id	sid	tid	token	lemma	pos
ejpam-176	1	1	5_basu.dvi	5_basu.dvi	NUM
ejpam-176	1	2	european	european	ADJ
ejpam-176	1	3	journal	journal	NOUN
ejpam-176	1	4	of	of	ADP
ejpam-176	1	5	pure	pure	ADJ
ejpam-176	1	6	and	and	CCONJ
ejpam-176	1	7	applied	apply	VERB
ejpam-176	1	8	mathematics	mathematic	NOUN
ejpam-176	1	9	vol	vol	NOUN
ejpam-176	1	10	.	.	PROPN
ejpam-176	2	1	2	2	NUM
ejpam-176	2	2	,	,	PUNCT
ejpam-176	2	3	no	no	INTJ
ejpam-176	2	4	.	.	NOUN
ejpam-176	2	5	1	1	NUM
ejpam-176	2	6	,	,	PUNCT
ejpam-176	2	7	2009	2009	NUM
ejpam-176	2	8	,	,	PUNCT
ejpam-176	2	9	(	(	PUNCT
ejpam-176	2	10	85	85	NUM
ejpam-176	2	11	-	-	SYM
ejpam-176	2	12	96	96	NUM
ejpam-176	2	13	)	)	PUNCT
ejpam-176	2	14	issn	issn	PROPN
ejpam-176	2	15	1307	1307	NUM
ejpam-176	2	16	-	-	SYM
ejpam-176	2	17	5543	5543	NUM
ejpam-176	2	18	–	–	PUNCT
ejpam-176	2	19	www.ejpam.com	www.ejpam.com	X
ejpam-176	2	20	locally	locally	ADV
ejpam-176	2	21	β	β	X
ejpam-176	2	22	-	-	ADJ
ejpam-176	2	23	closed	closed	ADJ
ejpam-176	2	24	spaces	space	NOUN
ejpam-176	2	25	c.	c.	PROPN
ejpam-176	2	26	k.	k.	PROPN
ejpam-176	2	27	basu1∗	basu1∗	PROPN
ejpam-176	2	28	and	and	CCONJ
ejpam-176	3	1	m.	m.	PROPN
ejpam-176	3	2	k.	k.	PROPN
ejpam-176	4	1	ghosh2	ghosh2	PROPN
ejpam-176	4	2	1	1	NUM
ejpam-176	4	3	department	department	NOUN
ejpam-176	4	4	of	of	ADP
ejpam-176	4	5	mathematics	mathematic	NOUN
ejpam-176	4	6	,	,	PUNCT
ejpam-176	4	7	university	university	NOUN
ejpam-176	4	8	of	of	ADP
ejpam-176	4	9	kalyani	kalyani	PROPN
ejpam-176	4	10	,	,	PUNCT
ejpam-176	4	11	kalyani-741235	kalyani-741235	NOUN
ejpam-176	4	12	,	,	PUNCT
ejpam-176	4	13	nadia	nadia	PROPN
ejpam-176	4	14	,	,	PUNCT
ejpam-176	4	15	west	west	PROPN
ejpam-176	4	16	bengal	bengal	PROPN
ejpam-176	4	17	,	,	PUNCT
ejpam-176	4	18	india	india	PROPN
ejpam-176	4	19	2	2	NUM
ejpam-176	4	20	dumkal	dumkal	NOUN
ejpam-176	4	21	college	college	NOUN
ejpam-176	4	22	,	,	PUNCT
ejpam-176	4	23	basantapur	basantapur	NOUN
ejpam-176	4	24	,	,	PUNCT
ejpam-176	4	25	basantapur-742406	basantapur-742406	ADJ
ejpam-176	4	26	,	,	PUNCT
ejpam-176	4	27	murshidabad	murshidabad	NOUN
ejpam-176	4	28	,	,	PUNCT
ejpam-176	4	29	west	west	PROPN
ejpam-176	4	30	bengal	bengal	PROPN
ejpam-176	4	31	,	,	PUNCT
ejpam-176	4	32	india	india	PROPN
ejpam-176	4	33	abstract	abstract	NOUN
ejpam-176	4	34	.	.	PUNCT
ejpam-176	5	1	in	in	ADP
ejpam-176	5	2	this	this	DET
ejpam-176	5	3	paper	paper	NOUN
ejpam-176	5	4	,	,	PUNCT
ejpam-176	5	5	we	we	PRON
ejpam-176	5	6	generalize	generalize	VERB
ejpam-176	5	7	the	the	DET
ejpam-176	5	8	notion	notion	NOUN
ejpam-176	5	9	of	of	ADP
ejpam-176	5	10	β	β	X
ejpam-176	5	11	-closed	-close	VERB
ejpam-176	5	12	-	-	NOUN
ejpam-176	5	13	ness	ness	NOUN
ejpam-176	5	14	[	[	X
ejpam-176	5	15	7	7	X
ejpam-176	5	16	]	]	PUNCT
ejpam-176	5	17	to	to	ADP
ejpam-176	5	18	arbitrary	arbitrary	ADJ
ejpam-176	5	19	subsets	subset	NOUN
ejpam-176	5	20	and	and	CCONJ
ejpam-176	5	21	in	in	ADP
ejpam-176	5	22	terms	term	NOUN
ejpam-176	5	23	of	of	ADP
ejpam-176	5	24	it	it	PRON
ejpam-176	5	25	we	we	PRON
ejpam-176	5	26	introduce	introduce	VERB
ejpam-176	5	27	the	the	DET
ejpam-176	5	28	class	class	NOUN
ejpam-176	5	29	of	of	ADP
ejpam-176	5	30	locally	locally	ADV
ejpam-176	5	31	β	β	X
ejpam-176	5	32	-closed	-close	VERB
ejpam-176	5	33	spaces	space	NOUN
ejpam-176	5	34	and	and	CCONJ
ejpam-176	5	35	also	also	ADV
ejpam-176	5	36	investigate	investigate	VERB
ejpam-176	5	37	of	of	ADP
ejpam-176	5	38	its	its	PRON
ejpam-176	5	39	several	several	ADJ
ejpam-176	5	40	properties	property	NOUN
ejpam-176	5	41	.	.	PUNCT
ejpam-176	6	1	it	it	PRON
ejpam-176	6	2	is	be	AUX
ejpam-176	6	3	observed	observe	VERB
ejpam-176	6	4	that	that	SCONJ
ejpam-176	6	5	although	although	SCONJ
ejpam-176	6	6	local	local	ADJ
ejpam-176	6	7	β	β	NOUN
ejpam-176	6	8	-closedness	-closedness	NOUN
ejpam-176	6	9	is	be	AUX
ejpam-176	6	10	independent	independent	ADJ
ejpam-176	6	11	of	of	ADP
ejpam-176	6	12	local	local	ADJ
ejpam-176	6	13	compact	compact	ADJ
ejpam-176	6	14	t2	t2	NOUN
ejpam-176	6	15	-	-	PUNCT
ejpam-176	6	16	ness	ness	NOUN
ejpam-176	6	17	but	but	CCONJ
ejpam-176	6	18	one	one	NOUN
ejpam-176	6	19	can	can	AUX
ejpam-176	6	20	be	be	AUX
ejpam-176	6	21	obtained	obtain	VERB
ejpam-176	6	22	from	from	ADP
ejpam-176	6	23	the	the	DET
ejpam-176	6	24	other	other	ADJ
ejpam-176	6	25	by	by	ADP
ejpam-176	6	26	the	the	DET
ejpam-176	6	27	help	help	NOUN
ejpam-176	6	28	of	of	ADP
ejpam-176	6	29	a	a	DET
ejpam-176	6	30	new	new	ADJ
ejpam-176	6	31	class	class	NOUN
ejpam-176	6	32	of	of	ADP
ejpam-176	6	33	functions	function	NOUN
ejpam-176	6	34	viz	viz	VERB
ejpam-176	6	35	.	.	PUNCT
ejpam-176	7	1	β	β	X
ejpam-176	7	2	-θ	-θ	PUNCT
ejpam-176	7	3	-closed	-close	VERB
ejpam-176	7	4	functions	function	NOUN
ejpam-176	7	5	which	which	PRON
ejpam-176	7	6	are	be	AUX
ejpam-176	7	7	independent	independent	ADJ
ejpam-176	7	8	not	not	PART
ejpam-176	7	9	only	only	ADV
ejpam-176	7	10	of	of	ADP
ejpam-176	7	11	closed	closed	ADJ
ejpam-176	7	12	functions	function	NOUN
ejpam-176	7	13	but	but	CCONJ
ejpam-176	7	14	also	also	ADV
ejpam-176	7	15	of	of	ADP
ejpam-176	7	16	continuous	continuous	ADJ
ejpam-176	7	17	functions	function	NOUN
ejpam-176	7	18	.	.	PUNCT
ejpam-176	8	1	ams	am	NOUN
ejpam-176	8	2	subject	subject	ADJ
ejpam-176	8	3	classifications	classification	NOUN
ejpam-176	8	4	:	:	PUNCT
ejpam-176	8	5	54c99	54c99	NUM
ejpam-176	8	6	,	,	PUNCT
ejpam-176	8	7	54d99	54d99	NUM
ejpam-176	8	8	key	key	ADJ
ejpam-176	8	9	words	word	NOUN
ejpam-176	8	10	:	:	PUNCT
ejpam-176	8	11	β	β	X
ejpam-176	8	12	-open	-open	PROPN
ejpam-176	8	13	,	,	PUNCT
ejpam-176	8	14	β	β	X
ejpam-176	8	15	-closed	-closed	PROPN
ejpam-176	8	16	,	,	PUNCT
ejpam-176	8	17	β	β	X
ejpam-176	8	18	-regular	-regular	NOUN
ejpam-176	8	19	,	,	PUNCT
ejpam-176	8	20	β	β	X
ejpam-176	8	21	-θ	-θ	PUNCT
ejpam-176	8	22	-open	-open	PROPN
ejpam-176	8	23	,	,	PUNCT
ejpam-176	8	24	β	β	X
ejpam-176	8	25	-θ	-θ	X
ejpam-176	8	26	-closed	-close	VERB
ejpam-176	8	27	functions	function	NOUN
ejpam-176	8	28	,	,	PUNCT
ejpam-176	8	29	locally	locally	ADV
ejpam-176	8	30	β	β	X
ejpam-176	8	31	-closed	-closed	ADJ
ejpam-176	8	32	,	,	PUNCT
ejpam-176	8	33	locally	locally	ADV
ejpam-176	8	34	compact	compact	ADJ
ejpam-176	8	35	t2	t2	NOUN
ejpam-176	8	36	.	.	PUNCT
ejpam-176	9	1	1	1	X
ejpam-176	9	2	.	.	X
ejpam-176	9	3	introduction	introduction	NOUN
ejpam-176	9	4	among	among	ADP
ejpam-176	9	5	various	various	ADJ
ejpam-176	9	6	generalized	generalized	ADJ
ejpam-176	9	7	open	open	ADJ
ejpam-176	9	8	sets	set	NOUN
ejpam-176	9	9	,	,	PUNCT
ejpam-176	9	10	the	the	DET
ejpam-176	9	11	notion	notion	NOUN
ejpam-176	9	12	of	of	ADP
ejpam-176	9	13	β	β	X
ejpam-176	9	14	-open	-open	NOUN
ejpam-176	9	15	sets	set	NOUN
ejpam-176	9	16	introduced	introduce	VERB
ejpam-176	9	17	by	by	ADP
ejpam-176	9	18	abd	abd	PROPN
ejpam-176	9	19	.	.	PUNCT
ejpam-176	10	1	elmonsef	elmonsef	PROPN
ejpam-176	10	2	et	et	PROPN
ejpam-176	10	3	al	al	PROPN
ejpam-176	10	4	.	.	PUNCT
ejpam-176	11	1	[	[	X
ejpam-176	11	2	1	1	X
ejpam-176	11	3	]	]	PUNCT
ejpam-176	11	4	which	which	PRON
ejpam-176	11	5	is	be	AUX
ejpam-176	11	6	equivalent	equivalent	ADJ
ejpam-176	11	7	to	to	ADP
ejpam-176	11	8	the	the	DET
ejpam-176	11	9	notion	notion	NOUN
ejpam-176	11	10	of	of	ADP
ejpam-176	11	11	semipre	semipre	NOUN
ejpam-176	11	12	-	-	PUNCT
ejpam-176	11	13	open	open	ADJ
ejpam-176	11	14	sets	set	NOUN
ejpam-176	11	15	due	due	ADJ
ejpam-176	11	16	to	to	PART
ejpam-176	11	17	andrijević	andrijević	VERB
ejpam-176	11	18	[	[	X
ejpam-176	11	19	4	4	NUM
ejpam-176	11	20	]	]	PUNCT
ejpam-176	11	21	,	,	PUNCT
ejpam-176	11	22	plays	play	VERB
ejpam-176	11	23	a	a	DET
ejpam-176	11	24	significant	significant	ADJ
ejpam-176	11	25	role	role	NOUN
ejpam-176	11	26	in	in	ADP
ejpam-176	11	27	general	general	ADJ
ejpam-176	11	28	topology	topology	NOUN
ejpam-176	11	29	and	and	CCONJ
ejpam-176	11	30	real	real	ADJ
ejpam-176	11	31	analysis	analysis	NOUN
ejpam-176	11	32	.	.	PUNCT
ejpam-176	12	1	now	now	ADV
ejpam-176	12	2	a	a	DET
ejpam-176	12	3	days	day	NOUN
ejpam-176	12	4	many	many	ADJ
ejpam-176	12	5	topologists	topologist	NOUN
ejpam-176	12	6	have	have	AUX
ejpam-176	12	7	focused	focus	VERB
ejpam-176	12	8	their	their	PRON
ejpam-176	12	9	research	research	NOUN
ejpam-176	12	10	on	on	ADP
ejpam-176	12	11	various	various	ADJ
ejpam-176	12	12	topics	topic	NOUN
ejpam-176	12	13	,	,	PUNCT
ejpam-176	12	14	using	use	VERB
ejpam-176	12	15	β	β	NOUN
ejpam-176	12	16	-open	-open	NOUN
ejpam-176	12	17	sets	set	NOUN
ejpam-176	12	18	.	.	PUNCT
ejpam-176	13	1	mention	mention	NOUN
ejpam-176	13	2	may	may	AUX
ejpam-176	13	3	be	be	AUX
ejpam-176	13	4	made	make	VERB
ejpam-176	13	5	of	of	ADP
ejpam-176	13	6	some	some	PRON
ejpam-176	13	7	of	of	ADP
ejpam-176	13	8	the	the	DET
ejpam-176	13	9	recent	recent	ADJ
ejpam-176	13	10	works	work	NOUN
ejpam-176	13	11	which	which	PRON
ejpam-176	13	12	are	be	AUX
ejpam-176	13	13	found	find	VERB
ejpam-176	13	14	in	in	ADP
ejpam-176	13	15	[	[	NOUN
ejpam-176	13	16	1,2,3	1,2,3	NUM
ejpam-176	13	17	,	,	PUNCT
ejpam-176	13	18	4,5,6,7,8,9,10,11,12,13,18,19,20,21,23	4,5,6,7,8,9,10,11,12,13,18,19,20,21,23	NOUN
ejpam-176	13	19	]	]	PUNCT
ejpam-176	13	20	.	.	PUNCT
ejpam-176	14	1	very	very	ADV
ejpam-176	14	2	recently	recently	ADV
ejpam-176	14	3	basu	basu	PROPN
ejpam-176	14	4	and	and	CCONJ
ejpam-176	14	5	ghosh	ghosh	PROPN
ejpam-176	15	1	[	[	X
ejpam-176	15	2	7	7	X
ejpam-176	15	3	]	]	PUNCT
ejpam-176	15	4	by	by	ADP
ejpam-176	15	5	the	the	DET
ejpam-176	15	6	help	help	NOUN
ejpam-176	15	7	of	of	ADP
ejpam-176	15	8	β	β	X
ejpam-176	15	9	-open	-open	NOUN
ejpam-176	15	10	sets	set	NOUN
ejpam-176	15	11	introduced	introduce	VERB
ejpam-176	15	12	a	a	DET
ejpam-176	15	13	covering	covering	NOUN
ejpam-176	15	14	property	property	NOUN
ejpam-176	15	15	known	know	VERB
ejpam-176	15	16	as	as	ADP
ejpam-176	15	17	β	β	NOUN
ejpam-176	15	18	-closedness	-closedness	PROPN
ejpam-176	15	19	and	and	CCONJ
ejpam-176	15	20	characterized	characterize	VERB
ejpam-176	15	21	such	such	ADJ
ejpam-176	15	22	spaces	space	NOUN
ejpam-176	15	23	from	from	ADP
ejpam-176	15	24	different	different	ADJ
ejpam-176	15	25	angles	angle	NOUN
ejpam-176	15	26	.	.	PUNCT
ejpam-176	16	1	in	in	ADP
ejpam-176	16	2	this	this	DET
ejpam-176	16	3	paper	paper	NOUN
ejpam-176	16	4	,	,	PUNCT
ejpam-176	16	5	we	we	PRON
ejpam-176	16	6	∗corresponding	∗corresponde	VERB
ejpam-176	16	7	author	author	NOUN
ejpam-176	16	8	.	.	PUNCT
ejpam-176	17	1	email	email	NOUN
ejpam-176	17	2	addresses	address	NOUN
ejpam-176	17	3	:	:	PUNCT
ejpam-176	17	4	kbasu1962	kbasu1962	PROPN
ejpam-176	17	5	�	�	PROPN
ejpam-176	17	6	yahoo	yahoo	PROPN
ejpam-176	17	7	.	.	PUNCT
ejpam-176	18	1	om	om	PROPN
ejpam-176	18	2	(	(	PUNCT
ejpam-176	18	3	c.	c.	PROPN
ejpam-176	18	4	basu	basu	PROPN
ejpam-176	18	5	)	)	PUNCT
ejpam-176	18	6	,	,	PUNCT
ejpam-176	18	7	manabghosh	manabghosh	PROPN
ejpam-176	18	8	�	�	PROPN
ejpam-176	18	9	gmail	gmail	NOUN
ejpam-176	18	10	.	.	PUNCT
ejpam-176	19	1	om	om	PROPN
ejpam-176	19	2	(	(	PUNCT
ejpam-176	19	3	m.	m.	PROPN
ejpam-176	19	4	ghosh	ghosh	PROPN
ejpam-176	19	5	)	)	PUNCT
ejpam-176	19	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-176	20	1	85	85	NUM
ejpam-176	20	2	c	c	NOUN
ejpam-176	20	3	©	©	PROPN
ejpam-176	20	4	2009	2009	NUM
ejpam-176	20	5	ejpam	ejpam	NOUN
ejpam-176	20	6	all	all	DET
ejpam-176	20	7	rights	right	NOUN
ejpam-176	20	8	reserved	reserve	VERB
ejpam-176	20	9	.	.	PUNCT
ejpam-176	21	1	c.	c.	PROPN
ejpam-176	21	2	basu	basu	PROPN
ejpam-176	21	3	and	and	CCONJ
ejpam-176	21	4	m.	m.	PROPN
ejpam-176	21	5	ghosh	ghosh	PROPN
ejpam-176	21	6	/	/	PUNCT
ejpam-176	21	7	eur	eur	PROPN
ejpam-176	21	8	.	.	PUNCT
ejpam-176	22	1	j.	j.	PROPN
ejpam-176	22	2	pure	pure	PROPN
ejpam-176	22	3	appl	appl	PROPN
ejpam-176	22	4	.	.	PROPN
ejpam-176	22	5	math	math	PROPN
ejpam-176	22	6	,	,	PUNCT
ejpam-176	22	7	2	2	NUM
ejpam-176	22	8	(	(	PUNCT
ejpam-176	22	9	2009	2009	NUM
ejpam-176	22	10	)	)	PUNCT
ejpam-176	22	11	,	,	PUNCT
ejpam-176	22	12	(	(	PUNCT
ejpam-176	22	13	85	85	NUM
ejpam-176	22	14	-	-	SYM
ejpam-176	22	15	96	96	NUM
ejpam-176	22	16	)	)	PUNCT
ejpam-176	22	17	86	86	NUM
ejpam-176	22	18	generalize	generalize	VERB
ejpam-176	22	19	the	the	DET
ejpam-176	22	20	concept	concept	NOUN
ejpam-176	22	21	of	of	ADP
ejpam-176	22	22	β	β	X
ejpam-176	22	23	-closedness	-closedness	NOUN
ejpam-176	22	24	to	to	ADP
ejpam-176	22	25	arbitrary	arbitrary	ADJ
ejpam-176	22	26	subsets	subset	NOUN
ejpam-176	22	27	and	and	CCONJ
ejpam-176	22	28	using	use	VERB
ejpam-176	22	29	such	such	ADJ
ejpam-176	22	30	sets	set	NOUN
ejpam-176	22	31	,	,	PUNCT
ejpam-176	22	32	we	we	PRON
ejpam-176	22	33	introduce	introduce	VERB
ejpam-176	22	34	and	and	CCONJ
ejpam-176	22	35	investigate	investigate	VERB
ejpam-176	22	36	locally	locally	ADV
ejpam-176	22	37	β	β	X
ejpam-176	22	38	-closed	-close	VERB
ejpam-176	22	39	spaces	space	NOUN
ejpam-176	22	40	.	.	PUNCT
ejpam-176	23	1	although	although	SCONJ
ejpam-176	23	2	we	we	PRON
ejpam-176	23	3	have	have	AUX
ejpam-176	23	4	seen	see	VERB
ejpam-176	23	5	that	that	SCONJ
ejpam-176	23	6	local	local	ADJ
ejpam-176	23	7	β	β	X
ejpam-176	23	8	-closedness	-closedness	NOUN
ejpam-176	23	9	is	be	AUX
ejpam-176	23	10	independent	independent	ADJ
ejpam-176	23	11	of	of	ADP
ejpam-176	23	12	local	local	ADJ
ejpam-176	23	13	compact	compact	ADJ
ejpam-176	23	14	t2	t2	NOUN
ejpam-176	23	15	-	-	PUNCT
ejpam-176	23	16	ness	ness	NOUN
ejpam-176	23	17	but	but	CCONJ
ejpam-176	23	18	our	our	PRON
ejpam-176	23	19	intension	intension	NOUN
ejpam-176	23	20	is	be	AUX
ejpam-176	23	21	to	to	PART
ejpam-176	23	22	achieve	achieve	VERB
ejpam-176	23	23	either	either	PRON
ejpam-176	23	24	of	of	ADP
ejpam-176	23	25	the	the	DET
ejpam-176	23	26	spaces	space	NOUN
ejpam-176	23	27	from	from	ADP
ejpam-176	23	28	the	the	DET
ejpam-176	23	29	other	other	ADJ
ejpam-176	23	30	.	.	PUNCT
ejpam-176	24	1	in	in	ADP
ejpam-176	24	2	this	this	DET
ejpam-176	24	3	regard	regard	NOUN
ejpam-176	24	4	,	,	PUNCT
ejpam-176	24	5	a	a	DET
ejpam-176	24	6	new	new	ADJ
ejpam-176	24	7	class	class	NOUN
ejpam-176	24	8	of	of	ADP
ejpam-176	24	9	functions	function	NOUN
ejpam-176	24	10	called	call	VERB
ejpam-176	24	11	β	β	X
ejpam-176	24	12	-θ	-θ	PUNCT
ejpam-176	24	13	-closed	-close	VERB
ejpam-176	24	14	function	function	NOUN
ejpam-176	24	15	is	be	AUX
ejpam-176	24	16	introduced	introduce	VERB
ejpam-176	24	17	,	,	PUNCT
ejpam-176	24	18	which	which	PRON
ejpam-176	24	19	quite	quite	ADV
ejpam-176	24	20	satisfactorily	satisfactorily	ADV
ejpam-176	24	21	enables	enable	VERB
ejpam-176	24	22	to	to	PART
ejpam-176	24	23	establish	establish	VERB
ejpam-176	24	24	our	our	PRON
ejpam-176	24	25	goal	goal	NOUN
ejpam-176	24	26	.	.	PUNCT
ejpam-176	25	1	in	in	ADP
ejpam-176	25	2	addition	addition	NOUN
ejpam-176	25	3	,	,	PUNCT
ejpam-176	25	4	a	a	DET
ejpam-176	25	5	sufficient	sufficient	ADJ
ejpam-176	25	6	condition	condition	NOUN
ejpam-176	25	7	for	for	ADP
ejpam-176	25	8	a	a	DET
ejpam-176	25	9	locally	locally	ADV
ejpam-176	25	10	β	β	X
ejpam-176	25	11	-closed	-close	VERB
ejpam-176	25	12	space	space	NOUN
ejpam-176	25	13	to	to	PART
ejpam-176	25	14	be	be	AUX
ejpam-176	25	15	extremally	extremally	ADV
ejpam-176	25	16	disconnected	disconnect	VERB
ejpam-176	25	17	is	be	AUX
ejpam-176	25	18	also	also	ADV
ejpam-176	25	19	established	establish	VERB
ejpam-176	25	20	.	.	PUNCT
ejpam-176	26	1	2	2	X
ejpam-176	26	2	.	.	NUM
ejpam-176	26	3	preliminaries	preliminary	NOUN
ejpam-176	26	4	throughout	throughout	ADP
ejpam-176	26	5	the	the	DET
ejpam-176	26	6	paper	paper	NOUN
ejpam-176	26	7	,	,	PUNCT
ejpam-176	26	8	spaces	space	VERB
ejpam-176	26	9	x	x	PUNCT
ejpam-176	26	10	and	and	CCONJ
ejpam-176	26	11	y	y	PROPN
ejpam-176	26	12	will	will	AUX
ejpam-176	26	13	always	always	ADV
ejpam-176	26	14	denote	denote	VERB
ejpam-176	26	15	topological	topological	ADJ
ejpam-176	26	16	spaces	space	NOUN
ejpam-176	26	17	without	without	ADP
ejpam-176	26	18	any	any	DET
ejpam-176	26	19	separation	separation	NOUN
ejpam-176	26	20	axioms	axiom	NOUN
ejpam-176	26	21	and	and	CCONJ
ejpam-176	26	22	ψ	ψ	X
ejpam-176	26	23	:	:	PUNCT
ejpam-176	26	24	x	x	X
ejpam-176	26	25	→	→	SYM
ejpam-176	26	26	y	y	PROPN
ejpam-176	26	27	will	will	AUX
ejpam-176	26	28	represent	represent	VERB
ejpam-176	26	29	a	a	DET
ejpam-176	26	30	(	(	PUNCT
ejpam-176	26	31	single	single	ADJ
ejpam-176	26	32	valued	value	VERB
ejpam-176	26	33	)	)	PUNCT
ejpam-176	26	34	function	function	NOUN
ejpam-176	26	35	.	.	PUNCT
ejpam-176	27	1	given	give	VERB
ejpam-176	27	2	a	a	DET
ejpam-176	27	3	set	set	NOUN
ejpam-176	27	4	a	a	PRON
ejpam-176	27	5	,	,	PUNCT
ejpam-176	27	6	its	its	PRON
ejpam-176	27	7	closure	closure	NOUN
ejpam-176	27	8	and	and	CCONJ
ejpam-176	27	9	interior	interior	ADJ
ejpam-176	27	10	are	be	AUX
ejpam-176	27	11	denoted	denote	VERB
ejpam-176	27	12	by	by	ADP
ejpam-176	27	13	cl(a	cl(a	NOUN
ejpam-176	27	14	)	)	PUNCT
ejpam-176	27	15	and	and	CCONJ
ejpam-176	27	16	int(a	int(a	PROPN
ejpam-176	27	17	)	)	PUNCT
ejpam-176	27	18	respectively	respectively	ADV
ejpam-176	27	19	.	.	PUNCT
ejpam-176	28	1	a	a	DET
ejpam-176	28	2	set	set	NOUN
ejpam-176	28	3	a	a	PRON
ejpam-176	28	4	is	be	AUX
ejpam-176	28	5	said	say	VERB
ejpam-176	28	6	to	to	PART
ejpam-176	28	7	be	be	AUX
ejpam-176	28	8	α	α	X
ejpam-176	28	9	-	-	ADJ
ejpam-176	28	10	open	open	ADJ
ejpam-176	28	11	[	[	X
ejpam-176	28	12	17	17	NUM
ejpam-176	28	13	]	]	X
ejpam-176	28	14	(	(	PUNCT
ejpam-176	28	15	resp	resp	NOUN
ejpam-176	28	16	.	.	PUNCT
ejpam-176	29	1	preopen	preopen	ADJ
ejpam-176	30	1	[	[	X
ejpam-176	30	2	16	16	NUM
ejpam-176	30	3	]	]	PUNCT
ejpam-176	30	4	,	,	PUNCT
ejpam-176	30	5	semi	semi	ADJ
ejpam-176	30	6	-	-	ADJ
ejpam-176	30	7	open	open	ADJ
ejpam-176	30	8	[	[	X
ejpam-176	30	9	14	14	NUM
ejpam-176	30	10	]	]	X
ejpam-176	30	11	,	,	PUNCT
ejpam-176	30	12	β	β	X
ejpam-176	30	13	-open	-open	NOUN
ejpam-176	31	1	[	[	X
ejpam-176	31	2	1	1	NUM
ejpam-176	31	3	]	]	PUNCT
ejpam-176	31	4	or	or	CCONJ
ejpam-176	31	5	semi	semi	ADJ
ejpam-176	31	6	-	-	ADJ
ejpam-176	31	7	preopen	preopen	ADJ
ejpam-176	31	8	[	[	X
ejpam-176	31	9	4	4	NUM
ejpam-176	31	10	]	]	PUNCT
ejpam-176	31	11	)	)	PUNCT
ejpam-176	31	12	if	if	SCONJ
ejpam-176	31	13	a	a	DET
ejpam-176	31	14	⊂	⊂	X
ejpam-176	31	15	int(cl(int(a	int(cl(int(a	NOUN
ejpam-176	31	16	)	)	PUNCT
ejpam-176	31	17	)	)	PUNCT
ejpam-176	31	18	)	)	PUNCT
ejpam-176	31	19	(	(	PUNCT
ejpam-176	31	20	resp	resp	NOUN
ejpam-176	31	21	.	.	PUNCT
ejpam-176	32	1	a⊂	a⊂	X
ejpam-176	33	1	int(cl(a	int(cl(a	PROPN
ejpam-176	33	2	)	)	PUNCT
ejpam-176	33	3	)	)	PUNCT
ejpam-176	33	4	,	,	PUNCT
ejpam-176	33	5	a⊂	a⊂	SYM
ejpam-176	33	6	cl(int(a	cl(int(a	NOUN
ejpam-176	33	7	)	)	PUNCT
ejpam-176	33	8	)	)	PUNCT
ejpam-176	33	9	,	,	PUNCT
ejpam-176	33	10	a⊂	a⊂	NOUN
ejpam-176	33	11	cl(int(cl(a	cl(int(cl(a	NOUN
ejpam-176	33	12	)	)	PUNCT
ejpam-176	33	13	)	)	PUNCT
ejpam-176	33	14	)	)	PUNCT
ejpam-176	33	15	)	)	PUNCT
ejpam-176	33	16	.	.	PUNCT
ejpam-176	34	1	the	the	DET
ejpam-176	34	2	complement	complement	NOUN
ejpam-176	34	3	of	of	ADP
ejpam-176	34	4	a	a	DET
ejpam-176	34	5	β	β	X
ejpam-176	34	6	-open	-open	NOUN
ejpam-176	34	7	(	(	PUNCT
ejpam-176	34	8	resp	resp	NOUN
ejpam-176	34	9	.	.	PUNCT
ejpam-176	35	1	semi	semi	ADJ
ejpam-176	35	2	-	-	ADJ
ejpam-176	35	3	open	open	ADJ
ejpam-176	35	4	)	)	PUNCT
ejpam-176	35	5	set	set	NOUN
ejpam-176	35	6	is	be	AUX
ejpam-176	35	7	said	say	VERB
ejpam-176	35	8	to	to	PART
ejpam-176	35	9	be	be	AUX
ejpam-176	35	10	β	β	X
ejpam-176	35	11	-closed	-close	VERB
ejpam-176	35	12	[	[	X
ejpam-176	35	13	1	1	NUM
ejpam-176	35	14	]	]	PUNCT
ejpam-176	35	15	or	or	CCONJ
ejpam-176	35	16	semi	semi	ADV
ejpam-176	35	17	-	-	ADJ
ejpam-176	35	18	preclosed	preclosed	ADJ
ejpam-176	35	19	[	[	X
ejpam-176	35	20	4	4	NUM
ejpam-176	35	21	]	]	PUNCT
ejpam-176	35	22	(	(	PUNCT
ejpam-176	35	23	resp	resp	NOUN
ejpam-176	35	24	.	.	PUNCT
ejpam-176	36	1	semiclosed	semiclose	VERB
ejpam-176	36	2	[	[	X
ejpam-176	36	3	14	14	NUM
ejpam-176	36	4	]	]	NUM
ejpam-176	36	5	)	)	PUNCT
ejpam-176	36	6	.	.	PUNCT
ejpam-176	37	1	the	the	DET
ejpam-176	37	2	intersection	intersection	NOUN
ejpam-176	37	3	of	of	ADP
ejpam-176	37	4	all	all	DET
ejpam-176	37	5	β	β	X
ejpam-176	37	6	-closed	-close	VERB
ejpam-176	37	7	(	(	PUNCT
ejpam-176	37	8	resp	resp	NOUN
ejpam-176	37	9	.	.	PUNCT
ejpam-176	38	1	semi	semi	ADJ
ejpam-176	38	2	-	-	ADJ
ejpam-176	38	3	closed	closed	ADJ
ejpam-176	38	4	)	)	PUNCT
ejpam-176	38	5	sets	set	NOUN
ejpam-176	38	6	containing	contain	VERB
ejpam-176	38	7	a	a	PRON
ejpam-176	38	8	is	be	AUX
ejpam-176	38	9	called	call	VERB
ejpam-176	38	10	the	the	DET
ejpam-176	38	11	β	β	NOUN
ejpam-176	38	12	-closure	-closure	NOUN
ejpam-176	38	13	[	[	X
ejpam-176	38	14	1	1	NUM
ejpam-176	38	15	]	]	PUNCT
ejpam-176	38	16	or	or	CCONJ
ejpam-176	38	17	semi	semi	ADJ
ejpam-176	38	18	-	-	ADJ
ejpam-176	38	19	preclosure	preclosure	ADJ
ejpam-176	38	20	[	[	X
ejpam-176	38	21	4	4	NUM
ejpam-176	38	22	]	]	PUNCT
ejpam-176	38	23	(	(	PUNCT
ejpam-176	38	24	resp	resp	NOUN
ejpam-176	38	25	.	.	PUNCT
ejpam-176	39	1	semiclosure	semiclosure	NOUN
ejpam-176	39	2	)	)	PUNCT
ejpam-176	39	3	of	of	ADP
ejpam-176	39	4	a	a	PRON
ejpam-176	39	5	and	and	CCONJ
ejpam-176	39	6	is	be	AUX
ejpam-176	39	7	denoted	denote	VERB
ejpam-176	39	8	by	by	ADP
ejpam-176	39	9	β	β	NOUN
ejpam-176	39	10	cl(a	cl(a	X
ejpam-176	39	11	)	)	PUNCT
ejpam-176	39	12	or	or	CCONJ
ejpam-176	39	13	sp	sp	NOUN
ejpam-176	39	14	-	-	PUNCT
ejpam-176	39	15	cl(a	cl(a	NUM
ejpam-176	39	16	)	)	PUNCT
ejpam-176	39	17	(	(	PUNCT
ejpam-176	39	18	resp	resp	NOUN
ejpam-176	39	19	.	.	PUNCT
ejpam-176	40	1	scl(a	scl(a	PROPN
ejpam-176	40	2	)	)	PUNCT
ejpam-176	40	3	)	)	PUNCT
ejpam-176	40	4	.	.	PUNCT
ejpam-176	41	1	a	a	DET
ejpam-176	41	2	set	set	NOUN
ejpam-176	41	3	a	a	PRON
ejpam-176	41	4	is	be	AUX
ejpam-176	41	5	called	call	VERB
ejpam-176	41	6	β	β	PRON
ejpam-176	41	7	-regular	-regular	ADJ
ejpam-176	41	8	[	[	X
ejpam-176	41	9	7	7	NUM
ejpam-176	41	10	]	]	SYM
ejpam-176	41	11	(=	(=	ADJ
ejpam-176	41	12	sp	sp	NOUN
ejpam-176	41	13	-	-	PUNCT
ejpam-176	41	14	regular	regular	NOUN
ejpam-176	41	15	[	[	X
ejpam-176	41	16	18	18	NUM
ejpam-176	41	17	]	]	SYM
ejpam-176	41	18	)	)	PUNCT
ejpam-176	41	19	if	if	SCONJ
ejpam-176	41	20	its	its	PRON
ejpam-176	41	21	both	both	PRON
ejpam-176	41	22	β	β	X
ejpam-176	41	23	-open	-open	NOUN
ejpam-176	41	24	as	as	ADV
ejpam-176	41	25	well	well	ADV
ejpam-176	41	26	as	as	ADP
ejpam-176	41	27	β	β	X
ejpam-176	41	28	-closed	-close	VERB
ejpam-176	41	29	.	.	PUNCT
ejpam-176	42	1	the	the	DET
ejpam-176	42	2	family	family	NOUN
ejpam-176	42	3	of	of	ADP
ejpam-176	42	4	all	all	DET
ejpam-176	42	5	β	β	X
ejpam-176	42	6	-open	-open	PROPN
ejpam-176	42	7	(	(	PUNCT
ejpam-176	42	8	resp	resp	NOUN
ejpam-176	42	9	.	.	PUNCT
ejpam-176	43	1	β	β	NOUN
ejpam-176	43	2	-regular	-regular	ADJ
ejpam-176	43	3	,	,	PUNCT
ejpam-176	43	4	regular	regular	ADJ
ejpam-176	43	5	open	open	ADJ
ejpam-176	43	6	)	)	PUNCT
ejpam-176	43	7	sets	set	NOUN
ejpam-176	43	8	containing	contain	VERB
ejpam-176	43	9	a	a	DET
ejpam-176	43	10	point	point	NOUN
ejpam-176	43	11	x	x	SYM
ejpam-176	43	12	∈	∈	NOUN
ejpam-176	43	13	x	x	PUNCT
ejpam-176	43	14	is	be	AUX
ejpam-176	43	15	denoted	denote	VERB
ejpam-176	43	16	by	by	ADP
ejpam-176	43	17	βo(x	βo(x	PUNCT
ejpam-176	43	18	,	,	PUNCT
ejpam-176	43	19	x	x	X
ejpam-176	43	20	)	)	PUNCT
ejpam-176	43	21	(	(	PUNCT
ejpam-176	43	22	resp	resp	NOUN
ejpam-176	43	23	.	.	PUNCT
ejpam-176	44	1	βr(x	βr(x	X
ejpam-176	44	2	,	,	PUNCT
ejpam-176	45	1	x	x	X
ejpam-176	45	2	)	)	PUNCT
ejpam-176	45	3	,	,	PUNCT
ejpam-176	45	4	ro(x	ro(x	PUNCT
ejpam-176	45	5	,	,	PUNCT
ejpam-176	45	6	x	x	NOUN
ejpam-176	45	7	)	)	PUNCT
ejpam-176	45	8	)	)	PUNCT
ejpam-176	45	9	.	.	PUNCT
ejpam-176	46	1	the	the	DET
ejpam-176	46	2	family	family	NOUN
ejpam-176	46	3	of	of	ADP
ejpam-176	46	4	all	all	DET
ejpam-176	46	5	β	β	X
ejpam-176	46	6	-open	-open	PROPN
ejpam-176	46	7	(	(	PUNCT
ejpam-176	46	8	resp	resp	NOUN
ejpam-176	46	9	.	.	PUNCT
ejpam-176	47	1	β	β	NOUN
ejpam-176	47	2	-regular	-regular	ADJ
ejpam-176	47	3	,	,	PUNCT
ejpam-176	47	4	regular	regular	ADJ
ejpam-176	47	5	open	open	ADJ
ejpam-176	47	6	)	)	PUNCT
ejpam-176	47	7	sets	set	NOUN
ejpam-176	47	8	in	in	ADP
ejpam-176	47	9	x	x	PUNCT
ejpam-176	47	10	is	be	AUX
ejpam-176	47	11	denoted	denote	VERB
ejpam-176	47	12	by	by	ADP
ejpam-176	47	13	βo(x	βo(x	PUNCT
ejpam-176	47	14	)	)	PUNCT
ejpam-176	47	15	(	(	PUNCT
ejpam-176	47	16	resp	resp	NOUN
ejpam-176	47	17	.	.	PUNCT
ejpam-176	47	18	βr(x	βr(x	PUNCT
ejpam-176	47	19	)	)	PUNCT
ejpam-176	47	20	,	,	PUNCT
ejpam-176	47	21	ro(x	ro(x	NUM
ejpam-176	47	22	)	)	PUNCT
ejpam-176	47	23	)	)	PUNCT
ejpam-176	47	24	.	.	PUNCT
ejpam-176	48	1	a	a	DET
ejpam-176	48	2	point	point	NOUN
ejpam-176	48	3	x	x	PUNCT
ejpam-176	48	4	of	of	ADP
ejpam-176	48	5	x	x	NOUN
ejpam-176	48	6	is	be	AUX
ejpam-176	48	7	in	in	ADP
ejpam-176	48	8	the	the	DET
ejpam-176	48	9	β	β	NOUN
ejpam-176	48	10	-θ	-θ	PUNCT
ejpam-176	48	11	-closure	-closure	PROPN
ejpam-176	48	12	[	[	X
ejpam-176	48	13	7	7	NUM
ejpam-176	48	14	]	]	SYM
ejpam-176	48	15	(=	(=	ADJ
ejpam-176	48	16	sp	sp	NOUN
ejpam-176	48	17	-	-	PUNCT
ejpam-176	48	18	θ	θ	NOUN
ejpam-176	48	19	-closure	-closure	NOUN
ejpam-176	48	20	[	[	X
ejpam-176	48	21	18	18	NUM
ejpam-176	48	22	]	]	PUNCT
ejpam-176	48	23	)	)	PUNCT
ejpam-176	48	24	of	of	ADP
ejpam-176	48	25	a	a	PRON
ejpam-176	48	26	,	,	PUNCT
ejpam-176	48	27	denoted	denote	VERB
ejpam-176	48	28	by	by	ADP
ejpam-176	48	29	x	x	PROPN
ejpam-176	48	30	∈	∈	PROPN
ejpam-176	48	31	β	β	X
ejpam-176	48	32	-θ	-θ	X
ejpam-176	48	33	-cl(a	-cl(a	PROPN
ejpam-176	48	34	)	)	PUNCT
ejpam-176	48	35	(	(	PUNCT
ejpam-176	48	36	resp	resp	NOUN
ejpam-176	48	37	.	.	PUNCT
ejpam-176	49	1	x	x	PUNCT
ejpam-176	49	2	∈sp	∈sp	NUM
ejpam-176	49	3	-	-	PUNCT
ejpam-176	49	4	θ	θ	NOUN
ejpam-176	49	5	-cl(s	-cl(s	NOUN
ejpam-176	49	6	)	)	PUNCT
ejpam-176	49	7	)	)	PUNCT
ejpam-176	50	1	if	if	SCONJ
ejpam-176	50	2	a∩β	a∩β	PRON
ejpam-176	50	3	cl(u	cl(u	NOUN
ejpam-176	50	4	)	)	PUNCT
ejpam-176	50	5	6=	6=	NUM
ejpam-176	50	6	;	;	PUNCT
ejpam-176	50	7	for	for	ADP
ejpam-176	50	8	each	each	DET
ejpam-176	50	9	u	u	PROPN
ejpam-176	50	10	∈	∈	PROPN
ejpam-176	50	11	βo(x	βo(x	PUNCT
ejpam-176	50	12	,	,	PUNCT
ejpam-176	50	13	x	x	X
ejpam-176	50	14	)	)	PUNCT
ejpam-176	50	15	.	.	PUNCT
ejpam-176	51	1	a	a	DET
ejpam-176	51	2	subset	subset	NOUN
ejpam-176	51	3	a	a	PRON
ejpam-176	51	4	is	be	AUX
ejpam-176	51	5	said	say	VERB
ejpam-176	51	6	to	to	PART
ejpam-176	51	7	be	be	AUX
ejpam-176	51	8	β	β	X
ejpam-176	51	9	-θ	-θ	PUNCT
ejpam-176	51	10	-closed	-closed	ADJ
ejpam-176	52	1	[	[	X
ejpam-176	52	2	7	7	NUM
ejpam-176	52	3	]	]	PUNCT
ejpam-176	52	4	(	(	PUNCT
ejpam-176	52	5	or	or	CCONJ
ejpam-176	52	6	sp	sp	NOUN
ejpam-176	52	7	-	-	PUNCT
ejpam-176	52	8	θ	θ	NOUN
ejpam-176	52	9	-closed	-close	VERB
ejpam-176	53	1	[	[	X
ejpam-176	53	2	18	18	NUM
ejpam-176	53	3	]	]	SYM
ejpam-176	53	4	)	)	PUNCT
ejpam-176	53	5	if	if	SCONJ
ejpam-176	53	6	a	a	DET
ejpam-176	53	7	=	=	X
ejpam-176	53	8	β	β	X
ejpam-176	53	9	-θ	-θ	ADJ
ejpam-176	53	10	-cl(a	-cl(a	PROPN
ejpam-176	53	11	)	)	PUNCT
ejpam-176	53	12	or	or	CCONJ
ejpam-176	53	13	a	a	DET
ejpam-176	53	14	=	=	ADJ
ejpam-176	53	15	sp	sp	NOUN
ejpam-176	53	16	-	-	PUNCT
ejpam-176	53	17	θ	θ	NOUN
ejpam-176	53	18	-cl(a	-cl(a	NUM
ejpam-176	53	19	)	)	PUNCT
ejpam-176	53	20	.	.	PUNCT
ejpam-176	54	1	the	the	DET
ejpam-176	54	2	complement	complement	NOUN
ejpam-176	54	3	of	of	ADP
ejpam-176	54	4	a	a	DET
ejpam-176	54	5	β	β	X
ejpam-176	54	6	-θ	-θ	X
ejpam-176	54	7	-closed	-close	VERB
ejpam-176	54	8	or	or	CCONJ
ejpam-176	54	9	sp	sp	NOUN
ejpam-176	54	10	-	-	PUNCT
ejpam-176	54	11	θ	θ	NOUN
ejpam-176	54	12	-closed	-close	VERB
ejpam-176	54	13	set	set	NOUN
ejpam-176	54	14	is	be	AUX
ejpam-176	54	15	said	say	VERB
ejpam-176	54	16	to	to	PART
ejpam-176	54	17	be	be	AUX
ejpam-176	54	18	β	β	X
ejpam-176	54	19	-θ	-θ	PUNCT
ejpam-176	54	20	-open	-open	PROPN
ejpam-176	55	1	[	[	X
ejpam-176	55	2	7	7	NUM
ejpam-176	55	3	]	]	PUNCT
ejpam-176	55	4	or	or	CCONJ
ejpam-176	55	5	sp	sp	NOUN
ejpam-176	55	6	-	-	PUNCT
ejpam-176	55	7	θ	θ	NOUN
ejpam-176	55	8	-open	-open	NOUN
ejpam-176	55	9	[	[	X
ejpam-176	55	10	18	18	NUM
ejpam-176	55	11	]	]	PUNCT
ejpam-176	55	12	.	.	PUNCT
ejpam-176	56	1	the	the	DET
ejpam-176	56	2	family	family	NOUN
ejpam-176	56	3	of	of	ADP
ejpam-176	56	4	all	all	DET
ejpam-176	56	5	β	β	X
ejpam-176	56	6	-θ	-θ	PUNCT
ejpam-176	56	7	-open	-open	ADJ
ejpam-176	56	8	sets	set	NOUN
ejpam-176	56	9	of	of	ADP
ejpam-176	56	10	x	x	SYM
ejpam-176	56	11	is	be	AUX
ejpam-176	56	12	denoted	denote	VERB
ejpam-176	56	13	by	by	ADP
ejpam-176	56	14	β	β	X
ejpam-176	56	15	-θ	-θ	VERB
ejpam-176	56	16	-o(x	-o(x	ADV
ejpam-176	56	17	)	)	PUNCT
ejpam-176	56	18	and	and	CCONJ
ejpam-176	56	19	that	that	SCONJ
ejpam-176	56	20	containing	contain	VERB
ejpam-176	56	21	a	a	DET
ejpam-176	56	22	point	point	NOUN
ejpam-176	56	23	x	x	PUNCT
ejpam-176	56	24	of	of	ADP
ejpam-176	56	25	x	x	PRON
ejpam-176	56	26	is	be	AUX
ejpam-176	56	27	denoted	denote	VERB
ejpam-176	56	28	by	by	ADP
ejpam-176	56	29	β	β	X
ejpam-176	56	30	-θ	-θ	PUNCT
ejpam-176	57	1	-o(x	-o(x	ADV
ejpam-176	57	2	,	,	PUNCT
ejpam-176	57	3	x	x	NOUN
ejpam-176	57	4	)	)	PUNCT
ejpam-176	57	5	.	.	PUNCT
ejpam-176	58	1	a	a	DET
ejpam-176	58	2	filter	filter	NOUN
ejpam-176	58	3	basef	basef	NOUN
ejpam-176	58	4	is	be	AUX
ejpam-176	58	5	said	say	VERB
ejpam-176	58	6	to	to	ADP
ejpam-176	58	7	β	β	X
ejpam-176	58	8	-θ	-θ	PUNCT
ejpam-176	58	9	-adhere	-adhere	PROPN
ejpam-176	58	10	at	at	ADP
ejpam-176	58	11	some	some	DET
ejpam-176	58	12	point	point	NOUN
ejpam-176	58	13	x	x	PUNCT
ejpam-176	58	14	of	of	ADP
ejpam-176	58	15	x	x	PRON
ejpam-176	58	16	if	if	SCONJ
ejpam-176	58	17	x	x	SYM
ejpam-176	58	18	∈	∈	NOUN
ejpam-176	58	19	β	β	X
ejpam-176	58	20	-θ	-θ	PUNCT
ejpam-176	58	21	-cl(f	-cl(f	PROPN
ejpam-176	58	22	)	)	PUNCT
ejpam-176	58	23	for	for	ADP
ejpam-176	58	24	each	each	DET
ejpam-176	58	25	f	f	PROPN
ejpam-176	58	26	∈	∈	PROPN
ejpam-176	58	27	f	f	PROPN
ejpam-176	58	28	and	and	CCONJ
ejpam-176	58	29	is	be	AUX
ejpam-176	58	30	said	say	VERB
ejpam-176	58	31	to	to	ADP
ejpam-176	58	32	β	β	X
ejpam-176	58	33	-θ	-θ	PUNCT
ejpam-176	58	34	-converge	-converge	VERB
ejpam-176	58	35	to	to	ADP
ejpam-176	58	36	a	a	DET
ejpam-176	58	37	point	point	NOUN
ejpam-176	58	38	x	x	PUNCT
ejpam-176	58	39	of	of	ADP
ejpam-176	58	40	x	x	PRON
ejpam-176	58	41	if	if	SCONJ
ejpam-176	58	42	for	for	ADP
ejpam-176	58	43	each	each	DET
ejpam-176	58	44	u	u	PROPN
ejpam-176	58	45	∈	∈	PROPN
ejpam-176	58	46	βo(x	βo(x	PUNCT
ejpam-176	58	47	,	,	PUNCT
ejpam-176	58	48	x	x	X
ejpam-176	58	49	)	)	PUNCT
ejpam-176	58	50	,	,	PUNCT
ejpam-176	58	51	there	there	PRON
ejpam-176	58	52	is	be	VERB
ejpam-176	58	53	an	an	DET
ejpam-176	58	54	f	f	PROPN
ejpam-176	58	55	∈	∈	PROPN
ejpam-176	58	56	f	f	PROPN
ejpam-176	58	57	such	such	ADJ
ejpam-176	58	58	that	that	SCONJ
ejpam-176	58	59	f	f	PROPN
ejpam-176	58	60	⊂	⊂	X
ejpam-176	58	61	β	β	X
ejpam-176	58	62	cl(u	cl(u	PROPN
ejpam-176	58	63	)	)	PUNCT
ejpam-176	58	64	.	.	PUNCT
ejpam-176	59	1	a	a	DET
ejpam-176	59	2	subset	subset	NOUN
ejpam-176	59	3	is	be	AUX
ejpam-176	59	4	said	say	VERB
ejpam-176	59	5	to	to	PART
ejpam-176	59	6	be	be	AUX
ejpam-176	59	7	an	an	DET
ejpam-176	59	8	n	n	ADV
ejpam-176	59	9	c	c	NOUN
ejpam-176	59	10	-	-	PUNCT
ejpam-176	59	11	set	set	VERB
ejpam-176	59	12	[	[	X
ejpam-176	59	13	22	22	NUM
ejpam-176	59	14	]	]	PUNCT
ejpam-176	59	15	if	if	SCONJ
ejpam-176	59	16	every	every	DET
ejpam-176	59	17	cover	cover	NOUN
ejpam-176	59	18	of	of	ADP
ejpam-176	59	19	a	a	PRON
ejpam-176	59	20	by	by	ADP
ejpam-176	59	21	regular	regular	ADJ
ejpam-176	59	22	open	open	ADJ
ejpam-176	59	23	sets	set	NOUN
ejpam-176	59	24	c.	c.	PROPN
ejpam-176	59	25	basu	basu	PROPN
ejpam-176	59	26	and	and	CCONJ
ejpam-176	59	27	m.	m.	PROPN
ejpam-176	59	28	ghosh	ghosh	PROPN
ejpam-176	59	29	/	/	PUNCT
ejpam-176	59	30	eur	eur	PROPN
ejpam-176	59	31	.	.	PUNCT
ejpam-176	60	1	j.	j.	PROPN
ejpam-176	60	2	pure	pure	PROPN
ejpam-176	60	3	appl	appl	PROPN
ejpam-176	60	4	.	.	PROPN
ejpam-176	60	5	math	math	PROPN
ejpam-176	60	6	,	,	PUNCT
ejpam-176	60	7	2	2	NUM
ejpam-176	60	8	(	(	PUNCT
ejpam-176	60	9	2009	2009	NUM
ejpam-176	60	10	)	)	PUNCT
ejpam-176	60	11	,	,	PUNCT
ejpam-176	60	12	(	(	PUNCT
ejpam-176	60	13	85	85	NUM
ejpam-176	60	14	-	-	SYM
ejpam-176	60	15	96	96	NUM
ejpam-176	60	16	)	)	PUNCT
ejpam-176	60	17	87	87	NUM
ejpam-176	60	18	of	of	ADP
ejpam-176	60	19	x	x	PUNCT
ejpam-176	60	20	has	have	VERB
ejpam-176	60	21	a	a	DET
ejpam-176	60	22	finite	finite	ADJ
ejpam-176	60	23	subcover	subcover	PROPN
ejpam-176	60	24	.	.	PUNCT
ejpam-176	61	1	we	we	PRON
ejpam-176	61	2	state	state	VERB
ejpam-176	61	3	the	the	DET
ejpam-176	61	4	following	follow	VERB
ejpam-176	61	5	results	result	NOUN
ejpam-176	61	6	which	which	PRON
ejpam-176	61	7	will	will	AUX
ejpam-176	61	8	be	be	AUX
ejpam-176	61	9	frequently	frequently	ADV
ejpam-176	61	10	used	use	VERB
ejpam-176	61	11	in	in	ADP
ejpam-176	61	12	the	the	DET
ejpam-176	61	13	sequel	sequel	NOUN
ejpam-176	61	14	.	.	PUNCT
ejpam-176	62	1	lemma	lemma	PROPN
ejpam-176	62	2	2.1	2.1	NUM
ejpam-176	62	3	(	(	PUNCT
ejpam-176	62	4	t.	t.	NOUN
ejpam-176	62	5	noiri	noiri	NOUN
ejpam-176	63	1	[	[	X
ejpam-176	63	2	18	18	NUM
ejpam-176	63	3	]	]	PUNCT
ejpam-176	63	4	,	,	PUNCT
ejpam-176	63	5	basu	basu	PROPN
ejpam-176	63	6	and	and	CCONJ
ejpam-176	63	7	ghosh	ghosh	PROPN
ejpam-176	64	1	[	[	X
ejpam-176	64	2	7	7	NUM
ejpam-176	64	3	]	]	NUM
ejpam-176	64	4	)	)	PUNCT
ejpam-176	64	5	.	.	PUNCT
ejpam-176	65	1	the	the	DET
ejpam-176	65	2	following	follow	VERB
ejpam-176	65	3	hold	hold	NOUN
ejpam-176	65	4	for	for	ADP
ejpam-176	65	5	a	a	DET
ejpam-176	65	6	subset	subset	NOUN
ejpam-176	65	7	a	a	PRON
ejpam-176	65	8	of	of	ADP
ejpam-176	65	9	a	a	DET
ejpam-176	65	10	space	space	NOUN
ejpam-176	65	11	x	x	X
ejpam-176	65	12	:	:	PUNCT
ejpam-176	65	13	1	1	X
ejpam-176	65	14	.	.	X
ejpam-176	65	15	a∈	a∈	PROPN
ejpam-176	65	16	βo(x	βo(x	PUNCT
ejpam-176	65	17	)	)	PUNCT
ejpam-176	65	18	if	if	SCONJ
ejpam-176	65	19	and	and	CCONJ
ejpam-176	65	20	only	only	ADV
ejpam-176	65	21	if	if	SCONJ
ejpam-176	65	22	β	β	X
ejpam-176	65	23	cl(a	cl(a	X
ejpam-176	65	24	)	)	PUNCT
ejpam-176	65	25	∈	∈	PROPN
ejpam-176	65	26	βr(x	βr(x	PUNCT
ejpam-176	65	27	)	)	PUNCT
ejpam-176	65	28	.	.	PUNCT
ejpam-176	66	1	2	2	X
ejpam-176	66	2	.	.	X
ejpam-176	66	3	β	β	X
ejpam-176	66	4	-θ	-θ	PUNCT
ejpam-176	66	5	-cl(a	-cl(a	X
ejpam-176	66	6	)	)	PUNCT
ejpam-176	66	7	=	=	VERB
ejpam-176	67	1	∩{v	∩{v	NOUN
ejpam-176	67	2	:	:	PUNCT
ejpam-176	67	3	a⊂	a⊂	X
ejpam-176	67	4	v	v	NOUN
ejpam-176	67	5	:	:	PUNCT
ejpam-176	67	6	and	and	CCONJ
ejpam-176	67	7	v	v	ADP
ejpam-176	67	8	∈	∈	PROPN
ejpam-176	67	9	βr(x	βr(x	PUNCT
ejpam-176	67	10	)	)	PUNCT
ejpam-176	67	11	}	}	PUNCT
ejpam-176	67	12	.	.	PUNCT
ejpam-176	68	1	3	3	X
ejpam-176	68	2	.	.	X
ejpam-176	68	3	x	x	SYM
ejpam-176	68	4	∈	∈	PROPN
ejpam-176	68	5	β	β	X
ejpam-176	68	6	-θ	-θ	X
ejpam-176	68	7	-cl(a	-cl(a	X
ejpam-176	68	8	)	)	PUNCT
ejpam-176	68	9	if	if	SCONJ
ejpam-176	68	10	and	and	CCONJ
ejpam-176	68	11	only	only	ADV
ejpam-176	68	12	if	if	SCONJ
ejpam-176	68	13	a∩	a∩	PROPN
ejpam-176	68	14	v	v	ADP
ejpam-176	68	15	6=	6=	NUM
ejpam-176	68	16	;	;	PUNCT
ejpam-176	68	17	for	for	ADP
ejpam-176	68	18	each	each	DET
ejpam-176	68	19	v	v	X
ejpam-176	68	20	∈	∈	PROPN
ejpam-176	68	21	βr(x	βr(x	PUNCT
ejpam-176	68	22	,	,	PUNCT
ejpam-176	68	23	x	x	X
ejpam-176	68	24	)	)	PUNCT
ejpam-176	68	25	.	.	PUNCT
ejpam-176	69	1	4	4	X
ejpam-176	69	2	.	.	X
ejpam-176	69	3	if	if	SCONJ
ejpam-176	69	4	a⊂	a⊂	NOUN
ejpam-176	69	5	b	b	NOUN
ejpam-176	69	6	,	,	PUNCT
ejpam-176	69	7	then	then	ADV
ejpam-176	69	8	β	β	X
ejpam-176	69	9	-θ	-θ	PROPN
ejpam-176	69	10	-cl(a	-cl(a	X
ejpam-176	69	11	)	)	PUNCT
ejpam-176	69	12	⊂	⊂	PROPN
ejpam-176	69	13	β	β	X
ejpam-176	69	14	-θ	-θ	PUNCT
ejpam-176	69	15	-cl(b	-cl(b	PROPN
ejpam-176	69	16	)	)	PUNCT
ejpam-176	69	17	.	.	PUNCT
ejpam-176	70	1	5	5	X
ejpam-176	70	2	.	.	X
ejpam-176	70	3	β	β	X
ejpam-176	70	4	-θ	-θ	PUNCT
ejpam-176	70	5	-cl(β	-cl(β	PUNCT
ejpam-176	70	6	-θ	-θ	PUNCT
ejpam-176	70	7	-cl(a	-cl(a	NUM
ejpam-176	70	8	)	)	PUNCT
ejpam-176	70	9	)	)	PUNCT
ejpam-176	71	1	=	=	PUNCT
ejpam-176	71	2	β	β	X
ejpam-176	71	3	-θ	-θ	PUNCT
ejpam-176	71	4	-cl(a	-cl(a	PROPN
ejpam-176	71	5	)	)	PUNCT
ejpam-176	71	6	.	.	PUNCT
ejpam-176	72	1	6	6	X
ejpam-176	72	2	.	.	X
ejpam-176	72	3	a∈	a∈	PROPN
ejpam-176	72	4	β	β	X
ejpam-176	73	1	-θ	-θ	PUNCT
ejpam-176	73	2	-o(x	-o(x	ADV
ejpam-176	73	3	)	)	PUNCT
ejpam-176	73	4	if	if	SCONJ
ejpam-176	73	5	and	and	CCONJ
ejpam-176	73	6	only	only	ADV
ejpam-176	73	7	if	if	SCONJ
ejpam-176	73	8	for	for	ADP
ejpam-176	73	9	each	each	DET
ejpam-176	73	10	x	x	SYM
ejpam-176	73	11	∈	∈	PROPN
ejpam-176	73	12	a	a	PRON
ejpam-176	73	13	,	,	PUNCT
ejpam-176	73	14	there	there	PRON
ejpam-176	73	15	exists	exist	VERB
ejpam-176	73	16	a	a	DET
ejpam-176	73	17	v	v	NOUN
ejpam-176	73	18	∈	∈	NOUN
ejpam-176	73	19	βr(x	βr(x	PUNCT
ejpam-176	73	20	,	,	PUNCT
ejpam-176	73	21	x	x	X
ejpam-176	73	22	)	)	PUNCT
ejpam-176	73	23	such	such	ADJ
ejpam-176	73	24	that	that	SCONJ
ejpam-176	73	25	x	x	SYM
ejpam-176	73	26	∈	∈	PROPN
ejpam-176	73	27	v	v	ADP
ejpam-176	73	28	⊂	⊂	PROPN
ejpam-176	73	29	a.	a.	NOUN
ejpam-176	73	30	7	7	NUM
ejpam-176	73	31	.	.	PUNCT
ejpam-176	74	1	β	β	X
ejpam-176	74	2	-θ	-θ	PUNCT
ejpam-176	74	3	-cl(a	-cl(a	X
ejpam-176	74	4	)	)	PUNCT
ejpam-176	74	5	is	be	AUX
ejpam-176	74	6	a	a	DET
ejpam-176	74	7	β	β	X
ejpam-176	74	8	-θ	-θ	PUNCT
ejpam-176	74	9	-closed	-close	VERB
ejpam-176	74	10	set	set	NOUN
ejpam-176	74	11	and	and	CCONJ
ejpam-176	74	12	union	union	NOUN
ejpam-176	74	13	of	of	ADP
ejpam-176	74	14	even	even	ADV
ejpam-176	74	15	two	two	NUM
ejpam-176	74	16	β	β	X
ejpam-176	74	17	-θ	-θ	PUNCT
ejpam-176	74	18	-closed	-close	VERB
ejpam-176	74	19	sets	set	NOUN
ejpam-176	74	20	is	be	AUX
ejpam-176	74	21	not	not	PART
ejpam-176	74	22	necessarily	necessarily	ADV
ejpam-176	74	23	a	a	DET
ejpam-176	74	24	β	β	X
ejpam-176	74	25	-θ	-θ	PUNCT
ejpam-176	74	26	closed	closed	ADJ
ejpam-176	74	27	set	set	NOUN
ejpam-176	74	28	.	.	PUNCT
ejpam-176	75	1	8	8	X
ejpam-176	75	2	.	.	X
ejpam-176	76	1	if	if	SCONJ
ejpam-176	76	2	a∈	a∈	PROPN
ejpam-176	76	3	βo(x	βo(x	PUNCT
ejpam-176	76	4	)	)	PUNCT
ejpam-176	76	5	,	,	PUNCT
ejpam-176	76	6	then	then	ADV
ejpam-176	76	7	β	β	X
ejpam-176	76	8	cl(a	cl(a	X
ejpam-176	76	9	)	)	PUNCT
ejpam-176	76	10	=	=	PUNCT
ejpam-176	76	11	β	β	X
ejpam-176	76	12	-θ	-θ	PUNCT
ejpam-176	76	13	-cl(a	-cl(a	PROPN
ejpam-176	76	14	)	)	PUNCT
ejpam-176	76	15	.	.	PUNCT
ejpam-176	77	1	9	9	X
ejpam-176	77	2	.	.	X
ejpam-176	77	3	a∈	a∈	PROPN
ejpam-176	77	4	βr(x	βr(x	PUNCT
ejpam-176	77	5	)	)	PUNCT
ejpam-176	77	6	if	if	SCONJ
ejpam-176	77	7	and	and	CCONJ
ejpam-176	77	8	only	only	ADV
ejpam-176	77	9	if	if	SCONJ
ejpam-176	77	10	a	a	PRON
ejpam-176	77	11	is	be	AUX
ejpam-176	77	12	β	β	X
ejpam-176	77	13	-θ	-θ	PUNCT
ejpam-176	77	14	-open	-open	ADJ
ejpam-176	77	15	and	and	CCONJ
ejpam-176	77	16	β	β	X
ejpam-176	77	17	-θ	-θ	X
ejpam-176	77	18	-closed	-closed	PROPN
ejpam-176	77	19	.	.	PUNCT
ejpam-176	77	20	10	10	NUM
ejpam-176	77	21	.	.	PUNCT
ejpam-176	78	1	β	β	NOUN
ejpam-176	78	2	-regular⇒	-regular⇒	X
ejpam-176	79	1	β	β	X
ejpam-176	79	2	-θ	-θ	PUNCT
ejpam-176	79	3	-open⇒	-open⇒	PUNCT
ejpam-176	79	4	β	β	X
ejpam-176	79	5	-open	-open	PROPN
ejpam-176	79	6	.	.	PUNCT
ejpam-176	80	1	but	but	CCONJ
ejpam-176	80	2	the	the	DET
ejpam-176	80	3	converses	converse	NOUN
ejpam-176	80	4	are	be	AUX
ejpam-176	80	5	not	not	PART
ejpam-176	80	6	necessarily	necessarily	ADV
ejpam-176	80	7	true	true	ADJ
ejpam-176	80	8	.	.	PUNCT
ejpam-176	81	1	3	3	X
ejpam-176	81	2	.	.	X
ejpam-176	81	3	β	β	NOUN
ejpam-176	81	4	-closed	-close	VERB
ejpam-176	81	5	subsets	subset	NOUN
ejpam-176	81	6	and	and	CCONJ
ejpam-176	81	7	β	β	X
ejpam-176	81	8	-θ	-θ	PUNCT
ejpam-176	81	9	-closed	-close	VERB
ejpam-176	81	10	functions	function	NOUN
ejpam-176	81	11	definition	definition	NOUN
ejpam-176	81	12	3.1	3.1	NUM
ejpam-176	81	13	.	.	PUNCT
ejpam-176	82	1	a	a	DET
ejpam-176	82	2	subset	subset	NOUN
ejpam-176	82	3	s	s	NOUN
ejpam-176	82	4	of	of	ADP
ejpam-176	82	5	a	a	DET
ejpam-176	82	6	topological	topological	ADJ
ejpam-176	82	7	space	space	NOUN
ejpam-176	82	8	x	x	PRON
ejpam-176	82	9	is	be	AUX
ejpam-176	82	10	said	say	VERB
ejpam-176	82	11	to	to	PART
ejpam-176	82	12	be	be	AUX
ejpam-176	82	13	β	β	X
ejpam-176	82	14	-closed	-close	VERB
ejpam-176	82	15	relative	relative	ADJ
ejpam-176	82	16	to	to	ADP
ejpam-176	82	17	x	x	SYM
ejpam-176	82	18	(	(	PUNCT
ejpam-176	82	19	β	β	X
ejpam-176	82	20	-set	-set	NUM
ejpam-176	82	21	,	,	PUNCT
ejpam-176	82	22	for	for	ADP
ejpam-176	82	23	short	short	ADJ
ejpam-176	82	24	)	)	PUNCT
ejpam-176	82	25	if	if	SCONJ
ejpam-176	82	26	for	for	ADP
ejpam-176	82	27	every	every	DET
ejpam-176	82	28	cover	cover	NOUN
ejpam-176	82	29	{	{	PUNCT
ejpam-176	82	30	vα	vα	X
ejpam-176	82	31	:	:	PUNCT
ejpam-176	82	32	α	α	PROPN
ejpam-176	82	33	∈	∈	PROPN
ejpam-176	83	1	i	i	X
ejpam-176	83	2	}	}	PUNCT
ejpam-176	83	3	of	of	ADP
ejpam-176	83	4	s	s	PRON
ejpam-176	83	5	by	by	ADP
ejpam-176	83	6	β	β	X
ejpam-176	83	7	-open	-open	NOUN
ejpam-176	83	8	sets	set	NOUN
ejpam-176	83	9	in	in	ADP
ejpam-176	83	10	x	x	X
ejpam-176	83	11	,	,	PUNCT
ejpam-176	83	12	there	there	PRON
ejpam-176	83	13	exists	exist	VERB
ejpam-176	83	14	a	a	DET
ejpam-176	83	15	finite	finite	NOUN
ejpam-176	83	16	subset	subset	VERB
ejpam-176	83	17	i0	i0	PROPN
ejpam-176	83	18	of	of	ADP
ejpam-176	83	19	i	i	PRON
ejpam-176	83	20	such	such	ADJ
ejpam-176	83	21	that	that	DET
ejpam-176	83	22	s	s	PROPN
ejpam-176	83	23	⊂	⊂	PROPN
ejpam-176	83	24	∪{β	∪{β	PROPN
ejpam-176	83	25	cl(vα	cl(vα	PROPN
ejpam-176	83	26	)	)	PUNCT
ejpam-176	83	27	:	:	PUNCT
ejpam-176	84	1	α	α	PROPN
ejpam-176	84	2	∈	∈	PROPN
ejpam-176	84	3	i0	i0	PROPN
ejpam-176	84	4	}	}	PUNCT
ejpam-176	84	5	.	.	PUNCT
ejpam-176	85	1	if	if	SCONJ
ejpam-176	85	2	in	in	ADP
ejpam-176	85	3	particular	particular	ADJ
ejpam-176	85	4	,	,	PUNCT
ejpam-176	85	5	if	if	SCONJ
ejpam-176	85	6	s	s	VERB
ejpam-176	85	7	=	=	NOUN
ejpam-176	85	8	x	x	X
ejpam-176	85	9	and	and	CCONJ
ejpam-176	85	10	s	s	VERB
ejpam-176	85	11	is	be	AUX
ejpam-176	85	12	β	β	AUX
ejpam-176	85	13	-closed	-close	VERB
ejpam-176	85	14	relative	relative	ADJ
ejpam-176	85	15	to	to	ADP
ejpam-176	85	16	x	x	SYM
ejpam-176	85	17	then	then	ADV
ejpam-176	85	18	x	x	X
ejpam-176	85	19	is	be	AUX
ejpam-176	85	20	β	β	X
ejpam-176	85	21	-closed	-close	VERB
ejpam-176	85	22	[	[	X
ejpam-176	85	23	7	7	NUM
ejpam-176	85	24	]	]	PUNCT
ejpam-176	85	25	.	.	PUNCT
ejpam-176	86	1	it	it	PRON
ejpam-176	86	2	is	be	AUX
ejpam-176	86	3	not	not	PART
ejpam-176	86	4	hard	hard	ADJ
ejpam-176	86	5	to	to	PART
ejpam-176	86	6	prove	prove	VERB
ejpam-176	86	7	the	the	DET
ejpam-176	86	8	theorem	theorem	ADJ
ejpam-176	86	9	3.2	3.2	NUM
ejpam-176	86	10	that	that	PRON
ejpam-176	86	11	gives	give	VERB
ejpam-176	86	12	several	several	ADJ
ejpam-176	86	13	characterizations	characterization	NOUN
ejpam-176	86	14	of	of	ADP
ejpam-176	86	15	a	a	DET
ejpam-176	86	16	subset	subset	NOUN
ejpam-176	86	17	of	of	ADP
ejpam-176	86	18	a	a	DET
ejpam-176	86	19	space	space	NOUN
ejpam-176	86	20	x	x	PUNCT
ejpam-176	86	21	which	which	PRON
ejpam-176	86	22	is	be	AUX
ejpam-176	86	23	β	β	AUX
ejpam-176	86	24	-closed	-close	VERB
ejpam-176	86	25	relative	relative	ADJ
ejpam-176	86	26	to	to	ADP
ejpam-176	86	27	x	x	PUNCT
ejpam-176	86	28	and	and	CCONJ
ejpam-176	86	29	will	will	AUX
ejpam-176	86	30	be	be	AUX
ejpam-176	86	31	utilized	utilize	VERB
ejpam-176	86	32	in	in	ADP
ejpam-176	86	33	establishing	establish	VERB
ejpam-176	86	34	several	several	ADJ
ejpam-176	86	35	results	result	NOUN
ejpam-176	86	36	.	.	PUNCT
ejpam-176	87	1	theorem	theorem	VERB
ejpam-176	87	2	3.1	3.1	NUM
ejpam-176	87	3	.	.	PUNCT
ejpam-176	88	1	for	for	ADP
ejpam-176	88	2	a	a	DET
ejpam-176	88	3	non	non	ADJ
ejpam-176	88	4	-	-	ADJ
ejpam-176	88	5	void	void	ADJ
ejpam-176	88	6	subset	subset	NOUN
ejpam-176	88	7	s	s	NOUN
ejpam-176	88	8	of	of	ADP
ejpam-176	88	9	a	a	DET
ejpam-176	88	10	space	space	NOUN
ejpam-176	88	11	,	,	PUNCT
ejpam-176	88	12	the	the	DET
ejpam-176	88	13	following	follow	VERB
ejpam-176	88	14	are	be	AUX
ejpam-176	88	15	equivalent	equivalent	ADJ
ejpam-176	88	16	:	:	PUNCT
ejpam-176	88	17	(	(	PUNCT
ejpam-176	88	18	a	a	X
ejpam-176	88	19	)	)	PUNCT
ejpam-176	88	20	s	s	VERB
ejpam-176	88	21	is	be	AUX
ejpam-176	88	22	β	β	AUX
ejpam-176	88	23	-closed	-close	VERB
ejpam-176	88	24	relative	relative	ADJ
ejpam-176	88	25	to	to	ADP
ejpam-176	88	26	x	x	PROPN
ejpam-176	88	27	.	.	PUNCT
ejpam-176	89	1	(	(	PUNCT
ejpam-176	89	2	b	b	X
ejpam-176	89	3	)	)	PUNCT
ejpam-176	89	4	every	every	DET
ejpam-176	89	5	filter	filter	NOUN
ejpam-176	89	6	base	base	NOUN
ejpam-176	89	7	on	on	ADP
ejpam-176	89	8	x	x	PUNCT
ejpam-176	89	9	which	which	PRON
ejpam-176	89	10	meets	meet	VERB
ejpam-176	89	11	s	s	PROPN
ejpam-176	89	12	,	,	PUNCT
ejpam-176	89	13	β	β	X
ejpam-176	89	14	-θ	-θ	PUNCT
ejpam-176	89	15	-adheres	-adhere	NOUN
ejpam-176	89	16	at	at	ADP
ejpam-176	89	17	some	some	DET
ejpam-176	89	18	point	point	NOUN
ejpam-176	89	19	of	of	ADP
ejpam-176	89	20	s.	s.	PROPN
ejpam-176	89	21	c.	c.	PROPN
ejpam-176	89	22	basu	basu	PROPN
ejpam-176	89	23	and	and	CCONJ
ejpam-176	89	24	m.	m.	PROPN
ejpam-176	89	25	ghosh	ghosh	PROPN
ejpam-176	89	26	/	/	PUNCT
ejpam-176	89	27	eur	eur	PROPN
ejpam-176	89	28	.	.	PUNCT
ejpam-176	90	1	j.	j.	PROPN
ejpam-176	90	2	pure	pure	PROPN
ejpam-176	90	3	appl	appl	PROPN
ejpam-176	90	4	.	.	PROPN
ejpam-176	90	5	math	math	PROPN
ejpam-176	90	6	,	,	PUNCT
ejpam-176	90	7	2	2	NUM
ejpam-176	90	8	(	(	PUNCT
ejpam-176	90	9	2009	2009	NUM
ejpam-176	90	10	)	)	PUNCT
ejpam-176	90	11	,	,	PUNCT
ejpam-176	90	12	(	(	PUNCT
ejpam-176	90	13	85	85	NUM
ejpam-176	90	14	-	-	SYM
ejpam-176	90	15	96	96	NUM
ejpam-176	90	16	)	)	PUNCT
ejpam-176	90	17	88	88	NUM
ejpam-176	90	18	(	(	PUNCT
ejpam-176	90	19	c	c	NOUN
ejpam-176	90	20	)	)	PUNCT
ejpam-176	90	21	every	every	DET
ejpam-176	90	22	maximal	maximal	ADJ
ejpam-176	90	23	filter	filter	NOUN
ejpam-176	90	24	base	base	NOUN
ejpam-176	90	25	on	on	ADP
ejpam-176	90	26	x	x	PUNCT
ejpam-176	90	27	which	which	PRON
ejpam-176	90	28	meets	meet	VERB
ejpam-176	90	29	s	s	PROPN
ejpam-176	90	30	,	,	PUNCT
ejpam-176	90	31	β	β	X
ejpam-176	90	32	-θ	-θ	PUNCT
ejpam-176	90	33	-converges	-converge	NOUN
ejpam-176	90	34	to	to	ADP
ejpam-176	90	35	some	some	DET
ejpam-176	90	36	point	point	NOUN
ejpam-176	90	37	of	of	ADP
ejpam-176	90	38	s.	s.	PROPN
ejpam-176	90	39	(	(	PUNCT
ejpam-176	90	40	d	d	X
ejpam-176	90	41	)	)	PUNCT
ejpam-176	90	42	every	every	DET
ejpam-176	90	43	cover	cover	NOUN
ejpam-176	90	44	of	of	ADP
ejpam-176	90	45	s	s	PRON
ejpam-176	90	46	by	by	ADP
ejpam-176	90	47	β	β	X
ejpam-176	90	48	-θ	-θ	PUNCT
ejpam-176	90	49	-open	-open	ADJ
ejpam-176	90	50	sets	set	NOUN
ejpam-176	90	51	of	of	ADP
ejpam-176	90	52	x	x	PUNCT
ejpam-176	90	53	has	have	VERB
ejpam-176	90	54	a	a	DET
ejpam-176	90	55	finite	finite	ADJ
ejpam-176	90	56	subcover	subcover	PROPN
ejpam-176	90	57	.	.	PUNCT
ejpam-176	91	1	(	(	PUNCT
ejpam-176	91	2	e	e	X
ejpam-176	91	3	)	)	PUNCT
ejpam-176	91	4	every	every	DET
ejpam-176	91	5	cover	cover	NOUN
ejpam-176	91	6	of	of	ADP
ejpam-176	91	7	s	s	PRON
ejpam-176	91	8	by	by	ADP
ejpam-176	91	9	β	β	NOUN
ejpam-176	91	10	-regular	-regular	ADJ
ejpam-176	91	11	sets	set	NOUN
ejpam-176	91	12	of	of	ADP
ejpam-176	91	13	x	x	PUNCT
ejpam-176	91	14	has	have	VERB
ejpam-176	91	15	a	a	DET
ejpam-176	91	16	finite	finite	ADJ
ejpam-176	91	17	subcover	subcover	PROPN
ejpam-176	91	18	.	.	PUNCT
ejpam-176	92	1	(	(	PUNCT
ejpam-176	92	2	f	f	X
ejpam-176	92	3	)	)	PUNCT
ejpam-176	92	4	for	for	ADP
ejpam-176	92	5	every	every	DET
ejpam-176	92	6	family	family	NOUN
ejpam-176	92	7	{	{	PUNCT
ejpam-176	92	8	uα	uα	NOUN
ejpam-176	92	9	:	:	PUNCT
ejpam-176	92	10	α	α	PROPN
ejpam-176	92	11	∈	∈	PROPN
ejpam-176	93	1	i	i	X
ejpam-176	93	2	}	}	PUNCT
ejpam-176	93	3	of	of	ADP
ejpam-176	93	4	β	β	X
ejpam-176	93	5	-regular	-regular	ADJ
ejpam-176	93	6	sets	set	NOUN
ejpam-176	93	7	of	of	ADP
ejpam-176	93	8	x	x	PUNCT
ejpam-176	93	9	with	with	ADP
ejpam-176	93	10	[	[	X
ejpam-176	93	11	∩α∈i	∩α∈i	NOUN
ejpam-176	93	12	uα	uα	PROPN
ejpam-176	93	13	]	]	X
ejpam-176	93	14	∩	∩	X
ejpam-176	93	15	s	s	PART
ejpam-176	93	16	=	=	PUNCT
ejpam-176	93	17	;	;	PUNCT
ejpam-176	93	18	,	,	PUNCT
ejpam-176	93	19	there	there	PRON
ejpam-176	93	20	is	be	VERB
ejpam-176	93	21	a	a	DET
ejpam-176	93	22	finite	finite	NOUN
ejpam-176	93	23	subset	subset	NOUN
ejpam-176	93	24	i0	i0	PROPN
ejpam-176	93	25	of	of	ADP
ejpam-176	93	26	i	i	PRON
ejpam-176	93	27	such	such	ADJ
ejpam-176	93	28	that	that	SCONJ
ejpam-176	94	1	[	[	X
ejpam-176	94	2	∩α∈i0	∩α∈i0	X
ejpam-176	94	3	uα]∩	uα]∩	NOUN
ejpam-176	94	4	s	s	PART
ejpam-176	94	5	=	=	PUNCT
ejpam-176	94	6	;	;	PUNCT
ejpam-176	94	7	.	.	PUNCT
ejpam-176	95	1	(	(	PUNCT
ejpam-176	95	2	g	g	NOUN
ejpam-176	95	3	)	)	PUNCT
ejpam-176	95	4	every	every	DET
ejpam-176	95	5	filter	filter	NOUN
ejpam-176	95	6	base	base	NOUN
ejpam-176	95	7	on	on	ADP
ejpam-176	95	8	s	s	PROPN
ejpam-176	95	9	,	,	PUNCT
ejpam-176	95	10	β	β	X
ejpam-176	95	11	-θ	-θ	PUNCT
ejpam-176	95	12	-adheres	-adhere	NOUN
ejpam-176	95	13	to	to	ADP
ejpam-176	95	14	some	some	DET
ejpam-176	95	15	point	point	NOUN
ejpam-176	95	16	of	of	ADP
ejpam-176	95	17	s.	s.	PROPN
ejpam-176	95	18	(	(	PUNCT
ejpam-176	95	19	h	h	NOUN
ejpam-176	95	20	)	)	PUNCT
ejpam-176	95	21	every	every	DET
ejpam-176	95	22	maximal	maximal	ADJ
ejpam-176	95	23	filter	filter	NOUN
ejpam-176	95	24	base	base	NOUN
ejpam-176	95	25	on	on	ADP
ejpam-176	95	26	s	s	PROPN
ejpam-176	95	27	,	,	PUNCT
ejpam-176	95	28	β	β	X
ejpam-176	95	29	-θ	-θ	PUNCT
ejpam-176	95	30	-converges	-converge	NOUN
ejpam-176	95	31	to	to	ADP
ejpam-176	95	32	some	some	DET
ejpam-176	95	33	point	point	NOUN
ejpam-176	95	34	of	of	ADP
ejpam-176	95	35	s.	s.	PROPN
ejpam-176	95	36	theorem	theorem	VERB
ejpam-176	95	37	3.2	3.2	NUM
ejpam-176	95	38	.	.	PUNCT
ejpam-176	96	1	for	for	ADP
ejpam-176	96	2	a	a	DET
ejpam-176	96	3	space	space	NOUN
ejpam-176	96	4	x	x	SYM
ejpam-176	96	5	,	,	PUNCT
ejpam-176	96	6	the	the	DET
ejpam-176	96	7	following	follow	VERB
ejpam-176	96	8	are	be	AUX
ejpam-176	96	9	equivalent	equivalent	ADJ
ejpam-176	96	10	:	:	PUNCT
ejpam-176	96	11	(	(	PUNCT
ejpam-176	96	12	a	a	X
ejpam-176	96	13	)	)	PUNCT
ejpam-176	96	14	x	x	X
ejpam-176	96	15	is	be	AUX
ejpam-176	96	16	β	β	X
ejpam-176	96	17	-closed	-close	VERB
ejpam-176	96	18	.	.	PUNCT
ejpam-176	97	1	(	(	PUNCT
ejpam-176	97	2	b	b	X
ejpam-176	97	3	)	)	PUNCT
ejpam-176	97	4	every	every	DET
ejpam-176	97	5	proper	proper	ADJ
ejpam-176	97	6	β	β	X
ejpam-176	97	7	-θ	-θ	X
ejpam-176	97	8	-closed	-close	VERB
ejpam-176	97	9	set	set	NOUN
ejpam-176	97	10	is	be	AUX
ejpam-176	97	11	β	β	AUX
ejpam-176	97	12	-closed	-close	VERB
ejpam-176	97	13	relative	relative	ADJ
ejpam-176	97	14	to	to	ADP
ejpam-176	97	15	x	x	PROPN
ejpam-176	97	16	.	.	PUNCT
ejpam-176	98	1	(	(	PUNCT
ejpam-176	98	2	c	c	X
ejpam-176	98	3	)	)	PUNCT
ejpam-176	98	4	every	every	DET
ejpam-176	98	5	proper	proper	ADJ
ejpam-176	98	6	β	β	SYM
ejpam-176	98	7	-regular	-regular	ADJ
ejpam-176	98	8	set	set	NOUN
ejpam-176	98	9	is	be	AUX
ejpam-176	98	10	β	β	AUX
ejpam-176	98	11	-closed	-close	VERB
ejpam-176	98	12	relative	relative	ADJ
ejpam-176	98	13	to	to	ADP
ejpam-176	98	14	x	x	X
ejpam-176	98	15	.	.	PUNCT
ejpam-176	99	1	proof	proof	NOUN
ejpam-176	99	2	:	:	PUNCT
ejpam-176	99	3	(	(	PUNCT
ejpam-176	99	4	a)⇒	a)⇒	PROPN
ejpam-176	99	5	(	(	PUNCT
ejpam-176	99	6	b	b	NOUN
ejpam-176	99	7	)	)	PUNCT
ejpam-176	99	8	:	:	PUNCT
ejpam-176	99	9	let	let	VERB
ejpam-176	99	10	{	{	PUNCT
ejpam-176	99	11	uα	uα	NOUN
ejpam-176	99	12	:	:	PUNCT
ejpam-176	99	13	α	α	PROPN
ejpam-176	99	14	∈	∈	PROPN
ejpam-176	100	1	i	i	PRON
ejpam-176	100	2	}	}	PUNCT
ejpam-176	100	3	be	be	VERB
ejpam-176	100	4	a	a	DET
ejpam-176	100	5	cover	cover	NOUN
ejpam-176	100	6	of	of	ADP
ejpam-176	100	7	a	a	DET
ejpam-176	100	8	proper	proper	ADJ
ejpam-176	100	9	β	β	X
ejpam-176	100	10	-θ	-θ	X
ejpam-176	100	11	-closed	-close	VERB
ejpam-176	100	12	set	set	NOUN
ejpam-176	100	13	s	s	VERB
ejpam-176	100	14	by	by	ADP
ejpam-176	100	15	β	β	NOUN
ejpam-176	100	16	-regular	-regular	ADJ
ejpam-176	100	17	sets	set	NOUN
ejpam-176	100	18	of	of	ADP
ejpam-176	100	19	x	x	X
ejpam-176	100	20	.	.	PUNCT
ejpam-176	101	1	since	since	SCONJ
ejpam-176	101	2	x	x	X
ejpam-176	101	3	−	−	PROPN
ejpam-176	101	4	s	s	VERB
ejpam-176	101	5	is	be	AUX
ejpam-176	101	6	β	β	X
ejpam-176	101	7	-θ	-θ	PUNCT
ejpam-176	101	8	-open	-open	ADJ
ejpam-176	101	9	,	,	PUNCT
ejpam-176	101	10	for	for	ADP
ejpam-176	101	11	each	each	DET
ejpam-176	101	12	x	x	SYM
ejpam-176	101	13	∈	∈	PROPN
ejpam-176	101	14	x	x	X
ejpam-176	101	15	−	−	NOUN
ejpam-176	101	16	s	s	X
ejpam-176	101	17	,	,	PUNCT
ejpam-176	101	18	there	there	PRON
ejpam-176	101	19	exists	exist	VERB
ejpam-176	101	20	a	a	DET
ejpam-176	101	21	vx	vx	PROPN
ejpam-176	101	22	∈	∈	PROPN
ejpam-176	101	23	βr(x	βr(x	PUNCT
ejpam-176	101	24	,	,	PUNCT
ejpam-176	101	25	x	x	X
ejpam-176	101	26	)	)	PUNCT
ejpam-176	101	27	such	such	ADJ
ejpam-176	101	28	that	that	SCONJ
ejpam-176	101	29	x	x	SYM
ejpam-176	101	30	∈	∈	PROPN
ejpam-176	101	31	vx	vx	X
ejpam-176	101	32	⊂	⊂	NOUN
ejpam-176	101	33	x	x	PUNCT
ejpam-176	101	34	−	−	PROPN
ejpam-176	101	35	s.	s.	PROPN
ejpam-176	101	36	hence	hence	ADV
ejpam-176	101	37	the	the	DET
ejpam-176	101	38	family	family	NOUN
ejpam-176	101	39	{	{	PUNCT
ejpam-176	101	40	vx	vx	PROPN
ejpam-176	101	41	:	:	PUNCT
ejpam-176	101	42	x	x	SYM
ejpam-176	101	43	∈	∈	NOUN
ejpam-176	101	44	x	x	X
ejpam-176	102	1	−	−	NOUN
ejpam-176	102	2	s	s	PART
ejpam-176	102	3	}	}	PUNCT
ejpam-176	102	4	∪	∪	ADJ
ejpam-176	102	5	{	{	PUNCT
ejpam-176	102	6	uα	uα	NOUN
ejpam-176	102	7	:	:	PUNCT
ejpam-176	102	8	α	α	PROPN
ejpam-176	102	9	∈	∈	PROPN
ejpam-176	103	1	i	i	PRON
ejpam-176	103	2	}	}	PUNCT
ejpam-176	103	3	is	be	AUX
ejpam-176	103	4	a	a	DET
ejpam-176	103	5	cover	cover	NOUN
ejpam-176	103	6	of	of	ADP
ejpam-176	103	7	x	x	PUNCT
ejpam-176	103	8	by	by	ADP
ejpam-176	103	9	β	β	NOUN
ejpam-176	103	10	-regular	-regular	ADJ
ejpam-176	103	11	sets	set	NOUN
ejpam-176	103	12	of	of	ADP
ejpam-176	103	13	x	x	X
ejpam-176	103	14	.	.	PUNCT
ejpam-176	104	1	since	since	SCONJ
ejpam-176	104	2	x	x	PROPN
ejpam-176	104	3	is	be	AUX
ejpam-176	104	4	β	β	X
ejpam-176	104	5	-closed	-close	VERB
ejpam-176	104	6	,	,	PUNCT
ejpam-176	104	7	there	there	PRON
ejpam-176	104	8	is	be	VERB
ejpam-176	104	9	a	a	DET
ejpam-176	104	10	finite	finite	NOUN
ejpam-176	104	11	subset	subset	NOUN
ejpam-176	104	12	i0	i0	PROPN
ejpam-176	104	13	of	of	ADP
ejpam-176	104	14	i	i	PRON
ejpam-176	104	15	such	such	ADJ
ejpam-176	104	16	that	that	PRON
ejpam-176	104	17	s	s	X
ejpam-176	105	1	⊂	⊂	PROPN
ejpam-176	105	2	∪{uα	∪{uα	NUM
ejpam-176	105	3	:	:	PUNCT
ejpam-176	105	4	α	α	PROPN
ejpam-176	105	5	∈	∈	PROPN
ejpam-176	105	6	i0	i0	PROPN
ejpam-176	105	7	}	}	PUNCT
ejpam-176	105	8	.	.	PUNCT
ejpam-176	106	1	therefore	therefore	ADV
ejpam-176	106	2	by	by	ADP
ejpam-176	106	3	theorem	theorem	NOUN
ejpam-176	106	4	3.2	3.2	NUM
ejpam-176	106	5	,	,	PUNCT
ejpam-176	106	6	s	s	PART
ejpam-176	106	7	is	be	AUX
ejpam-176	106	8	β	β	AUX
ejpam-176	106	9	-closed	-close	VERB
ejpam-176	106	10	relative	relative	ADJ
ejpam-176	106	11	to	to	ADP
ejpam-176	106	12	x	x	PROPN
ejpam-176	106	13	.	.	PUNCT
ejpam-176	107	1	(	(	PUNCT
ejpam-176	107	2	b)⇒	b)⇒	PROPN
ejpam-176	107	3	(	(	PUNCT
ejpam-176	107	4	c	c	NOUN
ejpam-176	107	5	)	)	PUNCT
ejpam-176	107	6	:	:	PUNCT
ejpam-176	107	7	since	since	SCONJ
ejpam-176	107	8	every	every	DET
ejpam-176	107	9	β	β	NOUN
ejpam-176	107	10	-regular	-regular	ADJ
ejpam-176	107	11	set	set	NOUN
ejpam-176	107	12	is	be	AUX
ejpam-176	107	13	β	β	X
ejpam-176	107	14	-θ	-θ	PUNCT
ejpam-176	107	15	-closed	-closed	PROPN
ejpam-176	107	16	,	,	PUNCT
ejpam-176	107	17	the	the	DET
ejpam-176	107	18	proof	proof	NOUN
ejpam-176	107	19	is	be	AUX
ejpam-176	107	20	obvious	obvious	ADJ
ejpam-176	107	21	.	.	PUNCT
ejpam-176	108	1	(	(	PUNCT
ejpam-176	108	2	c	c	X
ejpam-176	108	3	)	)	PUNCT
ejpam-176	108	4	⇒	⇒	NOUN
ejpam-176	108	5	(	(	PUNCT
ejpam-176	108	6	a	a	X
ejpam-176	108	7	)	)	PUNCT
ejpam-176	108	8	:	:	PUNCT
ejpam-176	108	9	let	let	VERB
ejpam-176	108	10	s	s	PRON
ejpam-176	108	11	6=	6=	PROPN
ejpam-176	108	12	;	;	PUNCT
ejpam-176	108	13	,	,	PUNCT
ejpam-176	108	14	x	x	PRON
ejpam-176	108	15	be	be	AUX
ejpam-176	108	16	a	a	DET
ejpam-176	108	17	β	β	NOUN
ejpam-176	108	18	-regular	-regular	ADJ
ejpam-176	108	19	set	set	NOUN
ejpam-176	108	20	.	.	PUNCT
ejpam-176	109	1	since	since	SCONJ
ejpam-176	109	2	x	x	X
ejpam-176	109	3	=	=	SYM
ejpam-176	109	4	s	s	X
ejpam-176	109	5	∪	∪	X
ejpam-176	109	6	(	(	PUNCT
ejpam-176	109	7	x	x	SYM
ejpam-176	109	8	−	−	PROPN
ejpam-176	109	9	s	s	PART
ejpam-176	109	10	)	)	PUNCT
ejpam-176	109	11	and	and	CCONJ
ejpam-176	109	12	s	s	PROPN
ejpam-176	109	13	and	and	CCONJ
ejpam-176	109	14	x	x	SYM
ejpam-176	109	15	−	−	NOUN
ejpam-176	109	16	s	s	VERB
ejpam-176	109	17	are	be	AUX
ejpam-176	109	18	both	both	PRON
ejpam-176	109	19	β	β	NOUN
ejpam-176	109	20	-regular	-regular	ADJ
ejpam-176	109	21	,	,	PUNCT
ejpam-176	109	22	the	the	DET
ejpam-176	109	23	proof	proof	NOUN
ejpam-176	109	24	is	be	AUX
ejpam-176	109	25	obvious	obvious	ADJ
ejpam-176	109	26	.	.	PUNCT
ejpam-176	110	1	theorem	theorem	VERB
ejpam-176	110	2	3.3	3.3	NUM
ejpam-176	110	3	.	.	PUNCT
ejpam-176	111	1	if	if	SCONJ
ejpam-176	111	2	s	s	PROPN
ejpam-176	111	3	is	be	AUX
ejpam-176	111	4	β	β	AUX
ejpam-176	111	5	-closed	-close	VERB
ejpam-176	111	6	relative	relative	ADJ
ejpam-176	111	7	to	to	ADP
ejpam-176	111	8	x	x	PUNCT
ejpam-176	111	9	where	where	SCONJ
ejpam-176	111	10	x	x	PRON
ejpam-176	111	11	is	be	AUX
ejpam-176	111	12	t2	t2	NOUN
ejpam-176	111	13	then	then	ADV
ejpam-176	111	14	s	s	VERB
ejpam-176	111	15	is	be	AUX
ejpam-176	111	16	a	a	DET
ejpam-176	111	17	β	β	X
ejpam-176	111	18	-θ	-θ	PUNCT
ejpam-176	111	19	-closed	-close	VERB
ejpam-176	111	20	set	set	NOUN
ejpam-176	111	21	.	.	PUNCT
ejpam-176	112	1	proof	proof	NOUN
ejpam-176	112	2	:	:	PUNCT
ejpam-176	112	3	let	let	VERB
ejpam-176	112	4	x	x	PROPN
ejpam-176	112	5	6∈	6∈	PROPN
ejpam-176	112	6	s.	s.	PROPN
ejpam-176	112	7	then	then	ADV
ejpam-176	112	8	for	for	ADP
ejpam-176	112	9	each	each	DET
ejpam-176	112	10	y	y	PROPN
ejpam-176	112	11	∈	∈	PROPN
ejpam-176	112	12	s	s	PART
ejpam-176	112	13	,	,	PUNCT
ejpam-176	112	14	there	there	PRON
ejpam-176	112	15	exists	exist	VERB
ejpam-176	112	16	an	an	DET
ejpam-176	112	17	open	open	ADJ
ejpam-176	112	18	set	set	NOUN
ejpam-176	112	19	uy	uy	NOUN
ejpam-176	112	20	containing	contain	VERB
ejpam-176	112	21	y	y	PRON
ejpam-176	112	22	such	such	ADJ
ejpam-176	112	23	that	that	SCONJ
ejpam-176	112	24	x	x	SYM
ejpam-176	112	25	6∈	6∈	PROPN
ejpam-176	112	26	cl(uy	cl(uy	NOUN
ejpam-176	112	27	)	)	PUNCT
ejpam-176	113	1	=	=	PUNCT
ejpam-176	113	2	vy	vy	INTJ
ejpam-176	113	3	(	(	PUNCT
ejpam-176	113	4	say	say	INTJ
ejpam-176	113	5	)	)	PUNCT
ejpam-176	113	6	.	.	PUNCT
ejpam-176	114	1	since	since	SCONJ
ejpam-176	114	2	each	each	DET
ejpam-176	114	3	vy	vy	NOUN
ejpam-176	114	4	is	be	AUX
ejpam-176	114	5	regular	regular	ADV
ejpam-176	114	6	closed	closed	ADJ
ejpam-176	114	7	and	and	CCONJ
ejpam-176	114	8	hence	hence	ADV
ejpam-176	114	9	is	be	AUX
ejpam-176	114	10	β	β	NOUN
ejpam-176	114	11	-regular	-regular	ADJ
ejpam-176	114	12	and	and	CCONJ
ejpam-176	114	13	s	s	NOUN
ejpam-176	114	14	⊂	⊂	PROPN
ejpam-176	114	15	∪y∈svy	∪y∈svy	PROPN
ejpam-176	114	16	,	,	PUNCT
ejpam-176	114	17	then	then	ADV
ejpam-176	114	18	by	by	ADP
ejpam-176	114	19	theorem	theorem	NOUN
ejpam-176	114	20	3.2	3.2	NUM
ejpam-176	114	21	,	,	PUNCT
ejpam-176	114	22	there	there	PRON
ejpam-176	114	23	exists	exist	VERB
ejpam-176	114	24	a	a	DET
ejpam-176	114	25	finite	finite	NOUN
ejpam-176	114	26	subset	subset	VERB
ejpam-176	114	27	s0	s0	NOUN
ejpam-176	114	28	of	of	ADP
ejpam-176	114	29	s	s	PRON
ejpam-176	114	30	such	such	ADJ
ejpam-176	114	31	that	that	PRON
ejpam-176	114	32	s	s	X
ejpam-176	115	1	⊂	⊂	X
ejpam-176	115	2	∪y∈s0	∪y∈s0	ADJ
ejpam-176	115	3	vy	vy	NOUN
ejpam-176	115	4	=	=	NOUN
ejpam-176	115	5	v	v	PROPN
ejpam-176	115	6	(	(	PUNCT
ejpam-176	115	7	say	say	INTJ
ejpam-176	115	8	)	)	PUNCT
ejpam-176	115	9	.	.	PUNCT
ejpam-176	116	1	now	now	ADV
ejpam-176	116	2	the	the	DET
ejpam-176	116	3	set	set	NOUN
ejpam-176	116	4	v	v	NOUN
ejpam-176	116	5	is	be	AUX
ejpam-176	116	6	being	be	AUX
ejpam-176	116	7	a	a	DET
ejpam-176	116	8	regular	regular	ADJ
ejpam-176	116	9	closed	close	VERB
ejpam-176	116	10	set	set	NOUN
ejpam-176	116	11	and	and	CCONJ
ejpam-176	116	12	hence	hence	ADV
ejpam-176	116	13	its	its	PRON
ejpam-176	116	14	complement	complement	NOUN
ejpam-176	116	15	x	x	PUNCT
ejpam-176	116	16	−	−	PROPN
ejpam-176	116	17	v	v	NUM
ejpam-176	116	18	∈	∈	PROPN
ejpam-176	116	19	ro(x	ro(x	PUNCT
ejpam-176	116	20	,	,	PUNCT
ejpam-176	116	21	x	x	X
ejpam-176	116	22	)	)	PUNCT
ejpam-176	116	23	.	.	PUNCT
ejpam-176	117	1	x	x	PUNCT
ejpam-176	118	1	−	−	NOUN
ejpam-176	118	2	v	v	NOUN
ejpam-176	118	3	is	be	AUX
ejpam-176	118	4	therefore	therefore	ADV
ejpam-176	118	5	β	β	PART
ejpam-176	118	6	-regular	-regular	ADJ
ejpam-176	118	7	set	set	VERB
ejpam-176	118	8	containing	contain	VERB
ejpam-176	118	9	x	x	X
ejpam-176	118	10	.	.	PUNCT
ejpam-176	119	1	so	so	ADV
ejpam-176	119	2	s	s	VERB
ejpam-176	119	3	is	be	AUX
ejpam-176	119	4	β	β	X
ejpam-176	119	5	-θ	-θ	PUNCT
ejpam-176	119	6	-closed	-closed	PROPN
ejpam-176	119	7	.	.	PUNCT
ejpam-176	120	1	lemma	lemma	PROPN
ejpam-176	120	2	3.1	3.1	NUM
ejpam-176	120	3	.	.	PUNCT
ejpam-176	121	1	(	(	PUNCT
ejpam-176	121	2	abd	abd	PROPN
ejpam-176	121	3	.	.	PUNCT
ejpam-176	122	1	el	el	PROPN
ejpam-176	122	2	-	-	PUNCT
ejpam-176	122	3	monsef	monsef	PROPN
ejpam-176	122	4	et	et	PROPN
ejpam-176	122	5	al	al	PROPN
ejpam-176	122	6	.	.	PUNCT
ejpam-176	123	1	[	[	X
ejpam-176	123	2	1	1	NUM
ejpam-176	123	3	]	]	PUNCT
ejpam-176	123	4	)	)	PUNCT
ejpam-176	123	5	let	let	VERB
ejpam-176	123	6	a	a	PRON
ejpam-176	123	7	and	and	CCONJ
ejpam-176	123	8	y	y	PROPN
ejpam-176	123	9	be	be	AUX
ejpam-176	123	10	subsets	subset	NOUN
ejpam-176	123	11	of	of	ADP
ejpam-176	123	12	a	a	DET
ejpam-176	123	13	space	space	NOUN
ejpam-176	123	14	x	x	INTJ
ejpam-176	123	15	.	.	PUNCT
ejpam-176	124	1	then	then	ADV
ejpam-176	124	2	(	(	PUNCT
ejpam-176	124	3	i	i	NOUN
ejpam-176	124	4	)	)	PUNCT
ejpam-176	124	5	if	if	SCONJ
ejpam-176	124	6	a∈	a∈	PROPN
ejpam-176	124	7	βo(x	βo(x	PUNCT
ejpam-176	124	8	)	)	PUNCT
ejpam-176	124	9	and	and	CCONJ
ejpam-176	124	10	y	y	PROPN
ejpam-176	124	11	is	be	AUX
ejpam-176	124	12	α	α	NOUN
ejpam-176	124	13	-	-	NOUN
ejpam-176	124	14	open	open	ADJ
ejpam-176	124	15	in	in	ADP
ejpam-176	124	16	x	x	X
ejpam-176	124	17	,	,	PUNCT
ejpam-176	124	18	then	then	ADV
ejpam-176	124	19	a∩	a∩	PROPN
ejpam-176	124	20	y	y	PROPN
ejpam-176	124	21	∈	∈	PROPN
ejpam-176	124	22	βo(y	βo(y	PUNCT
ejpam-176	124	23	)	)	PUNCT
ejpam-176	124	24	.	.	PUNCT
ejpam-176	125	1	(	(	PUNCT
ejpam-176	125	2	ii	ii	NOUN
ejpam-176	125	3	)	)	PUNCT
ejpam-176	125	4	if	if	SCONJ
ejpam-176	125	5	a∈	a∈	PROPN
ejpam-176	125	6	βo(y	βo(y	PUNCT
ejpam-176	125	7	)	)	PUNCT
ejpam-176	125	8	and	and	CCONJ
ejpam-176	125	9	y	y	PROPN
ejpam-176	125	10	∈	∈	PROPN
ejpam-176	125	11	βo(x	βo(x	PUNCT
ejpam-176	125	12	)	)	PUNCT
ejpam-176	125	13	,	,	PUNCT
ejpam-176	125	14	then	then	ADV
ejpam-176	125	15	a∈	a∈	PROPN
ejpam-176	125	16	βo(x	βo(x	PUNCT
ejpam-176	125	17	)	)	PUNCT
ejpam-176	125	18	.	.	PUNCT
ejpam-176	126	1	c.	c.	PROPN
ejpam-176	126	2	basu	basu	PROPN
ejpam-176	126	3	and	and	CCONJ
ejpam-176	126	4	m.	m.	PROPN
ejpam-176	126	5	ghosh	ghosh	PROPN
ejpam-176	126	6	/	/	PUNCT
ejpam-176	126	7	eur	eur	PROPN
ejpam-176	126	8	.	.	PUNCT
ejpam-176	127	1	j.	j.	PROPN
ejpam-176	127	2	pure	pure	PROPN
ejpam-176	127	3	appl	appl	PROPN
ejpam-176	127	4	.	.	PROPN
ejpam-176	127	5	math	math	PROPN
ejpam-176	127	6	,	,	PUNCT
ejpam-176	127	7	2	2	NUM
ejpam-176	127	8	(	(	PUNCT
ejpam-176	127	9	2009	2009	NUM
ejpam-176	127	10	)	)	PUNCT
ejpam-176	127	11	,	,	PUNCT
ejpam-176	127	12	(	(	PUNCT
ejpam-176	127	13	85	85	NUM
ejpam-176	127	14	-	-	SYM
ejpam-176	127	15	96	96	NUM
ejpam-176	127	16	)	)	PUNCT
ejpam-176	127	17	89	89	NUM
ejpam-176	127	18	lemma	lemma	PROPN
ejpam-176	127	19	3.2	3.2	NUM
ejpam-176	127	20	.	.	PUNCT
ejpam-176	128	1	[	[	X
ejpam-176	128	2	13	13	NUM
ejpam-176	128	3	]	]	PUNCT
ejpam-176	128	4	let	let	VERB
ejpam-176	128	5	x	x	PRON
ejpam-176	128	6	be	be	AUX
ejpam-176	128	7	a	a	DET
ejpam-176	128	8	space	space	NOUN
ejpam-176	128	9	and	and	CCONJ
ejpam-176	128	10	a	a	PRON
ejpam-176	128	11	,	,	PUNCT
ejpam-176	128	12	y	y	PROPN
ejpam-176	128	13	be	be	VERB
ejpam-176	128	14	subsets	subset	NOUN
ejpam-176	128	15	of	of	ADP
ejpam-176	128	16	x	x	SYM
ejpam-176	128	17	such	such	ADJ
ejpam-176	128	18	that	that	SCONJ
ejpam-176	128	19	a	a	DET
ejpam-176	128	20	⊂	⊂	X
ejpam-176	128	21	y	y	PROPN
ejpam-176	128	22	⊂	⊂	PROPN
ejpam-176	128	23	x	x	X
ejpam-176	128	24	and	and	CCONJ
ejpam-176	128	25	y	y	PROPN
ejpam-176	128	26	is	be	AUX
ejpam-176	128	27	α	α	NOUN
ejpam-176	128	28	-	-	NOUN
ejpam-176	128	29	open	open	ADJ
ejpam-176	128	30	in	in	ADP
ejpam-176	128	31	x	x	X
ejpam-176	128	32	.	.	PUNCT
ejpam-176	129	1	then	then	ADV
ejpam-176	129	2	the	the	DET
ejpam-176	129	3	following	follow	VERB
ejpam-176	129	4	properties	property	NOUN
ejpam-176	129	5	hold	hold	VERB
ejpam-176	129	6	:	:	PUNCT
ejpam-176	129	7	(	(	PUNCT
ejpam-176	129	8	i	i	NOUN
ejpam-176	129	9	)	)	PUNCT
ejpam-176	129	10	a∈	a∈	PROPN
ejpam-176	129	11	βo(y	βo(y	PUNCT
ejpam-176	129	12	)	)	PUNCT
ejpam-176	130	1	if	if	SCONJ
ejpam-176	130	2	and	and	CCONJ
ejpam-176	130	3	only	only	ADV
ejpam-176	130	4	if	if	SCONJ
ejpam-176	130	5	a∈	a∈	PROPN
ejpam-176	130	6	βo(x	βo(x	PUNCT
ejpam-176	130	7	)	)	PUNCT
ejpam-176	130	8	.	.	PUNCT
ejpam-176	131	1	(	(	PUNCT
ejpam-176	131	2	ii	ii	X
ejpam-176	131	3	)	)	PUNCT
ejpam-176	131	4	β	β	PROPN
ejpam-176	131	5	clx	clx	PROPN
ejpam-176	131	6	(	(	PUNCT
ejpam-176	131	7	a)∩	a)∩	X
ejpam-176	131	8	y	y	PROPN
ejpam-176	131	9	=	=	PUNCT
ejpam-176	131	10	β	β	X
ejpam-176	131	11	cly	cly	ADV
ejpam-176	131	12	(	(	PUNCT
ejpam-176	131	13	a	a	X
ejpam-176	131	14	)	)	PUNCT
ejpam-176	131	15	,	,	PUNCT
ejpam-176	131	16	where	where	SCONJ
ejpam-176	131	17	β	β	AUX
ejpam-176	131	18	cly	cly	ADV
ejpam-176	131	19	(	(	PUNCT
ejpam-176	131	20	a	a	X
ejpam-176	131	21	)	)	PUNCT
ejpam-176	131	22	denotes	denote	VERB
ejpam-176	131	23	the	the	DET
ejpam-176	131	24	β	β	NOUN
ejpam-176	131	25	-closure	-closure	NOUN
ejpam-176	131	26	of	of	ADP
ejpam-176	131	27	a	a	PRON
ejpam-176	131	28	in	in	ADP
ejpam-176	131	29	the	the	DET
ejpam-176	131	30	subspace	subspace	NOUN
ejpam-176	131	31	y	y	PROPN
ejpam-176	131	32	.	.	PUNCT
ejpam-176	131	33	theorem	theorem	VERB
ejpam-176	131	34	3.4	3.4	NUM
ejpam-176	131	35	.	.	PUNCT
ejpam-176	132	1	let	let	AUX
ejpam-176	132	2	(	(	PUNCT
ejpam-176	132	3	x	x	X
ejpam-176	132	4	,	,	PUNCT
ejpam-176	132	5	τ	τ	X
ejpam-176	132	6	)	)	PUNCT
ejpam-176	132	7	be	be	VERB
ejpam-176	132	8	a	a	DET
ejpam-176	132	9	space	space	NOUN
ejpam-176	132	10	and	and	CCONJ
ejpam-176	132	11	y	y	PROPN
ejpam-176	132	12	is	be	AUX
ejpam-176	132	13	α	α	NOUN
ejpam-176	132	14	-	-	NOUN
ejpam-176	132	15	open	open	ADJ
ejpam-176	132	16	in	in	ADP
ejpam-176	132	17	x	x	X
ejpam-176	132	18	,	,	PUNCT
ejpam-176	132	19	then	then	ADV
ejpam-176	132	20	βr(y	βr(y	PUNCT
ejpam-176	132	21	,	,	PUNCT
ejpam-176	132	22	τy	τy	X
ejpam-176	132	23	)	)	PUNCT
ejpam-176	133	1	=	=	SYM
ejpam-176	133	2	βr(x	βr(x	PUNCT
ejpam-176	133	3	,	,	PUNCT
ejpam-176	133	4	τ)∩	τ)∩	PROPN
ejpam-176	133	5	y	y	PROPN
ejpam-176	133	6	.	.	PUNCT
ejpam-176	134	1	proof	proof	NOUN
ejpam-176	134	2	:	:	PUNCT
ejpam-176	134	3	let	let	VERB
ejpam-176	134	4	a	a	DET
ejpam-176	134	5	∈	∈	NOUN
ejpam-176	134	6	βr(x	βr(x	PUNCT
ejpam-176	134	7	,	,	PUNCT
ejpam-176	134	8	τ	τ	X
ejpam-176	134	9	)	)	PUNCT
ejpam-176	134	10	∩	∩	PROPN
ejpam-176	134	11	y	y	PROPN
ejpam-176	134	12	.	.	PUNCT
ejpam-176	135	1	then	then	ADV
ejpam-176	135	2	a	a	DET
ejpam-176	135	3	=	=	X
ejpam-176	135	4	u	u	NOUN
ejpam-176	135	5	∩	∩	X
ejpam-176	135	6	y	y	PROPN
ejpam-176	135	7	for	for	ADP
ejpam-176	135	8	some	some	DET
ejpam-176	135	9	u	u	PROPN
ejpam-176	135	10	∈	∈	PROPN
ejpam-176	135	11	βr(x	βr(x	PUNCT
ejpam-176	135	12	,	,	PUNCT
ejpam-176	135	13	τ	τ	PROPN
ejpam-176	135	14	)	)	PUNCT
ejpam-176	135	15	.	.	PUNCT
ejpam-176	136	1	then	then	ADV
ejpam-176	136	2	by	by	ADP
ejpam-176	136	3	lemma	lemma	PROPN
ejpam-176	136	4	3.5	3.5	NUM
ejpam-176	136	5	,	,	PUNCT
ejpam-176	136	6	a	a	DET
ejpam-176	136	7	∈	∈	PROPN
ejpam-176	136	8	βo(y	βo(y	PUNCT
ejpam-176	136	9	,	,	PUNCT
ejpam-176	136	10	τy	τy	PRON
ejpam-176	136	11	)	)	PUNCT
ejpam-176	136	12	.	.	PUNCT
ejpam-176	137	1	now	now	ADV
ejpam-176	137	2	by	by	ADP
ejpam-176	137	3	lemma	lemma	PROPN
ejpam-176	137	4	3.6	3.6	NUM
ejpam-176	137	5	,	,	PUNCT
ejpam-176	137	6	we	we	PRON
ejpam-176	137	7	have	have	VERB
ejpam-176	137	8	β	β	X
ejpam-176	137	9	cly	cly	ADV
ejpam-176	137	10	(	(	PUNCT
ejpam-176	137	11	a	a	X
ejpam-176	137	12	)	)	PUNCT
ejpam-176	137	13	=	=	SYM
ejpam-176	137	14	β	β	X
ejpam-176	137	15	clx	clx	X
ejpam-176	137	16	(	(	PUNCT
ejpam-176	137	17	a	a	NOUN
ejpam-176	137	18	)	)	PUNCT
ejpam-176	137	19	∩	∩	NOUN
ejpam-176	137	20	y	y	PROPN
ejpam-176	137	21	⊂	⊂	PROPN
ejpam-176	137	22	β	β	PROPN
ejpam-176	137	23	clx	clx	PROPN
ejpam-176	137	24	(	(	PUNCT
ejpam-176	137	25	u	u	NOUN
ejpam-176	137	26	)	)	PUNCT
ejpam-176	137	27	∩	∩	NOUN
ejpam-176	137	28	y	y	PROPN
ejpam-176	137	29	=	=	SYM
ejpam-176	137	30	u	u	PROPN
ejpam-176	137	31	∩	∩	NOUN
ejpam-176	137	32	y	y	NOUN
ejpam-176	137	33	=	=	PUNCT
ejpam-176	137	34	a.	a.	NOUN
ejpam-176	138	1	so	so	ADV
ejpam-176	138	2	,	,	PUNCT
ejpam-176	138	3	a	a	PRON
ejpam-176	138	4	is	be	AUX
ejpam-176	138	5	β	β	AUX
ejpam-176	138	6	-closed	-close	VERB
ejpam-176	138	7	in	in	ADP
ejpam-176	138	8	(	(	PUNCT
ejpam-176	138	9	y	y	PROPN
ejpam-176	138	10	,	,	PUNCT
ejpam-176	138	11	τy	τy	NUM
ejpam-176	138	12	)	)	PUNCT
ejpam-176	138	13	and	and	CCONJ
ejpam-176	138	14	hence	hence	ADV
ejpam-176	138	15	a	a	DET
ejpam-176	138	16	∈	∈	NOUN
ejpam-176	138	17	βr(y	βr(y	NUM
ejpam-176	138	18	,	,	PUNCT
ejpam-176	138	19	τy	τy	PRON
ejpam-176	138	20	)	)	PUNCT
ejpam-176	138	21	.	.	PUNCT
ejpam-176	139	1	therefore	therefore	ADV
ejpam-176	139	2	,	,	PUNCT
ejpam-176	139	3	βr(x	βr(x	PUNCT
ejpam-176	139	4	,	,	PUNCT
ejpam-176	139	5	τ)∩	τ)∩	PROPN
ejpam-176	139	6	y	y	PROPN
ejpam-176	139	7	⊂	⊂	PROPN
ejpam-176	139	8	βr(y	βr(y	PROPN
ejpam-176	139	9	,	,	PUNCT
ejpam-176	139	10	τy	τy	PRON
ejpam-176	139	11	)	)	PUNCT
ejpam-176	139	12	.	.	PUNCT
ejpam-176	140	1	conversely	conversely	ADV
ejpam-176	140	2	,	,	PUNCT
ejpam-176	140	3	let	let	VERB
ejpam-176	140	4	w	w	PROPN
ejpam-176	140	5	∈	∈	PROPN
ejpam-176	140	6	βr(y	βr(y	VERB
ejpam-176	140	7	,	,	PUNCT
ejpam-176	140	8	τy	τy	PRON
ejpam-176	140	9	)	)	PUNCT
ejpam-176	140	10	.	.	PUNCT
ejpam-176	141	1	then	then	ADV
ejpam-176	141	2	by	by	ADP
ejpam-176	141	3	lemma	lemma	PROPN
ejpam-176	141	4	3.6(i	3.6(i	NUM
ejpam-176	141	5	)	)	PUNCT
ejpam-176	141	6	,	,	PUNCT
ejpam-176	141	7	w	w	PROPN
ejpam-176	141	8	∈	∈	PROPN
ejpam-176	141	9	βo(x	βo(x	PUNCT
ejpam-176	141	10	,	,	PUNCT
ejpam-176	141	11	τ	τ	PROPN
ejpam-176	141	12	)	)	PUNCT
ejpam-176	141	13	.	.	PUNCT
ejpam-176	142	1	clearly	clearly	ADV
ejpam-176	142	2	w	w	X
ejpam-176	142	3	=	=	X
ejpam-176	142	4	β	β	X
ejpam-176	142	5	cly	cly	ADV
ejpam-176	142	6	(	(	PUNCT
ejpam-176	142	7	w	w	NOUN
ejpam-176	142	8	)	)	PUNCT
ejpam-176	142	9	=	=	SYM
ejpam-176	142	10	β	β	X
ejpam-176	142	11	clx	clx	X
ejpam-176	142	12	(	(	PUNCT
ejpam-176	142	13	w	w	NOUN
ejpam-176	142	14	)	)	PUNCT
ejpam-176	142	15	∩	∩	NOUN
ejpam-176	142	16	y	y	PROPN
ejpam-176	142	17	(	(	PUNCT
ejpam-176	142	18	by	by	ADP
ejpam-176	142	19	lemma	lemma	PROPN
ejpam-176	142	20	3.6(ii	3.6(ii	NUM
ejpam-176	142	21	)	)	PUNCT
ejpam-176	142	22	)	)	PUNCT
ejpam-176	142	23	and	and	CCONJ
ejpam-176	142	24	hence	hence	ADV
ejpam-176	142	25	w	w	PROPN
ejpam-176	142	26	∈	∈	PROPN
ejpam-176	142	27	βr(x	βr(x	PUNCT
ejpam-176	142	28	,	,	PUNCT
ejpam-176	142	29	τ)∩	τ)∩	PROPN
ejpam-176	142	30	y	y	PROPN
ejpam-176	142	31	.	.	PUNCT
ejpam-176	142	32	theorem	theorem	VERB
ejpam-176	142	33	3.5	3.5	NUM
ejpam-176	142	34	.	.	PUNCT
ejpam-176	143	1	let	let	VERB
ejpam-176	143	2	y	y	PRON
ejpam-176	143	3	be	be	AUX
ejpam-176	143	4	an	an	DET
ejpam-176	143	5	α	α	NOUN
ejpam-176	143	6	-	-	ADJ
ejpam-176	143	7	open	open	ADJ
ejpam-176	143	8	set	set	NOUN
ejpam-176	143	9	in	in	ADP
ejpam-176	143	10	a	a	DET
ejpam-176	143	11	space	space	NOUN
ejpam-176	143	12	(	(	PUNCT
ejpam-176	143	13	x	x	X
ejpam-176	143	14	,	,	PUNCT
ejpam-176	143	15	τ	τ	PROPN
ejpam-176	143	16	)	)	PUNCT
ejpam-176	143	17	.	.	PUNCT
ejpam-176	144	1	then	then	ADV
ejpam-176	144	2	(	(	PUNCT
ejpam-176	144	3	y	y	PROPN
ejpam-176	144	4	,	,	PUNCT
ejpam-176	144	5	τy	τy	PART
ejpam-176	144	6	)	)	PUNCT
ejpam-176	144	7	is	be	AUX
ejpam-176	144	8	β	β	X
ejpam-176	144	9	-closed	-close	VERB
ejpam-176	144	10	if	if	SCONJ
ejpam-176	144	11	and	and	CCONJ
ejpam-176	144	12	only	only	ADV
ejpam-176	144	13	if	if	SCONJ
ejpam-176	144	14	y	y	PROPN
ejpam-176	144	15	is	be	AUX
ejpam-176	144	16	β	β	AUX
ejpam-176	144	17	-closed	-close	VERB
ejpam-176	144	18	relative	relative	ADJ
ejpam-176	144	19	to	to	ADP
ejpam-176	144	20	x	x	X
ejpam-176	144	21	.	.	PUNCT
ejpam-176	145	1	proof	proof	NOUN
ejpam-176	145	2	:	:	PUNCT
ejpam-176	145	3	let	let	VERB
ejpam-176	145	4	(	(	PUNCT
ejpam-176	145	5	y	y	PROPN
ejpam-176	145	6	,	,	PUNCT
ejpam-176	145	7	τy	τy	PART
ejpam-176	145	8	)	)	PUNCT
ejpam-176	145	9	be	be	VERB
ejpam-176	145	10	β	β	X
ejpam-176	145	11	-closed	-close	VERB
ejpam-176	145	12	.	.	PUNCT
ejpam-176	146	1	if	if	SCONJ
ejpam-176	146	2	u	u	PRON
ejpam-176	146	3	=	=	X
ejpam-176	146	4	{	{	PUNCT
ejpam-176	146	5	uα	uα	X
ejpam-176	146	6	:	:	PUNCT
ejpam-176	146	7	α	α	PROPN
ejpam-176	146	8	∈	∈	PROPN
ejpam-176	146	9	λ	λ	PROPN
ejpam-176	146	10	}	}	PUNCT
ejpam-176	146	11	is	be	AUX
ejpam-176	146	12	a	a	DET
ejpam-176	146	13	cover	cover	NOUN
ejpam-176	146	14	of	of	ADP
ejpam-176	146	15	y	y	PROPN
ejpam-176	146	16	by	by	ADP
ejpam-176	146	17	β	β	NOUN
ejpam-176	146	18	-regular	-regular	ADJ
ejpam-176	146	19	sets	set	NOUN
ejpam-176	146	20	of	of	ADP
ejpam-176	146	21	x	x	X
ejpam-176	146	22	.	.	PUNCT
ejpam-176	147	1	then	then	ADV
ejpam-176	147	2	by	by	ADP
ejpam-176	147	3	above	above	ADP
ejpam-176	147	4	theorem	theorem	VERB
ejpam-176	147	5	3.7,uy	3.7,uy	NUM
ejpam-176	147	6	=	=	SYM
ejpam-176	147	7	{	{	PUNCT
ejpam-176	147	8	uα∩y	uα∩y	PROPN
ejpam-176	147	9	:	:	PUNCT
ejpam-176	147	10	α	α	PROPN
ejpam-176	147	11	∈	∈	PROPN
ejpam-176	147	12	λ	λ	NOUN
ejpam-176	147	13	}	}	PUNCT
ejpam-176	147	14	is	be	AUX
ejpam-176	147	15	a	a	DET
ejpam-176	147	16	cover	cover	NOUN
ejpam-176	147	17	of	of	ADP
ejpam-176	147	18	y	y	PROPN
ejpam-176	147	19	by	by	ADP
ejpam-176	147	20	β	β	NOUN
ejpam-176	147	21	-regular	-regular	ADJ
ejpam-176	147	22	sets	set	NOUN
ejpam-176	147	23	of	of	ADP
ejpam-176	147	24	(	(	PUNCT
ejpam-176	147	25	y	y	PROPN
ejpam-176	147	26	,	,	PUNCT
ejpam-176	147	27	τy	τy	PRON
ejpam-176	147	28	)	)	PUNCT
ejpam-176	147	29	.	.	PUNCT
ejpam-176	148	1	since	since	SCONJ
ejpam-176	148	2	(	(	PUNCT
ejpam-176	148	3	y	y	PROPN
ejpam-176	148	4	,	,	PUNCT
ejpam-176	148	5	τy	τy	PART
ejpam-176	148	6	)	)	PUNCT
ejpam-176	148	7	is	be	AUX
ejpam-176	148	8	β	β	PROPN
ejpam-176	148	9	-closed	-close	VERB
ejpam-176	148	10	then	then	ADV
ejpam-176	148	11	y	y	PROPN
ejpam-176	148	12	is	be	AUX
ejpam-176	148	13	covered	cover	VERB
ejpam-176	148	14	by	by	ADP
ejpam-176	148	15	finite	finite	ADJ
ejpam-176	148	16	number	number	NOUN
ejpam-176	148	17	of	of	ADP
ejpam-176	148	18	sets	set	NOUN
ejpam-176	148	19	of	of	ADP
ejpam-176	148	20	u	u	PRON
ejpam-176	148	21	say	say	VERB
ejpam-176	148	22	,	,	PUNCT
ejpam-176	148	23	u1	u1	PROPN
ejpam-176	148	24	,	,	PUNCT
ejpam-176	148	25	......	......	PUNCT
ejpam-176	148	26	,	,	PUNCT
ejpam-176	148	27	un	un	PROPN
ejpam-176	148	28	and	and	CCONJ
ejpam-176	148	29	hence	hence	ADV
ejpam-176	148	30	y	y	PROPN
ejpam-176	148	31	is	be	AUX
ejpam-176	148	32	β	β	X
ejpam-176	148	33	-closed	-close	VERB
ejpam-176	148	34	relative	relative	ADJ
ejpam-176	148	35	to	to	ADP
ejpam-176	148	36	x	x	X
ejpam-176	148	37	.	.	PUNCT
ejpam-176	149	1	conversely	conversely	ADV
ejpam-176	149	2	,	,	PUNCT
ejpam-176	149	3	let	let	VERB
ejpam-176	149	4	y	y	PRON
ejpam-176	149	5	be	be	AUX
ejpam-176	149	6	β	β	AUX
ejpam-176	149	7	-closed	-close	VERB
ejpam-176	149	8	relative	relative	ADJ
ejpam-176	149	9	to	to	ADP
ejpam-176	149	10	x	x	X
ejpam-176	149	11	.	.	PUNCT
ejpam-176	150	1	let	let	VERB
ejpam-176	150	2	u	u	PRON
ejpam-176	150	3	=	=	PUNCT
ejpam-176	150	4	{	{	PUNCT
ejpam-176	150	5	uα	uα	X
ejpam-176	150	6	:	:	PUNCT
ejpam-176	150	7	α	α	PROPN
ejpam-176	150	8	∈	∈	PROPN
ejpam-176	150	9	λ	λ	NOUN
ejpam-176	150	10	}	}	PUNCT
ejpam-176	150	11	be	be	VERB
ejpam-176	150	12	a	a	DET
ejpam-176	150	13	cover	cover	NOUN
ejpam-176	150	14	of	of	ADP
ejpam-176	150	15	y	y	PROPN
ejpam-176	150	16	,	,	PUNCT
ejpam-176	150	17	where	where	SCONJ
ejpam-176	150	18	each	each	DET
ejpam-176	150	19	uα	uα	PROPN
ejpam-176	150	20	∈	∈	PROPN
ejpam-176	150	21	βr(y	βr(y	NUM
ejpam-176	150	22	,	,	PUNCT
ejpam-176	150	23	τy	τy	PRON
ejpam-176	150	24	)	)	PUNCT
ejpam-176	150	25	.	.	PUNCT
ejpam-176	151	1	then	then	ADV
ejpam-176	151	2	by	by	ADP
ejpam-176	151	3	above	above	ADP
ejpam-176	151	4	theorem	theorem	ADJ
ejpam-176	151	5	3.7	3.7	NUM
ejpam-176	151	6	,	,	PUNCT
ejpam-176	151	7	for	for	ADP
ejpam-176	151	8	each	each	DET
ejpam-176	151	9	α	α	PROPN
ejpam-176	151	10	∈	∈	PROPN
ejpam-176	151	11	λ	λ	NOUN
ejpam-176	151	12	,	,	PUNCT
ejpam-176	151	13	there	there	PRON
ejpam-176	151	14	exists	exist	VERB
ejpam-176	151	15	a	a	DET
ejpam-176	151	16	β	β	NOUN
ejpam-176	151	17	-regular	-regular	NOUN
ejpam-176	151	18	set	set	VERB
ejpam-176	151	19	vα	vα	ADP
ejpam-176	151	20	∈	∈	PROPN
ejpam-176	151	21	βr(x	βr(x	PUNCT
ejpam-176	151	22	)	)	PUNCT
ejpam-176	151	23	such	such	ADJ
ejpam-176	151	24	that	that	PRON
ejpam-176	151	25	uα	uα	PROPN
ejpam-176	151	26	=	=	SYM
ejpam-176	151	27	vα	vα	PROPN
ejpam-176	151	28	∩	∩	PROPN
ejpam-176	151	29	y	y	PROPN
ejpam-176	151	30	.	.	PUNCT
ejpam-176	152	1	therefore	therefore	ADV
ejpam-176	152	2	y	y	PROPN
ejpam-176	152	3	is	be	AUX
ejpam-176	152	4	covered	cover	VERB
ejpam-176	152	5	by	by	ADP
ejpam-176	152	6	the	the	DET
ejpam-176	152	7	family	family	NOUN
ejpam-176	152	8	u	u	NOUN
ejpam-176	152	9	=	=	PUNCT
ejpam-176	152	10	{	{	PUNCT
ejpam-176	152	11	vα	vα	X
ejpam-176	152	12	:	:	PUNCT
ejpam-176	152	13	α	α	PROPN
ejpam-176	152	14	∈	∈	PROPN
ejpam-176	152	15	λ	λ	NOUN
ejpam-176	152	16	}	}	PUNCT
ejpam-176	152	17	.	.	PUNCT
ejpam-176	153	1	since	since	SCONJ
ejpam-176	153	2	y	y	PROPN
ejpam-176	153	3	is	be	AUX
ejpam-176	153	4	β	β	AUX
ejpam-176	153	5	-closed	-close	VERB
ejpam-176	153	6	relative	relative	ADJ
ejpam-176	153	7	to	to	ADP
ejpam-176	153	8	x	x	PRON
ejpam-176	153	9	,	,	PUNCT
ejpam-176	153	10	there	there	PRON
ejpam-176	153	11	exits	exit	VERB
ejpam-176	153	12	vα1	vα1	NOUN
ejpam-176	153	13	,	,	PUNCT
ejpam-176	153	14	.....	.....	PUNCT
ejpam-176	153	15	,	,	PUNCT
ejpam-176	153	16	vαn	vαn	NOUN
ejpam-176	153	17	∈	∈	PROPN
ejpam-176	153	18	v	v	ADP
ejpam-176	153	19	such	such	ADJ
ejpam-176	153	20	that	that	SCONJ
ejpam-176	153	21	y	y	PROPN
ejpam-176	153	22	⊂	⊂	X
ejpam-176	153	23	∪n	∪n	PROPN
ejpam-176	153	24	i=1vαi	i=1vαi	INTJ
ejpam-176	153	25	.	.	PUNCT
ejpam-176	154	1	now	now	ADV
ejpam-176	154	2	as	as	SCONJ
ejpam-176	154	3	y	y	PROPN
ejpam-176	154	4	=	=	PROPN
ejpam-176	154	5	∪n	∪n	PROPN
ejpam-176	154	6	i=1	i=1	PROPN
ejpam-176	154	7	(	(	PUNCT
ejpam-176	154	8	vαi	vαi	PROPN
ejpam-176	154	9	∩	∩	ADJ
ejpam-176	154	10	y	y	PROPN
ejpam-176	154	11	)	)	PUNCT
ejpam-176	154	12	,	,	PUNCT
ejpam-176	154	13	{	{	PUNCT
ejpam-176	154	14	uα1	uα1	NOUN
ejpam-176	154	15	,	,	PUNCT
ejpam-176	154	16	.....	.....	PUNCT
ejpam-176	154	17	,	,	PUNCT
ejpam-176	154	18	uαn	uαn	PROPN
ejpam-176	154	19	}	}	PUNCT
ejpam-176	154	20	is	be	AUX
ejpam-176	154	21	a	a	DET
ejpam-176	154	22	finite	finite	NOUN
ejpam-176	154	23	subfamily	subfamily	ADV
ejpam-176	154	24	of	of	ADP
ejpam-176	154	25	u	u	PRON
ejpam-176	154	26	which	which	PRON
ejpam-176	154	27	covers	cover	VERB
ejpam-176	154	28	y	y	PRON
ejpam-176	154	29	.	.	PUNCT
ejpam-176	155	1	so	so	ADV
ejpam-176	155	2	(	(	PUNCT
ejpam-176	155	3	y	y	PROPN
ejpam-176	155	4	,	,	PUNCT
ejpam-176	155	5	τy	τy	PART
ejpam-176	155	6	)	)	PUNCT
ejpam-176	155	7	is	be	AUX
ejpam-176	155	8	β	β	X
ejpam-176	155	9	-closed	-close	VERB
ejpam-176	155	10	.	.	PUNCT
ejpam-176	156	1	theorem	theorem	VERB
ejpam-176	156	2	3.6	3.6	NUM
ejpam-176	156	3	.	.	PUNCT
ejpam-176	157	1	let	let	VERB
ejpam-176	157	2	a	a	PRON
ejpam-176	157	3	,	,	PUNCT
ejpam-176	157	4	y	y	PROPN
ejpam-176	157	5	be	be	VERB
ejpam-176	157	6	subsets	subset	NOUN
ejpam-176	157	7	of	of	ADP
ejpam-176	157	8	a	a	DET
ejpam-176	157	9	space	space	NOUN
ejpam-176	157	10	(	(	PUNCT
ejpam-176	157	11	x	x	X
ejpam-176	157	12	,	,	PUNCT
ejpam-176	157	13	τ	τ	X
ejpam-176	157	14	)	)	PUNCT
ejpam-176	157	15	such	such	ADJ
ejpam-176	157	16	that	that	SCONJ
ejpam-176	157	17	a	a	DET
ejpam-176	157	18	⊂	⊂	X
ejpam-176	157	19	y	y	PROPN
ejpam-176	157	20	⊂	⊂	PROPN
ejpam-176	157	21	x	x	X
ejpam-176	157	22	and	and	CCONJ
ejpam-176	157	23	y	y	PROPN
ejpam-176	157	24	be	be	AUX
ejpam-176	157	25	α	α	NOUN
ejpam-176	157	26	-	-	NOUN
ejpam-176	157	27	open	open	ADJ
ejpam-176	157	28	in	in	ADP
ejpam-176	157	29	(	(	PUNCT
ejpam-176	157	30	x	x	INTJ
ejpam-176	157	31	,	,	PUNCT
ejpam-176	157	32	τ	τ	PROPN
ejpam-176	157	33	)	)	PUNCT
ejpam-176	157	34	.	.	PUNCT
ejpam-176	158	1	then	then	ADV
ejpam-176	158	2	a	a	PRON
ejpam-176	158	3	is	be	AUX
ejpam-176	158	4	β	β	X
ejpam-176	158	5	-closed	-close	VERB
ejpam-176	158	6	relative	relative	ADJ
ejpam-176	158	7	to	to	ADP
ejpam-176	158	8	(	(	PUNCT
ejpam-176	158	9	y	y	PROPN
ejpam-176	158	10	,	,	PUNCT
ejpam-176	158	11	τy	τy	PRON
ejpam-176	158	12	)	)	PUNCT
ejpam-176	158	13	if	if	SCONJ
ejpam-176	158	14	and	and	CCONJ
ejpam-176	158	15	only	only	ADV
ejpam-176	158	16	if	if	SCONJ
ejpam-176	158	17	a	a	PRON
ejpam-176	158	18	is	be	AUX
ejpam-176	158	19	β	β	X
ejpam-176	158	20	-closed	-close	VERB
ejpam-176	158	21	relative	relative	ADJ
ejpam-176	158	22	to	to	ADP
ejpam-176	158	23	(	(	PUNCT
ejpam-176	158	24	x	x	INTJ
ejpam-176	158	25	,	,	PUNCT
ejpam-176	158	26	τ	τ	PROPN
ejpam-176	158	27	)	)	PUNCT
ejpam-176	158	28	.	.	PUNCT
ejpam-176	159	1	proof	proof	NOUN
ejpam-176	159	2	:	:	PUNCT
ejpam-176	159	3	the	the	DET
ejpam-176	159	4	proof	proof	NOUN
ejpam-176	159	5	is	be	AUX
ejpam-176	159	6	obvious	obvious	ADJ
ejpam-176	159	7	because	because	SCONJ
ejpam-176	159	8	of	of	ADP
ejpam-176	159	9	theorem	theorem	NOUN
ejpam-176	159	10	3.7	3.7	NUM
ejpam-176	159	11	.	.	PUNCT
ejpam-176	160	1	corollary	corollary	ADJ
ejpam-176	160	2	3.1	3.1	NUM
ejpam-176	160	3	.	.	PUNCT
ejpam-176	161	1	if	if	SCONJ
ejpam-176	161	2	y	y	PROPN
ejpam-176	161	3	,	,	PUNCT
ejpam-176	161	4	z	z	PROPN
ejpam-176	161	5	are	be	AUX
ejpam-176	161	6	open	open	ADJ
ejpam-176	161	7	subsets	subset	NOUN
ejpam-176	161	8	of	of	ADP
ejpam-176	161	9	a	a	DET
ejpam-176	161	10	space	space	NOUN
ejpam-176	161	11	x	x	INTJ
ejpam-176	161	12	such	such	ADJ
ejpam-176	161	13	that	that	SCONJ
ejpam-176	161	14	z	z	PROPN
ejpam-176	161	15	⊂	⊂	PROPN
ejpam-176	162	1	y	y	PROPN
ejpam-176	162	2	⊂	⊂	PROPN
ejpam-176	162	3	x	x	X
ejpam-176	162	4	then	then	ADV
ejpam-176	162	5	z	z	PROPN
ejpam-176	162	6	is	be	AUX
ejpam-176	162	7	a	a	DET
ejpam-176	162	8	β	β	X
ejpam-176	162	9	-closed	-close	VERB
ejpam-176	162	10	subspace	subspace	NOUN
ejpam-176	162	11	of	of	ADP
ejpam-176	162	12	y	y	PRON
ejpam-176	162	13	if	if	SCONJ
ejpam-176	163	1	and	and	CCONJ
ejpam-176	163	2	only	only	ADV
ejpam-176	163	3	if	if	SCONJ
ejpam-176	163	4	z	z	NOUN
ejpam-176	163	5	is	be	AUX
ejpam-176	163	6	a	a	DET
ejpam-176	163	7	β	β	X
ejpam-176	163	8	-closed	-close	VERB
ejpam-176	163	9	subspace	subspace	NOUN
ejpam-176	163	10	of	of	ADP
ejpam-176	163	11	x	x	PROPN
ejpam-176	163	12	.	.	PUNCT
ejpam-176	164	1	c.	c.	PROPN
ejpam-176	164	2	basu	basu	PROPN
ejpam-176	164	3	and	and	CCONJ
ejpam-176	164	4	m.	m.	PROPN
ejpam-176	164	5	ghosh	ghosh	PROPN
ejpam-176	164	6	/	/	PUNCT
ejpam-176	164	7	eur	eur	PROPN
ejpam-176	164	8	.	.	PUNCT
ejpam-176	165	1	j.	j.	PROPN
ejpam-176	165	2	pure	pure	PROPN
ejpam-176	165	3	appl	appl	PROPN
ejpam-176	165	4	.	.	PROPN
ejpam-176	165	5	math	math	PROPN
ejpam-176	165	6	,	,	PUNCT
ejpam-176	165	7	2	2	NUM
ejpam-176	165	8	(	(	PUNCT
ejpam-176	165	9	2009	2009	NUM
ejpam-176	165	10	)	)	PUNCT
ejpam-176	165	11	,	,	PUNCT
ejpam-176	165	12	(	(	PUNCT
ejpam-176	165	13	85	85	NUM
ejpam-176	165	14	-	-	SYM
ejpam-176	165	15	96	96	NUM
ejpam-176	165	16	)	)	PUNCT
ejpam-176	165	17	90	90	NUM
ejpam-176	165	18	proof	proof	NOUN
ejpam-176	165	19	:	:	PUNCT
ejpam-176	165	20	the	the	DET
ejpam-176	165	21	proof	proof	NOUN
ejpam-176	165	22	follows	follow	VERB
ejpam-176	165	23	from	from	ADP
ejpam-176	165	24	theorem	theorem	ADJ
ejpam-176	165	25	3.8	3.8	NUM
ejpam-176	165	26	and	and	CCONJ
ejpam-176	165	27	theorem	theorem	VERB
ejpam-176	165	28	3.9	3.9	NUM
ejpam-176	165	29	.	.	PUNCT
ejpam-176	166	1	definition	definition	NOUN
ejpam-176	166	2	3.2	3.2	NUM
ejpam-176	166	3	.	.	PUNCT
ejpam-176	167	1	a	a	DET
ejpam-176	167	2	function	function	NOUN
ejpam-176	167	3	ψ	ψ	NOUN
ejpam-176	167	4	:	:	PUNCT
ejpam-176	167	5	x	x	SYM
ejpam-176	167	6	→	→	SYM
ejpam-176	167	7	y	y	PROPN
ejpam-176	167	8	is	be	AUX
ejpam-176	167	9	said	say	VERB
ejpam-176	167	10	to	to	PART
ejpam-176	167	11	be	be	AUX
ejpam-176	167	12	β	β	X
ejpam-176	167	13	-θ	-θ	PUNCT
ejpam-176	167	14	-closed	-close	VERB
ejpam-176	167	15	if	if	SCONJ
ejpam-176	167	16	image	image	NOUN
ejpam-176	167	17	of	of	ADP
ejpam-176	167	18	each	each	DET
ejpam-176	167	19	β	β	X
ejpam-176	167	20	-θ	-θ	PUNCT
ejpam-176	167	21	-closed	-close	VERB
ejpam-176	167	22	set	set	NOUN
ejpam-176	167	23	is	be	AUX
ejpam-176	167	24	closed	close	VERB
ejpam-176	167	25	in	in	ADP
ejpam-176	167	26	y	y	PROPN
ejpam-176	167	27	.	.	PUNCT
ejpam-176	168	1	it	it	PRON
ejpam-176	168	2	is	be	AUX
ejpam-176	168	3	not	not	PART
ejpam-176	168	4	hard	hard	ADJ
ejpam-176	168	5	to	to	PART
ejpam-176	168	6	prove	prove	VERB
ejpam-176	168	7	the	the	DET
ejpam-176	168	8	following	follow	VERB
ejpam-176	168	9	characterizations	characterization	NOUN
ejpam-176	168	10	for	for	ADP
ejpam-176	168	11	β	β	X
ejpam-176	168	12	-θ	-θ	X
ejpam-176	168	13	-closed	-close	VERB
ejpam-176	168	14	function	function	NOUN
ejpam-176	168	15	.	.	PUNCT
ejpam-176	169	1	theorem	theorem	VERB
ejpam-176	169	2	3.7	3.7	NUM
ejpam-176	169	3	.	.	PUNCT
ejpam-176	170	1	for	for	ADP
ejpam-176	170	2	a	a	DET
ejpam-176	170	3	function	function	NOUN
ejpam-176	170	4	ψ	ψ	NOUN
ejpam-176	170	5	:	:	PUNCT
ejpam-176	170	6	x	x	X
ejpam-176	170	7	→	→	SYM
ejpam-176	170	8	y	y	PROPN
ejpam-176	170	9	,	,	PUNCT
ejpam-176	170	10	the	the	DET
ejpam-176	170	11	following	follow	VERB
ejpam-176	170	12	are	be	AUX
ejpam-176	170	13	equivalent	equivalent	ADJ
ejpam-176	170	14	:	:	PUNCT
ejpam-176	170	15	(	(	PUNCT
ejpam-176	170	16	i	i	NOUN
ejpam-176	170	17	)	)	PUNCT
ejpam-176	170	18	ψ	ψ	NOUN
ejpam-176	170	19	is	be	AUX
ejpam-176	170	20	β	β	X
ejpam-176	170	21	-θ	-θ	PUNCT
ejpam-176	170	22	-closed	-closed	PROPN
ejpam-176	170	23	.	.	PUNCT
ejpam-176	171	1	(	(	PUNCT
ejpam-176	171	2	ii	ii	NOUN
ejpam-176	171	3	)	)	PUNCT
ejpam-176	171	4	cl(ψ(b	cl(ψ(b	NOUN
ejpam-176	171	5	)	)	PUNCT
ejpam-176	171	6	)	)	PUNCT
ejpam-176	172	1	⊂ψ(β	⊂ψ(β	PROPN
ejpam-176	172	2	-θ	-θ	NUM
ejpam-176	172	3	-cl(b	-cl(b	NOUN
ejpam-176	172	4	)	)	PUNCT
ejpam-176	172	5	)	)	PUNCT
ejpam-176	172	6	,	,	PUNCT
ejpam-176	172	7	for	for	ADP
ejpam-176	172	8	each	each	DET
ejpam-176	172	9	b	b	PROPN
ejpam-176	172	10	⊂	⊂	PROPN
ejpam-176	172	11	x	x	X
ejpam-176	172	12	.	.	PUNCT
ejpam-176	173	1	(	(	PUNCT
ejpam-176	173	2	iii	iii	NOUN
ejpam-176	173	3	)	)	PUNCT
ejpam-176	173	4	for	for	ADP
ejpam-176	173	5	each	each	DET
ejpam-176	173	6	y	y	PROPN
ejpam-176	173	7	∈	∈	PROPN
ejpam-176	173	8	y	y	PROPN
ejpam-176	173	9	and	and	CCONJ
ejpam-176	173	10	each	each	DET
ejpam-176	173	11	β	β	X
ejpam-176	173	12	-θ	-θ	PUNCT
ejpam-176	173	13	-open	-open	PROPN
ejpam-176	173	14	set	set	VERB
ejpam-176	173	15	v	v	NOUN
ejpam-176	173	16	containing	contain	VERB
ejpam-176	173	17	ψ−1(y	ψ−1(y	PROPN
ejpam-176	173	18	)	)	PUNCT
ejpam-176	173	19	,	,	PUNCT
ejpam-176	173	20	there	there	PRON
ejpam-176	173	21	is	be	VERB
ejpam-176	173	22	an	an	DET
ejpam-176	173	23	open	open	ADJ
ejpam-176	173	24	set	set	NOUN
ejpam-176	173	25	u	u	NOUN
ejpam-176	173	26	containing	contain	VERB
ejpam-176	173	27	y	y	PRON
ejpam-176	173	28	satisfying	satisfy	VERB
ejpam-176	173	29	ψ−1(u)⊂	ψ−1(u)⊂	NOUN
ejpam-176	173	30	v	v	NOUN
ejpam-176	173	31	.	.	PUNCT
ejpam-176	174	1	(	(	PUNCT
ejpam-176	174	2	iv	iv	X
ejpam-176	174	3	)	)	PUNCT
ejpam-176	174	4	for	for	ADP
ejpam-176	174	5	each	each	PRON
ejpam-176	174	6	subset	subset	VERB
ejpam-176	174	7	a	a	DET
ejpam-176	174	8	of	of	ADP
ejpam-176	174	9	y	y	PROPN
ejpam-176	174	10	and	and	CCONJ
ejpam-176	174	11	each	each	DET
ejpam-176	174	12	β	β	X
ejpam-176	174	13	-θ	-θ	PUNCT
ejpam-176	174	14	-open	-open	PROPN
ejpam-176	174	15	set	set	NOUN
ejpam-176	174	16	v	v	NOUN
ejpam-176	174	17	containing	contain	VERB
ejpam-176	174	18	ψ−1(a	ψ−1(a	NOUN
ejpam-176	174	19	)	)	PUNCT
ejpam-176	174	20	there	there	PRON
ejpam-176	174	21	is	be	VERB
ejpam-176	174	22	an	an	DET
ejpam-176	174	23	open	open	ADJ
ejpam-176	174	24	set	set	NOUN
ejpam-176	174	25	u	u	NOUN
ejpam-176	174	26	containing	contain	VERB
ejpam-176	174	27	a	a	DET
ejpam-176	174	28	such	such	ADJ
ejpam-176	174	29	that	that	SCONJ
ejpam-176	174	30	ψ−1(u)⊂	ψ−1(u)⊂	NOUN
ejpam-176	174	31	v	v	X
ejpam-176	174	32	.	.	PUNCT
ejpam-176	175	1	(	(	PUNCT
ejpam-176	175	2	v	v	NOUN
ejpam-176	175	3	)	)	PUNCT
ejpam-176	175	4	{	{	PUNCT
ejpam-176	175	5	y	y	PROPN
ejpam-176	175	6	∈	∈	PROPN
ejpam-176	176	1	y	y	PROPN
ejpam-176	176	2	:	:	PUNCT
ejpam-176	176	3	ψ−1(y)⊂	ψ−1(y)⊂	PROPN
ejpam-176	176	4	v	v	X
ejpam-176	176	5	}	}	PUNCT
ejpam-176	176	6	is	be	AUX
ejpam-176	176	7	open	open	ADJ
ejpam-176	176	8	in	in	ADP
ejpam-176	176	9	y	y	PROPN
ejpam-176	176	10	whenever	whenever	SCONJ
ejpam-176	176	11	u	u	NOUN
ejpam-176	176	12	is	be	AUX
ejpam-176	176	13	β	β	X
ejpam-176	176	14	-θ	-θ	PUNCT
ejpam-176	176	15	-open	-open	VERB
ejpam-176	176	16	in	in	ADP
ejpam-176	176	17	x	x	X
ejpam-176	176	18	.	.	PUNCT
ejpam-176	177	1	(	(	PUNCT
ejpam-176	177	2	vi	vi	X
ejpam-176	177	3	)	)	PUNCT
ejpam-176	177	4	{	{	PUNCT
ejpam-176	177	5	y	y	PROPN
ejpam-176	177	6	∈	∈	PROPN
ejpam-176	177	7	y	y	PROPN
ejpam-176	177	8	:	:	PUNCT
ejpam-176	177	9	ψ−1(y)∩	ψ−1(y)∩	PROPN
ejpam-176	177	10	b	b	PROPN
ejpam-176	178	1	6=	6=	PROPN
ejpam-176	178	2	;	;	PUNCT
ejpam-176	178	3	}	}	PUNCT
ejpam-176	178	4	is	be	AUX
ejpam-176	178	5	closed	close	VERB
ejpam-176	178	6	in	in	ADP
ejpam-176	178	7	y	y	PROPN
ejpam-176	178	8	whenever	whenever	SCONJ
ejpam-176	178	9	b	b	PROPN
ejpam-176	178	10	is	be	AUX
ejpam-176	178	11	β	β	PART
ejpam-176	178	12	-θ	-θ	PUNCT
ejpam-176	178	13	-closed	-closed	ADJ
ejpam-176	178	14	in	in	ADP
ejpam-176	178	15	x	x	X
ejpam-176	178	16	.	.	PUNCT
ejpam-176	179	1	the	the	DET
ejpam-176	179	2	concepts	concept	NOUN
ejpam-176	179	3	of	of	ADP
ejpam-176	179	4	closed	closed	ADJ
ejpam-176	179	5	functions	function	NOUN
ejpam-176	179	6	and	and	CCONJ
ejpam-176	179	7	β	β	X
ejpam-176	179	8	-θ	-θ	PUNCT
ejpam-176	179	9	-closed	-close	VERB
ejpam-176	179	10	functions	function	NOUN
ejpam-176	179	11	are	be	AUX
ejpam-176	179	12	independent	independent	ADJ
ejpam-176	179	13	to	to	ADP
ejpam-176	179	14	each	each	DET
ejpam-176	179	15	other	other	ADJ
ejpam-176	179	16	.	.	PUNCT
ejpam-176	180	1	in	in	ADP
ejpam-176	180	2	addition	addition	NOUN
ejpam-176	180	3	,	,	PUNCT
ejpam-176	180	4	the	the	DET
ejpam-176	180	5	notions	notion	NOUN
ejpam-176	180	6	of	of	ADP
ejpam-176	180	7	continuity	continuity	NOUN
ejpam-176	180	8	and	and	CCONJ
ejpam-176	180	9	β	β	X
ejpam-176	180	10	-θ	-θ	ADJ
ejpam-176	180	11	-closedness	-closedness	PROPN
ejpam-176	180	12	are	be	AUX
ejpam-176	180	13	also	also	ADV
ejpam-176	180	14	independent	independent	ADJ
ejpam-176	180	15	.	.	PUNCT
ejpam-176	181	1	to	to	PART
ejpam-176	181	2	validitate	validitate	VERB
ejpam-176	181	3	these	these	PRON
ejpam-176	181	4	we	we	PRON
ejpam-176	181	5	establish	establish	VERB
ejpam-176	181	6	the	the	DET
ejpam-176	181	7	following	following	ADJ
ejpam-176	181	8	examples	example	NOUN
ejpam-176	181	9	:	:	PUNCT
ejpam-176	181	10	example	example	NOUN
ejpam-176	182	1	3.1	3.1	NUM
ejpam-176	182	2	.	.	PUNCT
ejpam-176	183	1	let	let	VERB
ejpam-176	183	2	x	x	PUNCT
ejpam-176	183	3	=	=	SYM
ejpam-176	183	4	r	r	NOUN
ejpam-176	183	5	,	,	PUNCT
ejpam-176	183	6	the	the	DET
ejpam-176	183	7	set	set	NOUN
ejpam-176	183	8	of	of	ADP
ejpam-176	183	9	reals	real	NOUN
ejpam-176	183	10	with	with	ADP
ejpam-176	183	11	the	the	DET
ejpam-176	183	12	topology	topology	NOUN
ejpam-176	183	13	τx	τx	INTJ
ejpam-176	183	14	in	in	ADP
ejpam-176	183	15	which	which	PRON
ejpam-176	183	16	the	the	DET
ejpam-176	183	17	non	non	ADJ
ejpam-176	183	18	-	-	ADJ
ejpam-176	183	19	void	void	ADJ
ejpam-176	183	20	open	open	ADJ
ejpam-176	183	21	sets	set	NOUN
ejpam-176	183	22	are	be	AUX
ejpam-176	183	23	subsets	subset	NOUN
ejpam-176	183	24	of	of	ADP
ejpam-176	183	25	x	x	PUNCT
ejpam-176	183	26	which	which	PRON
ejpam-176	183	27	contain	contain	VERB
ejpam-176	183	28	the	the	DET
ejpam-176	183	29	point	point	NOUN
ejpam-176	183	30	1	1	NUM
ejpam-176	183	31	.	.	PUNCT
ejpam-176	184	1	clearly	clearly	ADV
ejpam-176	184	2	every	every	DET
ejpam-176	184	3	non	non	ADJ
ejpam-176	184	4	-	-	ADJ
ejpam-176	184	5	void	void	ADJ
ejpam-176	184	6	β	β	X
ejpam-176	184	7	-open	-open	PROPN
ejpam-176	184	8	set	set	NOUN
ejpam-176	184	9	must	must	AUX
ejpam-176	184	10	contains	contain	VERB
ejpam-176	184	11	the	the	DET
ejpam-176	184	12	point	point	NOUN
ejpam-176	184	13	1	1	NUM
ejpam-176	184	14	and	and	CCONJ
ejpam-176	184	15	β	β	X
ejpam-176	184	16	-θ	-θ	PUNCT
ejpam-176	184	17	-closed	-close	VERB
ejpam-176	184	18	sets	set	NOUN
ejpam-176	184	19	are	be	AUX
ejpam-176	184	20	;	;	PUNCT
ejpam-176	184	21	and	and	CCONJ
ejpam-176	184	22	x	x	X
ejpam-176	184	23	only	only	ADV
ejpam-176	184	24	.	.	PUNCT
ejpam-176	185	1	let	let	VERB
ejpam-176	185	2	y	y	PROPN
ejpam-176	185	3	=	=	PUNCT
ejpam-176	185	4	{	{	PUNCT
ejpam-176	185	5	a	a	PRON
ejpam-176	185	6	,	,	PUNCT
ejpam-176	185	7	b	b	NOUN
ejpam-176	185	8	,	,	PUNCT
ejpam-176	185	9	c	c	NOUN
ejpam-176	185	10	}	}	PUNCT
ejpam-176	185	11	with	with	ADP
ejpam-176	185	12	the	the	DET
ejpam-176	185	13	topology	topology	NOUN
ejpam-176	185	14	τy	τy	ADP
ejpam-176	185	15	=	=	PUNCT
ejpam-176	185	16	{	{	PUNCT
ejpam-176	185	17	;	;	PUNCT
ejpam-176	185	18	,	,	PUNCT
ejpam-176	185	19	y	y	PROPN
ejpam-176	185	20	,	,	PUNCT
ejpam-176	185	21	{	{	PUNCT
ejpam-176	185	22	a	a	X
ejpam-176	185	23	}	}	PUNCT
ejpam-176	185	24	,	,	PUNCT
ejpam-176	185	25	{	{	PUNCT
ejpam-176	185	26	a	a	PRON
ejpam-176	185	27	,	,	PUNCT
ejpam-176	185	28	c	c	NOUN
ejpam-176	185	29	}	}	PUNCT
ejpam-176	185	30	}	}	PUNCT
ejpam-176	185	31	.	.	PUNCT
ejpam-176	186	1	let	let	VERB
ejpam-176	186	2	ψ	ψ	X
ejpam-176	186	3	:	:	PUNCT
ejpam-176	186	4	(	(	PUNCT
ejpam-176	186	5	x	x	X
ejpam-176	186	6	,	,	PUNCT
ejpam-176	186	7	τx	τx	PROPN
ejpam-176	186	8	)	)	PUNCT
ejpam-176	186	9	→	→	SYM
ejpam-176	186	10	(	(	PUNCT
ejpam-176	186	11	y	y	PROPN
ejpam-176	186	12	,	,	PUNCT
ejpam-176	186	13	τy	τy	PART
ejpam-176	186	14	)	)	PUNCT
ejpam-176	186	15	be	be	AUX
ejpam-176	186	16	defined	define	VERB
ejpam-176	186	17	as	as	ADP
ejpam-176	186	18	ψ(x	ψ(x	NOUN
ejpam-176	186	19	)	)	PUNCT
ejpam-176	186	20	=	=	NOUN
ejpam-176	187	1	a	a	PRON
ejpam-176	187	2	for	for	ADP
ejpam-176	187	3	all	all	DET
ejpam-176	187	4	x	x	SYM
ejpam-176	187	5	∈	∈	NOUN
ejpam-176	187	6	x	x	X
ejpam-176	187	7	.	.	PUNCT
ejpam-176	188	1	clearly	clearly	ADV
ejpam-176	188	2	ψ	ψ	X
ejpam-176	188	3	is	be	AUX
ejpam-176	188	4	continuous	continuous	ADJ
ejpam-176	188	5	but	but	CCONJ
ejpam-176	188	6	as	as	ADP
ejpam-176	188	7	ψ(x	ψ(x	NOUN
ejpam-176	188	8	)	)	PUNCT
ejpam-176	189	1	=	=	PRON
ejpam-176	189	2	{	{	PUNCT
ejpam-176	189	3	a	a	NOUN
ejpam-176	189	4	}	}	PUNCT
ejpam-176	189	5	,	,	PUNCT
ejpam-176	189	6	where	where	SCONJ
ejpam-176	189	7	{	{	PUNCT
ejpam-176	189	8	a	a	PRON
ejpam-176	189	9	}	}	PUNCT
ejpam-176	189	10	is	be	AUX
ejpam-176	189	11	not	not	PART
ejpam-176	189	12	closed	close	VERB
ejpam-176	189	13	in	in	ADP
ejpam-176	189	14	y	y	PROPN
ejpam-176	189	15	,	,	PUNCT
ejpam-176	189	16	ψ	ψ	X
ejpam-176	189	17	is	be	AUX
ejpam-176	189	18	not	not	PART
ejpam-176	189	19	a	a	DET
ejpam-176	189	20	β	β	X
ejpam-176	189	21	-θ	-θ	PUNCT
ejpam-176	189	22	-closed	-closed	ADJ
ejpam-176	189	23	function	function	NOUN
ejpam-176	189	24	.	.	PUNCT
ejpam-176	190	1	example	example	NOUN
ejpam-176	190	2	3.2	3.2	NUM
ejpam-176	190	3	.	.	PUNCT
ejpam-176	191	1	let	let	VERB
ejpam-176	191	2	x	x	PUNCT
ejpam-176	191	3	=	=	PRON
ejpam-176	191	4	{	{	PUNCT
ejpam-176	191	5	a	a	DET
ejpam-176	191	6	,	,	PUNCT
ejpam-176	191	7	b	b	NOUN
ejpam-176	191	8	,	,	PUNCT
ejpam-176	191	9	c	c	NOUN
ejpam-176	191	10	}	}	PUNCT
ejpam-176	191	11	,	,	PUNCT
ejpam-176	191	12	τ	τ	X
ejpam-176	191	13	=	=	PUNCT
ejpam-176	191	14	{	{	PUNCT
ejpam-176	191	15	;	;	PUNCT
ejpam-176	191	16	,	,	PUNCT
ejpam-176	191	17	x	x	X
ejpam-176	191	18	,	,	PUNCT
ejpam-176	191	19	{	{	PUNCT
ejpam-176	191	20	a	a	NOUN
ejpam-176	191	21	}	}	PUNCT
ejpam-176	191	22	,	,	PUNCT
ejpam-176	191	23	{	{	PUNCT
ejpam-176	191	24	a	a	DET
ejpam-176	191	25	,	,	PUNCT
ejpam-176	191	26	b	b	NOUN
ejpam-176	191	27	}	}	PUNCT
ejpam-176	191	28	,	,	PUNCT
ejpam-176	191	29	{	{	PUNCT
ejpam-176	191	30	a	a	PRON
ejpam-176	191	31	,	,	PUNCT
ejpam-176	191	32	c	c	NOUN
ejpam-176	191	33	}	}	PUNCT
ejpam-176	191	34	}	}	PUNCT
ejpam-176	191	35	and	and	CCONJ
ejpam-176	191	36	σ	σ	X
ejpam-176	191	37	=	=	PUNCT
ejpam-176	191	38	{	{	PUNCT
ejpam-176	191	39	;	;	PUNCT
ejpam-176	191	40	,	,	PUNCT
ejpam-176	191	41	x	x	X
ejpam-176	191	42	,	,	PUNCT
ejpam-176	191	43	{	{	PUNCT
ejpam-176	191	44	a	a	NOUN
ejpam-176	191	45	}	}	PUNCT
ejpam-176	191	46	,	,	PUNCT
ejpam-176	191	47	{	{	PUNCT
ejpam-176	191	48	a	a	DET
ejpam-176	191	49	,	,	PUNCT
ejpam-176	191	50	b	b	NOUN
ejpam-176	191	51	}	}	PUNCT
ejpam-176	191	52	}	}	PUNCT
ejpam-176	191	53	.	.	PUNCT
ejpam-176	192	1	consider	consider	VERB
ejpam-176	192	2	the	the	DET
ejpam-176	192	3	identity	identity	NOUN
ejpam-176	192	4	function	function	NOUN
ejpam-176	192	5	ψ1	ψ1	NOUN
ejpam-176	192	6	:	:	PUNCT
ejpam-176	192	7	(	(	PUNCT
ejpam-176	192	8	x	x	X
ejpam-176	192	9	,	,	PUNCT
ejpam-176	192	10	τ)→	τ)→	PROPN
ejpam-176	192	11	(	(	PUNCT
ejpam-176	192	12	x	x	X
ejpam-176	192	13	,	,	PUNCT
ejpam-176	192	14	σ	σ	PROPN
ejpam-176	192	15	)	)	PUNCT
ejpam-176	192	16	.	.	PUNCT
ejpam-176	193	1	clearlyψ1	clearlyψ1	PROPN
ejpam-176	193	2	is	be	AUX
ejpam-176	193	3	not	not	PART
ejpam-176	193	4	a	a	DET
ejpam-176	193	5	closed	closed	ADJ
ejpam-176	193	6	function	function	NOUN
ejpam-176	193	7	but	but	CCONJ
ejpam-176	193	8	ψ1	ψ1	NOUN
ejpam-176	193	9	is	be	AUX
ejpam-176	193	10	β	β	X
ejpam-176	193	11	-θ	-θ	PUNCT
ejpam-176	193	12	-closed	-close	VERB
ejpam-176	193	13	since	since	SCONJ
ejpam-176	193	14	the	the	DET
ejpam-176	193	15	only	only	ADJ
ejpam-176	193	16	β	β	X
ejpam-176	193	17	-θ	-θ	PUNCT
ejpam-176	193	18	-closed	-close	VERB
ejpam-176	193	19	sets	set	NOUN
ejpam-176	193	20	of	of	ADP
ejpam-176	193	21	(	(	PUNCT
ejpam-176	193	22	x	x	INTJ
ejpam-176	193	23	,	,	PUNCT
ejpam-176	193	24	τ	τ	X
ejpam-176	193	25	)	)	PUNCT
ejpam-176	193	26	are	be	AUX
ejpam-176	193	27	φ	φ	PROPN
ejpam-176	193	28	and	and	CCONJ
ejpam-176	193	29	x	x	X
ejpam-176	193	30	only	only	ADV
ejpam-176	193	31	.	.	PUNCT
ejpam-176	194	1	again	again	ADV
ejpam-176	194	2	the	the	DET
ejpam-176	194	3	identity	identity	NOUN
ejpam-176	194	4	function	function	NOUN
ejpam-176	194	5	ψ2	ψ2	NOUN
ejpam-176	194	6	:	:	PUNCT
ejpam-176	194	7	(	(	PUNCT
ejpam-176	194	8	x	x	X
ejpam-176	194	9	,	,	PUNCT
ejpam-176	194	10	σ	σ	PROPN
ejpam-176	194	11	)	)	PUNCT
ejpam-176	194	12	→	→	SYM
ejpam-176	194	13	(	(	PUNCT
ejpam-176	194	14	x	x	X
ejpam-176	194	15	,	,	PUNCT
ejpam-176	194	16	τ	τ	X
ejpam-176	194	17	)	)	PUNCT
ejpam-176	194	18	is	be	AUX
ejpam-176	194	19	clearly	clearly	ADV
ejpam-176	194	20	a	a	DET
ejpam-176	194	21	closed	closed	ADJ
ejpam-176	194	22	function	function	NOUN
ejpam-176	194	23	which	which	PRON
ejpam-176	194	24	is	be	AUX
ejpam-176	194	25	not	not	PART
ejpam-176	194	26	continuous	continuous	ADJ
ejpam-176	194	27	.	.	PUNCT
ejpam-176	195	1	since	since	SCONJ
ejpam-176	195	2	the	the	DET
ejpam-176	195	3	family	family	NOUN
ejpam-176	195	4	of	of	ADP
ejpam-176	195	5	c.	c.	PROPN
ejpam-176	195	6	basu	basu	PROPN
ejpam-176	195	7	and	and	CCONJ
ejpam-176	195	8	m.	m.	PROPN
ejpam-176	195	9	ghosh	ghosh	PROPN
ejpam-176	195	10	/	/	PUNCT
ejpam-176	195	11	eur	eur	PROPN
ejpam-176	195	12	.	.	PUNCT
ejpam-176	196	1	j.	j.	PROPN
ejpam-176	196	2	pure	pure	PROPN
ejpam-176	196	3	appl	appl	PROPN
ejpam-176	196	4	.	.	PROPN
ejpam-176	196	5	math	math	PROPN
ejpam-176	196	6	,	,	PUNCT
ejpam-176	196	7	2	2	NUM
ejpam-176	196	8	(	(	PUNCT
ejpam-176	196	9	2009	2009	NUM
ejpam-176	196	10	)	)	PUNCT
ejpam-176	196	11	,	,	PUNCT
ejpam-176	196	12	(	(	PUNCT
ejpam-176	196	13	85	85	NUM
ejpam-176	196	14	-	-	SYM
ejpam-176	196	15	96	96	NUM
ejpam-176	196	16	)	)	PUNCT
ejpam-176	196	17	91	91	NUM
ejpam-176	196	18	all	all	DET
ejpam-176	196	19	β	β	NOUN
ejpam-176	196	20	-open	-open	ADJ
ejpam-176	196	21	sets	set	NOUN
ejpam-176	196	22	of	of	ADP
ejpam-176	196	23	(	(	PUNCT
ejpam-176	196	24	x	x	PROPN
ejpam-176	196	25	,	,	PUNCT
ejpam-176	196	26	σ	σ	PROPN
ejpam-176	196	27	)	)	PUNCT
ejpam-176	196	28	is	be	AUX
ejpam-176	196	29	{	{	PUNCT
ejpam-176	196	30	;	;	PUNCT
ejpam-176	196	31	,	,	PUNCT
ejpam-176	196	32	x	x	X
ejpam-176	196	33	,	,	PUNCT
ejpam-176	196	34	{	{	PUNCT
ejpam-176	196	35	a	a	NOUN
ejpam-176	196	36	}	}	PUNCT
ejpam-176	196	37	,	,	PUNCT
ejpam-176	196	38	{	{	PUNCT
ejpam-176	196	39	a	a	DET
ejpam-176	196	40	,	,	PUNCT
ejpam-176	196	41	b	b	NOUN
ejpam-176	196	42	}	}	PUNCT
ejpam-176	196	43	,	,	PUNCT
ejpam-176	196	44	{	{	PUNCT
ejpam-176	196	45	a	a	PRON
ejpam-176	196	46	,	,	PUNCT
ejpam-176	196	47	c	c	NOUN
ejpam-176	196	48	}	}	PUNCT
ejpam-176	196	49	}	}	PUNCT
ejpam-176	196	50	then	then	ADV
ejpam-176	196	51	βr(x	βr(x	PUNCT
ejpam-176	196	52	,	,	PUNCT
ejpam-176	196	53	σ	σ	PROPN
ejpam-176	196	54	)	)	PUNCT
ejpam-176	196	55	=	=	PUNCT
ejpam-176	197	1	β	β	X
ejpam-176	197	2	-θ	-θ	PUNCT
ejpam-176	198	1	-o(x	-o(x	ADV
ejpam-176	198	2	,	,	PUNCT
ejpam-176	198	3	σ	σ	PROPN
ejpam-176	198	4	)	)	PUNCT
ejpam-176	198	5	=	=	PRON
ejpam-176	198	6	{	{	PUNCT
ejpam-176	198	7	;	;	PUNCT
ejpam-176	198	8	,	,	PUNCT
ejpam-176	198	9	x	x	SYM
ejpam-176	198	10	}	}	PUNCT
ejpam-176	198	11	.	.	PUNCT
ejpam-176	199	1	therefore	therefore	ADV
ejpam-176	199	2	ψ2	ψ2	NOUN
ejpam-176	199	3	is	be	AUX
ejpam-176	199	4	a	a	DET
ejpam-176	199	5	β	β	X
ejpam-176	199	6	-θ	-θ	PUNCT
ejpam-176	199	7	-closed	-closed	ADJ
ejpam-176	199	8	function	function	NOUN
ejpam-176	199	9	.	.	PUNCT
ejpam-176	200	1	example	example	NOUN
ejpam-176	200	2	3.3	3.3	NUM
ejpam-176	200	3	.	.	PUNCT
ejpam-176	201	1	the	the	DET
ejpam-176	201	2	identity	identity	NOUN
ejpam-176	201	3	function	function	NOUN
ejpam-176	201	4	ψ	ψ	X
ejpam-176	201	5	:	:	PUNCT
ejpam-176	201	6	(	(	PUNCT
ejpam-176	201	7	r	r	NOUN
ejpam-176	201	8	,	,	PUNCT
ejpam-176	201	9	u	u	NOUN
ejpam-176	201	10	)	)	PUNCT
ejpam-176	201	11	→	→	SYM
ejpam-176	201	12	(	(	PUNCT
ejpam-176	201	13	r	r	NOUN
ejpam-176	201	14	,	,	PUNCT
ejpam-176	201	15	u	u	NOUN
ejpam-176	201	16	)	)	PUNCT
ejpam-176	201	17	,	,	PUNCT
ejpam-176	201	18	where	where	SCONJ
ejpam-176	201	19	(	(	PUNCT
ejpam-176	201	20	r	r	NOUN
ejpam-176	201	21	,	,	PUNCT
ejpam-176	201	22	u	u	NOUN
ejpam-176	201	23	)	)	PUNCT
ejpam-176	201	24	is	be	AUX
ejpam-176	201	25	the	the	DET
ejpam-176	201	26	set	set	NOUN
ejpam-176	201	27	of	of	ADP
ejpam-176	201	28	reals	real	NOUN
ejpam-176	201	29	with	with	ADP
ejpam-176	201	30	the	the	DET
ejpam-176	201	31	usual	usual	ADJ
ejpam-176	201	32	topology	topology	NOUN
ejpam-176	201	33	u	u	NOUN
ejpam-176	201	34	is	be	AUX
ejpam-176	201	35	a	a	DET
ejpam-176	201	36	closed	closed	ADJ
ejpam-176	201	37	function	function	NOUN
ejpam-176	201	38	which	which	PRON
ejpam-176	201	39	is	be	AUX
ejpam-176	201	40	not	not	PART
ejpam-176	201	41	a	a	DET
ejpam-176	201	42	β	β	X
ejpam-176	201	43	-θ	-θ	PUNCT
ejpam-176	201	44	-closed	-closed	ADJ
ejpam-176	201	45	function	function	NOUN
ejpam-176	201	46	.	.	PUNCT
ejpam-176	202	1	in	in	ADP
ejpam-176	202	2	fact	fact	NOUN
ejpam-176	202	3	each	each	DET
ejpam-176	202	4	closed	closed	ADJ
ejpam-176	202	5	rays	ray	NOUN
ejpam-176	202	6	(	(	PUNCT
ejpam-176	202	7	−∞	−∞	NOUN
ejpam-176	202	8	,	,	PUNCT
ejpam-176	202	9	a	a	DET
ejpam-176	202	10	]	]	X
ejpam-176	202	11	,	,	PUNCT
ejpam-176	202	12	[	[	X
ejpam-176	202	13	b,∞	b,∞	NOUN
ejpam-176	202	14	)	)	PUNCT
ejpam-176	202	15	are	be	AUX
ejpam-176	202	16	β	β	X
ejpam-176	202	17	-open	-open	NOUN
ejpam-176	202	18	sets	set	NOUN
ejpam-176	202	19	in	in	ADP
ejpam-176	202	20	(	(	PUNCT
ejpam-176	202	21	r	r	NOUN
ejpam-176	202	22	,	,	PUNCT
ejpam-176	202	23	u	u	NOUN
ejpam-176	202	24	)	)	PUNCT
ejpam-176	202	25	.	.	PUNCT
ejpam-176	203	1	so	so	ADV
ejpam-176	203	2	for	for	ADP
ejpam-176	203	3	a	a	DET
ejpam-176	203	4	<	<	X
ejpam-176	203	5	b	b	PROPN
ejpam-176	203	6	,	,	PUNCT
ejpam-176	203	7	the	the	DET
ejpam-176	203	8	interval	interval	NOUN
ejpam-176	203	9	(	(	PUNCT
ejpam-176	203	10	a	a	DET
ejpam-176	203	11	,	,	PUNCT
ejpam-176	203	12	b	b	NOUN
ejpam-176	203	13	)	)	PUNCT
ejpam-176	203	14	is	be	AUX
ejpam-176	203	15	β	β	X
ejpam-176	203	16	-θ	-θ	PUNCT
ejpam-176	203	17	-closed	-closed	PROPN
ejpam-176	203	18	.	.	PUNCT
ejpam-176	204	1	but	but	CCONJ
ejpam-176	204	2	its	its	PRON
ejpam-176	204	3	image	image	NOUN
ejpam-176	204	4	ψ((a	ψ((a	NOUN
ejpam-176	204	5	,	,	PUNCT
ejpam-176	204	6	b	b	NOUN
ejpam-176	204	7	)	)	PUNCT
ejpam-176	204	8	)	)	PUNCT
ejpam-176	205	1	=	=	PRON
ejpam-176	205	2	(	(	PUNCT
ejpam-176	205	3	a	a	DET
ejpam-176	205	4	,	,	PUNCT
ejpam-176	205	5	b	b	NOUN
ejpam-176	205	6	)	)	PUNCT
ejpam-176	205	7	is	be	AUX
ejpam-176	205	8	not	not	PART
ejpam-176	205	9	closed	close	VERB
ejpam-176	205	10	in	in	ADP
ejpam-176	205	11	(	(	PUNCT
ejpam-176	205	12	r	r	NOUN
ejpam-176	205	13	,	,	PUNCT
ejpam-176	205	14	u	u	NOUN
ejpam-176	205	15	)	)	PUNCT
ejpam-176	205	16	.	.	PUNCT
ejpam-176	206	1	theorem	theorem	VERB
ejpam-176	206	2	3.8	3.8	NUM
ejpam-176	206	3	.	.	PUNCT
ejpam-176	207	1	let	let	VERB
ejpam-176	207	2	ψ	ψ	X
ejpam-176	207	3	:	:	PUNCT
ejpam-176	207	4	x	x	SYM
ejpam-176	207	5	→	→	SYM
ejpam-176	207	6	y	y	X
ejpam-176	207	7	be	be	AUX
ejpam-176	207	8	a	a	DET
ejpam-176	207	9	surjective	surjective	ADJ
ejpam-176	207	10	β	β	X
ejpam-176	207	11	-θ	-θ	PUNCT
ejpam-176	207	12	-closed	-close	VERB
ejpam-176	207	13	function	function	NOUN
ejpam-176	207	14	having	have	VERB
ejpam-176	207	15	β	β	X
ejpam-176	207	16	-closed	-close	VERB
ejpam-176	207	17	relative	relative	ADJ
ejpam-176	207	18	to	to	ADP
ejpam-176	207	19	x	x	SYM
ejpam-176	207	20	(	(	PUNCT
ejpam-176	207	21	i.e.	i.e.	X
ejpam-176	207	22	β	β	X
ejpam-176	207	23	-set	-set	NUM
ejpam-176	207	24	)	)	PUNCT
ejpam-176	207	25	point	point	NOUN
ejpam-176	207	26	inverses	inverse	NOUN
ejpam-176	207	27	.	.	PUNCT
ejpam-176	208	1	then	then	ADV
ejpam-176	208	2	ψ−1(a	ψ−1(a	PROPN
ejpam-176	208	3	)	)	PUNCT
ejpam-176	208	4	is	be	AUX
ejpam-176	208	5	β	β	X
ejpam-176	208	6	-closed	-close	VERB
ejpam-176	208	7	relative	relative	ADJ
ejpam-176	208	8	to	to	ADP
ejpam-176	208	9	x	x	PRON
ejpam-176	208	10	whenever	whenever	SCONJ
ejpam-176	208	11	a	a	PRON
ejpam-176	208	12	is	be	AUX
ejpam-176	208	13	compact	compact	ADJ
ejpam-176	208	14	in	in	ADP
ejpam-176	208	15	y	y	PROPN
ejpam-176	208	16	.	.	PUNCT
ejpam-176	209	1	proof	proof	NOUN
ejpam-176	209	2	:	:	PUNCT
ejpam-176	209	3	let	let	VERB
ejpam-176	209	4	v	v	VERB
ejpam-176	209	5	=	=	PUNCT
ejpam-176	209	6	{	{	PUNCT
ejpam-176	209	7	vλ	vλ	INTJ
ejpam-176	209	8	:	:	PUNCT
ejpam-176	209	9	λ	λ	PROPN
ejpam-176	209	10	∈	∈	PROPN
ejpam-176	209	11	λ	λ	PROPN
ejpam-176	209	12	}	}	PUNCT
ejpam-176	209	13	be	be	VERB
ejpam-176	209	14	a	a	DET
ejpam-176	209	15	β	β	X
ejpam-176	209	16	-θ	-θ	PUNCT
ejpam-176	209	17	-open	-open	ADJ
ejpam-176	209	18	cover	cover	NOUN
ejpam-176	209	19	of	of	ADP
ejpam-176	209	20	ψ−1(a	ψ−1(a	NOUN
ejpam-176	209	21	)	)	PUNCT
ejpam-176	209	22	.	.	PUNCT
ejpam-176	210	1	by	by	ADP
ejpam-176	210	2	hypothesis	hypothesis	NOUN
ejpam-176	210	3	and	and	CCONJ
ejpam-176	210	4	by	by	ADP
ejpam-176	210	5	theorem	theorem	NOUN
ejpam-176	210	6	3.2	3.2	NUM
ejpam-176	210	7	,	,	PUNCT
ejpam-176	210	8	for	for	ADP
ejpam-176	210	9	each	each	DET
ejpam-176	210	10	y	y	PROPN
ejpam-176	210	11	∈	∈	PROPN
ejpam-176	210	12	a	a	DET
ejpam-176	210	13	there	there	PRON
ejpam-176	210	14	exist	exist	VERB
ejpam-176	210	15	λ1	λ1	ADJ
ejpam-176	210	16	,	,	PUNCT
ejpam-176	210	17	......	......	PUNCT
ejpam-176	210	18	,	,	PUNCT
ejpam-176	210	19	λn	λn	X
ejpam-176	210	20	such	such	ADJ
ejpam-176	210	21	that	that	PRON
ejpam-176	210	22	ψ−1(y	ψ−1(y	PROPN
ejpam-176	210	23	)	)	PUNCT
ejpam-176	211	1	⊂	⊂	PRON
ejpam-176	211	2	∪n	∪n	X
ejpam-176	212	1	i=1	i=1	PROPN
ejpam-176	212	2	vλi	vλi	PROPN
ejpam-176	212	3	=	=	PROPN
ejpam-176	212	4	vy	vy	PROPN
ejpam-176	212	5	(	(	PUNCT
ejpam-176	212	6	say	say	INTJ
ejpam-176	212	7	)	)	PUNCT
ejpam-176	212	8	.	.	PUNCT
ejpam-176	213	1	since	since	SCONJ
ejpam-176	213	2	vy	vy	PROPN
ejpam-176	213	3	is	be	AUX
ejpam-176	213	4	β	β	X
ejpam-176	213	5	-θ	-θ	PUNCT
ejpam-176	213	6	-open	-open	ADJ
ejpam-176	213	7	and	and	CCONJ
ejpam-176	213	8	ψ	ψ	NOUN
ejpam-176	213	9	is	be	AUX
ejpam-176	213	10	β	β	X
ejpam-176	213	11	-θ	-θ	PUNCT
ejpam-176	213	12	-closed	-close	VERB
ejpam-176	213	13	,	,	PUNCT
ejpam-176	213	14	by	by	ADP
ejpam-176	213	15	theorem	theorem	NOUN
ejpam-176	213	16	3.12	3.12	NUM
ejpam-176	213	17	,	,	PUNCT
ejpam-176	213	18	there	there	PRON
ejpam-176	213	19	exists	exist	VERB
ejpam-176	213	20	an	an	DET
ejpam-176	213	21	open	open	ADJ
ejpam-176	213	22	set	set	NOUN
ejpam-176	213	23	uy	uy	NOUN
ejpam-176	213	24	containing	contain	VERB
ejpam-176	213	25	y	y	PRON
ejpam-176	213	26	such	such	ADJ
ejpam-176	213	27	that	that	PRON
ejpam-176	213	28	ψ−1(uy	ψ−1(uy	PROPN
ejpam-176	213	29	)	)	PUNCT
ejpam-176	213	30	⊂	⊂	PROPN
ejpam-176	213	31	vy	vy	NOUN
ejpam-176	213	32	.	.	PUNCT
ejpam-176	214	1	since	since	SCONJ
ejpam-176	214	2	a	a	PRON
ejpam-176	214	3	is	be	AUX
ejpam-176	214	4	compact	compact	ADJ
ejpam-176	214	5	,	,	PUNCT
ejpam-176	214	6	there	there	PRON
ejpam-176	214	7	exist	exist	VERB
ejpam-176	214	8	y1	y1	NOUN
ejpam-176	214	9	,	,	PUNCT
ejpam-176	214	10	.....	.....	PUNCT
ejpam-176	214	11	,	,	PUNCT
ejpam-176	214	12	yn	yn	PROPN
ejpam-176	214	13	∈	∈	PROPN
ejpam-176	214	14	a	a	DET
ejpam-176	214	15	such	such	ADJ
ejpam-176	214	16	that	that	PRON
ejpam-176	214	17	ψ−1(a)⊂	ψ−1(a)⊂	VERB
ejpam-176	215	1	∪k	∪k	NUM
ejpam-176	215	2	i=1	i=1	PROPN
ejpam-176	215	3	ψ−1(uyi	ψ−1(uyi	PUNCT
ejpam-176	215	4	)	)	PUNCT
ejpam-176	215	5	.	.	PUNCT
ejpam-176	216	1	hence	hence	ADV
ejpam-176	216	2	ψ−1(a)⊂	ψ−1(a)⊂	PUNCT
ejpam-176	216	3	∪k	∪k	PROPN
ejpam-176	216	4	i=1	i=1	PROPN
ejpam-176	216	5	vyi	vyi	PROPN
ejpam-176	216	6	,	,	PUNCT
ejpam-176	216	7	where	where	SCONJ
ejpam-176	216	8	each	each	DET
ejpam-176	216	9	vyi	vyi	NOUN
ejpam-176	216	10	is	be	AUX
ejpam-176	216	11	a	a	DET
ejpam-176	216	12	union	union	NOUN
ejpam-176	216	13	of	of	ADP
ejpam-176	216	14	finite	finite	ADJ
ejpam-176	216	15	number	number	NOUN
ejpam-176	216	16	of	of	ADP
ejpam-176	216	17	members	member	NOUN
ejpam-176	216	18	of	of	ADP
ejpam-176	216	19	v	v	NOUN
ejpam-176	216	20	.	.	PUNCT
ejpam-176	217	1	therefore	therefore	ADV
ejpam-176	217	2	ψ−1(a	ψ−1(a	PROPN
ejpam-176	217	3	)	)	PUNCT
ejpam-176	217	4	is	be	AUX
ejpam-176	217	5	β	β	X
ejpam-176	217	6	-closed	-close	VERB
ejpam-176	217	7	relative	relative	ADJ
ejpam-176	217	8	to	to	ADP
ejpam-176	217	9	x	x	PROPN
ejpam-176	217	10	.	.	PUNCT
ejpam-176	218	1	theorem	theorem	ADJ
ejpam-176	218	2	3.9	3.9	NUM
ejpam-176	218	3	.	.	PUNCT
ejpam-176	219	1	let	let	VERB
ejpam-176	219	2	ψ	ψ	X
ejpam-176	219	3	:	:	PUNCT
ejpam-176	219	4	x	x	SYM
ejpam-176	219	5	→	→	SYM
ejpam-176	219	6	y	y	X
ejpam-176	219	7	be	be	AUX
ejpam-176	219	8	a	a	DET
ejpam-176	219	9	surjective	surjective	ADJ
ejpam-176	219	10	β	β	X
ejpam-176	219	11	-θ	-θ	PUNCT
ejpam-176	219	12	-closed	-close	VERB
ejpam-176	219	13	function	function	NOUN
ejpam-176	219	14	having	have	VERB
ejpam-176	219	15	β	β	X
ejpam-176	219	16	-closed	-close	VERB
ejpam-176	219	17	relative	relative	ADJ
ejpam-176	219	18	to	to	ADP
ejpam-176	219	19	x	x	SYM
ejpam-176	219	20	(	(	PUNCT
ejpam-176	219	21	i.e.	i.e.	X
ejpam-176	219	22	β	β	X
ejpam-176	219	23	-set	-set	NUM
ejpam-176	219	24	)	)	PUNCT
ejpam-176	219	25	point	point	NOUN
ejpam-176	219	26	inverses	inverse	VERB
ejpam-176	219	27	.	.	PUNCT
ejpam-176	220	1	if	if	SCONJ
ejpam-176	220	2	y	y	PROPN
ejpam-176	220	3	is	be	AUX
ejpam-176	220	4	compact	compact	ADJ
ejpam-176	220	5	and	and	CCONJ
ejpam-176	220	6	x	x	ADJ
ejpam-176	220	7	is	be	AUX
ejpam-176	220	8	t2	t2	PROPN
ejpam-176	220	9	then	then	ADV
ejpam-176	220	10	ψ	ψ	NOUN
ejpam-176	220	11	is	be	AUX
ejpam-176	220	12	continuous	continuous	ADJ
ejpam-176	220	13	.	.	PUNCT
ejpam-176	221	1	proof	proof	NOUN
ejpam-176	221	2	:	:	PUNCT
ejpam-176	221	3	since	since	SCONJ
ejpam-176	221	4	y	y	PROPN
ejpam-176	221	5	is	be	AUX
ejpam-176	221	6	compact	compact	ADJ
ejpam-176	221	7	then	then	ADV
ejpam-176	221	8	by	by	ADP
ejpam-176	221	9	the	the	DET
ejpam-176	221	10	above	above	ADJ
ejpam-176	221	11	theorem	theorem	NOUN
ejpam-176	221	12	3.16	3.16	NUM
ejpam-176	221	13	,	,	PUNCT
ejpam-176	221	14	ψ−1(a	ψ−1(a	PROPN
ejpam-176	221	15	)	)	PUNCT
ejpam-176	221	16	is	be	AUX
ejpam-176	221	17	β	β	X
ejpam-176	221	18	-closed	-close	VERB
ejpam-176	221	19	relative	relative	ADJ
ejpam-176	221	20	to	to	ADP
ejpam-176	221	21	x	x	PRON
ejpam-176	221	22	whenever	whenever	SCONJ
ejpam-176	221	23	a	a	PRON
ejpam-176	221	24	is	be	AUX
ejpam-176	221	25	closed	close	VERB
ejpam-176	221	26	in	in	ADP
ejpam-176	221	27	y	y	PROPN
ejpam-176	221	28	.	.	PUNCT
ejpam-176	222	1	obviously	obviously	ADV
ejpam-176	222	2	ψ−1(a	ψ−1(a	PROPN
ejpam-176	222	3	)	)	PUNCT
ejpam-176	222	4	is	be	AUX
ejpam-176	222	5	an	an	DET
ejpam-176	222	6	nc	nc	NOUN
ejpam-176	222	7	-	-	PUNCT
ejpam-176	222	8	set	set	NOUN
ejpam-176	222	9	and	and	CCONJ
ejpam-176	222	10	since	since	SCONJ
ejpam-176	222	11	x	x	PRON
ejpam-176	222	12	is	be	AUX
ejpam-176	222	13	t2	t2	NOUN
ejpam-176	222	14	then	then	ADV
ejpam-176	222	15	ψ−1(a	ψ−1(a	PROPN
ejpam-176	222	16	)	)	PUNCT
ejpam-176	223	1	is	be	AUX
ejpam-176	223	2	closed	close	VERB
ejpam-176	223	3	as	as	ADV
ejpam-176	223	4	well	well	ADV
ejpam-176	223	5	in	in	ADP
ejpam-176	223	6	x	x	X
ejpam-176	223	7	.	.	PUNCT
ejpam-176	224	1	therefore	therefore	ADV
ejpam-176	224	2	ψ	ψ	X
ejpam-176	224	3	is	be	AUX
ejpam-176	224	4	continuous	continuous	ADJ
ejpam-176	224	5	.	.	PUNCT
ejpam-176	225	1	4	4	X
ejpam-176	225	2	.	.	X
ejpam-176	225	3	locally	locally	ADV
ejpam-176	225	4	β	β	X
ejpam-176	225	5	-closed	-close	VERB
ejpam-176	225	6	spaces	space	NOUN
ejpam-176	225	7	definition	definition	NOUN
ejpam-176	225	8	4.1	4.1	NUM
ejpam-176	225	9	.	.	PUNCT
ejpam-176	226	1	a	a	DET
ejpam-176	226	2	space	space	NOUN
ejpam-176	226	3	x	x	PUNCT
ejpam-176	226	4	is	be	AUX
ejpam-176	226	5	called	call	VERB
ejpam-176	226	6	locally	locally	ADV
ejpam-176	226	7	β	β	X
ejpam-176	226	8	-closed	-close	VERB
ejpam-176	226	9	if	if	SCONJ
ejpam-176	226	10	for	for	ADP
ejpam-176	226	11	each	each	DET
ejpam-176	226	12	x	x	SYM
ejpam-176	226	13	∈	∈	PROPN
ejpam-176	226	14	x	x	X
ejpam-176	226	15	,	,	PUNCT
ejpam-176	226	16	there	there	PRON
ejpam-176	226	17	exists	exist	VERB
ejpam-176	226	18	a	a	DET
ejpam-176	226	19	regular	regular	ADJ
ejpam-176	226	20	open	open	ADJ
ejpam-176	226	21	neighbourhood	neighbourhood	NOUN
ejpam-176	226	22	of	of	ADP
ejpam-176	226	23	which	which	PRON
ejpam-176	226	24	is	be	AUX
ejpam-176	226	25	a	a	DET
ejpam-176	226	26	β	β	X
ejpam-176	226	27	-closed	-close	VERB
ejpam-176	226	28	subspace	subspace	NOUN
ejpam-176	226	29	of	of	ADP
ejpam-176	226	30	x	x	X
ejpam-176	226	31	.	.	PUNCT
ejpam-176	226	32	remark	remark	PROPN
ejpam-176	226	33	4.1	4.1	NUM
ejpam-176	226	34	.	.	PUNCT
ejpam-176	227	1	every	every	DET
ejpam-176	227	2	β	β	X
ejpam-176	227	3	-closed	-close	VERB
ejpam-176	227	4	space	space	NOUN
ejpam-176	227	5	is	be	AUX
ejpam-176	227	6	locally	locally	ADV
ejpam-176	227	7	β	β	X
ejpam-176	227	8	-closed	-closed	PROPN
ejpam-176	227	9	.	.	PUNCT
ejpam-176	228	1	but	but	CCONJ
ejpam-176	228	2	the	the	DET
ejpam-176	228	3	converse	converse	NOUN
ejpam-176	228	4	is	be	AUX
ejpam-176	228	5	not	not	PART
ejpam-176	228	6	true	true	ADJ
ejpam-176	228	7	,	,	PUNCT
ejpam-176	228	8	in	in	ADP
ejpam-176	228	9	general	general	ADJ
ejpam-176	228	10	.	.	PUNCT
ejpam-176	229	1	any	any	DET
ejpam-176	229	2	infinite	infinite	NOUN
ejpam-176	229	3	set	set	NOUN
ejpam-176	229	4	with	with	ADP
ejpam-176	229	5	the	the	DET
ejpam-176	229	6	discrete	discrete	ADJ
ejpam-176	229	7	topology	topology	NOUN
ejpam-176	229	8	is	be	AUX
ejpam-176	229	9	an	an	DET
ejpam-176	229	10	example	example	NOUN
ejpam-176	229	11	of	of	ADP
ejpam-176	229	12	a	a	DET
ejpam-176	229	13	locally	locally	ADV
ejpam-176	229	14	β	β	X
ejpam-176	229	15	-closed	-close	VERB
ejpam-176	229	16	space	space	NOUN
ejpam-176	229	17	which	which	PRON
ejpam-176	229	18	is	be	AUX
ejpam-176	229	19	not	not	PART
ejpam-176	229	20	β	β	X
ejpam-176	229	21	-closed	-close	VERB
ejpam-176	229	22	.	.	PUNCT
ejpam-176	230	1	c.	c.	PROPN
ejpam-176	230	2	basu	basu	PROPN
ejpam-176	230	3	and	and	CCONJ
ejpam-176	230	4	m.	m.	PROPN
ejpam-176	230	5	ghosh	ghosh	PROPN
ejpam-176	230	6	/	/	PUNCT
ejpam-176	230	7	eur	eur	PROPN
ejpam-176	230	8	.	.	PUNCT
ejpam-176	231	1	j.	j.	PROPN
ejpam-176	231	2	pure	pure	PROPN
ejpam-176	231	3	appl	appl	PROPN
ejpam-176	231	4	.	.	PROPN
ejpam-176	231	5	math	math	PROPN
ejpam-176	231	6	,	,	PUNCT
ejpam-176	231	7	2	2	NUM
ejpam-176	231	8	(	(	PUNCT
ejpam-176	231	9	2009	2009	NUM
ejpam-176	231	10	)	)	PUNCT
ejpam-176	231	11	,	,	PUNCT
ejpam-176	231	12	(	(	PUNCT
ejpam-176	231	13	85	85	NUM
ejpam-176	231	14	-	-	SYM
ejpam-176	231	15	96	96	NUM
ejpam-176	231	16	)	)	PUNCT
ejpam-176	231	17	92	92	NUM
ejpam-176	231	18	theorem	theorem	VERB
ejpam-176	231	19	4.1	4.1	NUM
ejpam-176	231	20	.	.	PUNCT
ejpam-176	232	1	a	a	DET
ejpam-176	232	2	space	space	NOUN
ejpam-176	232	3	x	x	PUNCT
ejpam-176	232	4	is	be	AUX
ejpam-176	232	5	locally	locally	ADV
ejpam-176	232	6	β	β	X
ejpam-176	232	7	-closed	-close	VERB
ejpam-176	232	8	if	if	SCONJ
ejpam-176	232	9	and	and	CCONJ
ejpam-176	232	10	only	only	ADV
ejpam-176	232	11	if	if	SCONJ
ejpam-176	232	12	for	for	ADP
ejpam-176	232	13	each	each	DET
ejpam-176	232	14	x	x	SYM
ejpam-176	232	15	∈	∈	PROPN
ejpam-176	232	16	x	x	X
ejpam-176	232	17	,	,	PUNCT
ejpam-176	232	18	there	there	PRON
ejpam-176	232	19	is	be	VERB
ejpam-176	232	20	a	a	DET
ejpam-176	232	21	v	v	NOUN
ejpam-176	232	22	∈	∈	NOUN
ejpam-176	232	23	ro(x	ro(x	PUNCT
ejpam-176	232	24	,	,	PUNCT
ejpam-176	232	25	x	x	X
ejpam-176	232	26	)	)	PUNCT
ejpam-176	232	27	such	such	ADJ
ejpam-176	232	28	that	that	DET
ejpam-176	232	29	v	v	NOUN
ejpam-176	232	30	is	be	AUX
ejpam-176	232	31	locally	locally	ADV
ejpam-176	232	32	β	β	X
ejpam-176	232	33	-closed	-close	VERB
ejpam-176	232	34	.	.	PUNCT
ejpam-176	233	1	proof	proof	NOUN
ejpam-176	233	2	:	:	PUNCT
ejpam-176	233	3	the	the	DET
ejpam-176	233	4	necessity	necessity	NOUN
ejpam-176	233	5	part	part	NOUN
ejpam-176	233	6	is	be	AUX
ejpam-176	233	7	obvious	obvious	ADJ
ejpam-176	233	8	.	.	PUNCT
ejpam-176	234	1	for	for	ADP
ejpam-176	234	2	the	the	DET
ejpam-176	234	3	sufficiency	sufficiency	NOUN
ejpam-176	234	4	part	part	NOUN
ejpam-176	234	5	,	,	PUNCT
ejpam-176	234	6	let	let	VERB
ejpam-176	234	7	w	w	NOUN
ejpam-176	234	8	∈	∈	PROPN
ejpam-176	234	9	ro(x	ro(x	PUNCT
ejpam-176	234	10	)	)	PUNCT
ejpam-176	234	11	.	.	PUNCT
ejpam-176	235	1	we	we	PRON
ejpam-176	235	2	shall	shall	AUX
ejpam-176	235	3	prove	prove	VERB
ejpam-176	235	4	that	that	SCONJ
ejpam-176	235	5	if	if	SCONJ
ejpam-176	235	6	a∈	a∈	PROPN
ejpam-176	235	7	ro(w	ro(w	NUM
ejpam-176	235	8	)	)	PUNCT
ejpam-176	235	9	then	then	ADV
ejpam-176	235	10	a∈	a∈	PROPN
ejpam-176	235	11	ro(x	ro(x	PUNCT
ejpam-176	235	12	)	)	PUNCT
ejpam-176	235	13	.	.	PUNCT
ejpam-176	236	1	indeed	indeed	ADV
ejpam-176	236	2	,	,	PUNCT
ejpam-176	236	3	a=	a=	PROPN
ejpam-176	236	4	intw	intw	PROPN
ejpam-176	236	5	(	(	PUNCT
ejpam-176	236	6	clw	clw	PROPN
ejpam-176	236	7	(	(	PUNCT
ejpam-176	236	8	a	a	NOUN
ejpam-176	236	9	)	)	PUNCT
ejpam-176	236	10	)	)	PUNCT
ejpam-176	236	11	=	=	SYM
ejpam-176	236	12	intw	intw	NOUN
ejpam-176	236	13	(	(	PUNCT
ejpam-176	236	14	w∩clx	w∩clx	PROPN
ejpam-176	236	15	(	(	PUNCT
ejpam-176	236	16	a	a	NOUN
ejpam-176	236	17	)	)	PUNCT
ejpam-176	236	18	)	)	PUNCT
ejpam-176	237	1	=	=	SYM
ejpam-176	237	2	intx	intx	PROPN
ejpam-176	237	3	(	(	PUNCT
ejpam-176	237	4	w∩clx	w∩clx	PROPN
ejpam-176	237	5	(	(	PUNCT
ejpam-176	237	6	a	a	NOUN
ejpam-176	237	7	)	)	PUNCT
ejpam-176	237	8	)	)	PUNCT
ejpam-176	238	1	=	=	SYM
ejpam-176	238	2	intx	intx	PROPN
ejpam-176	238	3	(	(	PUNCT
ejpam-176	238	4	w	w	PROPN
ejpam-176	238	5	)	)	PUNCT
ejpam-176	238	6	∩intx	∩intx	VERB
ejpam-176	238	7	(	(	PUNCT
ejpam-176	238	8	clx	clx	X
ejpam-176	238	9	(	(	PUNCT
ejpam-176	238	10	a	a	NOUN
ejpam-176	238	11	)	)	PUNCT
ejpam-176	238	12	)	)	PUNCT
ejpam-176	238	13	=	=	SYM
ejpam-176	239	1	w	w	PROPN
ejpam-176	239	2	∩	∩	PROPN
ejpam-176	239	3	intx	intx	PROPN
ejpam-176	239	4	(	(	PUNCT
ejpam-176	239	5	clx	clx	PROPN
ejpam-176	239	6	(	(	PUNCT
ejpam-176	239	7	a	a	NOUN
ejpam-176	239	8	)	)	PUNCT
ejpam-176	239	9	)	)	PUNCT
ejpam-176	240	1	=	=	SYM
ejpam-176	240	2	intx	intx	PROPN
ejpam-176	240	3	(	(	PUNCT
ejpam-176	240	4	clx	clx	PROPN
ejpam-176	240	5	(	(	PUNCT
ejpam-176	240	6	a	a	NOUN
ejpam-176	240	7	)	)	PUNCT
ejpam-176	240	8	)	)	PUNCT
ejpam-176	240	9	(	(	PUNCT
ejpam-176	240	10	as	as	ADP
ejpam-176	240	11	a	a	DET
ejpam-176	240	12	⊂	⊂	PROPN
ejpam-176	240	13	w	w	NOUN
ejpam-176	240	14	)	)	PUNCT
ejpam-176	240	15	.	.	PUNCT
ejpam-176	241	1	by	by	ADP
ejpam-176	241	2	hypothesis	hypothesis	NOUN
ejpam-176	241	3	,	,	PUNCT
ejpam-176	241	4	for	for	ADP
ejpam-176	241	5	each	each	DET
ejpam-176	241	6	x	x	SYM
ejpam-176	241	7	∈	∈	PROPN
ejpam-176	241	8	x	x	X
ejpam-176	241	9	,	,	PUNCT
ejpam-176	241	10	there	there	PRON
ejpam-176	241	11	is	be	VERB
ejpam-176	241	12	a	a	DET
ejpam-176	241	13	w	w	NOUN
ejpam-176	241	14	∈	∈	PROPN
ejpam-176	241	15	ro(x	ro(x	PUNCT
ejpam-176	241	16	,	,	PUNCT
ejpam-176	241	17	x	x	X
ejpam-176	241	18	)	)	PUNCT
ejpam-176	241	19	such	such	ADJ
ejpam-176	241	20	that	that	SCONJ
ejpam-176	241	21	(	(	PUNCT
ejpam-176	241	22	w	w	NOUN
ejpam-176	241	23	,	,	PUNCT
ejpam-176	241	24	τw	τw	NOUN
ejpam-176	241	25	)	)	PUNCT
ejpam-176	241	26	is	be	AUX
ejpam-176	241	27	locally	locally	ADV
ejpam-176	241	28	β	β	X
ejpam-176	241	29	-closed	-closed	PROPN
ejpam-176	241	30	.	.	PUNCT
ejpam-176	242	1	then	then	ADV
ejpam-176	242	2	by	by	ADP
ejpam-176	242	3	definition	definition	NOUN
ejpam-176	242	4	for	for	ADP
ejpam-176	242	5	each	each	DET
ejpam-176	242	6	x	x	PUNCT
ejpam-176	242	7	∈w	∈w	NOUN
ejpam-176	242	8	,	,	PUNCT
ejpam-176	242	9	there	there	PRON
ejpam-176	242	10	is	be	VERB
ejpam-176	242	11	an	an	DET
ejpam-176	242	12	u	u	PROPN
ejpam-176	242	13	∈	∈	PROPN
ejpam-176	242	14	ro(w	ro(w	PRON
ejpam-176	242	15	)	)	PUNCT
ejpam-176	242	16	such	such	ADJ
ejpam-176	242	17	that	that	SCONJ
ejpam-176	242	18	x	x	SYM
ejpam-176	242	19	∈	∈	PROPN
ejpam-176	242	20	u	u	NOUN
ejpam-176	242	21	and	and	CCONJ
ejpam-176	242	22	u	u	NOUN
ejpam-176	242	23	is	be	AUX
ejpam-176	242	24	a	a	DET
ejpam-176	242	25	β	β	X
ejpam-176	242	26	-closed	-close	VERB
ejpam-176	242	27	subspace	subspace	NOUN
ejpam-176	242	28	of	of	ADP
ejpam-176	242	29	w	w	PROPN
ejpam-176	242	30	.	.	PUNCT
ejpam-176	243	1	then	then	ADV
ejpam-176	243	2	by	by	ADP
ejpam-176	243	3	the	the	DET
ejpam-176	243	4	argument	argument	NOUN
ejpam-176	243	5	given	give	VERB
ejpam-176	243	6	above	above	ADP
ejpam-176	243	7	u	u	NOUN
ejpam-176	243	8	∈	∈	PROPN
ejpam-176	243	9	ro(x	ro(x	PUNCT
ejpam-176	243	10	,	,	PUNCT
ejpam-176	243	11	x	x	X
ejpam-176	243	12	)	)	PUNCT
ejpam-176	243	13	and	and	CCONJ
ejpam-176	243	14	hence	hence	ADV
ejpam-176	243	15	by	by	ADP
ejpam-176	243	16	the	the	DET
ejpam-176	243	17	corollary	corollary	ADJ
ejpam-176	243	18	3.10	3.10	NUM
ejpam-176	243	19	,	,	PUNCT
ejpam-176	243	20	u	u	NOUN
ejpam-176	243	21	is	be	AUX
ejpam-176	243	22	a	a	DET
ejpam-176	243	23	β	β	X
ejpam-176	243	24	-closed	-close	VERB
ejpam-176	243	25	subspace	subspace	NOUN
ejpam-176	243	26	of	of	ADP
ejpam-176	243	27	x	x	X
ejpam-176	243	28	.	.	PUNCT
ejpam-176	244	1	so	so	ADV
ejpam-176	244	2	,	,	PUNCT
ejpam-176	244	3	(	(	PUNCT
ejpam-176	244	4	x	x	X
ejpam-176	244	5	,	,	PUNCT
ejpam-176	244	6	τ	τ	X
ejpam-176	244	7	)	)	PUNCT
ejpam-176	244	8	is	be	AUX
ejpam-176	244	9	locally	locally	ADV
ejpam-176	244	10	β	β	X
ejpam-176	244	11	-closed	-closed	PROPN
ejpam-176	244	12	.	.	PUNCT
ejpam-176	245	1	theorem	theorem	VERB
ejpam-176	245	2	4.2	4.2	NUM
ejpam-176	245	3	.	.	PUNCT
ejpam-176	246	1	for	for	ADP
ejpam-176	246	2	a	a	DET
ejpam-176	246	3	topological	topological	ADJ
ejpam-176	246	4	space	space	NOUN
ejpam-176	246	5	(	(	PUNCT
ejpam-176	246	6	x	x	X
ejpam-176	246	7	,	,	PUNCT
ejpam-176	246	8	τ	τ	PROPN
ejpam-176	246	9	)	)	PUNCT
ejpam-176	246	10	,	,	PUNCT
ejpam-176	246	11	the	the	DET
ejpam-176	246	12	following	follow	VERB
ejpam-176	246	13	are	be	AUX
ejpam-176	246	14	equivalent	equivalent	ADJ
ejpam-176	246	15	:	:	PUNCT
ejpam-176	246	16	(	(	PUNCT
ejpam-176	246	17	a	a	X
ejpam-176	246	18	)	)	PUNCT
ejpam-176	246	19	(	(	PUNCT
ejpam-176	246	20	x	x	X
ejpam-176	246	21	,	,	PUNCT
ejpam-176	246	22	τ	τ	X
ejpam-176	246	23	)	)	PUNCT
ejpam-176	246	24	is	be	AUX
ejpam-176	246	25	locally	locally	ADV
ejpam-176	246	26	β	β	X
ejpam-176	246	27	-closed	-close	VERB
ejpam-176	246	28	.	.	PUNCT
ejpam-176	247	1	(	(	PUNCT
ejpam-176	247	2	b	b	X
ejpam-176	247	3	)	)	PUNCT
ejpam-176	247	4	for	for	ADP
ejpam-176	247	5	each	each	DET
ejpam-176	247	6	point	point	NOUN
ejpam-176	247	7	x	x	PUNCT
ejpam-176	247	8	of	of	ADP
ejpam-176	247	9	x	x	SYM
ejpam-176	247	10	,	,	PUNCT
ejpam-176	247	11	there	there	PRON
ejpam-176	247	12	is	be	VERB
ejpam-176	247	13	a	a	DET
ejpam-176	247	14	v	v	NOUN
ejpam-176	247	15	∈	∈	NOUN
ejpam-176	247	16	ro(x	ro(x	PUNCT
ejpam-176	247	17	,	,	PUNCT
ejpam-176	247	18	x	x	X
ejpam-176	247	19	)	)	PUNCT
ejpam-176	247	20	which	which	PRON
ejpam-176	247	21	is	be	AUX
ejpam-176	247	22	β	β	X
ejpam-176	247	23	-closed	-close	VERB
ejpam-176	247	24	relative	relative	ADJ
ejpam-176	247	25	to	to	ADP
ejpam-176	247	26	x	x	PROPN
ejpam-176	247	27	.	.	PUNCT
ejpam-176	248	1	(	(	PUNCT
ejpam-176	248	2	c	c	X
ejpam-176	248	3	)	)	PUNCT
ejpam-176	248	4	each	each	DET
ejpam-176	248	5	point	point	NOUN
ejpam-176	248	6	x	x	PUNCT
ejpam-176	248	7	of	of	ADP
ejpam-176	248	8	x	x	PUNCT
ejpam-176	248	9	has	have	AUX
ejpam-176	248	10	an	an	DET
ejpam-176	248	11	open	open	ADJ
ejpam-176	248	12	neighbourhood	neighbourhood	NOUN
ejpam-176	248	13	v	v	NOUN
ejpam-176	248	14	of	of	ADP
ejpam-176	248	15	x	x	INTJ
ejpam-176	248	16	such	such	ADJ
ejpam-176	248	17	that	that	DET
ejpam-176	248	18	int(cl(v	int(cl(v	NOUN
ejpam-176	248	19	)	)	PUNCT
ejpam-176	248	20	)	)	PUNCT
ejpam-176	248	21	is	be	AUX
ejpam-176	248	22	β	β	X
ejpam-176	248	23	-closed	-close	VERB
ejpam-176	248	24	relative	relative	ADJ
ejpam-176	248	25	to	to	ADP
ejpam-176	248	26	x	x	PROPN
ejpam-176	248	27	.	.	PUNCT
ejpam-176	249	1	(	(	PUNCT
ejpam-176	249	2	d	d	X
ejpam-176	249	3	)	)	PUNCT
ejpam-176	249	4	for	for	ADP
ejpam-176	249	5	each	each	DET
ejpam-176	249	6	point	point	NOUN
ejpam-176	249	7	x	x	PUNCT
ejpam-176	249	8	of	of	ADP
ejpam-176	249	9	x	x	SYM
ejpam-176	249	10	,	,	PUNCT
ejpam-176	249	11	there	there	PRON
ejpam-176	249	12	is	be	VERB
ejpam-176	249	13	an	an	DET
ejpam-176	249	14	open	open	ADJ
ejpam-176	249	15	neighbourhood	neighbourhood	NOUN
ejpam-176	249	16	u	u	NOUN
ejpam-176	249	17	of	of	ADP
ejpam-176	249	18	x	x	SYM
ejpam-176	249	19	such	such	ADJ
ejpam-176	249	20	that	that	PRON
ejpam-176	249	21	scl(u	scl(u	PROPN
ejpam-176	249	22	)	)	PUNCT
ejpam-176	249	23	is	be	AUX
ejpam-176	249	24	β	β	X
ejpam-176	249	25	-closed	-close	VERB
ejpam-176	249	26	relative	relative	ADJ
ejpam-176	249	27	to	to	ADP
ejpam-176	249	28	x	x	PROPN
ejpam-176	249	29	.	.	PUNCT
ejpam-176	250	1	(	(	PUNCT
ejpam-176	250	2	e	e	NOUN
ejpam-176	250	3	)	)	PUNCT
ejpam-176	250	4	for	for	ADP
ejpam-176	250	5	each	each	DET
ejpam-176	250	6	point	point	NOUN
ejpam-176	250	7	x	x	PUNCT
ejpam-176	250	8	of	of	ADP
ejpam-176	250	9	x	x	SYM
ejpam-176	250	10	,	,	PUNCT
ejpam-176	250	11	there	there	PRON
ejpam-176	250	12	is	be	VERB
ejpam-176	250	13	an	an	DET
ejpam-176	250	14	open	open	ADJ
ejpam-176	250	15	neighbourhood	neighbourhood	NOUN
ejpam-176	250	16	u	u	NOUN
ejpam-176	250	17	of	of	ADP
ejpam-176	250	18	x	x	SYM
ejpam-176	250	19	such	such	ADJ
ejpam-176	250	20	that	that	SCONJ
ejpam-176	250	21	β	β	NOUN
ejpam-176	250	22	cl(u	cl(u	X
ejpam-176	250	23	)	)	PUNCT
ejpam-176	250	24	is	be	AUX
ejpam-176	250	25	β	β	AUX
ejpam-176	250	26	-closed	-close	VERB
ejpam-176	250	27	relative	relative	ADJ
ejpam-176	250	28	to	to	ADP
ejpam-176	250	29	x	x	PROPN
ejpam-176	250	30	.	.	PUNCT
ejpam-176	251	1	(	(	PUNCT
ejpam-176	251	2	f	f	X
ejpam-176	251	3	)	)	PUNCT
ejpam-176	251	4	for	for	ADP
ejpam-176	251	5	each	each	DET
ejpam-176	251	6	point	point	NOUN
ejpam-176	251	7	of	of	ADP
ejpam-176	251	8	x	x	X
ejpam-176	251	9	,	,	PUNCT
ejpam-176	251	10	there	there	PRON
ejpam-176	251	11	is	be	VERB
ejpam-176	251	12	an	an	DET
ejpam-176	251	13	α	α	NOUN
ejpam-176	251	14	-	-	ADJ
ejpam-176	251	15	open	open	ADJ
ejpam-176	251	16	set	set	VERB
ejpam-176	251	17	v	v	NOUN
ejpam-176	251	18	containing	contain	VERB
ejpam-176	251	19	x	x	PUNCT
ejpam-176	251	20	such	such	ADJ
ejpam-176	251	21	that	that	DET
ejpam-176	251	22	int(cl(v	int(cl(v	NOUN
ejpam-176	251	23	)	)	PUNCT
ejpam-176	251	24	)	)	PUNCT
ejpam-176	252	1	is	be	AUX
ejpam-176	252	2	a	a	DET
ejpam-176	252	3	β	β	X
ejpam-176	252	4	-closed	-close	VERB
ejpam-176	252	5	subspace	subspace	NOUN
ejpam-176	252	6	of	of	ADP
ejpam-176	252	7	x	x	X
ejpam-176	252	8	.	.	PUNCT
ejpam-176	253	1	proof	proof	NOUN
ejpam-176	253	2	:	:	PUNCT
ejpam-176	253	3	the	the	DET
ejpam-176	253	4	proof	proof	NOUN
ejpam-176	253	5	is	be	AUX
ejpam-176	253	6	followed	follow	VERB
ejpam-176	253	7	from	from	ADP
ejpam-176	253	8	the	the	DET
ejpam-176	253	9	facts	fact	NOUN
ejpam-176	253	10	that	that	SCONJ
ejpam-176	253	11	a	a	DET
ejpam-176	253	12	set	set	NOUN
ejpam-176	253	13	a	a	PRON
ejpam-176	253	14	is	be	AUX
ejpam-176	253	15	pre	pre	ADJ
ejpam-176	253	16	-	-	ADJ
ejpam-176	253	17	open	open	ADJ
ejpam-176	253	18	if	if	SCONJ
ejpam-176	253	19	and	and	CCONJ
ejpam-176	253	20	only	only	ADV
ejpam-176	253	21	if	if	SCONJ
ejpam-176	253	22	scl(a	scl(a	X
ejpam-176	253	23	)	)	PUNCT
ejpam-176	253	24	=	=	SYM
ejpam-176	253	25	int(cl(a	int(cl(a	PROPN
ejpam-176	253	26	)	)	PUNCT
ejpam-176	253	27	)	)	PUNCT
ejpam-176	253	28	and	and	CCONJ
ejpam-176	253	29	for	for	ADP
ejpam-176	253	30	an	an	DET
ejpam-176	253	31	open	open	ADJ
ejpam-176	253	32	set	set	NOUN
ejpam-176	253	33	u	u	NOUN
ejpam-176	253	34	,	,	PUNCT
ejpam-176	253	35	β	β	X
ejpam-176	253	36	cl(u	cl(u	NOUN
ejpam-176	253	37	)	)	PUNCT
ejpam-176	253	38	=	=	SYM
ejpam-176	253	39	int	int	NOUN
ejpam-176	253	40	cl(u	cl(u	NOUN
ejpam-176	253	41	)	)	PUNCT
ejpam-176	253	42	and	and	CCONJ
ejpam-176	253	43	from	from	ADP
ejpam-176	253	44	theorem	theorem	ADJ
ejpam-176	253	45	3.8	3.8	NUM
ejpam-176	253	46	.	.	PUNCT
ejpam-176	253	47	theorem	theorem	VERB
ejpam-176	253	48	4.3	4.3	NUM
ejpam-176	253	49	.	.	PUNCT
ejpam-176	254	1	a	a	DET
ejpam-176	254	2	space	space	NOUN
ejpam-176	254	3	(	(	PUNCT
ejpam-176	254	4	x	x	X
ejpam-176	254	5	,	,	PUNCT
ejpam-176	254	6	τ	τ	X
ejpam-176	254	7	)	)	PUNCT
ejpam-176	254	8	is	be	AUX
ejpam-176	254	9	locally	locally	ADV
ejpam-176	254	10	β	β	X
ejpam-176	254	11	-closed	-close	VERB
ejpam-176	254	12	if	if	SCONJ
ejpam-176	254	13	and	and	CCONJ
ejpam-176	254	14	only	only	ADV
ejpam-176	254	15	if	if	SCONJ
ejpam-176	254	16	(	(	PUNCT
ejpam-176	254	17	x	x	INTJ
ejpam-176	254	18	,	,	PUNCT
ejpam-176	254	19	τα	τα	PROPN
ejpam-176	254	20	)	)	PUNCT
ejpam-176	254	21	is	be	AUX
ejpam-176	254	22	locally	locally	ADV
ejpam-176	254	23	β	β	X
ejpam-176	254	24	-closed	-close	VERB
ejpam-176	254	25	.	.	PUNCT
ejpam-176	255	1	proof	proof	NOUN
ejpam-176	255	2	:	:	PUNCT
ejpam-176	255	3	since	since	SCONJ
ejpam-176	255	4	βo(x	βo(x	NUM
ejpam-176	255	5	,	,	PUNCT
ejpam-176	255	6	τ	τ	X
ejpam-176	255	7	)	)	PUNCT
ejpam-176	255	8	=	=	SYM
ejpam-176	255	9	βo(x	βo(x	NUM
ejpam-176	255	10	,	,	PUNCT
ejpam-176	255	11	τα	τα	PROPN
ejpam-176	255	12	)	)	PUNCT
ejpam-176	255	13	,	,	PUNCT
ejpam-176	255	14	the	the	DET
ejpam-176	255	15	proof	proof	NOUN
ejpam-176	255	16	is	be	AUX
ejpam-176	255	17	immediate	immediate	ADJ
ejpam-176	255	18	.	.	PUNCT
ejpam-176	256	1	the	the	DET
ejpam-176	256	2	following	follow	VERB
ejpam-176	256	3	examples	example	NOUN
ejpam-176	256	4	show	show	VERB
ejpam-176	256	5	that	that	SCONJ
ejpam-176	256	6	local	local	ADJ
ejpam-176	256	7	β	β	NOUN
ejpam-176	256	8	-closedness	-closedness	ADJ
ejpam-176	256	9	and	and	CCONJ
ejpam-176	256	10	local	local	ADJ
ejpam-176	256	11	compact	compact	ADJ
ejpam-176	256	12	t2	t2	NOUN
ejpam-176	256	13	-	-	PUNCT
ejpam-176	256	14	ness	ness	NOUN
ejpam-176	256	15	are	be	AUX
ejpam-176	256	16	independent	independent	ADJ
ejpam-176	256	17	to	to	ADP
ejpam-176	256	18	each	each	DET
ejpam-176	256	19	other	other	ADJ
ejpam-176	256	20	.	.	PUNCT
ejpam-176	257	1	c.	c.	PROPN
ejpam-176	257	2	basu	basu	PROPN
ejpam-176	257	3	and	and	CCONJ
ejpam-176	257	4	m.	m.	PROPN
ejpam-176	257	5	ghosh	ghosh	PROPN
ejpam-176	257	6	/	/	PUNCT
ejpam-176	257	7	eur	eur	PROPN
ejpam-176	257	8	.	.	PUNCT
ejpam-176	258	1	j.	j.	PROPN
ejpam-176	258	2	pure	pure	PROPN
ejpam-176	258	3	appl	appl	PROPN
ejpam-176	258	4	.	.	PROPN
ejpam-176	258	5	math	math	PROPN
ejpam-176	258	6	,	,	PUNCT
ejpam-176	258	7	2	2	NUM
ejpam-176	258	8	(	(	PUNCT
ejpam-176	258	9	2009	2009	NUM
ejpam-176	258	10	)	)	PUNCT
ejpam-176	258	11	,	,	PUNCT
ejpam-176	258	12	(	(	PUNCT
ejpam-176	258	13	85	85	NUM
ejpam-176	258	14	-	-	SYM
ejpam-176	258	15	96	96	NUM
ejpam-176	258	16	)	)	PUNCT
ejpam-176	258	17	93	93	NUM
ejpam-176	258	18	example	example	NOUN
ejpam-176	258	19	4.1	4.1	NUM
ejpam-176	258	20	.	.	PUNCT
ejpam-176	258	21	example	example	NOUN
ejpam-176	258	22	of	of	ADP
ejpam-176	258	23	a	a	DET
ejpam-176	258	24	locally	locally	ADV
ejpam-176	258	25	β	β	X
ejpam-176	258	26	-closed	-close	VERB
ejpam-176	258	27	space	space	NOUN
ejpam-176	258	28	which	which	PRON
ejpam-176	258	29	is	be	AUX
ejpam-176	258	30	not	not	PART
ejpam-176	258	31	locally	locally	ADV
ejpam-176	258	32	compact	compact	ADJ
ejpam-176	258	33	t2	t2	NOUN
ejpam-176	258	34	let	let	VERB
ejpam-176	258	35	x	x	PUNCT
ejpam-176	258	36	=	=	SYM
ejpam-176	258	37	r	r	NOUN
ejpam-176	258	38	,	,	PUNCT
ejpam-176	258	39	the	the	DET
ejpam-176	258	40	set	set	NOUN
ejpam-176	258	41	of	of	ADP
ejpam-176	258	42	reals	real	NOUN
ejpam-176	258	43	with	with	ADP
ejpam-176	258	44	the	the	DET
ejpam-176	258	45	countable	countable	ADJ
ejpam-176	258	46	complement	complement	NOUN
ejpam-176	258	47	topology	topology	NOUN
ejpam-176	258	48	τ	τ	X
ejpam-176	258	49	.	.	PUNCT
ejpam-176	258	50	clearly	clearly	ADV
ejpam-176	258	51	po(x	po(x	PUNCT
ejpam-176	258	52	)	)	PUNCT
ejpam-176	258	53	=	=	PUNCT
ejpam-176	258	54	{	{	PUNCT
ejpam-176	258	55	uncountable	uncountable	ADJ
ejpam-176	258	56	infinite	infinite	ADJ
ejpam-176	258	57	subset	subset	NOUN
ejpam-176	258	58	of	of	ADP
ejpam-176	258	59	x	x	PUNCT
ejpam-176	258	60	or	or	CCONJ
ejpam-176	258	61	φ	φ	NUM
ejpam-176	258	62	}	}	PUNCT
ejpam-176	258	63	=	=	PRON
ejpam-176	258	64	βo(x	βo(x	PUNCT
ejpam-176	258	65	)	)	PUNCT
ejpam-176	258	66	.	.	PUNCT
ejpam-176	259	1	since	since	SCONJ
ejpam-176	259	2	for	for	ADP
ejpam-176	259	3	a	a	DET
ejpam-176	259	4	subset	subset	NOUN
ejpam-176	259	5	s	s	NOUN
ejpam-176	259	6	of	of	ADP
ejpam-176	259	7	x	x	SYM
ejpam-176	259	8	,	,	PUNCT
ejpam-176	259	9	β	β	X
ejpam-176	259	10	cl(s	cl(s	NOUN
ejpam-176	259	11	)	)	PUNCT
ejpam-176	259	12	=	=	SYM
ejpam-176	259	13	s	s	NOUN
ejpam-176	259	14	∪	∪	VERB
ejpam-176	259	15	int(cl(int(s	int(cl(int(s	PROPN
ejpam-176	259	16	)	)	PUNCT
ejpam-176	259	17	)	)	PUNCT
ejpam-176	260	1	[	[	X
ejpam-176	260	2	6	6	NUM
ejpam-176	260	3	]	]	PUNCT
ejpam-176	260	4	,	,	PUNCT
ejpam-176	260	5	then	then	ADV
ejpam-176	260	6	β	β	X
ejpam-176	260	7	cl(v	cl(v	NOUN
ejpam-176	260	8	)	)	PUNCT
ejpam-176	260	9	=	=	PUNCT
ejpam-176	261	1	x	x	X
ejpam-176	261	2	for	for	ADP
ejpam-176	261	3	any	any	DET
ejpam-176	261	4	non	non	ADJ
ejpam-176	261	5	-	-	ADJ
ejpam-176	261	6	empty	empty	ADJ
ejpam-176	261	7	v	v	ADJ
ejpam-176	261	8	∈	∈	PROPN
ejpam-176	261	9	βo(x	βo(x	PUNCT
ejpam-176	261	10	)	)	PUNCT
ejpam-176	261	11	.	.	PUNCT
ejpam-176	262	1	therefore	therefore	ADV
ejpam-176	262	2	(	(	PUNCT
ejpam-176	262	3	x	x	X
ejpam-176	262	4	,	,	PUNCT
ejpam-176	262	5	τ	τ	X
ejpam-176	262	6	)	)	PUNCT
ejpam-176	262	7	is	be	AUX
ejpam-176	262	8	β	β	AUX
ejpam-176	262	9	closed	close	VERB
ejpam-176	262	10	and	and	CCONJ
ejpam-176	262	11	hence	hence	ADV
ejpam-176	262	12	is	be	AUX
ejpam-176	262	13	locally	locally	ADV
ejpam-176	262	14	β	β	X
ejpam-176	262	15	-closed	-close	VERB
ejpam-176	262	16	.	.	PUNCT
ejpam-176	263	1	clearly	clearly	ADV
ejpam-176	263	2	(	(	PUNCT
ejpam-176	263	3	x	x	X
ejpam-176	263	4	,	,	PUNCT
ejpam-176	263	5	τ	τ	X
ejpam-176	263	6	)	)	PUNCT
ejpam-176	263	7	is	be	AUX
ejpam-176	263	8	not	not	PART
ejpam-176	263	9	locally	locally	ADV
ejpam-176	263	10	compact	compact	ADJ
ejpam-176	263	11	t2	t2	NOUN
ejpam-176	263	12	.	.	PUNCT
ejpam-176	264	1	example	example	NOUN
ejpam-176	265	1	4.2	4.2	NUM
ejpam-176	265	2	.	.	PUNCT
ejpam-176	266	1	example	example	NOUN
ejpam-176	266	2	of	of	ADP
ejpam-176	266	3	a	a	DET
ejpam-176	266	4	locally	locally	ADV
ejpam-176	266	5	compact	compact	ADJ
ejpam-176	266	6	t2	t2	NOUN
ejpam-176	266	7	space	space	NOUN
ejpam-176	266	8	which	which	PRON
ejpam-176	266	9	is	be	AUX
ejpam-176	266	10	not	not	PART
ejpam-176	266	11	locally	locally	ADV
ejpam-176	266	12	β	β	X
ejpam-176	266	13	-closed	-close	VERB
ejpam-176	266	14	let	let	VERB
ejpam-176	266	15	x	x	SYM
ejpam-176	266	16	=	=	SYM
ejpam-176	266	17	r	r	NOUN
ejpam-176	266	18	,	,	PUNCT
ejpam-176	266	19	the	the	DET
ejpam-176	266	20	set	set	NOUN
ejpam-176	266	21	of	of	ADP
ejpam-176	266	22	reals	real	NOUN
ejpam-176	266	23	with	with	ADP
ejpam-176	266	24	the	the	DET
ejpam-176	266	25	usual	usual	ADJ
ejpam-176	266	26	topologyu	topologyu	NOUN
ejpam-176	266	27	.	.	PUNCT
ejpam-176	267	1	clearly	clearly	ADV
ejpam-176	267	2	(	(	PUNCT
ejpam-176	267	3	x	x	X
ejpam-176	267	4	,	,	PUNCT
ejpam-176	267	5	u	u	NOUN
ejpam-176	267	6	)	)	PUNCT
ejpam-176	267	7	is	be	AUX
ejpam-176	267	8	locally	locally	ADV
ejpam-176	267	9	compact	compact	ADJ
ejpam-176	267	10	t2	t2	NOUN
ejpam-176	267	11	but	but	CCONJ
ejpam-176	267	12	is	be	AUX
ejpam-176	267	13	not	not	PART
ejpam-176	267	14	a	a	DET
ejpam-176	267	15	locally	locally	ADV
ejpam-176	267	16	β	β	X
ejpam-176	267	17	-closed	-closed	ADJ
ejpam-176	267	18	space	space	NOUN
ejpam-176	267	19	.	.	PUNCT
ejpam-176	268	1	although	although	SCONJ
ejpam-176	268	2	we	we	PRON
ejpam-176	268	3	have	have	AUX
ejpam-176	268	4	seen	see	VERB
ejpam-176	268	5	from	from	ADP
ejpam-176	268	6	above	above	ADP
ejpam-176	268	7	examples	example	NOUN
ejpam-176	268	8	that	that	PRON
ejpam-176	268	9	local	local	ADJ
ejpam-176	268	10	β	β	X
ejpam-176	268	11	-closedness	-closedness	ADJ
ejpam-176	268	12	and	and	CCONJ
ejpam-176	268	13	local	local	ADJ
ejpam-176	268	14	compact	compact	ADJ
ejpam-176	268	15	t2	t2	NOUN
ejpam-176	268	16	-	-	PUNCT
ejpam-176	268	17	ness	ness	NOUN
ejpam-176	268	18	are	be	AUX
ejpam-176	268	19	independent	independent	ADJ
ejpam-176	268	20	concepts	concept	NOUN
ejpam-176	268	21	but	but	CCONJ
ejpam-176	268	22	the	the	DET
ejpam-176	268	23	next	next	ADJ
ejpam-176	268	24	two	two	NUM
ejpam-176	268	25	theorems	theorem	NOUN
ejpam-176	268	26	are	be	AUX
ejpam-176	268	27	two	two	NUM
ejpam-176	268	28	of	of	ADP
ejpam-176	268	29	our	our	PRON
ejpam-176	268	30	main	main	ADJ
ejpam-176	268	31	results	result	NOUN
ejpam-176	268	32	and	and	CCONJ
ejpam-176	268	33	relate	relate	VERB
ejpam-176	268	34	locally	locally	ADV
ejpam-176	268	35	compact	compact	ADJ
ejpam-176	268	36	t2	t2	NOUN
ejpam-176	268	37	spaces	space	NOUN
ejpam-176	268	38	to	to	ADP
ejpam-176	268	39	locally	locally	ADV
ejpam-176	268	40	β	β	X
ejpam-176	268	41	-closed	-close	VERB
ejpam-176	268	42	spaces	space	NOUN
ejpam-176	268	43	theorem	theorem	VERB
ejpam-176	268	44	4.4	4.4	NUM
ejpam-176	268	45	.	.	PUNCT
ejpam-176	269	1	let	let	VERB
ejpam-176	269	2	ψ	ψ	X
ejpam-176	269	3	:	:	PUNCT
ejpam-176	269	4	x	x	SYM
ejpam-176	269	5	→	→	SYM
ejpam-176	269	6	y	y	X
ejpam-176	269	7	be	be	AUX
ejpam-176	269	8	continuous	continuous	ADJ
ejpam-176	269	9	β	β	X
ejpam-176	269	10	-θ	-θ	X
ejpam-176	269	11	-closed	-close	VERB
ejpam-176	269	12	surjection	surjection	NOUN
ejpam-176	269	13	with	with	ADP
ejpam-176	269	14	point	point	NOUN
ejpam-176	269	15	inverses	inverse	NOUN
ejpam-176	269	16	are	be	AUX
ejpam-176	269	17	β	β	X
ejpam-176	269	18	closed	close	VERB
ejpam-176	269	19	sets	set	NOUN
ejpam-176	269	20	relative	relative	ADJ
ejpam-176	269	21	to	to	ADP
ejpam-176	269	22	x	x	SYM
ejpam-176	269	23	(	(	PUNCT
ejpam-176	269	24	i.e.	i.e.	X
ejpam-176	269	25	β	β	X
ejpam-176	269	26	-set	-set	NUM
ejpam-176	269	27	)	)	PUNCT
ejpam-176	269	28	.	.	PUNCT
ejpam-176	270	1	then	then	ADV
ejpam-176	270	2	x	x	X
ejpam-176	270	3	is	be	AUX
ejpam-176	270	4	locally	locally	ADV
ejpam-176	270	5	β	β	X
ejpam-176	270	6	-closed	-close	VERB
ejpam-176	270	7	whenever	whenever	SCONJ
ejpam-176	270	8	y	y	PROPN
ejpam-176	270	9	is	be	AUX
ejpam-176	270	10	locally	locally	ADV
ejpam-176	270	11	compact	compact	ADJ
ejpam-176	270	12	t2	t2	NOUN
ejpam-176	270	13	.	.	PUNCT
ejpam-176	271	1	proof	proof	NOUN
ejpam-176	271	2	:	:	PUNCT
ejpam-176	271	3	since	since	SCONJ
ejpam-176	271	4	y	y	PROPN
ejpam-176	271	5	is	be	AUX
ejpam-176	271	6	being	be	AUX
ejpam-176	271	7	a	a	DET
ejpam-176	271	8	locally	locally	ADV
ejpam-176	271	9	compact	compact	ADJ
ejpam-176	271	10	t2	t2	NOUN
ejpam-176	271	11	space	space	NOUN
ejpam-176	271	12	,	,	PUNCT
ejpam-176	271	13	for	for	ADP
ejpam-176	271	14	each	each	DET
ejpam-176	271	15	x	x	SYM
ejpam-176	271	16	∈	∈	PROPN
ejpam-176	271	17	x	x	X
ejpam-176	271	18	,	,	PUNCT
ejpam-176	271	19	there	there	PRON
ejpam-176	271	20	exists	exist	VERB
ejpam-176	271	21	an	an	DET
ejpam-176	271	22	open	open	ADJ
ejpam-176	271	23	neighbourhood	neighbourhood	NOUN
ejpam-176	271	24	v	v	NOUN
ejpam-176	271	25	of	of	ADP
ejpam-176	271	26	x	x	PUNCT
ejpam-176	271	27	such	such	ADJ
ejpam-176	271	28	that	that	SCONJ
ejpam-176	271	29	cl(v	cl(v	NOUN
ejpam-176	271	30	)	)	PUNCT
ejpam-176	271	31	is	be	AUX
ejpam-176	271	32	compact	compact	ADJ
ejpam-176	271	33	in	in	ADP
ejpam-176	271	34	y	y	PROPN
ejpam-176	271	35	.	.	PUNCT
ejpam-176	272	1	as	as	SCONJ
ejpam-176	272	2	ψ	ψ	PROPN
ejpam-176	272	3	is	be	AUX
ejpam-176	272	4	β	β	X
ejpam-176	272	5	-θ	-θ	PUNCT
ejpam-176	272	6	-closed	-close	VERB
ejpam-176	272	7	,	,	PUNCT
ejpam-176	272	8	by	by	ADP
ejpam-176	272	9	theorem	theorem	NOUN
ejpam-176	272	10	3.16	3.16	NUM
ejpam-176	272	11	,	,	PUNCT
ejpam-176	272	12	ψ−1(cl(v	ψ−1(cl(v	NOUN
ejpam-176	272	13	)	)	PUNCT
ejpam-176	272	14	)	)	PUNCT
ejpam-176	272	15	is	be	AUX
ejpam-176	272	16	a	a	DET
ejpam-176	272	17	β	β	X
ejpam-176	272	18	-closed	-close	VERB
ejpam-176	272	19	set	set	NOUN
ejpam-176	272	20	relative	relative	ADJ
ejpam-176	272	21	to	to	ADP
ejpam-176	272	22	x	x	PROPN
ejpam-176	272	23	.	.	PUNCT
ejpam-176	273	1	as	as	SCONJ
ejpam-176	273	2	ψ	ψ	NOUN
ejpam-176	273	3	is	be	AUX
ejpam-176	273	4	continuous	continuous	ADJ
ejpam-176	273	5	it	it	PRON
ejpam-176	273	6	is	be	AUX
ejpam-176	273	7	obvious	obvious	ADJ
ejpam-176	273	8	that	that	SCONJ
ejpam-176	273	9	int(cl(ψ−1(v	int(cl(ψ−1(v	PROPN
ejpam-176	273	10	)	)	PUNCT
ejpam-176	273	11	)	)	PUNCT
ejpam-176	274	1	⊂	⊂	PROPN
ejpam-176	274	2	ψ−1(cl(v	ψ−1(cl(v	NOUN
ejpam-176	274	3	)	)	PUNCT
ejpam-176	274	4	)	)	PUNCT
ejpam-176	274	5	.	.	PUNCT
ejpam-176	275	1	but	but	CCONJ
ejpam-176	275	2	int(cl(ψ−1(v	int(cl(ψ−1(v	PROPN
ejpam-176	275	3	)	)	PUNCT
ejpam-176	275	4	)	)	PUNCT
ejpam-176	275	5	is	be	AUX
ejpam-176	275	6	obviously	obviously	ADV
ejpam-176	275	7	β	β	PART
ejpam-176	275	8	-regular	-regular	ADJ
ejpam-176	275	9	set	set	VERB
ejpam-176	275	10	containing	contain	VERB
ejpam-176	275	11	x	x	PUNCT
ejpam-176	275	12	and	and	CCONJ
ejpam-176	275	13	hence	hence	ADV
ejpam-176	275	14	by	by	ADP
ejpam-176	275	15	theorem	theorem	ADJ
ejpam-176	275	16	3.3	3.3	NUM
ejpam-176	275	17	,	,	PUNCT
ejpam-176	275	18	int(cl(ψ−1(v	int(cl(ψ−1(v	PROPN
ejpam-176	275	19	)	)	PUNCT
ejpam-176	275	20	)	)	PUNCT
ejpam-176	275	21	is	be	AUX
ejpam-176	275	22	β	β	X
ejpam-176	275	23	-closed	-close	VERB
ejpam-176	275	24	relative	relative	ADJ
ejpam-176	275	25	to	to	ADP
ejpam-176	275	26	x	x	X
ejpam-176	275	27	.	.	PUNCT
ejpam-176	276	1	therefore	therefore	ADV
ejpam-176	276	2	by	by	ADP
ejpam-176	276	3	theorem	theorem	NOUN
ejpam-176	276	4	4.4	4.4	NUM
ejpam-176	276	5	,	,	PUNCT
ejpam-176	276	6	x	x	X
ejpam-176	276	7	is	be	AUX
ejpam-176	276	8	locally	locally	ADV
ejpam-176	276	9	β	β	X
ejpam-176	276	10	-closed	-closed	PROPN
ejpam-176	276	11	.	.	PUNCT
ejpam-176	277	1	remark	remark	PROPN
ejpam-176	277	2	4.2	4.2	NUM
ejpam-176	277	3	.	.	PUNCT
ejpam-176	278	1	in	in	ADP
ejpam-176	278	2	the	the	DET
ejpam-176	278	3	above	above	ADJ
ejpam-176	278	4	theorem	theorem	NOUN
ejpam-176	278	5	x	x	PRON
ejpam-176	278	6	is	be	AUX
ejpam-176	278	7	not	not	PART
ejpam-176	278	8	necessarily	necessarily	ADV
ejpam-176	278	9	t2	t2	NOUN
ejpam-176	278	10	.	.	PUNCT
ejpam-176	279	1	example	example	NOUN
ejpam-176	279	2	4.3	4.3	NUM
ejpam-176	279	3	.	.	PUNCT
ejpam-176	280	1	let	let	VERB
ejpam-176	280	2	x	x	PUNCT
ejpam-176	280	3	=	=	PUNCT
ejpam-176	280	4	any	any	DET
ejpam-176	280	5	finite	finite	NOUN
ejpam-176	280	6	set	set	VERB
ejpam-176	280	7	and	and	CCONJ
ejpam-176	280	8	τx	τx	ADP
ejpam-176	280	9	=	=	PUNCT
ejpam-176	280	10	{	{	PUNCT
ejpam-176	280	11	;	;	PUNCT
ejpam-176	280	12	,	,	PUNCT
ejpam-176	280	13	x	x	SYM
ejpam-176	280	14	}	}	PUNCT
ejpam-176	280	15	.	.	PUNCT
ejpam-176	281	1	let	let	VERB
ejpam-176	281	2	y	y	PROPN
ejpam-176	281	3	=	=	PRON
ejpam-176	281	4	{	{	PUNCT
ejpam-176	281	5	a	a	X
ejpam-176	281	6	}	}	PUNCT
ejpam-176	281	7	with	with	ADP
ejpam-176	281	8	the	the	DET
ejpam-176	281	9	discrete	discrete	ADJ
ejpam-176	281	10	topology	topology	NOUN
ejpam-176	281	11	.	.	PUNCT
ejpam-176	282	1	let	let	VERB
ejpam-176	282	2	ψ	ψ	X
ejpam-176	282	3	:	:	PUNCT
ejpam-176	282	4	x	x	SYM
ejpam-176	282	5	→	→	SYM
ejpam-176	282	6	y	y	PROPN
ejpam-176	282	7	be	be	AUX
ejpam-176	282	8	the	the	DET
ejpam-176	282	9	constant	constant	ADJ
ejpam-176	282	10	function	function	NOUN
ejpam-176	282	11	.	.	PUNCT
ejpam-176	283	1	then	then	ADV
ejpam-176	283	2	y	y	PROPN
ejpam-176	283	3	is	be	AUX
ejpam-176	283	4	locally	locally	ADV
ejpam-176	283	5	compact	compact	ADJ
ejpam-176	283	6	t2	t2	NOUN
ejpam-176	283	7	and	and	CCONJ
ejpam-176	283	8	ψ	ψ	NOUN
ejpam-176	283	9	is	be	AUX
ejpam-176	283	10	continuous	continuous	ADJ
ejpam-176	283	11	β	β	X
ejpam-176	283	12	-θ	-θ	PUNCT
ejpam-176	283	13	-closed	-close	VERB
ejpam-176	283	14	surjection	surjection	NOUN
ejpam-176	283	15	with	with	ADP
ejpam-176	283	16	β	β	X
ejpam-176	283	17	-closed	-close	VERB
ejpam-176	283	18	set	set	NOUN
ejpam-176	283	19	relative	relative	ADJ
ejpam-176	283	20	to	to	ADP
ejpam-176	283	21	x	x	SYM
ejpam-176	283	22	(	(	PUNCT
ejpam-176	283	23	i.e.	i.e.	X
ejpam-176	283	24	β	β	X
ejpam-176	283	25	-set	-set	NUM
ejpam-176	283	26	)	)	PUNCT
ejpam-176	283	27	point	point	NOUN
ejpam-176	283	28	inverses	inverse	NOUN
ejpam-176	283	29	.	.	PUNCT
ejpam-176	284	1	however	however	ADV
ejpam-176	284	2	x	x	PRON
ejpam-176	284	3	is	be	AUX
ejpam-176	284	4	not	not	PART
ejpam-176	284	5	t2	t2	NOUN
ejpam-176	284	6	.	.	PUNCT
ejpam-176	285	1	c.	c.	PROPN
ejpam-176	285	2	basu	basu	PROPN
ejpam-176	285	3	and	and	CCONJ
ejpam-176	285	4	m.	m.	PROPN
ejpam-176	285	5	ghosh	ghosh	PROPN
ejpam-176	285	6	/	/	PUNCT
ejpam-176	285	7	eur	eur	PROPN
ejpam-176	285	8	.	.	PUNCT
ejpam-176	286	1	j.	j.	PROPN
ejpam-176	286	2	pure	pure	PROPN
ejpam-176	286	3	appl	appl	PROPN
ejpam-176	286	4	.	.	PROPN
ejpam-176	286	5	math	math	PROPN
ejpam-176	286	6	,	,	PUNCT
ejpam-176	286	7	2	2	NUM
ejpam-176	286	8	(	(	PUNCT
ejpam-176	286	9	2009	2009	NUM
ejpam-176	286	10	)	)	PUNCT
ejpam-176	286	11	,	,	PUNCT
ejpam-176	286	12	(	(	PUNCT
ejpam-176	286	13	85	85	NUM
ejpam-176	286	14	-	-	SYM
ejpam-176	286	15	96	96	NUM
ejpam-176	286	16	)	)	PUNCT
ejpam-176	286	17	94	94	NUM
ejpam-176	286	18	definition	definition	NOUN
ejpam-176	286	19	4.2	4.2	NUM
ejpam-176	286	20	.	.	PUNCT
ejpam-176	287	1	[	[	X
ejpam-176	287	2	7	7	X
ejpam-176	287	3	]	]	X
ejpam-176	287	4	a	a	DET
ejpam-176	287	5	function	function	NOUN
ejpam-176	287	6	ψ	ψ	NOUN
ejpam-176	287	7	:	:	PUNCT
ejpam-176	287	8	x	x	SYM
ejpam-176	287	9	→	→	SYM
ejpam-176	287	10	y	y	PROPN
ejpam-176	287	11	is	be	AUX
ejpam-176	287	12	said	say	VERB
ejpam-176	287	13	to	to	PART
ejpam-176	287	14	be	be	AUX
ejpam-176	287	15	(	(	PUNCT
ejpam-176	287	16	θ	θ	PROPN
ejpam-176	287	17	,	,	PUNCT
ejpam-176	287	18	β)-continuous	β)-continuous	PUNCT
ejpam-176	287	19	if	if	SCONJ
ejpam-176	287	20	for	for	ADP
ejpam-176	287	21	each	each	DET
ejpam-176	287	22	x	x	SYM
ejpam-176	287	23	∈	∈	PROPN
ejpam-176	287	24	x	x	X
ejpam-176	287	25	and	and	CCONJ
ejpam-176	287	26	each	each	DET
ejpam-176	287	27	v	v	NOUN
ejpam-176	287	28	∈	∈	NOUN
ejpam-176	287	29	βr(y	βr(y	NUM
ejpam-176	287	30	,	,	PUNCT
ejpam-176	287	31	ψ(x	ψ(x	NOUN
ejpam-176	287	32	)	)	PUNCT
ejpam-176	287	33	)	)	PUNCT
ejpam-176	288	1	there	there	PRON
ejpam-176	288	2	is	be	VERB
ejpam-176	288	3	an	an	DET
ejpam-176	288	4	open	open	ADJ
ejpam-176	288	5	set	set	NOUN
ejpam-176	288	6	u	u	NOUN
ejpam-176	288	7	containing	contain	VERB
ejpam-176	288	8	x	x	PUNCT
ejpam-176	288	9	such	such	ADJ
ejpam-176	288	10	that	that	DET
ejpam-176	288	11	ψ(u)⊂	ψ(u)⊂	NOUN
ejpam-176	288	12	v	v	NOUN
ejpam-176	288	13	.	.	PUNCT
ejpam-176	289	1	theorem	theorem	VERB
ejpam-176	289	2	4.5	4.5	NUM
ejpam-176	289	3	.	.	PUNCT
ejpam-176	290	1	ifψ	ifψ	NOUN
ejpam-176	290	2	:	:	PUNCT
ejpam-176	290	3	x	x	X
ejpam-176	290	4	→	→	SYM
ejpam-176	290	5	y	y	PROPN
ejpam-176	290	6	is	be	AUX
ejpam-176	290	7	a	a	DET
ejpam-176	290	8	β	β	X
ejpam-176	290	9	-θ	-θ	PUNCT
ejpam-176	290	10	-closed	-close	VERB
ejpam-176	290	11	,	,	PUNCT
ejpam-176	290	12	(	(	PUNCT
ejpam-176	290	13	θ	θ	PROPN
ejpam-176	290	14	,	,	PUNCT
ejpam-176	290	15	β)-continuous	β)-continuous	ADJ
ejpam-176	290	16	surjection	surjection	NOUN
ejpam-176	290	17	with	with	SCONJ
ejpam-176	290	18	point	point	NOUN
ejpam-176	290	19	inverses	inverse	NOUN
ejpam-176	290	20	are	be	AUX
ejpam-176	290	21	β	β	X
ejpam-176	290	22	-closed	-close	VERB
ejpam-176	290	23	sets	set	NOUN
ejpam-176	290	24	relative	relative	ADJ
ejpam-176	290	25	to	to	ADP
ejpam-176	290	26	x	x	SYM
ejpam-176	290	27	(	(	PUNCT
ejpam-176	290	28	i.e.	i.e.	X
ejpam-176	290	29	β	β	X
ejpam-176	290	30	-sets	-set	NOUN
ejpam-176	290	31	)	)	PUNCT
ejpam-176	290	32	.	.	PUNCT
ejpam-176	291	1	then	then	ADV
ejpam-176	291	2	y	y	PROPN
ejpam-176	291	3	is	be	AUX
ejpam-176	291	4	locally	locally	ADV
ejpam-176	291	5	β	β	X
ejpam-176	291	6	-closed	-close	VERB
ejpam-176	291	7	if	if	SCONJ
ejpam-176	291	8	x	x	PRON
ejpam-176	291	9	is	be	AUX
ejpam-176	291	10	locally	locally	ADV
ejpam-176	291	11	compact	compact	ADJ
ejpam-176	291	12	t2	t2	NOUN
ejpam-176	291	13	.	.	PUNCT
ejpam-176	292	1	proof	proof	NOUN
ejpam-176	292	2	:	:	PUNCT
ejpam-176	292	3	first	first	ADV
ejpam-176	292	4	of	of	ADP
ejpam-176	292	5	all	all	PRON
ejpam-176	292	6	we	we	PRON
ejpam-176	292	7	claim	claim	VERB
ejpam-176	292	8	that	that	SCONJ
ejpam-176	292	9	y	y	PROPN
ejpam-176	292	10	is	be	AUX
ejpam-176	292	11	t2	t2	PROPN
ejpam-176	292	12	.	.	PUNCT
ejpam-176	293	1	indeed	indeed	ADV
ejpam-176	293	2	,	,	PUNCT
ejpam-176	293	3	by	by	ADP
ejpam-176	293	4	the	the	DET
ejpam-176	293	5	hypothesis	hypothesis	NOUN
ejpam-176	293	6	,	,	PUNCT
ejpam-176	293	7	for	for	ADP
ejpam-176	293	8	distinct	distinct	ADJ
ejpam-176	293	9	points	point	NOUN
ejpam-176	293	10	y1	y1	NOUN
ejpam-176	293	11	and	and	CCONJ
ejpam-176	293	12	y2	y2	PROPN
ejpam-176	293	13	in	in	ADP
ejpam-176	293	14	y	y	PROPN
ejpam-176	293	15	,	,	PUNCT
ejpam-176	293	16	ψ−1(yi	ψ−1(yi	PROPN
ejpam-176	293	17	)	)	PUNCT
ejpam-176	293	18	for	for	ADP
ejpam-176	293	19	i	i	PRON
ejpam-176	293	20	=	=	NOUN
ejpam-176	293	21	1,2	1,2	NUM
ejpam-176	293	22	are	be	AUX
ejpam-176	293	23	disjoint	disjoint	NOUN
ejpam-176	293	24	β	β	X
ejpam-176	293	25	-closed	-close	VERB
ejpam-176	293	26	sets	set	NOUN
ejpam-176	293	27	relative	relative	ADJ
ejpam-176	293	28	to	to	ADP
ejpam-176	293	29	x	x	PUNCT
ejpam-176	293	30	and	and	CCONJ
ejpam-176	293	31	hence	hence	ADV
ejpam-176	293	32	they	they	PRON
ejpam-176	293	33	are	be	AUX
ejpam-176	293	34	ncsets	ncset	NOUN
ejpam-176	293	35	.	.	PUNCT
ejpam-176	294	1	since	since	SCONJ
ejpam-176	294	2	y	y	PROPN
ejpam-176	294	3	is	be	AUX
ejpam-176	294	4	t2	t2	NOUN
ejpam-176	294	5	,	,	PUNCT
ejpam-176	294	6	one	one	PRON
ejpam-176	294	7	can	can	AUX
ejpam-176	294	8	check	check	VERB
ejpam-176	294	9	easily	easily	ADV
ejpam-176	294	10	that	that	SCONJ
ejpam-176	294	11	,	,	PUNCT
ejpam-176	294	12	there	there	PRON
ejpam-176	294	13	exist	exist	VERB
ejpam-176	294	14	disjoint	disjoint	NOUN
ejpam-176	294	15	w1	w1	NOUN
ejpam-176	294	16	,	,	PUNCT
ejpam-176	294	17	w2	w2	NOUN
ejpam-176	294	18	∈	∈	PROPN
ejpam-176	294	19	ro(x	ro(x	PUNCT
ejpam-176	294	20	)	)	PUNCT
ejpam-176	294	21	satisfying	satisfy	VERB
ejpam-176	294	22	ψ−1(yi	ψ−1(yi	NUM
ejpam-176	294	23	)	)	PUNCT
ejpam-176	295	1	⊂	⊂	PROPN
ejpam-176	295	2	ui	ui	PROPN
ejpam-176	295	3	for	for	ADP
ejpam-176	295	4	i	i	PROPN
ejpam-176	295	5	=	=	NOUN
ejpam-176	295	6	1,2	1,2	NUM
ejpam-176	295	7	.	.	PUNCT
ejpam-176	296	1	as	as	SCONJ
ejpam-176	296	2	every	every	DET
ejpam-176	296	3	regular	regular	ADJ
ejpam-176	296	4	open	open	ADJ
ejpam-176	296	5	set	set	NOUN
ejpam-176	296	6	is	be	AUX
ejpam-176	296	7	β	β	NOUN
ejpam-176	296	8	-regular	-regular	ADJ
ejpam-176	296	9	and	and	CCONJ
ejpam-176	296	10	hence	hence	ADV
ejpam-176	296	11	is	be	AUX
ejpam-176	296	12	β	β	X
ejpam-176	296	13	-θ	-θ	PUNCT
ejpam-176	296	14	-open	-open	ADJ
ejpam-176	296	15	and	and	CCONJ
ejpam-176	296	16	as	as	SCONJ
ejpam-176	296	17	ψ	ψ	NOUN
ejpam-176	296	18	is	be	AUX
ejpam-176	296	19	β	β	X
ejpam-176	296	20	-θ	-θ	PUNCT
ejpam-176	296	21	-closed	-closed	ADJ
ejpam-176	296	22	,	,	PUNCT
ejpam-176	296	23	then	then	ADV
ejpam-176	296	24	by	by	ADP
ejpam-176	296	25	theorem	theorem	NOUN
ejpam-176	296	26	3.12	3.12	NUM
ejpam-176	296	27	,	,	PUNCT
ejpam-176	296	28	there	there	PRON
ejpam-176	296	29	exist	exist	VERB
ejpam-176	296	30	open	open	ADJ
ejpam-176	296	31	sets	set	NOUN
ejpam-176	296	32	ui	ui	NOUN
ejpam-176	296	33	containing	contain	VERB
ejpam-176	296	34	yi	yi	PRON
ejpam-176	296	35	such	such	ADJ
ejpam-176	296	36	that	that	SCONJ
ejpam-176	296	37	ψ−1(ui	ψ−1(ui	PROPN
ejpam-176	296	38	)	)	PUNCT
ejpam-176	297	1	⊂	⊂	PROPN
ejpam-176	297	2	wi	wi	PROPN
ejpam-176	297	3	for	for	ADP
ejpam-176	297	4	i	i	PROPN
ejpam-176	297	5	=	=	NOUN
ejpam-176	297	6	1,2	1,2	NUM
ejpam-176	297	7	.	.	PUNCT
ejpam-176	298	1	therefore	therefore	ADV
ejpam-176	298	2	y	y	PROPN
ejpam-176	298	3	is	be	AUX
ejpam-176	298	4	t2	t2	NOUN
ejpam-176	298	5	.	.	PUNCT
ejpam-176	299	1	let	let	VERB
ejpam-176	299	2	y	y	PROPN
ejpam-176	299	3	∈	∈	PROPN
ejpam-176	299	4	y	y	PROPN
ejpam-176	299	5	.	.	PUNCT
ejpam-176	300	1	since	since	SCONJ
ejpam-176	300	2	x	x	PRON
ejpam-176	300	3	is	be	AUX
ejpam-176	300	4	a	a	DET
ejpam-176	300	5	locally	locally	ADV
ejpam-176	300	6	compact	compact	ADJ
ejpam-176	300	7	t2	t2	NOUN
ejpam-176	300	8	space	space	NOUN
ejpam-176	300	9	,	,	PUNCT
ejpam-176	300	10	then	then	ADV
ejpam-176	300	11	for	for	ADP
ejpam-176	300	12	each	each	DET
ejpam-176	300	13	x	x	SYM
ejpam-176	300	14	∈	∈	PROPN
ejpam-176	300	15	ψ−1(y	ψ−1(y	PROPN
ejpam-176	300	16	)	)	PUNCT
ejpam-176	300	17	,	,	PUNCT
ejpam-176	300	18	there	there	PRON
ejpam-176	300	19	exists	exist	VERB
ejpam-176	300	20	a	a	DET
ejpam-176	300	21	closed	closed	ADJ
ejpam-176	300	22	compact	compact	ADJ
ejpam-176	300	23	neighbourhood	neighbourhood	NOUN
ejpam-176	300	24	vx	vx	X
ejpam-176	300	25	of	of	ADP
ejpam-176	300	26	x	x	PROPN
ejpam-176	300	27	in	in	ADP
ejpam-176	300	28	x	x	X
ejpam-176	300	29	.	.	PUNCT
ejpam-176	301	1	now	now	ADV
ejpam-176	301	2	as	as	SCONJ
ejpam-176	301	3	the	the	DET
ejpam-176	301	4	family	family	NOUN
ejpam-176	301	5	{	{	PUNCT
ejpam-176	301	6	int(vx	int(vx	NOUN
ejpam-176	301	7	)	)	PUNCT
ejpam-176	301	8	:	:	PUNCT
ejpam-176	301	9	x	x	X
ejpam-176	301	10	∈	∈	PROPN
ejpam-176	301	11	ψ−1(y	ψ−1(y	PROPN
ejpam-176	301	12	)	)	PUNCT
ejpam-176	301	13	}	}	PUNCT
ejpam-176	301	14	is	be	AUX
ejpam-176	301	15	being	be	AUX
ejpam-176	301	16	a	a	DET
ejpam-176	301	17	β	β	NOUN
ejpam-176	301	18	-regular	-regular	ADJ
ejpam-176	301	19	cover	cover	NOUN
ejpam-176	301	20	(	(	PUNCT
ejpam-176	301	21	argument	argument	NOUN
ejpam-176	301	22	given	give	VERB
ejpam-176	301	23	above	above	ADV
ejpam-176	301	24	)	)	PUNCT
ejpam-176	301	25	of	of	ADP
ejpam-176	301	26	the	the	DET
ejpam-176	301	27	set	set	NOUN
ejpam-176	301	28	ψ−1(y	ψ−1(y	PROPN
ejpam-176	301	29	)	)	PUNCT
ejpam-176	301	30	which	which	PRON
ejpam-176	301	31	is	be	AUX
ejpam-176	301	32	β	β	X
ejpam-176	301	33	-closed	-close	VERB
ejpam-176	301	34	relative	relative	ADJ
ejpam-176	301	35	to	to	ADP
ejpam-176	301	36	x	x	PRON
ejpam-176	301	37	,	,	PUNCT
ejpam-176	301	38	then	then	ADV
ejpam-176	301	39	by	by	ADP
ejpam-176	301	40	theorem	theorem	NOUN
ejpam-176	301	41	3.2	3.2	NUM
ejpam-176	301	42	,	,	PUNCT
ejpam-176	301	43	there	there	PRON
ejpam-176	301	44	exist	exist	VERB
ejpam-176	301	45	x1	x1	PROPN
ejpam-176	301	46	,	,	PUNCT
ejpam-176	301	47	x2	x2	PROPN
ejpam-176	301	48	,	,	PUNCT
ejpam-176	301	49	....	....	PUNCT
ejpam-176	301	50	,	,	PUNCT
ejpam-176	301	51	xk	xk	PROPN
ejpam-176	301	52	∈	∈	PROPN
ejpam-176	301	53	ψ	ψ	X
ejpam-176	301	54	−1(y	−1(y	NOUN
ejpam-176	301	55	)	)	PUNCT
ejpam-176	301	56	such	such	ADJ
ejpam-176	301	57	that	that	PRON
ejpam-176	301	58	ψ−1(y	ψ−1(y	PROPN
ejpam-176	301	59	)	)	PUNCT
ejpam-176	302	1	⊂	⊂	PROPN
ejpam-176	302	2	∪k	∪k	PROPN
ejpam-176	302	3	i=1	i=1	X
ejpam-176	302	4	int(vxi	int(vxi	ADV
ejpam-176	302	5	)	)	PUNCT
ejpam-176	302	6	.	.	PUNCT
ejpam-176	303	1	hence	hence	ADV
ejpam-176	303	2	ψ−1(y	ψ−1(y	PROPN
ejpam-176	303	3	)	)	PUNCT
ejpam-176	304	1	⊂	⊂	PROPN
ejpam-176	304	2	∪k	∪k	PROPN
ejpam-176	304	3	i=1	i=1	X
ejpam-176	304	4	int(vxi	int(vxi	ADV
ejpam-176	304	5	)	)	PUNCT
ejpam-176	305	1	⊂	⊂	PRON
ejpam-176	305	2	int(∪k	int(∪k	PROPN
ejpam-176	305	3	i=1vxi	i=1vxi	PROPN
ejpam-176	305	4	)	)	PUNCT
ejpam-176	305	5	.	.	PUNCT
ejpam-176	306	1	since	since	SCONJ
ejpam-176	306	2	the	the	DET
ejpam-176	306	3	latter	latter	ADJ
ejpam-176	306	4	subset	subset	NOUN
ejpam-176	306	5	is	be	AUX
ejpam-176	306	6	β	β	X
ejpam-176	306	7	-θ	-θ	PUNCT
ejpam-176	306	8	-open	-open	ADJ
ejpam-176	306	9	and	and	CCONJ
ejpam-176	306	10	ψ	ψ	NOUN
ejpam-176	306	11	is	be	AUX
ejpam-176	306	12	β	β	X
ejpam-176	306	13	-θ	-θ	PUNCT
ejpam-176	306	14	-closed	-close	VERB
ejpam-176	306	15	then	then	ADV
ejpam-176	306	16	by	by	ADP
ejpam-176	306	17	theorem	theorem	NOUN
ejpam-176	306	18	3.12	3.12	NUM
ejpam-176	306	19	there	there	ADV
ejpam-176	306	20	exists	exist	VERB
ejpam-176	306	21	an	an	DET
ejpam-176	306	22	open	open	ADJ
ejpam-176	306	23	set	set	NOUN
ejpam-176	306	24	wy	wy	PROPN
ejpam-176	306	25	containing	contain	VERB
ejpam-176	306	26	y	y	PRON
ejpam-176	306	27	such	such	ADJ
ejpam-176	306	28	that	that	SCONJ
ejpam-176	306	29	ψ−1(wy)⊂	ψ−1(wy)⊂	PROPN
ejpam-176	306	30	int(∪k	int(∪k	PROPN
ejpam-176	306	31	i=1vxi	i=1vxi	NOUN
ejpam-176	306	32	)	)	PUNCT
ejpam-176	306	33	.	.	PUNCT
ejpam-176	307	1	hence	hence	ADV
ejpam-176	307	2	y	y	PROPN
ejpam-176	307	3	∈wy	∈wy	PROPN
ejpam-176	307	4	⊂	⊂	PROPN
ejpam-176	307	5	ψ(int(∪k	ψ(int(∪k	VERB
ejpam-176	307	6	i=1	i=1	PROPN
ejpam-176	307	7	vxi	vxi	PROPN
ejpam-176	307	8	)	)	PUNCT
ejpam-176	307	9	)	)	PUNCT
ejpam-176	308	1	⊂ψ(∪k	⊂ψ(∪k	PROPN
ejpam-176	308	2	i=1	i=1	PROPN
ejpam-176	308	3	vxi	vxi	PROPN
ejpam-176	308	4	)	)	PUNCT
ejpam-176	308	5	.	.	PUNCT
ejpam-176	309	1	as	as	SCONJ
ejpam-176	309	2	it	it	PRON
ejpam-176	309	3	is	be	AUX
ejpam-176	309	4	obvious	obvious	ADJ
ejpam-176	309	5	that	that	SCONJ
ejpam-176	309	6	(	(	PUNCT
ejpam-176	309	7	θ	θ	NOUN
ejpam-176	309	8	,	,	PUNCT
ejpam-176	309	9	β)-continuous	β)-continuous	ADJ
ejpam-176	309	10	image	image	NOUN
ejpam-176	309	11	of	of	ADP
ejpam-176	309	12	a	a	DET
ejpam-176	309	13	compact	compact	ADJ
ejpam-176	309	14	set	set	NOUN
ejpam-176	309	15	is	be	AUX
ejpam-176	309	16	a	a	DET
ejpam-176	309	17	β	β	X
ejpam-176	309	18	-closed	-close	VERB
ejpam-176	309	19	set	set	NOUN
ejpam-176	309	20	and	and	CCONJ
ejpam-176	309	21	y	y	PROPN
ejpam-176	309	22	is	be	AUX
ejpam-176	309	23	t2	t2	NOUN
ejpam-176	309	24	,	,	PUNCT
ejpam-176	309	25	ψ(∪k	ψ(∪k	NUM
ejpam-176	309	26	i=1vxi	i=1vxi	NOUN
ejpam-176	309	27	)	)	PUNCT
ejpam-176	309	28	is	be	AUX
ejpam-176	309	29	obviously	obviously	ADV
ejpam-176	309	30	closed	close	VERB
ejpam-176	309	31	.	.	PUNCT
ejpam-176	310	1	since	since	SCONJ
ejpam-176	310	2	y	y	PROPN
ejpam-176	310	3	∈	∈	PROPN
ejpam-176	310	4	wy	wy	PROPN
ejpam-176	310	5	⊂	⊂	PROPN
ejpam-176	310	6	int(cl(wy	int(cl(wy	PROPN
ejpam-176	310	7	)	)	PUNCT
ejpam-176	310	8	)	)	PUNCT
ejpam-176	311	1	⊂	⊂	PRON
ejpam-176	311	2	ψ(∪k	ψ(∪k	VERB
ejpam-176	311	3	i=1	i=1	PROPN
ejpam-176	311	4	vxi	vxi	PROPN
ejpam-176	311	5	)	)	PUNCT
ejpam-176	311	6	and	and	CCONJ
ejpam-176	311	7	int(cl(wy	int(cl(wy	PROPN
ejpam-176	311	8	)	)	PUNCT
ejpam-176	311	9	)	)	PUNCT
ejpam-176	311	10	is	be	AUX
ejpam-176	311	11	β	β	NOUN
ejpam-176	311	12	-regular	-regular	NOUN
ejpam-176	311	13	then	then	ADV
ejpam-176	311	14	int(cl(wy	int(cl(wy	PROPN
ejpam-176	311	15	)	)	PUNCT
ejpam-176	311	16	)	)	PUNCT
ejpam-176	311	17	is	be	AUX
ejpam-176	311	18	β	β	X
ejpam-176	311	19	-closed	-close	VERB
ejpam-176	311	20	relative	relative	ADJ
ejpam-176	311	21	to	to	ADP
ejpam-176	311	22	x	x	X
ejpam-176	311	23	.	.	PUNCT
ejpam-176	312	1	therefore	therefore	ADV
ejpam-176	312	2	by	by	ADP
ejpam-176	312	3	theorem	theorem	NOUN
ejpam-176	312	4	4.4	4.4	NUM
ejpam-176	312	5	,	,	PUNCT
ejpam-176	312	6	y	y	PROPN
ejpam-176	312	7	is	be	AUX
ejpam-176	312	8	locally	locally	ADV
ejpam-176	312	9	β	β	X
ejpam-176	312	10	-closed	-closed	PROPN
ejpam-176	312	11	.	.	PUNCT
ejpam-176	313	1	definition	definition	NOUN
ejpam-176	313	2	4.3	4.3	NUM
ejpam-176	313	3	.	.	PUNCT
ejpam-176	314	1	a	a	DET
ejpam-176	314	2	topological	topological	ADJ
ejpam-176	314	3	space	space	NOUN
ejpam-176	314	4	x	x	PUNCT
ejpam-176	314	5	is	be	AUX
ejpam-176	314	6	called	call	VERB
ejpam-176	314	7	γ	γ	NOUN
ejpam-176	314	8	-	-	ADJ
ejpam-176	314	9	perfect	perfect	ADJ
ejpam-176	314	10	if	if	SCONJ
ejpam-176	314	11	for	for	ADP
ejpam-176	314	12	each	each	DET
ejpam-176	314	13	u	u	PROPN
ejpam-176	314	14	∈	∈	PROPN
ejpam-176	314	15	ro(x	ro(x	PUNCT
ejpam-176	314	16	)	)	PUNCT
ejpam-176	314	17	and	and	CCONJ
ejpam-176	314	18	each	each	DET
ejpam-176	314	19	x	x	SYM
ejpam-176	314	20	6∈	6∈	PROPN
ejpam-176	314	21	u	u	NOUN
ejpam-176	314	22	,	,	PUNCT
ejpam-176	314	23	there	there	PRON
ejpam-176	314	24	exists	exist	VERB
ejpam-176	314	25	a	a	DET
ejpam-176	314	26	family	family	NOUN
ejpam-176	314	27	of	of	ADP
ejpam-176	314	28	open	open	ADJ
ejpam-176	314	29	sets	set	NOUN
ejpam-176	314	30	v	v	NOUN
ejpam-176	314	31	=	=	SYM
ejpam-176	314	32	{	{	PUNCT
ejpam-176	314	33	vα	vα	X
ejpam-176	314	34	:	:	PUNCT
ejpam-176	314	35	α	α	PROPN
ejpam-176	314	36	∈	∈	PROPN
ejpam-176	315	1	i	i	X
ejpam-176	315	2	}	}	PUNCT
ejpam-176	315	3	such	such	ADJ
ejpam-176	315	4	that	that	SCONJ
ejpam-176	315	5	u	u	PROPN
ejpam-176	315	6	⊂	⊂	PRON
ejpam-176	315	7	∪α∈i	∪α∈i	PROPN
ejpam-176	315	8	cl(vα)with	cl(vα)with	ADP
ejpam-176	315	9	x	x	PROPN
ejpam-176	315	10	6∈	6∈	PROPN
ejpam-176	315	11	∪α∈i	∪α∈i	PROPN
ejpam-176	315	12	cl(vα	cl(vα	NOUN
ejpam-176	315	13	)	)	PUNCT
ejpam-176	315	14	.	.	PUNCT
ejpam-176	316	1	theorem	theorem	VERB
ejpam-176	316	2	4.6	4.6	NUM
ejpam-176	316	3	.	.	PUNCT
ejpam-176	317	1	every	every	DET
ejpam-176	317	2	locally	locally	ADV
ejpam-176	317	3	β	β	X
ejpam-176	317	4	-closed	-close	VERB
ejpam-176	317	5	γ	γ	X
ejpam-176	317	6	-	-	ADJ
ejpam-176	317	7	perfect	perfect	ADJ
ejpam-176	317	8	space	space	NOUN
ejpam-176	317	9	is	be	AUX
ejpam-176	317	10	extremally	extremally	ADV
ejpam-176	317	11	disconnected	disconnect	VERB
ejpam-176	317	12	.	.	PUNCT
ejpam-176	318	1	proof	proof	NOUN
ejpam-176	318	2	:	:	PUNCT
ejpam-176	318	3	let	let	VERB
ejpam-176	318	4	u	u	PRON
ejpam-176	318	5	∈	∈	PROPN
ejpam-176	318	6	ro(x	ro(x	PUNCT
ejpam-176	318	7	)	)	PUNCT
ejpam-176	318	8	,	,	PUNCT
ejpam-176	318	9	where	where	SCONJ
ejpam-176	318	10	x	x	PRON
ejpam-176	318	11	is	be	AUX
ejpam-176	318	12	a	a	DET
ejpam-176	318	13	locally	locally	ADV
ejpam-176	318	14	β	β	X
ejpam-176	318	15	-closed	-close	VERB
ejpam-176	318	16	γ	γ	X
ejpam-176	318	17	-	-	ADJ
ejpam-176	318	18	perfect	perfect	ADJ
ejpam-176	318	19	space	space	NOUN
ejpam-176	318	20	.	.	PUNCT
ejpam-176	319	1	let	let	VERB
ejpam-176	319	2	x	x	SYM
ejpam-176	319	3	6∈	6∈	PROPN
ejpam-176	319	4	u	u	NOUN
ejpam-176	319	5	.	.	PUNCT
ejpam-176	320	1	since	since	SCONJ
ejpam-176	320	2	x	x	PRON
ejpam-176	320	3	is	be	AUX
ejpam-176	320	4	locally	locally	ADV
ejpam-176	320	5	β	β	X
ejpam-176	320	6	-closed	-close	VERB
ejpam-176	320	7	,	,	PUNCT
ejpam-176	320	8	there	there	PRON
ejpam-176	320	9	is	be	VERB
ejpam-176	320	10	a	a	DET
ejpam-176	320	11	v	v	NOUN
ejpam-176	320	12	∈	∈	NOUN
ejpam-176	320	13	ro(x	ro(x	PUNCT
ejpam-176	320	14	,	,	PUNCT
ejpam-176	320	15	x	x	X
ejpam-176	320	16	)	)	PUNCT
ejpam-176	320	17	such	such	ADJ
ejpam-176	320	18	that	that	DET
ejpam-176	320	19	v	v	NOUN
ejpam-176	320	20	is	be	AUX
ejpam-176	320	21	β	β	X
ejpam-176	320	22	-closed	-close	VERB
ejpam-176	320	23	relative	relative	ADJ
ejpam-176	320	24	to	to	ADP
ejpam-176	320	25	x	x	PROPN
ejpam-176	320	26	.	.	PUNCT
ejpam-176	321	1	let	let	VERB
ejpam-176	321	2	r=	r=	PROPN
ejpam-176	321	3	u	u	NOUN
ejpam-176	321	4	∩	∩	ADJ
ejpam-176	321	5	v	v	ADJ
ejpam-176	321	6	.	.	PUNCT
ejpam-176	322	1	case	case	NOUN
ejpam-176	322	2	-	-	PUNCT
ejpam-176	322	3	i	i	PRON
ejpam-176	322	4	:	:	PUNCT
ejpam-176	322	5	suppose	suppose	VERB
ejpam-176	322	6	r=	r=	ADJ
ejpam-176	322	7	;	;	PUNCT
ejpam-176	322	8	.	.	PUNCT
ejpam-176	323	1	then	then	ADV
ejpam-176	323	2	u	u	PRON
ejpam-176	323	3	will	will	AUX
ejpam-176	323	4	be	be	AUX
ejpam-176	323	5	obviously	obviously	ADV
ejpam-176	323	6	closed	close	VERB
ejpam-176	323	7	.	.	PUNCT
ejpam-176	324	1	case	case	NOUN
ejpam-176	324	2	-	-	PUNCT
ejpam-176	324	3	ii	ii	NOUN
ejpam-176	324	4	:	:	PUNCT
ejpam-176	324	5	suppose	suppose	VERB
ejpam-176	324	6	r	r	NOUN
ejpam-176	324	7	6=	6=	NUM
ejpam-176	324	8	;	;	PUNCT
ejpam-176	324	9	.	.	PUNCT
ejpam-176	325	1	then	then	ADV
ejpam-176	325	2	as	as	ADP
ejpam-176	325	3	r	r	NOUN
ejpam-176	325	4	∈	∈	PROPN
ejpam-176	325	5	ro(x	ro(x	PUNCT
ejpam-176	325	6	)	)	PUNCT
ejpam-176	325	7	⊂	⊂	PROPN
ejpam-176	325	8	βr(x	βr(x	PUNCT
ejpam-176	325	9	)	)	PUNCT
ejpam-176	325	10	and	and	CCONJ
ejpam-176	325	11	r	r	NOUN
ejpam-176	325	12	⊂	⊂	PROPN
ejpam-176	325	13	v	v	NOUN
ejpam-176	325	14	,	,	PUNCT
ejpam-176	325	15	where	where	SCONJ
ejpam-176	325	16	v	v	NOUN
ejpam-176	325	17	is	be	AUX
ejpam-176	325	18	β	β	X
ejpam-176	325	19	-closed	-close	VERB
ejpam-176	325	20	relative	relative	ADJ
ejpam-176	325	21	to	to	ADP
ejpam-176	325	22	x	x	PRON
ejpam-176	325	23	,	,	PUNCT
ejpam-176	325	24	r	r	NOUN
ejpam-176	325	25	is	be	AUX
ejpam-176	325	26	clearly	clearly	ADV
ejpam-176	325	27	β	β	X
ejpam-176	325	28	-closed	-close	VERB
ejpam-176	325	29	relative	relative	ADJ
ejpam-176	325	30	to	to	ADP
ejpam-176	325	31	x	x	X
ejpam-176	325	32	.	.	PUNCT
ejpam-176	326	1	since	since	SCONJ
ejpam-176	326	2	x	x	PROPN
ejpam-176	326	3	is	be	AUX
ejpam-176	326	4	γ	γ	X
ejpam-176	326	5	-	-	ADJ
ejpam-176	326	6	perfect	perfect	ADJ
ejpam-176	326	7	and	and	CCONJ
ejpam-176	326	8	r	r	NOUN
ejpam-176	326	9	∈	∈	PROPN
ejpam-176	326	10	ro(x	ro(x	PUNCT
ejpam-176	326	11	)	)	PUNCT
ejpam-176	326	12	with	with	ADP
ejpam-176	326	13	references	reference	NOUN
ejpam-176	326	14	95	95	NUM
ejpam-176	326	15	x	x	SYM
ejpam-176	326	16	6∈	6∈	NOUN
ejpam-176	326	17	r	r	NOUN
ejpam-176	326	18	the	the	DET
ejpam-176	326	19	there	there	PRON
ejpam-176	326	20	exists	exist	VERB
ejpam-176	326	21	a	a	DET
ejpam-176	326	22	family	family	NOUN
ejpam-176	326	23	of	of	ADP
ejpam-176	326	24	open	open	ADJ
ejpam-176	326	25	sets	set	NOUN
ejpam-176	326	26	v	v	NOUN
ejpam-176	326	27	=	=	SYM
ejpam-176	326	28	{	{	PUNCT
ejpam-176	326	29	vα	vα	X
ejpam-176	326	30	:	:	PUNCT
ejpam-176	326	31	α	α	PROPN
ejpam-176	326	32	∈	∈	PROPN
ejpam-176	327	1	i	i	X
ejpam-176	327	2	}	}	PUNCT
ejpam-176	327	3	such	such	ADJ
ejpam-176	327	4	that	that	SCONJ
ejpam-176	327	5	r	r	NOUN
ejpam-176	327	6	⊂	⊂	ADJ
ejpam-176	327	7	∪α∈i	∪α∈i	X
ejpam-176	327	8	cl(vα	cl(vα	NOUN
ejpam-176	327	9	)	)	PUNCT
ejpam-176	327	10	with	with	ADP
ejpam-176	327	11	x	x	SYM
ejpam-176	327	12	6∈	6∈	PROPN
ejpam-176	327	13	∪α∈i	∪α∈i	PROPN
ejpam-176	327	14	cl(vα	cl(vα	NOUN
ejpam-176	327	15	)	)	PUNCT
ejpam-176	327	16	.	.	PUNCT
ejpam-176	328	1	since	since	SCONJ
ejpam-176	328	2	every	every	DET
ejpam-176	328	3	regular	regular	ADJ
ejpam-176	328	4	closed	closed	ADJ
ejpam-176	328	5	set	set	NOUN
ejpam-176	328	6	is	be	AUX
ejpam-176	328	7	being	be	AUX
ejpam-176	328	8	β	β	X
ejpam-176	328	9	-regular	-regular	ADJ
ejpam-176	328	10	,	,	PUNCT
ejpam-176	328	11	the	the	DET
ejpam-176	328	12	family	family	NOUN
ejpam-176	328	13	{	{	PUNCT
ejpam-176	328	14	cl(vα	cl(vα	PROPN
ejpam-176	328	15	)	)	PUNCT
ejpam-176	328	16	:	:	PUNCT
ejpam-176	329	1	α	α	X
ejpam-176	329	2	∈	∈	PROPN
ejpam-176	330	1	i	i	PRON
ejpam-176	330	2	}	}	PUNCT
ejpam-176	330	3	is	be	AUX
ejpam-176	330	4	a	a	DET
ejpam-176	330	5	β	β	NOUN
ejpam-176	330	6	-regular	-regular	ADJ
ejpam-176	330	7	cover	cover	NOUN
ejpam-176	330	8	of	of	ADP
ejpam-176	330	9	the	the	DET
ejpam-176	330	10	set	set	NOUN
ejpam-176	330	11	r	r	NOUN
ejpam-176	330	12	which	which	PRON
ejpam-176	330	13	is	be	AUX
ejpam-176	330	14	β	β	AUX
ejpam-176	330	15	-closed	-close	VERB
ejpam-176	330	16	relative	relative	ADJ
ejpam-176	330	17	to	to	ADP
ejpam-176	330	18	x	x	PROPN
ejpam-176	330	19	.	.	PUNCT
ejpam-176	331	1	so	so	ADV
ejpam-176	331	2	there	there	PRON
ejpam-176	331	3	exist	exist	VERB
ejpam-176	331	4	α1	α1	NOUN
ejpam-176	331	5	,	,	PUNCT
ejpam-176	331	6	....	....	PUNCT
ejpam-176	332	1	,	,	PUNCT
ejpam-176	332	2	αn	αn	X
ejpam-176	332	3	∈	∈	PROPN
ejpam-176	333	1	i	i	PRON
ejpam-176	333	2	such	such	ADJ
ejpam-176	333	3	that	that	SCONJ
ejpam-176	333	4	r	r	NOUN
ejpam-176	333	5	⊂	⊂	X
ejpam-176	333	6	∪n	∪n	PROPN
ejpam-176	333	7	i=1	i=1	PROPN
ejpam-176	333	8	cl(vαi	cl(vαi	PROPN
ejpam-176	333	9	)	)	PUNCT
ejpam-176	333	10	.	.	PUNCT
ejpam-176	334	1	let	let	VERB
ejpam-176	334	2	w	w	NOUN
ejpam-176	334	3	=	=	PUNCT
ejpam-176	334	4	x	x	X
ejpam-176	334	5	−∪n	−∪n	PROPN
ejpam-176	334	6	i=1	i=1	PROPN
ejpam-176	334	7	cl(vαi	cl(vαi	NOUN
ejpam-176	334	8	)	)	PUNCT
ejpam-176	334	9	.	.	PUNCT
ejpam-176	335	1	clearly	clearly	ADV
ejpam-176	335	2	w	w	ADP
ejpam-176	335	3	∩	∩	ADJ
ejpam-176	335	4	v	v	NOUN
ejpam-176	335	5	is	be	AUX
ejpam-176	335	6	an	an	DET
ejpam-176	335	7	open	open	ADJ
ejpam-176	335	8	set	set	NOUN
ejpam-176	335	9	containing	contain	VERB
ejpam-176	335	10	x	x	SYM
ejpam-176	335	11	disjoint	disjoint	NOUN
ejpam-176	335	12	from	from	ADP
ejpam-176	335	13	u	u	PROPN
ejpam-176	335	14	.	.	PUNCT
ejpam-176	336	1	hence	hence	ADV
ejpam-176	336	2	u	u	NOUN
ejpam-176	336	3	is	be	AUX
ejpam-176	336	4	closed	closed	ADJ
ejpam-176	336	5	.	.	PUNCT
ejpam-176	337	1	therefore	therefore	ADV
ejpam-176	337	2	x	x	X
ejpam-176	337	3	is	be	AUX
ejpam-176	337	4	extremally	extremally	ADV
ejpam-176	337	5	disconnected	disconnect	VERB
ejpam-176	337	6	.	.	PUNCT
ejpam-176	338	1	references	reference	NOUN
ejpam-176	338	2	[	[	X
ejpam-176	338	3	1	1	NUM
ejpam-176	338	4	]	]	PUNCT
ejpam-176	338	5	m.	m.	PROPN
ejpam-176	338	6	e.	e.	PROPN
ejpam-176	338	7	abd	abd	PROPN
ejpam-176	338	8	.	.	PUNCT
ejpam-176	339	1	el	el	PROPN
ejpam-176	339	2	.	.	PROPN
ejpam-176	339	3	monsef	monsef	PROPN
ejpam-176	339	4	,	,	PUNCT
ejpam-176	339	5	s.	s.	PROPN
ejpam-176	339	6	n.	n.	PROPN
ejpam-176	339	7	el	el	PROPN
ejpam-176	339	8	-	-	PUNCT
ejpam-176	339	9	deeb	deeb	PROPN
ejpam-176	339	10	and	and	CCONJ
ejpam-176	339	11	r.	r.	PROPN
ejpam-176	339	12	a.	a.	PROPN
ejpam-176	339	13	mahmoud	mahmoud	PROPN
ejpam-176	339	14	,	,	PUNCT
ejpam-176	339	15	β	β	X
ejpam-176	339	16	-open	-open	NOUN
ejpam-176	339	17	sets	set	NOUN
ejpam-176	339	18	and	and	CCONJ
ejpam-176	339	19	β	β	PRON
ejpam-176	339	20	-continuous	-continuous	ADJ
ejpam-176	339	21	mappings	mapping	NOUN
ejpam-176	339	22	,	,	PUNCT
ejpam-176	339	23	bull	bull	NOUN
ejpam-176	339	24	.	.	PUNCT
ejpam-176	340	1	fac	fac	PROPN
ejpam-176	340	2	.	.	PUNCT
ejpam-176	341	1	sci	sci	PROPN
ejpam-176	341	2	.	.	PUNCT
ejpam-176	341	3	assiut	assiut	PROPN
ejpam-176	341	4	univ	univ	PROPN
ejpam-176	341	5	.	.	PROPN
ejpam-176	341	6	,	,	PUNCT
ejpam-176	341	7	12(1	12(1	NUM
ejpam-176	341	8	)	)	PUNCT
ejpam-176	341	9	(	(	PUNCT
ejpam-176	341	10	1983	1983	NUM
ejpam-176	341	11	)	)	PUNCT
ejpam-176	341	12	,	,	PUNCT
ejpam-176	341	13	77	77	NUM
ejpam-176	341	14	-	-	SYM
ejpam-176	341	15	90	90	NUM
ejpam-176	341	16	.	.	PUNCT
ejpam-176	342	1	[	[	X
ejpam-176	342	2	2	2	NUM
ejpam-176	342	3	]	]	PUNCT
ejpam-176	342	4	m.	m.	PROPN
ejpam-176	342	5	e.	e.	PROPN
ejpam-176	342	6	abd	abd	PROPN
ejpam-176	342	7	.	.	PUNCT
ejpam-176	343	1	el	el	PROPN
ejpam-176	343	2	.	.	PROPN
ejpam-176	343	3	monsef	monsef	PROPN
ejpam-176	343	4	,	,	PUNCT
ejpam-176	343	5	a.	a.	NOUN
ejpam-176	343	6	m.	m.	NOUN
ejpam-176	343	7	kozae	kozae	PROPN
ejpam-176	343	8	,	,	PUNCT
ejpam-176	343	9	some	some	DET
ejpam-176	343	10	generalized	generalized	ADJ
ejpam-176	343	11	forms	form	NOUN
ejpam-176	343	12	of	of	ADP
ejpam-176	343	13	compactness	compactness	NOUN
ejpam-176	343	14	and	and	CCONJ
ejpam-176	343	15	closedness	closedness	NOUN
ejpam-176	343	16	,	,	PUNCT
ejpam-176	343	17	delta	delta	PROPN
ejpam-176	343	18	j.	j.	PROPN
ejpam-176	343	19	sci	sci	PROPN
ejpam-176	343	20	.	.	PUNCT
ejpam-176	344	1	9(2	9(2	NUM
ejpam-176	344	2	)	)	PUNCT
ejpam-176	344	3	,	,	PUNCT
ejpam-176	344	4	1985	1985	NUM
ejpam-176	344	5	,	,	PUNCT
ejpam-176	344	6	257	257	NUM
ejpam-176	344	7	-	-	SYM
ejpam-176	344	8	269	269	NUM
ejpam-176	344	9	.	.	PUNCT
ejpam-176	345	1	[	[	X
ejpam-176	345	2	3	3	X
ejpam-176	345	3	]	]	PUNCT
ejpam-176	345	4	t.	t.	PROPN
ejpam-176	345	5	aho	aho	PROPN
ejpam-176	345	6	and	and	CCONJ
ejpam-176	345	7	t.	t.	PROPN
ejpam-176	345	8	nieminen	nieminen	PROPN
ejpam-176	345	9	,	,	PUNCT
ejpam-176	345	10	spaces	space	VERB
ejpam-176	345	11	in	in	ADP
ejpam-176	345	12	which	which	PRON
ejpam-176	345	13	preopen	preopen	ADJ
ejpam-176	345	14	subsets	subset	NOUN
ejpam-176	345	15	are	be	AUX
ejpam-176	345	16	semi	semi	ADJ
ejpam-176	345	17	-	-	ADJ
ejpam-176	345	18	open	open	ADJ
ejpam-176	345	19	,	,	PUNCT
ejpam-176	345	20	ricerche	ricerche	X
ejpam-176	345	21	mat	mat	PROPN
ejpam-176	345	22	.	.	PROPN
ejpam-176	345	23	,	,	PUNCT
ejpam-176	345	24	43	43	NUM
ejpam-176	345	25	(	(	PUNCT
ejpam-176	345	26	1994	1994	NUM
ejpam-176	345	27	)	)	PUNCT
ejpam-176	345	28	,	,	PUNCT
ejpam-176	345	29	45	45	NUM
ejpam-176	345	30	-	-	SYM
ejpam-176	345	31	59	59	NUM
ejpam-176	345	32	.	.	PUNCT
ejpam-176	346	1	[	[	X
ejpam-176	346	2	4	4	X
ejpam-176	346	3	]	]	X
ejpam-176	346	4	d.	d.	PROPN
ejpam-176	346	5	andrijević	andrijević	PROPN
ejpam-176	346	6	,	,	PUNCT
ejpam-176	346	7	semi	semi	ADJ
ejpam-176	346	8	-	-	ADJ
ejpam-176	346	9	preopen	preopen	ADJ
ejpam-176	346	10	sets	set	NOUN
ejpam-176	346	11	,	,	PUNCT
ejpam-176	346	12	math	math	NOUN
ejpam-176	346	13	.	.	PUNCT
ejpam-176	347	1	vesnik	vesnik	PROPN
ejpam-176	347	2	,	,	PUNCT
ejpam-176	347	3	38	38	NUM
ejpam-176	347	4	(	(	PUNCT
ejpam-176	347	5	1986	1986	NUM
ejpam-176	347	6	)	)	PUNCT
ejpam-176	347	7	,	,	PUNCT
ejpam-176	347	8	24	24	NUM
ejpam-176	347	9	-	-	SYM
ejpam-176	347	10	32	32	NUM
ejpam-176	347	11	.	.	PUNCT
ejpam-176	348	1	[	[	X
ejpam-176	348	2	5	5	X
ejpam-176	348	3	]	]	X
ejpam-176	348	4	d.	d.	PROPN
ejpam-176	348	5	andrijević	andrijević	PROPN
ejpam-176	348	6	,	,	PUNCT
ejpam-176	348	7	on	on	ADP
ejpam-176	348	8	spo	spo	PROPN
ejpam-176	348	9	-	-	PUNCT
ejpam-176	348	10	equivalent	equivalent	ADJ
ejpam-176	348	11	topologies	topology	NOUN
ejpam-176	348	12	,	,	PUNCT
ejpam-176	348	13	suppl	suppl	PROPN
ejpam-176	348	14	.	.	PUNCT
ejpam-176	348	15	rend	rend	VERB
ejpam-176	348	16	.	.	PUNCT
ejpam-176	349	1	cir	cir	PROPN
ejpam-176	349	2	.	.	PUNCT
ejpam-176	349	3	mat	mat	PROPN
ejpam-176	349	4	.	.	PUNCT
ejpam-176	349	5	palermo	palermo	NOUN
ejpam-176	349	6	,	,	PUNCT
ejpam-176	349	7	29	29	NUM
ejpam-176	349	8	(	(	PUNCT
ejpam-176	349	9	1992	1992	NUM
ejpam-176	349	10	)	)	PUNCT
ejpam-176	349	11	,	,	PUNCT
ejpam-176	349	12	317	317	NUM
ejpam-176	349	13	-	-	SYM
ejpam-176	349	14	328	328	NUM
ejpam-176	349	15	.	.	PUNCT
ejpam-176	350	1	[	[	X
ejpam-176	350	2	6	6	NUM
ejpam-176	350	3	]	]	X
ejpam-176	350	4	d.	d.	PROPN
ejpam-176	350	5	andrijević	andrijević	PROPN
ejpam-176	350	6	,	,	PUNCT
ejpam-176	350	7	on	on	ADP
ejpam-176	350	8	b	b	X
ejpam-176	350	9	-	-	PUNCT
ejpam-176	350	10	open	open	ADJ
ejpam-176	350	11	sets	set	NOUN
ejpam-176	350	12	,	,	PUNCT
ejpam-176	350	13	math	math	NOUN
ejpam-176	350	14	.	.	PUNCT
ejpam-176	351	1	vesnik	vesnik	PROPN
ejpam-176	351	2	,	,	PUNCT
ejpam-176	351	3	48	48	NUM
ejpam-176	351	4	(	(	PUNCT
ejpam-176	351	5	1996	1996	NUM
ejpam-176	351	6	)	)	PUNCT
ejpam-176	351	7	,	,	PUNCT
ejpam-176	351	8	59	59	NUM
ejpam-176	351	9	-	-	SYM
ejpam-176	351	10	64	64	NUM
ejpam-176	351	11	.	.	PUNCT
ejpam-176	352	1	[	[	X
ejpam-176	352	2	7	7	X
ejpam-176	352	3	]	]	X
ejpam-176	352	4	c.	c.	PROPN
ejpam-176	352	5	k.	k.	PROPN
ejpam-176	352	6	basu	basu	PROPN
ejpam-176	352	7	and	and	CCONJ
ejpam-176	352	8	m.	m.	PROPN
ejpam-176	352	9	k.	k.	PROPN
ejpam-176	352	10	ghosh	ghosh	PROPN
ejpam-176	352	11	,	,	PUNCT
ejpam-176	352	12	β	β	X
ejpam-176	352	13	-closed	-close	VERB
ejpam-176	352	14	spaces	space	NOUN
ejpam-176	352	15	and	and	CCONJ
ejpam-176	352	16	β	β	X
ejpam-176	352	17	-θ	-θ	PUNCT
ejpam-176	352	18	-subclosed	-subclose	VERB
ejpam-176	352	19	graphs	graph	NOUN
ejpam-176	352	20	,	,	PUNCT
ejpam-176	352	21	european	european	PROPN
ejpam-176	352	22	j.	j.	PROPN
ejpam-176	352	23	of	of	ADP
ejpam-176	352	24	pure	pure	ADJ
ejpam-176	352	25	and	and	CCONJ
ejpam-176	352	26	appl	appl	NOUN
ejpam-176	352	27	.	.	PROPN
ejpam-176	352	28	math	math	PROPN
ejpam-176	352	29	.	.	PUNCT
ejpam-176	352	30	,	,	PUNCT
ejpam-176	352	31	vol	vol	NOUN
ejpam-176	352	32	.	.	PROPN
ejpam-176	352	33	1	1	NUM
ejpam-176	352	34	,	,	PUNCT
ejpam-176	352	35	no	no	INTJ
ejpam-176	352	36	.	.	NOUN
ejpam-176	352	37	3	3	NUM
ejpam-176	352	38	,	,	PUNCT
ejpam-176	352	39	2008	2008	NUM
ejpam-176	352	40	(	(	PUNCT
ejpam-176	352	41	40	40	NUM
ejpam-176	352	42	-	-	SYM
ejpam-176	352	43	50	50	NUM
ejpam-176	352	44	)	)	PUNCT
ejpam-176	352	45	.	.	PUNCT
ejpam-176	353	1	[	[	X
ejpam-176	353	2	8	8	NUM
ejpam-176	353	3	]	]	X
ejpam-176	353	4	y.	y.	NOUN
ejpam-176	353	5	beceren	beceren	PROPN
ejpam-176	353	6	and	and	CCONJ
ejpam-176	353	7	t.	t.	PROPN
ejpam-176	353	8	noiri	noiri	PROPN
ejpam-176	353	9	,	,	PUNCT
ejpam-176	353	10	some	some	DET
ejpam-176	353	11	functions	function	NOUN
ejpam-176	353	12	defined	define	VERB
ejpam-176	353	13	by	by	ADP
ejpam-176	353	14	semi	semi	ADJ
ejpam-176	353	15	-	-	ADJ
ejpam-176	353	16	open	open	ADJ
ejpam-176	353	17	and	and	CCONJ
ejpam-176	353	18	β	β	X
ejpam-176	353	19	-open	-open	NOUN
ejpam-176	353	20	sets	set	NOUN
ejpam-176	353	21	,	,	PUNCT
ejpam-176	353	22	chaos	chaos	NOUN
ejpam-176	353	23	solitons	soliton	NOUN
ejpam-176	353	24	and	and	CCONJ
ejpam-176	353	25	fractals	fractal	NOUN
ejpam-176	353	26	,	,	PUNCT
ejpam-176	353	27	36	36	NUM
ejpam-176	353	28	(	(	PUNCT
ejpam-176	353	29	2008	2008	NUM
ejpam-176	353	30	)	)	PUNCT
ejpam-176	353	31	,	,	PUNCT
ejpam-176	353	32	1225	1225	NUM
ejpam-176	353	33	-	-	SYM
ejpam-176	353	34	1231	1231	NUM
ejpam-176	353	35	.	.	PUNCT
ejpam-176	354	1	[	[	X
ejpam-176	354	2	9	9	NUM
ejpam-176	354	3	]	]	X
ejpam-176	354	4	j.	j.	PROPN
ejpam-176	354	5	borsík	borsík	PROPN
ejpam-176	354	6	,	,	PUNCT
ejpam-176	354	7	oscillation	oscillation	NOUN
ejpam-176	354	8	for	for	ADP
ejpam-176	354	9	almost	almost	ADV
ejpam-176	354	10	continuity	continuity	NOUN
ejpam-176	354	11	,	,	PUNCT
ejpam-176	354	12	acta	acta	PROPN
ejpam-176	354	13	.	.	PUNCT
ejpam-176	354	14	math	math	NOUN
ejpam-176	354	15	.	.	PUNCT
ejpam-176	355	1	hungar	hungar	PROPN
ejpam-176	355	2	.	.	PUNCT
ejpam-176	355	3	,	,	PUNCT
ejpam-176	355	4	115(4)(2007	115(4)(2007	NUM
ejpam-176	355	5	)	)	PUNCT
ejpam-176	355	6	,	,	PUNCT
ejpam-176	355	7	319	319	NUM
ejpam-176	355	8	-	-	SYM
ejpam-176	355	9	332	332	NUM
ejpam-176	355	10	.	.	PUNCT
ejpam-176	356	1	[	[	X
ejpam-176	356	2	10	10	NUM
ejpam-176	356	3	]	]	PUNCT
ejpam-176	356	4	m.	m.	NOUN
ejpam-176	356	5	caldas	caldas	PROPN
ejpam-176	356	6	,	,	PUNCT
ejpam-176	356	7	s.	s.	PROPN
ejpam-176	356	8	jafari	jafari	PROPN
ejpam-176	356	9	,	,	PUNCT
ejpam-176	356	10	some	some	DET
ejpam-176	356	11	propertires	propertire	NOUN
ejpam-176	356	12	of	of	ADP
ejpam-176	356	13	contra	contra	PROPN
ejpam-176	356	14	β	β	PROPN
ejpam-176	356	15	-continuous	-continuous	ADJ
ejpam-176	356	16	functions	function	NOUN
ejpam-176	356	17	,	,	PUNCT
ejpam-176	356	18	mem	mem	PROPN
ejpam-176	356	19	.	.	PUNCT
ejpam-176	357	1	fac	fac	PROPN
ejpam-176	357	2	.	.	PUNCT
ejpam-176	358	1	sci	sci	PROPN
ejpam-176	358	2	.	.	PROPN
ejpam-176	358	3	kochi	kochi	PROPN
ejpam-176	358	4	.	.	PUNCT
ejpam-176	359	1	univ	univ	PROPN
ejpam-176	359	2	.	.	PUNCT
ejpam-176	360	1	(	(	PUNCT
ejpam-176	360	2	math	math	NOUN
ejpam-176	360	3	.	.	PUNCT
ejpam-176	360	4	)	)	PUNCT
ejpam-176	361	1	2001	2001	NUM
ejpam-176	361	2	;	;	PUNCT
ejpam-176	361	3	22	22	NUM
ejpam-176	361	4	:	:	SYM
ejpam-176	361	5	19	19	NUM
ejpam-176	361	6	-	-	SYM
ejpam-176	361	7	28	28	NUM
ejpam-176	361	8	.	.	PUNCT
ejpam-176	362	1	[	[	X
ejpam-176	362	2	11	11	NUM
ejpam-176	362	3	]	]	PUNCT
ejpam-176	362	4	z.	z.	PROPN
ejpam-176	362	5	duszynski	duszynski	PROPN
ejpam-176	362	6	,	,	PUNCT
ejpam-176	362	7	on	on	ADP
ejpam-176	362	8	some	some	DET
ejpam-176	362	9	concepts	concept	NOUN
ejpam-176	362	10	of	of	ADP
ejpam-176	362	11	weak	weak	ADJ
ejpam-176	362	12	connectedness	connectedness	NOUN
ejpam-176	362	13	of	of	ADP
ejpam-176	362	14	topological	topological	ADJ
ejpam-176	362	15	spaces	space	NOUN
ejpam-176	362	16	,	,	PUNCT
ejpam-176	362	17	acta	acta	PROPN
ejpam-176	362	18	.	.	PUNCT
ejpam-176	362	19	math	math	NOUN
ejpam-176	362	20	.	.	PUNCT
ejpam-176	363	1	hungar	hungar	PROPN
ejpam-176	363	2	.	.	PUNCT
ejpam-176	363	3	,	,	PUNCT
ejpam-176	363	4	110(1	110(1	NUM
ejpam-176	363	5	-	-	SYM
ejpam-176	363	6	2	2	NUM
ejpam-176	363	7	)	)	PUNCT
ejpam-176	363	8	,	,	PUNCT
ejpam-176	363	9	2006	2006	NUM
ejpam-176	363	10	,	,	PUNCT
ejpam-176	363	11	81	81	NUM
ejpam-176	363	12	-	-	SYM
ejpam-176	363	13	90	90	NUM
ejpam-176	363	14	.	.	PUNCT
ejpam-176	364	1	[	[	X
ejpam-176	364	2	12	12	NUM
ejpam-176	364	3	]	]	PUNCT
ejpam-176	364	4	m.	m.	NOUN
ejpam-176	364	5	ganster	ganster	NOUN
ejpam-176	364	6	and	and	CCONJ
ejpam-176	364	7	d.	d.	PROPN
ejpam-176	364	8	andrijevic	andrijevic	PROPN
ejpam-176	364	9	,	,	PUNCT
ejpam-176	364	10	on	on	ADP
ejpam-176	364	11	some	some	DET
ejpam-176	364	12	questions	question	NOUN
ejpam-176	364	13	concerning	concern	VERB
ejpam-176	364	14	semi	semi	ADJ
ejpam-176	364	15	-	-	ADJ
ejpam-176	364	16	preopen	preopen	ADJ
ejpam-176	364	17	sets	set	NOUN
ejpam-176	364	18	,	,	PUNCT
ejpam-176	364	19	journ	journ	NOUN
ejpam-176	364	20	.	.	PUNCT
ejpam-176	365	1	inst	inst	PROPN
ejpam-176	365	2	.	.	PUNCT
ejpam-176	365	3	math	math	NOUN
ejpam-176	365	4	.	.	PUNCT
ejpam-176	366	1	and	and	CCONJ
ejpam-176	366	2	comp	comp	PROPN
ejpam-176	366	3	.	.	PUNCT
ejpam-176	367	1	sci	sci	PROPN
ejpam-176	367	2	.	.	PUNCT
ejpam-176	368	1	(	(	PUNCT
ejpam-176	368	2	math	math	NOUN
ejpam-176	368	3	.	.	PUNCT
ejpam-176	369	1	ser	ser	PROPN
ejpam-176	369	2	.	.	PUNCT
ejpam-176	369	3	)	)	PUNCT
ejpam-176	370	1	1(1988	1(1988	NUM
ejpam-176	370	2	)	)	PUNCT
ejpam-176	370	3	,	,	PUNCT
ejpam-176	370	4	65	65	NUM
ejpam-176	370	5	-	-	SYM
ejpam-176	370	6	75	75	NUM
ejpam-176	370	7	.	.	PUNCT
ejpam-176	371	1	[	[	X
ejpam-176	371	2	13	13	NUM
ejpam-176	371	3	]	]	PUNCT
ejpam-176	371	4	s.	s.	PROPN
ejpam-176	371	5	jafari	jafari	PROPN
ejpam-176	371	6	and	and	CCONJ
ejpam-176	371	7	t.	t.	PROPN
ejpam-176	371	8	noiri	noiri	PROPN
ejpam-176	371	9	,	,	PUNCT
ejpam-176	371	10	properties	property	NOUN
ejpam-176	371	11	of	of	ADP
ejpam-176	371	12	β	β	X
ejpam-176	371	13	-connected	-connected	ADJ
ejpam-176	371	14	spaces	space	NOUN
ejpam-176	371	15	,	,	PUNCT
ejpam-176	371	16	acta	acta	PROPN
ejpam-176	371	17	math	math	PROPN
ejpam-176	371	18	.	.	PUNCT
ejpam-176	372	1	hungar	hungar	PROPN
ejpam-176	372	2	.	.	PUNCT
ejpam-176	372	3	,	,	PUNCT
ejpam-176	372	4	101	101	NUM
ejpam-176	372	5	(	(	PUNCT
ejpam-176	372	6	3)(2003	3)(2003	NUM
ejpam-176	372	7	)	)	PUNCT
ejpam-176	372	8	,	,	PUNCT
ejpam-176	372	9	227	227	NUM
ejpam-176	372	10	-	-	SYM
ejpam-176	372	11	236	236	NUM
ejpam-176	372	12	.	.	PUNCT
ejpam-176	373	1	[	[	X
ejpam-176	373	2	14	14	NUM
ejpam-176	373	3	]	]	X
ejpam-176	373	4	n.	n.	PROPN
ejpam-176	373	5	levine	levine	PROPN
ejpam-176	373	6	,	,	PUNCT
ejpam-176	373	7	semi	semi	ADJ
ejpam-176	373	8	-	-	ADJ
ejpam-176	373	9	open	open	ADJ
ejpam-176	373	10	sets	set	NOUN
ejpam-176	373	11	and	and	CCONJ
ejpam-176	373	12	semi	semi	ADJ
ejpam-176	373	13	-	-	NOUN
ejpam-176	373	14	continuity	continuity	NOUN
ejpam-176	373	15	in	in	ADP
ejpam-176	373	16	topological	topological	ADJ
ejpam-176	373	17	spaces	space	NOUN
ejpam-176	373	18	,	,	PUNCT
ejpam-176	373	19	amer	amer	PROPN
ejpam-176	373	20	.	.	PROPN
ejpam-176	373	21	math	math	PROPN
ejpam-176	373	22	.	.	PUNCT
ejpam-176	374	1	monthly	monthly	ADJ
ejpam-176	374	2	70	70	NUM
ejpam-176	374	3	(	(	PUNCT
ejpam-176	374	4	1963	1963	NUM
ejpam-176	374	5	)	)	PUNCT
ejpam-176	374	6	,	,	PUNCT
ejpam-176	374	7	36	36	NUM
ejpam-176	374	8	-	-	SYM
ejpam-176	374	9	41	41	NUM
ejpam-176	374	10	.	.	PUNCT
ejpam-176	374	11	references	reference	NOUN
ejpam-176	374	12	96	96	NUM
ejpam-176	375	1	[	[	X
ejpam-176	375	2	15	15	NUM
ejpam-176	375	3	]	]	X
ejpam-176	375	4	g.	g.	PROPN
ejpam-176	375	5	di	di	PROPN
ejpam-176	375	6	maio	maio	PROPN
ejpam-176	375	7	and	and	CCONJ
ejpam-176	375	8	t.	t.	PROPN
ejpam-176	375	9	noiri	noiri	PROPN
ejpam-176	375	10	,	,	PUNCT
ejpam-176	375	11	on	on	ADP
ejpam-176	375	12	s	s	ADJ
ejpam-176	375	13	-	-	PUNCT
ejpam-176	375	14	closed	closed	ADJ
ejpam-176	375	15	spaces	space	NOUN
ejpam-176	375	16	,	,	PUNCT
ejpam-176	375	17	ind	ind	PROPN
ejpam-176	375	18	.	.	PUNCT
ejpam-176	376	1	j.	j.	PROPN
ejpam-176	376	2	pure	pure	PROPN
ejpam-176	376	3	appl	appl	PROPN
ejpam-176	376	4	.	.	PUNCT
ejpam-176	376	5	math	math	NOUN
ejpam-176	376	6	.	.	PUNCT
ejpam-176	377	1	18	18	NUM
ejpam-176	377	2	(	(	PUNCT
ejpam-176	377	3	3	3	NUM
ejpam-176	377	4	)	)	PUNCT
ejpam-176	377	5	(	(	PUNCT
ejpam-176	377	6	1987	1987	NUM
ejpam-176	377	7	)	)	PUNCT
ejpam-176	377	8	,	,	PUNCT
ejpam-176	377	9	226	226	NUM
ejpam-176	377	10	-	-	SYM
ejpam-176	377	11	233	233	NUM
ejpam-176	377	12	.	.	PUNCT
ejpam-176	378	1	[	[	X
ejpam-176	378	2	16	16	NUM
ejpam-176	378	3	]	]	PUNCT
ejpam-176	378	4	a.	a.	NOUN
ejpam-176	378	5	s.	s.	PROPN
ejpam-176	378	6	mashhour	mashhour	PROPN
ejpam-176	378	7	,	,	PUNCT
ejpam-176	378	8	m.	m.	PROPN
ejpam-176	378	9	e.	e.	PROPN
ejpam-176	378	10	abd	abd	PROPN
ejpam-176	378	11	el	el	PROPN
ejpam-176	378	12	-	-	PROPN
ejpam-176	378	13	monsef	monsef	PROPN
ejpam-176	378	14	and	and	CCONJ
ejpam-176	378	15	s.	s.	PROPN
ejpam-176	378	16	n.	n.	PROPN
ejpam-176	378	17	el	el	PROPN
ejpam-176	378	18	-	-	PROPN
ejpam-176	378	19	deeb	deeb	PROPN
ejpam-176	378	20	,	,	PUNCT
ejpam-176	378	21	on	on	ADP
ejpam-176	378	22	precontinuous	precontinuous	ADJ
ejpam-176	378	23	and	and	CCONJ
ejpam-176	378	24	weak	weak	ADJ
ejpam-176	378	25	precontinuous	precontinuous	ADJ
ejpam-176	378	26	mappings	mapping	NOUN
ejpam-176	378	27	,	,	PUNCT
ejpam-176	378	28	proc	proc	NOUN
ejpam-176	378	29	.	.	PUNCT
ejpam-176	379	1	math	math	NOUN
ejpam-176	379	2	.	.	PUNCT
ejpam-176	380	1	phys	phy	NOUN
ejpam-176	380	2	.	.	PUNCT
ejpam-176	381	1	soc	soc	PROPN
ejpam-176	381	2	.	.	PUNCT
ejpam-176	382	1	egypt	egypt	PROPN
ejpam-176	382	2	,	,	PUNCT
ejpam-176	382	3	53	53	NUM
ejpam-176	382	4	(	(	PUNCT
ejpam-176	382	5	1982	1982	NUM
ejpam-176	382	6	)	)	PUNCT
ejpam-176	382	7	,	,	PUNCT
ejpam-176	382	8	47	47	NUM
ejpam-176	382	9	-	-	SYM
ejpam-176	382	10	53	53	NUM
ejpam-176	382	11	.	.	PUNCT
ejpam-176	383	1	[	[	X
ejpam-176	383	2	17	17	NUM
ejpam-176	383	3	]	]	X
ejpam-176	383	4	o.	o.	PROPN
ejpam-176	383	5	njastad	njastad	PROPN
ejpam-176	383	6	,	,	PUNCT
ejpam-176	383	7	on	on	ADP
ejpam-176	383	8	some	some	DET
ejpam-176	383	9	classes	class	NOUN
ejpam-176	383	10	of	of	ADP
ejpam-176	383	11	nearly	nearly	ADV
ejpam-176	383	12	open	open	ADJ
ejpam-176	383	13	sets	set	NOUN
ejpam-176	383	14	,	,	PUNCT
ejpam-176	383	15	pacific	pacific	PROPN
ejpam-176	383	16	jour	jour	PROPN
ejpam-176	383	17	.	.	PUNCT
ejpam-176	383	18	math	math	PROPN
ejpam-176	383	19	.	.	PUNCT
ejpam-176	383	20	,	,	PUNCT
ejpam-176	383	21	15	15	NUM
ejpam-176	383	22	(	(	PUNCT
ejpam-176	383	23	1965	1965	NUM
ejpam-176	383	24	)	)	PUNCT
ejpam-176	383	25	,	,	PUNCT
ejpam-176	383	26	961	961	NUM
ejpam-176	383	27	-	-	SYM
ejpam-176	383	28	970	970	NUM
ejpam-176	383	29	.	.	PUNCT
ejpam-176	384	1	[	[	X
ejpam-176	384	2	18	18	NUM
ejpam-176	384	3	]	]	PUNCT
ejpam-176	384	4	t.	t.	PROPN
ejpam-176	384	5	noiri	noiri	PROPN
ejpam-176	384	6	,	,	PUNCT
ejpam-176	384	7	weak	weak	ADJ
ejpam-176	384	8	and	and	CCONJ
ejpam-176	384	9	strong	strong	ADJ
ejpam-176	384	10	forms	form	NOUN
ejpam-176	384	11	of	of	ADP
ejpam-176	384	12	β	β	NOUN
ejpam-176	384	13	-irressolute	-irressolute	NOUN
ejpam-176	384	14	functions	function	NOUN
ejpam-176	384	15	,	,	PUNCT
ejpam-176	384	16	acta	acta	PROPN
ejpam-176	384	17	math	math	PROPN
ejpam-176	384	18	.	.	PUNCT
ejpam-176	385	1	hungar	hungar	PROPN
ejpam-176	385	2	.	.	PUNCT
ejpam-176	386	1	,	,	PUNCT
ejpam-176	386	2	99	99	NUM
ejpam-176	386	3	,	,	PUNCT
ejpam-176	386	4	no	no	INTJ
ejpam-176	386	5	.	.	NOUN
ejpam-176	386	6	4	4	NUM
ejpam-176	386	7	,	,	PUNCT
ejpam-176	386	8	(	(	PUNCT
ejpam-176	386	9	2003	2003	NUM
ejpam-176	386	10	)	)	PUNCT
ejpam-176	386	11	315	315	NUM
ejpam-176	386	12	-	-	SYM
ejpam-176	386	13	328	328	NUM
ejpam-176	386	14	.	.	PUNCT
ejpam-176	387	1	[	[	X
ejpam-176	387	2	19	19	NUM
ejpam-176	387	3	]	]	PUNCT
ejpam-176	387	4	v.	v.	CCONJ
ejpam-176	387	5	popa	popa	NOUN
ejpam-176	387	6	and	and	CCONJ
ejpam-176	387	7	t.	t.	PROPN
ejpam-176	387	8	noiri	noiri	PROPN
ejpam-176	387	9	,	,	PUNCT
ejpam-176	387	10	on	on	ADP
ejpam-176	387	11	β	β	X
ejpam-176	387	12	-continuous	-continuous	ADJ
ejpam-176	387	13	functions	function	NOUN
ejpam-176	387	14	,	,	PUNCT
ejpam-176	387	15	real	real	ADJ
ejpam-176	387	16	analysis	analysis	NOUN
ejpam-176	387	17	exchange	exchange	NOUN
ejpam-176	387	18	18(1992	18(1992	NUM
ejpam-176	387	19	-	-	SYM
ejpam-176	387	20	1993	1993	NUM
ejpam-176	387	21	)	)	PUNCT
ejpam-176	387	22	,	,	PUNCT
ejpam-176	387	23	544548	544548	NUM
ejpam-176	387	24	.	.	PUNCT
ejpam-176	388	1	[	[	X
ejpam-176	388	2	20	20	NUM
ejpam-176	388	3	]	]	PUNCT
ejpam-176	388	4	v.	v.	CCONJ
ejpam-176	388	5	popa	popa	NOUN
ejpam-176	388	6	and	and	CCONJ
ejpam-176	388	7	t.	t.	PROPN
ejpam-176	388	8	noiri	noiri	PROPN
ejpam-176	388	9	,	,	PUNCT
ejpam-176	388	10	weakly	weakly	ADJ
ejpam-176	388	11	β	β	X
ejpam-176	388	12	-continuous	-continuous	ADJ
ejpam-176	388	13	functions	function	NOUN
ejpam-176	388	14	,	,	PUNCT
ejpam-176	388	15	an	an	PROPN
ejpam-176	388	16	.	.	PUNCT
ejpam-176	388	17	univ	univ	PROPN
ejpam-176	388	18	.	.	PUNCT
ejpam-176	389	1	timisoara	timisoara	PROPN
ejpam-176	389	2	ser	ser	PROPN
ejpam-176	389	3	.	.	PROPN
ejpam-176	389	4	mat	mat	PROPN
ejpam-176	389	5	.	.	PUNCT
ejpam-176	389	6	inform	inform	NOUN
ejpam-176	389	7	.	.	PUNCT
ejpam-176	389	8	,	,	PUNCT
ejpam-176	389	9	32	32	NUM
ejpam-176	389	10	(	(	PUNCT
ejpam-176	389	11	1994	1994	NUM
ejpam-176	389	12	)	)	PUNCT
ejpam-176	389	13	,	,	PUNCT
ejpam-176	389	14	83	83	NUM
ejpam-176	389	15	-	-	SYM
ejpam-176	389	16	92	92	NUM
ejpam-176	389	17	.	.	PUNCT
ejpam-176	390	1	[	[	X
ejpam-176	390	2	21	21	NUM
ejpam-176	390	3	]	]	X
ejpam-176	390	4	v.	v.	CCONJ
ejpam-176	390	5	popa	popa	NOUN
ejpam-176	390	6	and	and	CCONJ
ejpam-176	390	7	t.	t.	PROPN
ejpam-176	390	8	noiri	noiri	PROPN
ejpam-176	390	9	,	,	PUNCT
ejpam-176	390	10	on	on	ADP
ejpam-176	390	11	upper	upper	ADJ
ejpam-176	390	12	and	and	CCONJ
ejpam-176	390	13	lower	low	ADJ
ejpam-176	390	14	β	β	X
ejpam-176	390	15	-continuous	-continuous	ADJ
ejpam-176	390	16	multifunctions	multifunction	NOUN
ejpam-176	390	17	,	,	PUNCT
ejpam-176	390	18	real	real	ADJ
ejpam-176	390	19	analysis	analysis	NOUN
ejpam-176	390	20	exchange	exchange	NOUN
ejpam-176	390	21	,	,	PUNCT
ejpam-176	390	22	22(1	22(1	NUM
ejpam-176	390	23	)	)	PUNCT
ejpam-176	390	24	,	,	PUNCT
ejpam-176	390	25	1996/1997	1996/1997	NUM
ejpam-176	390	26	,	,	PUNCT
ejpam-176	390	27	362	362	NUM
ejpam-176	390	28	-	-	SYM
ejpam-176	390	29	376	376	NUM
ejpam-176	390	30	.	.	PUNCT
ejpam-176	391	1	[	[	X
ejpam-176	391	2	22	22	NUM
ejpam-176	391	3	]	]	PUNCT
ejpam-176	391	4	m.	m.	NOUN
ejpam-176	391	5	k.	k.	PROPN
ejpam-176	391	6	singal	singal	PROPN
ejpam-176	391	7	and	and	CCONJ
ejpam-176	391	8	a.	a.	PROPN
ejpam-176	391	9	mathur	mathur	PROPN
ejpam-176	391	10	,	,	PUNCT
ejpam-176	391	11	on	on	ADP
ejpam-176	391	12	nearly	nearly	ADV
ejpam-176	391	13	compact	compact	ADJ
ejpam-176	391	14	spaces	space	NOUN
ejpam-176	391	15	,	,	PUNCT
ejpam-176	391	16	boll	boll	NOUN
ejpam-176	391	17	.	.	PUNCT
ejpam-176	391	18	un	un	PROPN
ejpam-176	391	19	.	.	PROPN
ejpam-176	391	20	mat	mat	PROPN
ejpam-176	391	21	.	.	PUNCT
ejpam-176	391	22	ital	ital	PROPN
ejpam-176	391	23	4(6	4(6	NUM
ejpam-176	391	24	)	)	PUNCT
ejpam-176	391	25	1969	1969	NUM
ejpam-176	391	26	,	,	PUNCT
ejpam-176	391	27	702	702	NUM
ejpam-176	391	28	-	-	SYM
ejpam-176	391	29	710	710	NUM
ejpam-176	391	30	.	.	PUNCT
ejpam-176	392	1	[	[	X
ejpam-176	392	2	23	23	NUM
ejpam-176	392	3	]	]	PUNCT
ejpam-176	392	4	t.	t.	PROPN
ejpam-176	392	5	h.	h.	PROPN
ejpam-176	392	6	halvac	halvac	PROPN
ejpam-176	392	7	,	,	PUNCT
ejpam-176	392	8	relations	relation	NOUN
ejpam-176	392	9	between	between	ADP
ejpam-176	392	10	new	new	ADJ
ejpam-176	392	11	topologies	topology	NOUN
ejpam-176	392	12	obtained	obtain	VERB
ejpam-176	392	13	from	from	ADP
ejpam-176	392	14	old	old	ADJ
ejpam-176	392	15	ones	one	NOUN
ejpam-176	392	16	,	,	PUNCT
ejpam-176	392	17	acta	acta	PROPN
ejpam-176	392	18	math	math	PROPN
ejpam-176	392	19	.	.	PUNCT
ejpam-176	393	1	hungar	hungar	PROPN
ejpam-176	393	2	.	.	PUNCT
ejpam-176	393	3	,	,	PUNCT
ejpam-176	393	4	64(3	64(3	NOUN
ejpam-176	393	5	)	)	PUNCT
ejpam-176	393	6	,	,	PUNCT
ejpam-176	393	7	(	(	PUNCT
ejpam-176	393	8	1994	1994	NUM
ejpam-176	393	9	)	)	PUNCT
ejpam-176	393	10	,	,	PUNCT
ejpam-176	393	11	231	231	NUM
ejpam-176	393	12	-	-	SYM
ejpam-176	393	13	235	235	NUM
ejpam-176	393	14	.	.	PUNCT