id	sid	tid	token	lemma	pos
ejpam-4597	1	1	european	european	PROPN
ejpam-4597	1	2	journal	journal	PROPN
ejpam-4597	1	3	of	of	ADP
ejpam-4597	1	4	pure	pure	ADJ
ejpam-4597	1	5	and	and	CCONJ
ejpam-4597	1	6	applied	apply	VERB
ejpam-4597	1	7	mathematics	mathematic	NOUN
ejpam-4597	1	8	vol	vol	NOUN
ejpam-4597	1	9	.	.	PUNCT
ejpam-4597	2	1	16	16	NUM
ejpam-4597	2	2	,	,	PUNCT
ejpam-4597	2	3	no	no	INTJ
ejpam-4597	2	4	.	.	NOUN
ejpam-4597	2	5	1	1	NUM
ejpam-4597	2	6	,	,	PUNCT
ejpam-4597	2	7	2023	2023	NUM
ejpam-4597	2	8	,	,	PUNCT
ejpam-4597	2	9	180	180	NUM
ejpam-4597	2	10	-	-	SYM
ejpam-4597	2	11	191	191	NUM
ejpam-4597	2	12	issn	issn	PROPN
ejpam-4597	2	13	1307	1307	NUM
ejpam-4597	2	14	-	-	SYM
ejpam-4597	2	15	5543	5543	NUM
ejpam-4597	2	16	–	–	PUNCT
ejpam-4597	3	1	ejpam.com	ejpam.com	X
ejpam-4597	3	2	published	publish	VERB
ejpam-4597	3	3	by	by	ADP
ejpam-4597	3	4	new	new	PROPN
ejpam-4597	3	5	york	york	PROPN
ejpam-4597	3	6	business	business	PROPN
ejpam-4597	3	7	global	global	PROPN
ejpam-4597	3	8	on	on	ADP
ejpam-4597	3	9	g	g	NOUN
ejpam-4597	3	10	-	-	PUNCT
ejpam-4597	3	11	regularity	regularity	NOUN
ejpam-4597	3	12	and	and	CCONJ
ejpam-4597	3	13	g	g	NOUN
ejpam-4597	3	14	-	-	PUNCT
ejpam-4597	3	15	normality	normality	NOUN
ejpam-4597	3	16	in	in	ADP
ejpam-4597	3	17	fuzzy	fuzzy	ADJ
ejpam-4597	3	18	soft	soft	ADJ
ejpam-4597	3	19	topological	topological	ADJ
ejpam-4597	3	20	spaces	space	NOUN
ejpam-4597	3	21	s.	s.	PROPN
ejpam-4597	3	22	saleh1,2,∗	saleh1,2,∗	PROPN
ejpam-4597	3	23	,	,	PUNCT
ejpam-4597	3	24	jawaher	jawaher	PROPN
ejpam-4597	3	25	al	al	PROPN
ejpam-4597	3	26	-	-	PUNCT
ejpam-4597	3	27	mufarrij3	mufarrij3	PROPN
ejpam-4597	3	28	1computer	1computer	NUM
ejpam-4597	3	29	science	science	NOUN
ejpam-4597	3	30	department	department	NOUN
ejpam-4597	3	31	,	,	PUNCT
ejpam-4597	3	32	cihan	cihan	VERB
ejpam-4597	3	33	university	university	NOUN
ejpam-4597	3	34	-	-	PUNCT
ejpam-4597	3	35	erbil	erbil	PROPN
ejpam-4597	3	36	,	,	PUNCT
ejpam-4597	3	37	kurdistan	kurdistan	ADJ
ejpam-4597	3	38	region	region	NOUN
ejpam-4597	3	39	,	,	PUNCT
ejpam-4597	3	40	iraq	iraq	PROPN
ejpam-4597	3	41	2department	2department	NUM
ejpam-4597	3	42	of	of	ADP
ejpam-4597	3	43	mathematics	mathematic	NOUN
ejpam-4597	3	44	,	,	PUNCT
ejpam-4597	3	45	hodeidah	hodeidah	PROPN
ejpam-4597	3	46	university	university	NOUN
ejpam-4597	3	47	,	,	PUNCT
ejpam-4597	3	48	hodeidah	hodeidah	PROPN
ejpam-4597	3	49	,	,	PUNCT
ejpam-4597	3	50	yemen	yemen	PROPN
ejpam-4597	3	51	.	.	PUNCT
ejpam-4597	4	1	3department	3department	NUM
ejpam-4597	4	2	of	of	ADP
ejpam-4597	4	3	mathematics	mathematic	NOUN
ejpam-4597	4	4	,	,	PUNCT
ejpam-4597	4	5	women	woman	NOUN
ejpam-4597	4	6	section	section	NOUN
ejpam-4597	4	7	,	,	PUNCT
ejpam-4597	4	8	king	king	PROPN
ejpam-4597	4	9	saud	saud	PROPN
ejpam-4597	4	10	university	university	PROPN
ejpam-4597	4	11	,	,	PUNCT
ejpam-4597	4	12	riyadh	riyadh	PROPN
ejpam-4597	4	13	12372	12372	NUM
ejpam-4597	4	14	,	,	PUNCT
ejpam-4597	4	15	ksa	ksa	PROPN
ejpam-4597	4	16	.	.	PROPN
ejpam-4597	4	17	abstract	abstract	PROPN
ejpam-4597	4	18	.	.	PUNCT
ejpam-4597	5	1	the	the	DET
ejpam-4597	5	2	main	main	ADJ
ejpam-4597	5	3	aim	aim	NOUN
ejpam-4597	5	4	of	of	ADP
ejpam-4597	5	5	this	this	DET
ejpam-4597	5	6	work	work	NOUN
ejpam-4597	5	7	is	be	AUX
ejpam-4597	5	8	to	to	PART
ejpam-4597	5	9	introduce	introduce	VERB
ejpam-4597	5	10	and	and	CCONJ
ejpam-4597	5	11	study	study	VERB
ejpam-4597	5	12	the	the	DET
ejpam-4597	5	13	notions	notion	NOUN
ejpam-4597	5	14	of	of	ADP
ejpam-4597	5	15	generalized	generalized	ADJ
ejpam-4597	5	16	regularity	regularity	NOUN
ejpam-4597	5	17	,	,	PUNCT
ejpam-4597	5	18	normality	normality	NOUN
ejpam-4597	5	19	,	,	PUNCT
ejpam-4597	5	20	and	and	CCONJ
ejpam-4597	5	21	symmetric	symmetric	ADJ
ejpam-4597	5	22	in	in	ADP
ejpam-4597	5	23	fuzzy	fuzzy	ADJ
ejpam-4597	5	24	soft	soft	ADJ
ejpam-4597	5	25	topological	topological	ADJ
ejpam-4597	5	26	spaces	space	NOUN
ejpam-4597	5	27	via	via	ADP
ejpam-4597	5	28	fuzzy	fuzzy	ADJ
ejpam-4597	5	29	soft	soft	ADJ
ejpam-4597	5	30	generalized	generalize	VERB
ejpam-4597	5	31	closed	closed	ADJ
ejpam-4597	5	32	sets	set	NOUN
ejpam-4597	5	33	.	.	PUNCT
ejpam-4597	6	1	some	some	PRON
ejpam-4597	6	2	of	of	ADP
ejpam-4597	6	3	their	their	PRON
ejpam-4597	6	4	basic	basic	ADJ
ejpam-4597	6	5	properties	property	NOUN
ejpam-4597	6	6	are	be	AUX
ejpam-4597	6	7	investigated	investigate	VERB
ejpam-4597	6	8	.	.	PUNCT
ejpam-4597	7	1	many	many	ADJ
ejpam-4597	7	2	related	related	ADJ
ejpam-4597	7	3	theorems	theorem	NOUN
ejpam-4597	7	4	and	and	CCONJ
ejpam-4597	7	5	relations	relation	NOUN
ejpam-4597	7	6	of	of	ADP
ejpam-4597	7	7	these	these	DET
ejpam-4597	7	8	notions	notion	NOUN
ejpam-4597	7	9	are	be	AUX
ejpam-4597	7	10	presented	present	VERB
ejpam-4597	7	11	.	.	PUNCT
ejpam-4597	8	1	moreover	moreover	ADV
ejpam-4597	8	2	,	,	PUNCT
ejpam-4597	8	3	the	the	DET
ejpam-4597	8	4	hereditary	hereditary	ADJ
ejpam-4597	8	5	property	property	NOUN
ejpam-4597	8	6	and	and	CCONJ
ejpam-4597	8	7	some	some	DET
ejpam-4597	8	8	preservation	preservation	NOUN
ejpam-4597	8	9	theorems	theorem	NOUN
ejpam-4597	8	10	are	be	AUX
ejpam-4597	8	11	discussed	discuss	VERB
ejpam-4597	8	12	.	.	PUNCT
ejpam-4597	9	1	2020	2020	NUM
ejpam-4597	9	2	mathematics	mathematic	NOUN
ejpam-4597	9	3	subject	subject	NOUN
ejpam-4597	9	4	classifications	classification	NOUN
ejpam-4597	9	5	:	:	PUNCT
ejpam-4597	9	6	54a40	54a40	NUM
ejpam-4597	9	7	,	,	PUNCT
ejpam-4597	9	8	54c08	54c08	NUM
ejpam-4597	9	9	,	,	PUNCT
ejpam-4597	9	10	54d15	54d15	PRON
ejpam-4597	9	11	key	key	ADJ
ejpam-4597	9	12	words	word	NOUN
ejpam-4597	9	13	and	and	CCONJ
ejpam-4597	9	14	phrases	phrase	NOUN
ejpam-4597	9	15	:	:	PUNCT
ejpam-4597	9	16	fuzzy	fuzzy	ADJ
ejpam-4597	9	17	soft	soft	ADJ
ejpam-4597	9	18	set	set	NOUN
ejpam-4597	9	19	,	,	PUNCT
ejpam-4597	9	20	fuzzy	fuzzy	ADJ
ejpam-4597	9	21	soft	soft	ADJ
ejpam-4597	9	22	g	g	NOUN
ejpam-4597	9	23	-	-	PUNCT
ejpam-4597	9	24	closed	close	VERB
ejpam-4597	9	25	set	set	NOUN
ejpam-4597	9	26	,	,	PUNCT
ejpam-4597	9	27	quasi	quasi	ADJ
ejpam-4597	9	28	coincident	coincident	NOUN
ejpam-4597	9	29	,	,	PUNCT
ejpam-4597	9	30	fuzzy	fuzzy	ADJ
ejpam-4597	9	31	soft	soft	ADJ
ejpam-4597	9	32	g	g	NOUN
ejpam-4597	9	33	-	-	PUNCT
ejpam-4597	9	34	continuous	continuous	ADJ
ejpam-4597	9	35	maps	map	NOUN
ejpam-4597	9	36	,	,	PUNCT
ejpam-4597	9	37	fuzzy	fuzzy	ADJ
ejpam-4597	9	38	soft	soft	ADJ
ejpam-4597	9	39	g	g	NOUN
ejpam-4597	9	40	-	-	PUNCT
ejpam-4597	9	41	regular	regular	ADJ
ejpam-4597	9	42	,	,	PUNCT
ejpam-4597	9	43	fuzzy	fuzzy	ADJ
ejpam-4597	9	44	soft	soft	ADJ
ejpam-4597	9	45	g	g	NOUN
ejpam-4597	9	46	-	-	PUNCT
ejpam-4597	9	47	normal	normal	ADJ
ejpam-4597	9	48	space	space	NOUN
ejpam-4597	9	49	1	1	NUM
ejpam-4597	9	50	.	.	PUNCT
ejpam-4597	10	1	introduction	introduction	NOUN
ejpam-4597	10	2	and	and	CCONJ
ejpam-4597	10	3	preliminaries	preliminary	NOUN
ejpam-4597	10	4	levine	levine	NOUN
ejpam-4597	10	5	[	[	X
ejpam-4597	10	6	18	18	NUM
ejpam-4597	10	7	]	]	PUNCT
ejpam-4597	10	8	introduced	introduce	VERB
ejpam-4597	10	9	the	the	DET
ejpam-4597	10	10	notion	notion	NOUN
ejpam-4597	10	11	of	of	ADP
ejpam-4597	10	12	generalized	generalized	ADJ
ejpam-4597	10	13	closed	close	VERB
ejpam-4597	10	14	set	set	NOUN
ejpam-4597	10	15	,	,	PUNCT
ejpam-4597	10	16	briefly	briefly	ADV
ejpam-4597	10	17	g	g	NOUN
ejpam-4597	10	18	-	-	PUNCT
ejpam-4597	10	19	closed	closed	ADJ
ejpam-4597	10	20	in	in	ADP
ejpam-4597	10	21	general	general	ADJ
ejpam-4597	10	22	topology	topology	NOUN
ejpam-4597	10	23	.	.	PUNCT
ejpam-4597	11	1	a	a	DET
ejpam-4597	11	2	subset	subset	NOUN
ejpam-4597	11	3	b	b	NOUN
ejpam-4597	11	4	of	of	ADP
ejpam-4597	11	5	a	a	DET
ejpam-4597	11	6	topological	topological	ADJ
ejpam-4597	11	7	space	space	NOUN
ejpam-4597	11	8	(	(	PUNCT
ejpam-4597	11	9	x	x	X
ejpam-4597	11	10	,	,	PUNCT
ejpam-4597	11	11	τ	τ	X
ejpam-4597	11	12	)	)	PUNCT
ejpam-4597	11	13	is	be	AUX
ejpam-4597	11	14	called	call	VERB
ejpam-4597	11	15	g	g	NOUN
ejpam-4597	11	16	-	-	PUNCT
ejpam-4597	11	17	closed	closed	ADJ
ejpam-4597	11	18	,	,	PUNCT
ejpam-4597	11	19	if	if	SCONJ
ejpam-4597	11	20	cl(b	cl(b	NOUN
ejpam-4597	11	21	)	)	PUNCT
ejpam-4597	11	22	⊆	⊆	NUM
ejpam-4597	11	23	u	u	NOUN
ejpam-4597	11	24	whenever	whenever	SCONJ
ejpam-4597	11	25	b	b	PROPN
ejpam-4597	11	26	⊆	⊆	NUM
ejpam-4597	11	27	u	u	NOUN
ejpam-4597	11	28	and	and	CCONJ
ejpam-4597	11	29	u	u	NOUN
ejpam-4597	11	30	is	be	AUX
ejpam-4597	11	31	open	open	ADJ
ejpam-4597	11	32	in	in	ADP
ejpam-4597	11	33	(	(	PUNCT
ejpam-4597	11	34	x	x	NOUN
ejpam-4597	11	35	,	,	PUNCT
ejpam-4597	11	36	τ	τ	PROPN
ejpam-4597	11	37	)	)	PUNCT
ejpam-4597	11	38	.	.	PUNCT
ejpam-4597	12	1	this	this	DET
ejpam-4597	12	2	notion	notion	NOUN
ejpam-4597	12	3	has	have	AUX
ejpam-4597	12	4	been	be	AUX
ejpam-4597	12	5	studied	study	VERB
ejpam-4597	12	6	extensively	extensively	ADV
ejpam-4597	12	7	in	in	ADP
ejpam-4597	12	8	topology	topology	NOUN
ejpam-4597	12	9	and	and	CCONJ
ejpam-4597	12	10	fuzzy	fuzzy	ADJ
ejpam-4597	12	11	topology	topology	NOUN
ejpam-4597	12	12	by	by	ADP
ejpam-4597	12	13	many	many	ADJ
ejpam-4597	12	14	authors	author	NOUN
ejpam-4597	12	15	as	as	ADP
ejpam-4597	12	16	in	in	ADP
ejpam-4597	12	17	(	(	PUNCT
ejpam-4597	12	18	[	[	X
ejpam-4597	12	19	3	3	NUM
ejpam-4597	12	20	,	,	PUNCT
ejpam-4597	12	21	5	5	NUM
ejpam-4597	12	22	,	,	PUNCT
ejpam-4597	12	23	7	7	NUM
ejpam-4597	12	24	,	,	PUNCT
ejpam-4597	12	25	8	8	NUM
ejpam-4597	12	26	,	,	PUNCT
ejpam-4597	12	27	13	13	NUM
ejpam-4597	12	28	,	,	PUNCT
ejpam-4597	12	29	17	17	NUM
ejpam-4597	12	30	,	,	PUNCT
ejpam-4597	12	31	25–27	25–27	NUM
ejpam-4597	12	32	,	,	PUNCT
ejpam-4597	12	33	32	32	NUM
ejpam-4597	12	34	]	]	PUNCT
ejpam-4597	12	35	)	)	PUNCT
ejpam-4597	12	36	.	.	PUNCT
ejpam-4597	13	1	the	the	DET
ejpam-4597	13	2	investigation	investigation	NOUN
ejpam-4597	13	3	of	of	ADP
ejpam-4597	13	4	g	g	NOUN
ejpam-4597	13	5	-	-	PUNCT
ejpam-4597	13	6	closed	close	VERB
ejpam-4597	13	7	sets	set	NOUN
ejpam-4597	13	8	has	have	AUX
ejpam-4597	13	9	led	lead	VERB
ejpam-4597	13	10	to	to	ADP
ejpam-4597	13	11	several	several	ADJ
ejpam-4597	13	12	new	new	ADJ
ejpam-4597	13	13	and	and	CCONJ
ejpam-4597	13	14	interesting	interesting	ADJ
ejpam-4597	13	15	concepts	concept	NOUN
ejpam-4597	13	16	,	,	PUNCT
ejpam-4597	13	17	e.g.	e.g.	ADV
ejpam-4597	13	18	g	g	NOUN
ejpam-4597	13	19	-	-	PUNCT
ejpam-4597	13	20	regular	regular	ADJ
ejpam-4597	13	21	,	,	PUNCT
ejpam-4597	13	22	g	g	NOUN
ejpam-4597	13	23	-	-	PUNCT
ejpam-4597	13	24	normal	normal	ADJ
ejpam-4597	13	25	spaces	space	NOUN
ejpam-4597	13	26	,	,	PUNCT
ejpam-4597	13	27	their	their	PRON
ejpam-4597	13	28	generalizations	generalization	NOUN
ejpam-4597	13	29	which	which	PRON
ejpam-4597	13	30	are	be	AUX
ejpam-4597	13	31	studied	study	VERB
ejpam-4597	13	32	in	in	ADP
ejpam-4597	13	33	(	(	PUNCT
ejpam-4597	13	34	[	[	X
ejpam-4597	13	35	12	12	NUM
ejpam-4597	13	36	,	,	PUNCT
ejpam-4597	13	37	15	15	NUM
ejpam-4597	13	38	,	,	PUNCT
ejpam-4597	13	39	21–24	21–24	NUM
ejpam-4597	13	40	]	]	NUM
ejpam-4597	13	41	)	)	PUNCT
ejpam-4597	13	42	,	,	PUNCT
ejpam-4597	13	43	and	and	CCONJ
ejpam-4597	13	44	new	new	ADJ
ejpam-4597	13	45	separation	separation	NOUN
ejpam-4597	13	46	axioms	axiom	VERB
ejpam-4597	13	47	weaker	weak	ADJ
ejpam-4597	13	48	than	than	SCONJ
ejpam-4597	13	49	t1	t1	NOUN
ejpam-4597	13	50	are	be	AUX
ejpam-4597	13	51	presented	present	VERB
ejpam-4597	13	52	.	.	PUNCT
ejpam-4597	14	1	in	in	ADP
ejpam-4597	14	2	recent	recent	ADJ
ejpam-4597	14	3	time	time	NOUN
ejpam-4597	14	4	,	,	PUNCT
ejpam-4597	14	5	the	the	DET
ejpam-4597	14	6	topological	topological	ADJ
ejpam-4597	14	7	structures	structure	NOUN
ejpam-4597	14	8	play	play	VERB
ejpam-4597	14	9	an	an	DET
ejpam-4597	14	10	important	important	ADJ
ejpam-4597	14	11	role	role	NOUN
ejpam-4597	14	12	in	in	ADP
ejpam-4597	14	13	many	many	ADJ
ejpam-4597	14	14	applications	application	NOUN
ejpam-4597	14	15	of	of	ADP
ejpam-4597	14	16	complex	complex	ADJ
ejpam-4597	14	17	real	real	ADJ
ejpam-4597	14	18	-	-	PUNCT
ejpam-4597	14	19	life	life	NOUN
ejpam-4597	14	20	problems	problem	NOUN
ejpam-4597	14	21	in	in	ADP
ejpam-4597	14	22	various	various	ADJ
ejpam-4597	14	23	field	field	NOUN
ejpam-4597	14	24	,	,	PUNCT
ejpam-4597	14	25	specially	specially	ADV
ejpam-4597	14	26	the	the	DET
ejpam-4597	14	27	fields	field	NOUN
ejpam-4597	14	28	that	that	PRON
ejpam-4597	14	29	concerned	concern	VERB
ejpam-4597	14	30	with	with	ADP
ejpam-4597	14	31	handling	handle	VERB
ejpam-4597	14	32	all	all	DET
ejpam-4597	14	33	cases	case	NOUN
ejpam-4597	14	34	that	that	PRON
ejpam-4597	14	35	contain	contain	VERB
ejpam-4597	14	36	uncertainties	uncertainty	NOUN
ejpam-4597	14	37	such	such	ADJ
ejpam-4597	14	38	as	as	ADP
ejpam-4597	14	39	medical	medical	ADJ
ejpam-4597	14	40	diagnosis	diagnosis	NOUN
ejpam-4597	14	41	and	and	CCONJ
ejpam-4597	14	42	decision	decision	NOUN
ejpam-4597	14	43	making,	making,	ADJ
ejpam-4597	14	44	...	...	PUNCT
ejpam-4597	14	45	etc	etc	X
ejpam-4597	14	46	see	see	VERB
ejpam-4597	14	47	e.	e.	PROPN
ejpam-4597	14	48	g.	g.	PROPN
ejpam-4597	15	1	(	(	PUNCT
ejpam-4597	15	2	[	[	X
ejpam-4597	15	3	10	10	NUM
ejpam-4597	15	4	,	,	PUNCT
ejpam-4597	15	5	11	11	NUM
ejpam-4597	15	6	]	]	NUM
ejpam-4597	15	7	)	)	PUNCT
ejpam-4597	15	8	.	.	PUNCT
ejpam-4597	16	1	after	after	ADP
ejpam-4597	16	2	the	the	DET
ejpam-4597	16	3	discovery	discovery	NOUN
ejpam-4597	16	4	of	of	ADP
ejpam-4597	16	5	fuzzy	fuzzy	ADJ
ejpam-4597	16	6	set	set	NOUN
ejpam-4597	16	7	theory	theory	NOUN
ejpam-4597	16	8	by	by	ADP
ejpam-4597	16	9	zadeh	zadeh	PROPN
ejpam-4597	17	1	[	[	X
ejpam-4597	17	2	33	33	NUM
ejpam-4597	17	3	]	]	PUNCT
ejpam-4597	17	4	,	,	PUNCT
ejpam-4597	17	5	many	many	ADJ
ejpam-4597	17	6	authors	author	NOUN
ejpam-4597	17	7	generalized	generalize	VERB
ejpam-4597	17	8	and	and	CCONJ
ejpam-4597	17	9	applied	apply	VERB
ejpam-4597	17	10	this	this	DET
ejpam-4597	17	11	idea	idea	NOUN
ejpam-4597	17	12	in	in	ADP
ejpam-4597	17	13	different	different	ADJ
ejpam-4597	17	14	aspects	aspect	NOUN
ejpam-4597	17	15	see	see	VERB
ejpam-4597	17	16	e.	e.	PROPN
ejpam-4597	17	17	g.	g.	PROPN
ejpam-4597	18	1	(	(	PUNCT
ejpam-4597	18	2	[	[	X
ejpam-4597	18	3	1	1	NUM
ejpam-4597	18	4	,	,	PUNCT
ejpam-4597	18	5	2	2	NUM
ejpam-4597	18	6	,	,	PUNCT
ejpam-4597	18	7	14	14	NUM
ejpam-4597	18	8	,	,	PUNCT
ejpam-4597	18	9	19	19	NUM
ejpam-4597	18	10	]	]	PUNCT
ejpam-4597	18	11	.	.	PUNCT
ejpam-4597	19	1	the	the	DET
ejpam-4597	19	2	concept	concept	NOUN
ejpam-4597	19	3	of	of	ADP
ejpam-4597	19	4	fuzzy	fuzzy	ADJ
ejpam-4597	19	5	topological	topological	ADJ
ejpam-4597	19	6	space	space	NOUN
ejpam-4597	19	7	was	be	AUX
ejpam-4597	19	8	introduced	introduce	VERB
ejpam-4597	19	9	by	by	ADP
ejpam-4597	19	10	chang	chang	PROPN
ejpam-4597	19	11	in	in	ADP
ejpam-4597	19	12	[	[	X
ejpam-4597	19	13	6	6	NUM
ejpam-4597	19	14	]	]	PUNCT
ejpam-4597	19	15	.	.	PUNCT
ejpam-4597	20	1	balasubramanian	balasubramanian	PROPN
ejpam-4597	20	2	et	et	PROPN
ejpam-4597	20	3	.	.	PUNCT
ejpam-4597	21	1	al	al	PROPN
ejpam-4597	22	1	[	[	X
ejpam-4597	22	2	5	5	NUM
ejpam-4597	22	3	]	]	PUNCT
ejpam-4597	22	4	introduced	introduce	VERB
ejpam-4597	22	5	the	the	DET
ejpam-4597	22	6	∗corresponding	∗corresponde	VERB
ejpam-4597	22	7	author	author	NOUN
ejpam-4597	22	8	.	.	PUNCT
ejpam-4597	23	1	doi	doi	NOUN
ejpam-4597	23	2	:	:	PUNCT
ejpam-4597	23	3	https://doi.org/10.29020/nybg.ejpam.v16i1.4597	https://doi.org/10.29020/nybg.ejpam.v16i1.4597	NOUN
ejpam-4597	23	4	email	email	NOUN
ejpam-4597	23	5	addresses	address	VERB
ejpam-4597	23	6	:	:	PUNCT
ejpam-4597	23	7	salem.saleh@cihanuniversity.edu.iq	salem.saleh@cihanuniversity.edu.iq	ADJ
ejpam-4597	23	8	(	(	PUNCT
ejpam-4597	23	9	s.	s.	PROPN
ejpam-4597	23	10	saleh	saleh	PROPN
ejpam-4597	23	11	)	)	PUNCT
ejpam-4597	23	12	,	,	PUNCT
ejpam-4597	23	13	jmufarij@ksu.edu.sa	jmufarij@ksu.edu.sa	PROPN
ejpam-4597	23	14	(	(	PUNCT
ejpam-4597	23	15	j.	j.	PROPN
ejpam-4597	23	16	al	al	PROPN
ejpam-4597	23	17	-	-	PUNCT
ejpam-4597	23	18	mufarrij	mufarrij	PROPN
ejpam-4597	23	19	)	)	PUNCT
ejpam-4597	23	20	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4597	24	1	180	180	NUM
ejpam-4597	24	2	©	©	PROPN
ejpam-4597	24	3	2023	2023	NUM
ejpam-4597	24	4	ejpam	ejpam	NOUN
ejpam-4597	24	5	all	all	DET
ejpam-4597	24	6	rights	right	NOUN
ejpam-4597	24	7	reserved	reserve	VERB
ejpam-4597	24	8	.	.	PUNCT
ejpam-4597	25	1	s.	s.	PROPN
ejpam-4597	25	2	saleh	saleh	PROPN
ejpam-4597	25	3	,	,	PUNCT
ejpam-4597	25	4	j.	j.	PROPN
ejpam-4597	25	5	al	al	PROPN
ejpam-4597	25	6	-	-	PUNCT
ejpam-4597	25	7	mufarrij	mufarrij	PROPN
ejpam-4597	25	8	/	/	SYM
ejpam-4597	25	9	eur	eur	PROPN
ejpam-4597	25	10	.	.	PUNCT
ejpam-4597	26	1	j.	j.	PROPN
ejpam-4597	26	2	pure	pure	PROPN
ejpam-4597	26	3	appl	appl	PROPN
ejpam-4597	26	4	.	.	PROPN
ejpam-4597	26	5	math	math	PROPN
ejpam-4597	26	6	,	,	PUNCT
ejpam-4597	26	7	16	16	NUM
ejpam-4597	26	8	(	(	PUNCT
ejpam-4597	26	9	1	1	NUM
ejpam-4597	26	10	)	)	PUNCT
ejpam-4597	26	11	(	(	PUNCT
ejpam-4597	26	12	2023	2023	NUM
ejpam-4597	26	13	)	)	PUNCT
ejpam-4597	26	14	,	,	PUNCT
ejpam-4597	26	15	180	180	NUM
ejpam-4597	26	16	-	-	SYM
ejpam-4597	26	17	191	191	NUM
ejpam-4597	26	18	181	181	NUM
ejpam-4597	26	19	concept	concept	NOUN
ejpam-4597	26	20	of	of	ADP
ejpam-4597	26	21	fuzzy	fuzzy	ADJ
ejpam-4597	26	22	generalized	generalize	VERB
ejpam-4597	26	23	closed	closed	ADJ
ejpam-4597	26	24	sets	set	NOUN
ejpam-4597	26	25	.	.	PUNCT
ejpam-4597	27	1	then	then	ADV
ejpam-4597	27	2	m.	m.	PROPN
ejpam-4597	27	3	el	el	PROPN
ejpam-4597	27	4	-	-	PROPN
ejpam-4597	27	5	shafei	shafei	NOUN
ejpam-4597	27	6	[	[	X
ejpam-4597	27	7	12	12	NUM
ejpam-4597	27	8	]	]	PUNCT
ejpam-4597	27	9	introduced	introduce	VERB
ejpam-4597	27	10	and	and	CCONJ
ejpam-4597	27	11	studied	study	VERB
ejpam-4597	27	12	some	some	DET
ejpam-4597	27	13	applications	application	NOUN
ejpam-4597	27	14	of	of	ADP
ejpam-4597	27	15	fuzzy	fuzzy	ADJ
ejpam-4597	27	16	generalized	generalize	VERB
ejpam-4597	27	17	closed	closed	ADJ
ejpam-4597	27	18	sets	set	NOUN
ejpam-4597	27	19	.	.	PUNCT
ejpam-4597	28	1	tanay	tanay	PROPN
ejpam-4597	28	2	et	et	PROPN
ejpam-4597	28	3	.	.	PUNCT
ejpam-4597	29	1	al	al	PROPN
ejpam-4597	29	2	.	.	PUNCT
ejpam-4597	30	1	[	[	X
ejpam-4597	30	2	30	30	NUM
ejpam-4597	30	3	]	]	PUNCT
ejpam-4597	30	4	defined	define	VERB
ejpam-4597	30	5	and	and	CCONJ
ejpam-4597	30	6	studied	study	VERB
ejpam-4597	30	7	the	the	DET
ejpam-4597	30	8	notion	notion	NOUN
ejpam-4597	30	9	of	of	ADP
ejpam-4597	30	10	topological	topological	ADJ
ejpam-4597	30	11	structure	structure	NOUN
ejpam-4597	30	12	for	for	ADP
ejpam-4597	30	13	fuzzy	fuzzy	ADJ
ejpam-4597	30	14	soft	soft	ADJ
ejpam-4597	30	15	sets	set	NOUN
ejpam-4597	30	16	and	and	CCONJ
ejpam-4597	30	17	studied	study	VERB
ejpam-4597	30	18	many	many	ADJ
ejpam-4597	30	19	related	relate	VERB
ejpam-4597	30	20	concepts	concept	NOUN
ejpam-4597	30	21	.	.	PUNCT
ejpam-4597	31	1	recently	recently	ADV
ejpam-4597	31	2	,	,	PUNCT
ejpam-4597	31	3	tarrannum	tarrannum	PROPN
ejpam-4597	31	4	et	et	PROPN
ejpam-4597	31	5	.	.	PUNCT
ejpam-4597	32	1	al	al	PROPN
ejpam-4597	32	2	.	.	PUNCT
ejpam-4597	33	1	[	[	X
ejpam-4597	33	2	31	31	NUM
ejpam-4597	33	3	]	]	PUNCT
ejpam-4597	33	4	introduced	introduce	VERB
ejpam-4597	33	5	the	the	DET
ejpam-4597	33	6	concept	concept	NOUN
ejpam-4597	33	7	of	of	ADP
ejpam-4597	33	8	fuzzy	fuzzy	ADJ
ejpam-4597	33	9	soft	soft	ADJ
ejpam-4597	33	10	generalized	generalize	VERB
ejpam-4597	33	11	closed	close	VERB
ejpam-4597	33	12	sets	set	NOUN
ejpam-4597	33	13	,	,	PUNCT
ejpam-4597	33	14	fuzzy	fuzzy	ADJ
ejpam-4597	33	15	soft	soft	ADJ
ejpam-4597	33	16	generalized	generalized	ADJ
ejpam-4597	33	17	continuous	continuous	ADJ
ejpam-4597	33	18	maps	map	NOUN
ejpam-4597	33	19	,	,	PUNCT
ejpam-4597	33	20	and	and	CCONJ
ejpam-4597	33	21	studied	study	VERB
ejpam-4597	33	22	some	some	DET
ejpam-4597	33	23	properties	property	NOUN
ejpam-4597	33	24	for	for	ADP
ejpam-4597	33	25	them	they	PRON
ejpam-4597	33	26	.	.	PUNCT
ejpam-4597	34	1	in	in	ADP
ejpam-4597	34	2	this	this	DET
ejpam-4597	34	3	paper	paper	NOUN
ejpam-4597	34	4	,	,	PUNCT
ejpam-4597	34	5	we	we	PRON
ejpam-4597	34	6	define	define	VERB
ejpam-4597	34	7	and	and	CCONJ
ejpam-4597	34	8	study	study	VERB
ejpam-4597	34	9	the	the	DET
ejpam-4597	34	10	notions	notion	NOUN
ejpam-4597	34	11	of	of	ADP
ejpam-4597	34	12	fuzzy	fuzzy	ADJ
ejpam-4597	34	13	soft	soft	ADJ
ejpam-4597	34	14	generalized	generalized	ADJ
ejpam-4597	34	15	regular	regular	ADJ
ejpam-4597	34	16	spaces	space	NOUN
ejpam-4597	34	17	,	,	PUNCT
ejpam-4597	34	18	generalized	generalize	VERB
ejpam-4597	34	19	normal	normal	ADJ
ejpam-4597	34	20	spaces	space	NOUN
ejpam-4597	34	21	,	,	PUNCT
ejpam-4597	34	22	and	and	CCONJ
ejpam-4597	34	23	symmetric	symmetric	ADJ
ejpam-4597	34	24	spaces	space	NOUN
ejpam-4597	34	25	by	by	ADP
ejpam-4597	34	26	utilizing	utilize	VERB
ejpam-4597	34	27	fuzzy	fuzzy	ADJ
ejpam-4597	34	28	soft	soft	ADJ
ejpam-4597	34	29	generalized	generalize	VERB
ejpam-4597	34	30	closed	closed	ADJ
ejpam-4597	34	31	sets	set	NOUN
ejpam-4597	34	32	.	.	PUNCT
ejpam-4597	35	1	we	we	PRON
ejpam-4597	35	2	obtain	obtain	VERB
ejpam-4597	35	3	some	some	DET
ejpam-4597	35	4	characterizations	characterization	NOUN
ejpam-4597	35	5	.	.	PUNCT
ejpam-4597	36	1	several	several	ADJ
ejpam-4597	36	2	related	related	ADJ
ejpam-4597	36	3	theorems	theorem	NOUN
ejpam-4597	36	4	and	and	CCONJ
ejpam-4597	36	5	relationships	relationship	NOUN
ejpam-4597	36	6	of	of	ADP
ejpam-4597	36	7	them	they	PRON
ejpam-4597	36	8	are	be	AUX
ejpam-4597	36	9	discussed	discuss	VERB
ejpam-4597	36	10	.	.	PUNCT
ejpam-4597	37	1	in	in	ADP
ejpam-4597	37	2	addition	addition	NOUN
ejpam-4597	37	3	,	,	PUNCT
ejpam-4597	37	4	the	the	DET
ejpam-4597	37	5	hereditary	hereditary	ADJ
ejpam-4597	37	6	property	property	NOUN
ejpam-4597	37	7	and	and	CCONJ
ejpam-4597	37	8	some	some	DET
ejpam-4597	37	9	preservation	preservation	NOUN
ejpam-4597	37	10	theorems	theorem	NOUN
ejpam-4597	37	11	are	be	AUX
ejpam-4597	37	12	presented	present	VERB
ejpam-4597	37	13	.	.	PUNCT
ejpam-4597	38	1	throughout	throughout	ADP
ejpam-4597	38	2	this	this	DET
ejpam-4597	38	3	work	work	NOUN
ejpam-4597	38	4	,	,	PUNCT
ejpam-4597	38	5	u	u	NOUN
ejpam-4597	38	6	refers	refer	VERB
ejpam-4597	38	7	to	to	ADP
ejpam-4597	38	8	an	an	DET
ejpam-4597	38	9	universe	universe	NOUN
ejpam-4597	38	10	set	set	NOUN
ejpam-4597	38	11	,	,	PUNCT
ejpam-4597	38	12	e	e	X
ejpam-4597	38	13	is	be	AUX
ejpam-4597	38	14	the	the	DET
ejpam-4597	38	15	set	set	NOUN
ejpam-4597	38	16	of	of	ADP
ejpam-4597	38	17	all	all	DET
ejpam-4597	38	18	parameters	parameter	NOUN
ejpam-4597	38	19	,	,	PUNCT
ejpam-4597	38	20	p	p	X
ejpam-4597	38	21	(	(	PUNCT
ejpam-4597	38	22	u	u	NOUN
ejpam-4597	38	23	)	)	PUNCT
ejpam-4597	38	24	is	be	AUX
ejpam-4597	38	25	the	the	DET
ejpam-4597	38	26	power	power	NOUN
ejpam-4597	38	27	set	set	NOUN
ejpam-4597	38	28	of	of	ADP
ejpam-4597	38	29	u	u	PROPN
ejpam-4597	38	30	,	,	PUNCT
ejpam-4597	38	31	iu	iu	ADV
ejpam-4597	38	32	is	be	AUX
ejpam-4597	38	33	the	the	DET
ejpam-4597	38	34	set	set	NOUN
ejpam-4597	38	35	of	of	ADP
ejpam-4597	38	36	all	all	DET
ejpam-4597	38	37	fuzzy	fuzzy	ADJ
ejpam-4597	38	38	sets	set	NOUN
ejpam-4597	38	39	on	on	ADP
ejpam-4597	38	40	u	u	NOUN
ejpam-4597	38	41	,	,	PUNCT
ejpam-4597	38	42	where	where	SCONJ
ejpam-4597	38	43	i	i	PRON
ejpam-4597	38	44	=	=	PUNCT
ejpam-4597	39	1	[	[	X
ejpam-4597	39	2	0	0	NUM
ejpam-4597	39	3	,	,	PUNCT
ejpam-4597	39	4	1	1	NUM
ejpam-4597	39	5	]	]	PUNCT
ejpam-4597	39	6	,	,	PUNCT
ejpam-4597	39	7	fsrefers	fsrefer	VERB
ejpam-4597	39	8	to	to	ADP
ejpam-4597	39	9	fuzzy	fuzzy	ADJ
ejpam-4597	39	10	soft	soft	ADJ
ejpam-4597	39	11	,	,	PUNCT
ejpam-4597	39	12	and	and	CCONJ
ejpam-4597	39	13	(	(	PUNCT
ejpam-4597	39	14	u	u	NOUN
ejpam-4597	39	15	,	,	PUNCT
ejpam-4597	39	16	δ	δ	PROPN
ejpam-4597	39	17	,	,	PUNCT
ejpam-4597	39	18	e	e	NOUN
ejpam-4597	39	19	)	)	PUNCT
ejpam-4597	39	20	means	mean	VERB
ejpam-4597	39	21	fuzzy	fuzzy	ADJ
ejpam-4597	39	22	soft	soft	ADJ
ejpam-4597	39	23	topological	topological	ADJ
ejpam-4597	39	24	space	space	NOUN
ejpam-4597	39	25	.	.	PUNCT
ejpam-4597	40	1	in	in	ADP
ejpam-4597	40	2	the	the	DET
ejpam-4597	40	3	next	next	ADJ
ejpam-4597	40	4	,	,	PUNCT
ejpam-4597	40	5	we	we	PRON
ejpam-4597	40	6	recall	recall	VERB
ejpam-4597	40	7	some	some	DET
ejpam-4597	40	8	basic	basic	ADJ
ejpam-4597	40	9	definitions	definition	NOUN
ejpam-4597	40	10	and	and	CCONJ
ejpam-4597	40	11	notations	notation	NOUN
ejpam-4597	40	12	which	which	PRON
ejpam-4597	40	13	are	be	AUX
ejpam-4597	40	14	used	use	VERB
ejpam-4597	40	15	in	in	ADP
ejpam-4597	40	16	this	this	DET
ejpam-4597	40	17	sequel	sequel	NOUN
ejpam-4597	40	18	.	.	PUNCT
ejpam-4597	41	1	a	a	DET
ejpam-4597	41	2	fuzzy	fuzzy	ADJ
ejpam-4597	41	3	set(or	set(or	NOUN
ejpam-4597	41	4	f	f	PROPN
ejpam-4597	41	5	-set	-set	PROPN
ejpam-4597	41	6	)	)	PUNCT
ejpam-4597	42	1	a	a	PRON
ejpam-4597	42	2	in	in	ADP
ejpam-4597	42	3	u	u	PROPN
ejpam-4597	42	4	is	be	AUX
ejpam-4597	42	5	a	a	DET
ejpam-4597	42	6	mapping	mapping	NOUN
ejpam-4597	42	7	a	a	PRON
ejpam-4597	42	8	:	:	PUNCT
ejpam-4597	42	9	u	u	NOUN
ejpam-4597	42	10	−→	−→	NOUN
ejpam-4597	42	11	i	i	PRON
ejpam-4597	42	12	assigns	assign	VERB
ejpam-4597	42	13	the	the	DET
ejpam-4597	42	14	value	value	NOUN
ejpam-4597	42	15	a(x	a(x	NOUN
ejpam-4597	42	16	)	)	PUNCT
ejpam-4597	42	17	∈	∈	NOUN
ejpam-4597	42	18	i	i	PRON
ejpam-4597	42	19	for	for	ADP
ejpam-4597	42	20	all	all	DET
ejpam-4597	42	21	x	x	SYM
ejpam-4597	42	22	∈	∈	PROPN
ejpam-4597	42	23	u	u	NOUN
ejpam-4597	42	24	.	.	PUNCT
ejpam-4597	43	1	an	an	DET
ejpam-4597	43	2	f	f	PROPN
ejpam-4597	43	3	-point	-point	PROPN
ejpam-4597	43	4	xα	xα	INTJ
ejpam-4597	43	5	is	be	AUX
ejpam-4597	43	6	an	an	DET
ejpam-4597	43	7	f	f	X
ejpam-4597	43	8	-set	-set	PUNCT
ejpam-4597	43	9	such	such	ADJ
ejpam-4597	43	10	that	that	PRON
ejpam-4597	43	11	xα(y	xα(y	NOUN
ejpam-4597	43	12	)	)	PUNCT
ejpam-4597	44	1	=	=	SYM
ejpam-4597	44	2	α	α	X
ejpam-4597	44	3	>	>	X
ejpam-4597	44	4	0	0	PUNCT
ejpam-4597	45	1	if	if	SCONJ
ejpam-4597	45	2	x	x	NOUN
ejpam-4597	45	3	=	=	SYM
ejpam-4597	45	4	y	y	PROPN
ejpam-4597	45	5	and	and	CCONJ
ejpam-4597	45	6	xα	xα	INTJ
ejpam-4597	45	7	(	(	PUNCT
ejpam-4597	45	8	y	y	X
ejpam-4597	45	9	)	)	PUNCT
ejpam-4597	45	10	=	=	SYM
ejpam-4597	46	1	0	0	NUM
ejpam-4597	47	1	otherwise	otherwise	ADV
ejpam-4597	47	2	for	for	ADP
ejpam-4597	47	3	all	all	DET
ejpam-4597	47	4	y	y	PROPN
ejpam-4597	47	5	∈	∈	PROPN
ejpam-4597	47	6	u.	u.	NOUN
ejpam-4597	48	1	we	we	PRON
ejpam-4597	48	2	write	write	VERB
ejpam-4597	48	3	xα	xα	ADP
ejpam-4597	48	4	∈	∈	PROPN
ejpam-4597	48	5	a	a	DET
ejpam-4597	48	6	if	if	SCONJ
ejpam-4597	48	7	α	α	NOUN
ejpam-4597	48	8	≤	≤	X
ejpam-4597	48	9	a(x	a(x	NOUN
ejpam-4597	48	10	)	)	PUNCT
ejpam-4597	48	11	.	.	PUNCT
ejpam-4597	49	1	the	the	DET
ejpam-4597	49	2	class	class	NOUN
ejpam-4597	49	3	of	of	ADP
ejpam-4597	49	4	all	all	DET
ejpam-4597	49	5	f	f	PROPN
ejpam-4597	49	6	-points	-point	NOUN
ejpam-4597	49	7	of	of	ADP
ejpam-4597	49	8	u	u	NOUN
ejpam-4597	49	9	is	be	AUX
ejpam-4597	49	10	denoted	denote	VERB
ejpam-4597	49	11	by	by	ADP
ejpam-4597	49	12	fp	fp	PROPN
ejpam-4597	49	13	(	(	PUNCT
ejpam-4597	49	14	u	u	NOUN
ejpam-4597	49	15	)	)	PUNCT
ejpam-4597	50	1	[	[	X
ejpam-4597	50	2	33	33	NUM
ejpam-4597	50	3	]	]	PUNCT
ejpam-4597	50	4	.	.	PUNCT
ejpam-4597	51	1	a	a	DET
ejpam-4597	51	2	fuzzy	fuzzy	ADJ
ejpam-4597	51	3	soft	soft	ADJ
ejpam-4597	51	4	set(or	set(or	ADJ
ejpam-4597	51	5	fs	fs	ADJ
ejpam-4597	51	6	-	-	PUNCT
ejpam-4597	51	7	set	set	ADJ
ejpam-4597	51	8	)	)	PUNCT
ejpam-4597	51	9	fe	fe	NOUN
ejpam-4597	51	10	=	=	PUNCT
ejpam-4597	51	11	(	(	PUNCT
ejpam-4597	51	12	f	f	X
ejpam-4597	51	13	,	,	PUNCT
ejpam-4597	51	14	e	e	NOUN
ejpam-4597	51	15	)	)	PUNCT
ejpam-4597	51	16	on	on	ADP
ejpam-4597	51	17	u	u	NOUN
ejpam-4597	51	18	is	be	AUX
ejpam-4597	51	19	a	a	DET
ejpam-4597	51	20	mapping	mapping	NOUN
ejpam-4597	51	21	f	f	NOUN
ejpam-4597	51	22	:	:	PUNCT
ejpam-4597	52	1	e	e	X
ejpam-4597	52	2	−→	−→	NOUN
ejpam-4597	52	3	iu	iu	ADP
ejpam-4597	52	4	where	where	SCONJ
ejpam-4597	52	5	f	f	X
ejpam-4597	52	6	(	(	PUNCT
ejpam-4597	52	7	e	e	NOUN
ejpam-4597	52	8	)	)	PUNCT
ejpam-4597	52	9	=	=	SYM
ejpam-4597	52	10	fe	fe	X
ejpam-4597	52	11	is	be	AUX
ejpam-4597	52	12	an	an	DET
ejpam-4597	52	13	f	f	X
ejpam-4597	52	14	-set	-set	PUNCT
ejpam-4597	52	15	on	on	ADP
ejpam-4597	52	16	u	u	PROPN
ejpam-4597	52	17	.	.	PUNCT
ejpam-4597	53	1	thus	thus	ADV
ejpam-4597	53	2	fe	fe	X
ejpam-4597	53	3	can	can	AUX
ejpam-4597	53	4	be	be	AUX
ejpam-4597	53	5	written	write	VERB
ejpam-4597	53	6	as	as	ADP
ejpam-4597	53	7	the	the	DET
ejpam-4597	53	8	set	set	NOUN
ejpam-4597	53	9	of	of	ADP
ejpam-4597	53	10	ordered	order	VERB
ejpam-4597	53	11	pairs	pair	NOUN
ejpam-4597	53	12	fe	fe	X
ejpam-4597	53	13	=	=	PUNCT
ejpam-4597	53	14	{	{	PUNCT
ejpam-4597	53	15	(	(	PUNCT
ejpam-4597	53	16	e	e	NOUN
ejpam-4597	53	17	,	,	PUNCT
ejpam-4597	53	18	f(e	f(e	NOUN
ejpam-4597	53	19	)	)	PUNCT
ejpam-4597	53	20	)	)	PUNCT
ejpam-4597	53	21	:	:	PUNCT
ejpam-4597	54	1	e	e	X
ejpam-4597	54	2	∈	∈	PROPN
ejpam-4597	54	3	e	e	NOUN
ejpam-4597	54	4	,	,	PUNCT
ejpam-4597	54	5	f(e	f(e	NOUN
ejpam-4597	54	6	)	)	PUNCT
ejpam-4597	54	7	∈	∈	PROPN
ejpam-4597	54	8	iu	iu	ADP
ejpam-4597	54	9	}	}	PUNCT
ejpam-4597	54	10	.	.	PUNCT
ejpam-4597	55	1	the	the	DET
ejpam-4597	55	2	class	class	NOUN
ejpam-4597	55	3	of	of	ADP
ejpam-4597	55	4	all	all	DET
ejpam-4597	55	5	fs	f	NOUN
ejpam-4597	55	6	-	-	NOUN
ejpam-4597	55	7	sets	set	NOUN
ejpam-4597	55	8	on	on	ADP
ejpam-4597	55	9	u	u	NOUN
ejpam-4597	55	10	is	be	AUX
ejpam-4597	55	11	denoted	denote	VERB
ejpam-4597	55	12	by	by	ADP
ejpam-4597	55	13	fss(u	fss(u	PROPN
ejpam-4597	55	14	)	)	PUNCT
ejpam-4597	56	1	[	[	X
ejpam-4597	56	2	19	19	NUM
ejpam-4597	56	3	]	]	PUNCT
ejpam-4597	56	4	.	.	PUNCT
ejpam-4597	57	1	for	for	ADP
ejpam-4597	57	2	two	two	NUM
ejpam-4597	57	3	fs	f	NOUN
ejpam-4597	57	4	-	-	PUNCT
ejpam-4597	57	5	sets	set	NOUN
ejpam-4597	57	6	fe	fe	NOUN
ejpam-4597	57	7	and	and	CCONJ
ejpam-4597	57	8	ge	ge	PROPN
ejpam-4597	57	9	on	on	ADP
ejpam-4597	57	10	u	u	PROPN
ejpam-4597	57	11	,	,	PUNCT
ejpam-4597	57	12	we	we	PRON
ejpam-4597	57	13	have[19	have[19	VERB
ejpam-4597	57	14	]	]	PUNCT
ejpam-4597	57	15	:	:	PUNCT
ejpam-4597	57	16	1	1	X
ejpam-4597	57	17	)	)	PUNCT
ejpam-4597	57	18	fe	fe	NOUN
ejpam-4597	57	19	is	be	AUX
ejpam-4597	57	20	called	call	VERB
ejpam-4597	57	21	a	a	DET
ejpam-4597	57	22	null	null	ADJ
ejpam-4597	57	23	(	(	PUNCT
ejpam-4597	57	24	resp	resp	NOUN
ejpam-4597	57	25	.	.	PUNCT
ejpam-4597	58	1	universal	universal	ADJ
ejpam-4597	58	2	)	)	PUNCT
ejpam-4597	58	3	fs	fs	NOUN
ejpam-4597	58	4	-	-	PUNCT
ejpam-4597	58	5	set	set	NOUN
ejpam-4597	58	6	,	,	PUNCT
ejpam-4597	58	7	symbolized	symbolize	VERB
ejpam-4597	58	8	by	by	ADP
ejpam-4597	58	9	0̃e(resp.1̃e	0̃e(resp.1̃e	SYM
ejpam-4597	58	10	)	)	PUNCT
ejpam-4597	58	11	if	if	SCONJ
ejpam-4597	58	12	f(e	f(e	NOUN
ejpam-4597	58	13	)	)	PUNCT
ejpam-4597	58	14	=	=	SYM
ejpam-4597	59	1	0(resp.f(e	0(resp.f(e	X
ejpam-4597	59	2	)	)	PUNCT
ejpam-4597	59	3	=	=	SYM
ejpam-4597	59	4	1	1	X
ejpam-4597	59	5	)	)	PUNCT
ejpam-4597	59	6	for	for	ADP
ejpam-4597	59	7	all	all	DET
ejpam-4597	59	8	e	e	PROPN
ejpam-4597	59	9	∈	∈	PROPN
ejpam-4597	59	10	e.	e.	PROPN
ejpam-4597	59	11	2	2	NUM
ejpam-4597	59	12	)	)	PUNCT
ejpam-4597	59	13	fe	fe	NOUN
ejpam-4597	59	14	is	be	AUX
ejpam-4597	59	15	a	a	DET
ejpam-4597	59	16	subset	subset	NOUN
ejpam-4597	59	17	of	of	ADP
ejpam-4597	59	18	ge	ge	PROPN
ejpam-4597	59	19	if	if	SCONJ
ejpam-4597	59	20	f	f	PROPN
ejpam-4597	59	21	(	(	PUNCT
ejpam-4597	59	22	e	e	NOUN
ejpam-4597	59	23	)	)	PUNCT
ejpam-4597	59	24	≤	≤	NOUN
ejpam-4597	59	25	g	g	NOUN
ejpam-4597	59	26	(	(	PUNCT
ejpam-4597	59	27	e	e	NOUN
ejpam-4597	59	28	)	)	PUNCT
ejpam-4597	59	29	∀	∀	X
ejpam-4597	59	30	e	e	X
ejpam-4597	59	31	∈	∈	PROPN
ejpam-4597	59	32	e	e	NOUN
ejpam-4597	59	33	,	,	PUNCT
ejpam-4597	59	34	symbolized	symbolize	VERB
ejpam-4597	59	35	by	by	ADP
ejpam-4597	59	36	f	f	PROPN
ejpam-4597	59	37	⊑	⊑	PROPN
ejpam-4597	59	38	g.	g.	PROPN
ejpam-4597	59	39	3	3	NUM
ejpam-4597	59	40	)	)	PUNCT
ejpam-4597	59	41	fe	fe	NOUN
ejpam-4597	59	42	and	and	CCONJ
ejpam-4597	59	43	ge	ge	PROPN
ejpam-4597	59	44	are	be	AUX
ejpam-4597	59	45	equal	equal	ADJ
ejpam-4597	59	46	if	if	SCONJ
ejpam-4597	59	47	fe	fe	PROPN
ejpam-4597	59	48	⊑	⊑	X
ejpam-4597	59	49	ge	ge	PROPN
ejpam-4597	59	50	and	and	CCONJ
ejpam-4597	59	51	ge	ge	PROPN
ejpam-4597	59	52	⊑	⊑	DET
ejpam-4597	59	53	fe	fe	X
ejpam-4597	59	54	.	.	PUNCT
ejpam-4597	60	1	it	it	PRON
ejpam-4597	60	2	is	be	AUX
ejpam-4597	60	3	symbolized	symbolize	VERB
ejpam-4597	60	4	by	by	ADP
ejpam-4597	60	5	fe	fe	X
ejpam-4597	60	6	=	=	PROPN
ejpam-4597	60	7	ge	ge	PROPN
ejpam-4597	60	8	.	.	PUNCT
ejpam-4597	61	1	4	4	X
ejpam-4597	61	2	)	)	PUNCT
ejpam-4597	61	3	the	the	DET
ejpam-4597	61	4	union	union	NOUN
ejpam-4597	61	5	of	of	ADP
ejpam-4597	61	6	fe	fe	PROPN
ejpam-4597	61	7	and	and	CCONJ
ejpam-4597	61	8	ge	ge	PROPN
ejpam-4597	61	9	is	be	AUX
ejpam-4597	61	10	an	an	DET
ejpam-4597	61	11	fs	fs	NOUN
ejpam-4597	61	12	-	-	PUNCT
ejpam-4597	61	13	set	set	ADJ
ejpam-4597	61	14	he	he	PRON
ejpam-4597	61	15	defined	define	VERB
ejpam-4597	61	16	by	by	ADP
ejpam-4597	61	17	h	h	PROPN
ejpam-4597	61	18	(	(	PUNCT
ejpam-4597	61	19	e	e	NOUN
ejpam-4597	61	20	)	)	PUNCT
ejpam-4597	62	1	=	=	SYM
ejpam-4597	62	2	f	f	X
ejpam-4597	62	3	(	(	PUNCT
ejpam-4597	62	4	e	e	NOUN
ejpam-4597	62	5	)	)	PUNCT
ejpam-4597	62	6	∨	∨	NOUN
ejpam-4597	62	7	g	g	PROPN
ejpam-4597	62	8	(	(	PUNCT
ejpam-4597	62	9	e	e	NOUN
ejpam-4597	62	10	)	)	PUNCT
ejpam-4597	62	11	for	for	ADP
ejpam-4597	62	12	all	all	PRON
ejpam-4597	62	13	e	e	PROPN
ejpam-4597	62	14	∈	∈	PROPN
ejpam-4597	62	15	e.	e.	PROPN
ejpam-4597	63	1	he	he	PRON
ejpam-4597	63	2	is	be	AUX
ejpam-4597	63	3	symbolized	symbolize	VERB
ejpam-4597	63	4	by	by	ADP
ejpam-4597	63	5	fe	fe	X
ejpam-4597	63	6	⊔	⊔	PROPN
ejpam-4597	63	7	ge	ge	PROPN
ejpam-4597	63	8	.	.	PUNCT
ejpam-4597	64	1	5	5	X
ejpam-4597	64	2	)	)	PUNCT
ejpam-4597	64	3	the	the	DET
ejpam-4597	64	4	intersection	intersection	NOUN
ejpam-4597	64	5	of	of	ADP
ejpam-4597	64	6	fe	fe	NOUN
ejpam-4597	64	7	and	and	CCONJ
ejpam-4597	64	8	ge	ge	PROPN
ejpam-4597	64	9	is	be	AUX
ejpam-4597	64	10	an	an	DET
ejpam-4597	64	11	fs	fs	VERB
ejpam-4597	64	12	-	-	PUNCT
ejpam-4597	64	13	set	set	VERB
ejpam-4597	64	14	le	le	NOUN
ejpam-4597	64	15	defined	define	VERB
ejpam-4597	64	16	by	by	ADP
ejpam-4597	64	17	l	l	PROPN
ejpam-4597	64	18	(	(	PUNCT
ejpam-4597	64	19	e	e	NOUN
ejpam-4597	64	20	)	)	PUNCT
ejpam-4597	64	21	=	=	SYM
ejpam-4597	64	22	f	f	X
ejpam-4597	64	23	(	(	PUNCT
ejpam-4597	64	24	e	e	NOUN
ejpam-4597	64	25	)	)	PUNCT
ejpam-4597	64	26	∧	∧	PROPN
ejpam-4597	64	27	g	g	NOUN
ejpam-4597	64	28	(	(	PUNCT
ejpam-4597	64	29	e	e	NOUN
ejpam-4597	64	30	)	)	PUNCT
ejpam-4597	64	31	for	for	ADP
ejpam-4597	64	32	all	all	DET
ejpam-4597	64	33	e	e	PROPN
ejpam-4597	64	34	∈	∈	PROPN
ejpam-4597	64	35	e.	e.	PROPN
ejpam-4597	64	36	le	le	PROPN
ejpam-4597	64	37	is	be	AUX
ejpam-4597	64	38	symbolized	symbolize	VERB
ejpam-4597	64	39	by	by	ADP
ejpam-4597	64	40	fe	fe	X
ejpam-4597	64	41	⊓	⊓	PROPN
ejpam-4597	64	42	ge	ge	PROPN
ejpam-4597	64	43	.	.	PUNCT
ejpam-4597	65	1	an	an	DET
ejpam-4597	65	2	fs	fs	NOUN
ejpam-4597	65	3	-	-	PUNCT
ejpam-4597	65	4	point	point	NOUN
ejpam-4597	65	5	xeα	xeα	NOUN
ejpam-4597	65	6	on	on	ADP
ejpam-4597	65	7	u	u	PROPN
ejpam-4597	65	8	is	be	AUX
ejpam-4597	65	9	an	an	DET
ejpam-4597	65	10	fs	fs	NOUN
ejpam-4597	65	11	-	-	PUNCT
ejpam-4597	65	12	set	set	VERB
ejpam-4597	65	13	(	(	PUNCT
ejpam-4597	65	14	xeα	xeα	PROPN
ejpam-4597	65	15	,	,	PUNCT
ejpam-4597	65	16	e	e	NOUN
ejpam-4597	65	17	)	)	PUNCT
ejpam-4597	65	18	given	give	VERB
ejpam-4597	65	19	by	by	ADP
ejpam-4597	65	20	xeα(e	xeα(e	PROPN
ejpam-4597	65	21	′	′	NUM
ejpam-4597	65	22	)	)	PUNCT
ejpam-4597	66	1	=	=	PUNCT
ejpam-4597	66	2	xα	xα	INTJ
ejpam-4597	66	3	if	if	SCONJ
ejpam-4597	66	4	e	e	X
ejpam-4597	66	5	′	′	NOUN
ejpam-4597	66	6	=	=	SYM
ejpam-4597	66	7	e	e	NOUN
ejpam-4597	66	8	and	and	CCONJ
ejpam-4597	66	9	xeα(e	xeα(e	PROPN
ejpam-4597	66	10	′	′	NUM
ejpam-4597	66	11	)	)	PUNCT
ejpam-4597	67	1	=	=	SYM
ejpam-4597	67	2	0	0	PUNCT
ejpam-4597	68	1	otherwise	otherwise	ADV
ejpam-4597	68	2	,	,	PUNCT
ejpam-4597	68	3	where	where	SCONJ
ejpam-4597	68	4	xα	xα	PRON
ejpam-4597	68	5	is	be	AUX
ejpam-4597	68	6	an	an	DET
ejpam-4597	68	7	f	f	PROPN
ejpam-4597	68	8	-point	-point	NOUN
ejpam-4597	68	9	in	in	ADP
ejpam-4597	68	10	u	u	NOUN
ejpam-4597	68	11	with	with	ADP
ejpam-4597	68	12	the	the	DET
ejpam-4597	68	13	support	support	NOUN
ejpam-4597	68	14	x	x	PUNCT
ejpam-4597	68	15	and	and	CCONJ
ejpam-4597	68	16	the	the	DET
ejpam-4597	68	17	value	value	NOUN
ejpam-4597	68	18	α	α	NOUN
ejpam-4597	68	19	,	,	PUNCT
ejpam-4597	68	20	α	α	PROPN
ejpam-4597	68	21	∈	∈	PROPN
ejpam-4597	68	22	(	(	PUNCT
ejpam-4597	68	23	0	0	NUM
ejpam-4597	68	24	,	,	PUNCT
ejpam-4597	68	25	1	1	NUM
ejpam-4597	68	26	]	]	PUNCT
ejpam-4597	68	27	.	.	PUNCT
ejpam-4597	69	1	an	an	DET
ejpam-4597	69	2	fs	fs	NOUN
ejpam-4597	69	3	-	-	PUNCT
ejpam-4597	69	4	point	point	NOUN
ejpam-4597	69	5	xeα∈̃fe	xeα∈̃fe	PUNCT
ejpam-4597	69	6	if	if	SCONJ
ejpam-4597	69	7	α	α	PRON
ejpam-4597	69	8	≤	≤	NUM
ejpam-4597	69	9	f(e)(x	f(e)(x	NOUN
ejpam-4597	69	10	)	)	PUNCT
ejpam-4597	69	11	.	.	PUNCT
ejpam-4597	70	1	the	the	DET
ejpam-4597	70	2	set	set	NOUN
ejpam-4597	70	3	of	of	ADP
ejpam-4597	70	4	all	all	DET
ejpam-4597	70	5	fs	f	NOUN
ejpam-4597	70	6	-	-	PUNCT
ejpam-4597	70	7	points	point	NOUN
ejpam-4597	70	8	in	in	ADP
ejpam-4597	70	9	u	u	NOUN
ejpam-4597	70	10	is	be	AUX
ejpam-4597	70	11	denoted	denote	VERB
ejpam-4597	70	12	by	by	ADP
ejpam-4597	70	13	fsp	fsp	PROPN
ejpam-4597	70	14	(	(	PUNCT
ejpam-4597	70	15	u	u	NOUN
ejpam-4597	70	16	)	)	PUNCT
ejpam-4597	70	17	.	.	PUNCT
ejpam-4597	71	1	we	we	PRON
ejpam-4597	71	2	can	can	AUX
ejpam-4597	71	3	write	write	VERB
ejpam-4597	71	4	xeα	xeα	PROPN
ejpam-4597	71	5	̸=	̸=	PROPN
ejpam-4597	71	6	yeβ	yeβ	NOUN
ejpam-4597	71	7	if	if	SCONJ
ejpam-4597	71	8	x	x	PROPN
ejpam-4597	71	9	̸=	̸=	PROPN
ejpam-4597	71	10	y	y	PROPN
ejpam-4597	72	1	[	[	X
ejpam-4597	72	2	4	4	NUM
ejpam-4597	72	3	,	,	PUNCT
ejpam-4597	72	4	9	9	NUM
ejpam-4597	72	5	]	]	PUNCT
ejpam-4597	72	6	.	.	PUNCT
ejpam-4597	73	1	the	the	DET
ejpam-4597	73	2	triple	triple	ADJ
ejpam-4597	73	3	(	(	PUNCT
ejpam-4597	73	4	u	u	NOUN
ejpam-4597	73	5	,	,	PUNCT
ejpam-4597	73	6	δ	δ	PROPN
ejpam-4597	73	7	,	,	PUNCT
ejpam-4597	73	8	e	e	NOUN
ejpam-4597	73	9	)	)	PUNCT
ejpam-4597	73	10	is	be	AUX
ejpam-4597	73	11	called	call	VERB
ejpam-4597	73	12	a	a	DET
ejpam-4597	73	13	fuzzy	fuzzy	ADJ
ejpam-4597	73	14	soft	soft	ADJ
ejpam-4597	73	15	topological	topological	ADJ
ejpam-4597	73	16	space	space	NOUN
ejpam-4597	73	17	(	(	PUNCT
ejpam-4597	73	18	or	or	CCONJ
ejpam-4597	73	19	fsts	fst	NOUN
ejpam-4597	73	20	)	)	PUNCT
ejpam-4597	73	21	where	where	SCONJ
ejpam-4597	73	22	e	e	NOUN
ejpam-4597	73	23	is	be	AUX
ejpam-4597	73	24	a	a	DET
ejpam-4597	73	25	s.	s.	PROPN
ejpam-4597	73	26	saleh	saleh	PROPN
ejpam-4597	73	27	,	,	PUNCT
ejpam-4597	73	28	j.	j.	PROPN
ejpam-4597	73	29	al	al	PROPN
ejpam-4597	73	30	-	-	PUNCT
ejpam-4597	73	31	mufarrij	mufarrij	PROPN
ejpam-4597	73	32	/	/	SYM
ejpam-4597	73	33	eur	eur	PROPN
ejpam-4597	73	34	.	.	PUNCT
ejpam-4597	74	1	j.	j.	PROPN
ejpam-4597	74	2	pure	pure	PROPN
ejpam-4597	74	3	appl	appl	PROPN
ejpam-4597	74	4	.	.	PROPN
ejpam-4597	74	5	math	math	PROPN
ejpam-4597	74	6	,	,	PUNCT
ejpam-4597	74	7	16	16	NUM
ejpam-4597	74	8	(	(	PUNCT
ejpam-4597	74	9	1	1	NUM
ejpam-4597	74	10	)	)	PUNCT
ejpam-4597	74	11	(	(	PUNCT
ejpam-4597	74	12	2023	2023	NUM
ejpam-4597	74	13	)	)	PUNCT
ejpam-4597	74	14	,	,	PUNCT
ejpam-4597	74	15	180	180	NUM
ejpam-4597	74	16	-	-	SYM
ejpam-4597	74	17	191	191	NUM
ejpam-4597	74	18	182	182	NUM
ejpam-4597	74	19	fixed	fix	VERB
ejpam-4597	74	20	set	set	NOUN
ejpam-4597	74	21	of	of	ADP
ejpam-4597	74	22	parameters	parameter	NOUN
ejpam-4597	74	23	and	and	CCONJ
ejpam-4597	74	24	δ	δ	PROPN
ejpam-4597	74	25	is	be	AUX
ejpam-4597	74	26	the	the	DET
ejpam-4597	74	27	class	class	NOUN
ejpam-4597	74	28	of	of	ADP
ejpam-4597	74	29	fs	f	NOUN
ejpam-4597	74	30	-	-	PUNCT
ejpam-4597	74	31	sets	set	NOUN
ejpam-4597	74	32	on	on	ADP
ejpam-4597	74	33	u	u	NOUN
ejpam-4597	74	34	which	which	PRON
ejpam-4597	74	35	is	be	AUX
ejpam-4597	74	36	closed	close	VERB
ejpam-4597	74	37	under	under	ADP
ejpam-4597	74	38	a	a	DET
ejpam-4597	74	39	finite	finite	ADJ
ejpam-4597	74	40	intersection	intersection	NOUN
ejpam-4597	74	41	,	,	PUNCT
ejpam-4597	74	42	an	an	DET
ejpam-4597	74	43	arbitrary	arbitrary	ADJ
ejpam-4597	74	44	union	union	NOUN
ejpam-4597	74	45	,	,	PUNCT
ejpam-4597	74	46	and	and	CCONJ
ejpam-4597	74	47	0e	0e	NOUN
ejpam-4597	74	48	,	,	PUNCT
ejpam-4597	74	49	1e	1e	PROPN
ejpam-4597	74	50	belong	belong	VERB
ejpam-4597	74	51	to	to	ADP
ejpam-4597	74	52	δ	δ	PROPN
ejpam-4597	74	53	.	.	PUNCT
ejpam-4597	75	1	the	the	DET
ejpam-4597	75	2	family	family	PROPN
ejpam-4597	75	3	fsos(u	fsos(u	PROPN
ejpam-4597	75	4	)	)	PUNCT
ejpam-4597	75	5	(	(	PUNCT
ejpam-4597	75	6	resp	resp	NOUN
ejpam-4597	75	7	.	.	PUNCT
ejpam-4597	76	1	fscs(u	fscs(u	ADP
ejpam-4597	76	2	)	)	PUNCT
ejpam-4597	76	3	)	)	PUNCT
ejpam-4597	77	1	refers	refer	VERB
ejpam-4597	77	2	to	to	ADP
ejpam-4597	77	3	the	the	DET
ejpam-4597	77	4	set	set	NOUN
ejpam-4597	77	5	of	of	ADP
ejpam-4597	77	6	all	all	DET
ejpam-4597	77	7	fs	fs	PROPN
ejpam-4597	77	8	-	-	PUNCT
ejpam-4597	77	9	open(resp	open(resp	PROPN
ejpam-4597	77	10	.	.	PUNCT
ejpam-4597	78	1	fs	fs	ADJ
ejpam-4597	78	2	-	-	PUNCT
ejpam-4597	78	3	closed	closed	ADJ
ejpam-4597	78	4	)	)	PUNCT
ejpam-4597	78	5	sets	set	NOUN
ejpam-4597	78	6	on	on	ADP
ejpam-4597	78	7	u	u	NOUN
ejpam-4597	78	8	[	[	X
ejpam-4597	78	9	4	4	NUM
ejpam-4597	78	10	,	,	PUNCT
ejpam-4597	78	11	30	30	NUM
ejpam-4597	78	12	]	]	PUNCT
ejpam-4597	78	13	.	.	PUNCT
ejpam-4597	79	1	notation	notation	NOUN
ejpam-4597	79	2	.	.	PUNCT
ejpam-4597	80	1	[	[	X
ejpam-4597	80	2	29	29	NUM
ejpam-4597	80	3	]	]	PUNCT
ejpam-4597	80	4	for	for	ADP
ejpam-4597	80	5	xeα	xeα	PROPN
ejpam-4597	80	6	∈	∈	PROPN
ejpam-4597	80	7	fsp	fsp	PROPN
ejpam-4597	80	8	(	(	PUNCT
ejpam-4597	80	9	u	u	NOUN
ejpam-4597	80	10	)	)	PUNCT
ejpam-4597	80	11	,	,	PUNCT
ejpam-4597	80	12	oxe	oxe	PROPN
ejpam-4597	80	13	α	α	PROPN
ejpam-4597	80	14	refers	refer	VERB
ejpam-4597	80	15	to	to	ADP
ejpam-4597	80	16	an	an	DET
ejpam-4597	80	17	fso	fso	NOUN
ejpam-4597	80	18	-	-	PUNCT
ejpam-4597	80	19	set	set	NOUN
ejpam-4597	80	20	contains	contain	VERB
ejpam-4597	80	21	xeα	xeα	PROPN
ejpam-4597	80	22	and	and	CCONJ
ejpam-4597	80	23	is	be	AUX
ejpam-4597	80	24	called	call	VERB
ejpam-4597	80	25	fso	fso	PROPN
ejpam-4597	80	26	-	-	PUNCT
ejpam-4597	80	27	nbd	nbd	PROPN
ejpam-4597	80	28	of	of	ADP
ejpam-4597	80	29	xeα	xeα	PROPN
ejpam-4597	80	30	,	,	PUNCT
ejpam-4597	80	31	ne	ne	PROPN
ejpam-4597	80	32	(	(	PUNCT
ejpam-4597	80	33	xeα	xeα	PROPN
ejpam-4597	80	34	)	)	PUNCT
ejpam-4597	80	35	refers	refer	VERB
ejpam-4597	80	36	to	to	ADP
ejpam-4597	80	37	the	the	DET
ejpam-4597	80	38	set	set	NOUN
ejpam-4597	80	39	of	of	ADP
ejpam-4597	80	40	all	all	DET
ejpam-4597	80	41	fso	fso	NOUN
ejpam-4597	80	42	-	-	PUNCT
ejpam-4597	80	43	nbds	nbds	NOUN
ejpam-4597	80	44	of	of	ADP
ejpam-4597	80	45	xeα	xeα	PROPN
ejpam-4597	80	46	.	.	PUNCT
ejpam-4597	81	1	in	in	ADP
ejpam-4597	81	2	general	general	ADJ
ejpam-4597	81	3	ofe	ofe	PROPN
ejpam-4597	81	4	refers	refer	VERB
ejpam-4597	81	5	to	to	ADP
ejpam-4597	81	6	an	an	DET
ejpam-4597	81	7	fso	fso	NOUN
ejpam-4597	81	8	-	-	PUNCT
ejpam-4597	81	9	set	set	NOUN
ejpam-4597	81	10	contains	contain	VERB
ejpam-4597	81	11	fe	fe	X
ejpam-4597	81	12	.	.	PUNCT
ejpam-4597	82	1	an	an	DET
ejpam-4597	82	2	fs	fs	NOUN
ejpam-4597	82	3	-	-	PUNCT
ejpam-4597	82	4	closure	closure	NOUN
ejpam-4597	82	5	of	of	ADP
ejpam-4597	82	6	an	an	DET
ejpam-4597	82	7	fs	fs	NOUN
ejpam-4597	82	8	-	-	PUNCT
ejpam-4597	82	9	set	set	VERB
ejpam-4597	82	10	he	he	PRON
ejpam-4597	82	11	in	in	ADP
ejpam-4597	82	12	(	(	PUNCT
ejpam-4597	82	13	u	u	NOUN
ejpam-4597	82	14	,	,	PUNCT
ejpam-4597	82	15	δ	δ	PROPN
ejpam-4597	82	16	,	,	PUNCT
ejpam-4597	82	17	e	e	NOUN
ejpam-4597	82	18	)	)	PUNCT
ejpam-4597	82	19	denoted	denote	VERB
ejpam-4597	82	20	by	by	ADP
ejpam-4597	82	21	cl(he	cl(he	NOUN
ejpam-4597	82	22	)	)	PUNCT
ejpam-4597	82	23	is	be	AUX
ejpam-4597	82	24	the	the	DET
ejpam-4597	82	25	smallest	small	ADJ
ejpam-4597	82	26	fscset	fscset	NOUN
ejpam-4597	82	27	on	on	ADP
ejpam-4597	82	28	u	u	NOUN
ejpam-4597	82	29	which	which	PRON
ejpam-4597	82	30	contains	contain	VERB
ejpam-4597	82	31	he	he	PRON
ejpam-4597	82	32	,	,	PUNCT
ejpam-4597	82	33	and	and	CCONJ
ejpam-4597	82	34	an	an	DET
ejpam-4597	82	35	fs	fs	ADJ
ejpam-4597	82	36	-	-	ADJ
ejpam-4597	82	37	interior	interior	NOUN
ejpam-4597	82	38	of	of	ADP
ejpam-4597	82	39	he	he	PRON
ejpam-4597	82	40	denoted	denote	VERB
ejpam-4597	82	41	by	by	ADP
ejpam-4597	82	42	int(he	int(he	NOUN
ejpam-4597	82	43	)	)	PUNCT
ejpam-4597	82	44	is	be	AUX
ejpam-4597	82	45	the	the	DET
ejpam-4597	82	46	largest	large	ADJ
ejpam-4597	82	47	fso	fso	NOUN
ejpam-4597	82	48	-	-	PUNCT
ejpam-4597	82	49	set	set	NOUN
ejpam-4597	82	50	contained	contain	VERB
ejpam-4597	82	51	in	in	ADP
ejpam-4597	82	52	he	he	PRON
ejpam-4597	82	53	.	.	PUNCT
ejpam-4597	83	1	it	it	PRON
ejpam-4597	83	2	is	be	AUX
ejpam-4597	83	3	clear	clear	ADJ
ejpam-4597	83	4	that	that	SCONJ
ejpam-4597	83	5	xeα∈̃int(he	xeα∈̃int(he	PROPN
ejpam-4597	83	6	)	)	PUNCT
ejpam-4597	83	7	if	if	SCONJ
ejpam-4597	83	8	and	and	CCONJ
ejpam-4597	83	9	only	only	ADV
ejpam-4597	83	10	if	if	SCONJ
ejpam-4597	83	11	there	there	PRON
ejpam-4597	83	12	exists	exist	VERB
ejpam-4597	83	13	oxe	oxe	PRON
ejpam-4597	83	14	α	α	PROPN
ejpam-4597	83	15	∈	∈	PROPN
ejpam-4597	83	16	δ	δ	PROPN
ejpam-4597	83	17	such	such	ADJ
ejpam-4597	83	18	that	that	SCONJ
ejpam-4597	83	19	oxe	oxe	PRON
ejpam-4597	83	20	α	α	NOUN
ejpam-4597	83	21	⊑	⊑	X
ejpam-4597	83	22	he	he	PRON
ejpam-4597	83	23	[	[	X
ejpam-4597	83	24	4	4	NUM
ejpam-4597	83	25	]	]	PUNCT
ejpam-4597	83	26	.	.	PUNCT
ejpam-4597	84	1	definition	definition	NOUN
ejpam-4597	84	2	1	1	NUM
ejpam-4597	84	3	.	.	PUNCT
ejpam-4597	85	1	[	[	X
ejpam-4597	85	2	16	16	NUM
ejpam-4597	85	3	]	]	PUNCT
ejpam-4597	85	4	let	let	VERB
ejpam-4597	85	5	fss(u	fss(u	NOUN
ejpam-4597	85	6	)	)	PUNCT
ejpam-4597	85	7	and	and	CCONJ
ejpam-4597	85	8	fss(v	fss(v	NOUN
ejpam-4597	85	9	)	)	PUNCT
ejpam-4597	85	10	be	be	VERB
ejpam-4597	85	11	two	two	NUM
ejpam-4597	85	12	classes	class	NOUN
ejpam-4597	85	13	of	of	ADP
ejpam-4597	85	14	all	all	DET
ejpam-4597	85	15	fs	f	NOUN
ejpam-4597	85	16	-	-	NOUN
ejpam-4597	85	17	sets	set	NOUN
ejpam-4597	85	18	on	on	ADP
ejpam-4597	85	19	u	u	PROPN
ejpam-4597	85	20	,	,	PUNCT
ejpam-4597	85	21	v	v	ADP
ejpam-4597	85	22	respectively	respectively	ADV
ejpam-4597	85	23	,	,	PUNCT
ejpam-4597	85	24	and	and	CCONJ
ejpam-4597	85	25	let	let	VERB
ejpam-4597	85	26	p	p	NOUN
ejpam-4597	85	27	:	:	PUNCT
ejpam-4597	85	28	u	u	VERB
ejpam-4597	85	29	−→	−→	NOUN
ejpam-4597	85	30	v	v	NOUN
ejpam-4597	85	31	and	and	CCONJ
ejpam-4597	85	32	u	u	NOUN
ejpam-4597	85	33	:	:	PUNCT
ejpam-4597	85	34	e	e	X
ejpam-4597	85	35	−→	−→	NOUN
ejpam-4597	85	36	k	k	PROPN
ejpam-4597	85	37	be	be	AUX
ejpam-4597	85	38	two	two	NUM
ejpam-4597	85	39	maps	map	NOUN
ejpam-4597	85	40	,	,	PUNCT
ejpam-4597	85	41	then	then	ADV
ejpam-4597	85	42	the	the	DET
ejpam-4597	85	43	map	map	NOUN
ejpam-4597	85	44	fup	fup	VERB
ejpam-4597	85	45	:	:	PUNCT
ejpam-4597	85	46	fss	fss	PROPN
ejpam-4597	85	47	(	(	PUNCT
ejpam-4597	85	48	u	u	NOUN
ejpam-4597	85	49	)	)	PUNCT
ejpam-4597	85	50	−→	−→	ADJ
ejpam-4597	85	51	fss	fss	ADJ
ejpam-4597	85	52	(	(	PUNCT
ejpam-4597	85	53	v	v	NOUN
ejpam-4597	85	54	)	)	PUNCT
ejpam-4597	85	55	is	be	AUX
ejpam-4597	85	56	called	call	VERB
ejpam-4597	85	57	an	an	DET
ejpam-4597	85	58	fs	fs	NOUN
ejpam-4597	85	59	-	-	PUNCT
ejpam-4597	85	60	map	map	NOUN
ejpam-4597	85	61	for	for	ADP
ejpam-4597	85	62	which	which	PRON
ejpam-4597	85	63	:	:	PUNCT
ejpam-4597	85	64	i	i	X
ejpam-4597	85	65	)	)	PUNCT
ejpam-4597	85	66	if	if	SCONJ
ejpam-4597	85	67	he	he	PRON
ejpam-4597	85	68	∈	∈	VERB
ejpam-4597	85	69	fss(ue	fss(ue	NUM
ejpam-4597	85	70	)	)	PUNCT
ejpam-4597	85	71	,	,	PUNCT
ejpam-4597	85	72	then	then	ADV
ejpam-4597	85	73	the	the	DET
ejpam-4597	85	74	image	image	NOUN
ejpam-4597	85	75	of	of	ADP
ejpam-4597	85	76	he	he	PRON
ejpam-4597	85	77	denoted	denote	VERB
ejpam-4597	85	78	by	by	ADP
ejpam-4597	85	79	fup(he	fup(he	NOUN
ejpam-4597	85	80	)	)	PUNCT
ejpam-4597	85	81	is	be	AUX
ejpam-4597	85	82	an	an	DET
ejpam-4597	85	83	fs	fs	NOUN
ejpam-4597	85	84	-	-	PUNCT
ejpam-4597	85	85	set	set	NOUN
ejpam-4597	85	86	on	on	ADP
ejpam-4597	85	87	v	v	NOUN
ejpam-4597	85	88	given	give	VERB
ejpam-4597	85	89	by	by	ADP
ejpam-4597	85	90	fup(he	fup(he	NOUN
ejpam-4597	85	91	)	)	PUNCT
ejpam-4597	85	92	(	(	PUNCT
ejpam-4597	85	93	k	k	X
ejpam-4597	85	94	)	)	PUNCT
ejpam-4597	85	95	=	=	SYM
ejpam-4597	85	96	sup{p(h	sup{p(h	PROPN
ejpam-4597	85	97	(	(	PUNCT
ejpam-4597	85	98	e	e	NOUN
ejpam-4597	85	99	)	)	PUNCT
ejpam-4597	85	100	)	)	PUNCT
ejpam-4597	85	101	:	:	PUNCT
ejpam-4597	86	1	e	e	X
ejpam-4597	86	2	∈	∈	PROPN
ejpam-4597	86	3	u−1	u−1	PROPN
ejpam-4597	86	4	(	(	PUNCT
ejpam-4597	86	5	k	k	NOUN
ejpam-4597	86	6	)	)	PUNCT
ejpam-4597	86	7	}	}	PUNCT
ejpam-4597	86	8	if	if	SCONJ
ejpam-4597	86	9	u−1	u−1	PROPN
ejpam-4597	86	10	(	(	PUNCT
ejpam-4597	86	11	k	k	NOUN
ejpam-4597	86	12	)	)	PUNCT
ejpam-4597	86	13	̸=	̸=	PROPN
ejpam-4597	86	14	∅	∅	NOUN
ejpam-4597	86	15	and	and	CCONJ
ejpam-4597	86	16	fup	fup	X
ejpam-4597	86	17	(	(	PUNCT
ejpam-4597	86	18	he	he	PRON
ejpam-4597	86	19	)	)	PUNCT
ejpam-4597	86	20	(	(	PUNCT
ejpam-4597	86	21	k	k	X
ejpam-4597	86	22	)	)	PUNCT
ejpam-4597	86	23	=	=	NOUN
ejpam-4597	86	24	0k	0k	NOUN
ejpam-4597	86	25	,	,	PUNCT
ejpam-4597	86	26	otherwise	otherwise	ADV
ejpam-4597	86	27	∀k	∀k	NOUN
ejpam-4597	86	28	∈	∈	PROPN
ejpam-4597	86	29	k.	k.	PROPN
ejpam-4597	86	30	ii	ii	PROPN
ejpam-4597	86	31	)	)	PUNCT
ejpam-4597	86	32	if	if	SCONJ
ejpam-4597	86	33	gk	gk	PROPN
ejpam-4597	86	34	∈	∈	PROPN
ejpam-4597	86	35	fss(v	fss(v	PROPN
ejpam-4597	86	36	)	)	PUNCT
ejpam-4597	86	37	,	,	PUNCT
ejpam-4597	86	38	then	then	ADV
ejpam-4597	86	39	the	the	DET
ejpam-4597	86	40	preimage	preimage	NOUN
ejpam-4597	86	41	of	of	ADP
ejpam-4597	86	42	gk	gk	PROPN
ejpam-4597	86	43	denoted	denote	VERB
ejpam-4597	86	44	by	by	ADP
ejpam-4597	86	45	f−1	f−1	PROPN
ejpam-4597	86	46	up	up	ADP
ejpam-4597	86	47	(	(	PUNCT
ejpam-4597	86	48	gk	gk	NOUN
ejpam-4597	86	49	)	)	PUNCT
ejpam-4597	86	50	is	be	AUX
ejpam-4597	86	51	an	an	DET
ejpam-4597	86	52	fs	fs	NOUN
ejpam-4597	86	53	-	-	PUNCT
ejpam-4597	86	54	set	set	NOUN
ejpam-4597	86	55	on	on	ADP
ejpam-4597	86	56	u	u	NOUN
ejpam-4597	86	57	defined	define	VERB
ejpam-4597	86	58	by	by	ADP
ejpam-4597	86	59	f−1	f−1	PROPN
ejpam-4597	86	60	up	up	ADP
ejpam-4597	86	61	(	(	PUNCT
ejpam-4597	86	62	gk)(e	gk)(e	NOUN
ejpam-4597	86	63	)	)	PUNCT
ejpam-4597	86	64	=	=	SYM
ejpam-4597	86	65	p−1(g	p−1(g	PROPN
ejpam-4597	86	66	(	(	PUNCT
ejpam-4597	86	67	u	u	NOUN
ejpam-4597	86	68	(	(	PUNCT
ejpam-4597	86	69	e	e	NOUN
ejpam-4597	86	70	)	)	PUNCT
ejpam-4597	86	71	)	)	PUNCT
ejpam-4597	86	72	)	)	PUNCT
ejpam-4597	86	73	for	for	ADP
ejpam-4597	86	74	all	all	DET
ejpam-4597	86	75	e	e	PROPN
ejpam-4597	86	76	∈	∈	PROPN
ejpam-4597	86	77	e.	e.	PROPN
ejpam-4597	86	78	an	an	DET
ejpam-4597	86	79	fs	fs	PROPN
ejpam-4597	86	80	-	-	PUNCT
ejpam-4597	86	81	map	map	NOUN
ejpam-4597	86	82	fup	fup	NOUN
ejpam-4597	86	83	is	be	AUX
ejpam-4597	86	84	called	call	VERB
ejpam-4597	86	85	one	one	NUM
ejpam-4597	86	86	-	-	PUNCT
ejpam-4597	86	87	one(onto	one(onto	NOUN
ejpam-4597	86	88	)	)	PUNCT
ejpam-4597	86	89	if	if	SCONJ
ejpam-4597	86	90	u	u	PROPN
ejpam-4597	86	91	and	and	CCONJ
ejpam-4597	86	92	p	p	NOUN
ejpam-4597	86	93	are	be	AUX
ejpam-4597	86	94	one	one	NUM
ejpam-4597	86	95	-	-	PUNCT
ejpam-4597	86	96	one(onto	one(onto	NUM
ejpam-4597	86	97	)	)	PUNCT
ejpam-4597	86	98	.	.	PUNCT
ejpam-4597	87	1	for	for	ADP
ejpam-4597	87	2	more	more	ADJ
ejpam-4597	87	3	details	detail	NOUN
ejpam-4597	87	4	about	about	ADP
ejpam-4597	87	5	the	the	DET
ejpam-4597	87	6	properties	property	NOUN
ejpam-4597	87	7	of	of	ADP
ejpam-4597	87	8	image	image	NOUN
ejpam-4597	87	9	and	and	CCONJ
ejpam-4597	87	10	preimage	preimage	NOUN
ejpam-4597	87	11	of	of	ADP
ejpam-4597	87	12	the	the	DET
ejpam-4597	87	13	fs	f	NOUN
ejpam-4597	87	14	-	-	PUNCT
ejpam-4597	87	15	sets	set	NOUN
ejpam-4597	87	16	see	see	VERB
ejpam-4597	87	17	[	[	X
ejpam-4597	87	18	16	16	NUM
ejpam-4597	87	19	]	]	PUNCT
ejpam-4597	87	20	.	.	PUNCT
ejpam-4597	88	1	definition	definition	NOUN
ejpam-4597	88	2	2	2	NUM
ejpam-4597	88	3	.	.	PUNCT
ejpam-4597	89	1	[	[	X
ejpam-4597	89	2	4	4	X
ejpam-4597	89	3	]	]	PUNCT
ejpam-4597	89	4	the	the	DET
ejpam-4597	89	5	fs	f	NOUN
ejpam-4597	89	6	-	-	PUNCT
ejpam-4597	89	7	sets	set	VERB
ejpam-4597	89	8	he	he	PRON
ejpam-4597	89	9	and	and	CCONJ
ejpam-4597	89	10	ge	ge	PROPN
ejpam-4597	89	11	on	on	ADP
ejpam-4597	89	12	u	u	PROPN
ejpam-4597	89	13	are	be	AUX
ejpam-4597	89	14	called	call	VERB
ejpam-4597	89	15	fs	fs	ADJ
ejpam-4597	89	16	-	-	PUNCT
ejpam-4597	89	17	quasi	quasi	ADJ
ejpam-4597	89	18	coincident	coincident	NOUN
ejpam-4597	89	19	,	,	PUNCT
ejpam-4597	89	20	denoted	denote	VERB
ejpam-4597	89	21	by	by	ADP
ejpam-4597	89	22	heqge	heqge	NOUN
ejpam-4597	89	23	if	if	SCONJ
ejpam-4597	89	24	there	there	PRON
ejpam-4597	89	25	is	be	VERB
ejpam-4597	89	26	e	e	X
ejpam-4597	89	27	∈	∈	NOUN
ejpam-4597	89	28	e	e	NOUN
ejpam-4597	89	29	and	and	CCONJ
ejpam-4597	89	30	x	x	SYM
ejpam-4597	89	31	∈	∈	PROPN
ejpam-4597	89	32	u	u	NOUN
ejpam-4597	89	33	such	such	ADJ
ejpam-4597	89	34	that	that	SCONJ
ejpam-4597	89	35	h(e)(x	h(e)(x	NOUN
ejpam-4597	89	36	)	)	PUNCT
ejpam-4597	89	37	+	+	CCONJ
ejpam-4597	89	38	g(e)(x	g(e)(x	VERB
ejpam-4597	89	39	)	)	PUNCT
ejpam-4597	89	40	>	>	X
ejpam-4597	90	1	1	1	X
ejpam-4597	90	2	.	.	PUNCT
ejpam-4597	91	1	if	if	SCONJ
ejpam-4597	91	2	he	he	PRON
ejpam-4597	91	3	is	be	AUX
ejpam-4597	91	4	not	not	PART
ejpam-4597	91	5	quasi	quasi	ADJ
ejpam-4597	91	6	coincident	coincident	NOUN
ejpam-4597	91	7	with	with	ADP
ejpam-4597	91	8	ge	ge	PROPN
ejpam-4597	91	9	,	,	PUNCT
ejpam-4597	91	10	we	we	PRON
ejpam-4597	91	11	write	write	VERB
ejpam-4597	91	12	he	he	PRON
ejpam-4597	91	13	q̃ge	q̃ge	PROPN
ejpam-4597	91	14	.	.	PUNCT
ejpam-4597	92	1	in	in	ADP
ejpam-4597	92	2	particular	particular	ADJ
ejpam-4597	92	3	,	,	PUNCT
ejpam-4597	92	4	xeαqge	xeαqge	VERB
ejpam-4597	92	5	if	if	SCONJ
ejpam-4597	92	6	α+	α+	PRON
ejpam-4597	92	7	g(e)(x	g(e)(x	NOUN
ejpam-4597	92	8	)	)	PUNCT
ejpam-4597	92	9	>	>	X
ejpam-4597	93	1	1	1	X
ejpam-4597	93	2	.	.	X
ejpam-4597	93	3	proposition	proposition	NOUN
ejpam-4597	93	4	1	1	NUM
ejpam-4597	93	5	.	.	PUNCT
ejpam-4597	94	1	[	[	X
ejpam-4597	94	2	4	4	NUM
ejpam-4597	94	3	,	,	PUNCT
ejpam-4597	94	4	29	29	NUM
ejpam-4597	94	5	]	]	PUNCT
ejpam-4597	94	6	(	(	PUNCT
ejpam-4597	94	7	i	i	NOUN
ejpam-4597	94	8	)	)	PUNCT
ejpam-4597	94	9	fe	fe	PROPN
ejpam-4597	94	10	q̃ge	q̃ge	PROPN
ejpam-4597	94	11	⇔	⇔	PROPN
ejpam-4597	94	12	fe	fe	PROPN
ejpam-4597	94	13	⊑	⊑	X
ejpam-4597	95	1	gce	gce	PROPN
ejpam-4597	95	2	.	.	PUNCT
ejpam-4597	96	1	(	(	PUNCT
ejpam-4597	96	2	ii	ii	NOUN
ejpam-4597	96	3	)	)	PUNCT
ejpam-4597	96	4	fe	fe	NOUN
ejpam-4597	96	5	⊓	⊓	PROPN
ejpam-4597	96	6	ge	ge	PROPN
ejpam-4597	96	7	=	=	SYM
ejpam-4597	96	8	0e	0e	PROPN
ejpam-4597	96	9	⇒	⇒	PROPN
ejpam-4597	96	10	fe	fe	X
ejpam-4597	96	11	q̃ge	q̃ge	PROPN
ejpam-4597	96	12	.	.	PUNCT
ejpam-4597	97	1	(	(	PUNCT
ejpam-4597	97	2	iii	iii	X
ejpam-4597	97	3	)	)	PUNCT
ejpam-4597	97	4	fe	fe	NOUN
ejpam-4597	97	5	q̃ge	q̃ge	PROPN
ejpam-4597	97	6	,	,	PUNCT
ejpam-4597	97	7	he	he	PRON
ejpam-4597	97	8	⊑	⊑	X
ejpam-4597	97	9	ge	ge	PROPN
ejpam-4597	97	10	⇒	⇒	PROPN
ejpam-4597	97	11	fe	fe	X
ejpam-4597	97	12	q̃he	q̃he	PROPN
ejpam-4597	97	13	.	.	PUNCT
ejpam-4597	98	1	(	(	PUNCT
ejpam-4597	98	2	iv	iv	X
ejpam-4597	98	3	)	)	PUNCT
ejpam-4597	98	4	xeαq̃fe	xeαq̃fe	PROPN
ejpam-4597	99	1	⇔	⇔	PROPN
ejpam-4597	99	2	xeα∈̃f	xeα∈̃f	PROPN
ejpam-4597	100	1	c	c	PROPN
ejpam-4597	100	2	e	e	X
ejpam-4597	100	3	.	.	PUNCT
ejpam-4597	101	1	(	(	PUNCT
ejpam-4597	101	2	v	v	NOUN
ejpam-4597	101	3	)	)	PUNCT
ejpam-4597	101	4	fe	fe	NOUN
ejpam-4597	102	1	⊑	⊑	X
ejpam-4597	102	2	ge	ge	PROPN
ejpam-4597	102	3	⇔	⇔	PROPN
ejpam-4597	102	4	(	(	PUNCT
ejpam-4597	102	5	xeαqfe	xeαqfe	PROPN
ejpam-4597	102	6	⇒	⇒	NOUN
ejpam-4597	102	7	xeαqge	xeαqge	PROPN
ejpam-4597	102	8	)	)	PUNCT
ejpam-4597	102	9	.	.	PUNCT
ejpam-4597	103	1	(	(	PUNCT
ejpam-4597	103	2	vi	vi	NOUN
ejpam-4597	103	3	)	)	PUNCT
ejpam-4597	103	4	fe	fe	NOUN
ejpam-4597	104	1	q̃f	q̃f	INTJ
ejpam-4597	104	2	c	c	PROPN
ejpam-4597	104	3	e	e	PROPN
ejpam-4597	104	4	.	.	PUNCT
ejpam-4597	105	1	lemma	lemma	PROPN
ejpam-4597	105	2	1	1	NUM
ejpam-4597	105	3	.	.	PUNCT
ejpam-4597	106	1	[	[	X
ejpam-4597	106	2	29	29	NUM
ejpam-4597	106	3	]	]	PUNCT
ejpam-4597	106	4	for	for	ADP
ejpam-4597	106	5	an	an	DET
ejpam-4597	106	6	fsts	fst	NOUN
ejpam-4597	106	7	(	(	PUNCT
ejpam-4597	106	8	u	u	NOUN
ejpam-4597	106	9	,	,	PUNCT
ejpam-4597	106	10	δ	δ	PROPN
ejpam-4597	106	11	,	,	PUNCT
ejpam-4597	106	12	e	e	NOUN
ejpam-4597	106	13	)	)	PUNCT
ejpam-4597	106	14	and	and	CCONJ
ejpam-4597	106	15	xeα	xeα	PROPN
ejpam-4597	106	16	∈	∈	PROPN
ejpam-4597	106	17	fsp	fsp	PROPN
ejpam-4597	106	18	(	(	PUNCT
ejpam-4597	106	19	u	u	NOUN
ejpam-4597	106	20	)	)	PUNCT
ejpam-4597	106	21	,	,	PUNCT
ejpam-4597	106	22	we	we	PRON
ejpam-4597	106	23	have	have	VERB
ejpam-4597	106	24	:	:	PUNCT
ejpam-4597	106	25	(	(	PUNCT
ejpam-4597	106	26	i	i	NOUN
ejpam-4597	106	27	)	)	PUNCT
ejpam-4597	106	28	ge	ge	PROPN
ejpam-4597	107	1	q̃fe	q̃fe	NOUN
ejpam-4597	107	2	if	if	SCONJ
ejpam-4597	107	3	and	and	CCONJ
ejpam-4597	107	4	only	only	ADV
ejpam-4597	107	5	if	if	SCONJ
ejpam-4597	107	6	ge	ge	PROPN
ejpam-4597	107	7	q̃cl(fe	q̃cl(fe	PROPN
ejpam-4597	107	8	)	)	PUNCT
ejpam-4597	107	9	∀	∀	PUNCT
ejpam-4597	107	10	ge	ge	PROPN
ejpam-4597	107	11	∈	∈	PROPN
ejpam-4597	107	12	δ	δ	PROPN
ejpam-4597	107	13	,	,	PUNCT
ejpam-4597	107	14	(	(	PUNCT
ejpam-4597	107	15	ii	ii	NOUN
ejpam-4597	107	16	)	)	PUNCT
ejpam-4597	107	17	xeαq̃cl(fe	xeαq̃cl(fe	PROPN
ejpam-4597	107	18	)	)	PUNCT
ejpam-4597	108	1	if	if	SCONJ
ejpam-4597	108	2	and	and	CCONJ
ejpam-4597	108	3	only	only	ADV
ejpam-4597	108	4	if	if	SCONJ
ejpam-4597	108	5	oxe	oxe	PRON
ejpam-4597	108	6	α	α	NOUN
ejpam-4597	108	7	q̃fe	q̃fe	NOUN
ejpam-4597	108	8	∀	∀	NOUN
ejpam-4597	108	9	oxe	oxe	VERB
ejpam-4597	108	10	α	α	PROPN
ejpam-4597	108	11	∈	∈	PROPN
ejpam-4597	108	12	δ	δ	PROPN
ejpam-4597	108	13	.	.	PUNCT
ejpam-4597	109	1	definition	definition	NOUN
ejpam-4597	109	2	3	3	NUM
ejpam-4597	109	3	.	.	PUNCT
ejpam-4597	110	1	[	[	X
ejpam-4597	110	2	20	20	NUM
ejpam-4597	110	3	]	]	PUNCT
ejpam-4597	110	4	an	an	DET
ejpam-4597	110	5	fs	fs	NOUN
ejpam-4597	110	6	-	-	PUNCT
ejpam-4597	110	7	set	set	VERB
ejpam-4597	110	8	he	he	PRON
ejpam-4597	110	9	in	in	ADP
ejpam-4597	110	10	(	(	PUNCT
ejpam-4597	110	11	u	u	NOUN
ejpam-4597	110	12	,	,	PUNCT
ejpam-4597	110	13	δ	δ	PROPN
ejpam-4597	110	14	,	,	PUNCT
ejpam-4597	110	15	e	e	NOUN
ejpam-4597	110	16	)	)	PUNCT
ejpam-4597	110	17	is	be	AUX
ejpam-4597	110	18	said	say	VERB
ejpam-4597	110	19	to	to	PART
ejpam-4597	110	20	be	be	AUX
ejpam-4597	110	21	regular	regular	ADJ
ejpam-4597	110	22	open	open	ADJ
ejpam-4597	110	23	(	(	PUNCT
ejpam-4597	110	24	resp	resp	NOUN
ejpam-4597	110	25	.	.	PUNCT
ejpam-4597	111	1	regular	regular	ADJ
ejpam-4597	111	2	closed	closed	ADJ
ejpam-4597	111	3	)	)	PUNCT
ejpam-4597	111	4	if	if	SCONJ
ejpam-4597	111	5	he	he	PRON
ejpam-4597	111	6	=	=	SYM
ejpam-4597	111	7	int(cl(he	int(cl(he	PROPN
ejpam-4597	111	8	)	)	PUNCT
ejpam-4597	111	9	)	)	PUNCT
ejpam-4597	112	1	(	(	PUNCT
ejpam-4597	112	2	resp	resp	NOUN
ejpam-4597	112	3	.	.	PUNCT
ejpam-4597	113	1	he	he	PRON
ejpam-4597	113	2	=	=	SYM
ejpam-4597	113	3	cl(int(he	cl(int(he	PROPN
ejpam-4597	113	4	)	)	PUNCT
ejpam-4597	113	5	)	)	PUNCT
ejpam-4597	113	6	.	.	PUNCT
ejpam-4597	114	1	the	the	DET
ejpam-4597	114	2	family	family	NOUN
ejpam-4597	114	3	of	of	ADP
ejpam-4597	114	4	all	all	DET
ejpam-4597	114	5	fs	fs	ADJ
ejpam-4597	114	6	-	-	ADJ
ejpam-4597	114	7	regular	regular	ADJ
ejpam-4597	114	8	open	open	ADJ
ejpam-4597	114	9	(	(	PUNCT
ejpam-4597	114	10	resp	resp	NOUN
ejpam-4597	114	11	.	.	PUNCT
ejpam-4597	115	1	all	all	DET
ejpam-4597	115	2	fs	fs	ADJ
ejpam-4597	115	3	-	-	PUNCT
ejpam-4597	115	4	regular	regular	ADJ
ejpam-4597	115	5	closed	closed	ADJ
ejpam-4597	115	6	)	)	PUNCT
ejpam-4597	115	7	on	on	ADP
ejpam-4597	115	8	u	u	NOUN
ejpam-4597	115	9	is	be	AUX
ejpam-4597	115	10	denoted	denote	VERB
ejpam-4597	115	11	by	by	ADP
ejpam-4597	115	12	fsro(u	fsro(u	NOUN
ejpam-4597	115	13	)	)	PUNCT
ejpam-4597	115	14	(	(	PUNCT
ejpam-4597	115	15	resp	resp	NOUN
ejpam-4597	115	16	.	.	PUNCT
ejpam-4597	116	1	fsrc(u	fsrc(u	NOUN
ejpam-4597	116	2	)	)	PUNCT
ejpam-4597	116	3	)	)	PUNCT
ejpam-4597	116	4	.	.	PUNCT
ejpam-4597	117	1	s.	s.	PROPN
ejpam-4597	117	2	saleh	saleh	PROPN
ejpam-4597	117	3	,	,	PUNCT
ejpam-4597	117	4	j.	j.	PROPN
ejpam-4597	117	5	al	al	PROPN
ejpam-4597	117	6	-	-	PUNCT
ejpam-4597	117	7	mufarrij	mufarrij	PROPN
ejpam-4597	117	8	/	/	SYM
ejpam-4597	117	9	eur	eur	PROPN
ejpam-4597	117	10	.	.	PUNCT
ejpam-4597	118	1	j.	j.	PROPN
ejpam-4597	118	2	pure	pure	PROPN
ejpam-4597	118	3	appl	appl	PROPN
ejpam-4597	118	4	.	.	PROPN
ejpam-4597	118	5	math	math	PROPN
ejpam-4597	118	6	,	,	PUNCT
ejpam-4597	118	7	16	16	NUM
ejpam-4597	118	8	(	(	PUNCT
ejpam-4597	118	9	1	1	NUM
ejpam-4597	118	10	)	)	PUNCT
ejpam-4597	118	11	(	(	PUNCT
ejpam-4597	118	12	2023	2023	NUM
ejpam-4597	118	13	)	)	PUNCT
ejpam-4597	118	14	,	,	PUNCT
ejpam-4597	118	15	180	180	NUM
ejpam-4597	118	16	-	-	SYM
ejpam-4597	118	17	191	191	NUM
ejpam-4597	118	18	183	183	NUM
ejpam-4597	118	19	definition	definition	NOUN
ejpam-4597	118	20	4	4	NUM
ejpam-4597	118	21	.	.	PUNCT
ejpam-4597	119	1	[	[	X
ejpam-4597	119	2	31	31	NUM
ejpam-4597	119	3	]	]	PUNCT
ejpam-4597	119	4	an	an	DET
ejpam-4597	119	5	fs	fs	ADJ
ejpam-4597	119	6	-	-	PUNCT
ejpam-4597	119	7	set	set	VERB
ejpam-4597	119	8	fe	fe	NOUN
ejpam-4597	119	9	in	in	ADP
ejpam-4597	119	10	(	(	PUNCT
ejpam-4597	119	11	u	u	NOUN
ejpam-4597	119	12	,	,	PUNCT
ejpam-4597	119	13	δ	δ	PROPN
ejpam-4597	119	14	,	,	PUNCT
ejpam-4597	119	15	e	e	NOUN
ejpam-4597	119	16	)	)	PUNCT
ejpam-4597	119	17	is	be	AUX
ejpam-4597	119	18	said	say	VERB
ejpam-4597	119	19	to	to	PART
ejpam-4597	119	20	be	be	AUX
ejpam-4597	119	21	fuzzy	fuzzy	ADJ
ejpam-4597	119	22	soft	soft	ADJ
ejpam-4597	119	23	generalized	generalized	ADJ
ejpam-4597	119	24	closed	close	VERB
ejpam-4597	119	25	(	(	PUNCT
ejpam-4597	119	26	or	or	CCONJ
ejpam-4597	119	27	fsg	fsg	PROPN
ejpam-4597	119	28	-	-	PUNCT
ejpam-4597	119	29	closed	closed	ADJ
ejpam-4597	119	30	)	)	PUNCT
ejpam-4597	119	31	if	if	SCONJ
ejpam-4597	119	32	cl(fe	cl(fe	PROPN
ejpam-4597	119	33	)	)	PUNCT
ejpam-4597	119	34	⊑	⊑	X
ejpam-4597	119	35	he	he	PRON
ejpam-4597	119	36	for	for	ADP
ejpam-4597	119	37	all	all	DET
ejpam-4597	119	38	fe	fe	X
ejpam-4597	119	39	⊑	⊑	X
ejpam-4597	120	1	he	he	PRON
ejpam-4597	120	2	and	and	CCONJ
ejpam-4597	120	3	he	he	PRON
ejpam-4597	120	4	∈	∈	PROPN
ejpam-4597	120	5	fsos(u	fsos(u	PROPN
ejpam-4597	120	6	)	)	PUNCT
ejpam-4597	120	7	.	.	PUNCT
ejpam-4597	121	1	the	the	DET
ejpam-4597	121	2	collection	collection	NOUN
ejpam-4597	121	3	of	of	ADP
ejpam-4597	121	4	all	all	DET
ejpam-4597	121	5	fsg	fsg	PROPN
ejpam-4597	121	6	-	-	PUNCT
ejpam-4597	121	7	closed	close	VERB
ejpam-4597	121	8	sets	set	NOUN
ejpam-4597	121	9	in	in	ADP
ejpam-4597	121	10	(	(	PUNCT
ejpam-4597	121	11	u	u	NOUN
ejpam-4597	121	12	,	,	PUNCT
ejpam-4597	121	13	δ	δ	PROPN
ejpam-4597	121	14	,	,	PUNCT
ejpam-4597	121	15	e	e	NOUN
ejpam-4597	121	16	)	)	PUNCT
ejpam-4597	121	17	is	be	AUX
ejpam-4597	121	18	denoted	denote	VERB
ejpam-4597	121	19	by	by	ADP
ejpam-4597	121	20	fsgcs(u	fsgcs(u	PROPN
ejpam-4597	121	21	)	)	PUNCT
ejpam-4597	121	22	.	.	PUNCT
ejpam-4597	122	1	the	the	DET
ejpam-4597	122	2	complement	complement	NOUN
ejpam-4597	122	3	of	of	ADP
ejpam-4597	122	4	an	an	DET
ejpam-4597	122	5	fsg	fsg	NOUN
ejpam-4597	122	6	-	-	PUNCT
ejpam-4597	122	7	closed	close	VERB
ejpam-4597	122	8	set	set	NOUN
ejpam-4597	122	9	is	be	AUX
ejpam-4597	122	10	called	call	VERB
ejpam-4597	122	11	an	an	DET
ejpam-4597	122	12	fsg	fsg	NOUN
ejpam-4597	122	13	-	-	PUNCT
ejpam-4597	122	14	open	open	ADJ
ejpam-4597	122	15	set	set	NOUN
ejpam-4597	122	16	.	.	PUNCT
ejpam-4597	123	1	note	note	NOUN
ejpam-4597	123	2	.	.	PUNCT
ejpam-4597	124	1	clearly	clearly	ADV
ejpam-4597	124	2	,	,	PUNCT
ejpam-4597	124	3	every	every	DET
ejpam-4597	124	4	fsc	fsc	PROPN
ejpam-4597	124	5	-	-	PUNCT
ejpam-4597	124	6	set	set	NOUN
ejpam-4597	124	7	is	be	AUX
ejpam-4597	124	8	an	an	DET
ejpam-4597	124	9	fsg	fsg	NOUN
ejpam-4597	124	10	-	-	PUNCT
ejpam-4597	124	11	closed	closed	ADJ
ejpam-4597	124	12	set	set	NOUN
ejpam-4597	124	13	.	.	PUNCT
ejpam-4597	125	1	definition	definition	NOUN
ejpam-4597	125	2	5	5	NUM
ejpam-4597	125	3	.	.	PUNCT
ejpam-4597	126	1	[	[	X
ejpam-4597	126	2	28	28	NUM
ejpam-4597	126	3	]	]	X
ejpam-4597	126	4	an	an	DET
ejpam-4597	126	5	fst	fst	NOUN
ejpam-4597	126	6	(	(	PUNCT
ejpam-4597	126	7	u	u	PROPN
ejpam-4597	126	8	,	,	PUNCT
ejpam-4597	126	9	δ	δ	PROPN
ejpam-4597	126	10	,	,	PUNCT
ejpam-4597	126	11	e	e	NOUN
ejpam-4597	126	12	)	)	PUNCT
ejpam-4597	126	13	is	be	AUX
ejpam-4597	126	14	said	say	VERB
ejpam-4597	126	15	to	to	PART
ejpam-4597	126	16	be	be	AUX
ejpam-4597	126	17	:	:	PUNCT
ejpam-4597	126	18	(	(	PUNCT
ejpam-4597	126	19	i	i	NOUN
ejpam-4597	126	20	)	)	PUNCT
ejpam-4597	126	21	fst0	fst0	PROPN
ejpam-4597	126	22	iff	iff	PROPN
ejpam-4597	126	23	for	for	ADP
ejpam-4597	126	24	any	any	DET
ejpam-4597	126	25	xeα	xeα	PROPN
ejpam-4597	126	26	,	,	PUNCT
ejpam-4597	126	27	y	y	PROPN
ejpam-4597	126	28	e	e	PROPN
ejpam-4597	126	29	β	β	PROPN
ejpam-4597	126	30	∈	∈	PROPN
ejpam-4597	126	31	fsp	fsp	PROPN
ejpam-4597	126	32	(	(	PUNCT
ejpam-4597	126	33	u	u	NOUN
ejpam-4597	126	34	)	)	PUNCT
ejpam-4597	126	35	with	with	ADP
ejpam-4597	126	36	xeαq̃y	xeαq̃y	PROPN
ejpam-4597	126	37	e	e	PROPN
ejpam-4597	126	38	β	β	PROPN
ejpam-4597	126	39	implies	imply	VERB
ejpam-4597	126	40	xeαq̃cl(y	xeαq̃cl(y	PROPN
ejpam-4597	126	41	e	e	NOUN
ejpam-4597	126	42	β	β	NOUN
ejpam-4597	126	43	)	)	PUNCT
ejpam-4597	126	44	or	or	CCONJ
ejpam-4597	126	45	cl(xeα)q̃y	cl(xeα)q̃y	NOUN
ejpam-4597	126	46	e	e	X
ejpam-4597	126	47	β	β	X
ejpam-4597	126	48	.	.	PUNCT
ejpam-4597	127	1	(	(	PUNCT
ejpam-4597	127	2	ii	ii	NOUN
ejpam-4597	127	3	)	)	PUNCT
ejpam-4597	127	4	fst1	fst1	PROPN
ejpam-4597	127	5	iff	iff	PROPN
ejpam-4597	127	6	for	for	ADP
ejpam-4597	127	7	any	any	DET
ejpam-4597	127	8	xeα	xeα	PROPN
ejpam-4597	127	9	,	,	PUNCT
ejpam-4597	127	10	y	y	PROPN
ejpam-4597	127	11	e	e	PROPN
ejpam-4597	127	12	β	β	PROPN
ejpam-4597	127	13	∈	∈	PROPN
ejpam-4597	127	14	fsp	fsp	PROPN
ejpam-4597	127	15	(	(	PUNCT
ejpam-4597	127	16	u	u	NOUN
ejpam-4597	127	17	)	)	PUNCT
ejpam-4597	127	18	with	with	ADP
ejpam-4597	127	19	xeαq̃y	xeαq̃y	PROPN
ejpam-4597	127	20	e	e	PROPN
ejpam-4597	127	21	β	β	PROPN
ejpam-4597	127	22	implies	imply	VERB
ejpam-4597	127	23	xeαq̃cl(y	xeαq̃cl(y	PROPN
ejpam-4597	127	24	e	e	NOUN
ejpam-4597	127	25	β	β	NOUN
ejpam-4597	127	26	)	)	PUNCT
ejpam-4597	127	27	and	and	CCONJ
ejpam-4597	127	28	cl(xeα)q̃y	cl(xeα)q̃y	NOUN
ejpam-4597	127	29	e	e	NOUN
ejpam-4597	127	30	β	β	X
ejpam-4597	127	31	.	.	PUNCT
ejpam-4597	128	1	(	(	PUNCT
ejpam-4597	128	2	iii	iii	NOUN
ejpam-4597	128	3	)	)	PUNCT
ejpam-4597	128	4	fst2	fst2	PROPN
ejpam-4597	128	5	iff	iff	NOUN
ejpam-4597	128	6	for	for	ADP
ejpam-4597	128	7	any	any	DET
ejpam-4597	128	8	xeα	xeα	NOUN
ejpam-4597	128	9	,	,	PUNCT
ejpam-4597	128	10	yeβ	yeβ	PROPN
ejpam-4597	128	11	∈	∈	PROPN
ejpam-4597	128	12	fsp	fsp	NOUN
ejpam-4597	128	13	(	(	PUNCT
ejpam-4597	128	14	u	u	NOUN
ejpam-4597	128	15	)	)	PUNCT
ejpam-4597	128	16	with	with	ADP
ejpam-4597	128	17	xeαq̃y	xeαq̃y	PROPN
ejpam-4597	128	18	e	e	PROPN
ejpam-4597	128	19	β	β	PROPN
ejpam-4597	128	20	,	,	PUNCT
ejpam-4597	128	21	there	there	PRON
ejpam-4597	128	22	are	be	VERB
ejpam-4597	128	23	oxe	oxe	PROPN
ejpam-4597	128	24	α	α	NOUN
ejpam-4597	128	25	,	,	PUNCT
ejpam-4597	128	26	oyeβ	oyeβ	NOUN
ejpam-4597	128	27	∈	∈	PROPN
ejpam-4597	128	28	δ	δ	NOUN
ejpam-4597	128	29	such	such	ADJ
ejpam-4597	128	30	that	that	SCONJ
ejpam-4597	128	31	oxe	oxe	PROPN
ejpam-4597	128	32	α	α	DET
ejpam-4597	128	33	q̃oyeβ	q̃oyeβ	PROPN
ejpam-4597	128	34	.	.	PUNCT
ejpam-4597	129	1	definition	definition	NOUN
ejpam-4597	129	2	6	6	NUM
ejpam-4597	129	3	.	.	PUNCT
ejpam-4597	130	1	[	[	X
ejpam-4597	130	2	28	28	NUM
ejpam-4597	130	3	]	]	X
ejpam-4597	130	4	an	an	DET
ejpam-4597	130	5	fsts	fst	NOUN
ejpam-4597	130	6	(	(	PUNCT
ejpam-4597	130	7	u	u	NOUN
ejpam-4597	130	8	,	,	PUNCT
ejpam-4597	130	9	δ	δ	PROPN
ejpam-4597	130	10	,	,	PUNCT
ejpam-4597	130	11	e	e	NOUN
ejpam-4597	130	12	)	)	PUNCT
ejpam-4597	130	13	is	be	AUX
ejpam-4597	130	14	said	say	VERB
ejpam-4597	130	15	to	to	PART
ejpam-4597	130	16	be	be	AUX
ejpam-4597	130	17	:	:	PUNCT
ejpam-4597	130	18	(	(	PUNCT
ejpam-4597	130	19	i	i	NOUN
ejpam-4597	130	20	)	)	PUNCT
ejpam-4597	130	21	fsr2(or	fsr2(or	ADV
ejpam-4597	130	22	fs	fs	PROPN
ejpam-4597	130	23	-	-	ADJ
ejpam-4597	130	24	regular	regular	ADJ
ejpam-4597	130	25	)	)	PUNCT
ejpam-4597	130	26	iff	iff	NOUN
ejpam-4597	130	27	for	for	ADP
ejpam-4597	130	28	any	any	DET
ejpam-4597	130	29	xeα	xeα	PROPN
ejpam-4597	130	30	∈	∈	PROPN
ejpam-4597	130	31	fsp	fsp	NOUN
ejpam-4597	130	32	(	(	PUNCT
ejpam-4597	130	33	u	u	NOUN
ejpam-4597	130	34	)	)	PUNCT
ejpam-4597	130	35	with	with	ADP
ejpam-4597	130	36	xeαq̃fe	xeαq̃fe	PROPN
ejpam-4597	130	37	,	,	PUNCT
ejpam-4597	130	38	fe	fe	X
ejpam-4597	130	39	is	be	AUX
ejpam-4597	130	40	an	an	DET
ejpam-4597	130	41	fsc	fsc	PROPN
ejpam-4597	130	42	-	-	PUNCT
ejpam-4597	130	43	set	set	NOUN
ejpam-4597	130	44	,	,	PUNCT
ejpam-4597	130	45	there	there	PRON
ejpam-4597	130	46	are	be	VERB
ejpam-4597	130	47	oxe	oxe	PROPN
ejpam-4597	130	48	α	α	NOUN
ejpam-4597	130	49	,	,	PUNCT
ejpam-4597	130	50	ofe	ofe	INTJ
ejpam-4597	130	51	∈	∈	PROPN
ejpam-4597	130	52	δ	δ	PROPN
ejpam-4597	130	53	such	such	ADJ
ejpam-4597	130	54	that	that	SCONJ
ejpam-4597	130	55	oxe	oxe	PRON
ejpam-4597	130	56	α	α	PRON
ejpam-4597	130	57	q̃ofe	q̃ofe	NOUN
ejpam-4597	130	58	.	.	PUNCT
ejpam-4597	131	1	(	(	PUNCT
ejpam-4597	131	2	ii	ii	NOUN
ejpam-4597	131	3	)	)	PUNCT
ejpam-4597	131	4	fsr3	fsr3	PROPN
ejpam-4597	131	5	(	(	PUNCT
ejpam-4597	131	6	or	or	CCONJ
ejpam-4597	131	7	fs	fs	ADJ
ejpam-4597	131	8	-	-	ADJ
ejpam-4597	131	9	normal	normal	ADJ
ejpam-4597	131	10	)	)	PUNCT
ejpam-4597	131	11	iff	iff	NOUN
ejpam-4597	131	12	for	for	ADP
ejpam-4597	131	13	any	any	DET
ejpam-4597	131	14	fsc	fsc	NOUN
ejpam-4597	131	15	-	-	PUNCT
ejpam-4597	131	16	sets	set	NOUN
ejpam-4597	131	17	fe	fe	X
ejpam-4597	131	18	,	,	PUNCT
ejpam-4597	131	19	ge	ge	PROPN
ejpam-4597	131	20	with	with	ADP
ejpam-4597	131	21	fe	fe	PROPN
ejpam-4597	131	22	q̃ge	q̃ge	PROPN
ejpam-4597	131	23	,	,	PUNCT
ejpam-4597	131	24	there	there	PRON
ejpam-4597	131	25	are	be	VERB
ejpam-4597	131	26	ofe	ofe	ADJ
ejpam-4597	131	27	,	,	PUNCT
ejpam-4597	131	28	oge	oge	PROPN
ejpam-4597	131	29	∈	∈	PROPN
ejpam-4597	131	30	δ	δ	PROPN
ejpam-4597	131	31	such	such	ADJ
ejpam-4597	131	32	that	that	SCONJ
ejpam-4597	131	33	ofe	ofe	ADJ
ejpam-4597	131	34	q̃oge	q̃oge	NOUN
ejpam-4597	131	35	.	.	PUNCT
ejpam-4597	132	1	(	(	PUNCT
ejpam-4597	132	2	iii	iii	NOUN
ejpam-4597	132	3	)	)	PUNCT
ejpam-4597	132	4	fst3	fst3	PROPN
ejpam-4597	132	5	(	(	PUNCT
ejpam-4597	132	6	resp	resp	NOUN
ejpam-4597	132	7	.	.	PUNCT
ejpam-4597	133	1	fst4	fst4	PROPN
ejpam-4597	133	2	)	)	PUNCT
ejpam-4597	134	1	iff	iff	VERB
ejpam-4597	134	2	it	it	PRON
ejpam-4597	134	3	is	be	AUX
ejpam-4597	134	4	fsr2	fsr2	PROPN
ejpam-4597	134	5	(	(	PUNCT
ejpam-4597	134	6	resp	resp	NOUN
ejpam-4597	134	7	.	.	PUNCT
ejpam-4597	135	1	fsr3	fsr3	PROPN
ejpam-4597	135	2	)	)	PUNCT
ejpam-4597	135	3	and	and	CCONJ
ejpam-4597	135	4	fst1	fst1	NOUN
ejpam-4597	135	5	.	.	PUNCT
ejpam-4597	136	1	theorem	theorem	NOUN
ejpam-4597	136	2	1	1	NUM
ejpam-4597	136	3	.	.	PUNCT
ejpam-4597	137	1	[	[	X
ejpam-4597	137	2	28	28	NUM
ejpam-4597	137	3	]	]	X
ejpam-4597	137	4	fst4	fst4	NOUN
ejpam-4597	137	5	⇒	⇒	NOUN
ejpam-4597	137	6	fst3	fst3	PROPN
ejpam-4597	137	7	⇒	⇒	PROPN
ejpam-4597	137	8	fst2	fst2	PROPN
ejpam-4597	137	9	⇒	⇒	PROPN
ejpam-4597	137	10	fst1	fst1	PROPN
ejpam-4597	137	11	⇒	⇒	PROPN
ejpam-4597	137	12	fst0	fst0	PROPN
ejpam-4597	137	13	.	.	PUNCT
ejpam-4597	138	1	definition	definition	NOUN
ejpam-4597	138	2	7	7	NUM
ejpam-4597	138	3	.	.	PUNCT
ejpam-4597	139	1	[	[	X
ejpam-4597	139	2	29	29	NUM
ejpam-4597	139	3	]	]	X
ejpam-4597	139	4	let	let	AUX
ejpam-4597	139	5	(	(	PUNCT
ejpam-4597	139	6	u	u	NOUN
ejpam-4597	139	7	,	,	PUNCT
ejpam-4597	139	8	τ	τ	X
ejpam-4597	139	9	)	)	PUNCT
ejpam-4597	139	10	be	be	VERB
ejpam-4597	139	11	a	a	DET
ejpam-4597	139	12	topological	topological	ADJ
ejpam-4597	139	13	space	space	NOUN
ejpam-4597	139	14	.	.	PUNCT
ejpam-4597	140	1	the	the	DET
ejpam-4597	140	2	family	family	NOUN
ejpam-4597	140	3	δ	δ	PROPN
ejpam-4597	140	4	=	=	PRON
ejpam-4597	140	5	{	{	PUNCT
ejpam-4597	140	6	χ̃a	χ̃a	X
ejpam-4597	140	7	:	:	PUNCT
ejpam-4597	140	8	a	a	DET
ejpam-4597	140	9	∈	∈	PROPN
ejpam-4597	140	10	τ	τ	PROPN
ejpam-4597	140	11	}	}	PUNCT
ejpam-4597	140	12	defines	define	VERB
ejpam-4597	140	13	an	an	DET
ejpam-4597	140	14	fst	fst	NOUN
ejpam-4597	140	15	on	on	ADP
ejpam-4597	140	16	u	u	NOUN
ejpam-4597	140	17	induced	induce	VERB
ejpam-4597	140	18	by	by	ADP
ejpam-4597	140	19	τ	τ	PROPN
ejpam-4597	140	20	.	.	PROPN
ejpam-4597	140	21	definition	definition	NOUN
ejpam-4597	140	22	8	8	NUM
ejpam-4597	140	23	.	.	PUNCT
ejpam-4597	141	1	[	[	X
ejpam-4597	141	2	31	31	NUM
ejpam-4597	141	3	]	]	PUNCT
ejpam-4597	141	4	an	an	DET
ejpam-4597	141	5	fs	fs	NOUN
ejpam-4597	141	6	-	-	PUNCT
ejpam-4597	141	7	map	map	NOUN
ejpam-4597	141	8	fup	fup	NOUN
ejpam-4597	141	9	:	:	PUNCT
ejpam-4597	141	10	(	(	PUNCT
ejpam-4597	141	11	u	u	NOUN
ejpam-4597	141	12	,	,	PUNCT
ejpam-4597	141	13	δ	δ	PROPN
ejpam-4597	141	14	,	,	PUNCT
ejpam-4597	141	15	e	e	NOUN
ejpam-4597	141	16	)	)	PUNCT
ejpam-4597	141	17	−→	−→	NOUN
ejpam-4597	141	18	(	(	PUNCT
ejpam-4597	141	19	v	v	NOUN
ejpam-4597	141	20	,	,	PUNCT
ejpam-4597	141	21	ϑ,k	ϑ,k	NOUN
ejpam-4597	141	22	)	)	PUNCT
ejpam-4597	141	23	is	be	AUX
ejpam-4597	141	24	said	say	VERB
ejpam-4597	141	25	to	to	PART
ejpam-4597	141	26	be	be	AUX
ejpam-4597	141	27	:	:	PUNCT
ejpam-4597	141	28	(	(	PUNCT
ejpam-4597	141	29	i	i	NOUN
ejpam-4597	141	30	)	)	PUNCT
ejpam-4597	141	31	fsg	fsg	NOUN
ejpam-4597	141	32	-	-	ADJ
ejpam-4597	141	33	continuous	continuous	ADJ
ejpam-4597	141	34	if	if	SCONJ
ejpam-4597	141	35	f−1	f−1	PROPN
ejpam-4597	141	36	up	up	ADP
ejpam-4597	141	37	(	(	PUNCT
ejpam-4597	141	38	he	he	PRON
ejpam-4597	141	39	)	)	PUNCT
ejpam-4597	141	40	∈	∈	PROPN
ejpam-4597	141	41	fsgcs(u	fsgcs(u	PROPN
ejpam-4597	141	42	)	)	PUNCT
ejpam-4597	141	43	for	for	ADP
ejpam-4597	141	44	any	any	DET
ejpam-4597	141	45	he	he	PRON
ejpam-4597	141	46	∈	∈	PROPN
ejpam-4597	141	47	fscs(v	fscs(v	PROPN
ejpam-4597	141	48	)	)	PUNCT
ejpam-4597	141	49	.	.	PUNCT
ejpam-4597	142	1	(	(	PUNCT
ejpam-4597	142	2	ii	ii	NOUN
ejpam-4597	142	3	)	)	PUNCT
ejpam-4597	142	4	fsgc	fsgc	VERB
ejpam-4597	142	5	-	-	PUNCT
ejpam-4597	142	6	irresolute	irresolute	ADJ
ejpam-4597	142	7	if	if	SCONJ
ejpam-4597	142	8	f−1	f−1	PROPN
ejpam-4597	142	9	up	up	ADP
ejpam-4597	142	10	(	(	PUNCT
ejpam-4597	142	11	ge	ge	PROPN
ejpam-4597	142	12	)	)	PUNCT
ejpam-4597	142	13	∈	∈	PROPN
ejpam-4597	142	14	fsgcs(u	fsgcs(u	PROPN
ejpam-4597	142	15	)	)	PUNCT
ejpam-4597	142	16	for	for	ADP
ejpam-4597	142	17	any	any	DET
ejpam-4597	142	18	ge	ge	PROPN
ejpam-4597	142	19	∈	∈	PROPN
ejpam-4597	142	20	fsgcs(v	fsgcs(v	PROPN
ejpam-4597	142	21	)	)	PUNCT
ejpam-4597	142	22	.	.	PUNCT
ejpam-4597	143	1	note	note	VERB
ejpam-4597	143	2	.	.	PUNCT
ejpam-4597	144	1	clearly	clearly	ADV
ejpam-4597	144	2	,	,	PUNCT
ejpam-4597	144	3	every	every	DET
ejpam-4597	144	4	fsgc	fsgc	VERB
ejpam-4597	144	5	-	-	PUNCT
ejpam-4597	144	6	irresolute	irresolute	ADJ
ejpam-4597	144	7	map	map	NOUN
ejpam-4597	144	8	is	be	AUX
ejpam-4597	144	9	fsg	fsg	NOUN
ejpam-4597	144	10	-	-	PUNCT
ejpam-4597	144	11	continuous	continuous	ADJ
ejpam-4597	144	12	.	.	PUNCT
ejpam-4597	145	1	2	2	X
ejpam-4597	145	2	.	.	NOUN
ejpam-4597	145	3	fuzzy	fuzzy	ADJ
ejpam-4597	145	4	soft	soft	ADJ
ejpam-4597	145	5	g	g	NOUN
ejpam-4597	145	6	-	-	PUNCT
ejpam-4597	145	7	regular	regular	ADJ
ejpam-4597	145	8	spaces	space	NOUN
ejpam-4597	145	9	definition	definition	NOUN
ejpam-4597	145	10	9	9	NUM
ejpam-4597	145	11	.	.	PUNCT
ejpam-4597	146	1	an	an	DET
ejpam-4597	146	2	fsts	fst	NOUN
ejpam-4597	146	3	(	(	PUNCT
ejpam-4597	146	4	u	u	NOUN
ejpam-4597	146	5	,	,	PUNCT
ejpam-4597	146	6	δ	δ	PROPN
ejpam-4597	146	7	,	,	PUNCT
ejpam-4597	146	8	e	e	NOUN
ejpam-4597	146	9	)	)	PUNCT
ejpam-4597	146	10	is	be	AUX
ejpam-4597	146	11	said	say	VERB
ejpam-4597	146	12	to	to	PART
ejpam-4597	146	13	be	be	AUX
ejpam-4597	146	14	:	:	PUNCT
ejpam-4597	146	15	(	(	PUNCT
ejpam-4597	146	16	i	i	NOUN
ejpam-4597	146	17	)	)	PUNCT
ejpam-4597	146	18	fst	fst	NOUN
ejpam-4597	146	19	1	1	NUM
ejpam-4597	146	20	2	2	NUM
ejpam-4597	146	21	iff	iff	VERB
ejpam-4597	146	22	any	any	DET
ejpam-4597	146	23	fsg	fsg	PROPN
ejpam-4597	146	24	-	-	PUNCT
ejpam-4597	146	25	closed	closed	ADJ
ejpam-4597	146	26	set	set	NOUN
ejpam-4597	146	27	on	on	ADP
ejpam-4597	146	28	u	u	NOUN
ejpam-4597	146	29	is	be	AUX
ejpam-4597	146	30	an	an	DET
ejpam-4597	146	31	fsc	fsc	PROPN
ejpam-4597	146	32	-	-	PUNCT
ejpam-4597	146	33	set	set	NOUN
ejpam-4597	146	34	.	.	PUNCT
ejpam-4597	147	1	(	(	PUNCT
ejpam-4597	147	2	ii	ii	NOUN
ejpam-4597	147	3	)	)	PUNCT
ejpam-4597	147	4	fst2	fst2	ADJ
ejpam-4597	147	5	1	1	NUM
ejpam-4597	147	6	2	2	NUM
ejpam-4597	147	7	iff	iff	NOUN
ejpam-4597	147	8	for	for	ADP
ejpam-4597	147	9	any	any	DET
ejpam-4597	147	10	xeα	xeα	NOUN
ejpam-4597	147	11	,	,	PUNCT
ejpam-4597	147	12	yeβ	yeβ	PROPN
ejpam-4597	147	13	∈	∈	PROPN
ejpam-4597	147	14	fsp	fsp	NOUN
ejpam-4597	147	15	(	(	PUNCT
ejpam-4597	147	16	u	u	NOUN
ejpam-4597	147	17	)	)	PUNCT
ejpam-4597	147	18	with	with	ADP
ejpam-4597	147	19	xeαq̃y	xeαq̃y	PROPN
ejpam-4597	147	20	e	e	PROPN
ejpam-4597	147	21	β	β	PROPN
ejpam-4597	147	22	,	,	PUNCT
ejpam-4597	147	23	there	there	PRON
ejpam-4597	147	24	are	be	VERB
ejpam-4597	147	25	oxe	oxe	PROPN
ejpam-4597	147	26	α	α	NOUN
ejpam-4597	147	27	,	,	PUNCT
ejpam-4597	147	28	oyeβ	oyeβ	NOUN
ejpam-4597	147	29	∈	∈	PROPN
ejpam-4597	147	30	δ	δ	PROPN
ejpam-4597	147	31	such	such	ADJ
ejpam-4597	147	32	that	that	SCONJ
ejpam-4597	147	33	cloxe	cloxe	VERB
ejpam-4597	147	34	α	α	X
ejpam-4597	147	35	q̃cloyeβ	q̃cloyeβ	NOUN
ejpam-4597	147	36	.	.	PUNCT
ejpam-4597	148	1	definition	definition	NOUN
ejpam-4597	148	2	10	10	NUM
ejpam-4597	148	3	.	.	PUNCT
ejpam-4597	149	1	an	an	DET
ejpam-4597	149	2	fsts(u	fsts(u	PROPN
ejpam-4597	149	3	,	,	PUNCT
ejpam-4597	149	4	δ	δ	PROPN
ejpam-4597	149	5	,	,	PUNCT
ejpam-4597	149	6	e	e	NOUN
ejpam-4597	149	7	)	)	PUNCT
ejpam-4597	149	8	is	be	AUX
ejpam-4597	149	9	said	say	VERB
ejpam-4597	149	10	to	to	PART
ejpam-4597	149	11	be	be	AUX
ejpam-4597	149	12	fsg	fsg	NOUN
ejpam-4597	149	13	-	-	ADJ
ejpam-4597	149	14	regular	regular	ADJ
ejpam-4597	149	15	(	(	PUNCT
ejpam-4597	149	16	or	or	CCONJ
ejpam-4597	149	17	fs	fs	PROPN
ejpam-4597	149	18	-	-	PUNCT
ejpam-4597	149	19	gr2	gr2	NOUN
ejpam-4597	149	20	)	)	PUNCT
ejpam-4597	149	21	if	if	SCONJ
ejpam-4597	149	22	for	for	ADP
ejpam-4597	149	23	any	any	DET
ejpam-4597	149	24	fsg	fsg	NOUN
ejpam-4597	149	25	-	-	PUNCT
ejpam-4597	149	26	closed	close	VERB
ejpam-4597	149	27	set	set	NOUN
ejpam-4597	149	28	he	he	PRON
ejpam-4597	149	29	and	and	CCONJ
ejpam-4597	149	30	any	any	DET
ejpam-4597	149	31	fs	fs	NOUN
ejpam-4597	149	32	-	-	PUNCT
ejpam-4597	149	33	point	point	NOUN
ejpam-4597	149	34	xeα	xeα	NOUN
ejpam-4597	149	35	with	with	ADP
ejpam-4597	149	36	xeαq̃he	xeαq̃he	PROPN
ejpam-4597	149	37	,	,	PUNCT
ejpam-4597	149	38	there	there	PRON
ejpam-4597	149	39	are	be	VERB
ejpam-4597	149	40	oxe	oxe	PROPN
ejpam-4597	149	41	α	α	NOUN
ejpam-4597	149	42	,	,	PUNCT
ejpam-4597	149	43	ohe	ohe	PROPN
ejpam-4597	149	44	∈δ	∈δ	VERB
ejpam-4597	149	45	such	such	ADJ
ejpam-4597	149	46	that	that	SCONJ
ejpam-4597	149	47	oxe	oxe	PRON
ejpam-4597	149	48	α	α	NOUN
ejpam-4597	149	49	q̃ohe	q̃ohe	NOUN
ejpam-4597	149	50	.	.	PUNCT
ejpam-4597	150	1	s.	s.	PROPN
ejpam-4597	150	2	saleh	saleh	PROPN
ejpam-4597	150	3	,	,	PUNCT
ejpam-4597	150	4	j.	j.	PROPN
ejpam-4597	150	5	al	al	PROPN
ejpam-4597	150	6	-	-	PUNCT
ejpam-4597	150	7	mufarrij	mufarrij	PROPN
ejpam-4597	150	8	/	/	SYM
ejpam-4597	150	9	eur	eur	PROPN
ejpam-4597	150	10	.	.	PUNCT
ejpam-4597	151	1	j.	j.	PROPN
ejpam-4597	151	2	pure	pure	PROPN
ejpam-4597	151	3	appl	appl	PROPN
ejpam-4597	151	4	.	.	PROPN
ejpam-4597	151	5	math	math	PROPN
ejpam-4597	151	6	,	,	PUNCT
ejpam-4597	151	7	16	16	NUM
ejpam-4597	151	8	(	(	PUNCT
ejpam-4597	151	9	1	1	NUM
ejpam-4597	151	10	)	)	PUNCT
ejpam-4597	151	11	(	(	PUNCT
ejpam-4597	151	12	2023	2023	NUM
ejpam-4597	151	13	)	)	PUNCT
ejpam-4597	151	14	,	,	PUNCT
ejpam-4597	151	15	180	180	NUM
ejpam-4597	151	16	-	-	SYM
ejpam-4597	151	17	191	191	NUM
ejpam-4597	151	18	184	184	NUM
ejpam-4597	151	19	remark	remark	NOUN
ejpam-4597	151	20	1	1	NUM
ejpam-4597	151	21	.	.	PUNCT
ejpam-4597	152	1	clearly	clearly	ADV
ejpam-4597	152	2	,	,	PUNCT
ejpam-4597	152	3	every	every	DET
ejpam-4597	152	4	fs	fs	ADJ
ejpam-4597	152	5	-	-	PUNCT
ejpam-4597	152	6	gr2	gr2	PROPN
ejpam-4597	152	7	space	space	NOUN
ejpam-4597	152	8	is	be	AUX
ejpam-4597	152	9	fsr2	fsr2	PROPN
ejpam-4597	152	10	.	.	PUNCT
ejpam-4597	153	1	the	the	DET
ejpam-4597	153	2	next	next	ADJ
ejpam-4597	153	3	example	example	NOUN
ejpam-4597	153	4	shows	show	VERB
ejpam-4597	153	5	that	that	SCONJ
ejpam-4597	153	6	the	the	DET
ejpam-4597	153	7	converse	converse	NOUN
ejpam-4597	153	8	is	be	AUX
ejpam-4597	153	9	not	not	PART
ejpam-4597	153	10	necessarily	necessarily	ADV
ejpam-4597	153	11	true	true	ADJ
ejpam-4597	153	12	.	.	PUNCT
ejpam-4597	154	1	example	example	NOUN
ejpam-4597	155	1	1	1	NUM
ejpam-4597	155	2	.	.	PUNCT
ejpam-4597	155	3	let	let	VERB
ejpam-4597	155	4	u	u	PRON
ejpam-4597	155	5	=	=	X
ejpam-4597	155	6	{	{	PUNCT
ejpam-4597	155	7	a	a	PRON
ejpam-4597	155	8	,	,	PUNCT
ejpam-4597	155	9	b	b	NOUN
ejpam-4597	155	10	}	}	PUNCT
ejpam-4597	155	11	,	,	PUNCT
ejpam-4597	155	12	e	e	X
ejpam-4597	155	13	=	=	PUNCT
ejpam-4597	155	14	{	{	PUNCT
ejpam-4597	155	15	e	e	PROPN
ejpam-4597	155	16	,	,	PUNCT
ejpam-4597	155	17	t	t	PROPN
ejpam-4597	155	18	}	}	PUNCT
ejpam-4597	155	19	,	,	PUNCT
ejpam-4597	155	20	and	and	CCONJ
ejpam-4597	155	21	δ	δ	PROPN
ejpam-4597	155	22	=	=	SYM
ejpam-4597	155	23	{	{	PUNCT
ejpam-4597	155	24	0e	0e	NOUN
ejpam-4597	155	25	,	,	PUNCT
ejpam-4597	155	26	1e	1e	PROPN
ejpam-4597	155	27	,	,	PUNCT
ejpam-4597	155	28	fe	fe	X
ejpam-4597	155	29	=	=	PUNCT
ejpam-4597	155	30	{	{	PUNCT
ejpam-4597	155	31	(	(	PUNCT
ejpam-4597	155	32	e	e	NOUN
ejpam-4597	155	33	,	,	PUNCT
ejpam-4597	155	34	{	{	PUNCT
ejpam-4597	155	35	a0.5	a0.5	VERB
ejpam-4597	155	36	,	,	PUNCT
ejpam-4597	155	37	b0.3	b0.3	NOUN
ejpam-4597	155	38	}	}	PUNCT
ejpam-4597	155	39	)	)	PUNCT
ejpam-4597	155	40	,	,	PUNCT
ejpam-4597	155	41	(	(	PUNCT
ejpam-4597	155	42	t	t	NOUN
ejpam-4597	155	43	,	,	PUNCT
ejpam-4597	155	44	{	{	PUNCT
ejpam-4597	155	45	a0.5	a0.5	VERB
ejpam-4597	155	46	,	,	PUNCT
ejpam-4597	155	47	b0.7	b0.7	VERB
ejpam-4597	155	48	}	}	PUNCT
ejpam-4597	155	49	)	)	PUNCT
ejpam-4597	155	50	}	}	PUNCT
ejpam-4597	155	51	,	,	PUNCT
ejpam-4597	155	52	ge	ge	PROPN
ejpam-4597	155	53	=	=	PRON
ejpam-4597	155	54	{	{	PUNCT
ejpam-4597	155	55	(	(	PUNCT
ejpam-4597	155	56	e	e	NOUN
ejpam-4597	155	57	,	,	PUNCT
ejpam-4597	155	58	{	{	PUNCT
ejpam-4597	155	59	a0.5	a0.5	VERB
ejpam-4597	155	60	,	,	PUNCT
ejpam-4597	155	61	b0.3	b0.3	NOUN
ejpam-4597	155	62	}	}	PUNCT
ejpam-4597	155	63	)	)	PUNCT
ejpam-4597	155	64	,	,	PUNCT
ejpam-4597	155	65	(	(	PUNCT
ejpam-4597	155	66	t	t	NOUN
ejpam-4597	155	67	,	,	PUNCT
ejpam-4597	155	68	{	{	PUNCT
ejpam-4597	155	69	a0.5	a0.5	VERB
ejpam-4597	155	70	,	,	PUNCT
ejpam-4597	155	71	b0.7	b0.7	VERB
ejpam-4597	155	72	}	}	PUNCT
ejpam-4597	155	73	)	)	PUNCT
ejpam-4597	155	74	}	}	PUNCT
ejpam-4597	155	75	}	}	PUNCT
ejpam-4597	155	76	,	,	PUNCT
ejpam-4597	155	77	then	then	ADV
ejpam-4597	155	78	δ	δ	PROPN
ejpam-4597	155	79	is	be	AUX
ejpam-4597	155	80	fst	fst	NOUN
ejpam-4597	155	81	on	on	ADP
ejpam-4597	155	82	u	u	PROPN
ejpam-4597	155	83	.	.	PUNCT
ejpam-4597	156	1	one	one	PRON
ejpam-4597	156	2	can	can	AUX
ejpam-4597	156	3	easy	easy	VERB
ejpam-4597	156	4	to	to	PART
ejpam-4597	156	5	verify	verify	VERB
ejpam-4597	156	6	that	that	SCONJ
ejpam-4597	156	7	(	(	PUNCT
ejpam-4597	156	8	u	u	NOUN
ejpam-4597	156	9	,	,	PUNCT
ejpam-4597	156	10	δ	δ	PROPN
ejpam-4597	156	11	,	,	PUNCT
ejpam-4597	156	12	e	e	NOUN
ejpam-4597	156	13	)	)	PUNCT
ejpam-4597	156	14	is	be	AUX
ejpam-4597	156	15	fsr2	fsr2	PROPN
ejpam-4597	156	16	but	but	CCONJ
ejpam-4597	156	17	not	not	PART
ejpam-4597	156	18	fs	fs	PROPN
ejpam-4597	156	19	-	-	PUNCT
ejpam-4597	156	20	gr2	gr2	NOUN
ejpam-4597	156	21	.	.	PUNCT
ejpam-4597	157	1	theorem	theorem	NOUN
ejpam-4597	157	2	2	2	NUM
ejpam-4597	157	3	.	.	PUNCT
ejpam-4597	158	1	an	an	DET
ejpam-4597	158	2	fsts	fst	NOUN
ejpam-4597	158	3	(	(	PUNCT
ejpam-4597	158	4	u	u	NOUN
ejpam-4597	158	5	,	,	PUNCT
ejpam-4597	158	6	δ	δ	PROPN
ejpam-4597	158	7	,	,	PUNCT
ejpam-4597	158	8	e	e	NOUN
ejpam-4597	158	9	)	)	PUNCT
ejpam-4597	158	10	is	be	AUX
ejpam-4597	158	11	fs	fs	X
ejpam-4597	158	12	gr2	gr2	PROPN
ejpam-4597	158	13	if	if	SCONJ
ejpam-4597	159	1	and	and	CCONJ
ejpam-4597	159	2	only	only	ADV
ejpam-4597	159	3	if	if	SCONJ
ejpam-4597	159	4	it	it	PRON
ejpam-4597	159	5	is	be	AUX
ejpam-4597	159	6	fsr2	fsr2	PROPN
ejpam-4597	159	7	and	and	CCONJ
ejpam-4597	159	8	fst	fst	PROPN
ejpam-4597	159	9	1	1	NUM
ejpam-4597	159	10	2	2	NUM
ejpam-4597	159	11	.	.	PUNCT
ejpam-4597	160	1	proof	proof	NOUN
ejpam-4597	160	2	.	.	PUNCT
ejpam-4597	161	1	if	if	SCONJ
ejpam-4597	161	2	(	(	PUNCT
ejpam-4597	161	3	u	u	NOUN
ejpam-4597	161	4	,	,	PUNCT
ejpam-4597	161	5	δ	δ	PROPN
ejpam-4597	161	6	,	,	PUNCT
ejpam-4597	161	7	e	e	NOUN
ejpam-4597	161	8	)	)	PUNCT
ejpam-4597	161	9	is	be	AUX
ejpam-4597	161	10	fs	fs	PROPN
ejpam-4597	161	11	-	-	PUNCT
ejpam-4597	161	12	gr2	gr2	NOUN
ejpam-4597	161	13	,	,	PUNCT
ejpam-4597	161	14	then	then	ADV
ejpam-4597	161	15	by	by	ADP
ejpam-4597	161	16	remark	remark	NOUN
ejpam-4597	161	17	1	1	NUM
ejpam-4597	161	18	it	it	PRON
ejpam-4597	161	19	is	be	AUX
ejpam-4597	161	20	fsr2	fsr2	PROPN
ejpam-4597	161	21	.	.	PUNCT
ejpam-4597	162	1	for	for	ADP
ejpam-4597	162	2	any	any	DET
ejpam-4597	162	3	fsg	fsg	PROPN
ejpam-4597	162	4	-	-	PUNCT
ejpam-4597	162	5	closed	close	VERB
ejpam-4597	162	6	set	set	VERB
ejpam-4597	162	7	fe	fe	NOUN
ejpam-4597	162	8	and	and	CCONJ
ejpam-4597	162	9	any	any	DET
ejpam-4597	162	10	fs	fs	ADJ
ejpam-4597	162	11	-	-	PUNCT
ejpam-4597	162	12	point	point	NOUN
ejpam-4597	162	13	xeα	xeα	NOUN
ejpam-4597	162	14	with	with	ADP
ejpam-4597	162	15	xeαq̃fe	xeαq̃fe	PROPN
ejpam-4597	162	16	i.e.	i.e.	X
ejpam-4597	162	17	xeα∈̃fc	xeα∈̃fc	PUNCT
ejpam-4597	162	18	e	e	X
ejpam-4597	162	19	,	,	PUNCT
ejpam-4597	162	20	there	there	PRON
ejpam-4597	162	21	are	be	VERB
ejpam-4597	162	22	oxe	oxe	PROPN
ejpam-4597	162	23	α	α	NOUN
ejpam-4597	162	24	,	,	PUNCT
ejpam-4597	162	25	ofe∈δ	ofe∈δ	VERB
ejpam-4597	162	26	such	such	ADJ
ejpam-4597	162	27	that	that	SCONJ
ejpam-4597	162	28	oxe	oxe	PRON
ejpam-4597	162	29	α	α	PRON
ejpam-4597	162	30	q̃ofe	q̃ofe	NOUN
ejpam-4597	162	31	=	=	PRON
ejpam-4597	162	32	⇒	⇒	VERB
ejpam-4597	162	33	oxe	oxe	NUM
ejpam-4597	162	34	α	α	NOUN
ejpam-4597	162	35	q̃fe	q̃fe	NOUN
ejpam-4597	162	36	=	=	NOUN
ejpam-4597	162	37	⇒	⇒	NOUN
ejpam-4597	163	1	xeαq̃cl	xeαq̃cl	PROPN
ejpam-4597	163	2	(	(	PUNCT
ejpam-4597	163	3	fe	fe	NOUN
ejpam-4597	163	4	)	)	PUNCT
ejpam-4597	163	5	implies	imply	VERB
ejpam-4597	163	6	that	that	SCONJ
ejpam-4597	163	7	xeα∈̃[cl	xeα∈̃[cl	PROPN
ejpam-4597	163	8	(	(	PUNCT
ejpam-4597	163	9	fe	fe	NOUN
ejpam-4597	163	10	)	)	PUNCT
ejpam-4597	163	11	]	]	PUNCT
ejpam-4597	164	1	c	c	X
ejpam-4597	164	2	.	.	PUNCT
ejpam-4597	165	1	thus	thus	ADV
ejpam-4597	165	2	fc	fc	X
ejpam-4597	165	3	e⊑[cl	e⊑[cl	PROPN
ejpam-4597	165	4	(	(	PUNCT
ejpam-4597	165	5	fe	fe	NOUN
ejpam-4597	165	6	)	)	PUNCT
ejpam-4597	165	7	]	]	PUNCT
ejpam-4597	166	1	c	c	NOUN
ejpam-4597	166	2	=	=	PUNCT
ejpam-4597	166	3	⇒	⇒	NOUN
ejpam-4597	166	4	cl	cl	NOUN
ejpam-4597	166	5	(	(	PUNCT
ejpam-4597	166	6	fe)⊑fe	fe)⊑fe	NOUN
ejpam-4597	166	7	and	and	CCONJ
ejpam-4597	166	8	so	so	ADV
ejpam-4597	166	9	,	,	PUNCT
ejpam-4597	166	10	fe	fe	X
ejpam-4597	166	11	=	=	NOUN
ejpam-4597	166	12	cl	cl	PROPN
ejpam-4597	166	13	(	(	PUNCT
ejpam-4597	166	14	fe	fe	NOUN
ejpam-4597	166	15	)	)	PUNCT
ejpam-4597	166	16	this	this	PRON
ejpam-4597	166	17	means	mean	VERB
ejpam-4597	166	18	every	every	DET
ejpam-4597	166	19	fsg	fsg	PROPN
ejpam-4597	166	20	-	-	PUNCT
ejpam-4597	166	21	closed	closed	ADJ
ejpam-4597	166	22	set	set	NOUN
ejpam-4597	166	23	in	in	ADP
ejpam-4597	166	24	(	(	PUNCT
ejpam-4597	166	25	u	u	NOUN
ejpam-4597	166	26	,	,	PUNCT
ejpam-4597	166	27	δ	δ	PROPN
ejpam-4597	166	28	,	,	PUNCT
ejpam-4597	166	29	e	e	NOUN
ejpam-4597	166	30	)	)	PUNCT
ejpam-4597	166	31	is	be	AUX
ejpam-4597	166	32	an	an	DET
ejpam-4597	166	33	fscset	fscset	NOUN
ejpam-4597	166	34	.	.	PUNCT
ejpam-4597	167	1	the	the	DET
ejpam-4597	167	2	result	result	NOUN
ejpam-4597	167	3	holds	hold	VERB
ejpam-4597	167	4	.	.	PUNCT
ejpam-4597	168	1	conversely	conversely	ADV
ejpam-4597	168	2	,	,	PUNCT
ejpam-4597	168	3	it	it	PRON
ejpam-4597	168	4	is	be	AUX
ejpam-4597	168	5	clear	clear	ADJ
ejpam-4597	168	6	.	.	PUNCT
ejpam-4597	169	1	theorem	theorem	VERB
ejpam-4597	169	2	3	3	NUM
ejpam-4597	169	3	.	.	PUNCT
ejpam-4597	170	1	an	an	DET
ejpam-4597	170	2	fsts(u	fsts(u	PROPN
ejpam-4597	170	3	,	,	PUNCT
ejpam-4597	170	4	δ	δ	PROPN
ejpam-4597	170	5	,	,	PUNCT
ejpam-4597	170	6	e	e	NOUN
ejpam-4597	170	7	)	)	PUNCT
ejpam-4597	170	8	is	be	AUX
ejpam-4597	170	9	fs	fs	PROPN
ejpam-4597	170	10	-	-	PUNCT
ejpam-4597	170	11	gr2	gr2	NOUN
ejpam-4597	170	12	if	if	SCONJ
ejpam-4597	171	1	and	and	CCONJ
ejpam-4597	171	2	only	only	ADV
ejpam-4597	171	3	if	if	SCONJ
ejpam-4597	171	4	for	for	SCONJ
ejpam-4597	171	5	any	any	DET
ejpam-4597	171	6	fs	fs	NOUN
ejpam-4597	171	7	-	-	PUNCT
ejpam-4597	171	8	point	point	NOUN
ejpam-4597	171	9	xeα	xeα	NOUN
ejpam-4597	171	10	and	and	CCONJ
ejpam-4597	171	11	any	any	DET
ejpam-4597	171	12	fsg	fsg	NOUN
ejpam-4597	171	13	-	-	PUNCT
ejpam-4597	171	14	open	open	NOUN
ejpam-4597	171	15	set	set	VERB
ejpam-4597	171	16	oxe	oxe	PRON
ejpam-4597	171	17	α	α	NOUN
ejpam-4597	171	18	,	,	PUNCT
ejpam-4597	171	19	there	there	PRON
ejpam-4597	171	20	is	be	VERB
ejpam-4597	171	21	an	an	DET
ejpam-4597	171	22	fso	fso	NOUN
ejpam-4597	171	23	-	-	PUNCT
ejpam-4597	171	24	set	set	VERB
ejpam-4597	171	25	o∗	o∗	PROPN
ejpam-4597	171	26	xe	xe	PROPN
ejpam-4597	171	27	α	α	PROPN
ejpam-4597	171	28	such	such	ADJ
ejpam-4597	171	29	that	that	DET
ejpam-4597	171	30	cl(o∗	cl(o∗	PROPN
ejpam-4597	171	31	xe	xe	PROPN
ejpam-4597	171	32	α	α	PROPN
ejpam-4597	171	33	)	)	PUNCT
ejpam-4597	172	1	⊑oxe	⊑oxe	X
ejpam-4597	172	2	α	α	NOUN
ejpam-4597	172	3	.	.	PUNCT
ejpam-4597	173	1	proof	proof	NOUN
ejpam-4597	173	2	.	.	PUNCT
ejpam-4597	174	1	let	let	VERB
ejpam-4597	174	2	(	(	PUNCT
ejpam-4597	174	3	u	u	NOUN
ejpam-4597	174	4	,	,	PUNCT
ejpam-4597	174	5	δ	δ	PROPN
ejpam-4597	174	6	,	,	PUNCT
ejpam-4597	174	7	e	e	NOUN
ejpam-4597	174	8	)	)	PUNCT
ejpam-4597	174	9	be	be	AUX
ejpam-4597	174	10	fs	f	NOUN
ejpam-4597	174	11	-	-	NOUN
ejpam-4597	174	12	gr2	gr2	PROPN
ejpam-4597	174	13	and	and	CCONJ
ejpam-4597	174	14	oxe	oxe	PRON
ejpam-4597	174	15	α	α	NOUN
ejpam-4597	174	16	be	be	AUX
ejpam-4597	174	17	any	any	DET
ejpam-4597	174	18	fsg	fsg	NOUN
ejpam-4597	174	19	-	-	PUNCT
ejpam-4597	174	20	open	open	ADJ
ejpam-4597	174	21	set	set	NOUN
ejpam-4597	174	22	containing	contain	VERB
ejpam-4597	174	23	fs	fs	NOUN
ejpam-4597	174	24	-	-	PUNCT
ejpam-4597	174	25	point	point	NOUN
ejpam-4597	174	26	xeα	xeα	PROPN
ejpam-4597	174	27	,	,	PUNCT
ejpam-4597	174	28	then	then	ADV
ejpam-4597	174	29	oc	oc	VERB
ejpam-4597	174	30	xe	xe	PROPN
ejpam-4597	174	31	α	α	PROPN
ejpam-4597	174	32	=	=	SYM
ejpam-4597	174	33	fe	fe	X
ejpam-4597	174	34	which	which	PRON
ejpam-4597	174	35	is	be	AUX
ejpam-4597	174	36	an	an	DET
ejpam-4597	174	37	fsg	fsg	PROPN
ejpam-4597	174	38	-	-	PUNCT
ejpam-4597	174	39	closed	closed	ADJ
ejpam-4597	174	40	set	set	NOUN
ejpam-4597	174	41	.	.	PUNCT
ejpam-4597	175	1	since	since	SCONJ
ejpam-4597	175	2	oxe	oxe	PROPN
ejpam-4597	175	3	α	α	PRON
ejpam-4597	175	4	q̃oc	q̃oc	PROPN
ejpam-4597	175	5	xe	xe	PROPN
ejpam-4597	175	6	α	α	PROPN
ejpam-4597	175	7	we	we	PRON
ejpam-4597	175	8	have	have	VERB
ejpam-4597	175	9	,	,	PUNCT
ejpam-4597	175	10	xeαq̃o	xeαq̃o	PROPN
ejpam-4597	175	11	c	c	PROPN
ejpam-4597	175	12	xe	xe	PROPN
ejpam-4597	175	13	α	α	PROPN
ejpam-4597	175	14	.	.	PUNCT
ejpam-4597	176	1	since	since	SCONJ
ejpam-4597	176	2	(	(	PUNCT
ejpam-4597	176	3	u	u	NOUN
ejpam-4597	176	4	,	,	PUNCT
ejpam-4597	176	5	δ	δ	PROPN
ejpam-4597	176	6	,	,	PUNCT
ejpam-4597	176	7	e	e	NOUN
ejpam-4597	176	8	)	)	PUNCT
ejpam-4597	176	9	is	be	AUX
ejpam-4597	176	10	fs	fs	PROPN
ejpam-4597	176	11	-	-	PUNCT
ejpam-4597	176	12	gr2	gr2	NOUN
ejpam-4597	176	13	,	,	PUNCT
ejpam-4597	176	14	there	there	PRON
ejpam-4597	176	15	are	be	VERB
ejpam-4597	176	16	o∗	o∗	PROPN
ejpam-4597	176	17	xe	xe	PROPN
ejpam-4597	176	18	α	α	PROPN
ejpam-4597	176	19	,	,	PUNCT
ejpam-4597	176	20	ooc	ooc	PRON
ejpam-4597	176	21	xeα	xeα	NOUN
ejpam-4597	176	22	∈	∈	PROPN
ejpam-4597	176	23	δ	δ	PROPN
ejpam-4597	176	24	such	such	ADJ
ejpam-4597	176	25	that	that	SCONJ
ejpam-4597	176	26	o∗	o∗	PROPN
ejpam-4597	176	27	xe	xe	PROPN
ejpam-4597	176	28	α	α	PROPN
ejpam-4597	176	29	q̃ooc	q̃ooc	ADV
ejpam-4597	176	30	xeα	xeα	PUNCT
ejpam-4597	176	31	=	=	NOUN
ejpam-4597	176	32	ofe	ofe	NOUN
ejpam-4597	176	33	implies	imply	VERB
ejpam-4597	176	34	o∗	o∗	PROPN
ejpam-4597	176	35	xe	xe	PROPN
ejpam-4597	176	36	α	α	PROPN
ejpam-4597	176	37	⊑	⊑	X
ejpam-4597	176	38	oc	oc	PROPN
ejpam-4597	176	39	fe	fe	X
ejpam-4597	176	40	and	and	CCONJ
ejpam-4597	176	41	so	so	ADV
ejpam-4597	176	42	,	,	PUNCT
ejpam-4597	176	43	cl(o∗	cl(o∗	PROPN
ejpam-4597	176	44	xe	xe	PROPN
ejpam-4597	176	45	α	α	PROPN
ejpam-4597	176	46	)	)	PUNCT
ejpam-4597	177	1	⊑	⊑	PROPN
ejpam-4597	177	2	oc	oc	PROPN
ejpam-4597	177	3	fe	fe	PROPN
ejpam-4597	177	4	.	.	PUNCT
ejpam-4597	178	1	since	since	SCONJ
ejpam-4597	178	2	oc	oc	AUX
ejpam-4597	178	3	xe	xe	PROPN
ejpam-4597	178	4	α	α	PROPN
ejpam-4597	178	5	⊑	⊑	X
ejpam-4597	178	6	ooc	ooc	PRON
ejpam-4597	178	7	xeα	xeα	PUNCT
ejpam-4597	179	1	=	=	PRON
ejpam-4597	179	2	ofe	ofe	INTJ
ejpam-4597	179	3	,	,	PUNCT
ejpam-4597	179	4	we	we	PRON
ejpam-4597	179	5	obtain	obtain	VERB
ejpam-4597	179	6	oc	oc	PRON
ejpam-4597	179	7	fe	fe	X
ejpam-4597	179	8	⊑	⊑	PRON
ejpam-4597	179	9	oxe	oxe	PROPN
ejpam-4597	179	10	α	α	NOUN
ejpam-4597	179	11	.	.	PUNCT
ejpam-4597	180	1	hence	hence	ADV
ejpam-4597	180	2	cl(o∗	cl(o∗	VERB
ejpam-4597	180	3	xe	xe	PROPN
ejpam-4597	180	4	α	α	PROPN
ejpam-4597	180	5	)	)	PUNCT
ejpam-4597	180	6	⊑	⊑	PROPN
ejpam-4597	180	7	oxe	oxe	PROPN
ejpam-4597	180	8	α	α	NOUN
ejpam-4597	180	9	.	.	PUNCT
ejpam-4597	181	1	conversely	conversely	ADV
ejpam-4597	181	2	,	,	PUNCT
ejpam-4597	181	3	let	let	VERB
ejpam-4597	181	4	xeα	xeα	PROPN
ejpam-4597	181	5	be	be	AUX
ejpam-4597	181	6	any	any	DET
ejpam-4597	181	7	fs	fs	ADJ
ejpam-4597	181	8	-	-	PUNCT
ejpam-4597	181	9	point	point	NOUN
ejpam-4597	181	10	and	and	CCONJ
ejpam-4597	181	11	ge	ge	PROPN
ejpam-4597	181	12	be	be	AUX
ejpam-4597	181	13	any	any	DET
ejpam-4597	181	14	fsg	fsg	NOUN
ejpam-4597	181	15	-	-	PUNCT
ejpam-4597	181	16	closed	closed	ADJ
ejpam-4597	181	17	set	set	NOUN
ejpam-4597	181	18	with	with	ADP
ejpam-4597	181	19	xeαq̃ge	xeαq̃ge	PROPN
ejpam-4597	181	20	,	,	PUNCT
ejpam-4597	181	21	then	then	ADV
ejpam-4597	181	22	xeα	xeα	PROPN
ejpam-4597	181	23	∈	∈	PROPN
ejpam-4597	181	24	gce	gce	PROPN
ejpam-4597	181	25	=	=	PUNCT
ejpam-4597	181	26	oxe	oxe	PROPN
ejpam-4597	181	27	α	α	PRON
ejpam-4597	181	28	which	which	PRON
ejpam-4597	181	29	is	be	AUX
ejpam-4597	181	30	an	an	DET
ejpam-4597	181	31	fsg	fsg	NOUN
ejpam-4597	181	32	-	-	PUNCT
ejpam-4597	181	33	open	open	ADJ
ejpam-4597	181	34	set	set	NOUN
ejpam-4597	181	35	containing	contain	VERB
ejpam-4597	181	36	xeα	xeα	PROPN
ejpam-4597	181	37	.	.	PUNCT
ejpam-4597	182	1	so	so	ADV
ejpam-4597	182	2	by	by	ADP
ejpam-4597	182	3	hypothesis	hypothesis	NOUN
ejpam-4597	182	4	,	,	PUNCT
ejpam-4597	182	5	there	there	PRON
ejpam-4597	182	6	exists	exist	VERB
ejpam-4597	182	7	an	an	DET
ejpam-4597	182	8	fso	fso	NOUN
ejpam-4597	182	9	-	-	PUNCT
ejpam-4597	182	10	set	set	VERB
ejpam-4597	182	11	o∗	o∗	PROPN
ejpam-4597	182	12	xe	xe	PROPN
ejpam-4597	182	13	α	α	PROPN
ejpam-4597	182	14	such	such	ADJ
ejpam-4597	182	15	that	that	DET
ejpam-4597	182	16	cl(o∗	cl(o∗	PROPN
ejpam-4597	182	17	xe	xe	PROPN
ejpam-4597	182	18	α	α	PROPN
ejpam-4597	182	19	)	)	PUNCT
ejpam-4597	182	20	⊑	⊑	X
ejpam-4597	182	21	oxe	oxe	PROPN
ejpam-4597	182	22	α	α	PROPN
ejpam-4597	182	23	=	=	SYM
ejpam-4597	182	24	gce	gce	PROPN
ejpam-4597	182	25	implies	imply	VERB
ejpam-4597	182	26	ge	ge	PROPN
ejpam-4597	182	27	⊑	⊑	X
ejpam-4597	183	1	[	[	X
ejpam-4597	183	2	cl(o∗	cl(o∗	X
ejpam-4597	183	3	xe	xe	PROPN
ejpam-4597	183	4	α	α	PROPN
ejpam-4597	183	5	)	)	PUNCT
ejpam-4597	184	1	]	]	X
ejpam-4597	184	2	c	c	X
ejpam-4597	184	3	=	=	SYM
ejpam-4597	184	4	oge	oge	PROPN
ejpam-4597	184	5	and	and	CCONJ
ejpam-4597	184	6	cl(o∗	cl(o∗	PROPN
ejpam-4597	184	7	xe	xe	PROPN
ejpam-4597	184	8	α	α	NOUN
ejpam-4597	184	9	)	)	PUNCT
ejpam-4597	184	10	q̃[cl(o∗	q̃[cl(o∗	NOUN
ejpam-4597	184	11	xe	xe	PROPN
ejpam-4597	184	12	α	α	PROPN
ejpam-4597	184	13	)	)	PUNCT
ejpam-4597	185	1	]	]	X
ejpam-4597	185	2	c	c	X
ejpam-4597	185	3	=	=	SYM
ejpam-4597	185	4	oge	oge	PROPN
ejpam-4597	185	5	.	.	PUNCT
ejpam-4597	186	1	therefore	therefore	ADV
ejpam-4597	186	2	o∗	o∗	PROPN
ejpam-4597	186	3	xe	xe	PROPN
ejpam-4597	186	4	α	α	PROPN
ejpam-4597	186	5	q̃o	q̃o	PROPN
ejpam-4597	186	6	ge	ge	PROPN
ejpam-4597	186	7	.	.	PUNCT
ejpam-4597	187	1	hence	hence	ADV
ejpam-4597	187	2	the	the	DET
ejpam-4597	187	3	result	result	NOUN
ejpam-4597	187	4	holds	hold	VERB
ejpam-4597	187	5	.	.	PUNCT
ejpam-4597	188	1	theorem	theorem	NOUN
ejpam-4597	188	2	4	4	NUM
ejpam-4597	188	3	.	.	PUNCT
ejpam-4597	189	1	an	an	DET
ejpam-4597	189	2	fsts	fst	NOUN
ejpam-4597	189	3	(	(	PUNCT
ejpam-4597	189	4	u	u	NOUN
ejpam-4597	189	5	,	,	PUNCT
ejpam-4597	189	6	δ	δ	PROPN
ejpam-4597	189	7	,	,	PUNCT
ejpam-4597	189	8	e	e	NOUN
ejpam-4597	189	9	)	)	PUNCT
ejpam-4597	189	10	is	be	AUX
ejpam-4597	189	11	fs	fs	PROPN
ejpam-4597	189	12	-	-	PUNCT
ejpam-4597	189	13	gr2	gr2	NOUN
ejpam-4597	189	14	if	if	SCONJ
ejpam-4597	190	1	and	and	CCONJ
ejpam-4597	190	2	only	only	ADV
ejpam-4597	190	3	if	if	SCONJ
ejpam-4597	190	4	for	for	ADP
ejpam-4597	190	5	any	any	DET
ejpam-4597	190	6	fsg	fsg	NOUN
ejpam-4597	190	7	-	-	PUNCT
ejpam-4597	190	8	closed	close	VERB
ejpam-4597	190	9	set	set	NOUN
ejpam-4597	190	10	ge	ge	PROPN
ejpam-4597	190	11	and	and	CCONJ
ejpam-4597	190	12	any	any	DET
ejpam-4597	190	13	fs	fs	NOUN
ejpam-4597	190	14	-	-	PUNCT
ejpam-4597	190	15	point	point	NOUN
ejpam-4597	190	16	xeα	xeα	NOUN
ejpam-4597	190	17	with	with	ADP
ejpam-4597	190	18	xeαq̃ge	xeαq̃ge	PROPN
ejpam-4597	190	19	,	,	PUNCT
ejpam-4597	190	20	there	there	PRON
ejpam-4597	190	21	are	be	VERB
ejpam-4597	190	22	oxe	oxe	PROPN
ejpam-4597	190	23	α	α	NOUN
ejpam-4597	190	24	,	,	PUNCT
ejpam-4597	190	25	oge	oge	PROPN
ejpam-4597	190	26	∈	∈	PROPN
ejpam-4597	190	27	δ	δ	PROPN
ejpam-4597	190	28	such	such	ADJ
ejpam-4597	190	29	that	that	SCONJ
ejpam-4597	190	30	cl(oxe	cl(oxe	PROPN
ejpam-4597	190	31	α	α	NOUN
ejpam-4597	190	32	)	)	PUNCT
ejpam-4597	190	33	q̃cl(oge	q̃cl(oge	NOUN
ejpam-4597	190	34	)	)	PUNCT
ejpam-4597	190	35	.	.	PUNCT
ejpam-4597	191	1	proof	proof	NOUN
ejpam-4597	191	2	.	.	PUNCT
ejpam-4597	192	1	let	let	VERB
ejpam-4597	192	2	(	(	PUNCT
ejpam-4597	192	3	u	u	NOUN
ejpam-4597	192	4	,	,	PUNCT
ejpam-4597	192	5	δ	δ	PROPN
ejpam-4597	192	6	,	,	PUNCT
ejpam-4597	192	7	e	e	NOUN
ejpam-4597	192	8	)	)	PUNCT
ejpam-4597	192	9	be	be	AUX
ejpam-4597	192	10	an	an	DET
ejpam-4597	192	11	fs	fs	ADJ
ejpam-4597	192	12	-	-	PUNCT
ejpam-4597	192	13	gr2	gr2	NOUN
ejpam-4597	192	14	space	space	NOUN
ejpam-4597	192	15	and	and	CCONJ
ejpam-4597	192	16	ge	ge	PROPN
ejpam-4597	192	17	be	be	AUX
ejpam-4597	192	18	any	any	DET
ejpam-4597	192	19	fsg	fsg	NOUN
ejpam-4597	192	20	-	-	PUNCT
ejpam-4597	192	21	closed	closed	ADJ
ejpam-4597	192	22	set	set	NOUN
ejpam-4597	192	23	with	with	ADP
ejpam-4597	192	24	xeαq̃ge	xeαq̃ge	PROPN
ejpam-4597	192	25	,	,	PUNCT
ejpam-4597	192	26	there	there	PRON
ejpam-4597	192	27	are	be	VERB
ejpam-4597	192	28	o∗	o∗	PROPN
ejpam-4597	192	29	xe	xe	PROPN
ejpam-4597	192	30	α	α	PROPN
ejpam-4597	192	31	,	,	PUNCT
ejpam-4597	192	32	ofe	ofe	INTJ
ejpam-4597	192	33	∈	∈	PROPN
ejpam-4597	192	34	δ	δ	PROPN
ejpam-4597	192	35	such	such	ADJ
ejpam-4597	192	36	that	that	SCONJ
ejpam-4597	192	37	ofe	ofe	INTJ
ejpam-4597	192	38	q̃o	q̃o	PROPN
ejpam-4597	192	39	∗	∗	PROPN
ejpam-4597	192	40	xe	xe	PROPN
ejpam-4597	192	41	α	α	PROPN
ejpam-4597	192	42	.	.	PUNCT
ejpam-4597	193	1	from	from	ADP
ejpam-4597	193	2	lemma	lemma	PROPN
ejpam-4597	193	3	1	1	NUM
ejpam-4597	193	4	,	,	PUNCT
ejpam-4597	193	5	we	we	PRON
ejpam-4597	193	6	get	get	VERB
ejpam-4597	193	7	cl(ofe	cl(ofe	PROPN
ejpam-4597	193	8	)	)	PUNCT
ejpam-4597	193	9	q̃o	q̃o	PROPN
ejpam-4597	193	10	∗	∗	PROPN
ejpam-4597	193	11	xe	xe	PROPN
ejpam-4597	193	12	α	α	PROPN
ejpam-4597	193	13	that	that	ADV
ejpam-4597	193	14	is	be	AUX
ejpam-4597	193	15	,	,	PUNCT
ejpam-4597	193	16	cl(ofe	cl(ofe	PROPN
ejpam-4597	193	17	)	)	PUNCT
ejpam-4597	193	18	q̃x	q̃x	PROPN
ejpam-4597	194	1	e	e	NOUN
ejpam-4597	194	2	α	α	PROPN
ejpam-4597	194	3	.	.	PUNCT
ejpam-4597	195	1	a	a	DET
ejpam-4597	195	2	gain	gain	NOUN
ejpam-4597	195	3	,	,	PUNCT
ejpam-4597	195	4	since	since	SCONJ
ejpam-4597	195	5	(	(	PUNCT
ejpam-4597	195	6	u	u	NOUN
ejpam-4597	195	7	,	,	PUNCT
ejpam-4597	195	8	δ	δ	PROPN
ejpam-4597	195	9	,	,	PUNCT
ejpam-4597	195	10	e	e	NOUN
ejpam-4597	195	11	)	)	PUNCT
ejpam-4597	195	12	is	be	AUX
ejpam-4597	195	13	fs	fs	PROPN
ejpam-4597	195	14	-	-	PUNCT
ejpam-4597	195	15	gr2	gr2	NOUN
ejpam-4597	195	16	,	,	PUNCT
ejpam-4597	195	17	there	there	PRON
ejpam-4597	195	18	are	be	VERB
ejpam-4597	195	19	o∗∗	o∗∗	PROPN
ejpam-4597	195	20	xe	xe	PROPN
ejpam-4597	195	21	α	α	PROPN
ejpam-4597	195	22	,	,	PUNCT
ejpam-4597	195	23	ocl(ofe	ocl(ofe	NOUN
ejpam-4597	195	24	)	)	PUNCT
ejpam-4597	196	1	∈	∈	PROPN
ejpam-4597	196	2	δ	δ	PROPN
ejpam-4597	196	3	such	such	ADJ
ejpam-4597	196	4	that	that	SCONJ
ejpam-4597	196	5	o∗∗	o∗∗	PROPN
ejpam-4597	196	6	xe	xe	PROPN
ejpam-4597	196	7	α	α	PROPN
ejpam-4597	196	8	q̃ocl(ofe	q̃ocl(ofe	ADJ
ejpam-4597	196	9	)	)	PUNCT
ejpam-4597	196	10	implies	imply	VERB
ejpam-4597	196	11	that	that	SCONJ
ejpam-4597	196	12	cl(o∗∗	cl(o∗∗	PROPN
ejpam-4597	196	13	xe	xe	PROPN
ejpam-4597	196	14	α	α	PROPN
ejpam-4597	196	15	)	)	PUNCT
ejpam-4597	196	16	q̃ocl(ofe	q̃ocl(ofe	ADJ
ejpam-4597	196	17	)	)	PUNCT
ejpam-4597	196	18	(	(	PUNCT
ejpam-4597	196	19	by	by	ADP
ejpam-4597	196	20	lemma	lemma	PROPN
ejpam-4597	196	21	1	1	NUM
ejpam-4597	196	22	)	)	PUNCT
ejpam-4597	196	23	.	.	PUNCT
ejpam-4597	197	1	take	take	VERB
ejpam-4597	197	2	oxe	oxe	PRON
ejpam-4597	197	3	α	α	NOUN
ejpam-4597	197	4	=	=	SYM
ejpam-4597	197	5	o∗	o∗	PROPN
ejpam-4597	197	6	xe	xe	PROPN
ejpam-4597	198	1	α	α	DET
ejpam-4597	198	2	⊓	⊓	PROPN
ejpam-4597	198	3	o∗∗	o∗∗	NOUN
ejpam-4597	198	4	xe	xe	PROPN
ejpam-4597	198	5	α	α	PROPN
ejpam-4597	198	6	and	and	CCONJ
ejpam-4597	198	7	by	by	ADP
ejpam-4597	198	8	the	the	DET
ejpam-4597	198	9	above	above	ADJ
ejpam-4597	198	10	theorem	theorem	NOUN
ejpam-4597	198	11	,	,	PUNCT
ejpam-4597	198	12	there	there	PRON
ejpam-4597	198	13	exists	exist	VERB
ejpam-4597	198	14	oxe	oxe	PRON
ejpam-4597	198	15	α	α	PROPN
ejpam-4597	198	16	∈	∈	PROPN
ejpam-4597	198	17	δ	δ	PROPN
ejpam-4597	198	18	such	such	ADJ
ejpam-4597	198	19	that	that	SCONJ
ejpam-4597	198	20	cl(oxe	cl(oxe	PROPN
ejpam-4597	198	21	α	α	PROPN
ejpam-4597	198	22	)	)	PUNCT
ejpam-4597	198	23	⊑	⊑	PROPN
ejpam-4597	199	1	o∗	o∗	PROPN
ejpam-4597	199	2	xe	xe	PROPN
ejpam-4597	199	3	α	α	PROPN
ejpam-4597	199	4	.	.	PUNCT
ejpam-4597	200	1	since	since	SCONJ
ejpam-4597	200	2	cl(ofe	cl(ofe	PROPN
ejpam-4597	200	3	)	)	PUNCT
ejpam-4597	200	4	q̃o	q̃o	PROPN
ejpam-4597	200	5	∗	∗	PROPN
ejpam-4597	200	6	xe	xe	PROPN
ejpam-4597	200	7	α	α	PROPN
ejpam-4597	200	8	,	,	PUNCT
ejpam-4597	200	9	we	we	PRON
ejpam-4597	200	10	get	get	VERB
ejpam-4597	200	11	cl(ofe	cl(ofe	NOUN
ejpam-4597	200	12	)	)	PUNCT
ejpam-4597	200	13	q̃cl(oxe	q̃cl(oxe	X
ejpam-4597	200	14	α	α	NOUN
ejpam-4597	200	15	)	)	PUNCT
ejpam-4597	200	16	.	.	PUNCT
ejpam-4597	201	1	conversely	conversely	ADV
ejpam-4597	201	2	,	,	PUNCT
ejpam-4597	201	3	it	it	PRON
ejpam-4597	201	4	follows	follow	VERB
ejpam-4597	201	5	directly	directly	ADV
ejpam-4597	201	6	from	from	ADP
ejpam-4597	201	7	hypothesis	hypothesis	NOUN
ejpam-4597	201	8	.	.	PUNCT
ejpam-4597	202	1	definition	definition	NOUN
ejpam-4597	202	2	11	11	NUM
ejpam-4597	202	3	.	.	PUNCT
ejpam-4597	203	1	an	an	DET
ejpam-4597	203	2	fsts	fst	NOUN
ejpam-4597	203	3	(	(	PUNCT
ejpam-4597	203	4	u	u	NOUN
ejpam-4597	203	5	,	,	PUNCT
ejpam-4597	203	6	δ	δ	PROPN
ejpam-4597	203	7	,	,	PUNCT
ejpam-4597	203	8	e	e	NOUN
ejpam-4597	203	9	)	)	PUNCT
ejpam-4597	203	10	is	be	AUX
ejpam-4597	203	11	said	say	VERB
ejpam-4597	203	12	to	to	PART
ejpam-4597	203	13	be	be	AUX
ejpam-4597	203	14	fs	f	NOUN
ejpam-4597	203	15	-	-	PUNCT
ejpam-4597	203	16	symmetric	symmetric	ADJ
ejpam-4597	203	17	iff	iff	PROPN
ejpam-4597	203	18	for	for	ADP
ejpam-4597	203	19	any	any	DET
ejpam-4597	203	20	fs	fs	ADJ
ejpam-4597	203	21	-	-	PUNCT
ejpam-4597	203	22	points	point	NOUN
ejpam-4597	203	23	xeα	xeα	PROPN
ejpam-4597	203	24	,	,	PUNCT
ejpam-4597	203	25	y	y	PROPN
ejpam-4597	203	26	e	e	PROPN
ejpam-4597	203	27	β	β	PROPN
ejpam-4597	203	28	∈	∈	PROPN
ejpam-4597	203	29	fsp	fsp	PROPN
ejpam-4597	203	30	(	(	PUNCT
ejpam-4597	203	31	u	u	NOUN
ejpam-4597	203	32	)	)	PUNCT
ejpam-4597	203	33	with	with	ADP
ejpam-4597	203	34	xeαq̃cl(y	xeαq̃cl(y	PROPN
ejpam-4597	203	35	e	e	PROPN
ejpam-4597	203	36	β	β	NOUN
ejpam-4597	203	37	)	)	PUNCT
ejpam-4597	203	38	implies	imply	VERB
ejpam-4597	203	39	yeβ	yeβ	PROPN
ejpam-4597	203	40	q̃cl(x	q̃cl(x	PROPN
ejpam-4597	203	41	e	e	PROPN
ejpam-4597	203	42	α	α	NOUN
ejpam-4597	203	43	)	)	PUNCT
ejpam-4597	203	44	.	.	PUNCT
ejpam-4597	204	1	theorem	theorem	ADJ
ejpam-4597	204	2	5	5	NUM
ejpam-4597	204	3	.	.	PUNCT
ejpam-4597	205	1	an	an	DET
ejpam-4597	205	2	fsts	fst	NOUN
ejpam-4597	205	3	(	(	PUNCT
ejpam-4597	205	4	u	u	NOUN
ejpam-4597	205	5	,	,	PUNCT
ejpam-4597	205	6	δ	δ	PROPN
ejpam-4597	205	7	,	,	PUNCT
ejpam-4597	205	8	e	e	NOUN
ejpam-4597	205	9	)	)	PUNCT
ejpam-4597	205	10	is	be	AUX
ejpam-4597	205	11	fs	f	NOUN
ejpam-4597	205	12	-	-	ADJ
ejpam-4597	205	13	symmetric	symmetric	ADJ
ejpam-4597	205	14	if	if	SCONJ
ejpam-4597	205	15	and	and	CCONJ
ejpam-4597	205	16	only	only	ADV
ejpam-4597	205	17	if	if	SCONJ
ejpam-4597	205	18	cl(xeα)q̃ge	cl(xeα)q̃ge	VERB
ejpam-4597	205	19	for	for	ADP
ejpam-4597	205	20	any	any	DET
ejpam-4597	205	21	fscset	fscset	NOUN
ejpam-4597	205	22	ge	ge	PROPN
ejpam-4597	205	23	with	with	ADP
ejpam-4597	205	24	xeαq̃ge	xeαq̃ge	PROPN
ejpam-4597	205	25	.	.	PUNCT
ejpam-4597	206	1	s.	s.	PROPN
ejpam-4597	206	2	saleh	saleh	PROPN
ejpam-4597	206	3	,	,	PUNCT
ejpam-4597	206	4	j.	j.	PROPN
ejpam-4597	206	5	al	al	PROPN
ejpam-4597	206	6	-	-	PUNCT
ejpam-4597	206	7	mufarrij	mufarrij	PROPN
ejpam-4597	206	8	/	/	SYM
ejpam-4597	206	9	eur	eur	PROPN
ejpam-4597	206	10	.	.	PUNCT
ejpam-4597	207	1	j.	j.	PROPN
ejpam-4597	207	2	pure	pure	PROPN
ejpam-4597	207	3	appl	appl	PROPN
ejpam-4597	207	4	.	.	PROPN
ejpam-4597	207	5	math	math	PROPN
ejpam-4597	207	6	,	,	PUNCT
ejpam-4597	207	7	16	16	NUM
ejpam-4597	207	8	(	(	PUNCT
ejpam-4597	207	9	1	1	NUM
ejpam-4597	207	10	)	)	PUNCT
ejpam-4597	207	11	(	(	PUNCT
ejpam-4597	207	12	2023	2023	NUM
ejpam-4597	207	13	)	)	PUNCT
ejpam-4597	207	14	,	,	PUNCT
ejpam-4597	207	15	180	180	NUM
ejpam-4597	207	16	-	-	SYM
ejpam-4597	207	17	191	191	NUM
ejpam-4597	207	18	185	185	NUM
ejpam-4597	207	19	proof	proof	NOUN
ejpam-4597	207	20	.	.	PUNCT
ejpam-4597	207	21	suppose	suppose	VERB
ejpam-4597	207	22	that	that	SCONJ
ejpam-4597	207	23	ge	ge	PROPN
ejpam-4597	207	24	is	be	AUX
ejpam-4597	207	25	an	an	DET
ejpam-4597	207	26	fsc	fsc	PROPN
ejpam-4597	207	27	-	-	PUNCT
ejpam-4597	207	28	set	set	NOUN
ejpam-4597	207	29	on	on	ADP
ejpam-4597	207	30	u	u	NOUN
ejpam-4597	207	31	with	with	ADP
ejpam-4597	207	32	xeαq̃ge	xeαq̃ge	PROPN
ejpam-4597	207	33	.	.	PUNCT
ejpam-4597	208	1	clearly	clearly	ADV
ejpam-4597	208	2	cl	cl	VERB
ejpam-4597	208	3	(	(	PUNCT
ejpam-4597	208	4	yet	yet	CCONJ
ejpam-4597	208	5	)	)	PUNCT
ejpam-4597	209	1	⊑	⊑	PROPN
ejpam-4597	209	2	ge	ge	PROPN
ejpam-4597	209	3	for	for	ADP
ejpam-4597	209	4	all	all	DET
ejpam-4597	209	5	yet	yet	ADV
ejpam-4597	209	6	∈̃ge	∈̃ge	ADJ
ejpam-4597	209	7	and	and	CCONJ
ejpam-4597	209	8	so	so	ADV
ejpam-4597	209	9	,	,	PUNCT
ejpam-4597	209	10	xeαq̃cl(y	xeαq̃cl(y	PROPN
ejpam-4597	209	11	e	e	PROPN
ejpam-4597	209	12	t	t	PROPN
ejpam-4597	209	13	)	)	PUNCT
ejpam-4597	209	14	.	.	PUNCT
ejpam-4597	210	1	since	since	SCONJ
ejpam-4597	210	2	(	(	PUNCT
ejpam-4597	210	3	u	u	NOUN
ejpam-4597	210	4	,	,	PUNCT
ejpam-4597	210	5	δ	δ	PROPN
ejpam-4597	210	6	,	,	PUNCT
ejpam-4597	210	7	e	e	NOUN
ejpam-4597	210	8	)	)	PUNCT
ejpam-4597	210	9	is	be	AUX
ejpam-4597	210	10	fs	fs	PROPN
ejpam-4597	210	11	-	-	ADJ
ejpam-4597	210	12	symmetric	symmetric	ADJ
ejpam-4597	210	13	,	,	PUNCT
ejpam-4597	210	14	we	we	PRON
ejpam-4597	210	15	have	have	VERB
ejpam-4597	210	16	yeβ	yeβ	PROPN
ejpam-4597	210	17	q̃cl(x	q̃cl(x	X
ejpam-4597	210	18	e	e	NOUN
ejpam-4597	210	19	α	α	NOUN
ejpam-4597	210	20	)	)	PUNCT
ejpam-4597	210	21	for	for	ADP
ejpam-4597	210	22	all	all	DET
ejpam-4597	210	23	yet	yet	ADV
ejpam-4597	210	24	∈̃ge	∈̃ge	ADJ
ejpam-4597	210	25	and	and	CCONJ
ejpam-4597	210	26	so	so	ADV
ejpam-4597	210	27	,	,	PUNCT
ejpam-4597	210	28	for	for	ADP
ejpam-4597	210	29	all	all	DET
ejpam-4597	210	30	yet	yet	ADV
ejpam-4597	210	31	∈̃ge	∈̃ge	NOUN
ejpam-4597	210	32	there	there	PRON
ejpam-4597	210	33	is	be	VERB
ejpam-4597	210	34	an	an	DET
ejpam-4597	210	35	fso	fso	NOUN
ejpam-4597	210	36	-	-	PUNCT
ejpam-4597	210	37	set	set	VERB
ejpam-4597	210	38	oyet	oyet	NOUN
ejpam-4597	210	39	containing	contain	VERB
ejpam-4597	210	40	yet	yet	ADV
ejpam-4597	210	41	such	such	ADJ
ejpam-4597	210	42	that	that	PRON
ejpam-4597	210	43	xeαq̃oyet	xeαq̃oyet	PROPN
ejpam-4597	210	44	.	.	PUNCT
ejpam-4597	211	1	put	put	VERB
ejpam-4597	211	2	he	he	PRON
ejpam-4597	211	3	=	=	PUNCT
ejpam-4597	211	4	⊔	⊔	PROPN
ejpam-4597	211	5	{	{	PUNCT
ejpam-4597	211	6	oyet	oyet	ADV
ejpam-4597	211	7	:	:	PUNCT
ejpam-4597	211	8	yet	yet	ADV
ejpam-4597	211	9	∈̃ge	∈̃ge	NOUN
ejpam-4597	211	10	and	and	CCONJ
ejpam-4597	211	11	xeαq̃oyet	xeαq̃oyet	PROPN
ejpam-4597	211	12	}	}	PUNCT
ejpam-4597	211	13	,	,	PUNCT
ejpam-4597	211	14	then	then	ADV
ejpam-4597	211	15	he	he	PRON
ejpam-4597	211	16	=	=	PUNCT
ejpam-4597	211	17	oge	oge	PROPN
ejpam-4597	211	18	and	and	CCONJ
ejpam-4597	211	19	xeαq̃he	xeαq̃he	PROPN
ejpam-4597	211	20	.	.	PUNCT
ejpam-4597	212	1	thus	thus	ADV
ejpam-4597	212	2	x	x	X
ejpam-4597	212	3	e	e	NOUN
ejpam-4597	212	4	α∈̃hce	α∈̃hce	PROPN
ejpam-4597	212	5	and	and	CCONJ
ejpam-4597	212	6	so	so	ADV
ejpam-4597	212	7	,	,	PUNCT
ejpam-4597	212	8	cl(xeα	cl(xeα	PROPN
ejpam-4597	212	9	)	)	PUNCT
ejpam-4597	212	10	⊑	⊑	PROPN
ejpam-4597	213	1	hce	hce	PROPN
ejpam-4597	213	2	implies	imply	VERB
ejpam-4597	213	3	cl(xeα)q̃he	cl(xeα)q̃he	NOUN
ejpam-4597	213	4	.	.	PUNCT
ejpam-4597	214	1	therefore	therefore	ADV
ejpam-4597	214	2	cl(xeα)q̃ge	cl(xeα)q̃ge	PUNCT
ejpam-4597	214	3	.	.	PUNCT
ejpam-4597	215	1	conversely	conversely	ADV
ejpam-4597	215	2	,	,	PUNCT
ejpam-4597	215	3	it	it	PRON
ejpam-4597	215	4	is	be	AUX
ejpam-4597	215	5	obvious	obvious	ADJ
ejpam-4597	215	6	.	.	PUNCT
ejpam-4597	216	1	corollary	corollary	ADJ
ejpam-4597	216	2	1	1	NUM
ejpam-4597	216	3	.	.	PUNCT
ejpam-4597	217	1	an	an	DET
ejpam-4597	217	2	fsts	fst	NOUN
ejpam-4597	217	3	(	(	PUNCT
ejpam-4597	217	4	u	u	NOUN
ejpam-4597	217	5	,	,	PUNCT
ejpam-4597	217	6	δ	δ	PROPN
ejpam-4597	217	7	,	,	PUNCT
ejpam-4597	217	8	e	e	NOUN
ejpam-4597	217	9	)	)	PUNCT
ejpam-4597	217	10	is	be	AUX
ejpam-4597	217	11	said	say	VERB
ejpam-4597	217	12	to	to	PART
ejpam-4597	217	13	be	be	AUX
ejpam-4597	217	14	fs	f	NOUN
ejpam-4597	217	15	-	-	ADJ
ejpam-4597	217	16	symmetric	symmetric	ADJ
ejpam-4597	217	17	if	if	SCONJ
ejpam-4597	217	18	and	and	CCONJ
ejpam-4597	217	19	only	only	ADV
ejpam-4597	217	20	if	if	SCONJ
ejpam-4597	217	21	every	every	DET
ejpam-4597	217	22	fs	fs	NOUN
ejpam-4597	217	23	-	-	PUNCT
ejpam-4597	217	24	point	point	NOUN
ejpam-4597	217	25	xeα	xeα	PROPN
ejpam-4597	217	26	∈	∈	PROPN
ejpam-4597	217	27	fsp	fsp	PROPN
ejpam-4597	217	28	(	(	PUNCT
ejpam-4597	217	29	u	u	NOUN
ejpam-4597	217	30	)	)	PUNCT
ejpam-4597	217	31	is	be	AUX
ejpam-4597	217	32	an	an	DET
ejpam-4597	217	33	fsg	fsg	PROPN
ejpam-4597	217	34	-	-	PUNCT
ejpam-4597	217	35	closed	closed	ADJ
ejpam-4597	217	36	set	set	NOUN
ejpam-4597	217	37	.	.	PUNCT
ejpam-4597	218	1	remark	remark	PROPN
ejpam-4597	218	2	2	2	NUM
ejpam-4597	218	3	.	.	PUNCT
ejpam-4597	219	1	clearly	clearly	ADV
ejpam-4597	219	2	,	,	PUNCT
ejpam-4597	219	3	every	every	DET
ejpam-4597	219	4	fst	fst	NOUN
ejpam-4597	219	5	1	1	NUM
ejpam-4597	219	6	space	space	NOUN
ejpam-4597	219	7	is	be	AUX
ejpam-4597	219	8	fs	fs	ADJ
ejpam-4597	219	9	-	-	NOUN
ejpam-4597	219	10	symmetric	symmetric	ADJ
ejpam-4597	219	11	.	.	PUNCT
ejpam-4597	220	1	the	the	DET
ejpam-4597	220	2	next	next	ADJ
ejpam-4597	220	3	example	example	NOUN
ejpam-4597	220	4	shows	show	VERB
ejpam-4597	220	5	that	that	SCONJ
ejpam-4597	220	6	the	the	DET
ejpam-4597	220	7	converse	converse	NOUN
ejpam-4597	220	8	may	may	AUX
ejpam-4597	220	9	not	not	PART
ejpam-4597	220	10	be	be	AUX
ejpam-4597	220	11	true	true	ADJ
ejpam-4597	220	12	.	.	PUNCT
ejpam-4597	221	1	example	example	NOUN
ejpam-4597	222	1	2	2	NUM
ejpam-4597	222	2	.	.	PUNCT
ejpam-4597	222	3	let	let	VERB
ejpam-4597	222	4	u	u	PRON
ejpam-4597	222	5	=	=	PUNCT
ejpam-4597	222	6	{	{	PUNCT
ejpam-4597	222	7	x	x	NOUN
ejpam-4597	222	8	}	}	PUNCT
ejpam-4597	222	9	,	,	PUNCT
ejpam-4597	222	10	e	e	X
ejpam-4597	222	11	=	=	PUNCT
ejpam-4597	222	12	{	{	PUNCT
ejpam-4597	222	13	e	e	NOUN
ejpam-4597	222	14	}	}	PUNCT
ejpam-4597	222	15	,	,	PUNCT
ejpam-4597	222	16	and	and	CCONJ
ejpam-4597	222	17	δ	δ	PROPN
ejpam-4597	222	18	=	=	SYM
ejpam-4597	222	19	{	{	PUNCT
ejpam-4597	222	20	0e	0e	NOUN
ejpam-4597	222	21	,	,	PUNCT
ejpam-4597	222	22	1e	1e	PROPN
ejpam-4597	222	23	,	,	PUNCT
ejpam-4597	222	24	xe0.5	xe0.5	X
ejpam-4597	222	25	}	}	PUNCT
ejpam-4597	222	26	,	,	PUNCT
ejpam-4597	222	27	then	then	ADV
ejpam-4597	222	28	one	one	PRON
ejpam-4597	222	29	can	can	AUX
ejpam-4597	222	30	verify	verify	VERB
ejpam-4597	222	31	δ	δ	PROPN
ejpam-4597	222	32	is	be	AUX
ejpam-4597	222	33	fs	fs	ADJ
ejpam-4597	222	34	-	-	ADJ
ejpam-4597	222	35	symmetric	symmetric	ADJ
ejpam-4597	222	36	but	but	CCONJ
ejpam-4597	222	37	not	not	PART
ejpam-4597	222	38	fst	fst	NOUN
ejpam-4597	222	39	1	1	NUM
ejpam-4597	222	40	.	.	PUNCT
ejpam-4597	223	1	moreover	moreover	ADV
ejpam-4597	223	2	,	,	PUNCT
ejpam-4597	223	3	δ	δ	PROPN
ejpam-4597	223	4	is	be	AUX
ejpam-4597	223	5	not	not	PART
ejpam-4597	223	6	ft	ft	ADP
ejpam-4597	223	7	1	1	NUM
ejpam-4597	223	8	2	2	NUM
ejpam-4597	223	9	.	.	PUNCT
ejpam-4597	224	1	proposition	proposition	NOUN
ejpam-4597	224	2	2	2	NUM
ejpam-4597	224	3	.	.	PUNCT
ejpam-4597	225	1	an	an	DET
ejpam-4597	225	2	fsts	fst	NOUN
ejpam-4597	225	3	(	(	PUNCT
ejpam-4597	225	4	u	u	NOUN
ejpam-4597	225	5	,	,	PUNCT
ejpam-4597	225	6	δ	δ	PROPN
ejpam-4597	225	7	,	,	PUNCT
ejpam-4597	225	8	e	e	NOUN
ejpam-4597	225	9	)	)	PUNCT
ejpam-4597	225	10	is	be	AUX
ejpam-4597	225	11	fst	fst	NOUN
ejpam-4597	225	12	1	1	NUM
ejpam-4597	225	13	if	if	SCONJ
ejpam-4597	225	14	and	and	CCONJ
ejpam-4597	225	15	only	only	ADV
ejpam-4597	225	16	if	if	SCONJ
ejpam-4597	225	17	it	it	PRON
ejpam-4597	225	18	is	be	AUX
ejpam-4597	225	19	fs	fs	ADJ
ejpam-4597	225	20	-	-	ADJ
ejpam-4597	225	21	symmetric	symmetric	ADJ
ejpam-4597	225	22	and	and	CCONJ
ejpam-4597	225	23	fst	fst	NOUN
ejpam-4597	225	24	0	0	NUM
ejpam-4597	225	25	.	.	PUNCT
ejpam-4597	226	1	proof	proof	NOUN
ejpam-4597	226	2	.	.	PUNCT
ejpam-4597	227	1	clearly	clearly	ADV
ejpam-4597	227	2	,	,	PUNCT
ejpam-4597	227	3	if	if	SCONJ
ejpam-4597	227	4	(	(	PUNCT
ejpam-4597	227	5	u	u	NOUN
ejpam-4597	227	6	,	,	PUNCT
ejpam-4597	227	7	δ	δ	PROPN
ejpam-4597	227	8	,	,	PUNCT
ejpam-4597	227	9	e	e	NOUN
ejpam-4597	227	10	)	)	PUNCT
ejpam-4597	227	11	is	be	AUX
ejpam-4597	227	12	fst	fst	NOUN
ejpam-4597	227	13	1	1	NUM
ejpam-4597	227	14	,	,	PUNCT
ejpam-4597	227	15	then	then	ADV
ejpam-4597	227	16	it	it	PRON
ejpam-4597	227	17	is	be	AUX
ejpam-4597	227	18	fs	fs	ADJ
ejpam-4597	227	19	-	-	ADJ
ejpam-4597	227	20	symmetric	symmetric	ADJ
ejpam-4597	227	21	and	and	CCONJ
ejpam-4597	227	22	fst	fst	NOUN
ejpam-4597	227	23	0	0	NUM
ejpam-4597	227	24	.	.	PUNCT
ejpam-4597	228	1	conversely	conversely	ADV
ejpam-4597	228	2	,	,	PUNCT
ejpam-4597	228	3	let	let	VERB
ejpam-4597	228	4	(	(	PUNCT
ejpam-4597	228	5	u	u	NOUN
ejpam-4597	228	6	,	,	PUNCT
ejpam-4597	228	7	δ	δ	PROPN
ejpam-4597	228	8	,	,	PUNCT
ejpam-4597	228	9	e	e	NOUN
ejpam-4597	228	10	)	)	PUNCT
ejpam-4597	228	11	be	be	AUX
ejpam-4597	228	12	fs	fs	PROPN
ejpam-4597	228	13	-	-	ADJ
ejpam-4597	228	14	symmetric	symmetric	ADJ
ejpam-4597	228	15	and	and	CCONJ
ejpam-4597	228	16	fst	fst	NOUN
ejpam-4597	228	17	0	0	PUNCT
ejpam-4597	228	18	.	.	PUNCT
ejpam-4597	228	19	suppose	suppose	VERB
ejpam-4597	228	20	xeαq̃y	xeαq̃y	PROPN
ejpam-4597	228	21	e	e	PROPN
ejpam-4597	228	22	t	t	PROPN
ejpam-4597	228	23	.	.	PUNCT
ejpam-4597	229	1	then	then	ADV
ejpam-4597	229	2	either	either	CCONJ
ejpam-4597	229	3	xeαq̃cl(y	xeαq̃cl(y	PROPN
ejpam-4597	229	4	e	e	PROPN
ejpam-4597	229	5	t	t	PROPN
ejpam-4597	229	6	)	)	PUNCT
ejpam-4597	229	7	or	or	CCONJ
ejpam-4597	229	8	yet	yet	ADV
ejpam-4597	229	9	q̃cl(x	q̃cl(x	NOUN
ejpam-4597	229	10	e	e	NOUN
ejpam-4597	229	11	α	α	NOUN
ejpam-4597	229	12	)	)	PUNCT
ejpam-4597	229	13	.	.	PUNCT
ejpam-4597	230	1	by	by	ADP
ejpam-4597	230	2	fs	f	NOUN
ejpam-4597	230	3	-	-	PUNCT
ejpam-4597	230	4	symmetry	symmetry	NOUN
ejpam-4597	230	5	,	,	PUNCT
ejpam-4597	230	6	we	we	PRON
ejpam-4597	230	7	have	have	VERB
ejpam-4597	230	8	xeαq̃cl(y	xeαq̃cl(y	PROPN
ejpam-4597	230	9	e	e	PROPN
ejpam-4597	230	10	t	t	PROPN
ejpam-4597	230	11	)	)	PUNCT
ejpam-4597	230	12	and	and	CCONJ
ejpam-4597	230	13	yet	yet	ADV
ejpam-4597	230	14	q̃cl(x	q̃cl(x	NOUN
ejpam-4597	230	15	e	e	NOUN
ejpam-4597	230	16	α	α	NOUN
ejpam-4597	230	17	)	)	PUNCT
ejpam-4597	230	18	for	for	ADP
ejpam-4597	230	19	any	any	DET
ejpam-4597	230	20	xeα	xeα	NOUN
ejpam-4597	230	21	,	,	PUNCT
ejpam-4597	230	22	yet	yet	CCONJ
ejpam-4597	230	23	∈	∈	PROPN
ejpam-4597	230	24	fsp	fsp	PROPN
ejpam-4597	230	25	(	(	PUNCT
ejpam-4597	230	26	u	u	NOUN
ejpam-4597	230	27	)	)	PUNCT
ejpam-4597	230	28	.	.	PUNCT
ejpam-4597	231	1	the	the	DET
ejpam-4597	231	2	result	result	NOUN
ejpam-4597	231	3	holds	hold	VERB
ejpam-4597	231	4	.	.	PUNCT
ejpam-4597	232	1	theorem	theorem	NOUN
ejpam-4597	232	2	6	6	NUM
ejpam-4597	232	3	.	.	PUNCT
ejpam-4597	233	1	every	every	DET
ejpam-4597	233	2	fs	fs	PROPN
ejpam-4597	233	3	-	-	PUNCT
ejpam-4597	233	4	gr2	gr2	PROPN
ejpam-4597	233	5	space	space	NOUN
ejpam-4597	233	6	is	be	AUX
ejpam-4597	233	7	fst	fst	NOUN
ejpam-4597	233	8	2	2	NUM
ejpam-4597	233	9	1	1	NUM
ejpam-4597	233	10	2	2	NUM
ejpam-4597	233	11	.	.	PUNCT
ejpam-4597	234	1	proof	proof	NOUN
ejpam-4597	234	2	.	.	PUNCT
ejpam-4597	235	1	let	let	VERB
ejpam-4597	235	2	(	(	PUNCT
ejpam-4597	235	3	u	u	NOUN
ejpam-4597	235	4	,	,	PUNCT
ejpam-4597	235	5	δ	δ	PROPN
ejpam-4597	235	6	,	,	PUNCT
ejpam-4597	235	7	e	e	NOUN
ejpam-4597	235	8	)	)	PUNCT
ejpam-4597	235	9	be	be	AUX
ejpam-4597	235	10	fs	fs	PROPN
ejpam-4597	235	11	-	-	NOUN
ejpam-4597	235	12	gr2	gr2	PROPN
ejpam-4597	235	13	and	and	CCONJ
ejpam-4597	235	14	xeα	xeα	PROPN
ejpam-4597	235	15	,	,	PUNCT
ejpam-4597	235	16	y	y	PROPN
ejpam-4597	235	17	e	e	PROPN
ejpam-4597	235	18	t	t	PROPN
ejpam-4597	235	19	∈	∈	PROPN
ejpam-4597	235	20	fsp	fsp	PROPN
ejpam-4597	235	21	(	(	PUNCT
ejpam-4597	235	22	u	u	NOUN
ejpam-4597	235	23	)	)	PUNCT
ejpam-4597	235	24	with	with	ADP
ejpam-4597	235	25	xeαq̃y	xeαq̃y	PROPN
ejpam-4597	235	26	e	e	PROPN
ejpam-4597	235	27	t	t	PROPN
ejpam-4597	235	28	.	.	PUNCT
ejpam-4597	236	1	then	then	ADV
ejpam-4597	236	2	(	(	PUNCT
ejpam-4597	236	3	u	u	NOUN
ejpam-4597	236	4	,	,	PUNCT
ejpam-4597	236	5	δ	δ	PROPN
ejpam-4597	236	6	,	,	PUNCT
ejpam-4597	236	7	e	e	NOUN
ejpam-4597	236	8	)	)	PUNCT
ejpam-4597	236	9	is	be	AUX
ejpam-4597	236	10	fs	fs	ADJ
ejpam-4597	236	11	-	-	ADJ
ejpam-4597	236	12	symmetric	symmetric	ADJ
ejpam-4597	236	13	and	and	CCONJ
ejpam-4597	236	14	so	so	ADV
ejpam-4597	236	15	xeα	xeα	PROPN
ejpam-4597	236	16	is	be	AUX
ejpam-4597	236	17	an	an	DET
ejpam-4597	236	18	fsg	fsg	PROPN
ejpam-4597	236	19	-	-	PUNCT
ejpam-4597	236	20	closed	close	VERB
ejpam-4597	236	21	set	set	NOUN
ejpam-4597	236	22	.	.	PUNCT
ejpam-4597	237	1	from	from	ADP
ejpam-4597	237	2	theorem	theorem	NOUN
ejpam-4597	237	3	4	4	NUM
ejpam-4597	237	4	there	there	PRON
ejpam-4597	237	5	are	be	VERB
ejpam-4597	237	6	fso	fso	NOUN
ejpam-4597	237	7	-	-	PUNCT
ejpam-4597	237	8	sets	set	NOUN
ejpam-4597	237	9	oxe	oxe	PRON
ejpam-4597	237	10	α	α	NOUN
ejpam-4597	237	11	and	and	CCONJ
ejpam-4597	237	12	oyet	oyet	ADV
ejpam-4597	237	13	such	such	ADJ
ejpam-4597	237	14	that	that	SCONJ
ejpam-4597	237	15	cl(oxe	cl(oxe	PROPN
ejpam-4597	237	16	α	α	PROPN
ejpam-4597	237	17	)	)	PUNCT
ejpam-4597	237	18	q̃cl(oyet	q̃cl(oyet	ADV
ejpam-4597	237	19	)	)	PUNCT
ejpam-4597	237	20	.	.	PUNCT
ejpam-4597	238	1	hence	hence	ADV
ejpam-4597	238	2	the	the	DET
ejpam-4597	238	3	result	result	NOUN
ejpam-4597	238	4	holds	hold	VERB
ejpam-4597	238	5	.	.	PUNCT
ejpam-4597	239	1	proposition	proposition	NOUN
ejpam-4597	239	2	3	3	NUM
ejpam-4597	239	3	.	.	X
ejpam-4597	240	1	for	for	ADP
ejpam-4597	240	2	an	an	DET
ejpam-4597	240	3	fs	fs	ADJ
ejpam-4597	240	4	-	-	PUNCT
ejpam-4597	240	5	symmetric	symmetric	ADJ
ejpam-4597	240	6	space	space	NOUN
ejpam-4597	240	7	(	(	PUNCT
ejpam-4597	240	8	u	u	NOUN
ejpam-4597	240	9	,	,	PUNCT
ejpam-4597	240	10	δ	δ	PROPN
ejpam-4597	240	11	,	,	PUNCT
ejpam-4597	240	12	e	e	NOUN
ejpam-4597	240	13	)	)	PUNCT
ejpam-4597	240	14	.	.	PUNCT
ejpam-4597	241	1	the	the	DET
ejpam-4597	241	2	next	next	ADJ
ejpam-4597	241	3	properties	property	NOUN
ejpam-4597	241	4	are	be	AUX
ejpam-4597	241	5	equivalent	equivalent	ADJ
ejpam-4597	241	6	:	:	PUNCT
ejpam-4597	241	7	(	(	PUNCT
ejpam-4597	241	8	1	1	X
ejpam-4597	241	9	)	)	PUNCT
ejpam-4597	241	10	(	(	PUNCT
ejpam-4597	241	11	u	u	NOUN
ejpam-4597	241	12	,	,	PUNCT
ejpam-4597	241	13	δ	δ	PROPN
ejpam-4597	241	14	,	,	PUNCT
ejpam-4597	241	15	e	e	NOUN
ejpam-4597	241	16	)	)	PUNCT
ejpam-4597	241	17	is	be	AUX
ejpam-4597	241	18	fst	fst	NOUN
ejpam-4597	241	19	0	0	NUM
ejpam-4597	241	20	,	,	PUNCT
ejpam-4597	241	21	(	(	PUNCT
ejpam-4597	241	22	2	2	NUM
ejpam-4597	241	23	)	)	PUNCT
ejpam-4597	241	24	(	(	PUNCT
ejpam-4597	241	25	u	u	NOUN
ejpam-4597	241	26	,	,	PUNCT
ejpam-4597	241	27	δ	δ	PROPN
ejpam-4597	241	28	,	,	PUNCT
ejpam-4597	241	29	e	e	NOUN
ejpam-4597	241	30	)	)	PUNCT
ejpam-4597	241	31	is	be	AUX
ejpam-4597	241	32	fst	fst	NOUN
ejpam-4597	241	33	1	1	NUM
ejpam-4597	241	34	2	2	NUM
ejpam-4597	241	35	,	,	PUNCT
ejpam-4597	241	36	(	(	PUNCT
ejpam-4597	241	37	3	3	NUM
ejpam-4597	241	38	)	)	PUNCT
ejpam-4597	241	39	(	(	PUNCT
ejpam-4597	241	40	u	u	NOUN
ejpam-4597	241	41	,	,	PUNCT
ejpam-4597	241	42	δ	δ	PROPN
ejpam-4597	241	43	,	,	PUNCT
ejpam-4597	241	44	e	e	NOUN
ejpam-4597	241	45	)	)	PUNCT
ejpam-4597	241	46	is	be	AUX
ejpam-4597	241	47	fst	fst	NOUN
ejpam-4597	241	48	1	1	NUM
ejpam-4597	241	49	.	.	PUNCT
ejpam-4597	242	1	proof	proof	NOUN
ejpam-4597	242	2	.	.	PUNCT
ejpam-4597	243	1	it	it	PRON
ejpam-4597	243	2	is	be	AUX
ejpam-4597	243	3	obvious	obvious	ADJ
ejpam-4597	243	4	.	.	PUNCT
ejpam-4597	244	1	definition	definition	NOUN
ejpam-4597	244	2	12	12	NUM
ejpam-4597	244	3	.	.	PUNCT
ejpam-4597	245	1	an	an	DET
ejpam-4597	245	2	fsts	fst	NOUN
ejpam-4597	245	3	(	(	PUNCT
ejpam-4597	245	4	u	u	NOUN
ejpam-4597	245	5	,	,	PUNCT
ejpam-4597	245	6	δ	δ	PROPN
ejpam-4597	245	7	,	,	PUNCT
ejpam-4597	245	8	e	e	NOUN
ejpam-4597	245	9	)	)	PUNCT
ejpam-4597	245	10	is	be	AUX
ejpam-4597	245	11	called	call	VERB
ejpam-4597	245	12	fsg3	fsg3	PROPN
ejpam-4597	245	13	iff	iff	PROPN
ejpam-4597	245	14	it	it	PRON
ejpam-4597	245	15	is	be	AUX
ejpam-4597	245	16	fs	fs	ADJ
ejpam-4597	245	17	-	-	PUNCT
ejpam-4597	245	18	gr2	gr2	NOUN
ejpam-4597	245	19	and	and	CCONJ
ejpam-4597	245	20	fs	f	NOUN
ejpam-4597	245	21	-	-	ADJ
ejpam-4597	245	22	symmetric	symmetric	ADJ
ejpam-4597	245	23	.	.	PUNCT
ejpam-4597	246	1	proposition	proposition	NOUN
ejpam-4597	246	2	4	4	NUM
ejpam-4597	246	3	.	.	PUNCT
ejpam-4597	247	1	every	every	DET
ejpam-4597	247	2	fsg3	fsg3	NOUN
ejpam-4597	247	3	space	space	NOUN
ejpam-4597	247	4	is	be	AUX
ejpam-4597	247	5	fst	fst	NOUN
ejpam-4597	247	6	2	2	NUM
ejpam-4597	247	7	.	.	PUNCT
ejpam-4597	248	1	proof	proof	NOUN
ejpam-4597	248	2	.	.	PUNCT
ejpam-4597	249	1	it	it	PRON
ejpam-4597	249	2	follows	follow	VERB
ejpam-4597	249	3	directly	directly	ADV
ejpam-4597	249	4	from	from	ADP
ejpam-4597	249	5	the	the	DET
ejpam-4597	249	6	above	above	ADJ
ejpam-4597	249	7	definition	definition	NOUN
ejpam-4597	249	8	,	,	PUNCT
ejpam-4597	249	9	definition	definition	NOUN
ejpam-4597	249	10	10	10	NUM
ejpam-4597	249	11	,	,	PUNCT
ejpam-4597	249	12	and	and	CCONJ
ejpam-4597	249	13	corollary	corollary	ADJ
ejpam-4597	249	14	1	1	NUM
ejpam-4597	249	15	.	.	PUNCT
ejpam-4597	250	1	the	the	DET
ejpam-4597	250	2	next	next	ADJ
ejpam-4597	250	3	example	example	NOUN
ejpam-4597	250	4	shows	show	VERB
ejpam-4597	250	5	that	that	SCONJ
ejpam-4597	250	6	the	the	DET
ejpam-4597	250	7	converse	converse	NOUN
ejpam-4597	250	8	of	of	ADP
ejpam-4597	250	9	the	the	DET
ejpam-4597	250	10	above	above	ADJ
ejpam-4597	250	11	proposition	proposition	NOUN
ejpam-4597	250	12	may	may	AUX
ejpam-4597	250	13	not	not	PART
ejpam-4597	250	14	be	be	AUX
ejpam-4597	250	15	true	true	ADJ
ejpam-4597	250	16	.	.	PUNCT
ejpam-4597	251	1	s.	s.	PROPN
ejpam-4597	251	2	saleh	saleh	PROPN
ejpam-4597	251	3	,	,	PUNCT
ejpam-4597	251	4	j.	j.	PROPN
ejpam-4597	251	5	al	al	PROPN
ejpam-4597	251	6	-	-	PUNCT
ejpam-4597	251	7	mufarrij	mufarrij	PROPN
ejpam-4597	251	8	/	/	SYM
ejpam-4597	251	9	eur	eur	PROPN
ejpam-4597	251	10	.	.	PUNCT
ejpam-4597	252	1	j.	j.	PROPN
ejpam-4597	252	2	pure	pure	PROPN
ejpam-4597	252	3	appl	appl	PROPN
ejpam-4597	252	4	.	.	PROPN
ejpam-4597	252	5	math	math	PROPN
ejpam-4597	252	6	,	,	PUNCT
ejpam-4597	252	7	16	16	NUM
ejpam-4597	252	8	(	(	PUNCT
ejpam-4597	252	9	1	1	NUM
ejpam-4597	252	10	)	)	PUNCT
ejpam-4597	252	11	(	(	PUNCT
ejpam-4597	252	12	2023	2023	NUM
ejpam-4597	252	13	)	)	PUNCT
ejpam-4597	252	14	,	,	PUNCT
ejpam-4597	252	15	180	180	NUM
ejpam-4597	252	16	-	-	SYM
ejpam-4597	252	17	191	191	NUM
ejpam-4597	252	18	186	186	NUM
ejpam-4597	252	19	example	example	NOUN
ejpam-4597	252	20	3	3	NUM
ejpam-4597	252	21	.	.	PUNCT
ejpam-4597	253	1	let	let	VERB
ejpam-4597	253	2	u	u	PRON
ejpam-4597	253	3	be	be	AUX
ejpam-4597	253	4	an	an	DET
ejpam-4597	253	5	infinite	infinite	ADJ
ejpam-4597	253	6	set	set	NOUN
ejpam-4597	253	7	and	and	CCONJ
ejpam-4597	253	8	e	e	NOUN
ejpam-4597	253	9	=	=	PUNCT
ejpam-4597	253	10	{	{	PUNCT
ejpam-4597	253	11	e	e	NOUN
ejpam-4597	253	12	}	}	PUNCT
ejpam-4597	253	13	.	.	PUNCT
ejpam-4597	254	1	for	for	ADP
ejpam-4597	254	2	x	x	SYM
ejpam-4597	254	3	,	,	PUNCT
ejpam-4597	254	4	y	y	PROPN
ejpam-4597	254	5	∈	∈	PROPN
ejpam-4597	254	6	u	u	PROPN
ejpam-4597	254	7	,	,	PUNCT
ejpam-4597	254	8	x	x	PROPN
ejpam-4597	254	9	̸=	̸=	PROPN
ejpam-4597	254	10	y	y	PROPN
ejpam-4597	254	11	,	,	PUNCT
ejpam-4597	254	12	let	let	VERB
ejpam-4597	254	13	he	he	PRON
ejpam-4597	254	14	be	be	AUX
ejpam-4597	254	15	an	an	DET
ejpam-4597	254	16	fs	fs	NOUN
ejpam-4597	254	17	-	-	PUNCT
ejpam-4597	254	18	set	set	NOUN
ejpam-4597	254	19	on	on	ADP
ejpam-4597	254	20	u	u	NOUN
ejpam-4597	254	21	given	give	VERB
ejpam-4597	254	22	by	by	ADP
ejpam-4597	254	23	h(e)(z	h(e)(z	NOUN
ejpam-4597	254	24	)	)	PUNCT
ejpam-4597	254	25	=	=	SYM
ejpam-4597	254	26	1	1	NUM
ejpam-4597	254	27	if	if	SCONJ
ejpam-4597	254	28	z	z	NOUN
ejpam-4597	254	29	=	=	SYM
ejpam-4597	254	30	x	x	SYM
ejpam-4597	254	31	,	,	PUNCT
ejpam-4597	254	32	h(e)(z	h(e)(z	X
ejpam-4597	254	33	)	)	PUNCT
ejpam-4597	255	1	=	=	SYM
ejpam-4597	255	2	0	0	PUNCT
ejpam-4597	256	1	if	if	SCONJ
ejpam-4597	256	2	z	z	NOUN
ejpam-4597	256	3	=	=	SYM
ejpam-4597	256	4	y	y	PROPN
ejpam-4597	256	5	,	,	PUNCT
ejpam-4597	256	6	and	and	CCONJ
ejpam-4597	256	7	h	h	NOUN
ejpam-4597	256	8	(	(	PUNCT
ejpam-4597	256	9	e	e	NOUN
ejpam-4597	256	10	)	)	PUNCT
ejpam-4597	256	11	(	(	PUNCT
ejpam-4597	256	12	z	z	NOUN
ejpam-4597	256	13	)	)	PUNCT
ejpam-4597	256	14	=	=	SYM
ejpam-4597	256	15	0.5	0.5	NUM
ejpam-4597	256	16	if	if	SCONJ
ejpam-4597	256	17	z	z	PROPN
ejpam-4597	256	18	̸=	̸=	PROPN
ejpam-4597	256	19	x	x	NUM
ejpam-4597	256	20	,	,	PUNCT
ejpam-4597	256	21	z	z	PROPN
ejpam-4597	256	22	̸=	̸=	PROPN
ejpam-4597	256	23	y.	y.	NOUN
ejpam-4597	256	24	now	now	ADV
ejpam-4597	256	25	for	for	ADP
ejpam-4597	256	26	any	any	DET
ejpam-4597	256	27	z	z	NOUN
ejpam-4597	256	28	∈	∈	PROPN
ejpam-4597	256	29	u	u	PROPN
ejpam-4597	256	30	.	.	PUNCT
ejpam-4597	257	1	consider	consider	VERB
ejpam-4597	257	2	the	the	DET
ejpam-4597	257	3	fst	fst	PROPN
ejpam-4597	257	4	δ	δ	PROPN
ejpam-4597	257	5	on	on	ADP
ejpam-4597	257	6	u	u	NOUN
ejpam-4597	257	7	generated	generate	VERB
ejpam-4597	257	8	by	by	ADP
ejpam-4597	257	9	the	the	DET
ejpam-4597	257	10	class	class	NOUN
ejpam-4597	257	11	{	{	PUNCT
ejpam-4597	257	12	(	(	PUNCT
ejpam-4597	257	13	he)x	he)x	PROPN
ejpam-4597	257	14	,	,	PUNCT
ejpam-4597	257	15	y	y	NOUN
ejpam-4597	257	16	:	:	PUNCT
ejpam-4597	257	17	x	x	X
ejpam-4597	257	18	,	,	PUNCT
ejpam-4597	257	19	y	y	PROPN
ejpam-4597	257	20	∈	∈	PROPN
ejpam-4597	257	21	u	u	PROPN
ejpam-4597	257	22	,	,	PUNCT
ejpam-4597	257	23	x	x	PROPN
ejpam-4597	257	24	̸=	̸=	PROPN
ejpam-4597	257	25	y	y	PROPN
ejpam-4597	257	26	}	}	PUNCT
ejpam-4597	257	27	.	.	PUNCT
ejpam-4597	258	1	then	then	ADV
ejpam-4597	258	2	one	one	PRON
ejpam-4597	258	3	can	can	AUX
ejpam-4597	258	4	check	check	VERB
ejpam-4597	258	5	that	that	SCONJ
ejpam-4597	258	6	δ	δ	PROPN
ejpam-4597	258	7	is	be	AUX
ejpam-4597	258	8	fst	fst	NOUN
ejpam-4597	258	9	2	2	NUM
ejpam-4597	258	10	but	but	CCONJ
ejpam-4597	258	11	not	not	PART
ejpam-4597	258	12	fs	fs	PROPN
ejpam-4597	258	13	-	-	PUNCT
ejpam-4597	258	14	gr2	gr2	NOUN
ejpam-4597	258	15	and	and	CCONJ
ejpam-4597	258	16	so	so	ADV
ejpam-4597	258	17	not	not	PART
ejpam-4597	258	18	fsg3	fsg3	PROPN
ejpam-4597	258	19	.	.	PUNCT
ejpam-4597	259	1	theorem	theorem	VERB
ejpam-4597	259	2	7	7	NUM
ejpam-4597	259	3	.	.	PUNCT
ejpam-4597	260	1	an	an	DET
ejpam-4597	260	2	fsts(u	fsts(u	PROPN
ejpam-4597	260	3	,	,	PUNCT
ejpam-4597	260	4	δ	δ	PROPN
ejpam-4597	260	5	,	,	PUNCT
ejpam-4597	260	6	e	e	NOUN
ejpam-4597	260	7	)	)	PUNCT
ejpam-4597	260	8	is	be	AUX
ejpam-4597	260	9	fsg3	fsg3	ADJ
ejpam-4597	260	10	if	if	SCONJ
ejpam-4597	261	1	and	and	CCONJ
ejpam-4597	261	2	only	only	ADV
ejpam-4597	261	3	if	if	SCONJ
ejpam-4597	261	4	it	it	PRON
ejpam-4597	261	5	is	be	AUX
ejpam-4597	261	6	fst	fst	NOUN
ejpam-4597	261	7	3	3	NUM
ejpam-4597	261	8	.	.	PUNCT
ejpam-4597	262	1	proof	proof	NOUN
ejpam-4597	262	2	.	.	PUNCT
ejpam-4597	263	1	let	let	VERB
ejpam-4597	263	2	(	(	PUNCT
ejpam-4597	263	3	u	u	NOUN
ejpam-4597	263	4	,	,	PUNCT
ejpam-4597	263	5	δ	δ	PROPN
ejpam-4597	263	6	,	,	PUNCT
ejpam-4597	263	7	e	e	NOUN
ejpam-4597	263	8	)	)	PUNCT
ejpam-4597	263	9	be	be	AUX
ejpam-4597	263	10	an	an	DET
ejpam-4597	263	11	fsg3	fsg3	NOUN
ejpam-4597	263	12	-	-	PUNCT
ejpam-4597	263	13	space	space	NOUN
ejpam-4597	263	14	,	,	PUNCT
ejpam-4597	263	15	then	then	ADV
ejpam-4597	263	16	it	it	PRON
ejpam-4597	263	17	is	be	AUX
ejpam-4597	263	18	fs	fs	ADJ
ejpam-4597	263	19	-	-	PUNCT
ejpam-4597	263	20	gr2	gr2	NOUN
ejpam-4597	263	21	and	and	CCONJ
ejpam-4597	263	22	fs	f	NOUN
ejpam-4597	263	23	-	-	PUNCT
ejpam-4597	263	24	symmetric	symmetric	ADJ
ejpam-4597	263	25	.	.	PUNCT
ejpam-4597	264	1	now	now	ADV
ejpam-4597	264	2	,	,	PUNCT
ejpam-4597	264	3	every	every	DET
ejpam-4597	264	4	fs	fs	PROPN
ejpam-4597	264	5	-	-	PUNCT
ejpam-4597	264	6	gr2	gr2	PROPN
ejpam-4597	264	7	is	be	AUX
ejpam-4597	264	8	fsr2	fsr2	PROPN
ejpam-4597	264	9	and	and	CCONJ
ejpam-4597	264	10	every	every	DET
ejpam-4597	264	11	fsg3	fsg3	NOUN
ejpam-4597	264	12	is	be	AUX
ejpam-4597	264	13	fst	fst	NOUN
ejpam-4597	264	14	2	2	NUM
ejpam-4597	264	15	.	.	PUNCT
ejpam-4597	265	1	thus	thus	ADV
ejpam-4597	265	2	(	(	PUNCT
ejpam-4597	265	3	u	u	NOUN
ejpam-4597	265	4	,	,	PUNCT
ejpam-4597	265	5	δ	δ	PROPN
ejpam-4597	265	6	,	,	PUNCT
ejpam-4597	265	7	e	e	NOUN
ejpam-4597	265	8	)	)	PUNCT
ejpam-4597	265	9	is	be	AUX
ejpam-4597	265	10	fsr2	fsr2	PROPN
ejpam-4597	265	11	and	and	CCONJ
ejpam-4597	265	12	fst	fst	NOUN
ejpam-4597	265	13	2	2	NUM
ejpam-4597	265	14	.	.	PUNCT
ejpam-4597	266	1	so	so	ADV
ejpam-4597	266	2	the	the	DET
ejpam-4597	266	3	result	result	NOUN
ejpam-4597	266	4	holds	hold	VERB
ejpam-4597	266	5	.	.	PUNCT
ejpam-4597	267	1	conversely	conversely	ADV
ejpam-4597	267	2	,	,	PUNCT
ejpam-4597	267	3	let	let	VERB
ejpam-4597	267	4	(	(	PUNCT
ejpam-4597	267	5	u	u	NOUN
ejpam-4597	267	6	,	,	PUNCT
ejpam-4597	267	7	δ	δ	PROPN
ejpam-4597	267	8	,	,	PUNCT
ejpam-4597	267	9	e	e	NOUN
ejpam-4597	267	10	)	)	PUNCT
ejpam-4597	267	11	be	be	AUX
ejpam-4597	267	12	fst	fst	NOUN
ejpam-4597	267	13	3	3	NUM
ejpam-4597	267	14	,	,	PUNCT
ejpam-4597	267	15	then	then	ADV
ejpam-4597	267	16	it	it	PRON
ejpam-4597	267	17	is	be	AUX
ejpam-4597	267	18	fsr2	fsr2	PROPN
ejpam-4597	267	19	and	and	CCONJ
ejpam-4597	267	20	ft	ft	PROPN
ejpam-4597	267	21	1	1	NUM
ejpam-4597	267	22	and	and	CCONJ
ejpam-4597	267	23	so	so	ADV
ejpam-4597	267	24	,	,	PUNCT
ejpam-4597	267	25	it	it	PRON
ejpam-4597	267	26	is	be	AUX
ejpam-4597	267	27	fst	fst	NOUN
ejpam-4597	267	28	1	1	NUM
ejpam-4597	267	29	2	2	NUM
ejpam-4597	267	30	and	and	CCONJ
ejpam-4597	267	31	fssymmetric	fssymmetric	ADJ
ejpam-4597	267	32	.	.	PUNCT
ejpam-4597	268	1	thus	thus	ADV
ejpam-4597	268	2	(	(	PUNCT
ejpam-4597	268	3	u	u	NOUN
ejpam-4597	268	4	,	,	PUNCT
ejpam-4597	268	5	δ	δ	PROPN
ejpam-4597	268	6	,	,	PUNCT
ejpam-4597	268	7	e	e	NOUN
ejpam-4597	268	8	)	)	PUNCT
ejpam-4597	268	9	is	be	AUX
ejpam-4597	268	10	fsr2	fsr2	PROPN
ejpam-4597	268	11	and	and	CCONJ
ejpam-4597	268	12	fst	fst	PROPN
ejpam-4597	268	13	1	1	NUM
ejpam-4597	268	14	2	2	NUM
ejpam-4597	268	15	which	which	PRON
ejpam-4597	268	16	implies	imply	VERB
ejpam-4597	268	17	that	that	SCONJ
ejpam-4597	268	18	(	(	PUNCT
ejpam-4597	268	19	u	u	NOUN
ejpam-4597	268	20	,	,	PUNCT
ejpam-4597	268	21	δ	δ	PROPN
ejpam-4597	268	22	,	,	PUNCT
ejpam-4597	268	23	e	e	NOUN
ejpam-4597	268	24	)	)	PUNCT
ejpam-4597	268	25	is	be	AUX
ejpam-4597	268	26	fs	fs	PROPN
ejpam-4597	268	27	-	-	PUNCT
ejpam-4597	268	28	gr2	gr2	NOUN
ejpam-4597	268	29	.	.	PUNCT
ejpam-4597	269	1	since	since	SCONJ
ejpam-4597	269	2	(	(	PUNCT
ejpam-4597	269	3	u	u	NOUN
ejpam-4597	269	4	,	,	PUNCT
ejpam-4597	269	5	δ	δ	PROPN
ejpam-4597	269	6	,	,	PUNCT
ejpam-4597	269	7	e	e	NOUN
ejpam-4597	269	8	)	)	PUNCT
ejpam-4597	269	9	is	be	AUX
ejpam-4597	269	10	fs	fs	PROPN
ejpam-4597	269	11	-	-	NOUN
ejpam-4597	269	12	symmetric	symmetric	ADJ
ejpam-4597	269	13	.	.	PUNCT
ejpam-4597	270	1	hence	hence	ADV
ejpam-4597	270	2	(	(	PUNCT
ejpam-4597	270	3	u	u	NOUN
ejpam-4597	270	4	,	,	PUNCT
ejpam-4597	270	5	δ	δ	PROPN
ejpam-4597	270	6	,	,	PUNCT
ejpam-4597	270	7	e	e	NOUN
ejpam-4597	270	8	)	)	PUNCT
ejpam-4597	270	9	is	be	AUX
ejpam-4597	270	10	fsg3	fsg3	PROPN
ejpam-4597	270	11	.	.	PUNCT
ejpam-4597	271	1	3	3	X
ejpam-4597	271	2	.	.	X
ejpam-4597	271	3	fuzzy	fuzzy	ADJ
ejpam-4597	271	4	soft	soft	ADJ
ejpam-4597	271	5	g	g	NOUN
ejpam-4597	271	6	-	-	PUNCT
ejpam-4597	271	7	normal	normal	ADJ
ejpam-4597	271	8	spaces	space	NOUN
ejpam-4597	271	9	definition	definition	NOUN
ejpam-4597	271	10	13	13	NUM
ejpam-4597	271	11	.	.	PUNCT
ejpam-4597	272	1	an	an	DET
ejpam-4597	272	2	fsts	fst	NOUN
ejpam-4597	272	3	(	(	PUNCT
ejpam-4597	272	4	u	u	NOUN
ejpam-4597	272	5	,	,	PUNCT
ejpam-4597	272	6	δ	δ	PROPN
ejpam-4597	272	7	,	,	PUNCT
ejpam-4597	272	8	e	e	NOUN
ejpam-4597	272	9	)	)	PUNCT
ejpam-4597	272	10	is	be	AUX
ejpam-4597	272	11	said	say	VERB
ejpam-4597	272	12	to	to	PART
ejpam-4597	272	13	be	be	AUX
ejpam-4597	272	14	fsg	fsg	NOUN
ejpam-4597	272	15	-	-	ADJ
ejpam-4597	272	16	normal	normal	ADJ
ejpam-4597	272	17	(	(	PUNCT
ejpam-4597	272	18	or	or	CCONJ
ejpam-4597	272	19	fs	f	NOUN
ejpam-4597	272	20	-	-	PUNCT
ejpam-4597	272	21	gr3	gr3	NOUN
ejpam-4597	272	22	)	)	PUNCT
ejpam-4597	272	23	if	if	SCONJ
ejpam-4597	272	24	for	for	ADP
ejpam-4597	272	25	every	every	DET
ejpam-4597	272	26	fsgclosed	fsgclosed	ADJ
ejpam-4597	272	27	sets	set	NOUN
ejpam-4597	272	28	fe	fe	NOUN
ejpam-4597	272	29	and	and	CCONJ
ejpam-4597	272	30	he	he	PRON
ejpam-4597	272	31	with	with	ADP
ejpam-4597	272	32	fe	fe	X
ejpam-4597	272	33	q̃he	q̃he	PROPN
ejpam-4597	272	34	,	,	PUNCT
ejpam-4597	272	35	there	there	PRON
ejpam-4597	272	36	are	be	VERB
ejpam-4597	272	37	fso	fso	NOUN
ejpam-4597	272	38	-	-	PUNCT
ejpam-4597	272	39	sets	set	NOUN
ejpam-4597	272	40	ofe	ofe	ADJ
ejpam-4597	272	41	and	and	CCONJ
ejpam-4597	272	42	ohe	ohe	NOUN
ejpam-4597	272	43	containing	contain	VERB
ejpam-4597	272	44	fe	fe	NOUN
ejpam-4597	272	45	and	and	CCONJ
ejpam-4597	272	46	he	he	PRON
ejpam-4597	272	47	respectively	respectively	ADV
ejpam-4597	272	48	,	,	PUNCT
ejpam-4597	272	49	such	such	ADJ
ejpam-4597	272	50	that	that	SCONJ
ejpam-4597	272	51	ofe	ofe	INTJ
ejpam-4597	272	52	q̃	q̃	PROPN
ejpam-4597	272	53	ohe	ohe	NOUN
ejpam-4597	272	54	.	.	PUNCT
ejpam-4597	273	1	remark	remark	PROPN
ejpam-4597	273	2	3	3	NUM
ejpam-4597	273	3	.	.	PUNCT
ejpam-4597	274	1	clearly	clearly	ADV
ejpam-4597	274	2	,	,	PUNCT
ejpam-4597	274	3	every	every	DET
ejpam-4597	274	4	fs	fs	ADJ
ejpam-4597	274	5	-	-	PUNCT
ejpam-4597	274	6	gr3	gr3	NOUN
ejpam-4597	274	7	space	space	NOUN
ejpam-4597	274	8	is	be	AUX
ejpam-4597	274	9	fsr3	fsr3	NOUN
ejpam-4597	274	10	.	.	PUNCT
ejpam-4597	275	1	theorem	theorem	VERB
ejpam-4597	275	2	8	8	NUM
ejpam-4597	275	3	.	.	PUNCT
ejpam-4597	276	1	an	an	DET
ejpam-4597	276	2	fsts	fst	NOUN
ejpam-4597	276	3	(	(	PUNCT
ejpam-4597	276	4	u	u	NOUN
ejpam-4597	276	5	,	,	PUNCT
ejpam-4597	276	6	δ	δ	PROPN
ejpam-4597	276	7	,	,	PUNCT
ejpam-4597	276	8	e	e	NOUN
ejpam-4597	276	9	)	)	PUNCT
ejpam-4597	276	10	is	be	AUX
ejpam-4597	276	11	fs	f	NOUN
ejpam-4597	276	12	-	-	PUNCT
ejpam-4597	276	13	gr3	gr3	NOUN
ejpam-4597	276	14	if	if	SCONJ
ejpam-4597	276	15	and	and	CCONJ
ejpam-4597	276	16	only	only	ADV
ejpam-4597	276	17	if	if	SCONJ
ejpam-4597	276	18	for	for	ADP
ejpam-4597	276	19	any	any	DET
ejpam-4597	276	20	fsg	fsg	NOUN
ejpam-4597	276	21	-	-	PUNCT
ejpam-4597	276	22	closed	close	VERB
ejpam-4597	276	23	set	set	VERB
ejpam-4597	276	24	fe	fe	NOUN
ejpam-4597	276	25	and	and	CCONJ
ejpam-4597	276	26	for	for	ADP
ejpam-4597	276	27	any	any	DET
ejpam-4597	276	28	fso	fso	NOUN
ejpam-4597	276	29	-	-	PUNCT
ejpam-4597	276	30	set	set	VERB
ejpam-4597	276	31	ofe	ofe	NOUN
ejpam-4597	276	32	containing	contain	VERB
ejpam-4597	276	33	fe	fe	NOUN
ejpam-4597	276	34	,	,	PUNCT
ejpam-4597	276	35	there	there	PRON
ejpam-4597	276	36	is	be	VERB
ejpam-4597	276	37	o∗	o∗	PROPN
ejpam-4597	276	38	fe	fe	X
ejpam-4597	276	39	∈	∈	PROPN
ejpam-4597	276	40	δ	δ	PROPN
ejpam-4597	276	41	such	such	ADJ
ejpam-4597	276	42	that	that	DET
ejpam-4597	276	43	cl(o∗	cl(o∗	PROPN
ejpam-4597	276	44	fe	fe	X
ejpam-4597	276	45	)	)	PUNCT
ejpam-4597	277	1	⊑	⊑	PROPN
ejpam-4597	277	2	ofe	ofe	INTJ
ejpam-4597	277	3	.	.	PUNCT
ejpam-4597	278	1	proof	proof	NOUN
ejpam-4597	278	2	.	.	PUNCT
ejpam-4597	279	1	let	let	VERB
ejpam-4597	279	2	(	(	PUNCT
ejpam-4597	279	3	u	u	NOUN
ejpam-4597	279	4	,	,	PUNCT
ejpam-4597	279	5	δ	δ	PROPN
ejpam-4597	279	6	,	,	PUNCT
ejpam-4597	279	7	e	e	NOUN
ejpam-4597	279	8	)	)	PUNCT
ejpam-4597	279	9	be	be	AUX
ejpam-4597	279	10	an	an	DET
ejpam-4597	279	11	fs	fs	ADJ
ejpam-4597	279	12	-	-	PUNCT
ejpam-4597	279	13	gr3	gr3	NOUN
ejpam-4597	279	14	space	space	NOUN
ejpam-4597	279	15	,	,	PUNCT
ejpam-4597	279	16	he	he	PRON
ejpam-4597	279	17	be	be	VERB
ejpam-4597	279	18	any	any	DET
ejpam-4597	279	19	fsg	fsg	NOUN
ejpam-4597	279	20	-	-	PUNCT
ejpam-4597	279	21	closed	closed	ADJ
ejpam-4597	279	22	set	set	NOUN
ejpam-4597	279	23	,	,	PUNCT
ejpam-4597	279	24	and	and	CCONJ
ejpam-4597	279	25	let	let	VERB
ejpam-4597	279	26	ohe	ohe	NOUN
ejpam-4597	279	27	be	be	AUX
ejpam-4597	279	28	any	any	DET
ejpam-4597	279	29	fso	fso	NOUN
ejpam-4597	279	30	-	-	PUNCT
ejpam-4597	279	31	set	set	NOUN
ejpam-4597	279	32	containing	contain	VERB
ejpam-4597	279	33	he	he	PRON
ejpam-4597	279	34	,	,	PUNCT
ejpam-4597	279	35	then	then	ADV
ejpam-4597	279	36	oc	oc	VERB
ejpam-4597	279	37	he	he	PRON
ejpam-4597	279	38	is	be	AUX
ejpam-4597	279	39	an	an	DET
ejpam-4597	279	40	fsc	fsc	PROPN
ejpam-4597	279	41	-	-	PUNCT
ejpam-4597	279	42	set	set	NOUN
ejpam-4597	279	43	.	.	PUNCT
ejpam-4597	280	1	it	it	PRON
ejpam-4597	280	2	is	be	AUX
ejpam-4597	280	3	known	know	VERB
ejpam-4597	280	4	that	that	SCONJ
ejpam-4597	280	5	ohe	ohe	PROPN
ejpam-4597	280	6	q̃oc	q̃oc	PROPN
ejpam-4597	280	7	he	he	PRON
ejpam-4597	280	8	and	and	CCONJ
ejpam-4597	280	9	so	so	ADV
ejpam-4597	280	10	,	,	PUNCT
ejpam-4597	280	11	he	he	PRON
ejpam-4597	280	12	q̃o	q̃o	VERB
ejpam-4597	280	13	c	c	VERB
ejpam-4597	280	14	he	he	PRON
ejpam-4597	280	15	.	.	PUNCT
ejpam-4597	281	1	since	since	SCONJ
ejpam-4597	281	2	(	(	PUNCT
ejpam-4597	281	3	u	u	NOUN
ejpam-4597	281	4	,	,	PUNCT
ejpam-4597	281	5	δ	δ	PROPN
ejpam-4597	281	6	,	,	PUNCT
ejpam-4597	281	7	e	e	NOUN
ejpam-4597	281	8	)	)	PUNCT
ejpam-4597	281	9	is	be	AUX
ejpam-4597	281	10	fs	f	NOUN
ejpam-4597	281	11	-	-	PUNCT
ejpam-4597	281	12	gr3	gr3	NOUN
ejpam-4597	281	13	,	,	PUNCT
ejpam-4597	281	14	there	there	PRON
ejpam-4597	281	15	are	be	VERB
ejpam-4597	281	16	fso	fso	NOUN
ejpam-4597	281	17	-	-	PUNCT
ejpam-4597	281	18	sets	set	NOUN
ejpam-4597	281	19	o∗	o∗	PROPN
ejpam-4597	281	20	he	he	PRON
ejpam-4597	281	21	and	and	CCONJ
ejpam-4597	281	22	ooc	ooc	ADV
ejpam-4597	281	23	he	he	PRON
ejpam-4597	281	24	such	such	ADJ
ejpam-4597	281	25	that	that	SCONJ
ejpam-4597	281	26	o∗	o∗	PROPN
ejpam-4597	281	27	he	he	PRON
ejpam-4597	281	28	q̃ooc	q̃ooc	ADV
ejpam-4597	281	29	he	he	PRON
ejpam-4597	281	30	and	and	CCONJ
ejpam-4597	281	31	so	so	ADV
ejpam-4597	281	32	,	,	PUNCT
ejpam-4597	281	33	o∗	o∗	PROPN
ejpam-4597	281	34	he	he	PRON
ejpam-4597	281	35	⊑	⊑	VERB
ejpam-4597	281	36	oc	oc	VERB
ejpam-4597	281	37	oc	oc	VERB
ejpam-4597	281	38	he	he	PRON
ejpam-4597	281	39	and	and	CCONJ
ejpam-4597	281	40	cl(o∗	cl(o∗	VERB
ejpam-4597	281	41	he	he	PRON
ejpam-4597	281	42	)	)	PUNCT
ejpam-4597	281	43	⊑	⊑	PRON
ejpam-4597	281	44	oc	oc	AUX
ejpam-4597	281	45	oc	oc	VERB
ejpam-4597	281	46	he	he	PRON
ejpam-4597	281	47	.	.	PUNCT
ejpam-4597	282	1	since	since	SCONJ
ejpam-4597	282	2	oc	oc	VERB
ejpam-4597	282	3	he	he	PRON
ejpam-4597	282	4	⊑ooc	⊑ooc	ADV
ejpam-4597	282	5	he	he	PRON
ejpam-4597	282	6	we	we	PRON
ejpam-4597	282	7	get	get	VERB
ejpam-4597	282	8	oc	oc	ADP
ejpam-4597	282	9	oc	oc	ADP
ejpam-4597	282	10	he	he	PRON
ejpam-4597	282	11	⊑ohe	⊑ohe	ADJ
ejpam-4597	282	12	and	and	CCONJ
ejpam-4597	282	13	cl(o∗	cl(o∗	VERB
ejpam-4597	282	14	he	he	PRON
ejpam-4597	282	15	)	)	PUNCT
ejpam-4597	283	1	⊑oc	⊑oc	PROPN
ejpam-4597	283	2	oc	oc	ADP
ejpam-4597	283	3	he	he	PRON
ejpam-4597	283	4	⊑o	⊑o	VERB
ejpam-4597	283	5	he	he	PRON
ejpam-4597	283	6	.	.	PUNCT
ejpam-4597	284	1	hence	hence	ADV
ejpam-4597	284	2	the	the	DET
ejpam-4597	284	3	result	result	NOUN
ejpam-4597	284	4	holds	hold	VERB
ejpam-4597	284	5	.	.	PUNCT
ejpam-4597	285	1	conversely	conversely	ADV
ejpam-4597	285	2	,	,	PUNCT
ejpam-4597	285	3	it	it	PRON
ejpam-4597	285	4	follows	follow	VERB
ejpam-4597	285	5	directly	directly	ADV
ejpam-4597	285	6	from	from	ADP
ejpam-4597	285	7	hypothesis	hypothesis	NOUN
ejpam-4597	285	8	.	.	PUNCT
ejpam-4597	286	1	theorem	theorem	VERB
ejpam-4597	286	2	9	9	NUM
ejpam-4597	286	3	.	.	PUNCT
ejpam-4597	287	1	an	an	DET
ejpam-4597	287	2	fsts	fst	NOUN
ejpam-4597	287	3	(	(	PUNCT
ejpam-4597	287	4	u	u	NOUN
ejpam-4597	287	5	,	,	PUNCT
ejpam-4597	287	6	δ	δ	PROPN
ejpam-4597	287	7	,	,	PUNCT
ejpam-4597	287	8	e	e	NOUN
ejpam-4597	287	9	)	)	PUNCT
ejpam-4597	287	10	is	be	AUX
ejpam-4597	287	11	fs	f	NOUN
ejpam-4597	287	12	-	-	PUNCT
ejpam-4597	287	13	gr3	gr3	NOUN
ejpam-4597	287	14	if	if	SCONJ
ejpam-4597	287	15	and	and	CCONJ
ejpam-4597	287	16	only	only	ADV
ejpam-4597	287	17	if	if	SCONJ
ejpam-4597	287	18	for	for	ADP
ejpam-4597	287	19	any	any	DET
ejpam-4597	287	20	fsg	fsg	NOUN
ejpam-4597	287	21	-	-	PUNCT
ejpam-4597	287	22	closed	close	VERB
ejpam-4597	287	23	sets	set	NOUN
ejpam-4597	287	24	fe	fe	X
ejpam-4597	287	25	and	and	CCONJ
ejpam-4597	287	26	ge	ge	PROPN
ejpam-4597	287	27	with	with	ADP
ejpam-4597	287	28	fe	fe	PROPN
ejpam-4597	287	29	q̃ge	q̃ge	PROPN
ejpam-4597	287	30	,	,	PUNCT
ejpam-4597	287	31	there	there	PRON
ejpam-4597	287	32	are	be	VERB
ejpam-4597	287	33	fso	fso	NOUN
ejpam-4597	287	34	-	-	PUNCT
ejpam-4597	287	35	sets	set	NOUN
ejpam-4597	287	36	ofe	ofe	ADJ
ejpam-4597	287	37	and	and	CCONJ
ejpam-4597	287	38	oge	oge	NOUN
ejpam-4597	287	39	containing	contain	VERB
ejpam-4597	287	40	fe	fe	NOUN
ejpam-4597	287	41	and	and	CCONJ
ejpam-4597	287	42	he	he	PRON
ejpam-4597	287	43	respectively	respectively	ADV
ejpam-4597	287	44	,	,	PUNCT
ejpam-4597	287	45	such	such	ADJ
ejpam-4597	287	46	that	that	DET
ejpam-4597	287	47	cl(ofe	cl(ofe	NOUN
ejpam-4597	287	48	)	)	PUNCT
ejpam-4597	287	49	q̃	q̃	PROPN
ejpam-4597	287	50	cl(oge	cl(oge	PROPN
ejpam-4597	287	51	)	)	PUNCT
ejpam-4597	287	52	.	.	PUNCT
ejpam-4597	288	1	proof	proof	NOUN
ejpam-4597	288	2	.	.	PUNCT
ejpam-4597	289	1	let	let	VERB
ejpam-4597	289	2	(	(	PUNCT
ejpam-4597	289	3	u	u	NOUN
ejpam-4597	289	4	,	,	PUNCT
ejpam-4597	289	5	δ	δ	PROPN
ejpam-4597	289	6	,	,	PUNCT
ejpam-4597	289	7	e	e	NOUN
ejpam-4597	289	8	)	)	PUNCT
ejpam-4597	289	9	be	be	AUX
ejpam-4597	289	10	fs	f	NOUN
ejpam-4597	289	11	-	-	PUNCT
ejpam-4597	289	12	gr3	gr3	NOUN
ejpam-4597	289	13	and	and	CCONJ
ejpam-4597	289	14	fe	fe	X
ejpam-4597	289	15	,	,	PUNCT
ejpam-4597	289	16	ge	ge	PROPN
ejpam-4597	289	17	be	be	AUX
ejpam-4597	289	18	any	any	DET
ejpam-4597	289	19	fsg	fsg	NOUN
ejpam-4597	289	20	-	-	PUNCT
ejpam-4597	289	21	closed	close	VERB
ejpam-4597	289	22	sets	set	NOUN
ejpam-4597	289	23	with	with	ADP
ejpam-4597	289	24	fe	fe	PROPN
ejpam-4597	289	25	q̃ge	q̃ge	PROPN
ejpam-4597	289	26	,	,	PUNCT
ejpam-4597	289	27	there	there	PRON
ejpam-4597	289	28	exist	exist	VERB
ejpam-4597	289	29	o	o	NOUN
ejpam-4597	289	30	#	#	NOUN
ejpam-4597	289	31	fe	fe	NOUN
ejpam-4597	289	32	,	,	PUNCT
ejpam-4597	289	33	oge	oge	PROPN
ejpam-4597	289	34	∈	∈	PROPN
ejpam-4597	289	35	δ	δ	PROPN
ejpam-4597	289	36	such	such	ADJ
ejpam-4597	289	37	that	that	SCONJ
ejpam-4597	290	1	o	o	NOUN
ejpam-4597	290	2	#	#	NOUN
ejpam-4597	290	3	fe	fe	NOUN
ejpam-4597	290	4	q̃oge	q̃oge	NOUN
ejpam-4597	290	5	=	=	NOUN
ejpam-4597	290	6	⇒	⇒	NOUN
ejpam-4597	290	7	o	o	NOUN
ejpam-4597	290	8	#	#	NOUN
ejpam-4597	290	9	fe	fe	X
ejpam-4597	290	10	q̃cl(oge	q̃cl(oge	NOUN
ejpam-4597	290	11	)	)	PUNCT
ejpam-4597	290	12	(	(	PUNCT
ejpam-4597	290	13	by	by	ADP
ejpam-4597	290	14	lemma	lemma	PROPN
ejpam-4597	290	15	1	1	NUM
ejpam-4597	290	16	)	)	PUNCT
ejpam-4597	290	17	.	.	PUNCT
ejpam-4597	291	1	a	a	DET
ejpam-4597	291	2	gain	gain	NOUN
ejpam-4597	291	3	,	,	PUNCT
ejpam-4597	291	4	since	since	SCONJ
ejpam-4597	291	5	(	(	PUNCT
ejpam-4597	291	6	u	u	NOUN
ejpam-4597	291	7	,	,	PUNCT
ejpam-4597	291	8	δ	δ	PROPN
ejpam-4597	291	9	,	,	PUNCT
ejpam-4597	291	10	e	e	NOUN
ejpam-4597	291	11	)	)	PUNCT
ejpam-4597	291	12	is	be	AUX
ejpam-4597	291	13	fs	f	NOUN
ejpam-4597	291	14	-	-	PUNCT
ejpam-4597	291	15	gr3	gr3	NOUN
ejpam-4597	291	16	,	,	PUNCT
ejpam-4597	291	17	then	then	ADV
ejpam-4597	291	18	there	there	PRON
ejpam-4597	291	19	are	be	VERB
ejpam-4597	291	20	o∗	o∗	PROPN
ejpam-4597	291	21	fe	fe	X
ejpam-4597	291	22	,	,	PUNCT
ejpam-4597	291	23	ocl(oge	ocl(oge	PROPN
ejpam-4597	291	24	)	)	PUNCT
ejpam-4597	292	1	∈	∈	PROPN
ejpam-4597	292	2	δ	δ	PROPN
ejpam-4597	292	3	such	such	ADJ
ejpam-4597	292	4	that	that	SCONJ
ejpam-4597	292	5	o∗	o∗	PROPN
ejpam-4597	292	6	fe	fe	X
ejpam-4597	292	7	q̃ocl(oge	q̃ocl(oge	PROPN
ejpam-4597	292	8	)	)	PUNCT
ejpam-4597	293	1	=	=	NOUN
ejpam-4597	293	2	⇒	⇒	NOUN
ejpam-4597	293	3	cl(o∗	cl(o∗	PROPN
ejpam-4597	293	4	fe	fe	X
ejpam-4597	293	5	)	)	PUNCT
ejpam-4597	293	6	q̃ocl(oge	q̃ocl(oge	PROPN
ejpam-4597	293	7	)	)	PUNCT
ejpam-4597	293	8	(	(	PUNCT
ejpam-4597	293	9	by	by	ADP
ejpam-4597	293	10	lemma	lemma	PROPN
ejpam-4597	293	11	1	1	NUM
ejpam-4597	293	12	)	)	PUNCT
ejpam-4597	293	13	.	.	PUNCT
ejpam-4597	294	1	now	now	ADV
ejpam-4597	294	2	we	we	PRON
ejpam-4597	294	3	put	put	VERB
ejpam-4597	294	4	ofe	ofe	ADJ
ejpam-4597	294	5	=	=	NOUN
ejpam-4597	294	6	o	o	NOUN
ejpam-4597	294	7	#	#	NOUN
ejpam-4597	294	8	fe	fe	NOUN
ejpam-4597	294	9	⊓	⊓	PROPN
ejpam-4597	294	10	o∗	o∗	PROPN
ejpam-4597	294	11	fe	fe	X
ejpam-4597	294	12	.	.	PUNCT
ejpam-4597	295	1	since	since	SCONJ
ejpam-4597	295	2	(	(	PUNCT
ejpam-4597	295	3	u	u	NOUN
ejpam-4597	295	4	,	,	PUNCT
ejpam-4597	295	5	δ	δ	PROPN
ejpam-4597	295	6	,	,	PUNCT
ejpam-4597	295	7	e	e	NOUN
ejpam-4597	295	8	)	)	PUNCT
ejpam-4597	295	9	is	be	AUX
ejpam-4597	295	10	fsgr3	fsgr3	ADJ
ejpam-4597	295	11	and	and	CCONJ
ejpam-4597	295	12	o	o	NOUN
ejpam-4597	295	13	#	#	NOUN
ejpam-4597	295	14	fe	fe	X
ejpam-4597	295	15	∈	∈	PROPN
ejpam-4597	295	16	δ	δ	PROPN
ejpam-4597	295	17	,	,	PUNCT
ejpam-4597	295	18	by	by	ADP
ejpam-4597	295	19	the	the	DET
ejpam-4597	295	20	above	above	ADJ
ejpam-4597	295	21	theorem	theorem	NOUN
ejpam-4597	295	22	there	there	PRON
ejpam-4597	295	23	is	be	VERB
ejpam-4597	295	24	ofe	ofe	ADJ
ejpam-4597	295	25	∈	∈	PROPN
ejpam-4597	295	26	δ	δ	PROPN
ejpam-4597	295	27	such	such	ADJ
ejpam-4597	295	28	that	that	DET
ejpam-4597	295	29	cl(ofe	cl(ofe	NOUN
ejpam-4597	295	30	)	)	PUNCT
ejpam-4597	296	1	⊑	⊑	X
ejpam-4597	297	1	o	o	NOUN
ejpam-4597	297	2	#	#	NOUN
ejpam-4597	297	3	fe	fe	NOUN
ejpam-4597	297	4	.	.	PUNCT
ejpam-4597	298	1	since	since	SCONJ
ejpam-4597	298	2	o	o	NOUN
ejpam-4597	298	3	#	#	NOUN
ejpam-4597	298	4	fe	fe	NOUN
ejpam-4597	298	5	q̃cl(oge	q̃cl(oge	NOUN
ejpam-4597	298	6	)	)	PUNCT
ejpam-4597	298	7	,	,	PUNCT
ejpam-4597	298	8	we	we	PRON
ejpam-4597	298	9	get	get	VERB
ejpam-4597	298	10	cl(ofe	cl(ofe	NOUN
ejpam-4597	298	11	)	)	PUNCT
ejpam-4597	298	12	q̃cl(oge	q̃cl(oge	PROPN
ejpam-4597	298	13	)	)	PUNCT
ejpam-4597	298	14	.	.	PUNCT
ejpam-4597	299	1	conversely	conversely	ADV
ejpam-4597	299	2	,	,	PUNCT
ejpam-4597	299	3	it	it	PRON
ejpam-4597	299	4	follows	follow	VERB
ejpam-4597	299	5	directly	directly	ADV
ejpam-4597	299	6	from	from	ADP
ejpam-4597	299	7	hypothesis	hypothesis	NOUN
ejpam-4597	299	8	.	.	PUNCT
ejpam-4597	300	1	s.	s.	PROPN
ejpam-4597	300	2	saleh	saleh	PROPN
ejpam-4597	300	3	,	,	PUNCT
ejpam-4597	300	4	j.	j.	PROPN
ejpam-4597	300	5	al	al	PROPN
ejpam-4597	300	6	-	-	PUNCT
ejpam-4597	300	7	mufarrij	mufarrij	PROPN
ejpam-4597	300	8	/	/	SYM
ejpam-4597	300	9	eur	eur	PROPN
ejpam-4597	300	10	.	.	PUNCT
ejpam-4597	301	1	j.	j.	PROPN
ejpam-4597	301	2	pure	pure	PROPN
ejpam-4597	301	3	appl	appl	PROPN
ejpam-4597	301	4	.	.	PROPN
ejpam-4597	301	5	math	math	PROPN
ejpam-4597	301	6	,	,	PUNCT
ejpam-4597	301	7	16	16	NUM
ejpam-4597	301	8	(	(	PUNCT
ejpam-4597	301	9	1	1	NUM
ejpam-4597	301	10	)	)	PUNCT
ejpam-4597	301	11	(	(	PUNCT
ejpam-4597	301	12	2023	2023	NUM
ejpam-4597	301	13	)	)	PUNCT
ejpam-4597	301	14	,	,	PUNCT
ejpam-4597	301	15	180	180	NUM
ejpam-4597	301	16	-	-	SYM
ejpam-4597	301	17	191	191	NUM
ejpam-4597	301	18	187	187	NUM
ejpam-4597	301	19	definition	definition	NOUN
ejpam-4597	301	20	14	14	NUM
ejpam-4597	301	21	.	.	PUNCT
ejpam-4597	302	1	an	an	DET
ejpam-4597	302	2	fsts(u	fsts(u	PROPN
ejpam-4597	302	3	,	,	PUNCT
ejpam-4597	302	4	δ	δ	PROPN
ejpam-4597	302	5	,	,	PUNCT
ejpam-4597	302	6	e	e	NOUN
ejpam-4597	302	7	)	)	PUNCT
ejpam-4597	302	8	is	be	AUX
ejpam-4597	302	9	called	call	VERB
ejpam-4597	302	10	fsg4	fsg4	ADJ
ejpam-4597	302	11	iff	iff	PROPN
ejpam-4597	302	12	it	it	PRON
ejpam-4597	302	13	is	be	AUX
ejpam-4597	302	14	fs	f	NOUN
ejpam-4597	302	15	-	-	PUNCT
ejpam-4597	302	16	gr3	gr3	NOUN
ejpam-4597	302	17	and	and	CCONJ
ejpam-4597	302	18	fs	f	NOUN
ejpam-4597	302	19	-	-	PUNCT
ejpam-4597	302	20	symmetric	symmetric	ADJ
ejpam-4597	302	21	.	.	PUNCT
ejpam-4597	303	1	theorem	theorem	NOUN
ejpam-4597	303	2	10	10	NUM
ejpam-4597	303	3	.	.	PUNCT
ejpam-4597	304	1	every	every	DET
ejpam-4597	304	2	fsg4	fsg4	ADJ
ejpam-4597	304	3	space	space	NOUN
ejpam-4597	304	4	is	be	AUX
ejpam-4597	304	5	fsg3	fsg3	PROPN
ejpam-4597	304	6	.	.	PUNCT
ejpam-4597	305	1	proof	proof	NOUN
ejpam-4597	305	2	.	.	PUNCT
ejpam-4597	306	1	let	let	VERB
ejpam-4597	306	2	(	(	PUNCT
ejpam-4597	306	3	u	u	NOUN
ejpam-4597	306	4	,	,	PUNCT
ejpam-4597	306	5	δ	δ	PROPN
ejpam-4597	306	6	,	,	PUNCT
ejpam-4597	306	7	e	e	NOUN
ejpam-4597	306	8	)	)	PUNCT
ejpam-4597	306	9	be	be	AUX
ejpam-4597	306	10	fsg4	fsg4	ADJ
ejpam-4597	306	11	,	,	PUNCT
ejpam-4597	306	12	then	then	ADV
ejpam-4597	306	13	it	it	PRON
ejpam-4597	306	14	is	be	AUX
ejpam-4597	306	15	fs	f	NOUN
ejpam-4597	306	16	-	-	PUNCT
ejpam-4597	306	17	gr3	gr3	NOUN
ejpam-4597	306	18	and	and	CCONJ
ejpam-4597	306	19	fs	f	NOUN
ejpam-4597	306	20	-	-	PUNCT
ejpam-4597	306	21	symmetric	symmetric	ADJ
ejpam-4597	306	22	.	.	PUNCT
ejpam-4597	307	1	let	let	VERB
ejpam-4597	307	2	he	he	PRON
ejpam-4597	307	3	be	be	AUX
ejpam-4597	307	4	an	an	DET
ejpam-4597	307	5	fsg	fsg	NOUN
ejpam-4597	307	6	-	-	PUNCT
ejpam-4597	307	7	closed	closed	ADJ
ejpam-4597	307	8	set	set	NOUN
ejpam-4597	307	9	with	with	ADP
ejpam-4597	307	10	xeαq̃he	xeαq̃he	PROPN
ejpam-4597	307	11	.	.	PUNCT
ejpam-4597	308	1	then	then	ADV
ejpam-4597	308	2	xeα	xeα	PROPN
ejpam-4597	308	3	is	be	AUX
ejpam-4597	308	4	an	an	DET
ejpam-4597	308	5	fsg	fsg	PROPN
ejpam-4597	308	6	-	-	PUNCT
ejpam-4597	308	7	closed	closed	ADJ
ejpam-4597	308	8	set	set	NOUN
ejpam-4597	308	9	,	,	PUNCT
ejpam-4597	308	10	because	because	SCONJ
ejpam-4597	308	11	u	u	NOUN
ejpam-4597	308	12	is	be	AUX
ejpam-4597	308	13	fs	f	NOUN
ejpam-4597	308	14	-	-	NOUN
ejpam-4597	308	15	symmetric	symmetric	ADJ
ejpam-4597	308	16	.	.	PUNCT
ejpam-4597	309	1	since	since	SCONJ
ejpam-4597	309	2	(	(	PUNCT
ejpam-4597	309	3	u	u	NOUN
ejpam-4597	309	4	,	,	PUNCT
ejpam-4597	309	5	δ	δ	PROPN
ejpam-4597	309	6	,	,	PUNCT
ejpam-4597	309	7	e	e	NOUN
ejpam-4597	309	8	)	)	PUNCT
ejpam-4597	309	9	is	be	AUX
ejpam-4597	309	10	fs	f	NOUN
ejpam-4597	309	11	-	-	PUNCT
ejpam-4597	309	12	gr3	gr3	NOUN
ejpam-4597	309	13	,	,	PUNCT
ejpam-4597	309	14	there	there	PRON
ejpam-4597	309	15	are	be	VERB
ejpam-4597	309	16	fso	fso	NOUN
ejpam-4597	309	17	-	-	PUNCT
ejpam-4597	309	18	sets	set	NOUN
ejpam-4597	309	19	oxe	oxe	PRON
ejpam-4597	309	20	α	α	NOUN
ejpam-4597	309	21	and	and	CCONJ
ejpam-4597	309	22	ohe	ohe	NOUN
ejpam-4597	309	23	such	such	ADJ
ejpam-4597	309	24	that	that	SCONJ
ejpam-4597	309	25	oxe	oxe	PRON
ejpam-4597	309	26	α	α	NOUN
ejpam-4597	309	27	q̃ohe	q̃ohe	NOUN
ejpam-4597	309	28	.	.	PUNCT
ejpam-4597	310	1	thus	thus	ADV
ejpam-4597	310	2	u	u	NOUN
ejpam-4597	310	3	is	be	AUX
ejpam-4597	310	4	fs	fs	ADJ
ejpam-4597	310	5	-	-	ADJ
ejpam-4597	310	6	gr2	gr2	NOUN
ejpam-4597	310	7	and	and	CCONJ
ejpam-4597	310	8	so	so	ADV
ejpam-4597	310	9	,	,	PUNCT
ejpam-4597	310	10	(	(	PUNCT
ejpam-4597	310	11	u	u	NOUN
ejpam-4597	310	12	,	,	PUNCT
ejpam-4597	310	13	δ	δ	PROPN
ejpam-4597	310	14	,	,	PUNCT
ejpam-4597	310	15	e	e	NOUN
ejpam-4597	310	16	)	)	PUNCT
ejpam-4597	310	17	is	be	AUX
ejpam-4597	310	18	fsg3	fsg3	PROPN
ejpam-4597	310	19	.	.	PUNCT
ejpam-4597	311	1	corollary	corollary	ADJ
ejpam-4597	311	2	2	2	NUM
ejpam-4597	311	3	.	.	PUNCT
ejpam-4597	312	1	every	every	DET
ejpam-4597	312	2	fs	fs	NOUN
ejpam-4597	312	3	-	-	PUNCT
ejpam-4597	312	4	gr3	gr3	NOUN
ejpam-4597	312	5	and	and	CCONJ
ejpam-4597	312	6	fs	fs	ADJ
ejpam-4597	312	7	-	-	PUNCT
ejpam-4597	312	8	symmetric	symmetric	ADJ
ejpam-4597	312	9	space	space	NOUN
ejpam-4597	312	10	is	be	AUX
ejpam-4597	312	11	fs	f	NOUN
ejpam-4597	312	12	-	-	ADJ
ejpam-4597	312	13	gr2	gr2	NOUN
ejpam-4597	312	14	.	.	PUNCT
ejpam-4597	313	1	proposition	proposition	NOUN
ejpam-4597	313	2	5	5	NUM
ejpam-4597	313	3	.	.	PUNCT
ejpam-4597	314	1	an	an	DET
ejpam-4597	314	2	fsts(u	fsts(u	PROPN
ejpam-4597	314	3	,	,	PUNCT
ejpam-4597	314	4	δ	δ	PROPN
ejpam-4597	314	5	,	,	PUNCT
ejpam-4597	314	6	e	e	NOUN
ejpam-4597	314	7	)	)	PUNCT
ejpam-4597	314	8	is	be	AUX
ejpam-4597	314	9	fs	f	NOUN
ejpam-4597	314	10	-	-	PUNCT
ejpam-4597	314	11	gr3	gr3	NOUN
ejpam-4597	314	12	if	if	SCONJ
ejpam-4597	314	13	and	and	CCONJ
ejpam-4597	314	14	only	only	ADV
ejpam-4597	314	15	if	if	SCONJ
ejpam-4597	314	16	it	it	PRON
ejpam-4597	314	17	is	be	AUX
ejpam-4597	314	18	fsr3	fsr3	PROPN
ejpam-4597	314	19	and	and	CCONJ
ejpam-4597	314	20	fst	fst	PROPN
ejpam-4597	314	21	1	1	NUM
ejpam-4597	314	22	2	2	NUM
ejpam-4597	314	23	.	.	PUNCT
ejpam-4597	315	1	proof	proof	NOUN
ejpam-4597	315	2	.	.	PUNCT
ejpam-4597	316	1	by	by	ADP
ejpam-4597	316	2	similar	similar	ADJ
ejpam-4597	316	3	way	way	NOUN
ejpam-4597	316	4	as	as	ADP
ejpam-4597	316	5	that	that	PRON
ejpam-4597	316	6	of	of	ADP
ejpam-4597	316	7	theorem	theorem	ADJ
ejpam-4597	316	8	2	2	NUM
ejpam-4597	316	9	.	.	PUNCT
ejpam-4597	316	10	theorem	theorem	VERB
ejpam-4597	316	11	11	11	NUM
ejpam-4597	316	12	.	.	PUNCT
ejpam-4597	317	1	an	an	DET
ejpam-4597	317	2	fsts(u	fsts(u	PROPN
ejpam-4597	317	3	,	,	PUNCT
ejpam-4597	317	4	δ	δ	PROPN
ejpam-4597	317	5	,	,	PUNCT
ejpam-4597	317	6	e	e	NOUN
ejpam-4597	317	7	)	)	PUNCT
ejpam-4597	317	8	is	be	AUX
ejpam-4597	317	9	fsg4	fsg4	ADJ
ejpam-4597	317	10	if	if	SCONJ
ejpam-4597	317	11	and	and	CCONJ
ejpam-4597	317	12	only	only	ADV
ejpam-4597	317	13	if	if	SCONJ
ejpam-4597	317	14	it	it	PRON
ejpam-4597	317	15	is	be	AUX
ejpam-4597	317	16	fst	fst	NOUN
ejpam-4597	317	17	4	4	NUM
ejpam-4597	317	18	.	.	PUNCT
ejpam-4597	318	1	proof	proof	NOUN
ejpam-4597	318	2	.	.	PUNCT
ejpam-4597	319	1	by	by	ADP
ejpam-4597	319	2	similar	similar	ADJ
ejpam-4597	319	3	way	way	NOUN
ejpam-4597	319	4	as	as	ADP
ejpam-4597	319	5	that	that	PRON
ejpam-4597	319	6	of	of	ADP
ejpam-4597	319	7	theorem	theorem	ADJ
ejpam-4597	319	8	7	7	NUM
ejpam-4597	319	9	.	.	NOUN
ejpam-4597	319	10	4	4	NUM
ejpam-4597	319	11	.	.	X
ejpam-4597	320	1	some	some	DET
ejpam-4597	320	2	properties	property	NOUN
ejpam-4597	320	3	and	and	CCONJ
ejpam-4597	320	4	relations	relation	NOUN
ejpam-4597	320	5	here	here	ADV
ejpam-4597	320	6	we	we	PRON
ejpam-4597	320	7	shall	shall	AUX
ejpam-4597	320	8	investigate	investigate	VERB
ejpam-4597	320	9	some	some	DET
ejpam-4597	320	10	preservation	preservation	NOUN
ejpam-4597	320	11	theorems	theorem	NOUN
ejpam-4597	320	12	and	and	CCONJ
ejpam-4597	320	13	relationships	relationship	NOUN
ejpam-4597	320	14	of	of	ADP
ejpam-4597	320	15	fs	fs	NOUN
ejpam-4597	320	16	-	-	PUNCT
ejpam-4597	320	17	gr2	gr2	NOUN
ejpam-4597	320	18	and	and	CCONJ
ejpam-4597	320	19	fs	f	NOUN
ejpam-4597	320	20	-	-	PUNCT
ejpam-4597	320	21	gr3	gr3	NOUN
ejpam-4597	320	22	spaces	space	NOUN
ejpam-4597	320	23	.	.	PUNCT
ejpam-4597	321	1	definition	definition	NOUN
ejpam-4597	321	2	15	15	NUM
ejpam-4597	321	3	.	.	PUNCT
ejpam-4597	322	1	[	[	X
ejpam-4597	322	2	31	31	NUM
ejpam-4597	322	3	]	]	PUNCT
ejpam-4597	322	4	an	an	DET
ejpam-4597	322	5	fs	fs	NOUN
ejpam-4597	322	6	-	-	PUNCT
ejpam-4597	322	7	map	map	NOUN
ejpam-4597	322	8	fup	fup	NOUN
ejpam-4597	322	9	:	:	PUNCT
ejpam-4597	322	10	(	(	PUNCT
ejpam-4597	322	11	u	u	NOUN
ejpam-4597	322	12	,	,	PUNCT
ejpam-4597	322	13	δ	δ	PROPN
ejpam-4597	322	14	,	,	PUNCT
ejpam-4597	322	15	e)−→(v	e)−→(v	PROPN
ejpam-4597	322	16	,	,	PUNCT
ejpam-4597	322	17	σ	σ	PROPN
ejpam-4597	322	18	,	,	PUNCT
ejpam-4597	322	19	k	k	NOUN
ejpam-4597	322	20	)	)	PUNCT
ejpam-4597	322	21	is	be	AUX
ejpam-4597	322	22	said	say	VERB
ejpam-4597	322	23	to	to	PART
ejpam-4597	322	24	be	be	AUX
ejpam-4597	322	25	:	:	PUNCT
ejpam-4597	322	26	(	(	PUNCT
ejpam-4597	322	27	i	i	NOUN
ejpam-4597	322	28	)	)	PUNCT
ejpam-4597	322	29	fsg	fsg	PROPN
ejpam-4597	322	30	-	-	PUNCT
ejpam-4597	322	31	closed	close	VERB
ejpam-4597	322	32	if	if	SCONJ
ejpam-4597	322	33	fup(he	fup(he	NOUN
ejpam-4597	322	34	)	)	PUNCT
ejpam-4597	322	35	is	be	AUX
ejpam-4597	322	36	fsg	fsg	NOUN
ejpam-4597	322	37	-	-	PUNCT
ejpam-4597	322	38	closed	closed	ADJ
ejpam-4597	322	39	in	in	ADP
ejpam-4597	322	40	(	(	PUNCT
ejpam-4597	322	41	v	v	NOUN
ejpam-4597	322	42	,	,	PUNCT
ejpam-4597	322	43	σ	σ	PROPN
ejpam-4597	322	44	,	,	PUNCT
ejpam-4597	322	45	k	k	NOUN
ejpam-4597	322	46	)	)	PUNCT
ejpam-4597	322	47	for	for	ADP
ejpam-4597	322	48	any	any	DET
ejpam-4597	322	49	fsc	fsc	PROPN
ejpam-4597	322	50	-	-	PUNCT
ejpam-4597	322	51	set	set	VERB
ejpam-4597	322	52	he	he	PRON
ejpam-4597	322	53	in	in	ADP
ejpam-4597	322	54	(	(	PUNCT
ejpam-4597	322	55	u	u	NOUN
ejpam-4597	322	56	,	,	PUNCT
ejpam-4597	322	57	δ	δ	PROPN
ejpam-4597	322	58	,	,	PUNCT
ejpam-4597	322	59	e	e	NOUN
ejpam-4597	322	60	)	)	PUNCT
ejpam-4597	322	61	.	.	PUNCT
ejpam-4597	323	1	(	(	PUNCT
ejpam-4597	323	2	ii	ii	X
ejpam-4597	323	3	)	)	PUNCT
ejpam-4597	323	4	fsg	fsg	PROPN
ejpam-4597	323	5	-	-	PUNCT
ejpam-4597	323	6	open	open	ADJ
ejpam-4597	323	7	if	if	SCONJ
ejpam-4597	323	8	fup(he	fup(he	NOUN
ejpam-4597	323	9	)	)	PUNCT
ejpam-4597	323	10	is	be	AUX
ejpam-4597	323	11	fsg	fsg	NOUN
ejpam-4597	323	12	-	-	PUNCT
ejpam-4597	323	13	open	open	ADJ
ejpam-4597	323	14	in	in	ADP
ejpam-4597	323	15	(	(	PUNCT
ejpam-4597	323	16	v	v	NOUN
ejpam-4597	323	17	,	,	PUNCT
ejpam-4597	323	18	σ	σ	PROPN
ejpam-4597	323	19	,	,	PUNCT
ejpam-4597	323	20	k	k	NOUN
ejpam-4597	323	21	)	)	PUNCT
ejpam-4597	323	22	for	for	ADP
ejpam-4597	323	23	any	any	DET
ejpam-4597	323	24	fso	fso	NOUN
ejpam-4597	323	25	-	-	PUNCT
ejpam-4597	323	26	set	set	VERB
ejpam-4597	323	27	he	he	PRON
ejpam-4597	323	28	in	in	ADP
ejpam-4597	323	29	(	(	PUNCT
ejpam-4597	323	30	u	u	NOUN
ejpam-4597	323	31	,	,	PUNCT
ejpam-4597	323	32	δ	δ	PROPN
ejpam-4597	323	33	,	,	PUNCT
ejpam-4597	323	34	e	e	NOUN
ejpam-4597	323	35	)	)	PUNCT
ejpam-4597	323	36	.	.	PUNCT
ejpam-4597	324	1	lemma	lemma	PROPN
ejpam-4597	324	2	2	2	X
ejpam-4597	324	3	.	.	PUNCT
ejpam-4597	325	1	if	if	SCONJ
ejpam-4597	325	2	fup	fup	VERB
ejpam-4597	325	3	:	:	PUNCT
ejpam-4597	325	4	(	(	PUNCT
ejpam-4597	325	5	u	u	NOUN
ejpam-4597	325	6	,	,	PUNCT
ejpam-4597	325	7	δ	δ	PROPN
ejpam-4597	325	8	,	,	PUNCT
ejpam-4597	325	9	e	e	NOUN
ejpam-4597	325	10	)	)	PUNCT
ejpam-4597	325	11	−→	−→	NOUN
ejpam-4597	325	12	(	(	PUNCT
ejpam-4597	325	13	v	v	NOUN
ejpam-4597	325	14	,	,	PUNCT
ejpam-4597	325	15	σ	σ	PROPN
ejpam-4597	325	16	,	,	PUNCT
ejpam-4597	325	17	k	k	NOUN
ejpam-4597	325	18	)	)	PUNCT
ejpam-4597	325	19	is	be	AUX
ejpam-4597	325	20	an	an	DET
ejpam-4597	325	21	fs	fs	NOUN
ejpam-4597	325	22	-	-	ADJ
ejpam-4597	325	23	open	open	ADJ
ejpam-4597	325	24	,	,	PUNCT
ejpam-4597	325	25	fsg	fsg	ADJ
ejpam-4597	325	26	-	-	PUNCT
ejpam-4597	325	27	continuous	continuous	ADJ
ejpam-4597	325	28	bijection	bijection	NOUN
ejpam-4597	325	29	map	map	NOUN
ejpam-4597	325	30	,	,	PUNCT
ejpam-4597	325	31	then	then	ADV
ejpam-4597	325	32	fup	fup	X
ejpam-4597	325	33	is	be	AUX
ejpam-4597	325	34	fsgc	fsgc	ADJ
ejpam-4597	325	35	-	-	PUNCT
ejpam-4597	325	36	irresolute	irresolute	ADJ
ejpam-4597	325	37	.	.	PUNCT
ejpam-4597	326	1	proof	proof	NOUN
ejpam-4597	326	2	.	.	PUNCT
ejpam-4597	327	1	let	let	VERB
ejpam-4597	327	2	he	he	PRON
ejpam-4597	327	3	∈	∈	VERB
ejpam-4597	327	4	fsgc(v	fsgc(v	NOUN
ejpam-4597	327	5	)	)	PUNCT
ejpam-4597	327	6	and	and	CCONJ
ejpam-4597	327	7	f−1	f−1	PROPN
ejpam-4597	327	8	up	up	ADP
ejpam-4597	327	9	(	(	PUNCT
ejpam-4597	327	10	he	he	PRON
ejpam-4597	327	11	)	)	PUNCT
ejpam-4597	328	1	⊑	⊑	PROPN
ejpam-4597	328	2	ge	ge	PROPN
ejpam-4597	328	3	,	,	PUNCT
ejpam-4597	328	4	where	where	SCONJ
ejpam-4597	328	5	ge	ge	PROPN
ejpam-4597	328	6	∈	∈	PROPN
ejpam-4597	328	7	fso(u	fso(u	PROPN
ejpam-4597	328	8	)	)	PUNCT
ejpam-4597	328	9	,	,	PUNCT
ejpam-4597	328	10	then	then	ADV
ejpam-4597	328	11	he	he	PRON
ejpam-4597	328	12	⊑	⊑	PRON
ejpam-4597	328	13	fup(ge	fup(ge	NOUN
ejpam-4597	328	14	)	)	PUNCT
ejpam-4597	328	15	.	.	PUNCT
ejpam-4597	329	1	since	since	SCONJ
ejpam-4597	329	2	fup	fup	PROPN
ejpam-4597	329	3	is	be	AUX
ejpam-4597	329	4	fs	fs	ADJ
ejpam-4597	329	5	-	-	ADJ
ejpam-4597	329	6	open	open	ADJ
ejpam-4597	329	7	,	,	PUNCT
ejpam-4597	329	8	we	we	PRON
ejpam-4597	329	9	have	have	VERB
ejpam-4597	329	10	fup(ge	fup(ge	NOUN
ejpam-4597	329	11	)	)	PUNCT
ejpam-4597	329	12	∈	∈	PROPN
ejpam-4597	329	13	fso(v	fso(v	PROPN
ejpam-4597	329	14	)	)	PUNCT
ejpam-4597	329	15	.	.	PUNCT
ejpam-4597	330	1	since	since	SCONJ
ejpam-4597	330	2	he	he	PRON
ejpam-4597	330	3	is	be	AUX
ejpam-4597	330	4	an	an	DET
ejpam-4597	330	5	fsg	fsg	PROPN
ejpam-4597	330	6	-	-	PUNCT
ejpam-4597	330	7	closed	closed	ADJ
ejpam-4597	330	8	set	set	NOUN
ejpam-4597	330	9	on	on	ADP
ejpam-4597	330	10	v	v	NUM
ejpam-4597	330	11	,	,	PUNCT
ejpam-4597	330	12	we	we	PRON
ejpam-4597	330	13	obtain	obtain	VERB
ejpam-4597	330	14	cl(he	cl(he	NOUN
ejpam-4597	330	15	)	)	PUNCT
ejpam-4597	330	16	⊑	⊑	PRON
ejpam-4597	330	17	fup(ge	fup(ge	NOUN
ejpam-4597	330	18	)	)	PUNCT
ejpam-4597	330	19	.	.	PUNCT
ejpam-4597	331	1	hence	hence	ADV
ejpam-4597	331	2	f−1	f−1	PROPN
ejpam-4597	331	3	up	up	ADP
ejpam-4597	331	4	(	(	PUNCT
ejpam-4597	331	5	cl(he	cl(he	NOUN
ejpam-4597	331	6	)	)	PUNCT
ejpam-4597	331	7	⊑	⊑	X
ejpam-4597	331	8	ge	ge	PROPN
ejpam-4597	331	9	(	(	PUNCT
ejpam-4597	331	10	because	because	SCONJ
ejpam-4597	331	11	fup	fup	X
ejpam-4597	331	12	is	be	AUX
ejpam-4597	331	13	oneone	oneone	NOUN
ejpam-4597	331	14	)	)	PUNCT
ejpam-4597	331	15	.	.	PUNCT
ejpam-4597	332	1	since	since	SCONJ
ejpam-4597	332	2	fup	fup	PROPN
ejpam-4597	332	3	is	be	AUX
ejpam-4597	332	4	fsg	fsg	NOUN
ejpam-4597	332	5	-	-	PUNCT
ejpam-4597	332	6	continuous	continuous	ADJ
ejpam-4597	332	7	,	,	PUNCT
ejpam-4597	332	8	we	we	PRON
ejpam-4597	332	9	have	have	VERB
ejpam-4597	332	10	f−1	f−1	PROPN
ejpam-4597	332	11	up	up	ADP
ejpam-4597	332	12	(	(	PUNCT
ejpam-4597	332	13	cl(he	cl(he	NOUN
ejpam-4597	332	14	)	)	PUNCT
ejpam-4597	332	15	is	be	AUX
ejpam-4597	332	16	an	an	DET
ejpam-4597	332	17	fsg	fsg	PROPN
ejpam-4597	332	18	-	-	PUNCT
ejpam-4597	332	19	closed	close	VERB
ejpam-4597	332	20	set	set	NOUN
ejpam-4597	332	21	in	in	ADP
ejpam-4597	332	22	u	u	NOUN
ejpam-4597	332	23	and	and	CCONJ
ejpam-4597	332	24	so	so	ADV
ejpam-4597	332	25	,	,	PUNCT
ejpam-4597	332	26	cl(f−1	cl(f−1	VERB
ejpam-4597	332	27	up	up	ADP
ejpam-4597	332	28	(	(	PUNCT
ejpam-4597	332	29	he	he	PRON
ejpam-4597	332	30	)	)	PUNCT
ejpam-4597	332	31	)	)	PUNCT
ejpam-4597	333	1	⊑	⊑	X
ejpam-4597	333	2	cl(f−1	cl(f−1	VERB
ejpam-4597	333	3	up	up	ADP
ejpam-4597	333	4	(	(	PUNCT
ejpam-4597	333	5	cl	cl	INTJ
ejpam-4597	333	6	(	(	PUNCT
ejpam-4597	333	7	he	he	PRON
ejpam-4597	333	8	)	)	PUNCT
ejpam-4597	333	9	)	)	PUNCT
ejpam-4597	333	10	)	)	PUNCT
ejpam-4597	334	1	⊑	⊑	PROPN
ejpam-4597	334	2	ge	ge	PROPN
ejpam-4597	334	3	.	.	PUNCT
ejpam-4597	335	1	hence	hence	ADV
ejpam-4597	335	2	f−1	f−1	PROPN
ejpam-4597	335	3	up	up	ADP
ejpam-4597	335	4	(	(	PUNCT
ejpam-4597	335	5	he	he	PRON
ejpam-4597	335	6	)	)	PUNCT
ejpam-4597	335	7	is	be	AUX
ejpam-4597	335	8	an	an	DET
ejpam-4597	335	9	fsg	fsg	PROPN
ejpam-4597	335	10	-	-	PUNCT
ejpam-4597	335	11	closed	closed	ADJ
ejpam-4597	335	12	set	set	NOUN
ejpam-4597	335	13	on	on	ADP
ejpam-4597	335	14	v	v	NUM
ejpam-4597	335	15	.	.	PUNCT
ejpam-4597	336	1	theorem	theorem	NOUN
ejpam-4597	336	2	12	12	NUM
ejpam-4597	336	3	.	.	PUNCT
ejpam-4597	337	1	if	if	SCONJ
ejpam-4597	337	2	fup	fup	VERB
ejpam-4597	337	3	:	:	PUNCT
ejpam-4597	337	4	(	(	PUNCT
ejpam-4597	337	5	u	u	NOUN
ejpam-4597	337	6	,	,	PUNCT
ejpam-4597	337	7	δ	δ	PROPN
ejpam-4597	337	8	,	,	PUNCT
ejpam-4597	337	9	e)−→(v	e)−→(v	PROPN
ejpam-4597	337	10	,	,	PUNCT
ejpam-4597	337	11	σ	σ	PROPN
ejpam-4597	337	12	,	,	PUNCT
ejpam-4597	337	13	k	k	NOUN
ejpam-4597	337	14	)	)	PUNCT
ejpam-4597	337	15	is	be	AUX
ejpam-4597	337	16	an	an	DET
ejpam-4597	337	17	fs	fs	NOUN
ejpam-4597	337	18	-	-	ADJ
ejpam-4597	337	19	open	open	ADJ
ejpam-4597	337	20	,	,	PUNCT
ejpam-4597	337	21	fsg	fsg	ADJ
ejpam-4597	337	22	-	-	PUNCT
ejpam-4597	337	23	continuous	continuous	ADJ
ejpam-4597	337	24	bijection	bijection	NOUN
ejpam-4597	337	25	map	map	NOUN
ejpam-4597	337	26	and	and	CCONJ
ejpam-4597	337	27	(	(	PUNCT
ejpam-4597	337	28	u	u	NOUN
ejpam-4597	337	29	,	,	PUNCT
ejpam-4597	337	30	δ	δ	PROPN
ejpam-4597	337	31	,	,	PUNCT
ejpam-4597	337	32	e	e	NOUN
ejpam-4597	337	33	)	)	PUNCT
ejpam-4597	337	34	is	be	AUX
ejpam-4597	337	35	fs	fs	PROPN
ejpam-4597	337	36	-	-	PUNCT
ejpam-4597	337	37	gr2	gr2	NOUN
ejpam-4597	337	38	,	,	PUNCT
ejpam-4597	337	39	then	then	ADV
ejpam-4597	337	40	(	(	PUNCT
ejpam-4597	337	41	v	v	NOUN
ejpam-4597	337	42	,	,	PUNCT
ejpam-4597	337	43	σ	σ	PROPN
ejpam-4597	337	44	,	,	PUNCT
ejpam-4597	337	45	k	k	NOUN
ejpam-4597	337	46	)	)	PUNCT
ejpam-4597	337	47	is	be	AUX
ejpam-4597	337	48	fs	fs	PROPN
ejpam-4597	337	49	-	-	PUNCT
ejpam-4597	337	50	gr2	gr2	NOUN
ejpam-4597	337	51	.	.	PUNCT
ejpam-4597	338	1	proof	proof	NOUN
ejpam-4597	338	2	.	.	PUNCT
ejpam-4597	339	1	let	let	VERB
ejpam-4597	339	2	he	he	PRON
ejpam-4597	339	3	∈	∈	VERB
ejpam-4597	339	4	fsgc(v	fsgc(v	NOUN
ejpam-4597	339	5	)	)	PUNCT
ejpam-4597	339	6	and	and	CCONJ
ejpam-4597	339	7	yeαq̃he	yeαq̃he	PROPN
ejpam-4597	339	8	.	.	PUNCT
ejpam-4597	340	1	since	since	SCONJ
ejpam-4597	340	2	fup	fup	PROPN
ejpam-4597	340	3	is	be	AUX
ejpam-4597	340	4	fs	fs	ADJ
ejpam-4597	340	5	-	-	ADJ
ejpam-4597	340	6	open	open	ADJ
ejpam-4597	340	7	,	,	PUNCT
ejpam-4597	340	8	fsg	fsg	ADJ
ejpam-4597	340	9	-	-	PUNCT
ejpam-4597	340	10	continuous	continuous	ADJ
ejpam-4597	340	11	bijective	bijective	ADJ
ejpam-4597	340	12	,	,	PUNCT
ejpam-4597	340	13	by	by	ADP
ejpam-4597	340	14	the	the	DET
ejpam-4597	340	15	above	above	ADJ
ejpam-4597	340	16	lemma	lemma	PROPN
ejpam-4597	340	17	,	,	PUNCT
ejpam-4597	340	18	fup	fup	X
ejpam-4597	340	19	is	be	AUX
ejpam-4597	340	20	fsgc	fsgc	ADJ
ejpam-4597	340	21	-	-	PUNCT
ejpam-4597	340	22	irresolute	irresolute	ADJ
ejpam-4597	340	23	and	and	CCONJ
ejpam-4597	340	24	so	so	ADV
ejpam-4597	340	25	,	,	PUNCT
ejpam-4597	340	26	f−1	f−1	PROPN
ejpam-4597	340	27	up	up	ADP
ejpam-4597	340	28	(	(	PUNCT
ejpam-4597	340	29	he	he	PRON
ejpam-4597	340	30	)	)	PUNCT
ejpam-4597	340	31	is	be	AUX
ejpam-4597	340	32	fsg	fsg	NOUN
ejpam-4597	340	33	-	-	PUNCT
ejpam-4597	340	34	closed	closed	ADJ
ejpam-4597	340	35	.	.	PUNCT
ejpam-4597	341	1	take	take	VERB
ejpam-4597	341	2	fup	fup	X
ejpam-4597	341	3	(	(	PUNCT
ejpam-4597	341	4	x	x	X
ejpam-4597	341	5	e	e	NOUN
ejpam-4597	341	6	α	α	NOUN
ejpam-4597	341	7	)	)	PUNCT
ejpam-4597	341	8	=	=	SYM
ejpam-4597	341	9	yeα	yeα	PROPN
ejpam-4597	341	10	,	,	PUNCT
ejpam-4597	341	11	then	then	ADV
ejpam-4597	341	12	xeαq̃f	xeαq̃f	PROPN
ejpam-4597	342	1	−1	−1	VERB
ejpam-4597	342	2	up	up	ADV
ejpam-4597	342	3	(	(	PUNCT
ejpam-4597	342	4	he	he	PRON
ejpam-4597	342	5	)	)	PUNCT
ejpam-4597	342	6	)	)	PUNCT
ejpam-4597	342	7	.	.	PUNCT
ejpam-4597	343	1	since	since	SCONJ
ejpam-4597	343	2	u	u	NOUN
ejpam-4597	343	3	is	be	AUX
ejpam-4597	343	4	fs	f	NOUN
ejpam-4597	343	5	-	-	NOUN
ejpam-4597	343	6	gr2	gr2	NOUN
ejpam-4597	343	7	,	,	PUNCT
ejpam-4597	343	8	there	there	PRON
ejpam-4597	343	9	are	be	VERB
ejpam-4597	343	10	fso	fso	NOUN
ejpam-4597	343	11	-	-	PUNCT
ejpam-4597	343	12	sets	set	NOUN
ejpam-4597	343	13	oxe	oxe	PRON
ejpam-4597	343	14	α	α	NOUN
ejpam-4597	343	15	and	and	CCONJ
ejpam-4597	343	16	of−1	of−1	VERB
ejpam-4597	343	17	up	up	ADP
ejpam-4597	343	18	(	(	PUNCT
ejpam-4597	343	19	he	he	PRON
ejpam-4597	343	20	)	)	PUNCT
ejpam-4597	343	21	such	such	ADJ
ejpam-4597	343	22	thatoxe	thatoxe	VERB
ejpam-4597	343	23	α	α	NOUN
ejpam-4597	343	24	q̃of−1	q̃of−1	NOUN
ejpam-4597	343	25	up	up	ADP
ejpam-4597	343	26	(	(	PUNCT
ejpam-4597	343	27	he	he	PRON
ejpam-4597	343	28	)	)	PUNCT
ejpam-4597	343	29	.	.	PUNCT
ejpam-4597	344	1	since	since	SCONJ
ejpam-4597	344	2	fup	fup	PROPN
ejpam-4597	344	3	is	be	AUX
ejpam-4597	344	4	fs	fs	ADJ
ejpam-4597	344	5	-	-	PUNCT
ejpam-4597	344	6	open	open	ADJ
ejpam-4597	344	7	and	and	CCONJ
ejpam-4597	344	8	bijective	bijective	ADJ
ejpam-4597	344	9	,	,	PUNCT
ejpam-4597	344	10	we	we	PRON
ejpam-4597	344	11	have	have	VERB
ejpam-4597	344	12	yeα∈̃fup(oxe	yeα∈̃fup(oxe	NUM
ejpam-4597	344	13	α	α	NOUN
ejpam-4597	344	14	)	)	PUNCT
ejpam-4597	344	15	,	,	PUNCT
ejpam-4597	344	16	he	he	PRON
ejpam-4597	344	17	⊑	⊑	PRON
ejpam-4597	344	18	fup(of−1	fup(of−1	PROPN
ejpam-4597	344	19	up	up	ADP
ejpam-4597	344	20	(	(	PUNCT
ejpam-4597	344	21	he	he	PRON
ejpam-4597	344	22	)	)	PUNCT
ejpam-4597	344	23	)	)	PUNCT
ejpam-4597	344	24	and	and	CCONJ
ejpam-4597	344	25	fup(oxe	fup(oxe	X
ejpam-4597	344	26	α	α	X
ejpam-4597	344	27	)	)	PUNCT
ejpam-4597	344	28	q̃fup(of−1	q̃fup(of−1	VERB
ejpam-4597	344	29	up	up	ADV
ejpam-4597	344	30	(	(	PUNCT
ejpam-4597	344	31	he	he	PRON
ejpam-4597	344	32	)	)	PUNCT
ejpam-4597	344	33	)	)	PUNCT
ejpam-4597	344	34	.	.	PUNCT
ejpam-4597	345	1	the	the	DET
ejpam-4597	345	2	result	result	NOUN
ejpam-4597	345	3	holds	hold	VERB
ejpam-4597	345	4	.	.	PUNCT
ejpam-4597	346	1	s.	s.	PROPN
ejpam-4597	346	2	saleh	saleh	PROPN
ejpam-4597	346	3	,	,	PUNCT
ejpam-4597	346	4	j.	j.	PROPN
ejpam-4597	346	5	al	al	PROPN
ejpam-4597	346	6	-	-	PUNCT
ejpam-4597	346	7	mufarrij	mufarrij	PROPN
ejpam-4597	346	8	/	/	SYM
ejpam-4597	346	9	eur	eur	PROPN
ejpam-4597	346	10	.	.	PUNCT
ejpam-4597	347	1	j.	j.	PROPN
ejpam-4597	347	2	pure	pure	PROPN
ejpam-4597	347	3	appl	appl	PROPN
ejpam-4597	347	4	.	.	PROPN
ejpam-4597	347	5	math	math	PROPN
ejpam-4597	347	6	,	,	PUNCT
ejpam-4597	347	7	16	16	NUM
ejpam-4597	347	8	(	(	PUNCT
ejpam-4597	347	9	1	1	NUM
ejpam-4597	347	10	)	)	PUNCT
ejpam-4597	347	11	(	(	PUNCT
ejpam-4597	347	12	2023	2023	NUM
ejpam-4597	347	13	)	)	PUNCT
ejpam-4597	347	14	,	,	PUNCT
ejpam-4597	347	15	180	180	NUM
ejpam-4597	347	16	-	-	SYM
ejpam-4597	347	17	191	191	NUM
ejpam-4597	347	18	188	188	NUM
ejpam-4597	347	19	theorem	theorem	NOUN
ejpam-4597	347	20	13	13	NUM
ejpam-4597	347	21	.	.	PUNCT
ejpam-4597	348	1	if	if	SCONJ
ejpam-4597	348	2	fup	fup	VERB
ejpam-4597	348	3	:	:	PUNCT
ejpam-4597	348	4	(	(	PUNCT
ejpam-4597	348	5	u	u	NOUN
ejpam-4597	348	6	,	,	PUNCT
ejpam-4597	348	7	δ	δ	PROPN
ejpam-4597	348	8	,	,	PUNCT
ejpam-4597	348	9	e)−→(v	e)−→(v	PROPN
ejpam-4597	348	10	,	,	PUNCT
ejpam-4597	348	11	σ	σ	PROPN
ejpam-4597	348	12	,	,	PUNCT
ejpam-4597	348	13	k	k	NOUN
ejpam-4597	348	14	)	)	PUNCT
ejpam-4597	348	15	is	be	AUX
ejpam-4597	348	16	an	an	DET
ejpam-4597	348	17	fsg	fsg	NOUN
ejpam-4597	348	18	-	-	PUNCT
ejpam-4597	348	19	continuous	continuous	ADJ
ejpam-4597	348	20	,	,	PUNCT
ejpam-4597	348	21	fsg	fsg	PROPN
ejpam-4597	348	22	-	-	PUNCT
ejpam-4597	348	23	closed	close	VERB
ejpam-4597	348	24	one	one	NUM
ejpam-4597	348	25	-	-	PUNCT
ejpam-4597	348	26	one	one	NUM
ejpam-4597	348	27	map	map	NOUN
ejpam-4597	348	28	and	and	CCONJ
ejpam-4597	348	29	(	(	PUNCT
ejpam-4597	348	30	v	v	NOUN
ejpam-4597	348	31	,	,	PUNCT
ejpam-4597	348	32	σ	σ	PROPN
ejpam-4597	348	33	,	,	PUNCT
ejpam-4597	348	34	k	k	NOUN
ejpam-4597	348	35	)	)	PUNCT
ejpam-4597	348	36	is	be	AUX
ejpam-4597	348	37	fs	fs	PROPN
ejpam-4597	348	38	-	-	PUNCT
ejpam-4597	348	39	gr2	gr2	NOUN
ejpam-4597	348	40	,	,	PUNCT
ejpam-4597	348	41	then	then	ADV
ejpam-4597	348	42	(	(	PUNCT
ejpam-4597	348	43	u	u	NOUN
ejpam-4597	348	44	,	,	PUNCT
ejpam-4597	348	45	δ	δ	PROPN
ejpam-4597	348	46	,	,	PUNCT
ejpam-4597	348	47	e	e	NOUN
ejpam-4597	348	48	)	)	PUNCT
ejpam-4597	348	49	is	be	AUX
ejpam-4597	348	50	fs	fs	PROPN
ejpam-4597	348	51	-	-	PUNCT
ejpam-4597	348	52	gr2	gr2	NOUN
ejpam-4597	348	53	.	.	PUNCT
ejpam-4597	349	1	proof	proof	NOUN
ejpam-4597	349	2	.	.	PUNCT
ejpam-4597	350	1	let	let	VERB
ejpam-4597	350	2	he	he	PRON
ejpam-4597	350	3	∈	∈	PROPN
ejpam-4597	350	4	fsgc(u	fsgc(u	PROPN
ejpam-4597	350	5	)	)	PUNCT
ejpam-4597	350	6	and	and	CCONJ
ejpam-4597	350	7	xeαq̃he	xeαq̃he	PROPN
ejpam-4597	350	8	.	.	PUNCT
ejpam-4597	351	1	by	by	ADP
ejpam-4597	351	2	fs	fs	NOUN
ejpam-4597	351	3	-	-	PUNCT
ejpam-4597	351	4	continuity	continuity	NOUN
ejpam-4597	351	5	and	and	CCONJ
ejpam-4597	351	6	fsg	fsg	PROPN
ejpam-4597	351	7	-	-	PUNCT
ejpam-4597	351	8	closedness	closedness	NOUN
ejpam-4597	351	9	we	we	PRON
ejpam-4597	351	10	have	have	VERB
ejpam-4597	351	11	fup(he	fup(he	NOUN
ejpam-4597	351	12	)	)	PUNCT
ejpam-4597	351	13	∈	∈	NOUN
ejpam-4597	351	14	fsgc(v	fsgc(v	NOUN
ejpam-4597	351	15	)	)	PUNCT
ejpam-4597	351	16	.	.	PUNCT
ejpam-4597	352	1	indeed	indeed	ADV
ejpam-4597	352	2	,	,	PUNCT
ejpam-4597	352	3	if	if	SCONJ
ejpam-4597	352	4	fup(he	fup(he	NOUN
ejpam-4597	352	5	)	)	PUNCT
ejpam-4597	352	6	⊑	⊑	PART
ejpam-4597	352	7	ge	ge	PROPN
ejpam-4597	352	8	and	and	CCONJ
ejpam-4597	352	9	ge	ge	PROPN
ejpam-4597	352	10	is	be	AUX
ejpam-4597	352	11	an	an	DET
ejpam-4597	352	12	fso	fso	NOUN
ejpam-4597	352	13	-	-	PUNCT
ejpam-4597	352	14	set	set	VERB
ejpam-4597	352	15	in	in	ADP
ejpam-4597	352	16	(	(	PUNCT
ejpam-4597	352	17	v	v	NOUN
ejpam-4597	352	18	,	,	PUNCT
ejpam-4597	352	19	σ	σ	PROPN
ejpam-4597	352	20	,	,	PUNCT
ejpam-4597	352	21	k	k	PROPN
ejpam-4597	352	22	)	)	PUNCT
ejpam-4597	352	23	,	,	PUNCT
ejpam-4597	352	24	we	we	PRON
ejpam-4597	352	25	have	have	VERB
ejpam-4597	352	26	he	he	PRON
ejpam-4597	352	27	⊑	⊑	DET
ejpam-4597	352	28	f−1	f−1	PROPN
ejpam-4597	352	29	up	up	ADP
ejpam-4597	352	30	(	(	PUNCT
ejpam-4597	352	31	ge	ge	PROPN
ejpam-4597	352	32	)	)	PUNCT
ejpam-4597	352	33	,	,	PUNCT
ejpam-4597	352	34	and	and	CCONJ
ejpam-4597	352	35	so	so	ADV
ejpam-4597	352	36	cl(he	cl(he	ADJ
ejpam-4597	352	37	)	)	PUNCT
ejpam-4597	352	38	⊑	⊑	X
ejpam-4597	353	1	f−1	f−1	PROPN
ejpam-4597	353	2	up	up	ADP
ejpam-4597	353	3	(	(	PUNCT
ejpam-4597	353	4	ge	ge	PROPN
ejpam-4597	353	5	)	)	PUNCT
ejpam-4597	353	6	.	.	PUNCT
ejpam-4597	354	1	thus	thus	ADV
ejpam-4597	354	2	fup(he	fup(he	VERB
ejpam-4597	354	3	)	)	PUNCT
ejpam-4597	354	4	⊑	⊑	PRON
ejpam-4597	354	5	fup(cl	fup(cl	NOUN
ejpam-4597	354	6	(	(	PUNCT
ejpam-4597	354	7	he	he	PRON
ejpam-4597	354	8	)	)	PUNCT
ejpam-4597	354	9	)	)	PUNCT
ejpam-4597	354	10	⊑	⊑	PROPN
ejpam-4597	354	11	fupf	fupf	VERB
ejpam-4597	354	12	−1	−1	ADV
ejpam-4597	354	13	up	up	ADP
ejpam-4597	354	14	(	(	PUNCT
ejpam-4597	354	15	ge	ge	PROPN
ejpam-4597	354	16	)	)	PUNCT
ejpam-4597	354	17	⊑	⊑	PROPN
ejpam-4597	354	18	ge	ge	PROPN
ejpam-4597	354	19	.	.	PUNCT
ejpam-4597	355	1	so	so	ADV
ejpam-4597	355	2	cl(he	cl(he	NOUN
ejpam-4597	355	3	)	)	PUNCT
ejpam-4597	355	4	⊑	⊑	PROPN
ejpam-4597	356	1	ge	ge	PROPN
ejpam-4597	356	2	.	.	PUNCT
ejpam-4597	357	1	thus	thus	ADV
ejpam-4597	357	2	fup(he	fup(he	VERB
ejpam-4597	357	3	)	)	PUNCT
ejpam-4597	357	4	is	be	AUX
ejpam-4597	357	5	fsg	fsg	NOUN
ejpam-4597	357	6	-	-	PUNCT
ejpam-4597	357	7	closed	closed	ADJ
ejpam-4597	357	8	.	.	PUNCT
ejpam-4597	358	1	since	since	SCONJ
ejpam-4597	358	2	fup	fup	PROPN
ejpam-4597	358	3	is	be	AUX
ejpam-4597	358	4	one	one	NUM
ejpam-4597	358	5	-	-	PUNCT
ejpam-4597	358	6	one	one	NUM
ejpam-4597	358	7	,	,	PUNCT
ejpam-4597	358	8	we	we	PRON
ejpam-4597	358	9	get	get	VERB
ejpam-4597	358	10	fup	fup	ADJ
ejpam-4597	358	11	(	(	PUNCT
ejpam-4597	358	12	x	x	X
ejpam-4597	358	13	e	e	NOUN
ejpam-4597	358	14	α	α	NOUN
ejpam-4597	358	15	)	)	PUNCT
ejpam-4597	358	16	q̃fup(he	q̃fup(he	NOUN
ejpam-4597	358	17	)	)	PUNCT
ejpam-4597	358	18	.	.	PUNCT
ejpam-4597	359	1	since	since	SCONJ
ejpam-4597	359	2	(	(	PUNCT
ejpam-4597	359	3	v	v	NOUN
ejpam-4597	359	4	,	,	PUNCT
ejpam-4597	359	5	σ	σ	PROPN
ejpam-4597	359	6	,	,	PUNCT
ejpam-4597	359	7	k	k	NOUN
ejpam-4597	359	8	)	)	PUNCT
ejpam-4597	359	9	is	be	AUX
ejpam-4597	359	10	fs	fs	PROPN
ejpam-4597	359	11	-	-	PUNCT
ejpam-4597	359	12	gr2	gr2	NOUN
ejpam-4597	359	13	,	,	PUNCT
ejpam-4597	359	14	there	there	PRON
ejpam-4597	359	15	exist	exist	VERB
ejpam-4597	359	16	fso	fso	NOUN
ejpam-4597	359	17	-	-	PUNCT
ejpam-4597	359	18	sets	set	NOUN
ejpam-4597	359	19	ofup(xe	ofup(xe	PROPN
ejpam-4597	359	20	α	α	NOUN
ejpam-4597	359	21	)	)	PUNCT
ejpam-4597	359	22	and	and	CCONJ
ejpam-4597	359	23	ofup(he	ofup(he	VERB
ejpam-4597	359	24	)	)	PUNCT
ejpam-4597	359	25	such	such	ADJ
ejpam-4597	359	26	that	that	SCONJ
ejpam-4597	359	27	ofup(xe	ofup(xe	PROPN
ejpam-4597	359	28	α	α	NOUN
ejpam-4597	359	29	)	)	PUNCT
ejpam-4597	359	30	q̃ofup(he	q̃ofup(he	PROPN
ejpam-4597	359	31	)	)	PUNCT
ejpam-4597	359	32	.	.	PUNCT
ejpam-4597	360	1	so	so	ADV
ejpam-4597	360	2	,	,	PUNCT
ejpam-4597	360	3	we	we	PRON
ejpam-4597	360	4	get	get	VERB
ejpam-4597	360	5	xeα∈̃f−1	xeα∈̃f−1	PROPN
ejpam-4597	360	6	up	up	ADP
ejpam-4597	360	7	(	(	PUNCT
ejpam-4597	360	8	ofup(xe	ofup(xe	PROPN
ejpam-4597	360	9	α	α	NUM
ejpam-4597	360	10	)	)	PUNCT
ejpam-4597	360	11	)	)	PUNCT
ejpam-4597	360	12	,	,	PUNCT
ejpam-4597	361	1	he	he	PRON
ejpam-4597	361	2	⊑	⊑	X
ejpam-4597	361	3	f−1	f−1	PROPN
ejpam-4597	361	4	up	up	ADP
ejpam-4597	361	5	(	(	PUNCT
ejpam-4597	361	6	ofup(he	ofup(he	NOUN
ejpam-4597	361	7	)	)	PUNCT
ejpam-4597	361	8	)	)	PUNCT
ejpam-4597	361	9	and	and	CCONJ
ejpam-4597	361	10	f−1	f−1	PROPN
ejpam-4597	361	11	up	up	ADP
ejpam-4597	361	12	(	(	PUNCT
ejpam-4597	361	13	ofup(xe	ofup(xe	PROPN
ejpam-4597	361	14	α	α	NUM
ejpam-4597	361	15	)	)	PUNCT
ejpam-4597	361	16	)	)	PUNCT
ejpam-4597	361	17	q̃f−1	q̃f−1	PROPN
ejpam-4597	361	18	up	up	ADV
ejpam-4597	361	19	(	(	PUNCT
ejpam-4597	361	20	ofup(he	ofup(he	NOUN
ejpam-4597	361	21	)	)	PUNCT
ejpam-4597	361	22	)	)	PUNCT
ejpam-4597	361	23	.	.	PUNCT
ejpam-4597	362	1	since	since	SCONJ
ejpam-4597	362	2	fup	fup	PROPN
ejpam-4597	362	3	is	be	AUX
ejpam-4597	362	4	fs	fs	ADJ
ejpam-4597	362	5	-	-	ADJ
ejpam-4597	362	6	continuous	continuous	ADJ
ejpam-4597	362	7	,	,	PUNCT
ejpam-4597	362	8	we	we	PRON
ejpam-4597	362	9	get	get	VERB
ejpam-4597	362	10	f−1	f−1	PROPN
ejpam-4597	362	11	up	up	ADP
ejpam-4597	362	12	(	(	PUNCT
ejpam-4597	362	13	ofup(xe	ofup(xe	PROPN
ejpam-4597	362	14	α	α	NUM
ejpam-4597	362	15	)	)	PUNCT
ejpam-4597	362	16	)	)	PUNCT
ejpam-4597	362	17	and	and	CCONJ
ejpam-4597	362	18	f−1	f−1	PROPN
ejpam-4597	362	19	up	up	ADP
ejpam-4597	362	20	(	(	PUNCT
ejpam-4597	362	21	ofup(he	ofup(he	NOUN
ejpam-4597	362	22	)	)	PUNCT
ejpam-4597	362	23	)	)	PUNCT
ejpam-4597	362	24	are	be	AUX
ejpam-4597	362	25	fso	fso	NOUN
ejpam-4597	362	26	-	-	PUNCT
ejpam-4597	362	27	sets	set	NOUN
ejpam-4597	362	28	in	in	ADP
ejpam-4597	362	29	(	(	PUNCT
ejpam-4597	362	30	u	u	NOUN
ejpam-4597	362	31	,	,	PUNCT
ejpam-4597	362	32	δ	δ	PROPN
ejpam-4597	362	33	,	,	PUNCT
ejpam-4597	362	34	e	e	NOUN
ejpam-4597	362	35	)	)	PUNCT
ejpam-4597	362	36	.	.	PUNCT
ejpam-4597	363	1	the	the	DET
ejpam-4597	363	2	result	result	NOUN
ejpam-4597	363	3	holds	hold	VERB
ejpam-4597	363	4	.	.	PUNCT
ejpam-4597	364	1	theorem	theorem	NOUN
ejpam-4597	364	2	14	14	NUM
ejpam-4597	364	3	.	.	PUNCT
ejpam-4597	365	1	if	if	SCONJ
ejpam-4597	365	2	fup	fup	VERB
ejpam-4597	365	3	:	:	PUNCT
ejpam-4597	365	4	(	(	PUNCT
ejpam-4597	365	5	u	u	NOUN
ejpam-4597	365	6	,	,	PUNCT
ejpam-4597	365	7	δ	δ	PROPN
ejpam-4597	365	8	,	,	PUNCT
ejpam-4597	365	9	e)−→(v	e)−→(v	PROPN
ejpam-4597	365	10	,	,	PUNCT
ejpam-4597	365	11	σ	σ	PROPN
ejpam-4597	365	12	,	,	PUNCT
ejpam-4597	365	13	k	k	NOUN
ejpam-4597	365	14	)	)	PUNCT
ejpam-4597	365	15	is	be	AUX
ejpam-4597	365	16	fs	fs	ADJ
ejpam-4597	365	17	-	-	ADJ
ejpam-4597	365	18	continuous	continuous	ADJ
ejpam-4597	365	19	,	,	PUNCT
ejpam-4597	365	20	fsg	fsg	PROPN
ejpam-4597	365	21	-	-	PUNCT
ejpam-4597	365	22	closed	close	VERB
ejpam-4597	365	23	one	one	NUM
ejpam-4597	365	24	-	-	PUNCT
ejpam-4597	365	25	one	one	NUM
ejpam-4597	365	26	and	and	CCONJ
ejpam-4597	365	27	(	(	PUNCT
ejpam-4597	365	28	v	v	NOUN
ejpam-4597	365	29	,	,	PUNCT
ejpam-4597	365	30	σ	σ	PROPN
ejpam-4597	365	31	,	,	PUNCT
ejpam-4597	365	32	k	k	NOUN
ejpam-4597	365	33	)	)	PUNCT
ejpam-4597	365	34	is	be	AUX
ejpam-4597	365	35	fs	f	NOUN
ejpam-4597	365	36	-	-	PUNCT
ejpam-4597	365	37	gr3	gr3	NOUN
ejpam-4597	365	38	,	,	PUNCT
ejpam-4597	365	39	then	then	ADV
ejpam-4597	365	40	(	(	PUNCT
ejpam-4597	365	41	u	u	NOUN
ejpam-4597	365	42	,	,	PUNCT
ejpam-4597	365	43	δ	δ	PROPN
ejpam-4597	365	44	,	,	PUNCT
ejpam-4597	365	45	e	e	NOUN
ejpam-4597	365	46	)	)	PUNCT
ejpam-4597	365	47	is	be	AUX
ejpam-4597	365	48	fs	f	NOUN
ejpam-4597	365	49	-	-	PUNCT
ejpam-4597	365	50	gr3	gr3	NOUN
ejpam-4597	365	51	.	.	PUNCT
ejpam-4597	366	1	proof	proof	NOUN
ejpam-4597	366	2	.	.	PUNCT
ejpam-4597	367	1	let	let	VERB
ejpam-4597	367	2	he	he	PRON
ejpam-4597	367	3	,	,	PUNCT
ejpam-4597	367	4	ge	ge	PROPN
ejpam-4597	367	5	∈	∈	PROPN
ejpam-4597	367	6	fsgcs(u	fsgcs(u	PROPN
ejpam-4597	367	7	)	)	PUNCT
ejpam-4597	367	8	with	with	ADP
ejpam-4597	367	9	he	he	PRON
ejpam-4597	367	10	q̃ge	q̃ge	PROPN
ejpam-4597	367	11	.	.	PUNCT
ejpam-4597	368	1	as	as	ADP
ejpam-4597	368	2	in	in	ADP
ejpam-4597	368	3	the	the	DET
ejpam-4597	368	4	above	above	ADJ
ejpam-4597	368	5	theorem	theorem	ADJ
ejpam-4597	368	6	fup	fup	NOUN
ejpam-4597	368	7	(	(	PUNCT
ejpam-4597	368	8	he	he	PRON
ejpam-4597	368	9	)	)	PUNCT
ejpam-4597	368	10	and	and	CCONJ
ejpam-4597	368	11	fup	fup	X
ejpam-4597	368	12	(	(	PUNCT
ejpam-4597	368	13	ge	ge	PROPN
ejpam-4597	368	14	)	)	PUNCT
ejpam-4597	368	15	∈	∈	PROPN
ejpam-4597	368	16	fsgc(v	fsgc(v	NOUN
ejpam-4597	368	17	)	)	PUNCT
ejpam-4597	368	18	.	.	PUNCT
ejpam-4597	369	1	since	since	SCONJ
ejpam-4597	369	2	fup	fup	PROPN
ejpam-4597	369	3	is	be	AUX
ejpam-4597	369	4	one	one	NUM
ejpam-4597	369	5	-	-	PUNCT
ejpam-4597	369	6	one	one	NUM
ejpam-4597	369	7	,	,	PUNCT
ejpam-4597	369	8	we	we	PRON
ejpam-4597	369	9	have	have	VERB
ejpam-4597	369	10	fup(he)q̃fup(ge	fup(he)q̃fup(ge	VERB
ejpam-4597	369	11	)	)	PUNCT
ejpam-4597	369	12	.	.	PUNCT
ejpam-4597	370	1	since	since	SCONJ
ejpam-4597	370	2	(	(	PUNCT
ejpam-4597	370	3	u	u	NOUN
ejpam-4597	370	4	,	,	PUNCT
ejpam-4597	370	5	δ	δ	PROPN
ejpam-4597	370	6	,	,	PUNCT
ejpam-4597	370	7	e	e	NOUN
ejpam-4597	370	8	)	)	PUNCT
ejpam-4597	370	9	is	be	AUX
ejpam-4597	370	10	fs	f	NOUN
ejpam-4597	370	11	-	-	PUNCT
ejpam-4597	370	12	gr3	gr3	NOUN
ejpam-4597	370	13	,	,	PUNCT
ejpam-4597	370	14	there	there	PRON
ejpam-4597	370	15	are	be	VERB
ejpam-4597	370	16	fso	fso	NOUN
ejpam-4597	370	17	-	-	PUNCT
ejpam-4597	370	18	sets	set	NOUN
ejpam-4597	370	19	ofup(he	ofup(he	NOUN
ejpam-4597	370	20	)	)	PUNCT
ejpam-4597	370	21	,	,	PUNCT
ejpam-4597	370	22	ofup(ge	ofup(ge	NOUN
ejpam-4597	370	23	)	)	PUNCT
ejpam-4597	370	24	such	such	ADJ
ejpam-4597	370	25	that	that	DET
ejpam-4597	370	26	ofup(he)q̃	ofup(he)q̃	PROPN
ejpam-4597	370	27	ofup(ge	ofup(ge	NOUN
ejpam-4597	370	28	)	)	PUNCT
ejpam-4597	370	29	.	.	PUNCT
ejpam-4597	371	1	so	so	ADV
ejpam-4597	371	2	we	we	PRON
ejpam-4597	371	3	get	get	VERB
ejpam-4597	371	4	,	,	PUNCT
ejpam-4597	371	5	he	he	PRON
ejpam-4597	371	6	⊑	⊑	X
ejpam-4597	371	7	f−1	f−1	PROPN
ejpam-4597	371	8	up	up	ADP
ejpam-4597	371	9	(	(	PUNCT
ejpam-4597	371	10	ofup(he	ofup(he	NOUN
ejpam-4597	371	11	)	)	PUNCT
ejpam-4597	371	12	)	)	PUNCT
ejpam-4597	371	13	,	,	PUNCT
ejpam-4597	371	14	ge	ge	PROPN
ejpam-4597	372	1	⊑	⊑	PROPN
ejpam-4597	372	2	f−1	f−1	PROPN
ejpam-4597	372	3	up	up	ADP
ejpam-4597	372	4	(	(	PUNCT
ejpam-4597	372	5	ofup(ge	ofup(ge	NOUN
ejpam-4597	372	6	)	)	PUNCT
ejpam-4597	372	7	)	)	PUNCT
ejpam-4597	372	8	and	and	CCONJ
ejpam-4597	372	9	f−1	f−1	PROPN
ejpam-4597	372	10	up	up	ADP
ejpam-4597	372	11	(	(	PUNCT
ejpam-4597	372	12	ofup(he))q̃f	ofup(he))q̃f	NUM
ejpam-4597	372	13	−1	−1	NOUN
ejpam-4597	372	14	up	up	ADP
ejpam-4597	372	15	(	(	PUNCT
ejpam-4597	372	16	ofup(ge	ofup(ge	NOUN
ejpam-4597	372	17	)	)	PUNCT
ejpam-4597	372	18	)	)	PUNCT
ejpam-4597	372	19	.	.	PUNCT
ejpam-4597	373	1	since	since	SCONJ
ejpam-4597	373	2	fup	fup	PROPN
ejpam-4597	373	3	is	be	AUX
ejpam-4597	373	4	fs	fs	ADJ
ejpam-4597	373	5	-	-	ADJ
ejpam-4597	373	6	continuous	continuous	ADJ
ejpam-4597	373	7	,	,	PUNCT
ejpam-4597	373	8	we	we	PRON
ejpam-4597	373	9	get	get	VERB
ejpam-4597	373	10	f−1	f−1	PROPN
ejpam-4597	373	11	up	up	ADP
ejpam-4597	373	12	(	(	PUNCT
ejpam-4597	373	13	ofup(he	ofup(he	NOUN
ejpam-4597	373	14	)	)	PUNCT
ejpam-4597	373	15	)	)	PUNCT
ejpam-4597	373	16	and	and	CCONJ
ejpam-4597	373	17	f−1	f−1	PROPN
ejpam-4597	373	18	up	up	ADP
ejpam-4597	373	19	(	(	PUNCT
ejpam-4597	373	20	ofup(ge	ofup(ge	NOUN
ejpam-4597	373	21	)	)	PUNCT
ejpam-4597	373	22	)	)	PUNCT
ejpam-4597	373	23	are	be	AUX
ejpam-4597	373	24	fso	fso	NOUN
ejpam-4597	373	25	-	-	PUNCT
ejpam-4597	373	26	sets	set	NOUN
ejpam-4597	373	27	in	in	ADP
ejpam-4597	373	28	(	(	PUNCT
ejpam-4597	373	29	u	u	NOUN
ejpam-4597	373	30	,	,	PUNCT
ejpam-4597	373	31	δ	δ	PROPN
ejpam-4597	373	32	,	,	PUNCT
ejpam-4597	373	33	e	e	NOUN
ejpam-4597	373	34	)	)	PUNCT
ejpam-4597	373	35	.	.	PUNCT
ejpam-4597	374	1	the	the	DET
ejpam-4597	374	2	proof	proof	NOUN
ejpam-4597	374	3	is	be	AUX
ejpam-4597	374	4	complete	complete	ADJ
ejpam-4597	374	5	.	.	PUNCT
ejpam-4597	375	1	theorem	theorem	NOUN
ejpam-4597	375	2	15	15	NUM
ejpam-4597	375	3	.	.	PUNCT
ejpam-4597	376	1	if	if	SCONJ
ejpam-4597	376	2	fup	fup	VERB
ejpam-4597	376	3	:	:	PUNCT
ejpam-4597	376	4	(	(	PUNCT
ejpam-4597	376	5	u	u	NOUN
ejpam-4597	376	6	,	,	PUNCT
ejpam-4597	376	7	δ	δ	PROPN
ejpam-4597	376	8	,	,	PUNCT
ejpam-4597	376	9	e)−→(v	e)−→(v	PROPN
ejpam-4597	376	10	,	,	PUNCT
ejpam-4597	376	11	σ	σ	PROPN
ejpam-4597	376	12	,	,	PUNCT
ejpam-4597	376	13	k	k	NOUN
ejpam-4597	376	14	)	)	PUNCT
ejpam-4597	376	15	is	be	AUX
ejpam-4597	376	16	fs	fs	ADJ
ejpam-4597	376	17	-	-	ADJ
ejpam-4597	376	18	open	open	ADJ
ejpam-4597	376	19	,	,	PUNCT
ejpam-4597	376	20	fsg	fsg	ADJ
ejpam-4597	376	21	-	-	PUNCT
ejpam-4597	376	22	continuous	continuous	ADJ
ejpam-4597	376	23	bijection	bijection	NOUN
ejpam-4597	376	24	,	,	PUNCT
ejpam-4597	376	25	and	and	CCONJ
ejpam-4597	376	26	(	(	PUNCT
ejpam-4597	376	27	u	u	NOUN
ejpam-4597	376	28	,	,	PUNCT
ejpam-4597	376	29	δ	δ	PROPN
ejpam-4597	376	30	,	,	PUNCT
ejpam-4597	376	31	e	e	NOUN
ejpam-4597	376	32	)	)	PUNCT
ejpam-4597	376	33	is	be	AUX
ejpam-4597	376	34	fs	f	NOUN
ejpam-4597	376	35	-	-	PUNCT
ejpam-4597	376	36	gr3	gr3	NOUN
ejpam-4597	376	37	,	,	PUNCT
ejpam-4597	376	38	then	then	ADV
ejpam-4597	376	39	(	(	PUNCT
ejpam-4597	376	40	v	v	NOUN
ejpam-4597	376	41	,	,	PUNCT
ejpam-4597	376	42	σ	σ	PROPN
ejpam-4597	376	43	,	,	PUNCT
ejpam-4597	376	44	k	k	NOUN
ejpam-4597	376	45	)	)	PUNCT
ejpam-4597	376	46	is	be	AUX
ejpam-4597	376	47	fs	f	NOUN
ejpam-4597	376	48	-	-	PUNCT
ejpam-4597	376	49	gr3	gr3	NOUN
ejpam-4597	376	50	.	.	PUNCT
ejpam-4597	377	1	proof	proof	NOUN
ejpam-4597	377	2	.	.	PUNCT
ejpam-4597	378	1	it	it	PRON
ejpam-4597	378	2	is	be	AUX
ejpam-4597	378	3	analogous	analogous	ADJ
ejpam-4597	378	4	to	to	ADP
ejpam-4597	378	5	that	that	PRON
ejpam-4597	378	6	of	of	ADP
ejpam-4597	378	7	the	the	DET
ejpam-4597	378	8	above	above	ADJ
ejpam-4597	378	9	theorem	theorem	PROPN
ejpam-4597	378	10	.	.	PUNCT
ejpam-4597	378	11	theorem	theorem	VERB
ejpam-4597	378	12	16	16	NUM
ejpam-4597	378	13	.	.	PUNCT
ejpam-4597	379	1	if	if	SCONJ
ejpam-4597	379	2	fup	fup	VERB
ejpam-4597	379	3	:	:	PUNCT
ejpam-4597	379	4	(	(	PUNCT
ejpam-4597	379	5	u	u	NOUN
ejpam-4597	379	6	,	,	PUNCT
ejpam-4597	379	7	δ	δ	PROPN
ejpam-4597	379	8	,	,	PUNCT
ejpam-4597	379	9	e)−→(v	e)−→(v	PROPN
ejpam-4597	379	10	,	,	PUNCT
ejpam-4597	379	11	σ	σ	PROPN
ejpam-4597	379	12	,	,	PUNCT
ejpam-4597	379	13	k	k	NOUN
ejpam-4597	379	14	)	)	PUNCT
ejpam-4597	379	15	is	be	AUX
ejpam-4597	379	16	fsgc	fsgc	ADJ
ejpam-4597	379	17	-	-	PUNCT
ejpam-4597	379	18	irresolute	irresolute	ADJ
ejpam-4597	379	19	,	,	PUNCT
ejpam-4597	379	20	fs	f	NOUN
ejpam-4597	379	21	-	-	VERB
ejpam-4597	379	22	open	open	ADJ
ejpam-4597	379	23	onto	onto	ADP
ejpam-4597	379	24	and	and	CCONJ
ejpam-4597	379	25	(	(	PUNCT
ejpam-4597	379	26	u	u	PROPN
ejpam-4597	379	27	,	,	PUNCT
ejpam-4597	379	28	δ	δ	PROPN
ejpam-4597	379	29	,	,	PUNCT
ejpam-4597	379	30	e	e	NOUN
ejpam-4597	379	31	)	)	PUNCT
ejpam-4597	379	32	is	be	AUX
ejpam-4597	379	33	fs	f	NOUN
ejpam-4597	379	34	-	-	PUNCT
ejpam-4597	379	35	gr3	gr3	NOUN
ejpam-4597	379	36	,	,	PUNCT
ejpam-4597	379	37	then	then	ADV
ejpam-4597	379	38	(	(	PUNCT
ejpam-4597	379	39	v	v	NOUN
ejpam-4597	379	40	,	,	PUNCT
ejpam-4597	379	41	σ	σ	PROPN
ejpam-4597	379	42	,	,	PUNCT
ejpam-4597	379	43	k	k	NOUN
ejpam-4597	379	44	)	)	PUNCT
ejpam-4597	379	45	is	be	AUX
ejpam-4597	379	46	fs	f	NOUN
ejpam-4597	379	47	-	-	PUNCT
ejpam-4597	379	48	gr3	gr3	NOUN
ejpam-4597	379	49	.	.	PUNCT
ejpam-4597	380	1	proof	proof	NOUN
ejpam-4597	380	2	.	.	PUNCT
ejpam-4597	381	1	it	it	PRON
ejpam-4597	381	2	is	be	AUX
ejpam-4597	381	3	similar	similar	ADJ
ejpam-4597	381	4	to	to	ADP
ejpam-4597	381	5	that	that	PRON
ejpam-4597	381	6	of	of	ADP
ejpam-4597	381	7	theorem	theorem	ADJ
ejpam-4597	381	8	14	14	NUM
ejpam-4597	381	9	.	.	PUNCT
ejpam-4597	382	1	the	the	DET
ejpam-4597	382	2	next	next	ADJ
ejpam-4597	382	3	two	two	NUM
ejpam-4597	382	4	theorems	theorem	NOUN
ejpam-4597	382	5	show	show	VERB
ejpam-4597	382	6	that	that	SCONJ
ejpam-4597	382	7	fs	fs	PROPN
ejpam-4597	382	8	-	-	PUNCT
ejpam-4597	382	9	gr2	gr2	PROPN
ejpam-4597	382	10	and	and	CCONJ
ejpam-4597	382	11	fs	f	NOUN
ejpam-4597	382	12	-	-	PUNCT
ejpam-4597	382	13	gr3	gr3	NOUN
ejpam-4597	382	14	are	be	AUX
ejpam-4597	382	15	hereditary	hereditary	ADJ
ejpam-4597	382	16	property	property	NOUN
ejpam-4597	382	17	.	.	PUNCT
ejpam-4597	383	1	theorem	theorem	VERB
ejpam-4597	383	2	17	17	NUM
ejpam-4597	383	3	.	.	PUNCT
ejpam-4597	384	1	every	every	DET
ejpam-4597	384	2	fs	fs	NOUN
ejpam-4597	384	3	-	-	PUNCT
ejpam-4597	384	4	subspace	subspace	NOUN
ejpam-4597	384	5	(	(	PUNCT
ejpam-4597	384	6	ṽe	ṽe	ADV
ejpam-4597	384	7	,	,	PUNCT
ejpam-4597	384	8	δv	δv	ADV
ejpam-4597	384	9	,	,	PUNCT
ejpam-4597	384	10	e	e	NOUN
ejpam-4597	384	11	)	)	PUNCT
ejpam-4597	384	12	of	of	ADP
ejpam-4597	384	13	fs	fs	PROPN
ejpam-4597	384	14	-	-	PUNCT
ejpam-4597	384	15	gr2	gr2	PROPN
ejpam-4597	384	16	is	be	AUX
ejpam-4597	384	17	fs	f	NOUN
ejpam-4597	384	18	-	-	PUNCT
ejpam-4597	384	19	gr2	gr2	NOUN
ejpam-4597	384	20	.	.	PUNCT
ejpam-4597	385	1	proof	proof	NOUN
ejpam-4597	385	2	.	.	PUNCT
ejpam-4597	386	1	let	let	VERB
ejpam-4597	386	2	(	(	PUNCT
ejpam-4597	386	3	u	u	NOUN
ejpam-4597	386	4	,	,	PUNCT
ejpam-4597	386	5	δ	δ	PROPN
ejpam-4597	386	6	,	,	PUNCT
ejpam-4597	386	7	e	e	NOUN
ejpam-4597	386	8	)	)	PUNCT
ejpam-4597	386	9	be	be	AUX
ejpam-4597	386	10	fs	fs	PROPN
ejpam-4597	386	11	-	-	NOUN
ejpam-4597	386	12	gr2	gr2	NOUN
ejpam-4597	386	13	.	.	PUNCT
ejpam-4597	387	1	suppose	suppose	VERB
ejpam-4597	387	2	that	that	SCONJ
ejpam-4597	387	3	he	he	PRON
ejpam-4597	387	4	any	any	DET
ejpam-4597	387	5	fsg	fsg	PROPN
ejpam-4597	387	6	-	-	PUNCT
ejpam-4597	387	7	closed	close	VERB
ejpam-4597	387	8	set	set	NOUN
ejpam-4597	387	9	in	in	ADP
ejpam-4597	387	10	(	(	PUNCT
ejpam-4597	387	11	ṽe	ṽe	ADV
ejpam-4597	387	12	,	,	PUNCT
ejpam-4597	387	13	δv	δv	ADV
ejpam-4597	387	14	,	,	PUNCT
ejpam-4597	387	15	e	e	X
ejpam-4597	387	16	)	)	PUNCT
ejpam-4597	387	17	with	with	ADP
ejpam-4597	387	18	xeαq̃he	xeαq̃he	PROPN
ejpam-4597	387	19	for	for	ADP
ejpam-4597	387	20	any	any	DET
ejpam-4597	387	21	fs	fs	NOUN
ejpam-4597	387	22	-	-	PUNCT
ejpam-4597	387	23	point	point	NOUN
ejpam-4597	387	24	in	in	ADP
ejpam-4597	387	25	(	(	PUNCT
ejpam-4597	387	26	ṽe	ṽe	ADV
ejpam-4597	387	27	,	,	PUNCT
ejpam-4597	387	28	δv	δv	ADV
ejpam-4597	387	29	,	,	PUNCT
ejpam-4597	387	30	e	e	NOUN
ejpam-4597	387	31	)	)	PUNCT
ejpam-4597	387	32	,	,	PUNCT
ejpam-4597	387	33	then	then	ADV
ejpam-4597	387	34	there	there	PRON
ejpam-4597	387	35	is	be	VERB
ejpam-4597	387	36	an	an	DET
ejpam-4597	387	37	fsc	fsc	PROPN
ejpam-4597	387	38	-	-	PUNCT
ejpam-4597	387	39	set	set	VERB
ejpam-4597	387	40	and	and	CCONJ
ejpam-4597	387	41	so	so	ADV
ejpam-4597	387	42	fsg	fsg	PROPN
ejpam-4597	387	43	-	-	PUNCT
ejpam-4597	387	44	closed	close	VERB
ejpam-4597	387	45	set	set	VERB
ejpam-4597	387	46	fe	fe	NOUN
ejpam-4597	387	47	in	in	ADP
ejpam-4597	387	48	(	(	PUNCT
ejpam-4597	387	49	u	u	NOUN
ejpam-4597	387	50	,	,	PUNCT
ejpam-4597	387	51	δ	δ	PROPN
ejpam-4597	387	52	,	,	PUNCT
ejpam-4597	387	53	e	e	NOUN
ejpam-4597	387	54	)	)	PUNCT
ejpam-4597	387	55	with	with	ADP
ejpam-4597	387	56	he	he	PRON
ejpam-4597	387	57	=	=	PUNCT
ejpam-4597	387	58	ṽe	ṽe	PUNCT
ejpam-4597	387	59	⊓	⊓	PROPN
ejpam-4597	387	60	fe	fe	NOUN
ejpam-4597	387	61	and	and	CCONJ
ejpam-4597	387	62	xeαq̃fe	xeαq̃fe	PROPN
ejpam-4597	387	63	.	.	PUNCT
ejpam-4597	388	1	since	since	SCONJ
ejpam-4597	388	2	(	(	PUNCT
ejpam-4597	388	3	u	u	NOUN
ejpam-4597	388	4	,	,	PUNCT
ejpam-4597	388	5	δ	δ	PROPN
ejpam-4597	388	6	,	,	PUNCT
ejpam-4597	388	7	e	e	NOUN
ejpam-4597	388	8	)	)	PUNCT
ejpam-4597	388	9	is	be	AUX
ejpam-4597	388	10	fs	fs	PROPN
ejpam-4597	388	11	-	-	PUNCT
ejpam-4597	388	12	gr2	gr2	NOUN
ejpam-4597	388	13	,	,	PUNCT
ejpam-4597	388	14	there	there	PRON
ejpam-4597	388	15	are	be	VERB
ejpam-4597	388	16	oxe	oxe	PROPN
ejpam-4597	388	17	α	α	NOUN
ejpam-4597	388	18	,	,	PUNCT
ejpam-4597	388	19	ofe	ofe	INTJ
ejpam-4597	388	20	∈	∈	PROPN
ejpam-4597	388	21	δ	δ	PROPN
ejpam-4597	388	22	such	such	ADJ
ejpam-4597	388	23	that	that	SCONJ
ejpam-4597	389	1	oxe	oxe	PRON
ejpam-4597	389	2	α	α	PRON
ejpam-4597	389	3	q̃ofe	q̃ofe	NOUN
ejpam-4597	389	4	.	.	PUNCT
ejpam-4597	390	1	now	now	ADV
ejpam-4597	390	2	take	take	VERB
ejpam-4597	390	3	o∗	o∗	PROPN
ejpam-4597	390	4	xe	xe	PROPN
ejpam-4597	390	5	α	α	PROPN
ejpam-4597	390	6	=	=	PUNCT
ejpam-4597	390	7	ṽe	ṽe	ADP
ejpam-4597	390	8	⊓oxe	⊓oxe	X
ejpam-4597	390	9	α	α	X
ejpam-4597	390	10	∈	∈	PROPN
ejpam-4597	390	11	δv	δv	ADV
ejpam-4597	391	1	and	and	CCONJ
ejpam-4597	391	2	o∗	o∗	PROPN
ejpam-4597	391	3	fe	fe	X
ejpam-4597	391	4	=	=	PUNCT
ejpam-4597	391	5	ṽe	ṽe	PROPN
ejpam-4597	391	6	⊓ofe	⊓ofe	PROPN
ejpam-4597	391	7	∈	∈	PROPN
ejpam-4597	391	8	δv	δv	ADV
ejpam-4597	391	9	,	,	PUNCT
ejpam-4597	391	10	then	then	ADV
ejpam-4597	391	11	o∗	o∗	PROPN
ejpam-4597	391	12	xe	xe	PROPN
ejpam-4597	391	13	α	α	PROPN
ejpam-4597	391	14	and	and	CCONJ
ejpam-4597	391	15	o∗	o∗	PROPN
ejpam-4597	391	16	fe	fe	X
ejpam-4597	391	17	are	be	AUX
ejpam-4597	391	18	fso	fso	NOUN
ejpam-4597	391	19	-	-	PUNCT
ejpam-4597	391	20	sets	set	NOUN
ejpam-4597	391	21	in	in	ADP
ejpam-4597	391	22	(	(	PUNCT
ejpam-4597	391	23	ṽe	ṽe	ADV
ejpam-4597	391	24	,	,	PUNCT
ejpam-4597	391	25	δv	δv	ADV
ejpam-4597	391	26	,	,	PUNCT
ejpam-4597	391	27	e	e	X
ejpam-4597	391	28	)	)	PUNCT
ejpam-4597	391	29	containing	contain	VERB
ejpam-4597	391	30	xeα	xeα	PROPN
ejpam-4597	391	31	and	and	CCONJ
ejpam-4597	391	32	fe	fe	NOUN
ejpam-4597	391	33	respectively	respectively	ADV
ejpam-4597	391	34	,	,	PUNCT
ejpam-4597	391	35	such	such	ADJ
ejpam-4597	391	36	that	that	SCONJ
ejpam-4597	391	37	o∗	o∗	PROPN
ejpam-4597	391	38	xe	xe	PROPN
ejpam-4597	391	39	α	α	PROPN
ejpam-4597	391	40	q̃o∗	q̃o∗	PROPN
ejpam-4597	391	41	fe	fe	X
ejpam-4597	391	42	.	.	PUNCT
ejpam-4597	392	1	the	the	DET
ejpam-4597	392	2	result	result	NOUN
ejpam-4597	392	3	holds	hold	VERB
ejpam-4597	392	4	.	.	PUNCT
ejpam-4597	393	1	theorem	theorem	NOUN
ejpam-4597	393	2	18	18	NUM
ejpam-4597	393	3	.	.	PUNCT
ejpam-4597	394	1	every	every	DET
ejpam-4597	394	2	fsc	fsc	PROPN
ejpam-4597	394	3	-	-	PUNCT
ejpam-4597	394	4	subspace	subspace	NOUN
ejpam-4597	394	5	(	(	PUNCT
ejpam-4597	394	6	ṽe	ṽe	ADV
ejpam-4597	394	7	,	,	PUNCT
ejpam-4597	394	8	δv	δv	ADV
ejpam-4597	394	9	,	,	PUNCT
ejpam-4597	394	10	e	e	NOUN
ejpam-4597	394	11	)	)	PUNCT
ejpam-4597	394	12	of	of	ADP
ejpam-4597	394	13	fs	fs	PROPN
ejpam-4597	394	14	-	-	PUNCT
ejpam-4597	394	15	gr3	gr3	PROPN
ejpam-4597	394	16	is	be	AUX
ejpam-4597	394	17	fs	f	NOUN
ejpam-4597	394	18	-	-	PUNCT
ejpam-4597	394	19	gr3	gr3	NOUN
ejpam-4597	394	20	.	.	PUNCT
ejpam-4597	395	1	proof	proof	NOUN
ejpam-4597	395	2	.	.	PUNCT
ejpam-4597	396	1	it	it	PRON
ejpam-4597	396	2	is	be	AUX
ejpam-4597	396	3	similar	similar	ADJ
ejpam-4597	396	4	to	to	ADP
ejpam-4597	396	5	that	that	PRON
ejpam-4597	396	6	of	of	ADP
ejpam-4597	396	7	the	the	DET
ejpam-4597	396	8	above	above	ADJ
ejpam-4597	396	9	theorem	theorem	PROPN
ejpam-4597	396	10	.	.	PROPN
ejpam-4597	397	1	references	reference	NOUN
ejpam-4597	397	2	189	189	NUM
ejpam-4597	397	3	theorem	theorem	NOUN
ejpam-4597	397	4	19	19	NUM
ejpam-4597	397	5	.	.	PUNCT
ejpam-4597	398	1	(	(	PUNCT
ejpam-4597	398	2	u	u	NOUN
ejpam-4597	398	3	,	,	PUNCT
ejpam-4597	398	4	δτ	δτ	VERB
ejpam-4597	398	5	,	,	PUNCT
ejpam-4597	398	6	e	e	X
ejpam-4597	398	7	)	)	PUNCT
ejpam-4597	398	8	is	be	AUX
ejpam-4597	398	9	fs	fs	PROPN
ejpam-4597	398	10	-	-	PUNCT
ejpam-4597	398	11	gr2	gr2	NOUN
ejpam-4597	398	12	if	if	SCONJ
ejpam-4597	398	13	and	and	CCONJ
ejpam-4597	398	14	only	only	ADV
ejpam-4597	398	15	if	if	SCONJ
ejpam-4597	398	16	(	(	PUNCT
ejpam-4597	398	17	u	u	NOUN
ejpam-4597	398	18	,	,	PUNCT
ejpam-4597	398	19	τ	τ	X
ejpam-4597	398	20	)	)	PUNCT
ejpam-4597	398	21	is	be	AUX
ejpam-4597	398	22	g	g	NOUN
ejpam-4597	398	23	-	-	PUNCT
ejpam-4597	398	24	regular	regular	ADJ
ejpam-4597	398	25	.	.	PUNCT
ejpam-4597	399	1	proof	proof	NOUN
ejpam-4597	399	2	.	.	PUNCT
ejpam-4597	400	1	let	let	VERB
ejpam-4597	400	2	(	(	PUNCT
ejpam-4597	400	3	u	u	NOUN
ejpam-4597	400	4	,	,	PUNCT
ejpam-4597	400	5	δτ	δτ	VERB
ejpam-4597	400	6	,	,	PUNCT
ejpam-4597	400	7	e	e	X
ejpam-4597	400	8	)	)	PUNCT
ejpam-4597	400	9	be	be	AUX
ejpam-4597	400	10	fs	fs	PROPN
ejpam-4597	400	11	-	-	NOUN
ejpam-4597	400	12	gr2	gr2	NOUN
ejpam-4597	400	13	and	and	CCONJ
ejpam-4597	400	14	b	b	NOUN
ejpam-4597	400	15	any	any	DET
ejpam-4597	400	16	closed	closed	ADJ
ejpam-4597	400	17	set	set	NOUN
ejpam-4597	400	18	in	in	ADP
ejpam-4597	400	19	(	(	PUNCT
ejpam-4597	400	20	u	u	NOUN
ejpam-4597	400	21	,	,	PUNCT
ejpam-4597	400	22	τ	τ	X
ejpam-4597	400	23	)	)	PUNCT
ejpam-4597	400	24	with	with	ADP
ejpam-4597	400	25	x	x	PROPN
ejpam-4597	400	26	/∈	/∈	PROPN
ejpam-4597	400	27	b	b	NOUN
ejpam-4597	400	28	,	,	PUNCT
ejpam-4597	400	29	then	then	ADV
ejpam-4597	400	30	b	b	PROPN
ejpam-4597	400	31	is	be	AUX
ejpam-4597	400	32	a	a	DET
ejpam-4597	400	33	g	g	NOUN
ejpam-4597	400	34	-	-	PUNCT
ejpam-4597	400	35	closed	close	VERB
ejpam-4597	400	36	set	set	NOUN
ejpam-4597	400	37	and	and	CCONJ
ejpam-4597	400	38	there	there	PRON
ejpam-4597	400	39	is	be	VERB
ejpam-4597	400	40	an	an	DET
ejpam-4597	400	41	fsc	fsc	PROPN
ejpam-4597	400	42	-	-	PUNCT
ejpam-4597	400	43	set	set	VERB
ejpam-4597	400	44	fe	fe	NOUN
ejpam-4597	400	45	such	such	ADJ
ejpam-4597	400	46	that	that	DET
ejpam-4597	400	47	fe	fe	X
ejpam-4597	400	48	=	=	PUNCT
ejpam-4597	400	49	χ̃b	χ̃b	PROPN
ejpam-4597	400	50	.	.	PUNCT
ejpam-4597	400	51	clearly	clearly	ADV
ejpam-4597	400	52	fe	fe	PROPN
ejpam-4597	400	53	is	be	AUX
ejpam-4597	400	54	an	an	DET
ejpam-4597	400	55	fsg	fsg	NOUN
ejpam-4597	400	56	-	-	PUNCT
ejpam-4597	400	57	closed	closed	ADJ
ejpam-4597	400	58	set	set	NOUN
ejpam-4597	400	59	with	with	ADP
ejpam-4597	400	60	xe1q̃fe	xe1q̃fe	PROPN
ejpam-4597	400	61	.	.	PUNCT
ejpam-4597	401	1	since	since	SCONJ
ejpam-4597	401	2	(	(	PUNCT
ejpam-4597	401	3	u	u	NOUN
ejpam-4597	401	4	,	,	PUNCT
ejpam-4597	401	5	δτ	δτ	VERB
ejpam-4597	401	6	,	,	PUNCT
ejpam-4597	401	7	e	e	X
ejpam-4597	401	8	)	)	PUNCT
ejpam-4597	401	9	is	be	AUX
ejpam-4597	401	10	fs	fs	PROPN
ejpam-4597	401	11	-	-	PUNCT
ejpam-4597	401	12	gr2	gr2	NOUN
ejpam-4597	401	13	,	,	PUNCT
ejpam-4597	401	14	there	there	PRON
ejpam-4597	401	15	are	be	VERB
ejpam-4597	401	16	oxe	oxe	X
ejpam-4597	401	17	1	1	NUM
ejpam-4597	401	18	,	,	PUNCT
ejpam-4597	401	19	ofe	ofe	INTJ
ejpam-4597	401	20	∈	∈	PROPN
ejpam-4597	401	21	δτ	δτ	VERB
ejpam-4597	401	22	such	such	ADJ
ejpam-4597	401	23	that	that	SCONJ
ejpam-4597	401	24	oxe	oxe	PRON
ejpam-4597	401	25	1	1	NUM
ejpam-4597	401	26	q̃ofe	q̃ofe	NOUN
ejpam-4597	401	27	.	.	PUNCT
ejpam-4597	402	1	thus	thus	ADV
ejpam-4597	402	2	there	there	PRON
ejpam-4597	402	3	are	be	VERB
ejpam-4597	402	4	ox	ox	ADJ
ejpam-4597	402	5	,	,	PUNCT
ejpam-4597	402	6	ob	ob	ADP
ejpam-4597	402	7	∈	∈	PROPN
ejpam-4597	402	8	τ	τ	X
ejpam-4597	402	9	such	such	ADJ
ejpam-4597	402	10	that	that	SCONJ
ejpam-4597	402	11	oxe	oxe	PROPN
ejpam-4597	402	12	1	1	NUM
ejpam-4597	402	13	=	=	SYM
ejpam-4597	402	14	χ̃ox	χ̃ox	PROPN
ejpam-4597	402	15	,	,	PUNCT
ejpam-4597	402	16	ofe	ofe	NOUN
ejpam-4597	402	17	=	=	PUNCT
ejpam-4597	402	18	χ̃ob	χ̃ob	PROPN
ejpam-4597	402	19	and	and	CCONJ
ejpam-4597	402	20	ox	ox	ADJ
ejpam-4597	402	21	∩ob	∩ob	NOUN
ejpam-4597	402	22	=	=	PUNCT
ejpam-4597	402	23	∅.	∅.	VERB
ejpam-4597	402	24	therefore	therefore	ADV
ejpam-4597	402	25	(	(	PUNCT
ejpam-4597	402	26	u	u	NOUN
ejpam-4597	402	27	,	,	PUNCT
ejpam-4597	402	28	τ	τ	X
ejpam-4597	402	29	)	)	PUNCT
ejpam-4597	402	30	is	be	AUX
ejpam-4597	402	31	g	g	NOUN
ejpam-4597	402	32	-	-	PUNCT
ejpam-4597	402	33	regular	regular	ADJ
ejpam-4597	402	34	.	.	PUNCT
ejpam-4597	403	1	conversely	conversely	ADV
ejpam-4597	403	2	,	,	PUNCT
ejpam-4597	403	3	let	let	VERB
ejpam-4597	403	4	(	(	PUNCT
ejpam-4597	403	5	u	u	NOUN
ejpam-4597	403	6	,	,	PUNCT
ejpam-4597	403	7	τ	τ	X
ejpam-4597	403	8	)	)	PUNCT
ejpam-4597	403	9	be	be	VERB
ejpam-4597	403	10	g	g	NOUN
ejpam-4597	403	11	-	-	PUNCT
ejpam-4597	403	12	regular	regular	ADJ
ejpam-4597	404	1	and	and	CCONJ
ejpam-4597	404	2	he	he	PRON
ejpam-4597	404	3	any	any	DET
ejpam-4597	404	4	closed	closed	ADJ
ejpam-4597	404	5	set	set	VERB
ejpam-4597	404	6	in	in	ADP
ejpam-4597	404	7	(	(	PUNCT
ejpam-4597	404	8	u	u	NOUN
ejpam-4597	404	9	,	,	PUNCT
ejpam-4597	404	10	δτ	δτ	VERB
ejpam-4597	404	11	,	,	PUNCT
ejpam-4597	404	12	e	e	NOUN
ejpam-4597	404	13	)	)	PUNCT
ejpam-4597	404	14	with	with	ADP
ejpam-4597	404	15	xeαq̃he	xeαq̃he	PROPN
ejpam-4597	404	16	.	.	PUNCT
ejpam-4597	405	1	then	then	ADV
ejpam-4597	405	2	he	he	PRON
ejpam-4597	405	3	is	be	AUX
ejpam-4597	405	4	an	an	DET
ejpam-4597	405	5	fsg	fsg	PROPN
ejpam-4597	405	6	-	-	PUNCT
ejpam-4597	405	7	closed	close	VERB
ejpam-4597	405	8	set	set	NOUN
ejpam-4597	405	9	and	and	CCONJ
ejpam-4597	405	10	there	there	PRON
ejpam-4597	405	11	is	be	VERB
ejpam-4597	405	12	a	a	DET
ejpam-4597	405	13	closed	closed	ADJ
ejpam-4597	405	14	set	set	VERB
ejpam-4597	405	15	f	f	PROPN
ejpam-4597	405	16	in	in	ADP
ejpam-4597	405	17	(	(	PUNCT
ejpam-4597	405	18	u	u	NOUN
ejpam-4597	405	19	,	,	PUNCT
ejpam-4597	405	20	τ	τ	X
ejpam-4597	405	21	)	)	PUNCT
ejpam-4597	405	22	such	such	ADJ
ejpam-4597	405	23	that	that	SCONJ
ejpam-4597	405	24	he	he	PRON
ejpam-4597	405	25	=	=	PUNCT
ejpam-4597	405	26	χ̃of	χ̃of	ADJ
ejpam-4597	405	27	and	and	CCONJ
ejpam-4597	405	28	x	x	SYM
ejpam-4597	405	29	/∈	/∈	PROPN
ejpam-4597	406	1	f	f	PROPN
ejpam-4597	406	2	.	.	PUNCT
ejpam-4597	407	1	clearly	clearly	ADV
ejpam-4597	407	2	f	f	PROPN
ejpam-4597	407	3	is	be	AUX
ejpam-4597	407	4	g	g	NOUN
ejpam-4597	407	5	-	-	PUNCT
ejpam-4597	407	6	closed	close	VERB
ejpam-4597	407	7	and	and	CCONJ
ejpam-4597	407	8	(	(	PUNCT
ejpam-4597	407	9	u	u	NOUN
ejpam-4597	407	10	,	,	PUNCT
ejpam-4597	407	11	τ	τ	X
ejpam-4597	407	12	)	)	PUNCT
ejpam-4597	407	13	is	be	AUX
ejpam-4597	407	14	g	g	NOUN
ejpam-4597	407	15	-	-	PUNCT
ejpam-4597	407	16	regular	regular	ADJ
ejpam-4597	407	17	,	,	PUNCT
ejpam-4597	407	18	then	then	ADV
ejpam-4597	407	19	there	there	PRON
ejpam-4597	407	20	are	be	VERB
ejpam-4597	407	21	ox	ox	ADJ
ejpam-4597	407	22	,	,	PUNCT
ejpam-4597	407	23	of	of	ADP
ejpam-4597	407	24	∈	∈	PROPN
ejpam-4597	407	25	τ	τ	X
ejpam-4597	407	26	with	with	ADP
ejpam-4597	407	27	ox	ox	NOUN
ejpam-4597	407	28	∩of	∩of	NOUN
ejpam-4597	407	29	=	=	NOUN
ejpam-4597	407	30	∅	∅	NOUN
ejpam-4597	407	31	and	and	CCONJ
ejpam-4597	407	32	so	so	ADV
ejpam-4597	407	33	,	,	PUNCT
ejpam-4597	407	34	there	there	PRON
ejpam-4597	407	35	are	be	VERB
ejpam-4597	407	36	oxe	oxe	PRON
ejpam-4597	407	37	α	α	NOUN
ejpam-4597	407	38	and	and	CCONJ
ejpam-4597	407	39	ohe	ohe	NOUN
ejpam-4597	407	40	∈	∈	PROPN
ejpam-4597	407	41	δτ	δτ	VERB
ejpam-4597	407	42	such	such	ADJ
ejpam-4597	407	43	that	that	SCONJ
ejpam-4597	407	44	oxe	oxe	PRON
ejpam-4597	407	45	α	α	PROPN
ejpam-4597	407	46	=	=	SYM
ejpam-4597	407	47	χ̃ox	χ̃ox	PROPN
ejpam-4597	407	48	,	,	PUNCT
ejpam-4597	407	49	ohe	ohe	NOUN
ejpam-4597	407	50	=	=	PUNCT
ejpam-4597	407	51	χ̃of	χ̃of	PROPN
ejpam-4597	407	52	and	and	CCONJ
ejpam-4597	407	53	oxe	oxe	PRON
ejpam-4597	407	54	α	α	NOUN
ejpam-4597	407	55	q̃ohe	q̃ohe	NOUN
ejpam-4597	407	56	.	.	PUNCT
ejpam-4597	408	1	hence	hence	ADV
ejpam-4597	408	2	(	(	PUNCT
ejpam-4597	408	3	u	u	NOUN
ejpam-4597	408	4	,	,	PUNCT
ejpam-4597	408	5	δτ	δτ	VERB
ejpam-4597	408	6	,	,	PUNCT
ejpam-4597	408	7	e	e	X
ejpam-4597	408	8	)	)	PUNCT
ejpam-4597	408	9	is	be	AUX
ejpam-4597	408	10	fs	fs	PROPN
ejpam-4597	408	11	-	-	PUNCT
ejpam-4597	408	12	gr2	gr2	NOUN
ejpam-4597	408	13	.	.	PUNCT
ejpam-4597	409	1	theorem	theorem	ADJ
ejpam-4597	409	2	20	20	NUM
ejpam-4597	409	3	.	.	PUNCT
ejpam-4597	410	1	(	(	PUNCT
ejpam-4597	410	2	u	u	NOUN
ejpam-4597	410	3	,	,	PUNCT
ejpam-4597	410	4	δτ	δτ	VERB
ejpam-4597	410	5	,	,	PUNCT
ejpam-4597	410	6	e	e	X
ejpam-4597	410	7	)	)	PUNCT
ejpam-4597	410	8	is	be	AUX
ejpam-4597	410	9	fs	f	NOUN
ejpam-4597	410	10	-	-	PUNCT
ejpam-4597	410	11	gr3	gr3	NOUN
ejpam-4597	410	12	if	if	SCONJ
ejpam-4597	410	13	and	and	CCONJ
ejpam-4597	410	14	only	only	ADV
ejpam-4597	410	15	if	if	SCONJ
ejpam-4597	410	16	(	(	PUNCT
ejpam-4597	410	17	u	u	NOUN
ejpam-4597	410	18	,	,	PUNCT
ejpam-4597	410	19	τ	τ	X
ejpam-4597	410	20	)	)	PUNCT
ejpam-4597	410	21	is	be	AUX
ejpam-4597	410	22	g	g	NOUN
ejpam-4597	410	23	-	-	PUNCT
ejpam-4597	410	24	normal	normal	ADJ
ejpam-4597	410	25	.	.	PUNCT
ejpam-4597	411	1	proof	proof	NOUN
ejpam-4597	411	2	.	.	PUNCT
ejpam-4597	412	1	it	it	PRON
ejpam-4597	412	2	is	be	AUX
ejpam-4597	412	3	similar	similar	ADJ
ejpam-4597	412	4	to	to	ADP
ejpam-4597	412	5	that	that	PRON
ejpam-4597	412	6	of	of	ADP
ejpam-4597	412	7	the	the	DET
ejpam-4597	412	8	above	above	ADJ
ejpam-4597	412	9	theorem	theorem	PROPN
ejpam-4597	412	10	.	.	PROPN
ejpam-4597	413	1	from	from	ADP
ejpam-4597	413	2	the	the	DET
ejpam-4597	413	3	obtained	obtain	VERB
ejpam-4597	413	4	results	result	NOUN
ejpam-4597	413	5	in	in	ADP
ejpam-4597	413	6	section	section	NOUN
ejpam-4597	413	7	2	2	NUM
ejpam-4597	413	8	,	,	PUNCT
ejpam-4597	413	9	3	3	NUM
ejpam-4597	413	10	.	.	X
ejpam-4597	414	1	we	we	PRON
ejpam-4597	414	2	conclude	conclude	VERB
ejpam-4597	414	3	the	the	DET
ejpam-4597	414	4	next	next	ADJ
ejpam-4597	414	5	relations	relation	NOUN
ejpam-4597	414	6	.	.	PUNCT
ejpam-4597	415	1	corollary	corollary	ADJ
ejpam-4597	415	2	3	3	NUM
ejpam-4597	415	3	.	.	PUNCT
ejpam-4597	416	1	for	for	ADP
ejpam-4597	416	2	an	an	DET
ejpam-4597	416	3	fsts	fst	NOUN
ejpam-4597	416	4	(	(	PUNCT
ejpam-4597	416	5	u	u	NOUN
ejpam-4597	416	6	,	,	PUNCT
ejpam-4597	416	7	τ	τ	PROPN
ejpam-4597	416	8	,	,	PUNCT
ejpam-4597	416	9	e	e	NOUN
ejpam-4597	416	10	)	)	PUNCT
ejpam-4597	416	11	,	,	PUNCT
ejpam-4597	416	12	the	the	DET
ejpam-4597	416	13	next	next	ADJ
ejpam-4597	416	14	implications	implication	NOUN
ejpam-4597	416	15	hold	hold	VERB
ejpam-4597	416	16	.	.	PUNCT
ejpam-4597	417	1	1	1	X
ejpam-4597	417	2	)	)	PUNCT
ejpam-4597	417	3	fsg4	fsg4	VERB
ejpam-4597	417	4	⇔	⇔	PROPN
ejpam-4597	417	5	fst4	fst4	PROPN
ejpam-4597	417	6	⇒	⇒	NOUN
ejpam-4597	417	7	fst3	fst3	PROPN
ejpam-4597	417	8	⇔	⇔	PROPN
ejpam-4597	417	9	fsg3	fsg3	PROPN
ejpam-4597	417	10	⇔	⇔	PROPN
ejpam-4597	417	11	fs	fs	PROPN
ejpam-4597	417	12	-	-	PUNCT
ejpam-4597	417	13	gr2	gr2	PROPN
ejpam-4597	417	14	∧	∧	PROPN
ejpam-4597	417	15	fs	fs	PROPN
ejpam-4597	417	16	-	-	PUNCT
ejpam-4597	417	17	symmetric	symmetric	ADJ
ejpam-4597	417	18	⇒	⇒	PROPN
ejpam-4597	417	19	fsr2	fsr2	PROPN
ejpam-4597	417	20	.	.	PUNCT
ejpam-4597	418	1	2)fsg3	2)fsg3	NUM
ejpam-4597	418	2	⇒	⇒	NOUN
ejpam-4597	418	3	fst2	fst2	ADJ
ejpam-4597	418	4	1	1	NUM
ejpam-4597	418	5	2	2	NUM
ejpam-4597	418	6	⇒	⇒	NOUN
ejpam-4597	418	7	fst2	fst2	PROPN
ejpam-4597	418	8	⇒	⇒	PROPN
ejpam-4597	418	9	fst1	fst1	PROPN
ejpam-4597	418	10	⇒	⇒	PROPN
ejpam-4597	418	11	fst0	fst0	PROPN
ejpam-4597	418	12	.	.	PUNCT
ejpam-4597	419	1	5	5	X
ejpam-4597	419	2	.	.	X
ejpam-4597	419	3	conclusion	conclusion	NOUN
ejpam-4597	419	4	the	the	DET
ejpam-4597	419	5	topological	topological	ADJ
ejpam-4597	419	6	structures	structure	NOUN
ejpam-4597	419	7	play	play	VERB
ejpam-4597	419	8	an	an	DET
ejpam-4597	419	9	important	important	ADJ
ejpam-4597	419	10	role	role	NOUN
ejpam-4597	419	11	in	in	ADP
ejpam-4597	419	12	many	many	ADJ
ejpam-4597	419	13	applications	application	NOUN
ejpam-4597	419	14	of	of	ADP
ejpam-4597	419	15	complex	complex	ADJ
ejpam-4597	419	16	reallife	reallife	NOUN
ejpam-4597	419	17	problems	problem	NOUN
ejpam-4597	419	18	in	in	ADP
ejpam-4597	419	19	various	various	ADJ
ejpam-4597	419	20	field	field	NOUN
ejpam-4597	419	21	,	,	PUNCT
ejpam-4597	419	22	specially	specially	ADV
ejpam-4597	419	23	the	the	DET
ejpam-4597	419	24	fields	field	NOUN
ejpam-4597	419	25	that	that	PRON
ejpam-4597	419	26	concerned	concern	VERB
ejpam-4597	419	27	with	with	ADP
ejpam-4597	419	28	handling	handle	VERB
ejpam-4597	419	29	all	all	DET
ejpam-4597	419	30	cases	case	NOUN
ejpam-4597	419	31	that	that	PRON
ejpam-4597	419	32	contain	contain	VERB
ejpam-4597	419	33	uncertainties	uncertainty	NOUN
ejpam-4597	419	34	such	such	ADJ
ejpam-4597	419	35	as	as	ADP
ejpam-4597	419	36	medical	medical	ADJ
ejpam-4597	419	37	diagnosis	diagnosis	NOUN
ejpam-4597	419	38	,	,	PUNCT
ejpam-4597	419	39	economic	economic	ADJ
ejpam-4597	419	40	,	,	PUNCT
ejpam-4597	419	41	and	and	CCONJ
ejpam-4597	419	42	decision	decision	NOUN
ejpam-4597	419	43	making,	making,	ADJ
ejpam-4597	419	44	..	..	PUNCT
ejpam-4597	419	45	etc	etc	X
ejpam-4597	419	46	.	.	X
ejpam-4597	420	1	in	in	ADP
ejpam-4597	420	2	this	this	DET
ejpam-4597	420	3	work	work	NOUN
ejpam-4597	420	4	,	,	PUNCT
ejpam-4597	420	5	we	we	PRON
ejpam-4597	420	6	introduced	introduce	VERB
ejpam-4597	420	7	and	and	CCONJ
ejpam-4597	420	8	studied	study	VERB
ejpam-4597	420	9	the	the	DET
ejpam-4597	420	10	new	new	ADJ
ejpam-4597	420	11	classes	class	NOUN
ejpam-4597	420	12	of	of	ADP
ejpam-4597	420	13	spaces	space	NOUN
ejpam-4597	420	14	namely	namely	ADV
ejpam-4597	420	15	,	,	PUNCT
ejpam-4597	420	16	fsg	fsg	PROPN
ejpam-4597	420	17	-	-	PUNCT
ejpam-4597	420	18	regular	regular	ADJ
ejpam-4597	420	19	and	and	CCONJ
ejpam-4597	420	20	fsg	fsg	ADJ
ejpam-4597	420	21	-	-	ADJ
ejpam-4597	420	22	normal	normal	ADJ
ejpam-4597	420	23	space	space	NOUN
ejpam-4597	420	24	via	via	ADP
ejpam-4597	420	25	fuzzy	fuzzy	ADJ
ejpam-4597	420	26	soft	soft	ADJ
ejpam-4597	420	27	generalized	generalize	VERB
ejpam-4597	420	28	closed	closed	ADJ
ejpam-4597	420	29	sets	set	NOUN
ejpam-4597	420	30	.	.	PUNCT
ejpam-4597	421	1	we	we	PRON
ejpam-4597	421	2	investigated	investigate	VERB
ejpam-4597	421	3	some	some	DET
ejpam-4597	421	4	characterizations	characterization	NOUN
ejpam-4597	421	5	for	for	ADP
ejpam-4597	421	6	them	they	PRON
ejpam-4597	421	7	.	.	PUNCT
ejpam-4597	422	1	some	some	DET
ejpam-4597	422	2	related	relate	VERB
ejpam-4597	422	3	theorems	theorem	NOUN
ejpam-4597	422	4	and	and	CCONJ
ejpam-4597	422	5	relations	relation	NOUN
ejpam-4597	422	6	are	be	AUX
ejpam-4597	422	7	presented	present	VERB
ejpam-4597	422	8	with	with	ADP
ejpam-4597	422	9	some	some	DET
ejpam-4597	422	10	necessary	necessary	ADJ
ejpam-4597	422	11	examples	example	NOUN
ejpam-4597	422	12	.	.	PUNCT
ejpam-4597	423	1	in	in	ADP
ejpam-4597	423	2	addition	addition	NOUN
ejpam-4597	423	3	,	,	PUNCT
ejpam-4597	423	4	the	the	DET
ejpam-4597	423	5	hereditary	hereditary	ADJ
ejpam-4597	423	6	property	property	NOUN
ejpam-4597	423	7	and	and	CCONJ
ejpam-4597	423	8	some	some	DET
ejpam-4597	423	9	preservation	preservation	NOUN
ejpam-4597	423	10	theorems	theorem	NOUN
ejpam-4597	423	11	.	.	PUNCT
ejpam-4597	424	1	in	in	ADP
ejpam-4597	424	2	the	the	DET
ejpam-4597	424	3	future	future	ADJ
ejpam-4597	424	4	work	work	NOUN
ejpam-4597	424	5	we	we	PRON
ejpam-4597	424	6	will	will	AUX
ejpam-4597	424	7	try	try	VERB
ejpam-4597	424	8	to	to	PART
ejpam-4597	424	9	present	present	VERB
ejpam-4597	424	10	some	some	DET
ejpam-4597	424	11	applications	application	NOUN
ejpam-4597	424	12	for	for	ADP
ejpam-4597	424	13	fuzzy	fuzzy	ADJ
ejpam-4597	424	14	soft	soft	ADJ
ejpam-4597	424	15	generalized	generalized	ADJ
ejpam-4597	424	16	sets	set	NOUN
ejpam-4597	424	17	in	in	ADP
ejpam-4597	424	18	different	different	ADJ
ejpam-4597	424	19	aspects	aspect	NOUN
ejpam-4597	424	20	.	.	PUNCT
ejpam-4597	425	1	6	6	X
ejpam-4597	425	2	.	.	X
ejpam-4597	425	3	conflicts	conflict	NOUN
ejpam-4597	425	4	of	of	ADP
ejpam-4597	425	5	interest	interest	NOUN
ejpam-4597	425	6	the	the	DET
ejpam-4597	425	7	authors	author	NOUN
ejpam-4597	425	8	declare	declare	VERB
ejpam-4597	425	9	no	no	DET
ejpam-4597	425	10	conflict	conflict	NOUN
ejpam-4597	425	11	of	of	ADP
ejpam-4597	425	12	interest	interest	NOUN
ejpam-4597	425	13	.	.	PUNCT
ejpam-4597	426	1	references	reference	NOUN
ejpam-4597	426	2	[	[	X
ejpam-4597	426	3	1	1	NUM
ejpam-4597	426	4	]	]	PUNCT
ejpam-4597	426	5	m.	m.	NOUN
ejpam-4597	426	6	e.	e.	PROPN
ejpam-4597	426	7	abd	abd	PROPN
ejpam-4597	426	8	el	el	PROPN
ejpam-4597	426	9	-	-	PUNCT
ejpam-4597	426	10	monsef	monsef	ADJ
ejpam-4597	426	11	,	,	PUNCT
ejpam-4597	426	12	m.	m.	NOUN
ejpam-4597	426	13	a.	a.	PROPN
ejpam-4597	426	14	el	el	PROPN
ejpam-4597	426	15	-	-	PROPN
ejpam-4597	426	16	gayar	gayar	NOUN
ejpam-4597	426	17	,	,	PUNCT
ejpam-4597	426	18	and	and	CCONJ
ejpam-4597	426	19	r.	r.	PROPN
ejpam-4597	426	20	m.	m.	PROPN
ejpam-4597	426	21	aqeel	aqeel	PROPN
ejpam-4597	426	22	.	.	PUNCT
ejpam-4597	427	1	a	a	DET
ejpam-4597	427	2	comparison	comparison	NOUN
ejpam-4597	427	3	of	of	ADP
ejpam-4597	427	4	three	three	NUM
ejpam-4597	427	5	types	type	NOUN
ejpam-4597	427	6	of	of	ADP
ejpam-4597	427	7	rough	rough	ADJ
ejpam-4597	427	8	fuzzy	fuzzy	ADJ
ejpam-4597	427	9	sets	set	NOUN
ejpam-4597	427	10	based	base	VERB
ejpam-4597	427	11	on	on	ADP
ejpam-4597	427	12	two	two	NUM
ejpam-4597	427	13	universal	universal	ADJ
ejpam-4597	427	14	sets	set	NOUN
ejpam-4597	427	15	.	.	PUNCT
ejpam-4597	428	1	international	international	ADJ
ejpam-4597	428	2	journal	journal	NOUN
ejpam-4597	428	3	of	of	ADP
ejpam-4597	428	4	machine	machine	NOUN
ejpam-4597	428	5	learning	learning	NOUN
ejpam-4597	428	6	and	and	CCONJ
ejpam-4597	428	7	cybernetics	cybernetic	NOUN
ejpam-4597	428	8	,	,	PUNCT
ejpam-4597	428	9	8(1):343–353	8(1):343–353	NUM
ejpam-4597	428	10	,	,	PUNCT
ejpam-4597	428	11	2017	2017	NUM
ejpam-4597	428	12	.	.	PUNCT
ejpam-4597	429	1	references	reference	NOUN
ejpam-4597	429	2	190	190	NUM
ejpam-4597	430	1	[	[	X
ejpam-4597	430	2	2	2	X
ejpam-4597	430	3	]	]	PUNCT
ejpam-4597	430	4	me	i	PRON
ejpam-4597	430	5	abd	abd	PROPN
ejpam-4597	430	6	el	el	PROPN
ejpam-4597	430	7	-	-	PROPN
ejpam-4597	430	8	monsef	monsef	PROPN
ejpam-4597	430	9	,	,	PUNCT
ejpam-4597	430	10	ma	ma	PROPN
ejpam-4597	430	11	el	el	PROPN
ejpam-4597	430	12	-	-	PROPN
ejpam-4597	430	13	gayar	gayar	NOUN
ejpam-4597	430	14	,	,	PUNCT
ejpam-4597	430	15	and	and	CCONJ
ejpam-4597	430	16	rm	rm	PROPN
ejpam-4597	430	17	aqeel	aqeel	PROPN
ejpam-4597	430	18	.	.	PUNCT
ejpam-4597	431	1	on	on	ADP
ejpam-4597	431	2	relationships	relationship	NOUN
ejpam-4597	431	3	between	between	ADP
ejpam-4597	431	4	revised	revise	VERB
ejpam-4597	431	5	rough	rough	ADJ
ejpam-4597	431	6	fuzzy	fuzzy	ADJ
ejpam-4597	431	7	approximation	approximation	NOUN
ejpam-4597	431	8	operators	operator	NOUN
ejpam-4597	431	9	and	and	CCONJ
ejpam-4597	431	10	fuzzy	fuzzy	ADJ
ejpam-4597	431	11	topological	topological	ADJ
ejpam-4597	431	12	spaces	space	NOUN
ejpam-4597	431	13	.	.	PUNCT
ejpam-4597	432	1	international	international	ADJ
ejpam-4597	432	2	journal	journal	NOUN
ejpam-4597	432	3	of	of	ADP
ejpam-4597	432	4	granular	granular	ADJ
ejpam-4597	432	5	computing	computing	NOUN
ejpam-4597	432	6	,	,	PUNCT
ejpam-4597	432	7	rough	rough	ADJ
ejpam-4597	432	8	sets	set	NOUN
ejpam-4597	432	9	and	and	CCONJ
ejpam-4597	432	10	intelligent	intelligent	ADJ
ejpam-4597	432	11	systems	system	NOUN
ejpam-4597	432	12	,	,	PUNCT
ejpam-4597	432	13	3(4):257–271	3(4):257–271	NUM
ejpam-4597	432	14	,	,	PUNCT
ejpam-4597	432	15	2014	2014	NUM
ejpam-4597	432	16	.	.	PUNCT
ejpam-4597	433	1	[	[	X
ejpam-4597	433	2	3	3	X
ejpam-4597	433	3	]	]	PUNCT
ejpam-4597	433	4	s.	s.	PROPN
ejpam-4597	433	5	p.	p.	PROPN
ejpam-4597	433	6	arya	arya	PROPN
ejpam-4597	433	7	and	and	CCONJ
ejpam-4597	433	8	m.	m.	PROPN
ejpam-4597	433	9	p.	p.	PROPN
ejpam-4597	433	10	bhamini	bhamini	PROPN
ejpam-4597	433	11	.	.	PUNCT
ejpam-4597	434	1	a	a	DET
ejpam-4597	434	2	generalisation	generalisation	NOUN
ejpam-4597	434	3	of	of	ADP
ejpam-4597	434	4	normal	normal	ADJ
ejpam-4597	434	5	spaces	space	NOUN
ejpam-4597	434	6	.	.	PUNCT
ejpam-4597	435	1	matematički	matematički	PROPN
ejpam-4597	435	2	vesnik	vesnik	PROPN
ejpam-4597	435	3	,	,	PUNCT
ejpam-4597	435	4	35(81):1–10	35(81):1–10	NUM
ejpam-4597	435	5	,	,	PUNCT
ejpam-4597	435	6	1983	1983	NUM
ejpam-4597	435	7	.	.	PUNCT
ejpam-4597	436	1	[	[	X
ejpam-4597	436	2	4	4	X
ejpam-4597	436	3	]	]	PUNCT
ejpam-4597	436	4	s.	s.	PROPN
ejpam-4597	436	5	atmaca	atmaca	PROPN
ejpam-4597	436	6	and	and	CCONJ
ejpam-4597	436	7	i.	i.	PROPN
ejpam-4597	436	8	zorlutuna	zorlutuna	PROPN
ejpam-4597	436	9	.	.	PUNCT
ejpam-4597	437	1	on	on	ADP
ejpam-4597	437	2	fuzzy	fuzzy	ADJ
ejpam-4597	437	3	soft	soft	ADJ
ejpam-4597	437	4	topological	topological	ADJ
ejpam-4597	437	5	spaces	space	NOUN
ejpam-4597	437	6	.	.	PUNCT
ejpam-4597	438	1	ann	ann	PROPN
ejpam-4597	438	2	.	.	PUNCT
ejpam-4597	438	3	fuzzy	fuzzy	ADJ
ejpam-4597	438	4	math	math	PROPN
ejpam-4597	438	5	.	.	PUNCT
ejpam-4597	439	1	inform	inform	NOUN
ejpam-4597	439	2	,	,	PUNCT
ejpam-4597	439	3	5(2):377–386	5(2):377–386	NUM
ejpam-4597	439	4	,	,	PUNCT
ejpam-4597	439	5	2013	2013	NUM
ejpam-4597	439	6	.	.	PUNCT
ejpam-4597	440	1	[	[	X
ejpam-4597	440	2	5	5	X
ejpam-4597	440	3	]	]	PUNCT
ejpam-4597	440	4	g.	g.	PROPN
ejpam-4597	440	5	balasubramanian	balasubramanian	PROPN
ejpam-4597	440	6	and	and	CCONJ
ejpam-4597	440	7	p.	p.	PROPN
ejpam-4597	440	8	sundaram	sundaram	PROPN
ejpam-4597	440	9	.	.	PUNCT
ejpam-4597	441	1	on	on	ADP
ejpam-4597	441	2	some	some	DET
ejpam-4597	441	3	generalizations	generalization	NOUN
ejpam-4597	441	4	of	of	ADP
ejpam-4597	441	5	fuzzy	fuzzy	ADJ
ejpam-4597	441	6	continuous	continuous	ADJ
ejpam-4597	441	7	functions	function	NOUN
ejpam-4597	441	8	.	.	PUNCT
ejpam-4597	442	1	fuzzy	fuzzy	ADJ
ejpam-4597	442	2	sets	set	NOUN
ejpam-4597	442	3	and	and	CCONJ
ejpam-4597	442	4	systems	system	NOUN
ejpam-4597	442	5	,	,	PUNCT
ejpam-4597	442	6	86(1):93–100	86(1):93–100	NUM
ejpam-4597	442	7	,	,	PUNCT
ejpam-4597	442	8	1997	1997	NUM
ejpam-4597	442	9	.	.	PUNCT
ejpam-4597	443	1	[	[	X
ejpam-4597	443	2	6	6	NUM
ejpam-4597	443	3	]	]	X
ejpam-4597	443	4	c.	c.	PROPN
ejpam-4597	443	5	chang	chang	PROPN
ejpam-4597	443	6	.	.	PUNCT
ejpam-4597	444	1	fuzzy	fuzzy	ADJ
ejpam-4597	444	2	topological	topological	ADJ
ejpam-4597	444	3	spaces	space	NOUN
ejpam-4597	444	4	.	.	PUNCT
ejpam-4597	445	1	journal	journal	PROPN
ejpam-4597	445	2	of	of	ADP
ejpam-4597	445	3	mathematical	mathematical	ADJ
ejpam-4597	445	4	analysis	analysis	NOUN
ejpam-4597	445	5	and	and	CCONJ
ejpam-4597	445	6	applications	application	NOUN
ejpam-4597	445	7	,	,	PUNCT
ejpam-4597	445	8	24(1):182–190	24(1):182–190	NUM
ejpam-4597	445	9	,	,	PUNCT
ejpam-4597	445	10	1968	1968	NUM
ejpam-4597	445	11	.	.	PUNCT
ejpam-4597	446	1	[	[	X
ejpam-4597	446	2	7	7	NUM
ejpam-4597	446	3	]	]	PUNCT
ejpam-4597	446	4	á.	á.	PRON
ejpam-4597	446	5	császár	császár	PROPN
ejpam-4597	446	6	.	.	PUNCT
ejpam-4597	447	1	generalized	generalize	VERB
ejpam-4597	447	2	open	open	ADJ
ejpam-4597	447	3	sets	set	NOUN
ejpam-4597	447	4	.	.	PUNCT
ejpam-4597	448	1	acta	acta	PROPN
ejpam-4597	448	2	mathematica	mathematica	PROPN
ejpam-4597	448	3	hungarica	hungarica	PROPN
ejpam-4597	448	4	,	,	PUNCT
ejpam-4597	448	5	75(1	75(1	NOUN
ejpam-4597	448	6	-	-	PUNCT
ejpam-4597	448	7	2):65–87	2):65–87	NUM
ejpam-4597	448	8	,	,	PUNCT
ejpam-4597	448	9	1997	1997	NUM
ejpam-4597	448	10	.	.	PUNCT
ejpam-4597	449	1	[	[	X
ejpam-4597	449	2	8	8	NUM
ejpam-4597	449	3	]	]	PUNCT
ejpam-4597	449	4	á.	á.	PROPN
ejpam-4597	449	5	császár	császár	NOUN
ejpam-4597	449	6	.	.	PUNCT
ejpam-4597	450	1	normal	normal	ADJ
ejpam-4597	450	2	generalized	generalized	ADJ
ejpam-4597	450	3	topologies	topology	NOUN
ejpam-4597	450	4	.	.	PUNCT
ejpam-4597	451	1	acta	acta	PROPN
ejpam-4597	451	2	mathematica	mathematica	PROPN
ejpam-4597	451	3	hungarica	hungarica	PROPN
ejpam-4597	451	4	,	,	PUNCT
ejpam-4597	451	5	115(4):309	115(4):309	NUM
ejpam-4597	451	6	–	–	PUNCT
ejpam-4597	451	7	313	313	NUM
ejpam-4597	451	8	,	,	PUNCT
ejpam-4597	451	9	2007	2007	NUM
ejpam-4597	451	10	.	.	PUNCT
ejpam-4597	452	1	[	[	X
ejpam-4597	452	2	9	9	NUM
ejpam-4597	452	3	]	]	SYM
ejpam-4597	452	4	i̇.	i̇.	PROPN
ejpam-4597	452	5	demir	demir	PROPN
ejpam-4597	452	6	and	and	CCONJ
ejpam-4597	452	7	o.	o.	PROPN
ejpam-4597	452	8	özbakır	özbakır	PROPN
ejpam-4597	452	9	.	.	PUNCT
ejpam-4597	453	1	some	some	DET
ejpam-4597	453	2	properties	property	NOUN
ejpam-4597	453	3	of	of	ADP
ejpam-4597	453	4	fuzzy	fuzzy	ADJ
ejpam-4597	453	5	soft	soft	ADJ
ejpam-4597	453	6	proximity	proximity	NOUN
ejpam-4597	453	7	spaces	space	NOUN
ejpam-4597	453	8	.	.	PUNCT
ejpam-4597	454	1	the	the	DET
ejpam-4597	454	2	scientific	scientific	ADJ
ejpam-4597	454	3	world	world	NOUN
ejpam-4597	454	4	journal	journal	NOUN
ejpam-4597	454	5	,	,	PUNCT
ejpam-4597	454	6	2015	2015	NUM
ejpam-4597	454	7	,	,	PUNCT
ejpam-4597	454	8	2015	2015	NUM
ejpam-4597	454	9	.	.	PUNCT
ejpam-4597	455	1	[	[	X
ejpam-4597	455	2	10	10	NUM
ejpam-4597	455	3	]	]	PUNCT
ejpam-4597	455	4	m.	m.	NOUN
ejpam-4597	455	5	k.	k.	PROPN
ejpam-4597	456	1	el	el	PROPN
ejpam-4597	456	2	-	-	PROPN
ejpam-4597	456	3	bably	bably	PROPN
ejpam-4597	456	4	and	and	CCONJ
ejpam-4597	456	5	e.	e.	PROPN
ejpam-4597	456	6	a.	a.	PROPN
ejpam-4597	456	7	abo	abo	PROPN
ejpam-4597	456	8	-	-	PUNCT
ejpam-4597	456	9	tabl	tabl	NOUN
ejpam-4597	456	10	.	.	PUNCT
ejpam-4597	457	1	a	a	DET
ejpam-4597	457	2	topological	topological	ADJ
ejpam-4597	457	3	reduction	reduction	NOUN
ejpam-4597	457	4	for	for	ADP
ejpam-4597	457	5	predicting	predict	VERB
ejpam-4597	457	6	of	of	ADP
ejpam-4597	457	7	a	a	DET
ejpam-4597	457	8	lung	lung	NOUN
ejpam-4597	457	9	cancer	cancer	NOUN
ejpam-4597	457	10	disease	disease	NOUN
ejpam-4597	457	11	based	base	VERB
ejpam-4597	457	12	on	on	ADP
ejpam-4597	457	13	generalized	generalized	ADJ
ejpam-4597	457	14	rough	rough	ADJ
ejpam-4597	457	15	sets	set	NOUN
ejpam-4597	457	16	.	.	PUNCT
ejpam-4597	458	1	journal	journal	NOUN
ejpam-4597	458	2	of	of	ADP
ejpam-4597	458	3	intelligent	intelligent	ADJ
ejpam-4597	458	4	&	&	CCONJ
ejpam-4597	458	5	fuzzy	fuzzy	ADJ
ejpam-4597	458	6	systems	system	NOUN
ejpam-4597	458	7	,	,	PUNCT
ejpam-4597	458	8	42(2):3045–3060	42(2):3045–3060	NOUN
ejpam-4597	458	9	,	,	PUNCT
ejpam-4597	458	10	2021	2021	NUM
ejpam-4597	458	11	.	.	PUNCT
ejpam-4597	459	1	[	[	X
ejpam-4597	459	2	11	11	NUM
ejpam-4597	459	3	]	]	PUNCT
ejpam-4597	459	4	m.	m.	NOUN
ejpam-4597	459	5	a.	a.	PROPN
ejpam-4597	459	6	el	el	PROPN
ejpam-4597	459	7	-	-	PROPN
ejpam-4597	459	8	gayar	gayar	PROPN
ejpam-4597	459	9	and	and	CCONJ
ejpam-4597	459	10	a.	a.	NOUN
ejpam-4597	459	11	a.	a.	PROPN
ejpam-4597	459	12	el	el	PROPN
ejpam-4597	459	13	atik	atik	PROPN
ejpam-4597	459	14	.	.	PUNCT
ejpam-4597	460	1	topological	topological	ADJ
ejpam-4597	460	2	models	model	NOUN
ejpam-4597	460	3	of	of	ADP
ejpam-4597	460	4	rough	rough	ADJ
ejpam-4597	460	5	sets	set	NOUN
ejpam-4597	460	6	and	and	CCONJ
ejpam-4597	460	7	decision	decision	NOUN
ejpam-4597	460	8	making	making	NOUN
ejpam-4597	460	9	of	of	ADP
ejpam-4597	460	10	covid-19	covid-19	PROPN
ejpam-4597	460	11	.	.	PUNCT
ejpam-4597	460	12	complexity	complexity	NOUN
ejpam-4597	460	13	,	,	PUNCT
ejpam-4597	460	14	2022	2022	NUM
ejpam-4597	460	15	,	,	PUNCT
ejpam-4597	460	16	2022	2022	NUM
ejpam-4597	460	17	.	.	PUNCT
ejpam-4597	461	1	[	[	X
ejpam-4597	461	2	12	12	NUM
ejpam-4597	461	3	]	]	PUNCT
ejpam-4597	461	4	m.	m.	PROPN
ejpam-4597	461	5	e.	e.	PROPN
ejpam-4597	461	6	el	el	PROPN
ejpam-4597	461	7	-	-	PROPN
ejpam-4597	461	8	shafei	shafei	PROPN
ejpam-4597	461	9	.	.	PUNCT
ejpam-4597	462	1	some	some	DET
ejpam-4597	462	2	applications	application	NOUN
ejpam-4597	462	3	of	of	ADP
ejpam-4597	462	4	generalized	generalized	ADJ
ejpam-4597	462	5	closed	closed	ADJ
ejpam-4597	462	6	sets	set	NOUN
ejpam-4597	462	7	in	in	ADP
ejpam-4597	462	8	fuzzy	fuzzy	ADJ
ejpam-4597	462	9	topological	topological	ADJ
ejpam-4597	462	10	spaces	space	NOUN
ejpam-4597	462	11	.	.	PUNCT
ejpam-4597	463	1	kyungpook	kyungpook	PROPN
ejpam-4597	463	2	mathematical	mathematical	PROPN
ejpam-4597	463	3	journal	journal	NOUN
ejpam-4597	463	4	,	,	PUNCT
ejpam-4597	463	5	45(1):13–19	45(1):13–19	NUM
ejpam-4597	463	6	,	,	PUNCT
ejpam-4597	463	7	2005	2005	NUM
ejpam-4597	463	8	.	.	PUNCT
ejpam-4597	464	1	[	[	X
ejpam-4597	464	2	13	13	NUM
ejpam-4597	464	3	]	]	X
ejpam-4597	464	4	r.	r.	PROPN
ejpam-4597	464	5	engelking	engelke	VERB
ejpam-4597	464	6	.	.	PUNCT
ejpam-4597	465	1	general	general	ADJ
ejpam-4597	465	2	topology	topology	NOUN
ejpam-4597	465	3	,	,	PUNCT
ejpam-4597	465	4	pwn	pwn	NOUN
ejpam-4597	465	5	-	-	PUNCT
ejpam-4597	465	6	polish	polish	PROPN
ejpam-4597	465	7	sci	sci	PROPN
ejpam-4597	465	8	.	.	PROPN
ejpam-4597	465	9	1977	1977	NUM
ejpam-4597	465	10	.	.	PUNCT
ejpam-4597	466	1	[	[	X
ejpam-4597	466	2	14	14	NUM
ejpam-4597	466	3	]	]	X
ejpam-4597	466	4	el	el	PROPN
ejpam-4597	466	5	-	-	ADJ
ejpam-4597	466	6	bably	bably	PROPN
ejpam-4597	466	7	m.	m.	PROPN
ejpam-4597	466	8	k.	k.	PROPN
ejpam-4597	466	9	,	,	PUNCT
ejpam-4597	466	10	ali	ali	PROPN
ejpam-4597	466	11	m.	m.	PROPN
ejpam-4597	466	12	i.	i.	PROPN
ejpam-4597	466	13	,	,	PUNCT
ejpam-4597	466	14	and	and	CCONJ
ejpam-4597	466	15	e.	e.	PROPN
ejpam-4597	466	16	a.	a.	PROPN
ejpam-4597	466	17	abo	abo	PROPN
ejpam-4597	466	18	-	-	PUNCT
ejpam-4597	466	19	tabl	tabl	NOUN
ejpam-4597	466	20	.	.	PUNCT
ejpam-4597	467	1	new	new	ADJ
ejpam-4597	467	2	topological	topological	ADJ
ejpam-4597	467	3	approaches	approach	NOUN
ejpam-4597	467	4	to	to	ADP
ejpam-4597	467	5	generalized	generalize	VERB
ejpam-4597	467	6	soft	soft	ADJ
ejpam-4597	467	7	rough	rough	ADJ
ejpam-4597	467	8	approximations	approximation	NOUN
ejpam-4597	467	9	with	with	ADP
ejpam-4597	467	10	medical	medical	ADJ
ejpam-4597	467	11	applications	application	NOUN
ejpam-4597	467	12	.	.	PUNCT
ejpam-4597	468	1	journal	journal	NOUN
ejpam-4597	468	2	of	of	ADP
ejpam-4597	468	3	mathematics	mathematic	NOUN
ejpam-4597	468	4	,	,	PUNCT
ejpam-4597	468	5	2021	2021	NUM
ejpam-4597	468	6	,	,	PUNCT
ejpam-4597	468	7	2021	2021	NUM
ejpam-4597	468	8	.	.	PUNCT
ejpam-4597	469	1	[	[	X
ejpam-4597	469	2	15	15	NUM
ejpam-4597	469	3	]	]	X
ejpam-4597	469	4	l.	l.	PROPN
ejpam-4597	469	5	kalantan	kalantan	PROPN
ejpam-4597	469	6	.	.	PUNCT
ejpam-4597	470	1	results	result	VERB
ejpam-4597	470	2	about	about	ADP
ejpam-4597	470	3	-	-	PUNCT
ejpam-4597	470	4	normality	normality	NOUN
ejpam-4597	470	5	.	.	PUNCT
ejpam-4597	471	1	topology	topology	NOUN
ejpam-4597	471	2	appl	appl	PROPN
ejpam-4597	471	3	.	.	PROPN
ejpam-4597	471	4	,	,	PUNCT
ejpam-4597	471	5	125:47–62	125:47–62	NUM
ejpam-4597	471	6	,	,	PUNCT
ejpam-4597	471	7	2002	2002	NUM
ejpam-4597	471	8	.	.	PUNCT
ejpam-4597	472	1	[	[	X
ejpam-4597	472	2	16	16	NUM
ejpam-4597	472	3	]	]	PUNCT
ejpam-4597	472	4	a.	a.	NOUN
ejpam-4597	472	5	kharal	kharal	PROPN
ejpam-4597	472	6	and	and	CCONJ
ejpam-4597	472	7	b.	b.	PROPN
ejpam-4597	472	8	ahmad	ahmad	PROPN
ejpam-4597	472	9	.	.	PUNCT
ejpam-4597	473	1	mappings	mapping	NOUN
ejpam-4597	473	2	on	on	ADP
ejpam-4597	473	3	fuzzy	fuzzy	ADJ
ejpam-4597	473	4	soft	soft	ADJ
ejpam-4597	473	5	classes	class	NOUN
ejpam-4597	473	6	.	.	PUNCT
ejpam-4597	474	1	advances	advance	NOUN
ejpam-4597	474	2	in	in	ADP
ejpam-4597	474	3	fuzzy	fuzzy	ADJ
ejpam-4597	474	4	systems	system	NOUN
ejpam-4597	474	5	,	,	PUNCT
ejpam-4597	474	6	2009	2009	NUM
ejpam-4597	474	7	,	,	PUNCT
ejpam-4597	474	8	2009	2009	NUM
ejpam-4597	474	9	.	.	PUNCT
ejpam-4597	475	1	[	[	X
ejpam-4597	475	2	17	17	NUM
ejpam-4597	475	3	]	]	X
ejpam-4597	475	4	n.	n.	PROPN
ejpam-4597	475	5	levine	levine	PROPN
ejpam-4597	475	6	.	.	PUNCT
ejpam-4597	476	1	semi	semi	ADJ
ejpam-4597	476	2	-	-	ADJ
ejpam-4597	476	3	open	open	ADJ
ejpam-4597	476	4	sets	set	NOUN
ejpam-4597	476	5	and	and	CCONJ
ejpam-4597	476	6	semi	semi	ADJ
ejpam-4597	476	7	-	-	NOUN
ejpam-4597	476	8	continuity	continuity	NOUN
ejpam-4597	476	9	in	in	ADP
ejpam-4597	476	10	topological	topological	ADJ
ejpam-4597	476	11	spaces	space	NOUN
ejpam-4597	476	12	.	.	PUNCT
ejpam-4597	477	1	the	the	DET
ejpam-4597	477	2	american	american	PROPN
ejpam-4597	477	3	mathematical	mathematical	PROPN
ejpam-4597	477	4	monthly	monthly	ADV
ejpam-4597	477	5	,	,	PUNCT
ejpam-4597	477	6	70(1):36–41	70(1):36–41	NUM
ejpam-4597	477	7	,	,	PUNCT
ejpam-4597	477	8	1963	1963	NUM
ejpam-4597	477	9	.	.	PUNCT
ejpam-4597	477	10	references	reference	NOUN
ejpam-4597	477	11	191	191	NUM
ejpam-4597	477	12	[	[	X
ejpam-4597	477	13	18	18	NUM
ejpam-4597	477	14	]	]	X
ejpam-4597	477	15	n.	n.	PROPN
ejpam-4597	477	16	levine	levine	PROPN
ejpam-4597	477	17	.	.	PUNCT
ejpam-4597	478	1	generalized	generalize	VERB
ejpam-4597	478	2	closed	closed	ADJ
ejpam-4597	478	3	sets	set	NOUN
ejpam-4597	478	4	in	in	ADP
ejpam-4597	478	5	topology	topology	NOUN
ejpam-4597	478	6	.	.	PUNCT
ejpam-4597	479	1	rendiconti	rendiconti	VERB
ejpam-4597	479	2	del	del	PROPN
ejpam-4597	479	3	circolo	circolo	PROPN
ejpam-4597	479	4	matematico	matematico	NOUN
ejpam-4597	479	5	di	di	NOUN
ejpam-4597	479	6	palermo	palermo	NOUN
ejpam-4597	479	7	,	,	PUNCT
ejpam-4597	479	8	19(1):89–96	19(1):89–96	NUM
ejpam-4597	479	9	,	,	PUNCT
ejpam-4597	479	10	1970	1970	NUM
ejpam-4597	479	11	.	.	PUNCT
ejpam-4597	480	1	[	[	X
ejpam-4597	480	2	19	19	NUM
ejpam-4597	480	3	]	]	PUNCT
ejpam-4597	480	4	p.	p.	PROPN
ejpam-4597	480	5	k.	k.	PROPN
ejpam-4597	481	1	maji	maji	PROPN
ejpam-4597	481	2	,	,	PUNCT
ejpam-4597	481	3	r.	r.	PROPN
ejpam-4597	481	4	biswas	biswas	PROPN
ejpam-4597	481	5	,	,	PUNCT
ejpam-4597	481	6	and	and	CCONJ
ejpam-4597	481	7	a.	a.	PROPN
ejpam-4597	481	8	roy	roy	PROPN
ejpam-4597	481	9	.	.	PROPN
ejpam-4597	481	10	fuzzy	fuzzy	ADJ
ejpam-4597	481	11	soft	soft	ADJ
ejpam-4597	481	12	sets	set	NOUN
ejpam-4597	481	13	.	.	PUNCT
ejpam-4597	482	1	j.	j.	PROPN
ejpam-4597	482	2	fuzzy	fuzzy	PROPN
ejpam-4597	482	3	math	math	PROPN
ejpam-4597	482	4	.	.	PUNCT
ejpam-4597	482	5	,	,	PUNCT
ejpam-4597	482	6	9(3	9(3	NUM
ejpam-4597	482	7	)	)	PUNCT
ejpam-4597	482	8	,	,	PUNCT
ejpam-4597	482	9	2001	2001	NUM
ejpam-4597	482	10	.	.	PUNCT
ejpam-4597	483	1	[	[	X
ejpam-4597	483	2	20	20	NUM
ejpam-4597	483	3	]	]	PUNCT
ejpam-4597	483	4	p.	p.	NOUN
ejpam-4597	483	5	mukherjee	mukherjee	PROPN
ejpam-4597	483	6	,	,	PUNCT
ejpam-4597	483	7	r.	r.	PROPN
ejpam-4597	483	8	p.	p.	PROPN
ejpam-4597	483	9	chakraborty	chakraborty	PROPN
ejpam-4597	483	10	,	,	PUNCT
ejpam-4597	483	11	and	and	CCONJ
ejpam-4597	483	12	c.	c.	PROPN
ejpam-4597	483	13	park	park	PROPN
ejpam-4597	483	14	.	.	PUNCT
ejpam-4597	484	1	on	on	ADP
ejpam-4597	484	2	fuzzy	fuzzy	ADJ
ejpam-4597	484	3	soft	soft	ADJ
ejpam-4597	484	4	δ	δ	NOUN
ejpam-4597	484	5	-	-	ADJ
ejpam-4597	484	6	open	open	ADJ
ejpam-4597	484	7	sets	set	NOUN
ejpam-4597	484	8	and	and	CCONJ
ejpam-4597	484	9	fuzzy	fuzzy	ADJ
ejpam-4597	484	10	soft	soft	ADJ
ejpam-4597	484	11	δ	δ	NOUN
ejpam-4597	484	12	-	-	NOUN
ejpam-4597	484	13	continuity	continuity	NOUN
ejpam-4597	484	14	.	.	PUNCT
ejpam-4597	485	1	ann	ann	PROPN
ejpam-4597	485	2	.	.	PUNCT
ejpam-4597	485	3	fuzzy	fuzzy	ADJ
ejpam-4597	485	4	math	math	PROPN
ejpam-4597	485	5	.	.	PUNCT
ejpam-4597	486	1	inform	inform	NOUN
ejpam-4597	486	2	,	,	PUNCT
ejpam-4597	486	3	11(2):327–340	11(2):327–340	NOUN
ejpam-4597	486	4	,	,	PUNCT
ejpam-4597	486	5	2016	2016	NUM
ejpam-4597	486	6	.	.	PUNCT
ejpam-4597	487	1	[	[	X
ejpam-4597	487	2	21	21	NUM
ejpam-4597	487	3	]	]	X
ejpam-4597	487	4	b.	b.	PROPN
ejpam-4597	487	5	m.	m.	PROPN
ejpam-4597	487	6	munshi	munshi	PROPN
ejpam-4597	487	7	.	.	PUNCT
ejpam-4597	488	1	separation	separation	NOUN
ejpam-4597	488	2	axioms	axiom	VERB
ejpam-4597	488	3	.	.	PUNCT
ejpam-4597	489	1	acta	acta	PROPN
ejpam-4597	489	2	ciencia	ciencia	PROPN
ejpam-4597	489	3	indica	indica	PROPN
ejpam-4597	489	4	,	,	PUNCT
ejpam-4597	489	5	12(2):140–145	12(2):140–145	PROPN
ejpam-4597	489	6	,	,	PUNCT
ejpam-4597	489	7	1986	1986	NUM
ejpam-4597	489	8	.	.	PUNCT
ejpam-4597	490	1	[	[	X
ejpam-4597	490	2	22	22	NUM
ejpam-4597	490	3	]	]	PUNCT
ejpam-4597	490	4	m.	m.	NOUN
ejpam-4597	490	5	navaneethakrishnan	navaneethakrishnan	NOUN
ejpam-4597	490	6	and	and	CCONJ
ejpam-4597	490	7	j.	j.	PROPN
ejpam-4597	490	8	p.	p.	PROPN
ejpam-4597	490	9	joseph	joseph	PROPN
ejpam-4597	490	10	.	.	PUNCT
ejpam-4597	491	1	g	g	NOUN
ejpam-4597	491	2	-	-	PUNCT
ejpam-4597	491	3	closed	close	VERB
ejpam-4597	491	4	sets	set	NOUN
ejpam-4597	491	5	in	in	ADP
ejpam-4597	491	6	ideal	ideal	ADJ
ejpam-4597	491	7	topological	topological	ADJ
ejpam-4597	491	8	spaces	space	NOUN
ejpam-4597	491	9	.	.	PUNCT
ejpam-4597	492	1	acta	acta	PROPN
ejpam-4597	492	2	mathematica	mathematica	PROPN
ejpam-4597	492	3	hungarica	hungarica	PROPN
ejpam-4597	492	4	,	,	PUNCT
ejpam-4597	492	5	119(4):365–371	119(4):365–371	NUM
ejpam-4597	492	6	,	,	PUNCT
ejpam-4597	492	7	2008	2008	NUM
ejpam-4597	492	8	.	.	PUNCT
ejpam-4597	493	1	[	[	X
ejpam-4597	493	2	23	23	NUM
ejpam-4597	493	3	]	]	X
ejpam-4597	493	4	m.	m.	NOUN
ejpam-4597	493	5	navaneethakrishnan	navaneethakrishnan	PROPN
ejpam-4597	493	6	,	,	PUNCT
ejpam-4597	493	7	j.	j.	PROPN
ejpam-4597	493	8	p.	p.	PROPN
ejpam-4597	493	9	joseph	joseph	PROPN
ejpam-4597	493	10	,	,	PUNCT
ejpam-4597	493	11	and	and	CCONJ
ejpam-4597	493	12	d	d	NOUN
ejpam-4597	493	13	sivaraj	sivaraj	NOUN
ejpam-4597	493	14	.	.	PUNCT
ejpam-4597	494	1	i	i	PRON
ejpam-4597	494	2	g	g	NOUN
ejpam-4597	494	3	-	-	PUNCT
ejpam-4597	494	4	normal	normal	ADJ
ejpam-4597	495	1	and	and	CCONJ
ejpam-4597	495	2	i	i	PRON
ejpam-4597	495	3	g	g	NOUN
ejpam-4597	495	4	-	-	PUNCT
ejpam-4597	495	5	regular	regular	ADJ
ejpam-4597	495	6	spaces	space	NOUN
ejpam-4597	495	7	.	.	PUNCT
ejpam-4597	496	1	acta	acta	PROPN
ejpam-4597	496	2	mathematica	mathematica	PROPN
ejpam-4597	496	3	hungarica	hungarica	PROPN
ejpam-4597	496	4	,	,	PUNCT
ejpam-4597	496	5	125(4):327–340	125(4):327–340	NUM
ejpam-4597	496	6	,	,	PUNCT
ejpam-4597	496	7	2009	2009	NUM
ejpam-4597	496	8	.	.	PUNCT
ejpam-4597	497	1	[	[	X
ejpam-4597	497	2	24	24	NUM
ejpam-4597	497	3	]	]	PUNCT
ejpam-4597	497	4	t.	t.	PROPN
ejpam-4597	497	5	noiri	noiri	PROPN
ejpam-4597	497	6	and	and	CCONJ
ejpam-4597	497	7	v.	v.	ADP
ejpam-4597	497	8	popa	popa	NOUN
ejpam-4597	497	9	.	.	PUNCT
ejpam-4597	498	1	on	on	ADP
ejpam-4597	498	2	g	g	NOUN
ejpam-4597	498	3	-	-	PUNCT
ejpam-4597	498	4	regular	regular	ADJ
ejpam-4597	498	5	spaces	space	NOUN
ejpam-4597	498	6	and	and	CCONJ
ejpam-4597	498	7	some	some	DET
ejpam-4597	498	8	functions	function	NOUN
ejpam-4597	498	9	.	.	PUNCT
ejpam-4597	499	1	mem	mem	PROPN
ejpam-4597	499	2	.	.	PUNCT
ejpam-4597	499	3	fac	fac	PROPN
ejpam-4597	499	4	.	.	PUNCT
ejpam-4597	500	1	sci	sci	PROPN
ejpam-4597	500	2	.	.	PROPN
ejpam-4597	500	3	kochi	kochi	PROPN
ejpam-4597	500	4	univ	univ	PROPN
ejpam-4597	500	5	.	.	PUNCT
ejpam-4597	501	1	math	math	PROPN
ejpam-4597	501	2	,	,	PUNCT
ejpam-4597	501	3	20:67–74	20:67–74	NUM
ejpam-4597	501	4	,	,	PUNCT
ejpam-4597	501	5	1999	1999	NUM
ejpam-4597	501	6	.	.	PUNCT
ejpam-4597	502	1	[	[	X
ejpam-4597	502	2	25	25	NUM
ejpam-4597	502	3	]	]	X
ejpam-4597	502	4	r.	r.	PROPN
ejpam-4597	502	5	parimelazhagan	parimelazhagan	PROPN
ejpam-4597	502	6	and	and	CCONJ
ejpam-4597	502	7	v.	v.	ADP
ejpam-4597	502	8	subramonia	subramonia	PROPN
ejpam-4597	502	9	.	.	PUNCT
ejpam-4597	503	1	strongly	strongly	ADV
ejpam-4597	503	2	g	g	ADP
ejpam-4597	503	3	*	*	PUNCT
ejpam-4597	503	4	closed	close	VERB
ejpam-4597	503	5	sets	set	NOUN
ejpam-4597	503	6	in	in	ADP
ejpam-4597	503	7	topological	topological	ADJ
ejpam-4597	503	8	spaces	space	NOUN
ejpam-4597	503	9	.	.	PUNCT
ejpam-4597	504	1	int	int	NOUN
ejpam-4597	504	2	.	.	PUNCT
ejpam-4597	505	1	jou	jou	INTJ
ejpam-4597	505	2	.	.	PROPN
ejpam-4597	505	3	of	of	ADP
ejpam-4597	505	4	math	math	NOUN
ejpam-4597	505	5	.	.	PUNCT
ejpam-4597	506	1	analy	analy	PROPN
ejpam-4597	506	2	,	,	PUNCT
ejpam-4597	506	3	6(30):1481–1489	6(30):1481–1489	NOUN
ejpam-4597	506	4	,	,	PUNCT
ejpam-4597	506	5	2012	2012	NUM
ejpam-4597	506	6	.	.	PUNCT
ejpam-4597	507	1	[	[	X
ejpam-4597	507	2	26	26	NUM
ejpam-4597	507	3	]	]	PUNCT
ejpam-4597	507	4	j.	j.	PROPN
ejpam-4597	507	5	k.	k.	PROPN
ejpam-4597	507	6	park	park	PROPN
ejpam-4597	507	7	and	and	CCONJ
ejpam-4597	507	8	j.	j.	PROPN
ejpam-4597	507	9	h.	h.	PROPN
ejpam-4597	507	10	park	park	PROPN
ejpam-4597	507	11	.	.	PUNCT
ejpam-4597	508	1	mildly	mildly	ADV
ejpam-4597	508	2	generalized	generalize	VERB
ejpam-4597	508	3	closed	closed	ADJ
ejpam-4597	508	4	sets	set	NOUN
ejpam-4597	508	5	,	,	PUNCT
ejpam-4597	508	6	almost	almost	ADV
ejpam-4597	508	7	normal	normal	ADJ
ejpam-4597	508	8	and	and	CCONJ
ejpam-4597	508	9	mildly	mildly	ADV
ejpam-4597	508	10	normal	normal	ADJ
ejpam-4597	508	11	spaces	space	NOUN
ejpam-4597	508	12	.	.	PUNCT
ejpam-4597	509	1	chaos	chaos	NOUN
ejpam-4597	509	2	,	,	PUNCT
ejpam-4597	509	3	solitons	soliton	NOUN
ejpam-4597	509	4	&	&	CCONJ
ejpam-4597	509	5	fractals	fractal	NOUN
ejpam-4597	509	6	,	,	PUNCT
ejpam-4597	509	7	20(5):1103–1111	20(5):1103–1111	NUM
ejpam-4597	509	8	,	,	PUNCT
ejpam-4597	509	9	2004	2004	NUM
ejpam-4597	509	10	.	.	PUNCT
ejpam-4597	510	1	[	[	X
ejpam-4597	510	2	27	27	NUM
ejpam-4597	510	3	]	]	PUNCT
ejpam-4597	510	4	t.	t.	PROPN
ejpam-4597	510	5	rajendrakumar	rajendrakumar	PROPN
ejpam-4597	510	6	and	and	CCONJ
ejpam-4597	510	7	g.	g.	PROPN
ejpam-4597	510	8	anandajothi	anandajothi	PROPN
ejpam-4597	510	9	.	.	PUNCT
ejpam-4597	511	1	on	on	ADP
ejpam-4597	511	2	fuzzy	fuzzy	ADJ
ejpam-4597	511	3	strongly	strongly	ADV
ejpam-4597	511	4	g	g	NOUN
ejpam-4597	511	5	-	-	PUNCT
ejpam-4597	511	6	closed	close	VERB
ejpam-4597	511	7	sets	set	NOUN
ejpam-4597	511	8	in	in	ADP
ejpam-4597	511	9	fuzzy	fuzzy	ADJ
ejpam-4597	511	10	topological	topological	ADJ
ejpam-4597	511	11	spaces	space	NOUN
ejpam-4597	511	12	.	.	PUNCT
ejpam-4597	512	1	intern	intern	PROPN
ejpam-4597	512	2	.	.	PUNCT
ejpam-4597	513	1	j.	j.	PROPN
ejpam-4597	513	2	fuzzy	fuzzy	PROPN
ejpam-4597	513	3	mathematical	mathematical	PROPN
ejpam-4597	513	4	archive	archive	NOUN
ejpam-4597	513	5	,	,	PUNCT
ejpam-4597	513	6	3:68–75	3:68–75	NUM
ejpam-4597	513	7	,	,	PUNCT
ejpam-4597	513	8	2013	2013	NUM
ejpam-4597	513	9	.	.	PUNCT
ejpam-4597	514	1	[	[	X
ejpam-4597	514	2	28	28	NUM
ejpam-4597	514	3	]	]	X
ejpam-4597	514	4	s.	s.	PROPN
ejpam-4597	514	5	saleh	saleh	PROPN
ejpam-4597	514	6	,	,	PUNCT
ejpam-4597	514	7	a.	a.	PROPN
ejpam-4597	514	8	m.	m.	PROPN
ejpam-4597	514	9	abd	abd	PROPN
ejpam-4597	514	10	el	el	PROPN
ejpam-4597	514	11	-	-	PROPN
ejpam-4597	514	12	latif	latif	PROPN
ejpam-4597	514	13	,	,	PUNCT
ejpam-4597	514	14	and	and	CCONJ
ejpam-4597	514	15	al	al	PROPN
ejpam-4597	514	16	-	-	PUNCT
ejpam-4597	514	17	salemi	salemi	PROPN
ejpam-4597	514	18	amany	amany	NOUN
ejpam-4597	514	19	.	.	PUNCT
ejpam-4597	515	1	on	on	ADP
ejpam-4597	515	2	separation	separation	NOUN
ejpam-4597	515	3	axioms	axiom	NOUN
ejpam-4597	515	4	in	in	ADP
ejpam-4597	515	5	fuzzy	fuzzy	ADJ
ejpam-4597	515	6	soft	soft	ADJ
ejpam-4597	515	7	topological	topological	ADJ
ejpam-4597	515	8	spaces	space	NOUN
ejpam-4597	515	9	.	.	PUNCT
ejpam-4597	516	1	south	south	ADJ
ejpam-4597	516	2	asian	asian	PROPN
ejpam-4597	516	3	j.	j.	PROPN
ejpam-4597	516	4	math	math	PROPN
ejpam-4597	516	5	.	.	PUNCT
ejpam-4597	516	6	,	,	PUNCT
ejpam-4597	516	7	8(2):92–102	8(2):92–102	NUM
ejpam-4597	516	8	,	,	PUNCT
ejpam-4597	516	9	2018	2018	NUM
ejpam-4597	516	10	.	.	PUNCT
ejpam-4597	517	1	[	[	X
ejpam-4597	517	2	29	29	NUM
ejpam-4597	517	3	]	]	PUNCT
ejpam-4597	517	4	s.	s.	PROPN
ejpam-4597	517	5	saleh	saleh	PROPN
ejpam-4597	517	6	and	and	CCONJ
ejpam-4597	517	7	amani	amani	PROPN
ejpam-4597	517	8	al	al	PROPN
ejpam-4597	517	9	-	-	PUNCT
ejpam-4597	517	10	salemi	salemi	PROPN
ejpam-4597	517	11	.	.	PUNCT
ejpam-4597	518	1	the	the	DET
ejpam-4597	518	2	r	r	NOUN
ejpam-4597	518	3	0	0	NUM
ejpam-4597	518	4	and	and	CCONJ
ejpam-4597	518	5	r	r	NOUN
ejpam-4597	518	6	1	1	NUM
ejpam-4597	518	7	properties	property	NOUN
ejpam-4597	518	8	in	in	ADP
ejpam-4597	518	9	fuzzy	fuzzy	ADJ
ejpam-4597	518	10	soft	soft	ADJ
ejpam-4597	518	11	topological	topological	ADJ
ejpam-4597	518	12	spaces	space	NOUN
ejpam-4597	518	13	.	.	PUNCT
ejpam-4597	519	1	journal	journal	NOUN
ejpam-4597	519	2	of	of	ADP
ejpam-4597	519	3	new	new	ADJ
ejpam-4597	519	4	theory	theory	NOUN
ejpam-4597	519	5	,	,	PUNCT
ejpam-4597	519	6	(	(	PUNCT
ejpam-4597	519	7	24):50–58	24):50–58	PROPN
ejpam-4597	519	8	,	,	PUNCT
ejpam-4597	519	9	2018	2018	NUM
ejpam-4597	519	10	.	.	PUNCT
ejpam-4597	520	1	[	[	X
ejpam-4597	520	2	30	30	NUM
ejpam-4597	520	3	]	]	X
ejpam-4597	520	4	b.	b.	PROPN
ejpam-4597	520	5	tanay	tanay	PROPN
ejpam-4597	520	6	and	and	CCONJ
ejpam-4597	520	7	m.	m.	PROPN
ejpam-4597	520	8	b.	b.	PROPN
ejpam-4597	520	9	kandemir	kandemir	PROPN
ejpam-4597	520	10	.	.	PUNCT
ejpam-4597	521	1	topological	topological	ADJ
ejpam-4597	521	2	structure	structure	NOUN
ejpam-4597	521	3	of	of	ADP
ejpam-4597	521	4	fuzzy	fuzzy	ADJ
ejpam-4597	521	5	soft	soft	ADJ
ejpam-4597	521	6	sets	set	NOUN
ejpam-4597	521	7	.	.	PUNCT
ejpam-4597	522	1	computers	computer	NOUN
ejpam-4597	522	2	&	&	CCONJ
ejpam-4597	522	3	mathematics	mathematics	PROPN
ejpam-4597	522	4	with	with	ADP
ejpam-4597	522	5	applications	application	NOUN
ejpam-4597	522	6	,	,	PUNCT
ejpam-4597	522	7	61(10):2952–2957	61(10):2952–2957	NOUN
ejpam-4597	522	8	,	,	PUNCT
ejpam-4597	522	9	2011	2011	NUM
ejpam-4597	522	10	.	.	PUNCT
ejpam-4597	523	1	[	[	X
ejpam-4597	523	2	31	31	NUM
ejpam-4597	523	3	]	]	PUNCT
ejpam-4597	523	4	z.	z.	PROPN
ejpam-4597	523	5	tarrannum	tarrannum	PROPN
ejpam-4597	523	6	and	and	CCONJ
ejpam-4597	523	7	a.	a.	NOUN
ejpam-4597	523	8	p.	p.	PROPN
ejpam-4597	523	9	narappanavar	narappanavar	NOUN
ejpam-4597	523	10	.	.	PUNCT
ejpam-4597	524	1	fuzzy	fuzzy	ADJ
ejpam-4597	524	2	soft	soft	ADJ
ejpam-4597	524	3	generalized	generalize	VERB
ejpam-4597	524	4	closed	closed	ADJ
ejpam-4597	524	5	sets	set	NOUN
ejpam-4597	524	6	in	in	ADP
ejpam-4597	524	7	fuzzy	fuzzy	ADJ
ejpam-4597	524	8	soft	soft	ADJ
ejpam-4597	524	9	topological	topological	ADJ
ejpam-4597	524	10	spaces	space	NOUN
ejpam-4597	524	11	.	.	PUNCT
ejpam-4597	525	1	international	international	ADJ
ejpam-4597	525	2	journal	journal	NOUN
ejpam-4597	525	3	of	of	ADP
ejpam-4597	525	4	applied	apply	VERB
ejpam-4597	525	5	engineering	engineering	NOUN
ejpam-4597	525	6	research	research	NOUN
ejpam-4597	525	7	,	,	PUNCT
ejpam-4597	525	8	14(3):633	14(3):633	NUM
ejpam-4597	525	9	–	–	PUNCT
ejpam-4597	525	10	636	636	NUM
ejpam-4597	525	11	,	,	PUNCT
ejpam-4597	525	12	2019	2019	NUM
ejpam-4597	525	13	.	.	PUNCT
ejpam-4597	526	1	[	[	X
ejpam-4597	526	2	32	32	NUM
ejpam-4597	526	3	]	]	X
ejpam-4597	526	4	m.k.r.s	m.k.r.s	PROPN
ejpam-4597	526	5	.	.	PUNCT
ejpam-4597	526	6	veera	veera	PROPN
ejpam-4597	526	7	kumar	kumar	PROPN
ejpam-4597	526	8	.	.	PROPN
ejpam-4597	526	9	between	between	ADP
ejpam-4597	526	10	closed	close	VERB
ejpam-4597	526	11	sets	set	NOUN
ejpam-4597	526	12	and	and	CCONJ
ejpam-4597	526	13	g	g	NOUN
ejpam-4597	526	14	-	-	PUNCT
ejpam-4597	526	15	closed	close	VERB
ejpam-4597	526	16	sets	set	NOUN
ejpam-4597	526	17	.	.	PUNCT
ejpam-4597	527	1	mem	mem	PROPN
ejpam-4597	527	2	.	.	PUNCT
ejpam-4597	527	3	fac	fac	PROPN
ejpam-4597	527	4	.	.	PUNCT
ejpam-4597	527	5	sci	sci	PROPN
ejpam-4597	527	6	.	.	PROPN
ejpam-4597	527	7	kochi	kochi	PROPN
ejpam-4597	527	8	univ	univ	PROPN
ejpam-4597	527	9	.	.	PUNCT
ejpam-4597	527	10	ser	ser	PROPN
ejpam-4597	527	11	.	.	PUNCT
ejpam-4597	528	1	a	a	DET
ejpam-4597	528	2	math	math	NOUN
ejpam-4597	528	3	.	.	PUNCT
ejpam-4597	528	4	,	,	PUNCT
ejpam-4597	528	5	21:1–19	21:1–19	NUM
ejpam-4597	528	6	,	,	PUNCT
ejpam-4597	528	7	2000	2000	NUM
ejpam-4597	528	8	.	.	PUNCT
ejpam-4597	529	1	[	[	X
ejpam-4597	529	2	33	33	NUM
ejpam-4597	529	3	]	]	PUNCT
ejpam-4597	529	4	l.	l.	PROPN
ejpam-4597	529	5	a.	a.	PROPN
ejpam-4597	529	6	zadeh	zadeh	PROPN
ejpam-4597	529	7	.	.	PUNCT
ejpam-4597	530	1	information	information	NOUN
ejpam-4597	530	2	and	and	CCONJ
ejpam-4597	530	3	control	control	NOUN
ejpam-4597	530	4	.	.	PUNCT
ejpam-4597	531	1	fuzzy	fuzzy	ADJ
ejpam-4597	531	2	sets	set	NOUN
ejpam-4597	531	3	,	,	PUNCT
ejpam-4597	531	4	8(3):338–353	8(3):338–353	NUM
ejpam-4597	531	5	,	,	PUNCT
ejpam-4597	531	6	1965	1965	NUM
ejpam-4597	531	7	.	.	PUNCT