id	sid	tid	token	lemma	pos
ejpam-2495	1	1	european	european	PROPN
ejpam-2495	1	2	journal	journal	PROPN
ejpam-2495	1	3	of	of	ADP
ejpam-2495	1	4	pure	pure	ADJ
ejpam-2495	1	5	and	and	CCONJ
ejpam-2495	1	6	applied	apply	VERB
ejpam-2495	1	7	mathematics	mathematic	NOUN
ejpam-2495	1	8	vol	vol	NOUN
ejpam-2495	1	9	.	.	PROPN
ejpam-2495	2	1	10	10	NUM
ejpam-2495	2	2	,	,	PUNCT
ejpam-2495	2	3	no	no	INTJ
ejpam-2495	2	4	.	.	NOUN
ejpam-2495	2	5	2	2	NUM
ejpam-2495	2	6	,	,	PUNCT
ejpam-2495	2	7	2017	2017	NUM
ejpam-2495	2	8	,	,	PUNCT
ejpam-2495	2	9	323	323	NUM
ejpam-2495	2	10	-	-	SYM
ejpam-2495	2	11	334	334	NUM
ejpam-2495	2	12	issn	issn	PROPN
ejpam-2495	2	13	1307	1307	NUM
ejpam-2495	2	14	-	-	SYM
ejpam-2495	2	15	5543	5543	NUM
ejpam-2495	2	16	–	–	PUNCT
ejpam-2495	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-2495	2	18	published	publish	VERB
ejpam-2495	2	19	by	by	ADP
ejpam-2495	2	20	new	new	PROPN
ejpam-2495	2	21	york	york	PROPN
ejpam-2495	2	22	business	business	PROPN
ejpam-2495	2	23	global	global	ADJ
ejpam-2495	2	24	btµcompactness	btµcompactness	NOUN
ejpam-2495	2	25	and	and	CCONJ
ejpam-2495	2	26	btµ	btµ	PROPN
ejpam-2495	2	27	connectedness	connectedness	NOUN
ejpam-2495	2	28	in	in	ADP
ejpam-2495	2	29	supra	supra	PROPN
ejpam-2495	2	30	topological	topological	PROPN
ejpam-2495	2	31	spaces	space	NOUN
ejpam-2495	2	32	k.krishnaveni1,∗	k.krishnaveni1,∗	PROPN
ejpam-2495	2	33	,	,	PUNCT
ejpam-2495	2	34	m.vigneshwaran	m.vigneshwaran	NOUN
ejpam-2495	2	35	2	2	NUM
ejpam-2495	2	36	1	1	NUM
ejpam-2495	2	37	research	research	NOUN
ejpam-2495	2	38	scholar	scholar	NOUN
ejpam-2495	2	39	,	,	PUNCT
ejpam-2495	2	40	department	department	NOUN
ejpam-2495	2	41	of	of	ADP
ejpam-2495	2	42	mathematics	mathematics	PROPN
ejpam-2495	2	43	,	,	PUNCT
ejpam-2495	2	44	coimbatore	coimbatore	PROPN
ejpam-2495	2	45	,	,	PUNCT
ejpam-2495	2	46	tamilnadu	tamilnadu	NOUN
ejpam-2495	2	47	,	,	PUNCT
ejpam-2495	2	48	india	india	PROPN
ejpam-2495	2	49	.	.	PROPN
ejpam-2495	2	50	2	2	NUM
ejpam-2495	2	51	department	department	NOUN
ejpam-2495	2	52	of	of	ADP
ejpam-2495	2	53	mathematics	mathematics	PROPN
ejpam-2495	2	54	,	,	PUNCT
ejpam-2495	2	55	coimbatore	coimbatore	PROPN
ejpam-2495	2	56	,	,	PUNCT
ejpam-2495	2	57	tamilnadu	tamilnadu	NOUN
ejpam-2495	2	58	,	,	PUNCT
ejpam-2495	2	59	india	india	PROPN
ejpam-2495	2	60	abstract	abstract	NOUN
ejpam-2495	2	61	.	.	PUNCT
ejpam-2495	3	1	in	in	ADP
ejpam-2495	3	2	this	this	DET
ejpam-2495	3	3	paper	paper	NOUN
ejpam-2495	3	4	we	we	PRON
ejpam-2495	3	5	newly	newly	ADV
ejpam-2495	3	6	originate	originate	VERB
ejpam-2495	3	7	the	the	DET
ejpam-2495	3	8	notion	notion	NOUN
ejpam-2495	3	9	of	of	ADP
ejpam-2495	3	10	btµ	btµ	NOUN
ejpam-2495	3	11	compact	compact	ADJ
ejpam-2495	3	12	space	space	NOUN
ejpam-2495	3	13	and	and	CCONJ
ejpam-2495	3	14	inspected	inspect	VERB
ejpam-2495	3	15	its	its	PRON
ejpam-2495	3	16	several	several	ADJ
ejpam-2495	3	17	effects	effect	NOUN
ejpam-2495	3	18	and	and	CCONJ
ejpam-2495	3	19	characterizations	characterization	NOUN
ejpam-2495	3	20	.	.	PUNCT
ejpam-2495	4	1	also	also	ADV
ejpam-2495	4	2	we	we	PRON
ejpam-2495	4	3	newly	newly	ADV
ejpam-2495	4	4	originate	originate	VERB
ejpam-2495	4	5	and	and	CCONJ
ejpam-2495	4	6	study	study	VERB
ejpam-2495	4	7	the	the	DET
ejpam-2495	4	8	concept	concept	NOUN
ejpam-2495	4	9	of	of	ADP
ejpam-2495	4	10	btµ	btµ	PROPN
ejpam-2495	4	11	lindelof	lindelof	PROPN
ejpam-2495	4	12	spaces	space	NOUN
ejpam-2495	4	13	and	and	CCONJ
ejpam-2495	4	14	connected	connected	ADJ
ejpam-2495	4	15	spaces	space	NOUN
ejpam-2495	4	16	.	.	PUNCT
ejpam-2495	5	1	2010	2010	NUM
ejpam-2495	5	2	mathematics	mathematic	NOUN
ejpam-2495	5	3	subject	subject	NOUN
ejpam-2495	5	4	classifications	classification	NOUN
ejpam-2495	5	5	:	:	PUNCT
ejpam-2495	5	6	54d05	54d05	NUM
ejpam-2495	5	7	,	,	PUNCT
ejpam-2495	5	8	54d20	54d20	NUM
ejpam-2495	5	9	,	,	PUNCT
ejpam-2495	5	10	54d30	54d30	ADJ
ejpam-2495	5	11	key	key	ADJ
ejpam-2495	5	12	words	word	NOUN
ejpam-2495	5	13	and	and	CCONJ
ejpam-2495	5	14	phrases	phrase	NOUN
ejpam-2495	5	15	:	:	PUNCT
ejpam-2495	5	16	btµ	btµ	NOUN
ejpam-2495	5	17	-open	-open	NOUN
ejpam-2495	5	18	sets	set	NOUN
ejpam-2495	5	19	;	;	PUNCT
ejpam-2495	5	20	btµ	btµ	NOUN
ejpam-2495	5	21	-compact	-compact	NOUN
ejpam-2495	5	22	spaces	space	NOUN
ejpam-2495	5	23	;	;	PUNCT
ejpam-2495	5	24	btµ	btµ	NOUN
ejpam-2495	5	25	lindelof	lindelof	PROPN
ejpam-2495	5	26	spaces	space	NOUN
ejpam-2495	5	27	and	and	CCONJ
ejpam-2495	5	28	btµ	btµ	NOUN
ejpam-2495	5	29	connected	connected	ADJ
ejpam-2495	5	30	spaces	space	NOUN
ejpam-2495	5	31	.	.	PUNCT
ejpam-2495	6	1	1	1	X
ejpam-2495	6	2	.	.	X
ejpam-2495	6	3	introduction	introduction	NOUN
ejpam-2495	6	4	the	the	DET
ejpam-2495	6	5	supra	supra	PROPN
ejpam-2495	6	6	topological	topological	ADJ
ejpam-2495	6	7	spaces	space	NOUN
ejpam-2495	6	8	was	be	AUX
ejpam-2495	6	9	introduced	introduce	VERB
ejpam-2495	6	10	by	by	ADP
ejpam-2495	6	11	mashhour.et.al	mashhour.et.al	PROPN
ejpam-2495	7	1	[	[	X
ejpam-2495	7	2	6	6	NUM
ejpam-2495	7	3	]	]	PUNCT
ejpam-2495	7	4	in	in	ADP
ejpam-2495	7	5	1983	1983	NUM
ejpam-2495	7	6	.	.	PUNCT
ejpam-2495	8	1	they	they	PRON
ejpam-2495	8	2	studied	study	VERB
ejpam-2495	8	3	s	s	PART
ejpam-2495	8	4	continuous	continuous	ADJ
ejpam-2495	8	5	maps	map	NOUN
ejpam-2495	8	6	and	and	CCONJ
ejpam-2495	8	7	s*continuous	s*continuous	ADJ
ejpam-2495	8	8	maps	map	NOUN
ejpam-2495	8	9	.	.	PUNCT
ejpam-2495	9	1	the	the	DET
ejpam-2495	9	2	supra	supra	PROPN
ejpam-2495	9	3	bopen	bopen	NOUN
ejpam-2495	9	4	set	set	NOUN
ejpam-2495	9	5	and	and	CCONJ
ejpam-2495	9	6	supra	supra	PROPN
ejpam-2495	9	7	b	b	X
ejpam-2495	9	8	-	-	PUNCT
ejpam-2495	9	9	continuity	continuity	NOUN
ejpam-2495	9	10	was	be	AUX
ejpam-2495	9	11	brought	bring	VERB
ejpam-2495	9	12	out	out	ADP
ejpam-2495	9	13	by	by	ADP
ejpam-2495	9	14	sayed.et.al	sayed.et.al	PROPN
ejpam-2495	10	1	[	[	X
ejpam-2495	10	2	8	8	NUM
ejpam-2495	10	3	]	]	PUNCT
ejpam-2495	10	4	in	in	ADP
ejpam-2495	10	5	2010	2010	NUM
ejpam-2495	10	6	.	.	PUNCT
ejpam-2495	11	1	recently	recently	ADV
ejpam-2495	11	2	krishnaveni	krishnaveni	PROPN
ejpam-2495	11	3	and	and	CCONJ
ejpam-2495	11	4	vigneshwaran	vigneshwaran	NOUN
ejpam-2495	11	5	[	[	X
ejpam-2495	11	6	4	4	X
ejpam-2495	11	7	]	]	PUNCT
ejpam-2495	11	8	came	come	VERB
ejpam-2495	11	9	out	out	ADP
ejpam-2495	11	10	with	with	ADP
ejpam-2495	11	11	supra	supra	PROPN
ejpam-2495	11	12	bt	bt	PROPN
ejpam-2495	11	13	-closed	-close	VERB
ejpam-2495	11	14	sets	set	NOUN
ejpam-2495	11	15	and	and	CCONJ
ejpam-2495	11	16	defined	define	VERB
ejpam-2495	11	17	their	their	PRON
ejpam-2495	11	18	properties	property	NOUN
ejpam-2495	11	19	.	.	PUNCT
ejpam-2495	12	1	in	in	ADP
ejpam-2495	12	2	2013	2013	NUM
ejpam-2495	12	3	,	,	PUNCT
ejpam-2495	12	4	jamal	jamal	PROPN
ejpam-2495	12	5	m.mustafa.et.al[3	m.mustafa.et.al[3	PROPN
ejpam-2495	12	6	]	]	PUNCT
ejpam-2495	12	7	came	come	VERB
ejpam-2495	12	8	out	out	ADP
ejpam-2495	12	9	with	with	ADP
ejpam-2495	12	10	the	the	DET
ejpam-2495	12	11	concect	concect	NOUN
ejpam-2495	12	12	of	of	ADP
ejpam-2495	12	13	supra	supra	PROPN
ejpam-2495	12	14	bconnected	bconnected	PROPN
ejpam-2495	12	15	and	and	CCONJ
ejpam-2495	12	16	supra	supra	PROPN
ejpam-2495	12	17	blindelof	blindelof	NOUN
ejpam-2495	12	18	spaces	space	VERB
ejpam-2495	12	19	.	.	PUNCT
ejpam-2495	13	1	now	now	ADV
ejpam-2495	13	2	we	we	PRON
ejpam-2495	13	3	bring	bring	VERB
ejpam-2495	13	4	up	up	ADP
ejpam-2495	13	5	with	with	ADP
ejpam-2495	13	6	the	the	DET
ejpam-2495	13	7	new	new	ADJ
ejpam-2495	13	8	concepts	concept	NOUN
ejpam-2495	13	9	of	of	ADP
ejpam-2495	13	10	supra	supra	PROPN
ejpam-2495	13	11	bt	bt	PROPN
ejpam-2495	13	12	-compact	-compact	PROPN
ejpam-2495	13	13	,	,	PUNCT
ejpam-2495	13	14	supra	supra	PROPN
ejpam-2495	13	15	bt	bt	PROPN
ejpam-2495	13	16	lindelof	lindelof	PROPN
ejpam-2495	13	17	,	,	PUNCT
ejpam-2495	13	18	countably	countably	ADV
ejpam-2495	13	19	supra	supra	PROPN
ejpam-2495	13	20	bt	bt	PROPN
ejpam-2495	14	1	compact	compact	ADJ
ejpam-2495	14	2	and	and	CCONJ
ejpam-2495	14	3	supra	supra	PROPN
ejpam-2495	14	4	bt	bt	PROPN
ejpam-2495	14	5	-connected	-connected	ADJ
ejpam-2495	14	6	spaces	space	NOUN
ejpam-2495	14	7	and	and	CCONJ
ejpam-2495	14	8	reviewed	review	VERB
ejpam-2495	14	9	several	several	ADJ
ejpam-2495	14	10	properties	property	NOUN
ejpam-2495	14	11	for	for	ADP
ejpam-2495	14	12	these	these	DET
ejpam-2495	14	13	concepts	concept	NOUN
ejpam-2495	14	14	.	.	PUNCT
ejpam-2495	15	1	2	2	X
ejpam-2495	15	2	.	.	X
ejpam-2495	15	3	preliminaries	preliminary	NOUN
ejpam-2495	15	4	definition	definition	NOUN
ejpam-2495	15	5	1	1	NUM
ejpam-2495	15	6	(	(	PUNCT
ejpam-2495	15	7	6,8	6,8	NUM
ejpam-2495	15	8	)	)	PUNCT
ejpam-2495	15	9	.	.	PUNCT
ejpam-2495	16	1	a	a	DET
ejpam-2495	16	2	subfamily	subfamily	NOUN
ejpam-2495	16	3	of	of	ADP
ejpam-2495	16	4	µ	µ	NOUN
ejpam-2495	16	5	of	of	ADP
ejpam-2495	16	6	x	x	VERB
ejpam-2495	16	7	is	be	AUX
ejpam-2495	16	8	said	say	VERB
ejpam-2495	16	9	to	to	PART
ejpam-2495	16	10	be	be	AUX
ejpam-2495	16	11	a	a	DET
ejpam-2495	16	12	supra	supra	ADJ
ejpam-2495	16	13	topology	topology	NOUN
ejpam-2495	16	14	on	on	ADP
ejpam-2495	16	15	x	x	SYM
ejpam-2495	16	16	,	,	PUNCT
ejpam-2495	16	17	if	if	SCONJ
ejpam-2495	16	18	(	(	PUNCT
ejpam-2495	16	19	i	i	NOUN
ejpam-2495	16	20	)	)	PUNCT
ejpam-2495	16	21	x	x	NOUN
ejpam-2495	16	22	,	,	PUNCT
ejpam-2495	16	23	φεµ	φεµ	ADJ
ejpam-2495	16	24	(	(	PUNCT
ejpam-2495	16	25	ii	ii	NOUN
ejpam-2495	16	26	)	)	PUNCT
ejpam-2495	16	27	if	if	SCONJ
ejpam-2495	16	28	aiεµ	aiεµ	PROPN
ejpam-2495	16	29	for	for	ADP
ejpam-2495	16	30	all	all	DET
ejpam-2495	16	31	iε	iε	PROPN
ejpam-2495	16	32	j	j	PROPN
ejpam-2495	16	33	then	then	ADV
ejpam-2495	16	34	∪aiεµ.	∪aiεµ.	VERB
ejpam-2495	16	35	the	the	DET
ejpam-2495	16	36	pair	pair	NOUN
ejpam-2495	16	37	(	(	PUNCT
ejpam-2495	16	38	x,µ	x,µ	NOUN
ejpam-2495	16	39	)	)	PUNCT
ejpam-2495	16	40	is	be	AUX
ejpam-2495	16	41	called	call	VERB
ejpam-2495	16	42	supra	supra	PROPN
ejpam-2495	16	43	topological	topological	ADJ
ejpam-2495	16	44	space	space	NOUN
ejpam-2495	16	45	.	.	PUNCT
ejpam-2495	17	1	the	the	DET
ejpam-2495	17	2	elements	element	NOUN
ejpam-2495	17	3	of	of	ADP
ejpam-2495	17	4	µ	µ	NOUN
ejpam-2495	17	5	are	be	AUX
ejpam-2495	17	6	called	call	VERB
ejpam-2495	17	7	supra	supra	PROPN
ejpam-2495	17	8	open	open	ADJ
ejpam-2495	17	9	sets	set	NOUN
ejpam-2495	17	10	in	in	ADP
ejpam-2495	17	11	(	(	PUNCT
ejpam-2495	17	12	x,µ	x,µ	NOUN
ejpam-2495	17	13	)	)	PUNCT
ejpam-2495	17	14	and	and	CCONJ
ejpam-2495	17	15	complement	complement	NOUN
ejpam-2495	17	16	of	of	ADP
ejpam-2495	17	17	a	a	DET
ejpam-2495	17	18	supra	supra	ADJ
ejpam-2495	17	19	open	open	ADJ
ejpam-2495	17	20	set	set	NOUN
ejpam-2495	17	21	is	be	AUX
ejpam-2495	17	22	called	call	VERB
ejpam-2495	17	23	a	a	DET
ejpam-2495	17	24	supra	supra	NOUN
ejpam-2495	17	25	closed	close	VERB
ejpam-2495	17	26	set	set	NOUN
ejpam-2495	17	27	.	.	PUNCT
ejpam-2495	18	1	∗corresponding	∗corresponde	VERB
ejpam-2495	18	2	author	author	NOUN
ejpam-2495	18	3	.	.	PUNCT
ejpam-2495	19	1	email	email	NOUN
ejpam-2495	19	2	addresses	address	NOUN
ejpam-2495	19	3	:	:	PUNCT
ejpam-2495	19	4	krishnavenikaliswami@gmail.com	krishnavenikaliswami@gmail.com	X
ejpam-2495	19	5	(	(	PUNCT
ejpam-2495	19	6	k.krishna	k.krishna	NOUN
ejpam-2495	19	7	)	)	PUNCT
ejpam-2495	19	8	,	,	PUNCT
ejpam-2495	19	9	vignesh.mat@gmail.com	vignesh.mat@gmail.com	X
ejpam-2495	19	10	(	(	PUNCT
ejpam-2495	19	11	m.vignesh	m.vignesh	NOUN
ejpam-2495	19	12	)	)	PUNCT
ejpam-2495	19	13	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2495	20	1	323	323	NUM
ejpam-2495	20	2	c	c	X
ejpam-2495	20	3	©	©	PROPN
ejpam-2495	20	4	2017	2017	NUM
ejpam-2495	20	5	ejpam	ejpam	VERB
ejpam-2495	20	6	all	all	DET
ejpam-2495	20	7	rights	right	NOUN
ejpam-2495	20	8	reserved	reserve	VERB
ejpam-2495	20	9	.	.	PUNCT
ejpam-2495	21	1	k.krishna	k.krishna	NOUN
ejpam-2495	21	2	,	,	PUNCT
ejpam-2495	21	3	m.vignesh	m.vignesh	NOUN
ejpam-2495	21	4	/	/	SYM
ejpam-2495	21	5	eur	eur	PROPN
ejpam-2495	21	6	.	.	PUNCT
ejpam-2495	22	1	j.	j.	PROPN
ejpam-2495	22	2	pure	pure	PROPN
ejpam-2495	22	3	appl	appl	PROPN
ejpam-2495	22	4	.	.	PROPN
ejpam-2495	22	5	math	math	PROPN
ejpam-2495	22	6	,	,	PUNCT
ejpam-2495	22	7	10	10	NUM
ejpam-2495	22	8	(	(	PUNCT
ejpam-2495	22	9	2	2	NUM
ejpam-2495	22	10	)	)	PUNCT
ejpam-2495	22	11	(	(	PUNCT
ejpam-2495	22	12	2017	2017	NUM
ejpam-2495	22	13	)	)	PUNCT
ejpam-2495	22	14	,	,	PUNCT
ejpam-2495	22	15	323	323	NUM
ejpam-2495	22	16	-	-	SYM
ejpam-2495	22	17	334	334	NUM
ejpam-2495	22	18	324	324	NUM
ejpam-2495	22	19	definition	definition	NOUN
ejpam-2495	22	20	2	2	NUM
ejpam-2495	22	21	(	(	PUNCT
ejpam-2495	22	22	6	6	NUM
ejpam-2495	22	23	)	)	PUNCT
ejpam-2495	22	24	.	.	PUNCT
ejpam-2495	23	1	(	(	PUNCT
ejpam-2495	23	2	i	i	NOUN
ejpam-2495	23	3	)	)	PUNCT
ejpam-2495	23	4	the	the	DET
ejpam-2495	23	5	supra	supra	ADJ
ejpam-2495	23	6	closure	closure	NOUN
ejpam-2495	23	7	of	of	ADP
ejpam-2495	23	8	a	a	DET
ejpam-2495	23	9	set	set	NOUN
ejpam-2495	23	10	a	a	PRON
ejpam-2495	23	11	is	be	AUX
ejpam-2495	23	12	denoted	denote	VERB
ejpam-2495	23	13	by	by	ADP
ejpam-2495	23	14	clµ(a	clµ(a	PROPN
ejpam-2495	23	15	)	)	PUNCT
ejpam-2495	23	16	and	and	CCONJ
ejpam-2495	23	17	is	be	AUX
ejpam-2495	23	18	defined	define	VERB
ejpam-2495	23	19	as	as	ADP
ejpam-2495	23	20	clµ(a	clµ(a	PROPN
ejpam-2495	23	21	)	)	PUNCT
ejpam-2495	24	1	=	=	VERB
ejpam-2495	24	2	∩{b	∩{b	NOUN
ejpam-2495	24	3	:	:	PUNCT
ejpam-2495	24	4	b	b	X
ejpam-2495	24	5	is	be	AUX
ejpam-2495	24	6	a	a	DET
ejpam-2495	24	7	supra	supra	NOUN
ejpam-2495	24	8	closed	close	VERB
ejpam-2495	24	9	set	set	VERB
ejpam-2495	24	10	and	and	CCONJ
ejpam-2495	24	11	a	a	DET
ejpam-2495	24	12	⊆	⊆	NUM
ejpam-2495	24	13	b	b	NOUN
ejpam-2495	24	14	}	}	PUNCT
ejpam-2495	24	15	.	.	PUNCT
ejpam-2495	25	1	(	(	PUNCT
ejpam-2495	25	2	ii	ii	X
ejpam-2495	25	3	)	)	PUNCT
ejpam-2495	25	4	the	the	DET
ejpam-2495	25	5	supra	supra	PROPN
ejpam-2495	25	6	interior	interior	NOUN
ejpam-2495	25	7	of	of	ADP
ejpam-2495	25	8	a	a	DET
ejpam-2495	25	9	set	set	NOUN
ejpam-2495	25	10	a	a	PRON
ejpam-2495	25	11	is	be	AUX
ejpam-2495	25	12	denoted	denote	VERB
ejpam-2495	25	13	by	by	ADP
ejpam-2495	25	14	intµ(a	intµ(a	PROPN
ejpam-2495	25	15	)	)	PUNCT
ejpam-2495	25	16	and	and	CCONJ
ejpam-2495	25	17	defined	define	VERB
ejpam-2495	25	18	as	as	ADP
ejpam-2495	25	19	intµ(a	intµ(a	PROPN
ejpam-2495	25	20	)	)	PUNCT
ejpam-2495	25	21	=	=	X
ejpam-2495	26	1	∪{b	∪{b	NOUN
ejpam-2495	26	2	:	:	PUNCT
ejpam-2495	26	3	b	b	X
ejpam-2495	26	4	is	be	AUX
ejpam-2495	26	5	a	a	DET
ejpam-2495	26	6	supra	supra	ADJ
ejpam-2495	26	7	open	open	ADJ
ejpam-2495	26	8	set	set	NOUN
ejpam-2495	26	9	and	and	CCONJ
ejpam-2495	26	10	a	a	DET
ejpam-2495	26	11	⊇	⊇	ADJ
ejpam-2495	26	12	b	b	NOUN
ejpam-2495	26	13	}	}	PUNCT
ejpam-2495	26	14	.	.	PUNCT
ejpam-2495	27	1	definition	definition	NOUN
ejpam-2495	27	2	3	3	NUM
ejpam-2495	27	3	(	(	PUNCT
ejpam-2495	27	4	8)	8)	NUM
ejpam-2495	27	5	.	.	PUNCT
ejpam-2495	28	1	let	let	AUX
ejpam-2495	28	2	(	(	PUNCT
ejpam-2495	28	3	x	x	X
ejpam-2495	28	4	,	,	PUNCT
ejpam-2495	28	5	τ	τ	X
ejpam-2495	28	6	)	)	PUNCT
ejpam-2495	28	7	be	be	VERB
ejpam-2495	28	8	a	a	DET
ejpam-2495	28	9	topological	topological	ADJ
ejpam-2495	28	10	spaces	space	NOUN
ejpam-2495	28	11	and	and	CCONJ
ejpam-2495	28	12	µ	µ	PRON
ejpam-2495	28	13	be	be	AUX
ejpam-2495	28	14	a	a	DET
ejpam-2495	28	15	supra	supra	ADJ
ejpam-2495	28	16	topolgy	topolgy	VERB
ejpam-2495	28	17	on	on	ADP
ejpam-2495	28	18	x.	x.	NOUN
ejpam-2495	28	19	we	we	PRON
ejpam-2495	28	20	call	call	VERB
ejpam-2495	28	21	µ	µ	PRON
ejpam-2495	28	22	a	a	DET
ejpam-2495	28	23	supra	supra	ADJ
ejpam-2495	28	24	topology	topology	NOUN
ejpam-2495	28	25	associated	associate	VERB
ejpam-2495	28	26	with	with	ADP
ejpam-2495	28	27	τ	τ	PROPN
ejpam-2495	28	28	if	if	SCONJ
ejpam-2495	28	29	τ	τ	PROPN
ejpam-2495	28	30	⊂	⊂	PROPN
ejpam-2495	28	31	µ.	µ.	PROPN
ejpam-2495	28	32	definition	definition	NOUN
ejpam-2495	28	33	4	4	NUM
ejpam-2495	28	34	(	(	PUNCT
ejpam-2495	28	35	8)	8)	NUM
ejpam-2495	28	36	.	.	PUNCT
ejpam-2495	29	1	let	let	AUX
ejpam-2495	29	2	(	(	PUNCT
ejpam-2495	29	3	x,µ	x,µ	NOUN
ejpam-2495	29	4	)	)	PUNCT
ejpam-2495	29	5	be	be	VERB
ejpam-2495	29	6	a	a	DET
ejpam-2495	29	7	supra	supra	ADJ
ejpam-2495	29	8	topological	topological	ADJ
ejpam-2495	29	9	space	space	NOUN
ejpam-2495	29	10	.	.	PUNCT
ejpam-2495	30	1	a	a	DET
ejpam-2495	30	2	set	set	NOUN
ejpam-2495	30	3	a	a	PRON
ejpam-2495	30	4	is	be	AUX
ejpam-2495	30	5	called	call	VERB
ejpam-2495	30	6	a	a	DET
ejpam-2495	30	7	supra	supra	PROPN
ejpam-2495	30	8	b	b	NOUN
ejpam-2495	30	9	-	-	PUNCT
ejpam-2495	30	10	open	open	ADJ
ejpam-2495	30	11	set	set	NOUN
ejpam-2495	30	12	if	if	SCONJ
ejpam-2495	30	13	a	a	DET
ejpam-2495	30	14	⊆	⊆	NUM
ejpam-2495	30	15	clµ(intµ(a	clµ(intµ(a	NOUN
ejpam-2495	30	16	)	)	PUNCT
ejpam-2495	30	17	)	)	PUNCT
ejpam-2495	30	18	∪	∪	ADP
ejpam-2495	30	19	intµ(clµ(a	intµ(clµ(a	NOUN
ejpam-2495	30	20	)	)	PUNCT
ejpam-2495	30	21	)	)	PUNCT
ejpam-2495	30	22	.	.	PUNCT
ejpam-2495	31	1	the	the	DET
ejpam-2495	31	2	complement	complement	NOUN
ejpam-2495	31	3	of	of	ADP
ejpam-2495	31	4	a	a	DET
ejpam-2495	31	5	supra	supra	PROPN
ejpam-2495	31	6	b	b	NOUN
ejpam-2495	31	7	-	-	PUNCT
ejpam-2495	31	8	open	open	ADJ
ejpam-2495	31	9	set	set	NOUN
ejpam-2495	31	10	is	be	AUX
ejpam-2495	31	11	called	call	VERB
ejpam-2495	31	12	a	a	DET
ejpam-2495	31	13	supra	supra	PROPN
ejpam-2495	31	14	b	b	PROPN
ejpam-2495	31	15	-	-	PUNCT
ejpam-2495	31	16	closed	closed	ADJ
ejpam-2495	31	17	set	set	NOUN
ejpam-2495	31	18	.	.	PUNCT
ejpam-2495	32	1	definition	definition	NOUN
ejpam-2495	32	2	5	5	NUM
ejpam-2495	32	3	(	(	PUNCT
ejpam-2495	32	4	4	4	NUM
ejpam-2495	32	5	)	)	PUNCT
ejpam-2495	32	6	.	.	PUNCT
ejpam-2495	33	1	a	a	DET
ejpam-2495	33	2	subset	subset	NOUN
ejpam-2495	33	3	a	a	PRON
ejpam-2495	33	4	of	of	ADP
ejpam-2495	33	5	a	a	DET
ejpam-2495	33	6	supra	supra	PROPN
ejpam-2495	33	7	topological	topological	PROPN
ejpam-2495	33	8	space(x,µ	space(x,µ	PROPN
ejpam-2495	33	9	)	)	PUNCT
ejpam-2495	33	10	is	be	AUX
ejpam-2495	33	11	called	call	VERB
ejpam-2495	33	12	btµ-closed	btµ-closed	ADJ
ejpam-2495	33	13	set	set	NOUN
ejpam-2495	33	14	if	if	SCONJ
ejpam-2495	33	15	bclµ(a	bclµ(a	PROPN
ejpam-2495	33	16	)	)	PUNCT
ejpam-2495	34	1	⊂	⊂	PROPN
ejpam-2495	34	2	u	u	NOUN
ejpam-2495	34	3	whenever	whenever	SCONJ
ejpam-2495	34	4	a⊂	a⊂	PUNCT
ejpam-2495	34	5	u	u	NOUN
ejpam-2495	34	6	and	and	CCONJ
ejpam-2495	34	7	u	u	NOUN
ejpam-2495	34	8	is	be	AUX
ejpam-2495	34	9	tµopen	tµopen	ADJ
ejpam-2495	34	10	in	in	ADP
ejpam-2495	34	11	(	(	PUNCT
ejpam-2495	34	12	x,µ	x,µ	NOUN
ejpam-2495	34	13	)	)	PUNCT
ejpam-2495	34	14	.	.	PUNCT
ejpam-2495	35	1	definition	definition	NOUN
ejpam-2495	35	2	6	6	NUM
ejpam-2495	35	3	(	(	PUNCT
ejpam-2495	35	4	4	4	NUM
ejpam-2495	35	5	)	)	PUNCT
ejpam-2495	35	6	.	.	PUNCT
ejpam-2495	36	1	let	let	VERB
ejpam-2495	36	2	(	(	PUNCT
ejpam-2495	36	3	x	x	X
ejpam-2495	36	4	,	,	PUNCT
ejpam-2495	36	5	τ	τ	X
ejpam-2495	36	6	)	)	PUNCT
ejpam-2495	36	7	and	and	CCONJ
ejpam-2495	36	8	(	(	PUNCT
ejpam-2495	36	9	y	y	PROPN
ejpam-2495	36	10	,	,	PUNCT
ejpam-2495	36	11	σ	σ	PROPN
ejpam-2495	36	12	)	)	PUNCT
ejpam-2495	36	13	be	be	VERB
ejpam-2495	36	14	two	two	NUM
ejpam-2495	36	15	topological	topological	ADJ
ejpam-2495	36	16	spaces	space	NOUN
ejpam-2495	36	17	and	and	CCONJ
ejpam-2495	36	18	µ	µ	PRON
ejpam-2495	36	19	be	be	AUX
ejpam-2495	36	20	an	an	DET
ejpam-2495	36	21	associated	associated	ADJ
ejpam-2495	36	22	supra	supra	NOUN
ejpam-2495	36	23	topology	topology	NOUN
ejpam-2495	36	24	with	with	ADP
ejpam-2495	36	25	τ	τ	PROPN
ejpam-2495	36	26	.	.	PUNCT
ejpam-2495	37	1	a	a	DET
ejpam-2495	37	2	function	function	NOUN
ejpam-2495	37	3	f:(x	f:(x	PROPN
ejpam-2495	37	4	,	,	PUNCT
ejpam-2495	37	5	τ	τ	PROPN
ejpam-2495	37	6	)	)	PUNCT
ejpam-2495	37	7	→(y	→(y	PROPN
ejpam-2495	37	8	,	,	PUNCT
ejpam-2495	37	9	σ	σ	PROPN
ejpam-2495	37	10	)	)	PUNCT
ejpam-2495	37	11	is	be	AUX
ejpam-2495	37	12	called	call	VERB
ejpam-2495	37	13	btµ	btµ	NOUN
ejpam-2495	37	14	continuous	continuous	ADJ
ejpam-2495	37	15	if	if	SCONJ
ejpam-2495	37	16	f−1(v	f−1(v	PROPN
ejpam-2495	37	17	)	)	PUNCT
ejpam-2495	37	18	is	be	AUX
ejpam-2495	37	19	btµ	btµ	NOUN
ejpam-2495	37	20	closed	close	VERB
ejpam-2495	37	21	in	in	ADP
ejpam-2495	37	22	(	(	PUNCT
ejpam-2495	37	23	x	x	X
ejpam-2495	37	24	,	,	PUNCT
ejpam-2495	37	25	τ	τ	X
ejpam-2495	37	26	)	)	PUNCT
ejpam-2495	37	27	for	for	SCONJ
ejpam-2495	37	28	every	every	DET
ejpam-2495	37	29	supra	supra	NOUN
ejpam-2495	37	30	closed	close	VERB
ejpam-2495	37	31	set	set	VERB
ejpam-2495	37	32	v	v	NOUN
ejpam-2495	37	33	of	of	ADP
ejpam-2495	37	34	(	(	PUNCT
ejpam-2495	37	35	y	y	PROPN
ejpam-2495	37	36	,	,	PUNCT
ejpam-2495	37	37	σ	σ	PROPN
ejpam-2495	37	38	)	)	PUNCT
ejpam-2495	37	39	.	.	PUNCT
ejpam-2495	38	1	definition	definition	NOUN
ejpam-2495	38	2	7	7	NUM
ejpam-2495	38	3	(	(	PUNCT
ejpam-2495	38	4	4	4	NUM
ejpam-2495	38	5	)	)	PUNCT
ejpam-2495	38	6	.	.	PUNCT
ejpam-2495	39	1	let	let	VERB
ejpam-2495	39	2	(	(	PUNCT
ejpam-2495	39	3	x	x	X
ejpam-2495	39	4	,	,	PUNCT
ejpam-2495	39	5	τ	τ	X
ejpam-2495	39	6	)	)	PUNCT
ejpam-2495	39	7	and	and	CCONJ
ejpam-2495	39	8	(	(	PUNCT
ejpam-2495	39	9	y	y	PROPN
ejpam-2495	39	10	,	,	PUNCT
ejpam-2495	39	11	σ	σ	PROPN
ejpam-2495	39	12	)	)	PUNCT
ejpam-2495	39	13	be	be	VERB
ejpam-2495	39	14	two	two	NUM
ejpam-2495	39	15	topological	topological	ADJ
ejpam-2495	39	16	spaces	space	NOUN
ejpam-2495	39	17	and	and	CCONJ
ejpam-2495	39	18	µ	µ	PRON
ejpam-2495	39	19	be	be	AUX
ejpam-2495	39	20	an	an	DET
ejpam-2495	39	21	associated	associated	ADJ
ejpam-2495	39	22	supra	supra	NOUN
ejpam-2495	39	23	topology	topology	NOUN
ejpam-2495	39	24	with	with	ADP
ejpam-2495	39	25	τ	τ	PROPN
ejpam-2495	39	26	.	.	PUNCT
ejpam-2495	40	1	a	a	DET
ejpam-2495	40	2	function	function	NOUN
ejpam-2495	40	3	f:(x	f:(x	NOUN
ejpam-2495	40	4	,	,	PUNCT
ejpam-2495	40	5	τ)→(y	τ)→(y	PROPN
ejpam-2495	40	6	,	,	PUNCT
ejpam-2495	40	7	σ	σ	PROPN
ejpam-2495	40	8	)	)	PUNCT
ejpam-2495	40	9	is	be	AUX
ejpam-2495	40	10	called	call	VERB
ejpam-2495	40	11	btµ	btµ	NOUN
ejpam-2495	40	12	irresolute	irresolute	VERB
ejpam-2495	40	13	if	if	SCONJ
ejpam-2495	40	14	f−1(v	f−1(v	PROPN
ejpam-2495	40	15	)	)	PUNCT
ejpam-2495	40	16	is	be	AUX
ejpam-2495	40	17	btµ	btµ	NOUN
ejpam-2495	40	18	closed	close	VERB
ejpam-2495	40	19	in	in	ADP
ejpam-2495	40	20	(	(	PUNCT
ejpam-2495	40	21	x	x	X
ejpam-2495	40	22	,	,	PUNCT
ejpam-2495	40	23	τ	τ	X
ejpam-2495	40	24	)	)	PUNCT
ejpam-2495	40	25	for	for	SCONJ
ejpam-2495	40	26	every	every	DET
ejpam-2495	40	27	btµ	btµ	NOUN
ejpam-2495	40	28	closed	close	VERB
ejpam-2495	40	29	set	set	VERB
ejpam-2495	40	30	v	v	ADP
ejpam-2495	40	31	of	of	ADP
ejpam-2495	40	32	(	(	PUNCT
ejpam-2495	40	33	y	y	PROPN
ejpam-2495	40	34	,	,	PUNCT
ejpam-2495	40	35	σ	σ	PROPN
ejpam-2495	40	36	)	)	PUNCT
ejpam-2495	40	37	.	.	PUNCT
ejpam-2495	41	1	definition	definition	NOUN
ejpam-2495	41	2	8	8	NUM
ejpam-2495	41	3	(	(	PUNCT
ejpam-2495	41	4	4	4	NUM
ejpam-2495	41	5	)	)	PUNCT
ejpam-2495	41	6	.	.	PUNCT
ejpam-2495	42	1	a	a	DET
ejpam-2495	42	2	supra	supra	PROPN
ejpam-2495	42	3	topological	topological	ADJ
ejpam-2495	42	4	space	space	NOUN
ejpam-2495	42	5	(	(	PUNCT
ejpam-2495	42	6	x,µ	x,µ	NOUN
ejpam-2495	42	7	)	)	PUNCT
ejpam-2495	42	8	is	be	AUX
ejpam-2495	42	9	called	call	VERB
ejpam-2495	42	10	btt	btt	PROPN
ejpam-2495	42	11	µ	µ	PROPN
ejpam-2495	42	12	c	c	NOUN
ejpam-2495	42	13	space	space	NOUN
ejpam-2495	42	14	,	,	PUNCT
ejpam-2495	42	15	if	if	SCONJ
ejpam-2495	42	16	every	every	DET
ejpam-2495	42	17	btµclosed	btµclose	VERB
ejpam-2495	42	18	set	set	NOUN
ejpam-2495	42	19	is	be	AUX
ejpam-2495	42	20	supra	supra	NOUN
ejpam-2495	42	21	closed	close	VERB
ejpam-2495	42	22	set	set	NOUN
ejpam-2495	42	23	.	.	PUNCT
ejpam-2495	43	1	definition	definition	NOUN
ejpam-2495	43	2	9	9	NUM
ejpam-2495	43	3	(	(	PUNCT
ejpam-2495	43	4	5	5	NUM
ejpam-2495	43	5	)	)	PUNCT
ejpam-2495	43	6	.	.	PUNCT
ejpam-2495	44	1	let	let	VERB
ejpam-2495	44	2	(	(	PUNCT
ejpam-2495	44	3	x	x	X
ejpam-2495	44	4	,	,	PUNCT
ejpam-2495	44	5	τ	τ	X
ejpam-2495	44	6	)	)	PUNCT
ejpam-2495	44	7	and	and	CCONJ
ejpam-2495	44	8	(	(	PUNCT
ejpam-2495	44	9	y	y	PROPN
ejpam-2495	44	10	,	,	PUNCT
ejpam-2495	44	11	σ	σ	PROPN
ejpam-2495	44	12	)	)	PUNCT
ejpam-2495	44	13	be	be	VERB
ejpam-2495	44	14	two	two	NUM
ejpam-2495	44	15	topological	topological	ADJ
ejpam-2495	44	16	spaces	space	NOUN
ejpam-2495	44	17	and	and	CCONJ
ejpam-2495	44	18	µ	µ	PRON
ejpam-2495	44	19	be	be	AUX
ejpam-2495	44	20	an	an	DET
ejpam-2495	44	21	associated	associated	ADJ
ejpam-2495	44	22	supra	supra	NOUN
ejpam-2495	44	23	topology	topology	NOUN
ejpam-2495	44	24	with	with	ADP
ejpam-2495	44	25	τ	τ	PROPN
ejpam-2495	44	26	.	.	PUNCT
ejpam-2495	45	1	a	a	DET
ejpam-2495	45	2	function	function	NOUN
ejpam-2495	45	3	f:(x	f:(x	PROPN
ejpam-2495	45	4	,	,	PUNCT
ejpam-2495	45	5	τ	τ	PROPN
ejpam-2495	45	6	)	)	PUNCT
ejpam-2495	45	7	→(y	→(y	PROPN
ejpam-2495	45	8	,	,	PUNCT
ejpam-2495	45	9	σ	σ	PROPN
ejpam-2495	45	10	)	)	PUNCT
ejpam-2495	45	11	is	be	AUX
ejpam-2495	45	12	called	call	VERB
ejpam-2495	45	13	strongly	strongly	ADV
ejpam-2495	45	14	btµ	btµ	NOUN
ejpam-2495	45	15	continuous	continuous	ADJ
ejpam-2495	45	16	if	if	SCONJ
ejpam-2495	45	17	the	the	DET
ejpam-2495	45	18	inverse	inverse	ADJ
ejpam-2495	45	19	image	image	NOUN
ejpam-2495	45	20	of	of	ADP
ejpam-2495	45	21	every	every	DET
ejpam-2495	45	22	btµ-closed	btµ-close	VERB
ejpam-2495	45	23	in	in	ADP
ejpam-2495	45	24	y	y	PROPN
ejpam-2495	45	25	is	be	AUX
ejpam-2495	45	26	supra	supra	PROPN
ejpam-2495	45	27	closed	close	VERB
ejpam-2495	45	28	in	in	ADP
ejpam-2495	45	29	x.	x.	NOUN
ejpam-2495	45	30	definition	definition	NOUN
ejpam-2495	45	31	10	10	NUM
ejpam-2495	45	32	(	(	PUNCT
ejpam-2495	45	33	5	5	NUM
ejpam-2495	45	34	)	)	PUNCT
ejpam-2495	45	35	.	.	PUNCT
ejpam-2495	46	1	let	let	VERB
ejpam-2495	46	2	(	(	PUNCT
ejpam-2495	46	3	x	x	X
ejpam-2495	46	4	,	,	PUNCT
ejpam-2495	46	5	τ	τ	X
ejpam-2495	46	6	)	)	PUNCT
ejpam-2495	46	7	and	and	CCONJ
ejpam-2495	46	8	(	(	PUNCT
ejpam-2495	46	9	y	y	PROPN
ejpam-2495	46	10	,	,	PUNCT
ejpam-2495	46	11	σ	σ	PROPN
ejpam-2495	46	12	)	)	PUNCT
ejpam-2495	46	13	be	be	VERB
ejpam-2495	46	14	two	two	NUM
ejpam-2495	46	15	topological	topological	ADJ
ejpam-2495	46	16	spaces	space	NOUN
ejpam-2495	46	17	and	and	CCONJ
ejpam-2495	46	18	µ	µ	PRON
ejpam-2495	46	19	be	be	AUX
ejpam-2495	46	20	an	an	DET
ejpam-2495	46	21	associated	associated	ADJ
ejpam-2495	46	22	supra	supra	NOUN
ejpam-2495	46	23	topology	topology	NOUN
ejpam-2495	46	24	with	with	ADP
ejpam-2495	46	25	τ	τ	PROPN
ejpam-2495	46	26	.	.	PUNCT
ejpam-2495	47	1	a	a	DET
ejpam-2495	47	2	function	function	NOUN
ejpam-2495	47	3	f:(x	f:(x	PROPN
ejpam-2495	47	4	,	,	PUNCT
ejpam-2495	47	5	τ	τ	PROPN
ejpam-2495	47	6	)	)	PUNCT
ejpam-2495	47	7	→(y	→(y	PROPN
ejpam-2495	47	8	,	,	PUNCT
ejpam-2495	47	9	σ	σ	PROPN
ejpam-2495	47	10	)	)	PUNCT
ejpam-2495	47	11	is	be	AUX
ejpam-2495	47	12	called	call	VERB
ejpam-2495	47	13	perfectly	perfectly	ADV
ejpam-2495	47	14	btµ	btµ	NOUN
ejpam-2495	47	15	continuous	continuous	ADJ
ejpam-2495	47	16	if	if	SCONJ
ejpam-2495	47	17	the	the	DET
ejpam-2495	47	18	inverse	inverse	ADJ
ejpam-2495	47	19	image	image	NOUN
ejpam-2495	47	20	of	of	ADP
ejpam-2495	47	21	every	every	DET
ejpam-2495	47	22	btµ-closed	btµ-close	VERB
ejpam-2495	47	23	in	in	ADP
ejpam-2495	47	24	y	y	PROPN
ejpam-2495	47	25	is	be	AUX
ejpam-2495	47	26	both	both	PRON
ejpam-2495	47	27	supra	supra	PROPN
ejpam-2495	47	28	closed	closed	ADJ
ejpam-2495	47	29	and	and	CCONJ
ejpam-2495	47	30	supra	supra	NOUN
ejpam-2495	47	31	open	open	ADJ
ejpam-2495	47	32	in	in	ADP
ejpam-2495	47	33	x.	x.	PROPN
ejpam-2495	47	34	3	3	NUM
ejpam-2495	47	35	.	.	PUNCT
ejpam-2495	47	36	supra	supra	PROPN
ejpam-2495	47	37	bt	bt	PROPN
ejpam-2495	47	38	compactness	compactness	NOUN
ejpam-2495	47	39	definition	definition	NOUN
ejpam-2495	47	40	11	11	NUM
ejpam-2495	47	41	.	.	PUNCT
ejpam-2495	48	1	a	a	DET
ejpam-2495	48	2	collection	collection	NOUN
ejpam-2495	48	3	{	{	PUNCT
ejpam-2495	48	4	ai	ai	NOUN
ejpam-2495	48	5	:	:	PUNCT
ejpam-2495	48	6	i	i	PRON
ejpam-2495	48	7	∈	∈	VERB
ejpam-2495	48	8	i	i	X
ejpam-2495	48	9	}	}	PUNCT
ejpam-2495	48	10	of	of	ADP
ejpam-2495	48	11	btµ	btµ	NOUN
ejpam-2495	48	12	open	open	ADJ
ejpam-2495	48	13	sets	set	NOUN
ejpam-2495	48	14	in	in	ADP
ejpam-2495	48	15	a	a	DET
ejpam-2495	48	16	supra	supra	ADJ
ejpam-2495	48	17	topological	topological	ADJ
ejpam-2495	48	18	space	space	NOUN
ejpam-2495	48	19	(	(	PUNCT
ejpam-2495	48	20	x,µ	x,µ	NOUN
ejpam-2495	48	21	)	)	PUNCT
ejpam-2495	48	22	is	be	AUX
ejpam-2495	48	23	called	call	VERB
ejpam-2495	48	24	a	a	DET
ejpam-2495	48	25	btµ-open	btµ-open	ADJ
ejpam-2495	48	26	cover	cover	NOUN
ejpam-2495	48	27	of	of	ADP
ejpam-2495	48	28	a	a	DET
ejpam-2495	48	29	subset	subset	NOUN
ejpam-2495	48	30	b	b	NOUN
ejpam-2495	48	31	of	of	ADP
ejpam-2495	48	32	x	x	PRON
ejpam-2495	48	33	if	if	SCONJ
ejpam-2495	48	34	b⊂	b⊂	PROPN
ejpam-2495	48	35	⋃	⋃	PROPN
ejpam-2495	48	36	{	{	PUNCT
ejpam-2495	48	37	ai	ai	NOUN
ejpam-2495	48	38	:	:	PUNCT
ejpam-2495	48	39	i	i	PRON
ejpam-2495	48	40	∈	∈	VERB
ejpam-2495	49	1	i	i	PRON
ejpam-2495	49	2	}	}	PUNCT
ejpam-2495	49	3	holds	hold	VERB
ejpam-2495	49	4	.	.	PUNCT
ejpam-2495	50	1	definition	definition	NOUN
ejpam-2495	50	2	12	12	NUM
ejpam-2495	50	3	.	.	PUNCT
ejpam-2495	51	1	a	a	DET
ejpam-2495	51	2	supra	supra	PROPN
ejpam-2495	51	3	topological	topological	ADJ
ejpam-2495	51	4	space	space	NOUN
ejpam-2495	51	5	(	(	PUNCT
ejpam-2495	51	6	x,µ	x,µ	NOUN
ejpam-2495	51	7	)	)	PUNCT
ejpam-2495	51	8	is	be	AUX
ejpam-2495	51	9	btµ	btµ	NOUN
ejpam-2495	51	10	compact	compact	ADJ
ejpam-2495	51	11	if	if	SCONJ
ejpam-2495	51	12	every	every	DET
ejpam-2495	51	13	btµ	btµ	NOUN
ejpam-2495	51	14	open	open	ADJ
ejpam-2495	51	15	cover	cover	NOUN
ejpam-2495	51	16	of	of	ADP
ejpam-2495	51	17	x	x	PUNCT
ejpam-2495	51	18	has	have	VERB
ejpam-2495	51	19	a	a	DET
ejpam-2495	51	20	finite	finite	ADJ
ejpam-2495	51	21	subcover	subcover	PROPN
ejpam-2495	51	22	.	.	PUNCT
ejpam-2495	52	1	definition	definition	NOUN
ejpam-2495	52	2	13	13	NUM
ejpam-2495	52	3	.	.	PUNCT
ejpam-2495	53	1	a	a	DET
ejpam-2495	53	2	subset	subset	NOUN
ejpam-2495	53	3	b	b	NOUN
ejpam-2495	53	4	of	of	ADP
ejpam-2495	53	5	a	a	DET
ejpam-2495	53	6	supra	supra	ADJ
ejpam-2495	53	7	topological	topological	ADJ
ejpam-2495	53	8	space	space	NOUN
ejpam-2495	53	9	(	(	PUNCT
ejpam-2495	53	10	x,µ	x,µ	NOUN
ejpam-2495	53	11	)	)	PUNCT
ejpam-2495	53	12	is	be	AUX
ejpam-2495	53	13	said	say	VERB
ejpam-2495	53	14	to	to	PART
ejpam-2495	53	15	be	be	AUX
ejpam-2495	53	16	btµ	btµ	PROPN
ejpam-2495	53	17	compact	compact	ADJ
ejpam-2495	53	18	relative	relative	ADJ
ejpam-2495	53	19	to	to	ADP
ejpam-2495	53	20	(	(	PUNCT
ejpam-2495	53	21	x,µ	x,µ	NOUN
ejpam-2495	53	22	)	)	PUNCT
ejpam-2495	53	23	if	if	SCONJ
ejpam-2495	53	24	,	,	PUNCT
ejpam-2495	53	25	for	for	SCONJ
ejpam-2495	53	26	every	every	DET
ejpam-2495	53	27	collection	collection	NOUN
ejpam-2495	53	28	{	{	PUNCT
ejpam-2495	53	29	ai	ai	INTJ
ejpam-2495	53	30	:	:	PUNCT
ejpam-2495	53	31	i	i	PRON
ejpam-2495	53	32	∈	∈	VERB
ejpam-2495	54	1	i	i	X
ejpam-2495	54	2	}	}	PUNCT
ejpam-2495	54	3	of	of	ADP
ejpam-2495	54	4	btµ	btµ	NOUN
ejpam-2495	54	5	open	open	ADJ
ejpam-2495	54	6	subsets	subset	NOUN
ejpam-2495	54	7	of	of	ADP
ejpam-2495	54	8	x	x	SYM
ejpam-2495	54	9	such	such	ADJ
ejpam-2495	54	10	that	that	SCONJ
ejpam-2495	54	11	b⊂	b⊂	PROPN
ejpam-2495	54	12	⋃	⋃	PROPN
ejpam-2495	54	13	{	{	PUNCT
ejpam-2495	54	14	ai	ai	NOUN
ejpam-2495	54	15	:	:	PUNCT
ejpam-2495	54	16	i	i	PRON
ejpam-2495	54	17	∈	∈	PROPN
ejpam-2495	55	1	i	i	PRON
ejpam-2495	55	2	}	}	PUNCT
ejpam-2495	55	3	there	there	PRON
ejpam-2495	55	4	exist	exist	VERB
ejpam-2495	55	5	a	a	DET
ejpam-2495	55	6	finite	finite	NOUN
ejpam-2495	55	7	subset	subset	NOUN
ejpam-2495	55	8	io	io	PROPN
ejpam-2495	55	9	of	of	ADP
ejpam-2495	55	10	i	i	PRON
ejpam-2495	55	11	such	such	ADJ
ejpam-2495	55	12	that	that	PRON
ejpam-2495	55	13	b	b	NOUN
ejpam-2495	55	14	⊆	⊆	NUM
ejpam-2495	55	15	⋃	⋃	NUM
ejpam-2495	55	16	{	{	PUNCT
ejpam-2495	55	17	ai	ai	VERB
ejpam-2495	55	18	:	:	PUNCT
ejpam-2495	55	19	i	i	PROPN
ejpam-2495	55	20	∈	∈	PROPN
ejpam-2495	55	21	io	io	NOUN
ejpam-2495	55	22	}	}	PUNCT
ejpam-2495	55	23	.	.	PUNCT
ejpam-2495	56	1	k.krishna	k.krishna	NOUN
ejpam-2495	56	2	,	,	PUNCT
ejpam-2495	56	3	m.vignesh	m.vignesh	NOUN
ejpam-2495	56	4	/	/	SYM
ejpam-2495	56	5	eur	eur	PROPN
ejpam-2495	56	6	.	.	PUNCT
ejpam-2495	57	1	j.	j.	PROPN
ejpam-2495	57	2	pure	pure	PROPN
ejpam-2495	57	3	appl	appl	PROPN
ejpam-2495	57	4	.	.	PROPN
ejpam-2495	57	5	math	math	PROPN
ejpam-2495	57	6	,	,	PUNCT
ejpam-2495	57	7	10	10	NUM
ejpam-2495	57	8	(	(	PUNCT
ejpam-2495	57	9	2	2	NUM
ejpam-2495	57	10	)	)	PUNCT
ejpam-2495	57	11	(	(	PUNCT
ejpam-2495	57	12	2017	2017	NUM
ejpam-2495	57	13	)	)	PUNCT
ejpam-2495	57	14	,	,	PUNCT
ejpam-2495	57	15	323	323	NUM
ejpam-2495	57	16	-	-	SYM
ejpam-2495	57	17	334	334	NUM
ejpam-2495	57	18	325	325	NUM
ejpam-2495	57	19	definition	definition	NOUN
ejpam-2495	57	20	14	14	NUM
ejpam-2495	57	21	.	.	PUNCT
ejpam-2495	58	1	a	a	DET
ejpam-2495	58	2	subset	subset	NOUN
ejpam-2495	58	3	b	b	NOUN
ejpam-2495	58	4	of	of	ADP
ejpam-2495	58	5	a	a	DET
ejpam-2495	58	6	supra	supra	ADJ
ejpam-2495	58	7	topological	topological	ADJ
ejpam-2495	58	8	space	space	NOUN
ejpam-2495	58	9	(	(	PUNCT
ejpam-2495	58	10	x,µ	x,µ	NOUN
ejpam-2495	58	11	)	)	PUNCT
ejpam-2495	58	12	is	be	AUX
ejpam-2495	58	13	said	say	VERB
ejpam-2495	58	14	to	to	PART
ejpam-2495	58	15	be	be	AUX
ejpam-2495	58	16	btµ	btµ	PROPN
ejpam-2495	58	17	compact	compact	ADJ
ejpam-2495	58	18	if	if	SCONJ
ejpam-2495	58	19	b	b	PROPN
ejpam-2495	58	20	is	be	AUX
ejpam-2495	58	21	btµ	btµ	NOUN
ejpam-2495	58	22	compact	compact	ADJ
ejpam-2495	58	23	as	as	ADP
ejpam-2495	58	24	a	a	DET
ejpam-2495	58	25	subspace	subspace	NOUN
ejpam-2495	58	26	of	of	ADP
ejpam-2495	58	27	x.	x.	PROPN
ejpam-2495	58	28	theorem	theorem	NOUN
ejpam-2495	58	29	1	1	NUM
ejpam-2495	58	30	.	.	PUNCT
ejpam-2495	59	1	every	every	DET
ejpam-2495	59	2	btµ	btµ	NOUN
ejpam-2495	59	3	compact	compact	ADJ
ejpam-2495	59	4	space	space	NOUN
ejpam-2495	59	5	is	be	AUX
ejpam-2495	59	6	supra	supra	ADJ
ejpam-2495	59	7	compact	compact	ADJ
ejpam-2495	59	8	.	.	PUNCT
ejpam-2495	60	1	proof	proof	NOUN
ejpam-2495	60	2	.	.	PUNCT
ejpam-2495	61	1	let	let	VERB
ejpam-2495	61	2	{	{	PUNCT
ejpam-2495	61	3	ai	ai	VERB
ejpam-2495	61	4	:	:	PUNCT
ejpam-2495	61	5	i	i	PRON
ejpam-2495	61	6	∈	∈	PROPN
ejpam-2495	61	7	i	i	PRON
ejpam-2495	61	8	}	}	PUNCT
ejpam-2495	61	9	be	be	VERB
ejpam-2495	61	10	a	a	DET
ejpam-2495	61	11	supra	supra	ADJ
ejpam-2495	61	12	open	open	ADJ
ejpam-2495	61	13	cover	cover	NOUN
ejpam-2495	61	14	of	of	ADP
ejpam-2495	61	15	(	(	PUNCT
ejpam-2495	61	16	x,µ	x,µ	NOUN
ejpam-2495	61	17	)	)	PUNCT
ejpam-2495	61	18	.	.	PUNCT
ejpam-2495	62	1	by	by	ADP
ejpam-2495	62	2	[	[	X
ejpam-2495	62	3	4	4	X
ejpam-2495	62	4	]	]	PUNCT
ejpam-2495	62	5	{	{	PUNCT
ejpam-2495	62	6	ai	ai	INTJ
ejpam-2495	62	7	:	:	PUNCT
ejpam-2495	62	8	i	i	PRON
ejpam-2495	62	9	∈	∈	PROPN
ejpam-2495	62	10	i	i	PRON
ejpam-2495	62	11	}	}	PUNCT
ejpam-2495	62	12	is	be	AUX
ejpam-2495	62	13	a	a	DET
ejpam-2495	62	14	btµ	btµ	NOUN
ejpam-2495	62	15	open	open	ADJ
ejpam-2495	62	16	cover	cover	NOUN
ejpam-2495	62	17	of	of	ADP
ejpam-2495	62	18	(	(	PUNCT
ejpam-2495	62	19	x,µ	x,µ	NOUN
ejpam-2495	62	20	)	)	PUNCT
ejpam-2495	62	21	.	.	PUNCT
ejpam-2495	63	1	since	since	SCONJ
ejpam-2495	63	2	(	(	PUNCT
ejpam-2495	63	3	x,µ	x,µ	NOUN
ejpam-2495	63	4	)	)	PUNCT
ejpam-2495	63	5	is	be	AUX
ejpam-2495	63	6	btµ	btµ	PROPN
ejpam-2495	63	7	compact	compact	ADJ
ejpam-2495	63	8	,	,	PUNCT
ejpam-2495	63	9	btµ	btµ	NOUN
ejpam-2495	63	10	open	open	ADJ
ejpam-2495	63	11	cover	cover	NOUN
ejpam-2495	63	12	{	{	PUNCT
ejpam-2495	63	13	ai	ai	VERB
ejpam-2495	63	14	:	:	PUNCT
ejpam-2495	63	15	i	i	PRON
ejpam-2495	63	16	∈	∈	VERB
ejpam-2495	64	1	i	i	X
ejpam-2495	64	2	}	}	PUNCT
ejpam-2495	64	3	of	of	ADP
ejpam-2495	64	4	(	(	PUNCT
ejpam-2495	64	5	x,µ	x,µ	NOUN
ejpam-2495	64	6	)	)	PUNCT
ejpam-2495	64	7	has	have	VERB
ejpam-2495	64	8	a	a	DET
ejpam-2495	64	9	finite	finite	ADJ
ejpam-2495	64	10	subcover	subcover	PROPN
ejpam-2495	64	11	say	say	VERB
ejpam-2495	64	12	{	{	PUNCT
ejpam-2495	64	13	ai	ai	VERB
ejpam-2495	64	14	:	:	PUNCT
ejpam-2495	64	15	i	i	NOUN
ejpam-2495	64	16	=	=	NOUN
ejpam-2495	64	17	1	1	NUM
ejpam-2495	64	18	,	,	PUNCT
ejpam-2495	64	19	2	2	NUM
ejpam-2495	64	20	,	,	PUNCT
ejpam-2495	64	21	·	·	PUNCT
ejpam-2495	64	22	·	·	PUNCT
ejpam-2495	64	23	·	·	PUNCT
ejpam-2495	64	24	,	,	PUNCT
ejpam-2495	64	25	n	n	CCONJ
ejpam-2495	64	26	}	}	PUNCT
ejpam-2495	64	27	for	for	ADP
ejpam-2495	64	28	x.	x.	NOUN
ejpam-2495	64	29	hence	hence	ADV
ejpam-2495	64	30	(	(	PUNCT
ejpam-2495	64	31	x,µ	x,µ	NOUN
ejpam-2495	64	32	)	)	PUNCT
ejpam-2495	64	33	is	be	AUX
ejpam-2495	64	34	a	a	DET
ejpam-2495	64	35	supra	supra	ADJ
ejpam-2495	64	36	compact	compact	ADJ
ejpam-2495	64	37	space	space	NOUN
ejpam-2495	64	38	.	.	PUNCT
ejpam-2495	65	1	theorem	theorem	NOUN
ejpam-2495	65	2	2	2	NUM
ejpam-2495	65	3	.	.	PUNCT
ejpam-2495	66	1	every	every	DET
ejpam-2495	66	2	btµ	btµ	NOUN
ejpam-2495	66	3	closed	close	VERB
ejpam-2495	66	4	subset	subset	NOUN
ejpam-2495	66	5	of	of	ADP
ejpam-2495	66	6	a	a	DET
ejpam-2495	66	7	btµ	btµ	NOUN
ejpam-2495	66	8	compact	compact	ADJ
ejpam-2495	66	9	space	space	NOUN
ejpam-2495	66	10	is	be	AUX
ejpam-2495	66	11	btµ	btµ	NOUN
ejpam-2495	66	12	compact	compact	ADJ
ejpam-2495	66	13	relative	relative	ADJ
ejpam-2495	66	14	to	to	ADP
ejpam-2495	66	15	x.	x.	NOUN
ejpam-2495	66	16	proof	proof	NOUN
ejpam-2495	66	17	.	.	PUNCT
ejpam-2495	67	1	let	let	VERB
ejpam-2495	67	2	a	a	DET
ejpam-2495	67	3	be	be	AUX
ejpam-2495	67	4	a	a	DET
ejpam-2495	67	5	btµ	btµ	NOUN
ejpam-2495	67	6	closed	close	VERB
ejpam-2495	67	7	subset	subset	NOUN
ejpam-2495	67	8	of	of	ADP
ejpam-2495	67	9	a	a	DET
ejpam-2495	67	10	supra	supra	ADJ
ejpam-2495	67	11	topological	topological	ADJ
ejpam-2495	67	12	space	space	NOUN
ejpam-2495	67	13	(	(	PUNCT
ejpam-2495	67	14	x,µ	x,µ	NOUN
ejpam-2495	67	15	)	)	PUNCT
ejpam-2495	67	16	.	.	PUNCT
ejpam-2495	68	1	then	then	ADV
ejpam-2495	68	2	ac	ac	PROPN
ejpam-2495	68	3	is	be	AUX
ejpam-2495	68	4	btµ	btµ	NOUN
ejpam-2495	68	5	open	open	ADJ
ejpam-2495	68	6	in	in	ADP
ejpam-2495	68	7	(	(	PUNCT
ejpam-2495	68	8	x,µ	x,µ	NOUN
ejpam-2495	68	9	)	)	PUNCT
ejpam-2495	68	10	.	.	PUNCT
ejpam-2495	69	1	let	let	VERB
ejpam-2495	69	2	s	s	PRON
ejpam-2495	69	3	=	=	VERB
ejpam-2495	69	4	{	{	PUNCT
ejpam-2495	69	5	ai	ai	INTJ
ejpam-2495	69	6	:	:	PUNCT
ejpam-2495	69	7	i	i	PRON
ejpam-2495	69	8	∈	∈	PROPN
ejpam-2495	69	9	i	i	PRON
ejpam-2495	69	10	}	}	PUNCT
ejpam-2495	69	11	be	be	VERB
ejpam-2495	69	12	an	an	DET
ejpam-2495	69	13	btµ	btµ	NOUN
ejpam-2495	69	14	open	open	ADJ
ejpam-2495	69	15	cover	cover	NOUN
ejpam-2495	69	16	of	of	ADP
ejpam-2495	69	17	a	a	PRON
ejpam-2495	69	18	by	by	ADP
ejpam-2495	69	19	btµ	btµ	NOUN
ejpam-2495	69	20	open	open	NOUN
ejpam-2495	69	21	subset	subset	VERB
ejpam-2495	69	22	in	in	ADP
ejpam-2495	69	23	(	(	PUNCT
ejpam-2495	69	24	x,µ	x,µ	NOUN
ejpam-2495	69	25	)	)	PUNCT
ejpam-2495	69	26	.	.	PUNCT
ejpam-2495	70	1	let	let	VERB
ejpam-2495	70	2	s	s	PRON
ejpam-2495	70	3	*	*	PUNCT
ejpam-2495	70	4	=	=	PUNCT
ejpam-2495	70	5	s∪ac	s∪ac	PART
ejpam-2495	70	6	is	be	AUX
ejpam-2495	70	7	a	a	DET
ejpam-2495	70	8	btµ	btµ	NOUN
ejpam-2495	70	9	open	open	ADJ
ejpam-2495	70	10	cover	cover	NOUN
ejpam-2495	70	11	of	of	ADP
ejpam-2495	70	12	(	(	PUNCT
ejpam-2495	70	13	x,µ	x,µ	NOUN
ejpam-2495	70	14	)	)	PUNCT
ejpam-2495	70	15	.	.	PUNCT
ejpam-2495	71	1	that	that	PRON
ejpam-2495	71	2	is	be	AUX
ejpam-2495	71	3	x	x	X
ejpam-2495	71	4	=	=	PRON
ejpam-2495	71	5	(	(	PUNCT
ejpam-2495	71	6	⋃	⋃	PROPN
ejpam-2495	71	7	i∈i	i∈i	ADJ
ejpam-2495	71	8	ai	ai	NOUN
ejpam-2495	71	9	)	)	PUNCT
ejpam-2495	71	10	⋃	⋃	NOUN
ejpam-2495	71	11	ac	ac	NOUN
ejpam-2495	71	12	.	.	PUNCT
ejpam-2495	72	1	by	by	ADP
ejpam-2495	72	2	hypothesis	hypothesis	NOUN
ejpam-2495	72	3	(	(	PUNCT
ejpam-2495	72	4	x,µ	x,µ	NOUN
ejpam-2495	72	5	)	)	PUNCT
ejpam-2495	72	6	is	be	AUX
ejpam-2495	72	7	a	a	DET
ejpam-2495	72	8	btµcompact	btµcompact	NOUN
ejpam-2495	72	9	and	and	CCONJ
ejpam-2495	72	10	hence	hence	ADV
ejpam-2495	72	11	s	s	AUX
ejpam-2495	72	12	*	*	PUNCT
ejpam-2495	72	13	is	be	AUX
ejpam-2495	72	14	reducible	reducible	ADJ
ejpam-2495	72	15	to	to	ADP
ejpam-2495	72	16	a	a	DET
ejpam-2495	72	17	finite	finite	ADJ
ejpam-2495	72	18	sub	sub	NOUN
ejpam-2495	72	19	cover	cover	NOUN
ejpam-2495	72	20	of	of	ADP
ejpam-2495	72	21	(	(	PUNCT
ejpam-2495	72	22	x,µ	x,µ	NOUN
ejpam-2495	72	23	)	)	PUNCT
ejpam-2495	72	24	say	say	VERB
ejpam-2495	72	25	x	x	X
ejpam-2495	72	26	=	=	PUNCT
ejpam-2495	72	27	ai1	ai1	X
ejpam-2495	72	28	∪	∪	X
ejpam-2495	72	29	ai2∪	ai2∪	PROPN
ejpam-2495	72	30	,	,	PUNCT
ejpam-2495	72	31	·	·	PUNCT
ejpam-2495	72	32	·	·	PUNCT
ejpam-2495	72	33	·	·	PUNCT
ejpam-2495	72	34	,	,	PUNCT
ejpam-2495	73	1	∪ain	∪ain	VERB
ejpam-2495	73	2	∪	∪	PROPN
ejpam-2495	73	3	ac	ac	PROPN
ejpam-2495	73	4	,	,	PUNCT
ejpam-2495	73	5	aik	aik	NOUN
ejpam-2495	73	6	∈	∈	PROPN
ejpam-2495	73	7	s∗.	s∗.	ADJ
ejpam-2495	73	8	but	but	CCONJ
ejpam-2495	73	9	a	a	PRON
ejpam-2495	73	10	and	and	CCONJ
ejpam-2495	73	11	ac	ac	PROPN
ejpam-2495	73	12	are	be	AUX
ejpam-2495	73	13	disjoint	disjoint	ADJ
ejpam-2495	73	14	.	.	PUNCT
ejpam-2495	74	1	hence	hence	ADV
ejpam-2495	74	2	a	a	DET
ejpam-2495	74	3	⊂	⊂	ADV
ejpam-2495	74	4	ai1	ai1	X
ejpam-2495	74	5	∪ai2∪	∪ai2∪	AUX
ejpam-2495	74	6	,	,	PUNCT
ejpam-2495	74	7	·	·	PUNCT
ejpam-2495	74	8	·	·	PUNCT
ejpam-2495	74	9	·	·	PUNCT
ejpam-2495	74	10	,	,	PUNCT
ejpam-2495	74	11	∪ain	∪ain	NOUN
ejpam-2495	74	12	∈	∈	PROPN
ejpam-2495	74	13	s.	s.	PROPN
ejpam-2495	74	14	thus	thus	ADV
ejpam-2495	74	15	a	a	DET
ejpam-2495	74	16	btµ	btµ	NOUN
ejpam-2495	74	17	-open	-open	NOUN
ejpam-2495	74	18	cover	cover	NOUN
ejpam-2495	74	19	s	s	NOUN
ejpam-2495	74	20	of	of	ADP
ejpam-2495	74	21	a	a	PRON
ejpam-2495	74	22	contains	contain	VERB
ejpam-2495	74	23	a	a	DET
ejpam-2495	74	24	finite	finite	ADJ
ejpam-2495	74	25	subcover	subcover	PROPN
ejpam-2495	74	26	.	.	PUNCT
ejpam-2495	75	1	hence	hence	ADV
ejpam-2495	75	2	a	a	PRON
ejpam-2495	75	3	is	be	AUX
ejpam-2495	75	4	btµcompact	btµcompact	NOUN
ejpam-2495	75	5	relative	relative	ADJ
ejpam-2495	75	6	to	to	ADP
ejpam-2495	75	7	(	(	PUNCT
ejpam-2495	75	8	x,µ	x,µ	NOUN
ejpam-2495	75	9	)	)	PUNCT
ejpam-2495	75	10	.	.	PUNCT
ejpam-2495	76	1	theorem	theorem	NOUN
ejpam-2495	76	2	3	3	NUM
ejpam-2495	76	3	.	.	PUNCT
ejpam-2495	77	1	a	a	DET
ejpam-2495	77	2	btµ	btµ	NOUN
ejpam-2495	77	3	continuous	continuous	ADJ
ejpam-2495	77	4	image	image	NOUN
ejpam-2495	77	5	of	of	ADP
ejpam-2495	77	6	a	a	DET
ejpam-2495	77	7	btµ	btµ	NOUN
ejpam-2495	77	8	compact	compact	ADJ
ejpam-2495	77	9	space	space	NOUN
ejpam-2495	77	10	is	be	AUX
ejpam-2495	77	11	supra	supra	ADJ
ejpam-2495	77	12	compact	compact	ADJ
ejpam-2495	77	13	.	.	PUNCT
ejpam-2495	78	1	proof	proof	NOUN
ejpam-2495	78	2	.	.	PUNCT
ejpam-2495	79	1	let	let	VERB
ejpam-2495	79	2	f	f	X
ejpam-2495	79	3	:	:	PUNCT
ejpam-2495	79	4	x	x	X
ejpam-2495	79	5	→	→	SYM
ejpam-2495	79	6	y	y	X
ejpam-2495	79	7	be	be	AUX
ejpam-2495	79	8	a	a	DET
ejpam-2495	79	9	btµcontinuous	btµcontinuous	ADJ
ejpam-2495	79	10	map	map	NOUN
ejpam-2495	79	11	from	from	ADP
ejpam-2495	79	12	a	a	DET
ejpam-2495	79	13	btµ	btµ	NOUN
ejpam-2495	79	14	compact	compact	ADJ
ejpam-2495	79	15	x	x	X
ejpam-2495	79	16	onto	onto	ADP
ejpam-2495	79	17	a	a	DET
ejpam-2495	79	18	supra	supra	ADJ
ejpam-2495	79	19	topological	topological	ADJ
ejpam-2495	79	20	space	space	NOUN
ejpam-2495	79	21	y.	y.	PROPN
ejpam-2495	79	22	let	let	VERB
ejpam-2495	79	23	{	{	PUNCT
ejpam-2495	79	24	ai	ai	VERB
ejpam-2495	79	25	:	:	PUNCT
ejpam-2495	79	26	i	i	PRON
ejpam-2495	79	27	∈	∈	PROPN
ejpam-2495	80	1	i	i	PRON
ejpam-2495	80	2	}	}	PUNCT
ejpam-2495	80	3	be	be	VERB
ejpam-2495	80	4	a	a	DET
ejpam-2495	80	5	supra	supra	ADJ
ejpam-2495	80	6	open	open	ADJ
ejpam-2495	80	7	cover	cover	NOUN
ejpam-2495	80	8	of	of	ADP
ejpam-2495	80	9	y.	y.	NOUN
ejpam-2495	80	10	then	then	ADV
ejpam-2495	80	11	f−1	f−1	PROPN
ejpam-2495	80	12	{	{	PUNCT
ejpam-2495	80	13	ai	ai	VERB
ejpam-2495	80	14	:	:	PUNCT
ejpam-2495	80	15	i	i	PRON
ejpam-2495	80	16	∈	∈	PROPN
ejpam-2495	81	1	i	i	PRON
ejpam-2495	81	2	}	}	PUNCT
ejpam-2495	81	3	is	be	AUX
ejpam-2495	81	4	a	a	DET
ejpam-2495	81	5	btµ	btµ	NOUN
ejpam-2495	81	6	open	open	ADJ
ejpam-2495	81	7	cover	cover	NOUN
ejpam-2495	81	8	of	of	ADP
ejpam-2495	81	9	x	x	PRON
ejpam-2495	81	10	,	,	PUNCT
ejpam-2495	81	11	as	as	SCONJ
ejpam-2495	81	12	f	f	PROPN
ejpam-2495	81	13	is	be	AUX
ejpam-2495	81	14	btµ	btµ	NOUN
ejpam-2495	81	15	continuous	continuous	ADJ
ejpam-2495	81	16	.	.	PUNCT
ejpam-2495	82	1	since	since	SCONJ
ejpam-2495	82	2	x	x	PROPN
ejpam-2495	82	3	is	be	AUX
ejpam-2495	82	4	btµ	btµ	PROPN
ejpam-2495	82	5	compact	compact	ADJ
ejpam-2495	82	6	,	,	PUNCT
ejpam-2495	82	7	the	the	DET
ejpam-2495	82	8	btµ	btµ	NOUN
ejpam-2495	82	9	open	open	VERB
ejpam-2495	82	10	cover	cover	NOUN
ejpam-2495	82	11	of	of	ADP
ejpam-2495	82	12	x	x	X
ejpam-2495	82	13	,	,	PUNCT
ejpam-2495	82	14	f−1	f−1	PROPN
ejpam-2495	82	15	{	{	PUNCT
ejpam-2495	82	16	ai	ai	VERB
ejpam-2495	82	17	:	:	PUNCT
ejpam-2495	82	18	i	i	PRON
ejpam-2495	82	19	∈	∈	PROPN
ejpam-2495	83	1	i	i	PRON
ejpam-2495	83	2	}	}	PUNCT
ejpam-2495	83	3	has	have	VERB
ejpam-2495	83	4	a	a	DET
ejpam-2495	83	5	finite	finite	ADJ
ejpam-2495	83	6	sub	sub	NOUN
ejpam-2495	83	7	cover	cover	NOUN
ejpam-2495	83	8	say	say	VERB
ejpam-2495	83	9	{	{	PUNCT
ejpam-2495	83	10	f−1(ai	f−1(ai	NOUN
ejpam-2495	83	11	)	)	PUNCT
ejpam-2495	83	12	:	:	PUNCT
ejpam-2495	84	1	i	i	NOUN
ejpam-2495	84	2	=	=	NOUN
ejpam-2495	84	3	1	1	NUM
ejpam-2495	84	4	,	,	PUNCT
ejpam-2495	84	5	2	2	NUM
ejpam-2495	84	6	,	,	PUNCT
ejpam-2495	84	7	·	·	PUNCT
ejpam-2495	84	8	·	·	PUNCT
ejpam-2495	84	9	·	·	PUNCT
ejpam-2495	84	10	,	,	PUNCT
ejpam-2495	84	11	n	n	CCONJ
ejpam-2495	84	12	}	}	PUNCT
ejpam-2495	84	13	.	.	PUNCT
ejpam-2495	85	1	therefore	therefore	ADV
ejpam-2495	85	2	x	x	X
ejpam-2495	85	3	=	=	SYM
ejpam-2495	85	4	⋃n	⋃n	PROPN
ejpam-2495	85	5	i=1	i=1	PROPN
ejpam-2495	85	6	f	f	PROPN
ejpam-2495	85	7	−1(ai	−1(ai	NOUN
ejpam-2495	85	8	)	)	PUNCT
ejpam-2495	85	9	,	,	PUNCT
ejpam-2495	85	10	which	which	PRON
ejpam-2495	85	11	implies	imply	VERB
ejpam-2495	85	12	f(x	f(x	PROPN
ejpam-2495	85	13	)	)	PUNCT
ejpam-2495	86	1	=	=	PRON
ejpam-2495	86	2	n⋃	n⋃	VERB
ejpam-2495	86	3	i=1	i=1	PRON
ejpam-2495	86	4	(	(	PUNCT
ejpam-2495	86	5	ai	ai	NOUN
ejpam-2495	86	6	)	)	PUNCT
ejpam-2495	86	7	,	,	PUNCT
ejpam-2495	86	8	then	then	ADV
ejpam-2495	86	9	y	y	PROPN
ejpam-2495	86	10	=	=	PRON
ejpam-2495	86	11	n⋃	n⋃	VERB
ejpam-2495	86	12	i=1	i=1	PROPN
ejpam-2495	86	13	(	(	PUNCT
ejpam-2495	86	14	ai	ai	NOUN
ejpam-2495	86	15	)	)	PUNCT
ejpam-2495	86	16	.	.	PUNCT
ejpam-2495	87	1	that	that	PRON
ejpam-2495	87	2	is	be	AUX
ejpam-2495	87	3	{	{	PUNCT
ejpam-2495	87	4	a1	a1	PROPN
ejpam-2495	87	5	,	,	PUNCT
ejpam-2495	87	6	a2	a2	PROPN
ejpam-2495	87	7	,	,	PUNCT
ejpam-2495	87	8	·	·	PUNCT
ejpam-2495	87	9	·	·	PUNCT
ejpam-2495	87	10	·	·	PUNCT
ejpam-2495	87	11	,	,	PUNCT
ejpam-2495	87	12	an	an	PRON
ejpam-2495	87	13	}	}	PUNCT
ejpam-2495	87	14	is	be	AUX
ejpam-2495	87	15	a	a	DET
ejpam-2495	87	16	finite	finite	ADJ
ejpam-2495	87	17	sub	sub	NOUN
ejpam-2495	87	18	cover	cover	NOUN
ejpam-2495	87	19	of	of	ADP
ejpam-2495	87	20	{	{	PUNCT
ejpam-2495	87	21	ai	ai	INTJ
ejpam-2495	87	22	:	:	PUNCT
ejpam-2495	87	23	i	i	PRON
ejpam-2495	87	24	∈	∈	VERB
ejpam-2495	87	25	i	i	X
ejpam-2495	87	26	}	}	PUNCT
ejpam-2495	87	27	for	for	ADP
ejpam-2495	87	28	y.	y.	PROPN
ejpam-2495	87	29	hence	hence	ADV
ejpam-2495	87	30	y	y	PROPN
ejpam-2495	87	31	is	be	AUX
ejpam-2495	87	32	supra	supra	ADJ
ejpam-2495	87	33	compact	compact	ADJ
ejpam-2495	87	34	.	.	PUNCT
ejpam-2495	88	1	theorem	theorem	VERB
ejpam-2495	88	2	4	4	NUM
ejpam-2495	88	3	.	.	PUNCT
ejpam-2495	89	1	if	if	SCONJ
ejpam-2495	89	2	a	a	DET
ejpam-2495	89	3	map	map	NOUN
ejpam-2495	89	4	f	f	X
ejpam-2495	89	5	:	:	PUNCT
ejpam-2495	89	6	(	(	PUNCT
ejpam-2495	89	7	x	x	X
ejpam-2495	89	8	,	,	PUNCT
ejpam-2495	89	9	τ)→	τ)→	PROPN
ejpam-2495	89	10	(	(	PUNCT
ejpam-2495	89	11	y	y	PROPN
ejpam-2495	89	12	,	,	PUNCT
ejpam-2495	89	13	σ	σ	PROPN
ejpam-2495	89	14	)	)	PUNCT
ejpam-2495	89	15	is	be	AUX
ejpam-2495	89	16	btµ	btµ	NOUN
ejpam-2495	89	17	irresolute	irresolute	ADJ
ejpam-2495	89	18	and	and	CCONJ
ejpam-2495	89	19	a	a	DET
ejpam-2495	89	20	subset	subset	NOUN
ejpam-2495	89	21	s	s	NOUN
ejpam-2495	89	22	of	of	ADP
ejpam-2495	89	23	x	x	SYM
ejpam-2495	89	24	is	be	AUX
ejpam-2495	89	25	btµ	btµ	NOUN
ejpam-2495	89	26	compact	compact	ADJ
ejpam-2495	89	27	relative	relative	ADJ
ejpam-2495	89	28	to	to	ADP
ejpam-2495	89	29	(	(	PUNCT
ejpam-2495	89	30	x	x	X
ejpam-2495	89	31	,	,	PUNCT
ejpam-2495	89	32	τ	τ	PROPN
ejpam-2495	89	33	)	)	PUNCT
ejpam-2495	89	34	,	,	PUNCT
ejpam-2495	89	35	then	then	ADV
ejpam-2495	89	36	the	the	DET
ejpam-2495	89	37	image	image	NOUN
ejpam-2495	89	38	f(s	f(	VERB
ejpam-2495	89	39	)	)	PUNCT
ejpam-2495	89	40	is	be	AUX
ejpam-2495	89	41	btµ	btµ	PROPN
ejpam-2495	89	42	compact	compact	ADJ
ejpam-2495	89	43	relative	relative	ADJ
ejpam-2495	89	44	to	to	ADP
ejpam-2495	89	45	(	(	PUNCT
ejpam-2495	89	46	y	y	PROPN
ejpam-2495	89	47	,	,	PUNCT
ejpam-2495	89	48	σ	σ	PROPN
ejpam-2495	89	49	)	)	PUNCT
ejpam-2495	89	50	.	.	PUNCT
ejpam-2495	90	1	proof	proof	NOUN
ejpam-2495	90	2	.	.	PUNCT
ejpam-2495	91	1	let	let	VERB
ejpam-2495	91	2	{	{	PUNCT
ejpam-2495	91	3	ai	ai	VERB
ejpam-2495	91	4	:	:	PUNCT
ejpam-2495	91	5	i	i	PRON
ejpam-2495	91	6	∈	∈	PROPN
ejpam-2495	91	7	i	i	PRON
ejpam-2495	91	8	}	}	PUNCT
ejpam-2495	91	9	be	be	VERB
ejpam-2495	91	10	a	a	DET
ejpam-2495	91	11	collection	collection	NOUN
ejpam-2495	91	12	of	of	ADP
ejpam-2495	91	13	btµ	btµ	NOUN
ejpam-2495	91	14	open	open	ADJ
ejpam-2495	91	15	cover	cover	NOUN
ejpam-2495	91	16	of	of	ADP
ejpam-2495	91	17	(	(	PUNCT
ejpam-2495	91	18	y	y	PROPN
ejpam-2495	91	19	,	,	PUNCT
ejpam-2495	91	20	σ	σ	PROPN
ejpam-2495	91	21	)	)	PUNCT
ejpam-2495	91	22	,	,	PUNCT
ejpam-2495	91	23	such	such	ADJ
ejpam-2495	91	24	that	that	DET
ejpam-2495	91	25	f(s)⊆⋃	f(s)⊆⋃	PROPN
ejpam-2495	91	26	i∈i	i∈i	ADJ
ejpam-2495	91	27	ai	ai	VERB
ejpam-2495	91	28	.	.	PUNCT
ejpam-2495	92	1	then	then	ADV
ejpam-2495	92	2	s	s	VERB
ejpam-2495	92	3	⊆	⊆	NUM
ejpam-2495	92	4	n⋃	n⋃	NOUN
ejpam-2495	92	5	i=1	i=1	PROPN
ejpam-2495	92	6	f−1(ai	f−1(ai	PROPN
ejpam-2495	92	7	)	)	PUNCT
ejpam-2495	92	8	,	,	PUNCT
ejpam-2495	92	9	where	where	SCONJ
ejpam-2495	92	10	{	{	PUNCT
ejpam-2495	92	11	f−1(ai	f−1(ai	NOUN
ejpam-2495	92	12	)	)	PUNCT
ejpam-2495	92	13	:	:	PUNCT
ejpam-2495	93	1	i	i	PRON
ejpam-2495	93	2	∈	∈	PROPN
ejpam-2495	93	3	i	i	X
ejpam-2495	93	4	)	)	PUNCT
ejpam-2495	93	5	}	}	PUNCT
ejpam-2495	93	6	is	be	AUX
ejpam-2495	93	7	btµopen	btµopen	ADJ
ejpam-2495	93	8	set	set	VERB
ejpam-2495	93	9	in	in	ADP
ejpam-2495	93	10	(	(	PUNCT
ejpam-2495	93	11	x	x	NOUN
ejpam-2495	93	12	,	,	PUNCT
ejpam-2495	93	13	τ	τ	PROPN
ejpam-2495	93	14	)	)	PUNCT
ejpam-2495	93	15	.	.	PUNCT
ejpam-2495	94	1	since	since	SCONJ
ejpam-2495	94	2	s	s	PROPN
ejpam-2495	94	3	is	be	AUX
ejpam-2495	94	4	btµ	btµ	NOUN
ejpam-2495	94	5	-compact	-compact	NOUN
ejpam-2495	94	6	relative	relative	ADJ
ejpam-2495	94	7	to	to	ADP
ejpam-2495	94	8	(	(	PUNCT
ejpam-2495	94	9	x	x	X
ejpam-2495	94	10	,	,	PUNCT
ejpam-2495	94	11	τ	τ	X
ejpam-2495	94	12	)	)	PUNCT
ejpam-2495	94	13	,	,	PUNCT
ejpam-2495	94	14	there	there	PRON
ejpam-2495	94	15	exist	exist	VERB
ejpam-2495	94	16	finite	finite	ADJ
ejpam-2495	94	17	subcollection	subcollection	NOUN
ejpam-2495	94	18	{	{	PUNCT
ejpam-2495	94	19	a1	a1	PROPN
ejpam-2495	94	20	,	,	PUNCT
ejpam-2495	94	21	a2	a2	PROPN
ejpam-2495	94	22	,	,	PUNCT
ejpam-2495	94	23	·	·	PUNCT
ejpam-2495	94	24	·	·	PUNCT
ejpam-2495	94	25	·	·	PUNCT
ejpam-2495	94	26	,	,	PUNCT
ejpam-2495	94	27	an	an	X
ejpam-2495	94	28	}	}	PUNCT
ejpam-2495	94	29	such	such	ADJ
ejpam-2495	94	30	that	that	DET
ejpam-2495	94	31	s	s	VERB
ejpam-2495	94	32	⊆	⊆	NUM
ejpam-2495	94	33	n⋃	n⋃	NOUN
ejpam-2495	94	34	i=1	i=1	PROPN
ejpam-2495	94	35	f−1(ai	f−1(ai	PROPN
ejpam-2495	94	36	)	)	PUNCT
ejpam-2495	94	37	.	.	PUNCT
ejpam-2495	95	1	that	that	PRON
ejpam-2495	95	2	is	be	AUX
ejpam-2495	95	3	f(s	f(	NOUN
ejpam-2495	95	4	)	)	PUNCT
ejpam-2495	95	5	⊆	⊆	NUM
ejpam-2495	95	6	n⋃	n⋃	NOUN
ejpam-2495	95	7	i=1	i=1	PROPN
ejpam-2495	95	8	ai	ai	VERB
ejpam-2495	95	9	.	.	PUNCT
ejpam-2495	96	1	hence	hence	ADV
ejpam-2495	96	2	f(s	f(	VERB
ejpam-2495	96	3	)	)	PUNCT
ejpam-2495	96	4	is	be	AUX
ejpam-2495	96	5	btµ	btµ	PROPN
ejpam-2495	96	6	compact	compact	ADJ
ejpam-2495	96	7	relative	relative	ADJ
ejpam-2495	96	8	to	to	ADP
ejpam-2495	96	9	(	(	PUNCT
ejpam-2495	96	10	y	y	PROPN
ejpam-2495	96	11	,	,	PUNCT
ejpam-2495	96	12	σ	σ	PROPN
ejpam-2495	96	13	)	)	PUNCT
ejpam-2495	96	14	.	.	PUNCT
ejpam-2495	97	1	theorem	theorem	NOUN
ejpam-2495	97	2	5	5	NUM
ejpam-2495	97	3	.	.	PUNCT
ejpam-2495	98	1	if	if	SCONJ
ejpam-2495	98	2	a	a	DET
ejpam-2495	98	3	map	map	NOUN
ejpam-2495	98	4	f	f	X
ejpam-2495	98	5	:	:	PUNCT
ejpam-2495	98	6	(	(	PUNCT
ejpam-2495	98	7	x	x	X
ejpam-2495	98	8	,	,	PUNCT
ejpam-2495	98	9	τ)→	τ)→	PROPN
ejpam-2495	98	10	(	(	PUNCT
ejpam-2495	98	11	y	y	PROPN
ejpam-2495	98	12	,	,	PUNCT
ejpam-2495	98	13	σ	σ	PROPN
ejpam-2495	98	14	)	)	PUNCT
ejpam-2495	98	15	is	be	AUX
ejpam-2495	98	16	strongly	strongly	ADV
ejpam-2495	98	17	btµ	btµ	ADJ
ejpam-2495	98	18	continuous	continuous	ADJ
ejpam-2495	98	19	map	map	NOUN
ejpam-2495	98	20	from	from	ADP
ejpam-2495	98	21	a	a	DET
ejpam-2495	98	22	supra	supra	ADJ
ejpam-2495	98	23	compact	compact	ADJ
ejpam-2495	98	24	space	space	NOUN
ejpam-2495	98	25	(	(	PUNCT
ejpam-2495	98	26	x	x	X
ejpam-2495	98	27	,	,	PUNCT
ejpam-2495	98	28	τ	τ	X
ejpam-2495	98	29	)	)	PUNCT
ejpam-2495	98	30	onto	onto	ADP
ejpam-2495	98	31	a	a	DET
ejpam-2495	98	32	supra	supra	ADJ
ejpam-2495	98	33	topological	topological	ADJ
ejpam-2495	98	34	space	space	NOUN
ejpam-2495	98	35	(	(	PUNCT
ejpam-2495	98	36	y	y	PROPN
ejpam-2495	98	37	,	,	PUNCT
ejpam-2495	98	38	σ	σ	PROPN
ejpam-2495	98	39	)	)	PUNCT
ejpam-2495	98	40	,	,	PUNCT
ejpam-2495	98	41	then	then	ADV
ejpam-2495	98	42	(	(	PUNCT
ejpam-2495	98	43	y	y	PROPN
ejpam-2495	98	44	,	,	PUNCT
ejpam-2495	98	45	σ	σ	PROPN
ejpam-2495	98	46	)	)	PUNCT
ejpam-2495	98	47	is	be	AUX
ejpam-2495	98	48	btµ	btµ	NOUN
ejpam-2495	98	49	compact	compact	ADJ
ejpam-2495	98	50	.	.	PUNCT
ejpam-2495	99	1	k.krishna	k.krishna	NOUN
ejpam-2495	99	2	,	,	PUNCT
ejpam-2495	99	3	m.vignesh	m.vignesh	NOUN
ejpam-2495	99	4	/	/	SYM
ejpam-2495	99	5	eur	eur	PROPN
ejpam-2495	99	6	.	.	PUNCT
ejpam-2495	100	1	j.	j.	PROPN
ejpam-2495	100	2	pure	pure	PROPN
ejpam-2495	100	3	appl	appl	PROPN
ejpam-2495	100	4	.	.	PROPN
ejpam-2495	100	5	math	math	PROPN
ejpam-2495	100	6	,	,	PUNCT
ejpam-2495	100	7	10	10	NUM
ejpam-2495	100	8	(	(	PUNCT
ejpam-2495	100	9	2	2	NUM
ejpam-2495	100	10	)	)	PUNCT
ejpam-2495	100	11	(	(	PUNCT
ejpam-2495	100	12	2017	2017	NUM
ejpam-2495	100	13	)	)	PUNCT
ejpam-2495	100	14	,	,	PUNCT
ejpam-2495	100	15	323	323	NUM
ejpam-2495	100	16	-	-	SYM
ejpam-2495	100	17	334	334	NUM
ejpam-2495	100	18	326	326	NUM
ejpam-2495	100	19	proof	proof	NOUN
ejpam-2495	100	20	.	.	PUNCT
ejpam-2495	101	1	let	let	VERB
ejpam-2495	101	2	{	{	PUNCT
ejpam-2495	101	3	ai	ai	VERB
ejpam-2495	101	4	:	:	PUNCT
ejpam-2495	101	5	i	i	PRON
ejpam-2495	101	6	∈	∈	PROPN
ejpam-2495	101	7	i	i	PRON
ejpam-2495	101	8	}	}	PUNCT
ejpam-2495	101	9	be	be	VERB
ejpam-2495	101	10	a	a	DET
ejpam-2495	101	11	btµ	btµ	NOUN
ejpam-2495	101	12	open	open	ADJ
ejpam-2495	101	13	cover	cover	NOUN
ejpam-2495	101	14	of	of	ADP
ejpam-2495	101	15	(	(	PUNCT
ejpam-2495	101	16	y	y	PROPN
ejpam-2495	101	17	,	,	PUNCT
ejpam-2495	101	18	σ	σ	PROPN
ejpam-2495	101	19	)	)	PUNCT
ejpam-2495	101	20	.	.	PUNCT
ejpam-2495	102	1	since	since	SCONJ
ejpam-2495	102	2	f	f	PROPN
ejpam-2495	102	3	is	be	AUX
ejpam-2495	102	4	strongly	strongly	ADV
ejpam-2495	102	5	btµ	btµ	PROPN
ejpam-2495	102	6	continuous	continuous	ADJ
ejpam-2495	102	7	,	,	PUNCT
ejpam-2495	102	8	{	{	PUNCT
ejpam-2495	102	9	f−1(ai	f−1(ai	NOUN
ejpam-2495	102	10	:	:	PUNCT
ejpam-2495	102	11	i	i	PROPN
ejpam-2495	102	12	∈	∈	PROPN
ejpam-2495	102	13	i	i	X
ejpam-2495	102	14	)	)	PUNCT
ejpam-2495	102	15	}	}	PUNCT
ejpam-2495	102	16	is	be	AUX
ejpam-2495	102	17	an	an	DET
ejpam-2495	102	18	supra	supra	ADJ
ejpam-2495	102	19	open	open	ADJ
ejpam-2495	102	20	cover	cover	NOUN
ejpam-2495	102	21	of	of	ADP
ejpam-2495	102	22	(	(	PUNCT
ejpam-2495	102	23	x	x	X
ejpam-2495	102	24	,	,	PUNCT
ejpam-2495	102	25	τ	τ	PROPN
ejpam-2495	102	26	)	)	PUNCT
ejpam-2495	102	27	.	.	PUNCT
ejpam-2495	103	1	again	again	ADV
ejpam-2495	103	2	,	,	PUNCT
ejpam-2495	103	3	since	since	SCONJ
ejpam-2495	103	4	(	(	PUNCT
ejpam-2495	103	5	x	x	X
ejpam-2495	103	6	,	,	PUNCT
ejpam-2495	103	7	τ	τ	X
ejpam-2495	103	8	)	)	PUNCT
ejpam-2495	103	9	is	be	AUX
ejpam-2495	103	10	supra	supra	ADJ
ejpam-2495	103	11	compact	compact	ADJ
ejpam-2495	103	12	,	,	PUNCT
ejpam-2495	103	13	the	the	DET
ejpam-2495	103	14	supra	supra	PROPN
ejpam-2495	103	15	open	open	ADJ
ejpam-2495	103	16	cover	cover	NOUN
ejpam-2495	103	17	{	{	PUNCT
ejpam-2495	103	18	f−1(ai	f−1(ai	NOUN
ejpam-2495	103	19	)	)	PUNCT
ejpam-2495	103	20	:	:	PUNCT
ejpam-2495	104	1	i	i	PRON
ejpam-2495	104	2	∈	∈	PROPN
ejpam-2495	104	3	i	i	X
ejpam-2495	104	4	)	)	PUNCT
ejpam-2495	104	5	}	}	PUNCT
ejpam-2495	104	6	of	of	ADP
ejpam-2495	104	7	(	(	PUNCT
ejpam-2495	104	8	x	x	X
ejpam-2495	104	9	,	,	PUNCT
ejpam-2495	104	10	τ	τ	X
ejpam-2495	104	11	)	)	PUNCT
ejpam-2495	104	12	has	have	AUX
ejpam-2495	104	13	a	a	DET
ejpam-2495	104	14	finite	finite	ADJ
ejpam-2495	104	15	sub	sub	NOUN
ejpam-2495	104	16	cover	cover	NOUN
ejpam-2495	104	17	say	say	VERB
ejpam-2495	104	18	{	{	PUNCT
ejpam-2495	104	19	f−1(ai	f−1(ai	NOUN
ejpam-2495	104	20	)	)	PUNCT
ejpam-2495	104	21	:	:	PUNCT
ejpam-2495	105	1	i	i	NOUN
ejpam-2495	105	2	=	=	NOUN
ejpam-2495	105	3	1	1	NUM
ejpam-2495	105	4	,	,	PUNCT
ejpam-2495	105	5	2	2	NUM
ejpam-2495	105	6	,	,	PUNCT
ejpam-2495	105	7	·	·	PUNCT
ejpam-2495	105	8	·	·	PUNCT
ejpam-2495	105	9	·	·	PUNCT
ejpam-2495	105	10	,	,	PUNCT
ejpam-2495	105	11	n	n	CCONJ
ejpam-2495	105	12	}	}	PUNCT
ejpam-2495	105	13	.	.	PUNCT
ejpam-2495	106	1	therefore	therefore	ADV
ejpam-2495	106	2	x	x	X
ejpam-2495	106	3	=	=	PRON
ejpam-2495	106	4	n⋃	n⋃	VERB
ejpam-2495	106	5	i=1	i=1	PROPN
ejpam-2495	106	6	f−1(ai	f−1(ai	PROPN
ejpam-2495	106	7	)	)	PUNCT
ejpam-2495	106	8	,	,	PUNCT
ejpam-2495	106	9	which	which	PRON
ejpam-2495	106	10	implies	imply	VERB
ejpam-2495	106	11	f(x	f(x	PROPN
ejpam-2495	106	12	)	)	PUNCT
ejpam-2495	107	1	=	=	PRON
ejpam-2495	107	2	n⋃	n⋃	VERB
ejpam-2495	107	3	i=1	i=1	PRON
ejpam-2495	107	4	(	(	PUNCT
ejpam-2495	107	5	ai	ai	NOUN
ejpam-2495	107	6	)	)	PUNCT
ejpam-2495	107	7	,	,	PUNCT
ejpam-2495	107	8	so	so	SCONJ
ejpam-2495	107	9	that	that	SCONJ
ejpam-2495	107	10	y	y	PROPN
ejpam-2495	107	11	=	=	PRON
ejpam-2495	107	12	n⋃	n⋃	VERB
ejpam-2495	107	13	i=1	i=1	PROPN
ejpam-2495	107	14	(	(	PUNCT
ejpam-2495	107	15	ai	ai	NOUN
ejpam-2495	107	16	)	)	PUNCT
ejpam-2495	107	17	.	.	PUNCT
ejpam-2495	108	1	that	that	PRON
ejpam-2495	108	2	is	be	AUX
ejpam-2495	108	3	a1	a1	PROPN
ejpam-2495	108	4	,	,	PUNCT
ejpam-2495	108	5	a2	a2	PROPN
ejpam-2495	108	6	,	,	PUNCT
ejpam-2495	108	7	·	·	PUNCT
ejpam-2495	108	8	·	·	PUNCT
ejpam-2495	108	9	·	·	PUNCT
ejpam-2495	108	10	,	,	PUNCT
ejpam-2495	108	11	an	an	PRON
ejpam-2495	108	12	is	be	AUX
ejpam-2495	108	13	a	a	DET
ejpam-2495	108	14	finite	finite	ADJ
ejpam-2495	108	15	sub	sub	NOUN
ejpam-2495	108	16	cover	cover	NOUN
ejpam-2495	108	17	of	of	ADP
ejpam-2495	108	18	{	{	PUNCT
ejpam-2495	108	19	ai	ai	INTJ
ejpam-2495	108	20	:	:	PUNCT
ejpam-2495	108	21	i	i	PRON
ejpam-2495	109	1	∈	∈	VERB
ejpam-2495	110	1	i	i	X
ejpam-2495	110	2	}	}	PUNCT
ejpam-2495	110	3	for	for	ADP
ejpam-2495	110	4	(	(	PUNCT
ejpam-2495	110	5	y	y	PROPN
ejpam-2495	110	6	,	,	PUNCT
ejpam-2495	110	7	σ	σ	PROPN
ejpam-2495	110	8	)	)	PUNCT
ejpam-2495	110	9	.	.	PUNCT
ejpam-2495	111	1	hence	hence	ADV
ejpam-2495	111	2	(	(	PUNCT
ejpam-2495	111	3	y	y	PROPN
ejpam-2495	111	4	,	,	PUNCT
ejpam-2495	111	5	σ	σ	PROPN
ejpam-2495	111	6	)	)	PUNCT
ejpam-2495	111	7	is	be	AUX
ejpam-2495	111	8	btµ	btµ	PROPN
ejpam-2495	111	9	-compact	-compact	PROPN
ejpam-2495	111	10	.	.	PUNCT
ejpam-2495	112	1	theorem	theorem	VERB
ejpam-2495	112	2	6	6	NUM
ejpam-2495	112	3	.	.	PUNCT
ejpam-2495	113	1	if	if	SCONJ
ejpam-2495	113	2	a	a	DET
ejpam-2495	113	3	map	map	NOUN
ejpam-2495	113	4	f	f	X
ejpam-2495	113	5	:	:	PUNCT
ejpam-2495	113	6	(	(	PUNCT
ejpam-2495	113	7	x	x	X
ejpam-2495	113	8	,	,	PUNCT
ejpam-2495	113	9	τ)→	τ)→	PROPN
ejpam-2495	113	10	(	(	PUNCT
ejpam-2495	113	11	y	y	PROPN
ejpam-2495	113	12	,	,	PUNCT
ejpam-2495	113	13	σ	σ	PROPN
ejpam-2495	113	14	)	)	PUNCT
ejpam-2495	113	15	is	be	AUX
ejpam-2495	113	16	perfectly	perfectly	ADV
ejpam-2495	113	17	btµcontinuous	btµcontinuous	ADJ
ejpam-2495	113	18	map	map	NOUN
ejpam-2495	113	19	from	from	ADP
ejpam-2495	113	20	a	a	DET
ejpam-2495	113	21	compact	compact	ADJ
ejpam-2495	113	22	space	space	NOUN
ejpam-2495	113	23	(	(	PUNCT
ejpam-2495	113	24	x	x	X
ejpam-2495	113	25	,	,	PUNCT
ejpam-2495	113	26	τ	τ	X
ejpam-2495	113	27	)	)	PUNCT
ejpam-2495	113	28	onto	onto	ADP
ejpam-2495	113	29	a	a	DET
ejpam-2495	113	30	supra	supra	ADJ
ejpam-2495	113	31	topological	topological	ADJ
ejpam-2495	113	32	space	space	NOUN
ejpam-2495	113	33	(	(	PUNCT
ejpam-2495	113	34	y	y	PROPN
ejpam-2495	113	35	,	,	PUNCT
ejpam-2495	113	36	σ	σ	PROPN
ejpam-2495	113	37	)	)	PUNCT
ejpam-2495	113	38	,	,	PUNCT
ejpam-2495	113	39	then	then	ADV
ejpam-2495	113	40	(	(	PUNCT
ejpam-2495	113	41	y	y	PROPN
ejpam-2495	113	42	,	,	PUNCT
ejpam-2495	113	43	σ	σ	PROPN
ejpam-2495	113	44	)	)	PUNCT
ejpam-2495	113	45	is	be	AUX
ejpam-2495	113	46	btµ	btµ	NOUN
ejpam-2495	113	47	compact	compact	ADJ
ejpam-2495	113	48	.	.	PUNCT
ejpam-2495	114	1	proof	proof	NOUN
ejpam-2495	114	2	.	.	PUNCT
ejpam-2495	115	1	let	let	VERB
ejpam-2495	115	2	{	{	PUNCT
ejpam-2495	115	3	ai	ai	VERB
ejpam-2495	115	4	:	:	PUNCT
ejpam-2495	115	5	i	i	PRON
ejpam-2495	115	6	∈	∈	PROPN
ejpam-2495	115	7	i	i	PRON
ejpam-2495	115	8	}	}	PUNCT
ejpam-2495	115	9	be	be	VERB
ejpam-2495	115	10	a	a	DET
ejpam-2495	115	11	btµ	btµ	NOUN
ejpam-2495	115	12	open	open	ADJ
ejpam-2495	115	13	cover	cover	NOUN
ejpam-2495	115	14	of	of	ADP
ejpam-2495	115	15	(	(	PUNCT
ejpam-2495	115	16	y	y	PROPN
ejpam-2495	115	17	,	,	PUNCT
ejpam-2495	115	18	σ	σ	PROPN
ejpam-2495	115	19	)	)	PUNCT
ejpam-2495	115	20	.	.	PUNCT
ejpam-2495	116	1	since	since	SCONJ
ejpam-2495	116	2	f	f	PROPN
ejpam-2495	116	3	is	be	AUX
ejpam-2495	116	4	perfectly	perfectly	ADV
ejpam-2495	116	5	btµcontinuous	btµcontinuous	ADJ
ejpam-2495	116	6	,	,	PUNCT
ejpam-2495	116	7	{	{	PUNCT
ejpam-2495	116	8	f−1(ai	f−1(ai	NOUN
ejpam-2495	116	9	)	)	PUNCT
ejpam-2495	116	10	:	:	PUNCT
ejpam-2495	117	1	i	i	PRON
ejpam-2495	117	2	∈	∈	PROPN
ejpam-2495	117	3	i	i	X
ejpam-2495	117	4	)	)	PUNCT
ejpam-2495	117	5	}	}	PUNCT
ejpam-2495	117	6	is	be	AUX
ejpam-2495	117	7	a	a	DET
ejpam-2495	117	8	supra	supra	ADJ
ejpam-2495	117	9	open	open	ADJ
ejpam-2495	117	10	cover	cover	NOUN
ejpam-2495	117	11	of	of	ADP
ejpam-2495	117	12	(	(	PUNCT
ejpam-2495	117	13	x	x	X
ejpam-2495	117	14	,	,	PUNCT
ejpam-2495	117	15	τ	τ	PROPN
ejpam-2495	117	16	)	)	PUNCT
ejpam-2495	117	17	.	.	PUNCT
ejpam-2495	118	1	again	again	ADV
ejpam-2495	118	2	,	,	PUNCT
ejpam-2495	118	3	since	since	SCONJ
ejpam-2495	118	4	(	(	PUNCT
ejpam-2495	118	5	x	x	X
ejpam-2495	118	6	,	,	PUNCT
ejpam-2495	118	7	τ	τ	X
ejpam-2495	118	8	)	)	PUNCT
ejpam-2495	118	9	is	be	AUX
ejpam-2495	118	10	supra	supra	ADJ
ejpam-2495	118	11	compact	compact	ADJ
ejpam-2495	118	12	,	,	PUNCT
ejpam-2495	118	13	the	the	DET
ejpam-2495	118	14	supra	supra	PROPN
ejpam-2495	118	15	open	open	ADJ
ejpam-2495	118	16	cover	cover	NOUN
ejpam-2495	118	17	{	{	PUNCT
ejpam-2495	118	18	f−1(ai	f−1(ai	NOUN
ejpam-2495	118	19	)	)	PUNCT
ejpam-2495	118	20	:	:	PUNCT
ejpam-2495	119	1	i	i	PRON
ejpam-2495	119	2	∈	∈	VERB
ejpam-2495	119	3	i	i	PRON
ejpam-2495	119	4	}	}	PUNCT
ejpam-2495	119	5	of	of	ADP
ejpam-2495	119	6	(	(	PUNCT
ejpam-2495	119	7	x	x	X
ejpam-2495	119	8	,	,	PUNCT
ejpam-2495	119	9	τ	τ	X
ejpam-2495	119	10	)	)	PUNCT
ejpam-2495	119	11	has	have	VERB
ejpam-2495	119	12	a	a	DET
ejpam-2495	119	13	finite	finite	ADJ
ejpam-2495	119	14	sub	sub	NOUN
ejpam-2495	119	15	cover	cover	NOUN
ejpam-2495	119	16	say	say	VERB
ejpam-2495	119	17	{	{	PUNCT
ejpam-2495	119	18	f−1(ai	f−1(ai	NOUN
ejpam-2495	119	19	)	)	PUNCT
ejpam-2495	119	20	:	:	PUNCT
ejpam-2495	120	1	i	i	NOUN
ejpam-2495	120	2	=	=	NOUN
ejpam-2495	120	3	1	1	NUM
ejpam-2495	120	4	,	,	PUNCT
ejpam-2495	120	5	2	2	NUM
ejpam-2495	120	6	,	,	PUNCT
ejpam-2495	120	7	·	·	PUNCT
ejpam-2495	120	8	·	·	PUNCT
ejpam-2495	120	9	·	·	PUNCT
ejpam-2495	120	10	,	,	PUNCT
ejpam-2495	120	11	n	n	CCONJ
ejpam-2495	120	12	}	}	PUNCT
ejpam-2495	120	13	.	.	PUNCT
ejpam-2495	121	1	therefore	therefore	ADV
ejpam-2495	121	2	x	x	X
ejpam-2495	121	3	=	=	PRON
ejpam-2495	121	4	n⋃	n⋃	VERB
ejpam-2495	121	5	i=1	i=1	PROPN
ejpam-2495	121	6	f−1(ai	f−1(ai	PROPN
ejpam-2495	121	7	)	)	PUNCT
ejpam-2495	121	8	,	,	PUNCT
ejpam-2495	121	9	which	which	PRON
ejpam-2495	121	10	implies	imply	VERB
ejpam-2495	121	11	f(x	f(x	PROPN
ejpam-2495	121	12	)	)	PUNCT
ejpam-2495	122	1	=	=	PRON
ejpam-2495	122	2	n⋃	n⋃	VERB
ejpam-2495	122	3	i=1	i=1	PROPN
ejpam-2495	122	4	ai	ai	VERB
ejpam-2495	122	5	,	,	PUNCT
ejpam-2495	122	6	so	so	SCONJ
ejpam-2495	122	7	that	that	SCONJ
ejpam-2495	122	8	y	y	PROPN
ejpam-2495	122	9	=	=	PUNCT
ejpam-2495	122	10	n⋃	n⋃	VERB
ejpam-2495	122	11	i=1	i=1	PROPN
ejpam-2495	122	12	ai	ai	VERB
ejpam-2495	122	13	.	.	PUNCT
ejpam-2495	123	1	that	that	PRON
ejpam-2495	123	2	is	be	AUX
ejpam-2495	123	3	a1	a1	PROPN
ejpam-2495	123	4	,	,	PUNCT
ejpam-2495	123	5	a2	a2	PROPN
ejpam-2495	123	6	,	,	PUNCT
ejpam-2495	123	7	·	·	PUNCT
ejpam-2495	123	8	·	·	PUNCT
ejpam-2495	123	9	·	·	PUNCT
ejpam-2495	123	10	,	,	PUNCT
ejpam-2495	123	11	an	an	PRON
ejpam-2495	123	12	is	be	AUX
ejpam-2495	123	13	a	a	DET
ejpam-2495	123	14	finite	finite	ADJ
ejpam-2495	123	15	sub	sub	NOUN
ejpam-2495	123	16	cover	cover	NOUN
ejpam-2495	123	17	of	of	ADP
ejpam-2495	123	18	{	{	PUNCT
ejpam-2495	123	19	ai	ai	INTJ
ejpam-2495	123	20	:	:	PUNCT
ejpam-2495	123	21	i	i	PRON
ejpam-2495	124	1	∈	∈	VERB
ejpam-2495	125	1	i	i	X
ejpam-2495	125	2	}	}	PUNCT
ejpam-2495	125	3	for	for	ADP
ejpam-2495	125	4	(	(	PUNCT
ejpam-2495	125	5	y	y	PROPN
ejpam-2495	125	6	,	,	PUNCT
ejpam-2495	125	7	σ	σ	PROPN
ejpam-2495	125	8	)	)	PUNCT
ejpam-2495	125	9	.	.	PUNCT
ejpam-2495	126	1	hence	hence	ADV
ejpam-2495	126	2	(	(	PUNCT
ejpam-2495	126	3	y	y	PROPN
ejpam-2495	126	4	,	,	PUNCT
ejpam-2495	126	5	σ	σ	PROPN
ejpam-2495	126	6	)	)	PUNCT
ejpam-2495	126	7	is	be	AUX
ejpam-2495	126	8	btµ	btµ	PROPN
ejpam-2495	126	9	-compact	-compact	PROPN
ejpam-2495	126	10	.	.	PUNCT
ejpam-2495	127	1	theorem	theorem	VERB
ejpam-2495	127	2	7	7	NUM
ejpam-2495	127	3	.	.	PUNCT
ejpam-2495	128	1	if	if	SCONJ
ejpam-2495	128	2	a	a	DET
ejpam-2495	128	3	map	map	NOUN
ejpam-2495	128	4	f	f	X
ejpam-2495	128	5	:	:	PUNCT
ejpam-2495	128	6	(	(	PUNCT
ejpam-2495	128	7	x	x	X
ejpam-2495	128	8	,	,	PUNCT
ejpam-2495	128	9	τ	τ	X
ejpam-2495	128	10	)	)	PUNCT
ejpam-2495	128	11	→	→	SYM
ejpam-2495	128	12	(	(	PUNCT
ejpam-2495	128	13	y	y	PROPN
ejpam-2495	128	14	,	,	PUNCT
ejpam-2495	128	15	σ	σ	PROPN
ejpam-2495	128	16	)	)	PUNCT
ejpam-2495	128	17	be	be	VERB
ejpam-2495	128	18	btµ	btµ	NOUN
ejpam-2495	128	19	irresolute	irresolute	ADJ
ejpam-2495	128	20	map	map	NOUN
ejpam-2495	128	21	from	from	ADP
ejpam-2495	128	22	btµ	btµ	PROPN
ejpam-2495	128	23	compact	compact	ADJ
ejpam-2495	128	24	space	space	NOUN
ejpam-2495	128	25	(	(	PUNCT
ejpam-2495	128	26	x	x	X
ejpam-2495	128	27	,	,	PUNCT
ejpam-2495	128	28	τ	τ	X
ejpam-2495	128	29	)	)	PUNCT
ejpam-2495	128	30	onto	onto	ADP
ejpam-2495	128	31	supra	supra	PROPN
ejpam-2495	128	32	topological	topological	ADJ
ejpam-2495	128	33	space	space	NOUN
ejpam-2495	128	34	(	(	PUNCT
ejpam-2495	128	35	y	y	PROPN
ejpam-2495	128	36	,	,	PUNCT
ejpam-2495	128	37	σ	σ	PROPN
ejpam-2495	128	38	)	)	PUNCT
ejpam-2495	128	39	then	then	ADV
ejpam-2495	128	40	(	(	PUNCT
ejpam-2495	128	41	y	y	PROPN
ejpam-2495	128	42	,	,	PUNCT
ejpam-2495	128	43	σ	σ	PROPN
ejpam-2495	128	44	)	)	PUNCT
ejpam-2495	128	45	btµ	btµ	NOUN
ejpam-2495	128	46	compact	compact	ADJ
ejpam-2495	128	47	.	.	PUNCT
ejpam-2495	129	1	proof	proof	NOUN
ejpam-2495	129	2	.	.	PUNCT
ejpam-2495	130	1	if	if	SCONJ
ejpam-2495	130	2	a	a	DET
ejpam-2495	130	3	map	map	NOUN
ejpam-2495	130	4	f	f	X
ejpam-2495	130	5	:	:	PUNCT
ejpam-2495	130	6	(	(	PUNCT
ejpam-2495	130	7	x	x	X
ejpam-2495	130	8	,	,	PUNCT
ejpam-2495	130	9	τ)→	τ)→	PROPN
ejpam-2495	130	10	(	(	PUNCT
ejpam-2495	130	11	y	y	PROPN
ejpam-2495	130	12	,	,	PUNCT
ejpam-2495	130	13	σ	σ	PROPN
ejpam-2495	130	14	)	)	PUNCT
ejpam-2495	130	15	is	be	AUX
ejpam-2495	130	16	btµ	btµ	PROPN
ejpam-2495	130	17	irresolute	irresolute	ADJ
ejpam-2495	130	18	map	map	NOUN
ejpam-2495	130	19	from	from	ADP
ejpam-2495	130	20	a	a	DET
ejpam-2495	130	21	btµcompact	btµcompact	NOUN
ejpam-2495	130	22	space	space	NOUN
ejpam-2495	130	23	(	(	PUNCT
ejpam-2495	130	24	x	x	X
ejpam-2495	130	25	,	,	PUNCT
ejpam-2495	130	26	τ	τ	X
ejpam-2495	130	27	)	)	PUNCT
ejpam-2495	130	28	onto	onto	ADP
ejpam-2495	130	29	a	a	DET
ejpam-2495	130	30	supra	supra	ADJ
ejpam-2495	130	31	topological	topological	ADJ
ejpam-2495	130	32	space	space	NOUN
ejpam-2495	130	33	(	(	PUNCT
ejpam-2495	130	34	y	y	PROPN
ejpam-2495	130	35	,	,	PUNCT
ejpam-2495	130	36	σ	σ	PROPN
ejpam-2495	130	37	)	)	PUNCT
ejpam-2495	130	38	.	.	PUNCT
ejpam-2495	131	1	let	let	VERB
ejpam-2495	131	2	{	{	PUNCT
ejpam-2495	131	3	ai	ai	VERB
ejpam-2495	131	4	:	:	PUNCT
ejpam-2495	131	5	i	i	PRON
ejpam-2495	131	6	∈	∈	PROPN
ejpam-2495	131	7	i	i	PRON
ejpam-2495	131	8	}	}	PUNCT
ejpam-2495	131	9	be	be	VERB
ejpam-2495	131	10	a	a	DET
ejpam-2495	131	11	btµ	btµ	NOUN
ejpam-2495	131	12	open	open	ADJ
ejpam-2495	131	13	cover	cover	NOUN
ejpam-2495	131	14	of	of	ADP
ejpam-2495	131	15	(	(	PUNCT
ejpam-2495	131	16	y	y	PROPN
ejpam-2495	131	17	,	,	PUNCT
ejpam-2495	131	18	σ	σ	PROPN
ejpam-2495	131	19	)	)	PUNCT
ejpam-2495	131	20	.	.	PUNCT
ejpam-2495	132	1	then	then	ADV
ejpam-2495	132	2	{	{	PUNCT
ejpam-2495	132	3	f−1(ai	f−1(ai	NOUN
ejpam-2495	132	4	)	)	PUNCT
ejpam-2495	132	5	:	:	PUNCT
ejpam-2495	133	1	i	i	PRON
ejpam-2495	133	2	∈	∈	VERB
ejpam-2495	133	3	i	i	PRON
ejpam-2495	133	4	}	}	PUNCT
ejpam-2495	133	5	is	be	AUX
ejpam-2495	133	6	an	an	DET
ejpam-2495	133	7	btµ	btµ	NOUN
ejpam-2495	133	8	open	open	ADJ
ejpam-2495	133	9	cover	cover	NOUN
ejpam-2495	133	10	of	of	ADP
ejpam-2495	133	11	(	(	PUNCT
ejpam-2495	133	12	x	x	X
ejpam-2495	133	13	,	,	PUNCT
ejpam-2495	133	14	τ	τ	PROPN
ejpam-2495	133	15	)	)	PUNCT
ejpam-2495	133	16	,	,	PUNCT
ejpam-2495	133	17	since	since	SCONJ
ejpam-2495	133	18	f	f	PROPN
ejpam-2495	133	19	is	be	AUX
ejpam-2495	133	20	btµ	btµ	NOUN
ejpam-2495	133	21	irresolute	irresolute	ADJ
ejpam-2495	133	22	.	.	PUNCT
ejpam-2495	134	1	as	as	SCONJ
ejpam-2495	134	2	(	(	PUNCT
ejpam-2495	134	3	x	x	NOUN
ejpam-2495	134	4	,	,	PUNCT
ejpam-2495	134	5	τ	τ	X
ejpam-2495	134	6	)	)	PUNCT
ejpam-2495	134	7	is	be	AUX
ejpam-2495	134	8	btµ	btµ	PROPN
ejpam-2495	134	9	compact	compact	ADJ
ejpam-2495	134	10	,	,	PUNCT
ejpam-2495	134	11	the	the	DET
ejpam-2495	134	12	btµ	btµ	NOUN
ejpam-2495	134	13	open	open	ADJ
ejpam-2495	134	14	cover	cover	VERB
ejpam-2495	134	15	{	{	PUNCT
ejpam-2495	134	16	f−1(ai	f−1(ai	NOUN
ejpam-2495	134	17	)	)	PUNCT
ejpam-2495	134	18	:	:	PUNCT
ejpam-2495	135	1	i	i	PRON
ejpam-2495	135	2	∈	∈	VERB
ejpam-2495	135	3	i	i	PRON
ejpam-2495	135	4	}	}	PUNCT
ejpam-2495	135	5	of	of	ADP
ejpam-2495	135	6	(	(	PUNCT
ejpam-2495	135	7	x	x	X
ejpam-2495	135	8	,	,	PUNCT
ejpam-2495	135	9	τ	τ	X
ejpam-2495	135	10	)	)	PUNCT
ejpam-2495	135	11	has	have	VERB
ejpam-2495	135	12	a	a	DET
ejpam-2495	135	13	finite	finite	ADJ
ejpam-2495	135	14	sub	sub	NOUN
ejpam-2495	135	15	cover	cover	NOUN
ejpam-2495	135	16	say	say	VERB
ejpam-2495	135	17	{	{	PUNCT
ejpam-2495	135	18	f−1(ai	f−1(ai	NOUN
ejpam-2495	135	19	)	)	PUNCT
ejpam-2495	135	20	:	:	PUNCT
ejpam-2495	136	1	i	i	NOUN
ejpam-2495	136	2	=	=	NOUN
ejpam-2495	136	3	1	1	NUM
ejpam-2495	136	4	,	,	PUNCT
ejpam-2495	136	5	2	2	NUM
ejpam-2495	136	6	,	,	PUNCT
ejpam-2495	136	7	·	·	PUNCT
ejpam-2495	136	8	·	·	PUNCT
ejpam-2495	136	9	·	·	PUNCT
ejpam-2495	136	10	,	,	PUNCT
ejpam-2495	136	11	n	n	CCONJ
ejpam-2495	136	12	}	}	PUNCT
ejpam-2495	136	13	.	.	PUNCT
ejpam-2495	137	1	therefore	therefore	ADV
ejpam-2495	137	2	x	x	X
ejpam-2495	137	3	=	=	PRON
ejpam-2495	137	4	n⋃	n⋃	VERB
ejpam-2495	137	5	i=1	i=1	PROPN
ejpam-2495	137	6	f−1(ai	f−1(ai	PROPN
ejpam-2495	137	7	)	)	PUNCT
ejpam-2495	137	8	,	,	PUNCT
ejpam-2495	137	9	which	which	PRON
ejpam-2495	137	10	implies	imply	VERB
ejpam-2495	137	11	f(x	f(x	PROPN
ejpam-2495	137	12	)	)	PUNCT
ejpam-2495	138	1	=	=	PRON
ejpam-2495	138	2	n⋃	n⋃	VERB
ejpam-2495	138	3	i=1	i=1	PROPN
ejpam-2495	138	4	ai	ai	VERB
ejpam-2495	138	5	,	,	PUNCT
ejpam-2495	138	6	so	so	SCONJ
ejpam-2495	138	7	that	that	SCONJ
ejpam-2495	138	8	y	y	PROPN
ejpam-2495	138	9	=	=	PUNCT
ejpam-2495	138	10	n⋃	n⋃	VERB
ejpam-2495	138	11	i=1	i=1	PROPN
ejpam-2495	138	12	ai	ai	VERB
ejpam-2495	138	13	.	.	PUNCT
ejpam-2495	139	1	that	that	PRON
ejpam-2495	139	2	is	be	AUX
ejpam-2495	139	3	a1	a1	PROPN
ejpam-2495	139	4	,	,	PUNCT
ejpam-2495	139	5	a2	a2	PROPN
ejpam-2495	139	6	,	,	PUNCT
ejpam-2495	139	7	·	·	PUNCT
ejpam-2495	139	8	·	·	PUNCT
ejpam-2495	139	9	·	·	PUNCT
ejpam-2495	139	10	,	,	PUNCT
ejpam-2495	139	11	an	an	PRON
ejpam-2495	139	12	is	be	AUX
ejpam-2495	139	13	a	a	DET
ejpam-2495	139	14	finite	finite	ADJ
ejpam-2495	139	15	sub	sub	NOUN
ejpam-2495	139	16	cover	cover	NOUN
ejpam-2495	139	17	of	of	ADP
ejpam-2495	139	18	{	{	PUNCT
ejpam-2495	139	19	ai	ai	INTJ
ejpam-2495	139	20	:	:	PUNCT
ejpam-2495	139	21	i	i	PRON
ejpam-2495	140	1	∈	∈	VERB
ejpam-2495	141	1	i	i	X
ejpam-2495	141	2	}	}	PUNCT
ejpam-2495	141	3	for	for	ADP
ejpam-2495	141	4	(	(	PUNCT
ejpam-2495	141	5	y	y	PROPN
ejpam-2495	141	6	,	,	PUNCT
ejpam-2495	141	7	σ	σ	PROPN
ejpam-2495	141	8	)	)	PUNCT
ejpam-2495	141	9	.	.	PUNCT
ejpam-2495	142	1	hence	hence	ADV
ejpam-2495	142	2	(	(	PUNCT
ejpam-2495	142	3	y	y	PROPN
ejpam-2495	142	4	,	,	PUNCT
ejpam-2495	142	5	σ	σ	PROPN
ejpam-2495	142	6	)	)	PUNCT
ejpam-2495	142	7	is	be	AUX
ejpam-2495	142	8	btµ	btµ	PROPN
ejpam-2495	142	9	-compact	-compact	PROPN
ejpam-2495	142	10	.	.	PUNCT
ejpam-2495	143	1	theorem	theorem	VERB
ejpam-2495	143	2	8	8	NUM
ejpam-2495	143	3	.	.	PUNCT
ejpam-2495	144	1	if	if	SCONJ
ejpam-2495	144	2	(	(	PUNCT
ejpam-2495	144	3	x	x	X
ejpam-2495	144	4	,	,	PUNCT
ejpam-2495	144	5	τ	τ	X
ejpam-2495	144	6	)	)	PUNCT
ejpam-2495	144	7	is	be	AUX
ejpam-2495	144	8	compact	compact	ADJ
ejpam-2495	144	9	and	and	CCONJ
ejpam-2495	144	10	btt	btt	PROPN
ejpam-2495	144	11	µ	µ	PROPN
ejpam-2495	144	12	c	c	NOUN
ejpam-2495	144	13	space	space	NOUN
ejpam-2495	144	14	,	,	PUNCT
ejpam-2495	144	15	then	then	ADV
ejpam-2495	144	16	(	(	PUNCT
ejpam-2495	144	17	x	x	X
ejpam-2495	144	18	,	,	PUNCT
ejpam-2495	144	19	τ	τ	X
ejpam-2495	144	20	)	)	PUNCT
ejpam-2495	144	21	is	be	AUX
ejpam-2495	144	22	btµ	btµ	NOUN
ejpam-2495	144	23	compact	compact	ADJ
ejpam-2495	144	24	.	.	PUNCT
ejpam-2495	145	1	proof	proof	NOUN
ejpam-2495	145	2	.	.	PUNCT
ejpam-2495	146	1	let	let	VERB
ejpam-2495	146	2	(	(	PUNCT
ejpam-2495	146	3	x	x	X
ejpam-2495	146	4	,	,	PUNCT
ejpam-2495	146	5	τ	τ	X
ejpam-2495	146	6	)	)	PUNCT
ejpam-2495	146	7	is	be	AUX
ejpam-2495	146	8	btµ	btµ	NOUN
ejpam-2495	146	9	compact	compact	ADJ
ejpam-2495	146	10	space	space	NOUN
ejpam-2495	146	11	.	.	PUNCT
ejpam-2495	147	1	let	let	VERB
ejpam-2495	147	2	{	{	PUNCT
ejpam-2495	147	3	ai	ai	VERB
ejpam-2495	147	4	:	:	PUNCT
ejpam-2495	147	5	i	i	PRON
ejpam-2495	147	6	∈	∈	PROPN
ejpam-2495	147	7	i	i	PRON
ejpam-2495	147	8	}	}	PUNCT
ejpam-2495	147	9	be	be	VERB
ejpam-2495	147	10	a	a	DET
ejpam-2495	147	11	btµ	btµ	NOUN
ejpam-2495	147	12	open	open	ADJ
ejpam-2495	147	13	cover	cover	NOUN
ejpam-2495	147	14	of	of	ADP
ejpam-2495	147	15	(	(	PUNCT
ejpam-2495	147	16	x	x	NOUN
ejpam-2495	147	17	,	,	PUNCT
ejpam-2495	147	18	)	)	PUNCT
ejpam-2495	147	19	.	.	PUNCT
ejpam-2495	148	1	since	since	SCONJ
ejpam-2495	148	2	by	by	ADP
ejpam-2495	148	3	btt	btt	PROPN
ejpam-2495	148	4	µ	µ	PROPN
ejpam-2495	148	5	c	c	NOUN
ejpam-2495	148	6	-space,{ai	-space,{ai	NOUN
ejpam-2495	148	7	:	:	PUNCT
ejpam-2495	149	1	i	i	PRON
ejpam-2495	149	2	∈	∈	VERB
ejpam-2495	149	3	i	i	PRON
ejpam-2495	149	4	}	}	PUNCT
ejpam-2495	149	5	is	be	AUX
ejpam-2495	149	6	a	a	DET
ejpam-2495	149	7	supra	supra	ADJ
ejpam-2495	149	8	open	open	ADJ
ejpam-2495	149	9	cover	cover	NOUN
ejpam-2495	149	10	of	of	ADP
ejpam-2495	149	11	(	(	PUNCT
ejpam-2495	149	12	x	x	X
ejpam-2495	149	13	,	,	PUNCT
ejpam-2495	149	14	τ	τ	PROPN
ejpam-2495	149	15	)	)	PUNCT
ejpam-2495	149	16	.	.	PUNCT
ejpam-2495	150	1	since	since	SCONJ
ejpam-2495	150	2	(	(	PUNCT
ejpam-2495	150	3	x	x	X
ejpam-2495	150	4	,	,	PUNCT
ejpam-2495	150	5	τ	τ	X
ejpam-2495	150	6	)	)	PUNCT
ejpam-2495	150	7	is	be	AUX
ejpam-2495	150	8	compact	compact	ADJ
ejpam-2495	150	9	,	,	PUNCT
ejpam-2495	151	1	supra	supra	ADJ
ejpam-2495	151	2	open	open	ADJ
ejpam-2495	151	3	cover	cover	NOUN
ejpam-2495	151	4	{	{	PUNCT
ejpam-2495	151	5	ai	ai	VERB
ejpam-2495	151	6	:	:	PUNCT
ejpam-2495	151	7	i	i	PRON
ejpam-2495	151	8	∈	∈	VERB
ejpam-2495	152	1	i	i	X
ejpam-2495	152	2	}	}	PUNCT
ejpam-2495	152	3	of	of	ADP
ejpam-2495	152	4	(	(	PUNCT
ejpam-2495	152	5	x	x	X
ejpam-2495	152	6	,	,	PUNCT
ejpam-2495	152	7	τ	τ	X
ejpam-2495	152	8	)	)	PUNCT
ejpam-2495	152	9	has	have	VERB
ejpam-2495	152	10	a	a	DET
ejpam-2495	152	11	finite	finite	ADJ
ejpam-2495	152	12	sub	sub	NOUN
ejpam-2495	152	13	cover	cover	NOUN
ejpam-2495	152	14	say	say	VERB
ejpam-2495	152	15	{	{	PUNCT
ejpam-2495	152	16	ai	ai	VERB
ejpam-2495	152	17	:	:	PUNCT
ejpam-2495	152	18	i	i	NOUN
ejpam-2495	152	19	=	=	NOUN
ejpam-2495	152	20	1	1	NUM
ejpam-2495	152	21	,	,	PUNCT
ejpam-2495	152	22	2	2	NUM
ejpam-2495	152	23	,	,	PUNCT
ejpam-2495	152	24	·	·	PUNCT
ejpam-2495	152	25	·	·	PUNCT
ejpam-2495	152	26	·	·	PUNCT
ejpam-2495	152	27	,	,	PUNCT
ejpam-2495	152	28	n	n	CCONJ
ejpam-2495	152	29	}	}	PUNCT
ejpam-2495	152	30	for	for	ADP
ejpam-2495	152	31	x.	x.	NOUN
ejpam-2495	152	32	hence	hence	ADV
ejpam-2495	152	33	(	(	PUNCT
ejpam-2495	152	34	x	x	X
ejpam-2495	152	35	,	,	PUNCT
ejpam-2495	152	36	τ	τ	X
ejpam-2495	152	37	)	)	PUNCT
ejpam-2495	152	38	is	be	AUX
ejpam-2495	152	39	a	a	DET
ejpam-2495	152	40	btµ	btµ	NOUN
ejpam-2495	152	41	compact	compact	ADJ
ejpam-2495	152	42	space	space	NOUN
ejpam-2495	152	43	.	.	PUNCT
ejpam-2495	153	1	k.krishna	k.krishna	NOUN
ejpam-2495	153	2	,	,	PUNCT
ejpam-2495	153	3	m.vignesh	m.vignesh	NOUN
ejpam-2495	153	4	/	/	SYM
ejpam-2495	153	5	eur	eur	PROPN
ejpam-2495	153	6	.	.	PUNCT
ejpam-2495	154	1	j.	j.	PROPN
ejpam-2495	154	2	pure	pure	PROPN
ejpam-2495	154	3	appl	appl	PROPN
ejpam-2495	154	4	.	.	PROPN
ejpam-2495	154	5	math	math	PROPN
ejpam-2495	154	6	,	,	PUNCT
ejpam-2495	154	7	10	10	NUM
ejpam-2495	154	8	(	(	PUNCT
ejpam-2495	154	9	2	2	NUM
ejpam-2495	154	10	)	)	PUNCT
ejpam-2495	154	11	(	(	PUNCT
ejpam-2495	154	12	2017	2017	NUM
ejpam-2495	154	13	)	)	PUNCT
ejpam-2495	154	14	,	,	PUNCT
ejpam-2495	154	15	323	323	NUM
ejpam-2495	154	16	-	-	SYM
ejpam-2495	154	17	334	334	NUM
ejpam-2495	154	18	327	327	NUM
ejpam-2495	154	19	theorem	theorem	NOUN
ejpam-2495	154	20	9	9	NUM
ejpam-2495	154	21	.	.	PUNCT
ejpam-2495	155	1	a	a	DET
ejpam-2495	155	2	supra	supra	PROPN
ejpam-2495	155	3	topological	topological	ADJ
ejpam-2495	155	4	space	space	NOUN
ejpam-2495	155	5	(	(	PUNCT
ejpam-2495	155	6	x	x	X
ejpam-2495	155	7	,	,	PUNCT
ejpam-2495	155	8	τ	τ	X
ejpam-2495	155	9	)	)	PUNCT
ejpam-2495	155	10	is	be	AUX
ejpam-2495	155	11	btµ	btµ	NOUN
ejpam-2495	155	12	compact	compact	ADJ
ejpam-2495	155	13	if	if	SCONJ
ejpam-2495	155	14	and	and	CCONJ
ejpam-2495	155	15	only	only	ADV
ejpam-2495	155	16	if	if	SCONJ
ejpam-2495	155	17	every	every	DET
ejpam-2495	155	18	family	family	NOUN
ejpam-2495	155	19	of	of	ADP
ejpam-2495	155	20	btµ-closed	btµ-closed	ADJ
ejpam-2495	155	21	sets	set	NOUN
ejpam-2495	155	22	of	of	ADP
ejpam-2495	155	23	(	(	PUNCT
ejpam-2495	155	24	x	x	X
ejpam-2495	155	25	,	,	PUNCT
ejpam-2495	155	26	τ	τ	X
ejpam-2495	155	27	)	)	PUNCT
ejpam-2495	155	28	having	have	VERB
ejpam-2495	155	29	finite	finite	ADJ
ejpam-2495	155	30	intersection	intersection	NOUN
ejpam-2495	155	31	property	property	NOUN
ejpam-2495	155	32	has	have	VERB
ejpam-2495	155	33	a	a	DET
ejpam-2495	155	34	non	non	X
ejpam-2495	155	35	empty	empty	ADJ
ejpam-2495	155	36	intersection	intersection	NOUN
ejpam-2495	155	37	.	.	PUNCT
ejpam-2495	156	1	proof	proof	NOUN
ejpam-2495	156	2	.	.	PUNCT
ejpam-2495	157	1	suppose	suppose	VERB
ejpam-2495	157	2	(	(	PUNCT
ejpam-2495	157	3	x	x	X
ejpam-2495	157	4	,	,	PUNCT
ejpam-2495	157	5	τ	τ	X
ejpam-2495	157	6	)	)	PUNCT
ejpam-2495	157	7	is	be	AUX
ejpam-2495	157	8	btµcompact	btµcompact	NOUN
ejpam-2495	157	9	,	,	PUNCT
ejpam-2495	157	10	let	let	VERB
ejpam-2495	157	11	{	{	PUNCT
ejpam-2495	157	12	ai	ai	VERB
ejpam-2495	157	13	:	:	PUNCT
ejpam-2495	157	14	i	i	PRON
ejpam-2495	157	15	∈	∈	PROPN
ejpam-2495	158	1	i	i	PRON
ejpam-2495	158	2	}	}	PUNCT
ejpam-2495	158	3	be	be	VERB
ejpam-2495	158	4	a	a	DET
ejpam-2495	158	5	family	family	NOUN
ejpam-2495	158	6	of	of	ADP
ejpam-2495	158	7	btµclosed	btµclose	VERB
ejpam-2495	158	8	sets	set	NOUN
ejpam-2495	158	9	with	with	ADP
ejpam-2495	158	10	finite	finite	ADJ
ejpam-2495	158	11	intersection	intersection	NOUN
ejpam-2495	158	12	property	property	NOUN
ejpam-2495	158	13	.	.	PUNCT
ejpam-2495	159	1	suppose	suppose	VERB
ejpam-2495	159	2	⋂	⋂	PROPN
ejpam-2495	159	3	i∈i	i∈i	ADJ
ejpam-2495	159	4	ai	ai	PROPN
ejpam-2495	159	5	=	=	PROPN
ejpam-2495	159	6	φ	φ	PROPN
ejpam-2495	159	7	,	,	PUNCT
ejpam-2495	159	8	then	then	ADV
ejpam-2495	159	9	x	x	SYM
ejpam-2495	159	10	⋂	⋂	PROPN
ejpam-2495	160	1	i∈i	i∈i	ADJ
ejpam-2495	160	2	ai=	ai=	PROPN
ejpam-2495	160	3	x.	x.	NOUN
ejpam-2495	161	1	this	this	DET
ejpam-2495	161	2	implies⋃	implies⋃	NOUN
ejpam-2495	161	3	i∈i	i∈i	ADJ
ejpam-2495	161	4	(	(	PUNCT
ejpam-2495	161	5	x−ai	x−ai	PROPN
ejpam-2495	161	6	)	)	PUNCT
ejpam-2495	161	7	=	=	PUNCT
ejpam-2495	162	1	x.	x.	NOUN
ejpam-2495	162	2	thus	thus	ADV
ejpam-2495	162	3	the	the	DET
ejpam-2495	162	4	cover	cover	NOUN
ejpam-2495	162	5	{	{	PUNCT
ejpam-2495	162	6	x	x	NOUN
ejpam-2495	162	7	−ai	−ai	NOUN
ejpam-2495	162	8	:	:	PUNCT
ejpam-2495	162	9	i	i	PRON
ejpam-2495	162	10	∈	∈	VERB
ejpam-2495	163	1	i	i	PRON
ejpam-2495	163	2	}	}	PUNCT
ejpam-2495	163	3	is	be	AUX
ejpam-2495	163	4	a	a	DET
ejpam-2495	163	5	btµopen	btµopen	ADJ
ejpam-2495	163	6	cover	cover	NOUN
ejpam-2495	163	7	of	of	ADP
ejpam-2495	163	8	(	(	PUNCT
ejpam-2495	163	9	x	x	X
ejpam-2495	163	10	,	,	PUNCT
ejpam-2495	163	11	τ	τ	PROPN
ejpam-2495	163	12	)	)	PUNCT
ejpam-2495	163	13	.	.	PUNCT
ejpam-2495	164	1	then	then	ADV
ejpam-2495	164	2	,	,	PUNCT
ejpam-2495	164	3	the	the	DET
ejpam-2495	164	4	btµ-open	btµ-open	ADJ
ejpam-2495	164	5	cover	cover	NOUN
ejpam-2495	164	6	{	{	PUNCT
ejpam-2495	164	7	x	x	NOUN
ejpam-2495	164	8	−ai	−ai	NOUN
ejpam-2495	164	9	:	:	PUNCT
ejpam-2495	164	10	i	i	PRON
ejpam-2495	164	11	∈	∈	VERB
ejpam-2495	164	12	i	i	PRON
ejpam-2495	164	13	}	}	PUNCT
ejpam-2495	164	14	has	have	VERB
ejpam-2495	164	15	a	a	DET
ejpam-2495	164	16	finite	finite	ADJ
ejpam-2495	164	17	sub	sub	NOUN
ejpam-2495	164	18	cover	cover	NOUN
ejpam-2495	164	19	say	say	VERB
ejpam-2495	165	1	x-{x	x-{x	PROPN
ejpam-2495	165	2	−ai	−ai	NOUN
ejpam-2495	165	3	:	:	PUNCT
ejpam-2495	165	4	i	i	NOUN
ejpam-2495	165	5	=	=	NOUN
ejpam-2495	165	6	1	1	NUM
ejpam-2495	165	7	,	,	PUNCT
ejpam-2495	165	8	2	2	NUM
ejpam-2495	165	9	,	,	PUNCT
ejpam-2495	165	10	·	·	PUNCT
ejpam-2495	165	11	·	·	PUNCT
ejpam-2495	165	12	·	·	PUNCT
ejpam-2495	165	13	,	,	PUNCT
ejpam-2495	165	14	n	n	CCONJ
ejpam-2495	165	15	}	}	PUNCT
ejpam-2495	165	16	.	.	PUNCT
ejpam-2495	166	1	this	this	PRON
ejpam-2495	166	2	implies	imply	VERB
ejpam-2495	166	3	x	x	PUNCT
ejpam-2495	166	4	=	=	SYM
ejpam-2495	166	5	⋃	⋃	PROPN
ejpam-2495	166	6	i∈i	i∈i	ADJ
ejpam-2495	166	7	(	(	PUNCT
ejpam-2495	166	8	x	x	X
ejpam-2495	166	9	−	−	NOUN
ejpam-2495	166	10	ai	ai	NOUN
ejpam-2495	166	11	)	)	PUNCT
ejpam-2495	166	12	which	which	PRON
ejpam-2495	166	13	implies	imply	VERB
ejpam-2495	166	14	x	x	NOUN
ejpam-2495	166	15	=	=	SYM
ejpam-2495	166	16	x	x	SYM
ejpam-2495	166	17	n⋂	n⋂	VERB
ejpam-2495	166	18	i=1	i=1	PROPN
ejpam-2495	166	19	ai	ai	VERB
ejpam-2495	166	20	,	,	PUNCT
ejpam-2495	166	21	which	which	PRON
ejpam-2495	166	22	implies	imply	VERB
ejpam-2495	166	23	x	x	NOUN
ejpam-2495	166	24	-	-	PUNCT
ejpam-2495	166	25	x	x	SYM
ejpam-2495	166	26	=	=	PUNCT
ejpam-2495	166	27	x	x	X
ejpam-2495	166	28	-	-	PUNCT
ejpam-2495	166	29	[	[	PUNCT
ejpam-2495	166	30	x	x	PART
ejpam-2495	166	31	−	−	NOUN
ejpam-2495	166	32	n⋂	n⋂	NOUN
ejpam-2495	166	33	i=1	i=1	PROPN
ejpam-2495	166	34	ai	ai	VERB
ejpam-2495	166	35	]	]	PUNCT
ejpam-2495	166	36	which	which	PRON
ejpam-2495	166	37	implies	imply	VERB
ejpam-2495	166	38	φ	φ	PROPN
ejpam-2495	166	39	=	=	SYM
ejpam-2495	166	40	n⋂	n⋂	PROPN
ejpam-2495	166	41	i=1	i=1	PROPN
ejpam-2495	166	42	ai	ai	VERB
ejpam-2495	166	43	.	.	PUNCT
ejpam-2495	167	1	this	this	PRON
ejpam-2495	167	2	disproves	disprove	VERB
ejpam-2495	167	3	the	the	DET
ejpam-2495	167	4	assumption	assumption	NOUN
ejpam-2495	167	5	.	.	PUNCT
ejpam-2495	168	1	hence	hence	ADV
ejpam-2495	168	2	n⋂	n⋂	VERB
ejpam-2495	168	3	i=1	i=1	PROPN
ejpam-2495	168	4	ai	ai	VERB
ejpam-2495	168	5	6=	6=	PROPN
ejpam-2495	168	6	φ	φ	PROPN
ejpam-2495	168	7	conversely	conversely	ADV
ejpam-2495	168	8	suppose	suppose	VERB
ejpam-2495	168	9	(	(	PUNCT
ejpam-2495	168	10	x	x	X
ejpam-2495	168	11	,	,	PUNCT
ejpam-2495	168	12	τ	τ	PROPN
ejpam-2495	168	13	)	)	PUNCT
ejpam-2495	168	14	is	be	AUX
ejpam-2495	168	15	not	not	PART
ejpam-2495	168	16	btµcompact	btµcompact	NOUN
ejpam-2495	168	17	.	.	PUNCT
ejpam-2495	169	1	then	then	ADV
ejpam-2495	169	2	there	there	PRON
ejpam-2495	169	3	exit	exit	VERB
ejpam-2495	169	4	an	an	DET
ejpam-2495	169	5	btµopen	btµopen	ADJ
ejpam-2495	169	6	cover	cover	NOUN
ejpam-2495	169	7	of	of	ADP
ejpam-2495	169	8	(	(	PUNCT
ejpam-2495	169	9	x	x	X
ejpam-2495	169	10	,	,	PUNCT
ejpam-2495	169	11	τ	τ	X
ejpam-2495	169	12	)	)	PUNCT
ejpam-2495	169	13	say	say	VERB
ejpam-2495	169	14	{	{	PUNCT
ejpam-2495	169	15	gi	gi	INTJ
ejpam-2495	169	16	:	:	PUNCT
ejpam-2495	169	17	i	i	PRON
ejpam-2495	169	18	∈	∈	VERB
ejpam-2495	170	1	i	i	PRON
ejpam-2495	170	2	}	}	PUNCT
ejpam-2495	170	3	having	have	VERB
ejpam-2495	170	4	no	no	DET
ejpam-2495	170	5	finite	finite	ADJ
ejpam-2495	170	6	sub	sub	NOUN
ejpam-2495	170	7	cover	cover	NOUN
ejpam-2495	170	8	.	.	PUNCT
ejpam-2495	171	1	this	this	PRON
ejpam-2495	171	2	implies	imply	VERB
ejpam-2495	171	3	for	for	ADP
ejpam-2495	171	4	any	any	DET
ejpam-2495	171	5	finite	finite	ADJ
ejpam-2495	171	6	sub	sub	NOUN
ejpam-2495	171	7	family	family	NOUN
ejpam-2495	171	8	gi	gi	NOUN
ejpam-2495	171	9	:	:	PUNCT
ejpam-2495	171	10	i	i	PRON
ejpam-2495	171	11	=	=	NOUN
ejpam-2495	171	12	1	1	NUM
ejpam-2495	171	13	,	,	PUNCT
ejpam-2495	171	14	2	2	NUM
ejpam-2495	171	15	,	,	PUNCT
ejpam-2495	171	16	·	·	PUNCT
ejpam-2495	171	17	·	·	PUNCT
ejpam-2495	171	18	·	·	PUNCT
ejpam-2495	171	19	,	,	PUNCT
ejpam-2495	171	20	n	n	X
ejpam-2495	171	21	of	of	ADP
ejpam-2495	171	22	{	{	PUNCT
ejpam-2495	171	23	gi	gi	X
ejpam-2495	171	24	:	:	PUNCT
ejpam-2495	171	25	i	i	PRON
ejpam-2495	171	26	∈	∈	PROPN
ejpam-2495	172	1	i	i	X
ejpam-2495	172	2	}	}	PUNCT
ejpam-2495	172	3	,	,	PUNCT
ejpam-2495	172	4	we	we	PRON
ejpam-2495	172	5	have	have	VERB
ejpam-2495	172	6	n⋃	n⋃	VERB
ejpam-2495	172	7	i=1	i=1	PROPN
ejpam-2495	172	8	gi	gi	PROPN
ejpam-2495	172	9	6=	6=	PROPN
ejpam-2495	173	1	x	x	SYM
ejpam-2495	173	2	,	,	PUNCT
ejpam-2495	173	3	which	which	PRON
ejpam-2495	173	4	implies	imply	VERB
ejpam-2495	173	5	x	x	X
ejpam-2495	173	6	n⋃	n⋃	VERB
ejpam-2495	173	7	i=1	i=1	PROPN
ejpam-2495	173	8	gi	gi	PROPN
ejpam-2495	173	9	6=	6=	NUM
ejpam-2495	173	10	x	x	SYM
ejpam-2495	173	11	x	x	X
ejpam-2495	173	12	,	,	PUNCT
ejpam-2495	173	13	therefore	therefore	ADV
ejpam-2495	173	14	⋂	⋂	PROPN
ejpam-2495	173	15	i∈i	i∈i	ADJ
ejpam-2495	173	16	(	(	PUNCT
ejpam-2495	173	17	x	x	X
ejpam-2495	173	18	−	−	PROPN
ejpam-2495	173	19	gi	gi	NOUN
ejpam-2495	173	20	)	)	PUNCT
ejpam-2495	173	21	6=	6=	ADP
ejpam-2495	173	22	φ	φ	PROPN
ejpam-2495	173	23	.	.	PUNCT
ejpam-2495	174	1	then	then	ADV
ejpam-2495	174	2	the	the	DET
ejpam-2495	174	3	family	family	NOUN
ejpam-2495	174	4	{	{	PUNCT
ejpam-2495	174	5	x	x	PROPN
ejpam-2495	174	6	−gi	−gi	NOUN
ejpam-2495	174	7	:	:	PUNCT
ejpam-2495	174	8	i	i	PRON
ejpam-2495	174	9	∈	∈	VERB
ejpam-2495	174	10	i	i	X
ejpam-2495	174	11	}	}	PUNCT
ejpam-2495	174	12	of	of	ADP
ejpam-2495	174	13	btµ	btµ	NOUN
ejpam-2495	174	14	closed	close	VERB
ejpam-2495	174	15	sets	set	NOUN
ejpam-2495	174	16	has	have	VERB
ejpam-2495	174	17	a	a	DET
ejpam-2495	174	18	finite	finite	ADJ
ejpam-2495	174	19	intersection	intersection	NOUN
ejpam-2495	174	20	property	property	NOUN
ejpam-2495	174	21	.	.	PUNCT
ejpam-2495	175	1	also	also	ADV
ejpam-2495	175	2	by	by	ADP
ejpam-2495	175	3	assumption	assumption	NOUN
ejpam-2495	175	4	⋂	⋂	PROPN
ejpam-2495	175	5	i∈i	i∈i	ADJ
ejpam-2495	175	6	(	(	PUNCT
ejpam-2495	175	7	x	x	X
ejpam-2495	175	8	−	−	PROPN
ejpam-2495	175	9	gi	gi	NOUN
ejpam-2495	175	10	)	)	PUNCT
ejpam-2495	175	11	6=	6=	NUM
ejpam-2495	175	12	φ	φ	NUM
ejpam-2495	175	13	which	which	PRON
ejpam-2495	175	14	implies	imply	VERB
ejpam-2495	175	15	x	x	X
ejpam-2495	175	16	n⋃	n⋃	VERB
ejpam-2495	175	17	i=1	i=1	PROPN
ejpam-2495	175	18	gi	gi	PROPN
ejpam-2495	175	19	6=	6=	PROPN
ejpam-2495	175	20	φ	φ	PROPN
ejpam-2495	175	21	,	,	PUNCT
ejpam-2495	175	22	so	so	SCONJ
ejpam-2495	175	23	that	that	SCONJ
ejpam-2495	175	24	n⋃	n⋃	VERB
ejpam-2495	175	25	i=1	i=1	PROPN
ejpam-2495	175	26	gi	gi	INTJ
ejpam-2495	176	1	6=	6=	NUM
ejpam-2495	176	2	x.	x.	NOUN
ejpam-2495	177	1	this	this	PRON
ejpam-2495	177	2	implies	imply	VERB
ejpam-2495	177	3	{	{	PUNCT
ejpam-2495	177	4	gi	gi	INTJ
ejpam-2495	177	5	:	:	PUNCT
ejpam-2495	177	6	i	i	PRON
ejpam-2495	177	7	∈	∈	VERB
ejpam-2495	178	1	i	i	PRON
ejpam-2495	178	2	}	}	PUNCT
ejpam-2495	178	3	is	be	AUX
ejpam-2495	178	4	not	not	PART
ejpam-2495	178	5	a	a	DET
ejpam-2495	178	6	cover	cover	NOUN
ejpam-2495	178	7	of	of	ADP
ejpam-2495	178	8	(	(	PUNCT
ejpam-2495	178	9	x	x	X
ejpam-2495	178	10	,	,	PUNCT
ejpam-2495	178	11	τ	τ	PROPN
ejpam-2495	178	12	)	)	PUNCT
ejpam-2495	178	13	.	.	PUNCT
ejpam-2495	179	1	this	this	PRON
ejpam-2495	179	2	disproves	disprove	VERB
ejpam-2495	179	3	the	the	DET
ejpam-2495	179	4	fact	fact	NOUN
ejpam-2495	179	5	that	that	SCONJ
ejpam-2495	179	6	{	{	PUNCT
ejpam-2495	179	7	gi	gi	X
ejpam-2495	179	8	:	:	PUNCT
ejpam-2495	179	9	i	i	PRON
ejpam-2495	179	10	∈	∈	VERB
ejpam-2495	179	11	i	i	PRON
ejpam-2495	179	12	}	}	PUNCT
ejpam-2495	179	13	is	be	AUX
ejpam-2495	179	14	a	a	DET
ejpam-2495	179	15	cover	cover	NOUN
ejpam-2495	179	16	for	for	ADP
ejpam-2495	179	17	(	(	PUNCT
ejpam-2495	179	18	x	x	X
ejpam-2495	179	19	,	,	PUNCT
ejpam-2495	179	20	τ	τ	PROPN
ejpam-2495	179	21	)	)	PUNCT
ejpam-2495	179	22	.	.	PUNCT
ejpam-2495	180	1	therefore	therefore	ADV
ejpam-2495	180	2	a	a	DET
ejpam-2495	180	3	btµ	btµ	NOUN
ejpam-2495	180	4	open	open	ADJ
ejpam-2495	180	5	cover	cover	NOUN
ejpam-2495	180	6	{	{	PUNCT
ejpam-2495	180	7	gi	gi	INTJ
ejpam-2495	180	8	:	:	PUNCT
ejpam-2495	181	1	i	i	PRON
ejpam-2495	181	2	∈	∈	VERB
ejpam-2495	181	3	i	i	X
ejpam-2495	181	4	}	}	PUNCT
ejpam-2495	181	5	of	of	ADP
ejpam-2495	181	6	(	(	PUNCT
ejpam-2495	181	7	x	x	X
ejpam-2495	181	8	,	,	PUNCT
ejpam-2495	181	9	τ	τ	X
ejpam-2495	181	10	)	)	PUNCT
ejpam-2495	181	11	has	have	VERB
ejpam-2495	181	12	a	a	DET
ejpam-2495	181	13	finite	finite	ADJ
ejpam-2495	181	14	sub	sub	NOUN
ejpam-2495	181	15	cover	cover	NOUN
ejpam-2495	181	16	{	{	PUNCT
ejpam-2495	181	17	gi	gi	INTJ
ejpam-2495	181	18	:	:	PUNCT
ejpam-2495	181	19	i	i	NOUN
ejpam-2495	181	20	=	=	NOUN
ejpam-2495	181	21	1	1	NUM
ejpam-2495	181	22	,	,	PUNCT
ejpam-2495	181	23	2	2	NUM
ejpam-2495	181	24	,	,	PUNCT
ejpam-2495	181	25	·	·	PUNCT
ejpam-2495	181	26	·	·	PUNCT
ejpam-2495	181	27	·	·	PUNCT
ejpam-2495	181	28	,	,	PUNCT
ejpam-2495	181	29	n	n	CCONJ
ejpam-2495	181	30	}	}	PUNCT
ejpam-2495	181	31	.	.	PUNCT
ejpam-2495	182	1	hence	hence	ADV
ejpam-2495	182	2	(	(	PUNCT
ejpam-2495	182	3	x	x	X
ejpam-2495	182	4	,	,	PUNCT
ejpam-2495	182	5	τ	τ	X
ejpam-2495	182	6	)	)	PUNCT
ejpam-2495	182	7	is	be	AUX
ejpam-2495	182	8	btµ	btµ	PROPN
ejpam-2495	182	9	compact	compact	ADJ
ejpam-2495	182	10	.	.	PUNCT
ejpam-2495	183	1	theorem	theorem	ADJ
ejpam-2495	183	2	10	10	NUM
ejpam-2495	183	3	.	.	PUNCT
ejpam-2495	184	1	let	let	VERB
ejpam-2495	184	2	a	a	DET
ejpam-2495	184	3	be	be	AUX
ejpam-2495	184	4	a	a	DET
ejpam-2495	184	5	btµ	btµ	NOUN
ejpam-2495	184	6	compact	compact	ADV
ejpam-2495	184	7	set	set	VERB
ejpam-2495	184	8	relative	relative	ADJ
ejpam-2495	184	9	to	to	ADP
ejpam-2495	184	10	a	a	DET
ejpam-2495	184	11	supra	supra	ADJ
ejpam-2495	184	12	topological	topological	ADJ
ejpam-2495	184	13	space	space	NOUN
ejpam-2495	184	14	x	x	PUNCT
ejpam-2495	184	15	and	and	CCONJ
ejpam-2495	184	16	b	b	X
ejpam-2495	184	17	be	be	AUX
ejpam-2495	184	18	a	a	DET
ejpam-2495	184	19	btµ	btµ	NOUN
ejpam-2495	184	20	-closed	-close	VERB
ejpam-2495	184	21	subset	subset	NOUN
ejpam-2495	184	22	of	of	ADP
ejpam-2495	184	23	x.	x.	NOUN
ejpam-2495	184	24	then	then	ADV
ejpam-2495	184	25	a∩	a∩	PROPN
ejpam-2495	184	26	b	b	PROPN
ejpam-2495	184	27	is	be	AUX
ejpam-2495	184	28	btµ	btµ	PROPN
ejpam-2495	184	29	compact	compact	ADJ
ejpam-2495	184	30	relative	relative	ADJ
ejpam-2495	184	31	to	to	ADP
ejpam-2495	184	32	x.	x.	NOUN
ejpam-2495	184	33	proof	proof	NOUN
ejpam-2495	184	34	.	.	PUNCT
ejpam-2495	185	1	let	let	VERB
ejpam-2495	185	2	a	a	PRON
ejpam-2495	185	3	is	be	AUX
ejpam-2495	185	4	btµ	btµ	NOUN
ejpam-2495	185	5	compact	compact	ADJ
ejpam-2495	185	6	relative	relative	ADJ
ejpam-2495	185	7	to	to	ADP
ejpam-2495	185	8	x.	x.	NOUN
ejpam-2495	185	9	suppose	suppose	VERB
ejpam-2495	185	10	that	that	SCONJ
ejpam-2495	185	11	{	{	PUNCT
ejpam-2495	185	12	ai	ai	VERB
ejpam-2495	185	13	:	:	PUNCT
ejpam-2495	185	14	i	i	PRON
ejpam-2495	185	15	∈	∈	PROPN
ejpam-2495	185	16	i	i	PRON
ejpam-2495	185	17	}	}	PUNCT
ejpam-2495	185	18	is	be	AUX
ejpam-2495	185	19	a	a	DET
ejpam-2495	185	20	cover	cover	NOUN
ejpam-2495	185	21	of	of	ADP
ejpam-2495	185	22	a∩	a∩	PROPN
ejpam-2495	185	23	b	b	PROPN
ejpam-2495	185	24	by	by	ADP
ejpam-2495	185	25	btµ	btµ	NOUN
ejpam-2495	185	26	open	open	ADJ
ejpam-2495	185	27	sets	set	NOUN
ejpam-2495	185	28	in	in	ADP
ejpam-2495	185	29	x.	x.	NOUN
ejpam-2495	185	30	then	then	ADV
ejpam-2495	185	31	{	{	PUNCT
ejpam-2495	185	32	ai	ai	INTJ
ejpam-2495	185	33	:	:	PUNCT
ejpam-2495	185	34	i	i	PRON
ejpam-2495	185	35	∈	∈	VERB
ejpam-2495	185	36	i	i	PRON
ejpam-2495	185	37	}	}	PUNCT
ejpam-2495	185	38	∪	∪	VERB
ejpam-2495	185	39	{	{	PUNCT
ejpam-2495	185	40	bc	bc	PROPN
ejpam-2495	185	41	}	}	PUNCT
ejpam-2495	185	42	is	be	AUX
ejpam-2495	185	43	a	a	DET
ejpam-2495	185	44	cover	cover	NOUN
ejpam-2495	185	45	of	of	ADP
ejpam-2495	185	46	a	a	PRON
ejpam-2495	185	47	by	by	ADP
ejpam-2495	185	48	btµ	btµ	NOUN
ejpam-2495	185	49	-open	-open	PROPN
ejpam-2495	185	50	sets	set	NOUN
ejpam-2495	185	51	in	in	ADP
ejpam-2495	185	52	x	x	NOUN
ejpam-2495	185	53	,	,	PUNCT
ejpam-2495	185	54	but	but	CCONJ
ejpam-2495	185	55	a	a	PRON
ejpam-2495	185	56	is	be	AUX
ejpam-2495	185	57	btµ	btµ	NOUN
ejpam-2495	185	58	compact	compact	ADJ
ejpam-2495	185	59	relative	relative	ADJ
ejpam-2495	185	60	to	to	ADP
ejpam-2495	185	61	x	x	PRON
ejpam-2495	185	62	,	,	PUNCT
ejpam-2495	185	63	so	so	SCONJ
ejpam-2495	185	64	there	there	PRON
ejpam-2495	185	65	exist	exist	VERB
ejpam-2495	185	66	i1	i1	PROPN
ejpam-2495	185	67	,	,	PUNCT
ejpam-2495	185	68	i2	i2	PROPN
ejpam-2495	185	69	,	,	PUNCT
ejpam-2495	185	70	·	·	PUNCT
ejpam-2495	185	71	·	·	PUNCT
ejpam-2495	185	72	·	·	PUNCT
ejpam-2495	185	73	,	,	PUNCT
ejpam-2495	185	74	in	in	ADP
ejpam-2495	185	75	such	such	ADJ
ejpam-2495	185	76	that	that	SCONJ
ejpam-2495	185	77	a	a	DET
ejpam-2495	185	78	⊆	⊆	NUM
ejpam-2495	185	79	⋃	⋃	NOUN
ejpam-2495	185	80	{	{	PUNCT
ejpam-2495	185	81	aij	aij	PROPN
ejpam-2495	185	82	:	:	PUNCT
ejpam-2495	185	83	j	j	PROPN
ejpam-2495	185	84	=	=	SYM
ejpam-2495	185	85	1	1	NUM
ejpam-2495	185	86	,	,	PUNCT
ejpam-2495	185	87	2	2	NUM
ejpam-2495	185	88	,	,	PUNCT
ejpam-2495	185	89	·	·	PUNCT
ejpam-2495	185	90	·	·	PUNCT
ejpam-2495	185	91	·	·	PUNCT
ejpam-2495	185	92	,	,	PUNCT
ejpam-2495	185	93	n	n	CCONJ
ejpam-2495	185	94	}	}	PUNCT
ejpam-2495	185	95	∪	∪	X
ejpam-2495	185	96	bc	bc	PROPN
ejpam-2495	185	97	.	.	PUNCT
ejpam-2495	186	1	then	then	ADV
ejpam-2495	186	2	a∩b	a∩b	PROPN
ejpam-2495	186	3	⊆	⊆	NUM
ejpam-2495	186	4	⋃{⋃	⋃{⋃	PROPN
ejpam-2495	186	5	aij	aij	PROPN
ejpam-2495	186	6	∩b	∩b	NOUN
ejpam-2495	186	7	,	,	PUNCT
ejpam-2495	186	8	j	j	NOUN
ejpam-2495	186	9	=	=	SYM
ejpam-2495	186	10	1	1	NUM
ejpam-2495	186	11	,	,	PUNCT
ejpam-2495	186	12	2	2	NUM
ejpam-2495	186	13	,	,	PUNCT
ejpam-2495	186	14	·	·	PUNCT
ejpam-2495	186	15	·	·	PUNCT
ejpam-2495	186	16	·	·	PUNCT
ejpam-2495	186	17	,	,	PUNCT
ejpam-2495	186	18	n	n	CCONJ
ejpam-2495	186	19	}	}	PUNCT
ejpam-2495	186	20	⊆⋃	⊆⋃	PROPN
ejpam-2495	186	21	{	{	PUNCT
ejpam-2495	186	22	aij	aij	PROPN
ejpam-2495	186	23	:	:	PUNCT
ejpam-2495	186	24	j	j	PROPN
ejpam-2495	186	25	=	=	SYM
ejpam-2495	186	26	1	1	NUM
ejpam-2495	186	27	,	,	PUNCT
ejpam-2495	186	28	2	2	NUM
ejpam-2495	186	29	,	,	PUNCT
ejpam-2495	186	30	·	·	PUNCT
ejpam-2495	186	31	·	·	PUNCT
ejpam-2495	186	32	·	·	PUNCT
ejpam-2495	186	33	,	,	PUNCT
ejpam-2495	186	34	n	n	CCONJ
ejpam-2495	186	35	}	}	PUNCT
ejpam-2495	186	36	.	.	PUNCT
ejpam-2495	187	1	hence	hence	ADV
ejpam-2495	187	2	a∩	a∩	PROPN
ejpam-2495	187	3	b	b	PROPN
ejpam-2495	187	4	is	be	AUX
ejpam-2495	187	5	btµ	btµ	NOUN
ejpam-2495	187	6	compact	compact	ADJ
ejpam-2495	187	7	relative	relative	ADJ
ejpam-2495	187	8	to	to	ADP
ejpam-2495	187	9	x.	x.	NOUN
ejpam-2495	187	10	theorem	theorem	VERB
ejpam-2495	187	11	11	11	NUM
ejpam-2495	187	12	.	.	PUNCT
ejpam-2495	188	1	if	if	SCONJ
ejpam-2495	188	2	a	a	DET
ejpam-2495	188	3	function	function	NOUN
ejpam-2495	188	4	f	f	X
ejpam-2495	188	5	:	:	PUNCT
ejpam-2495	188	6	(	(	PUNCT
ejpam-2495	188	7	x	x	X
ejpam-2495	188	8	,	,	PUNCT
ejpam-2495	188	9	τ	τ	X
ejpam-2495	188	10	)	)	PUNCT
ejpam-2495	188	11	→	→	SYM
ejpam-2495	188	12	(	(	PUNCT
ejpam-2495	188	13	y	y	PROPN
ejpam-2495	188	14	,	,	PUNCT
ejpam-2495	188	15	σ	σ	PROPN
ejpam-2495	188	16	)	)	PUNCT
ejpam-2495	188	17	is	be	AUX
ejpam-2495	188	18	btµ	btµ	NOUN
ejpam-2495	188	19	irresolute	irresolute	ADJ
ejpam-2495	188	20	and	and	CCONJ
ejpam-2495	188	21	a	a	DET
ejpam-2495	188	22	subset	subset	NOUN
ejpam-2495	188	23	of	of	ADP
ejpam-2495	188	24	x	x	SYM
ejpam-2495	188	25	is	be	AUX
ejpam-2495	188	26	btµ	btµ	NOUN
ejpam-2495	188	27	compact	compact	ADJ
ejpam-2495	188	28	relative	relative	ADJ
ejpam-2495	188	29	to	to	ADP
ejpam-2495	188	30	x	x	PRON
ejpam-2495	188	31	,	,	PUNCT
ejpam-2495	188	32	then	then	ADV
ejpam-2495	188	33	f(b	f(b	PROPN
ejpam-2495	188	34	)	)	PUNCT
ejpam-2495	188	35	is	be	AUX
ejpam-2495	188	36	btµ	btµ	NOUN
ejpam-2495	188	37	compact	compact	ADJ
ejpam-2495	188	38	relative	relative	ADV
ejpam-2495	188	39	to	to	ADP
ejpam-2495	188	40	y.	y.	NOUN
ejpam-2495	188	41	proof	proof	NOUN
ejpam-2495	188	42	.	.	PUNCT
ejpam-2495	189	1	let	let	VERB
ejpam-2495	189	2	{	{	PUNCT
ejpam-2495	189	3	ai	ai	VERB
ejpam-2495	189	4	:	:	PUNCT
ejpam-2495	189	5	i	i	PRON
ejpam-2495	189	6	∈	∈	PROPN
ejpam-2495	189	7	i	i	PRON
ejpam-2495	189	8	}	}	PUNCT
ejpam-2495	189	9	be	be	VERB
ejpam-2495	189	10	a	a	DET
ejpam-2495	189	11	cover	cover	NOUN
ejpam-2495	189	12	of	of	ADP
ejpam-2495	189	13	f(b	f(b	PROPN
ejpam-2495	189	14	)	)	PUNCT
ejpam-2495	189	15	by	by	ADP
ejpam-2495	189	16	btµ	btµ	PROPN
ejpam-2495	189	17	-open	-open	PROPN
ejpam-2495	189	18	subsets	subset	NOUN
ejpam-2495	189	19	of	of	ADP
ejpam-2495	189	20	y.	y.	PROPN
ejpam-2495	189	21	then	then	ADV
ejpam-2495	189	22	{	{	PUNCT
ejpam-2495	189	23	f−1(ai	f−1(ai	NOUN
ejpam-2495	189	24	)	)	PUNCT
ejpam-2495	189	25	:	:	PUNCT
ejpam-2495	190	1	i	i	PRON
ejpam-2495	190	2	∈	∈	VERB
ejpam-2495	190	3	i	i	PRON
ejpam-2495	190	4	}	}	PUNCT
ejpam-2495	190	5	is	be	AUX
ejpam-2495	190	6	a	a	DET
ejpam-2495	190	7	cover	cover	NOUN
ejpam-2495	190	8	of	of	ADP
ejpam-2495	190	9	b	b	NOUN
ejpam-2495	190	10	by	by	ADP
ejpam-2495	190	11	btµ	btµ	PROPN
ejpam-2495	190	12	-open	-open	PROPN
ejpam-2495	190	13	subsets	subset	NOUN
ejpam-2495	190	14	of	of	ADP
ejpam-2495	190	15	x.	x.	NOUN
ejpam-2495	190	16	since	since	SCONJ
ejpam-2495	190	17	b	b	PROPN
ejpam-2495	190	18	is	be	AUX
ejpam-2495	190	19	btµ	btµ	NOUN
ejpam-2495	190	20	-compact	-compact	NOUN
ejpam-2495	190	21	relative	relative	ADJ
ejpam-2495	190	22	to	to	ADP
ejpam-2495	190	23	x	x	PRON
ejpam-2495	190	24	,	,	PUNCT
ejpam-2495	190	25	{	{	PUNCT
ejpam-2495	190	26	f−1(ai	f−1(ai	NOUN
ejpam-2495	190	27	)	)	PUNCT
ejpam-2495	190	28	:	:	PUNCT
ejpam-2495	191	1	i	i	PRON
ejpam-2495	191	2	∈	∈	VERB
ejpam-2495	191	3	i	i	PRON
ejpam-2495	191	4	}	}	PUNCT
ejpam-2495	191	5	has	have	VERB
ejpam-2495	191	6	a	a	DET
ejpam-2495	191	7	finite	finite	ADJ
ejpam-2495	191	8	subcover	subcover	PROPN
ejpam-2495	191	9	say	say	VERB
ejpam-2495	191	10	{	{	PUNCT
ejpam-2495	191	11	f−1(a1	f−1(a1	NOUN
ejpam-2495	191	12	)	)	PUNCT
ejpam-2495	191	13	,	,	PUNCT
ejpam-2495	191	14	f	f	PROPN
ejpam-2495	191	15	−1(a2	−1(a2	NOUN
ejpam-2495	191	16	)	)	PUNCT
ejpam-2495	191	17	,	,	PUNCT
ejpam-2495	191	18	·	·	PUNCT
ejpam-2495	191	19	·	·	PUNCT
ejpam-2495	191	20	·	·	PUNCT
ejpam-2495	191	21	,	,	PUNCT
ejpam-2495	191	22	f−1(an	f−1(an	NOUN
ejpam-2495	191	23	)	)	PUNCT
ejpam-2495	191	24	}	}	PUNCT
ejpam-2495	191	25	for	for	ADP
ejpam-2495	191	26	b.	b.	PROPN
ejpam-2495	191	27	now	now	ADV
ejpam-2495	191	28	k.krishna	k.krishna	NOUN
ejpam-2495	191	29	,	,	PUNCT
ejpam-2495	191	30	m.vignesh	m.vignesh	NOUN
ejpam-2495	191	31	/	/	SYM
ejpam-2495	191	32	eur	eur	PROPN
ejpam-2495	191	33	.	.	PUNCT
ejpam-2495	192	1	j.	j.	PROPN
ejpam-2495	192	2	pure	pure	PROPN
ejpam-2495	192	3	appl	appl	PROPN
ejpam-2495	192	4	.	.	PROPN
ejpam-2495	192	5	math	math	PROPN
ejpam-2495	192	6	,	,	PUNCT
ejpam-2495	192	7	10	10	NUM
ejpam-2495	192	8	(	(	PUNCT
ejpam-2495	192	9	2	2	NUM
ejpam-2495	192	10	)	)	PUNCT
ejpam-2495	192	11	(	(	PUNCT
ejpam-2495	192	12	2017	2017	NUM
ejpam-2495	192	13	)	)	PUNCT
ejpam-2495	192	14	,	,	PUNCT
ejpam-2495	192	15	323	323	NUM
ejpam-2495	192	16	-	-	SYM
ejpam-2495	192	17	334	334	NUM
ejpam-2495	192	18	328	328	NUM
ejpam-2495	192	19	{	{	PUNCT
ejpam-2495	192	20	a1	a1	PROPN
ejpam-2495	192	21	,	,	PUNCT
ejpam-2495	192	22	a2	a2	PROPN
ejpam-2495	192	23	,	,	PUNCT
ejpam-2495	192	24	·	·	PUNCT
ejpam-2495	192	25	·	·	PUNCT
ejpam-2495	192	26	·	·	PUNCT
ejpam-2495	192	27	,	,	PUNCT
ejpam-2495	192	28	an	an	PRON
ejpam-2495	192	29	}	}	PUNCT
ejpam-2495	192	30	is	be	AUX
ejpam-2495	192	31	a	a	DET
ejpam-2495	192	32	finite	finite	ADJ
ejpam-2495	192	33	subcover	subcover	NOUN
ejpam-2495	192	34	of	of	ADP
ejpam-2495	192	35	{	{	PUNCT
ejpam-2495	192	36	ai	ai	PROPN
ejpam-2495	192	37	:	:	PUNCT
ejpam-2495	192	38	i	i	PRON
ejpam-2495	192	39	∈	∈	VERB
ejpam-2495	193	1	i	i	X
ejpam-2495	193	2	}	}	PUNCT
ejpam-2495	193	3	for	for	ADP
ejpam-2495	193	4	f(b	f(b	PROPN
ejpam-2495	193	5	)	)	PUNCT
ejpam-2495	193	6	.	.	PUNCT
ejpam-2495	194	1	so	so	ADV
ejpam-2495	194	2	f(b	f(b	PROPN
ejpam-2495	194	3	)	)	PUNCT
ejpam-2495	194	4	is	be	AUX
ejpam-2495	194	5	btµ	btµ	NOUN
ejpam-2495	194	6	-compact	-compact	PROPN
ejpam-2495	194	7	relative	relative	ADJ
ejpam-2495	194	8	to	to	ADP
ejpam-2495	194	9	y.	y.	PROPN
ejpam-2495	194	10	4	4	NUM
ejpam-2495	194	11	.	.	PUNCT
ejpam-2495	195	1	countably	countably	ADV
ejpam-2495	195	2	supra	supra	PROPN
ejpam-2495	195	3	bt	bt	PROPN
ejpam-2495	195	4	compactness	compactness	NOUN
ejpam-2495	195	5	in	in	ADP
ejpam-2495	195	6	supra	supra	PROPN
ejpam-2495	195	7	topological	topological	ADJ
ejpam-2495	195	8	spaces	space	NOUN
ejpam-2495	195	9	in	in	ADP
ejpam-2495	195	10	this	this	DET
ejpam-2495	195	11	section	section	NOUN
ejpam-2495	195	12	,	,	PUNCT
ejpam-2495	195	13	we	we	PRON
ejpam-2495	195	14	concentrate	concentrate	VERB
ejpam-2495	195	15	on	on	ADP
ejpam-2495	195	16	the	the	DET
ejpam-2495	195	17	concept	concept	NOUN
ejpam-2495	195	18	of	of	ADP
ejpam-2495	195	19	countably	countably	ADV
ejpam-2495	195	20	btµcompactness	btµcompactness	NOUN
ejpam-2495	195	21	and	and	CCONJ
ejpam-2495	195	22	their	their	PRON
ejpam-2495	195	23	properties	property	NOUN
ejpam-2495	195	24	.	.	PUNCT
ejpam-2495	196	1	definition	definition	NOUN
ejpam-2495	196	2	15	15	NUM
ejpam-2495	196	3	.	.	PUNCT
ejpam-2495	197	1	a	a	DET
ejpam-2495	197	2	supra	supra	PROPN
ejpam-2495	197	3	topological	topological	ADJ
ejpam-2495	197	4	space	space	NOUN
ejpam-2495	197	5	(	(	PUNCT
ejpam-2495	197	6	x	x	X
ejpam-2495	197	7	,	,	PUNCT
ejpam-2495	197	8	τ	τ	X
ejpam-2495	197	9	)	)	PUNCT
ejpam-2495	197	10	is	be	AUX
ejpam-2495	197	11	said	say	VERB
ejpam-2495	197	12	to	to	PART
ejpam-2495	197	13	be	be	AUX
ejpam-2495	197	14	countably	countably	ADV
ejpam-2495	197	15	btµ	btµ	ADJ
ejpam-2495	197	16	compact	compact	ADJ
ejpam-2495	197	17	if	if	SCONJ
ejpam-2495	197	18	every	every	DET
ejpam-2495	197	19	countable	countable	ADJ
ejpam-2495	197	20	btµ	btµ	NOUN
ejpam-2495	197	21	open	open	ADJ
ejpam-2495	197	22	cover	cover	NOUN
ejpam-2495	197	23	of	of	ADP
ejpam-2495	197	24	x	x	PUNCT
ejpam-2495	197	25	has	have	VERB
ejpam-2495	197	26	a	a	DET
ejpam-2495	197	27	finite	finite	ADJ
ejpam-2495	197	28	subcover	subcover	PROPN
ejpam-2495	197	29	.	.	PUNCT
ejpam-2495	198	1	theorem	theorem	VERB
ejpam-2495	198	2	12	12	NUM
ejpam-2495	198	3	.	.	PUNCT
ejpam-2495	199	1	if	if	SCONJ
ejpam-2495	199	2	(	(	PUNCT
ejpam-2495	199	3	x	x	X
ejpam-2495	199	4	,	,	PUNCT
ejpam-2495	199	5	τ	τ	X
ejpam-2495	199	6	)	)	PUNCT
ejpam-2495	199	7	is	be	AUX
ejpam-2495	199	8	a	a	DET
ejpam-2495	199	9	countably	countably	ADV
ejpam-2495	199	10	btµ	btµ	ADJ
ejpam-2495	199	11	compact	compact	ADJ
ejpam-2495	199	12	space	space	NOUN
ejpam-2495	199	13	,	,	PUNCT
ejpam-2495	199	14	then	then	ADV
ejpam-2495	199	15	(	(	PUNCT
ejpam-2495	199	16	x	x	X
ejpam-2495	199	17	,	,	PUNCT
ejpam-2495	199	18	τ	τ	X
ejpam-2495	199	19	)	)	PUNCT
ejpam-2495	199	20	is	be	AUX
ejpam-2495	199	21	countably	countably	ADV
ejpam-2495	199	22	supra	supra	ADJ
ejpam-2495	199	23	compact	compact	ADJ
ejpam-2495	199	24	.	.	PUNCT
ejpam-2495	200	1	proof	proof	NOUN
ejpam-2495	200	2	.	.	PUNCT
ejpam-2495	201	1	let	let	VERB
ejpam-2495	201	2	(	(	PUNCT
ejpam-2495	201	3	x	x	X
ejpam-2495	201	4	,	,	PUNCT
ejpam-2495	201	5	τ	τ	X
ejpam-2495	201	6	)	)	PUNCT
ejpam-2495	201	7	is	be	AUX
ejpam-2495	201	8	countably	countably	ADV
ejpam-2495	201	9	btµ	btµ	ADJ
ejpam-2495	201	10	compact	compact	ADJ
ejpam-2495	201	11	space	space	NOUN
ejpam-2495	201	12	.	.	PUNCT
ejpam-2495	202	1	let	let	VERB
ejpam-2495	202	2	{	{	PUNCT
ejpam-2495	202	3	ai	ai	VERB
ejpam-2495	202	4	:	:	PUNCT
ejpam-2495	202	5	i	i	PRON
ejpam-2495	202	6	∈	∈	PROPN
ejpam-2495	202	7	i	i	PRON
ejpam-2495	202	8	}	}	PUNCT
ejpam-2495	202	9	be	be	VERB
ejpam-2495	202	10	a	a	DET
ejpam-2495	202	11	countable	countable	ADJ
ejpam-2495	202	12	supra	supra	NOUN
ejpam-2495	202	13	open	open	ADJ
ejpam-2495	202	14	cover	cover	NOUN
ejpam-2495	202	15	of	of	ADP
ejpam-2495	202	16	(	(	PUNCT
ejpam-2495	202	17	x	x	X
ejpam-2495	202	18	,	,	PUNCT
ejpam-2495	202	19	τ	τ	PROPN
ejpam-2495	202	20	)	)	PUNCT
ejpam-2495	202	21	.	.	PUNCT
ejpam-2495	203	1	by	by	ADP
ejpam-2495	203	2	[	[	X
ejpam-2495	203	3	4	4	NUM
ejpam-2495	203	4	]	]	PUNCT
ejpam-2495	203	5	,	,	PUNCT
ejpam-2495	203	6	{	{	PUNCT
ejpam-2495	203	7	ai	ai	VERB
ejpam-2495	203	8	:	:	PUNCT
ejpam-2495	203	9	i	i	PRON
ejpam-2495	203	10	∈	∈	PROPN
ejpam-2495	203	11	i	i	PRON
ejpam-2495	203	12	}	}	PUNCT
ejpam-2495	203	13	is	be	AUX
ejpam-2495	203	14	a	a	DET
ejpam-2495	203	15	countable	countable	ADJ
ejpam-2495	203	16	btµ	btµ	NOUN
ejpam-2495	203	17	open	open	ADJ
ejpam-2495	203	18	cover	cover	NOUN
ejpam-2495	203	19	of	of	ADP
ejpam-2495	203	20	(	(	PUNCT
ejpam-2495	203	21	x	x	X
ejpam-2495	203	22	,	,	PUNCT
ejpam-2495	203	23	τ	τ	PROPN
ejpam-2495	203	24	)	)	PUNCT
ejpam-2495	203	25	.	.	PUNCT
ejpam-2495	204	1	since	since	SCONJ
ejpam-2495	204	2	(	(	PUNCT
ejpam-2495	204	3	x	x	X
ejpam-2495	204	4	,	,	PUNCT
ejpam-2495	204	5	τ	τ	X
ejpam-2495	204	6	)	)	PUNCT
ejpam-2495	204	7	is	be	AUX
ejpam-2495	204	8	countably	countably	ADV
ejpam-2495	204	9	btµ	btµ	PROPN
ejpam-2495	204	10	compact	compact	ADJ
ejpam-2495	204	11	,	,	PUNCT
ejpam-2495	204	12	countable	countable	ADJ
ejpam-2495	204	13	btµ	btµ	NOUN
ejpam-2495	204	14	open	open	ADJ
ejpam-2495	204	15	cover	cover	NOUN
ejpam-2495	204	16	{	{	PUNCT
ejpam-2495	204	17	ai	ai	VERB
ejpam-2495	204	18	:	:	PUNCT
ejpam-2495	204	19	i	i	PRON
ejpam-2495	204	20	∈	∈	VERB
ejpam-2495	205	1	i	i	X
ejpam-2495	205	2	}	}	PUNCT
ejpam-2495	205	3	of	of	ADP
ejpam-2495	205	4	(	(	PUNCT
ejpam-2495	205	5	x	x	X
ejpam-2495	205	6	,	,	PUNCT
ejpam-2495	205	7	τ	τ	X
ejpam-2495	205	8	)	)	PUNCT
ejpam-2495	205	9	has	have	VERB
ejpam-2495	205	10	a	a	DET
ejpam-2495	205	11	finite	finite	ADJ
ejpam-2495	205	12	subcover	subcover	PROPN
ejpam-2495	205	13	say	say	VERB
ejpam-2495	205	14	{	{	PUNCT
ejpam-2495	205	15	ai	ai	VERB
ejpam-2495	205	16	:	:	PUNCT
ejpam-2495	205	17	i	i	NOUN
ejpam-2495	205	18	=	=	NOUN
ejpam-2495	205	19	1	1	NUM
ejpam-2495	205	20	,	,	PUNCT
ejpam-2495	205	21	2	2	NUM
ejpam-2495	205	22	,	,	PUNCT
ejpam-2495	205	23	·	·	PUNCT
ejpam-2495	205	24	·	·	PUNCT
ejpam-2495	205	25	·	·	PUNCT
ejpam-2495	205	26	,	,	PUNCT
ejpam-2495	205	27	n	n	CCONJ
ejpam-2495	205	28	}	}	PUNCT
ejpam-2495	205	29	for	for	ADP
ejpam-2495	205	30	x.	x.	NOUN
ejpam-2495	205	31	hence	hence	ADV
ejpam-2495	205	32	(	(	PUNCT
ejpam-2495	205	33	x	x	X
ejpam-2495	205	34	,	,	PUNCT
ejpam-2495	205	35	τ	τ	X
ejpam-2495	205	36	)	)	PUNCT
ejpam-2495	205	37	is	be	AUX
ejpam-2495	205	38	a	a	DET
ejpam-2495	205	39	countably	countably	ADV
ejpam-2495	205	40	supra	supra	ADJ
ejpam-2495	205	41	compact	compact	ADJ
ejpam-2495	205	42	space	space	NOUN
ejpam-2495	205	43	.	.	PUNCT
ejpam-2495	206	1	theorem	theorem	VERB
ejpam-2495	206	2	13	13	NUM
ejpam-2495	206	3	.	.	PUNCT
ejpam-2495	207	1	if	if	SCONJ
ejpam-2495	207	2	(	(	PUNCT
ejpam-2495	207	3	x	x	X
ejpam-2495	207	4	,	,	PUNCT
ejpam-2495	207	5	τ	τ	X
ejpam-2495	207	6	)	)	PUNCT
ejpam-2495	207	7	is	be	AUX
ejpam-2495	207	8	countably	countably	ADV
ejpam-2495	207	9	supra	supra	ADJ
ejpam-2495	207	10	compact	compact	PROPN
ejpam-2495	207	11	and	and	CCONJ
ejpam-2495	207	12	btt	btt	PROPN
ejpam-2495	207	13	µ	µ	PROPN
ejpam-2495	207	14	c	c	NOUN
ejpam-2495	207	15	-space	-space	NOUN
ejpam-2495	207	16	,	,	PUNCT
ejpam-2495	207	17	then	then	ADV
ejpam-2495	207	18	(	(	PUNCT
ejpam-2495	207	19	x	x	X
ejpam-2495	207	20	,	,	PUNCT
ejpam-2495	207	21	τ	τ	X
ejpam-2495	207	22	)	)	PUNCT
ejpam-2495	207	23	is	be	AUX
ejpam-2495	207	24	countably	countably	ADV
ejpam-2495	207	25	btµ	btµ	NOUN
ejpam-2495	207	26	compact	compact	ADJ
ejpam-2495	207	27	.	.	PUNCT
ejpam-2495	208	1	proof	proof	NOUN
ejpam-2495	208	2	.	.	PUNCT
ejpam-2495	209	1	let	let	VERB
ejpam-2495	209	2	(	(	PUNCT
ejpam-2495	209	3	x	x	X
ejpam-2495	209	4	,	,	PUNCT
ejpam-2495	209	5	τ	τ	X
ejpam-2495	209	6	)	)	PUNCT
ejpam-2495	209	7	is	be	AUX
ejpam-2495	209	8	countably	countably	ADV
ejpam-2495	209	9	btµ	btµ	ADJ
ejpam-2495	209	10	compact	compact	ADJ
ejpam-2495	209	11	space	space	NOUN
ejpam-2495	209	12	.	.	PUNCT
ejpam-2495	210	1	let	let	VERB
ejpam-2495	210	2	{	{	PUNCT
ejpam-2495	210	3	ai	ai	VERB
ejpam-2495	210	4	:	:	PUNCT
ejpam-2495	210	5	i	i	PRON
ejpam-2495	210	6	∈	∈	PROPN
ejpam-2495	210	7	i	i	PRON
ejpam-2495	210	8	}	}	PUNCT
ejpam-2495	210	9	be	be	VERB
ejpam-2495	210	10	a	a	DET
ejpam-2495	210	11	countable	countable	ADJ
ejpam-2495	210	12	btµ	btµ	NOUN
ejpam-2495	210	13	open	open	ADJ
ejpam-2495	210	14	cover	cover	NOUN
ejpam-2495	210	15	of	of	ADP
ejpam-2495	210	16	(	(	PUNCT
ejpam-2495	210	17	x	x	X
ejpam-2495	210	18	,	,	PUNCT
ejpam-2495	210	19	τ	τ	PROPN
ejpam-2495	210	20	)	)	PUNCT
ejpam-2495	210	21	.	.	PUNCT
ejpam-2495	211	1	since	since	SCONJ
ejpam-2495	211	2	by	by	ADP
ejpam-2495	211	3	btt	btt	PROPN
ejpam-2495	211	4	µ	µ	PROPN
ejpam-2495	211	5	c	c	NOUN
ejpam-2495	211	6	space	space	NOUN
ejpam-2495	211	7	{	{	PUNCT
ejpam-2495	211	8	ai	ai	VERB
ejpam-2495	211	9	:	:	PUNCT
ejpam-2495	211	10	i	i	PRON
ejpam-2495	211	11	∈	∈	PROPN
ejpam-2495	212	1	i	i	PRON
ejpam-2495	212	2	}	}	PUNCT
ejpam-2495	212	3	is	be	AUX
ejpam-2495	212	4	a	a	DET
ejpam-2495	212	5	countable	countable	ADJ
ejpam-2495	212	6	open	open	ADJ
ejpam-2495	212	7	cover	cover	NOUN
ejpam-2495	212	8	of	of	ADP
ejpam-2495	212	9	(	(	PUNCT
ejpam-2495	212	10	x	x	X
ejpam-2495	212	11	,	,	PUNCT
ejpam-2495	212	12	τ	τ	PROPN
ejpam-2495	212	13	)	)	PUNCT
ejpam-2495	212	14	.	.	PUNCT
ejpam-2495	213	1	since	since	SCONJ
ejpam-2495	213	2	(	(	PUNCT
ejpam-2495	213	3	x	x	X
ejpam-2495	213	4	,	,	PUNCT
ejpam-2495	213	5	τ	τ	X
ejpam-2495	213	6	)	)	PUNCT
ejpam-2495	213	7	is	be	AUX
ejpam-2495	213	8	countably	countably	ADV
ejpam-2495	213	9	supra	supra	ADJ
ejpam-2495	213	10	compact	compact	ADJ
ejpam-2495	213	11	,	,	PUNCT
ejpam-2495	213	12	countable	countable	ADJ
ejpam-2495	213	13	supra	supra	ADJ
ejpam-2495	213	14	open	open	ADJ
ejpam-2495	213	15	cover	cover	NOUN
ejpam-2495	213	16	{	{	PUNCT
ejpam-2495	213	17	ai	ai	VERB
ejpam-2495	213	18	:	:	PUNCT
ejpam-2495	213	19	i	i	PRON
ejpam-2495	213	20	∈	∈	VERB
ejpam-2495	214	1	i	i	X
ejpam-2495	214	2	}	}	PUNCT
ejpam-2495	214	3	of	of	ADP
ejpam-2495	214	4	(	(	PUNCT
ejpam-2495	214	5	x	x	X
ejpam-2495	214	6	,	,	PUNCT
ejpam-2495	214	7	τ	τ	X
ejpam-2495	214	8	)	)	PUNCT
ejpam-2495	214	9	has	have	VERB
ejpam-2495	214	10	a	a	DET
ejpam-2495	214	11	finite	finite	ADJ
ejpam-2495	214	12	sub	sub	NOUN
ejpam-2495	214	13	cover	cover	NOUN
ejpam-2495	214	14	say	say	VERB
ejpam-2495	214	15	{	{	PUNCT
ejpam-2495	214	16	ai	ai	VERB
ejpam-2495	214	17	:	:	PUNCT
ejpam-2495	214	18	i	i	NOUN
ejpam-2495	214	19	=	=	NOUN
ejpam-2495	214	20	1	1	NUM
ejpam-2495	214	21	,	,	PUNCT
ejpam-2495	214	22	2	2	NUM
ejpam-2495	214	23	,	,	PUNCT
ejpam-2495	214	24	·	·	PUNCT
ejpam-2495	214	25	·	·	PUNCT
ejpam-2495	214	26	·	·	PUNCT
ejpam-2495	214	27	,	,	PUNCT
ejpam-2495	214	28	n	n	CCONJ
ejpam-2495	214	29	}	}	PUNCT
ejpam-2495	214	30	for	for	ADP
ejpam-2495	214	31	x.	x.	NOUN
ejpam-2495	214	32	hence	hence	ADV
ejpam-2495	214	33	(	(	PUNCT
ejpam-2495	214	34	x	x	X
ejpam-2495	214	35	,	,	PUNCT
ejpam-2495	214	36	τ	τ	X
ejpam-2495	214	37	)	)	PUNCT
ejpam-2495	214	38	is	be	AUX
ejpam-2495	214	39	a	a	DET
ejpam-2495	214	40	countably	countably	ADV
ejpam-2495	214	41	btµ	btµ	ADJ
ejpam-2495	214	42	compact	compact	ADJ
ejpam-2495	214	43	space	space	NOUN
ejpam-2495	214	44	.	.	PUNCT
ejpam-2495	215	1	theorem	theorem	VERB
ejpam-2495	215	2	14	14	NUM
ejpam-2495	215	3	.	.	PUNCT
ejpam-2495	216	1	every	every	DET
ejpam-2495	216	2	btµ	btµ	NOUN
ejpam-2495	216	3	compact	compact	ADJ
ejpam-2495	216	4	space	space	NOUN
ejpam-2495	216	5	is	be	AUX
ejpam-2495	216	6	countably	countably	ADV
ejpam-2495	216	7	btµ	btµ	NOUN
ejpam-2495	216	8	-compact	-compact	PROPN
ejpam-2495	216	9	.	.	PUNCT
ejpam-2495	217	1	proof	proof	NOUN
ejpam-2495	217	2	.	.	PUNCT
ejpam-2495	218	1	let	let	VERB
ejpam-2495	218	2	(	(	PUNCT
ejpam-2495	218	3	x	x	X
ejpam-2495	218	4	,	,	PUNCT
ejpam-2495	218	5	τ	τ	X
ejpam-2495	218	6	)	)	PUNCT
ejpam-2495	218	7	is	be	AUX
ejpam-2495	218	8	btµ-compact	btµ-compact	ADJ
ejpam-2495	218	9	space	space	NOUN
ejpam-2495	218	10	.	.	PUNCT
ejpam-2495	219	1	let	let	VERB
ejpam-2495	219	2	{	{	PUNCT
ejpam-2495	219	3	ai	ai	VERB
ejpam-2495	219	4	:	:	PUNCT
ejpam-2495	219	5	i	i	PRON
ejpam-2495	219	6	∈	∈	PROPN
ejpam-2495	219	7	i	i	PRON
ejpam-2495	219	8	}	}	PUNCT
ejpam-2495	219	9	be	be	VERB
ejpam-2495	219	10	a	a	DET
ejpam-2495	219	11	countable	countable	ADJ
ejpam-2495	219	12	btµpen	btµpen	NOUN
ejpam-2495	219	13	cover	cover	NOUN
ejpam-2495	219	14	of	of	ADP
ejpam-2495	219	15	(	(	PUNCT
ejpam-2495	219	16	x	x	X
ejpam-2495	219	17	,	,	PUNCT
ejpam-2495	219	18	τ	τ	PROPN
ejpam-2495	219	19	)	)	PUNCT
ejpam-2495	219	20	.	.	PUNCT
ejpam-2495	220	1	since	since	SCONJ
ejpam-2495	220	2	(	(	PUNCT
ejpam-2495	220	3	x	x	X
ejpam-2495	220	4	,	,	PUNCT
ejpam-2495	220	5	τ	τ	X
ejpam-2495	220	6	)	)	PUNCT
ejpam-2495	220	7	is	be	AUX
ejpam-2495	220	8	btµcompact	btµcompact	NOUN
ejpam-2495	220	9	,	,	PUNCT
ejpam-2495	220	10	btµpen	btµpen	ADJ
ejpam-2495	220	11	cover{ai	cover{ai	NOUN
ejpam-2495	220	12	:	:	PUNCT
ejpam-2495	220	13	i	i	PRON
ejpam-2495	220	14	∈	∈	VERB
ejpam-2495	221	1	i	i	X
ejpam-2495	221	2	}	}	PUNCT
ejpam-2495	221	3	of	of	ADP
ejpam-2495	221	4	(	(	PUNCT
ejpam-2495	221	5	x	x	X
ejpam-2495	221	6	,	,	PUNCT
ejpam-2495	221	7	τ	τ	X
ejpam-2495	221	8	)	)	PUNCT
ejpam-2495	221	9	has	have	VERB
ejpam-2495	221	10	a	a	DET
ejpam-2495	221	11	finite	finite	ADJ
ejpam-2495	221	12	subcover	subcover	PROPN
ejpam-2495	221	13	say	say	VERB
ejpam-2495	221	14	{	{	PUNCT
ejpam-2495	221	15	ai	ai	VERB
ejpam-2495	221	16	:	:	PUNCT
ejpam-2495	221	17	i	i	NOUN
ejpam-2495	221	18	=	=	NOUN
ejpam-2495	221	19	1	1	NUM
ejpam-2495	221	20	,	,	PUNCT
ejpam-2495	221	21	2	2	NUM
ejpam-2495	221	22	,	,	PUNCT
ejpam-2495	221	23	·	·	PUNCT
ejpam-2495	221	24	·	·	PUNCT
ejpam-2495	221	25	·	·	PUNCT
ejpam-2495	221	26	,	,	PUNCT
ejpam-2495	221	27	n	n	CCONJ
ejpam-2495	221	28	}	}	PUNCT
ejpam-2495	221	29	for	for	ADP
ejpam-2495	221	30	(	(	PUNCT
ejpam-2495	221	31	x	x	X
ejpam-2495	221	32	,	,	PUNCT
ejpam-2495	221	33	τ	τ	PROPN
ejpam-2495	221	34	)	)	PUNCT
ejpam-2495	221	35	.	.	PUNCT
ejpam-2495	222	1	hence	hence	ADV
ejpam-2495	222	2	(	(	PUNCT
ejpam-2495	222	3	x	x	X
ejpam-2495	222	4	,	,	PUNCT
ejpam-2495	222	5	τ	τ	X
ejpam-2495	222	6	)	)	PUNCT
ejpam-2495	222	7	is	be	AUX
ejpam-2495	222	8	a	a	DET
ejpam-2495	222	9	countably	countably	ADV
ejpam-2495	222	10	btµ-compact	btµ-compact	ADJ
ejpam-2495	222	11	space	space	NOUN
ejpam-2495	222	12	.	.	PUNCT
ejpam-2495	223	1	theorem	theorem	NOUN
ejpam-2495	223	2	15	15	NUM
ejpam-2495	223	3	.	.	PUNCT
ejpam-2495	224	1	let	let	VERB
ejpam-2495	224	2	f	f	NOUN
ejpam-2495	224	3	:	:	PUNCT
ejpam-2495	224	4	(	(	PUNCT
ejpam-2495	224	5	x	x	X
ejpam-2495	224	6	,	,	PUNCT
ejpam-2495	224	7	τ	τ	X
ejpam-2495	224	8	)	)	PUNCT
ejpam-2495	224	9	→	→	SYM
ejpam-2495	224	10	(	(	PUNCT
ejpam-2495	224	11	y	y	PROPN
ejpam-2495	224	12	,	,	PUNCT
ejpam-2495	224	13	σ	σ	PROPN
ejpam-2495	224	14	)	)	PUNCT
ejpam-2495	224	15	be	be	VERB
ejpam-2495	224	16	a	a	DET
ejpam-2495	224	17	btµ	btµ	NOUN
ejpam-2495	224	18	continuous	continuous	ADJ
ejpam-2495	224	19	injective	injective	ADJ
ejpam-2495	224	20	mapping	mapping	NOUN
ejpam-2495	224	21	.	.	PUNCT
ejpam-2495	225	1	if	if	SCONJ
ejpam-2495	225	2	x	x	PRON
ejpam-2495	225	3	is	be	AUX
ejpam-2495	225	4	countably	countably	ADV
ejpam-2495	225	5	btµ	btµ	ADJ
ejpam-2495	225	6	compact	compact	ADJ
ejpam-2495	225	7	space	space	NOUN
ejpam-2495	225	8	then	then	ADV
ejpam-2495	225	9	(	(	PUNCT
ejpam-2495	225	10	y	y	PROPN
ejpam-2495	225	11	,	,	PUNCT
ejpam-2495	225	12	σ	σ	PROPN
ejpam-2495	225	13	)	)	PUNCT
ejpam-2495	225	14	is	be	AUX
ejpam-2495	225	15	countably	countably	ADV
ejpam-2495	225	16	supra	supra	ADJ
ejpam-2495	225	17	compact	compact	ADJ
ejpam-2495	225	18	.	.	PUNCT
ejpam-2495	226	1	proof	proof	NOUN
ejpam-2495	226	2	.	.	PUNCT
ejpam-2495	227	1	let	let	VERB
ejpam-2495	227	2	f	f	NOUN
ejpam-2495	227	3	:	:	PUNCT
ejpam-2495	227	4	(	(	PUNCT
ejpam-2495	227	5	x	x	X
ejpam-2495	227	6	,	,	PUNCT
ejpam-2495	227	7	τ	τ	X
ejpam-2495	227	8	)	)	PUNCT
ejpam-2495	227	9	→	→	SYM
ejpam-2495	227	10	(	(	PUNCT
ejpam-2495	227	11	y	y	PROPN
ejpam-2495	227	12	,	,	PUNCT
ejpam-2495	227	13	σ	σ	PROPN
ejpam-2495	227	14	)	)	PUNCT
ejpam-2495	227	15	be	be	VERB
ejpam-2495	227	16	a	a	DET
ejpam-2495	227	17	btµ	btµ	NOUN
ejpam-2495	227	18	continuous	continuous	ADJ
ejpam-2495	227	19	map	map	NOUN
ejpam-2495	227	20	from	from	ADP
ejpam-2495	227	21	a	a	DET
ejpam-2495	227	22	countably	countably	ADV
ejpam-2495	227	23	btµ	btµ	NOUN
ejpam-2495	227	24	compact	compact	ADJ
ejpam-2495	227	25	(	(	PUNCT
ejpam-2495	227	26	x	x	X
ejpam-2495	227	27	,	,	PUNCT
ejpam-2495	227	28	τ	τ	X
ejpam-2495	227	29	)	)	PUNCT
ejpam-2495	227	30	onto	onto	ADP
ejpam-2495	227	31	a	a	DET
ejpam-2495	227	32	supra	supra	ADJ
ejpam-2495	227	33	topological	topological	ADJ
ejpam-2495	227	34	space	space	NOUN
ejpam-2495	227	35	(	(	PUNCT
ejpam-2495	227	36	y	y	PROPN
ejpam-2495	227	37	,	,	PUNCT
ejpam-2495	227	38	σ	σ	PROPN
ejpam-2495	227	39	)	)	PUNCT
ejpam-2495	227	40	.	.	PUNCT
ejpam-2495	228	1	let	let	VERB
ejpam-2495	228	2	{	{	PUNCT
ejpam-2495	228	3	ai	ai	VERB
ejpam-2495	228	4	:	:	PUNCT
ejpam-2495	228	5	i	i	PRON
ejpam-2495	228	6	∈	∈	PROPN
ejpam-2495	228	7	i	i	PRON
ejpam-2495	228	8	}	}	PUNCT
ejpam-2495	228	9	be	be	VERB
ejpam-2495	228	10	a	a	DET
ejpam-2495	228	11	countable	countable	ADJ
ejpam-2495	228	12	supra	supra	NOUN
ejpam-2495	228	13	open	open	ADJ
ejpam-2495	228	14	cover	cover	NOUN
ejpam-2495	228	15	of	of	ADP
ejpam-2495	228	16	y.	y.	NOUN
ejpam-2495	228	17	then	then	ADV
ejpam-2495	228	18	{	{	PUNCT
ejpam-2495	228	19	f−1(ai	f−1(ai	NOUN
ejpam-2495	228	20	)	)	PUNCT
ejpam-2495	228	21	:	:	PUNCT
ejpam-2495	229	1	i	i	PRON
ejpam-2495	229	2	∈	∈	VERB
ejpam-2495	229	3	i	i	PRON
ejpam-2495	229	4	}	}	PUNCT
ejpam-2495	229	5	is	be	AUX
ejpam-2495	229	6	a	a	DET
ejpam-2495	229	7	countable	countable	ADJ
ejpam-2495	229	8	btµ	btµ	NOUN
ejpam-2495	229	9	open	open	ADJ
ejpam-2495	229	10	cover	cover	NOUN
ejpam-2495	229	11	of	of	ADP
ejpam-2495	229	12	x	x	PRON
ejpam-2495	229	13	,	,	PUNCT
ejpam-2495	229	14	as	as	SCONJ
ejpam-2495	229	15	f	f	PROPN
ejpam-2495	229	16	is	be	AUX
ejpam-2495	229	17	btµ	btµ	NOUN
ejpam-2495	229	18	continuous	continuous	ADJ
ejpam-2495	229	19	.	.	PUNCT
ejpam-2495	230	1	since	since	SCONJ
ejpam-2495	230	2	x	x	PRON
ejpam-2495	230	3	is	be	AUX
ejpam-2495	230	4	countably	countably	ADV
ejpam-2495	230	5	btµcompact	btµcompact	NOUN
ejpam-2495	230	6	,	,	PUNCT
ejpam-2495	230	7	the	the	DET
ejpam-2495	230	8	countable	countable	ADJ
ejpam-2495	230	9	btµ-open	btµ-open	ADJ
ejpam-2495	230	10	cover	cover	NOUN
ejpam-2495	230	11	{	{	PUNCT
ejpam-2495	230	12	f−1(ai	f−1(ai	NOUN
ejpam-2495	230	13	)	)	PUNCT
ejpam-2495	230	14	:	:	PUNCT
ejpam-2495	231	1	i	i	PRON
ejpam-2495	231	2	∈	∈	VERB
ejpam-2495	231	3	i	i	PRON
ejpam-2495	231	4	}	}	PUNCT
ejpam-2495	231	5	of	of	ADP
ejpam-2495	231	6	x	x	PUNCT
ejpam-2495	231	7	has	have	AUX
ejpam-2495	231	8	a	a	DET
ejpam-2495	231	9	finite	finite	ADJ
ejpam-2495	231	10	sub	sub	NOUN
ejpam-2495	231	11	cover	cover	NOUN
ejpam-2495	231	12	say	say	VERB
ejpam-2495	231	13	{	{	PUNCT
ejpam-2495	231	14	f−1(ai	f−1(ai	NOUN
ejpam-2495	231	15	)	)	PUNCT
ejpam-2495	231	16	:	:	PUNCT
ejpam-2495	232	1	i	i	NOUN
ejpam-2495	232	2	=	=	NOUN
ejpam-2495	232	3	1	1	NUM
ejpam-2495	232	4	,	,	PUNCT
ejpam-2495	232	5	2	2	NUM
ejpam-2495	232	6	,	,	PUNCT
ejpam-2495	232	7	·	·	PUNCT
ejpam-2495	232	8	·	·	PUNCT
ejpam-2495	232	9	·	·	PUNCT
ejpam-2495	232	10	,	,	PUNCT
ejpam-2495	232	11	n	n	CCONJ
ejpam-2495	232	12	}	}	PUNCT
ejpam-2495	232	13	.	.	PUNCT
ejpam-2495	233	1	therefore	therefore	ADV
ejpam-2495	233	2	x	x	X
ejpam-2495	233	3	k.krishna	k.krishna	NOUN
ejpam-2495	233	4	,	,	PUNCT
ejpam-2495	233	5	m.vignesh	m.vignesh	NOUN
ejpam-2495	233	6	/	/	SYM
ejpam-2495	233	7	eur	eur	PROPN
ejpam-2495	233	8	.	.	PUNCT
ejpam-2495	234	1	j.	j.	PROPN
ejpam-2495	234	2	pure	pure	PROPN
ejpam-2495	234	3	appl	appl	PROPN
ejpam-2495	234	4	.	.	PROPN
ejpam-2495	234	5	math	math	PROPN
ejpam-2495	234	6	,	,	PUNCT
ejpam-2495	234	7	10	10	NUM
ejpam-2495	234	8	(	(	PUNCT
ejpam-2495	234	9	2	2	NUM
ejpam-2495	234	10	)	)	PUNCT
ejpam-2495	234	11	(	(	PUNCT
ejpam-2495	234	12	2017	2017	NUM
ejpam-2495	234	13	)	)	PUNCT
ejpam-2495	234	14	,	,	PUNCT
ejpam-2495	234	15	323	323	NUM
ejpam-2495	234	16	-	-	SYM
ejpam-2495	234	17	334	334	NUM
ejpam-2495	234	18	329	329	NUM
ejpam-2495	234	19	=	=	NOUN
ejpam-2495	234	20	n⋃	n⋃	VERB
ejpam-2495	234	21	i=1	i=1	PRON
ejpam-2495	234	22	{	{	PUNCT
ejpam-2495	234	23	f−1(ai	f−1(ai	PROPN
ejpam-2495	234	24	)	)	PUNCT
ejpam-2495	234	25	}	}	PUNCT
ejpam-2495	234	26	,	,	PUNCT
ejpam-2495	234	27	which	which	PRON
ejpam-2495	234	28	implies	imply	VERB
ejpam-2495	234	29	f(x	f(x	PROPN
ejpam-2495	234	30	)	)	PUNCT
ejpam-2495	235	1	=	=	PRON
ejpam-2495	235	2	n⋃	n⋃	VERB
ejpam-2495	235	3	i=1	i=1	PROPN
ejpam-2495	235	4	ai	ai	VERB
ejpam-2495	235	5	,	,	PUNCT
ejpam-2495	235	6	then	then	ADV
ejpam-2495	235	7	y	y	PROPN
ejpam-2495	235	8	=	=	PUNCT
ejpam-2495	235	9	n⋃	n⋃	VERB
ejpam-2495	235	10	i=1	i=1	PROPN
ejpam-2495	235	11	ai	ai	VERB
ejpam-2495	235	12	.	.	PUNCT
ejpam-2495	236	1	that	that	PRON
ejpam-2495	236	2	is	be	AUX
ejpam-2495	236	3	{	{	PUNCT
ejpam-2495	236	4	a1	a1	PROPN
ejpam-2495	236	5	,	,	PUNCT
ejpam-2495	236	6	a2	a2	PROPN
ejpam-2495	236	7	,	,	PUNCT
ejpam-2495	236	8	·	·	PUNCT
ejpam-2495	236	9	·	·	PUNCT
ejpam-2495	236	10	·	·	PUNCT
ejpam-2495	236	11	,	,	PUNCT
ejpam-2495	236	12	an	an	PRON
ejpam-2495	236	13	}	}	PUNCT
ejpam-2495	236	14	is	be	AUX
ejpam-2495	236	15	a	a	DET
ejpam-2495	236	16	finite	finite	ADJ
ejpam-2495	236	17	sub	sub	NOUN
ejpam-2495	236	18	cover	cover	NOUN
ejpam-2495	236	19	of	of	ADP
ejpam-2495	236	20	{	{	PUNCT
ejpam-2495	236	21	ai	ai	INTJ
ejpam-2495	236	22	:	:	PUNCT
ejpam-2495	236	23	i	i	PRON
ejpam-2495	236	24	∈	∈	VERB
ejpam-2495	236	25	i	i	X
ejpam-2495	236	26	}	}	PUNCT
ejpam-2495	236	27	for	for	ADP
ejpam-2495	236	28	y.	y.	PROPN
ejpam-2495	236	29	hence	hence	ADV
ejpam-2495	236	30	y	y	PROPN
ejpam-2495	236	31	is	be	AUX
ejpam-2495	236	32	countably	countably	ADV
ejpam-2495	236	33	supra	supra	ADJ
ejpam-2495	236	34	compact	compact	PROPN
ejpam-2495	236	35	.	.	PUNCT
ejpam-2495	237	1	theorem	theorem	VERB
ejpam-2495	237	2	16	16	NUM
ejpam-2495	237	3	.	.	PUNCT
ejpam-2495	238	1	if	if	SCONJ
ejpam-2495	238	2	a	a	DET
ejpam-2495	238	3	map	map	NOUN
ejpam-2495	238	4	f	f	X
ejpam-2495	238	5	:	:	PUNCT
ejpam-2495	238	6	(	(	PUNCT
ejpam-2495	238	7	x	x	X
ejpam-2495	238	8	,	,	PUNCT
ejpam-2495	238	9	τ	τ	X
ejpam-2495	238	10	)	)	PUNCT
ejpam-2495	238	11	→	→	SYM
ejpam-2495	238	12	(	(	PUNCT
ejpam-2495	238	13	y	y	PROPN
ejpam-2495	238	14	,	,	PUNCT
ejpam-2495	238	15	σ	σ	PROPN
ejpam-2495	238	16	)	)	PUNCT
ejpam-2495	238	17	is	be	AUX
ejpam-2495	238	18	perfectly	perfectly	ADV
ejpam-2495	238	19	btµ	btµ	ADJ
ejpam-2495	238	20	continuous	continuous	ADJ
ejpam-2495	238	21	map	map	NOUN
ejpam-2495	238	22	from	from	ADP
ejpam-2495	238	23	a	a	DET
ejpam-2495	238	24	countably	countably	ADV
ejpam-2495	238	25	supra	supra	ADJ
ejpam-2495	238	26	compact	compact	ADJ
ejpam-2495	238	27	space	space	NOUN
ejpam-2495	238	28	(	(	PUNCT
ejpam-2495	238	29	x	x	X
ejpam-2495	238	30	,	,	PUNCT
ejpam-2495	238	31	τ	τ	X
ejpam-2495	238	32	)	)	PUNCT
ejpam-2495	238	33	onto	onto	ADP
ejpam-2495	238	34	a	a	DET
ejpam-2495	238	35	supra	supra	ADJ
ejpam-2495	238	36	topological	topological	ADJ
ejpam-2495	238	37	space	space	NOUN
ejpam-2495	238	38	(	(	PUNCT
ejpam-2495	238	39	y	y	PROPN
ejpam-2495	238	40	,	,	PUNCT
ejpam-2495	238	41	σ	σ	PROPN
ejpam-2495	238	42	)	)	PUNCT
ejpam-2495	238	43	,	,	PUNCT
ejpam-2495	238	44	then	then	ADV
ejpam-2495	238	45	(	(	PUNCT
ejpam-2495	238	46	y	y	PROPN
ejpam-2495	238	47	,	,	PUNCT
ejpam-2495	238	48	σ	σ	PROPN
ejpam-2495	238	49	)	)	PUNCT
ejpam-2495	238	50	is	be	AUX
ejpam-2495	238	51	countably	countably	ADV
ejpam-2495	238	52	btµ	btµ	NOUN
ejpam-2495	238	53	compact	compact	ADJ
ejpam-2495	238	54	.	.	PUNCT
ejpam-2495	239	1	proof	proof	NOUN
ejpam-2495	239	2	.	.	PUNCT
ejpam-2495	240	1	let	let	VERB
ejpam-2495	240	2	{	{	PUNCT
ejpam-2495	240	3	ai	ai	VERB
ejpam-2495	240	4	:	:	PUNCT
ejpam-2495	240	5	i	i	PRON
ejpam-2495	240	6	∈	∈	PROPN
ejpam-2495	240	7	i	i	PRON
ejpam-2495	240	8	}	}	PUNCT
ejpam-2495	240	9	be	be	VERB
ejpam-2495	240	10	a	a	DET
ejpam-2495	240	11	countable	countable	ADJ
ejpam-2495	240	12	btµ	btµ	NOUN
ejpam-2495	240	13	open	open	ADJ
ejpam-2495	240	14	cover	cover	NOUN
ejpam-2495	240	15	of	of	ADP
ejpam-2495	240	16	(	(	PUNCT
ejpam-2495	240	17	y	y	PROPN
ejpam-2495	240	18	,	,	PUNCT
ejpam-2495	240	19	σ	σ	PROPN
ejpam-2495	240	20	)	)	PUNCT
ejpam-2495	240	21	.	.	PUNCT
ejpam-2495	241	1	since	since	SCONJ
ejpam-2495	241	2	f	f	PROPN
ejpam-2495	241	3	is	be	AUX
ejpam-2495	241	4	perfectly	perfectly	ADV
ejpam-2495	241	5	btµ	btµ	ADJ
ejpam-2495	241	6	continuous	continuous	ADJ
ejpam-2495	241	7	,	,	PUNCT
ejpam-2495	241	8	{	{	PUNCT
ejpam-2495	241	9	f−1(ai	f−1(ai	NOUN
ejpam-2495	241	10	)	)	PUNCT
ejpam-2495	241	11	:	:	PUNCT
ejpam-2495	241	12	i	i	PRON
ejpam-2495	241	13	∈	∈	VERB
ejpam-2495	241	14	i	i	PRON
ejpam-2495	241	15	}	}	PUNCT
ejpam-2495	241	16	is	be	AUX
ejpam-2495	241	17	a	a	DET
ejpam-2495	241	18	countable	countable	ADJ
ejpam-2495	241	19	supra	supra	NOUN
ejpam-2495	241	20	open	open	ADJ
ejpam-2495	241	21	cover	cover	NOUN
ejpam-2495	241	22	of	of	ADP
ejpam-2495	241	23	(	(	PUNCT
ejpam-2495	241	24	x	x	X
ejpam-2495	241	25	,	,	PUNCT
ejpam-2495	241	26	τ	τ	PROPN
ejpam-2495	241	27	)	)	PUNCT
ejpam-2495	241	28	.	.	PUNCT
ejpam-2495	242	1	again	again	ADV
ejpam-2495	242	2	,	,	PUNCT
ejpam-2495	242	3	since	since	SCONJ
ejpam-2495	242	4	(	(	PUNCT
ejpam-2495	242	5	x	x	X
ejpam-2495	242	6	,	,	PUNCT
ejpam-2495	242	7	τ	τ	PROPN
ejpam-2495	242	8	)	)	PUNCT
ejpam-2495	242	9	is	be	AUX
ejpam-2495	242	10	countably	countably	ADV
ejpam-2495	242	11	supra	supra	ADJ
ejpam-2495	242	12	compact	compact	ADJ
ejpam-2495	242	13	,	,	PUNCT
ejpam-2495	242	14	the	the	DET
ejpam-2495	242	15	countable	countable	ADJ
ejpam-2495	242	16	supra	supra	PROPN
ejpam-2495	242	17	open	open	ADJ
ejpam-2495	242	18	cover	cover	NOUN
ejpam-2495	242	19	{	{	PUNCT
ejpam-2495	242	20	f−1(ai	f−1(ai	NOUN
ejpam-2495	242	21	)	)	PUNCT
ejpam-2495	242	22	:	:	PUNCT
ejpam-2495	243	1	i	i	PRON
ejpam-2495	243	2	∈	∈	VERB
ejpam-2495	243	3	i	i	PRON
ejpam-2495	243	4	}	}	PUNCT
ejpam-2495	243	5	of	of	ADP
ejpam-2495	243	6	(	(	PUNCT
ejpam-2495	243	7	x	x	X
ejpam-2495	243	8	,	,	PUNCT
ejpam-2495	243	9	τ	τ	X
ejpam-2495	243	10	)	)	PUNCT
ejpam-2495	243	11	has	have	VERB
ejpam-2495	243	12	a	a	DET
ejpam-2495	243	13	finite	finite	ADJ
ejpam-2495	243	14	sub	sub	NOUN
ejpam-2495	243	15	cover	cover	NOUN
ejpam-2495	243	16	say	say	VERB
ejpam-2495	243	17	{	{	PUNCT
ejpam-2495	243	18	f−1(ai	f−1(ai	NOUN
ejpam-2495	243	19	)	)	PUNCT
ejpam-2495	243	20	:	:	PUNCT
ejpam-2495	244	1	i	i	NOUN
ejpam-2495	244	2	=	=	NOUN
ejpam-2495	244	3	1	1	NUM
ejpam-2495	244	4	,	,	PUNCT
ejpam-2495	244	5	2	2	NUM
ejpam-2495	244	6	,	,	PUNCT
ejpam-2495	244	7	·	·	PUNCT
ejpam-2495	244	8	·	·	PUNCT
ejpam-2495	244	9	·	·	PUNCT
ejpam-2495	244	10	,	,	PUNCT
ejpam-2495	244	11	n	n	CCONJ
ejpam-2495	244	12	}	}	PUNCT
ejpam-2495	244	13	.	.	PUNCT
ejpam-2495	245	1	therefore	therefore	ADV
ejpam-2495	245	2	x	x	X
ejpam-2495	245	3	=	=	PRON
ejpam-2495	245	4	n⋃	n⋃	VERB
ejpam-2495	245	5	i=1	i=1	PRON
ejpam-2495	245	6	{	{	PUNCT
ejpam-2495	245	7	f−1(ai	f−1(ai	PROPN
ejpam-2495	245	8	)	)	PUNCT
ejpam-2495	245	9	}	}	PUNCT
ejpam-2495	245	10	,	,	PUNCT
ejpam-2495	245	11	which	which	PRON
ejpam-2495	245	12	implies	imply	VERB
ejpam-2495	245	13	f(x	f(x	PROPN
ejpam-2495	245	14	)	)	PUNCT
ejpam-2495	245	15	=	=	PRON
ejpam-2495	245	16	n⋃	n⋃	VERB
ejpam-2495	245	17	i=1	i=1	PRON
ejpam-2495	245	18	{	{	PUNCT
ejpam-2495	245	19	(	(	PUNCT
ejpam-2495	245	20	ai	ai	NOUN
ejpam-2495	245	21	)	)	PUNCT
ejpam-2495	245	22	}	}	PUNCT
ejpam-2495	245	23	,	,	PUNCT
ejpam-2495	245	24	so	so	SCONJ
ejpam-2495	245	25	that	that	SCONJ
ejpam-2495	245	26	y	y	PROPN
ejpam-2495	245	27	=	=	PRON
ejpam-2495	245	28	n⋃	n⋃	PROPN
ejpam-2495	245	29	i=1	i=1	PRON
ejpam-2495	245	30	{	{	PUNCT
ejpam-2495	245	31	(	(	PUNCT
ejpam-2495	245	32	ai	ai	NOUN
ejpam-2495	245	33	)	)	PUNCT
ejpam-2495	245	34	}	}	PUNCT
ejpam-2495	245	35	.	.	PUNCT
ejpam-2495	246	1	that	that	PRON
ejpam-2495	246	2	is	be	AUX
ejpam-2495	246	3	{	{	PUNCT
ejpam-2495	246	4	a1	a1	PROPN
ejpam-2495	246	5	,	,	PUNCT
ejpam-2495	246	6	a2	a2	PROPN
ejpam-2495	246	7	,	,	PUNCT
ejpam-2495	246	8	·	·	PUNCT
ejpam-2495	246	9	·	·	PUNCT
ejpam-2495	246	10	·	·	PUNCT
ejpam-2495	246	11	,	,	PUNCT
ejpam-2495	246	12	an	an	PRON
ejpam-2495	246	13	}	}	PUNCT
ejpam-2495	246	14	is	be	AUX
ejpam-2495	246	15	a	a	DET
ejpam-2495	246	16	finite	finite	ADJ
ejpam-2495	246	17	sub	sub	NOUN
ejpam-2495	246	18	cover	cover	NOUN
ejpam-2495	246	19	of	of	ADP
ejpam-2495	246	20	{	{	PUNCT
ejpam-2495	246	21	ai	ai	INTJ
ejpam-2495	246	22	:	:	PUNCT
ejpam-2495	246	23	i	i	PRON
ejpam-2495	246	24	∈	∈	VERB
ejpam-2495	247	1	i	i	X
ejpam-2495	247	2	}	}	PUNCT
ejpam-2495	247	3	for	for	ADP
ejpam-2495	247	4	(	(	PUNCT
ejpam-2495	247	5	y	y	PROPN
ejpam-2495	247	6	,	,	PUNCT
ejpam-2495	247	7	σ	σ	PROPN
ejpam-2495	247	8	)	)	PUNCT
ejpam-2495	247	9	.	.	PUNCT
ejpam-2495	248	1	hence	hence	ADV
ejpam-2495	248	2	(	(	PUNCT
ejpam-2495	248	3	y	y	PROPN
ejpam-2495	248	4	,	,	PUNCT
ejpam-2495	248	5	σ	σ	PROPN
ejpam-2495	248	6	)	)	PUNCT
ejpam-2495	248	7	is	be	AUX
ejpam-2495	248	8	countably	countably	ADV
ejpam-2495	248	9	btµ	btµ	NOUN
ejpam-2495	248	10	-compact	-compact	PROPN
ejpam-2495	248	11	.	.	PUNCT
ejpam-2495	249	1	theorem	theorem	VERB
ejpam-2495	249	2	17	17	NUM
ejpam-2495	249	3	.	.	PUNCT
ejpam-2495	250	1	if	if	SCONJ
ejpam-2495	250	2	a	a	DET
ejpam-2495	250	3	map	map	NOUN
ejpam-2495	250	4	f	f	X
ejpam-2495	250	5	:	:	PUNCT
ejpam-2495	250	6	(	(	PUNCT
ejpam-2495	250	7	x	x	X
ejpam-2495	250	8	,	,	PUNCT
ejpam-2495	250	9	τ	τ	X
ejpam-2495	250	10	)	)	PUNCT
ejpam-2495	250	11	→	→	SYM
ejpam-2495	250	12	(	(	PUNCT
ejpam-2495	250	13	y	y	PROPN
ejpam-2495	250	14	,	,	PUNCT
ejpam-2495	250	15	σ	σ	PROPN
ejpam-2495	250	16	)	)	PUNCT
ejpam-2495	250	17	is	be	AUX
ejpam-2495	250	18	strongly	strongly	ADV
ejpam-2495	250	19	btµcontinuous	btµcontinuous	ADJ
ejpam-2495	250	20	map	map	NOUN
ejpam-2495	250	21	from	from	ADP
ejpam-2495	250	22	a	a	DET
ejpam-2495	250	23	countably	countably	ADV
ejpam-2495	250	24	supra	supra	ADJ
ejpam-2495	250	25	compact	compact	ADJ
ejpam-2495	250	26	space	space	NOUN
ejpam-2495	250	27	(	(	PUNCT
ejpam-2495	250	28	x	x	X
ejpam-2495	250	29	,	,	PUNCT
ejpam-2495	250	30	τ	τ	X
ejpam-2495	250	31	)	)	PUNCT
ejpam-2495	250	32	onto	onto	ADP
ejpam-2495	250	33	a	a	DET
ejpam-2495	250	34	supra	supra	ADJ
ejpam-2495	250	35	topological	topological	ADJ
ejpam-2495	250	36	space	space	NOUN
ejpam-2495	250	37	(	(	PUNCT
ejpam-2495	250	38	y	y	PROPN
ejpam-2495	250	39	,	,	PUNCT
ejpam-2495	250	40	σ	σ	PROPN
ejpam-2495	250	41	)	)	PUNCT
ejpam-2495	250	42	,	,	PUNCT
ejpam-2495	250	43	then	then	ADV
ejpam-2495	250	44	(	(	PUNCT
ejpam-2495	250	45	y	y	PROPN
ejpam-2495	250	46	,	,	PUNCT
ejpam-2495	250	47	σ	σ	PROPN
ejpam-2495	250	48	)	)	PUNCT
ejpam-2495	250	49	is	be	AUX
ejpam-2495	250	50	countably	countably	ADV
ejpam-2495	250	51	btµ	btµ	NOUN
ejpam-2495	250	52	compact	compact	ADJ
ejpam-2495	250	53	.	.	PUNCT
ejpam-2495	251	1	proof	proof	NOUN
ejpam-2495	251	2	.	.	PUNCT
ejpam-2495	252	1	let	let	VERB
ejpam-2495	252	2	{	{	PUNCT
ejpam-2495	252	3	ai	ai	VERB
ejpam-2495	252	4	:	:	PUNCT
ejpam-2495	252	5	i	i	PRON
ejpam-2495	252	6	∈	∈	PROPN
ejpam-2495	252	7	i	i	PRON
ejpam-2495	252	8	}	}	PUNCT
ejpam-2495	252	9	be	be	VERB
ejpam-2495	252	10	a	a	DET
ejpam-2495	252	11	countable	countable	ADJ
ejpam-2495	252	12	btµ	btµ	NOUN
ejpam-2495	252	13	open	open	ADJ
ejpam-2495	252	14	cover	cover	NOUN
ejpam-2495	252	15	of	of	ADP
ejpam-2495	252	16	(	(	PUNCT
ejpam-2495	252	17	y	y	PROPN
ejpam-2495	252	18	,	,	PUNCT
ejpam-2495	252	19	σ	σ	PROPN
ejpam-2495	252	20	)	)	PUNCT
ejpam-2495	252	21	.	.	PUNCT
ejpam-2495	253	1	since	since	SCONJ
ejpam-2495	253	2	f	f	PROPN
ejpam-2495	253	3	is	be	AUX
ejpam-2495	253	4	strongly	strongly	ADV
ejpam-2495	253	5	btµ	btµ	PROPN
ejpam-2495	253	6	continuous	continuous	ADJ
ejpam-2495	253	7	,	,	PUNCT
ejpam-2495	253	8	{	{	PUNCT
ejpam-2495	253	9	f−1(ai	f−1(ai	NOUN
ejpam-2495	253	10	)	)	PUNCT
ejpam-2495	253	11	:	:	PUNCT
ejpam-2495	253	12	i	i	NOUN
ejpam-2495	253	13	=	=	NOUN
ejpam-2495	253	14	1	1	NUM
ejpam-2495	253	15	,	,	PUNCT
ejpam-2495	253	16	2	2	NUM
ejpam-2495	253	17	,	,	PUNCT
ejpam-2495	253	18	·	·	PUNCT
ejpam-2495	253	19	·	·	PUNCT
ejpam-2495	253	20	·	·	PUNCT
ejpam-2495	253	21	,	,	PUNCT
ejpam-2495	253	22	n	n	CCONJ
ejpam-2495	253	23	}	}	PUNCT
ejpam-2495	253	24	is	be	AUX
ejpam-2495	253	25	an	an	DET
ejpam-2495	253	26	countable	countable	ADJ
ejpam-2495	253	27	supra	supra	NOUN
ejpam-2495	253	28	open	open	ADJ
ejpam-2495	253	29	cover	cover	NOUN
ejpam-2495	253	30	of	of	ADP
ejpam-2495	253	31	(	(	PUNCT
ejpam-2495	253	32	x	x	X
ejpam-2495	253	33	,	,	PUNCT
ejpam-2495	253	34	τ	τ	PROPN
ejpam-2495	253	35	)	)	PUNCT
ejpam-2495	253	36	.	.	PUNCT
ejpam-2495	254	1	again	again	ADV
ejpam-2495	254	2	,	,	PUNCT
ejpam-2495	254	3	since	since	SCONJ
ejpam-2495	254	4	(	(	PUNCT
ejpam-2495	254	5	x	x	X
ejpam-2495	254	6	,	,	PUNCT
ejpam-2495	254	7	τ	τ	X
ejpam-2495	254	8	)	)	PUNCT
ejpam-2495	254	9	is	be	AUX
ejpam-2495	254	10	countably	countably	ADV
ejpam-2495	254	11	supra	supra	ADJ
ejpam-2495	254	12	compact	compact	ADJ
ejpam-2495	254	13	,	,	PUNCT
ejpam-2495	254	14	the	the	DET
ejpam-2495	254	15	countable	countable	ADJ
ejpam-2495	254	16	supra	supra	PROPN
ejpam-2495	254	17	open	open	ADJ
ejpam-2495	254	18	cover	cover	NOUN
ejpam-2495	254	19	{	{	PUNCT
ejpam-2495	254	20	f−1(ai	f−1(ai	NOUN
ejpam-2495	254	21	)	)	PUNCT
ejpam-2495	254	22	:	:	PUNCT
ejpam-2495	255	1	i	i	PRON
ejpam-2495	255	2	∈	∈	VERB
ejpam-2495	255	3	i	i	PRON
ejpam-2495	255	4	}	}	PUNCT
ejpam-2495	255	5	of	of	ADP
ejpam-2495	255	6	(	(	PUNCT
ejpam-2495	255	7	x	x	X
ejpam-2495	255	8	,	,	PUNCT
ejpam-2495	255	9	τ	τ	X
ejpam-2495	255	10	)	)	PUNCT
ejpam-2495	255	11	has	have	VERB
ejpam-2495	255	12	a	a	DET
ejpam-2495	255	13	finite	finite	ADJ
ejpam-2495	255	14	sub	sub	NOUN
ejpam-2495	255	15	cover	cover	NOUN
ejpam-2495	255	16	say	say	VERB
ejpam-2495	255	17	{	{	PUNCT
ejpam-2495	255	18	f−1(ai	f−1(ai	NOUN
ejpam-2495	255	19	)	)	PUNCT
ejpam-2495	255	20	:	:	PUNCT
ejpam-2495	256	1	i	i	NOUN
ejpam-2495	256	2	=	=	NOUN
ejpam-2495	256	3	1	1	NUM
ejpam-2495	256	4	,	,	PUNCT
ejpam-2495	256	5	2	2	NUM
ejpam-2495	256	6	,	,	PUNCT
ejpam-2495	256	7	·	·	PUNCT
ejpam-2495	256	8	·	·	PUNCT
ejpam-2495	256	9	·	·	PUNCT
ejpam-2495	256	10	,	,	PUNCT
ejpam-2495	256	11	n	n	CCONJ
ejpam-2495	256	12	}	}	PUNCT
ejpam-2495	256	13	.	.	PUNCT
ejpam-2495	257	1	therefore	therefore	ADV
ejpam-2495	257	2	x	x	X
ejpam-2495	257	3	=	=	PRON
ejpam-2495	257	4	n⋃	n⋃	VERB
ejpam-2495	257	5	i=1	i=1	PRON
ejpam-2495	257	6	{	{	PUNCT
ejpam-2495	257	7	f−1(ai	f−1(ai	PROPN
ejpam-2495	257	8	)	)	PUNCT
ejpam-2495	257	9	}	}	PUNCT
ejpam-2495	257	10	,	,	PUNCT
ejpam-2495	257	11	which	which	PRON
ejpam-2495	257	12	implies	imply	VERB
ejpam-2495	257	13	f(x	f(x	PROPN
ejpam-2495	257	14	)	)	PUNCT
ejpam-2495	257	15	=	=	PRON
ejpam-2495	257	16	n⋃	n⋃	VERB
ejpam-2495	257	17	i=1	i=1	PROPN
ejpam-2495	257	18	ai	ai	VERB
ejpam-2495	257	19	,	,	PUNCT
ejpam-2495	257	20	so	so	SCONJ
ejpam-2495	257	21	that	that	SCONJ
ejpam-2495	257	22	y=	y=	PRON
ejpam-2495	257	23	n⋃	n⋃	VERB
ejpam-2495	257	24	i=1	i=1	PROPN
ejpam-2495	257	25	ai	ai	VERB
ejpam-2495	257	26	.	.	PUNCT
ejpam-2495	258	1	that	that	PRON
ejpam-2495	258	2	is	be	AUX
ejpam-2495	258	3	{	{	PUNCT
ejpam-2495	258	4	a1	a1	PROPN
ejpam-2495	258	5	,	,	PUNCT
ejpam-2495	258	6	a2	a2	PROPN
ejpam-2495	258	7	,	,	PUNCT
ejpam-2495	258	8	·	·	PUNCT
ejpam-2495	258	9	·	·	PUNCT
ejpam-2495	258	10	·	·	PUNCT
ejpam-2495	258	11	,	,	PUNCT
ejpam-2495	258	12	an	an	PRON
ejpam-2495	258	13	}	}	PUNCT
ejpam-2495	258	14	is	be	AUX
ejpam-2495	258	15	a	a	DET
ejpam-2495	258	16	finite	finite	ADJ
ejpam-2495	258	17	sub	sub	NOUN
ejpam-2495	258	18	cover	cover	NOUN
ejpam-2495	258	19	of	of	ADP
ejpam-2495	258	20	{	{	PUNCT
ejpam-2495	258	21	ai	ai	INTJ
ejpam-2495	258	22	:	:	PUNCT
ejpam-2495	258	23	i	i	PRON
ejpam-2495	258	24	∈	∈	VERB
ejpam-2495	259	1	i	i	X
ejpam-2495	259	2	}	}	PUNCT
ejpam-2495	259	3	for	for	ADP
ejpam-2495	259	4	(	(	PUNCT
ejpam-2495	259	5	y	y	PROPN
ejpam-2495	259	6	,	,	PUNCT
ejpam-2495	259	7	σ	σ	PROPN
ejpam-2495	259	8	)	)	PUNCT
ejpam-2495	259	9	.	.	PUNCT
ejpam-2495	260	1	hence	hence	ADV
ejpam-2495	260	2	(	(	PUNCT
ejpam-2495	260	3	y	y	PROPN
ejpam-2495	260	4	,	,	PUNCT
ejpam-2495	260	5	σ	σ	PROPN
ejpam-2495	260	6	)	)	PUNCT
ejpam-2495	260	7	is	be	AUX
ejpam-2495	260	8	countably	countably	ADV
ejpam-2495	260	9	btµ	btµ	NOUN
ejpam-2495	260	10	-compact	-compact	PROPN
ejpam-2495	260	11	.	.	PUNCT
ejpam-2495	261	1	theorem	theorem	VERB
ejpam-2495	261	2	18	18	NUM
ejpam-2495	261	3	.	.	PUNCT
ejpam-2495	262	1	the	the	DET
ejpam-2495	262	2	image	image	NOUN
ejpam-2495	262	3	of	of	ADP
ejpam-2495	262	4	a	a	DET
ejpam-2495	262	5	countably	countably	ADV
ejpam-2495	262	6	btµ	btµ	ADJ
ejpam-2495	262	7	compact	compact	ADJ
ejpam-2495	262	8	space	space	NOUN
ejpam-2495	262	9	under	under	ADP
ejpam-2495	262	10	a	a	DET
ejpam-2495	262	11	btµirresolute	btµirresolute	NOUN
ejpam-2495	262	12	map	map	NOUN
ejpam-2495	262	13	is	be	AUX
ejpam-2495	262	14	countably	countably	ADV
ejpam-2495	262	15	btµcompact	btµcompact	NOUN
ejpam-2495	262	16	.	.	PUNCT
ejpam-2495	263	1	proof	proof	NOUN
ejpam-2495	263	2	.	.	PUNCT
ejpam-2495	264	1	if	if	SCONJ
ejpam-2495	264	2	a	a	DET
ejpam-2495	264	3	map	map	NOUN
ejpam-2495	264	4	f	f	X
ejpam-2495	264	5	:	:	PUNCT
ejpam-2495	264	6	(	(	PUNCT
ejpam-2495	264	7	x	x	X
ejpam-2495	264	8	,	,	PUNCT
ejpam-2495	264	9	τ)→	τ)→	PROPN
ejpam-2495	264	10	(	(	PUNCT
ejpam-2495	264	11	y	y	PROPN
ejpam-2495	264	12	,	,	PUNCT
ejpam-2495	264	13	σ	σ	PROPN
ejpam-2495	264	14	)	)	PUNCT
ejpam-2495	264	15	is	be	AUX
ejpam-2495	264	16	btµ	btµ	PROPN
ejpam-2495	264	17	irresolute	irresolute	ADJ
ejpam-2495	264	18	map	map	NOUN
ejpam-2495	264	19	from	from	ADP
ejpam-2495	264	20	a	a	DET
ejpam-2495	264	21	countably	countably	ADV
ejpam-2495	264	22	btµ	btµ	ADJ
ejpam-2495	264	23	compact	compact	ADJ
ejpam-2495	264	24	space	space	NOUN
ejpam-2495	264	25	(	(	PUNCT
ejpam-2495	264	26	x	x	X
ejpam-2495	264	27	,	,	PUNCT
ejpam-2495	264	28	τ	τ	X
ejpam-2495	264	29	)	)	PUNCT
ejpam-2495	264	30	onto	onto	ADP
ejpam-2495	264	31	a	a	DET
ejpam-2495	264	32	supra	supra	ADJ
ejpam-2495	264	33	topological	topological	ADJ
ejpam-2495	264	34	space	space	NOUN
ejpam-2495	264	35	(	(	PUNCT
ejpam-2495	264	36	y	y	PROPN
ejpam-2495	264	37	,	,	PUNCT
ejpam-2495	264	38	σ	σ	PROPN
ejpam-2495	264	39	)	)	PUNCT
ejpam-2495	264	40	.	.	PUNCT
ejpam-2495	265	1	let	let	VERB
ejpam-2495	265	2	{	{	PUNCT
ejpam-2495	265	3	ai	ai	VERB
ejpam-2495	265	4	:	:	PUNCT
ejpam-2495	265	5	i	i	PRON
ejpam-2495	265	6	∈	∈	PROPN
ejpam-2495	265	7	i	i	PRON
ejpam-2495	265	8	}	}	PUNCT
ejpam-2495	265	9	be	be	VERB
ejpam-2495	265	10	a	a	DET
ejpam-2495	265	11	countable	countable	ADJ
ejpam-2495	265	12	btµ	btµ	NOUN
ejpam-2495	265	13	open	open	ADJ
ejpam-2495	265	14	cover	cover	NOUN
ejpam-2495	265	15	of	of	ADP
ejpam-2495	265	16	(	(	PUNCT
ejpam-2495	265	17	y	y	PROPN
ejpam-2495	265	18	,	,	PUNCT
ejpam-2495	265	19	σ	σ	PROPN
ejpam-2495	265	20	)	)	PUNCT
ejpam-2495	265	21	.then	.then	X
ejpam-2495	266	1	{	{	PUNCT
ejpam-2495	266	2	f−1(ai	f−1(ai	NOUN
ejpam-2495	266	3	)	)	PUNCT
ejpam-2495	266	4	:	:	PUNCT
ejpam-2495	267	1	i	i	NOUN
ejpam-2495	267	2	=	=	NOUN
ejpam-2495	267	3	1	1	NUM
ejpam-2495	267	4	,	,	PUNCT
ejpam-2495	267	5	2	2	NUM
ejpam-2495	267	6	,	,	PUNCT
ejpam-2495	267	7	·	·	PUNCT
ejpam-2495	267	8	·	·	PUNCT
ejpam-2495	267	9	·	·	PUNCT
ejpam-2495	267	10	,	,	PUNCT
ejpam-2495	267	11	n	n	CCONJ
ejpam-2495	267	12	}	}	PUNCT
ejpam-2495	267	13	is	be	AUX
ejpam-2495	267	14	an	an	DET
ejpam-2495	267	15	countable	countable	ADJ
ejpam-2495	267	16	btµ	btµ	NOUN
ejpam-2495	267	17	open	open	ADJ
ejpam-2495	267	18	cover	cover	NOUN
ejpam-2495	267	19	of	of	ADP
ejpam-2495	267	20	(	(	PUNCT
ejpam-2495	267	21	x	x	X
ejpam-2495	267	22	,	,	PUNCT
ejpam-2495	267	23	τ	τ	PROPN
ejpam-2495	267	24	)	)	PUNCT
ejpam-2495	267	25	,	,	PUNCT
ejpam-2495	267	26	since	since	SCONJ
ejpam-2495	267	27	f	f	PROPN
ejpam-2495	267	28	is	be	AUX
ejpam-2495	267	29	btµ	btµ	NOUN
ejpam-2495	267	30	irresolute	irresolute	ADJ
ejpam-2495	267	31	.	.	PUNCT
ejpam-2495	268	1	as	as	SCONJ
ejpam-2495	268	2	(	(	PUNCT
ejpam-2495	268	3	x	x	NOUN
ejpam-2495	268	4	,	,	PUNCT
ejpam-2495	268	5	τ	τ	X
ejpam-2495	268	6	)	)	PUNCT
ejpam-2495	268	7	is	be	AUX
ejpam-2495	268	8	countably	countably	ADV
ejpam-2495	268	9	btµ	btµ	PROPN
ejpam-2495	268	10	compact	compact	ADJ
ejpam-2495	268	11	,	,	PUNCT
ejpam-2495	268	12	the	the	DET
ejpam-2495	268	13	countable	countable	ADJ
ejpam-2495	268	14	btµopen	btµopen	ADJ
ejpam-2495	268	15	cover	cover	NOUN
ejpam-2495	268	16	{	{	PUNCT
ejpam-2495	268	17	f−1(ai	f−1(ai	NOUN
ejpam-2495	268	18	)	)	PUNCT
ejpam-2495	268	19	:	:	PUNCT
ejpam-2495	269	1	i	i	PRON
ejpam-2495	269	2	∈	∈	VERB
ejpam-2495	269	3	i	i	PRON
ejpam-2495	269	4	}	}	PUNCT
ejpam-2495	269	5	of	of	ADP
ejpam-2495	269	6	(	(	PUNCT
ejpam-2495	269	7	x	x	X
ejpam-2495	269	8	,	,	PUNCT
ejpam-2495	269	9	τ	τ	X
ejpam-2495	269	10	)	)	PUNCT
ejpam-2495	269	11	has	have	VERB
ejpam-2495	269	12	a	a	DET
ejpam-2495	269	13	finite	finite	ADJ
ejpam-2495	269	14	sub	sub	NOUN
ejpam-2495	269	15	cover	cover	NOUN
ejpam-2495	269	16	say	say	VERB
ejpam-2495	269	17	{	{	PUNCT
ejpam-2495	269	18	f−1(ai	f−1(ai	NOUN
ejpam-2495	269	19	)	)	PUNCT
ejpam-2495	269	20	:	:	PUNCT
ejpam-2495	270	1	i	i	NOUN
ejpam-2495	270	2	=	=	NOUN
ejpam-2495	270	3	1	1	NUM
ejpam-2495	270	4	,	,	PUNCT
ejpam-2495	270	5	2	2	NUM
ejpam-2495	270	6	,	,	PUNCT
ejpam-2495	270	7	·	·	PUNCT
ejpam-2495	270	8	·	·	PUNCT
ejpam-2495	270	9	·	·	PUNCT
ejpam-2495	270	10	,	,	PUNCT
ejpam-2495	270	11	n	n	CCONJ
ejpam-2495	270	12	}	}	PUNCT
ejpam-2495	270	13	.	.	PUNCT
ejpam-2495	271	1	therefore	therefore	ADV
ejpam-2495	271	2	x	x	X
ejpam-2495	271	3	=	=	PRON
ejpam-2495	271	4	n⋃	n⋃	VERB
ejpam-2495	271	5	i=1	i=1	PRON
ejpam-2495	271	6	{	{	PUNCT
ejpam-2495	271	7	f−1(ai	f−1(ai	PROPN
ejpam-2495	271	8	)	)	PUNCT
ejpam-2495	271	9	}	}	PUNCT
ejpam-2495	271	10	,	,	PUNCT
ejpam-2495	271	11	which	which	PRON
ejpam-2495	271	12	implies	imply	VERB
ejpam-2495	271	13	f(x	f(x	PROPN
ejpam-2495	271	14	)	)	PUNCT
ejpam-2495	271	15	=	=	PRON
ejpam-2495	271	16	n⋃	n⋃	VERB
ejpam-2495	271	17	i=1	i=1	PRON
ejpam-2495	271	18	{	{	PUNCT
ejpam-2495	271	19	(	(	PUNCT
ejpam-2495	271	20	ai	ai	NOUN
ejpam-2495	271	21	)	)	PUNCT
ejpam-2495	271	22	}	}	PUNCT
ejpam-2495	271	23	,	,	PUNCT
ejpam-2495	271	24	so	so	SCONJ
ejpam-2495	271	25	that	that	SCONJ
ejpam-2495	271	26	y	y	PROPN
ejpam-2495	271	27	=	=	PRON
ejpam-2495	271	28	n⋃	n⋃	PROPN
ejpam-2495	271	29	i=1	i=1	PRON
ejpam-2495	271	30	{	{	PUNCT
ejpam-2495	271	31	(	(	PUNCT
ejpam-2495	271	32	ai	ai	NOUN
ejpam-2495	271	33	)	)	PUNCT
ejpam-2495	271	34	}	}	PUNCT
ejpam-2495	271	35	.	.	PUNCT
ejpam-2495	272	1	that	that	PRON
ejpam-2495	272	2	is	be	AUX
ejpam-2495	272	3	{	{	PUNCT
ejpam-2495	272	4	a1	a1	PROPN
ejpam-2495	272	5	,	,	PUNCT
ejpam-2495	272	6	a2	a2	PROPN
ejpam-2495	272	7	,	,	PUNCT
ejpam-2495	272	8	·	·	PUNCT
ejpam-2495	272	9	·	·	PUNCT
ejpam-2495	272	10	·	·	PUNCT
ejpam-2495	272	11	,	,	PUNCT
ejpam-2495	272	12	an	an	PRON
ejpam-2495	272	13	}	}	PUNCT
ejpam-2495	272	14	is	be	AUX
ejpam-2495	272	15	a	a	DET
ejpam-2495	272	16	finite	finite	ADJ
ejpam-2495	272	17	sub	sub	NOUN
ejpam-2495	272	18	cover	cover	NOUN
ejpam-2495	272	19	of	of	ADP
ejpam-2495	272	20	{	{	PUNCT
ejpam-2495	272	21	ai	ai	INTJ
ejpam-2495	272	22	:	:	PUNCT
ejpam-2495	272	23	i	i	PRON
ejpam-2495	272	24	∈	∈	VERB
ejpam-2495	273	1	i	i	X
ejpam-2495	273	2	}	}	PUNCT
ejpam-2495	273	3	for	for	ADP
ejpam-2495	273	4	(	(	PUNCT
ejpam-2495	273	5	y	y	PROPN
ejpam-2495	273	6	,	,	PUNCT
ejpam-2495	273	7	σ	σ	PROPN
ejpam-2495	273	8	)	)	PUNCT
ejpam-2495	273	9	.	.	PUNCT
ejpam-2495	274	1	hence	hence	ADV
ejpam-2495	274	2	(	(	PUNCT
ejpam-2495	274	3	y	y	PROPN
ejpam-2495	274	4	,	,	PUNCT
ejpam-2495	274	5	σ	σ	PROPN
ejpam-2495	274	6	)	)	PUNCT
ejpam-2495	274	7	is	be	AUX
ejpam-2495	274	8	countably	countably	ADV
ejpam-2495	274	9	btµ	btµ	NOUN
ejpam-2495	274	10	-compact	-compact	PROPN
ejpam-2495	274	11	.	.	PUNCT
ejpam-2495	275	1	k.krishna	k.krishna	NOUN
ejpam-2495	275	2	,	,	PUNCT
ejpam-2495	275	3	m.vignesh	m.vignesh	NOUN
ejpam-2495	275	4	/	/	SYM
ejpam-2495	275	5	eur	eur	PROPN
ejpam-2495	275	6	.	.	PUNCT
ejpam-2495	276	1	j.	j.	PROPN
ejpam-2495	276	2	pure	pure	PROPN
ejpam-2495	276	3	appl	appl	PROPN
ejpam-2495	276	4	.	.	PROPN
ejpam-2495	276	5	math	math	PROPN
ejpam-2495	276	6	,	,	PUNCT
ejpam-2495	276	7	10	10	NUM
ejpam-2495	276	8	(	(	PUNCT
ejpam-2495	276	9	2	2	NUM
ejpam-2495	276	10	)	)	PUNCT
ejpam-2495	276	11	(	(	PUNCT
ejpam-2495	276	12	2017	2017	NUM
ejpam-2495	276	13	)	)	PUNCT
ejpam-2495	276	14	,	,	PUNCT
ejpam-2495	276	15	323	323	NUM
ejpam-2495	276	16	-	-	SYM
ejpam-2495	276	17	334	334	NUM
ejpam-2495	276	18	330	330	NUM
ejpam-2495	276	19	5	5	NUM
ejpam-2495	276	20	.	.	PUNCT
ejpam-2495	277	1	supra	supra	PROPN
ejpam-2495	277	2	bt	bt	PROPN
ejpam-2495	277	3	-	-	ADJ
ejpam-2495	277	4	lindelof	lindelof	ADJ
ejpam-2495	277	5	space	space	NOUN
ejpam-2495	277	6	in	in	ADP
ejpam-2495	277	7	this	this	DET
ejpam-2495	277	8	section	section	NOUN
ejpam-2495	277	9	,	,	PUNCT
ejpam-2495	277	10	we	we	PRON
ejpam-2495	277	11	concentrate	concentrate	VERB
ejpam-2495	277	12	on	on	ADP
ejpam-2495	277	13	the	the	DET
ejpam-2495	277	14	concept	concept	NOUN
ejpam-2495	277	15	of	of	ADP
ejpam-2495	277	16	btµlindelof	btµlindelof	NOUN
ejpam-2495	277	17	space	space	NOUN
ejpam-2495	277	18	and	and	CCONJ
ejpam-2495	277	19	their	their	PRON
ejpam-2495	277	20	properties	property	NOUN
ejpam-2495	277	21	.	.	PUNCT
ejpam-2495	278	1	definition	definition	NOUN
ejpam-2495	278	2	16	16	NUM
ejpam-2495	278	3	.	.	PUNCT
ejpam-2495	279	1	a	a	DET
ejpam-2495	279	2	supra	supra	PROPN
ejpam-2495	279	3	topological	topological	ADJ
ejpam-2495	279	4	space	space	NOUN
ejpam-2495	279	5	(	(	PUNCT
ejpam-2495	279	6	x	x	X
ejpam-2495	279	7	,	,	PUNCT
ejpam-2495	279	8	τ	τ	X
ejpam-2495	279	9	)	)	PUNCT
ejpam-2495	279	10	is	be	AUX
ejpam-2495	279	11	said	say	VERB
ejpam-2495	279	12	to	to	PART
ejpam-2495	279	13	be	be	AUX
ejpam-2495	279	14	btµ	btµ	PROPN
ejpam-2495	279	15	lindelof	lindelof	PROPN
ejpam-2495	279	16	space	space	NOUN
ejpam-2495	279	17	if	if	SCONJ
ejpam-2495	279	18	every	every	DET
ejpam-2495	279	19	btµ	btµ	NOUN
ejpam-2495	279	20	open	open	ADJ
ejpam-2495	279	21	cover	cover	NOUN
ejpam-2495	279	22	of	of	ADP
ejpam-2495	279	23	x	x	PUNCT
ejpam-2495	279	24	has	have	VERB
ejpam-2495	279	25	a	a	DET
ejpam-2495	279	26	countable	countable	ADJ
ejpam-2495	279	27	subcover	subcover	PROPN
ejpam-2495	279	28	.	.	PUNCT
ejpam-2495	280	1	theorem	theorem	VERB
ejpam-2495	280	2	19	19	NUM
ejpam-2495	280	3	.	.	PUNCT
ejpam-2495	281	1	every	every	DET
ejpam-2495	281	2	btµ	btµ	NOUN
ejpam-2495	281	3	lindelof	lindelof	PROPN
ejpam-2495	281	4	space	space	NOUN
ejpam-2495	281	5	is	be	AUX
ejpam-2495	281	6	supra	supra	ADJ
ejpam-2495	281	7	lindelof	lindelof	PROPN
ejpam-2495	281	8	space	space	NOUN
ejpam-2495	281	9	.	.	PUNCT
ejpam-2495	282	1	proof	proof	NOUN
ejpam-2495	282	2	.	.	PUNCT
ejpam-2495	283	1	let	let	VERB
ejpam-2495	283	2	{	{	PUNCT
ejpam-2495	283	3	ai	ai	VERB
ejpam-2495	283	4	:	:	PUNCT
ejpam-2495	283	5	i	i	PRON
ejpam-2495	283	6	∈	∈	PROPN
ejpam-2495	283	7	i	i	PRON
ejpam-2495	283	8	}	}	PUNCT
ejpam-2495	283	9	be	be	VERB
ejpam-2495	283	10	a	a	DET
ejpam-2495	283	11	supra	supra	ADJ
ejpam-2495	283	12	open	open	ADJ
ejpam-2495	283	13	cover	cover	NOUN
ejpam-2495	283	14	of	of	ADP
ejpam-2495	283	15	(	(	PUNCT
ejpam-2495	283	16	x	x	X
ejpam-2495	283	17	,	,	PUNCT
ejpam-2495	283	18	τ	τ	PROPN
ejpam-2495	283	19	)	)	PUNCT
ejpam-2495	283	20	.	.	PUNCT
ejpam-2495	284	1	by	by	ADP
ejpam-2495	284	2	[	[	X
ejpam-2495	284	3	4	4	NUM
ejpam-2495	284	4	]	]	PUNCT
ejpam-2495	284	5	,	,	PUNCT
ejpam-2495	284	6	{	{	PUNCT
ejpam-2495	284	7	ai	ai	VERB
ejpam-2495	284	8	:	:	PUNCT
ejpam-2495	284	9	i	i	PRON
ejpam-2495	284	10	∈	∈	PROPN
ejpam-2495	284	11	i	i	PRON
ejpam-2495	284	12	}	}	PUNCT
ejpam-2495	284	13	is	be	AUX
ejpam-2495	284	14	a	a	DET
ejpam-2495	284	15	btµ	btµ	NOUN
ejpam-2495	284	16	open	open	ADJ
ejpam-2495	284	17	cover	cover	NOUN
ejpam-2495	284	18	of	of	ADP
ejpam-2495	284	19	(	(	PUNCT
ejpam-2495	284	20	x	x	X
ejpam-2495	284	21	,	,	PUNCT
ejpam-2495	284	22	τ	τ	PROPN
ejpam-2495	284	23	)	)	PUNCT
ejpam-2495	284	24	.	.	PUNCT
ejpam-2495	285	1	since	since	SCONJ
ejpam-2495	285	2	(	(	PUNCT
ejpam-2495	285	3	x	x	X
ejpam-2495	285	4	,	,	PUNCT
ejpam-2495	285	5	τ	τ	X
ejpam-2495	285	6	)	)	PUNCT
ejpam-2495	285	7	is	be	AUX
ejpam-2495	285	8	btµ	btµ	PROPN
ejpam-2495	285	9	lindelof	lindelof	PROPN
ejpam-2495	285	10	space	space	NOUN
ejpam-2495	285	11	,	,	PUNCT
ejpam-2495	285	12	btµopen	btµopen	ADJ
ejpam-2495	285	13	cover	cover	NOUN
ejpam-2495	285	14	{	{	PUNCT
ejpam-2495	285	15	ai	ai	INTJ
ejpam-2495	285	16	:	:	PUNCT
ejpam-2495	285	17	i	i	PRON
ejpam-2495	285	18	∈	∈	VERB
ejpam-2495	286	1	i	i	X
ejpam-2495	286	2	}	}	PUNCT
ejpam-2495	286	3	of	of	ADP
ejpam-2495	286	4	(	(	PUNCT
ejpam-2495	286	5	x	x	X
ejpam-2495	286	6	,	,	PUNCT
ejpam-2495	286	7	τ	τ	X
ejpam-2495	286	8	)	)	PUNCT
ejpam-2495	286	9	has	have	VERB
ejpam-2495	286	10	a	a	DET
ejpam-2495	286	11	countable	countable	ADJ
ejpam-2495	286	12	subcover	subcover	NOUN
ejpam-2495	286	13	say	say	VERB
ejpam-2495	286	14	{	{	PUNCT
ejpam-2495	286	15	ai	ai	VERB
ejpam-2495	286	16	:	:	PUNCT
ejpam-2495	286	17	i	i	NOUN
ejpam-2495	286	18	=	=	NOUN
ejpam-2495	286	19	1	1	NUM
ejpam-2495	286	20	,	,	PUNCT
ejpam-2495	286	21	2	2	NUM
ejpam-2495	286	22	,	,	PUNCT
ejpam-2495	286	23	·	·	PUNCT
ejpam-2495	286	24	·	·	PUNCT
ejpam-2495	286	25	·	·	PUNCT
ejpam-2495	286	26	,	,	PUNCT
ejpam-2495	286	27	n	n	CCONJ
ejpam-2495	286	28	}	}	PUNCT
ejpam-2495	286	29	for	for	ADP
ejpam-2495	286	30	x.	x.	NOUN
ejpam-2495	286	31	hence	hence	ADV
ejpam-2495	286	32	(	(	PUNCT
ejpam-2495	286	33	x	x	X
ejpam-2495	286	34	,	,	PUNCT
ejpam-2495	286	35	τ	τ	X
ejpam-2495	286	36	)	)	PUNCT
ejpam-2495	286	37	is	be	AUX
ejpam-2495	286	38	a	a	DET
ejpam-2495	286	39	supra	supra	ADJ
ejpam-2495	286	40	lindelof	lindelof	PROPN
ejpam-2495	286	41	space	space	NOUN
ejpam-2495	286	42	.	.	PUNCT
ejpam-2495	287	1	theorem	theorem	VERB
ejpam-2495	287	2	20	20	NUM
ejpam-2495	287	3	.	.	PUNCT
ejpam-2495	288	1	if	if	SCONJ
ejpam-2495	288	2	(	(	PUNCT
ejpam-2495	288	3	x	x	X
ejpam-2495	288	4	,	,	PUNCT
ejpam-2495	288	5	τ	τ	X
ejpam-2495	288	6	)	)	PUNCT
ejpam-2495	288	7	is	be	AUX
ejpam-2495	288	8	supra	supra	PROPN
ejpam-2495	288	9	lindelof	lindelof	PROPN
ejpam-2495	288	10	space	space	NOUN
ejpam-2495	288	11	and	and	CCONJ
ejpam-2495	288	12	btt	btt	PROPN
ejpam-2495	288	13	µ	µ	PROPN
ejpam-2495	288	14	c	c	NOUN
ejpam-2495	288	15	-space	-space	NOUN
ejpam-2495	288	16	,	,	PUNCT
ejpam-2495	288	17	then	then	ADV
ejpam-2495	288	18	(	(	PUNCT
ejpam-2495	288	19	x	x	X
ejpam-2495	288	20	,	,	PUNCT
ejpam-2495	288	21	τ	τ	PROPN
ejpam-2495	288	22	)	)	PUNCT
ejpam-2495	288	23	is	be	AUX
ejpam-2495	288	24	btµ	btµ	PROPN
ejpam-2495	288	25	lindelof	lindelof	PROPN
ejpam-2495	288	26	space	space	NOUN
ejpam-2495	288	27	.	.	PUNCT
ejpam-2495	289	1	proof	proof	NOUN
ejpam-2495	289	2	.	.	PUNCT
ejpam-2495	290	1	let	let	VERB
ejpam-2495	290	2	{	{	PUNCT
ejpam-2495	290	3	ai	ai	VERB
ejpam-2495	290	4	:	:	PUNCT
ejpam-2495	290	5	i	i	PRON
ejpam-2495	290	6	∈	∈	PROPN
ejpam-2495	290	7	i	i	PRON
ejpam-2495	290	8	}	}	PUNCT
ejpam-2495	290	9	be	be	VERB
ejpam-2495	290	10	a	a	DET
ejpam-2495	290	11	btµ	btµ	NOUN
ejpam-2495	290	12	open	open	ADJ
ejpam-2495	290	13	cover	cover	NOUN
ejpam-2495	290	14	of	of	ADP
ejpam-2495	290	15	(	(	PUNCT
ejpam-2495	290	16	x	x	X
ejpam-2495	290	17	,	,	PUNCT
ejpam-2495	290	18	τ	τ	PROPN
ejpam-2495	290	19	)	)	PUNCT
ejpam-2495	290	20	.	.	PUNCT
ejpam-2495	291	1	since	since	SCONJ
ejpam-2495	291	2	by	by	ADP
ejpam-2495	291	3	btt	btt	PROPN
ejpam-2495	291	4	µ	µ	PROPN
ejpam-2495	291	5	c	c	NOUN
ejpam-2495	291	6	-space,{ai	-space,{ai	NOUN
ejpam-2495	291	7	:	:	PUNCT
ejpam-2495	292	1	i	i	PRON
ejpam-2495	292	2	∈	∈	VERB
ejpam-2495	292	3	i	i	PRON
ejpam-2495	292	4	}	}	PUNCT
ejpam-2495	292	5	is	be	AUX
ejpam-2495	292	6	a	a	DET
ejpam-2495	292	7	supra	supra	ADJ
ejpam-2495	292	8	open	open	ADJ
ejpam-2495	292	9	cover	cover	NOUN
ejpam-2495	292	10	of	of	ADP
ejpam-2495	292	11	(	(	PUNCT
ejpam-2495	292	12	x	x	X
ejpam-2495	292	13	,	,	PUNCT
ejpam-2495	292	14	τ	τ	PROPN
ejpam-2495	292	15	)	)	PUNCT
ejpam-2495	292	16	.	.	PUNCT
ejpam-2495	293	1	since	since	SCONJ
ejpam-2495	293	2	(	(	PUNCT
ejpam-2495	293	3	x	x	X
ejpam-2495	293	4	,	,	PUNCT
ejpam-2495	293	5	τ	τ	X
ejpam-2495	293	6	)	)	PUNCT
ejpam-2495	293	7	is	be	AUX
ejpam-2495	293	8	compact	compact	ADJ
ejpam-2495	293	9	,	,	PUNCT
ejpam-2495	294	1	supra	supra	ADJ
ejpam-2495	294	2	open	open	ADJ
ejpam-2495	294	3	cover	cover	NOUN
ejpam-2495	294	4	{	{	PUNCT
ejpam-2495	294	5	ai	ai	VERB
ejpam-2495	294	6	:	:	PUNCT
ejpam-2495	294	7	i	i	PRON
ejpam-2495	294	8	∈	∈	VERB
ejpam-2495	295	1	i	i	X
ejpam-2495	295	2	}	}	PUNCT
ejpam-2495	295	3	of	of	ADP
ejpam-2495	295	4	(	(	PUNCT
ejpam-2495	295	5	x	x	X
ejpam-2495	295	6	,	,	PUNCT
ejpam-2495	295	7	τ	τ	X
ejpam-2495	295	8	)	)	PUNCT
ejpam-2495	295	9	has	have	VERB
ejpam-2495	295	10	a	a	DET
ejpam-2495	295	11	countable	countable	ADJ
ejpam-2495	295	12	sub	sub	NOUN
ejpam-2495	295	13	cover	cover	NOUN
ejpam-2495	295	14	say	say	VERB
ejpam-2495	295	15	{	{	PUNCT
ejpam-2495	295	16	ai	ai	VERB
ejpam-2495	295	17	:	:	PUNCT
ejpam-2495	295	18	i	i	NOUN
ejpam-2495	295	19	=	=	NOUN
ejpam-2495	295	20	1	1	NUM
ejpam-2495	295	21	,	,	PUNCT
ejpam-2495	295	22	2	2	NUM
ejpam-2495	295	23	,	,	PUNCT
ejpam-2495	295	24	·	·	PUNCT
ejpam-2495	295	25	·	·	PUNCT
ejpam-2495	295	26	·	·	PUNCT
ejpam-2495	295	27	,	,	PUNCT
ejpam-2495	295	28	n	n	CCONJ
ejpam-2495	295	29	}	}	PUNCT
ejpam-2495	295	30	for	for	ADP
ejpam-2495	295	31	x.	x.	NOUN
ejpam-2495	295	32	hence	hence	ADV
ejpam-2495	295	33	(	(	PUNCT
ejpam-2495	295	34	x	x	X
ejpam-2495	295	35	,	,	PUNCT
ejpam-2495	295	36	τ	τ	X
ejpam-2495	295	37	)	)	PUNCT
ejpam-2495	295	38	is	be	AUX
ejpam-2495	295	39	a	a	DET
ejpam-2495	295	40	btµ	btµ	NOUN
ejpam-2495	295	41	lindelof	lindelof	PROPN
ejpam-2495	295	42	space	space	NOUN
ejpam-2495	295	43	.	.	PUNCT
ejpam-2495	296	1	theorem	theorem	PROPN
ejpam-2495	296	2	21	21	NUM
ejpam-2495	296	3	.	.	PUNCT
ejpam-2495	297	1	every	every	DET
ejpam-2495	297	2	btµ	btµ	NOUN
ejpam-2495	297	3	compact	compact	ADJ
ejpam-2495	297	4	space	space	NOUN
ejpam-2495	297	5	is	be	AUX
ejpam-2495	297	6	btµ	btµ	PROPN
ejpam-2495	297	7	lindelof	lindelof	PROPN
ejpam-2495	297	8	space	space	NOUN
ejpam-2495	297	9	.	.	PUNCT
ejpam-2495	298	1	proof	proof	NOUN
ejpam-2495	298	2	.	.	PUNCT
ejpam-2495	299	1	let	let	VERB
ejpam-2495	299	2	{	{	PUNCT
ejpam-2495	299	3	ai	ai	VERB
ejpam-2495	299	4	:	:	PUNCT
ejpam-2495	299	5	i	i	PRON
ejpam-2495	299	6	∈	∈	PROPN
ejpam-2495	299	7	i	i	PRON
ejpam-2495	299	8	}	}	PUNCT
ejpam-2495	299	9	be	be	VERB
ejpam-2495	299	10	a	a	DET
ejpam-2495	299	11	btµ	btµ	NOUN
ejpam-2495	299	12	open	open	ADJ
ejpam-2495	299	13	cover	cover	NOUN
ejpam-2495	299	14	of	of	ADP
ejpam-2495	299	15	(	(	PUNCT
ejpam-2495	299	16	x	x	X
ejpam-2495	299	17	,	,	PUNCT
ejpam-2495	299	18	τ	τ	PROPN
ejpam-2495	299	19	)	)	PUNCT
ejpam-2495	299	20	.	.	PUNCT
ejpam-2495	300	1	then	then	ADV
ejpam-2495	300	2	{	{	PUNCT
ejpam-2495	300	3	ai	ai	INTJ
ejpam-2495	300	4	:	:	PUNCT
ejpam-2495	300	5	i	i	PRON
ejpam-2495	300	6	∈	∈	PROPN
ejpam-2495	301	1	i	i	PRON
ejpam-2495	301	2	}	}	PUNCT
ejpam-2495	301	3	has	have	VERB
ejpam-2495	301	4	a	a	DET
ejpam-2495	301	5	finite	finite	ADJ
ejpam-2495	301	6	subcover	subcover	PROPN
ejpam-2495	301	7	say	say	VERB
ejpam-2495	301	8	{	{	PUNCT
ejpam-2495	301	9	ai	ai	VERB
ejpam-2495	301	10	:	:	PUNCT
ejpam-2495	301	11	i	i	NOUN
ejpam-2495	301	12	=	=	NOUN
ejpam-2495	301	13	1	1	NUM
ejpam-2495	301	14	,	,	PUNCT
ejpam-2495	301	15	2	2	NUM
ejpam-2495	301	16	,	,	PUNCT
ejpam-2495	301	17	·	·	PUNCT
ejpam-2495	301	18	·	·	PUNCT
ejpam-2495	301	19	·	·	PUNCT
ejpam-2495	301	20	,	,	PUNCT
ejpam-2495	301	21	n	n	CCONJ
ejpam-2495	301	22	}	}	PUNCT
ejpam-2495	301	23	.	.	PUNCT
ejpam-2495	302	1	since	since	SCONJ
ejpam-2495	302	2	(	(	PUNCT
ejpam-2495	302	3	x	x	X
ejpam-2495	302	4	,	,	PUNCT
ejpam-2495	302	5	τ	τ	X
ejpam-2495	302	6	)	)	PUNCT
ejpam-2495	302	7	is	be	AUX
ejpam-2495	302	8	btµ	btµ	NOUN
ejpam-2495	302	9	compact	compact	ADJ
ejpam-2495	302	10	space	space	NOUN
ejpam-2495	302	11	.	.	PUNCT
ejpam-2495	303	1	since	since	SCONJ
ejpam-2495	303	2	every	every	DET
ejpam-2495	303	3	finite	finite	PROPN
ejpam-2495	303	4	subcover	subcover	PROPN
ejpam-2495	303	5	is	be	AUX
ejpam-2495	303	6	always	always	ADV
ejpam-2495	303	7	countable	countable	ADJ
ejpam-2495	303	8	subcover	subcover	NOUN
ejpam-2495	303	9	and	and	CCONJ
ejpam-2495	303	10	therefore	therefore	ADV
ejpam-2495	303	11	{	{	PUNCT
ejpam-2495	303	12	ai	ai	INTJ
ejpam-2495	303	13	:	:	PUNCT
ejpam-2495	303	14	i	i	NOUN
ejpam-2495	303	15	=	=	NOUN
ejpam-2495	303	16	1	1	NUM
ejpam-2495	303	17	,	,	PUNCT
ejpam-2495	303	18	2	2	NUM
ejpam-2495	303	19	,	,	PUNCT
ejpam-2495	303	20	·	·	PUNCT
ejpam-2495	303	21	·	·	PUNCT
ejpam-2495	303	22	·	·	PUNCT
ejpam-2495	303	23	,	,	PUNCT
ejpam-2495	303	24	n	n	CCONJ
ejpam-2495	303	25	}	}	PUNCT
ejpam-2495	303	26	is	be	AUX
ejpam-2495	303	27	countable	countable	ADJ
ejpam-2495	303	28	subcover	subcover	NOUN
ejpam-2495	303	29	of	of	ADP
ejpam-2495	303	30	{	{	PUNCT
ejpam-2495	303	31	ai	ai	PROPN
ejpam-2495	303	32	:	:	PUNCT
ejpam-2495	303	33	i	i	PRON
ejpam-2495	303	34	∈	∈	PROPN
ejpam-2495	304	1	i	i	PRON
ejpam-2495	304	2	}	}	PUNCT
ejpam-2495	304	3	.	.	PUNCT
ejpam-2495	305	1	hence	hence	ADV
ejpam-2495	305	2	(	(	PUNCT
ejpam-2495	305	3	x	x	X
ejpam-2495	305	4	,	,	PUNCT
ejpam-2495	305	5	τ	τ	X
ejpam-2495	305	6	)	)	PUNCT
ejpam-2495	305	7	is	be	AUX
ejpam-2495	305	8	btµ	btµ	PROPN
ejpam-2495	305	9	lindelof	lindelof	PROPN
ejpam-2495	305	10	space	space	NOUN
ejpam-2495	305	11	.	.	PUNCT
ejpam-2495	306	1	theorem	theorem	VERB
ejpam-2495	306	2	22	22	NUM
ejpam-2495	306	3	.	.	PUNCT
ejpam-2495	307	1	a	a	DET
ejpam-2495	307	2	btµ	btµ	NOUN
ejpam-2495	307	3	continuous	continuous	ADJ
ejpam-2495	307	4	image	image	NOUN
ejpam-2495	307	5	of	of	ADP
ejpam-2495	307	6	a	a	DET
ejpam-2495	307	7	btµ	btµ	NOUN
ejpam-2495	307	8	lindelof	lindelof	PROPN
ejpam-2495	307	9	space	space	NOUN
ejpam-2495	307	10	is	be	AUX
ejpam-2495	307	11	supra	supra	ADJ
ejpam-2495	307	12	lindelof	lindelof	PROPN
ejpam-2495	307	13	space	space	NOUN
ejpam-2495	307	14	.	.	PUNCT
ejpam-2495	308	1	proof	proof	NOUN
ejpam-2495	308	2	.	.	PUNCT
ejpam-2495	309	1	let	let	VERB
ejpam-2495	309	2	f	f	NOUN
ejpam-2495	309	3	:	:	PUNCT
ejpam-2495	309	4	(	(	PUNCT
ejpam-2495	309	5	x	x	X
ejpam-2495	309	6	,	,	PUNCT
ejpam-2495	309	7	τ)→	τ)→	PROPN
ejpam-2495	309	8	(	(	PUNCT
ejpam-2495	309	9	y	y	NOUN
ejpam-2495	309	10	,	,	PUNCT
ejpam-2495	309	11	σ)be	σ)be	PROPN
ejpam-2495	309	12	a	a	DET
ejpam-2495	309	13	btµ	btµ	NOUN
ejpam-2495	309	14	continuous	continuous	ADJ
ejpam-2495	309	15	map	map	NOUN
ejpam-2495	309	16	from	from	ADP
ejpam-2495	309	17	a	a	DET
ejpam-2495	309	18	btµ	btµ	NOUN
ejpam-2495	309	19	lindelof	lindelof	NOUN
ejpam-2495	309	20	space	space	NOUN
ejpam-2495	309	21	x	x	X
ejpam-2495	309	22	onto	onto	ADP
ejpam-2495	309	23	a	a	DET
ejpam-2495	309	24	supra	supra	ADJ
ejpam-2495	309	25	topological	topological	ADJ
ejpam-2495	309	26	space	space	NOUN
ejpam-2495	309	27	y.	y.	PROPN
ejpam-2495	309	28	let	let	VERB
ejpam-2495	309	29	{	{	PUNCT
ejpam-2495	309	30	ai	ai	VERB
ejpam-2495	309	31	:	:	PUNCT
ejpam-2495	309	32	i	i	PRON
ejpam-2495	309	33	∈	∈	PROPN
ejpam-2495	310	1	i	i	PRON
ejpam-2495	310	2	}	}	PUNCT
ejpam-2495	310	3	be	be	VERB
ejpam-2495	310	4	a	a	DET
ejpam-2495	310	5	supra	supra	ADJ
ejpam-2495	310	6	open	open	ADJ
ejpam-2495	310	7	cover	cover	NOUN
ejpam-2495	310	8	of	of	ADP
ejpam-2495	310	9	y.	y.	NOUN
ejpam-2495	310	10	then	then	ADV
ejpam-2495	310	11	{	{	PUNCT
ejpam-2495	310	12	f−1(ai	f−1(ai	PROPN
ejpam-2495	310	13	)	)	PUNCT
ejpam-2495	310	14	:	:	PUNCT
ejpam-2495	311	1	i	i	PRON
ejpam-2495	311	2	∈	∈	VERB
ejpam-2495	311	3	i	i	PRON
ejpam-2495	311	4	}	}	PUNCT
ejpam-2495	311	5	is	be	AUX
ejpam-2495	311	6	a	a	DET
ejpam-2495	311	7	btµ	btµ	NOUN
ejpam-2495	311	8	open	open	ADJ
ejpam-2495	311	9	cover	cover	NOUN
ejpam-2495	311	10	of	of	ADP
ejpam-2495	311	11	x	x	PRON
ejpam-2495	311	12	,	,	PUNCT
ejpam-2495	311	13	as	as	SCONJ
ejpam-2495	311	14	f	f	PROPN
ejpam-2495	311	15	is	be	AUX
ejpam-2495	311	16	btµ	btµ	NOUN
ejpam-2495	311	17	continuous	continuous	ADJ
ejpam-2495	311	18	.	.	PUNCT
ejpam-2495	312	1	since	since	SCONJ
ejpam-2495	312	2	x	x	PROPN
ejpam-2495	312	3	is	be	AUX
ejpam-2495	312	4	btµ	btµ	PROPN
ejpam-2495	312	5	lindelof	lindelof	PROPN
ejpam-2495	312	6	space	space	NOUN
ejpam-2495	312	7	,	,	PUNCT
ejpam-2495	312	8	the	the	DET
ejpam-2495	312	9	btµ	btµ	NOUN
ejpam-2495	312	10	open	open	ADJ
ejpam-2495	312	11	cover	cover	VERB
ejpam-2495	312	12	{	{	PUNCT
ejpam-2495	312	13	f−1(ai	f−1(ai	NOUN
ejpam-2495	312	14	)	)	PUNCT
ejpam-2495	312	15	:	:	PUNCT
ejpam-2495	313	1	i	i	PRON
ejpam-2495	313	2	∈	∈	VERB
ejpam-2495	313	3	i	i	PRON
ejpam-2495	313	4	}	}	PUNCT
ejpam-2495	313	5	of	of	ADP
ejpam-2495	313	6	x	x	PUNCT
ejpam-2495	313	7	has	have	VERB
ejpam-2495	313	8	a	a	DET
ejpam-2495	313	9	countable	countable	ADJ
ejpam-2495	313	10	sub	sub	NOUN
ejpam-2495	313	11	cover	cover	NOUN
ejpam-2495	313	12	say	say	VERB
ejpam-2495	313	13	{	{	PUNCT
ejpam-2495	313	14	f−1(ai	f−1(ai	NOUN
ejpam-2495	313	15	)	)	PUNCT
ejpam-2495	313	16	:	:	PUNCT
ejpam-2495	314	1	i	i	NOUN
ejpam-2495	314	2	=	=	NOUN
ejpam-2495	314	3	1	1	NUM
ejpam-2495	314	4	,	,	PUNCT
ejpam-2495	314	5	2	2	NUM
ejpam-2495	314	6	,	,	PUNCT
ejpam-2495	314	7	·	·	PUNCT
ejpam-2495	314	8	·	·	PUNCT
ejpam-2495	314	9	·	·	PUNCT
ejpam-2495	314	10	,	,	PUNCT
ejpam-2495	314	11	n	n	CCONJ
ejpam-2495	314	12	}	}	PUNCT
ejpam-2495	314	13	.	.	PUNCT
ejpam-2495	315	1	therefore	therefore	ADV
ejpam-2495	315	2	x	x	X
ejpam-2495	315	3	=	=	PRON
ejpam-2495	315	4	n⋃	n⋃	VERB
ejpam-2495	315	5	i=1	i=1	PRON
ejpam-2495	315	6	{	{	PUNCT
ejpam-2495	315	7	f−1(ai	f−1(ai	PROPN
ejpam-2495	315	8	)	)	PUNCT
ejpam-2495	315	9	}	}	PUNCT
ejpam-2495	315	10	,	,	PUNCT
ejpam-2495	315	11	which	which	PRON
ejpam-2495	315	12	implies	imply	VERB
ejpam-2495	315	13	f(x	f(x	PROPN
ejpam-2495	315	14	)	)	PUNCT
ejpam-2495	315	15	=	=	PRON
ejpam-2495	315	16	n⋃	n⋃	VERB
ejpam-2495	315	17	i=1	i=1	PROPN
ejpam-2495	315	18	ai	ai	VERB
ejpam-2495	315	19	,	,	PUNCT
ejpam-2495	315	20	then	then	ADV
ejpam-2495	315	21	y	y	PROPN
ejpam-2495	315	22	=	=	PUNCT
ejpam-2495	315	23	n⋃	n⋃	VERB
ejpam-2495	315	24	i=1	i=1	PROPN
ejpam-2495	315	25	ai	ai	VERB
ejpam-2495	315	26	.	.	PUNCT
ejpam-2495	316	1	that	that	PRON
ejpam-2495	316	2	is	be	AUX
ejpam-2495	316	3	{	{	PUNCT
ejpam-2495	316	4	a1	a1	PROPN
ejpam-2495	316	5	,	,	PUNCT
ejpam-2495	316	6	a2	a2	PROPN
ejpam-2495	316	7	,	,	PUNCT
ejpam-2495	316	8	·	·	PUNCT
ejpam-2495	316	9	·	·	PUNCT
ejpam-2495	316	10	·	·	PUNCT
ejpam-2495	316	11	,	,	PUNCT
ejpam-2495	316	12	an	an	PRON
ejpam-2495	316	13	}	}	PUNCT
ejpam-2495	316	14	is	be	AUX
ejpam-2495	316	15	a	a	DET
ejpam-2495	316	16	countable	countable	ADJ
ejpam-2495	316	17	sub	sub	NOUN
ejpam-2495	316	18	cover	cover	NOUN
ejpam-2495	316	19	of	of	ADP
ejpam-2495	316	20	{	{	PUNCT
ejpam-2495	316	21	ai	ai	INTJ
ejpam-2495	316	22	:	:	PUNCT
ejpam-2495	316	23	i	i	PRON
ejpam-2495	316	24	∈	∈	VERB
ejpam-2495	317	1	i	i	X
ejpam-2495	317	2	}	}	PUNCT
ejpam-2495	317	3	for	for	ADP
ejpam-2495	317	4	y.	y.	PROPN
ejpam-2495	317	5	hence	hence	ADV
ejpam-2495	317	6	y	y	PROPN
ejpam-2495	317	7	is	be	AUX
ejpam-2495	317	8	supra	supra	PROPN
ejpam-2495	317	9	lindelof	lindelof	PROPN
ejpam-2495	317	10	space	space	NOUN
ejpam-2495	317	11	.	.	PUNCT
ejpam-2495	318	1	theorem	theorem	VERB
ejpam-2495	318	2	23	23	NUM
ejpam-2495	318	3	.	.	PUNCT
ejpam-2495	319	1	the	the	DET
ejpam-2495	319	2	image	image	NOUN
ejpam-2495	319	3	of	of	ADP
ejpam-2495	319	4	a	a	DET
ejpam-2495	319	5	btµ	btµ	NOUN
ejpam-2495	319	6	lindelof	lindelof	PROPN
ejpam-2495	319	7	space	space	NOUN
ejpam-2495	319	8	under	under	ADP
ejpam-2495	319	9	a	a	DET
ejpam-2495	319	10	btµ	btµ	NOUN
ejpam-2495	319	11	irresolute	irresolute	NOUN
ejpam-2495	319	12	map	map	NOUN
ejpam-2495	319	13	is	be	AUX
ejpam-2495	319	14	btµ	btµ	PROPN
ejpam-2495	319	15	lindelof	lindelof	PROPN
ejpam-2495	319	16	space	space	NOUN
ejpam-2495	319	17	.	.	PUNCT
ejpam-2495	320	1	k.krishna	k.krishna	NOUN
ejpam-2495	320	2	,	,	PUNCT
ejpam-2495	320	3	m.vignesh	m.vignesh	NOUN
ejpam-2495	320	4	/	/	SYM
ejpam-2495	320	5	eur	eur	PROPN
ejpam-2495	320	6	.	.	PUNCT
ejpam-2495	321	1	j.	j.	PROPN
ejpam-2495	321	2	pure	pure	PROPN
ejpam-2495	321	3	appl	appl	PROPN
ejpam-2495	321	4	.	.	PROPN
ejpam-2495	321	5	math	math	PROPN
ejpam-2495	321	6	,	,	PUNCT
ejpam-2495	321	7	10	10	NUM
ejpam-2495	321	8	(	(	PUNCT
ejpam-2495	321	9	2	2	NUM
ejpam-2495	321	10	)	)	PUNCT
ejpam-2495	321	11	(	(	PUNCT
ejpam-2495	321	12	2017	2017	NUM
ejpam-2495	321	13	)	)	PUNCT
ejpam-2495	321	14	,	,	PUNCT
ejpam-2495	321	15	323	323	NUM
ejpam-2495	321	16	-	-	SYM
ejpam-2495	321	17	334	334	NUM
ejpam-2495	321	18	331	331	NUM
ejpam-2495	321	19	proof	proof	NOUN
ejpam-2495	321	20	.	.	PUNCT
ejpam-2495	322	1	if	if	SCONJ
ejpam-2495	322	2	a	a	DET
ejpam-2495	322	3	map	map	NOUN
ejpam-2495	322	4	f	f	X
ejpam-2495	322	5	:	:	PUNCT
ejpam-2495	322	6	(	(	PUNCT
ejpam-2495	322	7	x	x	X
ejpam-2495	322	8	,	,	PUNCT
ejpam-2495	322	9	τ)→	τ)→	PROPN
ejpam-2495	322	10	(	(	PUNCT
ejpam-2495	322	11	y	y	PROPN
ejpam-2495	322	12	,	,	PUNCT
ejpam-2495	322	13	σ	σ	PROPN
ejpam-2495	322	14	)	)	PUNCT
ejpam-2495	322	15	is	be	AUX
ejpam-2495	322	16	btµ	btµ	PROPN
ejpam-2495	322	17	irresolute	irresolute	ADJ
ejpam-2495	322	18	map	map	NOUN
ejpam-2495	322	19	from	from	ADP
ejpam-2495	322	20	a	a	DET
ejpam-2495	322	21	btµ	btµ	NOUN
ejpam-2495	322	22	lindelof	lindelof	NOUN
ejpam-2495	322	23	space	space	NOUN
ejpam-2495	322	24	(	(	PUNCT
ejpam-2495	322	25	x	x	X
ejpam-2495	322	26	,	,	PUNCT
ejpam-2495	322	27	τ	τ	X
ejpam-2495	322	28	)	)	PUNCT
ejpam-2495	322	29	onto	onto	ADP
ejpam-2495	322	30	a	a	DET
ejpam-2495	322	31	supra	supra	ADJ
ejpam-2495	322	32	topological	topological	ADJ
ejpam-2495	322	33	space	space	NOUN
ejpam-2495	322	34	(	(	PUNCT
ejpam-2495	322	35	y	y	PROPN
ejpam-2495	322	36	,	,	PUNCT
ejpam-2495	322	37	σ	σ	PROPN
ejpam-2495	322	38	)	)	PUNCT
ejpam-2495	322	39	.	.	PUNCT
ejpam-2495	323	1	let	let	VERB
ejpam-2495	323	2	{	{	PUNCT
ejpam-2495	323	3	ai	ai	VERB
ejpam-2495	323	4	:	:	PUNCT
ejpam-2495	323	5	i	i	PRON
ejpam-2495	323	6	∈	∈	PROPN
ejpam-2495	323	7	i	i	PRON
ejpam-2495	323	8	}	}	PUNCT
ejpam-2495	323	9	be	be	VERB
ejpam-2495	323	10	a	a	DET
ejpam-2495	323	11	btµ	btµ	NOUN
ejpam-2495	323	12	open	open	ADJ
ejpam-2495	323	13	cover	cover	NOUN
ejpam-2495	323	14	of	of	ADP
ejpam-2495	323	15	(	(	PUNCT
ejpam-2495	323	16	y	y	PROPN
ejpam-2495	323	17	,	,	PUNCT
ejpam-2495	323	18	σ).then	σ).then	PROPN
ejpam-2495	323	19	{	{	PUNCT
ejpam-2495	323	20	f−1(ai	f−1(ai	PROPN
ejpam-2495	323	21	)	)	PUNCT
ejpam-2495	323	22	:	:	PUNCT
ejpam-2495	324	1	i	i	PRON
ejpam-2495	324	2	∈	∈	VERB
ejpam-2495	324	3	i	i	PRON
ejpam-2495	324	4	}	}	PUNCT
ejpam-2495	324	5	is	be	AUX
ejpam-2495	324	6	an	an	DET
ejpam-2495	324	7	btµ	btµ	NOUN
ejpam-2495	324	8	open	open	ADJ
ejpam-2495	324	9	cover	cover	NOUN
ejpam-2495	324	10	of	of	ADP
ejpam-2495	324	11	(	(	PUNCT
ejpam-2495	324	12	x	x	X
ejpam-2495	324	13	,	,	PUNCT
ejpam-2495	324	14	τ	τ	PROPN
ejpam-2495	324	15	)	)	PUNCT
ejpam-2495	324	16	.	.	PUNCT
ejpam-2495	325	1	since	since	SCONJ
ejpam-2495	325	2	f	f	PROPN
ejpam-2495	325	3	is	be	AUX
ejpam-2495	325	4	btµ	btµ	NOUN
ejpam-2495	325	5	irresolute	irresolute	ADJ
ejpam-2495	325	6	.	.	PUNCT
ejpam-2495	326	1	as	as	SCONJ
ejpam-2495	326	2	(	(	PUNCT
ejpam-2495	326	3	x	x	NOUN
ejpam-2495	326	4	,	,	PUNCT
ejpam-2495	326	5	τ	τ	X
ejpam-2495	326	6	)	)	PUNCT
ejpam-2495	326	7	is	be	AUX
ejpam-2495	326	8	btµ	btµ	PROPN
ejpam-2495	326	9	lindelof	lindelof	PROPN
ejpam-2495	326	10	space	space	NOUN
ejpam-2495	326	11	,	,	PUNCT
ejpam-2495	326	12	the	the	DET
ejpam-2495	326	13	btµ	btµ	NOUN
ejpam-2495	326	14	open	open	ADJ
ejpam-2495	326	15	cover	cover	VERB
ejpam-2495	326	16	{	{	PUNCT
ejpam-2495	326	17	f−1(ai	f−1(ai	NOUN
ejpam-2495	326	18	)	)	PUNCT
ejpam-2495	326	19	:	:	PUNCT
ejpam-2495	327	1	i	i	PRON
ejpam-2495	327	2	∈	∈	VERB
ejpam-2495	327	3	i	i	PRON
ejpam-2495	327	4	}	}	PUNCT
ejpam-2495	327	5	of	of	ADP
ejpam-2495	327	6	(	(	PUNCT
ejpam-2495	327	7	x	x	X
ejpam-2495	327	8	,	,	PUNCT
ejpam-2495	327	9	τ	τ	X
ejpam-2495	327	10	)	)	PUNCT
ejpam-2495	327	11	has	have	VERB
ejpam-2495	327	12	a	a	DET
ejpam-2495	327	13	countable	countable	ADJ
ejpam-2495	327	14	sub	sub	NOUN
ejpam-2495	327	15	cover	cover	NOUN
ejpam-2495	327	16	say	say	VERB
ejpam-2495	327	17	{	{	PUNCT
ejpam-2495	327	18	f−1(ai	f−1(ai	NOUN
ejpam-2495	327	19	)	)	PUNCT
ejpam-2495	327	20	:	:	PUNCT
ejpam-2495	328	1	i	i	NOUN
ejpam-2495	328	2	=	=	NOUN
ejpam-2495	328	3	1	1	NUM
ejpam-2495	328	4	,	,	PUNCT
ejpam-2495	328	5	2	2	NUM
ejpam-2495	328	6	,	,	PUNCT
ejpam-2495	328	7	·	·	PUNCT
ejpam-2495	328	8	·	·	PUNCT
ejpam-2495	328	9	·	·	PUNCT
ejpam-2495	328	10	,	,	PUNCT
ejpam-2495	328	11	n	n	CCONJ
ejpam-2495	328	12	}	}	PUNCT
ejpam-2495	328	13	.	.	PUNCT
ejpam-2495	329	1	therefore	therefore	ADV
ejpam-2495	329	2	x	x	X
ejpam-2495	329	3	=	=	PRON
ejpam-2495	329	4	n⋃	n⋃	VERB
ejpam-2495	329	5	i=1	i=1	PRON
ejpam-2495	329	6	{	{	PUNCT
ejpam-2495	329	7	f−1(ai	f−1(ai	PROPN
ejpam-2495	329	8	)	)	PUNCT
ejpam-2495	329	9	}	}	PUNCT
ejpam-2495	329	10	,	,	PUNCT
ejpam-2495	329	11	which	which	PRON
ejpam-2495	329	12	implies	imply	VERB
ejpam-2495	329	13	f(x	f(x	PROPN
ejpam-2495	329	14	)	)	PUNCT
ejpam-2495	329	15	=	=	PRON
ejpam-2495	329	16	n⋃	n⋃	VERB
ejpam-2495	329	17	i=1	i=1	PROPN
ejpam-2495	329	18	ai	ai	VERB
ejpam-2495	329	19	,	,	PUNCT
ejpam-2495	329	20	so	so	SCONJ
ejpam-2495	329	21	that	that	SCONJ
ejpam-2495	329	22	y=	y=	PRON
ejpam-2495	329	23	n⋃	n⋃	VERB
ejpam-2495	329	24	i=1	i=1	PROPN
ejpam-2495	329	25	ai	ai	VERB
ejpam-2495	329	26	.	.	PUNCT
ejpam-2495	330	1	that	that	PRON
ejpam-2495	330	2	is	be	AUX
ejpam-2495	330	3	{	{	PUNCT
ejpam-2495	330	4	a1	a1	PROPN
ejpam-2495	330	5	,	,	PUNCT
ejpam-2495	330	6	a2	a2	PROPN
ejpam-2495	330	7	,	,	PUNCT
ejpam-2495	330	8	·	·	PUNCT
ejpam-2495	330	9	·	·	PUNCT
ejpam-2495	330	10	·	·	PUNCT
ejpam-2495	330	11	,	,	PUNCT
ejpam-2495	330	12	an	an	PRON
ejpam-2495	330	13	}	}	PUNCT
ejpam-2495	330	14	is	be	AUX
ejpam-2495	330	15	a	a	DET
ejpam-2495	330	16	countable	countable	ADJ
ejpam-2495	330	17	sub	sub	NOUN
ejpam-2495	330	18	cover	cover	NOUN
ejpam-2495	330	19	of	of	ADP
ejpam-2495	330	20	{	{	PUNCT
ejpam-2495	330	21	ai	ai	INTJ
ejpam-2495	330	22	:	:	PUNCT
ejpam-2495	330	23	i	i	PRON
ejpam-2495	330	24	∈	∈	VERB
ejpam-2495	331	1	i	i	X
ejpam-2495	331	2	}	}	PUNCT
ejpam-2495	331	3	for	for	ADP
ejpam-2495	331	4	(	(	PUNCT
ejpam-2495	331	5	y	y	PROPN
ejpam-2495	331	6	,	,	PUNCT
ejpam-2495	331	7	σ	σ	PROPN
ejpam-2495	331	8	)	)	PUNCT
ejpam-2495	331	9	.	.	PUNCT
ejpam-2495	332	1	hence	hence	ADV
ejpam-2495	332	2	(	(	PUNCT
ejpam-2495	332	3	y	y	PROPN
ejpam-2495	332	4	,	,	PUNCT
ejpam-2495	332	5	σ	σ	PROPN
ejpam-2495	332	6	)	)	PUNCT
ejpam-2495	332	7	is	be	AUX
ejpam-2495	332	8	btµ	btµ	PROPN
ejpam-2495	332	9	lindelof	lindelof	PROPN
ejpam-2495	332	10	space	space	NOUN
ejpam-2495	332	11	.	.	PUNCT
ejpam-2495	333	1	theorem	theorem	VERB
ejpam-2495	333	2	24	24	NUM
ejpam-2495	333	3	.	.	PUNCT
ejpam-2495	334	1	if	if	SCONJ
ejpam-2495	334	2	(	(	PUNCT
ejpam-2495	334	3	x	x	X
ejpam-2495	334	4	,	,	PUNCT
ejpam-2495	334	5	τ	τ	X
ejpam-2495	334	6	)	)	PUNCT
ejpam-2495	334	7	is	be	AUX
ejpam-2495	334	8	btµ	btµ	PROPN
ejpam-2495	334	9	lindelof	lindelof	PROPN
ejpam-2495	334	10	space	space	NOUN
ejpam-2495	334	11	and	and	CCONJ
ejpam-2495	334	12	countably	countably	ADV
ejpam-2495	334	13	btµ	btµ	ADJ
ejpam-2495	334	14	compact	compact	ADJ
ejpam-2495	334	15	space	space	NOUN
ejpam-2495	334	16	then	then	ADV
ejpam-2495	334	17	(	(	PUNCT
ejpam-2495	334	18	x	x	X
ejpam-2495	334	19	,	,	PUNCT
ejpam-2495	334	20	τ	τ	X
ejpam-2495	334	21	)	)	PUNCT
ejpam-2495	334	22	is	be	AUX
ejpam-2495	334	23	btµ	btµ	NOUN
ejpam-2495	334	24	compact	compact	ADJ
ejpam-2495	334	25	space	space	NOUN
ejpam-2495	334	26	.	.	PUNCT
ejpam-2495	335	1	proof	proof	NOUN
ejpam-2495	335	2	.	.	PUNCT
ejpam-2495	336	1	suppose	suppose	VERB
ejpam-2495	336	2	(	(	PUNCT
ejpam-2495	336	3	x	x	X
ejpam-2495	336	4	,	,	PUNCT
ejpam-2495	336	5	τ	τ	X
ejpam-2495	336	6	)	)	PUNCT
ejpam-2495	336	7	is	be	AUX
ejpam-2495	336	8	btµ	btµ	PROPN
ejpam-2495	336	9	lindelof	lindelof	PROPN
ejpam-2495	336	10	space	space	NOUN
ejpam-2495	336	11	and	and	CCONJ
ejpam-2495	336	12	countably	countably	ADV
ejpam-2495	336	13	btµ	btµ	ADJ
ejpam-2495	336	14	compact	compact	ADJ
ejpam-2495	336	15	space	space	NOUN
ejpam-2495	336	16	.	.	PUNCT
ejpam-2495	337	1	let	let	VERB
ejpam-2495	337	2	{	{	PUNCT
ejpam-2495	337	3	ai	ai	VERB
ejpam-2495	337	4	:	:	PUNCT
ejpam-2495	337	5	i	i	PRON
ejpam-2495	337	6	∈	∈	PROPN
ejpam-2495	337	7	i	i	PRON
ejpam-2495	337	8	}	}	PUNCT
ejpam-2495	337	9	be	be	VERB
ejpam-2495	337	10	a	a	DET
ejpam-2495	337	11	btµ	btµ	NOUN
ejpam-2495	337	12	open	open	ADJ
ejpam-2495	337	13	cover	cover	NOUN
ejpam-2495	337	14	of	of	ADP
ejpam-2495	337	15	(	(	PUNCT
ejpam-2495	337	16	x	x	X
ejpam-2495	337	17	,	,	PUNCT
ejpam-2495	337	18	τ	τ	PROPN
ejpam-2495	337	19	)	)	PUNCT
ejpam-2495	337	20	.	.	PUNCT
ejpam-2495	338	1	since	since	SCONJ
ejpam-2495	338	2	(	(	PUNCT
ejpam-2495	338	3	x	x	X
ejpam-2495	338	4	,	,	PUNCT
ejpam-2495	338	5	τ	τ	X
ejpam-2495	338	6	)	)	PUNCT
ejpam-2495	338	7	is	be	AUX
ejpam-2495	338	8	btµ	btµ	PROPN
ejpam-2495	338	9	lindelof	lindelof	PROPN
ejpam-2495	338	10	space	space	NOUN
ejpam-2495	338	11	,	,	PUNCT
ejpam-2495	338	12	{	{	PUNCT
ejpam-2495	338	13	ai	ai	VERB
ejpam-2495	338	14	:	:	PUNCT
ejpam-2495	338	15	i	i	PRON
ejpam-2495	338	16	∈	∈	PROPN
ejpam-2495	339	1	i	i	PRON
ejpam-2495	339	2	}	}	PUNCT
ejpam-2495	339	3	has	have	VERB
ejpam-2495	339	4	a	a	DET
ejpam-2495	339	5	countable	countable	ADJ
ejpam-2495	339	6	subcover	subcover	NOUN
ejpam-2495	339	7	say	say	VERB
ejpam-2495	339	8	{	{	PUNCT
ejpam-2495	339	9	ain	ain	NOUN
ejpam-2495	339	10	:	:	PUNCT
ejpam-2495	339	11	i	i	PROPN
ejpam-2495	339	12	∈	∈	VERB
ejpam-2495	340	1	i	i	PRON
ejpam-2495	340	2	,	,	PUNCT
ejpam-2495	340	3	n	n	PROPN
ejpam-2495	340	4	∈	∈	PROPN
ejpam-2495	340	5	n	n	CCONJ
ejpam-2495	340	6	}	}	PUNCT
ejpam-2495	340	7	,	,	PUNCT
ejpam-2495	340	8	therefore	therefore	ADV
ejpam-2495	340	9	{	{	PUNCT
ejpam-2495	340	10	ain	ain	NOUN
ejpam-2495	340	11	:	:	PUNCT
ejpam-2495	340	12	i	i	PROPN
ejpam-2495	340	13	∈	∈	VERB
ejpam-2495	340	14	i	i	PRON
ejpam-2495	340	15	,	,	PUNCT
ejpam-2495	340	16	n	n	PROPN
ejpam-2495	340	17	∈	∈	PROPN
ejpam-2495	340	18	n	n	CCONJ
ejpam-2495	340	19	}	}	PUNCT
ejpam-2495	340	20	is	be	AUX
ejpam-2495	340	21	a	a	DET
ejpam-2495	340	22	countable	countable	ADJ
ejpam-2495	340	23	subcover	subcover	NOUN
ejpam-2495	340	24	of	of	ADP
ejpam-2495	340	25	(	(	PUNCT
ejpam-2495	340	26	x	x	X
ejpam-2495	340	27	,	,	PUNCT
ejpam-2495	340	28	τ	τ	X
ejpam-2495	340	29	)	)	PUNCT
ejpam-2495	340	30	and	and	CCONJ
ejpam-2495	340	31	{	{	PUNCT
ejpam-2495	340	32	ain	ain	NOUN
ejpam-2495	340	33	:	:	PUNCT
ejpam-2495	340	34	i	i	PROPN
ejpam-2495	340	35	∈	∈	VERB
ejpam-2495	341	1	i	i	PRON
ejpam-2495	341	2	,	,	PUNCT
ejpam-2495	341	3	n	n	PROPN
ejpam-2495	341	4	∈	∈	PROPN
ejpam-2495	341	5	n	n	CCONJ
ejpam-2495	341	6	}	}	PUNCT
ejpam-2495	341	7	is	be	AUX
ejpam-2495	341	8	subfamily	subfamily	ADV
ejpam-2495	341	9	of	of	ADP
ejpam-2495	341	10	{	{	PUNCT
ejpam-2495	341	11	ai	ai	VERB
ejpam-2495	341	12	:	:	PUNCT
ejpam-2495	341	13	i	i	PRON
ejpam-2495	341	14	∈	∈	VERB
ejpam-2495	341	15	i	i	X
ejpam-2495	341	16	}	}	PUNCT
ejpam-2495	341	17	and	and	CCONJ
ejpam-2495	341	18	so	so	ADV
ejpam-2495	341	19	{	{	PUNCT
ejpam-2495	341	20	ain	ain	NOUN
ejpam-2495	341	21	:	:	PUNCT
ejpam-2495	341	22	i	i	PROPN
ejpam-2495	341	23	∈	∈	VERB
ejpam-2495	341	24	i	i	PRON
ejpam-2495	341	25	,	,	PUNCT
ejpam-2495	341	26	n	n	PROPN
ejpam-2495	341	27	∈	∈	PROPN
ejpam-2495	341	28	n	n	CCONJ
ejpam-2495	341	29	}	}	PUNCT
ejpam-2495	341	30	is	be	AUX
ejpam-2495	341	31	a	a	DET
ejpam-2495	341	32	countable	countable	ADJ
ejpam-2495	341	33	btµ	btµ	NOUN
ejpam-2495	341	34	open	open	ADJ
ejpam-2495	341	35	cover	cover	NOUN
ejpam-2495	341	36	of	of	ADP
ejpam-2495	341	37	(	(	PUNCT
ejpam-2495	341	38	x	x	X
ejpam-2495	341	39	,	,	PUNCT
ejpam-2495	341	40	τ	τ	PROPN
ejpam-2495	341	41	)	)	PUNCT
ejpam-2495	341	42	.	.	PUNCT
ejpam-2495	342	1	again	again	ADV
ejpam-2495	342	2	,	,	PUNCT
ejpam-2495	342	3	since	since	SCONJ
ejpam-2495	342	4	(	(	PUNCT
ejpam-2495	342	5	x	x	X
ejpam-2495	342	6	,	,	PUNCT
ejpam-2495	342	7	τ	τ	X
ejpam-2495	342	8	)	)	PUNCT
ejpam-2495	342	9	is	be	AUX
ejpam-2495	342	10	countably	countably	ADV
ejpam-2495	342	11	btµ	btµ	NOUN
ejpam-2495	342	12	compact	compact	ADJ
ejpam-2495	342	13	,	,	PUNCT
ejpam-2495	342	14	{	{	PUNCT
ejpam-2495	342	15	ain	ain	NOUN
ejpam-2495	342	16	:	:	PUNCT
ejpam-2495	342	17	i	i	PROPN
ejpam-2495	342	18	∈	∈	VERB
ejpam-2495	342	19	i	i	PRON
ejpam-2495	342	20	,	,	PUNCT
ejpam-2495	342	21	n	n	PROPN
ejpam-2495	342	22	∈	∈	PROPN
ejpam-2495	342	23	n	n	CCONJ
ejpam-2495	342	24	}	}	PUNCT
ejpam-2495	342	25	has	have	VERB
ejpam-2495	342	26	a	a	DET
ejpam-2495	342	27	finite	finite	ADJ
ejpam-2495	342	28	subcover	subcover	NOUN
ejpam-2495	342	29	and	and	CCONJ
ejpam-2495	342	30	{	{	PUNCT
ejpam-2495	342	31	aik	aik	NOUN
ejpam-2495	342	32	:	:	PUNCT
ejpam-2495	343	1	i	i	PRON
ejpam-2495	343	2	∈	∈	VERB
ejpam-2495	344	1	i	i	PRON
ejpam-2495	344	2	,	,	PUNCT
ejpam-2495	344	3	k	k	PROPN
ejpam-2495	344	4	=	=	SYM
ejpam-2495	344	5	1	1	NUM
ejpam-2495	344	6	,	,	PUNCT
ejpam-2495	344	7	2n	2n	NUM
ejpam-2495	344	8	}	}	PUNCT
ejpam-2495	344	9	.	.	PUNCT
ejpam-2495	345	1	therefore	therefore	ADV
ejpam-2495	345	2	{	{	PUNCT
ejpam-2495	345	3	aik	aik	NOUN
ejpam-2495	345	4	:	:	PUNCT
ejpam-2495	345	5	i	i	PRON
ejpam-2495	345	6	∈	∈	VERB
ejpam-2495	346	1	i	i	PRON
ejpam-2495	346	2	,	,	PUNCT
ejpam-2495	346	3	k	k	PROPN
ejpam-2495	346	4	=	=	SYM
ejpam-2495	346	5	1	1	NUM
ejpam-2495	346	6	,	,	PUNCT
ejpam-2495	346	7	2	2	NUM
ejpam-2495	346	8	,	,	PUNCT
ejpam-2495	346	9	·	·	PUNCT
ejpam-2495	346	10	·	·	PUNCT
ejpam-2495	346	11	·	·	PUNCT
ejpam-2495	346	12	,	,	PUNCT
ejpam-2495	346	13	n	n	CCONJ
ejpam-2495	346	14	}	}	PUNCT
ejpam-2495	346	15	is	be	AUX
ejpam-2495	346	16	a	a	DET
ejpam-2495	346	17	finite	finite	ADJ
ejpam-2495	346	18	subcover	subcover	NOUN
ejpam-2495	346	19	of	of	ADP
ejpam-2495	346	20	{	{	PUNCT
ejpam-2495	346	21	ai	ai	PROPN
ejpam-2495	346	22	:	:	PUNCT
ejpam-2495	346	23	i	i	PRON
ejpam-2495	346	24	∈	∈	VERB
ejpam-2495	347	1	i	i	X
ejpam-2495	347	2	}	}	PUNCT
ejpam-2495	347	3	for	for	ADP
ejpam-2495	347	4	(	(	PUNCT
ejpam-2495	347	5	x	x	X
ejpam-2495	347	6	,	,	PUNCT
ejpam-2495	347	7	τ	τ	PROPN
ejpam-2495	347	8	)	)	PUNCT
ejpam-2495	347	9	.	.	PUNCT
ejpam-2495	348	1	hence	hence	ADV
ejpam-2495	348	2	(	(	PUNCT
ejpam-2495	348	3	x	x	X
ejpam-2495	348	4	,	,	PUNCT
ejpam-2495	348	5	τ	τ	X
ejpam-2495	348	6	)	)	PUNCT
ejpam-2495	348	7	is	be	AUX
ejpam-2495	348	8	btµ	btµ	NOUN
ejpam-2495	348	9	compact	compact	ADJ
ejpam-2495	348	10	space	space	NOUN
ejpam-2495	348	11	.	.	PUNCT
ejpam-2495	349	1	theorem	theorem	VERB
ejpam-2495	349	2	25	25	NUM
ejpam-2495	349	3	.	.	PUNCT
ejpam-2495	350	1	if	if	SCONJ
ejpam-2495	350	2	a	a	DET
ejpam-2495	350	3	function	function	NOUN
ejpam-2495	350	4	f	f	X
ejpam-2495	350	5	:	:	PUNCT
ejpam-2495	350	6	(	(	PUNCT
ejpam-2495	350	7	x	x	X
ejpam-2495	350	8	,	,	PUNCT
ejpam-2495	350	9	τ	τ	X
ejpam-2495	350	10	)	)	PUNCT
ejpam-2495	350	11	→	→	SYM
ejpam-2495	350	12	(	(	PUNCT
ejpam-2495	350	13	y	y	PROPN
ejpam-2495	350	14	,	,	PUNCT
ejpam-2495	350	15	σ	σ	PROPN
ejpam-2495	350	16	)	)	PUNCT
ejpam-2495	350	17	is	be	AUX
ejpam-2495	350	18	btµ	btµ	NOUN
ejpam-2495	350	19	irresolute	irresolute	ADJ
ejpam-2495	350	20	and	and	CCONJ
ejpam-2495	350	21	a	a	DET
ejpam-2495	350	22	subset	subset	NOUN
ejpam-2495	350	23	of	of	ADP
ejpam-2495	350	24	x	x	SYM
ejpam-2495	350	25	is	be	AUX
ejpam-2495	350	26	btµ	btµ	PROPN
ejpam-2495	350	27	lindelof	lindelof	PROPN
ejpam-2495	350	28	relative	relative	ADJ
ejpam-2495	350	29	to	to	ADP
ejpam-2495	350	30	x	x	NOUN
ejpam-2495	350	31	,	,	PUNCT
ejpam-2495	350	32	then	then	ADV
ejpam-2495	350	33	f(b	f(b	PROPN
ejpam-2495	350	34	)	)	PUNCT
ejpam-2495	350	35	is	be	AUX
ejpam-2495	350	36	btµ	btµ	PROPN
ejpam-2495	350	37	lindelof	lindelof	PROPN
ejpam-2495	350	38	relative	relative	ADJ
ejpam-2495	350	39	to	to	ADP
ejpam-2495	350	40	y.	y.	NOUN
ejpam-2495	350	41	proof	proof	NOUN
ejpam-2495	350	42	.	.	PUNCT
ejpam-2495	351	1	let	let	VERB
ejpam-2495	351	2	{	{	PUNCT
ejpam-2495	351	3	ai	ai	VERB
ejpam-2495	351	4	:	:	PUNCT
ejpam-2495	351	5	i	i	PRON
ejpam-2495	351	6	∈	∈	PROPN
ejpam-2495	351	7	i	i	PRON
ejpam-2495	351	8	}	}	PUNCT
ejpam-2495	351	9	be	be	VERB
ejpam-2495	351	10	a	a	DET
ejpam-2495	351	11	cover	cover	NOUN
ejpam-2495	351	12	of	of	ADP
ejpam-2495	351	13	f(b	f(b	PROPN
ejpam-2495	351	14	)	)	PUNCT
ejpam-2495	351	15	by	by	ADP
ejpam-2495	351	16	btµ	btµ	PROPN
ejpam-2495	351	17	-open	-open	PROPN
ejpam-2495	351	18	subsets	subset	NOUN
ejpam-2495	351	19	of	of	ADP
ejpam-2495	351	20	y.	y.	PROPN
ejpam-2495	351	21	then	then	ADV
ejpam-2495	351	22	{	{	PUNCT
ejpam-2495	351	23	f−1(ai	f−1(ai	NOUN
ejpam-2495	351	24	)	)	PUNCT
ejpam-2495	351	25	:	:	PUNCT
ejpam-2495	352	1	i	i	PRON
ejpam-2495	352	2	∈	∈	VERB
ejpam-2495	352	3	i	i	PRON
ejpam-2495	352	4	}	}	PUNCT
ejpam-2495	352	5	is	be	AUX
ejpam-2495	352	6	a	a	DET
ejpam-2495	352	7	cover	cover	NOUN
ejpam-2495	352	8	of	of	ADP
ejpam-2495	352	9	b	b	NOUN
ejpam-2495	352	10	by	by	ADP
ejpam-2495	352	11	btµ	btµ	PROPN
ejpam-2495	352	12	-open	-open	PROPN
ejpam-2495	352	13	subsets	subset	NOUN
ejpam-2495	352	14	of	of	ADP
ejpam-2495	352	15	x.	x.	NOUN
ejpam-2495	352	16	since	since	SCONJ
ejpam-2495	352	17	b	b	PROPN
ejpam-2495	352	18	is	be	AUX
ejpam-2495	352	19	btµ	btµ	PROPN
ejpam-2495	352	20	-lindelof	-lindelof	NOUN
ejpam-2495	352	21	relative	relative	ADJ
ejpam-2495	352	22	to	to	ADP
ejpam-2495	352	23	x	x	PRON
ejpam-2495	352	24	,	,	PUNCT
ejpam-2495	352	25	{	{	PUNCT
ejpam-2495	352	26	f−1(ai	f−1(ai	NOUN
ejpam-2495	352	27	)	)	PUNCT
ejpam-2495	352	28	:	:	PUNCT
ejpam-2495	353	1	i	i	PRON
ejpam-2495	353	2	∈	∈	VERB
ejpam-2495	353	3	i	i	PRON
ejpam-2495	353	4	}	}	PUNCT
ejpam-2495	353	5	has	have	VERB
ejpam-2495	353	6	a	a	DET
ejpam-2495	353	7	countable	countable	ADJ
ejpam-2495	353	8	subcover	subcover	NOUN
ejpam-2495	353	9	say	say	VERB
ejpam-2495	353	10	{	{	PUNCT
ejpam-2495	353	11	f−1(a1	f−1(a1	NOUN
ejpam-2495	353	12	)	)	PUNCT
ejpam-2495	353	13	,	,	PUNCT
ejpam-2495	353	14	f	f	PROPN
ejpam-2495	353	15	−1(a2	−1(a2	NOUN
ejpam-2495	353	16	)	)	PUNCT
ejpam-2495	353	17	,	,	PUNCT
ejpam-2495	353	18	·	·	PUNCT
ejpam-2495	353	19	·	·	PUNCT
ejpam-2495	353	20	·	·	PUNCT
ejpam-2495	353	21	,	,	PUNCT
ejpam-2495	353	22	f−1(an	f−1(an	NOUN
ejpam-2495	353	23	)	)	PUNCT
ejpam-2495	353	24	}	}	PUNCT
ejpam-2495	353	25	for	for	ADP
ejpam-2495	353	26	b.	b.	PROPN
ejpam-2495	353	27	now	now	ADV
ejpam-2495	353	28	{	{	PUNCT
ejpam-2495	353	29	a1	a1	PROPN
ejpam-2495	353	30	,	,	PUNCT
ejpam-2495	353	31	a2	a2	PROPN
ejpam-2495	353	32	,	,	PUNCT
ejpam-2495	353	33	·	·	PUNCT
ejpam-2495	353	34	·	·	PUNCT
ejpam-2495	353	35	·	·	PUNCT
ejpam-2495	353	36	,	,	PUNCT
ejpam-2495	353	37	an	an	PRON
ejpam-2495	353	38	}	}	PUNCT
ejpam-2495	353	39	is	be	AUX
ejpam-2495	353	40	a	a	DET
ejpam-2495	353	41	countable	countable	ADJ
ejpam-2495	353	42	subcover	subcover	NOUN
ejpam-2495	353	43	of	of	ADP
ejpam-2495	353	44	{	{	PUNCT
ejpam-2495	353	45	ai	ai	PROPN
ejpam-2495	353	46	:	:	PUNCT
ejpam-2495	353	47	i	i	PRON
ejpam-2495	353	48	∈	∈	VERB
ejpam-2495	354	1	i	i	X
ejpam-2495	354	2	}	}	PUNCT
ejpam-2495	354	3	for	for	ADP
ejpam-2495	354	4	f(b	f(b	PROPN
ejpam-2495	354	5	)	)	PUNCT
ejpam-2495	354	6	.	.	PUNCT
ejpam-2495	355	1	so	so	ADV
ejpam-2495	355	2	f(b	f(b	PROPN
ejpam-2495	355	3	)	)	PUNCT
ejpam-2495	355	4	is	be	AUX
ejpam-2495	355	5	btµ	btµ	PROPN
ejpam-2495	355	6	-lindelof	-lindelof	PROPN
ejpam-2495	355	7	relative	relative	ADJ
ejpam-2495	355	8	to	to	ADP
ejpam-2495	355	9	y.	y.	PROPN
ejpam-2495	355	10	6	6	NUM
ejpam-2495	355	11	.	.	PUNCT
ejpam-2495	356	1	supra	supra	PROPN
ejpam-2495	356	2	bt	bt	NOUN
ejpam-2495	357	1	-	-	NOUN
ejpam-2495	358	1	connectedness	connectedness	NOUN
ejpam-2495	358	2	in	in	ADP
ejpam-2495	358	3	supra	supra	PROPN
ejpam-2495	358	4	topological	topological	ADJ
ejpam-2495	358	5	space	space	NOUN
ejpam-2495	358	6	definition	definition	NOUN
ejpam-2495	358	7	17	17	NUM
ejpam-2495	358	8	.	.	PUNCT
ejpam-2495	359	1	a	a	DET
ejpam-2495	359	2	supra	supra	PROPN
ejpam-2495	359	3	topological	topological	ADJ
ejpam-2495	359	4	space	space	NOUN
ejpam-2495	359	5	(	(	PUNCT
ejpam-2495	359	6	x,µ	x,µ	NOUN
ejpam-2495	359	7	)	)	PUNCT
ejpam-2495	359	8	is	be	AUX
ejpam-2495	359	9	said	say	VERB
ejpam-2495	359	10	to	to	PART
ejpam-2495	359	11	be	be	AUX
ejpam-2495	359	12	btµ	btµ	NOUN
ejpam-2495	359	13	connected	connect	VERB
ejpam-2495	359	14	if	if	SCONJ
ejpam-2495	359	15	x	x	PRON
ejpam-2495	359	16	can	can	AUX
ejpam-2495	359	17	not	not	PART
ejpam-2495	359	18	be	be	AUX
ejpam-2495	359	19	written	write	VERB
ejpam-2495	359	20	as	as	ADP
ejpam-2495	359	21	a	a	DET
ejpam-2495	359	22	disjoint	disjoint	NOUN
ejpam-2495	359	23	union	union	NOUN
ejpam-2495	359	24	of	of	ADP
ejpam-2495	359	25	two	two	NUM
ejpam-2495	359	26	non	non	ADJ
ejpam-2495	359	27	empty	empty	ADJ
ejpam-2495	359	28	btµ	btµ	NOUN
ejpam-2495	359	29	-open	-open	NOUN
ejpam-2495	359	30	sets	set	NOUN
ejpam-2495	359	31	.	.	PUNCT
ejpam-2495	360	1	a	a	DET
ejpam-2495	360	2	subsets	subset	NOUN
ejpam-2495	360	3	of	of	ADP
ejpam-2495	360	4	(	(	PUNCT
ejpam-2495	360	5	x,µ	x,µ	NOUN
ejpam-2495	360	6	)	)	PUNCT
ejpam-2495	360	7	is	be	AUX
ejpam-2495	360	8	btµ	btµ	NOUN
ejpam-2495	360	9	-connected	-connected	ADJ
ejpam-2495	360	10	if	if	SCONJ
ejpam-2495	360	11	it	it	PRON
ejpam-2495	360	12	is	be	AUX
ejpam-2495	360	13	btµ	btµ	NOUN
ejpam-2495	360	14	-connected	-connected	ADJ
ejpam-2495	360	15	as	as	ADP
ejpam-2495	360	16	a	a	DET
ejpam-2495	360	17	subspace	subspace	NOUN
ejpam-2495	360	18	.	.	PUNCT
ejpam-2495	361	1	theorem	theorem	NOUN
ejpam-2495	361	2	26	26	NUM
ejpam-2495	361	3	.	.	PUNCT
ejpam-2495	362	1	every	every	DET
ejpam-2495	362	2	btµ	btµ	NOUN
ejpam-2495	362	3	-connected	-connected	ADJ
ejpam-2495	362	4	space	space	NOUN
ejpam-2495	362	5	is	be	AUX
ejpam-2495	362	6	supra	supra	NOUN
ejpam-2495	362	7	connected	connect	VERB
ejpam-2495	362	8	.	.	PUNCT
ejpam-2495	363	1	proof	proof	NOUN
ejpam-2495	363	2	.	.	PUNCT
ejpam-2495	364	1	let	let	VERB
ejpam-2495	364	2	a	a	PRON
ejpam-2495	364	3	and	and	CCONJ
ejpam-2495	364	4	b	b	NOUN
ejpam-2495	364	5	are	be	AUX
ejpam-2495	364	6	supra	supra	ADJ
ejpam-2495	364	7	open	open	ADJ
ejpam-2495	364	8	sets	set	NOUN
ejpam-2495	364	9	in	in	ADP
ejpam-2495	364	10	x.	x.	NOUN
ejpam-2495	364	11	since	since	SCONJ
ejpam-2495	364	12	every	every	DET
ejpam-2495	364	13	supra	supra	PROPN
ejpam-2495	364	14	open	open	ADJ
ejpam-2495	364	15	sets	set	NOUN
ejpam-2495	364	16	is	be	AUX
ejpam-2495	364	17	btµ	btµ	NOUN
ejpam-2495	364	18	-open	-open	NOUN
ejpam-2495	364	19	set	set	NOUN
ejpam-2495	364	20	.	.	PUNCT
ejpam-2495	365	1	therefore	therefore	ADV
ejpam-2495	365	2	a	a	PRON
ejpam-2495	365	3	and	and	CCONJ
ejpam-2495	365	4	b	b	NOUN
ejpam-2495	365	5	are	be	AUX
ejpam-2495	365	6	btµ	btµ	NOUN
ejpam-2495	365	7	-open	-open	ADJ
ejpam-2495	365	8	and	and	CCONJ
ejpam-2495	365	9	x	x	NOUN
ejpam-2495	365	10	is	be	AUX
ejpam-2495	365	11	btµ	btµ	NOUN
ejpam-2495	365	12	connected	connected	ADJ
ejpam-2495	365	13	space	space	NOUN
ejpam-2495	365	14	.	.	PUNCT
ejpam-2495	366	1	therefore	therefore	ADV
ejpam-2495	366	2	x	x	X
ejpam-2495	366	3	6=	6=	ADP
ejpam-2495	366	4	a	a	DET
ejpam-2495	366	5	∪b	∪b	NOUN
ejpam-2495	366	6	.	.	PUNCT
ejpam-2495	367	1	therefore	therefore	ADV
ejpam-2495	367	2	x	x	X
ejpam-2495	367	3	is	be	AUX
ejpam-2495	367	4	supra	supra	PROPN
ejpam-2495	367	5	connected	connect	VERB
ejpam-2495	367	6	.	.	PUNCT
ejpam-2495	368	1	k.krishna	k.krishna	NOUN
ejpam-2495	368	2	,	,	PUNCT
ejpam-2495	368	3	m.vignesh	m.vignesh	NOUN
ejpam-2495	368	4	/	/	SYM
ejpam-2495	368	5	eur	eur	PROPN
ejpam-2495	368	6	.	.	PUNCT
ejpam-2495	369	1	j.	j.	PROPN
ejpam-2495	369	2	pure	pure	PROPN
ejpam-2495	369	3	appl	appl	PROPN
ejpam-2495	369	4	.	.	PROPN
ejpam-2495	369	5	math	math	PROPN
ejpam-2495	369	6	,	,	PUNCT
ejpam-2495	369	7	10	10	NUM
ejpam-2495	369	8	(	(	PUNCT
ejpam-2495	369	9	2	2	NUM
ejpam-2495	369	10	)	)	PUNCT
ejpam-2495	369	11	(	(	PUNCT
ejpam-2495	369	12	2017	2017	NUM
ejpam-2495	369	13	)	)	PUNCT
ejpam-2495	369	14	,	,	PUNCT
ejpam-2495	369	15	323	323	NUM
ejpam-2495	369	16	-	-	SYM
ejpam-2495	369	17	334	334	NUM
ejpam-2495	369	18	332	332	NUM
ejpam-2495	369	19	example	example	NOUN
ejpam-2495	369	20	1	1	NUM
ejpam-2495	369	21	.	.	PUNCT
ejpam-2495	370	1	let	let	VERB
ejpam-2495	370	2	x={a	x={a	PROPN
ejpam-2495	370	3	,	,	PUNCT
ejpam-2495	370	4	b	b	PROPN
ejpam-2495	370	5	,	,	PUNCT
ejpam-2495	370	6	c	c	NOUN
ejpam-2495	370	7	}	}	PUNCT
ejpam-2495	370	8	and	and	CCONJ
ejpam-2495	370	9	τ	τ	PROPN
ejpam-2495	370	10	=	=	SYM
ejpam-2495	370	11	{	{	PUNCT
ejpam-2495	370	12	x	x	PROPN
ejpam-2495	370	13	,	,	PUNCT
ejpam-2495	370	14	φ	φ	PROPN
ejpam-2495	370	15	,	,	PUNCT
ejpam-2495	370	16	{	{	PUNCT
ejpam-2495	370	17	a	a	X
ejpam-2495	370	18	}	}	PUNCT
ejpam-2495	370	19	}	}	PUNCT
ejpam-2495	370	20	.	.	PUNCT
ejpam-2495	371	1	then	then	ADV
ejpam-2495	371	2	it	it	PRON
ejpam-2495	371	3	is	be	AUX
ejpam-2495	371	4	btµ	btµ	PROPN
ejpam-2495	371	5	-connected	-connected	ADJ
ejpam-2495	371	6	.	.	PUNCT
ejpam-2495	372	1	remark	remark	PROPN
ejpam-2495	372	2	1	1	NUM
ejpam-2495	372	3	.	.	PUNCT
ejpam-2495	373	1	the	the	DET
ejpam-2495	373	2	converse	converse	NOUN
ejpam-2495	373	3	of	of	ADP
ejpam-2495	373	4	the	the	DET
ejpam-2495	373	5	above	above	ADJ
ejpam-2495	373	6	theorem	theorem	NOUN
ejpam-2495	373	7	need	need	AUX
ejpam-2495	373	8	not	not	PART
ejpam-2495	373	9	be	be	AUX
ejpam-2495	373	10	true	true	ADJ
ejpam-2495	373	11	in	in	ADP
ejpam-2495	373	12	general	general	ADJ
ejpam-2495	373	13	,	,	PUNCT
ejpam-2495	373	14	which	which	PRON
ejpam-2495	373	15	follows	follow	VERB
ejpam-2495	373	16	from	from	ADP
ejpam-2495	373	17	the	the	DET
ejpam-2495	373	18	following	follow	VERB
ejpam-2495	373	19	example	example	NOUN
ejpam-2495	373	20	.	.	PUNCT
ejpam-2495	374	1	example	example	NOUN
ejpam-2495	375	1	2	2	NUM
ejpam-2495	375	2	.	.	PUNCT
ejpam-2495	375	3	let	let	VERB
ejpam-2495	375	4	x={a	x={a	PROPN
ejpam-2495	375	5	,	,	PUNCT
ejpam-2495	375	6	b	b	PROPN
ejpam-2495	375	7	,	,	PUNCT
ejpam-2495	375	8	c	c	NOUN
ejpam-2495	375	9	}	}	PUNCT
ejpam-2495	375	10	and	and	CCONJ
ejpam-2495	375	11	τ	τ	PROPN
ejpam-2495	375	12	=	=	SYM
ejpam-2495	375	13	{	{	PUNCT
ejpam-2495	375	14	x	x	PROPN
ejpam-2495	375	15	,	,	PUNCT
ejpam-2495	375	16	φ	φ	PROPN
ejpam-2495	375	17	,	,	PUNCT
ejpam-2495	375	18	{	{	PUNCT
ejpam-2495	375	19	a	a	NOUN
ejpam-2495	375	20	}	}	PUNCT
ejpam-2495	375	21	,	,	PUNCT
ejpam-2495	375	22	{	{	PUNCT
ejpam-2495	375	23	b	b	NOUN
ejpam-2495	375	24	}	}	PUNCT
ejpam-2495	375	25	,	,	PUNCT
ejpam-2495	375	26	{	{	PUNCT
ejpam-2495	375	27	a	a	PRON
ejpam-2495	375	28	,	,	PUNCT
ejpam-2495	375	29	b}}.clearly	b}}.clearly	ADV
ejpam-2495	375	30	(	(	PUNCT
ejpam-2495	375	31	x	x	X
ejpam-2495	375	32	,	,	PUNCT
ejpam-2495	375	33	τ	τ	X
ejpam-2495	375	34	)	)	PUNCT
ejpam-2495	375	35	is	be	AUX
ejpam-2495	375	36	supra	supra	ADJ
ejpam-2495	375	37	connected	connect	VERB
ejpam-2495	375	38	.	.	PUNCT
ejpam-2495	376	1	the	the	DET
ejpam-2495	376	2	btµ	btµ	NOUN
ejpam-2495	376	3	open	open	VERB
ejpam-2495	376	4	sets	set	NOUN
ejpam-2495	376	5	of	of	ADP
ejpam-2495	376	6	x	x	SYM
ejpam-2495	376	7	are	be	AUX
ejpam-2495	376	8	{	{	PUNCT
ejpam-2495	376	9	x	x	NOUN
ejpam-2495	376	10	,	,	PUNCT
ejpam-2495	376	11	φ	φ	NUM
ejpam-2495	376	12	,	,	PUNCT
ejpam-2495	376	13	{	{	PUNCT
ejpam-2495	376	14	b	b	NOUN
ejpam-2495	376	15	,	,	PUNCT
ejpam-2495	376	16	c	c	NOUN
ejpam-2495	376	17	}	}	PUNCT
ejpam-2495	376	18	,	,	PUNCT
ejpam-2495	376	19	{	{	PUNCT
ejpam-2495	376	20	a	a	X
ejpam-2495	376	21	,	,	PUNCT
ejpam-2495	376	22	c	c	NOUN
ejpam-2495	376	23	}	}	PUNCT
ejpam-2495	376	24	,	,	PUNCT
ejpam-2495	376	25	{	{	PUNCT
ejpam-2495	376	26	a	a	DET
ejpam-2495	376	27	,	,	PUNCT
ejpam-2495	376	28	b	b	NOUN
ejpam-2495	376	29	}	}	PUNCT
ejpam-2495	376	30	,	,	PUNCT
ejpam-2495	376	31	{	{	PUNCT
ejpam-2495	376	32	b	b	NOUN
ejpam-2495	376	33	}	}	PUNCT
ejpam-2495	376	34	,	,	PUNCT
ejpam-2495	376	35	{	{	PUNCT
ejpam-2495	376	36	a	a	X
ejpam-2495	376	37	}	}	PUNCT
ejpam-2495	376	38	}	}	PUNCT
ejpam-2495	376	39	.	.	PUNCT
ejpam-2495	377	1	therefore	therefore	ADV
ejpam-2495	377	2	(	(	PUNCT
ejpam-2495	377	3	x	x	X
ejpam-2495	377	4	,	,	PUNCT
ejpam-2495	377	5	τ	τ	X
ejpam-2495	377	6	)	)	PUNCT
ejpam-2495	377	7	is	be	AUX
ejpam-2495	377	8	not	not	PART
ejpam-2495	377	9	a	a	DET
ejpam-2495	377	10	btµ	btµ	NOUN
ejpam-2495	377	11	-connected	-connected	ADJ
ejpam-2495	377	12	space	space	NOUN
ejpam-2495	377	13	,	,	PUNCT
ejpam-2495	377	14	since	since	SCONJ
ejpam-2495	377	15	x	x	PROPN
ejpam-2495	377	16	=	=	PRON
ejpam-2495	377	17	{	{	PUNCT
ejpam-2495	377	18	b	b	NOUN
ejpam-2495	377	19	,	,	PUNCT
ejpam-2495	377	20	c	c	NOUN
ejpam-2495	377	21	}	}	PUNCT
ejpam-2495	377	22	∪	∪	X
ejpam-2495	377	23	{	{	PUNCT
ejpam-2495	377	24	a	a	NOUN
ejpam-2495	377	25	}	}	PUNCT
ejpam-2495	377	26	where	where	SCONJ
ejpam-2495	377	27	{	{	PUNCT
ejpam-2495	377	28	b	b	NOUN
ejpam-2495	377	29	,	,	PUNCT
ejpam-2495	377	30	c	c	NOUN
ejpam-2495	377	31	}	}	PUNCT
ejpam-2495	377	32	and	and	CCONJ
ejpam-2495	377	33	{	{	PUNCT
ejpam-2495	377	34	a	a	PRON
ejpam-2495	377	35	}	}	PUNCT
ejpam-2495	377	36	are	be	AUX
ejpam-2495	377	37	non	non	X
ejpam-2495	377	38	empty	empty	ADJ
ejpam-2495	377	39	btµ	btµ	NOUN
ejpam-2495	377	40	-open	-open	NOUN
ejpam-2495	377	41	sets	set	NOUN
ejpam-2495	377	42	.	.	PUNCT
ejpam-2495	378	1	theorem	theorem	VERB
ejpam-2495	378	2	27	27	NUM
ejpam-2495	378	3	.	.	PUNCT
ejpam-2495	379	1	for	for	ADP
ejpam-2495	379	2	a	a	DET
ejpam-2495	379	3	supra	supra	ADJ
ejpam-2495	379	4	topological	topological	ADJ
ejpam-2495	379	5	space	space	NOUN
ejpam-2495	379	6	(	(	PUNCT
ejpam-2495	379	7	x	x	X
ejpam-2495	379	8	,	,	PUNCT
ejpam-2495	379	9	τ	τ	X
ejpam-2495	379	10	)	)	PUNCT
ejpam-2495	379	11	the	the	DET
ejpam-2495	379	12	following	follow	VERB
ejpam-2495	379	13	are	be	AUX
ejpam-2495	379	14	equivalent	equivalent	ADJ
ejpam-2495	379	15	(	(	PUNCT
ejpam-2495	379	16	i	i	NOUN
ejpam-2495	379	17	)	)	PUNCT
ejpam-2495	379	18	(	(	PUNCT
ejpam-2495	379	19	x	x	X
ejpam-2495	379	20	,	,	PUNCT
ejpam-2495	379	21	τ	τ	X
ejpam-2495	379	22	)	)	PUNCT
ejpam-2495	379	23	is	be	AUX
ejpam-2495	379	24	btµ	btµ	NOUN
ejpam-2495	379	25	-connected	-connected	ADJ
ejpam-2495	379	26	.	.	PUNCT
ejpam-2495	380	1	(	(	PUNCT
ejpam-2495	380	2	ii	ii	NOUN
ejpam-2495	380	3	)	)	PUNCT
ejpam-2495	380	4	the	the	DET
ejpam-2495	380	5	only	only	ADJ
ejpam-2495	380	6	subset	subset	NOUN
ejpam-2495	380	7	of	of	ADP
ejpam-2495	380	8	(	(	PUNCT
ejpam-2495	380	9	x	x	X
ejpam-2495	380	10	,	,	PUNCT
ejpam-2495	380	11	τ	τ	X
ejpam-2495	380	12	)	)	PUNCT
ejpam-2495	380	13	which	which	PRON
ejpam-2495	380	14	are	be	AUX
ejpam-2495	380	15	both	both	PRON
ejpam-2495	380	16	btµ	btµ	NOUN
ejpam-2495	380	17	open	open	ADJ
ejpam-2495	380	18	and	and	CCONJ
ejpam-2495	380	19	btµ	btµ	NOUN
ejpam-2495	380	20	-closed	-close	VERB
ejpam-2495	380	21	are	be	AUX
ejpam-2495	380	22	the	the	DET
ejpam-2495	380	23	empty	empty	ADJ
ejpam-2495	380	24	set	set	NOUN
ejpam-2495	380	25	x	x	X
ejpam-2495	380	26	and	and	CCONJ
ejpam-2495	380	27	φ	φ	NUM
ejpam-2495	380	28	.	.	PUNCT
ejpam-2495	381	1	(	(	PUNCT
ejpam-2495	381	2	iii	iii	X
ejpam-2495	381	3	)	)	PUNCT
ejpam-2495	381	4	each	each	DET
ejpam-2495	381	5	btµ	btµ	NOUN
ejpam-2495	381	6	-continuous	-continuous	ADJ
ejpam-2495	381	7	map	map	NOUN
ejpam-2495	381	8	of	of	ADP
ejpam-2495	381	9	(	(	PUNCT
ejpam-2495	381	10	x	x	X
ejpam-2495	381	11	,	,	PUNCT
ejpam-2495	381	12	τ	τ	X
ejpam-2495	381	13	)	)	PUNCT
ejpam-2495	381	14	into	into	ADP
ejpam-2495	381	15	a	a	DET
ejpam-2495	381	16	discrete	discrete	ADJ
ejpam-2495	381	17	space	space	NOUN
ejpam-2495	381	18	(	(	PUNCT
ejpam-2495	381	19	y	y	PROPN
ejpam-2495	381	20	,	,	PUNCT
ejpam-2495	381	21	σ	σ	PROPN
ejpam-2495	381	22	)	)	PUNCT
ejpam-2495	381	23	with	with	ADP
ejpam-2495	381	24	atleast	atleast	ADJ
ejpam-2495	381	25	two	two	NUM
ejpam-2495	381	26	points	point	NOUN
ejpam-2495	381	27	is	be	AUX
ejpam-2495	381	28	a	a	DET
ejpam-2495	381	29	constant	constant	ADJ
ejpam-2495	381	30	map	map	NOUN
ejpam-2495	381	31	.	.	PUNCT
ejpam-2495	382	1	proof	proof	NOUN
ejpam-2495	382	2	.	.	PUNCT
ejpam-2495	383	1	(	(	PUNCT
ejpam-2495	383	2	1)⇒(2	1)⇒(2	X
ejpam-2495	383	3	)	)	PUNCT
ejpam-2495	383	4	let	let	VERB
ejpam-2495	383	5	g	g	NOUN
ejpam-2495	383	6	be	be	AUX
ejpam-2495	383	7	a	a	DET
ejpam-2495	383	8	btµ-open	btµ-open	ADJ
ejpam-2495	383	9	and	and	CCONJ
ejpam-2495	383	10	btµclosed	btµclose	VERB
ejpam-2495	383	11	subset	subset	NOUN
ejpam-2495	383	12	of	of	ADP
ejpam-2495	383	13	(	(	PUNCT
ejpam-2495	383	14	x	x	X
ejpam-2495	383	15	,	,	PUNCT
ejpam-2495	383	16	τ).then	τ).then	ADJ
ejpam-2495	383	17	x	x	NOUN
ejpam-2495	383	18	-	-	PUNCT
ejpam-2495	383	19	g	g	PROPN
ejpam-2495	383	20	is	be	AUX
ejpam-2495	383	21	also	also	ADV
ejpam-2495	383	22	both	both	PRON
ejpam-2495	383	23	btµ-open	btµ-open	ADJ
ejpam-2495	383	24	and	and	CCONJ
ejpam-2495	383	25	btµ	btµ	NOUN
ejpam-2495	383	26	-closed	-close	VERB
ejpam-2495	383	27	.	.	PUNCT
ejpam-2495	384	1	then	then	ADV
ejpam-2495	384	2	x	x	X
ejpam-2495	384	3	=	=	PUNCT
ejpam-2495	384	4	g∪(x	g∪(x	NOUN
ejpam-2495	384	5	-	-	PUNCT
ejpam-2495	384	6	g	g	NOUN
ejpam-2495	384	7	)	)	PUNCT
ejpam-2495	384	8	a	a	DET
ejpam-2495	384	9	disjoint	disjoint	NOUN
ejpam-2495	384	10	union	union	NOUN
ejpam-2495	384	11	of	of	ADP
ejpam-2495	384	12	two	two	NUM
ejpam-2495	384	13	non	non	X
ejpam-2495	384	14	empty	empty	ADJ
ejpam-2495	384	15	btµ	btµ	NOUN
ejpam-2495	384	16	-open	-open	PROPN
ejpam-2495	384	17	sets	set	NOUN
ejpam-2495	384	18	which	which	PRON
ejpam-2495	384	19	contradicts	contradict	VERB
ejpam-2495	384	20	the	the	DET
ejpam-2495	384	21	fact	fact	NOUN
ejpam-2495	384	22	that	that	SCONJ
ejpam-2495	384	23	(	(	PUNCT
ejpam-2495	384	24	x	x	X
ejpam-2495	384	25	,	,	PUNCT
ejpam-2495	384	26	τ	τ	X
ejpam-2495	384	27	)	)	PUNCT
ejpam-2495	384	28	is	be	AUX
ejpam-2495	384	29	btµ-connected	btµ-connected	ADJ
ejpam-2495	384	30	.	.	PUNCT
ejpam-2495	385	1	hence	hence	ADV
ejpam-2495	385	2	g	g	PROPN
ejpam-2495	385	3	=	=	SYM
ejpam-2495	385	4	φ	φ	PROPN
ejpam-2495	385	5	(	(	PUNCT
ejpam-2495	385	6	or	or	CCONJ
ejpam-2495	385	7	)	)	PUNCT
ejpam-2495	385	8	x.	x.	NOUN
ejpam-2495	386	1	(	(	PUNCT
ejpam-2495	386	2	2)⇒(1)suppose	2)⇒(1)suppose	NUM
ejpam-2495	386	3	that	that	PRON
ejpam-2495	386	4	x	x	X
ejpam-2495	387	1	=	=	PUNCT
ejpam-2495	387	2	a∪	a∪	PROPN
ejpam-2495	387	3	b	b	NOUN
ejpam-2495	387	4	where	where	SCONJ
ejpam-2495	387	5	a	a	PRON
ejpam-2495	387	6	and	and	CCONJ
ejpam-2495	387	7	b	b	NOUN
ejpam-2495	387	8	are	be	AUX
ejpam-2495	387	9	disjoint	disjoint	VERB
ejpam-2495	387	10	non	non	ADJ
ejpam-2495	387	11	empty	empty	ADJ
ejpam-2495	387	12	btµ-open	btµ-open	ADJ
ejpam-2495	387	13	subsets	subset	NOUN
ejpam-2495	387	14	of	of	ADP
ejpam-2495	387	15	(	(	PUNCT
ejpam-2495	387	16	x	x	X
ejpam-2495	387	17	,	,	PUNCT
ejpam-2495	387	18	τ	τ	PROPN
ejpam-2495	387	19	)	)	PUNCT
ejpam-2495	387	20	.	.	PUNCT
ejpam-2495	388	1	since	since	SCONJ
ejpam-2495	388	2	a	a	DET
ejpam-2495	388	3	=	=	SYM
ejpam-2495	388	4	x	x	PROPN
ejpam-2495	388	5	-	-	PUNCT
ejpam-2495	388	6	b	b	NOUN
ejpam-2495	388	7	,	,	PUNCT
ejpam-2495	388	8	then	then	ADV
ejpam-2495	388	9	a	a	PRON
ejpam-2495	388	10	is	be	AUX
ejpam-2495	388	11	both	both	DET
ejpam-2495	388	12	btµ	btµ	NOUN
ejpam-2495	388	13	-open	-open	ADJ
ejpam-2495	388	14	and	and	CCONJ
ejpam-2495	388	15	btµclosed	btµclose	VERB
ejpam-2495	388	16	.	.	PUNCT
ejpam-2495	389	1	by	by	ADP
ejpam-2495	389	2	assumption	assumption	NOUN
ejpam-2495	389	3	a	a	DET
ejpam-2495	389	4	=	=	NOUN
ejpam-2495	389	5	φ	φ	NOUN
ejpam-2495	389	6	or	or	CCONJ
ejpam-2495	389	7	x	x	NOUN
ejpam-2495	389	8	,	,	PUNCT
ejpam-2495	389	9	which	which	PRON
ejpam-2495	389	10	is	be	AUX
ejpam-2495	389	11	a	a	DET
ejpam-2495	389	12	contradiction	contradiction	NOUN
ejpam-2495	389	13	.	.	PUNCT
ejpam-2495	390	1	hence	hence	ADV
ejpam-2495	390	2	(	(	PUNCT
ejpam-2495	390	3	x	x	X
ejpam-2495	390	4	,	,	PUNCT
ejpam-2495	390	5	τ	τ	X
ejpam-2495	390	6	)	)	PUNCT
ejpam-2495	390	7	is	be	AUX
ejpam-2495	390	8	btµ-connected	btµ-connected	ADJ
ejpam-2495	390	9	.	.	PUNCT
ejpam-2495	391	1	(	(	PUNCT
ejpam-2495	391	2	2)⇒(3	2)⇒(3	X
ejpam-2495	391	3	)	)	PUNCT
ejpam-2495	391	4	let	let	VERB
ejpam-2495	391	5	f	f	NOUN
ejpam-2495	391	6	:	:	PUNCT
ejpam-2495	391	7	(	(	PUNCT
ejpam-2495	391	8	x	x	X
ejpam-2495	391	9	,	,	PUNCT
ejpam-2495	391	10	τ)→	τ)→	PROPN
ejpam-2495	391	11	(	(	PUNCT
ejpam-2495	391	12	y	y	PROPN
ejpam-2495	391	13	,	,	PUNCT
ejpam-2495	391	14	σ	σ	PROPN
ejpam-2495	391	15	)	)	PUNCT
ejpam-2495	391	16	be	be	VERB
ejpam-2495	391	17	a	a	DET
ejpam-2495	391	18	btµ-continuous	btµ-continuous	ADJ
ejpam-2495	391	19	map	map	NOUN
ejpam-2495	391	20	,	,	PUNCT
ejpam-2495	391	21	where	where	SCONJ
ejpam-2495	391	22	(	(	PUNCT
ejpam-2495	391	23	y	y	PROPN
ejpam-2495	391	24	,	,	PUNCT
ejpam-2495	391	25	σ	σ	PROPN
ejpam-2495	391	26	)	)	PUNCT
ejpam-2495	391	27	is	be	AUX
ejpam-2495	391	28	discrete	discrete	ADJ
ejpam-2495	391	29	space	space	NOUN
ejpam-2495	391	30	with	with	ADP
ejpam-2495	391	31	atleast	atleast	ADJ
ejpam-2495	391	32	two	two	NUM
ejpam-2495	391	33	points	point	NOUN
ejpam-2495	391	34	.	.	PUNCT
ejpam-2495	392	1	then	then	ADV
ejpam-2495	392	2	f−1(y	f−1(y	PROPN
ejpam-2495	392	3	)	)	PUNCT
ejpam-2495	392	4	is	be	AUX
ejpam-2495	392	5	btµ	btµ	NOUN
ejpam-2495	392	6	-closed	-close	VERB
ejpam-2495	392	7	and	and	CCONJ
ejpam-2495	392	8	btµ	btµ	NOUN
ejpam-2495	392	9	-open	-open	PROPN
ejpam-2495	392	10	for	for	ADP
ejpam-2495	392	11	each	each	DET
ejpam-2495	392	12	y∈	y∈	PROPN
ejpam-2495	392	13	y.	y.	NOUN
ejpam-2495	392	14	that	that	PRON
ejpam-2495	392	15	is	be	AUX
ejpam-2495	392	16	(	(	PUNCT
ejpam-2495	392	17	x	x	X
ejpam-2495	392	18	,	,	PUNCT
ejpam-2495	392	19	τ	τ	X
ejpam-2495	392	20	)	)	PUNCT
ejpam-2495	392	21	is	be	AUX
ejpam-2495	392	22	covered	cover	VERB
ejpam-2495	392	23	by	by	ADP
ejpam-2495	392	24	btµ-closed	btµ-closed	ADJ
ejpam-2495	392	25	and	and	CCONJ
ejpam-2495	392	26	btµ-open	btµ-open	ADJ
ejpam-2495	392	27	covering	covering	NOUN
ejpam-2495	392	28	{	{	PUNCT
ejpam-2495	392	29	f−1	f−1	PROPN
ejpam-2495	392	30	{	{	PUNCT
ejpam-2495	392	31	y	y	NOUN
ejpam-2495	392	32	}	}	PUNCT
ejpam-2495	392	33	:	:	PUNCT
ejpam-2495	392	34	y	y	PROPN
ejpam-2495	392	35	∈	∈	PROPN
ejpam-2495	392	36	y	y	PROPN
ejpam-2495	392	37	}	}	PUNCT
ejpam-2495	392	38	.by	.by	PROPN
ejpam-2495	393	1	assumption	assumption	NOUN
ejpam-2495	393	2	,	,	PUNCT
ejpam-2495	393	3	{	{	PUNCT
ejpam-2495	393	4	f−1	f−1	PROPN
ejpam-2495	393	5	{	{	PUNCT
ejpam-2495	393	6	y	y	NOUN
ejpam-2495	393	7	}	}	PUNCT
ejpam-2495	393	8	}	}	PUNCT
ejpam-2495	393	9	=	=	SYM
ejpam-2495	393	10	φ	φ	PROPN
ejpam-2495	393	11	or	or	CCONJ
ejpam-2495	393	12	x	x	PROPN
ejpam-2495	393	13	for	for	ADP
ejpam-2495	393	14	each	each	DET
ejpam-2495	393	15	y∈	y∈	NOUN
ejpam-2495	393	16	y.	y.	NOUN
ejpam-2495	393	17	if	if	SCONJ
ejpam-2495	393	18	f−1	f−1	PROPN
ejpam-2495	393	19	{	{	PUNCT
ejpam-2495	393	20	y	y	NOUN
ejpam-2495	393	21	}	}	PUNCT
ejpam-2495	393	22	=	=	SYM
ejpam-2495	393	23	φ	φ	PROPN
ejpam-2495	393	24	for	for	ADP
ejpam-2495	393	25	each	each	DET
ejpam-2495	393	26	y	y	PROPN
ejpam-2495	393	27	∈	∈	PROPN
ejpam-2495	393	28	y	y	PROPN
ejpam-2495	393	29	,	,	PUNCT
ejpam-2495	393	30	then	then	ADV
ejpam-2495	393	31	f	f	PROPN
ejpam-2495	393	32	fails	fail	VERB
ejpam-2495	393	33	to	to	PART
ejpam-2495	393	34	be	be	AUX
ejpam-2495	393	35	a	a	DET
ejpam-2495	393	36	map	map	NOUN
ejpam-2495	393	37	.	.	PUNCT
ejpam-2495	394	1	therefore	therefore	ADV
ejpam-2495	394	2	their	their	PRON
ejpam-2495	394	3	exist	exist	NOUN
ejpam-2495	394	4	atleast	atleast	ADJ
ejpam-2495	394	5	one	one	NUM
ejpam-2495	394	6	point	point	NOUN
ejpam-2495	394	7	say	say	VERB
ejpam-2495	394	8	f−1	f−1	PROPN
ejpam-2495	394	9	{	{	PUNCT
ejpam-2495	394	10	y1	y1	PROPN
ejpam-2495	394	11	}	}	PUNCT
ejpam-2495	394	12	6=	6=	NUM
ejpam-2495	394	13	φ	φ	PROPN
ejpam-2495	394	14	,	,	PUNCT
ejpam-2495	394	15	y1	y1	PROPN
ejpam-2495	394	16	∈	∈	PROPN
ejpam-2495	394	17	y	y	PROPN
ejpam-2495	394	18	such	such	ADJ
ejpam-2495	394	19	that	that	PRON
ejpam-2495	394	20	f−1({y1	f−1({y1	PROPN
ejpam-2495	394	21	}	}	PUNCT
ejpam-2495	394	22	)	)	PUNCT
ejpam-2495	395	1	=	=	PUNCT
ejpam-2495	396	1	x.	x.	NOUN
ejpam-2495	396	2	this	this	PRON
ejpam-2495	396	3	shows	show	VERB
ejpam-2495	396	4	that	that	SCONJ
ejpam-2495	396	5	f	f	PROPN
ejpam-2495	396	6	is	be	AUX
ejpam-2495	396	7	a	a	DET
ejpam-2495	396	8	constant	constant	ADJ
ejpam-2495	396	9	map	map	NOUN
ejpam-2495	396	10	.	.	PUNCT
ejpam-2495	397	1	(	(	PUNCT
ejpam-2495	397	2	3)⇒(2	3)⇒(2	NOUN
ejpam-2495	397	3	)	)	PUNCT
ejpam-2495	397	4	let	let	VERB
ejpam-2495	397	5	g	g	NOUN
ejpam-2495	397	6	be	be	AUX
ejpam-2495	397	7	both	both	PRON
ejpam-2495	397	8	btµ	btµ	NOUN
ejpam-2495	397	9	-open	-open	ADJ
ejpam-2495	397	10	and	and	CCONJ
ejpam-2495	397	11	btµ	btµ	NOUN
ejpam-2495	397	12	-closed	-close	VERB
ejpam-2495	397	13	in	in	ADP
ejpam-2495	397	14	(	(	PUNCT
ejpam-2495	397	15	x	x	NOUN
ejpam-2495	397	16	,	,	PUNCT
ejpam-2495	397	17	τ	τ	PROPN
ejpam-2495	397	18	)	)	PUNCT
ejpam-2495	397	19	.	.	PUNCT
ejpam-2495	398	1	suppose	suppose	VERB
ejpam-2495	398	2	g	g	PROPN
ejpam-2495	398	3	6=	6=	PROPN
ejpam-2495	398	4	φ	φ	PROPN
ejpam-2495	398	5	.	.	PUNCT
ejpam-2495	399	1	let	let	VERB
ejpam-2495	399	2	f	f	NOUN
ejpam-2495	399	3	:	:	PUNCT
ejpam-2495	399	4	(	(	PUNCT
ejpam-2495	399	5	x	x	X
ejpam-2495	399	6	,	,	PUNCT
ejpam-2495	399	7	τ)→	τ)→	PROPN
ejpam-2495	399	8	(	(	PUNCT
ejpam-2495	399	9	y	y	PROPN
ejpam-2495	399	10	,	,	PUNCT
ejpam-2495	399	11	σ	σ	PROPN
ejpam-2495	399	12	)	)	PUNCT
ejpam-2495	399	13	be	be	VERB
ejpam-2495	399	14	a	a	DET
ejpam-2495	399	15	btµ	btµ	NOUN
ejpam-2495	399	16	-continuous	-continuous	ADJ
ejpam-2495	399	17	map	map	NOUN
ejpam-2495	399	18	defined	define	VERB
ejpam-2495	399	19	by	by	ADP
ejpam-2495	399	20	f(g	f(g	NOUN
ejpam-2495	399	21	)	)	PUNCT
ejpam-2495	399	22	=	=	PRON
ejpam-2495	400	1	{	{	PUNCT
ejpam-2495	400	2	a	a	NOUN
ejpam-2495	400	3	}	}	PUNCT
ejpam-2495	400	4	and	and	CCONJ
ejpam-2495	400	5	f(x	f(x	PROPN
ejpam-2495	400	6	-	-	PUNCT
ejpam-2495	400	7	g	g	NOUN
ejpam-2495	400	8	)	)	PUNCT
ejpam-2495	400	9	=	=	PUNCT
ejpam-2495	400	10	{	{	PUNCT
ejpam-2495	400	11	b	b	NOUN
ejpam-2495	400	12	}	}	PUNCT
ejpam-2495	400	13	where	where	SCONJ
ejpam-2495	400	14	a	a	DET
ejpam-2495	400	15	6=	6=	SYM
ejpam-2495	400	16	b	b	NOUN
ejpam-2495	400	17	and	and	CCONJ
ejpam-2495	400	18	a	a	PRON
ejpam-2495	400	19	,	,	PUNCT
ejpam-2495	400	20	b∈	b∈	PROPN
ejpam-2495	400	21	y.	y.	PROPN
ejpam-2495	400	22	by	by	ADP
ejpam-2495	400	23	assumption	assumption	NOUN
ejpam-2495	400	24	,	,	PUNCT
ejpam-2495	400	25	f	f	PROPN
ejpam-2495	400	26	is	be	AUX
ejpam-2495	400	27	constant	constant	ADJ
ejpam-2495	400	28	so	so	ADV
ejpam-2495	400	29	g	g	PROPN
ejpam-2495	400	30	=	=	PROPN
ejpam-2495	400	31	x.	x.	NOUN
ejpam-2495	400	32	theorem	theorem	VERB
ejpam-2495	400	33	28	28	NUM
ejpam-2495	400	34	.	.	PUNCT
ejpam-2495	401	1	let	let	VERB
ejpam-2495	401	2	f	f	NOUN
ejpam-2495	401	3	:	:	PUNCT
ejpam-2495	401	4	(	(	PUNCT
ejpam-2495	401	5	x	x	X
ejpam-2495	401	6	,	,	PUNCT
ejpam-2495	401	7	τ)→	τ)→	PROPN
ejpam-2495	401	8	(	(	PUNCT
ejpam-2495	401	9	y	y	PROPN
ejpam-2495	401	10	,	,	PUNCT
ejpam-2495	401	11	σ	σ	PROPN
ejpam-2495	401	12	)	)	PUNCT
ejpam-2495	401	13	be	be	VERB
ejpam-2495	401	14	a	a	DET
ejpam-2495	401	15	btµ	btµ	NOUN
ejpam-2495	401	16	-continuous	-continuous	ADJ
ejpam-2495	401	17	surjection	surjection	NOUN
ejpam-2495	401	18	and	and	CCONJ
ejpam-2495	401	19	(	(	PUNCT
ejpam-2495	401	20	x	x	X
ejpam-2495	401	21	,	,	PUNCT
ejpam-2495	401	22	τ	τ	X
ejpam-2495	401	23	)	)	PUNCT
ejpam-2495	401	24	is	be	AUX
ejpam-2495	401	25	btµ	btµ	NOUN
ejpam-2495	401	26	connected	connect	VERB
ejpam-2495	401	27	,	,	PUNCT
ejpam-2495	401	28	then	then	ADV
ejpam-2495	401	29	(	(	PUNCT
ejpam-2495	401	30	y	y	PROPN
ejpam-2495	401	31	,	,	PUNCT
ejpam-2495	401	32	σ	σ	PROPN
ejpam-2495	401	33	)	)	PUNCT
ejpam-2495	401	34	is	be	AUX
ejpam-2495	401	35	supra	supra	ADJ
ejpam-2495	401	36	connected	connect	VERB
ejpam-2495	401	37	.	.	PUNCT
ejpam-2495	402	1	proof	proof	NOUN
ejpam-2495	402	2	.	.	PUNCT
ejpam-2495	403	1	suppose	suppose	VERB
ejpam-2495	403	2	(	(	PUNCT
ejpam-2495	403	3	y	y	PROPN
ejpam-2495	403	4	,	,	PUNCT
ejpam-2495	403	5	σ	σ	PROPN
ejpam-2495	403	6	)	)	PUNCT
ejpam-2495	403	7	is	be	AUX
ejpam-2495	403	8	not	not	PART
ejpam-2495	403	9	supra	supra	NOUN
ejpam-2495	403	10	connected	connect	VERB
ejpam-2495	403	11	.	.	PUNCT
ejpam-2495	404	1	let	let	VERB
ejpam-2495	404	2	y	y	PROPN
ejpam-2495	404	3	=	=	PUNCT
ejpam-2495	405	1	a∪	a∪	PROPN
ejpam-2495	406	1	b	b	NOUN
ejpam-2495	406	2	,	,	PUNCT
ejpam-2495	406	3	where	where	SCONJ
ejpam-2495	406	4	a	a	PRON
ejpam-2495	406	5	and	and	CCONJ
ejpam-2495	406	6	b	b	NOUN
ejpam-2495	406	7	are	be	AUX
ejpam-2495	406	8	disjoint	disjoint	VERB
ejpam-2495	406	9	non	non	ADJ
ejpam-2495	406	10	empty	empty	ADJ
ejpam-2495	406	11	supra	supra	ADJ
ejpam-2495	406	12	open	open	ADJ
ejpam-2495	406	13	subsets	subset	NOUN
ejpam-2495	406	14	in	in	ADP
ejpam-2495	406	15	(	(	PUNCT
ejpam-2495	406	16	y	y	PROPN
ejpam-2495	406	17	,	,	PUNCT
ejpam-2495	406	18	σ	σ	PROPN
ejpam-2495	406	19	)	)	PUNCT
ejpam-2495	406	20	.	.	PUNCT
ejpam-2495	407	1	since	since	SCONJ
ejpam-2495	407	2	f	f	PROPN
ejpam-2495	407	3	is	be	AUX
ejpam-2495	407	4	btµ	btµ	PROPN
ejpam-2495	407	5	-continuous	-continuous	ADJ
ejpam-2495	407	6	,	,	PUNCT
ejpam-2495	407	7	x	x	SYM
ejpam-2495	407	8	=	=	PUNCT
ejpam-2495	407	9	f−1(a	f−1(a	NOUN
ejpam-2495	407	10	)	)	PUNCT
ejpam-2495	408	1	⋃	⋃	NOUN
ejpam-2495	408	2	f−1(b	f−1(b	PROPN
ejpam-2495	408	3	)	)	PUNCT
ejpam-2495	408	4	,	,	PUNCT
ejpam-2495	408	5	where	where	SCONJ
ejpam-2495	408	6	f−1(a	f−1(a	NOUN
ejpam-2495	408	7	)	)	PUNCT
ejpam-2495	408	8	and	and	CCONJ
ejpam-2495	408	9	f−1(b	f−1(b	PROPN
ejpam-2495	408	10	)	)	PUNCT
ejpam-2495	408	11	are	be	AUX
ejpam-2495	408	12	disjoint	disjoint	X
ejpam-2495	408	13	non	non	ADJ
ejpam-2495	408	14	empty	empty	ADJ
ejpam-2495	408	15	btµ	btµ	NOUN
ejpam-2495	408	16	-open	-open	ADJ
ejpam-2495	408	17	subsets	subset	NOUN
ejpam-2495	408	18	in	in	ADP
ejpam-2495	408	19	(	(	PUNCT
ejpam-2495	408	20	x	x	NOUN
ejpam-2495	408	21	,	,	PUNCT
ejpam-2495	408	22	τ	τ	PROPN
ejpam-2495	408	23	)	)	PUNCT
ejpam-2495	408	24	.	.	PUNCT
ejpam-2495	409	1	this	this	PRON
ejpam-2495	409	2	disproves	disprove	VERB
ejpam-2495	409	3	the	the	DET
ejpam-2495	409	4	fact	fact	NOUN
ejpam-2495	409	5	that	that	SCONJ
ejpam-2495	409	6	(	(	PUNCT
ejpam-2495	409	7	x	x	X
ejpam-2495	409	8	,	,	PUNCT
ejpam-2495	409	9	τ	τ	X
ejpam-2495	409	10	)	)	PUNCT
ejpam-2495	409	11	is	be	AUX
ejpam-2495	409	12	btµ	btµ	NOUN
ejpam-2495	409	13	-connected	-connected	ADJ
ejpam-2495	409	14	.	.	PUNCT
ejpam-2495	410	1	hence	hence	ADV
ejpam-2495	410	2	(	(	PUNCT
ejpam-2495	410	3	y	y	PROPN
ejpam-2495	410	4	,	,	PUNCT
ejpam-2495	410	5	σ	σ	PROPN
ejpam-2495	410	6	)	)	PUNCT
ejpam-2495	410	7	is	be	AUX
ejpam-2495	410	8	supra	supra	PROPN
ejpam-2495	410	9	connected	connect	VERB
ejpam-2495	410	10	.	.	PUNCT
ejpam-2495	411	1	k.krishna	k.krishna	NOUN
ejpam-2495	411	2	,	,	PUNCT
ejpam-2495	411	3	m.vignesh	m.vignesh	NOUN
ejpam-2495	411	4	/	/	SYM
ejpam-2495	411	5	eur	eur	PROPN
ejpam-2495	411	6	.	.	PUNCT
ejpam-2495	412	1	j.	j.	PROPN
ejpam-2495	412	2	pure	pure	PROPN
ejpam-2495	412	3	appl	appl	PROPN
ejpam-2495	412	4	.	.	PROPN
ejpam-2495	412	5	math	math	PROPN
ejpam-2495	412	6	,	,	PUNCT
ejpam-2495	412	7	10	10	NUM
ejpam-2495	412	8	(	(	PUNCT
ejpam-2495	412	9	2	2	NUM
ejpam-2495	412	10	)	)	PUNCT
ejpam-2495	412	11	(	(	PUNCT
ejpam-2495	412	12	2017	2017	NUM
ejpam-2495	412	13	)	)	PUNCT
ejpam-2495	412	14	,	,	PUNCT
ejpam-2495	412	15	323	323	NUM
ejpam-2495	412	16	-	-	SYM
ejpam-2495	412	17	334	334	NUM
ejpam-2495	412	18	333	333	NUM
ejpam-2495	412	19	theorem	theorem	NOUN
ejpam-2495	412	20	29	29	NUM
ejpam-2495	412	21	.	.	PUNCT
ejpam-2495	413	1	if	if	SCONJ
ejpam-2495	413	2	f	f	PROPN
ejpam-2495	413	3	:	:	PUNCT
ejpam-2495	413	4	(	(	PUNCT
ejpam-2495	413	5	x	x	X
ejpam-2495	413	6	,	,	PUNCT
ejpam-2495	413	7	τ)→	τ)→	PROPN
ejpam-2495	413	8	(	(	PUNCT
ejpam-2495	413	9	y	y	PROPN
ejpam-2495	413	10	,	,	PUNCT
ejpam-2495	413	11	σ	σ	PROPN
ejpam-2495	413	12	)	)	PUNCT
ejpam-2495	413	13	is	be	AUX
ejpam-2495	413	14	a	a	DET
ejpam-2495	413	15	btµ-irresolute	btµ-irresolute	ADJ
ejpam-2495	413	16	surjection	surjection	NOUN
ejpam-2495	413	17	and	and	CCONJ
ejpam-2495	413	18	x	x	NOUN
ejpam-2495	413	19	is	be	AUX
ejpam-2495	413	20	btµ-connected	btµ-connected	ADJ
ejpam-2495	413	21	,	,	PUNCT
ejpam-2495	413	22	then	then	ADV
ejpam-2495	413	23	y	y	PROPN
ejpam-2495	413	24	is	be	AUX
ejpam-2495	413	25	btµ-connected	btµ-connected	ADJ
ejpam-2495	413	26	.	.	PUNCT
ejpam-2495	414	1	proof	proof	NOUN
ejpam-2495	414	2	.	.	PUNCT
ejpam-2495	415	1	suppose	suppose	VERB
ejpam-2495	415	2	that	that	SCONJ
ejpam-2495	415	3	y	y	PROPN
ejpam-2495	415	4	is	be	AUX
ejpam-2495	415	5	btµ-connected	btµ-connected	ADJ
ejpam-2495	415	6	.	.	PUNCT
ejpam-2495	416	1	let	let	VERB
ejpam-2495	416	2	y	y	NOUN
ejpam-2495	416	3	=	=	SYM
ejpam-2495	416	4	a∪b	a∪b	PROPN
ejpam-2495	416	5	,	,	PUNCT
ejpam-2495	416	6	where	where	SCONJ
ejpam-2495	416	7	a	a	PRON
ejpam-2495	416	8	and	and	CCONJ
ejpam-2495	416	9	b	b	NOUN
ejpam-2495	416	10	are	be	AUX
ejpam-2495	416	11	non	non	X
ejpam-2495	416	12	empty	empty	ADJ
ejpam-2495	416	13	btµ-open	btµ-open	ADJ
ejpam-2495	416	14	set	set	NOUN
ejpam-2495	416	15	in	in	ADP
ejpam-2495	416	16	y.	y.	NOUN
ejpam-2495	416	17	since	since	SCONJ
ejpam-2495	416	18	f	f	PROPN
ejpam-2495	416	19	is	be	AUX
ejpam-2495	416	20	btµ	btµ	NOUN
ejpam-2495	416	21	-irresolute	-irresolute	ADJ
ejpam-2495	416	22	and	and	CCONJ
ejpam-2495	416	23	onto	onto	ADP
ejpam-2495	416	24	,	,	PUNCT
ejpam-2495	416	25	x	x	PROPN
ejpam-2495	416	26	=	=	SYM
ejpam-2495	416	27	f−1(a)∪f−1(b	f−1(a)∪f−1(b	PROPN
ejpam-2495	416	28	)	)	PUNCT
ejpam-2495	416	29	,	,	PUNCT
ejpam-2495	416	30	where	where	SCONJ
ejpam-2495	416	31	f−1(a	f−1(a	NOUN
ejpam-2495	416	32	)	)	PUNCT
ejpam-2495	416	33	and	and	CCONJ
ejpam-2495	416	34	f−1(b	f−1(b	PROPN
ejpam-2495	416	35	)	)	PUNCT
ejpam-2495	416	36	are	be	AUX
ejpam-2495	416	37	disjoint	disjoint	ADJ
ejpam-2495	416	38	non	non	ADJ
ejpam-2495	416	39	empty	empty	ADJ
ejpam-2495	416	40	btµ-open	btµ-open	ADJ
ejpam-2495	416	41	sets	set	NOUN
ejpam-2495	416	42	in	in	ADP
ejpam-2495	416	43	(	(	PUNCT
ejpam-2495	416	44	x	x	NOUN
ejpam-2495	416	45	,	,	PUNCT
ejpam-2495	416	46	τ	τ	PROPN
ejpam-2495	416	47	)	)	PUNCT
ejpam-2495	416	48	.	.	PUNCT
ejpam-2495	417	1	this	this	PRON
ejpam-2495	417	2	contradicts	contradict	VERB
ejpam-2495	417	3	the	the	DET
ejpam-2495	417	4	fact	fact	NOUN
ejpam-2495	417	5	that	that	SCONJ
ejpam-2495	417	6	(	(	PUNCT
ejpam-2495	417	7	x	x	X
ejpam-2495	417	8	,	,	PUNCT
ejpam-2495	417	9	τ	τ	X
ejpam-2495	417	10	)	)	PUNCT
ejpam-2495	417	11	is	be	AUX
ejpam-2495	417	12	btµconnected	btµconnecte	VERB
ejpam-2495	417	13	.	.	PUNCT
ejpam-2495	418	1	hence	hence	ADV
ejpam-2495	418	2	(	(	PUNCT
ejpam-2495	418	3	y	y	PROPN
ejpam-2495	418	4	,	,	PUNCT
ejpam-2495	418	5	σ	σ	PROPN
ejpam-2495	418	6	)	)	PUNCT
ejpam-2495	418	7	is	be	AUX
ejpam-2495	418	8	btµ	btµ	NOUN
ejpam-2495	418	9	-connected	-connected	ADJ
ejpam-2495	418	10	.	.	PUNCT
ejpam-2495	419	1	theorem	theorem	NOUN
ejpam-2495	419	2	30	30	NUM
ejpam-2495	419	3	.	.	PUNCT
ejpam-2495	420	1	suppose	suppose	VERB
ejpam-2495	420	2	that	that	SCONJ
ejpam-2495	420	3	x	x	PRON
ejpam-2495	420	4	is	be	AUX
ejpam-2495	420	5	a	a	DET
ejpam-2495	420	6	btt	btt	NOUN
ejpam-2495	420	7	µ	µ	PROPN
ejpam-2495	420	8	c	c	NOUN
ejpam-2495	420	9	-space	-space	NOUN
ejpam-2495	420	10	and	and	CCONJ
ejpam-2495	420	11	x	x	VERB
ejpam-2495	420	12	is	be	AUX
ejpam-2495	420	13	supra	supra	ADJ
ejpam-2495	420	14	connected	connect	VERB
ejpam-2495	420	15	then	then	ADV
ejpam-2495	420	16	btµ	btµ	PROPN
ejpam-2495	420	17	connected	connect	VERB
ejpam-2495	420	18	.	.	PUNCT
ejpam-2495	421	1	proof	proof	NOUN
ejpam-2495	421	2	.	.	PUNCT
ejpam-2495	422	1	suppose	suppose	VERB
ejpam-2495	422	2	that	that	SCONJ
ejpam-2495	422	3	x	x	PRON
ejpam-2495	422	4	is	be	AUX
ejpam-2495	422	5	supra	supra	PROPN
ejpam-2495	422	6	connected	connect	VERB
ejpam-2495	422	7	.	.	PUNCT
ejpam-2495	423	1	then	then	ADV
ejpam-2495	423	2	x	x	PRON
ejpam-2495	423	3	can	can	AUX
ejpam-2495	423	4	not	not	PART
ejpam-2495	423	5	be	be	AUX
ejpam-2495	423	6	expressed	express	VERB
ejpam-2495	423	7	as	as	ADP
ejpam-2495	423	8	disjoint	disjoint	NOUN
ejpam-2495	423	9	union	union	NOUN
ejpam-2495	423	10	of	of	ADP
ejpam-2495	423	11	two	two	NUM
ejpam-2495	423	12	non	non	X
ejpam-2495	423	13	empty	empty	ADJ
ejpam-2495	423	14	proper	proper	ADJ
ejpam-2495	423	15	subset	subset	NOUN
ejpam-2495	423	16	of	of	ADP
ejpam-2495	423	17	x.	x.	PROPN
ejpam-2495	423	18	suppose	suppose	VERB
ejpam-2495	423	19	x	x	PRON
ejpam-2495	423	20	is	be	AUX
ejpam-2495	423	21	not	not	PART
ejpam-2495	423	22	btµ	btµ	NOUN
ejpam-2495	423	23	-connected	-connected	ADJ
ejpam-2495	423	24	space	space	NOUN
ejpam-2495	423	25	.	.	PUNCT
ejpam-2495	424	1	let	let	VERB
ejpam-2495	424	2	a	a	PRON
ejpam-2495	424	3	and	and	CCONJ
ejpam-2495	424	4	b	b	NOUN
ejpam-2495	424	5	be	be	AUX
ejpam-2495	424	6	any	any	DET
ejpam-2495	424	7	two	two	NUM
ejpam-2495	424	8	btµ-open	btµ-open	ADJ
ejpam-2495	424	9	subsets	subset	NOUN
ejpam-2495	424	10	of	of	ADP
ejpam-2495	424	11	x	x	SYM
ejpam-2495	424	12	such	such	ADJ
ejpam-2495	424	13	that	that	SCONJ
ejpam-2495	424	14	x	x	X
ejpam-2495	425	1	=	=	PUNCT
ejpam-2495	425	2	a∪	a∪	PROPN
ejpam-2495	425	3	b	b	NOUN
ejpam-2495	425	4	,	,	PUNCT
ejpam-2495	425	5	where	where	SCONJ
ejpam-2495	425	6	a∩b	a∩b	PROPN
ejpam-2495	425	7	=	=	SYM
ejpam-2495	425	8	φ	φ	PROPN
ejpam-2495	425	9	and	and	CCONJ
ejpam-2495	425	10	a⊂x	a⊂x	NOUN
ejpam-2495	425	11	,	,	PUNCT
ejpam-2495	425	12	b⊂	b⊂	PROPN
ejpam-2495	425	13	x.	x.	NOUN
ejpam-2495	425	14	since	since	SCONJ
ejpam-2495	425	15	x	x	PRON
ejpam-2495	425	16	is	be	AUX
ejpam-2495	425	17	btt	btt	PROPN
ejpam-2495	425	18	µ	µ	PROPN
ejpam-2495	425	19	c	c	NOUN
ejpam-2495	425	20	-space	-space	NOUN
ejpam-2495	425	21	and	and	CCONJ
ejpam-2495	425	22	a	a	DET
ejpam-2495	425	23	,	,	PUNCT
ejpam-2495	425	24	b	b	NOUN
ejpam-2495	425	25	are	be	AUX
ejpam-2495	425	26	btµ	btµ	PROPN
ejpam-2495	425	27	-open	-open	NOUN
ejpam-2495	425	28	.	.	PUNCT
ejpam-2495	426	1	a	a	PRON
ejpam-2495	426	2	,	,	PUNCT
ejpam-2495	426	3	b	b	NOUN
ejpam-2495	426	4	are	be	AUX
ejpam-2495	426	5	open	open	ADJ
ejpam-2495	426	6	subsets	subset	NOUN
ejpam-2495	426	7	of	of	ADP
ejpam-2495	426	8	x	x	PRON
ejpam-2495	426	9	,	,	PUNCT
ejpam-2495	426	10	which	which	PRON
ejpam-2495	426	11	contradicts	contradict	VERB
ejpam-2495	426	12	that	that	SCONJ
ejpam-2495	426	13	x	x	PRON
ejpam-2495	426	14	is	be	AUX
ejpam-2495	426	15	supra	supra	PROPN
ejpam-2495	426	16	connected	connect	VERB
ejpam-2495	426	17	.	.	PUNCT
ejpam-2495	427	1	therefore	therefore	ADV
ejpam-2495	427	2	x	x	X
ejpam-2495	427	3	is	be	AUX
ejpam-2495	427	4	btµ	btµ	NOUN
ejpam-2495	427	5	-connected	-connected	ADJ
ejpam-2495	427	6	.	.	PUNCT
ejpam-2495	428	1	theorem	theorem	NOUN
ejpam-2495	428	2	31	31	NUM
ejpam-2495	428	3	.	.	PUNCT
ejpam-2495	429	1	if	if	SCONJ
ejpam-2495	429	2	the	the	DET
ejpam-2495	429	3	btµ	btµ	NOUN
ejpam-2495	429	4	-open	-open	NOUN
ejpam-2495	429	5	sets	set	NOUN
ejpam-2495	429	6	c	c	NOUN
ejpam-2495	429	7	and	and	CCONJ
ejpam-2495	429	8	d	d	PROPN
ejpam-2495	429	9	form	form	VERB
ejpam-2495	429	10	a	a	DET
ejpam-2495	429	11	separation	separation	NOUN
ejpam-2495	429	12	of	of	ADP
ejpam-2495	429	13	x	x	PUNCT
ejpam-2495	429	14	and	and	CCONJ
ejpam-2495	429	15	if	if	SCONJ
ejpam-2495	429	16	y	y	PROPN
ejpam-2495	429	17	is	be	AUX
ejpam-2495	429	18	btµconnected	btµconnecte	VERB
ejpam-2495	429	19	subspace	subspace	NOUN
ejpam-2495	429	20	of	of	ADP
ejpam-2495	429	21	x	x	PRON
ejpam-2495	429	22	,	,	PUNCT
ejpam-2495	429	23	then	then	ADV
ejpam-2495	429	24	y	y	PROPN
ejpam-2495	429	25	lies	lie	VERB
ejpam-2495	429	26	entirely	entirely	ADV
ejpam-2495	429	27	within	within	ADP
ejpam-2495	429	28	c	c	PROPN
ejpam-2495	429	29	or	or	CCONJ
ejpam-2495	429	30	d.	d.	PROPN
ejpam-2495	429	31	proof	proof	NOUN
ejpam-2495	429	32	.	.	PUNCT
ejpam-2495	430	1	since	since	SCONJ
ejpam-2495	430	2	c	c	PROPN
ejpam-2495	430	3	and	and	CCONJ
ejpam-2495	430	4	d	d	PROPN
ejpam-2495	430	5	are	be	AUX
ejpam-2495	430	6	both	both	PRON
ejpam-2495	430	7	btµ	btµ	NOUN
ejpam-2495	430	8	-open	-open	VERB
ejpam-2495	430	9	in	in	ADP
ejpam-2495	430	10	x.	x.	NOUN
ejpam-2495	430	11	the	the	DET
ejpam-2495	430	12	set	set	NOUN
ejpam-2495	430	13	c∩y	c∩y	NOUN
ejpam-2495	430	14	and	and	CCONJ
ejpam-2495	430	15	d∩y	d∩y	NOUN
ejpam-2495	430	16	are	be	AUX
ejpam-2495	430	17	btµ	btµ	NOUN
ejpam-2495	430	18	-open	-open	ADJ
ejpam-2495	430	19	in	in	ADP
ejpam-2495	430	20	y	y	PROPN
ejpam-2495	430	21	,	,	PUNCT
ejpam-2495	430	22	these	these	DET
ejpam-2495	430	23	two	two	NUM
ejpam-2495	430	24	sets	set	NOUN
ejpam-2495	430	25	are	be	AUX
ejpam-2495	430	26	disjoint	disjoint	ADJ
ejpam-2495	430	27	and	and	CCONJ
ejpam-2495	430	28	their	their	PRON
ejpam-2495	430	29	union	union	NOUN
ejpam-2495	430	30	is	be	AUX
ejpam-2495	430	31	y.	y.	NOUN
ejpam-2495	430	32	if	if	SCONJ
ejpam-2495	430	33	they	they	PRON
ejpam-2495	430	34	were	be	AUX
ejpam-2495	430	35	both	both	PRON
ejpam-2495	430	36	non	non	X
ejpam-2495	430	37	empty	empty	ADJ
ejpam-2495	430	38	,	,	PUNCT
ejpam-2495	430	39	they	they	PRON
ejpam-2495	430	40	would	would	AUX
ejpam-2495	430	41	constitute	constitute	VERB
ejpam-2495	430	42	a	a	DET
ejpam-2495	430	43	separation	separation	NOUN
ejpam-2495	430	44	of	of	ADP
ejpam-2495	430	45	y.	y.	PROPN
ejpam-2495	430	46	therefore	therefore	ADV
ejpam-2495	430	47	,	,	PUNCT
ejpam-2495	430	48	one	one	NUM
ejpam-2495	430	49	of	of	ADP
ejpam-2495	430	50	them	they	PRON
ejpam-2495	430	51	is	be	AUX
ejpam-2495	430	52	empty	empty	ADJ
ejpam-2495	430	53	.	.	PUNCT
ejpam-2495	431	1	hence	hence	ADV
ejpam-2495	431	2	y	y	PROPN
ejpam-2495	431	3	must	must	AUX
ejpam-2495	431	4	lie	lie	VERB
ejpam-2495	431	5	entirely	entirely	ADV
ejpam-2495	431	6	in	in	ADP
ejpam-2495	431	7	c	c	PROPN
ejpam-2495	431	8	or	or	CCONJ
ejpam-2495	431	9	d.	d.	PROPN
ejpam-2495	431	10	theorem	theorem	VERB
ejpam-2495	431	11	32	32	NUM
ejpam-2495	431	12	.	.	PUNCT
ejpam-2495	432	1	let	let	VERB
ejpam-2495	432	2	a	a	PRON
ejpam-2495	432	3	be	be	AUX
ejpam-2495	432	4	a	a	DET
ejpam-2495	432	5	btµ-connected	btµ-connected	ADJ
ejpam-2495	432	6	subspace	subspace	NOUN
ejpam-2495	432	7	of	of	ADP
ejpam-2495	432	8	x.	x.	NOUN
ejpam-2495	432	9	if	if	SCONJ
ejpam-2495	432	10	a	a	PRON
ejpam-2495	432	11	⊂	⊂	X
ejpam-2495	432	12	b	b	X
ejpam-2495	432	13	⊂	⊂	PROPN
ejpam-2495	432	14	btµcl(a),then	btµcl(a),then	PROPN
ejpam-2495	432	15	b	b	PROPN
ejpam-2495	432	16	is	be	AUX
ejpam-2495	432	17	also	also	ADV
ejpam-2495	432	18	btµ-connected	btµ-connected	ADJ
ejpam-2495	432	19	.	.	PUNCT
ejpam-2495	433	1	proof	proof	NOUN
ejpam-2495	433	2	.	.	PUNCT
ejpam-2495	434	1	let	let	VERB
ejpam-2495	434	2	a	a	DET
ejpam-2495	434	3	be	be	AUX
ejpam-2495	434	4	btµ	btµ	NOUN
ejpam-2495	434	5	-connected.let	-connected.let	NOUN
ejpam-2495	434	6	a	a	DET
ejpam-2495	434	7	⊂	⊂	PROPN
ejpam-2495	434	8	b	b	PROPN
ejpam-2495	434	9	⊂	⊂	PROPN
ejpam-2495	434	10	btµcl(a	btµcl(a	PROPN
ejpam-2495	434	11	)	)	PUNCT
ejpam-2495	434	12	.	.	PUNCT
ejpam-2495	435	1	suppose	suppose	VERB
ejpam-2495	435	2	that	that	SCONJ
ejpam-2495	435	3	b	b	X
ejpam-2495	435	4	=	=	SYM
ejpam-2495	435	5	c	c	NOUN
ejpam-2495	435	6	∪d	∪d	X
ejpam-2495	435	7	is	be	AUX
ejpam-2495	435	8	a	a	DET
ejpam-2495	435	9	separation	separation	NOUN
ejpam-2495	435	10	of	of	ADP
ejpam-2495	435	11	b	b	NOUN
ejpam-2495	435	12	by	by	ADP
ejpam-2495	435	13	btµ	btµ	NOUN
ejpam-2495	435	14	-open	-open	NOUN
ejpam-2495	435	15	sets.thus	sets.thu	NOUN
ejpam-2495	435	16	by	by	ADP
ejpam-2495	435	17	previous	previous	ADJ
ejpam-2495	435	18	theorem	theorem	NOUN
ejpam-2495	435	19	above	above	ADP
ejpam-2495	435	20	a	a	PRON
ejpam-2495	435	21	must	must	AUX
ejpam-2495	435	22	lie	lie	VERB
ejpam-2495	435	23	entirely	entirely	ADV
ejpam-2495	435	24	in	in	ADP
ejpam-2495	435	25	c	c	NOUN
ejpam-2495	435	26	or	or	CCONJ
ejpam-2495	435	27	d.suppose	d.suppose	PRON
ejpam-2495	435	28	that	that	PRON
ejpam-2495	435	29	a⊂	a⊂	VERB
ejpam-2495	435	30	c	c	NOUN
ejpam-2495	435	31	,	,	PUNCT
ejpam-2495	435	32	then	then	ADV
ejpam-2495	435	33	btµcl(a	btµcl(a	NUM
ejpam-2495	435	34	)	)	PUNCT
ejpam-2495	435	35	⊆	⊆	NUM
ejpam-2495	435	36	btµcl(c).since	btµcl(c).since	NOUN
ejpam-2495	435	37	btµcl(c	btµcl(c	NOUN
ejpam-2495	435	38	)	)	PUNCT
ejpam-2495	435	39	and	and	CCONJ
ejpam-2495	435	40	d	d	PROPN
ejpam-2495	435	41	are	be	AUX
ejpam-2495	435	42	disjoint	disjoint	ADJ
ejpam-2495	435	43	,	,	PUNCT
ejpam-2495	435	44	b	b	NOUN
ejpam-2495	435	45	can	can	AUX
ejpam-2495	435	46	not	not	PART
ejpam-2495	435	47	intersect	intersect	VERB
ejpam-2495	435	48	d.this	d.this	PRON
ejpam-2495	435	49	disproves	disprove	NOUN
ejpam-2495	435	50	the	the	DET
ejpam-2495	435	51	fact	fact	NOUN
ejpam-2495	435	52	that	that	SCONJ
ejpam-2495	435	53	d	d	NOUN
ejpam-2495	435	54	is	be	AUX
ejpam-2495	435	55	non	non	X
ejpam-2495	435	56	empty	empty	ADJ
ejpam-2495	435	57	subset	subset	NOUN
ejpam-2495	435	58	of	of	ADP
ejpam-2495	435	59	b.so	b.so	PROPN
ejpam-2495	435	60	d	d	PROPN
ejpam-2495	435	61	=	=	NOUN
ejpam-2495	435	62	φwhich	φwhich	PRON
ejpam-2495	435	63	implies	imply	VERB
ejpam-2495	435	64	b	b	NOUN
ejpam-2495	435	65	is	be	AUX
ejpam-2495	435	66	btµ-connected	btµ-connected	ADJ
ejpam-2495	435	67	.	.	PUNCT
ejpam-2495	436	1	7	7	X
ejpam-2495	436	2	.	.	NUM
ejpam-2495	436	3	references	reference	NOUN
ejpam-2495	436	4	1	1	NUM
ejpam-2495	436	5	d.andrijevic	d.andrijevic	ADJ
ejpam-2495	436	6	,	,	PUNCT
ejpam-2495	436	7	on	on	ADP
ejpam-2495	436	8	bopen	bopen	NOUN
ejpam-2495	436	9	sets	set	NOUN
ejpam-2495	436	10	,	,	PUNCT
ejpam-2495	436	11	mat.vesnik	mat.vesnik	X
ejpam-2495	436	12	,	,	PUNCT
ejpam-2495	436	13	48(1996	48(1996	NOUN
ejpam-2495	436	14	)	)	PUNCT
ejpam-2495	436	15	,	,	PUNCT
ejpam-2495	436	16	no.1	no.1	NOUN
ejpam-2495	436	17	-	-	PUNCT
ejpam-2495	436	18	2,59	2,59	NUM
ejpam-2495	436	19	-	-	PUNCT
ejpam-2495	436	20	64	64	NUM
ejpam-2495	436	21	.	.	NOUN
ejpam-2495	436	22	2	2	NUM
ejpam-2495	436	23	r.devi	r.devi	NOUN
ejpam-2495	436	24	,	,	PUNCT
ejpam-2495	436	25	s.sampathkumar	s.sampathkumar	ADJ
ejpam-2495	436	26	and	and	CCONJ
ejpam-2495	436	27	m.caldas	m.calda	NOUN
ejpam-2495	436	28	,	,	PUNCT
ejpam-2495	436	29	on	on	ADP
ejpam-2495	436	30	supra	supra	PROPN
ejpam-2495	436	31	α	α	PROPN
ejpam-2495	436	32	open	open	ADJ
ejpam-2495	436	33	sets	set	NOUN
ejpam-2495	436	34	and	and	CCONJ
ejpam-2495	436	35	s	s	NOUN
ejpam-2495	436	36	-	-	ADJ
ejpam-2495	436	37	continuous	continuous	ADJ
ejpam-2495	436	38	maps	map	NOUN
ejpam-2495	436	39	,	,	PUNCT
ejpam-2495	436	40	general	general	ADJ
ejpam-2495	436	41	mathematics	mathematic	NOUN
ejpam-2495	436	42	,	,	PUNCT
ejpam-2495	436	43	16(2	16(2	NUM
ejpam-2495	436	44	)	)	PUNCT
ejpam-2495	436	45	,	,	PUNCT
ejpam-2495	436	46	(	(	PUNCT
ejpam-2495	436	47	2008	2008	NUM
ejpam-2495	436	48	)	)	PUNCT
ejpam-2495	436	49	,	,	PUNCT
ejpam-2495	436	50	77	77	NUM
ejpam-2495	436	51	-	-	SYM
ejpam-2495	436	52	84	84	NUM
ejpam-2495	436	53	.	.	PUNCT
ejpam-2495	437	1	3	3	NUM
ejpam-2495	437	2	jamal	jamal	PROPN
ejpam-2495	437	3	m.mustafa	m.mustafa	PROPN
ejpam-2495	437	4	,	,	PUNCT
ejpam-2495	437	5	supra	supra	PROPN
ejpam-2495	437	6	b	b	PROPN
ejpam-2495	437	7	-	-	PUNCT
ejpam-2495	437	8	compact	compact	ADJ
ejpam-2495	437	9	and	and	CCONJ
ejpam-2495	437	10	supra	supra	ADJ
ejpam-2495	437	11	b	b	PROPN
ejpam-2495	437	12	-	-	PUNCT
ejpam-2495	437	13	lindelof	lindelof	PROPN
ejpam-2495	437	14	spaces	space	NOUN
ejpam-2495	437	15	,	,	PUNCT
ejpam-2495	437	16	j.mat.app	j.mat.app	PROPN
ejpam-2495	437	17	.	.	PUNCT
ejpam-2495	438	1	36,(2013),7983	36,(2013),7983	NUM
ejpam-2495	438	2	.	.	PUNCT
ejpam-2495	439	1	4	4	NUM
ejpam-2495	439	2	k.krishnaveni	k.krishnaveni	NOUN
ejpam-2495	439	3	and	and	CCONJ
ejpam-2495	439	4	m.vigneshwaran	m.vigneshwaran	NOUN
ejpam-2495	439	5	,	,	PUNCT
ejpam-2495	439	6	on	on	ADP
ejpam-2495	439	7	btµ	btµ	NOUN
ejpam-2495	439	8	-closed	-close	VERB
ejpam-2495	439	9	sets	set	NOUN
ejpam-2495	439	10	in	in	ADP
ejpam-2495	439	11	supra	supra	ADJ
ejpam-2495	439	12	topological	topological	ADJ
ejpam-2495	439	13	spaces	space	NOUN
ejpam-2495	439	14	,	,	PUNCT
ejpam-2495	439	15	int.j	int.j	PROPN
ejpam-2495	439	16	.	.	PUNCT
ejpam-2495	440	1	mat.arc	mat.arc	X
ejpam-2495	440	2	.	.	PUNCT
ejpam-2495	440	3	,	,	PUNCT
ejpam-2495	440	4	4(2),(2013),1	4(2),(2013),1	PROPN
ejpam-2495	440	5	-	-	PUNCT
ejpam-2495	440	6	6	6	NUM
ejpam-2495	440	7	.	.	PUNCT
ejpam-2495	441	1	k.krishna	k.krishna	NOUN
ejpam-2495	441	2	,	,	PUNCT
ejpam-2495	441	3	m.vignesh	m.vignesh	NOUN
ejpam-2495	441	4	/	/	SYM
ejpam-2495	441	5	eur	eur	PROPN
ejpam-2495	441	6	.	.	PUNCT
ejpam-2495	442	1	j.	j.	PROPN
ejpam-2495	442	2	pure	pure	PROPN
ejpam-2495	442	3	appl	appl	PROPN
ejpam-2495	442	4	.	.	PROPN
ejpam-2495	442	5	math	math	PROPN
ejpam-2495	442	6	,	,	PUNCT
ejpam-2495	442	7	10	10	NUM
ejpam-2495	442	8	(	(	PUNCT
ejpam-2495	442	9	2	2	NUM
ejpam-2495	442	10	)	)	PUNCT
ejpam-2495	442	11	(	(	PUNCT
ejpam-2495	442	12	2017	2017	NUM
ejpam-2495	442	13	)	)	PUNCT
ejpam-2495	442	14	,	,	PUNCT
ejpam-2495	442	15	323	323	NUM
ejpam-2495	442	16	-	-	SYM
ejpam-2495	442	17	334	334	NUM
ejpam-2495	442	18	334	334	NUM
ejpam-2495	442	19	5	5	NUM
ejpam-2495	442	20	k.krishnaveni	k.krishnaveni	NOUN
ejpam-2495	442	21	and	and	CCONJ
ejpam-2495	442	22	m.vigneshwaran	m.vigneshwaran	NOUN
ejpam-2495	442	23	,	,	PUNCT
ejpam-2495	442	24	some	some	DET
ejpam-2495	442	25	stronger	strong	ADJ
ejpam-2495	442	26	forms	form	NOUN
ejpam-2495	442	27	of	of	ADP
ejpam-2495	442	28	supra	supra	ADJ
ejpam-2495	442	29	btµ	btµ	PROPN
ejpam-2495	442	30	continuous	continuous	ADJ
ejpam-2495	442	31	function	function	NOUN
ejpam-2495	442	32	,	,	PUNCT
ejpam-2495	442	33	int.j.mat	int.j.mat	NOUN
ejpam-2495	442	34	.	.	PUNCT
ejpam-2495	443	1	stat.inv	stat.inv	NOUN
ejpam-2495	443	2	.	.	NOUN
ejpam-2495	443	3	,1(2),(2013	,1(2),(2013	PUNCT
ejpam-2495	443	4	)	)	PUNCT
ejpam-2495	443	5	,	,	PUNCT
ejpam-2495	443	6	84	84	NUM
ejpam-2495	443	7	-	-	SYM
ejpam-2495	443	8	87	87	NUM
ejpam-2495	443	9	.	.	PUNCT
ejpam-2495	444	1	6	6	NUM
ejpam-2495	444	2	a.s.mashhour	a.s.mashhour	ADJ
ejpam-2495	444	3	,	,	PUNCT
ejpam-2495	444	4	a.a.allam	a.a.allam	PROPN
ejpam-2495	444	5	,	,	PUNCT
ejpam-2495	444	6	f.s.mohamoud	f.s.mohamoud	NOUN
ejpam-2495	444	7	and	and	CCONJ
ejpam-2495	444	8	f.h.khedr	f.h.khedr	NOUN
ejpam-2495	444	9	,	,	PUNCT
ejpam-2495	444	10	on	on	ADP
ejpam-2495	444	11	supra	supra	PROPN
ejpam-2495	444	12	topological	topological	ADJ
ejpam-2495	444	13	spaces	space	NOUN
ejpam-2495	444	14	,	,	PUNCT
ejpam-2495	444	15	indian	indian	ADJ
ejpam-2495	444	16	j.pure	j.pure	NOUN
ejpam-2495	444	17	and	and	CCONJ
ejpam-2495	444	18	appl.math	appl.math	PROPN
ejpam-2495	444	19	.	.	PROPN
ejpam-2495	444	20	,	,	PUNCT
ejpam-2495	444	21	no.4,14(1983	no.4,14(1983	PROPN
ejpam-2495	444	22	)	)	PUNCT
ejpam-2495	444	23	,	,	PUNCT
ejpam-2495	444	24	502510	502510	NUM
ejpam-2495	444	25	.	.	PUNCT
ejpam-2495	445	1	7	7	NUM
ejpam-2495	445	2	p.g.patil	p.g.patil	PROPN
ejpam-2495	445	3	,	,	PUNCT
ejpam-2495	445	4	w	w	NOUN
ejpam-2495	445	5	-compactness	-compactness	NOUN
ejpam-2495	445	6	and	and	CCONJ
ejpam-2495	445	7	w	w	NOUN
ejpam-2495	445	8	-	-	NOUN
ejpam-2495	445	9	connectedness	connectedness	NOUN
ejpam-2495	445	10	in	in	ADP
ejpam-2495	445	11	topological	topological	ADJ
ejpam-2495	445	12	spaces	space	NOUN
ejpam-2495	445	13	,	,	PUNCT
ejpam-2495	445	14	thai	thai	PROPN
ejpam-2495	445	15	.	.	PUNCT
ejpam-2495	446	1	j.	j.	PROPN
ejpam-2495	446	2	mat	mat	PROPN
ejpam-2495	446	3	.	.	PROPN
ejpam-2495	446	4	,	,	PUNCT
ejpam-2495	446	5	(	(	PUNCT
ejpam-2495	446	6	12),(2014),499	12),(2014),499	NUM
ejpam-2495	446	7	-	-	SYM
ejpam-2495	446	8	507	507	NUM
ejpam-2495	446	9	.	.	NOUN
ejpam-2495	446	10	8	8	NUM
ejpam-2495	446	11	o.r	o.r	PROPN
ejpam-2495	446	12	.	.	PROPN
ejpam-2495	446	13	sayed	sayed	PROPN
ejpam-2495	446	14	and	and	CCONJ
ejpam-2495	446	15	takashi	takashi	PROPN
ejpam-2495	446	16	noiri	noiri	PROPN
ejpam-2495	446	17	,	,	PUNCT
ejpam-2495	446	18	on	on	ADP
ejpam-2495	446	19	b	b	X
ejpam-2495	446	20	-	-	PUNCT
ejpam-2495	446	21	open	open	ADJ
ejpam-2495	446	22	sets	set	NOUN
ejpam-2495	446	23	and	and	CCONJ
ejpam-2495	446	24	supra	supra	PROPN
ejpam-2495	446	25	b	b	NOUN
ejpam-2495	446	26	-	-	PUNCT
ejpam-2495	446	27	continuity	continuity	NOUN
ejpam-2495	446	28	on	on	ADP
ejpam-2495	446	29	topological	topological	ADJ
ejpam-2495	446	30	spaces	space	NOUN
ejpam-2495	446	31	,	,	PUNCT
ejpam-2495	446	32	eur.j.pure	eur.j.pure	ADJ
ejpam-2495	446	33	and	and	CCONJ
ejpam-2495	446	34	app	app	PROPN
ejpam-2495	446	35	.	.	PUNCT
ejpam-2495	446	36	mat	mat	PROPN
ejpam-2495	446	37	.	.	PROPN
ejpam-2495	446	38	,3(2)(2010	,3(2)(2010	PROPN
ejpam-2495	446	39	)	)	PUNCT
ejpam-2495	446	40	,	,	PUNCT
ejpam-2495	446	41	295	295	NUM
ejpam-2495	446	42	-	-	SYM
ejpam-2495	446	43	302	302	NUM
ejpam-2495	446	44	.	.	PUNCT