id	sid	tid	token	lemma	pos
ejpam-141	1	1	2_dung.dvi	2_dung.dvi	NUM
ejpam-141	1	2	european	european	ADJ
ejpam-141	1	3	journal	journal	NOUN
ejpam-141	1	4	of	of	ADP
ejpam-141	1	5	pure	pure	ADJ
ejpam-141	1	6	and	and	CCONJ
ejpam-141	1	7	applied	apply	VERB
ejpam-141	1	8	mathematics	mathematic	NOUN
ejpam-141	1	9	vol	vol	NOUN
ejpam-141	1	10	.	.	PROPN
ejpam-141	1	11	2	2	NUM
ejpam-141	1	12	,	,	PUNCT
ejpam-141	1	13	no	no	INTJ
ejpam-141	1	14	.	.	NOUN
ejpam-141	1	15	2	2	NUM
ejpam-141	1	16	,	,	PUNCT
ejpam-141	1	17	2009	2009	NUM
ejpam-141	1	18	,	,	PUNCT
ejpam-141	1	19	(	(	PUNCT
ejpam-141	1	20	182	182	NUM
ejpam-141	1	21	-	-	SYM
ejpam-141	1	22	194	194	NUM
ejpam-141	1	23	)	)	PUNCT
ejpam-141	1	24	issn	issn	PROPN
ejpam-141	1	25	1307	1307	NUM
ejpam-141	1	26	-	-	SYM
ejpam-141	1	27	5543	5543	NUM
ejpam-141	1	28	–	–	PUNCT
ejpam-141	1	29	www.ejpam.com	www.ejpam.com	X
ejpam-141	1	30	on	on	ADP
ejpam-141	1	31	1	1	NUM
ejpam-141	1	32	-	-	PUNCT
ejpam-141	1	33	sequence	sequence	NOUN
ejpam-141	1	34	-	-	PUNCT
ejpam-141	1	35	covering	cover	VERB
ejpam-141	1	36	π	π	PROPN
ejpam-141	1	37	-	-	PUNCT
ejpam-141	1	38	s	s	NOUN
ejpam-141	1	39	-	-	PUNCT
ejpam-141	1	40	images	image	NOUN
ejpam-141	1	41	of	of	ADP
ejpam-141	1	42	locally	locally	ADV
ejpam-141	1	43	separable	separable	ADJ
ejpam-141	1	44	metric	metric	ADJ
ejpam-141	1	45	spaces	space	NOUN
ejpam-141	1	46	nguyen	nguyen	PROPN
ejpam-141	1	47	van	van	PROPN
ejpam-141	1	48	dung	dung	PROPN
ejpam-141	1	49	mathematics	mathematics	PROPN
ejpam-141	1	50	faculty	faculty	NOUN
ejpam-141	1	51	,	,	PUNCT
ejpam-141	1	52	dongthap	dongthap	PROPN
ejpam-141	1	53	university	university	PROPN
ejpam-141	1	54	caolanh	caolanh	NOUN
ejpam-141	1	55	city	city	PROPN
ejpam-141	1	56	,	,	PUNCT
ejpam-141	1	57	dongthap	dongthap	PROPN
ejpam-141	1	58	province	province	PROPN
ejpam-141	1	59	,	,	PUNCT
ejpam-141	1	60	vietnam	vietnam	PROPN
ejpam-141	1	61	abstract	abstract	NOUN
ejpam-141	1	62	.	.	PUNCT
ejpam-141	2	1	in	in	ADP
ejpam-141	2	2	this	this	DET
ejpam-141	2	3	paper	paper	NOUN
ejpam-141	2	4	,	,	PUNCT
ejpam-141	2	5	we	we	PRON
ejpam-141	2	6	give	give	VERB
ejpam-141	2	7	a	a	DET
ejpam-141	2	8	characterization	characterization	NOUN
ejpam-141	2	9	on	on	ADP
ejpam-141	2	10	1	1	NUM
ejpam-141	2	11	-	-	PUNCT
ejpam-141	2	12	sequence	sequence	NOUN
ejpam-141	2	13	-	-	PUNCT
ejpam-141	2	14	covering	cover	VERB
ejpam-141	2	15	π	π	PROPN
ejpam-141	2	16	-	-	PUNCT
ejpam-141	2	17	s	s	NOUN
ejpam-141	2	18	-	-	PUNCT
ejpam-141	2	19	images	image	NOUN
ejpam-141	2	20	of	of	ADP
ejpam-141	2	21	locally	locally	ADV
ejpam-141	2	22	separable	separable	ADJ
ejpam-141	2	23	metric	metric	ADJ
ejpam-141	2	24	spaces	space	NOUN
ejpam-141	2	25	by	by	ADP
ejpam-141	2	26	means	mean	NOUN
ejpam-141	2	27	of	of	ADP
ejpam-141	2	28	point	point	NOUN
ejpam-141	2	29	-	-	PUNCT
ejpam-141	2	30	countable	countable	ADJ
ejpam-141	2	31	σ	σ	NOUN
ejpam-141	2	32	-	-	PUNCT
ejpam-141	2	33	strong	strong	ADJ
ejpam-141	2	34	sn	sn	NOUN
ejpam-141	2	35	-	-	PUNCT
ejpam-141	2	36	network	network	NOUN
ejpam-141	2	37	consisting	consist	VERB
ejpam-141	2	38	of	of	ADP
ejpam-141	2	39	cosmic	cosmic	ADJ
ejpam-141	2	40	spaces	space	NOUN
ejpam-141	2	41	(	(	PUNCT
ejpam-141	2	42	sn	sn	NOUN
ejpam-141	2	43	-	-	PUNCT
ejpam-141	2	44	second	second	ADJ
ejpam-141	2	45	countable	countable	ADJ
ejpam-141	2	46	spaces	space	NOUN
ejpam-141	2	47	,	,	PUNCT
ejpam-141	2	48	ℵ0	ℵ0	NOUN
ejpam-141	2	49	-	-	NOUN
ejpam-141	2	50	spaces	space	NOUN
ejpam-141	2	51	)	)	PUNCT
ejpam-141	2	52	.	.	PUNCT
ejpam-141	3	1	as	as	ADP
ejpam-141	3	2	an	an	DET
ejpam-141	3	3	application	application	NOUN
ejpam-141	3	4	,	,	PUNCT
ejpam-141	3	5	we	we	PRON
ejpam-141	3	6	get	get	VERB
ejpam-141	3	7	a	a	DET
ejpam-141	3	8	new	new	ADJ
ejpam-141	3	9	characterization	characterization	NOUN
ejpam-141	3	10	on	on	ADP
ejpam-141	3	11	1	1	NUM
ejpam-141	3	12	-	-	PUNCT
ejpam-141	3	13	sequence	sequence	NOUN
ejpam-141	3	14	-	-	PUNCT
ejpam-141	3	15	covering	covering	NOUN
ejpam-141	3	16	,	,	PUNCT
ejpam-141	3	17	quotient	quotient	NOUN
ejpam-141	3	18	π	π	PROPN
ejpam-141	3	19	-	-	PUNCT
ejpam-141	3	20	s	s	NOUN
ejpam-141	3	21	-	-	PUNCT
ejpam-141	3	22	images	image	NOUN
ejpam-141	3	23	of	of	ADP
ejpam-141	3	24	locally	locally	ADV
ejpam-141	3	25	separable	separable	ADJ
ejpam-141	3	26	metric	metric	ADJ
ejpam-141	3	27	spaces	space	NOUN
ejpam-141	3	28	,	,	PUNCT
ejpam-141	3	29	which	which	PRON
ejpam-141	3	30	is	be	AUX
ejpam-141	3	31	helpful	helpful	ADJ
ejpam-141	3	32	in	in	ADP
ejpam-141	3	33	solving	solve	VERB
ejpam-141	3	34	y.	y.	PROPN
ejpam-141	3	35	tanaka	tanaka	PROPN
ejpam-141	3	36	and	and	CCONJ
ejpam-141	3	37	s.	s.	PROPN
ejpam-141	3	38	xia	xia	PROPN
ejpam-141	3	39	’s	’s	PART
ejpam-141	3	40	question	question	NOUN
ejpam-141	3	41	in	in	ADP
ejpam-141	3	42	[	[	X
ejpam-141	3	43	21	21	NUM
ejpam-141	3	44	]	]	PUNCT
ejpam-141	3	45	.	.	PUNCT
ejpam-141	4	1	ams	am	NOUN
ejpam-141	4	2	subject	subject	ADJ
ejpam-141	4	3	classifications	classification	NOUN
ejpam-141	4	4	:	:	PUNCT
ejpam-141	4	5	54d65	54d65	NUM
ejpam-141	4	6	,	,	PUNCT
ejpam-141	4	7	54e35	54e35	NUM
ejpam-141	4	8	,	,	PUNCT
ejpam-141	4	9	54e40	54e40	NUM
ejpam-141	4	10	key	key	ADJ
ejpam-141	4	11	words	word	NOUN
ejpam-141	4	12	:	:	PUNCT
ejpam-141	4	13	1	1	NUM
ejpam-141	4	14	-	-	PUNCT
ejpam-141	4	15	sequence	sequence	NOUN
ejpam-141	4	16	-	-	PUNCT
ejpam-141	4	17	covering	covering	NOUN
ejpam-141	4	18	,	,	PUNCT
ejpam-141	4	19	σ	σ	NOUN
ejpam-141	4	20	-	-	PUNCT
ejpam-141	4	21	strong	strong	ADJ
ejpam-141	4	22	sn	sn	NOUN
ejpam-141	4	23	-	-	PUNCT
ejpam-141	4	24	network	network	NOUN
ejpam-141	4	25	,	,	PUNCT
ejpam-141	4	26	π	π	PROPN
ejpam-141	4	27	-	-	PUNCT
ejpam-141	4	28	s	s	NOUN
ejpam-141	4	29	-	-	PUNCT
ejpam-141	4	30	mapping	mapping	NOUN
ejpam-141	4	31	1	1	NUM
ejpam-141	4	32	.	.	PUNCT
ejpam-141	4	33	introduction	introduction	NOUN
ejpam-141	4	34	to	to	PART
ejpam-141	4	35	determine	determine	VERB
ejpam-141	4	36	what	what	PRON
ejpam-141	4	37	spaces	space	VERB
ejpam-141	4	38	the	the	DET
ejpam-141	4	39	images	image	NOUN
ejpam-141	4	40	of	of	ADP
ejpam-141	4	41	şniceť	şniceť	ADJ
ejpam-141	4	42	spaces	space	NOUN
ejpam-141	4	43	under	under	ADP
ejpam-141	4	44	şniceť	şniceť	ADJ
ejpam-141	4	45	mappings	mapping	NOUN
ejpam-141	4	46	are	be	AUX
ejpam-141	4	47	is	be	AUX
ejpam-141	4	48	one	one	NUM
ejpam-141	4	49	of	of	ADP
ejpam-141	4	50	the	the	DET
ejpam-141	4	51	central	central	ADJ
ejpam-141	4	52	questions	question	NOUN
ejpam-141	4	53	of	of	ADP
ejpam-141	4	54	general	general	ADJ
ejpam-141	4	55	topology	topology	NOUN
ejpam-141	5	1	[	[	X
ejpam-141	5	2	1	1	NUM
ejpam-141	5	3	]	]	PUNCT
ejpam-141	5	4	.	.	PUNCT
ejpam-141	6	1	in	in	ADP
ejpam-141	6	2	the	the	DET
ejpam-141	6	3	past	past	NOUN
ejpam-141	6	4	,	,	PUNCT
ejpam-141	6	5	many	many	ADJ
ejpam-141	6	6	noteworthy	noteworthy	ADJ
ejpam-141	6	7	results	result	NOUN
ejpam-141	6	8	on	on	ADP
ejpam-141	6	9	images	image	NOUN
ejpam-141	6	10	of	of	ADP
ejpam-141	6	11	metric	metric	ADJ
ejpam-141	6	12	spaces	space	NOUN
ejpam-141	6	13	have	have	AUX
ejpam-141	6	14	been	be	AUX
ejpam-141	6	15	obtained	obtain	VERB
ejpam-141	6	16	.	.	PUNCT
ejpam-141	7	1	for	for	ADP
ejpam-141	7	2	a	a	DET
ejpam-141	7	3	survey	survey	NOUN
ejpam-141	7	4	in	in	ADP
ejpam-141	7	5	this	this	DET
ejpam-141	7	6	field	field	NOUN
ejpam-141	7	7	,	,	PUNCT
ejpam-141	7	8	email	email	NOUN
ejpam-141	7	9	addresses	address	NOUN
ejpam-141	7	10	:	:	PUNCT
ejpam-141	7	11	nvdung�staff.dthu.edu.vn	nvdung�staff.dthu.edu.vn	NUM
ejpam-141	7	12	;	;	PUNCT
ejpam-141	7	13	nguyendungt	nguyendungt	PROPN
ejpam-141	7	14	�	�	PROPN
ejpam-141	7	15	yahoo	yahoo	PROPN
ejpam-141	7	16	.	.	PUNCT
ejpam-141	8	1	om	om	PROPN
ejpam-141	8	2	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-141	8	3	182	182	NUM
ejpam-141	9	1	c	c	NOUN
ejpam-141	9	2	©	©	PROPN
ejpam-141	9	3	2009	2009	NUM
ejpam-141	9	4	ejpam	ejpam	NOUN
ejpam-141	9	5	all	all	DET
ejpam-141	9	6	rights	right	NOUN
ejpam-141	9	7	reserved	reserve	VERB
ejpam-141	9	8	.	.	PUNCT
ejpam-141	10	1	n.	n.	NOUN
ejpam-141	10	2	dung	dung	PROPN
ejpam-141	10	3	/	/	SYM
ejpam-141	10	4	eur	eur	PROPN
ejpam-141	10	5	.	.	PUNCT
ejpam-141	11	1	j.	j.	PROPN
ejpam-141	11	2	pure	pure	PROPN
ejpam-141	11	3	appl	appl	PROPN
ejpam-141	11	4	.	.	PROPN
ejpam-141	11	5	math	math	PROPN
ejpam-141	11	6	,	,	PUNCT
ejpam-141	11	7	2	2	NUM
ejpam-141	11	8	(	(	PUNCT
ejpam-141	11	9	2009	2009	NUM
ejpam-141	11	10	)	)	PUNCT
ejpam-141	11	11	,	,	PUNCT
ejpam-141	11	12	(	(	PUNCT
ejpam-141	11	13	182	182	NUM
ejpam-141	11	14	-	-	SYM
ejpam-141	11	15	194	194	NUM
ejpam-141	11	16	)	)	PUNCT
ejpam-141	11	17	183	183	NUM
ejpam-141	11	18	see	see	VERB
ejpam-141	11	19	[	[	X
ejpam-141	11	20	19	19	NUM
ejpam-141	11	21	]	]	PUNCT
ejpam-141	11	22	,	,	PUNCT
ejpam-141	11	23	for	for	ADP
ejpam-141	11	24	example	example	NOUN
ejpam-141	11	25	.	.	PUNCT
ejpam-141	12	1	related	relate	VERB
ejpam-141	12	2	to	to	ADP
ejpam-141	12	3	characterizations	characterization	NOUN
ejpam-141	12	4	on	on	ADP
ejpam-141	12	5	images	image	NOUN
ejpam-141	12	6	of	of	ADP
ejpam-141	12	7	metric	metric	ADJ
ejpam-141	12	8	spaces	space	NOUN
ejpam-141	12	9	,	,	PUNCT
ejpam-141	12	10	y.	y.	PROPN
ejpam-141	12	11	tanaka	tanaka	PROPN
ejpam-141	12	12	and	and	CCONJ
ejpam-141	12	13	s.	s.	PROPN
ejpam-141	12	14	xia	xia	PROPN
ejpam-141	12	15	posed	pose	VERB
ejpam-141	12	16	the	the	DET
ejpam-141	12	17	following	following	ADJ
ejpam-141	12	18	question	question	NOUN
ejpam-141	12	19	in	in	ADP
ejpam-141	12	20	[	[	X
ejpam-141	12	21	21	21	NUM
ejpam-141	12	22	]	]	PUNCT
ejpam-141	12	23	.	.	PUNCT
ejpam-141	13	1	question	question	NOUN
ejpam-141	13	2	1.1	1.1	NUM
ejpam-141	13	3	(	(	PUNCT
ejpam-141	13	4	[	[	X
ejpam-141	13	5	21	21	NUM
ejpam-141	13	6	]	]	PUNCT
ejpam-141	13	7	)	)	PUNCT
ejpam-141	13	8	.	.	PUNCT
ejpam-141	14	1	what	what	PRON
ejpam-141	14	2	is	be	AUX
ejpam-141	14	3	a	a	DET
ejpam-141	14	4	nice	nice	ADJ
ejpam-141	14	5	characterization	characterization	NOUN
ejpam-141	14	6	for	for	ADP
ejpam-141	14	7	a	a	DET
ejpam-141	14	8	quotient	quotient	NOUN
ejpam-141	14	9	s	s	NOUN
ejpam-141	14	10	-	-	NOUN
ejpam-141	14	11	image	image	NOUN
ejpam-141	14	12	of	of	ADP
ejpam-141	14	13	a	a	DET
ejpam-141	14	14	locally	locally	ADV
ejpam-141	14	15	separable	separable	ADJ
ejpam-141	14	16	metric	metric	ADJ
ejpam-141	14	17	space	space	NOUN
ejpam-141	14	18	?	?	PUNCT
ejpam-141	15	1	this	this	DET
ejpam-141	15	2	question	question	NOUN
ejpam-141	15	3	was	be	AUX
ejpam-141	15	4	partly	partly	ADV
ejpam-141	15	5	answered	answer	VERB
ejpam-141	15	6	by	by	ADP
ejpam-141	15	7	many	many	ADJ
ejpam-141	15	8	authors	author	NOUN
ejpam-141	15	9	[	[	X
ejpam-141	15	10	13	13	NUM
ejpam-141	15	11	]	]	PUNCT
ejpam-141	15	12	,	,	PUNCT
ejpam-141	15	13	[	[	X
ejpam-141	15	14	14	14	NUM
ejpam-141	15	15	]	]	PUNCT
ejpam-141	15	16	,	,	PUNCT
ejpam-141	15	17	[	[	X
ejpam-141	15	18	20	20	NUM
ejpam-141	15	19	]	]	PUNCT
ejpam-141	15	20	.	.	PUNCT
ejpam-141	16	1	it	it	PRON
ejpam-141	16	2	is	be	AUX
ejpam-141	16	3	known	know	VERB
ejpam-141	16	4	that	that	SCONJ
ejpam-141	16	5	1	1	NUM
ejpam-141	16	6	-	-	PUNCT
ejpam-141	16	7	sequence	sequence	NOUN
ejpam-141	16	8	-	-	PUNCT
ejpam-141	16	9	covering	cover	VERB
ejpam-141	16	10	s	s	NOUN
ejpam-141	16	11	-	-	PUNCT
ejpam-141	16	12	images	image	NOUN
ejpam-141	16	13	of	of	ADP
ejpam-141	16	14	metric	metric	ADJ
ejpam-141	16	15	spaces	space	NOUN
ejpam-141	16	16	have	have	AUX
ejpam-141	16	17	been	be	AUX
ejpam-141	16	18	characterized	characterize	VERB
ejpam-141	16	19	by	by	ADP
ejpam-141	16	20	pointcountable	pointcountable	ADJ
ejpam-141	16	21	sn	sn	PROPN
ejpam-141	16	22	-	-	PUNCT
ejpam-141	16	23	networks	network	NOUN
ejpam-141	16	24	,	,	PUNCT
ejpam-141	16	25	and	and	CCONJ
ejpam-141	16	26	1	1	NUM
ejpam-141	16	27	-	-	PUNCT
ejpam-141	16	28	sequence	sequence	NOUN
ejpam-141	16	29	-	-	PUNCT
ejpam-141	16	30	coveringπ	coveringπ	NOUN
ejpam-141	16	31	-	-	PUNCT
ejpam-141	16	32	images	image	NOUN
ejpam-141	16	33	of	of	ADP
ejpam-141	16	34	metric	metric	ADJ
ejpam-141	16	35	spaces	space	NOUN
ejpam-141	16	36	have	have	AUX
ejpam-141	16	37	been	be	AUX
ejpam-141	16	38	characterized	characterize	VERB
ejpam-141	16	39	byσ	byσ	ADJ
ejpam-141	16	40	-	-	PUNCT
ejpam-141	16	41	strong	strong	ADJ
ejpam-141	16	42	sn	sn	NOUN
ejpam-141	16	43	-	-	PUNCT
ejpam-141	16	44	networks	network	NOUN
ejpam-141	17	1	[	[	X
ejpam-141	17	2	16	16	NUM
ejpam-141	17	3	]	]	PUNCT
ejpam-141	17	4	.	.	PUNCT
ejpam-141	18	1	also	also	ADV
ejpam-141	18	2	,	,	PUNCT
ejpam-141	18	3	as	as	ADP
ejpam-141	18	4	in	in	ADP
ejpam-141	18	5	the	the	DET
ejpam-141	18	6	proofs	proof	NOUN
ejpam-141	18	7	of	of	ADP
ejpam-141	18	8	[	[	X
ejpam-141	18	9	10	10	NUM
ejpam-141	18	10	]	]	PUNCT
ejpam-141	18	11	,	,	PUNCT
ejpam-141	18	12	1	1	NUM
ejpam-141	18	13	-	-	PUNCT
ejpam-141	18	14	sequencecovering	sequencecovering	NOUN
ejpam-141	18	15	π	π	PROPN
ejpam-141	18	16	-	-	PUNCT
ejpam-141	18	17	s	s	NOUN
ejpam-141	18	18	-	-	PUNCT
ejpam-141	18	19	images	image	NOUN
ejpam-141	18	20	of	of	ADP
ejpam-141	18	21	metric	metric	ADJ
ejpam-141	18	22	spaces	space	NOUN
ejpam-141	18	23	can	can	AUX
ejpam-141	18	24	be	be	AUX
ejpam-141	18	25	characterized	characterize	VERB
ejpam-141	18	26	by	by	ADP
ejpam-141	18	27	point	point	NOUN
ejpam-141	18	28	-	-	PUNCT
ejpam-141	18	29	countable	countable	ADJ
ejpam-141	18	30	σstrong	σstrong	ADJ
ejpam-141	18	31	sn	sn	PROPN
ejpam-141	18	32	-	-	PUNCT
ejpam-141	18	33	networks	network	NOUN
ejpam-141	18	34	.	.	PUNCT
ejpam-141	19	1	recently	recently	ADV
ejpam-141	19	2	,	,	PUNCT
ejpam-141	19	3	the	the	DET
ejpam-141	19	4	characterizations	characterization	NOUN
ejpam-141	19	5	on	on	ADP
ejpam-141	19	6	images	image	NOUN
ejpam-141	19	7	of	of	ADP
ejpam-141	19	8	locally	locally	ADV
ejpam-141	19	9	separable	separable	ADJ
ejpam-141	19	10	metric	metric	ADJ
ejpam-141	19	11	spaces	space	NOUN
ejpam-141	19	12	cause	cause	VERB
ejpam-141	19	13	attention	attention	NOUN
ejpam-141	19	14	once	once	ADV
ejpam-141	19	15	again	again	ADV
ejpam-141	19	16	,	,	PUNCT
ejpam-141	19	17	and	and	CCONJ
ejpam-141	19	18	1	1	NUM
ejpam-141	19	19	-	-	PUNCT
ejpam-141	19	20	sequence	sequence	NOUN
ejpam-141	19	21	-	-	PUNCT
ejpam-141	19	22	covering	cover	VERB
ejpam-141	19	23	s	s	NOUN
ejpam-141	19	24	-	-	PUNCT
ejpam-141	19	25	images	image	NOUN
ejpam-141	19	26	of	of	ADP
ejpam-141	19	27	locally	locally	ADV
ejpam-141	19	28	separable	separable	ADJ
ejpam-141	19	29	metric	metric	ADJ
ejpam-141	19	30	spaces	space	NOUN
ejpam-141	19	31	have	have	AUX
ejpam-141	19	32	been	be	AUX
ejpam-141	19	33	characterized	characterize	VERB
ejpam-141	19	34	by	by	ADP
ejpam-141	19	35	point	point	NOUN
ejpam-141	19	36	-	-	PUNCT
ejpam-141	19	37	countable	countable	ADJ
ejpam-141	19	38	sn	sn	NOUN
ejpam-141	19	39	-	-	PUNCT
ejpam-141	19	40	network	network	NOUN
ejpam-141	19	41	consisting	consist	VERB
ejpam-141	19	42	of	of	ADP
ejpam-141	19	43	cosmic	cosmic	ADJ
ejpam-141	19	44	spaces	space	NOUN
ejpam-141	19	45	(	(	PUNCT
ejpam-141	19	46	ℵ0	ℵ0	NOUN
ejpam-141	19	47	-	-	NOUN
ejpam-141	19	48	spaces	space	NOUN
ejpam-141	19	49	)	)	PUNCT
ejpam-141	20	1	[	[	X
ejpam-141	20	2	5	5	NUM
ejpam-141	20	3	]	]	PUNCT
ejpam-141	20	4	.	.	PUNCT
ejpam-141	21	1	taking	take	VERB
ejpam-141	21	2	these	these	DET
ejpam-141	21	3	results	result	NOUN
ejpam-141	21	4	into	into	ADP
ejpam-141	21	5	account	account	NOUN
ejpam-141	21	6	,	,	PUNCT
ejpam-141	21	7	it	it	PRON
ejpam-141	21	8	is	be	AUX
ejpam-141	21	9	natural	natural	ADJ
ejpam-141	21	10	to	to	PART
ejpam-141	21	11	be	be	AUX
ejpam-141	21	12	interested	interested	ADJ
ejpam-141	21	13	in	in	ADP
ejpam-141	21	14	the	the	DET
ejpam-141	21	15	following	follow	VERB
ejpam-141	21	16	question	question	NOUN
ejpam-141	21	17	.	.	PUNCT
ejpam-141	22	1	question	question	NOUN
ejpam-141	22	2	1.2	1.2	NUM
ejpam-141	22	3	.	.	PUNCT
ejpam-141	23	1	are	be	AUX
ejpam-141	23	2	the	the	DET
ejpam-141	23	3	following	follow	VERB
ejpam-141	23	4	equivalent	equivalent	NOUN
ejpam-141	23	5	for	for	ADP
ejpam-141	23	6	a	a	DET
ejpam-141	23	7	space	space	NOUN
ejpam-141	23	8	x	x	NOUN
ejpam-141	23	9	?	?	NOUN
ejpam-141	24	1	1	1	NUM
ejpam-141	24	2	.	.	X
ejpam-141	24	3	x	x	PUNCT
ejpam-141	24	4	is	be	AUX
ejpam-141	24	5	an	an	DET
ejpam-141	24	6	1	1	NUM
ejpam-141	24	7	-	-	PUNCT
ejpam-141	24	8	sequence	sequence	NOUN
ejpam-141	24	9	-	-	PUNCT
ejpam-141	24	10	covering	cover	VERB
ejpam-141	24	11	π	π	PROPN
ejpam-141	24	12	-	-	PUNCT
ejpam-141	24	13	s	s	NOUN
ejpam-141	24	14	-	-	PUNCT
ejpam-141	24	15	image	image	NOUN
ejpam-141	24	16	of	of	ADP
ejpam-141	24	17	a	a	DET
ejpam-141	24	18	locally	locally	ADV
ejpam-141	24	19	separable	separable	ADJ
ejpam-141	24	20	metric	metric	ADJ
ejpam-141	24	21	space	space	NOUN
ejpam-141	24	22	.	.	PUNCT
ejpam-141	25	1	2	2	X
ejpam-141	25	2	.	.	X
ejpam-141	25	3	x	x	PUNCT
ejpam-141	25	4	has	have	VERB
ejpam-141	25	5	a	a	DET
ejpam-141	25	6	point	point	NOUN
ejpam-141	25	7	-	-	PUNCT
ejpam-141	25	8	countable	countable	ADJ
ejpam-141	25	9	σ	σ	NOUN
ejpam-141	25	10	-	-	PUNCT
ejpam-141	25	11	strong	strong	ADJ
ejpam-141	25	12	sn	sn	NOUN
ejpam-141	25	13	-	-	PUNCT
ejpam-141	25	14	network	network	NOUN
ejpam-141	25	15	consisting	consist	VERB
ejpam-141	25	16	of	of	ADP
ejpam-141	25	17	cosmic	cosmic	ADJ
ejpam-141	25	18	spaces	space	NOUN
ejpam-141	25	19	(	(	PUNCT
ejpam-141	25	20	ℵ0spaces	ℵ0space	NOUN
ejpam-141	25	21	)	)	PUNCT
ejpam-141	25	22	.	.	PUNCT
ejpam-141	26	1	in	in	ADP
ejpam-141	26	2	this	this	DET
ejpam-141	26	3	paper	paper	NOUN
ejpam-141	26	4	,	,	PUNCT
ejpam-141	26	5	we	we	PRON
ejpam-141	26	6	give	give	VERB
ejpam-141	26	7	a	a	DET
ejpam-141	26	8	characterization	characterization	NOUN
ejpam-141	26	9	on	on	ADP
ejpam-141	26	10	1	1	NUM
ejpam-141	26	11	-	-	PUNCT
ejpam-141	26	12	sequence	sequence	NOUN
ejpam-141	26	13	-	-	PUNCT
ejpam-141	26	14	covering	cover	VERB
ejpam-141	26	15	π	π	PROPN
ejpam-141	26	16	-	-	PUNCT
ejpam-141	26	17	s	s	NOUN
ejpam-141	26	18	-	-	PUNCT
ejpam-141	26	19	images	image	NOUN
ejpam-141	26	20	of	of	ADP
ejpam-141	26	21	locally	locally	ADV
ejpam-141	26	22	separable	separable	ADJ
ejpam-141	26	23	metric	metric	ADJ
ejpam-141	26	24	spaces	space	NOUN
ejpam-141	26	25	by	by	ADP
ejpam-141	26	26	means	mean	NOUN
ejpam-141	26	27	of	of	ADP
ejpam-141	26	28	point	point	NOUN
ejpam-141	26	29	-	-	PUNCT
ejpam-141	26	30	countable	countable	ADJ
ejpam-141	26	31	σ	σ	NOUN
ejpam-141	26	32	-	-	PUNCT
ejpam-141	26	33	strong	strong	ADJ
ejpam-141	26	34	sn	sn	NOUN
ejpam-141	26	35	-	-	PUNCT
ejpam-141	26	36	network	network	NOUN
ejpam-141	26	37	consisting	consist	VERB
ejpam-141	26	38	of	of	ADP
ejpam-141	26	39	cosmic	cosmic	ADJ
ejpam-141	26	40	spaces	space	NOUN
ejpam-141	26	41	(	(	PUNCT
ejpam-141	26	42	sn	sn	NOUN
ejpam-141	26	43	-	-	PUNCT
ejpam-141	26	44	second	second	ADJ
ejpam-141	26	45	countable	countable	ADJ
ejpam-141	26	46	spaces	space	NOUN
ejpam-141	26	47	,	,	PUNCT
ejpam-141	26	48	ℵ0	ℵ0	NOUN
ejpam-141	26	49	-	-	NOUN
ejpam-141	26	50	spaces	space	NOUN
ejpam-141	26	51	)	)	PUNCT
ejpam-141	26	52	.	.	PUNCT
ejpam-141	27	1	as	as	ADP
ejpam-141	27	2	an	an	DET
ejpam-141	27	3	application	application	NOUN
ejpam-141	27	4	,	,	PUNCT
ejpam-141	27	5	we	we	PRON
ejpam-141	27	6	get	get	VERB
ejpam-141	27	7	a	a	DET
ejpam-141	27	8	new	new	ADJ
ejpam-141	27	9	characterization	characterization	NOUN
ejpam-141	27	10	on	on	ADP
ejpam-141	27	11	1	1	NUM
ejpam-141	27	12	-	-	PUNCT
ejpam-141	27	13	sequence	sequence	NOUN
ejpam-141	27	14	-	-	PUNCT
ejpam-141	27	15	covering	covering	NOUN
ejpam-141	27	16	,	,	PUNCT
ejpam-141	27	17	quotient	quotient	NOUN
ejpam-141	27	18	π	π	PROPN
ejpam-141	27	19	-	-	PUNCT
ejpam-141	27	20	s	s	NOUN
ejpam-141	27	21	-	-	PUNCT
ejpam-141	27	22	images	image	NOUN
ejpam-141	27	23	of	of	ADP
ejpam-141	27	24	locally	locally	ADV
ejpam-141	27	25	separable	separable	ADJ
ejpam-141	27	26	metric	metric	ADJ
ejpam-141	27	27	spaces	space	NOUN
ejpam-141	27	28	,	,	PUNCT
ejpam-141	27	29	which	which	PRON
ejpam-141	27	30	is	be	AUX
ejpam-141	27	31	helpful	helpful	ADJ
ejpam-141	27	32	in	in	ADP
ejpam-141	27	33	solving	solve	VERB
ejpam-141	27	34	the	the	DET
ejpam-141	27	35	above	above	ADJ
ejpam-141	27	36	question	question	NOUN
ejpam-141	27	37	1.1	1.1	NUM
ejpam-141	27	38	of	of	ADP
ejpam-141	27	39	y.	y.	PROPN
ejpam-141	27	40	tanaka	tanaka	PROPN
ejpam-141	27	41	and	and	CCONJ
ejpam-141	27	42	s.	s.	PROPN
ejpam-141	27	43	xia	xia	PROPN
ejpam-141	27	44	.	.	PUNCT
ejpam-141	28	1	n.	n.	PROPN
ejpam-141	28	2	dung	dung	PROPN
ejpam-141	28	3	/	/	SYM
ejpam-141	28	4	eur	eur	PROPN
ejpam-141	28	5	.	.	PUNCT
ejpam-141	29	1	j.	j.	PROPN
ejpam-141	29	2	pure	pure	PROPN
ejpam-141	29	3	appl	appl	PROPN
ejpam-141	29	4	.	.	PROPN
ejpam-141	29	5	math	math	PROPN
ejpam-141	29	6	,	,	PUNCT
ejpam-141	29	7	2	2	NUM
ejpam-141	29	8	(	(	PUNCT
ejpam-141	29	9	2009	2009	NUM
ejpam-141	29	10	)	)	PUNCT
ejpam-141	29	11	,	,	PUNCT
ejpam-141	29	12	(	(	PUNCT
ejpam-141	29	13	182	182	NUM
ejpam-141	29	14	-	-	SYM
ejpam-141	29	15	194	194	NUM
ejpam-141	29	16	)	)	PUNCT
ejpam-141	29	17	184	184	NUM
ejpam-141	29	18	throughout	throughout	ADP
ejpam-141	29	19	this	this	DET
ejpam-141	29	20	paper	paper	NOUN
ejpam-141	29	21	,	,	PUNCT
ejpam-141	29	22	all	all	DET
ejpam-141	29	23	spaces	space	NOUN
ejpam-141	29	24	are	be	AUX
ejpam-141	29	25	regular	regular	ADJ
ejpam-141	29	26	and	and	CCONJ
ejpam-141	29	27	t1	t1	VERB
ejpam-141	29	28	,	,	PUNCT
ejpam-141	29	29	n	n	PRON
ejpam-141	29	30	denotes	denote	VERB
ejpam-141	29	31	the	the	DET
ejpam-141	29	32	set	set	NOUN
ejpam-141	29	33	of	of	ADP
ejpam-141	29	34	all	all	DET
ejpam-141	29	35	natural	natural	ADJ
ejpam-141	29	36	numbers	number	NOUN
ejpam-141	29	37	,	,	PUNCT
ejpam-141	29	38	ω	ω	NUM
ejpam-141	29	39	=	=	SYM
ejpam-141	29	40	n	n	NOUN
ejpam-141	29	41	∪	∪	X
ejpam-141	29	42	{	{	PUNCT
ejpam-141	29	43	0	0	NUM
ejpam-141	29	44	}	}	PUNCT
ejpam-141	29	45	,	,	PUNCT
ejpam-141	29	46	and	and	CCONJ
ejpam-141	29	47	a	a	DET
ejpam-141	29	48	convergent	convergent	NOUN
ejpam-141	29	49	sequence	sequence	NOUN
ejpam-141	29	50	includes	include	VERB
ejpam-141	29	51	its	its	PRON
ejpam-141	29	52	limit	limit	NOUN
ejpam-141	29	53	point	point	NOUN
ejpam-141	29	54	.	.	PUNCT
ejpam-141	30	1	let	let	VERB
ejpam-141	30	2	p	p	PRON
ejpam-141	30	3	be	be	AUX
ejpam-141	30	4	a	a	DET
ejpam-141	30	5	family	family	NOUN
ejpam-141	30	6	of	of	ADP
ejpam-141	30	7	subsets	subset	NOUN
ejpam-141	30	8	of	of	ADP
ejpam-141	30	9	x	x	PUNCT
ejpam-141	30	10	and	and	CCONJ
ejpam-141	30	11	x	x	SYM
ejpam-141	30	12	∈	∈	NOUN
ejpam-141	30	13	x	x	X
ejpam-141	30	14	.	.	PUNCT
ejpam-141	31	1	then	then	ADV
ejpam-141	31	2	⋂	⋂	PROPN
ejpam-141	31	3	p	p	NOUN
ejpam-141	31	4	,	,	PUNCT
ejpam-141	31	5	and	and	CCONJ
ejpam-141	31	6	st(x	st(x	PROPN
ejpam-141	31	7	,	,	PUNCT
ejpam-141	31	8	p	p	NOUN
ejpam-141	31	9	)	)	PUNCT
ejpam-141	31	10	denote	denote	VERB
ejpam-141	31	11	the	the	DET
ejpam-141	31	12	intersection	intersection	NOUN
ejpam-141	31	13	⋂	⋂	PROPN
ejpam-141	31	14	{	{	PUNCT
ejpam-141	31	15	p	p	X
ejpam-141	31	16	:	:	PUNCT
ejpam-141	31	17	p	p	X
ejpam-141	31	18	∈	∈	PROPN
ejpam-141	31	19	p	p	X
ejpam-141	31	20	}	}	PUNCT
ejpam-141	31	21	,	,	PUNCT
ejpam-141	31	22	and	and	CCONJ
ejpam-141	31	23	the	the	DET
ejpam-141	31	24	union	union	NOUN
ejpam-141	31	25	⋃	⋃	PROPN
ejpam-141	31	26	{	{	PUNCT
ejpam-141	31	27	p	p	NOUN
ejpam-141	31	28	∈	∈	PROPN
ejpam-141	31	29	p	p	X
ejpam-141	31	30	:	:	PUNCT
ejpam-141	31	31	x	x	SYM
ejpam-141	31	32	∈	∈	PROPN
ejpam-141	31	33	p	p	X
ejpam-141	31	34	}	}	PUNCT
ejpam-141	31	35	,	,	PUNCT
ejpam-141	31	36	respectively	respectively	ADV
ejpam-141	31	37	.	.	PUNCT
ejpam-141	32	1	a	a	DET
ejpam-141	32	2	convergent	convergent	NOUN
ejpam-141	32	3	sequence	sequence	NOUN
ejpam-141	32	4	{	{	PUNCT
ejpam-141	32	5	xn	xn	PROPN
ejpam-141	32	6	:	:	PUNCT
ejpam-141	32	7	n	n	CCONJ
ejpam-141	32	8	∈ω	∈ω	NOUN
ejpam-141	32	9	}	}	PUNCT
ejpam-141	32	10	converging	converge	VERB
ejpam-141	32	11	to	to	ADP
ejpam-141	32	12	x0	x0	PROPN
ejpam-141	32	13	is	be	AUX
ejpam-141	32	14	eventually	eventually	ADV
ejpam-141	32	15	in	in	ADP
ejpam-141	32	16	a	a	DET
ejpam-141	32	17	subset	subset	NOUN
ejpam-141	32	18	a	a	PRON
ejpam-141	32	19	of	of	ADP
ejpam-141	32	20	x	x	SYM
ejpam-141	32	21	,	,	PUNCT
ejpam-141	32	22	if	if	SCONJ
ejpam-141	32	23	{	{	PUNCT
ejpam-141	32	24	xn	xn	NOUN
ejpam-141	32	25	:	:	PUNCT
ejpam-141	32	26	n	n	CCONJ
ejpam-141	32	27	≥	≥	X
ejpam-141	32	28	n0	n0	NUM
ejpam-141	32	29	}	}	PUNCT
ejpam-141	32	30	∪	∪	X
ejpam-141	32	31	{	{	PUNCT
ejpam-141	32	32	x0	x0	PROPN
ejpam-141	32	33	}	}	PUNCT
ejpam-141	32	34	⊂	⊂	PROPN
ejpam-141	32	35	a	a	PRON
ejpam-141	32	36	for	for	ADP
ejpam-141	32	37	some	some	DET
ejpam-141	32	38	n0	n0	PROPN
ejpam-141	32	39	∈	∈	PROPN
ejpam-141	32	40	n.	n.	NOUN
ejpam-141	32	41	for	for	ADP
ejpam-141	32	42	terms	term	NOUN
ejpam-141	32	43	which	which	PRON
ejpam-141	32	44	are	be	AUX
ejpam-141	32	45	not	not	PART
ejpam-141	32	46	defined	define	VERB
ejpam-141	32	47	here	here	ADV
ejpam-141	32	48	,	,	PUNCT
ejpam-141	32	49	please	please	INTJ
ejpam-141	32	50	refer	refer	VERB
ejpam-141	32	51	to	to	ADP
ejpam-141	32	52	[	[	X
ejpam-141	32	53	3	3	NUM
ejpam-141	32	54	]	]	PUNCT
ejpam-141	32	55	.	.	PUNCT
ejpam-141	33	1	2	2	X
ejpam-141	33	2	.	.	X
ejpam-141	33	3	main	main	ADJ
ejpam-141	33	4	results	result	NOUN
ejpam-141	33	5	definition	definition	NOUN
ejpam-141	33	6	2.1	2.1	NUM
ejpam-141	33	7	.	.	PUNCT
ejpam-141	34	1	let	let	VERB
ejpam-141	34	2	p	p	PRON
ejpam-141	34	3	be	be	AUX
ejpam-141	34	4	a	a	DET
ejpam-141	34	5	subset	subset	NOUN
ejpam-141	34	6	of	of	ADP
ejpam-141	34	7	a	a	DET
ejpam-141	34	8	space	space	NOUN
ejpam-141	34	9	x	x	X
ejpam-141	34	10	.	.	PUNCT
ejpam-141	35	1	(	(	PUNCT
ejpam-141	35	2	1	1	X
ejpam-141	35	3	)	)	PUNCT
ejpam-141	35	4	p	p	NOUN
ejpam-141	35	5	is	be	AUX
ejpam-141	35	6	a	a	DET
ejpam-141	35	7	sequential	sequential	ADJ
ejpam-141	35	8	neighborhood	neighborhood	NOUN
ejpam-141	35	9	of	of	ADP
ejpam-141	35	10	x	x	PUNCT
ejpam-141	36	1	[	[	X
ejpam-141	36	2	4	4	NUM
ejpam-141	36	3	]	]	PUNCT
ejpam-141	36	4	,	,	PUNCT
ejpam-141	36	5	if	if	SCONJ
ejpam-141	36	6	for	for	ADP
ejpam-141	36	7	every	every	DET
ejpam-141	36	8	convergent	convergent	NOUN
ejpam-141	36	9	sequence	sequence	NOUN
ejpam-141	36	10	s	s	AUX
ejpam-141	36	11	converging	converge	VERB
ejpam-141	36	12	to	to	ADP
ejpam-141	36	13	x	x	PUNCT
ejpam-141	36	14	in	in	ADP
ejpam-141	36	15	x	x	X
ejpam-141	36	16	,	,	PUNCT
ejpam-141	36	17	s	s	X
ejpam-141	36	18	is	be	AUX
ejpam-141	36	19	eventually	eventually	ADV
ejpam-141	36	20	in	in	ADP
ejpam-141	36	21	p.	p.	NOUN
ejpam-141	36	22	(	(	PUNCT
ejpam-141	36	23	2	2	X
ejpam-141	36	24	)	)	PUNCT
ejpam-141	36	25	p	p	NOUN
ejpam-141	36	26	is	be	AUX
ejpam-141	36	27	a	a	DET
ejpam-141	36	28	sequentially	sequentially	ADV
ejpam-141	36	29	open	open	ADJ
ejpam-141	36	30	subset	subset	NOUN
ejpam-141	36	31	of	of	ADP
ejpam-141	36	32	x	x	PUNCT
ejpam-141	37	1	[	[	X
ejpam-141	37	2	4	4	NUM
ejpam-141	37	3	]	]	PUNCT
ejpam-141	37	4	,	,	PUNCT
ejpam-141	37	5	if	if	SCONJ
ejpam-141	37	6	for	for	ADP
ejpam-141	37	7	every	every	DET
ejpam-141	37	8	x	x	SYM
ejpam-141	37	9	∈	∈	PROPN
ejpam-141	37	10	p	p	NOUN
ejpam-141	37	11	,	,	PUNCT
ejpam-141	37	12	p	p	PRON
ejpam-141	37	13	is	be	AUX
ejpam-141	37	14	a	a	DET
ejpam-141	37	15	sequential	sequential	ADJ
ejpam-141	37	16	neighborhood	neighborhood	NOUN
ejpam-141	37	17	of	of	ADP
ejpam-141	37	18	x.	x.	NOUN
ejpam-141	37	19	definition	definition	NOUN
ejpam-141	37	20	2.2	2.2	NUM
ejpam-141	37	21	.	.	PUNCT
ejpam-141	38	1	let	let	VERB
ejpam-141	38	2	p	p	PRON
ejpam-141	38	3	be	be	AUX
ejpam-141	38	4	a	a	DET
ejpam-141	38	5	family	family	NOUN
ejpam-141	38	6	of	of	ADP
ejpam-141	38	7	subsets	subset	NOUN
ejpam-141	38	8	of	of	ADP
ejpam-141	38	9	a	a	DET
ejpam-141	38	10	space	space	NOUN
ejpam-141	38	11	x	x	X
ejpam-141	38	12	.	.	PUNCT
ejpam-141	39	1	(	(	PUNCT
ejpam-141	39	2	1	1	X
ejpam-141	39	3	)	)	PUNCT
ejpam-141	39	4	for	for	ADP
ejpam-141	39	5	each	each	PRON
ejpam-141	39	6	x	x	SYM
ejpam-141	39	7	∈	∈	PROPN
ejpam-141	39	8	x	x	X
ejpam-141	39	9	,	,	PUNCT
ejpam-141	39	10	p	p	NOUN
ejpam-141	39	11	is	be	AUX
ejpam-141	39	12	a	a	DET
ejpam-141	39	13	network	network	NOUN
ejpam-141	39	14	at	at	ADP
ejpam-141	39	15	x	x	SYM
ejpam-141	39	16	in	in	ADP
ejpam-141	39	17	x	x	SYM
ejpam-141	39	18	,	,	PUNCT
ejpam-141	39	19	if	if	SCONJ
ejpam-141	39	20	x	x	SYM
ejpam-141	39	21	∈	∈	PROPN
ejpam-141	39	22	⋂	⋂	PROPN
ejpam-141	39	23	p	p	NOUN
ejpam-141	39	24	,	,	PUNCT
ejpam-141	39	25	and	and	CCONJ
ejpam-141	39	26	if	if	SCONJ
ejpam-141	39	27	x	x	SYM
ejpam-141	39	28	∈	∈	PROPN
ejpam-141	39	29	u	u	NOUN
ejpam-141	39	30	with	with	ADP
ejpam-141	39	31	u	u	NOUN
ejpam-141	39	32	open	open	ADJ
ejpam-141	39	33	in	in	ADP
ejpam-141	39	34	x	x	X
ejpam-141	39	35	,	,	PUNCT
ejpam-141	39	36	there	there	PRON
ejpam-141	39	37	exists	exist	VERB
ejpam-141	39	38	p	p	PROPN
ejpam-141	39	39	∈	∈	PROPN
ejpam-141	39	40	p	p	NOUN
ejpam-141	39	41	such	such	ADJ
ejpam-141	39	42	that	that	SCONJ
ejpam-141	39	43	x	x	SYM
ejpam-141	39	44	∈	∈	PROPN
ejpam-141	39	45	p	p	X
ejpam-141	39	46	⊂	⊂	PROPN
ejpam-141	39	47	u.	u.	PROPN
ejpam-141	39	48	(	(	PUNCT
ejpam-141	39	49	2	2	NUM
ejpam-141	39	50	)	)	PUNCT
ejpam-141	39	51	p	p	NOUN
ejpam-141	39	52	is	be	AUX
ejpam-141	39	53	a	a	DET
ejpam-141	39	54	cs	cs	ADJ
ejpam-141	39	55	-	-	NOUN
ejpam-141	39	56	network	network	NOUN
ejpam-141	39	57	of	of	ADP
ejpam-141	39	58	x	x	PUNCT
ejpam-141	40	1	[	[	X
ejpam-141	40	2	8	8	NUM
ejpam-141	40	3	]	]	PUNCT
ejpam-141	40	4	,	,	PUNCT
ejpam-141	40	5	if	if	SCONJ
ejpam-141	40	6	for	for	ADP
ejpam-141	40	7	every	every	DET
ejpam-141	40	8	convergent	convergent	NOUN
ejpam-141	40	9	sequence	sequence	NOUN
ejpam-141	40	10	s	s	AUX
ejpam-141	40	11	converging	converge	VERB
ejpam-141	40	12	to	to	ADP
ejpam-141	40	13	x	x	SYM
ejpam-141	40	14	∈	∈	PROPN
ejpam-141	40	15	u	u	NOUN
ejpam-141	40	16	with	with	ADP
ejpam-141	40	17	u	u	NOUN
ejpam-141	40	18	open	open	ADJ
ejpam-141	40	19	in	in	ADP
ejpam-141	40	20	x	x	X
ejpam-141	40	21	,	,	PUNCT
ejpam-141	40	22	there	there	PRON
ejpam-141	40	23	exists	exist	VERB
ejpam-141	40	24	p	p	PROPN
ejpam-141	40	25	∈	∈	PROPN
ejpam-141	40	26	p	p	NOUN
ejpam-141	40	27	such	such	ADJ
ejpam-141	40	28	that	that	DET
ejpam-141	40	29	s	s	NOUN
ejpam-141	40	30	is	be	AUX
ejpam-141	40	31	eventually	eventually	ADV
ejpam-141	40	32	in	in	ADP
ejpam-141	40	33	p	p	PROPN
ejpam-141	40	34	⊂	⊂	PROPN
ejpam-141	40	35	u.	u.	PROPN
ejpam-141	40	36	(	(	PUNCT
ejpam-141	40	37	3	3	X
ejpam-141	40	38	)	)	PUNCT
ejpam-141	40	39	p	p	NOUN
ejpam-141	40	40	is	be	AUX
ejpam-141	40	41	an	an	DET
ejpam-141	40	42	sn	sn	NOUN
ejpam-141	40	43	-	-	PUNCT
ejpam-141	40	44	cover	cover	NOUN
ejpam-141	40	45	of	of	ADP
ejpam-141	40	46	x	x	PUNCT
ejpam-141	41	1	[	[	X
ejpam-141	41	2	14	14	NUM
ejpam-141	41	3	]	]	X
ejpam-141	41	4	,	,	PUNCT
ejpam-141	41	5	if	if	SCONJ
ejpam-141	41	6	each	each	DET
ejpam-141	41	7	element	element	NOUN
ejpam-141	41	8	of	of	ADP
ejpam-141	41	9	p	p	PROPN
ejpam-141	41	10	is	be	AUX
ejpam-141	41	11	a	a	DET
ejpam-141	41	12	sequential	sequential	ADJ
ejpam-141	41	13	neighborhood	neighborhood	NOUN
ejpam-141	41	14	of	of	ADP
ejpam-141	41	15	some	some	DET
ejpam-141	41	16	point	point	NOUN
ejpam-141	41	17	in	in	ADP
ejpam-141	41	18	x	x	X
ejpam-141	41	19	,	,	PUNCT
ejpam-141	41	20	and	and	CCONJ
ejpam-141	41	21	for	for	ADP
ejpam-141	41	22	each	each	DET
ejpam-141	41	23	x	x	SYM
ejpam-141	41	24	∈	∈	PROPN
ejpam-141	41	25	x	x	X
ejpam-141	41	26	,	,	PUNCT
ejpam-141	41	27	some	some	DET
ejpam-141	41	28	p	p	PROPN
ejpam-141	41	29	∈	∈	PROPN
ejpam-141	41	30	p	p	NOUN
ejpam-141	41	31	is	be	AUX
ejpam-141	41	32	a	a	DET
ejpam-141	41	33	sequential	sequential	ADJ
ejpam-141	41	34	neighborhood	neighborhood	NOUN
ejpam-141	41	35	of	of	ADP
ejpam-141	41	36	x.	x.	NOUN
ejpam-141	41	37	definition	definition	NOUN
ejpam-141	41	38	2.3	2.3	NUM
ejpam-141	41	39	.	.	PUNCT
ejpam-141	42	1	let	let	VERB
ejpam-141	42	2	x	x	PRON
ejpam-141	42	3	be	be	AUX
ejpam-141	42	4	a	a	DET
ejpam-141	42	5	space	space	NOUN
ejpam-141	42	6	.	.	PUNCT
ejpam-141	43	1	(	(	PUNCT
ejpam-141	43	2	1	1	X
ejpam-141	43	3	)	)	PUNCT
ejpam-141	43	4	x	x	X
ejpam-141	43	5	is	be	AUX
ejpam-141	43	6	an	an	DET
ejpam-141	43	7	ℵ0	ℵ0	NOUN
ejpam-141	43	8	-	-	PUNCT
ejpam-141	43	9	space	space	NOUN
ejpam-141	43	10	[	[	X
ejpam-141	43	11	17	17	NUM
ejpam-141	43	12	]	]	X
ejpam-141	43	13	(	(	PUNCT
ejpam-141	43	14	resp	resp	NOUN
ejpam-141	43	15	.	.	PUNCT
ejpam-141	44	1	,	,	PUNCT
ejpam-141	44	2	cosmic	cosmic	ADJ
ejpam-141	44	3	space	space	NOUN
ejpam-141	44	4	[	[	X
ejpam-141	44	5	17	17	NUM
ejpam-141	44	6	]	]	PUNCT
ejpam-141	44	7	,	,	PUNCT
ejpam-141	44	8	sn	sn	ADJ
ejpam-141	44	9	-	-	PUNCT
ejpam-141	44	10	second	second	ADJ
ejpam-141	44	11	countable	countable	ADJ
ejpam-141	44	12	space	space	NOUN
ejpam-141	44	13	[	[	X
ejpam-141	44	14	7	7	NUM
ejpam-141	44	15	]	]	NUM
ejpam-141	44	16	)	)	PUNCT
ejpam-141	44	17	,	,	PUNCT
ejpam-141	44	18	if	if	SCONJ
ejpam-141	44	19	x	x	PRON
ejpam-141	44	20	has	have	VERB
ejpam-141	44	21	a	a	DET
ejpam-141	44	22	countable	countable	ADJ
ejpam-141	44	23	cs	cs	ADJ
ejpam-141	44	24	-	-	NOUN
ejpam-141	44	25	network	network	NOUN
ejpam-141	44	26	(	(	PUNCT
ejpam-141	44	27	resp	resp	NOUN
ejpam-141	44	28	.	.	PUNCT
ejpam-141	44	29	,	,	PUNCT
ejpam-141	44	30	countable	countable	ADJ
ejpam-141	44	31	network	network	NOUN
ejpam-141	44	32	,	,	PUNCT
ejpam-141	44	33	countable	countable	ADJ
ejpam-141	44	34	sn	sn	NOUN
ejpam-141	44	35	-	-	PUNCT
ejpam-141	44	36	network	network	NOUN
ejpam-141	44	37	)	)	PUNCT
ejpam-141	44	38	.	.	PUNCT
ejpam-141	45	1	(	(	PUNCT
ejpam-141	45	2	2	2	X
ejpam-141	45	3	)	)	PUNCT
ejpam-141	45	4	x	x	X
ejpam-141	45	5	is	be	AUX
ejpam-141	45	6	a	a	DET
ejpam-141	45	7	sequential	sequential	ADJ
ejpam-141	45	8	space	space	NOUN
ejpam-141	45	9	[	[	X
ejpam-141	45	10	4	4	NUM
ejpam-141	45	11	]	]	PUNCT
ejpam-141	45	12	,	,	PUNCT
ejpam-141	45	13	if	if	SCONJ
ejpam-141	45	14	every	every	DET
ejpam-141	45	15	sequentially	sequentially	ADV
ejpam-141	45	16	open	open	ADJ
ejpam-141	45	17	subset	subset	NOUN
ejpam-141	45	18	of	of	ADP
ejpam-141	45	19	x	x	PUNCT
ejpam-141	45	20	is	be	AUX
ejpam-141	45	21	open	open	ADJ
ejpam-141	45	22	.	.	PUNCT
ejpam-141	46	1	n.	n.	NOUN
ejpam-141	46	2	dung	dung	PROPN
ejpam-141	46	3	/	/	SYM
ejpam-141	46	4	eur	eur	PROPN
ejpam-141	46	5	.	.	PUNCT
ejpam-141	47	1	j.	j.	PROPN
ejpam-141	47	2	pure	pure	PROPN
ejpam-141	47	3	appl	appl	PROPN
ejpam-141	47	4	.	.	PROPN
ejpam-141	47	5	math	math	PROPN
ejpam-141	47	6	,	,	PUNCT
ejpam-141	47	7	2	2	NUM
ejpam-141	47	8	(	(	PUNCT
ejpam-141	47	9	2009	2009	NUM
ejpam-141	47	10	)	)	PUNCT
ejpam-141	47	11	,	,	PUNCT
ejpam-141	47	12	(	(	PUNCT
ejpam-141	47	13	182	182	NUM
ejpam-141	47	14	-	-	SYM
ejpam-141	47	15	194	194	NUM
ejpam-141	47	16	)	)	PUNCT
ejpam-141	47	17	185	185	NUM
ejpam-141	47	18	(	(	PUNCT
ejpam-141	47	19	3	3	NUM
ejpam-141	47	20	)	)	PUNCT
ejpam-141	47	21	x	x	X
ejpam-141	47	22	is	be	AUX
ejpam-141	47	23	sequentially	sequentially	ADV
ejpam-141	47	24	separable	separable	ADJ
ejpam-141	47	25	[	[	X
ejpam-141	47	26	2	2	NUM
ejpam-141	47	27	]	]	PUNCT
ejpam-141	47	28	,	,	PUNCT
ejpam-141	47	29	if	if	SCONJ
ejpam-141	47	30	x	x	PRON
ejpam-141	47	31	has	have	VERB
ejpam-141	47	32	a	a	DET
ejpam-141	47	33	countable	countable	ADJ
ejpam-141	47	34	subset	subset	NOUN
ejpam-141	47	35	d	d	SCONJ
ejpam-141	47	36	such	such	ADJ
ejpam-141	47	37	that	that	PRON
ejpam-141	47	38	for	for	ADP
ejpam-141	47	39	each	each	DET
ejpam-141	47	40	x	x	SYM
ejpam-141	47	41	∈	∈	PROPN
ejpam-141	47	42	x	x	X
ejpam-141	47	43	,	,	PUNCT
ejpam-141	47	44	there	there	PRON
ejpam-141	47	45	exists	exist	VERB
ejpam-141	47	46	a	a	DET
ejpam-141	47	47	sequence	sequence	NOUN
ejpam-141	47	48	l	l	NOUN
ejpam-141	48	1	⊂	⊂	PUNCT
ejpam-141	49	1	d	d	X
ejpam-141	49	2	converging	converge	VERB
ejpam-141	49	3	to	to	ADP
ejpam-141	49	4	x	x	PRON
ejpam-141	49	5	,	,	PUNCT
ejpam-141	49	6	where	where	SCONJ
ejpam-141	49	7	d	d	NOUN
ejpam-141	49	8	is	be	AUX
ejpam-141	49	9	a	a	DET
ejpam-141	49	10	sequentially	sequentially	ADV
ejpam-141	49	11	dense	dense	ADJ
ejpam-141	49	12	subset	subset	NOUN
ejpam-141	49	13	of	of	ADP
ejpam-141	49	14	x	x	PROPN
ejpam-141	49	15	.	.	PUNCT
ejpam-141	50	1	definition	definition	NOUN
ejpam-141	50	2	2.4	2.4	NUM
ejpam-141	50	3	.	.	PUNCT
ejpam-141	51	1	let	let	VERB
ejpam-141	51	2	p	p	NOUN
ejpam-141	51	3	=	=	VERB
ejpam-141	51	4	⋃	⋃	PROPN
ejpam-141	51	5	{	{	PUNCT
ejpam-141	51	6	px	px	X
ejpam-141	51	7	:	:	PUNCT
ejpam-141	51	8	x	x	SYM
ejpam-141	51	9	∈	∈	PROPN
ejpam-141	51	10	x	x	PRON
ejpam-141	51	11	}	}	PUNCT
ejpam-141	51	12	be	be	AUX
ejpam-141	51	13	a	a	DET
ejpam-141	51	14	family	family	NOUN
ejpam-141	51	15	of	of	ADP
ejpam-141	51	16	subsets	subset	NOUN
ejpam-141	51	17	of	of	ADP
ejpam-141	51	18	a	a	DET
ejpam-141	51	19	space	space	NOUN
ejpam-141	51	20	x	x	PUNCT
ejpam-141	51	21	satisfying	satisfy	VERB
ejpam-141	51	22	that	that	SCONJ
ejpam-141	51	23	,	,	PUNCT
ejpam-141	51	24	for	for	ADP
ejpam-141	51	25	each	each	PRON
ejpam-141	51	26	x	x	SYM
ejpam-141	51	27	∈	∈	PROPN
ejpam-141	51	28	x	x	X
ejpam-141	51	29	,	,	PUNCT
ejpam-141	51	30	px	px	PROPN
ejpam-141	51	31	is	be	AUX
ejpam-141	51	32	a	a	DET
ejpam-141	51	33	network	network	NOUN
ejpam-141	51	34	at	at	ADP
ejpam-141	51	35	x	x	X
ejpam-141	51	36	in	in	ADP
ejpam-141	51	37	x	x	X
ejpam-141	51	38	,	,	PUNCT
ejpam-141	51	39	and	and	CCONJ
ejpam-141	51	40	if	if	SCONJ
ejpam-141	51	41	u	u	NOUN
ejpam-141	51	42	,	,	PUNCT
ejpam-141	51	43	v	v	NOUN
ejpam-141	51	44	∈	∈	PROPN
ejpam-141	51	45	px	px	NOUN
ejpam-141	51	46	,	,	PUNCT
ejpam-141	51	47	then	then	ADV
ejpam-141	51	48	w	w	PROPN
ejpam-141	51	49	⊂	⊂	PROPN
ejpam-141	51	50	u	u	PROPN
ejpam-141	51	51	∩	∩	NOUN
ejpam-141	51	52	v	v	NOUN
ejpam-141	51	53	for	for	ADP
ejpam-141	51	54	some	some	DET
ejpam-141	51	55	w	w	PROPN
ejpam-141	51	56	∈	∈	PROPN
ejpam-141	51	57	px	px	NOUN
ejpam-141	51	58	.	.	PUNCT
ejpam-141	52	1	(	(	PUNCT
ejpam-141	52	2	1	1	X
ejpam-141	52	3	)	)	PUNCT
ejpam-141	52	4	p	p	NOUN
ejpam-141	52	5	is	be	AUX
ejpam-141	52	6	a	a	DET
ejpam-141	52	7	weak	weak	ADJ
ejpam-141	52	8	base	base	NOUN
ejpam-141	52	9	of	of	ADP
ejpam-141	52	10	x	x	PUNCT
ejpam-141	53	1	[	[	X
ejpam-141	53	2	18	18	NUM
ejpam-141	53	3	]	]	X
ejpam-141	53	4	,	,	PUNCT
ejpam-141	53	5	if	if	SCONJ
ejpam-141	53	6	g	g	PROPN
ejpam-141	53	7	⊂	⊂	PROPN
ejpam-141	53	8	x	x	PUNCT
ejpam-141	53	9	such	such	ADJ
ejpam-141	53	10	that	that	PRON
ejpam-141	53	11	for	for	ADP
ejpam-141	53	12	each	each	DET
ejpam-141	53	13	x	x	SYM
ejpam-141	53	14	∈	∈	PROPN
ejpam-141	53	15	g	g	NOUN
ejpam-141	53	16	,	,	PUNCT
ejpam-141	53	17	there	there	PRON
ejpam-141	53	18	exists	exist	VERB
ejpam-141	53	19	p	p	PROPN
ejpam-141	53	20	∈	∈	PROPN
ejpam-141	53	21	px	px	NOUN
ejpam-141	53	22	satisfying	satisfy	VERB
ejpam-141	53	23	p	p	PROPN
ejpam-141	53	24	⊂	⊂	PROPN
ejpam-141	53	25	g	g	PROPN
ejpam-141	53	26	,	,	PUNCT
ejpam-141	53	27	then	then	ADV
ejpam-141	53	28	g	g	PROPN
ejpam-141	53	29	is	be	AUX
ejpam-141	53	30	open	open	ADJ
ejpam-141	53	31	in	in	ADP
ejpam-141	53	32	x	x	X
ejpam-141	53	33	(	(	PUNCT
ejpam-141	53	34	2)p	2)p	NUM
ejpam-141	53	35	is	be	AUX
ejpam-141	53	36	an	an	DET
ejpam-141	53	37	sn	sn	NOUN
ejpam-141	53	38	-	-	PUNCT
ejpam-141	53	39	network	network	NOUN
ejpam-141	53	40	of	of	ADP
ejpam-141	53	41	x	x	PUNCT
ejpam-141	54	1	[	[	X
ejpam-141	54	2	12	12	NUM
ejpam-141	54	3	]	]	PUNCT
ejpam-141	54	4	,	,	PUNCT
ejpam-141	54	5	if	if	SCONJ
ejpam-141	54	6	each	each	DET
ejpam-141	54	7	member	member	NOUN
ejpam-141	54	8	ofpx	ofpx	PROPN
ejpam-141	54	9	is	be	AUX
ejpam-141	54	10	a	a	DET
ejpam-141	54	11	sequential	sequential	ADJ
ejpam-141	54	12	neighborhood	neighborhood	NOUN
ejpam-141	54	13	of	of	ADP
ejpam-141	54	14	x	x	PUNCT
ejpam-141	54	15	in	in	ADP
ejpam-141	54	16	x	x	X
ejpam-141	54	17	.	.	PUNCT
ejpam-141	55	1	(	(	PUNCT
ejpam-141	55	2	3	3	X
ejpam-141	55	3	)	)	PUNCT
ejpam-141	55	4	the	the	DET
ejpam-141	55	5	above	above	ADJ
ejpam-141	55	6	px	px	PROPN
ejpam-141	55	7	is	be	AUX
ejpam-141	55	8	respectively	respectively	ADV
ejpam-141	55	9	a	a	DET
ejpam-141	55	10	weak	weak	ADJ
ejpam-141	55	11	base	base	NOUN
ejpam-141	55	12	,	,	PUNCT
ejpam-141	55	13	and	and	CCONJ
ejpam-141	55	14	an	an	DET
ejpam-141	55	15	sn	sn	NOUN
ejpam-141	55	16	-	-	PUNCT
ejpam-141	55	17	network	network	NOUN
ejpam-141	55	18	at	at	ADP
ejpam-141	55	19	x	x	X
ejpam-141	55	20	in	in	ADP
ejpam-141	55	21	x	x	PUNCT
ejpam-141	56	1	[	[	X
ejpam-141	56	2	11	11	NUM
ejpam-141	56	3	]	]	PUNCT
ejpam-141	56	4	.	.	PUNCT
ejpam-141	57	1	remark	remark	VERB
ejpam-141	57	2	2.5	2.5	NUM
ejpam-141	57	3	(	(	PUNCT
ejpam-141	57	4	[	[	X
ejpam-141	57	5	14	14	NUM
ejpam-141	57	6	]	]	NUM
ejpam-141	57	7	)	)	PUNCT
ejpam-141	57	8	.	.	PUNCT
ejpam-141	58	1	an	an	DET
ejpam-141	58	2	sn	sn	NOUN
ejpam-141	58	3	-	-	PUNCT
ejpam-141	58	4	network	network	NOUN
ejpam-141	58	5	of	of	ADP
ejpam-141	58	6	a	a	DET
ejpam-141	58	7	sequential	sequential	ADJ
ejpam-141	58	8	space	space	NOUN
ejpam-141	58	9	is	be	AUX
ejpam-141	58	10	a	a	DET
ejpam-141	58	11	weak	weak	ADJ
ejpam-141	58	12	base	base	NOUN
ejpam-141	58	13	.	.	PUNCT
ejpam-141	59	1	definition	definition	NOUN
ejpam-141	59	2	2.6	2.6	NUM
ejpam-141	59	3	.	.	PUNCT
ejpam-141	60	1	let	let	VERB
ejpam-141	60	2	f	f	NOUN
ejpam-141	60	3	:	:	PUNCT
ejpam-141	60	4	x	x	PUNCT
ejpam-141	60	5	−→	−→	NOUN
ejpam-141	60	6	y	y	NOUN
ejpam-141	60	7	be	be	AUX
ejpam-141	60	8	a	a	DET
ejpam-141	60	9	mapping	mapping	NOUN
ejpam-141	60	10	.	.	PUNCT
ejpam-141	61	1	(	(	PUNCT
ejpam-141	61	2	1	1	X
ejpam-141	61	3	)	)	PUNCT
ejpam-141	61	4	f	f	PROPN
ejpam-141	61	5	is	be	AUX
ejpam-141	61	6	an	an	DET
ejpam-141	61	7	1	1	NUM
ejpam-141	61	8	-	-	PUNCT
ejpam-141	61	9	sequence	sequence	NOUN
ejpam-141	61	10	-	-	PUNCT
ejpam-141	61	11	covering	cover	VERB
ejpam-141	61	12	mapping	mapping	NOUN
ejpam-141	61	13	[	[	X
ejpam-141	61	14	12	12	NUM
ejpam-141	61	15	]	]	PUNCT
ejpam-141	61	16	,	,	PUNCT
ejpam-141	61	17	if	if	SCONJ
ejpam-141	61	18	for	for	ADP
ejpam-141	61	19	every	every	DET
ejpam-141	61	20	y	y	PROPN
ejpam-141	61	21	∈	∈	PROPN
ejpam-141	61	22	y	y	PROPN
ejpam-141	61	23	,	,	PUNCT
ejpam-141	61	24	there	there	PRON
ejpam-141	61	25	exists	exist	VERB
ejpam-141	61	26	x	x	PUNCT
ejpam-141	61	27	y	y	PROPN
ejpam-141	61	28	∈	∈	PROPN
ejpam-141	61	29	f	f	PROPN
ejpam-141	61	30	−1(y	−1(y	NOUN
ejpam-141	61	31	)	)	PUNCT
ejpam-141	61	32	such	such	ADJ
ejpam-141	61	33	that	that	SCONJ
ejpam-141	61	34	whenever	whenever	SCONJ
ejpam-141	61	35	{	{	PUNCT
ejpam-141	61	36	yn	yn	X
ejpam-141	61	37	:	:	PUNCT
ejpam-141	61	38	n	n	CCONJ
ejpam-141	61	39	∈	∈	PROPN
ejpam-141	61	40	n	n	CCONJ
ejpam-141	61	41	}	}	PUNCT
ejpam-141	61	42	is	be	AUX
ejpam-141	61	43	a	a	DET
ejpam-141	61	44	sequence	sequence	NOUN
ejpam-141	61	45	converging	converge	VERB
ejpam-141	61	46	to	to	ADP
ejpam-141	61	47	y	y	PROPN
ejpam-141	61	48	in	in	ADP
ejpam-141	61	49	y	y	PROPN
ejpam-141	61	50	there	there	PRON
ejpam-141	61	51	exists	exist	VERB
ejpam-141	61	52	a	a	DET
ejpam-141	61	53	sequence	sequence	NOUN
ejpam-141	61	54	{	{	PUNCT
ejpam-141	61	55	xn	xn	PROPN
ejpam-141	61	56	:	:	PUNCT
ejpam-141	62	1	n	n	CCONJ
ejpam-141	62	2	∈	∈	PROPN
ejpam-141	62	3	n	n	CCONJ
ejpam-141	62	4	}	}	PUNCT
ejpam-141	62	5	converging	converge	VERB
ejpam-141	62	6	to	to	ADP
ejpam-141	62	7	x	x	PROPN
ejpam-141	62	8	y	y	PROPN
ejpam-141	62	9	in	in	ADP
ejpam-141	62	10	x	x	PUNCT
ejpam-141	62	11	with	with	ADP
ejpam-141	62	12	each	each	DET
ejpam-141	62	13	xn	xn	PROPN
ejpam-141	62	14	∈	∈	PROPN
ejpam-141	62	15	f	f	PROPN
ejpam-141	62	16	−1(yn	−1(yn	NOUN
ejpam-141	62	17	)	)	PUNCT
ejpam-141	62	18	.	.	PUNCT
ejpam-141	63	1	(	(	PUNCT
ejpam-141	63	2	2	2	X
ejpam-141	63	3	)	)	PUNCT
ejpam-141	63	4	f	f	PROPN
ejpam-141	63	5	is	be	AUX
ejpam-141	63	6	an	an	DET
ejpam-141	63	7	1	1	NUM
ejpam-141	63	8	-	-	PUNCT
ejpam-141	63	9	sequentially	sequentially	ADV
ejpam-141	63	10	quotient	quotient	NOUN
ejpam-141	63	11	mapping	mapping	NOUN
ejpam-141	64	1	[	[	X
ejpam-141	64	2	16	16	NUM
ejpam-141	64	3	]	]	X
ejpam-141	64	4	,	,	PUNCT
ejpam-141	64	5	if	if	SCONJ
ejpam-141	64	6	for	for	ADP
ejpam-141	64	7	every	every	DET
ejpam-141	64	8	y	y	PROPN
ejpam-141	64	9	∈	∈	PROPN
ejpam-141	64	10	y	y	PROPN
ejpam-141	64	11	,	,	PUNCT
ejpam-141	64	12	there	there	PRON
ejpam-141	64	13	exists	exist	VERB
ejpam-141	64	14	x	x	PUNCT
ejpam-141	64	15	y	y	PROPN
ejpam-141	64	16	∈	∈	PROPN
ejpam-141	64	17	f	f	PROPN
ejpam-141	64	18	−1(y	−1(y	NOUN
ejpam-141	64	19	)	)	PUNCT
ejpam-141	64	20	such	such	ADJ
ejpam-141	64	21	that	that	SCONJ
ejpam-141	64	22	whenever	whenever	SCONJ
ejpam-141	64	23	{	{	PUNCT
ejpam-141	64	24	yn	yn	X
ejpam-141	64	25	:	:	PUNCT
ejpam-141	64	26	n	n	CCONJ
ejpam-141	64	27	∈	∈	PROPN
ejpam-141	64	28	n	n	CCONJ
ejpam-141	64	29	}	}	PUNCT
ejpam-141	64	30	is	be	AUX
ejpam-141	64	31	a	a	DET
ejpam-141	64	32	sequence	sequence	NOUN
ejpam-141	64	33	converging	converge	VERB
ejpam-141	64	34	to	to	ADP
ejpam-141	64	35	y	y	PROPN
ejpam-141	64	36	in	in	ADP
ejpam-141	64	37	y	y	PROPN
ejpam-141	64	38	there	there	PRON
ejpam-141	64	39	exists	exist	VERB
ejpam-141	64	40	a	a	DET
ejpam-141	64	41	sequence	sequence	NOUN
ejpam-141	64	42	{	{	PUNCT
ejpam-141	64	43	xk	xk	NOUN
ejpam-141	64	44	:	:	PUNCT
ejpam-141	64	45	k	k	PROPN
ejpam-141	64	46	∈	∈	PROPN
ejpam-141	64	47	n	n	CCONJ
ejpam-141	64	48	}	}	PUNCT
ejpam-141	64	49	converging	converge	VERB
ejpam-141	64	50	to	to	ADP
ejpam-141	64	51	x	x	PROPN
ejpam-141	64	52	y	y	PROPN
ejpam-141	64	53	in	in	ADP
ejpam-141	64	54	x	x	PUNCT
ejpam-141	64	55	with	with	ADP
ejpam-141	64	56	each	each	DET
ejpam-141	64	57	xk	xk	PROPN
ejpam-141	64	58	∈	∈	PROPN
ejpam-141	64	59	f	f	PROPN
ejpam-141	64	60	−1(ynk	−1(ynk	PROPN
ejpam-141	64	61	)	)	PUNCT
ejpam-141	64	62	.	.	PUNCT
ejpam-141	65	1	(	(	PUNCT
ejpam-141	65	2	3	3	X
ejpam-141	65	3	)	)	PUNCT
ejpam-141	65	4	f	f	PROPN
ejpam-141	65	5	is	be	AUX
ejpam-141	65	6	a	a	DET
ejpam-141	65	7	π	π	NOUN
ejpam-141	65	8	-	-	NOUN
ejpam-141	65	9	mapping	mapping	NOUN
ejpam-141	65	10	[	[	X
ejpam-141	65	11	1	1	NUM
ejpam-141	65	12	]	]	PUNCT
ejpam-141	65	13	,	,	PUNCT
ejpam-141	65	14	if	if	SCONJ
ejpam-141	65	15	for	for	ADP
ejpam-141	65	16	every	every	DET
ejpam-141	65	17	y	y	PROPN
ejpam-141	65	18	∈	∈	PROPN
ejpam-141	65	19	y	y	PROPN
ejpam-141	65	20	and	and	CCONJ
ejpam-141	65	21	for	for	ADP
ejpam-141	65	22	every	every	DET
ejpam-141	65	23	neighborhood	neighborhood	NOUN
ejpam-141	65	24	u	u	NOUN
ejpam-141	65	25	of	of	ADP
ejpam-141	65	26	y	y	PROPN
ejpam-141	65	27	in	in	ADP
ejpam-141	65	28	y	y	PROPN
ejpam-141	65	29	,	,	PUNCT
ejpam-141	65	30	d	d	PROPN
ejpam-141	65	31	(	(	PUNCT
ejpam-141	65	32	f	f	PROPN
ejpam-141	65	33	−1(y	−1(y	PROPN
ejpam-141	65	34	)	)	PUNCT
ejpam-141	65	35	,	,	PUNCT
ejpam-141	65	36	x	x	PUNCT
ejpam-141	65	37	−	−	PROPN
ejpam-141	65	38	f	f	PROPN
ejpam-141	65	39	−1(u	−1(u	NOUN
ejpam-141	65	40	)	)	PUNCT
ejpam-141	65	41	)	)	PUNCT
ejpam-141	65	42	>	>	X
ejpam-141	66	1	0	0	NUM
ejpam-141	66	2	,	,	PUNCT
ejpam-141	66	3	where	where	SCONJ
ejpam-141	66	4	x	x	PRON
ejpam-141	66	5	is	be	AUX
ejpam-141	66	6	a	a	DET
ejpam-141	66	7	metric	metric	ADJ
ejpam-141	66	8	space	space	NOUN
ejpam-141	66	9	with	with	ADP
ejpam-141	66	10	a	a	DET
ejpam-141	66	11	metric	metric	ADJ
ejpam-141	66	12	d.	d.	NOUN
ejpam-141	66	13	(	(	PUNCT
ejpam-141	66	14	4	4	NUM
ejpam-141	66	15	)	)	PUNCT
ejpam-141	66	16	f	f	PROPN
ejpam-141	66	17	is	be	AUX
ejpam-141	66	18	an	an	DET
ejpam-141	66	19	s	s	NOUN
ejpam-141	66	20	-	-	NOUN
ejpam-141	66	21	mapping	mapping	NOUN
ejpam-141	66	22	[	[	X
ejpam-141	66	23	1	1	NUM
ejpam-141	66	24	]	]	PUNCT
ejpam-141	66	25	,	,	PUNCT
ejpam-141	66	26	if	if	SCONJ
ejpam-141	66	27	f	f	PROPN
ejpam-141	66	28	−1(y	−1(y	PROPN
ejpam-141	66	29	)	)	PUNCT
ejpam-141	66	30	is	be	AUX
ejpam-141	66	31	separable	separable	ADJ
ejpam-141	66	32	for	for	ADP
ejpam-141	66	33	every	every	DET
ejpam-141	66	34	y	y	PROPN
ejpam-141	66	35	∈	∈	PROPN
ejpam-141	66	36	y	y	PROPN
ejpam-141	66	37	.	.	PUNCT
ejpam-141	67	1	(	(	PUNCT
ejpam-141	67	2	5	5	X
ejpam-141	67	3	)	)	PUNCT
ejpam-141	67	4	f	f	PROPN
ejpam-141	67	5	is	be	AUX
ejpam-141	67	6	a	a	DET
ejpam-141	67	7	π	π	PROPN
ejpam-141	67	8	-	-	PUNCT
ejpam-141	67	9	s	s	NOUN
ejpam-141	67	10	-	-	PUNCT
ejpam-141	67	11	mapping	mapping	NOUN
ejpam-141	67	12	[	[	X
ejpam-141	67	13	10	10	NUM
ejpam-141	67	14	]	]	PUNCT
ejpam-141	67	15	,	,	PUNCT
ejpam-141	67	16	if	if	SCONJ
ejpam-141	67	17	f	f	PROPN
ejpam-141	67	18	is	be	AUX
ejpam-141	67	19	both	both	PRON
ejpam-141	67	20	π	π	NOUN
ejpam-141	67	21	-	-	NOUN
ejpam-141	67	22	mapping	mapping	ADJ
ejpam-141	67	23	and	and	CCONJ
ejpam-141	67	24	s	s	NOUN
ejpam-141	67	25	-	-	NOUN
ejpam-141	67	26	mapping	mapping	NOUN
ejpam-141	67	27	.	.	PUNCT
ejpam-141	68	1	definition	definition	NOUN
ejpam-141	68	2	2.7	2.7	NUM
ejpam-141	68	3	.	.	PUNCT
ejpam-141	69	1	let	let	VERB
ejpam-141	69	2	{	{	PUNCT
ejpam-141	69	3	pn	pn	VERB
ejpam-141	69	4	:	:	PUNCT
ejpam-141	69	5	n	n	CCONJ
ejpam-141	69	6	∈	∈	PROPN
ejpam-141	69	7	n	n	CCONJ
ejpam-141	69	8	}	}	PUNCT
ejpam-141	69	9	be	be	AUX
ejpam-141	69	10	a	a	DET
ejpam-141	69	11	refinement	refinement	NOUN
ejpam-141	69	12	sequence	sequence	NOUN
ejpam-141	69	13	of	of	ADP
ejpam-141	69	14	a	a	DET
ejpam-141	69	15	space	space	NOUN
ejpam-141	69	16	x	x	SYM
ejpam-141	69	17	,	,	PUNCT
ejpam-141	69	18	i.e.	i.e.	X
ejpam-141	69	19	,	,	PUNCT
ejpam-141	69	20	each	each	DET
ejpam-141	69	21	pn	pn	PROPN
ejpam-141	69	22	is	be	AUX
ejpam-141	69	23	a	a	DET
ejpam-141	69	24	cover	cover	NOUN
ejpam-141	69	25	of	of	ADP
ejpam-141	69	26	x	x	PUNCT
ejpam-141	69	27	and	and	CCONJ
ejpam-141	69	28	pn+1	pn+1	PROPN
ejpam-141	69	29	is	be	AUX
ejpam-141	69	30	a	a	DET
ejpam-141	69	31	refinement	refinement	NOUN
ejpam-141	69	32	of	of	ADP
ejpam-141	69	33	pn	pn	PROPN
ejpam-141	69	34	.	.	PUNCT
ejpam-141	69	35	n.	n.	PROPN
ejpam-141	69	36	dung	dung	PROPN
ejpam-141	69	37	/	/	SYM
ejpam-141	69	38	eur	eur	PROPN
ejpam-141	69	39	.	.	PUNCT
ejpam-141	70	1	j.	j.	PROPN
ejpam-141	70	2	pure	pure	PROPN
ejpam-141	70	3	appl	appl	PROPN
ejpam-141	70	4	.	.	PROPN
ejpam-141	70	5	math	math	PROPN
ejpam-141	70	6	,	,	PUNCT
ejpam-141	70	7	2	2	NUM
ejpam-141	70	8	(	(	PUNCT
ejpam-141	70	9	2009	2009	NUM
ejpam-141	70	10	)	)	PUNCT
ejpam-141	70	11	,	,	PUNCT
ejpam-141	70	12	(	(	PUNCT
ejpam-141	70	13	182	182	NUM
ejpam-141	70	14	-	-	SYM
ejpam-141	70	15	194	194	NUM
ejpam-141	70	16	)	)	PUNCT
ejpam-141	70	17	186	186	NUM
ejpam-141	70	18	(	(	PUNCT
ejpam-141	70	19	1	1	NUM
ejpam-141	70	20	)	)	PUNCT
ejpam-141	70	21	⋃	⋃	NOUN
ejpam-141	70	22	{	{	PUNCT
ejpam-141	70	23	pn	pn	NOUN
ejpam-141	70	24	:	:	PUNCT
ejpam-141	70	25	n	n	CCONJ
ejpam-141	70	26	∈	∈	PROPN
ejpam-141	70	27	n	n	CCONJ
ejpam-141	70	28	}	}	PUNCT
ejpam-141	70	29	is	be	AUX
ejpam-141	70	30	σ	σ	NOUN
ejpam-141	70	31	-	-	PUNCT
ejpam-141	70	32	strong	strong	ADJ
ejpam-141	70	33	network	network	NOUN
ejpam-141	70	34	of	of	ADP
ejpam-141	70	35	x	x	PROPN
ejpam-141	71	1	[	[	X
ejpam-141	71	2	9	9	NUM
ejpam-141	71	3	]	]	PUNCT
ejpam-141	71	4	,	,	PUNCT
ejpam-141	71	5	if	if	SCONJ
ejpam-141	71	6	{	{	PUNCT
ejpam-141	71	7	st(x	st(x	X
ejpam-141	71	8	,	,	PUNCT
ejpam-141	71	9	pn	pn	PROPN
ejpam-141	71	10	)	)	PUNCT
ejpam-141	71	11	:	:	PUNCT
ejpam-141	71	12	n	n	CCONJ
ejpam-141	71	13	∈	∈	PROPN
ejpam-141	71	14	n	n	CCONJ
ejpam-141	71	15	}	}	PUNCT
ejpam-141	71	16	is	be	AUX
ejpam-141	71	17	a	a	DET
ejpam-141	71	18	network	network	NOUN
ejpam-141	71	19	at	at	ADP
ejpam-141	71	20	x	x	SYM
ejpam-141	71	21	in	in	ADP
ejpam-141	71	22	x	x	PUNCT
ejpam-141	71	23	for	for	ADP
ejpam-141	71	24	every	every	DET
ejpam-141	71	25	x	x	SYM
ejpam-141	71	26	∈	∈	PROPN
ejpam-141	71	27	x	x	X
ejpam-141	71	28	.	.	PUNCT
ejpam-141	72	1	(	(	PUNCT
ejpam-141	72	2	2	2	X
ejpam-141	72	3	)	)	PUNCT
ejpam-141	72	4	⋃	⋃	NOUN
ejpam-141	72	5	{	{	PUNCT
ejpam-141	72	6	pn	pn	NOUN
ejpam-141	72	7	:	:	PUNCT
ejpam-141	72	8	n	n	CCONJ
ejpam-141	72	9	∈	∈	PROPN
ejpam-141	72	10	n	n	CCONJ
ejpam-141	72	11	}	}	PUNCT
ejpam-141	72	12	is	be	AUX
ejpam-141	72	13	weak	weak	ADJ
ejpam-141	72	14	development	development	NOUN
ejpam-141	72	15	of	of	ADP
ejpam-141	72	16	x	x	PUNCT
ejpam-141	73	1	[	[	X
ejpam-141	73	2	10	10	NUM
ejpam-141	73	3	]	]	PUNCT
ejpam-141	73	4	,	,	PUNCT
ejpam-141	73	5	if	if	SCONJ
ejpam-141	73	6	{	{	PUNCT
ejpam-141	73	7	st(x	st(x	X
ejpam-141	73	8	,	,	PUNCT
ejpam-141	73	9	pn	pn	PROPN
ejpam-141	73	10	)	)	PUNCT
ejpam-141	73	11	:	:	PUNCT
ejpam-141	74	1	n	n	CCONJ
ejpam-141	74	2	∈	∈	PROPN
ejpam-141	74	3	n	n	CCONJ
ejpam-141	74	4	}	}	PUNCT
ejpam-141	74	5	is	be	AUX
ejpam-141	74	6	a	a	DET
ejpam-141	74	7	weak	weak	ADJ
ejpam-141	74	8	base	base	NOUN
ejpam-141	74	9	at	at	ADP
ejpam-141	74	10	x	x	X
ejpam-141	74	11	in	in	ADP
ejpam-141	74	12	x	x	PUNCT
ejpam-141	74	13	for	for	ADP
ejpam-141	74	14	every	every	DET
ejpam-141	74	15	x	x	SYM
ejpam-141	74	16	∈	∈	PROPN
ejpam-141	74	17	x	x	X
ejpam-141	74	18	.	.	PUNCT
ejpam-141	75	1	(	(	PUNCT
ejpam-141	75	2	3	3	X
ejpam-141	75	3	)	)	PUNCT
ejpam-141	75	4	⋃	⋃	NOUN
ejpam-141	75	5	{	{	PUNCT
ejpam-141	75	6	pn	pn	NOUN
ejpam-141	75	7	:	:	PUNCT
ejpam-141	75	8	n	n	CCONJ
ejpam-141	75	9	∈	∈	PROPN
ejpam-141	75	10	n	n	CCONJ
ejpam-141	75	11	}	}	PUNCT
ejpam-141	75	12	is	be	AUX
ejpam-141	75	13	a	a	DET
ejpam-141	75	14	σ	σ	NOUN
ejpam-141	75	15	-	-	PUNCT
ejpam-141	75	16	strong	strong	ADJ
ejpam-141	75	17	sn	sn	NOUN
ejpam-141	75	18	-	-	PUNCT
ejpam-141	75	19	network	network	NOUN
ejpam-141	75	20	of	of	ADP
ejpam-141	75	21	x	x	SYM
ejpam-141	75	22	,	,	PUNCT
ejpam-141	75	23	if	if	SCONJ
ejpam-141	75	24	⋃	⋃	PROPN
ejpam-141	75	25	{	{	PUNCT
ejpam-141	75	26	pn	pn	NOUN
ejpam-141	75	27	:	:	PUNCT
ejpam-141	75	28	n	n	CCONJ
ejpam-141	75	29	∈	∈	PROPN
ejpam-141	75	30	n	n	CCONJ
ejpam-141	75	31	}	}	PUNCT
ejpam-141	75	32	is	be	AUX
ejpam-141	75	33	a	a	DET
ejpam-141	75	34	σ	σ	PROPN
ejpam-141	75	35	-	-	PUNCT
ejpam-141	75	36	strong	strong	ADJ
ejpam-141	75	37	network	network	NOUN
ejpam-141	75	38	and	and	CCONJ
ejpam-141	75	39	each	each	DET
ejpam-141	75	40	pn	pn	PROPN
ejpam-141	75	41	is	be	AUX
ejpam-141	75	42	an	an	DET
ejpam-141	75	43	sn	sn	NOUN
ejpam-141	75	44	-	-	PUNCT
ejpam-141	75	45	cover	cover	NOUN
ejpam-141	75	46	of	of	ADP
ejpam-141	75	47	x	x	X
ejpam-141	75	48	.	.	PUNCT
ejpam-141	76	1	a	a	DET
ejpam-141	76	2	σ	σ	NOUN
ejpam-141	76	3	-	-	PUNCT
ejpam-141	76	4	strong	strong	ADJ
ejpam-141	76	5	sn	sn	NOUN
ejpam-141	76	6	-	-	PUNCT
ejpam-141	76	7	network	network	NOUN
ejpam-141	76	8	of	of	ADP
ejpam-141	76	9	x	x	X
ejpam-141	76	10	is	be	AUX
ejpam-141	76	11	a	a	DET
ejpam-141	76	12	point	point	NOUN
ejpam-141	76	13	-	-	PUNCT
ejpam-141	76	14	star	star	NOUN
ejpam-141	76	15	network	network	NOUN
ejpam-141	76	16	of	of	ADP
ejpam-141	76	17	sn	sn	PROPN
ejpam-141	76	18	-	-	PUNCT
ejpam-141	76	19	covers	cover	NOUN
ejpam-141	76	20	in	in	ADP
ejpam-141	76	21	the	the	DET
ejpam-141	76	22	sense	sense	NOUN
ejpam-141	76	23	of	of	ADP
ejpam-141	76	24	[	[	X
ejpam-141	76	25	16	16	NUM
ejpam-141	76	26	]	]	PUNCT
ejpam-141	76	27	.	.	PUNCT
ejpam-141	77	1	(	(	PUNCT
ejpam-141	77	2	4	4	NUM
ejpam-141	77	3	)	)	PUNCT
ejpam-141	77	4	⋃	⋃	NOUN
ejpam-141	77	5	{	{	PUNCT
ejpam-141	77	6	pn	pn	NOUN
ejpam-141	77	7	:	:	PUNCT
ejpam-141	77	8	n	n	CCONJ
ejpam-141	77	9	∈	∈	PROPN
ejpam-141	77	10	n	n	CCONJ
ejpam-141	77	11	}	}	PUNCT
ejpam-141	77	12	is	be	AUX
ejpam-141	77	13	an	an	DET
ejpam-141	77	14	sn	sn	NOUN
ejpam-141	77	15	-	-	PUNCT
ejpam-141	77	16	weak	weak	ADJ
ejpam-141	77	17	-	-	PUNCT
ejpam-141	77	18	development	development	NOUN
ejpam-141	77	19	of	of	ADP
ejpam-141	77	20	x	x	SYM
ejpam-141	77	21	,	,	PUNCT
ejpam-141	77	22	if	if	SCONJ
ejpam-141	77	23	⋃	⋃	PROPN
ejpam-141	77	24	{	{	PUNCT
ejpam-141	77	25	pn	pn	NOUN
ejpam-141	77	26	:	:	PUNCT
ejpam-141	77	27	n	n	CCONJ
ejpam-141	77	28	∈	∈	PROPN
ejpam-141	77	29	n	n	CCONJ
ejpam-141	77	30	}	}	PUNCT
ejpam-141	77	31	is	be	AUX
ejpam-141	77	32	a	a	DET
ejpam-141	77	33	weakdevelopment	weakdevelopment	NOUN
ejpam-141	77	34	and	and	CCONJ
ejpam-141	77	35	each	each	DET
ejpam-141	77	36	pn	pn	PROPN
ejpam-141	77	37	is	be	AUX
ejpam-141	77	38	an	an	DET
ejpam-141	77	39	sn	sn	NOUN
ejpam-141	77	40	-	-	PUNCT
ejpam-141	77	41	cover	cover	NOUN
ejpam-141	77	42	of	of	ADP
ejpam-141	77	43	x	x	X
ejpam-141	77	44	.	.	PUNCT
ejpam-141	78	1	definition	definition	NOUN
ejpam-141	78	2	2.8	2.8	NUM
ejpam-141	78	3	.	.	PUNCT
ejpam-141	79	1	let	let	VERB
ejpam-141	79	2	p	p	NOUN
ejpam-141	79	3	=	=	VERB
ejpam-141	79	4	⋃	⋃	PROPN
ejpam-141	79	5	{	{	PUNCT
ejpam-141	79	6	pn	pn	NOUN
ejpam-141	79	7	:	:	PUNCT
ejpam-141	79	8	n	n	CCONJ
ejpam-141	79	9	∈	∈	PROPN
ejpam-141	79	10	n	n	CCONJ
ejpam-141	79	11	}	}	PUNCT
ejpam-141	79	12	be	be	AUX
ejpam-141	79	13	a	a	DET
ejpam-141	79	14	σ	σ	NOUN
ejpam-141	79	15	-	-	PUNCT
ejpam-141	79	16	strong	strong	ADJ
ejpam-141	79	17	network	network	NOUN
ejpam-141	79	18	of	of	ADP
ejpam-141	79	19	x	x	X
ejpam-141	79	20	.	.	PUNCT
ejpam-141	80	1	for	for	ADP
ejpam-141	80	2	every	every	DET
ejpam-141	80	3	n	n	PRON
ejpam-141	80	4	∈	∈	PROPN
ejpam-141	80	5	n	n	CCONJ
ejpam-141	80	6	,	,	PUNCT
ejpam-141	80	7	put	put	VERB
ejpam-141	80	8	pn	pn	NOUN
ejpam-141	80	9	=	=	PUNCT
ejpam-141	80	10	{	{	PUNCT
ejpam-141	80	11	pα	pα	INTJ
ejpam-141	80	12	:	:	PUNCT
ejpam-141	80	13	α	α	PROPN
ejpam-141	80	14	∈	∈	PROPN
ejpam-141	80	15	an	an	PRON
ejpam-141	80	16	}	}	PUNCT
ejpam-141	80	17	,	,	PUNCT
ejpam-141	80	18	and	and	CCONJ
ejpam-141	80	19	endowed	endow	VERB
ejpam-141	80	20	an	an	DET
ejpam-141	80	21	with	with	ADP
ejpam-141	80	22	discrete	discrete	ADJ
ejpam-141	80	23	topology	topology	NOUN
ejpam-141	80	24	.	.	PUNCT
ejpam-141	81	1	put	put	VERB
ejpam-141	81	2	m	m	PROPN
ejpam-141	81	3	=	=	NOUN
ejpam-141	81	4	n	n	PRON
ejpam-141	81	5	a	a	NOUN
ejpam-141	81	6	=	=	X
ejpam-141	81	7	(	(	PUNCT
ejpam-141	81	8	αn	αn	NOUN
ejpam-141	81	9	)	)	PUNCT
ejpam-141	81	10	∈	∈	NOUN
ejpam-141	81	11	∏	∏	PROPN
ejpam-141	81	12	n∈n	n∈n	NOUN
ejpam-141	81	13	an	an	PRON
ejpam-141	81	14	:	:	PUNCT
ejpam-141	81	15	{	{	PUNCT
ejpam-141	81	16	pαn	pαn	NOUN
ejpam-141	81	17	:	:	PUNCT
ejpam-141	81	18	n	n	CCONJ
ejpam-141	81	19	∈	∈	PROPN
ejpam-141	81	20	n	n	CCONJ
ejpam-141	81	21	}	}	PUNCT
ejpam-141	81	22	forms	form	VERB
ejpam-141	81	23	a	a	DET
ejpam-141	81	24	network	network	NOUN
ejpam-141	81	25	at	at	ADP
ejpam-141	81	26	some	some	DET
ejpam-141	81	27	point	point	NOUN
ejpam-141	81	28	xa	xa	PROPN
ejpam-141	82	1	in	in	ADP
ejpam-141	82	2	x	x	X
ejpam-141	82	3	o	o	NOUN
ejpam-141	82	4	.	.	PUNCT
ejpam-141	83	1	then	then	ADV
ejpam-141	83	2	m	m	PROPN
ejpam-141	83	3	,	,	PUNCT
ejpam-141	83	4	which	which	PRON
ejpam-141	83	5	is	be	AUX
ejpam-141	83	6	a	a	DET
ejpam-141	83	7	subspace	subspace	NOUN
ejpam-141	83	8	of	of	ADP
ejpam-141	83	9	the	the	DET
ejpam-141	83	10	product	product	NOUN
ejpam-141	83	11	space	space	NOUN
ejpam-141	83	12	∏	∏	PROPN
ejpam-141	83	13	n∈n	n∈n	NOUN
ejpam-141	83	14	an	an	PROPN
ejpam-141	83	15	,	,	PUNCT
ejpam-141	83	16	is	be	AUX
ejpam-141	83	17	a	a	DET
ejpam-141	83	18	metric	metric	ADJ
ejpam-141	83	19	space	space	NOUN
ejpam-141	83	20	,	,	PUNCT
ejpam-141	83	21	xa	xa	PROPN
ejpam-141	83	22	is	be	AUX
ejpam-141	83	23	unique	unique	ADJ
ejpam-141	83	24	,	,	PUNCT
ejpam-141	83	25	and	and	CCONJ
ejpam-141	83	26	xa	xa	PROPN
ejpam-141	83	27	=	=	SYM
ejpam-141	83	28	⋂	⋂	PROPN
ejpam-141	83	29	n∈n	n∈n	ADJ
ejpam-141	83	30	pαn	pαn	NOUN
ejpam-141	83	31	for	for	ADP
ejpam-141	83	32	every	every	DET
ejpam-141	83	33	a	a	DET
ejpam-141	83	34	∈	∈	PROPN
ejpam-141	83	35	m.	m.	NOUN
ejpam-141	83	36	define	define	VERB
ejpam-141	83	37	f	f	PROPN
ejpam-141	83	38	:	:	PUNCT
ejpam-141	83	39	m	m	VERB
ejpam-141	83	40	→	→	PUNCT
ejpam-141	83	41	x	x	PUNCT
ejpam-141	83	42	by	by	ADP
ejpam-141	83	43	choosing	choose	VERB
ejpam-141	83	44	f	f	PROPN
ejpam-141	83	45	(	(	PUNCT
ejpam-141	83	46	a	a	NOUN
ejpam-141	83	47	)	)	PUNCT
ejpam-141	83	48	=	=	SYM
ejpam-141	83	49	xa	xa	PROPN
ejpam-141	83	50	,	,	PUNCT
ejpam-141	83	51	then	then	ADV
ejpam-141	83	52	f	f	PROPN
ejpam-141	83	53	is	be	AUX
ejpam-141	83	54	a	a	DET
ejpam-141	83	55	mapping	mapping	NOUN
ejpam-141	83	56	and	and	CCONJ
ejpam-141	83	57	(	(	PUNCT
ejpam-141	83	58	f	f	PROPN
ejpam-141	83	59	,	,	PUNCT
ejpam-141	83	60	m	m	PROPN
ejpam-141	83	61	,	,	PUNCT
ejpam-141	83	62	x	x	SYM
ejpam-141	83	63	,	,	PUNCT
ejpam-141	83	64	{	{	PUNCT
ejpam-141	83	65	pn	pn	NOUN
ejpam-141	83	66	}	}	PUNCT
ejpam-141	83	67	)	)	PUNCT
ejpam-141	83	68	is	be	AUX
ejpam-141	83	69	a	a	DET
ejpam-141	83	70	ponomarev	ponomarev	NOUN
ejpam-141	83	71	-	-	NOUN
ejpam-141	83	72	system	system	NOUN
ejpam-141	83	73	[	[	X
ejpam-141	83	74	15	15	NUM
ejpam-141	83	75	]	]	PUNCT
ejpam-141	83	76	.	.	PUNCT
ejpam-141	84	1	theorem	theorem	VERB
ejpam-141	84	2	2.9	2.9	NUM
ejpam-141	84	3	.	.	PUNCT
ejpam-141	85	1	the	the	DET
ejpam-141	85	2	following	follow	VERB
ejpam-141	85	3	are	be	AUX
ejpam-141	85	4	equivalent	equivalent	ADJ
ejpam-141	85	5	for	for	ADP
ejpam-141	85	6	a	a	DET
ejpam-141	85	7	space	space	NOUN
ejpam-141	85	8	x	x	X
ejpam-141	85	9	.	.	PUNCT
ejpam-141	86	1	1	1	X
ejpam-141	86	2	.	.	X
ejpam-141	86	3	x	x	PUNCT
ejpam-141	86	4	is	be	AUX
ejpam-141	86	5	an	an	DET
ejpam-141	86	6	1	1	NUM
ejpam-141	86	7	-	-	PUNCT
ejpam-141	86	8	sequence	sequence	NOUN
ejpam-141	86	9	-	-	PUNCT
ejpam-141	86	10	covering	cover	VERB
ejpam-141	86	11	π	π	PROPN
ejpam-141	86	12	-	-	PUNCT
ejpam-141	86	13	s	s	NOUN
ejpam-141	86	14	-	-	PUNCT
ejpam-141	86	15	image	image	NOUN
ejpam-141	86	16	of	of	ADP
ejpam-141	86	17	a	a	DET
ejpam-141	86	18	locally	locally	ADV
ejpam-141	86	19	separable	separable	ADJ
ejpam-141	86	20	metric	metric	ADJ
ejpam-141	86	21	space	space	NOUN
ejpam-141	86	22	.	.	PUNCT
ejpam-141	87	1	2	2	X
ejpam-141	87	2	.	.	X
ejpam-141	87	3	x	x	X
ejpam-141	87	4	is	be	AUX
ejpam-141	87	5	an	an	DET
ejpam-141	87	6	1	1	NUM
ejpam-141	87	7	-	-	PUNCT
ejpam-141	87	8	sequentially	sequentially	ADV
ejpam-141	87	9	-	-	PUNCT
ejpam-141	87	10	quotient	quotient	NOUN
ejpam-141	87	11	π	π	PROPN
ejpam-141	87	12	-	-	PUNCT
ejpam-141	87	13	s	s	NOUN
ejpam-141	87	14	-	-	PUNCT
ejpam-141	87	15	image	image	NOUN
ejpam-141	87	16	of	of	ADP
ejpam-141	87	17	a	a	DET
ejpam-141	87	18	locally	locally	ADV
ejpam-141	87	19	separable	separable	ADJ
ejpam-141	87	20	metric	metric	ADJ
ejpam-141	87	21	space	space	NOUN
ejpam-141	87	22	.	.	PUNCT
ejpam-141	88	1	3	3	X
ejpam-141	88	2	.	.	X
ejpam-141	88	3	x	x	PUNCT
ejpam-141	88	4	has	have	VERB
ejpam-141	88	5	a	a	DET
ejpam-141	88	6	point	point	NOUN
ejpam-141	88	7	-	-	PUNCT
ejpam-141	88	8	countable	countable	ADJ
ejpam-141	88	9	σ	σ	NOUN
ejpam-141	88	10	-	-	PUNCT
ejpam-141	88	11	strong	strong	ADJ
ejpam-141	88	12	sn	sn	NOUN
ejpam-141	88	13	-	-	PUNCT
ejpam-141	88	14	network	network	NOUN
ejpam-141	88	15	consisting	consist	VERB
ejpam-141	88	16	of	of	ADP
ejpam-141	88	17	sn	sn	NOUN
ejpam-141	88	18	-	-	PUNCT
ejpam-141	88	19	second	second	ADJ
ejpam-141	88	20	countable	countable	ADJ
ejpam-141	88	21	spaces	space	NOUN
ejpam-141	88	22	.	.	PUNCT
ejpam-141	89	1	4	4	X
ejpam-141	89	2	.	.	X
ejpam-141	89	3	x	x	PUNCT
ejpam-141	89	4	has	have	VERB
ejpam-141	89	5	a	a	DET
ejpam-141	89	6	point	point	NOUN
ejpam-141	89	7	-	-	PUNCT
ejpam-141	89	8	countable	countable	ADJ
ejpam-141	89	9	σ	σ	NOUN
ejpam-141	89	10	-	-	PUNCT
ejpam-141	89	11	strong	strong	ADJ
ejpam-141	89	12	sn	sn	NOUN
ejpam-141	89	13	-	-	PUNCT
ejpam-141	89	14	network	network	NOUN
ejpam-141	89	15	consisting	consist	VERB
ejpam-141	89	16	of	of	ADP
ejpam-141	89	17	ℵ0	ℵ0	NOUN
ejpam-141	89	18	-	-	NOUN
ejpam-141	89	19	spaces	space	NOUN
ejpam-141	89	20	.	.	PUNCT
ejpam-141	90	1	5	5	X
ejpam-141	90	2	.	.	X
ejpam-141	90	3	x	x	PUNCT
ejpam-141	90	4	has	have	VERB
ejpam-141	90	5	a	a	DET
ejpam-141	90	6	point	point	NOUN
ejpam-141	90	7	-	-	PUNCT
ejpam-141	90	8	countable	countable	ADJ
ejpam-141	90	9	σ	σ	NOUN
ejpam-141	90	10	-	-	PUNCT
ejpam-141	90	11	strong	strong	ADJ
ejpam-141	90	12	sn	sn	NOUN
ejpam-141	90	13	-	-	PUNCT
ejpam-141	90	14	network	network	NOUN
ejpam-141	90	15	consisting	consist	VERB
ejpam-141	90	16	of	of	ADP
ejpam-141	90	17	cosmic	cosmic	ADJ
ejpam-141	90	18	spaces	space	NOUN
ejpam-141	90	19	.	.	PUNCT
ejpam-141	91	1	n.	n.	NOUN
ejpam-141	91	2	dung	dung	PROPN
ejpam-141	91	3	/	/	SYM
ejpam-141	91	4	eur	eur	PROPN
ejpam-141	91	5	.	.	PUNCT
ejpam-141	92	1	j.	j.	PROPN
ejpam-141	92	2	pure	pure	PROPN
ejpam-141	92	3	appl	appl	PROPN
ejpam-141	92	4	.	.	PROPN
ejpam-141	92	5	math	math	PROPN
ejpam-141	92	6	,	,	PUNCT
ejpam-141	92	7	2	2	NUM
ejpam-141	92	8	(	(	PUNCT
ejpam-141	92	9	2009	2009	NUM
ejpam-141	92	10	)	)	PUNCT
ejpam-141	92	11	,	,	PUNCT
ejpam-141	92	12	(	(	PUNCT
ejpam-141	92	13	182	182	NUM
ejpam-141	92	14	-	-	SYM
ejpam-141	92	15	194	194	NUM
ejpam-141	92	16	)	)	PUNCT
ejpam-141	92	17	187	187	NUM
ejpam-141	92	18	proof	proof	NOUN
ejpam-141	92	19	.	.	PUNCT
ejpam-141	93	1	(	(	PUNCT
ejpam-141	93	2	1)⇒	1)⇒	NUM
ejpam-141	93	3	(	(	PUNCT
ejpam-141	93	4	2	2	NUM
ejpam-141	93	5	)	)	PUNCT
ejpam-141	93	6	.	.	PUNCT
ejpam-141	94	1	it	it	PRON
ejpam-141	94	2	is	be	AUX
ejpam-141	94	3	obvious	obvious	ADJ
ejpam-141	94	4	.	.	PUNCT
ejpam-141	95	1	(	(	PUNCT
ejpam-141	95	2	2	2	X
ejpam-141	95	3	)	)	PUNCT
ejpam-141	95	4	⇒	⇒	NOUN
ejpam-141	95	5	(	(	PUNCT
ejpam-141	95	6	3	3	NUM
ejpam-141	95	7	)	)	PUNCT
ejpam-141	95	8	.	.	PUNCT
ejpam-141	96	1	let	let	VERB
ejpam-141	96	2	f	f	NOUN
ejpam-141	96	3	:	:	PUNCT
ejpam-141	96	4	m	m	AUX
ejpam-141	96	5	−→	−→	ADJ
ejpam-141	96	6	x	x	VERB
ejpam-141	96	7	be	be	AUX
ejpam-141	96	8	an	an	DET
ejpam-141	96	9	1	1	NUM
ejpam-141	96	10	-	-	PUNCT
ejpam-141	96	11	sequentially	sequentially	ADV
ejpam-141	96	12	-	-	PUNCT
ejpam-141	96	13	quotient	quotient	NOUN
ejpam-141	97	1	π	π	PROPN
ejpam-141	97	2	-	-	PUNCT
ejpam-141	97	3	s	s	NOUN
ejpam-141	97	4	-	-	NOUN
ejpam-141	97	5	mapping	mapping	NOUN
ejpam-141	97	6	from	from	ADP
ejpam-141	97	7	a	a	DET
ejpam-141	97	8	locally	locally	ADV
ejpam-141	97	9	separable	separable	ADJ
ejpam-141	97	10	metric	metric	ADJ
ejpam-141	97	11	space	space	NOUN
ejpam-141	97	12	m	m	VERB
ejpam-141	97	13	with	with	ADP
ejpam-141	97	14	a	a	DET
ejpam-141	97	15	metric	metric	ADJ
ejpam-141	97	16	d	d	NOUN
ejpam-141	97	17	onto	onto	ADP
ejpam-141	97	18	x	x	X
ejpam-141	97	19	.	.	PUNCT
ejpam-141	98	1	for	for	ADP
ejpam-141	98	2	each	each	DET
ejpam-141	98	3	x	x	SYM
ejpam-141	98	4	∈	∈	PROPN
ejpam-141	98	5	x	x	X
ejpam-141	98	6	,	,	PUNCT
ejpam-141	98	7	there	there	PRON
ejpam-141	98	8	exists	exist	VERB
ejpam-141	98	9	ax	ax	NOUN
ejpam-141	98	10	∈	∈	PROPN
ejpam-141	98	11	f	f	PROPN
ejpam-141	98	12	−1(x	−1(x	NOUN
ejpam-141	98	13	)	)	PUNCT
ejpam-141	98	14	such	such	ADJ
ejpam-141	98	15	that	that	SCONJ
ejpam-141	98	16	whenever	whenever	SCONJ
ejpam-141	98	17	{	{	PUNCT
ejpam-141	98	18	xn	xn	NOUN
ejpam-141	98	19	:	:	PUNCT
ejpam-141	98	20	n	n	CCONJ
ejpam-141	98	21	∈	∈	PROPN
ejpam-141	98	22	n	n	CCONJ
ejpam-141	98	23	}	}	PUNCT
ejpam-141	98	24	is	be	AUX
ejpam-141	98	25	a	a	DET
ejpam-141	98	26	sequence	sequence	NOUN
ejpam-141	98	27	converging	converge	VERB
ejpam-141	98	28	to	to	ADP
ejpam-141	98	29	x	x	PUNCT
ejpam-141	98	30	in	in	ADP
ejpam-141	98	31	x	x	SYM
ejpam-141	98	32	there	there	PRON
ejpam-141	98	33	exists	exist	VERB
ejpam-141	98	34	a	a	DET
ejpam-141	98	35	sequence	sequence	NOUN
ejpam-141	98	36	{	{	PUNCT
ejpam-141	98	37	ak	ak	PROPN
ejpam-141	98	38	:	:	PUNCT
ejpam-141	98	39	k	k	PROPN
ejpam-141	98	40	∈	∈	PROPN
ejpam-141	98	41	n	n	CCONJ
ejpam-141	98	42	}	}	PUNCT
ejpam-141	98	43	converging	converge	VERB
ejpam-141	98	44	to	to	PART
ejpam-141	98	45	ax	ax	VERB
ejpam-141	98	46	in	in	ADP
ejpam-141	98	47	m	m	PROPN
ejpam-141	98	48	with	with	ADP
ejpam-141	98	49	each	each	DET
ejpam-141	98	50	ak	ak	PROPN
ejpam-141	98	51	∈	∈	PROPN
ejpam-141	98	52	f	f	PROPN
ejpam-141	98	53	−1(xnk	−1(xnk	PROPN
ejpam-141	98	54	)	)	PUNCT
ejpam-141	98	55	.	.	PUNCT
ejpam-141	99	1	since	since	SCONJ
ejpam-141	99	2	m	m	PROPN
ejpam-141	99	3	is	be	AUX
ejpam-141	99	4	locally	locally	ADV
ejpam-141	99	5	separable	separable	ADJ
ejpam-141	99	6	metric	metric	ADJ
ejpam-141	99	7	,	,	PUNCT
ejpam-141	99	8	m	m	VERB
ejpam-141	99	9	=	=	NOUN
ejpam-141	99	10	⊕λ∈λmλ	⊕λ∈λmλ	ADJ
ejpam-141	99	11	by	by	ADP
ejpam-141	99	12	[	[	X
ejpam-141	99	13	3	3	NUM
ejpam-141	99	14	,	,	PUNCT
ejpam-141	99	15	4.4.f	4.4.f	PROPN
ejpam-141	99	16	]	]	PUNCT
ejpam-141	99	17	,	,	PUNCT
ejpam-141	99	18	where	where	SCONJ
ejpam-141	99	19	each	each	DET
ejpam-141	99	20	mλ	mλ	NOUN
ejpam-141	99	21	is	be	AUX
ejpam-141	99	22	a	a	DET
ejpam-141	99	23	separable	separable	ADJ
ejpam-141	99	24	metric	metric	ADJ
ejpam-141	99	25	space	space	NOUN
ejpam-141	99	26	with	with	ADP
ejpam-141	99	27	a	a	DET
ejpam-141	99	28	metric	metric	ADJ
ejpam-141	99	29	dλ	dλ	NOUN
ejpam-141	99	30	.	.	PUNCT
ejpam-141	100	1	for	for	ADP
ejpam-141	100	2	each	each	DET
ejpam-141	100	3	λ	λ	PROPN
ejpam-141	100	4	∈	∈	PROPN
ejpam-141	100	5	λ	λ	PROPN
ejpam-141	100	6	,	,	PUNCT
ejpam-141	100	7	let	let	VERB
ejpam-141	100	8	dλ	dλ	NOUN
ejpam-141	100	9	be	be	AUX
ejpam-141	100	10	a	a	DET
ejpam-141	100	11	countable	countable	ADJ
ejpam-141	100	12	dense	dense	ADJ
ejpam-141	100	13	subset	subset	NOUN
ejpam-141	100	14	of	of	ADP
ejpam-141	100	15	mλ	mλ	NOUN
ejpam-141	100	16	.	.	PUNCT
ejpam-141	101	1	for	for	ADP
ejpam-141	101	2	each	each	DET
ejpam-141	101	3	n	n	PRON
ejpam-141	101	4	∈	∈	PROPN
ejpam-141	101	5	n	n	CCONJ
ejpam-141	101	6	,	,	PUNCT
ejpam-141	101	7	put	put	VERB
ejpam-141	101	8	bλ	bλ	ADP
ejpam-141	101	9	,	,	PUNCT
ejpam-141	101	10	n	n	CCONJ
ejpam-141	101	11	,	,	PUNCT
ejpam-141	101	12	x	x	SYM
ejpam-141	101	13	=	=	PRON
ejpam-141	101	14	{	{	PUNCT
ejpam-141	101	15	b(a	b(a	PROPN
ejpam-141	101	16	,	,	PUNCT
ejpam-141	101	17	1	1	NUM
ejpam-141	101	18	/	/	SYM
ejpam-141	101	19	n	n	CCONJ
ejpam-141	101	20	)	)	PUNCT
ejpam-141	101	21	:	:	PUNCT
ejpam-141	101	22	a	a	DET
ejpam-141	101	23	∈	∈	PROPN
ejpam-141	101	24	dλ	dλ	NOUN
ejpam-141	101	25	,	,	PUNCT
ejpam-141	101	26	ax	ax	NOUN
ejpam-141	101	27	∈	∈	PROPN
ejpam-141	101	28	b(a	b(a	NOUN
ejpam-141	101	29	,	,	PUNCT
ejpam-141	101	30	1	1	NUM
ejpam-141	101	31	/	/	SYM
ejpam-141	101	32	n	n	CCONJ
ejpam-141	101	33	)	)	PUNCT
ejpam-141	101	34	}	}	PUNCT
ejpam-141	101	35	,	,	PUNCT
ejpam-141	101	36	where	where	SCONJ
ejpam-141	101	37	b(a	b(a	NOUN
ejpam-141	101	38	,	,	PUNCT
ejpam-141	101	39	1	1	NUM
ejpam-141	101	40	/	/	SYM
ejpam-141	101	41	n	n	CCONJ
ejpam-141	101	42	)	)	PUNCT
ejpam-141	101	43	=	=	PRON
ejpam-141	102	1	{	{	PUNCT
ejpam-141	102	2	b	b	X
ejpam-141	102	3	∈	∈	ADJ
ejpam-141	102	4	mλ	mλ	NOUN
ejpam-141	102	5	:	:	PUNCT
ejpam-141	102	6	dλ(a	dλ(a	NOUN
ejpam-141	102	7	,	,	PUNCT
ejpam-141	102	8	b	b	NOUN
ejpam-141	102	9	)	)	PUNCT
ejpam-141	102	10	<	<	X
ejpam-141	102	11	1	1	NUM
ejpam-141	102	12	/	/	SYM
ejpam-141	102	13	n	n	CCONJ
ejpam-141	102	14	}	}	PUNCT
ejpam-141	102	15	,	,	PUNCT
ejpam-141	102	16	and	and	CCONJ
ejpam-141	102	17	put	put	VERB
ejpam-141	102	18	bn	bn	NUM
ejpam-141	102	19	,	,	PUNCT
ejpam-141	102	20	x	x	PUNCT
ejpam-141	102	21	=	=	SYM
ejpam-141	102	22	⋃	⋃	NOUN
ejpam-141	102	23	{	{	PUNCT
ejpam-141	102	24	bλ	bλ	NOUN
ejpam-141	102	25	,	,	PUNCT
ejpam-141	102	26	n	n	CCONJ
ejpam-141	102	27	,	,	PUNCT
ejpam-141	102	28	x	x	PUNCT
ejpam-141	102	29	:	:	PUNCT
ejpam-141	102	30	λ	λ	X
ejpam-141	102	31	∈	∈	NOUN
ejpam-141	102	32	λ},bn	λ},bn	NOUN
ejpam-141	102	33	=	=	SYM
ejpam-141	102	34	⋃	⋃	X
ejpam-141	102	35	{	{	PUNCT
ejpam-141	102	36	bn	bn	NOUN
ejpam-141	102	37	,	,	PUNCT
ejpam-141	102	38	x	x	X
ejpam-141	102	39	:	:	PUNCT
ejpam-141	102	40	x	x	SYM
ejpam-141	102	41	∈	∈	NOUN
ejpam-141	102	42	x},bx	x},bx	PROPN
ejpam-141	102	43	=	=	PUNCT
ejpam-141	102	44	⋃	⋃	PROPN
ejpam-141	102	45	{	{	PUNCT
ejpam-141	102	46	bn	bn	NOUN
ejpam-141	102	47	,	,	PUNCT
ejpam-141	102	48	x	x	SYM
ejpam-141	102	49	:	:	PUNCT
ejpam-141	102	50	n	n	CCONJ
ejpam-141	102	51	∈	∈	PROPN
ejpam-141	102	52	n	n	CCONJ
ejpam-141	102	53	}	}	PUNCT
ejpam-141	102	54	,	,	PUNCT
ejpam-141	102	55	b	b	X
ejpam-141	102	56	=	=	SYM
ejpam-141	102	57	⋃	⋃	NOUN
ejpam-141	102	58	{	{	PUNCT
ejpam-141	102	59	bn	bn	NOUN
ejpam-141	102	60	:	:	PUNCT
ejpam-141	102	61	n	n	CCONJ
ejpam-141	102	62	∈	∈	PROPN
ejpam-141	102	63	n}=	n}=	PROPN
ejpam-141	102	64	⋃	⋃	PROPN
ejpam-141	102	65	{	{	PUNCT
ejpam-141	102	66	bx	bx	NOUN
ejpam-141	102	67	:	:	PUNCT
ejpam-141	102	68	x	x	SYM
ejpam-141	102	69	∈	∈	NOUN
ejpam-141	102	70	x	x	X
ejpam-141	102	71	}	}	PUNCT
ejpam-141	102	72	,	,	PUNCT
ejpam-141	102	73	and	and	CCONJ
ejpam-141	102	74	pn	pn	VERB
ejpam-141	102	75	,	,	PUNCT
ejpam-141	102	76	x	x	X
ejpam-141	102	77	=	=	SYM
ejpam-141	102	78	f	f	X
ejpam-141	102	79	(	(	PUNCT
ejpam-141	102	80	bn	bn	PROPN
ejpam-141	102	81	,	,	PUNCT
ejpam-141	102	82	x),pn	x),pn	NOUN
ejpam-141	102	83	=	=	SYM
ejpam-141	102	84	⋃	⋃	PROPN
ejpam-141	102	85	{	{	PUNCT
ejpam-141	102	86	pn	pn	NOUN
ejpam-141	102	87	,	,	PUNCT
ejpam-141	102	88	x	x	INTJ
ejpam-141	102	89	:	:	PUNCT
ejpam-141	102	90	x	x	SYM
ejpam-141	102	91	∈	∈	PROPN
ejpam-141	103	1	x},px	x},px	PRON
ejpam-141	103	2	=	=	PRON
ejpam-141	104	1	⋃	⋃	NOUN
ejpam-141	104	2	{	{	PUNCT
ejpam-141	104	3	pn	pn	NOUN
ejpam-141	104	4	,	,	PUNCT
ejpam-141	104	5	x	x	INTJ
ejpam-141	104	6	:	:	PUNCT
ejpam-141	104	7	n	n	CCONJ
ejpam-141	104	8	∈	∈	PROPN
ejpam-141	104	9	n	n	CCONJ
ejpam-141	104	10	}	}	PUNCT
ejpam-141	104	11	,	,	PUNCT
ejpam-141	104	12	p	p	X
ejpam-141	104	13	=	=	X
ejpam-141	104	14	⋃	⋃	PROPN
ejpam-141	104	15	{	{	PUNCT
ejpam-141	104	16	pn	pn	NOUN
ejpam-141	104	17	:	:	PUNCT
ejpam-141	104	18	n	n	CCONJ
ejpam-141	104	19	∈	∈	PROPN
ejpam-141	104	20	n}=	n}=	ADV
ejpam-141	104	21	⋃	⋃	PROPN
ejpam-141	104	22	{	{	PUNCT
ejpam-141	104	23	px	px	X
ejpam-141	104	24	:	:	PUNCT
ejpam-141	104	25	x	x	SYM
ejpam-141	104	26	∈	∈	NOUN
ejpam-141	104	27	x	x	NOUN
ejpam-141	104	28	}	}	PUNCT
ejpam-141	104	29	.	.	PUNCT
ejpam-141	105	1	then	then	ADV
ejpam-141	105	2	{	{	PUNCT
ejpam-141	105	3	pn	pn	X
ejpam-141	105	4	:	:	PUNCT
ejpam-141	105	5	n	n	CCONJ
ejpam-141	105	6	∈	∈	PROPN
ejpam-141	105	7	n	n	CCONJ
ejpam-141	105	8	}	}	PUNCT
ejpam-141	105	9	is	be	AUX
ejpam-141	105	10	a	a	DET
ejpam-141	105	11	refinement	refinement	NOUN
ejpam-141	105	12	sequence	sequence	NOUN
ejpam-141	105	13	of	of	ADP
ejpam-141	105	14	x	x	X
ejpam-141	105	15	.	.	PUNCT
ejpam-141	106	1	we	we	PRON
ejpam-141	106	2	shall	shall	AUX
ejpam-141	106	3	prove	prove	VERB
ejpam-141	106	4	that	that	SCONJ
ejpam-141	106	5	p	p	NOUN
ejpam-141	106	6	is	be	AUX
ejpam-141	106	7	a	a	DET
ejpam-141	106	8	pointcountable	pointcountable	ADJ
ejpam-141	106	9	σ	σ	VERB
ejpam-141	106	10	-	-	PUNCT
ejpam-141	106	11	strong	strong	ADJ
ejpam-141	106	12	sn	sn	NOUN
ejpam-141	106	13	-	-	PUNCT
ejpam-141	106	14	network	network	NOUN
ejpam-141	106	15	of	of	ADP
ejpam-141	106	16	x	x	SYM
ejpam-141	106	17	consisting	consist	VERB
ejpam-141	106	18	of	of	ADP
ejpam-141	106	19	sn	sn	NOUN
ejpam-141	106	20	-	-	PUNCT
ejpam-141	106	21	second	second	ADJ
ejpam-141	106	22	countable	countable	ADJ
ejpam-141	106	23	spaces	space	NOUN
ejpam-141	106	24	by	by	ADP
ejpam-141	106	25	the	the	DET
ejpam-141	106	26	following	follow	VERB
ejpam-141	106	27	facts	fact	NOUN
ejpam-141	106	28	(	(	PUNCT
ejpam-141	106	29	a	a	X
ejpam-141	106	30	)	)	PUNCT
ejpam-141	106	31	,	,	PUNCT
ejpam-141	106	32	(	(	PUNCT
ejpam-141	106	33	b	b	NOUN
ejpam-141	106	34	)	)	PUNCT
ejpam-141	106	35	,	,	PUNCT
ejpam-141	106	36	(	(	PUNCT
ejpam-141	106	37	c	c	NOUN
ejpam-141	106	38	)	)	PUNCT
ejpam-141	106	39	,	,	PUNCT
ejpam-141	106	40	and	and	CCONJ
ejpam-141	106	41	(	(	PUNCT
ejpam-141	106	42	d	d	NOUN
ejpam-141	106	43	)	)	PUNCT
ejpam-141	106	44	.	.	PUNCT
ejpam-141	107	1	(	(	PUNCT
ejpam-141	107	2	a	a	X
ejpam-141	107	3	)	)	PUNCT
ejpam-141	107	4	⋃	⋃	NOUN
ejpam-141	107	5	{	{	PUNCT
ejpam-141	107	6	pn	pn	NOUN
ejpam-141	107	7	:	:	PUNCT
ejpam-141	107	8	n	n	CCONJ
ejpam-141	107	9	∈	∈	PROPN
ejpam-141	107	10	n	n	CCONJ
ejpam-141	107	11	}	}	PUNCT
ejpam-141	107	12	is	be	AUX
ejpam-141	107	13	a	a	DET
ejpam-141	107	14	σ	σ	PROPN
ejpam-141	107	15	-	-	PUNCT
ejpam-141	107	16	strong	strong	ADJ
ejpam-141	107	17	network	network	NOUN
ejpam-141	107	18	of	of	ADP
ejpam-141	107	19	x	x	X
ejpam-141	107	20	.	.	PUNCT
ejpam-141	108	1	let	let	VERB
ejpam-141	108	2	x	x	PUNCT
ejpam-141	108	3	∈	∈	PROPN
ejpam-141	108	4	u	u	NOUN
ejpam-141	108	5	with	with	ADP
ejpam-141	108	6	u	u	NOUN
ejpam-141	108	7	open	open	ADJ
ejpam-141	108	8	in	in	ADP
ejpam-141	108	9	x	x	X
ejpam-141	108	10	.	.	PUNCT
ejpam-141	109	1	since	since	SCONJ
ejpam-141	109	2	f	f	PROPN
ejpam-141	109	3	is	be	AUX
ejpam-141	109	4	a	a	DET
ejpam-141	109	5	π	π	PROPN
ejpam-141	109	6	-	-	NOUN
ejpam-141	109	7	mapping	mapping	NOUN
ejpam-141	109	8	,	,	PUNCT
ejpam-141	110	1	d	d	X
ejpam-141	110	2	(	(	PUNCT
ejpam-141	110	3	f	f	PROPN
ejpam-141	110	4	−1(x	−1(x	PROPN
ejpam-141	110	5	)	)	PUNCT
ejpam-141	110	6	,	,	PUNCT
ejpam-141	110	7	m	m	VERB
ejpam-141	110	8	−	−	PROPN
ejpam-141	110	9	f	f	PROPN
ejpam-141	110	10	−1(u	−1(u	NOUN
ejpam-141	110	11	)	)	PUNCT
ejpam-141	110	12	)	)	PUNCT
ejpam-141	110	13	>	>	X
ejpam-141	111	1	0	0	X
ejpam-141	111	2	.	.	PUNCT
ejpam-141	112	1	it	it	PRON
ejpam-141	112	2	implies	imply	VERB
ejpam-141	112	3	that	that	SCONJ
ejpam-141	113	1	d	d	X
ejpam-141	113	2	(	(	PUNCT
ejpam-141	113	3	f	f	PROPN
ejpam-141	113	4	−1(x	−1(x	PROPN
ejpam-141	113	5	)	)	PUNCT
ejpam-141	113	6	,	,	PUNCT
ejpam-141	113	7	m	m	VERB
ejpam-141	113	8	−	−	PROPN
ejpam-141	113	9	f	f	PROPN
ejpam-141	113	10	−1(u	−1(u	NOUN
ejpam-141	113	11	)	)	PUNCT
ejpam-141	113	12	)	)	PUNCT
ejpam-141	113	13	>	>	X
ejpam-141	113	14	2	2	NUM
ejpam-141	113	15	/	/	SYM
ejpam-141	113	16	n	n	NOUN
ejpam-141	113	17	for	for	ADP
ejpam-141	113	18	some	some	DET
ejpam-141	113	19	n	n	PRON
ejpam-141	113	20	∈	∈	PROPN
ejpam-141	113	21	n.	n.	NOUN
ejpam-141	113	22	let	let	VERB
ejpam-141	113	23	x	x	SYM
ejpam-141	113	24	∈	∈	PROPN
ejpam-141	113	25	f	f	X
ejpam-141	113	26	(	(	PUNCT
ejpam-141	113	27	b(a	b(a	PROPN
ejpam-141	113	28	,	,	PUNCT
ejpam-141	113	29	1	1	NUM
ejpam-141	113	30	/	/	SYM
ejpam-141	113	31	n	n	CCONJ
ejpam-141	113	32	)	)	PUNCT
ejpam-141	113	33	)	)	PUNCT
ejpam-141	114	1	∈	∈	PROPN
ejpam-141	114	2	pn	pn	NOUN
ejpam-141	114	3	for	for	ADP
ejpam-141	114	4	some	some	DET
ejpam-141	114	5	b(a	b(a	NOUN
ejpam-141	114	6	,	,	PUNCT
ejpam-141	114	7	1	1	NUM
ejpam-141	114	8	/	/	SYM
ejpam-141	114	9	n	n	CCONJ
ejpam-141	114	10	)	)	PUNCT
ejpam-141	114	11	∈	∈	PROPN
ejpam-141	114	12	bλ	bλ	NOUN
ejpam-141	114	13	,	,	PUNCT
ejpam-141	114	14	n	n	CCONJ
ejpam-141	114	15	,	,	PUNCT
ejpam-141	114	16	x	x	X
ejpam-141	114	17	.	.	PUNCT
ejpam-141	115	1	we	we	PRON
ejpam-141	115	2	shall	shall	AUX
ejpam-141	115	3	prove	prove	VERB
ejpam-141	115	4	that	that	SCONJ
ejpam-141	115	5	b(a	b(a	NOUN
ejpam-141	115	6	,	,	PUNCT
ejpam-141	115	7	1	1	NUM
ejpam-141	115	8	/	/	SYM
ejpam-141	115	9	n	n	CCONJ
ejpam-141	115	10	)	)	PUNCT
ejpam-141	115	11	⊂	⊂	PROPN
ejpam-141	115	12	f	f	X
ejpam-141	115	13	−1(u	−1(u	NOUN
ejpam-141	115	14	)	)	PUNCT
ejpam-141	115	15	.	.	PUNCT
ejpam-141	116	1	in	in	ADP
ejpam-141	116	2	fact	fact	NOUN
ejpam-141	116	3	,	,	PUNCT
ejpam-141	116	4	if	if	SCONJ
ejpam-141	116	5	b(a	b(a	NOUN
ejpam-141	116	6	,	,	PUNCT
ejpam-141	116	7	1	1	NUM
ejpam-141	116	8	/	/	SYM
ejpam-141	116	9	n	n	CCONJ
ejpam-141	116	10	)	)	PUNCT
ejpam-141	116	11	6⊂	6⊂	NUM
ejpam-141	116	12	f	f	PROPN
ejpam-141	116	13	−1(u	−1(u	NOUN
ejpam-141	116	14	)	)	PUNCT
ejpam-141	116	15	,	,	PUNCT
ejpam-141	116	16	then	then	ADV
ejpam-141	116	17	there	there	PRON
ejpam-141	116	18	exists	exist	VERB
ejpam-141	116	19	b	b	PROPN
ejpam-141	116	20	∈	∈	PROPN
ejpam-141	116	21	b(a	b(a	NOUN
ejpam-141	116	22	,	,	PUNCT
ejpam-141	116	23	1	1	NUM
ejpam-141	116	24	/	/	SYM
ejpam-141	116	25	n	n	CCONJ
ejpam-141	116	26	)	)	PUNCT
ejpam-141	116	27	−	−	PROPN
ejpam-141	116	28	f	f	PROPN
ejpam-141	116	29	−1(u	−1(u	NOUN
ejpam-141	116	30	)	)	PUNCT
ejpam-141	116	31	.	.	PUNCT
ejpam-141	117	1	since	since	SCONJ
ejpam-141	117	2	f	f	PROPN
ejpam-141	117	3	−1(x	−1(x	PROPN
ejpam-141	117	4	)	)	PUNCT
ejpam-141	117	5	∩	∩	ADJ
ejpam-141	117	6	n.	n.	NOUN
ejpam-141	117	7	dung	dung	PROPN
ejpam-141	117	8	/	/	SYM
ejpam-141	117	9	eur	eur	PROPN
ejpam-141	117	10	.	.	PUNCT
ejpam-141	118	1	j.	j.	PROPN
ejpam-141	118	2	pure	pure	PROPN
ejpam-141	118	3	appl	appl	PROPN
ejpam-141	118	4	.	.	PROPN
ejpam-141	118	5	math	math	PROPN
ejpam-141	118	6	,	,	PUNCT
ejpam-141	118	7	2	2	NUM
ejpam-141	118	8	(	(	PUNCT
ejpam-141	118	9	2009	2009	NUM
ejpam-141	118	10	)	)	PUNCT
ejpam-141	118	11	,	,	PUNCT
ejpam-141	118	12	(	(	PUNCT
ejpam-141	118	13	182	182	NUM
ejpam-141	118	14	-	-	SYM
ejpam-141	118	15	194	194	NUM
ejpam-141	118	16	)	)	PUNCT
ejpam-141	118	17	188	188	NUM
ejpam-141	118	18	b(a	b(a	NOUN
ejpam-141	118	19	,	,	PUNCT
ejpam-141	118	20	1	1	NUM
ejpam-141	118	21	/	/	SYM
ejpam-141	118	22	n	n	CCONJ
ejpam-141	118	23	)	)	PUNCT
ejpam-141	118	24	6=	6=	NUM
ejpam-141	118	25	;	;	PUNCT
ejpam-141	118	26	,	,	PUNCT
ejpam-141	118	27	there	there	PRON
ejpam-141	118	28	exists	exist	VERB
ejpam-141	118	29	c	c	PROPN
ejpam-141	118	30	∈	∈	PROPN
ejpam-141	118	31	f	f	PROPN
ejpam-141	118	32	−1(x	−1(x	NOUN
ejpam-141	118	33	)	)	PUNCT
ejpam-141	118	34	∩	∩	NOUN
ejpam-141	118	35	b(a	b(a	NOUN
ejpam-141	118	36	,	,	PUNCT
ejpam-141	118	37	1	1	NUM
ejpam-141	118	38	/	/	SYM
ejpam-141	118	39	n	n	CCONJ
ejpam-141	118	40	)	)	PUNCT
ejpam-141	118	41	.	.	PUNCT
ejpam-141	119	1	then	then	ADV
ejpam-141	119	2	d	d	X
ejpam-141	119	3	(	(	PUNCT
ejpam-141	119	4	f	f	PROPN
ejpam-141	119	5	−1(x	−1(x	PROPN
ejpam-141	119	6	)	)	PUNCT
ejpam-141	119	7	,	,	PUNCT
ejpam-141	119	8	m	m	VERB
ejpam-141	119	9	−	−	PROPN
ejpam-141	119	10	f	f	PROPN
ejpam-141	119	11	−1(u	−1(u	NOUN
ejpam-141	119	12	)	)	PUNCT
ejpam-141	119	13	)	)	PUNCT
ejpam-141	119	14	≤	≤	PROPN
ejpam-141	119	15	d(c	d(c	PROPN
ejpam-141	119	16	,	,	PUNCT
ejpam-141	119	17	b	b	NOUN
ejpam-141	119	18	)	)	PUNCT
ejpam-141	119	19	≤	≤	NOUN
ejpam-141	119	20	d(c	d(c	PROPN
ejpam-141	119	21	,	,	PUNCT
ejpam-141	119	22	a)+	a)+	NOUN
ejpam-141	119	23	d(a	d(a	PROPN
ejpam-141	119	24	,	,	PUNCT
ejpam-141	119	25	b	b	NOUN
ejpam-141	119	26	)	)	PUNCT
ejpam-141	119	27	<	<	X
ejpam-141	119	28	2	2	NUM
ejpam-141	119	29	/	/	SYM
ejpam-141	119	30	n.	n.	NOUN
ejpam-141	119	31	it	it	PRON
ejpam-141	119	32	is	be	AUX
ejpam-141	119	33	a	a	DET
ejpam-141	119	34	contradiction	contradiction	NOUN
ejpam-141	119	35	.	.	PUNCT
ejpam-141	120	1	then	then	ADV
ejpam-141	120	2	we	we	PRON
ejpam-141	120	3	get	get	VERB
ejpam-141	120	4	f	f	PROPN
ejpam-141	120	5	(	(	PUNCT
ejpam-141	120	6	b(a	b(a	PROPN
ejpam-141	120	7	,	,	PUNCT
ejpam-141	120	8	1	1	NUM
ejpam-141	120	9	/	/	SYM
ejpam-141	120	10	n	n	CCONJ
ejpam-141	120	11	)	)	PUNCT
ejpam-141	120	12	)	)	PUNCT
ejpam-141	121	1	⊂	⊂	PROPN
ejpam-141	121	2	u	u	PROPN
ejpam-141	121	3	.	.	PUNCT
ejpam-141	122	1	therefore	therefore	ADV
ejpam-141	122	2	,	,	PUNCT
ejpam-141	122	3	st(x	st(x	X
ejpam-141	122	4	,	,	PUNCT
ejpam-141	122	5	pn	pn	NOUN
ejpam-141	122	6	)	)	PUNCT
ejpam-141	122	7	=	=	SYM
ejpam-141	122	8	⋃	⋃	NOUN
ejpam-141	122	9	{	{	PUNCT
ejpam-141	122	10	f	f	X
ejpam-141	122	11	(	(	PUNCT
ejpam-141	122	12	b(a	b(a	PROPN
ejpam-141	122	13	,	,	PUNCT
ejpam-141	122	14	1	1	NUM
ejpam-141	122	15	/	/	SYM
ejpam-141	122	16	n	n	CCONJ
ejpam-141	122	17	)	)	PUNCT
ejpam-141	122	18	)	)	PUNCT
ejpam-141	122	19	:	:	PUNCT
ejpam-141	123	1	x	x	X
ejpam-141	123	2	∈	∈	PROPN
ejpam-141	123	3	f	f	X
ejpam-141	123	4	(	(	PUNCT
ejpam-141	123	5	b(a	b(a	PROPN
ejpam-141	123	6	,	,	PUNCT
ejpam-141	123	7	1	1	NUM
ejpam-141	123	8	/	/	SYM
ejpam-141	123	9	n	n	CCONJ
ejpam-141	123	10	)	)	PUNCT
ejpam-141	123	11	)	)	PUNCT
ejpam-141	123	12	,	,	PUNCT
ejpam-141	123	13	a	a	DET
ejpam-141	123	14	∈	∈	PROPN
ejpam-141	123	15	dλ	dλ	NOUN
ejpam-141	123	16	,	,	PUNCT
ejpam-141	123	17	λ	λ	PROPN
ejpam-141	123	18	∈	∈	PROPN
ejpam-141	123	19	λ	λ	PROPN
ejpam-141	123	20	}	}	PUNCT
ejpam-141	123	21	⊂	⊂	PROPN
ejpam-141	123	22	u	u	NOUN
ejpam-141	123	23	.	.	PUNCT
ejpam-141	124	1	it	it	PRON
ejpam-141	124	2	implies	imply	VERB
ejpam-141	124	3	that	that	SCONJ
ejpam-141	124	4	p	p	PROPN
ejpam-141	124	5	is	be	AUX
ejpam-141	124	6	a	a	DET
ejpam-141	124	7	σ	σ	PROPN
ejpam-141	124	8	-	-	PUNCT
ejpam-141	124	9	strong	strong	ADJ
ejpam-141	124	10	network	network	NOUN
ejpam-141	124	11	of	of	ADP
ejpam-141	124	12	x	x	X
ejpam-141	124	13	.	.	PUNCT
ejpam-141	125	1	(	(	PUNCT
ejpam-141	125	2	b	b	X
ejpam-141	125	3	)	)	PUNCT
ejpam-141	125	4	each	each	DET
ejpam-141	125	5	pn	pn	PROPN
ejpam-141	125	6	is	be	AUX
ejpam-141	125	7	an	an	DET
ejpam-141	125	8	sn	sn	NOUN
ejpam-141	125	9	-	-	PUNCT
ejpam-141	125	10	cover	cover	NOUN
ejpam-141	125	11	of	of	ADP
ejpam-141	125	12	x	x	X
ejpam-141	125	13	.	.	PUNCT
ejpam-141	126	1	let	let	VERB
ejpam-141	126	2	x	x	PUNCT
ejpam-141	126	3	∈	∈	PROPN
ejpam-141	126	4	x	x	X
ejpam-141	126	5	and	and	CCONJ
ejpam-141	126	6	p	p	X
ejpam-141	126	7	=	=	SYM
ejpam-141	126	8	f	f	X
ejpam-141	126	9	(	(	PUNCT
ejpam-141	126	10	b	b	X
ejpam-141	126	11	)	)	PUNCT
ejpam-141	126	12	∈	∈	PROPN
ejpam-141	126	13	pn	pn	NOUN
ejpam-141	126	14	,	,	PUNCT
ejpam-141	126	15	x	x	NOUN
ejpam-141	126	16	for	for	ADP
ejpam-141	126	17	some	some	DET
ejpam-141	126	18	b	b	NOUN
ejpam-141	126	19	∈	∈	PROPN
ejpam-141	126	20	bn	bn	NOUN
ejpam-141	126	21	,	,	PUNCT
ejpam-141	126	22	x	x	X
ejpam-141	126	23	.	.	PUNCT
ejpam-141	127	1	we	we	PRON
ejpam-141	127	2	shall	shall	AUX
ejpam-141	127	3	prove	prove	VERB
ejpam-141	127	4	that	that	SCONJ
ejpam-141	127	5	p	p	NOUN
ejpam-141	127	6	is	be	AUX
ejpam-141	127	7	a	a	DET
ejpam-141	127	8	sequential	sequential	ADJ
ejpam-141	127	9	neighborhood	neighborhood	NOUN
ejpam-141	127	10	of	of	ADP
ejpam-141	127	11	x	x	PRON
ejpam-141	127	12	.	.	PUNCT
ejpam-141	128	1	let	let	VERB
ejpam-141	128	2	s	s	PRON
ejpam-141	128	3	be	be	AUX
ejpam-141	128	4	a	a	DET
ejpam-141	128	5	convergent	convergent	NOUN
ejpam-141	128	6	sequence	sequence	NOUN
ejpam-141	128	7	converging	converge	VERB
ejpam-141	128	8	to	to	ADP
ejpam-141	128	9	x	x	PUNCT
ejpam-141	128	10	in	in	ADP
ejpam-141	128	11	x	x	X
ejpam-141	128	12	.	.	PUNCT
ejpam-141	129	1	then	then	ADV
ejpam-141	129	2	there	there	PRON
ejpam-141	129	3	exists	exist	VERB
ejpam-141	129	4	a	a	DET
ejpam-141	129	5	convergent	convergent	NOUN
ejpam-141	129	6	sequence	sequence	NOUN
ejpam-141	129	7	l	l	NOUN
ejpam-141	129	8	converging	converge	VERB
ejpam-141	129	9	to	to	PART
ejpam-141	129	10	ax	ax	VERB
ejpam-141	129	11	in	in	ADP
ejpam-141	129	12	m	m	PRON
ejpam-141	129	13	such	such	ADJ
ejpam-141	129	14	that	that	SCONJ
ejpam-141	129	15	f	f	PROPN
ejpam-141	129	16	(	(	PUNCT
ejpam-141	129	17	l	l	NOUN
ejpam-141	129	18	)	)	PUNCT
ejpam-141	129	19	is	be	AUX
ejpam-141	129	20	a	a	DET
ejpam-141	129	21	subsequence	subsequence	NOUN
ejpam-141	129	22	of	of	ADP
ejpam-141	129	23	s.	s.	PROPN
ejpam-141	129	24	since	since	SCONJ
ejpam-141	129	25	b	b	PROPN
ejpam-141	129	26	is	be	AUX
ejpam-141	129	27	open	open	ADJ
ejpam-141	129	28	,	,	PUNCT
ejpam-141	129	29	l	l	NOUN
ejpam-141	129	30	is	be	AUX
ejpam-141	129	31	eventually	eventually	ADV
ejpam-141	129	32	in	in	ADP
ejpam-141	129	33	b.	b.	PROPN
ejpam-141	130	1	hence	hence	ADV
ejpam-141	130	2	f	f	PROPN
ejpam-141	130	3	(	(	PUNCT
ejpam-141	130	4	lλ	lλ	INTJ
ejpam-141	130	5	)	)	PUNCT
ejpam-141	130	6	is	be	AUX
ejpam-141	130	7	eventually	eventually	ADV
ejpam-141	130	8	in	in	ADP
ejpam-141	130	9	p.	p.	NOUN
ejpam-141	130	10	it	it	PRON
ejpam-141	130	11	implies	imply	VERB
ejpam-141	130	12	that	that	SCONJ
ejpam-141	130	13	s	s	VERB
ejpam-141	130	14	is	be	AUX
ejpam-141	130	15	frequently	frequently	ADV
ejpam-141	130	16	in	in	ADP
ejpam-141	130	17	p.	p.	NOUN
ejpam-141	130	18	it	it	PRON
ejpam-141	130	19	follows	follow	VERB
ejpam-141	130	20	from	from	ADP
ejpam-141	130	21	[	[	X
ejpam-141	130	22	6	6	NUM
ejpam-141	130	23	,	,	PUNCT
ejpam-141	130	24	remark	remark	VERB
ejpam-141	130	25	1.4	1.4	NUM
ejpam-141	130	26	]	]	PUNCT
ejpam-141	130	27	that	that	SCONJ
ejpam-141	130	28	p	p	PROPN
ejpam-141	130	29	is	be	AUX
ejpam-141	130	30	a	a	DET
ejpam-141	130	31	sequential	sequential	ADJ
ejpam-141	130	32	neighborhood	neighborhood	NOUN
ejpam-141	130	33	of	of	ADP
ejpam-141	130	34	x	x	X
ejpam-141	130	35	.	.	PUNCT
ejpam-141	131	1	therefore	therefore	ADV
ejpam-141	131	2	,	,	PUNCT
ejpam-141	131	3	pn	pn	PROPN
ejpam-141	131	4	is	be	AUX
ejpam-141	131	5	an	an	DET
ejpam-141	131	6	sn	sn	NOUN
ejpam-141	131	7	-	-	PUNCT
ejpam-141	131	8	cover	cover	NOUN
ejpam-141	131	9	of	of	ADP
ejpam-141	131	10	x	x	X
ejpam-141	131	11	.	.	PUNCT
ejpam-141	132	1	(	(	PUNCT
ejpam-141	132	2	c	c	X
ejpam-141	132	3	)	)	PUNCT
ejpam-141	132	4	p	p	NOUN
ejpam-141	132	5	is	be	AUX
ejpam-141	132	6	point	point	NOUN
ejpam-141	132	7	-	-	PUNCT
ejpam-141	132	8	countable	countable	ADJ
ejpam-141	132	9	.	.	PUNCT
ejpam-141	133	1	let	let	VERB
ejpam-141	133	2	x	x	PUNCT
ejpam-141	133	3	∈	∈	PROPN
ejpam-141	133	4	x	x	X
ejpam-141	133	5	.	.	PUNCT
ejpam-141	134	1	since	since	SCONJ
ejpam-141	134	2	f	f	PROPN
ejpam-141	134	3	is	be	AUX
ejpam-141	134	4	an	an	DET
ejpam-141	134	5	s	s	NOUN
ejpam-141	134	6	-	-	NOUN
ejpam-141	134	7	mapping	mapping	NOUN
ejpam-141	134	8	,	,	PUNCT
ejpam-141	134	9	f	f	PROPN
ejpam-141	134	10	−1(x	−1(x	NOUN
ejpam-141	134	11	)	)	PUNCT
ejpam-141	134	12	is	be	AUX
ejpam-141	134	13	separable	separable	ADJ
ejpam-141	134	14	.	.	PUNCT
ejpam-141	135	1	it	it	PRON
ejpam-141	135	2	implies	imply	VERB
ejpam-141	135	3	that	that	SCONJ
ejpam-141	135	4	f	f	PROPN
ejpam-141	135	5	−1(x	−1(x	NOUN
ejpam-141	135	6	)	)	PUNCT
ejpam-141	135	7	meets	meet	VERB
ejpam-141	135	8	at	at	ADP
ejpam-141	135	9	most	most	ADV
ejpam-141	135	10	countably	countably	ADV
ejpam-141	135	11	many	many	ADJ
ejpam-141	135	12	mλ	mλ	NOUN
ejpam-141	135	13	’s	’s	NOUN
ejpam-141	135	14	.	.	PUNCT
ejpam-141	136	1	then	then	ADV
ejpam-141	136	2	f	f	PROPN
ejpam-141	136	3	−1(x	−1(x	NOUN
ejpam-141	136	4	)	)	PUNCT
ejpam-141	136	5	meets	meet	VERB
ejpam-141	136	6	at	at	ADP
ejpam-141	136	7	most	most	ADV
ejpam-141	136	8	countably	countably	ADV
ejpam-141	136	9	many	many	ADJ
ejpam-141	136	10	members	member	NOUN
ejpam-141	136	11	of	of	ADP
ejpam-141	136	12	bn	bn	NOUN
ejpam-141	136	13	,	,	PUNCT
ejpam-141	136	14	i.e.	i.e.	X
ejpam-141	136	15	,	,	PUNCT
ejpam-141	136	16	x	x	PRON
ejpam-141	136	17	meets	meet	VERB
ejpam-141	136	18	at	at	ADP
ejpam-141	136	19	most	most	ADV
ejpam-141	136	20	countable	countable	ADJ
ejpam-141	136	21	many	many	ADJ
ejpam-141	136	22	members	member	NOUN
ejpam-141	136	23	of	of	ADP
ejpam-141	136	24	pn	pn	PROPN
ejpam-141	136	25	.	.	PUNCT
ejpam-141	137	1	therefore	therefore	ADV
ejpam-141	137	2	,	,	PUNCT
ejpam-141	137	3	p	p	PRON
ejpam-141	137	4	is	be	AUX
ejpam-141	137	5	point	point	NOUN
ejpam-141	137	6	-	-	PUNCT
ejpam-141	137	7	countable	countable	ADJ
ejpam-141	137	8	.	.	PUNCT
ejpam-141	138	1	(	(	PUNCT
ejpam-141	138	2	d	d	X
ejpam-141	138	3	)	)	PUNCT
ejpam-141	138	4	each	each	DET
ejpam-141	138	5	p	p	PROPN
ejpam-141	138	6	∈	∈	PROPN
ejpam-141	138	7	p	p	NOUN
ejpam-141	138	8	is	be	AUX
ejpam-141	138	9	an	an	DET
ejpam-141	138	10	sn	sn	NOUN
ejpam-141	138	11	-	-	PUNCT
ejpam-141	138	12	second	second	ADJ
ejpam-141	138	13	countable	countable	ADJ
ejpam-141	138	14	space	space	NOUN
ejpam-141	138	15	.	.	PUNCT
ejpam-141	139	1	let	let	VERB
ejpam-141	139	2	p	p	NOUN
ejpam-141	139	3	=	=	PUNCT
ejpam-141	139	4	f	f	X
ejpam-141	139	5	(	(	PUNCT
ejpam-141	139	6	b	b	NOUN
ejpam-141	139	7	)	)	PUNCT
ejpam-141	139	8	for	for	ADP
ejpam-141	139	9	some	some	DET
ejpam-141	139	10	b	b	PROPN
ejpam-141	139	11	∈	∈	PROPN
ejpam-141	139	12	b	b	PROPN
ejpam-141	139	13	.	.	PUNCT
ejpam-141	140	1	since	since	SCONJ
ejpam-141	140	2	b	b	PROPN
ejpam-141	140	3	is	be	AUX
ejpam-141	140	4	separable	separable	ADJ
ejpam-141	140	5	metric	metric	ADJ
ejpam-141	140	6	,	,	PUNCT
ejpam-141	140	7	p	p	PRON
ejpam-141	140	8	is	be	AUX
ejpam-141	140	9	sequentially	sequentially	ADV
ejpam-141	140	10	separable	separable	ADJ
ejpam-141	140	11	by	by	ADP
ejpam-141	140	12	[	[	X
ejpam-141	140	13	14	14	NUM
ejpam-141	140	14	,	,	PUNCT
ejpam-141	140	15	lemma	lemma	PROPN
ejpam-141	140	16	2.2	2.2	NUM
ejpam-141	140	17	]	]	PUNCT
ejpam-141	140	18	.	.	PUNCT
ejpam-141	141	1	let	let	VERB
ejpam-141	141	2	dp	dp	NOUN
ejpam-141	141	3	be	be	AUX
ejpam-141	141	4	a	a	DET
ejpam-141	141	5	sequentially	sequentially	ADV
ejpam-141	141	6	dense	dense	ADJ
ejpam-141	141	7	subset	subset	NOUN
ejpam-141	141	8	of	of	ADP
ejpam-141	141	9	p.	p.	NOUN
ejpam-141	141	10	for	for	ADP
ejpam-141	141	11	each	each	DET
ejpam-141	141	12	x	x	SYM
ejpam-141	141	13	∈	∈	PROPN
ejpam-141	141	14	p	p	NOUN
ejpam-141	141	15	,	,	PUNCT
ejpam-141	141	16	put	put	VERB
ejpam-141	141	17	qx	qx	NOUN
ejpam-141	141	18	=	=	PUNCT
ejpam-141	141	19	{	{	PUNCT
ejpam-141	141	20	q	q	NOUN
ejpam-141	141	21	∩	∩	ADJ
ejpam-141	141	22	p	p	NOUN
ejpam-141	141	23	:	:	PUNCT
ejpam-141	141	24	q	q	PROPN
ejpam-141	141	25	∈	∈	PROPN
ejpam-141	141	26	px	px	NOUN
ejpam-141	141	27	,	,	PUNCT
ejpam-141	141	28	q	q	NOUN
ejpam-141	141	29	∩	∩	ADJ
ejpam-141	141	30	dp	dp	NOUN
ejpam-141	141	31	6=	6=	NOUN
ejpam-141	141	32	;	;	PUNCT
ejpam-141	141	33	}	}	PUNCT
ejpam-141	141	34	,	,	PUNCT
ejpam-141	141	35	and	and	CCONJ
ejpam-141	141	36	put	put	VERB
ejpam-141	141	37	q	q	NOUN
ejpam-141	141	38	=	=	X
ejpam-141	141	39	⋃	⋃	NOUN
ejpam-141	141	40	{	{	PUNCT
ejpam-141	141	41	qx	qx	NOUN
ejpam-141	141	42	:	:	PUNCT
ejpam-141	141	43	x	x	SYM
ejpam-141	141	44	∈	∈	PROPN
ejpam-141	141	45	p	p	X
ejpam-141	141	46	}	}	PUNCT
ejpam-141	141	47	.	.	PUNCT
ejpam-141	142	1	since	since	SCONJ
ejpam-141	142	2	p	p	NOUN
ejpam-141	142	3	is	be	AUX
ejpam-141	142	4	point	point	NOUN
ejpam-141	142	5	-	-	PUNCT
ejpam-141	142	6	countable	countable	ADJ
ejpam-141	142	7	and	and	CCONJ
ejpam-141	142	8	dp	dp	NOUN
ejpam-141	142	9	is	be	AUX
ejpam-141	142	10	countable	countable	ADJ
ejpam-141	142	11	,	,	PUNCT
ejpam-141	142	12	q	q	PUNCT
ejpam-141	142	13	is	be	AUX
ejpam-141	142	14	countable	countable	ADJ
ejpam-141	142	15	.	.	PUNCT
ejpam-141	143	1	it	it	PRON
ejpam-141	143	2	suffices	suffice	VERB
ejpam-141	143	3	to	to	PART
ejpam-141	143	4	prove	prove	VERB
ejpam-141	143	5	the	the	DET
ejpam-141	143	6	following	follow	VERB
ejpam-141	143	7	facts	fact	NOUN
ejpam-141	143	8	(	(	PUNCT
ejpam-141	143	9	i	i	NOUN
ejpam-141	143	10	)	)	PUNCT
ejpam-141	143	11	,	,	PUNCT
ejpam-141	143	12	(	(	PUNCT
ejpam-141	143	13	ii	ii	NOUN
ejpam-141	143	14	)	)	PUNCT
ejpam-141	143	15	,	,	PUNCT
ejpam-141	143	16	and	and	CCONJ
ejpam-141	143	17	(	(	PUNCT
ejpam-141	143	18	iv	iv	X
ejpam-141	143	19	)	)	PUNCT
ejpam-141	143	20	for	for	ADP
ejpam-141	143	21	every	every	DET
ejpam-141	143	22	x	x	SYM
ejpam-141	143	23	∈	∈	PROPN
ejpam-141	143	24	p.	p.	NOUN
ejpam-141	143	25	(	(	PUNCT
ejpam-141	143	26	i	i	NOUN
ejpam-141	143	27	)	)	PUNCT
ejpam-141	143	28	qx	qx	PROPN
ejpam-141	143	29	is	be	AUX
ejpam-141	143	30	a	a	DET
ejpam-141	143	31	network	network	NOUN
ejpam-141	143	32	at	at	ADP
ejpam-141	143	33	x	x	PUNCT
ejpam-141	143	34	in	in	ADP
ejpam-141	143	35	p.	p.	NOUN
ejpam-141	143	36	let	let	VERB
ejpam-141	143	37	x	x	PUNCT
ejpam-141	143	38	∈	∈	PROPN
ejpam-141	143	39	u	u	NOUN
ejpam-141	143	40	with	with	ADP
ejpam-141	143	41	u	u	NOUN
ejpam-141	143	42	open	open	ADJ
ejpam-141	143	43	in	in	ADP
ejpam-141	143	44	p.	p.	NOUN
ejpam-141	143	45	then	then	ADV
ejpam-141	143	46	x	x	X
ejpam-141	143	47	∈	∈	NOUN
ejpam-141	143	48	v	v	NOUN
ejpam-141	143	49	with	with	ADP
ejpam-141	143	50	v	v	NOUN
ejpam-141	143	51	open	open	ADJ
ejpam-141	143	52	in	in	ADP
ejpam-141	143	53	x	x	X
ejpam-141	143	54	and	and	CCONJ
ejpam-141	143	55	v	v	ADP
ejpam-141	143	56	∩	∩	ADJ
ejpam-141	143	57	p	p	X
ejpam-141	143	58	=	=	SYM
ejpam-141	143	59	u	u	PROPN
ejpam-141	143	60	.	.	PUNCT
ejpam-141	144	1	let	let	VERB
ejpam-141	144	2	s	s	PRON
ejpam-141	144	3	be	be	AUX
ejpam-141	144	4	a	a	DET
ejpam-141	144	5	sequence	sequence	NOUN
ejpam-141	144	6	in	in	ADP
ejpam-141	144	7	dp	dp	NOUN
ejpam-141	144	8	converging	converge	VERB
ejpam-141	144	9	to	to	ADP
ejpam-141	144	10	x	x	PROPN
ejpam-141	144	11	.	.	PUNCT
ejpam-141	145	1	since	since	SCONJ
ejpam-141	145	2	p	p	NOUN
ejpam-141	145	3	is	be	AUX
ejpam-141	145	4	a	a	DET
ejpam-141	145	5	σ	σ	NOUN
ejpam-141	145	6	-	-	PUNCT
ejpam-141	145	7	strong	strong	ADJ
ejpam-141	145	8	sn	sn	NOUN
ejpam-141	145	9	-	-	PUNCT
ejpam-141	145	10	network	network	NOUN
ejpam-141	145	11	of	of	ADP
ejpam-141	145	12	x	x	X
ejpam-141	145	13	,	,	PUNCT
ejpam-141	145	14	s	s	NOUN
ejpam-141	145	15	∪	∪	X
ejpam-141	145	16	{	{	PUNCT
ejpam-141	145	17	x	x	NOUN
ejpam-141	145	18	}	}	PUNCT
ejpam-141	145	19	is	be	AUX
ejpam-141	145	20	eventually	eventually	ADV
ejpam-141	145	21	in	in	ADP
ejpam-141	145	22	q	q	PROPN
ejpam-141	145	23	⊂	⊂	PROPN
ejpam-141	145	24	v	v	NOUN
ejpam-141	145	25	with	with	ADP
ejpam-141	145	26	some	some	DET
ejpam-141	145	27	q	q	PROPN
ejpam-141	145	28	∈	∈	PROPN
ejpam-141	145	29	px	px	NOUN
ejpam-141	145	30	.	.	PUNCT
ejpam-141	146	1	it	it	PRON
ejpam-141	146	2	implies	imply	VERB
ejpam-141	146	3	that	that	SCONJ
ejpam-141	146	4	q	q	NOUN
ejpam-141	146	5	∩	∩	ADJ
ejpam-141	146	6	dp	dp	NOUN
ejpam-141	146	7	6=	6=	NOUN
ejpam-141	146	8	;	;	PUNCT
ejpam-141	146	9	,	,	PUNCT
ejpam-141	146	10	and	and	CCONJ
ejpam-141	146	11	x	x	X
ejpam-141	146	12	∈	∈	PROPN
ejpam-141	146	13	q	q	PROPN
ejpam-141	146	14	∩	∩	PROPN
ejpam-141	146	15	p	p	PROPN
ejpam-141	146	16	⊂	⊂	PROPN
ejpam-141	146	17	v	v	ADP
ejpam-141	146	18	∩	∩	NOUN
ejpam-141	146	19	p	p	X
ejpam-141	146	20	=	=	SYM
ejpam-141	146	21	u	u	PROPN
ejpam-141	146	22	.	.	PUNCT
ejpam-141	147	1	therefore	therefore	ADV
ejpam-141	147	2	,	,	PUNCT
ejpam-141	147	3	qx	qx	PROPN
ejpam-141	147	4	is	be	AUX
ejpam-141	147	5	a	a	DET
ejpam-141	147	6	network	network	NOUN
ejpam-141	147	7	at	at	ADP
ejpam-141	147	8	x	x	PUNCT
ejpam-141	147	9	in	in	ADP
ejpam-141	147	10	p.	p.	PROPN
ejpam-141	147	11	n.	n.	PROPN
ejpam-141	147	12	dung	dung	PROPN
ejpam-141	147	13	/	/	SYM
ejpam-141	147	14	eur	eur	PROPN
ejpam-141	147	15	.	.	PUNCT
ejpam-141	148	1	j.	j.	PROPN
ejpam-141	148	2	pure	pure	PROPN
ejpam-141	148	3	appl	appl	PROPN
ejpam-141	148	4	.	.	PROPN
ejpam-141	148	5	math	math	PROPN
ejpam-141	148	6	,	,	PUNCT
ejpam-141	148	7	2	2	NUM
ejpam-141	148	8	(	(	PUNCT
ejpam-141	148	9	2009	2009	NUM
ejpam-141	148	10	)	)	PUNCT
ejpam-141	148	11	,	,	PUNCT
ejpam-141	148	12	(	(	PUNCT
ejpam-141	148	13	182	182	NUM
ejpam-141	148	14	-	-	SYM
ejpam-141	148	15	194	194	NUM
ejpam-141	148	16	)	)	PUNCT
ejpam-141	148	17	189	189	NUM
ejpam-141	148	18	(	(	PUNCT
ejpam-141	148	19	ii	ii	NOUN
ejpam-141	148	20	)	)	PUNCT
ejpam-141	149	1	if	if	SCONJ
ejpam-141	149	2	q1,q2	q1,q2	PROPN
ejpam-141	149	3	∈	∈	PROPN
ejpam-141	149	4	qx	qx	PROPN
ejpam-141	149	5	,	,	PUNCT
ejpam-141	149	6	then	then	ADV
ejpam-141	149	7	q	q	PROPN
ejpam-141	149	8	⊂q1	⊂q1	PROPN
ejpam-141	149	9	∩q2	∩q2	NOUN
ejpam-141	149	10	for	for	ADP
ejpam-141	149	11	some	some	DET
ejpam-141	149	12	q	q	NOUN
ejpam-141	149	13	∈	∈	PROPN
ejpam-141	149	14	qx	qx	INTJ
ejpam-141	149	15	.	.	PUNCT
ejpam-141	150	1	let	let	VERB
ejpam-141	150	2	q1	q1	PROPN
ejpam-141	150	3	=	=	SYM
ejpam-141	150	4	f	f	PROPN
ejpam-141	150	5	(	(	PUNCT
ejpam-141	150	6	b1)∩	b1)∩	PROPN
ejpam-141	150	7	p	p	X
ejpam-141	150	8	,	,	PUNCT
ejpam-141	150	9	q2	q2	NOUN
ejpam-141	150	10	=	=	SYM
ejpam-141	150	11	f	f	PROPN
ejpam-141	150	12	(	(	PUNCT
ejpam-141	150	13	b2)∩	b2)∩	PROPN
ejpam-141	150	14	p	p	NOUN
ejpam-141	150	15	for	for	ADP
ejpam-141	150	16	some	some	DET
ejpam-141	150	17	b1	b1	NOUN
ejpam-141	150	18	,	,	PUNCT
ejpam-141	150	19	b2	b2	NOUN
ejpam-141	150	20	∈bx	∈bx	PROPN
ejpam-141	150	21	.	.	PUNCT
ejpam-141	151	1	let	let	VERB
ejpam-141	151	2	s	s	PRON
ejpam-141	151	3	be	be	AUX
ejpam-141	151	4	a	a	DET
ejpam-141	151	5	sequence	sequence	NOUN
ejpam-141	151	6	in	in	ADP
ejpam-141	151	7	dp	dp	NOUN
ejpam-141	151	8	converging	converge	VERB
ejpam-141	151	9	to	to	ADP
ejpam-141	151	10	x	x	PROPN
ejpam-141	151	11	.	.	PUNCT
ejpam-141	152	1	then	then	ADV
ejpam-141	152	2	there	there	PRON
ejpam-141	152	3	exists	exist	VERB
ejpam-141	152	4	a	a	DET
ejpam-141	152	5	sequence	sequence	NOUN
ejpam-141	152	6	l	l	NOUN
ejpam-141	152	7	converging	converge	VERB
ejpam-141	152	8	to	to	PART
ejpam-141	152	9	ax	ax	VERB
ejpam-141	152	10	in	in	ADP
ejpam-141	152	11	m	m	PRON
ejpam-141	152	12	such	such	ADJ
ejpam-141	152	13	that	that	SCONJ
ejpam-141	152	14	f	f	PROPN
ejpam-141	152	15	(	(	PUNCT
ejpam-141	152	16	l	l	NOUN
ejpam-141	152	17	)	)	PUNCT
ejpam-141	152	18	is	be	AUX
ejpam-141	152	19	a	a	DET
ejpam-141	152	20	subsequence	subsequence	NOUN
ejpam-141	152	21	of	of	ADP
ejpam-141	152	22	s.	s.	PROPN
ejpam-141	152	23	since	since	SCONJ
ejpam-141	152	24	bx	bx	PROPN
ejpam-141	152	25	is	be	AUX
ejpam-141	152	26	a	a	DET
ejpam-141	152	27	base	base	NOUN
ejpam-141	152	28	at	at	ADP
ejpam-141	152	29	ax	ax	NOUN
ejpam-141	152	30	in	in	ADP
ejpam-141	152	31	m	m	PROPN
ejpam-141	152	32	,	,	PUNCT
ejpam-141	152	33	there	there	PRON
ejpam-141	152	34	exists	exist	VERB
ejpam-141	152	35	c	c	NOUN
ejpam-141	152	36	∈	∈	PROPN
ejpam-141	152	37	bx	bx	NOUN
ejpam-141	152	38	such	such	ADJ
ejpam-141	152	39	that	that	SCONJ
ejpam-141	152	40	l	l	NOUN
ejpam-141	152	41	∪	∪	X
ejpam-141	152	42	{	{	PUNCT
ejpam-141	152	43	ax	ax	NOUN
ejpam-141	152	44	}	}	PUNCT
ejpam-141	152	45	is	be	AUX
ejpam-141	152	46	eventually	eventually	ADV
ejpam-141	152	47	in	in	ADP
ejpam-141	152	48	c	c	PROPN
ejpam-141	152	49	⊂	⊂	PROPN
ejpam-141	152	50	b1	b1	PROPN
ejpam-141	152	51	∩	∩	ADJ
ejpam-141	152	52	b2	b2	NOUN
ejpam-141	152	53	.	.	PUNCT
ejpam-141	153	1	then	then	ADV
ejpam-141	153	2	s	s	AUX
ejpam-141	153	3	∪	∪	X
ejpam-141	153	4	{	{	PUNCT
ejpam-141	153	5	x	x	NOUN
ejpam-141	153	6	}	}	PUNCT
ejpam-141	153	7	is	be	AUX
ejpam-141	153	8	frequently	frequently	ADV
ejpam-141	153	9	in	in	ADP
ejpam-141	153	10	f	f	PROPN
ejpam-141	153	11	(	(	PUNCT
ejpam-141	153	12	c	c	NOUN
ejpam-141	153	13	)	)	PUNCT
ejpam-141	153	14	.	.	PUNCT
ejpam-141	154	1	it	it	PRON
ejpam-141	154	2	implies	imply	VERB
ejpam-141	154	3	that	that	SCONJ
ejpam-141	154	4	f	f	PROPN
ejpam-141	154	5	(	(	PUNCT
ejpam-141	154	6	c)∩	c)∩	PROPN
ejpam-141	154	7	dp	dp	PROPN
ejpam-141	154	8	6=	6=	NUM
ejpam-141	154	9	;	;	PUNCT
ejpam-141	154	10	.	.	PUNCT
ejpam-141	155	1	put	put	VERB
ejpam-141	155	2	q	q	NOUN
ejpam-141	155	3	=	=	X
ejpam-141	155	4	f	f	X
ejpam-141	155	5	(	(	PUNCT
ejpam-141	155	6	c)∩	c)∩	PROPN
ejpam-141	156	1	p.	p.	NOUN
ejpam-141	156	2	then	then	ADV
ejpam-141	156	3	q	q	PROPN
ejpam-141	156	4	∈	∈	PROPN
ejpam-141	156	5	qx	qx	PROPN
ejpam-141	156	6	,	,	PUNCT
ejpam-141	156	7	and	and	CCONJ
ejpam-141	156	8	q	q	PROPN
ejpam-141	156	9	⊂q1	⊂q1	PROPN
ejpam-141	156	10	∩q2	∩q2	PROPN
ejpam-141	156	11	.	.	PUNCT
ejpam-141	157	1	(	(	PUNCT
ejpam-141	157	2	iii	iii	X
ejpam-141	157	3	)	)	PUNCT
ejpam-141	158	1	each	each	DET
ejpam-141	158	2	q	q	PROPN
ejpam-141	158	3	∈	∈	PROPN
ejpam-141	158	4	qx	qx	PROPN
ejpam-141	158	5	is	be	AUX
ejpam-141	158	6	a	a	DET
ejpam-141	158	7	sequential	sequential	ADJ
ejpam-141	158	8	neighborhood	neighborhood	NOUN
ejpam-141	158	9	of	of	ADP
ejpam-141	158	10	x	x	PUNCT
ejpam-141	158	11	in	in	ADP
ejpam-141	158	12	p.	p.	NOUN
ejpam-141	158	13	let	let	VERB
ejpam-141	158	14	q	q	NOUN
ejpam-141	158	15	=	=	SYM
ejpam-141	158	16	f	f	X
ejpam-141	158	17	(	(	PUNCT
ejpam-141	158	18	c)∩	c)∩	X
ejpam-141	158	19	p	p	NOUN
ejpam-141	158	20	with	with	ADP
ejpam-141	158	21	some	some	DET
ejpam-141	158	22	c	c	NOUN
ejpam-141	158	23	∈bx	∈bx	PROPN
ejpam-141	158	24	,	,	PUNCT
ejpam-141	158	25	and	and	CCONJ
ejpam-141	158	26	f	f	X
ejpam-141	158	27	(	(	PUNCT
ejpam-141	158	28	c)∩dp	c)∩dp	NOUN
ejpam-141	158	29	6=	6=	NUM
ejpam-141	158	30	;	;	PUNCT
ejpam-141	158	31	,	,	PUNCT
ejpam-141	158	32	and	and	CCONJ
ejpam-141	158	33	let	let	VERB
ejpam-141	158	34	s	s	PRON
ejpam-141	158	35	be	be	AUX
ejpam-141	158	36	a	a	DET
ejpam-141	158	37	convergent	convergent	NOUN
ejpam-141	158	38	sequence	sequence	NOUN
ejpam-141	158	39	converging	converge	VERB
ejpam-141	158	40	to	to	ADP
ejpam-141	158	41	x	x	PUNCT
ejpam-141	158	42	in	in	ADP
ejpam-141	158	43	p.	p.	NOUN
ejpam-141	158	44	then	then	ADV
ejpam-141	158	45	there	there	PRON
ejpam-141	158	46	exists	exist	VERB
ejpam-141	158	47	a	a	DET
ejpam-141	158	48	convergent	convergent	NOUN
ejpam-141	158	49	sequence	sequence	NOUN
ejpam-141	158	50	l	l	NOUN
ejpam-141	158	51	converging	converge	VERB
ejpam-141	158	52	to	to	PART
ejpam-141	158	53	ax	ax	VERB
ejpam-141	158	54	in	in	ADP
ejpam-141	158	55	m	m	PRON
ejpam-141	158	56	such	such	ADJ
ejpam-141	158	57	that	that	SCONJ
ejpam-141	158	58	f	f	PROPN
ejpam-141	158	59	(	(	PUNCT
ejpam-141	158	60	l	l	NOUN
ejpam-141	158	61	)	)	PUNCT
ejpam-141	158	62	is	be	AUX
ejpam-141	158	63	a	a	DET
ejpam-141	158	64	subsequence	subsequence	NOUN
ejpam-141	158	65	of	of	ADP
ejpam-141	158	66	s.	s.	PROPN
ejpam-141	158	67	since	since	SCONJ
ejpam-141	158	68	l	l	PROPN
ejpam-141	158	69	is	be	AUX
ejpam-141	158	70	eventually	eventually	ADV
ejpam-141	158	71	in	in	ADP
ejpam-141	158	72	c	c	PROPN
ejpam-141	158	73	,	,	PUNCT
ejpam-141	158	74	s	s	VERB
ejpam-141	158	75	is	be	AUX
ejpam-141	158	76	frequently	frequently	ADV
ejpam-141	158	77	in	in	ADP
ejpam-141	158	78	q.	q.	PROPN
ejpam-141	158	79	it	it	PRON
ejpam-141	158	80	follows	follow	VERB
ejpam-141	158	81	from	from	ADP
ejpam-141	158	82	[	[	X
ejpam-141	158	83	6	6	NUM
ejpam-141	158	84	,	,	PUNCT
ejpam-141	158	85	remark	remark	VERB
ejpam-141	158	86	1.4	1.4	NUM
ejpam-141	158	87	]	]	PUNCT
ejpam-141	158	88	that	that	PRON
ejpam-141	158	89	q	q	NOUN
ejpam-141	158	90	is	be	AUX
ejpam-141	158	91	a	a	DET
ejpam-141	158	92	sequential	sequential	ADJ
ejpam-141	158	93	neighborhood	neighborhood	NOUN
ejpam-141	158	94	of	of	ADP
ejpam-141	158	95	x	x	PUNCT
ejpam-141	158	96	in	in	ADP
ejpam-141	158	97	p.	p.	NOUN
ejpam-141	158	98	(	(	PUNCT
ejpam-141	158	99	3)⇒	3)⇒	NUM
ejpam-141	158	100	(	(	PUNCT
ejpam-141	158	101	4)⇒	4)⇒	NUM
ejpam-141	158	102	(	(	PUNCT
ejpam-141	158	103	5	5	NUM
ejpam-141	158	104	)	)	PUNCT
ejpam-141	158	105	.	.	PUNCT
ejpam-141	159	1	it	it	PRON
ejpam-141	159	2	is	be	AUX
ejpam-141	159	3	obvious	obvious	ADJ
ejpam-141	159	4	.	.	PUNCT
ejpam-141	160	1	(	(	PUNCT
ejpam-141	160	2	5	5	X
ejpam-141	160	3	)	)	PUNCT
ejpam-141	160	4	⇒	⇒	NOUN
ejpam-141	160	5	(	(	PUNCT
ejpam-141	160	6	1	1	NUM
ejpam-141	160	7	)	)	PUNCT
ejpam-141	160	8	.	.	PUNCT
ejpam-141	161	1	let	let	VERB
ejpam-141	161	2	p	p	NOUN
ejpam-141	161	3	=	=	VERB
ejpam-141	161	4	⋃	⋃	PROPN
ejpam-141	161	5	{	{	PUNCT
ejpam-141	161	6	pn	pn	NOUN
ejpam-141	161	7	:	:	PUNCT
ejpam-141	161	8	n	n	CCONJ
ejpam-141	161	9	∈	∈	PROPN
ejpam-141	161	10	n	n	CCONJ
ejpam-141	161	11	}	}	PUNCT
ejpam-141	161	12	be	be	AUX
ejpam-141	161	13	a	a	DET
ejpam-141	161	14	point	point	NOUN
ejpam-141	161	15	-	-	PUNCT
ejpam-141	161	16	countable	countable	ADJ
ejpam-141	161	17	σ	σ	NOUN
ejpam-141	161	18	-	-	PUNCT
ejpam-141	161	19	strong	strong	ADJ
ejpam-141	161	20	sn	sn	NOUN
ejpam-141	161	21	-	-	PUNCT
ejpam-141	161	22	network	network	NOUN
ejpam-141	161	23	of	of	ADP
ejpam-141	161	24	x	x	SYM
ejpam-141	161	25	consisting	consist	VERB
ejpam-141	161	26	of	of	ADP
ejpam-141	161	27	cosmic	cosmic	ADJ
ejpam-141	161	28	spaces	space	NOUN
ejpam-141	161	29	.	.	PUNCT
ejpam-141	162	1	for	for	ADP
ejpam-141	162	2	each	each	DET
ejpam-141	162	3	n	n	PRON
ejpam-141	162	4	∈	∈	PROPN
ejpam-141	162	5	n	n	CCONJ
ejpam-141	162	6	,	,	PUNCT
ejpam-141	162	7	put	put	VERB
ejpam-141	162	8	pn	pn	NOUN
ejpam-141	162	9	=	=	PUNCT
ejpam-141	162	10	{	{	PUNCT
ejpam-141	162	11	pn	pn	PROPN
ejpam-141	162	12	,	,	PUNCT
ejpam-141	162	13	λ	λ	PROPN
ejpam-141	162	14	:	:	PUNCT
ejpam-141	162	15	λ	λ	X
ejpam-141	162	16	∈	∈	PROPN
ejpam-141	162	17	λn	λn	NOUN
ejpam-141	162	18	}	}	PUNCT
ejpam-141	162	19	=	=	SYM
ejpam-141	162	20	⋃	⋃	NOUN
ejpam-141	162	21	{	{	PUNCT
ejpam-141	162	22	pn	pn	NOUN
ejpam-141	162	23	,	,	PUNCT
ejpam-141	162	24	x	x	INTJ
ejpam-141	162	25	:	:	PUNCT
ejpam-141	162	26	x	x	SYM
ejpam-141	162	27	∈	∈	NOUN
ejpam-141	162	28	x	x	X
ejpam-141	162	29	}	}	PUNCT
ejpam-141	162	30	,	,	PUNCT
ejpam-141	162	31	where	where	SCONJ
ejpam-141	162	32	each	each	DET
ejpam-141	162	33	pn	pn	PROPN
ejpam-141	162	34	,	,	PUNCT
ejpam-141	162	35	x	x	PUNCT
ejpam-141	162	36	is	be	AUX
ejpam-141	162	37	an	an	DET
ejpam-141	162	38	sn	sn	NOUN
ejpam-141	162	39	-	-	PUNCT
ejpam-141	162	40	cover	cover	NOUN
ejpam-141	162	41	at	at	ADP
ejpam-141	162	42	x	x	X
ejpam-141	162	43	in	in	ADP
ejpam-141	162	44	x	x	X
ejpam-141	162	45	.	.	PUNCT
ejpam-141	163	1	since	since	SCONJ
ejpam-141	163	2	each	each	DET
ejpam-141	163	3	pn	pn	PROPN
ejpam-141	163	4	,	,	PUNCT
ejpam-141	163	5	λ	λ	PROPN
ejpam-141	163	6	is	be	AUX
ejpam-141	163	7	a	a	DET
ejpam-141	163	8	cosmic	cosmic	ADJ
ejpam-141	163	9	space	space	NOUN
ejpam-141	163	10	,	,	PUNCT
ejpam-141	163	11	pn	pn	PROPN
ejpam-141	163	12	,	,	PUNCT
ejpam-141	163	13	λ	λ	PROPN
ejpam-141	163	14	is	be	AUX
ejpam-141	163	15	a	a	DET
ejpam-141	163	16	sequentially	sequentially	ADV
ejpam-141	163	17	separable	separable	ADJ
ejpam-141	163	18	space	space	NOUN
ejpam-141	163	19	by	by	ADP
ejpam-141	163	20	[	[	X
ejpam-141	163	21	14	14	NUM
ejpam-141	163	22	,	,	PUNCT
ejpam-141	163	23	corollary	corollary	ADJ
ejpam-141	163	24	2.6	2.6	NUM
ejpam-141	163	25	]	]	PUNCT
ejpam-141	163	26	.	.	PUNCT
ejpam-141	164	1	then	then	ADV
ejpam-141	164	2	pn	pn	PROPN
ejpam-141	164	3	,	,	PUNCT
ejpam-141	164	4	λ	λ	PROPN
ejpam-141	164	5	has	have	VERB
ejpam-141	164	6	a	a	DET
ejpam-141	164	7	countable	countable	ADJ
ejpam-141	164	8	sequentially	sequentially	ADV
ejpam-141	164	9	dense	dense	ADJ
ejpam-141	164	10	subset	subset	NOUN
ejpam-141	164	11	dn	dn	PROPN
ejpam-141	164	12	,	,	PUNCT
ejpam-141	164	13	λ	λ	PROPN
ejpam-141	164	14	.	.	PROPN
ejpam-141	164	15	for	for	ADP
ejpam-141	164	16	each	each	DET
ejpam-141	164	17	i	i	PRON
ejpam-141	164	18	∈	∈	PROPN
ejpam-141	165	1	n	n	CCONJ
ejpam-141	166	1	and	and	CCONJ
ejpam-141	166	2	x	x	PROPN
ejpam-141	166	3	∈	∈	PROPN
ejpam-141	166	4	pn	pn	PROPN
ejpam-141	166	5	,	,	PUNCT
ejpam-141	166	6	λ	λ	PROPN
ejpam-141	166	7	,	,	PUNCT
ejpam-141	166	8	put	put	VERB
ejpam-141	166	9	qn	qn	NOUN
ejpam-141	166	10	,	,	PUNCT
ejpam-141	166	11	λ	λ	PROPN
ejpam-141	166	12	,	,	PUNCT
ejpam-141	166	13	i	i	PRON
ejpam-141	166	14	,	,	PUNCT
ejpam-141	167	1	x	x	SYM
ejpam-141	167	2	=	=	PRON
ejpam-141	167	3	{	{	PUNCT
ejpam-141	167	4	p∩	p∩	PROPN
ejpam-141	167	5	pn	pn	PROPN
ejpam-141	167	6	,	,	PUNCT
ejpam-141	167	7	λ	λ	PROPN
ejpam-141	167	8	:	:	PUNCT
ejpam-141	167	9	p	p	X
ejpam-141	167	10	∈	∈	PROPN
ejpam-141	167	11	pi	pi	NOUN
ejpam-141	167	12	,	,	PUNCT
ejpam-141	167	13	x	x	X
ejpam-141	167	14	,	,	PUNCT
ejpam-141	167	15	p∩dn	p∩dn	PROPN
ejpam-141	167	16	,	,	PUNCT
ejpam-141	167	17	λ	λ	PROPN
ejpam-141	167	18	6=	6=	NUM
ejpam-141	167	19	;	;	PUNCT
ejpam-141	167	20	}	}	PUNCT
ejpam-141	167	21	,	,	PUNCT
ejpam-141	167	22	and	and	CCONJ
ejpam-141	167	23	putqn	putqn	PROPN
ejpam-141	167	24	,	,	PUNCT
ejpam-141	167	25	λ	λ	PROPN
ejpam-141	167	26	,	,	PUNCT
ejpam-141	167	27	i	i	PRON
ejpam-141	167	28	=	=	PUNCT
ejpam-141	167	29	⋃	⋃	NOUN
ejpam-141	167	30	{	{	PUNCT
ejpam-141	167	31	qn	qn	NOUN
ejpam-141	167	32	,	,	PUNCT
ejpam-141	167	33	λ	λ	PROPN
ejpam-141	167	34	,	,	PUNCT
ejpam-141	167	35	i	i	PRON
ejpam-141	167	36	,	,	PUNCT
ejpam-141	167	37	x	x	X
ejpam-141	167	38	:	:	PUNCT
ejpam-141	167	39	x	x	X
ejpam-141	167	40	∈	∈	PROPN
ejpam-141	167	41	pn	pn	PROPN
ejpam-141	167	42	,	,	PUNCT
ejpam-141	167	43	λ	λ	NOUN
ejpam-141	167	44	}	}	PUNCT
ejpam-141	167	45	,	,	PUNCT
ejpam-141	167	46	and	and	CCONJ
ejpam-141	167	47	qn	qn	INTJ
ejpam-141	167	48	,	,	PUNCT
ejpam-141	167	49	λ	λ	NOUN
ejpam-141	167	50	=	=	PUNCT
ejpam-141	167	51	⋃	⋃	NOUN
ejpam-141	167	52	{	{	PUNCT
ejpam-141	167	53	qn	qn	NOUN
ejpam-141	167	54	,	,	PUNCT
ejpam-141	167	55	λ	λ	PROPN
ejpam-141	167	56	,	,	PUNCT
ejpam-141	167	57	i	i	PRON
ejpam-141	167	58	:	:	PUNCT
ejpam-141	168	1	i	i	PROPN
ejpam-141	168	2	∈	∈	PROPN
ejpam-141	168	3	n	n	CCONJ
ejpam-141	168	4	}	}	PUNCT
ejpam-141	168	5	.	.	PUNCT
ejpam-141	169	1	since	since	SCONJ
ejpam-141	169	2	p	p	NOUN
ejpam-141	169	3	is	be	AUX
ejpam-141	169	4	a	a	DET
ejpam-141	169	5	point	point	NOUN
ejpam-141	169	6	-	-	PUNCT
ejpam-141	169	7	countable	countable	ADJ
ejpam-141	169	8	and	and	CCONJ
ejpam-141	169	9	dn	dn	NOUN
ejpam-141	169	10	,	,	PUNCT
ejpam-141	169	11	λ	λ	PROPN
ejpam-141	169	12	is	be	AUX
ejpam-141	169	13	countable	countable	ADJ
ejpam-141	169	14	,	,	PUNCT
ejpam-141	169	15	qn	qn	INTJ
ejpam-141	169	16	,	,	PUNCT
ejpam-141	169	17	λ	λ	PROPN
ejpam-141	169	18	is	be	AUX
ejpam-141	169	19	a	a	DET
ejpam-141	169	20	countable	countable	NOUN
ejpam-141	169	21	.	.	PUNCT
ejpam-141	170	1	it	it	PRON
ejpam-141	170	2	is	be	AUX
ejpam-141	170	3	easy	easy	ADJ
ejpam-141	170	4	to	to	PART
ejpam-141	170	5	see	see	VERB
ejpam-141	170	6	that	that	SCONJ
ejpam-141	170	7	{	{	PUNCT
ejpam-141	170	8	qn	qn	INTJ
ejpam-141	170	9	,	,	PUNCT
ejpam-141	170	10	λ	λ	PROPN
ejpam-141	170	11	,	,	PUNCT
ejpam-141	170	12	i	i	PRON
ejpam-141	170	13	:	:	PUNCT
ejpam-141	170	14	i	i	PROPN
ejpam-141	170	15	∈	∈	PROPN
ejpam-141	170	16	n	n	CCONJ
ejpam-141	170	17	}	}	PUNCT
ejpam-141	170	18	is	be	AUX
ejpam-141	170	19	a	a	DET
ejpam-141	170	20	refinement	refinement	NOUN
ejpam-141	170	21	sequence	sequence	NOUN
ejpam-141	170	22	of	of	ADP
ejpam-141	170	23	pn	pn	PROPN
ejpam-141	170	24	,	,	PUNCT
ejpam-141	170	25	λ	λ	PROPN
ejpam-141	170	26	.	.	PROPN
ejpam-141	170	27	for	for	ADP
ejpam-141	170	28	each	each	DET
ejpam-141	170	29	x	x	SYM
ejpam-141	170	30	∈	∈	PROPN
ejpam-141	170	31	u	u	NOUN
ejpam-141	170	32	with	with	ADP
ejpam-141	170	33	u	u	NOUN
ejpam-141	170	34	open	open	ADJ
ejpam-141	170	35	in	in	ADP
ejpam-141	170	36	pn	pn	PROPN
ejpam-141	170	37	,	,	PUNCT
ejpam-141	170	38	λ	λ	PROPN
ejpam-141	170	39	,	,	PUNCT
ejpam-141	170	40	we	we	PRON
ejpam-141	170	41	get	get	VERB
ejpam-141	170	42	x	x	PUNCT
ejpam-141	170	43	∈	∈	NOUN
ejpam-141	170	44	v	v	NOUN
ejpam-141	170	45	with	with	ADP
ejpam-141	170	46	v	v	NOUN
ejpam-141	170	47	open	open	ADJ
ejpam-141	170	48	in	in	ADP
ejpam-141	170	49	x	x	X
ejpam-141	170	50	and	and	CCONJ
ejpam-141	170	51	v∩pn	v∩pn	PROPN
ejpam-141	170	52	,	,	PUNCT
ejpam-141	170	53	λ	λ	X
ejpam-141	170	54	=	=	SYM
ejpam-141	170	55	u	u	PROPN
ejpam-141	170	56	.	.	PUNCT
ejpam-141	171	1	since	since	SCONJ
ejpam-141	171	2	p	p	NOUN
ejpam-141	171	3	is	be	AUX
ejpam-141	171	4	a	a	DET
ejpam-141	171	5	σ	σ	PROPN
ejpam-141	171	6	-	-	PUNCT
ejpam-141	171	7	strong	strong	ADJ
ejpam-141	171	8	network	network	NOUN
ejpam-141	171	9	of	of	ADP
ejpam-141	171	10	x	x	SYM
ejpam-141	171	11	,	,	PUNCT
ejpam-141	171	12	there	there	PRON
ejpam-141	171	13	exists	exist	VERB
ejpam-141	171	14	i	i	PRON
ejpam-141	171	15	∈	∈	PROPN
ejpam-141	171	16	n	n	PRON
ejpam-141	171	17	such	such	ADJ
ejpam-141	171	18	that	that	SCONJ
ejpam-141	171	19	x	x	SYM
ejpam-141	171	20	∈	∈	PROPN
ejpam-141	171	21	st(x	st(x	X
ejpam-141	171	22	,	,	PUNCT
ejpam-141	171	23	pi)⊂	pi)⊂	PROPN
ejpam-141	171	24	v	v	NOUN
ejpam-141	171	25	.	.	PUNCT
ejpam-141	172	1	let	let	VERB
ejpam-141	172	2	l	l	NOUN
ejpam-141	172	3	be	be	AUX
ejpam-141	172	4	a	a	DET
ejpam-141	172	5	sequence	sequence	NOUN
ejpam-141	172	6	in	in	ADP
ejpam-141	172	7	dn	dn	NOUN
ejpam-141	172	8	,	,	PUNCT
ejpam-141	172	9	λ	λ	NOUN
ejpam-141	172	10	converging	converge	VERB
ejpam-141	172	11	to	to	ADP
ejpam-141	172	12	x	x	PROPN
ejpam-141	172	13	.	.	PUNCT
ejpam-141	173	1	since	since	SCONJ
ejpam-141	173	2	pi	pi	NOUN
ejpam-141	173	3	is	be	AUX
ejpam-141	173	4	an	an	DET
ejpam-141	173	5	sn	sn	NOUN
ejpam-141	173	6	-	-	PUNCT
ejpam-141	173	7	cover	cover	NOUN
ejpam-141	173	8	of	of	ADP
ejpam-141	173	9	x	x	X
ejpam-141	173	10	,	,	PUNCT
ejpam-141	173	11	l∪{x	l∪{x	NOUN
ejpam-141	173	12	}	}	PUNCT
ejpam-141	173	13	is	be	AUX
ejpam-141	173	14	eventually	eventually	ADV
ejpam-141	173	15	in	in	ADP
ejpam-141	173	16	p	p	PROPN
ejpam-141	173	17	⊂	⊂	PROPN
ejpam-141	173	18	v	v	NOUN
ejpam-141	173	19	for	for	ADP
ejpam-141	173	20	some	some	DET
ejpam-141	173	21	p	p	PROPN
ejpam-141	173	22	∈	∈	PROPN
ejpam-141	173	23	pi	pi	NOUN
ejpam-141	173	24	,	,	PUNCT
ejpam-141	173	25	x	x	PROPN
ejpam-141	173	26	.	.	PUNCT
ejpam-141	174	1	then	then	ADV
ejpam-141	174	2	p	p	X
ejpam-141	174	3	∩	∩	ADJ
ejpam-141	174	4	dn	dn	NOUN
ejpam-141	174	5	,	,	PUNCT
ejpam-141	174	6	λ	λ	PROPN
ejpam-141	174	7	6=	6=	NUM
ejpam-141	174	8	;	;	PUNCT
ejpam-141	174	9	,	,	PUNCT
ejpam-141	174	10	and	and	CCONJ
ejpam-141	174	11	p	p	PROPN
ejpam-141	174	12	∩	∩	ADJ
ejpam-141	174	13	pn	pn	NOUN
ejpam-141	174	14	,	,	PUNCT
ejpam-141	174	15	λ	λ	PROPN
ejpam-141	174	16	∈	∈	PROPN
ejpam-141	174	17	qn	qn	PROPN
ejpam-141	174	18	,	,	PUNCT
ejpam-141	174	19	λ	λ	PROPN
ejpam-141	174	20	,	,	PUNCT
ejpam-141	174	21	i.	i.	NOUN
ejpam-141	174	22	it	it	PRON
ejpam-141	174	23	implies	imply	VERB
ejpam-141	174	24	that	that	SCONJ
ejpam-141	174	25	x	x	SYM
ejpam-141	174	26	∈	∈	PROPN
ejpam-141	174	27	st(x	st(x	X
ejpam-141	174	28	,	,	PUNCT
ejpam-141	174	29	qn	qn	INTJ
ejpam-141	174	30	,	,	PUNCT
ejpam-141	174	31	λ	λ	PROPN
ejpam-141	174	32	,	,	PUNCT
ejpam-141	174	33	i	i	NOUN
ejpam-141	174	34	)	)	PUNCT
ejpam-141	174	35	=	=	SYM
ejpam-141	174	36	st(x	st(x	X
ejpam-141	174	37	,	,	PUNCT
ejpam-141	174	38	pi	pi	NOUN
ejpam-141	174	39	)	)	PUNCT
ejpam-141	174	40	∩	∩	PROPN
ejpam-141	174	41	pn	pn	PROPN
ejpam-141	174	42	,	,	PUNCT
ejpam-141	174	43	λ	λ	PROPN
ejpam-141	174	44	⊂	⊂	PROPN
ejpam-141	174	45	v	v	ADP
ejpam-141	174	46	∩	∩	ADJ
ejpam-141	174	47	pn	pn	NOUN
ejpam-141	174	48	,	,	PUNCT
ejpam-141	174	49	λ	λ	PROPN
ejpam-141	174	50	=	=	SYM
ejpam-141	174	51	u	u	PROPN
ejpam-141	174	52	.	.	PUNCT
ejpam-141	175	1	therefore	therefore	ADV
ejpam-141	175	2	,	,	PUNCT
ejpam-141	175	3	{	{	PUNCT
ejpam-141	175	4	qn	qn	INTJ
ejpam-141	175	5	,	,	PUNCT
ejpam-141	175	6	λ	λ	PROPN
ejpam-141	175	7	,	,	PUNCT
ejpam-141	175	8	i	i	PRON
ejpam-141	175	9	:	:	PUNCT
ejpam-141	175	10	i	i	PROPN
ejpam-141	175	11	∈	∈	PROPN
ejpam-141	175	12	n	n	CCONJ
ejpam-141	175	13	}	}	PUNCT
ejpam-141	175	14	is	be	AUX
ejpam-141	175	15	a	a	DET
ejpam-141	175	16	σ	σ	PROPN
ejpam-141	175	17	-	-	PUNCT
ejpam-141	175	18	strong	strong	ADJ
ejpam-141	175	19	network	network	NOUN
ejpam-141	175	20	of	of	ADP
ejpam-141	175	21	pn	pn	PROPN
ejpam-141	175	22	,	,	PUNCT
ejpam-141	175	23	λ	λ	PROPN
ejpam-141	175	24	.	.	PUNCT
ejpam-141	175	25	n.	n.	PROPN
ejpam-141	175	26	dung	dung	PROPN
ejpam-141	175	27	/	/	SYM
ejpam-141	175	28	eur	eur	PROPN
ejpam-141	175	29	.	.	PUNCT
ejpam-141	176	1	j.	j.	PROPN
ejpam-141	176	2	pure	pure	PROPN
ejpam-141	176	3	appl	appl	PROPN
ejpam-141	176	4	.	.	PROPN
ejpam-141	176	5	math	math	PROPN
ejpam-141	176	6	,	,	PUNCT
ejpam-141	176	7	2	2	NUM
ejpam-141	176	8	(	(	PUNCT
ejpam-141	176	9	2009	2009	NUM
ejpam-141	176	10	)	)	PUNCT
ejpam-141	176	11	,	,	PUNCT
ejpam-141	176	12	(	(	PUNCT
ejpam-141	176	13	182	182	NUM
ejpam-141	176	14	-	-	SYM
ejpam-141	176	15	194	194	NUM
ejpam-141	176	16	)	)	PUNCT
ejpam-141	176	17	190	190	NUM
ejpam-141	176	18	for	for	ADP
ejpam-141	176	19	each	each	DET
ejpam-141	176	20	x	x	SYM
ejpam-141	176	21	∈	∈	PROPN
ejpam-141	176	22	pn	pn	PROPN
ejpam-141	176	23	,	,	PUNCT
ejpam-141	176	24	λ	λ	PROPN
ejpam-141	176	25	and	and	CCONJ
ejpam-141	176	26	i	i	PROPN
ejpam-141	176	27	∈	∈	PROPN
ejpam-141	176	28	n	n	CCONJ
ejpam-141	176	29	,	,	PUNCT
ejpam-141	176	30	let	let	VERB
ejpam-141	176	31	q	q	PROPN
ejpam-141	176	32	∈	∈	PROPN
ejpam-141	176	33	qn	qn	PROPN
ejpam-141	176	34	,	,	PUNCT
ejpam-141	176	35	λ	λ	PROPN
ejpam-141	176	36	,	,	PUNCT
ejpam-141	176	37	i	i	PRON
ejpam-141	176	38	,	,	PUNCT
ejpam-141	176	39	x	x	PROPN
ejpam-141	176	40	.	.	PUNCT
ejpam-141	177	1	then	then	ADV
ejpam-141	177	2	q	q	X
ejpam-141	178	1	=	=	SYM
ejpam-141	178	2	p	p	NOUN
ejpam-141	178	3	∩	∩	ADJ
ejpam-141	178	4	pn	pn	PROPN
ejpam-141	178	5	,	,	PUNCT
ejpam-141	178	6	λ	λ	PROPN
ejpam-141	178	7	,	,	PUNCT
ejpam-141	178	8	where	where	SCONJ
ejpam-141	178	9	p	p	PROPN
ejpam-141	178	10	∈	∈	PROPN
ejpam-141	178	11	pi	pi	NOUN
ejpam-141	178	12	,	,	PUNCT
ejpam-141	178	13	x	x	X
ejpam-141	178	14	and	and	CCONJ
ejpam-141	178	15	p	p	PROPN
ejpam-141	178	16	∩	∩	ADJ
ejpam-141	178	17	dn	dn	NOUN
ejpam-141	178	18	,	,	PUNCT
ejpam-141	178	19	λ	λ	PROPN
ejpam-141	178	20	6=	6=	NUM
ejpam-141	178	21	;	;	PUNCT
ejpam-141	178	22	.	.	PUNCT
ejpam-141	179	1	let	let	VERB
ejpam-141	179	2	s	s	PRON
ejpam-141	179	3	be	be	AUX
ejpam-141	179	4	a	a	DET
ejpam-141	179	5	convergent	convergent	NOUN
ejpam-141	179	6	sequence	sequence	NOUN
ejpam-141	179	7	converging	converge	VERB
ejpam-141	179	8	to	to	ADP
ejpam-141	179	9	x	x	PUNCT
ejpam-141	179	10	in	in	ADP
ejpam-141	179	11	pn	pn	PROPN
ejpam-141	179	12	,	,	PUNCT
ejpam-141	179	13	λ	λ	PROPN
ejpam-141	179	14	.	.	PUNCT
ejpam-141	180	1	since	since	SCONJ
ejpam-141	180	2	pi	pi	NOUN
ejpam-141	180	3	is	be	AUX
ejpam-141	180	4	an	an	DET
ejpam-141	180	5	sn	sn	NOUN
ejpam-141	180	6	-	-	PUNCT
ejpam-141	180	7	cover	cover	NOUN
ejpam-141	180	8	of	of	ADP
ejpam-141	180	9	x	x	PRON
ejpam-141	180	10	,	,	PUNCT
ejpam-141	180	11	s	s	X
ejpam-141	180	12	is	be	AUX
ejpam-141	180	13	eventually	eventually	ADV
ejpam-141	180	14	in	in	ADP
ejpam-141	180	15	p.	p.	NOUN
ejpam-141	180	16	it	it	PRON
ejpam-141	180	17	implies	imply	VERB
ejpam-141	180	18	that	that	SCONJ
ejpam-141	180	19	s	s	VERB
ejpam-141	180	20	is	be	AUX
ejpam-141	180	21	eventually	eventually	ADV
ejpam-141	180	22	in	in	ADP
ejpam-141	180	23	p	p	NOUN
ejpam-141	180	24	∩	∩	ADJ
ejpam-141	180	25	pn	pn	PROPN
ejpam-141	180	26	,	,	PUNCT
ejpam-141	180	27	λ	λ	PROPN
ejpam-141	180	28	.	.	PUNCT
ejpam-141	180	29	therefore	therefore	ADV
ejpam-141	180	30	,	,	PUNCT
ejpam-141	180	31	qn	qn	INTJ
ejpam-141	180	32	,	,	PUNCT
ejpam-141	180	33	λ	λ	PROPN
ejpam-141	180	34	is	be	AUX
ejpam-141	180	35	a	a	DET
ejpam-141	180	36	σ	σ	NOUN
ejpam-141	180	37	-	-	PUNCT
ejpam-141	180	38	strong	strong	ADJ
ejpam-141	180	39	sn	sn	NOUN
ejpam-141	180	40	-	-	PUNCT
ejpam-141	180	41	network	network	NOUN
ejpam-141	180	42	of	of	ADP
ejpam-141	180	43	pn	pn	PROPN
ejpam-141	180	44	,	,	PUNCT
ejpam-141	180	45	λ	λ	PROPN
ejpam-141	180	46	.	.	PUNCT
ejpam-141	180	47	by	by	ADP
ejpam-141	180	48	the	the	DET
ejpam-141	180	49	above	above	ADJ
ejpam-141	180	50	,	,	PUNCT
ejpam-141	180	51	the	the	DET
ejpam-141	180	52	ponomarev	ponomarev	NOUN
ejpam-141	180	53	-	-	PUNCT
ejpam-141	180	54	system	system	NOUN
ejpam-141	180	55	(	(	PUNCT
ejpam-141	180	56	fn	fn	NOUN
ejpam-141	180	57	,	,	PUNCT
ejpam-141	180	58	λ	λ	PROPN
ejpam-141	180	59	,	,	PUNCT
ejpam-141	180	60	mn	mn	PROPN
ejpam-141	180	61	,	,	PUNCT
ejpam-141	180	62	λ	λ	PROPN
ejpam-141	180	63	,	,	PUNCT
ejpam-141	180	64	pn	pn	PROPN
ejpam-141	180	65	,	,	PUNCT
ejpam-141	180	66	λ	λ	PROPN
ejpam-141	180	67	,	,	PUNCT
ejpam-141	180	68	{	{	PUNCT
ejpam-141	180	69	qn	qn	INTJ
ejpam-141	180	70	,	,	PUNCT
ejpam-141	180	71	λ	λ	PROPN
ejpam-141	180	72	,	,	PUNCT
ejpam-141	180	73	i	i	NOUN
ejpam-141	180	74	}	}	PUNCT
ejpam-141	180	75	)	)	PUNCT
ejpam-141	180	76	exists	exist	VERB
ejpam-141	180	77	.	.	PUNCT
ejpam-141	181	1	since	since	SCONJ
ejpam-141	181	2	each	each	DET
ejpam-141	181	3	qn	qn	NOUN
ejpam-141	181	4	,	,	PUNCT
ejpam-141	181	5	λ	λ	PROPN
ejpam-141	181	6	,	,	PUNCT
ejpam-141	181	7	i	i	PRON
ejpam-141	181	8	is	be	AUX
ejpam-141	181	9	countable	countable	ADJ
ejpam-141	181	10	,	,	PUNCT
ejpam-141	181	11	mn	mn	PROPN
ejpam-141	181	12	,	,	PUNCT
ejpam-141	181	13	λ	λ	PROPN
ejpam-141	181	14	is	be	AUX
ejpam-141	181	15	a	a	DET
ejpam-141	181	16	separable	separable	ADJ
ejpam-141	181	17	metric	metric	ADJ
ejpam-141	181	18	space	space	NOUN
ejpam-141	181	19	with	with	ADP
ejpam-141	181	20	the	the	DET
ejpam-141	181	21	metric	metric	ADJ
ejpam-141	181	22	dn	dn	NOUN
ejpam-141	181	23	,	,	PUNCT
ejpam-141	181	24	λ	λ	NOUN
ejpam-141	181	25	described	describe	VERB
ejpam-141	181	26	as	as	ADP
ejpam-141	181	27	follows	follow	VERB
ejpam-141	181	28	.	.	PUNCT
ejpam-141	182	1	for	for	ADP
ejpam-141	182	2	a	a	DET
ejpam-141	182	3	=	=	X
ejpam-141	182	4	(	(	PUNCT
ejpam-141	182	5	αi	αi	NOUN
ejpam-141	182	6	)	)	PUNCT
ejpam-141	182	7	,	,	PUNCT
ejpam-141	182	8	b	b	X
ejpam-141	182	9	=	=	SYM
ejpam-141	182	10	(	(	PUNCT
ejpam-141	182	11	βi	βi	NOUN
ejpam-141	182	12	)	)	PUNCT
ejpam-141	182	13	∈	∈	PROPN
ejpam-141	182	14	mn	mn	PROPN
ejpam-141	182	15	,	,	PUNCT
ejpam-141	182	16	λ	λ	PROPN
ejpam-141	182	17	,	,	PUNCT
ejpam-141	182	18	if	if	SCONJ
ejpam-141	182	19	a	a	DET
ejpam-141	182	20	=	=	SYM
ejpam-141	182	21	b	b	NOUN
ejpam-141	182	22	,	,	PUNCT
ejpam-141	182	23	then	then	ADV
ejpam-141	182	24	dn	dn	PROPN
ejpam-141	182	25	,	,	PUNCT
ejpam-141	182	26	λ(a	λ(a	PROPN
ejpam-141	182	27	,	,	PUNCT
ejpam-141	182	28	b	b	NOUN
ejpam-141	182	29	)	)	PUNCT
ejpam-141	182	30	=	=	SYM
ejpam-141	182	31	0	0	NUM
ejpam-141	182	32	,	,	PUNCT
ejpam-141	182	33	and	and	CCONJ
ejpam-141	182	34	otherwise	otherwise	ADV
ejpam-141	182	35	,	,	PUNCT
ejpam-141	182	36	dn	dn	INTJ
ejpam-141	182	37	,	,	PUNCT
ejpam-141	182	38	λ(a	λ(a	PROPN
ejpam-141	182	39	,	,	PUNCT
ejpam-141	182	40	b	b	NOUN
ejpam-141	182	41	)	)	PUNCT
ejpam-141	182	42	=	=	SYM
ejpam-141	182	43	1	1	NUM
ejpam-141	182	44	/	/	SYM
ejpam-141	182	45	min{i	min{i	PROPN
ejpam-141	182	46	∈	∈	PROPN
ejpam-141	182	47	n	n	CCONJ
ejpam-141	182	48	:	:	PUNCT
ejpam-141	182	49	αi	αi	PROPN
ejpam-141	182	50	6=	6=	PUNCT
ejpam-141	182	51	βi	βi	PRON
ejpam-141	182	52	}	}	PUNCT
ejpam-141	182	53	.	.	PUNCT
ejpam-141	183	1	put	put	VERB
ejpam-141	183	2	m	m	PROPN
ejpam-141	183	3	=	=	PUNCT
ejpam-141	183	4	⊕{mn	⊕{mn	PROPN
ejpam-141	183	5	,	,	PUNCT
ejpam-141	183	6	λ	λ	NOUN
ejpam-141	183	7	:	:	PUNCT
ejpam-141	183	8	λ	λ	X
ejpam-141	183	9	∈	∈	PROPN
ejpam-141	183	10	λn	λn	NOUN
ejpam-141	183	11	,	,	PUNCT
ejpam-141	183	12	n	n	PROPN
ejpam-141	183	13	∈	∈	PROPN
ejpam-141	183	14	n	n	CCONJ
ejpam-141	183	15	}	}	PUNCT
ejpam-141	183	16	and	and	CCONJ
ejpam-141	183	17	define	define	VERB
ejpam-141	183	18	f	f	X
ejpam-141	183	19	:	:	PUNCT
ejpam-141	183	20	m	m	VERB
ejpam-141	183	21	−→	−→	ADJ
ejpam-141	183	22	x	x	PUNCT
ejpam-141	183	23	by	by	ADP
ejpam-141	183	24	choosing	choose	VERB
ejpam-141	183	25	f	f	PROPN
ejpam-141	183	26	(	(	PUNCT
ejpam-141	183	27	a	a	NOUN
ejpam-141	183	28	)	)	PUNCT
ejpam-141	183	29	=	=	SYM
ejpam-141	183	30	fn	fn	NOUN
ejpam-141	183	31	,	,	PUNCT
ejpam-141	183	32	λ(a	λ(a	NOUN
ejpam-141	183	33	)	)	PUNCT
ejpam-141	184	1	if	if	SCONJ
ejpam-141	184	2	a	a	DET
ejpam-141	184	3	∈	∈	PROPN
ejpam-141	184	4	mn	mn	PROPN
ejpam-141	184	5	,	,	PUNCT
ejpam-141	184	6	λ	λ	PROPN
ejpam-141	184	7	with	with	ADP
ejpam-141	184	8	λ	λ	PROPN
ejpam-141	184	9	∈	∈	PROPN
ejpam-141	184	10	λn	λn	NOUN
ejpam-141	184	11	,	,	PUNCT
ejpam-141	184	12	n	n	PROPN
ejpam-141	184	13	∈	∈	PROPN
ejpam-141	184	14	n.	n.	NOUN
ejpam-141	184	15	then	then	ADV
ejpam-141	184	16	f	f	PROPN
ejpam-141	184	17	is	be	AUX
ejpam-141	184	18	a	a	DET
ejpam-141	184	19	mapping	mapping	NOUN
ejpam-141	184	20	,	,	PUNCT
ejpam-141	184	21	and	and	CCONJ
ejpam-141	184	22	m	m	PROPN
ejpam-141	184	23	is	be	AUX
ejpam-141	184	24	a	a	DET
ejpam-141	184	25	locally	locally	ADV
ejpam-141	184	26	separable	separable	ADJ
ejpam-141	184	27	metric	metric	ADJ
ejpam-141	184	28	space	space	NOUN
ejpam-141	184	29	with	with	ADP
ejpam-141	184	30	the	the	DET
ejpam-141	184	31	metric	metric	NOUN
ejpam-141	184	32	d	d	NOUN
ejpam-141	184	33	described	describe	VERB
ejpam-141	184	34	as	as	ADP
ejpam-141	184	35	follows	follow	VERB
ejpam-141	184	36	.	.	PUNCT
ejpam-141	185	1	for	for	ADP
ejpam-141	185	2	each	each	DET
ejpam-141	185	3	a	a	PROPN
ejpam-141	185	4	,	,	PUNCT
ejpam-141	185	5	b	b	X
ejpam-141	185	6	∈	∈	ADV
ejpam-141	185	7	m	m	PRON
ejpam-141	185	8	,	,	PUNCT
ejpam-141	185	9	if	if	SCONJ
ejpam-141	185	10	a	a	PRON
ejpam-141	185	11	,	,	PUNCT
ejpam-141	185	12	b	b	PROPN
ejpam-141	185	13	∈	∈	PROPN
ejpam-141	185	14	mn	mn	PROPN
ejpam-141	185	15	,	,	PUNCT
ejpam-141	185	16	λ	λ	PROPN
ejpam-141	185	17	for	for	ADP
ejpam-141	185	18	some	some	DET
ejpam-141	185	19	λ	λ	PROPN
ejpam-141	185	20	∈	∈	PROPN
ejpam-141	185	21	λn	λn	NOUN
ejpam-141	185	22	and	and	CCONJ
ejpam-141	185	23	n	n	CCONJ
ejpam-141	185	24	∈	∈	PROPN
ejpam-141	185	25	n	n	CCONJ
ejpam-141	185	26	,	,	PUNCT
ejpam-141	185	27	then	then	ADV
ejpam-141	185	28	d(a	d(a	PROPN
ejpam-141	185	29	,	,	PUNCT
ejpam-141	185	30	b	b	NOUN
ejpam-141	185	31	)	)	PUNCT
ejpam-141	185	32	=	=	SYM
ejpam-141	185	33	dn	dn	PROPN
ejpam-141	185	34	,	,	PUNCT
ejpam-141	185	35	λ(a	λ(a	PROPN
ejpam-141	185	36	,	,	PUNCT
ejpam-141	185	37	b	b	NOUN
ejpam-141	185	38	)	)	PUNCT
ejpam-141	185	39	,	,	PUNCT
ejpam-141	185	40	and	and	CCONJ
ejpam-141	185	41	otherwise	otherwise	ADV
ejpam-141	185	42	,	,	PUNCT
ejpam-141	185	43	d(a	d(a	PROPN
ejpam-141	185	44	,	,	PUNCT
ejpam-141	185	45	b	b	NOUN
ejpam-141	185	46	)	)	PUNCT
ejpam-141	185	47	=	=	SYM
ejpam-141	186	1	1	1	X
ejpam-141	186	2	.	.	PUNCT
ejpam-141	187	1	we	we	PRON
ejpam-141	187	2	shall	shall	AUX
ejpam-141	187	3	prove	prove	VERB
ejpam-141	187	4	that	that	SCONJ
ejpam-141	187	5	f	f	PROPN
ejpam-141	187	6	is	be	AUX
ejpam-141	187	7	a	a	DET
ejpam-141	187	8	sequencecovering	sequencecovering	NOUN
ejpam-141	187	9	π	π	PROPN
ejpam-141	187	10	-	-	PUNCT
ejpam-141	187	11	s	s	NOUN
ejpam-141	187	12	-	-	PUNCT
ejpam-141	187	13	mapping	mapping	NOUN
ejpam-141	187	14	by	by	ADP
ejpam-141	187	15	the	the	DET
ejpam-141	187	16	following	follow	VERB
ejpam-141	187	17	facts	fact	NOUN
ejpam-141	187	18	(	(	PUNCT
ejpam-141	187	19	a	a	X
ejpam-141	187	20	)	)	PUNCT
ejpam-141	187	21	,	,	PUNCT
ejpam-141	187	22	(	(	PUNCT
ejpam-141	187	23	b	b	NOUN
ejpam-141	187	24	)	)	PUNCT
ejpam-141	187	25	,	,	PUNCT
ejpam-141	187	26	and	and	CCONJ
ejpam-141	187	27	(	(	PUNCT
ejpam-141	187	28	c	c	NOUN
ejpam-141	187	29	)	)	PUNCT
ejpam-141	187	30	.	.	PUNCT
ejpam-141	188	1	(	(	PUNCT
ejpam-141	188	2	a	a	X
ejpam-141	188	3	)	)	PUNCT
ejpam-141	188	4	f	f	PROPN
ejpam-141	188	5	is	be	AUX
ejpam-141	188	6	a	a	DET
ejpam-141	188	7	π	π	NOUN
ejpam-141	188	8	-	-	NOUN
ejpam-141	188	9	mapping	mapping	NOUN
ejpam-141	188	10	.	.	PUNCT
ejpam-141	189	1	let	let	VERB
ejpam-141	189	2	x	x	PUNCT
ejpam-141	189	3	∈	∈	PROPN
ejpam-141	189	4	u	u	NOUN
ejpam-141	189	5	with	with	ADP
ejpam-141	189	6	u	u	NOUN
ejpam-141	189	7	open	open	ADJ
ejpam-141	189	8	in	in	ADP
ejpam-141	189	9	x	x	X
ejpam-141	189	10	.	.	PUNCT
ejpam-141	190	1	then	then	ADV
ejpam-141	190	2	st(x	st(x	PUNCT
ejpam-141	190	3	,	,	PUNCT
ejpam-141	190	4	pm	pm	NOUN
ejpam-141	190	5	)	)	PUNCT
ejpam-141	191	1	⊂	⊂	PROPN
ejpam-141	191	2	u	u	NOUN
ejpam-141	191	3	for	for	ADP
ejpam-141	191	4	some	some	DET
ejpam-141	191	5	m	m	NOUN
ejpam-141	191	6	∈	∈	PROPN
ejpam-141	191	7	n.	n.	NOUN
ejpam-141	191	8	for	for	ADP
ejpam-141	191	9	each	each	DET
ejpam-141	191	10	n	n	PRON
ejpam-141	191	11	∈	∈	PROPN
ejpam-141	191	12	n	n	NOUN
ejpam-141	191	13	and	and	CCONJ
ejpam-141	191	14	λ	λ	PROPN
ejpam-141	191	15	∈	∈	PROPN
ejpam-141	191	16	λn	λn	NOUN
ejpam-141	191	17	with	with	ADP
ejpam-141	191	18	x	x	PROPN
ejpam-141	191	19	∈	∈	PROPN
ejpam-141	191	20	pn	pn	PROPN
ejpam-141	191	21	,	,	PUNCT
ejpam-141	191	22	λ	λ	PROPN
ejpam-141	191	23	,	,	PUNCT
ejpam-141	191	24	we	we	PRON
ejpam-141	191	25	get	get	VERB
ejpam-141	191	26	st(x	st(x	PUNCT
ejpam-141	191	27	,	,	PUNCT
ejpam-141	191	28	qn	qn	INTJ
ejpam-141	191	29	,	,	PUNCT
ejpam-141	191	30	λ	λ	PROPN
ejpam-141	191	31	,	,	PUNCT
ejpam-141	191	32	m)⊂	m)⊂	PROPN
ejpam-141	191	33	un	un	PROPN
ejpam-141	191	34	,	,	PUNCT
ejpam-141	191	35	λ	λ	PROPN
ejpam-141	191	36	,	,	PUNCT
ejpam-141	191	37	where	where	SCONJ
ejpam-141	191	38	un	un	PROPN
ejpam-141	191	39	,	,	PUNCT
ejpam-141	191	40	λ	λ	NOUN
ejpam-141	191	41	=	=	SYM
ejpam-141	191	42	u	u	PROPN
ejpam-141	191	43	∩	∩	X
ejpam-141	191	44	pn	pn	PROPN
ejpam-141	191	45	,	,	PUNCT
ejpam-141	191	46	λ	λ	PROPN
ejpam-141	191	47	.	.	PROPN
ejpam-141	191	48	for	for	ADP
ejpam-141	191	49	each	each	DET
ejpam-141	191	50	a	a	DET
ejpam-141	191	51	=	=	X
ejpam-141	191	52	(	(	PUNCT
ejpam-141	191	53	αi	αi	NOUN
ejpam-141	191	54	)	)	PUNCT
ejpam-141	191	55	∈	∈	PROPN
ejpam-141	191	56	mn	mn	PROPN
ejpam-141	191	57	,	,	PUNCT
ejpam-141	191	58	λ	λ	PROPN
ejpam-141	191	59	,	,	PUNCT
ejpam-141	191	60	if	if	SCONJ
ejpam-141	191	61	dn	dn	PROPN
ejpam-141	191	62	,	,	PUNCT
ejpam-141	191	63	λ	λ	PROPN
ejpam-141	191	64	(	(	PUNCT
ejpam-141	191	65	f	f	PROPN
ejpam-141	191	66	−1	−1	NOUN
ejpam-141	191	67	n	n	CCONJ
ejpam-141	191	68	,	,	PUNCT
ejpam-141	191	69	λ	λ	PROPN
ejpam-141	191	70	(	(	PUNCT
ejpam-141	191	71	x	x	NOUN
ejpam-141	191	72	)	)	PUNCT
ejpam-141	191	73	,	,	PUNCT
ejpam-141	191	74	a	a	X
ejpam-141	191	75	)	)	PUNCT
ejpam-141	191	76	<	<	X
ejpam-141	191	77	1	1	NUM
ejpam-141	191	78	/	/	SYM
ejpam-141	191	79	m	m	PROPN
ejpam-141	191	80	,	,	PUNCT
ejpam-141	191	81	then	then	ADV
ejpam-141	191	82	there	there	PRON
ejpam-141	191	83	exists	exist	VERB
ejpam-141	191	84	b	b	NOUN
ejpam-141	191	85	=	=	SYM
ejpam-141	191	86	(	(	PUNCT
ejpam-141	191	87	βi	βi	NOUN
ejpam-141	191	88	)	)	PUNCT
ejpam-141	191	89	∈	∈	PROPN
ejpam-141	191	90	f	f	PROPN
ejpam-141	191	91	−1	−1	NOUN
ejpam-141	191	92	n	n	CCONJ
ejpam-141	191	93	,	,	PUNCT
ejpam-141	191	94	λ	λ	PROPN
ejpam-141	191	95	(	(	PUNCT
ejpam-141	191	96	x	x	NOUN
ejpam-141	191	97	)	)	PUNCT
ejpam-141	191	98	such	such	ADJ
ejpam-141	191	99	that	that	DET
ejpam-141	191	100	dn	dn	NOUN
ejpam-141	191	101	,	,	PUNCT
ejpam-141	191	102	λ(a	λ(a	PROPN
ejpam-141	191	103	,	,	PUNCT
ejpam-141	191	104	b	b	NOUN
ejpam-141	191	105	)	)	PUNCT
ejpam-141	191	106	<	<	X
ejpam-141	191	107	1	1	NUM
ejpam-141	191	108	/	/	SYM
ejpam-141	191	109	m.	m.	NOUN
ejpam-141	191	110	hence	hence	ADV
ejpam-141	191	111	αi	αi	VERB
ejpam-141	191	112	=	=	PUNCT
ejpam-141	192	1	βi	βi	PROPN
ejpam-141	192	2	if	if	SCONJ
ejpam-141	192	3	i	i	PRON
ejpam-141	192	4	≤	≤	X
ejpam-141	192	5	m.	m.	NOUN
ejpam-141	192	6	since	since	SCONJ
ejpam-141	192	7	x	x	PROPN
ejpam-141	192	8	∈	∈	PROPN
ejpam-141	192	9	qβm	qβm	PROPN
ejpam-141	192	10	⊂	⊂	PROPN
ejpam-141	192	11	st(x	st(x	PROPN
ejpam-141	192	12	,	,	PUNCT
ejpam-141	192	13	qn	qn	INTJ
ejpam-141	192	14	,	,	PUNCT
ejpam-141	192	15	λ	λ	PROPN
ejpam-141	192	16	,	,	PUNCT
ejpam-141	192	17	m	m	NOUN
ejpam-141	192	18	)	)	PUNCT
ejpam-141	192	19	⊂	⊂	PROPN
ejpam-141	192	20	un	un	PROPN
ejpam-141	192	21	,	,	PUNCT
ejpam-141	192	22	λ	λ	PROPN
ejpam-141	192	23	,	,	PUNCT
ejpam-141	192	24	fn	fn	NOUN
ejpam-141	192	25	,	,	PUNCT
ejpam-141	192	26	λ(a	λ(a	PROPN
ejpam-141	192	27	)	)	PUNCT
ejpam-141	193	1	∈	∈	PROPN
ejpam-141	193	2	qαm	qαm	NOUN
ejpam-141	193	3	=	=	SYM
ejpam-141	193	4	qβm	qβm	PROPN
ejpam-141	193	5	⊂	⊂	ADJ
ejpam-141	193	6	un	un	PROPN
ejpam-141	193	7	,	,	PUNCT
ejpam-141	193	8	λ	λ	X
ejpam-141	193	9	.	.	PUNCT
ejpam-141	194	1	it	it	PRON
ejpam-141	194	2	implies	imply	VERB
ejpam-141	194	3	that	that	SCONJ
ejpam-141	194	4	a	a	DET
ejpam-141	194	5	∈	∈	PROPN
ejpam-141	194	6	f	f	PROPN
ejpam-141	194	7	−1	−1	NOUN
ejpam-141	194	8	n	n	CCONJ
ejpam-141	194	9	,	,	PUNCT
ejpam-141	194	10	λ	λ	PROPN
ejpam-141	194	11	(	(	PUNCT
ejpam-141	194	12	un	un	PROPN
ejpam-141	194	13	,	,	PUNCT
ejpam-141	194	14	λ	λ	NOUN
ejpam-141	194	15	)	)	PUNCT
ejpam-141	194	16	.	.	PUNCT
ejpam-141	195	1	therefore	therefore	ADV
ejpam-141	195	2	,	,	PUNCT
ejpam-141	195	3	if	if	SCONJ
ejpam-141	195	4	a	a	DET
ejpam-141	195	5	∈	∈	PROPN
ejpam-141	195	6	mn	mn	PROPN
ejpam-141	195	7	,	,	PUNCT
ejpam-141	195	8	λ	λ	PROPN
ejpam-141	195	9	−	−	PROPN
ejpam-141	195	10	f	f	PROPN
ejpam-141	195	11	−1	−1	NOUN
ejpam-141	195	12	n	n	CCONJ
ejpam-141	195	13	,	,	PUNCT
ejpam-141	195	14	λ	λ	PROPN
ejpam-141	195	15	(	(	PUNCT
ejpam-141	195	16	un	un	PROPN
ejpam-141	195	17	,	,	PUNCT
ejpam-141	195	18	λ	λ	NOUN
ejpam-141	195	19	)	)	PUNCT
ejpam-141	195	20	,	,	PUNCT
ejpam-141	195	21	then	then	ADV
ejpam-141	195	22	dn	dn	PROPN
ejpam-141	195	23	,	,	PUNCT
ejpam-141	195	24	λ	λ	PROPN
ejpam-141	195	25	(	(	PUNCT
ejpam-141	195	26	f	f	PROPN
ejpam-141	195	27	−1	−1	NOUN
ejpam-141	195	28	n	n	CCONJ
ejpam-141	195	29	,	,	PUNCT
ejpam-141	195	30	λ	λ	PROPN
ejpam-141	195	31	(	(	PUNCT
ejpam-141	195	32	x	x	NOUN
ejpam-141	195	33	)	)	PUNCT
ejpam-141	195	34	,	,	PUNCT
ejpam-141	195	35	a	a	X
ejpam-141	195	36	)	)	PUNCT
ejpam-141	195	37	≥	≥	NOUN
ejpam-141	195	38	1	1	NUM
ejpam-141	195	39	/	/	SYM
ejpam-141	195	40	m.	m.	NOUN
ejpam-141	195	41	hence	hence	ADV
ejpam-141	195	42	dn	dn	PROPN
ejpam-141	195	43	,	,	PUNCT
ejpam-141	195	44	λ	λ	PROPN
ejpam-141	195	45	(	(	PUNCT
ejpam-141	195	46	f	f	PROPN
ejpam-141	195	47	−1	−1	NOUN
ejpam-141	195	48	n	n	CCONJ
ejpam-141	195	49	,	,	PUNCT
ejpam-141	195	50	λ	λ	PROPN
ejpam-141	195	51	(	(	PUNCT
ejpam-141	195	52	x	x	NOUN
ejpam-141	195	53	)	)	PUNCT
ejpam-141	195	54	,	,	PUNCT
ejpam-141	195	55	mn	mn	PROPN
ejpam-141	195	56	,	,	PUNCT
ejpam-141	195	57	λ	λ	PROPN
ejpam-141	195	58	−	−	PROPN
ejpam-141	195	59	f	f	PROPN
ejpam-141	195	60	−1	−1	NOUN
ejpam-141	195	61	n	n	CCONJ
ejpam-141	195	62	,	,	PUNCT
ejpam-141	195	63	λ	λ	PROPN
ejpam-141	195	64	(	(	PUNCT
ejpam-141	195	65	un	un	PROPN
ejpam-141	195	66	,	,	PUNCT
ejpam-141	195	67	λ	λ	NOUN
ejpam-141	195	68	)	)	PUNCT
ejpam-141	195	69	)	)	PUNCT
ejpam-141	195	70	≥	≥	NOUN
ejpam-141	195	71	1	1	NUM
ejpam-141	195	72	/	/	SYM
ejpam-141	195	73	m.	m.	NOUN
ejpam-141	196	1	so	so	SCONJ
ejpam-141	196	2	we	we	PRON
ejpam-141	196	3	get	get	VERB
ejpam-141	196	4	d	d	X
ejpam-141	196	5	(	(	PUNCT
ejpam-141	196	6	f	f	PROPN
ejpam-141	196	7	−1(x	−1(x	PROPN
ejpam-141	196	8	)	)	PUNCT
ejpam-141	196	9	,	,	PUNCT
ejpam-141	196	10	m	m	VERB
ejpam-141	196	11	−	−	PROPN
ejpam-141	196	12	f	f	PROPN
ejpam-141	196	13	−1(u	−1(u	NOUN
ejpam-141	196	14	)	)	PUNCT
ejpam-141	196	15	)	)	PUNCT
ejpam-141	197	1	=	=	SYM
ejpam-141	197	2	inf	inf	PROPN
ejpam-141	197	3	�	�	PROPN
ejpam-141	197	4	d(a	d(a	PROPN
ejpam-141	197	5	,	,	PUNCT
ejpam-141	197	6	b	b	NOUN
ejpam-141	197	7	)	)	PUNCT
ejpam-141	197	8	:	:	PUNCT
ejpam-141	197	9	a	a	DET
ejpam-141	197	10	∈	∈	PROPN
ejpam-141	197	11	f	f	X
ejpam-141	197	12	−1(x	−1(x	NOUN
ejpam-141	197	13	)	)	PUNCT
ejpam-141	197	14	,	,	PUNCT
ejpam-141	198	1	b	b	X
ejpam-141	198	2	∈	∈	PROPN
ejpam-141	198	3	m	m	VERB
ejpam-141	198	4	−	−	PROPN
ejpam-141	198	5	f	f	PROPN
ejpam-141	198	6	−1(u	−1(u	X
ejpam-141	198	7	)	)	PUNCT
ejpam-141	198	8	=	=	NOUN
ejpam-141	198	9	min	min	NOUN
ejpam-141	198	10	n	n	ADP
ejpam-141	198	11	1	1	NUM
ejpam-141	198	12	,	,	PUNCT
ejpam-141	198	13	inf	inf	PROPN
ejpam-141	198	14	�	�	PROPN
ejpam-141	198	15	dn	dn	PROPN
ejpam-141	198	16	,	,	PUNCT
ejpam-141	198	17	λ	λ	PROPN
ejpam-141	198	18	(	(	PUNCT
ejpam-141	198	19	f	f	PROPN
ejpam-141	198	20	−1	−1	NOUN
ejpam-141	198	21	n	n	CCONJ
ejpam-141	198	22	,	,	PUNCT
ejpam-141	198	23	λ	λ	PROPN
ejpam-141	198	24	(	(	PUNCT
ejpam-141	198	25	x	x	NOUN
ejpam-141	198	26	)	)	PUNCT
ejpam-141	198	27	,	,	PUNCT
ejpam-141	198	28	mn	mn	PROPN
ejpam-141	198	29	,	,	PUNCT
ejpam-141	198	30	λ−	λ−	PROPN
ejpam-141	198	31	f	f	PROPN
ejpam-141	198	32	−1	−1	NOUN
ejpam-141	198	33	n	n	PROPN
ejpam-141	198	34	,	,	PUNCT
ejpam-141	198	35	λ	λ	PROPN
ejpam-141	198	36	(	(	PUNCT
ejpam-141	198	37	un	un	PROPN
ejpam-141	198	38	,	,	PUNCT
ejpam-141	198	39	λ	λ	NOUN
ejpam-141	198	40	)	)	PUNCT
ejpam-141	198	41	)	)	PUNCT
ejpam-141	198	42	:	:	PUNCT
ejpam-141	199	1	λ	λ	X
ejpam-141	199	2	∈	∈	PROPN
ejpam-141	199	3	λn	λn	NOUN
ejpam-141	199	4	,	,	PUNCT
ejpam-141	199	5	n	n	PROPN
ejpam-141	199	6	∈	∈	PROPN
ejpam-141	199	7	n	n	PRON
ejpam-141	199	8	o	o	NOUN
ejpam-141	199	9	≥	≥	NUM
ejpam-141	199	10	1	1	NUM
ejpam-141	199	11	/	/	SYM
ejpam-141	199	12	m	m	PROPN
ejpam-141	199	13	>	>	X
ejpam-141	199	14	0	0	X
ejpam-141	199	15	.	.	PUNCT
ejpam-141	200	1	it	it	PRON
ejpam-141	200	2	implies	imply	VERB
ejpam-141	200	3	that	that	SCONJ
ejpam-141	200	4	f	f	PROPN
ejpam-141	200	5	is	be	AUX
ejpam-141	200	6	a	a	DET
ejpam-141	200	7	π	π	NOUN
ejpam-141	200	8	-	-	NOUN
ejpam-141	200	9	mapping	mapping	NOUN
ejpam-141	200	10	.	.	PUNCT
ejpam-141	201	1	(	(	PUNCT
ejpam-141	201	2	b	b	X
ejpam-141	201	3	)	)	PUNCT
ejpam-141	201	4	f	f	PROPN
ejpam-141	201	5	is	be	AUX
ejpam-141	201	6	an	an	DET
ejpam-141	201	7	s	s	NOUN
ejpam-141	201	8	-	-	NOUN
ejpam-141	201	9	mapping	mapping	NOUN
ejpam-141	201	10	.	.	PUNCT
ejpam-141	202	1	n.	n.	NOUN
ejpam-141	202	2	dung	dung	PROPN
ejpam-141	202	3	/	/	SYM
ejpam-141	202	4	eur	eur	PROPN
ejpam-141	202	5	.	.	PUNCT
ejpam-141	203	1	j.	j.	PROPN
ejpam-141	203	2	pure	pure	PROPN
ejpam-141	203	3	appl	appl	PROPN
ejpam-141	203	4	.	.	PROPN
ejpam-141	203	5	math	math	PROPN
ejpam-141	203	6	,	,	PUNCT
ejpam-141	203	7	2	2	NUM
ejpam-141	203	8	(	(	PUNCT
ejpam-141	203	9	2009	2009	NUM
ejpam-141	203	10	)	)	PUNCT
ejpam-141	203	11	,	,	PUNCT
ejpam-141	203	12	(	(	PUNCT
ejpam-141	203	13	182	182	NUM
ejpam-141	203	14	-	-	SYM
ejpam-141	203	15	194	194	NUM
ejpam-141	203	16	)	)	PUNCT
ejpam-141	203	17	191	191	NUM
ejpam-141	203	18	let	let	VERB
ejpam-141	203	19	x	x	X
ejpam-141	203	20	∈	∈	PROPN
ejpam-141	203	21	x	x	X
ejpam-141	203	22	.	.	PUNCT
ejpam-141	204	1	for	for	ADP
ejpam-141	204	2	each	each	DET
ejpam-141	204	3	n	n	PRON
ejpam-141	204	4	∈	∈	PROPN
ejpam-141	204	5	n	n	CCONJ
ejpam-141	204	6	,	,	PUNCT
ejpam-141	204	7	since	since	SCONJ
ejpam-141	204	8	pn	pn	PROPN
ejpam-141	204	9	is	be	AUX
ejpam-141	204	10	point	point	NOUN
ejpam-141	204	11	-	-	PUNCT
ejpam-141	204	12	countable	countable	ADJ
ejpam-141	204	13	,	,	PUNCT
ejpam-141	204	14	λn	λn	NOUN
ejpam-141	204	15	,	,	PUNCT
ejpam-141	204	16	x	x	SYM
ejpam-141	204	17	=	=	PRON
ejpam-141	204	18	{	{	PUNCT
ejpam-141	204	19	λ	λ	X
ejpam-141	204	20	∈	∈	NOUN
ejpam-141	204	21	λn	λn	NOUN
ejpam-141	204	22	:	:	PUNCT
ejpam-141	204	23	x	x	X
ejpam-141	204	24	∈	∈	PROPN
ejpam-141	204	25	pn	pn	PROPN
ejpam-141	204	26	,	,	PUNCT
ejpam-141	204	27	λ	λ	PROPN
ejpam-141	204	28	}	}	PUNCT
ejpam-141	204	29	is	be	AUX
ejpam-141	204	30	countable	countable	ADJ
ejpam-141	204	31	.	.	PUNCT
ejpam-141	205	1	since	since	SCONJ
ejpam-141	205	2	each	each	DET
ejpam-141	205	3	mn	mn	PROPN
ejpam-141	205	4	,	,	PUNCT
ejpam-141	205	5	λ	λ	PROPN
ejpam-141	205	6	is	be	AUX
ejpam-141	205	7	separable	separable	ADJ
ejpam-141	205	8	metric	metric	ADJ
ejpam-141	205	9	,	,	PUNCT
ejpam-141	205	10	f	f	PROPN
ejpam-141	205	11	−1	−1	NOUN
ejpam-141	205	12	n	n	CCONJ
ejpam-141	205	13	,	,	PUNCT
ejpam-141	205	14	λ	λ	PROPN
ejpam-141	205	15	(	(	PUNCT
ejpam-141	205	16	x	x	X
ejpam-141	205	17	)	)	PUNCT
ejpam-141	205	18	is	be	AUX
ejpam-141	205	19	separable	separable	ADJ
ejpam-141	205	20	.	.	PUNCT
ejpam-141	206	1	it	it	PRON
ejpam-141	206	2	implies	imply	VERB
ejpam-141	206	3	that	that	SCONJ
ejpam-141	206	4	f	f	PROPN
ejpam-141	206	5	−1(x	−1(x	NOUN
ejpam-141	206	6	)	)	PUNCT
ejpam-141	206	7	=	=	SYM
ejpam-141	206	8	⋃	⋃	NOUN
ejpam-141	206	9	{	{	PUNCT
ejpam-141	206	10	f	f	NOUN
ejpam-141	206	11	−1	−1	NOUN
ejpam-141	206	12	n	n	CCONJ
ejpam-141	206	13	,	,	PUNCT
ejpam-141	206	14	λ	λ	X
ejpam-141	206	15	(	(	PUNCT
ejpam-141	206	16	x	x	NOUN
ejpam-141	206	17	)	)	PUNCT
ejpam-141	206	18	:	:	PUNCT
ejpam-141	207	1	λ	λ	X
ejpam-141	207	2	∈	∈	PROPN
ejpam-141	207	3	λn	λn	NOUN
ejpam-141	207	4	,	,	PUNCT
ejpam-141	207	5	x	x	INTJ
ejpam-141	207	6	,	,	PUNCT
ejpam-141	207	7	n	n	CCONJ
ejpam-141	207	8	∈	∈	PROPN
ejpam-141	207	9	n	n	CCONJ
ejpam-141	207	10	}	}	PUNCT
ejpam-141	207	11	is	be	AUX
ejpam-141	207	12	separable	separable	ADJ
ejpam-141	207	13	.	.	PUNCT
ejpam-141	208	1	then	then	ADV
ejpam-141	208	2	f	f	PROPN
ejpam-141	208	3	is	be	AUX
ejpam-141	208	4	an	an	DET
ejpam-141	208	5	s	s	NOUN
ejpam-141	208	6	-	-	NOUN
ejpam-141	208	7	mapping	mapping	NOUN
ejpam-141	208	8	.	.	PUNCT
ejpam-141	209	1	(	(	PUNCT
ejpam-141	209	2	c	c	X
ejpam-141	209	3	)	)	PUNCT
ejpam-141	209	4	f	f	PROPN
ejpam-141	209	5	is	be	AUX
ejpam-141	209	6	1	1	NUM
ejpam-141	209	7	-	-	PUNCT
ejpam-141	209	8	sequence	sequence	NOUN
ejpam-141	209	9	-	-	PUNCT
ejpam-141	209	10	covering	covering	NOUN
ejpam-141	209	11	.	.	PUNCT
ejpam-141	210	1	for	for	ADP
ejpam-141	210	2	each	each	DET
ejpam-141	210	3	x	x	SYM
ejpam-141	210	4	∈	∈	PROPN
ejpam-141	210	5	x	x	X
ejpam-141	210	6	,	,	PUNCT
ejpam-141	210	7	since	since	SCONJ
ejpam-141	210	8	p	p	NOUN
ejpam-141	210	9	is	be	AUX
ejpam-141	210	10	a	a	DET
ejpam-141	210	11	σ	σ	NOUN
ejpam-141	210	12	-	-	PUNCT
ejpam-141	210	13	strong	strong	ADJ
ejpam-141	210	14	sn	sn	NOUN
ejpam-141	210	15	-	-	PUNCT
ejpam-141	210	16	network	network	NOUN
ejpam-141	210	17	of	of	ADP
ejpam-141	210	18	x	x	SYM
ejpam-141	210	19	,	,	PUNCT
ejpam-141	210	20	there	there	PRON
ejpam-141	210	21	exists	exist	VERB
ejpam-141	210	22	pn	pn	PROPN
ejpam-141	210	23	,	,	PUNCT
ejpam-141	210	24	λ	λ	PROPN
ejpam-141	210	25	∈	∈	PROPN
ejpam-141	210	26	p	p	NOUN
ejpam-141	210	27	such	such	ADJ
ejpam-141	210	28	that	that	PRON
ejpam-141	210	29	for	for	ADP
ejpam-141	210	30	each	each	DET
ejpam-141	210	31	convergent	convergent	NOUN
ejpam-141	210	32	sequence	sequence	NOUN
ejpam-141	210	33	s	s	AUX
ejpam-141	210	34	converging	converge	VERB
ejpam-141	210	35	to	to	ADP
ejpam-141	210	36	x	x	PUNCT
ejpam-141	210	37	in	in	ADP
ejpam-141	210	38	x	x	X
ejpam-141	210	39	,	,	PUNCT
ejpam-141	210	40	s	s	X
ejpam-141	210	41	is	be	AUX
ejpam-141	210	42	eventually	eventually	ADV
ejpam-141	210	43	in	in	ADP
ejpam-141	210	44	pn	pn	PROPN
ejpam-141	210	45	,	,	PUNCT
ejpam-141	210	46	λ	λ	PROPN
ejpam-141	210	47	.	.	PUNCT
ejpam-141	211	1	since	since	SCONJ
ejpam-141	211	2	qn	qn	PROPN
ejpam-141	211	3	,	,	PUNCT
ejpam-141	211	4	λ	λ	PROPN
ejpam-141	211	5	is	be	AUX
ejpam-141	211	6	a	a	DET
ejpam-141	211	7	countable	countable	ADJ
ejpam-141	211	8	σ	σ	NOUN
ejpam-141	211	9	-	-	PUNCT
ejpam-141	211	10	strong	strong	ADJ
ejpam-141	211	11	sn	sn	NOUN
ejpam-141	211	12	-	-	PUNCT
ejpam-141	211	13	network	network	NOUN
ejpam-141	211	14	of	of	ADP
ejpam-141	211	15	pn	pn	PROPN
ejpam-141	211	16	,	,	PUNCT
ejpam-141	211	17	λ	λ	PROPN
ejpam-141	211	18	,	,	PUNCT
ejpam-141	211	19	fn	fn	NOUN
ejpam-141	211	20	,	,	PUNCT
ejpam-141	211	21	λ	λ	PROPN
ejpam-141	211	22	is	be	AUX
ejpam-141	211	23	an	an	DET
ejpam-141	211	24	1	1	NUM
ejpam-141	211	25	-	-	PUNCT
ejpam-141	211	26	sequencecovering	sequencecovere	VERB
ejpam-141	211	27	mapping	mapping	NOUN
ejpam-141	211	28	as	as	ADP
ejpam-141	211	29	in	in	ADP
ejpam-141	211	30	the	the	DET
ejpam-141	211	31	proof	proof	NOUN
ejpam-141	211	32	(	(	PUNCT
ejpam-141	211	33	3	3	X
ejpam-141	211	34	)	)	PUNCT
ejpam-141	211	35	⇒	⇒	NOUN
ejpam-141	211	36	(	(	PUNCT
ejpam-141	211	37	1	1	NUM
ejpam-141	211	38	)	)	PUNCT
ejpam-141	211	39	of	of	ADP
ejpam-141	211	40	[	[	X
ejpam-141	211	41	16	16	NUM
ejpam-141	211	42	,	,	PUNCT
ejpam-141	211	43	theorem	theorem	VERB
ejpam-141	211	44	11	11	NUM
ejpam-141	211	45	]	]	PUNCT
ejpam-141	211	46	.	.	PUNCT
ejpam-141	212	1	then	then	ADV
ejpam-141	212	2	there	there	PRON
ejpam-141	212	3	exists	exist	VERB
ejpam-141	212	4	ax	ax	PROPN
ejpam-141	212	5	∈	∈	PROPN
ejpam-141	212	6	mn	mn	PROPN
ejpam-141	212	7	,	,	PUNCT
ejpam-141	212	8	λ	λ	PROPN
ejpam-141	212	9	such	such	ADJ
ejpam-141	212	10	that	that	SCONJ
ejpam-141	212	11	whenever	whenever	SCONJ
ejpam-141	212	12	hn	hn	PROPN
ejpam-141	212	13	,	,	PUNCT
ejpam-141	212	14	λ	λ	PROPN
ejpam-141	212	15	is	be	AUX
ejpam-141	212	16	a	a	DET
ejpam-141	212	17	convergent	convergent	NOUN
ejpam-141	212	18	sequence	sequence	NOUN
ejpam-141	212	19	converging	converge	VERB
ejpam-141	212	20	to	to	ADP
ejpam-141	212	21	x	x	PUNCT
ejpam-141	212	22	in	in	ADP
ejpam-141	212	23	pn	pn	PROPN
ejpam-141	212	24	,	,	PUNCT
ejpam-141	212	25	λ	λ	VERB
ejpam-141	212	26	there	there	PRON
ejpam-141	212	27	exists	exist	VERB
ejpam-141	212	28	a	a	DET
ejpam-141	212	29	convergent	convergent	NOUN
ejpam-141	212	30	sequence	sequence	NOUN
ejpam-141	212	31	kn	kn	PROPN
ejpam-141	212	32	,	,	PUNCT
ejpam-141	212	33	λ	λ	X
ejpam-141	212	34	converging	converge	VERB
ejpam-141	212	35	to	to	PART
ejpam-141	212	36	ax	ax	VERB
ejpam-141	212	37	in	in	ADP
ejpam-141	212	38	mn	mn	PROPN
ejpam-141	212	39	,	,	PUNCT
ejpam-141	212	40	λ	λ	PROPN
ejpam-141	212	41	with	with	ADP
ejpam-141	212	42	fn	fn	NOUN
ejpam-141	212	43	,	,	PUNCT
ejpam-141	212	44	λ(kn	λ(kn	PROPN
ejpam-141	212	45	,	,	PUNCT
ejpam-141	212	46	λ	λ	NOUN
ejpam-141	212	47	)	)	PUNCT
ejpam-141	212	48	=	=	SYM
ejpam-141	212	49	hn	hn	PROPN
ejpam-141	212	50	,	,	PUNCT
ejpam-141	212	51	λ	λ	PROPN
ejpam-141	212	52	.	.	PROPN
ejpam-141	212	53	put	put	VERB
ejpam-141	212	54	hn	hn	NOUN
ejpam-141	212	55	,	,	PUNCT
ejpam-141	212	56	λ	λ	X
ejpam-141	212	57	=	=	SYM
ejpam-141	212	58	s	s	PART
ejpam-141	212	59	∩	∩	ADJ
ejpam-141	212	60	pn	pn	PROPN
ejpam-141	212	61	,	,	PUNCT
ejpam-141	212	62	λ	λ	PROPN
ejpam-141	212	63	,	,	PUNCT
ejpam-141	212	64	then	then	ADV
ejpam-141	212	65	hn	hn	PROPN
ejpam-141	212	66	,	,	PUNCT
ejpam-141	212	67	λ	λ	PROPN
ejpam-141	212	68	is	be	AUX
ejpam-141	212	69	a	a	DET
ejpam-141	212	70	convergent	convergent	NOUN
ejpam-141	212	71	sequence	sequence	NOUN
ejpam-141	212	72	converging	converge	VERB
ejpam-141	212	73	to	to	ADP
ejpam-141	212	74	x	x	PUNCT
ejpam-141	212	75	in	in	ADP
ejpam-141	212	76	pn	pn	PROPN
ejpam-141	212	77	,	,	PUNCT
ejpam-141	212	78	λ	λ	PROPN
ejpam-141	212	79	.	.	PUNCT
ejpam-141	213	1	since	since	SCONJ
ejpam-141	213	2	s−	s−	PROPN
ejpam-141	213	3	pn	pn	PROPN
ejpam-141	213	4	,	,	PUNCT
ejpam-141	213	5	λ	λ	PROPN
ejpam-141	213	6	is	be	AUX
ejpam-141	213	7	finite	finite	ADJ
ejpam-141	213	8	,	,	PUNCT
ejpam-141	213	9	s−	s−	PROPN
ejpam-141	213	10	pn	pn	PROPN
ejpam-141	213	11	,	,	PUNCT
ejpam-141	213	12	λ	λ	PROPN
ejpam-141	213	13	=	=	SYM
ejpam-141	213	14	f	f	X
ejpam-141	213	15	(	(	PUNCT
ejpam-141	213	16	f	f	X
ejpam-141	213	17	)	)	PUNCT
ejpam-141	213	18	for	for	ADP
ejpam-141	213	19	some	some	DET
ejpam-141	213	20	finite	finite	NOUN
ejpam-141	213	21	subset	subset	NOUN
ejpam-141	213	22	f	f	PROPN
ejpam-141	213	23	of	of	ADP
ejpam-141	213	24	m	m	PROPN
ejpam-141	213	25	.	.	PUNCT
ejpam-141	214	1	put	put	VERB
ejpam-141	214	2	k	k	PROPN
ejpam-141	214	3	=	=	SYM
ejpam-141	214	4	kn	kn	PROPN
ejpam-141	214	5	,	,	PUNCT
ejpam-141	214	6	λ	λ	PROPN
ejpam-141	214	7	∪	∪	PROPN
ejpam-141	214	8	f	f	PROPN
ejpam-141	214	9	,	,	PUNCT
ejpam-141	214	10	then	then	ADV
ejpam-141	214	11	k	k	PROPN
ejpam-141	214	12	is	be	AUX
ejpam-141	214	13	a	a	DET
ejpam-141	214	14	convergent	convergent	NOUN
ejpam-141	214	15	sequence	sequence	NOUN
ejpam-141	214	16	converging	converge	VERB
ejpam-141	214	17	to	to	PART
ejpam-141	214	18	ax	ax	VERB
ejpam-141	214	19	in	in	ADP
ejpam-141	214	20	m	m	PROPN
ejpam-141	214	21	satisfying	satisfy	VERB
ejpam-141	214	22	f	f	X
ejpam-141	214	23	(	(	PUNCT
ejpam-141	214	24	k	k	NOUN
ejpam-141	214	25	)	)	PUNCT
ejpam-141	214	26	=	=	VERB
ejpam-141	215	1	s.	s.	PROPN
ejpam-141	215	2	it	it	PRON
ejpam-141	215	3	implies	imply	VERB
ejpam-141	215	4	that	that	SCONJ
ejpam-141	215	5	f	f	PROPN
ejpam-141	215	6	is	be	AUX
ejpam-141	215	7	1	1	NUM
ejpam-141	215	8	-	-	PUNCT
ejpam-141	215	9	sequence	sequence	NOUN
ejpam-141	215	10	-	-	PUNCT
ejpam-141	215	11	covering	covering	NOUN
ejpam-141	215	12	.	.	PUNCT
ejpam-141	216	1	corollary	corollary	ADJ
ejpam-141	216	2	2.10	2.10	NUM
ejpam-141	216	3	.	.	PUNCT
ejpam-141	217	1	the	the	DET
ejpam-141	217	2	following	follow	VERB
ejpam-141	217	3	are	be	AUX
ejpam-141	217	4	equivalent	equivalent	ADJ
ejpam-141	217	5	for	for	ADP
ejpam-141	217	6	a	a	DET
ejpam-141	217	7	space	space	NOUN
ejpam-141	217	8	x	x	X
ejpam-141	217	9	.	.	PUNCT
ejpam-141	218	1	1	1	X
ejpam-141	218	2	.	.	X
ejpam-141	218	3	x	x	PUNCT
ejpam-141	218	4	is	be	AUX
ejpam-141	218	5	an	an	DET
ejpam-141	218	6	1	1	NUM
ejpam-141	218	7	-	-	PUNCT
ejpam-141	218	8	sequence	sequence	NOUN
ejpam-141	218	9	-	-	PUNCT
ejpam-141	218	10	covering	covering	NOUN
ejpam-141	218	11	,	,	PUNCT
ejpam-141	218	12	quotient	quotient	NOUN
ejpam-141	218	13	π	π	PROPN
ejpam-141	218	14	-	-	PUNCT
ejpam-141	218	15	s	s	NOUN
ejpam-141	218	16	-	-	PUNCT
ejpam-141	218	17	image	image	NOUN
ejpam-141	218	18	of	of	ADP
ejpam-141	218	19	a	a	DET
ejpam-141	218	20	locally	locally	ADV
ejpam-141	218	21	separable	separable	ADJ
ejpam-141	218	22	metric	metric	ADJ
ejpam-141	218	23	space	space	NOUN
ejpam-141	218	24	.	.	PUNCT
ejpam-141	219	1	2	2	X
ejpam-141	219	2	.	.	X
ejpam-141	219	3	x	x	X
ejpam-141	219	4	is	be	AUX
ejpam-141	219	5	an	an	DET
ejpam-141	219	6	1	1	NUM
ejpam-141	219	7	-	-	PUNCT
ejpam-141	219	8	sequentially	sequentially	ADV
ejpam-141	219	9	-	-	PUNCT
ejpam-141	219	10	quotient	quotient	NOUN
ejpam-141	219	11	,	,	PUNCT
ejpam-141	219	12	quotient	quotient	VERB
ejpam-141	219	13	π	π	PROPN
ejpam-141	219	14	-	-	PUNCT
ejpam-141	219	15	s	s	NOUN
ejpam-141	219	16	-	-	PUNCT
ejpam-141	219	17	image	image	NOUN
ejpam-141	219	18	of	of	ADP
ejpam-141	219	19	a	a	DET
ejpam-141	219	20	locally	locally	ADV
ejpam-141	219	21	separable	separable	ADJ
ejpam-141	219	22	metric	metric	ADJ
ejpam-141	219	23	space	space	NOUN
ejpam-141	219	24	.	.	PUNCT
ejpam-141	220	1	3	3	X
ejpam-141	220	2	.	.	X
ejpam-141	220	3	x	x	PUNCT
ejpam-141	220	4	has	have	VERB
ejpam-141	220	5	a	a	DET
ejpam-141	220	6	point	point	NOUN
ejpam-141	220	7	-	-	PUNCT
ejpam-141	220	8	countable	countable	ADJ
ejpam-141	220	9	sn	sn	NOUN
ejpam-141	220	10	-	-	PUNCT
ejpam-141	220	11	weak	weak	ADJ
ejpam-141	220	12	-	-	PUNCT
ejpam-141	220	13	development	development	NOUN
ejpam-141	220	14	consisting	consisting	NOUN
ejpam-141	220	15	of	of	ADP
ejpam-141	220	16	sn	sn	NOUN
ejpam-141	220	17	-	-	PUNCT
ejpam-141	220	18	second	second	ADJ
ejpam-141	220	19	countable	countable	ADJ
ejpam-141	220	20	spaces	space	NOUN
ejpam-141	220	21	.	.	PUNCT
ejpam-141	221	1	4	4	X
ejpam-141	221	2	.	.	X
ejpam-141	221	3	x	x	PUNCT
ejpam-141	221	4	has	have	VERB
ejpam-141	221	5	a	a	DET
ejpam-141	221	6	point	point	NOUN
ejpam-141	221	7	-	-	PUNCT
ejpam-141	221	8	countable	countable	ADJ
ejpam-141	221	9	sn	sn	NOUN
ejpam-141	221	10	-	-	PUNCT
ejpam-141	221	11	weak	weak	ADJ
ejpam-141	221	12	-	-	PUNCT
ejpam-141	221	13	development	development	NOUN
ejpam-141	221	14	consisting	consisting	NOUN
ejpam-141	221	15	of	of	ADP
ejpam-141	221	16	ℵ0	ℵ0	NOUN
ejpam-141	221	17	-	-	NOUN
ejpam-141	221	18	spaces	space	NOUN
ejpam-141	221	19	.	.	PUNCT
ejpam-141	222	1	5	5	X
ejpam-141	222	2	.	.	X
ejpam-141	222	3	x	x	PUNCT
ejpam-141	222	4	has	have	VERB
ejpam-141	222	5	a	a	DET
ejpam-141	222	6	point	point	NOUN
ejpam-141	222	7	-	-	PUNCT
ejpam-141	222	8	countable	countable	ADJ
ejpam-141	222	9	sn	sn	NOUN
ejpam-141	222	10	-	-	PUNCT
ejpam-141	222	11	weak	weak	ADJ
ejpam-141	222	12	-	-	PUNCT
ejpam-141	222	13	development	development	NOUN
ejpam-141	222	14	consisting	consisting	NOUN
ejpam-141	222	15	of	of	ADP
ejpam-141	222	16	cosmic	cosmic	ADJ
ejpam-141	222	17	spaces	space	NOUN
ejpam-141	222	18	.	.	PUNCT
ejpam-141	223	1	proof	proof	NOUN
ejpam-141	223	2	.	.	PUNCT
ejpam-141	224	1	(	(	PUNCT
ejpam-141	224	2	1)⇒	1)⇒	NUM
ejpam-141	224	3	(	(	PUNCT
ejpam-141	224	4	2	2	NUM
ejpam-141	224	5	)	)	PUNCT
ejpam-141	224	6	.	.	PUNCT
ejpam-141	225	1	it	it	PRON
ejpam-141	225	2	is	be	AUX
ejpam-141	225	3	obvious	obvious	ADJ
ejpam-141	225	4	.	.	PUNCT
ejpam-141	226	1	n.	n.	NOUN
ejpam-141	226	2	dung	dung	PROPN
ejpam-141	226	3	/	/	SYM
ejpam-141	226	4	eur	eur	PROPN
ejpam-141	226	5	.	.	PUNCT
ejpam-141	227	1	j.	j.	PROPN
ejpam-141	227	2	pure	pure	PROPN
ejpam-141	227	3	appl	appl	PROPN
ejpam-141	227	4	.	.	PROPN
ejpam-141	227	5	math	math	PROPN
ejpam-141	227	6	,	,	PUNCT
ejpam-141	227	7	2	2	NUM
ejpam-141	227	8	(	(	PUNCT
ejpam-141	227	9	2009	2009	NUM
ejpam-141	227	10	)	)	PUNCT
ejpam-141	227	11	,	,	PUNCT
ejpam-141	227	12	(	(	PUNCT
ejpam-141	227	13	182	182	NUM
ejpam-141	227	14	-	-	SYM
ejpam-141	227	15	194	194	NUM
ejpam-141	227	16	)	)	PUNCT
ejpam-141	227	17	192	192	NUM
ejpam-141	227	18	(	(	PUNCT
ejpam-141	227	19	2)⇒	2)⇒	NUM
ejpam-141	227	20	(	(	PUNCT
ejpam-141	227	21	3	3	NUM
ejpam-141	227	22	)	)	PUNCT
ejpam-141	227	23	.	.	PUNCT
ejpam-141	228	1	by	by	ADP
ejpam-141	228	2	theorem	theorem	NOUN
ejpam-141	228	3	2.9	2.9	NUM
ejpam-141	228	4	,	,	PUNCT
ejpam-141	228	5	x	x	PUNCT
ejpam-141	228	6	has	have	VERB
ejpam-141	228	7	a	a	DET
ejpam-141	228	8	point	point	NOUN
ejpam-141	228	9	-	-	PUNCT
ejpam-141	228	10	countable	countable	ADJ
ejpam-141	228	11	σ	σ	NOUN
ejpam-141	228	12	-	-	PUNCT
ejpam-141	228	13	strong	strong	ADJ
ejpam-141	228	14	sn	sn	NOUN
ejpam-141	228	15	-	-	PUNCT
ejpam-141	228	16	network	network	NOUN
ejpam-141	228	17	⋃	⋃	PUNCT
ejpam-141	228	18	{	{	PUNCT
ejpam-141	228	19	pn	pn	NOUN
ejpam-141	228	20	:	:	PUNCT
ejpam-141	228	21	n	n	CCONJ
ejpam-141	228	22	∈	∈	PROPN
ejpam-141	228	23	n	n	CCONJ
ejpam-141	228	24	}	}	PUNCT
ejpam-141	228	25	consisting	consist	VERB
ejpam-141	228	26	of	of	ADP
ejpam-141	228	27	sn	sn	NOUN
ejpam-141	228	28	-	-	PUNCT
ejpam-141	228	29	second	second	ADJ
ejpam-141	228	30	countable	countable	ADJ
ejpam-141	228	31	spaces	space	NOUN
ejpam-141	228	32	.	.	PUNCT
ejpam-141	229	1	we	we	PRON
ejpam-141	229	2	shall	shall	AUX
ejpam-141	229	3	prove	prove	VERB
ejpam-141	229	4	that	that	SCONJ
ejpam-141	229	5	,	,	PUNCT
ejpam-141	229	6	for	for	ADP
ejpam-141	229	7	every	every	DET
ejpam-141	229	8	x	x	SYM
ejpam-141	229	9	∈	∈	PROPN
ejpam-141	229	10	x	x	X
ejpam-141	229	11	,	,	PUNCT
ejpam-141	229	12	{	{	PUNCT
ejpam-141	229	13	st(x	st(x	X
ejpam-141	229	14	,	,	PUNCT
ejpam-141	229	15	pn	pn	PROPN
ejpam-141	229	16	)	)	PUNCT
ejpam-141	229	17	:	:	PUNCT
ejpam-141	229	18	n	n	CCONJ
ejpam-141	229	19	∈	∈	PROPN
ejpam-141	229	20	n	n	CCONJ
ejpam-141	229	21	}	}	PUNCT
ejpam-141	229	22	is	be	AUX
ejpam-141	229	23	a	a	DET
ejpam-141	229	24	weak	weak	ADJ
ejpam-141	229	25	base	base	NOUN
ejpam-141	229	26	at	at	ADP
ejpam-141	229	27	x	x	PUNCT
ejpam-141	229	28	in	in	ADP
ejpam-141	229	29	x	x	PUNCT
ejpam-141	229	30	by	by	ADP
ejpam-141	229	31	the	the	DET
ejpam-141	229	32	following	follow	VERB
ejpam-141	229	33	facts	fact	NOUN
ejpam-141	229	34	(	(	PUNCT
ejpam-141	229	35	a	a	X
ejpam-141	229	36	)	)	PUNCT
ejpam-141	229	37	,	,	PUNCT
ejpam-141	229	38	(	(	PUNCT
ejpam-141	229	39	b	b	NOUN
ejpam-141	229	40	)	)	PUNCT
ejpam-141	229	41	,	,	PUNCT
ejpam-141	229	42	and	and	CCONJ
ejpam-141	229	43	(	(	PUNCT
ejpam-141	229	44	c	c	NOUN
ejpam-141	229	45	)	)	PUNCT
ejpam-141	229	46	.	.	PUNCT
ejpam-141	230	1	(	(	PUNCT
ejpam-141	230	2	a	a	X
ejpam-141	230	3	)	)	PUNCT
ejpam-141	230	4	{	{	PUNCT
ejpam-141	230	5	st(x	st(x	PROPN
ejpam-141	230	6	,	,	PUNCT
ejpam-141	230	7	pn	pn	PROPN
ejpam-141	230	8	)	)	PUNCT
ejpam-141	230	9	:	:	PUNCT
ejpam-141	231	1	n	n	CCONJ
ejpam-141	231	2	∈	∈	PROPN
ejpam-141	231	3	n	n	CCONJ
ejpam-141	231	4	}	}	PUNCT
ejpam-141	231	5	is	be	AUX
ejpam-141	231	6	a	a	DET
ejpam-141	231	7	network	network	NOUN
ejpam-141	231	8	at	at	ADP
ejpam-141	231	9	x	x	X
ejpam-141	231	10	in	in	ADP
ejpam-141	231	11	x	x	X
ejpam-141	231	12	.	.	PUNCT
ejpam-141	232	1	it	it	PRON
ejpam-141	232	2	follows	follow	VERB
ejpam-141	232	3	from	from	ADP
ejpam-141	232	4	the	the	DET
ejpam-141	232	5	fact	fact	NOUN
ejpam-141	232	6	that	that	SCONJ
ejpam-141	232	7	⋃	⋃	ADV
ejpam-141	232	8	{	{	PUNCT
ejpam-141	232	9	pn	pn	NOUN
ejpam-141	232	10	:	:	PUNCT
ejpam-141	232	11	n	n	CCONJ
ejpam-141	232	12	∈	∈	PROPN
ejpam-141	232	13	n	n	CCONJ
ejpam-141	232	14	}	}	PUNCT
ejpam-141	232	15	is	be	AUX
ejpam-141	232	16	a	a	DET
ejpam-141	232	17	σ	σ	PROPN
ejpam-141	232	18	-	-	PUNCT
ejpam-141	232	19	strong	strong	ADJ
ejpam-141	232	20	network	network	NOUN
ejpam-141	232	21	of	of	ADP
ejpam-141	232	22	x	x	X
ejpam-141	232	23	.	.	PUNCT
ejpam-141	233	1	(	(	PUNCT
ejpam-141	233	2	b	b	X
ejpam-141	233	3	)	)	PUNCT
ejpam-141	233	4	if	if	SCONJ
ejpam-141	233	5	st(x	st(x	PROPN
ejpam-141	233	6	,	,	PUNCT
ejpam-141	233	7	pk	pk	NOUN
ejpam-141	233	8	)	)	PUNCT
ejpam-141	233	9	,	,	PUNCT
ejpam-141	233	10	st(x	st(x	X
ejpam-141	233	11	,	,	PUNCT
ejpam-141	233	12	pl	pl	NOUN
ejpam-141	233	13	)	)	PUNCT
ejpam-141	233	14	∈	∈	PROPN
ejpam-141	233	15	{	{	PUNCT
ejpam-141	233	16	st(x	st(x	X
ejpam-141	233	17	,	,	PUNCT
ejpam-141	233	18	pn	pn	PROPN
ejpam-141	233	19	)	)	PUNCT
ejpam-141	233	20	:	:	PUNCT
ejpam-141	233	21	n	n	X
ejpam-141	233	22	∈	∈	PROPN
ejpam-141	233	23	n	n	CCONJ
ejpam-141	233	24	}	}	PUNCT
ejpam-141	233	25	,	,	PUNCT
ejpam-141	233	26	then	then	ADV
ejpam-141	233	27	there	there	PRON
ejpam-141	233	28	exists	exist	VERB
ejpam-141	233	29	m	m	VERB
ejpam-141	233	30	∈	∈	PROPN
ejpam-141	233	31	n	n	PRON
ejpam-141	233	32	such	such	ADJ
ejpam-141	233	33	that	that	PRON
ejpam-141	233	34	st(x	st(x	PROPN
ejpam-141	233	35	,	,	PUNCT
ejpam-141	233	36	pm	pm	NOUN
ejpam-141	233	37	)	)	PUNCT
ejpam-141	233	38	⊂	⊂	PROPN
ejpam-141	233	39	st(x	st(x	PROPN
ejpam-141	233	40	,	,	PUNCT
ejpam-141	233	41	pk)∩	pk)∩	PROPN
ejpam-141	233	42	st(x	st(x	X
ejpam-141	233	43	,	,	PUNCT
ejpam-141	233	44	pl	pl	PROPN
ejpam-141	233	45	)	)	PUNCT
ejpam-141	233	46	.	.	PUNCT
ejpam-141	234	1	it	it	PRON
ejpam-141	234	2	is	be	AUX
ejpam-141	234	3	clear	clear	ADJ
ejpam-141	234	4	by	by	ADP
ejpam-141	234	5	choosing	choose	VERB
ejpam-141	234	6	m	m	PROPN
ejpam-141	234	7	=	=	NOUN
ejpam-141	234	8	max{k	max{k	NOUN
ejpam-141	234	9	,	,	PUNCT
ejpam-141	234	10	l	l	NOUN
ejpam-141	234	11	}	}	PUNCT
ejpam-141	234	12	.	.	PUNCT
ejpam-141	235	1	(	(	PUNCT
ejpam-141	235	2	c	c	X
ejpam-141	235	3	)	)	PUNCT
ejpam-141	235	4	since	since	SCONJ
ejpam-141	235	5	x	x	PRON
ejpam-141	235	6	is	be	AUX
ejpam-141	235	7	a	a	DET
ejpam-141	235	8	quotient	quotient	NOUN
ejpam-141	235	9	image	image	NOUN
ejpam-141	235	10	of	of	ADP
ejpam-141	235	11	a	a	DET
ejpam-141	235	12	metric	metric	ADJ
ejpam-141	235	13	space	space	NOUN
ejpam-141	235	14	,	,	PUNCT
ejpam-141	235	15	x	x	X
ejpam-141	235	16	is	be	AUX
ejpam-141	235	17	sequential	sequential	ADJ
ejpam-141	235	18	.	.	PUNCT
ejpam-141	236	1	it	it	PRON
ejpam-141	236	2	is	be	AUX
ejpam-141	236	3	easy	easy	ADJ
ejpam-141	236	4	to	to	PART
ejpam-141	236	5	see	see	VERB
ejpam-141	236	6	that	that	SCONJ
ejpam-141	236	7	each	each	DET
ejpam-141	236	8	st(x	st(x	PROPN
ejpam-141	236	9	,	,	PUNCT
ejpam-141	236	10	pn	pn	PROPN
ejpam-141	236	11	)	)	PUNCT
ejpam-141	236	12	is	be	AUX
ejpam-141	236	13	a	a	DET
ejpam-141	236	14	sequential	sequential	ADJ
ejpam-141	236	15	neighborhood	neighborhood	NOUN
ejpam-141	236	16	of	of	ADP
ejpam-141	236	17	x	x	PUNCT
ejpam-141	236	18	in	in	ADP
ejpam-141	236	19	x	x	PROPN
ejpam-141	236	20	.	.	PUNCT
ejpam-141	237	1	note	note	VERB
ejpam-141	237	2	that	that	SCONJ
ejpam-141	237	3	{	{	PUNCT
ejpam-141	237	4	st(x	st(x	PROPN
ejpam-141	237	5	,	,	PUNCT
ejpam-141	237	6	pn	pn	PROPN
ejpam-141	237	7	)	)	PUNCT
ejpam-141	237	8	:	:	PUNCT
ejpam-141	237	9	n	n	CCONJ
ejpam-141	237	10	∈	∈	PROPN
ejpam-141	237	11	n	n	CCONJ
ejpam-141	237	12	}	}	PUNCT
ejpam-141	237	13	is	be	AUX
ejpam-141	237	14	a	a	DET
ejpam-141	237	15	network	network	NOUN
ejpam-141	237	16	at	at	ADP
ejpam-141	237	17	x	x	X
ejpam-141	237	18	in	in	ADP
ejpam-141	237	19	x	x	X
ejpam-141	237	20	.	.	PUNCT
ejpam-141	238	1	then	then	ADV
ejpam-141	238	2	{	{	PUNCT
ejpam-141	238	3	st(x	st(x	PROPN
ejpam-141	238	4	,	,	PUNCT
ejpam-141	238	5	pn	pn	PROPN
ejpam-141	238	6	)	)	PUNCT
ejpam-141	238	7	:	:	PUNCT
ejpam-141	238	8	n	n	CCONJ
ejpam-141	238	9	∈	∈	PROPN
ejpam-141	238	10	n	n	CCONJ
ejpam-141	238	11	}	}	PUNCT
ejpam-141	238	12	is	be	AUX
ejpam-141	238	13	an	an	DET
ejpam-141	238	14	sn	sn	NOUN
ejpam-141	238	15	-	-	PUNCT
ejpam-141	238	16	network	network	NOUN
ejpam-141	238	17	at	at	ADP
ejpam-141	238	18	x	x	X
ejpam-141	238	19	in	in	ADP
ejpam-141	238	20	x	x	X
ejpam-141	238	21	.	.	PUNCT
ejpam-141	239	1	it	it	PRON
ejpam-141	239	2	implies	imply	VERB
ejpam-141	239	3	that	that	SCONJ
ejpam-141	239	4	{	{	PUNCT
ejpam-141	239	5	st(x	st(x	X
ejpam-141	239	6	,	,	PUNCT
ejpam-141	239	7	pn	pn	PROPN
ejpam-141	239	8	)	)	PUNCT
ejpam-141	239	9	:	:	PUNCT
ejpam-141	239	10	n	n	CCONJ
ejpam-141	239	11	∈	∈	PROPN
ejpam-141	239	12	n	n	CCONJ
ejpam-141	239	13	}	}	PUNCT
ejpam-141	239	14	is	be	AUX
ejpam-141	239	15	a	a	DET
ejpam-141	239	16	weak	weak	ADJ
ejpam-141	239	17	base	base	NOUN
ejpam-141	239	18	at	at	ADP
ejpam-141	239	19	x	x	X
ejpam-141	239	20	by	by	ADP
ejpam-141	239	21	remark	remark	NOUN
ejpam-141	239	22	2.5	2.5	NUM
ejpam-141	239	23	.	.	PUNCT
ejpam-141	240	1	(	(	PUNCT
ejpam-141	240	2	3)⇒	3)⇒	NUM
ejpam-141	240	3	(	(	PUNCT
ejpam-141	240	4	4)⇒	4)⇒	NUM
ejpam-141	240	5	(	(	PUNCT
ejpam-141	240	6	5	5	NUM
ejpam-141	240	7	)	)	PUNCT
ejpam-141	240	8	.	.	PUNCT
ejpam-141	241	1	it	it	PRON
ejpam-141	241	2	is	be	AUX
ejpam-141	241	3	obvious	obvious	ADJ
ejpam-141	241	4	.	.	PUNCT
ejpam-141	242	1	(	(	PUNCT
ejpam-141	242	2	5	5	X
ejpam-141	242	3	)	)	PUNCT
ejpam-141	242	4	⇒	⇒	NOUN
ejpam-141	242	5	(	(	PUNCT
ejpam-141	242	6	1	1	NUM
ejpam-141	242	7	)	)	PUNCT
ejpam-141	242	8	.	.	PUNCT
ejpam-141	243	1	let	let	VERB
ejpam-141	243	2	p	p	NOUN
ejpam-141	243	3	=	=	VERB
ejpam-141	243	4	⋃	⋃	PROPN
ejpam-141	243	5	{	{	PUNCT
ejpam-141	243	6	pn	pn	NOUN
ejpam-141	243	7	:	:	PUNCT
ejpam-141	243	8	n	n	CCONJ
ejpam-141	243	9	∈	∈	PROPN
ejpam-141	243	10	n	n	CCONJ
ejpam-141	243	11	}	}	PUNCT
ejpam-141	243	12	be	be	AUX
ejpam-141	243	13	a	a	DET
ejpam-141	243	14	point	point	NOUN
ejpam-141	243	15	-	-	PUNCT
ejpam-141	243	16	countable	countable	ADJ
ejpam-141	243	17	sn	sn	NOUN
ejpam-141	243	18	-	-	PUNCT
ejpam-141	243	19	weak	weak	ADJ
ejpam-141	243	20	-	-	PUNCT
ejpam-141	243	21	development	development	NOUN
ejpam-141	243	22	of	of	ADP
ejpam-141	243	23	x	x	SYM
ejpam-141	243	24	consisting	consist	VERB
ejpam-141	243	25	of	of	ADP
ejpam-141	243	26	cosmic	cosmic	ADJ
ejpam-141	243	27	spaces	space	NOUN
ejpam-141	243	28	.	.	PUNCT
ejpam-141	244	1	by	by	ADP
ejpam-141	244	2	theorem	theorem	NOUN
ejpam-141	244	3	2.9	2.9	NUM
ejpam-141	244	4	,	,	PUNCT
ejpam-141	244	5	x	x	X
ejpam-141	244	6	is	be	AUX
ejpam-141	244	7	an	an	DET
ejpam-141	244	8	1	1	NUM
ejpam-141	244	9	-	-	PUNCT
ejpam-141	244	10	sequence	sequence	NOUN
ejpam-141	244	11	-	-	PUNCT
ejpam-141	244	12	covering	cover	VERB
ejpam-141	244	13	πs	πs	NOUN
ejpam-141	244	14	-	-	PUNCT
ejpam-141	244	15	image	image	NOUN
ejpam-141	244	16	of	of	ADP
ejpam-141	244	17	a	a	DET
ejpam-141	244	18	locally	locally	ADV
ejpam-141	244	19	separable	separable	ADJ
ejpam-141	244	20	metric	metric	ADJ
ejpam-141	244	21	space	space	NOUN
ejpam-141	244	22	under	under	ADP
ejpam-141	244	23	the	the	DET
ejpam-141	244	24	mapping	mapping	NOUN
ejpam-141	244	25	f	f	NOUN
ejpam-141	244	26	.	.	PUNCT
ejpam-141	245	1	since	since	SCONJ
ejpam-141	245	2	x	x	PRON
ejpam-141	245	3	has	have	VERB
ejpam-141	245	4	a	a	DET
ejpam-141	245	5	weak	weak	ADJ
ejpam-141	245	6	-	-	PUNCT
ejpam-141	245	7	development	development	NOUN
ejpam-141	245	8	,	,	PUNCT
ejpam-141	245	9	x	x	X
ejpam-141	245	10	is	be	AUX
ejpam-141	245	11	sequential	sequential	ADJ
ejpam-141	245	12	.	.	PUNCT
ejpam-141	246	1	in	in	ADP
ejpam-141	246	2	fact	fact	NOUN
ejpam-141	246	3	,	,	PUNCT
ejpam-141	246	4	let	let	VERB
ejpam-141	246	5	a	a	PRON
ejpam-141	246	6	be	be	AUX
ejpam-141	246	7	a	a	DET
ejpam-141	246	8	sequentially	sequentially	ADV
ejpam-141	246	9	open	open	ADJ
ejpam-141	246	10	subset	subset	NOUN
ejpam-141	246	11	of	of	ADP
ejpam-141	246	12	x	x	PUNCT
ejpam-141	246	13	and	and	CCONJ
ejpam-141	246	14	x	x	SYM
ejpam-141	246	15	∈	∈	NOUN
ejpam-141	246	16	a.	a.	NOUN
ejpam-141	246	17	for	for	ADP
ejpam-141	246	18	each	each	DET
ejpam-141	246	19	n	n	PRON
ejpam-141	246	20	∈	∈	PROPN
ejpam-141	246	21	n	n	CCONJ
ejpam-141	246	22	,	,	PUNCT
ejpam-141	246	23	if	if	SCONJ
ejpam-141	246	24	st(x	st(x	PROPN
ejpam-141	246	25	,	,	PUNCT
ejpam-141	246	26	pn	pn	PROPN
ejpam-141	246	27	)	)	PUNCT
ejpam-141	246	28	6⊂	6⊂	NUM
ejpam-141	246	29	a	a	PRON
ejpam-141	246	30	,	,	PUNCT
ejpam-141	246	31	then	then	ADV
ejpam-141	246	32	there	there	PRON
ejpam-141	246	33	exists	exist	VERB
ejpam-141	246	34	xn	xn	PROPN
ejpam-141	246	35	∈	∈	PROPN
ejpam-141	246	36	st(x	st(x	X
ejpam-141	246	37	,	,	PUNCT
ejpam-141	246	38	pn	pn	PROPN
ejpam-141	246	39	)	)	PUNCT
ejpam-141	246	40	−	−	NOUN
ejpam-141	246	41	a.	a.	NOUN
ejpam-141	247	1	we	we	PRON
ejpam-141	247	2	get	get	VERB
ejpam-141	247	3	that	that	PRON
ejpam-141	247	4	{	{	PUNCT
ejpam-141	247	5	xn	xn	NOUN
ejpam-141	247	6	:	:	PUNCT
ejpam-141	248	1	n	n	CCONJ
ejpam-141	248	2	∈	∈	PROPN
ejpam-141	248	3	n	n	CCONJ
ejpam-141	248	4	}	}	PUNCT
ejpam-141	248	5	is	be	AUX
ejpam-141	248	6	a	a	DET
ejpam-141	248	7	sequence	sequence	NOUN
ejpam-141	248	8	converging	converge	VERB
ejpam-141	248	9	to	to	ADP
ejpam-141	248	10	x	x	PROPN
ejpam-141	248	11	.	.	PUNCT
ejpam-141	249	1	then	then	ADV
ejpam-141	249	2	{	{	PUNCT
ejpam-141	249	3	xn	xn	PROPN
ejpam-141	249	4	:	:	PUNCT
ejpam-141	249	5	n	n	CCONJ
ejpam-141	249	6	∈	∈	PROPN
ejpam-141	249	7	n	n	CCONJ
ejpam-141	249	8	}	}	PUNCT
ejpam-141	249	9	∪	∪	X
ejpam-141	249	10	{	{	PUNCT
ejpam-141	249	11	x	x	NOUN
ejpam-141	249	12	}	}	PUNCT
ejpam-141	249	13	is	be	AUX
ejpam-141	249	14	eventually	eventually	ADV
ejpam-141	249	15	in	in	ADP
ejpam-141	249	16	a.	a.	NOUN
ejpam-141	249	17	it	it	PRON
ejpam-141	249	18	is	be	AUX
ejpam-141	249	19	a	a	DET
ejpam-141	249	20	contradiction	contradiction	NOUN
ejpam-141	249	21	.	.	PUNCT
ejpam-141	250	1	therefore	therefore	ADV
ejpam-141	250	2	,	,	PUNCT
ejpam-141	250	3	st(x	st(x	PUNCT
ejpam-141	250	4	,	,	PUNCT
ejpam-141	250	5	pn)⊂	pn)⊂	PROPN
ejpam-141	250	6	a	a	PRON
ejpam-141	250	7	for	for	ADP
ejpam-141	250	8	some	some	DET
ejpam-141	250	9	n	n	PRON
ejpam-141	250	10	∈	∈	NOUN
ejpam-141	250	11	n.	n.	NOUN
ejpam-141	250	12	hence	hence	ADV
ejpam-141	250	13	a	a	PRON
ejpam-141	250	14	is	be	AUX
ejpam-141	250	15	open	open	ADJ
ejpam-141	250	16	,	,	PUNCT
ejpam-141	250	17	i.e.	i.e.	X
ejpam-141	250	18	,	,	PUNCT
ejpam-141	250	19	x	x	X
ejpam-141	250	20	is	be	AUX
ejpam-141	250	21	sequential	sequential	ADJ
ejpam-141	250	22	.	.	PUNCT
ejpam-141	251	1	since	since	SCONJ
ejpam-141	251	2	x	x	PRON
ejpam-141	251	3	is	be	AUX
ejpam-141	251	4	sequential	sequential	ADJ
ejpam-141	251	5	,	,	PUNCT
ejpam-141	251	6	f	f	PROPN
ejpam-141	251	7	is	be	AUX
ejpam-141	251	8	quotient	quotient	NOUN
ejpam-141	251	9	by	by	ADP
ejpam-141	251	10	[	[	X
ejpam-141	251	11	14	14	NUM
ejpam-141	251	12	,	,	PUNCT
ejpam-141	251	13	lemma	lemma	PROPN
ejpam-141	251	14	3.5	3.5	NUM
ejpam-141	251	15	]	]	PUNCT
ejpam-141	251	16	.	.	PUNCT
ejpam-141	252	1	it	it	PRON
ejpam-141	252	2	implies	imply	VERB
ejpam-141	252	3	that	that	SCONJ
ejpam-141	252	4	x	x	PRON
ejpam-141	252	5	is	be	AUX
ejpam-141	252	6	an	an	DET
ejpam-141	252	7	1	1	NUM
ejpam-141	252	8	-	-	PUNCT
ejpam-141	252	9	sequence	sequence	NOUN
ejpam-141	252	10	-	-	PUNCT
ejpam-141	252	11	covering	covering	NOUN
ejpam-141	252	12	,	,	PUNCT
ejpam-141	252	13	quotient	quotient	NOUN
ejpam-141	252	14	π	π	PROPN
ejpam-141	252	15	-	-	PUNCT
ejpam-141	252	16	s	s	NOUN
ejpam-141	252	17	-	-	PUNCT
ejpam-141	252	18	image	image	NOUN
ejpam-141	252	19	of	of	ADP
ejpam-141	252	20	a	a	DET
ejpam-141	252	21	locally	locally	ADV
ejpam-141	252	22	separable	separable	ADJ
ejpam-141	252	23	metric	metric	ADJ
ejpam-141	252	24	space	space	NOUN
ejpam-141	252	25	.	.	PUNCT
ejpam-141	253	1	remark	remark	PROPN
ejpam-141	253	2	2.11	2.11	NUM
ejpam-141	253	3	.	.	PUNCT
ejpam-141	254	1	corollary	corollary	ADJ
ejpam-141	254	2	2.10	2.10	NUM
ejpam-141	254	3	is	be	AUX
ejpam-141	254	4	a	a	DET
ejpam-141	254	5	partly	partly	ADV
ejpam-141	254	6	answer	answer	NOUN
ejpam-141	254	7	of	of	ADP
ejpam-141	254	8	question	question	NOUN
ejpam-141	254	9	1.1	1.1	NUM
ejpam-141	254	10	.	.	PUNCT
ejpam-141	255	1	references	reference	NOUN
ejpam-141	255	2	193	193	NUM
ejpam-141	255	3	references	reference	NOUN
ejpam-141	255	4	[	[	X
ejpam-141	255	5	1	1	NUM
ejpam-141	255	6	]	]	PUNCT
ejpam-141	255	7	a.	a.	NOUN
ejpam-141	255	8	v.	v.	ADP
ejpam-141	255	9	arhangel’skii	arhangel’skii	ADJ
ejpam-141	255	10	,	,	PUNCT
ejpam-141	255	11	mappings	mapping	NOUN
ejpam-141	255	12	and	and	CCONJ
ejpam-141	255	13	spaces	space	NOUN
ejpam-141	255	14	,	,	PUNCT
ejpam-141	255	15	russian	russian	ADJ
ejpam-141	255	16	math	math	NOUN
ejpam-141	255	17	.	.	PUNCT
ejpam-141	256	1	surveys	survey	NOUN
ejpam-141	256	2	21	21	NUM
ejpam-141	256	3	:	:	SYM
ejpam-141	256	4	115	115	NUM
ejpam-141	256	5	–	–	SYM
ejpam-141	256	6	162	162	NUM
ejpam-141	256	7	(	(	PUNCT
ejpam-141	256	8	1966	1966	NUM
ejpam-141	256	9	)	)	PUNCT
ejpam-141	256	10	.	.	PUNCT
ejpam-141	257	1	[	[	X
ejpam-141	257	2	2	2	X
ejpam-141	257	3	]	]	PUNCT
ejpam-141	257	4	s.	s.	PROPN
ejpam-141	257	5	w.	w.	PROPN
ejpam-141	257	6	davis	davis	PROPN
ejpam-141	257	7	,	,	PUNCT
ejpam-141	257	8	more	more	ADJ
ejpam-141	257	9	on	on	ADP
ejpam-141	257	10	cauchy	cauchy	ADJ
ejpam-141	257	11	conditions	condition	NOUN
ejpam-141	257	12	,	,	PUNCT
ejpam-141	257	13	topology	topology	NOUN
ejpam-141	257	14	proc	proc	NOUN
ejpam-141	257	15	.	.	PUNCT
ejpam-141	258	1	9	9	NUM
ejpam-141	258	2	:	:	SYM
ejpam-141	258	3	31	31	NUM
ejpam-141	258	4	–	–	PUNCT
ejpam-141	258	5	36	36	NUM
ejpam-141	258	6	(	(	PUNCT
ejpam-141	258	7	1984	1984	NUM
ejpam-141	258	8	)	)	PUNCT
ejpam-141	258	9	.	.	PUNCT
ejpam-141	259	1	[	[	X
ejpam-141	259	2	3	3	X
ejpam-141	259	3	]	]	X
ejpam-141	259	4	r.	r.	PROPN
ejpam-141	259	5	engelking	engelking	NOUN
ejpam-141	259	6	,	,	PUNCT
ejpam-141	259	7	general	general	ADJ
ejpam-141	259	8	topology	topology	NOUN
ejpam-141	259	9	,	,	PUNCT
ejpam-141	259	10	sigma	sigma	PROPN
ejpam-141	259	11	series	series	PROPN
ejpam-141	259	12	in	in	ADP
ejpam-141	259	13	pure	pure	ADJ
ejpam-141	259	14	mathematics	mathematic	NOUN
ejpam-141	259	15	,	,	PUNCT
ejpam-141	259	16	vol	vol	NOUN
ejpam-141	259	17	.	.	PROPN
ejpam-141	259	18	6	6	NUM
ejpam-141	259	19	,	,	PUNCT
ejpam-141	259	20	heldermann	heldermann	PROPN
ejpam-141	259	21	verlag	verlag	PROPN
ejpam-141	259	22	,	,	PUNCT
ejpam-141	259	23	berlin	berlin	PROPN
ejpam-141	259	24	,	,	PUNCT
ejpam-141	259	25	1988	1988	NUM
ejpam-141	259	26	.	.	PUNCT
ejpam-141	260	1	[	[	X
ejpam-141	260	2	4	4	X
ejpam-141	260	3	]	]	PUNCT
ejpam-141	260	4	s.	s.	PROPN
ejpam-141	260	5	p.	p.	PROPN
ejpam-141	260	6	franklin	franklin	PROPN
ejpam-141	260	7	,	,	PUNCT
ejpam-141	260	8	spaces	space	NOUN
ejpam-141	260	9	in	in	ADP
ejpam-141	260	10	which	which	PRON
ejpam-141	260	11	sequences	sequence	NOUN
ejpam-141	260	12	suffice	suffice	VERB
ejpam-141	260	13	,	,	PUNCT
ejpam-141	260	14	fund	fund	PROPN
ejpam-141	260	15	.	.	PUNCT
ejpam-141	261	1	math	math	NOUN
ejpam-141	261	2	.	.	PUNCT
ejpam-141	262	1	57	57	NUM
ejpam-141	262	2	:	:	SYM
ejpam-141	262	3	107	107	NUM
ejpam-141	262	4	–	–	PUNCT
ejpam-141	262	5	115	115	NUM
ejpam-141	262	6	(	(	PUNCT
ejpam-141	262	7	1965	1965	NUM
ejpam-141	262	8	)	)	PUNCT
ejpam-141	262	9	.	.	PUNCT
ejpam-141	263	1	[	[	X
ejpam-141	263	2	5	5	X
ejpam-141	263	3	]	]	X
ejpam-141	263	4	y.	y.	PROPN
ejpam-141	263	5	ge	ge	PROPN
ejpam-141	263	6	,	,	PUNCT
ejpam-141	263	7	2	2	NUM
ejpam-141	263	8	-	-	PUNCT
ejpam-141	263	9	sequence	sequence	NOUN
ejpam-141	263	10	-	-	PUNCT
ejpam-141	263	11	covering	cover	VERB
ejpam-141	263	12	mappings	mapping	NOUN
ejpam-141	263	13	in	in	ADP
ejpam-141	263	14	ponomarev	ponomarev	NOUN
ejpam-141	263	15	-	-	NOUN
ejpam-141	263	16	systems	system	NOUN
ejpam-141	263	17	,	,	PUNCT
ejpam-141	263	18	chinese	chinese	PROPN
ejpam-141	263	19	adv	adv	PROPN
ejpam-141	263	20	.	.	PUNCT
ejpam-141	263	21	math	math	PROPN
ejpam-141	263	22	.	.	PUNCT
ejpam-141	264	1	(	(	PUNCT
ejpam-141	264	2	china	china	PROPN
ejpam-141	264	3	)	)	PUNCT
ejpam-141	264	4	,	,	PUNCT
ejpam-141	264	5	to	to	PART
ejpam-141	264	6	appear	appear	VERB
ejpam-141	264	7	.	.	PUNCT
ejpam-141	265	1	[	[	X
ejpam-141	265	2	6	6	NUM
ejpam-141	265	3	]	]	X
ejpam-141	265	4	y.	y.	PROPN
ejpam-141	265	5	ge	ge	PROPN
ejpam-141	265	6	,	,	PUNCT
ejpam-141	265	7	on	on	ADP
ejpam-141	265	8	compact	compact	ADJ
ejpam-141	265	9	images	image	NOUN
ejpam-141	265	10	of	of	ADP
ejpam-141	265	11	locally	locally	ADV
ejpam-141	265	12	separable	separable	ADJ
ejpam-141	265	13	metric	metric	ADJ
ejpam-141	265	14	spaces	space	NOUN
ejpam-141	265	15	,	,	PUNCT
ejpam-141	265	16	topology	topology	NOUN
ejpam-141	265	17	proc	proc	NOUN
ejpam-141	265	18	.	.	PROPN
ejpam-141	266	1	27	27	NUM
ejpam-141	266	2	,	,	PUNCT
ejpam-141	266	3	1	1	NUM
ejpam-141	266	4	:	:	SYM
ejpam-141	266	5	351	351	NUM
ejpam-141	266	6	–	–	PUNCT
ejpam-141	266	7	360	360	NUM
ejpam-141	266	8	(	(	PUNCT
ejpam-141	266	9	2003	2003	NUM
ejpam-141	266	10	)	)	PUNCT
ejpam-141	266	11	.	.	PUNCT
ejpam-141	267	1	[	[	X
ejpam-141	267	2	7	7	X
ejpam-141	267	3	]	]	X
ejpam-141	267	4	y.	y.	PROPN
ejpam-141	267	5	ge	ge	PROPN
ejpam-141	267	6	,	,	PUNCT
ejpam-141	267	7	spaces	space	VERB
ejpam-141	267	8	with	with	ADP
ejpam-141	267	9	countable	countable	ADJ
ejpam-141	267	10	sn	sn	NOUN
ejpam-141	267	11	-	-	PUNCT
ejpam-141	267	12	networks	network	NOUN
ejpam-141	267	13	,	,	PUNCT
ejpam-141	267	14	comment	comment	NOUN
ejpam-141	267	15	.	.	PUNCT
ejpam-141	268	1	math	math	NOUN
ejpam-141	268	2	.	.	PUNCT
ejpam-141	269	1	univ	univ	PROPN
ejpam-141	269	2	.	.	PUNCT
ejpam-141	270	1	carolina	carolina	PROPN
ejpam-141	270	2	45	45	NUM
ejpam-141	270	3	:	:	SYM
ejpam-141	270	4	169	169	NUM
ejpam-141	270	5	–	–	PUNCT
ejpam-141	270	6	176	176	NUM
ejpam-141	270	7	(	(	PUNCT
ejpam-141	270	8	2004	2004	NUM
ejpam-141	270	9	)	)	PUNCT
ejpam-141	270	10	.	.	PUNCT
ejpam-141	271	1	[	[	X
ejpam-141	271	2	8	8	X
ejpam-141	271	3	]	]	PUNCT
ejpam-141	271	4	j.	j.	PROPN
ejpam-141	271	5	a.	a.	PROPN
ejpam-141	271	6	gurthrie	gurthrie	PROPN
ejpam-141	271	7	,	,	PUNCT
ejpam-141	271	8	a	a	DET
ejpam-141	271	9	characterization	characterization	NOUN
ejpam-141	271	10	of	of	ADP
ejpam-141	271	11	ℵ0	ℵ0	NOUN
ejpam-141	271	12	-	-	PUNCT
ejpam-141	271	13	spaces	space	NOUN
ejpam-141	271	14	,	,	PUNCT
ejpam-141	271	15	general	general	ADJ
ejpam-141	271	16	topology	topology	NOUN
ejpam-141	271	17	appl	appl	NOUN
ejpam-141	271	18	.	.	PUNCT
ejpam-141	272	1	1	1	NUM
ejpam-141	272	2	:	:	SYM
ejpam-141	272	3	105	105	NUM
ejpam-141	272	4	–	–	SYM
ejpam-141	272	5	110	110	NUM
ejpam-141	272	6	(	(	PUNCT
ejpam-141	272	7	1971	1971	NUM
ejpam-141	272	8	)	)	PUNCT
ejpam-141	272	9	.	.	PUNCT
ejpam-141	273	1	[	[	X
ejpam-141	273	2	9	9	NUM
ejpam-141	273	3	]	]	X
ejpam-141	273	4	y.	y.	PROPN
ejpam-141	273	5	ikeda	ikeda	PROPN
ejpam-141	273	6	,	,	PUNCT
ejpam-141	273	7	c.	c.	PROPN
ejpam-141	273	8	liu	liu	PROPN
ejpam-141	273	9	,	,	PUNCT
ejpam-141	273	10	and	and	CCONJ
ejpam-141	273	11	y.	y.	PROPN
ejpam-141	273	12	tanaka	tanaka	PROPN
ejpam-141	273	13	,	,	PUNCT
ejpam-141	273	14	quotient	quotient	VERB
ejpam-141	273	15	compact	compact	ADJ
ejpam-141	273	16	images	image	NOUN
ejpam-141	273	17	of	of	ADP
ejpam-141	273	18	metric	metric	ADJ
ejpam-141	273	19	spaces	space	NOUN
ejpam-141	273	20	,	,	PUNCT
ejpam-141	273	21	and	and	CCONJ
ejpam-141	273	22	related	related	ADJ
ejpam-141	273	23	matters	matter	NOUN
ejpam-141	273	24	,	,	PUNCT
ejpam-141	273	25	topology	topology	NOUN
ejpam-141	273	26	appl	appl	NOUN
ejpam-141	273	27	.	.	PROPN
ejpam-141	274	1	122	122	NUM
ejpam-141	274	2	,	,	PUNCT
ejpam-141	274	3	237	237	NUM
ejpam-141	274	4	–	–	PUNCT
ejpam-141	274	5	252	252	NUM
ejpam-141	274	6	(	(	PUNCT
ejpam-141	274	7	2002	2002	NUM
ejpam-141	274	8	)	)	PUNCT
ejpam-141	274	9	.	.	PUNCT
ejpam-141	275	1	[	[	X
ejpam-141	275	2	10	10	NUM
ejpam-141	275	3	]	]	PUNCT
ejpam-141	275	4	z.	z.	PROPN
ejpam-141	275	5	li	li	PROPN
ejpam-141	275	6	,	,	PUNCT
ejpam-141	275	7	on	on	ADP
ejpam-141	275	8	π	π	PROPN
ejpam-141	275	9	-	-	PUNCT
ejpam-141	275	10	s	s	NOUN
ejpam-141	275	11	-	-	PUNCT
ejpam-141	275	12	images	image	NOUN
ejpam-141	275	13	of	of	ADP
ejpam-141	275	14	metric	metric	ADJ
ejpam-141	275	15	spaces	space	NOUN
ejpam-141	275	16	,	,	PUNCT
ejpam-141	275	17	int	int	NOUN
ejpam-141	275	18	.	.	PUNCT
ejpam-141	276	1	j.	j.	PROPN
ejpam-141	276	2	math	math	PROPN
ejpam-141	276	3	.	.	PUNCT
ejpam-141	277	1	sci	sci	PROPN
ejpam-141	277	2	.	.	PROPN
ejpam-141	278	1	7	7	NUM
ejpam-141	278	2	:	:	SYM
ejpam-141	278	3	1101	1101	NUM
ejpam-141	278	4	–	–	PUNCT
ejpam-141	278	5	1107	1107	NUM
ejpam-141	278	6	(	(	PUNCT
ejpam-141	278	7	2005	2005	NUM
ejpam-141	278	8	)	)	PUNCT
ejpam-141	278	9	.	.	PUNCT
ejpam-141	279	1	[	[	X
ejpam-141	279	2	11	11	NUM
ejpam-141	279	3	]	]	PUNCT
ejpam-141	279	4	z.	z.	PROPN
ejpam-141	279	5	li	li	PROPN
ejpam-141	279	6	,	,	PUNCT
ejpam-141	279	7	q.	q.	PROPN
ejpam-141	279	8	li	li	PROPN
ejpam-141	279	9	,	,	PUNCT
ejpam-141	279	10	and	and	CCONJ
ejpam-141	279	11	x.	x.	NOUN
ejpam-141	279	12	zhou	zhou	PROPN
ejpam-141	279	13	,	,	PUNCT
ejpam-141	279	14	on	on	ADP
ejpam-141	279	15	sequence	sequence	NOUN
ejpam-141	279	16	-	-	PUNCT
ejpam-141	279	17	covering	cover	VERB
ejpam-141	279	18	msss	msss	NOUN
ejpam-141	279	19	-	-	PUNCT
ejpam-141	279	20	maps	map	NOUN
ejpam-141	279	21	,	,	PUNCT
ejpam-141	279	22	mat	mat	PROPN
ejpam-141	279	23	.	.	PROPN
ejpam-141	279	24	vesnik	vesnik	PROPN
ejpam-141	279	25	59	59	NUM
ejpam-141	279	26	:	:	SYM
ejpam-141	279	27	15	15	NUM
ejpam-141	279	28	–	–	SYM
ejpam-141	279	29	21	21	NUM
ejpam-141	279	30	(	(	PUNCT
ejpam-141	279	31	2007	2007	NUM
ejpam-141	279	32	)	)	PUNCT
ejpam-141	279	33	.	.	PUNCT
ejpam-141	280	1	[	[	X
ejpam-141	280	2	12	12	NUM
ejpam-141	280	3	]	]	PUNCT
ejpam-141	280	4	s.	s.	PROPN
ejpam-141	280	5	lin	lin	PROPN
ejpam-141	280	6	,	,	PUNCT
ejpam-141	280	7	on	on	ADP
ejpam-141	280	8	sequence	sequence	NOUN
ejpam-141	280	9	-	-	PUNCT
ejpam-141	280	10	covering	cover	VERB
ejpam-141	280	11	s	s	NOUN
ejpam-141	280	12	-	-	PUNCT
ejpam-141	280	13	mappings	mapping	NOUN
ejpam-141	280	14	,	,	PUNCT
ejpam-141	280	15	adv	adv	PROPN
ejpam-141	280	16	.	.	PUNCT
ejpam-141	280	17	math	math	PROPN
ejpam-141	280	18	.	.	PUNCT
ejpam-141	281	1	(	(	PUNCT
ejpam-141	281	2	china	china	PROPN
ejpam-141	281	3	)	)	PUNCT
ejpam-141	281	4	25	25	NUM
ejpam-141	281	5	:	:	SYM
ejpam-141	281	6	548	548	NUM
ejpam-141	281	7	–	–	PUNCT
ejpam-141	281	8	551	551	NUM
ejpam-141	281	9	(	(	PUNCT
ejpam-141	281	10	1996	1996	NUM
ejpam-141	281	11	)	)	PUNCT
ejpam-141	281	12	.	.	PUNCT
ejpam-141	282	1	[	[	X
ejpam-141	282	2	13	13	NUM
ejpam-141	282	3	]	]	PUNCT
ejpam-141	282	4	s.	s.	PROPN
ejpam-141	282	5	lin	lin	PROPN
ejpam-141	282	6	,	,	PUNCT
ejpam-141	282	7	c.	c.	PROPN
ejpam-141	282	8	liu	liu	PROPN
ejpam-141	282	9	,	,	PUNCT
ejpam-141	282	10	and	and	CCONJ
ejpam-141	282	11	m.	m.	PROPN
ejpam-141	282	12	dai	dai	PROPN
ejpam-141	282	13	,	,	PUNCT
ejpam-141	282	14	images	image	NOUN
ejpam-141	282	15	on	on	ADP
ejpam-141	282	16	locally	locally	ADV
ejpam-141	282	17	separable	separable	ADJ
ejpam-141	282	18	metric	metric	ADJ
ejpam-141	282	19	spaces	space	NOUN
ejpam-141	282	20	,	,	PUNCT
ejpam-141	282	21	acta	acta	PROPN
ejpam-141	282	22	math	math	PROPN
ejpam-141	282	23	.	.	PUNCT
ejpam-141	283	1	sinica	sinica	PROPN
ejpam-141	283	2	(	(	PUNCT
ejpam-141	283	3	n.s	n.s	PROPN
ejpam-141	283	4	.	.	PROPN
ejpam-141	283	5	)	)	PUNCT
ejpam-141	283	6	13	13	NUM
ejpam-141	283	7	,	,	PUNCT
ejpam-141	283	8	1	1	NUM
ejpam-141	283	9	:	:	SYM
ejpam-141	283	10	1	1	NUM
ejpam-141	283	11	–	–	SYM
ejpam-141	283	12	8	8	NUM
ejpam-141	283	13	(	(	PUNCT
ejpam-141	283	14	1997	1997	NUM
ejpam-141	283	15	)	)	PUNCT
ejpam-141	283	16	.	.	PUNCT
ejpam-141	284	1	[	[	X
ejpam-141	284	2	14	14	NUM
ejpam-141	284	3	]	]	X
ejpam-141	284	4	s.	s.	PROPN
ejpam-141	284	5	lin	lin	PROPN
ejpam-141	284	6	and	and	CCONJ
ejpam-141	284	7	p.	p.	PROPN
ejpam-141	284	8	yan	yan	PROPN
ejpam-141	284	9	,	,	PUNCT
ejpam-141	284	10	sequence	sequence	NOUN
ejpam-141	284	11	-	-	PUNCT
ejpam-141	284	12	covering	cover	VERB
ejpam-141	284	13	maps	map	NOUN
ejpam-141	284	14	of	of	ADP
ejpam-141	284	15	metric	metric	ADJ
ejpam-141	284	16	spaces	space	NOUN
ejpam-141	284	17	,	,	PUNCT
ejpam-141	284	18	topology	topology	NOUN
ejpam-141	284	19	appl	appl	NOUN
ejpam-141	284	20	.	.	PUNCT
ejpam-141	285	1	109	109	NUM
ejpam-141	285	2	:	:	SYM
ejpam-141	285	3	301	301	NUM
ejpam-141	285	4	–	–	PUNCT
ejpam-141	285	5	314	314	NUM
ejpam-141	285	6	(	(	PUNCT
ejpam-141	285	7	2001	2001	NUM
ejpam-141	285	8	)	)	PUNCT
ejpam-141	285	9	.	.	PUNCT
ejpam-141	286	1	[	[	X
ejpam-141	286	2	15	15	NUM
ejpam-141	286	3	]	]	X
ejpam-141	286	4	s.	s.	PROPN
ejpam-141	286	5	lin	lin	PROPN
ejpam-141	286	6	and	and	CCONJ
ejpam-141	286	7	p.	p.	PROPN
ejpam-141	286	8	yan	yan	PROPN
ejpam-141	286	9	,	,	PUNCT
ejpam-141	286	10	notes	note	VERB
ejpam-141	286	11	on	on	ADP
ejpam-141	286	12	c	c	PROPN
ejpam-141	286	13	f	f	PROPN
ejpam-141	286	14	p	p	NOUN
ejpam-141	286	15	-	-	PUNCT
ejpam-141	286	16	covers	cover	VERB
ejpam-141	286	17	,	,	PUNCT
ejpam-141	286	18	comment	comment	NOUN
ejpam-141	286	19	.	.	PUNCT
ejpam-141	287	1	math	math	NOUN
ejpam-141	287	2	.	.	PUNCT
ejpam-141	288	1	univ	univ	PROPN
ejpam-141	288	2	.	.	PUNCT
ejpam-141	289	1	carolina	carolina	PROPN
ejpam-141	289	2	44	44	NUM
ejpam-141	289	3	,	,	PUNCT
ejpam-141	289	4	2	2	NUM
ejpam-141	289	5	:	:	SYM
ejpam-141	289	6	295	295	NUM
ejpam-141	289	7	–	–	SYM
ejpam-141	289	8	306	306	NUM
ejpam-141	289	9	(	(	PUNCT
ejpam-141	289	10	2003	2003	NUM
ejpam-141	289	11	)	)	PUNCT
ejpam-141	289	12	.	.	PUNCT
ejpam-141	290	1	[	[	X
ejpam-141	290	2	16	16	NUM
ejpam-141	290	3	]	]	PUNCT
ejpam-141	290	4	s.	s.	PROPN
ejpam-141	290	5	lin	lin	PROPN
ejpam-141	290	6	,	,	PUNCT
ejpam-141	290	7	j	j	PROPN
ejpam-141	290	8	-	-	PROPN
ejpam-141	290	9	c.	c.	PROPN
ejpam-141	290	10	zhu	zhu	PROPN
ejpam-141	290	11	,	,	PUNCT
ejpam-141	290	12	y.	y.	PROPN
ejpam-141	290	13	ge	ge	PROPN
ejpam-141	290	14	,	,	PUNCT
ejpam-141	290	15	and	and	CCONJ
ejpam-141	290	16	j	j	PROPN
ejpam-141	290	17	-	-	PUNCT
ejpam-141	290	18	s.	s.	PROPN
ejpam-141	290	19	gu	gu	PROPN
ejpam-141	290	20	,	,	PUNCT
ejpam-141	290	21	almost	almost	ADV
ejpam-141	290	22	-	-	PUNCT
ejpam-141	290	23	open	open	ADJ
ejpam-141	290	24	maps	map	NOUN
ejpam-141	290	25	,	,	PUNCT
ejpam-141	290	26	sequence	sequence	NOUN
ejpam-141	290	27	-	-	PUNCT
ejpam-141	290	28	covering	cover	VERB
ejpam-141	290	29	maps	map	NOUN
ejpam-141	290	30	and	and	CCONJ
ejpam-141	290	31	sn	sn	NOUN
ejpam-141	290	32	-	-	PUNCT
ejpam-141	290	33	networks	network	NOUN
ejpam-141	290	34	,	,	PUNCT
ejpam-141	290	35	indian	indian	ADJ
ejpam-141	290	36	j.	j.	PROPN
ejpam-141	290	37	pure	pure	PROPN
ejpam-141	290	38	appl	appl	PROPN
ejpam-141	290	39	.	.	PUNCT
ejpam-141	290	40	math	math	NOUN
ejpam-141	290	41	.	.	PUNCT
ejpam-141	291	1	37	37	NUM
ejpam-141	291	2	,	,	PUNCT
ejpam-141	291	3	2	2	NUM
ejpam-141	291	4	:	:	SYM
ejpam-141	291	5	111	111	NUM
ejpam-141	291	6	–	–	SYM
ejpam-141	291	7	119	119	NUM
ejpam-141	291	8	(	(	PUNCT
ejpam-141	291	9	2006	2006	NUM
ejpam-141	291	10	)	)	PUNCT
ejpam-141	291	11	.	.	PUNCT
ejpam-141	292	1	references	reference	NOUN
ejpam-141	292	2	194	194	NUM
ejpam-141	293	1	[	[	X
ejpam-141	293	2	17	17	NUM
ejpam-141	293	3	]	]	X
ejpam-141	293	4	e.	e.	PROPN
ejpam-141	293	5	michael	michael	PROPN
ejpam-141	293	6	,	,	PUNCT
ejpam-141	293	7	ℵ0	ℵ0	PROPN
ejpam-141	293	8	-	-	NOUN
ejpam-141	293	9	spaces	space	NOUN
ejpam-141	293	10	,	,	PUNCT
ejpam-141	293	11	j.	j.	PROPN
ejpam-141	293	12	math	math	PROPN
ejpam-141	293	13	.	.	PUNCT
ejpam-141	293	14	mech	mech	PROPN
ejpam-141	293	15	.	.	PUNCT
ejpam-141	294	1	15	15	NUM
ejpam-141	294	2	:	:	SYM
ejpam-141	294	3	983–1002	983–1002	NUM
ejpam-141	294	4	(	(	PUNCT
ejpam-141	294	5	1966	1966	NUM
ejpam-141	294	6	)	)	PUNCT
ejpam-141	294	7	.	.	PUNCT
ejpam-141	295	1	[	[	X
ejpam-141	295	2	18	18	NUM
ejpam-141	295	3	]	]	X
ejpam-141	295	4	f.	f.	PROPN
ejpam-141	295	5	siwiec	siwiec	PROPN
ejpam-141	295	6	,	,	PUNCT
ejpam-141	295	7	on	on	ADP
ejpam-141	295	8	defining	define	VERB
ejpam-141	295	9	a	a	DET
ejpam-141	295	10	space	space	NOUN
ejpam-141	295	11	by	by	ADP
ejpam-141	295	12	a	a	DET
ejpam-141	295	13	weak	weak	ADJ
ejpam-141	295	14	-	-	PUNCT
ejpam-141	295	15	base	base	NOUN
ejpam-141	295	16	,	,	PUNCT
ejpam-141	295	17	pacific	pacific	PROPN
ejpam-141	295	18	j.	j.	PROPN
ejpam-141	295	19	math	math	PROPN
ejpam-141	295	20	.	.	PUNCT
ejpam-141	296	1	52	52	NUM
ejpam-141	296	2	:	:	SYM
ejpam-141	296	3	233	233	NUM
ejpam-141	296	4	–	–	SYM
ejpam-141	296	5	245	245	NUM
ejpam-141	296	6	(	(	PUNCT
ejpam-141	296	7	1974	1974	NUM
ejpam-141	296	8	)	)	PUNCT
ejpam-141	296	9	.	.	PUNCT
ejpam-141	297	1	[	[	X
ejpam-141	297	2	19	19	NUM
ejpam-141	297	3	]	]	X
ejpam-141	297	4	y.	y.	PROPN
ejpam-141	297	5	tanaka	tanaka	PROPN
ejpam-141	297	6	,	,	PUNCT
ejpam-141	297	7	theory	theory	NOUN
ejpam-141	297	8	of	of	ADP
ejpam-141	297	9	k	k	PROPN
ejpam-141	297	10	-	-	PUNCT
ejpam-141	297	11	networks	network	NOUN
ejpam-141	297	12	ii	ii	PROPN
ejpam-141	297	13	,	,	PUNCT
ejpam-141	297	14	questions	question	NOUN
ejpam-141	297	15	answers	answer	NOUN
ejpam-141	297	16	in	in	ADP
ejpam-141	297	17	gen	gen	PROPN
ejpam-141	297	18	.	.	PROPN
ejpam-141	297	19	topology	topology	PROPN
ejpam-141	297	20	19	19	NUM
ejpam-141	297	21	:	:	SYM
ejpam-141	297	22	27	27	NUM
ejpam-141	297	23	–	–	SYM
ejpam-141	297	24	46	46	NUM
ejpam-141	297	25	(	(	PUNCT
ejpam-141	297	26	2001	2001	NUM
ejpam-141	297	27	)	)	PUNCT
ejpam-141	297	28	.	.	PUNCT
ejpam-141	298	1	[	[	X
ejpam-141	298	2	20	20	NUM
ejpam-141	298	3	]	]	X
ejpam-141	298	4	y.	y.	PROPN
ejpam-141	298	5	tanaka	tanaka	PROPN
ejpam-141	298	6	and	and	CCONJ
ejpam-141	298	7	y.	y.	PROPN
ejpam-141	298	8	ge	ge	PROPN
ejpam-141	298	9	,	,	PUNCT
ejpam-141	298	10	around	around	ADP
ejpam-141	298	11	quotient	quotient	NOUN
ejpam-141	298	12	compact	compact	ADJ
ejpam-141	298	13	images	image	NOUN
ejpam-141	298	14	of	of	ADP
ejpam-141	298	15	metric	metric	ADJ
ejpam-141	298	16	spaces	space	NOUN
ejpam-141	298	17	,	,	PUNCT
ejpam-141	298	18	and	and	CCONJ
ejpam-141	298	19	symmetric	symmetric	ADJ
ejpam-141	298	20	spaces	space	NOUN
ejpam-141	298	21	,	,	PUNCT
ejpam-141	298	22	houston	houston	PROPN
ejpam-141	298	23	j.	j.	PROPN
ejpam-141	298	24	math	math	PROPN
ejpam-141	298	25	.	.	PUNCT
ejpam-141	299	1	32	32	NUM
ejpam-141	299	2	,	,	PUNCT
ejpam-141	299	3	1	1	NUM
ejpam-141	299	4	:	:	SYM
ejpam-141	299	5	99	99	NUM
ejpam-141	299	6	–	–	SYM
ejpam-141	299	7	117	117	NUM
ejpam-141	299	8	(	(	PUNCT
ejpam-141	299	9	2006	2006	NUM
ejpam-141	299	10	)	)	PUNCT
ejpam-141	299	11	.	.	PUNCT
ejpam-141	300	1	[	[	X
ejpam-141	300	2	21	21	NUM
ejpam-141	300	3	]	]	X
ejpam-141	300	4	y.	y.	PROPN
ejpam-141	300	5	tanaka	tanaka	PROPN
ejpam-141	300	6	and	and	CCONJ
ejpam-141	300	7	s.	s.	PROPN
ejpam-141	300	8	xia	xia	PROPN
ejpam-141	300	9	,	,	PUNCT
ejpam-141	300	10	certain	certain	ADJ
ejpam-141	300	11	s	s	NOUN
ejpam-141	300	12	-	-	PUNCT
ejpam-141	300	13	images	image	NOUN
ejpam-141	300	14	of	of	ADP
ejpam-141	300	15	locally	locally	ADV
ejpam-141	300	16	separable	separable	ADJ
ejpam-141	300	17	metric	metric	ADJ
ejpam-141	300	18	spaces	space	NOUN
ejpam-141	300	19	,	,	PUNCT
ejpam-141	300	20	questions	question	NOUN
ejpam-141	300	21	answers	answer	VERB
ejpam-141	300	22	gen	gen	PROPN
ejpam-141	300	23	.	.	PROPN
ejpam-141	300	24	topology	topology	PROPN
ejpam-141	300	25	14	14	NUM
ejpam-141	300	26	:	:	SYM
ejpam-141	300	27	217	217	NUM
ejpam-141	300	28	–	–	SYM
ejpam-141	300	29	231	231	NUM
ejpam-141	300	30	(	(	PUNCT
ejpam-141	300	31	1996	1996	NUM
ejpam-141	300	32	)	)	PUNCT
ejpam-141	300	33	.	.	PUNCT
ejpam-141	301	1	[	[	X
ejpam-141	301	2	22	22	NUM
ejpam-141	301	3	]	]	PUNCT
ejpam-141	301	4	p.	p.	PROPN
ejpam-141	301	5	yan	yan	PROPN
ejpam-141	301	6	,	,	PUNCT
ejpam-141	301	7	on	on	ADP
ejpam-141	301	8	strong	strong	ADJ
ejpam-141	301	9	sequence	sequence	NOUN
ejpam-141	301	10	-	-	PUNCT
ejpam-141	301	11	covering	cover	VERB
ejpam-141	301	12	compact	compact	ADJ
ejpam-141	301	13	mappings	mapping	NOUN
ejpam-141	301	14	,	,	PUNCT
ejpam-141	301	15	northeast	northeast	ADJ
ejpam-141	301	16	.	.	PUNCT
ejpam-141	301	17	math	math	NOUN
ejpam-141	301	18	.	.	PUNCT
ejpam-141	302	1	j.	j.	PROPN
ejpam-141	302	2	14	14	NUM
ejpam-141	302	3	:	:	PUNCT
ejpam-141	302	4	341	341	NUM
ejpam-141	302	5	–	–	PUNCT
ejpam-141	302	6	344	344	NUM
ejpam-141	302	7	(	(	PUNCT
ejpam-141	302	8	1998	1998	NUM
ejpam-141	302	9	)	)	PUNCT
ejpam-141	302	10	.	.	PUNCT