id	sid	tid	token	lemma	pos
ejpam-2199	1	1	compile	compile	NOUN
ejpam-2199	1	2	/	/	SYM
ejpam-2199	1	3	output.dvi	output.dvi	NOUN
ejpam-2199	1	4	european	european	ADJ
ejpam-2199	1	5	journal	journal	NOUN
ejpam-2199	1	6	of	of	ADP
ejpam-2199	1	7	pure	pure	ADJ
ejpam-2199	1	8	and	and	CCONJ
ejpam-2199	1	9	applied	apply	VERB
ejpam-2199	1	10	mathematics	mathematic	NOUN
ejpam-2199	1	11	vol	vol	NOUN
ejpam-2199	1	12	.	.	PROPN
ejpam-2199	1	13	8	8	NUM
ejpam-2199	1	14	,	,	PUNCT
ejpam-2199	1	15	no	no	INTJ
ejpam-2199	1	16	.	.	NOUN
ejpam-2199	1	17	4	4	NUM
ejpam-2199	1	18	,	,	PUNCT
ejpam-2199	1	19	2015	2015	NUM
ejpam-2199	1	20	,	,	PUNCT
ejpam-2199	1	21	514	514	NUM
ejpam-2199	1	22	-	-	SYM
ejpam-2199	1	23	525	525	NUM
ejpam-2199	1	24	issn	issn	PROPN
ejpam-2199	1	25	1307	1307	NUM
ejpam-2199	1	26	-	-	SYM
ejpam-2199	1	27	5543	5543	NUM
ejpam-2199	1	28	–	–	PUNCT
ejpam-2199	1	29	www.ejpam.com	www.ejpam.com	X
ejpam-2199	1	30	on	on	ADP
ejpam-2199	1	31	locally	locally	ADV
ejpam-2199	1	32	hurewicz	hurewicz	NOUN
ejpam-2199	1	33	spaces	space	NOUN
ejpam-2199	1	34	clarice	clarice	PROPN
ejpam-2199	1	35	aparecida	aparecida	PROPN
ejpam-2199	1	36	roika1	roika1	PROPN
ejpam-2199	1	37	,	,	PUNCT
ejpam-2199	1	38	soraya	soraya	PROPN
ejpam-2199	1	39	r.t	r.t	PROPN
ejpam-2199	1	40	kudri1∗	kudri1∗	PROPN
ejpam-2199	1	41	,	,	PUNCT
ejpam-2199	1	42	tomaz	tomaz	NOUN
ejpam-2199	1	43	.	.	PUNCT
ejpam-2199	2	1	k.	k.	PROPN
ejpam-2199	2	2	breuckmann1	breuckmann1	PROPN
ejpam-2199	3	1	1department	1department	NUM
ejpam-2199	3	2	of	of	ADP
ejpam-2199	3	3	mathematics	mathematic	NOUN
ejpam-2199	3	4	,	,	PUNCT
ejpam-2199	3	5	federal	federal	ADJ
ejpam-2199	3	6	university	university	PROPN
ejpam-2199	3	7	of	of	ADP
ejpam-2199	3	8	paraná	paraná	PROPN
ejpam-2199	3	9	,	,	PUNCT
ejpam-2199	3	10	p.	p.	PROPN
ejpam-2199	3	11	o.	o.	PROPN
ejpam-2199	3	12	box	box	PROPN
ejpam-2199	3	13	019081	019081	NUM
ejpam-2199	3	14	,	,	PUNCT
ejpam-2199	3	15	curitiba	curitiba	PROPN
ejpam-2199	3	16	,	,	PUNCT
ejpam-2199	3	17	pr	pr	NOUN
ejpam-2199	3	18	,	,	PUNCT
ejpam-2199	3	19	81531990	81531990	NUM
ejpam-2199	3	20	,	,	PUNCT
ejpam-2199	3	21	brazil	brazil	PROPN
ejpam-2199	3	22	.	.	PUNCT
ejpam-2199	4	1	abstract	abstract	ADJ
ejpam-2199	4	2	.	.	PUNCT
ejpam-2199	5	1	in	in	ADP
ejpam-2199	5	2	this	this	DET
ejpam-2199	5	3	paper	paper	NOUN
ejpam-2199	5	4	we	we	PRON
ejpam-2199	5	5	define	define	VERB
ejpam-2199	5	6	locally	locally	ADV
ejpam-2199	5	7	hurewicz	hurewicz	ADJ
ejpam-2199	5	8	spaces	space	NOUN
ejpam-2199	5	9	,	,	PUNCT
ejpam-2199	5	10	weakly	weakly	ADV
ejpam-2199	5	11	locally	locally	ADV
ejpam-2199	5	12	hurewicz	hurewicz	NOUN
ejpam-2199	5	13	spaces	space	NOUN
ejpam-2199	5	14	and	and	CCONJ
ejpam-2199	5	15	relatively	relatively	ADV
ejpam-2199	5	16	locally	locally	ADV
ejpam-2199	5	17	hurewicz	hurewicz	ADJ
ejpam-2199	5	18	spaces	space	NOUN
ejpam-2199	5	19	.	.	PUNCT
ejpam-2199	6	1	we	we	PRON
ejpam-2199	6	2	obtain	obtain	VERB
ejpam-2199	6	3	some	some	DET
ejpam-2199	6	4	results	result	NOUN
ejpam-2199	6	5	and	and	CCONJ
ejpam-2199	6	6	prove	prove	VERB
ejpam-2199	6	7	the	the	DET
ejpam-2199	6	8	equivalence	equivalence	NOUN
ejpam-2199	6	9	of	of	ADP
ejpam-2199	6	10	those	those	DET
ejpam-2199	6	11	definitions	definition	NOUN
ejpam-2199	6	12	in	in	ADP
ejpam-2199	6	13	hausdorff	hausdorff	NOUN
ejpam-2199	6	14	c	c	NOUN
ejpam-2199	6	15	-	-	PUNCT
ejpam-2199	6	16	spaces	space	NOUN
ejpam-2199	6	17	.	.	PUNCT
ejpam-2199	7	1	2010	2010	NUM
ejpam-2199	7	2	mathematics	mathematic	NOUN
ejpam-2199	7	3	subject	subject	NOUN
ejpam-2199	7	4	classifications	classification	NOUN
ejpam-2199	7	5	:	:	PUNCT
ejpam-2199	7	6	54d20	54d20	NUM
ejpam-2199	7	7	key	key	ADJ
ejpam-2199	7	8	words	word	NOUN
ejpam-2199	7	9	and	and	CCONJ
ejpam-2199	7	10	phrases	phrase	NOUN
ejpam-2199	7	11	:	:	PUNCT
ejpam-2199	7	12	hurewicz	hurewicz	NOUN
ejpam-2199	7	13	spaces	space	NOUN
ejpam-2199	7	14	,	,	PUNCT
ejpam-2199	7	15	locally	locally	ADV
ejpam-2199	7	16	hurewicz	hurewicz	NOUN
ejpam-2199	7	17	spaces	space	NOUN
ejpam-2199	7	18	.	.	PUNCT
ejpam-2199	8	1	1	1	X
ejpam-2199	8	2	.	.	X
ejpam-2199	8	3	introduction	introduction	NOUN
ejpam-2199	8	4	in	in	ADP
ejpam-2199	8	5	[	[	X
ejpam-2199	8	6	3	3	NUM
ejpam-2199	8	7	]	]	X
ejpam-2199	8	8	hurewicz	hurewicz	NOUN
ejpam-2199	8	9	introduced	introduce	VERB
ejpam-2199	8	10	the	the	DET
ejpam-2199	8	11	notion	notion	NOUN
ejpam-2199	8	12	of	of	ADP
ejpam-2199	8	13	hurewicz	hurewicz	NOUN
ejpam-2199	8	14	topological	topological	ADJ
ejpam-2199	8	15	spaces	space	NOUN
ejpam-2199	8	16	.	.	PUNCT
ejpam-2199	9	1	those	those	DET
ejpam-2199	9	2	spaces	space	NOUN
ejpam-2199	9	3	generalize	generalize	VERB
ejpam-2199	9	4	compact	compact	ADJ
ejpam-2199	9	5	spaces	space	NOUN
ejpam-2199	9	6	and	and	CCONJ
ejpam-2199	9	7	are	be	AUX
ejpam-2199	9	8	contained	contain	VERB
ejpam-2199	9	9	in	in	ADP
ejpam-2199	9	10	the	the	DET
ejpam-2199	9	11	class	class	NOUN
ejpam-2199	9	12	of	of	ADP
ejpam-2199	9	13	lindelöf	lindelöf	NOUN
ejpam-2199	9	14	spaces	space	NOUN
ejpam-2199	9	15	.	.	PUNCT
ejpam-2199	10	1	the	the	DET
ejpam-2199	10	2	principal	principal	ADJ
ejpam-2199	10	3	purpose	purpose	NOUN
ejpam-2199	10	4	of	of	ADP
ejpam-2199	10	5	this	this	DET
ejpam-2199	10	6	work	work	NOUN
ejpam-2199	10	7	is	be	AUX
ejpam-2199	10	8	to	to	PART
ejpam-2199	10	9	localize	localize	VERB
ejpam-2199	10	10	the	the	DET
ejpam-2199	10	11	hurewicz	hurewicz	NOUN
ejpam-2199	10	12	property	property	NOUN
ejpam-2199	10	13	,	,	PUNCT
ejpam-2199	10	14	introducing	introduce	VERB
ejpam-2199	10	15	here	here	ADV
ejpam-2199	10	16	the	the	DET
ejpam-2199	10	17	locally	locally	ADV
ejpam-2199	10	18	hurewicz	hurewicz	NOUN
ejpam-2199	10	19	spaces	space	NOUN
ejpam-2199	10	20	.	.	PUNCT
ejpam-2199	11	1	in	in	ADP
ejpam-2199	11	2	general	general	ADJ
ejpam-2199	11	3	topology	topology	NOUN
ejpam-2199	11	4	there	there	PRON
ejpam-2199	11	5	are	be	VERB
ejpam-2199	11	6	three	three	NUM
ejpam-2199	11	7	ways	way	NOUN
ejpam-2199	11	8	to	to	PART
ejpam-2199	11	9	define	define	VERB
ejpam-2199	11	10	local	local	ADJ
ejpam-2199	11	11	compactness	compactness	NOUN
ejpam-2199	11	12	,	,	PUNCT
ejpam-2199	11	13	which	which	PRON
ejpam-2199	11	14	here	here	ADV
ejpam-2199	11	15	are	be	AUX
ejpam-2199	11	16	called	call	VERB
ejpam-2199	11	17	local	local	ADJ
ejpam-2199	11	18	compactness	compactness	NOUN
ejpam-2199	11	19	,	,	PUNCT
ejpam-2199	11	20	weak	weak	ADJ
ejpam-2199	11	21	local	local	ADJ
ejpam-2199	11	22	compactness	compactness	NOUN
ejpam-2199	11	23	and	and	CCONJ
ejpam-2199	11	24	relative	relative	ADJ
ejpam-2199	11	25	local	local	ADJ
ejpam-2199	11	26	compactness	compactness	NOUN
ejpam-2199	11	27	.	.	PUNCT
ejpam-2199	12	1	in	in	ADP
ejpam-2199	12	2	this	this	DET
ejpam-2199	12	3	paper	paper	NOUN
ejpam-2199	12	4	we	we	PRON
ejpam-2199	12	5	define	define	VERB
ejpam-2199	12	6	locally	locally	ADV
ejpam-2199	12	7	hurewicz	hurewicz	ADJ
ejpam-2199	12	8	spaces	space	NOUN
ejpam-2199	12	9	,	,	PUNCT
ejpam-2199	12	10	weakly	weakly	ADV
ejpam-2199	12	11	locally	locally	ADV
ejpam-2199	12	12	hurewicz	hurewicz	NOUN
ejpam-2199	12	13	spaces	space	NOUN
ejpam-2199	12	14	and	and	CCONJ
ejpam-2199	12	15	relatively	relatively	ADV
ejpam-2199	12	16	locally	locally	ADV
ejpam-2199	12	17	hurewicz	hurewicz	ADJ
ejpam-2199	12	18	spaces	space	NOUN
ejpam-2199	12	19	,	,	PUNCT
ejpam-2199	12	20	prove	prove	VERB
ejpam-2199	12	21	their	their	PRON
ejpam-2199	12	22	equivalence	equivalence	NOUN
ejpam-2199	12	23	in	in	ADP
ejpam-2199	12	24	hausdorff	hausdorff	NOUN
ejpam-2199	12	25	c	c	NOUN
ejpam-2199	12	26	-	-	PUNCT
ejpam-2199	12	27	spaces	space	NOUN
ejpam-2199	12	28	and	and	CCONJ
ejpam-2199	12	29	study	study	VERB
ejpam-2199	12	30	some	some	PRON
ejpam-2199	12	31	of	of	ADP
ejpam-2199	12	32	their	their	PRON
ejpam-2199	12	33	properties	property	NOUN
ejpam-2199	12	34	.	.	PUNCT
ejpam-2199	13	1	2	2	X
ejpam-2199	13	2	.	.	NUM
ejpam-2199	13	3	preliminaries	preliminary	NOUN
ejpam-2199	13	4	throughout	throughout	ADP
ejpam-2199	13	5	this	this	DET
ejpam-2199	13	6	paper	paper	NOUN
ejpam-2199	13	7	we	we	PRON
ejpam-2199	13	8	use	use	VERB
ejpam-2199	13	9	the	the	DET
ejpam-2199	13	10	notation	notation	NOUN
ejpam-2199	13	11	f	f	PROPN
ejpam-2199	13	12	⊂<∞	⊂<∞	NOUN
ejpam-2199	13	13	x	x	SYM
ejpam-2199	13	14	as	as	ADP
ejpam-2199	13	15	abbreviation	abbreviation	NOUN
ejpam-2199	13	16	for	for	SCONJ
ejpam-2199	13	17	"	"	PUNCT
ejpam-2199	13	18	f	f	PROPN
ejpam-2199	13	19	is	be	AUX
ejpam-2199	13	20	a	a	DET
ejpam-2199	13	21	finite	finite	NOUN
ejpam-2199	13	22	subset	subset	NOUN
ejpam-2199	13	23	of	of	ADP
ejpam-2199	13	24	x	x	X
ejpam-2199	13	25	"	"	PUNCT
ejpam-2199	13	26	.	.	PUNCT
ejpam-2199	14	1	definition	definition	NOUN
ejpam-2199	14	2	1	1	NUM
ejpam-2199	14	3	.	.	PUNCT
ejpam-2199	15	1	[	[	X
ejpam-2199	15	2	4	4	X
ejpam-2199	15	3	]	]	X
ejpam-2199	15	4	a	a	DET
ejpam-2199	15	5	topological	topological	ADJ
ejpam-2199	15	6	space	space	NOUN
ejpam-2199	15	7	〈	〈	NOUN
ejpam-2199	15	8	x	x	X
ejpam-2199	15	9	,	,	PUNCT
ejpam-2199	15	10	t	t	PROPN
ejpam-2199	15	11	〉	〉	NOUN
ejpam-2199	15	12	is	be	AUX
ejpam-2199	15	13	locally	locally	ADV
ejpam-2199	15	14	compact	compact	ADJ
ejpam-2199	15	15	if	if	SCONJ
ejpam-2199	16	1	and	and	CCONJ
ejpam-2199	16	2	only	only	ADV
ejpam-2199	16	3	if	if	SCONJ
ejpam-2199	16	4	for	for	ADP
ejpam-2199	16	5	each	each	DET
ejpam-2199	16	6	x	x	SYM
ejpam-2199	16	7	∈	∈	PROPN
ejpam-2199	16	8	x	x	X
ejpam-2199	16	9	and	and	CCONJ
ejpam-2199	16	10	for	for	ADP
ejpam-2199	16	11	every	every	DET
ejpam-2199	16	12	neighborhood	neighborhood	NOUN
ejpam-2199	16	13	v	v	NOUN
ejpam-2199	16	14	of	of	ADP
ejpam-2199	16	15	x	x	NOUN
ejpam-2199	16	16	,	,	PUNCT
ejpam-2199	16	17	there	there	PRON
ejpam-2199	16	18	are	be	VERB
ejpam-2199	16	19	u	u	PROPN
ejpam-2199	16	20	∈	∈	PROPN
ejpam-2199	16	21	t	t	NOUN
ejpam-2199	16	22	and	and	CCONJ
ejpam-2199	16	23	a	a	DET
ejpam-2199	16	24	compact	compact	ADJ
ejpam-2199	16	25	subset	subset	NOUN
ejpam-2199	16	26	c	c	NOUN
ejpam-2199	16	27	of	of	ADP
ejpam-2199	16	28	x	x	INTJ
ejpam-2199	16	29	such	such	ADJ
ejpam-2199	16	30	that	that	SCONJ
ejpam-2199	16	31	x	x	SYM
ejpam-2199	16	32	∈	∈	PROPN
ejpam-2199	16	33	u	u	X
ejpam-2199	16	34	⊂	⊂	X
ejpam-2199	16	35	c	c	X
ejpam-2199	16	36	⊂	⊂	PROPN
ejpam-2199	16	37	v	v	PROPN
ejpam-2199	16	38	.	.	PUNCT
ejpam-2199	17	1	definition	definition	NOUN
ejpam-2199	17	2	2	2	NUM
ejpam-2199	17	3	.	.	PUNCT
ejpam-2199	18	1	[	[	X
ejpam-2199	18	2	5	5	NUM
ejpam-2199	18	3	]	]	PUNCT
ejpam-2199	18	4	a	a	DET
ejpam-2199	18	5	topological	topological	ADJ
ejpam-2199	18	6	space	space	NOUN
ejpam-2199	18	7	〈	〈	NOUN
ejpam-2199	18	8	x	x	X
ejpam-2199	18	9	,	,	PUNCT
ejpam-2199	18	10	t	t	PROPN
ejpam-2199	18	11	〉	〉	NOUN
ejpam-2199	18	12	is	be	AUX
ejpam-2199	18	13	weakly	weakly	ADV
ejpam-2199	18	14	locally	locally	ADV
ejpam-2199	18	15	compact	compact	ADJ
ejpam-2199	18	16	if	if	SCONJ
ejpam-2199	19	1	and	and	CCONJ
ejpam-2199	19	2	only	only	ADV
ejpam-2199	19	3	if	if	SCONJ
ejpam-2199	19	4	for	for	ADP
ejpam-2199	19	5	each	each	DET
ejpam-2199	19	6	x	x	SYM
ejpam-2199	19	7	∈	∈	PROPN
ejpam-2199	19	8	x	x	VERB
ejpam-2199	19	9	there	there	PRON
ejpam-2199	19	10	are	be	VERB
ejpam-2199	19	11	u	u	PROPN
ejpam-2199	19	12	∈	∈	PROPN
ejpam-2199	19	13	t	t	NOUN
ejpam-2199	19	14	and	and	CCONJ
ejpam-2199	19	15	a	a	DET
ejpam-2199	19	16	compact	compact	ADJ
ejpam-2199	19	17	subset	subset	NOUN
ejpam-2199	19	18	c	c	NOUN
ejpam-2199	19	19	of	of	ADP
ejpam-2199	19	20	x	x	INTJ
ejpam-2199	19	21	such	such	ADJ
ejpam-2199	19	22	that	that	SCONJ
ejpam-2199	19	23	x	x	SYM
ejpam-2199	19	24	∈	∈	PROPN
ejpam-2199	19	25	u	u	NOUN
ejpam-2199	19	26	⊂	⊂	PROPN
ejpam-2199	19	27	c.	c.	PROPN
ejpam-2199	19	28	∗corresponding	∗corresponde	VERB
ejpam-2199	19	29	author	author	NOUN
ejpam-2199	19	30	.	.	PUNCT
ejpam-2199	20	1	email	email	NOUN
ejpam-2199	20	2	address	address	NOUN
ejpam-2199	20	3	:	:	PUNCT
ejpam-2199	20	4	soraya@onda.com.br	soraya@onda.com.br	NOUN
ejpam-2199	20	5	(	(	PUNCT
ejpam-2199	20	6	s.r.t.kudri	s.r.t.kudri	PROPN
ejpam-2199	20	7	)	)	PUNCT
ejpam-2199	20	8	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2199	21	1	514	514	NUM
ejpam-2199	21	2	c	c	X
ejpam-2199	21	3	©	©	PROPN
ejpam-2199	21	4	2015	2015	NUM
ejpam-2199	21	5	ejpam	ejpam	NOUN
ejpam-2199	21	6	all	all	DET
ejpam-2199	21	7	rights	right	NOUN
ejpam-2199	21	8	reserved	reserve	VERB
ejpam-2199	21	9	.	.	PUNCT
ejpam-2199	22	1	c.	c.	PROPN
ejpam-2199	22	2	roika	roika	PROPN
ejpam-2199	22	3	,	,	PUNCT
ejpam-2199	22	4	s.	s.	PROPN
ejpam-2199	22	5	kudri	kudri	PROPN
ejpam-2199	22	6	,	,	PUNCT
ejpam-2199	22	7	t.	t.	PROPN
ejpam-2199	22	8	breuckmann	breuckmann	PROPN
ejpam-2199	22	9	/	/	SYM
ejpam-2199	22	10	eur	eur	PROPN
ejpam-2199	22	11	.	.	PUNCT
ejpam-2199	23	1	j.	j.	PROPN
ejpam-2199	23	2	pure	pure	PROPN
ejpam-2199	23	3	appl	appl	PROPN
ejpam-2199	23	4	.	.	PROPN
ejpam-2199	23	5	math	math	PROPN
ejpam-2199	23	6	,	,	PUNCT
ejpam-2199	23	7	8	8	NUM
ejpam-2199	23	8	(	(	PUNCT
ejpam-2199	23	9	2015	2015	NUM
ejpam-2199	23	10	)	)	PUNCT
ejpam-2199	23	11	,	,	PUNCT
ejpam-2199	23	12	514	514	NUM
ejpam-2199	23	13	-	-	SYM
ejpam-2199	23	14	525	525	NUM
ejpam-2199	23	15	515	515	NUM
ejpam-2199	23	16	definition	definition	NOUN
ejpam-2199	23	17	3	3	NUM
ejpam-2199	23	18	.	.	PUNCT
ejpam-2199	24	1	[	[	X
ejpam-2199	24	2	2	2	X
ejpam-2199	24	3	]	]	PUNCT
ejpam-2199	24	4	a	a	DET
ejpam-2199	24	5	topological	topological	ADJ
ejpam-2199	24	6	space	space	NOUN
ejpam-2199	24	7	〈	〈	NOUN
ejpam-2199	24	8	x	x	X
ejpam-2199	24	9	,	,	PUNCT
ejpam-2199	24	10	t	t	PROPN
ejpam-2199	24	11	〉	〉	NOUN
ejpam-2199	24	12	is	be	AUX
ejpam-2199	24	13	relatively	relatively	ADV
ejpam-2199	24	14	locally	locally	ADV
ejpam-2199	24	15	compact	compact	ADJ
ejpam-2199	24	16	if	if	SCONJ
ejpam-2199	25	1	and	and	CCONJ
ejpam-2199	25	2	only	only	ADV
ejpam-2199	25	3	if	if	SCONJ
ejpam-2199	25	4	for	for	ADP
ejpam-2199	25	5	each	each	DET
ejpam-2199	25	6	x	x	SYM
ejpam-2199	25	7	∈	∈	PROPN
ejpam-2199	25	8	x	x	VERB
ejpam-2199	25	9	there	there	PRON
ejpam-2199	25	10	are	be	VERB
ejpam-2199	25	11	u	u	PROPN
ejpam-2199	25	12	∈	∈	PROPN
ejpam-2199	25	13	t	t	NOUN
ejpam-2199	25	14	such	such	ADJ
ejpam-2199	25	15	that	that	SCONJ
ejpam-2199	25	16	x	x	SYM
ejpam-2199	25	17	∈	∈	PROPN
ejpam-2199	25	18	u	u	NOUN
ejpam-2199	25	19	and	and	CCONJ
ejpam-2199	25	20	u	u	NOUN
ejpam-2199	25	21	is	be	AUX
ejpam-2199	25	22	compact	compact	ADJ
ejpam-2199	25	23	.	.	PUNCT
ejpam-2199	26	1	definition	definition	NOUN
ejpam-2199	26	2	4	4	NUM
ejpam-2199	26	3	.	.	PUNCT
ejpam-2199	27	1	[	[	X
ejpam-2199	27	2	1	1	X
ejpam-2199	27	3	]	]	PUNCT
ejpam-2199	27	4	in	in	ADP
ejpam-2199	27	5	any	any	DET
ejpam-2199	27	6	nonempty	nonempty	ADV
ejpam-2199	27	7	set	set	VERB
ejpam-2199	27	8	x	x	PUNCT
ejpam-2199	27	9	we	we	PRON
ejpam-2199	27	10	can	can	AUX
ejpam-2199	27	11	define	define	VERB
ejpam-2199	27	12	a	a	DET
ejpam-2199	27	13	topology	topology	NOUN
ejpam-2199	27	14	t	t	NOUN
ejpam-2199	27	15	by	by	ADP
ejpam-2199	27	16	considering	consider	VERB
ejpam-2199	27	17	as	as	SCONJ
ejpam-2199	27	18	open	open	ADJ
ejpam-2199	27	19	sets	set	VERB
ejpam-2199	27	20	the	the	DET
ejpam-2199	27	21	empty	empty	ADJ
ejpam-2199	27	22	set	set	NOUN
ejpam-2199	27	23	and	and	CCONJ
ejpam-2199	27	24	all	all	DET
ejpam-2199	27	25	subsets	subset	NOUN
ejpam-2199	27	26	of	of	ADP
ejpam-2199	27	27	x	x	PUNCT
ejpam-2199	27	28	containing	contain	VERB
ejpam-2199	27	29	a	a	DET
ejpam-2199	27	30	particular	particular	ADJ
ejpam-2199	27	31	point	point	NOUN
ejpam-2199	27	32	p	p	X
ejpam-2199	27	33	∈	∈	PROPN
ejpam-2199	27	34	x	x	X
ejpam-2199	27	35	.	.	PUNCT
ejpam-2199	28	1	we	we	PRON
ejpam-2199	28	2	shall	shall	AUX
ejpam-2199	28	3	call	call	VERB
ejpam-2199	28	4	it	it	PRON
ejpam-2199	28	5	the	the	DET
ejpam-2199	28	6	particular	particular	ADJ
ejpam-2199	28	7	point	point	NOUN
ejpam-2199	28	8	p	p	PRON
ejpam-2199	28	9	topology	topology	NOUN
ejpam-2199	28	10	.	.	PUNCT
ejpam-2199	29	1	definition	definition	NOUN
ejpam-2199	29	2	5	5	NUM
ejpam-2199	29	3	.	.	PUNCT
ejpam-2199	30	1	[	[	X
ejpam-2199	30	2	3	3	X
ejpam-2199	30	3	]	]	PUNCT
ejpam-2199	30	4	a	a	DET
ejpam-2199	30	5	topological	topological	ADJ
ejpam-2199	30	6	space	space	NOUN
ejpam-2199	30	7	〈	〈	NOUN
ejpam-2199	30	8	x	x	X
ejpam-2199	30	9	,	,	PUNCT
ejpam-2199	30	10	t	t	PROPN
ejpam-2199	30	11	〉	〉	NOUN
ejpam-2199	30	12	is	be	AUX
ejpam-2199	30	13	hurewicz	hurewicz	NOUN
ejpam-2199	30	14	if	if	SCONJ
ejpam-2199	30	15	and	and	CCONJ
ejpam-2199	30	16	only	only	ADV
ejpam-2199	30	17	if	if	SCONJ
ejpam-2199	30	18	for	for	ADP
ejpam-2199	30	19	each	each	DET
ejpam-2199	30	20	sequence	sequence	NOUN
ejpam-2199	30	21	{	{	PUNCT
ejpam-2199	30	22	un}n∈n	un}n∈n	NOUN
ejpam-2199	30	23	of	of	ADP
ejpam-2199	30	24	open	open	ADJ
ejpam-2199	30	25	coverings	covering	NOUN
ejpam-2199	30	26	of	of	ADP
ejpam-2199	30	27	x	x	SYM
ejpam-2199	30	28	,	,	PUNCT
ejpam-2199	30	29	there	there	PRON
ejpam-2199	30	30	exists	exist	VERB
ejpam-2199	30	31	a	a	DET
ejpam-2199	30	32	sequence	sequence	NOUN
ejpam-2199	30	33	{	{	PUNCT
ejpam-2199	30	34	vn}n∈n	vn}n∈n	ADP
ejpam-2199	30	35	such	such	ADJ
ejpam-2199	30	36	that	that	PRON
ejpam-2199	30	37	:	:	PUNCT
ejpam-2199	30	38	(	(	PUNCT
ejpam-2199	30	39	i	i	NOUN
ejpam-2199	30	40	)	)	PUNCT
ejpam-2199	30	41	for	for	ADP
ejpam-2199	30	42	each	each	DET
ejpam-2199	30	43	n	n	PRON
ejpam-2199	30	44	∈	∈	PROPN
ejpam-2199	30	45	n	n	CCONJ
ejpam-2199	30	46	,	,	PUNCT
ejpam-2199	30	47	vn	vn	PROPN
ejpam-2199	30	48	⊂<∞	⊂<∞	PROPN
ejpam-2199	30	49	un	un	PROPN
ejpam-2199	30	50	.	.	PROPN
ejpam-2199	30	51	(	(	PUNCT
ejpam-2199	30	52	ii	ii	NOUN
ejpam-2199	30	53	)	)	PUNCT
ejpam-2199	30	54	∀x	∀x	VERB
ejpam-2199	30	55	∈	∈	PROPN
ejpam-2199	30	56	x	x	X
ejpam-2199	30	57	,	,	PUNCT
ejpam-2199	30	58	∃n0	∃n0	NOUN
ejpam-2199	30	59	∈	∈	PROPN
ejpam-2199	30	60	n	n	PRON
ejpam-2199	30	61	such	such	ADJ
ejpam-2199	30	62	that	that	SCONJ
ejpam-2199	30	63	∀n	∀n	NUM
ejpam-2199	30	64	∈	∈	NOUN
ejpam-2199	30	65	n	n	ADV
ejpam-2199	30	66	if	if	SCONJ
ejpam-2199	30	67	n≥	n≥	PROPN
ejpam-2199	30	68	n0	n0	NUM
ejpam-2199	30	69	,	,	PUNCT
ejpam-2199	30	70	there	there	PRON
ejpam-2199	30	71	exists	exist	VERB
ejpam-2199	30	72	v	v	ADP
ejpam-2199	30	73	∈	∈	PROPN
ejpam-2199	30	74	vn	vn	NOUN
ejpam-2199	30	75	with	with	ADP
ejpam-2199	30	76	x	x	PROPN
ejpam-2199	30	77	∈	∈	PROPN
ejpam-2199	30	78	v	v	NOUN
ejpam-2199	30	79	.	.	PUNCT
ejpam-2199	30	80	example	example	NOUN
ejpam-2199	31	1	1	1	NUM
ejpam-2199	31	2	.	.	PUNCT
ejpam-2199	32	1	the	the	DET
ejpam-2199	32	2	real	real	ADJ
ejpam-2199	32	3	line	line	NOUN
ejpam-2199	32	4	r	r	NOUN
ejpam-2199	32	5	in	in	ADP
ejpam-2199	32	6	its	its	PRON
ejpam-2199	32	7	usual	usual	ADJ
ejpam-2199	32	8	topology	topology	NOUN
ejpam-2199	32	9	is	be	AUX
ejpam-2199	32	10	a	a	DET
ejpam-2199	32	11	hurewicz	hurewicz	NOUN
ejpam-2199	32	12	space	space	NOUN
ejpam-2199	32	13	.	.	PUNCT
ejpam-2199	33	1	let	let	VERB
ejpam-2199	33	2	{	{	PUNCT
ejpam-2199	33	3	un}n∈n	un}n∈n	PRON
ejpam-2199	33	4	be	be	AUX
ejpam-2199	33	5	a	a	DET
ejpam-2199	33	6	sequence	sequence	NOUN
ejpam-2199	33	7	of	of	ADP
ejpam-2199	33	8	open	open	ADJ
ejpam-2199	33	9	coverings	covering	NOUN
ejpam-2199	33	10	of	of	ADP
ejpam-2199	33	11	r	r	NOUN
ejpam-2199	33	12	,	,	PUNCT
ejpam-2199	33	13	where	where	SCONJ
ejpam-2199	33	14	un	un	PROPN
ejpam-2199	33	15	=	=	PRON
ejpam-2199	33	16	{	{	PUNCT
ejpam-2199	33	17	un	un	PROPN
ejpam-2199	33	18	j	j	PROPN
ejpam-2199	33	19	}	}	PUNCT
ejpam-2199	33	20	j∈jn	j∈jn	NOUN
ejpam-2199	33	21	.	.	PUNCT
ejpam-2199	34	1	since	since	SCONJ
ejpam-2199	34	2	for	for	ADP
ejpam-2199	34	3	each	each	DET
ejpam-2199	34	4	n	n	PRON
ejpam-2199	34	5	∈	∈	PROPN
ejpam-2199	34	6	n	n	CCONJ
ejpam-2199	34	7	,	,	PUNCT
ejpam-2199	34	8	[	[	X
ejpam-2199	34	9	−n	−n	ADJ
ejpam-2199	34	10	,	,	PUNCT
ejpam-2199	34	11	n	n	CCONJ
ejpam-2199	34	12	]	]	X
ejpam-2199	34	13	⊂	⊂	X
ejpam-2199	34	14	r	r	NOUN
ejpam-2199	34	15	is	be	AUX
ejpam-2199	34	16	compact	compact	ADJ
ejpam-2199	34	17	,	,	PUNCT
ejpam-2199	34	18	∃in	∃in	PROPN
ejpam-2199	34	19	⊂<∞	⊂<∞	PROPN
ejpam-2199	34	20	jn	jn	PROPN
ejpam-2199	34	21	such	such	ADJ
ejpam-2199	34	22	that	that	DET
ejpam-2199	34	23	vn	vn	PROPN
ejpam-2199	34	24	=	=	PRON
ejpam-2199	34	25	{	{	PUNCT
ejpam-2199	34	26	un	un	PROPN
ejpam-2199	34	27	j	j	PROPN
ejpam-2199	34	28	}	}	PUNCT
ejpam-2199	34	29	j∈in	j∈in	PROPN
ejpam-2199	34	30	covers	cover	VERB
ejpam-2199	34	31	[	[	X
ejpam-2199	34	32	−n	−n	ADJ
ejpam-2199	34	33	,	,	PUNCT
ejpam-2199	34	34	n	n	CCONJ
ejpam-2199	34	35	]	]	PUNCT
ejpam-2199	34	36	,	,	PUNCT
ejpam-2199	34	37	then	then	ADV
ejpam-2199	34	38	the	the	DET
ejpam-2199	34	39	sequence	sequence	NOUN
ejpam-2199	34	40	{	{	PUNCT
ejpam-2199	34	41	vn}n∈n	vn}n∈n	X
ejpam-2199	34	42	is	be	AUX
ejpam-2199	34	43	such	such	ADJ
ejpam-2199	34	44	that	that	SCONJ
ejpam-2199	34	45	:	:	PUNCT
ejpam-2199	34	46	(	(	PUNCT
ejpam-2199	34	47	i	i	NOUN
ejpam-2199	34	48	)	)	PUNCT
ejpam-2199	34	49	∀n	∀n	PROPN
ejpam-2199	34	50	∈	∈	PROPN
ejpam-2199	34	51	n	n	CCONJ
ejpam-2199	34	52	,	,	PUNCT
ejpam-2199	34	53	in	in	ADP
ejpam-2199	34	54	⊂<∞	⊂<∞	PROPN
ejpam-2199	34	55	jn	jn	PROPN
ejpam-2199	34	56	and	and	CCONJ
ejpam-2199	34	57	vn	vn	PROPN
ejpam-2199	34	58	=	=	PUNCT
ejpam-2199	34	59	{	{	PUNCT
ejpam-2199	34	60	un	un	PROPN
ejpam-2199	34	61	j	j	PROPN
ejpam-2199	34	62	}	}	PUNCT
ejpam-2199	34	63	j∈in	j∈in	PROPN
ejpam-2199	34	64	,	,	PUNCT
ejpam-2199	34	65	then	then	ADV
ejpam-2199	34	66	we	we	PRON
ejpam-2199	34	67	have	have	VERB
ejpam-2199	34	68	vn	vn	PROPN
ejpam-2199	34	69	⊂<∞	⊂<∞	PROPN
ejpam-2199	34	70	un	un	PROPN
ejpam-2199	34	71	.	.	PROPN
ejpam-2199	34	72	(	(	PUNCT
ejpam-2199	34	73	ii	ii	NOUN
ejpam-2199	34	74	)	)	PUNCT
ejpam-2199	34	75	for	for	ADP
ejpam-2199	34	76	each	each	DET
ejpam-2199	34	77	x	x	SYM
ejpam-2199	34	78	∈	∈	PROPN
ejpam-2199	34	79	r	r	NOUN
ejpam-2199	34	80	,	,	PUNCT
ejpam-2199	34	81	we	we	PRON
ejpam-2199	34	82	have	have	VERB
ejpam-2199	34	83	that	that	SCONJ
ejpam-2199	34	84	there	there	PRON
ejpam-2199	34	85	is	be	VERB
ejpam-2199	34	86	n0	n0	NUM
ejpam-2199	34	87	∈	∈	PROPN
ejpam-2199	34	88	n	n	CCONJ
ejpam-2199	34	89	such	such	ADJ
ejpam-2199	34	90	that	that	DET
ejpam-2199	34	91	|x	|x	NOUN
ejpam-2199	34	92	|	|	ADV
ejpam-2199	34	93	≤	≤	PUNCT
ejpam-2199	34	94	n0	n0	NUM
ejpam-2199	34	95	.	.	PUNCT
ejpam-2199	35	1	for	for	ADP
ejpam-2199	35	2	n	n	PRON
ejpam-2199	35	3	∈	∈	PROPN
ejpam-2199	35	4	n	n	CCONJ
ejpam-2199	35	5	,	,	PUNCT
ejpam-2199	35	6	if	if	SCONJ
ejpam-2199	35	7	n≥	n≥	PROPN
ejpam-2199	35	8	n0	n0	NUM
ejpam-2199	35	9	,	,	PUNCT
ejpam-2199	35	10	then	then	ADV
ejpam-2199	35	11	|x	|x	NOUN
ejpam-2199	35	12	|	|	ADV
ejpam-2199	35	13	≤	≤	NUM
ejpam-2199	35	14	n	n	CCONJ
ejpam-2199	35	15	,	,	PUNCT
ejpam-2199	35	16	i.e.	i.e.	X
ejpam-2199	35	17	,	,	PUNCT
ejpam-2199	35	18	x	x	SYM
ejpam-2199	35	19	∈	∈	PROPN
ejpam-2199	35	20	[	[	X
ejpam-2199	35	21	−n	−n	NOUN
ejpam-2199	35	22	,	,	PUNCT
ejpam-2199	35	23	n	n	CCONJ
ejpam-2199	35	24	]	]	PUNCT
ejpam-2199	35	25	.	.	PUNCT
ejpam-2199	36	1	but	but	CCONJ
ejpam-2199	36	2	vn	vn	PROPN
ejpam-2199	36	3	=	=	SYM
ejpam-2199	36	4	{	{	PUNCT
ejpam-2199	36	5	un	un	PROPN
ejpam-2199	36	6	j	j	PROPN
ejpam-2199	36	7	}	}	PUNCT
ejpam-2199	36	8	j∈in	j∈in	PROPN
ejpam-2199	36	9	covers	cover	VERB
ejpam-2199	36	10	[	[	X
ejpam-2199	36	11	−n	−n	ADJ
ejpam-2199	36	12	,	,	PUNCT
ejpam-2199	36	13	n	n	CCONJ
ejpam-2199	36	14	]	]	PUNCT
ejpam-2199	36	15	,	,	PUNCT
ejpam-2199	36	16	so	so	CCONJ
ejpam-2199	36	17	there	there	PRON
ejpam-2199	36	18	exists	exist	VERB
ejpam-2199	36	19	j	j	PROPN
ejpam-2199	36	20	∈	∈	PROPN
ejpam-2199	36	21	in	in	ADP
ejpam-2199	36	22	such	such	ADJ
ejpam-2199	36	23	that	that	SCONJ
ejpam-2199	36	24	x	x	SYM
ejpam-2199	36	25	∈	∈	PROPN
ejpam-2199	36	26	un	un	PROPN
ejpam-2199	36	27	j	j	PROPN
ejpam-2199	36	28	∈	∈	PROPN
ejpam-2199	36	29	vn	vn	PROPN
ejpam-2199	36	30	.	.	PUNCT
ejpam-2199	37	1	proposition	proposition	NOUN
ejpam-2199	37	2	1	1	NUM
ejpam-2199	37	3	.	.	PUNCT
ejpam-2199	38	1	let	let	VERB
ejpam-2199	38	2	x	x	PUNCT
ejpam-2199	38	3	=	=	SYM
ejpam-2199	38	4	⋃	⋃	NOUN
ejpam-2199	38	5	i∈n	i∈n	NOUN
ejpam-2199	38	6	ki	ki	PROPN
ejpam-2199	38	7	,	,	PUNCT
ejpam-2199	38	8	where	where	SCONJ
ejpam-2199	38	9	∀i	∀i	NOUN
ejpam-2199	38	10	∈	∈	NOUN
ejpam-2199	38	11	n	n	CCONJ
ejpam-2199	38	12	,	,	PUNCT
ejpam-2199	38	13	ki	ki	PROPN
ejpam-2199	38	14	is	be	AUX
ejpam-2199	38	15	compact	compact	ADJ
ejpam-2199	38	16	and	and	CCONJ
ejpam-2199	38	17	ki	ki	PROPN
ejpam-2199	38	18	⊂	⊂	PROPN
ejpam-2199	38	19	ki+1	ki+1	PROPN
ejpam-2199	38	20	,	,	PUNCT
ejpam-2199	38	21	then	then	ADV
ejpam-2199	38	22	x	x	PUNCT
ejpam-2199	38	23	is	be	AUX
ejpam-2199	38	24	hurewicz	hurewicz	NOUN
ejpam-2199	38	25	.	.	PUNCT
ejpam-2199	39	1	proof	proof	NOUN
ejpam-2199	39	2	.	.	PUNCT
ejpam-2199	40	1	let	let	VERB
ejpam-2199	40	2	{	{	PUNCT
ejpam-2199	40	3	un}n∈n	un}n∈n	PRON
ejpam-2199	40	4	be	be	AUX
ejpam-2199	40	5	a	a	DET
ejpam-2199	40	6	sequence	sequence	NOUN
ejpam-2199	40	7	of	of	ADP
ejpam-2199	40	8	open	open	ADJ
ejpam-2199	40	9	coverings	covering	NOUN
ejpam-2199	40	10	of	of	ADP
ejpam-2199	40	11	x	x	SYM
ejpam-2199	40	12	,	,	PUNCT
ejpam-2199	40	13	where	where	SCONJ
ejpam-2199	40	14	each	each	DET
ejpam-2199	40	15	un	un	PROPN
ejpam-2199	41	1	=	=	PRON
ejpam-2199	41	2	{	{	PUNCT
ejpam-2199	41	3	un	un	PROPN
ejpam-2199	41	4	j	j	PROPN
ejpam-2199	41	5	}	}	PUNCT
ejpam-2199	41	6	j∈jn	j∈jn	NOUN
ejpam-2199	41	7	.	.	PUNCT
ejpam-2199	42	1	since	since	SCONJ
ejpam-2199	42	2	∀n	∀n	NUM
ejpam-2199	42	3	∈	∈	PROPN
ejpam-2199	42	4	n	n	CCONJ
ejpam-2199	42	5	,	,	PUNCT
ejpam-2199	42	6	kn	kn	PROPN
ejpam-2199	42	7	⊂	⊂	PROPN
ejpam-2199	42	8	x	x	INTJ
ejpam-2199	42	9	we	we	PRON
ejpam-2199	42	10	have	have	VERB
ejpam-2199	42	11	that	that	DET
ejpam-2199	42	12	un	un	PROPN
ejpam-2199	42	13	covers	cover	VERB
ejpam-2199	42	14	kn	kn	PROPN
ejpam-2199	42	15	and	and	CCONJ
ejpam-2199	42	16	by	by	ADP
ejpam-2199	42	17	the	the	DET
ejpam-2199	42	18	compactness	compactness	NOUN
ejpam-2199	42	19	of	of	ADP
ejpam-2199	42	20	kn	kn	PROPN
ejpam-2199	42	21	there	there	PRON
ejpam-2199	42	22	is	be	VERB
ejpam-2199	42	23	in	in	ADP
ejpam-2199	42	24	⊂<∞	⊂<∞	PROPN
ejpam-2199	42	25	jn	jn	PROPN
ejpam-2199	42	26	such	such	ADJ
ejpam-2199	42	27	that	that	SCONJ
ejpam-2199	42	28	kn	kn	PROPN
ejpam-2199	42	29	⊂	⊂	PROPN
ejpam-2199	42	30	⋃	⋃	PROPN
ejpam-2199	42	31	j∈in	j∈in	PROPN
ejpam-2199	42	32	un	un	PROPN
ejpam-2199	42	33	j	j	PROPN
ejpam-2199	42	34	.	.	PUNCT
ejpam-2199	43	1	for	for	ADP
ejpam-2199	43	2	each	each	DET
ejpam-2199	43	3	n	n	PRON
ejpam-2199	43	4	∈	∈	PROPN
ejpam-2199	43	5	n	n	ADV
ejpam-2199	43	6	let	let	VERB
ejpam-2199	43	7	vn	vn	VERB
ejpam-2199	43	8	=	=	PRON
ejpam-2199	43	9	{	{	PUNCT
ejpam-2199	43	10	un	un	PROPN
ejpam-2199	43	11	j	j	PROPN
ejpam-2199	43	12	}	}	PUNCT
ejpam-2199	43	13	j∈in	j∈in	PROPN
ejpam-2199	43	14	,	,	PUNCT
ejpam-2199	43	15	then	then	ADV
ejpam-2199	43	16	the	the	DET
ejpam-2199	43	17	sequence	sequence	NOUN
ejpam-2199	43	18	{	{	PUNCT
ejpam-2199	43	19	vn	vn	PROPN
ejpam-2199	43	20	j}n∈n	j}n∈n	ADV
ejpam-2199	43	21	is	be	AUX
ejpam-2199	43	22	such	such	ADJ
ejpam-2199	43	23	that	that	SCONJ
ejpam-2199	43	24	:	:	PUNCT
ejpam-2199	43	25	(	(	PUNCT
ejpam-2199	43	26	i	i	NOUN
ejpam-2199	43	27	)	)	PUNCT
ejpam-2199	43	28	∀n	∀n	PROPN
ejpam-2199	43	29	∈	∈	PROPN
ejpam-2199	43	30	n	n	CCONJ
ejpam-2199	43	31	,	,	PUNCT
ejpam-2199	43	32	vn	vn	PROPN
ejpam-2199	43	33	⊂<∞	⊂<∞	PROPN
ejpam-2199	43	34	un	un	PROPN
ejpam-2199	43	35	.	.	PROPN
ejpam-2199	43	36	(	(	PUNCT
ejpam-2199	43	37	ii	ii	NOUN
ejpam-2199	43	38	)	)	PUNCT
ejpam-2199	43	39	for	for	ADP
ejpam-2199	43	40	each	each	DET
ejpam-2199	43	41	x	x	SYM
ejpam-2199	43	42	∈	∈	PROPN
ejpam-2199	43	43	x	x	X
ejpam-2199	43	44	,	,	PUNCT
ejpam-2199	43	45	since	since	SCONJ
ejpam-2199	43	46	x	x	X
ejpam-2199	43	47	=	=	SYM
ejpam-2199	43	48	⋃	⋃	NOUN
ejpam-2199	43	49	i∈n	i∈n	NOUN
ejpam-2199	43	50	ki	ki	PROPN
ejpam-2199	43	51	there	there	PRON
ejpam-2199	43	52	exists	exist	VERB
ejpam-2199	43	53	n0	n0	PROPN
ejpam-2199	43	54	∈	∈	PROPN
ejpam-2199	43	55	n	n	PRON
ejpam-2199	43	56	such	such	ADJ
ejpam-2199	43	57	that	that	SCONJ
ejpam-2199	43	58	x	x	SYM
ejpam-2199	43	59	∈	∈	NUM
ejpam-2199	43	60	kn0	kn0	NOUN
ejpam-2199	44	1	⊂	⊂	X
ejpam-2199	44	2	⋃	⋃	PROPN
ejpam-2199	44	3	j∈in0	j∈in0	NUM
ejpam-2199	44	4	un0	un0	NOUN
ejpam-2199	44	5	j	j	NOUN
ejpam-2199	44	6	,	,	PUNCT
ejpam-2199	44	7	then	then	ADV
ejpam-2199	44	8	x	x	PART
ejpam-2199	44	9	∈	∈	PROPN
ejpam-2199	44	10	un0	un0	NOUN
ejpam-2199	44	11	j0	j0	PROPN
ejpam-2199	44	12	for	for	ADP
ejpam-2199	44	13	some	some	DET
ejpam-2199	44	14	j0	j0	PROPN
ejpam-2199	44	15	∈	∈	PROPN
ejpam-2199	44	16	in0	in0	NOUN
ejpam-2199	44	17	,	,	PUNCT
ejpam-2199	44	18	then	then	ADV
ejpam-2199	44	19	un0	un0	NOUN
ejpam-2199	44	20	j0	j0	PROPN
ejpam-2199	44	21	∈	∈	PROPN
ejpam-2199	44	22	vn	vn	PROPN
ejpam-2199	44	23	.	.	PROPN
ejpam-2199	45	1	from	from	ADP
ejpam-2199	45	2	ki	ki	PROPN
ejpam-2199	46	1	⊂	⊂	PROPN
ejpam-2199	46	2	ki+1	ki+1	INTJ
ejpam-2199	47	1	we	we	PRON
ejpam-2199	47	2	wave	wave	VERB
ejpam-2199	47	3	that	that	SCONJ
ejpam-2199	47	4	∀n	∀n	NUM
ejpam-2199	47	5	∈	∈	PROPN
ejpam-2199	47	6	n	n	CCONJ
ejpam-2199	47	7	,	,	PUNCT
ejpam-2199	47	8	n≥	n≥	PROPN
ejpam-2199	47	9	n0	n0	NUM
ejpam-2199	47	10	,	,	PUNCT
ejpam-2199	47	11	x	x	PROPN
ejpam-2199	47	12	∈	∈	NUM
ejpam-2199	47	13	kn0	kn0	NOUN
ejpam-2199	48	1	⊂	⊂	PROPN
ejpam-2199	48	2	kn	kn	PROPN
ejpam-2199	49	1	⊂	⊂	PROPN
ejpam-2199	49	2	⋃	⋃	PROPN
ejpam-2199	49	3	j∈in	j∈in	PROPN
ejpam-2199	49	4	un	un	PROPN
ejpam-2199	49	5	j	j	PROPN
ejpam-2199	49	6	.	.	PUNCT
ejpam-2199	50	1	hence	hence	ADV
ejpam-2199	50	2	there	there	PRON
ejpam-2199	50	3	is	be	VERB
ejpam-2199	50	4	j	j	PROPN
ejpam-2199	50	5	∈	∈	PROPN
ejpam-2199	50	6	in	in	ADP
ejpam-2199	50	7	such	such	ADJ
ejpam-2199	50	8	that	that	SCONJ
ejpam-2199	50	9	x	x	SYM
ejpam-2199	50	10	∈	∈	PROPN
ejpam-2199	50	11	un	un	PROPN
ejpam-2199	50	12	j	j	PROPN
ejpam-2199	50	13	∈	∈	PROPN
ejpam-2199	50	14	vn	vn	PROPN
ejpam-2199	50	15	.	.	PUNCT
ejpam-2199	51	1	so	so	ADV
ejpam-2199	51	2	x	x	X
ejpam-2199	51	3	is	be	AUX
ejpam-2199	51	4	hurewicz	hurewicz	NOUN
ejpam-2199	51	5	.	.	PUNCT
ejpam-2199	52	1	proposition	proposition	NOUN
ejpam-2199	52	2	2	2	NUM
ejpam-2199	52	3	.	.	PUNCT
ejpam-2199	53	1	let	let	VERB
ejpam-2199	53	2	x	x	PUNCT
ejpam-2199	53	3	=	=	SYM
ejpam-2199	53	4	⋃	⋃	NOUN
ejpam-2199	53	5	i∈n	i∈n	NOUN
ejpam-2199	53	6	ki	ki	PROPN
ejpam-2199	53	7	,	,	PUNCT
ejpam-2199	53	8	where	where	SCONJ
ejpam-2199	53	9	for	for	ADP
ejpam-2199	53	10	each	each	DET
ejpam-2199	53	11	i	i	PROPN
ejpam-2199	53	12	∈	∈	PROPN
ejpam-2199	53	13	n	n	CCONJ
ejpam-2199	53	14	,	,	PUNCT
ejpam-2199	53	15	ki	ki	PROPN
ejpam-2199	53	16	is	be	AUX
ejpam-2199	53	17	compact	compact	ADJ
ejpam-2199	53	18	,	,	PUNCT
ejpam-2199	53	19	then	then	ADV
ejpam-2199	53	20	x	x	X
ejpam-2199	53	21	is	be	AUX
ejpam-2199	53	22	hurewicz	hurewicz	NOUN
ejpam-2199	53	23	.	.	PUNCT
ejpam-2199	54	1	proof	proof	NOUN
ejpam-2199	54	2	.	.	PUNCT
ejpam-2199	55	1	let	let	VERB
ejpam-2199	55	2	x	x	PUNCT
ejpam-2199	55	3	=	=	SYM
ejpam-2199	55	4	⋃	⋃	NOUN
ejpam-2199	55	5	i∈n	i∈n	NOUN
ejpam-2199	55	6	ki	ki	PROPN
ejpam-2199	55	7	.	.	PUNCT
ejpam-2199	56	1	consider	consider	VERB
ejpam-2199	56	2	for	for	ADP
ejpam-2199	56	3	each	each	DET
ejpam-2199	56	4	i	i	PROPN
ejpam-2199	56	5	∈	∈	PROPN
ejpam-2199	56	6	n	n	CCONJ
ejpam-2199	56	7	,	,	PUNCT
ejpam-2199	56	8	k	k	PROPN
ejpam-2199	56	9	′i	′i	NOUN
ejpam-2199	57	1	=	=	PUNCT
ejpam-2199	57	2	i	i	PRON
ejpam-2199	57	3	⋃	⋃	VERB
ejpam-2199	57	4	j=1	j=1	PROPN
ejpam-2199	57	5	k	k	PROPN
ejpam-2199	57	6	j	j	PROPN
ejpam-2199	57	7	.	.	PUNCT
ejpam-2199	58	1	we	we	PRON
ejpam-2199	58	2	have	have	VERB
ejpam-2199	58	3	that	that	PRON
ejpam-2199	58	4	k	k	PROPN
ejpam-2199	58	5	′i	′i	PROPN
ejpam-2199	58	6	is	be	AUX
ejpam-2199	58	7	compact	compact	ADJ
ejpam-2199	58	8	,	,	PUNCT
ejpam-2199	58	9	k	k	PROPN
ejpam-2199	58	10	′i	′i	PROPN
ejpam-2199	58	11	⊂	⊂	PROPN
ejpam-2199	58	12	k	k	PROPN
ejpam-2199	58	13	′i+1	′i+1	PROPN
ejpam-2199	59	1	and	and	CCONJ
ejpam-2199	59	2	x	x	X
ejpam-2199	59	3	=	=	SYM
ejpam-2199	59	4	⋃	⋃	NOUN
ejpam-2199	59	5	i∈n	i∈n	NOUN
ejpam-2199	59	6	k	k	PROPN
ejpam-2199	59	7	′i	′i	NOUN
ejpam-2199	59	8	then	then	ADV
ejpam-2199	59	9	by	by	ADP
ejpam-2199	59	10	the	the	DET
ejpam-2199	59	11	previous	previous	ADJ
ejpam-2199	59	12	proposition	proposition	NOUN
ejpam-2199	59	13	x	x	PUNCT
ejpam-2199	59	14	is	be	AUX
ejpam-2199	59	15	hurewicz	hurewicz	NOUN
ejpam-2199	59	16	.	.	PUNCT
ejpam-2199	60	1	c.	c.	NOUN
ejpam-2199	60	2	roika	roika	PROPN
ejpam-2199	60	3	,	,	PUNCT
ejpam-2199	60	4	s.	s.	PROPN
ejpam-2199	60	5	kudri	kudri	PROPN
ejpam-2199	60	6	,	,	PUNCT
ejpam-2199	60	7	t.	t.	PROPN
ejpam-2199	60	8	breuckmann	breuckmann	PROPN
ejpam-2199	60	9	/	/	SYM
ejpam-2199	60	10	eur	eur	PROPN
ejpam-2199	60	11	.	.	PUNCT
ejpam-2199	61	1	j.	j.	PROPN
ejpam-2199	61	2	pure	pure	PROPN
ejpam-2199	61	3	appl	appl	PROPN
ejpam-2199	61	4	.	.	PROPN
ejpam-2199	61	5	math	math	PROPN
ejpam-2199	61	6	,	,	PUNCT
ejpam-2199	61	7	8	8	NUM
ejpam-2199	61	8	(	(	PUNCT
ejpam-2199	61	9	2015	2015	NUM
ejpam-2199	61	10	)	)	PUNCT
ejpam-2199	61	11	,	,	PUNCT
ejpam-2199	61	12	514	514	NUM
ejpam-2199	61	13	-	-	SYM
ejpam-2199	61	14	525	525	NUM
ejpam-2199	61	15	516	516	NUM
ejpam-2199	61	16	corollary	corollary	ADJ
ejpam-2199	61	17	1	1	NUM
ejpam-2199	61	18	.	.	PUNCT
ejpam-2199	62	1	if	if	SCONJ
ejpam-2199	62	2	a	a	DET
ejpam-2199	62	3	topological	topological	ADJ
ejpam-2199	62	4	space	space	NOUN
ejpam-2199	62	5	〈	〈	NOUN
ejpam-2199	62	6	x	x	X
ejpam-2199	62	7	,	,	PUNCT
ejpam-2199	62	8	t	t	PROPN
ejpam-2199	62	9	〉	〉	NOUN
ejpam-2199	62	10	is	be	AUX
ejpam-2199	62	11	compact	compact	ADJ
ejpam-2199	62	12	,	,	PUNCT
ejpam-2199	62	13	then	then	ADV
ejpam-2199	62	14	〈	〈	PROPN
ejpam-2199	62	15	x	x	X
ejpam-2199	62	16	,	,	PUNCT
ejpam-2199	62	17	t	t	PROPN
ejpam-2199	62	18	〉	〉	NOUN
ejpam-2199	62	19	is	be	AUX
ejpam-2199	62	20	hurewicz	hurewicz	NOUN
ejpam-2199	62	21	.	.	PUNCT
ejpam-2199	63	1	proof	proof	NOUN
ejpam-2199	63	2	.	.	PUNCT
ejpam-2199	64	1	it	it	PRON
ejpam-2199	64	2	follows	follow	VERB
ejpam-2199	64	3	immediately	immediately	ADV
ejpam-2199	64	4	from	from	ADP
ejpam-2199	64	5	the	the	DET
ejpam-2199	64	6	proposition	proposition	NOUN
ejpam-2199	64	7	2	2	NUM
ejpam-2199	64	8	.	.	X
ejpam-2199	64	9	proposition	proposition	NOUN
ejpam-2199	64	10	3	3	NUM
ejpam-2199	64	11	.	.	PUNCT
ejpam-2199	65	1	if	if	SCONJ
ejpam-2199	65	2	a	a	DET
ejpam-2199	65	3	topological	topological	ADJ
ejpam-2199	65	4	space	space	NOUN
ejpam-2199	65	5	〈	〈	NOUN
ejpam-2199	65	6	x	x	X
ejpam-2199	65	7	,	,	PUNCT
ejpam-2199	65	8	t	t	PROPN
ejpam-2199	65	9	〉	〉	NOUN
ejpam-2199	65	10	is	be	AUX
ejpam-2199	65	11	hurewicz	hurewicz	NOUN
ejpam-2199	65	12	,	,	PUNCT
ejpam-2199	65	13	then	then	ADV
ejpam-2199	65	14	〈	〈	PROPN
ejpam-2199	65	15	x	x	X
ejpam-2199	65	16	,	,	PUNCT
ejpam-2199	65	17	t	t	PROPN
ejpam-2199	65	18	〉	〉	NOUN
ejpam-2199	65	19	is	be	AUX
ejpam-2199	65	20	lindelöf	lindelöf	NOUN
ejpam-2199	65	21	.	.	PUNCT
ejpam-2199	66	1	proof	proof	NOUN
ejpam-2199	66	2	.	.	PUNCT
ejpam-2199	67	1	let	let	VERB
ejpam-2199	67	2	u	u	PRON
ejpam-2199	67	3	=	=	PUNCT
ejpam-2199	67	4	{	{	PUNCT
ejpam-2199	67	5	u	u	NOUN
ejpam-2199	67	6	j	j	PROPN
ejpam-2199	67	7	}	}	PUNCT
ejpam-2199	67	8	j∈j	j∈j	NOUN
ejpam-2199	67	9	be	be	VERB
ejpam-2199	67	10	an	an	DET
ejpam-2199	67	11	open	open	ADJ
ejpam-2199	67	12	covering	covering	NOUN
ejpam-2199	67	13	of	of	ADP
ejpam-2199	67	14	x	x	X
ejpam-2199	67	15	.	.	PUNCT
ejpam-2199	68	1	consider	consider	VERB
ejpam-2199	68	2	the	the	DET
ejpam-2199	68	3	sequence	sequence	NOUN
ejpam-2199	68	4	{	{	PUNCT
ejpam-2199	68	5	un}n∈n	un}n∈n	NOUN
ejpam-2199	68	6	,	,	PUNCT
ejpam-2199	68	7	where	where	SCONJ
ejpam-2199	68	8	un	un	PROPN
ejpam-2199	68	9	=	=	PROPN
ejpam-2199	68	10	u.	u.	PROPN
ejpam-2199	68	11	since	since	SCONJ
ejpam-2199	68	12	x	x	PRON
ejpam-2199	68	13	is	be	AUX
ejpam-2199	68	14	hurewicz	hurewicz	NOUN
ejpam-2199	68	15	,	,	PUNCT
ejpam-2199	68	16	there	there	PRON
ejpam-2199	68	17	exists	exist	VERB
ejpam-2199	68	18	a	a	DET
ejpam-2199	68	19	sequence	sequence	NOUN
ejpam-2199	68	20	{	{	PUNCT
ejpam-2199	68	21	vn}n∈n	vn}n∈n	ADP
ejpam-2199	68	22	such	such	ADJ
ejpam-2199	68	23	that	that	PRON
ejpam-2199	68	24	:	:	PUNCT
ejpam-2199	68	25	(	(	PUNCT
ejpam-2199	68	26	i	i	NOUN
ejpam-2199	68	27	)	)	PUNCT
ejpam-2199	68	28	∀n	∀n	PROPN
ejpam-2199	69	1	∈	∈	PROPN
ejpam-2199	69	2	n	n	CCONJ
ejpam-2199	69	3	,	,	PUNCT
ejpam-2199	69	4	vn	vn	PROPN
ejpam-2199	69	5	⊂<∞	⊂<∞	PROPN
ejpam-2199	69	6	un	un	PROPN
ejpam-2199	70	1	=	=	PROPN
ejpam-2199	70	2	u	u	PROPN
ejpam-2199	70	3	,	,	PUNCT
ejpam-2199	70	4	i.e.	i.e.	X
ejpam-2199	70	5	,	,	PUNCT
ejpam-2199	70	6	∃in	∃in	ADJ
ejpam-2199	70	7	⊂<∞	⊂<∞	PROPN
ejpam-2199	70	8	j	j	PROPN
ejpam-2199	70	9	such	such	ADJ
ejpam-2199	70	10	that	that	DET
ejpam-2199	70	11	vn	vn	PROPN
ejpam-2199	70	12	=	=	PUNCT
ejpam-2199	70	13	{	{	PUNCT
ejpam-2199	70	14	u	u	PROPN
ejpam-2199	70	15	j	j	PROPN
ejpam-2199	70	16	}	}	PUNCT
ejpam-2199	70	17	j∈in	j∈in	PROPN
ejpam-2199	70	18	.	.	PUNCT
ejpam-2199	71	1	(	(	PUNCT
ejpam-2199	71	2	ii	ii	NOUN
ejpam-2199	71	3	)	)	PUNCT
ejpam-2199	71	4	for	for	ADP
ejpam-2199	71	5	each	each	DET
ejpam-2199	71	6	x	x	SYM
ejpam-2199	71	7	∈	∈	PROPN
ejpam-2199	71	8	x	x	X
ejpam-2199	71	9	,	,	PUNCT
ejpam-2199	71	10	∃n0	∃n0	NOUN
ejpam-2199	71	11	∈	∈	PROPN
ejpam-2199	71	12	n	n	PRON
ejpam-2199	71	13	such	such	ADJ
ejpam-2199	71	14	that	that	SCONJ
ejpam-2199	71	15	∀n	∀n	NUM
ejpam-2199	71	16	∈	∈	NOUN
ejpam-2199	71	17	n	n	ADV
ejpam-2199	71	18	if	if	SCONJ
ejpam-2199	71	19	n≥	n≥	PROPN
ejpam-2199	71	20	n0	n0	X
ejpam-2199	71	21	then	then	ADV
ejpam-2199	71	22	there	there	PRON
ejpam-2199	71	23	exists	exist	VERB
ejpam-2199	71	24	v	v	ADP
ejpam-2199	71	25	∈	∈	PROPN
ejpam-2199	71	26	vn	vn	NOUN
ejpam-2199	71	27	with	with	ADP
ejpam-2199	71	28	x	x	PROPN
ejpam-2199	71	29	∈	∈	PROPN
ejpam-2199	71	30	v	v	NOUN
ejpam-2199	71	31	.	.	PUNCT
ejpam-2199	72	1	considering	consider	VERB
ejpam-2199	72	2	v	v	NUM
ejpam-2199	72	3	=	=	SYM
ejpam-2199	72	4	{	{	PUNCT
ejpam-2199	72	5	u	u	PROPN
ejpam-2199	72	6	j	j	PROPN
ejpam-2199	72	7	;	;	PUNCT
ejpam-2199	72	8	j	j	PROPN
ejpam-2199	72	9	∈	∈	PROPN
ejpam-2199	72	10	in	in	ADP
ejpam-2199	72	11	,	,	PUNCT
ejpam-2199	72	12	n	n	CCONJ
ejpam-2199	72	13	∈	∈	PROPN
ejpam-2199	72	14	n	n	CCONJ
ejpam-2199	72	15	}	}	PUNCT
ejpam-2199	72	16	,	,	PUNCT
ejpam-2199	72	17	we	we	PRON
ejpam-2199	72	18	have	have	VERB
ejpam-2199	72	19	that	that	DET
ejpam-2199	72	20	v	v	NOUN
ejpam-2199	72	21	is	be	AUX
ejpam-2199	72	22	a	a	DET
ejpam-2199	72	23	countable	countable	ADJ
ejpam-2199	72	24	subcovering	subcovering	NOUN
ejpam-2199	72	25	of	of	ADP
ejpam-2199	72	26	x	x	X
ejpam-2199	72	27	,	,	PUNCT
ejpam-2199	72	28	because	because	SCONJ
ejpam-2199	72	29	for	for	ADP
ejpam-2199	72	30	each	each	DET
ejpam-2199	72	31	n	n	PRON
ejpam-2199	72	32	∈	∈	PROPN
ejpam-2199	72	33	n	n	CCONJ
ejpam-2199	72	34	,	,	PUNCT
ejpam-2199	72	35	in	in	ADP
ejpam-2199	72	36	is	be	AUX
ejpam-2199	72	37	finite	finite	ADJ
ejpam-2199	72	38	and	and	CCONJ
ejpam-2199	72	39	for	for	ADP
ejpam-2199	72	40	each	each	DET
ejpam-2199	72	41	x	x	SYM
ejpam-2199	72	42	∈	∈	PROPN
ejpam-2199	72	43	x	x	X
ejpam-2199	72	44	,	,	PUNCT
ejpam-2199	72	45	by	by	ADP
ejpam-2199	72	46	(	(	PUNCT
ejpam-2199	72	47	ii	ii	NOUN
ejpam-2199	72	48	)	)	PUNCT
ejpam-2199	72	49	there	there	PRON
ejpam-2199	72	50	exists	exist	VERB
ejpam-2199	72	51	n0	n0	PROPN
ejpam-2199	72	52	∈	∈	PROPN
ejpam-2199	72	53	n	n	PRON
ejpam-2199	73	1	such	such	ADJ
ejpam-2199	73	2	that	that	SCONJ
ejpam-2199	73	3	∀n	∀n	NUM
ejpam-2199	73	4	∈	∈	NOUN
ejpam-2199	73	5	n	n	ADV
ejpam-2199	73	6	if	if	SCONJ
ejpam-2199	73	7	n	n	NUM
ejpam-2199	73	8	≥	≥	X
ejpam-2199	73	9	n0	n0	NUM
ejpam-2199	73	10	,	,	PUNCT
ejpam-2199	73	11	then	then	ADV
ejpam-2199	73	12	there	there	PRON
ejpam-2199	73	13	is	be	VERB
ejpam-2199	73	14	v	v	ADP
ejpam-2199	73	15	∈	∈	PROPN
ejpam-2199	73	16	vn	vn	NOUN
ejpam-2199	73	17	such	such	ADJ
ejpam-2199	73	18	that	that	SCONJ
ejpam-2199	73	19	x	x	SYM
ejpam-2199	73	20	∈	∈	NOUN
ejpam-2199	73	21	v	v	NOUN
ejpam-2199	73	22	,	,	PUNCT
ejpam-2199	73	23	then	then	ADV
ejpam-2199	73	24	there	there	PRON
ejpam-2199	73	25	exists	exist	VERB
ejpam-2199	73	26	v	v	ADP
ejpam-2199	73	27	∈	∈	PROPN
ejpam-2199	73	28	vn0	vn0	NOUN
ejpam-2199	73	29	,	,	PUNCT
ejpam-2199	73	30	such	such	ADJ
ejpam-2199	73	31	that	that	SCONJ
ejpam-2199	73	32	x	x	SYM
ejpam-2199	73	33	∈	∈	NOUN
ejpam-2199	73	34	v	v	NOUN
ejpam-2199	73	35	,	,	PUNCT
ejpam-2199	73	36	but	but	CCONJ
ejpam-2199	73	37	from	from	ADP
ejpam-2199	73	38	v	v	NUM
ejpam-2199	73	39	∈	∈	NOUN
ejpam-2199	73	40	vn0	vn0	NOUN
ejpam-2199	73	41	,	,	PUNCT
ejpam-2199	73	42	we	we	PRON
ejpam-2199	73	43	have	have	VERB
ejpam-2199	73	44	that	that	PRON
ejpam-2199	73	45	,	,	PUNCT
ejpam-2199	73	46	v	v	NOUN
ejpam-2199	73	47	=	=	SYM
ejpam-2199	73	48	u	u	X
ejpam-2199	73	49	j	j	PROPN
ejpam-2199	73	50	,	,	PUNCT
ejpam-2199	73	51	for	for	ADP
ejpam-2199	73	52	some	some	DET
ejpam-2199	73	53	j	j	PROPN
ejpam-2199	73	54	∈	∈	PROPN
ejpam-2199	73	55	in0	in0	NOUN
ejpam-2199	73	56	,	,	PUNCT
ejpam-2199	73	57	then	then	ADV
ejpam-2199	73	58	v	v	ADP
ejpam-2199	73	59	∈	∈	PROPN
ejpam-2199	74	1	v.	v.	ADP
ejpam-2199	75	1	so	so	ADV
ejpam-2199	75	2	x	x	X
ejpam-2199	75	3	is	be	AUX
ejpam-2199	75	4	a	a	DET
ejpam-2199	75	5	lindelöf	lindelöf	NOUN
ejpam-2199	75	6	space	space	NOUN
ejpam-2199	75	7	.	.	PUNCT
ejpam-2199	76	1	example	example	NOUN
ejpam-2199	77	1	2	2	NUM
ejpam-2199	77	2	.	.	PUNCT
ejpam-2199	77	3	the	the	DET
ejpam-2199	77	4	real	real	ADJ
ejpam-2199	77	5	line	line	NOUN
ejpam-2199	77	6	r	r	NOUN
ejpam-2199	77	7	in	in	ADP
ejpam-2199	77	8	the	the	DET
ejpam-2199	77	9	particular	particular	ADJ
ejpam-2199	77	10	point	point	NOUN
ejpam-2199	77	11	p	p	NOUN
ejpam-2199	77	12	topology	topology	NOUN
ejpam-2199	77	13	is	be	AUX
ejpam-2199	77	14	not	not	PART
ejpam-2199	77	15	a	a	DET
ejpam-2199	77	16	lindelöf	lindelöf	NOUN
ejpam-2199	77	17	space	space	NOUN
ejpam-2199	77	18	.	.	PUNCT
ejpam-2199	78	1	in	in	ADP
ejpam-2199	78	2	fact	fact	NOUN
ejpam-2199	78	3	,	,	PUNCT
ejpam-2199	78	4	since	since	SCONJ
ejpam-2199	78	5	{	{	PUNCT
ejpam-2199	78	6	{	{	PUNCT
ejpam-2199	78	7	x	x	INTJ
ejpam-2199	78	8	,	,	PUNCT
ejpam-2199	78	9	p	p	X
ejpam-2199	78	10	}	}	PUNCT
ejpam-2199	78	11	;	;	PUNCT
ejpam-2199	78	12	x	x	X
ejpam-2199	78	13	∈	∈	PROPN
ejpam-2199	78	14	r	r	NOUN
ejpam-2199	78	15	}	}	PUNCT
ejpam-2199	78	16	is	be	AUX
ejpam-2199	78	17	an	an	DET
ejpam-2199	78	18	open	open	ADJ
ejpam-2199	78	19	covering	covering	NOUN
ejpam-2199	78	20	of	of	ADP
ejpam-2199	78	21	r	r	NOUN
ejpam-2199	78	22	which	which	PRON
ejpam-2199	78	23	does	do	AUX
ejpam-2199	78	24	not	not	PART
ejpam-2199	78	25	have	have	VERB
ejpam-2199	78	26	a	a	DET
ejpam-2199	78	27	countable	countable	ADJ
ejpam-2199	78	28	subcovering	subcovering	NOUN
ejpam-2199	78	29	.	.	PUNCT
ejpam-2199	79	1	by	by	ADP
ejpam-2199	79	2	the	the	DET
ejpam-2199	79	3	previous	previous	ADJ
ejpam-2199	79	4	proposition	proposition	NOUN
ejpam-2199	79	5	,	,	PUNCT
ejpam-2199	79	6	the	the	DET
ejpam-2199	79	7	real	real	ADJ
ejpam-2199	79	8	line	line	NOUN
ejpam-2199	79	9	in	in	ADP
ejpam-2199	79	10	the	the	DET
ejpam-2199	79	11	particular	particular	ADJ
ejpam-2199	79	12	point	point	NOUN
ejpam-2199	79	13	p	p	NOUN
ejpam-2199	79	14	topology	topology	NOUN
ejpam-2199	79	15	is	be	AUX
ejpam-2199	79	16	not	not	PART
ejpam-2199	79	17	hurewicz	hurewicz	ADJ
ejpam-2199	79	18	.	.	PUNCT
ejpam-2199	80	1	proposition	proposition	NOUN
ejpam-2199	80	2	4	4	NUM
ejpam-2199	80	3	.	.	PUNCT
ejpam-2199	81	1	let	let	VERB
ejpam-2199	81	2	x	x	PRON
ejpam-2199	81	3	and	and	CCONJ
ejpam-2199	81	4	y	y	PROPN
ejpam-2199	81	5	be	be	AUX
ejpam-2199	81	6	topological	topological	ADJ
ejpam-2199	81	7	spaces	space	NOUN
ejpam-2199	81	8	and	and	CCONJ
ejpam-2199	81	9	let	let	VERB
ejpam-2199	81	10	x	x	PRON
ejpam-2199	81	11	be	be	AUX
ejpam-2199	81	12	hurewicz	hurewicz	ADJ
ejpam-2199	81	13	.	.	PUNCT
ejpam-2199	82	1	if	if	SCONJ
ejpam-2199	82	2	f	f	PROPN
ejpam-2199	82	3	:	:	PUNCT
ejpam-2199	82	4	x	x	X
ejpam-2199	82	5	→	→	SYM
ejpam-2199	82	6	y	y	PROPN
ejpam-2199	82	7	is	be	AUX
ejpam-2199	82	8	a	a	DET
ejpam-2199	82	9	surjective	surjective	ADJ
ejpam-2199	82	10	continuous	continuous	ADJ
ejpam-2199	82	11	function	function	NOUN
ejpam-2199	82	12	,	,	PUNCT
ejpam-2199	82	13	then	then	ADV
ejpam-2199	82	14	y	y	PROPN
ejpam-2199	82	15	is	be	AUX
ejpam-2199	82	16	hurewicz	hurewicz	ADJ
ejpam-2199	82	17	.	.	PUNCT
ejpam-2199	83	1	proof	proof	NOUN
ejpam-2199	83	2	.	.	PUNCT
ejpam-2199	84	1	let	let	VERB
ejpam-2199	84	2	{	{	PUNCT
ejpam-2199	84	3	un}n∈n	un}n∈n	PRON
ejpam-2199	84	4	be	be	AUX
ejpam-2199	84	5	a	a	DET
ejpam-2199	84	6	sequence	sequence	NOUN
ejpam-2199	84	7	of	of	ADP
ejpam-2199	84	8	open	open	ADJ
ejpam-2199	84	9	coverings	covering	NOUN
ejpam-2199	84	10	of	of	ADP
ejpam-2199	84	11	y	y	PROPN
ejpam-2199	84	12	,	,	PUNCT
ejpam-2199	84	13	where	where	SCONJ
ejpam-2199	84	14	each	each	DET
ejpam-2199	84	15	un	un	PROPN
ejpam-2199	85	1	=	=	PRON
ejpam-2199	85	2	{	{	PUNCT
ejpam-2199	85	3	un	un	PROPN
ejpam-2199	85	4	j	j	PROPN
ejpam-2199	85	5	}	}	PUNCT
ejpam-2199	85	6	j∈jn	j∈jn	NOUN
ejpam-2199	85	7	.	.	PUNCT
ejpam-2199	86	1	consider	consider	VERB
ejpam-2199	86	2	for	for	ADP
ejpam-2199	86	3	each	each	DET
ejpam-2199	86	4	n	n	PRON
ejpam-2199	86	5	∈	∈	PROPN
ejpam-2199	86	6	n	n	CCONJ
ejpam-2199	86	7	,	,	PUNCT
ejpam-2199	86	8	wn	wn	PROPN
ejpam-2199	86	9	=	=	X
ejpam-2199	86	10	{	{	PUNCT
ejpam-2199	86	11	f	f	PROPN
ejpam-2199	86	12	−1(un	−1(un	PROPN
ejpam-2199	86	13	j	j	PROPN
ejpam-2199	86	14	)	)	PUNCT
ejpam-2199	86	15	}	}	PUNCT
ejpam-2199	86	16	j∈jn	j∈jn	NOUN
ejpam-2199	86	17	.	.	PUNCT
ejpam-2199	87	1	by	by	ADP
ejpam-2199	87	2	the	the	DET
ejpam-2199	87	3	continuity	continuity	NOUN
ejpam-2199	87	4	of	of	ADP
ejpam-2199	87	5	f	f	PRON
ejpam-2199	87	6	we	we	PRON
ejpam-2199	87	7	have	have	VERB
ejpam-2199	87	8	that	that	PRON
ejpam-2199	87	9	,	,	PUNCT
ejpam-2199	87	10	f	f	PROPN
ejpam-2199	87	11	−1(un	−1(un	PROPN
ejpam-2199	87	12	j	j	PROPN
ejpam-2199	87	13	)	)	PUNCT
ejpam-2199	87	14	is	be	AUX
ejpam-2199	87	15	open	open	ADJ
ejpam-2199	87	16	in	in	ADP
ejpam-2199	87	17	x	x	PUNCT
ejpam-2199	88	1	and	and	CCONJ
ejpam-2199	88	2	we	we	PRON
ejpam-2199	88	3	also	also	ADV
ejpam-2199	88	4	have	have	VERB
ejpam-2199	88	5	that	that	PRON
ejpam-2199	88	6	wn	wn	PROPN
ejpam-2199	88	7	is	be	AUX
ejpam-2199	88	8	a	a	DET
ejpam-2199	88	9	covering	covering	NOUN
ejpam-2199	88	10	of	of	ADP
ejpam-2199	88	11	x	x	PUNCT
ejpam-2199	88	12	,	,	PUNCT
ejpam-2199	88	13	because	because	SCONJ
ejpam-2199	88	14	if	if	SCONJ
ejpam-2199	88	15	x	x	SYM
ejpam-2199	88	16	∈	∈	NOUN
ejpam-2199	88	17	x	x	INTJ
ejpam-2199	88	18	we	we	PRON
ejpam-2199	88	19	have	have	VERB
ejpam-2199	88	20	that	that	DET
ejpam-2199	88	21	f	f	PROPN
ejpam-2199	88	22	(	(	PUNCT
ejpam-2199	88	23	x	x	X
ejpam-2199	88	24	)	)	PUNCT
ejpam-2199	88	25	∈	∈	PROPN
ejpam-2199	88	26	y	y	PROPN
ejpam-2199	88	27	,	,	PUNCT
ejpam-2199	88	28	hence	hence	ADV
ejpam-2199	88	29	∃	∃	PROPN
ejpam-2199	88	30	j	j	PROPN
ejpam-2199	88	31	∈	∈	PROPN
ejpam-2199	88	32	jn	jn	PROPN
ejpam-2199	89	1	such	such	ADJ
ejpam-2199	89	2	that	that	SCONJ
ejpam-2199	89	3	f	f	PROPN
ejpam-2199	89	4	(	(	PUNCT
ejpam-2199	89	5	x	x	X
ejpam-2199	89	6	)	)	PUNCT
ejpam-2199	89	7	∈	∈	PROPN
ejpam-2199	89	8	un	un	PROPN
ejpam-2199	89	9	j	j	PROPN
ejpam-2199	89	10	,	,	PUNCT
ejpam-2199	89	11	then	then	ADV
ejpam-2199	89	12	x	x	SYM
ejpam-2199	89	13	∈	∈	PROPN
ejpam-2199	89	14	f	f	PROPN
ejpam-2199	89	15	−1(un	−1(un	PROPN
ejpam-2199	89	16	j	j	PROPN
ejpam-2199	89	17	)	)	PUNCT
ejpam-2199	89	18	.	.	PUNCT
ejpam-2199	90	1	therefore	therefore	ADV
ejpam-2199	90	2	,	,	PUNCT
ejpam-2199	90	3	{	{	PUNCT
ejpam-2199	90	4	wn}n∈n	wn}n∈n	X
ejpam-2199	90	5	is	be	AUX
ejpam-2199	90	6	a	a	DET
ejpam-2199	90	7	sequence	sequence	NOUN
ejpam-2199	90	8	of	of	ADP
ejpam-2199	90	9	open	open	ADJ
ejpam-2199	90	10	coverings	covering	NOUN
ejpam-2199	90	11	of	of	ADP
ejpam-2199	90	12	x	x	X
ejpam-2199	90	13	.	.	PUNCT
ejpam-2199	91	1	since	since	SCONJ
ejpam-2199	91	2	x	x	PROPN
ejpam-2199	91	3	is	be	AUX
ejpam-2199	91	4	hurewicz	hurewicz	NOUN
ejpam-2199	91	5	,	,	PUNCT
ejpam-2199	91	6	there	there	PRON
ejpam-2199	91	7	is	be	VERB
ejpam-2199	91	8	a	a	DET
ejpam-2199	91	9	sequence	sequence	NOUN
ejpam-2199	91	10	{	{	PUNCT
ejpam-2199	91	11	hn}n∈n	hn}n∈n	ADP
ejpam-2199	91	12	,	,	PUNCT
ejpam-2199	91	13	such	such	ADJ
ejpam-2199	91	14	that	that	SCONJ
ejpam-2199	91	15	:	:	PUNCT
ejpam-2199	91	16	(	(	PUNCT
ejpam-2199	91	17	i	i	NOUN
ejpam-2199	91	18	)	)	PUNCT
ejpam-2199	91	19	∀n	∀n	PROPN
ejpam-2199	91	20	∈	∈	PROPN
ejpam-2199	91	21	n	n	CCONJ
ejpam-2199	91	22	,	,	PUNCT
ejpam-2199	91	23	hn	hn	PROPN
ejpam-2199	91	24	⊂<∞wn	⊂<∞wn	PROPN
ejpam-2199	91	25	,	,	PUNCT
ejpam-2199	91	26	i.	i.	PROPN
ejpam-2199	91	27	e.	e.	PROPN
ejpam-2199	91	28	,	,	PUNCT
ejpam-2199	91	29	there	there	PRON
ejpam-2199	91	30	is	be	VERB
ejpam-2199	91	31	in	in	ADP
ejpam-2199	91	32	⊂<∞	⊂<∞	PROPN
ejpam-2199	91	33	jn	jn	PROPN
ejpam-2199	91	34	,	,	PUNCT
ejpam-2199	91	35	such	such	ADJ
ejpam-2199	91	36	that	that	SCONJ
ejpam-2199	91	37	hn	hn	PRON
ejpam-2199	91	38	=	=	X
ejpam-2199	91	39	{	{	PUNCT
ejpam-2199	91	40	f	f	PROPN
ejpam-2199	91	41	−1(un	−1(un	PROPN
ejpam-2199	91	42	j	j	PROPN
ejpam-2199	91	43	)	)	PUNCT
ejpam-2199	91	44	}	}	PUNCT
ejpam-2199	91	45	j∈in	j∈in	NOUN
ejpam-2199	91	46	.	.	PUNCT
ejpam-2199	92	1	(	(	PUNCT
ejpam-2199	92	2	ii	ii	NOUN
ejpam-2199	92	3	)	)	PUNCT
ejpam-2199	92	4	for	for	ADP
ejpam-2199	92	5	each	each	DET
ejpam-2199	92	6	x	x	SYM
ejpam-2199	92	7	∈	∈	PROPN
ejpam-2199	92	8	x	x	X
ejpam-2199	92	9	,	,	PUNCT
ejpam-2199	92	10	∃n0	∃n0	NOUN
ejpam-2199	92	11	∈	∈	PROPN
ejpam-2199	92	12	n	n	PRON
ejpam-2199	92	13	such	such	ADJ
ejpam-2199	92	14	that	that	SCONJ
ejpam-2199	92	15	∀n	∀n	NUM
ejpam-2199	92	16	∈	∈	NOUN
ejpam-2199	92	17	n	n	ADV
ejpam-2199	92	18	if	if	SCONJ
ejpam-2199	92	19	n≥	n≥	PROPN
ejpam-2199	92	20	n0	n0	NUM
ejpam-2199	92	21	,	,	PUNCT
ejpam-2199	92	22	then	then	ADV
ejpam-2199	92	23	there	there	PRON
ejpam-2199	92	24	exists	exist	VERB
ejpam-2199	92	25	v	v	ADP
ejpam-2199	92	26	∈	∈	NOUN
ejpam-2199	92	27	hn	hn	PROPN
ejpam-2199	92	28	with	with	ADP
ejpam-2199	92	29	x	x	PROPN
ejpam-2199	92	30	∈	∈	PROPN
ejpam-2199	92	31	v	v	NOUN
ejpam-2199	92	32	,	,	PUNCT
ejpam-2199	92	33	i.e.	i.e.	X
ejpam-2199	92	34	,	,	PUNCT
ejpam-2199	92	35	there	there	PRON
ejpam-2199	92	36	is	be	VERB
ejpam-2199	92	37	j	j	PROPN
ejpam-2199	92	38	∈	∈	PROPN
ejpam-2199	92	39	in	in	ADP
ejpam-2199	92	40	with	with	ADP
ejpam-2199	92	41	x	x	PROPN
ejpam-2199	92	42	∈	∈	PROPN
ejpam-2199	92	43	f	f	PROPN
ejpam-2199	92	44	−1(un	−1(un	PROPN
ejpam-2199	92	45	j	j	PROPN
ejpam-2199	92	46	)	)	PUNCT
ejpam-2199	92	47	.	.	PUNCT
ejpam-2199	93	1	consider	consider	VERB
ejpam-2199	93	2	∀n	∀n	NUM
ejpam-2199	93	3	∈	∈	PROPN
ejpam-2199	93	4	n	n	CCONJ
ejpam-2199	93	5	,	,	PUNCT
ejpam-2199	93	6	vn	vn	PROPN
ejpam-2199	93	7	=	=	PRON
ejpam-2199	93	8	{	{	PUNCT
ejpam-2199	93	9	un	un	PROPN
ejpam-2199	93	10	j	j	PROPN
ejpam-2199	93	11	}	}	PUNCT
ejpam-2199	93	12	j∈in	j∈in	PROPN
ejpam-2199	93	13	.	.	PUNCT
ejpam-2199	94	1	then	then	ADV
ejpam-2199	94	2	the	the	DET
ejpam-2199	94	3	sequence	sequence	NOUN
ejpam-2199	94	4	{	{	PUNCT
ejpam-2199	94	5	vn}n∈n	vn}n∈n	X
ejpam-2199	94	6	is	be	AUX
ejpam-2199	94	7	such	such	ADJ
ejpam-2199	94	8	that	that	SCONJ
ejpam-2199	94	9	:	:	PUNCT
ejpam-2199	94	10	(	(	PUNCT
ejpam-2199	94	11	i	i	NOUN
ejpam-2199	94	12	)	)	PUNCT
ejpam-2199	94	13	∀n	∀n	PROPN
ejpam-2199	94	14	∈	∈	PROPN
ejpam-2199	94	15	n	n	CCONJ
ejpam-2199	94	16	,	,	PUNCT
ejpam-2199	94	17	vn	vn	PROPN
ejpam-2199	94	18	⊂<∞	⊂<∞	PROPN
ejpam-2199	94	19	un	un	PROPN
ejpam-2199	94	20	.	.	PROPN
ejpam-2199	94	21	(	(	PUNCT
ejpam-2199	94	22	ii	ii	NOUN
ejpam-2199	94	23	)	)	PUNCT
ejpam-2199	94	24	for	for	ADP
ejpam-2199	94	25	each	each	DET
ejpam-2199	94	26	y	y	PROPN
ejpam-2199	94	27	∈	∈	PROPN
ejpam-2199	94	28	y	y	PROPN
ejpam-2199	94	29	,	,	PUNCT
ejpam-2199	94	30	since	since	SCONJ
ejpam-2199	94	31	f	f	PROPN
ejpam-2199	94	32	is	be	AUX
ejpam-2199	94	33	surjective	surjective	ADJ
ejpam-2199	94	34	∃x	∃x	PROPN
ejpam-2199	94	35	∈	∈	PROPN
ejpam-2199	94	36	x	x	PUNCT
ejpam-2199	94	37	such	such	ADJ
ejpam-2199	94	38	that	that	SCONJ
ejpam-2199	94	39	f	f	PROPN
ejpam-2199	94	40	(	(	PUNCT
ejpam-2199	94	41	x	x	X
ejpam-2199	94	42	)	)	PUNCT
ejpam-2199	94	43	=	=	SYM
ejpam-2199	94	44	y	y	PROPN
ejpam-2199	94	45	.	.	PUNCT
ejpam-2199	95	1	by	by	ADP
ejpam-2199	95	2	previous	previous	ADJ
ejpam-2199	95	3	(	(	PUNCT
ejpam-2199	95	4	ii	ii	NOUN
ejpam-2199	95	5	)	)	PUNCT
ejpam-2199	95	6	there	there	PRON
ejpam-2199	95	7	exists	exist	VERB
ejpam-2199	95	8	n0	n0	PROPN
ejpam-2199	95	9	∈	∈	PROPN
ejpam-2199	95	10	n	n	CCONJ
ejpam-2199	95	11	,	,	PUNCT
ejpam-2199	95	12	such	such	ADJ
ejpam-2199	95	13	that	that	SCONJ
ejpam-2199	95	14	∀n	∀n	NUM
ejpam-2199	95	15	∈	∈	NOUN
ejpam-2199	95	16	n	n	ADV
ejpam-2199	95	17	if	if	SCONJ
ejpam-2199	95	18	n	n	NUM
ejpam-2199	95	19	≥	≥	X
ejpam-2199	95	20	n0	n0	NUM
ejpam-2199	95	21	,	,	PUNCT
ejpam-2199	95	22	then	then	ADV
ejpam-2199	95	23	there	there	PRON
ejpam-2199	95	24	exists	exist	VERB
ejpam-2199	95	25	j	j	PROPN
ejpam-2199	95	26	∈	∈	PROPN
ejpam-2199	95	27	in	in	ADP
ejpam-2199	95	28	with	with	ADP
ejpam-2199	95	29	x	x	PROPN
ejpam-2199	95	30	∈	∈	PROPN
ejpam-2199	95	31	f	f	PROPN
ejpam-2199	95	32	−1(un	−1(un	PROPN
ejpam-2199	95	33	j	j	PROPN
ejpam-2199	95	34	)	)	PUNCT
ejpam-2199	95	35	.	.	PUNCT
ejpam-2199	96	1	since	since	SCONJ
ejpam-2199	96	2	j	j	PROPN
ejpam-2199	96	3	∈	∈	PROPN
ejpam-2199	96	4	in	in	ADP
ejpam-2199	96	5	we	we	PRON
ejpam-2199	96	6	have	have	VERB
ejpam-2199	96	7	that	that	DET
ejpam-2199	96	8	y	y	PROPN
ejpam-2199	96	9	=	=	SYM
ejpam-2199	96	10	f	f	PROPN
ejpam-2199	96	11	(	(	PUNCT
ejpam-2199	96	12	x	x	X
ejpam-2199	96	13	)	)	PUNCT
ejpam-2199	96	14	∈	∈	PROPN
ejpam-2199	96	15	f	f	PROPN
ejpam-2199	96	16	(	(	PUNCT
ejpam-2199	96	17	f	f	PROPN
ejpam-2199	96	18	−1(un	−1(un	PROPN
ejpam-2199	96	19	j	j	PROPN
ejpam-2199	96	20	)	)	PUNCT
ejpam-2199	96	21	)	)	PUNCT
ejpam-2199	97	1	⊂	⊂	PROPN
ejpam-2199	97	2	un	un	PROPN
ejpam-2199	97	3	j	j	PROPN
ejpam-2199	97	4	∈	∈	PROPN
ejpam-2199	97	5	vn	vn	PROPN
ejpam-2199	97	6	.	.	PUNCT
ejpam-2199	98	1	so	so	ADV
ejpam-2199	98	2	y	y	PROPN
ejpam-2199	98	3	is	be	AUX
ejpam-2199	98	4	hurewicz	hurewicz	NOUN
ejpam-2199	98	5	.	.	PUNCT
ejpam-2199	99	1	c.	c.	NOUN
ejpam-2199	99	2	roika	roika	PROPN
ejpam-2199	99	3	,	,	PUNCT
ejpam-2199	99	4	s.	s.	PROPN
ejpam-2199	99	5	kudri	kudri	PROPN
ejpam-2199	99	6	,	,	PUNCT
ejpam-2199	99	7	t.	t.	PROPN
ejpam-2199	99	8	breuckmann	breuckmann	PROPN
ejpam-2199	99	9	/	/	SYM
ejpam-2199	99	10	eur	eur	PROPN
ejpam-2199	99	11	.	.	PUNCT
ejpam-2199	100	1	j.	j.	PROPN
ejpam-2199	100	2	pure	pure	PROPN
ejpam-2199	100	3	appl	appl	PROPN
ejpam-2199	100	4	.	.	PROPN
ejpam-2199	100	5	math	math	PROPN
ejpam-2199	100	6	,	,	PUNCT
ejpam-2199	100	7	8	8	NUM
ejpam-2199	100	8	(	(	PUNCT
ejpam-2199	100	9	2015	2015	NUM
ejpam-2199	100	10	)	)	PUNCT
ejpam-2199	100	11	,	,	PUNCT
ejpam-2199	100	12	514	514	NUM
ejpam-2199	100	13	-	-	SYM
ejpam-2199	100	14	525	525	NUM
ejpam-2199	100	15	517	517	NUM
ejpam-2199	100	16	definition	definition	NOUN
ejpam-2199	100	17	6	6	NUM
ejpam-2199	100	18	.	.	PUNCT
ejpam-2199	101	1	let	let	VERB
ejpam-2199	101	2	x	x	PRON
ejpam-2199	101	3	be	be	AUX
ejpam-2199	101	4	a	a	DET
ejpam-2199	101	5	topological	topological	ADJ
ejpam-2199	101	6	space	space	NOUN
ejpam-2199	101	7	and	and	CCONJ
ejpam-2199	101	8	y	y	PROPN
ejpam-2199	101	9	a	a	DET
ejpam-2199	101	10	subset	subset	NOUN
ejpam-2199	101	11	of	of	ADP
ejpam-2199	101	12	x	x	X
ejpam-2199	101	13	.	.	PUNCT
ejpam-2199	102	1	we	we	PRON
ejpam-2199	102	2	say	say	VERB
ejpam-2199	102	3	that	that	SCONJ
ejpam-2199	102	4	y	y	PROPN
ejpam-2199	102	5	is	be	AUX
ejpam-2199	102	6	hurewicz	hurewicz	ADJ
ejpam-2199	102	7	if	if	SCONJ
ejpam-2199	103	1	and	and	CCONJ
ejpam-2199	103	2	only	only	ADV
ejpam-2199	103	3	if	if	SCONJ
ejpam-2199	103	4	y	y	PROPN
ejpam-2199	103	5	is	be	AUX
ejpam-2199	103	6	a	a	DET
ejpam-2199	103	7	hurewicz	hurewicz	NOUN
ejpam-2199	103	8	subspace	subspace	NOUN
ejpam-2199	103	9	of	of	ADP
ejpam-2199	103	10	x	x	X
ejpam-2199	103	11	.	.	PUNCT
ejpam-2199	104	1	proposition	proposition	NOUN
ejpam-2199	104	2	5	5	NUM
ejpam-2199	104	3	.	.	PUNCT
ejpam-2199	105	1	let	let	VERB
ejpam-2199	105	2	y	y	PRON
ejpam-2199	105	3	be	be	AUX
ejpam-2199	105	4	a	a	DET
ejpam-2199	105	5	subspace	subspace	NOUN
ejpam-2199	105	6	of	of	ADP
ejpam-2199	105	7	x	x	X
ejpam-2199	105	8	.	.	PUNCT
ejpam-2199	106	1	y	y	PROPN
ejpam-2199	106	2	is	be	AUX
ejpam-2199	106	3	hurewicz	hurewicz	ADJ
ejpam-2199	106	4	if	if	SCONJ
ejpam-2199	107	1	and	and	CCONJ
ejpam-2199	107	2	only	only	ADV
ejpam-2199	107	3	if	if	SCONJ
ejpam-2199	107	4	for	for	ADP
ejpam-2199	107	5	each	each	DET
ejpam-2199	107	6	sequence	sequence	NOUN
ejpam-2199	107	7	{	{	PUNCT
ejpam-2199	107	8	un}n∈n	un}n∈n	NOUN
ejpam-2199	107	9	of	of	ADP
ejpam-2199	107	10	coverings	covering	NOUN
ejpam-2199	107	11	of	of	ADP
ejpam-2199	107	12	y	y	PRON
ejpam-2199	107	13	by	by	ADP
ejpam-2199	107	14	open	open	ADJ
ejpam-2199	107	15	sets	set	NOUN
ejpam-2199	107	16	in	in	ADP
ejpam-2199	107	17	x	x	X
ejpam-2199	107	18	,	,	PUNCT
ejpam-2199	107	19	there	there	PRON
ejpam-2199	107	20	is	be	VERB
ejpam-2199	107	21	a	a	DET
ejpam-2199	107	22	sequence	sequence	NOUN
ejpam-2199	107	23	{	{	PUNCT
ejpam-2199	107	24	vn}n∈n	vn}n∈n	ADP
ejpam-2199	107	25	such	such	ADJ
ejpam-2199	107	26	that	that	PRON
ejpam-2199	107	27	:	:	PUNCT
ejpam-2199	107	28	(	(	PUNCT
ejpam-2199	107	29	i	i	NOUN
ejpam-2199	107	30	)	)	PUNCT
ejpam-2199	107	31	∀n	∀n	PROPN
ejpam-2199	107	32	∈	∈	PROPN
ejpam-2199	107	33	n	n	CCONJ
ejpam-2199	107	34	,	,	PUNCT
ejpam-2199	107	35	vn	vn	PROPN
ejpam-2199	107	36	⊂<∞	⊂<∞	PROPN
ejpam-2199	107	37	un	un	PROPN
ejpam-2199	107	38	.	.	PROPN
ejpam-2199	107	39	(	(	PUNCT
ejpam-2199	107	40	ii	ii	PROPN
ejpam-2199	107	41	)	)	PUNCT
ejpam-2199	107	42	∀y	∀y	PROPN
ejpam-2199	107	43	∈	∈	PROPN
ejpam-2199	107	44	y	y	PROPN
ejpam-2199	107	45	,	,	PUNCT
ejpam-2199	107	46	∃n0	∃n0	NOUN
ejpam-2199	107	47	∈	∈	PROPN
ejpam-2199	107	48	n	n	CCONJ
ejpam-2199	107	49	,	,	PUNCT
ejpam-2199	107	50	such	such	ADJ
ejpam-2199	107	51	that	that	SCONJ
ejpam-2199	107	52	∀n	∀n	NUM
ejpam-2199	107	53	∈	∈	NOUN
ejpam-2199	107	54	n	n	ADV
ejpam-2199	107	55	if	if	SCONJ
ejpam-2199	107	56	n≥	n≥	PROPN
ejpam-2199	107	57	n0	n0	NUM
ejpam-2199	107	58	,	,	PUNCT
ejpam-2199	107	59	then	then	ADV
ejpam-2199	107	60	there	there	PRON
ejpam-2199	107	61	exists	exist	VERB
ejpam-2199	107	62	v	v	ADP
ejpam-2199	107	63	∈	∈	PROPN
ejpam-2199	107	64	vn	vn	NOUN
ejpam-2199	107	65	with	with	ADP
ejpam-2199	107	66	y	y	PROPN
ejpam-2199	107	67	∈	∈	PROPN
ejpam-2199	107	68	v	v	NOUN
ejpam-2199	107	69	.	.	PUNCT
ejpam-2199	108	1	proof	proof	NOUN
ejpam-2199	108	2	.	.	PUNCT
ejpam-2199	109	1	(	(	PUNCT
ejpam-2199	109	2	⇒	⇒	PROPN
ejpam-2199	109	3	)	)	PUNCT
ejpam-2199	109	4	considering	consider	VERB
ejpam-2199	109	5	y	y	PROPN
ejpam-2199	109	6	hurewicz	hurewicz	NOUN
ejpam-2199	109	7	,	,	PUNCT
ejpam-2199	109	8	let	let	VERB
ejpam-2199	109	9	{	{	PUNCT
ejpam-2199	109	10	un}n∈n	un}n∈n	PRON
ejpam-2199	109	11	be	be	AUX
ejpam-2199	109	12	a	a	DET
ejpam-2199	109	13	sequence	sequence	NOUN
ejpam-2199	109	14	of	of	ADP
ejpam-2199	109	15	coverings	covering	NOUN
ejpam-2199	109	16	of	of	ADP
ejpam-2199	109	17	y	y	PRON
ejpam-2199	109	18	by	by	ADP
ejpam-2199	109	19	open	open	ADJ
ejpam-2199	109	20	sets	set	NOUN
ejpam-2199	109	21	in	in	ADP
ejpam-2199	109	22	x	x	SYM
ejpam-2199	109	23	,	,	PUNCT
ejpam-2199	109	24	where	where	SCONJ
ejpam-2199	109	25	∀n	∀n	NUM
ejpam-2199	109	26	∈	∈	PROPN
ejpam-2199	109	27	n	n	CCONJ
ejpam-2199	109	28	,	,	PUNCT
ejpam-2199	109	29	un	un	PROPN
ejpam-2199	109	30	=	=	PROPN
ejpam-2199	109	31	{	{	PUNCT
ejpam-2199	109	32	un	un	PROPN
ejpam-2199	109	33	j	j	PROPN
ejpam-2199	109	34	}	}	PUNCT
ejpam-2199	109	35	j∈jn	j∈jn	NOUN
ejpam-2199	109	36	.	.	PUNCT
ejpam-2199	110	1	consider	consider	VERB
ejpam-2199	110	2	the	the	DET
ejpam-2199	110	3	sequence	sequence	NOUN
ejpam-2199	110	4	{	{	PUNCT
ejpam-2199	110	5	wn}n∈n	wn}n∈n	X
ejpam-2199	110	6	where	where	SCONJ
ejpam-2199	110	7	each	each	DET
ejpam-2199	110	8	wn	wn	NOUN
ejpam-2199	110	9	=	=	PRON
ejpam-2199	110	10	{	{	PUNCT
ejpam-2199	110	11	wn	wn	PROPN
ejpam-2199	110	12	j	j	PROPN
ejpam-2199	110	13	}	}	PUNCT
ejpam-2199	110	14	j∈jn	j∈jn	PROPN
ejpam-2199	110	15	with	with	ADP
ejpam-2199	110	16	wn	wn	PROPN
ejpam-2199	110	17	j	j	PROPN
ejpam-2199	110	18	=	=	PROPN
ejpam-2199	110	19	un	un	PROPN
ejpam-2199	110	20	j	j	PROPN
ejpam-2199	110	21	∩	∩	PROPN
ejpam-2199	110	22	y	y	PROPN
ejpam-2199	110	23	.	.	PUNCT
ejpam-2199	111	1	then	then	ADV
ejpam-2199	111	2	wn	wn	PROPN
ejpam-2199	111	3	is	be	AUX
ejpam-2199	111	4	a	a	DET
ejpam-2199	111	5	covering	covering	NOUN
ejpam-2199	111	6	of	of	ADP
ejpam-2199	111	7	y	y	PROPN
ejpam-2199	111	8	since	since	SCONJ
ejpam-2199	111	9	for	for	ADP
ejpam-2199	111	10	each	each	DET
ejpam-2199	111	11	y	y	PROPN
ejpam-2199	111	12	∈	∈	PROPN
ejpam-2199	111	13	y	y	PROPN
ejpam-2199	111	14	by	by	ADP
ejpam-2199	111	15	the	the	DET
ejpam-2199	111	16	fact	fact	NOUN
ejpam-2199	111	17	that	that	SCONJ
ejpam-2199	111	18	un	un	PROPN
ejpam-2199	111	19	be	be	VERB
ejpam-2199	111	20	a	a	DET
ejpam-2199	111	21	covering	covering	NOUN
ejpam-2199	111	22	of	of	ADP
ejpam-2199	111	23	y	y	NOUN
ejpam-2199	111	24	we	we	PRON
ejpam-2199	111	25	have	have	VERB
ejpam-2199	111	26	that	that	SCONJ
ejpam-2199	111	27	there	there	PRON
ejpam-2199	111	28	is	be	VERB
ejpam-2199	111	29	j	j	PROPN
ejpam-2199	111	30	∈	∈	PROPN
ejpam-2199	111	31	jn	jn	PROPN
ejpam-2199	111	32	with	with	ADP
ejpam-2199	111	33	y	y	PROPN
ejpam-2199	111	34	∈	∈	PROPN
ejpam-2199	112	1	un	un	PROPN
ejpam-2199	112	2	j	j	PROPN
ejpam-2199	112	3	,	,	PUNCT
ejpam-2199	112	4	then	then	ADV
ejpam-2199	112	5	y	y	PROPN
ejpam-2199	112	6	∈	∈	PROPN
ejpam-2199	112	7	un	un	PROPN
ejpam-2199	112	8	j	j	PROPN
ejpam-2199	112	9	∩	∩	PROPN
ejpam-2199	112	10	y	y	PROPN
ejpam-2199	112	11	=	=	PROPN
ejpam-2199	112	12	wn	wn	PROPN
ejpam-2199	112	13	j	j	PROPN
ejpam-2199	112	14	andwn	andwn	NOUN
ejpam-2199	112	15	is	be	AUX
ejpam-2199	112	16	formed	form	VERB
ejpam-2199	112	17	by	by	ADP
ejpam-2199	112	18	open	open	ADJ
ejpam-2199	112	19	sets	set	NOUN
ejpam-2199	112	20	in	in	ADP
ejpam-2199	112	21	y	y	PROPN
ejpam-2199	112	22	,	,	PUNCT
ejpam-2199	112	23	but	but	CCONJ
ejpam-2199	112	24	y	y	PROPN
ejpam-2199	112	25	is	be	AUX
ejpam-2199	112	26	hurewicz	hurewicz	NOUN
ejpam-2199	112	27	then	then	ADV
ejpam-2199	112	28	there	there	PRON
ejpam-2199	112	29	exists	exist	VERB
ejpam-2199	112	30	a	a	DET
ejpam-2199	112	31	sequence	sequence	NOUN
ejpam-2199	112	32	{	{	PUNCT
ejpam-2199	112	33	hn}n∈n	hn}n∈n	ADP
ejpam-2199	112	34	,	,	PUNCT
ejpam-2199	112	35	such	such	ADJ
ejpam-2199	112	36	that	that	SCONJ
ejpam-2199	112	37	:	:	PUNCT
ejpam-2199	112	38	(	(	PUNCT
ejpam-2199	112	39	i	i	NOUN
ejpam-2199	112	40	)	)	PUNCT
ejpam-2199	112	41	∀n	∀n	PROPN
ejpam-2199	112	42	∈	∈	PROPN
ejpam-2199	112	43	n	n	CCONJ
ejpam-2199	112	44	,	,	PUNCT
ejpam-2199	112	45	hn	hn	PROPN
ejpam-2199	112	46	⊂<∞wn	⊂<∞wn	PROPN
ejpam-2199	112	47	,	,	PUNCT
ejpam-2199	112	48	i.	i.	PROPN
ejpam-2199	112	49	e.	e.	PROPN
ejpam-2199	112	50	,	,	PUNCT
ejpam-2199	112	51	∃in	∃in	PROPN
ejpam-2199	112	52	⊂<∞	⊂<∞	PROPN
ejpam-2199	112	53	jn	jn	PROPN
ejpam-2199	112	54	such	such	ADJ
ejpam-2199	112	55	that	that	SCONJ
ejpam-2199	112	56	hn	hn	PROPN
ejpam-2199	112	57	=	=	X
ejpam-2199	112	58	{	{	PUNCT
ejpam-2199	112	59	wn	wn	PROPN
ejpam-2199	112	60	j	j	PROPN
ejpam-2199	112	61	}	}	PUNCT
ejpam-2199	112	62	j∈jn	j∈jn	PROPN
ejpam-2199	112	63	.	.	PUNCT
ejpam-2199	113	1	(	(	PUNCT
ejpam-2199	113	2	ii	ii	NOUN
ejpam-2199	113	3	)	)	PUNCT
ejpam-2199	113	4	for	for	ADP
ejpam-2199	113	5	each	each	DET
ejpam-2199	113	6	y	y	PROPN
ejpam-2199	113	7	∈	∈	PROPN
ejpam-2199	113	8	y,∃n0	y,∃n0	NOUN
ejpam-2199	113	9	∈	∈	PROPN
ejpam-2199	113	10	n	n	PRON
ejpam-2199	113	11	such	such	ADJ
ejpam-2199	113	12	that	that	SCONJ
ejpam-2199	113	13	∀n	∀n	NUM
ejpam-2199	113	14	∈	∈	NOUN
ejpam-2199	113	15	n	n	ADV
ejpam-2199	113	16	if	if	SCONJ
ejpam-2199	113	17	n≥	n≥	PROPN
ejpam-2199	113	18	n0	n0	NUM
ejpam-2199	113	19	,	,	PUNCT
ejpam-2199	113	20	then	then	ADV
ejpam-2199	113	21	there	there	PRON
ejpam-2199	113	22	exists	exist	VERB
ejpam-2199	113	23	v	v	ADP
ejpam-2199	113	24	∈	∈	PROPN
ejpam-2199	113	25	hn	hn	PROPN
ejpam-2199	113	26	with	with	ADP
ejpam-2199	113	27	y	y	PROPN
ejpam-2199	113	28	∈	∈	PROPN
ejpam-2199	113	29	v	v	PROPN
ejpam-2199	113	30	.	.	PUNCT
ejpam-2199	114	1	consider	consider	VERB
ejpam-2199	114	2	∀n	∀n	NUM
ejpam-2199	114	3	∈	∈	PROPN
ejpam-2199	114	4	n	n	CCONJ
ejpam-2199	114	5	,	,	PUNCT
ejpam-2199	114	6	vn	vn	PROPN
ejpam-2199	114	7	=	=	PRON
ejpam-2199	114	8	{	{	PUNCT
ejpam-2199	114	9	un	un	PROPN
ejpam-2199	114	10	j	j	PROPN
ejpam-2199	114	11	}	}	PUNCT
ejpam-2199	114	12	j∈in	j∈in	PROPN
ejpam-2199	114	13	,	,	PUNCT
ejpam-2199	114	14	then	then	ADV
ejpam-2199	114	15	the	the	DET
ejpam-2199	114	16	sequence	sequence	NOUN
ejpam-2199	114	17	{	{	PUNCT
ejpam-2199	114	18	vn}n∈n	vn}n∈n	X
ejpam-2199	114	19	is	be	AUX
ejpam-2199	114	20	such	such	ADJ
ejpam-2199	114	21	that	that	SCONJ
ejpam-2199	114	22	:	:	PUNCT
ejpam-2199	114	23	(	(	PUNCT
ejpam-2199	114	24	i	i	NOUN
ejpam-2199	114	25	)	)	PUNCT
ejpam-2199	114	26	∀n	∀n	PROPN
ejpam-2199	114	27	∈	∈	PROPN
ejpam-2199	114	28	n	n	CCONJ
ejpam-2199	114	29	,	,	PUNCT
ejpam-2199	114	30	vn	vn	PROPN
ejpam-2199	114	31	⊂<∞	⊂<∞	PROPN
ejpam-2199	114	32	un	un	PROPN
ejpam-2199	114	33	.	.	PROPN
ejpam-2199	114	34	(	(	PUNCT
ejpam-2199	114	35	ii	ii	NOUN
ejpam-2199	114	36	)	)	PUNCT
ejpam-2199	114	37	if	if	SCONJ
ejpam-2199	114	38	y	y	PROPN
ejpam-2199	114	39	∈	∈	PROPN
ejpam-2199	114	40	y	y	PROPN
ejpam-2199	114	41	,	,	PUNCT
ejpam-2199	114	42	from	from	ADP
ejpam-2199	114	43	previous	previous	ADJ
ejpam-2199	114	44	(	(	PUNCT
ejpam-2199	114	45	ii	ii	NOUN
ejpam-2199	114	46	)	)	PUNCT
ejpam-2199	114	47	∃n0	∃n0	NOUN
ejpam-2199	114	48	∈	∈	PROPN
ejpam-2199	114	49	n	n	CCONJ
ejpam-2199	114	50	,	,	PUNCT
ejpam-2199	114	51	such	such	ADJ
ejpam-2199	114	52	that	that	SCONJ
ejpam-2199	114	53	∀n	∀n	NUM
ejpam-2199	114	54	∈	∈	NOUN
ejpam-2199	114	55	n	n	ADV
ejpam-2199	114	56	if	if	SCONJ
ejpam-2199	114	57	n≥	n≥	PROPN
ejpam-2199	114	58	n0	n0	X
ejpam-2199	114	59	then	then	ADV
ejpam-2199	114	60	there	there	PRON
ejpam-2199	114	61	exists	exist	VERB
ejpam-2199	114	62	v	v	ADP
ejpam-2199	114	63	∈	∈	PROPN
ejpam-2199	114	64	hn	hn	PROPN
ejpam-2199	114	65	with	with	ADP
ejpam-2199	114	66	y	y	PROPN
ejpam-2199	114	67	∈	∈	PROPN
ejpam-2199	114	68	v	v	NOUN
ejpam-2199	114	69	.	.	PUNCT
ejpam-2199	115	1	therefore	therefore	ADV
ejpam-2199	115	2	there	there	PRON
ejpam-2199	115	3	is	be	VERB
ejpam-2199	115	4	j	j	PROPN
ejpam-2199	115	5	∈	∈	PROPN
ejpam-2199	115	6	in	in	ADP
ejpam-2199	115	7	with	with	ADP
ejpam-2199	115	8	v	v	NOUN
ejpam-2199	115	9	=	=	NOUN
ejpam-2199	115	10	wn	wn	PROPN
ejpam-2199	115	11	j	j	PROPN
ejpam-2199	115	12	=	=	PROPN
ejpam-2199	115	13	un	un	PROPN
ejpam-2199	115	14	j	j	PROPN
ejpam-2199	115	15	∩	∩	PROPN
ejpam-2199	115	16	y	y	PROPN
ejpam-2199	115	17	.	.	PUNCT
ejpam-2199	116	1	since	since	SCONJ
ejpam-2199	116	2	j	j	PROPN
ejpam-2199	116	3	∈	∈	PROPN
ejpam-2199	116	4	in	in	ADP
ejpam-2199	116	5	we	we	PRON
ejpam-2199	116	6	have	have	VERB
ejpam-2199	116	7	that	that	DET
ejpam-2199	116	8	un	un	PROPN
ejpam-2199	116	9	j	j	PROPN
ejpam-2199	116	10	∈	∈	PROPN
ejpam-2199	116	11	vn	vn	PROPN
ejpam-2199	116	12	and	and	CCONJ
ejpam-2199	116	13	y	y	PROPN
ejpam-2199	116	14	∈	∈	PROPN
ejpam-2199	116	15	un	un	PROPN
ejpam-2199	116	16	j	j	PROPN
ejpam-2199	116	17	.	.	PUNCT
ejpam-2199	117	1	(	(	PUNCT
ejpam-2199	117	2	⇐	⇐	ADJ
ejpam-2199	117	3	)	)	PUNCT
ejpam-2199	117	4	let	let	VERB
ejpam-2199	117	5	{	{	PUNCT
ejpam-2199	117	6	un}n∈n	un}n∈n	PRON
ejpam-2199	117	7	be	be	AUX
ejpam-2199	117	8	a	a	DET
ejpam-2199	117	9	sequence	sequence	NOUN
ejpam-2199	117	10	of	of	ADP
ejpam-2199	117	11	coverings	covering	NOUN
ejpam-2199	117	12	of	of	ADP
ejpam-2199	117	13	y	y	PRON
ejpam-2199	117	14	by	by	ADP
ejpam-2199	117	15	open	open	ADJ
ejpam-2199	117	16	sets	set	NOUN
ejpam-2199	117	17	in	in	ADP
ejpam-2199	117	18	y	y	PROPN
ejpam-2199	117	19	,	,	PUNCT
ejpam-2199	117	20	where	where	SCONJ
ejpam-2199	117	21	eachun	eachun	PROPN
ejpam-2199	117	22	=	=	PRON
ejpam-2199	117	23	{	{	PUNCT
ejpam-2199	117	24	un	un	PROPN
ejpam-2199	117	25	j	j	PROPN
ejpam-2199	117	26	}	}	PUNCT
ejpam-2199	117	27	j∈jn	j∈jn	NOUN
ejpam-2199	117	28	.	.	PUNCT
ejpam-2199	118	1	since	since	SCONJ
ejpam-2199	118	2	y	y	PROPN
ejpam-2199	118	3	is	be	AUX
ejpam-2199	118	4	subspace	subspace	NOUN
ejpam-2199	118	5	of	of	ADP
ejpam-2199	118	6	x	x	PRON
ejpam-2199	118	7	,	,	PUNCT
ejpam-2199	118	8	for	for	ADP
ejpam-2199	118	9	each	each	DET
ejpam-2199	118	10	n	n	PRON
ejpam-2199	118	11	∈	∈	PROPN
ejpam-2199	118	12	n	n	NOUN
ejpam-2199	118	13	and	and	CCONJ
ejpam-2199	118	14	for	for	ADP
ejpam-2199	118	15	each	each	DET
ejpam-2199	118	16	j	j	PROPN
ejpam-2199	118	17	∈	∈	PROPN
ejpam-2199	118	18	jn	jn	PROPN
ejpam-2199	118	19	there	there	PRON
ejpam-2199	118	20	exists	exist	VERB
ejpam-2199	118	21	a	a	DET
ejpam-2199	118	22	open	open	ADJ
ejpam-2199	118	23	set	set	NOUN
ejpam-2199	118	24	vn	vn	PROPN
ejpam-2199	118	25	j	j	PROPN
ejpam-2199	118	26	in	in	ADP
ejpam-2199	118	27	x	x	X
ejpam-2199	118	28	such	such	ADJ
ejpam-2199	118	29	that	that	SCONJ
ejpam-2199	118	30	un	un	PROPN
ejpam-2199	118	31	j	j	PROPN
ejpam-2199	118	32	=	=	PROPN
ejpam-2199	118	33	vn	vn	PROPN
ejpam-2199	118	34	j∩y	j∩y	NOUN
ejpam-2199	118	35	.	.	PUNCT
ejpam-2199	119	1	consider	consider	VERB
ejpam-2199	119	2	∀n	∀n	NUM
ejpam-2199	119	3	∈	∈	PROPN
ejpam-2199	119	4	n	n	CCONJ
ejpam-2199	119	5	,	,	PUNCT
ejpam-2199	119	6	wn	wn	PROPN
ejpam-2199	119	7	=	=	PROPN
ejpam-2199	119	8	{	{	PUNCT
ejpam-2199	119	9	vn	vn	PROPN
ejpam-2199	119	10	j	j	PROPN
ejpam-2199	119	11	}	}	PUNCT
ejpam-2199	119	12	j∈in	j∈in	PROPN
ejpam-2199	119	13	,	,	PUNCT
ejpam-2199	119	14	thenwn	thenwn	PROPN
ejpam-2199	119	15	is	be	AUX
ejpam-2199	119	16	a	a	DET
ejpam-2199	119	17	covering	covering	NOUN
ejpam-2199	119	18	of	of	ADP
ejpam-2199	119	19	y	y	PROPN
ejpam-2199	119	20	because	because	SCONJ
ejpam-2199	119	21	,	,	PUNCT
ejpam-2199	119	22	if	if	SCONJ
ejpam-2199	119	23	y	y	PROPN
ejpam-2199	119	24	∈	∈	PROPN
ejpam-2199	119	25	y	y	PROPN
ejpam-2199	119	26	,	,	PUNCT
ejpam-2199	119	27	∃	∃	PROPN
ejpam-2199	119	28	j	j	PROPN
ejpam-2199	119	29	∈	∈	PROPN
ejpam-2199	119	30	jn	jn	PROPN
ejpam-2199	119	31	such	such	ADJ
ejpam-2199	119	32	that	that	SCONJ
ejpam-2199	119	33	y	y	PROPN
ejpam-2199	119	34	∈	∈	PROPN
ejpam-2199	119	35	un	un	PROPN
ejpam-2199	119	36	j	j	PROPN
ejpam-2199	119	37	,	,	PUNCT
ejpam-2199	119	38	then	then	ADV
ejpam-2199	119	39	y	y	PROPN
ejpam-2199	119	40	∈	∈	PROPN
ejpam-2199	119	41	vn	vn	PROPN
ejpam-2199	119	42	j	j	PROPN
ejpam-2199	119	43	and	and	CCONJ
ejpam-2199	119	44	the	the	DET
ejpam-2199	119	45	sequence	sequence	NOUN
ejpam-2199	119	46	{	{	PUNCT
ejpam-2199	119	47	wn	wn	PROPN
ejpam-2199	119	48	j	j	PROPN
ejpam-2199	119	49	}	}	PUNCT
ejpam-2199	119	50	j∈jn	j∈jn	PROPN
ejpam-2199	119	51	is	be	AUX
ejpam-2199	119	52	a	a	DET
ejpam-2199	119	53	sequence	sequence	NOUN
ejpam-2199	119	54	of	of	ADP
ejpam-2199	119	55	coverings	covering	NOUN
ejpam-2199	119	56	of	of	ADP
ejpam-2199	119	57	y	y	PRON
ejpam-2199	119	58	by	by	ADP
ejpam-2199	119	59	open	open	ADJ
ejpam-2199	119	60	sets	set	NOUN
ejpam-2199	119	61	in	in	ADP
ejpam-2199	119	62	x	x	X
ejpam-2199	119	63	,	,	PUNCT
ejpam-2199	119	64	then	then	ADV
ejpam-2199	119	65	there	there	PRON
ejpam-2199	119	66	exists	exist	VERB
ejpam-2199	119	67	a	a	DET
ejpam-2199	119	68	sequence	sequence	NOUN
ejpam-2199	119	69	{	{	PUNCT
ejpam-2199	119	70	hn}n∈n	hn}n∈n	ADP
ejpam-2199	119	71	,	,	PUNCT
ejpam-2199	119	72	such	such	ADJ
ejpam-2199	119	73	that	that	SCONJ
ejpam-2199	119	74	:	:	PUNCT
ejpam-2199	119	75	(	(	PUNCT
ejpam-2199	119	76	i	i	NOUN
ejpam-2199	119	77	)	)	PUNCT
ejpam-2199	119	78	∀n	∀n	PROPN
ejpam-2199	119	79	∈	∈	PROPN
ejpam-2199	119	80	n	n	CCONJ
ejpam-2199	119	81	,	,	PUNCT
ejpam-2199	119	82	hn	hn	PROPN
ejpam-2199	119	83	⊂<∞wn	⊂<∞wn	PROPN
ejpam-2199	119	84	,	,	PUNCT
ejpam-2199	119	85	i.	i.	PROPN
ejpam-2199	119	86	e.	e.	PROPN
ejpam-2199	119	87	,	,	PUNCT
ejpam-2199	119	88	∃in	∃in	PROPN
ejpam-2199	119	89	⊂<∞	⊂<∞	PROPN
ejpam-2199	119	90	jn	jn	PROPN
ejpam-2199	119	91	,	,	PUNCT
ejpam-2199	119	92	such	such	ADJ
ejpam-2199	119	93	that	that	SCONJ
ejpam-2199	119	94	hn	hn	PROPN
ejpam-2199	119	95	=	=	X
ejpam-2199	119	96	{	{	PUNCT
ejpam-2199	119	97	vn	vn	PROPN
ejpam-2199	119	98	j	j	PROPN
ejpam-2199	119	99	}	}	PUNCT
ejpam-2199	119	100	j∈in	j∈in	PROPN
ejpam-2199	119	101	.	.	PUNCT
ejpam-2199	120	1	(	(	PUNCT
ejpam-2199	120	2	ii	ii	NOUN
ejpam-2199	120	3	)	)	PUNCT
ejpam-2199	120	4	∀y	∀y	PROPN
ejpam-2199	120	5	∈	∈	PROPN
ejpam-2199	120	6	y,∃n0	y,∃n0	NOUN
ejpam-2199	120	7	∈	∈	PROPN
ejpam-2199	120	8	n	n	PRON
ejpam-2199	120	9	such	such	ADJ
ejpam-2199	120	10	that	that	SCONJ
ejpam-2199	120	11	∀n	∀n	NUM
ejpam-2199	120	12	∈	∈	NOUN
ejpam-2199	120	13	n	n	ADV
ejpam-2199	120	14	if	if	SCONJ
ejpam-2199	120	15	n≥	n≥	PROPN
ejpam-2199	120	16	n0	n0	X
ejpam-2199	120	17	then	then	ADV
ejpam-2199	120	18	there	there	PRON
ejpam-2199	120	19	exists	exist	VERB
ejpam-2199	120	20	v	v	ADP
ejpam-2199	120	21	∈	∈	PROPN
ejpam-2199	120	22	hn	hn	PROPN
ejpam-2199	120	23	with	with	ADP
ejpam-2199	120	24	y	y	PROPN
ejpam-2199	120	25	∈	∈	PROPN
ejpam-2199	120	26	v	v	PROPN
ejpam-2199	120	27	.	.	PUNCT
ejpam-2199	121	1	consider	consider	VERB
ejpam-2199	121	2	∀n	∀n	NUM
ejpam-2199	121	3	∈	∈	PROPN
ejpam-2199	121	4	n	n	CCONJ
ejpam-2199	121	5	,	,	PUNCT
ejpam-2199	121	6	vn	vn	PROPN
ejpam-2199	121	7	=	=	PRON
ejpam-2199	121	8	{	{	PUNCT
ejpam-2199	121	9	un	un	PROPN
ejpam-2199	121	10	j	j	PROPN
ejpam-2199	121	11	}	}	PUNCT
ejpam-2199	121	12	j∈in	j∈in	PROPN
ejpam-2199	121	13	,	,	PUNCT
ejpam-2199	121	14	then	then	ADV
ejpam-2199	121	15	the	the	DET
ejpam-2199	121	16	sequence	sequence	NOUN
ejpam-2199	121	17	{	{	PUNCT
ejpam-2199	121	18	vn}n∈n	vn}n∈n	X
ejpam-2199	121	19	is	be	AUX
ejpam-2199	121	20	such	such	ADJ
ejpam-2199	121	21	that	that	SCONJ
ejpam-2199	121	22	:	:	PUNCT
ejpam-2199	121	23	(	(	PUNCT
ejpam-2199	121	24	i	i	NOUN
ejpam-2199	121	25	)	)	PUNCT
ejpam-2199	121	26	∀n	∀n	PROPN
ejpam-2199	121	27	∈	∈	PROPN
ejpam-2199	121	28	n	n	CCONJ
ejpam-2199	121	29	,	,	PUNCT
ejpam-2199	121	30	vn	vn	PROPN
ejpam-2199	121	31	⊂<∞	⊂<∞	PROPN
ejpam-2199	121	32	un	un	PROPN
ejpam-2199	121	33	.	.	PROPN
ejpam-2199	121	34	(	(	PUNCT
ejpam-2199	121	35	ii	ii	NOUN
ejpam-2199	121	36	)	)	PUNCT
ejpam-2199	122	1	if	if	SCONJ
ejpam-2199	122	2	y	y	PROPN
ejpam-2199	122	3	∈	∈	PROPN
ejpam-2199	122	4	y	y	PROPN
ejpam-2199	122	5	,	,	PUNCT
ejpam-2199	122	6	from	from	ADP
ejpam-2199	122	7	previous	previous	ADJ
ejpam-2199	122	8	(	(	PUNCT
ejpam-2199	122	9	ii	ii	NOUN
ejpam-2199	122	10	)	)	PUNCT
ejpam-2199	122	11	∃n0	∃n0	NOUN
ejpam-2199	122	12	∈	∈	PROPN
ejpam-2199	122	13	n	n	CCONJ
ejpam-2199	122	14	,	,	PUNCT
ejpam-2199	122	15	such	such	ADJ
ejpam-2199	122	16	that	that	SCONJ
ejpam-2199	122	17	∀n	∀n	NUM
ejpam-2199	122	18	∈	∈	NOUN
ejpam-2199	122	19	n	n	ADV
ejpam-2199	122	20	if	if	SCONJ
ejpam-2199	122	21	n	n	NUM
ejpam-2199	122	22	≥	≥	NOUN
ejpam-2199	122	23	n0	n0	X
ejpam-2199	122	24	then	then	ADV
ejpam-2199	122	25	there	there	PRON
ejpam-2199	122	26	is	be	VERB
ejpam-2199	122	27	v	v	ADP
ejpam-2199	122	28	∈	∈	NOUN
ejpam-2199	122	29	hn	hn	PROPN
ejpam-2199	122	30	with	with	ADP
ejpam-2199	122	31	y	y	PROPN
ejpam-2199	122	32	∈	∈	PROPN
ejpam-2199	122	33	v	v	NOUN
ejpam-2199	122	34	.	.	PUNCT
ejpam-2199	123	1	since	since	SCONJ
ejpam-2199	123	2	v	v	NUM
ejpam-2199	123	3	∈	∈	NOUN
ejpam-2199	124	1	hn	hn	INTJ
ejpam-2199	124	2	we	we	PRON
ejpam-2199	124	3	have	have	VERB
ejpam-2199	124	4	that	that	SCONJ
ejpam-2199	124	5	there	there	PRON
ejpam-2199	124	6	exists	exist	VERB
ejpam-2199	124	7	j	j	PROPN
ejpam-2199	124	8	∈	∈	PROPN
ejpam-2199	124	9	in	in	ADP
ejpam-2199	124	10	with	with	ADP
ejpam-2199	124	11	y	y	PROPN
ejpam-2199	124	12	∈	∈	PROPN
ejpam-2199	124	13	vn	vn	PROPN
ejpam-2199	124	14	j	j	PROPN
ejpam-2199	124	15	,	,	PUNCT
ejpam-2199	124	16	but	but	CCONJ
ejpam-2199	125	1	y	y	PROPN
ejpam-2199	125	2	∈	∈	PROPN
ejpam-2199	125	3	y	y	PROPN
ejpam-2199	125	4	,	,	PUNCT
ejpam-2199	125	5	then	then	ADV
ejpam-2199	125	6	y	y	PROPN
ejpam-2199	125	7	∈	∈	PROPN
ejpam-2199	125	8	vn	vn	PROPN
ejpam-2199	125	9	j	j	PROPN
ejpam-2199	125	10	∩	∩	PROPN
ejpam-2199	125	11	y	y	PROPN
ejpam-2199	125	12	=	=	PROPN
ejpam-2199	125	13	un	un	PROPN
ejpam-2199	125	14	j	j	PROPN
ejpam-2199	125	15	∈	∈	PROPN
ejpam-2199	125	16	vn	vn	PROPN
ejpam-2199	125	17	,	,	PUNCT
ejpam-2199	125	18	because	because	SCONJ
ejpam-2199	125	19	j	j	PROPN
ejpam-2199	125	20	∈	∈	PROPN
ejpam-2199	125	21	in	in	ADP
ejpam-2199	125	22	.	.	PUNCT
ejpam-2199	126	1	so	so	ADV
ejpam-2199	126	2	y	y	PROPN
ejpam-2199	126	3	is	be	AUX
ejpam-2199	126	4	a	a	DET
ejpam-2199	126	5	hurewicz	hurewicz	NOUN
ejpam-2199	126	6	space	space	NOUN
ejpam-2199	126	7	.	.	PUNCT
ejpam-2199	127	1	c.	c.	PROPN
ejpam-2199	127	2	roika	roika	PROPN
ejpam-2199	127	3	,	,	PUNCT
ejpam-2199	127	4	s.	s.	PROPN
ejpam-2199	127	5	kudri	kudri	PROPN
ejpam-2199	127	6	,	,	PUNCT
ejpam-2199	127	7	t.	t.	PROPN
ejpam-2199	127	8	breuckmann	breuckmann	PROPN
ejpam-2199	127	9	/	/	SYM
ejpam-2199	127	10	eur	eur	PROPN
ejpam-2199	127	11	.	.	PUNCT
ejpam-2199	128	1	j.	j.	PROPN
ejpam-2199	128	2	pure	pure	PROPN
ejpam-2199	128	3	appl	appl	PROPN
ejpam-2199	128	4	.	.	PROPN
ejpam-2199	128	5	math	math	PROPN
ejpam-2199	128	6	,	,	PUNCT
ejpam-2199	128	7	8	8	NUM
ejpam-2199	128	8	(	(	PUNCT
ejpam-2199	128	9	2015	2015	NUM
ejpam-2199	128	10	)	)	PUNCT
ejpam-2199	128	11	,	,	PUNCT
ejpam-2199	128	12	514	514	NUM
ejpam-2199	128	13	-	-	SYM
ejpam-2199	128	14	525	525	NUM
ejpam-2199	128	15	518	518	NUM
ejpam-2199	128	16	proposition	proposition	NOUN
ejpam-2199	128	17	6	6	NUM
ejpam-2199	128	18	.	.	PUNCT
ejpam-2199	129	1	if	if	SCONJ
ejpam-2199	129	2	f	f	PROPN
ejpam-2199	129	3	is	be	AUX
ejpam-2199	129	4	a	a	DET
ejpam-2199	129	5	closed	closed	ADJ
ejpam-2199	129	6	subspace	subspace	NOUN
ejpam-2199	129	7	of	of	ADP
ejpam-2199	129	8	a	a	DET
ejpam-2199	129	9	hurewicz	hurewicz	NOUN
ejpam-2199	129	10	space	space	NOUN
ejpam-2199	129	11	x	x	INTJ
ejpam-2199	129	12	,	,	PUNCT
ejpam-2199	129	13	then	then	ADV
ejpam-2199	129	14	f	f	PROPN
ejpam-2199	129	15	is	be	AUX
ejpam-2199	129	16	hurewicz	hurewicz	NOUN
ejpam-2199	129	17	.	.	PUNCT
ejpam-2199	130	1	proof	proof	NOUN
ejpam-2199	130	2	.	.	PUNCT
ejpam-2199	131	1	let	let	VERB
ejpam-2199	131	2	{	{	PUNCT
ejpam-2199	131	3	un}n∈n	un}n∈n	PRON
ejpam-2199	131	4	be	be	AUX
ejpam-2199	131	5	a	a	DET
ejpam-2199	131	6	sequence	sequence	NOUN
ejpam-2199	131	7	of	of	ADP
ejpam-2199	131	8	coverings	covering	NOUN
ejpam-2199	131	9	of	of	ADP
ejpam-2199	131	10	f	f	PROPN
ejpam-2199	131	11	by	by	ADP
ejpam-2199	131	12	open	open	ADJ
ejpam-2199	131	13	sets	set	NOUN
ejpam-2199	131	14	in	in	ADP
ejpam-2199	131	15	x	x	SYM
ejpam-2199	131	16	,	,	PUNCT
ejpam-2199	131	17	where	where	SCONJ
ejpam-2199	131	18	each	each	DET
ejpam-2199	131	19	un	un	PROPN
ejpam-2199	132	1	=	=	PRON
ejpam-2199	132	2	{	{	PUNCT
ejpam-2199	132	3	un	un	PROPN
ejpam-2199	132	4	j	j	PROPN
ejpam-2199	132	5	}	}	PUNCT
ejpam-2199	132	6	j∈jn	j∈jn	NOUN
ejpam-2199	132	7	.	.	PUNCT
ejpam-2199	133	1	since	since	SCONJ
ejpam-2199	133	2	f	f	PROPN
ejpam-2199	133	3	is	be	AUX
ejpam-2199	133	4	a	a	DET
ejpam-2199	133	5	closed	closed	ADJ
ejpam-2199	133	6	set	set	NOUN
ejpam-2199	133	7	,	,	PUNCT
ejpam-2199	133	8	f	f	PROPN
ejpam-2199	133	9	c	c	PROPN
ejpam-2199	133	10	is	be	AUX
ejpam-2199	133	11	an	an	DET
ejpam-2199	133	12	open	open	ADJ
ejpam-2199	133	13	set	set	NOUN
ejpam-2199	133	14	.	.	PUNCT
ejpam-2199	134	1	considerwn	considerwn	PROPN
ejpam-2199	134	2	=	=	SYM
ejpam-2199	134	3	{	{	PUNCT
ejpam-2199	134	4	un	un	PROPN
ejpam-2199	134	5	j	j	PROPN
ejpam-2199	134	6	}	}	PUNCT
ejpam-2199	134	7	j∈in	j∈in	PROPN
ejpam-2199	134	8	∪	∪	PROPN
ejpam-2199	134	9	f	f	PROPN
ejpam-2199	134	10	c	c	PROPN
ejpam-2199	134	11	,	,	PUNCT
ejpam-2199	134	12	then	then	ADV
ejpam-2199	134	13	wn	wn	PROPN
ejpam-2199	134	14	is	be	AUX
ejpam-2199	134	15	an	an	DET
ejpam-2199	134	16	open	open	ADJ
ejpam-2199	134	17	covering	covering	NOUN
ejpam-2199	134	18	of	of	ADP
ejpam-2199	134	19	x	x	X
ejpam-2199	134	20	.	.	PUNCT
ejpam-2199	135	1	let	let	VERB
ejpam-2199	135	2	{	{	PUNCT
ejpam-2199	135	3	wn}n∈n	wn}n∈n	X
ejpam-2199	135	4	be	be	AUX
ejpam-2199	135	5	a	a	DET
ejpam-2199	135	6	sequence	sequence	NOUN
ejpam-2199	135	7	of	of	ADP
ejpam-2199	135	8	open	open	ADJ
ejpam-2199	135	9	coverings	covering	NOUN
ejpam-2199	135	10	of	of	ADP
ejpam-2199	135	11	x	x	X
ejpam-2199	135	12	.	.	PUNCT
ejpam-2199	136	1	since	since	SCONJ
ejpam-2199	136	2	x	x	PROPN
ejpam-2199	136	3	is	be	AUX
ejpam-2199	136	4	hurewicz	hurewicz	NOUN
ejpam-2199	136	5	,	,	PUNCT
ejpam-2199	136	6	there	there	PRON
ejpam-2199	136	7	exists	exist	VERB
ejpam-2199	136	8	a	a	DET
ejpam-2199	136	9	sequence	sequence	NOUN
ejpam-2199	136	10	{	{	PUNCT
ejpam-2199	136	11	hn}n∈n	hn}n∈n	ADP
ejpam-2199	136	12	,	,	PUNCT
ejpam-2199	136	13	such	such	ADJ
ejpam-2199	136	14	that	that	SCONJ
ejpam-2199	136	15	:	:	PUNCT
ejpam-2199	136	16	(	(	PUNCT
ejpam-2199	136	17	i	i	NOUN
ejpam-2199	136	18	)	)	PUNCT
ejpam-2199	136	19	∀n	∀n	PROPN
ejpam-2199	136	20	∈	∈	PROPN
ejpam-2199	136	21	n	n	CCONJ
ejpam-2199	136	22	,	,	PUNCT
ejpam-2199	136	23	hn	hn	PROPN
ejpam-2199	136	24	⊂<∞	⊂<∞	PROPN
ejpam-2199	136	25	wn	wn	PROPN
ejpam-2199	136	26	,	,	PUNCT
ejpam-2199	136	27	i.	i.	PROPN
ejpam-2199	136	28	e.	e.	PROPN
ejpam-2199	136	29	,	,	PUNCT
ejpam-2199	136	30	there	there	PRON
ejpam-2199	136	31	exists	exist	VERB
ejpam-2199	136	32	a	a	DET
ejpam-2199	136	33	finite	finite	NOUN
ejpam-2199	136	34	set	set	VERB
ejpam-2199	136	35	in	in	ADP
ejpam-2199	136	36	,	,	PUNCT
ejpam-2199	136	37	such	such	ADJ
ejpam-2199	136	38	that	that	SCONJ
ejpam-2199	136	39	hn	hn	PROPN
ejpam-2199	136	40	=	=	X
ejpam-2199	136	41	{	{	PUNCT
ejpam-2199	136	42	vn	vn	PROPN
ejpam-2199	136	43	j	j	PROPN
ejpam-2199	136	44	}	}	PUNCT
ejpam-2199	136	45	j∈in	j∈in	PROPN
ejpam-2199	136	46	where	where	SCONJ
ejpam-2199	136	47	vn	vn	PROPN
ejpam-2199	136	48	j	j	PROPN
ejpam-2199	136	49	=	=	PUNCT
ejpam-2199	136	50	uni	uni	PROPN
ejpam-2199	136	51	for	for	ADP
ejpam-2199	136	52	some	some	PRON
ejpam-2199	136	53	i	i	PRON
ejpam-2199	136	54	∈	∈	PROPN
ejpam-2199	136	55	jn	jn	PROPN
ejpam-2199	137	1	or	or	CCONJ
ejpam-2199	137	2	vn	vn	INTJ
ejpam-2199	137	3	j	j	PROPN
ejpam-2199	138	1	=	=	PUNCT
ejpam-2199	138	2	f	f	PROPN
ejpam-2199	138	3	c	c	PROPN
ejpam-2199	138	4	.	.	PUNCT
ejpam-2199	139	1	(	(	PUNCT
ejpam-2199	139	2	ii	ii	NOUN
ejpam-2199	139	3	)	)	PUNCT
ejpam-2199	139	4	for	for	ADP
ejpam-2199	139	5	each	each	DET
ejpam-2199	139	6	x	x	SYM
ejpam-2199	139	7	∈	∈	PROPN
ejpam-2199	139	8	x	x	X
ejpam-2199	139	9	,	,	PUNCT
ejpam-2199	139	10	∃n0	∃n0	NOUN
ejpam-2199	139	11	∈	∈	PROPN
ejpam-2199	139	12	n	n	PRON
ejpam-2199	139	13	such	such	ADJ
ejpam-2199	139	14	that	that	SCONJ
ejpam-2199	139	15	∀n	∀n	NUM
ejpam-2199	139	16	∈	∈	NOUN
ejpam-2199	139	17	n	n	ADV
ejpam-2199	139	18	if	if	SCONJ
ejpam-2199	139	19	n≥	n≥	PROPN
ejpam-2199	139	20	n0	n0	X
ejpam-2199	139	21	then	then	ADV
ejpam-2199	139	22	,	,	PUNCT
ejpam-2199	139	23	there	there	PRON
ejpam-2199	139	24	exists	exist	VERB
ejpam-2199	139	25	v	v	ADP
ejpam-2199	139	26	∈	∈	NOUN
ejpam-2199	139	27	hn	hn	PROPN
ejpam-2199	139	28	with	with	ADP
ejpam-2199	139	29	x	x	PROPN
ejpam-2199	139	30	∈	∈	PROPN
ejpam-2199	139	31	v	v	NOUN
ejpam-2199	139	32	.	.	PUNCT
ejpam-2199	140	1	consider	consider	VERB
ejpam-2199	140	2	vn	vn	NOUN
ejpam-2199	140	3	=	=	SYM
ejpam-2199	140	4	{	{	PUNCT
ejpam-2199	140	5	un	un	PROPN
ejpam-2199	140	6	j	j	PROPN
ejpam-2199	140	7	∈	∈	PROPN
ejpam-2199	140	8	un	un	PROPN
ejpam-2199	140	9	;	;	PUNCT
ejpam-2199	140	10	un	un	PROPN
ejpam-2199	140	11	j	j	PROPN
ejpam-2199	140	12	∈	∈	PROPN
ejpam-2199	140	13	hn	hn	PROPN
ejpam-2199	140	14	}	}	PUNCT
ejpam-2199	140	15	,	,	PUNCT
ejpam-2199	140	16	then	then	ADV
ejpam-2199	140	17	the	the	DET
ejpam-2199	140	18	sequence	sequence	NOUN
ejpam-2199	140	19	{	{	PUNCT
ejpam-2199	140	20	vn}n∈n	vn}n∈n	NUM
ejpam-2199	140	21	,	,	PUNCT
ejpam-2199	140	22	is	be	AUX
ejpam-2199	140	23	such	such	ADJ
ejpam-2199	140	24	that	that	SCONJ
ejpam-2199	140	25	:	:	PUNCT
ejpam-2199	140	26	(	(	PUNCT
ejpam-2199	140	27	i	i	NOUN
ejpam-2199	140	28	)	)	PUNCT
ejpam-2199	140	29	∀n	∀n	PROPN
ejpam-2199	140	30	∈	∈	PROPN
ejpam-2199	140	31	n	n	CCONJ
ejpam-2199	140	32	,	,	PUNCT
ejpam-2199	140	33	we	we	PRON
ejpam-2199	140	34	have	have	VERB
ejpam-2199	140	35	that	that	DET
ejpam-2199	140	36	vn	vn	PROPN
ejpam-2199	140	37	⊂<∞	⊂<∞	PROPN
ejpam-2199	140	38	un	un	PROPN
ejpam-2199	140	39	.	.	PROPN
ejpam-2199	140	40	(	(	PUNCT
ejpam-2199	140	41	ii	ii	NOUN
ejpam-2199	140	42	)	)	PUNCT
ejpam-2199	140	43	let	let	VERB
ejpam-2199	140	44	y	y	PROPN
ejpam-2199	140	45	∈	∈	PROPN
ejpam-2199	140	46	f	f	PROPN
ejpam-2199	140	47	.	.	PUNCT
ejpam-2199	141	1	then	then	ADV
ejpam-2199	141	2	from	from	ADP
ejpam-2199	141	3	previous	previous	ADJ
ejpam-2199	141	4	(	(	PUNCT
ejpam-2199	141	5	ii	ii	NOUN
ejpam-2199	141	6	)	)	PUNCT
ejpam-2199	141	7	∃n0	∃n0	NOUN
ejpam-2199	141	8	∈	∈	PROPN
ejpam-2199	141	9	n	n	PRON
ejpam-2199	141	10	such	such	ADJ
ejpam-2199	141	11	that	that	SCONJ
ejpam-2199	141	12	∀n	∀n	NUM
ejpam-2199	141	13	∈	∈	NOUN
ejpam-2199	141	14	n	n	ADV
ejpam-2199	141	15	if	if	SCONJ
ejpam-2199	141	16	n	n	NUM
ejpam-2199	141	17	≥	≥	X
ejpam-2199	141	18	n0	n0	NUM
ejpam-2199	141	19	,	,	PUNCT
ejpam-2199	141	20	there	there	PRON
ejpam-2199	141	21	exists	exist	VERB
ejpam-2199	141	22	v	v	ADP
ejpam-2199	141	23	∈	∈	PROPN
ejpam-2199	141	24	hn	hn	PROPN
ejpam-2199	141	25	with	with	ADP
ejpam-2199	141	26	y	y	PROPN
ejpam-2199	141	27	∈	∈	PROPN
ejpam-2199	141	28	v	v	NOUN
ejpam-2199	141	29	.	.	PUNCT
ejpam-2199	142	1	since	since	SCONJ
ejpam-2199	142	2	v	v	NUM
ejpam-2199	142	3	∈	∈	NOUN
ejpam-2199	142	4	hn	hn	NOUN
ejpam-2199	142	5	,	,	PUNCT
ejpam-2199	142	6	we	we	PRON
ejpam-2199	142	7	have	have	VERB
ejpam-2199	142	8	that	that	PRON
ejpam-2199	142	9	v	v	NOUN
ejpam-2199	142	10	=	=	SYM
ejpam-2199	142	11	un	un	PROPN
ejpam-2199	142	12	j	j	PROPN
ejpam-2199	142	13	∈	∈	PROPN
ejpam-2199	142	14	un	un	PROPN
ejpam-2199	142	15	or	or	CCONJ
ejpam-2199	142	16	v	v	NOUN
ejpam-2199	142	17	=	=	SYM
ejpam-2199	142	18	f	f	NOUN
ejpam-2199	142	19	c	c	NOUN
ejpam-2199	142	20	,	,	PUNCT
ejpam-2199	142	21	but	but	CCONJ
ejpam-2199	142	22	since	since	SCONJ
ejpam-2199	142	23	y	y	PROPN
ejpam-2199	142	24	/∈	/∈	PUNCT
ejpam-2199	143	1	f	f	AUX
ejpam-2199	143	2	we	we	PRON
ejpam-2199	143	3	have	have	VERB
ejpam-2199	143	4	v	v	NOUN
ejpam-2199	143	5	=	=	SYM
ejpam-2199	143	6	uni	uni	PROPN
ejpam-2199	143	7	∈	∈	PROPN
ejpam-2199	143	8	un	un	NOUN
ejpam-2199	143	9	,	,	PUNCT
ejpam-2199	143	10	thus	thus	ADV
ejpam-2199	143	11	v	v	ADP
ejpam-2199	143	12	∈	∈	PROPN
ejpam-2199	143	13	vn	vn	NOUN
ejpam-2199	143	14	,	,	PUNCT
ejpam-2199	143	15	therefore	therefore	ADV
ejpam-2199	143	16	y	y	PROPN
ejpam-2199	143	17	∈	∈	PROPN
ejpam-2199	143	18	v	v	ADP
ejpam-2199	143	19	∈	∈	PROPN
ejpam-2199	143	20	vn	vn	X
ejpam-2199	143	21	.	.	PUNCT
ejpam-2199	144	1	by	by	ADP
ejpam-2199	144	2	proposition	proposition	NOUN
ejpam-2199	144	3	5	5	NUM
ejpam-2199	144	4	f	f	NOUN
ejpam-2199	144	5	is	be	AUX
ejpam-2199	144	6	a	a	DET
ejpam-2199	144	7	hurewicz	hurewicz	NOUN
ejpam-2199	144	8	space	space	NOUN
ejpam-2199	144	9	.	.	PUNCT
ejpam-2199	145	1	proposition	proposition	NOUN
ejpam-2199	145	2	7	7	NUM
ejpam-2199	145	3	.	.	PUNCT
ejpam-2199	146	1	let	let	VERB
ejpam-2199	146	2	x	x	PRON
ejpam-2199	146	3	be	be	AUX
ejpam-2199	146	4	a	a	DET
ejpam-2199	146	5	topological	topological	ADJ
ejpam-2199	146	6	space	space	NOUN
ejpam-2199	146	7	and	and	CCONJ
ejpam-2199	146	8	let	let	VERB
ejpam-2199	146	9	h	h	NOUN
ejpam-2199	146	10	and	and	CCONJ
ejpam-2199	146	11	y	y	PROPN
ejpam-2199	146	12	be	be	AUX
ejpam-2199	146	13	subspaces	subspace	NOUN
ejpam-2199	146	14	of	of	ADP
ejpam-2199	146	15	x	x	PRON
ejpam-2199	146	16	,	,	PUNCT
ejpam-2199	146	17	with	with	ADP
ejpam-2199	146	18	h	h	NOUN
ejpam-2199	146	19	hurewicz	hurewicz	NOUN
ejpam-2199	146	20	and	and	CCONJ
ejpam-2199	146	21	y	y	PROPN
ejpam-2199	146	22	closed	close	VERB
ejpam-2199	146	23	,	,	PUNCT
ejpam-2199	146	24	then	then	ADV
ejpam-2199	146	25	h	h	PROPN
ejpam-2199	146	26	∩	∩	NOUN
ejpam-2199	146	27	y	y	PROPN
ejpam-2199	146	28	is	be	AUX
ejpam-2199	146	29	hurewicz	hurewicz	ADJ
ejpam-2199	146	30	.	.	PUNCT
ejpam-2199	147	1	proof	proof	NOUN
ejpam-2199	147	2	.	.	PUNCT
ejpam-2199	148	1	let	let	VERB
ejpam-2199	148	2	{	{	PUNCT
ejpam-2199	148	3	un}n∈n	un}n∈n	PRON
ejpam-2199	148	4	be	be	AUX
ejpam-2199	148	5	a	a	DET
ejpam-2199	148	6	sequence	sequence	NOUN
ejpam-2199	148	7	of	of	ADP
ejpam-2199	148	8	coverings	covering	NOUN
ejpam-2199	148	9	of	of	ADP
ejpam-2199	148	10	h	h	NOUN
ejpam-2199	148	11	∩	∩	NOUN
ejpam-2199	148	12	y	y	PROPN
ejpam-2199	148	13	by	by	ADP
ejpam-2199	148	14	open	open	ADJ
ejpam-2199	148	15	sets	set	NOUN
ejpam-2199	148	16	in	in	ADP
ejpam-2199	148	17	x	x	SYM
ejpam-2199	148	18	,	,	PUNCT
ejpam-2199	148	19	where	where	SCONJ
ejpam-2199	148	20	each	each	DET
ejpam-2199	148	21	un	un	PROPN
ejpam-2199	149	1	=	=	PRON
ejpam-2199	149	2	{	{	PUNCT
ejpam-2199	149	3	un	un	PROPN
ejpam-2199	149	4	j	j	PROPN
ejpam-2199	149	5	}	}	PUNCT
ejpam-2199	149	6	j∈jn	j∈jn	NOUN
ejpam-2199	149	7	.	.	PUNCT
ejpam-2199	150	1	consider	consider	VERB
ejpam-2199	150	2	∀n	∀n	NUM
ejpam-2199	150	3	∈	∈	PROPN
ejpam-2199	150	4	n	n	CCONJ
ejpam-2199	150	5	,	,	PUNCT
ejpam-2199	150	6	hn	hn	PROPN
ejpam-2199	150	7	=	=	PRON
ejpam-2199	150	8	{	{	PUNCT
ejpam-2199	150	9	un	un	PROPN
ejpam-2199	150	10	j	j	PROPN
ejpam-2199	150	11	}	}	PUNCT
ejpam-2199	150	12	j∈jn	j∈jn	PROPN
ejpam-2199	150	13	∪	∪	VERB
ejpam-2199	150	14	y	y	PROPN
ejpam-2199	150	15	c	c	PROPN
ejpam-2199	150	16	,	,	PUNCT
ejpam-2199	150	17	then	then	ADV
ejpam-2199	150	18	hn	hn	PROPN
ejpam-2199	150	19	is	be	AUX
ejpam-2199	150	20	a	a	DET
ejpam-2199	150	21	covering	covering	NOUN
ejpam-2199	150	22	of	of	ADP
ejpam-2199	150	23	h	h	NOUN
ejpam-2199	150	24	by	by	ADP
ejpam-2199	150	25	open	open	ADJ
ejpam-2199	150	26	sets	set	NOUN
ejpam-2199	150	27	in	in	ADP
ejpam-2199	150	28	x	x	X
ejpam-2199	150	29	,	,	PUNCT
ejpam-2199	150	30	because	because	SCONJ
ejpam-2199	150	31	y	y	PROPN
ejpam-2199	150	32	is	be	AUX
ejpam-2199	150	33	a	a	DET
ejpam-2199	150	34	closed	closed	ADJ
ejpam-2199	150	35	set	set	NOUN
ejpam-2199	150	36	we	we	PRON
ejpam-2199	150	37	have	have	VERB
ejpam-2199	150	38	that	that	PRON
ejpam-2199	150	39	y	y	PROPN
ejpam-2199	150	40	c	c	PROPN
ejpam-2199	150	41	is	be	AUX
ejpam-2199	150	42	an	an	DET
ejpam-2199	150	43	open	open	ADJ
ejpam-2199	150	44	set	set	NOUN
ejpam-2199	150	45	in	in	ADP
ejpam-2199	150	46	x	x	PUNCT
ejpam-2199	150	47	and	and	CCONJ
ejpam-2199	150	48	for	for	ADP
ejpam-2199	150	49	each	each	DET
ejpam-2199	150	50	x	x	SYM
ejpam-2199	150	51	∈	∈	PROPN
ejpam-2199	150	52	h	h	NOUN
ejpam-2199	150	53	if	if	SCONJ
ejpam-2199	150	54	x	x	SYM
ejpam-2199	150	55	∈	∈	PROPN
ejpam-2199	150	56	y	y	NOUN
ejpam-2199	150	57	then	then	ADV
ejpam-2199	150	58	x	x	SYM
ejpam-2199	150	59	∈	∈	NOUN
ejpam-2199	150	60	h	h	NOUN
ejpam-2199	150	61	∩	∩	PROPN
ejpam-2199	150	62	y	y	PROPN
ejpam-2199	150	63	,	,	PUNCT
ejpam-2199	150	64	then	then	ADV
ejpam-2199	150	65	there	there	PRON
ejpam-2199	150	66	exists	exist	VERB
ejpam-2199	150	67	j	j	PROPN
ejpam-2199	150	68	∈	∈	PROPN
ejpam-2199	150	69	jn	jn	PROPN
ejpam-2199	151	1	such	such	ADJ
ejpam-2199	151	2	that	that	SCONJ
ejpam-2199	151	3	x	x	PROPN
ejpam-2199	151	4	∈	∈	PROPN
ejpam-2199	151	5	un	un	PROPN
ejpam-2199	151	6	j	j	PROPN
ejpam-2199	151	7	,	,	PUNCT
ejpam-2199	151	8	if	if	SCONJ
ejpam-2199	151	9	x	x	X
ejpam-2199	151	10	/∈	/∈	PUNCT
ejpam-2199	152	1	y	y	NOUN
ejpam-2199	153	1	then	then	ADV
ejpam-2199	153	2	x	x	SYM
ejpam-2199	153	3	∈	∈	PROPN
ejpam-2199	153	4	y	y	NOUN
ejpam-2199	153	5	c	c	PROPN
ejpam-2199	153	6	.	.	PUNCT
ejpam-2199	154	1	therefore	therefore	ADV
ejpam-2199	154	2	we	we	PRON
ejpam-2199	154	3	have	have	VERB
ejpam-2199	154	4	that	that	SCONJ
ejpam-2199	154	5	the	the	DET
ejpam-2199	154	6	sequence	sequence	NOUN
ejpam-2199	154	7	{	{	PUNCT
ejpam-2199	154	8	hn}n∈n	hn}n∈n	ADV
ejpam-2199	154	9	is	be	AUX
ejpam-2199	154	10	a	a	DET
ejpam-2199	154	11	sequence	sequence	NOUN
ejpam-2199	154	12	of	of	ADP
ejpam-2199	154	13	open	open	ADJ
ejpam-2199	154	14	coverings	covering	NOUN
ejpam-2199	154	15	of	of	ADP
ejpam-2199	154	16	h	h	NOUN
ejpam-2199	154	17	by	by	ADP
ejpam-2199	154	18	open	open	ADJ
ejpam-2199	154	19	sets	set	NOUN
ejpam-2199	154	20	in	in	ADP
ejpam-2199	154	21	x	x	SYM
ejpam-2199	154	22	,	,	PUNCT
ejpam-2199	154	23	since	since	SCONJ
ejpam-2199	154	24	h	h	NOUN
ejpam-2199	154	25	is	be	AUX
ejpam-2199	154	26	hurewicz	hurewicz	ADJ
ejpam-2199	154	27	in	in	ADP
ejpam-2199	154	28	x	x	PUNCT
ejpam-2199	154	29	by	by	ADP
ejpam-2199	154	30	proposition	proposition	NOUN
ejpam-2199	154	31	5	5	NUM
ejpam-2199	154	32	,	,	PUNCT
ejpam-2199	154	33	there	there	PRON
ejpam-2199	154	34	is	be	VERB
ejpam-2199	154	35	a	a	DET
ejpam-2199	154	36	sequence	sequence	NOUN
ejpam-2199	154	37	{	{	PUNCT
ejpam-2199	154	38	wn}n∈n	wn}n∈n	X
ejpam-2199	154	39	such	such	ADJ
ejpam-2199	154	40	that	that	PRON
ejpam-2199	154	41	:	:	PUNCT
ejpam-2199	154	42	(	(	PUNCT
ejpam-2199	154	43	i	i	NOUN
ejpam-2199	154	44	)	)	PUNCT
ejpam-2199	154	45	∀n	∀n	PROPN
ejpam-2199	155	1	∈	∈	PROPN
ejpam-2199	155	2	n	n	CCONJ
ejpam-2199	155	3	,	,	PUNCT
ejpam-2199	155	4	wn	wn	PROPN
ejpam-2199	155	5	⊂<∞	⊂<∞	PROPN
ejpam-2199	155	6	hn	hn	PROPN
ejpam-2199	155	7	,	,	PUNCT
ejpam-2199	155	8	i.	i.	PROPN
ejpam-2199	155	9	e.	e.	PROPN
ejpam-2199	155	10	,	,	PUNCT
ejpam-2199	155	11	there	there	PRON
ejpam-2199	155	12	exists	exist	VERB
ejpam-2199	155	13	a	a	DET
ejpam-2199	155	14	finite	finite	NOUN
ejpam-2199	155	15	subset	subset	VERB
ejpam-2199	155	16	in	in	ADP
ejpam-2199	155	17	such	such	ADJ
ejpam-2199	155	18	thatwn	thatwn	NOUN
ejpam-2199	155	19	=	=	SYM
ejpam-2199	155	20	{	{	PUNCT
ejpam-2199	155	21	vn	vn	PROPN
ejpam-2199	155	22	j	j	PROPN
ejpam-2199	155	23	}	}	PUNCT
ejpam-2199	155	24	j∈in	j∈in	PROPN
ejpam-2199	155	25	where	where	SCONJ
ejpam-2199	155	26	vn	vn	PROPN
ejpam-2199	155	27	j	j	PROPN
ejpam-2199	155	28	=	=	PUNCT
ejpam-2199	155	29	uni	uni	PROPN
ejpam-2199	155	30	for	for	ADP
ejpam-2199	155	31	some	some	PRON
ejpam-2199	155	32	i	i	PRON
ejpam-2199	155	33	∈	∈	PROPN
ejpam-2199	155	34	jn	jn	PROPN
ejpam-2199	155	35	or	or	CCONJ
ejpam-2199	155	36	vn	vn	INTJ
ejpam-2199	155	37	j	j	PROPN
ejpam-2199	156	1	=	=	PUNCT
ejpam-2199	156	2	y	y	PROPN
ejpam-2199	156	3	c	c	PROPN
ejpam-2199	156	4	.	.	PUNCT
ejpam-2199	157	1	(	(	PUNCT
ejpam-2199	157	2	ii	ii	NOUN
ejpam-2199	157	3	)	)	PUNCT
ejpam-2199	157	4	for	for	ADP
ejpam-2199	157	5	each	each	DET
ejpam-2199	157	6	x	x	SYM
ejpam-2199	157	7	∈	∈	PROPN
ejpam-2199	157	8	h	h	NOUN
ejpam-2199	157	9	,	,	PUNCT
ejpam-2199	157	10	∃n0	∃n0	NOUN
ejpam-2199	157	11	∈	∈	PROPN
ejpam-2199	157	12	n	n	PRON
ejpam-2199	157	13	such	such	ADJ
ejpam-2199	157	14	that	that	SCONJ
ejpam-2199	157	15	∀n	∀n	NUM
ejpam-2199	157	16	∈	∈	NOUN
ejpam-2199	157	17	n	n	ADV
ejpam-2199	157	18	if	if	SCONJ
ejpam-2199	157	19	n≥	n≥	PROPN
ejpam-2199	157	20	n0	n0	X
ejpam-2199	157	21	then	then	ADV
ejpam-2199	157	22	there	there	PRON
ejpam-2199	157	23	exists	exist	VERB
ejpam-2199	157	24	v	v	ADP
ejpam-2199	157	25	∈wn	∈wn	NOUN
ejpam-2199	157	26	with	with	ADP
ejpam-2199	157	27	x	x	PROPN
ejpam-2199	157	28	∈	∈	PROPN
ejpam-2199	157	29	v	v	NOUN
ejpam-2199	157	30	.	.	PUNCT
ejpam-2199	158	1	consider	consider	VERB
ejpam-2199	158	2	vn	vn	NOUN
ejpam-2199	158	3	=	=	SYM
ejpam-2199	158	4	{	{	PUNCT
ejpam-2199	158	5	un	un	PROPN
ejpam-2199	158	6	j	j	PROPN
ejpam-2199	158	7	∈	∈	PROPN
ejpam-2199	159	1	hn	hn	PROPN
ejpam-2199	159	2	;	;	PUNCT
ejpam-2199	159	3	un	un	PROPN
ejpam-2199	159	4	j	j	PROPN
ejpam-2199	159	5	∈	∈	PROPN
ejpam-2199	159	6	un	un	PROPN
ejpam-2199	159	7	}	}	PUNCT
ejpam-2199	159	8	,	,	PUNCT
ejpam-2199	159	9	then	then	ADV
ejpam-2199	159	10	the	the	DET
ejpam-2199	159	11	sequence	sequence	NOUN
ejpam-2199	159	12	{	{	PUNCT
ejpam-2199	159	13	vn}n∈n	vn}n∈n	NUM
ejpam-2199	159	14	,	,	PUNCT
ejpam-2199	159	15	is	be	AUX
ejpam-2199	159	16	such	such	ADJ
ejpam-2199	159	17	that	that	SCONJ
ejpam-2199	159	18	:	:	PUNCT
ejpam-2199	159	19	(	(	PUNCT
ejpam-2199	159	20	i	i	NOUN
ejpam-2199	159	21	)	)	PUNCT
ejpam-2199	159	22	∀n	∀n	PROPN
ejpam-2199	159	23	∈	∈	PROPN
ejpam-2199	159	24	n	n	CCONJ
ejpam-2199	159	25	,	,	PUNCT
ejpam-2199	159	26	vn	vn	PROPN
ejpam-2199	159	27	⊂<∞	⊂<∞	PROPN
ejpam-2199	159	28	un	un	PROPN
ejpam-2199	159	29	,	,	PUNCT
ejpam-2199	159	30	because	because	SCONJ
ejpam-2199	159	31	hn	hn	PROPN
ejpam-2199	159	32	is	be	AUX
ejpam-2199	159	33	formed	form	VERB
ejpam-2199	159	34	by	by	ADP
ejpam-2199	159	35	finite	finite	ADJ
ejpam-2199	159	36	elements	element	NOUN
ejpam-2199	159	37	.	.	PUNCT
ejpam-2199	160	1	(	(	PUNCT
ejpam-2199	160	2	ii	ii	NOUN
ejpam-2199	160	3	)	)	PUNCT
ejpam-2199	160	4	for	for	ADP
ejpam-2199	160	5	each	each	DET
ejpam-2199	160	6	x	x	SYM
ejpam-2199	160	7	∈	∈	PROPN
ejpam-2199	160	8	h	h	NOUN
ejpam-2199	160	9	∩	∩	ADJ
ejpam-2199	160	10	y	y	PROPN
ejpam-2199	160	11	,	,	PUNCT
ejpam-2199	160	12	we	we	PRON
ejpam-2199	160	13	have	have	VERB
ejpam-2199	160	14	that	that	DET
ejpam-2199	160	15	x	x	PUNCT
ejpam-2199	160	16	∈	∈	PROPN
ejpam-2199	160	17	h	h	NOUN
ejpam-2199	160	18	and	and	CCONJ
ejpam-2199	160	19	x	x	PUNCT
ejpam-2199	160	20	∈	∈	PROPN
ejpam-2199	160	21	y	y	NOUN
ejpam-2199	160	22	.	.	PUNCT
ejpam-2199	161	1	if	if	SCONJ
ejpam-2199	161	2	x	x	SYM
ejpam-2199	161	3	∈	∈	PROPN
ejpam-2199	161	4	h	h	NOUN
ejpam-2199	161	5	,	,	PUNCT
ejpam-2199	161	6	by	by	ADP
ejpam-2199	161	7	previous	previous	ADJ
ejpam-2199	161	8	(	(	PUNCT
ejpam-2199	161	9	ii	ii	NOUN
ejpam-2199	161	10	)	)	PUNCT
ejpam-2199	161	11	∃n0	∃n0	NOUN
ejpam-2199	161	12	∈	∈	PROPN
ejpam-2199	161	13	n	n	PRON
ejpam-2199	161	14	such	such	ADJ
ejpam-2199	161	15	that	that	SCONJ
ejpam-2199	161	16	∀n	∀n	NUM
ejpam-2199	161	17	∈	∈	NOUN
ejpam-2199	161	18	n	n	ADV
ejpam-2199	161	19	if	if	SCONJ
ejpam-2199	161	20	n≥	n≥	PROPN
ejpam-2199	161	21	n0	n0	X
ejpam-2199	161	22	then	then	ADV
ejpam-2199	161	23	there	there	PRON
ejpam-2199	161	24	exists	exist	VERB
ejpam-2199	161	25	v	v	ADP
ejpam-2199	161	26	∈wn	∈wn	NOUN
ejpam-2199	161	27	with	with	ADP
ejpam-2199	161	28	x	x	PROPN
ejpam-2199	161	29	∈	∈	PROPN
ejpam-2199	161	30	v	v	NOUN
ejpam-2199	161	31	.	.	PUNCT
ejpam-2199	162	1	from	from	ADP
ejpam-2199	162	2	v	v	NUM
ejpam-2199	162	3	∈	∈	NOUN
ejpam-2199	162	4	hn	hn	NOUN
ejpam-2199	162	5	,	,	PUNCT
ejpam-2199	162	6	we	we	PRON
ejpam-2199	162	7	have	have	VERB
ejpam-2199	162	8	that	that	PRON
ejpam-2199	162	9	v	v	NOUN
ejpam-2199	162	10	=	=	SYM
ejpam-2199	162	11	uni	uni	PROPN
ejpam-2199	162	12	∈	∈	PROPN
ejpam-2199	162	13	un	un	PROPN
ejpam-2199	162	14	or	or	CCONJ
ejpam-2199	162	15	v	v	NOUN
ejpam-2199	162	16	=	=	SYM
ejpam-2199	162	17	y	y	PROPN
ejpam-2199	162	18	c	c	PROPN
ejpam-2199	162	19	.	.	PUNCT
ejpam-2199	163	1	since	since	SCONJ
ejpam-2199	163	2	x	x	PROPN
ejpam-2199	163	3	/∈	/∈	PROPN
ejpam-2199	163	4	y	y	PROPN
ejpam-2199	163	5	c	c	PROPN
ejpam-2199	163	6	,	,	PUNCT
ejpam-2199	163	7	then	then	ADV
ejpam-2199	163	8	v	v	X
ejpam-2199	163	9	=	=	SYM
ejpam-2199	163	10	uni	uni	PROPN
ejpam-2199	163	11	∈	∈	PROPN
ejpam-2199	163	12	un	un	NOUN
ejpam-2199	163	13	,	,	PUNCT
ejpam-2199	163	14	hence	hence	ADV
ejpam-2199	163	15	v	v	NOUN
ejpam-2199	163	16	∈	∈	PROPN
ejpam-2199	163	17	vn	vn	NOUN
ejpam-2199	163	18	,	,	PUNCT
ejpam-2199	163	19	then	then	ADV
ejpam-2199	163	20	x	x	PART
ejpam-2199	163	21	∈	∈	PROPN
ejpam-2199	163	22	v	v	ADP
ejpam-2199	163	23	∈	∈	PROPN
ejpam-2199	163	24	vn	vn	X
ejpam-2199	163	25	.	.	PUNCT
ejpam-2199	164	1	by	by	ADP
ejpam-2199	164	2	proposition	proposition	NOUN
ejpam-2199	164	3	5	5	NUM
ejpam-2199	164	4	h	h	NOUN
ejpam-2199	164	5	∩	∩	NOUN
ejpam-2199	164	6	y	y	PROPN
ejpam-2199	164	7	is	be	AUX
ejpam-2199	164	8	a	a	DET
ejpam-2199	164	9	hurewicz	hurewicz	NOUN
ejpam-2199	164	10	space	space	NOUN
ejpam-2199	164	11	.	.	PUNCT
ejpam-2199	165	1	c.	c.	PROPN
ejpam-2199	165	2	roika	roika	PROPN
ejpam-2199	165	3	,	,	PUNCT
ejpam-2199	165	4	s.	s.	PROPN
ejpam-2199	165	5	kudri	kudri	PROPN
ejpam-2199	165	6	,	,	PUNCT
ejpam-2199	165	7	t.	t.	PROPN
ejpam-2199	165	8	breuckmann	breuckmann	PROPN
ejpam-2199	165	9	/	/	SYM
ejpam-2199	165	10	eur	eur	PROPN
ejpam-2199	165	11	.	.	PUNCT
ejpam-2199	166	1	j.	j.	PROPN
ejpam-2199	166	2	pure	pure	PROPN
ejpam-2199	166	3	appl	appl	PROPN
ejpam-2199	166	4	.	.	PROPN
ejpam-2199	166	5	math	math	PROPN
ejpam-2199	166	6	,	,	PUNCT
ejpam-2199	166	7	8	8	NUM
ejpam-2199	166	8	(	(	PUNCT
ejpam-2199	166	9	2015	2015	NUM
ejpam-2199	166	10	)	)	PUNCT
ejpam-2199	166	11	,	,	PUNCT
ejpam-2199	166	12	514	514	NUM
ejpam-2199	166	13	-	-	SYM
ejpam-2199	166	14	525	525	NUM
ejpam-2199	166	15	519	519	NUM
ejpam-2199	166	16	3	3	NUM
ejpam-2199	166	17	.	.	PUNCT
ejpam-2199	167	1	c	c	X
ejpam-2199	167	2	-	-	PUNCT
ejpam-2199	167	3	space	space	NOUN
ejpam-2199	167	4	definition	definition	NOUN
ejpam-2199	167	5	7	7	NUM
ejpam-2199	167	6	.	.	PUNCT
ejpam-2199	168	1	a	a	DET
ejpam-2199	168	2	topological	topological	ADJ
ejpam-2199	168	3	space	space	NOUN
ejpam-2199	168	4	〈	〈	NOUN
ejpam-2199	168	5	x	x	X
ejpam-2199	168	6	,	,	PUNCT
ejpam-2199	168	7	t	t	PROPN
ejpam-2199	168	8	〉	〉	NOUN
ejpam-2199	168	9	is	be	AUX
ejpam-2199	168	10	a	a	DET
ejpam-2199	168	11	c	c	NOUN
ejpam-2199	168	12	-	-	PUNCT
ejpam-2199	168	13	space	space	NOUN
ejpam-2199	168	14	if	if	SCONJ
ejpam-2199	168	15	and	and	CCONJ
ejpam-2199	168	16	only	only	ADV
ejpam-2199	168	17	if	if	SCONJ
ejpam-2199	168	18	,	,	PUNCT
ejpam-2199	168	19	for	for	ADP
ejpam-2199	168	20	each	each	DET
ejpam-2199	168	21	x	x	SYM
ejpam-2199	168	22	∈	∈	PROPN
ejpam-2199	168	23	x	x	X
ejpam-2199	168	24	and	and	CCONJ
ejpam-2199	168	25	for	for	ADP
ejpam-2199	168	26	each	each	DET
ejpam-2199	168	27	sequence	sequence	NOUN
ejpam-2199	168	28	{	{	PUNCT
ejpam-2199	168	29	an}n∈n	an}n∈n	ADV
ejpam-2199	168	30	,	,	PUNCT
ejpam-2199	168	31	where	where	SCONJ
ejpam-2199	168	32	an	an	PRON
ejpam-2199	168	33	=	=	X
ejpam-2199	168	34	{	{	PUNCT
ejpam-2199	168	35	an	an	DET
ejpam-2199	168	36	j	j	PROPN
ejpam-2199	168	37	∈	∈	PROPN
ejpam-2199	168	38	t	t	NOUN
ejpam-2199	168	39	;	;	PUNCT
ejpam-2199	168	40	1	1	NUM
ejpam-2199	168	41	≤	≤	NUM
ejpam-2199	168	42	j	j	PROPN
ejpam-2199	168	43	≤	≤	PROPN
ejpam-2199	168	44	kn	kn	PROPN
ejpam-2199	168	45	}	}	PUNCT
ejpam-2199	168	46	with	with	ADP
ejpam-2199	168	47	x	x	PROPN
ejpam-2199	168	48	∈	∈	PROPN
ejpam-2199	168	49	kn	kn	NOUN
ejpam-2199	168	50	⋂	⋂	PROPN
ejpam-2199	168	51	j=1	j=1	PROPN
ejpam-2199	168	52	an	an	DET
ejpam-2199	168	53	j	j	PROPN
ejpam-2199	168	54	,	,	PUNCT
ejpam-2199	168	55	there	there	PRON
ejpam-2199	168	56	exists	exist	VERB
ejpam-2199	168	57	v	v	ADP
ejpam-2199	168	58	∈	∈	PROPN
ejpam-2199	168	59	t	t	NOUN
ejpam-2199	168	60	such	such	ADJ
ejpam-2199	168	61	that	that	SCONJ
ejpam-2199	168	62	∀n	∀n	NUM
ejpam-2199	168	63	∈	∈	PROPN
ejpam-2199	168	64	n	n	CCONJ
ejpam-2199	168	65	,	,	PUNCT
ejpam-2199	168	66	x	x	PROPN
ejpam-2199	168	67	∈	∈	NOUN
ejpam-2199	168	68	v	v	ADP
ejpam-2199	168	69	⊂	⊂	PROPN
ejpam-2199	168	70	kn	kn	PROPN
ejpam-2199	168	71	⋂	⋂	PROPN
ejpam-2199	168	72	j=1	j=1	PROPN
ejpam-2199	168	73	an	an	DET
ejpam-2199	168	74	j	j	PROPN
ejpam-2199	168	75	.	.	PUNCT
ejpam-2199	168	76	example	example	NOUN
ejpam-2199	169	1	3	3	X
ejpam-2199	169	2	.	.	X
ejpam-2199	169	3	consider	consider	VERB
ejpam-2199	169	4	x	x	PRON
ejpam-2199	169	5	6=	6=	NUM
ejpam-2199	169	6	;	;	PUNCT
ejpam-2199	169	7	,	,	PUNCT
ejpam-2199	169	8	with	with	ADP
ejpam-2199	169	9	the	the	DET
ejpam-2199	169	10	discrete	discrete	ADJ
ejpam-2199	169	11	topology	topology	NOUN
ejpam-2199	169	12	.	.	PUNCT
ejpam-2199	170	1	x	x	PRON
ejpam-2199	170	2	is	be	AUX
ejpam-2199	170	3	a	a	DET
ejpam-2199	170	4	c	c	NOUN
ejpam-2199	170	5	-	-	PUNCT
ejpam-2199	170	6	space	space	NOUN
ejpam-2199	170	7	,	,	PUNCT
ejpam-2199	170	8	because	because	SCONJ
ejpam-2199	170	9	for	for	ADP
ejpam-2199	170	10	each	each	DET
ejpam-2199	170	11	x	x	SYM
ejpam-2199	170	12	∈	∈	PROPN
ejpam-2199	170	13	x	x	X
ejpam-2199	170	14	and	and	CCONJ
ejpam-2199	170	15	for	for	ADP
ejpam-2199	170	16	each	each	DET
ejpam-2199	170	17	sequence	sequence	NOUN
ejpam-2199	170	18	{	{	PUNCT
ejpam-2199	170	19	an}n∈n	an}n∈n	VERB
ejpam-2199	170	20	where	where	SCONJ
ejpam-2199	170	21	for	for	ADP
ejpam-2199	170	22	each	each	DET
ejpam-2199	170	23	n	n	PRON
ejpam-2199	170	24	∈	∈	PROPN
ejpam-2199	170	25	n	n	CCONJ
ejpam-2199	170	26	,	,	PUNCT
ejpam-2199	170	27	an	an	DET
ejpam-2199	170	28	=	=	X
ejpam-2199	170	29	{	{	PUNCT
ejpam-2199	170	30	an	an	DET
ejpam-2199	170	31	j	j	PROPN
ejpam-2199	170	32	}	}	PUNCT
ejpam-2199	170	33	kn	kn	PROPN
ejpam-2199	170	34	j=1	j=1	PROPN
ejpam-2199	170	35	with	with	ADP
ejpam-2199	170	36	an	an	DET
ejpam-2199	170	37	j	j	NOUN
ejpam-2199	170	38	open	open	ADJ
ejpam-2199	170	39	and	and	CCONJ
ejpam-2199	170	40	x	x	SYM
ejpam-2199	170	41	∈	∈	PROPN
ejpam-2199	170	42	kn	kn	NOUN
ejpam-2199	170	43	⋂	⋂	PROPN
ejpam-2199	170	44	j=1	j=1	PROPN
ejpam-2199	170	45	an	an	DET
ejpam-2199	170	46	j	j	PROPN
ejpam-2199	170	47	,	,	PUNCT
ejpam-2199	170	48	then	then	ADV
ejpam-2199	170	49	{	{	PUNCT
ejpam-2199	170	50	x	x	X
ejpam-2199	170	51	}	}	PUNCT
ejpam-2199	170	52	is	be	AUX
ejpam-2199	170	53	an	an	DET
ejpam-2199	170	54	open	open	ADJ
ejpam-2199	170	55	set	set	NOUN
ejpam-2199	170	56	such	such	ADJ
ejpam-2199	170	57	that	that	SCONJ
ejpam-2199	170	58	∀n	∀n	NUM
ejpam-2199	170	59	∈	∈	PROPN
ejpam-2199	170	60	n	n	CCONJ
ejpam-2199	170	61	,	,	PUNCT
ejpam-2199	170	62	x	x	SYM
ejpam-2199	170	63	∈	∈	NOUN
ejpam-2199	170	64	{	{	PUNCT
ejpam-2199	170	65	x	x	NOUN
ejpam-2199	170	66	}	}	PUNCT
ejpam-2199	170	67	⊂	⊂	PROPN
ejpam-2199	170	68	kn	kn	PROPN
ejpam-2199	171	1	⋂	⋂	PROPN
ejpam-2199	171	2	j=1	j=1	PROPN
ejpam-2199	171	3	an	an	DET
ejpam-2199	171	4	j	j	PROPN
ejpam-2199	171	5	.	.	PUNCT
ejpam-2199	172	1	example	example	NOUN
ejpam-2199	173	1	4	4	NUM
ejpam-2199	173	2	.	.	PUNCT
ejpam-2199	174	1	the	the	DET
ejpam-2199	174	2	real	real	ADJ
ejpam-2199	174	3	line	line	NOUN
ejpam-2199	174	4	r	r	NOUN
ejpam-2199	174	5	in	in	ADP
ejpam-2199	174	6	its	its	PRON
ejpam-2199	174	7	usual	usual	ADJ
ejpam-2199	174	8	topology	topology	NOUN
ejpam-2199	174	9	is	be	AUX
ejpam-2199	174	10	not	not	PART
ejpam-2199	174	11	a	a	DET
ejpam-2199	174	12	c	c	NOUN
ejpam-2199	174	13	-	-	NOUN
ejpam-2199	174	14	space	space	NOUN
ejpam-2199	174	15	,	,	PUNCT
ejpam-2199	174	16	because	because	SCONJ
ejpam-2199	174	17	0	0	NUM
ejpam-2199	174	18	∈	∈	PROPN
ejpam-2199	174	19	r	r	NOUN
ejpam-2199	174	20	and	and	CCONJ
ejpam-2199	174	21	considering	consider	VERB
ejpam-2199	174	22	the	the	DET
ejpam-2199	174	23	sequence	sequence	NOUN
ejpam-2199	174	24	{	{	PUNCT
ejpam-2199	174	25	an}n∈n	an}n∈n	ADV
ejpam-2199	174	26	,	,	PUNCT
ejpam-2199	174	27	where	where	SCONJ
ejpam-2199	174	28	each	each	DET
ejpam-2199	174	29	an	an	X
ejpam-2199	174	30	=	=	X
ejpam-2199	174	31	{	{	PUNCT
ejpam-2199	174	32	(	(	PUNCT
ejpam-2199	174	33	−	−	PROPN
ejpam-2199	174	34	1	1	NUM
ejpam-2199	174	35	k	k	NOUN
ejpam-2199	174	36	,	,	PUNCT
ejpam-2199	174	37	1	1	NUM
ejpam-2199	174	38	k	k	NOUN
ejpam-2199	174	39	)	)	PUNCT
ejpam-2199	174	40	;	;	PUNCT
ejpam-2199	174	41	∀k	∀k	X
ejpam-2199	174	42	∈	∈	PROPN
ejpam-2199	174	43	n	n	CCONJ
ejpam-2199	174	44	,	,	PUNCT
ejpam-2199	174	45	1	1	NUM
ejpam-2199	174	46	≤	≤	NUM
ejpam-2199	174	47	k	k	NOUN
ejpam-2199	174	48	≤	≤	PROPN
ejpam-2199	174	49	n	n	CCONJ
ejpam-2199	174	50	}	}	PUNCT
ejpam-2199	174	51	,	,	PUNCT
ejpam-2199	174	52	we	we	PRON
ejpam-2199	174	53	have	have	VERB
ejpam-2199	174	54	that	that	PRON
ejpam-2199	174	55	for	for	ADP
ejpam-2199	174	56	each	each	DET
ejpam-2199	174	57	n	n	PRON
ejpam-2199	174	58	∈	∈	PROPN
ejpam-2199	174	59	n	n	CCONJ
ejpam-2199	174	60	,	,	PUNCT
ejpam-2199	174	61	0	0	NUM
ejpam-2199	174	62	∈	∈	PROPN
ejpam-2199	174	63	n	n	PRON
ejpam-2199	174	64	⋂	⋂	PROPN
ejpam-2199	174	65	k=1	k=1	X
ejpam-2199	174	66	(	(	PUNCT
ejpam-2199	174	67	−1	−1	NOUN
ejpam-2199	174	68	k	k	PROPN
ejpam-2199	174	69	,	,	PUNCT
ejpam-2199	174	70	1	1	NUM
ejpam-2199	174	71	k	k	NOUN
ejpam-2199	174	72	)	)	PUNCT
ejpam-2199	174	73	,	,	PUNCT
ejpam-2199	174	74	but	but	CCONJ
ejpam-2199	174	75	there	there	PRON
ejpam-2199	174	76	is	be	VERB
ejpam-2199	174	77	not	not	PART
ejpam-2199	174	78	an	an	DET
ejpam-2199	174	79	open	open	ADJ
ejpam-2199	174	80	set	set	NOUN
ejpam-2199	174	81	u	u	NOUN
ejpam-2199	174	82	in	in	ADP
ejpam-2199	174	83	r	r	NOUN
ejpam-2199	174	84	such	such	ADJ
ejpam-2199	174	85	that	that	SCONJ
ejpam-2199	174	86	∀n	∀n	NUM
ejpam-2199	174	87	∈	∈	PROPN
ejpam-2199	174	88	n	n	CCONJ
ejpam-2199	174	89	,	,	PUNCT
ejpam-2199	174	90	0	0	NUM
ejpam-2199	174	91	∈	∈	PROPN
ejpam-2199	174	92	u	u	NOUN
ejpam-2199	174	93	⊂	⊂	PROPN
ejpam-2199	174	94	n	n	PROPN
ejpam-2199	174	95	⋂	⋂	PROPN
ejpam-2199	174	96	k=1	k=1	X
ejpam-2199	174	97	(	(	PUNCT
ejpam-2199	174	98	−1	−1	NOUN
ejpam-2199	174	99	k	k	PROPN
ejpam-2199	174	100	,	,	PUNCT
ejpam-2199	174	101	1	1	NUM
ejpam-2199	174	102	k	k	NOUN
ejpam-2199	174	103	)	)	PUNCT
ejpam-2199	174	104	.	.	PUNCT
ejpam-2199	175	1	lemma	lemma	PROPN
ejpam-2199	175	2	1	1	X
ejpam-2199	175	3	.	.	PUNCT
ejpam-2199	176	1	let	let	VERB
ejpam-2199	176	2	x	x	PRON
ejpam-2199	176	3	be	be	AUX
ejpam-2199	176	4	a	a	DET
ejpam-2199	176	5	hausdorff	hausdorff	NOUN
ejpam-2199	176	6	c	c	NOUN
ejpam-2199	176	7	-	-	PUNCT
ejpam-2199	176	8	space	space	NOUN
ejpam-2199	176	9	,	,	PUNCT
ejpam-2199	176	10	a	a	DET
ejpam-2199	176	11	a	a	DET
ejpam-2199	176	12	hurewicz	hurewicz	NOUN
ejpam-2199	176	13	subspace	subspace	NOUN
ejpam-2199	176	14	of	of	ADP
ejpam-2199	176	15	x	x	PUNCT
ejpam-2199	176	16	and	and	CCONJ
ejpam-2199	176	17	x0	x0	PROPN
ejpam-2199	176	18	/∈	/∈	PUNCT
ejpam-2199	177	1	a	a	PRON
ejpam-2199	177	2	,	,	PUNCT
ejpam-2199	177	3	then	then	ADV
ejpam-2199	177	4	there	there	PRON
ejpam-2199	177	5	are	be	VERB
ejpam-2199	177	6	disjoint	disjoint	ADJ
ejpam-2199	177	7	open	open	ADJ
ejpam-2199	177	8	sets	set	NOUN
ejpam-2199	177	9	v	v	NOUN
ejpam-2199	177	10	and	and	CCONJ
ejpam-2199	177	11	u	u	NOUN
ejpam-2199	177	12	in	in	ADP
ejpam-2199	177	13	x	x	PUNCT
ejpam-2199	177	14	containing	contain	VERB
ejpam-2199	177	15	x0	x0	PROPN
ejpam-2199	177	16	and	and	CCONJ
ejpam-2199	177	17	a	a	PRON
ejpam-2199	177	18	,	,	PUNCT
ejpam-2199	177	19	respectively	respectively	ADV
ejpam-2199	177	20	.	.	PUNCT
ejpam-2199	178	1	proof	proof	NOUN
ejpam-2199	178	2	.	.	PUNCT
ejpam-2199	179	1	consider	consider	VERB
ejpam-2199	179	2	a	a	DET
ejpam-2199	179	3	∈	∈	NOUN
ejpam-2199	179	4	a	a	PRON
ejpam-2199	179	5	,	,	PUNCT
ejpam-2199	179	6	with	with	ADP
ejpam-2199	179	7	x0	x0	PROPN
ejpam-2199	179	8	/∈	/∈	PUNCT
ejpam-2199	180	1	a	a	PRON
ejpam-2199	180	2	we	we	PRON
ejpam-2199	180	3	have	have	VERB
ejpam-2199	180	4	that	that	PRON
ejpam-2199	180	5	x0	x0	PROPN
ejpam-2199	181	1	6=	6=	PROPN
ejpam-2199	182	1	a	a	PRON
ejpam-2199	182	2	,	,	PUNCT
ejpam-2199	182	3	since	since	SCONJ
ejpam-2199	182	4	x	x	PRON
ejpam-2199	182	5	is	be	AUX
ejpam-2199	182	6	a	a	DET
ejpam-2199	182	7	hausdorff	hausdorff	NOUN
ejpam-2199	182	8	space	space	NOUN
ejpam-2199	182	9	,	,	PUNCT
ejpam-2199	182	10	there	there	PRON
ejpam-2199	182	11	are	be	VERB
ejpam-2199	182	12	va	va	PROPN
ejpam-2199	182	13	and	and	CCONJ
ejpam-2199	182	14	ua	ua	PROPN
ejpam-2199	182	15	disjoint	disjoint	VERB
ejpam-2199	182	16	open	open	ADJ
ejpam-2199	182	17	sets	set	NOUN
ejpam-2199	182	18	in	in	ADP
ejpam-2199	182	19	x	x	PUNCT
ejpam-2199	182	20	containing	contain	VERB
ejpam-2199	182	21	x0	x0	PROPN
ejpam-2199	182	22	and	and	CCONJ
ejpam-2199	182	23	a	a	PRON
ejpam-2199	182	24	,	,	PUNCT
ejpam-2199	182	25	respectively	respectively	ADV
ejpam-2199	182	26	.	.	PUNCT
ejpam-2199	183	1	by	by	ADP
ejpam-2199	183	2	considering	consider	VERB
ejpam-2199	183	3	∀n	∀n	NUM
ejpam-2199	183	4	∈	∈	PROPN
ejpam-2199	183	5	n	n	X
ejpam-2199	183	6	,	,	PUNCT
ejpam-2199	183	7	un	un	PROPN
ejpam-2199	183	8	=	=	PROPN
ejpam-2199	183	9	{	{	PUNCT
ejpam-2199	183	10	ua}a∈a	ua}a∈a	ADP
ejpam-2199	183	11	,	,	PUNCT
ejpam-2199	183	12	we	we	PRON
ejpam-2199	183	13	have	have	VERB
ejpam-2199	183	14	that	that	SCONJ
ejpam-2199	183	15	{	{	PUNCT
ejpam-2199	183	16	un}n∈n	un}n∈n	NOUN
ejpam-2199	183	17	is	be	AUX
ejpam-2199	183	18	a	a	DET
ejpam-2199	183	19	sequence	sequence	NOUN
ejpam-2199	183	20	of	of	ADP
ejpam-2199	183	21	coverings	covering	NOUN
ejpam-2199	183	22	of	of	ADP
ejpam-2199	183	23	a	a	PRON
ejpam-2199	183	24	by	by	ADP
ejpam-2199	183	25	open	open	ADJ
ejpam-2199	183	26	sets	set	NOUN
ejpam-2199	183	27	in	in	ADP
ejpam-2199	183	28	x	x	X
ejpam-2199	183	29	.	.	PUNCT
ejpam-2199	184	1	since	since	SCONJ
ejpam-2199	184	2	,	,	PUNCT
ejpam-2199	184	3	a	a	PRON
ejpam-2199	184	4	is	be	AUX
ejpam-2199	184	5	hurewicz	hurewicz	VERB
ejpam-2199	184	6	by	by	ADP
ejpam-2199	184	7	proposition	proposition	NOUN
ejpam-2199	184	8	5	5	NUM
ejpam-2199	184	9	there	there	ADV
ejpam-2199	184	10	exists	exist	VERB
ejpam-2199	184	11	a	a	DET
ejpam-2199	184	12	sequence	sequence	NOUN
ejpam-2199	184	13	{	{	PUNCT
ejpam-2199	184	14	wn}n∈n	wn}n∈n	X
ejpam-2199	184	15	such	such	ADJ
ejpam-2199	184	16	that	that	PRON
ejpam-2199	184	17	:	:	PUNCT
ejpam-2199	184	18	(	(	PUNCT
ejpam-2199	184	19	i	i	NOUN
ejpam-2199	184	20	)	)	PUNCT
ejpam-2199	184	21	∀n	∀n	PROPN
ejpam-2199	185	1	∈	∈	PROPN
ejpam-2199	185	2	n	n	CCONJ
ejpam-2199	185	3	,	,	PUNCT
ejpam-2199	185	4	wn	wn	PROPN
ejpam-2199	185	5	⊂<∞	⊂<∞	PROPN
ejpam-2199	185	6	un	un	PROPN
ejpam-2199	185	7	,	,	PUNCT
ejpam-2199	185	8	i.	i.	PROPN
ejpam-2199	185	9	e.	e.	PROPN
ejpam-2199	185	10	,	,	PUNCT
ejpam-2199	185	11	∃in	∃in	PROPN
ejpam-2199	185	12	⊂<∞	⊂<∞	PROPN
ejpam-2199	185	13	a	a	X
ejpam-2199	185	14	,	,	PUNCT
ejpam-2199	185	15	such	such	ADJ
ejpam-2199	185	16	thatwn	thatwn	NOUN
ejpam-2199	185	17	=	=	SYM
ejpam-2199	185	18	{	{	PUNCT
ejpam-2199	185	19	ua}a∈a	ua}a∈a	NOUN
ejpam-2199	185	20	.	.	PUNCT
ejpam-2199	185	21	(	(	PUNCT
ejpam-2199	185	22	ii	ii	NOUN
ejpam-2199	185	23	)	)	PUNCT
ejpam-2199	185	24	for	for	ADP
ejpam-2199	185	25	each	each	DET
ejpam-2199	185	26	y	y	PROPN
ejpam-2199	185	27	∈	∈	PROPN
ejpam-2199	185	28	a	a	DET
ejpam-2199	185	29	,	,	PUNCT
ejpam-2199	185	30	∃n0	∃n0	NOUN
ejpam-2199	185	31	∈	∈	PROPN
ejpam-2199	185	32	n	n	CCONJ
ejpam-2199	185	33	,	,	PUNCT
ejpam-2199	185	34	such	such	ADJ
ejpam-2199	185	35	that	that	SCONJ
ejpam-2199	185	36	∀n	∀n	NUM
ejpam-2199	185	37	∈	∈	NOUN
ejpam-2199	185	38	n	n	ADV
ejpam-2199	185	39	if	if	SCONJ
ejpam-2199	185	40	n≥	n≥	PROPN
ejpam-2199	185	41	n0	n0	NUM
ejpam-2199	185	42	,	,	PUNCT
ejpam-2199	185	43	there	there	PRON
ejpam-2199	185	44	exists	exist	VERB
ejpam-2199	185	45	a	a	DET
ejpam-2199	185	46	∈	∈	NOUN
ejpam-2199	185	47	in	in	ADP
ejpam-2199	185	48	with	with	ADP
ejpam-2199	185	49	y	y	PROPN
ejpam-2199	185	50	∈	∈	PROPN
ejpam-2199	185	51	ua	ua	PROPN
ejpam-2199	185	52	.	.	PUNCT
ejpam-2199	185	53	consider	consider	VERB
ejpam-2199	185	54	now	now	ADV
ejpam-2199	185	55	,	,	PUNCT
ejpam-2199	185	56	∀n	∀n	NUM
ejpam-2199	185	57	∈	∈	PROPN
ejpam-2199	185	58	n	n	CCONJ
ejpam-2199	185	59	,	,	PUNCT
ejpam-2199	185	60	vn	vn	PROPN
ejpam-2199	185	61	=	=	PUNCT
ejpam-2199	185	62	{	{	PUNCT
ejpam-2199	185	63	va}a∈in	va}a∈in	PROPN
ejpam-2199	185	64	,	,	PUNCT
ejpam-2199	185	65	since	since	SCONJ
ejpam-2199	185	66	for	for	ADP
ejpam-2199	185	67	each	each	DET
ejpam-2199	185	68	a	a	DET
ejpam-2199	185	69	∈	∈	PROPN
ejpam-2199	185	70	a	a	PRON
ejpam-2199	185	71	,	,	PUNCT
ejpam-2199	185	72	x0	x0	PROPN
ejpam-2199	185	73	∈	∈	PROPN
ejpam-2199	185	74	va	va	NOUN
ejpam-2199	185	75	then	then	ADV
ejpam-2199	185	76	∀n	∀n	NUM
ejpam-2199	185	77	∈	∈	PROPN
ejpam-2199	185	78	n	n	CCONJ
ejpam-2199	185	79	,	,	PUNCT
ejpam-2199	185	80	x0	x0	PROPN
ejpam-2199	185	81	∈	∈	PROPN
ejpam-2199	185	82	⋂	⋂	PROPN
ejpam-2199	185	83	a∈in	a∈in	PROPN
ejpam-2199	185	84	va	va	PROPN
ejpam-2199	185	85	,	,	PUNCT
ejpam-2199	185	86	but	but	CCONJ
ejpam-2199	185	87	since	since	SCONJ
ejpam-2199	185	88	x	x	PRON
ejpam-2199	185	89	is	be	AUX
ejpam-2199	185	90	a	a	DET
ejpam-2199	185	91	c	c	NOUN
ejpam-2199	185	92	-	-	PUNCT
ejpam-2199	185	93	space	space	NOUN
ejpam-2199	185	94	we	we	PRON
ejpam-2199	185	95	have	have	VERB
ejpam-2199	185	96	that	that	SCONJ
ejpam-2199	185	97	there	there	PRON
ejpam-2199	185	98	exists	exist	VERB
ejpam-2199	185	99	an	an	DET
ejpam-2199	185	100	open	open	ADJ
ejpam-2199	185	101	set	set	NOUN
ejpam-2199	185	102	v	v	NOUN
ejpam-2199	185	103	in	in	ADP
ejpam-2199	185	104	x	x	PUNCT
ejpam-2199	185	105	such	such	ADJ
ejpam-2199	185	106	that	that	SCONJ
ejpam-2199	185	107	∀n	∀n	NUM
ejpam-2199	185	108	∈	∈	PROPN
ejpam-2199	185	109	n	n	CCONJ
ejpam-2199	185	110	,	,	PUNCT
ejpam-2199	185	111	x0	x0	PROPN
ejpam-2199	185	112	∈	∈	PROPN
ejpam-2199	185	113	v	v	ADP
ejpam-2199	185	114	⊂	⊂	PROPN
ejpam-2199	185	115	⋂	⋂	PROPN
ejpam-2199	185	116	a∈in	a∈in	PROPN
ejpam-2199	185	117	va	va	PROPN
ejpam-2199	185	118	.	.	PUNCT
ejpam-2199	185	119	consider	consider	VERB
ejpam-2199	185	120	u	u	NOUN
ejpam-2199	185	121	=	=	PROPN
ejpam-2199	185	122	⋃	⋃	PROPN
ejpam-2199	185	123	n∈n	n∈n	X
ejpam-2199	185	124	�	�	PROPN
ejpam-2199	185	125	⋃	⋃	PROPN
ejpam-2199	185	126	a∈in	a∈in	PROPN
ejpam-2199	185	127	ua	ua	PROPN
ejpam-2199	185	128	�	�	PROPN
ejpam-2199	185	129	.	.	PUNCT
ejpam-2199	186	1	we	we	PRON
ejpam-2199	186	2	have	have	VERB
ejpam-2199	186	3	that	that	SCONJ
ejpam-2199	186	4	u	u	NOUN
ejpam-2199	186	5	is	be	AUX
ejpam-2199	186	6	an	an	DET
ejpam-2199	186	7	open	open	ADJ
ejpam-2199	186	8	set	set	NOUN
ejpam-2199	186	9	in	in	ADP
ejpam-2199	186	10	x	x	PUNCT
ejpam-2199	186	11	and	and	CCONJ
ejpam-2199	186	12	a⊂	a⊂	VERB
ejpam-2199	186	13	u	u	NOUN
ejpam-2199	186	14	,	,	PUNCT
ejpam-2199	186	15	because	because	SCONJ
ejpam-2199	186	16	for	for	ADP
ejpam-2199	186	17	each	each	DET
ejpam-2199	186	18	y	y	PROPN
ejpam-2199	186	19	∈	∈	PROPN
ejpam-2199	186	20	a	a	DET
ejpam-2199	186	21	by	by	ADP
ejpam-2199	186	22	(	(	PUNCT
ejpam-2199	186	23	ii	ii	NOUN
ejpam-2199	186	24	)	)	PUNCT
ejpam-2199	186	25	∃n0	∃n0	NOUN
ejpam-2199	186	26	∈	∈	PROPN
ejpam-2199	187	1	n	n	PRON
ejpam-2199	187	2	such	such	ADJ
ejpam-2199	187	3	that	that	SCONJ
ejpam-2199	187	4	∀n	∀n	NUM
ejpam-2199	187	5	∈	∈	NOUN
ejpam-2199	187	6	n	n	ADV
ejpam-2199	187	7	if	if	SCONJ
ejpam-2199	187	8	n	n	PRON
ejpam-2199	187	9	≥	≥	NOUN
ejpam-2199	187	10	n0	n0	X
ejpam-2199	187	11	there	there	PRON
ejpam-2199	187	12	exists	exist	VERB
ejpam-2199	187	13	a	a	DET
ejpam-2199	187	14	∈	∈	NOUN
ejpam-2199	187	15	in	in	ADP
ejpam-2199	187	16	such	such	ADJ
ejpam-2199	187	17	that	that	SCONJ
ejpam-2199	187	18	y	y	PROPN
ejpam-2199	187	19	∈	∈	PROPN
ejpam-2199	187	20	ua	ua	PROPN
ejpam-2199	187	21	.	.	PUNCT
ejpam-2199	188	1	hence	hence	ADV
ejpam-2199	188	2	⋃	⋃	ADP
ejpam-2199	188	3	a∈in	a∈in	PROPN
ejpam-2199	188	4	ua	ua	PROPN
ejpam-2199	188	5	⊂	⊂	PROPN
ejpam-2199	188	6	⋃	⋃	PROPN
ejpam-2199	188	7	n∈n	n∈n	X
ejpam-2199	188	8	�	�	PROPN
ejpam-2199	188	9	⋃	⋃	PROPN
ejpam-2199	188	10	a∈in	a∈in	PROPN
ejpam-2199	188	11	ua	ua	PROPN
ejpam-2199	188	12	�	�	PROPN
ejpam-2199	188	13	=	=	SYM
ejpam-2199	188	14	u	u	PROPN
ejpam-2199	188	15	.	.	PUNCT
ejpam-2199	189	1	now	now	ADV
ejpam-2199	189	2	we	we	PRON
ejpam-2199	189	3	prove	prove	VERB
ejpam-2199	189	4	that	that	SCONJ
ejpam-2199	189	5	v	v	NOUN
ejpam-2199	189	6	and	and	CCONJ
ejpam-2199	189	7	u	u	NOUN
ejpam-2199	189	8	are	be	AUX
ejpam-2199	189	9	disjoint	disjoint	NOUN
ejpam-2199	189	10	sets	set	NOUN
ejpam-2199	189	11	.	.	PUNCT
ejpam-2199	190	1	suppose	suppose	VERB
ejpam-2199	190	2	that	that	SCONJ
ejpam-2199	190	3	there	there	PRON
ejpam-2199	190	4	exists	exist	VERB
ejpam-2199	190	5	y	y	PROPN
ejpam-2199	190	6	∈	∈	PROPN
ejpam-2199	190	7	v	v	ADP
ejpam-2199	190	8	∩	∩	ADJ
ejpam-2199	190	9	u	u	NOUN
ejpam-2199	190	10	.	.	PUNCT
ejpam-2199	191	1	then	then	ADV
ejpam-2199	191	2	y	y	PROPN
ejpam-2199	191	3	∈	∈	PROPN
ejpam-2199	191	4	u	u	NOUN
ejpam-2199	191	5	=	=	PUNCT
ejpam-2199	191	6	⋃	⋃	PROPN
ejpam-2199	191	7	n∈n	n∈n	X
ejpam-2199	191	8	�	�	PROPN
ejpam-2199	191	9	⋃	⋃	PROPN
ejpam-2199	191	10	a∈in	a∈in	PROPN
ejpam-2199	191	11	ua	ua	PROPN
ejpam-2199	191	12	�	�	PROPN
ejpam-2199	191	13	hence	hence	ADV
ejpam-2199	191	14	∃n0	∃n0	NOUN
ejpam-2199	191	15	∈	∈	PROPN
ejpam-2199	191	16	n	n	PRON
ejpam-2199	191	17	such	such	ADJ
ejpam-2199	191	18	that	that	SCONJ
ejpam-2199	191	19	y	y	PROPN
ejpam-2199	191	20	∈	∈	PROPN
ejpam-2199	191	21	⋃	⋃	PROPN
ejpam-2199	191	22	a∈in	a∈in	PROPN
ejpam-2199	191	23	ua	ua	PROPN
ejpam-2199	191	24	then	then	ADV
ejpam-2199	191	25	∃a0	∃a0	VERB
ejpam-2199	191	26	∈	∈	PROPN
ejpam-2199	191	27	in0	in0	NOUN
ejpam-2199	191	28	such	such	ADJ
ejpam-2199	191	29	that	that	SCONJ
ejpam-2199	191	30	y	y	PROPN
ejpam-2199	191	31	∈	∈	PROPN
ejpam-2199	192	1	ua0	ua0	ADV
ejpam-2199	192	2	,	,	PUNCT
ejpam-2199	192	3	but	but	CCONJ
ejpam-2199	192	4	since	since	SCONJ
ejpam-2199	192	5	y	y	PROPN
ejpam-2199	192	6	∈	∈	PROPN
ejpam-2199	192	7	v	v	NOUN
ejpam-2199	192	8	and	and	CCONJ
ejpam-2199	192	9	∀n	∀n	NUM
ejpam-2199	192	10	∈	∈	PROPN
ejpam-2199	192	11	n	n	PRON
ejpam-2199	192	12	v	v	NOUN
ejpam-2199	192	13	⊂	⊂	PROPN
ejpam-2199	192	14	⋂	⋂	PROPN
ejpam-2199	192	15	a∈in	a∈in	PROPN
ejpam-2199	192	16	va	va	PROPN
ejpam-2199	192	17	then	then	ADV
ejpam-2199	192	18	we	we	PRON
ejpam-2199	192	19	have	have	VERB
ejpam-2199	192	20	that	that	PRON
ejpam-2199	192	21	v	v	ADP
ejpam-2199	192	22	⊂	⊂	PROPN
ejpam-2199	192	23	⋂	⋂	PROPN
ejpam-2199	192	24	a∈in0	a∈in0	PUNCT
ejpam-2199	192	25	va	va	NOUN
ejpam-2199	192	26	,	,	PUNCT
ejpam-2199	192	27	hence	hence	ADV
ejpam-2199	192	28	y	y	PROPN
ejpam-2199	192	29	∈	∈	PROPN
ejpam-2199	192	30	v	v	ADP
ejpam-2199	192	31	⊂	⊂	PROPN
ejpam-2199	192	32	⋂	⋂	PROPN
ejpam-2199	192	33	a∈in0	a∈in0	PUNCT
ejpam-2199	192	34	va	va	NOUN
ejpam-2199	192	35	then	then	ADV
ejpam-2199	192	36	∀a	∀a	VERB
ejpam-2199	192	37	∈	∈	PROPN
ejpam-2199	192	38	in0	in0	NOUN
ejpam-2199	192	39	y	y	PROPN
ejpam-2199	192	40	∈	∈	PROPN
ejpam-2199	192	41	va	va	NOUN
ejpam-2199	192	42	which	which	PRON
ejpam-2199	192	43	implies	imply	VERB
ejpam-2199	192	44	that	that	SCONJ
ejpam-2199	192	45	y	y	PROPN
ejpam-2199	192	46	∈	∈	PROPN
ejpam-2199	192	47	va0	va0	NOUN
ejpam-2199	192	48	and	and	CCONJ
ejpam-2199	192	49	then	then	ADV
ejpam-2199	192	50	va0	va0	PROPN
ejpam-2199	192	51	∩	∩	PROPN
ejpam-2199	192	52	ua0	ua0	PROPN
ejpam-2199	192	53	6=	6=	NUM
ejpam-2199	192	54	;	;	PUNCT
ejpam-2199	192	55	,	,	PUNCT
ejpam-2199	192	56	contradiction	contradiction	NOUN
ejpam-2199	192	57	.	.	PUNCT
ejpam-2199	193	1	c.	c.	PROPN
ejpam-2199	193	2	roika	roika	PROPN
ejpam-2199	193	3	,	,	PUNCT
ejpam-2199	193	4	s.	s.	PROPN
ejpam-2199	193	5	kudri	kudri	PROPN
ejpam-2199	193	6	,	,	PUNCT
ejpam-2199	193	7	t.	t.	PROPN
ejpam-2199	193	8	breuckmann	breuckmann	PROPN
ejpam-2199	193	9	/	/	SYM
ejpam-2199	193	10	eur	eur	PROPN
ejpam-2199	193	11	.	.	PUNCT
ejpam-2199	194	1	j.	j.	PROPN
ejpam-2199	194	2	pure	pure	PROPN
ejpam-2199	194	3	appl	appl	PROPN
ejpam-2199	194	4	.	.	PROPN
ejpam-2199	194	5	math	math	PROPN
ejpam-2199	194	6	,	,	PUNCT
ejpam-2199	194	7	8	8	NUM
ejpam-2199	194	8	(	(	PUNCT
ejpam-2199	194	9	2015	2015	NUM
ejpam-2199	194	10	)	)	PUNCT
ejpam-2199	194	11	,	,	PUNCT
ejpam-2199	194	12	514	514	NUM
ejpam-2199	194	13	-	-	SYM
ejpam-2199	194	14	525	525	NUM
ejpam-2199	194	15	520	520	NUM
ejpam-2199	194	16	proposition	proposition	NOUN
ejpam-2199	194	17	8	8	NUM
ejpam-2199	194	18	.	.	PUNCT
ejpam-2199	195	1	let	let	VERB
ejpam-2199	195	2	〈	〈	PROPN
ejpam-2199	195	3	x	x	PROPN
ejpam-2199	195	4	,	,	PUNCT
ejpam-2199	195	5	t	t	PROPN
ejpam-2199	195	6	〉	〉	NOUN
ejpam-2199	195	7	be	be	VERB
ejpam-2199	195	8	a	a	DET
ejpam-2199	195	9	hausdorff	hausdorff	NOUN
ejpam-2199	195	10	c	c	NOUN
ejpam-2199	195	11	-	-	PUNCT
ejpam-2199	195	12	space	space	NOUN
ejpam-2199	195	13	and	and	CCONJ
ejpam-2199	195	14	a	a	DET
ejpam-2199	195	15	be	be	AUX
ejpam-2199	195	16	a	a	DET
ejpam-2199	195	17	hurewicz	hurewicz	NOUN
ejpam-2199	195	18	subspace	subspace	NOUN
ejpam-2199	195	19	of	of	ADP
ejpam-2199	195	20	x	x	SYM
ejpam-2199	195	21	,	,	PUNCT
ejpam-2199	195	22	then	then	ADV
ejpam-2199	195	23	a	a	PRON
ejpam-2199	195	24	is	be	AUX
ejpam-2199	195	25	closed	closed	ADJ
ejpam-2199	195	26	.	.	PUNCT
ejpam-2199	196	1	proof	proof	NOUN
ejpam-2199	196	2	.	.	PUNCT
ejpam-2199	197	1	we	we	PRON
ejpam-2199	197	2	are	be	AUX
ejpam-2199	197	3	going	go	VERB
ejpam-2199	197	4	to	to	PART
ejpam-2199	197	5	show	show	VERB
ejpam-2199	197	6	that	that	SCONJ
ejpam-2199	197	7	if	if	SCONJ
ejpam-2199	197	8	x	x	SYM
ejpam-2199	197	9	∈	∈	NOUN
ejpam-2199	197	10	ac	ac	VERB
ejpam-2199	197	11	there	there	PRON
ejpam-2199	197	12	is	be	VERB
ejpam-2199	197	13	u	u	PROPN
ejpam-2199	197	14	∈	∈	PROPN
ejpam-2199	197	15	t	t	NOUN
ejpam-2199	197	16	such	such	ADJ
ejpam-2199	197	17	that	that	SCONJ
ejpam-2199	197	18	x	x	SYM
ejpam-2199	197	19	∈	∈	PROPN
ejpam-2199	197	20	u	u	X
ejpam-2199	197	21	⊂	⊂	X
ejpam-2199	197	22	ac	ac	PROPN
ejpam-2199	197	23	.	.	PUNCT
ejpam-2199	198	1	since	since	SCONJ
ejpam-2199	198	2	x	x	PROPN
ejpam-2199	198	3	/∈	/∈	PROPN
ejpam-2199	198	4	a	a	X
ejpam-2199	198	5	,	,	PUNCT
ejpam-2199	198	6	a	a	PRON
ejpam-2199	198	7	is	be	AUX
ejpam-2199	198	8	hurewicz	hurewicz	NOUN
ejpam-2199	198	9	and	and	CCONJ
ejpam-2199	198	10	x	x	NOUN
ejpam-2199	198	11	is	be	AUX
ejpam-2199	198	12	a	a	DET
ejpam-2199	198	13	hausdorff	hausdorff	NOUN
ejpam-2199	198	14	c	c	NOUN
ejpam-2199	198	15	-	-	PUNCT
ejpam-2199	198	16	space	space	NOUN
ejpam-2199	198	17	then	then	ADV
ejpam-2199	198	18	by	by	ADP
ejpam-2199	198	19	lemma	lemma	PROPN
ejpam-2199	198	20	1	1	NUM
ejpam-2199	198	21	,	,	PUNCT
ejpam-2199	198	22	there	there	PRON
ejpam-2199	198	23	are	be	VERB
ejpam-2199	198	24	v	v	NOUN
ejpam-2199	198	25	and	and	CCONJ
ejpam-2199	198	26	u	u	PRON
ejpam-2199	198	27	disjoint	disjoint	ADJ
ejpam-2199	198	28	open	open	ADJ
ejpam-2199	198	29	sets	set	NOUN
ejpam-2199	198	30	containing	contain	VERB
ejpam-2199	198	31	x	x	PROPN
ejpam-2199	198	32	and	and	CCONJ
ejpam-2199	198	33	a	a	PRON
ejpam-2199	198	34	,	,	PUNCT
ejpam-2199	198	35	respectively	respectively	ADV
ejpam-2199	198	36	.	.	PUNCT
ejpam-2199	199	1	hence	hence	ADV
ejpam-2199	199	2	we	we	PRON
ejpam-2199	199	3	have	have	VERB
ejpam-2199	199	4	that	that	PRON
ejpam-2199	199	5	x	x	SYM
ejpam-2199	199	6	∈	∈	PROPN
ejpam-2199	199	7	v	v	ADP
ejpam-2199	199	8	⊂	⊂	PROPN
ejpam-2199	199	9	ac	ac	PROPN
ejpam-2199	199	10	,	,	PUNCT
ejpam-2199	199	11	because	because	SCONJ
ejpam-2199	199	12	since	since	SCONJ
ejpam-2199	199	13	a⊂	a⊂	VERB
ejpam-2199	199	14	u	u	NOUN
ejpam-2199	199	15	and	and	CCONJ
ejpam-2199	199	16	u	u	NOUN
ejpam-2199	199	17	∩	∩	NOUN
ejpam-2199	199	18	v	v	NOUN
ejpam-2199	199	19	=	=	PUNCT
ejpam-2199	199	20	;	;	PUNCT
ejpam-2199	199	21	then	then	ADV
ejpam-2199	199	22	a∩	a∩	PROPN
ejpam-2199	199	23	v	v	NOUN
ejpam-2199	199	24	=	=	PUNCT
ejpam-2199	199	25	;	;	PUNCT
ejpam-2199	199	26	.	.	PUNCT
ejpam-2199	200	1	so	so	ADV
ejpam-2199	200	2	ac	ac	PROPN
ejpam-2199	200	3	is	be	AUX
ejpam-2199	200	4	open	open	ADJ
ejpam-2199	200	5	,	,	PUNCT
ejpam-2199	200	6	hence	hence	ADV
ejpam-2199	200	7	a	a	PRON
ejpam-2199	200	8	is	be	AUX
ejpam-2199	200	9	closed	closed	ADJ
ejpam-2199	200	10	.	.	PUNCT
ejpam-2199	201	1	proposition	proposition	NOUN
ejpam-2199	201	2	9	9	NUM
ejpam-2199	201	3	.	.	PUNCT
ejpam-2199	202	1	let	let	VERB
ejpam-2199	202	2	〈	〈	PROPN
ejpam-2199	202	3	x	x	X
ejpam-2199	202	4	,	,	PUNCT
ejpam-2199	202	5	tx	tx	PROPN
ejpam-2199	202	6	〉	〉	NOUN
ejpam-2199	202	7	be	be	VERB
ejpam-2199	202	8	a	a	DET
ejpam-2199	202	9	topological	topological	ADJ
ejpam-2199	202	10	c	c	NOUN
ejpam-2199	202	11	-	-	PUNCT
ejpam-2199	202	12	space	space	NOUN
ejpam-2199	202	13	and	and	CCONJ
ejpam-2199	202	14	let	let	VERB
ejpam-2199	202	15	〈	〈	PROPN
ejpam-2199	202	16	y	y	PROPN
ejpam-2199	202	17	,	,	PUNCT
ejpam-2199	202	18	ty	ty	NUM
ejpam-2199	202	19	〉	〉	NOUN
ejpam-2199	202	20	be	be	VERB
ejpam-2199	202	21	a	a	DET
ejpam-2199	202	22	subspace	subspace	NOUN
ejpam-2199	202	23	of	of	ADP
ejpam-2199	202	24	x	x	PRON
ejpam-2199	202	25	,	,	PUNCT
ejpam-2199	202	26	then	then	ADV
ejpam-2199	202	27	y	y	PROPN
ejpam-2199	202	28	is	be	AUX
ejpam-2199	202	29	a	a	DET
ejpam-2199	202	30	c	c	NOUN
ejpam-2199	202	31	-	-	PUNCT
ejpam-2199	202	32	space	space	NOUN
ejpam-2199	202	33	.	.	PUNCT
ejpam-2199	203	1	proof	proof	NOUN
ejpam-2199	203	2	.	.	PUNCT
ejpam-2199	204	1	let	let	VERB
ejpam-2199	204	2	x	x	SYM
ejpam-2199	204	3	∈	∈	PROPN
ejpam-2199	204	4	y	y	PROPN
ejpam-2199	204	5	,	,	PUNCT
ejpam-2199	204	6	consider	consider	VERB
ejpam-2199	204	7	{	{	PUNCT
ejpam-2199	204	8	an}n∈n	an}n∈n	PUNCT
ejpam-2199	204	9	a	a	DET
ejpam-2199	204	10	sequence	sequence	NOUN
ejpam-2199	204	11	such	such	ADJ
ejpam-2199	204	12	that	that	PRON
ejpam-2199	204	13	for	for	ADP
ejpam-2199	204	14	each	each	DET
ejpam-2199	204	15	n	n	PRON
ejpam-2199	204	16	∈	∈	PROPN
ejpam-2199	204	17	n	n	CCONJ
ejpam-2199	204	18	,	,	PUNCT
ejpam-2199	204	19	an	an	DET
ejpam-2199	204	20	=	=	X
ejpam-2199	204	21	{	{	PUNCT
ejpam-2199	204	22	an	an	DET
ejpam-2199	204	23	j	j	PROPN
ejpam-2199	204	24	∈	∈	PROPN
ejpam-2199	204	25	ty	ty	INTJ
ejpam-2199	204	26	;	;	PUNCT
ejpam-2199	204	27	j	j	PROPN
ejpam-2199	204	28	=	=	NOUN
ejpam-2199	204	29	1	1	NUM
ejpam-2199	204	30	.	.	PUNCT
ejpam-2199	204	31	.	.	PUNCT
ejpam-2199	204	32	.	.	PUNCT
ejpam-2199	205	1	,	,	PUNCT
ejpam-2199	205	2	kn	kn	PROPN
ejpam-2199	205	3	}	}	PUNCT
ejpam-2199	205	4	and	and	CCONJ
ejpam-2199	205	5	x	x	PUNCT
ejpam-2199	205	6	∈	∈	PROPN
ejpam-2199	205	7	kn	kn	NOUN
ejpam-2199	206	1	⋂	⋂	PROPN
ejpam-2199	206	2	j=1	j=1	PROPN
ejpam-2199	206	3	an	an	DET
ejpam-2199	206	4	j	j	PROPN
ejpam-2199	206	5	then	then	ADV
ejpam-2199	206	6	,	,	PUNCT
ejpam-2199	206	7	since	since	SCONJ
ejpam-2199	206	8	y	y	PROPN
ejpam-2199	206	9	is	be	AUX
ejpam-2199	206	10	subspace	subspace	NOUN
ejpam-2199	206	11	of	of	ADP
ejpam-2199	206	12	x	x	SYM
ejpam-2199	206	13	,	,	PUNCT
ejpam-2199	206	14	∀n	∀n	NUM
ejpam-2199	206	15	∈	∈	PROPN
ejpam-2199	206	16	n	n	NOUN
ejpam-2199	206	17	and	and	CCONJ
ejpam-2199	206	18	∀	∀	NUM
ejpam-2199	206	19	j	j	NOUN
ejpam-2199	206	20	=	=	SYM
ejpam-2199	206	21	1	1	NUM
ejpam-2199	206	22	,	,	PUNCT
ejpam-2199	206	23	.	.	PUNCT
ejpam-2199	206	24	.	.	PUNCT
ejpam-2199	206	25	.	.	PUNCT
ejpam-2199	207	1	,	,	PUNCT
ejpam-2199	207	2	kn	kn	PROPN
ejpam-2199	207	3	,	,	PUNCT
ejpam-2199	207	4	there	there	PRON
ejpam-2199	207	5	exists	exist	VERB
ejpam-2199	207	6	un	un	PROPN
ejpam-2199	207	7	j	j	PROPN
ejpam-2199	207	8	∈	∈	PROPN
ejpam-2199	207	9	tx	tx	VERB
ejpam-2199	207	10	such	such	ADJ
ejpam-2199	207	11	that	that	SCONJ
ejpam-2199	207	12	an	an	DET
ejpam-2199	207	13	j	j	PROPN
ejpam-2199	207	14	=	=	PROPN
ejpam-2199	207	15	un	un	PROPN
ejpam-2199	207	16	j	j	PROPN
ejpam-2199	207	17	∩	∩	PROPN
ejpam-2199	207	18	y	y	PROPN
ejpam-2199	207	19	.	.	PUNCT
ejpam-2199	208	1	hence	hence	ADV
ejpam-2199	208	2	an	an	DET
ejpam-2199	208	3	j	j	PROPN
ejpam-2199	208	4	⊂	⊂	PROPN
ejpam-2199	208	5	un	un	PROPN
ejpam-2199	208	6	j	j	PROPN
ejpam-2199	208	7	,	,	PUNCT
ejpam-2199	208	8	then	then	ADV
ejpam-2199	208	9	∀n	∀n	NUM
ejpam-2199	208	10	∈	∈	PROPN
ejpam-2199	208	11	n	n	CCONJ
ejpam-2199	208	12	,	,	PUNCT
ejpam-2199	208	13	x	x	PROPN
ejpam-2199	208	14	∈	∈	PROPN
ejpam-2199	208	15	kn	kn	PROPN
ejpam-2199	208	16	⋂	⋂	PROPN
ejpam-2199	208	17	j=1	j=1	PROPN
ejpam-2199	208	18	un	un	PROPN
ejpam-2199	208	19	j	j	PROPN
ejpam-2199	208	20	.	.	PUNCT
ejpam-2199	209	1	since	since	SCONJ
ejpam-2199	209	2	x	x	PRON
ejpam-2199	209	3	is	be	AUX
ejpam-2199	209	4	a	a	DET
ejpam-2199	209	5	c	c	NOUN
ejpam-2199	209	6	-	-	PUNCT
ejpam-2199	209	7	space	space	NOUN
ejpam-2199	209	8	,	,	PUNCT
ejpam-2199	209	9	there	there	PRON
ejpam-2199	209	10	exists	exist	VERB
ejpam-2199	209	11	u	u	PROPN
ejpam-2199	209	12	∈	∈	PROPN
ejpam-2199	209	13	tx	tx	ADP
ejpam-2199	209	14	such	such	ADJ
ejpam-2199	209	15	that	that	PRON
ejpam-2199	209	16	for	for	ADP
ejpam-2199	209	17	each	each	DET
ejpam-2199	209	18	n	n	PRON
ejpam-2199	209	19	∈	∈	PROPN
ejpam-2199	209	20	n	n	CCONJ
ejpam-2199	209	21	,	,	PUNCT
ejpam-2199	209	22	x	x	PUNCT
ejpam-2199	209	23	∈	∈	PROPN
ejpam-2199	209	24	u	u	NOUN
ejpam-2199	209	25	⊂	⊂	PROPN
ejpam-2199	209	26	kn	kn	PROPN
ejpam-2199	209	27	⋂	⋂	PROPN
ejpam-2199	209	28	j=1	j=1	PROPN
ejpam-2199	209	29	un	un	PROPN
ejpam-2199	209	30	j	j	PROPN
ejpam-2199	209	31	,	,	PUNCT
ejpam-2199	209	32	hence	hence	ADV
ejpam-2199	209	33	v	v	NOUN
ejpam-2199	209	34	=	=	SYM
ejpam-2199	209	35	u	u	NOUN
ejpam-2199	209	36	∩	∩	PROPN
ejpam-2199	209	37	y	y	PROPN
ejpam-2199	209	38	,	,	PUNCT
ejpam-2199	209	39	v	v	PROPN
ejpam-2199	209	40	∈	∈	NOUN
ejpam-2199	209	41	ty	ty	INTJ
ejpam-2199	209	42	,	,	PUNCT
ejpam-2199	209	43	x	x	PUNCT
ejpam-2199	209	44	∈	∈	PROPN
ejpam-2199	209	45	v	v	NOUN
ejpam-2199	209	46	and	and	CCONJ
ejpam-2199	209	47	for	for	ADP
ejpam-2199	209	48	each	each	DET
ejpam-2199	209	49	n	n	PRON
ejpam-2199	209	50	∈	∈	PROPN
ejpam-2199	209	51	n	n	PRON
ejpam-2199	209	52	v	v	NOUN
ejpam-2199	209	53	=	=	SYM
ejpam-2199	209	54	u	u	NOUN
ejpam-2199	209	55	∩	∩	PROPN
ejpam-2199	209	56	y	y	PROPN
ejpam-2199	209	57	⊂	⊂	PROPN
ejpam-2199	209	58	kn	kn	PROPN
ejpam-2199	210	1	⋂	⋂	PROPN
ejpam-2199	210	2	j=1	j=1	PROPN
ejpam-2199	210	3	un	un	PROPN
ejpam-2199	210	4	j	j	PROPN
ejpam-2199	210	5	!	!	PUNCT
ejpam-2199	211	1	∩	∩	PROPN
ejpam-2199	211	2	y	y	PROPN
ejpam-2199	211	3	=	=	SYM
ejpam-2199	211	4	kn	kn	PROPN
ejpam-2199	211	5	⋂	⋂	PROPN
ejpam-2199	211	6	j=1	j=1	PROPN
ejpam-2199	211	7	(	(	PUNCT
ejpam-2199	211	8	un	un	PROPN
ejpam-2199	211	9	j	j	PROPN
ejpam-2199	211	10	∩	∩	PROPN
ejpam-2199	211	11	y	y	PROPN
ejpam-2199	211	12	)	)	PUNCT
ejpam-2199	212	1	=	=	NOUN
ejpam-2199	213	1	kn	kn	PROPN
ejpam-2199	213	2	⋂	⋂	PROPN
ejpam-2199	213	3	j=1	j=1	PROPN
ejpam-2199	213	4	an	an	DET
ejpam-2199	213	5	j	j	PROPN
ejpam-2199	213	6	.	.	PUNCT
ejpam-2199	214	1	so	so	ADV
ejpam-2199	214	2	y	y	PROPN
ejpam-2199	214	3	is	be	AUX
ejpam-2199	214	4	a	a	DET
ejpam-2199	214	5	c	c	NOUN
ejpam-2199	214	6	-	-	PUNCT
ejpam-2199	214	7	space	space	NOUN
ejpam-2199	214	8	.	.	PUNCT
ejpam-2199	215	1	proposition	proposition	NOUN
ejpam-2199	215	2	10	10	NUM
ejpam-2199	215	3	.	.	PUNCT
ejpam-2199	216	1	let	let	VERB
ejpam-2199	216	2	〈	〈	PROPN
ejpam-2199	216	3	x	x	X
ejpam-2199	216	4	,	,	PUNCT
ejpam-2199	216	5	tx	tx	PROPN
ejpam-2199	216	6	〉	〉	NOUN
ejpam-2199	216	7	be	be	VERB
ejpam-2199	216	8	a	a	DET
ejpam-2199	216	9	topological	topological	ADJ
ejpam-2199	216	10	c	c	NOUN
ejpam-2199	216	11	-	-	PUNCT
ejpam-2199	216	12	space	space	NOUN
ejpam-2199	216	13	,	,	PUNCT
ejpam-2199	216	14	〈	〈	PROPN
ejpam-2199	216	15	y	y	PROPN
ejpam-2199	216	16	,	,	PUNCT
ejpam-2199	216	17	ty	ty	NUM
ejpam-2199	216	18	〉	〉	NOUN
ejpam-2199	216	19	be	be	VERB
ejpam-2199	216	20	a	a	DET
ejpam-2199	216	21	topological	topological	ADJ
ejpam-2199	216	22	space	space	NOUN
ejpam-2199	216	23	and	and	CCONJ
ejpam-2199	216	24	f	f	NOUN
ejpam-2199	216	25	:	:	PUNCT
ejpam-2199	216	26	x	x	X
ejpam-2199	216	27	→	→	SYM
ejpam-2199	216	28	y	y	X
ejpam-2199	216	29	be	be	AUX
ejpam-2199	216	30	an	an	DET
ejpam-2199	216	31	open	open	ADJ
ejpam-2199	216	32	,	,	PUNCT
ejpam-2199	216	33	continuous	continuous	ADJ
ejpam-2199	216	34	and	and	CCONJ
ejpam-2199	216	35	surjective	surjective	ADJ
ejpam-2199	216	36	function	function	NOUN
ejpam-2199	216	37	.	.	PUNCT
ejpam-2199	217	1	then	then	ADV
ejpam-2199	217	2	y	y	PROPN
ejpam-2199	217	3	is	be	AUX
ejpam-2199	217	4	a	a	DET
ejpam-2199	217	5	c	c	NOUN
ejpam-2199	217	6	-	-	PUNCT
ejpam-2199	217	7	space	space	NOUN
ejpam-2199	217	8	.	.	PUNCT
ejpam-2199	218	1	proof	proof	NOUN
ejpam-2199	218	2	.	.	PUNCT
ejpam-2199	219	1	let	let	VERB
ejpam-2199	219	2	y	y	PROPN
ejpam-2199	219	3	∈	∈	PROPN
ejpam-2199	219	4	y	y	PROPN
ejpam-2199	219	5	and	and	CCONJ
ejpam-2199	219	6	{	{	PUNCT
ejpam-2199	219	7	an}n∈n	an}n∈n	PUNCT
ejpam-2199	219	8	a	a	DET
ejpam-2199	219	9	sequence	sequence	NOUN
ejpam-2199	219	10	such	such	ADJ
ejpam-2199	219	11	that	that	PRON
ejpam-2199	219	12	for	for	ADP
ejpam-2199	219	13	each	each	DET
ejpam-2199	219	14	n	n	PRON
ejpam-2199	219	15	∈	∈	PROPN
ejpam-2199	219	16	n	n	CCONJ
ejpam-2199	219	17	,	,	PUNCT
ejpam-2199	219	18	an	an	DET
ejpam-2199	219	19	=	=	X
ejpam-2199	219	20	{	{	PUNCT
ejpam-2199	219	21	an	an	DET
ejpam-2199	219	22	j	j	PROPN
ejpam-2199	219	23	∈	∈	PROPN
ejpam-2199	219	24	ty	ty	INTJ
ejpam-2199	219	25	;	;	PUNCT
ejpam-2199	219	26	j	j	PROPN
ejpam-2199	219	27	=	=	NOUN
ejpam-2199	219	28	1	1	NUM
ejpam-2199	219	29	.	.	PUNCT
ejpam-2199	219	30	.	.	PUNCT
ejpam-2199	219	31	.	.	PUNCT
ejpam-2199	220	1	,	,	PUNCT
ejpam-2199	220	2	kn	kn	PROPN
ejpam-2199	220	3	}	}	PUNCT
ejpam-2199	220	4	and	and	CCONJ
ejpam-2199	220	5	y	y	PROPN
ejpam-2199	220	6	∈	∈	PROPN
ejpam-2199	221	1	kn	kn	PROPN
ejpam-2199	221	2	⋂	⋂	PROPN
ejpam-2199	221	3	j=1	j=1	PROPN
ejpam-2199	221	4	an	an	DET
ejpam-2199	221	5	j	j	PROPN
ejpam-2199	221	6	.	.	PUNCT
ejpam-2199	222	1	since	since	SCONJ
ejpam-2199	222	2	f	f	PROPN
ejpam-2199	222	3	is	be	AUX
ejpam-2199	222	4	a	a	DET
ejpam-2199	222	5	surjection	surjection	NOUN
ejpam-2199	222	6	,	,	PUNCT
ejpam-2199	222	7	∃x	∃x	PROPN
ejpam-2199	222	8	∈	∈	PROPN
ejpam-2199	222	9	x	x	X
ejpam-2199	222	10	such	such	ADJ
ejpam-2199	222	11	that	that	SCONJ
ejpam-2199	222	12	f	f	PROPN
ejpam-2199	222	13	(	(	PUNCT
ejpam-2199	222	14	x	x	X
ejpam-2199	222	15	)	)	PUNCT
ejpam-2199	222	16	=	=	SYM
ejpam-2199	222	17	y	y	PROPN
ejpam-2199	222	18	.	.	PUNCT
ejpam-2199	223	1	for	for	ADP
ejpam-2199	223	2	each	each	DET
ejpam-2199	223	3	n	n	PRON
ejpam-2199	223	4	∈	∈	PROPN
ejpam-2199	223	5	n	n	NOUN
ejpam-2199	223	6	and	and	CCONJ
ejpam-2199	223	7	for	for	ADP
ejpam-2199	223	8	each	each	PRON
ejpam-2199	223	9	j	j	NOUN
ejpam-2199	223	10	=	=	SYM
ejpam-2199	223	11	1	1	NUM
ejpam-2199	223	12	,	,	PUNCT
ejpam-2199	223	13	.	.	PUNCT
ejpam-2199	223	14	.	.	PUNCT
ejpam-2199	223	15	.	.	PUNCT
ejpam-2199	224	1	,	,	PUNCT
ejpam-2199	224	2	kn	kn	PROPN
ejpam-2199	224	3	,	,	PUNCT
ejpam-2199	224	4	since	since	SCONJ
ejpam-2199	224	5	f	f	PROPN
ejpam-2199	224	6	is	be	AUX
ejpam-2199	224	7	continuous	continuous	ADJ
ejpam-2199	224	8	and	and	CCONJ
ejpam-2199	224	9	an	an	DET
ejpam-2199	224	10	j	j	PROPN
ejpam-2199	224	11	∈	∈	PROPN
ejpam-2199	225	1	ty	ty	INTJ
ejpam-2199	225	2	,	,	PUNCT
ejpam-2199	225	3	we	we	PRON
ejpam-2199	225	4	have	have	VERB
ejpam-2199	225	5	f	f	PROPN
ejpam-2199	225	6	−1(an	−1(an	PROPN
ejpam-2199	225	7	j	j	PROPN
ejpam-2199	225	8	)	)	PUNCT
ejpam-2199	225	9	∈	∈	PROPN
ejpam-2199	225	10	tx	tx	PROPN
ejpam-2199	225	11	.	.	PUNCT
ejpam-2199	226	1	hence	hence	ADV
ejpam-2199	226	2	for	for	ADP
ejpam-2199	226	3	each	each	DET
ejpam-2199	226	4	n	n	PRON
ejpam-2199	226	5	∈	∈	PROPN
ejpam-2199	226	6	n	n	CCONJ
ejpam-2199	226	7	,	,	PUNCT
ejpam-2199	226	8	x	x	PROPN
ejpam-2199	226	9	∈	∈	PROPN
ejpam-2199	226	10	f	f	PROPN
ejpam-2199	226	11	−1({y	−1({y	PROPN
ejpam-2199	226	12	}	}	PUNCT
ejpam-2199	226	13	)	)	PUNCT
ejpam-2199	227	1	⊂	⊂	PROPN
ejpam-2199	227	2	f	f	X
ejpam-2199	228	1	−1	−1	PROPN
ejpam-2199	228	2	(	(	PUNCT
ejpam-2199	228	3	kn	kn	PROPN
ejpam-2199	228	4	⋂	⋂	PROPN
ejpam-2199	228	5	j=1	j=1	PROPN
ejpam-2199	228	6	an	an	DET
ejpam-2199	228	7	j	j	NOUN
ejpam-2199	228	8	)	)	PUNCT
ejpam-2199	229	1	=	=	SYM
ejpam-2199	229	2	kn	kn	PROPN
ejpam-2199	229	3	⋂	⋂	PROPN
ejpam-2199	229	4	j=1	j=1	PROPN
ejpam-2199	229	5	f	f	PROPN
ejpam-2199	229	6	−1(an	−1(an	PROPN
ejpam-2199	229	7	j	j	PROPN
ejpam-2199	229	8	)	)	PUNCT
ejpam-2199	229	9	.	.	PUNCT
ejpam-2199	230	1	because	because	SCONJ
ejpam-2199	230	2	x	x	PRON
ejpam-2199	230	3	is	be	AUX
ejpam-2199	230	4	a	a	DET
ejpam-2199	230	5	c	c	NOUN
ejpam-2199	230	6	-	-	PUNCT
ejpam-2199	230	7	space	space	NOUN
ejpam-2199	230	8	,	,	PUNCT
ejpam-2199	230	9	there	there	PRON
ejpam-2199	230	10	exists	exist	VERB
ejpam-2199	230	11	u	u	PROPN
ejpam-2199	230	12	∈	∈	PROPN
ejpam-2199	230	13	tx	tx	ADP
ejpam-2199	230	14	such	such	ADJ
ejpam-2199	230	15	that	that	PRON
ejpam-2199	230	16	for	for	ADP
ejpam-2199	230	17	each	each	DET
ejpam-2199	230	18	n	n	PRON
ejpam-2199	230	19	∈	∈	PROPN
ejpam-2199	230	20	n	n	CCONJ
ejpam-2199	230	21	,	,	PUNCT
ejpam-2199	230	22	x	x	PUNCT
ejpam-2199	230	23	∈	∈	PROPN
ejpam-2199	230	24	u	u	NOUN
ejpam-2199	230	25	⊂	⊂	PROPN
ejpam-2199	230	26	kn	kn	PROPN
ejpam-2199	230	27	⋂	⋂	PROPN
ejpam-2199	230	28	j=1	j=1	PROPN
ejpam-2199	230	29	f	f	PROPN
ejpam-2199	230	30	−1(an	−1(an	PROPN
ejpam-2199	230	31	j	j	PROPN
ejpam-2199	230	32	)	)	PUNCT
ejpam-2199	230	33	,	,	PUNCT
ejpam-2199	230	34	then	then	ADV
ejpam-2199	230	35	for	for	ADP
ejpam-2199	230	36	each	each	DET
ejpam-2199	230	37	n	n	PRON
ejpam-2199	230	38	∈	∈	PROPN
ejpam-2199	230	39	n	n	CCONJ
ejpam-2199	230	40	y	y	NOUN
ejpam-2199	230	41	=	=	SYM
ejpam-2199	230	42	f	f	PROPN
ejpam-2199	230	43	(	(	PUNCT
ejpam-2199	230	44	x	x	X
ejpam-2199	230	45	)	)	PUNCT
ejpam-2199	230	46	∈	∈	PROPN
ejpam-2199	230	47	f	f	X
ejpam-2199	230	48	(	(	PUNCT
ejpam-2199	230	49	u	u	NOUN
ejpam-2199	230	50	)	)	PUNCT
ejpam-2199	231	1	⊂	⊂	PROPN
ejpam-2199	231	2	f	f	X
ejpam-2199	232	1	(	(	PUNCT
ejpam-2199	232	2	kn	kn	NOUN
ejpam-2199	232	3	⋂	⋂	PROPN
ejpam-2199	232	4	j=1	j=1	PROPN
ejpam-2199	232	5	f	f	PROPN
ejpam-2199	232	6	−1(an	−1(an	PROPN
ejpam-2199	232	7	j	j	PROPN
ejpam-2199	232	8	)	)	PUNCT
ejpam-2199	232	9	)	)	PUNCT
ejpam-2199	233	1	⊂	⊂	PROPN
ejpam-2199	234	1	kn	kn	PROPN
ejpam-2199	234	2	⋂	⋂	PROPN
ejpam-2199	234	3	j=1	j=1	PROPN
ejpam-2199	234	4	an	an	DET
ejpam-2199	234	5	j	j	PROPN
ejpam-2199	234	6	,	,	PUNCT
ejpam-2199	234	7	since	since	SCONJ
ejpam-2199	234	8	f	f	PROPN
ejpam-2199	234	9	is	be	AUX
ejpam-2199	234	10	an	an	DET
ejpam-2199	234	11	open	open	ADJ
ejpam-2199	234	12	function	function	NOUN
ejpam-2199	234	13	we	we	PRON
ejpam-2199	234	14	have	have	VERB
ejpam-2199	234	15	that	that	PRON
ejpam-2199	234	16	f	f	PROPN
ejpam-2199	234	17	(	(	PUNCT
ejpam-2199	234	18	u	u	NOUN
ejpam-2199	234	19	)	)	PUNCT
ejpam-2199	234	20	is	be	AUX
ejpam-2199	234	21	an	an	DET
ejpam-2199	234	22	open	open	ADJ
ejpam-2199	234	23	set	set	NOUN
ejpam-2199	234	24	.	.	PUNCT
ejpam-2199	235	1	so	so	ADV
ejpam-2199	235	2	y	y	PROPN
ejpam-2199	235	3	is	be	AUX
ejpam-2199	235	4	a	a	DET
ejpam-2199	235	5	c	c	NOUN
ejpam-2199	235	6	-	-	PUNCT
ejpam-2199	235	7	space	space	NOUN
ejpam-2199	235	8	.	.	PUNCT
ejpam-2199	236	1	c.	c.	PROPN
ejpam-2199	236	2	roika	roika	PROPN
ejpam-2199	236	3	,	,	PUNCT
ejpam-2199	236	4	s.	s.	PROPN
ejpam-2199	236	5	kudri	kudri	PROPN
ejpam-2199	236	6	,	,	PUNCT
ejpam-2199	236	7	t.	t.	PROPN
ejpam-2199	236	8	breuckmann	breuckmann	PROPN
ejpam-2199	236	9	/	/	SYM
ejpam-2199	236	10	eur	eur	PROPN
ejpam-2199	236	11	.	.	PUNCT
ejpam-2199	237	1	j.	j.	PROPN
ejpam-2199	237	2	pure	pure	PROPN
ejpam-2199	237	3	appl	appl	PROPN
ejpam-2199	237	4	.	.	PROPN
ejpam-2199	237	5	math	math	PROPN
ejpam-2199	237	6	,	,	PUNCT
ejpam-2199	237	7	8	8	NUM
ejpam-2199	237	8	(	(	PUNCT
ejpam-2199	237	9	2015	2015	NUM
ejpam-2199	237	10	)	)	PUNCT
ejpam-2199	237	11	,	,	PUNCT
ejpam-2199	237	12	514	514	NUM
ejpam-2199	237	13	-	-	SYM
ejpam-2199	237	14	525	525	NUM
ejpam-2199	237	15	521	521	NUM
ejpam-2199	237	16	4	4	NUM
ejpam-2199	237	17	.	.	PUNCT
ejpam-2199	238	1	locally	locally	ADV
ejpam-2199	238	2	hurewicz	hurewicz	NOUN
ejpam-2199	238	3	spaces	space	NOUN
ejpam-2199	238	4	definition	definition	NOUN
ejpam-2199	238	5	8	8	NUM
ejpam-2199	238	6	.	.	PUNCT
ejpam-2199	239	1	a	a	DET
ejpam-2199	239	2	topological	topological	ADJ
ejpam-2199	239	3	space	space	NOUN
ejpam-2199	239	4	〈	〈	NOUN
ejpam-2199	239	5	x	x	X
ejpam-2199	239	6	,	,	PUNCT
ejpam-2199	239	7	t	t	PROPN
ejpam-2199	239	8	〉	〉	NOUN
ejpam-2199	239	9	is	be	AUX
ejpam-2199	239	10	locally	locally	ADV
ejpam-2199	239	11	hurewicz	hurewicz	NOUN
ejpam-2199	239	12	if	if	SCONJ
ejpam-2199	239	13	and	and	CCONJ
ejpam-2199	239	14	only	only	ADV
ejpam-2199	239	15	if	if	SCONJ
ejpam-2199	239	16	,	,	PUNCT
ejpam-2199	239	17	for	for	ADP
ejpam-2199	239	18	each	each	DET
ejpam-2199	239	19	x	x	SYM
ejpam-2199	239	20	∈	∈	PROPN
ejpam-2199	239	21	x	x	X
ejpam-2199	239	22	and	and	CCONJ
ejpam-2199	239	23	for	for	ADP
ejpam-2199	239	24	each	each	DET
ejpam-2199	239	25	v	v	NUM
ejpam-2199	239	26	∈	∈	PROPN
ejpam-2199	239	27	t	t	NOUN
ejpam-2199	239	28	with	with	ADP
ejpam-2199	239	29	x	x	PROPN
ejpam-2199	239	30	∈	∈	PROPN
ejpam-2199	239	31	v	v	NOUN
ejpam-2199	239	32	,	,	PUNCT
ejpam-2199	239	33	there	there	PRON
ejpam-2199	239	34	exists	exist	VERB
ejpam-2199	239	35	u	u	PROPN
ejpam-2199	239	36	∈	∈	PROPN
ejpam-2199	239	37	t	t	PROPN
ejpam-2199	239	38	and	and	CCONJ
ejpam-2199	239	39	h	h	NOUN
ejpam-2199	239	40	hurewicz	hurewicz	NOUN
ejpam-2199	239	41	,	,	PUNCT
ejpam-2199	239	42	where	where	SCONJ
ejpam-2199	239	43	x	x	SYM
ejpam-2199	239	44	∈	∈	PROPN
ejpam-2199	239	45	u	u	X
ejpam-2199	239	46	⊂	⊂	PROPN
ejpam-2199	239	47	h	h	PROPN
ejpam-2199	239	48	⊂	⊂	PROPN
ejpam-2199	239	49	v	v	PROPN
ejpam-2199	239	50	.	.	PUNCT
ejpam-2199	240	1	definition	definition	NOUN
ejpam-2199	240	2	9	9	NUM
ejpam-2199	240	3	.	.	PUNCT
ejpam-2199	241	1	a	a	DET
ejpam-2199	241	2	topological	topological	ADJ
ejpam-2199	241	3	space	space	NOUN
ejpam-2199	241	4	〈	〈	NOUN
ejpam-2199	241	5	x	x	X
ejpam-2199	241	6	,	,	PUNCT
ejpam-2199	241	7	t	t	PROPN
ejpam-2199	241	8	〉	〉	NOUN
ejpam-2199	241	9	is	be	AUX
ejpam-2199	241	10	weakly	weakly	ADV
ejpam-2199	241	11	locally	locally	ADV
ejpam-2199	241	12	hurewicz	hurewicz	NOUN
ejpam-2199	241	13	if	if	SCONJ
ejpam-2199	241	14	and	and	CCONJ
ejpam-2199	241	15	only	only	ADV
ejpam-2199	241	16	if	if	SCONJ
ejpam-2199	241	17	,	,	PUNCT
ejpam-2199	241	18	for	for	ADP
ejpam-2199	241	19	each	each	DET
ejpam-2199	241	20	x	x	SYM
ejpam-2199	241	21	∈	∈	PROPN
ejpam-2199	241	22	x	x	X
ejpam-2199	241	23	,	,	PUNCT
ejpam-2199	241	24	there	there	PRON
ejpam-2199	241	25	exists	exist	VERB
ejpam-2199	241	26	u	u	PROPN
ejpam-2199	241	27	∈	∈	PROPN
ejpam-2199	241	28	t	t	PROPN
ejpam-2199	241	29	and	and	CCONJ
ejpam-2199	241	30	h	h	NOUN
ejpam-2199	241	31	hurewicz	hurewicz	NOUN
ejpam-2199	241	32	,	,	PUNCT
ejpam-2199	241	33	such	such	ADJ
ejpam-2199	241	34	that	that	SCONJ
ejpam-2199	241	35	x	x	SYM
ejpam-2199	241	36	∈	∈	PROPN
ejpam-2199	241	37	u.	u.	NOUN
ejpam-2199	241	38	definition	definition	NOUN
ejpam-2199	241	39	10	10	NUM
ejpam-2199	241	40	.	.	PUNCT
ejpam-2199	242	1	a	a	DET
ejpam-2199	242	2	topological	topological	ADJ
ejpam-2199	242	3	space	space	NOUN
ejpam-2199	242	4	〈	〈	NOUN
ejpam-2199	242	5	x	x	X
ejpam-2199	242	6	,	,	PUNCT
ejpam-2199	242	7	t	t	PROPN
ejpam-2199	242	8	〉	〉	NOUN
ejpam-2199	242	9	is	be	AUX
ejpam-2199	242	10	relatively	relatively	ADV
ejpam-2199	242	11	locally	locally	ADV
ejpam-2199	242	12	hurewicz	hurewicz	NOUN
ejpam-2199	242	13	if	if	SCONJ
ejpam-2199	242	14	and	and	CCONJ
ejpam-2199	242	15	only	only	ADV
ejpam-2199	242	16	if	if	SCONJ
ejpam-2199	242	17	,	,	PUNCT
ejpam-2199	242	18	for	for	ADP
ejpam-2199	242	19	each	each	DET
ejpam-2199	242	20	x	x	SYM
ejpam-2199	242	21	∈	∈	PROPN
ejpam-2199	242	22	x	x	X
ejpam-2199	242	23	,	,	PUNCT
ejpam-2199	242	24	there	there	PRON
ejpam-2199	242	25	exists	exist	VERB
ejpam-2199	242	26	u	u	PROPN
ejpam-2199	242	27	∈	∈	PROPN
ejpam-2199	242	28	t	t	PROPN
ejpam-2199	242	29	with	with	ADP
ejpam-2199	242	30	u	u	NOUN
ejpam-2199	242	31	hurewicz	hurewicz	NOUN
ejpam-2199	242	32	,	,	PUNCT
ejpam-2199	242	33	such	such	ADJ
ejpam-2199	242	34	that	that	SCONJ
ejpam-2199	242	35	x	x	SYM
ejpam-2199	242	36	∈	∈	PROPN
ejpam-2199	242	37	u.	u.	NOUN
ejpam-2199	242	38	proposition	proposition	NOUN
ejpam-2199	242	39	11	11	NUM
ejpam-2199	242	40	.	.	PUNCT
ejpam-2199	243	1	if	if	SCONJ
ejpam-2199	243	2	〈	〈	PROPN
ejpam-2199	243	3	x	x	X
ejpam-2199	243	4	,	,	PUNCT
ejpam-2199	243	5	t	t	PROPN
ejpam-2199	243	6	〉	〉	NOUN
ejpam-2199	243	7	is	be	AUX
ejpam-2199	243	8	a	a	DET
ejpam-2199	243	9	hurewicz	hurewicz	NOUN
ejpam-2199	243	10	topological	topological	ADJ
ejpam-2199	243	11	space	space	NOUN
ejpam-2199	243	12	then	then	ADV
ejpam-2199	243	13	〈	〈	PROPN
ejpam-2199	243	14	x	x	X
ejpam-2199	243	15	,	,	PUNCT
ejpam-2199	243	16	t	t	PROPN
ejpam-2199	243	17	〉	〉	NOUN
ejpam-2199	243	18	is	be	AUX
ejpam-2199	243	19	weakly	weakly	ADV
ejpam-2199	243	20	locally	locally	ADV
ejpam-2199	243	21	hurewicz	hurewicz	NOUN
ejpam-2199	243	22	.	.	PUNCT
ejpam-2199	244	1	proof	proof	NOUN
ejpam-2199	244	2	.	.	PUNCT
ejpam-2199	245	1	for	for	SCONJ
ejpam-2199	245	2	each	each	DET
ejpam-2199	245	3	x	x	SYM
ejpam-2199	245	4	∈	∈	PROPN
ejpam-2199	245	5	x	x	PUNCT
ejpam-2199	245	6	,	,	PUNCT
ejpam-2199	245	7	consider	consider	VERB
ejpam-2199	245	8	u	u	PRON
ejpam-2199	245	9	=	=	NOUN
ejpam-2199	245	10	x	x	X
ejpam-2199	245	11	and	and	CCONJ
ejpam-2199	245	12	h	h	NOUN
ejpam-2199	246	1	=	=	SYM
ejpam-2199	246	2	x	x	X
ejpam-2199	246	3	,	,	PUNCT
ejpam-2199	246	4	then	then	ADV
ejpam-2199	246	5	u	u	PROPN
ejpam-2199	246	6	∈	∈	PROPN
ejpam-2199	246	7	t	t	PROPN
ejpam-2199	246	8	,	,	PUNCT
ejpam-2199	246	9	h	h	NOUN
ejpam-2199	246	10	is	be	AUX
ejpam-2199	246	11	hurewicz	hurewicz	ADJ
ejpam-2199	246	12	and	and	CCONJ
ejpam-2199	246	13	x	x	SYM
ejpam-2199	246	14	∈	∈	PROPN
ejpam-2199	246	15	u	u	PROPN
ejpam-2199	246	16	⊂	⊂	PROPN
ejpam-2199	246	17	h.	h.	PROPN
ejpam-2199	247	1	hence	hence	ADV
ejpam-2199	247	2	x	x	X
ejpam-2199	247	3	is	be	AUX
ejpam-2199	247	4	weakly	weakly	ADV
ejpam-2199	247	5	locally	locally	ADV
ejpam-2199	247	6	hurewicz	hurewicz	NOUN
ejpam-2199	247	7	.	.	PUNCT
ejpam-2199	248	1	proposition	proposition	NOUN
ejpam-2199	248	2	12	12	NUM
ejpam-2199	248	3	.	.	PUNCT
ejpam-2199	249	1	if	if	SCONJ
ejpam-2199	249	2	〈	〈	PROPN
ejpam-2199	249	3	x	x	X
ejpam-2199	249	4	,	,	PUNCT
ejpam-2199	249	5	t	t	PROPN
ejpam-2199	249	6	〉	〉	NOUN
ejpam-2199	249	7	is	be	AUX
ejpam-2199	249	8	a	a	DET
ejpam-2199	249	9	hurewicz	hurewicz	NOUN
ejpam-2199	249	10	topological	topological	ADJ
ejpam-2199	249	11	space	space	NOUN
ejpam-2199	249	12	then	then	ADV
ejpam-2199	249	13	〈	〈	PROPN
ejpam-2199	249	14	x	x	X
ejpam-2199	249	15	,	,	PUNCT
ejpam-2199	249	16	t	t	PROPN
ejpam-2199	249	17	〉	〉	NOUN
ejpam-2199	249	18	is	be	AUX
ejpam-2199	249	19	relatively	relatively	ADV
ejpam-2199	249	20	locally	locally	ADV
ejpam-2199	249	21	hurewicz	hurewicz	NOUN
ejpam-2199	249	22	.	.	PUNCT
ejpam-2199	250	1	proof	proof	NOUN
ejpam-2199	250	2	.	.	PUNCT
ejpam-2199	251	1	for	for	SCONJ
ejpam-2199	251	2	each	each	DET
ejpam-2199	251	3	x	x	SYM
ejpam-2199	251	4	∈	∈	PROPN
ejpam-2199	251	5	x	x	PUNCT
ejpam-2199	251	6	,	,	PUNCT
ejpam-2199	251	7	consider	consider	VERB
ejpam-2199	251	8	u	u	PRON
ejpam-2199	251	9	=	=	NOUN
ejpam-2199	251	10	x	x	X
ejpam-2199	251	11	.	.	PUNCT
ejpam-2199	252	1	then	then	ADV
ejpam-2199	252	2	x	x	SYM
ejpam-2199	252	3	∈	∈	PROPN
ejpam-2199	252	4	u	u	NOUN
ejpam-2199	252	5	and	and	CCONJ
ejpam-2199	252	6	u	u	NOUN
ejpam-2199	252	7	=	=	NOUN
ejpam-2199	252	8	x	x	INTJ
ejpam-2199	252	9	,	,	PUNCT
ejpam-2199	252	10	hence	hence	ADV
ejpam-2199	252	11	u	u	NOUN
ejpam-2199	252	12	is	be	AUX
ejpam-2199	252	13	hurewicz	hurewicz	ADJ
ejpam-2199	252	14	.	.	PUNCT
ejpam-2199	253	1	therefore	therefore	ADV
ejpam-2199	253	2	x	x	X
ejpam-2199	253	3	is	be	AUX
ejpam-2199	253	4	relatively	relatively	ADV
ejpam-2199	253	5	locally	locally	ADV
ejpam-2199	253	6	hurewicz	hurewicz	NOUN
ejpam-2199	253	7	.	.	PUNCT
ejpam-2199	254	1	proposition	proposition	NOUN
ejpam-2199	254	2	13	13	NUM
ejpam-2199	254	3	.	.	PUNCT
ejpam-2199	255	1	if	if	SCONJ
ejpam-2199	255	2	〈	〈	PROPN
ejpam-2199	255	3	x	x	X
ejpam-2199	255	4	,	,	PUNCT
ejpam-2199	255	5	t	t	PROPN
ejpam-2199	255	6	〉	〉	NOUN
ejpam-2199	255	7	is	be	AUX
ejpam-2199	255	8	a	a	DET
ejpam-2199	255	9	locally	locally	ADV
ejpam-2199	255	10	hurewicz	hurewicz	ADJ
ejpam-2199	255	11	topological	topological	ADJ
ejpam-2199	255	12	space	space	NOUN
ejpam-2199	255	13	then	then	ADV
ejpam-2199	255	14	〈	〈	PROPN
ejpam-2199	255	15	x	x	X
ejpam-2199	255	16	,	,	PUNCT
ejpam-2199	255	17	t	t	PROPN
ejpam-2199	255	18	〉	〉	NOUN
ejpam-2199	255	19	is	be	AUX
ejpam-2199	255	20	weakly	weakly	ADV
ejpam-2199	255	21	locally	locally	ADV
ejpam-2199	255	22	hurewicz	hurewicz	NOUN
ejpam-2199	255	23	.	.	PUNCT
ejpam-2199	256	1	proof	proof	NOUN
ejpam-2199	256	2	.	.	PUNCT
ejpam-2199	257	1	for	for	ADP
ejpam-2199	257	2	each	each	DET
ejpam-2199	257	3	x	x	SYM
ejpam-2199	257	4	∈	∈	PROPN
ejpam-2199	257	5	x	x	X
ejpam-2199	257	6	,	,	PUNCT
ejpam-2199	257	7	since	since	SCONJ
ejpam-2199	257	8	x	x	PRON
ejpam-2199	257	9	is	be	AUX
ejpam-2199	257	10	locally	locally	ADV
ejpam-2199	257	11	hurewicz	hurewicz	NOUN
ejpam-2199	257	12	,	,	PUNCT
ejpam-2199	257	13	for	for	ADP
ejpam-2199	257	14	v	v	NOUN
ejpam-2199	257	15	=	=	SYM
ejpam-2199	257	16	x	x	SYM
ejpam-2199	257	17	there	there	PRON
ejpam-2199	257	18	are	be	VERB
ejpam-2199	257	19	u	u	PRON
ejpam-2199	257	20	open	open	ADJ
ejpam-2199	257	21	set	set	VERB
ejpam-2199	257	22	in	in	ADP
ejpam-2199	257	23	x	x	PUNCT
ejpam-2199	257	24	and	and	CCONJ
ejpam-2199	257	25	h	h	NOUN
ejpam-2199	257	26	hurewicz	hurewicz	NOUN
ejpam-2199	257	27	such	such	ADJ
ejpam-2199	257	28	that	that	SCONJ
ejpam-2199	257	29	x	x	SYM
ejpam-2199	257	30	∈	∈	PROPN
ejpam-2199	257	31	u	u	X
ejpam-2199	257	32	⊂	⊂	PROPN
ejpam-2199	257	33	h	h	PROPN
ejpam-2199	257	34	⊂	⊂	PROPN
ejpam-2199	257	35	x	x	X
ejpam-2199	257	36	.	.	PUNCT
ejpam-2199	258	1	hence	hence	ADV
ejpam-2199	258	2	x	x	X
ejpam-2199	258	3	is	be	AUX
ejpam-2199	258	4	a	a	DET
ejpam-2199	258	5	weakly	weakly	ADJ
ejpam-2199	258	6	locally	locally	ADV
ejpam-2199	258	7	hurewicz	hurewicz	ADJ
ejpam-2199	258	8	space	space	NOUN
ejpam-2199	258	9	.	.	PUNCT
ejpam-2199	259	1	proposition	proposition	NOUN
ejpam-2199	259	2	14	14	NUM
ejpam-2199	259	3	.	.	PUNCT
ejpam-2199	260	1	if	if	SCONJ
ejpam-2199	260	2	〈	〈	PROPN
ejpam-2199	260	3	x	x	X
ejpam-2199	260	4	,	,	PUNCT
ejpam-2199	260	5	t	t	PROPN
ejpam-2199	260	6	〉	〉	NOUN
ejpam-2199	260	7	is	be	AUX
ejpam-2199	260	8	a	a	DET
ejpam-2199	260	9	relatively	relatively	ADV
ejpam-2199	260	10	locally	locally	ADV
ejpam-2199	260	11	hurewicz	hurewicz	ADJ
ejpam-2199	260	12	topological	topological	ADJ
ejpam-2199	260	13	space	space	NOUN
ejpam-2199	260	14	then	then	ADV
ejpam-2199	260	15	〈	〈	PROPN
ejpam-2199	260	16	x	x	X
ejpam-2199	260	17	,	,	PUNCT
ejpam-2199	260	18	t	t	PROPN
ejpam-2199	260	19	〉	〉	NOUN
ejpam-2199	260	20	is	be	AUX
ejpam-2199	260	21	weakly	weakly	ADV
ejpam-2199	260	22	locally	locally	ADV
ejpam-2199	260	23	hurewicz	hurewicz	NOUN
ejpam-2199	260	24	.	.	PUNCT
ejpam-2199	261	1	proof	proof	NOUN
ejpam-2199	261	2	.	.	PUNCT
ejpam-2199	262	1	for	for	ADP
ejpam-2199	262	2	each	each	DET
ejpam-2199	262	3	x	x	SYM
ejpam-2199	262	4	∈	∈	PROPN
ejpam-2199	262	5	x	x	X
ejpam-2199	262	6	,	,	PUNCT
ejpam-2199	262	7	because	because	SCONJ
ejpam-2199	262	8	x	x	PRON
ejpam-2199	262	9	is	be	AUX
ejpam-2199	262	10	locally	locally	ADV
ejpam-2199	262	11	hurewicz	hurewicz	NOUN
ejpam-2199	262	12	,	,	PUNCT
ejpam-2199	262	13	there	there	PRON
ejpam-2199	262	14	exists	exist	VERB
ejpam-2199	262	15	u	u	PRON
ejpam-2199	262	16	open	open	ADJ
ejpam-2199	262	17	set	set	VERB
ejpam-2199	262	18	in	in	ADP
ejpam-2199	262	19	x	x	X
ejpam-2199	262	20	,	,	PUNCT
ejpam-2199	262	21	with	with	ADP
ejpam-2199	262	22	u	u	NOUN
ejpam-2199	262	23	hurewicz	hurewicz	NOUN
ejpam-2199	262	24	such	such	ADJ
ejpam-2199	262	25	that	that	SCONJ
ejpam-2199	262	26	x	x	SYM
ejpam-2199	262	27	∈	∈	PROPN
ejpam-2199	262	28	u	u	NOUN
ejpam-2199	262	29	.	.	PUNCT
ejpam-2199	263	1	then	then	ADV
ejpam-2199	263	2	x	x	SYM
ejpam-2199	263	3	∈	∈	PROPN
ejpam-2199	263	4	u	u	NOUN
ejpam-2199	263	5	⊂	⊂	PROPN
ejpam-2199	263	6	u	u	PROPN
ejpam-2199	263	7	with	with	ADP
ejpam-2199	263	8	u	u	NOUN
ejpam-2199	263	9	hurewicz	hurewicz	NOUN
ejpam-2199	263	10	.	.	PUNCT
ejpam-2199	264	1	hence	hence	ADV
ejpam-2199	264	2	x	x	PRON
ejpam-2199	264	3	is	be	AUX
ejpam-2199	264	4	a	a	DET
ejpam-2199	264	5	weakly	weakly	ADJ
ejpam-2199	264	6	locally	locally	ADV
ejpam-2199	264	7	hurewicz	hurewicz	ADJ
ejpam-2199	264	8	space	space	NOUN
ejpam-2199	264	9	.	.	PUNCT
ejpam-2199	265	1	proposition	proposition	NOUN
ejpam-2199	265	2	15	15	NUM
ejpam-2199	265	3	.	.	PUNCT
ejpam-2199	266	1	a	a	DET
ejpam-2199	266	2	hausdorff	hausdorff	NOUN
ejpam-2199	266	3	c	c	NOUN
ejpam-2199	266	4	-	-	PUNCT
ejpam-2199	266	5	space	space	NOUN
ejpam-2199	266	6	〈	〈	NOUN
ejpam-2199	266	7	x	x	PROPN
ejpam-2199	266	8	,	,	PUNCT
ejpam-2199	266	9	t	t	PROPN
ejpam-2199	266	10	〉	〉	NOUN
ejpam-2199	266	11	is	be	AUX
ejpam-2199	266	12	locally	locally	ADV
ejpam-2199	266	13	hurewicz	hurewicz	NOUN
ejpam-2199	266	14	if	if	SCONJ
ejpam-2199	266	15	and	and	CCONJ
ejpam-2199	266	16	only	only	ADV
ejpam-2199	266	17	if	if	SCONJ
ejpam-2199	266	18	,	,	PUNCT
ejpam-2199	266	19	x	x	PUNCT
ejpam-2199	266	20	is	be	AUX
ejpam-2199	266	21	weakly	weakly	ADV
ejpam-2199	266	22	locally	locally	ADV
ejpam-2199	266	23	hurewicz	hurewicz	NOUN
ejpam-2199	266	24	.	.	PUNCT
ejpam-2199	267	1	proof	proof	NOUN
ejpam-2199	267	2	.	.	PUNCT
ejpam-2199	268	1	(	(	PUNCT
ejpam-2199	268	2	⇒	⇒	NOUN
ejpam-2199	268	3	)	)	PUNCT
ejpam-2199	268	4	proposition	proposition	NOUN
ejpam-2199	268	5	13	13	NUM
ejpam-2199	268	6	.	.	PUNCT
ejpam-2199	269	1	(	(	PUNCT
ejpam-2199	269	2	⇐	⇐	ADJ
ejpam-2199	269	3	)	)	PUNCT
ejpam-2199	269	4	consider	consider	VERB
ejpam-2199	269	5	x	x	X
ejpam-2199	269	6	∈	∈	PROPN
ejpam-2199	269	7	x	x	X
ejpam-2199	269	8	and	and	CCONJ
ejpam-2199	269	9	v	v	ADP
ejpam-2199	269	10	a	a	DET
ejpam-2199	269	11	neighborhood	neighborhood	NOUN
ejpam-2199	269	12	of	of	ADP
ejpam-2199	269	13	x	x	X
ejpam-2199	269	14	.	.	PUNCT
ejpam-2199	270	1	since	since	SCONJ
ejpam-2199	270	2	x	x	PRON
ejpam-2199	270	3	is	be	AUX
ejpam-2199	270	4	weakly	weakly	ADV
ejpam-2199	270	5	locally	locally	ADV
ejpam-2199	270	6	hurewicz	hurewicz	NOUN
ejpam-2199	270	7	there	there	PRON
ejpam-2199	270	8	exist	exist	VERB
ejpam-2199	270	9	u	u	PROPN
ejpam-2199	270	10	∈	∈	PROPN
ejpam-2199	270	11	t	t	PROPN
ejpam-2199	270	12	and	and	CCONJ
ejpam-2199	270	13	h	h	NOUN
ejpam-2199	270	14	hurewicz	hurewicz	NOUN
ejpam-2199	270	15	with	with	ADP
ejpam-2199	270	16	x	x	PROPN
ejpam-2199	270	17	∈	∈	PROPN
ejpam-2199	270	18	u	u	NOUN
ejpam-2199	270	19	⊂	⊂	PROPN
ejpam-2199	270	20	h.	h.	PROPN
ejpam-2199	270	21	consider	consider	VERB
ejpam-2199	270	22	a	a	DET
ejpam-2199	270	23	=	=	NOUN
ejpam-2199	270	24	h	h	NOUN
ejpam-2199	270	25	∩	∩	NOUN
ejpam-2199	270	26	v	v	ADP
ejpam-2199	270	27	c	c	NOUN
ejpam-2199	270	28	,	,	PUNCT
ejpam-2199	270	29	since	since	SCONJ
ejpam-2199	270	30	x	x	PROPN
ejpam-2199	270	31	∈	∈	NOUN
ejpam-2199	270	32	v	v	NOUN
ejpam-2199	270	33	we	we	PRON
ejpam-2199	270	34	have	have	VERB
ejpam-2199	270	35	that	that	PRON
ejpam-2199	271	1	x	x	SYM
ejpam-2199	271	2	/∈	/∈	PUNCT
ejpam-2199	272	1	a	a	PRON
ejpam-2199	272	2	and	and	CCONJ
ejpam-2199	272	3	a	a	PRON
ejpam-2199	272	4	is	be	AUX
ejpam-2199	272	5	hurewicz	hurewicz	NOUN
ejpam-2199	272	6	because	because	SCONJ
ejpam-2199	272	7	h	h	NOUN
ejpam-2199	272	8	is	be	AUX
ejpam-2199	272	9	hurewicz	hurewicz	ADJ
ejpam-2199	272	10	and	and	CCONJ
ejpam-2199	272	11	x	x	X
ejpam-2199	272	12	is	be	AUX
ejpam-2199	272	13	a	a	DET
ejpam-2199	272	14	hausdorff	hausdorff	NOUN
ejpam-2199	272	15	c	c	NOUN
ejpam-2199	272	16	-	-	PUNCT
ejpam-2199	272	17	space	space	NOUN
ejpam-2199	272	18	by	by	ADP
ejpam-2199	272	19	proposition	proposition	NOUN
ejpam-2199	272	20	8	8	NUM
ejpam-2199	272	21	h	h	NOUN
ejpam-2199	272	22	is	be	AUX
ejpam-2199	272	23	closed	closed	ADJ
ejpam-2199	272	24	,	,	PUNCT
ejpam-2199	272	25	then	then	ADV
ejpam-2199	272	26	a	a	DET
ejpam-2199	272	27	=	=	ADJ
ejpam-2199	272	28	h	h	NOUN
ejpam-2199	272	29	∩	∩	NOUN
ejpam-2199	272	30	v	v	ADP
ejpam-2199	272	31	c	c	NOUN
ejpam-2199	272	32	,	,	PUNCT
ejpam-2199	272	33	is	be	AUX
ejpam-2199	272	34	a	a	DET
ejpam-2199	272	35	closed	closed	ADJ
ejpam-2199	272	36	set	set	NOUN
ejpam-2199	272	37	.	.	PUNCT
ejpam-2199	273	1	since	since	SCONJ
ejpam-2199	273	2	a	a	DET
ejpam-2199	273	3	⊂	⊂	PROPN
ejpam-2199	273	4	h	h	NOUN
ejpam-2199	273	5	by	by	ADP
ejpam-2199	273	6	proposition	proposition	NOUN
ejpam-2199	273	7	6	6	NUM
ejpam-2199	273	8	a	a	PRON
ejpam-2199	273	9	is	be	AUX
ejpam-2199	273	10	hurewicz	hurewicz	NOUN
ejpam-2199	273	11	,	,	PUNCT
ejpam-2199	273	12	then	then	ADV
ejpam-2199	273	13	by	by	ADP
ejpam-2199	273	14	lemma	lemma	PROPN
ejpam-2199	273	15	1	1	NUM
ejpam-2199	273	16	there	there	PRON
ejpam-2199	273	17	are	be	VERB
ejpam-2199	273	18	wx	wx	PROPN
ejpam-2199	273	19	and	and	CCONJ
ejpam-2199	273	20	wa	wa	PROPN
ejpam-2199	273	21	disjoint	disjoint	VERB
ejpam-2199	273	22	open	open	ADJ
ejpam-2199	273	23	sets	set	NOUN
ejpam-2199	273	24	containing	contain	VERB
ejpam-2199	273	25	x	x	PROPN
ejpam-2199	273	26	and	and	CCONJ
ejpam-2199	273	27	a	a	PRON
ejpam-2199	273	28	,	,	PUNCT
ejpam-2199	273	29	respectively	respectively	ADV
ejpam-2199	273	30	.	.	PUNCT
ejpam-2199	274	1	consider	consider	VERB
ejpam-2199	274	2	u	u	PRON
ejpam-2199	274	3	=	=	NOUN
ejpam-2199	274	4	wx	wx	X
ejpam-2199	274	5	∩	∩	X
ejpam-2199	274	6	int(h	int(h	X
ejpam-2199	274	7	)	)	PUNCT
ejpam-2199	274	8	.	.	PUNCT
ejpam-2199	275	1	then	then	ADV
ejpam-2199	275	2	u	u	PRON
ejpam-2199	275	3	is	be	AUX
ejpam-2199	275	4	an	an	DET
ejpam-2199	275	5	open	open	ADJ
ejpam-2199	275	6	set	set	NOUN
ejpam-2199	275	7	containing	contain	VERB
ejpam-2199	275	8	x	x	PROPN
ejpam-2199	275	9	and	and	CCONJ
ejpam-2199	275	10	u	u	X
ejpam-2199	275	11	⊂	⊂	PROPN
ejpam-2199	275	12	int(h	int(h	PROPN
ejpam-2199	275	13	)	)	PUNCT
ejpam-2199	276	1	⊂	⊂	PROPN
ejpam-2199	276	2	h	h	NOUN
ejpam-2199	276	3	,	,	PUNCT
ejpam-2199	276	4	then	then	ADV
ejpam-2199	276	5	u	u	X
ejpam-2199	276	6	⊂	⊂	PROPN
ejpam-2199	276	7	h	h	PROPN
ejpam-2199	277	1	=	=	SYM
ejpam-2199	277	2	h.	h.	PROPN
ejpam-2199	277	3	therefore	therefore	ADV
ejpam-2199	277	4	u	u	PROPN
ejpam-2199	277	5	is	be	AUX
ejpam-2199	277	6	a	a	DET
ejpam-2199	277	7	closed	closed	ADJ
ejpam-2199	277	8	subspace	subspace	NOUN
ejpam-2199	277	9	of	of	ADP
ejpam-2199	277	10	a	a	DET
ejpam-2199	277	11	hurewicz	hurewicz	NOUN
ejpam-2199	277	12	space	space	NOUN
ejpam-2199	277	13	hence	hence	ADV
ejpam-2199	277	14	by	by	ADP
ejpam-2199	277	15	proposition	proposition	NOUN
ejpam-2199	277	16	6	6	NUM
ejpam-2199	277	17	u	u	NOUN
ejpam-2199	277	18	is	be	AUX
ejpam-2199	277	19	hurewicz	hurewicz	NOUN
ejpam-2199	277	20	.	.	PUNCT
ejpam-2199	278	1	c.	c.	NOUN
ejpam-2199	278	2	roika	roika	PROPN
ejpam-2199	278	3	,	,	PUNCT
ejpam-2199	278	4	s.	s.	PROPN
ejpam-2199	278	5	kudri	kudri	PROPN
ejpam-2199	278	6	,	,	PUNCT
ejpam-2199	278	7	t.	t.	PROPN
ejpam-2199	278	8	breuckmann	breuckmann	PROPN
ejpam-2199	278	9	/	/	SYM
ejpam-2199	278	10	eur	eur	PROPN
ejpam-2199	278	11	.	.	PUNCT
ejpam-2199	279	1	j.	j.	PROPN
ejpam-2199	279	2	pure	pure	PROPN
ejpam-2199	279	3	appl	appl	PROPN
ejpam-2199	279	4	.	.	PROPN
ejpam-2199	279	5	math	math	PROPN
ejpam-2199	279	6	,	,	PUNCT
ejpam-2199	279	7	8	8	NUM
ejpam-2199	279	8	(	(	PUNCT
ejpam-2199	279	9	2015	2015	NUM
ejpam-2199	279	10	)	)	PUNCT
ejpam-2199	279	11	,	,	PUNCT
ejpam-2199	279	12	514	514	NUM
ejpam-2199	279	13	-	-	SYM
ejpam-2199	279	14	525	525	NUM
ejpam-2199	279	15	522	522	NUM
ejpam-2199	279	16	now	now	ADV
ejpam-2199	279	17	we	we	PRON
ejpam-2199	279	18	prove	prove	VERB
ejpam-2199	279	19	,	,	PUNCT
ejpam-2199	279	20	that	that	SCONJ
ejpam-2199	279	21	u	u	PROPN
ejpam-2199	279	22	⊂	⊂	X
ejpam-2199	279	23	v	v	INTJ
ejpam-2199	279	24	.	.	PUNCT
ejpam-2199	280	1	we	we	PRON
ejpam-2199	280	2	have	have	VERB
ejpam-2199	280	3	u	u	NOUN
ejpam-2199	280	4	∩	∩	NOUN
ejpam-2199	280	5	a	a	X
ejpam-2199	280	6	=	=	X
ejpam-2199	280	7	;	;	PUNCT
ejpam-2199	280	8	.	.	PUNCT
ejpam-2199	281	1	in	in	ADP
ejpam-2199	281	2	fact	fact	NOUN
ejpam-2199	281	3	,	,	PUNCT
ejpam-2199	281	4	supposing	suppose	VERB
ejpam-2199	281	5	by	by	ADP
ejpam-2199	281	6	contradiction	contradiction	NOUN
ejpam-2199	281	7	that	that	SCONJ
ejpam-2199	281	8	∃y	∃y	PROPN
ejpam-2199	281	9	∈	∈	PROPN
ejpam-2199	281	10	u	u	PROPN
ejpam-2199	281	11	∩	∩	NOUN
ejpam-2199	281	12	a	a	X
ejpam-2199	281	13	,	,	PUNCT
ejpam-2199	281	14	then	then	ADV
ejpam-2199	281	15	y	y	PROPN
ejpam-2199	281	16	∈	∈	PROPN
ejpam-2199	281	17	u	u	PROPN
ejpam-2199	281	18	∩	∩	NOUN
ejpam-2199	281	19	a	a	X
ejpam-2199	281	20	,	,	PUNCT
ejpam-2199	281	21	then	then	ADV
ejpam-2199	281	22	y	y	PROPN
ejpam-2199	281	23	∈	∈	PROPN
ejpam-2199	281	24	u	u	NOUN
ejpam-2199	281	25	hence	hence	ADV
ejpam-2199	281	26	any	any	DET
ejpam-2199	281	27	neighborhood	neighborhood	NOUN
ejpam-2199	281	28	of	of	ADP
ejpam-2199	281	29	y	y	PROPN
ejpam-2199	281	30	intersects	intersect	NOUN
ejpam-2199	281	31	u	u	NOUN
ejpam-2199	281	32	and	and	CCONJ
ejpam-2199	281	33	y	y	PROPN
ejpam-2199	281	34	∈	∈	PROPN
ejpam-2199	281	35	a	a	DET
ejpam-2199	281	36	⊂	⊂	PROPN
ejpam-2199	281	37	wa	wa	PROPN
ejpam-2199	281	38	then	then	ADV
ejpam-2199	281	39	wa	wa	PROPN
ejpam-2199	281	40	∩	∩	PROPN
ejpam-2199	281	41	u	u	PROPN
ejpam-2199	281	42	6=	6=	PROPN
ejpam-2199	281	43	;	;	PUNCT
ejpam-2199	281	44	,	,	PUNCT
ejpam-2199	281	45	but	but	CCONJ
ejpam-2199	281	46	u	u	NOUN
ejpam-2199	281	47	⊂	⊂	PROPN
ejpam-2199	281	48	wx	wx	PROPN
ejpam-2199	281	49	he	he	PRON
ejpam-2199	281	50	have	have	VERB
ejpam-2199	281	51	that	that	DET
ejpam-2199	281	52	wa	wa	ADV
ejpam-2199	281	53	∩wx	∩wx	PROPN
ejpam-2199	281	54	6=	6=	PROPN
ejpam-2199	281	55	;	;	PUNCT
ejpam-2199	281	56	,	,	PUNCT
ejpam-2199	281	57	contradiction	contradiction	NOUN
ejpam-2199	281	58	.	.	PUNCT
ejpam-2199	282	1	hence	hence	ADV
ejpam-2199	282	2	u	u	PROPN
ejpam-2199	282	3	⊂	⊂	PROPN
ejpam-2199	282	4	h	h	NOUN
ejpam-2199	282	5	and	and	CCONJ
ejpam-2199	282	6	u	u	PROPN
ejpam-2199	282	7	∩	∩	NOUN
ejpam-2199	282	8	a=	a=	VERB
ejpam-2199	282	9	;	;	PUNCT
ejpam-2199	282	10	,	,	PUNCT
ejpam-2199	282	11	which	which	PRON
ejpam-2199	282	12	implies	imply	VERB
ejpam-2199	282	13	that	that	SCONJ
ejpam-2199	282	14	u	u	PROPN
ejpam-2199	282	15	⊂	⊂	PROPN
ejpam-2199	282	16	v	v	PROPN
ejpam-2199	282	17	,	,	PUNCT
ejpam-2199	282	18	then	then	ADV
ejpam-2199	282	19	we	we	PRON
ejpam-2199	282	20	have	have	VERB
ejpam-2199	282	21	that	that	PRON
ejpam-2199	282	22	x	x	PUNCT
ejpam-2199	282	23	∈	∈	PROPN
ejpam-2199	282	24	u	u	NOUN
ejpam-2199	282	25	⊂	⊂	PROPN
ejpam-2199	282	26	u	u	X
ejpam-2199	282	27	⊂	⊂	PROPN
ejpam-2199	282	28	v	v	PROPN
ejpam-2199	282	29	.	.	PUNCT
ejpam-2199	283	1	therefore	therefore	ADV
ejpam-2199	283	2	,	,	PUNCT
ejpam-2199	283	3	x	x	X
ejpam-2199	283	4	is	be	AUX
ejpam-2199	283	5	a	a	DET
ejpam-2199	283	6	locally	locally	ADV
ejpam-2199	283	7	hurewicz	hurewicz	ADJ
ejpam-2199	283	8	space	space	NOUN
ejpam-2199	283	9	.	.	PUNCT
ejpam-2199	284	1	proposition	proposition	NOUN
ejpam-2199	284	2	16	16	NUM
ejpam-2199	284	3	.	.	PUNCT
ejpam-2199	285	1	a	a	DET
ejpam-2199	285	2	hausdorff	hausdorff	NOUN
ejpam-2199	285	3	c	c	NOUN
ejpam-2199	285	4	-	-	PUNCT
ejpam-2199	285	5	space	space	NOUN
ejpam-2199	285	6	〈	〈	NOUN
ejpam-2199	285	7	x	x	PROPN
ejpam-2199	285	8	,	,	PUNCT
ejpam-2199	285	9	t	t	PROPN
ejpam-2199	285	10	〉	〉	NOUN
ejpam-2199	285	11	is	be	AUX
ejpam-2199	285	12	relatively	relatively	ADV
ejpam-2199	285	13	locally	locally	ADV
ejpam-2199	285	14	hurewicz	hurewicz	NOUN
ejpam-2199	285	15	if	if	SCONJ
ejpam-2199	285	16	and	and	CCONJ
ejpam-2199	285	17	only	only	ADV
ejpam-2199	285	18	if	if	SCONJ
ejpam-2199	285	19	,	,	PUNCT
ejpam-2199	285	20	x	x	PUNCT
ejpam-2199	285	21	is	be	AUX
ejpam-2199	285	22	weakly	weakly	ADV
ejpam-2199	285	23	locally	locally	ADV
ejpam-2199	285	24	hurewicz	hurewicz	NOUN
ejpam-2199	285	25	.	.	PUNCT
ejpam-2199	286	1	proof	proof	NOUN
ejpam-2199	286	2	.	.	PUNCT
ejpam-2199	287	1	(	(	PUNCT
ejpam-2199	287	2	⇒	⇒	NOUN
ejpam-2199	287	3	)	)	PUNCT
ejpam-2199	287	4	proposition	proposition	NOUN
ejpam-2199	287	5	14	14	NUM
ejpam-2199	287	6	.	.	PUNCT
ejpam-2199	288	1	(	(	PUNCT
ejpam-2199	288	2	⇐	⇐	ADJ
ejpam-2199	288	3	)	)	PUNCT
ejpam-2199	288	4	consider	consider	VERB
ejpam-2199	288	5	x	x	X
ejpam-2199	288	6	∈	∈	NOUN
ejpam-2199	288	7	x	x	X
ejpam-2199	288	8	.	.	PUNCT
ejpam-2199	289	1	because	because	SCONJ
ejpam-2199	289	2	x	x	PRON
ejpam-2199	289	3	is	be	AUX
ejpam-2199	289	4	weakly	weakly	ADV
ejpam-2199	289	5	locally	locally	ADV
ejpam-2199	289	6	hurewicz	hurewicz	NOUN
ejpam-2199	289	7	,	,	PUNCT
ejpam-2199	289	8	there	there	PRON
ejpam-2199	289	9	are	be	VERB
ejpam-2199	289	10	u	u	PROPN
ejpam-2199	289	11	∈	∈	PROPN
ejpam-2199	289	12	t	t	NOUN
ejpam-2199	289	13	and	and	CCONJ
ejpam-2199	289	14	h	h	NOUN
ejpam-2199	289	15	hurewicz	hurewicz	NOUN
ejpam-2199	289	16	such	such	ADJ
ejpam-2199	289	17	that	that	SCONJ
ejpam-2199	289	18	x	x	SYM
ejpam-2199	289	19	∈	∈	PROPN
ejpam-2199	289	20	u	u	NOUN
ejpam-2199	289	21	⊂	⊂	PROPN
ejpam-2199	289	22	h.	h.	PROPN
ejpam-2199	290	1	so	so	ADV
ejpam-2199	290	2	u	u	PROPN
ejpam-2199	290	3	⊂	⊂	PROPN
ejpam-2199	290	4	h	h	NOUN
ejpam-2199	290	5	and	and	CCONJ
ejpam-2199	290	6	since	since	SCONJ
ejpam-2199	290	7	h	h	NOUN
ejpam-2199	290	8	is	be	AUX
ejpam-2199	290	9	a	a	DET
ejpam-2199	290	10	hurewicz	hurewicz	NOUN
ejpam-2199	290	11	subspace	subspace	NOUN
ejpam-2199	290	12	of	of	ADP
ejpam-2199	290	13	a	a	DET
ejpam-2199	290	14	hausdorff	hausdorff	NOUN
ejpam-2199	290	15	c	c	NOUN
ejpam-2199	290	16	-	-	PUNCT
ejpam-2199	290	17	space	space	NOUN
ejpam-2199	290	18	by	by	ADP
ejpam-2199	290	19	proposition	proposition	NOUN
ejpam-2199	290	20	8	8	NUM
ejpam-2199	290	21	h	h	NOUN
ejpam-2199	290	22	is	be	AUX
ejpam-2199	290	23	closed	closed	ADJ
ejpam-2199	290	24	.	.	PUNCT
ejpam-2199	291	1	then	then	ADV
ejpam-2199	291	2	u	u	PROPN
ejpam-2199	291	3	⊂	⊂	PROPN
ejpam-2199	291	4	h	h	NOUN
ejpam-2199	291	5	,	,	PUNCT
ejpam-2199	291	6	but	but	CCONJ
ejpam-2199	291	7	u	u	PRON
ejpam-2199	291	8	being	be	AUX
ejpam-2199	291	9	closed	close	VERB
ejpam-2199	291	10	by	by	ADP
ejpam-2199	291	11	proposition	proposition	NOUN
ejpam-2199	291	12	6	6	NUM
ejpam-2199	291	13	u	u	NOUN
ejpam-2199	291	14	is	be	AUX
ejpam-2199	291	15	hurewicz	hurewicz	NOUN
ejpam-2199	291	16	,	,	PUNCT
ejpam-2199	291	17	then	then	ADV
ejpam-2199	291	18	x	x	PART
ejpam-2199	291	19	∈	∈	PROPN
ejpam-2199	291	20	u	u	NOUN
ejpam-2199	291	21	,	,	PUNCT
ejpam-2199	291	22	with	with	ADP
ejpam-2199	291	23	u	u	NOUN
ejpam-2199	291	24	hurewicz	hurewicz	NOUN
ejpam-2199	291	25	.	.	PUNCT
ejpam-2199	292	1	so	so	ADV
ejpam-2199	292	2	x	x	X
ejpam-2199	292	3	is	be	AUX
ejpam-2199	292	4	relatively	relatively	ADV
ejpam-2199	292	5	locally	locally	ADV
ejpam-2199	292	6	hurewicz	hurewicz	ADJ
ejpam-2199	292	7	space	space	NOUN
ejpam-2199	292	8	.	.	PUNCT
ejpam-2199	293	1	proposition	proposition	NOUN
ejpam-2199	293	2	17	17	NUM
ejpam-2199	293	3	.	.	PUNCT
ejpam-2199	294	1	if	if	SCONJ
ejpam-2199	294	2	〈	〈	PROPN
ejpam-2199	294	3	x	x	X
ejpam-2199	294	4	,	,	PUNCT
ejpam-2199	294	5	t	t	PROPN
ejpam-2199	294	6	〉	〉	NOUN
ejpam-2199	294	7	is	be	AUX
ejpam-2199	294	8	a	a	DET
ejpam-2199	294	9	locally	locally	ADV
ejpam-2199	294	10	compact	compact	ADJ
ejpam-2199	294	11	topological	topological	ADJ
ejpam-2199	294	12	space	space	NOUN
ejpam-2199	294	13	then	then	ADV
ejpam-2199	294	14	〈	〈	PROPN
ejpam-2199	294	15	x	x	X
ejpam-2199	294	16	,	,	PUNCT
ejpam-2199	294	17	t	t	PROPN
ejpam-2199	294	18	〉	〉	NOUN
ejpam-2199	294	19	is	be	AUX
ejpam-2199	294	20	locally	locally	ADV
ejpam-2199	294	21	hurewicz	hurewicz	NOUN
ejpam-2199	294	22	.	.	PUNCT
ejpam-2199	295	1	proof	proof	NOUN
ejpam-2199	295	2	.	.	PUNCT
ejpam-2199	296	1	for	for	ADP
ejpam-2199	296	2	each	each	DET
ejpam-2199	296	3	x	x	SYM
ejpam-2199	296	4	∈	∈	PROPN
ejpam-2199	296	5	x	x	X
ejpam-2199	296	6	and	and	CCONJ
ejpam-2199	296	7	v	v	ADP
ejpam-2199	296	8	a	a	DET
ejpam-2199	296	9	neighborhood	neighborhood	NOUN
ejpam-2199	296	10	of	of	ADP
ejpam-2199	296	11	x	x	SYM
ejpam-2199	296	12	,	,	PUNCT
ejpam-2199	296	13	since	since	SCONJ
ejpam-2199	296	14	x	x	PRON
ejpam-2199	296	15	is	be	AUX
ejpam-2199	296	16	locally	locally	ADV
ejpam-2199	296	17	compact	compact	ADJ
ejpam-2199	296	18	there	there	PRON
ejpam-2199	296	19	are	be	VERB
ejpam-2199	296	20	u	u	PROPN
ejpam-2199	296	21	∈	∈	PROPN
ejpam-2199	296	22	t	t	NOUN
ejpam-2199	296	23	and	and	CCONJ
ejpam-2199	296	24	a	a	DET
ejpam-2199	296	25	compact	compact	ADJ
ejpam-2199	296	26	set	set	NOUN
ejpam-2199	296	27	c	c	NOUN
ejpam-2199	296	28	with	with	ADP
ejpam-2199	296	29	x	x	PROPN
ejpam-2199	296	30	∈	∈	PROPN
ejpam-2199	296	31	u	u	NOUN
ejpam-2199	296	32	⊂	⊂	X
ejpam-2199	296	33	c	c	X
ejpam-2199	296	34	⊂	⊂	PROPN
ejpam-2199	296	35	v	v	PROPN
ejpam-2199	296	36	,	,	PUNCT
ejpam-2199	296	37	but	but	CCONJ
ejpam-2199	296	38	by	by	ADP
ejpam-2199	296	39	corollary	corollary	ADJ
ejpam-2199	296	40	1	1	NUM
ejpam-2199	296	41	,	,	PUNCT
ejpam-2199	296	42	c	c	PROPN
ejpam-2199	296	43	is	be	AUX
ejpam-2199	296	44	hurewicz	hurewicz	NOUN
ejpam-2199	296	45	then	then	ADV
ejpam-2199	296	46	x	x	PUNCT
ejpam-2199	296	47	is	be	AUX
ejpam-2199	296	48	locally	locally	ADV
ejpam-2199	296	49	hurewicz	hurewicz	NOUN
ejpam-2199	296	50	.	.	PUNCT
ejpam-2199	297	1	proposition	proposition	NOUN
ejpam-2199	297	2	18	18	NUM
ejpam-2199	297	3	.	.	PUNCT
ejpam-2199	298	1	if	if	SCONJ
ejpam-2199	298	2	〈	〈	PROPN
ejpam-2199	298	3	x	x	X
ejpam-2199	298	4	,	,	PUNCT
ejpam-2199	298	5	t	t	PROPN
ejpam-2199	298	6	〉	〉	NOUN
ejpam-2199	298	7	is	be	AUX
ejpam-2199	298	8	a	a	DET
ejpam-2199	298	9	weakly	weakly	ADJ
ejpam-2199	298	10	locally	locally	ADV
ejpam-2199	298	11	compact	compact	ADJ
ejpam-2199	298	12	topological	topological	ADJ
ejpam-2199	298	13	space	space	NOUN
ejpam-2199	298	14	then	then	ADV
ejpam-2199	298	15	〈	〈	PROPN
ejpam-2199	298	16	x	x	X
ejpam-2199	298	17	,	,	PUNCT
ejpam-2199	298	18	t	t	PROPN
ejpam-2199	298	19	〉	〉	NOUN
ejpam-2199	298	20	is	be	AUX
ejpam-2199	298	21	weakly	weakly	ADV
ejpam-2199	298	22	locally	locally	ADV
ejpam-2199	298	23	hurewicz	hurewicz	NOUN
ejpam-2199	298	24	.	.	PUNCT
ejpam-2199	299	1	proof	proof	NOUN
ejpam-2199	299	2	.	.	PUNCT
ejpam-2199	300	1	consider	consider	VERB
ejpam-2199	300	2	x	x	X
ejpam-2199	300	3	∈	∈	NOUN
ejpam-2199	300	4	x	x	X
ejpam-2199	300	5	.	.	PUNCT
ejpam-2199	301	1	because	because	SCONJ
ejpam-2199	301	2	x	x	PRON
ejpam-2199	301	3	is	be	AUX
ejpam-2199	301	4	weakly	weakly	ADV
ejpam-2199	301	5	locally	locally	ADV
ejpam-2199	301	6	compact	compact	ADJ
ejpam-2199	301	7	there	there	PRON
ejpam-2199	301	8	are	be	VERB
ejpam-2199	301	9	u	u	PROPN
ejpam-2199	301	10	∈	∈	PROPN
ejpam-2199	301	11	t	t	NOUN
ejpam-2199	301	12	and	and	CCONJ
ejpam-2199	301	13	a	a	DET
ejpam-2199	301	14	compact	compact	ADJ
ejpam-2199	301	15	set	set	NOUN
ejpam-2199	301	16	c	c	PROPN
ejpam-2199	301	17	such	such	ADJ
ejpam-2199	301	18	that	that	SCONJ
ejpam-2199	301	19	x	x	SYM
ejpam-2199	301	20	∈	∈	PROPN
ejpam-2199	301	21	u	u	NOUN
ejpam-2199	301	22	⊂	⊂	PROPN
ejpam-2199	301	23	c	c	X
ejpam-2199	301	24	.	.	PUNCT
ejpam-2199	302	1	since	since	SCONJ
ejpam-2199	302	2	by	by	ADP
ejpam-2199	302	3	corollary	corollary	ADJ
ejpam-2199	302	4	1	1	NUM
ejpam-2199	302	5	c	c	NOUN
ejpam-2199	302	6	is	be	AUX
ejpam-2199	302	7	hurewicz	hurewicz	NOUN
ejpam-2199	302	8	we	we	PRON
ejpam-2199	302	9	have	have	VERB
ejpam-2199	302	10	x	x	X
ejpam-2199	302	11	weakly	weakly	ADJ
ejpam-2199	302	12	locally	locally	ADV
ejpam-2199	302	13	hurewicz	hurewicz	NOUN
ejpam-2199	302	14	.	.	PUNCT
ejpam-2199	303	1	proposition	proposition	NOUN
ejpam-2199	303	2	19	19	NUM
ejpam-2199	303	3	.	.	PUNCT
ejpam-2199	304	1	if	if	SCONJ
ejpam-2199	304	2	〈	〈	PROPN
ejpam-2199	304	3	x	x	X
ejpam-2199	304	4	,	,	PUNCT
ejpam-2199	304	5	t	t	PROPN
ejpam-2199	304	6	〉	〉	NOUN
ejpam-2199	304	7	is	be	AUX
ejpam-2199	304	8	a	a	DET
ejpam-2199	304	9	relatively	relatively	ADV
ejpam-2199	304	10	locally	locally	ADV
ejpam-2199	304	11	compact	compact	ADJ
ejpam-2199	304	12	topological	topological	ADJ
ejpam-2199	304	13	space	space	NOUN
ejpam-2199	304	14	then	then	ADV
ejpam-2199	304	15	〈	〈	PROPN
ejpam-2199	304	16	x	x	X
ejpam-2199	304	17	,	,	PUNCT
ejpam-2199	304	18	t	t	PROPN
ejpam-2199	304	19	〉	〉	NOUN
ejpam-2199	304	20	is	be	AUX
ejpam-2199	304	21	relatively	relatively	ADV
ejpam-2199	304	22	locally	locally	ADV
ejpam-2199	304	23	hurewicz	hurewicz	NOUN
ejpam-2199	304	24	.	.	PUNCT
ejpam-2199	305	1	proof	proof	NOUN
ejpam-2199	305	2	.	.	PUNCT
ejpam-2199	306	1	consider	consider	VERB
ejpam-2199	306	2	x	x	X
ejpam-2199	306	3	∈	∈	NOUN
ejpam-2199	306	4	x	x	X
ejpam-2199	306	5	.	.	PUNCT
ejpam-2199	307	1	because	because	SCONJ
ejpam-2199	307	2	x	x	PRON
ejpam-2199	307	3	is	be	AUX
ejpam-2199	307	4	relatively	relatively	ADV
ejpam-2199	307	5	locally	locally	ADV
ejpam-2199	307	6	compact	compact	ADJ
ejpam-2199	307	7	there	there	PRON
ejpam-2199	307	8	is	be	VERB
ejpam-2199	307	9	u	u	PROPN
ejpam-2199	307	10	∈	∈	PROPN
ejpam-2199	307	11	t	t	NOUN
ejpam-2199	307	12	with	with	ADP
ejpam-2199	307	13	u	u	PROPN
ejpam-2199	307	14	compact	compact	ADJ
ejpam-2199	307	15	with	with	ADP
ejpam-2199	307	16	x	x	SYM
ejpam-2199	307	17	∈	∈	PROPN
ejpam-2199	307	18	u	u	NOUN
ejpam-2199	307	19	.	.	PUNCT
ejpam-2199	308	1	by	by	ADP
ejpam-2199	308	2	corollary	corollary	ADJ
ejpam-2199	308	3	1	1	NUM
ejpam-2199	308	4	,	,	PUNCT
ejpam-2199	308	5	u	u	NOUN
ejpam-2199	308	6	is	be	AUX
ejpam-2199	308	7	hurewicz	hurewicz	ADJ
ejpam-2199	308	8	.	.	PUNCT
ejpam-2199	309	1	therefore	therefore	ADV
ejpam-2199	309	2	x	x	X
ejpam-2199	309	3	relatively	relatively	ADV
ejpam-2199	309	4	locally	locally	ADV
ejpam-2199	309	5	hurewicz	hurewicz	NOUN
ejpam-2199	309	6	.	.	PUNCT
ejpam-2199	310	1	example	example	NOUN
ejpam-2199	310	2	5	5	NUM
ejpam-2199	310	3	.	.	X
ejpam-2199	311	1	consider	consider	VERB
ejpam-2199	311	2	r	r	NOUN
ejpam-2199	311	3	in	in	ADP
ejpam-2199	311	4	its	its	PRON
ejpam-2199	311	5	topology	topology	NOUN
ejpam-2199	311	6	,	,	PUNCT
ejpam-2199	311	7	we	we	PRON
ejpam-2199	311	8	have	have	VERB
ejpam-2199	311	9	that	that	PRON
ejpam-2199	311	10	r	r	NOUN
ejpam-2199	311	11	is	be	AUX
ejpam-2199	311	12	hurewicz	hurewicz	NOUN
ejpam-2199	311	13	,	,	PUNCT
ejpam-2199	311	14	then	then	ADV
ejpam-2199	311	15	by	by	ADP
ejpam-2199	311	16	proposition	proposition	NOUN
ejpam-2199	311	17	11	11	NUM
ejpam-2199	311	18	and	and	CCONJ
ejpam-2199	311	19	by	by	ADP
ejpam-2199	311	20	proposition	proposition	NOUN
ejpam-2199	311	21	12	12	NUM
ejpam-2199	311	22	we	we	PRON
ejpam-2199	311	23	have	have	VERB
ejpam-2199	311	24	that	that	PRON
ejpam-2199	311	25	r	r	NOUN
ejpam-2199	311	26	is	be	AUX
ejpam-2199	311	27	weakly	weakly	ADV
ejpam-2199	311	28	locally	locally	ADV
ejpam-2199	311	29	hurewicz	hurewicz	NOUN
ejpam-2199	312	1	and	and	CCONJ
ejpam-2199	312	2	relatively	relatively	ADV
ejpam-2199	312	3	locally	locally	ADV
ejpam-2199	312	4	hurewicz	hurewicz	NOUN
ejpam-2199	312	5	.	.	PUNCT
ejpam-2199	313	1	we	we	PRON
ejpam-2199	313	2	have	have	VERB
ejpam-2199	313	3	that	that	PRON
ejpam-2199	313	4	r	r	NOUN
ejpam-2199	313	5	is	be	AUX
ejpam-2199	313	6	not	not	PART
ejpam-2199	313	7	a	a	DET
ejpam-2199	313	8	c	c	NOUN
ejpam-2199	313	9	-	-	NOUN
ejpam-2199	313	10	space	space	NOUN
ejpam-2199	313	11	,	,	PUNCT
ejpam-2199	313	12	but	but	CCONJ
ejpam-2199	313	13	it	it	PRON
ejpam-2199	313	14	is	be	AUX
ejpam-2199	313	15	a	a	DET
ejpam-2199	313	16	locally	locally	ADV
ejpam-2199	313	17	hurewicz	hurewicz	NOUN
ejpam-2199	313	18	space	space	NOUN
ejpam-2199	313	19	because	because	SCONJ
ejpam-2199	313	20	for	for	ADP
ejpam-2199	313	21	each	each	DET
ejpam-2199	313	22	x	x	SYM
ejpam-2199	313	23	∈	∈	PROPN
ejpam-2199	313	24	r	r	NOUN
ejpam-2199	313	25	and	and	CCONJ
ejpam-2199	313	26	v	v	NOUN
ejpam-2199	313	27	open	open	ADJ
ejpam-2199	313	28	in	in	ADP
ejpam-2199	313	29	r	r	NOUN
ejpam-2199	313	30	,	,	PUNCT
ejpam-2199	313	31	there	there	PRON
ejpam-2199	313	32	exists	exist	VERB
ejpam-2199	313	33	ǫ	ǫ	PRON
ejpam-2199	313	34	>	>	X
ejpam-2199	313	35	0	0	NUM
ejpam-2199	313	36	such	such	ADJ
ejpam-2199	313	37	that	that	SCONJ
ejpam-2199	313	38	x	x	SYM
ejpam-2199	313	39	∈	∈	PROPN
ejpam-2199	313	40	(	(	PUNCT
ejpam-2199	313	41	x	x	X
ejpam-2199	313	42	−	−	NOUN
ejpam-2199	313	43	ǫ	ǫ	NOUN
ejpam-2199	313	44	,	,	PUNCT
ejpam-2199	313	45	x	x	PUNCT
ejpam-2199	314	1	+	+	SYM
ejpam-2199	314	2	ǫ	ǫ	X
ejpam-2199	314	3	)	)	PUNCT
ejpam-2199	314	4	⊂	⊂	PROPN
ejpam-2199	314	5	v	v	ADP
ejpam-2199	314	6	,	,	PUNCT
ejpam-2199	314	7	but	but	CCONJ
ejpam-2199	314	8	(	(	PUNCT
ejpam-2199	314	9	x	x	X
ejpam-2199	314	10	−	−	PROPN
ejpam-2199	314	11	ǫ2	ǫ2	NOUN
ejpam-2199	314	12	,	,	PUNCT
ejpam-2199	314	13	x	x	PROPN
ejpam-2199	314	14	+	+	NUM
ejpam-2199	314	15	ǫ2	ǫ2	NOUN
ejpam-2199	314	16	)	)	PUNCT
ejpam-2199	314	17	is	be	AUX
ejpam-2199	314	18	such	such	ADJ
ejpam-2199	314	19	that	that	SCONJ
ejpam-2199	314	20	x	x	SYM
ejpam-2199	314	21	∈	∈	PROPN
ejpam-2199	314	22	(	(	PUNCT
ejpam-2199	314	23	x	x	SYM
ejpam-2199	314	24	−	−	PROPN
ejpam-2199	314	25	ǫ2	ǫ2	NOUN
ejpam-2199	314	26	,	,	PUNCT
ejpam-2199	314	27	x	x	PROPN
ejpam-2199	314	28	+	+	NUM
ejpam-2199	314	29	ǫ2	ǫ2	NOUN
ejpam-2199	314	30	)	)	PUNCT
ejpam-2199	314	31	⊂	⊂	PROPN
ejpam-2199	315	1	[	[	X
ejpam-2199	315	2	x	x	X
ejpam-2199	315	3	−	−	X
ejpam-2199	315	4	ǫ	ǫ	NUM
ejpam-2199	315	5	2	2	NUM
ejpam-2199	315	6	,	,	PUNCT
ejpam-2199	315	7	x	x	PROPN
ejpam-2199	315	8	+	+	NUM
ejpam-2199	315	9	ǫ2	ǫ2	NOUN
ejpam-2199	315	10	]	]	X
ejpam-2199	315	11	⊂	⊂	X
ejpam-2199	315	12	(	(	PUNCT
ejpam-2199	315	13	x	x	X
ejpam-2199	315	14	−	−	NOUN
ejpam-2199	315	15	ǫ	ǫ	NOUN
ejpam-2199	315	16	,	,	PUNCT
ejpam-2199	315	17	x	x	PUNCT
ejpam-2199	316	1	+	+	SYM
ejpam-2199	316	2	ǫ	ǫ	X
ejpam-2199	316	3	)	)	PUNCT
ejpam-2199	316	4	⊂	⊂	PROPN
ejpam-2199	316	5	v	v	ADP
ejpam-2199	316	6	,	,	PUNCT
ejpam-2199	316	7	where	where	SCONJ
ejpam-2199	316	8	(	(	PUNCT
ejpam-2199	316	9	x	x	X
ejpam-2199	316	10	−	−	PROPN
ejpam-2199	316	11	ǫ2	ǫ2	NOUN
ejpam-2199	316	12	,	,	PUNCT
ejpam-2199	316	13	x	x	PROPN
ejpam-2199	316	14	+	+	NUM
ejpam-2199	316	15	ǫ2	ǫ2	NOUN
ejpam-2199	316	16	)	)	PUNCT
ejpam-2199	316	17	is	be	AUX
ejpam-2199	316	18	an	an	DET
ejpam-2199	316	19	open	open	ADJ
ejpam-2199	316	20	set	set	NOUN
ejpam-2199	316	21	and	and	CCONJ
ejpam-2199	316	22	[	[	X
ejpam-2199	316	23	x	x	X
ejpam-2199	316	24	−	−	PROPN
ejpam-2199	316	25	ǫ2	ǫ2	NOUN
ejpam-2199	316	26	,	,	PUNCT
ejpam-2199	316	27	x	x	PROPN
ejpam-2199	317	1	+	+	NUM
ejpam-2199	317	2	ǫ2	ǫ2	NOUN
ejpam-2199	317	3	]	]	PUNCT
ejpam-2199	317	4	is	be	AUX
ejpam-2199	317	5	compact	compact	ADJ
ejpam-2199	317	6	,	,	PUNCT
ejpam-2199	317	7	hence	hence	ADV
ejpam-2199	317	8	by	by	ADP
ejpam-2199	317	9	corollary	corollary	ADJ
ejpam-2199	317	10	1	1	NUM
ejpam-2199	317	11	is	be	AUX
ejpam-2199	317	12	hurewicz	hurewicz	NOUN
ejpam-2199	317	13	.	.	PUNCT
ejpam-2199	318	1	c.	c.	NOUN
ejpam-2199	318	2	roika	roika	PROPN
ejpam-2199	318	3	,	,	PUNCT
ejpam-2199	318	4	s.	s.	PROPN
ejpam-2199	318	5	kudri	kudri	PROPN
ejpam-2199	318	6	,	,	PUNCT
ejpam-2199	318	7	t.	t.	PROPN
ejpam-2199	318	8	breuckmann	breuckmann	PROPN
ejpam-2199	318	9	/	/	SYM
ejpam-2199	318	10	eur	eur	PROPN
ejpam-2199	318	11	.	.	PUNCT
ejpam-2199	319	1	j.	j.	PROPN
ejpam-2199	319	2	pure	pure	PROPN
ejpam-2199	319	3	appl	appl	PROPN
ejpam-2199	319	4	.	.	PROPN
ejpam-2199	319	5	math	math	PROPN
ejpam-2199	319	6	,	,	PUNCT
ejpam-2199	319	7	8	8	NUM
ejpam-2199	319	8	(	(	PUNCT
ejpam-2199	319	9	2015	2015	NUM
ejpam-2199	319	10	)	)	PUNCT
ejpam-2199	319	11	,	,	PUNCT
ejpam-2199	319	12	514	514	NUM
ejpam-2199	319	13	-	-	SYM
ejpam-2199	319	14	525	525	NUM
ejpam-2199	319	15	523	523	NUM
ejpam-2199	319	16	example	example	NOUN
ejpam-2199	319	17	6	6	NUM
ejpam-2199	319	18	.	.	PUNCT
ejpam-2199	320	1	consider	consider	VERB
ejpam-2199	320	2	r	r	NOUN
ejpam-2199	320	3	with	with	ADP
ejpam-2199	320	4	the	the	DET
ejpam-2199	320	5	discrete	discrete	ADJ
ejpam-2199	320	6	topology	topology	NOUN
ejpam-2199	320	7	.	.	PUNCT
ejpam-2199	321	1	we	we	PRON
ejpam-2199	321	2	have	have	VERB
ejpam-2199	321	3	that	that	PRON
ejpam-2199	321	4	r	r	NOUN
ejpam-2199	321	5	is	be	AUX
ejpam-2199	321	6	not	not	PART
ejpam-2199	321	7	lindelöf	lindelöf	ADJ
ejpam-2199	321	8	,	,	PUNCT
ejpam-2199	321	9	because	because	SCONJ
ejpam-2199	321	10	{	{	PUNCT
ejpam-2199	321	11	{	{	PUNCT
ejpam-2199	321	12	x}/x	x}/x	PROPN
ejpam-2199	321	13	∈	∈	PROPN
ejpam-2199	321	14	r	r	NOUN
ejpam-2199	321	15	}	}	PUNCT
ejpam-2199	321	16	is	be	AUX
ejpam-2199	321	17	an	an	DET
ejpam-2199	321	18	open	open	ADJ
ejpam-2199	321	19	covering	covering	NOUN
ejpam-2199	321	20	of	of	ADP
ejpam-2199	321	21	r	r	NOUN
ejpam-2199	321	22	which	which	PRON
ejpam-2199	321	23	does	do	AUX
ejpam-2199	321	24	not	not	PART
ejpam-2199	321	25	have	have	VERB
ejpam-2199	321	26	a	a	DET
ejpam-2199	321	27	countable	countable	ADJ
ejpam-2199	321	28	subcovering	subcovering	NOUN
ejpam-2199	321	29	,	,	PUNCT
ejpam-2199	321	30	hence	hence	ADV
ejpam-2199	321	31	by	by	ADP
ejpam-2199	321	32	proposition	proposition	NOUN
ejpam-2199	321	33	3	3	NUM
ejpam-2199	321	34	r	r	NOUN
ejpam-2199	321	35	with	with	ADP
ejpam-2199	321	36	the	the	DET
ejpam-2199	321	37	discrete	discrete	ADJ
ejpam-2199	321	38	topology	topology	NOUN
ejpam-2199	321	39	is	be	AUX
ejpam-2199	321	40	not	not	PART
ejpam-2199	321	41	hurewicz	hurewicz	NOUN
ejpam-2199	321	42	,	,	PUNCT
ejpam-2199	321	43	but	but	CCONJ
ejpam-2199	321	44	for	for	SCONJ
ejpam-2199	321	45	each	each	DET
ejpam-2199	321	46	x	x	SYM
ejpam-2199	321	47	∈	∈	PROPN
ejpam-2199	321	48	r	r	NOUN
ejpam-2199	321	49	,	,	PUNCT
ejpam-2199	321	50	{	{	PUNCT
ejpam-2199	321	51	x	x	NOUN
ejpam-2199	321	52	}	}	PUNCT
ejpam-2199	321	53	is	be	AUX
ejpam-2199	321	54	a	a	DET
ejpam-2199	321	55	compact	compact	ADJ
ejpam-2199	321	56	set	set	NOUN
ejpam-2199	321	57	,	,	PUNCT
ejpam-2199	321	58	then	then	ADV
ejpam-2199	321	59	{	{	PUNCT
ejpam-2199	321	60	x	x	X
ejpam-2199	321	61	}	}	PUNCT
ejpam-2199	321	62	is	be	AUX
ejpam-2199	321	63	hurewicz	hurewicz	ADJ
ejpam-2199	321	64	.	.	PUNCT
ejpam-2199	322	1	then	then	ADV
ejpam-2199	322	2	we	we	PRON
ejpam-2199	322	3	have	have	VERB
ejpam-2199	322	4	that	that	DET
ejpam-2199	322	5	r	r	NOUN
ejpam-2199	322	6	with	with	ADP
ejpam-2199	322	7	the	the	DET
ejpam-2199	322	8	discrete	discrete	ADJ
ejpam-2199	322	9	topology	topology	NOUN
ejpam-2199	322	10	is	be	AUX
ejpam-2199	322	11	locally	locally	ADV
ejpam-2199	322	12	hurewicz	hurewicz	NOUN
ejpam-2199	322	13	,	,	PUNCT
ejpam-2199	322	14	because	because	SCONJ
ejpam-2199	322	15	for	for	ADP
ejpam-2199	322	16	each	each	DET
ejpam-2199	322	17	x	x	SYM
ejpam-2199	322	18	∈	∈	PROPN
ejpam-2199	322	19	r	r	NOUN
ejpam-2199	322	20	and	and	CCONJ
ejpam-2199	322	21	a	a	DET
ejpam-2199	322	22	neighborhood	neighborhood	NOUN
ejpam-2199	322	23	v	v	NOUN
ejpam-2199	322	24	of	of	ADP
ejpam-2199	322	25	x	x	PRON
ejpam-2199	322	26	,	,	PUNCT
ejpam-2199	322	27	we	we	PRON
ejpam-2199	322	28	have	have	VERB
ejpam-2199	322	29	that	that	PRON
ejpam-2199	322	30	x	x	SYM
ejpam-2199	322	31	∈	∈	PROPN
ejpam-2199	322	32	{	{	PUNCT
ejpam-2199	322	33	x	x	NOUN
ejpam-2199	322	34	}	}	PUNCT
ejpam-2199	322	35	⊂	⊂	PROPN
ejpam-2199	322	36	v	v	NOUN
ejpam-2199	322	37	,	,	PUNCT
ejpam-2199	322	38	where	where	SCONJ
ejpam-2199	322	39	{	{	PUNCT
ejpam-2199	322	40	x	x	X
ejpam-2199	322	41	}	}	PUNCT
ejpam-2199	322	42	is	be	AUX
ejpam-2199	322	43	an	an	DET
ejpam-2199	322	44	open	open	ADJ
ejpam-2199	322	45	set	set	NOUN
ejpam-2199	322	46	and	and	CCONJ
ejpam-2199	322	47	hurewicz	hurewicz	NOUN
ejpam-2199	322	48	.	.	PUNCT
ejpam-2199	323	1	since	since	SCONJ
ejpam-2199	323	2	r	r	NOUN
ejpam-2199	323	3	with	with	ADP
ejpam-2199	323	4	the	the	DET
ejpam-2199	323	5	discrete	discrete	ADJ
ejpam-2199	323	6	topological	topological	NOUN
ejpam-2199	323	7	is	be	AUX
ejpam-2199	323	8	a	a	DET
ejpam-2199	323	9	hausdorff	hausdorff	NOUN
ejpam-2199	323	10	c	c	NOUN
ejpam-2199	323	11	-	-	PUNCT
ejpam-2199	323	12	space	space	NOUN
ejpam-2199	323	13	,	,	PUNCT
ejpam-2199	323	14	we	we	PRON
ejpam-2199	323	15	have	have	VERB
ejpam-2199	323	16	that	that	PRON
ejpam-2199	323	17	r	r	NOUN
ejpam-2199	323	18	is	be	AUX
ejpam-2199	323	19	weakly	weakly	ADV
ejpam-2199	323	20	locally	locally	ADV
ejpam-2199	323	21	hurewicz	hurewicz	NOUN
ejpam-2199	323	22	and	and	CCONJ
ejpam-2199	323	23	relatively	relatively	ADV
ejpam-2199	323	24	locally	locally	ADV
ejpam-2199	323	25	hurewicz	hurewicz	NOUN
ejpam-2199	323	26	.	.	PUNCT
ejpam-2199	323	27	example	example	NOUN
ejpam-2199	324	1	7	7	NUM
ejpam-2199	324	2	.	.	X
ejpam-2199	325	1	consider	consider	VERB
ejpam-2199	325	2	r	r	NOUN
ejpam-2199	325	3	with	with	ADP
ejpam-2199	325	4	the	the	DET
ejpam-2199	325	5	particular	particular	ADJ
ejpam-2199	325	6	point	point	NOUN
ejpam-2199	325	7	p	p	NOUN
ejpam-2199	325	8	topology	topology	NOUN
ejpam-2199	325	9	(	(	PUNCT
ejpam-2199	325	10	definition	definition	NOUN
ejpam-2199	325	11	4	4	NUM
ejpam-2199	325	12	)	)	PUNCT
ejpam-2199	325	13	,	,	PUNCT
ejpam-2199	325	14	by	by	ADP
ejpam-2199	325	15	example	example	NOUN
ejpam-2199	325	16	2	2	NUM
ejpam-2199	325	17	we	we	PRON
ejpam-2199	325	18	have	have	VERB
ejpam-2199	325	19	that	that	PRON
ejpam-2199	325	20	r	r	NOUN
ejpam-2199	325	21	is	be	AUX
ejpam-2199	325	22	not	not	PART
ejpam-2199	325	23	hurewicz	hurewicz	ADJ
ejpam-2199	325	24	.	.	PUNCT
ejpam-2199	326	1	given	give	VERB
ejpam-2199	326	2	a	a	DET
ejpam-2199	326	3	nonempty	nonempty	ADJ
ejpam-2199	326	4	open	open	NOUN
ejpam-2199	326	5	set	set	NOUN
ejpam-2199	326	6	a	a	PRON
ejpam-2199	326	7	in	in	ADP
ejpam-2199	326	8	r	r	NOUN
ejpam-2199	326	9	,	,	PUNCT
ejpam-2199	326	10	we	we	PRON
ejpam-2199	326	11	have	have	VERB
ejpam-2199	326	12	that	that	PRON
ejpam-2199	326	13	a	a	DET
ejpam-2199	326	14	=	=	SYM
ejpam-2199	326	15	r	r	NOUN
ejpam-2199	326	16	,	,	PUNCT
ejpam-2199	326	17	because	because	SCONJ
ejpam-2199	326	18	for	for	ADP
ejpam-2199	326	19	y	y	PROPN
ejpam-2199	326	20	∈	∈	PROPN
ejpam-2199	326	21	r	r	NOUN
ejpam-2199	326	22	,	,	PUNCT
ejpam-2199	326	23	we	we	PRON
ejpam-2199	326	24	have	have	VERB
ejpam-2199	326	25	that	that	SCONJ
ejpam-2199	326	26	any	any	DET
ejpam-2199	326	27	neighborhood	neighborhood	NOUN
ejpam-2199	326	28	of	of	ADP
ejpam-2199	326	29	y	y	PRON
ejpam-2199	326	30	being	be	AUX
ejpam-2199	326	31	nonempty	nonempty	ADV
ejpam-2199	326	32	contains	contain	VERB
ejpam-2199	326	33	p	p	PRON
ejpam-2199	326	34	,	,	PUNCT
ejpam-2199	326	35	then	then	ADV
ejpam-2199	326	36	intersects	intersect	VERB
ejpam-2199	326	37	a.	a.	NOUN
ejpam-2199	326	38	hence	hence	ADV
ejpam-2199	326	39	r	r	NOUN
ejpam-2199	326	40	is	be	AUX
ejpam-2199	326	41	not	not	PART
ejpam-2199	326	42	relatively	relatively	ADV
ejpam-2199	326	43	locally	locally	ADV
ejpam-2199	326	44	hurewicz	hurewicz	NOUN
ejpam-2199	326	45	,	,	PUNCT
ejpam-2199	326	46	because	because	SCONJ
ejpam-2199	326	47	for	for	ADP
ejpam-2199	326	48	each	each	DET
ejpam-2199	326	49	x	x	SYM
ejpam-2199	326	50	∈	∈	NOUN
ejpam-2199	326	51	r	r	NOUN
ejpam-2199	326	52	any	any	DET
ejpam-2199	326	53	neighborhood	neighborhood	NOUN
ejpam-2199	326	54	v	v	NOUN
ejpam-2199	326	55	of	of	ADP
ejpam-2199	326	56	x	x	PUNCT
ejpam-2199	326	57	is	be	AUX
ejpam-2199	326	58	a	a	DET
ejpam-2199	326	59	nonempty	nonempty	ADJ
ejpam-2199	326	60	set	set	NOUN
ejpam-2199	326	61	,	,	PUNCT
ejpam-2199	326	62	then	then	ADV
ejpam-2199	326	63	v	v	NOUN
ejpam-2199	326	64	=	=	SYM
ejpam-2199	326	65	r	r	NOUN
ejpam-2199	326	66	,	,	PUNCT
ejpam-2199	326	67	but	but	CCONJ
ejpam-2199	326	68	since	since	SCONJ
ejpam-2199	326	69	r	r	NOUN
ejpam-2199	326	70	is	be	AUX
ejpam-2199	326	71	not	not	PART
ejpam-2199	326	72	hurewicz	hurewicz	NOUN
ejpam-2199	326	73	,	,	PUNCT
ejpam-2199	326	74	then	then	ADV
ejpam-2199	326	75	we	we	PRON
ejpam-2199	326	76	can	can	AUX
ejpam-2199	326	77	not	not	PART
ejpam-2199	326	78	obtain	obtain	VERB
ejpam-2199	326	79	a	a	DET
ejpam-2199	326	80	neighborhood	neighborhood	NOUN
ejpam-2199	326	81	of	of	ADP
ejpam-2199	326	82	x	x	SYM
ejpam-2199	326	83	where	where	SCONJ
ejpam-2199	326	84	the	the	DET
ejpam-2199	326	85	closure	closure	NOUN
ejpam-2199	326	86	is	be	AUX
ejpam-2199	326	87	hurewicz	hurewicz	NOUN
ejpam-2199	326	88	.	.	PUNCT
ejpam-2199	327	1	but	but	CCONJ
ejpam-2199	327	2	r	r	NOUN
ejpam-2199	327	3	is	be	AUX
ejpam-2199	327	4	weakly	weakly	ADV
ejpam-2199	327	5	locally	locally	ADV
ejpam-2199	327	6	compact	compact	ADJ
ejpam-2199	327	7	,	,	PUNCT
ejpam-2199	327	8	because	because	SCONJ
ejpam-2199	327	9	for	for	ADP
ejpam-2199	327	10	each	each	DET
ejpam-2199	327	11	x	x	SYM
ejpam-2199	327	12	∈	∈	NOUN
ejpam-2199	327	13	r	r	NOUN
ejpam-2199	327	14	we	we	PRON
ejpam-2199	327	15	have	have	VERB
ejpam-2199	327	16	that	that	PRON
ejpam-2199	327	17	x	x	SYM
ejpam-2199	327	18	∈	∈	PROPN
ejpam-2199	327	19	{	{	PUNCT
ejpam-2199	327	20	x	x	NOUN
ejpam-2199	327	21	,	,	PUNCT
ejpam-2199	327	22	p	p	X
ejpam-2199	327	23	}	}	PUNCT
ejpam-2199	327	24	and	and	CCONJ
ejpam-2199	327	25	{	{	PUNCT
ejpam-2199	327	26	x	x	X
ejpam-2199	327	27	,	,	PUNCT
ejpam-2199	327	28	p	p	X
ejpam-2199	327	29	}	}	PUNCT
ejpam-2199	327	30	is	be	AUX
ejpam-2199	327	31	an	an	DET
ejpam-2199	327	32	open	open	ADJ
ejpam-2199	327	33	and	and	CCONJ
ejpam-2199	327	34	compact	compact	ADJ
ejpam-2199	327	35	set	set	NOUN
ejpam-2199	327	36	,	,	PUNCT
ejpam-2199	327	37	hence	hence	ADV
ejpam-2199	327	38	by	by	ADP
ejpam-2199	327	39	proposition	proposition	NOUN
ejpam-2199	327	40	18	18	NUM
ejpam-2199	327	41	,	,	PUNCT
ejpam-2199	327	42	r	r	NOUN
ejpam-2199	327	43	is	be	AUX
ejpam-2199	327	44	weakly	weakly	ADV
ejpam-2199	327	45	locally	locally	ADV
ejpam-2199	327	46	hurewicz	hurewicz	NOUN
ejpam-2199	327	47	.	.	PUNCT
ejpam-2199	328	1	proposition	proposition	NOUN
ejpam-2199	328	2	20	20	NUM
ejpam-2199	328	3	.	.	PUNCT
ejpam-2199	329	1	let	let	VERB
ejpam-2199	329	2	〈	〈	PROPN
ejpam-2199	329	3	x	x	X
ejpam-2199	329	4	,	,	PUNCT
ejpam-2199	329	5	tx	tx	PROPN
ejpam-2199	329	6	〉	〉	NOUN
ejpam-2199	329	7	and	and	CCONJ
ejpam-2199	329	8	〈	〈	PROPN
ejpam-2199	329	9	y	y	PROPN
ejpam-2199	329	10	,	,	PUNCT
ejpam-2199	329	11	ty	ty	NUM
ejpam-2199	329	12	〉	〉	NOUN
ejpam-2199	329	13	be	be	VERB
ejpam-2199	329	14	topological	topological	ADJ
ejpam-2199	329	15	spaces	space	NOUN
ejpam-2199	329	16	,	,	PUNCT
ejpam-2199	329	17	where	where	SCONJ
ejpam-2199	329	18	x	x	PRON
ejpam-2199	329	19	is	be	AUX
ejpam-2199	329	20	locally	locally	ADV
ejpam-2199	329	21	hurewicz	hurewicz	NOUN
ejpam-2199	329	22	and	and	CCONJ
ejpam-2199	329	23	let	let	VERB
ejpam-2199	329	24	f	f	NOUN
ejpam-2199	329	25	:	:	PUNCT
ejpam-2199	329	26	x	x	X
ejpam-2199	329	27	→	→	SYM
ejpam-2199	329	28	y	y	X
ejpam-2199	329	29	be	be	AUX
ejpam-2199	329	30	a	a	DET
ejpam-2199	329	31	continuous	continuous	ADJ
ejpam-2199	329	32	,	,	PUNCT
ejpam-2199	329	33	open	open	ADJ
ejpam-2199	329	34	and	and	CCONJ
ejpam-2199	329	35	surjective	surjective	ADJ
ejpam-2199	329	36	function	function	NOUN
ejpam-2199	329	37	,	,	PUNCT
ejpam-2199	329	38	then	then	ADV
ejpam-2199	329	39	y	y	PROPN
ejpam-2199	329	40	is	be	AUX
ejpam-2199	329	41	locally	locally	ADV
ejpam-2199	329	42	hurewicz	hurewicz	NOUN
ejpam-2199	329	43	.	.	PUNCT
ejpam-2199	330	1	proof	proof	NOUN
ejpam-2199	330	2	.	.	PUNCT
ejpam-2199	331	1	consider	consider	VERB
ejpam-2199	331	2	y	y	PROPN
ejpam-2199	331	3	∈	∈	PROPN
ejpam-2199	331	4	y	y	PROPN
ejpam-2199	331	5	and	and	CCONJ
ejpam-2199	331	6	v	v	ADP
ejpam-2199	331	7	a	a	DET
ejpam-2199	331	8	neighborhood	neighborhood	NOUN
ejpam-2199	331	9	of	of	ADP
ejpam-2199	331	10	y	y	PROPN
ejpam-2199	331	11	,	,	PUNCT
ejpam-2199	331	12	then	then	ADV
ejpam-2199	331	13	∃x	∃x	PROPN
ejpam-2199	331	14	∈	∈	PROPN
ejpam-2199	331	15	x	x	X
ejpam-2199	331	16	such	such	ADJ
ejpam-2199	331	17	that	that	SCONJ
ejpam-2199	331	18	f	f	PROPN
ejpam-2199	331	19	(	(	PUNCT
ejpam-2199	331	20	x	x	X
ejpam-2199	331	21	)	)	PUNCT
ejpam-2199	331	22	=	=	SYM
ejpam-2199	331	23	y	y	PROPN
ejpam-2199	331	24	.	.	PUNCT
ejpam-2199	332	1	by	by	ADP
ejpam-2199	332	2	the	the	DET
ejpam-2199	332	3	continuity	continuity	NOUN
ejpam-2199	332	4	of	of	ADP
ejpam-2199	332	5	f	f	PROPN
ejpam-2199	332	6	,	,	PUNCT
ejpam-2199	332	7	we	we	PRON
ejpam-2199	332	8	have	have	VERB
ejpam-2199	332	9	that	that	PRON
ejpam-2199	332	10	f	f	PROPN
ejpam-2199	332	11	−1(v	−1(v	PROPN
ejpam-2199	332	12	)	)	PUNCT
ejpam-2199	333	1	∈	∈	PROPN
ejpam-2199	333	2	tx	tx	PROPN
ejpam-2199	333	3	.	.	PUNCT
ejpam-2199	334	1	because	because	SCONJ
ejpam-2199	334	2	x	x	PRON
ejpam-2199	334	3	is	be	AUX
ejpam-2199	334	4	locally	locally	ADV
ejpam-2199	334	5	hurewicz	hurewicz	NOUN
ejpam-2199	334	6	,	,	PUNCT
ejpam-2199	334	7	there	there	PRON
ejpam-2199	334	8	are	be	VERB
ejpam-2199	334	9	u	u	PRON
ejpam-2199	334	10	open	open	ADJ
ejpam-2199	334	11	set	set	VERB
ejpam-2199	334	12	in	in	ADP
ejpam-2199	334	13	x	x	PUNCT
ejpam-2199	335	1	and	and	CCONJ
ejpam-2199	335	2	h	h	NOUN
ejpam-2199	335	3	hurewicz	hurewicz	NOUN
ejpam-2199	335	4	such	such	ADJ
ejpam-2199	335	5	that	that	SCONJ
ejpam-2199	335	6	x	x	SYM
ejpam-2199	335	7	∈	∈	PROPN
ejpam-2199	335	8	u	u	X
ejpam-2199	335	9	⊂	⊂	PROPN
ejpam-2199	335	10	h	h	PROPN
ejpam-2199	335	11	⊂	⊂	PROPN
ejpam-2199	335	12	f	f	PROPN
ejpam-2199	335	13	−1(v	−1(v	PROPN
ejpam-2199	335	14	)	)	PUNCT
ejpam-2199	335	15	,	,	PUNCT
ejpam-2199	335	16	then	then	ADV
ejpam-2199	335	17	y	y	PROPN
ejpam-2199	335	18	=	=	SYM
ejpam-2199	335	19	f	f	PROPN
ejpam-2199	335	20	(	(	PUNCT
ejpam-2199	335	21	x	x	X
ejpam-2199	335	22	)	)	PUNCT
ejpam-2199	335	23	∈	∈	PROPN
ejpam-2199	335	24	f	f	X
ejpam-2199	335	25	(	(	PUNCT
ejpam-2199	335	26	u	u	NOUN
ejpam-2199	335	27	)	)	PUNCT
ejpam-2199	336	1	⊂	⊂	PROPN
ejpam-2199	336	2	f	f	X
ejpam-2199	336	3	(	(	PUNCT
ejpam-2199	336	4	h	h	NOUN
ejpam-2199	336	5	)	)	PUNCT
ejpam-2199	337	1	⊂	⊂	PROPN
ejpam-2199	337	2	f	f	X
ejpam-2199	337	3	(	(	PUNCT
ejpam-2199	337	4	f	f	PROPN
ejpam-2199	337	5	−1(v	−1(v	PROPN
ejpam-2199	337	6	)	)	PUNCT
ejpam-2199	337	7	)	)	PUNCT
ejpam-2199	338	1	⊂	⊂	PROPN
ejpam-2199	338	2	v	v	ADP
ejpam-2199	338	3	,	,	PUNCT
ejpam-2199	338	4	since	since	SCONJ
ejpam-2199	338	5	f	f	PROPN
ejpam-2199	338	6	is	be	AUX
ejpam-2199	338	7	an	an	DET
ejpam-2199	338	8	open	open	ADJ
ejpam-2199	338	9	function	function	NOUN
ejpam-2199	338	10	f	f	PROPN
ejpam-2199	338	11	(	(	PUNCT
ejpam-2199	338	12	u	u	NOUN
ejpam-2199	338	13	)	)	PUNCT
ejpam-2199	338	14	is	be	AUX
ejpam-2199	338	15	open	open	ADJ
ejpam-2199	338	16	in	in	ADP
ejpam-2199	338	17	y	y	PROPN
ejpam-2199	338	18	and	and	CCONJ
ejpam-2199	338	19	since	since	SCONJ
ejpam-2199	338	20	f	f	PROPN
ejpam-2199	338	21	is	be	AUX
ejpam-2199	338	22	continuous	continuous	ADJ
ejpam-2199	338	23	f	f	X
ejpam-2199	338	24	(	(	PUNCT
ejpam-2199	338	25	h	h	NOUN
ejpam-2199	338	26	)	)	PUNCT
ejpam-2199	338	27	is	be	AUX
ejpam-2199	338	28	hurewicz	hurewicz	VERB
ejpam-2199	338	29	by	by	ADP
ejpam-2199	338	30	proposition	proposition	NOUN
ejpam-2199	338	31	4	4	NUM
ejpam-2199	338	32	.	.	PUNCT
ejpam-2199	339	1	so	so	ADV
ejpam-2199	339	2	y	y	PROPN
ejpam-2199	339	3	is	be	AUX
ejpam-2199	339	4	a	a	DET
ejpam-2199	339	5	locally	locally	ADV
ejpam-2199	339	6	hurewicz	hurewicz	ADJ
ejpam-2199	339	7	space	space	NOUN
ejpam-2199	339	8	.	.	PUNCT
ejpam-2199	340	1	proposition	proposition	NOUN
ejpam-2199	340	2	21	21	NUM
ejpam-2199	340	3	.	.	PUNCT
ejpam-2199	341	1	let	let	VERB
ejpam-2199	341	2	〈	〈	PROPN
ejpam-2199	341	3	x	x	X
ejpam-2199	341	4	,	,	PUNCT
ejpam-2199	341	5	tx	tx	PROPN
ejpam-2199	341	6	〉	〉	NOUN
ejpam-2199	341	7	and	and	CCONJ
ejpam-2199	341	8	〈	〈	PROPN
ejpam-2199	341	9	y	y	PROPN
ejpam-2199	341	10	,	,	PUNCT
ejpam-2199	341	11	ty	ty	NUM
ejpam-2199	341	12	〉	〉	NOUN
ejpam-2199	341	13	be	be	VERB
ejpam-2199	341	14	topological	topological	ADJ
ejpam-2199	341	15	spaces	space	NOUN
ejpam-2199	341	16	,	,	PUNCT
ejpam-2199	341	17	where	where	SCONJ
ejpam-2199	341	18	x	x	PRON
ejpam-2199	341	19	is	be	AUX
ejpam-2199	341	20	weakly	weakly	ADV
ejpam-2199	341	21	locally	locally	ADV
ejpam-2199	341	22	hurewicz	hurewicz	NOUN
ejpam-2199	341	23	and	and	CCONJ
ejpam-2199	341	24	let	let	VERB
ejpam-2199	341	25	f	f	NOUN
ejpam-2199	341	26	:	:	PUNCT
ejpam-2199	341	27	x	x	X
ejpam-2199	341	28	→	→	SYM
ejpam-2199	341	29	y	y	X
ejpam-2199	341	30	be	be	AUX
ejpam-2199	341	31	a	a	DET
ejpam-2199	341	32	continuous	continuous	ADJ
ejpam-2199	341	33	,	,	PUNCT
ejpam-2199	341	34	open	open	ADJ
ejpam-2199	341	35	and	and	CCONJ
ejpam-2199	341	36	surjective	surjective	ADJ
ejpam-2199	341	37	function	function	NOUN
ejpam-2199	341	38	,	,	PUNCT
ejpam-2199	341	39	then	then	ADV
ejpam-2199	341	40	y	y	PROPN
ejpam-2199	341	41	is	be	AUX
ejpam-2199	341	42	weakly	weakly	ADV
ejpam-2199	341	43	locally	locally	ADV
ejpam-2199	341	44	hurewicz	hurewicz	NOUN
ejpam-2199	341	45	.	.	PUNCT
ejpam-2199	342	1	proof	proof	NOUN
ejpam-2199	342	2	.	.	PUNCT
ejpam-2199	343	1	by	by	AUX
ejpam-2199	343	2	consider	consider	VERB
ejpam-2199	343	3	y	y	PROPN
ejpam-2199	343	4	∈	∈	PROPN
ejpam-2199	343	5	y	y	PROPN
ejpam-2199	343	6	,	,	PUNCT
ejpam-2199	343	7	∃x	∃x	PROPN
ejpam-2199	343	8	∈	∈	PROPN
ejpam-2199	343	9	x	x	X
ejpam-2199	344	1	such	such	ADJ
ejpam-2199	344	2	that	that	SCONJ
ejpam-2199	344	3	f	f	PROPN
ejpam-2199	344	4	(	(	PUNCT
ejpam-2199	344	5	x	x	X
ejpam-2199	344	6	)	)	PUNCT
ejpam-2199	344	7	=	=	SYM
ejpam-2199	344	8	y	y	PROPN
ejpam-2199	344	9	.	.	PUNCT
ejpam-2199	345	1	because	because	SCONJ
ejpam-2199	345	2	x	x	PRON
ejpam-2199	345	3	is	be	AUX
ejpam-2199	345	4	weakly	weakly	ADV
ejpam-2199	345	5	locally	locally	ADV
ejpam-2199	345	6	hurewicz	hurewicz	NOUN
ejpam-2199	345	7	,	,	PUNCT
ejpam-2199	345	8	there	there	PRON
ejpam-2199	345	9	are	be	VERB
ejpam-2199	345	10	u	u	PROPN
ejpam-2199	345	11	∈	∈	PROPN
ejpam-2199	345	12	tx	tx	NOUN
ejpam-2199	345	13	and	and	CCONJ
ejpam-2199	345	14	h	h	NOUN
ejpam-2199	345	15	hurewicz	hurewicz	NOUN
ejpam-2199	345	16	with	with	ADP
ejpam-2199	345	17	x	x	PROPN
ejpam-2199	345	18	∈	∈	PROPN
ejpam-2199	345	19	u	u	NOUN
ejpam-2199	345	20	⊂	⊂	PROPN
ejpam-2199	345	21	h	h	NOUN
ejpam-2199	345	22	,	,	PUNCT
ejpam-2199	345	23	then	then	ADV
ejpam-2199	345	24	y	y	PROPN
ejpam-2199	345	25	=	=	SYM
ejpam-2199	345	26	f	f	PROPN
ejpam-2199	345	27	(	(	PUNCT
ejpam-2199	345	28	x	x	X
ejpam-2199	345	29	)	)	PUNCT
ejpam-2199	345	30	∈	∈	PROPN
ejpam-2199	345	31	f	f	X
ejpam-2199	345	32	(	(	PUNCT
ejpam-2199	345	33	u	u	NOUN
ejpam-2199	345	34	)	)	PUNCT
ejpam-2199	345	35	⊂	⊂	PROPN
ejpam-2199	345	36	f	f	X
ejpam-2199	345	37	(	(	PUNCT
ejpam-2199	345	38	h	h	NOUN
ejpam-2199	345	39	)	)	PUNCT
ejpam-2199	345	40	,	,	PUNCT
ejpam-2199	345	41	since	since	SCONJ
ejpam-2199	345	42	f	f	PROPN
ejpam-2199	345	43	is	be	AUX
ejpam-2199	345	44	an	an	DET
ejpam-2199	345	45	open	open	ADJ
ejpam-2199	345	46	we	we	PRON
ejpam-2199	345	47	have	have	VERB
ejpam-2199	345	48	that	that	PRON
ejpam-2199	345	49	f	f	PROPN
ejpam-2199	345	50	(	(	PUNCT
ejpam-2199	345	51	u	u	NOUN
ejpam-2199	345	52	)	)	PUNCT
ejpam-2199	345	53	∈	∈	NOUN
ejpam-2199	345	54	ty	ty	INTJ
ejpam-2199	345	55	and	and	CCONJ
ejpam-2199	345	56	by	by	ADP
ejpam-2199	345	57	the	the	DET
ejpam-2199	345	58	continuity	continuity	NOUN
ejpam-2199	345	59	of	of	ADP
ejpam-2199	345	60	f	f	PROPN
ejpam-2199	345	61	and	and	CCONJ
ejpam-2199	345	62	proposition	proposition	NOUN
ejpam-2199	345	63	4	4	NUM
ejpam-2199	345	64	f	f	NOUN
ejpam-2199	345	65	(	(	PUNCT
ejpam-2199	345	66	h	h	NOUN
ejpam-2199	345	67	)	)	PUNCT
ejpam-2199	345	68	is	be	AUX
ejpam-2199	345	69	hurewicz	hurewicz	NOUN
ejpam-2199	345	70	.	.	PUNCT
ejpam-2199	346	1	so	so	ADV
ejpam-2199	346	2	y	y	PROPN
ejpam-2199	346	3	is	be	AUX
ejpam-2199	346	4	a	a	DET
ejpam-2199	346	5	weakly	weakly	ADJ
ejpam-2199	346	6	locally	locally	ADV
ejpam-2199	346	7	hurewicz	hurewicz	ADJ
ejpam-2199	346	8	space	space	NOUN
ejpam-2199	346	9	.	.	PUNCT
ejpam-2199	347	1	proposition	proposition	NOUN
ejpam-2199	347	2	22	22	NUM
ejpam-2199	347	3	.	.	PUNCT
ejpam-2199	348	1	let	let	VERB
ejpam-2199	348	2	〈	〈	PROPN
ejpam-2199	348	3	x	x	X
ejpam-2199	348	4	,	,	PUNCT
ejpam-2199	348	5	tx	tx	PROPN
ejpam-2199	348	6	〉	〉	NOUN
ejpam-2199	348	7	and	and	CCONJ
ejpam-2199	348	8	〈	〈	PROPN
ejpam-2199	348	9	y	y	PROPN
ejpam-2199	348	10	,	,	PUNCT
ejpam-2199	348	11	ty	ty	NUM
ejpam-2199	348	12	〉	〉	NOUN
ejpam-2199	348	13	be	be	VERB
ejpam-2199	348	14	topological	topological	ADJ
ejpam-2199	348	15	spaces	space	NOUN
ejpam-2199	348	16	,	,	PUNCT
ejpam-2199	348	17	with	with	SCONJ
ejpam-2199	348	18	x	x	X
ejpam-2199	348	19	is	be	AUX
ejpam-2199	348	20	relatively	relatively	ADV
ejpam-2199	348	21	locally	locally	ADV
ejpam-2199	348	22	hurewicz	hurewicz	NOUN
ejpam-2199	348	23	and	and	CCONJ
ejpam-2199	348	24	y	y	PROPN
ejpam-2199	348	25	a	a	DET
ejpam-2199	348	26	hausdorff	hausdorff	NOUN
ejpam-2199	348	27	c	c	NOUN
ejpam-2199	348	28	-	-	PUNCT
ejpam-2199	348	29	space	space	NOUN
ejpam-2199	348	30	and	and	CCONJ
ejpam-2199	348	31	let	let	VERB
ejpam-2199	348	32	f	f	NOUN
ejpam-2199	348	33	:	:	PUNCT
ejpam-2199	348	34	x	x	X
ejpam-2199	348	35	→	→	SYM
ejpam-2199	348	36	y	y	X
ejpam-2199	348	37	be	be	AUX
ejpam-2199	348	38	a	a	DET
ejpam-2199	348	39	continuous	continuous	ADJ
ejpam-2199	348	40	,	,	PUNCT
ejpam-2199	348	41	open	open	ADJ
ejpam-2199	348	42	surjection	surjection	NOUN
ejpam-2199	348	43	,	,	PUNCT
ejpam-2199	348	44	then	then	ADV
ejpam-2199	348	45	y	y	PROPN
ejpam-2199	348	46	is	be	AUX
ejpam-2199	348	47	relatively	relatively	ADV
ejpam-2199	348	48	locally	locally	ADV
ejpam-2199	348	49	hurewicz	hurewicz	NOUN
ejpam-2199	348	50	.	.	PUNCT
ejpam-2199	349	1	proof	proof	NOUN
ejpam-2199	349	2	.	.	PUNCT
ejpam-2199	350	1	consider	consider	VERB
ejpam-2199	350	2	y	y	PROPN
ejpam-2199	350	3	∈	∈	PROPN
ejpam-2199	350	4	y	y	PROPN
ejpam-2199	350	5	,	,	PUNCT
ejpam-2199	350	6	then	then	ADV
ejpam-2199	350	7	∃x	∃x	PROPN
ejpam-2199	350	8	∈	∈	PROPN
ejpam-2199	350	9	x	x	PUNCT
ejpam-2199	350	10	with	with	ADP
ejpam-2199	350	11	f	f	PROPN
ejpam-2199	350	12	(	(	PUNCT
ejpam-2199	350	13	x	x	NOUN
ejpam-2199	350	14	)	)	PUNCT
ejpam-2199	350	15	=	=	SYM
ejpam-2199	350	16	y	y	PROPN
ejpam-2199	350	17	.	.	PUNCT
ejpam-2199	351	1	from	from	ADP
ejpam-2199	351	2	the	the	DET
ejpam-2199	351	3	fact	fact	NOUN
ejpam-2199	351	4	that	that	SCONJ
ejpam-2199	351	5	x	x	PRON
ejpam-2199	351	6	is	be	AUX
ejpam-2199	351	7	relatively	relatively	ADV
ejpam-2199	351	8	locally	locally	ADV
ejpam-2199	351	9	hurewicz	hurewicz	NOUN
ejpam-2199	351	10	,	,	PUNCT
ejpam-2199	351	11	there	there	PRON
ejpam-2199	351	12	is	be	VERB
ejpam-2199	351	13	u	u	PROPN
ejpam-2199	351	14	∈	∈	PROPN
ejpam-2199	351	15	tx	tx	NOUN
ejpam-2199	351	16	,	,	PUNCT
ejpam-2199	351	17	with	with	ADP
ejpam-2199	351	18	u	u	NOUN
ejpam-2199	351	19	hurewicz	hurewicz	NOUN
ejpam-2199	351	20	with	with	ADP
ejpam-2199	351	21	x	x	PROPN
ejpam-2199	351	22	∈	∈	PROPN
ejpam-2199	351	23	u	u	NOUN
ejpam-2199	351	24	,	,	PUNCT
ejpam-2199	351	25	then	then	ADV
ejpam-2199	351	26	y	y	PROPN
ejpam-2199	351	27	=	=	SYM
ejpam-2199	351	28	f	f	PROPN
ejpam-2199	351	29	(	(	PUNCT
ejpam-2199	351	30	x	x	X
ejpam-2199	351	31	)	)	PUNCT
ejpam-2199	351	32	∈	∈	PROPN
ejpam-2199	351	33	f	f	X
ejpam-2199	351	34	(	(	PUNCT
ejpam-2199	351	35	u	u	NOUN
ejpam-2199	351	36	)	)	PUNCT
ejpam-2199	351	37	and	and	CCONJ
ejpam-2199	351	38	c.	c.	PROPN
ejpam-2199	351	39	roika	roika	PROPN
ejpam-2199	351	40	,	,	PUNCT
ejpam-2199	351	41	s.	s.	PROPN
ejpam-2199	351	42	kudri	kudri	PROPN
ejpam-2199	351	43	,	,	PUNCT
ejpam-2199	351	44	t.	t.	PROPN
ejpam-2199	351	45	breuckmann	breuckmann	PROPN
ejpam-2199	351	46	/	/	SYM
ejpam-2199	351	47	eur	eur	PROPN
ejpam-2199	351	48	.	.	PUNCT
ejpam-2199	352	1	j.	j.	PROPN
ejpam-2199	352	2	pure	pure	PROPN
ejpam-2199	352	3	appl	appl	PROPN
ejpam-2199	352	4	.	.	PROPN
ejpam-2199	352	5	math	math	PROPN
ejpam-2199	352	6	,	,	PUNCT
ejpam-2199	352	7	8	8	NUM
ejpam-2199	352	8	(	(	PUNCT
ejpam-2199	352	9	2015	2015	NUM
ejpam-2199	352	10	)	)	PUNCT
ejpam-2199	352	11	,	,	PUNCT
ejpam-2199	352	12	514	514	NUM
ejpam-2199	352	13	-	-	SYM
ejpam-2199	352	14	525	525	NUM
ejpam-2199	352	15	524	524	NUM
ejpam-2199	352	16	since	since	SCONJ
ejpam-2199	352	17	u	u	PRON
ejpam-2199	352	18	hurewicz	hurewicz	NOUN
ejpam-2199	352	19	and	and	CCONJ
ejpam-2199	352	20	f	f	PROPN
ejpam-2199	352	21	is	be	AUX
ejpam-2199	352	22	continuous	continuous	ADJ
ejpam-2199	352	23	by	by	ADP
ejpam-2199	352	24	proposition	proposition	NOUN
ejpam-2199	352	25	4	4	NUM
ejpam-2199	352	26	f	f	NOUN
ejpam-2199	352	27	(	(	PUNCT
ejpam-2199	352	28	u	u	NOUN
ejpam-2199	352	29	)	)	PUNCT
ejpam-2199	352	30	is	be	AUX
ejpam-2199	352	31	hurewicz	hurewicz	NOUN
ejpam-2199	352	32	,	,	PUNCT
ejpam-2199	352	33	but	but	CCONJ
ejpam-2199	352	34	f	f	X
ejpam-2199	352	35	(	(	PUNCT
ejpam-2199	352	36	u	u	NOUN
ejpam-2199	352	37	)	)	PUNCT
ejpam-2199	352	38	⊂	⊂	PROPN
ejpam-2199	352	39	f	f	X
ejpam-2199	352	40	(	(	PUNCT
ejpam-2199	352	41	u	u	NOUN
ejpam-2199	352	42	)	)	PUNCT
ejpam-2199	352	43	.	.	PUNCT
ejpam-2199	353	1	since	since	SCONJ
ejpam-2199	353	2	y	y	PROPN
ejpam-2199	353	3	is	be	AUX
ejpam-2199	353	4	a	a	DET
ejpam-2199	353	5	hausdorff	hausdorff	NOUN
ejpam-2199	353	6	c	c	NOUN
ejpam-2199	353	7	-	-	PUNCT
ejpam-2199	353	8	space	space	NOUN
ejpam-2199	353	9	and	and	CCONJ
ejpam-2199	353	10	f	f	PROPN
ejpam-2199	353	11	(	(	PUNCT
ejpam-2199	353	12	u	u	NOUN
ejpam-2199	353	13	)	)	PUNCT
ejpam-2199	353	14	is	be	AUX
ejpam-2199	353	15	hurewicz	hurewicz	NOUN
ejpam-2199	353	16	,	,	PUNCT
ejpam-2199	353	17	we	we	PRON
ejpam-2199	353	18	have	have	VERB
ejpam-2199	353	19	that	that	PRON
ejpam-2199	353	20	f	f	PROPN
ejpam-2199	353	21	(	(	PUNCT
ejpam-2199	353	22	u	u	NOUN
ejpam-2199	353	23	)	)	PUNCT
ejpam-2199	353	24	is	be	AUX
ejpam-2199	353	25	closed	close	VERB
ejpam-2199	353	26	,	,	PUNCT
ejpam-2199	353	27	then	then	ADV
ejpam-2199	353	28	f	f	PROPN
ejpam-2199	353	29	(	(	PUNCT
ejpam-2199	353	30	u	u	NOUN
ejpam-2199	353	31	)	)	PUNCT
ejpam-2199	354	1	⊂	⊂	PROPN
ejpam-2199	354	2	f	f	X
ejpam-2199	354	3	(	(	PUNCT
ejpam-2199	354	4	u	u	NOUN
ejpam-2199	354	5	)	)	PUNCT
ejpam-2199	354	6	,	,	PUNCT
ejpam-2199	354	7	then	then	ADV
ejpam-2199	354	8	f	f	PROPN
ejpam-2199	354	9	(	(	PUNCT
ejpam-2199	354	10	u	u	NOUN
ejpam-2199	354	11	)	)	PUNCT
ejpam-2199	354	12	is	be	AUX
ejpam-2199	354	13	a	a	DET
ejpam-2199	354	14	closed	closed	ADJ
ejpam-2199	354	15	subspace	subspace	NOUN
ejpam-2199	354	16	of	of	ADP
ejpam-2199	354	17	a	a	DET
ejpam-2199	354	18	hausdorff	hausdorff	NOUN
ejpam-2199	354	19	space	space	NOUN
ejpam-2199	354	20	,	,	PUNCT
ejpam-2199	354	21	then	then	ADV
ejpam-2199	354	22	f	f	PROPN
ejpam-2199	354	23	(	(	PUNCT
ejpam-2199	354	24	u	u	NOUN
ejpam-2199	354	25	)	)	PUNCT
ejpam-2199	354	26	is	be	AUX
ejpam-2199	354	27	hurewicz	hurewicz	NOUN
ejpam-2199	354	28	,	,	PUNCT
ejpam-2199	354	29	so	so	ADV
ejpam-2199	355	1	y	y	PROPN
ejpam-2199	355	2	∈	∈	PROPN
ejpam-2199	355	3	f	f	X
ejpam-2199	355	4	(	(	PUNCT
ejpam-2199	355	5	u	u	NOUN
ejpam-2199	355	6	)	)	PUNCT
ejpam-2199	355	7	⊂	⊂	PROPN
ejpam-2199	355	8	f	f	X
ejpam-2199	355	9	(	(	PUNCT
ejpam-2199	355	10	u	u	NOUN
ejpam-2199	355	11	)	)	PUNCT
ejpam-2199	355	12	,	,	PUNCT
ejpam-2199	355	13	with	with	ADP
ejpam-2199	355	14	f	f	PROPN
ejpam-2199	355	15	(	(	PUNCT
ejpam-2199	355	16	u	u	NOUN
ejpam-2199	355	17	)	)	PUNCT
ejpam-2199	355	18	is	be	AUX
ejpam-2199	355	19	open	open	ADJ
ejpam-2199	355	20	and	and	CCONJ
ejpam-2199	355	21	f	f	PROPN
ejpam-2199	355	22	(	(	PUNCT
ejpam-2199	355	23	u	u	NOUN
ejpam-2199	355	24	)	)	PUNCT
ejpam-2199	355	25	hurewicz	hurewicz	NOUN
ejpam-2199	355	26	.	.	PUNCT
ejpam-2199	356	1	so	so	ADV
ejpam-2199	356	2	y	y	PROPN
ejpam-2199	356	3	is	be	AUX
ejpam-2199	356	4	a	a	DET
ejpam-2199	356	5	relatively	relatively	ADV
ejpam-2199	356	6	locally	locally	ADV
ejpam-2199	356	7	hurewicz	hurewicz	ADJ
ejpam-2199	356	8	space	space	NOUN
ejpam-2199	356	9	.	.	PUNCT
ejpam-2199	357	1	proposition	proposition	NOUN
ejpam-2199	357	2	23	23	NUM
ejpam-2199	357	3	.	.	PUNCT
ejpam-2199	358	1	let	let	VERB
ejpam-2199	358	2	〈	〈	PROPN
ejpam-2199	358	3	x	x	X
ejpam-2199	358	4	,	,	PUNCT
ejpam-2199	358	5	tx	tx	PROPN
ejpam-2199	358	6	〉	〉	NOUN
ejpam-2199	358	7	be	be	VERB
ejpam-2199	358	8	a	a	DET
ejpam-2199	358	9	locally	locally	ADV
ejpam-2199	358	10	hurewicz	hurewicz	ADJ
ejpam-2199	358	11	topological	topological	ADJ
ejpam-2199	358	12	space	space	NOUN
ejpam-2199	358	13	and	and	CCONJ
ejpam-2199	358	14	let	let	VERB
ejpam-2199	358	15	〈	〈	PROPN
ejpam-2199	358	16	y	y	PROPN
ejpam-2199	358	17	,	,	PUNCT
ejpam-2199	358	18	ty	ty	NUM
ejpam-2199	358	19	〉	〉	NOUN
ejpam-2199	358	20	be	be	VERB
ejpam-2199	358	21	a	a	DET
ejpam-2199	358	22	closed	closed	ADJ
ejpam-2199	358	23	subspace	subspace	NOUN
ejpam-2199	358	24	of	of	ADP
ejpam-2199	358	25	x	x	PRON
ejpam-2199	358	26	,	,	PUNCT
ejpam-2199	358	27	then	then	ADV
ejpam-2199	358	28	y	y	PROPN
ejpam-2199	358	29	is	be	AUX
ejpam-2199	358	30	locally	locally	ADV
ejpam-2199	358	31	hurewicz	hurewicz	NOUN
ejpam-2199	358	32	.	.	PUNCT
ejpam-2199	359	1	proof	proof	NOUN
ejpam-2199	359	2	.	.	PUNCT
ejpam-2199	360	1	consider	consider	VERB
ejpam-2199	360	2	y	y	PROPN
ejpam-2199	360	3	∈	∈	PROPN
ejpam-2199	360	4	y	y	PROPN
ejpam-2199	360	5	and	and	CCONJ
ejpam-2199	360	6	v	v	ADP
ejpam-2199	360	7	an	an	DET
ejpam-2199	360	8	open	open	ADJ
ejpam-2199	360	9	set	set	NOUN
ejpam-2199	360	10	in	in	ADP
ejpam-2199	360	11	y	y	PROPN
ejpam-2199	360	12	such	such	ADJ
ejpam-2199	360	13	that	that	SCONJ
ejpam-2199	360	14	y	y	PROPN
ejpam-2199	360	15	∈	∈	PROPN
ejpam-2199	360	16	v	v	NOUN
ejpam-2199	360	17	.	.	PUNCT
ejpam-2199	361	1	then	then	ADV
ejpam-2199	361	2	y	y	PROPN
ejpam-2199	361	3	∈	∈	PROPN
ejpam-2199	361	4	x	x	X
ejpam-2199	362	1	and	and	CCONJ
ejpam-2199	362	2	there	there	PRON
ejpam-2199	362	3	is	be	VERB
ejpam-2199	362	4	v	v	NOUN
ejpam-2199	362	5	′	′	NOUN
ejpam-2199	362	6	opens	open	VERB
ejpam-2199	362	7	in	in	ADP
ejpam-2199	362	8	x	x	SYM
ejpam-2199	362	9	,	,	PUNCT
ejpam-2199	362	10	such	such	ADJ
ejpam-2199	362	11	that	that	DET
ejpam-2199	362	12	v	v	NOUN
ejpam-2199	362	13	=	=	SYM
ejpam-2199	362	14	v	v	NOUN
ejpam-2199	362	15	′	′	NOUN
ejpam-2199	362	16	∩	∩	NOUN
ejpam-2199	362	17	x	x	X
ejpam-2199	362	18	.	.	PUNCT
ejpam-2199	363	1	since	since	SCONJ
ejpam-2199	363	2	x	x	PRON
ejpam-2199	363	3	is	be	AUX
ejpam-2199	363	4	locally	locally	ADV
ejpam-2199	363	5	hurewicz	hurewicz	NOUN
ejpam-2199	363	6	,	,	PUNCT
ejpam-2199	363	7	there	there	PRON
ejpam-2199	363	8	are	be	VERB
ejpam-2199	363	9	u	u	NOUN
ejpam-2199	363	10	′	′	NOUN
ejpam-2199	363	11	open	open	ADJ
ejpam-2199	363	12	in	in	ADP
ejpam-2199	363	13	x	x	PUNCT
ejpam-2199	364	1	and	and	CCONJ
ejpam-2199	364	2	h	h	NOUN
ejpam-2199	364	3	hurewicz	hurewicz	NOUN
ejpam-2199	364	4	such	such	ADJ
ejpam-2199	364	5	that	that	SCONJ
ejpam-2199	364	6	y	y	PROPN
ejpam-2199	364	7	∈	∈	PROPN
ejpam-2199	364	8	u	u	NOUN
ejpam-2199	365	1	′	′	NOUN
ejpam-2199	365	2	⊂	⊂	PROPN
ejpam-2199	365	3	h	h	PROPN
ejpam-2199	366	1	⊂	⊂	PROPN
ejpam-2199	366	2	v	v	PROPN
ejpam-2199	366	3	′	′	NUM
ejpam-2199	366	4	,	,	PUNCT
ejpam-2199	366	5	but	but	CCONJ
ejpam-2199	366	6	since	since	SCONJ
ejpam-2199	366	7	y	y	PROPN
ejpam-2199	366	8	∈	∈	PROPN
ejpam-2199	366	9	y	y	NOUN
ejpam-2199	366	10	we	we	PRON
ejpam-2199	366	11	have	have	VERB
ejpam-2199	366	12	that	that	DET
ejpam-2199	366	13	y	y	PROPN
ejpam-2199	366	14	∈	∈	PROPN
ejpam-2199	366	15	u	u	NOUN
ejpam-2199	366	16	′	′	NOUN
ejpam-2199	366	17	∩	∩	PROPN
ejpam-2199	366	18	y	y	PROPN
ejpam-2199	366	19	⊂	⊂	PROPN
ejpam-2199	366	20	h	h	PROPN
ejpam-2199	366	21	∩	∩	PROPN
ejpam-2199	366	22	y	y	PROPN
ejpam-2199	366	23	⊂	⊂	PROPN
ejpam-2199	366	24	v	v	ADP
ejpam-2199	366	25	′	′	NUM
ejpam-2199	366	26	∩	∩	ADJ
ejpam-2199	366	27	y	y	PROPN
ejpam-2199	366	28	=	=	SYM
ejpam-2199	366	29	v	v	PROPN
ejpam-2199	366	30	,	,	PUNCT
ejpam-2199	366	31	where	where	SCONJ
ejpam-2199	366	32	u	u	NOUN
ejpam-2199	366	33	′	′	PROPN
ejpam-2199	366	34	∩	∩	NOUN
ejpam-2199	366	35	y	y	PROPN
ejpam-2199	366	36	is	be	AUX
ejpam-2199	366	37	open	open	ADJ
ejpam-2199	366	38	in	in	ADP
ejpam-2199	366	39	y	y	PROPN
ejpam-2199	366	40	and	and	CCONJ
ejpam-2199	366	41	h	h	PROPN
ejpam-2199	366	42	∩	∩	NOUN
ejpam-2199	366	43	y	y	PROPN
ejpam-2199	366	44	is	be	AUX
ejpam-2199	366	45	hurewicz	hurewicz	VERB
ejpam-2199	366	46	by	by	ADP
ejpam-2199	366	47	proposition	proposition	NOUN
ejpam-2199	366	48	7	7	NUM
ejpam-2199	366	49	.	.	PUNCT
ejpam-2199	367	1	therefore	therefore	ADV
ejpam-2199	367	2	y	y	PROPN
ejpam-2199	367	3	is	be	AUX
ejpam-2199	367	4	locally	locally	ADV
ejpam-2199	367	5	hurewicz	hurewicz	NOUN
ejpam-2199	367	6	.	.	PUNCT
ejpam-2199	368	1	proposition	proposition	NOUN
ejpam-2199	368	2	24	24	NUM
ejpam-2199	368	3	.	.	PUNCT
ejpam-2199	369	1	let	let	VERB
ejpam-2199	369	2	〈	〈	PROPN
ejpam-2199	369	3	x	x	X
ejpam-2199	369	4	,	,	PUNCT
ejpam-2199	369	5	tx	tx	PROPN
ejpam-2199	369	6	〉	〉	NOUN
ejpam-2199	369	7	be	be	VERB
ejpam-2199	369	8	a	a	DET
ejpam-2199	369	9	weakly	weakly	ADJ
ejpam-2199	369	10	locally	locally	ADV
ejpam-2199	369	11	hurewicz	hurewicz	ADJ
ejpam-2199	369	12	topological	topological	ADJ
ejpam-2199	369	13	space	space	NOUN
ejpam-2199	369	14	and	and	CCONJ
ejpam-2199	369	15	let	let	VERB
ejpam-2199	369	16	〈	〈	PROPN
ejpam-2199	369	17	y	y	PROPN
ejpam-2199	369	18	,	,	PUNCT
ejpam-2199	369	19	ty	ty	NUM
ejpam-2199	369	20	〉	〉	NOUN
ejpam-2199	369	21	be	be	VERB
ejpam-2199	369	22	a	a	DET
ejpam-2199	369	23	closed	closed	ADJ
ejpam-2199	369	24	subspace	subspace	NOUN
ejpam-2199	369	25	of	of	ADP
ejpam-2199	369	26	x	x	PRON
ejpam-2199	369	27	,	,	PUNCT
ejpam-2199	369	28	then	then	ADV
ejpam-2199	369	29	y	y	PROPN
ejpam-2199	369	30	is	be	AUX
ejpam-2199	369	31	weakly	weakly	ADV
ejpam-2199	369	32	locally	locally	ADV
ejpam-2199	369	33	hurewicz	hurewicz	NOUN
ejpam-2199	369	34	.	.	PUNCT
ejpam-2199	370	1	proof	proof	NOUN
ejpam-2199	370	2	.	.	PUNCT
ejpam-2199	371	1	consider	consider	VERB
ejpam-2199	371	2	y	y	PROPN
ejpam-2199	371	3	∈	∈	PROPN
ejpam-2199	371	4	y	y	PROPN
ejpam-2199	371	5	.	.	PUNCT
ejpam-2199	372	1	then	then	ADV
ejpam-2199	372	2	there	there	PRON
ejpam-2199	372	3	is	be	VERB
ejpam-2199	372	4	u	u	PROPN
ejpam-2199	372	5	∈	∈	PROPN
ejpam-2199	372	6	tx	tx	PROPN
ejpam-2199	372	7	and	and	CCONJ
ejpam-2199	372	8	h	h	NOUN
ejpam-2199	372	9	hurewicz	hurewicz	NOUN
ejpam-2199	372	10	in	in	ADP
ejpam-2199	372	11	x	x	INTJ
ejpam-2199	372	12	such	such	ADJ
ejpam-2199	372	13	that	that	SCONJ
ejpam-2199	372	14	y	y	PROPN
ejpam-2199	372	15	∈	∈	PROPN
ejpam-2199	372	16	u	u	PROPN
ejpam-2199	372	17	⊂	⊂	PROPN
ejpam-2199	372	18	h.	h.	PROPN
ejpam-2199	373	1	so	so	ADV
ejpam-2199	373	2	we	we	PRON
ejpam-2199	373	3	have	have	VERB
ejpam-2199	373	4	that	that	PRON
ejpam-2199	373	5	y	y	PROPN
ejpam-2199	373	6	∈	∈	PROPN
ejpam-2199	373	7	u	u	PROPN
ejpam-2199	373	8	∩	∩	PROPN
ejpam-2199	373	9	y	y	PROPN
ejpam-2199	373	10	⊂	⊂	PROPN
ejpam-2199	373	11	h	h	PROPN
ejpam-2199	373	12	∩	∩	PROPN
ejpam-2199	373	13	y	y	PROPN
ejpam-2199	373	14	,	,	PUNCT
ejpam-2199	373	15	where	where	SCONJ
ejpam-2199	373	16	u	u	PROPN
ejpam-2199	373	17	∩	∩	NOUN
ejpam-2199	373	18	y	y	PROPN
ejpam-2199	373	19	is	be	AUX
ejpam-2199	373	20	open	open	ADJ
ejpam-2199	373	21	in	in	ADP
ejpam-2199	373	22	y	y	PROPN
ejpam-2199	373	23	and	and	CCONJ
ejpam-2199	373	24	h	h	PROPN
ejpam-2199	373	25	∩	∩	NOUN
ejpam-2199	373	26	y	y	PROPN
ejpam-2199	373	27	is	be	AUX
ejpam-2199	373	28	hurewicz	hurewicz	VERB
ejpam-2199	373	29	by	by	ADP
ejpam-2199	373	30	proposition	proposition	NOUN
ejpam-2199	373	31	7	7	NUM
ejpam-2199	373	32	,	,	PUNCT
ejpam-2199	373	33	then	then	ADV
ejpam-2199	373	34	y	y	PROPN
ejpam-2199	373	35	is	be	AUX
ejpam-2199	373	36	weakly	weakly	ADV
ejpam-2199	373	37	locally	locally	ADV
ejpam-2199	373	38	hurewicz	hurewicz	NOUN
ejpam-2199	373	39	.	.	PUNCT
ejpam-2199	374	1	proposition	proposition	NOUN
ejpam-2199	374	2	25	25	NUM
ejpam-2199	374	3	.	.	PUNCT
ejpam-2199	375	1	let	let	VERB
ejpam-2199	375	2	〈	〈	PROPN
ejpam-2199	375	3	x	x	X
ejpam-2199	375	4	,	,	PUNCT
ejpam-2199	375	5	tx	tx	PROPN
ejpam-2199	375	6	〉	〉	NOUN
ejpam-2199	375	7	be	be	VERB
ejpam-2199	375	8	a	a	DET
ejpam-2199	375	9	relatively	relatively	ADV
ejpam-2199	375	10	locally	locally	ADV
ejpam-2199	375	11	hurewicz	hurewicz	ADJ
ejpam-2199	375	12	topological	topological	ADJ
ejpam-2199	375	13	space	space	NOUN
ejpam-2199	375	14	and	and	CCONJ
ejpam-2199	375	15	let	let	VERB
ejpam-2199	375	16	〈	〈	PROPN
ejpam-2199	375	17	y	y	PROPN
ejpam-2199	375	18	,	,	PUNCT
ejpam-2199	375	19	ty	ty	NUM
ejpam-2199	375	20	〉	〉	NOUN
ejpam-2199	375	21	be	be	VERB
ejpam-2199	375	22	a	a	DET
ejpam-2199	375	23	closed	closed	ADJ
ejpam-2199	375	24	subspace	subspace	NOUN
ejpam-2199	375	25	of	of	ADP
ejpam-2199	375	26	x	x	PRON
ejpam-2199	375	27	,	,	PUNCT
ejpam-2199	375	28	then	then	ADV
ejpam-2199	375	29	y	y	PROPN
ejpam-2199	375	30	is	be	AUX
ejpam-2199	375	31	relatively	relatively	ADV
ejpam-2199	375	32	locally	locally	ADV
ejpam-2199	375	33	hurewicz	hurewicz	NOUN
ejpam-2199	375	34	.	.	PUNCT
ejpam-2199	376	1	proof	proof	NOUN
ejpam-2199	376	2	.	.	PUNCT
ejpam-2199	377	1	consider	consider	VERB
ejpam-2199	377	2	y	y	PROPN
ejpam-2199	377	3	∈	∈	PROPN
ejpam-2199	377	4	y	y	PROPN
ejpam-2199	377	5	.	.	PUNCT
ejpam-2199	378	1	then	then	ADV
ejpam-2199	378	2	there	there	PRON
ejpam-2199	378	3	exists	exist	VERB
ejpam-2199	378	4	u	u	PROPN
ejpam-2199	378	5	∈	∈	PROPN
ejpam-2199	378	6	tx	tx	PROPN
ejpam-2199	378	7	with	with	ADP
ejpam-2199	378	8	u	u	NOUN
ejpam-2199	378	9	hurewicz	hurewicz	NOUN
ejpam-2199	378	10	and	and	CCONJ
ejpam-2199	378	11	y	y	PROPN
ejpam-2199	378	12	∈	∈	PROPN
ejpam-2199	378	13	u	u	PROPN
ejpam-2199	378	14	.	.	PUNCT
ejpam-2199	379	1	then	then	ADV
ejpam-2199	379	2	y	y	PROPN
ejpam-2199	379	3	∈	∈	PROPN
ejpam-2199	379	4	u∩y	u∩y	PROPN
ejpam-2199	379	5	and	and	CCONJ
ejpam-2199	379	6	by	by	ADP
ejpam-2199	379	7	proposition	proposition	NOUN
ejpam-2199	379	8	7	7	NUM
ejpam-2199	379	9	u∩y	u∩y	PROPN
ejpam-2199	379	10	is	be	AUX
ejpam-2199	379	11	hurewicz	hurewicz	NOUN
ejpam-2199	379	12	,	,	PUNCT
ejpam-2199	379	13	but	but	CCONJ
ejpam-2199	379	14	u	u	NOUN
ejpam-2199	379	15	∩	∩	PROPN
ejpam-2199	379	16	y	y	PROPN
ejpam-2199	379	17	⊂	⊂	PROPN
ejpam-2199	379	18	u∩y	u∩y	PROPN
ejpam-2199	379	19	=	=	SYM
ejpam-2199	379	20	u∩y	u∩y	PROPN
ejpam-2199	379	21	.	.	PUNCT
ejpam-2199	380	1	by	by	ADP
ejpam-2199	380	2	proposition	proposition	NOUN
ejpam-2199	380	3	6	6	NUM
ejpam-2199	380	4	we	we	PRON
ejpam-2199	380	5	have	have	VERB
ejpam-2199	380	6	that	that	DET
ejpam-2199	380	7	u	u	PROPN
ejpam-2199	380	8	∩	∩	NOUN
ejpam-2199	380	9	y	y	PROPN
ejpam-2199	380	10	is	be	AUX
ejpam-2199	380	11	hurewicz	hurewicz	NOUN
ejpam-2199	380	12	,	,	PUNCT
ejpam-2199	380	13	hence	hence	ADV
ejpam-2199	380	14	y	y	PROPN
ejpam-2199	380	15	is	be	AUX
ejpam-2199	380	16	relatively	relatively	ADV
ejpam-2199	380	17	locally	locally	ADV
ejpam-2199	380	18	hurewicz	hurewicz	NOUN
ejpam-2199	380	19	.	.	PUNCT
ejpam-2199	381	1	proposition	proposition	NOUN
ejpam-2199	381	2	26	26	NUM
ejpam-2199	381	3	.	.	PUNCT
ejpam-2199	382	1	let	let	VERB
ejpam-2199	382	2	x	x	PRON
ejpam-2199	382	3	be	be	AUX
ejpam-2199	382	4	a	a	DET
ejpam-2199	382	5	weakly	weakly	ADJ
ejpam-2199	382	6	locally	locally	ADV
ejpam-2199	382	7	hurewicz	hurewicz	ADJ
ejpam-2199	382	8	topological	topological	ADJ
ejpam-2199	382	9	space	space	NOUN
ejpam-2199	382	10	then	then	ADV
ejpam-2199	382	11	a⊂	a⊂	VERB
ejpam-2199	382	12	x	x	PUNCT
ejpam-2199	382	13	is	be	AUX
ejpam-2199	382	14	open	open	ADJ
ejpam-2199	382	15	in	in	ADP
ejpam-2199	382	16	x	x	SYM
ejpam-2199	382	17	if	if	SCONJ
ejpam-2199	382	18	and	and	CCONJ
ejpam-2199	382	19	only	only	ADV
ejpam-2199	382	20	if	if	SCONJ
ejpam-2199	382	21	,	,	PUNCT
ejpam-2199	382	22	a∩	a∩	PROPN
ejpam-2199	382	23	h	h	NOUN
ejpam-2199	382	24	is	be	AUX
ejpam-2199	382	25	open	open	ADJ
ejpam-2199	382	26	in	in	ADP
ejpam-2199	382	27	h	h	NOUN
ejpam-2199	382	28	for	for	ADP
ejpam-2199	382	29	each	each	DET
ejpam-2199	382	30	h	h	NOUN
ejpam-2199	382	31	hurewicz	hurewicz	NOUN
ejpam-2199	382	32	.	.	PUNCT
ejpam-2199	383	1	proof	proof	NOUN
ejpam-2199	383	2	.	.	PUNCT
ejpam-2199	384	1	(	(	PUNCT
ejpam-2199	384	2	⇒	⇒	PROPN
ejpam-2199	384	3	)	)	PUNCT
ejpam-2199	384	4	if	if	SCONJ
ejpam-2199	384	5	a	a	PRON
ejpam-2199	384	6	is	be	AUX
ejpam-2199	384	7	open	open	ADJ
ejpam-2199	384	8	in	in	ADP
ejpam-2199	384	9	x	x	PUNCT
ejpam-2199	384	10	then	then	ADV
ejpam-2199	384	11	a∩	a∩	PROPN
ejpam-2199	384	12	h	h	NOUN
ejpam-2199	384	13	is	be	AUX
ejpam-2199	384	14	open	open	ADJ
ejpam-2199	384	15	in	in	ADP
ejpam-2199	384	16	h.	h.	PROPN
ejpam-2199	384	17	(	(	PUNCT
ejpam-2199	384	18	⇐	⇐	ADJ
ejpam-2199	384	19	)	)	PUNCT
ejpam-2199	384	20	consider	consider	VERB
ejpam-2199	384	21	a	a	DET
ejpam-2199	384	22	∈	∈	NOUN
ejpam-2199	384	23	a.	a.	NOUN
ejpam-2199	384	24	we	we	PRON
ejpam-2199	384	25	have	have	VERB
ejpam-2199	384	26	that	that	PRON
ejpam-2199	384	27	a	a	DET
ejpam-2199	384	28	∈	∈	NOUN
ejpam-2199	384	29	x	x	X
ejpam-2199	384	30	and	and	CCONJ
ejpam-2199	384	31	since	since	SCONJ
ejpam-2199	384	32	x	x	PRON
ejpam-2199	384	33	is	be	AUX
ejpam-2199	384	34	weakly	weakly	ADV
ejpam-2199	384	35	locally	locally	ADV
ejpam-2199	384	36	hurewicz	hurewicz	NOUN
ejpam-2199	384	37	there	there	PRON
ejpam-2199	384	38	are	be	VERB
ejpam-2199	384	39	u	u	PROPN
ejpam-2199	384	40	∈	∈	PROPN
ejpam-2199	384	41	tx	tx	NOUN
ejpam-2199	384	42	and	and	CCONJ
ejpam-2199	384	43	h	h	NOUN
ejpam-2199	384	44	hurewicz	hurewicz	NOUN
ejpam-2199	384	45	in	in	ADP
ejpam-2199	384	46	x	x	INTJ
ejpam-2199	384	47	such	such	ADJ
ejpam-2199	384	48	that	that	SCONJ
ejpam-2199	384	49	a	a	DET
ejpam-2199	384	50	∈	∈	PROPN
ejpam-2199	384	51	u	u	NOUN
ejpam-2199	384	52	⊂	⊂	PROPN
ejpam-2199	384	53	h.	h.	PROPN
ejpam-2199	384	54	since	since	SCONJ
ejpam-2199	384	55	h	h	PROPN
ejpam-2199	384	56	is	be	AUX
ejpam-2199	384	57	hurewicz	hurewicz	NOUN
ejpam-2199	384	58	,	,	PUNCT
ejpam-2199	384	59	a∩	a∩	PROPN
ejpam-2199	384	60	h	h	NOUN
ejpam-2199	384	61	is	be	AUX
ejpam-2199	384	62	open	open	ADJ
ejpam-2199	384	63	in	in	ADP
ejpam-2199	384	64	h	h	NOUN
ejpam-2199	384	65	,	,	PUNCT
ejpam-2199	384	66	then	then	ADV
ejpam-2199	384	67	since	since	SCONJ
ejpam-2199	384	68	a∩u	a∩u	PROPN
ejpam-2199	384	69	=	=	SYM
ejpam-2199	384	70	(	(	PUNCT
ejpam-2199	384	71	a∩h)∩u	a∩h)∩u	NOUN
ejpam-2199	384	72	we	we	PRON
ejpam-2199	384	73	have	have	VERB
ejpam-2199	384	74	that	that	DET
ejpam-2199	384	75	a∩u	a∩u	PROPN
ejpam-2199	384	76	is	be	AUX
ejpam-2199	384	77	open	open	ADJ
ejpam-2199	384	78	in	in	ADP
ejpam-2199	384	79	u	u	PROPN
ejpam-2199	384	80	,	,	PUNCT
ejpam-2199	384	81	then	then	ADV
ejpam-2199	384	82	there	there	PRON
ejpam-2199	384	83	is	be	VERB
ejpam-2199	384	84	v	v	ADP
ejpam-2199	384	85	∈	∈	NOUN
ejpam-2199	384	86	tx	tx	NOUN
ejpam-2199	384	87	such	such	ADJ
ejpam-2199	384	88	that	that	SCONJ
ejpam-2199	384	89	a∩	a∩	PROPN
ejpam-2199	384	90	u	u	NOUN
ejpam-2199	384	91	=	=	SYM
ejpam-2199	384	92	u	u	PROPN
ejpam-2199	384	93	∩	∩	NOUN
ejpam-2199	384	94	v	v	NOUN
ejpam-2199	384	95	,	,	PUNCT
ejpam-2199	384	96	but	but	CCONJ
ejpam-2199	384	97	since	since	SCONJ
ejpam-2199	384	98	u	u	NOUN
ejpam-2199	384	99	and	and	CCONJ
ejpam-2199	384	100	v	v	NOUN
ejpam-2199	384	101	are	be	AUX
ejpam-2199	384	102	open	open	ADJ
ejpam-2199	384	103	in	in	ADP
ejpam-2199	384	104	x	x	VERB
ejpam-2199	384	105	we	we	PRON
ejpam-2199	384	106	have	have	VERB
ejpam-2199	384	107	that	that	SCONJ
ejpam-2199	384	108	u	u	PROPN
ejpam-2199	384	109	∩	∩	NOUN
ejpam-2199	384	110	v	v	NOUN
ejpam-2199	384	111	is	be	AUX
ejpam-2199	384	112	open	open	ADJ
ejpam-2199	384	113	in	in	ADP
ejpam-2199	384	114	x	x	PUNCT
ejpam-2199	384	115	and	and	CCONJ
ejpam-2199	384	116	u	u	PROPN
ejpam-2199	384	117	∩	∩	NOUN
ejpam-2199	384	118	a	a	PRON
ejpam-2199	384	119	is	be	AUX
ejpam-2199	384	120	open	open	ADJ
ejpam-2199	384	121	in	in	ADP
ejpam-2199	384	122	x	x	X
ejpam-2199	384	123	,	,	PUNCT
ejpam-2199	384	124	hence	hence	ADV
ejpam-2199	384	125	a	a	DET
ejpam-2199	384	126	∈	∈	PROPN
ejpam-2199	384	127	a∩	a∩	PROPN
ejpam-2199	384	128	u	u	X
ejpam-2199	384	129	⊂	⊂	PROPN
ejpam-2199	384	130	a	a	X
ejpam-2199	384	131	,	,	PUNCT
ejpam-2199	384	132	whit	whit	NOUN
ejpam-2199	384	133	a∩	a∩	PROPN
ejpam-2199	384	134	u	u	NOUN
ejpam-2199	384	135	open	open	ADJ
ejpam-2199	384	136	in	in	ADP
ejpam-2199	384	137	x	x	X
ejpam-2199	384	138	.	.	PUNCT
ejpam-2199	385	1	then	then	ADV
ejpam-2199	385	2	a	a	PRON
ejpam-2199	385	3	is	be	AUX
ejpam-2199	385	4	open	open	ADJ
ejpam-2199	385	5	.	.	PUNCT
ejpam-2199	386	1	proposition	proposition	NOUN
ejpam-2199	386	2	27	27	NUM
ejpam-2199	386	3	.	.	PUNCT
ejpam-2199	387	1	let	let	VERB
ejpam-2199	387	2	x	x	PRON
ejpam-2199	387	3	be	be	AUX
ejpam-2199	387	4	a	a	DET
ejpam-2199	387	5	locally	locally	ADV
ejpam-2199	387	6	hurewicz	hurewicz	ADJ
ejpam-2199	387	7	topological	topological	ADJ
ejpam-2199	387	8	space	space	NOUN
ejpam-2199	387	9	,	,	PUNCT
ejpam-2199	387	10	then	then	ADV
ejpam-2199	387	11	a	a	DET
ejpam-2199	387	12	subset	subset	NOUN
ejpam-2199	387	13	a	a	PRON
ejpam-2199	387	14	of	of	ADP
ejpam-2199	387	15	x	x	NOUN
ejpam-2199	387	16	is	be	AUX
ejpam-2199	387	17	open	open	ADJ
ejpam-2199	387	18	in	in	ADP
ejpam-2199	387	19	x	x	SYM
ejpam-2199	387	20	if	if	SCONJ
ejpam-2199	388	1	and	and	CCONJ
ejpam-2199	388	2	only	only	ADV
ejpam-2199	388	3	if	if	SCONJ
ejpam-2199	388	4	,	,	PUNCT
ejpam-2199	388	5	a∩	a∩	PROPN
ejpam-2199	388	6	h	h	NOUN
ejpam-2199	388	7	is	be	AUX
ejpam-2199	388	8	open	open	ADJ
ejpam-2199	388	9	in	in	ADP
ejpam-2199	388	10	h	h	NOUN
ejpam-2199	388	11	for	for	ADP
ejpam-2199	388	12	each	each	DET
ejpam-2199	388	13	h	h	NOUN
ejpam-2199	388	14	hurewicz	hurewicz	NOUN
ejpam-2199	388	15	.	.	PUNCT
ejpam-2199	389	1	references	reference	NOUN
ejpam-2199	389	2	525	525	NUM
ejpam-2199	389	3	proof	proof	NOUN
ejpam-2199	389	4	.	.	PUNCT
ejpam-2199	390	1	(	(	PUNCT
ejpam-2199	390	2	⇒	⇒	PROPN
ejpam-2199	390	3	)	)	PUNCT
ejpam-2199	390	4	if	if	SCONJ
ejpam-2199	390	5	a	a	PRON
ejpam-2199	390	6	is	be	AUX
ejpam-2199	390	7	open	open	ADJ
ejpam-2199	390	8	in	in	ADP
ejpam-2199	390	9	x	x	PUNCT
ejpam-2199	390	10	then	then	ADV
ejpam-2199	390	11	a∩	a∩	PROPN
ejpam-2199	390	12	h	h	NOUN
ejpam-2199	390	13	is	be	AUX
ejpam-2199	390	14	open	open	ADJ
ejpam-2199	390	15	in	in	ADP
ejpam-2199	390	16	h.	h.	PROPN
ejpam-2199	390	17	(	(	PUNCT
ejpam-2199	390	18	⇐	⇐	ADJ
ejpam-2199	390	19	)	)	PUNCT
ejpam-2199	390	20	let	let	VERB
ejpam-2199	390	21	a⊂	a⊂	NOUN
ejpam-2199	390	22	x	x	ADP
ejpam-2199	390	23	such	such	ADJ
ejpam-2199	390	24	that	that	SCONJ
ejpam-2199	390	25	a∩	a∩	PROPN
ejpam-2199	390	26	h	h	NOUN
ejpam-2199	390	27	is	be	AUX
ejpam-2199	390	28	open	open	ADJ
ejpam-2199	390	29	in	in	ADP
ejpam-2199	390	30	h	h	NOUN
ejpam-2199	390	31	for	for	ADP
ejpam-2199	390	32	each	each	DET
ejpam-2199	390	33	h	h	NOUN
ejpam-2199	390	34	hurewicz	hurewicz	NOUN
ejpam-2199	390	35	,	,	PUNCT
ejpam-2199	390	36	then	then	ADV
ejpam-2199	390	37	by	by	ADP
ejpam-2199	390	38	proposition	proposition	NOUN
ejpam-2199	390	39	13	13	NUM
ejpam-2199	390	40	we	we	PRON
ejpam-2199	390	41	have	have	VERB
ejpam-2199	390	42	that	that	PRON
ejpam-2199	390	43	x	x	PRON
ejpam-2199	390	44	is	be	AUX
ejpam-2199	390	45	weakly	weakly	ADV
ejpam-2199	390	46	locally	locally	ADV
ejpam-2199	390	47	hurewicz	hurewicz	NOUN
ejpam-2199	390	48	and	and	CCONJ
ejpam-2199	390	49	by	by	ADP
ejpam-2199	390	50	proposition	proposition	NOUN
ejpam-2199	390	51	26	26	NUM
ejpam-2199	390	52	we	we	PRON
ejpam-2199	390	53	have	have	VERB
ejpam-2199	390	54	that	that	SCONJ
ejpam-2199	390	55	a	a	PRON
ejpam-2199	390	56	is	be	AUX
ejpam-2199	390	57	open	open	ADJ
ejpam-2199	390	58	in	in	ADP
ejpam-2199	390	59	x	x	X
ejpam-2199	390	60	.	.	PUNCT
ejpam-2199	391	1	proposition	proposition	NOUN
ejpam-2199	391	2	28	28	NUM
ejpam-2199	391	3	.	.	PUNCT
ejpam-2199	392	1	let	let	VERB
ejpam-2199	392	2	x	x	PRON
ejpam-2199	392	3	be	be	AUX
ejpam-2199	392	4	a	a	DET
ejpam-2199	392	5	relatively	relatively	ADV
ejpam-2199	392	6	locally	locally	ADV
ejpam-2199	392	7	hurewicz	hurewicz	ADJ
ejpam-2199	392	8	topological	topological	ADJ
ejpam-2199	392	9	space	space	NOUN
ejpam-2199	392	10	and	and	CCONJ
ejpam-2199	392	11	a	a	DET
ejpam-2199	392	12	⊂	⊂	PROPN
ejpam-2199	392	13	x	x	X
ejpam-2199	392	14	,	,	PUNCT
ejpam-2199	392	15	then	then	ADV
ejpam-2199	392	16	a	a	PRON
ejpam-2199	392	17	is	be	AUX
ejpam-2199	392	18	open	open	ADJ
ejpam-2199	392	19	in	in	ADP
ejpam-2199	392	20	x	x	SYM
ejpam-2199	392	21	if	if	SCONJ
ejpam-2199	392	22	and	and	CCONJ
ejpam-2199	392	23	only	only	ADV
ejpam-2199	392	24	if	if	SCONJ
ejpam-2199	392	25	,	,	PUNCT
ejpam-2199	392	26	a∩	a∩	PROPN
ejpam-2199	392	27	h	h	NOUN
ejpam-2199	392	28	is	be	AUX
ejpam-2199	392	29	open	open	ADJ
ejpam-2199	392	30	in	in	ADP
ejpam-2199	392	31	h	h	NOUN
ejpam-2199	392	32	for	for	ADP
ejpam-2199	392	33	each	each	DET
ejpam-2199	392	34	h	h	NOUN
ejpam-2199	392	35	hurewicz	hurewicz	NOUN
ejpam-2199	392	36	.	.	PUNCT
ejpam-2199	393	1	proof	proof	NOUN
ejpam-2199	393	2	.	.	PUNCT
ejpam-2199	394	1	(	(	PUNCT
ejpam-2199	394	2	⇒	⇒	PROPN
ejpam-2199	394	3	)	)	PUNCT
ejpam-2199	394	4	if	if	SCONJ
ejpam-2199	394	5	a	a	PRON
ejpam-2199	394	6	is	be	AUX
ejpam-2199	394	7	open	open	ADJ
ejpam-2199	394	8	in	in	ADP
ejpam-2199	394	9	x	x	PUNCT
ejpam-2199	394	10	then	then	ADV
ejpam-2199	394	11	a∩	a∩	PROPN
ejpam-2199	394	12	h	h	NOUN
ejpam-2199	394	13	is	be	AUX
ejpam-2199	394	14	open	open	ADJ
ejpam-2199	394	15	in	in	ADP
ejpam-2199	394	16	h.	h.	PROPN
ejpam-2199	394	17	(	(	PUNCT
ejpam-2199	394	18	⇐	⇐	PROPN
ejpam-2199	394	19	)	)	PUNCT
ejpam-2199	394	20	if	if	SCONJ
ejpam-2199	394	21	a∩h	a∩h	NOUN
ejpam-2199	394	22	is	be	AUX
ejpam-2199	394	23	open	open	ADJ
ejpam-2199	394	24	in	in	ADP
ejpam-2199	394	25	h	h	NOUN
ejpam-2199	394	26	for	for	ADP
ejpam-2199	394	27	each	each	DET
ejpam-2199	394	28	h	h	NOUN
ejpam-2199	394	29	hurewicz	hurewicz	NOUN
ejpam-2199	394	30	,	,	PUNCT
ejpam-2199	394	31	by	by	ADP
ejpam-2199	394	32	proposition	proposition	NOUN
ejpam-2199	394	33	14	14	NUM
ejpam-2199	394	34	we	we	PRON
ejpam-2199	394	35	have	have	VERB
ejpam-2199	394	36	that	that	PRON
ejpam-2199	394	37	x	x	PRON
ejpam-2199	394	38	is	be	AUX
ejpam-2199	394	39	weakly	weakly	ADV
ejpam-2199	394	40	locally	locally	ADV
ejpam-2199	394	41	hurewicz	hurewicz	NOUN
ejpam-2199	394	42	and	and	CCONJ
ejpam-2199	394	43	by	by	ADP
ejpam-2199	394	44	proposition	proposition	NOUN
ejpam-2199	394	45	26	26	NUM
ejpam-2199	394	46	we	we	PRON
ejpam-2199	394	47	have	have	VERB
ejpam-2199	394	48	that	that	SCONJ
ejpam-2199	394	49	a	a	PRON
ejpam-2199	394	50	is	be	AUX
ejpam-2199	394	51	open	open	ADJ
ejpam-2199	394	52	in	in	ADP
ejpam-2199	394	53	x	x	X
ejpam-2199	394	54	.	.	PUNCT
ejpam-2199	395	1	references	reference	NOUN
ejpam-2199	395	2	[	[	X
ejpam-2199	395	3	1	1	NUM
ejpam-2199	395	4	]	]	PUNCT
ejpam-2199	395	5	f.	f.	PROPN
ejpam-2199	395	6	cammaroto	cammaroto	PROPN
ejpam-2199	395	7	and	and	CCONJ
ejpam-2199	395	8	g.	g.	PROPN
ejpam-2199	395	9	santoro	santoro	PROPN
ejpam-2199	395	10	.	.	PUNCT
ejpam-2199	396	1	some	some	DET
ejpam-2199	396	2	counterexamples	counterexample	NOUN
ejpam-2199	396	3	and	and	CCONJ
ejpam-2199	396	4	properties	property	NOUN
ejpam-2199	396	5	on	on	ADP
ejpam-2199	396	6	generalizations	generalization	NOUN
ejpam-2199	396	7	of	of	ADP
ejpam-2199	396	8	lindelöf	lindelöf	NOUN
ejpam-2199	396	9	spaces	space	NOUN
ejpam-2199	396	10	,	,	PUNCT
ejpam-2199	396	11	international	international	ADJ
ejpam-2199	396	12	journal	journal	NOUN
ejpam-2199	396	13	of	of	ADP
ejpam-2199	396	14	mathematical	mathematical	ADJ
ejpam-2199	396	15	sciences	sciences	PROPN
ejpam-2199	396	16	,	,	PUNCT
ejpam-2199	396	17	19(4	19(4	NOUN
ejpam-2199	396	18	)	)	PUNCT
ejpam-2199	396	19	,	,	PUNCT
ejpam-2199	396	20	737–746	737–746	NUM
ejpam-2199	396	21	.	.	NOUN
ejpam-2199	396	22	1996	1996	NUM
ejpam-2199	396	23	.	.	PUNCT
ejpam-2199	397	1	[	[	X
ejpam-2199	397	2	2	2	X
ejpam-2199	397	3	]	]	PUNCT
ejpam-2199	397	4	j.	j.	PROPN
ejpam-2199	397	5	dugundji	dugundji	PROPN
ejpam-2199	397	6	.	.	PUNCT
ejpam-2199	398	1	topology	topology	PROPN
ejpam-2199	398	2	,	,	PUNCT
ejpam-2199	398	3	allyn	allyn	PROPN
ejpam-2199	398	4	an	an	DET
ejpam-2199	398	5	bacon	bacon	NOUN
ejpam-2199	398	6	,	,	PUNCT
ejpam-2199	398	7	boston	boston	PROPN
ejpam-2199	398	8	,	,	PUNCT
ejpam-2199	398	9	1988	1988	NUM
ejpam-2199	398	10	.	.	PUNCT
ejpam-2199	399	1	[	[	X
ejpam-2199	399	2	3	3	X
ejpam-2199	399	3	]	]	PUNCT
ejpam-2199	399	4	w.	w.	NOUN
ejpam-2199	399	5	hurewicz	hurewicz	PROPN
ejpam-2199	399	6	.	.	PUNCT
ejpam-2199	400	1	über	über	PROPN
ejpam-2199	400	2	eine	eine	PROPN
ejpam-2199	400	3	verallgeneinerung	verallgeneinerung	PROPN
ejpam-2199	400	4	des	des	PROPN
ejpam-2199	400	5	borelschen	borelschen	PROPN
ejpam-2199	400	6	theorems	theorem	NOUN
ejpam-2199	400	7	,	,	PUNCT
ejpam-2199	400	8	mathematische	mathematische	NOUN
ejpam-2199	400	9	zeitschrift	zeitschrift	NOUN
ejpam-2199	400	10	,	,	PUNCT
ejpam-2199	400	11	24	24	NUM
ejpam-2199	400	12	,	,	PUNCT
ejpam-2199	400	13	401–421	401–421	NUM
ejpam-2199	400	14	.	.	NOUN
ejpam-2199	400	15	1925	1925	NUM
ejpam-2199	400	16	.	.	PUNCT
ejpam-2199	401	1	[	[	X
ejpam-2199	401	2	4	4	X
ejpam-2199	401	3	]	]	X
ejpam-2199	401	4	e.l	e.l	PROPN
ejpam-2199	401	5	.	.	PROPN
ejpam-2199	401	6	lima	lima	PROPN
ejpam-2199	401	7	.	.	PUNCT
ejpam-2199	402	1	elementos	elementos	PROPN
ejpam-2199	402	2	de	de	PROPN
ejpam-2199	402	3	topologia	topologia	PROPN
ejpam-2199	402	4	geral	geral	NOUN
ejpam-2199	402	5	,	,	PUNCT
ejpam-2199	402	6	editora	editora	PROPN
ejpam-2199	402	7	da	da	PROPN
ejpam-2199	402	8	universidade	universidade	PROPN
ejpam-2199	402	9	de	de	PROPN
ejpam-2199	402	10	são	são	PROPN
ejpam-2199	402	11	paulo	paulo	PROPN
ejpam-2199	402	12	,	,	PUNCT
ejpam-2199	402	13	1970	1970	NUM
ejpam-2199	402	14	.	.	PUNCT
ejpam-2199	403	1	[	[	X
ejpam-2199	403	2	5	5	X
ejpam-2199	403	3	]	]	PUNCT
ejpam-2199	403	4	j.	j.	PROPN
ejpam-2199	403	5	munkres	munkres	PROPN
ejpam-2199	403	6	.	.	PUNCT
ejpam-2199	404	1	topology	topology	NOUN
ejpam-2199	404	2	:	:	PUNCT
ejpam-2199	404	3	a	a	DET
ejpam-2199	404	4	first	first	ADJ
ejpam-2199	404	5	course	course	NOUN
ejpam-2199	404	6	,	,	PUNCT
ejpam-2199	404	7	prentice	prentice	NOUN
ejpam-2199	404	8	-	-	PUNCT
ejpam-2199	404	9	hall	hall	NOUN
ejpam-2199	404	10	,	,	PUNCT
ejpam-2199	404	11	englewood	englewood	PROPN
ejpam-2199	404	12	cliffs	cliffs	PROPN
ejpam-2199	404	13	,	,	PUNCT
ejpam-2199	404	14	new	new	PROPN
ejpam-2199	404	15	jersey	jersey	PROPN
ejpam-2199	404	16	,	,	PUNCT
ejpam-2199	404	17	1999	1999	NUM
ejpam-2199	404	18	.	.	PUNCT