id	sid	tid	token	lemma	pos
ejpam-3131	1	1	european	european	PROPN
ejpam-3131	1	2	journal	journal	PROPN
ejpam-3131	1	3	of	of	ADP
ejpam-3131	1	4	pure	pure	ADJ
ejpam-3131	1	5	and	and	CCONJ
ejpam-3131	1	6	applied	apply	VERB
ejpam-3131	1	7	mathematics	mathematic	NOUN
ejpam-3131	1	8	vol	vol	NOUN
ejpam-3131	1	9	.	.	PUNCT
ejpam-3131	2	1	11	11	NUM
ejpam-3131	2	2	,	,	PUNCT
ejpam-3131	2	3	no	no	INTJ
ejpam-3131	2	4	.	.	NOUN
ejpam-3131	2	5	1	1	NUM
ejpam-3131	2	6	,	,	PUNCT
ejpam-3131	2	7	2018	2018	NUM
ejpam-3131	2	8	,	,	PUNCT
ejpam-3131	2	9	299	299	NUM
ejpam-3131	2	10	-	-	SYM
ejpam-3131	2	11	314	314	NUM
ejpam-3131	2	12	issn	issn	PROPN
ejpam-3131	2	13	1307	1307	NUM
ejpam-3131	2	14	-	-	SYM
ejpam-3131	2	15	5543	5543	NUM
ejpam-3131	2	16	–	–	PUNCT
ejpam-3131	3	1	www.ejpam.com	www.ejpam.com	X
ejpam-3131	3	2	published	publish	VERB
ejpam-3131	3	3	by	by	ADP
ejpam-3131	3	4	new	new	PROPN
ejpam-3131	3	5	york	york	PROPN
ejpam-3131	3	6	business	business	PROPN
ejpam-3131	3	7	global	global	PROPN
ejpam-3131	3	8	between	between	ADP
ejpam-3131	3	9	closed	closed	ADJ
ejpam-3131	3	10	and	and	CCONJ
ejpam-3131	3	11	ig	ig	NOUN
ejpam-3131	3	12	-	-	ADJ
ejpam-3131	3	13	closed	close	VERB
ejpam-3131	3	14	sets	set	NOUN
ejpam-3131	3	15	néstor	néstor	NOUN
ejpam-3131	3	16	raúl	raúl	PROPN
ejpam-3131	3	17	pachón	pachón	PROPN
ejpam-3131	3	18	rubiano	rubiano	PROPN
ejpam-3131	3	19	departamento	departamento	PROPN
ejpam-3131	3	20	de	de	PROPN
ejpam-3131	3	21	matemáticas	matemáticas	PROPN
ejpam-3131	3	22	,	,	PUNCT
ejpam-3131	3	23	escuela	escuela	PROPN
ejpam-3131	3	24	colombiana	colombiana	PROPN
ejpam-3131	3	25	de	de	PROPN
ejpam-3131	3	26	ingeniería	ingeniería	PROPN
ejpam-3131	3	27	,	,	PUNCT
ejpam-3131	3	28	bogotá	bogotá	PROPN
ejpam-3131	3	29	,	,	PUNCT
ejpam-3131	3	30	colombia	colombia	PROPN
ejpam-3131	3	31	.	.	PUNCT
ejpam-3131	3	32	departamento	departamento	PROPN
ejpam-3131	3	33	de	de	PROPN
ejpam-3131	3	34	matemáticas	matemáticas	PROPN
ejpam-3131	3	35	,	,	PUNCT
ejpam-3131	3	36	universidad	universidad	PROPN
ejpam-3131	3	37	nacional	nacional	NOUN
ejpam-3131	3	38	,	,	PUNCT
ejpam-3131	3	39	bogotá	bogotá	NOUN
ejpam-3131	3	40	,	,	PUNCT
ejpam-3131	3	41	colombia	colombia	PROPN
ejpam-3131	3	42	.	.	PUNCT
ejpam-3131	4	1	abstract	abstract	ADJ
ejpam-3131	4	2	.	.	PUNCT
ejpam-3131	5	1	the	the	DET
ejpam-3131	5	2	concept	concept	NOUN
ejpam-3131	5	3	of	of	ADP
ejpam-3131	5	4	closed	closed	ADJ
ejpam-3131	5	5	sets	set	NOUN
ejpam-3131	5	6	is	be	AUX
ejpam-3131	5	7	a	a	DET
ejpam-3131	5	8	central	central	ADJ
ejpam-3131	5	9	object	object	NOUN
ejpam-3131	5	10	in	in	ADP
ejpam-3131	5	11	general	general	ADJ
ejpam-3131	5	12	topology	topology	NOUN
ejpam-3131	5	13	.	.	PUNCT
ejpam-3131	6	1	in	in	ADP
ejpam-3131	6	2	order	order	NOUN
ejpam-3131	6	3	to	to	PART
ejpam-3131	6	4	extend	extend	VERB
ejpam-3131	6	5	many	many	ADJ
ejpam-3131	6	6	of	of	ADP
ejpam-3131	6	7	important	important	ADJ
ejpam-3131	6	8	properties	property	NOUN
ejpam-3131	6	9	of	of	ADP
ejpam-3131	6	10	closed	closed	ADJ
ejpam-3131	6	11	sets	set	NOUN
ejpam-3131	6	12	to	to	ADP
ejpam-3131	6	13	a	a	DET
ejpam-3131	6	14	larger	large	ADJ
ejpam-3131	6	15	families	family	NOUN
ejpam-3131	6	16	,	,	PUNCT
ejpam-3131	6	17	norman	norman	PROPN
ejpam-3131	6	18	levine	levine	PROPN
ejpam-3131	6	19	initiated	initiate	VERB
ejpam-3131	6	20	the	the	DET
ejpam-3131	6	21	study	study	NOUN
ejpam-3131	6	22	of	of	ADP
ejpam-3131	6	23	generalized	generalized	ADJ
ejpam-3131	6	24	closed	closed	ADJ
ejpam-3131	6	25	sets	set	NOUN
ejpam-3131	6	26	.	.	PUNCT
ejpam-3131	7	1	in	in	ADP
ejpam-3131	7	2	this	this	DET
ejpam-3131	7	3	paper	paper	NOUN
ejpam-3131	7	4	we	we	PRON
ejpam-3131	7	5	introduce	introduce	VERB
ejpam-3131	7	6	,	,	PUNCT
ejpam-3131	7	7	via	via	ADP
ejpam-3131	7	8	ideals	ideal	NOUN
ejpam-3131	7	9	,	,	PUNCT
ejpam-3131	7	10	new	new	ADJ
ejpam-3131	7	11	generalizations	generalization	NOUN
ejpam-3131	7	12	of	of	ADP
ejpam-3131	7	13	closed	closed	ADJ
ejpam-3131	7	14	subsets	subset	NOUN
ejpam-3131	7	15	,	,	PUNCT
ejpam-3131	7	16	which	which	PRON
ejpam-3131	7	17	are	be	AUX
ejpam-3131	7	18	strong	strong	ADJ
ejpam-3131	7	19	forms	form	NOUN
ejpam-3131	7	20	of	of	ADP
ejpam-3131	7	21	the	the	DET
ejpam-3131	7	22	ig	ig	PROPN
ejpam-3131	7	23	-	-	PUNCT
ejpam-3131	7	24	closed	close	VERB
ejpam-3131	7	25	sets	set	NOUN
ejpam-3131	7	26	,	,	PUNCT
ejpam-3131	7	27	called	call	VERB
ejpam-3131	7	28	ρig	ρig	NOUN
ejpam-3131	7	29	-	-	PUNCT
ejpam-3131	7	30	closed	close	VERB
ejpam-3131	7	31	sets	set	NOUN
ejpam-3131	7	32	and	and	CCONJ
ejpam-3131	7	33	closed	close	VERB
ejpam-3131	7	34	-	-	PUNCT
ejpam-3131	7	35	i	i	PRON
ejpam-3131	7	36	sets	set	VERB
ejpam-3131	7	37	.	.	PUNCT
ejpam-3131	8	1	we	we	PRON
ejpam-3131	8	2	present	present	VERB
ejpam-3131	8	3	some	some	DET
ejpam-3131	8	4	properties	property	NOUN
ejpam-3131	8	5	and	and	CCONJ
ejpam-3131	8	6	applications	application	NOUN
ejpam-3131	8	7	of	of	ADP
ejpam-3131	8	8	these	these	DET
ejpam-3131	8	9	new	new	ADJ
ejpam-3131	8	10	sets	set	NOUN
ejpam-3131	8	11	and	and	CCONJ
ejpam-3131	8	12	compare	compare	VERB
ejpam-3131	8	13	the	the	DET
ejpam-3131	8	14	ρig	ρig	NOUN
ejpam-3131	8	15	-	-	PUNCT
ejpam-3131	8	16	closed	close	VERB
ejpam-3131	8	17	sets	set	NOUN
ejpam-3131	8	18	and	and	CCONJ
ejpam-3131	8	19	the	the	DET
ejpam-3131	8	20	closed	closed	ADJ
ejpam-3131	8	21	-	-	PUNCT
ejpam-3131	8	22	i	i	PRON
ejpam-3131	8	23	sets	set	VERB
ejpam-3131	8	24	with	with	ADP
ejpam-3131	8	25	the	the	DET
ejpam-3131	8	26	g	g	NOUN
ejpam-3131	8	27	-	-	PUNCT
ejpam-3131	8	28	closed	close	VERB
ejpam-3131	8	29	sets	set	NOUN
ejpam-3131	8	30	introduced	introduce	VERB
ejpam-3131	8	31	by	by	ADP
ejpam-3131	8	32	levine	levine	PROPN
ejpam-3131	8	33	.	.	PUNCT
ejpam-3131	9	1	we	we	PRON
ejpam-3131	9	2	show	show	VERB
ejpam-3131	9	3	that	that	SCONJ
ejpam-3131	9	4	i	i	PRON
ejpam-3131	9	5	-	-	PUNCT
ejpam-3131	9	6	closed	closed	ADJ
ejpam-3131	9	7	and	and	CCONJ
ejpam-3131	9	8	closed	closed	ADJ
ejpam-3131	9	9	-	-	PUNCT
ejpam-3131	9	10	i	i	PRON
ejpam-3131	9	11	are	be	AUX
ejpam-3131	9	12	independent	independent	ADJ
ejpam-3131	9	13	concepts	concept	NOUN
ejpam-3131	9	14	,	,	PUNCT
ejpam-3131	9	15	as	as	ADV
ejpam-3131	9	16	well	well	ADV
ejpam-3131	9	17	as	as	ADP
ejpam-3131	9	18	i∗-closed	i∗-close	VERB
ejpam-3131	9	19	sets	set	NOUN
ejpam-3131	9	20	and	and	CCONJ
ejpam-3131	9	21	closed	close	VERB
ejpam-3131	9	22	-	-	PUNCT
ejpam-3131	9	23	i	i	PRON
ejpam-3131	9	24	concepts	concept	NOUN
ejpam-3131	9	25	.	.	PUNCT
ejpam-3131	10	1	2010	2010	NUM
ejpam-3131	10	2	mathematics	mathematic	NOUN
ejpam-3131	10	3	subject	subject	NOUN
ejpam-3131	10	4	classifications	classification	NOUN
ejpam-3131	10	5	:	:	PUNCT
ejpam-3131	10	6	54d30	54d30	NUM
ejpam-3131	10	7	,	,	PUNCT
ejpam-3131	10	8	54c10	54c10	NUM
ejpam-3131	10	9	key	key	ADJ
ejpam-3131	10	10	words	word	NOUN
ejpam-3131	10	11	and	and	CCONJ
ejpam-3131	10	12	phrases	phrase	NOUN
ejpam-3131	10	13	:	:	PUNCT
ejpam-3131	10	14	g	g	NOUN
ejpam-3131	10	15	-	-	PUNCT
ejpam-3131	10	16	closed	closed	ADJ
ejpam-3131	10	17	,	,	PUNCT
ejpam-3131	10	18	ig	ig	NOUN
ejpam-3131	10	19	-	-	PUNCT
ejpam-3131	10	20	closed	closed	ADJ
ejpam-3131	10	21	,	,	PUNCT
ejpam-3131	10	22	i	i	PRON
ejpam-3131	10	23	-	-	PUNCT
ejpam-3131	10	24	compact	compact	ADJ
ejpam-3131	10	25	,	,	PUNCT
ejpam-3131	10	26	i	i	PRON
ejpam-3131	10	27	-	-	PUNCT
ejpam-3131	10	28	normal	normal	ADJ
ejpam-3131	10	29	,	,	PUNCT
ejpam-3131	10	30	i	i	PROPN
ejpam-3131	10	31	-	-	PUNCT
ejpam-3131	10	32	qhc	qhc	PROPN
ejpam-3131	10	33	,	,	PUNCT
ejpam-3131	10	34	ρc(i)-compact	ρc(i)-compact	PROPN
ejpam-3131	10	35	.	.	PUNCT
ejpam-3131	11	1	1	1	X
ejpam-3131	11	2	.	.	X
ejpam-3131	11	3	introduction	introduction	NOUN
ejpam-3131	11	4	and	and	CCONJ
ejpam-3131	11	5	preliminaries	preliminary	NOUN
ejpam-3131	11	6	the	the	DET
ejpam-3131	11	7	g	g	NOUN
ejpam-3131	11	8	-	-	PUNCT
ejpam-3131	11	9	closed	close	VERB
ejpam-3131	11	10	sets	set	NOUN
ejpam-3131	11	11	,	,	PUNCT
ejpam-3131	11	12	which	which	PRON
ejpam-3131	11	13	is	be	AUX
ejpam-3131	11	14	a	a	DET
ejpam-3131	11	15	extension	extension	NOUN
ejpam-3131	11	16	of	of	ADP
ejpam-3131	11	17	closed	closed	ADJ
ejpam-3131	11	18	sets	set	NOUN
ejpam-3131	11	19	,	,	PUNCT
ejpam-3131	11	20	was	be	AUX
ejpam-3131	11	21	introduced	introduce	VERB
ejpam-3131	11	22	by	by	ADP
ejpam-3131	11	23	levine	levine	PROPN
ejpam-3131	11	24	and	and	CCONJ
ejpam-3131	11	25	the	the	DET
ejpam-3131	11	26	ig	ig	NOUN
ejpam-3131	11	27	-	-	PUNCT
ejpam-3131	11	28	closed	closed	ADJ
ejpam-3131	11	29	sets	set	NOUN
ejpam-3131	11	30	,	,	PUNCT
ejpam-3131	11	31	which	which	PRON
ejpam-3131	11	32	is	be	AUX
ejpam-3131	11	33	a	a	DET
ejpam-3131	11	34	generalization	generalization	NOUN
ejpam-3131	11	35	of	of	ADP
ejpam-3131	11	36	g	g	NOUN
ejpam-3131	11	37	-	-	PUNCT
ejpam-3131	11	38	closed	close	VERB
ejpam-3131	11	39	sets	set	NOUN
ejpam-3131	11	40	,	,	PUNCT
ejpam-3131	11	41	was	be	AUX
ejpam-3131	11	42	defined	define	VERB
ejpam-3131	11	43	by	by	ADP
ejpam-3131	11	44	jafari	jafari	NOUN
ejpam-3131	11	45	-	-	NOUN
ejpam-3131	11	46	rajesh	rajesh	PROPN
ejpam-3131	11	47	,	,	PUNCT
ejpam-3131	11	48	in	in	ADP
ejpam-3131	11	49	terms	term	NOUN
ejpam-3131	11	50	of	of	ADP
ejpam-3131	11	51	ideals	ideal	NOUN
ejpam-3131	11	52	.	.	PUNCT
ejpam-3131	12	1	in	in	ADP
ejpam-3131	12	2	this	this	DET
ejpam-3131	12	3	paper	paper	NOUN
ejpam-3131	12	4	we	we	PRON
ejpam-3131	12	5	introduce	introduce	VERB
ejpam-3131	12	6	and	and	CCONJ
ejpam-3131	12	7	study	study	VERB
ejpam-3131	12	8	new	new	ADJ
ejpam-3131	12	9	intermediate	intermediate	ADJ
ejpam-3131	12	10	concepts	concept	NOUN
ejpam-3131	12	11	between	between	ADP
ejpam-3131	12	12	closed	closed	ADJ
ejpam-3131	12	13	and	and	CCONJ
ejpam-3131	12	14	ig	ig	ADJ
ejpam-3131	12	15	-	-	ADJ
ejpam-3131	12	16	closed	closed	ADJ
ejpam-3131	12	17	sets	set	NOUN
ejpam-3131	12	18	,	,	PUNCT
ejpam-3131	12	19	via	via	ADP
ejpam-3131	12	20	ideals	ideal	NOUN
ejpam-3131	12	21	.	.	PUNCT
ejpam-3131	13	1	we	we	PRON
ejpam-3131	13	2	also	also	ADV
ejpam-3131	13	3	present	present	VERB
ejpam-3131	13	4	some	some	DET
ejpam-3131	13	5	applications	application	NOUN
ejpam-3131	13	6	of	of	ADP
ejpam-3131	13	7	these	these	DET
ejpam-3131	13	8	new	new	ADJ
ejpam-3131	13	9	sets	set	NOUN
ejpam-3131	13	10	,	,	PUNCT
ejpam-3131	13	11	related	relate	VERB
ejpam-3131	13	12	to	to	ADP
ejpam-3131	13	13	compactness	compactness	NOUN
ejpam-3131	13	14	and	and	CCONJ
ejpam-3131	13	15	normality	normality	NOUN
ejpam-3131	13	16	.	.	PUNCT
ejpam-3131	14	1	an	an	DET
ejpam-3131	14	2	ideal	ideal	NOUN
ejpam-3131	14	3	i	i	PRON
ejpam-3131	14	4	in	in	ADP
ejpam-3131	14	5	a	a	DET
ejpam-3131	14	6	set	set	NOUN
ejpam-3131	14	7	x	x	PUNCT
ejpam-3131	14	8	is	be	AUX
ejpam-3131	14	9	a	a	DET
ejpam-3131	14	10	subset	subset	NOUN
ejpam-3131	14	11	of	of	ADP
ejpam-3131	14	12	p(x	p(x	PROPN
ejpam-3131	14	13	)	)	PUNCT
ejpam-3131	14	14	,	,	PUNCT
ejpam-3131	14	15	the	the	DET
ejpam-3131	14	16	power	power	NOUN
ejpam-3131	14	17	set	set	NOUN
ejpam-3131	14	18	of	of	ADP
ejpam-3131	14	19	x	x	PROPN
ejpam-3131	14	20	,	,	PUNCT
ejpam-3131	14	21	such	such	ADJ
ejpam-3131	14	22	that	that	SCONJ
ejpam-3131	14	23	:	:	PUNCT
ejpam-3131	14	24	(	(	PUNCT
ejpam-3131	14	25	i	i	NOUN
ejpam-3131	14	26	)	)	PUNCT
ejpam-3131	14	27	if	if	SCONJ
ejpam-3131	14	28	a	a	PRON
ejpam-3131	14	29	⊆	⊆	NUM
ejpam-3131	14	30	b	b	SYM
ejpam-3131	14	31	⊆	⊆	NUM
ejpam-3131	14	32	x	x	PUNCT
ejpam-3131	14	33	and	and	CCONJ
ejpam-3131	14	34	b	b	X
ejpam-3131	14	35	∈	∈	PROPN
ejpam-3131	15	1	i	i	PRON
ejpam-3131	15	2	then	then	ADV
ejpam-3131	15	3	a	a	DET
ejpam-3131	15	4	∈	∈	PROPN
ejpam-3131	15	5	i	i	X
ejpam-3131	15	6	,	,	PUNCT
ejpam-3131	15	7	and	and	CCONJ
ejpam-3131	15	8	(	(	PUNCT
ejpam-3131	15	9	ii	ii	NOUN
ejpam-3131	15	10	)	)	PUNCT
ejpam-3131	15	11	if	if	SCONJ
ejpam-3131	15	12	a	a	DET
ejpam-3131	15	13	∈	∈	X
ejpam-3131	15	14	i	i	PRON
ejpam-3131	15	15	and	and	CCONJ
ejpam-3131	15	16	b	b	X
ejpam-3131	15	17	∈	∈	PROPN
ejpam-3131	16	1	i	i	PRON
ejpam-3131	16	2	then	then	ADV
ejpam-3131	16	3	a	a	DET
ejpam-3131	16	4	∪b	∪b	PUNCT
ejpam-3131	16	5	∈	∈	PROPN
ejpam-3131	16	6	i.	i.	NOUN
ejpam-3131	16	7	some	some	DET
ejpam-3131	16	8	simple	simple	ADJ
ejpam-3131	16	9	and	and	CCONJ
ejpam-3131	16	10	useful	useful	ADJ
ejpam-3131	16	11	ideals	ideal	NOUN
ejpam-3131	16	12	in	in	ADP
ejpam-3131	16	13	x	x	PUNCT
ejpam-3131	16	14	are	be	AUX
ejpam-3131	16	15	:	:	PUNCT
ejpam-3131	16	16	(	(	PUNCT
ejpam-3131	16	17	i	i	NOUN
ejpam-3131	16	18	)	)	PUNCT
ejpam-3131	16	19	p(a	p(a	PROPN
ejpam-3131	16	20	)	)	PUNCT
ejpam-3131	16	21	,	,	PUNCT
ejpam-3131	16	22	where	where	SCONJ
ejpam-3131	16	23	a	a	DET
ejpam-3131	16	24	⊆	⊆	NUM
ejpam-3131	16	25	x	x	SYM
ejpam-3131	16	26	,	,	PUNCT
ejpam-3131	16	27	(	(	PUNCT
ejpam-3131	16	28	ii	ii	NOUN
ejpam-3131	16	29	)	)	PUNCT
ejpam-3131	16	30	if	if	SCONJ
ejpam-3131	16	31	(	(	PUNCT
ejpam-3131	16	32	x	x	X
ejpam-3131	16	33	)	)	PUNCT
ejpam-3131	16	34	,	,	PUNCT
ejpam-3131	16	35	the	the	DET
ejpam-3131	16	36	ideal	ideal	NOUN
ejpam-3131	16	37	of	of	ADP
ejpam-3131	16	38	all	all	DET
ejpam-3131	16	39	finite	finite	ADJ
ejpam-3131	16	40	subsets	subset	NOUN
ejpam-3131	16	41	of	of	ADP
ejpam-3131	16	42	x	x	NOUN
ejpam-3131	16	43	,	,	PUNCT
ejpam-3131	16	44	and	and	CCONJ
ejpam-3131	16	45	(	(	PUNCT
ejpam-3131	16	46	iii	iii	NOUN
ejpam-3131	16	47	)	)	PUNCT
ejpam-3131	16	48	ic	ic	PROPN
ejpam-3131	16	49	(	(	PUNCT
ejpam-3131	16	50	x	x	NOUN
ejpam-3131	16	51	)	)	PUNCT
ejpam-3131	16	52	,	,	PUNCT
ejpam-3131	16	53	the	the	DET
ejpam-3131	16	54	ideal	ideal	NOUN
ejpam-3131	16	55	of	of	ADP
ejpam-3131	16	56	all	all	DET
ejpam-3131	16	57	countable	countable	ADJ
ejpam-3131	16	58	subsets	subset	NOUN
ejpam-3131	16	59	of	of	ADP
ejpam-3131	16	60	x.	x.	NOUN
ejpam-3131	16	61	email	email	NOUN
ejpam-3131	16	62	addresses	address	NOUN
ejpam-3131	16	63	:	:	PUNCT
ejpam-3131	16	64	nestor.pachon@escuelaing.edu.co	nestor.pachon@escuelaing.edu.co	ADJ
ejpam-3131	16	65	,	,	PUNCT
ejpam-3131	16	66	nrpachonr@unal.edu.co	nrpachonr@unal.edu.co	INTJ
ejpam-3131	16	67	(	(	PUNCT
ejpam-3131	16	68	n.r	n.r	PROPN
ejpam-3131	16	69	.	.	PROPN
ejpam-3131	16	70	pachón	pachón	PROPN
ejpam-3131	16	71	)	)	PUNCT
ejpam-3131	16	72	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3131	16	73	299	299	NUM
ejpam-3131	16	74	©	©	PROPN
ejpam-3131	16	75	2018	2018	NUM
ejpam-3131	16	76	ejpam	ejpam	VERB
ejpam-3131	16	77	all	all	DET
ejpam-3131	16	78	rights	right	NOUN
ejpam-3131	16	79	reserved	reserve	VERB
ejpam-3131	16	80	.	.	PUNCT
ejpam-3131	17	1	n.r	n.r	PROPN
ejpam-3131	17	2	.	.	PROPN
ejpam-3131	17	3	pachón	pachón	PROPN
ejpam-3131	17	4	/	/	SYM
ejpam-3131	17	5	eur	eur	PROPN
ejpam-3131	17	6	.	.	PUNCT
ejpam-3131	18	1	j.	j.	PROPN
ejpam-3131	18	2	pure	pure	PROPN
ejpam-3131	18	3	appl	appl	PROPN
ejpam-3131	18	4	.	.	PROPN
ejpam-3131	18	5	math	math	PROPN
ejpam-3131	18	6	,	,	PUNCT
ejpam-3131	18	7	11	11	NUM
ejpam-3131	18	8	(	(	PUNCT
ejpam-3131	18	9	1	1	NUM
ejpam-3131	18	10	)	)	PUNCT
ejpam-3131	18	11	(	(	PUNCT
ejpam-3131	18	12	2018	2018	NUM
ejpam-3131	18	13	)	)	PUNCT
ejpam-3131	18	14	,	,	PUNCT
ejpam-3131	18	15	299	299	NUM
ejpam-3131	18	16	-	-	SYM
ejpam-3131	18	17	314	314	NUM
ejpam-3131	18	18	300	300	NUM
ejpam-3131	18	19	if	if	SCONJ
ejpam-3131	18	20	(	(	PUNCT
ejpam-3131	18	21	x	x	NOUN
ejpam-3131	18	22	,	,	PUNCT
ejpam-3131	18	23	τ	τ	X
ejpam-3131	18	24	)	)	PUNCT
ejpam-3131	18	25	is	be	AUX
ejpam-3131	18	26	a	a	DET
ejpam-3131	18	27	topological	topological	ADJ
ejpam-3131	18	28	space	space	NOUN
ejpam-3131	18	29	and	and	CCONJ
ejpam-3131	18	30	i	i	PRON
ejpam-3131	18	31	is	be	AUX
ejpam-3131	18	32	an	an	DET
ejpam-3131	18	33	ideal	ideal	NOUN
ejpam-3131	18	34	in	in	ADP
ejpam-3131	18	35	x	x	NOUN
ejpam-3131	18	36	,	,	PUNCT
ejpam-3131	18	37	then	then	ADV
ejpam-3131	18	38	(	(	PUNCT
ejpam-3131	18	39	x	x	X
ejpam-3131	18	40	,	,	PUNCT
ejpam-3131	18	41	τ	τ	PROPN
ejpam-3131	18	42	,	,	PUNCT
ejpam-3131	18	43	i	i	PROPN
ejpam-3131	18	44	)	)	PUNCT
ejpam-3131	18	45	is	be	AUX
ejpam-3131	18	46	called	call	VERB
ejpam-3131	18	47	an	an	DET
ejpam-3131	18	48	ideal	ideal	ADJ
ejpam-3131	18	49	space	space	NOUN
ejpam-3131	18	50	.	.	PUNCT
ejpam-3131	19	1	if	if	SCONJ
ejpam-3131	19	2	(	(	PUNCT
ejpam-3131	19	3	x	x	NOUN
ejpam-3131	19	4	,	,	PUNCT
ejpam-3131	19	5	τ	τ	X
ejpam-3131	19	6	)	)	PUNCT
ejpam-3131	19	7	is	be	AUX
ejpam-3131	19	8	a	a	DET
ejpam-3131	19	9	topological	topological	ADJ
ejpam-3131	19	10	space	space	NOUN
ejpam-3131	19	11	and	and	CCONJ
ejpam-3131	19	12	a	a	DET
ejpam-3131	19	13	⊆	⊆	NUM
ejpam-3131	19	14	x	x	SYM
ejpam-3131	19	15	then	then	ADV
ejpam-3131	19	16	the	the	DET
ejpam-3131	19	17	closure	closure	NOUN
ejpam-3131	19	18	and	and	CCONJ
ejpam-3131	19	19	the	the	DET
ejpam-3131	19	20	interior	interior	NOUN
ejpam-3131	19	21	of	of	ADP
ejpam-3131	19	22	a	a	PRON
ejpam-3131	19	23	are	be	AUX
ejpam-3131	19	24	denoted	denote	VERB
ejpam-3131	19	25	by	by	ADP
ejpam-3131	19	26	a	a	PRON
ejpam-3131	19	27	(	(	PUNCT
ejpam-3131	19	28	or	or	CCONJ
ejpam-3131	19	29	adhτ	adhτ	NOUN
ejpam-3131	19	30	(	(	PUNCT
ejpam-3131	19	31	a	a	NOUN
ejpam-3131	19	32	)	)	PUNCT
ejpam-3131	19	33	)	)	PUNCT
ejpam-3131	20	1	and	and	CCONJ
ejpam-3131	20	2	0	0	NUM
ejpam-3131	20	3	a	a	PRON
ejpam-3131	20	4	(	(	PUNCT
ejpam-3131	20	5	or	or	CCONJ
ejpam-3131	20	6	intτ	intτ	NOUN
ejpam-3131	20	7	(	(	PUNCT
ejpam-3131	20	8	a	a	NOUN
ejpam-3131	20	9	)	)	PUNCT
ejpam-3131	20	10	)	)	PUNCT
ejpam-3131	20	11	,	,	PUNCT
ejpam-3131	20	12	respectively	respectively	ADV
ejpam-3131	20	13	.	.	PUNCT
ejpam-3131	21	1	if	if	SCONJ
ejpam-3131	21	2	a	a	PRON
ejpam-3131	21	3	and	and	CCONJ
ejpam-3131	21	4	b	b	NOUN
ejpam-3131	21	5	are	be	AUX
ejpam-3131	21	6	subsets	subset	NOUN
ejpam-3131	21	7	of	of	ADP
ejpam-3131	21	8	the	the	DET
ejpam-3131	21	9	space	space	NOUN
ejpam-3131	21	10	(	(	PUNCT
ejpam-3131	21	11	x	x	X
ejpam-3131	21	12	,	,	PUNCT
ejpam-3131	21	13	τ	τ	X
ejpam-3131	21	14	)	)	PUNCT
ejpam-3131	21	15	and	and	CCONJ
ejpam-3131	21	16	a	a	DET
ejpam-3131	21	17	∩b	∩b	NOUN
ejpam-3131	21	18	=	=	NOUN
ejpam-3131	21	19	∅	∅	NOUN
ejpam-3131	21	20	=	=	PUNCT
ejpam-3131	21	21	a	a	DET
ejpam-3131	21	22	∩b	∩b	NOUN
ejpam-3131	21	23	then	then	ADV
ejpam-3131	21	24	a	a	PRON
ejpam-3131	21	25	and	and	CCONJ
ejpam-3131	21	26	b	b	NOUN
ejpam-3131	21	27	are	be	AUX
ejpam-3131	21	28	called	call	VERB
ejpam-3131	21	29	separated	separate	VERB
ejpam-3131	21	30	.	.	PUNCT
ejpam-3131	22	1	if	if	SCONJ
ejpam-3131	22	2	a	a	DET
ejpam-3131	22	3	⊆	⊆	NUM
ejpam-3131	22	4	0	0	NUM
ejpam-3131	22	5	a	a	DET
ejpam-3131	22	6	then	then	ADV
ejpam-3131	22	7	a	a	PRON
ejpam-3131	22	8	is	be	AUX
ejpam-3131	22	9	said	say	VERB
ejpam-3131	22	10	to	to	PART
ejpam-3131	22	11	be	be	AUX
ejpam-3131	22	12	pre	pre	ADJ
ejpam-3131	22	13	-	-	ADJ
ejpam-3131	22	14	open	open	ADJ
ejpam-3131	22	15	[	[	X
ejpam-3131	22	16	6	6	NUM
ejpam-3131	22	17	]	]	PUNCT
ejpam-3131	22	18	.	.	PUNCT
ejpam-3131	23	1	if	if	SCONJ
ejpam-3131	23	2	0	0	NUM
ejpam-3131	23	3	a	a	DET
ejpam-3131	23	4	⊆	⊆	NUM
ejpam-3131	23	5	a	a	DET
ejpam-3131	23	6	then	then	ADV
ejpam-3131	23	7	a	a	PRON
ejpam-3131	23	8	is	be	AUX
ejpam-3131	23	9	defined	define	VERB
ejpam-3131	23	10	to	to	PART
ejpam-3131	23	11	be	be	AUX
ejpam-3131	23	12	pre	pre	ADJ
ejpam-3131	23	13	-	-	ADJ
ejpam-3131	23	14	closed	closed	ADJ
ejpam-3131	23	15	[	[	X
ejpam-3131	23	16	6	6	NUM
ejpam-3131	23	17	]	]	PUNCT
ejpam-3131	23	18	.	.	PUNCT
ejpam-3131	24	1	it	it	PRON
ejpam-3131	24	2	is	be	AUX
ejpam-3131	24	3	clear	clear	ADJ
ejpam-3131	24	4	that	that	SCONJ
ejpam-3131	24	5	a	a	PRON
ejpam-3131	24	6	is	be	AUX
ejpam-3131	24	7	pre	pre	ADJ
ejpam-3131	24	8	-	-	ADJ
ejpam-3131	24	9	open	open	ADJ
ejpam-3131	24	10	if	if	SCONJ
ejpam-3131	24	11	and	and	CCONJ
ejpam-3131	24	12	only	only	ADV
ejpam-3131	24	13	if	if	SCONJ
ejpam-3131	24	14	x\a	x\a	PROPN
ejpam-3131	24	15	is	be	AUX
ejpam-3131	24	16	pre	pre	ADJ
ejpam-3131	24	17	-	-	ADJ
ejpam-3131	24	18	closed	closed	ADJ
ejpam-3131	24	19	.	.	PUNCT
ejpam-3131	25	1	if	if	SCONJ
ejpam-3131	25	2	(	(	PUNCT
ejpam-3131	25	3	x	x	NOUN
ejpam-3131	25	4	,	,	PUNCT
ejpam-3131	25	5	τ	τ	X
ejpam-3131	25	6	)	)	PUNCT
ejpam-3131	25	7	is	be	AUX
ejpam-3131	25	8	a	a	DET
ejpam-3131	25	9	topological	topological	ADJ
ejpam-3131	25	10	space	space	NOUN
ejpam-3131	25	11	and	and	CCONJ
ejpam-3131	25	12	a	a	DET
ejpam-3131	25	13	⊆	⊆	NUM
ejpam-3131	25	14	x	x	SYM
ejpam-3131	25	15	then	then	ADV
ejpam-3131	25	16	a	a	PRON
ejpam-3131	25	17	is	be	AUX
ejpam-3131	25	18	said	say	VERB
ejpam-3131	25	19	to	to	PART
ejpam-3131	25	20	be	be	AUX
ejpam-3131	25	21	g	g	NOUN
ejpam-3131	25	22	-	-	PUNCT
ejpam-3131	25	23	closed	closed	ADJ
ejpam-3131	25	24	[	[	X
ejpam-3131	25	25	5	5	NUM
ejpam-3131	25	26	]	]	PUNCT
ejpam-3131	25	27	if	if	SCONJ
ejpam-3131	25	28	,	,	PUNCT
ejpam-3131	25	29	for	for	ADP
ejpam-3131	25	30	each	each	DET
ejpam-3131	25	31	u	u	PROPN
ejpam-3131	25	32	∈	∈	PROPN
ejpam-3131	25	33	τ	τ	X
ejpam-3131	25	34	,	,	PUNCT
ejpam-3131	25	35	a	a	DET
ejpam-3131	25	36	⊆	⊆	NUM
ejpam-3131	25	37	u	u	NOUN
ejpam-3131	25	38	implies	imply	VERB
ejpam-3131	25	39	a	a	DET
ejpam-3131	25	40	⊆	⊆	NUM
ejpam-3131	25	41	u	u	NOUN
ejpam-3131	25	42	.	.	PUNCT
ejpam-3131	26	1	an	an	DET
ejpam-3131	26	2	ideal	ideal	ADJ
ejpam-3131	26	3	space	space	NOUN
ejpam-3131	26	4	(	(	PUNCT
ejpam-3131	26	5	x	x	X
ejpam-3131	26	6	,	,	PUNCT
ejpam-3131	26	7	τ	τ	PROPN
ejpam-3131	26	8	,	,	PUNCT
ejpam-3131	26	9	i	i	PROPN
ejpam-3131	26	10	)	)	PUNCT
ejpam-3131	26	11	is	be	AUX
ejpam-3131	26	12	defined	define	VERB
ejpam-3131	26	13	to	to	PART
ejpam-3131	26	14	be	be	AUX
ejpam-3131	26	15	i	i	NOUN
ejpam-3131	26	16	-	-	NOUN
ejpam-3131	26	17	normal	normal	ADJ
ejpam-3131	26	18	[	[	X
ejpam-3131	26	19	1	1	NUM
ejpam-3131	26	20	]	]	X
ejpam-3131	26	21	if	if	SCONJ
ejpam-3131	26	22	for	for	ADP
ejpam-3131	26	23	every	every	DET
ejpam-3131	26	24	pair	pair	NOUN
ejpam-3131	26	25	of	of	ADP
ejpam-3131	26	26	disjoint	disjoint	NOUN
ejpam-3131	26	27	closed	close	VERB
ejpam-3131	26	28	subsets	subset	NOUN
ejpam-3131	26	29	f	f	PROPN
ejpam-3131	26	30	and	and	CCONJ
ejpam-3131	26	31	g	g	NOUN
ejpam-3131	26	32	,	,	PUNCT
ejpam-3131	26	33	there	there	PRON
ejpam-3131	26	34	exist	exist	VERB
ejpam-3131	26	35	disjoint	disjoint	ADJ
ejpam-3131	26	36	open	open	ADJ
ejpam-3131	26	37	sets	set	NOUN
ejpam-3131	26	38	u	u	NOUN
ejpam-3131	26	39	and	and	CCONJ
ejpam-3131	26	40	v	v	ADP
ejpam-3131	26	41	such	such	ADJ
ejpam-3131	27	1	that	that	SCONJ
ejpam-3131	27	2	f\u	f\u	PROPN
ejpam-3131	27	3	∈	∈	PROPN
ejpam-3131	28	1	i	i	PRON
ejpam-3131	28	2	and	and	CCONJ
ejpam-3131	28	3	g\v	g\v	PROPN
ejpam-3131	28	4	∈	∈	PROPN
ejpam-3131	28	5	i.	i.	NOUN
ejpam-3131	28	6	the	the	DET
ejpam-3131	28	7	symbol	symbol	NOUN
ejpam-3131	28	8	□	□	PUNCT
ejpam-3131	28	9	is	be	AUX
ejpam-3131	28	10	used	use	VERB
ejpam-3131	28	11	to	to	PART
ejpam-3131	28	12	indicate	indicate	VERB
ejpam-3131	28	13	the	the	DET
ejpam-3131	28	14	end	end	NOUN
ejpam-3131	28	15	of	of	ADP
ejpam-3131	28	16	a	a	DET
ejpam-3131	28	17	proof	proof	NOUN
ejpam-3131	28	18	.	.	PUNCT
ejpam-3131	29	1	2	2	X
ejpam-3131	29	2	.	.	X
ejpam-3131	29	3	ρig	ρig	NOUN
ejpam-3131	29	4	-	-	PUNCT
ejpam-3131	29	5	closed	close	VERB
ejpam-3131	29	6	sets	set	NOUN
ejpam-3131	29	7	the	the	DET
ejpam-3131	29	8	generalized	generalize	VERB
ejpam-3131	29	9	closed	close	VERB
ejpam-3131	29	10	sets	set	NOUN
ejpam-3131	29	11	via	via	ADP
ejpam-3131	29	12	ideals	ideal	NOUN
ejpam-3131	29	13	,	,	PUNCT
ejpam-3131	29	14	that	that	SCONJ
ejpam-3131	29	15	we	we	PRON
ejpam-3131	29	16	consider	consider	VERB
ejpam-3131	29	17	,	,	PUNCT
ejpam-3131	29	18	are	be	AUX
ejpam-3131	29	19	due	due	ADJ
ejpam-3131	29	20	to	to	ADP
ejpam-3131	29	21	jafari	jafari	PROPN
ejpam-3131	29	22	-	-	PROPN
ejpam-3131	29	23	rajesh	rajesh	PROPN
ejpam-3131	29	24	and	and	CCONJ
ejpam-3131	29	25	these	these	PRON
ejpam-3131	29	26	are	be	AUX
ejpam-3131	29	27	extensions	extension	NOUN
ejpam-3131	29	28	of	of	ADP
ejpam-3131	29	29	the	the	DET
ejpam-3131	29	30	g	g	NOUN
ejpam-3131	29	31	-	-	PUNCT
ejpam-3131	29	32	closed	close	VERB
ejpam-3131	29	33	sets	set	NOUN
ejpam-3131	29	34	of	of	ADP
ejpam-3131	29	35	levine	levine	PROPN
ejpam-3131	29	36	.	.	PUNCT
ejpam-3131	30	1	in	in	ADP
ejpam-3131	30	2	this	this	DET
ejpam-3131	30	3	section	section	NOUN
ejpam-3131	30	4	we	we	PRON
ejpam-3131	30	5	define	define	VERB
ejpam-3131	30	6	the	the	DET
ejpam-3131	30	7	ρigclosed	ρigclose	VERB
ejpam-3131	30	8	sets	set	NOUN
ejpam-3131	30	9	,	,	PUNCT
ejpam-3131	30	10	which	which	PRON
ejpam-3131	30	11	is	be	AUX
ejpam-3131	30	12	a	a	DET
ejpam-3131	30	13	new	new	ADJ
ejpam-3131	30	14	intermediate	intermediate	ADJ
ejpam-3131	30	15	concept	concept	NOUN
ejpam-3131	30	16	between	between	ADP
ejpam-3131	30	17	closed	closed	ADJ
ejpam-3131	30	18	and	and	CCONJ
ejpam-3131	30	19	ig	ig	NOUN
ejpam-3131	30	20	-	-	ADJ
ejpam-3131	30	21	closed	close	VERB
ejpam-3131	30	22	sets	set	NOUN
ejpam-3131	30	23	.	.	PUNCT
ejpam-3131	31	1	some	some	DET
ejpam-3131	31	2	properties	property	NOUN
ejpam-3131	31	3	,	,	PUNCT
ejpam-3131	31	4	characterizations	characterization	NOUN
ejpam-3131	31	5	and	and	CCONJ
ejpam-3131	31	6	applications	application	NOUN
ejpam-3131	31	7	are	be	AUX
ejpam-3131	31	8	presented	present	VERB
ejpam-3131	31	9	.	.	PUNCT
ejpam-3131	32	1	if	if	SCONJ
ejpam-3131	32	2	(	(	PUNCT
ejpam-3131	32	3	x	x	X
ejpam-3131	32	4	,	,	PUNCT
ejpam-3131	32	5	τ	τ	PROPN
ejpam-3131	32	6	,	,	PUNCT
ejpam-3131	32	7	i	i	PROPN
ejpam-3131	32	8	)	)	PUNCT
ejpam-3131	32	9	is	be	AUX
ejpam-3131	32	10	an	an	DET
ejpam-3131	32	11	ideal	ideal	ADJ
ejpam-3131	32	12	space	space	NOUN
ejpam-3131	32	13	and	and	CCONJ
ejpam-3131	32	14	a	a	DET
ejpam-3131	32	15	⊆	⊆	NUM
ejpam-3131	32	16	x	x	SYM
ejpam-3131	32	17	then	then	ADV
ejpam-3131	32	18	a	a	PRON
ejpam-3131	32	19	is	be	AUX
ejpam-3131	32	20	defined	define	VERB
ejpam-3131	32	21	to	to	PART
ejpam-3131	32	22	be	be	AUX
ejpam-3131	32	23	ig	ig	NOUN
ejpam-3131	32	24	-	-	ADJ
ejpam-3131	32	25	closed	closed	ADJ
ejpam-3131	32	26	[	[	X
ejpam-3131	32	27	2	2	NUM
ejpam-3131	32	28	]	]	PUNCT
ejpam-3131	32	29	if	if	SCONJ
ejpam-3131	32	30	,	,	PUNCT
ejpam-3131	32	31	for	for	ADP
ejpam-3131	32	32	all	all	PRON
ejpam-3131	32	33	u	u	PROPN
ejpam-3131	32	34	∈	∈	PROPN
ejpam-3131	32	35	τ	τ	X
ejpam-3131	32	36	,	,	PUNCT
ejpam-3131	32	37	a	a	DET
ejpam-3131	32	38	⊆	⊆	NUM
ejpam-3131	32	39	u	u	NOUN
ejpam-3131	32	40	implies	imply	VERB
ejpam-3131	32	41	a\u	a\u	PROPN
ejpam-3131	32	42	∈	∈	PROPN
ejpam-3131	32	43	i.	i.	NOUN
ejpam-3131	32	44	it	it	PRON
ejpam-3131	32	45	is	be	AUX
ejpam-3131	32	46	noted	note	VERB
ejpam-3131	32	47	that	that	SCONJ
ejpam-3131	32	48	closed	closed	ADJ
ejpam-3131	32	49	→	→	SYM
ejpam-3131	32	50	g	g	NOUN
ejpam-3131	32	51	-	-	PUNCT
ejpam-3131	32	52	closed	close	VERB
ejpam-3131	32	53	→	→	SYM
ejpam-3131	32	54	ig	ig	NOUN
ejpam-3131	32	55	-	-	PUNCT
ejpam-3131	32	56	closed	closed	ADJ
ejpam-3131	32	57	.	.	PUNCT
ejpam-3131	33	1	definition	definition	NOUN
ejpam-3131	33	2	2.1	2.1	NUM
ejpam-3131	33	3	.	.	PUNCT
ejpam-3131	34	1	if	if	SCONJ
ejpam-3131	34	2	(	(	PUNCT
ejpam-3131	34	3	x	x	X
ejpam-3131	34	4	,	,	PUNCT
ejpam-3131	34	5	τ	τ	PROPN
ejpam-3131	34	6	,	,	PUNCT
ejpam-3131	34	7	i	i	PROPN
ejpam-3131	34	8	)	)	PUNCT
ejpam-3131	34	9	is	be	AUX
ejpam-3131	34	10	an	an	DET
ejpam-3131	34	11	ideal	ideal	ADJ
ejpam-3131	34	12	topological	topological	ADJ
ejpam-3131	34	13	space	space	NOUN
ejpam-3131	34	14	and	and	CCONJ
ejpam-3131	34	15	a	a	DET
ejpam-3131	34	16	⊆	⊆	NUM
ejpam-3131	34	17	x	x	SYM
ejpam-3131	34	18	then	then	ADV
ejpam-3131	34	19	a	a	PRON
ejpam-3131	34	20	is	be	AUX
ejpam-3131	34	21	said	say	VERB
ejpam-3131	34	22	to	to	PART
ejpam-3131	34	23	be	be	AUX
ejpam-3131	34	24	ρig	ρig	NOUN
ejpam-3131	34	25	-	-	PUNCT
ejpam-3131	34	26	closed	closed	ADJ
ejpam-3131	34	27	if	if	SCONJ
ejpam-3131	34	28	for	for	ADP
ejpam-3131	34	29	each	each	DET
ejpam-3131	34	30	u	u	PROPN
ejpam-3131	34	31	∈	∈	PROPN
ejpam-3131	34	32	τ	τ	X
ejpam-3131	34	33	,	,	PUNCT
ejpam-3131	34	34	if	if	SCONJ
ejpam-3131	34	35	a\u	a\u	PROPN
ejpam-3131	34	36	∈	∈	PROPN
ejpam-3131	34	37	i	i	PRON
ejpam-3131	34	38	then	then	ADV
ejpam-3131	34	39	a\u	a\u	PROPN
ejpam-3131	34	40	∈	∈	PROPN
ejpam-3131	34	41	i.	i.	NOUN
ejpam-3131	34	42	it	it	PRON
ejpam-3131	34	43	is	be	AUX
ejpam-3131	34	44	clear	clear	ADJ
ejpam-3131	34	45	that	that	SCONJ
ejpam-3131	34	46	closed	closed	ADJ
ejpam-3131	34	47	→	→	SYM
ejpam-3131	34	48	ρig	ρig	ADV
ejpam-3131	34	49	-	-	PUNCT
ejpam-3131	34	50	closed	close	VERB
ejpam-3131	34	51	→	→	SYM
ejpam-3131	34	52	ig	ig	PROPN
ejpam-3131	34	53	-	-	PUNCT
ejpam-3131	34	54	closed	close	VERB
ejpam-3131	34	55	the	the	DET
ejpam-3131	34	56	converse	converse	NOUN
ejpam-3131	34	57	are	be	AUX
ejpam-3131	34	58	not	not	PART
ejpam-3131	34	59	true	true	ADJ
ejpam-3131	34	60	,	,	PUNCT
ejpam-3131	34	61	as	as	SCONJ
ejpam-3131	34	62	we	we	PRON
ejpam-3131	34	63	can	can	AUX
ejpam-3131	34	64	see	see	VERB
ejpam-3131	34	65	in	in	ADP
ejpam-3131	34	66	the	the	DET
ejpam-3131	34	67	next	next	ADJ
ejpam-3131	34	68	example	example	NOUN
ejpam-3131	34	69	.	.	PUNCT
ejpam-3131	35	1	example	example	NOUN
ejpam-3131	36	1	2.2	2.2	NUM
ejpam-3131	36	2	.	.	PUNCT
ejpam-3131	37	1	(	(	PUNCT
ejpam-3131	37	2	1	1	X
ejpam-3131	37	3	)	)	PUNCT
ejpam-3131	37	4	if	if	SCONJ
ejpam-3131	37	5	u	u	NOUN
ejpam-3131	37	6	is	be	AUX
ejpam-3131	37	7	the	the	DET
ejpam-3131	37	8	usual	usual	ADJ
ejpam-3131	37	9	topology	topology	NOUN
ejpam-3131	37	10	in	in	ADP
ejpam-3131	37	11	the	the	DET
ejpam-3131	37	12	set	set	NOUN
ejpam-3131	37	13	r	r	NOUN
ejpam-3131	37	14	,	,	PUNCT
ejpam-3131	37	15	then	then	ADV
ejpam-3131	37	16	all	all	DET
ejpam-3131	37	17	a	a	DET
ejpam-3131	37	18	⊆	⊆	NUM
ejpam-3131	37	19	r	r	NOUN
ejpam-3131	37	20	is	be	AUX
ejpam-3131	37	21	ρig	ρig	NOUN
ejpam-3131	37	22	-	-	PUNCT
ejpam-3131	37	23	closed	close	VERB
ejpam-3131	37	24	in	in	ADP
ejpam-3131	37	25	the	the	DET
ejpam-3131	37	26	ideal	ideal	ADJ
ejpam-3131	37	27	space	space	NOUN
ejpam-3131	37	28	(	(	PUNCT
ejpam-3131	37	29	r	r	NOUN
ejpam-3131	37	30	,	,	PUNCT
ejpam-3131	37	31	u	u	NOUN
ejpam-3131	37	32	,	,	PUNCT
ejpam-3131	37	33	i	i	PROPN
ejpam-3131	37	34	=	=	SYM
ejpam-3131	37	35	p(r	p(r	PROPN
ejpam-3131	37	36	)	)	PUNCT
ejpam-3131	37	37	)	)	PUNCT
ejpam-3131	37	38	,	,	PUNCT
ejpam-3131	37	39	but	but	CCONJ
ejpam-3131	37	40	(	(	PUNCT
ejpam-3131	37	41	0	0	NUM
ejpam-3131	37	42	,	,	PUNCT
ejpam-3131	37	43	1	1	NUM
ejpam-3131	37	44	)	)	PUNCT
ejpam-3131	37	45	is	be	AUX
ejpam-3131	37	46	not	not	PART
ejpam-3131	37	47	g	g	NOUN
ejpam-3131	37	48	-	-	PUNCT
ejpam-3131	37	49	closed	closed	ADJ
ejpam-3131	37	50	.	.	PUNCT
ejpam-3131	38	1	then	then	ADV
ejpam-3131	38	2	ρig	ρig	ADJ
ejpam-3131	38	3	-	-	PUNCT
ejpam-3131	38	4	closed↛g	closed↛g	NOUN
ejpam-3131	38	5	-	-	PUNCT
ejpam-3131	38	6	closed	close	VERB
ejpam-3131	38	7	and	and	CCONJ
ejpam-3131	38	8	so	so	ADV
ejpam-3131	38	9	ρig	ρig	ADV
ejpam-3131	38	10	-	-	PUNCT
ejpam-3131	38	11	closed↛closed	closed↛close	VERB
ejpam-3131	38	12	.	.	PUNCT
ejpam-3131	39	1	(	(	PUNCT
ejpam-3131	39	2	2	2	X
ejpam-3131	39	3	)	)	PUNCT
ejpam-3131	39	4	if	if	SCONJ
ejpam-3131	39	5	c	c	NOUN
ejpam-3131	39	6	=	=	SYM
ejpam-3131	39	7	{	{	PUNCT
ejpam-3131	39	8	∅,r}∪{(r,∞	∅,r}∪{(r,∞	PROPN
ejpam-3131	39	9	)	)	PUNCT
ejpam-3131	39	10	:	:	PUNCT
ejpam-3131	39	11	r	r	NOUN
ejpam-3131	39	12	∈	∈	PROPN
ejpam-3131	39	13	r	r	NOUN
ejpam-3131	39	14	}	}	PUNCT
ejpam-3131	39	15	then	then	ADV
ejpam-3131	39	16	z	z	NOUN
ejpam-3131	39	17	is	be	AUX
ejpam-3131	39	18	not	not	PART
ejpam-3131	39	19	ρig	ρig	NOUN
ejpam-3131	39	20	-	-	PUNCT
ejpam-3131	39	21	closed	close	VERB
ejpam-3131	39	22	in	in	ADP
ejpam-3131	39	23	the	the	DET
ejpam-3131	39	24	space	space	NOUN
ejpam-3131	39	25	(	(	PUNCT
ejpam-3131	39	26	r	r	NOUN
ejpam-3131	39	27	,	,	PUNCT
ejpam-3131	39	28	c	c	X
ejpam-3131	39	29	,	,	PUNCT
ejpam-3131	39	30	i	i	PRON
ejpam-3131	39	31	=	=	PUNCT
ejpam-3131	39	32	ic	ic	PROPN
ejpam-3131	39	33	(	(	PUNCT
ejpam-3131	39	34	r	r	NOUN
ejpam-3131	39	35	)	)	PUNCT
ejpam-3131	39	36	)	)	PUNCT
ejpam-3131	39	37	,	,	PUNCT
ejpam-3131	40	1	because	because	SCONJ
ejpam-3131	40	2	z\	z\	PROPN
ejpam-3131	40	3	(	(	PUNCT
ejpam-3131	40	4	0,∞	0,∞	NUM
ejpam-3131	40	5	)	)	PUNCT
ejpam-3131	40	6	∈	∈	PROPN
ejpam-3131	40	7	i	i	PRON
ejpam-3131	40	8	but	but	CCONJ
ejpam-3131	40	9	z\	z\	NUM
ejpam-3131	40	10	(	(	PUNCT
ejpam-3131	40	11	0,∞	0,∞	NUM
ejpam-3131	40	12	)	)	PUNCT
ejpam-3131	40	13	=	=	SYM
ejpam-3131	40	14	(	(	PUNCT
ejpam-3131	40	15	−∞	−∞	NOUN
ejpam-3131	40	16	,	,	PUNCT
ejpam-3131	40	17	0	0	NUM
ejpam-3131	40	18	]	]	PUNCT
ejpam-3131	40	19	/∈	/∈	PUNCT
ejpam-3131	41	1	i.	i.	PROPN
ejpam-3131	41	2	however	however	ADV
ejpam-3131	41	3	z	z	PROPN
ejpam-3131	41	4	is	be	AUX
ejpam-3131	41	5	g	g	NOUN
ejpam-3131	41	6	-	-	PUNCT
ejpam-3131	41	7	closed	closed	ADJ
ejpam-3131	41	8	,	,	PUNCT
ejpam-3131	41	9	and	and	CCONJ
ejpam-3131	41	10	then	then	ADV
ejpam-3131	41	11	z	z	PROPN
ejpam-3131	41	12	is	be	AUX
ejpam-3131	41	13	ig	ig	PRON
ejpam-3131	41	14	-	-	ADJ
ejpam-3131	41	15	closed	closed	ADJ
ejpam-3131	41	16	.	.	PUNCT
ejpam-3131	42	1	thus	thus	ADV
ejpam-3131	42	2	g	g	PROPN
ejpam-3131	42	3	-	-	PUNCT
ejpam-3131	42	4	closed↛	closed↛	ADJ
ejpam-3131	42	5	ρig	ρig	NOUN
ejpam-3131	42	6	-	-	PUNCT
ejpam-3131	42	7	closed	close	VERB
ejpam-3131	42	8	and	and	CCONJ
ejpam-3131	42	9	ig	ig	NOUN
ejpam-3131	42	10	-	-	PUNCT
ejpam-3131	42	11	closed	close	VERB
ejpam-3131	42	12	↛	↛	NOUN
ejpam-3131	42	13	ρig	ρig	NOUN
ejpam-3131	42	14	-	-	PUNCT
ejpam-3131	42	15	closed	closed	ADJ
ejpam-3131	42	16	.	.	PUNCT
ejpam-3131	43	1	observe	observe	VERB
ejpam-3131	43	2	that	that	SCONJ
ejpam-3131	43	3	g	g	NOUN
ejpam-3131	43	4	-	-	PUNCT
ejpam-3131	43	5	closed	close	VERB
ejpam-3131	43	6	and	and	CCONJ
ejpam-3131	43	7	ρig	ρig	ADV
ejpam-3131	43	8	-	-	PUNCT
ejpam-3131	43	9	closed	close	VERB
ejpam-3131	43	10	are	be	AUX
ejpam-3131	43	11	independent	independent	ADJ
ejpam-3131	43	12	concepts	concept	NOUN
ejpam-3131	43	13	.	.	PUNCT
ejpam-3131	44	1	an	an	DET
ejpam-3131	44	2	application	application	NOUN
ejpam-3131	44	3	of	of	ADP
ejpam-3131	44	4	ρig	ρig	NOUN
ejpam-3131	44	5	-	-	PUNCT
ejpam-3131	44	6	closed	close	VERB
ejpam-3131	44	7	sets	set	NOUN
ejpam-3131	44	8	is	be	AUX
ejpam-3131	44	9	shown	show	VERB
ejpam-3131	44	10	in	in	ADP
ejpam-3131	44	11	the	the	DET
ejpam-3131	44	12	next	next	ADJ
ejpam-3131	44	13	theorem	theorem	NOUN
ejpam-3131	44	14	.	.	PUNCT
ejpam-3131	45	1	if	if	SCONJ
ejpam-3131	45	2	(	(	PUNCT
ejpam-3131	45	3	x	x	X
ejpam-3131	45	4	,	,	PUNCT
ejpam-3131	45	5	τ	τ	PROPN
ejpam-3131	45	6	,	,	PUNCT
ejpam-3131	45	7	i	i	PROPN
ejpam-3131	45	8	)	)	PUNCT
ejpam-3131	45	9	is	be	AUX
ejpam-3131	45	10	an	an	DET
ejpam-3131	45	11	ideal	ideal	ADJ
ejpam-3131	45	12	space	space	NOUN
ejpam-3131	45	13	then	then	ADV
ejpam-3131	45	14	a	a	DET
ejpam-3131	45	15	subset	subset	NOUN
ejpam-3131	45	16	a	a	PRON
ejpam-3131	45	17	is	be	AUX
ejpam-3131	45	18	said	say	VERB
ejpam-3131	45	19	to	to	PART
ejpam-3131	45	20	be	be	AUX
ejpam-3131	45	21	:	:	PUNCT
ejpam-3131	45	22	(	(	PUNCT
ejpam-3131	45	23	1	1	X
ejpam-3131	45	24	)	)	PUNCT
ejpam-3131	45	25	i	i	NOUN
ejpam-3131	45	26	-	-	NOUN
ejpam-3131	45	27	compact	compact	ADJ
ejpam-3131	45	28	[	[	X
ejpam-3131	45	29	8	8	NUM
ejpam-3131	45	30	]	]	X
ejpam-3131	45	31	if	if	SCONJ
ejpam-3131	45	32	for	for	ADP
ejpam-3131	45	33	each	each	DET
ejpam-3131	45	34	open	open	ADJ
ejpam-3131	45	35	cover	cover	NOUN
ejpam-3131	45	36	{	{	PUNCT
ejpam-3131	45	37	vα}α∈λ	vα}α∈λ	NOUN
ejpam-3131	45	38	of	of	ADP
ejpam-3131	45	39	a	a	PRON
ejpam-3131	45	40	,	,	PUNCT
ejpam-3131	45	41	there	there	PRON
ejpam-3131	45	42	exists	exist	VERB
ejpam-3131	45	43	λ0	λ0	NOUN
ejpam-3131	45	44	⊆	⊆	NUM
ejpam-3131	45	45	λ	λ	PROPN
ejpam-3131	45	46	,	,	PUNCT
ejpam-3131	45	47	finite	finite	NOUN
ejpam-3131	45	48	,	,	PUNCT
ejpam-3131	45	49	such	such	ADJ
ejpam-3131	45	50	that	that	SCONJ
ejpam-3131	45	51	a\	a\	NOUN
ejpam-3131	45	52	∪	∪	ADP
ejpam-3131	45	53	α∈λ0	α∈λ0	NOUN
ejpam-3131	45	54	vα	vα	ADP
ejpam-3131	45	55	∈	∈	PROPN
ejpam-3131	45	56	i	i	PRON
ejpam-3131	45	57	,	,	PUNCT
ejpam-3131	45	58	and	and	CCONJ
ejpam-3131	45	59	n.r	n.r	PROPN
ejpam-3131	45	60	.	.	PROPN
ejpam-3131	45	61	pachón	pachón	PROPN
ejpam-3131	45	62	/	/	SYM
ejpam-3131	45	63	eur	eur	PROPN
ejpam-3131	45	64	.	.	PUNCT
ejpam-3131	46	1	j.	j.	PROPN
ejpam-3131	46	2	pure	pure	PROPN
ejpam-3131	46	3	appl	appl	PROPN
ejpam-3131	46	4	.	.	PROPN
ejpam-3131	46	5	math	math	PROPN
ejpam-3131	46	6	,	,	PUNCT
ejpam-3131	46	7	11	11	NUM
ejpam-3131	46	8	(	(	PUNCT
ejpam-3131	46	9	1	1	NUM
ejpam-3131	46	10	)	)	PUNCT
ejpam-3131	46	11	(	(	PUNCT
ejpam-3131	46	12	2018	2018	NUM
ejpam-3131	46	13	)	)	PUNCT
ejpam-3131	46	14	,	,	PUNCT
ejpam-3131	46	15	299	299	NUM
ejpam-3131	46	16	-	-	SYM
ejpam-3131	46	17	314	314	NUM
ejpam-3131	46	18	301	301	NUM
ejpam-3131	46	19	(	(	PUNCT
ejpam-3131	46	20	2	2	NUM
ejpam-3131	46	21	)	)	PUNCT
ejpam-3131	46	22	ρi	ρi	NOUN
ejpam-3131	46	23	-	-	ADJ
ejpam-3131	46	24	compact	compact	ADJ
ejpam-3131	46	25	[	[	X
ejpam-3131	46	26	9	9	NUM
ejpam-3131	46	27	]	]	X
ejpam-3131	46	28	if	if	SCONJ
ejpam-3131	46	29	for	for	ADP
ejpam-3131	46	30	each	each	DET
ejpam-3131	46	31	family	family	NOUN
ejpam-3131	46	32	{	{	PUNCT
ejpam-3131	46	33	vα}α∈λ	vα}α∈λ	X
ejpam-3131	46	34	of	of	ADP
ejpam-3131	46	35	open	open	ADJ
ejpam-3131	46	36	subsets	subset	NOUN
ejpam-3131	46	37	of	of	ADP
ejpam-3131	46	38	x	x	PRON
ejpam-3131	46	39	,	,	PUNCT
ejpam-3131	46	40	if	if	SCONJ
ejpam-3131	46	41	a\	a\	PRON
ejpam-3131	46	42	∪	∪	ADP
ejpam-3131	46	43	α∈λ	α∈λ	NOUN
ejpam-3131	46	44	vα	vα	ADP
ejpam-3131	46	45	∈	∈	PROPN
ejpam-3131	47	1	i	i	PRON
ejpam-3131	47	2	there	there	PRON
ejpam-3131	47	3	exists	exist	VERB
ejpam-3131	47	4	λ0	λ0	NOUN
ejpam-3131	47	5	⊆	⊆	NUM
ejpam-3131	47	6	λ	λ	PROPN
ejpam-3131	47	7	,	,	PUNCT
ejpam-3131	47	8	finite	finite	NOUN
ejpam-3131	47	9	,	,	PUNCT
ejpam-3131	47	10	such	such	ADJ
ejpam-3131	47	11	that	that	SCONJ
ejpam-3131	47	12	a\	a\	NOUN
ejpam-3131	47	13	∪	∪	ADP
ejpam-3131	47	14	α∈λ0	α∈λ0	NOUN
ejpam-3131	47	15	vα	vα	ADP
ejpam-3131	47	16	∈	∈	PROPN
ejpam-3131	47	17	i.	i.	NOUN
ejpam-3131	47	18	the	the	DET
ejpam-3131	47	19	space	space	NOUN
ejpam-3131	47	20	(	(	PUNCT
ejpam-3131	47	21	x	x	X
ejpam-3131	47	22	,	,	PUNCT
ejpam-3131	47	23	τ	τ	PROPN
ejpam-3131	47	24	,	,	PUNCT
ejpam-3131	47	25	i	i	PROPN
ejpam-3131	47	26	)	)	PUNCT
ejpam-3131	47	27	is	be	AUX
ejpam-3131	47	28	i	i	NOUN
ejpam-3131	47	29	-	-	ADJ
ejpam-3131	47	30	compact	compact	ADJ
ejpam-3131	47	31	if	if	SCONJ
ejpam-3131	47	32	x	x	PRON
ejpam-3131	47	33	is	be	AUX
ejpam-3131	47	34	i	i	NOUN
ejpam-3131	47	35	-	-	NOUN
ejpam-3131	47	36	compact	compact	ADJ
ejpam-3131	47	37	,	,	PUNCT
ejpam-3131	47	38	and	and	CCONJ
ejpam-3131	47	39	(	(	PUNCT
ejpam-3131	47	40	x	x	X
ejpam-3131	47	41	,	,	PUNCT
ejpam-3131	47	42	τ	τ	PROPN
ejpam-3131	47	43	,	,	PUNCT
ejpam-3131	47	44	i	i	PROPN
ejpam-3131	47	45	)	)	PUNCT
ejpam-3131	47	46	is	be	AUX
ejpam-3131	47	47	ρi	ρi	NOUN
ejpam-3131	47	48	-	-	ADJ
ejpam-3131	47	49	compact	compact	ADJ
ejpam-3131	47	50	if	if	SCONJ
ejpam-3131	47	51	x	x	PRON
ejpam-3131	47	52	is	be	AUX
ejpam-3131	47	53	ρi	ρi	NOUN
ejpam-3131	47	54	-	-	ADJ
ejpam-3131	47	55	compact	compact	ADJ
ejpam-3131	47	56	.	.	PUNCT
ejpam-3131	48	1	theorem	theorem	VERB
ejpam-3131	48	2	2.3	2.3	NUM
ejpam-3131	48	3	.	.	PUNCT
ejpam-3131	49	1	if	if	SCONJ
ejpam-3131	49	2	the	the	DET
ejpam-3131	49	3	ideal	ideal	ADJ
ejpam-3131	49	4	space	space	NOUN
ejpam-3131	49	5	(	(	PUNCT
ejpam-3131	49	6	x	x	X
ejpam-3131	49	7	,	,	PUNCT
ejpam-3131	49	8	τ	τ	PROPN
ejpam-3131	49	9	,	,	PUNCT
ejpam-3131	49	10	i	i	PROPN
ejpam-3131	49	11	)	)	PUNCT
ejpam-3131	49	12	is	be	AUX
ejpam-3131	49	13	ρi	ρi	NOUN
ejpam-3131	49	14	-	-	ADJ
ejpam-3131	49	15	compact	compact	ADJ
ejpam-3131	49	16	and	and	CCONJ
ejpam-3131	49	17	a	a	DET
ejpam-3131	49	18	⊆	⊆	NUM
ejpam-3131	49	19	x	x	SYM
ejpam-3131	49	20	we	we	PRON
ejpam-3131	49	21	have	have	VERB
ejpam-3131	49	22	that	that	PRON
ejpam-3131	49	23	:	:	PUNCT
ejpam-3131	49	24	(	(	PUNCT
ejpam-3131	49	25	1	1	X
ejpam-3131	49	26	)	)	PUNCT
ejpam-3131	49	27	if	if	SCONJ
ejpam-3131	49	28	a	a	PRON
ejpam-3131	49	29	is	be	AUX
ejpam-3131	49	30	closed	close	VERB
ejpam-3131	49	31	then	then	ADV
ejpam-3131	49	32	a	a	PRON
ejpam-3131	49	33	is	be	AUX
ejpam-3131	49	34	ρi	ρi	NOUN
ejpam-3131	49	35	-	-	ADJ
ejpam-3131	49	36	compact	compact	ADJ
ejpam-3131	49	37	.	.	PUNCT
ejpam-3131	50	1	(	(	PUNCT
ejpam-3131	50	2	2	2	X
ejpam-3131	50	3	)	)	PUNCT
ejpam-3131	50	4	if	if	SCONJ
ejpam-3131	50	5	a	a	PRON
ejpam-3131	50	6	is	be	AUX
ejpam-3131	50	7	ρig	ρig	NOUN
ejpam-3131	50	8	-	-	PUNCT
ejpam-3131	50	9	closed	close	VERB
ejpam-3131	50	10	then	then	ADV
ejpam-3131	50	11	a	a	PRON
ejpam-3131	50	12	is	be	AUX
ejpam-3131	50	13	ρi	ρi	NOUN
ejpam-3131	50	14	-	-	ADJ
ejpam-3131	50	15	compact	compact	ADJ
ejpam-3131	50	16	.	.	PUNCT
ejpam-3131	51	1	(	(	PUNCT
ejpam-3131	51	2	3	3	X
ejpam-3131	51	3	)	)	PUNCT
ejpam-3131	51	4	if	if	SCONJ
ejpam-3131	51	5	a	a	PRON
ejpam-3131	51	6	is	be	AUX
ejpam-3131	51	7	ig	ig	NOUN
ejpam-3131	51	8	-	-	VERB
ejpam-3131	51	9	closed	closed	ADJ
ejpam-3131	51	10	then	then	ADV
ejpam-3131	51	11	a	a	PRON
ejpam-3131	51	12	is	be	AUX
ejpam-3131	51	13	i	i	NOUN
ejpam-3131	51	14	-	-	PUNCT
ejpam-3131	51	15	compact	compact	ADJ
ejpam-3131	51	16	.	.	PUNCT
ejpam-3131	52	1	proof	proof	NOUN
ejpam-3131	52	2	.	.	PUNCT
ejpam-3131	53	1	(	(	PUNCT
ejpam-3131	53	2	1	1	X
ejpam-3131	53	3	)	)	PUNCT
ejpam-3131	53	4	let	let	AUX
ejpam-3131	53	5	{	{	PUNCT
ejpam-3131	53	6	vα}α∈λ	vα}α∈λ	ADV
ejpam-3131	53	7	be	be	AUX
ejpam-3131	53	8	a	a	DET
ejpam-3131	53	9	collection	collection	NOUN
ejpam-3131	53	10	of	of	ADP
ejpam-3131	53	11	open	open	ADJ
ejpam-3131	53	12	sets	set	NOUN
ejpam-3131	53	13	of	of	ADP
ejpam-3131	53	14	x	x	PUNCT
ejpam-3131	53	15	such	such	ADJ
ejpam-3131	53	16	that	that	SCONJ
ejpam-3131	53	17	a\	a\	NOUN
ejpam-3131	53	18	∪	∪	ADP
ejpam-3131	53	19	α∈λ	α∈λ	NOUN
ejpam-3131	53	20	vα	vα	ADP
ejpam-3131	53	21	∈	∈	PROPN
ejpam-3131	54	1	i	i	PRON
ejpam-3131	54	2	,	,	PUNCT
ejpam-3131	54	3	this	this	PRON
ejpam-3131	54	4	is	be	AUX
ejpam-3131	54	5	,	,	PUNCT
ejpam-3131	54	6	x\	x\	PROPN
ejpam-3131	54	7	[	[	PUNCT
ejpam-3131	54	8	(	(	PUNCT
ejpam-3131	54	9	x\a	x\a	PROPN
ejpam-3131	54	10	)	)	PUNCT
ejpam-3131	54	11	∪	∪	ADP
ejpam-3131	54	12	∪	∪	ADJ
ejpam-3131	54	13	α∈λ	α∈λ	NOUN
ejpam-3131	54	14	vα	vα	X
ejpam-3131	54	15	]	]	PUNCT
ejpam-3131	54	16	∈	∈	PROPN
ejpam-3131	54	17	i.	i.	NOUN
ejpam-3131	54	18	there	there	PRON
ejpam-3131	54	19	exists	exist	VERB
ejpam-3131	54	20	λ0	λ0	NOUN
ejpam-3131	54	21	⊆	⊆	NUM
ejpam-3131	54	22	λ	λ	PROPN
ejpam-3131	54	23	,	,	PUNCT
ejpam-3131	54	24	finite	finite	NOUN
ejpam-3131	54	25	,	,	PUNCT
ejpam-3131	54	26	with	with	ADP
ejpam-3131	54	27	x\	x\	PROPN
ejpam-3131	54	28	[	[	PUNCT
ejpam-3131	54	29	(	(	PUNCT
ejpam-3131	54	30	x\a	x\a	PROPN
ejpam-3131	54	31	)	)	PUNCT
ejpam-3131	54	32	∪	∪	X
ejpam-3131	54	33	∪	∪	ADJ
ejpam-3131	54	34	α∈λ0	α∈λ0	NOUN
ejpam-3131	54	35	vα	vα	X
ejpam-3131	54	36	]	]	X
ejpam-3131	54	37	∈	∈	PROPN
ejpam-3131	55	1	i	i	PRON
ejpam-3131	55	2	,	,	PUNCT
ejpam-3131	55	3	this	this	PRON
ejpam-3131	55	4	is	be	AUX
ejpam-3131	55	5	,	,	PUNCT
ejpam-3131	55	6	a\	a\	NOUN
ejpam-3131	55	7	∪	∪	ADJ
ejpam-3131	55	8	α∈λ0	α∈λ0	NOUN
ejpam-3131	55	9	vα	vα	ADP
ejpam-3131	55	10	∈	∈	PROPN
ejpam-3131	55	11	i.	i.	NOUN
ejpam-3131	55	12	(	(	PUNCT
ejpam-3131	55	13	2	2	X
ejpam-3131	55	14	)	)	PUNCT
ejpam-3131	55	15	let	let	AUX
ejpam-3131	55	16	{	{	PUNCT
ejpam-3131	55	17	vα}α∈λ	vα}α∈λ	ADV
ejpam-3131	55	18	be	be	AUX
ejpam-3131	55	19	a	a	DET
ejpam-3131	55	20	collection	collection	NOUN
ejpam-3131	55	21	of	of	ADP
ejpam-3131	55	22	open	open	ADJ
ejpam-3131	55	23	sets	set	NOUN
ejpam-3131	55	24	of	of	ADP
ejpam-3131	55	25	x	x	PUNCT
ejpam-3131	55	26	such	such	ADJ
ejpam-3131	55	27	that	that	SCONJ
ejpam-3131	55	28	a\	a\	NOUN
ejpam-3131	55	29	∪	∪	ADP
ejpam-3131	55	30	α∈λ	α∈λ	NOUN
ejpam-3131	55	31	vα	vα	ADP
ejpam-3131	55	32	∈	∈	PROPN
ejpam-3131	55	33	i.	i.	NOUN
ejpam-3131	55	34	since	since	SCONJ
ejpam-3131	55	35	a	a	PRON
ejpam-3131	55	36	is	be	AUX
ejpam-3131	55	37	ρig	ρig	NOUN
ejpam-3131	55	38	-	-	PUNCT
ejpam-3131	55	39	closed	closed	ADJ
ejpam-3131	55	40	we	we	PRON
ejpam-3131	55	41	have	have	VERB
ejpam-3131	55	42	that	that	SCONJ
ejpam-3131	55	43	a\	a\	NOUN
ejpam-3131	55	44	∪	∪	ADJ
ejpam-3131	55	45	α∈λ	α∈λ	NOUN
ejpam-3131	55	46	vα	vα	ADP
ejpam-3131	55	47	∈	∈	PROPN
ejpam-3131	55	48	i.	i.	NOUN
ejpam-3131	55	49	given	give	VERB
ejpam-3131	55	50	that	that	SCONJ
ejpam-3131	55	51	a	a	PRON
ejpam-3131	55	52	is	be	AUX
ejpam-3131	55	53	ρi	ρi	NOUN
ejpam-3131	55	54	-	-	ADJ
ejpam-3131	55	55	compact	compact	ADJ
ejpam-3131	55	56	,	,	PUNCT
ejpam-3131	55	57	there	there	PRON
ejpam-3131	55	58	exists	exist	VERB
ejpam-3131	55	59	λ0	λ0	NOUN
ejpam-3131	55	60	⊆	⊆	NUM
ejpam-3131	55	61	λ	λ	PROPN
ejpam-3131	55	62	,	,	PUNCT
ejpam-3131	55	63	finite	finite	NOUN
ejpam-3131	55	64	,	,	PUNCT
ejpam-3131	55	65	with	with	ADP
ejpam-3131	55	66	a\	a\	NOUN
ejpam-3131	55	67	∪	∪	ADJ
ejpam-3131	55	68	α∈λ0	α∈λ0	NOUN
ejpam-3131	55	69	vα	vα	ADP
ejpam-3131	55	70	∈	∈	NOUN
ejpam-3131	55	71	i.	i.	NOUN
ejpam-3131	55	72	hence	hence	ADV
ejpam-3131	55	73	a\	a\	ADV
ejpam-3131	55	74	∪	∪	ADP
ejpam-3131	55	75	α∈λ0	α∈λ0	NOUN
ejpam-3131	55	76	vα	vα	ADP
ejpam-3131	55	77	∈	∈	PROPN
ejpam-3131	55	78	i.	i.	NOUN
ejpam-3131	55	79	(	(	PUNCT
ejpam-3131	55	80	3	3	X
ejpam-3131	55	81	)	)	PUNCT
ejpam-3131	55	82	let	let	AUX
ejpam-3131	55	83	{	{	PUNCT
ejpam-3131	55	84	vα}α∈λ	vα}α∈λ	ADV
ejpam-3131	55	85	be	be	AUX
ejpam-3131	55	86	a	a	DET
ejpam-3131	55	87	collection	collection	NOUN
ejpam-3131	55	88	of	of	ADP
ejpam-3131	55	89	open	open	ADJ
ejpam-3131	55	90	sets	set	NOUN
ejpam-3131	55	91	of	of	ADP
ejpam-3131	55	92	x	x	SYM
ejpam-3131	55	93	such	such	ADJ
ejpam-3131	55	94	that	that	SCONJ
ejpam-3131	55	95	a	a	DET
ejpam-3131	55	96	⊆	⊆	NUM
ejpam-3131	55	97	∪	∪	ADJ
ejpam-3131	55	98	α∈λ	α∈λ	NOUN
ejpam-3131	55	99	vα	vα	PROPN
ejpam-3131	55	100	.	.	PUNCT
ejpam-3131	56	1	given	give	VERB
ejpam-3131	56	2	that	that	SCONJ
ejpam-3131	56	3	a	a	PRON
ejpam-3131	56	4	is	be	AUX
ejpam-3131	56	5	ig	ig	PROPN
ejpam-3131	56	6	-	-	PUNCT
ejpam-3131	56	7	closed	closed	ADJ
ejpam-3131	56	8	we	we	PRON
ejpam-3131	56	9	have	have	VERB
ejpam-3131	56	10	that	that	SCONJ
ejpam-3131	56	11	a\	a\	NOUN
ejpam-3131	56	12	∪	∪	ADJ
ejpam-3131	56	13	α∈λ	α∈λ	NOUN
ejpam-3131	56	14	vα	vα	ADP
ejpam-3131	56	15	∈	∈	PROPN
ejpam-3131	56	16	i.	i.	NOUN
ejpam-3131	56	17	but	but	CCONJ
ejpam-3131	56	18	a	a	PRON
ejpam-3131	56	19	is	be	AUX
ejpam-3131	56	20	ρi	ρi	NOUN
ejpam-3131	56	21	-	-	ADJ
ejpam-3131	56	22	compact	compact	ADJ
ejpam-3131	56	23	,	,	PUNCT
ejpam-3131	56	24	and	and	CCONJ
ejpam-3131	56	25	so	so	ADV
ejpam-3131	56	26	there	there	PRON
ejpam-3131	56	27	exists	exist	VERB
ejpam-3131	56	28	λ0	λ0	NOUN
ejpam-3131	56	29	⊆	⊆	NUM
ejpam-3131	56	30	λ	λ	PROPN
ejpam-3131	56	31	,	,	PUNCT
ejpam-3131	56	32	finite	finite	NOUN
ejpam-3131	56	33	,	,	PUNCT
ejpam-3131	56	34	with	with	ADP
ejpam-3131	56	35	a\	a\	NOUN
ejpam-3131	56	36	∪	∪	ADJ
ejpam-3131	56	37	α∈λ0	α∈λ0	NOUN
ejpam-3131	56	38	vα	vα	ADP
ejpam-3131	56	39	∈	∈	PROPN
ejpam-3131	56	40	i.	i.	NOUN
ejpam-3131	56	41	thus	thus	ADV
ejpam-3131	56	42	a\	a\	ADV
ejpam-3131	56	43	∪	∪	ADJ
ejpam-3131	56	44	α∈λ0	α∈λ0	NOUN
ejpam-3131	56	45	vα	vα	ADP
ejpam-3131	56	46	∈	∈	PROPN
ejpam-3131	56	47	i.	i.	NOUN
ejpam-3131	56	48	□	□	PUNCT
ejpam-3131	56	49	we	we	PRON
ejpam-3131	56	50	recall	recall	VERB
ejpam-3131	56	51	that	that	SCONJ
ejpam-3131	56	52	an	an	DET
ejpam-3131	56	53	ideal	ideal	ADJ
ejpam-3131	56	54	space	space	NOUN
ejpam-3131	56	55	(	(	PUNCT
ejpam-3131	56	56	x	x	X
ejpam-3131	56	57	,	,	PUNCT
ejpam-3131	56	58	τ	τ	PROPN
ejpam-3131	56	59	,	,	PUNCT
ejpam-3131	56	60	i	i	PROPN
ejpam-3131	56	61	)	)	PUNCT
ejpam-3131	56	62	is	be	AUX
ejpam-3131	56	63	said	say	VERB
ejpam-3131	56	64	to	to	PART
ejpam-3131	56	65	be	be	AUX
ejpam-3131	56	66	ig	ig	NOUN
ejpam-3131	56	67	-	-	ADJ
ejpam-3131	56	68	normal	normal	ADJ
ejpam-3131	56	69	if	if	SCONJ
ejpam-3131	56	70	for	for	ADP
ejpam-3131	56	71	every	every	DET
ejpam-3131	56	72	pair	pair	NOUN
ejpam-3131	56	73	of	of	ADP
ejpam-3131	56	74	disjoint	disjoint	NOUN
ejpam-3131	56	75	g	g	NOUN
ejpam-3131	56	76	-	-	PUNCT
ejpam-3131	56	77	closed	close	VERB
ejpam-3131	56	78	subsets	subset	NOUN
ejpam-3131	56	79	f	f	PROPN
ejpam-3131	56	80	and	and	CCONJ
ejpam-3131	56	81	g	g	PROPN
ejpam-3131	56	82	of	of	ADP
ejpam-3131	56	83	x	x	SYM
ejpam-3131	56	84	,	,	PUNCT
ejpam-3131	56	85	there	there	PRON
ejpam-3131	56	86	exist	exist	VERB
ejpam-3131	56	87	disjoint	disjoint	ADJ
ejpam-3131	56	88	open	open	ADJ
ejpam-3131	56	89	sets	set	NOUN
ejpam-3131	56	90	u	u	NOUN
ejpam-3131	56	91	and	and	CCONJ
ejpam-3131	56	92	v	v	ADP
ejpam-3131	56	93	such	such	ADJ
ejpam-3131	57	1	that	that	SCONJ
ejpam-3131	57	2	f\u	f\u	PROPN
ejpam-3131	57	3	∈	∈	PROPN
ejpam-3131	58	1	i	i	PRON
ejpam-3131	58	2	and	and	CCONJ
ejpam-3131	58	3	g\v	g\v	PROPN
ejpam-3131	58	4	∈	∈	PROPN
ejpam-3131	58	5	i.	i.	NOUN
ejpam-3131	58	6	renukadevi	renukadevi	PROPN
ejpam-3131	58	7	-	-	PUNCT
ejpam-3131	58	8	sivaraj	sivaraj	PROPN
ejpam-3131	58	9	have	have	AUX
ejpam-3131	58	10	shown	show	VERB
ejpam-3131	58	11	that	that	SCONJ
ejpam-3131	58	12	if	if	SCONJ
ejpam-3131	58	13	(	(	PUNCT
ejpam-3131	58	14	x	x	NOUN
ejpam-3131	58	15	,	,	PUNCT
ejpam-3131	58	16	τ	τ	PROPN
ejpam-3131	58	17	,	,	PUNCT
ejpam-3131	58	18	i	i	PROPN
ejpam-3131	58	19	)	)	PUNCT
ejpam-3131	58	20	is	be	AUX
ejpam-3131	58	21	i	i	NOUN
ejpam-3131	58	22	-	-	ADJ
ejpam-3131	58	23	compact	compact	ADJ
ejpam-3131	58	24	and	and	CCONJ
ejpam-3131	58	25	(	(	PUNCT
ejpam-3131	58	26	x	x	NOUN
ejpam-3131	58	27	,	,	PUNCT
ejpam-3131	58	28	τ	τ	X
ejpam-3131	58	29	)	)	PUNCT
ejpam-3131	58	30	is	be	AUX
ejpam-3131	58	31	t2	t2	NOUN
ejpam-3131	58	32	then	then	ADV
ejpam-3131	58	33	(	(	PUNCT
ejpam-3131	58	34	x	x	X
ejpam-3131	58	35	,	,	PUNCT
ejpam-3131	58	36	τ	τ	PROPN
ejpam-3131	58	37	,	,	PUNCT
ejpam-3131	58	38	i	i	PROPN
ejpam-3131	58	39	)	)	PUNCT
ejpam-3131	58	40	is	be	AUX
ejpam-3131	58	41	i	i	NOUN
ejpam-3131	58	42	-	-	PUNCT
ejpam-3131	58	43	normal	normal	ADJ
ejpam-3131	58	44	.	.	PUNCT
ejpam-3131	59	1	in	in	ADP
ejpam-3131	59	2	contrast	contrast	NOUN
ejpam-3131	59	3	we	we	PRON
ejpam-3131	59	4	have	have	VERB
ejpam-3131	59	5	the	the	DET
ejpam-3131	59	6	following	follow	VERB
ejpam-3131	59	7	result	result	NOUN
ejpam-3131	59	8	.	.	PUNCT
ejpam-3131	60	1	theorem	theorem	VERB
ejpam-3131	60	2	2.4	2.4	NUM
ejpam-3131	60	3	.	.	PUNCT
ejpam-3131	61	1	if	if	SCONJ
ejpam-3131	61	2	(	(	PUNCT
ejpam-3131	61	3	x	x	X
ejpam-3131	61	4	,	,	PUNCT
ejpam-3131	61	5	τ	τ	PROPN
ejpam-3131	61	6	,	,	PUNCT
ejpam-3131	61	7	i	i	PROPN
ejpam-3131	61	8	)	)	PUNCT
ejpam-3131	61	9	is	be	AUX
ejpam-3131	61	10	ρi	ρi	NOUN
ejpam-3131	61	11	-	-	ADJ
ejpam-3131	61	12	compact	compact	ADJ
ejpam-3131	61	13	and	and	CCONJ
ejpam-3131	61	14	(	(	PUNCT
ejpam-3131	61	15	x	x	NOUN
ejpam-3131	61	16	,	,	PUNCT
ejpam-3131	61	17	τ	τ	X
ejpam-3131	61	18	)	)	PUNCT
ejpam-3131	61	19	is	be	AUX
ejpam-3131	61	20	t2	t2	NOUN
ejpam-3131	61	21	then	then	ADV
ejpam-3131	61	22	(	(	PUNCT
ejpam-3131	61	23	x	x	X
ejpam-3131	61	24	,	,	PUNCT
ejpam-3131	61	25	τ	τ	PROPN
ejpam-3131	61	26	,	,	PUNCT
ejpam-3131	61	27	i	i	PROPN
ejpam-3131	61	28	)	)	PUNCT
ejpam-3131	61	29	is	be	AUX
ejpam-3131	61	30	ig	ig	NOUN
ejpam-3131	61	31	-	-	ADJ
ejpam-3131	61	32	normal	normal	ADJ
ejpam-3131	61	33	.	.	PUNCT
ejpam-3131	62	1	proof	proof	NOUN
ejpam-3131	62	2	.	.	PUNCT
ejpam-3131	63	1	suppose	suppose	VERB
ejpam-3131	63	2	that	that	SCONJ
ejpam-3131	63	3	f	f	PROPN
ejpam-3131	63	4	and	and	CCONJ
ejpam-3131	63	5	g	g	PROPN
ejpam-3131	63	6	are	be	AUX
ejpam-3131	63	7	disjoint	disjoint	ADJ
ejpam-3131	63	8	g	g	NOUN
ejpam-3131	63	9	-	-	PUNCT
ejpam-3131	63	10	closed	close	VERB
ejpam-3131	63	11	sets	set	NOUN
ejpam-3131	63	12	.	.	PUNCT
ejpam-3131	64	1	it	it	PRON
ejpam-3131	64	2	is	be	AUX
ejpam-3131	64	3	noted	note	VERB
ejpam-3131	64	4	that	that	SCONJ
ejpam-3131	64	5	,	,	PUNCT
ejpam-3131	64	6	by	by	ADP
ejpam-3131	64	7	theorem	theorem	NOUN
ejpam-3131	64	8	2.3	2.3	NUM
ejpam-3131	64	9	,	,	PUNCT
ejpam-3131	64	10	f	f	PROPN
ejpam-3131	64	11	and	and	CCONJ
ejpam-3131	64	12	g	g	PROPN
ejpam-3131	64	13	are	be	AUX
ejpam-3131	64	14	i	i	NOUN
ejpam-3131	64	15	-	-	ADJ
ejpam-3131	64	16	compact	compact	ADJ
ejpam-3131	64	17	subsets	subset	NOUN
ejpam-3131	64	18	of	of	ADP
ejpam-3131	64	19	x.	x.	NOUN
ejpam-3131	64	20	let	let	VERB
ejpam-3131	64	21	g	g	PROPN
ejpam-3131	64	22	∈	∈	PROPN
ejpam-3131	64	23	g	g	PROPN
ejpam-3131	64	24	,	,	PUNCT
ejpam-3131	64	25	arbitrary	arbitrary	ADJ
ejpam-3131	64	26	.	.	PUNCT
ejpam-3131	65	1	for	for	ADP
ejpam-3131	65	2	each	each	DET
ejpam-3131	65	3	f	f	PROPN
ejpam-3131	65	4	∈	∈	PROPN
ejpam-3131	65	5	f	f	NOUN
ejpam-3131	65	6	there	there	PRON
ejpam-3131	65	7	are	be	VERB
ejpam-3131	65	8	disjoint	disjoint	NOUN
ejpam-3131	65	9	uf	uf	PROPN
ejpam-3131	65	10	∈	∈	PROPN
ejpam-3131	65	11	τ	τ	X
ejpam-3131	65	12	and	and	CCONJ
ejpam-3131	65	13	vf	vf	X
ejpam-3131	65	14	∈	∈	PROPN
ejpam-3131	65	15	τ	τ	X
ejpam-3131	65	16	such	such	ADJ
ejpam-3131	65	17	that	that	SCONJ
ejpam-3131	65	18	f	f	PROPN
ejpam-3131	65	19	∈	∈	PROPN
ejpam-3131	65	20	uf	uf	PROPN
ejpam-3131	65	21	and	and	CCONJ
ejpam-3131	65	22	g	g	PROPN
ejpam-3131	65	23	∈	∈	PROPN
ejpam-3131	65	24	vf	vf	X
ejpam-3131	65	25	.	.	PUNCT
ejpam-3131	66	1	given	give	VERB
ejpam-3131	66	2	that	that	SCONJ
ejpam-3131	66	3	f	f	PROPN
ejpam-3131	66	4	⊆	⊆	NUM
ejpam-3131	66	5	∪	∪	VERB
ejpam-3131	66	6	f∈f	f∈f	NOUN
ejpam-3131	66	7	uf	uf	NOUN
ejpam-3131	66	8	and	and	CCONJ
ejpam-3131	66	9	n.r	n.r	PROPN
ejpam-3131	66	10	.	.	PROPN
ejpam-3131	66	11	pachón	pachón	PROPN
ejpam-3131	66	12	/	/	SYM
ejpam-3131	66	13	eur	eur	PROPN
ejpam-3131	66	14	.	.	PUNCT
ejpam-3131	67	1	j.	j.	PROPN
ejpam-3131	67	2	pure	pure	PROPN
ejpam-3131	67	3	appl	appl	PROPN
ejpam-3131	67	4	.	.	PROPN
ejpam-3131	67	5	math	math	PROPN
ejpam-3131	67	6	,	,	PUNCT
ejpam-3131	67	7	11	11	NUM
ejpam-3131	67	8	(	(	PUNCT
ejpam-3131	67	9	1	1	NUM
ejpam-3131	67	10	)	)	PUNCT
ejpam-3131	67	11	(	(	PUNCT
ejpam-3131	67	12	2018	2018	NUM
ejpam-3131	67	13	)	)	PUNCT
ejpam-3131	67	14	,	,	PUNCT
ejpam-3131	67	15	299	299	NUM
ejpam-3131	67	16	-	-	SYM
ejpam-3131	67	17	314	314	NUM
ejpam-3131	67	18	302	302	NUM
ejpam-3131	67	19	f	f	NOUN
ejpam-3131	67	20	is	be	AUX
ejpam-3131	67	21	i	i	NOUN
ejpam-3131	67	22	-	-	PUNCT
ejpam-3131	67	23	compact	compact	ADJ
ejpam-3131	67	24	,	,	PUNCT
ejpam-3131	67	25	there	there	PRON
ejpam-3131	67	26	exists	exist	VERB
ejpam-3131	67	27	f0	f0	PROPN
ejpam-3131	67	28	⊆	⊆	NUM
ejpam-3131	67	29	f	f	PROPN
ejpam-3131	67	30	,	,	PUNCT
ejpam-3131	67	31	finite	finite	PROPN
ejpam-3131	67	32	,	,	PUNCT
ejpam-3131	67	33	with	with	ADP
ejpam-3131	67	34	f\	f\	SYM
ejpam-3131	67	35	∪	∪	ADP
ejpam-3131	67	36	f∈f0	f∈f0	PROPN
ejpam-3131	67	37	uf	uf	PROPN
ejpam-3131	67	38	∈	∈	PROPN
ejpam-3131	67	39	i.	i.	NOUN
ejpam-3131	67	40	let	let	VERB
ejpam-3131	67	41	tg	tg	PROPN
ejpam-3131	67	42	=	=	PUNCT
ejpam-3131	67	43	∪	∪	ADP
ejpam-3131	67	44	f∈f0	f∈f0	PROPN
ejpam-3131	67	45	uf	uf	PROPN
ejpam-3131	67	46	and	and	CCONJ
ejpam-3131	67	47	wg	wg	PROPN
ejpam-3131	67	48	=	=	NOUN
ejpam-3131	67	49	∩	∩	NOUN
ejpam-3131	67	50	f∈f0	f∈f0	X
ejpam-3131	67	51	vf	vf	X
ejpam-3131	67	52	.	.	PUNCT
ejpam-3131	68	1	it	it	PRON
ejpam-3131	68	2	is	be	AUX
ejpam-3131	68	3	noted	note	VERB
ejpam-3131	68	4	that	that	SCONJ
ejpam-3131	68	5	tg	tg	PROPN
ejpam-3131	68	6	∩wg	∩wg	NOUN
ejpam-3131	68	7	=	=	PUNCT
ejpam-3131	68	8	∅	∅	NOUN
ejpam-3131	68	9	and	and	CCONJ
ejpam-3131	68	10	f\tg	f\tg	PROPN
ejpam-3131	68	11	∈	∈	PROPN
ejpam-3131	68	12	i.	i.	NOUN
ejpam-3131	68	13	now	now	ADV
ejpam-3131	68	14	,	,	PUNCT
ejpam-3131	68	15	since	since	SCONJ
ejpam-3131	68	16	g	g	PROPN
ejpam-3131	68	17	⊆	⊆	NUM
ejpam-3131	68	18	∪	∪	ADP
ejpam-3131	68	19	g∈g	g∈g	PROPN
ejpam-3131	68	20	wg	wg	PROPN
ejpam-3131	68	21	and	and	CCONJ
ejpam-3131	68	22	g	g	PROPN
ejpam-3131	68	23	is	be	AUX
ejpam-3131	68	24	i	i	NOUN
ejpam-3131	68	25	-	-	PUNCT
ejpam-3131	68	26	compact	compact	ADJ
ejpam-3131	68	27	,	,	PUNCT
ejpam-3131	68	28	there	there	PRON
ejpam-3131	68	29	exists	exist	VERB
ejpam-3131	68	30	g0	g0	ADJ
ejpam-3131	68	31	⊆	⊆	NUM
ejpam-3131	68	32	g	g	NOUN
ejpam-3131	68	33	,	,	PUNCT
ejpam-3131	68	34	finite	finite	NOUN
ejpam-3131	68	35	,	,	PUNCT
ejpam-3131	68	36	with	with	ADP
ejpam-3131	68	37	g\	g\	PRON
ejpam-3131	68	38	∪	∪	ADJ
ejpam-3131	68	39	g∈g0	g∈g0	NOUN
ejpam-3131	68	40	wg	wg	PROPN
ejpam-3131	68	41	∈	∈	PROPN
ejpam-3131	68	42	i.	i.	NOUN
ejpam-3131	68	43	if	if	SCONJ
ejpam-3131	68	44	v	v	NOUN
ejpam-3131	68	45	=	=	SYM
ejpam-3131	68	46	∪	∪	ADP
ejpam-3131	68	47	g∈g0	g∈g0	ADJ
ejpam-3131	68	48	wg	wg	PROPN
ejpam-3131	68	49	and	and	CCONJ
ejpam-3131	68	50	u	u	NOUN
ejpam-3131	68	51	=	=	NOUN
ejpam-3131	68	52	∩	∩	NOUN
ejpam-3131	68	53	g∈g0	g∈g0	NOUN
ejpam-3131	69	1	tg	tg	PROPN
ejpam-3131	69	2	then	then	ADV
ejpam-3131	69	3	u	u	PROPN
ejpam-3131	69	4	and	and	CCONJ
ejpam-3131	69	5	v	v	NOUN
ejpam-3131	69	6	are	be	AUX
ejpam-3131	69	7	disjoint	disjoint	NOUN
ejpam-3131	69	8	,	,	PUNCT
ejpam-3131	69	9	g\v	g\v	PROPN
ejpam-3131	69	10	∈	∈	DET
ejpam-3131	69	11	i	i	PRON
ejpam-3131	69	12	and	and	CCONJ
ejpam-3131	69	13	f\u	f\u	AUX
ejpam-3131	69	14	=	=	SYM
ejpam-3131	69	15	∪	∪	ADJ
ejpam-3131	69	16	g∈g0	g∈g0	NOUN
ejpam-3131	69	17	(	(	PUNCT
ejpam-3131	69	18	x\tg	x\tg	PROPN
ejpam-3131	69	19	)	)	PUNCT
ejpam-3131	69	20	∈	∈	PROPN
ejpam-3131	69	21	i.	i.	NOUN
ejpam-3131	69	22	□	□	PUNCT
ejpam-3131	69	23	if	if	SCONJ
ejpam-3131	69	24	i	i	PRON
ejpam-3131	69	25	is	be	AUX
ejpam-3131	69	26	an	an	DET
ejpam-3131	69	27	ideal	ideal	NOUN
ejpam-3131	69	28	in	in	ADP
ejpam-3131	69	29	x	x	X
ejpam-3131	69	30	and	and	CCONJ
ejpam-3131	69	31	b	b	X
ejpam-3131	69	32	⊆	⊆	NUM
ejpam-3131	69	33	x	x	SYM
ejpam-3131	69	34	,	,	PUNCT
ejpam-3131	69	35	it	it	PRON
ejpam-3131	69	36	is	be	AUX
ejpam-3131	69	37	easy	easy	ADJ
ejpam-3131	69	38	to	to	PART
ejpam-3131	69	39	see	see	VERB
ejpam-3131	69	40	that	that	SCONJ
ejpam-3131	69	41	the	the	DET
ejpam-3131	69	42	set	set	NOUN
ejpam-3131	69	43	ib	ib	NOUN
ejpam-3131	69	44	=	=	PUNCT
ejpam-3131	69	45	{	{	PUNCT
ejpam-3131	69	46	i	i	PRON
ejpam-3131	69	47	∩b	∩b	VERB
ejpam-3131	69	48	:	:	PUNCT
ejpam-3131	69	49	i	i	PRON
ejpam-3131	69	50	∈	∈	VERB
ejpam-3131	69	51	i	i	PRON
ejpam-3131	69	52	}	}	PUNCT
ejpam-3131	69	53	is	be	AUX
ejpam-3131	69	54	an	an	DET
ejpam-3131	69	55	ideal	ideal	NOUN
ejpam-3131	69	56	in	in	ADP
ejpam-3131	69	57	b.	b.	PROPN
ejpam-3131	69	58	theorem	theorem	PROPN
ejpam-3131	69	59	2.5	2.5	NUM
ejpam-3131	69	60	.	.	PUNCT
ejpam-3131	70	1	let	let	VERB
ejpam-3131	70	2	(	(	PUNCT
ejpam-3131	70	3	x	x	X
ejpam-3131	70	4	,	,	PUNCT
ejpam-3131	70	5	τ	τ	PROPN
ejpam-3131	70	6	,	,	PUNCT
ejpam-3131	70	7	i	i	PRON
ejpam-3131	70	8	)	)	PUNCT
ejpam-3131	70	9	be	be	VERB
ejpam-3131	70	10	an	an	DET
ejpam-3131	70	11	ideal	ideal	ADJ
ejpam-3131	70	12	space	space	NOUN
ejpam-3131	70	13	.	.	PUNCT
ejpam-3131	71	1	if	if	SCONJ
ejpam-3131	71	2	a	a	DET
ejpam-3131	71	3	⊆	⊆	NUM
ejpam-3131	71	4	x	x	NOUN
ejpam-3131	71	5	and	and	CCONJ
ejpam-3131	71	6	b	b	NOUN
ejpam-3131	71	7	⊆	⊆	NUM
ejpam-3131	71	8	x	x	PUNCT
ejpam-3131	71	9	then	then	ADV
ejpam-3131	71	10	:	:	PUNCT
ejpam-3131	71	11	(	(	PUNCT
ejpam-3131	71	12	1	1	X
ejpam-3131	71	13	)	)	PUNCT
ejpam-3131	71	14	if	if	SCONJ
ejpam-3131	71	15	a	a	PRON
ejpam-3131	71	16	and	and	CCONJ
ejpam-3131	71	17	b	b	NOUN
ejpam-3131	71	18	are	be	AUX
ejpam-3131	71	19	ρig	ρig	ADV
ejpam-3131	71	20	-	-	PUNCT
ejpam-3131	71	21	closed	close	VERB
ejpam-3131	71	22	then	then	ADV
ejpam-3131	71	23	a	a	DET
ejpam-3131	71	24	∪b	∪b	PRON
ejpam-3131	71	25	is	be	AUX
ejpam-3131	71	26	ρig	ρig	ADV
ejpam-3131	71	27	-	-	PUNCT
ejpam-3131	71	28	closed	closed	ADJ
ejpam-3131	71	29	.	.	PUNCT
ejpam-3131	72	1	(	(	PUNCT
ejpam-3131	72	2	2	2	X
ejpam-3131	72	3	)	)	PUNCT
ejpam-3131	72	4	a	a	PRON
ejpam-3131	72	5	is	be	AUX
ejpam-3131	72	6	ρig	ρig	NOUN
ejpam-3131	72	7	-	-	PUNCT
ejpam-3131	72	8	closed	close	VERB
ejpam-3131	72	9	if	if	SCONJ
ejpam-3131	72	10	and	and	CCONJ
ejpam-3131	72	11	only	only	ADV
ejpam-3131	72	12	if	if	SCONJ
ejpam-3131	72	13	,	,	PUNCT
ejpam-3131	72	14	for	for	ADP
ejpam-3131	72	15	each	each	DET
ejpam-3131	72	16	closed	close	VERB
ejpam-3131	72	17	set	set	VERB
ejpam-3131	72	18	f	f	NOUN
ejpam-3131	72	19	,	,	PUNCT
ejpam-3131	72	20	if	if	SCONJ
ejpam-3131	72	21	f\	f\	PRON
ejpam-3131	73	1	(	(	PUNCT
ejpam-3131	73	2	a\a	a\a	X
ejpam-3131	73	3	)	)	PUNCT
ejpam-3131	73	4	∈	∈	PROPN
ejpam-3131	74	1	i	i	PRON
ejpam-3131	74	2	then	then	ADV
ejpam-3131	74	3	f	f	PROPN
ejpam-3131	74	4	∈	∈	PROPN
ejpam-3131	74	5	i.	i.	NOUN
ejpam-3131	74	6	(	(	PUNCT
ejpam-3131	74	7	3	3	X
ejpam-3131	74	8	)	)	PUNCT
ejpam-3131	74	9	if	if	SCONJ
ejpam-3131	74	10	a\b	a\b	ADP
ejpam-3131	74	11	∈	∈	PROPN
ejpam-3131	74	12	i	i	PRON
ejpam-3131	74	13	,	,	PUNCT
ejpam-3131	74	14	b\a	b\a	NOUN
ejpam-3131	74	15	∈	∈	PROPN
ejpam-3131	75	1	i	i	PRON
ejpam-3131	75	2	and	and	CCONJ
ejpam-3131	75	3	a	a	PRON
ejpam-3131	75	4	is	be	AUX
ejpam-3131	75	5	ρig	ρig	NOUN
ejpam-3131	75	6	-	-	PUNCT
ejpam-3131	75	7	closed	closed	ADJ
ejpam-3131	75	8	then	then	ADV
ejpam-3131	75	9	b	b	NOUN
ejpam-3131	75	10	is	be	AUX
ejpam-3131	75	11	ρig	ρig	ADV
ejpam-3131	75	12	-	-	PUNCT
ejpam-3131	75	13	closed	closed	ADJ
ejpam-3131	75	14	.	.	PUNCT
ejpam-3131	76	1	(	(	PUNCT
ejpam-3131	76	2	4	4	X
ejpam-3131	76	3	)	)	PUNCT
ejpam-3131	76	4	if	if	SCONJ
ejpam-3131	76	5	a	a	DET
ejpam-3131	76	6	⊆	⊆	NUM
ejpam-3131	76	7	b	b	SYM
ejpam-3131	76	8	⊆	⊆	NUM
ejpam-3131	76	9	a	a	PRON
ejpam-3131	76	10	and	and	CCONJ
ejpam-3131	76	11	a	a	PRON
ejpam-3131	76	12	is	be	AUX
ejpam-3131	76	13	ρig	ρig	NOUN
ejpam-3131	76	14	-	-	PUNCT
ejpam-3131	76	15	closed	closed	ADJ
ejpam-3131	76	16	,	,	PUNCT
ejpam-3131	76	17	then	then	ADV
ejpam-3131	76	18	b	b	PROPN
ejpam-3131	76	19	is	be	AUX
ejpam-3131	76	20	ρig	ρig	ADV
ejpam-3131	76	21	-	-	PUNCT
ejpam-3131	76	22	closed	closed	ADJ
ejpam-3131	76	23	.	.	PUNCT
ejpam-3131	77	1	(	(	PUNCT
ejpam-3131	77	2	5	5	X
ejpam-3131	77	3	)	)	PUNCT
ejpam-3131	77	4	if	if	SCONJ
ejpam-3131	77	5	a	a	PRON
ejpam-3131	77	6	is	be	AUX
ejpam-3131	77	7	ρig	ρig	NOUN
ejpam-3131	77	8	-	-	PUNCT
ejpam-3131	77	9	closed	closed	ADJ
ejpam-3131	77	10	and	and	CCONJ
ejpam-3131	77	11	b	b	NOUN
ejpam-3131	77	12	is	be	AUX
ejpam-3131	77	13	closed	closed	ADJ
ejpam-3131	77	14	,	,	PUNCT
ejpam-3131	77	15	then	then	ADV
ejpam-3131	77	16	a	a	DET
ejpam-3131	77	17	∩b	∩b	NOUN
ejpam-3131	77	18	is	be	AUX
ejpam-3131	77	19	ρig	ρig	ADV
ejpam-3131	77	20	-	-	PUNCT
ejpam-3131	77	21	closed	closed	ADJ
ejpam-3131	77	22	.	.	PUNCT
ejpam-3131	78	1	(	(	PUNCT
ejpam-3131	78	2	6	6	NUM
ejpam-3131	78	3	)	)	PUNCT
ejpam-3131	78	4	if	if	SCONJ
ejpam-3131	78	5	a	a	DET
ejpam-3131	78	6	⊆	⊆	NUM
ejpam-3131	78	7	b	b	NOUN
ejpam-3131	78	8	and	and	CCONJ
ejpam-3131	78	9	a	a	PRON
ejpam-3131	78	10	is	be	AUX
ejpam-3131	78	11	ρig	ρig	NOUN
ejpam-3131	78	12	-	-	PUNCT
ejpam-3131	78	13	closed	close	VERB
ejpam-3131	78	14	in	in	ADP
ejpam-3131	78	15	the	the	DET
ejpam-3131	78	16	space	space	NOUN
ejpam-3131	78	17	(	(	PUNCT
ejpam-3131	78	18	x	x	X
ejpam-3131	78	19	,	,	PUNCT
ejpam-3131	78	20	τ	τ	PROPN
ejpam-3131	78	21	,	,	PUNCT
ejpam-3131	78	22	i	i	PROPN
ejpam-3131	78	23	)	)	PUNCT
ejpam-3131	78	24	,	,	PUNCT
ejpam-3131	78	25	then	then	ADV
ejpam-3131	78	26	a	a	PRON
ejpam-3131	78	27	is	be	AUX
ejpam-3131	78	28	ρ(ib)g	ρ(ib)g	NOUN
ejpam-3131	78	29	-	-	PUNCT
ejpam-3131	78	30	closed	close	VERB
ejpam-3131	78	31	in	in	ADP
ejpam-3131	78	32	the	the	DET
ejpam-3131	78	33	space	space	NOUN
ejpam-3131	78	34	(	(	PUNCT
ejpam-3131	78	35	b	b	NOUN
ejpam-3131	78	36	,	,	PUNCT
ejpam-3131	78	37	τb	τb	ADJ
ejpam-3131	78	38	,	,	PUNCT
ejpam-3131	78	39	ib	ib	NOUN
ejpam-3131	78	40	)	)	PUNCT
ejpam-3131	78	41	,	,	PUNCT
ejpam-3131	78	42	where	where	SCONJ
ejpam-3131	78	43	τb	τb	ADV
ejpam-3131	78	44	=	=	SYM
ejpam-3131	78	45	{	{	PUNCT
ejpam-3131	78	46	u	u	NOUN
ejpam-3131	78	47	∩b	∩b	NOUN
ejpam-3131	78	48	:	:	PUNCT
ejpam-3131	78	49	u	u	NOUN
ejpam-3131	78	50	∈	∈	PROPN
ejpam-3131	78	51	τ	τ	X
ejpam-3131	78	52	}	}	PUNCT
ejpam-3131	78	53	.	.	PUNCT
ejpam-3131	79	1	proof	proof	NOUN
ejpam-3131	79	2	.	.	PUNCT
ejpam-3131	80	1	(	(	PUNCT
ejpam-3131	80	2	1	1	X
ejpam-3131	80	3	)	)	PUNCT
ejpam-3131	80	4	suppose	suppose	VERB
ejpam-3131	80	5	that	that	SCONJ
ejpam-3131	80	6	u	u	PROPN
ejpam-3131	80	7	∈	∈	PROPN
ejpam-3131	80	8	τ	τ	X
ejpam-3131	80	9	and	and	CCONJ
ejpam-3131	80	10	(	(	PUNCT
ejpam-3131	80	11	a	a	DET
ejpam-3131	80	12	∪b	∪b	NOUN
ejpam-3131	80	13	)	)	PUNCT
ejpam-3131	80	14	\u	\u	PRON
ejpam-3131	80	15	∈	∈	PROPN
ejpam-3131	80	16	i.	i.	NOUN
ejpam-3131	80	17	then	then	ADV
ejpam-3131	80	18	a\u	a\u	PROPN
ejpam-3131	80	19	∈	∈	PROPN
ejpam-3131	80	20	i	i	PRON
ejpam-3131	80	21	and	and	CCONJ
ejpam-3131	80	22	b\u	b\u	ADP
ejpam-3131	80	23	∈	∈	PROPN
ejpam-3131	80	24	i	i	PRON
ejpam-3131	80	25	,	,	PUNCT
ejpam-3131	80	26	and	and	CCONJ
ejpam-3131	80	27	so	so	ADV
ejpam-3131	80	28	a\u	a\u	PROPN
ejpam-3131	80	29	∈	∈	PROPN
ejpam-3131	80	30	i	i	PRON
ejpam-3131	80	31	and	and	CCONJ
ejpam-3131	80	32	b\u	b\u	ADP
ejpam-3131	80	33	∈	∈	PROPN
ejpam-3131	80	34	i.	i.	NOUN
ejpam-3131	80	35	this	this	PRON
ejpam-3131	80	36	implies	imply	VERB
ejpam-3131	80	37	that	that	SCONJ
ejpam-3131	80	38	a	a	DET
ejpam-3131	80	39	∪b\u	∪b\u	PROPN
ejpam-3131	80	40	∈	∈	PROPN
ejpam-3131	80	41	i.	i.	NOUN
ejpam-3131	80	42	(	(	PUNCT
ejpam-3131	80	43	2	2	NUM
ejpam-3131	80	44	)	)	PUNCT
ejpam-3131	80	45	(	(	PUNCT
ejpam-3131	80	46	→	→	NOUN
ejpam-3131	80	47	)	)	PUNCT
ejpam-3131	80	48	suppose	suppose	VERB
ejpam-3131	80	49	that	that	SCONJ
ejpam-3131	80	50	a	a	PRON
ejpam-3131	80	51	is	be	AUX
ejpam-3131	80	52	ρig	ρig	NOUN
ejpam-3131	80	53	-	-	PUNCT
ejpam-3131	80	54	closed	closed	ADJ
ejpam-3131	80	55	,	,	PUNCT
ejpam-3131	80	56	f	f	PROPN
ejpam-3131	80	57	⊆	⊆	NUM
ejpam-3131	81	1	x	x	PUNCT
ejpam-3131	81	2	is	be	AUX
ejpam-3131	81	3	closed	close	VERB
ejpam-3131	81	4	and	and	CCONJ
ejpam-3131	81	5	that	that	SCONJ
ejpam-3131	81	6	f\	f\	VERB
ejpam-3131	81	7	(	(	PUNCT
ejpam-3131	81	8	a\a	a\a	X
ejpam-3131	81	9	)	)	PUNCT
ejpam-3131	81	10	∈	∈	PROPN
ejpam-3131	82	1	i	i	PRON
ejpam-3131	82	2	,	,	PUNCT
ejpam-3131	82	3	this	this	PRON
ejpam-3131	82	4	is	be	AUX
ejpam-3131	82	5	,	,	PUNCT
ejpam-3131	82	6	f	f	PROPN
ejpam-3131	82	7	∩	∩	X
ejpam-3131	82	8	[	[	X
ejpam-3131	82	9	(	(	PUNCT
ejpam-3131	82	10	x\a	x\a	PROPN
ejpam-3131	82	11	)	)	PUNCT
ejpam-3131	82	12	∪a	∪a	NUM
ejpam-3131	82	13	]	]	PUNCT
ejpam-3131	83	1	∈	∈	PROPN
ejpam-3131	83	2	i.	i.	NOUN
ejpam-3131	83	3	then	then	ADV
ejpam-3131	83	4	f	f	PROPN
ejpam-3131	83	5	∩	∩	X
ejpam-3131	83	6	(	(	PUNCT
ejpam-3131	83	7	x\a	x\a	X
ejpam-3131	83	8	)	)	PUNCT
ejpam-3131	83	9	∈	∈	PROPN
ejpam-3131	84	1	i	i	PRON
ejpam-3131	84	2	and	and	CCONJ
ejpam-3131	84	3	a\	a\	PROPN
ejpam-3131	84	4	(	(	PUNCT
ejpam-3131	84	5	x\f	x\f	PROPN
ejpam-3131	84	6	)	)	PUNCT
ejpam-3131	85	1	=	=	SYM
ejpam-3131	85	2	f	f	PROPN
ejpam-3131	85	3	∩	∩	PROPN
ejpam-3131	85	4	a	a	DET
ejpam-3131	85	5	∈	∈	PROPN
ejpam-3131	85	6	i.	i.	NOUN
ejpam-3131	85	7	since	since	SCONJ
ejpam-3131	85	8	a	a	PRON
ejpam-3131	85	9	is	be	AUX
ejpam-3131	85	10	ρig	ρig	NOUN
ejpam-3131	85	11	-	-	PUNCT
ejpam-3131	85	12	closed	closed	ADJ
ejpam-3131	85	13	we	we	PRON
ejpam-3131	85	14	have	have	VERB
ejpam-3131	85	15	that	that	DET
ejpam-3131	85	16	a\	a\	NOUN
ejpam-3131	85	17	(	(	PUNCT
ejpam-3131	85	18	x\f	x\f	PROPN
ejpam-3131	85	19	)	)	PUNCT
ejpam-3131	85	20	∈	∈	PROPN
ejpam-3131	86	1	i	i	PRON
ejpam-3131	86	2	,	,	PUNCT
ejpam-3131	86	3	this	this	PRON
ejpam-3131	86	4	is	be	AUX
ejpam-3131	86	5	f	f	PROPN
ejpam-3131	86	6	∩	∩	PROPN
ejpam-3131	86	7	a	a	DET
ejpam-3131	86	8	∈	∈	PROPN
ejpam-3131	86	9	i.	i.	NOUN
ejpam-3131	86	10	thus	thus	ADV
ejpam-3131	86	11	f	f	PROPN
ejpam-3131	86	12	=(	=(	PROPN
ejpam-3131	86	13	f	f	PROPN
ejpam-3131	86	14	∩a	∩a	PROPN
ejpam-3131	86	15	)	)	PUNCT
ejpam-3131	86	16	∪	∪	ADP
ejpam-3131	86	17	[	[	PUNCT
ejpam-3131	86	18	f	f	NOUN
ejpam-3131	86	19	∩	∩	NOUN
ejpam-3131	86	20	(	(	PUNCT
ejpam-3131	86	21	x\a	x\a	PROPN
ejpam-3131	86	22	)	)	PUNCT
ejpam-3131	86	23	]	]	PUNCT
ejpam-3131	87	1	∈	∈	PROPN
ejpam-3131	87	2	i.	i.	PROPN
ejpam-3131	87	3	(	(	PUNCT
ejpam-3131	87	4	←	←	PROPN
ejpam-3131	87	5	)	)	PUNCT
ejpam-3131	87	6	let	let	VERB
ejpam-3131	87	7	u	u	PRON
ejpam-3131	87	8	∈	∈	PROPN
ejpam-3131	87	9	τ	τ	X
ejpam-3131	87	10	with	with	ADP
ejpam-3131	87	11	a\u	a\u	PROPN
ejpam-3131	87	12	∈	∈	PROPN
ejpam-3131	87	13	i.	i.	NOUN
ejpam-3131	87	14	given	give	VERB
ejpam-3131	87	15	that	that	SCONJ
ejpam-3131	87	16	a\u	a\u	PROPN
ejpam-3131	87	17	=	=	SYM
ejpam-3131	87	18	(	(	PUNCT
ejpam-3131	87	19	a\u	a\u	PROPN
ejpam-3131	87	20	)	)	PUNCT
ejpam-3131	87	21	\	\	PUNCT
ejpam-3131	88	1	(	(	PUNCT
ejpam-3131	88	2	a\a	a\a	NOUN
ejpam-3131	88	3	)	)	PUNCT
ejpam-3131	88	4	and	and	CCONJ
ejpam-3131	88	5	a\u	a\u	PROPN
ejpam-3131	88	6	is	be	AUX
ejpam-3131	88	7	closed	close	VERB
ejpam-3131	88	8	,	,	PUNCT
ejpam-3131	88	9	the	the	DET
ejpam-3131	88	10	hypothesis	hypothesis	NOUN
ejpam-3131	88	11	implies	imply	VERB
ejpam-3131	88	12	that	that	SCONJ
ejpam-3131	88	13	a\u	a\u	PROPN
ejpam-3131	88	14	∈	∈	PROPN
ejpam-3131	88	15	i.	i.	NOUN
ejpam-3131	88	16	(	(	PUNCT
ejpam-3131	88	17	3	3	X
ejpam-3131	88	18	)	)	PUNCT
ejpam-3131	88	19	suppose	suppose	VERB
ejpam-3131	88	20	that	that	SCONJ
ejpam-3131	88	21	v	v	X
ejpam-3131	88	22	∈	∈	X
ejpam-3131	88	23	τ	τ	X
ejpam-3131	88	24	and	and	CCONJ
ejpam-3131	88	25	b\v	b\v	PROPN
ejpam-3131	88	26	∈	∈	PROPN
ejpam-3131	88	27	i.	i.	NOUN
ejpam-3131	88	28	since	since	SCONJ
ejpam-3131	88	29	a\v	a\v	NOUN
ejpam-3131	88	30	⊆	⊆	NUM
ejpam-3131	88	31	(	(	PUNCT
ejpam-3131	88	32	a\b	a\b	NOUN
ejpam-3131	88	33	)	)	PUNCT
ejpam-3131	88	34	∪	∪	NOUN
ejpam-3131	88	35	(	(	PUNCT
ejpam-3131	88	36	b\v	b\v	NOUN
ejpam-3131	88	37	)	)	PUNCT
ejpam-3131	88	38	∈	∈	PROPN
ejpam-3131	89	1	i	i	PRON
ejpam-3131	89	2	then	then	ADV
ejpam-3131	89	3	a\v	a\v	NOUN
ejpam-3131	89	4	∈	∈	PROPN
ejpam-3131	89	5	i.	i.	NOUN
ejpam-3131	89	6	given	give	VERB
ejpam-3131	89	7	that	that	SCONJ
ejpam-3131	89	8	a	a	PRON
ejpam-3131	89	9	is	be	AUX
ejpam-3131	89	10	ρig	ρig	NOUN
ejpam-3131	89	11	-	-	PUNCT
ejpam-3131	89	12	closed	closed	ADJ
ejpam-3131	89	13	we	we	PRON
ejpam-3131	89	14	have	have	VERB
ejpam-3131	89	15	that	that	DET
ejpam-3131	89	16	a\v	a\v	PROPN
ejpam-3131	89	17	∈	∈	PROPN
ejpam-3131	89	18	i.	i.	NOUN
ejpam-3131	89	19	hence	hence	ADV
ejpam-3131	89	20	(	(	PUNCT
ejpam-3131	89	21	a\v	a\v	NOUN
ejpam-3131	89	22	)	)	PUNCT
ejpam-3131	89	23	∪	∪	NOUN
ejpam-3131	89	24	(	(	PUNCT
ejpam-3131	89	25	b\a	b\a	NOUN
ejpam-3131	89	26	)	)	PUNCT
ejpam-3131	89	27	∈	∈	PROPN
ejpam-3131	89	28	i.	i.	NOUN
ejpam-3131	90	1	but	but	CCONJ
ejpam-3131	90	2	b\v	b\v	PROPN
ejpam-3131	90	3	⊆	⊆	NUM
ejpam-3131	90	4	(	(	PUNCT
ejpam-3131	90	5	a\v	a\v	NOUN
ejpam-3131	90	6	)	)	PUNCT
ejpam-3131	90	7	∪	∪	NOUN
ejpam-3131	90	8	(	(	PUNCT
ejpam-3131	90	9	b\a	b\a	NOUN
ejpam-3131	90	10	)	)	PUNCT
ejpam-3131	90	11	and	and	CCONJ
ejpam-3131	90	12	so	so	ADV
ejpam-3131	90	13	b\v	b\v	PROPN
ejpam-3131	90	14	∈	∈	PROPN
ejpam-3131	90	15	i.	i.	NOUN
ejpam-3131	90	16	(	(	PUNCT
ejpam-3131	90	17	4	4	X
ejpam-3131	90	18	)	)	PUNCT
ejpam-3131	90	19	it	it	PRON
ejpam-3131	90	20	is	be	AUX
ejpam-3131	90	21	a	a	DET
ejpam-3131	90	22	consequence	consequence	NOUN
ejpam-3131	90	23	of	of	ADP
ejpam-3131	90	24	(	(	PUNCT
ejpam-3131	90	25	3	3	NUM
ejpam-3131	90	26	)	)	PUNCT
ejpam-3131	90	27	.	.	PUNCT
ejpam-3131	91	1	n.r	n.r	PROPN
ejpam-3131	91	2	.	.	PROPN
ejpam-3131	91	3	pachón	pachón	PROPN
ejpam-3131	91	4	/	/	SYM
ejpam-3131	91	5	eur	eur	PROPN
ejpam-3131	91	6	.	.	PUNCT
ejpam-3131	92	1	j.	j.	PROPN
ejpam-3131	92	2	pure	pure	PROPN
ejpam-3131	92	3	appl	appl	PROPN
ejpam-3131	92	4	.	.	PROPN
ejpam-3131	92	5	math	math	PROPN
ejpam-3131	92	6	,	,	PUNCT
ejpam-3131	92	7	11	11	NUM
ejpam-3131	92	8	(	(	PUNCT
ejpam-3131	92	9	1	1	NUM
ejpam-3131	92	10	)	)	PUNCT
ejpam-3131	92	11	(	(	PUNCT
ejpam-3131	92	12	2018	2018	NUM
ejpam-3131	92	13	)	)	PUNCT
ejpam-3131	92	14	,	,	PUNCT
ejpam-3131	92	15	299	299	NUM
ejpam-3131	92	16	-	-	SYM
ejpam-3131	92	17	314	314	NUM
ejpam-3131	92	18	303	303	NUM
ejpam-3131	92	19	(	(	PUNCT
ejpam-3131	92	20	5	5	NUM
ejpam-3131	92	21	)	)	PUNCT
ejpam-3131	92	22	if	if	SCONJ
ejpam-3131	92	23	u	u	PROPN
ejpam-3131	92	24	∈	∈	PROPN
ejpam-3131	92	25	τ	τ	X
ejpam-3131	92	26	and	and	CCONJ
ejpam-3131	92	27	(	(	PUNCT
ejpam-3131	92	28	a	a	DET
ejpam-3131	92	29	∩b	∩b	NOUN
ejpam-3131	92	30	)	)	PUNCT
ejpam-3131	92	31	\u	\u	X
ejpam-3131	92	32	∈	∈	PROPN
ejpam-3131	93	1	i	i	PRON
ejpam-3131	93	2	,	,	PUNCT
ejpam-3131	93	3	this	this	PRON
ejpam-3131	93	4	is	be	AUX
ejpam-3131	93	5	,	,	PUNCT
ejpam-3131	93	6	a\	a\	PROPN
ejpam-3131	94	1	[	[	X
ejpam-3131	94	2	u	u	NOUN
ejpam-3131	94	3	∪	∪	VERB
ejpam-3131	94	4	(	(	PUNCT
ejpam-3131	94	5	x\b	x\b	PROPN
ejpam-3131	94	6	)	)	PUNCT
ejpam-3131	94	7	]	]	PUNCT
ejpam-3131	95	1	∈	∈	PROPN
ejpam-3131	96	1	i	i	PRON
ejpam-3131	96	2	,	,	PUNCT
ejpam-3131	96	3	then	then	ADV
ejpam-3131	96	4	a\	a\	PROPN
ejpam-3131	97	1	[	[	X
ejpam-3131	97	2	u	u	NOUN
ejpam-3131	97	3	∪	∪	VERB
ejpam-3131	97	4	(	(	PUNCT
ejpam-3131	97	5	x\b	x\b	PROPN
ejpam-3131	97	6	)	)	PUNCT
ejpam-3131	97	7	]	]	PUNCT
ejpam-3131	98	1	∈	∈	PROPN
ejpam-3131	99	1	i	i	PRON
ejpam-3131	99	2	because	because	SCONJ
ejpam-3131	99	3	a	a	PRON
ejpam-3131	99	4	is	be	AUX
ejpam-3131	99	5	ρig	ρig	NOUN
ejpam-3131	99	6	-	-	PUNCT
ejpam-3131	99	7	closed	closed	ADJ
ejpam-3131	99	8	.	.	PUNCT
ejpam-3131	100	1	thus	thus	ADV
ejpam-3131	100	2	(	(	PUNCT
ejpam-3131	100	3	a	a	DET
ejpam-3131	100	4	∩b	∩b	NOUN
ejpam-3131	100	5	)	)	PUNCT
ejpam-3131	100	6	\u	\u	PRON
ejpam-3131	100	7	∈	∈	PROPN
ejpam-3131	100	8	i.	i.	NOUN
ejpam-3131	100	9	now	now	ADV
ejpam-3131	100	10	,	,	PUNCT
ejpam-3131	100	11	a	a	DET
ejpam-3131	100	12	∩b\u	∩b\u	NOUN
ejpam-3131	100	13	⊆	⊆	NUM
ejpam-3131	100	14	(	(	PUNCT
ejpam-3131	100	15	a	a	DET
ejpam-3131	100	16	∩b	∩b	NOUN
ejpam-3131	100	17	)	)	PUNCT
ejpam-3131	100	18	\u	\u	PRON
ejpam-3131	100	19	=(	=(	VERB
ejpam-3131	100	20	a	a	DET
ejpam-3131	100	21	∩b	∩b	NOUN
ejpam-3131	100	22	)	)	PUNCT
ejpam-3131	100	23	\u	\u	PRON
ejpam-3131	100	24	and	and	CCONJ
ejpam-3131	100	25	so	so	ADV
ejpam-3131	100	26	a	a	DET
ejpam-3131	100	27	∩b\u	∩b\u	PROPN
ejpam-3131	100	28	∈	∈	PROPN
ejpam-3131	100	29	i.	i.	NOUN
ejpam-3131	100	30	(	(	PUNCT
ejpam-3131	100	31	6	6	NUM
ejpam-3131	100	32	)	)	PUNCT
ejpam-3131	100	33	suppose	suppose	VERB
ejpam-3131	100	34	that	that	SCONJ
ejpam-3131	100	35	v	v	X
ejpam-3131	100	36	∈	∈	NOUN
ejpam-3131	100	37	τb	τb	ADP
ejpam-3131	100	38	and	and	CCONJ
ejpam-3131	100	39	a\v	a\v	NOUN
ejpam-3131	100	40	=	=	PROPN
ejpam-3131	100	41	i0	i0	PROPN
ejpam-3131	100	42	∈	∈	PROPN
ejpam-3131	100	43	ib	ib	INTJ
ejpam-3131	100	44	.	.	PUNCT
ejpam-3131	101	1	there	there	PRON
ejpam-3131	101	2	are	be	VERB
ejpam-3131	101	3	u	u	PROPN
ejpam-3131	101	4	∈	∈	PROPN
ejpam-3131	101	5	τ	τ	X
ejpam-3131	102	1	and	and	CCONJ
ejpam-3131	102	2	i	i	PRON
ejpam-3131	102	3	∈	∈	PROPN
ejpam-3131	102	4	i	i	PRON
ejpam-3131	102	5	with	with	ADP
ejpam-3131	102	6	v	v	NOUN
ejpam-3131	102	7	=	=	SYM
ejpam-3131	102	8	b	b	NOUN
ejpam-3131	102	9	∩	∩	ADJ
ejpam-3131	102	10	u	u	NOUN
ejpam-3131	102	11	and	and	CCONJ
ejpam-3131	102	12	i0	i0	PROPN
ejpam-3131	102	13	=	=	PROPN
ejpam-3131	103	1	i	i	PROPN
ejpam-3131	103	2	∩	∩	PROPN
ejpam-3131	103	3	b.	b.	PROPN
ejpam-3131	103	4	then	then	ADV
ejpam-3131	103	5	a\v	a\v	NOUN
ejpam-3131	103	6	=	=	SYM
ejpam-3131	103	7	a\	a\	NOUN
ejpam-3131	103	8	(	(	PUNCT
ejpam-3131	103	9	b	b	PROPN
ejpam-3131	103	10	∩	∩	ADJ
ejpam-3131	103	11	u	u	NOUN
ejpam-3131	103	12	)	)	PUNCT
ejpam-3131	103	13	=	=	SYM
ejpam-3131	103	14	b	b	NOUN
ejpam-3131	103	15	∩	∩	X
ejpam-3131	103	16	i	i	PRON
ejpam-3131	103	17	and	and	CCONJ
ejpam-3131	103	18	this	this	PRON
ejpam-3131	103	19	implies	imply	VERB
ejpam-3131	103	20	that	that	SCONJ
ejpam-3131	103	21	a\u	a\u	PROPN
ejpam-3131	103	22	⊆	⊆	NUM
ejpam-3131	103	23	a\	a\	PROPN
ejpam-3131	103	24	(	(	PUNCT
ejpam-3131	103	25	b	b	PROPN
ejpam-3131	103	26	∩	∩	ADJ
ejpam-3131	103	27	u	u	NOUN
ejpam-3131	103	28	)	)	PUNCT
ejpam-3131	103	29	=	=	SYM
ejpam-3131	103	30	b	b	NOUN
ejpam-3131	103	31	∩	∩	NOUN
ejpam-3131	103	32	i	i	PROPN
ejpam-3131	103	33	⊆	⊆	NUM
ejpam-3131	103	34	i.	i.	NOUN
ejpam-3131	103	35	thus	thus	ADV
ejpam-3131	103	36	a\u	a\u	PROPN
ejpam-3131	103	37	∈	∈	PROPN
ejpam-3131	103	38	i.	i.	NOUN
ejpam-3131	103	39	since	since	SCONJ
ejpam-3131	103	40	a	a	PRON
ejpam-3131	103	41	is	be	AUX
ejpam-3131	103	42	ρig	ρig	NOUN
ejpam-3131	103	43	-	-	PUNCT
ejpam-3131	103	44	closed	closed	ADJ
ejpam-3131	103	45	we	we	PRON
ejpam-3131	103	46	have	have	VERB
ejpam-3131	103	47	that	that	SCONJ
ejpam-3131	103	48	a\u	a\u	PROPN
ejpam-3131	103	49	∈	∈	PROPN
ejpam-3131	103	50	i.	i.	NOUN
ejpam-3131	103	51	this	this	PRON
ejpam-3131	103	52	implies	imply	VERB
ejpam-3131	103	53	that	that	SCONJ
ejpam-3131	103	54	(	(	PUNCT
ejpam-3131	103	55	a\u	a\u	NOUN
ejpam-3131	103	56	)	)	PUNCT
ejpam-3131	103	57	∩	∩	PROPN
ejpam-3131	103	58	b	b	X
ejpam-3131	103	59	∈	∈	PROPN
ejpam-3131	103	60	ib	ib	NOUN
ejpam-3131	103	61	,	,	PUNCT
ejpam-3131	103	62	this	this	PRON
ejpam-3131	103	63	is	be	AUX
ejpam-3131	103	64	,	,	PUNCT
ejpam-3131	103	65	(	(	PUNCT
ejpam-3131	103	66	a	a	DET
ejpam-3131	103	67	∩b	∩b	NOUN
ejpam-3131	103	68	)	)	PUNCT
ejpam-3131	104	1	\u	\u	PRON
ejpam-3131	104	2	∈	∈	NOUN
ejpam-3131	104	3	ib	ib	NOUN
ejpam-3131	104	4	,	,	PUNCT
ejpam-3131	104	5	and	and	CCONJ
ejpam-3131	104	6	finally	finally	ADV
ejpam-3131	104	7	adhτb	adhτb	VERB
ejpam-3131	104	8	(	(	PUNCT
ejpam-3131	104	9	a	a	NOUN
ejpam-3131	104	10	)	)	PUNCT
ejpam-3131	104	11	\v	\v	NOUN
ejpam-3131	105	1	=	=	PRON
ejpam-3131	105	2	adhτb	adhτb	ADJ
ejpam-3131	105	3	(	(	PUNCT
ejpam-3131	105	4	a	a	X
ejpam-3131	105	5	)	)	PUNCT
ejpam-3131	105	6	\	\	NOUN
ejpam-3131	106	1	(	(	PUNCT
ejpam-3131	106	2	u	u	NOUN
ejpam-3131	106	3	∩b	∩b	PROPN
ejpam-3131	106	4	)	)	PUNCT
ejpam-3131	106	5	=	=	PUNCT
ejpam-3131	106	6	(	(	PUNCT
ejpam-3131	106	7	b	b	X
ejpam-3131	106	8	∩a	∩a	PROPN
ejpam-3131	106	9	)	)	PUNCT
ejpam-3131	106	10	\	\	PUNCT
ejpam-3131	107	1	(	(	PUNCT
ejpam-3131	107	2	u	u	NOUN
ejpam-3131	107	3	∩b	∩b	PROPN
ejpam-3131	107	4	)	)	PUNCT
ejpam-3131	107	5	=	=	PUNCT
ejpam-3131	107	6	(	(	PUNCT
ejpam-3131	107	7	b	b	X
ejpam-3131	107	8	∩a	∩a	NOUN
ejpam-3131	107	9	)	)	PUNCT
ejpam-3131	107	10	\u	\u	PRON
ejpam-3131	107	11	∈	∈	PROPN
ejpam-3131	107	12	ib	ib	VERB
ejpam-3131	107	13	.	.	PUNCT
ejpam-3131	108	1	□	□	PUNCT
ejpam-3131	108	2	example	example	NOUN
ejpam-3131	108	3	2.6	2.6	NUM
ejpam-3131	108	4	.	.	PUNCT
ejpam-3131	109	1	let	let	VERB
ejpam-3131	109	2	c	c	NOUN
ejpam-3131	109	3	=	=	PRON
ejpam-3131	109	4	{	{	PUNCT
ejpam-3131	109	5	∅,r	∅,r	ADV
ejpam-3131	109	6	}	}	PUNCT
ejpam-3131	109	7	∪	∪	X
ejpam-3131	109	8	{	{	PUNCT
ejpam-3131	109	9	(	(	PUNCT
ejpam-3131	109	10	r,∞	r,∞	PROPN
ejpam-3131	109	11	)	)	PUNCT
ejpam-3131	109	12	:	:	PUNCT
ejpam-3131	110	1	r	r	NOUN
ejpam-3131	110	2	∈	∈	PROPN
ejpam-3131	110	3	r	r	NOUN
ejpam-3131	110	4	}	}	PUNCT
ejpam-3131	110	5	,	,	PUNCT
ejpam-3131	110	6	i	i	PRON
ejpam-3131	110	7	=	=	PUNCT
ejpam-3131	110	8	if	if	SCONJ
ejpam-3131	110	9	(	(	PUNCT
ejpam-3131	110	10	r	r	NOUN
ejpam-3131	110	11	)	)	PUNCT
ejpam-3131	110	12	,	,	PUNCT
ejpam-3131	110	13	a	a	DET
ejpam-3131	110	14	=	=	X
ejpam-3131	110	15	2z	2z	NUM
ejpam-3131	110	16	and	and	CCONJ
ejpam-3131	110	17	b	b	X
ejpam-3131	110	18	=	=	SYM
ejpam-3131	110	19	{	{	PUNCT
ejpam-3131	110	20	p	p	NOUN
ejpam-3131	110	21	∈	∈	PROPN
ejpam-3131	110	22	z	z	NOUN
ejpam-3131	110	23	:	:	PUNCT
ejpam-3131	110	24	|p|	|p|	PRON
ejpam-3131	110	25	is	be	AUX
ejpam-3131	110	26	a	a	DET
ejpam-3131	110	27	prime	prime	ADJ
ejpam-3131	110	28	number	number	NOUN
ejpam-3131	110	29	}	}	PUNCT
ejpam-3131	110	30	.	.	PUNCT
ejpam-3131	111	1	we	we	PRON
ejpam-3131	111	2	have	have	VERB
ejpam-3131	111	3	that	that	PRON
ejpam-3131	111	4	,	,	PUNCT
ejpam-3131	111	5	in	in	ADP
ejpam-3131	111	6	the	the	DET
ejpam-3131	111	7	space	space	NOUN
ejpam-3131	111	8	(	(	PUNCT
ejpam-3131	111	9	r	r	NOUN
ejpam-3131	111	10	,	,	PUNCT
ejpam-3131	111	11	c	c	X
ejpam-3131	111	12	,	,	PUNCT
ejpam-3131	111	13	i	i	PROPN
ejpam-3131	111	14	)	)	PUNCT
ejpam-3131	111	15	,	,	PUNCT
ejpam-3131	111	16	a	a	PRON
ejpam-3131	111	17	and	and	CCONJ
ejpam-3131	111	18	b	b	NOUN
ejpam-3131	111	19	are	be	AUX
ejpam-3131	111	20	ρig	ρig	ADV
ejpam-3131	111	21	-	-	PUNCT
ejpam-3131	111	22	closed	close	VERB
ejpam-3131	111	23	sets	set	NOUN
ejpam-3131	111	24	,	,	PUNCT
ejpam-3131	111	25	because	because	SCONJ
ejpam-3131	111	26	if	if	SCONJ
ejpam-3131	111	27	u	u	PROPN
ejpam-3131	111	28	∈	∈	PROPN
ejpam-3131	111	29	c	c	NOUN
ejpam-3131	111	30	and	and	CCONJ
ejpam-3131	111	31	a\u	a\u	PROPN
ejpam-3131	111	32	∈	∈	PROPN
ejpam-3131	111	33	i	i	PRON
ejpam-3131	111	34	(	(	PUNCT
ejpam-3131	111	35	or	or	CCONJ
ejpam-3131	111	36	b\u	b\u	ADP
ejpam-3131	111	37	∈	∈	PROPN
ejpam-3131	111	38	i	i	PROPN
ejpam-3131	111	39	)	)	PUNCT
ejpam-3131	111	40	then	then	ADV
ejpam-3131	111	41	u	u	X
ejpam-3131	111	42	=	=	NOUN
ejpam-3131	111	43	r	r	NOUN
ejpam-3131	111	44	and	and	CCONJ
ejpam-3131	111	45	so	so	ADV
ejpam-3131	111	46	a\u	a\u	PROPN
ejpam-3131	111	47	∈	∈	PROPN
ejpam-3131	111	48	i	i	PRON
ejpam-3131	111	49	(	(	PUNCT
ejpam-3131	111	50	or	or	CCONJ
ejpam-3131	111	51	b\u	b\u	ADP
ejpam-3131	111	52	∈	∈	PROPN
ejpam-3131	111	53	i	i	PROPN
ejpam-3131	111	54	)	)	PUNCT
ejpam-3131	111	55	.	.	PUNCT
ejpam-3131	112	1	however	however	ADV
ejpam-3131	112	2	a	a	DET
ejpam-3131	112	3	∩	∩	ADJ
ejpam-3131	112	4	b	b	NOUN
ejpam-3131	112	5	is	be	AUX
ejpam-3131	112	6	not	not	PART
ejpam-3131	112	7	ρig	ρig	NOUN
ejpam-3131	112	8	-	-	PUNCT
ejpam-3131	112	9	closed	closed	ADJ
ejpam-3131	112	10	since	since	SCONJ
ejpam-3131	112	11	a	a	DET
ejpam-3131	112	12	∩	∩	ADJ
ejpam-3131	112	13	b	b	NOUN
ejpam-3131	112	14	=	=	SYM
ejpam-3131	112	15	{	{	PUNCT
ejpam-3131	112	16	−2	−2	NOUN
ejpam-3131	112	17	,	,	PUNCT
ejpam-3131	112	18	2	2	NUM
ejpam-3131	112	19	}	}	PUNCT
ejpam-3131	112	20	,	,	PUNCT
ejpam-3131	112	21	(	(	PUNCT
ejpam-3131	112	22	a	a	DET
ejpam-3131	112	23	∩b	∩b	NOUN
ejpam-3131	112	24	)	)	PUNCT
ejpam-3131	112	25	\	\	PUNCT
ejpam-3131	112	26	(	(	PUNCT
ejpam-3131	112	27	0,∞	0,∞	NUM
ejpam-3131	112	28	)	)	PUNCT
ejpam-3131	112	29	∈	∈	PROPN
ejpam-3131	113	1	i	i	PRON
ejpam-3131	113	2	,	,	PUNCT
ejpam-3131	113	3	but	but	CCONJ
ejpam-3131	113	4	a	a	DET
ejpam-3131	113	5	∩b\	∩b\	PROPN
ejpam-3131	113	6	(	(	PUNCT
ejpam-3131	113	7	0,∞	0,∞	NUM
ejpam-3131	113	8	)	)	PUNCT
ejpam-3131	113	9	=	=	SYM
ejpam-3131	113	10	(	(	PUNCT
ejpam-3131	113	11	−∞	−∞	NOUN
ejpam-3131	113	12	,	,	PUNCT
ejpam-3131	113	13	0	0	NUM
ejpam-3131	113	14	]	]	PUNCT
ejpam-3131	113	15	/∈	/∈	PUNCT
ejpam-3131	114	1	i.	i.	PROPN
ejpam-3131	114	2	the	the	DET
ejpam-3131	114	3	following	following	ADJ
ejpam-3131	114	4	result	result	NOUN
ejpam-3131	114	5	is	be	AUX
ejpam-3131	114	6	due	due	ADJ
ejpam-3131	114	7	to	to	ADP
ejpam-3131	114	8	newcomb	newcomb	PROPN
ejpam-3131	114	9	.	.	PUNCT
ejpam-3131	115	1	lemma	lemma	PROPN
ejpam-3131	115	2	2.7	2.7	NUM
ejpam-3131	115	3	.	.	PUNCT
ejpam-3131	116	1	if	if	SCONJ
ejpam-3131	116	2	f	f	PROPN
ejpam-3131	116	3	:	:	PUNCT
ejpam-3131	116	4	x	x	X
ejpam-3131	116	5	→	→	SYM
ejpam-3131	116	6	y	y	PROPN
ejpam-3131	116	7	is	be	AUX
ejpam-3131	116	8	a	a	DET
ejpam-3131	116	9	function	function	NOUN
ejpam-3131	116	10	we	we	PRON
ejpam-3131	116	11	have	have	VERB
ejpam-3131	116	12	that	that	PRON
ejpam-3131	116	13	:	:	PUNCT
ejpam-3131	116	14	(	(	PUNCT
ejpam-3131	116	15	1	1	X
ejpam-3131	116	16	)	)	PUNCT
ejpam-3131	116	17	if	if	SCONJ
ejpam-3131	116	18	i	i	PRON
ejpam-3131	116	19	is	be	AUX
ejpam-3131	116	20	an	an	DET
ejpam-3131	116	21	ideal	ideal	NOUN
ejpam-3131	116	22	in	in	ADP
ejpam-3131	116	23	x	x	NOUN
ejpam-3131	116	24	,	,	PUNCT
ejpam-3131	116	25	then	then	ADV
ejpam-3131	116	26	f(i	f(i	NUM
ejpam-3131	116	27	)	)	PUNCT
ejpam-3131	117	1	=	=	PRON
ejpam-3131	117	2	{	{	PUNCT
ejpam-3131	117	3	f(i	f(i	PROPN
ejpam-3131	117	4	)	)	PUNCT
ejpam-3131	117	5	:	:	PUNCT
ejpam-3131	118	1	i	i	PRON
ejpam-3131	118	2	∈	∈	VERB
ejpam-3131	118	3	i	i	PRON
ejpam-3131	118	4	}	}	PUNCT
ejpam-3131	118	5	is	be	AUX
ejpam-3131	118	6	an	an	DET
ejpam-3131	118	7	ideal	ideal	NOUN
ejpam-3131	118	8	in	in	ADP
ejpam-3131	118	9	y	y	PROPN
ejpam-3131	118	10	.	.	PUNCT
ejpam-3131	119	1	(	(	PUNCT
ejpam-3131	119	2	2	2	X
ejpam-3131	119	3	)	)	PUNCT
ejpam-3131	119	4	if	if	SCONJ
ejpam-3131	119	5	f	f	PROPN
ejpam-3131	119	6	is	be	AUX
ejpam-3131	119	7	inyective	inyective	ADJ
ejpam-3131	119	8	and	and	CCONJ
ejpam-3131	119	9	j	j	PROPN
ejpam-3131	119	10	is	be	AUX
ejpam-3131	119	11	an	an	DET
ejpam-3131	119	12	ideal	ideal	NOUN
ejpam-3131	119	13	in	in	ADP
ejpam-3131	119	14	y	y	PROPN
ejpam-3131	119	15	,	,	PUNCT
ejpam-3131	119	16	then	then	ADV
ejpam-3131	119	17	the	the	DET
ejpam-3131	119	18	set	set	ADJ
ejpam-3131	119	19	f−1	f−1	PROPN
ejpam-3131	119	20	(	(	PUNCT
ejpam-3131	119	21	j	j	PROPN
ejpam-3131	119	22	)	)	PUNCT
ejpam-3131	119	23	=	=	PRON
ejpam-3131	119	24	{	{	PUNCT
ejpam-3131	119	25	f−1(j	f−1(j	PROPN
ejpam-3131	119	26	)	)	PUNCT
ejpam-3131	119	27	:	:	PUNCT
ejpam-3131	120	1	j	j	PROPN
ejpam-3131	120	2	∈	∈	PROPN
ejpam-3131	120	3	j	j	PROPN
ejpam-3131	120	4	}	}	PUNCT
ejpam-3131	120	5	is	be	AUX
ejpam-3131	120	6	an	an	DET
ejpam-3131	120	7	ideal	ideal	NOUN
ejpam-3131	120	8	in	in	ADP
ejpam-3131	120	9	x.	x.	NOUN
ejpam-3131	120	10	theorem	theorem	VERB
ejpam-3131	120	11	2.8	2.8	NUM
ejpam-3131	120	12	.	.	PUNCT
ejpam-3131	121	1	(	(	PUNCT
ejpam-3131	121	2	1	1	X
ejpam-3131	121	3	)	)	PUNCT
ejpam-3131	121	4	if	if	SCONJ
ejpam-3131	121	5	f	f	PROPN
ejpam-3131	121	6	:	:	PUNCT
ejpam-3131	121	7	(	(	PUNCT
ejpam-3131	121	8	x	x	X
ejpam-3131	121	9	,	,	PUNCT
ejpam-3131	121	10	τ	τ	X
ejpam-3131	121	11	)	)	PUNCT
ejpam-3131	121	12	→	→	SYM
ejpam-3131	121	13	(	(	PUNCT
ejpam-3131	121	14	y	y	PROPN
ejpam-3131	121	15	,	,	PUNCT
ejpam-3131	121	16	β	β	NOUN
ejpam-3131	121	17	)	)	PUNCT
ejpam-3131	121	18	is	be	AUX
ejpam-3131	121	19	a	a	DET
ejpam-3131	121	20	continuous	continuous	ADJ
ejpam-3131	121	21	,	,	PUNCT
ejpam-3131	121	22	closed	closed	ADJ
ejpam-3131	121	23	and	and	CCONJ
ejpam-3131	121	24	inyective	inyective	ADJ
ejpam-3131	121	25	function	function	NOUN
ejpam-3131	121	26	,	,	PUNCT
ejpam-3131	121	27	i	i	PRON
ejpam-3131	121	28	is	be	AUX
ejpam-3131	121	29	an	an	DET
ejpam-3131	121	30	ideal	ideal	NOUN
ejpam-3131	121	31	on	on	ADP
ejpam-3131	121	32	x	x	PROPN
ejpam-3131	121	33	,	,	PUNCT
ejpam-3131	121	34	j	j	PROPN
ejpam-3131	121	35	=	=	SYM
ejpam-3131	121	36	f(i	f(i	PROPN
ejpam-3131	121	37	)	)	PUNCT
ejpam-3131	121	38	and	and	CCONJ
ejpam-3131	121	39	if	if	SCONJ
ejpam-3131	121	40	a	a	DET
ejpam-3131	121	41	⊆	⊆	NUM
ejpam-3131	121	42	x	x	NOUN
ejpam-3131	121	43	is	be	AUX
ejpam-3131	121	44	ρig	ρig	ADV
ejpam-3131	121	45	-	-	PUNCT
ejpam-3131	121	46	closed	closed	ADJ
ejpam-3131	121	47	,	,	PUNCT
ejpam-3131	121	48	then	then	ADV
ejpam-3131	121	49	f(a	f(a	PROPN
ejpam-3131	121	50	)	)	PUNCT
ejpam-3131	121	51	is	be	AUX
ejpam-3131	121	52	ρjg	ρjg	NOUN
ejpam-3131	121	53	-	-	PUNCT
ejpam-3131	121	54	closed	closed	ADJ
ejpam-3131	121	55	.	.	PUNCT
ejpam-3131	122	1	(	(	PUNCT
ejpam-3131	122	2	2	2	X
ejpam-3131	122	3	)	)	PUNCT
ejpam-3131	122	4	if	if	SCONJ
ejpam-3131	122	5	f	f	PROPN
ejpam-3131	122	6	:	:	PUNCT
ejpam-3131	122	7	(	(	PUNCT
ejpam-3131	122	8	x	x	X
ejpam-3131	122	9	,	,	PUNCT
ejpam-3131	122	10	τ)→	τ)→	PROPN
ejpam-3131	122	11	(	(	PUNCT
ejpam-3131	122	12	y	y	NOUN
ejpam-3131	122	13	,	,	PUNCT
ejpam-3131	122	14	β	β	NOUN
ejpam-3131	122	15	)	)	PUNCT
ejpam-3131	122	16	is	be	AUX
ejpam-3131	122	17	a	a	DET
ejpam-3131	122	18	continuous	continuous	ADJ
ejpam-3131	122	19	,	,	PUNCT
ejpam-3131	122	20	closed	closed	ADJ
ejpam-3131	122	21	and	and	CCONJ
ejpam-3131	122	22	inyective	inyective	ADJ
ejpam-3131	122	23	function	function	NOUN
ejpam-3131	122	24	,	,	PUNCT
ejpam-3131	122	25	i	i	PRON
ejpam-3131	122	26	is	be	AUX
ejpam-3131	122	27	an	an	DET
ejpam-3131	122	28	ideal	ideal	NOUN
ejpam-3131	122	29	on	on	ADP
ejpam-3131	122	30	x	x	PROPN
ejpam-3131	122	31	,	,	PUNCT
ejpam-3131	122	32	j	j	PROPN
ejpam-3131	123	1	=	=	PRON
ejpam-3131	123	2	{	{	PUNCT
ejpam-3131	123	3	v	v	ADP
ejpam-3131	123	4	⊆	⊆	NUM
ejpam-3131	123	5	y	y	NOUN
ejpam-3131	123	6	:	:	PUNCT
ejpam-3131	123	7	f−1	f−1	PROPN
ejpam-3131	123	8	(	(	PUNCT
ejpam-3131	123	9	v	v	NOUN
ejpam-3131	123	10	)	)	PUNCT
ejpam-3131	123	11	∈	∈	PROPN
ejpam-3131	124	1	i	i	PRON
ejpam-3131	124	2	}	}	PUNCT
ejpam-3131	124	3	and	and	CCONJ
ejpam-3131	124	4	if	if	SCONJ
ejpam-3131	124	5	a	a	DET
ejpam-3131	124	6	⊆	⊆	NUM
ejpam-3131	124	7	x	x	NOUN
ejpam-3131	124	8	is	be	AUX
ejpam-3131	124	9	ρig	ρig	ADV
ejpam-3131	124	10	-	-	PUNCT
ejpam-3131	124	11	closed	closed	ADJ
ejpam-3131	124	12	,	,	PUNCT
ejpam-3131	124	13	then	then	ADV
ejpam-3131	124	14	f(a	f(a	PROPN
ejpam-3131	124	15	)	)	PUNCT
ejpam-3131	124	16	is	be	AUX
ejpam-3131	124	17	ρjg	ρjg	NOUN
ejpam-3131	124	18	-	-	PUNCT
ejpam-3131	124	19	closed	closed	ADJ
ejpam-3131	124	20	.	.	PUNCT
ejpam-3131	125	1	(	(	PUNCT
ejpam-3131	125	2	3	3	X
ejpam-3131	125	3	)	)	PUNCT
ejpam-3131	125	4	if	if	SCONJ
ejpam-3131	125	5	f	f	PROPN
ejpam-3131	125	6	:	:	PUNCT
ejpam-3131	125	7	(	(	PUNCT
ejpam-3131	125	8	x	x	X
ejpam-3131	125	9	,	,	PUNCT
ejpam-3131	125	10	τ)→	τ)→	PROPN
ejpam-3131	125	11	(	(	PUNCT
ejpam-3131	125	12	y	y	NOUN
ejpam-3131	125	13	,	,	PUNCT
ejpam-3131	125	14	β	β	NOUN
ejpam-3131	125	15	)	)	PUNCT
ejpam-3131	125	16	is	be	AUX
ejpam-3131	125	17	a	a	DET
ejpam-3131	125	18	continuous	continuous	ADJ
ejpam-3131	125	19	,	,	PUNCT
ejpam-3131	125	20	open	open	ADJ
ejpam-3131	125	21	and	and	CCONJ
ejpam-3131	125	22	inyective	inyective	ADJ
ejpam-3131	125	23	function	function	NOUN
ejpam-3131	125	24	,	,	PUNCT
ejpam-3131	125	25	i	i	PRON
ejpam-3131	125	26	is	be	AUX
ejpam-3131	125	27	an	an	DET
ejpam-3131	125	28	ideal	ideal	NOUN
ejpam-3131	125	29	on	on	ADP
ejpam-3131	125	30	x	x	PROPN
ejpam-3131	125	31	,	,	PUNCT
ejpam-3131	125	32	j	j	PROPN
ejpam-3131	126	1	=	=	PRON
ejpam-3131	126	2	{	{	PUNCT
ejpam-3131	126	3	v	v	ADP
ejpam-3131	126	4	⊆	⊆	NUM
ejpam-3131	126	5	y	y	NOUN
ejpam-3131	126	6	:	:	PUNCT
ejpam-3131	126	7	f−1	f−1	PROPN
ejpam-3131	126	8	(	(	PUNCT
ejpam-3131	126	9	v	v	NOUN
ejpam-3131	126	10	)	)	PUNCT
ejpam-3131	126	11	∈	∈	PROPN
ejpam-3131	127	1	i	i	PRON
ejpam-3131	127	2	}	}	PUNCT
ejpam-3131	127	3	and	and	CCONJ
ejpam-3131	127	4	if	if	SCONJ
ejpam-3131	127	5	b	b	PROPN
ejpam-3131	127	6	⊆	⊆	NUM
ejpam-3131	127	7	y	y	PROPN
ejpam-3131	127	8	is	be	AUX
ejpam-3131	127	9	ρjg	ρjg	NOUN
ejpam-3131	127	10	-	-	PUNCT
ejpam-3131	127	11	closed	closed	ADJ
ejpam-3131	127	12	,	,	PUNCT
ejpam-3131	127	13	then	then	ADV
ejpam-3131	127	14	f−1(b	f−1(b	PROPN
ejpam-3131	127	15	)	)	PUNCT
ejpam-3131	127	16	is	be	AUX
ejpam-3131	127	17	ρig	ρig	ADV
ejpam-3131	127	18	-	-	PUNCT
ejpam-3131	127	19	closed	closed	ADJ
ejpam-3131	127	20	.	.	PUNCT
ejpam-3131	128	1	(	(	PUNCT
ejpam-3131	128	2	4	4	X
ejpam-3131	128	3	)	)	PUNCT
ejpam-3131	128	4	if	if	SCONJ
ejpam-3131	128	5	f	f	PROPN
ejpam-3131	128	6	:	:	PUNCT
ejpam-3131	128	7	(	(	PUNCT
ejpam-3131	128	8	x	x	X
ejpam-3131	128	9	,	,	PUNCT
ejpam-3131	128	10	τ)→	τ)→	PROPN
ejpam-3131	128	11	(	(	PUNCT
ejpam-3131	128	12	y	y	NOUN
ejpam-3131	128	13	,	,	PUNCT
ejpam-3131	128	14	β	β	NOUN
ejpam-3131	128	15	)	)	PUNCT
ejpam-3131	128	16	is	be	AUX
ejpam-3131	128	17	an	an	DET
ejpam-3131	128	18	inyective	inyective	NOUN
ejpam-3131	128	19	,	,	PUNCT
ejpam-3131	128	20	continuous	continuous	ADJ
ejpam-3131	128	21	and	and	CCONJ
ejpam-3131	128	22	closed	closed	ADJ
ejpam-3131	128	23	function	function	NOUN
ejpam-3131	128	24	,	,	PUNCT
ejpam-3131	128	25	j	j	PROPN
ejpam-3131	128	26	is	be	AUX
ejpam-3131	128	27	an	an	DET
ejpam-3131	128	28	ideal	ideal	NOUN
ejpam-3131	128	29	in	in	ADP
ejpam-3131	128	30	y	y	PROPN
ejpam-3131	128	31	and	and	CCONJ
ejpam-3131	128	32	if	if	SCONJ
ejpam-3131	128	33	a	a	PRON
ejpam-3131	128	34	is	be	AUX
ejpam-3131	128	35	ρ	ρ	NOUN
ejpam-3131	128	36	(	(	PUNCT
ejpam-3131	128	37	f−1(j	f−1(j	PROPN
ejpam-3131	128	38	)	)	PUNCT
ejpam-3131	128	39	)	)	PUNCT
ejpam-3131	129	1	g	g	PROPN
ejpam-3131	129	2	-closed	-close	VERB
ejpam-3131	129	3	,	,	PUNCT
ejpam-3131	129	4	then	then	ADV
ejpam-3131	129	5	f(a	f(a	PROPN
ejpam-3131	129	6	)	)	PUNCT
ejpam-3131	129	7	is	be	AUX
ejpam-3131	129	8	ρjg	ρjg	NOUN
ejpam-3131	129	9	-	-	PUNCT
ejpam-3131	129	10	closed	closed	ADJ
ejpam-3131	129	11	.	.	PUNCT
ejpam-3131	130	1	proof	proof	NOUN
ejpam-3131	130	2	.	.	PUNCT
ejpam-3131	131	1	(	(	PUNCT
ejpam-3131	131	2	1	1	X
ejpam-3131	131	3	)	)	PUNCT
ejpam-3131	131	4	if	if	SCONJ
ejpam-3131	131	5	v	v	NUM
ejpam-3131	131	6	∈	∈	PROPN
ejpam-3131	131	7	β	β	X
ejpam-3131	131	8	and	and	CCONJ
ejpam-3131	131	9	f(a)\v	f(a)\v	PROPN
ejpam-3131	131	10	∈	∈	PROPN
ejpam-3131	131	11	j	j	PROPN
ejpam-3131	131	12	then	then	ADV
ejpam-3131	131	13	a\f−1(v	a\f−1(v	VERB
ejpam-3131	131	14	)	)	PUNCT
ejpam-3131	132	1	∈	∈	PROPN
ejpam-3131	133	1	i	i	PRON
ejpam-3131	133	2	,	,	PUNCT
ejpam-3131	133	3	because	because	SCONJ
ejpam-3131	133	4	f	f	PROPN
ejpam-3131	133	5	is	be	AUX
ejpam-3131	133	6	inyective	inyective	ADJ
ejpam-3131	133	7	.	.	PUNCT
ejpam-3131	134	1	given	give	VERB
ejpam-3131	134	2	that	that	SCONJ
ejpam-3131	134	3	a	a	PRON
ejpam-3131	134	4	is	be	AUX
ejpam-3131	134	5	ρig	ρig	NOUN
ejpam-3131	134	6	-	-	PUNCT
ejpam-3131	134	7	closed	closed	ADJ
ejpam-3131	134	8	we	we	PRON
ejpam-3131	134	9	have	have	VERB
ejpam-3131	134	10	that	that	DET
ejpam-3131	134	11	a\f−1(v	a\f−1(v	NOUN
ejpam-3131	134	12	)	)	PUNCT
ejpam-3131	135	1	∈	∈	PROPN
ejpam-3131	136	1	i	i	PRON
ejpam-3131	136	2	,	,	PUNCT
ejpam-3131	136	3	and	and	CCONJ
ejpam-3131	136	4	so	so	ADV
ejpam-3131	136	5	f	f	X
ejpam-3131	136	6	[	[	PUNCT
ejpam-3131	136	7	a\f−1(v	a\f−1(v	NOUN
ejpam-3131	136	8	)	)	PUNCT
ejpam-3131	136	9	]	]	PUNCT
ejpam-3131	137	1	∈	∈	PROPN
ejpam-3131	137	2	f(i	f(i	NUM
ejpam-3131	137	3	)	)	PUNCT
ejpam-3131	137	4	.	.	PUNCT
ejpam-3131	138	1	but	but	CCONJ
ejpam-3131	138	2	f	f	X
ejpam-3131	138	3	(	(	PUNCT
ejpam-3131	138	4	a	a	PRON
ejpam-3131	138	5	)	)	PUNCT
ejpam-3131	138	6	\v	\v	PROPN
ejpam-3131	139	1	⊆	⊆	NUM
ejpam-3131	139	2	f	f	X
ejpam-3131	139	3	(	(	PUNCT
ejpam-3131	139	4	a	a	X
ejpam-3131	139	5	)	)	PUNCT
ejpam-3131	139	6	\f(f−1(v	\f(f−1(v	PROPN
ejpam-3131	139	7	)	)	PUNCT
ejpam-3131	139	8	)	)	PUNCT
ejpam-3131	140	1	⊆	⊆	NUM
ejpam-3131	140	2	f	f	X
ejpam-3131	140	3	[	[	X
ejpam-3131	140	4	a\f−1(v	a\f−1(v	NOUN
ejpam-3131	140	5	)	)	PUNCT
ejpam-3131	140	6	]	]	PUNCT
ejpam-3131	140	7	.	.	PUNCT
ejpam-3131	141	1	moreover	moreover	ADV
ejpam-3131	141	2	f(a	f(a	NOUN
ejpam-3131	141	3	)	)	PUNCT
ejpam-3131	141	4	⊆	⊆	NUM
ejpam-3131	141	5	f(a	f(a	NOUN
ejpam-3131	141	6	)	)	PUNCT
ejpam-3131	141	7	,	,	PUNCT
ejpam-3131	141	8	since	since	SCONJ
ejpam-3131	141	9	f	f	PROPN
ejpam-3131	141	10	is	be	AUX
ejpam-3131	141	11	closed	closed	ADJ
ejpam-3131	141	12	.	.	PUNCT
ejpam-3131	142	1	in	in	ADP
ejpam-3131	142	2	consequence	consequence	NOUN
ejpam-3131	142	3	f(a)\v	f(a)\v	PROPN
ejpam-3131	142	4	∈	∈	PROPN
ejpam-3131	142	5	f(i	f(i	NUM
ejpam-3131	142	6	)	)	PUNCT
ejpam-3131	142	7	.	.	PUNCT
ejpam-3131	143	1	(	(	PUNCT
ejpam-3131	143	2	2	2	X
ejpam-3131	143	3	)	)	PUNCT
ejpam-3131	143	4	it	it	PRON
ejpam-3131	143	5	is	be	AUX
ejpam-3131	143	6	similar	similar	ADJ
ejpam-3131	143	7	to	to	ADP
ejpam-3131	143	8	(	(	PUNCT
ejpam-3131	143	9	1	1	NUM
ejpam-3131	143	10	)	)	PUNCT
ejpam-3131	143	11	.	.	PUNCT
ejpam-3131	144	1	n.r	n.r	PROPN
ejpam-3131	144	2	.	.	PROPN
ejpam-3131	144	3	pachón	pachón	PROPN
ejpam-3131	144	4	/	/	SYM
ejpam-3131	144	5	eur	eur	PROPN
ejpam-3131	144	6	.	.	PUNCT
ejpam-3131	145	1	j.	j.	PROPN
ejpam-3131	145	2	pure	pure	PROPN
ejpam-3131	145	3	appl	appl	PROPN
ejpam-3131	145	4	.	.	PROPN
ejpam-3131	145	5	math	math	PROPN
ejpam-3131	145	6	,	,	PUNCT
ejpam-3131	145	7	11	11	NUM
ejpam-3131	145	8	(	(	PUNCT
ejpam-3131	145	9	1	1	NUM
ejpam-3131	145	10	)	)	PUNCT
ejpam-3131	145	11	(	(	PUNCT
ejpam-3131	145	12	2018	2018	NUM
ejpam-3131	145	13	)	)	PUNCT
ejpam-3131	145	14	,	,	PUNCT
ejpam-3131	145	15	299	299	NUM
ejpam-3131	145	16	-	-	SYM
ejpam-3131	145	17	314	314	NUM
ejpam-3131	145	18	304	304	NUM
ejpam-3131	145	19	(	(	PUNCT
ejpam-3131	145	20	3	3	NUM
ejpam-3131	145	21	)	)	PUNCT
ejpam-3131	145	22	if	if	SCONJ
ejpam-3131	145	23	u	u	PROPN
ejpam-3131	145	24	∈	∈	PROPN
ejpam-3131	145	25	τ	τ	X
ejpam-3131	145	26	and	and	CCONJ
ejpam-3131	145	27	f−1(b)\u	f−1(b)\u	PROPN
ejpam-3131	145	28	∈	∈	PROPN
ejpam-3131	145	29	i	i	PRON
ejpam-3131	145	30	,	,	PUNCT
ejpam-3131	145	31	this	this	PRON
ejpam-3131	145	32	is	be	AUX
ejpam-3131	145	33	,	,	PUNCT
ejpam-3131	145	34	f−1	f−1	PROPN
ejpam-3131	146	1	[	[	X
ejpam-3131	146	2	b\f(u	b\f(u	PROPN
ejpam-3131	146	3	)	)	PUNCT
ejpam-3131	146	4	]	]	PUNCT
ejpam-3131	147	1	∈	∈	PROPN
ejpam-3131	148	1	i	i	PRON
ejpam-3131	148	2	,	,	PUNCT
ejpam-3131	148	3	then	then	ADV
ejpam-3131	148	4	b\f(u	b\f(u	PROPN
ejpam-3131	148	5	)	)	PUNCT
ejpam-3131	149	1	∈	∈	PROPN
ejpam-3131	149	2	j	j	PROPN
ejpam-3131	149	3	.	.	PUNCT
ejpam-3131	150	1	given	give	VERB
ejpam-3131	150	2	that	that	PRON
ejpam-3131	150	3	b	b	NOUN
ejpam-3131	150	4	is	be	AUX
ejpam-3131	150	5	ρjg	ρjg	NOUN
ejpam-3131	150	6	-	-	PUNCT
ejpam-3131	150	7	closed	closed	ADJ
ejpam-3131	150	8	we	we	PRON
ejpam-3131	150	9	have	have	VERB
ejpam-3131	150	10	that	that	DET
ejpam-3131	150	11	b\f(u	b\f(u	PROPN
ejpam-3131	150	12	)	)	PUNCT
ejpam-3131	150	13	∈	∈	PROPN
ejpam-3131	150	14	j	j	PROPN
ejpam-3131	150	15	.	.	PUNCT
ejpam-3131	151	1	in	in	ADP
ejpam-3131	151	2	consequence	consequence	PROPN
ejpam-3131	151	3	f−1	f−1	PROPN
ejpam-3131	151	4	[	[	PUNCT
ejpam-3131	151	5	b\f(u	b\f(u	PROPN
ejpam-3131	151	6	)	)	PUNCT
ejpam-3131	151	7	]	]	PUNCT
ejpam-3131	152	1	∈	∈	PROPN
ejpam-3131	153	1	i	i	PRON
ejpam-3131	153	2	,	,	PUNCT
ejpam-3131	153	3	this	this	PRON
ejpam-3131	153	4	is	be	AUX
ejpam-3131	153	5	f−1	f−1	PROPN
ejpam-3131	153	6	(	(	PUNCT
ejpam-3131	153	7	b	b	NOUN
ejpam-3131	153	8	)	)	PUNCT
ejpam-3131	153	9	\u	\u	PRON
ejpam-3131	153	10	∈	∈	PROPN
ejpam-3131	153	11	i.	i.	NOUN
ejpam-3131	153	12	since	since	SCONJ
ejpam-3131	153	13	f	f	PROPN
ejpam-3131	153	14	is	be	AUX
ejpam-3131	153	15	continuous	continuous	ADJ
ejpam-3131	153	16	we	we	PRON
ejpam-3131	153	17	have	have	VERB
ejpam-3131	153	18	that	that	DET
ejpam-3131	153	19	f−1(b	f−1(b	PROPN
ejpam-3131	153	20	)	)	PUNCT
ejpam-3131	153	21	⊆	⊆	NUM
ejpam-3131	153	22	f−1(b	f−1(b	PROPN
ejpam-3131	153	23	)	)	PUNCT
ejpam-3131	153	24	,	,	PUNCT
ejpam-3131	153	25	and	and	CCONJ
ejpam-3131	153	26	so	so	ADV
ejpam-3131	153	27	f−1	f−1	PROPN
ejpam-3131	153	28	(	(	PUNCT
ejpam-3131	153	29	b)\u	b)\u	PROPN
ejpam-3131	153	30	∈	∈	PROPN
ejpam-3131	153	31	i.	i.	NOUN
ejpam-3131	153	32	(	(	PUNCT
ejpam-3131	153	33	4	4	NUM
ejpam-3131	153	34	)	)	PUNCT
ejpam-3131	153	35	if	if	SCONJ
ejpam-3131	153	36	w	w	PROPN
ejpam-3131	153	37	∈	∈	PROPN
ejpam-3131	153	38	β	β	X
ejpam-3131	153	39	and	and	CCONJ
ejpam-3131	153	40	f(a)\w	f(a)\w	NOUN
ejpam-3131	153	41	∈	∈	PROPN
ejpam-3131	153	42	j	j	NOUN
ejpam-3131	153	43	then	then	ADV
ejpam-3131	153	44	a\f−1	a\f−1	PROPN
ejpam-3131	153	45	(	(	PUNCT
ejpam-3131	153	46	w	w	NOUN
ejpam-3131	153	47	)	)	PUNCT
ejpam-3131	154	1	=	=	SYM
ejpam-3131	154	2	f−1	f−1	PROPN
ejpam-3131	155	1	[	[	X
ejpam-3131	155	2	f	f	X
ejpam-3131	155	3	(	(	PUNCT
ejpam-3131	155	4	a	a	NOUN
ejpam-3131	155	5	)	)	PUNCT
ejpam-3131	155	6	\w	\w	ADJ
ejpam-3131	155	7	]	]	PUNCT
ejpam-3131	155	8	∈	∈	PROPN
ejpam-3131	155	9	f−1	f−1	PROPN
ejpam-3131	155	10	(	(	PUNCT
ejpam-3131	155	11	j	j	PROPN
ejpam-3131	155	12	)	)	PUNCT
ejpam-3131	155	13	.	.	PUNCT
ejpam-3131	156	1	since	since	SCONJ
ejpam-3131	156	2	a	a	DET
ejpam-3131	156	3	is	be	AUX
ejpam-3131	156	4	ρ	ρ	NOUN
ejpam-3131	156	5	(	(	PUNCT
ejpam-3131	156	6	f−1(j	f−1(j	PROPN
ejpam-3131	156	7	)	)	PUNCT
ejpam-3131	156	8	)	)	PUNCT
ejpam-3131	156	9	g	g	NOUN
ejpam-3131	156	10	-closed	-close	VERB
ejpam-3131	156	11	there	there	PRON
ejpam-3131	156	12	is	be	VERB
ejpam-3131	156	13	j	j	PROPN
ejpam-3131	156	14	∈	∈	PROPN
ejpam-3131	156	15	j	j	PROPN
ejpam-3131	156	16	with	with	ADP
ejpam-3131	156	17	a\f−1	a\f−1	PROPN
ejpam-3131	156	18	(	(	PUNCT
ejpam-3131	156	19	w	w	NOUN
ejpam-3131	156	20	)	)	PUNCT
ejpam-3131	156	21	=	=	SYM
ejpam-3131	156	22	f−1	f−1	PROPN
ejpam-3131	156	23	(	(	PUNCT
ejpam-3131	156	24	j	j	NOUN
ejpam-3131	156	25	)	)	PUNCT
ejpam-3131	156	26	.	.	PUNCT
ejpam-3131	157	1	but	but	CCONJ
ejpam-3131	157	2	f	f	X
ejpam-3131	157	3	(	(	PUNCT
ejpam-3131	157	4	a)\w	a)\w	VERB
ejpam-3131	157	5	⊆	⊆	NUM
ejpam-3131	157	6	f	f	X
ejpam-3131	157	7	(	(	PUNCT
ejpam-3131	157	8	a	a	NOUN
ejpam-3131	157	9	)	)	PUNCT
ejpam-3131	157	10	\w	\w	VERB
ejpam-3131	157	11	⊆	⊆	NUM
ejpam-3131	157	12	f	f	X
ejpam-3131	157	13	(	(	PUNCT
ejpam-3131	157	14	a	a	NOUN
ejpam-3131	157	15	)	)	PUNCT
ejpam-3131	157	16	\f	\f	PUNCT
ejpam-3131	158	1	[	[	PUNCT
ejpam-3131	158	2	f−1	f−1	PROPN
ejpam-3131	158	3	(	(	PUNCT
ejpam-3131	158	4	w	w	PROPN
ejpam-3131	158	5	)	)	PUNCT
ejpam-3131	158	6	]	]	PUNCT
ejpam-3131	159	1	⊆	⊆	NUM
ejpam-3131	159	2	f	f	X
ejpam-3131	159	3	[	[	PUNCT
ejpam-3131	159	4	a\f−1	a\f−1	PROPN
ejpam-3131	159	5	(	(	PUNCT
ejpam-3131	159	6	w	w	NOUN
ejpam-3131	159	7	)	)	PUNCT
ejpam-3131	159	8	]	]	PUNCT
ejpam-3131	160	1	=	=	PUNCT
ejpam-3131	160	2	f	f	X
ejpam-3131	160	3	(	(	PUNCT
ejpam-3131	160	4	f−1	f−1	PROPN
ejpam-3131	160	5	(	(	PUNCT
ejpam-3131	160	6	j	j	NOUN
ejpam-3131	160	7	)	)	PUNCT
ejpam-3131	160	8	)	)	PUNCT
ejpam-3131	161	1	⊆	⊆	NUM
ejpam-3131	161	2	j	j	NOUN
ejpam-3131	161	3	,	,	PUNCT
ejpam-3131	161	4	and	and	CCONJ
ejpam-3131	161	5	so	so	ADV
ejpam-3131	161	6	f	f	PROPN
ejpam-3131	161	7	(	(	PUNCT
ejpam-3131	161	8	a)\w	a)\w	PROPN
ejpam-3131	161	9	∈	∈	PROPN
ejpam-3131	161	10	j	j	PROPN
ejpam-3131	161	11	.	.	PUNCT
ejpam-3131	162	1	□	□	PUNCT
ejpam-3131	162	2	definition	definition	NOUN
ejpam-3131	162	3	2.9	2.9	NUM
ejpam-3131	162	4	.	.	PUNCT
ejpam-3131	163	1	if	if	SCONJ
ejpam-3131	163	2	(	(	PUNCT
ejpam-3131	163	3	x	x	X
ejpam-3131	163	4	,	,	PUNCT
ejpam-3131	163	5	τ	τ	PROPN
ejpam-3131	163	6	,	,	PUNCT
ejpam-3131	163	7	i	i	PROPN
ejpam-3131	163	8	)	)	PUNCT
ejpam-3131	163	9	is	be	AUX
ejpam-3131	163	10	an	an	DET
ejpam-3131	163	11	ideal	ideal	ADJ
ejpam-3131	163	12	topological	topological	ADJ
ejpam-3131	163	13	space	space	NOUN
ejpam-3131	163	14	and	and	CCONJ
ejpam-3131	163	15	a	a	DET
ejpam-3131	163	16	⊆	⊆	NUM
ejpam-3131	163	17	x	x	SYM
ejpam-3131	163	18	then	then	ADV
ejpam-3131	163	19	a	a	PRON
ejpam-3131	163	20	is	be	AUX
ejpam-3131	163	21	said	say	VERB
ejpam-3131	163	22	to	to	PART
ejpam-3131	163	23	be	be	AUX
ejpam-3131	163	24	ρig	ρig	NOUN
ejpam-3131	163	25	-	-	PUNCT
ejpam-3131	163	26	open	open	ADJ
ejpam-3131	163	27	if	if	SCONJ
ejpam-3131	163	28	x\a	x\a	PROPN
ejpam-3131	163	29	is	be	AUX
ejpam-3131	163	30	ρig	ρig	ADV
ejpam-3131	163	31	-	-	PUNCT
ejpam-3131	163	32	closed	closed	ADJ
ejpam-3131	163	33	.	.	PUNCT
ejpam-3131	164	1	the	the	DET
ejpam-3131	164	2	following	following	ADJ
ejpam-3131	164	3	result	result	NOUN
ejpam-3131	164	4	is	be	AUX
ejpam-3131	164	5	a	a	DET
ejpam-3131	164	6	consequence	consequence	NOUN
ejpam-3131	164	7	of	of	ADP
ejpam-3131	164	8	theorem	theorem	ADJ
ejpam-3131	164	9	2.5	2.5	NUM
ejpam-3131	164	10	.	.	PUNCT
ejpam-3131	165	1	theorem	theorem	VERB
ejpam-3131	165	2	2.10	2.10	NUM
ejpam-3131	165	3	.	.	PUNCT
ejpam-3131	166	1	let	let	VERB
ejpam-3131	166	2	(	(	PUNCT
ejpam-3131	166	3	x	x	X
ejpam-3131	166	4	,	,	PUNCT
ejpam-3131	166	5	τ	τ	PROPN
ejpam-3131	166	6	,	,	PUNCT
ejpam-3131	166	7	i	i	PRON
ejpam-3131	166	8	)	)	PUNCT
ejpam-3131	166	9	be	be	VERB
ejpam-3131	166	10	an	an	DET
ejpam-3131	166	11	ideal	ideal	ADJ
ejpam-3131	166	12	space	space	NOUN
ejpam-3131	166	13	.	.	PUNCT
ejpam-3131	167	1	if	if	SCONJ
ejpam-3131	167	2	a	a	DET
ejpam-3131	167	3	⊆	⊆	NUM
ejpam-3131	167	4	x	x	NOUN
ejpam-3131	167	5	and	and	CCONJ
ejpam-3131	167	6	b	b	NOUN
ejpam-3131	167	7	⊆	⊆	NUM
ejpam-3131	167	8	x	x	PUNCT
ejpam-3131	167	9	then	then	ADV
ejpam-3131	167	10	:	:	PUNCT
ejpam-3131	167	11	(	(	PUNCT
ejpam-3131	167	12	1	1	X
ejpam-3131	167	13	)	)	PUNCT
ejpam-3131	167	14	if	if	SCONJ
ejpam-3131	167	15	a	a	PRON
ejpam-3131	167	16	and	and	CCONJ
ejpam-3131	167	17	b	b	NOUN
ejpam-3131	167	18	are	be	AUX
ejpam-3131	167	19	ρig	ρig	ADV
ejpam-3131	167	20	-	-	PUNCT
ejpam-3131	167	21	open	open	ADJ
ejpam-3131	167	22	then	then	ADV
ejpam-3131	167	23	a	a	DET
ejpam-3131	167	24	∩b	∩b	NOUN
ejpam-3131	167	25	is	be	AUX
ejpam-3131	167	26	ρig	ρig	ADV
ejpam-3131	167	27	-	-	PUNCT
ejpam-3131	167	28	open	open	ADJ
ejpam-3131	167	29	.	.	PUNCT
ejpam-3131	168	1	(	(	PUNCT
ejpam-3131	168	2	2	2	X
ejpam-3131	168	3	)	)	PUNCT
ejpam-3131	168	4	a	a	PRON
ejpam-3131	168	5	is	be	AUX
ejpam-3131	168	6	ρig	ρig	NOUN
ejpam-3131	168	7	-	-	PUNCT
ejpam-3131	168	8	open	open	ADJ
ejpam-3131	168	9	if	if	SCONJ
ejpam-3131	168	10	and	and	CCONJ
ejpam-3131	168	11	only	only	ADV
ejpam-3131	168	12	if	if	SCONJ
ejpam-3131	168	13	,	,	PUNCT
ejpam-3131	168	14	for	for	ADP
ejpam-3131	168	15	each	each	DET
ejpam-3131	168	16	closed	close	VERB
ejpam-3131	168	17	set	set	VERB
ejpam-3131	168	18	f	f	NOUN
ejpam-3131	168	19	,	,	PUNCT
ejpam-3131	169	1	if	if	SCONJ
ejpam-3131	169	2	f\	f\	PRON
ejpam-3131	169	3	(	(	PUNCT
ejpam-3131	169	4	a\	a\	NOUN
ejpam-3131	169	5	0	0	NUM
ejpam-3131	169	6	a	a	PRON
ejpam-3131	169	7	)	)	PUNCT
ejpam-3131	169	8	∈	∈	PROPN
ejpam-3131	169	9	i	i	PRON
ejpam-3131	169	10	then	then	ADV
ejpam-3131	169	11	f	f	PROPN
ejpam-3131	169	12	∈	∈	PROPN
ejpam-3131	169	13	i.	i.	NOUN
ejpam-3131	169	14	(	(	PUNCT
ejpam-3131	169	15	3	3	X
ejpam-3131	169	16	)	)	PUNCT
ejpam-3131	169	17	if	if	SCONJ
ejpam-3131	169	18	b\a	b\a	NOUN
ejpam-3131	169	19	∈	∈	PROPN
ejpam-3131	169	20	i	i	PRON
ejpam-3131	169	21	,	,	PUNCT
ejpam-3131	169	22	0	0	PUNCT
ejpam-3131	170	1	a\	a\	NOUN
ejpam-3131	170	2	0	0	NUM
ejpam-3131	170	3	b	b	X
ejpam-3131	170	4	∈	∈	PROPN
ejpam-3131	171	1	i	i	PRON
ejpam-3131	171	2	and	and	CCONJ
ejpam-3131	171	3	a	a	PRON
ejpam-3131	171	4	is	be	AUX
ejpam-3131	171	5	ρig	ρig	NOUN
ejpam-3131	171	6	-	-	PUNCT
ejpam-3131	171	7	open	open	ADJ
ejpam-3131	171	8	then	then	ADV
ejpam-3131	171	9	b	b	NOUN
ejpam-3131	171	10	is	be	AUX
ejpam-3131	171	11	ρig	ρig	ADV
ejpam-3131	171	12	-	-	PUNCT
ejpam-3131	171	13	open	open	ADJ
ejpam-3131	171	14	.	.	PUNCT
ejpam-3131	172	1	(	(	PUNCT
ejpam-3131	172	2	4	4	X
ejpam-3131	172	3	)	)	PUNCT
ejpam-3131	172	4	if	if	SCONJ
ejpam-3131	172	5	0	0	NUM
ejpam-3131	172	6	a	a	DET
ejpam-3131	172	7	⊆	⊆	NUM
ejpam-3131	172	8	b	b	SYM
ejpam-3131	172	9	⊆	⊆	NUM
ejpam-3131	172	10	a	a	PRON
ejpam-3131	172	11	and	and	CCONJ
ejpam-3131	172	12	a	a	PRON
ejpam-3131	172	13	is	be	AUX
ejpam-3131	172	14	ρig	ρig	NOUN
ejpam-3131	172	15	-	-	PUNCT
ejpam-3131	172	16	open	open	ADJ
ejpam-3131	172	17	,	,	PUNCT
ejpam-3131	172	18	then	then	ADV
ejpam-3131	172	19	b	b	PROPN
ejpam-3131	172	20	is	be	AUX
ejpam-3131	172	21	ρig	ρig	ADV
ejpam-3131	172	22	-	-	PUNCT
ejpam-3131	172	23	open	open	ADJ
ejpam-3131	172	24	.	.	PUNCT
ejpam-3131	173	1	(	(	PUNCT
ejpam-3131	173	2	5	5	X
ejpam-3131	173	3	)	)	PUNCT
ejpam-3131	173	4	if	if	SCONJ
ejpam-3131	173	5	a	a	PRON
ejpam-3131	173	6	is	be	AUX
ejpam-3131	173	7	ρig	ρig	NOUN
ejpam-3131	173	8	-	-	PUNCT
ejpam-3131	173	9	open	open	ADJ
ejpam-3131	173	10	and	and	CCONJ
ejpam-3131	173	11	b	b	NOUN
ejpam-3131	173	12	is	be	AUX
ejpam-3131	173	13	open	open	ADJ
ejpam-3131	173	14	,	,	PUNCT
ejpam-3131	173	15	then	then	ADV
ejpam-3131	173	16	a	a	DET
ejpam-3131	173	17	∪b	∪b	PRON
ejpam-3131	173	18	is	be	AUX
ejpam-3131	173	19	ρig	ρig	ADV
ejpam-3131	173	20	-	-	PUNCT
ejpam-3131	173	21	open	open	ADJ
ejpam-3131	173	22	.	.	PUNCT
ejpam-3131	174	1	next	next	ADV
ejpam-3131	174	2	we	we	PRON
ejpam-3131	174	3	present	present	VERB
ejpam-3131	174	4	other	other	ADJ
ejpam-3131	174	5	useful	useful	ADJ
ejpam-3131	174	6	properties	property	NOUN
ejpam-3131	174	7	of	of	ADP
ejpam-3131	174	8	ρig	ρig	NOUN
ejpam-3131	174	9	-	-	PUNCT
ejpam-3131	174	10	open	open	ADJ
ejpam-3131	174	11	sets	set	NOUN
ejpam-3131	174	12	.	.	PUNCT
ejpam-3131	175	1	theorem	theorem	VERB
ejpam-3131	175	2	2.11	2.11	NUM
ejpam-3131	175	3	.	.	PUNCT
ejpam-3131	176	1	if	if	SCONJ
ejpam-3131	176	2	(	(	PUNCT
ejpam-3131	176	3	x	x	X
ejpam-3131	176	4	,	,	PUNCT
ejpam-3131	176	5	τ	τ	PROPN
ejpam-3131	176	6	,	,	PUNCT
ejpam-3131	176	7	i	i	PROPN
ejpam-3131	176	8	)	)	PUNCT
ejpam-3131	176	9	is	be	AUX
ejpam-3131	176	10	an	an	DET
ejpam-3131	176	11	ideal	ideal	ADJ
ejpam-3131	176	12	space	space	NOUN
ejpam-3131	176	13	then	then	ADV
ejpam-3131	176	14	a	a	DET
ejpam-3131	176	15	⊆	⊆	NUM
ejpam-3131	176	16	x	x	X
ejpam-3131	176	17	is	be	AUX
ejpam-3131	176	18	ρig	ρig	NOUN
ejpam-3131	176	19	-	-	PUNCT
ejpam-3131	176	20	open	open	ADJ
ejpam-3131	176	21	if	if	SCONJ
ejpam-3131	176	22	and	and	CCONJ
ejpam-3131	176	23	only	only	ADV
ejpam-3131	176	24	if	if	SCONJ
ejpam-3131	176	25	,	,	PUNCT
ejpam-3131	176	26	for	for	ADP
ejpam-3131	176	27	each	each	DET
ejpam-3131	176	28	f	f	PROPN
ejpam-3131	176	29	⊆	⊆	NUM
ejpam-3131	176	30	x	x	SYM
ejpam-3131	176	31	,	,	PUNCT
ejpam-3131	176	32	closed	closed	ADJ
ejpam-3131	176	33	,	,	PUNCT
ejpam-3131	176	34	if	if	SCONJ
ejpam-3131	176	35	f\a	f\a	PROPN
ejpam-3131	176	36	∈	∈	PROPN
ejpam-3131	177	1	i	i	PRON
ejpam-3131	177	2	then	then	ADV
ejpam-3131	177	3	f\	f\	X
ejpam-3131	177	4	0	0	PUNCT
ejpam-3131	177	5	a	a	DET
ejpam-3131	177	6	∈	∈	PROPN
ejpam-3131	177	7	i.	i.	NOUN
ejpam-3131	177	8	proof	proof	NOUN
ejpam-3131	177	9	.	.	PUNCT
ejpam-3131	178	1	(	(	PUNCT
ejpam-3131	178	2	→	→	NOUN
ejpam-3131	178	3	)	)	PUNCT
ejpam-3131	178	4	suppose	suppose	VERB
ejpam-3131	178	5	that	that	SCONJ
ejpam-3131	178	6	f	f	PROPN
ejpam-3131	178	7	⊆	⊆	NUM
ejpam-3131	178	8	x	x	PUNCT
ejpam-3131	178	9	is	be	AUX
ejpam-3131	178	10	closed	close	VERB
ejpam-3131	178	11	and	and	CCONJ
ejpam-3131	178	12	that	that	SCONJ
ejpam-3131	178	13	f\a	f\a	PROPN
ejpam-3131	178	14	∈	∈	PROPN
ejpam-3131	178	15	i	i	PRON
ejpam-3131	178	16	,	,	PUNCT
ejpam-3131	178	17	this	this	PRON
ejpam-3131	178	18	is	be	AUX
ejpam-3131	178	19	,	,	PUNCT
ejpam-3131	178	20	(	(	PUNCT
ejpam-3131	178	21	x\a	x\a	PROPN
ejpam-3131	178	22	)	)	PUNCT
ejpam-3131	178	23	\	\	PUNCT
ejpam-3131	179	1	(	(	PUNCT
ejpam-3131	179	2	x\f	x\f	SYM
ejpam-3131	179	3	)	)	PUNCT
ejpam-3131	179	4	∈	∈	PROPN
ejpam-3131	179	5	i.	i.	NOUN
ejpam-3131	179	6	given	give	VERB
ejpam-3131	179	7	that	that	SCONJ
ejpam-3131	179	8	x\a	x\a	PROPN
ejpam-3131	179	9	is	be	AUX
ejpam-3131	179	10	ρig	ρig	ADV
ejpam-3131	179	11	-	-	PUNCT
ejpam-3131	179	12	closed	closed	ADJ
ejpam-3131	179	13	we	we	PRON
ejpam-3131	179	14	have	have	VERB
ejpam-3131	180	1	that	that	PRON
ejpam-3131	180	2	x\a\	x\a\	PROPN
ejpam-3131	180	3	(	(	PUNCT
ejpam-3131	180	4	x\f	x\f	PROPN
ejpam-3131	180	5	)	)	PUNCT
ejpam-3131	180	6	∈	∈	PROPN
ejpam-3131	181	1	i	i	PRON
ejpam-3131	181	2	or	or	CCONJ
ejpam-3131	181	3	,	,	PUNCT
ejpam-3131	181	4	equivalently	equivalently	ADV
ejpam-3131	181	5	,	,	PUNCT
ejpam-3131	181	6	f\	f\	PROPN
ejpam-3131	181	7	0	0	PUNCT
ejpam-3131	181	8	a	a	DET
ejpam-3131	181	9	∈	∈	PROPN
ejpam-3131	181	10	i.	i.	NOUN
ejpam-3131	181	11	(	(	PUNCT
ejpam-3131	181	12	←	←	PROPN
ejpam-3131	181	13	)	)	PUNCT
ejpam-3131	181	14	suppose	suppose	VERB
ejpam-3131	181	15	that	that	SCONJ
ejpam-3131	181	16	v	v	X
ejpam-3131	181	17	∈	∈	X
ejpam-3131	181	18	τ	τ	X
ejpam-3131	181	19	and	and	CCONJ
ejpam-3131	181	20	(	(	PUNCT
ejpam-3131	181	21	x\a	x\a	PROPN
ejpam-3131	181	22	)	)	PUNCT
ejpam-3131	181	23	\v	\v	PROPN
ejpam-3131	182	1	∈	∈	PROPN
ejpam-3131	183	1	i	i	PRON
ejpam-3131	183	2	,	,	PUNCT
ejpam-3131	183	3	this	this	PRON
ejpam-3131	183	4	is	be	AUX
ejpam-3131	183	5	,	,	PUNCT
ejpam-3131	183	6	(	(	PUNCT
ejpam-3131	183	7	x\v	x\v	PROPN
ejpam-3131	183	8	)	)	PUNCT
ejpam-3131	183	9	\a	\a	PROPN
ejpam-3131	184	1	∈	∈	PROPN
ejpam-3131	184	2	i.	i.	NOUN
ejpam-3131	184	3	the	the	DET
ejpam-3131	184	4	hypothesis	hypothesis	NOUN
ejpam-3131	184	5	implies	imply	VERB
ejpam-3131	184	6	that	that	SCONJ
ejpam-3131	184	7	(	(	PUNCT
ejpam-3131	184	8	x\v	x\v	PROPN
ejpam-3131	184	9	)	)	PUNCT
ejpam-3131	184	10	\	\	PROPN
ejpam-3131	184	11	0	0	PUNCT
ejpam-3131	185	1	a	a	DET
ejpam-3131	185	2	∈	∈	PROPN
ejpam-3131	185	3	i	i	X
ejpam-3131	185	4	,	,	PUNCT
ejpam-3131	185	5	or	or	CCONJ
ejpam-3131	185	6	equivalently	equivalently	ADV
ejpam-3131	185	7	,	,	PUNCT
ejpam-3131	185	8	(	(	PUNCT
ejpam-3131	185	9	x\	x\	PROPN
ejpam-3131	185	10	0	0	NUM
ejpam-3131	185	11	a	a	PRON
ejpam-3131	185	12	)	)	PUNCT
ejpam-3131	185	13	\v	\v	PROPN
ejpam-3131	185	14	∈	∈	PROPN
ejpam-3131	185	15	i.	i.	NOUN
ejpam-3131	185	16	hence	hence	ADV
ejpam-3131	185	17	x\a\v	x\a\v	PROPN
ejpam-3131	185	18	∈	∈	PROPN
ejpam-3131	186	1	i	i	PRON
ejpam-3131	186	2	and	and	CCONJ
ejpam-3131	186	3	so	so	ADV
ejpam-3131	186	4	x\a	x\a	PROPN
ejpam-3131	186	5	is	be	AUX
ejpam-3131	186	6	ρig	ρig	ADV
ejpam-3131	186	7	-	-	PUNCT
ejpam-3131	186	8	closed	closed	ADJ
ejpam-3131	186	9	.	.	PUNCT
ejpam-3131	187	1	□	□	PUNCT
ejpam-3131	187	2	theorem	theorem	VERB
ejpam-3131	187	3	2.12	2.12	NUM
ejpam-3131	187	4	.	.	PUNCT
ejpam-3131	188	1	if	if	SCONJ
ejpam-3131	188	2	(	(	PUNCT
ejpam-3131	188	3	x	x	X
ejpam-3131	188	4	,	,	PUNCT
ejpam-3131	188	5	τ	τ	PROPN
ejpam-3131	188	6	,	,	PUNCT
ejpam-3131	188	7	i	i	PROPN
ejpam-3131	188	8	)	)	PUNCT
ejpam-3131	188	9	is	be	AUX
ejpam-3131	188	10	an	an	DET
ejpam-3131	188	11	ideal	ideal	ADJ
ejpam-3131	188	12	space	space	NOUN
ejpam-3131	188	13	,	,	PUNCT
ejpam-3131	188	14	then	then	ADV
ejpam-3131	188	15	a	a	DET
ejpam-3131	188	16	⊆	⊆	NUM
ejpam-3131	188	17	x	x	X
ejpam-3131	188	18	is	be	AUX
ejpam-3131	188	19	ρig	ρig	ADV
ejpam-3131	188	20	-	-	PUNCT
ejpam-3131	188	21	closed	close	VERB
ejpam-3131	188	22	if	if	SCONJ
ejpam-3131	189	1	and	and	CCONJ
ejpam-3131	189	2	only	only	ADV
ejpam-3131	189	3	if	if	SCONJ
ejpam-3131	189	4	a\a	a\a	PRON
ejpam-3131	189	5	is	be	AUX
ejpam-3131	189	6	ρig	ρig	ADV
ejpam-3131	189	7	-	-	PUNCT
ejpam-3131	189	8	open	open	ADJ
ejpam-3131	189	9	.	.	PUNCT
ejpam-3131	190	1	n.r	n.r	PROPN
ejpam-3131	190	2	.	.	PROPN
ejpam-3131	190	3	pachón	pachón	PROPN
ejpam-3131	190	4	/	/	SYM
ejpam-3131	190	5	eur	eur	PROPN
ejpam-3131	190	6	.	.	PUNCT
ejpam-3131	191	1	j.	j.	PROPN
ejpam-3131	191	2	pure	pure	PROPN
ejpam-3131	191	3	appl	appl	PROPN
ejpam-3131	191	4	.	.	PROPN
ejpam-3131	191	5	math	math	PROPN
ejpam-3131	191	6	,	,	PUNCT
ejpam-3131	191	7	11	11	NUM
ejpam-3131	191	8	(	(	PUNCT
ejpam-3131	191	9	1	1	NUM
ejpam-3131	191	10	)	)	PUNCT
ejpam-3131	191	11	(	(	PUNCT
ejpam-3131	191	12	2018	2018	NUM
ejpam-3131	191	13	)	)	PUNCT
ejpam-3131	191	14	,	,	PUNCT
ejpam-3131	191	15	299	299	NUM
ejpam-3131	191	16	-	-	SYM
ejpam-3131	191	17	314	314	NUM
ejpam-3131	191	18	305	305	NUM
ejpam-3131	191	19	proof	proof	NOUN
ejpam-3131	191	20	.	.	PUNCT
ejpam-3131	192	1	(	(	PUNCT
ejpam-3131	192	2	→	→	NOUN
ejpam-3131	192	3	)	)	PUNCT
ejpam-3131	192	4	suppose	suppose	VERB
ejpam-3131	192	5	that	that	SCONJ
ejpam-3131	192	6	f	f	PROPN
ejpam-3131	192	7	⊆	⊆	NUM
ejpam-3131	192	8	x	x	PUNCT
ejpam-3131	192	9	is	be	AUX
ejpam-3131	192	10	closed	close	VERB
ejpam-3131	192	11	and	and	CCONJ
ejpam-3131	192	12	that	that	SCONJ
ejpam-3131	192	13	f\	f\	VERB
ejpam-3131	192	14	(	(	PUNCT
ejpam-3131	192	15	a\a	a\a	X
ejpam-3131	192	16	)	)	PUNCT
ejpam-3131	192	17	∈	∈	PROPN
ejpam-3131	192	18	i.	i.	NOUN
ejpam-3131	192	19	by	by	ADP
ejpam-3131	192	20	the	the	DET
ejpam-3131	192	21	theorem	theorem	ADJ
ejpam-3131	192	22	2.5	2.5	NUM
ejpam-3131	192	23	we	we	PRON
ejpam-3131	192	24	have	have	VERB
ejpam-3131	192	25	that	that	PRON
ejpam-3131	192	26	f	f	PROPN
ejpam-3131	192	27	∈	∈	PROPN
ejpam-3131	193	1	i	i	PRON
ejpam-3131	193	2	,	,	PUNCT
ejpam-3131	193	3	and	and	CCONJ
ejpam-3131	193	4	so	so	ADV
ejpam-3131	193	5	f\int	f\int	NOUN
ejpam-3131	193	6	(	(	PUNCT
ejpam-3131	193	7	a\a	a\a	X
ejpam-3131	193	8	)	)	PUNCT
ejpam-3131	193	9	∈	∈	PROPN
ejpam-3131	194	1	i	i	PRON
ejpam-3131	194	2	,	,	PUNCT
ejpam-3131	194	3	because	because	SCONJ
ejpam-3131	194	4	int	int	NOUN
ejpam-3131	194	5	(	(	PUNCT
ejpam-3131	194	6	a\a	a\a	X
ejpam-3131	194	7	)	)	PUNCT
ejpam-3131	194	8	=	=	PUNCT
ejpam-3131	194	9	∅.	∅.	VERB
ejpam-3131	194	10	thus	thus	ADV
ejpam-3131	194	11	a\a	a\a	X
ejpam-3131	194	12	is	be	AUX
ejpam-3131	194	13	ρig	ρig	ADV
ejpam-3131	194	14	-	-	PUNCT
ejpam-3131	194	15	open	open	ADJ
ejpam-3131	194	16	.	.	PUNCT
ejpam-3131	195	1	(	(	PUNCT
ejpam-3131	195	2	←	←	PROPN
ejpam-3131	195	3	)	)	PUNCT
ejpam-3131	195	4	suppose	suppose	VERB
ejpam-3131	195	5	that	that	SCONJ
ejpam-3131	195	6	u	u	PROPN
ejpam-3131	195	7	∈	∈	PROPN
ejpam-3131	195	8	τ	τ	X
ejpam-3131	195	9	and	and	CCONJ
ejpam-3131	195	10	that	that	SCONJ
ejpam-3131	195	11	a\u	a\u	PROPN
ejpam-3131	195	12	∈	∈	PROPN
ejpam-3131	195	13	i.	i.	NOUN
ejpam-3131	195	14	given	give	VERB
ejpam-3131	195	15	that	that	SCONJ
ejpam-3131	195	16	(	(	PUNCT
ejpam-3131	195	17	a\u	a\u	PROPN
ejpam-3131	195	18	)	)	PUNCT
ejpam-3131	195	19	\	\	PUNCT
ejpam-3131	196	1	(	(	PUNCT
ejpam-3131	196	2	a\a	a\a	X
ejpam-3131	196	3	)	)	PUNCT
ejpam-3131	196	4	=	=	PUNCT
ejpam-3131	196	5	a\u	a\u	PROPN
ejpam-3131	196	6	∈	∈	PROPN
ejpam-3131	196	7	i	i	PRON
ejpam-3131	196	8	and	and	CCONJ
ejpam-3131	196	9	a\a	a\a	PROPN
ejpam-3131	196	10	is	be	AUX
ejpam-3131	196	11	ρig	ρig	ADV
ejpam-3131	196	12	-	-	PUNCT
ejpam-3131	196	13	open	open	ADJ
ejpam-3131	196	14	,	,	PUNCT
ejpam-3131	196	15	the	the	DET
ejpam-3131	196	16	theorem	theorem	ADJ
ejpam-3131	196	17	2.11	2.11	NUM
ejpam-3131	196	18	implies	imply	VERB
ejpam-3131	196	19	(	(	PUNCT
ejpam-3131	196	20	a\u	a\u	PROPN
ejpam-3131	196	21	)	)	PUNCT
ejpam-3131	197	1	\int	\int	PROPN
ejpam-3131	197	2	(	(	PUNCT
ejpam-3131	197	3	a\a	a\a	X
ejpam-3131	197	4	)	)	PUNCT
ejpam-3131	197	5	∈	∈	PROPN
ejpam-3131	198	1	i	i	PRON
ejpam-3131	198	2	,	,	PUNCT
ejpam-3131	198	3	this	this	PRON
ejpam-3131	198	4	is	be	AUX
ejpam-3131	198	5	,	,	PUNCT
ejpam-3131	198	6	a\u	a\u	PROPN
ejpam-3131	198	7	∈	∈	PROPN
ejpam-3131	198	8	i.	i.	NOUN
ejpam-3131	198	9	□	□	PUNCT
ejpam-3131	198	10	theorem	theorem	VERB
ejpam-3131	198	11	2.13	2.13	NUM
ejpam-3131	198	12	.	.	PUNCT
ejpam-3131	199	1	if	if	SCONJ
ejpam-3131	199	2	a	a	PRON
ejpam-3131	199	3	and	and	CCONJ
ejpam-3131	199	4	b	b	NOUN
ejpam-3131	199	5	are	be	AUX
ejpam-3131	199	6	ρig	ρig	ADV
ejpam-3131	199	7	-	-	PUNCT
ejpam-3131	199	8	open	open	ADJ
ejpam-3131	199	9	subsets	subset	NOUN
ejpam-3131	199	10	of	of	ADP
ejpam-3131	199	11	an	an	DET
ejpam-3131	199	12	ideal	ideal	ADJ
ejpam-3131	199	13	space	space	NOUN
ejpam-3131	199	14	(	(	PUNCT
ejpam-3131	199	15	x	x	X
ejpam-3131	199	16	,	,	PUNCT
ejpam-3131	199	17	τ	τ	PROPN
ejpam-3131	199	18	,	,	PUNCT
ejpam-3131	199	19	i	i	PROPN
ejpam-3131	199	20	)	)	PUNCT
ejpam-3131	199	21	,	,	PUNCT
ejpam-3131	199	22	such	such	ADJ
ejpam-3131	199	23	that	that	SCONJ
ejpam-3131	199	24	a	a	DET
ejpam-3131	199	25	∩b	∩b	NOUN
ejpam-3131	199	26	∈	∈	X
ejpam-3131	199	27	i	i	PRON
ejpam-3131	199	28	and	and	CCONJ
ejpam-3131	199	29	a	a	DET
ejpam-3131	199	30	∩b	∩b	NOUN
ejpam-3131	199	31	∈	∈	PROPN
ejpam-3131	199	32	i	i	PRON
ejpam-3131	199	33	,	,	PUNCT
ejpam-3131	199	34	then	then	ADV
ejpam-3131	199	35	a	a	DET
ejpam-3131	199	36	∪b	∪b	PRON
ejpam-3131	199	37	is	be	AUX
ejpam-3131	199	38	ρig	ρig	ADV
ejpam-3131	199	39	-	-	PUNCT
ejpam-3131	199	40	open	open	ADJ
ejpam-3131	199	41	.	.	PUNCT
ejpam-3131	200	1	proof	proof	NOUN
ejpam-3131	200	2	.	.	PUNCT
ejpam-3131	201	1	suppose	suppose	VERB
ejpam-3131	201	2	that	that	SCONJ
ejpam-3131	201	3	f	f	PROPN
ejpam-3131	201	4	⊆	⊆	NUM
ejpam-3131	201	5	x	x	PUNCT
ejpam-3131	201	6	is	be	AUX
ejpam-3131	201	7	closed	close	VERB
ejpam-3131	201	8	and	and	CCONJ
ejpam-3131	201	9	that	that	SCONJ
ejpam-3131	201	10	f\	f\	VERB
ejpam-3131	201	11	(	(	PUNCT
ejpam-3131	201	12	a	a	DET
ejpam-3131	201	13	∪b	∪b	NOUN
ejpam-3131	201	14	)	)	PUNCT
ejpam-3131	201	15	∈	∈	PROPN
ejpam-3131	201	16	i.	i.	NOUN
ejpam-3131	201	17	we	we	PRON
ejpam-3131	201	18	have	have	VERB
ejpam-3131	201	19	that	that	PRON
ejpam-3131	201	20	:	:	PUNCT
ejpam-3131	201	21	(	(	PUNCT
ejpam-3131	201	22	a	a	X
ejpam-3131	201	23	)	)	PUNCT
ejpam-3131	201	24	f\a	f\a	PROPN
ejpam-3131	201	25	∪b	∪b	PUNCT
ejpam-3131	201	26	∈	∈	PROPN
ejpam-3131	201	27	i.	i.	NOUN
ejpam-3131	201	28	(	(	PUNCT
ejpam-3131	201	29	b	b	NOUN
ejpam-3131	201	30	)	)	PUNCT
ejpam-3131	201	31	(	(	PUNCT
ejpam-3131	201	32	f	f	X
ejpam-3131	201	33	∩a	∩a	PROPN
ejpam-3131	201	34	)	)	PUNCT
ejpam-3131	201	35	\a	\a	VERB
ejpam-3131	202	1	∈	∈	PROPN
ejpam-3131	202	2	i	i	PRON
ejpam-3131	202	3	,	,	PUNCT
ejpam-3131	202	4	because	because	SCONJ
ejpam-3131	202	5	(	(	PUNCT
ejpam-3131	202	6	f	f	X
ejpam-3131	202	7	∩a	∩a	PROPN
ejpam-3131	202	8	)	)	PUNCT
ejpam-3131	202	9	\a	\a	VERB
ejpam-3131	203	1	⊆	⊆	X
ejpam-3131	203	2	(	(	PUNCT
ejpam-3131	203	3	a	a	DET
ejpam-3131	203	4	∩b	∩b	NOUN
ejpam-3131	203	5	)	)	PUNCT
ejpam-3131	203	6	∪	∪	ADP
ejpam-3131	203	7	[	[	X
ejpam-3131	203	8	f\	f\	X
ejpam-3131	203	9	(	(	PUNCT
ejpam-3131	203	10	a	a	DET
ejpam-3131	203	11	∪b	∪b	NOUN
ejpam-3131	203	12	)	)	PUNCT
ejpam-3131	203	13	]	]	PUNCT
ejpam-3131	204	1	∈	∈	PROPN
ejpam-3131	204	2	i.	i.	NOUN
ejpam-3131	204	3	(	(	PUNCT
ejpam-3131	204	4	c	c	X
ejpam-3131	204	5	)	)	PUNCT
ejpam-3131	204	6	(	(	PUNCT
ejpam-3131	204	7	f	f	NOUN
ejpam-3131	204	8	∩b	∩b	PROPN
ejpam-3131	204	9	)	)	PUNCT
ejpam-3131	204	10	\b	\b	NOUN
ejpam-3131	204	11	∈	∈	PROPN
ejpam-3131	204	12	i.	i.	NOUN
ejpam-3131	204	13	(	(	PUNCT
ejpam-3131	204	14	d	d	NOUN
ejpam-3131	204	15	)	)	PUNCT
ejpam-3131	204	16	(	(	PUNCT
ejpam-3131	204	17	f	f	X
ejpam-3131	204	18	∩a	∩a	PROPN
ejpam-3131	204	19	)	)	PUNCT
ejpam-3131	204	20	\	\	PROPN
ejpam-3131	204	21	0	0	PUNCT
ejpam-3131	205	1	a	a	DET
ejpam-3131	205	2	∈	∈	PROPN
ejpam-3131	205	3	i	i	PRON
ejpam-3131	205	4	,	,	PUNCT
ejpam-3131	205	5	because	because	SCONJ
ejpam-3131	205	6	f	f	PROPN
ejpam-3131	205	7	∩a	∩a	PROPN
ejpam-3131	205	8	is	be	AUX
ejpam-3131	205	9	closed	close	VERB
ejpam-3131	205	10	and	and	CCONJ
ejpam-3131	205	11	a	a	PRON
ejpam-3131	205	12	is	be	AUX
ejpam-3131	205	13	ρig	ρig	ADV
ejpam-3131	205	14	-	-	PUNCT
ejpam-3131	205	15	open	open	ADJ
ejpam-3131	205	16	.	.	PUNCT
ejpam-3131	206	1	(	(	PUNCT
ejpam-3131	206	2	e	e	X
ejpam-3131	206	3	)	)	PUNCT
ejpam-3131	206	4	(	(	PUNCT
ejpam-3131	206	5	f	f	NOUN
ejpam-3131	206	6	∩b	∩b	PROPN
ejpam-3131	206	7	)	)	PUNCT
ejpam-3131	206	8	\	\	PROPN
ejpam-3131	206	9	0	0	PUNCT
ejpam-3131	207	1	b	b	X
ejpam-3131	207	2	∈	∈	PROPN
ejpam-3131	207	3	i.	i.	NOUN
ejpam-3131	207	4	(	(	PUNCT
ejpam-3131	207	5	f	f	X
ejpam-3131	207	6	)	)	PUNCT
ejpam-3131	208	1	[	[	PUNCT
ejpam-3131	208	2	f	f	X
ejpam-3131	208	3	∩a	∩a	PROPN
ejpam-3131	208	4	∪b	∪b	X
ejpam-3131	208	5	]	]	PUNCT
ejpam-3131	208	6	\	\	PROPN
ejpam-3131	209	1	(	(	PUNCT
ejpam-3131	209	2	0	0	NUM
ejpam-3131	209	3	a	a	DET
ejpam-3131	209	4	∪	∪	ADJ
ejpam-3131	209	5	0	0	NUM
ejpam-3131	209	6	b	b	X
ejpam-3131	209	7	)	)	PUNCT
ejpam-3131	209	8	∈	∈	PROPN
ejpam-3131	209	9	i.	i.	NOUN
ejpam-3131	209	10	in	in	ADP
ejpam-3131	209	11	fact	fact	NOUN
ejpam-3131	209	12	,	,	PUNCT
ejpam-3131	209	13	given	give	VERB
ejpam-3131	209	14	that	that	SCONJ
ejpam-3131	209	15	[	[	X
ejpam-3131	209	16	(	(	PUNCT
ejpam-3131	209	17	f	f	X
ejpam-3131	209	18	∩a	∩a	PROPN
ejpam-3131	209	19	)	)	PUNCT
ejpam-3131	209	20	\	\	PROPN
ejpam-3131	209	21	0	0	PUNCT
ejpam-3131	210	1	a	a	PRON
ejpam-3131	210	2	]	]	PUNCT
ejpam-3131	210	3	∪	∪	X
ejpam-3131	210	4	[	[	X
ejpam-3131	210	5	(	(	PUNCT
ejpam-3131	210	6	f	f	NOUN
ejpam-3131	210	7	∩b	∩b	PROPN
ejpam-3131	210	8	)	)	PUNCT
ejpam-3131	210	9	\	\	PROPN
ejpam-3131	211	1	0	0	NUM
ejpam-3131	211	2	b	b	X
ejpam-3131	211	3	]	]	X
ejpam-3131	211	4	∈	∈	PROPN
ejpam-3131	212	1	i	i	PRON
ejpam-3131	212	2	and	and	CCONJ
ejpam-3131	212	3	(	(	PUNCT
ejpam-3131	212	4	a	a	PRON
ejpam-3131	212	5	∪b	∪b	X
ejpam-3131	212	6	)	)	PUNCT
ejpam-3131	212	7	\	\	NOUN
ejpam-3131	213	1	(	(	PUNCT
ejpam-3131	213	2	0	0	NUM
ejpam-3131	213	3	a	a	DET
ejpam-3131	213	4	∪	∪	ADJ
ejpam-3131	213	5	0	0	NUM
ejpam-3131	213	6	b	b	NOUN
ejpam-3131	213	7	)	)	PUNCT
ejpam-3131	213	8	⊆	⊆	NUM
ejpam-3131	213	9	(	(	PUNCT
ejpam-3131	213	10	a\	a\	NOUN
ejpam-3131	213	11	0	0	NUM
ejpam-3131	213	12	a	a	PRON
ejpam-3131	213	13	)	)	PUNCT
ejpam-3131	213	14	∪	∪	NOUN
ejpam-3131	213	15	(	(	PUNCT
ejpam-3131	213	16	b\	b\	X
ejpam-3131	213	17	0	0	NUM
ejpam-3131	213	18	b	b	NOUN
ejpam-3131	213	19	)	)	PUNCT
ejpam-3131	213	20	,	,	PUNCT
ejpam-3131	213	21	we	we	PRON
ejpam-3131	213	22	have	have	VERB
ejpam-3131	213	23	that	that	PRON
ejpam-3131	213	24	[	[	PUNCT
ejpam-3131	213	25	f	f	X
ejpam-3131	213	26	∩a	∩a	PROPN
ejpam-3131	213	27	∪b	∪b	X
ejpam-3131	213	28	]	]	PUNCT
ejpam-3131	213	29	\	\	PROPN
ejpam-3131	214	1	(	(	PUNCT
ejpam-3131	214	2	0	0	NUM
ejpam-3131	214	3	a	a	DET
ejpam-3131	214	4	∪	∪	ADJ
ejpam-3131	214	5	0	0	NUM
ejpam-3131	214	6	b	b	NOUN
ejpam-3131	214	7	)	)	PUNCT
ejpam-3131	214	8	=	=	SYM
ejpam-3131	214	9	f	f	PROPN
ejpam-3131	214	10	∩	∩	X
ejpam-3131	214	11	[	[	X
ejpam-3131	214	12	(	(	PUNCT
ejpam-3131	214	13	a	a	DET
ejpam-3131	214	14	∪b	∪b	X
ejpam-3131	214	15	)	)	PUNCT
ejpam-3131	214	16	\	\	NOUN
ejpam-3131	215	1	(	(	PUNCT
ejpam-3131	215	2	0	0	NUM
ejpam-3131	215	3	a	a	DET
ejpam-3131	215	4	∪	∪	ADJ
ejpam-3131	215	5	0	0	NUM
ejpam-3131	215	6	b	b	NOUN
ejpam-3131	215	7	)	)	PUNCT
ejpam-3131	215	8	]	]	PUNCT
ejpam-3131	216	1	⊆	⊆	NUM
ejpam-3131	216	2	f	f	X
ejpam-3131	216	3	∩	∩	NOUN
ejpam-3131	216	4	[	[	X
ejpam-3131	216	5	(	(	PUNCT
ejpam-3131	216	6	a\	a\	NOUN
ejpam-3131	216	7	0	0	NUM
ejpam-3131	216	8	a	a	PRON
ejpam-3131	216	9	)	)	PUNCT
ejpam-3131	216	10	∪	∪	NOUN
ejpam-3131	216	11	(	(	PUNCT
ejpam-3131	216	12	b\	b\	X
ejpam-3131	216	13	0	0	NUM
ejpam-3131	216	14	b	b	NOUN
ejpam-3131	216	15	)	)	PUNCT
ejpam-3131	216	16	]	]	PUNCT
ejpam-3131	217	1	=[	=[	NOUN
ejpam-3131	217	2	(	(	PUNCT
ejpam-3131	217	3	f	f	NOUN
ejpam-3131	217	4	∩a	∩a	PROPN
ejpam-3131	217	5	)	)	PUNCT
ejpam-3131	217	6	\	\	PROPN
ejpam-3131	217	7	0	0	PUNCT
ejpam-3131	218	1	a	a	DET
ejpam-3131	218	2	]	]	PUNCT
ejpam-3131	218	3	∪	∪	X
ejpam-3131	218	4	[	[	X
ejpam-3131	218	5	(	(	PUNCT
ejpam-3131	218	6	f	f	NOUN
ejpam-3131	218	7	∩b	∩b	PROPN
ejpam-3131	218	8	)	)	PUNCT
ejpam-3131	218	9	\	\	PROPN
ejpam-3131	218	10	0	0	NUM
ejpam-3131	218	11	b	b	NOUN
ejpam-3131	218	12	]	]	PUNCT
ejpam-3131	218	13	,	,	PUNCT
ejpam-3131	218	14	and	and	CCONJ
ejpam-3131	218	15	so	so	ADV
ejpam-3131	218	16	[	[	PUNCT
ejpam-3131	218	17	f	f	X
ejpam-3131	218	18	∩a	∩a	PROPN
ejpam-3131	218	19	∪b	∪b	X
ejpam-3131	218	20	]	]	PUNCT
ejpam-3131	218	21	\	\	PROPN
ejpam-3131	219	1	(	(	PUNCT
ejpam-3131	219	2	0	0	NUM
ejpam-3131	219	3	a	a	DET
ejpam-3131	219	4	∪	∪	ADJ
ejpam-3131	219	5	0	0	NUM
ejpam-3131	219	6	b	b	X
ejpam-3131	219	7	)	)	PUNCT
ejpam-3131	219	8	∈	∈	PROPN
ejpam-3131	219	9	i.	i.	NOUN
ejpam-3131	219	10	(	(	PUNCT
ejpam-3131	219	11	g	g	NOUN
ejpam-3131	219	12	)	)	PUNCT
ejpam-3131	219	13	f\	f\	X
ejpam-3131	219	14	0	0	PUNCT
ejpam-3131	219	15	(	(	PUNCT
ejpam-3131	219	16	a	a	DET
ejpam-3131	219	17	∪b	∪b	NOUN
ejpam-3131	219	18	)	)	PUNCT
ejpam-3131	219	19	∈	∈	PROPN
ejpam-3131	220	1	i	i	PRON
ejpam-3131	220	2	,	,	PUNCT
ejpam-3131	220	3	because	because	SCONJ
ejpam-3131	220	4	f\	f\	NOUN
ejpam-3131	220	5	0	0	PUNCT
ejpam-3131	220	6	(	(	PUNCT
ejpam-3131	220	7	a	a	DET
ejpam-3131	220	8	∪b	∪b	NOUN
ejpam-3131	220	9	)	)	PUNCT
ejpam-3131	220	10	⊆	⊆	NUM
ejpam-3131	220	11	f\	f\	SYM
ejpam-3131	220	12	(	(	PUNCT
ejpam-3131	220	13	0	0	ADP
ejpam-3131	220	14	a	a	DET
ejpam-3131	220	15	∪	∪	ADJ
ejpam-3131	220	16	0	0	NUM
ejpam-3131	220	17	b	b	NOUN
ejpam-3131	220	18	)	)	PUNCT
ejpam-3131	220	19	⊆	⊆	NUM
ejpam-3131	221	1	[	[	X
ejpam-3131	221	2	(	(	PUNCT
ejpam-3131	221	3	f	f	X
ejpam-3131	221	4	∩a	∩a	PROPN
ejpam-3131	221	5	∪b	∪b	X
ejpam-3131	221	6	)	)	PUNCT
ejpam-3131	221	7	\	\	NOUN
ejpam-3131	222	1	(	(	PUNCT
ejpam-3131	222	2	0	0	NUM
ejpam-3131	222	3	a	a	DET
ejpam-3131	222	4	∪	∪	ADJ
ejpam-3131	222	5	0	0	NUM
ejpam-3131	222	6	b	b	NOUN
ejpam-3131	222	7	)	)	PUNCT
ejpam-3131	222	8	]	]	PUNCT
ejpam-3131	222	9	∪	∪	X
ejpam-3131	222	10	(	(	PUNCT
ejpam-3131	222	11	f\a	f\a	X
ejpam-3131	222	12	∪b	∪b	X
ejpam-3131	222	13	)	)	PUNCT
ejpam-3131	222	14	∈	∈	PROPN
ejpam-3131	222	15	i.	i.	NOUN
ejpam-3131	222	16	therefore	therefore	ADV
ejpam-3131	222	17	a	a	PRON
ejpam-3131	222	18	∪b	∪b	VERB
ejpam-3131	222	19	is	be	AUX
ejpam-3131	222	20	ρig	ρig	ADV
ejpam-3131	222	21	-	-	PUNCT
ejpam-3131	222	22	open	open	ADJ
ejpam-3131	222	23	.	.	PUNCT
ejpam-3131	223	1	□	□	PUNCT
ejpam-3131	223	2	corollary	corollary	ADJ
ejpam-3131	223	3	2.14	2.14	NUM
ejpam-3131	223	4	.	.	PUNCT
ejpam-3131	224	1	(	(	PUNCT
ejpam-3131	224	2	1	1	X
ejpam-3131	224	3	)	)	PUNCT
ejpam-3131	224	4	if	if	SCONJ
ejpam-3131	224	5	a	a	PRON
ejpam-3131	224	6	and	and	CCONJ
ejpam-3131	224	7	b	b	NOUN
ejpam-3131	224	8	are	be	AUX
ejpam-3131	224	9	separated	separate	VERB
ejpam-3131	224	10	ρig	ρig	ADV
ejpam-3131	224	11	-	-	PUNCT
ejpam-3131	224	12	open	open	ADJ
ejpam-3131	224	13	subsets	subset	NOUN
ejpam-3131	224	14	of	of	ADP
ejpam-3131	224	15	an	an	DET
ejpam-3131	224	16	ideal	ideal	ADJ
ejpam-3131	224	17	space	space	NOUN
ejpam-3131	224	18	(	(	PUNCT
ejpam-3131	224	19	x	x	X
ejpam-3131	224	20	,	,	PUNCT
ejpam-3131	224	21	τ	τ	PROPN
ejpam-3131	224	22	,	,	PUNCT
ejpam-3131	224	23	i	i	PROPN
ejpam-3131	224	24	)	)	PUNCT
ejpam-3131	224	25	then	then	ADV
ejpam-3131	224	26	a	a	DET
ejpam-3131	224	27	∪b	∪b	VERB
ejpam-3131	224	28	is	be	AUX
ejpam-3131	224	29	ρig	ρig	ADV
ejpam-3131	224	30	-	-	PUNCT
ejpam-3131	224	31	open	open	ADJ
ejpam-3131	224	32	.	.	PUNCT
ejpam-3131	225	1	(	(	PUNCT
ejpam-3131	225	2	2	2	X
ejpam-3131	225	3	)	)	PUNCT
ejpam-3131	225	4	if	if	SCONJ
ejpam-3131	225	5	a	a	PRON
ejpam-3131	225	6	and	and	CCONJ
ejpam-3131	225	7	b	b	NOUN
ejpam-3131	225	8	are	be	AUX
ejpam-3131	225	9	ρig	ρig	ADV
ejpam-3131	225	10	-	-	PUNCT
ejpam-3131	225	11	closed	closed	ADJ
ejpam-3131	225	12	subsets	subset	NOUN
ejpam-3131	225	13	of	of	ADP
ejpam-3131	225	14	an	an	DET
ejpam-3131	225	15	ideal	ideal	ADJ
ejpam-3131	225	16	space	space	NOUN
ejpam-3131	225	17	(	(	PUNCT
ejpam-3131	225	18	x	x	X
ejpam-3131	225	19	,	,	PUNCT
ejpam-3131	225	20	τ	τ	PROPN
ejpam-3131	225	21	,	,	PUNCT
ejpam-3131	225	22	i	i	PROPN
ejpam-3131	225	23	)	)	PUNCT
ejpam-3131	225	24	,	,	PUNCT
ejpam-3131	225	25	such	such	ADJ
ejpam-3131	225	26	that	that	SCONJ
ejpam-3131	225	27	x\	x\	PROPN
ejpam-3131	225	28	(	(	PUNCT
ejpam-3131	225	29	0	0	NUM
ejpam-3131	225	30	a	a	PRON
ejpam-3131	225	31	∪b	∪b	X
ejpam-3131	225	32	)	)	PUNCT
ejpam-3131	225	33	∈	∈	PROPN
ejpam-3131	225	34	i	i	PRON
ejpam-3131	225	35	and	and	CCONJ
ejpam-3131	225	36	x\	x\	PROPN
ejpam-3131	225	37	(	(	PUNCT
ejpam-3131	225	38	a	a	DET
ejpam-3131	225	39	∪	∪	ADJ
ejpam-3131	225	40	0	0	NUM
ejpam-3131	225	41	b	b	NOUN
ejpam-3131	225	42	)	)	PUNCT
ejpam-3131	225	43	∈	∈	PROPN
ejpam-3131	226	1	i	i	PRON
ejpam-3131	226	2	,	,	PUNCT
ejpam-3131	226	3	then	then	ADV
ejpam-3131	226	4	a	a	DET
ejpam-3131	226	5	∩b	∩b	NOUN
ejpam-3131	226	6	is	be	AUX
ejpam-3131	226	7	ρig	ρig	ADV
ejpam-3131	226	8	-	-	PUNCT
ejpam-3131	226	9	closed	closed	ADJ
ejpam-3131	226	10	.	.	PUNCT
ejpam-3131	227	1	n.r	n.r	PROPN
ejpam-3131	227	2	.	.	PROPN
ejpam-3131	227	3	pachón	pachón	PROPN
ejpam-3131	227	4	/	/	SYM
ejpam-3131	227	5	eur	eur	PROPN
ejpam-3131	227	6	.	.	PUNCT
ejpam-3131	228	1	j.	j.	PROPN
ejpam-3131	228	2	pure	pure	PROPN
ejpam-3131	228	3	appl	appl	PROPN
ejpam-3131	228	4	.	.	PROPN
ejpam-3131	228	5	math	math	PROPN
ejpam-3131	228	6	,	,	PUNCT
ejpam-3131	228	7	11	11	NUM
ejpam-3131	228	8	(	(	PUNCT
ejpam-3131	228	9	1	1	NUM
ejpam-3131	228	10	)	)	PUNCT
ejpam-3131	228	11	(	(	PUNCT
ejpam-3131	228	12	2018	2018	NUM
ejpam-3131	228	13	)	)	PUNCT
ejpam-3131	228	14	,	,	PUNCT
ejpam-3131	228	15	299	299	NUM
ejpam-3131	228	16	-	-	SYM
ejpam-3131	228	17	314	314	NUM
ejpam-3131	228	18	306	306	NUM
ejpam-3131	228	19	we	we	PRON
ejpam-3131	228	20	end	end	VERB
ejpam-3131	228	21	this	this	DET
ejpam-3131	228	22	section	section	NOUN
ejpam-3131	228	23	with	with	ADP
ejpam-3131	228	24	an	an	DET
ejpam-3131	228	25	application	application	NOUN
ejpam-3131	228	26	to	to	ADP
ejpam-3131	228	27	ρig	ρig	NOUN
ejpam-3131	228	28	-	-	PUNCT
ejpam-3131	228	29	open	open	ADJ
ejpam-3131	228	30	sets	set	NOUN
ejpam-3131	228	31	to	to	ADP
ejpam-3131	228	32	i	i	NOUN
ejpam-3131	228	33	-	-	PUNCT
ejpam-3131	228	34	normality	normality	NOUN
ejpam-3131	228	35	.	.	PUNCT
ejpam-3131	229	1	theorem	theorem	VERB
ejpam-3131	229	2	2.15	2.15	NUM
ejpam-3131	229	3	.	.	PUNCT
ejpam-3131	230	1	the	the	DET
ejpam-3131	230	2	ideal	ideal	ADJ
ejpam-3131	230	3	space	space	NOUN
ejpam-3131	230	4	(	(	PUNCT
ejpam-3131	230	5	x	x	X
ejpam-3131	230	6	,	,	PUNCT
ejpam-3131	230	7	τ	τ	PROPN
ejpam-3131	230	8	,	,	PUNCT
ejpam-3131	230	9	i	i	PROPN
ejpam-3131	230	10	)	)	PUNCT
ejpam-3131	230	11	is	be	AUX
ejpam-3131	230	12	i	i	NOUN
ejpam-3131	230	13	-	-	PUNCT
ejpam-3131	230	14	normal	normal	ADJ
ejpam-3131	230	15	if	if	SCONJ
ejpam-3131	230	16	and	and	CCONJ
ejpam-3131	230	17	only	only	ADV
ejpam-3131	230	18	if	if	SCONJ
ejpam-3131	230	19	,	,	PUNCT
ejpam-3131	230	20	for	for	ADP
ejpam-3131	230	21	each	each	DET
ejpam-3131	230	22	pair	pair	NOUN
ejpam-3131	230	23	of	of	ADP
ejpam-3131	230	24	disjoint	disjoint	NOUN
ejpam-3131	230	25	closed	close	VERB
ejpam-3131	230	26	sets	set	NOUN
ejpam-3131	230	27	f	f	PROPN
ejpam-3131	230	28	and	and	CCONJ
ejpam-3131	230	29	g	g	NOUN
ejpam-3131	230	30	,	,	PUNCT
ejpam-3131	230	31	there	there	PRON
ejpam-3131	230	32	are	be	VERB
ejpam-3131	230	33	disjoint	disjoint	ADJ
ejpam-3131	230	34	ρig	ρig	ADV
ejpam-3131	230	35	-	-	PUNCT
ejpam-3131	230	36	open	open	ADJ
ejpam-3131	230	37	sets	set	NOUN
ejpam-3131	230	38	a	a	PRON
ejpam-3131	230	39	and	and	CCONJ
ejpam-3131	230	40	b	b	NOUN
ejpam-3131	230	41	such	such	ADJ
ejpam-3131	230	42	that	that	SCONJ
ejpam-3131	230	43	f\a	f\a	PROPN
ejpam-3131	230	44	∈	∈	PROPN
ejpam-3131	230	45	i	i	PRON
ejpam-3131	230	46	and	and	CCONJ
ejpam-3131	230	47	g\b	g\b	ADP
ejpam-3131	230	48	∈	∈	PROPN
ejpam-3131	230	49	i.	i.	NOUN
ejpam-3131	230	50	proof	proof	NOUN
ejpam-3131	230	51	.	.	PUNCT
ejpam-3131	231	1	(	(	PUNCT
ejpam-3131	231	2	→	→	NOUN
ejpam-3131	231	3	)	)	PUNCT
ejpam-3131	231	4	this	this	PRON
ejpam-3131	231	5	is	be	AUX
ejpam-3131	231	6	simple	simple	ADJ
ejpam-3131	231	7	because	because	SCONJ
ejpam-3131	231	8	open	open	ADJ
ejpam-3131	231	9	→	→	SYM
ejpam-3131	231	10	ρig	ρig	ADV
ejpam-3131	231	11	-	-	PUNCT
ejpam-3131	231	12	open	open	ADJ
ejpam-3131	231	13	.	.	PUNCT
ejpam-3131	232	1	(	(	PUNCT
ejpam-3131	232	2	←	←	PROPN
ejpam-3131	232	3	)	)	PUNCT
ejpam-3131	232	4	if	if	SCONJ
ejpam-3131	232	5	f	f	PROPN
ejpam-3131	232	6	and	and	CCONJ
ejpam-3131	232	7	g	g	PROPN
ejpam-3131	232	8	are	be	AUX
ejpam-3131	232	9	disjoint	disjoint	ADJ
ejpam-3131	232	10	closed	closed	ADJ
ejpam-3131	232	11	sets	set	NOUN
ejpam-3131	232	12	,	,	PUNCT
ejpam-3131	232	13	then	then	ADV
ejpam-3131	232	14	there	there	PRON
ejpam-3131	232	15	exist	exist	VERB
ejpam-3131	232	16	disjoint	disjoint	ADJ
ejpam-3131	232	17	ρig	ρig	NOUN
ejpam-3131	232	18	-	-	PUNCT
ejpam-3131	232	19	open	open	ADJ
ejpam-3131	232	20	sets	set	NOUN
ejpam-3131	232	21	a	a	PRON
ejpam-3131	232	22	and	and	CCONJ
ejpam-3131	232	23	b	b	NOUN
ejpam-3131	232	24	with	with	ADP
ejpam-3131	232	25	f\a	f\a	PROPN
ejpam-3131	232	26	∈	∈	PROPN
ejpam-3131	232	27	i	i	PRON
ejpam-3131	232	28	and	and	CCONJ
ejpam-3131	232	29	g\b	g\b	ADP
ejpam-3131	232	30	∈	∈	PROPN
ejpam-3131	232	31	i.	i.	NOUN
ejpam-3131	232	32	the	the	DET
ejpam-3131	232	33	theorem	theorem	ADJ
ejpam-3131	232	34	2.11	2.11	NUM
ejpam-3131	232	35	implies	imply	VERB
ejpam-3131	232	36	that	that	SCONJ
ejpam-3131	232	37	f\	f\	VERB
ejpam-3131	232	38	0	0	PUNCT
ejpam-3131	232	39	a	a	DET
ejpam-3131	232	40	∈	∈	NOUN
ejpam-3131	233	1	i	i	PRON
ejpam-3131	233	2	and	and	CCONJ
ejpam-3131	233	3	g\	g\	PRON
ejpam-3131	233	4	0	0	NUM
ejpam-3131	233	5	b	b	PROPN
ejpam-3131	233	6	∈	∈	PROPN
ejpam-3131	233	7	i.	i.	NOUN
ejpam-3131	233	8	moreover	moreover	ADV
ejpam-3131	233	9	0	0	NUM
ejpam-3131	233	10	a	a	DET
ejpam-3131	233	11	and	and	CCONJ
ejpam-3131	233	12	0	0	NUM
ejpam-3131	233	13	b	b	NOUN
ejpam-3131	233	14	are	be	AUX
ejpam-3131	233	15	disjoint	disjoint	ADJ
ejpam-3131	233	16	open	open	ADJ
ejpam-3131	233	17	sets	set	NOUN
ejpam-3131	233	18	.	.	PUNCT
ejpam-3131	234	1	□	□	PUNCT
ejpam-3131	234	2	3	3	X
ejpam-3131	234	3	.	.	X
ejpam-3131	234	4	closed	close	VERB
ejpam-3131	234	5	-	-	PUNCT
ejpam-3131	234	6	i	i	PRON
ejpam-3131	234	7	sets	set	VERB
ejpam-3131	234	8	in	in	ADP
ejpam-3131	234	9	this	this	DET
ejpam-3131	234	10	section	section	NOUN
ejpam-3131	234	11	we	we	PRON
ejpam-3131	234	12	introduce	introduce	VERB
ejpam-3131	234	13	the	the	DET
ejpam-3131	234	14	closed	closed	ADJ
ejpam-3131	234	15	-	-	PUNCT
ejpam-3131	234	16	i	i	PRON
ejpam-3131	234	17	sets	set	VERB
ejpam-3131	234	18	,	,	PUNCT
ejpam-3131	234	19	an	an	DET
ejpam-3131	234	20	intermediate	intermediate	ADJ
ejpam-3131	234	21	concept	concept	NOUN
ejpam-3131	234	22	between	between	ADP
ejpam-3131	234	23	closed	close	VERB
ejpam-3131	234	24	sets	set	NOUN
ejpam-3131	234	25	and	and	CCONJ
ejpam-3131	234	26	ρig	ρig	ADV
ejpam-3131	234	27	-	-	PUNCT
ejpam-3131	234	28	closed	close	VERB
ejpam-3131	234	29	sets	set	NOUN
ejpam-3131	234	30	.	.	PUNCT
ejpam-3131	235	1	we	we	PRON
ejpam-3131	235	2	also	also	ADV
ejpam-3131	235	3	consider	consider	VERB
ejpam-3131	235	4	some	some	DET
ejpam-3131	235	5	applications	application	NOUN
ejpam-3131	235	6	of	of	ADP
ejpam-3131	235	7	these	these	DET
ejpam-3131	235	8	sets	set	NOUN
ejpam-3131	235	9	.	.	PUNCT
ejpam-3131	236	1	given	give	VERB
ejpam-3131	236	2	an	an	DET
ejpam-3131	236	3	ideal	ideal	ADJ
ejpam-3131	236	4	space	space	NOUN
ejpam-3131	236	5	(	(	PUNCT
ejpam-3131	236	6	x	x	X
ejpam-3131	236	7	,	,	PUNCT
ejpam-3131	236	8	τ	τ	PROPN
ejpam-3131	236	9	,	,	PUNCT
ejpam-3131	236	10	i	i	PROPN
ejpam-3131	236	11	)	)	PUNCT
ejpam-3131	236	12	and	and	CCONJ
ejpam-3131	236	13	a	a	DET
ejpam-3131	236	14	set	set	NOUN
ejpam-3131	236	15	a	a	DET
ejpam-3131	236	16	⊆	⊆	NUM
ejpam-3131	236	17	x	x	SYM
ejpam-3131	236	18	,	,	PUNCT
ejpam-3131	236	19	we	we	PRON
ejpam-3131	236	20	denote	denote	VERB
ejpam-3131	236	21	by	by	ADP
ejpam-3131	236	22	a∗	a∗	PROPN
ejpam-3131	236	23	(	(	PUNCT
ejpam-3131	236	24	i	i	NOUN
ejpam-3131	236	25	)	)	PUNCT
ejpam-3131	236	26	=	=	PRON
ejpam-3131	237	1	{	{	PUNCT
ejpam-3131	237	2	x	x	PUNCT
ejpam-3131	237	3	∈	∈	PROPN
ejpam-3131	237	4	x	x	X
ejpam-3131	237	5	:	:	PUNCT
ejpam-3131	237	6	u	u	NOUN
ejpam-3131	237	7	∩a	∩a	NOUN
ejpam-3131	237	8	/∈	/∈	PUNCT
ejpam-3131	238	1	i	i	PRON
ejpam-3131	238	2	,	,	PUNCT
ejpam-3131	238	3	for	for	ADP
ejpam-3131	238	4	every	every	DET
ejpam-3131	238	5	u	u	PROPN
ejpam-3131	238	6	∈	∈	PROPN
ejpam-3131	238	7	τ	τ	X
ejpam-3131	238	8	with	with	ADP
ejpam-3131	238	9	x	x	PROPN
ejpam-3131	238	10	∈	∈	PROPN
ejpam-3131	238	11	u	u	NOUN
ejpam-3131	238	12	}	}	PUNCT
ejpam-3131	238	13	,	,	PUNCT
ejpam-3131	238	14	written	write	VERB
ejpam-3131	238	15	simply	simply	ADV
ejpam-3131	238	16	as	as	ADP
ejpam-3131	238	17	a∗	a∗	NOUN
ejpam-3131	238	18	when	when	SCONJ
ejpam-3131	238	19	there	there	PRON
ejpam-3131	238	20	is	be	VERB
ejpam-3131	238	21	no	no	DET
ejpam-3131	238	22	chance	chance	NOUN
ejpam-3131	238	23	for	for	ADP
ejpam-3131	238	24	confusion	confusion	NOUN
ejpam-3131	238	25	.	.	PUNCT
ejpam-3131	239	1	it	it	PRON
ejpam-3131	239	2	is	be	AUX
ejpam-3131	239	3	clear	clear	ADJ
ejpam-3131	239	4	that	that	SCONJ
ejpam-3131	239	5	a∗	a∗	PROPN
ejpam-3131	239	6	⊆	⊆	NUM
ejpam-3131	239	7	a.	a.	NOUN
ejpam-3131	239	8	a	a	DET
ejpam-3131	239	9	kuratowski	kuratowski	ADJ
ejpam-3131	239	10	closure	closure	NOUN
ejpam-3131	239	11	operator	operator	NOUN
ejpam-3131	239	12	for	for	ADP
ejpam-3131	239	13	a	a	DET
ejpam-3131	239	14	topology	topology	NOUN
ejpam-3131	239	15	τ∗	τ∗	NOUN
ejpam-3131	239	16	(	(	PUNCT
ejpam-3131	239	17	i	i	NOUN
ejpam-3131	239	18	)	)	PUNCT
ejpam-3131	239	19	,	,	PUNCT
ejpam-3131	239	20	finer	fine	ADJ
ejpam-3131	239	21	than	than	ADP
ejpam-3131	239	22	τ	τ	PROPN
ejpam-3131	239	23	,	,	PUNCT
ejpam-3131	239	24	is	be	AUX
ejpam-3131	239	25	defined	define	VERB
ejpam-3131	239	26	by	by	ADP
ejpam-3131	239	27	cl∗	cl∗	PROPN
ejpam-3131	239	28	(	(	PUNCT
ejpam-3131	239	29	a	a	X
ejpam-3131	239	30	)	)	PUNCT
ejpam-3131	239	31	=	=	SYM
ejpam-3131	240	1	a∪a∗	a∪a∗	PROPN
ejpam-3131	240	2	,	,	PUNCT
ejpam-3131	240	3	for	for	ADP
ejpam-3131	240	4	all	all	DET
ejpam-3131	240	5	a	a	DET
ejpam-3131	240	6	⊆	⊆	NUM
ejpam-3131	240	7	x.	x.	NOUN
ejpam-3131	240	8	when	when	SCONJ
ejpam-3131	240	9	there	there	PRON
ejpam-3131	240	10	is	be	VERB
ejpam-3131	240	11	no	no	DET
ejpam-3131	240	12	chance	chance	NOUN
ejpam-3131	240	13	for	for	SCONJ
ejpam-3131	240	14	confusion	confusion	NOUN
ejpam-3131	240	15	τ∗	τ∗	NOUN
ejpam-3131	240	16	(	(	PUNCT
ejpam-3131	240	17	i	i	NOUN
ejpam-3131	240	18	)	)	PUNCT
ejpam-3131	240	19	is	be	AUX
ejpam-3131	240	20	denoted	denote	VERB
ejpam-3131	240	21	by	by	ADP
ejpam-3131	240	22	τ∗.	τ∗.	NOUN
ejpam-3131	240	23	the	the	DET
ejpam-3131	240	24	topology	topology	NOUN
ejpam-3131	240	25	τ∗	τ∗	NOUN
ejpam-3131	240	26	has	have	VERB
ejpam-3131	240	27	as	as	ADP
ejpam-3131	240	28	a	a	DET
ejpam-3131	240	29	base	base	NOUN
ejpam-3131	240	30	β	β	X
ejpam-3131	240	31	(	(	PUNCT
ejpam-3131	240	32	τ	τ	PROPN
ejpam-3131	240	33	,	,	PUNCT
ejpam-3131	240	34	i	i	NOUN
ejpam-3131	240	35	)	)	PUNCT
ejpam-3131	240	36	=	=	PRON
ejpam-3131	240	37	{	{	PUNCT
ejpam-3131	240	38	v	v	NUM
ejpam-3131	240	39	\i	\i	NOUN
ejpam-3131	240	40	:	:	PUNCT
ejpam-3131	240	41	v	v	X
ejpam-3131	240	42	∈	∈	X
ejpam-3131	240	43	τ	τ	X
ejpam-3131	240	44	and	and	CCONJ
ejpam-3131	240	45	i	i	PRON
ejpam-3131	240	46	∈	∈	PROPN
ejpam-3131	241	1	i	i	PRON
ejpam-3131	241	2	}	}	PUNCT
ejpam-3131	242	1	[	[	X
ejpam-3131	242	2	12	12	NUM
ejpam-3131	242	3	]	]	PUNCT
ejpam-3131	242	4	.	.	PUNCT
ejpam-3131	243	1	in	in	ADP
ejpam-3131	243	2	1990	1990	NUM
ejpam-3131	243	3	,	,	PUNCT
ejpam-3131	243	4	d.	d.	PROPN
ejpam-3131	243	5	jancovic	jancovic	PROPN
ejpam-3131	243	6	and	and	CCONJ
ejpam-3131	243	7	t.	t.	PROPN
ejpam-3131	243	8	r.	r.	PROPN
ejpam-3131	243	9	hamlett	hamlett	PROPN
ejpam-3131	243	10	introduced	introduce	VERB
ejpam-3131	243	11	the	the	DET
ejpam-3131	243	12	notion	notion	NOUN
ejpam-3131	243	13	of	of	ADP
ejpam-3131	243	14	i	i	NOUN
ejpam-3131	243	15	-	-	PUNCT
ejpam-3131	243	16	open	open	ADJ
ejpam-3131	243	17	sets	set	NOUN
ejpam-3131	243	18	.	.	PUNCT
ejpam-3131	244	1	if	if	SCONJ
ejpam-3131	244	2	(	(	PUNCT
ejpam-3131	244	3	x	x	X
ejpam-3131	244	4	,	,	PUNCT
ejpam-3131	244	5	τ	τ	PROPN
ejpam-3131	244	6	,	,	PUNCT
ejpam-3131	244	7	i	i	PROPN
ejpam-3131	244	8	)	)	PUNCT
ejpam-3131	244	9	is	be	AUX
ejpam-3131	244	10	an	an	DET
ejpam-3131	244	11	ideal	ideal	ADJ
ejpam-3131	244	12	space	space	NOUN
ejpam-3131	244	13	and	and	CCONJ
ejpam-3131	244	14	a	a	DET
ejpam-3131	244	15	⊆	⊆	NUM
ejpam-3131	244	16	x	x	SYM
ejpam-3131	244	17	,	,	PUNCT
ejpam-3131	244	18	a	a	PRON
ejpam-3131	244	19	is	be	AUX
ejpam-3131	244	20	said	say	VERB
ejpam-3131	244	21	to	to	PART
ejpam-3131	244	22	be	be	AUX
ejpam-3131	244	23	i	i	NOUN
ejpam-3131	244	24	-	-	NOUN
ejpam-3131	244	25	open	open	ADJ
ejpam-3131	244	26	[	[	X
ejpam-3131	244	27	3	3	NUM
ejpam-3131	244	28	]	]	X
ejpam-3131	244	29	if	if	SCONJ
ejpam-3131	244	30	a	a	DET
ejpam-3131	244	31	⊆	⊆	NUM
ejpam-3131	244	32	int	int	NOUN
ejpam-3131	244	33	(	(	PUNCT
ejpam-3131	244	34	a∗	a∗	PROPN
ejpam-3131	244	35	)	)	PUNCT
ejpam-3131	244	36	.	.	PUNCT
ejpam-3131	245	1	a	a	PRON
ejpam-3131	245	2	is	be	AUX
ejpam-3131	245	3	said	say	VERB
ejpam-3131	245	4	to	to	PART
ejpam-3131	245	5	be	be	AUX
ejpam-3131	245	6	i	i	NOUN
ejpam-3131	245	7	-	-	PUNCT
ejpam-3131	245	8	closed	closed	ADJ
ejpam-3131	245	9	if	if	SCONJ
ejpam-3131	245	10	x\a	x\a	PROPN
ejpam-3131	245	11	is	be	AUX
ejpam-3131	245	12	i	i	PRON
ejpam-3131	245	13	-	-	PUNCT
ejpam-3131	245	14	open	open	ADJ
ejpam-3131	245	15	.	.	PUNCT
ejpam-3131	246	1	in	in	ADP
ejpam-3131	246	2	1992	1992	NUM
ejpam-3131	246	3	,	,	PUNCT
ejpam-3131	246	4	d.	d.	PROPN
ejpam-3131	246	5	jancovic	jancovic	PROPN
ejpam-3131	246	6	and	and	CCONJ
ejpam-3131	246	7	t.	t.	PROPN
ejpam-3131	246	8	r.	r.	PROPN
ejpam-3131	246	9	hamlett	hamlett	PROPN
ejpam-3131	246	10	introduced	introduce	VERB
ejpam-3131	246	11	the	the	DET
ejpam-3131	246	12	notion	notion	NOUN
ejpam-3131	246	13	of	of	ADP
ejpam-3131	246	14	i∗-open	i∗-open	ADJ
ejpam-3131	246	15	sets	set	NOUN
ejpam-3131	246	16	.	.	PUNCT
ejpam-3131	247	1	if	if	SCONJ
ejpam-3131	247	2	(	(	PUNCT
ejpam-3131	247	3	x	x	X
ejpam-3131	247	4	,	,	PUNCT
ejpam-3131	247	5	τ	τ	PROPN
ejpam-3131	247	6	,	,	PUNCT
ejpam-3131	247	7	i	i	PROPN
ejpam-3131	247	8	)	)	PUNCT
ejpam-3131	247	9	is	be	AUX
ejpam-3131	247	10	an	an	DET
ejpam-3131	247	11	ideal	ideal	ADJ
ejpam-3131	247	12	space	space	NOUN
ejpam-3131	247	13	and	and	CCONJ
ejpam-3131	247	14	a	a	DET
ejpam-3131	247	15	⊆	⊆	NUM
ejpam-3131	247	16	x	x	SYM
ejpam-3131	247	17	,	,	PUNCT
ejpam-3131	247	18	a	a	PRON
ejpam-3131	247	19	is	be	AUX
ejpam-3131	247	20	said	say	VERB
ejpam-3131	247	21	to	to	PART
ejpam-3131	247	22	be	be	AUX
ejpam-3131	247	23	i∗-closed	i∗-close	VERB
ejpam-3131	247	24	[	[	X
ejpam-3131	247	25	4	4	NUM
ejpam-3131	247	26	]	]	X
ejpam-3131	247	27	if	if	SCONJ
ejpam-3131	247	28	a∗	a∗	PROPN
ejpam-3131	247	29	⊆	⊆	SYM
ejpam-3131	247	30	a	a	PRON
ejpam-3131	247	31	or	or	CCONJ
ejpam-3131	247	32	,	,	PUNCT
ejpam-3131	247	33	equivalently	equivalently	ADV
ejpam-3131	247	34	,	,	PUNCT
ejpam-3131	247	35	if	if	SCONJ
ejpam-3131	247	36	a	a	PRON
ejpam-3131	247	37	is	be	AUX
ejpam-3131	247	38	closed	close	VERB
ejpam-3131	247	39	in	in	ADP
ejpam-3131	247	40	(	(	PUNCT
ejpam-3131	247	41	x	x	NOUN
ejpam-3131	247	42	,	,	PUNCT
ejpam-3131	247	43	τ∗	τ∗	NOUN
ejpam-3131	247	44	)	)	PUNCT
ejpam-3131	247	45	.	.	PUNCT
ejpam-3131	248	1	a	a	PRON
ejpam-3131	248	2	is	be	AUX
ejpam-3131	248	3	said	say	VERB
ejpam-3131	248	4	to	to	PART
ejpam-3131	248	5	be	be	AUX
ejpam-3131	248	6	i∗-open	i∗-open	ADJ
ejpam-3131	248	7	if	if	SCONJ
ejpam-3131	248	8	x\a	x\a	PROPN
ejpam-3131	248	9	is	be	AUX
ejpam-3131	248	10	i∗-closed	i∗-close	VERB
ejpam-3131	248	11	.	.	PUNCT
ejpam-3131	249	1	definition	definition	NOUN
ejpam-3131	249	2	3.1	3.1	NUM
ejpam-3131	249	3	.	.	PUNCT
ejpam-3131	250	1	if	if	SCONJ
ejpam-3131	250	2	(	(	PUNCT
ejpam-3131	250	3	x	x	X
ejpam-3131	250	4	,	,	PUNCT
ejpam-3131	250	5	τ	τ	PROPN
ejpam-3131	250	6	,	,	PUNCT
ejpam-3131	250	7	i	i	PROPN
ejpam-3131	250	8	)	)	PUNCT
ejpam-3131	250	9	is	be	AUX
ejpam-3131	250	10	an	an	DET
ejpam-3131	250	11	ideal	ideal	ADJ
ejpam-3131	250	12	space	space	NOUN
ejpam-3131	250	13	and	and	CCONJ
ejpam-3131	250	14	a	a	DET
ejpam-3131	250	15	⊆	⊆	NUM
ejpam-3131	250	16	x	x	SYM
ejpam-3131	250	17	,	,	PUNCT
ejpam-3131	250	18	then	then	ADV
ejpam-3131	250	19	a	a	PRON
ejpam-3131	250	20	is	be	AUX
ejpam-3131	250	21	said	say	VERB
ejpam-3131	250	22	to	to	PART
ejpam-3131	250	23	be	be	AUX
ejpam-3131	250	24	closed	close	VERB
ejpam-3131	250	25	-	-	PUNCT
ejpam-3131	250	26	i	i	PRON
ejpam-3131	250	27	if	if	SCONJ
ejpam-3131	250	28	a\a	a\a	PUNCT
ejpam-3131	250	29	∈	∈	PROPN
ejpam-3131	250	30	i.	i.	NOUN
ejpam-3131	250	31	a	a	DET
ejpam-3131	250	32	subset	subset	PROPN
ejpam-3131	250	33	b	b	NOUN
ejpam-3131	250	34	is	be	AUX
ejpam-3131	250	35	defined	define	VERB
ejpam-3131	250	36	to	to	PART
ejpam-3131	250	37	be	be	AUX
ejpam-3131	250	38	open	open	ADJ
ejpam-3131	250	39	-	-	PUNCT
ejpam-3131	250	40	i	i	PRON
ejpam-3131	250	41	if	if	SCONJ
ejpam-3131	250	42	x\b	x\b	PROPN
ejpam-3131	250	43	is	be	AUX
ejpam-3131	250	44	closed	closed	ADJ
ejpam-3131	250	45	-	-	PUNCT
ejpam-3131	250	46	i.	i.	NOUN
ejpam-3131	250	47	it	it	PRON
ejpam-3131	250	48	is	be	AUX
ejpam-3131	250	49	observed	observe	VERB
ejpam-3131	250	50	that	that	SCONJ
ejpam-3131	250	51	:	:	PUNCT
ejpam-3131	250	52	(	(	PUNCT
ejpam-3131	250	53	1	1	X
ejpam-3131	250	54	)	)	PUNCT
ejpam-3131	250	55	closed	closed	ADJ
ejpam-3131	250	56	→	→	SYM
ejpam-3131	250	57	closed	closed	ADJ
ejpam-3131	250	58	-	-	PUNCT
ejpam-3131	250	59	i.	i.	NOUN
ejpam-3131	250	60	(	(	PUNCT
ejpam-3131	250	61	2	2	NUM
ejpam-3131	250	62	)	)	PUNCT
ejpam-3131	250	63	a	a	PRON
ejpam-3131	250	64	is	be	AUX
ejpam-3131	250	65	open	open	ADJ
ejpam-3131	250	66	-	-	PUNCT
ejpam-3131	250	67	i	i	PRON
ejpam-3131	250	68	if	if	SCONJ
ejpam-3131	251	1	and	and	CCONJ
ejpam-3131	251	2	only	only	ADV
ejpam-3131	251	3	if	if	SCONJ
ejpam-3131	251	4	a\	a\	PROPN
ejpam-3131	251	5	0	0	NUM
ejpam-3131	251	6	a	a	DET
ejpam-3131	251	7	∈	∈	PROPN
ejpam-3131	251	8	i.	i.	NOUN
ejpam-3131	251	9	(	(	PUNCT
ejpam-3131	251	10	3	3	X
ejpam-3131	251	11	)	)	PUNCT
ejpam-3131	251	12	a	a	PRON
ejpam-3131	251	13	is	be	AUX
ejpam-3131	251	14	closed	closed	ADJ
ejpam-3131	251	15	-	-	PUNCT
ejpam-3131	251	16	i	i	PRON
ejpam-3131	251	17	and	and	CCONJ
ejpam-3131	251	18	open	open	ADJ
ejpam-3131	251	19	-	-	PUNCT
ejpam-3131	251	20	i	i	PRON
ejpam-3131	251	21	if	if	SCONJ
ejpam-3131	252	1	and	and	CCONJ
ejpam-3131	252	2	only	only	ADV
ejpam-3131	252	3	if	if	SCONJ
ejpam-3131	252	4	fr(a	fr(a	VERB
ejpam-3131	252	5	)	)	PUNCT
ejpam-3131	252	6	∈	∈	PROPN
ejpam-3131	253	1	i	i	PRON
ejpam-3131	253	2	,	,	PUNCT
ejpam-3131	253	3	where	where	SCONJ
ejpam-3131	253	4	fr(a	fr(a	ADV
ejpam-3131	253	5	)	)	PUNCT
ejpam-3131	253	6	is	be	AUX
ejpam-3131	253	7	the	the	DET
ejpam-3131	253	8	frontier	frontier	NOUN
ejpam-3131	253	9	of	of	ADP
ejpam-3131	253	10	a.	a.	NOUN
ejpam-3131	253	11	(	(	PUNCT
ejpam-3131	253	12	4	4	NUM
ejpam-3131	253	13	)	)	PUNCT
ejpam-3131	253	14	a	a	PRON
ejpam-3131	253	15	is	be	AUX
ejpam-3131	253	16	closed	closed	ADJ
ejpam-3131	253	17	-	-	PUNCT
ejpam-3131	253	18	i	i	PRON
ejpam-3131	253	19	if	if	SCONJ
ejpam-3131	254	1	and	and	CCONJ
ejpam-3131	254	2	only	only	ADV
ejpam-3131	254	3	if	if	SCONJ
ejpam-3131	254	4	a\a	a\a	PRON
ejpam-3131	254	5	is	be	AUX
ejpam-3131	254	6	open	open	ADJ
ejpam-3131	254	7	-	-	PUNCT
ejpam-3131	254	8	i.	i.	NOUN
ejpam-3131	254	9	(	(	PUNCT
ejpam-3131	254	10	5	5	NUM
ejpam-3131	254	11	)	)	PUNCT
ejpam-3131	255	1	each	each	DET
ejpam-3131	255	2	i	i	PRON
ejpam-3131	255	3	∈	∈	PROPN
ejpam-3131	256	1	i	i	PRON
ejpam-3131	256	2	is	be	AUX
ejpam-3131	256	3	open	open	ADJ
ejpam-3131	256	4	-	-	PUNCT
ejpam-3131	256	5	i.	i.	NOUN
ejpam-3131	256	6	(	(	PUNCT
ejpam-3131	256	7	6	6	NUM
ejpam-3131	256	8	)	)	PUNCT
ejpam-3131	256	9	if	if	SCONJ
ejpam-3131	256	10	a	a	PRON
ejpam-3131	256	11	is	be	AUX
ejpam-3131	256	12	open	open	ADJ
ejpam-3131	256	13	then	then	ADV
ejpam-3131	256	14	a	a	PRON
ejpam-3131	256	15	is	be	AUX
ejpam-3131	256	16	open	open	ADJ
ejpam-3131	256	17	-	-	PUNCT
ejpam-3131	256	18	i.	i.	NOUN
ejpam-3131	256	19	n.r	n.r	PROPN
ejpam-3131	256	20	.	.	PROPN
ejpam-3131	256	21	pachón	pachón	PROPN
ejpam-3131	256	22	/	/	SYM
ejpam-3131	256	23	eur	eur	PROPN
ejpam-3131	256	24	.	.	PUNCT
ejpam-3131	257	1	j.	j.	PROPN
ejpam-3131	257	2	pure	pure	PROPN
ejpam-3131	257	3	appl	appl	PROPN
ejpam-3131	257	4	.	.	PROPN
ejpam-3131	257	5	math	math	PROPN
ejpam-3131	257	6	,	,	PUNCT
ejpam-3131	257	7	11	11	NUM
ejpam-3131	257	8	(	(	PUNCT
ejpam-3131	257	9	1	1	NUM
ejpam-3131	257	10	)	)	PUNCT
ejpam-3131	257	11	(	(	PUNCT
ejpam-3131	257	12	2018	2018	NUM
ejpam-3131	257	13	)	)	PUNCT
ejpam-3131	257	14	,	,	PUNCT
ejpam-3131	257	15	299	299	NUM
ejpam-3131	257	16	-	-	SYM
ejpam-3131	257	17	314	314	NUM
ejpam-3131	257	18	307	307	NUM
ejpam-3131	257	19	example	example	NOUN
ejpam-3131	257	20	3.2	3.2	NUM
ejpam-3131	257	21	.	.	PUNCT
ejpam-3131	258	1	(	(	PUNCT
ejpam-3131	258	2	1	1	X
ejpam-3131	258	3	)	)	PUNCT
ejpam-3131	258	4	if	if	SCONJ
ejpam-3131	258	5	u	u	NOUN
ejpam-3131	258	6	is	be	AUX
ejpam-3131	258	7	the	the	DET
ejpam-3131	258	8	usual	usual	ADJ
ejpam-3131	258	9	topology	topology	NOUN
ejpam-3131	258	10	in	in	ADP
ejpam-3131	258	11	r	r	NOUN
ejpam-3131	258	12	and	and	CCONJ
ejpam-3131	258	13	if	if	SCONJ
ejpam-3131	258	14	i	i	PRON
ejpam-3131	258	15	=	=	PUNCT
ejpam-3131	258	16	if	if	SCONJ
ejpam-3131	258	17	(	(	PUNCT
ejpam-3131	258	18	r	r	NOUN
ejpam-3131	258	19	)	)	PUNCT
ejpam-3131	258	20	,	,	PUNCT
ejpam-3131	258	21	then	then	ADV
ejpam-3131	258	22	[	[	X
ejpam-3131	258	23	0	0	NUM
ejpam-3131	258	24	,	,	PUNCT
ejpam-3131	258	25	1	1	NUM
ejpam-3131	258	26	)	)	PUNCT
ejpam-3131	258	27	is	be	AUX
ejpam-3131	258	28	closed	closed	ADJ
ejpam-3131	258	29	-	-	PUNCT
ejpam-3131	258	30	i	i	PRON
ejpam-3131	258	31	but	but	CCONJ
ejpam-3131	259	1	[	[	X
ejpam-3131	259	2	0	0	NUM
ejpam-3131	259	3	,	,	PUNCT
ejpam-3131	259	4	1	1	NUM
ejpam-3131	259	5	)	)	PUNCT
ejpam-3131	259	6	is	be	AUX
ejpam-3131	259	7	not	not	PART
ejpam-3131	259	8	closed	close	VERB
ejpam-3131	259	9	.	.	PUNCT
ejpam-3131	260	1	since	since	SCONJ
ejpam-3131	260	2	q\q	q\q	PROPN
ejpam-3131	260	3	/∈	/∈	PUNCT
ejpam-3131	261	1	i	i	PRON
ejpam-3131	261	2	then	then	ADV
ejpam-3131	261	3	q	q	X
ejpam-3131	261	4	is	be	AUX
ejpam-3131	261	5	not	not	PART
ejpam-3131	261	6	closed	closed	ADJ
ejpam-3131	261	7	-	-	PUNCT
ejpam-3131	261	8	i.	i.	NOUN
ejpam-3131	261	9	(	(	PUNCT
ejpam-3131	261	10	2	2	NUM
ejpam-3131	261	11	)	)	PUNCT
ejpam-3131	261	12	if	if	SCONJ
ejpam-3131	261	13	x	x	PRON
ejpam-3131	261	14	=	=	X
ejpam-3131	261	15	{	{	PUNCT
ejpam-3131	261	16	a	a	PRON
ejpam-3131	261	17	,	,	PUNCT
ejpam-3131	261	18	b	b	NOUN
ejpam-3131	261	19	,	,	PUNCT
ejpam-3131	261	20	c	c	NOUN
ejpam-3131	261	21	,	,	PUNCT
ejpam-3131	261	22	d	d	NOUN
ejpam-3131	261	23	}	}	PUNCT
ejpam-3131	261	24	,	,	PUNCT
ejpam-3131	261	25	τ	τ	X
ejpam-3131	261	26	=	=	PUNCT
ejpam-3131	261	27	{	{	PUNCT
ejpam-3131	261	28	∅	∅	NOUN
ejpam-3131	261	29	,	,	PUNCT
ejpam-3131	261	30	x	x	X
ejpam-3131	261	31	,	,	PUNCT
ejpam-3131	261	32	{	{	PUNCT
ejpam-3131	261	33	c	c	NOUN
ejpam-3131	261	34	}	}	PUNCT
ejpam-3131	261	35	,	,	PUNCT
ejpam-3131	261	36	{	{	PUNCT
ejpam-3131	261	37	a	a	DET
ejpam-3131	261	38	,	,	PUNCT
ejpam-3131	261	39	b	b	NOUN
ejpam-3131	261	40	}	}	PUNCT
ejpam-3131	261	41	,	,	PUNCT
ejpam-3131	261	42	{	{	PUNCT
ejpam-3131	261	43	a	a	PRON
ejpam-3131	261	44	,	,	PUNCT
ejpam-3131	261	45	b	b	NOUN
ejpam-3131	261	46	,	,	PUNCT
ejpam-3131	261	47	c	c	NOUN
ejpam-3131	261	48	}	}	PUNCT
ejpam-3131	261	49	}	}	PUNCT
ejpam-3131	261	50	and	and	CCONJ
ejpam-3131	261	51	i	i	PRON
ejpam-3131	261	52	=	=	PUNCT
ejpam-3131	261	53	{	{	PUNCT
ejpam-3131	261	54	∅	∅	NOUN
ejpam-3131	261	55	,	,	PUNCT
ejpam-3131	261	56	{	{	PUNCT
ejpam-3131	261	57	a	a	X
ejpam-3131	261	58	}	}	PUNCT
ejpam-3131	261	59	}	}	PUNCT
ejpam-3131	261	60	,	,	PUNCT
ejpam-3131	261	61	then	then	ADV
ejpam-3131	261	62	the	the	DET
ejpam-3131	261	63	set	set	NOUN
ejpam-3131	261	64	a	a	X
ejpam-3131	261	65	=	=	SYM
ejpam-3131	261	66	{	{	PUNCT
ejpam-3131	261	67	b	b	PROPN
ejpam-3131	261	68	,	,	PUNCT
ejpam-3131	261	69	c	c	NOUN
ejpam-3131	261	70	,	,	PUNCT
ejpam-3131	261	71	d	d	NOUN
ejpam-3131	261	72	}	}	PUNCT
ejpam-3131	261	73	is	be	AUX
ejpam-3131	261	74	i	i	PRON
ejpam-3131	261	75	-	-	PUNCT
ejpam-3131	261	76	open	open	ADJ
ejpam-3131	261	77	[	[	X
ejpam-3131	261	78	7	7	NUM
ejpam-3131	261	79	]	]	PUNCT
ejpam-3131	261	80	.	.	PUNCT
ejpam-3131	262	1	now	now	ADV
ejpam-3131	262	2	,	,	PUNCT
ejpam-3131	262	3	since	since	SCONJ
ejpam-3131	262	4	a\	a\	PROPN
ejpam-3131	262	5	0	0	NUM
ejpam-3131	262	6	a	a	PRON
ejpam-3131	262	7	=	=	X
ejpam-3131	262	8	{	{	PUNCT
ejpam-3131	262	9	b	b	NOUN
ejpam-3131	262	10	,	,	PUNCT
ejpam-3131	262	11	d	d	NOUN
ejpam-3131	262	12	}	}	PUNCT
ejpam-3131	262	13	/∈	/∈	PUNCT
ejpam-3131	263	1	i	i	PRON
ejpam-3131	263	2	then	then	ADV
ejpam-3131	263	3	a	a	PRON
ejpam-3131	263	4	is	be	AUX
ejpam-3131	263	5	not	not	PART
ejpam-3131	263	6	open	open	ADJ
ejpam-3131	263	7	-	-	PUNCT
ejpam-3131	263	8	i.	i.	NOUN
ejpam-3131	263	9	it	it	PRON
ejpam-3131	263	10	is	be	AUX
ejpam-3131	263	11	noted	note	VERB
ejpam-3131	263	12	that	that	SCONJ
ejpam-3131	263	13	{	{	PUNCT
ejpam-3131	263	14	a	a	PRON
ejpam-3131	263	15	,	,	PUNCT
ejpam-3131	263	16	c	c	NOUN
ejpam-3131	263	17	}	}	PUNCT
ejpam-3131	263	18	/∈	/∈	PUNCT
ejpam-3131	264	1	τ	τ	PROPN
ejpam-3131	264	2	but	but	CCONJ
ejpam-3131	264	3	{	{	PUNCT
ejpam-3131	264	4	a	a	X
ejpam-3131	264	5	,	,	PUNCT
ejpam-3131	264	6	c	c	NOUN
ejpam-3131	264	7	}	}	PUNCT
ejpam-3131	264	8	is	be	AUX
ejpam-3131	264	9	open	open	ADJ
ejpam-3131	264	10	-	-	PUNCT
ejpam-3131	264	11	i.	i.	NOUN
ejpam-3131	264	12	moreover	moreover	ADV
ejpam-3131	264	13	,	,	PUNCT
ejpam-3131	264	14	since	since	SCONJ
ejpam-3131	264	15	a\a	a\a	NOUN
ejpam-3131	264	16	=	=	PRON
ejpam-3131	264	17	{	{	PUNCT
ejpam-3131	264	18	a	a	PRON
ejpam-3131	264	19	}	}	PUNCT
ejpam-3131	264	20	∈	∈	NOUN
ejpam-3131	264	21	i	i	PRON
ejpam-3131	264	22	and	and	CCONJ
ejpam-3131	264	23	a∗	a∗	PROPN
ejpam-3131	264	24	=	=	SYM
ejpam-3131	264	25	{	{	PUNCT
ejpam-3131	264	26	a	a	PRON
ejpam-3131	264	27	,	,	PUNCT
ejpam-3131	264	28	b	b	NOUN
ejpam-3131	264	29	,	,	PUNCT
ejpam-3131	264	30	d	d	NOUN
ejpam-3131	264	31	}	}	PUNCT
ejpam-3131	264	32	⊈	⊈	PROPN
ejpam-3131	265	1	a	a	DET
ejpam-3131	265	2	then	then	ADV
ejpam-3131	265	3	a	a	PRON
ejpam-3131	265	4	is	be	AUX
ejpam-3131	265	5	closed	closed	ADJ
ejpam-3131	265	6	-	-	PUNCT
ejpam-3131	265	7	i	i	PRON
ejpam-3131	265	8	but	but	CCONJ
ejpam-3131	265	9	a	a	PRON
ejpam-3131	265	10	is	be	AUX
ejpam-3131	265	11	not	not	PART
ejpam-3131	265	12	i∗-closed	i∗-close	VERB
ejpam-3131	265	13	.	.	PUNCT
ejpam-3131	266	1	now	now	ADV
ejpam-3131	266	2	,	,	PUNCT
ejpam-3131	266	3	if	if	SCONJ
ejpam-3131	266	4	b	b	X
ejpam-3131	266	5	=	=	X
ejpam-3131	266	6	{	{	PUNCT
ejpam-3131	266	7	a	a	NOUN
ejpam-3131	266	8	}	}	PUNCT
ejpam-3131	266	9	then	then	ADV
ejpam-3131	266	10	b\b	b\b	PUNCT
ejpam-3131	266	11	=	=	SYM
ejpam-3131	266	12	{	{	PUNCT
ejpam-3131	266	13	b	b	PROPN
ejpam-3131	266	14	,	,	PUNCT
ejpam-3131	266	15	d	d	NOUN
ejpam-3131	266	16	}	}	PUNCT
ejpam-3131	266	17	/∈	/∈	PUNCT
ejpam-3131	267	1	i	i	PRON
ejpam-3131	267	2	and	and	CCONJ
ejpam-3131	267	3	b∗	b∗	ADJ
ejpam-3131	267	4	=	=	PUNCT
ejpam-3131	267	5	∅	∅	NOUN
ejpam-3131	268	1	⊆	⊆	NUM
ejpam-3131	268	2	b.	b.	NOUN
ejpam-3131	268	3	then	then	ADV
ejpam-3131	268	4	b	b	PROPN
ejpam-3131	268	5	is	be	AUX
ejpam-3131	268	6	i∗-closed	i∗-close	VERB
ejpam-3131	268	7	but	but	CCONJ
ejpam-3131	268	8	b	b	NOUN
ejpam-3131	268	9	is	be	AUX
ejpam-3131	268	10	not	not	PART
ejpam-3131	268	11	closed	closed	ADJ
ejpam-3131	268	12	-	-	PUNCT
ejpam-3131	268	13	i.	i.	NOUN
ejpam-3131	268	14	(	(	PUNCT
ejpam-3131	268	15	3	3	NUM
ejpam-3131	268	16	)	)	PUNCT
ejpam-3131	268	17	if	if	SCONJ
ejpam-3131	268	18	i	i	PRON
ejpam-3131	268	19	=	=	SYM
ejpam-3131	268	20	{	{	PUNCT
ejpam-3131	268	21	∅	∅	NOUN
ejpam-3131	268	22	,	,	PUNCT
ejpam-3131	268	23	{	{	PUNCT
ejpam-3131	268	24	c	c	NOUN
ejpam-3131	268	25	}	}	PUNCT
ejpam-3131	268	26	,	,	PUNCT
ejpam-3131	268	27	{	{	PUNCT
ejpam-3131	268	28	d	d	X
ejpam-3131	268	29	}	}	PUNCT
ejpam-3131	268	30	,	,	PUNCT
ejpam-3131	268	31	{	{	PUNCT
ejpam-3131	268	32	c	c	X
ejpam-3131	268	33	,	,	PUNCT
ejpam-3131	268	34	d	d	NOUN
ejpam-3131	268	35	}	}	PUNCT
ejpam-3131	268	36	}	}	PUNCT
ejpam-3131	268	37	and	and	CCONJ
ejpam-3131	268	38	τ	τ	PROPN
ejpam-3131	268	39	=	=	SYM
ejpam-3131	268	40	{	{	PUNCT
ejpam-3131	268	41	∅	∅	NOUN
ejpam-3131	268	42	,	,	PUNCT
ejpam-3131	268	43	x	x	X
ejpam-3131	268	44	,	,	PUNCT
ejpam-3131	268	45	{	{	PUNCT
ejpam-3131	268	46	d	d	NOUN
ejpam-3131	268	47	}	}	PUNCT
ejpam-3131	268	48	,	,	PUNCT
ejpam-3131	268	49	{	{	PUNCT
ejpam-3131	268	50	a	a	X
ejpam-3131	268	51	,	,	PUNCT
ejpam-3131	268	52	c	c	NOUN
ejpam-3131	268	53	}	}	PUNCT
ejpam-3131	268	54	,	,	PUNCT
ejpam-3131	268	55	{	{	PUNCT
ejpam-3131	268	56	a	a	X
ejpam-3131	268	57	,	,	PUNCT
ejpam-3131	268	58	c	c	NOUN
ejpam-3131	268	59	,	,	PUNCT
ejpam-3131	268	60	d	d	NOUN
ejpam-3131	268	61	}	}	PUNCT
ejpam-3131	268	62	}	}	PUNCT
ejpam-3131	268	63	,	,	PUNCT
ejpam-3131	268	64	where	where	SCONJ
ejpam-3131	268	65	x	x	X
ejpam-3131	268	66	=	=	PRON
ejpam-3131	268	67	{	{	PUNCT
ejpam-3131	268	68	a	a	PRON
ejpam-3131	268	69	,	,	PUNCT
ejpam-3131	268	70	b	b	NOUN
ejpam-3131	268	71	,	,	PUNCT
ejpam-3131	268	72	c	c	NOUN
ejpam-3131	268	73	,	,	PUNCT
ejpam-3131	268	74	d	d	NOUN
ejpam-3131	268	75	}	}	PUNCT
ejpam-3131	268	76	,	,	PUNCT
ejpam-3131	268	77	then	then	ADV
ejpam-3131	268	78	the	the	DET
ejpam-3131	268	79	set	set	NOUN
ejpam-3131	268	80	a	a	X
ejpam-3131	268	81	=	=	X
ejpam-3131	268	82	{	{	PUNCT
ejpam-3131	268	83	a	a	X
ejpam-3131	268	84	,	,	PUNCT
ejpam-3131	268	85	c	c	NOUN
ejpam-3131	268	86	,	,	PUNCT
ejpam-3131	268	87	d	d	NOUN
ejpam-3131	268	88	}	}	PUNCT
ejpam-3131	268	89	is	be	AUX
ejpam-3131	268	90	open	open	ADJ
ejpam-3131	268	91	-	-	PUNCT
ejpam-3131	268	92	i.	i.	NOUN
ejpam-3131	268	93	however	however	ADV
ejpam-3131	268	94	a	a	PRON
ejpam-3131	268	95	is	be	AUX
ejpam-3131	268	96	not	not	PART
ejpam-3131	268	97	i	i	PRON
ejpam-3131	268	98	-	-	PUNCT
ejpam-3131	268	99	open	open	ADJ
ejpam-3131	268	100	[	[	X
ejpam-3131	268	101	7	7	NUM
ejpam-3131	268	102	]	]	PUNCT
ejpam-3131	268	103	.	.	PUNCT
ejpam-3131	269	1	hence	hence	ADV
ejpam-3131	269	2	,	,	PUNCT
ejpam-3131	269	3	in	in	ADP
ejpam-3131	269	4	general	general	ADJ
ejpam-3131	269	5	,	,	PUNCT
ejpam-3131	269	6	open	open	ADJ
ejpam-3131	269	7	↛	↛	PUNCT
ejpam-3131	269	8	i	i	PRON
ejpam-3131	269	9	-	-	PUNCT
ejpam-3131	269	10	open	open	ADJ
ejpam-3131	269	11	.	.	PUNCT
ejpam-3131	270	1	in	in	ADP
ejpam-3131	270	2	consequence	consequence	NOUN
ejpam-3131	270	3	the	the	DET
ejpam-3131	270	4	i	i	NOUN
ejpam-3131	270	5	-	-	PUNCT
ejpam-3131	270	6	closed	close	VERB
ejpam-3131	270	7	and	and	CCONJ
ejpam-3131	270	8	closed	closed	ADJ
ejpam-3131	270	9	-	-	PUNCT
ejpam-3131	270	10	i	i	PRON
ejpam-3131	270	11	are	be	AUX
ejpam-3131	270	12	independent	independent	ADJ
ejpam-3131	270	13	concepts	concept	NOUN
ejpam-3131	270	14	,	,	PUNCT
ejpam-3131	270	15	as	as	ADV
ejpam-3131	270	16	well	well	ADV
ejpam-3131	270	17	as	as	ADP
ejpam-3131	270	18	i∗-closed	i∗-close	VERB
ejpam-3131	270	19	and	and	CCONJ
ejpam-3131	270	20	closed	closed	ADJ
ejpam-3131	270	21	-	-	PUNCT
ejpam-3131	270	22	i	i	PRON
ejpam-3131	270	23	concepts	concept	NOUN
ejpam-3131	270	24	.	.	PUNCT
ejpam-3131	271	1	theorem	theorem	VERB
ejpam-3131	271	2	3.3	3.3	NUM
ejpam-3131	271	3	.	.	PUNCT
ejpam-3131	272	1	let	let	VERB
ejpam-3131	272	2	(	(	PUNCT
ejpam-3131	272	3	x	x	X
ejpam-3131	272	4	,	,	PUNCT
ejpam-3131	272	5	τ	τ	PROPN
ejpam-3131	272	6	,	,	PUNCT
ejpam-3131	272	7	i	i	PRON
ejpam-3131	272	8	)	)	PUNCT
ejpam-3131	272	9	be	be	VERB
ejpam-3131	272	10	an	an	DET
ejpam-3131	272	11	ideal	ideal	ADJ
ejpam-3131	272	12	space	space	NOUN
ejpam-3131	272	13	.	.	PUNCT
ejpam-3131	273	1	if	if	SCONJ
ejpam-3131	273	2	a	a	DET
ejpam-3131	273	3	⊆	⊆	NUM
ejpam-3131	273	4	x	x	NOUN
ejpam-3131	273	5	and	and	CCONJ
ejpam-3131	273	6	b	b	NOUN
ejpam-3131	273	7	⊆	⊆	NUM
ejpam-3131	273	8	x	x	PUNCT
ejpam-3131	273	9	then	then	ADV
ejpam-3131	273	10	:	:	PUNCT
ejpam-3131	273	11	(	(	PUNCT
ejpam-3131	273	12	1	1	X
ejpam-3131	273	13	)	)	PUNCT
ejpam-3131	273	14	if	if	SCONJ
ejpam-3131	273	15	a	a	PRON
ejpam-3131	273	16	is	be	AUX
ejpam-3131	273	17	closed	closed	ADJ
ejpam-3131	273	18	-	-	PUNCT
ejpam-3131	273	19	i	i	PRON
ejpam-3131	273	20	then	then	ADV
ejpam-3131	273	21	a	a	PRON
ejpam-3131	273	22	is	be	AUX
ejpam-3131	273	23	ρig	ρig	ADV
ejpam-3131	273	24	-	-	PUNCT
ejpam-3131	273	25	closed	closed	ADJ
ejpam-3131	273	26	.	.	PUNCT
ejpam-3131	274	1	(	(	PUNCT
ejpam-3131	274	2	2	2	X
ejpam-3131	274	3	)	)	PUNCT
ejpam-3131	274	4	if	if	SCONJ
ejpam-3131	274	5	a	a	PRON
ejpam-3131	274	6	is	be	AUX
ejpam-3131	274	7	closed	closed	ADJ
ejpam-3131	274	8	-	-	PUNCT
ejpam-3131	274	9	i	i	PRON
ejpam-3131	274	10	then	then	ADV
ejpam-3131	274	11	(	(	PUNCT
ejpam-3131	274	12	a	a	PRON
ejpam-3131	274	13	)	)	PUNCT
ejpam-3131	274	14	∗	∗	NOUN
ejpam-3131	274	15	\a	\a	VERB
ejpam-3131	274	16	∈	∈	PROPN
ejpam-3131	275	1	i	i	PRON
ejpam-3131	275	2	,	,	PUNCT
ejpam-3131	275	3	and	and	CCONJ
ejpam-3131	275	4	so	so	ADV
ejpam-3131	275	5	(	(	PUNCT
ejpam-3131	275	6	0	0	NUM
ejpam-3131	275	7	a	a	PRON
ejpam-3131	275	8	)	)	PUNCT
ejpam-3131	275	9	∗	∗	NOUN
ejpam-3131	275	10	\a	\a	VERB
ejpam-3131	275	11	∈	∈	PROPN
ejpam-3131	275	12	i.	i.	NOUN
ejpam-3131	275	13	(	(	PUNCT
ejpam-3131	275	14	3	3	X
ejpam-3131	275	15	)	)	PUNCT
ejpam-3131	275	16	if	if	SCONJ
ejpam-3131	275	17	a	a	PRON
ejpam-3131	275	18	and	and	CCONJ
ejpam-3131	275	19	b	b	NOUN
ejpam-3131	275	20	are	be	AUX
ejpam-3131	275	21	closed	closed	ADJ
ejpam-3131	275	22	-	-	PUNCT
ejpam-3131	275	23	i	i	PRON
ejpam-3131	275	24	then	then	ADV
ejpam-3131	275	25	a	a	DET
ejpam-3131	275	26	∪b	∪b	X
ejpam-3131	275	27	and	and	CCONJ
ejpam-3131	275	28	a	a	DET
ejpam-3131	275	29	∩b	∩b	NOUN
ejpam-3131	275	30	are	be	AUX
ejpam-3131	275	31	closed	closed	ADJ
ejpam-3131	275	32	-	-	PUNCT
ejpam-3131	275	33	i.	i.	NOUN
ejpam-3131	275	34	(	(	PUNCT
ejpam-3131	275	35	4	4	NUM
ejpam-3131	275	36	)	)	PUNCT
ejpam-3131	275	37	if	if	SCONJ
ejpam-3131	275	38	a\b	a\b	ADP
ejpam-3131	275	39	∈	∈	PROPN
ejpam-3131	275	40	i	i	PRON
ejpam-3131	275	41	,	,	PUNCT
ejpam-3131	275	42	b\a	b\a	NOUN
ejpam-3131	275	43	∈	∈	PROPN
ejpam-3131	276	1	i	i	PRON
ejpam-3131	276	2	and	and	CCONJ
ejpam-3131	276	3	a	a	PRON
ejpam-3131	276	4	is	be	AUX
ejpam-3131	276	5	closed	closed	ADJ
ejpam-3131	276	6	-	-	PUNCT
ejpam-3131	276	7	i	i	PRON
ejpam-3131	276	8	then	then	ADV
ejpam-3131	276	9	b	b	PROPN
ejpam-3131	276	10	is	be	AUX
ejpam-3131	276	11	closed	closed	ADJ
ejpam-3131	276	12	-	-	PUNCT
ejpam-3131	276	13	i.	i.	NOUN
ejpam-3131	276	14	(	(	PUNCT
ejpam-3131	276	15	5	5	NUM
ejpam-3131	276	16	)	)	PUNCT
ejpam-3131	276	17	if	if	SCONJ
ejpam-3131	276	18	a	a	DET
ejpam-3131	276	19	⊆	⊆	NUM
ejpam-3131	276	20	b	b	SYM
ejpam-3131	276	21	⊆	⊆	NUM
ejpam-3131	276	22	a	a	PRON
ejpam-3131	276	23	and	and	CCONJ
ejpam-3131	276	24	a	a	PRON
ejpam-3131	276	25	is	be	AUX
ejpam-3131	276	26	closed	closed	ADJ
ejpam-3131	276	27	-	-	PUNCT
ejpam-3131	276	28	i	i	NOUN
ejpam-3131	276	29	,	,	PUNCT
ejpam-3131	276	30	then	then	ADV
ejpam-3131	276	31	b	b	PROPN
ejpam-3131	276	32	is	be	AUX
ejpam-3131	276	33	closed	closed	ADJ
ejpam-3131	276	34	-	-	PUNCT
ejpam-3131	276	35	i.	i.	NOUN
ejpam-3131	276	36	(	(	PUNCT
ejpam-3131	276	37	6	6	NUM
ejpam-3131	276	38	)	)	PUNCT
ejpam-3131	276	39	if	if	SCONJ
ejpam-3131	276	40	a	a	PRON
ejpam-3131	276	41	is	be	AUX
ejpam-3131	276	42	pre	pre	ADJ
ejpam-3131	276	43	-	-	ADJ
ejpam-3131	276	44	open	open	ADJ
ejpam-3131	276	45	and	and	CCONJ
ejpam-3131	276	46	closed	closed	ADJ
ejpam-3131	277	1	-	-	PUNCT
ejpam-3131	277	2	i	i	PRON
ejpam-3131	277	3	then	then	ADV
ejpam-3131	277	4	a	a	PRON
ejpam-3131	277	5	is	be	AUX
ejpam-3131	277	6	open	open	ADJ
ejpam-3131	277	7	-	-	PUNCT
ejpam-3131	277	8	i.	i.	NOUN
ejpam-3131	277	9	(	(	PUNCT
ejpam-3131	277	10	7	7	NUM
ejpam-3131	277	11	)	)	PUNCT
ejpam-3131	277	12	if	if	SCONJ
ejpam-3131	277	13	a	a	DET
ejpam-3131	277	14	⊆	⊆	NUM
ejpam-3131	277	15	b	b	NOUN
ejpam-3131	277	16	and	and	CCONJ
ejpam-3131	277	17	a	a	PRON
ejpam-3131	277	18	is	be	AUX
ejpam-3131	277	19	closed	closed	ADJ
ejpam-3131	277	20	-	-	PUNCT
ejpam-3131	277	21	i	i	PRON
ejpam-3131	277	22	in	in	ADP
ejpam-3131	277	23	(	(	PUNCT
ejpam-3131	277	24	x	x	NOUN
ejpam-3131	277	25	,	,	PUNCT
ejpam-3131	277	26	τ	τ	PROPN
ejpam-3131	277	27	,	,	PUNCT
ejpam-3131	277	28	i	i	PROPN
ejpam-3131	277	29	)	)	PUNCT
ejpam-3131	277	30	,	,	PUNCT
ejpam-3131	277	31	then	then	ADV
ejpam-3131	277	32	a	a	PRON
ejpam-3131	277	33	is	be	AUX
ejpam-3131	277	34	closed	closed	ADJ
ejpam-3131	277	35	-	-	PUNCT
ejpam-3131	277	36	ib	ib	NOUN
ejpam-3131	277	37	in	in	ADP
ejpam-3131	277	38	(	(	PUNCT
ejpam-3131	277	39	b	b	NOUN
ejpam-3131	277	40	,	,	PUNCT
ejpam-3131	277	41	τb	τb	ADJ
ejpam-3131	277	42	,	,	PUNCT
ejpam-3131	277	43	ib	ib	NOUN
ejpam-3131	277	44	)	)	PUNCT
ejpam-3131	277	45	.	.	PUNCT
ejpam-3131	278	1	(	(	PUNCT
ejpam-3131	278	2	8)	8)	NUM
ejpam-3131	278	3	if	if	SCONJ
ejpam-3131	278	4	a	a	DET
ejpam-3131	278	5	⊆	⊆	NUM
ejpam-3131	278	6	b	b	NOUN
ejpam-3131	278	7	,	,	PUNCT
ejpam-3131	278	8	a	a	PRON
ejpam-3131	278	9	is	be	AUX
ejpam-3131	278	10	closed	closed	ADJ
ejpam-3131	278	11	-	-	PUNCT
ejpam-3131	278	12	ib	ib	NOUN
ejpam-3131	278	13	in	in	ADP
ejpam-3131	278	14	(	(	PUNCT
ejpam-3131	278	15	b	b	NOUN
ejpam-3131	278	16	,	,	PUNCT
ejpam-3131	278	17	τb	τb	ADJ
ejpam-3131	278	18	,	,	PUNCT
ejpam-3131	278	19	ib	ib	NOUN
ejpam-3131	278	20	)	)	PUNCT
ejpam-3131	278	21	,	,	PUNCT
ejpam-3131	278	22	b	b	PROPN
ejpam-3131	278	23	is	be	AUX
ejpam-3131	278	24	closed	closed	ADJ
ejpam-3131	278	25	-	-	PUNCT
ejpam-3131	278	26	i	i	PRON
ejpam-3131	278	27	in	in	ADP
ejpam-3131	278	28	(	(	PUNCT
ejpam-3131	278	29	x	x	NOUN
ejpam-3131	278	30	,	,	PUNCT
ejpam-3131	278	31	τ	τ	PROPN
ejpam-3131	278	32	,	,	PUNCT
ejpam-3131	278	33	i	i	PROPN
ejpam-3131	278	34	)	)	PUNCT
ejpam-3131	278	35	,	,	PUNCT
ejpam-3131	278	36	then	then	ADV
ejpam-3131	278	37	a	a	PRON
ejpam-3131	278	38	is	be	AUX
ejpam-3131	278	39	closed	closed	ADJ
ejpam-3131	278	40	-	-	PUNCT
ejpam-3131	278	41	i	i	PRON
ejpam-3131	278	42	in	in	ADP
ejpam-3131	278	43	(	(	PUNCT
ejpam-3131	278	44	x	x	NOUN
ejpam-3131	278	45	,	,	PUNCT
ejpam-3131	278	46	τ	τ	PROPN
ejpam-3131	278	47	,	,	PUNCT
ejpam-3131	278	48	i	i	PROPN
ejpam-3131	278	49	)	)	PUNCT
ejpam-3131	278	50	.	.	PUNCT
ejpam-3131	279	1	proof	proof	NOUN
ejpam-3131	279	2	.	.	PUNCT
ejpam-3131	280	1	(	(	PUNCT
ejpam-3131	280	2	1	1	X
ejpam-3131	280	3	)	)	PUNCT
ejpam-3131	280	4	suppose	suppose	VERB
ejpam-3131	280	5	that	that	SCONJ
ejpam-3131	280	6	u	u	PROPN
ejpam-3131	280	7	∈	∈	PROPN
ejpam-3131	280	8	τ	τ	X
ejpam-3131	280	9	and	and	CCONJ
ejpam-3131	280	10	a\u	a\u	PROPN
ejpam-3131	280	11	∈	∈	PROPN
ejpam-3131	280	12	i.	i.	NOUN
ejpam-3131	280	13	given	give	VERB
ejpam-3131	280	14	that	that	SCONJ
ejpam-3131	280	15	a\u	a\u	PROPN
ejpam-3131	280	16	⊆	⊆	NUM
ejpam-3131	280	17	(	(	PUNCT
ejpam-3131	280	18	a\a	a\a	NOUN
ejpam-3131	280	19	)	)	PUNCT
ejpam-3131	280	20	∪	∪	NOUN
ejpam-3131	280	21	(	(	PUNCT
ejpam-3131	280	22	a\u	a\u	NOUN
ejpam-3131	280	23	)	)	PUNCT
ejpam-3131	280	24	∈	∈	PROPN
ejpam-3131	280	25	i	i	PRON
ejpam-3131	280	26	,	,	PUNCT
ejpam-3131	280	27	we	we	PRON
ejpam-3131	280	28	have	have	VERB
ejpam-3131	280	29	that	that	SCONJ
ejpam-3131	280	30	a\u	a\u	PROPN
ejpam-3131	280	31	∈	∈	PROPN
ejpam-3131	280	32	i.	i.	NOUN
ejpam-3131	280	33	(	(	PUNCT
ejpam-3131	280	34	2	2	NUM
ejpam-3131	280	35	)	)	PUNCT
ejpam-3131	280	36	since	since	SCONJ
ejpam-3131	280	37	a	a	PRON
ejpam-3131	280	38	is	be	AUX
ejpam-3131	280	39	closed	close	VERB
ejpam-3131	280	40	then	then	ADV
ejpam-3131	280	41	(	(	PUNCT
ejpam-3131	280	42	a	a	PRON
ejpam-3131	280	43	)	)	PUNCT
ejpam-3131	280	44	∗	∗	NOUN
ejpam-3131	280	45	⊆	⊆	NUM
ejpam-3131	280	46	a	a	PRON
ejpam-3131	280	47	,	,	PUNCT
ejpam-3131	280	48	and	and	CCONJ
ejpam-3131	281	1	so	so	ADV
ejpam-3131	281	2	(	(	PUNCT
ejpam-3131	281	3	0	0	NUM
ejpam-3131	281	4	a	a	DET
ejpam-3131	281	5	)	)	PUNCT
ejpam-3131	281	6	∗	∗	NOUN
ejpam-3131	281	7	\a	\a	VERB
ejpam-3131	282	1	⊆	⊆	NUM
ejpam-3131	282	2	(	(	PUNCT
ejpam-3131	282	3	a	a	PRON
ejpam-3131	282	4	)	)	PUNCT
ejpam-3131	282	5	∗	∗	NOUN
ejpam-3131	282	6	\a	\a	VERB
ejpam-3131	282	7	⊆	⊆	NUM
ejpam-3131	282	8	a\a	a\a	NOUN
ejpam-3131	282	9	∈	∈	PROPN
ejpam-3131	282	10	i.	i.	NOUN
ejpam-3131	282	11	(	(	PUNCT
ejpam-3131	282	12	3	3	X
ejpam-3131	282	13	)	)	PUNCT
ejpam-3131	282	14	it	it	PRON
ejpam-3131	282	15	is	be	AUX
ejpam-3131	282	16	enough	enough	ADJ
ejpam-3131	282	17	to	to	PART
ejpam-3131	282	18	note	note	VERB
ejpam-3131	282	19	that	that	SCONJ
ejpam-3131	282	20	a	a	DET
ejpam-3131	282	21	∪b\	∪b\	X
ejpam-3131	282	22	(	(	PUNCT
ejpam-3131	282	23	a	a	DET
ejpam-3131	282	24	∪b	∪b	NOUN
ejpam-3131	282	25	)	)	PUNCT
ejpam-3131	282	26	=	=	SYM
ejpam-3131	282	27	(	(	PUNCT
ejpam-3131	282	28	a	a	DET
ejpam-3131	282	29	∪b	∪b	X
ejpam-3131	282	30	)	)	PUNCT
ejpam-3131	282	31	\	\	NOUN
ejpam-3131	282	32	(	(	PUNCT
ejpam-3131	282	33	a	a	DET
ejpam-3131	282	34	∪b	∪b	NOUN
ejpam-3131	282	35	)	)	PUNCT
ejpam-3131	282	36	⊆	⊆	NUM
ejpam-3131	282	37	(	(	PUNCT
ejpam-3131	282	38	a\a	a\a	NOUN
ejpam-3131	282	39	)	)	PUNCT
ejpam-3131	282	40	∪	∪	NOUN
ejpam-3131	282	41	(	(	PUNCT
ejpam-3131	282	42	b\b	b\b	NOUN
ejpam-3131	282	43	)	)	PUNCT
ejpam-3131	282	44	∈	∈	PROPN
ejpam-3131	283	1	i	i	PRON
ejpam-3131	283	2	,	,	PUNCT
ejpam-3131	283	3	and	and	CCONJ
ejpam-3131	283	4	that	that	SCONJ
ejpam-3131	283	5	a	a	DET
ejpam-3131	283	6	∩b\	∩b\	PROPN
ejpam-3131	283	7	(	(	PUNCT
ejpam-3131	283	8	a	a	DET
ejpam-3131	283	9	∩b	∩b	NOUN
ejpam-3131	283	10	)	)	PUNCT
ejpam-3131	283	11	⊆	⊆	NUM
ejpam-3131	283	12	(	(	PUNCT
ejpam-3131	283	13	a	a	DET
ejpam-3131	283	14	∩b	∩b	NOUN
ejpam-3131	283	15	)	)	PUNCT
ejpam-3131	283	16	\	\	PUNCT
ejpam-3131	283	17	(	(	PUNCT
ejpam-3131	283	18	a	a	DET
ejpam-3131	283	19	∩b	∩b	NOUN
ejpam-3131	283	20	)	)	PUNCT
ejpam-3131	283	21	⊆	⊆	NUM
ejpam-3131	283	22	(	(	PUNCT
ejpam-3131	283	23	a\a	a\a	NOUN
ejpam-3131	283	24	)	)	PUNCT
ejpam-3131	283	25	∪	∪	NOUN
ejpam-3131	283	26	(	(	PUNCT
ejpam-3131	283	27	b\b	b\b	NOUN
ejpam-3131	283	28	)	)	PUNCT
ejpam-3131	283	29	∈	∈	PROPN
ejpam-3131	283	30	i.	i.	NOUN
ejpam-3131	283	31	(	(	PUNCT
ejpam-3131	283	32	4	4	NUM
ejpam-3131	283	33	)	)	PUNCT
ejpam-3131	283	34	since	since	SCONJ
ejpam-3131	283	35	b\b	b\b	PROPN
ejpam-3131	283	36	⊆	⊆	NUM
ejpam-3131	283	37	(	(	PUNCT
ejpam-3131	283	38	a\a	a\a	NOUN
ejpam-3131	283	39	)	)	PUNCT
ejpam-3131	283	40	∪	∪	NOUN
ejpam-3131	283	41	(	(	PUNCT
ejpam-3131	283	42	b\a	b\a	NOUN
ejpam-3131	283	43	)	)	PUNCT
ejpam-3131	283	44	∪	∪	NOUN
ejpam-3131	283	45	(	(	PUNCT
ejpam-3131	283	46	a\b	a\b	NOUN
ejpam-3131	283	47	)	)	PUNCT
ejpam-3131	283	48	∈	∈	PROPN
ejpam-3131	284	1	i	i	PRON
ejpam-3131	284	2	,	,	PUNCT
ejpam-3131	284	3	we	we	PRON
ejpam-3131	284	4	have	have	VERB
ejpam-3131	284	5	that	that	PRON
ejpam-3131	284	6	b\b	b\b	PROPN
ejpam-3131	284	7	∈	∈	PROPN
ejpam-3131	284	8	i.	i.	PROPN
ejpam-3131	284	9	n.r	n.r	PROPN
ejpam-3131	284	10	.	.	PROPN
ejpam-3131	284	11	pachón	pachón	PROPN
ejpam-3131	284	12	/	/	SYM
ejpam-3131	284	13	eur	eur	PROPN
ejpam-3131	284	14	.	.	PUNCT
ejpam-3131	285	1	j.	j.	PROPN
ejpam-3131	285	2	pure	pure	PROPN
ejpam-3131	285	3	appl	appl	PROPN
ejpam-3131	285	4	.	.	PROPN
ejpam-3131	285	5	math	math	PROPN
ejpam-3131	285	6	,	,	PUNCT
ejpam-3131	285	7	11	11	NUM
ejpam-3131	285	8	(	(	PUNCT
ejpam-3131	285	9	1	1	NUM
ejpam-3131	285	10	)	)	PUNCT
ejpam-3131	285	11	(	(	PUNCT
ejpam-3131	285	12	2018	2018	NUM
ejpam-3131	285	13	)	)	PUNCT
ejpam-3131	285	14	,	,	PUNCT
ejpam-3131	285	15	299	299	NUM
ejpam-3131	285	16	-	-	SYM
ejpam-3131	285	17	314	314	NUM
ejpam-3131	285	18	308	308	NUM
ejpam-3131	285	19	(	(	PUNCT
ejpam-3131	285	20	5	5	NUM
ejpam-3131	285	21	)	)	PUNCT
ejpam-3131	285	22	it	it	PRON
ejpam-3131	285	23	is	be	AUX
ejpam-3131	285	24	a	a	DET
ejpam-3131	285	25	consequence	consequence	NOUN
ejpam-3131	285	26	of	of	ADP
ejpam-3131	285	27	(	(	PUNCT
ejpam-3131	285	28	4	4	NUM
ejpam-3131	285	29	)	)	PUNCT
ejpam-3131	285	30	.	.	PUNCT
ejpam-3131	286	1	(	(	PUNCT
ejpam-3131	286	2	6	6	NUM
ejpam-3131	286	3	)	)	PUNCT
ejpam-3131	286	4	by	by	ADP
ejpam-3131	286	5	hypothesis	hypothesis	NOUN
ejpam-3131	286	6	,	,	PUNCT
ejpam-3131	286	7	a\	a\	NOUN
ejpam-3131	286	8	0	0	NUM
ejpam-3131	286	9	a	a	DET
ejpam-3131	286	10	⊆	⊆	NUM
ejpam-3131	286	11	a\a	a\a	NOUN
ejpam-3131	286	12	∈	∈	PROPN
ejpam-3131	286	13	i.	i.	NOUN
ejpam-3131	286	14	(	(	PUNCT
ejpam-3131	286	15	7	7	NUM
ejpam-3131	286	16	)	)	PUNCT
ejpam-3131	286	17	given	give	VERB
ejpam-3131	286	18	that	that	DET
ejpam-3131	286	19	adhτb	adhτb	NOUN
ejpam-3131	286	20	(	(	PUNCT
ejpam-3131	286	21	a	a	NOUN
ejpam-3131	286	22	)	)	PUNCT
ejpam-3131	286	23	\a	\a	VERB
ejpam-3131	286	24	=	=	SYM
ejpam-3131	286	25	(	(	PUNCT
ejpam-3131	286	26	a	a	DET
ejpam-3131	286	27	∩b	∩b	NOUN
ejpam-3131	286	28	)	)	PUNCT
ejpam-3131	286	29	\a	\a	VERB
ejpam-3131	286	30	=	=	SYM
ejpam-3131	287	1	(	(	PUNCT
ejpam-3131	287	2	a\a	a\a	X
ejpam-3131	287	3	)	)	PUNCT
ejpam-3131	287	4	∩b	∩b	NOUN
ejpam-3131	287	5	∈	∈	PROPN
ejpam-3131	287	6	ib	ib	NOUN
ejpam-3131	287	7	,	,	PUNCT
ejpam-3131	287	8	then	then	ADV
ejpam-3131	287	9	adhτb	adhτb	VERB
ejpam-3131	287	10	(	(	PUNCT
ejpam-3131	287	11	a	a	NOUN
ejpam-3131	287	12	)	)	PUNCT
ejpam-3131	287	13	\a	\a	VERB
ejpam-3131	287	14	∈	∈	PROPN
ejpam-3131	287	15	ib	ib	NOUN
ejpam-3131	287	16	.	.	PUNCT
ejpam-3131	288	1	(	(	PUNCT
ejpam-3131	288	2	8)	8)	NUM
ejpam-3131	288	3	we	we	PRON
ejpam-3131	288	4	have	have	VERB
ejpam-3131	288	5	that	that	PRON
ejpam-3131	288	6	b\b	b\b	PROPN
ejpam-3131	288	7	∈	∈	PROPN
ejpam-3131	288	8	i	i	PRON
ejpam-3131	288	9	and	and	CCONJ
ejpam-3131	288	10	adhτb	adhτb	ADJ
ejpam-3131	288	11	(	(	PUNCT
ejpam-3131	288	12	a	a	NOUN
ejpam-3131	288	13	)	)	PUNCT
ejpam-3131	288	14	\a	\a	VERB
ejpam-3131	289	1	∈	∈	PROPN
ejpam-3131	289	2	ib	ib	NOUN
ejpam-3131	289	3	⊆	⊆	NUM
ejpam-3131	289	4	i.	i.	NOUN
ejpam-3131	289	5	now	now	ADV
ejpam-3131	289	6	,	,	PUNCT
ejpam-3131	289	7	adhτb	adhτb	ADJ
ejpam-3131	289	8	(	(	PUNCT
ejpam-3131	289	9	a	a	NOUN
ejpam-3131	289	10	)	)	PUNCT
ejpam-3131	289	11	=	=	PUNCT
ejpam-3131	289	12	a	a	DET
ejpam-3131	289	13	∩	∩	ADJ
ejpam-3131	289	14	b	b	NOUN
ejpam-3131	289	15	and	and	CCONJ
ejpam-3131	289	16	a\a	a\a	ADJ
ejpam-3131	289	17	⊆	⊆	NUM
ejpam-3131	290	1	[	[	X
ejpam-3131	290	2	(	(	PUNCT
ejpam-3131	290	3	a	a	DET
ejpam-3131	290	4	∩b	∩b	NOUN
ejpam-3131	290	5	)	)	PUNCT
ejpam-3131	290	6	\a	\a	VERB
ejpam-3131	290	7	]	]	PUNCT
ejpam-3131	290	8	∪	∪	X
ejpam-3131	290	9	(	(	PUNCT
ejpam-3131	290	10	b\b	b\b	NOUN
ejpam-3131	290	11	)	)	PUNCT
ejpam-3131	290	12	∈	∈	PROPN
ejpam-3131	290	13	i.	i.	NOUN
ejpam-3131	290	14	□	□	PUNCT
ejpam-3131	290	15	example	example	NOUN
ejpam-3131	290	16	3.4	3.4	NUM
ejpam-3131	290	17	.	.	PUNCT
ejpam-3131	291	1	(	(	PUNCT
ejpam-3131	291	2	1	1	X
ejpam-3131	291	3	)	)	PUNCT
ejpam-3131	291	4	in	in	ADP
ejpam-3131	291	5	the	the	DET
ejpam-3131	291	6	space	space	NOUN
ejpam-3131	291	7	(	(	PUNCT
ejpam-3131	291	8	r	r	NOUN
ejpam-3131	291	9	,	,	PUNCT
ejpam-3131	291	10	c	c	X
ejpam-3131	291	11	,	,	PUNCT
ejpam-3131	291	12	i	i	NOUN
ejpam-3131	291	13	)	)	PUNCT
ejpam-3131	291	14	of	of	ADP
ejpam-3131	291	15	example	example	NOUN
ejpam-3131	291	16	2.2	2.2	NUM
ejpam-3131	291	17	,	,	PUNCT
ejpam-3131	291	18	z	z	NOUN
ejpam-3131	291	19	is	be	AUX
ejpam-3131	291	20	g	g	NOUN
ejpam-3131	291	21	-	-	PUNCT
ejpam-3131	291	22	closed	closed	ADJ
ejpam-3131	291	23	but	but	CCONJ
ejpam-3131	291	24	z	z	NOUN
ejpam-3131	291	25	is	be	AUX
ejpam-3131	291	26	not	not	PART
ejpam-3131	291	27	closedi	closedi	ADJ
ejpam-3131	291	28	,	,	PUNCT
ejpam-3131	291	29	because	because	SCONJ
ejpam-3131	291	30	z	z	NOUN
ejpam-3131	291	31	is	be	AUX
ejpam-3131	291	32	not	not	PART
ejpam-3131	291	33	ρig	ρig	ADV
ejpam-3131	291	34	-	-	PUNCT
ejpam-3131	291	35	closed	closed	ADJ
ejpam-3131	291	36	.	.	PUNCT
ejpam-3131	292	1	(	(	PUNCT
ejpam-3131	292	2	2	2	X
ejpam-3131	292	3	)	)	PUNCT
ejpam-3131	292	4	if	if	SCONJ
ejpam-3131	292	5	c	c	AUX
ejpam-3131	292	6	=	=	PUNCT
ejpam-3131	292	7	{	{	PUNCT
ejpam-3131	292	8	∅,r	∅,r	ADV
ejpam-3131	292	9	}	}	PUNCT
ejpam-3131	292	10	∪	∪	X
ejpam-3131	292	11	{	{	PUNCT
ejpam-3131	292	12	(	(	PUNCT
ejpam-3131	292	13	r,∞	r,∞	PROPN
ejpam-3131	292	14	)	)	PUNCT
ejpam-3131	292	15	:	:	PUNCT
ejpam-3131	293	1	r	r	NOUN
ejpam-3131	293	2	∈	∈	NOUN
ejpam-3131	293	3	r	r	NOUN
ejpam-3131	293	4	}	}	PUNCT
ejpam-3131	293	5	and	and	CCONJ
ejpam-3131	293	6	i	i	PRON
ejpam-3131	293	7	=	=	NOUN
ejpam-3131	293	8	p	p	X
ejpam-3131	293	9	(	(	PUNCT
ejpam-3131	293	10	(	(	PUNCT
ejpam-3131	293	11	0,∞	0,∞	NOUN
ejpam-3131	293	12	)	)	PUNCT
ejpam-3131	293	13	)	)	PUNCT
ejpam-3131	293	14	,	,	PUNCT
ejpam-3131	293	15	then	then	ADV
ejpam-3131	293	16	the	the	DET
ejpam-3131	293	17	set	set	NOUN
ejpam-3131	293	18	a	a	X
ejpam-3131	293	19	=	=	SYM
ejpam-3131	293	20	(	(	PUNCT
ejpam-3131	293	21	−∞	−∞	NOUN
ejpam-3131	293	22	,	,	PUNCT
ejpam-3131	293	23	0	0	NUM
ejpam-3131	293	24	)	)	PUNCT
ejpam-3131	293	25	is	be	AUX
ejpam-3131	293	26	ρig	ρig	NOUN
ejpam-3131	293	27	-	-	PUNCT
ejpam-3131	293	28	closed	close	VERB
ejpam-3131	293	29	in	in	ADP
ejpam-3131	293	30	the	the	DET
ejpam-3131	293	31	space	space	NOUN
ejpam-3131	293	32	(	(	PUNCT
ejpam-3131	293	33	r	r	NOUN
ejpam-3131	293	34	,	,	PUNCT
ejpam-3131	293	35	c	c	X
ejpam-3131	293	36	,	,	PUNCT
ejpam-3131	293	37	i	i	PROPN
ejpam-3131	293	38	)	)	PUNCT
ejpam-3131	293	39	because	because	SCONJ
ejpam-3131	293	40	if	if	SCONJ
ejpam-3131	293	41	u	u	PROPN
ejpam-3131	293	42	∈	∈	PROPN
ejpam-3131	293	43	c	c	NOUN
ejpam-3131	293	44	and	and	CCONJ
ejpam-3131	293	45	a\u	a\u	PROPN
ejpam-3131	293	46	∈	∈	PROPN
ejpam-3131	294	1	i	i	PRON
ejpam-3131	294	2	then	then	ADV
ejpam-3131	294	3	u	u	VERB
ejpam-3131	294	4	=	=	SYM
ejpam-3131	294	5	r	r	NOUN
ejpam-3131	294	6	,	,	PUNCT
ejpam-3131	294	7	and	and	CCONJ
ejpam-3131	294	8	so	so	ADV
ejpam-3131	294	9	a\u	a\u	PROPN
ejpam-3131	294	10	∈	∈	PROPN
ejpam-3131	294	11	i.	i.	NOUN
ejpam-3131	294	12	however	however	ADV
ejpam-3131	294	13	,	,	PUNCT
ejpam-3131	294	14	since	since	SCONJ
ejpam-3131	294	15	a\a	a\a	ADJ
ejpam-3131	294	16	=	=	PUNCT
ejpam-3131	294	17	{	{	PUNCT
ejpam-3131	294	18	0	0	NUM
ejpam-3131	294	19	}	}	PUNCT
ejpam-3131	294	20	/∈	/∈	PUNCT
ejpam-3131	295	1	i	i	PRON
ejpam-3131	295	2	,	,	PUNCT
ejpam-3131	295	3	we	we	PRON
ejpam-3131	295	4	have	have	VERB
ejpam-3131	295	5	that	that	SCONJ
ejpam-3131	295	6	a	a	PRON
ejpam-3131	295	7	is	be	AUX
ejpam-3131	295	8	not	not	PART
ejpam-3131	295	9	closed	closed	ADJ
ejpam-3131	295	10	-	-	PUNCT
ejpam-3131	295	11	i.	i.	NOUN
ejpam-3131	295	12	thus	thus	ADV
ejpam-3131	295	13	,	,	PUNCT
ejpam-3131	295	14	in	in	ADP
ejpam-3131	295	15	general	general	ADJ
ejpam-3131	295	16	,	,	PUNCT
ejpam-3131	295	17	ρig	ρig	ADV
ejpam-3131	295	18	-	-	PUNCT
ejpam-3131	295	19	closed	closed	ADJ
ejpam-3131	295	20	↛closed	↛closed	ADJ
ejpam-3131	295	21	-	-	PUNCT
ejpam-3131	295	22	i.	i.	NOUN
ejpam-3131	295	23	(	(	PUNCT
ejpam-3131	295	24	3	3	NUM
ejpam-3131	295	25	)	)	PUNCT
ejpam-3131	295	26	if	if	SCONJ
ejpam-3131	295	27	u	u	NOUN
ejpam-3131	295	28	is	be	AUX
ejpam-3131	295	29	the	the	DET
ejpam-3131	295	30	usual	usual	ADJ
ejpam-3131	295	31	topology	topology	NOUN
ejpam-3131	295	32	in	in	ADP
ejpam-3131	295	33	r	r	NOUN
ejpam-3131	295	34	and	and	CCONJ
ejpam-3131	295	35	i	i	PRON
ejpam-3131	295	36	=	=	NOUN
ejpam-3131	296	1	p	p	X
ejpam-3131	296	2	(	(	PUNCT
ejpam-3131	296	3	{	{	PUNCT
ejpam-3131	296	4	0	0	NUM
ejpam-3131	296	5	,	,	PUNCT
ejpam-3131	296	6	1	1	NUM
ejpam-3131	296	7	}	}	PUNCT
ejpam-3131	296	8	)	)	PUNCT
ejpam-3131	296	9	,	,	PUNCT
ejpam-3131	296	10	then	then	ADV
ejpam-3131	296	11	the	the	DET
ejpam-3131	296	12	set	set	NOUN
ejpam-3131	296	13	a	a	X
ejpam-3131	296	14	=	=	SYM
ejpam-3131	296	15	(	(	PUNCT
ejpam-3131	296	16	0	0	NUM
ejpam-3131	296	17	,	,	PUNCT
ejpam-3131	296	18	1	1	NUM
ejpam-3131	296	19	)	)	PUNCT
ejpam-3131	296	20	is	be	AUX
ejpam-3131	296	21	not	not	PART
ejpam-3131	296	22	g	g	NOUN
ejpam-3131	296	23	-	-	PUNCT
ejpam-3131	296	24	closed	closed	ADJ
ejpam-3131	296	25	.	.	PUNCT
ejpam-3131	297	1	however	however	ADV
ejpam-3131	297	2	,	,	PUNCT
ejpam-3131	297	3	given	give	VERB
ejpam-3131	297	4	that	that	DET
ejpam-3131	297	5	a\a	a\a	NOUN
ejpam-3131	297	6	=	=	PUNCT
ejpam-3131	297	7	{	{	PUNCT
ejpam-3131	297	8	0	0	NUM
ejpam-3131	297	9	,	,	PUNCT
ejpam-3131	297	10	1	1	NUM
ejpam-3131	297	11	}	}	PUNCT
ejpam-3131	297	12	∈	∈	PROPN
ejpam-3131	297	13	i	i	PRON
ejpam-3131	297	14	,	,	PUNCT
ejpam-3131	297	15	we	we	PRON
ejpam-3131	297	16	conclude	conclude	VERB
ejpam-3131	297	17	that	that	SCONJ
ejpam-3131	297	18	(	(	PUNCT
ejpam-3131	297	19	0	0	NUM
ejpam-3131	297	20	,	,	PUNCT
ejpam-3131	297	21	1	1	NUM
ejpam-3131	297	22	)	)	PUNCT
ejpam-3131	297	23	is	be	AUX
ejpam-3131	297	24	closed	closed	ADJ
ejpam-3131	297	25	-	-	PUNCT
ejpam-3131	297	26	i.	i.	NOUN
ejpam-3131	297	27	so	so	ADV
ejpam-3131	297	28	,	,	PUNCT
ejpam-3131	297	29	in	in	ADP
ejpam-3131	297	30	general	general	ADJ
ejpam-3131	297	31	,	,	PUNCT
ejpam-3131	297	32	closed	closed	ADJ
ejpam-3131	297	33	-	-	PUNCT
ejpam-3131	297	34	i	i	PRON
ejpam-3131	297	35	↛g	↛g	NOUN
ejpam-3131	297	36	-	-	VERB
ejpam-3131	297	37	closed	closed	ADJ
ejpam-3131	297	38	.	.	PUNCT
ejpam-3131	298	1	thus	thus	ADV
ejpam-3131	298	2	,	,	PUNCT
ejpam-3131	298	3	closed	closed	ADJ
ejpam-3131	298	4	-	-	PUNCT
ejpam-3131	298	5	i	i	NOUN
ejpam-3131	298	6	and	and	CCONJ
ejpam-3131	298	7	g	g	NOUN
ejpam-3131	298	8	-	-	PUNCT
ejpam-3131	298	9	closed	closed	ADJ
ejpam-3131	298	10	are	be	AUX
ejpam-3131	298	11	independent	independent	ADJ
ejpam-3131	298	12	concepts	concept	NOUN
ejpam-3131	298	13	.	.	PUNCT
ejpam-3131	299	1	we	we	PRON
ejpam-3131	299	2	have	have	VERB
ejpam-3131	299	3	the	the	DET
ejpam-3131	299	4	following	follow	VERB
ejpam-3131	299	5	diagram	diagram	NOUN
ejpam-3131	299	6	.	.	PUNCT
ejpam-3131	300	1	g	g	PROPN
ejpam-3131	300	2	−	−	PROPN
ejpam-3131	300	3	closed	close	VERB
ejpam-3131	300	4	closed	closed	ADJ
ejpam-3131	300	5	closed−	closed−	NOUN
ejpam-3131	300	6	i	i	PRON
ejpam-3131	300	7	ρig	ρig	PRON
ejpam-3131	300	8	−	−	PROPN
ejpam-3131	300	9	closed	close	VERB
ejpam-3131	300	10	ig	ig	PRON
ejpam-3131	300	11	−	−	PROPN
ejpam-3131	300	12	closed	close	VERB
ejpam-3131	300	13	in	in	ADP
ejpam-3131	300	14	the	the	DET
ejpam-3131	300	15	theorem	theorem	ADJ
ejpam-3131	300	16	3.5	3.5	NUM
ejpam-3131	300	17	we	we	PRON
ejpam-3131	300	18	review	review	VERB
ejpam-3131	300	19	the	the	DET
ejpam-3131	300	20	behavior	behavior	NOUN
ejpam-3131	300	21	of	of	ADP
ejpam-3131	300	22	closed	closed	ADJ
ejpam-3131	300	23	-	-	PUNCT
ejpam-3131	300	24	i	i	PRON
ejpam-3131	300	25	sets	set	VERB
ejpam-3131	300	26	under	under	ADP
ejpam-3131	300	27	continuous	continuous	ADJ
ejpam-3131	300	28	or	or	CCONJ
ejpam-3131	300	29	closed	closed	ADJ
ejpam-3131	300	30	functions	function	NOUN
ejpam-3131	300	31	.	.	PUNCT
ejpam-3131	301	1	theorem	theorem	VERB
ejpam-3131	301	2	3.5	3.5	NUM
ejpam-3131	301	3	.	.	PUNCT
ejpam-3131	302	1	(	(	PUNCT
ejpam-3131	302	2	1	1	X
ejpam-3131	302	3	)	)	PUNCT
ejpam-3131	302	4	if	if	SCONJ
ejpam-3131	302	5	(	(	PUNCT
ejpam-3131	302	6	y	y	NOUN
ejpam-3131	302	7	,	,	PUNCT
ejpam-3131	302	8	β	β	X
ejpam-3131	302	9	,	,	PUNCT
ejpam-3131	302	10	j	j	PROPN
ejpam-3131	302	11	)	)	PUNCT
ejpam-3131	302	12	is	be	AUX
ejpam-3131	302	13	an	an	DET
ejpam-3131	302	14	ideal	ideal	ADJ
ejpam-3131	302	15	space	space	NOUN
ejpam-3131	302	16	,	,	PUNCT
ejpam-3131	302	17	f	f	X
ejpam-3131	302	18	:	:	PUNCT
ejpam-3131	302	19	(	(	PUNCT
ejpam-3131	302	20	x	x	X
ejpam-3131	302	21	,	,	PUNCT
ejpam-3131	302	22	τ)→	τ)→	PROPN
ejpam-3131	302	23	(	(	PUNCT
ejpam-3131	302	24	y	y	NOUN
ejpam-3131	302	25	,	,	PUNCT
ejpam-3131	302	26	β	β	NOUN
ejpam-3131	302	27	)	)	PUNCT
ejpam-3131	302	28	is	be	AUX
ejpam-3131	302	29	a	a	DET
ejpam-3131	302	30	continuous	continuous	ADJ
ejpam-3131	302	31	and	and	CCONJ
ejpam-3131	302	32	inyective	inyective	ADJ
ejpam-3131	302	33	function	function	NOUN
ejpam-3131	302	34	and	and	CCONJ
ejpam-3131	302	35	b	b	NOUN
ejpam-3131	303	1	is	be	AUX
ejpam-3131	303	2	closed	closed	ADJ
ejpam-3131	303	3	-	-	PUNCT
ejpam-3131	303	4	j	j	NOUN
ejpam-3131	303	5	,	,	PUNCT
ejpam-3131	303	6	then	then	ADV
ejpam-3131	303	7	f−1	f−1	PROPN
ejpam-3131	303	8	(	(	PUNCT
ejpam-3131	303	9	b	b	NOUN
ejpam-3131	303	10	)	)	PUNCT
ejpam-3131	303	11	is	be	AUX
ejpam-3131	303	12	closed	closed	ADJ
ejpam-3131	303	13	-	-	PUNCT
ejpam-3131	303	14	f−1	f−1	PROPN
ejpam-3131	303	15	(	(	PUNCT
ejpam-3131	303	16	j	j	PROPN
ejpam-3131	303	17	)	)	PUNCT
ejpam-3131	303	18	.	.	PUNCT
ejpam-3131	304	1	(	(	PUNCT
ejpam-3131	304	2	2	2	X
ejpam-3131	304	3	)	)	PUNCT
ejpam-3131	304	4	if	if	SCONJ
ejpam-3131	304	5	(	(	PUNCT
ejpam-3131	304	6	x	x	NOUN
ejpam-3131	304	7	,	,	PUNCT
ejpam-3131	304	8	τ	τ	PROPN
ejpam-3131	304	9	,	,	PUNCT
ejpam-3131	304	10	i	i	PROPN
ejpam-3131	304	11	)	)	PUNCT
ejpam-3131	304	12	is	be	AUX
ejpam-3131	304	13	an	an	DET
ejpam-3131	304	14	ideal	ideal	ADJ
ejpam-3131	304	15	space	space	NOUN
ejpam-3131	304	16	,	,	PUNCT
ejpam-3131	304	17	f	f	X
ejpam-3131	304	18	:	:	PUNCT
ejpam-3131	304	19	(	(	PUNCT
ejpam-3131	304	20	x	x	X
ejpam-3131	304	21	,	,	PUNCT
ejpam-3131	304	22	τ)→	τ)→	PROPN
ejpam-3131	304	23	(	(	PUNCT
ejpam-3131	304	24	y	y	NOUN
ejpam-3131	304	25	,	,	PUNCT
ejpam-3131	304	26	β	β	NOUN
ejpam-3131	304	27	)	)	PUNCT
ejpam-3131	304	28	is	be	AUX
ejpam-3131	304	29	a	a	DET
ejpam-3131	304	30	closed	closed	ADJ
ejpam-3131	304	31	function	function	NOUN
ejpam-3131	304	32	and	and	CCONJ
ejpam-3131	304	33	a	a	PRON
ejpam-3131	304	34	is	be	AUX
ejpam-3131	304	35	closed	closed	ADJ
ejpam-3131	304	36	-	-	PUNCT
ejpam-3131	304	37	i	i	NOUN
ejpam-3131	304	38	,	,	PUNCT
ejpam-3131	304	39	then	then	ADV
ejpam-3131	304	40	f	f	X
ejpam-3131	304	41	(	(	PUNCT
ejpam-3131	304	42	a	a	PRON
ejpam-3131	304	43	)	)	PUNCT
ejpam-3131	304	44	is	be	AUX
ejpam-3131	304	45	closed	closed	ADJ
ejpam-3131	304	46	-	-	PUNCT
ejpam-3131	304	47	f(i	f(i	NUM
ejpam-3131	304	48	)	)	PUNCT
ejpam-3131	304	49	.	.	PUNCT
ejpam-3131	305	1	(	(	PUNCT
ejpam-3131	305	2	3	3	X
ejpam-3131	305	3	)	)	PUNCT
ejpam-3131	305	4	if	if	SCONJ
ejpam-3131	305	5	(	(	PUNCT
ejpam-3131	305	6	x	x	NOUN
ejpam-3131	305	7	,	,	PUNCT
ejpam-3131	305	8	τ	τ	PROPN
ejpam-3131	305	9	,	,	PUNCT
ejpam-3131	305	10	i	i	PROPN
ejpam-3131	305	11	)	)	PUNCT
ejpam-3131	305	12	is	be	AUX
ejpam-3131	305	13	an	an	DET
ejpam-3131	305	14	ideal	ideal	ADJ
ejpam-3131	305	15	space	space	NOUN
ejpam-3131	305	16	,	,	PUNCT
ejpam-3131	305	17	f	f	X
ejpam-3131	305	18	:	:	PUNCT
ejpam-3131	305	19	(	(	PUNCT
ejpam-3131	305	20	x	x	X
ejpam-3131	305	21	,	,	PUNCT
ejpam-3131	305	22	τ	τ	X
ejpam-3131	305	23	)	)	PUNCT
ejpam-3131	305	24	→	→	SYM
ejpam-3131	305	25	(	(	PUNCT
ejpam-3131	305	26	y	y	PROPN
ejpam-3131	305	27	,	,	PUNCT
ejpam-3131	305	28	β	β	NOUN
ejpam-3131	305	29	)	)	PUNCT
ejpam-3131	305	30	is	be	AUX
ejpam-3131	305	31	a	a	DET
ejpam-3131	305	32	continuous	continuous	ADJ
ejpam-3131	305	33	function	function	NOUN
ejpam-3131	305	34	,	,	PUNCT
ejpam-3131	306	1	j	j	PROPN
ejpam-3131	306	2	=	=	PRON
ejpam-3131	306	3	{	{	PUNCT
ejpam-3131	306	4	d	d	PROPN
ejpam-3131	306	5	⊆	⊆	NUM
ejpam-3131	306	6	y	y	NOUN
ejpam-3131	306	7	:	:	PUNCT
ejpam-3131	306	8	f−1	f−1	PROPN
ejpam-3131	306	9	(	(	PUNCT
ejpam-3131	306	10	d	d	X
ejpam-3131	306	11	)	)	PUNCT
ejpam-3131	306	12	∈	∈	PROPN
ejpam-3131	307	1	i	i	PRON
ejpam-3131	307	2	}	}	PUNCT
ejpam-3131	307	3	and	and	CCONJ
ejpam-3131	307	4	b	b	NOUN
ejpam-3131	307	5	is	be	AUX
ejpam-3131	307	6	closed	closed	ADJ
ejpam-3131	307	7	-	-	PUNCT
ejpam-3131	307	8	j	j	NOUN
ejpam-3131	307	9	,	,	PUNCT
ejpam-3131	307	10	then	then	ADV
ejpam-3131	307	11	f−1	f−1	PROPN
ejpam-3131	307	12	(	(	PUNCT
ejpam-3131	307	13	b	b	NOUN
ejpam-3131	307	14	)	)	PUNCT
ejpam-3131	307	15	is	be	AUX
ejpam-3131	307	16	closed	closed	ADJ
ejpam-3131	307	17	-	-	PUNCT
ejpam-3131	307	18	i.	i.	NOUN
ejpam-3131	307	19	(	(	PUNCT
ejpam-3131	307	20	4	4	NUM
ejpam-3131	307	21	)	)	PUNCT
ejpam-3131	307	22	if	if	SCONJ
ejpam-3131	307	23	f	f	PROPN
ejpam-3131	307	24	:	:	PUNCT
ejpam-3131	307	25	(	(	PUNCT
ejpam-3131	307	26	x	x	X
ejpam-3131	307	27	,	,	PUNCT
ejpam-3131	307	28	τ)→	τ)→	PROPN
ejpam-3131	307	29	(	(	PUNCT
ejpam-3131	307	30	y	y	NOUN
ejpam-3131	307	31	,	,	PUNCT
ejpam-3131	307	32	β	β	NOUN
ejpam-3131	307	33	)	)	PUNCT
ejpam-3131	307	34	is	be	AUX
ejpam-3131	307	35	an	an	DET
ejpam-3131	307	36	inyective	inyective	ADJ
ejpam-3131	307	37	and	and	CCONJ
ejpam-3131	307	38	closed	closed	ADJ
ejpam-3131	307	39	function	function	NOUN
ejpam-3131	307	40	,	,	PUNCT
ejpam-3131	307	41	j	j	PROPN
ejpam-3131	307	42	is	be	AUX
ejpam-3131	307	43	an	an	DET
ejpam-3131	307	44	ideal	ideal	NOUN
ejpam-3131	307	45	in	in	ADP
ejpam-3131	307	46	y	y	PROPN
ejpam-3131	307	47	and	and	CCONJ
ejpam-3131	307	48	if	if	SCONJ
ejpam-3131	307	49	a	a	PRON
ejpam-3131	307	50	is	be	AUX
ejpam-3131	307	51	closed	closed	ADJ
ejpam-3131	307	52	-	-	PUNCT
ejpam-3131	307	53	f−1(j	f−1(j	NOUN
ejpam-3131	307	54	)	)	PUNCT
ejpam-3131	307	55	,	,	PUNCT
ejpam-3131	307	56	then	then	ADV
ejpam-3131	307	57	f(a	f(a	PROPN
ejpam-3131	307	58	)	)	PUNCT
ejpam-3131	307	59	is	be	AUX
ejpam-3131	307	60	closed	closed	ADJ
ejpam-3131	307	61	-	-	PUNCT
ejpam-3131	307	62	j	j	NOUN
ejpam-3131	307	63	.	.	PUNCT
ejpam-3131	308	1	n.r	n.r	PROPN
ejpam-3131	308	2	.	.	PROPN
ejpam-3131	308	3	pachón	pachón	PROPN
ejpam-3131	308	4	/	/	SYM
ejpam-3131	308	5	eur	eur	PROPN
ejpam-3131	308	6	.	.	PUNCT
ejpam-3131	309	1	j.	j.	PROPN
ejpam-3131	309	2	pure	pure	PROPN
ejpam-3131	309	3	appl	appl	PROPN
ejpam-3131	309	4	.	.	PROPN
ejpam-3131	309	5	math	math	PROPN
ejpam-3131	309	6	,	,	PUNCT
ejpam-3131	309	7	11	11	NUM
ejpam-3131	309	8	(	(	PUNCT
ejpam-3131	309	9	1	1	NUM
ejpam-3131	309	10	)	)	PUNCT
ejpam-3131	309	11	(	(	PUNCT
ejpam-3131	309	12	2018	2018	NUM
ejpam-3131	309	13	)	)	PUNCT
ejpam-3131	309	14	,	,	PUNCT
ejpam-3131	309	15	299	299	NUM
ejpam-3131	309	16	-	-	SYM
ejpam-3131	309	17	314	314	NUM
ejpam-3131	309	18	309	309	NUM
ejpam-3131	309	19	proof	proof	NOUN
ejpam-3131	309	20	.	.	PUNCT
ejpam-3131	310	1	(	(	PUNCT
ejpam-3131	310	2	1	1	X
ejpam-3131	310	3	)	)	PUNCT
ejpam-3131	310	4	we	we	PRON
ejpam-3131	310	5	have	have	VERB
ejpam-3131	310	6	that	that	DET
ejpam-3131	310	7	f−1	f−1	PROPN
ejpam-3131	310	8	(	(	PUNCT
ejpam-3131	310	9	b)\f−1	b)\f−1	PROPN
ejpam-3131	310	10	(	(	PUNCT
ejpam-3131	310	11	b	b	NOUN
ejpam-3131	310	12	)	)	PUNCT
ejpam-3131	310	13	⊆	⊆	NUM
ejpam-3131	310	14	f−1	f−1	PROPN
ejpam-3131	310	15	(	(	PUNCT
ejpam-3131	310	16	b	b	NOUN
ejpam-3131	310	17	)	)	PUNCT
ejpam-3131	310	18	\f−1(b	\f−1(b	ADJ
ejpam-3131	310	19	)	)	PUNCT
ejpam-3131	310	20	=	=	SYM
ejpam-3131	310	21	f−1	f−1	PROPN
ejpam-3131	310	22	(	(	PUNCT
ejpam-3131	310	23	b\b	b\b	NOUN
ejpam-3131	310	24	)	)	PUNCT
ejpam-3131	310	25	∈	∈	PROPN
ejpam-3131	310	26	f−1(j	f−1(j	NOUN
ejpam-3131	310	27	)	)	PUNCT
ejpam-3131	310	28	,	,	PUNCT
ejpam-3131	310	29	given	give	VERB
ejpam-3131	310	30	that	that	SCONJ
ejpam-3131	310	31	b\b	b\b	PROPN
ejpam-3131	310	32	∈	∈	PROPN
ejpam-3131	310	33	j	j	PROPN
ejpam-3131	310	34	.	.	PUNCT
ejpam-3131	311	1	(	(	PUNCT
ejpam-3131	311	2	2	2	X
ejpam-3131	311	3	)	)	PUNCT
ejpam-3131	311	4	since	since	SCONJ
ejpam-3131	311	5	f(a)\f(a	f(a)\f(a	NOUN
ejpam-3131	311	6	)	)	PUNCT
ejpam-3131	311	7	⊆	⊆	NUM
ejpam-3131	311	8	f	f	X
ejpam-3131	311	9	(	(	PUNCT
ejpam-3131	311	10	a	a	NOUN
ejpam-3131	311	11	)	)	PUNCT
ejpam-3131	311	12	\f	\f	X
ejpam-3131	311	13	(	(	PUNCT
ejpam-3131	311	14	a	a	X
ejpam-3131	311	15	)	)	PUNCT
ejpam-3131	311	16	⊆	⊆	NUM
ejpam-3131	311	17	f	f	X
ejpam-3131	311	18	(	(	PUNCT
ejpam-3131	311	19	a\a	a\a	X
ejpam-3131	311	20	)	)	PUNCT
ejpam-3131	311	21	∈	∈	PROPN
ejpam-3131	311	22	f	f	X
ejpam-3131	311	23	(	(	PUNCT
ejpam-3131	311	24	i	i	NOUN
ejpam-3131	311	25	)	)	PUNCT
ejpam-3131	311	26	,	,	PUNCT
ejpam-3131	311	27	then	then	ADV
ejpam-3131	311	28	f(a)\f(a	f(a)\f(a	VERB
ejpam-3131	311	29	)	)	PUNCT
ejpam-3131	311	30	∈	∈	PROPN
ejpam-3131	311	31	f	f	X
ejpam-3131	311	32	(	(	PUNCT
ejpam-3131	311	33	i	i	NOUN
ejpam-3131	311	34	)	)	PUNCT
ejpam-3131	311	35	.	.	PUNCT
ejpam-3131	312	1	(	(	PUNCT
ejpam-3131	312	2	3	3	X
ejpam-3131	312	3	)	)	PUNCT
ejpam-3131	312	4	given	give	VERB
ejpam-3131	312	5	that	that	PRON
ejpam-3131	312	6	b\b	b\b	PROPN
ejpam-3131	312	7	∈	∈	PROPN
ejpam-3131	312	8	j	j	PROPN
ejpam-3131	312	9	then	then	ADV
ejpam-3131	312	10	f−1	f−1	PROPN
ejpam-3131	312	11	(	(	PUNCT
ejpam-3131	312	12	b	b	NOUN
ejpam-3131	312	13	)	)	PUNCT
ejpam-3131	312	14	\f−1	\f−1	NOUN
ejpam-3131	312	15	(	(	PUNCT
ejpam-3131	312	16	b	b	NOUN
ejpam-3131	312	17	)	)	PUNCT
ejpam-3131	312	18	=	=	SYM
ejpam-3131	312	19	f−1	f−1	PROPN
ejpam-3131	312	20	(	(	PUNCT
ejpam-3131	312	21	b\b	b\b	NOUN
ejpam-3131	312	22	)	)	PUNCT
ejpam-3131	312	23	∈	∈	PROPN
ejpam-3131	312	24	i.	i.	NOUN
ejpam-3131	312	25	but	but	CCONJ
ejpam-3131	312	26	f−1	f−1	PROPN
ejpam-3131	312	27	(	(	PUNCT
ejpam-3131	312	28	b)\f−1	b)\f−1	PROPN
ejpam-3131	312	29	(	(	PUNCT
ejpam-3131	312	30	b	b	NOUN
ejpam-3131	312	31	)	)	PUNCT
ejpam-3131	312	32	⊆	⊆	NUM
ejpam-3131	312	33	f−1	f−1	PROPN
ejpam-3131	312	34	(	(	PUNCT
ejpam-3131	312	35	b	b	NOUN
ejpam-3131	312	36	)	)	PUNCT
ejpam-3131	312	37	\f−1	\f−1	NOUN
ejpam-3131	312	38	(	(	PUNCT
ejpam-3131	312	39	b	b	NOUN
ejpam-3131	312	40	)	)	PUNCT
ejpam-3131	312	41	and	and	CCONJ
ejpam-3131	312	42	so	so	ADV
ejpam-3131	312	43	f−1	f−1	PROPN
ejpam-3131	312	44	(	(	PUNCT
ejpam-3131	312	45	b)\f−1	b)\f−1	PROPN
ejpam-3131	312	46	(	(	PUNCT
ejpam-3131	312	47	b	b	NOUN
ejpam-3131	312	48	)	)	PUNCT
ejpam-3131	312	49	∈	∈	PROPN
ejpam-3131	312	50	i.	i.	NOUN
ejpam-3131	312	51	(	(	PUNCT
ejpam-3131	312	52	4	4	X
ejpam-3131	312	53	)	)	PUNCT
ejpam-3131	312	54	there	there	PRON
ejpam-3131	312	55	is	be	VERB
ejpam-3131	312	56	j	j	PROPN
ejpam-3131	312	57	∈	∈	PROPN
ejpam-3131	312	58	j	j	PROPN
ejpam-3131	312	59	such	such	ADJ
ejpam-3131	312	60	that	that	PRON
ejpam-3131	312	61	a\a	a\a	NOUN
ejpam-3131	312	62	=	=	SYM
ejpam-3131	312	63	f−1	f−1	PROPN
ejpam-3131	312	64	(	(	PUNCT
ejpam-3131	312	65	j	j	NOUN
ejpam-3131	312	66	)	)	PUNCT
ejpam-3131	312	67	,	,	PUNCT
ejpam-3131	312	68	and	and	CCONJ
ejpam-3131	312	69	so	so	ADV
ejpam-3131	312	70	f	f	PROPN
ejpam-3131	312	71	(	(	PUNCT
ejpam-3131	312	72	a)\f	a)\f	PROPN
ejpam-3131	312	73	(	(	PUNCT
ejpam-3131	312	74	a	a	NOUN
ejpam-3131	312	75	)	)	PUNCT
ejpam-3131	312	76	⊆	⊆	NUM
ejpam-3131	312	77	f	f	X
ejpam-3131	312	78	(	(	PUNCT
ejpam-3131	312	79	a	a	NOUN
ejpam-3131	312	80	)	)	PUNCT
ejpam-3131	312	81	\f	\f	X
ejpam-3131	313	1	(	(	PUNCT
ejpam-3131	313	2	a	a	X
ejpam-3131	313	3	)	)	PUNCT
ejpam-3131	313	4	⊆	⊆	NUM
ejpam-3131	313	5	f	f	X
ejpam-3131	313	6	(	(	PUNCT
ejpam-3131	313	7	a\a	a\a	X
ejpam-3131	313	8	)	)	PUNCT
ejpam-3131	314	1	=	=	SYM
ejpam-3131	314	2	f	f	X
ejpam-3131	314	3	(	(	PUNCT
ejpam-3131	314	4	f−1	f−1	PROPN
ejpam-3131	314	5	(	(	PUNCT
ejpam-3131	314	6	j	j	NOUN
ejpam-3131	314	7	)	)	PUNCT
ejpam-3131	314	8	)	)	PUNCT
ejpam-3131	315	1	⊆	⊆	NUM
ejpam-3131	315	2	j	j	NOUN
ejpam-3131	315	3	.	.	PUNCT
ejpam-3131	316	1	hence	hence	ADV
ejpam-3131	316	2	f	f	PROPN
ejpam-3131	316	3	(	(	PUNCT
ejpam-3131	316	4	a)\f	a)\f	PROPN
ejpam-3131	316	5	(	(	PUNCT
ejpam-3131	316	6	a	a	NOUN
ejpam-3131	316	7	)	)	PUNCT
ejpam-3131	316	8	∈	∈	PROPN
ejpam-3131	316	9	j	j	PROPN
ejpam-3131	316	10	.	.	PUNCT
ejpam-3131	317	1	□	□	PUNCT
ejpam-3131	317	2	the	the	DET
ejpam-3131	317	3	following	follow	VERB
ejpam-3131	317	4	theorem	theorem	NOUN
ejpam-3131	317	5	is	be	AUX
ejpam-3131	317	6	a	a	DET
ejpam-3131	317	7	consequence	consequence	NOUN
ejpam-3131	317	8	of	of	ADP
ejpam-3131	317	9	theorem	theorem	ADJ
ejpam-3131	317	10	3.3	3.3	NUM
ejpam-3131	317	11	.	.	PUNCT
ejpam-3131	318	1	theorem	theorem	VERB
ejpam-3131	318	2	3.6	3.6	NUM
ejpam-3131	318	3	.	.	PUNCT
ejpam-3131	319	1	let	let	VERB
ejpam-3131	319	2	(	(	PUNCT
ejpam-3131	319	3	x	x	X
ejpam-3131	319	4	,	,	PUNCT
ejpam-3131	319	5	τ	τ	PROPN
ejpam-3131	319	6	,	,	PUNCT
ejpam-3131	319	7	i	i	PRON
ejpam-3131	319	8	)	)	PUNCT
ejpam-3131	319	9	be	be	VERB
ejpam-3131	319	10	an	an	DET
ejpam-3131	319	11	ideal	ideal	ADJ
ejpam-3131	319	12	space	space	NOUN
ejpam-3131	319	13	.	.	PUNCT
ejpam-3131	320	1	if	if	SCONJ
ejpam-3131	320	2	a	a	DET
ejpam-3131	320	3	⊆	⊆	NUM
ejpam-3131	320	4	x	x	NOUN
ejpam-3131	320	5	and	and	CCONJ
ejpam-3131	320	6	b	b	NOUN
ejpam-3131	320	7	⊆	⊆	NUM
ejpam-3131	320	8	x	x	PUNCT
ejpam-3131	320	9	then	then	ADV
ejpam-3131	320	10	:	:	PUNCT
ejpam-3131	320	11	(	(	PUNCT
ejpam-3131	320	12	1	1	X
ejpam-3131	320	13	)	)	PUNCT
ejpam-3131	320	14	if	if	SCONJ
ejpam-3131	320	15	a	a	PRON
ejpam-3131	320	16	is	be	AUX
ejpam-3131	320	17	open	open	ADJ
ejpam-3131	320	18	-	-	PUNCT
ejpam-3131	320	19	i	i	PRON
ejpam-3131	320	20	then	then	ADV
ejpam-3131	320	21	a	a	PRON
ejpam-3131	320	22	is	be	AUX
ejpam-3131	320	23	ρig	ρig	ADV
ejpam-3131	320	24	-	-	PUNCT
ejpam-3131	320	25	open	open	ADJ
ejpam-3131	320	26	.	.	PUNCT
ejpam-3131	321	1	(	(	PUNCT
ejpam-3131	321	2	2	2	X
ejpam-3131	321	3	)	)	PUNCT
ejpam-3131	321	4	if	if	SCONJ
ejpam-3131	321	5	a	a	PRON
ejpam-3131	321	6	and	and	CCONJ
ejpam-3131	321	7	b	b	NOUN
ejpam-3131	321	8	are	be	AUX
ejpam-3131	321	9	open	open	ADJ
ejpam-3131	321	10	-	-	PUNCT
ejpam-3131	321	11	i	i	PRON
ejpam-3131	321	12	then	then	ADV
ejpam-3131	321	13	a	a	DET
ejpam-3131	321	14	∪b	∪b	X
ejpam-3131	321	15	and	and	CCONJ
ejpam-3131	321	16	a	a	DET
ejpam-3131	321	17	∩b	∩b	NOUN
ejpam-3131	321	18	are	be	AUX
ejpam-3131	321	19	open	open	ADJ
ejpam-3131	321	20	-	-	PUNCT
ejpam-3131	321	21	i.	i.	NOUN
ejpam-3131	321	22	(	(	PUNCT
ejpam-3131	321	23	3	3	NUM
ejpam-3131	321	24	)	)	PUNCT
ejpam-3131	321	25	if	if	SCONJ
ejpam-3131	321	26	b\a	b\a	NOUN
ejpam-3131	321	27	∈	∈	PROPN
ejpam-3131	322	1	i	i	PRON
ejpam-3131	322	2	,	,	PUNCT
ejpam-3131	322	3	0	0	PUNCT
ejpam-3131	323	1	a\	a\	NOUN
ejpam-3131	323	2	0	0	NUM
ejpam-3131	323	3	b	b	X
ejpam-3131	323	4	∈	∈	PROPN
ejpam-3131	324	1	i	i	PRON
ejpam-3131	324	2	and	and	CCONJ
ejpam-3131	324	3	a	a	PRON
ejpam-3131	324	4	is	be	AUX
ejpam-3131	324	5	open	open	ADJ
ejpam-3131	324	6	-	-	PUNCT
ejpam-3131	324	7	i	i	PRON
ejpam-3131	324	8	then	then	ADV
ejpam-3131	324	9	b	b	NOUN
ejpam-3131	324	10	is	be	AUX
ejpam-3131	324	11	open	open	ADJ
ejpam-3131	324	12	-	-	PUNCT
ejpam-3131	324	13	i.	i.	NOUN
ejpam-3131	324	14	(	(	PUNCT
ejpam-3131	324	15	4	4	NUM
ejpam-3131	324	16	)	)	PUNCT
ejpam-3131	324	17	if	if	SCONJ
ejpam-3131	324	18	0	0	NUM
ejpam-3131	324	19	a	a	DET
ejpam-3131	324	20	⊆	⊆	NUM
ejpam-3131	324	21	b	b	SYM
ejpam-3131	324	22	⊆	⊆	NUM
ejpam-3131	324	23	a	a	PRON
ejpam-3131	324	24	and	and	CCONJ
ejpam-3131	324	25	a	a	PRON
ejpam-3131	324	26	is	be	AUX
ejpam-3131	324	27	open	open	ADJ
ejpam-3131	324	28	-	-	PUNCT
ejpam-3131	324	29	i	i	NOUN
ejpam-3131	324	30	,	,	PUNCT
ejpam-3131	324	31	then	then	ADV
ejpam-3131	324	32	b	b	NOUN
ejpam-3131	324	33	is	be	AUX
ejpam-3131	324	34	open	open	ADJ
ejpam-3131	324	35	-	-	PUNCT
ejpam-3131	324	36	i.	i.	NOUN
ejpam-3131	324	37	(	(	PUNCT
ejpam-3131	324	38	5	5	NUM
ejpam-3131	324	39	)	)	PUNCT
ejpam-3131	324	40	if	if	SCONJ
ejpam-3131	324	41	a	a	PRON
ejpam-3131	324	42	is	be	AUX
ejpam-3131	324	43	pre	pre	ADJ
ejpam-3131	324	44	-	-	ADJ
ejpam-3131	324	45	closed	closed	ADJ
ejpam-3131	324	46	and	and	CCONJ
ejpam-3131	324	47	open	open	ADJ
ejpam-3131	324	48	-	-	PUNCT
ejpam-3131	324	49	i	i	PRON
ejpam-3131	324	50	then	then	ADV
ejpam-3131	324	51	0	0	NUM
ejpam-3131	325	1	a	a	PRON
ejpam-3131	325	2	is	be	AUX
ejpam-3131	325	3	closed	closed	ADJ
ejpam-3131	325	4	-	-	PUNCT
ejpam-3131	325	5	i.	i.	NOUN
ejpam-3131	325	6	(	(	PUNCT
ejpam-3131	325	7	6	6	NUM
ejpam-3131	325	8	)	)	PUNCT
ejpam-3131	325	9	if	if	SCONJ
ejpam-3131	325	10	a	a	DET
ejpam-3131	325	11	⊆	⊆	NUM
ejpam-3131	325	12	b	b	NOUN
ejpam-3131	325	13	and	and	CCONJ
ejpam-3131	325	14	a	a	PRON
ejpam-3131	325	15	is	be	AUX
ejpam-3131	325	16	open	open	ADJ
ejpam-3131	325	17	-	-	PUNCT
ejpam-3131	325	18	i	i	PRON
ejpam-3131	325	19	in	in	ADP
ejpam-3131	325	20	(	(	PUNCT
ejpam-3131	325	21	x	x	NOUN
ejpam-3131	325	22	,	,	PUNCT
ejpam-3131	325	23	τ	τ	PROPN
ejpam-3131	325	24	,	,	PUNCT
ejpam-3131	325	25	i	i	PROPN
ejpam-3131	325	26	)	)	PUNCT
ejpam-3131	325	27	,	,	PUNCT
ejpam-3131	325	28	then	then	ADV
ejpam-3131	325	29	a	a	PRON
ejpam-3131	325	30	is	be	AUX
ejpam-3131	325	31	open	open	ADJ
ejpam-3131	325	32	-	-	PUNCT
ejpam-3131	325	33	ib	ib	NOUN
ejpam-3131	325	34	in	in	ADP
ejpam-3131	325	35	(	(	PUNCT
ejpam-3131	325	36	b	b	NOUN
ejpam-3131	325	37	,	,	PUNCT
ejpam-3131	325	38	τb	τb	ADJ
ejpam-3131	325	39	,	,	PUNCT
ejpam-3131	325	40	ib	ib	NOUN
ejpam-3131	325	41	)	)	PUNCT
ejpam-3131	325	42	.	.	PUNCT
ejpam-3131	326	1	some	some	DET
ejpam-3131	326	2	applications	application	NOUN
ejpam-3131	326	3	of	of	ADP
ejpam-3131	326	4	the	the	DET
ejpam-3131	326	5	closed	closed	ADJ
ejpam-3131	326	6	-	-	PUNCT
ejpam-3131	326	7	i	i	NOUN
ejpam-3131	326	8	and	and	CCONJ
ejpam-3131	326	9	open	open	ADJ
ejpam-3131	326	10	-	-	PUNCT
ejpam-3131	326	11	i	i	PRON
ejpam-3131	326	12	sets	set	NOUN
ejpam-3131	326	13	are	be	AUX
ejpam-3131	326	14	shown	show	VERB
ejpam-3131	326	15	now	now	ADV
ejpam-3131	326	16	.	.	PUNCT
ejpam-3131	327	1	a	a	DET
ejpam-3131	327	2	subset	subset	NOUN
ejpam-3131	327	3	a	a	PRON
ejpam-3131	327	4	of	of	ADP
ejpam-3131	327	5	an	an	DET
ejpam-3131	327	6	ideal	ideal	ADJ
ejpam-3131	327	7	space	space	NOUN
ejpam-3131	327	8	(	(	PUNCT
ejpam-3131	327	9	x	x	X
ejpam-3131	327	10	,	,	PUNCT
ejpam-3131	327	11	τ	τ	PROPN
ejpam-3131	327	12	,	,	PUNCT
ejpam-3131	327	13	i	i	PROPN
ejpam-3131	327	14	)	)	PUNCT
ejpam-3131	327	15	is	be	AUX
ejpam-3131	327	16	said	say	VERB
ejpam-3131	327	17	to	to	PART
ejpam-3131	327	18	be	be	AUX
ejpam-3131	327	19	σi	σi	NOUN
ejpam-3131	327	20	-	-	ADJ
ejpam-3131	327	21	compact	compact	ADJ
ejpam-3131	328	1	[	[	X
ejpam-3131	328	2	9	9	NUM
ejpam-3131	328	3	]	]	X
ejpam-3131	328	4	if	if	SCONJ
ejpam-3131	328	5	for	for	ADP
ejpam-3131	328	6	each	each	DET
ejpam-3131	328	7	nonempty	nonempty	ADJ
ejpam-3131	328	8	collection	collection	NOUN
ejpam-3131	328	9	{	{	PUNCT
ejpam-3131	328	10	vα}α∈λ	vα}α∈λ	X
ejpam-3131	328	11	of	of	ADP
ejpam-3131	328	12	nonempty	nonempty	X
ejpam-3131	328	13	open	open	ADJ
ejpam-3131	328	14	sets	set	NOUN
ejpam-3131	328	15	,	,	PUNCT
ejpam-3131	328	16	if	if	SCONJ
ejpam-3131	328	17	a\	a\	PUNCT
ejpam-3131	328	18	∪	∪	ADP
ejpam-3131	328	19	α∈λ	α∈λ	NOUN
ejpam-3131	328	20	vα	vα	ADP
ejpam-3131	328	21	∈	∈	PROPN
ejpam-3131	328	22	i	i	PRON
ejpam-3131	328	23	then	then	ADV
ejpam-3131	328	24	there	there	PRON
ejpam-3131	328	25	exists	exist	VERB
ejpam-3131	328	26	λ0	λ0	NOUN
ejpam-3131	328	27	⊆	⊆	NUM
ejpam-3131	328	28	λ	λ	PROPN
ejpam-3131	328	29	,	,	PUNCT
ejpam-3131	328	30	finite	finite	NOUN
ejpam-3131	328	31	,	,	PUNCT
ejpam-3131	328	32	such	such	ADJ
ejpam-3131	328	33	that	that	SCONJ
ejpam-3131	328	34	a	a	DET
ejpam-3131	328	35	⊆	⊆	NUM
ejpam-3131	328	36	∪	∪	ADJ
ejpam-3131	328	37	α∈λ0	α∈λ0	NOUN
ejpam-3131	328	38	vα	vα	PROPN
ejpam-3131	328	39	.	.	PUNCT
ejpam-3131	329	1	the	the	DET
ejpam-3131	329	2	space	space	NOUN
ejpam-3131	329	3	(	(	PUNCT
ejpam-3131	329	4	x	x	X
ejpam-3131	329	5	,	,	PUNCT
ejpam-3131	329	6	τ	τ	PROPN
ejpam-3131	329	7	,	,	PUNCT
ejpam-3131	329	8	i	i	PROPN
ejpam-3131	329	9	)	)	PUNCT
ejpam-3131	329	10	is	be	AUX
ejpam-3131	329	11	σi	σi	NOUN
ejpam-3131	329	12	-	-	ADJ
ejpam-3131	329	13	compact	compact	ADJ
ejpam-3131	329	14	if	if	SCONJ
ejpam-3131	329	15	x	x	PRON
ejpam-3131	329	16	is	be	AUX
ejpam-3131	329	17	σi	σi	NOUN
ejpam-3131	329	18	-	-	NOUN
ejpam-3131	329	19	compact	compact	ADJ
ejpam-3131	329	20	.	.	PUNCT
ejpam-3131	330	1	it	it	PRON
ejpam-3131	330	2	is	be	AUX
ejpam-3131	330	3	simple	simple	ADJ
ejpam-3131	330	4	to	to	PART
ejpam-3131	330	5	see	see	VERB
ejpam-3131	330	6	that	that	SCONJ
ejpam-3131	330	7	if	if	SCONJ
ejpam-3131	330	8	(	(	PUNCT
ejpam-3131	330	9	x	x	NOUN
ejpam-3131	330	10	,	,	PUNCT
ejpam-3131	330	11	τ	τ	PROPN
ejpam-3131	330	12	,	,	PUNCT
ejpam-3131	330	13	i	i	PROPN
ejpam-3131	330	14	)	)	PUNCT
ejpam-3131	330	15	is	be	AUX
ejpam-3131	330	16	σi	σi	NOUN
ejpam-3131	330	17	-	-	ADJ
ejpam-3131	330	18	compact	compact	ADJ
ejpam-3131	330	19	and	and	CCONJ
ejpam-3131	330	20	if	if	SCONJ
ejpam-3131	330	21	a	a	DET
ejpam-3131	330	22	⊆	⊆	NUM
ejpam-3131	330	23	x	x	NOUN
ejpam-3131	330	24	is	be	AUX
ejpam-3131	330	25	closed	close	VERB
ejpam-3131	330	26	then	then	ADV
ejpam-3131	330	27	a	a	PRON
ejpam-3131	330	28	is	be	AUX
ejpam-3131	330	29	σi	σi	NOUN
ejpam-3131	330	30	-	-	ADJ
ejpam-3131	330	31	compact	compact	ADJ
ejpam-3131	330	32	.	.	PUNCT
ejpam-3131	331	1	theorem	theorem	VERB
ejpam-3131	331	2	3.7	3.7	NUM
ejpam-3131	331	3	.	.	PUNCT
ejpam-3131	332	1	if	if	SCONJ
ejpam-3131	332	2	(	(	PUNCT
ejpam-3131	332	3	x	x	X
ejpam-3131	332	4	,	,	PUNCT
ejpam-3131	332	5	τ	τ	PROPN
ejpam-3131	332	6	,	,	PUNCT
ejpam-3131	332	7	i	i	PROPN
ejpam-3131	332	8	)	)	PUNCT
ejpam-3131	332	9	is	be	AUX
ejpam-3131	332	10	an	an	DET
ejpam-3131	332	11	ideal	ideal	ADJ
ejpam-3131	332	12	space	space	NOUN
ejpam-3131	332	13	and	and	CCONJ
ejpam-3131	332	14	a	a	DET
ejpam-3131	332	15	⊆	⊆	NUM
ejpam-3131	332	16	x	x	NOUN
ejpam-3131	332	17	is	be	AUX
ejpam-3131	332	18	closed	closed	ADJ
ejpam-3131	332	19	-	-	PUNCT
ejpam-3131	332	20	i	i	PRON
ejpam-3131	332	21	we	we	PRON
ejpam-3131	332	22	have	have	VERB
ejpam-3131	332	23	that	that	PRON
ejpam-3131	332	24	:	:	PUNCT
ejpam-3131	332	25	(	(	PUNCT
ejpam-3131	332	26	1	1	X
ejpam-3131	332	27	)	)	PUNCT
ejpam-3131	332	28	if	if	SCONJ
ejpam-3131	332	29	(	(	PUNCT
ejpam-3131	332	30	x	x	NOUN
ejpam-3131	332	31	,	,	PUNCT
ejpam-3131	332	32	τ	τ	PROPN
ejpam-3131	332	33	,	,	PUNCT
ejpam-3131	332	34	i	i	PROPN
ejpam-3131	332	35	)	)	PUNCT
ejpam-3131	332	36	is	be	AUX
ejpam-3131	332	37	ρi	ρi	NOUN
ejpam-3131	332	38	-	-	ADJ
ejpam-3131	332	39	compact	compact	ADJ
ejpam-3131	332	40	then	then	ADV
ejpam-3131	332	41	a	a	PRON
ejpam-3131	332	42	is	be	AUX
ejpam-3131	332	43	ρi	ρi	NOUN
ejpam-3131	332	44	-	-	ADJ
ejpam-3131	332	45	compact	compact	ADJ
ejpam-3131	332	46	.	.	PUNCT
ejpam-3131	333	1	(	(	PUNCT
ejpam-3131	333	2	2	2	X
ejpam-3131	333	3	)	)	PUNCT
ejpam-3131	333	4	if	if	SCONJ
ejpam-3131	333	5	(	(	PUNCT
ejpam-3131	333	6	x	x	NOUN
ejpam-3131	333	7	,	,	PUNCT
ejpam-3131	333	8	τ	τ	PROPN
ejpam-3131	333	9	,	,	PUNCT
ejpam-3131	333	10	i	i	PROPN
ejpam-3131	333	11	)	)	PUNCT
ejpam-3131	333	12	is	be	AUX
ejpam-3131	333	13	σi	σi	NOUN
ejpam-3131	333	14	-	-	ADJ
ejpam-3131	333	15	compact	compact	ADJ
ejpam-3131	333	16	then	then	ADV
ejpam-3131	333	17	a	a	PRON
ejpam-3131	333	18	is	be	AUX
ejpam-3131	333	19	σi	σi	NOUN
ejpam-3131	333	20	-	-	ADJ
ejpam-3131	333	21	compact	compact	ADJ
ejpam-3131	333	22	.	.	PUNCT
ejpam-3131	334	1	proof	proof	NOUN
ejpam-3131	334	2	.	.	PUNCT
ejpam-3131	335	1	(	(	PUNCT
ejpam-3131	335	2	1	1	X
ejpam-3131	335	3	)	)	PUNCT
ejpam-3131	335	4	it	it	PRON
ejpam-3131	335	5	is	be	AUX
ejpam-3131	335	6	a	a	DET
ejpam-3131	335	7	consequence	consequence	NOUN
ejpam-3131	335	8	of	of	ADP
ejpam-3131	335	9	theorem	theorem	ADJ
ejpam-3131	335	10	2.3	2.3	NUM
ejpam-3131	335	11	,	,	PUNCT
ejpam-3131	335	12	because	because	SCONJ
ejpam-3131	335	13	closed	close	VERB
ejpam-3131	335	14	-	-	PUNCT
ejpam-3131	335	15	i	i	PRON
ejpam-3131	335	16	→	→	SYM
ejpam-3131	335	17	ρig	ρig	ADV
ejpam-3131	335	18	-	-	PUNCT
ejpam-3131	335	19	closed	closed	ADJ
ejpam-3131	335	20	.	.	PUNCT
ejpam-3131	336	1	n.r	n.r	PROPN
ejpam-3131	336	2	.	.	PROPN
ejpam-3131	336	3	pachón	pachón	PROPN
ejpam-3131	336	4	/	/	SYM
ejpam-3131	336	5	eur	eur	PROPN
ejpam-3131	336	6	.	.	PUNCT
ejpam-3131	337	1	j.	j.	PROPN
ejpam-3131	337	2	pure	pure	PROPN
ejpam-3131	337	3	appl	appl	PROPN
ejpam-3131	337	4	.	.	PROPN
ejpam-3131	337	5	math	math	PROPN
ejpam-3131	337	6	,	,	PUNCT
ejpam-3131	337	7	11	11	NUM
ejpam-3131	337	8	(	(	PUNCT
ejpam-3131	337	9	1	1	NUM
ejpam-3131	337	10	)	)	PUNCT
ejpam-3131	337	11	(	(	PUNCT
ejpam-3131	337	12	2018	2018	NUM
ejpam-3131	337	13	)	)	PUNCT
ejpam-3131	337	14	,	,	PUNCT
ejpam-3131	337	15	299	299	NUM
ejpam-3131	337	16	-	-	SYM
ejpam-3131	337	17	314	314	NUM
ejpam-3131	337	18	310	310	NUM
ejpam-3131	337	19	(	(	PUNCT
ejpam-3131	337	20	2	2	NUM
ejpam-3131	337	21	)	)	PUNCT
ejpam-3131	337	22	let	let	AUX
ejpam-3131	337	23	{	{	PUNCT
ejpam-3131	337	24	vα}α∈λ	vα}α∈λ	ADV
ejpam-3131	337	25	be	be	AUX
ejpam-3131	337	26	a	a	DET
ejpam-3131	337	27	nonempty	nonempty	ADJ
ejpam-3131	337	28	collection	collection	NOUN
ejpam-3131	337	29	of	of	ADP
ejpam-3131	337	30	nonempty	nonempty	X
ejpam-3131	337	31	open	open	ADJ
ejpam-3131	337	32	sets	set	NOUN
ejpam-3131	337	33	with	with	ADP
ejpam-3131	337	34	a\	a\	NOUN
ejpam-3131	337	35	∪	∪	ADJ
ejpam-3131	337	36	α∈λ	α∈λ	NOUN
ejpam-3131	337	37	vα	vα	ADP
ejpam-3131	337	38	∈	∈	PROPN
ejpam-3131	337	39	i.	i.	NOUN
ejpam-3131	337	40	since	since	SCONJ
ejpam-3131	337	41	a\a	a\a	PROPN
ejpam-3131	337	42	∈	∈	PROPN
ejpam-3131	337	43	i	i	PRON
ejpam-3131	337	44	and	and	CCONJ
ejpam-3131	337	45	a\	a\	ADV
ejpam-3131	337	46	∪	∪	ADJ
ejpam-3131	337	47	α∈λ	α∈λ	NOUN
ejpam-3131	337	48	vα	vα	ADP
ejpam-3131	337	49	⊆	⊆	NUM
ejpam-3131	338	1	(	(	PUNCT
ejpam-3131	338	2	a\	a\	NOUN
ejpam-3131	338	3	∪	∪	VERB
ejpam-3131	338	4	α∈λ	α∈λ	NOUN
ejpam-3131	338	5	vα	vα	NOUN
ejpam-3131	338	6	)	)	PUNCT
ejpam-3131	338	7	∪	∪	NOUN
ejpam-3131	338	8	(	(	PUNCT
ejpam-3131	338	9	a\a	a\a	X
ejpam-3131	338	10	)	)	PUNCT
ejpam-3131	338	11	∈	∈	PROPN
ejpam-3131	339	1	i	i	PRON
ejpam-3131	339	2	then	then	ADV
ejpam-3131	339	3	a\	a\	PUNCT
ejpam-3131	339	4	∪	∪	ADJ
ejpam-3131	339	5	α∈λ	α∈λ	NOUN
ejpam-3131	339	6	vα	vα	ADP
ejpam-3131	339	7	∈	∈	PROPN
ejpam-3131	339	8	i.	i.	NOUN
ejpam-3131	340	1	but	but	CCONJ
ejpam-3131	340	2	a	a	PRON
ejpam-3131	340	3	is	be	AUX
ejpam-3131	340	4	σi	σi	NOUN
ejpam-3131	340	5	-	-	ADJ
ejpam-3131	340	6	compact	compact	ADJ
ejpam-3131	341	1	and	and	CCONJ
ejpam-3131	341	2	so	so	ADV
ejpam-3131	341	3	there	there	PRON
ejpam-3131	341	4	exists	exist	VERB
ejpam-3131	341	5	λ0	λ0	NOUN
ejpam-3131	341	6	⊆	⊆	NUM
ejpam-3131	341	7	λ	λ	PROPN
ejpam-3131	341	8	,	,	PUNCT
ejpam-3131	341	9	finite	finite	NOUN
ejpam-3131	341	10	,	,	PUNCT
ejpam-3131	341	11	such	such	ADJ
ejpam-3131	341	12	that	that	SCONJ
ejpam-3131	341	13	a	a	DET
ejpam-3131	341	14	⊆	⊆	NUM
ejpam-3131	341	15	a	a	DET
ejpam-3131	341	16	⊆	⊆	NUM
ejpam-3131	341	17	∪	∪	ADJ
ejpam-3131	341	18	α∈λ0	α∈λ0	NOUN
ejpam-3131	341	19	vα	vα	NOUN
ejpam-3131	341	20	.	.	PUNCT
ejpam-3131	342	1	□	□	PUNCT
ejpam-3131	342	2	theorem	theorem	VERB
ejpam-3131	342	3	3.8	3.8	NUM
ejpam-3131	342	4	.	.	PUNCT
ejpam-3131	343	1	the	the	DET
ejpam-3131	343	2	ideal	ideal	ADJ
ejpam-3131	343	3	space	space	NOUN
ejpam-3131	343	4	(	(	PUNCT
ejpam-3131	343	5	x	x	X
ejpam-3131	343	6	,	,	PUNCT
ejpam-3131	343	7	τ	τ	PROPN
ejpam-3131	343	8	,	,	PUNCT
ejpam-3131	343	9	i	i	PROPN
ejpam-3131	343	10	)	)	PUNCT
ejpam-3131	343	11	is	be	AUX
ejpam-3131	343	12	i	i	NOUN
ejpam-3131	343	13	-	-	PUNCT
ejpam-3131	343	14	normal	normal	ADJ
ejpam-3131	343	15	if	if	SCONJ
ejpam-3131	343	16	and	and	CCONJ
ejpam-3131	343	17	only	only	ADV
ejpam-3131	343	18	if	if	SCONJ
ejpam-3131	343	19	,	,	PUNCT
ejpam-3131	343	20	for	for	ADP
ejpam-3131	343	21	each	each	DET
ejpam-3131	343	22	pair	pair	NOUN
ejpam-3131	343	23	of	of	ADP
ejpam-3131	343	24	disjoint	disjoint	NOUN
ejpam-3131	343	25	closed	close	VERB
ejpam-3131	343	26	sets	set	NOUN
ejpam-3131	343	27	f	f	PROPN
ejpam-3131	343	28	and	and	CCONJ
ejpam-3131	343	29	g	g	NOUN
ejpam-3131	343	30	,	,	PUNCT
ejpam-3131	343	31	there	there	PRON
ejpam-3131	343	32	are	be	VERB
ejpam-3131	343	33	disjoint	disjoint	ADJ
ejpam-3131	343	34	open	open	ADJ
ejpam-3131	343	35	-	-	PUNCT
ejpam-3131	343	36	i	i	PRON
ejpam-3131	343	37	sets	set	VERB
ejpam-3131	343	38	a	a	DET
ejpam-3131	343	39	and	and	CCONJ
ejpam-3131	343	40	b	b	NOUN
ejpam-3131	343	41	such	such	ADJ
ejpam-3131	343	42	that	that	SCONJ
ejpam-3131	343	43	f\a	f\a	PROPN
ejpam-3131	343	44	∈	∈	PROPN
ejpam-3131	343	45	i	i	PRON
ejpam-3131	343	46	and	and	CCONJ
ejpam-3131	343	47	g\b	g\b	ADP
ejpam-3131	343	48	∈	∈	PROPN
ejpam-3131	343	49	i.	i.	NOUN
ejpam-3131	343	50	proof	proof	NOUN
ejpam-3131	343	51	.	.	PUNCT
ejpam-3131	344	1	(	(	PUNCT
ejpam-3131	344	2	→	→	NOUN
ejpam-3131	344	3	)	)	PUNCT
ejpam-3131	344	4	it	it	PRON
ejpam-3131	344	5	is	be	AUX
ejpam-3131	344	6	clear	clear	ADJ
ejpam-3131	344	7	because	because	SCONJ
ejpam-3131	344	8	open→open	open→open	ADJ
ejpam-3131	344	9	-	-	PUNCT
ejpam-3131	344	10	i.	i.	NOUN
ejpam-3131	344	11	(	(	PUNCT
ejpam-3131	344	12	←	←	PROPN
ejpam-3131	344	13	)	)	PUNCT
ejpam-3131	344	14	it	it	PRON
ejpam-3131	344	15	is	be	AUX
ejpam-3131	344	16	a	a	DET
ejpam-3131	344	17	consequence	consequence	NOUN
ejpam-3131	344	18	of	of	ADP
ejpam-3131	344	19	theorem	theorem	NOUN
ejpam-3131	344	20	2.15	2.15	NUM
ejpam-3131	344	21	since	since	SCONJ
ejpam-3131	344	22	open	open	ADJ
ejpam-3131	344	23	-	-	PUNCT
ejpam-3131	344	24	i	i	PRON
ejpam-3131	344	25	→	→	SYM
ejpam-3131	344	26	ρig	ρig	ADV
ejpam-3131	344	27	-	-	PUNCT
ejpam-3131	344	28	open	open	ADJ
ejpam-3131	344	29	.	.	PUNCT
ejpam-3131	345	1	□	□	PUNCT
ejpam-3131	345	2	remark	remark	NOUN
ejpam-3131	345	3	3.9	3.9	NUM
ejpam-3131	345	4	.	.	PUNCT
ejpam-3131	346	1	if	if	SCONJ
ejpam-3131	346	2	(	(	PUNCT
ejpam-3131	346	3	x	x	X
ejpam-3131	346	4	,	,	PUNCT
ejpam-3131	346	5	τ	τ	PROPN
ejpam-3131	346	6	,	,	PUNCT
ejpam-3131	346	7	i	i	PROPN
ejpam-3131	346	8	)	)	PUNCT
ejpam-3131	346	9	is	be	AUX
ejpam-3131	346	10	an	an	DET
ejpam-3131	346	11	ideal	ideal	ADJ
ejpam-3131	346	12	space	space	NOUN
ejpam-3131	346	13	and	and	CCONJ
ejpam-3131	346	14	a	a	DET
ejpam-3131	346	15	⊆	⊆	NUM
ejpam-3131	346	16	x	x	SYM
ejpam-3131	346	17	,	,	PUNCT
ejpam-3131	346	18	then	then	ADV
ejpam-3131	346	19	:	:	PUNCT
ejpam-3131	346	20	(	(	PUNCT
ejpam-3131	346	21	1	1	X
ejpam-3131	346	22	)	)	PUNCT
ejpam-3131	346	23	τ	τ	PROPN
ejpam-3131	346	24	⊕	⊕	PROPN
ejpam-3131	346	25	i	i	PRON
ejpam-3131	346	26	is	be	AUX
ejpam-3131	346	27	the	the	DET
ejpam-3131	346	28	topology	topology	NOUN
ejpam-3131	346	29	generated	generate	VERB
ejpam-3131	346	30	for	for	ADP
ejpam-3131	346	31	the	the	DET
ejpam-3131	346	32	base	base	NOUN
ejpam-3131	346	33	τ	τ	PROPN
ejpam-3131	346	34	∪	∪	ADP
ejpam-3131	346	35	i.	i.	PROPN
ejpam-3131	346	36	it	it	PRON
ejpam-3131	346	37	is	be	AUX
ejpam-3131	346	38	noted	note	VERB
ejpam-3131	346	39	that	that	SCONJ
ejpam-3131	346	40	τ	τ	PROPN
ejpam-3131	346	41	⊕	⊕	PROPN
ejpam-3131	346	42	i	i	PRON
ejpam-3131	346	43	=	=	PUNCT
ejpam-3131	346	44	{	{	PUNCT
ejpam-3131	346	45	v	v	ADP
ejpam-3131	346	46	∪	∪	ADV
ejpam-3131	346	47	∪	∪	X
ejpam-3131	346	48	c	c	NOUN
ejpam-3131	346	49	:	:	PUNCT
ejpam-3131	346	50	v	v	NUM
ejpam-3131	346	51	∈	∈	X
ejpam-3131	346	52	τ	τ	X
ejpam-3131	346	53	and	and	CCONJ
ejpam-3131	346	54	c	c	PROPN
ejpam-3131	346	55	⊆	⊆	NUM
ejpam-3131	346	56	p(i	p(i	PROPN
ejpam-3131	346	57	)	)	PUNCT
ejpam-3131	346	58	}	}	PUNCT
ejpam-3131	346	59	.	.	PUNCT
ejpam-3131	347	1	(	(	PUNCT
ejpam-3131	347	2	2	2	X
ejpam-3131	347	3	)	)	PUNCT
ejpam-3131	347	4	i(a	i(a	PROPN
ejpam-3131	347	5	)	)	PUNCT
ejpam-3131	347	6	is	be	AUX
ejpam-3131	347	7	the	the	DET
ejpam-3131	347	8	set	set	NOUN
ejpam-3131	347	9	∪	∪	ADP
ejpam-3131	347	10	i∈i	i∈i	ADJ
ejpam-3131	347	11	,	,	PUNCT
ejpam-3131	347	12	i⊆a	i⊆a	PROPN
ejpam-3131	347	13	i.	i.	NOUN
ejpam-3131	347	14	in	in	ADP
ejpam-3131	347	15	the	the	DET
ejpam-3131	347	16	next	next	ADJ
ejpam-3131	347	17	theorem	theorem	NOUN
ejpam-3131	347	18	3.10	3.10	NUM
ejpam-3131	347	19	we	we	PRON
ejpam-3131	347	20	show	show	VERB
ejpam-3131	347	21	that	that	SCONJ
ejpam-3131	347	22	τ	τ	PROPN
ejpam-3131	347	23	⊕	⊕	PROPN
ejpam-3131	347	24	i	i	PRON
ejpam-3131	347	25	is	be	AUX
ejpam-3131	347	26	the	the	DET
ejpam-3131	347	27	smallest	small	ADJ
ejpam-3131	347	28	topology	topology	NOUN
ejpam-3131	347	29	in	in	ADP
ejpam-3131	347	30	x	x	NOUN
ejpam-3131	347	31	,	,	PUNCT
ejpam-3131	347	32	that	that	PRON
ejpam-3131	347	33	contains	contain	VERB
ejpam-3131	347	34	τ	τ	PROPN
ejpam-3131	347	35	,	,	PUNCT
ejpam-3131	347	36	such	such	ADJ
ejpam-3131	347	37	that	that	SCONJ
ejpam-3131	347	38	all	all	DET
ejpam-3131	347	39	open	open	ADJ
ejpam-3131	347	40	-	-	PUNCT
ejpam-3131	347	41	i	i	PRON
ejpam-3131	347	42	set	set	VERB
ejpam-3131	347	43	is	be	AUX
ejpam-3131	347	44	an	an	DET
ejpam-3131	347	45	open	open	ADJ
ejpam-3131	347	46	set	set	NOUN
ejpam-3131	347	47	.	.	PUNCT
ejpam-3131	348	1	theorem	theorem	VERB
ejpam-3131	348	2	3.10	3.10	NUM
ejpam-3131	348	3	.	.	PUNCT
ejpam-3131	349	1	if	if	SCONJ
ejpam-3131	349	2	(	(	PUNCT
ejpam-3131	349	3	x	x	X
ejpam-3131	349	4	,	,	PUNCT
ejpam-3131	349	5	τ	τ	PROPN
ejpam-3131	349	6	,	,	PUNCT
ejpam-3131	349	7	i	i	PROPN
ejpam-3131	349	8	)	)	PUNCT
ejpam-3131	349	9	is	be	AUX
ejpam-3131	349	10	an	an	DET
ejpam-3131	349	11	ideal	ideal	ADJ
ejpam-3131	349	12	space	space	NOUN
ejpam-3131	349	13	we	we	PRON
ejpam-3131	349	14	have	have	VERB
ejpam-3131	349	15	that	that	PRON
ejpam-3131	349	16	:	:	PUNCT
ejpam-3131	349	17	(	(	PUNCT
ejpam-3131	349	18	1	1	X
ejpam-3131	349	19	)	)	PUNCT
ejpam-3131	350	1	if	if	SCONJ
ejpam-3131	350	2	a	a	DET
ejpam-3131	350	3	⊆	⊆	NUM
ejpam-3131	350	4	x	x	SYM
ejpam-3131	350	5	then	then	ADV
ejpam-3131	350	6	intτ⊕i	intτ⊕i	PROPN
ejpam-3131	350	7	(	(	PUNCT
ejpam-3131	350	8	a	a	X
ejpam-3131	350	9	)	)	PUNCT
ejpam-3131	350	10	=	=	VERB
ejpam-3131	350	11	intτ	intτ	ADJ
ejpam-3131	350	12	(	(	PUNCT
ejpam-3131	350	13	a	a	X
ejpam-3131	350	14	)	)	PUNCT
ejpam-3131	350	15	∪	∪	PROPN
ejpam-3131	350	16	i(a	i(a	PROPN
ejpam-3131	350	17	)	)	PUNCT
ejpam-3131	350	18	.	.	PUNCT
ejpam-3131	351	1	(	(	PUNCT
ejpam-3131	351	2	2	2	X
ejpam-3131	351	3	)	)	PUNCT
ejpam-3131	351	4	a	a	DET
ejpam-3131	351	5	set	set	NOUN
ejpam-3131	351	6	f	f	NOUN
ejpam-3131	351	7	⊆	⊆	NUM
ejpam-3131	351	8	x	x	PUNCT
ejpam-3131	351	9	is	be	AUX
ejpam-3131	351	10	closed	close	VERB
ejpam-3131	351	11	in	in	ADP
ejpam-3131	351	12	the	the	DET
ejpam-3131	351	13	space	space	NOUN
ejpam-3131	351	14	(	(	PUNCT
ejpam-3131	351	15	x	x	X
ejpam-3131	351	16	,	,	PUNCT
ejpam-3131	351	17	τ	τ	PROPN
ejpam-3131	351	18	⊕	⊕	PROPN
ejpam-3131	351	19	i	i	NOUN
ejpam-3131	351	20	)	)	PUNCT
ejpam-3131	351	21	if	if	SCONJ
ejpam-3131	351	22	and	and	CCONJ
ejpam-3131	351	23	only	only	ADV
ejpam-3131	351	24	if	if	SCONJ
ejpam-3131	351	25	there	there	PRON
ejpam-3131	351	26	exists	exist	VERB
ejpam-3131	351	27	g	g	PROPN
ejpam-3131	351	28	⊆	⊆	NUM
ejpam-3131	351	29	x	x	NOUN
ejpam-3131	351	30	,	,	PUNCT
ejpam-3131	351	31	closed	close	VERB
ejpam-3131	351	32	in	in	ADP
ejpam-3131	351	33	(	(	PUNCT
ejpam-3131	351	34	x	x	NOUN
ejpam-3131	351	35	,	,	PUNCT
ejpam-3131	351	36	τ	τ	PROPN
ejpam-3131	351	37	)	)	PUNCT
ejpam-3131	351	38	,	,	PUNCT
ejpam-3131	351	39	and	and	CCONJ
ejpam-3131	351	40	a	a	DET
ejpam-3131	351	41	collection	collection	NOUN
ejpam-3131	351	42	c	c	PROPN
ejpam-3131	351	43	⊆	⊆	NUM
ejpam-3131	351	44	p(i	p(i	PROPN
ejpam-3131	351	45	)	)	PUNCT
ejpam-3131	351	46	,	,	PUNCT
ejpam-3131	351	47	such	such	ADJ
ejpam-3131	351	48	that	that	SCONJ
ejpam-3131	351	49	f	f	NOUN
ejpam-3131	352	1	=	=	PUNCT
ejpam-3131	352	2	g\	g\	PRON
ejpam-3131	352	3	∪	∪	ADJ
ejpam-3131	352	4	c.	c.	NOUN
ejpam-3131	352	5	(	(	PUNCT
ejpam-3131	352	6	3	3	NUM
ejpam-3131	352	7	)	)	PUNCT
ejpam-3131	352	8	if	if	SCONJ
ejpam-3131	352	9	a	a	DET
ejpam-3131	352	10	⊆	⊆	NUM
ejpam-3131	352	11	x	x	SYM
ejpam-3131	352	12	then	then	ADV
ejpam-3131	352	13	adhτ⊕i	adhτ⊕i	PROPN
ejpam-3131	352	14	(	(	PUNCT
ejpam-3131	352	15	a	a	X
ejpam-3131	352	16	)	)	PUNCT
ejpam-3131	352	17	=	=	SYM
ejpam-3131	352	18	adhτ	adhτ	NOUN
ejpam-3131	352	19	(	(	PUNCT
ejpam-3131	352	20	a	a	NOUN
ejpam-3131	352	21	)	)	PUNCT
ejpam-3131	352	22	\i(x\a	\i(x\a	PROPN
ejpam-3131	352	23	)	)	PUNCT
ejpam-3131	352	24	.	.	PUNCT
ejpam-3131	353	1	(	(	PUNCT
ejpam-3131	353	2	4	4	X
ejpam-3131	353	3	)	)	PUNCT
ejpam-3131	353	4	τ	τ	PROPN
ejpam-3131	353	5	⊕	⊕	PROPN
ejpam-3131	353	6	i	i	PRON
ejpam-3131	353	7	is	be	AUX
ejpam-3131	353	8	the	the	DET
ejpam-3131	353	9	smallest	small	ADJ
ejpam-3131	353	10	topology	topology	NOUN
ejpam-3131	353	11	β	β	NOUN
ejpam-3131	353	12	in	in	ADP
ejpam-3131	353	13	x	x	PROPN
ejpam-3131	353	14	such	such	ADJ
ejpam-3131	353	15	that	that	SCONJ
ejpam-3131	353	16	:	:	PUNCT
ejpam-3131	353	17	(	(	PUNCT
ejpam-3131	353	18	a	a	X
ejpam-3131	353	19	)	)	PUNCT
ejpam-3131	353	20	τ	τ	PROPN
ejpam-3131	353	21	⊆	⊆	NUM
ejpam-3131	353	22	β	β	X
ejpam-3131	353	23	and	and	CCONJ
ejpam-3131	353	24	(	(	PUNCT
ejpam-3131	353	25	b	b	NOUN
ejpam-3131	353	26	)	)	PUNCT
ejpam-3131	353	27	in	in	ADP
ejpam-3131	353	28	the	the	DET
ejpam-3131	353	29	space	space	NOUN
ejpam-3131	353	30	(	(	PUNCT
ejpam-3131	353	31	x	x	X
ejpam-3131	353	32	,	,	PUNCT
ejpam-3131	353	33	β	β	X
ejpam-3131	353	34	,	,	PUNCT
ejpam-3131	353	35	i	i	PROPN
ejpam-3131	353	36	)	)	PUNCT
ejpam-3131	353	37	,	,	PUNCT
ejpam-3131	353	38	for	for	ADP
ejpam-3131	353	39	each	each	DET
ejpam-3131	353	40	a	a	DET
ejpam-3131	353	41	⊆	⊆	NUM
ejpam-3131	353	42	x	x	SYM
ejpam-3131	353	43	,	,	PUNCT
ejpam-3131	353	44	a	a	PRON
ejpam-3131	353	45	is	be	AUX
ejpam-3131	353	46	open	open	ADJ
ejpam-3131	353	47	-	-	PUNCT
ejpam-3131	353	48	i	i	PRON
ejpam-3131	353	49	if	if	SCONJ
ejpam-3131	354	1	and	and	CCONJ
ejpam-3131	354	2	only	only	ADV
ejpam-3131	354	3	if	if	SCONJ
ejpam-3131	354	4	a	a	PRON
ejpam-3131	354	5	is	be	AUX
ejpam-3131	354	6	open	open	ADJ
ejpam-3131	354	7	.	.	PUNCT
ejpam-3131	355	1	proof	proof	NOUN
ejpam-3131	355	2	.	.	PUNCT
ejpam-3131	356	1	(	(	PUNCT
ejpam-3131	356	2	1	1	X
ejpam-3131	356	3	)	)	PUNCT
ejpam-3131	356	4	it	it	PRON
ejpam-3131	356	5	is	be	AUX
ejpam-3131	356	6	clear	clear	ADJ
ejpam-3131	357	1	that	that	SCONJ
ejpam-3131	357	2	intτ	intτ	ADV
ejpam-3131	357	3	(	(	PUNCT
ejpam-3131	357	4	a)∪i(a	a)∪i(a	ADJ
ejpam-3131	357	5	)	)	PUNCT
ejpam-3131	357	6	∈	∈	PROPN
ejpam-3131	357	7	τ	τ	X
ejpam-3131	357	8	⊕i	⊕i	NOUN
ejpam-3131	357	9	and	and	CCONJ
ejpam-3131	357	10	that	that	ADV
ejpam-3131	357	11	intτ	intτ	ADV
ejpam-3131	357	12	(	(	PUNCT
ejpam-3131	357	13	a)∪i(a	a)∪i(a	ADJ
ejpam-3131	357	14	)	)	PUNCT
ejpam-3131	357	15	⊆	⊆	NUM
ejpam-3131	357	16	a	a	PRON
ejpam-3131	357	17	,	,	PUNCT
ejpam-3131	357	18	and	and	CCONJ
ejpam-3131	357	19	so	so	ADV
ejpam-3131	357	20	intτ	intτ	ADV
ejpam-3131	357	21	(	(	PUNCT
ejpam-3131	357	22	a)∪	a)∪	ADV
ejpam-3131	357	23	i(a	i(a	PROPN
ejpam-3131	357	24	)	)	PUNCT
ejpam-3131	358	1	⊆	⊆	NUM
ejpam-3131	358	2	intτ⊕i	intτ⊕i	PROPN
ejpam-3131	358	3	(	(	PUNCT
ejpam-3131	358	4	a	a	NOUN
ejpam-3131	358	5	)	)	PUNCT
ejpam-3131	358	6	.	.	PUNCT
ejpam-3131	359	1	now	now	ADV
ejpam-3131	359	2	,	,	PUNCT
ejpam-3131	359	3	suppose	suppose	VERB
ejpam-3131	359	4	that	that	SCONJ
ejpam-3131	359	5	w	w	PROPN
ejpam-3131	359	6	∈	∈	PROPN
ejpam-3131	359	7	τ	τ	PROPN
ejpam-3131	359	8	⊕	⊕	NUM
ejpam-3131	359	9	i	i	PRON
ejpam-3131	359	10	and	and	CCONJ
ejpam-3131	359	11	that	that	SCONJ
ejpam-3131	359	12	w	w	ADP
ejpam-3131	359	13	⊆	⊆	NUM
ejpam-3131	359	14	a.	a.	NOUN
ejpam-3131	359	15	there	there	PRON
ejpam-3131	359	16	exist	exist	VERB
ejpam-3131	359	17	v	v	ADP
ejpam-3131	359	18	∈	∈	PROPN
ejpam-3131	359	19	τ	τ	X
ejpam-3131	359	20	and	and	CCONJ
ejpam-3131	359	21	a	a	DET
ejpam-3131	359	22	collection	collection	NOUN
ejpam-3131	359	23	{	{	PUNCT
ejpam-3131	359	24	iα}α∈λ	iα}α∈λ	NOUN
ejpam-3131	359	25	of	of	ADP
ejpam-3131	359	26	elements	element	NOUN
ejpam-3131	359	27	in	in	ADP
ejpam-3131	359	28	i	i	PRON
ejpam-3131	359	29	,	,	PUNCT
ejpam-3131	359	30	such	such	ADJ
ejpam-3131	359	31	that	that	SCONJ
ejpam-3131	359	32	w	w	NOUN
ejpam-3131	359	33	=	=	PUNCT
ejpam-3131	359	34	v	v	NOUN
ejpam-3131	359	35	∪	∪	ADV
ejpam-3131	359	36	∪	∪	ADJ
ejpam-3131	359	37	α∈λ	α∈λ	NOUN
ejpam-3131	359	38	iα	iα	PROPN
ejpam-3131	359	39	.	.	PUNCT
ejpam-3131	360	1	since	since	SCONJ
ejpam-3131	360	2	v	v	NUM
ejpam-3131	360	3	⊆	⊆	NUM
ejpam-3131	360	4	a	a	DET
ejpam-3131	360	5	then	then	ADV
ejpam-3131	360	6	v	v	ADP
ejpam-3131	360	7	⊆	⊆	NUM
ejpam-3131	360	8	intτ	intτ	ADV
ejpam-3131	360	9	(	(	PUNCT
ejpam-3131	360	10	a	a	NOUN
ejpam-3131	360	11	)	)	PUNCT
ejpam-3131	360	12	.	.	PUNCT
ejpam-3131	361	1	given	give	VERB
ejpam-3131	361	2	that	that	PRON
ejpam-3131	361	3	,	,	PUNCT
ejpam-3131	361	4	for	for	ADP
ejpam-3131	361	5	all	all	PRON
ejpam-3131	361	6	α	α	PRON
ejpam-3131	361	7	∈	∈	PROPN
ejpam-3131	361	8	λ	λ	NOUN
ejpam-3131	361	9	,	,	PUNCT
ejpam-3131	361	10	iα	iα	VERB
ejpam-3131	361	11	⊆	⊆	NUM
ejpam-3131	361	12	a	a	DET
ejpam-3131	361	13	then	then	ADV
ejpam-3131	361	14	∪	∪	ADJ
ejpam-3131	361	15	α∈λ	α∈λ	NOUN
ejpam-3131	361	16	iα	iα	NOUN
ejpam-3131	361	17	⊆	⊆	NUM
ejpam-3131	361	18	i(a	i(a	NOUN
ejpam-3131	361	19	)	)	PUNCT
ejpam-3131	361	20	,	,	PUNCT
ejpam-3131	361	21	and	and	CCONJ
ejpam-3131	361	22	so	so	ADV
ejpam-3131	361	23	w	w	ADP
ejpam-3131	361	24	⊆	⊆	NUM
ejpam-3131	361	25	intτ	intτ	ADJ
ejpam-3131	361	26	(	(	PUNCT
ejpam-3131	361	27	a	a	X
ejpam-3131	361	28	)	)	PUNCT
ejpam-3131	361	29	∪	∪	PROPN
ejpam-3131	361	30	i(a	i(a	PROPN
ejpam-3131	361	31	)	)	PUNCT
ejpam-3131	361	32	.	.	PUNCT
ejpam-3131	362	1	in	in	ADP
ejpam-3131	362	2	particular	particular	ADJ
ejpam-3131	362	3	intτ⊕i	intτ⊕i	PROPN
ejpam-3131	362	4	(	(	PUNCT
ejpam-3131	362	5	a	a	X
ejpam-3131	362	6	)	)	PUNCT
ejpam-3131	362	7	⊆	⊆	NUM
ejpam-3131	362	8	intτ	intτ	ADV
ejpam-3131	362	9	(	(	PUNCT
ejpam-3131	362	10	a	a	X
ejpam-3131	362	11	)	)	PUNCT
ejpam-3131	362	12	∪	∪	PROPN
ejpam-3131	362	13	i(a	i(a	PROPN
ejpam-3131	362	14	)	)	PUNCT
ejpam-3131	362	15	.	.	PUNCT
ejpam-3131	363	1	n.r	n.r	PROPN
ejpam-3131	363	2	.	.	PROPN
ejpam-3131	363	3	pachón	pachón	PROPN
ejpam-3131	363	4	/	/	SYM
ejpam-3131	363	5	eur	eur	PROPN
ejpam-3131	363	6	.	.	PUNCT
ejpam-3131	364	1	j.	j.	PROPN
ejpam-3131	364	2	pure	pure	PROPN
ejpam-3131	364	3	appl	appl	PROPN
ejpam-3131	364	4	.	.	PROPN
ejpam-3131	364	5	math	math	PROPN
ejpam-3131	364	6	,	,	PUNCT
ejpam-3131	364	7	11	11	NUM
ejpam-3131	364	8	(	(	PUNCT
ejpam-3131	364	9	1	1	NUM
ejpam-3131	364	10	)	)	PUNCT
ejpam-3131	364	11	(	(	PUNCT
ejpam-3131	364	12	2018	2018	NUM
ejpam-3131	364	13	)	)	PUNCT
ejpam-3131	364	14	,	,	PUNCT
ejpam-3131	364	15	299	299	NUM
ejpam-3131	364	16	-	-	SYM
ejpam-3131	364	17	314	314	NUM
ejpam-3131	364	18	311	311	NUM
ejpam-3131	364	19	(	(	PUNCT
ejpam-3131	364	20	2	2	NUM
ejpam-3131	364	21	)	)	PUNCT
ejpam-3131	364	22	it	it	PRON
ejpam-3131	364	23	is	be	AUX
ejpam-3131	364	24	obvious	obvious	ADJ
ejpam-3131	364	25	.	.	PUNCT
ejpam-3131	365	1	(	(	PUNCT
ejpam-3131	365	2	3	3	X
ejpam-3131	365	3	)	)	PUNCT
ejpam-3131	365	4	given	give	VERB
ejpam-3131	365	5	that	that	SCONJ
ejpam-3131	365	6	a	a	DET
ejpam-3131	365	7	⊆	⊆	NUM
ejpam-3131	365	8	adhτ	adhτ	NOUN
ejpam-3131	365	9	(	(	PUNCT
ejpam-3131	365	10	a	a	NOUN
ejpam-3131	365	11	)	)	PUNCT
ejpam-3131	365	12	\i(x\a	\i(x\a	PROPN
ejpam-3131	365	13	)	)	PUNCT
ejpam-3131	365	14	and	and	CCONJ
ejpam-3131	365	15	adhτ	adhτ	NOUN
ejpam-3131	365	16	(	(	PUNCT
ejpam-3131	365	17	a	a	X
ejpam-3131	365	18	)	)	PUNCT
ejpam-3131	365	19	\i(x\a	\i(x\a	PROPN
ejpam-3131	365	20	)	)	PUNCT
ejpam-3131	365	21	is	be	AUX
ejpam-3131	365	22	closed	close	VERB
ejpam-3131	365	23	in	in	ADP
ejpam-3131	365	24	(	(	PUNCT
ejpam-3131	365	25	x	x	X
ejpam-3131	365	26	,	,	PUNCT
ejpam-3131	365	27	τ	τ	PROPN
ejpam-3131	365	28	⊕	⊕	PROPN
ejpam-3131	365	29	i	i	PROPN
ejpam-3131	365	30	)	)	PUNCT
ejpam-3131	365	31	then	then	ADV
ejpam-3131	365	32	adhτ⊕i	adhτ⊕i	PROPN
ejpam-3131	365	33	(	(	PUNCT
ejpam-3131	365	34	a	a	X
ejpam-3131	365	35	)	)	PUNCT
ejpam-3131	365	36	⊆	⊆	NUM
ejpam-3131	365	37	adhτ	adhτ	NOUN
ejpam-3131	365	38	(	(	PUNCT
ejpam-3131	365	39	a	a	NOUN
ejpam-3131	365	40	)	)	PUNCT
ejpam-3131	365	41	\i(x\a	\i(x\a	PROPN
ejpam-3131	365	42	)	)	PUNCT
ejpam-3131	365	43	.	.	PUNCT
ejpam-3131	366	1	now	now	ADV
ejpam-3131	366	2	,	,	PUNCT
ejpam-3131	366	3	suppose	suppose	VERB
ejpam-3131	366	4	that	that	SCONJ
ejpam-3131	366	5	f	f	PROPN
ejpam-3131	366	6	is	be	AUX
ejpam-3131	366	7	closed	close	VERB
ejpam-3131	366	8	in	in	ADP
ejpam-3131	366	9	(	(	PUNCT
ejpam-3131	366	10	x	x	X
ejpam-3131	366	11	,	,	PUNCT
ejpam-3131	366	12	τ	τ	PROPN
ejpam-3131	366	13	⊕	⊕	PROPN
ejpam-3131	366	14	i	i	PROPN
ejpam-3131	366	15	)	)	PUNCT
ejpam-3131	366	16	and	and	CCONJ
ejpam-3131	366	17	that	that	SCONJ
ejpam-3131	366	18	a	a	DET
ejpam-3131	366	19	⊆	⊆	NUM
ejpam-3131	366	20	f	f	NOUN
ejpam-3131	366	21	.	.	PUNCT
ejpam-3131	367	1	there	there	PRON
ejpam-3131	367	2	exists	exist	VERB
ejpam-3131	367	3	g	g	PROPN
ejpam-3131	367	4	⊆	⊆	NUM
ejpam-3131	367	5	x	x	NOUN
ejpam-3131	367	6	,	,	PUNCT
ejpam-3131	367	7	closed	close	VERB
ejpam-3131	367	8	in	in	ADP
ejpam-3131	367	9	(	(	PUNCT
ejpam-3131	367	10	x	x	NOUN
ejpam-3131	367	11	,	,	PUNCT
ejpam-3131	367	12	τ	τ	PROPN
ejpam-3131	367	13	)	)	PUNCT
ejpam-3131	367	14	,	,	PUNCT
ejpam-3131	367	15	and	and	CCONJ
ejpam-3131	367	16	a	a	DET
ejpam-3131	367	17	collection	collection	NOUN
ejpam-3131	367	18	c	c	PROPN
ejpam-3131	367	19	⊆	⊆	NUM
ejpam-3131	367	20	p(i	p(i	PROPN
ejpam-3131	367	21	)	)	PUNCT
ejpam-3131	367	22	,	,	PUNCT
ejpam-3131	367	23	such	such	ADJ
ejpam-3131	367	24	that	that	SCONJ
ejpam-3131	367	25	f	f	NOUN
ejpam-3131	367	26	=	=	PUNCT
ejpam-3131	368	1	g\	g\	X
ejpam-3131	368	2	∪	∪	ADP
ejpam-3131	368	3	c.	c.	NOUN
ejpam-3131	368	4	since	since	SCONJ
ejpam-3131	368	5	adhτ	adhτ	NOUN
ejpam-3131	368	6	(	(	PUNCT
ejpam-3131	368	7	a	a	NOUN
ejpam-3131	368	8	)	)	PUNCT
ejpam-3131	368	9	⊆	⊆	NUM
ejpam-3131	368	10	g	g	NOUN
ejpam-3131	368	11	and	and	CCONJ
ejpam-3131	368	12	∪	∪	ADJ
ejpam-3131	368	13	c	c	NOUN
ejpam-3131	368	14	⊆	⊆	NUM
ejpam-3131	368	15	i	i	PRON
ejpam-3131	368	16	(	(	PUNCT
ejpam-3131	368	17	x\a	x\a	PROPN
ejpam-3131	368	18	)	)	PUNCT
ejpam-3131	368	19	we	we	PRON
ejpam-3131	368	20	have	have	VERB
ejpam-3131	368	21	that	that	DET
ejpam-3131	368	22	adhτ	adhτ	NOUN
ejpam-3131	368	23	(	(	PUNCT
ejpam-3131	368	24	a	a	NOUN
ejpam-3131	368	25	)	)	PUNCT
ejpam-3131	368	26	\i	\i	ADJ
ejpam-3131	368	27	(	(	PUNCT
ejpam-3131	368	28	x\a	x\a	PROPN
ejpam-3131	368	29	)	)	PUNCT
ejpam-3131	368	30	⊆	⊆	NUM
ejpam-3131	369	1	g\	g\	X
ejpam-3131	369	2	∪	∪	ADP
ejpam-3131	369	3	c	c	NOUN
ejpam-3131	369	4	=	=	SYM
ejpam-3131	369	5	f	f	PROPN
ejpam-3131	369	6	.	.	PUNCT
ejpam-3131	370	1	in	in	ADP
ejpam-3131	370	2	particular	particular	ADJ
ejpam-3131	370	3	,	,	PUNCT
ejpam-3131	370	4	adhτ	adhτ	NOUN
ejpam-3131	370	5	(	(	PUNCT
ejpam-3131	370	6	a	a	NOUN
ejpam-3131	370	7	)	)	PUNCT
ejpam-3131	370	8	\i	\i	ADJ
ejpam-3131	370	9	(	(	PUNCT
ejpam-3131	370	10	x\a	x\a	PROPN
ejpam-3131	370	11	)	)	PUNCT
ejpam-3131	370	12	⊆	⊆	NUM
ejpam-3131	370	13	adhτ⊕i	adhτ⊕i	PROPN
ejpam-3131	370	14	(	(	PUNCT
ejpam-3131	370	15	a	a	NOUN
ejpam-3131	370	16	)	)	PUNCT
ejpam-3131	370	17	.	.	PUNCT
ejpam-3131	371	1	(	(	PUNCT
ejpam-3131	371	2	4	4	X
ejpam-3131	371	3	)	)	PUNCT
ejpam-3131	371	4	(	(	PUNCT
ejpam-3131	371	5	i	i	NOUN
ejpam-3131	371	6	)	)	PUNCT
ejpam-3131	371	7	suppose	suppose	VERB
ejpam-3131	371	8	that	that	SCONJ
ejpam-3131	371	9	b	b	X
ejpam-3131	371	10	⊆	⊆	NUM
ejpam-3131	371	11	x	x	PUNCT
ejpam-3131	371	12	is	be	AUX
ejpam-3131	371	13	open	open	ADJ
ejpam-3131	371	14	-	-	PUNCT
ejpam-3131	371	15	i	i	PRON
ejpam-3131	371	16	in	in	ADP
ejpam-3131	371	17	the	the	DET
ejpam-3131	371	18	space	space	NOUN
ejpam-3131	371	19	(	(	PUNCT
ejpam-3131	371	20	x	x	X
ejpam-3131	371	21	,	,	PUNCT
ejpam-3131	371	22	τ	τ	PROPN
ejpam-3131	371	23	⊕	⊕	PROPN
ejpam-3131	371	24	i	i	PRON
ejpam-3131	371	25	,	,	PUNCT
ejpam-3131	371	26	i	i	PROPN
ejpam-3131	371	27	)	)	PUNCT
ejpam-3131	371	28	,	,	PUNCT
ejpam-3131	371	29	this	this	PRON
ejpam-3131	371	30	is	be	AUX
ejpam-3131	371	31	b\intτ⊕i	b\intτ⊕i	ADJ
ejpam-3131	371	32	(	(	PUNCT
ejpam-3131	371	33	b	b	NOUN
ejpam-3131	371	34	)	)	PUNCT
ejpam-3131	371	35	∈	∈	PROPN
ejpam-3131	371	36	i⊆τ	i⊆τ	PROPN
ejpam-3131	371	37	⊕	⊕	PROPN
ejpam-3131	371	38	i.	i.	PROPN
ejpam-3131	371	39	since	since	SCONJ
ejpam-3131	371	40	b	b	PROPN
ejpam-3131	372	1	=	=	PUNCT
ejpam-3131	372	2	[	[	X
ejpam-3131	372	3	b\intτ⊕i	b\intτ⊕i	INTJ
ejpam-3131	372	4	(	(	PUNCT
ejpam-3131	372	5	b	b	NOUN
ejpam-3131	372	6	)	)	PUNCT
ejpam-3131	372	7	]	]	PUNCT
ejpam-3131	372	8	∪	∪	ADP
ejpam-3131	372	9	intτ⊕i	intτ⊕i	PROPN
ejpam-3131	372	10	(	(	PUNCT
ejpam-3131	372	11	b	b	X
ejpam-3131	372	12	)	)	PUNCT
ejpam-3131	372	13	then	then	ADV
ejpam-3131	372	14	b	b	X
ejpam-3131	372	15	∈	∈	PROPN
ejpam-3131	372	16	τ	τ	PROPN
ejpam-3131	372	17	⊕	⊕	PROPN
ejpam-3131	372	18	i.	i.	PROPN
ejpam-3131	372	19	(	(	PUNCT
ejpam-3131	372	20	ii	ii	PROPN
ejpam-3131	372	21	)	)	PUNCT
ejpam-3131	372	22	suppose	suppose	VERB
ejpam-3131	372	23	that	that	SCONJ
ejpam-3131	372	24	β	β	PROPN
ejpam-3131	372	25	is	be	AUX
ejpam-3131	372	26	a	a	DET
ejpam-3131	372	27	topology	topology	NOUN
ejpam-3131	372	28	in	in	ADP
ejpam-3131	372	29	x	x	SYM
ejpam-3131	372	30	such	such	ADJ
ejpam-3131	372	31	that	that	SCONJ
ejpam-3131	372	32	τ	τ	PROPN
ejpam-3131	372	33	⊆	⊆	NUM
ejpam-3131	372	34	β	β	X
ejpam-3131	372	35	and	and	CCONJ
ejpam-3131	372	36	that	that	SCONJ
ejpam-3131	372	37	in	in	ADP
ejpam-3131	372	38	the	the	DET
ejpam-3131	372	39	space	space	NOUN
ejpam-3131	372	40	(	(	PUNCT
ejpam-3131	372	41	x	x	X
ejpam-3131	372	42	,	,	PUNCT
ejpam-3131	372	43	β	β	X
ejpam-3131	372	44	,	,	PUNCT
ejpam-3131	372	45	i	i	PROPN
ejpam-3131	372	46	)	)	PUNCT
ejpam-3131	372	47	,	,	PUNCT
ejpam-3131	372	48	for	for	ADP
ejpam-3131	372	49	each	each	DET
ejpam-3131	372	50	a	a	DET
ejpam-3131	372	51	⊆	⊆	NUM
ejpam-3131	372	52	x	x	SYM
ejpam-3131	372	53	,	,	PUNCT
ejpam-3131	372	54	a	a	PRON
ejpam-3131	372	55	is	be	AUX
ejpam-3131	372	56	open	open	ADJ
ejpam-3131	372	57	-	-	PUNCT
ejpam-3131	372	58	i	i	PRON
ejpam-3131	372	59	if	if	SCONJ
ejpam-3131	372	60	and	and	CCONJ
ejpam-3131	372	61	only	only	ADV
ejpam-3131	372	62	if	if	SCONJ
ejpam-3131	372	63	a	a	PRON
ejpam-3131	372	64	is	be	AUX
ejpam-3131	372	65	open	open	ADJ
ejpam-3131	372	66	.	.	PUNCT
ejpam-3131	373	1	given	give	VERB
ejpam-3131	373	2	that	that	SCONJ
ejpam-3131	373	3	all	all	DET
ejpam-3131	373	4	i	i	PRON
ejpam-3131	373	5	∈	∈	VERB
ejpam-3131	374	1	i	i	PRON
ejpam-3131	374	2	is	be	AUX
ejpam-3131	374	3	open	open	ADJ
ejpam-3131	374	4	-	-	PUNCT
ejpam-3131	374	5	i	i	PRON
ejpam-3131	374	6	in	in	ADP
ejpam-3131	374	7	(	(	PUNCT
ejpam-3131	374	8	x	x	NOUN
ejpam-3131	374	9	,	,	PUNCT
ejpam-3131	374	10	β	β	X
ejpam-3131	374	11	,	,	PUNCT
ejpam-3131	374	12	i	i	PROPN
ejpam-3131	374	13	)	)	PUNCT
ejpam-3131	374	14	then	then	ADV
ejpam-3131	374	15	,	,	PUNCT
ejpam-3131	374	16	by	by	ADP
ejpam-3131	374	17	hypothesis	hypothesis	NOUN
ejpam-3131	374	18	,	,	PUNCT
ejpam-3131	374	19	i	i	PRON
ejpam-3131	374	20	⊆	⊆	NUM
ejpam-3131	374	21	β	β	X
ejpam-3131	374	22	.	.	PUNCT
ejpam-3131	375	1	hence	hence	ADV
ejpam-3131	375	2	τ⊕i⊆β	τ⊕i⊆β	NOUN
ejpam-3131	375	3	.	.	PUNCT
ejpam-3131	376	1	□	□	PUNCT
ejpam-3131	376	2	remark	remark	NOUN
ejpam-3131	376	3	3.11	3.11	NUM
ejpam-3131	376	4	.	.	PUNCT
ejpam-3131	377	1	if	if	SCONJ
ejpam-3131	377	2	i	i	PRON
ejpam-3131	377	3	is	be	AUX
ejpam-3131	377	4	an	an	DET
ejpam-3131	377	5	ideal	ideal	NOUN
ejpam-3131	377	6	in	in	ADP
ejpam-3131	377	7	x	x	PUNCT
ejpam-3131	377	8	and	and	CCONJ
ejpam-3131	377	9	j	j	PROPN
ejpam-3131	377	10	is	be	AUX
ejpam-3131	377	11	an	an	DET
ejpam-3131	377	12	ideal	ideal	NOUN
ejpam-3131	377	13	in	in	ADP
ejpam-3131	377	14	y	y	PROPN
ejpam-3131	377	15	,	,	PUNCT
ejpam-3131	377	16	then	then	ADV
ejpam-3131	377	17	i	i	PRON
ejpam-3131	377	18	⊗	⊗	PROPN
ejpam-3131	377	19	j	j	PROPN
ejpam-3131	377	20	is	be	AUX
ejpam-3131	377	21	the	the	DET
ejpam-3131	377	22	set	set	NOUN
ejpam-3131	377	23	of	of	ADP
ejpam-3131	377	24	all	all	PRON
ejpam-3131	377	25	d	d	PROPN
ejpam-3131	377	26	⊆	⊆	NUM
ejpam-3131	377	27	x	x	SYM
ejpam-3131	377	28	×	×	PROPN
ejpam-3131	377	29	y	y	PROPN
ejpam-3131	377	30	such	such	ADJ
ejpam-3131	377	31	that	that	SCONJ
ejpam-3131	377	32	there	there	PRON
ejpam-3131	377	33	exist	exist	VERB
ejpam-3131	377	34	i	i	PRON
ejpam-3131	377	35	∈	∈	PROPN
ejpam-3131	378	1	i	i	PRON
ejpam-3131	378	2	,	,	PUNCT
ejpam-3131	378	3	a	a	DET
ejpam-3131	378	4	⊆	⊆	NUM
ejpam-3131	378	5	x	x	NOUN
ejpam-3131	378	6	,	,	PUNCT
ejpam-3131	378	7	j	j	PROPN
ejpam-3131	378	8	∈	∈	PROPN
ejpam-3131	378	9	j	j	PROPN
ejpam-3131	378	10	and	and	CCONJ
ejpam-3131	378	11	b	b	PROPN
ejpam-3131	378	12	⊆	⊆	NUM
ejpam-3131	378	13	y	y	PROPN
ejpam-3131	378	14	,	,	PUNCT
ejpam-3131	378	15	with	with	ADP
ejpam-3131	378	16	d	d	PROPN
ejpam-3131	378	17	⊆	⊆	NUM
ejpam-3131	378	18	(	(	PUNCT
ejpam-3131	378	19	a×	a×	PROPN
ejpam-3131	378	20	j	j	NOUN
ejpam-3131	378	21	)	)	PUNCT
ejpam-3131	378	22	∪	∪	NOUN
ejpam-3131	378	23	(	(	PUNCT
ejpam-3131	378	24	i	i	PRON
ejpam-3131	378	25	×b	×b	NOUN
ejpam-3131	378	26	)	)	PUNCT
ejpam-3131	378	27	.	.	PUNCT
ejpam-3131	379	1	theorem	theorem	VERB
ejpam-3131	379	2	3.12	3.12	NUM
ejpam-3131	379	3	.	.	PUNCT
ejpam-3131	380	1	(	(	PUNCT
ejpam-3131	380	2	1	1	X
ejpam-3131	380	3	)	)	PUNCT
ejpam-3131	380	4	if	if	SCONJ
ejpam-3131	380	5	i	i	PRON
ejpam-3131	380	6	is	be	AUX
ejpam-3131	380	7	an	an	DET
ejpam-3131	380	8	ideal	ideal	NOUN
ejpam-3131	380	9	in	in	ADP
ejpam-3131	380	10	x	x	PUNCT
ejpam-3131	380	11	and	and	CCONJ
ejpam-3131	380	12	j	j	PROPN
ejpam-3131	380	13	is	be	AUX
ejpam-3131	380	14	an	an	DET
ejpam-3131	380	15	ideal	ideal	NOUN
ejpam-3131	380	16	in	in	ADP
ejpam-3131	380	17	y	y	PROPN
ejpam-3131	380	18	,	,	PUNCT
ejpam-3131	380	19	then	then	ADV
ejpam-3131	380	20	i	i	PRON
ejpam-3131	380	21	⊗	⊗	PROPN
ejpam-3131	380	22	j	j	PROPN
ejpam-3131	380	23	is	be	AUX
ejpam-3131	380	24	an	an	DET
ejpam-3131	380	25	ideal	ideal	NOUN
ejpam-3131	380	26	in	in	ADP
ejpam-3131	380	27	x	x	PUNCT
ejpam-3131	380	28	×	×	PROPN
ejpam-3131	380	29	y	y	PROPN
ejpam-3131	380	30	.	.	PUNCT
ejpam-3131	381	1	(	(	PUNCT
ejpam-3131	381	2	2	2	X
ejpam-3131	381	3	)	)	PUNCT
ejpam-3131	381	4	if	if	SCONJ
ejpam-3131	381	5	a	a	PRON
ejpam-3131	381	6	is	be	AUX
ejpam-3131	381	7	open	open	ADJ
ejpam-3131	381	8	-	-	PUNCT
ejpam-3131	381	9	i	i	PRON
ejpam-3131	381	10	in	in	ADP
ejpam-3131	381	11	the	the	DET
ejpam-3131	381	12	space	space	NOUN
ejpam-3131	381	13	(	(	PUNCT
ejpam-3131	381	14	x	x	X
ejpam-3131	381	15	,	,	PUNCT
ejpam-3131	381	16	τ	τ	PROPN
ejpam-3131	381	17	,	,	PUNCT
ejpam-3131	381	18	i	i	PROPN
ejpam-3131	381	19	)	)	PUNCT
ejpam-3131	381	20	and	and	CCONJ
ejpam-3131	381	21	b	b	NOUN
ejpam-3131	381	22	is	be	AUX
ejpam-3131	381	23	open	open	ADJ
ejpam-3131	381	24	-	-	PUNCT
ejpam-3131	381	25	j	j	NOUN
ejpam-3131	381	26	in	in	ADP
ejpam-3131	381	27	the	the	DET
ejpam-3131	381	28	space	space	NOUN
ejpam-3131	381	29	(	(	PUNCT
ejpam-3131	381	30	y	y	PROPN
ejpam-3131	381	31	,	,	PUNCT
ejpam-3131	381	32	β	β	X
ejpam-3131	381	33	,	,	PUNCT
ejpam-3131	381	34	j	j	PROPN
ejpam-3131	381	35	)	)	PUNCT
ejpam-3131	381	36	,	,	PUNCT
ejpam-3131	381	37	then	then	ADV
ejpam-3131	381	38	a×b	a×b	PROPN
ejpam-3131	381	39	is	be	AUX
ejpam-3131	381	40	open	open	ADJ
ejpam-3131	381	41	-	-	PUNCT
ejpam-3131	381	42	i	i	PRON
ejpam-3131	381	43	⊗	⊗	PROPN
ejpam-3131	381	44	j	j	PROPN
ejpam-3131	381	45	in	in	ADP
ejpam-3131	381	46	the	the	DET
ejpam-3131	381	47	space	space	NOUN
ejpam-3131	381	48	(	(	PUNCT
ejpam-3131	381	49	x	x	SYM
ejpam-3131	381	50	×	×	PROPN
ejpam-3131	381	51	y	y	PROPN
ejpam-3131	381	52	,	,	PUNCT
ejpam-3131	381	53	τ	τ	PROPN
ejpam-3131	381	54	×	×	PROPN
ejpam-3131	381	55	β	β	X
ejpam-3131	381	56	,	,	PUNCT
ejpam-3131	381	57	i	i	PROPN
ejpam-3131	381	58	⊗	⊗	PROPN
ejpam-3131	381	59	j	j	PROPN
ejpam-3131	381	60	)	)	PUNCT
ejpam-3131	381	61	.	.	PUNCT
ejpam-3131	382	1	proof	proof	NOUN
ejpam-3131	382	2	.	.	PUNCT
ejpam-3131	383	1	(	(	PUNCT
ejpam-3131	383	2	1	1	X
ejpam-3131	383	3	)	)	PUNCT
ejpam-3131	383	4	it	it	PRON
ejpam-3131	383	5	is	be	AUX
ejpam-3131	383	6	clear	clear	ADJ
ejpam-3131	383	7	that	that	SCONJ
ejpam-3131	383	8	if	if	SCONJ
ejpam-3131	383	9	v	v	ADP
ejpam-3131	383	10	⊆	⊆	NUM
ejpam-3131	383	11	w	w	ADP
ejpam-3131	383	12	⊆	⊆	NUM
ejpam-3131	383	13	x	x	SYM
ejpam-3131	383	14	×	×	PROPN
ejpam-3131	383	15	y	y	PROPN
ejpam-3131	383	16	and	and	CCONJ
ejpam-3131	383	17	w	w	PROPN
ejpam-3131	383	18	∈	∈	PROPN
ejpam-3131	383	19	i	i	PRON
ejpam-3131	383	20	⊗	⊗	PROPN
ejpam-3131	383	21	j	j	PROPN
ejpam-3131	383	22	,	,	PUNCT
ejpam-3131	383	23	then	then	ADV
ejpam-3131	383	24	v	v	X
ejpam-3131	383	25	∈	∈	PROPN
ejpam-3131	384	1	i	i	PRON
ejpam-3131	384	2	⊗	⊗	PROPN
ejpam-3131	384	3	j	j	PROPN
ejpam-3131	384	4	.	.	PUNCT
ejpam-3131	384	5	suppose	suppose	VERB
ejpam-3131	384	6	that	that	SCONJ
ejpam-3131	384	7	{	{	PUNCT
ejpam-3131	384	8	d1	d1	NOUN
ejpam-3131	384	9	,	,	PUNCT
ejpam-3131	384	10	d2	d2	PROPN
ejpam-3131	384	11	}	}	PUNCT
ejpam-3131	384	12	⊆	⊆	NUM
ejpam-3131	384	13	i	i	NOUN
ejpam-3131	384	14	⊗	⊗	PROPN
ejpam-3131	384	15	j	j	PROPN
ejpam-3131	384	16	.	.	PUNCT
ejpam-3131	385	1	there	there	PRON
ejpam-3131	385	2	are	be	VERB
ejpam-3131	385	3	{	{	PUNCT
ejpam-3131	385	4	i1	i1	PROPN
ejpam-3131	385	5	,	,	PUNCT
ejpam-3131	385	6	i2	i2	PROPN
ejpam-3131	385	7	}	}	PUNCT
ejpam-3131	385	8	⊆	⊆	NUM
ejpam-3131	385	9	i	i	PRON
ejpam-3131	385	10	,	,	PUNCT
ejpam-3131	385	11	{	{	PUNCT
ejpam-3131	385	12	j1	j1	PROPN
ejpam-3131	385	13	,	,	PUNCT
ejpam-3131	385	14	j2	j2	PROPN
ejpam-3131	385	15	}	}	PUNCT
ejpam-3131	385	16	⊆	⊆	NUM
ejpam-3131	385	17	j	j	PROPN
ejpam-3131	385	18	,	,	PUNCT
ejpam-3131	385	19	{	{	PUNCT
ejpam-3131	385	20	a1	a1	NOUN
ejpam-3131	385	21	,	,	PUNCT
ejpam-3131	385	22	a2	a2	PROPN
ejpam-3131	385	23	}	}	PUNCT
ejpam-3131	385	24	⊆	⊆	NUM
ejpam-3131	385	25	p	p	NOUN
ejpam-3131	385	26	(	(	PUNCT
ejpam-3131	385	27	x	x	NOUN
ejpam-3131	385	28	)	)	PUNCT
ejpam-3131	385	29	and	and	CCONJ
ejpam-3131	385	30	{	{	PUNCT
ejpam-3131	385	31	b1	b1	NOUN
ejpam-3131	385	32	,	,	PUNCT
ejpam-3131	385	33	b2	b2	NOUN
ejpam-3131	385	34	}	}	PUNCT
ejpam-3131	385	35	⊆	⊆	NUM
ejpam-3131	385	36	p	p	NOUN
ejpam-3131	385	37	(	(	PUNCT
ejpam-3131	385	38	y	y	PROPN
ejpam-3131	385	39	)	)	PUNCT
ejpam-3131	385	40	such	such	ADJ
ejpam-3131	385	41	that	that	SCONJ
ejpam-3131	385	42	d1	d1	PROPN
ejpam-3131	385	43	⊆	⊆	NUM
ejpam-3131	385	44	(	(	PUNCT
ejpam-3131	385	45	a1	a1	NOUN
ejpam-3131	385	46	×	×	PROPN
ejpam-3131	385	47	j1	j1	PROPN
ejpam-3131	385	48	)	)	PUNCT
ejpam-3131	385	49	∪	∪	NOUN
ejpam-3131	385	50	(	(	PUNCT
ejpam-3131	385	51	i1	i1	PROPN
ejpam-3131	385	52	×b1	×b1	PROPN
ejpam-3131	385	53	)	)	PUNCT
ejpam-3131	385	54	and	and	CCONJ
ejpam-3131	385	55	d2	d2	PROPN
ejpam-3131	385	56	⊆	⊆	NUM
ejpam-3131	385	57	(	(	PUNCT
ejpam-3131	385	58	a2	a2	PROPN
ejpam-3131	385	59	×	×	PROPN
ejpam-3131	385	60	j2)∪(i2	j2)∪(i2	PROPN
ejpam-3131	385	61	×b2	×b2	PROPN
ejpam-3131	385	62	)	)	PUNCT
ejpam-3131	385	63	.	.	PUNCT
ejpam-3131	386	1	hence	hence	ADV
ejpam-3131	386	2	d1∪d2	d1∪d2	VERB
ejpam-3131	386	3	⊆	⊆	X
ejpam-3131	386	4	(	(	PUNCT
ejpam-3131	386	5	a1	a1	NOUN
ejpam-3131	386	6	×	×	NOUN
ejpam-3131	386	7	j1)∪(a2	j1)∪(a2	PROPN
ejpam-3131	386	8	×	×	PROPN
ejpam-3131	386	9	j2)∪(i1	j2)∪(i1	NOUN
ejpam-3131	386	10	×b1)∪(i2	×b1)∪(i2	NOUN
ejpam-3131	386	11	×b2	×b2	NOUN
ejpam-3131	386	12	)	)	PUNCT
ejpam-3131	386	13	⊆	⊆	NUM
ejpam-3131	387	1	[	[	X
ejpam-3131	387	2	(	(	PUNCT
ejpam-3131	387	3	a1	a1	PROPN
ejpam-3131	387	4	∪a2)×	∪a2)×	PROPN
ejpam-3131	387	5	(	(	PUNCT
ejpam-3131	387	6	j1	j1	PROPN
ejpam-3131	387	7	∪	∪	PROPN
ejpam-3131	387	8	j2	j2	PROPN
ejpam-3131	387	9	)	)	PUNCT
ejpam-3131	387	10	]	]	PUNCT
ejpam-3131	387	11	∪	∪	X
ejpam-3131	387	12	[	[	X
ejpam-3131	387	13	(	(	PUNCT
ejpam-3131	387	14	i1	i1	PROPN
ejpam-3131	387	15	∪	∪	X
ejpam-3131	387	16	i2)×	i2)×	X
ejpam-3131	387	17	(	(	PUNCT
ejpam-3131	387	18	b1	b1	NOUN
ejpam-3131	387	19	∪b2	∪b2	ADJ
ejpam-3131	387	20	)	)	PUNCT
ejpam-3131	387	21	]	]	PUNCT
ejpam-3131	387	22	.	.	PUNCT
ejpam-3131	388	1	this	this	PRON
ejpam-3131	388	2	implies	imply	VERB
ejpam-3131	388	3	that	that	SCONJ
ejpam-3131	388	4	d1	d1	PROPN
ejpam-3131	388	5	∪d2	∪d2	X
ejpam-3131	389	1	∈	∈	PROPN
ejpam-3131	390	1	i	i	PRON
ejpam-3131	390	2	⊗	⊗	PROPN
ejpam-3131	390	3	j	j	PROPN
ejpam-3131	390	4	.	.	PUNCT
ejpam-3131	391	1	(	(	PUNCT
ejpam-3131	391	2	2	2	X
ejpam-3131	391	3	)	)	PUNCT
ejpam-3131	391	4	since	since	SCONJ
ejpam-3131	391	5	a\	a\	NOUN
ejpam-3131	391	6	0	0	NUM
ejpam-3131	391	7	a	a	DET
ejpam-3131	391	8	∈	∈	NOUN
ejpam-3131	392	1	i	i	PRON
ejpam-3131	392	2	and	and	CCONJ
ejpam-3131	392	3	b\	b\	ADJ
ejpam-3131	392	4	0	0	PUNCT
ejpam-3131	393	1	b	b	X
ejpam-3131	393	2	∈	∈	PROPN
ejpam-3131	393	3	j	j	PROPN
ejpam-3131	393	4	,	,	PUNCT
ejpam-3131	393	5	we	we	PRON
ejpam-3131	393	6	have	have	VERB
ejpam-3131	393	7	that	that	PRON
ejpam-3131	393	8	(	(	PUNCT
ejpam-3131	393	9	a×b	a×b	PROPN
ejpam-3131	393	10	)	)	PUNCT
ejpam-3131	393	11	\int	\int	NOUN
ejpam-3131	393	12	(	(	PUNCT
ejpam-3131	393	13	a×b	a×b	PROPN
ejpam-3131	393	14	)	)	PUNCT
ejpam-3131	393	15	=	=	SYM
ejpam-3131	393	16	(	(	PUNCT
ejpam-3131	393	17	a×b	a×b	PROPN
ejpam-3131	393	18	)	)	PUNCT
ejpam-3131	393	19	\	\	PUNCT
ejpam-3131	394	1	(	(	PUNCT
ejpam-3131	394	2	0	0	NUM
ejpam-3131	394	3	a×	a×	NOUN
ejpam-3131	394	4	0	0	NUM
ejpam-3131	394	5	b	b	X
ejpam-3131	394	6	)	)	PUNCT
ejpam-3131	394	7	=[	=[	NOUN
ejpam-3131	394	8	(	(	PUNCT
ejpam-3131	394	9	a\	a\	NOUN
ejpam-3131	394	10	0	0	NUM
ejpam-3131	394	11	a	a	PRON
ejpam-3131	394	12	)	)	PUNCT
ejpam-3131	394	13	×b	×b	NOUN
ejpam-3131	394	14	]	]	PUNCT
ejpam-3131	394	15	∪	∪	ADP
ejpam-3131	394	16	[	[	PUNCT
ejpam-3131	394	17	a×	a×	NOUN
ejpam-3131	394	18	(	(	PUNCT
ejpam-3131	394	19	b\	b\	X
ejpam-3131	394	20	0	0	NUM
ejpam-3131	394	21	b	b	NOUN
ejpam-3131	394	22	)	)	PUNCT
ejpam-3131	394	23	]	]	PUNCT
ejpam-3131	395	1	∈	∈	PROPN
ejpam-3131	396	1	i	i	PRON
ejpam-3131	396	2	⊗	⊗	PROPN
ejpam-3131	396	3	j	j	PROPN
ejpam-3131	396	4	.	.	PUNCT
ejpam-3131	397	1	□	□	PUNCT
ejpam-3131	397	2	4	4	X
ejpam-3131	397	3	.	.	X
ejpam-3131	397	4	other	other	ADJ
ejpam-3131	397	5	characteristics	characteristic	NOUN
ejpam-3131	397	6	of	of	ADP
ejpam-3131	397	7	the	the	DET
ejpam-3131	397	8	topology	topology	NOUN
ejpam-3131	397	9	τ	τ	PROPN
ejpam-3131	397	10	⊕	⊕	NUM
ejpam-3131	397	11	i	i	PRON
ejpam-3131	397	12	in	in	ADP
ejpam-3131	397	13	this	this	DET
ejpam-3131	397	14	section	section	NOUN
ejpam-3131	397	15	we	we	PRON
ejpam-3131	397	16	present	present	VERB
ejpam-3131	397	17	some	some	DET
ejpam-3131	397	18	properties	property	NOUN
ejpam-3131	397	19	of	of	ADP
ejpam-3131	397	20	the	the	DET
ejpam-3131	397	21	topology	topology	NOUN
ejpam-3131	397	22	τ	τ	X
ejpam-3131	397	23	⊕i	⊕i	NOUN
ejpam-3131	397	24	,	,	PUNCT
ejpam-3131	397	25	related	relate	VERB
ejpam-3131	397	26	to	to	ADP
ejpam-3131	397	27	normality	normality	NOUN
ejpam-3131	397	28	,	,	PUNCT
ejpam-3131	397	29	compactness	compactness	NOUN
ejpam-3131	397	30	and	and	CCONJ
ejpam-3131	397	31	c	c	NOUN
ejpam-3131	397	32	-	-	PUNCT
ejpam-3131	397	33	compactness	compactness	NOUN
ejpam-3131	397	34	.	.	PUNCT
ejpam-3131	398	1	n.r	n.r	PROPN
ejpam-3131	398	2	.	.	PROPN
ejpam-3131	398	3	pachón	pachón	PROPN
ejpam-3131	398	4	/	/	SYM
ejpam-3131	398	5	eur	eur	PROPN
ejpam-3131	398	6	.	.	PUNCT
ejpam-3131	399	1	j.	j.	PROPN
ejpam-3131	399	2	pure	pure	PROPN
ejpam-3131	399	3	appl	appl	PROPN
ejpam-3131	399	4	.	.	PROPN
ejpam-3131	399	5	math	math	PROPN
ejpam-3131	399	6	,	,	PUNCT
ejpam-3131	399	7	11	11	NUM
ejpam-3131	399	8	(	(	PUNCT
ejpam-3131	399	9	1	1	NUM
ejpam-3131	399	10	)	)	PUNCT
ejpam-3131	399	11	(	(	PUNCT
ejpam-3131	399	12	2018	2018	NUM
ejpam-3131	399	13	)	)	PUNCT
ejpam-3131	399	14	,	,	PUNCT
ejpam-3131	399	15	299	299	NUM
ejpam-3131	399	16	-	-	SYM
ejpam-3131	399	17	314	314	NUM
ejpam-3131	399	18	312	312	NUM
ejpam-3131	399	19	remark	remark	NOUN
ejpam-3131	399	20	4.1	4.1	NUM
ejpam-3131	399	21	.	.	PUNCT
ejpam-3131	400	1	if	if	SCONJ
ejpam-3131	400	2	(	(	PUNCT
ejpam-3131	400	3	x	x	X
ejpam-3131	400	4	,	,	PUNCT
ejpam-3131	400	5	τ	τ	PROPN
ejpam-3131	400	6	,	,	PUNCT
ejpam-3131	400	7	i	i	PROPN
ejpam-3131	400	8	)	)	PUNCT
ejpam-3131	400	9	is	be	AUX
ejpam-3131	400	10	an	an	DET
ejpam-3131	400	11	ideal	ideal	ADJ
ejpam-3131	400	12	space	space	NOUN
ejpam-3131	400	13	then	then	ADV
ejpam-3131	400	14	i⊛	i⊛	VERB
ejpam-3131	400	15	=	=	SYM
ejpam-3131	400	16	{	{	PUNCT
ejpam-3131	400	17	∪	∪	X
ejpam-3131	400	18	c	c	NOUN
ejpam-3131	400	19	:	:	PUNCT
ejpam-3131	400	20	c	c	PROPN
ejpam-3131	400	21	⊆	⊆	NUM
ejpam-3131	400	22	p(i	p(i	PROPN
ejpam-3131	400	23	)	)	PUNCT
ejpam-3131	400	24	}	}	PUNCT
ejpam-3131	400	25	and	and	CCONJ
ejpam-3131	400	26	i	i	PRON
ejpam-3131	400	27	=	=	PRON
ejpam-3131	400	28	{	{	PUNCT
ejpam-3131	400	29	j	j	NOUN
ejpam-3131	400	30	:	:	PUNCT
ejpam-3131	400	31	j	j	PROPN
ejpam-3131	400	32	⊆	⊆	NUM
ejpam-3131	400	33	i	i	PROPN
ejpam-3131	400	34	,	,	PUNCT
ejpam-3131	400	35	for	for	ADP
ejpam-3131	400	36	some	some	DET
ejpam-3131	400	37	i	i	PRON
ejpam-3131	400	38	∈	∈	PROPN
ejpam-3131	401	1	i	i	PRON
ejpam-3131	401	2	}	}	PUNCT
ejpam-3131	401	3	it	it	PRON
ejpam-3131	401	4	is	be	AUX
ejpam-3131	401	5	clear	clear	ADJ
ejpam-3131	401	6	that	that	SCONJ
ejpam-3131	401	7	i⊛	i⊛	PROPN
ejpam-3131	401	8	=	=	SYM
ejpam-3131	401	9	p(ui	p(ui	NOUN
ejpam-3131	401	10	)	)	PUNCT
ejpam-3131	401	11	,	,	PUNCT
ejpam-3131	401	12	where	where	SCONJ
ejpam-3131	401	13	ui	ui	PROPN
ejpam-3131	401	14	=	=	PUNCT
ejpam-3131	401	15	∪	∪	ADP
ejpam-3131	401	16	i∈i	i∈i	ADJ
ejpam-3131	401	17	i.	i.	NOUN
ejpam-3131	401	18	it	it	PRON
ejpam-3131	401	19	is	be	AUX
ejpam-3131	401	20	easy	easy	ADJ
ejpam-3131	401	21	to	to	PART
ejpam-3131	401	22	see	see	VERB
ejpam-3131	401	23	that	that	SCONJ
ejpam-3131	401	24	i	i	PRON
ejpam-3131	401	25	is	be	AUX
ejpam-3131	401	26	an	an	DET
ejpam-3131	401	27	ideal	ideal	NOUN
ejpam-3131	401	28	in	in	ADP
ejpam-3131	401	29	x	x	PRON
ejpam-3131	401	30	,	,	PUNCT
ejpam-3131	401	31	that	that	SCONJ
ejpam-3131	401	32	i	i	PRON
ejpam-3131	401	33	⊆	⊆	NUM
ejpam-3131	401	34	i⊛	i⊛	NOUN
ejpam-3131	401	35	,	,	PUNCT
ejpam-3131	401	36	i	i	PRON
ejpam-3131	401	37	⊆	⊆	NUM
ejpam-3131	401	38	i	i	PRON
ejpam-3131	401	39	,	,	PUNCT
ejpam-3131	401	40	and	and	CCONJ
ejpam-3131	401	41	that	that	SCONJ
ejpam-3131	401	42	if	if	SCONJ
ejpam-3131	401	43	i	i	PRON
ejpam-3131	401	44	∈	∈	VERB
ejpam-3131	401	45	i	i	PRON
ejpam-3131	401	46	then	then	ADV
ejpam-3131	401	47	i	i	PROPN
ejpam-3131	401	48	∈	∈	PROPN
ejpam-3131	401	49	i.	i.	NOUN
ejpam-3131	401	50	moreover	moreover	ADV
ejpam-3131	401	51	,	,	PUNCT
ejpam-3131	401	52	if	if	SCONJ
ejpam-3131	401	53	τ	τ	PROPN
ejpam-3131	401	54	is	be	AUX
ejpam-3131	401	55	a	a	DET
ejpam-3131	401	56	topology	topology	NOUN
ejpam-3131	401	57	in	in	ADP
ejpam-3131	401	58	x	x	NOUN
ejpam-3131	401	59	,	,	PUNCT
ejpam-3131	401	60	it	it	PRON
ejpam-3131	401	61	is	be	AUX
ejpam-3131	401	62	clear	clear	ADJ
ejpam-3131	401	63	that	that	SCONJ
ejpam-3131	401	64	τ	τ	PROPN
ejpam-3131	401	65	⊕	⊕	PROPN
ejpam-3131	401	66	i	i	PRON
ejpam-3131	401	67	=	=	SYM
ejpam-3131	401	68	τ	τ	PROPN
ejpam-3131	401	69	⊕	⊕	PROPN
ejpam-3131	401	70	i⊛.	i⊛.	PROPN
ejpam-3131	401	71	theorem	theorem	VERB
ejpam-3131	401	72	4.2	4.2	NUM
ejpam-3131	401	73	.	.	PUNCT
ejpam-3131	402	1	if	if	SCONJ
ejpam-3131	402	2	i	i	PRON
ejpam-3131	402	3	is	be	AUX
ejpam-3131	402	4	an	an	DET
ejpam-3131	402	5	ideal	ideal	NOUN
ejpam-3131	402	6	in	in	ADP
ejpam-3131	402	7	x	x	PRON
ejpam-3131	402	8	,	,	PUNCT
ejpam-3131	402	9	τ	τ	PROPN
ejpam-3131	402	10	is	be	AUX
ejpam-3131	402	11	a	a	DET
ejpam-3131	402	12	topology	topology	NOUN
ejpam-3131	402	13	in	in	ADP
ejpam-3131	402	14	x	x	PUNCT
ejpam-3131	402	15	and	and	CCONJ
ejpam-3131	402	16	(	(	PUNCT
ejpam-3131	402	17	x	x	X
ejpam-3131	402	18	,	,	PUNCT
ejpam-3131	402	19	τ	τ	PROPN
ejpam-3131	402	20	⊕	⊕	PROPN
ejpam-3131	402	21	i	i	PROPN
ejpam-3131	402	22	)	)	PUNCT
ejpam-3131	402	23	is	be	AUX
ejpam-3131	402	24	a	a	DET
ejpam-3131	402	25	normal	normal	ADJ
ejpam-3131	402	26	space	space	NOUN
ejpam-3131	402	27	,	,	PUNCT
ejpam-3131	402	28	then	then	ADV
ejpam-3131	402	29	(	(	PUNCT
ejpam-3131	402	30	x	x	X
ejpam-3131	402	31	,	,	PUNCT
ejpam-3131	402	32	τ	τ	PROPN
ejpam-3131	402	33	,	,	PUNCT
ejpam-3131	402	34	i⊛	i⊛	PROPN
ejpam-3131	402	35	)	)	PUNCT
ejpam-3131	402	36	is	be	AUX
ejpam-3131	402	37	i⊛-normal	i⊛-normal	NOUN
ejpam-3131	402	38	.	.	PUNCT
ejpam-3131	403	1	proof	proof	NOUN
ejpam-3131	403	2	.	.	PUNCT
ejpam-3131	404	1	suppose	suppose	VERB
ejpam-3131	404	2	that	that	SCONJ
ejpam-3131	404	3	f	f	PROPN
ejpam-3131	404	4	and	and	CCONJ
ejpam-3131	404	5	g	g	PROPN
ejpam-3131	404	6	are	be	AUX
ejpam-3131	404	7	disjoint	disjoint	NOUN
ejpam-3131	404	8	closed	closed	ADJ
ejpam-3131	404	9	sets	set	NOUN
ejpam-3131	404	10	in	in	ADP
ejpam-3131	404	11	(	(	PUNCT
ejpam-3131	404	12	x	x	NOUN
ejpam-3131	404	13	,	,	PUNCT
ejpam-3131	404	14	τ	τ	PROPN
ejpam-3131	404	15	)	)	PUNCT
ejpam-3131	404	16	.	.	PUNCT
ejpam-3131	405	1	since	since	SCONJ
ejpam-3131	405	2	f	f	PROPN
ejpam-3131	405	3	and	and	CCONJ
ejpam-3131	405	4	g	g	PROPN
ejpam-3131	405	5	are	be	AUX
ejpam-3131	405	6	closed	close	VERB
ejpam-3131	405	7	sets	set	NOUN
ejpam-3131	405	8	in	in	ADP
ejpam-3131	405	9	(	(	PUNCT
ejpam-3131	405	10	x	x	X
ejpam-3131	405	11	,	,	PUNCT
ejpam-3131	405	12	τ	τ	PROPN
ejpam-3131	405	13	⊕	⊕	PROPN
ejpam-3131	405	14	i	i	PROPN
ejpam-3131	405	15	)	)	PUNCT
ejpam-3131	405	16	,	,	PUNCT
ejpam-3131	405	17	there	there	PRON
ejpam-3131	405	18	exists	exist	VERB
ejpam-3131	405	19	disjoint	disjoint	NOUN
ejpam-3131	405	20	sets	set	VERB
ejpam-3131	405	21	u	u	NOUN
ejpam-3131	405	22	∪	∪	ADP
ejpam-3131	405	23	∪	∪	ADJ
ejpam-3131	405	24	α∈λ1	α∈λ1	PROPN
ejpam-3131	405	25	iα	iα	ADP
ejpam-3131	405	26	∈	∈	PROPN
ejpam-3131	406	1	τ	τ	PROPN
ejpam-3131	406	2	⊕	⊕	PROPN
ejpam-3131	407	1	i	i	PRON
ejpam-3131	407	2	and	and	CCONJ
ejpam-3131	407	3	v	v	ADP
ejpam-3131	407	4	∪	∪	NOUN
ejpam-3131	407	5	∪	∪	NOUN
ejpam-3131	407	6	α∈λ2	α∈λ2	NOUN
ejpam-3131	407	7	iα	iα	NOUN
ejpam-3131	407	8	∈	∈	PROPN
ejpam-3131	407	9	τ	τ	PROPN
ejpam-3131	407	10	⊕	⊕	NUM
ejpam-3131	407	11	i	i	PRON
ejpam-3131	407	12	such	such	ADJ
ejpam-3131	407	13	that	that	SCONJ
ejpam-3131	407	14	f	f	PROPN
ejpam-3131	407	15	⊆	⊆	NUM
ejpam-3131	407	16	u	u	NOUN
ejpam-3131	407	17	∪	∪	ADP
ejpam-3131	407	18	∪	∪	ADJ
ejpam-3131	407	19	α∈λ1	α∈λ1	PROPN
ejpam-3131	407	20	iα	iα	NOUN
ejpam-3131	407	21	and	and	CCONJ
ejpam-3131	407	22	g	g	PROPN
ejpam-3131	407	23	⊆	⊆	NUM
ejpam-3131	407	24	v	v	ADP
ejpam-3131	407	25	∪	∪	NOUN
ejpam-3131	407	26	∪	∪	X
ejpam-3131	407	27	α∈λ2	α∈λ2	PROPN
ejpam-3131	407	28	iα	iα	NOUN
ejpam-3131	407	29	.	.	PUNCT
ejpam-3131	408	1	thus	thus	ADV
ejpam-3131	408	2	f\u	f\u	PROPN
ejpam-3131	408	3	⊆	⊆	NUM
ejpam-3131	408	4	∪	∪	X
ejpam-3131	408	5	α∈λ1	α∈λ1	ADP
ejpam-3131	408	6	iα	iα	NOUN
ejpam-3131	408	7	∈	∈	PROPN
ejpam-3131	408	8	i⊛	i⊛	PROPN
ejpam-3131	408	9	and	and	CCONJ
ejpam-3131	408	10	g\v	g\v	VERB
ejpam-3131	408	11	⊆	⊆	NUM
ejpam-3131	408	12	∪	∪	NOUN
ejpam-3131	408	13	α∈λ2	α∈λ2	ADJ
ejpam-3131	408	14	iα	iα	NOUN
ejpam-3131	408	15	∈	∈	PROPN
ejpam-3131	408	16	i⊛.	i⊛.	PROPN
ejpam-3131	408	17	moreover	moreover	ADV
ejpam-3131	408	18	u	u	NOUN
ejpam-3131	408	19	and	and	CCONJ
ejpam-3131	408	20	v	v	NOUN
ejpam-3131	408	21	are	be	AUX
ejpam-3131	408	22	disjoint	disjoint	ADJ
ejpam-3131	408	23	open	open	ADJ
ejpam-3131	408	24	sets	set	NOUN
ejpam-3131	408	25	in	in	ADP
ejpam-3131	408	26	(	(	PUNCT
ejpam-3131	408	27	x	x	NOUN
ejpam-3131	408	28	,	,	PUNCT
ejpam-3131	408	29	τ	τ	PROPN
ejpam-3131	408	30	)	)	PUNCT
ejpam-3131	408	31	.	.	PUNCT
ejpam-3131	409	1	□	□	PUNCT
ejpam-3131	409	2	a	a	DET
ejpam-3131	409	3	space	space	NOUN
ejpam-3131	409	4	(	(	PUNCT
ejpam-3131	409	5	x	x	X
ejpam-3131	409	6	,	,	PUNCT
ejpam-3131	409	7	τ	τ	X
ejpam-3131	409	8	)	)	PUNCT
ejpam-3131	409	9	is	be	AUX
ejpam-3131	409	10	said	say	VERB
ejpam-3131	409	11	to	to	PART
ejpam-3131	409	12	be	be	AUX
ejpam-3131	409	13	:	:	PUNCT
ejpam-3131	409	14	(	(	PUNCT
ejpam-3131	409	15	1	1	X
ejpam-3131	409	16	)	)	PUNCT
ejpam-3131	409	17	qhc	qhc	NOUN
ejpam-3131	410	1	[	[	X
ejpam-3131	410	2	11	11	NUM
ejpam-3131	410	3	]	]	X
ejpam-3131	410	4	if	if	SCONJ
ejpam-3131	410	5	for	for	ADP
ejpam-3131	410	6	each	each	DET
ejpam-3131	410	7	open	open	ADJ
ejpam-3131	410	8	cover	cover	NOUN
ejpam-3131	410	9	{	{	PUNCT
ejpam-3131	410	10	vα}α∈λ	vα}α∈λ	NOUN
ejpam-3131	410	11	of	of	ADP
ejpam-3131	410	12	x	x	PRON
ejpam-3131	410	13	,	,	PUNCT
ejpam-3131	410	14	there	there	PRON
ejpam-3131	410	15	exists	exist	VERB
ejpam-3131	410	16	λ0	λ0	NOUN
ejpam-3131	410	17	⊆	⊆	NUM
ejpam-3131	410	18	λ	λ	PROPN
ejpam-3131	410	19	,	,	PUNCT
ejpam-3131	410	20	finite	finite	NOUN
ejpam-3131	410	21	,	,	PUNCT
ejpam-3131	410	22	such	such	ADJ
ejpam-3131	410	23	that	that	SCONJ
ejpam-3131	410	24	x	x	X
ejpam-3131	410	25	=	=	SYM
ejpam-3131	410	26	∪	∪	ADP
ejpam-3131	410	27	α∈λ0	α∈λ0	NOUN
ejpam-3131	410	28	vα	vα	PROPN
ejpam-3131	410	29	.	.	PUNCT
ejpam-3131	411	1	(	(	PUNCT
ejpam-3131	411	2	2	2	NUM
ejpam-3131	411	3	)	)	PUNCT
ejpam-3131	411	4	c	c	NOUN
ejpam-3131	411	5	-	-	PUNCT
ejpam-3131	411	6	compact	compact	ADJ
ejpam-3131	412	1	[	[	X
ejpam-3131	412	2	13	13	NUM
ejpam-3131	412	3	]	]	X
ejpam-3131	412	4	if	if	SCONJ
ejpam-3131	412	5	for	for	ADP
ejpam-3131	412	6	each	each	DET
ejpam-3131	412	7	closed	close	VERB
ejpam-3131	412	8	set	set	VERB
ejpam-3131	412	9	f	f	NOUN
ejpam-3131	412	10	and	and	CCONJ
ejpam-3131	412	11	each	each	DET
ejpam-3131	412	12	open	open	ADJ
ejpam-3131	412	13	cover	cover	NOUN
ejpam-3131	412	14	{	{	PUNCT
ejpam-3131	412	15	vα}α∈λ	vα}α∈λ	NOUN
ejpam-3131	412	16	of	of	ADP
ejpam-3131	412	17	f	f	PROPN
ejpam-3131	412	18	,	,	PUNCT
ejpam-3131	412	19	there	there	PRON
ejpam-3131	412	20	exists	exist	VERB
ejpam-3131	412	21	λ0	λ0	NOUN
ejpam-3131	412	22	⊆	⊆	NUM
ejpam-3131	412	23	λ	λ	PROPN
ejpam-3131	412	24	,	,	PUNCT
ejpam-3131	412	25	finite	finite	NOUN
ejpam-3131	412	26	,	,	PUNCT
ejpam-3131	412	27	such	such	ADJ
ejpam-3131	412	28	that	that	SCONJ
ejpam-3131	412	29	f	f	PROPN
ejpam-3131	412	30	⊆	⊆	NUM
ejpam-3131	412	31	∪	∪	VERB
ejpam-3131	412	32	α∈λ0	α∈λ0	NOUN
ejpam-3131	412	33	vα	vα	PROPN
ejpam-3131	412	34	.	.	PUNCT
ejpam-3131	413	1	an	an	DET
ejpam-3131	413	2	ideal	ideal	ADJ
ejpam-3131	413	3	space	space	NOUN
ejpam-3131	413	4	(	(	PUNCT
ejpam-3131	413	5	x	x	X
ejpam-3131	413	6	,	,	PUNCT
ejpam-3131	413	7	τ	τ	PROPN
ejpam-3131	413	8	,	,	PUNCT
ejpam-3131	413	9	i	i	PROPN
ejpam-3131	413	10	)	)	PUNCT
ejpam-3131	413	11	is	be	AUX
ejpam-3131	413	12	defined	define	VERB
ejpam-3131	413	13	to	to	PART
ejpam-3131	413	14	be	be	AUX
ejpam-3131	413	15	:	:	PUNCT
ejpam-3131	413	16	(	(	PUNCT
ejpam-3131	413	17	1	1	X
ejpam-3131	413	18	)	)	PUNCT
ejpam-3131	413	19	ρi	ρi	NOUN
ejpam-3131	413	20	-	-	PUNCT
ejpam-3131	413	21	qhc	qhc	NOUN
ejpam-3131	414	1	[	[	X
ejpam-3131	414	2	10	10	NUM
ejpam-3131	414	3	]	]	X
ejpam-3131	414	4	if	if	SCONJ
ejpam-3131	414	5	for	for	ADP
ejpam-3131	414	6	each	each	DET
ejpam-3131	414	7	collection	collection	NOUN
ejpam-3131	414	8	{	{	PUNCT
ejpam-3131	414	9	vα}α∈λ	vα}α∈λ	X
ejpam-3131	414	10	of	of	ADP
ejpam-3131	414	11	open	open	ADJ
ejpam-3131	414	12	sets	set	NOUN
ejpam-3131	414	13	,	,	PUNCT
ejpam-3131	414	14	if	if	SCONJ
ejpam-3131	414	15	x\	x\	NOUN
ejpam-3131	414	16	∪	∪	VERB
ejpam-3131	414	17	α∈λ	α∈λ	NOUN
ejpam-3131	414	18	vα	vα	ADP
ejpam-3131	414	19	∈	∈	PROPN
ejpam-3131	414	20	i	i	PRON
ejpam-3131	414	21	there	there	PRON
ejpam-3131	414	22	exists	exist	VERB
ejpam-3131	414	23	λ0	λ0	NOUN
ejpam-3131	414	24	⊆	⊆	NUM
ejpam-3131	414	25	λ	λ	PROPN
ejpam-3131	414	26	,	,	PUNCT
ejpam-3131	414	27	finite	finite	NOUN
ejpam-3131	414	28	,	,	PUNCT
ejpam-3131	414	29	such	such	ADJ
ejpam-3131	414	30	that	that	SCONJ
ejpam-3131	414	31	x\	x\	NOUN
ejpam-3131	414	32	∪	∪	ADP
ejpam-3131	414	33	α∈λ0	α∈λ0	NOUN
ejpam-3131	414	34	vα	vα	ADP
ejpam-3131	414	35	∈	∈	PROPN
ejpam-3131	414	36	i.	i.	NOUN
ejpam-3131	414	37	(	(	PUNCT
ejpam-3131	414	38	2	2	NUM
ejpam-3131	414	39	)	)	PUNCT
ejpam-3131	414	40	ρc(i)-compact	ρc(i)-compact	PROPN
ejpam-3131	415	1	[	[	X
ejpam-3131	415	2	10	10	NUM
ejpam-3131	415	3	]	]	X
ejpam-3131	415	4	if	if	SCONJ
ejpam-3131	415	5	for	for	ADP
ejpam-3131	415	6	each	each	DET
ejpam-3131	415	7	closed	close	VERB
ejpam-3131	415	8	set	set	VERB
ejpam-3131	415	9	f	f	NOUN
ejpam-3131	415	10	and	and	CCONJ
ejpam-3131	415	11	each	each	DET
ejpam-3131	415	12	collection	collection	NOUN
ejpam-3131	415	13	{	{	PUNCT
ejpam-3131	415	14	vα}α∈λ	vα}α∈λ	X
ejpam-3131	415	15	of	of	ADP
ejpam-3131	415	16	open	open	ADJ
ejpam-3131	415	17	sets	set	NOUN
ejpam-3131	415	18	,	,	PUNCT
ejpam-3131	415	19	if	if	SCONJ
ejpam-3131	415	20	f\	f\	NOUN
ejpam-3131	415	21	∪	∪	ADP
ejpam-3131	415	22	α∈λ	α∈λ	NOUN
ejpam-3131	415	23	vα	vα	ADP
ejpam-3131	415	24	∈	∈	PROPN
ejpam-3131	416	1	i	i	PRON
ejpam-3131	416	2	there	there	PRON
ejpam-3131	416	3	exists	exist	VERB
ejpam-3131	416	4	λ0	λ0	NOUN
ejpam-3131	416	5	⊆	⊆	NUM
ejpam-3131	416	6	λ	λ	PROPN
ejpam-3131	416	7	,	,	PUNCT
ejpam-3131	416	8	finite	finite	NOUN
ejpam-3131	416	9	,	,	PUNCT
ejpam-3131	416	10	such	such	ADJ
ejpam-3131	416	11	that	that	SCONJ
ejpam-3131	416	12	f\	f\	NOUN
ejpam-3131	416	13	∪	∪	ADP
ejpam-3131	416	14	α∈λ0	α∈λ0	NOUN
ejpam-3131	416	15	vα	vα	ADP
ejpam-3131	416	16	∈	∈	PROPN
ejpam-3131	416	17	i.	i.	NOUN
ejpam-3131	416	18	theorem	theorem	VERB
ejpam-3131	416	19	4.3	4.3	NUM
ejpam-3131	416	20	.	.	PUNCT
ejpam-3131	417	1	(	(	PUNCT
ejpam-3131	417	2	1	1	X
ejpam-3131	417	3	)	)	PUNCT
ejpam-3131	417	4	if	if	SCONJ
ejpam-3131	417	5	the	the	DET
ejpam-3131	417	6	space	space	NOUN
ejpam-3131	417	7	(	(	PUNCT
ejpam-3131	417	8	x	x	X
ejpam-3131	417	9	,	,	PUNCT
ejpam-3131	417	10	τ	τ	PROPN
ejpam-3131	417	11	,	,	PUNCT
ejpam-3131	417	12	i⊛	i⊛	PROPN
ejpam-3131	417	13	)	)	PUNCT
ejpam-3131	417	14	is	be	AUX
ejpam-3131	417	15	ρi⊛-compact	ρi⊛-compact	NOUN
ejpam-3131	417	16	then	then	ADV
ejpam-3131	417	17	the	the	DET
ejpam-3131	417	18	space	space	NOUN
ejpam-3131	417	19	(	(	PUNCT
ejpam-3131	417	20	x	x	X
ejpam-3131	417	21	,	,	PUNCT
ejpam-3131	417	22	τ	τ	PROPN
ejpam-3131	417	23	⊕	⊕	PROPN
ejpam-3131	417	24	i	i	PROPN
ejpam-3131	417	25	,	,	PUNCT
ejpam-3131	417	26	i⊛	i⊛	PROPN
ejpam-3131	417	27	)	)	PUNCT
ejpam-3131	417	28	is	be	AUX
ejpam-3131	417	29	i⊛-compact	i⊛-compact	PROPN
ejpam-3131	417	30	.	.	PUNCT
ejpam-3131	418	1	(	(	PUNCT
ejpam-3131	418	2	2	2	X
ejpam-3131	418	3	)	)	PUNCT
ejpam-3131	418	4	if	if	SCONJ
ejpam-3131	418	5	the	the	DET
ejpam-3131	418	6	space	space	NOUN
ejpam-3131	418	7	(	(	PUNCT
ejpam-3131	418	8	x	x	X
ejpam-3131	418	9	,	,	PUNCT
ejpam-3131	418	10	τ	τ	PROPN
ejpam-3131	418	11	,	,	PUNCT
ejpam-3131	418	12	i⊛	i⊛	PROPN
ejpam-3131	418	13	)	)	PUNCT
ejpam-3131	418	14	is	be	AUX
ejpam-3131	418	15	σi⊛-compact	σi⊛-compact	NOUN
ejpam-3131	418	16	then	then	ADV
ejpam-3131	418	17	(	(	PUNCT
ejpam-3131	418	18	x	x	X
ejpam-3131	418	19	,	,	PUNCT
ejpam-3131	418	20	τ	τ	PROPN
ejpam-3131	418	21	⊕	⊕	PROPN
ejpam-3131	418	22	i	i	PROPN
ejpam-3131	418	23	)	)	PUNCT
ejpam-3131	418	24	is	be	AUX
ejpam-3131	418	25	compact	compact	ADJ
ejpam-3131	418	26	.	.	PUNCT
ejpam-3131	419	1	(	(	PUNCT
ejpam-3131	419	2	3	3	X
ejpam-3131	419	3	)	)	PUNCT
ejpam-3131	419	4	if	if	SCONJ
ejpam-3131	419	5	the	the	DET
ejpam-3131	419	6	space	space	NOUN
ejpam-3131	419	7	(	(	PUNCT
ejpam-3131	419	8	x	x	X
ejpam-3131	419	9	,	,	PUNCT
ejpam-3131	419	10	τ	τ	PROPN
ejpam-3131	419	11	⊕	⊕	PROPN
ejpam-3131	419	12	i	i	PROPN
ejpam-3131	419	13	)	)	PUNCT
ejpam-3131	419	14	is	be	AUX
ejpam-3131	419	15	compact	compact	ADJ
ejpam-3131	419	16	then	then	ADV
ejpam-3131	419	17	the	the	DET
ejpam-3131	419	18	space	space	NOUN
ejpam-3131	419	19	(	(	PUNCT
ejpam-3131	419	20	x	x	X
ejpam-3131	419	21	,	,	PUNCT
ejpam-3131	419	22	τ	τ	PROPN
ejpam-3131	419	23	,	,	PUNCT
ejpam-3131	419	24	i	i	PROPN
ejpam-3131	419	25	)	)	PUNCT
ejpam-3131	419	26	is	be	AUX
ejpam-3131	419	27	ρi	ρi	NOUN
ejpam-3131	419	28	-	-	ADJ
ejpam-3131	419	29	compact	compact	ADJ
ejpam-3131	419	30	.	.	PUNCT
ejpam-3131	420	1	(	(	PUNCT
ejpam-3131	420	2	4	4	X
ejpam-3131	420	3	)	)	PUNCT
ejpam-3131	420	4	if	if	SCONJ
ejpam-3131	420	5	the	the	DET
ejpam-3131	420	6	space	space	NOUN
ejpam-3131	420	7	(	(	PUNCT
ejpam-3131	420	8	x	x	X
ejpam-3131	420	9	,	,	PUNCT
ejpam-3131	420	10	τ	τ	PROPN
ejpam-3131	420	11	⊕	⊕	PROPN
ejpam-3131	420	12	i	i	PROPN
ejpam-3131	420	13	)	)	PUNCT
ejpam-3131	420	14	is	be	AUX
ejpam-3131	420	15	c	c	NOUN
ejpam-3131	420	16	-	-	ADJ
ejpam-3131	420	17	compact	compact	ADJ
ejpam-3131	420	18	then	then	ADV
ejpam-3131	420	19	the	the	DET
ejpam-3131	420	20	space	space	NOUN
ejpam-3131	420	21	(	(	PUNCT
ejpam-3131	420	22	x	x	X
ejpam-3131	420	23	,	,	PUNCT
ejpam-3131	420	24	τ	τ	PROPN
ejpam-3131	420	25	,	,	PUNCT
ejpam-3131	420	26	i	i	PROPN
ejpam-3131	420	27	)	)	PUNCT
ejpam-3131	420	28	is	be	AUX
ejpam-3131	420	29	ρc(i)-compact	ρc(i)-compact	ADJ
ejpam-3131	420	30	.	.	PUNCT
ejpam-3131	421	1	(	(	PUNCT
ejpam-3131	421	2	5	5	X
ejpam-3131	421	3	)	)	PUNCT
ejpam-3131	421	4	if	if	SCONJ
ejpam-3131	421	5	(	(	PUNCT
ejpam-3131	421	6	x	x	X
ejpam-3131	421	7	,	,	PUNCT
ejpam-3131	421	8	τ	τ	PROPN
ejpam-3131	421	9	⊕	⊕	PROPN
ejpam-3131	421	10	i	i	PROPN
ejpam-3131	421	11	)	)	PUNCT
ejpam-3131	421	12	is	be	AUX
ejpam-3131	421	13	qhc	qhc	NOUN
ejpam-3131	421	14	then	then	ADV
ejpam-3131	421	15	the	the	DET
ejpam-3131	421	16	space	space	NOUN
ejpam-3131	421	17	(	(	PUNCT
ejpam-3131	421	18	x	x	X
ejpam-3131	421	19	,	,	PUNCT
ejpam-3131	421	20	τ	τ	PROPN
ejpam-3131	421	21	,	,	PUNCT
ejpam-3131	421	22	i	i	PROPN
ejpam-3131	421	23	)	)	PUNCT
ejpam-3131	421	24	is	be	AUX
ejpam-3131	421	25	ρi	ρi	NOUN
ejpam-3131	421	26	-	-	PUNCT
ejpam-3131	421	27	qhc	qhc	PROPN
ejpam-3131	421	28	.	.	PUNCT
ejpam-3131	422	1	references	reference	NOUN
ejpam-3131	422	2	313	313	NUM
ejpam-3131	422	3	proof	proof	NOUN
ejpam-3131	422	4	.	.	PUNCT
ejpam-3131	423	1	(	(	PUNCT
ejpam-3131	423	2	1	1	X
ejpam-3131	423	3	)	)	PUNCT
ejpam-3131	423	4	suppose	suppose	VERB
ejpam-3131	423	5	that	that	SCONJ
ejpam-3131	423	6	x	x	X
ejpam-3131	423	7	=	=	PUNCT
ejpam-3131	423	8	∪	∪	ADP
ejpam-3131	423	9	α∈λ	α∈λ	NOUN
ejpam-3131	423	10	wα	wα	NOUN
ejpam-3131	423	11	,	,	PUNCT
ejpam-3131	423	12	where	where	SCONJ
ejpam-3131	423	13	wα	wα	PROPN
ejpam-3131	423	14	∈	∈	PROPN
ejpam-3131	423	15	τ	τ	PROPN
ejpam-3131	423	16	⊕	⊕	NUM
ejpam-3131	423	17	i	i	PRON
ejpam-3131	423	18	for	for	ADP
ejpam-3131	423	19	each	each	DET
ejpam-3131	423	20	α	α	NOUN
ejpam-3131	423	21	∈	∈	PROPN
ejpam-3131	423	22	λ	λ	PROPN
ejpam-3131	423	23	.	.	PROPN
ejpam-3131	423	24	for	for	ADP
ejpam-3131	423	25	all	all	PRON
ejpam-3131	423	26	α	α	PRON
ejpam-3131	423	27	∈	∈	PROPN
ejpam-3131	423	28	λ	λ	NOUN
ejpam-3131	423	29	,	,	PUNCT
ejpam-3131	423	30	there	there	PRON
ejpam-3131	423	31	exist	exist	VERB
ejpam-3131	423	32	vα	vα	ADP
ejpam-3131	423	33	∈	∈	PROPN
ejpam-3131	423	34	τ	τ	X
ejpam-3131	423	35	and	and	CCONJ
ejpam-3131	423	36	a	a	DET
ejpam-3131	423	37	collection	collection	NOUN
ejpam-3131	423	38	{	{	PUNCT
ejpam-3131	423	39	ij}j∈λα	ij}j∈λα	PROPN
ejpam-3131	423	40	of	of	ADP
ejpam-3131	423	41	elements	element	NOUN
ejpam-3131	423	42	in	in	ADP
ejpam-3131	423	43	i	i	PRON
ejpam-3131	423	44	,	,	PUNCT
ejpam-3131	423	45	such	such	ADJ
ejpam-3131	423	46	that	that	DET
ejpam-3131	423	47	wα	wα	NOUN
ejpam-3131	423	48	=	=	SYM
ejpam-3131	423	49	vα∪	vα∪	NUM
ejpam-3131	423	50	∪	∪	X
ejpam-3131	423	51	j∈λα	j∈λα	ADJ
ejpam-3131	423	52	ij	ij	NOUN
ejpam-3131	423	53	.	.	PUNCT
ejpam-3131	424	1	hence	hence	ADV
ejpam-3131	424	2	x	x	X
ejpam-3131	424	3	=	=	PUNCT
ejpam-3131	424	4	∪	∪	ADP
ejpam-3131	424	5	α∈λ	α∈λ	NOUN
ejpam-3131	424	6	vα	vα	ADP
ejpam-3131	424	7	∪	∪	ADP
ejpam-3131	424	8	∪	∪	ADJ
ejpam-3131	424	9	α∈λ	α∈λ	NOUN
ejpam-3131	424	10	∪	∪	X
ejpam-3131	424	11	j∈λα	j∈λα	ADJ
ejpam-3131	424	12	ij	ij	NOUN
ejpam-3131	424	13	.	.	PUNCT
ejpam-3131	425	1	then	then	ADV
ejpam-3131	425	2	x\	x\	NOUN
ejpam-3131	425	3	∪	∪	ADP
ejpam-3131	425	4	α∈λ	α∈λ	NOUN
ejpam-3131	425	5	vα	vα	ADP
ejpam-3131	425	6	∈	∈	PROPN
ejpam-3131	425	7	i⊛	i⊛	PROPN
ejpam-3131	425	8	and	and	CCONJ
ejpam-3131	425	9	since	since	SCONJ
ejpam-3131	425	10	(	(	PUNCT
ejpam-3131	425	11	x	x	X
ejpam-3131	425	12	,	,	PUNCT
ejpam-3131	425	13	τ	τ	PROPN
ejpam-3131	425	14	,	,	PUNCT
ejpam-3131	425	15	i⊛	i⊛	PROPN
ejpam-3131	425	16	)	)	PUNCT
ejpam-3131	425	17	is	be	AUX
ejpam-3131	425	18	ρi⊛-compact	ρi⊛-compact	ADJ
ejpam-3131	425	19	,	,	PUNCT
ejpam-3131	425	20	there	there	PRON
ejpam-3131	425	21	exists	exist	VERB
ejpam-3131	425	22	λ0	λ0	NOUN
ejpam-3131	425	23	⊆	⊆	NUM
ejpam-3131	425	24	λ	λ	PROPN
ejpam-3131	425	25	,	,	PUNCT
ejpam-3131	425	26	finite	finite	NOUN
ejpam-3131	425	27	,	,	PUNCT
ejpam-3131	425	28	with	with	ADP
ejpam-3131	425	29	x\	x\	NOUN
ejpam-3131	425	30	∪	∪	VERB
ejpam-3131	425	31	α∈λ0	α∈λ0	NOUN
ejpam-3131	425	32	vα	vα	ADP
ejpam-3131	425	33	∈	∈	PROPN
ejpam-3131	425	34	i⊛.	i⊛.	PROPN
ejpam-3131	425	35	this	this	PRON
ejpam-3131	425	36	implies	imply	VERB
ejpam-3131	425	37	that	that	SCONJ
ejpam-3131	425	38	x\	x\	NOUN
ejpam-3131	425	39	∪	∪	ADP
ejpam-3131	425	40	α∈λ0	α∈λ0	PROPN
ejpam-3131	425	41	wα	wα	NOUN
ejpam-3131	425	42	∈	∈	PROPN
ejpam-3131	425	43	i⊛.	i⊛.	PROPN
ejpam-3131	425	44	(	(	PUNCT
ejpam-3131	425	45	3	3	X
ejpam-3131	425	46	)	)	PUNCT
ejpam-3131	425	47	suppose	suppose	VERB
ejpam-3131	425	48	that	that	SCONJ
ejpam-3131	425	49	x\	x\	NOUN
ejpam-3131	425	50	∪	∪	ADP
ejpam-3131	425	51	α∈λ	α∈λ	NOUN
ejpam-3131	425	52	vα	vα	ADP
ejpam-3131	425	53	∈	∈	PROPN
ejpam-3131	425	54	i	i	PRON
ejpam-3131	425	55	,	,	PUNCT
ejpam-3131	425	56	where	where	SCONJ
ejpam-3131	425	57	{	{	PUNCT
ejpam-3131	425	58	vα}α∈λ	vα}α∈λ	CCONJ
ejpam-3131	425	59	is	be	AUX
ejpam-3131	425	60	a	a	DET
ejpam-3131	425	61	collection	collection	NOUN
ejpam-3131	425	62	of	of	ADP
ejpam-3131	425	63	elements	element	NOUN
ejpam-3131	425	64	in	in	ADP
ejpam-3131	425	65	τ	τ	PROPN
ejpam-3131	425	66	.	.	PUNCT
ejpam-3131	426	1	there	there	PRON
ejpam-3131	426	2	exists	exist	VERB
ejpam-3131	426	3	i	i	PRON
ejpam-3131	426	4	∈	∈	VERB
ejpam-3131	427	1	i	i	PRON
ejpam-3131	427	2	such	such	ADJ
ejpam-3131	427	3	that	that	SCONJ
ejpam-3131	427	4	x\	x\	NOUN
ejpam-3131	427	5	∪	∪	ADP
ejpam-3131	427	6	α∈λ	α∈λ	NOUN
ejpam-3131	427	7	vα	vα	ADP
ejpam-3131	428	1	=	=	PUNCT
ejpam-3131	428	2	i	i	PROPN
ejpam-3131	428	3	,	,	PUNCT
ejpam-3131	428	4	and	and	CCONJ
ejpam-3131	428	5	so	so	ADV
ejpam-3131	428	6	x	x	X
ejpam-3131	429	1	=	=	SYM
ejpam-3131	429	2	i∪	i∪	VERB
ejpam-3131	429	3	∪	∪	VERB
ejpam-3131	429	4	α∈λ	α∈λ	NOUN
ejpam-3131	429	5	vα	vα	PROPN
ejpam-3131	429	6	.	.	PUNCT
ejpam-3131	430	1	given	give	VERB
ejpam-3131	430	2	that	that	SCONJ
ejpam-3131	430	3	(	(	PUNCT
ejpam-3131	430	4	x	x	X
ejpam-3131	430	5	,	,	PUNCT
ejpam-3131	430	6	τ	τ	PROPN
ejpam-3131	430	7	⊕	⊕	PROPN
ejpam-3131	430	8	i	i	PROPN
ejpam-3131	430	9	)	)	PUNCT
ejpam-3131	430	10	is	be	AUX
ejpam-3131	430	11	compact	compact	ADJ
ejpam-3131	430	12	there	there	ADV
ejpam-3131	430	13	exists	exist	VERB
ejpam-3131	430	14	λ0	λ0	NOUN
ejpam-3131	430	15	⊆	⊆	NUM
ejpam-3131	430	16	λ	λ	PROPN
ejpam-3131	430	17	,	,	PUNCT
ejpam-3131	430	18	finite	finite	NOUN
ejpam-3131	430	19	,	,	PUNCT
ejpam-3131	430	20	with	with	ADP
ejpam-3131	430	21	x	x	X
ejpam-3131	431	1	=	=	SYM
ejpam-3131	431	2	i∪	i∪	VERB
ejpam-3131	431	3	∪	∪	VERB
ejpam-3131	431	4	α∈λ0	α∈λ0	NOUN
ejpam-3131	431	5	vα	vα	PROPN
ejpam-3131	431	6	.	.	PUNCT
ejpam-3131	432	1	hence	hence	ADV
ejpam-3131	432	2	x\	x\	NOUN
ejpam-3131	432	3	∪	∪	ADP
ejpam-3131	432	4	α∈λ0	α∈λ0	NOUN
ejpam-3131	432	5	vα	vα	ADP
ejpam-3131	432	6	⊆	⊆	NUM
ejpam-3131	432	7	i	i	PRON
ejpam-3131	432	8	∈	∈	PROPN
ejpam-3131	433	1	i	i	PRON
ejpam-3131	433	2	and	and	CCONJ
ejpam-3131	433	3	x\	x\	PROPN
ejpam-3131	433	4	∪	∪	VERB
ejpam-3131	433	5	α∈λ0	α∈λ0	NOUN
ejpam-3131	433	6	vα	vα	ADP
ejpam-3131	433	7	∈	∈	PROPN
ejpam-3131	433	8	i.	i.	NOUN
ejpam-3131	433	9	(	(	PUNCT
ejpam-3131	433	10	4	4	X
ejpam-3131	433	11	)	)	PUNCT
ejpam-3131	433	12	suppose	suppose	VERB
ejpam-3131	433	13	that	that	SCONJ
ejpam-3131	433	14	f\	f\	NOUN
ejpam-3131	433	15	∪	∪	ADP
ejpam-3131	433	16	α∈λ	α∈λ	NOUN
ejpam-3131	433	17	vα	vα	ADP
ejpam-3131	433	18	∈	∈	PROPN
ejpam-3131	434	1	i	i	PRON
ejpam-3131	434	2	,	,	PUNCT
ejpam-3131	434	3	where	where	SCONJ
ejpam-3131	434	4	{	{	PUNCT
ejpam-3131	434	5	vα}α∈λ	vα}α∈λ	CCONJ
ejpam-3131	434	6	is	be	AUX
ejpam-3131	434	7	a	a	DET
ejpam-3131	434	8	collection	collection	NOUN
ejpam-3131	434	9	of	of	ADP
ejpam-3131	434	10	elements	element	NOUN
ejpam-3131	434	11	in	in	ADP
ejpam-3131	434	12	τ	τ	PROPN
ejpam-3131	434	13	and	and	CCONJ
ejpam-3131	434	14	f	f	PROPN
ejpam-3131	434	15	is	be	AUX
ejpam-3131	434	16	closed	close	VERB
ejpam-3131	434	17	in	in	ADP
ejpam-3131	434	18	(	(	PUNCT
ejpam-3131	434	19	x	x	NOUN
ejpam-3131	434	20	,	,	PUNCT
ejpam-3131	434	21	τ	τ	PROPN
ejpam-3131	434	22	)	)	PUNCT
ejpam-3131	434	23	.	.	PUNCT
ejpam-3131	435	1	there	there	PRON
ejpam-3131	435	2	exists	exist	VERB
ejpam-3131	435	3	j	j	PROPN
ejpam-3131	435	4	∈	∈	PROPN
ejpam-3131	435	5	i	i	PRON
ejpam-3131	435	6	with	with	ADP
ejpam-3131	435	7	f\	f\	SYM
ejpam-3131	435	8	∪	∪	ADJ
ejpam-3131	435	9	α∈λ	α∈λ	NOUN
ejpam-3131	435	10	vα	vα	ADP
ejpam-3131	436	1	=	=	SYM
ejpam-3131	436	2	j	j	PROPN
ejpam-3131	436	3	,	,	PUNCT
ejpam-3131	436	4	and	and	CCONJ
ejpam-3131	437	1	so	so	ADV
ejpam-3131	437	2	f	f	PROPN
ejpam-3131	437	3	⊆	⊆	NUM
ejpam-3131	437	4	j	j	PROPN
ejpam-3131	437	5	∪	∪	ADP
ejpam-3131	437	6	∪	∪	ADJ
ejpam-3131	437	7	α∈λ	α∈λ	NOUN
ejpam-3131	437	8	vα	vα	PROPN
ejpam-3131	437	9	.	.	PUNCT
ejpam-3131	438	1	given	give	VERB
ejpam-3131	438	2	that	that	SCONJ
ejpam-3131	438	3	(	(	PUNCT
ejpam-3131	438	4	x	x	X
ejpam-3131	438	5	,	,	PUNCT
ejpam-3131	438	6	τ	τ	PROPN
ejpam-3131	438	7	⊕	⊕	PROPN
ejpam-3131	438	8	i	i	PROPN
ejpam-3131	438	9	)	)	PUNCT
ejpam-3131	438	10	is	be	AUX
ejpam-3131	438	11	c	c	NOUN
ejpam-3131	438	12	-	-	ADJ
ejpam-3131	438	13	compact	compact	ADJ
ejpam-3131	438	14	and	and	CCONJ
ejpam-3131	438	15	f	f	PROPN
ejpam-3131	438	16	is	be	AUX
ejpam-3131	438	17	closed	close	VERB
ejpam-3131	438	18	in	in	ADP
ejpam-3131	438	19	(	(	PUNCT
ejpam-3131	438	20	x	x	X
ejpam-3131	438	21	,	,	PUNCT
ejpam-3131	438	22	τ	τ	PROPN
ejpam-3131	438	23	⊕	⊕	PROPN
ejpam-3131	438	24	i	i	PROPN
ejpam-3131	438	25	)	)	PUNCT
ejpam-3131	438	26	,	,	PUNCT
ejpam-3131	438	27	there	there	PRON
ejpam-3131	438	28	exists	exist	VERB
ejpam-3131	438	29	λ0	λ0	NOUN
ejpam-3131	438	30	⊆	⊆	NUM
ejpam-3131	438	31	λ	λ	PROPN
ejpam-3131	438	32	,	,	PUNCT
ejpam-3131	438	33	finite	finite	NOUN
ejpam-3131	438	34	,	,	PUNCT
ejpam-3131	438	35	with	with	ADP
ejpam-3131	438	36	f	f	PROPN
ejpam-3131	438	37	⊆	⊆	PROPN
ejpam-3131	438	38	adhτ⊕i	adhτ⊕i	PROPN
ejpam-3131	438	39	(	(	PUNCT
ejpam-3131	438	40	j	j	NOUN
ejpam-3131	438	41	)	)	PUNCT
ejpam-3131	438	42	∪	∪	ADP
ejpam-3131	438	43	∪	∪	SYM
ejpam-3131	438	44	α∈λ0	α∈λ0	NOUN
ejpam-3131	438	45	adhτ⊕i(vα	adhτ⊕i(vα	NOUN
ejpam-3131	438	46	)	)	PUNCT
ejpam-3131	438	47	⊆	⊆	NUM
ejpam-3131	438	48	j	j	PROPN
ejpam-3131	438	49	∪	∪	X
ejpam-3131	438	50	∪	∪	ADJ
ejpam-3131	438	51	α∈λ0	α∈λ0	NOUN
ejpam-3131	438	52	vα	vα	PROPN
ejpam-3131	438	53	.	.	PUNCT
ejpam-3131	439	1	hence	hence	ADV
ejpam-3131	439	2	f\	f\	X
ejpam-3131	439	3	∪	∪	ADP
ejpam-3131	439	4	α∈λ0	α∈λ0	NOUN
ejpam-3131	439	5	vα	vα	ADP
ejpam-3131	439	6	⊆	⊆	NUM
ejpam-3131	439	7	j	j	PROPN
ejpam-3131	439	8	∈	∈	PROPN
ejpam-3131	439	9	i	i	PRON
ejpam-3131	439	10	and	and	CCONJ
ejpam-3131	439	11	f\	f\	VERB
ejpam-3131	439	12	∪	∪	ADP
ejpam-3131	439	13	α∈λ0	α∈λ0	NOUN
ejpam-3131	439	14	vα	vα	ADP
ejpam-3131	439	15	∈	∈	PROPN
ejpam-3131	439	16	i.	i.	NOUN
ejpam-3131	439	17	parts	part	NOUN
ejpam-3131	439	18	(	(	PUNCT
ejpam-3131	439	19	2	2	NUM
ejpam-3131	439	20	)	)	PUNCT
ejpam-3131	439	21	and	and	CCONJ
ejpam-3131	439	22	(	(	PUNCT
ejpam-3131	439	23	5	5	X
ejpam-3131	439	24	)	)	PUNCT
ejpam-3131	440	1	have	have	VERB
ejpam-3131	440	2	similar	similar	ADJ
ejpam-3131	440	3	demonstrations	demonstration	NOUN
ejpam-3131	440	4	.	.	PUNCT
ejpam-3131	441	1	□	□	PUNCT
ejpam-3131	441	2	acknowledgements	acknowledgement	NOUN
ejpam-3131	441	3	the	the	DET
ejpam-3131	441	4	author	author	NOUN
ejpam-3131	441	5	wishes	wish	VERB
ejpam-3131	441	6	to	to	PART
ejpam-3131	441	7	express	express	VERB
ejpam-3131	441	8	his	his	PRON
ejpam-3131	441	9	gratitude	gratitude	NOUN
ejpam-3131	441	10	to	to	ADP
ejpam-3131	441	11	the	the	DET
ejpam-3131	441	12	escuela	escuela	PROPN
ejpam-3131	441	13	colombiana	colombiana	PROPN
ejpam-3131	441	14	de	de	PROPN
ejpam-3131	441	15	ingeniería	ingeniería	PROPN
ejpam-3131	441	16	julio	julio	PROPN
ejpam-3131	441	17	garavito	garavito	PROPN
ejpam-3131	441	18	for	for	ADP
ejpam-3131	441	19	financing	finance	VERB
ejpam-3131	441	20	the	the	DET
ejpam-3131	441	21	research	research	NOUN
ejpam-3131	441	22	that	that	PRON
ejpam-3131	441	23	led	lead	VERB
ejpam-3131	441	24	to	to	ADP
ejpam-3131	441	25	this	this	DET
ejpam-3131	441	26	article	article	NOUN
ejpam-3131	441	27	.	.	PUNCT
ejpam-3131	442	1	likewise	likewise	ADV
ejpam-3131	442	2	,	,	PUNCT
ejpam-3131	442	3	the	the	DET
ejpam-3131	442	4	author	author	NOUN
ejpam-3131	442	5	thanks	thank	NOUN
ejpam-3131	442	6	professor	professor	PROPN
ejpam-3131	442	7	carlos	carlos	PROPN
ejpam-3131	442	8	abel	abel	PROPN
ejpam-3131	442	9	alvarez	alvarez	PROPN
ejpam-3131	442	10	,	,	PUNCT
ejpam-3131	442	11	of	of	ADP
ejpam-3131	442	12	the	the	DET
ejpam-3131	442	13	mathematics	mathematic	NOUN
ejpam-3131	442	14	program	program	NOUN
ejpam-3131	442	15	of	of	ADP
ejpam-3131	442	16	this	this	DET
ejpam-3131	442	17	institution	institution	NOUN
ejpam-3131	442	18	,	,	PUNCT
ejpam-3131	442	19	for	for	ADP
ejpam-3131	442	20	his	his	PRON
ejpam-3131	442	21	support	support	NOUN
ejpam-3131	442	22	in	in	ADP
ejpam-3131	442	23	the	the	DET
ejpam-3131	442	24	final	final	ADJ
ejpam-3131	442	25	version	version	NOUN
ejpam-3131	442	26	in	in	ADP
ejpam-3131	442	27	latex	latex	NOUN
ejpam-3131	442	28	of	of	ADP
ejpam-3131	442	29	this	this	DET
ejpam-3131	442	30	paper	paper	NOUN
ejpam-3131	442	31	.	.	PUNCT
ejpam-3131	443	1	references	reference	NOUN
ejpam-3131	443	2	[	[	X
ejpam-3131	443	3	1	1	X
ejpam-3131	443	4	]	]	PUNCT
ejpam-3131	443	5	v.	v.	CCONJ
ejpam-3131	443	6	renuka	renuka	PROPN
ejpam-3131	443	7	devi	devi	PROPN
ejpam-3131	443	8	and	and	CCONJ
ejpam-3131	443	9	d.	d.	PROPN
ejpam-3131	443	10	sivaraj	sivaraj	PROPN
ejpam-3131	443	11	.	.	PUNCT
ejpam-3131	444	1	a	a	DET
ejpam-3131	444	2	generalization	generalization	NOUN
ejpam-3131	444	3	of	of	ADP
ejpam-3131	444	4	normal	normal	ADJ
ejpam-3131	444	5	spaces	space	NOUN
ejpam-3131	444	6	.	.	PUNCT
ejpam-3131	445	1	archivum	archivum	PROPN
ejpam-3131	445	2	mathematicum	mathematicum	PROPN
ejpam-3131	445	3	,	,	PUNCT
ejpam-3131	445	4	44:265–270	44:265–270	PROPN
ejpam-3131	445	5	,	,	PUNCT
ejpam-3131	445	6	2008	2008	NUM
ejpam-3131	445	7	.	.	PUNCT
ejpam-3131	446	1	[	[	X
ejpam-3131	446	2	2	2	X
ejpam-3131	446	3	]	]	PUNCT
ejpam-3131	446	4	s.	s.	PROPN
ejpam-3131	446	5	jafari	jafari	PROPN
ejpam-3131	446	6	and	and	CCONJ
ejpam-3131	446	7	n.	n.	PROPN
ejpam-3131	446	8	rajesh	rajesh	PROPN
ejpam-3131	446	9	.	.	PUNCT
ejpam-3131	447	1	generalized	generalize	VERB
ejpam-3131	447	2	closed	close	VERB
ejpam-3131	447	3	sets	set	NOUN
ejpam-3131	447	4	with	with	ADP
ejpam-3131	447	5	respect	respect	NOUN
ejpam-3131	447	6	to	to	ADP
ejpam-3131	447	7	an	an	DET
ejpam-3131	447	8	ideal	ideal	NOUN
ejpam-3131	447	9	.	.	PUNCT
ejpam-3131	448	1	eur	eur	PROPN
ejpam-3131	448	2	.	.	PUNCT
ejpam-3131	448	3	jour	jour	PROPN
ejpam-3131	448	4	.	.	PROPN
ejpam-3131	449	1	of	of	ADP
ejpam-3131	449	2	pure	pure	ADJ
ejpam-3131	449	3	and	and	CCONJ
ejpam-3131	449	4	app	app	PROPN
ejpam-3131	449	5	.	.	PROPN
ejpam-3131	449	6	math	math	PROPN
ejpam-3131	449	7	,	,	PUNCT
ejpam-3131	449	8	4(2):147–151	4(2):147–151	NUM
ejpam-3131	449	9	,	,	PUNCT
ejpam-3131	449	10	2011	2011	NUM
ejpam-3131	449	11	.	.	PUNCT
ejpam-3131	450	1	references	reference	NOUN
ejpam-3131	450	2	314	314	NUM
ejpam-3131	451	1	[	[	X
ejpam-3131	451	2	3	3	NUM
ejpam-3131	451	3	]	]	X
ejpam-3131	451	4	d.	d.	NOUN
ejpam-3131	451	5	jancovic	jancovic	PROPN
ejpam-3131	451	6	and	and	CCONJ
ejpam-3131	451	7	t.	t.	PROPN
ejpam-3131	451	8	r.	r.	PROPN
ejpam-3131	451	9	hamlett	hamlett	PROPN
ejpam-3131	451	10	.	.	PUNCT
ejpam-3131	452	1	new	new	ADJ
ejpam-3131	452	2	topologies	topology	NOUN
ejpam-3131	452	3	from	from	ADP
ejpam-3131	452	4	old	old	ADJ
ejpam-3131	452	5	via	via	ADP
ejpam-3131	452	6	ideals	ideal	NOUN
ejpam-3131	452	7	.	.	PUNCT
ejpam-3131	453	1	amer	amer	PROPN
ejpam-3131	453	2	.	.	PUNCT
ejpam-3131	453	3	math	math	PROPN
ejpam-3131	453	4	.	.	PUNCT
ejpam-3131	454	1	monthly	monthly	ADJ
ejpam-3131	454	2	,	,	PUNCT
ejpam-3131	454	3	97:295–310	97:295–310	PROPN
ejpam-3131	454	4	,	,	PUNCT
ejpam-3131	454	5	1990	1990	NUM
ejpam-3131	454	6	.	.	PUNCT
ejpam-3131	455	1	[	[	X
ejpam-3131	455	2	4	4	X
ejpam-3131	455	3	]	]	X
ejpam-3131	455	4	d.	d.	NOUN
ejpam-3131	455	5	jancovic	jancovic	PROPN
ejpam-3131	455	6	and	and	CCONJ
ejpam-3131	455	7	t.	t.	PROPN
ejpam-3131	455	8	r.	r.	PROPN
ejpam-3131	455	9	hamlett	hamlett	PROPN
ejpam-3131	455	10	.	.	PUNCT
ejpam-3131	456	1	compatible	compatible	ADJ
ejpam-3131	456	2	extensions	extension	NOUN
ejpam-3131	456	3	of	of	ADP
ejpam-3131	456	4	ideals	ideal	NOUN
ejpam-3131	456	5	.	.	PUNCT
ejpam-3131	457	1	bollettino	bollettino	PROPN
ejpam-3131	457	2	u.	u.	PROPN
ejpam-3131	457	3	m.	m.	PROPN
ejpam-3131	457	4	i.	i.	PROPN
ejpam-3131	457	5	,	,	PUNCT
ejpam-3131	457	6	(	(	PUNCT
ejpam-3131	457	7	7):453–465	7):453–465	NOUN
ejpam-3131	457	8	,	,	PUNCT
ejpam-3131	457	9	1992	1992	NUM
ejpam-3131	457	10	.	.	PUNCT
ejpam-3131	458	1	[	[	X
ejpam-3131	458	2	5	5	NUM
ejpam-3131	458	3	]	]	X
ejpam-3131	458	4	n.	n.	PROPN
ejpam-3131	458	5	levine	levine	PROPN
ejpam-3131	458	6	.	.	PUNCT
ejpam-3131	459	1	generalized	generalize	VERB
ejpam-3131	459	2	closed	closed	ADJ
ejpam-3131	459	3	sets	set	NOUN
ejpam-3131	459	4	in	in	ADP
ejpam-3131	459	5	topology	topology	NOUN
ejpam-3131	459	6	.	.	PUNCT
ejpam-3131	460	1	rend	rend	VERB
ejpam-3131	460	2	.	.	PUNCT
ejpam-3131	461	1	circ	circ	PROPN
ejpam-3131	461	2	.	.	PUNCT
ejpam-3131	462	1	mat	mat	PROPN
ejpam-3131	462	2	.	.	PUNCT
ejpam-3131	462	3	palermo	palermo	NOUN
ejpam-3131	462	4	,	,	PUNCT
ejpam-3131	462	5	19(2):89	19(2):89	NUM
ejpam-3131	462	6	–	–	PUNCT
ejpam-3131	462	7	96	96	NUM
ejpam-3131	462	8	,	,	PUNCT
ejpam-3131	462	9	1970	1970	NUM
ejpam-3131	462	10	.	.	PUNCT
ejpam-3131	463	1	[	[	X
ejpam-3131	463	2	6	6	NUM
ejpam-3131	463	3	]	]	PUNCT
ejpam-3131	463	4	a.	a.	NOUN
ejpam-3131	463	5	s.	s.	PROPN
ejpam-3131	463	6	mashhour	mashhour	PROPN
ejpam-3131	463	7	,	,	PUNCT
ejpam-3131	463	8	m.	m.	PROPN
ejpam-3131	463	9	e.	e.	PROPN
ejpam-3131	463	10	abd	abd	PROPN
ejpam-3131	463	11	el	el	PROPN
ejpam-3131	463	12	-	-	PROPN
ejpam-3131	463	13	monsef	monsef	ADJ
ejpam-3131	463	14	,	,	PUNCT
ejpam-3131	463	15	and	and	CCONJ
ejpam-3131	463	16	s.	s.	PROPN
ejpam-3131	463	17	n.	n.	PROPN
ejpam-3131	463	18	el	el	PROPN
ejpam-3131	463	19	-	-	PUNCT
ejpam-3131	463	20	deep	deep	ADJ
ejpam-3131	463	21	.	.	PUNCT
ejpam-3131	464	1	on	on	ADP
ejpam-3131	464	2	precontinuous	precontinuous	ADJ
ejpam-3131	464	3	and	and	CCONJ
ejpam-3131	464	4	weak	weak	ADJ
ejpam-3131	464	5	precontinuous	precontinuous	ADJ
ejpam-3131	464	6	mappings	mapping	NOUN
ejpam-3131	464	7	.	.	PUNCT
ejpam-3131	465	1	proc	proc	NOUN
ejpam-3131	465	2	.	.	PUNCT
ejpam-3131	466	1	math	math	NOUN
ejpam-3131	466	2	.	.	PUNCT
ejpam-3131	467	1	and	and	CCONJ
ejpam-3131	467	2	phys	phy	NOUN
ejpam-3131	467	3	.	.	PUNCT
ejpam-3131	468	1	soc	soc	PROPN
ejpam-3131	468	2	.	.	PUNCT
ejpam-3131	469	1	of	of	ADP
ejpam-3131	469	2	egypt	egypt	PROPN
ejpam-3131	469	3	,	,	PUNCT
ejpam-3131	469	4	53:47–53	53:47–53	NUM
ejpam-3131	469	5	,	,	PUNCT
ejpam-3131	469	6	1982	1982	NUM
ejpam-3131	469	7	.	.	PUNCT
ejpam-3131	470	1	[	[	X
ejpam-3131	470	2	7	7	X
ejpam-3131	470	3	]	]	X
ejpam-3131	470	4	abd	abd	PROPN
ejpam-3131	470	5	el	el	PROPN
ejpam-3131	470	6	monsef	monsef	PROPN
ejpam-3131	470	7	,	,	PUNCT
ejpam-3131	470	8	e.	e.	PROPN
ejpam-3131	470	9	f.	f.	PROPN
ejpam-3131	470	10	lashien	lashien	PROPN
ejpam-3131	470	11	,	,	PUNCT
ejpam-3131	470	12	and	and	CCONJ
ejpam-3131	470	13	a.	a.	NOUN
ejpam-3131	470	14	a.	a.	NOUN
ejpam-3131	470	15	nasef	nasef	PROPN
ejpam-3131	470	16	.	.	PUNCT
ejpam-3131	471	1	on	on	ADP
ejpam-3131	471	2	i	i	NOUN
ejpam-3131	471	3	-	-	PUNCT
ejpam-3131	471	4	open	open	ADJ
ejpam-3131	471	5	sets	set	NOUN
ejpam-3131	471	6	and	and	CCONJ
ejpam-3131	471	7	i	i	NOUN
ejpam-3131	471	8	-	-	PUNCT
ejpam-3131	471	9	continuous	continuous	ADJ
ejpam-3131	471	10	functions	function	NOUN
ejpam-3131	471	11	.	.	PUNCT
ejpam-3131	472	1	kyungpook	kyungpook	PROPN
ejpam-3131	472	2	math	math	PROPN
ejpam-3131	472	3	.	.	PUNCT
ejpam-3131	473	1	jour	jour	PROPN
ejpam-3131	473	2	.	.	PROPN
ejpam-3131	473	3	,	,	PUNCT
ejpam-3131	473	4	32(1):21–30	32(1):21–30	NUM
ejpam-3131	473	5	,	,	PUNCT
ejpam-3131	473	6	1992	1992	NUM
ejpam-3131	473	7	.	.	PUNCT
ejpam-3131	474	1	[	[	X
ejpam-3131	474	2	8	8	NUM
ejpam-3131	474	3	]	]	X
ejpam-3131	474	4	r.	r.	PROPN
ejpam-3131	474	5	l.	l.	PROPN
ejpam-3131	474	6	newcomb	newcomb	PROPN
ejpam-3131	474	7	.	.	PUNCT
ejpam-3131	475	1	topologies	topology	NOUN
ejpam-3131	475	2	which	which	PRON
ejpam-3131	475	3	are	be	AUX
ejpam-3131	475	4	compact	compact	ADJ
ejpam-3131	475	5	modulo	modulo	NOUN
ejpam-3131	475	6	an	an	DET
ejpam-3131	475	7	ideal	ideal	NOUN
ejpam-3131	475	8	.	.	PUNCT
ejpam-3131	476	1	phd	phd	NOUN
ejpam-3131	476	2	thesis	thesis	PROPN
ejpam-3131	476	3	,	,	PUNCT
ejpam-3131	476	4	univ	univ	PROPN
ejpam-3131	476	5	.	.	PROPN
ejpam-3131	476	6	of	of	ADP
ejpam-3131	476	7	calif	calif	PROPN
ejpam-3131	476	8	.	.	PUNCT
ejpam-3131	477	1	at	at	ADP
ejpam-3131	477	2	santa	santa	PROPN
ejpam-3131	477	3	barbara	barbara	PROPN
ejpam-3131	477	4	.	.	PUNCT
ejpam-3131	478	1	california	california	PROPN
ejpam-3131	478	2	,	,	PUNCT
ejpam-3131	478	3	1967	1967	NUM
ejpam-3131	478	4	.	.	PUNCT
ejpam-3131	479	1	[	[	X
ejpam-3131	479	2	9	9	NUM
ejpam-3131	479	3	]	]	X
ejpam-3131	479	4	n.	n.	PROPN
ejpam-3131	479	5	r.	r.	PROPN
ejpam-3131	479	6	pachón	pachón	PROPN
ejpam-3131	479	7	.	.	PUNCT
ejpam-3131	480	1	new	new	ADJ
ejpam-3131	480	2	forms	form	NOUN
ejpam-3131	480	3	of	of	ADP
ejpam-3131	480	4	strong	strong	ADJ
ejpam-3131	480	5	compactness	compactness	NOUN
ejpam-3131	480	6	in	in	ADP
ejpam-3131	480	7	terms	term	NOUN
ejpam-3131	480	8	of	of	ADP
ejpam-3131	480	9	ideals	ideal	NOUN
ejpam-3131	480	10	.	.	PUNCT
ejpam-3131	481	1	int	int	NOUN
ejpam-3131	481	2	.	.	PUNCT
ejpam-3131	482	1	jour	jour	PROPN
ejpam-3131	482	2	.	.	PROPN
ejpam-3131	483	1	of	of	ADP
ejpam-3131	483	2	pure	pure	ADJ
ejpam-3131	483	3	and	and	CCONJ
ejpam-3131	483	4	app	app	PROPN
ejpam-3131	483	5	.	.	PROPN
ejpam-3131	483	6	math	math	PROPN
ejpam-3131	483	7	.	.	PUNCT
ejpam-3131	483	8	,	,	PUNCT
ejpam-3131	483	9	106(2):481–493	106(2):481–493	NUM
ejpam-3131	483	10	,	,	PUNCT
ejpam-3131	483	11	2016	2016	NUM
ejpam-3131	483	12	.	.	PUNCT
ejpam-3131	484	1	[	[	X
ejpam-3131	484	2	10	10	NUM
ejpam-3131	484	3	]	]	X
ejpam-3131	484	4	n.	n.	PROPN
ejpam-3131	484	5	r.	r.	PROPN
ejpam-3131	484	6	pachón	pachón	PROPN
ejpam-3131	484	7	.	.	PUNCT
ejpam-3131	484	8	ρc(i)-compact	ρc(i)-compact	PROPN
ejpam-3131	484	9	and	and	CCONJ
ejpam-3131	484	10	ρi	ρi	NOUN
ejpam-3131	484	11	-	-	PUNCT
ejpam-3131	484	12	qhc	qhc	NOUN
ejpam-3131	484	13	spaces	space	NOUN
ejpam-3131	484	14	.	.	PUNCT
ejpam-3131	485	1	int	int	NOUN
ejpam-3131	485	2	.	.	PUNCT
ejpam-3131	486	1	jour	jour	PROPN
ejpam-3131	486	2	.	.	PROPN
ejpam-3131	487	1	of	of	ADP
ejpam-3131	487	2	pure	pure	ADJ
ejpam-3131	487	3	and	and	CCONJ
ejpam-3131	487	4	app	app	PROPN
ejpam-3131	487	5	.	.	PROPN
ejpam-3131	487	6	math	math	PROPN
ejpam-3131	487	7	.	.	PUNCT
ejpam-3131	487	8	,	,	PUNCT
ejpam-3131	487	9	108(2):199–214	108(2):199–214	NUM
ejpam-3131	487	10	,	,	PUNCT
ejpam-3131	487	11	2016	2016	NUM
ejpam-3131	487	12	.	.	PUNCT
ejpam-3131	488	1	[	[	X
ejpam-3131	488	2	11	11	NUM
ejpam-3131	488	3	]	]	X
ejpam-3131	488	4	j.	j.	PROPN
ejpam-3131	488	5	porter	porter	PROPN
ejpam-3131	488	6	and	and	CCONJ
ejpam-3131	488	7	j.	j.	PROPN
ejpam-3131	488	8	thomas	thomas	PROPN
ejpam-3131	488	9	.	.	PUNCT
ejpam-3131	489	1	on	on	ADP
ejpam-3131	489	2	h	h	NOUN
ejpam-3131	489	3	-	-	PUNCT
ejpam-3131	489	4	closed	closed	ADJ
ejpam-3131	489	5	and	and	CCONJ
ejpam-3131	489	6	minimal	minimal	ADJ
ejpam-3131	489	7	hausdorff	hausdorff	NOUN
ejpam-3131	489	8	spaces	space	NOUN
ejpam-3131	489	9	.	.	PUNCT
ejpam-3131	490	1	trans	trans	PROPN
ejpam-3131	490	2	.	.	PUNCT
ejpam-3131	491	1	amer	amer	PROPN
ejpam-3131	491	2	.	.	PUNCT
ejpam-3131	491	3	math	math	PROPN
ejpam-3131	491	4	.	.	PUNCT
ejpam-3131	492	1	soc	soc	PROPN
ejpam-3131	492	2	.	.	PUNCT
ejpam-3131	492	3	,	,	PUNCT
ejpam-3131	492	4	138:159–170	138:159–170	NUM
ejpam-3131	492	5	,	,	PUNCT
ejpam-3131	492	6	1969	1969	NUM
ejpam-3131	492	7	.	.	PUNCT
ejpam-3131	493	1	[	[	X
ejpam-3131	493	2	12	12	NUM
ejpam-3131	493	3	]	]	X
ejpam-3131	493	4	r.	r.	PROPN
ejpam-3131	493	5	vaidyanathaswamy	vaidyanathaswamy	PROPN
ejpam-3131	493	6	.	.	PUNCT
ejpam-3131	494	1	the	the	DET
ejpam-3131	494	2	localization	localization	NOUN
ejpam-3131	494	3	theory	theory	NOUN
ejpam-3131	494	4	in	in	ADP
ejpam-3131	494	5	set	set	NOUN
ejpam-3131	494	6	-	-	PUNCT
ejpam-3131	494	7	topology	topology	NOUN
ejpam-3131	494	8	.	.	PUNCT
ejpam-3131	495	1	proc	proc	PROPN
ejpam-3131	495	2	.	.	PUNCT
ejpam-3131	496	1	indian	indian	PROPN
ejpam-3131	496	2	acad	acad	PROPN
ejpam-3131	496	3	.	.	PUNCT
ejpam-3131	497	1	sci	sci	PROPN
ejpam-3131	497	2	.	.	PROPN
ejpam-3131	497	3	,	,	PUNCT
ejpam-3131	497	4	20:51–61	20:51–61	NUM
ejpam-3131	497	5	,	,	PUNCT
ejpam-3131	497	6	1945	1945	NUM
ejpam-3131	497	7	.	.	PUNCT
ejpam-3131	498	1	[	[	X
ejpam-3131	498	2	13	13	NUM
ejpam-3131	498	3	]	]	X
ejpam-3131	498	4	g.	g.	PROPN
ejpam-3131	498	5	viglino	viglino	PROPN
ejpam-3131	498	6	.	.	PUNCT
ejpam-3131	499	1	c	c	X
ejpam-3131	499	2	-	-	PUNCT
ejpam-3131	499	3	compact	compact	ADJ
ejpam-3131	499	4	spaces	space	NOUN
ejpam-3131	499	5	.	.	PUNCT
ejpam-3131	500	1	duke	duke	PROPN
ejpam-3131	500	2	mathematical	mathematical	PROPN
ejpam-3131	500	3	journal	journal	PROPN
ejpam-3131	500	4	,	,	PUNCT
ejpam-3131	500	5	36(4):761–764	36(4):761–764	NUM
ejpam-3131	500	6	,	,	PUNCT
ejpam-3131	500	7	1969	1969	NUM
ejpam-3131	500	8	.	.	PUNCT