	594	31	a	a	PRON
ejpam-5062	594	32	is	be	AUX
ejpam-5062	594	33	α−	α−	ADP
ejpam-5062	594	34	sspo	sspo	NOUN
ejpam-5062	594	35	compact	compact	ADJ
ejpam-5062	594	36	.	.	PUNCT
ejpam-5062	595	1	in	in	ADP
ejpam-5062	595	2	similar	similar	ADJ
ejpam-5062	595	3	way	way	NOUN
ejpam-5062	595	4	we	we	PRON
ejpam-5062	595	5	can	can	AUX
ejpam-5062	595	6	prove	prove	VERB
ejpam-5062	595	7	the	the	DET
ejpam-5062	595	8	case	case	NOUN
ejpam-5062	595	9	when	when	SCONJ
ejpam-5062	595	10	a	a	PRON
ejpam-5062	595	11	is	be	AUX
ejpam-5062	595	12	an	an	DET
ejpam-5062	595	13	α∗	α∗	NOUN
ejpam-5062	595	14	−	−	NOUN
ejpam-5062	595	15	sspo	sspo	NOUN
ejpam-5062	595	16	lindelof	lindelof	PROPN
ejpam-5062	595	17	set	set	PROPN
ejpam-5062	595	18	.	.	PUNCT
ejpam-5062	596	1	theorem	theorem	VERB
ejpam-5062	596	2	36	36	NUM
ejpam-5062	596	3	.	.	PUNCT
ejpam-5062	597	1	let	let	VERB
ejpam-5062	597	2	a	a	DET
ejpam-5062	597	3	be	be	AUX
ejpam-5062	597	4	an	an	DET
ejpam-5062	597	5	α−sspo	α−sspo	NOUN
ejpam-5062	597	6	lindelof	lindelof	X
ejpam-5062	597	7	(	(	PUNCT
ejpam-5062	597	8	α∗−sspo	α∗−sspo	PROPN
ejpam-5062	597	9	lindelof	lindelof	PROPN
ejpam-5062	597	10	)	)	PUNCT
ejpam-5062	597	11	fuzzy	fuzzy	ADJ
ejpam-5062	597	12	set	set	VERB
ejpam-5062	597	13	in	in	ADP
ejpam-5062	597	14	(	(	PUNCT
ejpam-5062	597	15	x	x	NOUN
ejpam-5062	597	16	,	,	PUNCT
ejpam-5062	597	17	τ	τ	X
ejpam-5062	597	18	)	)	PUNCT
ejpam-5062	597	19	and	and	CCONJ
ejpam-5062	597	20	let	let	VERB
ejpam-5062	597	21	b	b	PROPN
ejpam-5062	597	22	∈	∈	PROPN
ejpam-5062	597	23	fsspc(τ	fsspc(τ	NOUN
ejpam-5062	597	24	)	)	PUNCT
ejpam-5062	597	25	,	,	PUNCT
ejpam-5062	597	26	then	then	ADV
ejpam-5062	597	27	a	a	DET
ejpam-5062	597	28	∧	∧	PROPN
ejpam-5062	597	29	b	b	PROPN
ejpam-5062	597	30	is	be	AUX
ejpam-5062	597	31	an	an	DET
ejpam-5062	597	32	α	α	NOUN
ejpam-5062	597	33	−	−	NOUN
ejpam-5062	597	34	sspo	sspo	NOUN
ejpam-5062	597	35	lindelof	lindelof	PROPN
ejpam-5062	597	36	(	(	PUNCT
ejpam-5062	597	37	α∗	α∗	NOUN
ejpam-5062	597	38	−	−	PROPN
ejpam-5062	597	39	sspo	sspo	NOUN
ejpam-5062	597	40	lindelof	lindelof	NOUN
ejpam-5062	597	41	)	)	PUNCT
ejpam-5062	597	42	fuzzy	fuzzy	ADJ
ejpam-5062	597	43	set	set	VERB
ejpam-5062	597	44	in	in	ADP
ejpam-5062	597	45	the	the	DET
ejpam-5062	597	46	fuzzy	fuzzy	ADJ
ejpam-5062	597	47	topological	topological	ADJ
ejpam-5062	597	48	space	space	NOUN
ejpam-5062	597	49	(	(	PUNCT
ejpam-5062	597	50	x	x	X
ejpam-5062	597	51	,	,	PUNCT
ejpam-5062	597	52	τ	τ	PROPN
ejpam-5062	597	53	)	)	PUNCT
ejpam-5062	597	54	.	.	PUNCT
ejpam-5062	598	1	proof	proof	NOUN
ejpam-5062	598	2	.	.	PUNCT
ejpam-5062	599	1	similar	similar	ADJ
ejpam-5062	599	2	to	to	ADP
ejpam-5062	599	3	theorem	theorem	NOUN
ejpam-5062	599	4	22	22	NUM
ejpam-5062	599	5	.	.	PUNCT
ejpam-5062	600	1	corollary	corollary	ADJ
ejpam-5062	600	2	11	11	NUM
ejpam-5062	600	3	.	.	PUNCT
ejpam-5062	601	1	let	let	VERB
ejpam-5062	601	2	x	x	PRON
ejpam-5062	601	3	be	be	AUX
ejpam-5062	601	4	an	an	DET
ejpam-5062	601	5	α−	α−	NOUN
ejpam-5062	601	6	sspo	sspo	NOUN
ejpam-5062	601	7	lindelof	lindelof	PROPN
ejpam-5062	601	8	(	(	PUNCT
ejpam-5062	601	9	α∗	α∗	NOUN
ejpam-5062	601	10	−	−	PROPN
ejpam-5062	601	11	sspo	sspo	NOUN
ejpam-5062	601	12	lindelof	lindelof	NOUN
ejpam-5062	601	13	)	)	PUNCT
ejpam-5062	601	14	space	space	NOUN
ejpam-5062	601	15	,	,	PUNCT
ejpam-5062	601	16	then	then	ADV
ejpam-5062	601	17	any	any	DET
ejpam-5062	601	18	fuzzy	fuzzy	ADJ
ejpam-5062	601	19	set	set	VERB
ejpam-5062	601	20	b	b	PROPN
ejpam-5062	601	21	∈	∈	PROPN
ejpam-5062	601	22	fsspc(τ	fsspc(τ	NOUN
ejpam-5062	601	23	)	)	PUNCT
ejpam-5062	601	24	is	be	AUX
ejpam-5062	601	25	an	an	DET
ejpam-5062	601	26	α	α	NOUN
ejpam-5062	601	27	−	−	NOUN
ejpam-5062	601	28	sspo	sspo	NOUN
ejpam-5062	601	29	lindelof	lindelof	PROPN
ejpam-5062	601	30	(	(	PUNCT
ejpam-5062	601	31	α∗	α∗	NOUN
ejpam-5062	601	32	−	−	PROPN
ejpam-5062	601	33	sspo	sspo	NOUN
ejpam-5062	601	34	lindelof	lindelof	NOUN
ejpam-5062	601	35	)	)	PUNCT
ejpam-5062	601	36	fuzzy	fuzzy	ADJ
ejpam-5062	601	37	set	set	VERB
ejpam-5062	601	38	in	in	ADP
ejpam-5062	601	39	the	the	DET
ejpam-5062	601	40	fuzzy	fuzzy	ADJ
ejpam-5062	601	41	topological	topological	ADJ
ejpam-5062	601	42	space	space	NOUN
ejpam-5062	601	43	(	(	PUNCT
ejpam-5062	601	44	x	x	X
ejpam-5062	601	45	,	,	PUNCT
ejpam-5062	601	46	τ	τ	PROPN
ejpam-5062	601	47	)	)	PUNCT
ejpam-5062	601	48	.	.	PUNCT
ejpam-5062	602	1	proof	proof	NOUN
ejpam-5062	602	2	.	.	PUNCT
ejpam-5062	603	1	it	it	PRON
ejpam-5062	603	2	follows	follow	VERB
ejpam-5062	603	3	directly	directly	ADV
ejpam-5062	603	4	from	from	ADP
ejpam-5062	603	5	theorem	theorem	ADJ
ejpam-5062	603	6	36	36	NUM
ejpam-5062	603	7	.	.	PUNCT
ejpam-5062	604	1	theorem	theorem	VERB
ejpam-5062	604	2	37	37	NUM
ejpam-5062	604	3	.	.	PUNCT
ejpam-5062	605	1	let	let	VERB
ejpam-5062	605	2	a	a	DET
ejpam-5062	605	3	,	,	PUNCT
ejpam-5062	605	4	b	b	PROPN
ejpam-5062	605	5	be	be	AUX
ejpam-5062	605	6	α−sspo	α−sspo	X
ejpam-5062	605	7	lindelof	lindelof	PROPN
ejpam-5062	605	8	(	(	PUNCT
ejpam-5062	605	9	α∗−sspo	α∗−sspo	PROPN
ejpam-5062	605	10	lindelof	lindelof	PROPN
ejpam-5062	605	11	)	)	PUNCT
ejpam-5062	605	12	fuzzy	fuzzy	ADJ
ejpam-5062	605	13	sets	set	NOUN
ejpam-5062	605	14	in	in	ADP
ejpam-5062	605	15	(	(	PUNCT
ejpam-5062	605	16	x	x	NOUN
ejpam-5062	605	17	,	,	PUNCT
ejpam-5062	605	18	τ	τ	PROPN
ejpam-5062	605	19	)	)	PUNCT
ejpam-5062	605	20	,	,	PUNCT
ejpam-5062	605	21	then	then	ADV
ejpam-5062	605	22	the	the	DET
ejpam-5062	605	23	fuzzy	fuzzy	ADJ
ejpam-5062	605	24	set	set	VERB
ejpam-5062	605	25	a	a	DET
ejpam-5062	605	26	∨	∨	PROPN
ejpam-5062	605	27	b	b	PROPN
ejpam-5062	605	28	is	be	AUX
ejpam-5062	605	29	also	also	ADV
ejpam-5062	605	30	an	an	DET
ejpam-5062	605	31	α	α	NOUN
ejpam-5062	605	32	−	−	NOUN
ejpam-5062	605	33	sspo	sspo	NOUN
ejpam-5062	605	34	lindelof	lindelof	PROPN
ejpam-5062	605	35	(	(	PUNCT
ejpam-5062	605	36	α∗	α∗	NOUN
ejpam-5062	605	37	−	−	PROPN
ejpam-5062	605	38	sspo	sspo	NOUN
ejpam-5062	605	39	lindelof	lindelof	NOUN
ejpam-5062	605	40	)	)	PUNCT
ejpam-5062	605	41	fuzzy	fuzzy	ADJ
ejpam-5062	605	42	set	set	VERB
ejpam-5062	605	43	in	in	ADP
ejpam-5062	605	44	(	(	PUNCT
ejpam-5062	605	45	x	x	NOUN
ejpam-5062	605	46	,	,	PUNCT
ejpam-5062	605	47	τ	τ	PROPN
ejpam-5062	605	48	)	)	PUNCT
ejpam-5062	605	49	.	.	PUNCT
ejpam-5062	606	1	proof	proof	NOUN
ejpam-5062	606	2	.	.	PUNCT
ejpam-5062	607	1	in	in	ADP
ejpam-5062	607	2	similar	similar	ADJ
ejpam-5062	607	3	way	way	NOUN
ejpam-5062	607	4	as	as	SCONJ
ejpam-5062	607	5	theorem	theorem	ADJ
ejpam-5062	607	6	23	23	NUM
ejpam-5062	607	7	.	.	PUNCT
ejpam-5062	607	8	theorem	theorem	VERB
ejpam-5062	607	9	38	38	NUM
ejpam-5062	607	10	.	.	PUNCT
ejpam-5062	608	1	if	if	SCONJ
ejpam-5062	608	2	f	f	PROPN
ejpam-5062	608	3	:	:	PUNCT
ejpam-5062	608	4	x	x	X
ejpam-5062	608	5	→	→	SYM
ejpam-5062	608	6	y	y	PROPN
ejpam-5062	608	7	is	be	AUX
ejpam-5062	608	8	a	a	DET
ejpam-5062	608	9	fuzzy	fuzzy	ADJ
ejpam-5062	608	10	sspo	sspo	NOUN
ejpam-5062	608	11	-	-	PUNCT
ejpam-5062	608	12	irresolute	irresolute	ADJ
ejpam-5062	608	13	mapping	mapping	NOUN
ejpam-5062	608	14	from	from	ADP
ejpam-5062	608	15	the	the	DET
ejpam-5062	608	16	fuzzy	fuzzy	ADJ
ejpam-5062	608	17	topological	topological	ADJ
ejpam-5062	608	18	space	space	NOUN
ejpam-5062	608	19	x	x	PUNCT
ejpam-5062	608	20	to	to	ADP
ejpam-5062	608	21	a	a	DET
ejpam-5062	608	22	fuzzy	fuzzy	ADJ
ejpam-5062	608	23	topological	topological	ADJ
ejpam-5062	608	24	space	space	NOUN
ejpam-5062	608	25	y	y	PROPN
ejpam-5062	608	26	.	.	PUNCT
ejpam-5062	609	1	if	if	SCONJ
ejpam-5062	609	2	the	the	DET
ejpam-5062	609	3	fuzzy	fuzzy	NOUN
ejpam-5062	609	4	set	set	VERB
ejpam-5062	609	5	a	a	PRON
ejpam-5062	609	6	is	be	AUX
ejpam-5062	609	7	an	an	DET
ejpam-5062	609	8	α	α	NOUN
ejpam-5062	609	9	−	−	NOUN
ejpam-5062	609	10	sspo	sspo	NOUN
ejpam-5062	609	11	lindelof	lindelof	PROPN
ejpam-5062	609	12	(	(	PUNCT
ejpam-5062	609	13	α∗	α∗	NOUN
ejpam-5062	609	14	−	−	PROPN
ejpam-5062	609	15	sspo	sspo	NOUN
ejpam-5062	609	16	lindelof	lindelof	NOUN
ejpam-5062	609	17	)	)	PUNCT
ejpam-5062	609	18	fuzzy	fuzzy	ADJ
ejpam-5062	609	19	set	set	VERB
ejpam-5062	609	20	in	in	ADP
ejpam-5062	609	21	x	x	SYM
ejpam-5062	609	22	then	then	ADV
ejpam-5062	609	23	f(a	f(a	PROPN
ejpam-5062	609	24	)	)	PUNCT
ejpam-5062	609	25	is	be	AUX
ejpam-5062	609	26	an	an	DET
ejpam-5062	609	27	α−	α−	X
ejpam-5062	609	28	sspo	sspo	NOUN
ejpam-5062	609	29	lindelof	lindelof	PROPN
ejpam-5062	609	30	(	(	PUNCT
ejpam-5062	609	31	α∗	α∗	NOUN
ejpam-5062	609	32	−	−	PROPN
ejpam-5062	609	33	sspo	sspo	NOUN
ejpam-5062	609	34	lindelof	lindelof	NOUN
ejpam-5062	609	35	)	)	PUNCT
ejpam-5062	609	36	fuzzy	fuzzy	ADJ
ejpam-5062	609	37	set	set	VERB
ejpam-5062	609	38	in	in	ADP
ejpam-5062	609	39	y	y	PROPN
ejpam-5062	609	40	.	.	PUNCT
ejpam-5062	610	1	proof	proof	NOUN
ejpam-5062	610	2	.	.	PUNCT
ejpam-5062	611	1	in	in	ADP
ejpam-5062	611	2	a	a	DET
ejpam-5062	611	3	similar	similar	ADJ
ejpam-5062	611	4	way	way	NOUN
ejpam-5062	611	5	as	as	SCONJ
ejpam-5062	611	6	theorem	theorem	ADJ
ejpam-5062	611	7	24	24	NUM
ejpam-5062	611	8	.	.	PUNCT
ejpam-5062	611	9	corollary	corollary	ADJ
ejpam-5062	611	10	12	12	NUM
ejpam-5062	611	11	.	.	PUNCT
ejpam-5062	612	1	if	if	SCONJ
ejpam-5062	612	2	f	f	PROPN
ejpam-5062	612	3	:	:	PUNCT
ejpam-5062	612	4	x	x	X
ejpam-5062	612	5	→	→	SYM
ejpam-5062	612	6	y	y	PROPN
ejpam-5062	612	7	is	be	AUX
ejpam-5062	612	8	a	a	DET
ejpam-5062	612	9	fuzzy	fuzzy	ADJ
ejpam-5062	612	10	sspo	sspo	NOUN
ejpam-5062	612	11	-	-	PUNCT
ejpam-5062	612	12	irresolute	irresolute	ADJ
ejpam-5062	612	13	mapping	mapping	NOUN
ejpam-5062	612	14	from	from	ADP
ejpam-5062	612	15	the	the	DET
ejpam-5062	612	16	fuzzy	fuzzy	ADJ
ejpam-5062	612	17	topological	topological	ADJ
ejpam-5062	612	18	space	space	NOUN
ejpam-5062	612	19	x	x	PUNCT
ejpam-5062	612	20	to	to	ADP
ejpam-5062	612	21	a	a	DET
ejpam-5062	612	22	fuzzy	fuzzy	ADJ
ejpam-5062	612	23	topological	topological	ADJ
ejpam-5062	612	24	space	space	NOUN
ejpam-5062	612	25	y	y	PROPN
ejpam-5062	612	26	.	.	PUNCT
ejpam-5062	613	1	if	if	SCONJ
ejpam-5062	613	2	x	x	PRON
ejpam-5062	613	3	is	be	AUX
ejpam-5062	613	4	an	an	DET
ejpam-5062	613	5	α	α	NOUN
ejpam-5062	613	6	−	−	NOUN
ejpam-5062	613	7	sspo	sspo	NOUN
ejpam-5062	613	8	lindelof	lindelof	PROPN
ejpam-5062	613	9	(	(	PUNCT
ejpam-5062	613	10	α∗	α∗	NOUN
ejpam-5062	613	11	−	−	PROPN
ejpam-5062	613	12	sspo	sspo	NOUN
ejpam-5062	613	13	lindelof	lindelof	PROPN
ejpam-5062	613	14	)	)	PUNCT
ejpam-5062	613	15	then	then	ADV
ejpam-5062	613	16	f(x	f(x	PROPN
ejpam-5062	613	17	)	)	PUNCT
ejpam-5062	613	18	is	be	AUX
ejpam-5062	613	19	an	an	DET
ejpam-5062	613	20	α−	α−	X
ejpam-5062	613	21	sspo	sspo	NOUN
ejpam-5062	613	22	lindelof	lindelof	PROPN
ejpam-5062	613	23	(	(	PUNCT
ejpam-5062	613	24	α∗	α∗	NOUN
ejpam-5062	613	25	−	−	PROPN
ejpam-5062	613	26	sspo	sspo	NOUN
ejpam-5062	613	27	lindelof	lindelof	NOUN
ejpam-5062	613	28	)	)	PUNCT
ejpam-5062	613	29	fuzzy	fuzzy	ADJ
ejpam-5062	613	30	set	set	VERB
ejpam-5062	613	31	in	in	ADP
ejpam-5062	613	32	y	y	PROPN
ejpam-5062	613	33	.	.	PUNCT
ejpam-5062	614	1	proof	proof	NOUN
ejpam-5062	614	2	.	.	PUNCT
ejpam-5062	615	1	it	it	PRON
ejpam-5062	615	2	follows	follow	VERB
ejpam-5062	615	3	directly	directly	ADV
ejpam-5062	615	4	from	from	ADP
ejpam-5062	615	5	theorem	theorem	ADJ
ejpam-5062	615	6	38	38	NUM
ejpam-5062	615	7	.	.	PUNCT
ejpam-5062	616	1	corollary	corollary	ADJ
ejpam-5062	616	2	13	13	NUM
ejpam-5062	616	3	.	.	PUNCT
ejpam-5062	617	1	let	let	VERB
ejpam-5062	617	2	f	f	NOUN
ejpam-5062	617	3	:	:	PUNCT
ejpam-5062	617	4	x	x	X
ejpam-5062	617	5	→	→	SYM
ejpam-5062	617	6	y	y	PROPN
ejpam-5062	617	7	is	be	AUX
ejpam-5062	617	8	a	a	DET
ejpam-5062	617	9	fuzzy	fuzzy	ADJ
ejpam-5062	617	10	sspo	sspo	NOUN
ejpam-5062	617	11	-	-	PUNCT
ejpam-5062	617	12	irresolute	irresolute	ADJ
ejpam-5062	617	13	and	and	CCONJ
ejpam-5062	617	14	surjective	surjective	ADJ
ejpam-5062	617	15	mapping	mapping	NOUN
ejpam-5062	617	16	from	from	ADP
ejpam-5062	617	17	the	the	DET
ejpam-5062	617	18	fuzzy	fuzzy	ADJ
ejpam-5062	617	19	topological	topological	ADJ
ejpam-5062	617	20	space	space	NOUN
ejpam-5062	617	21	x	x	PUNCT
ejpam-5062	617	22	to	to	ADP
ejpam-5062	617	23	a	a	DET
ejpam-5062	617	24	fuzzy	fuzzy	ADJ
ejpam-5062	617	25	topological	topological	ADJ
ejpam-5062	617	26	space	space	NOUN
ejpam-5062	617	27	y	y	PROPN
ejpam-5062	617	28	.	.	PUNCT
ejpam-5062	618	1	if	if	SCONJ
ejpam-5062	618	2	x	x	PRON
ejpam-5062	618	3	is	be	AUX
ejpam-5062	618	4	an	an	DET
ejpam-5062	618	5	α−sspo	α−sspo	NOUN
ejpam-5062	618	6	lindelof	lindelof	NOUN
ejpam-5062	618	7	(	(	PUNCT
ejpam-5062	618	8	α∗	α∗	NOUN
ejpam-5062	618	9	−	−	PROPN
ejpam-5062	618	10	sspo	sspo	NOUN
ejpam-5062	618	11	lindelof	lindelof	PROPN
ejpam-5062	618	12	)	)	PUNCT
ejpam-5062	618	13	then	then	ADV
ejpam-5062	618	14	y	y	PROPN
ejpam-5062	618	15	is	be	AUX
ejpam-5062	618	16	an	an	DET
ejpam-5062	618	17	α−	α−	X
ejpam-5062	618	18	sspo	sspo	NOUN
ejpam-5062	618	19	lindelof	lindelof	PROPN
ejpam-5062	618	20	(	(	PUNCT
ejpam-5062	618	21	α∗	α∗	AUX
ejpam-5062	618	22	−	−	PROPN
ejpam-5062	618	23	sspo	sspo	NOUN
ejpam-5062	618	24	lindelof	lindelof	NOUN
ejpam-5062	618	25	)	)	PUNCT
ejpam-5062	618	26	.	.	PUNCT
ejpam-5062	619	1	references	reference	NOUN
ejpam-5062	619	2	660	660	NUM
ejpam-5062	619	3	proof	proof	NOUN
ejpam-5062	619	4	.	.	PUNCT
ejpam-5062	620	1	it	it	PRON
ejpam-5062	620	2	follows	follow	VERB
ejpam-5062	620	3	from	from	ADP
ejpam-5062	620	4	theorem	theorem	ADJ
ejpam-5062	620	5	38	38	NUM
ejpam-5062	620	6	.	.	PUNCT
ejpam-5062	621	1	we	we	PRON
ejpam-5062	621	2	can	can	AUX
ejpam-5062	621	3	also	also	ADV
ejpam-5062	621	4	show	show	VERB
ejpam-5062	621	5	that	that	SCONJ
ejpam-5062	621	6	the	the	DET
ejpam-5062	621	7	following	follow	VERB
ejpam-5062	621	8	assertion	assertion	NOUN
ejpam-5062	621	9	are	be	AUX
ejpam-5062	621	10	true	true	ADJ
ejpam-5062	621	11	.	.	PUNCT
ejpam-5062	622	1	theorem	theorem	VERB
ejpam-5062	622	2	39	39	NUM
ejpam-5062	622	3	.	.	PUNCT
ejpam-5062	623	1	let	let	VERB
ejpam-5062	623	2	the	the	DET
ejpam-5062	623	3	mapping	mapping	NOUN
ejpam-5062	623	4	f	f	X
ejpam-5062	623	5	:	:	PUNCT
ejpam-5062	623	6	x	x	X
ejpam-5062	623	7	→	→	SYM
ejpam-5062	623	8	y	y	X
ejpam-5062	623	9	be	be	AUX
ejpam-5062	623	10	a	a	DET
ejpam-5062	623	11	fuzzy	fuzzy	ADJ
ejpam-5062	623	12	strong	strong	ADJ
ejpam-5062	623	13	semi	semi	ADJ
ejpam-5062	623	14	pre	pre	ADJ
ejpam-5062	623	15	-	-	ADJ
ejpam-5062	623	16	continuous	continuous	ADJ
ejpam-5062	623	17	and	and	CCONJ
ejpam-5062	623	18	surjective	surjective	ADJ
ejpam-5062	623	19	mapping	mapping	NOUN
ejpam-5062	623	20	from	from	ADP
ejpam-5062	623	21	the	the	DET
ejpam-5062	623	22	fuzzy	fuzzy	ADJ
ejpam-5062	623	23	topological	topological	ADJ
ejpam-5062	623	24	space	space	NOUN
ejpam-5062	623	25	x	x	PUNCT
ejpam-5062	623	26	to	to	ADP
ejpam-5062	623	27	a	a	DET
ejpam-5062	623	28	fuzzy	fuzzy	ADJ
ejpam-5062	623	29	topological	topological	ADJ
ejpam-5062	623	30	space	space	NOUN
ejpam-5062	623	31	y	y	PROPN
ejpam-5062	623	32	.	.	PUNCT
ejpam-5062	624	1	if	if	SCONJ
ejpam-5062	624	2	the	the	DET
ejpam-5062	624	3	space	space	NOUN
ejpam-5062	624	4	x	x	PUNCT
ejpam-5062	624	5	is	be	AUX
ejpam-5062	624	6	an	an	DET
ejpam-5062	624	7	α	α	NOUN
ejpam-5062	624	8	−	−	NOUN
ejpam-5062	624	9	sspo	sspo	NOUN
ejpam-5062	624	10	lindelof	lindelof	PROPN
ejpam-5062	624	11	(	(	PUNCT
ejpam-5062	624	12	α∗	α∗	NOUN
ejpam-5062	624	13	−	−	PROPN
ejpam-5062	624	14	sspo	sspo	NOUN
ejpam-5062	624	15	lindelof	lindelof	PROPN
ejpam-5062	624	16	)	)	PUNCT
ejpam-5062	624	17	then	then	ADV
ejpam-5062	624	18	y	y	PROPN
ejpam-5062	624	19	will	will	AUX
ejpam-5062	624	20	be	be	AUX
ejpam-5062	624	21	an	an	DET
ejpam-5062	624	22	αlindelof	αlindelof	ADJ
ejpam-5062	624	23	(	(	PUNCT
ejpam-5062	624	24	α∗lindelof	α∗lindelof	NOUN
ejpam-5062	624	25	)	)	PUNCT
ejpam-5062	624	26	space	space	NOUN
ejpam-5062	624	27	.	.	PUNCT
ejpam-5062	625	1	theorem	theorem	NOUN
ejpam-5062	625	2	40	40	NUM
ejpam-5062	625	3	.	.	PUNCT
ejpam-5062	626	1	let	let	VERB
ejpam-5062	626	2	the	the	DET
ejpam-5062	626	3	mapping	mapping	NOUN
ejpam-5062	626	4	f	f	X
ejpam-5062	626	5	:	:	PUNCT
ejpam-5062	626	6	x	x	X
ejpam-5062	626	7	→	→	SYM
ejpam-5062	626	8	y	y	X
ejpam-5062	626	9	be	be	AUX
ejpam-5062	626	10	a	a	DET
ejpam-5062	626	11	fuzzy	fuzzy	ADJ
ejpam-5062	626	12	sspo	sspo	NOUN
ejpam-5062	626	13	homeomorphism	homeomorphism	PROPN
ejpam-5062	626	14	from	from	ADP
ejpam-5062	626	15	the	the	DET
ejpam-5062	626	16	fuzzy	fuzzy	ADJ
ejpam-5062	626	17	topological	topological	ADJ
ejpam-5062	626	18	space	space	NOUN
ejpam-5062	626	19	x	x	PUNCT
ejpam-5062	626	20	to	to	ADP
ejpam-5062	626	21	a	a	DET
ejpam-5062	626	22	fuzzy	fuzzy	ADJ
ejpam-5062	626	23	topological	topological	ADJ
ejpam-5062	626	24	space	space	NOUN
ejpam-5062	626	25	y	y	PROPN
ejpam-5062	626	26	and	and	CCONJ
ejpam-5062	626	27	let	let	VERB
ejpam-5062	626	28	a	a	DET
ejpam-5062	626	29	be	be	AUX
ejpam-5062	626	30	a	a	DET
ejpam-5062	626	31	fuzzy	fuzzy	ADJ
ejpam-5062	626	32	set	set	NOUN
ejpam-5062	626	33	in	in	ADP
ejpam-5062	626	34	x.	x.	NOUN
ejpam-5062	626	35	if	if	SCONJ
ejpam-5062	626	36	the	the	DET
ejpam-5062	626	37	set	set	NOUN
ejpam-5062	626	38	a	a	PRON
ejpam-5062	626	39	is	be	AUX
ejpam-5062	626	40	an	an	DET
ejpam-5062	626	41	α	α	NOUN
ejpam-5062	626	42	−	−	NOUN
ejpam-5062	626	43	sspo	sspo	NOUN
ejpam-5062	626	44	lindelof	lindelof	PROPN
ejpam-5062	626	45	(	(	PUNCT
ejpam-5062	626	46	α∗	α∗	NOUN
ejpam-5062	626	47	−	−	PROPN
ejpam-5062	626	48	sspo	sspo	NOUN
ejpam-5062	626	49	lindelof	lindelof	NOUN
ejpam-5062	626	50	)	)	PUNCT
ejpam-5062	626	51	set	set	VERB
ejpam-5062	626	52	in	in	ADP
ejpam-5062	626	53	x	x	SYM
ejpam-5062	626	54	then	then	ADV
ejpam-5062	626	55	f(a	f(a	NOUN
ejpam-5062	626	56	)	)	PUNCT
ejpam-5062	626	57	will	will	AUX
ejpam-5062	626	58	also	also	ADV
ejpam-5062	626	59	be	be	AUX
ejpam-5062	626	60	an	an	DET
ejpam-5062	626	61	α−	α−	NOUN
ejpam-5062	626	62	sspo	sspo	NOUN
ejpam-5062	626	63	lindelof	lindelof	PROPN
ejpam-5062	626	64	(	(	PUNCT
ejpam-5062	626	65	α∗	α∗	NOUN
ejpam-5062	626	66	−	−	PROPN
ejpam-5062	626	67	sspo	sspo	NOUN
ejpam-5062	626	68	lindelof	lindelof	NOUN
ejpam-5062	626	69	)	)	PUNCT
ejpam-5062	626	70	fuzzy	fuzzy	ADJ
ejpam-5062	626	71	set	set	VERB
ejpam-5062	626	72	in	in	ADP
ejpam-5062	626	73	y	y	PROPN
ejpam-5062	626	74	.	.	PUNCT
ejpam-5062	627	1	corollary	corollary	ADJ
ejpam-5062	627	2	14	14	NUM
ejpam-5062	627	3	.	.	PUNCT
ejpam-5062	628	1	let	let	VERB
ejpam-5062	628	2	the	the	DET
ejpam-5062	628	3	mapping	mapping	NOUN
ejpam-5062	628	4	f	f	X
ejpam-5062	628	5	:	:	PUNCT
ejpam-5062	628	6	x	x	X
ejpam-5062	628	7	→	→	SYM
ejpam-5062	628	8	y	y	X
ejpam-5062	628	9	be	be	AUX
ejpam-5062	628	10	a	a	DET
ejpam-5062	628	11	fuzzy	fuzzy	ADJ
ejpam-5062	628	12	sspo	sspo	NOUN
ejpam-5062	628	13	homeomorphism	homeomorphism	PROPN
ejpam-5062	628	14	from	from	ADP
ejpam-5062	628	15	the	the	DET
ejpam-5062	628	16	fuzzy	fuzzy	ADJ
ejpam-5062	628	17	topological	topological	ADJ
ejpam-5062	628	18	space	space	NOUN
ejpam-5062	628	19	x	x	PUNCT
ejpam-5062	628	20	to	to	ADP
ejpam-5062	628	21	a	a	DET
ejpam-5062	628	22	fuzzy	fuzzy	ADJ
ejpam-5062	628	23	topological	topological	ADJ
ejpam-5062	628	24	spacey	spacey	NOUN
ejpam-5062	628	25	.	.	PUNCT
ejpam-5062	629	1	if	if	SCONJ
ejpam-5062	629	2	x	x	PRON
ejpam-5062	629	3	is	be	AUX
ejpam-5062	629	4	an	an	DET
ejpam-5062	629	5	α	α	NOUN
ejpam-5062	629	6	−	−	NOUN
ejpam-5062	629	7	sspo	sspo	NOUN
ejpam-5062	629	8	lindelof	lindelof	PROPN
ejpam-5062	629	9	(	(	PUNCT
ejpam-5062	629	10	α∗−sspo	α∗−sspo	PROPN
ejpam-5062	629	11	lindelof	lindelof	PROPN
ejpam-5062	629	12	)	)	PUNCT
ejpam-5062	629	13	then	then	ADV
ejpam-5062	629	14	y	y	PROPN
ejpam-5062	629	15	will	will	AUX
ejpam-5062	629	16	also	also	ADV
ejpam-5062	629	17	be	be	AUX
ejpam-5062	629	18	an	an	DET
ejpam-5062	629	19	α−sspo	α−sspo	NOUN
ejpam-5062	629	20	lindelof	lindelof	X
ejpam-5062	629	21	(	(	PUNCT
ejpam-5062	629	22	α∗−sspo	α∗−sspo	PROPN
ejpam-5062	629	23	lindelof	lindelof	PROPN
ejpam-5062	629	24	)	)	PUNCT
ejpam-5062	629	25	.	.	PUNCT
ejpam-5062	630	1	6	6	X
ejpam-5062	630	2	.	.	X
ejpam-5062	630	3	conclusion	conclusion	NOUN
ejpam-5062	630	4	in	in	ADP
ejpam-5062	630	5	this	this	DET
ejpam-5062	630	6	paper	paper	NOUN
ejpam-5062	630	7	we	we	PRON
ejpam-5062	630	8	have	have	AUX
ejpam-5062	630	9	investigated	investigate	VERB
ejpam-5062	630	10	properties	property	NOUN
ejpam-5062	630	11	of	of	ADP
ejpam-5062	630	12	a	a	DET
ejpam-5062	630	13	new	new	ADJ
ejpam-5062	630	14	form	form	NOUN
ejpam-5062	630	15	of	of	ADP
ejpam-5062	630	16	fuzzy	fuzzy	ADJ
ejpam-5062	630	17	pre	pre	ADJ
ejpam-5062	630	18	-	-	NOUN
ejpam-5062	630	19	separation	separation	NOUN
ejpam-5062	630	20	axioms	axiom	NOUN
ejpam-5062	630	21	as	as	ADV
ejpam-5062	630	22	well	well	ADV
ejpam-5062	630	23	as	as	ADP
ejpam-5062	630	24	the	the	DET
ejpam-5062	630	25	new	new	ADJ
ejpam-5062	630	26	form	form	NOUN
ejpam-5062	630	27	of	of	ADP
ejpam-5062	630	28	fuzzy	fuzzy	ADJ
ejpam-5062	630	29	compactness	compactness	NOUN
ejpam-5062	630	30	induced	induce	VERB
ejpam-5062	630	31	by	by	ADP
ejpam-5062	630	32	the	the	DET
ejpam-5062	630	33	new	new	ADJ
ejpam-5062	630	34	class	class	NOUN
ejpam-5062	630	35	of	of	ADP
ejpam-5062	630	36	fuzzy	fuzzy	ADJ
ejpam-5062	630	37	generalized	generalize	VERB
ejpam-5062	630	38	opened	open	VERB
ejpam-5062	630	39	sets	set	NOUN
ejpam-5062	630	40	.	.	PUNCT
ejpam-5062	631	1	we	we	PRON
ejpam-5062	631	2	also	also	ADV
ejpam-5062	631	3	investigated	investigate	VERB
ejpam-5062	631	4	their	their	PRON
ejpam-5062	631	5	properties	property	NOUN
ejpam-5062	631	6	in	in	ADP
ejpam-5062	631	7	regards	regard	NOUN
ejpam-5062	631	8	to	to	ADP
ejpam-5062	631	9	the	the	DET
ejpam-5062	631	10	fuzzy	fuzzy	ADJ
ejpam-5062	631	11	strong	strong	ADJ
ejpam-5062	631	12	semi	semi	ADJ
ejpam-5062	631	13	pre	pre	ADJ
ejpam-5062	631	14	-	-	ADJ
ejpam-5062	631	15	continuous	continuous	ADJ
ejpam-5062	631	16	functions	function	NOUN
ejpam-5062	631	17	as	as	ADV
ejpam-5062	631	18	well	well	ADV
ejpam-5062	631	19	as	as	ADP
ejpam-5062	631	20	the	the	DET
ejpam-5062	631	21	fuzzy	fuzzy	ADJ
ejpam-5062	631	22	sspo	sspo	NOUN
ejpam-5062	631	23	-	-	PUNCT
ejpam-5062	631	24	irresolute	irresolute	ADJ
ejpam-5062	631	25	mappings	mapping	NOUN
ejpam-5062	631	26	.	.	PUNCT
ejpam-5062	632	1	we	we	PRON
ejpam-5062	632	2	have	have	AUX
ejpam-5062	632	3	shown	show	VERB
ejpam-5062	632	4	that	that	SCONJ
ejpam-5062	632	5	the	the	DET
ejpam-5062	632	6	concept	concept	NOUN
ejpam-5062	632	7	of	of	ADP
ejpam-5062	632	8	fuzzy	fuzzy	ADJ
ejpam-5062	632	9	strong	strong	ADJ
ejpam-5062	632	10	pre	pre	ADJ
ejpam-5062	632	11	-	-	NOUN
ejpam-5062	632	12	separation	separation	NOUN
ejpam-5062	632	13	axioms	axiom	NOUN
ejpam-5062	632	14	is	be	AUX
ejpam-5062	632	15	stronger	strong	ADJ
ejpam-5062	632	16	than	than	ADP
ejpam-5062	632	17	the	the	DET
ejpam-5062	632	18	ordinary	ordinary	ADJ
ejpam-5062	632	19	fuzzy	fuzzy	ADJ
ejpam-5062	632	20	separation	separation	NOUN
ejpam-5062	632	21	axioms	axiom	NOUN
ejpam-5062	632	22	.	.	PUNCT
ejpam-5062	633	1	from	from	ADP
ejpam-5062	633	2	the	the	DET
ejpam-5062	633	3	properties	property	NOUN
ejpam-5062	633	4	that	that	PRON
ejpam-5062	633	5	we	we	PRON
ejpam-5062	633	6	investigated	investigate	VERB
ejpam-5062	633	7	,	,	PUNCT
ejpam-5062	633	8	the	the	DET
ejpam-5062	633	9	concept	concept	NOUN
ejpam-5062	633	10	of	of	ADP
ejpam-5062	633	11	α−sspo	α−sspo	PROPN
ejpam-5062	633	12	lindelof	lindelof	PROPN
ejpam-5062	633	13	space	space	NOUN
ejpam-5062	633	14	,	,	PUNCT
ejpam-5062	633	15	fuzzy	fuzzy	ADJ
ejpam-5062	633	16	sspo	sspo	NOUN
ejpam-5062	633	17	-	-	PUNCT
ejpam-5062	633	18	separability	separability	NOUN
ejpam-5062	633	19	and	and	CCONJ
ejpam-5062	633	20	the	the	DET
ejpam-5062	633	21	existence	existence	NOUN
ejpam-5062	633	22	of	of	ADP
ejpam-5062	633	23	a	a	DET
ejpam-5062	633	24	base	base	NOUN
ejpam-5062	633	25	consisting	consist	VERB
ejpam-5062	633	26	of	of	ADP
ejpam-5062	633	27	fuzzy	fuzzy	ADJ
ejpam-5062	633	28	strongly	strongly	ADV
ejpam-5062	633	29	semi	semi	ADV
ejpam-5062	633	30	pre	pre	ADJ
ejpam-5062	633	31	-	-	ADJ
ejpam-5062	633	32	open	open	ADJ
ejpam-5062	633	33	sets	set	NOUN
ejpam-5062	633	34	,	,	PUNCT
ejpam-5062	633	35	the	the	DET
ejpam-5062	633	36	strongest	strong	ADJ
ejpam-5062	633	37	concept	concept	NOUN
ejpam-5062	633	38	appears	appear	VERB
ejpam-5062	633	39	to	to	PART
ejpam-5062	633	40	be	be	AUX
ejpam-5062	633	41	the	the	DET
ejpam-5062	633	42	concept	concept	NOUN
ejpam-5062	633	43	of	of	ADP
ejpam-5062	633	44	the	the	DET
ejpam-5062	633	45	existence	existence	NOUN
ejpam-5062	633	46	of	of	ADP
ejpam-5062	633	47	a	a	DET
ejpam-5062	633	48	base	base	NOUN
ejpam-5062	633	49	consisting	consist	VERB
ejpam-5062	633	50	of	of	ADP
ejpam-5062	633	51	fuzzy	fuzzy	ADJ
ejpam-5062	633	52	strongly	strongly	ADV
ejpam-5062	633	53	semi	semi	ADV
ejpam-5062	633	54	pre	pre	ADJ
ejpam-5062	633	55	-	-	ADJ
ejpam-5062	633	56	open	open	ADJ
ejpam-5062	633	57	sets	set	NOUN
ejpam-5062	633	58	.	.	PUNCT
ejpam-5062	634	1	our	our	PRON
ejpam-5062	634	2	future	future	ADJ
ejpam-5062	634	3	work	work	NOUN
ejpam-5062	634	4	will	will	AUX
ejpam-5062	634	5	be	be	AUX
ejpam-5062	634	6	focused	focus	VERB
ejpam-5062	634	7	on	on	ADP
ejpam-5062	634	8	introducing	introduce	VERB
ejpam-5062	634	9	new	new	ADJ
ejpam-5062	634	10	form	form	NOUN
ejpam-5062	634	11	of	of	ADP
ejpam-5062	634	12	fuzzy	fuzzy	ADJ
ejpam-5062	634	13	connectedness	connectedness	NOUN
ejpam-5062	634	14	which	which	PRON
ejpam-5062	634	15	will	will	AUX
ejpam-5062	634	16	be	be	AUX
ejpam-5062	634	17	stronger	strong	ADJ
ejpam-5062	634	18	than	than	ADP
ejpam-5062	634	19	the	the	DET
ejpam-5062	634	20	concepts	concept	NOUN
ejpam-5062	634	21	of	of	ADP
ejpam-5062	634	22	fuzzy	fuzzy	ADJ
ejpam-5062	634	23	connectedness	connectedness	NOUN
ejpam-5062	634	24	introduced	introduce	VERB
ejpam-5062	634	25	by	by	ADP
ejpam-5062	634	26	other	other	ADJ
ejpam-5062	634	27	authors	author	NOUN
ejpam-5062	634	28	.	.	PUNCT
ejpam-5062	635	1	based	base	VERB
ejpam-5062	635	2	on	on	ADP
ejpam-5062	635	3	this	this	DET
ejpam-5062	635	4	work	work	NOUN
ejpam-5062	635	5	,	,	PUNCT
ejpam-5062	635	6	we	we	PRON
ejpam-5062	635	7	also	also	ADV
ejpam-5062	635	8	intent	intent	VERB
ejpam-5062	635	9	to	to	PART
ejpam-5062	635	10	introduce	introduce	VERB
ejpam-5062	635	11	the	the	DET
ejpam-5062	635	12	new	new	ADJ
ejpam-5062	635	13	concept	concept	NOUN
ejpam-5062	635	14	of	of	ADP
ejpam-5062	635	15	generalized	generalized	ADJ
ejpam-5062	635	16	open	open	ADJ
ejpam-5062	635	17	sets	set	NOUN
ejpam-5062	635	18	in	in	ADP
ejpam-5062	635	19	the	the	DET
ejpam-5062	635	20	intuitionistic	intuitionistic	ADJ
ejpam-5062	635	21	fuzzy	fuzzy	ADJ
ejpam-5062	635	22	topological	topological	ADJ
ejpam-5062	635	23	spaces	space	NOUN
ejpam-5062	635	24	.	.	PUNCT
ejpam-5062	636	1	references	reference	NOUN
ejpam-5062	636	2	[	[	X
ejpam-5062	636	3	1	1	NUM
ejpam-5062	636	4	]	]	X
ejpam-5062	636	5	n.	n.	NOUN
ejpam-5062	636	6	ajmal	ajmal	PROPN
ejpam-5062	636	7	and	and	CCONJ
ejpam-5062	636	8	s.k	s.k	PROPN
ejpam-5062	636	9	.	.	PROPN
ejpam-5062	636	10	azad	azad	PROPN
ejpam-5062	636	11	.	.	PUNCT
ejpam-5062	637	1	fuzzy	fuzzy	ADJ
ejpam-5062	637	2	almost	almost	ADV
ejpam-5062	637	3	continuity	continuity	NOUN
ejpam-5062	637	4	and	and	CCONJ
ejpam-5062	637	5	its	its	PRON
ejpam-5062	637	6	pointwise	pointwise	ADJ
ejpam-5062	637	7	characterization	characterization	NOUN
ejpam-5062	637	8	by	by	ADP
ejpam-5062	637	9	dual	dual	ADJ
ejpam-5062	637	10	points	point	NOUN
ejpam-5062	637	11	and	and	CCONJ
ejpam-5062	637	12	fuzzy	fuzzy	ADJ
ejpam-5062	637	13	nets	net	NOUN
ejpam-5062	637	14	.	.	PUNCT
ejpam-5062	638	1	fuzzy	fuzzy	ADJ
ejpam-5062	638	2	sets	set	NOUN
ejpam-5062	638	3	and	and	CCONJ
ejpam-5062	638	4	systems	system	NOUN
ejpam-5062	638	5	,	,	PUNCT
ejpam-5062	638	6	34:81–101	34:81–101	NUM
ejpam-5062	638	7	,	,	PUNCT
ejpam-5062	638	8	1990	1990	NUM
ejpam-5062	638	9	.	.	PUNCT
ejpam-5062	639	1	[	[	X
ejpam-5062	639	2	2	2	NUM
ejpam-5062	639	3	]	]	X
ejpam-5062	639	4	k.k	k.k	PROPN
ejpam-5062	639	5	.	.	PROPN
ejpam-5062	639	6	azad	azad	PROPN
ejpam-5062	639	7	.	.	PUNCT
ejpam-5062	640	1	on	on	ADP
ejpam-5062	640	2	fuzzy	fuzzy	ADJ
ejpam-5062	640	3	semicontinuity	semicontinuity	NOUN
ejpam-5062	640	4	,	,	PUNCT
ejpam-5062	640	5	fuzzy	fuzzy	ADJ
ejpam-5062	640	6	almost	almost	ADV
ejpam-5062	640	7	continuity	continuity	NOUN
ejpam-5062	640	8	and	and	CCONJ
ejpam-5062	640	9	fuzzy	fuzzy	ADJ
ejpam-5062	640	10	weakly	weakly	ADJ
ejpam-5062	640	11	continuity	continuity	NOUN
ejpam-5062	640	12	.	.	PUNCT
ejpam-5062	641	1	j.	j.	PROPN
ejpam-5062	641	2	math	math	PROPN
ejpam-5062	641	3	.	.	PUNCT
ejpam-5062	642	1	anal	anal	PROPN
ejpam-5062	642	2	.	.	PUNCT
ejpam-5062	642	3	appl	appl	PROPN
ejpam-5062	642	4	.	.	PROPN
ejpam-5062	642	5	,	,	PUNCT
ejpam-5062	642	6	82(3):14–32	82(3):14–32	NUM
ejpam-5062	642	7	,	,	PUNCT
ejpam-5062	642	8	1981	1981	NUM
ejpam-5062	642	9	.	.	PUNCT
ejpam-5062	643	1	[	[	X
ejpam-5062	643	2	3	3	X
ejpam-5062	643	3	]	]	X
ejpam-5062	643	4	a.s	a.s	PROPN
ejpam-5062	643	5	.	.	PROPN
ejpam-5062	643	6	binshahna	binshahna	PROPN
ejpam-5062	643	7	.	.	PUNCT
ejpam-5062	644	1	on	on	ADP
ejpam-5062	644	2	fuzzy	fuzzy	ADJ
ejpam-5062	644	3	strong	strong	ADJ
ejpam-5062	644	4	semicontinuity	semicontinuity	NOUN
ejpam-5062	644	5	and	and	CCONJ
ejpam-5062	644	6	fuzzy	fuzzy	ADJ
ejpam-5062	644	7	precontinuity	precontinuity	NOUN
ejpam-5062	644	8	.	.	PUNCT
ejpam-5062	645	1	fuzzy	fuzzy	ADJ
ejpam-5062	645	2	sets	set	NOUN
ejpam-5062	645	3	and	and	CCONJ
ejpam-5062	645	4	systems	system	NOUN
ejpam-5062	645	5	,	,	PUNCT
ejpam-5062	645	6	44(3):303–308	44(3):303–308	PROPN
ejpam-5062	645	7	,	,	PUNCT
ejpam-5062	645	8	1991	1991	NUM
ejpam-5062	645	9	.	.	PUNCT
ejpam-5062	646	1	[	[	X
ejpam-5062	646	2	4	4	X
ejpam-5062	646	3	]	]	X
ejpam-5062	646	4	c.l	c.l	PROPN
ejpam-5062	646	5	chang	chang	PROPN
ejpam-5062	646	6	.	.	PUNCT
ejpam-5062	647	1	fuzzy	fuzzy	ADJ
ejpam-5062	647	2	topological	topological	ADJ
ejpam-5062	647	3	spaces	space	NOUN
ejpam-5062	647	4	.	.	PUNCT
ejpam-5062	648	1	j.math.anal.appl	j.math.anal.appl	NOUN
ejpam-5062	648	2	.	.	PUNCT
ejpam-5062	648	3	,	,	PUNCT
ejpam-5062	648	4	24(1):182–190	24(1):182–190	NUM
ejpam-5062	648	5	,	,	PUNCT
ejpam-5062	648	6	1968	1968	NUM
ejpam-5062	648	7	.	.	PUNCT
ejpam-5062	649	1	references	reference	NOUN
ejpam-5062	649	2	661	661	NUM
ejpam-5062	649	3	[	[	X
ejpam-5062	649	4	5	5	NUM
ejpam-5062	649	5	]	]	X
ejpam-5062	649	6	t.e	t.e	PROPN
ejpam-5062	649	7	.	.	PROPN
ejpam-5062	649	8	gantner	gantner	PROPN
ejpam-5062	649	9	and	and	CCONJ
ejpam-5062	649	10	r.c	r.c	PROPN
ejpam-5062	649	11	steinlage	steinlage	NOUN
ejpam-5062	649	12	.	.	PUNCT
ejpam-5062	650	1	compactness	compactness	NOUN
ejpam-5062	650	2	in	in	ADP
ejpam-5062	650	3	fuzzy	fuzzy	ADJ
ejpam-5062	650	4	topological	topological	ADJ
ejpam-5062	650	5	spaces	space	NOUN
ejpam-5062	650	6	.	.	PUNCT
ejpam-5062	651	1	j.	j.	PROPN
ejpam-5062	651	2	math	math	PROPN
ejpam-5062	651	3	.	.	PUNCT
ejpam-5062	652	1	anal	anal	PROPN
ejpam-5062	652	2	.	.	PUNCT
ejpam-5062	653	1	appl	appl	PROPN
ejpam-5062	653	2	.	.	PROPN
ejpam-5062	653	3	,	,	PUNCT
ejpam-5062	653	4	62(3):547–562	62(3):547–562	PROPN
ejpam-5062	653	5	,	,	PUNCT
ejpam-5062	653	6	1978	1978	NUM
ejpam-5062	653	7	.	.	PUNCT
ejpam-5062	654	1	[	[	X
ejpam-5062	654	2	6	6	NUM
ejpam-5062	654	3	]	]	X
ejpam-5062	654	4	m.h	m.h	PROPN
ejpam-5062	654	5	.	.	PROPN
ejpam-5062	654	6	ghanim	ghanim	PROPN
ejpam-5062	654	7	,	,	PUNCT
ejpam-5062	654	8	e.e	e.e	PROPN
ejpam-5062	654	9	.	.	PROPN
ejpam-5062	654	10	kerre	kerre	PROPN
ejpam-5062	654	11	,	,	PUNCT
ejpam-5062	654	12	and	and	CCONJ
ejpam-5062	654	13	a.s	a.s	PROPN
ejpam-5062	654	14	.	.	PROPN
ejpam-5062	654	15	mashhour	mashhour	PROPN
ejpam-5062	654	16	.	.	PUNCT
ejpam-5062	655	1	separation	separation	NOUN
ejpam-5062	655	2	axioms	axiom	NOUN
ejpam-5062	655	3	,	,	PUNCT
ejpam-5062	655	4	subspaces	subspace	NOUN
ejpam-5062	655	5	and	and	CCONJ
ejpam-5062	655	6	sums	sum	NOUN
ejpam-5062	655	7	in	in	ADP
ejpam-5062	655	8	fuzzy	fuzzy	ADJ
ejpam-5062	655	9	topology	topology	NOUN
ejpam-5062	655	10	.	.	PUNCT
ejpam-5062	656	1	j.	j.	PROPN
ejpam-5062	656	2	math	math	PROPN
ejpam-5062	656	3	.	.	PUNCT
ejpam-5062	657	1	anal	anal	PROPN
ejpam-5062	657	2	.	.	PUNCT
ejpam-5062	658	1	appl	appl	PROPN
ejpam-5062	658	2	.	.	PROPN
ejpam-5062	658	3	,	,	PUNCT
ejpam-5062	659	1	102(1):189–202	102(1):189–202	NUM
ejpam-5062	659	2	,	,	PUNCT
ejpam-5062	659	3	1984	1984	NUM
ejpam-5062	659	4	.	.	PUNCT
ejpam-5062	660	1	[	[	X
ejpam-5062	660	2	7	7	X
ejpam-5062	660	3	]	]	X
ejpam-5062	660	4	j.a	j.a	PROPN
ejpam-5062	660	5	.	.	PROPN
ejpam-5062	660	6	goguen	goguen	PROPN
ejpam-5062	660	7	.	.	PUNCT
ejpam-5062	661	1	the	the	DET
ejpam-5062	661	2	fuzzy	fuzzy	ADJ
ejpam-5062	661	3	tychonoff	tychonoff	NOUN
ejpam-5062	661	4	theorem	theorem	VERB
ejpam-5062	661	5	.	.	PUNCT
ejpam-5062	662	1	j.	j.	PROPN
ejpam-5062	662	2	math	math	PROPN
ejpam-5062	662	3	.	.	PUNCT
ejpam-5062	663	1	anal	anal	PROPN
ejpam-5062	663	2	.	.	PUNCT
ejpam-5062	664	1	appl	appl	PROPN
ejpam-5062	664	2	.	.	PROPN
ejpam-5062	665	1	,	,	PUNCT
ejpam-5062	665	2	43(3):734–742	43(3):734–742	PROPN
ejpam-5062	665	3	,	,	PUNCT
ejpam-5062	665	4	1973	1973	NUM
ejpam-5062	665	5	.	.	PUNCT
ejpam-5062	666	1	[	[	X
ejpam-5062	666	2	8	8	NUM
ejpam-5062	666	3	]	]	X
ejpam-5062	666	4	v.	v.	CCONJ
ejpam-5062	666	5	gregori	gregori	PROPN
ejpam-5062	666	6	and	and	CCONJ
ejpam-5062	666	7	h.p.a	h.p.a	PROPN
ejpam-5062	666	8	.	.	PUNCT
ejpam-5062	667	1	kunzi	kunzi	PROPN
ejpam-5062	667	2	.	.	PUNCT
ejpam-5062	668	1	α	α	X
ejpam-5062	668	2	-	-	PUNCT
ejpam-5062	668	3	fuzzy	fuzzy	ADJ
ejpam-5062	668	4	compactness	compactness	NOUN
ejpam-5062	668	5	in	in	ADP
ejpam-5062	668	6	i	i	PROPN
ejpam-5062	668	7	-	-	PUNCT
ejpam-5062	668	8	topological	topological	ADJ
ejpam-5062	668	9	spaces	space	NOUN
ejpam-5062	668	10	.	.	PUNCT
ejpam-5062	669	1	international	international	ADJ
ejpam-5062	669	2	journal	journal	PROPN
ejpam-5062	669	3	of	of	ADP
ejpam-5062	669	4	mathematics	mathematics	PROPN
ejpam-5062	669	5	and	and	CCONJ
ejpam-5062	669	6	mathematical	mathematical	ADJ
ejpam-5062	669	7	sciences	science	NOUN
ejpam-5062	669	8	,	,	PUNCT
ejpam-5062	669	9	41(article	41(article	NUM
ejpam-5062	669	10	i	i	PROPN
ejpam-5062	669	11	d	d	PROPN
ejpam-5062	669	12	476231):2609–2617	476231):2609–2617	PROPN
ejpam-5062	669	13	,	,	PUNCT
ejpam-5062	669	14	2003	2003	NUM
ejpam-5062	669	15	.	.	PUNCT
ejpam-5062	670	1	[	[	X
ejpam-5062	670	2	9	9	NUM
ejpam-5062	670	3	]	]	X
ejpam-5062	670	4	u.	u.	NOUN
ejpam-5062	670	5	hohle	hohle	PROPN
ejpam-5062	670	6	.	.	PUNCT
ejpam-5062	671	1	probabilistische	probabilistische	PROPN
ejpam-5062	671	2	topologien	topologien	PROPN
ejpam-5062	671	3	.	.	PUNCT
ejpam-5062	672	1	manustcipta	manustcipta	NOUN
ejpam-5062	672	2	math	math	PROPN
ejpam-5062	672	3	.	.	PUNCT
ejpam-5062	672	4	,	,	PUNCT
ejpam-5062	673	1	26:223–245	26:223–245	PROPN
ejpam-5062	673	2	,	,	PUNCT
ejpam-5062	673	3	1978	1978	NUM
ejpam-5062	673	4	.	.	PUNCT
ejpam-5062	674	1	[	[	X
ejpam-5062	674	2	10	10	NUM
ejpam-5062	674	3	]	]	X
ejpam-5062	674	4	u.	u.	PROPN
ejpam-5062	674	5	hohle	hohle	PROPN
ejpam-5062	674	6	.	.	PUNCT
ejpam-5062	675	1	probabilistische	probabilistische	PROPN
ejpam-5062	675	2	kompakte	kompakte	PROPN
ejpam-5062	675	3	l	l	PROPN
ejpam-5062	675	4	-	-	PUNCT
ejpam-5062	675	5	unscharfe	unscharfe	ADJ
ejpam-5062	675	6	mengen	mengen	PROPN
ejpam-5062	675	7	.	.	PUNCT
ejpam-5062	676	1	manuscripta	manuscripta	NOUN
ejpam-5062	676	2	math	math	PROPN
ejpam-5062	676	3	.	.	PUNCT
ejpam-5062	676	4	,	,	PUNCT
ejpam-5062	677	1	26:331–347	26:331–347	PROPN
ejpam-5062	677	2	,	,	PUNCT
ejpam-5062	677	3	1979	1979	NUM
ejpam-5062	677	4	.	.	PUNCT
ejpam-5062	678	1	[	[	X
ejpam-5062	678	2	11	11	NUM
ejpam-5062	678	3	]	]	X
ejpam-5062	678	4	b.	b.	PROPN
ejpam-5062	678	5	hutton	hutton	PROPN
ejpam-5062	678	6	and	and	CCONJ
ejpam-5062	678	7	i.	i.	PROPN
ejpam-5062	678	8	reilly	reilly	PROPN
ejpam-5062	678	9	.	.	PUNCT
ejpam-5062	679	1	separation	separation	NOUN
ejpam-5062	679	2	axioms	axiom	VERB
ejpam-5062	679	3	in	in	ADP
ejpam-5062	679	4	fuzzy	fuzzy	ADJ
ejpam-5062	679	5	topological	topological	ADJ
ejpam-5062	679	6	spaces	space	NOUN
ejpam-5062	679	7	.	.	PUNCT
ejpam-5062	680	1	fuzzy	fuzzy	ADJ
ejpam-5062	680	2	sets	set	NOUN
ejpam-5062	680	3	and	and	CCONJ
ejpam-5062	680	4	systems	system	NOUN
ejpam-5062	680	5	,	,	PUNCT
ejpam-5062	680	6	3(1):93–104	3(1):93–104	NOUN
ejpam-5062	680	7	,	,	PUNCT
ejpam-5062	680	8	1980	1980	NUM
ejpam-5062	680	9	.	.	PUNCT
ejpam-5062	681	1	[	[	X
ejpam-5062	681	2	12	12	NUM
ejpam-5062	681	3	]	]	PUNCT
ejpam-5062	681	4	b.	b.	PROPN
ejpam-5062	681	5	krsteska	krsteska	PROPN
ejpam-5062	681	6	.	.	PUNCT
ejpam-5062	682	1	fuzzy	fuzzy	ADJ
ejpam-5062	682	2	strongly	strongly	ADV
ejpam-5062	682	3	preopen	preopen	ADJ
ejpam-5062	682	4	sets	set	NOUN
ejpam-5062	682	5	and	and	CCONJ
ejpam-5062	682	6	fuzzy	fuzzy	ADJ
ejpam-5062	682	7	strong	strong	ADJ
ejpam-5062	682	8	precontinuity	precontinuity	NOUN
ejpam-5062	682	9	.	.	PUNCT
ejpam-5062	683	1	mat	mat	PROPN
ejpam-5062	683	2	.	.	PUNCT
ejpam-5062	683	3	vesnik	vesnik	PROPN
ejpam-5062	683	4	,	,	PUNCT
ejpam-5062	683	5	50:111–123	50:111–123	PROPN
ejpam-5062	683	6	,	,	PUNCT
ejpam-5062	683	7	1998	1998	NUM
ejpam-5062	683	8	.	.	PUNCT
ejpam-5062	684	1	[	[	X
ejpam-5062	684	2	13	13	NUM
ejpam-5062	684	3	]	]	PUNCT
ejpam-5062	684	4	b.	b.	PROPN
ejpam-5062	684	5	krsteska	krsteska	PROPN
ejpam-5062	684	6	.	.	PUNCT
ejpam-5062	685	1	jedna	jedna	PROPN
ejpam-5062	685	2	klasa	klasa	PROPN
ejpam-5062	685	3	uopstenih	uopstenih	PROPN
ejpam-5062	685	4	otvorenih	otvorenih	ADP
ejpam-5062	685	5	skupova	skupova	PROPN
ejpam-5062	685	6	.	.	PUNCT
ejpam-5062	686	1	phd	phd	NOUN
ejpam-5062	686	2	thesis	thesis	PROPN
ejpam-5062	686	3	,	,	PUNCT
ejpam-5062	686	4	university	university	NOUN
ejpam-5062	686	5	of	of	ADP
ejpam-5062	686	6	belgrade	belgrade	PROPN
ejpam-5062	686	7	,	,	PUNCT
ejpam-5062	686	8	1999	1999	NUM
ejpam-5062	686	9	.	.	PUNCT
ejpam-5062	687	1	[	[	X
ejpam-5062	687	2	14	14	NUM
ejpam-5062	687	3	]	]	PUNCT
ejpam-5062	687	4	b.	b.	PROPN
ejpam-5062	687	5	krsteska	krsteska	PROPN
ejpam-5062	687	6	.	.	PUNCT
ejpam-5062	688	1	some	some	DET
ejpam-5062	688	2	fuzzy	fuzzy	ADJ
ejpam-5062	688	3	sp	sp	NOUN
ejpam-5062	688	4	-	-	PUNCT
ejpam-5062	688	5	topological	topological	ADJ
ejpam-5062	688	6	properties	property	NOUN
ejpam-5062	688	7	.	.	PUNCT
ejpam-5062	689	1	mat	mat	PROPN
ejpam-5062	689	2	.	.	PROPN
ejpam-5062	689	3	vesnik	vesnik	PROPN
ejpam-5062	689	4	,	,	PUNCT
ejpam-5062	689	5	51:39–51	51:39–51	PROPN
ejpam-5062	689	6	,	,	PUNCT
ejpam-5062	689	7	1999	1999	NUM
ejpam-5062	689	8	.	.	PUNCT
ejpam-5062	690	1	[	[	X
ejpam-5062	690	2	15	15	NUM
ejpam-5062	690	3	]	]	X
ejpam-5062	690	4	r.	r.	PROPN
ejpam-5062	690	5	lowen	lowen	PROPN
ejpam-5062	690	6	.	.	PUNCT
ejpam-5062	691	1	topologies	topology	NOUN
ejpam-5062	691	2	floues	floue	NOUN
ejpam-5062	691	3	.	.	PUNCT
ejpam-5062	692	1	cr	cr	PROPN
ejpam-5062	692	2	acad	acad	PROPN
ejpam-5062	692	3	.	.	PUNCT
ejpam-5062	693	1	sc	sc	PROPN
ejpam-5062	693	2	.	.	PUNCT
ejpam-5062	693	3	paris	paris	PROPN
ejpam-5062	693	4	278	278	NUM
ejpam-5062	693	5	,	,	PUNCT
ejpam-5062	693	6	pages	page	NOUN
ejpam-5062	693	7	925–928	925–928	NUM
ejpam-5062	693	8	,	,	PUNCT
ejpam-5062	693	9	1974	1974	NUM
ejpam-5062	693	10	.	.	PUNCT
ejpam-5062	694	1	[	[	X
ejpam-5062	694	2	16	16	NUM
ejpam-5062	694	3	]	]	X
ejpam-5062	694	4	r.	r.	PROPN
ejpam-5062	694	5	lowen	lowen	PROPN
ejpam-5062	694	6	.	.	PUNCT
ejpam-5062	695	1	initial	initial	ADJ
ejpam-5062	695	2	and	and	CCONJ
ejpam-5062	695	3	final	final	ADJ
ejpam-5062	695	4	topologies	topology	NOUN
ejpam-5062	695	5	and	and	CCONJ
ejpam-5062	695	6	the	the	DET
ejpam-5062	695	7	fuzzy	fuzzy	ADJ
ejpam-5062	695	8	tychonoff	tychonoff	NOUN
ejpam-5062	695	9	theorem	theorem	VERB
ejpam-5062	695	10	.	.	PUNCT
ejpam-5062	696	1	j.	j.	PROPN
ejpam-5062	696	2	math	math	PROPN
ejpam-5062	696	3	.	.	PUNCT
ejpam-5062	697	1	anal	anal	PROPN
ejpam-5062	697	2	.	.	PUNCT
ejpam-5062	697	3	appl	appl	PROPN
ejpam-5062	697	4	.	.	PROPN
ejpam-5062	697	5	,	,	PUNCT
ejpam-5062	697	6	58(1):11–21	58(1):11–21	NUM
ejpam-5062	697	7	,	,	PUNCT
ejpam-5062	697	8	1977	1977	NUM
ejpam-5062	697	9	.	.	PUNCT
ejpam-5062	698	1	[	[	X
ejpam-5062	698	2	17	17	NUM
ejpam-5062	698	3	]	]	PUNCT
ejpam-5062	698	4	sh.v	sh.v	NOUN
ejpam-5062	698	5	.	.	PUNCT
ejpam-5062	699	1	makolli	makolli	PROPN
ejpam-5062	699	2	and	and	CCONJ
ejpam-5062	699	3	b.	b.	PROPN
ejpam-5062	699	4	krsteska	krsteska	PROPN
ejpam-5062	699	5	.	.	PUNCT
ejpam-5062	700	1	a	a	DET
ejpam-5062	700	2	note	note	NOUN
ejpam-5062	700	3	on	on	ADP
ejpam-5062	700	4	fuzzy	fuzzy	ADJ
ejpam-5062	700	5	strongly	strongly	ADV
ejpam-5062	700	6	semi	semi	ADV
ejpam-5062	700	7	pre	pre	ADJ
ejpam-5062	700	8	-	-	ADJ
ejpam-5062	700	9	open	open	ADJ
ejpam-5062	700	10	sets	set	NOUN
ejpam-5062	700	11	and	and	CCONJ
ejpam-5062	700	12	fuzzy	fuzzy	ADJ
ejpam-5062	700	13	strong	strong	ADJ
ejpam-5062	700	14	semi	semi	ADJ
ejpam-5062	700	15	pre	pre	ADJ
ejpam-5062	700	16	-	-	NOUN
ejpam-5062	700	17	continuity	continuity	NOUN
ejpam-5062	700	18	.	.	PUNCT
ejpam-5062	701	1	international	international	ADJ
ejpam-5062	701	2	j.	j.	PROPN
ejpam-5062	701	3	of	of	ADP
ejpam-5062	701	4	math	math	PROPN
ejpam-5062	701	5	.	.	PUNCT
ejpam-5062	702	1	sci	sci	PROPN
ejpam-5062	702	2	.	.	PROPN
ejpam-5062	702	3	&	&	CCONJ
ejpam-5062	702	4	engg	engg	PROPN
ejpam-5062	702	5	.	.	PUNCT
ejpam-5062	703	1	appls	appls	PROPN
ejpam-5062	703	2	.	.	PUNCT
ejpam-5062	703	3	,	,	PUNCT
ejpam-5062	703	4	16(2):9–23	16(2):9–23	NUM
ejpam-5062	703	5	,	,	PUNCT
ejpam-5062	703	6	2022	2022	NUM
ejpam-5062	703	7	.	.	PUNCT
ejpam-5062	704	1	[	[	X
ejpam-5062	704	2	18	18	NUM
ejpam-5062	704	3	]	]	SYM
ejpam-5062	704	4	sh.v	sh.v	NOUN
ejpam-5062	704	5	.	.	PUNCT
ejpam-5062	704	6	makolli	makolli	PROPN
ejpam-5062	704	7	and	and	CCONJ
ejpam-5062	704	8	b.	b.	PROPN
ejpam-5062	704	9	krsteska	krsteska	PROPN
ejpam-5062	704	10	.	.	PUNCT
ejpam-5062	705	1	a	a	DET
ejpam-5062	705	2	note	note	NOUN
ejpam-5062	705	3	regarding	regard	VERB
ejpam-5062	705	4	some	some	DET
ejpam-5062	705	5	fuzzy	fuzzy	ADJ
ejpam-5062	705	6	sspo	sspo	NOUN
ejpam-5062	705	7	mappings	mapping	NOUN
ejpam-5062	705	8	.	.	PUNCT
ejpam-5062	706	1	mat.bilt	mat.bilt	PROPN
ejpam-5062	706	2	.	.	PROPN
ejpam-5062	706	3	,	,	PUNCT
ejpam-5062	706	4	46(2):83–96	46(2):83–96	NUM
ejpam-5062	706	5	,	,	PUNCT
ejpam-5062	706	6	2022	2022	NUM
ejpam-5062	706	7	.	.	PUNCT
ejpam-5062	707	1	[	[	X
ejpam-5062	707	2	19	19	NUM
ejpam-5062	707	3	]	]	X
ejpam-5062	707	4	s.r	s.r	PROPN
ejpam-5062	707	5	.	.	PROPN
ejpam-5062	707	6	malghan	malghan	PROPN
ejpam-5062	707	7	and	and	CCONJ
ejpam-5062	707	8	s.s	s.s	PROPN
ejpam-5062	707	9	.	.	PROPN
ejpam-5062	707	10	benchalli	benchalli	PROPN
ejpam-5062	707	11	.	.	PUNCT
ejpam-5062	708	1	on	on	ADP
ejpam-5062	708	2	fuzzy	fuzzy	ADJ
ejpam-5062	708	3	topological	topological	ADJ
ejpam-5062	708	4	spaces	space	NOUN
ejpam-5062	708	5	.	.	PUNCT
ejpam-5062	709	1	glasnik	glasnik	PROPN
ejpam-5062	709	2	mat	mat	PROPN
ejpam-5062	709	3	.	.	PROPN
ejpam-5062	709	4	,	,	PUNCT
ejpam-5062	709	5	16(2):313–325	16(2):313–325	PROPN
ejpam-5062	709	6	,	,	PUNCT
ejpam-5062	709	7	1981	1981	NUM
ejpam-5062	709	8	.	.	PUNCT
ejpam-5062	710	1	[	[	X
ejpam-5062	710	2	20	20	NUM
ejpam-5062	710	3	]	]	X
ejpam-5062	710	4	s.r	s.r	PROPN
ejpam-5062	710	5	.	.	PROPN
ejpam-5062	710	6	malghan	malghan	PROPN
ejpam-5062	710	7	and	and	CCONJ
ejpam-5062	710	8	s.s	s.s	PROPN
ejpam-5062	710	9	.	.	PROPN
ejpam-5062	710	10	benchalli	benchalli	PROPN
ejpam-5062	710	11	.	.	PUNCT
ejpam-5062	711	1	open	open	ADJ
ejpam-5062	711	2	maps	map	NOUN
ejpam-5062	711	3	,	,	PUNCT
ejpam-5062	711	4	closed	closed	ADJ
ejpam-5062	711	5	maps	map	NOUN
ejpam-5062	711	6	and	and	CCONJ
ejpam-5062	711	7	local	local	ADJ
ejpam-5062	711	8	compactness	compactness	NOUN
ejpam-5062	711	9	in	in	ADP
ejpam-5062	711	10	the	the	DET
ejpam-5062	711	11	fuzzy	fuzzy	ADJ
ejpam-5062	711	12	topological	topological	ADJ
ejpam-5062	711	13	spaces	space	NOUN
ejpam-5062	711	14	.	.	PUNCT
ejpam-5062	712	1	j.	j.	PROPN
ejpam-5062	712	2	math	math	PROPN
ejpam-5062	712	3	.	.	PUNCT
ejpam-5062	713	1	anal	anal	PROPN
ejpam-5062	713	2	.	.	PUNCT
ejpam-5062	714	1	appl	appl	PROPN
ejpam-5062	714	2	.	.	PROPN
ejpam-5062	715	1	,	,	PUNCT
ejpam-5062	715	2	99(2):338–349	99(2):338–349	NUM
ejpam-5062	715	3	,	,	PUNCT
ejpam-5062	715	4	1984	1984	NUM
ejpam-5062	715	5	.	.	PUNCT
ejpam-5062	716	1	[	[	X
ejpam-5062	716	2	21	21	NUM
ejpam-5062	716	3	]	]	X
ejpam-5062	716	4	a.s	a.s	PROPN
ejpam-5062	716	5	.	.	PROPN
ejpam-5062	716	6	mashhour	mashhour	PROPN
ejpam-5062	716	7	,	,	PUNCT
ejpam-5062	716	8	m.h	m.h	PROPN
ejpam-5062	716	9	.	.	PROPN
ejpam-5062	716	10	ghanim	ghanim	PROPN
ejpam-5062	716	11	,	,	PUNCT
ejpam-5062	716	12	and	and	CCONJ
ejpam-5062	716	13	m.a	m.a	PROPN
ejpam-5062	716	14	.	.	PROPN
ejpam-5062	716	15	fath	fath	PROPN
ejpam-5062	716	16	alla	alla	PROPN
ejpam-5062	716	17	.	.	PUNCT
ejpam-5062	717	1	on	on	ADP
ejpam-5062	717	2	fuzzy	fuzzy	ADJ
ejpam-5062	717	3	non	non	ADJ
ejpam-5062	717	4	-	-	ADJ
ejpam-5062	717	5	continuous	continuous	ADJ
ejpam-5062	717	6	mapping	mapping	NOUN
ejpam-5062	717	7	.	.	PUNCT
ejpam-5062	718	1	bull	bull	NOUN
ejpam-5062	718	2	.	.	PUNCT
ejpam-5062	719	1	cal	cal	PROPN
ejpam-5062	719	2	.	.	PUNCT
ejpam-5062	720	1	math	math	NOUN
ejpam-5062	720	2	.	.	PUNCT
ejpam-5062	721	1	soc	soc	PROPN
ejpam-5062	721	2	.	.	PUNCT
ejpam-5062	721	3	,	,	PUNCT
ejpam-5062	721	4	78:57–69	78:57–69	NUM
ejpam-5062	721	5	,	,	PUNCT
ejpam-5062	721	6	1986	1986	NUM
ejpam-5062	721	7	.	.	PUNCT
ejpam-5062	722	1	references	reference	NOUN
ejpam-5062	722	2	662	662	NUM
ejpam-5062	722	3	[	[	X
ejpam-5062	722	4	22	22	NUM
ejpam-5062	722	5	]	]	X
ejpam-5062	722	6	m.n	m.n	PROPN
ejpam-5062	722	7	.	.	PROPN
ejpam-5062	722	8	mukherjee	mukherjee	PROPN
ejpam-5062	722	9	and	and	CCONJ
ejpam-5062	722	10	s.p	s.p	PROPN
ejpam-5062	722	11	.	.	PUNCT
ejpam-5062	722	12	sinha	sinha	PROPN
ejpam-5062	722	13	.	.	PROPN
ejpam-5062	722	14	irresolute	irresolute	PROPN
ejpam-5062	722	15	and	and	CCONJ
ejpam-5062	722	16	almost	almost	ADV
ejpam-5062	722	17	open	open	ADJ
ejpam-5062	722	18	functions	function	NOUN
ejpam-5062	722	19	between	between	ADP
ejpam-5062	722	20	fuzzy	fuzzy	ADJ
ejpam-5062	722	21	topological	topological	ADJ
ejpam-5062	722	22	spaces	space	NOUN
ejpam-5062	722	23	.	.	PUNCT
ejpam-5062	723	1	fuzzy	fuzzy	ADJ
ejpam-5062	723	2	sets	set	NOUN
ejpam-5062	723	3	and	and	CCONJ
ejpam-5062	723	4	systems	system	NOUN
ejpam-5062	723	5	,	,	PUNCT
ejpam-5062	723	6	29:381–388	29:381–388	NUM
ejpam-5062	723	7	,	,	PUNCT
ejpam-5062	723	8	1989	1989	NUM
ejpam-5062	723	9	.	.	PUNCT
ejpam-5062	724	1	[	[	X
ejpam-5062	724	2	23	23	NUM
ejpam-5062	724	3	]	]	SYM
ejpam-5062	724	4	p.m.	p.m.	NOUN
ejpam-5062	725	1	pu	pu	PROPN
ejpam-5062	725	2	and	and	CCONJ
ejpam-5062	725	3	y.m	y.m	PROPN
ejpam-5062	725	4	.	.	PROPN
ejpam-5062	726	1	liu	liu	PROPN
ejpam-5062	726	2	.	.	PUNCT
ejpam-5062	726	3	fuzzy	fuzzy	ADJ
ejpam-5062	726	4	topology	topology	PROPN
ejpam-5062	726	5	.	.	PUNCT
ejpam-5062	727	1	i.	i.	PROPN
ejpam-5062	727	2	neighborhood	neighborhood	PROPN
ejpam-5062	727	3	structure	structure	NOUN
ejpam-5062	727	4	of	of	ADP
ejpam-5062	727	5	a	a	DET
ejpam-5062	727	6	fuzzy	fuzzy	ADJ
ejpam-5062	727	7	point	point	NOUN
ejpam-5062	727	8	and	and	CCONJ
ejpam-5062	727	9	moore	moore	PROPN
ejpam-5062	727	10	-	-	PUNCT
ejpam-5062	727	11	smith	smith	PROPN
ejpam-5062	727	12	convergence	convergence	NOUN
ejpam-5062	727	13	.	.	PUNCT
ejpam-5062	728	1	j.	j.	PROPN
ejpam-5062	728	2	math	math	PROPN
ejpam-5062	728	3	.	.	PUNCT
ejpam-5062	729	1	anal	anal	PROPN
ejpam-5062	729	2	.	.	PUNCT
ejpam-5062	730	1	appl	appl	PROPN
ejpam-5062	730	2	.	.	PROPN
ejpam-5062	730	3	,	,	PUNCT
ejpam-5062	731	1	76:571–599	76:571–599	NUM
ejpam-5062	731	2	,	,	PUNCT
ejpam-5062	731	3	1980	1980	NUM
ejpam-5062	731	4	.	.	PUNCT
ejpam-5062	732	1	[	[	X
ejpam-5062	732	2	24	24	NUM
ejpam-5062	732	3	]	]	X
ejpam-5062	732	4	s.	s.	PROPN
ejpam-5062	732	5	rodabaugh	rodabaugh	PROPN
ejpam-5062	732	6	.	.	PUNCT
ejpam-5062	733	1	the	the	DET
ejpam-5062	733	2	hausdorff	hausdorff	NOUN
ejpam-5062	733	3	separation	separation	NOUN
ejpam-5062	733	4	axiom	axiom	NOUN
ejpam-5062	733	5	for	for	ADP
ejpam-5062	733	6	fuzzy	fuzzy	ADJ
ejpam-5062	733	7	topological	topological	ADJ
ejpam-5062	733	8	spaces	space	NOUN
ejpam-5062	733	9	.	.	PUNCT
ejpam-5062	734	1	topol	topol	NOUN
ejpam-5062	734	2	.	.	PUNCT
ejpam-5062	734	3	appl	appl	PROPN
ejpam-5062	734	4	.	.	PROPN
ejpam-5062	734	5	,	,	PUNCT
ejpam-5062	734	6	11:319–334	11:319–334	PROPN
ejpam-5062	734	7	,	,	PUNCT
ejpam-5062	734	8	1980	1980	NUM
ejpam-5062	734	9	.	.	PUNCT
ejpam-5062	735	1	[	[	X
ejpam-5062	735	2	25	25	NUM
ejpam-5062	735	3	]	]	PUNCT
ejpam-5062	735	4	s.	s.	PROPN
ejpam-5062	735	5	saleh	saleh	PROPN
ejpam-5062	735	6	,	,	PUNCT
ejpam-5062	735	7	m.a	m.a	PROPN
ejpam-5062	735	8	.	.	PROPN
ejpam-5062	735	9	tareq	tareq	PROPN
ejpam-5062	735	10	,	,	PUNCT
ejpam-5062	735	11	a.a	a.a	PROPN
ejpam-5062	735	12	.	.	PROPN
ejpam-5062	735	13	azzam	azzam	PROPN
ejpam-5062	735	14	,	,	PUNCT
ejpam-5062	735	15	and	and	CCONJ
ejpam-5062	735	16	m.	m.	PROPN
ejpam-5062	735	17	hosny	hosny	PROPN
ejpam-5062	735	18	.	.	PUNCT
ejpam-5062	736	1	stronger	strong	ADJ
ejpam-5062	736	2	forms	form	NOUN
ejpam-5062	736	3	of	of	ADP
ejpam-5062	736	4	fuzzy	fuzzy	ADJ
ejpam-5062	736	5	pre	pre	NOUN
ejpam-5062	736	6	-	-	NOUN
ejpam-5062	736	7	separation	separation	NOUN
ejpam-5062	736	8	and	and	CCONJ
ejpam-5062	736	9	regularity	regularity	NOUN
ejpam-5062	736	10	axioms	axiom	NOUN
ejpam-5062	736	11	via	via	ADP
ejpam-5062	736	12	fuzzy	fuzzy	ADJ
ejpam-5062	736	13	topology	topology	NOUN
ejpam-5062	736	14	.	.	PUNCT
ejpam-5062	737	1	mathematics	mathematic	NOUN
ejpam-5062	737	2	,	,	PUNCT
ejpam-5062	737	3	11(4801):https://doi.org/10.3390/.	11(4801):https://doi.org/10.3390/.	NOUN
ejpam-5062	737	4	,	,	PUNCT
ejpam-5062	737	5	2023	2023	NUM
ejpam-5062	737	6	.	.	PUNCT
ejpam-5062	738	1	[	[	X
ejpam-5062	738	2	26	26	NUM
ejpam-5062	738	3	]	]	PUNCT
ejpam-5062	738	4	s.	s.	PROPN
ejpam-5062	738	5	saleh	saleh	PROPN
ejpam-5062	738	6	,	,	PUNCT
ejpam-5062	738	7	m.a	m.a	PROPN
ejpam-5062	738	8	.	.	PROPN
ejpam-5062	738	9	tareq	tareq	PROPN
ejpam-5062	738	10	,	,	PUNCT
ejpam-5062	738	11	and	and	CCONJ
ejpam-5062	738	12	a.	a.	NOUN
ejpam-5062	738	13	mhemdi	mhemdi	PROPN
ejpam-5062	738	14	.	.	PUNCT
ejpam-5062	739	1	some	some	DET
ejpam-5062	739	2	new	new	ADJ
ejpam-5062	739	3	types	type	NOUN
ejpam-5062	739	4	of	of	ADP
ejpam-5062	739	5	fuzzy	fuzzy	ADJ
ejpam-5062	739	6	soft	soft	ADJ
ejpam-5062	739	7	compact	compact	ADJ
ejpam-5062	739	8	spaces	space	NOUN
ejpam-5062	739	9	.	.	PUNCT
ejpam-5062	740	1	hindawi	hindawi	ADJ
ejpam-5062	740	2	journal	journal	PROPN
ejpam-5062	740	3	of	of	ADP
ejpam-5062	740	4	mathematics	mathematic	NOUN
ejpam-5062	740	5	,	,	PUNCT
ejpam-5062	740	6	(	(	PUNCT
ejpam-5062	740	7	article	article	NOUN
ejpam-5062	740	8	i	i	PROPN
ejpam-5062	740	9	d	d	PROPN
ejpam-5062	740	10	5065592):https://doi.org/10.1155/2023/5065592	5065592):https://doi.org/10.1155/2023/5065592	NUM
ejpam-5062	740	11	,	,	PUNCT
ejpam-5062	740	12	2023	2023	NUM
ejpam-5062	740	13	.	.	PUNCT
ejpam-5062	741	1	[	[	X
ejpam-5062	741	2	27	27	NUM
ejpam-5062	741	3	]	]	X
ejpam-5062	741	4	m.k	m.k	PROPN
ejpam-5062	741	5	.	.	PROPN
ejpam-5062	741	6	singal	singal	PROPN
ejpam-5062	741	7	and	and	CCONJ
ejpam-5062	741	8	n.	n.	PROPN
ejpam-5062	741	9	prakash	prakash	PROPN
ejpam-5062	741	10	.	.	PUNCT
ejpam-5062	741	11	fuzzy	fuzzy	ADJ
ejpam-5062	741	12	pre	pre	ADJ
ejpam-5062	741	13	-	-	ADJ
ejpam-5062	741	14	open	open	ADJ
ejpam-5062	741	15	sets	set	NOUN
ejpam-5062	741	16	and	and	CCONJ
ejpam-5062	741	17	fuzzy	fuzzy	ADJ
ejpam-5062	741	18	preseparation	preseparation	NOUN
ejpam-5062	741	19	axioms	axiom	NOUN
ejpam-5062	741	20	.	.	PUNCT
ejpam-5062	742	1	fuzzy	fuzzy	ADJ
ejpam-5062	742	2	sets	set	NOUN
ejpam-5062	742	3	and	and	CCONJ
ejpam-5062	742	4	systems	system	NOUN
ejpam-5062	742	5	,	,	PUNCT
ejpam-5062	742	6	44:273–281	44:273–281	NUM
ejpam-5062	742	7	,	,	PUNCT
ejpam-5062	742	8	1991	1991	NUM
ejpam-5062	742	9	.	.	PUNCT
ejpam-5062	743	1	[	[	X
ejpam-5062	743	2	28	28	NUM
ejpam-5062	743	3	]	]	X
ejpam-5062	743	4	m.a	m.a	PROPN
ejpam-5062	743	5	.	.	PROPN
ejpam-5062	743	6	tareq	tareq	PROPN
ejpam-5062	743	7	,	,	PUNCT
ejpam-5062	743	8	s.	s.	PROPN
ejpam-5062	743	9	saleh	saleh	PROPN
ejpam-5062	743	10	,	,	PUNCT
ejpam-5062	743	11	a.m.	a.m.	PROPN
ejpam-5062	744	1	abd	abd	PROPN
ejpam-5062	744	2	el	el	PROPN
ejpam-5062	744	3	-	-	PROPN
ejpam-5062	744	4	latif	latif	PROPN
ejpam-5062	744	5	,	,	PUNCT
ejpam-5062	744	6	and	and	CCONJ
ejpam-5062	744	7	a.	a.	NOUN
ejpam-5062	744	8	mhemdi	mhemdi	PROPN
ejpam-5062	744	9	.	.	PUNCT
ejpam-5062	745	1	novel	novel	ADJ
ejpam-5062	745	2	categories	category	NOUN
ejpam-5062	745	3	of	of	ADP
ejpam-5062	745	4	spaces	space	NOUN
ejpam-5062	745	5	in	in	ADP
ejpam-5062	745	6	the	the	DET
ejpam-5062	745	7	frame	frame	NOUN
ejpam-5062	745	8	of	of	ADP
ejpam-5062	745	9	fuzzy	fuzzy	ADJ
ejpam-5062	745	10	soft	soft	ADJ
ejpam-5062	745	11	topologies	topology	NOUN
ejpam-5062	745	12	.	.	PUNCT
ejpam-5062	746	1	aims	aim	VERB
ejpam-5062	746	2	mathematics	mathematic	NOUN
ejpam-5062	746	3	,	,	PUNCT
ejpam-5062	746	4	9(3):6305–6320	9(3):6305–6320	NUM
ejpam-5062	746	5	,	,	PUNCT
ejpam-5062	746	6	2024	2024	NUM
ejpam-5062	746	7	.	.	PUNCT
ejpam-5062	747	1	[	[	X
ejpam-5062	747	2	29	29	NUM
ejpam-5062	747	3	]	]	X
ejpam-5062	747	4	m.d	m.d	PROPN
ejpam-5062	747	5	.	.	PROPN
ejpam-5062	747	6	weiss	weiss	PROPN
ejpam-5062	747	7	.	.	PUNCT
ejpam-5062	748	1	fixed	fix	VERB
ejpam-5062	748	2	points	point	NOUN
ejpam-5062	748	3	,	,	PUNCT
ejpam-5062	748	4	separation	separation	NOUN
ejpam-5062	748	5	,	,	PUNCT
ejpam-5062	748	6	and	and	CCONJ
ejpam-5062	748	7	induced	induce	VERB
ejpam-5062	748	8	topologies	topology	NOUN
ejpam-5062	748	9	for	for	ADP
ejpam-5062	748	10	fuzzy	fuzzy	ADJ
ejpam-5062	748	11	sets	set	NOUN
ejpam-5062	748	12	.	.	PUNCT
ejpam-5062	749	1	j.	j.	PROPN
ejpam-5062	749	2	math	math	PROPN
ejpam-5062	749	3	.	.	PUNCT
ejpam-5062	750	1	anal	anal	PROPN
ejpam-5062	750	2	.	.	PUNCT
ejpam-5062	751	1	appl	appl	PROPN
ejpam-5062	751	2	.	.	PROPN
ejpam-5062	751	3	,	,	PUNCT
ejpam-5062	752	1	50:142–150	50:142–150	PROPN
ejpam-5062	752	2	,	,	PUNCT
ejpam-5062	752	3	1975	1975	NUM
ejpam-5062	752	4	.	.	PUNCT
ejpam-5062	753	1	[	[	X
ejpam-5062	753	2	30	30	NUM
ejpam-5062	753	3	]	]	X
ejpam-5062	753	4	c.k	c.k	PROPN
ejpam-5062	753	5	.	.	PROPN
ejpam-5062	753	6	wong	wong	PROPN
ejpam-5062	753	7	.	.	PROPN
ejpam-5062	753	8	fuzzy	fuzzy	ADJ
ejpam-5062	753	9	points	point	NOUN
ejpam-5062	753	10	and	and	CCONJ
ejpam-5062	753	11	local	local	ADJ
ejpam-5062	753	12	properties	property	NOUN
ejpam-5062	753	13	of	of	ADP
ejpam-5062	753	14	fuzzy	fuzzy	ADJ
ejpam-5062	753	15	topology	topology	NOUN
ejpam-5062	753	16	.	.	PUNCT
ejpam-5062	754	1	j.	j.	PROPN
ejpam-5062	754	2	math	math	PROPN
ejpam-5062	754	3	.	.	PUNCT
ejpam-5062	755	1	anal	anal	PROPN
ejpam-5062	755	2	.	.	PUNCT
ejpam-5062	756	1	appl	appl	PROPN
ejpam-5062	756	2	.	.	PROPN
ejpam-5062	756	3	,	,	PUNCT
ejpam-5062	756	4	46(2):316–328	46(2):316–328	PROPN
ejpam-5062	756	5	,	,	PUNCT
ejpam-5062	756	6	1974	1974	NUM
ejpam-5062	756	7	.	.	PUNCT
ejpam-5062	757	1	[	[	X
ejpam-5062	757	2	31	31	NUM
ejpam-5062	757	3	]	]	X
ejpam-5062	757	4	c.k	c.k	PROPN
ejpam-5062	757	5	.	.	PUNCT
ejpam-5062	757	6	wong	wong	PROPN
ejpam-5062	757	7	.	.	PROPN
ejpam-5062	757	8	fuzzy	fuzzy	ADJ
ejpam-5062	757	9	topology	topology	NOUN
ejpam-5062	757	10	:	:	PUNCT
ejpam-5062	757	11	product	product	NOUN
ejpam-5062	757	12	and	and	CCONJ
ejpam-5062	757	13	quotient	quotient	NOUN
ejpam-5062	757	14	theorems	theorem	NOUN
ejpam-5062	757	15	.	.	PUNCT
ejpam-5062	758	1	j.	j.	PROPN
ejpam-5062	758	2	math	math	PROPN
ejpam-5062	758	3	.	.	PUNCT
ejpam-5062	759	1	anal	anal	PROPN
ejpam-5062	759	2	.	.	PUNCT
ejpam-5062	760	1	appl	appl	PROPN
ejpam-5062	760	2	.	.	PROPN
ejpam-5062	760	3	,	,	PUNCT
ejpam-5062	760	4	45(2):512–521	45(2):512–521	PROPN
ejpam-5062	760	5	,	,	PUNCT
ejpam-5062	760	6	1974	1974	NUM
ejpam-5062	760	7	.	.	PUNCT
ejpam-5062	761	1	[	[	X
ejpam-5062	761	2	32	32	NUM
ejpam-5062	761	3	]	]	PUNCT
ejpam-5062	761	4	p.	p.	NOUN
ejpam-5062	761	5	wuyts	wuyts	PROPN
ejpam-5062	761	6	and	and	CCONJ
ejpam-5062	761	7	r.	r.	PROPN
ejpam-5062	761	8	lowen	lowen	PROPN
ejpam-5062	761	9	.	.	PUNCT
ejpam-5062	762	1	on	on	ADP
ejpam-5062	762	2	separation	separation	NOUN
ejpam-5062	762	3	axioms	axiom	NOUN
ejpam-5062	762	4	in	in	ADP
ejpam-5062	762	5	fuzzy	fuzzy	ADJ
ejpam-5062	762	6	topological	topological	ADJ
ejpam-5062	762	7	spaces	space	NOUN
ejpam-5062	762	8	,	,	PUNCT
ejpam-5062	762	9	fuzzy	fuzzy	ADJ
ejpam-5062	762	10	neighborhood	neighborhood	NOUN
ejpam-5062	762	11	spaces	space	NOUN
ejpam-5062	762	12	,	,	PUNCT
ejpam-5062	762	13	and	and	CCONJ
ejpam-5062	762	14	fuzzy	fuzzy	ADJ
ejpam-5062	762	15	uniform	uniform	ADJ
ejpam-5062	762	16	spaces	space	NOUN
ejpam-5062	762	17	.	.	PUNCT
ejpam-5062	763	1	journal	journal	PROPN
ejpam-5062	763	2	of	of	ADP
ejpam-5062	763	3	mathematical	mathematical	ADJ
ejpam-5062	763	4	analysis	analysis	NOUN
ejpam-5062	763	5	and	and	CCONJ
ejpam-5062	763	6	applications	application	NOUN
ejpam-5062	763	7	,	,	PUNCT
ejpam-5062	763	8	93(1):27–41	93(1):27–41	NUM
ejpam-5062	763	9	,	,	PUNCT
ejpam-5062	763	10	1983	1983	NUM
ejpam-5062	763	11	.	.	PUNCT
ejpam-5062	764	1	[	[	X
ejpam-5062	764	2	33	33	NUM
ejpam-5062	764	3	]	]	X
ejpam-5062	764	4	l.a	l.a	PROPN
ejpam-5062	764	5	.	.	PROPN
ejpam-5062	764	6	zadeh	zadeh	PROPN
ejpam-5062	764	7	.	.	PUNCT
ejpam-5062	764	8	fuzzy	fuzzy	ADJ
ejpam-5062	764	9	sets	set	NOUN
ejpam-5062	764	10	.	.	PUNCT
ejpam-5062	765	1	information	information	NOUN
ejpam-5062	765	2	and	and	CCONJ
ejpam-5062	765	3	control	control	NOUN
ejpam-5062	765	4	,	,	PUNCT
ejpam-5062	765	5	8(3):338–353	8(3):338–353	NUM
ejpam-5062	765	6	,	,	PUNCT
ejpam-5062	765	7	1965	1965	NUM
ejpam-5062	765	8	.	.	PUNCT