id	sid	tid	token	lemma	pos
ejpam-146	1	1	european	european	PROPN
ejpam-146	1	2	journal	journal	PROPN
ejpam-146	1	3	of	of	ADP
ejpam-146	1	4	pure	pure	ADJ
ejpam-146	1	5	and	and	CCONJ
ejpam-146	1	6	applied	apply	VERB
ejpam-146	1	7	mathematics	mathematic	NOUN
ejpam-146	1	8	vol	vol	NOUN
ejpam-146	1	9	.	.	PROPN
ejpam-146	2	1	1	1	NUM
ejpam-146	2	2	,	,	PUNCT
ejpam-146	2	3	no	no	INTJ
ejpam-146	2	4	.	.	NOUN
ejpam-146	2	5	3	3	NUM
ejpam-146	2	6	,	,	PUNCT
ejpam-146	2	7	2008	2008	NUM
ejpam-146	2	8	,	,	PUNCT
ejpam-146	2	9	(	(	PUNCT
ejpam-146	2	10	40	40	NUM
ejpam-146	2	11	-	-	SYM
ejpam-146	2	12	50	50	NUM
ejpam-146	2	13	)	)	PUNCT
ejpam-146	2	14	issn	issn	PROPN
ejpam-146	2	15	1307	1307	NUM
ejpam-146	2	16	-	-	SYM
ejpam-146	2	17	5543	5543	NUM
ejpam-146	2	18	–	–	PUNCT
ejpam-146	2	19	www.ejpam.com	www.ejpam.com	X
ejpam-146	2	20	β	β	X
ejpam-146	2	21	-	-	ADJ
ejpam-146	2	22	closed	closed	ADJ
ejpam-146	2	23	spaces	space	NOUN
ejpam-146	2	24	and	and	CCONJ
ejpam-146	2	25	β	β	NOUN
ejpam-146	2	26	-	-	PUNCT
ejpam-146	2	27	θ	θ	NOUN
ejpam-146	2	28	-subclosed	-subclose	VERB
ejpam-146	2	29	graphs	graph	NOUN
ejpam-146	2	30	c.	c.	PROPN
ejpam-146	2	31	k.	k.	PROPN
ejpam-146	2	32	basu1,∗	basu1,∗	PROPN
ejpam-146	2	33	,	,	PUNCT
ejpam-146	3	1	m.	m.	NOUN
ejpam-146	3	2	k.	k.	PROPN
ejpam-146	4	1	ghosh2	ghosh2	PROPN
ejpam-146	4	2	1	1	NUM
ejpam-146	4	3	department	department	NOUN
ejpam-146	4	4	of	of	ADP
ejpam-146	4	5	mathematics	mathematic	NOUN
ejpam-146	4	6	,	,	PUNCT
ejpam-146	4	7	university	university	NOUN
ejpam-146	4	8	of	of	ADP
ejpam-146	4	9	kalyani	kalyani	PROPN
ejpam-146	4	10	,	,	PUNCT
ejpam-146	4	11	kalyani-741235	kalyani-741235	NOUN
ejpam-146	4	12	,	,	PUNCT
ejpam-146	4	13	nadia	nadia	PROPN
ejpam-146	4	14	,	,	PUNCT
ejpam-146	4	15	west	west	PROPN
ejpam-146	4	16	bengal	bengal	PROPN
ejpam-146	4	17	,	,	PUNCT
ejpam-146	4	18	india	india	PROPN
ejpam-146	4	19	2	2	NUM
ejpam-146	4	20	dumkal	dumkal	NOUN
ejpam-146	4	21	college	college	NOUN
ejpam-146	4	22	,	,	PUNCT
ejpam-146	4	23	basantapur	basantapur	NOUN
ejpam-146	4	24	,	,	PUNCT
ejpam-146	4	25	dumkal-742303	dumkal-742303	NOUN
ejpam-146	4	26	,	,	PUNCT
ejpam-146	4	27	murshidabad	murshidabad	NOUN
ejpam-146	4	28	,	,	PUNCT
ejpam-146	4	29	west	west	PROPN
ejpam-146	4	30	bengal	bengal	PROPN
ejpam-146	4	31	,	,	PUNCT
ejpam-146	4	32	india	india	PROPN
ejpam-146	4	33	abstract	abstract	NOUN
ejpam-146	4	34	.	.	PUNCT
ejpam-146	5	1	the	the	DET
ejpam-146	5	2	purpose	purpose	NOUN
ejpam-146	5	3	of	of	ADP
ejpam-146	5	4	this	this	DET
ejpam-146	5	5	paper	paper	NOUN
ejpam-146	5	6	is	be	AUX
ejpam-146	5	7	to	to	PART
ejpam-146	5	8	achieve	achieve	VERB
ejpam-146	5	9	various	various	ADJ
ejpam-146	5	10	characterizations	characterization	NOUN
ejpam-146	5	11	of	of	ADP
ejpam-146	5	12	β	β	NOUN
ejpam-146	5	13	-	-	ADJ
ejpam-146	5	14	closed	closed	ADJ
ejpam-146	5	15	spaces	space	NOUN
ejpam-146	5	16	[	[	X
ejpam-146	5	17	2	2	NUM
ejpam-146	5	18	]	]	PUNCT
ejpam-146	5	19	,	,	PUNCT
ejpam-146	5	20	specially	specially	ADV
ejpam-146	5	21	,	,	PUNCT
ejpam-146	5	22	in	in	ADP
ejpam-146	5	23	terms	term	NOUN
ejpam-146	5	24	of	of	ADP
ejpam-146	5	25	new	new	ADJ
ejpam-146	5	26	types	type	NOUN
ejpam-146	5	27	of	of	ADP
ejpam-146	5	28	graphs	graph	NOUN
ejpam-146	5	29	under	under	ADP
ejpam-146	5	30	the	the	DET
ejpam-146	5	31	terminology	terminology	NOUN
ejpam-146	5	32	β	β	NOUN
ejpam-146	5	33	-	-	PUNCT
ejpam-146	5	34	θ	θ	NOUN
ejpam-146	5	35	-subclosed	-subclose	VERB
ejpam-146	5	36	graphs	graph	NOUN
ejpam-146	5	37	of	of	ADP
ejpam-146	5	38	functions	function	NOUN
ejpam-146	5	39	and	and	CCONJ
ejpam-146	5	40	in	in	ADP
ejpam-146	5	41	terms	term	NOUN
ejpam-146	5	42	of	of	ADP
ejpam-146	5	43	a	a	DET
ejpam-146	5	44	generalized	generalize	VERB
ejpam-146	5	45	complete	complete	ADJ
ejpam-146	5	46	accumulation	accumulation	NOUN
ejpam-146	5	47	point	point	NOUN
ejpam-146	5	48	.	.	PUNCT
ejpam-146	6	1	apart	apart	ADV
ejpam-146	6	2	from	from	ADP
ejpam-146	6	3	several	several	ADJ
ejpam-146	6	4	properties	property	NOUN
ejpam-146	6	5	,	,	PUNCT
ejpam-146	6	6	a	a	DET
ejpam-146	6	7	sufficient	sufficient	ADJ
ejpam-146	6	8	condition	condition	NOUN
ejpam-146	6	9	for	for	ADP
ejpam-146	6	10	common	common	ADJ
ejpam-146	6	11	fixed	fix	VERB
ejpam-146	6	12	points	point	NOUN
ejpam-146	6	13	of	of	ADP
ejpam-146	6	14	a	a	DET
ejpam-146	6	15	family	family	NOUN
ejpam-146	6	16	of	of	ADP
ejpam-146	6	17	functions	function	NOUN
ejpam-146	6	18	having	have	VERB
ejpam-146	6	19	β	β	NOUN
ejpam-146	6	20	-	-	PUNCT
ejpam-146	6	21	θ	θ	NOUN
ejpam-146	6	22	-subclosed	-subclose	VERB
ejpam-146	6	23	graphs	graph	NOUN
ejpam-146	6	24	is	be	AUX
ejpam-146	6	25	also	also	ADV
ejpam-146	6	26	given	give	VERB
ejpam-146	6	27	.	.	PUNCT
ejpam-146	7	1	ams	am	NOUN
ejpam-146	7	2	subject	subject	ADJ
ejpam-146	7	3	classifications	classification	NOUN
ejpam-146	7	4	:	:	PUNCT
ejpam-146	7	5	54d20	54d20	NUM
ejpam-146	7	6	,	,	PUNCT
ejpam-146	7	7	54d25	54d25	NUM
ejpam-146	7	8	,	,	PUNCT
ejpam-146	7	9	54d30	54d30	NUM
ejpam-146	7	10	,	,	PUNCT
ejpam-146	7	11	54c50	54c50	NUM
ejpam-146	7	12	.	.	PUNCT
ejpam-146	8	1	key	key	ADJ
ejpam-146	8	2	words	word	NOUN
ejpam-146	8	3	:	:	PUNCT
ejpam-146	8	4	β	β	X
ejpam-146	8	5	-	-	ADJ
ejpam-146	8	6	open	open	ADJ
ejpam-146	8	7	set	set	NOUN
ejpam-146	8	8	,	,	PUNCT
ejpam-146	8	9	β	β	NOUN
ejpam-146	8	10	-	-	NOUN
ejpam-146	8	11	closure	closure	NOUN
ejpam-146	8	12	,	,	PUNCT
ejpam-146	8	13	β	β	NOUN
ejpam-146	8	14	-	-	ADJ
ejpam-146	8	15	closed	closed	ADJ
ejpam-146	8	16	space	space	NOUN
ejpam-146	8	17	,	,	PUNCT
ejpam-146	8	18	β	β	ADJ
ejpam-146	8	19	-	-	ADJ
ejpam-146	8	20	regular	regular	ADJ
ejpam-146	8	21	sets	set	NOUN
ejpam-146	8	22	,	,	PUNCT
ejpam-146	8	23	β	β	X
ejpam-146	8	24	-	-	PUNCT
ejpam-146	8	25	θ	θ	NOUN
ejpam-146	8	26	-closed	-close	VERB
ejpam-146	8	27	sets	set	NOUN
ejpam-146	8	28	,	,	PUNCT
ejpam-146	8	29	(	(	PUNCT
ejpam-146	8	30	θ	θ	NOUN
ejpam-146	8	31	,	,	PUNCT
ejpam-146	8	32	β)-continuity	β)-continuity	NOUN
ejpam-146	8	33	,	,	PUNCT
ejpam-146	8	34	β	β	X
ejpam-146	8	35	-	-	PUNCT
ejpam-146	8	36	θ	θ	NOUN
ejpam-146	8	37	-subclosed	-subclose	VERB
ejpam-146	8	38	graph	graph	NOUN
ejpam-146	8	39	,	,	PUNCT
ejpam-146	8	40	β	β	NOUN
ejpam-146	8	41	-	-	ADJ
ejpam-146	8	42	θ	θ	NOUN
ejpam-146	8	43	-complete	-complete	ADJ
ejpam-146	8	44	accumulation	accumulation	NOUN
ejpam-146	8	45	point	point	NOUN
ejpam-146	8	46	.	.	PUNCT
ejpam-146	9	1	1	1	X
ejpam-146	9	2	.	.	X
ejpam-146	9	3	introduction	introduction	NOUN
ejpam-146	9	4	motivated	motivate	VERB
ejpam-146	9	5	by	by	ADP
ejpam-146	9	6	the	the	DET
ejpam-146	9	7	various	various	ADJ
ejpam-146	9	8	usefulness	usefulness	NOUN
ejpam-146	9	9	of	of	ADP
ejpam-146	9	10	compactness	compactness	NOUN
ejpam-146	9	11	many	many	ADJ
ejpam-146	9	12	mathematicians	mathematician	NOUN
ejpam-146	9	13	have	have	AUX
ejpam-146	9	14	tried	try	VERB
ejpam-146	9	15	to	to	PART
ejpam-146	9	16	generalize	generalize	VERB
ejpam-146	9	17	this	this	DET
ejpam-146	9	18	notion	notion	NOUN
ejpam-146	9	19	.	.	PUNCT
ejpam-146	10	1	in	in	ADP
ejpam-146	10	2	the	the	DET
ejpam-146	10	3	course	course	NOUN
ejpam-146	10	4	of	of	ADP
ejpam-146	10	5	their	their	PRON
ejpam-146	10	6	attempts	attempt	NOUN
ejpam-146	10	7	,	,	PUNCT
ejpam-146	10	8	several	several	ADJ
ejpam-146	10	9	weaker	weak	ADJ
ejpam-146	10	10	and	and	CCONJ
ejpam-146	10	11	stronger	strong	ADJ
ejpam-146	10	12	versions	version	NOUN
ejpam-146	10	13	of	of	ADP
ejpam-146	10	14	compactness	compactness	NOUN
ejpam-146	10	15	have	have	AUX
ejpam-146	10	16	been	be	AUX
ejpam-146	10	17	studied	study	VERB
ejpam-146	10	18	in	in	ADP
ejpam-146	10	19	detail	detail	NOUN
ejpam-146	10	20	.	.	PUNCT
ejpam-146	11	1	it	it	PRON
ejpam-146	11	2	is	be	AUX
ejpam-146	11	3	seen	see	VERB
ejpam-146	11	4	from	from	ADP
ejpam-146	11	5	the	the	DET
ejpam-146	11	6	literature	literature	NOUN
ejpam-146	11	7	that	that	PRON
ejpam-146	11	8	certain	certain	ADJ
ejpam-146	11	9	open	open	ADJ
ejpam-146	11	10	-	-	PUNCT
ejpam-146	11	11	like	like	ADJ
ejpam-146	11	12	sets	set	NOUN
ejpam-146	11	13	have	have	AUX
ejpam-146	11	14	been	be	AUX
ejpam-146	11	15	employed	employ	VERB
ejpam-146	11	16	for	for	ADP
ejpam-146	11	17	such	such	ADJ
ejpam-146	11	18	investigations	investigation	NOUN
ejpam-146	11	19	.	.	PUNCT
ejpam-146	12	1	in	in	ADP
ejpam-146	12	2	[	[	X
ejpam-146	12	3	1	1	NUM
ejpam-146	12	4	]	]	X
ejpam-146	12	5	monsef	monsef	PROPN
ejpam-146	12	6	et	et	PROPN
ejpam-146	12	7	.	.	PUNCT
ejpam-146	13	1	al	al	PROPN
ejpam-146	13	2	introduced	introduce	VERB
ejpam-146	13	3	the	the	DET
ejpam-146	13	4	notion	notion	NOUN
ejpam-146	13	5	of	of	ADP
ejpam-146	13	6	β	β	ADJ
ejpam-146	13	7	-	-	ADJ
ejpam-146	13	8	open	open	ADJ
ejpam-146	13	9	sets	set	NOUN
ejpam-146	13	10	(	(	PUNCT
ejpam-146	13	11	semi	semi	ADJ
ejpam-146	13	12	-	-	ADJ
ejpam-146	13	13	preopen	preopen	ADJ
ejpam-146	13	14	sets	set	NOUN
ejpam-146	13	15	[	[	X
ejpam-146	13	16	4	4	NUM
ejpam-146	13	17	]	]	PUNCT
ejpam-146	13	18	)	)	PUNCT
ejpam-146	13	19	and	and	CCONJ
ejpam-146	13	20	since	since	SCONJ
ejpam-146	13	21	its	its	PRON
ejpam-146	13	22	introduction	introduction	NOUN
ejpam-146	13	23	such	such	ADJ
ejpam-146	13	24	sets	set	NOUN
ejpam-146	13	25	along	along	ADP
ejpam-146	13	26	with	with	ADP
ejpam-146	13	27	some	some	PRON
ejpam-146	13	28	of	of	ADP
ejpam-146	13	29	their	their	PRON
ejpam-146	13	30	relevant	relevant	ADJ
ejpam-146	13	31	concepts	concept	NOUN
ejpam-146	13	32	have	have	AUX
ejpam-146	13	33	been	be	AUX
ejpam-146	13	34	investigated	investigate	VERB
ejpam-146	13	35	by	by	ADP
ejpam-146	13	36	many	many	ADJ
ejpam-146	13	37	.	.	PUNCT
ejpam-146	14	1	mention	mention	VERB
ejpam-146	14	2	may	may	AUX
ejpam-146	14	3	be	be	AUX
ejpam-146	14	4	made	make	VERB
ejpam-146	14	5	[	[	X
ejpam-146	14	6	2	2	NUM
ejpam-146	14	7	,	,	PUNCT
ejpam-146	14	8	3	3	NUM
ejpam-146	14	9	,	,	PUNCT
ejpam-146	14	10	4	4	NUM
ejpam-146	14	11	,	,	PUNCT
ejpam-146	14	12	5	5	NUM
ejpam-146	14	13	,	,	PUNCT
ejpam-146	14	14	6	6	NUM
ejpam-146	14	15	,	,	PUNCT
ejpam-146	14	16	9	9	NUM
ejpam-146	14	17	,	,	PUNCT
ejpam-146	14	18	10	10	NUM
ejpam-146	14	19	,	,	PUNCT
ejpam-146	14	20	16	16	NUM
ejpam-146	14	21	]	]	PUNCT
ejpam-146	14	22	.	.	PUNCT
ejpam-146	15	1	monsef	monsef	PROPN
ejpam-146	15	2	et	et	PROPN
ejpam-146	15	3	.	.	PUNCT
ejpam-146	16	1	al	al	PROPN
ejpam-146	17	1	[	[	X
ejpam-146	17	2	2	2	NUM
ejpam-146	17	3	]	]	PUNCT
ejpam-146	17	4	have	have	AUX
ejpam-146	17	5	taken	take	VERB
ejpam-146	17	6	up	up	ADP
ejpam-146	17	7	an	an	DET
ejpam-146	17	8	investigation	investigation	NOUN
ejpam-146	17	9	of	of	ADP
ejpam-146	17	10	a	a	DET
ejpam-146	17	11	sort	sort	NOUN
ejpam-146	17	12	of	of	ADV
ejpam-146	17	13	covering	cover	VERB
ejpam-146	17	14	property	property	NOUN
ejpam-146	17	15	,	,	PUNCT
ejpam-146	17	16	known	know	VERB
ejpam-146	17	17	as	as	ADP
ejpam-146	17	18	β	β	NOUN
ejpam-146	17	19	-	-	NOUN
ejpam-146	17	20	closedness	closedness	ADJ
ejpam-146	17	21	with	with	ADP
ejpam-146	17	22	the	the	DET
ejpam-146	17	23	help	help	NOUN
ejpam-146	17	24	of	of	ADP
ejpam-146	17	25	the	the	DET
ejpam-146	17	26	notion	notion	NOUN
ejpam-146	17	27	of	of	ADP
ejpam-146	17	28	β	β	ADJ
ejpam-146	17	29	-	-	ADJ
ejpam-146	17	30	open	open	ADJ
ejpam-146	17	31	sets	set	NOUN
ejpam-146	17	32	.	.	PUNCT
ejpam-146	18	1	a	a	DET
ejpam-146	18	2	topological	topological	ADJ
ejpam-146	18	3	space	space	NOUN
ejpam-146	18	4	x	x	PRON
ejpam-146	18	5	is	be	AUX
ejpam-146	18	6	said	say	VERB
ejpam-146	18	7	to	to	PART
ejpam-146	18	8	be	be	AUX
ejpam-146	18	9	β	β	X
ejpam-146	18	10	-	-	VERB
ejpam-146	18	11	closed	closed	ADJ
ejpam-146	18	12	[	[	X
ejpam-146	18	13	2	2	NUM
ejpam-146	18	14	]	]	PUNCT
ejpam-146	18	15	if	if	SCONJ
ejpam-146	18	16	every	every	DET
ejpam-146	18	17	β	β	NOUN
ejpam-146	18	18	-	-	ADJ
ejpam-146	18	19	open	open	ADJ
ejpam-146	18	20	cover	cover	NOUN
ejpam-146	18	21	of	of	ADP
ejpam-146	18	22	x	x	PUNCT
ejpam-146	18	23	admits	admit	VERB
ejpam-146	18	24	a	a	DET
ejpam-146	18	25	finite	finite	NOUN
ejpam-146	18	26	subfamily	subfamily	ADV
ejpam-146	18	27	whose	whose	DET
ejpam-146	18	28	β	β	NOUN
ejpam-146	18	29	-	-	NOUN
ejpam-146	18	30	closures	closure	NOUN
ejpam-146	18	31	cover	cover	VERB
ejpam-146	18	32	x	x	X
ejpam-146	18	33	.	.	PUNCT
ejpam-146	19	1	in	in	ADP
ejpam-146	19	2	this	this	DET
ejpam-146	19	3	paper	paper	NOUN
ejpam-146	19	4	we	we	PRON
ejpam-146	19	5	intend	intend	VERB
ejpam-146	19	6	to	to	PART
ejpam-146	19	7	undertake	undertake	VERB
ejpam-146	19	8	a	a	DET
ejpam-146	19	9	further	further	ADJ
ejpam-146	19	10	study	study	NOUN
ejpam-146	19	11	of	of	ADP
ejpam-146	19	12	such	such	ADJ
ejpam-146	19	13	concept	concept	NOUN
ejpam-146	19	14	.	.	PUNCT
ejpam-146	20	1	joseph	joseph	PROPN
ejpam-146	20	2	and	and	CCONJ
ejpam-146	20	3	kwack	kwack	VERB
ejpam-146	20	4	[	[	X
ejpam-146	20	5	11	11	NUM
ejpam-146	20	6	]	]	PUNCT
ejpam-146	20	7	have	have	AUX
ejpam-146	20	8	characterized	characterize	VERB
ejpam-146	20	9	s	s	NOUN
ejpam-146	20	10	-	-	PUNCT
ejpam-146	20	11	closed	closed	ADJ
ejpam-146	20	12	spaces	space	NOUN
ejpam-146	20	13	in	in	ADP
ejpam-146	20	14	various	various	ADJ
ejpam-146	20	15	ways	way	NOUN
ejpam-146	20	16	adopting	adopt	VERB
ejpam-146	20	17	the	the	DET
ejpam-146	20	18	techniques	technique	NOUN
ejpam-146	20	19	which	which	PRON
ejpam-146	20	20	have	have	AUX
ejpam-146	20	21	been	be	AUX
ejpam-146	20	22	found	find	VERB
ejpam-146	20	23	useful	useful	ADJ
ejpam-146	20	24	for	for	ADP
ejpam-146	20	25	compact	compact	ADJ
ejpam-146	20	26	spaces	space	NOUN
ejpam-146	20	27	and	and	CCONJ
ejpam-146	20	28	some	some	PRON
ejpam-146	20	29	of	of	ADP
ejpam-146	20	30	its	its	PRON
ejpam-146	20	31	generalizations	generalization	NOUN
ejpam-146	20	32	like	like	ADP
ejpam-146	20	33	h	h	NOUN
ejpam-146	20	34	-	-	PUNCT
ejpam-146	20	35	closed	closed	ADJ
ejpam-146	20	36	spaces	space	NOUN
ejpam-146	20	37	and	and	CCONJ
ejpam-146	20	38	minimal	minimal	ADJ
ejpam-146	20	39	hausdorff	hausdorff	NOUN
ejpam-146	20	40	spaces	space	NOUN
ejpam-146	20	41	.	.	PUNCT
ejpam-146	21	1	analogue	analogue	NOUN
ejpam-146	21	2	of	of	ADP
ejpam-146	21	3	such	such	ADJ
ejpam-146	21	4	characterizations	characterization	NOUN
ejpam-146	21	5	for	for	ADP
ejpam-146	21	6	β	β	NOUN
ejpam-146	21	7	-	-	ADJ
ejpam-146	21	8	closed	closed	ADJ
ejpam-146	21	9	spaces	space	NOUN
ejpam-146	21	10	are	be	AUX
ejpam-146	21	11	given	give	VERB
ejpam-146	21	12	here	here	ADV
ejpam-146	21	13	.	.	PUNCT
ejpam-146	22	1	in	in	ADP
ejpam-146	22	2	section	section	NOUN
ejpam-146	22	3	§	§	PROPN
ejpam-146	22	4	2	2	NUM
ejpam-146	22	5	,	,	PUNCT
ejpam-146	22	6	we	we	PRON
ejpam-146	22	7	state	state	VERB
ejpam-146	22	8	some	some	DET
ejpam-146	22	9	existing	exist	VERB
ejpam-146	22	10	definitions	definition	NOUN
ejpam-146	22	11	and	and	CCONJ
ejpam-146	22	12	results	result	NOUN
ejpam-146	22	13	as	as	ADP
ejpam-146	22	14	a	a	DET
ejpam-146	22	15	prerequisite	prerequisite	NOUN
ejpam-146	22	16	for	for	ADP
ejpam-146	22	17	the	the	DET
ejpam-146	22	18	development	development	NOUN
ejpam-146	22	19	of	of	ADP
ejpam-146	22	20	subsequent	subsequent	ADJ
ejpam-146	22	21	sections	section	NOUN
ejpam-146	22	22	.	.	PUNCT
ejpam-146	23	1	in	in	ADP
ejpam-146	23	2	section	section	NOUN
ejpam-146	23	3	§	§	PROPN
ejpam-146	23	4	3	3	NUM
ejpam-146	23	5	,	,	PUNCT
ejpam-146	23	6	we	we	PRON
ejpam-146	23	7	derive	derive	VERB
ejpam-146	23	8	various	various	ADJ
ejpam-146	23	9	characterizations	characterization	NOUN
ejpam-146	23	10	of	of	ADP
ejpam-146	23	11	β	β	NOUN
ejpam-146	23	12	-	-	ADJ
ejpam-146	23	13	closed	closed	ADJ
ejpam-146	23	14	spaces	space	NOUN
ejpam-146	23	15	,	,	PUNCT
ejpam-146	23	16	specially	specially	ADV
ejpam-146	23	17	,	,	PUNCT
ejpam-146	23	18	in	in	ADP
ejpam-146	23	19	terms	term	NOUN
ejpam-146	23	20	of	of	ADP
ejpam-146	23	21	filter	filter	NOUN
ejpam-146	23	22	bases	basis	NOUN
ejpam-146	23	23	,	,	PUNCT
ejpam-146	23	24	in	in	ADP
ejpam-146	23	25	terms	term	NOUN
ejpam-146	23	26	of	of	ADP
ejpam-146	23	27	nets	net	NOUN
ejpam-146	23	28	with	with	ADP
ejpam-146	23	29	well	well	ADV
ejpam-146	23	30	ordered	order	VERB
ejpam-146	23	31	directed	direct	VERB
ejpam-146	23	32	sets	set	NOUN
ejpam-146	23	33	and	and	CCONJ
ejpam-146	23	34	in	in	ADP
ejpam-146	23	35	terms	term	NOUN
ejpam-146	23	36	of	of	ADP
ejpam-146	23	37	a	a	DET
ejpam-146	23	38	generalized	generalize	VERB
ejpam-146	23	39	complete	complete	ADJ
ejpam-146	23	40	accumulation	accumulation	NOUN
ejpam-146	23	41	point	point	NOUN
ejpam-146	23	42	.	.	PUNCT
ejpam-146	24	1	section	section	NOUN
ejpam-146	24	2	§	§	NOUN
ejpam-146	24	3	4	4	NUM
ejpam-146	24	4	concerns	concern	NOUN
ejpam-146	24	5	from	from	ADP
ejpam-146	24	6	∗corresponding	∗corresponde	VERB
ejpam-146	24	7	author	author	NOUN
ejpam-146	24	8	.	.	PUNCT
ejpam-146	25	1	email	email	NOUN
ejpam-146	25	2	addresses	address	NOUN
ejpam-146	25	3	:	:	PUNCT
ejpam-146	25	4	ckbasu1962@yahoo.com	ckbasu1962@yahoo.com	X
ejpam-146	26	1	(	(	PUNCT
ejpam-146	26	2	c.	c.	PROPN
ejpam-146	26	3	k.	k.	PROPN
ejpam-146	26	4	basu	basu	PROPN
ejpam-146	26	5	)	)	PUNCT
ejpam-146	27	1	manabghosh@gmail.com	manabghosh@gmail.com	X
ejpam-146	28	1	(	(	PUNCT
ejpam-146	28	2	m.	m.	PROPN
ejpam-146	28	3	k.	k.	PROPN
ejpam-146	28	4	ghosh	ghosh	PROPN
ejpam-146	28	5	)	)	PUNCT
ejpam-146	29	1	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-146	30	1	40	40	NUM
ejpam-146	31	1	c	c	X
ejpam-146	31	2	©	©	NOUN
ejpam-146	31	3	2008	2008	NUM
ejpam-146	31	4	ejpam	ejpam	VERB
ejpam-146	31	5	all	all	DET
ejpam-146	31	6	rights	right	NOUN
ejpam-146	31	7	reserved	reserve	VERB
ejpam-146	31	8	.	.	PUNCT
ejpam-146	32	1	c.	c.	PROPN
ejpam-146	32	2	k.	k.	PROPN
ejpam-146	32	3	basu	basu	PROPN
ejpam-146	32	4	,	,	PUNCT
ejpam-146	32	5	m.	m.	PROPN
ejpam-146	32	6	k.	k.	PROPN
ejpam-146	32	7	ghosh	ghosh	PROPN
ejpam-146	32	8	/	/	PUNCT
ejpam-146	32	9	eur	eur	PROPN
ejpam-146	32	10	.	.	PUNCT
ejpam-146	33	1	j.	j.	PROPN
ejpam-146	33	2	pure	pure	PROPN
ejpam-146	33	3	appl	appl	PROPN
ejpam-146	33	4	.	.	PROPN
ejpam-146	33	5	math	math	PROPN
ejpam-146	33	6	,	,	PUNCT
ejpam-146	33	7	1	1	NUM
ejpam-146	33	8	(	(	PUNCT
ejpam-146	33	9	2008	2008	NUM
ejpam-146	33	10	)	)	PUNCT
ejpam-146	33	11	,	,	PUNCT
ejpam-146	33	12	(	(	PUNCT
ejpam-146	33	13	40	40	NUM
ejpam-146	33	14	-	-	SYM
ejpam-146	33	15	50	50	NUM
ejpam-146	33	16	)	)	PUNCT
ejpam-146	33	17	41	41	NUM
ejpam-146	33	18	several	several	ADJ
ejpam-146	33	19	points	point	NOUN
ejpam-146	33	20	of	of	ADP
ejpam-146	33	21	view	view	NOUN
ejpam-146	33	22	.	.	PUNCT
ejpam-146	34	1	first	first	ADV
ejpam-146	34	2	,	,	PUNCT
ejpam-146	34	3	in	in	ADP
ejpam-146	34	4	introducing	introduce	VERB
ejpam-146	34	5	and	and	CCONJ
ejpam-146	34	6	characterizing	characterize	VERB
ejpam-146	34	7	the	the	DET
ejpam-146	34	8	notions	notion	NOUN
ejpam-146	34	9	of	of	ADP
ejpam-146	34	10	(	(	PUNCT
ejpam-146	34	11	θ	θ	PROPN
ejpam-146	34	12	,	,	PUNCT
ejpam-146	34	13	β)-continuity	β)-continuity	NOUN
ejpam-146	34	14	and	and	CCONJ
ejpam-146	34	15	β	β	X
ejpam-146	34	16	-	-	ADJ
ejpam-146	34	17	θ	θ	NOUN
ejpam-146	34	18	-subclosedness	-subclosedness	NOUN
ejpam-146	34	19	of	of	ADP
ejpam-146	34	20	graphs	graph	NOUN
ejpam-146	34	21	of	of	ADP
ejpam-146	34	22	functions	function	NOUN
ejpam-146	34	23	,	,	PUNCT
ejpam-146	34	24	second	second	ADJ
ejpam-146	34	25	,	,	PUNCT
ejpam-146	34	26	to	to	PART
ejpam-146	34	27	obtain	obtain	VERB
ejpam-146	34	28	several	several	ADJ
ejpam-146	34	29	relevant	relevant	ADJ
ejpam-146	34	30	properties	property	NOUN
ejpam-146	34	31	of	of	ADP
ejpam-146	34	32	such	such	ADJ
ejpam-146	34	33	functions	function	NOUN
ejpam-146	34	34	along	along	ADP
ejpam-146	34	35	with	with	ADP
ejpam-146	34	36	a	a	DET
ejpam-146	34	37	theorem	theorem	NOUN
ejpam-146	34	38	that	that	PRON
ejpam-146	34	39	concerns	concern	NOUN
ejpam-146	34	40	on	on	ADP
ejpam-146	34	41	common	common	ADJ
ejpam-146	34	42	fixed	fix	VERB
ejpam-146	34	43	points	point	NOUN
ejpam-146	34	44	of	of	ADP
ejpam-146	34	45	a	a	DET
ejpam-146	34	46	family	family	NOUN
ejpam-146	34	47	of	of	ADP
ejpam-146	34	48	functions	function	NOUN
ejpam-146	34	49	having	have	VERB
ejpam-146	34	50	β	β	NOUN
ejpam-146	34	51	-	-	PUNCT
ejpam-146	34	52	θ	θ	NOUN
ejpam-146	34	53	-subclosed	-subclose	VERB
ejpam-146	34	54	graphs	graph	NOUN
ejpam-146	34	55	and	and	CCONJ
ejpam-146	34	56	finally	finally	ADV
ejpam-146	34	57	,	,	PUNCT
ejpam-146	34	58	to	to	PART
ejpam-146	34	59	exploit	exploit	VERB
ejpam-146	34	60	these	these	DET
ejpam-146	34	61	ideas	idea	NOUN
ejpam-146	34	62	in	in	ADP
ejpam-146	34	63	achieving	achieve	VERB
ejpam-146	34	64	some	some	DET
ejpam-146	34	65	characterizations	characterization	NOUN
ejpam-146	34	66	of	of	ADP
ejpam-146	34	67	β	β	NOUN
ejpam-146	34	68	-	-	ADJ
ejpam-146	34	69	closed	closed	ADJ
ejpam-146	34	70	spaces	space	NOUN
ejpam-146	34	71	.	.	PUNCT
ejpam-146	35	1	throughout	throughout	ADP
ejpam-146	35	2	this	this	DET
ejpam-146	35	3	paper	paper	NOUN
ejpam-146	35	4	,	,	PUNCT
ejpam-146	35	5	spaces	space	NOUN
ejpam-146	35	6	always	always	ADV
ejpam-146	35	7	mean	mean	VERB
ejpam-146	35	8	a	a	DET
ejpam-146	35	9	topological	topological	ADJ
ejpam-146	35	10	space	space	NOUN
ejpam-146	35	11	without	without	ADP
ejpam-146	35	12	any	any	DET
ejpam-146	35	13	separation	separation	NOUN
ejpam-146	35	14	axioms	axiom	NOUN
ejpam-146	35	15	and	and	CCONJ
ejpam-146	35	16	ψ	ψ	X
ejpam-146	35	17	:	:	PUNCT
ejpam-146	35	18	x	x	X
ejpam-146	35	19	→	→	SYM
ejpam-146	35	20	y	y	PROPN
ejpam-146	35	21	denotes	denote	VERB
ejpam-146	35	22	a	a	DET
ejpam-146	35	23	single	single	ADJ
ejpam-146	35	24	valued	value	VERB
ejpam-146	35	25	function	function	NOUN
ejpam-146	35	26	of	of	ADP
ejpam-146	35	27	a	a	DET
ejpam-146	35	28	space	space	NOUN
ejpam-146	35	29	(	(	PUNCT
ejpam-146	35	30	x	x	X
ejpam-146	35	31	,	,	PUNCT
ejpam-146	35	32	τ	τ	PROPN
ejpam-146	35	33	)	)	PUNCT
ejpam-146	35	34	into	into	ADP
ejpam-146	35	35	a	a	DET
ejpam-146	35	36	space	space	NOUN
ejpam-146	35	37	(	(	PUNCT
ejpam-146	35	38	y	y	NOUN
ejpam-146	35	39	,	,	PUNCT
ejpam-146	35	40	τ1	τ1	NOUN
ejpam-146	35	41	)	)	PUNCT
ejpam-146	35	42	.	.	PUNCT
ejpam-146	36	1	the	the	DET
ejpam-146	36	2	closure	closure	NOUN
ejpam-146	36	3	and	and	CCONJ
ejpam-146	36	4	the	the	DET
ejpam-146	36	5	interior	interior	NOUN
ejpam-146	36	6	of	of	ADP
ejpam-146	36	7	a	a	DET
ejpam-146	36	8	subset	subset	NOUN
ejpam-146	36	9	s	s	NOUN
ejpam-146	36	10	of	of	ADP
ejpam-146	36	11	a	a	DET
ejpam-146	36	12	space	space	NOUN
ejpam-146	36	13	x	x	PRON
ejpam-146	36	14	are	be	AUX
ejpam-146	36	15	denoted	denote	VERB
ejpam-146	36	16	by	by	ADP
ejpam-146	36	17	cl(s	cl(	NOUN
ejpam-146	36	18	)	)	PUNCT
ejpam-146	36	19	and	and	CCONJ
ejpam-146	36	20	int(s	int(s	PROPN
ejpam-146	36	21	)	)	PUNCT
ejpam-146	36	22	respectively	respectively	ADV
ejpam-146	36	23	.	.	PUNCT
ejpam-146	37	1	we	we	PRON
ejpam-146	37	2	recall	recall	VERB
ejpam-146	37	3	the	the	DET
ejpam-146	37	4	following	follow	VERB
ejpam-146	37	5	well	well	ADV
ejpam-146	37	6	known	know	VERB
ejpam-146	37	7	definitions	definition	NOUN
ejpam-146	37	8	:	:	PUNCT
ejpam-146	37	9	a	a	DET
ejpam-146	37	10	subset	subset	NOUN
ejpam-146	37	11	s	s	NOUN
ejpam-146	37	12	of	of	ADP
ejpam-146	37	13	a	a	DET
ejpam-146	37	14	space	space	NOUN
ejpam-146	37	15	(	(	PUNCT
ejpam-146	37	16	x	x	X
ejpam-146	37	17	,	,	PUNCT
ejpam-146	37	18	τ	τ	PROPN
ejpam-146	37	19	)	)	PUNCT
ejpam-146	37	20	or	or	CCONJ
ejpam-146	37	21	x	x	X
ejpam-146	37	22	is	be	AUX
ejpam-146	37	23	said	say	VERB
ejpam-146	37	24	to	to	PART
ejpam-146	37	25	be	be	AUX
ejpam-146	37	26	α	α	X
ejpam-146	37	27	-	-	ADJ
ejpam-146	37	28	open	open	ADJ
ejpam-146	37	29	[	[	X
ejpam-146	37	30	15	15	NUM
ejpam-146	37	31	]	]	X
ejpam-146	37	32	(	(	PUNCT
ejpam-146	37	33	resp	resp	NOUN
ejpam-146	37	34	.	.	PUNCT
ejpam-146	38	1	semi	semi	ADJ
ejpam-146	38	2	-	-	ADJ
ejpam-146	38	3	open	open	ADJ
ejpam-146	38	4	[	[	X
ejpam-146	38	5	12	12	NUM
ejpam-146	38	6	]	]	PUNCT
ejpam-146	38	7	,	,	PUNCT
ejpam-146	38	8	preopen	preopen	ADJ
ejpam-146	38	9	[	[	X
ejpam-146	38	10	14	14	NUM
ejpam-146	38	11	]	]	PUNCT
ejpam-146	38	12	,	,	PUNCT
ejpam-146	38	13	β	β	X
ejpam-146	38	14	-	-	VERB
ejpam-146	38	15	open	open	ADJ
ejpam-146	38	16	[	[	X
ejpam-146	38	17	1	1	NUM
ejpam-146	38	18	]	]	PUNCT
ejpam-146	38	19	or	or	CCONJ
ejpam-146	38	20	semi	semi	ADJ
ejpam-146	38	21	-	-	ADJ
ejpam-146	38	22	preopen	preopen	ADJ
ejpam-146	38	23	[	[	X
ejpam-146	38	24	4	4	NUM
ejpam-146	38	25	]	]	PUNCT
ejpam-146	38	26	)	)	PUNCT
ejpam-146	38	27	if	if	SCONJ
ejpam-146	38	28	s	s	VERB
ejpam-146	38	29	⊂	⊂	X
ejpam-146	38	30	int(cl(int(s	int(cl(int(s	PROPN
ejpam-146	38	31	)	)	PUNCT
ejpam-146	38	32	)	)	PUNCT
ejpam-146	38	33	)	)	PUNCT
ejpam-146	39	1	(	(	PUNCT
ejpam-146	39	2	resp	resp	NOUN
ejpam-146	39	3	.	.	PUNCT
ejpam-146	40	1	s	s	PART
ejpam-146	40	2	⊂	⊂	PROPN
ejpam-146	40	3	cl(int(s	cl(int(s	PROPN
ejpam-146	40	4	)	)	PUNCT
ejpam-146	40	5	,	,	PUNCT
ejpam-146	41	1	s	s	PROPN
ejpam-146	41	2	⊂	⊂	PROPN
ejpam-146	41	3	int(cl(s	int(cl(s	PROPN
ejpam-146	41	4	)	)	PUNCT
ejpam-146	41	5	)	)	PUNCT
ejpam-146	41	6	,	,	PUNCT
ejpam-146	41	7	s	s	PROPN
ejpam-146	41	8	⊂	⊂	PROPN
ejpam-146	41	9	cl(int(cl(s	cl(int(cl(s	PROPN
ejpam-146	41	10	)	)	PUNCT
ejpam-146	41	11	)	)	PUNCT
ejpam-146	41	12	)	)	PUNCT
ejpam-146	41	13	)	)	PUNCT
ejpam-146	41	14	.	.	PUNCT
ejpam-146	42	1	we	we	PRON
ejpam-146	42	2	denote	denote	VERB
ejpam-146	42	3	the	the	DET
ejpam-146	42	4	classes	class	NOUN
ejpam-146	42	5	of	of	ADP
ejpam-146	42	6	all	all	DET
ejpam-146	42	7	open	open	ADJ
ejpam-146	42	8	(	(	PUNCT
ejpam-146	42	9	resp	resp	NOUN
ejpam-146	42	10	.	.	PUNCT
ejpam-146	43	1	α	α	X
ejpam-146	43	2	-	-	ADJ
ejpam-146	43	3	open	open	ADJ
ejpam-146	43	4	,	,	PUNCT
ejpam-146	43	5	semi	semi	ADJ
ejpam-146	43	6	-	-	ADJ
ejpam-146	43	7	open	open	ADJ
ejpam-146	43	8	,	,	PUNCT
ejpam-146	43	9	preopen	preopen	ADJ
ejpam-146	43	10	,	,	PUNCT
ejpam-146	43	11	β	β	NOUN
ejpam-146	43	12	-	-	ADJ
ejpam-146	43	13	open	open	ADJ
ejpam-146	43	14	)	)	PUNCT
ejpam-146	43	15	sets	set	NOUN
ejpam-146	43	16	in	in	ADP
ejpam-146	43	17	a	a	DET
ejpam-146	43	18	space	space	NOUN
ejpam-146	43	19	(	(	PUNCT
ejpam-146	43	20	x	x	X
ejpam-146	43	21	,	,	PUNCT
ejpam-146	43	22	τ	τ	PROPN
ejpam-146	43	23	)	)	PUNCT
ejpam-146	43	24	by	by	ADP
ejpam-146	43	25	o(x	o(x	PROPN
ejpam-146	43	26	)	)	PUNCT
ejpam-146	43	27	(	(	PUNCT
ejpam-146	43	28	resp	resp	NOUN
ejpam-146	43	29	.	.	PUNCT
ejpam-146	43	30	τα	τα	PUNCT
ejpam-146	44	1	=	=	SYM
ejpam-146	44	2	α(x	α(x	PROPN
ejpam-146	44	3	)	)	PUNCT
ejpam-146	44	4	,	,	PUNCT
ejpam-146	44	5	so(x	so(x	X
ejpam-146	44	6	)	)	PUNCT
ejpam-146	44	7	,	,	PUNCT
ejpam-146	44	8	po(x	po(x	NUM
ejpam-146	44	9	)	)	PUNCT
ejpam-146	44	10	,	,	PUNCT
ejpam-146	44	11	βo(x	βo(x	PUNCT
ejpam-146	44	12	)	)	PUNCT
ejpam-146	45	1	=	=	SYM
ejpam-146	45	2	spo(x	spo(x	PROPN
ejpam-146	45	3	)	)	PUNCT
ejpam-146	45	4	)	)	PUNCT
ejpam-146	45	5	)	)	PUNCT
ejpam-146	45	6	and	and	CCONJ
ejpam-146	45	7	that	that	SCONJ
ejpam-146	45	8	containing	contain	VERB
ejpam-146	45	9	a	a	DET
ejpam-146	45	10	point	point	NOUN
ejpam-146	45	11	x	x	PUNCT
ejpam-146	45	12	of	of	ADP
ejpam-146	45	13	(	(	PUNCT
ejpam-146	45	14	x	x	PROPN
ejpam-146	45	15	,	,	PUNCT
ejpam-146	45	16	τ	τ	PROPN
ejpam-146	45	17	)	)	PUNCT
ejpam-146	45	18	by	by	ADP
ejpam-146	45	19	o(x	o(x	PROPN
ejpam-146	45	20	,	,	PUNCT
ejpam-146	45	21	x	x	X
ejpam-146	45	22	)	)	PUNCT
ejpam-146	45	23	(	(	PUNCT
ejpam-146	45	24	resp	resp	NOUN
ejpam-146	45	25	.	.	PUNCT
ejpam-146	46	1	α(x	α(x	PROPN
ejpam-146	46	2	,	,	PUNCT
ejpam-146	46	3	x	x	NOUN
ejpam-146	46	4	)	)	PUNCT
ejpam-146	46	5	,	,	PUNCT
ejpam-146	46	6	so(x	so(x	NOUN
ejpam-146	46	7	,	,	PUNCT
ejpam-146	46	8	x	x	NOUN
ejpam-146	46	9	)	)	PUNCT
ejpam-146	46	10	,	,	PUNCT
ejpam-146	46	11	po(x	po(x	PUNCT
ejpam-146	46	12	,	,	PUNCT
ejpam-146	46	13	x	x	X
ejpam-146	46	14	)	)	PUNCT
ejpam-146	46	15	,	,	PUNCT
ejpam-146	46	16	βo(x	βo(x	PUNCT
ejpam-146	46	17	,	,	PUNCT
ejpam-146	46	18	x	x	X
ejpam-146	46	19	)	)	PUNCT
ejpam-146	46	20	)	)	PUNCT
ejpam-146	46	21	.	.	PUNCT
ejpam-146	47	1	moreover	moreover	ADV
ejpam-146	47	2	it	it	PRON
ejpam-146	47	3	is	be	AUX
ejpam-146	47	4	well	well	ADV
ejpam-146	47	5	known	know	VERB
ejpam-146	47	6	that	that	SCONJ
ejpam-146	47	7	τ	τ	PROPN
ejpam-146	47	8	⊂	⊂	PROPN
ejpam-146	47	9	τα	τα	PUNCT
ejpam-146	47	10	=	=	X
ejpam-146	47	11	po(x	po(x	NUM
ejpam-146	47	12	)	)	PUNCT
ejpam-146	47	13	∩	∩	NOUN
ejpam-146	47	14	so(x	so(x	NUM
ejpam-146	47	15	)	)	PUNCT
ejpam-146	48	1	⊂	⊂	PROPN
ejpam-146	48	2	po(x	po(x	ADV
ejpam-146	48	3	)	)	PUNCT
ejpam-146	48	4	∪	∪	X
ejpam-146	48	5	so(x	so(x	NOUN
ejpam-146	48	6	)	)	PUNCT
ejpam-146	49	1	⊂	⊂	PROPN
ejpam-146	49	2	βo(x	βo(x	PUNCT
ejpam-146	49	3	)	)	PUNCT
ejpam-146	49	4	.	.	PUNCT
ejpam-146	50	1	the	the	DET
ejpam-146	50	2	complement	complement	NOUN
ejpam-146	50	3	of	of	ADP
ejpam-146	50	4	a	a	DET
ejpam-146	50	5	β	β	X
ejpam-146	50	6	-	-	ADJ
ejpam-146	50	7	open	open	ADJ
ejpam-146	50	8	set	set	NOUN
ejpam-146	50	9	is	be	AUX
ejpam-146	50	10	called	call	VERB
ejpam-146	50	11	β	β	NOUN
ejpam-146	50	12	-	-	VERB
ejpam-146	50	13	closed	closed	ADJ
ejpam-146	50	14	.	.	PUNCT
ejpam-146	51	1	preclosed	preclose	VERB
ejpam-146	51	2	and	and	CCONJ
ejpam-146	51	3	semi	semi	ADJ
ejpam-146	51	4	-	-	ADJ
ejpam-146	51	5	closed	closed	ADJ
ejpam-146	51	6	sets	set	NOUN
ejpam-146	51	7	are	be	AUX
ejpam-146	51	8	similarly	similarly	ADV
ejpam-146	51	9	defined	define	VERB
ejpam-146	51	10	.	.	PUNCT
ejpam-146	52	1	the	the	DET
ejpam-146	52	2	β	β	NOUN
ejpam-146	52	3	-	-	NOUN
ejpam-146	52	4	closure	closure	NOUN
ejpam-146	52	5	(	(	PUNCT
ejpam-146	52	6	resp	resp	NOUN
ejpam-146	52	7	.	.	PUNCT
ejpam-146	53	1	preclosure	preclosure	ADJ
ejpam-146	53	2	,	,	PUNCT
ejpam-146	53	3	semi	semi	ADJ
ejpam-146	53	4	closure	closure	NOUN
ejpam-146	53	5	)	)	PUNCT
ejpam-146	53	6	of	of	ADP
ejpam-146	53	7	s	s	PRON
ejpam-146	53	8	denoted	denote	VERB
ejpam-146	53	9	by	by	ADP
ejpam-146	53	10	β	β	NOUN
ejpam-146	53	11	cl(s	cl(s	PROPN
ejpam-146	53	12	)	)	PUNCT
ejpam-146	53	13	(	(	PUNCT
ejpam-146	53	14	resp	resp	NOUN
ejpam-146	53	15	.	.	PUNCT
ejpam-146	54	1	pcl(s	pcl(s	PROPN
ejpam-146	54	2	)	)	PUNCT
ejpam-146	54	3	,	,	PUNCT
ejpam-146	54	4	scl(s	scl(s	PROPN
ejpam-146	54	5	)	)	PUNCT
ejpam-146	54	6	)	)	PUNCT
ejpam-146	54	7	is	be	AUX
ejpam-146	54	8	the	the	DET
ejpam-146	54	9	intersection	intersection	NOUN
ejpam-146	54	10	of	of	ADP
ejpam-146	54	11	all	all	DET
ejpam-146	54	12	β	β	NOUN
ejpam-146	54	13	-	-	VERB
ejpam-146	54	14	closed	closed	ADJ
ejpam-146	54	15	(	(	PUNCT
ejpam-146	54	16	resp	resp	NOUN
ejpam-146	54	17	.	.	PUNCT
ejpam-146	55	1	pre	pre	PROPN
ejpam-146	56	1	closed	closed	ADJ
ejpam-146	56	2	,	,	PUNCT
ejpam-146	56	3	semi	semi	ADJ
ejpam-146	56	4	-	-	ADJ
ejpam-146	56	5	closed	closed	ADJ
ejpam-146	56	6	)	)	PUNCT
ejpam-146	56	7	subsets	subset	NOUN
ejpam-146	56	8	of	of	ADP
ejpam-146	56	9	x	x	PUNCT
ejpam-146	56	10	containing	contain	VERB
ejpam-146	56	11	s.	s.	PROPN
ejpam-146	56	12	β	β	PROPN
ejpam-146	56	13	-	-	NOUN
ejpam-146	56	14	interior	interior	ADJ
ejpam-146	56	15	of	of	ADP
ejpam-146	56	16	s	s	PROPN
ejpam-146	56	17	,	,	PUNCT
ejpam-146	56	18	denoted	denote	VERB
ejpam-146	56	19	by	by	ADP
ejpam-146	56	20	β	β	X
ejpam-146	56	21	int(s	int(s	PROPN
ejpam-146	56	22	)	)	PUNCT
ejpam-146	56	23	is	be	AUX
ejpam-146	56	24	defined	define	VERB
ejpam-146	56	25	as	as	ADP
ejpam-146	56	26	usual	usual	ADJ
ejpam-146	56	27	.	.	PUNCT
ejpam-146	57	1	a	a	DET
ejpam-146	57	2	space	space	NOUN
ejpam-146	57	3	x	x	PUNCT
ejpam-146	57	4	is	be	AUX
ejpam-146	57	5	called	call	VERB
ejpam-146	57	6	qhc	qhc	NOUN
ejpam-146	58	1	[	[	X
ejpam-146	58	2	7	7	NUM
ejpam-146	58	3	]	]	X
ejpam-146	58	4	(	(	PUNCT
ejpam-146	58	5	resp	resp	NOUN
ejpam-146	58	6	.	.	PUNCT
ejpam-146	59	1	s	s	X
ejpam-146	59	2	-	-	PUNCT
ejpam-146	59	3	closed	closed	ADJ
ejpam-146	59	4	[	[	X
ejpam-146	59	5	17	17	NUM
ejpam-146	59	6	]	]	NUM
ejpam-146	59	7	)	)	PUNCT
ejpam-146	59	8	,	,	PUNCT
ejpam-146	59	9	s	s	X
ejpam-146	59	10	-	-	PUNCT
ejpam-146	59	11	closed	closed	ADJ
ejpam-146	60	1	[	[	X
ejpam-146	60	2	13	13	NUM
ejpam-146	60	3	]	]	PUNCT
ejpam-146	60	4	,	,	PUNCT
ejpam-146	60	5	p	p	NOUN
ejpam-146	60	6	-	-	PUNCT
ejpam-146	60	7	closed	closed	ADJ
ejpam-146	60	8	[	[	X
ejpam-146	60	9	8	8	NUM
ejpam-146	60	10	]	]	PUNCT
ejpam-146	60	11	)	)	PUNCT
ejpam-146	60	12	if	if	SCONJ
ejpam-146	60	13	every	every	DET
ejpam-146	60	14	open	open	ADJ
ejpam-146	60	15	(	(	PUNCT
ejpam-146	60	16	resp	resp	NOUN
ejpam-146	60	17	.	.	PUNCT
ejpam-146	61	1	semi	semi	ADJ
ejpam-146	61	2	-	-	ADJ
ejpam-146	61	3	open	open	ADJ
ejpam-146	61	4	,	,	PUNCT
ejpam-146	61	5	semi	semi	ADJ
ejpam-146	61	6	-	-	ADJ
ejpam-146	61	7	open	open	ADJ
ejpam-146	61	8	,	,	PUNCT
ejpam-146	61	9	preopen	preopen	ADJ
ejpam-146	61	10	)	)	PUNCT
ejpam-146	61	11	cover	cover	NOUN
ejpam-146	61	12	of	of	ADP
ejpam-146	61	13	x	x	PUNCT
ejpam-146	61	14	has	have	VERB
ejpam-146	61	15	a	a	DET
ejpam-146	61	16	finite	finite	NOUN
ejpam-146	61	17	subfamily	subfamily	ADV
ejpam-146	61	18	,	,	PUNCT
ejpam-146	61	19	whose	whose	DET
ejpam-146	61	20	closures	closure	NOUN
ejpam-146	61	21	(	(	PUNCT
ejpam-146	61	22	resp	resp	NOUN
ejpam-146	61	23	.	.	PUNCT
ejpam-146	62	1	closures	closure	NOUN
ejpam-146	62	2	,	,	PUNCT
ejpam-146	62	3	semi	semi	ADJ
ejpam-146	62	4	-	-	NOUN
ejpam-146	62	5	closures	closure	NOUN
ejpam-146	62	6	,	,	PUNCT
ejpam-146	62	7	pre	pre	ADJ
ejpam-146	62	8	-	-	NOUN
ejpam-146	62	9	closures	closure	NOUN
ejpam-146	62	10	)	)	PUNCT
ejpam-146	62	11	cover	cover	NOUN
ejpam-146	62	12	x	x	X
ejpam-146	62	13	.	.	PUNCT
ejpam-146	63	1	for	for	ADP
ejpam-146	63	2	any	any	DET
ejpam-146	63	3	filter	filter	NOUN
ejpam-146	63	4	base	base	NOUN
ejpam-146	63	5	f	f	PROPN
ejpam-146	63	6	,	,	PUNCT
ejpam-146	63	7	adherence	adherence	NOUN
ejpam-146	63	8	of	of	ADP
ejpam-146	63	9	f	f	PROPN
ejpam-146	63	10	is	be	AUX
ejpam-146	63	11	written	write	VERB
ejpam-146	63	12	as	as	ADP
ejpam-146	63	13	adf	adf	PROPN
ejpam-146	63	14	.	.	PUNCT
ejpam-146	64	1	a	a	DET
ejpam-146	64	2	filter	filter	NOUN
ejpam-146	64	3	base	base	NOUN
ejpam-146	64	4	f	f	PROPN
ejpam-146	64	5	is	be	AUX
ejpam-146	64	6	said	say	VERB
ejpam-146	64	7	to	to	ADP
ejpam-146	64	8	(	(	PUNCT
ejpam-146	64	9	a	a	X
ejpam-146	64	10	)	)	PUNCT
ejpam-146	64	11	β	β	NOUN
ejpam-146	64	12	-	-	NOUN
ejpam-146	64	13	θ	θ	NOUN
ejpam-146	64	14	-adhere	-adhere	NOUN
ejpam-146	64	15	at	at	ADP
ejpam-146	64	16	x	x	X
ejpam-146	64	17	(	(	PUNCT
ejpam-146	64	18	written	write	VERB
ejpam-146	64	19	as	as	ADP
ejpam-146	64	20	x	x	PROPN
ejpam-146	64	21	∈	∈	PROPN
ejpam-146	64	22	β	β	NOUN
ejpam-146	64	23	-	-	NOUN
ejpam-146	64	24	θ	θ	NOUN
ejpam-146	64	25	-adf	-adf	NOUN
ejpam-146	64	26	)	)	PUNCT
ejpam-146	65	1	if	if	SCONJ
ejpam-146	65	2	for	for	ADP
ejpam-146	65	3	each	each	DET
ejpam-146	65	4	f	f	PROPN
ejpam-146	65	5	∈	∈	PROPN
ejpam-146	65	6	f	f	PROPN
ejpam-146	65	7	and	and	CCONJ
ejpam-146	65	8	each	each	DET
ejpam-146	65	9	v	v	NOUN
ejpam-146	65	10	∈	∈	NOUN
ejpam-146	65	11	βo(x	βo(x	PUNCT
ejpam-146	65	12	,	,	PUNCT
ejpam-146	65	13	x	x	X
ejpam-146	65	14	)	)	PUNCT
ejpam-146	65	15	,	,	PUNCT
ejpam-146	65	16	f	f	PROPN
ejpam-146	65	17	∩	∩	PROPN
ejpam-146	65	18	β	β	X
ejpam-146	65	19	cl(v	cl(v	NOUN
ejpam-146	65	20	)	)	PUNCT
ejpam-146	65	21	6=	6=	NUM
ejpam-146	65	22	;	;	PUNCT
ejpam-146	65	23	.	.	PUNCT
ejpam-146	66	1	(	(	PUNCT
ejpam-146	66	2	b	b	X
ejpam-146	66	3	)	)	PUNCT
ejpam-146	66	4	β	β	NOUN
ejpam-146	66	5	-	-	PUNCT
ejpam-146	66	6	θ	θ	NOUN
ejpam-146	66	7	-converge	-converge	NOUN
ejpam-146	66	8	to	to	ADP
ejpam-146	66	9	x	x	SYM
ejpam-146	66	10	if	if	SCONJ
ejpam-146	66	11	for	for	ADP
ejpam-146	66	12	each	each	DET
ejpam-146	66	13	v	v	NOUN
ejpam-146	66	14	∈	∈	NOUN
ejpam-146	66	15	βo(x	βo(x	PUNCT
ejpam-146	66	16	,	,	PUNCT
ejpam-146	66	17	x	x	X
ejpam-146	66	18	)	)	PUNCT
ejpam-146	66	19	,	,	PUNCT
ejpam-146	66	20	there	there	PRON
ejpam-146	66	21	is	be	VERB
ejpam-146	66	22	an	an	DET
ejpam-146	66	23	f	f	PROPN
ejpam-146	66	24	∈	∈	PROPN
ejpam-146	66	25	f	f	PROPN
ejpam-146	66	26	such	such	ADJ
ejpam-146	66	27	that	that	SCONJ
ejpam-146	66	28	f	f	PROPN
ejpam-146	66	29	⊂	⊂	X
ejpam-146	66	30	β	β	X
ejpam-146	66	31	cl(v	cl(v	NOUN
ejpam-146	66	32	)	)	PUNCT
ejpam-146	66	33	.	.	PUNCT
ejpam-146	67	1	the	the	DET
ejpam-146	67	2	corresponding	corresponding	ADJ
ejpam-146	67	3	definitions	definition	NOUN
ejpam-146	67	4	of	of	ADP
ejpam-146	67	5	nets	net	NOUN
ejpam-146	67	6	are	be	AUX
ejpam-146	67	7	obvious	obvious	ADJ
ejpam-146	67	8	.	.	PUNCT
ejpam-146	68	1	2	2	X
ejpam-146	68	2	.	.	X
ejpam-146	68	3	prerequisites	prerequisite	VERB
ejpam-146	68	4	the	the	DET
ejpam-146	68	5	following	follow	VERB
ejpam-146	68	6	definitions	definition	NOUN
ejpam-146	68	7	and	and	CCONJ
ejpam-146	68	8	results	result	NOUN
ejpam-146	68	9	which	which	PRON
ejpam-146	68	10	already	already	ADV
ejpam-146	68	11	have	have	AUX
ejpam-146	68	12	been	be	AUX
ejpam-146	68	13	found	find	VERB
ejpam-146	68	14	in	in	ADP
ejpam-146	68	15	literature	literature	NOUN
ejpam-146	68	16	[	[	X
ejpam-146	68	17	16	16	NUM
ejpam-146	68	18	]	]	PUNCT
ejpam-146	68	19	in	in	ADP
ejpam-146	68	20	the	the	DET
ejpam-146	68	21	language	language	NOUN
ejpam-146	68	22	of	of	ADP
ejpam-146	68	23	semipre	semipre	NOUN
ejpam-146	68	24	-	-	PUNCT
ejpam-146	68	25	open	open	ADJ
ejpam-146	68	26	sets	set	NOUN
ejpam-146	68	27	are	be	AUX
ejpam-146	68	28	being	be	AUX
ejpam-146	68	29	restated	restate	VERB
ejpam-146	68	30	in	in	ADP
ejpam-146	68	31	the	the	DET
ejpam-146	68	32	language	language	NOUN
ejpam-146	68	33	of	of	ADP
ejpam-146	68	34	β	β	ADJ
ejpam-146	68	35	-	-	ADJ
ejpam-146	68	36	open	open	ADJ
ejpam-146	68	37	sets	set	NOUN
ejpam-146	68	38	which	which	PRON
ejpam-146	68	39	will	will	AUX
ejpam-146	68	40	be	be	AUX
ejpam-146	68	41	frequently	frequently	ADV
ejpam-146	68	42	used	use	VERB
ejpam-146	68	43	in	in	ADP
ejpam-146	68	44	the	the	DET
ejpam-146	68	45	subsequent	subsequent	ADJ
ejpam-146	68	46	sections	section	NOUN
ejpam-146	68	47	.	.	PUNCT
ejpam-146	69	1	definition	definition	NOUN
ejpam-146	69	2	2.1	2.1	NUM
ejpam-146	69	3	.	.	PUNCT
ejpam-146	70	1	a	a	DET
ejpam-146	70	2	subset	subset	NOUN
ejpam-146	70	3	s	s	NOUN
ejpam-146	70	4	of	of	ADP
ejpam-146	70	5	a	a	DET
ejpam-146	70	6	space	space	NOUN
ejpam-146	70	7	(	(	PUNCT
ejpam-146	70	8	x	x	X
ejpam-146	70	9	,	,	PUNCT
ejpam-146	70	10	τ	τ	X
ejpam-146	70	11	)	)	PUNCT
ejpam-146	70	12	is	be	AUX
ejpam-146	70	13	said	say	VERB
ejpam-146	70	14	to	to	PART
ejpam-146	70	15	be	be	AUX
ejpam-146	70	16	β	β	X
ejpam-146	70	17	-	-	ADJ
ejpam-146	70	18	regular	regular	ADJ
ejpam-146	70	19	(=	(=	NOUN
ejpam-146	70	20	semipre	semipre	NOUN
ejpam-146	70	21	-	-	PUNCT
ejpam-146	70	22	regular	regular	ADJ
ejpam-146	71	1	[	[	X
ejpam-146	71	2	16	16	NUM
ejpam-146	71	3	]	]	SYM
ejpam-146	71	4	)	)	PUNCT
ejpam-146	71	5	if	if	SCONJ
ejpam-146	71	6	it	it	PRON
ejpam-146	71	7	is	be	AUX
ejpam-146	71	8	both	both	PRON
ejpam-146	71	9	β	β	NOUN
ejpam-146	71	10	-	-	VERB
ejpam-146	71	11	open	open	ADJ
ejpam-146	71	12	as	as	ADV
ejpam-146	71	13	well	well	ADV
ejpam-146	71	14	as	as	ADP
ejpam-146	71	15	β	β	NOUN
ejpam-146	71	16	-	-	VERB
ejpam-146	71	17	closed	closed	ADJ
ejpam-146	71	18	.	.	PUNCT
ejpam-146	72	1	the	the	DET
ejpam-146	72	2	family	family	NOUN
ejpam-146	72	3	of	of	ADP
ejpam-146	72	4	all	all	DET
ejpam-146	72	5	β	β	ADJ
ejpam-146	72	6	-	-	ADJ
ejpam-146	72	7	regular	regular	ADJ
ejpam-146	72	8	sets	set	NOUN
ejpam-146	72	9	of	of	ADP
ejpam-146	72	10	a	a	DET
ejpam-146	72	11	space	space	NOUN
ejpam-146	72	12	x	x	PUNCT
ejpam-146	72	13	and	and	CCONJ
ejpam-146	72	14	that	that	SCONJ
ejpam-146	72	15	containing	contain	VERB
ejpam-146	72	16	a	a	DET
ejpam-146	72	17	point	point	NOUN
ejpam-146	72	18	x	x	PUNCT
ejpam-146	72	19	of	of	ADP
ejpam-146	72	20	x	x	PRON
ejpam-146	72	21	are	be	AUX
ejpam-146	72	22	respectively	respectively	ADV
ejpam-146	72	23	denoted	denote	VERB
ejpam-146	72	24	by	by	ADP
ejpam-146	72	25	βr(x	βr(x	PUNCT
ejpam-146	72	26	)	)	PUNCT
ejpam-146	72	27	and	and	CCONJ
ejpam-146	72	28	βr(x	βr(x	NUM
ejpam-146	72	29	,	,	PUNCT
ejpam-146	72	30	x	x	X
ejpam-146	72	31	)	)	PUNCT
ejpam-146	72	32	.	.	PUNCT
ejpam-146	73	1	lemma	lemma	PROPN
ejpam-146	73	2	2.2	2.2	NUM
ejpam-146	74	1	[	[	X
ejpam-146	74	2	16	16	NUM
ejpam-146	74	3	]	]	PUNCT
ejpam-146	74	4	.	.	PUNCT
ejpam-146	75	1	for	for	ADP
ejpam-146	75	2	a	a	DET
ejpam-146	75	3	subset	subset	NOUN
ejpam-146	75	4	a	a	PRON
ejpam-146	75	5	of	of	ADP
ejpam-146	75	6	a	a	DET
ejpam-146	75	7	space	space	NOUN
ejpam-146	75	8	x	x	SYM
ejpam-146	75	9	,	,	PUNCT
ejpam-146	75	10	a∈	a∈	PROPN
ejpam-146	75	11	βo(x	βo(x	PUNCT
ejpam-146	75	12	)	)	PUNCT
ejpam-146	76	1	if	if	SCONJ
ejpam-146	76	2	and	and	CCONJ
ejpam-146	76	3	only	only	ADV
ejpam-146	76	4	if	if	SCONJ
ejpam-146	76	5	β	β	X
ejpam-146	76	6	cl(a	cl(a	X
ejpam-146	76	7	)	)	PUNCT
ejpam-146	76	8	∈	∈	PROPN
ejpam-146	76	9	βr(x	βr(x	PUNCT
ejpam-146	76	10	)	)	PUNCT
ejpam-146	76	11	.	.	PUNCT
ejpam-146	77	1	definition	definition	NOUN
ejpam-146	77	2	2.3	2.3	NUM
ejpam-146	77	3	.	.	PUNCT
ejpam-146	78	1	a	a	DET
ejpam-146	78	2	point	point	NOUN
ejpam-146	78	3	x	x	X
ejpam-146	78	4	∈	∈	NOUN
ejpam-146	78	5	x	x	PUNCT
ejpam-146	78	6	is	be	AUX
ejpam-146	78	7	said	say	VERB
ejpam-146	78	8	to	to	PART
ejpam-146	78	9	be	be	AUX
ejpam-146	78	10	in	in	ADP
ejpam-146	78	11	the	the	DET
ejpam-146	78	12	β	β	NOUN
ejpam-146	78	13	-	-	ADJ
ejpam-146	78	14	θ	θ	NOUN
ejpam-146	78	15	-closure	-closure	NOUN
ejpam-146	78	16	(=	(=	NOUN
ejpam-146	78	17	sp	sp	NOUN
ejpam-146	78	18	-	-	PUNCT
ejpam-146	78	19	θ	θ	NOUN
ejpam-146	78	20	-closure	-closure	NOUN
ejpam-146	79	1	[	[	X
ejpam-146	79	2	16	16	NUM
ejpam-146	79	3	]	]	PUNCT
ejpam-146	79	4	)	)	PUNCT
ejpam-146	79	5	of	of	ADP
ejpam-146	79	6	a	a	PRON
ejpam-146	79	7	,	,	PUNCT
ejpam-146	79	8	denoted	denote	VERB
ejpam-146	79	9	by	by	ADP
ejpam-146	79	10	β	β	NOUN
ejpam-146	79	11	-	-	NOUN
ejpam-146	79	12	θ	θ	NOUN
ejpam-146	79	13	-cl(a	-cl(a	NUM
ejpam-146	79	14	)	)	PUNCT
ejpam-146	79	15	,	,	PUNCT
ejpam-146	79	16	if	if	SCONJ
ejpam-146	79	17	a∩	a∩	PROPN
ejpam-146	79	18	β	β	X
ejpam-146	79	19	cl(v	cl(v	NOUN
ejpam-146	79	20	)	)	PUNCT
ejpam-146	79	21	6=	6=	NUM
ejpam-146	79	22	;	;	PUNCT
ejpam-146	79	23	for	for	ADP
ejpam-146	79	24	every	every	DET
ejpam-146	79	25	v	v	NOUN
ejpam-146	79	26	∈	∈	NOUN
ejpam-146	79	27	βo(x	βo(x	NUM
ejpam-146	79	28	,	,	PUNCT
ejpam-146	79	29	x	x	X
ejpam-146	79	30	)	)	PUNCT
ejpam-146	79	31	.	.	PUNCT
ejpam-146	80	1	if	if	SCONJ
ejpam-146	80	2	β	β	X
ejpam-146	80	3	-	-	NOUN
ejpam-146	80	4	θ	θ	NOUN
ejpam-146	80	5	-cl(a	-cl(a	NOUN
ejpam-146	80	6	)	)	PUNCT
ejpam-146	80	7	=	=	SYM
ejpam-146	80	8	a	a	PRON
ejpam-146	80	9	,	,	PUNCT
ejpam-146	80	10	then	then	ADV
ejpam-146	80	11	a	a	PRON
ejpam-146	80	12	is	be	AUX
ejpam-146	80	13	said	say	VERB
ejpam-146	80	14	to	to	PART
ejpam-146	80	15	be	be	AUX
ejpam-146	80	16	β	β	NOUN
ejpam-146	80	17	-	-	NOUN
ejpam-146	80	18	θ	θ	NOUN
ejpam-146	80	19	-closed	-close	VERB
ejpam-146	80	20	(=	(=	ADJ
ejpam-146	80	21	sp	sp	NOUN
ejpam-146	80	22	-	-	PUNCT
ejpam-146	80	23	θ	θ	NOUN
ejpam-146	80	24	-closed	-close	VERB
ejpam-146	80	25	[	[	X
ejpam-146	80	26	16	16	NUM
ejpam-146	80	27	]	]	PUNCT
ejpam-146	80	28	)	)	PUNCT
ejpam-146	80	29	.	.	PUNCT
ejpam-146	81	1	the	the	DET
ejpam-146	81	2	complement	complement	NOUN
ejpam-146	81	3	of	of	ADP
ejpam-146	81	4	a	a	DET
ejpam-146	81	5	β	β	NOUN
ejpam-146	81	6	-	-	PUNCT
ejpam-146	81	7	θ	θ	NOUN
ejpam-146	81	8	-closed	-close	VERB
ejpam-146	81	9	set	set	NOUN
ejpam-146	81	10	is	be	AUX
ejpam-146	81	11	said	say	VERB
ejpam-146	81	12	to	to	PART
ejpam-146	81	13	be	be	AUX
ejpam-146	81	14	c.	c.	PROPN
ejpam-146	81	15	k.	k.	PROPN
ejpam-146	81	16	basu	basu	PROPN
ejpam-146	81	17	,	,	PUNCT
ejpam-146	81	18	m.	m.	PROPN
ejpam-146	81	19	k.	k.	PROPN
ejpam-146	81	20	ghosh	ghosh	PROPN
ejpam-146	81	21	/	/	PUNCT
ejpam-146	81	22	eur	eur	PROPN
ejpam-146	81	23	.	.	PUNCT
ejpam-146	82	1	j.	j.	PROPN
ejpam-146	82	2	pure	pure	PROPN
ejpam-146	82	3	appl	appl	PROPN
ejpam-146	82	4	.	.	PROPN
ejpam-146	82	5	math	math	PROPN
ejpam-146	82	6	,	,	PUNCT
ejpam-146	82	7	1	1	NUM
ejpam-146	82	8	(	(	PUNCT
ejpam-146	82	9	2008	2008	NUM
ejpam-146	82	10	)	)	PUNCT
ejpam-146	82	11	,	,	PUNCT
ejpam-146	82	12	(	(	PUNCT
ejpam-146	82	13	40	40	NUM
ejpam-146	82	14	-	-	SYM
ejpam-146	82	15	50	50	NUM
ejpam-146	82	16	)	)	PUNCT
ejpam-146	82	17	42	42	NUM
ejpam-146	82	18	β	β	NOUN
ejpam-146	82	19	-	-	PUNCT
ejpam-146	82	20	θ	θ	NOUN
ejpam-146	82	21	-open	-open	NOUN
ejpam-146	82	22	(=	(=	NOUN
ejpam-146	82	23	sp	sp	NOUN
ejpam-146	82	24	-	-	PUNCT
ejpam-146	82	25	θ	θ	NOUN
ejpam-146	82	26	-open	-open	NOUN
ejpam-146	83	1	[	[	X
ejpam-146	83	2	16	16	NUM
ejpam-146	83	3	]	]	PUNCT
ejpam-146	83	4	)	)	PUNCT
ejpam-146	83	5	.	.	PUNCT
ejpam-146	84	1	lemma	lemma	PROPN
ejpam-146	85	1	2.4	2.4	NUM
ejpam-146	86	1	[	[	SYM
ejpam-146	86	2	16	16	NUM
ejpam-146	86	3	]	]	PUNCT
ejpam-146	86	4	.	.	PUNCT
ejpam-146	87	1	for	for	ADP
ejpam-146	87	2	a	a	DET
ejpam-146	87	3	subset	subset	NOUN
ejpam-146	87	4	a	a	PRON
ejpam-146	87	5	of	of	ADP
ejpam-146	87	6	a	a	DET
ejpam-146	87	7	space	space	NOUN
ejpam-146	87	8	x	x	SYM
ejpam-146	87	9	,	,	PUNCT
ejpam-146	87	10	β	β	X
ejpam-146	87	11	-	-	NOUN
ejpam-146	87	12	θ	θ	NOUN
ejpam-146	87	13	-cl(a	-cl(a	NOUN
ejpam-146	87	14	)	)	PUNCT
ejpam-146	87	15	=	=	SYM
ejpam-146	87	16	∩{r	∩{r	NOUN
ejpam-146	87	17	:	:	PUNCT
ejpam-146	87	18	a⊂	a⊂	X
ejpam-146	87	19	r	r	NOUN
ejpam-146	87	20	and	and	CCONJ
ejpam-146	87	21	r	r	NOUN
ejpam-146	87	22	∈	∈	PROPN
ejpam-146	87	23	βr(x	βr(x	PUNCT
ejpam-146	87	24	)	)	PUNCT
ejpam-146	87	25	}	}	PUNCT
ejpam-146	87	26	.	.	PUNCT
ejpam-146	88	1	lemma	lemma	PROPN
ejpam-146	88	2	2.5	2.5	NUM
ejpam-146	89	1	[	[	X
ejpam-146	89	2	16	16	NUM
ejpam-146	89	3	]	]	PUNCT
ejpam-146	89	4	.	.	PUNCT
ejpam-146	90	1	let	let	VERB
ejpam-146	90	2	a	a	PRON
ejpam-146	90	3	and	and	CCONJ
ejpam-146	90	4	b	b	NOUN
ejpam-146	90	5	be	be	AUX
ejpam-146	90	6	any	any	DET
ejpam-146	90	7	subsets	subset	NOUN
ejpam-146	90	8	of	of	ADP
ejpam-146	90	9	a	a	DET
ejpam-146	90	10	space	space	NOUN
ejpam-146	90	11	x	x	X
ejpam-146	90	12	.	.	PUNCT
ejpam-146	91	1	then	then	ADV
ejpam-146	91	2	the	the	DET
ejpam-146	91	3	following	follow	VERB
ejpam-146	91	4	properties	property	NOUN
ejpam-146	91	5	hold	hold	VERB
ejpam-146	91	6	:	:	PUNCT
ejpam-146	91	7	(	(	PUNCT
ejpam-146	91	8	i	i	NOUN
ejpam-146	91	9	)	)	PUNCT
ejpam-146	91	10	x	x	SYM
ejpam-146	92	1	∈	∈	PROPN
ejpam-146	92	2	β	β	PROPN
ejpam-146	92	3	-	-	PUNCT
ejpam-146	92	4	θ	θ	NOUN
ejpam-146	92	5	-cl(a	-cl(a	NOUN
ejpam-146	92	6	)	)	PUNCT
ejpam-146	92	7	if	if	SCONJ
ejpam-146	92	8	and	and	CCONJ
ejpam-146	92	9	only	only	ADV
ejpam-146	92	10	if	if	SCONJ
ejpam-146	92	11	a∩	a∩	PROPN
ejpam-146	92	12	v	v	ADP
ejpam-146	92	13	6=	6=	NUM
ejpam-146	92	14	;	;	PUNCT
ejpam-146	92	15	for	for	ADP
ejpam-146	92	16	each	each	DET
ejpam-146	92	17	v	v	X
ejpam-146	92	18	∈	∈	PROPN
ejpam-146	92	19	βr(x	βr(x	PUNCT
ejpam-146	92	20	,	,	PUNCT
ejpam-146	92	21	x	x	X
ejpam-146	92	22	)	)	PUNCT
ejpam-146	92	23	.	.	PUNCT
ejpam-146	93	1	(	(	PUNCT
ejpam-146	93	2	ii	ii	NOUN
ejpam-146	93	3	)	)	PUNCT
ejpam-146	93	4	if	if	SCONJ
ejpam-146	93	5	a⊂	a⊂	PRON
ejpam-146	93	6	b	b	NOUN
ejpam-146	93	7	then	then	ADV
ejpam-146	93	8	β	β	X
ejpam-146	93	9	-	-	PUNCT
ejpam-146	93	10	θ	θ	NOUN
ejpam-146	93	11	-cl(a)⊂	-cl(a)⊂	SYM
ejpam-146	93	12	β	β	X
ejpam-146	93	13	-	-	NOUN
ejpam-146	93	14	θ	θ	NOUN
ejpam-146	93	15	-cl(b	-cl(b	NOUN
ejpam-146	93	16	)	)	PUNCT
ejpam-146	93	17	.	.	PUNCT
ejpam-146	94	1	(	(	PUNCT
ejpam-146	94	2	iii	iii	NOUN
ejpam-146	94	3	)	)	PUNCT
ejpam-146	94	4	β	β	NOUN
ejpam-146	94	5	-	-	PUNCT
ejpam-146	94	6	θ	θ	NOUN
ejpam-146	94	7	-cl(β	-cl(β	PROPN
ejpam-146	94	8	-	-	PUNCT
ejpam-146	94	9	θ	θ	NOUN
ejpam-146	94	10	-cl(a	-cl(a	NUM
ejpam-146	94	11	)	)	PUNCT
ejpam-146	94	12	)	)	PUNCT
ejpam-146	95	1	=	=	PUNCT
ejpam-146	95	2	β	β	X
ejpam-146	95	3	-	-	NOUN
ejpam-146	95	4	θ	θ	NOUN
ejpam-146	95	5	-cl(a	-cl(a	NUM
ejpam-146	95	6	)	)	PUNCT
ejpam-146	95	7	.	.	PUNCT
ejpam-146	96	1	(	(	PUNCT
ejpam-146	96	2	iv	iv	X
ejpam-146	96	3	)	)	PUNCT
ejpam-146	96	4	intersection	intersection	NOUN
ejpam-146	96	5	of	of	ADP
ejpam-146	96	6	an	an	DET
ejpam-146	96	7	arbitrary	arbitrary	ADJ
ejpam-146	96	8	family	family	NOUN
ejpam-146	96	9	of	of	ADP
ejpam-146	96	10	β	β	PROPN
ejpam-146	96	11	-	-	PUNCT
ejpam-146	96	12	θ	θ	NOUN
ejpam-146	96	13	-closed	-close	VERB
ejpam-146	96	14	sets	set	NOUN
ejpam-146	96	15	in	in	ADP
ejpam-146	96	16	x	x	VERB
ejpam-146	96	17	is	be	AUX
ejpam-146	96	18	β	β	X
ejpam-146	96	19	-	-	NOUN
ejpam-146	96	20	θ	θ	NOUN
ejpam-146	96	21	-closed	-close	VERB
ejpam-146	96	22	in	in	ADP
ejpam-146	96	23	x	x	X
ejpam-146	96	24	.	.	PUNCT
ejpam-146	97	1	(	(	PUNCT
ejpam-146	97	2	v	v	NOUN
ejpam-146	97	3	)	)	PUNCT
ejpam-146	97	4	a	a	PRON
ejpam-146	97	5	is	be	AUX
ejpam-146	97	6	β	β	NOUN
ejpam-146	97	7	-	-	ADJ
ejpam-146	97	8	θ	θ	NOUN
ejpam-146	97	9	-open	-open	NOUN
ejpam-146	97	10	if	if	SCONJ
ejpam-146	97	11	and	and	CCONJ
ejpam-146	97	12	only	only	ADV
ejpam-146	97	13	if	if	SCONJ
ejpam-146	97	14	for	for	ADP
ejpam-146	97	15	each	each	DET
ejpam-146	97	16	x	x	SYM
ejpam-146	97	17	∈	∈	PROPN
ejpam-146	97	18	a	a	PRON
ejpam-146	97	19	,	,	PUNCT
ejpam-146	97	20	there	there	PRON
ejpam-146	97	21	exists	exist	VERB
ejpam-146	97	22	v	v	ADP
ejpam-146	97	23	∈	∈	PROPN
ejpam-146	97	24	βr(x	βr(x	PUNCT
ejpam-146	97	25	,	,	PUNCT
ejpam-146	97	26	x	x	X
ejpam-146	97	27	)	)	PUNCT
ejpam-146	97	28	such	such	ADJ
ejpam-146	97	29	that	that	SCONJ
ejpam-146	97	30	x	x	SYM
ejpam-146	97	31	∈	∈	PROPN
ejpam-146	97	32	v	v	ADP
ejpam-146	97	33	⊂	⊂	PROPN
ejpam-146	97	34	a.	a.	NOUN
ejpam-146	97	35	(	(	PUNCT
ejpam-146	97	36	vi	vi	NOUN
ejpam-146	97	37	)	)	PUNCT
ejpam-146	97	38	if	if	SCONJ
ejpam-146	97	39	a∈	a∈	PROPN
ejpam-146	97	40	βo(x	βo(x	PUNCT
ejpam-146	97	41	)	)	PUNCT
ejpam-146	97	42	then	then	ADV
ejpam-146	97	43	β	β	X
ejpam-146	97	44	cl(a	cl(a	X
ejpam-146	97	45	)	)	PUNCT
ejpam-146	97	46	=	=	SYM
ejpam-146	97	47	β	β	X
ejpam-146	97	48	-	-	NOUN
ejpam-146	97	49	θ	θ	NOUN
ejpam-146	97	50	-cl(a	-cl(a	NUM
ejpam-146	97	51	)	)	PUNCT
ejpam-146	97	52	.	.	PUNCT
ejpam-146	98	1	(	(	PUNCT
ejpam-146	98	2	vii	vii	PROPN
ejpam-146	98	3	)	)	PUNCT
ejpam-146	98	4	if	if	SCONJ
ejpam-146	98	5	a∈	a∈	PROPN
ejpam-146	98	6	βr(x	βr(x	NUM
ejpam-146	98	7	)	)	PUNCT
ejpam-146	98	8	then	then	ADV
ejpam-146	98	9	a	a	PRON
ejpam-146	98	10	is	be	AUX
ejpam-146	98	11	β	β	X
ejpam-146	98	12	-	-	PUNCT
ejpam-146	98	13	θ	θ	NOUN
ejpam-146	98	14	-closed	-close	VERB
ejpam-146	98	15	.	.	PUNCT
ejpam-146	99	1	remark	remark	NOUN
ejpam-146	99	2	2.6	2.6	NUM
ejpam-146	100	1	[	[	X
ejpam-146	100	2	16	16	NUM
ejpam-146	100	3	]	]	PUNCT
ejpam-146	100	4	.	.	PUNCT
ejpam-146	101	1	t.	t.	PROPN
ejpam-146	101	2	noiri	noiri	PROPN
ejpam-146	102	1	[	[	X
ejpam-146	102	2	16	16	NUM
ejpam-146	102	3	]	]	PUNCT
ejpam-146	102	4	has	have	AUX
ejpam-146	102	5	shown	show	VERB
ejpam-146	102	6	that	that	SCONJ
ejpam-146	102	7	β	β	NOUN
ejpam-146	102	8	-	-	ADJ
ejpam-146	102	9	regular	regular	ADJ
ejpam-146	102	10	⇒	⇒	NOUN
ejpam-146	102	11	β	β	X
ejpam-146	102	12	-	-	ADJ
ejpam-146	102	13	θ	θ	NOUN
ejpam-146	102	14	-open	-open	NOUN
ejpam-146	102	15	⇒	⇒	NOUN
ejpam-146	102	16	β	β	X
ejpam-146	102	17	-	-	VERB
ejpam-146	102	18	open	open	ADJ
ejpam-146	102	19	.	.	PUNCT
ejpam-146	103	1	but	but	CCONJ
ejpam-146	103	2	the	the	DET
ejpam-146	103	3	converses	converse	NOUN
ejpam-146	103	4	are	be	AUX
ejpam-146	103	5	not	not	PART
ejpam-146	103	6	necessarily	necessarily	ADV
ejpam-146	103	7	true	true	ADJ
ejpam-146	103	8	.	.	PUNCT
ejpam-146	104	1	3	3	X
ejpam-146	104	2	.	.	X
ejpam-146	104	3	β	β	X
ejpam-146	104	4	-	-	PUNCT
ejpam-146	104	5	closed	closed	ADJ
ejpam-146	104	6	spaces	space	NOUN
ejpam-146	104	7	definition	definition	NOUN
ejpam-146	104	8	3.1	3.1	NUM
ejpam-146	104	9	.	.	PUNCT
ejpam-146	105	1	a	a	DET
ejpam-146	105	2	space	space	NOUN
ejpam-146	105	3	x	x	PUNCT
ejpam-146	105	4	is	be	AUX
ejpam-146	105	5	said	say	VERB
ejpam-146	105	6	to	to	PART
ejpam-146	105	7	be	be	AUX
ejpam-146	105	8	β	β	X
ejpam-146	105	9	-	-	VERB
ejpam-146	105	10	closed	closed	ADJ
ejpam-146	105	11	[	[	X
ejpam-146	105	12	2	2	NUM
ejpam-146	105	13	]	]	PUNCT
ejpam-146	105	14	if	if	SCONJ
ejpam-146	105	15	every	every	DET
ejpam-146	105	16	cover	cover	NOUN
ejpam-146	105	17	of	of	ADP
ejpam-146	105	18	x	x	PUNCT
ejpam-146	105	19	by	by	ADP
ejpam-146	105	20	β	β	ADJ
ejpam-146	105	21	-	-	ADJ
ejpam-146	105	22	open	open	ADJ
ejpam-146	105	23	sets	set	NOUN
ejpam-146	105	24	has	have	VERB
ejpam-146	105	25	a	a	DET
ejpam-146	105	26	finite	finite	NOUN
ejpam-146	105	27	subfamily	subfamily	ADV
ejpam-146	105	28	whose	whose	DET
ejpam-146	105	29	β	β	NOUN
ejpam-146	105	30	-	-	NOUN
ejpam-146	105	31	closures	closure	NOUN
ejpam-146	105	32	cover	cover	VERB
ejpam-146	105	33	x	x	X
ejpam-146	105	34	.	.	PUNCT
ejpam-146	106	1	the	the	DET
ejpam-146	106	2	following	follow	VERB
ejpam-146	106	3	characterizations	characterization	NOUN
ejpam-146	106	4	of	of	ADP
ejpam-146	106	5	β	β	NOUN
ejpam-146	106	6	-	-	ADJ
ejpam-146	106	7	closed	closed	ADJ
ejpam-146	106	8	spaces	space	NOUN
ejpam-146	106	9	are	be	AUX
ejpam-146	106	10	quite	quite	ADV
ejpam-146	106	11	obvious	obvious	ADJ
ejpam-146	106	12	.	.	PUNCT
ejpam-146	107	1	theorem	theorem	VERB
ejpam-146	107	2	3.2	3.2	NUM
ejpam-146	107	3	.	.	PUNCT
ejpam-146	108	1	for	for	ADP
ejpam-146	108	2	a	a	DET
ejpam-146	108	3	space	space	NOUN
ejpam-146	108	4	x	x	SYM
ejpam-146	108	5	,	,	PUNCT
ejpam-146	108	6	the	the	DET
ejpam-146	108	7	following	follow	VERB
ejpam-146	108	8	are	be	AUX
ejpam-146	108	9	equivalent	equivalent	ADJ
ejpam-146	108	10	:	:	PUNCT
ejpam-146	108	11	(	(	PUNCT
ejpam-146	108	12	a	a	X
ejpam-146	108	13	)	)	PUNCT
ejpam-146	108	14	x	x	X
ejpam-146	108	15	is	be	AUX
ejpam-146	108	16	β	β	NOUN
ejpam-146	108	17	-	-	VERB
ejpam-146	108	18	closed	closed	ADJ
ejpam-146	108	19	.	.	PUNCT
ejpam-146	109	1	(	(	PUNCT
ejpam-146	109	2	b	b	X
ejpam-146	109	3	)	)	PUNCT
ejpam-146	109	4	every	every	DET
ejpam-146	109	5	cover	cover	NOUN
ejpam-146	109	6	of	of	ADP
ejpam-146	109	7	x	x	PUNCT
ejpam-146	109	8	by	by	ADP
ejpam-146	109	9	β	β	ADJ
ejpam-146	109	10	-	-	ADJ
ejpam-146	109	11	regular	regular	ADJ
ejpam-146	109	12	sets	set	NOUN
ejpam-146	109	13	has	have	VERB
ejpam-146	109	14	a	a	DET
ejpam-146	109	15	finite	finite	ADJ
ejpam-146	109	16	subcover	subcover	PROPN
ejpam-146	109	17	.	.	PUNCT
ejpam-146	110	1	(	(	PUNCT
ejpam-146	110	2	c	c	X
ejpam-146	110	3	)	)	PUNCT
ejpam-146	110	4	for	for	ADP
ejpam-146	110	5	every	every	DET
ejpam-146	110	6	family	family	NOUN
ejpam-146	110	7	{	{	PUNCT
ejpam-146	110	8	uα	uα	PROPN
ejpam-146	110	9	∈	∈	PROPN
ejpam-146	110	10	βr(x	βr(x	PUNCT
ejpam-146	110	11	)	)	PUNCT
ejpam-146	110	12	:	:	PUNCT
ejpam-146	111	1	α	α	X
ejpam-146	111	2	∈	∈	PROPN
ejpam-146	112	1	i	i	X
ejpam-146	112	2	}	}	PUNCT
ejpam-146	112	3	such	such	ADJ
ejpam-146	112	4	that	that	SCONJ
ejpam-146	112	5	∩{uα	∩{uα	NOUN
ejpam-146	112	6	:	:	PUNCT
ejpam-146	112	7	α	α	X
ejpam-146	112	8	∈	∈	PROPN
ejpam-146	113	1	i	i	X
ejpam-146	113	2	}	}	PUNCT
ejpam-146	113	3	=	=	SYM
ejpam-146	113	4	;	;	PUNCT
ejpam-146	113	5	,	,	PUNCT
ejpam-146	113	6	there	there	PRON
ejpam-146	113	7	exists	exist	VERB
ejpam-146	113	8	a	a	DET
ejpam-146	113	9	finite	finite	NOUN
ejpam-146	113	10	subset	subset	VERB
ejpam-146	113	11	i0	i0	PROPN
ejpam-146	113	12	of	of	ADP
ejpam-146	113	13	i	i	PRON
ejpam-146	113	14	such	such	ADJ
ejpam-146	113	15	that	that	SCONJ
ejpam-146	113	16	∩{uα	∩{uα	NOUN
ejpam-146	113	17	:	:	PUNCT
ejpam-146	113	18	α	α	PROPN
ejpam-146	113	19	∈	∈	PROPN
ejpam-146	113	20	i0}=	i0}=	NOUN
ejpam-146	113	21	;	;	PUNCT
ejpam-146	113	22	.	.	PUNCT
ejpam-146	114	1	(	(	PUNCT
ejpam-146	114	2	d	d	X
ejpam-146	114	3	)	)	PUNCT
ejpam-146	114	4	every	every	DET
ejpam-146	114	5	cover	cover	NOUN
ejpam-146	114	6	of	of	ADP
ejpam-146	114	7	x	x	PUNCT
ejpam-146	114	8	by	by	ADP
ejpam-146	114	9	β	β	NOUN
ejpam-146	114	10	-	-	ADJ
ejpam-146	114	11	θ	θ	NOUN
ejpam-146	114	12	-open	-open	NOUN
ejpam-146	114	13	sets	set	NOUN
ejpam-146	114	14	has	have	VERB
ejpam-146	114	15	a	a	DET
ejpam-146	114	16	finite	finite	ADJ
ejpam-146	114	17	subcover	subcover	PROPN
ejpam-146	114	18	.	.	PUNCT
ejpam-146	115	1	definition	definition	NOUN
ejpam-146	115	2	3.3	3.3	NUM
ejpam-146	115	3	.	.	PUNCT
ejpam-146	116	1	a	a	DET
ejpam-146	116	2	point	point	NOUN
ejpam-146	116	3	x	x	X
ejpam-146	116	4	in	in	ADP
ejpam-146	116	5	a	a	DET
ejpam-146	116	6	space	space	NOUN
ejpam-146	116	7	x	x	PUNCT
ejpam-146	116	8	is	be	AUX
ejpam-146	116	9	called	call	VERB
ejpam-146	116	10	a	a	DET
ejpam-146	116	11	β	β	NOUN
ejpam-146	116	12	-	-	ADJ
ejpam-146	116	13	θ	θ	NOUN
ejpam-146	116	14	-complete	-complete	ADJ
ejpam-146	116	15	accumulation	accumulation	NOUN
ejpam-146	116	16	point	point	NOUN
ejpam-146	116	17	(	(	PUNCT
ejpam-146	116	18	β	β	NOUN
ejpam-146	116	19	-	-	ADJ
ejpam-146	116	20	θ	θ	ADJ
ejpam-146	116	21	c.a.p	c.a.p	NOUN
ejpam-146	116	22	.	.	PUNCT
ejpam-146	116	23	,	,	PUNCT
ejpam-146	116	24	for	for	ADP
ejpam-146	116	25	short	short	ADJ
ejpam-146	116	26	)	)	PUNCT
ejpam-146	116	27	of	of	ADP
ejpam-146	116	28	a	a	DET
ejpam-146	116	29	subset	subset	NOUN
ejpam-146	116	30	s	s	NOUN
ejpam-146	116	31	of	of	ADP
ejpam-146	116	32	x	x	SYM
ejpam-146	116	33	if	if	SCONJ
ejpam-146	116	34	|s|	|s|	PROPN
ejpam-146	116	35	=	=	SYM
ejpam-146	116	36	|s	|s	PROPN
ejpam-146	116	37	∩	∩	NOUN
ejpam-146	116	38	v	v	ADP
ejpam-146	116	39	|	|	ADV
ejpam-146	116	40	for	for	ADP
ejpam-146	116	41	each	each	DET
ejpam-146	116	42	v	v	X
ejpam-146	116	43	∈	∈	PROPN
ejpam-146	116	44	βr(x	βr(x	PUNCT
ejpam-146	116	45	,	,	PUNCT
ejpam-146	116	46	x	x	X
ejpam-146	116	47	)	)	PUNCT
ejpam-146	116	48	,	,	PUNCT
ejpam-146	116	49	where	where	SCONJ
ejpam-146	116	50	|s|	|s|	PROPN
ejpam-146	116	51	denotes	denote	VERB
ejpam-146	116	52	the	the	DET
ejpam-146	116	53	cardinality	cardinality	NOUN
ejpam-146	116	54	of	of	ADP
ejpam-146	116	55	the	the	DET
ejpam-146	116	56	subset	subset	PROPN
ejpam-146	116	57	s.	s.	PROPN
ejpam-146	116	58	theorem	theorem	VERB
ejpam-146	116	59	3.4	3.4	NUM
ejpam-146	116	60	.	.	PUNCT
ejpam-146	117	1	the	the	DET
ejpam-146	117	2	following	follow	VERB
ejpam-146	117	3	are	be	AUX
ejpam-146	117	4	equivalent	equivalent	ADJ
ejpam-146	117	5	for	for	ADP
ejpam-146	117	6	a	a	DET
ejpam-146	117	7	space	space	NOUN
ejpam-146	117	8	x	x	X
ejpam-146	117	9	(	(	PUNCT
ejpam-146	117	10	a	a	NOUN
ejpam-146	117	11	)	)	PUNCT
ejpam-146	117	12	x	x	X
ejpam-146	117	13	is	be	AUX
ejpam-146	117	14	β	β	NOUN
ejpam-146	117	15	-	-	VERB
ejpam-146	117	16	closed	closed	ADJ
ejpam-146	117	17	.	.	PUNCT
ejpam-146	118	1	(	(	PUNCT
ejpam-146	118	2	b	b	X
ejpam-146	118	3	)	)	PUNCT
ejpam-146	118	4	every	every	DET
ejpam-146	118	5	infinite	infinite	NOUN
ejpam-146	118	6	subset	subset	NOUN
ejpam-146	118	7	x	x	PART
ejpam-146	118	8	has	have	VERB
ejpam-146	118	9	a	a	DET
ejpam-146	118	10	β	β	NOUN
ejpam-146	118	11	-	-	NOUN
ejpam-146	118	12	θ	θ	NOUN
ejpam-146	118	13	-c.a.p	-c.a.p	PROPN
ejpam-146	118	14	.	.	PUNCT
ejpam-146	119	1	in	in	ADP
ejpam-146	119	2	x	x	X
ejpam-146	119	3	.	.	PUNCT
ejpam-146	120	1	(	(	PUNCT
ejpam-146	120	2	c	c	X
ejpam-146	120	3	)	)	PUNCT
ejpam-146	120	4	each	each	DET
ejpam-146	120	5	net	net	NOUN
ejpam-146	120	6	with	with	ADP
ejpam-146	120	7	a	a	DET
ejpam-146	120	8	well	well	ADV
ejpam-146	120	9	ordered	order	VERB
ejpam-146	120	10	directed	direct	VERB
ejpam-146	120	11	set	set	NOUN
ejpam-146	120	12	as	as	ADP
ejpam-146	120	13	its	its	PRON
ejpam-146	120	14	domain	domain	NOUN
ejpam-146	120	15	β	β	NOUN
ejpam-146	120	16	-	-	NOUN
ejpam-146	120	17	θ	θ	NOUN
ejpam-146	120	18	-adheres	-adhere	NOUN
ejpam-146	120	19	to	to	ADP
ejpam-146	120	20	a	a	DET
ejpam-146	120	21	point	point	NOUN
ejpam-146	120	22	in	in	ADP
ejpam-146	120	23	x	x	X
ejpam-146	120	24	.	.	PUNCT
ejpam-146	121	1	proof	proof	NOUN
ejpam-146	121	2	.	.	PUNCT
ejpam-146	122	1	(	(	PUNCT
ejpam-146	122	2	a)⇒	a)⇒	PROPN
ejpam-146	122	3	(	(	PUNCT
ejpam-146	122	4	b	b	NOUN
ejpam-146	122	5	)	)	PUNCT
ejpam-146	122	6	:	:	PUNCT
ejpam-146	122	7	let	let	VERB
ejpam-146	122	8	i	i	PRON
ejpam-146	122	9	be	be	AUX
ejpam-146	122	10	an	an	DET
ejpam-146	122	11	infinite	infinite	NOUN
ejpam-146	122	12	subset	subset	NOUN
ejpam-146	122	13	in	in	ADP
ejpam-146	122	14	a	a	DET
ejpam-146	122	15	β	β	X
ejpam-146	122	16	-	-	ADJ
ejpam-146	122	17	closed	closed	ADJ
ejpam-146	122	18	space	space	NOUN
ejpam-146	122	19	x	x	PUNCT
ejpam-146	122	20	and	and	CCONJ
ejpam-146	122	21	also	also	ADV
ejpam-146	122	22	let	let	VERB
ejpam-146	122	23	n	n	X
ejpam-146	122	24	=	=	PRON
ejpam-146	122	25	{	{	PUNCT
ejpam-146	122	26	x	x	PUNCT
ejpam-146	122	27	∈	∈	NOUN
ejpam-146	122	28	x	x	X
ejpam-146	122	29	:	:	PUNCT
ejpam-146	122	30	x	x	X
ejpam-146	122	31	is	be	AUX
ejpam-146	122	32	not	not	PART
ejpam-146	122	33	a	a	DET
ejpam-146	122	34	β	β	NOUN
ejpam-146	122	35	-	-	NOUN
ejpam-146	122	36	θ	θ	NOUN
ejpam-146	122	37	-c.a.p	-c.a.p	PROPN
ejpam-146	122	38	.	.	PROPN
ejpam-146	122	39	of	of	ADP
ejpam-146	122	40	i	i	PRON
ejpam-146	122	41	}	}	PUNCT
ejpam-146	122	42	.	.	PUNCT
ejpam-146	123	1	so	so	ADV
ejpam-146	123	2	for	for	ADP
ejpam-146	123	3	each	each	DET
ejpam-146	123	4	x	x	SYM
ejpam-146	123	5	∈	∈	PROPN
ejpam-146	123	6	n	n	X
ejpam-146	123	7	,	,	PUNCT
ejpam-146	123	8	there	there	PRON
ejpam-146	123	9	exists	exist	VERB
ejpam-146	123	10	a	a	DET
ejpam-146	123	11	bx	bx	NOUN
ejpam-146	123	12	∈	∈	PROPN
ejpam-146	123	13	βr(x	βr(x	PUNCT
ejpam-146	123	14	,	,	PUNCT
ejpam-146	123	15	x	x	X
ejpam-146	123	16	)	)	PUNCT
ejpam-146	123	17	such	such	ADJ
ejpam-146	123	18	that	that	SCONJ
ejpam-146	123	19	|i	|i	VERB
ejpam-146	123	20	∩	∩	PROPN
ejpam-146	123	21	bx	bx	NOUN
ejpam-146	123	22	|	|	ADV
ejpam-146	123	23	<	<	X
ejpam-146	123	24	|i	|i	X
ejpam-146	124	1	|	|	ADV
ejpam-146	124	2	.	.	PUNCT
ejpam-146	125	1	if	if	SCONJ
ejpam-146	125	2	n	n	PRON
ejpam-146	125	3	is	be	AUX
ejpam-146	125	4	the	the	DET
ejpam-146	125	5	whole	whole	ADJ
ejpam-146	125	6	space	space	NOUN
ejpam-146	125	7	,	,	PUNCT
ejpam-146	125	8	then	then	ADV
ejpam-146	125	9	it	it	PRON
ejpam-146	125	10	follows	follow	VERB
ejpam-146	125	11	from	from	ADP
ejpam-146	125	12	the	the	DET
ejpam-146	125	13	theorem	theorem	ADJ
ejpam-146	125	14	3.2	3.2	NUM
ejpam-146	125	15	that	that	SCONJ
ejpam-146	125	16	the	the	DET
ejpam-146	125	17	cover	cover	NOUN
ejpam-146	125	18	{	{	PUNCT
ejpam-146	125	19	bx	bx	NOUN
ejpam-146	125	20	:	:	PUNCT
ejpam-146	125	21	x	x	SYM
ejpam-146	125	22	∈	∈	PROPN
ejpam-146	125	23	n	n	CCONJ
ejpam-146	125	24	}	}	PUNCT
ejpam-146	125	25	has	have	VERB
ejpam-146	125	26	a	a	DET
ejpam-146	125	27	finite	finite	ADJ
ejpam-146	125	28	subcover	subcover	PROPN
ejpam-146	125	29	,	,	PUNCT
ejpam-146	125	30	say	say	VERB
ejpam-146	125	31	,	,	PUNCT
ejpam-146	125	32	{	{	PUNCT
ejpam-146	125	33	bx1	bx1	NOUN
ejpam-146	125	34	,	,	PUNCT
ejpam-146	125	35	bx2	bx2	PROPN
ejpam-146	125	36	,	,	PUNCT
ejpam-146	125	37	.....	.....	PUNCT
ejpam-146	125	38	,	,	PUNCT
ejpam-146	125	39	bxk	bxk	NOUN
ejpam-146	125	40	}	}	PUNCT
ejpam-146	125	41	.	.	PUNCT
ejpam-146	126	1	now	now	ADV
ejpam-146	126	2	i	i	PRON
ejpam-146	126	3	⊂	⊂	PUNCT
ejpam-146	126	4	∪{bx	∪{bx	PROPN
ejpam-146	127	1	i	i	PRON
ejpam-146	127	2	∩	∩	VERB
ejpam-146	127	3	i	i	PRON
ejpam-146	127	4	:	:	PUNCT
ejpam-146	127	5	i	i	NOUN
ejpam-146	127	6	=	=	SYM
ejpam-146	127	7	1,2	1,2	NUM
ejpam-146	127	8	,	,	PUNCT
ejpam-146	127	9	.....	.....	PUNCT
ejpam-146	127	10	k	k	X
ejpam-146	127	11	}	}	PUNCT
ejpam-146	127	12	and	and	CCONJ
ejpam-146	127	13	|i	|i	VERB
ejpam-146	127	14	|=	|=	NOUN
ejpam-146	127	15	max{|bx	max{|bx	NOUN
ejpam-146	127	16	i	i	PRON
ejpam-146	127	17	∩	∩	VERB
ejpam-146	127	18	i	i	PRON
ejpam-146	128	1	|	|	ADV
ejpam-146	128	2	:	:	PUNCT
ejpam-146	129	1	i	i	NOUN
ejpam-146	129	2	=	=	SYM
ejpam-146	129	3	1,2	1,2	NUM
ejpam-146	129	4	,	,	PUNCT
ejpam-146	129	5	.....	.....	PUNCT
ejpam-146	129	6	k	k	X
ejpam-146	129	7	}	}	PUNCT
ejpam-146	129	8	—	—	PUNCT
ejpam-146	129	9	a	a	DET
ejpam-146	129	10	contradiction	contradiction	NOUN
ejpam-146	129	11	.	.	PUNCT
ejpam-146	130	1	so	so	ADV
ejpam-146	130	2	,	,	PUNCT
ejpam-146	130	3	i	i	PRON
ejpam-146	130	4	has	have	VERB
ejpam-146	130	5	a	a	DET
ejpam-146	130	6	β	β	NOUN
ejpam-146	130	7	-	-	NOUN
ejpam-146	130	8	θ	θ	NOUN
ejpam-146	130	9	-c.a.p	-c.a.p	PROPN
ejpam-146	130	10	.	.	PUNCT
ejpam-146	131	1	in	in	ADP
ejpam-146	131	2	x	x	PROPN
ejpam-146	131	3	.	.	PUNCT
ejpam-146	131	4	c.	c.	PROPN
ejpam-146	131	5	k.	k.	PROPN
ejpam-146	131	6	basu	basu	PROPN
ejpam-146	131	7	,	,	PUNCT
ejpam-146	131	8	m.	m.	PROPN
ejpam-146	131	9	k.	k.	PROPN
ejpam-146	131	10	ghosh	ghosh	PROPN
ejpam-146	131	11	/	/	PUNCT
ejpam-146	131	12	eur	eur	PROPN
ejpam-146	131	13	.	.	PUNCT
ejpam-146	132	1	j.	j.	PROPN
ejpam-146	132	2	pure	pure	PROPN
ejpam-146	132	3	appl	appl	PROPN
ejpam-146	132	4	.	.	PROPN
ejpam-146	132	5	math	math	PROPN
ejpam-146	132	6	,	,	PUNCT
ejpam-146	132	7	1	1	NUM
ejpam-146	132	8	(	(	PUNCT
ejpam-146	132	9	2008	2008	NUM
ejpam-146	132	10	)	)	PUNCT
ejpam-146	132	11	,	,	PUNCT
ejpam-146	132	12	(	(	PUNCT
ejpam-146	132	13	40	40	NUM
ejpam-146	132	14	-	-	SYM
ejpam-146	132	15	50	50	NUM
ejpam-146	132	16	)	)	PUNCT
ejpam-146	132	17	43	43	NUM
ejpam-146	132	18	(	(	PUNCT
ejpam-146	132	19	b	b	NOUN
ejpam-146	132	20	)	)	PUNCT
ejpam-146	132	21	⇒	⇒	NOUN
ejpam-146	132	22	(	(	PUNCT
ejpam-146	132	23	a	a	X
ejpam-146	132	24	)	)	PUNCT
ejpam-146	132	25	:	:	PUNCT
ejpam-146	132	26	conversely	conversely	ADV
ejpam-146	132	27	,	,	PUNCT
ejpam-146	132	28	let	let	VERB
ejpam-146	132	29	x	x	PRON
ejpam-146	132	30	be	be	AUX
ejpam-146	132	31	not	not	PART
ejpam-146	132	32	β	β	NOUN
ejpam-146	132	33	-	-	VERB
ejpam-146	132	34	closed	closed	ADJ
ejpam-146	132	35	.	.	PUNCT
ejpam-146	133	1	then	then	ADV
ejpam-146	133	2	by	by	ADP
ejpam-146	133	3	theorem	theorem	NOUN
ejpam-146	133	4	3.2	3.2	NUM
ejpam-146	133	5	there	there	PRON
ejpam-146	133	6	exists	exist	VERB
ejpam-146	133	7	a	a	DET
ejpam-146	133	8	cover	cover	NOUN
ejpam-146	133	9	u	u	NOUN
ejpam-146	133	10	of	of	ADP
ejpam-146	133	11	x	x	PUNCT
ejpam-146	133	12	by	by	ADP
ejpam-146	133	13	β	β	ADJ
ejpam-146	133	14	-	-	ADJ
ejpam-146	133	15	regular	regular	ADJ
ejpam-146	133	16	sets	set	NOUN
ejpam-146	133	17	with	with	ADP
ejpam-146	133	18	no	no	DET
ejpam-146	133	19	finite	finite	PROPN
ejpam-146	133	20	subcover	subcover	PROPN
ejpam-146	133	21	.	.	PUNCT
ejpam-146	134	1	consider	consider	VERB
ejpam-146	134	2	β	β	X
ejpam-146	134	3	=	=	NOUN
ejpam-146	134	4	min{|u	min{|u	PROPN
ejpam-146	134	5	?	?	PUNCT
ejpam-146	135	1	|	|	ADV
ejpam-146	135	2	:	:	PUNCT
ejpam-146	135	3	u	u	NOUN
ejpam-146	135	4	?	?	PUNCT
ejpam-146	136	1	⊂	⊂	PROPN
ejpam-146	136	2	u	u	NOUN
ejpam-146	136	3	and	and	CCONJ
ejpam-146	136	4	u	u	NOUN
ejpam-146	136	5	?	?	PUNCT
ejpam-146	136	6	is	be	AUX
ejpam-146	136	7	cover	cover	NOUN
ejpam-146	136	8	of	of	ADP
ejpam-146	136	9	x	x	PUNCT
ejpam-146	136	10	}	}	PUNCT
ejpam-146	136	11	where	where	SCONJ
ejpam-146	136	12	|.|	|.|	NOUN
ejpam-146	136	13	denotes	denote	VERB
ejpam-146	136	14	the	the	DET
ejpam-146	136	15	cardinality	cardinality	NOUN
ejpam-146	136	16	.	.	PUNCT
ejpam-146	137	1	let	let	VERB
ejpam-146	137	2	u0	u0	PROPN
ejpam-146	137	3	⊂	⊂	PROPN
ejpam-146	137	4	u	u	PRON
ejpam-146	137	5	be	be	AUX
ejpam-146	137	6	a	a	DET
ejpam-146	137	7	cover	cover	NOUN
ejpam-146	137	8	of	of	ADP
ejpam-146	137	9	x	x	PUNCT
ejpam-146	137	10	for	for	ADP
ejpam-146	137	11	which	which	PRON
ejpam-146	137	12	|u0|	|u0|	X
ejpam-146	137	13	=	=	SYM
ejpam-146	137	14	β	β	X
ejpam-146	137	15	.	.	PUNCT
ejpam-146	138	1	clearly	clearly	ADV
ejpam-146	138	2	β	β	X
ejpam-146	138	3	≥	≥	PRON
ejpam-146	138	4	ℵ0	ℵ0	PROPN
ejpam-146	138	5	.	.	PUNCT
ejpam-146	139	1	by	by	ADP
ejpam-146	139	2	well	well	ADV
ejpam-146	139	3	ordering	ordering	NOUN
ejpam-146	139	4	of	of	ADP
ejpam-146	139	5	u0	u0	NOUN
ejpam-146	139	6	by	by	ADP
ejpam-146	139	7	some	some	DET
ejpam-146	139	8	minimal	minimal	ADJ
ejpam-146	139	9	well	well	ADV
ejpam-146	139	10	-	-	PUNCT
ejpam-146	139	11	ordering	order	VERB
ejpam-146	139	12	≺	≺	NOUN
ejpam-146	139	13	,	,	PUNCT
ejpam-146	139	14	we	we	PRON
ejpam-146	139	15	have	have	AUX
ejpam-146	139	16	|{u	|{u	VERB
ejpam-146	139	17	:	:	PUNCT
ejpam-146	140	1	u	u	PROPN
ejpam-146	140	2	∈	∈	PROPN
ejpam-146	140	3	u0	u0	ADJ
ejpam-146	140	4	and	and	CCONJ
ejpam-146	140	5	u	u	NOUN
ejpam-146	140	6	≺	≺	NOUN
ejpam-146	140	7	u0}|	u0}|	SYM
ejpam-146	140	8	<	<	X
ejpam-146	140	9	|{u	|{u	PROPN
ejpam-146	140	10	;	;	PUNCT
ejpam-146	140	11	u	u	PROPN
ejpam-146	140	12	∈	∈	PROPN
ejpam-146	140	13	u0}|	u0}|	PROPN
ejpam-146	140	14	,	,	PUNCT
ejpam-146	140	15	for	for	ADP
ejpam-146	140	16	each	each	DET
ejpam-146	140	17	u0	u0	PROPN
ejpam-146	140	18	∈	∈	PROPN
ejpam-146	140	19	u0	u0	NOUN
ejpam-146	140	20	.	.	PUNCT
ejpam-146	141	1	clearly	clearly	ADV
ejpam-146	141	2	x	x	PRON
ejpam-146	141	3	can	can	AUX
ejpam-146	141	4	not	not	PART
ejpam-146	141	5	have	have	VERB
ejpam-146	141	6	any	any	DET
ejpam-146	141	7	subcover	subcover	NOUN
ejpam-146	141	8	with	with	ADP
ejpam-146	141	9	cardinality	cardinality	PROPN
ejpam-146	141	10	less	less	ADJ
ejpam-146	141	11	than	than	ADP
ejpam-146	141	12	β	β	PRON
ejpam-146	141	13	and	and	CCONJ
ejpam-146	141	14	hence	hence	ADV
ejpam-146	141	15	for	for	ADP
ejpam-146	141	16	each	each	DET
ejpam-146	141	17	u	u	PROPN
ejpam-146	141	18	∈	∈	PROPN
ejpam-146	141	19	u0	u0	NOUN
ejpam-146	141	20	,	,	PUNCT
ejpam-146	141	21	there	there	PRON
ejpam-146	141	22	exists	exist	VERB
ejpam-146	141	23	a	a	DET
ejpam-146	141	24	point	point	NOUN
ejpam-146	142	1	xu	xu	X
ejpam-146	142	2	∈	∈	PROPN
ejpam-146	142	3	x	x	PUNCT
ejpam-146	142	4	−∪{u0	−∪{u0	NOUN
ejpam-146	142	5	∪	∪	X
ejpam-146	142	6	{	{	PUNCT
ejpam-146	142	7	xu0	xu0	PROPN
ejpam-146	142	8	}	}	PUNCT
ejpam-146	142	9	:	:	PUNCT
ejpam-146	142	10	u0	u0	PROPN
ejpam-146	142	11	∈	∈	PROPN
ejpam-146	142	12	u0	u0	ADJ
ejpam-146	142	13	and	and	CCONJ
ejpam-146	142	14	u0	u0	ADJ
ejpam-146	142	15	≺	≺	NOUN
ejpam-146	142	16	u	u	NOUN
ejpam-146	142	17	}	}	PUNCT
ejpam-146	142	18	.	.	PUNCT
ejpam-146	143	1	this	this	PRON
ejpam-146	143	2	can	can	AUX
ejpam-146	143	3	always	always	ADV
ejpam-146	143	4	be	be	AUX
ejpam-146	143	5	done	do	VERB
ejpam-146	143	6	otherwise	otherwise	ADV
ejpam-146	143	7	one	one	NUM
ejpam-146	143	8	can	can	AUX
ejpam-146	143	9	choose	choose	VERB
ejpam-146	143	10	fromu0	fromu0	ADJ
ejpam-146	143	11	a	a	DET
ejpam-146	143	12	cover	cover	NOUN
ejpam-146	143	13	of	of	ADP
ejpam-146	143	14	smaller	small	ADJ
ejpam-146	143	15	cardinality	cardinality	NOUN
ejpam-146	143	16	.	.	PUNCT
ejpam-146	144	1	let	let	VERB
ejpam-146	144	2	s	s	PRON
ejpam-146	144	3	=	=	PUNCT
ejpam-146	144	4	{	{	PUNCT
ejpam-146	144	5	xu	xu	INTJ
ejpam-146	144	6	:	:	PUNCT
ejpam-146	144	7	u	u	PROPN
ejpam-146	144	8	∈u0	∈u0	PROPN
ejpam-146	144	9	}	}	PUNCT
ejpam-146	144	10	and	and	CCONJ
ejpam-146	144	11	x	x	AUX
ejpam-146	144	12	be	be	AUX
ejpam-146	144	13	any	any	DET
ejpam-146	144	14	point	point	NOUN
ejpam-146	144	15	of	of	ADP
ejpam-146	144	16	x	x	X
ejpam-146	144	17	.	.	PUNCT
ejpam-146	145	1	since	since	SCONJ
ejpam-146	145	2	u	u	NOUN
ejpam-146	145	3	is	be	AUX
ejpam-146	145	4	a	a	DET
ejpam-146	145	5	cover	cover	NOUN
ejpam-146	145	6	of	of	ADP
ejpam-146	145	7	x	x	X
ejpam-146	145	8	,	,	PUNCT
ejpam-146	145	9	x	x	PUNCT
ejpam-146	145	10	∈	∈	PROPN
ejpam-146	145	11	u	u	NOUN
ejpam-146	145	12	?	?	PUNCT
ejpam-146	146	1	for	for	ADP
ejpam-146	146	2	some	some	DET
ejpam-146	146	3	u	u	NOUN
ejpam-146	146	4	?	?	PUNCT
ejpam-146	147	1	∈	∈	PROPN
ejpam-146	147	2	u0	u0	PROPN
ejpam-146	147	3	.	.	PUNCT
ejpam-146	148	1	but	but	CCONJ
ejpam-146	148	2	by	by	ADP
ejpam-146	148	3	the	the	DET
ejpam-146	148	4	choice	choice	NOUN
ejpam-146	148	5	of	of	ADP
ejpam-146	148	6	xu	xu	PROPN
ejpam-146	148	7	,	,	PUNCT
ejpam-146	148	8	xu	xu	PROPN
ejpam-146	149	1	∈	∈	PROPN
ejpam-146	150	1	u	u	NOUN
ejpam-146	150	2	?	?	PROPN
ejpam-146	150	3	implies	imply	VERB
ejpam-146	150	4	u	u	PROPN
ejpam-146	150	5	≺	≺	NOUN
ejpam-146	150	6	u	u	NOUN
ejpam-146	150	7	?	?	PUNCT
ejpam-146	150	8	.	.	PUNCT
ejpam-146	151	1	therefore	therefore	ADV
ejpam-146	151	2	,	,	PUNCT
ejpam-146	151	3	w	w	PROPN
ejpam-146	151	4	=	=	PRON
ejpam-146	151	5	{	{	PUNCT
ejpam-146	151	6	u	u	NOUN
ejpam-146	151	7	∈	∈	PROPN
ejpam-146	151	8	u0	u0	NOUN
ejpam-146	151	9	and	and	CCONJ
ejpam-146	151	10	xu	xu	PROPN
ejpam-146	151	11	∈	∈	PROPN
ejpam-146	151	12	u	u	NOUN
ejpam-146	151	13	?	?	PUNCT
ejpam-146	151	14	}	}	PUNCT
ejpam-146	151	15	⊂	⊂	PRON
ejpam-146	151	16	{	{	PUNCT
ejpam-146	151	17	u	u	NOUN
ejpam-146	151	18	∈	∈	PROPN
ejpam-146	151	19	u0	u0	NOUN
ejpam-146	151	20	:	:	PUNCT
ejpam-146	151	21	u	u	NOUN
ejpam-146	151	22	≺	≺	NOUN
ejpam-146	151	23	u	u	NOUN
ejpam-146	151	24	?	?	PUNCT
ejpam-146	151	25	}	}	PUNCT
ejpam-146	151	26	.	.	PUNCT
ejpam-146	152	1	but	but	CCONJ
ejpam-146	152	2	|w	|w	NOUN
ejpam-146	152	3	|	|	ADV
ejpam-146	152	4	<	<	X
ejpam-146	152	5	β	β	X
ejpam-146	152	6	,	,	PUNCT
ejpam-146	152	7	by	by	ADP
ejpam-146	152	8	the	the	DET
ejpam-146	152	9	minimality	minimality	NOUN
ejpam-146	152	10	of	of	ADP
ejpam-146	152	11	≺.	≺.	PROPN
ejpam-146	152	12	so	so	ADV
ejpam-146	152	13	,	,	PUNCT
ejpam-146	152	14	|s	|s	PROPN
ejpam-146	152	15	∩	∩	NOUN
ejpam-146	152	16	u?|	u?|	PROPN
ejpam-146	152	17	<	<	X
ejpam-146	152	18	β	β	X
ejpam-146	152	19	.	.	PUNCT
ejpam-146	153	1	since	since	SCONJ
ejpam-146	153	2	for	for	ADP
ejpam-146	153	3	u1	u1	NOUN
ejpam-146	153	4	,	,	PUNCT
ejpam-146	153	5	u2	u2	PROPN
ejpam-146	153	6	∈	∈	PROPN
ejpam-146	153	7	u0	u0	NOUN
ejpam-146	153	8	with	with	ADP
ejpam-146	153	9	u1	u1	PROPN
ejpam-146	153	10	6=	6=	PROPN
ejpam-146	153	11	u2	u2	PROPN
ejpam-146	153	12	,	,	PUNCT
ejpam-146	153	13	we	we	PRON
ejpam-146	153	14	have	have	AUX
ejpam-146	153	15	xu1	xu1	VERB
ejpam-146	154	1	6=	6=	X
ejpam-146	154	2	xu2	xu2	PROPN
ejpam-146	154	3	,	,	PUNCT
ejpam-146	154	4	then	then	ADV
ejpam-146	154	5	|s|	|s|	PROPN
ejpam-146	154	6	=	=	SYM
ejpam-146	154	7	β	β	X
ejpam-146	154	8	≥	≥	NOUN
ejpam-146	154	9	ℵ0	ℵ0	PROPN
ejpam-146	154	10	.	.	PUNCT
ejpam-146	155	1	therefore	therefore	ADV
ejpam-146	155	2	the	the	DET
ejpam-146	155	3	infinite	infinite	ADJ
ejpam-146	155	4	set	set	NOUN
ejpam-146	155	5	s	s	PART
ejpam-146	155	6	has	have	VERB
ejpam-146	155	7	no	no	DET
ejpam-146	155	8	β	β	NOUN
ejpam-146	155	9	-	-	NOUN
ejpam-146	155	10	θ	θ	NOUN
ejpam-146	155	11	-c.a.p	-c.a.p	PROPN
ejpam-146	155	12	.	.	PUNCT
ejpam-146	156	1	in	in	ADP
ejpam-146	156	2	x	x	X
ejpam-146	156	3	—	—	PUNCT
ejpam-146	156	4	a	a	DET
ejpam-146	156	5	contradiction	contradiction	NOUN
ejpam-146	156	6	.	.	PUNCT
ejpam-146	157	1	so	so	ADV
ejpam-146	157	2	,	,	PUNCT
ejpam-146	157	3	x	x	X
ejpam-146	157	4	is	be	AUX
ejpam-146	157	5	β	β	NOUN
ejpam-146	157	6	-	-	VERB
ejpam-146	157	7	closed	closed	ADJ
ejpam-146	157	8	.	.	PUNCT
ejpam-146	158	1	(	(	PUNCT
ejpam-146	158	2	c)⇒	c)⇒	X
ejpam-146	158	3	(	(	PUNCT
ejpam-146	158	4	b	b	NOUN
ejpam-146	158	5	)	)	PUNCT
ejpam-146	158	6	:	:	PUNCT
ejpam-146	158	7	let	let	VERB
ejpam-146	158	8	i	i	PRON
ejpam-146	158	9	be	be	AUX
ejpam-146	158	10	an	an	DET
ejpam-146	158	11	infinite	infinite	ADJ
ejpam-146	158	12	subset	subset	NOUN
ejpam-146	158	13	of	of	ADP
ejpam-146	158	14	x	x	X
ejpam-146	158	15	.	.	PUNCT
ejpam-146	159	1	by	by	ADP
ejpam-146	159	2	zorn	zorn	PROPN
ejpam-146	159	3	’s	’s	PART
ejpam-146	159	4	lemma	lemma	PROPN
ejpam-146	159	5	,	,	PUNCT
ejpam-146	159	6	i	i	PRON
ejpam-146	159	7	can	can	AUX
ejpam-146	159	8	be	be	AUX
ejpam-146	159	9	assumed	assume	VERB
ejpam-146	159	10	to	to	PART
ejpam-146	159	11	be	be	AUX
ejpam-146	159	12	net	net	ADJ
ejpam-146	159	13	with	with	ADP
ejpam-146	159	14	a	a	DET
ejpam-146	159	15	well	well	ADV
ejpam-146	159	16	ordered	order	VERB
ejpam-146	159	17	directed	direct	VERB
ejpam-146	159	18	set	set	NOUN
ejpam-146	159	19	as	as	ADP
ejpam-146	159	20	its	its	PRON
ejpam-146	159	21	domain	domain	NOUN
ejpam-146	159	22	.	.	PUNCT
ejpam-146	160	1	so	so	ADV
ejpam-146	160	2	,	,	PUNCT
ejpam-146	160	3	it	it	PRON
ejpam-146	160	4	has	have	VERB
ejpam-146	160	5	a	a	DET
ejpam-146	160	6	β	β	NOUN
ejpam-146	160	7	-	-	ADJ
ejpam-146	160	8	θ	θ	NOUN
ejpam-146	160	9	-adherent	-adherent	NOUN
ejpam-146	160	10	point	point	NOUN
ejpam-146	160	11	say	say	VERB
ejpam-146	160	12	,	,	PUNCT
ejpam-146	160	13	x	x	PUNCT
ejpam-146	160	14	and	and	CCONJ
ejpam-146	160	15	clearly	clearly	ADV
ejpam-146	160	16	x	x	PUNCT
ejpam-146	160	17	is	be	AUX
ejpam-146	160	18	an	an	DET
ejpam-146	160	19	β	β	NOUN
ejpam-146	160	20	-	-	NOUN
ejpam-146	160	21	θ	θ	NOUN
ejpam-146	160	22	-c.a.p	-c.a.p	PROPN
ejpam-146	160	23	.	.	PUNCT
ejpam-146	161	1	of	of	ADP
ejpam-146	161	2	i	i	PRON
ejpam-146	161	3	.	.	PUNCT
ejpam-146	162	1	(	(	PUNCT
ejpam-146	162	2	a	a	X
ejpam-146	162	3	)	)	PUNCT
ejpam-146	162	4	⇒	⇒	NOUN
ejpam-146	162	5	(	(	PUNCT
ejpam-146	162	6	c	c	NOUN
ejpam-146	162	7	)	)	PUNCT
ejpam-146	162	8	:	:	PUNCT
ejpam-146	162	9	let	let	VERB
ejpam-146	162	10	{	{	PUNCT
ejpam-146	162	11	xλ}λ∈d	xλ}λ∈d	PRON
ejpam-146	162	12	be	be	AUX
ejpam-146	162	13	a	a	DET
ejpam-146	162	14	net	net	NOUN
ejpam-146	162	15	with	with	ADP
ejpam-146	162	16	well	well	ADV
ejpam-146	162	17	ordered	order	VERB
ejpam-146	162	18	directed	direct	VERB
ejpam-146	162	19	set	set	NOUN
ejpam-146	162	20	d	d	PROPN
ejpam-146	162	21	,	,	PUNCT
ejpam-146	162	22	having	have	VERB
ejpam-146	162	23	no	no	DET
ejpam-146	162	24	β	β	NOUN
ejpam-146	162	25	-	-	ADJ
ejpam-146	162	26	θ	θ	ADJ
ejpam-146	162	27	-adherent	-adherent	NOUN
ejpam-146	162	28	point	point	NOUN
ejpam-146	162	29	in	in	ADP
ejpam-146	162	30	x	x	SYM
ejpam-146	162	31	,	,	PUNCT
ejpam-146	162	32	so	so	ADV
ejpam-146	162	33	,	,	PUNCT
ejpam-146	162	34	for	for	ADP
ejpam-146	162	35	each	each	DET
ejpam-146	162	36	x	x	SYM
ejpam-146	162	37	∈	∈	PROPN
ejpam-146	162	38	x	x	X
ejpam-146	162	39	,	,	PUNCT
ejpam-146	162	40	there	there	PRON
ejpam-146	162	41	is	be	VERB
ejpam-146	162	42	a	a	DET
ejpam-146	162	43	β	β	NOUN
ejpam-146	162	44	-	-	ADJ
ejpam-146	162	45	regular	regular	ADJ
ejpam-146	162	46	set	set	VERB
ejpam-146	162	47	ux	ux	PROPN
ejpam-146	162	48	∈	∈	PROPN
ejpam-146	162	49	βr(x	βr(x	PUNCT
ejpam-146	162	50	,	,	PUNCT
ejpam-146	162	51	x	x	X
ejpam-146	162	52	)	)	PUNCT
ejpam-146	162	53	and	and	CCONJ
ejpam-146	162	54	a	a	DET
ejpam-146	162	55	λx	λx	NOUN
ejpam-146	162	56	∈	∈	PROPN
ejpam-146	163	1	d	d	ADP
ejpam-146	163	2	such	such	ADJ
ejpam-146	163	3	that	that	SCONJ
ejpam-146	163	4	xλ	xλ	PROPN
ejpam-146	163	5	∈	∈	PROPN
ejpam-146	163	6	x	x	PUNCT
ejpam-146	163	7	−	−	PROPN
ejpam-146	163	8	ux	ux	INTJ
ejpam-146	163	9	,	,	PUNCT
ejpam-146	163	10	∀	∀	X
ejpam-146	163	11	λ	λ	NOUN
ejpam-146	163	12	≥	≥	NOUN
ejpam-146	163	13	λx	λx	NOUN
ejpam-146	163	14	.	.	PUNCT
ejpam-146	164	1	since	since	SCONJ
ejpam-146	164	2	x	x	PROPN
ejpam-146	164	3	is	be	AUX
ejpam-146	164	4	β	β	NOUN
ejpam-146	164	5	-	-	VERB
ejpam-146	164	6	closed	closed	ADJ
ejpam-146	164	7	,	,	PUNCT
ejpam-146	164	8	the	the	DET
ejpam-146	164	9	cover	cover	NOUN
ejpam-146	164	10	{	{	PUNCT
ejpam-146	164	11	ux	ux	NOUN
ejpam-146	164	12	:	:	PUNCT
ejpam-146	164	13	x	x	SYM
ejpam-146	164	14	∈	∈	PROPN
ejpam-146	164	15	x	x	PUNCT
ejpam-146	164	16	}	}	PUNCT
ejpam-146	164	17	has	have	VERB
ejpam-146	164	18	a	a	DET
ejpam-146	164	19	finite	finite	ADJ
ejpam-146	164	20	subcover	subcover	PROPN
ejpam-146	164	21	,	,	PUNCT
ejpam-146	164	22	say	say	VERB
ejpam-146	164	23	,	,	PUNCT
ejpam-146	164	24	{	{	PUNCT
ejpam-146	164	25	ux1	ux1	NOUN
ejpam-146	164	26	,	,	PUNCT
ejpam-146	164	27	......	......	PUNCT
ejpam-146	164	28	,	,	PUNCT
ejpam-146	164	29	uxk	uxk	NOUN
ejpam-146	164	30	}	}	PUNCT
ejpam-146	164	31	.	.	PUNCT
ejpam-146	165	1	let	let	VERB
ejpam-146	165	2	{	{	PUNCT
ejpam-146	165	3	λx1	λx1	X
ejpam-146	165	4	,	,	PUNCT
ejpam-146	165	5	.....	.....	PUNCT
ejpam-146	165	6	,	,	PUNCT
ejpam-146	165	7	λxk	λxk	PROPN
ejpam-146	165	8	}	}	PUNCT
ejpam-146	165	9	be	be	AUX
ejpam-146	165	10	the	the	DET
ejpam-146	165	11	corresponding	corresponding	ADJ
ejpam-146	165	12	elements	element	NOUN
ejpam-146	165	13	in	in	ADP
ejpam-146	165	14	d	d	ADP
ejpam-146	165	15	which	which	PRON
ejpam-146	165	16	is	be	AUX
ejpam-146	165	17	finite	finite	ADJ
ejpam-146	165	18	and	and	CCONJ
ejpam-146	165	19	hence	hence	ADV
ejpam-146	165	20	by	by	ADP
ejpam-146	165	21	the	the	DET
ejpam-146	165	22	well	well	ADJ
ejpam-146	165	23	orderedness	orderedness	NOUN
ejpam-146	165	24	of	of	ADP
ejpam-146	165	25	d	d	NOUN
ejpam-146	165	26	,	,	PUNCT
ejpam-146	165	27	there	there	PRON
ejpam-146	165	28	exists	exist	VERB
ejpam-146	165	29	a	a	DET
ejpam-146	165	30	largest	large	ADJ
ejpam-146	165	31	element	element	NOUN
ejpam-146	165	32	say	say	VERB
ejpam-146	165	33	λxk	λxk	NOUN
ejpam-146	165	34	in	in	ADP
ejpam-146	165	35	d.	d.	PROPN
ejpam-146	165	36	then	then	ADV
ejpam-146	165	37	xλ	xλ	PROPN
ejpam-146	165	38	∈	∈	PROPN
ejpam-146	165	39	∩k	∩k	PROPN
ejpam-146	165	40	i=1(x	i=1(x	PROPN
ejpam-146	165	41	−	−	NUM
ejpam-146	165	42	ux	ux	INTJ
ejpam-146	166	1	i	i	INTJ
ejpam-146	166	2	)	)	PUNCT
ejpam-146	167	1	=	=	PUNCT
ejpam-146	167	2	x	x	PUNCT
ejpam-146	168	1	−	−	PROPN
ejpam-146	168	2	∪k	∪k	NUM
ejpam-146	168	3	i=1ux	i=1ux	PROPN
ejpam-146	169	1	i	i	PROPN
ejpam-146	169	2	=	=	PUNCT
ejpam-146	169	3	;	;	PUNCT
ejpam-146	169	4	,	,	PUNCT
ejpam-146	169	5	for	for	ADP
ejpam-146	169	6	λ	λ	PROPN
ejpam-146	169	7	>	>	X
ejpam-146	169	8	λxk	λxk	PROPN
ejpam-146	169	9	—	—	PUNCT
ejpam-146	169	10	a	a	DET
ejpam-146	169	11	contradiction	contradiction	NOUN
ejpam-146	169	12	.	.	PUNCT
ejpam-146	170	1	therefore	therefore	ADV
ejpam-146	170	2	the	the	DET
ejpam-146	170	3	net	net	NOUN
ejpam-146	170	4	{	{	PUNCT
ejpam-146	170	5	xλ}λ∈d	xλ}λ∈d	PRON
ejpam-146	170	6	has	have	VERB
ejpam-146	170	7	a	a	DET
ejpam-146	170	8	β	β	NOUN
ejpam-146	170	9	-	-	ADJ
ejpam-146	170	10	θ	θ	ADJ
ejpam-146	170	11	-adherent	-adherent	NOUN
ejpam-146	170	12	point	point	NOUN
ejpam-146	170	13	in	in	ADP
ejpam-146	170	14	x	x	X
ejpam-146	170	15	.	.	PUNCT
ejpam-146	171	1	theorem	theorem	VERB
ejpam-146	171	2	3.5	3.5	NUM
ejpam-146	171	3	.	.	PUNCT
ejpam-146	172	1	the	the	DET
ejpam-146	172	2	following	follow	VERB
ejpam-146	172	3	are	be	AUX
ejpam-146	172	4	equivalent	equivalent	ADJ
ejpam-146	172	5	for	for	ADP
ejpam-146	172	6	a	a	DET
ejpam-146	172	7	space	space	NOUN
ejpam-146	172	8	x	x	X
ejpam-146	172	9	(	(	PUNCT
ejpam-146	172	10	a	a	NOUN
ejpam-146	172	11	)	)	PUNCT
ejpam-146	172	12	x	x	X
ejpam-146	172	13	is	be	AUX
ejpam-146	172	14	β	β	NOUN
ejpam-146	172	15	-	-	VERB
ejpam-146	172	16	closed	closed	ADJ
ejpam-146	172	17	.	.	PUNCT
ejpam-146	173	1	(	(	PUNCT
ejpam-146	173	2	b	b	X
ejpam-146	173	3	)	)	PUNCT
ejpam-146	173	4	each	each	DET
ejpam-146	173	5	family	family	NOUN
ejpam-146	173	6	of	of	ADP
ejpam-146	173	7	β	β	PROPN
ejpam-146	173	8	-	-	PUNCT
ejpam-146	173	9	θ	θ	NOUN
ejpam-146	173	10	-closed	-close	VERB
ejpam-146	173	11	sets	set	NOUN
ejpam-146	173	12	with	with	ADP
ejpam-146	173	13	the	the	DET
ejpam-146	173	14	finite	finite	ADJ
ejpam-146	173	15	intersection	intersection	NOUN
ejpam-146	173	16	property	property	NOUN
ejpam-146	173	17	has	have	VERB
ejpam-146	173	18	nonempty	nonempty	ADJ
ejpam-146	173	19	intersection	intersection	NOUN
ejpam-146	173	20	.	.	PUNCT
ejpam-146	174	1	(	(	PUNCT
ejpam-146	174	2	c	c	X
ejpam-146	174	3	)	)	PUNCT
ejpam-146	174	4	each	each	DET
ejpam-146	174	5	filter	filter	NOUN
ejpam-146	174	6	base	base	NOUN
ejpam-146	174	7	on	on	ADP
ejpam-146	174	8	x	x	PUNCT
ejpam-146	174	9	has	have	VERB
ejpam-146	174	10	at	at	ADV
ejpam-146	174	11	least	least	ADV
ejpam-146	174	12	one	one	NUM
ejpam-146	174	13	β	β	NOUN
ejpam-146	174	14	-	-	PUNCT
ejpam-146	174	15	θ	θ	NOUN
ejpam-146	174	16	-adherent	-adherent	NOUN
ejpam-146	174	17	point	point	NOUN
ejpam-146	174	18	.	.	PUNCT
ejpam-146	175	1	(	(	PUNCT
ejpam-146	175	2	d	d	X
ejpam-146	175	3	)	)	PUNCT
ejpam-146	175	4	each	each	DET
ejpam-146	175	5	filter	filter	NOUN
ejpam-146	175	6	base	base	NOUN
ejpam-146	175	7	on	on	ADP
ejpam-146	175	8	x	x	PUNCT
ejpam-146	175	9	with	with	ADP
ejpam-146	175	10	atmost	atmost	PROPN
ejpam-146	175	11	one	one	NUM
ejpam-146	175	12	β	β	NOUN
ejpam-146	175	13	-	-	PUNCT
ejpam-146	175	14	θ	θ	NOUN
ejpam-146	175	15	-adherent	-adherent	NOUN
ejpam-146	175	16	point	point	NOUN
ejpam-146	175	17	is	be	AUX
ejpam-146	175	18	β	β	X
ejpam-146	175	19	-	-	PUNCT
ejpam-146	175	20	θ	θ	NOUN
ejpam-146	175	21	-convergent	-convergent	NOUN
ejpam-146	175	22	.	.	PUNCT
ejpam-146	176	1	(	(	PUNCT
ejpam-146	176	2	e	e	X
ejpam-146	176	3	)	)	PUNCT
ejpam-146	176	4	every	every	DET
ejpam-146	176	5	maximal	maximal	ADJ
ejpam-146	176	6	filter	filter	NOUN
ejpam-146	176	7	base	base	NOUN
ejpam-146	176	8	β	β	NOUN
ejpam-146	176	9	-	-	NOUN
ejpam-146	176	10	θ	θ	NOUN
ejpam-146	176	11	-converges	-converge	NOUN
ejpam-146	176	12	to	to	ADP
ejpam-146	176	13	some	some	DET
ejpam-146	176	14	point	point	NOUN
ejpam-146	176	15	in	in	ADP
ejpam-146	176	16	x	x	X
ejpam-146	176	17	.	.	PUNCT
ejpam-146	177	1	proof	proof	NOUN
ejpam-146	177	2	.	.	PUNCT
ejpam-146	178	1	(	(	PUNCT
ejpam-146	178	2	a)⇔	a)⇔	PROPN
ejpam-146	178	3	(	(	PUNCT
ejpam-146	178	4	b	b	NOUN
ejpam-146	178	5	)	)	PUNCT
ejpam-146	178	6	:	:	PUNCT
ejpam-146	178	7	obvious	obvious	ADJ
ejpam-146	178	8	.	.	PUNCT
ejpam-146	179	1	(	(	PUNCT
ejpam-146	179	2	b)⇒	b)⇒	NOUN
ejpam-146	179	3	(	(	PUNCT
ejpam-146	179	4	c	c	NOUN
ejpam-146	179	5	)	)	PUNCT
ejpam-146	179	6	:	:	PUNCT
ejpam-146	180	1	letf	letf	ADV
ejpam-146	180	2	=	=	SYM
ejpam-146	180	3	{	{	PUNCT
ejpam-146	180	4	fα	fα	PART
ejpam-146	180	5	:	:	PUNCT
ejpam-146	180	6	α	α	PROPN
ejpam-146	180	7	∈	∈	PROPN
ejpam-146	180	8	i	i	PRON
ejpam-146	180	9	}	}	PUNCT
ejpam-146	180	10	be	be	VERB
ejpam-146	180	11	a	a	DET
ejpam-146	180	12	filter	filter	NOUN
ejpam-146	180	13	base	base	NOUN
ejpam-146	180	14	on	on	ADP
ejpam-146	180	15	x	x	X
ejpam-146	180	16	.	.	PUNCT
ejpam-146	180	17	thenf	thenf	PROPN
ejpam-146	180	18	?	?	PUNCT
ejpam-146	181	1	=	=	PRON
ejpam-146	181	2	{	{	PUNCT
ejpam-146	181	3	β	β	NOUN
ejpam-146	181	4	-	-	NOUN
ejpam-146	181	5	θ	θ	NOUN
ejpam-146	181	6	-cl(fα	-cl(fα	PUNCT
ejpam-146	181	7	)	)	PUNCT
ejpam-146	181	8	:	:	PUNCT
ejpam-146	182	1	α	α	X
ejpam-146	182	2	∈	∈	PROPN
ejpam-146	183	1	i	i	PRON
ejpam-146	183	2	}	}	PUNCT
ejpam-146	183	3	is	be	AUX
ejpam-146	183	4	a	a	DET
ejpam-146	183	5	family	family	NOUN
ejpam-146	183	6	of	of	ADP
ejpam-146	183	7	β	β	PROPN
ejpam-146	183	8	-	-	PUNCT
ejpam-146	183	9	θ	θ	NOUN
ejpam-146	183	10	-closed	-close	VERB
ejpam-146	183	11	sets	set	NOUN
ejpam-146	183	12	with	with	ADP
ejpam-146	183	13	the	the	DET
ejpam-146	183	14	finite	finite	ADJ
ejpam-146	183	15	intersection	intersection	NOUN
ejpam-146	183	16	property	property	NOUN
ejpam-146	183	17	.	.	PUNCT
ejpam-146	184	1	then	then	ADV
ejpam-146	184	2	by	by	ADP
ejpam-146	184	3	(	(	PUNCT
ejpam-146	184	4	b	b	NOUN
ejpam-146	184	5	)	)	PUNCT
ejpam-146	184	6	β	β	NOUN
ejpam-146	184	7	-	-	NOUN
ejpam-146	184	8	θ	θ	NOUN
ejpam-146	184	9	-adf	-adf	PUNCT
ejpam-146	184	10	=	=	PUNCT
ejpam-146	184	11	∩f	∩f	NOUN
ejpam-146	184	12	?	?	PUNCT
ejpam-146	184	13	6=	6=	NUM
ejpam-146	184	14	;	;	PUNCT
ejpam-146	184	15	.	.	PUNCT
ejpam-146	185	1	(	(	PUNCT
ejpam-146	185	2	c)⇒	c)⇒	X
ejpam-146	185	3	(	(	PUNCT
ejpam-146	185	4	b	b	NOUN
ejpam-146	185	5	)	)	PUNCT
ejpam-146	185	6	:	:	PUNCT
ejpam-146	185	7	let	let	VERB
ejpam-146	185	8	ω	ω	PROPN
ejpam-146	185	9	=	=	PRON
ejpam-146	185	10	{	{	PUNCT
ejpam-146	185	11	fα	fα	ADP
ejpam-146	185	12	:	:	PUNCT
ejpam-146	185	13	α	α	PROPN
ejpam-146	185	14	∈	∈	PROPN
ejpam-146	186	1	i	i	PRON
ejpam-146	186	2	}	}	PUNCT
ejpam-146	186	3	be	be	VERB
ejpam-146	186	4	a	a	DET
ejpam-146	186	5	family	family	NOUN
ejpam-146	186	6	of	of	ADP
ejpam-146	186	7	β	β	PROPN
ejpam-146	186	8	-	-	PUNCT
ejpam-146	186	9	θ	θ	NOUN
ejpam-146	186	10	-closed	-close	VERB
ejpam-146	186	11	sets	set	NOUN
ejpam-146	186	12	having	have	VERB
ejpam-146	186	13	finite	finite	ADJ
ejpam-146	186	14	intersection	intersection	NOUN
ejpam-146	186	15	property	property	NOUN
ejpam-146	186	16	.	.	PUNCT
ejpam-146	187	1	let	let	VERB
ejpam-146	187	2	ω	ω	X
ejpam-146	187	3	?	?	PROPN
ejpam-146	187	4	be	be	VERB
ejpam-146	187	5	the	the	DET
ejpam-146	187	6	family	family	NOUN
ejpam-146	187	7	of	of	ADP
ejpam-146	187	8	all	all	DET
ejpam-146	187	9	sets	set	NOUN
ejpam-146	187	10	of	of	ADP
ejpam-146	187	11	ω	ω	NUM
ejpam-146	187	12	together	together	ADV
ejpam-146	187	13	with	with	ADP
ejpam-146	187	14	their	their	PRON
ejpam-146	187	15	all	all	DET
ejpam-146	187	16	finite	finite	ADJ
ejpam-146	187	17	intersections	intersection	NOUN
ejpam-146	187	18	.	.	PUNCT
ejpam-146	188	1	clearly	clearly	ADV
ejpam-146	188	2	,	,	PUNCT
ejpam-146	188	3	ω	ω	X
ejpam-146	188	4	?	?	PROPN
ejpam-146	188	5	is	be	AUX
ejpam-146	188	6	a	a	DET
ejpam-146	188	7	filter	filter	NOUN
ejpam-146	188	8	base	base	NOUN
ejpam-146	188	9	on	on	ADP
ejpam-146	188	10	x	x	PUNCT
ejpam-146	188	11	and	and	CCONJ
ejpam-146	188	12	hence	hence	ADV
ejpam-146	188	13	by	by	ADV
ejpam-146	188	14	(	(	PUNCT
ejpam-146	188	15	c	c	NOUN
ejpam-146	188	16	)	)	PUNCT
ejpam-146	188	17	,	,	PUNCT
ejpam-146	188	18	ω	ω	X
ejpam-146	188	19	?	?	PUNCT
ejpam-146	188	20	β	β	X
ejpam-146	188	21	-	-	PUNCT
ejpam-146	188	22	θ	θ	NOUN
ejpam-146	188	23	-adheres	-adhere	NOUN
ejpam-146	188	24	to	to	ADP
ejpam-146	188	25	some	some	DET
ejpam-146	188	26	point	point	NOUN
ejpam-146	188	27	say	say	VERB
ejpam-146	188	28	x	x	PUNCT
ejpam-146	188	29	in	in	ADP
ejpam-146	188	30	x	x	X
ejpam-146	188	31	.	.	PUNCT
ejpam-146	189	1	so	so	ADV
ejpam-146	189	2	,	,	PUNCT
ejpam-146	189	3	x	x	PUNCT
ejpam-146	189	4	∈	∈	NOUN
ejpam-146	189	5	∩ω	∩ω	PUNCT
ejpam-146	189	6	?	?	PUNCT
ejpam-146	190	1	⊂	⊂	PROPN
ejpam-146	190	2	∩ω	∩ω	PROPN
ejpam-146	190	3	.	.	PUNCT
ejpam-146	191	1	(	(	PUNCT
ejpam-146	191	2	c	c	X
ejpam-146	191	3	)	)	PUNCT
ejpam-146	191	4	⇒	⇒	NOUN
ejpam-146	191	5	(	(	PUNCT
ejpam-146	191	6	d	d	NOUN
ejpam-146	191	7	)	)	PUNCT
ejpam-146	191	8	:	:	PUNCT
ejpam-146	191	9	let	let	VERB
ejpam-146	191	10	f	f	PROPN
ejpam-146	191	11	=	=	PRON
ejpam-146	191	12	{	{	PUNCT
ejpam-146	191	13	fα	fα	PART
ejpam-146	191	14	:	:	PUNCT
ejpam-146	191	15	α	α	PROPN
ejpam-146	191	16	∈	∈	PROPN
ejpam-146	191	17	i	i	PRON
ejpam-146	191	18	}	}	PUNCT
ejpam-146	191	19	be	be	VERB
ejpam-146	191	20	a	a	DET
ejpam-146	191	21	filter	filter	NOUN
ejpam-146	191	22	base	base	NOUN
ejpam-146	191	23	on	on	ADP
ejpam-146	191	24	x	x	PUNCT
ejpam-146	191	25	with	with	ADP
ejpam-146	191	26	β	β	NOUN
ejpam-146	191	27	-	-	NOUN
ejpam-146	191	28	θ	θ	NOUN
ejpam-146	191	29	-adf	-adf	NOUN
ejpam-146	191	30	⊂	⊂	PRON
ejpam-146	191	31	{	{	PUNCT
ejpam-146	191	32	x	x	X
ejpam-146	191	33	}	}	PUNCT
ejpam-146	191	34	for	for	ADP
ejpam-146	191	35	some	some	DET
ejpam-146	191	36	x	x	SYM
ejpam-146	191	37	∈	∈	PROPN
ejpam-146	191	38	x	x	X
ejpam-146	191	39	.	.	PUNCT
ejpam-146	192	1	then	then	ADV
ejpam-146	192	2	by	by	ADP
ejpam-146	192	3	(	(	PUNCT
ejpam-146	192	4	c	c	NOUN
ejpam-146	192	5	)	)	PUNCT
ejpam-146	192	6	,	,	PUNCT
ejpam-146	192	7	β	β	X
ejpam-146	192	8	-	-	NOUN
ejpam-146	192	9	θ	θ	NOUN
ejpam-146	192	10	-adf	-adf	PUNCT
ejpam-146	192	11	=	=	PUNCT
ejpam-146	192	12	{	{	PUNCT
ejpam-146	192	13	x	x	NOUN
ejpam-146	192	14	}	}	PUNCT
ejpam-146	192	15	.	.	PUNCT
ejpam-146	193	1	suppose	suppose	VERB
ejpam-146	193	2	that	that	SCONJ
ejpam-146	193	3	there	there	PRON
ejpam-146	193	4	exists	exist	VERB
ejpam-146	193	5	an	an	DET
ejpam-146	193	6	u	u	PROPN
ejpam-146	193	7	∈	∈	PROPN
ejpam-146	193	8	βr(x	βr(x	PUNCT
ejpam-146	193	9	,	,	PUNCT
ejpam-146	193	10	x	x	X
ejpam-146	193	11	)	)	PUNCT
ejpam-146	193	12	such	such	ADJ
ejpam-146	193	13	that	that	DET
ejpam-146	193	14	fα	fα	ADP
ejpam-146	193	15	∩	∩	NOUN
ejpam-146	193	16	(	(	PUNCT
ejpam-146	193	17	x	x	SYM
ejpam-146	193	18	−	−	PROPN
ejpam-146	193	19	u	u	NOUN
ejpam-146	193	20	)	)	PUNCT
ejpam-146	193	21	6=	6=	NUM
ejpam-146	193	22	;	;	PUNCT
ejpam-146	193	23	,	,	PUNCT
ejpam-146	193	24	for	for	ADP
ejpam-146	193	25	all	all	DET
ejpam-146	193	26	α	α	NOUN
ejpam-146	193	27	∈	∈	NOUN
ejpam-146	193	28	i	i	PRON
ejpam-146	193	29	.	.	PUNCT
ejpam-146	194	1	then	then	ADV
ejpam-146	194	2	f	f	X
ejpam-146	194	3	?	?	PUNCT
ejpam-146	195	1	=	=	PRON
ejpam-146	195	2	{	{	PUNCT
ejpam-146	196	1	fα	fα	ADP
ejpam-146	196	2	−	−	PROPN
ejpam-146	196	3	u	u	NOUN
ejpam-146	196	4	:	:	PUNCT
ejpam-146	196	5	α	α	PROPN
ejpam-146	196	6	∈	∈	PROPN
ejpam-146	197	1	i	i	PRON
ejpam-146	197	2	}	}	PUNCT
ejpam-146	197	3	is	be	AUX
ejpam-146	197	4	a	a	DET
ejpam-146	197	5	filter	filter	NOUN
ejpam-146	197	6	base	base	NOUN
ejpam-146	197	7	on	on	ADP
ejpam-146	197	8	x	x	X
ejpam-146	197	9	.	.	PUNCT
ejpam-146	198	1	but	but	CCONJ
ejpam-146	198	2	by	by	ADP
ejpam-146	198	3	(	(	PUNCT
ejpam-146	198	4	c	c	NOUN
ejpam-146	198	5	)	)	PUNCT
ejpam-146	198	6	,	,	PUNCT
ejpam-146	198	7	f	f	PROPN
ejpam-146	198	8	?	?	PUNCT
ejpam-146	198	9	has	have	AUX
ejpam-146	198	10	at	at	ADV
ejpam-146	198	11	least	least	ADV
ejpam-146	198	12	one	one	NUM
ejpam-146	198	13	β	β	NOUN
ejpam-146	198	14	-	-	PUNCT
ejpam-146	198	15	θ	θ	NOUN
ejpam-146	198	16	-adherent	-adherent	NOUN
ejpam-146	198	17	point	point	NOUN
ejpam-146	198	18	.	.	PUNCT
ejpam-146	199	1	now	now	ADV
ejpam-146	199	2	,	,	PUNCT
ejpam-146	199	3	∩α∈iβ	∩α∈iβ	PROPN
ejpam-146	199	4	-	-	PUNCT
ejpam-146	199	5	θ	θ	PROPN
ejpam-146	199	6	-cl(fα	-cl(fα	PUNCT
ejpam-146	199	7	−	−	PROPN
ejpam-146	199	8	u	u	NOUN
ejpam-146	199	9	)	)	PUNCT
ejpam-146	199	10	⊂	⊂	PROPN
ejpam-146	199	11	(	(	PUNCT
ejpam-146	199	12	∩α∈iβ	∩α∈iβ	NOUN
ejpam-146	199	13	-	-	PUNCT
ejpam-146	199	14	θ	θ	PROPN
ejpam-146	199	15	cl(fα	cl(fα	NOUN
ejpam-146	199	16	)	)	PUNCT
ejpam-146	199	17	)	)	PUNCT
ejpam-146	199	18	∩	∩	NOUN
ejpam-146	199	19	(	(	PUNCT
ejpam-146	199	20	x	x	SYM
ejpam-146	199	21	−	−	PROPN
ejpam-146	199	22	u	u	NOUN
ejpam-146	199	23	)	)	PUNCT
ejpam-146	199	24	=	=	SYM
ejpam-146	199	25	{	{	PUNCT
ejpam-146	199	26	x	x	NOUN
ejpam-146	199	27	}	}	PUNCT
ejpam-146	199	28	∩	∩	NOUN
ejpam-146	199	29	(	(	PUNCT
ejpam-146	199	30	x	x	SYM
ejpam-146	199	31	−	−	PROPN
ejpam-146	199	32	u	u	NOUN
ejpam-146	199	33	)	)	PUNCT
ejpam-146	199	34	=	=	SYM
ejpam-146	199	35	;	;	PUNCT
ejpam-146	199	36	—	—	PUNCT
ejpam-146	199	37	a	a	DET
ejpam-146	199	38	contradiction	contradiction	NOUN
ejpam-146	199	39	.	.	PUNCT
ejpam-146	200	1	so	so	ADV
ejpam-146	200	2	for	for	ADP
ejpam-146	200	3	each	each	DET
ejpam-146	200	4	u	u	PROPN
ejpam-146	200	5	∈	∈	PROPN
ejpam-146	200	6	βr(x	βr(x	PUNCT
ejpam-146	200	7	,	,	PUNCT
ejpam-146	200	8	x	x	X
ejpam-146	200	9	)	)	PUNCT
ejpam-146	200	10	there	there	ADV
ejpam-146	200	11	c.	c.	PROPN
ejpam-146	200	12	k.	k.	PROPN
ejpam-146	200	13	basu	basu	PROPN
ejpam-146	200	14	,	,	PUNCT
ejpam-146	200	15	m.	m.	PROPN
ejpam-146	200	16	k.	k.	PROPN
ejpam-146	200	17	ghosh	ghosh	PROPN
ejpam-146	200	18	/	/	PUNCT
ejpam-146	200	19	eur	eur	PROPN
ejpam-146	200	20	.	.	PUNCT
ejpam-146	201	1	j.	j.	PROPN
ejpam-146	201	2	pure	pure	PROPN
ejpam-146	201	3	appl	appl	PROPN
ejpam-146	201	4	.	.	PROPN
ejpam-146	201	5	math	math	PROPN
ejpam-146	201	6	,	,	PUNCT
ejpam-146	201	7	1	1	NUM
ejpam-146	201	8	(	(	PUNCT
ejpam-146	201	9	2008	2008	NUM
ejpam-146	201	10	)	)	PUNCT
ejpam-146	201	11	,	,	PUNCT
ejpam-146	201	12	(	(	PUNCT
ejpam-146	201	13	40	40	NUM
ejpam-146	201	14	-	-	SYM
ejpam-146	201	15	50	50	NUM
ejpam-146	201	16	)	)	PUNCT
ejpam-146	201	17	44	44	NUM
ejpam-146	201	18	exists	exist	VERB
ejpam-146	201	19	an	an	DET
ejpam-146	201	20	fα	fα	NOUN
ejpam-146	201	21	∈	∈	PROPN
ejpam-146	201	22	f	f	NOUN
ejpam-146	201	23	with	with	ADP
ejpam-146	201	24	fα	fα	ADP
ejpam-146	201	25	⊂	⊂	PROPN
ejpam-146	201	26	u	u	PROPN
ejpam-146	201	27	.	.	PUNCT
ejpam-146	202	1	therefore	therefore	ADV
ejpam-146	202	2	f	f	X
ejpam-146	202	3	β	β	PROPN
ejpam-146	202	4	-	-	ADJ
ejpam-146	202	5	θ	θ	NOUN
ejpam-146	202	6	-converges	-converge	NOUN
ejpam-146	202	7	to	to	ADP
ejpam-146	202	8	x	x	X
ejpam-146	202	9	.	.	PUNCT
ejpam-146	203	1	(	(	PUNCT
ejpam-146	203	2	d)⇒	d)⇒	NOUN
ejpam-146	203	3	(	(	PUNCT
ejpam-146	203	4	c	c	NOUN
ejpam-146	203	5	)	)	PUNCT
ejpam-146	203	6	:	:	PUNCT
ejpam-146	203	7	suppose	suppose	VERB
ejpam-146	203	8	that	that	SCONJ
ejpam-146	203	9	f	f	PROPN
ejpam-146	203	10	=	=	PRON
ejpam-146	203	11	{	{	PUNCT
ejpam-146	203	12	fα	fα	PART
ejpam-146	203	13	:	:	PUNCT
ejpam-146	203	14	α	α	PROPN
ejpam-146	204	1	∈	∈	PROPN
ejpam-146	205	1	i	i	PRON
ejpam-146	205	2	}	}	PUNCT
ejpam-146	205	3	is	be	AUX
ejpam-146	205	4	a	a	DET
ejpam-146	205	5	filter	filter	NOUN
ejpam-146	205	6	base	base	NOUN
ejpam-146	205	7	on	on	ADP
ejpam-146	205	8	x	x	PUNCT
ejpam-146	205	9	with	with	ADP
ejpam-146	205	10	no	no	DET
ejpam-146	205	11	β	β	NOUN
ejpam-146	205	12	-	-	ADJ
ejpam-146	205	13	θ	θ	ADJ
ejpam-146	205	14	-adherent	-adherent	NOUN
ejpam-146	205	15	point	point	NOUN
ejpam-146	205	16	in	in	ADP
ejpam-146	205	17	x	x	X
ejpam-146	205	18	.	.	PUNCT
ejpam-146	206	1	by	by	ADP
ejpam-146	206	2	hypothesis	hypothesis	NOUN
ejpam-146	206	3	(	(	PUNCT
ejpam-146	206	4	d	d	NOUN
ejpam-146	206	5	)	)	PUNCT
ejpam-146	206	6	,	,	PUNCT
ejpam-146	206	7	f	f	PROPN
ejpam-146	206	8	β	β	X
ejpam-146	206	9	-	-	ADJ
ejpam-146	206	10	θ	θ	NOUN
ejpam-146	206	11	-converges	-converge	NOUN
ejpam-146	206	12	to	to	ADP
ejpam-146	206	13	a	a	DET
ejpam-146	206	14	point	point	NOUN
ejpam-146	206	15	say	say	VERB
ejpam-146	206	16	x	x	PUNCT
ejpam-146	206	17	in	in	ADP
ejpam-146	206	18	x	x	X
ejpam-146	206	19	.	.	PUNCT
ejpam-146	207	1	let	let	VERB
ejpam-146	207	2	fα	fα	ADP
ejpam-146	207	3	∈	∈	VERB
ejpam-146	207	4	f	f	PROPN
ejpam-146	207	5	and	and	CCONJ
ejpam-146	207	6	u	u	PROPN
ejpam-146	207	7	∈	∈	PROPN
ejpam-146	207	8	βr(x	βr(x	PUNCT
ejpam-146	207	9	,	,	PUNCT
ejpam-146	207	10	x	x	X
ejpam-146	207	11	)	)	PUNCT
ejpam-146	207	12	.	.	PUNCT
ejpam-146	208	1	then	then	ADV
ejpam-146	208	2	there	there	PRON
ejpam-146	208	3	exists	exist	VERB
ejpam-146	208	4	an	an	DET
ejpam-146	208	5	f	f	NOUN
ejpam-146	208	6	′	′	NUM
ejpam-146	209	1	α	α	PROPN
ejpam-146	209	2	∈	∈	PROPN
ejpam-146	209	3	f	f	PROPN
ejpam-146	209	4	such	such	ADJ
ejpam-146	210	1	that	that	SCONJ
ejpam-146	210	2	f	f	PROPN
ejpam-146	211	1	′	′	NUM
ejpam-146	211	2	α	α	PROPN
ejpam-146	211	3	⊂	⊂	PROPN
ejpam-146	211	4	u	u	PROPN
ejpam-146	211	5	.	.	PUNCT
ejpam-146	212	1	since	since	SCONJ
ejpam-146	212	2	f	f	PROPN
ejpam-146	212	3	is	be	AUX
ejpam-146	212	4	a	a	DET
ejpam-146	212	5	filter	filter	NOUN
ejpam-146	212	6	base	base	NOUN
ejpam-146	212	7	on	on	ADP
ejpam-146	212	8	x	x	X
ejpam-146	212	9	,	,	PUNCT
ejpam-146	212	10	there	there	PRON
ejpam-146	212	11	exists	exist	VERB
ejpam-146	212	12	an	an	DET
ejpam-146	212	13	fα	fα	NOUN
ejpam-146	212	14	?	?	PUNCT
ejpam-146	213	1	∈	∈	PROPN
ejpam-146	213	2	f	f	PROPN
ejpam-146	213	3	such	such	ADJ
ejpam-146	213	4	that	that	DET
ejpam-146	213	5	fα	fα	NOUN
ejpam-146	213	6	?	?	PUNCT
ejpam-146	214	1	⊂	⊂	PROPN
ejpam-146	214	2	fα	fα	ADP
ejpam-146	214	3	∩	∩	NOUN
ejpam-146	214	4	f	f	PROPN
ejpam-146	215	1	′	′	NUM
ejpam-146	215	2	α	α	PROPN
ejpam-146	215	3	⊂	⊂	X
ejpam-146	215	4	fα	fα	ADP
ejpam-146	215	5	∩	∩	ADJ
ejpam-146	215	6	u	u	PROPN
ejpam-146	215	7	.	.	PUNCT
ejpam-146	216	1	since	since	SCONJ
ejpam-146	216	2	f?α	f?α	NUM
ejpam-146	216	3	is	be	AUX
ejpam-146	216	4	non	non	ADJ
ejpam-146	216	5	-	-	ADJ
ejpam-146	216	6	empty	empty	ADJ
ejpam-146	216	7	,	,	PUNCT
ejpam-146	216	8	fα	fα	ADP
ejpam-146	216	9	∩	∩	ADJ
ejpam-146	216	10	u	u	NOUN
ejpam-146	216	11	6=	6=	PROPN
ejpam-146	216	12	;	;	PUNCT
ejpam-146	216	13	.	.	PUNCT
ejpam-146	217	1	so	so	ADV
ejpam-146	217	2	,	,	PUNCT
ejpam-146	217	3	x	x	PUNCT
ejpam-146	217	4	∈	∈	PROPN
ejpam-146	217	5	βθ	βθ	ADJ
ejpam-146	217	6	-cl(fα	-cl(fα	PUNCT
ejpam-146	217	7	)	)	PUNCT
ejpam-146	217	8	and	and	CCONJ
ejpam-146	217	9	this	this	PRON
ejpam-146	217	10	holds	hold	VERB
ejpam-146	217	11	for	for	ADP
ejpam-146	217	12	every	every	DET
ejpam-146	217	13	fα	fα	NOUN
ejpam-146	217	14	∈	∈	PROPN
ejpam-146	217	15	f	f	X
ejpam-146	217	16	.	.	PUNCT
ejpam-146	218	1	therefore	therefore	ADV
ejpam-146	218	2	,	,	PUNCT
ejpam-146	218	3	x	x	X
ejpam-146	218	4	is	be	AUX
ejpam-146	218	5	a	a	DET
ejpam-146	218	6	β	β	NOUN
ejpam-146	218	7	-	-	ADJ
ejpam-146	218	8	θ	θ	ADJ
ejpam-146	218	9	-adherent	-adherent	NOUN
ejpam-146	218	10	point	point	NOUN
ejpam-146	218	11	of	of	ADP
ejpam-146	218	12	f	f	PROPN
ejpam-146	218	13	—	—	PUNCT
ejpam-146	218	14	a	a	DET
ejpam-146	218	15	contradiction	contradiction	NOUN
ejpam-146	218	16	.	.	PUNCT
ejpam-146	219	1	(	(	PUNCT
ejpam-146	219	2	e)⇒	e)⇒	NOUN
ejpam-146	219	3	(	(	PUNCT
ejpam-146	219	4	c	c	NOUN
ejpam-146	219	5	)	)	PUNCT
ejpam-146	219	6	:	:	PUNCT
ejpam-146	219	7	let	let	VERB
ejpam-146	219	8	f	f	PRON
ejpam-146	219	9	be	be	AUX
ejpam-146	219	10	a	a	DET
ejpam-146	219	11	filter	filter	NOUN
ejpam-146	219	12	base	base	NOUN
ejpam-146	219	13	on	on	ADP
ejpam-146	219	14	x	x	PUNCT
ejpam-146	219	15	and	and	CCONJ
ejpam-146	219	16	f	f	PROPN
ejpam-146	219	17	?	?	PUNCT
ejpam-146	220	1	be	be	AUX
ejpam-146	220	2	a	a	DET
ejpam-146	220	3	maximal	maximal	ADJ
ejpam-146	220	4	filter	filter	NOUN
ejpam-146	220	5	base	base	NOUN
ejpam-146	220	6	such	such	ADJ
ejpam-146	220	7	that	that	SCONJ
ejpam-146	220	8	f	f	X
ejpam-146	220	9	⊂f	⊂f	PROPN
ejpam-146	220	10	?	?	PUNCT
ejpam-146	220	11	.	.	PUNCT
ejpam-146	221	1	by	by	ADP
ejpam-146	221	2	(	(	PUNCT
ejpam-146	221	3	e	e	NOUN
ejpam-146	221	4	)	)	PUNCT
ejpam-146	221	5	,	,	PUNCT
ejpam-146	221	6	f	f	PROPN
ejpam-146	221	7	?	?	PUNCT
ejpam-146	221	8	β	β	X
ejpam-146	221	9	-	-	PUNCT
ejpam-146	221	10	θ	θ	NOUN
ejpam-146	221	11	-converges	-converge	NOUN
ejpam-146	221	12	to	to	ADP
ejpam-146	221	13	some	some	DET
ejpam-146	221	14	point	point	NOUN
ejpam-146	221	15	x	x	PUNCT
ejpam-146	221	16	in	in	ADP
ejpam-146	221	17	x	x	X
ejpam-146	221	18	.	.	PUNCT
ejpam-146	222	1	for	for	ADP
ejpam-146	222	2	each	each	DET
ejpam-146	222	3	u	u	PROPN
ejpam-146	222	4	∈	∈	PROPN
ejpam-146	222	5	βr(x	βr(x	PUNCT
ejpam-146	222	6	,	,	PUNCT
ejpam-146	222	7	x	x	X
ejpam-146	222	8	)	)	PUNCT
ejpam-146	222	9	,	,	PUNCT
ejpam-146	222	10	there	there	PRON
ejpam-146	222	11	exists	exist	VERB
ejpam-146	222	12	an	an	DET
ejpam-146	222	13	f	f	NOUN
ejpam-146	222	14	?	?	PUNCT
ejpam-146	223	1	∈	∈	PROPN
ejpam-146	224	1	f	f	NOUN
ejpam-146	224	2	?	?	PUNCT
ejpam-146	225	1	such	such	ADJ
ejpam-146	225	2	that	that	DET
ejpam-146	225	3	f	f	X
ejpam-146	225	4	?	?	PUNCT
ejpam-146	226	1	⊂	⊂	PROPN
ejpam-146	226	2	u	u	PROPN
ejpam-146	226	3	.	.	PUNCT
ejpam-146	227	1	so	so	ADV
ejpam-146	227	2	for	for	ADP
ejpam-146	227	3	each	each	DET
ejpam-146	227	4	f	f	PROPN
ejpam-146	227	5	∈	∈	PROPN
ejpam-146	227	6	f	f	PROPN
ejpam-146	227	7	,	,	PUNCT
ejpam-146	227	8	;	;	PUNCT
ejpam-146	227	9	6=	6=	NUM
ejpam-146	227	10	f	f	PROPN
ejpam-146	227	11	∩	∩	PROPN
ejpam-146	227	12	f	f	X
ejpam-146	227	13	?	?	PUNCT
ejpam-146	228	1	⊂	⊂	PROPN
ejpam-146	228	2	f	f	X
ejpam-146	229	1	∩u	∩u	INTJ
ejpam-146	229	2	.	.	PUNCT
ejpam-146	230	1	therefore	therefore	ADV
ejpam-146	230	2	x	x	X
ejpam-146	230	3	is	be	AUX
ejpam-146	230	4	a	a	DET
ejpam-146	230	5	β	β	NOUN
ejpam-146	230	6	-	-	ADJ
ejpam-146	230	7	θ	θ	ADJ
ejpam-146	230	8	-adherent	-adherent	NOUN
ejpam-146	230	9	point	point	NOUN
ejpam-146	230	10	of	of	ADP
ejpam-146	230	11	f	f	PROPN
ejpam-146	230	12	.	.	PUNCT
ejpam-146	231	1	(	(	PUNCT
ejpam-146	231	2	c)⇒	c)⇒	X
ejpam-146	231	3	(	(	PUNCT
ejpam-146	231	4	e	e	NOUN
ejpam-146	231	5	)	)	PUNCT
ejpam-146	231	6	:	:	PUNCT
ejpam-146	231	7	obvious	obvious	ADJ
ejpam-146	231	8	.	.	PUNCT
ejpam-146	232	1	remark	remark	NOUN
ejpam-146	232	2	3.6	3.6	NUM
ejpam-146	232	3	.	.	PUNCT
ejpam-146	233	1	equivalent	equivalent	ADJ
ejpam-146	233	2	formulations	formulation	NOUN
ejpam-146	233	3	of	of	ADP
ejpam-146	233	4	the	the	DET
ejpam-146	233	5	characterizations	characterization	NOUN
ejpam-146	233	6	of	of	ADP
ejpam-146	233	7	β	β	NOUN
ejpam-146	233	8	-	-	ADJ
ejpam-146	233	9	closed	closed	ADJ
ejpam-146	233	10	spaces	space	NOUN
ejpam-146	233	11	in	in	ADP
ejpam-146	233	12	terms	term	NOUN
ejpam-146	233	13	of	of	ADP
ejpam-146	233	14	nets	net	NOUN
ejpam-146	233	15	and	and	CCONJ
ejpam-146	233	16	ultranets	ultranet	NOUN
ejpam-146	233	17	are	be	AUX
ejpam-146	233	18	quite	quite	ADV
ejpam-146	233	19	similar	similar	ADJ
ejpam-146	233	20	to	to	ADP
ejpam-146	233	21	the	the	DET
ejpam-146	233	22	above	above	ADJ
ejpam-146	233	23	theorem	theorem	NOUN
ejpam-146	233	24	and	and	CCONJ
ejpam-146	233	25	are	be	AUX
ejpam-146	233	26	omitted	omit	VERB
ejpam-146	233	27	.	.	PUNCT
ejpam-146	234	1	theorem	theorem	VERB
ejpam-146	234	2	3.7	3.7	NUM
ejpam-146	234	3	.	.	PUNCT
ejpam-146	235	1	(	(	PUNCT
ejpam-146	235	2	x	x	X
ejpam-146	235	3	,	,	PUNCT
ejpam-146	235	4	τ	τ	X
ejpam-146	235	5	)	)	PUNCT
ejpam-146	235	6	is	be	AUX
ejpam-146	235	7	β	β	NOUN
ejpam-146	235	8	-	-	VERB
ejpam-146	235	9	closed	closed	ADJ
ejpam-146	235	10	if	if	SCONJ
ejpam-146	235	11	and	and	CCONJ
ejpam-146	235	12	only	only	ADV
ejpam-146	235	13	if	if	SCONJ
ejpam-146	235	14	(	(	PUNCT
ejpam-146	235	15	x	x	INTJ
ejpam-146	235	16	,	,	PUNCT
ejpam-146	235	17	τα	τα	PROPN
ejpam-146	235	18	)	)	PUNCT
ejpam-146	235	19	is	be	AUX
ejpam-146	235	20	β	β	NOUN
ejpam-146	235	21	-	-	VERB
ejpam-146	235	22	closed	closed	ADJ
ejpam-146	235	23	.	.	PUNCT
ejpam-146	236	1	proof	proof	NOUN
ejpam-146	236	2	.	.	PUNCT
ejpam-146	237	1	the	the	DET
ejpam-146	237	2	result	result	NOUN
ejpam-146	237	3	follows	follow	VERB
ejpam-146	237	4	from	from	ADP
ejpam-146	237	5	the	the	DET
ejpam-146	237	6	well	well	ADV
ejpam-146	237	7	known	know	VERB
ejpam-146	237	8	fact	fact	NOUN
ejpam-146	237	9	that	that	SCONJ
ejpam-146	237	10	in	in	ADP
ejpam-146	237	11	any	any	DET
ejpam-146	237	12	space	space	NOUN
ejpam-146	237	13	(	(	PUNCT
ejpam-146	237	14	x	x	X
ejpam-146	237	15	,	,	PUNCT
ejpam-146	237	16	τ	τ	PROPN
ejpam-146	237	17	)	)	PUNCT
ejpam-146	237	18	,	,	PUNCT
ejpam-146	237	19	βo(x	βo(x	PUNCT
ejpam-146	237	20	,	,	PUNCT
ejpam-146	237	21	τ	τ	X
ejpam-146	237	22	)	)	PUNCT
ejpam-146	237	23	=	=	SYM
ejpam-146	237	24	βo(x	βo(x	NUM
ejpam-146	237	25	,	,	PUNCT
ejpam-146	237	26	τα	τα	PROPN
ejpam-146	237	27	)	)	PUNCT
ejpam-146	237	28	.	.	PUNCT
ejpam-146	238	1	since	since	SCONJ
ejpam-146	238	2	every	every	DET
ejpam-146	238	3	open	open	ADJ
ejpam-146	238	4	set	set	NOUN
ejpam-146	238	5	is	be	AUX
ejpam-146	238	6	β	β	NOUN
ejpam-146	238	7	-	-	ADJ
ejpam-146	238	8	open	open	ADJ
ejpam-146	238	9	,	,	PUNCT
ejpam-146	238	10	the	the	DET
ejpam-146	238	11	following	follow	VERB
ejpam-146	238	12	theorem	theorem	NOUN
ejpam-146	238	13	is	be	AUX
ejpam-146	238	14	quite	quite	ADV
ejpam-146	238	15	obvious	obvious	ADJ
ejpam-146	238	16	.	.	PUNCT
ejpam-146	239	1	theorem	theorem	VERB
ejpam-146	239	2	3.8	3.8	NUM
ejpam-146	239	3	.	.	PUNCT
ejpam-146	240	1	(	(	PUNCT
ejpam-146	240	2	a	a	X
ejpam-146	240	3	)	)	PUNCT
ejpam-146	240	4	every	every	DET
ejpam-146	240	5	β	β	X
ejpam-146	240	6	-	-	ADJ
ejpam-146	240	7	closed	closed	ADJ
ejpam-146	240	8	space	space	NOUN
ejpam-146	240	9	is	be	AUX
ejpam-146	240	10	quasi	quasi	ADJ
ejpam-146	240	11	h	h	NOUN
ejpam-146	240	12	-	-	PUNCT
ejpam-146	240	13	closed	closed	ADJ
ejpam-146	240	14	.	.	PUNCT
ejpam-146	241	1	(	(	PUNCT
ejpam-146	241	2	b	b	X
ejpam-146	241	3	)	)	PUNCT
ejpam-146	241	4	every	every	DET
ejpam-146	241	5	β	β	ADJ
ejpam-146	241	6	-	-	ADJ
ejpam-146	241	7	compact	compact	ADJ
ejpam-146	241	8	space	space	NOUN
ejpam-146	241	9	[	[	X
ejpam-146	241	10	2	2	NUM
ejpam-146	241	11	]	]	PUNCT
ejpam-146	241	12	(	(	PUNCT
ejpam-146	241	13	a	a	DET
ejpam-146	241	14	space	space	NOUN
ejpam-146	241	15	is	be	AUX
ejpam-146	241	16	β	β	NOUN
ejpam-146	241	17	-	-	ADJ
ejpam-146	241	18	compact	compact	ADJ
ejpam-146	241	19	if	if	SCONJ
ejpam-146	241	20	every	every	DET
ejpam-146	241	21	β	β	NOUN
ejpam-146	241	22	-	-	ADJ
ejpam-146	241	23	open	open	ADJ
ejpam-146	241	24	cover	cover	NOUN
ejpam-146	241	25	of	of	ADP
ejpam-146	241	26	has	have	VERB
ejpam-146	241	27	a	a	DET
ejpam-146	241	28	finite	finite	ADJ
ejpam-146	241	29	subcover	subcover	PROPN
ejpam-146	241	30	)	)	PUNCT
ejpam-146	241	31	is	be	AUX
ejpam-146	241	32	β	β	NOUN
ejpam-146	241	33	-	-	VERB
ejpam-146	241	34	closed	closed	ADJ
ejpam-146	241	35	.	.	PUNCT
ejpam-146	242	1	remark	remark	NOUN
ejpam-146	242	2	3.9	3.9	NUM
ejpam-146	242	3	.	.	PUNCT
ejpam-146	243	1	the	the	DET
ejpam-146	243	2	converse	converse	NOUN
ejpam-146	243	3	of	of	ADP
ejpam-146	243	4	the	the	DET
ejpam-146	243	5	results	result	NOUN
ejpam-146	243	6	(	(	PUNCT
ejpam-146	243	7	a	a	X
ejpam-146	243	8	)	)	PUNCT
ejpam-146	243	9	and	and	CCONJ
ejpam-146	243	10	(	(	PUNCT
ejpam-146	243	11	b	b	NOUN
ejpam-146	243	12	)	)	PUNCT
ejpam-146	243	13	in	in	ADP
ejpam-146	243	14	theorem	theorem	ADJ
ejpam-146	243	15	3.8	3.8	NUM
ejpam-146	243	16	are	be	AUX
ejpam-146	243	17	not	not	PART
ejpam-146	243	18	true	true	ADJ
ejpam-146	243	19	in	in	ADP
ejpam-146	243	20	general	general	ADJ
ejpam-146	243	21	.	.	PUNCT
ejpam-146	244	1	furthermore	furthermore	ADV
ejpam-146	244	2	the	the	DET
ejpam-146	244	3	concepts	concept	NOUN
ejpam-146	244	4	of	of	ADP
ejpam-146	244	5	compactness	compactness	NOUN
ejpam-146	244	6	and	and	CCONJ
ejpam-146	244	7	β	β	NOUN
ejpam-146	244	8	-	-	NOUN
ejpam-146	244	9	closedness	closedness	NOUN
ejpam-146	244	10	are	be	AUX
ejpam-146	244	11	independent	independent	ADJ
ejpam-146	244	12	.	.	PUNCT
ejpam-146	244	13	example	example	NOUN
ejpam-146	245	1	3.10	3.10	NUM
ejpam-146	245	2	.	.	PUNCT
ejpam-146	245	3	example	example	NOUN
ejpam-146	245	4	of	of	ADP
ejpam-146	245	5	a	a	DET
ejpam-146	245	6	compact	compact	ADJ
ejpam-146	245	7	(	(	PUNCT
ejpam-146	245	8	and	and	CCONJ
ejpam-146	245	9	hence	hence	ADV
ejpam-146	245	10	quasi	quasi	VERB
ejpam-146	245	11	h	h	NOUN
ejpam-146	245	12	-	-	PUNCT
ejpam-146	245	13	closed	closed	ADJ
ejpam-146	245	14	)	)	PUNCT
ejpam-146	245	15	space	space	NOUN
ejpam-146	245	16	which	which	PRON
ejpam-146	245	17	is	be	AUX
ejpam-146	245	18	not	not	PART
ejpam-146	245	19	β	β	NOUN
ejpam-146	245	20	-	-	VERB
ejpam-146	245	21	closed	closed	ADJ
ejpam-146	245	22	.	.	PUNCT
ejpam-146	246	1	let	let	VERB
ejpam-146	246	2	x	x	SYM
ejpam-146	246	3	=	=	PUNCT
ejpam-146	246	4	n	n	CCONJ
ejpam-146	246	5	be	be	VERB
ejpam-146	246	6	the	the	DET
ejpam-146	246	7	set	set	NOUN
ejpam-146	246	8	of	of	ADP
ejpam-146	246	9	all	all	DET
ejpam-146	246	10	naturals	natural	NOUN
ejpam-146	246	11	with	with	ADP
ejpam-146	246	12	the	the	DET
ejpam-146	246	13	co	co	NOUN
ejpam-146	246	14	-	-	ADJ
ejpam-146	246	15	finite	finite	ADJ
ejpam-146	246	16	topology	topology	NOUN
ejpam-146	246	17	τ	τ	NOUN
ejpam-146	246	18	.	.	PUNCT
ejpam-146	246	19	here	here	ADV
ejpam-146	246	20	so(x	so(x	PUNCT
ejpam-146	246	21	)	)	PUNCT
ejpam-146	247	1	=	=	SYM
ejpam-146	247	2	τ	τ	PROPN
ejpam-146	247	3	and	and	CCONJ
ejpam-146	247	4	po(x	po(x	NUM
ejpam-146	247	5	)	)	PUNCT
ejpam-146	247	6	=	=	SYM
ejpam-146	247	7	βo(x	βo(x	PUNCT
ejpam-146	247	8	)	)	PUNCT
ejpam-146	248	1	=	=	PUNCT
ejpam-146	248	2	{	{	PUNCT
ejpam-146	248	3	s	s	X
ejpam-146	248	4	⊂	⊂	PROPN
ejpam-146	248	5	x	x	X
ejpam-146	248	6	:	:	PUNCT
ejpam-146	248	7	s	s	X
ejpam-146	248	8	is	be	AUX
ejpam-146	248	9	infinite	infinite	ADJ
ejpam-146	248	10	}	}	PUNCT
ejpam-146	248	11	∪	∪	X
ejpam-146	248	12	{	{	PUNCT
ejpam-146	248	13	;	;	PUNCT
ejpam-146	248	14	}	}	PUNCT
ejpam-146	248	15	.	.	PUNCT
ejpam-146	249	1	since	since	SCONJ
ejpam-146	249	2	for	for	ADP
ejpam-146	249	3	a	a	DET
ejpam-146	249	4	subset	subset	NOUN
ejpam-146	249	5	s	s	PART
ejpam-146	249	6	,	,	PUNCT
ejpam-146	249	7	β	β	X
ejpam-146	249	8	cl(s	cl(s	NOUN
ejpam-146	249	9	)	)	PUNCT
ejpam-146	249	10	=	=	SYM
ejpam-146	249	11	s	s	NOUN
ejpam-146	249	12	∪	∪	VERB
ejpam-146	249	13	int(cl(int(s	int(cl(int(s	PROPN
ejpam-146	249	14	)	)	PUNCT
ejpam-146	249	15	)	)	PUNCT
ejpam-146	249	16	)	)	PUNCT
ejpam-146	249	17	,	,	PUNCT
ejpam-146	249	18	so	so	CCONJ
ejpam-146	249	19	the	the	DET
ejpam-146	249	20	β	β	X
ejpam-146	249	21	cl(ai	cl(ai	PROPN
ejpam-146	249	22	)	)	PUNCT
ejpam-146	249	23	=	=	VERB
ejpam-146	249	24	ai	ai	VERB
ejpam-146	249	25	when	when	SCONJ
ejpam-146	249	26	ai	ai	VERB
ejpam-146	249	27	=	=	NOUN
ejpam-146	249	28	ne	ne	PROPN
ejpam-146	249	29	∪	∪	X
ejpam-146	249	30	{	{	PUNCT
ejpam-146	249	31	i	i	NOUN
ejpam-146	249	32	}	}	PUNCT
ejpam-146	249	33	,	,	PUNCT
ejpam-146	249	34	i	i	PRON
ejpam-146	249	35	∈	∈	PROPN
ejpam-146	249	36	n	n	ADV
ejpam-146	249	37	and	and	CCONJ
ejpam-146	249	38	ne	ne	PROPN
ejpam-146	249	39	be	be	AUX
ejpam-146	249	40	the	the	DET
ejpam-146	249	41	set	set	NOUN
ejpam-146	249	42	of	of	ADP
ejpam-146	249	43	all	all	DET
ejpam-146	249	44	even	even	ADV
ejpam-146	249	45	positive	positive	ADJ
ejpam-146	249	46	integers	integer	NOUN
ejpam-146	249	47	.	.	PUNCT
ejpam-146	250	1	if	if	SCONJ
ejpam-146	250	2	we	we	PRON
ejpam-146	250	3	take	take	VERB
ejpam-146	250	4	the	the	DET
ejpam-146	250	5	β	β	NOUN
ejpam-146	250	6	-	-	ADJ
ejpam-146	250	7	open	open	ADJ
ejpam-146	250	8	cover	cover	NOUN
ejpam-146	250	9	u	u	NOUN
ejpam-146	250	10	=	=	PUNCT
ejpam-146	250	11	{	{	PUNCT
ejpam-146	250	12	ai	ai	INTJ
ejpam-146	250	13	:	:	PUNCT
ejpam-146	250	14	i	i	PROPN
ejpam-146	250	15	=	=	SYM
ejpam-146	250	16	1,3	1,3	NUM
ejpam-146	250	17	,	,	PUNCT
ejpam-146	250	18	5,7	5,7	NUM
ejpam-146	250	19	,	,	PUNCT
ejpam-146	250	20	...	...	PUNCT
ejpam-146	250	21	}	}	PUNCT
ejpam-146	250	22	of	of	ADP
ejpam-146	250	23	x	x	INTJ
ejpam-146	250	24	,	,	PUNCT
ejpam-146	250	25	where	where	SCONJ
ejpam-146	250	26	ai	ai	VERB
ejpam-146	250	27	=	=	SYM
ejpam-146	250	28	ne	ne	PROPN
ejpam-146	250	29	∪	∪	X
ejpam-146	250	30	{	{	PUNCT
ejpam-146	250	31	i	i	NOUN
ejpam-146	250	32	}	}	PUNCT
ejpam-146	250	33	then	then	ADV
ejpam-146	250	34	it	it	PRON
ejpam-146	250	35	has	have	VERB
ejpam-146	250	36	no	no	DET
ejpam-146	250	37	finite	finite	NOUN
ejpam-146	250	38	subfamily	subfamily	ADV
ejpam-146	250	39	whose	whose	DET
ejpam-146	250	40	β	β	NOUN
ejpam-146	250	41	-	-	NOUN
ejpam-146	250	42	closures	closure	NOUN
ejpam-146	250	43	cover	cover	VERB
ejpam-146	250	44	x	x	X
ejpam-146	250	45	.	.	PUNCT
ejpam-146	251	1	so	so	ADV
ejpam-146	251	2	(	(	PUNCT
ejpam-146	251	3	x	x	X
ejpam-146	251	4	,	,	PUNCT
ejpam-146	251	5	τ	τ	X
ejpam-146	251	6	)	)	PUNCT
ejpam-146	251	7	is	be	AUX
ejpam-146	251	8	not	not	PART
ejpam-146	251	9	βclosed	βclose	VERB
ejpam-146	251	10	but	but	CCONJ
ejpam-146	251	11	(	(	PUNCT
ejpam-146	251	12	x	x	X
ejpam-146	251	13	,	,	PUNCT
ejpam-146	251	14	τ	τ	X
ejpam-146	251	15	)	)	PUNCT
ejpam-146	251	16	is	be	AUX
ejpam-146	251	17	obviously	obviously	ADV
ejpam-146	251	18	compact	compact	ADJ
ejpam-146	252	1	and	and	CCONJ
ejpam-146	252	2	hence	hence	ADV
ejpam-146	252	3	it	it	PRON
ejpam-146	252	4	is	be	AUX
ejpam-146	252	5	quasi	quasi	ADJ
ejpam-146	252	6	h	h	NOUN
ejpam-146	252	7	-	-	PUNCT
ejpam-146	252	8	closed	closed	ADJ
ejpam-146	252	9	.	.	PUNCT
ejpam-146	253	1	example	example	NOUN
ejpam-146	254	1	3.11	3.11	NUM
ejpam-146	254	2	.	.	PUNCT
ejpam-146	254	3	example	example	NOUN
ejpam-146	254	4	of	of	ADP
ejpam-146	254	5	an	an	DET
ejpam-146	254	6	infinite	infinite	ADJ
ejpam-146	254	7	β	β	NOUN
ejpam-146	254	8	-	-	ADJ
ejpam-146	254	9	closed	closed	ADJ
ejpam-146	254	10	space	space	NOUN
ejpam-146	254	11	which	which	PRON
ejpam-146	254	12	is	be	AUX
ejpam-146	254	13	neither	neither	CCONJ
ejpam-146	254	14	β	β	ADJ
ejpam-146	254	15	-	-	ADJ
ejpam-146	254	16	compact	compact	ADJ
ejpam-146	254	17	nor	nor	CCONJ
ejpam-146	254	18	compact	compact	ADJ
ejpam-146	254	19	.	.	PUNCT
ejpam-146	255	1	let	let	VERB
ejpam-146	255	2	x	x	PRON
ejpam-146	255	3	be	be	AUX
ejpam-146	255	4	the	the	DET
ejpam-146	255	5	set	set	NOUN
ejpam-146	255	6	of	of	ADP
ejpam-146	255	7	reals	real	NOUN
ejpam-146	255	8	with	with	ADP
ejpam-146	255	9	the	the	DET
ejpam-146	255	10	topology	topology	NOUN
ejpam-146	255	11	τ	τ	PROPN
ejpam-146	255	12	in	in	ADP
ejpam-146	255	13	which	which	PRON
ejpam-146	255	14	non	non	ADJ
ejpam-146	255	15	-	-	ADJ
ejpam-146	255	16	void	void	ADJ
ejpam-146	255	17	open	open	ADJ
ejpam-146	255	18	sets	set	NOUN
ejpam-146	255	19	are	be	AUX
ejpam-146	255	20	those	those	DET
ejpam-146	255	21	subsets	subset	NOUN
ejpam-146	255	22	of	of	ADP
ejpam-146	255	23	x	x	PUNCT
ejpam-146	255	24	which	which	PRON
ejpam-146	255	25	contain	contain	VERB
ejpam-146	255	26	the	the	DET
ejpam-146	255	27	point	point	NOUN
ejpam-146	255	28	1	1	NUM
ejpam-146	255	29	.	.	PUNCT
ejpam-146	256	1	clearly	clearly	ADV
ejpam-146	256	2	the	the	DET
ejpam-146	256	3	space	space	NOUN
ejpam-146	256	4	(	(	PUNCT
ejpam-146	256	5	x	x	X
ejpam-146	256	6	,	,	PUNCT
ejpam-146	256	7	τ	τ	X
ejpam-146	256	8	)	)	PUNCT
ejpam-146	256	9	is	be	AUX
ejpam-146	256	10	not	not	PART
ejpam-146	256	11	compact	compact	ADJ
ejpam-146	256	12	and	and	CCONJ
ejpam-146	256	13	hence	hence	ADV
ejpam-146	256	14	not	not	PART
ejpam-146	256	15	βcompact	βcompact	ADJ
ejpam-146	256	16	(	(	PUNCT
ejpam-146	256	17	as	as	SCONJ
ejpam-146	256	18	every	every	DET
ejpam-146	256	19	β	β	ADJ
ejpam-146	256	20	-	-	ADJ
ejpam-146	256	21	compact	compact	ADJ
ejpam-146	256	22	space	space	NOUN
ejpam-146	256	23	is	be	AUX
ejpam-146	256	24	obviously	obviously	ADV
ejpam-146	256	25	compact	compact	ADJ
ejpam-146	256	26	)	)	PUNCT
ejpam-146	256	27	.	.	PUNCT
ejpam-146	257	1	we	we	PRON
ejpam-146	257	2	claim	claim	VERB
ejpam-146	257	3	that	that	SCONJ
ejpam-146	257	4	in	in	ADP
ejpam-146	257	5	this	this	DET
ejpam-146	257	6	space	space	NOUN
ejpam-146	257	7	(	(	PUNCT
ejpam-146	257	8	x	x	X
ejpam-146	257	9	,	,	PUNCT
ejpam-146	257	10	τ	τ	PROPN
ejpam-146	257	11	)	)	PUNCT
ejpam-146	257	12	every	every	DET
ejpam-146	257	13	non	non	ADJ
ejpam-146	257	14	-	-	ADJ
ejpam-146	257	15	void	void	ADJ
ejpam-146	257	16	β	β	X
ejpam-146	257	17	-	-	ADJ
ejpam-146	257	18	open	open	ADJ
ejpam-146	257	19	set	set	NOUN
ejpam-146	257	20	must	must	AUX
ejpam-146	257	21	contains	contain	VERB
ejpam-146	257	22	the	the	DET
ejpam-146	257	23	point	point	NOUN
ejpam-146	257	24	1	1	NUM
ejpam-146	257	25	.	.	PUNCT
ejpam-146	258	1	indeed	indeed	ADV
ejpam-146	258	2	,	,	PUNCT
ejpam-146	258	3	let	let	VERB
ejpam-146	258	4	s	s	PRON
ejpam-146	258	5	be	be	AUX
ejpam-146	258	6	a	a	DET
ejpam-146	258	7	non	non	ADJ
ejpam-146	258	8	-	-	ADJ
ejpam-146	258	9	void	void	ADJ
ejpam-146	258	10	subset	subset	NOUN
ejpam-146	258	11	of	of	ADP
ejpam-146	258	12	x	x	PROPN
ejpam-146	258	13	c.	c.	PROPN
ejpam-146	258	14	k.	k.	PROPN
ejpam-146	258	15	basu	basu	PROPN
ejpam-146	258	16	,	,	PUNCT
ejpam-146	258	17	m.	m.	PROPN
ejpam-146	258	18	k.	k.	PROPN
ejpam-146	258	19	ghosh	ghosh	PROPN
ejpam-146	258	20	/	/	PUNCT
ejpam-146	258	21	eur	eur	PROPN
ejpam-146	258	22	.	.	PUNCT
ejpam-146	259	1	j.	j.	PROPN
ejpam-146	259	2	pure	pure	PROPN
ejpam-146	259	3	appl	appl	PROPN
ejpam-146	259	4	.	.	PROPN
ejpam-146	259	5	math	math	PROPN
ejpam-146	259	6	,	,	PUNCT
ejpam-146	259	7	1	1	NUM
ejpam-146	259	8	(	(	PUNCT
ejpam-146	259	9	2008	2008	NUM
ejpam-146	259	10	)	)	PUNCT
ejpam-146	259	11	,	,	PUNCT
ejpam-146	259	12	(	(	PUNCT
ejpam-146	259	13	40	40	NUM
ejpam-146	259	14	-	-	SYM
ejpam-146	259	15	50	50	NUM
ejpam-146	259	16	)	)	PUNCT
ejpam-146	259	17	45	45	NUM
ejpam-146	259	18	such	such	ADJ
ejpam-146	259	19	that	that	SCONJ
ejpam-146	259	20	1	1	NUM
ejpam-146	259	21	6∈	6∈	NOUN
ejpam-146	259	22	s.	s.	PROPN
ejpam-146	259	23	since	since	SCONJ
ejpam-146	259	24	a	a	DET
ejpam-146	259	25	subset	subset	NOUN
ejpam-146	259	26	a	a	PRON
ejpam-146	259	27	is	be	AUX
ejpam-146	259	28	β	β	NOUN
ejpam-146	259	29	-	-	NOUN
ejpam-146	259	30	open	open	ADJ
ejpam-146	259	31	if	if	SCONJ
ejpam-146	259	32	a	a	DET
ejpam-146	259	33	⊂	⊂	PROPN
ejpam-146	259	34	cl(int(cl(a	cl(int(cl(a	NOUN
ejpam-146	259	35	)	)	PUNCT
ejpam-146	259	36	)	)	PUNCT
ejpam-146	259	37	)	)	PUNCT
ejpam-146	260	1	,	,	PUNCT
ejpam-146	260	2	then	then	ADV
ejpam-146	260	3	s	s	AUX
ejpam-146	260	4	can	can	AUX
ejpam-146	260	5	not	not	PART
ejpam-146	260	6	be	be	AUX
ejpam-146	260	7	β	β	X
ejpam-146	260	8	-	-	ADJ
ejpam-146	260	9	open	open	ADJ
ejpam-146	260	10	.	.	PUNCT
ejpam-146	261	1	hence	hence	ADV
ejpam-146	261	2	x	x	X
ejpam-146	261	3	is	be	AUX
ejpam-146	261	4	the	the	DET
ejpam-146	261	5	only	only	ADJ
ejpam-146	261	6	β	β	X
ejpam-146	261	7	-	-	ADJ
ejpam-146	261	8	closed	closed	ADJ
ejpam-146	261	9	set	set	NOUN
ejpam-146	261	10	containing	contain	VERB
ejpam-146	261	11	any	any	DET
ejpam-146	261	12	non	non	ADJ
ejpam-146	261	13	-	-	ADJ
ejpam-146	261	14	void	void	ADJ
ejpam-146	261	15	β	β	ADJ
ejpam-146	261	16	-	-	ADJ
ejpam-146	261	17	open	open	ADJ
ejpam-146	261	18	set	set	NOUN
ejpam-146	261	19	.	.	PUNCT
ejpam-146	262	1	thus	thus	ADV
ejpam-146	262	2	the	the	DET
ejpam-146	262	3	β	β	NOUN
ejpam-146	262	4	-	-	NOUN
ejpam-146	262	5	closure	closure	NOUN
ejpam-146	262	6	of	of	ADP
ejpam-146	262	7	a	a	DET
ejpam-146	262	8	single	single	ADJ
ejpam-146	262	9	non	non	ADJ
ejpam-146	262	10	-	-	ADJ
ejpam-146	262	11	void	void	ADJ
ejpam-146	262	12	β	β	X
ejpam-146	262	13	-	-	ADJ
ejpam-146	262	14	open	open	ADJ
ejpam-146	262	15	set	set	NOUN
ejpam-146	262	16	is	be	AUX
ejpam-146	262	17	x	x	PUNCT
ejpam-146	262	18	and	and	CCONJ
ejpam-146	262	19	therefore	therefore	ADV
ejpam-146	262	20	x	x	X
ejpam-146	262	21	is	be	AUX
ejpam-146	262	22	β	β	NOUN
ejpam-146	262	23	-	-	VERB
ejpam-146	262	24	closed	closed	ADJ
ejpam-146	262	25	.	.	PUNCT
ejpam-146	263	1	we	we	PRON
ejpam-146	263	2	recall	recall	VERB
ejpam-146	263	3	that	that	SCONJ
ejpam-146	263	4	a	a	DET
ejpam-146	263	5	space	space	NOUN
ejpam-146	263	6	(	(	PUNCT
ejpam-146	263	7	x	x	X
ejpam-146	263	8	,	,	PUNCT
ejpam-146	263	9	τ	τ	X
ejpam-146	263	10	)	)	PUNCT
ejpam-146	263	11	is	be	AUX
ejpam-146	263	12	said	say	VERB
ejpam-146	263	13	to	to	PART
ejpam-146	263	14	be	be	AUX
ejpam-146	263	15	submaximal	submaximal	ADJ
ejpam-146	263	16	[	[	X
ejpam-146	263	17	7	7	NUM
ejpam-146	263	18	]	]	PUNCT
ejpam-146	263	19	if	if	SCONJ
ejpam-146	263	20	every	every	DET
ejpam-146	263	21	dense	dense	ADJ
ejpam-146	263	22	subset	subset	NOUN
ejpam-146	263	23	of	of	ADP
ejpam-146	263	24	x	x	PUNCT
ejpam-146	263	25	is	be	AUX
ejpam-146	263	26	open	open	ADJ
ejpam-146	263	27	and	and	CCONJ
ejpam-146	263	28	extremally	extremally	ADV
ejpam-146	263	29	disconnected	disconnect	VERB
ejpam-146	263	30	[	[	X
ejpam-146	263	31	15	15	NUM
ejpam-146	263	32	]	]	X
ejpam-146	263	33	if	if	SCONJ
ejpam-146	263	34	the	the	DET
ejpam-146	263	35	closure	closure	NOUN
ejpam-146	263	36	of	of	ADP
ejpam-146	263	37	each	each	DET
ejpam-146	263	38	open	open	ADJ
ejpam-146	263	39	set	set	NOUN
ejpam-146	263	40	is	be	AUX
ejpam-146	263	41	open	open	ADJ
ejpam-146	263	42	in	in	ADP
ejpam-146	263	43	x	x	X
ejpam-146	263	44	.	.	PUNCT
ejpam-146	264	1	theorem	theorem	ADJ
ejpam-146	264	2	3.12	3.12	NUM
ejpam-146	264	3	.	.	PUNCT
ejpam-146	265	1	let	let	AUX
ejpam-146	265	2	(	(	PUNCT
ejpam-146	265	3	x	x	X
ejpam-146	265	4	,	,	PUNCT
ejpam-146	265	5	τ	τ	X
ejpam-146	265	6	)	)	PUNCT
ejpam-146	265	7	be	be	VERB
ejpam-146	265	8	a	a	DET
ejpam-146	265	9	extremally	extremally	ADV
ejpam-146	265	10	disconnected	disconnected	ADJ
ejpam-146	265	11	space	space	NOUN
ejpam-146	265	12	.	.	PUNCT
ejpam-146	266	1	then	then	ADV
ejpam-146	266	2	(	(	PUNCT
ejpam-146	266	3	x	x	X
ejpam-146	266	4	,	,	PUNCT
ejpam-146	266	5	τ	τ	X
ejpam-146	266	6	)	)	PUNCT
ejpam-146	266	7	is	be	AUX
ejpam-146	266	8	β	β	NOUN
ejpam-146	266	9	-	-	VERB
ejpam-146	266	10	closed	closed	ADJ
ejpam-146	266	11	if	if	SCONJ
ejpam-146	266	12	and	and	CCONJ
ejpam-146	266	13	only	only	ADV
ejpam-146	266	14	if	if	SCONJ
ejpam-146	266	15	(	(	PUNCT
ejpam-146	266	16	x	x	X
ejpam-146	266	17	,	,	PUNCT
ejpam-146	266	18	τ	τ	X
ejpam-146	266	19	)	)	PUNCT
ejpam-146	266	20	is	be	AUX
ejpam-146	266	21	p	p	NOUN
ejpam-146	266	22	-	-	PUNCT
ejpam-146	266	23	closed	closed	ADJ
ejpam-146	266	24	.	.	PUNCT
ejpam-146	267	1	proof	proof	NOUN
ejpam-146	267	2	.	.	PUNCT
ejpam-146	268	1	as	as	ADP
ejpam-146	268	2	a	a	DET
ejpam-146	268	3	space	space	NOUN
ejpam-146	268	4	(	(	PUNCT
ejpam-146	268	5	x	x	X
ejpam-146	268	6	,	,	PUNCT
ejpam-146	268	7	τ	τ	X
ejpam-146	268	8	)	)	PUNCT
ejpam-146	268	9	is	be	AUX
ejpam-146	268	10	extremally	extremally	ADV
ejpam-146	268	11	disconnected	disconnected	ADJ
ejpam-146	268	12	if	if	SCONJ
ejpam-146	268	13	and	and	CCONJ
ejpam-146	268	14	only	only	ADV
ejpam-146	268	15	po(x	po(x	PUNCT
ejpam-146	268	16	)	)	PUNCT
ejpam-146	268	17	=	=	SYM
ejpam-146	268	18	βo(x	βo(x	PUNCT
ejpam-146	268	19	)	)	PUNCT
ejpam-146	268	20	,	,	PUNCT
ejpam-146	268	21	the	the	DET
ejpam-146	268	22	result	result	NOUN
ejpam-146	268	23	follows	follow	VERB
ejpam-146	268	24	immediately	immediately	ADV
ejpam-146	268	25	.	.	PUNCT
ejpam-146	269	1	theorem	theorem	VERB
ejpam-146	269	2	3.13	3.13	NUM
ejpam-146	269	3	.	.	PUNCT
ejpam-146	270	1	if	if	SCONJ
ejpam-146	270	2	(	(	PUNCT
ejpam-146	270	3	x	x	X
ejpam-146	270	4	,	,	PUNCT
ejpam-146	270	5	τ	τ	X
ejpam-146	270	6	)	)	PUNCT
ejpam-146	270	7	is	be	AUX
ejpam-146	270	8	submaximal	submaximal	ADJ
ejpam-146	270	9	and	and	CCONJ
ejpam-146	270	10	extremally	extremally	ADV
ejpam-146	270	11	disconnected	disconnect	VERB
ejpam-146	270	12	then	then	ADV
ejpam-146	270	13	the	the	DET
ejpam-146	270	14	following	following	NOUN
ejpam-146	270	15	are	be	AUX
ejpam-146	270	16	equivalent	equivalent	ADJ
ejpam-146	270	17	:	:	PUNCT
ejpam-146	270	18	(	(	PUNCT
ejpam-146	270	19	a	a	X
ejpam-146	270	20	)	)	PUNCT
ejpam-146	270	21	(	(	PUNCT
ejpam-146	270	22	x	x	X
ejpam-146	270	23	,	,	PUNCT
ejpam-146	270	24	τ	τ	X
ejpam-146	270	25	)	)	PUNCT
ejpam-146	270	26	is	be	AUX
ejpam-146	270	27	β	β	NOUN
ejpam-146	270	28	-	-	VERB
ejpam-146	270	29	closed	closed	ADJ
ejpam-146	270	30	.	.	PUNCT
ejpam-146	271	1	(	(	PUNCT
ejpam-146	271	2	b	b	X
ejpam-146	271	3	)	)	PUNCT
ejpam-146	271	4	(	(	PUNCT
ejpam-146	271	5	x	x	X
ejpam-146	271	6	,	,	PUNCT
ejpam-146	271	7	τ	τ	X
ejpam-146	271	8	)	)	PUNCT
ejpam-146	271	9	is	be	AUX
ejpam-146	271	10	p	p	NOUN
ejpam-146	271	11	-	-	PUNCT
ejpam-146	271	12	closed	closed	ADJ
ejpam-146	271	13	.	.	PUNCT
ejpam-146	272	1	(	(	PUNCT
ejpam-146	272	2	c	c	X
ejpam-146	272	3	)	)	PUNCT
ejpam-146	272	4	(	(	PUNCT
ejpam-146	272	5	x	x	X
ejpam-146	272	6	,	,	PUNCT
ejpam-146	272	7	τ	τ	X
ejpam-146	272	8	)	)	PUNCT
ejpam-146	272	9	is	be	AUX
ejpam-146	272	10	s	s	NOUN
ejpam-146	272	11	-	-	PUNCT
ejpam-146	272	12	closed	closed	ADJ
ejpam-146	272	13	.	.	PUNCT
ejpam-146	273	1	(	(	PUNCT
ejpam-146	273	2	d	d	X
ejpam-146	273	3	)	)	PUNCT
ejpam-146	273	4	(	(	PUNCT
ejpam-146	273	5	x	x	X
ejpam-146	273	6	,	,	PUNCT
ejpam-146	273	7	τα	τα	PROPN
ejpam-146	273	8	)	)	PUNCT
ejpam-146	273	9	is	be	AUX
ejpam-146	273	10	β	β	NOUN
ejpam-146	273	11	-	-	VERB
ejpam-146	273	12	closed	closed	ADJ
ejpam-146	273	13	.	.	PUNCT
ejpam-146	274	1	(	(	PUNCT
ejpam-146	274	2	e	e	X
ejpam-146	274	3	)	)	PUNCT
ejpam-146	274	4	(	(	PUNCT
ejpam-146	274	5	x	x	X
ejpam-146	274	6	,	,	PUNCT
ejpam-146	274	7	τ	τ	X
ejpam-146	274	8	)	)	PUNCT
ejpam-146	274	9	is	be	AUX
ejpam-146	274	10	qhc	qhc	PROPN
ejpam-146	274	11	.	.	PUNCT
ejpam-146	275	1	(	(	PUNCT
ejpam-146	275	2	f	f	PROPN
ejpam-146	275	3	)	)	PUNCT
ejpam-146	275	4	(	(	PUNCT
ejpam-146	275	5	x	x	X
ejpam-146	275	6	,	,	PUNCT
ejpam-146	275	7	τα	τα	PROPN
ejpam-146	275	8	)	)	PUNCT
ejpam-146	275	9	is	be	AUX
ejpam-146	275	10	s	s	NOUN
ejpam-146	275	11	-	-	PUNCT
ejpam-146	275	12	closed	closed	ADJ
ejpam-146	275	13	.	.	PUNCT
ejpam-146	276	1	proof	proof	NOUN
ejpam-146	276	2	.	.	PUNCT
ejpam-146	277	1	the	the	DET
ejpam-146	277	2	proof	proof	NOUN
ejpam-146	277	3	follows	follow	VERB
ejpam-146	277	4	from	from	ADP
ejpam-146	277	5	the	the	DET
ejpam-146	277	6	fact	fact	NOUN
ejpam-146	277	7	that	that	SCONJ
ejpam-146	277	8	if	if	SCONJ
ejpam-146	277	9	(	(	PUNCT
ejpam-146	277	10	x	x	X
ejpam-146	277	11	,	,	PUNCT
ejpam-146	277	12	τ	τ	X
ejpam-146	277	13	)	)	PUNCT
ejpam-146	277	14	is	be	AUX
ejpam-146	277	15	a	a	DET
ejpam-146	277	16	submaximal	submaximal	ADJ
ejpam-146	277	17	extremally	extremally	ADV
ejpam-146	277	18	disconnected	disconnect	VERB
ejpam-146	277	19	space	space	NOUN
ejpam-146	277	20	then	then	ADV
ejpam-146	277	21	τ=	τ=	INTJ
ejpam-146	277	22	τα	τα	PUNCT
ejpam-146	277	23	=	=	X
ejpam-146	277	24	so(x	so(x	X
ejpam-146	277	25	)	)	PUNCT
ejpam-146	278	1	=	=	SYM
ejpam-146	278	2	po(x	po(x	X
ejpam-146	278	3	)	)	PUNCT
ejpam-146	278	4	=	=	PUNCT
ejpam-146	278	5	βo(x	βo(x	PUNCT
ejpam-146	278	6	)	)	PUNCT
ejpam-146	279	1	[	[	X
ejpam-146	279	2	6	6	NUM
ejpam-146	279	3	]	]	PUNCT
ejpam-146	279	4	.	.	PUNCT
ejpam-146	280	1	§	§	PROPN
ejpam-146	280	2	4	4	NUM
ejpam-146	280	3	.	.	PUNCT
ejpam-146	280	4	(	(	PUNCT
ejpam-146	280	5	θ	θ	NOUN
ejpam-146	280	6	,	,	PUNCT
ejpam-146	280	7	β)-continuity	β)-continuity	NOUN
ejpam-146	280	8	and	and	CCONJ
ejpam-146	280	9	β	β	X
ejpam-146	280	10	-	-	PUNCT
ejpam-146	280	11	θ	θ	NOUN
ejpam-146	280	12	-subclosed	-subclose	VERB
ejpam-146	280	13	graph	graph	NOUN
ejpam-146	280	14	definition	definition	NOUN
ejpam-146	280	15	4.1	4.1	NUM
ejpam-146	280	16	.	.	PUNCT
ejpam-146	281	1	a	a	DET
ejpam-146	281	2	function	function	NOUN
ejpam-146	281	3	ψ	ψ	NOUN
ejpam-146	281	4	:	:	PUNCT
ejpam-146	281	5	x	x	SYM
ejpam-146	281	6	→	→	SYM
ejpam-146	281	7	y	y	PROPN
ejpam-146	281	8	is	be	AUX
ejpam-146	281	9	(	(	PUNCT
ejpam-146	281	10	θ	θ	PROPN
ejpam-146	281	11	,	,	PUNCT
ejpam-146	281	12	β)-continuous	β)-continuous	PUNCT
ejpam-146	281	13	if	if	SCONJ
ejpam-146	281	14	each	each	DET
ejpam-146	281	15	filter	filter	NOUN
ejpam-146	281	16	base	base	NOUN
ejpam-146	281	17	f	f	PROPN
ejpam-146	281	18	on	on	ADP
ejpam-146	281	19	x	x	SYM
ejpam-146	281	20	,	,	PUNCT
ejpam-146	281	21	satisfies	satisfie	NOUN
ejpam-146	281	22	ψ(adf	ψ(adf	X
ejpam-146	281	23	)	)	PUNCT
ejpam-146	282	1	⊂	⊂	PROPN
ejpam-146	282	2	β	β	PROPN
ejpam-146	282	3	-	-	PUNCT
ejpam-146	282	4	θ	θ	NOUN
ejpam-146	282	5	-adψ(f	-adψ(f	PROPN
ejpam-146	282	6	)	)	PUNCT
ejpam-146	282	7	.	.	PUNCT
ejpam-146	283	1	theorem	theorem	VERB
ejpam-146	283	2	4.2	4.2	NUM
ejpam-146	283	3	.	.	PUNCT
ejpam-146	284	1	for	for	ADP
ejpam-146	284	2	a	a	DET
ejpam-146	284	3	function	function	NOUN
ejpam-146	284	4	ψ	ψ	NOUN
ejpam-146	284	5	:	:	PUNCT
ejpam-146	284	6	x	x	X
ejpam-146	284	7	→	→	SYM
ejpam-146	284	8	y	y	PROPN
ejpam-146	284	9	,	,	PUNCT
ejpam-146	284	10	the	the	DET
ejpam-146	284	11	following	follow	VERB
ejpam-146	284	12	are	be	AUX
ejpam-146	284	13	equivalent	equivalent	ADJ
ejpam-146	284	14	:	:	PUNCT
ejpam-146	284	15	(	(	PUNCT
ejpam-146	284	16	a	a	X
ejpam-146	284	17	)	)	PUNCT
ejpam-146	284	18	ψ	ψ	NOUN
ejpam-146	284	19	is	be	AUX
ejpam-146	284	20	(	(	PUNCT
ejpam-146	284	21	θ	θ	NOUN
ejpam-146	284	22	,	,	PUNCT
ejpam-146	284	23	β)-continuous	β)-continuous	PROPN
ejpam-146	284	24	.	.	PUNCT
ejpam-146	285	1	(	(	PUNCT
ejpam-146	285	2	b	b	X
ejpam-146	285	3	)	)	PUNCT
ejpam-146	285	4	for	for	ADP
ejpam-146	285	5	each	each	PRON
ejpam-146	285	6	a⊂	a⊂	NOUN
ejpam-146	285	7	x	x	SYM
ejpam-146	285	8	,	,	PUNCT
ejpam-146	285	9	ψ(cl(a))⊂	ψ(cl(a))⊂	NOUN
ejpam-146	285	10	β	β	X
ejpam-146	285	11	-	-	ADJ
ejpam-146	285	12	θ	θ	NOUN
ejpam-146	285	13	-cl(ψ(a	-cl(ψ(a	PROPN
ejpam-146	285	14	)	)	PUNCT
ejpam-146	285	15	)	)	PUNCT
ejpam-146	285	16	.	.	PUNCT
ejpam-146	286	1	(	(	PUNCT
ejpam-146	286	2	c	c	X
ejpam-146	286	3	)	)	PUNCT
ejpam-146	286	4	for	for	ADP
ejpam-146	286	5	each	each	DET
ejpam-146	286	6	x	x	SYM
ejpam-146	286	7	∈	∈	PROPN
ejpam-146	286	8	x	x	X
ejpam-146	286	9	and	and	CCONJ
ejpam-146	286	10	each	each	DET
ejpam-146	286	11	v	v	NOUN
ejpam-146	286	12	∈	∈	PROPN
ejpam-146	286	13	βo(y	βo(y	PUNCT
ejpam-146	286	14	,	,	PUNCT
ejpam-146	286	15	ψ(x	ψ(x	NOUN
ejpam-146	286	16	)	)	PUNCT
ejpam-146	286	17	)	)	PUNCT
ejpam-146	286	18	,	,	PUNCT
ejpam-146	286	19	there	there	PRON
ejpam-146	286	20	exists	exist	VERB
ejpam-146	286	21	an	an	DET
ejpam-146	286	22	open	open	ADJ
ejpam-146	286	23	set	set	NOUN
ejpam-146	286	24	u	u	NOUN
ejpam-146	286	25	containing	contain	VERB
ejpam-146	286	26	x	x	PUNCT
ejpam-146	286	27	such	such	ADJ
ejpam-146	286	28	that	that	DET
ejpam-146	286	29	ψ(u)⊂	ψ(u)⊂	NOUN
ejpam-146	286	30	β	β	NOUN
ejpam-146	286	31	-	-	NOUN
ejpam-146	286	32	cl(v	cl(v	X
ejpam-146	286	33	)	)	PUNCT
ejpam-146	286	34	.	.	PUNCT
ejpam-146	287	1	(	(	PUNCT
ejpam-146	287	2	d	d	X
ejpam-146	287	3	)	)	PUNCT
ejpam-146	287	4	for	for	ADP
ejpam-146	287	5	each	each	DET
ejpam-146	287	6	w	w	PROPN
ejpam-146	287	7	∈	∈	PROPN
ejpam-146	287	8	βr(y	βr(y	NUM
ejpam-146	287	9	,	,	PUNCT
ejpam-146	287	10	ψ(x	ψ(x	NOUN
ejpam-146	287	11	)	)	PUNCT
ejpam-146	287	12	)	)	PUNCT
ejpam-146	287	13	,	,	PUNCT
ejpam-146	287	14	there	there	PRON
ejpam-146	287	15	is	be	VERB
ejpam-146	287	16	an	an	DET
ejpam-146	287	17	open	open	ADJ
ejpam-146	287	18	set	set	NOUN
ejpam-146	287	19	u	u	NOUN
ejpam-146	287	20	containing	contain	VERB
ejpam-146	287	21	x	x	PUNCT
ejpam-146	287	22	such	such	ADJ
ejpam-146	287	23	that	that	DET
ejpam-146	287	24	ψ(u)⊂w	ψ(u)⊂w	NOUN
ejpam-146	287	25	.	.	PUNCT
ejpam-146	288	1	(	(	PUNCT
ejpam-146	288	2	e	e	X
ejpam-146	288	3	)	)	PUNCT
ejpam-146	288	4	for	for	ADP
ejpam-146	288	5	each	each	DET
ejpam-146	288	6	β	β	NOUN
ejpam-146	288	7	-	-	PUNCT
ejpam-146	288	8	θ	θ	NOUN
ejpam-146	288	9	-closed	-close	VERB
ejpam-146	288	10	set	set	PROPN
ejpam-146	288	11	b	b	PROPN
ejpam-146	288	12	of	of	ADP
ejpam-146	288	13	y	y	PROPN
ejpam-146	288	14	,	,	PUNCT
ejpam-146	288	15	ψ−1(b	ψ−1(b	PROPN
ejpam-146	288	16	)	)	PUNCT
ejpam-146	288	17	is	be	AUX
ejpam-146	288	18	closed	close	VERB
ejpam-146	288	19	in	in	ADP
ejpam-146	288	20	x	x	X
ejpam-146	288	21	.	.	PUNCT
ejpam-146	289	1	(	(	PUNCT
ejpam-146	289	2	f	f	X
ejpam-146	289	3	)	)	PUNCT
ejpam-146	289	4	for	for	ADP
ejpam-146	289	5	each	each	DET
ejpam-146	289	6	b	b	PROPN
ejpam-146	289	7	⊂	⊂	PROPN
ejpam-146	289	8	y	y	PROPN
ejpam-146	289	9	cl(ψ−1(b))⊂ψ−1(β	cl(ψ−1(b))⊂ψ−1(β	PROPN
ejpam-146	289	10	-	-	PUNCT
ejpam-146	289	11	θ	θ	NOUN
ejpam-146	289	12	-cl(b	-cl(b	NOUN
ejpam-146	289	13	)	)	PUNCT
ejpam-146	289	14	)	)	PUNCT
ejpam-146	289	15	.	.	PUNCT
ejpam-146	290	1	(	(	PUNCT
ejpam-146	290	2	g	g	NOUN
ejpam-146	290	3	)	)	PUNCT
ejpam-146	290	4	for	for	ADP
ejpam-146	290	5	each	each	DET
ejpam-146	290	6	x	x	SYM
ejpam-146	290	7	∈	∈	PROPN
ejpam-146	290	8	x	x	X
ejpam-146	290	9	and	and	CCONJ
ejpam-146	290	10	each	each	DET
ejpam-146	290	11	filter	filter	NOUN
ejpam-146	290	12	base	base	NOUN
ejpam-146	290	13	f	f	PROPN
ejpam-146	290	14	on	on	ADP
ejpam-146	290	15	x	x	PUNCT
ejpam-146	290	16	with	with	ADP
ejpam-146	290	17	f	f	PROPN
ejpam-146	290	18	→	→	SYM
ejpam-146	290	19	x	x	SYM
ejpam-146	290	20	,	,	PUNCT
ejpam-146	290	21	the	the	DET
ejpam-146	290	22	filter	filter	NOUN
ejpam-146	290	23	base	base	NOUN
ejpam-146	290	24	ψ(f	ψ(f	PROPN
ejpam-146	290	25	)	)	PUNCT
ejpam-146	290	26	β	β	X
ejpam-146	290	27	-	-	PUNCT
ejpam-146	290	28	θ	θ	NOUN
ejpam-146	290	29	converges	converge	NOUN
ejpam-146	290	30	to	to	ADP
ejpam-146	290	31	ψ(x	ψ(x	NUM
ejpam-146	290	32	)	)	PUNCT
ejpam-146	290	33	.	.	PUNCT
ejpam-146	291	1	(	(	PUNCT
ejpam-146	291	2	h	h	NOUN
ejpam-146	291	3	)	)	PUNCT
ejpam-146	291	4	for	for	ADP
ejpam-146	291	5	each	each	DET
ejpam-146	291	6	x	x	SYM
ejpam-146	291	7	∈	∈	PROPN
ejpam-146	291	8	x	x	X
ejpam-146	291	9	and	and	CCONJ
ejpam-146	291	10	every	every	DET
ejpam-146	291	11	net	net	NOUN
ejpam-146	291	12	(	(	PUNCT
ejpam-146	291	13	xλ	xλ	NOUN
ejpam-146	291	14	)	)	PUNCT
ejpam-146	291	15	in	in	ADP
ejpam-146	291	16	x	x	PUNCT
ejpam-146	291	17	with	with	ADP
ejpam-146	291	18	(	(	PUNCT
ejpam-146	291	19	xλ)→	xλ)→	X
ejpam-146	291	20	x	x	X
ejpam-146	291	21	,	,	PUNCT
ejpam-146	291	22	ψ(xλ	ψ(xλ	PROPN
ejpam-146	291	23	)	)	PUNCT
ejpam-146	291	24	β	β	NOUN
ejpam-146	291	25	-	-	PUNCT
ejpam-146	291	26	θ	θ	NOUN
ejpam-146	291	27	-converges	-converge	NOUN
ejpam-146	291	28	to	to	ADP
ejpam-146	291	29	ψ(x	ψ(x	NUM
ejpam-146	291	30	)	)	PUNCT
ejpam-146	291	31	.	.	PUNCT
ejpam-146	292	1	theorem	theorem	VERB
ejpam-146	292	2	4.3	4.3	NUM
ejpam-146	292	3	.	.	PUNCT
ejpam-146	293	1	if	if	SCONJ
ejpam-146	293	2	ψ	ψ	X
ejpam-146	293	3	:	:	PUNCT
ejpam-146	293	4	x	x	X
ejpam-146	293	5	→	→	SYM
ejpam-146	293	6	y	y	PROPN
ejpam-146	293	7	is	be	AUX
ejpam-146	293	8	(	(	PUNCT
ejpam-146	293	9	θ	θ	PROPN
ejpam-146	293	10	,	,	PUNCT
ejpam-146	293	11	β)-continuous	β)-continuous	PUNCT
ejpam-146	293	12	and	and	CCONJ
ejpam-146	293	13	y	y	PROPN
ejpam-146	293	14	is	be	AUX
ejpam-146	293	15	hausdorff	hausdorff	NOUN
ejpam-146	293	16	then	then	ADV
ejpam-146	293	17	the	the	DET
ejpam-146	293	18	graph	graph	NOUN
ejpam-146	293	19	g(ψ	g(ψ	PROPN
ejpam-146	293	20	)	)	PUNCT
ejpam-146	293	21	of	of	ADP
ejpam-146	293	22	ψ	ψ	NOUN
ejpam-146	293	23	is	be	AUX
ejpam-146	293	24	closed	close	VERB
ejpam-146	293	25	in	in	ADP
ejpam-146	293	26	x	x	PUNCT
ejpam-146	293	27	×	×	PROPN
ejpam-146	293	28	y	y	PROPN
ejpam-146	293	29	.	.	PUNCT
ejpam-146	294	1	proof	proof	NOUN
ejpam-146	294	2	.	.	PUNCT
ejpam-146	295	1	let	let	VERB
ejpam-146	295	2	(	(	PUNCT
ejpam-146	295	3	x	x	X
ejpam-146	295	4	,	,	PUNCT
ejpam-146	295	5	y	y	PROPN
ejpam-146	295	6	)	)	PUNCT
ejpam-146	295	7	6∈	6∈	NOUN
ejpam-146	296	1	g(ψ	g(ψ	PROPN
ejpam-146	296	2	)	)	PUNCT
ejpam-146	296	3	.	.	PUNCT
ejpam-146	297	1	then	then	ADV
ejpam-146	297	2	y	y	PROPN
ejpam-146	297	3	6=	6=	PROPN
ejpam-146	297	4	ψ(x	ψ(x	PROPN
ejpam-146	297	5	)	)	PUNCT
ejpam-146	297	6	.	.	PUNCT
ejpam-146	298	1	as	as	SCONJ
ejpam-146	298	2	y	y	PROPN
ejpam-146	298	3	is	be	AUX
ejpam-146	298	4	being	be	AUX
ejpam-146	298	5	hausdorff	hausdorff	NOUN
ejpam-146	298	6	,	,	PUNCT
ejpam-146	298	7	there	there	PRON
ejpam-146	298	8	are	be	VERB
ejpam-146	298	9	disjoint	disjoint	NOUN
ejpam-146	298	10	open	open	PROPN
ejpam-146	298	11	c.	c.	PROPN
ejpam-146	298	12	k.	k.	PROPN
ejpam-146	298	13	basu	basu	PROPN
ejpam-146	298	14	,	,	PUNCT
ejpam-146	298	15	m.	m.	PROPN
ejpam-146	298	16	k.	k.	PROPN
ejpam-146	298	17	ghosh	ghosh	PROPN
ejpam-146	298	18	/	/	PUNCT
ejpam-146	298	19	eur	eur	PROPN
ejpam-146	298	20	.	.	PUNCT
ejpam-146	299	1	j.	j.	PROPN
ejpam-146	299	2	pure	pure	PROPN
ejpam-146	299	3	appl	appl	PROPN
ejpam-146	299	4	.	.	PROPN
ejpam-146	299	5	math	math	PROPN
ejpam-146	299	6	,	,	PUNCT
ejpam-146	299	7	1	1	NUM
ejpam-146	299	8	(	(	PUNCT
ejpam-146	299	9	2008	2008	NUM
ejpam-146	299	10	)	)	PUNCT
ejpam-146	299	11	,	,	PUNCT
ejpam-146	299	12	(	(	PUNCT
ejpam-146	299	13	40	40	NUM
ejpam-146	299	14	-	-	SYM
ejpam-146	299	15	50	50	NUM
ejpam-146	299	16	)	)	PUNCT
ejpam-146	299	17	46	46	NUM
ejpam-146	299	18	sets	set	VERB
ejpam-146	299	19	u	u	NOUN
ejpam-146	299	20	and	and	CCONJ
ejpam-146	299	21	v	v	NOUN
ejpam-146	299	22	in	in	ADP
ejpam-146	299	23	y	y	NOUN
ejpam-146	299	24	containing	contain	VERB
ejpam-146	299	25	y	y	PROPN
ejpam-146	299	26	and	and	CCONJ
ejpam-146	299	27	ψ(x	ψ(x	NUM
ejpam-146	299	28	)	)	PUNCT
ejpam-146	299	29	respectively	respectively	ADV
ejpam-146	299	30	such	such	ADJ
ejpam-146	299	31	that	that	SCONJ
ejpam-146	299	32	u	u	PROPN
ejpam-146	299	33	∩	∩	NOUN
ejpam-146	299	34	β	β	NOUN
ejpam-146	299	35	-	-	NOUN
ejpam-146	299	36	cl(v	cl(v	X
ejpam-146	299	37	)	)	PUNCT
ejpam-146	299	38	=	=	SYM
ejpam-146	299	39	;	;	PUNCT
ejpam-146	299	40	.	.	PUNCT
ejpam-146	300	1	by	by	ADP
ejpam-146	300	2	(	(	PUNCT
ejpam-146	300	3	θ	θ	PROPN
ejpam-146	300	4	,	,	PUNCT
ejpam-146	300	5	β)continuity	β)continuity	NOUN
ejpam-146	300	6	of	of	ADP
ejpam-146	300	7	ψ	ψ	X
ejpam-146	300	8	,	,	PUNCT
ejpam-146	300	9	there	there	PRON
ejpam-146	300	10	is	be	VERB
ejpam-146	300	11	a	a	DET
ejpam-146	300	12	w	w	NOUN
ejpam-146	300	13	∈	∈	NOUN
ejpam-146	300	14	o(x	o(x	ADJ
ejpam-146	300	15	,	,	PUNCT
ejpam-146	300	16	x	x	X
ejpam-146	300	17	)	)	PUNCT
ejpam-146	300	18	such	such	ADJ
ejpam-146	300	19	that	that	SCONJ
ejpam-146	300	20	ψ(w	ψ(w	PROPN
ejpam-146	300	21	)	)	PUNCT
ejpam-146	301	1	⊂	⊂	PROPN
ejpam-146	302	1	β	β	NOUN
ejpam-146	302	2	-	-	PUNCT
ejpam-146	302	3	cl(v	cl(v	X
ejpam-146	302	4	)	)	PUNCT
ejpam-146	302	5	.	.	PUNCT
ejpam-146	303	1	then	then	ADV
ejpam-146	303	2	w	w	PROPN
ejpam-146	303	3	×	×	PROPN
ejpam-146	303	4	u	u	NOUN
ejpam-146	303	5	is	be	AUX
ejpam-146	303	6	an	an	DET
ejpam-146	303	7	open	open	ADJ
ejpam-146	303	8	set	set	NOUN
ejpam-146	303	9	in	in	ADP
ejpam-146	303	10	x	x	SYM
ejpam-146	303	11	×	×	PROPN
ejpam-146	303	12	y	y	NOUN
ejpam-146	303	13	containing	contain	VERB
ejpam-146	303	14	(	(	PUNCT
ejpam-146	303	15	x	x	INTJ
ejpam-146	303	16	,	,	PUNCT
ejpam-146	303	17	y	y	PROPN
ejpam-146	303	18	)	)	PUNCT
ejpam-146	303	19	such	such	ADJ
ejpam-146	303	20	that	that	SCONJ
ejpam-146	303	21	g(ψ)∩	g(ψ)∩	PROPN
ejpam-146	303	22	(	(	PUNCT
ejpam-146	303	23	w	w	PROPN
ejpam-146	303	24	×	×	PROPN
ejpam-146	303	25	u	u	NOUN
ejpam-146	303	26	)	)	PUNCT
ejpam-146	303	27	=	=	SYM
ejpam-146	303	28	;	;	PUNCT
ejpam-146	303	29	.	.	PUNCT
ejpam-146	304	1	therefore	therefore	ADV
ejpam-146	304	2	g(ψ	g(ψ	PROPN
ejpam-146	304	3	)	)	PUNCT
ejpam-146	304	4	is	be	AUX
ejpam-146	304	5	closed	close	VERB
ejpam-146	304	6	.	.	PUNCT
ejpam-146	305	1	theorem	theorem	VERB
ejpam-146	305	2	4.4	4.4	NUM
ejpam-146	305	3	.	.	PUNCT
ejpam-146	306	1	let	let	VERB
ejpam-146	306	2	g(ψ	g(ψ	PROPN
ejpam-146	306	3	)	)	PUNCT
ejpam-146	306	4	:	:	PUNCT
ejpam-146	307	1	x	x	X
ejpam-146	307	2	→	→	SYM
ejpam-146	307	3	x	x	SYM
ejpam-146	307	4	×	×	NOUN
ejpam-146	307	5	y	y	NOUN
ejpam-146	307	6	be	be	AUX
ejpam-146	307	7	the	the	DET
ejpam-146	307	8	graph	graph	NOUN
ejpam-146	307	9	function	function	NOUN
ejpam-146	307	10	of	of	ADP
ejpam-146	307	11	the	the	DET
ejpam-146	307	12	function	function	NOUN
ejpam-146	307	13	ψ	ψ	NOUN
ejpam-146	307	14	:	:	PUNCT
ejpam-146	307	15	x	x	X
ejpam-146	307	16	→	→	SYM
ejpam-146	307	17	y	y	PROPN
ejpam-146	307	18	.	.	PUNCT
ejpam-146	308	1	then	then	ADV
ejpam-146	308	2	ψ	ψ	X
ejpam-146	308	3	is	be	AUX
ejpam-146	308	4	(	(	PUNCT
ejpam-146	308	5	θ	θ	PROPN
ejpam-146	308	6	,	,	PUNCT
ejpam-146	308	7	β)-continuous	β)-continuous	PUNCT
ejpam-146	308	8	if	if	SCONJ
ejpam-146	308	9	g(ψ	g(ψ	PROPN
ejpam-146	308	10	)	)	PUNCT
ejpam-146	308	11	is	be	AUX
ejpam-146	308	12	so	so	ADV
ejpam-146	308	13	.	.	PUNCT
ejpam-146	309	1	proof	proof	NOUN
ejpam-146	309	2	.	.	PUNCT
ejpam-146	310	1	let	let	VERB
ejpam-146	310	2	x	x	PUNCT
ejpam-146	310	3	∈	∈	PROPN
ejpam-146	310	4	x	x	X
ejpam-146	310	5	and	and	CCONJ
ejpam-146	310	6	w	w	PROPN
ejpam-146	310	7	be	be	AUX
ejpam-146	310	8	any	any	DET
ejpam-146	310	9	β	β	NOUN
ejpam-146	310	10	-	-	ADJ
ejpam-146	310	11	open	open	ADJ
ejpam-146	310	12	set	set	ADJ
ejpam-146	310	13	containing	contain	VERB
ejpam-146	310	14	ψ(x	ψ(x	NOUN
ejpam-146	310	15	)	)	PUNCT
ejpam-146	310	16	in	in	ADP
ejpam-146	310	17	y	y	PROPN
ejpam-146	310	18	.	.	PUNCT
ejpam-146	311	1	if	if	SCONJ
ejpam-146	311	2	u	u	PROPN
ejpam-146	311	3	∈	∈	PROPN
ejpam-146	311	4	βo(x	βo(x	PUNCT
ejpam-146	311	5	)	)	PUNCT
ejpam-146	311	6	and	and	CCONJ
ejpam-146	311	7	w	w	PROPN
ejpam-146	311	8	∈	∈	PROPN
ejpam-146	311	9	βo(y	βo(y	PUNCT
ejpam-146	311	10	)	)	PUNCT
ejpam-146	311	11	then	then	ADV
ejpam-146	311	12	we	we	PRON
ejpam-146	311	13	claim	claim	VERB
ejpam-146	311	14	that	that	SCONJ
ejpam-146	311	15	u	u	PRON
ejpam-146	311	16	×w	×w	VERB
ejpam-146	311	17	∈	∈	PROPN
ejpam-146	311	18	βo(x	βo(x	PUNCT
ejpam-146	311	19	×	×	PROPN
ejpam-146	311	20	y	y	PROPN
ejpam-146	311	21	)	)	PUNCT
ejpam-146	311	22	.	.	PUNCT
ejpam-146	312	1	indeed	indeed	ADV
ejpam-146	312	2	,	,	PUNCT
ejpam-146	312	3	since	since	SCONJ
ejpam-146	312	4	u	u	NOUN
ejpam-146	312	5	and	and	CCONJ
ejpam-146	312	6	w	w	PROPN
ejpam-146	312	7	are	be	AUX
ejpam-146	312	8	β	β	X
ejpam-146	312	9	-	-	ADJ
ejpam-146	312	10	open	open	ADJ
ejpam-146	312	11	sets	set	NOUN
ejpam-146	312	12	,	,	PUNCT
ejpam-146	312	13	there	there	PRON
ejpam-146	312	14	exists	exist	VERB
ejpam-146	312	15	v	v	ADP
ejpam-146	312	16	∈	∈	PROPN
ejpam-146	312	17	po(x	po(x	NUM
ejpam-146	312	18	)	)	PUNCT
ejpam-146	312	19	and	and	CCONJ
ejpam-146	313	1	k	k	PROPN
ejpam-146	313	2	∈	∈	PROPN
ejpam-146	313	3	po(y	po(y	NUM
ejpam-146	313	4	)	)	PUNCT
ejpam-146	313	5	such	such	ADJ
ejpam-146	313	6	that	that	PRON
ejpam-146	313	7	v	v	ADP
ejpam-146	313	8	⊂	⊂	PROPN
ejpam-146	313	9	u	u	X
ejpam-146	313	10	⊂	⊂	PROPN
ejpam-146	313	11	cl(v	cl(v	X
ejpam-146	313	12	)	)	PUNCT
ejpam-146	313	13	and	and	CCONJ
ejpam-146	313	14	k	k	PROPN
ejpam-146	313	15	⊂w	⊂w	PROPN
ejpam-146	313	16	⊂	⊂	PROPN
ejpam-146	313	17	cl(k	cl(k	NOUN
ejpam-146	313	18	)	)	PUNCT
ejpam-146	313	19	.	.	PUNCT
ejpam-146	314	1	clearly	clearly	ADV
ejpam-146	314	2	v	v	ADP
ejpam-146	314	3	×k	×k	NOUN
ejpam-146	314	4	⊂	⊂	PROPN
ejpam-146	314	5	u	u	PROPN
ejpam-146	314	6	×w	×w	VERB
ejpam-146	314	7	⊂	⊂	PRON
ejpam-146	314	8	cl(v	cl(v	NOUN
ejpam-146	314	9	)	)	PUNCT
ejpam-146	314	10	×	×	NOUN
ejpam-146	314	11	cl(k	cl(k	NOUN
ejpam-146	314	12	)	)	PUNCT
ejpam-146	314	13	=	=	SYM
ejpam-146	314	14	cl(v	cl(v	X
ejpam-146	314	15	×k	×k	NOUN
ejpam-146	314	16	)	)	PUNCT
ejpam-146	314	17	,	,	PUNCT
ejpam-146	314	18	and	and	CCONJ
ejpam-146	314	19	v	v	X
ejpam-146	314	20	×k	×k	PROPN
ejpam-146	314	21	∈	∈	NOUN
ejpam-146	314	22	po(x	po(x	NUM
ejpam-146	314	23	×	×	PROPN
ejpam-146	314	24	y	y	PROPN
ejpam-146	314	25	)	)	PUNCT
ejpam-146	314	26	.	.	PUNCT
ejpam-146	315	1	so	so	ADV
ejpam-146	315	2	u	u	NOUN
ejpam-146	315	3	×w	×w	NOUN
ejpam-146	315	4	is	be	AUX
ejpam-146	315	5	β	β	NOUN
ejpam-146	315	6	-	-	VERB
ejpam-146	315	7	open	open	ADJ
ejpam-146	315	8	in	in	ADP
ejpam-146	315	9	x	x	X
ejpam-146	315	10	×y	×y	NOUN
ejpam-146	315	11	.	.	PUNCT
ejpam-146	316	1	thus	thus	ADV
ejpam-146	316	2	x	x	PUNCT
ejpam-146	316	3	×w	×w	NOUN
ejpam-146	316	4	∈	∈	PROPN
ejpam-146	316	5	βo(x	βo(x	PUNCT
ejpam-146	316	6	×y	×y	X
ejpam-146	316	7	)	)	PUNCT
ejpam-146	316	8	containing	contain	VERB
ejpam-146	316	9	g(ψ)(x	g(ψ)(x	PROPN
ejpam-146	316	10	)	)	PUNCT
ejpam-146	316	11	.	.	PUNCT
ejpam-146	317	1	since	since	SCONJ
ejpam-146	317	2	g(ψ	g(ψ	PROPN
ejpam-146	317	3	)	)	PUNCT
ejpam-146	317	4	is	be	AUX
ejpam-146	317	5	(	(	PUNCT
ejpam-146	317	6	θ	θ	PROPN
ejpam-146	317	7	,	,	PUNCT
ejpam-146	317	8	β)-continuous	β)-continuous	PROPN
ejpam-146	317	9	,	,	PUNCT
ejpam-146	317	10	there	there	PRON
ejpam-146	317	11	exists	exist	VERB
ejpam-146	317	12	an	an	DET
ejpam-146	317	13	open	open	ADJ
ejpam-146	317	14	set	set	NOUN
ejpam-146	317	15	o	o	NOUN
ejpam-146	317	16	containing	contain	VERB
ejpam-146	317	17	x	x	PUNCT
ejpam-146	317	18	such	such	ADJ
ejpam-146	317	19	that	that	SCONJ
ejpam-146	317	20	g(ψ)(o)⊂	g(ψ)(o)⊂	PROPN
ejpam-146	317	21	β	β	X
ejpam-146	317	22	cl(x	cl(x	NOUN
ejpam-146	317	23	×w	×w	NOUN
ejpam-146	317	24	)	)	PUNCT
ejpam-146	317	25	⊂	⊂	PROPN
ejpam-146	318	1	x	x	X
ejpam-146	318	2	×β	×β	PROPN
ejpam-146	318	3	cl(w	cl(w	NOUN
ejpam-146	318	4	)	)	PUNCT
ejpam-146	318	5	.	.	PUNCT
ejpam-146	319	1	therefore	therefore	ADV
ejpam-146	319	2	we	we	PRON
ejpam-146	319	3	have	have	VERB
ejpam-146	319	4	ψ(o)⊂	ψ(o)⊂	PROPN
ejpam-146	319	5	β	β	X
ejpam-146	319	6	cl(w	cl(w	NOUN
ejpam-146	319	7	)	)	PUNCT
ejpam-146	319	8	and	and	CCONJ
ejpam-146	319	9	hence	hence	ADV
ejpam-146	319	10	ψ	ψ	X
ejpam-146	319	11	is	be	AUX
ejpam-146	319	12	(	(	PUNCT
ejpam-146	319	13	θ	θ	NOUN
ejpam-146	319	14	,	,	PUNCT
ejpam-146	319	15	β)-continuous	β)-continuous	PUNCT
ejpam-146	319	16	.	.	PUNCT
ejpam-146	320	1	definition	definition	NOUN
ejpam-146	320	2	4.5	4.5	NUM
ejpam-146	320	3	.	.	PUNCT
ejpam-146	321	1	a	a	DET
ejpam-146	321	2	function	function	NOUN
ejpam-146	321	3	ψ	ψ	NOUN
ejpam-146	321	4	:	:	PUNCT
ejpam-146	321	5	x	x	SYM
ejpam-146	321	6	→	→	SYM
ejpam-146	321	7	y	y	PROPN
ejpam-146	321	8	has	have	VERB
ejpam-146	321	9	a	a	DET
ejpam-146	321	10	β	β	NOUN
ejpam-146	321	11	-	-	PUNCT
ejpam-146	321	12	θ	θ	NOUN
ejpam-146	321	13	-subclosed	-subclose	VERB
ejpam-146	321	14	graph	graph	NOUN
ejpam-146	321	15	if	if	SCONJ
ejpam-146	321	16	β	β	NOUN
ejpam-146	321	17	-	-	PUNCT
ejpam-146	321	18	θ	θ	NOUN
ejpam-146	321	19	-adψ(ω	-adψ(ω	PROPN
ejpam-146	321	20	)	)	PUNCT
ejpam-146	322	1	⊂	⊂	PROPN
ejpam-146	322	2	{	{	PUNCT
ejpam-146	322	3	ψ(x	ψ(x	NOUN
ejpam-146	322	4	)	)	PUNCT
ejpam-146	322	5	}	}	PUNCT
ejpam-146	322	6	for	for	ADP
ejpam-146	322	7	each	each	DET
ejpam-146	322	8	x	x	SYM
ejpam-146	322	9	∈	∈	PROPN
ejpam-146	322	10	x	x	X
ejpam-146	322	11	and	and	CCONJ
ejpam-146	322	12	each	each	DET
ejpam-146	322	13	filter	filter	NOUN
ejpam-146	322	14	base	base	NOUN
ejpam-146	322	15	ω	ω	PROPN
ejpam-146	322	16	on	on	ADP
ejpam-146	322	17	x	x	X
ejpam-146	322	18	−	−	PROPN
ejpam-146	322	19	{	{	PUNCT
ejpam-146	322	20	x	x	NOUN
ejpam-146	322	21	}	}	PUNCT
ejpam-146	322	22	with	with	ADP
ejpam-146	322	23	ω→	ω→	PROPN
ejpam-146	322	24	x	x	SYM
ejpam-146	322	25	.	.	PUNCT
ejpam-146	323	1	equivalently	equivalently	ADV
ejpam-146	323	2	,	,	PUNCT
ejpam-146	323	3	ψ	ψ	PRON
ejpam-146	323	4	has	have	VERB
ejpam-146	323	5	a	a	DET
ejpam-146	323	6	β	β	NOUN
ejpam-146	323	7	-	-	PUNCT
ejpam-146	323	8	θ	θ	NOUN
ejpam-146	323	9	-subclosed	-subclose	VERB
ejpam-146	323	10	graph	graph	NOUN
ejpam-146	323	11	if	if	SCONJ
ejpam-146	323	12	and	and	CCONJ
ejpam-146	323	13	only	only	ADV
ejpam-146	323	14	if	if	SCONJ
ejpam-146	323	15	for	for	ADP
ejpam-146	323	16	each	each	DET
ejpam-146	323	17	x	x	SYM
ejpam-146	323	18	∈	∈	PROPN
ejpam-146	323	19	x	x	X
ejpam-146	323	20	and	and	CCONJ
ejpam-146	323	21	each	each	DET
ejpam-146	323	22	net	net	NOUN
ejpam-146	323	23	(	(	PUNCT
ejpam-146	323	24	xλ	xλ	NOUN
ejpam-146	323	25	)	)	PUNCT
ejpam-146	323	26	in	in	ADP
ejpam-146	323	27	x	x	X
ejpam-146	323	28	−	−	PROPN
ejpam-146	323	29	{	{	PUNCT
ejpam-146	323	30	x	x	NOUN
ejpam-146	323	31	}	}	PUNCT
ejpam-146	323	32	with	with	ADP
ejpam-146	323	33	xλ→	xλ→	PROPN
ejpam-146	323	34	x	x	X
ejpam-146	323	35	,	,	PUNCT
ejpam-146	323	36	ψ(xλ	ψ(xλ	PROPN
ejpam-146	323	37	)	)	PUNCT
ejpam-146	323	38	β	β	NOUN
ejpam-146	323	39	-	-	PUNCT
ejpam-146	323	40	θ	θ	NOUN
ejpam-146	323	41	-adheres	-adhere	NOUN
ejpam-146	323	42	to	to	ADP
ejpam-146	323	43	atmost	atmost	PROPN
ejpam-146	323	44	ψ(x	ψ(x	PROPN
ejpam-146	323	45	)	)	PUNCT
ejpam-146	323	46	.	.	PUNCT
ejpam-146	324	1	theorem	theorem	VERB
ejpam-146	324	2	4.6	4.6	NUM
ejpam-146	324	3	.	.	PUNCT
ejpam-146	325	1	the	the	DET
ejpam-146	325	2	following	follow	VERB
ejpam-146	325	3	are	be	AUX
ejpam-146	325	4	equivalent	equivalent	ADJ
ejpam-146	325	5	for	for	ADP
ejpam-146	325	6	spaces	space	NOUN
ejpam-146	325	7	x	x	X
ejpam-146	325	8	,	,	PUNCT
ejpam-146	325	9	y	y	PROPN
ejpam-146	325	10	and	and	CCONJ
ejpam-146	325	11	for	for	ADP
ejpam-146	325	12	the	the	DET
ejpam-146	325	13	function	function	NOUN
ejpam-146	325	14	ψ	ψ	NOUN
ejpam-146	325	15	:	:	PUNCT
ejpam-146	325	16	x	x	SYM
ejpam-146	325	17	→	→	SYM
ejpam-146	325	18	y	y	PROPN
ejpam-146	325	19	(	(	PUNCT
ejpam-146	325	20	a	a	NOUN
ejpam-146	325	21	)	)	PUNCT
ejpam-146	325	22	ψ	ψ	NOUN
ejpam-146	325	23	has	have	AUX
ejpam-146	325	24	a	a	DET
ejpam-146	325	25	β	β	NOUN
ejpam-146	325	26	-	-	PUNCT
ejpam-146	325	27	θ	θ	NOUN
ejpam-146	325	28	-subclosed	-subclose	VERB
ejpam-146	325	29	graph	graph	NOUN
ejpam-146	325	30	.	.	PUNCT
ejpam-146	326	1	(	(	PUNCT
ejpam-146	326	2	b	b	X
ejpam-146	326	3	)	)	PUNCT
ejpam-146	326	4	for	for	ADP
ejpam-146	326	5	each	each	DET
ejpam-146	326	6	(	(	PUNCT
ejpam-146	326	7	x	x	PROPN
ejpam-146	326	8	,	,	PUNCT
ejpam-146	326	9	y	y	PROPN
ejpam-146	326	10	)	)	PUNCT
ejpam-146	326	11	6∈	6∈	NOUN
ejpam-146	326	12	g(ψ	g(ψ	PROPN
ejpam-146	326	13	)	)	PUNCT
ejpam-146	326	14	,	,	PUNCT
ejpam-146	326	15	there	there	PRON
ejpam-146	326	16	are	be	VERB
ejpam-146	326	17	open	open	ADJ
ejpam-146	326	18	sets	set	NOUN
ejpam-146	326	19	w	w	NOUN
ejpam-146	326	20	containing	contain	VERB
ejpam-146	326	21	x	x	PUNCT
ejpam-146	326	22	in	in	ADP
ejpam-146	326	23	x	x	X
ejpam-146	326	24	and	and	CCONJ
ejpam-146	326	25	some	some	DET
ejpam-146	326	26	β	β	NOUN
ejpam-146	326	27	-	-	ADJ
ejpam-146	326	28	open	open	ADJ
ejpam-146	326	29	set	set	VERB
ejpam-146	326	30	v	v	NOUN
ejpam-146	326	31	containing	contain	VERB
ejpam-146	326	32	y	y	NOUN
ejpam-146	326	33	in	in	ADP
ejpam-146	326	34	y	y	PROPN
ejpam-146	326	35	satisfying	satisfy	VERB
ejpam-146	326	36	g(ψ)∩	g(ψ)∩	PROPN
ejpam-146	326	37	(	(	PUNCT
ejpam-146	326	38	w	w	NOUN
ejpam-146	326	39	−	−	PROPN
ejpam-146	326	40	{	{	PUNCT
ejpam-146	326	41	x})×	x})×	PROPN
ejpam-146	326	42	β	β	PROPN
ejpam-146	326	43	cl(v	cl(v	NOUN
ejpam-146	326	44	)	)	PUNCT
ejpam-146	326	45	)	)	PUNCT
ejpam-146	327	1	=	=	SYM
ejpam-146	327	2	;	;	PUNCT
ejpam-146	327	3	.	.	PUNCT
ejpam-146	328	1	(	(	PUNCT
ejpam-146	328	2	c	c	X
ejpam-146	328	3	)	)	PUNCT
ejpam-146	328	4	for	for	ADP
ejpam-146	328	5	each	each	DET
ejpam-146	328	6	(	(	PUNCT
ejpam-146	328	7	x	x	PROPN
ejpam-146	328	8	,	,	PUNCT
ejpam-146	328	9	y	y	PROPN
ejpam-146	328	10	)	)	PUNCT
ejpam-146	328	11	6∈	6∈	NOUN
ejpam-146	328	12	g(ψ	g(ψ	PROPN
ejpam-146	328	13	)	)	PUNCT
ejpam-146	328	14	,	,	PUNCT
ejpam-146	328	15	there	there	PRON
ejpam-146	328	16	exist	exist	VERB
ejpam-146	328	17	an	an	DET
ejpam-146	328	18	open	open	ADJ
ejpam-146	328	19	set	set	NOUN
ejpam-146	328	20	w	w	NOUN
ejpam-146	328	21	containing	contain	VERB
ejpam-146	328	22	x	x	PUNCT
ejpam-146	328	23	in	in	ADP
ejpam-146	328	24	x	x	X
ejpam-146	328	25	and	and	CCONJ
ejpam-146	328	26	some	some	DET
ejpam-146	328	27	β	β	NOUN
ejpam-146	328	28	-	-	ADJ
ejpam-146	328	29	open	open	ADJ
ejpam-146	328	30	set	set	VERB
ejpam-146	328	31	v	v	NOUN
ejpam-146	328	32	containing	contain	VERB
ejpam-146	328	33	y	y	PROPN
ejpam-146	328	34	in	in	ADP
ejpam-146	328	35	y	y	PROPN
ejpam-146	329	1	such	such	ADJ
ejpam-146	329	2	that	that	PRON
ejpam-146	329	3	g(ψ)∩	g(ψ)∩	PROPN
ejpam-146	329	4	(	(	PUNCT
ejpam-146	329	5	w	w	PROPN
ejpam-146	329	6	×	×	PROPN
ejpam-146	329	7	(	(	PUNCT
ejpam-146	329	8	β	β	X
ejpam-146	329	9	cl(v	cl(v	NOUN
ejpam-146	329	10	)	)	PUNCT
ejpam-146	329	11	−	−	PROPN
ejpam-146	329	12	{	{	PUNCT
ejpam-146	329	13	ψ(x	ψ(x	NOUN
ejpam-146	329	14	)	)	PUNCT
ejpam-146	329	15	}	}	PUNCT
ejpam-146	329	16	)	)	PUNCT
ejpam-146	329	17	)	)	PUNCT
ejpam-146	329	18	=	=	SYM
ejpam-146	329	19	;	;	PUNCT
ejpam-146	329	20	.	.	PUNCT
ejpam-146	330	1	(	(	PUNCT
ejpam-146	330	2	d	d	X
ejpam-146	330	3	)	)	PUNCT
ejpam-146	330	4	for	for	ADP
ejpam-146	330	5	each	each	DET
ejpam-146	330	6	(	(	PUNCT
ejpam-146	330	7	x	x	PROPN
ejpam-146	330	8	,	,	PUNCT
ejpam-146	330	9	y	y	PROPN
ejpam-146	330	10	)	)	PUNCT
ejpam-146	330	11	6∈	6∈	NOUN
ejpam-146	330	12	g(ψ	g(ψ	PROPN
ejpam-146	330	13	)	)	PUNCT
ejpam-146	330	14	,	,	PUNCT
ejpam-146	330	15	there	there	PRON
ejpam-146	330	16	exist	exist	VERB
ejpam-146	330	17	an	an	DET
ejpam-146	330	18	open	open	ADJ
ejpam-146	330	19	set	set	NOUN
ejpam-146	330	20	w	w	NOUN
ejpam-146	330	21	containing	contain	VERB
ejpam-146	330	22	x	x	PUNCT
ejpam-146	330	23	in	in	ADP
ejpam-146	330	24	x	x	X
ejpam-146	330	25	and	and	CCONJ
ejpam-146	330	26	β	β	X
ejpam-146	330	27	-	-	ADJ
ejpam-146	330	28	open	open	ADJ
ejpam-146	330	29	set	set	VERB
ejpam-146	330	30	v	v	NOUN
ejpam-146	330	31	containing	contain	VERB
ejpam-146	330	32	y	y	PROPN
ejpam-146	330	33	in	in	ADP
ejpam-146	330	34	y	y	PROPN
ejpam-146	330	35	such	such	ADJ
ejpam-146	330	36	that	that	SCONJ
ejpam-146	330	37	ψ(w	ψ(w	PROPN
ejpam-146	330	38	)	)	PUNCT
ejpam-146	330	39	∩	∩	NOUN
ejpam-146	330	40	(	(	PUNCT
ejpam-146	330	41	β	β	X
ejpam-146	330	42	cl(v	cl(v	NOUN
ejpam-146	330	43	)	)	PUNCT
ejpam-146	330	44	−	−	PROPN
ejpam-146	330	45	{	{	PUNCT
ejpam-146	330	46	ψ(x	ψ(x	NOUN
ejpam-146	330	47	)	)	PUNCT
ejpam-146	330	48	}	}	PUNCT
ejpam-146	330	49	)	)	PUNCT
ejpam-146	331	1	=	=	SYM
ejpam-146	331	2	;	;	PUNCT
ejpam-146	331	3	.	.	PUNCT
ejpam-146	332	1	proof	proof	NOUN
ejpam-146	332	2	.	.	PUNCT
ejpam-146	333	1	(	(	PUNCT
ejpam-146	333	2	a	a	X
ejpam-146	333	3	)	)	PUNCT
ejpam-146	333	4	⇒	⇒	NOUN
ejpam-146	333	5	(	(	PUNCT
ejpam-146	333	6	b	b	NOUN
ejpam-146	333	7	)	)	PUNCT
ejpam-146	333	8	:	:	PUNCT
ejpam-146	333	9	let	let	VERB
ejpam-146	333	10	ψ	ψ	X
ejpam-146	333	11	:	:	PUNCT
ejpam-146	333	12	x	x	SYM
ejpam-146	333	13	→	→	SYM
ejpam-146	333	14	y	y	X
ejpam-146	333	15	be	be	AUX
ejpam-146	333	16	a	a	DET
ejpam-146	333	17	function	function	NOUN
ejpam-146	333	18	having	have	VERB
ejpam-146	333	19	β	β	NOUN
ejpam-146	333	20	-	-	PUNCT
ejpam-146	333	21	θ	θ	NOUN
ejpam-146	333	22	-subclosed	-subclose	VERB
ejpam-146	333	23	graph	graph	NOUN
ejpam-146	333	24	and	and	CCONJ
ejpam-146	333	25	(	(	PUNCT
ejpam-146	333	26	x	x	X
ejpam-146	333	27	,	,	PUNCT
ejpam-146	333	28	y	y	PROPN
ejpam-146	333	29	)	)	PUNCT
ejpam-146	333	30	6∈	6∈	NOUN
ejpam-146	333	31	g(ψ	g(ψ	PROPN
ejpam-146	333	32	)	)	PUNCT
ejpam-146	333	33	.	.	PUNCT
ejpam-146	334	1	consider	consider	VERB
ejpam-146	334	2	f	f	NOUN
ejpam-146	334	3	=	=	PRON
ejpam-146	334	4	{	{	PUNCT
ejpam-146	334	5	w	w	NOUN
ejpam-146	334	6	−	−	PROPN
ejpam-146	334	7	{	{	PUNCT
ejpam-146	334	8	x	x	NOUN
ejpam-146	334	9	}	}	PUNCT
ejpam-146	334	10	:	:	PUNCT
ejpam-146	334	11	w	w	X
ejpam-146	334	12	∈	∈	PROPN
ejpam-146	334	13	o(x	o(x	ADJ
ejpam-146	334	14	,	,	PUNCT
ejpam-146	334	15	x	x	X
ejpam-146	334	16	)	)	PUNCT
ejpam-146	334	17	}	}	PUNCT
ejpam-146	334	18	.	.	PUNCT
ejpam-146	335	1	if	if	SCONJ
ejpam-146	335	2	f	f	PROPN
ejpam-146	335	3	is	be	AUX
ejpam-146	335	4	a	a	DET
ejpam-146	335	5	filter	filter	NOUN
ejpam-146	335	6	base	base	NOUN
ejpam-146	335	7	then	then	ADV
ejpam-146	335	8	f	f	PROPN
ejpam-146	335	9	→	→	SYM
ejpam-146	335	10	x	x	X
ejpam-146	335	11	and	and	CCONJ
ejpam-146	335	12	since	since	SCONJ
ejpam-146	335	13	ψ	ψ	NOUN
ejpam-146	335	14	has	have	VERB
ejpam-146	335	15	a	a	DET
ejpam-146	335	16	β	β	NOUN
ejpam-146	335	17	-	-	PUNCT
ejpam-146	335	18	θ	θ	NOUN
ejpam-146	335	19	-subclosed	-subclose	VERB
ejpam-146	335	20	graph	graph	NOUN
ejpam-146	335	21	,	,	PUNCT
ejpam-146	335	22	y	y	PROPN
ejpam-146	335	23	6∈	6∈	PROPN
ejpam-146	335	24	β	β	PROPN
ejpam-146	335	25	-	-	PUNCT
ejpam-146	335	26	θ	θ	NOUN
ejpam-146	335	27	-adψ(f	-adψ(f	PROPN
ejpam-146	335	28	)	)	PUNCT
ejpam-146	335	29	.	.	PUNCT
ejpam-146	336	1	hence	hence	ADV
ejpam-146	336	2	there	there	PRON
ejpam-146	336	3	exist	exist	VERB
ejpam-146	336	4	an	an	DET
ejpam-146	336	5	f(=	f(=	PROPN
ejpam-146	336	6	w	w	ADP
ejpam-146	336	7	−	−	PROPN
ejpam-146	336	8	{	{	PUNCT
ejpam-146	336	9	x	x	NOUN
ejpam-146	336	10	}	}	PUNCT
ejpam-146	336	11	,	,	PUNCT
ejpam-146	336	12	for	for	ADP
ejpam-146	336	13	some	some	DET
ejpam-146	336	14	w	w	NOUN
ejpam-146	336	15	∈	∈	PROPN
ejpam-146	336	16	o(x	o(x	ADJ
ejpam-146	336	17	,	,	PUNCT
ejpam-146	336	18	x	x	NOUN
ejpam-146	336	19	)	)	PUNCT
ejpam-146	336	20	)	)	PUNCT
ejpam-146	337	1	∈	∈	PROPN
ejpam-146	337	2	f	f	PROPN
ejpam-146	337	3	and	and	CCONJ
ejpam-146	337	4	a	a	DET
ejpam-146	337	5	β	β	NOUN
ejpam-146	337	6	-	-	ADJ
ejpam-146	337	7	open	open	ADJ
ejpam-146	337	8	set	set	NOUN
ejpam-146	337	9	v	v	NOUN
ejpam-146	337	10	containing	contain	VERB
ejpam-146	337	11	y	y	PROPN
ejpam-146	337	12	in	in	ADP
ejpam-146	337	13	y	y	PROPN
ejpam-146	337	14	such	such	ADJ
ejpam-146	337	15	that	that	DET
ejpam-146	337	16	ψ(f	ψ(f	NOUN
ejpam-146	337	17	)	)	PUNCT
ejpam-146	337	18	∩	∩	NOUN
ejpam-146	337	19	β	β	X
ejpam-146	337	20	cl(v	cl(v	NOUN
ejpam-146	337	21	)	)	PUNCT
ejpam-146	337	22	=	=	SYM
ejpam-146	337	23	;	;	PUNCT
ejpam-146	337	24	i.e.	i.e.	X
ejpam-146	337	25	ψ(w	ψ(w	X
ejpam-146	337	26	−{x})∩β	−{x})∩β	ADJ
ejpam-146	337	27	cl(v	cl(v	NOUN
ejpam-146	337	28	)	)	PUNCT
ejpam-146	337	29	=	=	SYM
ejpam-146	337	30	;	;	PUNCT
ejpam-146	337	31	.	.	PUNCT
ejpam-146	338	1	therefore	therefore	ADV
ejpam-146	338	2	g(ψ)∩	g(ψ)∩	PROPN
ejpam-146	338	3	(	(	PUNCT
ejpam-146	338	4	w	w	PROPN
ejpam-146	338	5	−{x}×β	−{x}×β	PROPN
ejpam-146	338	6	cl(v	cl(v	NOUN
ejpam-146	338	7	)	)	PUNCT
ejpam-146	338	8	)	)	PUNCT
ejpam-146	339	1	=	=	PUNCT
ejpam-146	339	2	;	;	PUNCT
ejpam-146	339	3	.	.	PUNCT
ejpam-146	340	1	if	if	SCONJ
ejpam-146	340	2	f	f	PROPN
ejpam-146	340	3	is	be	AUX
ejpam-146	340	4	not	not	PART
ejpam-146	340	5	a	a	DET
ejpam-146	340	6	filter	filter	NOUN
ejpam-146	340	7	base	base	NOUN
ejpam-146	340	8	then	then	ADV
ejpam-146	340	9	w	w	X
ejpam-146	340	10	=	=	SYM
ejpam-146	340	11	{	{	PUNCT
ejpam-146	340	12	x	x	NOUN
ejpam-146	340	13	}	}	PUNCT
ejpam-146	340	14	for	for	ADP
ejpam-146	340	15	some	some	DET
ejpam-146	340	16	w	w	NOUN
ejpam-146	340	17	∈	∈	PROPN
ejpam-146	340	18	o(x	o(x	ADJ
ejpam-146	340	19	,	,	PUNCT
ejpam-146	340	20	x	x	X
ejpam-146	340	21	)	)	PUNCT
ejpam-146	340	22	and	and	CCONJ
ejpam-146	340	23	the	the	DET
ejpam-146	340	24	rest	rest	NOUN
ejpam-146	340	25	is	be	AUX
ejpam-146	340	26	obvious	obvious	ADJ
ejpam-146	340	27	.	.	PUNCT
ejpam-146	341	1	(	(	PUNCT
ejpam-146	341	2	b)⇒	b)⇒	NOUN
ejpam-146	341	3	(	(	PUNCT
ejpam-146	341	4	c	c	NOUN
ejpam-146	341	5	)	)	PUNCT
ejpam-146	341	6	:	:	PUNCT
ejpam-146	341	7	if	if	SCONJ
ejpam-146	341	8	possible	possible	ADJ
ejpam-146	341	9	,	,	PUNCT
ejpam-146	341	10	let	let	VERB
ejpam-146	341	11	(	(	PUNCT
ejpam-146	341	12	z	z	NOUN
ejpam-146	341	13	,	,	PUNCT
ejpam-146	341	14	ψ(z	ψ(z	NOUN
ejpam-146	341	15	)	)	PUNCT
ejpam-146	341	16	)	)	PUNCT
ejpam-146	342	1	∈	∈	PROPN
ejpam-146	342	2	g(ψ)∩	g(ψ)∩	PROPN
ejpam-146	342	3	(	(	PUNCT
ejpam-146	342	4	w	w	PROPN
ejpam-146	342	5	×β	×β	PROPN
ejpam-146	342	6	cl(v	cl(v	NOUN
ejpam-146	342	7	)	)	PUNCT
ejpam-146	342	8	−{ψ(x	−{ψ(x	NUM
ejpam-146	342	9	)	)	PUNCT
ejpam-146	342	10	}	}	PUNCT
ejpam-146	342	11	)	)	PUNCT
ejpam-146	343	1	=	=	SYM
ejpam-146	343	2	;	;	PUNCT
ejpam-146	343	3	where	where	SCONJ
ejpam-146	343	4	w	w	NOUN
ejpam-146	343	5	and	and	CCONJ
ejpam-146	343	6	v	v	NOUN
ejpam-146	343	7	are	be	AUX
ejpam-146	343	8	sets	set	NOUN
ejpam-146	343	9	as	as	ADP
ejpam-146	343	10	in	in	ADP
ejpam-146	343	11	the	the	DET
ejpam-146	343	12	hypothesis	hypothesis	NOUN
ejpam-146	343	13	(	(	PUNCT
ejpam-146	343	14	b	b	NOUN
ejpam-146	343	15	)	)	PUNCT
ejpam-146	343	16	.	.	PUNCT
ejpam-146	344	1	then	then	ADV
ejpam-146	344	2	z	z	NOUN
ejpam-146	344	3	∈w	∈w	NOUN
ejpam-146	344	4	and	and	CCONJ
ejpam-146	344	5	ψ(z	ψ(z	PROPN
ejpam-146	344	6	)	)	PUNCT
ejpam-146	344	7	∈	∈	PROPN
ejpam-146	344	8	β	β	X
ejpam-146	344	9	cl(v	cl(v	X
ejpam-146	344	10	)	)	PUNCT
ejpam-146	344	11	−	−	PROPN
ejpam-146	344	12	{	{	PUNCT
ejpam-146	344	13	ψ(x	ψ(x	NOUN
ejpam-146	344	14	)	)	PUNCT
ejpam-146	344	15	}	}	PUNCT
ejpam-146	344	16	.	.	PUNCT
ejpam-146	345	1	clearly	clearly	ADV
ejpam-146	345	2	ψ(z	ψ(z	VERB
ejpam-146	345	3	)	)	PUNCT
ejpam-146	345	4	6	6	NUM
ejpam-146	345	5	=	=	SYM
ejpam-146	345	6	ψ(x	ψ(x	NOUN
ejpam-146	345	7	)	)	PUNCT
ejpam-146	345	8	and	and	CCONJ
ejpam-146	345	9	hence	hence	ADV
ejpam-146	345	10	z	z	PROPN
ejpam-146	345	11	6=	6=	NUM
ejpam-146	345	12	x	x	X
ejpam-146	345	13	.	.	PUNCT
ejpam-146	346	1	since	since	SCONJ
ejpam-146	346	2	z	z	PROPN
ejpam-146	346	3	∈w	∈w	PROPN
ejpam-146	346	4	−{x	−{x	NUM
ejpam-146	346	5	}	}	PUNCT
ejpam-146	346	6	and	and	CCONJ
ejpam-146	346	7	ψ(z	ψ(z	PROPN
ejpam-146	346	8	)	)	PUNCT
ejpam-146	346	9	∈	∈	PROPN
ejpam-146	346	10	β	β	X
ejpam-146	346	11	cl(v	cl(v	X
ejpam-146	346	12	)	)	PUNCT
ejpam-146	346	13	then	then	ADV
ejpam-146	346	14	ψ(z	ψ(z	PROPN
ejpam-146	346	15	)	)	PUNCT
ejpam-146	346	16	∈ψ(w	∈ψ(w	PROPN
ejpam-146	346	17	−{x})∩	−{x})∩	ADV
ejpam-146	346	18	β	β	X
ejpam-146	346	19	cl(v	cl(v	NOUN
ejpam-146	346	20	)	)	PUNCT
ejpam-146	346	21	=	=	PUNCT
ejpam-146	346	22	;	;	PUNCT
ejpam-146	346	23	=	=	SYM
ejpam-146	346	24	g(ψ)∩	g(ψ)∩	X
ejpam-146	346	25	(	(	PUNCT
ejpam-146	346	26	(	(	PUNCT
ejpam-146	346	27	w	w	NOUN
ejpam-146	346	28	−	−	PROPN
ejpam-146	346	29	{	{	PUNCT
ejpam-146	346	30	x})×	x})×	PROPN
ejpam-146	346	31	β	β	PROPN
ejpam-146	346	32	cl(v	cl(v	NOUN
ejpam-146	346	33	)	)	PUNCT
ejpam-146	346	34	)	)	PUNCT
ejpam-146	346	35	—	—	PUNCT
ejpam-146	346	36	a	a	DET
ejpam-146	346	37	contradiction	contradiction	NOUN
ejpam-146	346	38	.	.	PUNCT
ejpam-146	347	1	(	(	PUNCT
ejpam-146	347	2	c)⇒	c)⇒	X
ejpam-146	347	3	(	(	PUNCT
ejpam-146	347	4	d	d	NOUN
ejpam-146	347	5	)	)	PUNCT
ejpam-146	347	6	:	:	PUNCT
ejpam-146	347	7	obvious	obvious	ADJ
ejpam-146	347	8	.	.	PUNCT
ejpam-146	348	1	(	(	PUNCT
ejpam-146	348	2	d	d	X
ejpam-146	348	3	)	)	PUNCT
ejpam-146	348	4	⇒	⇒	NOUN
ejpam-146	348	5	(	(	PUNCT
ejpam-146	348	6	a	a	X
ejpam-146	348	7	)	)	PUNCT
ejpam-146	348	8	:	:	PUNCT
ejpam-146	348	9	suppose	suppose	VERB
ejpam-146	348	10	f	f	PROPN
ejpam-146	348	11	is	be	AUX
ejpam-146	348	12	filter	filter	NOUN
ejpam-146	348	13	base	base	NOUN
ejpam-146	348	14	in	in	ADP
ejpam-146	348	15	x	x	X
ejpam-146	348	16	−	−	PROPN
ejpam-146	348	17	{	{	PUNCT
ejpam-146	348	18	x	x	NOUN
ejpam-146	348	19	}	}	PUNCT
ejpam-146	348	20	such	such	ADJ
ejpam-146	348	21	that	that	SCONJ
ejpam-146	348	22	f	f	PROPN
ejpam-146	348	23	→	→	SYM
ejpam-146	348	24	x	x	AUX
ejpam-146	348	25	and	and	CCONJ
ejpam-146	348	26	also	also	ADV
ejpam-146	348	27	suppose	suppose	VERB
ejpam-146	348	28	that	that	SCONJ
ejpam-146	348	29	y	y	PROPN
ejpam-146	348	30	6=	6=	PROPN
ejpam-146	348	31	ψ(x	ψ(x	PROPN
ejpam-146	348	32	)	)	PUNCT
ejpam-146	348	33	.	.	PUNCT
ejpam-146	349	1	then	then	ADV
ejpam-146	349	2	(	(	PUNCT
ejpam-146	349	3	x	x	X
ejpam-146	349	4	,	,	PUNCT
ejpam-146	349	5	y	y	PROPN
ejpam-146	349	6	)	)	PUNCT
ejpam-146	349	7	6∈	6∈	NOUN
ejpam-146	349	8	g(ψ	g(ψ	PROPN
ejpam-146	349	9	)	)	PUNCT
ejpam-146	349	10	.	.	PUNCT
ejpam-146	350	1	so	so	ADV
ejpam-146	350	2	by	by	ADP
ejpam-146	350	3	hypothesis	hypothesis	NOUN
ejpam-146	350	4	(	(	PUNCT
ejpam-146	350	5	d	d	NOUN
ejpam-146	350	6	)	)	PUNCT
ejpam-146	350	7	,	,	PUNCT
ejpam-146	350	8	there	there	PRON
ejpam-146	350	9	is	be	VERB
ejpam-146	350	10	an	an	DET
ejpam-146	350	11	open	open	ADJ
ejpam-146	350	12	set	set	NOUN
ejpam-146	350	13	w	w	NOUN
ejpam-146	350	14	containing	contain	VERB
ejpam-146	350	15	x	x	PUNCT
ejpam-146	350	16	in	in	ADP
ejpam-146	350	17	x	x	X
ejpam-146	350	18	and	and	CCONJ
ejpam-146	350	19	a	a	DET
ejpam-146	350	20	β	β	NOUN
ejpam-146	350	21	-	-	ADJ
ejpam-146	350	22	open	open	ADJ
ejpam-146	350	23	set	set	NOUN
ejpam-146	350	24	v	v	NOUN
ejpam-146	350	25	containing	contain	VERB
ejpam-146	350	26	y	y	PROPN
ejpam-146	350	27	in	in	ADP
ejpam-146	350	28	y	y	PROPN
ejpam-146	350	29	such	such	ADJ
ejpam-146	350	30	that	that	SCONJ
ejpam-146	350	31	ψ(w	ψ(w	PROPN
ejpam-146	350	32	)	)	PUNCT
ejpam-146	350	33	∩	∩	NOUN
ejpam-146	350	34	(	(	PUNCT
ejpam-146	350	35	β	β	X
ejpam-146	350	36	cl(v	cl(v	NOUN
ejpam-146	350	37	)	)	PUNCT
ejpam-146	350	38	−	−	PROPN
ejpam-146	350	39	{	{	PUNCT
ejpam-146	350	40	ψ(x	ψ(x	NOUN
ejpam-146	350	41	)	)	PUNCT
ejpam-146	350	42	}	}	PUNCT
ejpam-146	350	43	)	)	PUNCT
ejpam-146	350	44	=	=	SYM
ejpam-146	351	1	;	;	PUNCT
ejpam-146	351	2	.	.	PUNCT
ejpam-146	352	1	since	since	SCONJ
ejpam-146	352	2	f	f	PROPN
ejpam-146	352	3	→	→	PUNCT
ejpam-146	352	4	x	x	PROPN
ejpam-146	352	5	then	then	ADV
ejpam-146	352	6	f	f	PROPN
ejpam-146	352	7	⊂	⊂	PROPN
ejpam-146	352	8	w	w	PROPN
ejpam-146	352	9	for	for	ADP
ejpam-146	352	10	some	some	DET
ejpam-146	352	11	f	f	PROPN
ejpam-146	352	12	∈	∈	PROPN
ejpam-146	352	13	f	f	PROPN
ejpam-146	352	14	.	.	PUNCT
ejpam-146	353	1	therefore	therefore	ADV
ejpam-146	353	2	ψ(f	ψ(f	NOUN
ejpam-146	353	3	)	)	PUNCT
ejpam-146	353	4	∩	∩	NOUN
ejpam-146	353	5	(	(	PUNCT
ejpam-146	353	6	β	β	X
ejpam-146	353	7	cl(v	cl(v	NOUN
ejpam-146	353	8	)	)	PUNCT
ejpam-146	353	9	−	−	PROPN
ejpam-146	353	10	{	{	PUNCT
ejpam-146	353	11	ψ(x	ψ(x	NOUN
ejpam-146	353	12	)	)	PUNCT
ejpam-146	353	13	}	}	PUNCT
ejpam-146	353	14	)	)	PUNCT
ejpam-146	353	15	=	=	SYM
ejpam-146	353	16	;	;	PUNCT
ejpam-146	353	17	.	.	PUNCT
ejpam-146	354	1	now	now	ADV
ejpam-146	354	2	as	as	SCONJ
ejpam-146	354	3	f	f	PROPN
ejpam-146	354	4	is	be	AUX
ejpam-146	354	5	a	a	DET
ejpam-146	354	6	filter	filter	NOUN
ejpam-146	354	7	base	base	NOUN
ejpam-146	354	8	in	in	ADP
ejpam-146	354	9	x	x	X
ejpam-146	354	10	−	−	PROPN
ejpam-146	354	11	{	{	PUNCT
ejpam-146	354	12	x	x	NOUN
ejpam-146	354	13	}	}	PUNCT
ejpam-146	354	14	,	,	PUNCT
ejpam-146	354	15	ψ(f	ψ(f	NOUN
ejpam-146	354	16	)	)	PUNCT
ejpam-146	354	17	∩	∩	NOUN
ejpam-146	354	18	β	β	X
ejpam-146	354	19	cl(v	cl(v	X
ejpam-146	354	20	)	)	PUNCT
ejpam-146	354	21	=	=	SYM
ejpam-146	354	22	;	;	PUNCT
ejpam-146	354	23	.	.	PUNCT
ejpam-146	355	1	so	so	ADV
ejpam-146	355	2	,	,	PUNCT
ejpam-146	355	3	y	y	PROPN
ejpam-146	355	4	6∈	6∈	PROPN
ejpam-146	355	5	β	β	PROPN
ejpam-146	355	6	-	-	PUNCT
ejpam-146	355	7	θ	θ	NOUN
ejpam-146	355	8	-adψ(f	-adψ(f	PROPN
ejpam-146	355	9	)	)	PUNCT
ejpam-146	355	10	.	.	PUNCT
ejpam-146	356	1	therefore	therefore	ADV
ejpam-146	356	2	β	β	X
ejpam-146	356	3	-	-	PUNCT
ejpam-146	356	4	θ	θ	PROPN
ejpam-146	356	5	c.	c.	PROPN
ejpam-146	356	6	k.	k.	PROPN
ejpam-146	356	7	basu	basu	PROPN
ejpam-146	356	8	,	,	PUNCT
ejpam-146	356	9	m.	m.	PROPN
ejpam-146	356	10	k.	k.	PROPN
ejpam-146	356	11	ghosh	ghosh	PROPN
ejpam-146	356	12	/	/	PUNCT
ejpam-146	356	13	eur	eur	PROPN
ejpam-146	356	14	.	.	PUNCT
ejpam-146	357	1	j.	j.	PROPN
ejpam-146	357	2	pure	pure	PROPN
ejpam-146	357	3	appl	appl	PROPN
ejpam-146	357	4	.	.	PROPN
ejpam-146	357	5	math	math	PROPN
ejpam-146	357	6	,	,	PUNCT
ejpam-146	357	7	1	1	NUM
ejpam-146	357	8	(	(	PUNCT
ejpam-146	357	9	2008	2008	NUM
ejpam-146	357	10	)	)	PUNCT
ejpam-146	357	11	,	,	PUNCT
ejpam-146	357	12	(	(	PUNCT
ejpam-146	357	13	40	40	NUM
ejpam-146	357	14	-	-	SYM
ejpam-146	357	15	50	50	NUM
ejpam-146	357	16	)	)	PUNCT
ejpam-146	357	17	47	47	NUM
ejpam-146	357	18	adψ(f	adψ(f	NOUN
ejpam-146	357	19	)	)	PUNCT
ejpam-146	357	20	⊂	⊂	PROPN
ejpam-146	357	21	{	{	PUNCT
ejpam-146	357	22	ψ(x	ψ(x	NOUN
ejpam-146	357	23	)	)	PUNCT
ejpam-146	357	24	}	}	PUNCT
ejpam-146	357	25	.	.	PUNCT
ejpam-146	358	1	theorem	theorem	VERB
ejpam-146	358	2	4.7	4.7	NUM
ejpam-146	358	3	.	.	PUNCT
ejpam-146	359	1	if	if	SCONJ
ejpam-146	359	2	φ	φ	PROPN
ejpam-146	359	3	:	:	PUNCT
ejpam-146	359	4	x	x	X
ejpam-146	359	5	→	→	SYM
ejpam-146	359	6	y	y	PROPN
ejpam-146	359	7	is	be	AUX
ejpam-146	359	8	(	(	PUNCT
ejpam-146	359	9	θ	θ	PROPN
ejpam-146	359	10	,	,	PUNCT
ejpam-146	359	11	β)-continuous	β)-continuous	PUNCT
ejpam-146	359	12	and	and	CCONJ
ejpam-146	359	13	if	if	SCONJ
ejpam-146	359	14	ψ	ψ	X
ejpam-146	359	15	:	:	PUNCT
ejpam-146	359	16	x	x	X
ejpam-146	359	17	→	→	SYM
ejpam-146	359	18	y	y	PROPN
ejpam-146	359	19	has	have	VERB
ejpam-146	359	20	a	a	DET
ejpam-146	359	21	β	β	NOUN
ejpam-146	359	22	-	-	PUNCT
ejpam-146	359	23	θ	θ	NOUN
ejpam-146	359	24	-subclosed	-subclose	VERB
ejpam-146	359	25	graph	graph	NOUN
ejpam-146	359	26	then	then	ADV
ejpam-146	359	27	the	the	DET
ejpam-146	359	28	set	set	NOUN
ejpam-146	359	29	∆x	∆x	PROPN
ejpam-146	359	30	(	(	PUNCT
ejpam-146	359	31	φ	φ	PROPN
ejpam-146	359	32	,	,	PUNCT
ejpam-146	359	33	ψ	ψ	NOUN
ejpam-146	359	34	)	)	PUNCT
ejpam-146	359	35	=	=	SYM
ejpam-146	359	36	{	{	PUNCT
ejpam-146	359	37	x	x	PUNCT
ejpam-146	359	38	∈	∈	PROPN
ejpam-146	359	39	x	x	X
ejpam-146	359	40	:	:	PUNCT
ejpam-146	359	41	φ(x	φ(x	VERB
ejpam-146	359	42	)	)	PUNCT
ejpam-146	359	43	=	=	NOUN
ejpam-146	359	44	ψ(x	ψ(x	NOUN
ejpam-146	359	45	)	)	PUNCT
ejpam-146	359	46	}	}	PUNCT
ejpam-146	359	47	is	be	AUX
ejpam-146	359	48	a	a	DET
ejpam-146	359	49	closed	closed	ADJ
ejpam-146	359	50	subset	subset	NOUN
ejpam-146	359	51	of	of	ADP
ejpam-146	359	52	x	x	X
ejpam-146	359	53	.	.	PUNCT
ejpam-146	360	1	proof	proof	NOUN
ejpam-146	360	2	.	.	PUNCT
ejpam-146	361	1	suppose	suppose	VERB
ejpam-146	361	2	x0	x0	PROPN
ejpam-146	361	3	∈	∈	PROPN
ejpam-146	361	4	cl(∆x	cl(∆x	X
ejpam-146	362	1	(	(	PUNCT
ejpam-146	362	2	φ	φ	NOUN
ejpam-146	362	3	,	,	PUNCT
ejpam-146	362	4	ψ))−∆x	ψ))−∆x	PROPN
ejpam-146	362	5	(	(	PUNCT
ejpam-146	362	6	φ	φ	X
ejpam-146	362	7	,	,	PUNCT
ejpam-146	362	8	ψ	ψ	NOUN
ejpam-146	362	9	)	)	PUNCT
ejpam-146	362	10	.	.	PUNCT
ejpam-146	363	1	then	then	ADV
ejpam-146	363	2	there	there	PRON
ejpam-146	363	3	is	be	VERB
ejpam-146	363	4	a	a	DET
ejpam-146	363	5	filter	filter	NOUN
ejpam-146	363	6	base	base	NOUN
ejpam-146	363	7	f	f	PROPN
ejpam-146	363	8	on	on	ADP
ejpam-146	363	9	∆x	∆x	PROPN
ejpam-146	363	10	(	(	PUNCT
ejpam-146	363	11	φ	φ	PROPN
ejpam-146	363	12	,	,	PUNCT
ejpam-146	363	13	ψ	ψ	NOUN
ejpam-146	363	14	)	)	PUNCT
ejpam-146	363	15	such	such	ADJ
ejpam-146	363	16	that	that	SCONJ
ejpam-146	363	17	f	f	PROPN
ejpam-146	363	18	→	→	SYM
ejpam-146	363	19	x0	x0	PROPN
ejpam-146	363	20	.	.	PUNCT
ejpam-146	364	1	since	since	SCONJ
ejpam-146	364	2	ψ(f	ψ(f	NOUN
ejpam-146	364	3	)	)	PUNCT
ejpam-146	364	4	=	=	SYM
ejpam-146	364	5	φ(f	φ(f	PROPN
ejpam-146	364	6	)	)	PUNCT
ejpam-146	364	7	,	,	PUNCT
ejpam-146	364	8	for	for	ADP
ejpam-146	364	9	each	each	DET
ejpam-146	364	10	f	f	PROPN
ejpam-146	364	11	∈	∈	PROPN
ejpam-146	364	12	f	f	PROPN
ejpam-146	364	13	and	and	CCONJ
ejpam-146	364	14	since	since	SCONJ
ejpam-146	364	15	ψ	ψ	NOUN
ejpam-146	364	16	has	have	VERB
ejpam-146	364	17	a	a	DET
ejpam-146	364	18	β	β	NOUN
ejpam-146	364	19	-	-	PUNCT
ejpam-146	364	20	θ	θ	NOUN
ejpam-146	364	21	-subclosed	-subclose	VERB
ejpam-146	364	22	graph	graph	NOUN
ejpam-146	364	23	,	,	PUNCT
ejpam-146	364	24	we	we	PRON
ejpam-146	364	25	have	have	VERB
ejpam-146	364	26	β	β	NOUN
ejpam-146	364	27	-	-	NOUN
ejpam-146	364	28	θ	θ	NOUN
ejpam-146	364	29	-adφ(f	-adφ(f	PROPN
ejpam-146	364	30	)	)	PUNCT
ejpam-146	365	1	=	=	PUNCT
ejpam-146	365	2	β	β	X
ejpam-146	365	3	-	-	NOUN
ejpam-146	365	4	θ	θ	NOUN
ejpam-146	365	5	-adψ(f	-adψ(f	PROPN
ejpam-146	365	6	)	)	PUNCT
ejpam-146	365	7	⊂	⊂	PROPN
ejpam-146	365	8	{	{	PUNCT
ejpam-146	365	9	ψ(x	ψ(x	NOUN
ejpam-146	365	10	)	)	PUNCT
ejpam-146	365	11	}	}	PUNCT
ejpam-146	365	12	.	.	PUNCT
ejpam-146	366	1	as	as	SCONJ
ejpam-146	366	2	φ	φ	PROPN
ejpam-146	366	3	is	be	AUX
ejpam-146	366	4	(	(	PUNCT
ejpam-146	366	5	θ	θ	PROPN
ejpam-146	366	6	,	,	PUNCT
ejpam-146	366	7	β)-continuous	β)-continuous	PUNCT
ejpam-146	366	8	then	then	ADV
ejpam-146	366	9	for	for	ADP
ejpam-146	366	10	each	each	DET
ejpam-146	366	11	f	f	PROPN
ejpam-146	366	12	∈	∈	PROPN
ejpam-146	366	13	f	f	PROPN
ejpam-146	366	14	,	,	PUNCT
ejpam-146	366	15	we	we	PRON
ejpam-146	366	16	have	have	VERB
ejpam-146	366	17	x0	x0	PROPN
ejpam-146	366	18	∈	∈	PROPN
ejpam-146	366	19	cl(f	cl(f	PROPN
ejpam-146	366	20	)	)	PUNCT
ejpam-146	366	21	⊂	⊂	PROPN
ejpam-146	366	22	cl(φ−1(φ(f	cl(φ−1(φ(f	NOUN
ejpam-146	366	23	)	)	PUNCT
ejpam-146	366	24	)	)	PUNCT
ejpam-146	366	25	)	)	PUNCT
ejpam-146	367	1	⊂	⊂	PROPN
ejpam-146	367	2	φ−1(β	φ−1(β	PROPN
ejpam-146	367	3	-	-	PUNCT
ejpam-146	367	4	θ	θ	NOUN
ejpam-146	367	5	-cl(φ(f	-cl(φ(f	PUNCT
ejpam-146	367	6	)	)	PUNCT
ejpam-146	367	7	)	)	PUNCT
ejpam-146	367	8	(	(	PUNCT
ejpam-146	367	9	last	last	ADJ
ejpam-146	367	10	inclusion	inclusion	NOUN
ejpam-146	367	11	follows	follow	VERB
ejpam-146	367	12	from	from	ADP
ejpam-146	367	13	theorem	theorem	ADJ
ejpam-146	367	14	4.2	4.2	NUM
ejpam-146	367	15	)	)	PUNCT
ejpam-146	367	16	.	.	PUNCT
ejpam-146	368	1	so	so	ADV
ejpam-146	368	2	,	,	PUNCT
ejpam-146	368	3	φ(x0	φ(x0	NOUN
ejpam-146	368	4	)	)	PUNCT
ejpam-146	368	5	∈	∈	PROPN
ejpam-146	368	6	β	β	PROPN
ejpam-146	368	7	-	-	PUNCT
ejpam-146	368	8	θ	θ	NOUN
ejpam-146	368	9	-cl(φ(f	-cl(φ(f	PUNCT
ejpam-146	368	10	)	)	PUNCT
ejpam-146	368	11	)	)	PUNCT
ejpam-146	368	12	for	for	ADP
ejpam-146	368	13	each	each	DET
ejpam-146	368	14	f	f	PROPN
ejpam-146	368	15	∈	∈	PROPN
ejpam-146	368	16	f	f	PROPN
ejpam-146	368	17	.	.	PUNCT
ejpam-146	369	1	therefore	therefore	ADV
ejpam-146	369	2	,	,	PUNCT
ejpam-146	369	3	φ(x0	φ(x0	NOUN
ejpam-146	369	4	)	)	PUNCT
ejpam-146	369	5	∈	∈	NOUN
ejpam-146	369	6	βθ	βθ	PROPN
ejpam-146	369	7	-adφ(f	-adφ(f	PROPN
ejpam-146	369	8	)	)	PUNCT
ejpam-146	369	9	and	and	CCONJ
ejpam-146	369	10	hence	hence	ADV
ejpam-146	369	11	φ(x0	φ(x0	NOUN
ejpam-146	369	12	)	)	PUNCT
ejpam-146	370	1	=	=	NOUN
ejpam-146	370	2	ψ(x0	ψ(x0	NOUN
ejpam-146	370	3	)	)	PUNCT
ejpam-146	370	4	—	—	PUNCT
ejpam-146	370	5	a	a	DET
ejpam-146	370	6	contradiction	contradiction	NOUN
ejpam-146	370	7	.	.	PUNCT
ejpam-146	371	1	so	so	ADV
ejpam-146	371	2	∆x	∆x	PROPN
ejpam-146	371	3	(	(	PUNCT
ejpam-146	371	4	φ	φ	PROPN
ejpam-146	371	5	,	,	PUNCT
ejpam-146	371	6	ψ	ψ	NOUN
ejpam-146	371	7	)	)	PUNCT
ejpam-146	371	8	is	be	AUX
ejpam-146	371	9	closed	close	VERB
ejpam-146	371	10	in	in	ADP
ejpam-146	371	11	x	x	X
ejpam-146	371	12	.	.	PUNCT
ejpam-146	372	1	definition	definition	NOUN
ejpam-146	372	2	4.8	4.8	NUM
ejpam-146	372	3	.	.	PUNCT
ejpam-146	373	1	a	a	DET
ejpam-146	373	2	topological	topological	ADJ
ejpam-146	373	3	space	space	NOUN
ejpam-146	373	4	x	x	PRON
ejpam-146	373	5	is	be	AUX
ejpam-146	373	6	said	say	VERB
ejpam-146	373	7	to	to	PART
ejpam-146	373	8	be	be	AUX
ejpam-146	373	9	β	β	X
ejpam-146	373	10	-	-	VERB
ejpam-146	373	11	connected	connect	VERB
ejpam-146	374	1	[	[	X
ejpam-146	374	2	3	3	X
ejpam-146	374	3	]	]	PUNCT
ejpam-146	374	4	if	if	SCONJ
ejpam-146	374	5	x	x	PRON
ejpam-146	374	6	can	can	AUX
ejpam-146	374	7	not	not	PART
ejpam-146	374	8	be	be	AUX
ejpam-146	374	9	expressed	express	VERB
ejpam-146	374	10	as	as	ADP
ejpam-146	374	11	the	the	DET
ejpam-146	374	12	union	union	NOUN
ejpam-146	374	13	of	of	ADP
ejpam-146	374	14	two	two	NUM
ejpam-146	374	15	non	non	ADJ
ejpam-146	374	16	-	-	ADJ
ejpam-146	374	17	empty	empty	ADJ
ejpam-146	374	18	disjoint	disjoint	NOUN
ejpam-146	374	19	β	β	NOUN
ejpam-146	374	20	-	-	ADJ
ejpam-146	374	21	open	open	ADJ
ejpam-146	374	22	sets	set	NOUN
ejpam-146	374	23	.	.	PUNCT
ejpam-146	375	1	corollary	corollary	ADJ
ejpam-146	375	2	4.9	4.9	NUM
ejpam-146	375	3	.	.	PUNCT
ejpam-146	376	1	if	if	SCONJ
ejpam-146	376	2	x	x	PRON
ejpam-146	376	3	is	be	AUX
ejpam-146	376	4	β	β	VERB
ejpam-146	376	5	-	-	VERB
ejpam-146	376	6	connected	connected	ADJ
ejpam-146	376	7	and	and	CCONJ
ejpam-146	376	8	if	if	SCONJ
ejpam-146	376	9	ψ	ψ	X
ejpam-146	376	10	:	:	PUNCT
ejpam-146	376	11	x	x	SYM
ejpam-146	376	12	→	→	PUNCT
ejpam-146	376	13	x	x	X
ejpam-146	376	14	has	have	VERB
ejpam-146	376	15	a	a	DET
ejpam-146	376	16	β	β	NOUN
ejpam-146	376	17	-	-	PUNCT
ejpam-146	376	18	θ	θ	NOUN
ejpam-146	376	19	-subclosed	-subclose	VERB
ejpam-146	376	20	graph	graph	NOUN
ejpam-146	376	21	then	then	ADV
ejpam-146	376	22	the	the	DET
ejpam-146	376	23	set	set	NOUN
ejpam-146	376	24	of	of	ADP
ejpam-146	376	25	fixed	fix	VERB
ejpam-146	376	26	points	point	NOUN
ejpam-146	376	27	of	of	ADP
ejpam-146	376	28	ψ	ψ	NOUN
ejpam-146	376	29	is	be	AUX
ejpam-146	376	30	a	a	DET
ejpam-146	376	31	closed	closed	ADJ
ejpam-146	376	32	subset	subset	NOUN
ejpam-146	376	33	of	of	ADP
ejpam-146	376	34	x	x	X
ejpam-146	376	35	.	.	PUNCT
ejpam-146	377	1	proof	proof	NOUN
ejpam-146	377	2	.	.	PUNCT
ejpam-146	378	1	since	since	SCONJ
ejpam-146	378	2	x	x	PROPN
ejpam-146	378	3	is	be	AUX
ejpam-146	378	4	β	β	VERB
ejpam-146	378	5	-	-	VERB
ejpam-146	378	6	connected	connected	ADJ
ejpam-146	378	7	and	and	CCONJ
ejpam-146	378	8	also	also	ADV
ejpam-146	378	9	since	since	SCONJ
ejpam-146	378	10	β	β	NOUN
ejpam-146	378	11	cl(v	cl(v	X
ejpam-146	378	12	)	)	PUNCT
ejpam-146	378	13	∈	∈	PROPN
ejpam-146	378	14	βo(x	βo(x	PUNCT
ejpam-146	378	15	)	)	PUNCT
ejpam-146	378	16	for	for	ADP
ejpam-146	378	17	v	v	NOUN
ejpam-146	378	18	∈	∈	NOUN
ejpam-146	378	19	βo(x	βo(x	PUNCT
ejpam-146	378	20	)	)	PUNCT
ejpam-146	378	21	(	(	PUNCT
ejpam-146	378	22	by	by	ADP
ejpam-146	378	23	lemma	lemma	PROPN
ejpam-146	378	24	2.2	2.2	NUM
ejpam-146	378	25	)	)	PUNCT
ejpam-146	378	26	,	,	PUNCT
ejpam-146	378	27	for	for	ADP
ejpam-146	378	28	a	a	DET
ejpam-146	378	29	nonempty	nonempty	ADJ
ejpam-146	378	30	β	β	NOUN
ejpam-146	378	31	-	-	ADJ
ejpam-146	378	32	open	open	ADJ
ejpam-146	378	33	set	set	NOUN
ejpam-146	378	34	w	w	PROPN
ejpam-146	378	35	of	of	ADP
ejpam-146	378	36	x	x	SYM
ejpam-146	378	37	,	,	PUNCT
ejpam-146	378	38	β	β	X
ejpam-146	378	39	cl(w	cl(w	NOUN
ejpam-146	378	40	)	)	PUNCT
ejpam-146	379	1	=	=	PUNCT
ejpam-146	380	1	x	x	X
ejpam-146	380	2	.	.	PUNCT
ejpam-146	381	1	so	so	ADV
ejpam-146	381	2	,	,	PUNCT
ejpam-146	381	3	the	the	DET
ejpam-146	381	4	identity	identity	NOUN
ejpam-146	381	5	function	function	NOUN
ejpam-146	381	6	φ	φ	NOUN
ejpam-146	381	7	:	:	PUNCT
ejpam-146	381	8	x	x	X
ejpam-146	381	9	→	→	PUNCT
ejpam-146	381	10	x	x	X
ejpam-146	381	11	is	be	AUX
ejpam-146	381	12	always	always	ADV
ejpam-146	381	13	(	(	PUNCT
ejpam-146	381	14	θ	θ	NOUN
ejpam-146	381	15	,	,	PUNCT
ejpam-146	381	16	β)-continuous	β)-continuous	PUNCT
ejpam-146	381	17	.	.	PUNCT
ejpam-146	382	1	hence	hence	ADV
ejpam-146	382	2	by	by	ADP
ejpam-146	382	3	the	the	DET
ejpam-146	382	4	above	above	ADJ
ejpam-146	382	5	theorem	theorem	NOUN
ejpam-146	382	6	4.7	4.7	NUM
ejpam-146	382	7	,	,	PUNCT
ejpam-146	382	8	the	the	DET
ejpam-146	382	9	result	result	NOUN
ejpam-146	382	10	is	be	AUX
ejpam-146	382	11	being	be	AUX
ejpam-146	382	12	followed	follow	VERB
ejpam-146	382	13	.	.	PUNCT
ejpam-146	383	1	the	the	DET
ejpam-146	383	2	following	follow	VERB
ejpam-146	383	3	theorem	theorem	NOUN
ejpam-146	383	4	establishes	establishe	NOUN
ejpam-146	383	5	on	on	ADP
ejpam-146	383	6	common	common	ADJ
ejpam-146	383	7	fixed	fix	VERB
ejpam-146	383	8	points	point	NOUN
ejpam-146	383	9	of	of	ADP
ejpam-146	383	10	a	a	DET
ejpam-146	383	11	family	family	NOUN
ejpam-146	383	12	of	of	ADP
ejpam-146	383	13	functions	function	NOUN
ejpam-146	383	14	having	have	VERB
ejpam-146	383	15	β	β	NOUN
ejpam-146	383	16	-	-	PUNCT
ejpam-146	383	17	θ	θ	NOUN
ejpam-146	383	18	-subclosed	-subclose	VERB
ejpam-146	383	19	graphs	graph	NOUN
ejpam-146	383	20	.	.	PUNCT
ejpam-146	384	1	theorem	theorem	VERB
ejpam-146	384	2	4.10	4.10	NUM
ejpam-146	384	3	.	.	PUNCT
ejpam-146	385	1	let	let	VERB
ejpam-146	385	2	ω	ω	NUM
ejpam-146	385	3	be	be	AUX
ejpam-146	385	4	a	a	DET
ejpam-146	385	5	family	family	NOUN
ejpam-146	385	6	of	of	ADP
ejpam-146	385	7	functions	function	NOUN
ejpam-146	385	8	from	from	ADP
ejpam-146	385	9	a	a	DET
ejpam-146	385	10	β	β	X
ejpam-146	385	11	-	-	VERB
ejpam-146	385	12	connected	connected	ADJ
ejpam-146	385	13	β	β	ADJ
ejpam-146	385	14	-	-	ADJ
ejpam-146	385	15	closed	closed	ADJ
ejpam-146	385	16	space	space	NOUN
ejpam-146	385	17	x	x	PUNCT
ejpam-146	385	18	into	into	ADP
ejpam-146	385	19	itself	itself	PRON
ejpam-146	385	20	with	with	ADP
ejpam-146	385	21	β	β	NOUN
ejpam-146	385	22	-	-	PUNCT
ejpam-146	385	23	θ	θ	NOUN
ejpam-146	385	24	-subclosed	-subclose	VERB
ejpam-146	385	25	graphs	graph	NOUN
ejpam-146	385	26	.	.	PUNCT
ejpam-146	386	1	if	if	SCONJ
ejpam-146	386	2	for	for	ADP
ejpam-146	386	3	each	each	DET
ejpam-146	386	4	finite	finite	PROPN
ejpam-146	386	5	ω0	ω0	PROPN
ejpam-146	386	6	⊂	⊂	PROPN
ejpam-146	386	7	ω	ω	PROPN
ejpam-146	386	8	there	there	PRON
ejpam-146	386	9	is	be	VERB
ejpam-146	386	10	an	an	DET
ejpam-146	386	11	x	x	SYM
ejpam-146	386	12	∈	∈	PROPN
ejpam-146	386	13	x	x	X
ejpam-146	386	14	such	such	ADJ
ejpam-146	386	15	that	that	DET
ejpam-146	386	16	ψ(x	ψ(x	NOUN
ejpam-146	386	17	)	)	PUNCT
ejpam-146	387	1	=	=	SYM
ejpam-146	387	2	x	x	PUNCT
ejpam-146	387	3	for	for	ADP
ejpam-146	387	4	all	all	DET
ejpam-146	387	5	ψ	ψ	DET
ejpam-146	387	6	∈	∈	NOUN
ejpam-146	387	7	ω0	ω0	NOUN
ejpam-146	387	8	then	then	ADV
ejpam-146	387	9	there	there	PRON
ejpam-146	387	10	exists	exist	VERB
ejpam-146	387	11	an	an	DET
ejpam-146	387	12	x	x	SYM
ejpam-146	387	13	∈	∈	PROPN
ejpam-146	387	14	x	x	X
ejpam-146	387	15	such	such	ADJ
ejpam-146	387	16	that	that	DET
ejpam-146	387	17	ψ(x	ψ(x	NOUN
ejpam-146	387	18	)	)	PUNCT
ejpam-146	388	1	=	=	SYM
ejpam-146	388	2	x	x	PUNCT
ejpam-146	388	3	for	for	ADP
ejpam-146	388	4	all	all	DET
ejpam-146	388	5	ψ	ψ	PRON
ejpam-146	388	6	∈	∈	PROPN
ejpam-146	388	7	ω	ω	PROPN
ejpam-146	388	8	.	.	PUNCT
ejpam-146	389	1	proof	proof	NOUN
ejpam-146	389	2	.	.	PUNCT
ejpam-146	390	1	since	since	SCONJ
ejpam-146	390	2	x	x	PROPN
ejpam-146	390	3	is	be	AUX
ejpam-146	390	4	β	β	VERB
ejpam-146	390	5	-	-	VERB
ejpam-146	390	6	connected	connect	VERB
ejpam-146	390	7	,	,	PUNCT
ejpam-146	390	8	the	the	DET
ejpam-146	390	9	identity	identity	NOUN
ejpam-146	390	10	function	function	NOUN
ejpam-146	390	11	φ	φ	NOUN
ejpam-146	390	12	:	:	PUNCT
ejpam-146	390	13	x	x	X
ejpam-146	390	14	→	→	PUNCT
ejpam-146	390	15	x	x	X
ejpam-146	390	16	is	be	AUX
ejpam-146	390	17	(	(	PUNCT
ejpam-146	390	18	θ	θ	NOUN
ejpam-146	390	19	,	,	PUNCT
ejpam-146	390	20	β)-continuous	β)-continuous	PROPN
ejpam-146	390	21	.	.	PUNCT
ejpam-146	391	1	now	now	ADV
ejpam-146	391	2	by	by	ADP
ejpam-146	391	3	theorem	theorem	NOUN
ejpam-146	391	4	4.7	4.7	NUM
ejpam-146	391	5	,	,	PUNCT
ejpam-146	391	6	f	f	X
ejpam-146	391	7	=	=	PRON
ejpam-146	391	8	{	{	PUNCT
ejpam-146	391	9	∆x	∆x	PROPN
ejpam-146	391	10	(	(	PUNCT
ejpam-146	391	11	φ	φ	PROPN
ejpam-146	391	12	,	,	PUNCT
ejpam-146	391	13	ψ	ψ	NOUN
ejpam-146	391	14	)	)	PUNCT
ejpam-146	391	15	:	:	PUNCT
ejpam-146	391	16	ψ	ψ	X
ejpam-146	391	17	∈	∈	PROPN
ejpam-146	391	18	ω	ω	PROPN
ejpam-146	391	19	}	}	PUNCT
ejpam-146	391	20	is	be	AUX
ejpam-146	391	21	a	a	DET
ejpam-146	391	22	family	family	NOUN
ejpam-146	391	23	of	of	ADP
ejpam-146	391	24	closed	closed	ADJ
ejpam-146	391	25	subsets	subset	NOUN
ejpam-146	391	26	of	of	ADP
ejpam-146	391	27	x	x	X
ejpam-146	391	28	.	.	PUNCT
ejpam-146	392	1	by	by	ADP
ejpam-146	392	2	hypothesis	hypothesis	NOUN
ejpam-146	392	3	,	,	PUNCT
ejpam-146	392	4	ω	ω	PROPN
ejpam-146	392	5	has	have	AUX
ejpam-146	392	6	finite	finite	VERB
ejpam-146	392	7	the	the	DET
ejpam-146	392	8	intersection	intersection	NOUN
ejpam-146	392	9	property	property	NOUN
ejpam-146	392	10	.	.	PUNCT
ejpam-146	393	1	let	let	VERB
ejpam-146	393	2	f0	f0	PROPN
ejpam-146	393	3	be	be	AUX
ejpam-146	393	4	the	the	DET
ejpam-146	393	5	filter	filter	NOUN
ejpam-146	393	6	base	base	NOUN
ejpam-146	393	7	generated	generate	VERB
ejpam-146	393	8	by	by	ADP
ejpam-146	393	9	f	f	PROPN
ejpam-146	393	10	.	.	PUNCT
ejpam-146	394	1	since	since	SCONJ
ejpam-146	394	2	x	x	PROPN
ejpam-146	394	3	is	be	AUX
ejpam-146	394	4	β	β	NOUN
ejpam-146	394	5	-	-	VERB
ejpam-146	394	6	closed	closed	ADJ
ejpam-146	394	7	,	,	PUNCT
ejpam-146	394	8	by	by	ADP
ejpam-146	394	9	theorem	theorem	NOUN
ejpam-146	394	10	3.2	3.2	NUM
ejpam-146	394	11	,	,	PUNCT
ejpam-146	394	12	β	β	NOUN
ejpam-146	394	13	-	-	NOUN
ejpam-146	394	14	θ	θ	NOUN
ejpam-146	394	15	-adf0	-adf0	PROPN
ejpam-146	394	16	6=	6=	NUM
ejpam-146	394	17	;	;	PUNCT
ejpam-146	394	18	.	.	PUNCT
ejpam-146	395	1	hence	hence	ADV
ejpam-146	395	2	;	;	PUNCT
ejpam-146	395	3	6=	6=	SYM
ejpam-146	395	4	β	β	X
ejpam-146	395	5	-	-	PUNCT
ejpam-146	395	6	θ	θ	NOUN
ejpam-146	395	7	-adf0	-adf0	PUNCT
ejpam-146	396	1	⊂	⊂	PROPN
ejpam-146	396	2	∩ψ∈ω∆x	∩ψ∈ω∆x	PROPN
ejpam-146	396	3	(	(	PUNCT
ejpam-146	396	4	φ	φ	X
ejpam-146	396	5	,	,	PUNCT
ejpam-146	396	6	ψ	ψ	NOUN
ejpam-146	396	7	)	)	PUNCT
ejpam-146	396	8	.	.	PUNCT
ejpam-146	397	1	therefore	therefore	ADV
ejpam-146	397	2	,	,	PUNCT
ejpam-146	397	3	there	there	PRON
ejpam-146	397	4	is	be	VERB
ejpam-146	397	5	at	at	ADV
ejpam-146	397	6	least	least	ADJ
ejpam-146	397	7	one	one	NUM
ejpam-146	397	8	x	x	SYM
ejpam-146	397	9	∈	∈	NOUN
ejpam-146	397	10	x	x	SYM
ejpam-146	397	11	satisfying	satisfy	VERB
ejpam-146	397	12	ψ(x	ψ(x	NOUN
ejpam-146	397	13	)	)	PUNCT
ejpam-146	397	14	=	=	SYM
ejpam-146	397	15	φ(x	φ(x	NOUN
ejpam-146	397	16	)	)	PUNCT
ejpam-146	397	17	=	=	SYM
ejpam-146	398	1	x	x	PUNCT
ejpam-146	398	2	for	for	ADP
ejpam-146	398	3	all	all	PRON
ejpam-146	398	4	ψ	ψ	PRON
ejpam-146	398	5	∈	∈	PROPN
ejpam-146	398	6	ω	ω	PROPN
ejpam-146	398	7	.	.	PUNCT
ejpam-146	398	8	theorem	theorem	PROPN
ejpam-146	398	9	4.11	4.11	NUM
ejpam-146	398	10	.	.	PUNCT
ejpam-146	399	1	if	if	SCONJ
ejpam-146	399	2	a	a	DET
ejpam-146	399	3	⊂	⊂	X
ejpam-146	399	4	x	x	X
ejpam-146	399	5	and	and	CCONJ
ejpam-146	399	6	ψ	ψ	X
ejpam-146	399	7	:	:	PUNCT
ejpam-146	399	8	x	x	X
ejpam-146	399	9	→	→	SYM
ejpam-146	399	10	y	y	PROPN
ejpam-146	399	11	has	have	VERB
ejpam-146	399	12	a	a	DET
ejpam-146	399	13	β	β	NOUN
ejpam-146	399	14	-	-	PUNCT
ejpam-146	399	15	θ	θ	NOUN
ejpam-146	399	16	-subclosed	-subclose	VERB
ejpam-146	399	17	graph	graph	NOUN
ejpam-146	399	18	then	then	ADV
ejpam-146	399	19	the	the	DET
ejpam-146	399	20	restriction	restriction	NOUN
ejpam-146	399	21	ψa	ψa	ADP
ejpam-146	399	22	:	:	PUNCT
ejpam-146	399	23	a→	a→	PUNCT
ejpam-146	399	24	y	y	PROPN
ejpam-146	399	25	has	have	VERB
ejpam-146	399	26	a	a	DET
ejpam-146	399	27	β	β	NOUN
ejpam-146	399	28	-	-	PUNCT
ejpam-146	399	29	θ	θ	NOUN
ejpam-146	399	30	-subclosed	-subclose	VERB
ejpam-146	399	31	graph	graph	NOUN
ejpam-146	399	32	.	.	PUNCT
ejpam-146	400	1	proof	proof	NOUN
ejpam-146	400	2	.	.	PUNCT
ejpam-146	401	1	straightforward	straightforward	ADJ
ejpam-146	401	2	.	.	PUNCT
ejpam-146	402	1	it	it	PRON
ejpam-146	402	2	is	be	AUX
ejpam-146	402	3	well	well	ADV
ejpam-146	402	4	known	know	VERB
ejpam-146	402	5	that	that	PRON
ejpam-146	402	6	inverse	inverse	VERB
ejpam-146	402	7	the	the	DET
ejpam-146	402	8	image	image	NOUN
ejpam-146	402	9	of	of	ADP
ejpam-146	402	10	a	a	DET
ejpam-146	402	11	compact	compact	ADJ
ejpam-146	402	12	set	set	NOUN
ejpam-146	402	13	of	of	ADP
ejpam-146	402	14	a	a	DET
ejpam-146	402	15	function	function	NOUN
ejpam-146	402	16	with	with	ADP
ejpam-146	402	17	closed	closed	ADJ
ejpam-146	402	18	graph	graph	NOUN
ejpam-146	402	19	is	be	AUX
ejpam-146	402	20	closed	close	VERB
ejpam-146	402	21	.	.	PUNCT
ejpam-146	403	1	the	the	DET
ejpam-146	403	2	following	follow	VERB
ejpam-146	403	3	theorem	theorem	NOUN
ejpam-146	403	4	shows	show	VERB
ejpam-146	403	5	a	a	DET
ejpam-146	403	6	analogous	analogous	ADJ
ejpam-146	403	7	result	result	NOUN
ejpam-146	403	8	for	for	ADP
ejpam-146	403	9	functions	function	NOUN
ejpam-146	403	10	having	have	VERB
ejpam-146	403	11	β	β	NOUN
ejpam-146	403	12	-	-	PUNCT
ejpam-146	403	13	θ	θ	NOUN
ejpam-146	403	14	-subclosed	-subclose	VERB
ejpam-146	403	15	graph	graph	NOUN
ejpam-146	403	16	(	(	PUNCT
ejpam-146	403	17	a	a	DET
ejpam-146	403	18	subset	subset	NOUN
ejpam-146	403	19	b	b	NOUN
ejpam-146	403	20	of	of	ADP
ejpam-146	403	21	x	x	PROPN
ejpam-146	403	22	is	be	AUX
ejpam-146	403	23	called	call	VERB
ejpam-146	403	24	β	β	NOUN
ejpam-146	403	25	-	-	VERB
ejpam-146	403	26	closed	close	VERB
ejpam-146	403	27	with	with	ADP
ejpam-146	403	28	respect	respect	NOUN
ejpam-146	403	29	to	to	ADP
ejpam-146	403	30	x	x	SYM
ejpam-146	403	31	written	write	VERB
ejpam-146	403	32	as	as	ADP
ejpam-146	403	33	β	β	NOUN
ejpam-146	403	34	-	-	VERB
ejpam-146	403	35	set	set	VERB
ejpam-146	403	36	if	if	SCONJ
ejpam-146	403	37	every	every	DET
ejpam-146	403	38	cover	cover	NOUN
ejpam-146	403	39	of	of	ADP
ejpam-146	403	40	b	b	NOUN
ejpam-146	403	41	by	by	ADP
ejpam-146	403	42	β	β	ADJ
ejpam-146	403	43	-	-	ADJ
ejpam-146	403	44	open	open	ADJ
ejpam-146	403	45	sets	set	NOUN
ejpam-146	403	46	of	of	ADP
ejpam-146	403	47	x	x	PUNCT
ejpam-146	403	48	has	have	VERB
ejpam-146	403	49	a	a	DET
ejpam-146	403	50	finite	finite	NOUN
ejpam-146	403	51	subfamily	subfamily	ADV
ejpam-146	403	52	whose	whose	DET
ejpam-146	403	53	β	β	NOUN
ejpam-146	403	54	-	-	NOUN
ejpam-146	403	55	closures	closure	NOUN
ejpam-146	403	56	cover	cover	VERB
ejpam-146	403	57	b	b	NOUN
ejpam-146	403	58	)	)	PUNCT
ejpam-146	403	59	.	.	PUNCT
ejpam-146	404	1	theorem	theorem	VERB
ejpam-146	404	2	4.12	4.12	NUM
ejpam-146	404	3	.	.	PUNCT
ejpam-146	405	1	if	if	SCONJ
ejpam-146	405	2	ψ	ψ	X
ejpam-146	405	3	:	:	PUNCT
ejpam-146	405	4	x	x	X
ejpam-146	405	5	→	→	SYM
ejpam-146	405	6	y	y	PROPN
ejpam-146	405	7	is	be	AUX
ejpam-146	405	8	a	a	DET
ejpam-146	405	9	function	function	NOUN
ejpam-146	405	10	with	with	ADP
ejpam-146	405	11	a	a	DET
ejpam-146	405	12	β	β	NOUN
ejpam-146	405	13	-	-	PUNCT
ejpam-146	405	14	θ	θ	NOUN
ejpam-146	405	15	-subclosed	-subclose	VERB
ejpam-146	405	16	graph	graph	NOUN
ejpam-146	405	17	then	then	ADV
ejpam-146	405	18	ψ−1(b	ψ−1(b	NOUN
ejpam-146	405	19	)	)	PUNCT
ejpam-146	405	20	is	be	AUX
ejpam-146	405	21	closed	close	VERB
ejpam-146	405	22	in	in	ADP
ejpam-146	405	23	x	x	PUNCT
ejpam-146	405	24	for	for	ADP
ejpam-146	405	25	each	each	DET
ejpam-146	405	26	β	β	NOUN
ejpam-146	405	27	-	-	PUNCT
ejpam-146	405	28	set	set	VERB
ejpam-146	405	29	b	b	NOUN
ejpam-146	405	30	in	in	ADP
ejpam-146	405	31	y	y	PROPN
ejpam-146	405	32	.	.	PUNCT
ejpam-146	406	1	c.	c.	PROPN
ejpam-146	406	2	k.	k.	PROPN
ejpam-146	406	3	basu	basu	PROPN
ejpam-146	406	4	,	,	PUNCT
ejpam-146	406	5	m.	m.	PROPN
ejpam-146	406	6	k.	k.	PROPN
ejpam-146	406	7	ghosh	ghosh	PROPN
ejpam-146	406	8	/	/	PUNCT
ejpam-146	406	9	eur	eur	PROPN
ejpam-146	406	10	.	.	PUNCT
ejpam-146	407	1	j.	j.	PROPN
ejpam-146	407	2	pure	pure	PROPN
ejpam-146	407	3	appl	appl	PROPN
ejpam-146	407	4	.	.	PROPN
ejpam-146	407	5	math	math	PROPN
ejpam-146	407	6	,	,	PUNCT
ejpam-146	407	7	1	1	NUM
ejpam-146	407	8	(	(	PUNCT
ejpam-146	407	9	2008	2008	NUM
ejpam-146	407	10	)	)	PUNCT
ejpam-146	407	11	,	,	PUNCT
ejpam-146	407	12	(	(	PUNCT
ejpam-146	407	13	40	40	NUM
ejpam-146	407	14	-	-	SYM
ejpam-146	407	15	50	50	NUM
ejpam-146	407	16	)	)	PUNCT
ejpam-146	407	17	48	48	NUM
ejpam-146	407	18	proof	proof	NOUN
ejpam-146	407	19	.	.	PUNCT
ejpam-146	408	1	let	let	VERB
ejpam-146	408	2	x	x	SYM
ejpam-146	408	3	∈	∈	PROPN
ejpam-146	408	4	cl(ψ−1(b	cl(ψ−1(b	NOUN
ejpam-146	408	5	)	)	PUNCT
ejpam-146	408	6	)	)	PUNCT
ejpam-146	409	1	−	−	PROPN
ejpam-146	409	2	ψ−1(b	ψ−1(b	NOUN
ejpam-146	409	3	)	)	PUNCT
ejpam-146	409	4	.	.	PUNCT
ejpam-146	410	1	then	then	ADV
ejpam-146	410	2	there	there	PRON
ejpam-146	410	3	is	be	VERB
ejpam-146	410	4	a	a	DET
ejpam-146	410	5	filter	filter	NOUN
ejpam-146	410	6	base	base	NOUN
ejpam-146	410	7	f	f	PROPN
ejpam-146	410	8	on	on	ADP
ejpam-146	410	9	ψ−1(b	ψ−1(b	NOUN
ejpam-146	410	10	)	)	PUNCT
ejpam-146	411	1	such	such	ADJ
ejpam-146	411	2	that	that	SCONJ
ejpam-146	411	3	f	f	PROPN
ejpam-146	411	4	→	→	SYM
ejpam-146	411	5	x	x	X
ejpam-146	411	6	.	.	PUNCT
ejpam-146	412	1	since	since	SCONJ
ejpam-146	412	2	ψ	ψ	NOUN
ejpam-146	412	3	has	have	VERB
ejpam-146	412	4	a	a	DET
ejpam-146	412	5	β	β	NOUN
ejpam-146	412	6	-	-	PUNCT
ejpam-146	412	7	θ	θ	NOUN
ejpam-146	412	8	-subclosed	-subclose	VERB
ejpam-146	412	9	graph	graph	NOUN
ejpam-146	412	10	,	,	PUNCT
ejpam-146	412	11	β	β	NOUN
ejpam-146	412	12	-	-	NOUN
ejpam-146	412	13	θ	θ	NOUN
ejpam-146	412	14	-adψ(f	-adψ(f	PROPN
ejpam-146	412	15	)	)	PUNCT
ejpam-146	412	16	⊂	⊂	PROPN
ejpam-146	412	17	{	{	PUNCT
ejpam-146	412	18	ψ(x	ψ(x	NOUN
ejpam-146	412	19	)	)	PUNCT
ejpam-146	412	20	}	}	PUNCT
ejpam-146	412	21	.	.	PUNCT
ejpam-146	413	1	now	now	ADV
ejpam-146	413	2	as	as	SCONJ
ejpam-146	413	3	b	b	PROPN
ejpam-146	413	4	is	be	AUX
ejpam-146	413	5	being	be	AUX
ejpam-146	413	6	a	a	DET
ejpam-146	413	7	β	β	NOUN
ejpam-146	413	8	-	-	NOUN
ejpam-146	413	9	set	set	ADJ
ejpam-146	413	10	,	,	PUNCT
ejpam-146	413	11	it	it	PRON
ejpam-146	413	12	can	can	AUX
ejpam-146	413	13	be	be	AUX
ejpam-146	413	14	easily	easily	ADV
ejpam-146	413	15	verified	verify	VERB
ejpam-146	413	16	that	that	SCONJ
ejpam-146	413	17	b	b	NUM
ejpam-146	413	18	∩	∩	NOUN
ejpam-146	413	19	β	β	X
ejpam-146	413	20	-	-	NOUN
ejpam-146	413	21	θ	θ	NOUN
ejpam-146	413	22	-adψ(f	-adψ(f	PROPN
ejpam-146	413	23	)	)	PUNCT
ejpam-146	413	24	6=	6=	NUM
ejpam-146	413	25	;	;	PUNCT
ejpam-146	413	26	.	.	PUNCT
ejpam-146	414	1	therefore	therefore	ADV
ejpam-146	414	2	ψ(x	ψ(x	PROPN
ejpam-146	414	3	)	)	PUNCT
ejpam-146	414	4	∈	∈	PROPN
ejpam-146	414	5	b	b	NOUN
ejpam-146	414	6	and	and	CCONJ
ejpam-146	414	7	hence	hence	ADV
ejpam-146	414	8	x	x	X
ejpam-146	415	1	∈ψ−1(b)—a	∈ψ−1(b)—a	ADJ
ejpam-146	415	2	contradiction	contradiction	NOUN
ejpam-146	415	3	.	.	PUNCT
ejpam-146	416	1	theorem	theorem	VERB
ejpam-146	416	2	4.13	4.13	NUM
ejpam-146	416	3	.	.	PUNCT
ejpam-146	417	1	the	the	DET
ejpam-146	417	2	following	follow	VERB
ejpam-146	417	3	are	be	AUX
ejpam-146	417	4	equivalent	equivalent	ADJ
ejpam-146	417	5	for	for	ADP
ejpam-146	417	6	a	a	DET
ejpam-146	417	7	β	β	NOUN
ejpam-146	417	8	-	-	ADJ
ejpam-146	417	9	t2	t2	ADJ
ejpam-146	417	10	space	space	NOUN
ejpam-146	417	11	(	(	PUNCT
ejpam-146	417	12	x	x	X
ejpam-146	417	13	,	,	PUNCT
ejpam-146	417	14	τ	τ	X
ejpam-146	417	15	):	):	PUNCT
ejpam-146	417	16	(	(	PUNCT
ejpam-146	417	17	a	a	NOUN
ejpam-146	417	18	)	)	PUNCT
ejpam-146	417	19	(	(	PUNCT
ejpam-146	417	20	x	x	X
ejpam-146	417	21	,	,	PUNCT
ejpam-146	417	22	τ	τ	X
ejpam-146	417	23	)	)	PUNCT
ejpam-146	417	24	is	be	AUX
ejpam-146	417	25	β	β	NOUN
ejpam-146	417	26	-	-	VERB
ejpam-146	417	27	closed	closed	ADJ
ejpam-146	417	28	.	.	PUNCT
ejpam-146	418	1	(	(	PUNCT
ejpam-146	418	2	b	b	X
ejpam-146	418	3	)	)	PUNCT
ejpam-146	418	4	for	for	ADP
ejpam-146	418	5	any	any	DET
ejpam-146	418	6	space	space	NOUN
ejpam-146	418	7	y	y	NOUN
ejpam-146	418	8	,	,	PUNCT
ejpam-146	418	9	every	every	DET
ejpam-146	418	10	functions	function	NOUN
ejpam-146	418	11	f	f	X
ejpam-146	419	1	:	:	PUNCT
ejpam-146	419	2	y	y	PROPN
ejpam-146	419	3	→	→	PUNCT
ejpam-146	419	4	x	x	X
ejpam-146	419	5	with	with	ADP
ejpam-146	419	6	β	β	X
ejpam-146	419	7	-	-	PUNCT
ejpam-146	419	8	θ	θ	NOUN
ejpam-146	419	9	-subclosed	-subclose	VERB
ejpam-146	419	10	graph	graph	NOUN
ejpam-146	419	11	is	be	AUX
ejpam-146	419	12	(	(	PUNCT
ejpam-146	419	13	θ	θ	NOUN
ejpam-146	419	14	,	,	PUNCT
ejpam-146	419	15	β)-continuous	β)-continuous	PROPN
ejpam-146	419	16	.	.	PUNCT
ejpam-146	420	1	(	(	PUNCT
ejpam-146	420	2	c	c	X
ejpam-146	420	3	)	)	PUNCT
ejpam-146	420	4	for	for	ADP
ejpam-146	420	5	all	all	DET
ejpam-146	420	6	spaces	space	NOUN
ejpam-146	420	7	y	y	PROPN
ejpam-146	420	8	,	,	PUNCT
ejpam-146	420	9	z	z	PROPN
ejpam-146	420	10	and	and	CCONJ
ejpam-146	420	11	all	all	DET
ejpam-146	420	12	functions	function	NOUN
ejpam-146	420	13	φ	φ	X
ejpam-146	420	14	:	:	PUNCT
ejpam-146	421	1	y	y	PROPN
ejpam-146	421	2	→	→	PUNCT
ejpam-146	421	3	x	x	X
ejpam-146	421	4	and	and	CCONJ
ejpam-146	421	5	ψ	ψ	X
ejpam-146	421	6	:	:	PUNCT
ejpam-146	421	7	z	z	X
ejpam-146	421	8	→	→	SYM
ejpam-146	421	9	x	x	X
ejpam-146	421	10	with	with	ADP
ejpam-146	421	11	β	β	X
ejpam-146	421	12	-	-	PUNCT
ejpam-146	421	13	θ	θ	NOUN
ejpam-146	421	14	-subclosed	-subclose	VERB
ejpam-146	421	15	graphs	graph	NOUN
ejpam-146	421	16	,	,	PUNCT
ejpam-146	421	17	the	the	DET
ejpam-146	421	18	set	set	ADJ
ejpam-146	421	19	d(φ	d(φ	PROPN
ejpam-146	421	20	,	,	PUNCT
ejpam-146	421	21	ψ	ψ	NOUN
ejpam-146	421	22	)	)	PUNCT
ejpam-146	421	23	=	=	SYM
ejpam-146	421	24	{	{	PUNCT
ejpam-146	421	25	(	(	PUNCT
ejpam-146	421	26	y	y	PROPN
ejpam-146	421	27	,	,	PUNCT
ejpam-146	421	28	z	z	NOUN
ejpam-146	421	29	)	)	PUNCT
ejpam-146	421	30	∈	∈	PROPN
ejpam-146	422	1	y	y	PROPN
ejpam-146	422	2	×	×	PROPN
ejpam-146	422	3	z	z	NOUN
ejpam-146	422	4	:	:	PUNCT
ejpam-146	422	5	φ(y	φ(y	ADJ
ejpam-146	422	6	)	)	PUNCT
ejpam-146	422	7	=	=	SYM
ejpam-146	422	8	ψ(z	ψ(z	PROPN
ejpam-146	422	9	)	)	PUNCT
ejpam-146	422	10	}	}	PUNCT
ejpam-146	422	11	is	be	AUX
ejpam-146	422	12	closed	close	VERB
ejpam-146	422	13	in	in	ADP
ejpam-146	422	14	y	y	PROPN
ejpam-146	422	15	×	×	PROPN
ejpam-146	422	16	z	z	NOUN
ejpam-146	422	17	.	.	PUNCT
ejpam-146	423	1	(	(	PUNCT
ejpam-146	423	2	d	d	X
ejpam-146	423	3	)	)	PUNCT
ejpam-146	423	4	for	for	ADP
ejpam-146	423	5	any	any	DET
ejpam-146	423	6	space	space	NOUN
ejpam-146	423	7	y	y	NOUN
ejpam-146	423	8	and	and	CCONJ
ejpam-146	423	9	every	every	DET
ejpam-146	423	10	function	function	NOUN
ejpam-146	423	11	ψ	ψ	NOUN
ejpam-146	423	12	:	:	PUNCT
ejpam-146	423	13	y	y	PROPN
ejpam-146	423	14	→	→	PUNCT
ejpam-146	423	15	x	x	SYM
ejpam-146	423	16	having	have	VERB
ejpam-146	423	17	β	β	NOUN
ejpam-146	423	18	-	-	PUNCT
ejpam-146	423	19	θ	θ	NOUN
ejpam-146	423	20	-subclosed	-subclose	VERB
ejpam-146	423	21	graph	graph	NOUN
ejpam-146	423	22	,	,	PUNCT
ejpam-146	423	23	the	the	DET
ejpam-146	423	24	set	set	NOUN
ejpam-146	423	25	d(ψ	d(ψ	NOUN
ejpam-146	423	26	)	)	PUNCT
ejpam-146	424	1	=	=	PRON
ejpam-146	424	2	{	{	PUNCT
ejpam-146	424	3	(	(	PUNCT
ejpam-146	424	4	y1	y1	INTJ
ejpam-146	424	5	,	,	PUNCT
ejpam-146	424	6	y2	y2	NOUN
ejpam-146	424	7	)	)	PUNCT
ejpam-146	424	8	∈	∈	PROPN
ejpam-146	425	1	y	y	PROPN
ejpam-146	425	2	×	×	NOUN
ejpam-146	425	3	y	y	PROPN
ejpam-146	425	4	:	:	PUNCT
ejpam-146	425	5	ψ(y1	ψ(y1	VERB
ejpam-146	425	6	)	)	PUNCT
ejpam-146	425	7	=	=	NOUN
ejpam-146	425	8	ψ(y2	ψ(y2	NOUN
ejpam-146	425	9	)	)	PUNCT
ejpam-146	425	10	}	}	PUNCT
ejpam-146	425	11	is	be	AUX
ejpam-146	425	12	closed	close	VERB
ejpam-146	425	13	in	in	ADP
ejpam-146	425	14	y	y	PROPN
ejpam-146	425	15	×	×	PROPN
ejpam-146	425	16	y	y	PROPN
ejpam-146	425	17	.	.	PUNCT
ejpam-146	426	1	proof	proof	NOUN
ejpam-146	426	2	.	.	PUNCT
ejpam-146	427	1	(	(	PUNCT
ejpam-146	427	2	a)⇒	a)⇒	PROPN
ejpam-146	427	3	(	(	PUNCT
ejpam-146	427	4	b	b	NOUN
ejpam-146	427	5	)	)	PUNCT
ejpam-146	427	6	:	:	PUNCT
ejpam-146	427	7	let	let	VERB
ejpam-146	427	8	f	f	PRON
ejpam-146	427	9	:	:	PUNCT
ejpam-146	427	10	y	y	PROPN
ejpam-146	427	11	→	→	PUNCT
ejpam-146	427	12	x	x	X
ejpam-146	427	13	be	be	AUX
ejpam-146	427	14	a	a	DET
ejpam-146	427	15	function	function	NOUN
ejpam-146	427	16	which	which	PRON
ejpam-146	427	17	has	have	VERB
ejpam-146	427	18	a	a	DET
ejpam-146	427	19	β	β	NOUN
ejpam-146	427	20	-	-	PUNCT
ejpam-146	427	21	θ	θ	NOUN
ejpam-146	427	22	-subclosed	-subclose	VERB
ejpam-146	427	23	graph	graph	NOUN
ejpam-146	427	24	.	.	PUNCT
ejpam-146	428	1	to	to	PART
ejpam-146	428	2	show	show	VERB
ejpam-146	428	3	f	f	PROPN
ejpam-146	428	4	is	be	AUX
ejpam-146	428	5	(	(	PUNCT
ejpam-146	428	6	θ	θ	PROPN
ejpam-146	428	7	,	,	PUNCT
ejpam-146	428	8	β)-continuous	β)-continuous	PROPN
ejpam-146	428	9	,	,	PUNCT
ejpam-146	428	10	we	we	PRON
ejpam-146	428	11	will	will	AUX
ejpam-146	428	12	have	have	VERB
ejpam-146	428	13	to	to	PART
ejpam-146	428	14	show	show	VERB
ejpam-146	428	15	that	that	SCONJ
ejpam-146	428	16	f	f	PROPN
ejpam-146	428	17	(	(	PUNCT
ejpam-146	428	18	adf	adf	PROPN
ejpam-146	428	19	)	)	PUNCT
ejpam-146	428	20	⊂	⊂	PROPN
ejpam-146	428	21	β	β	PROPN
ejpam-146	428	22	-	-	PUNCT
ejpam-146	428	23	θ	θ	NOUN
ejpam-146	428	24	-ad	-ad	NOUN
ejpam-146	428	25	f	f	PROPN
ejpam-146	428	26	(	(	PUNCT
ejpam-146	428	27	f	f	PROPN
ejpam-146	428	28	)	)	PUNCT
ejpam-146	428	29	,	,	PUNCT
ejpam-146	428	30	for	for	ADP
ejpam-146	428	31	any	any	DET
ejpam-146	428	32	filter	filter	NOUN
ejpam-146	428	33	base	base	NOUN
ejpam-146	428	34	f	f	PROPN
ejpam-146	428	35	on	on	ADP
ejpam-146	428	36	y	y	PROPN
ejpam-146	428	37	.	.	PUNCT
ejpam-146	429	1	let	let	VERB
ejpam-146	429	2	x	x	SYM
ejpam-146	429	3	∈	∈	PROPN
ejpam-146	429	4	f	f	X
ejpam-146	429	5	(	(	PUNCT
ejpam-146	429	6	adf	adf	PROPN
ejpam-146	429	7	)	)	PUNCT
ejpam-146	429	8	.	.	PUNCT
ejpam-146	430	1	then	then	ADV
ejpam-146	430	2	x	x	X
ejpam-146	430	3	=	=	SYM
ejpam-146	430	4	f	f	X
ejpam-146	430	5	(	(	PUNCT
ejpam-146	430	6	y	y	NOUN
ejpam-146	430	7	)	)	PUNCT
ejpam-146	430	8	for	for	ADP
ejpam-146	430	9	some	some	DET
ejpam-146	430	10	y	y	PROPN
ejpam-146	430	11	∈	∈	PROPN
ejpam-146	430	12	adf	adf	NOUN
ejpam-146	430	13	.	.	PUNCT
ejpam-146	431	1	let	let	VERB
ejpam-146	431	2	f0	f0	PROPN
ejpam-146	431	3	=	=	PRON
ejpam-146	431	4	{	{	PUNCT
ejpam-146	431	5	(	(	PUNCT
ejpam-146	431	6	u	u	NOUN
ejpam-146	431	7	∩	∩	NOUN
ejpam-146	431	8	f)−	f)−	PROPN
ejpam-146	431	9	{	{	PUNCT
ejpam-146	431	10	y	y	NOUN
ejpam-146	431	11	}	}	PUNCT
ejpam-146	431	12	:	:	PUNCT
ejpam-146	431	13	f	f	PROPN
ejpam-146	431	14	∈	∈	PROPN
ejpam-146	431	15	f	f	PROPN
ejpam-146	431	16	and	and	CCONJ
ejpam-146	431	17	u	u	PROPN
ejpam-146	431	18	∈	∈	PROPN
ejpam-146	431	19	o(y	o(y	PROPN
ejpam-146	431	20	,	,	PUNCT
ejpam-146	431	21	y	y	NOUN
ejpam-146	431	22	)	)	PUNCT
ejpam-146	431	23	}	}	PUNCT
ejpam-146	431	24	.	.	PUNCT
ejpam-146	432	1	case	case	NOUN
ejpam-146	432	2	-	-	PUNCT
ejpam-146	432	3	i	i	PRON
ejpam-146	432	4	:	:	PUNCT
ejpam-146	432	5	let	let	VERB
ejpam-146	432	6	f0	f0	PROPN
ejpam-146	432	7	be	be	AUX
ejpam-146	432	8	a	a	DET
ejpam-146	432	9	filter	filter	NOUN
ejpam-146	432	10	base	base	NOUN
ejpam-146	432	11	on	on	ADP
ejpam-146	432	12	y	y	PROPN
ejpam-146	432	13	−	−	PROPN
ejpam-146	432	14	{	{	PUNCT
ejpam-146	432	15	y	y	NOUN
ejpam-146	432	16	}	}	PUNCT
ejpam-146	432	17	.	.	PUNCT
ejpam-146	433	1	then	then	ADV
ejpam-146	433	2	clearly	clearly	ADV
ejpam-146	433	3	f	f	PROPN
ejpam-146	433	4	→	→	SYM
ejpam-146	433	5	y	y	PROPN
ejpam-146	433	6	in	in	ADP
ejpam-146	433	7	y	y	PROPN
ejpam-146	433	8	.	.	PUNCT
ejpam-146	434	1	since	since	SCONJ
ejpam-146	434	2	f	f	PROPN
ejpam-146	434	3	has	have	VERB
ejpam-146	434	4	a	a	DET
ejpam-146	434	5	βθ	βθ	ADV
ejpam-146	434	6	-subclosed	-subclose	VERB
ejpam-146	434	7	graph	graph	NOUN
ejpam-146	434	8	,	,	PUNCT
ejpam-146	434	9	β	β	NOUN
ejpam-146	434	10	-	-	NOUN
ejpam-146	434	11	θ	θ	NOUN
ejpam-146	434	12	-ad	-ad	NOUN
ejpam-146	434	13	f	f	PROPN
ejpam-146	434	14	(	(	PUNCT
ejpam-146	434	15	f0	f0	PROPN
ejpam-146	434	16	)	)	PUNCT
ejpam-146	434	17	⊂	⊂	PROPN
ejpam-146	434	18	{	{	PUNCT
ejpam-146	434	19	f	f	X
ejpam-146	434	20	(	(	PUNCT
ejpam-146	434	21	y	y	NOUN
ejpam-146	434	22	)	)	PUNCT
ejpam-146	434	23	}	}	PUNCT
ejpam-146	434	24	.	.	PUNCT
ejpam-146	435	1	also	also	ADV
ejpam-146	435	2	,	,	PUNCT
ejpam-146	435	3	as	as	SCONJ
ejpam-146	435	4	x	x	PROPN
ejpam-146	435	5	is	be	AUX
ejpam-146	435	6	β	β	NOUN
ejpam-146	435	7	-	-	VERB
ejpam-146	435	8	closed	closed	ADJ
ejpam-146	435	9	,	,	PUNCT
ejpam-146	435	10	by	by	ADP
ejpam-146	435	11	theorem	theorem	NOUN
ejpam-146	435	12	3.5	3.5	NUM
ejpam-146	435	13	,	,	PUNCT
ejpam-146	435	14	we	we	PRON
ejpam-146	435	15	get	get	VERB
ejpam-146	435	16	β	β	NOUN
ejpam-146	435	17	-	-	NOUN
ejpam-146	435	18	θ	θ	NOUN
ejpam-146	435	19	-ad	-ad	NOUN
ejpam-146	435	20	f	f	PROPN
ejpam-146	435	21	(	(	PUNCT
ejpam-146	435	22	f0	f0	PROPN
ejpam-146	435	23	)	)	PUNCT
ejpam-146	435	24	=	=	PRON
ejpam-146	435	25	{	{	PUNCT
ejpam-146	435	26	f	f	X
ejpam-146	435	27	(	(	PUNCT
ejpam-146	435	28	y	y	NOUN
ejpam-146	435	29	)	)	PUNCT
ejpam-146	435	30	}	}	PUNCT
ejpam-146	435	31	.	.	PUNCT
ejpam-146	436	1	so	so	ADV
ejpam-146	436	2	x	x	X
ejpam-146	436	3	=	=	SYM
ejpam-146	436	4	f	f	X
ejpam-146	436	5	(	(	PUNCT
ejpam-146	436	6	y	y	NOUN
ejpam-146	436	7	)	)	PUNCT
ejpam-146	436	8	∈	∈	PROPN
ejpam-146	436	9	β	β	NOUN
ejpam-146	436	10	-	-	NOUN
ejpam-146	436	11	θ	θ	NOUN
ejpam-146	436	12	-ad	-ad	NOUN
ejpam-146	436	13	f	f	PROPN
ejpam-146	436	14	(	(	PUNCT
ejpam-146	436	15	f0)⊆	f0)⊆	PROPN
ejpam-146	436	16	β	β	PROPN
ejpam-146	436	17	-	-	NOUN
ejpam-146	436	18	θad	θad	NOUN
ejpam-146	436	19	f	f	NOUN
ejpam-146	436	20	(	(	PUNCT
ejpam-146	436	21	f	f	PROPN
ejpam-146	436	22	)	)	PUNCT
ejpam-146	436	23	.	.	PUNCT
ejpam-146	437	1	case	case	NOUN
ejpam-146	437	2	-	-	PUNCT
ejpam-146	437	3	ii	ii	NOUN
ejpam-146	437	4	:	:	PUNCT
ejpam-146	437	5	letf0	letf0	X
ejpam-146	437	6	be	be	AUX
ejpam-146	437	7	not	not	PART
ejpam-146	437	8	a	a	DET
ejpam-146	437	9	filter	filter	NOUN
ejpam-146	437	10	base	base	NOUN
ejpam-146	437	11	on	on	ADP
ejpam-146	437	12	y	y	PROPN
ejpam-146	437	13	−{y	−{y	NOUN
ejpam-146	437	14	}	}	PUNCT
ejpam-146	437	15	.	.	PUNCT
ejpam-146	438	1	then	then	ADV
ejpam-146	438	2	u0∩	u0∩	PROPN
ejpam-146	438	3	f0	f0	PROPN
ejpam-146	438	4	=	=	PUNCT
ejpam-146	438	5	{	{	PUNCT
ejpam-146	438	6	y	y	NOUN
ejpam-146	438	7	}	}	PUNCT
ejpam-146	438	8	for	for	ADP
ejpam-146	438	9	some	some	DET
ejpam-146	438	10	u0	u0	ADJ
ejpam-146	438	11	∈	∈	PROPN
ejpam-146	438	12	o(y	o(y	PROPN
ejpam-146	438	13	,	,	PUNCT
ejpam-146	438	14	y	y	NOUN
ejpam-146	438	15	)	)	PUNCT
ejpam-146	438	16	and	and	CCONJ
ejpam-146	438	17	f0	f0	PROPN
ejpam-146	438	18	∈	∈	PROPN
ejpam-146	438	19	f0	f0	PROPN
ejpam-146	438	20	.	.	PUNCT
ejpam-146	439	1	we	we	PRON
ejpam-146	439	2	claim	claim	VERB
ejpam-146	439	3	that	that	SCONJ
ejpam-146	439	4	y	y	PROPN
ejpam-146	439	5	∈	∈	PROPN
ejpam-146	439	6	f	f	PROPN
ejpam-146	439	7	for	for	ADP
ejpam-146	439	8	each	each	DET
ejpam-146	439	9	f	f	PROPN
ejpam-146	439	10	∈	∈	PROPN
ejpam-146	439	11	f	f	PROPN
ejpam-146	439	12	.	.	PUNCT
ejpam-146	440	1	indeed	indeed	ADV
ejpam-146	440	2	,	,	PUNCT
ejpam-146	440	3	if	if	SCONJ
ejpam-146	440	4	it	it	PRON
ejpam-146	440	5	is	be	AUX
ejpam-146	440	6	not	not	PART
ejpam-146	440	7	true	true	ADJ
ejpam-146	440	8	,	,	PUNCT
ejpam-146	440	9	then	then	ADV
ejpam-146	440	10	for	for	ADP
ejpam-146	440	11	some	some	PRON
ejpam-146	440	12	f	f	NOUN
ejpam-146	441	1	′	′	NUM
ejpam-146	441	2	∈	∈	PROPN
ejpam-146	441	3	f	f	PROPN
ejpam-146	441	4	,	,	PUNCT
ejpam-146	441	5	y	y	PROPN
ejpam-146	441	6	6∈	6∈	PROPN
ejpam-146	442	1	f	f	NOUN
ejpam-146	442	2	′	′	INTJ
ejpam-146	442	3	.	.	PUNCT
ejpam-146	443	1	select	select	VERB
ejpam-146	443	2	an	an	DET
ejpam-146	443	3	f	f	X
ejpam-146	443	4	′′	′′	PROPN
ejpam-146	443	5	∈	∈	PROPN
ejpam-146	443	6	f	f	PROPN
ejpam-146	443	7	such	such	ADJ
ejpam-146	443	8	that	that	SCONJ
ejpam-146	443	9	f	f	PROPN
ejpam-146	443	10	′′	′′	PROPN
ejpam-146	443	11	⊆	⊆	NUM
ejpam-146	443	12	f0	f0	PROPN
ejpam-146	443	13	∩	∩	NOUN
ejpam-146	443	14	f	f	PROPN
ejpam-146	443	15	′	′	NOUN
ejpam-146	443	16	.	.	PUNCT
ejpam-146	444	1	so	so	ADV
ejpam-146	444	2	,	,	PUNCT
ejpam-146	444	3	(	(	PUNCT
ejpam-146	444	4	u0	u0	X
ejpam-146	444	5	∩	∩	ADJ
ejpam-146	444	6	f	f	PROPN
ejpam-146	444	7	′′	′′	PROPN
ejpam-146	444	8	)	)	PUNCT
ejpam-146	444	9	−	−	PROPN
ejpam-146	444	10	{	{	PUNCT
ejpam-146	444	11	y	y	NOUN
ejpam-146	444	12	}	}	PUNCT
ejpam-146	444	13	⊆	⊆	NUM
ejpam-146	444	14	(	(	PUNCT
ejpam-146	444	15	u0	u0	ADJ
ejpam-146	444	16	∩	∩	ADJ
ejpam-146	444	17	f0)−	f0)−	PROPN
ejpam-146	444	18	{	{	PUNCT
ejpam-146	444	19	y	y	NOUN
ejpam-146	444	20	}	}	PUNCT
ejpam-146	444	21	=	=	SYM
ejpam-146	444	22	;	;	PUNCT
ejpam-146	444	23	.	.	PUNCT
ejpam-146	445	1	therefore	therefore	ADV
ejpam-146	445	2	,	,	PUNCT
ejpam-146	445	3	u0	u0	ADJ
ejpam-146	445	4	∩	∩	ADJ
ejpam-146	445	5	f	f	X
ejpam-146	445	6	′′	′′	PROPN
ejpam-146	445	7	=	=	PRON
ejpam-146	445	8	{	{	PUNCT
ejpam-146	445	9	y	y	NOUN
ejpam-146	445	10	}	}	PUNCT
ejpam-146	445	11	and	and	CCONJ
ejpam-146	445	12	hence	hence	ADV
ejpam-146	445	13	y	y	PROPN
ejpam-146	445	14	∈	∈	PROPN
ejpam-146	445	15	f	f	PROPN
ejpam-146	446	1	′′	′′	PROPN
ejpam-146	446	2	⊆	⊆	NUM
ejpam-146	446	3	f0	f0	PROPN
ejpam-146	446	4	∩	∩	NOUN
ejpam-146	446	5	f	f	PROPN
ejpam-146	446	6	′	′	NOUN
ejpam-146	446	7	.	.	PUNCT
ejpam-146	447	1	this	this	PRON
ejpam-146	447	2	shows	show	VERB
ejpam-146	447	3	y	y	PROPN
ejpam-146	447	4	∈	∈	PROPN
ejpam-146	448	1	f	f	NOUN
ejpam-146	449	1	′	′	NUM
ejpam-146	449	2	—	—	PUNCT
ejpam-146	449	3	a	a	DET
ejpam-146	449	4	contradiction	contradiction	NOUN
ejpam-146	449	5	.	.	PUNCT
ejpam-146	450	1	so	so	ADV
ejpam-146	450	2	,	,	PUNCT
ejpam-146	450	3	x	x	PROPN
ejpam-146	451	1	=	=	SYM
ejpam-146	451	2	f	f	X
ejpam-146	451	3	(	(	PUNCT
ejpam-146	451	4	y	y	NOUN
ejpam-146	451	5	)	)	PUNCT
ejpam-146	451	6	∈	∈	PROPN
ejpam-146	451	7	f	f	X
ejpam-146	451	8	(	(	PUNCT
ejpam-146	451	9	f	f	X
ejpam-146	451	10	)	)	PUNCT
ejpam-146	451	11	for	for	ADP
ejpam-146	451	12	each	each	DET
ejpam-146	451	13	f	f	PROPN
ejpam-146	451	14	∈	∈	PROPN
ejpam-146	451	15	f	f	PROPN
ejpam-146	451	16	and	and	CCONJ
ejpam-146	451	17	hence	hence	ADV
ejpam-146	451	18	x	x	X
ejpam-146	451	19	∈	∈	ADJ
ejpam-146	451	20	β	β	NOUN
ejpam-146	451	21	-	-	NOUN
ejpam-146	451	22	θ	θ	NOUN
ejpam-146	451	23	-ad	-ad	NOUN
ejpam-146	451	24	f	f	PROPN
ejpam-146	451	25	(	(	PUNCT
ejpam-146	451	26	f	f	PROPN
ejpam-146	451	27	)	)	PUNCT
ejpam-146	451	28	.	.	PUNCT
ejpam-146	452	1	therefore	therefore	ADV
ejpam-146	452	2	,	,	PUNCT
ejpam-146	452	3	in	in	ADP
ejpam-146	452	4	any	any	DET
ejpam-146	452	5	case	case	NOUN
ejpam-146	452	6	,	,	PUNCT
ejpam-146	452	7	f	f	PROPN
ejpam-146	452	8	is	be	AUX
ejpam-146	452	9	(	(	PUNCT
ejpam-146	452	10	θ	θ	NOUN
ejpam-146	452	11	,	,	PUNCT
ejpam-146	452	12	β)-continuous	β)-continuous	ADJ
ejpam-146	452	13	.	.	PUNCT
ejpam-146	453	1	(	(	PUNCT
ejpam-146	453	2	b)⇒	b)⇒	NOUN
ejpam-146	453	3	(	(	PUNCT
ejpam-146	453	4	a	a	NOUN
ejpam-146	453	5	)	)	PUNCT
ejpam-146	453	6	:	:	PUNCT
ejpam-146	453	7	if	if	SCONJ
ejpam-146	453	8	possible	possible	ADJ
ejpam-146	453	9	let	let	VERB
ejpam-146	453	10	(	(	PUNCT
ejpam-146	453	11	x	x	X
ejpam-146	453	12	,	,	PUNCT
ejpam-146	453	13	τ	τ	X
ejpam-146	453	14	)	)	PUNCT
ejpam-146	453	15	be	be	VERB
ejpam-146	453	16	not	not	PART
ejpam-146	453	17	β	β	NOUN
ejpam-146	453	18	-	-	VERB
ejpam-146	453	19	closed	closed	ADJ
ejpam-146	453	20	.	.	PUNCT
ejpam-146	454	1	then	then	ADV
ejpam-146	454	2	by	by	ADP
ejpam-146	454	3	theorem	theorem	NOUN
ejpam-146	454	4	3.5	3.5	NUM
ejpam-146	454	5	,	,	PUNCT
ejpam-146	454	6	there	there	PRON
ejpam-146	454	7	exists	exist	VERB
ejpam-146	454	8	a	a	DET
ejpam-146	454	9	filter	filter	NOUN
ejpam-146	454	10	base	base	NOUN
ejpam-146	454	11	f	f	PROPN
ejpam-146	454	12	on	on	ADP
ejpam-146	454	13	x	x	PUNCT
ejpam-146	454	14	with	with	ADP
ejpam-146	454	15	β	β	NOUN
ejpam-146	454	16	-	-	NOUN
ejpam-146	454	17	θ	θ	NOUN
ejpam-146	454	18	-adf	-adf	NUM
ejpam-146	454	19	=	=	PUNCT
ejpam-146	454	20	;	;	PUNCT
ejpam-146	454	21	.	.	PUNCT
ejpam-146	455	1	choose	choose	VERB
ejpam-146	455	2	xo	xo	PROPN
ejpam-146	455	3	∈	∈	PROPN
ejpam-146	455	4	x	x	PUNCT
ejpam-146	455	5	and	and	CCONJ
ejpam-146	455	6	let	let	VERB
ejpam-146	455	7	τ0	τ0	NOUN
ejpam-146	455	8	=	=	PUNCT
ejpam-146	455	9	{	{	PUNCT
ejpam-146	455	10	b	b	X
ejpam-146	455	11	⊂	⊂	NOUN
ejpam-146	455	12	x	x	X
ejpam-146	455	13	:	:	PUNCT
ejpam-146	455	14	x0	x0	PROPN
ejpam-146	455	15	6∈	6∈	PROPN
ejpam-146	456	1	b	b	X
ejpam-146	456	2	}	}	PUNCT
ejpam-146	456	3	∪	∪	ADJ
ejpam-146	456	4	{	{	PUNCT
ejpam-146	456	5	b	b	NOUN
ejpam-146	456	6	⊂	⊂	PROPN
ejpam-146	456	7	x	x	X
ejpam-146	456	8	:	:	PUNCT
ejpam-146	456	9	x0	x0	PROPN
ejpam-146	456	10	∈	∈	PROPN
ejpam-146	456	11	b	b	PROPN
ejpam-146	456	12	and	and	CCONJ
ejpam-146	456	13	f	f	PROPN
ejpam-146	456	14	⊂	⊂	PROPN
ejpam-146	456	15	b	b	PROPN
ejpam-146	456	16	for	for	ADP
ejpam-146	456	17	some	some	DET
ejpam-146	456	18	f	f	NOUN
ejpam-146	456	19	∈	∈	PROPN
ejpam-146	456	20	f	f	X
ejpam-146	456	21	}	}	PUNCT
ejpam-146	456	22	.	.	PUNCT
ejpam-146	457	1	in	in	ADP
ejpam-146	457	2	[	[	X
ejpam-146	457	3	11	11	NUM
ejpam-146	457	4	]	]	PUNCT
ejpam-146	457	5	it	it	PRON
ejpam-146	457	6	has	have	AUX
ejpam-146	457	7	been	be	AUX
ejpam-146	457	8	shown	show	VERB
ejpam-146	457	9	that	that	SCONJ
ejpam-146	457	10	τ0	τ0	NOUN
ejpam-146	457	11	is	be	AUX
ejpam-146	457	12	a	a	DET
ejpam-146	457	13	topology	topology	NOUN
ejpam-146	457	14	on	on	ADP
ejpam-146	457	15	x	x	X
ejpam-146	457	16	.	.	PUNCT
ejpam-146	458	1	we	we	PRON
ejpam-146	458	2	shall	shall	AUX
ejpam-146	458	3	show	show	VERB
ejpam-146	458	4	that	that	SCONJ
ejpam-146	458	5	the	the	DET
ejpam-146	458	6	identity	identity	NOUN
ejpam-146	458	7	function	function	NOUN
ejpam-146	458	8	f	f	NOUN
ejpam-146	458	9	:	:	PUNCT
ejpam-146	458	10	(	(	PUNCT
ejpam-146	458	11	x	x	X
ejpam-146	458	12	,	,	PUNCT
ejpam-146	458	13	τ0	τ0	NOUN
ejpam-146	458	14	)	)	PUNCT
ejpam-146	458	15	→	→	SYM
ejpam-146	458	16	(	(	PUNCT
ejpam-146	458	17	x	x	X
ejpam-146	458	18	,	,	PUNCT
ejpam-146	458	19	τ	τ	X
ejpam-146	458	20	)	)	PUNCT
ejpam-146	458	21	has	have	VERB
ejpam-146	458	22	a	a	DET
ejpam-146	458	23	β	β	NOUN
ejpam-146	458	24	-	-	PUNCT
ejpam-146	458	25	θ	θ	NOUN
ejpam-146	458	26	-subclosed	-subclose	VERB
ejpam-146	458	27	graph	graph	NOUN
ejpam-146	458	28	but	but	CCONJ
ejpam-146	458	29	f	f	PROPN
ejpam-146	458	30	is	be	AUX
ejpam-146	458	31	not	not	PART
ejpam-146	458	32	(	(	PUNCT
ejpam-146	458	33	θ	θ	PROPN
ejpam-146	458	34	,	,	PUNCT
ejpam-146	458	35	β)-continuous	β)-continuous	PROPN
ejpam-146	458	36	.	.	PUNCT
ejpam-146	459	1	for	for	ADP
ejpam-146	459	2	this	this	PRON
ejpam-146	459	3	let	let	VERB
ejpam-146	459	4	g	g	NOUN
ejpam-146	459	5	be	be	AUX
ejpam-146	459	6	a	a	DET
ejpam-146	459	7	filter	filter	NOUN
ejpam-146	459	8	base	base	NOUN
ejpam-146	459	9	on	on	ADP
ejpam-146	459	10	x	x	X
ejpam-146	459	11	−	−	PROPN
ejpam-146	459	12	{	{	PUNCT
ejpam-146	459	13	x	x	NOUN
ejpam-146	459	14	}	}	PUNCT
ejpam-146	459	15	such	such	ADJ
ejpam-146	459	16	that	that	SCONJ
ejpam-146	459	17	g	g	NOUN
ejpam-146	459	18	→	→	SYM
ejpam-146	459	19	x	x	X
ejpam-146	459	20	in	in	ADP
ejpam-146	459	21	(	(	PUNCT
ejpam-146	459	22	x	x	INTJ
ejpam-146	459	23	,	,	PUNCT
ejpam-146	459	24	τ0	τ0	NOUN
ejpam-146	459	25	)	)	PUNCT
ejpam-146	459	26	.	.	PUNCT
ejpam-146	460	1	we	we	PRON
ejpam-146	460	2	claim	claim	VERB
ejpam-146	460	3	that	that	SCONJ
ejpam-146	460	4	x	x	X
ejpam-146	460	5	=	=	SYM
ejpam-146	460	6	x0	x0	PROPN
ejpam-146	460	7	.	.	PUNCT
ejpam-146	461	1	if	if	SCONJ
ejpam-146	461	2	not	not	PART
ejpam-146	461	3	then	then	ADV
ejpam-146	461	4	{	{	PUNCT
ejpam-146	461	5	x	x	X
ejpam-146	461	6	}	}	PUNCT
ejpam-146	461	7	is	be	AUX
ejpam-146	461	8	an	an	DET
ejpam-146	461	9	open	open	ADJ
ejpam-146	461	10	set	set	NOUN
ejpam-146	461	11	in	in	ADP
ejpam-146	461	12	(	(	PUNCT
ejpam-146	461	13	x	x	INTJ
ejpam-146	461	14	,	,	PUNCT
ejpam-146	461	15	τ0	τ0	NOUN
ejpam-146	461	16	)	)	PUNCT
ejpam-146	461	17	and	and	CCONJ
ejpam-146	461	18	hence	hence	ADV
ejpam-146	461	19	the	the	DET
ejpam-146	461	20	filter	filter	NOUN
ejpam-146	461	21	base	base	NOUN
ejpam-146	461	22	g	g	NOUN
ejpam-146	461	23	on	on	ADP
ejpam-146	461	24	x−{x	x−{x	PROPN
ejpam-146	461	25	}	}	PUNCT
ejpam-146	461	26	can	can	AUX
ejpam-146	461	27	not	not	PART
ejpam-146	461	28	converge	converge	VERB
ejpam-146	461	29	to	to	ADP
ejpam-146	461	30	x	x	PUNCT
ejpam-146	461	31	in	in	ADP
ejpam-146	461	32	(	(	PUNCT
ejpam-146	461	33	x	x	INTJ
ejpam-146	461	34	,	,	PUNCT
ejpam-146	461	35	τ0	τ0	NOUN
ejpam-146	461	36	)	)	PUNCT
ejpam-146	461	37	—	—	PUNCT
ejpam-146	461	38	a	a	DET
ejpam-146	461	39	contradiction	contradiction	NOUN
ejpam-146	461	40	.	.	PUNCT
ejpam-146	462	1	also	also	ADV
ejpam-146	462	2	we	we	PRON
ejpam-146	462	3	claim	claim	VERB
ejpam-146	462	4	thatf	thatf	VERB
ejpam-146	462	5	⊂	⊂	PROPN
ejpam-146	462	6	g	g	PROPN
ejpam-146	462	7	.	.	PUNCT
ejpam-146	463	1	indeed	indeed	ADV
ejpam-146	463	2	,	,	PUNCT
ejpam-146	463	3	for	for	ADP
ejpam-146	463	4	each	each	DET
ejpam-146	463	5	f	f	PROPN
ejpam-146	463	6	∈	∈	PROPN
ejpam-146	463	7	f	f	PROPN
ejpam-146	463	8	,	,	PUNCT
ejpam-146	463	9	we	we	PRON
ejpam-146	463	10	have	have	VERB
ejpam-146	463	11	f	f	PROPN
ejpam-146	463	12	∪	∪	X
ejpam-146	463	13	{	{	PUNCT
ejpam-146	463	14	x0	x0	PROPN
ejpam-146	463	15	}	}	PUNCT
ejpam-146	463	16	∈	∈	PROPN
ejpam-146	463	17	τ0	τ0	NOUN
ejpam-146	463	18	and	and	CCONJ
ejpam-146	463	19	since	since	SCONJ
ejpam-146	463	20	g	g	PROPN
ejpam-146	463	21	→	→	SYM
ejpam-146	463	22	x	x	SYM
ejpam-146	463	23	=	=	SYM
ejpam-146	463	24	x0	x0	PROPN
ejpam-146	463	25	in	in	ADP
ejpam-146	463	26	(	(	PUNCT
ejpam-146	463	27	x	x	INTJ
ejpam-146	463	28	,	,	PUNCT
ejpam-146	463	29	τ0	τ0	NOUN
ejpam-146	463	30	)	)	PUNCT
ejpam-146	463	31	,	,	PUNCT
ejpam-146	463	32	there	there	PRON
ejpam-146	463	33	exists	exist	VERB
ejpam-146	463	34	a	a	DET
ejpam-146	463	35	g	g	PROPN
ejpam-146	463	36	∈	∈	PROPN
ejpam-146	463	37	g	g	NOUN
ejpam-146	463	38	such	such	ADJ
ejpam-146	463	39	that	that	SCONJ
ejpam-146	463	40	g	g	PROPN
ejpam-146	463	41	⊂	⊂	PROPN
ejpam-146	463	42	f	f	PROPN
ejpam-146	463	43	∪	∪	X
ejpam-146	463	44	{	{	PUNCT
ejpam-146	463	45	x0	x0	PROPN
ejpam-146	463	46	}	}	PUNCT
ejpam-146	463	47	.	.	PUNCT
ejpam-146	464	1	so	so	ADV
ejpam-146	464	2	,	,	PUNCT
ejpam-146	464	3	g	g	PROPN
ejpam-146	464	4	⊂	⊂	PROPN
ejpam-146	464	5	f	f	PROPN
ejpam-146	464	6	and	and	CCONJ
ejpam-146	464	7	hence	hence	ADV
ejpam-146	464	8	f	f	PROPN
ejpam-146	464	9	∈	∈	PROPN
ejpam-146	464	10	g	g	PROPN
ejpam-146	464	11	.	.	PUNCT
ejpam-146	465	1	hence	hence	ADV
ejpam-146	465	2	,	,	PUNCT
ejpam-146	465	3	β	β	X
ejpam-146	465	4	-	-	NOUN
ejpam-146	465	5	θ	θ	NOUN
ejpam-146	465	6	-ad	-ad	NOUN
ejpam-146	465	7	f	f	PROPN
ejpam-146	465	8	(	(	PUNCT
ejpam-146	465	9	g	g	PROPN
ejpam-146	465	10	)	)	PUNCT
ejpam-146	465	11	=	=	SYM
ejpam-146	465	12	β	β	X
ejpam-146	465	13	-	-	PUNCT
ejpam-146	465	14	θ	θ	NOUN
ejpam-146	465	15	-adg	-adg	NOUN
ejpam-146	465	16	⊆	⊆	NUM
ejpam-146	465	17	βθ	βθ	NOUN
ejpam-146	465	18	-adf	-adf	NUM
ejpam-146	465	19	=	=	PUNCT
ejpam-146	465	20	;	;	PUNCT
ejpam-146	465	21	.	.	PUNCT
ejpam-146	466	1	therefore	therefore	ADV
ejpam-146	466	2	,	,	PUNCT
ejpam-146	466	3	f	f	PROPN
ejpam-146	466	4	has	have	VERB
ejpam-146	466	5	a	a	DET
ejpam-146	466	6	β	β	NOUN
ejpam-146	466	7	-	-	PUNCT
ejpam-146	466	8	θ	θ	NOUN
ejpam-146	466	9	-subclosed	-subclose	VERB
ejpam-146	466	10	graph	graph	NOUN
ejpam-146	466	11	.	.	PUNCT
ejpam-146	467	1	but	but	CCONJ
ejpam-146	467	2	this	this	DET
ejpam-146	467	3	f	f	NOUN
ejpam-146	467	4	is	be	AUX
ejpam-146	467	5	not	not	PART
ejpam-146	467	6	(	(	PUNCT
ejpam-146	467	7	θ	θ	PROPN
ejpam-146	467	8	,	,	PUNCT
ejpam-146	467	9	β)-continuous	β)-continuous	PROPN
ejpam-146	467	10	.	.	PUNCT
ejpam-146	468	1	in	in	ADP
ejpam-146	468	2	fact	fact	NOUN
ejpam-146	468	3	,	,	PUNCT
ejpam-146	468	4	x0	x0	PROPN
ejpam-146	468	5	∈	∈	PROPN
ejpam-146	468	6	adf	adf	PROPN
ejpam-146	468	7	in	in	ADP
ejpam-146	468	8	(	(	PUNCT
ejpam-146	468	9	x	x	INTJ
ejpam-146	468	10	,	,	PUNCT
ejpam-146	468	11	τ0	τ0	NOUN
ejpam-146	468	12	)	)	PUNCT
ejpam-146	468	13	but	but	CCONJ
ejpam-146	468	14	f	f	X
ejpam-146	468	15	(	(	PUNCT
ejpam-146	468	16	x0	x0	PROPN
ejpam-146	468	17	)	)	PUNCT
ejpam-146	469	1	=	=	SYM
ejpam-146	470	1	x0	x0	PROPN
ejpam-146	470	2	6∈	6∈	PROPN
ejpam-146	470	3	β	β	X
ejpam-146	470	4	-	-	PUNCT
ejpam-146	470	5	θ	θ	NOUN
ejpam-146	470	6	-ad	-ad	NOUN
ejpam-146	470	7	f	f	PROPN
ejpam-146	470	8	(	(	PUNCT
ejpam-146	470	9	f	f	PROPN
ejpam-146	470	10	)	)	PUNCT
ejpam-146	470	11	.	.	PUNCT
ejpam-146	471	1	this	this	PRON
ejpam-146	471	2	contradicts	contradict	VERB
ejpam-146	471	3	the	the	DET
ejpam-146	471	4	hypothesis	hypothesis	NOUN
ejpam-146	471	5	(	(	PUNCT
ejpam-146	471	6	b	b	NOUN
ejpam-146	471	7	)	)	PUNCT
ejpam-146	471	8	.	.	PUNCT
ejpam-146	472	1	so	so	ADV
ejpam-146	472	2	(	(	PUNCT
ejpam-146	472	3	x	x	X
ejpam-146	472	4	,	,	PUNCT
ejpam-146	472	5	τ	τ	X
ejpam-146	472	6	)	)	PUNCT
ejpam-146	472	7	is	be	AUX
ejpam-146	472	8	β	β	NOUN
ejpam-146	472	9	-	-	VERB
ejpam-146	472	10	closed	closed	ADJ
ejpam-146	472	11	.	.	PUNCT
ejpam-146	473	1	(	(	PUNCT
ejpam-146	473	2	b	b	X
ejpam-146	473	3	)	)	PUNCT
ejpam-146	473	4	⇒	⇒	NOUN
ejpam-146	473	5	(	(	PUNCT
ejpam-146	473	6	c	c	NOUN
ejpam-146	473	7	)	)	PUNCT
ejpam-146	473	8	:	:	PUNCT
ejpam-146	474	1	let	let	VERB
ejpam-146	474	2	(	(	PUNCT
ejpam-146	474	3	y	y	NOUN
ejpam-146	474	4	,	,	PUNCT
ejpam-146	474	5	z	z	NOUN
ejpam-146	474	6	)	)	PUNCT
ejpam-146	474	7	be	be	AUX
ejpam-146	474	8	a	a	DET
ejpam-146	474	9	limit	limit	NOUN
ejpam-146	474	10	point	point	NOUN
ejpam-146	474	11	of	of	ADP
ejpam-146	474	12	d(φ	d(φ	PROPN
ejpam-146	474	13	,	,	PUNCT
ejpam-146	474	14	ψ	ψ	NOUN
ejpam-146	474	15	)	)	PUNCT
ejpam-146	474	16	.	.	PUNCT
ejpam-146	475	1	then	then	ADV
ejpam-146	475	2	there	there	PRON
ejpam-146	475	3	exists	exist	VERB
ejpam-146	475	4	a	a	DET
ejpam-146	475	5	net	net	NOUN
ejpam-146	475	6	{	{	PUNCT
ejpam-146	475	7	(	(	PUNCT
ejpam-146	475	8	yλ	yλ	PROPN
ejpam-146	475	9	,	,	PUNCT
ejpam-146	475	10	zλ	zλ	X
ejpam-146	475	11	)	)	PUNCT
ejpam-146	475	12	:	:	PUNCT
ejpam-146	476	1	λ	λ	X
ejpam-146	476	2	∈	∈	PROPN
ejpam-146	476	3	i	i	X
ejpam-146	476	4	}	}	PUNCT
ejpam-146	476	5	in	in	ADP
ejpam-146	476	6	d(φ	d(φ	PROPN
ejpam-146	476	7	,	,	PUNCT
ejpam-146	476	8	ψ	ψ	NOUN
ejpam-146	476	9	)	)	PUNCT
ejpam-146	476	10	−	−	NOUN
ejpam-146	476	11	{	{	PUNCT
ejpam-146	476	12	(	(	PUNCT
ejpam-146	476	13	y	y	PROPN
ejpam-146	476	14	,	,	PUNCT
ejpam-146	476	15	z	z	NOUN
ejpam-146	476	16	)	)	PUNCT
ejpam-146	476	17	}	}	PUNCT
ejpam-146	476	18	with	with	ADP
ejpam-146	476	19	{	{	PUNCT
ejpam-146	476	20	(	(	PUNCT
ejpam-146	476	21	yλ	yλ	PROPN
ejpam-146	476	22	,	,	PUNCT
ejpam-146	476	23	zλ	zλ	X
ejpam-146	476	24	)	)	PUNCT
ejpam-146	476	25	→	→	SYM
ejpam-146	476	26	(	(	PUNCT
ejpam-146	476	27	y	y	PROPN
ejpam-146	476	28	,	,	PUNCT
ejpam-146	476	29	z	z	NOUN
ejpam-146	476	30	)	)	PUNCT
ejpam-146	476	31	.	.	PUNCT
ejpam-146	477	1	so	so	ADV
ejpam-146	477	2	,	,	PUNCT
ejpam-146	477	3	either	either	CCONJ
ejpam-146	477	4	(	(	PUNCT
ejpam-146	477	5	yλ	yλ	X
ejpam-146	477	6	)	)	PUNCT
ejpam-146	477	7	is	be	AUX
ejpam-146	477	8	in	in	ADP
ejpam-146	477	9	y	y	PROPN
ejpam-146	477	10	−	−	PROPN
ejpam-146	477	11	{	{	PUNCT
ejpam-146	477	12	y	y	NOUN
ejpam-146	477	13	}	}	PUNCT
ejpam-146	477	14	or	or	CCONJ
ejpam-146	477	15	(	(	PUNCT
ejpam-146	477	16	zλ	zλ	X
ejpam-146	477	17	)	)	PUNCT
ejpam-146	477	18	is	be	AUX
ejpam-146	477	19	in	in	ADP
ejpam-146	477	20	z	z	PROPN
ejpam-146	477	21	−	−	PROPN
ejpam-146	477	22	{	{	PUNCT
ejpam-146	477	23	z	z	NOUN
ejpam-146	477	24	}	}	PUNCT
ejpam-146	477	25	,	,	PUNCT
ejpam-146	477	26	say	say	VERB
ejpam-146	477	27	(	(	PUNCT
ejpam-146	477	28	yλ	yλ	NOUN
ejpam-146	477	29	)	)	PUNCT
ejpam-146	477	30	is	be	AUX
ejpam-146	477	31	in	in	ADP
ejpam-146	477	32	y	y	PROPN
ejpam-146	477	33	−	−	PROPN
ejpam-146	477	34	{	{	PUNCT
ejpam-146	477	35	y	y	NOUN
ejpam-146	477	36	}	}	PUNCT
ejpam-146	477	37	;	;	PUNCT
ejpam-146	477	38	since	since	SCONJ
ejpam-146	477	39	φ	φ	PROPN
ejpam-146	477	40	has	have	VERB
ejpam-146	477	41	a	a	DET
ejpam-146	477	42	β	β	NOUN
ejpam-146	477	43	-	-	PUNCT
ejpam-146	477	44	θ	θ	NOUN
ejpam-146	477	45	-subclosed	-subclose	VERB
ejpam-146	477	46	graph	graph	NOUN
ejpam-146	477	47	,	,	PUNCT
ejpam-146	477	48	φ(yλ	φ(yλ	NOUN
ejpam-146	477	49	)	)	PUNCT
ejpam-146	477	50	has	have	AUX
ejpam-146	477	51	atmost	atmost	PROPN
ejpam-146	477	52	one	one	NUM
ejpam-146	477	53	βθ	βθ	PROPN
ejpam-146	477	54	-adherent	-adherent	NOUN
ejpam-146	477	55	point	point	NOUN
ejpam-146	477	56	say	say	VERB
ejpam-146	477	57	,	,	PUNCT
ejpam-146	477	58	φ(y	φ(y	PROPN
ejpam-146	477	59	)	)	PUNCT
ejpam-146	477	60	.	.	PUNCT
ejpam-146	478	1	now	now	ADV
ejpam-146	478	2	as	as	ADP
ejpam-146	478	3	by	by	ADP
ejpam-146	478	4	hypothesis	hypothesis	NOUN
ejpam-146	478	5	(	(	PUNCT
ejpam-146	478	6	b	b	NOUN
ejpam-146	478	7	)	)	PUNCT
ejpam-146	478	8	,	,	PUNCT
ejpam-146	478	9	φ	φ	PROPN
ejpam-146	478	10	is	be	AUX
ejpam-146	478	11	(	(	PUNCT
ejpam-146	478	12	θ	θ	PROPN
ejpam-146	478	13	,	,	PUNCT
ejpam-146	478	14	β)-continuous	β)-continuous	NUM
ejpam-146	478	15	,	,	PUNCT
ejpam-146	478	16	hence	hence	ADV
ejpam-146	478	17	φ(yλ	φ(yλ	ADJ
ejpam-146	478	18	)	)	PUNCT
ejpam-146	478	19	β	β	NOUN
ejpam-146	478	20	-	-	NOUN
ejpam-146	478	21	θ	θ	NOUN
ejpam-146	478	22	-converges	-converge	NOUN
ejpam-146	478	23	to	to	PART
ejpam-146	478	24	φ(y	φ(y	VERB
ejpam-146	478	25	)	)	PUNCT
ejpam-146	478	26	only	only	ADV
ejpam-146	478	27	.	.	PUNCT
ejpam-146	479	1	but	but	CCONJ
ejpam-146	479	2	as	as	ADP
ejpam-146	479	3	φ(yλ	φ(yλ	NOUN
ejpam-146	479	4	)	)	PUNCT
ejpam-146	479	5	=	=	PUNCT
ejpam-146	479	6	ψ(zλ	ψ(zλ	NOUN
ejpam-146	479	7	)	)	PUNCT
ejpam-146	479	8	for	for	ADP
ejpam-146	479	9	each	each	DET
ejpam-146	479	10	λ	λ	PROPN
ejpam-146	479	11	∈	∈	PROPN
ejpam-146	479	12	i	i	PRON
ejpam-146	479	13	,	,	PUNCT
ejpam-146	479	14	the	the	DET
ejpam-146	479	15	net	net	ADJ
ejpam-146	479	16	ψ(zλ	ψ(zλ	NOUN
ejpam-146	479	17	)	)	PUNCT
ejpam-146	479	18	is	be	AUX
ejpam-146	479	19	also	also	ADV
ejpam-146	479	20	β	β	NOUN
ejpam-146	479	21	-	-	PUNCT
ejpam-146	479	22	θ	θ	NOUN
ejpam-146	479	23	-converging	-converging	NOUN
ejpam-146	479	24	to	to	PART
ejpam-146	479	25	φ(y	φ(y	VERB
ejpam-146	479	26	)	)	PUNCT
ejpam-146	479	27	only	only	ADV
ejpam-146	479	28	.	.	PUNCT
ejpam-146	480	1	since	since	SCONJ
ejpam-146	480	2	ψ	ψ	NOUN
ejpam-146	480	3	is	be	AUX
ejpam-146	480	4	(	(	PUNCT
ejpam-146	480	5	θ	θ	PROPN
ejpam-146	480	6	,	,	PUNCT
ejpam-146	480	7	β)-continuous	β)-continuous	PUNCT
ejpam-146	480	8	(	(	PUNCT
ejpam-146	480	9	by	by	ADP
ejpam-146	480	10	hypothesis	hypothesis	NOUN
ejpam-146	480	11	(	(	PUNCT
ejpam-146	480	12	b	b	NOUN
ejpam-146	480	13	)	)	PUNCT
ejpam-146	480	14	)	)	PUNCT
ejpam-146	480	15	ψ(zλ	ψ(zλ	NOUN
ejpam-146	480	16	)	)	PUNCT
ejpam-146	480	17	β	β	NOUN
ejpam-146	480	18	-	-	PUNCT
ejpam-146	480	19	θ	θ	PROPN
ejpam-146	480	20	c.	c.	PROPN
ejpam-146	480	21	k.	k.	PROPN
ejpam-146	480	22	basu	basu	PROPN
ejpam-146	480	23	,	,	PUNCT
ejpam-146	480	24	m.	m.	PROPN
ejpam-146	480	25	k.	k.	PROPN
ejpam-146	480	26	ghosh	ghosh	PROPN
ejpam-146	480	27	/	/	PUNCT
ejpam-146	480	28	eur	eur	PROPN
ejpam-146	480	29	.	.	PUNCT
ejpam-146	481	1	j.	j.	PROPN
ejpam-146	481	2	pure	pure	PROPN
ejpam-146	481	3	appl	appl	PROPN
ejpam-146	481	4	.	.	PROPN
ejpam-146	481	5	math	math	PROPN
ejpam-146	481	6	,	,	PUNCT
ejpam-146	481	7	1	1	NUM
ejpam-146	481	8	(	(	PUNCT
ejpam-146	481	9	2008	2008	NUM
ejpam-146	481	10	)	)	PUNCT
ejpam-146	481	11	,	,	PUNCT
ejpam-146	481	12	(	(	PUNCT
ejpam-146	481	13	40	40	NUM
ejpam-146	481	14	-	-	SYM
ejpam-146	481	15	50	50	NUM
ejpam-146	481	16	)	)	PUNCT
ejpam-146	481	17	49	49	NUM
ejpam-146	481	18	converges	converge	NOUN
ejpam-146	481	19	to	to	ADP
ejpam-146	481	20	ψ(z	ψ(z	VERB
ejpam-146	481	21	)	)	PUNCT
ejpam-146	481	22	.	.	PUNCT
ejpam-146	482	1	since	since	SCONJ
ejpam-146	482	2	x	x	PROPN
ejpam-146	482	3	is	be	AUX
ejpam-146	482	4	β	β	NOUN
ejpam-146	482	5	-	-	NOUN
ejpam-146	482	6	t2	t2	NOUN
ejpam-146	482	7	,	,	PUNCT
ejpam-146	482	8	we	we	PRON
ejpam-146	482	9	have	have	AUX
ejpam-146	482	10	φ(y	φ(y	NOUN
ejpam-146	482	11	)	)	PUNCT
ejpam-146	482	12	=	=	SYM
ejpam-146	482	13	ψ(z	ψ(z	PROPN
ejpam-146	482	14	)	)	PUNCT
ejpam-146	482	15	and	and	CCONJ
ejpam-146	482	16	so	so	ADV
ejpam-146	482	17	(	(	PUNCT
ejpam-146	482	18	y	y	PROPN
ejpam-146	482	19	,	,	PUNCT
ejpam-146	482	20	z	z	NOUN
ejpam-146	482	21	)	)	PUNCT
ejpam-146	482	22	∈	∈	PROPN
ejpam-146	482	23	d.	d.	PROPN
ejpam-146	482	24	therefore	therefore	ADV
ejpam-146	482	25	,	,	PUNCT
ejpam-146	482	26	d	d	PROPN
ejpam-146	482	27	is	be	AUX
ejpam-146	482	28	closed	close	VERB
ejpam-146	482	29	in	in	ADP
ejpam-146	482	30	y	y	PROPN
ejpam-146	482	31	×	×	PROPN
ejpam-146	482	32	z	z	NOUN
ejpam-146	482	33	.	.	PUNCT
ejpam-146	483	1	(	(	PUNCT
ejpam-146	483	2	c)⇒	c)⇒	X
ejpam-146	483	3	(	(	PUNCT
ejpam-146	483	4	d	d	NOUN
ejpam-146	483	5	)	)	PUNCT
ejpam-146	483	6	:	:	PUNCT
ejpam-146	483	7	obvious	obvious	ADJ
ejpam-146	483	8	.	.	PUNCT
ejpam-146	484	1	(	(	PUNCT
ejpam-146	484	2	d	d	X
ejpam-146	484	3	)	)	PUNCT
ejpam-146	484	4	⇒	⇒	NOUN
ejpam-146	484	5	(	(	PUNCT
ejpam-146	484	6	a	a	X
ejpam-146	484	7	)	)	PUNCT
ejpam-146	484	8	:	:	PUNCT
ejpam-146	484	9	suppose	suppose	VERB
ejpam-146	484	10	(	(	PUNCT
ejpam-146	484	11	x	x	X
ejpam-146	484	12	,	,	PUNCT
ejpam-146	484	13	τ	τ	X
ejpam-146	484	14	)	)	PUNCT
ejpam-146	484	15	is	be	AUX
ejpam-146	484	16	not	not	PART
ejpam-146	484	17	β	β	NOUN
ejpam-146	484	18	-	-	VERB
ejpam-146	484	19	closed	closed	ADJ
ejpam-146	484	20	.	.	PUNCT
ejpam-146	485	1	so	so	ADV
ejpam-146	485	2	by	by	ADP
ejpam-146	485	3	remark	remark	NOUN
ejpam-146	485	4	3.6	3.6	NUM
ejpam-146	485	5	,	,	PUNCT
ejpam-146	485	6	there	there	PRON
ejpam-146	485	7	exists	exist	VERB
ejpam-146	485	8	a	a	DET
ejpam-146	485	9	net	net	NOUN
ejpam-146	485	10	(	(	PUNCT
ejpam-146	485	11	xλ)λ∈i	xλ)λ∈i	NUM
ejpam-146	485	12	in	in	ADP
ejpam-146	485	13	x	x	PUNCT
ejpam-146	485	14	which	which	PRON
ejpam-146	485	15	has	have	VERB
ejpam-146	485	16	no	no	DET
ejpam-146	485	17	β	β	NOUN
ejpam-146	485	18	-	-	PUNCT
ejpam-146	485	19	θ	θ	ADJ
ejpam-146	485	20	-adherent	-adherent	NOUN
ejpam-146	485	21	point	point	NOUN
ejpam-146	485	22	.	.	PUNCT
ejpam-146	486	1	we	we	PRON
ejpam-146	486	2	may	may	AUX
ejpam-146	486	3	choose	choose	VERB
ejpam-146	486	4	x0	x0	PROPN
ejpam-146	486	5	,	,	PUNCT
ejpam-146	486	6	x1	x1	PROPN
ejpam-146	486	7	∈	∈	PROPN
ejpam-146	486	8	x	x	PUNCT
ejpam-146	486	9	with	with	ADP
ejpam-146	486	10	x0	x0	PROPN
ejpam-146	486	11	6=	6=	PRON
ejpam-146	486	12	x1	x1	PROPN
ejpam-146	486	13	and	and	CCONJ
ejpam-146	486	14	assume	assume	VERB
ejpam-146	486	15	without	without	ADP
ejpam-146	486	16	loss	loss	NOUN
ejpam-146	486	17	of	of	ADP
ejpam-146	486	18	generality	generality	NOUN
ejpam-146	486	19	that	that	PRON
ejpam-146	486	20	(	(	PUNCT
ejpam-146	486	21	xλ)λ∈i	xλ)λ∈i	PROPN
ejpam-146	486	22	is	be	AUX
ejpam-146	486	23	a	a	DET
ejpam-146	486	24	net	net	NOUN
ejpam-146	486	25	in	in	ADP
ejpam-146	486	26	x	x	PART
ejpam-146	486	27	−	−	PROPN
ejpam-146	486	28	{	{	PUNCT
ejpam-146	486	29	x0	x0	PROPN
ejpam-146	486	30	,	,	PUNCT
ejpam-146	486	31	x1	x1	PROPN
ejpam-146	486	32	}	}	PUNCT
ejpam-146	486	33	.	.	PUNCT
ejpam-146	487	1	let	let	VERB
ejpam-146	487	2	z	z	NOUN
ejpam-146	487	3	=	=	PUNCT
ejpam-146	487	4	x	x	PROPN
ejpam-146	487	5	and	and	CCONJ
ejpam-146	487	6	τ	τ	PROPN
ejpam-146	487	7	?	?	PUNCT
ejpam-146	488	1	=	=	PRON
ejpam-146	488	2	{	{	PUNCT
ejpam-146	488	3	u	u	X
ejpam-146	488	4	⊂	⊂	PROPN
ejpam-146	488	5	z	z	NOUN
ejpam-146	488	6	:	:	PUNCT
ejpam-146	488	7	u	u	NOUN
ejpam-146	488	8	∩	∩	NOUN
ejpam-146	488	9	{	{	PUNCT
ejpam-146	488	10	x0	x0	PROPN
ejpam-146	488	11	,	,	PUNCT
ejpam-146	488	12	x1	x1	PROPN
ejpam-146	488	13	}	}	PUNCT
ejpam-146	488	14	=	=	SYM
ejpam-146	488	15	;	;	PUNCT
ejpam-146	488	16	}	}	PUNCT
ejpam-146	488	17	or	or	CCONJ
ejpam-146	488	18	{	{	PUNCT
ejpam-146	488	19	u	u	X
ejpam-146	488	20	⊂	⊂	PROPN
ejpam-146	488	21	z	z	NOUN
ejpam-146	488	22	:	:	PUNCT
ejpam-146	488	23	u	u	NOUN
ejpam-146	488	24	∩	∩	NOUN
ejpam-146	488	25	{	{	PUNCT
ejpam-146	488	26	x0	x0	PROPN
ejpam-146	488	27	,	,	PUNCT
ejpam-146	488	28	x1	x1	PROPN
ejpam-146	488	29	}	}	PUNCT
ejpam-146	488	30	6=	6=	NUM
ejpam-146	488	31	;	;	PUNCT
ejpam-146	488	32	and	and	CCONJ
ejpam-146	488	33	sλ	sλ	NOUN
ejpam-146	488	34	=	=	SYM
ejpam-146	488	35	{	{	PUNCT
ejpam-146	488	36	xλ	xλ	NOUN
ejpam-146	488	37	:	:	PUNCT
ejpam-146	488	38	λ	λ	X
ejpam-146	488	39	≥	≥	NOUN
ejpam-146	488	40	λ0	λ0	NOUN
ejpam-146	488	41	}	}	PUNCT
ejpam-146	488	42	⊂	⊂	PROPN
ejpam-146	488	43	u	u	NOUN
ejpam-146	488	44	for	for	ADP
ejpam-146	488	45	some	some	DET
ejpam-146	488	46	λ0	λ0	NOUN
ejpam-146	488	47	∈	∈	NOUN
ejpam-146	488	48	i	i	X
ejpam-146	488	49	}	}	PUNCT
ejpam-146	488	50	.	.	PUNCT
ejpam-146	489	1	clearly	clearly	ADV
ejpam-146	489	2	τ	τ	X
ejpam-146	489	3	?	?	PROPN
ejpam-146	489	4	is	be	AUX
ejpam-146	489	5	a	a	DET
ejpam-146	489	6	topology	topology	NOUN
ejpam-146	489	7	on	on	ADP
ejpam-146	489	8	z	z	PROPN
ejpam-146	489	9	.	.	PUNCT
ejpam-146	490	1	let	let	VERB
ejpam-146	490	2	ψ	ψ	X
ejpam-146	490	3	:	:	PUNCT
ejpam-146	490	4	(	(	PUNCT
ejpam-146	490	5	z	z	NOUN
ejpam-146	490	6	,	,	PUNCT
ejpam-146	490	7	τ	τ	PROPN
ejpam-146	490	8	?	?	PUNCT
ejpam-146	490	9	)	)	PUNCT
ejpam-146	490	10	→	→	SYM
ejpam-146	490	11	(	(	PUNCT
ejpam-146	490	12	x	x	X
ejpam-146	490	13	,	,	PUNCT
ejpam-146	490	14	τ	τ	X
ejpam-146	490	15	)	)	PUNCT
ejpam-146	490	16	be	be	AUX
ejpam-146	490	17	define	define	ADJ
ejpam-146	490	18	by	by	ADP
ejpam-146	490	19	ψ(x0	ψ(x0	NOUN
ejpam-146	490	20	)	)	PUNCT
ejpam-146	491	1	=	=	SYM
ejpam-146	491	2	x1	x1	PROPN
ejpam-146	491	3	,	,	PUNCT
ejpam-146	491	4	ψ(x1	ψ(x1	NOUN
ejpam-146	491	5	)	)	PUNCT
ejpam-146	491	6	=	=	SYM
ejpam-146	491	7	ψ(x0	ψ(x0	NOUN
ejpam-146	491	8	)	)	PUNCT
ejpam-146	491	9	and	and	CCONJ
ejpam-146	491	10	ψ(x	ψ(x	NUM
ejpam-146	491	11	)	)	PUNCT
ejpam-146	492	1	=	=	NOUN
ejpam-146	492	2	x	x	X
ejpam-146	492	3	if	if	SCONJ
ejpam-146	492	4	x	x	SYM
ejpam-146	492	5	6∈	6∈	PROPN
ejpam-146	492	6	{	{	PUNCT
ejpam-146	492	7	x0	x0	PROPN
ejpam-146	492	8	,	,	PUNCT
ejpam-146	492	9	x1	x1	PROPN
ejpam-146	492	10	}	}	PUNCT
ejpam-146	492	11	.	.	PUNCT
ejpam-146	493	1	we	we	PRON
ejpam-146	493	2	arrive	arrive	VERB
ejpam-146	493	3	at	at	ADP
ejpam-146	493	4	a	a	DET
ejpam-146	493	5	contradiction	contradiction	NOUN
ejpam-146	493	6	by	by	ADP
ejpam-146	493	7	showing	show	VERB
ejpam-146	493	8	that	that	SCONJ
ejpam-146	493	9	d(ψ	d(ψ	NOUN
ejpam-146	493	10	)	)	PUNCT
ejpam-146	493	11	is	be	AUX
ejpam-146	493	12	not	not	PART
ejpam-146	493	13	closed	closed	ADJ
ejpam-146	493	14	but	but	CCONJ
ejpam-146	493	15	this	this	DET
ejpam-146	493	16	function	function	NOUN
ejpam-146	493	17	ψ	ψ	NOUN
ejpam-146	493	18	has	have	VERB
ejpam-146	493	19	a	a	DET
ejpam-146	493	20	β	β	NOUN
ejpam-146	493	21	-	-	PUNCT
ejpam-146	493	22	θ	θ	NOUN
ejpam-146	493	23	-subclosed	-subclose	VERB
ejpam-146	493	24	graph	graph	NOUN
ejpam-146	493	25	.	.	PUNCT
ejpam-146	494	1	from	from	ADP
ejpam-146	494	2	the	the	DET
ejpam-146	494	3	definition	definition	NOUN
ejpam-146	494	4	,	,	PUNCT
ejpam-146	494	5	it	it	PRON
ejpam-146	494	6	is	be	AUX
ejpam-146	494	7	clear	clear	ADJ
ejpam-146	494	8	that	that	SCONJ
ejpam-146	494	9	(	(	PUNCT
ejpam-146	494	10	x0	x0	PROPN
ejpam-146	494	11	,	,	PUNCT
ejpam-146	494	12	x1	x1	PROPN
ejpam-146	494	13	)	)	PUNCT
ejpam-146	494	14	6∈	6∈	PROPN
ejpam-146	494	15	d(ψ	d(ψ	PROPN
ejpam-146	494	16	)	)	PUNCT
ejpam-146	494	17	.	.	PUNCT
ejpam-146	495	1	but	but	CCONJ
ejpam-146	495	2	(	(	PUNCT
ejpam-146	495	3	x0	x0	PROPN
ejpam-146	495	4	,	,	PUNCT
ejpam-146	495	5	x1	x1	PROPN
ejpam-146	495	6	)	)	PUNCT
ejpam-146	495	7	is	be	AUX
ejpam-146	495	8	a	a	DET
ejpam-146	495	9	limit	limit	NOUN
ejpam-146	495	10	point	point	NOUN
ejpam-146	495	11	of	of	ADP
ejpam-146	495	12	d(ψ	d(ψ	NOUN
ejpam-146	495	13	)	)	PUNCT
ejpam-146	495	14	.	.	PUNCT
ejpam-146	496	1	indeed	indeed	ADV
ejpam-146	496	2	,	,	PUNCT
ejpam-146	496	3	let	let	VERB
ejpam-146	496	4	w	w	NOUN
ejpam-146	496	5	be	be	AUX
ejpam-146	496	6	an	an	DET
ejpam-146	496	7	open	open	ADJ
ejpam-146	496	8	set	set	NOUN
ejpam-146	496	9	containing	contain	VERB
ejpam-146	496	10	(	(	PUNCT
ejpam-146	496	11	x0	x0	PROPN
ejpam-146	496	12	,	,	PUNCT
ejpam-146	496	13	x1	x1	PROPN
ejpam-146	496	14	)	)	PUNCT
ejpam-146	496	15	in	in	ADP
ejpam-146	496	16	z×	z×	NUM
ejpam-146	496	17	z	z	NOUN
ejpam-146	496	18	.	.	PUNCT
ejpam-146	497	1	the	the	DET
ejpam-146	497	2	definition	definition	NOUN
ejpam-146	497	3	of	of	ADP
ejpam-146	497	4	τ	τ	PROPN
ejpam-146	497	5	?	?	PUNCT
ejpam-146	497	6	ensures	ensure	VERB
ejpam-146	497	7	that	that	PRON
ejpam-146	497	8	(	(	PUNCT
ejpam-146	497	9	sλ1	sλ1	INTJ
ejpam-146	497	10	∪{x0})×	∪{x0})×	NOUN
ejpam-146	497	11	(	(	PUNCT
ejpam-146	497	12	sλ2	sλ2	NOUN
ejpam-146	497	13	∪{x1})⊆w	∪{x1})⊆w	NOUN
ejpam-146	497	14	for	for	ADP
ejpam-146	497	15	some	some	DET
ejpam-146	497	16	λ1,λ2	λ1,λ2	PROPN
ejpam-146	497	17	∈	∈	PROPN
ejpam-146	497	18	i	i	PRON
ejpam-146	497	19	.	.	PUNCT
ejpam-146	498	1	now	now	ADV
ejpam-146	498	2	(	(	PUNCT
ejpam-146	498	3	xλ	xλ	NOUN
ejpam-146	498	4	,	,	PUNCT
ejpam-146	498	5	xλ	xλ	NOUN
ejpam-146	498	6	)	)	PUNCT
ejpam-146	498	7	∈w	∈w	NOUN
ejpam-146	498	8	∩	∩	NOUN
ejpam-146	498	9	d(ψ	d(ψ	NOUN
ejpam-146	498	10	)	)	PUNCT
ejpam-146	498	11	for	for	SCONJ
ejpam-146	498	12	λ	λ	PROPN
ejpam-146	498	13	>	>	X
ejpam-146	498	14	λ1,λ2	λ1,λ2	PROPN
ejpam-146	498	15	provides	provide	VERB
ejpam-146	498	16	(	(	PUNCT
ejpam-146	498	17	x0	x0	PROPN
ejpam-146	498	18	,	,	PUNCT
ejpam-146	498	19	x1	x1	PROPN
ejpam-146	498	20	)	)	PUNCT
ejpam-146	498	21	is	be	AUX
ejpam-146	498	22	a	a	DET
ejpam-146	498	23	limit	limit	NOUN
ejpam-146	498	24	point	point	NOUN
ejpam-146	498	25	of	of	ADP
ejpam-146	498	26	d(ψ	d(ψ	NOUN
ejpam-146	498	27	)	)	PUNCT
ejpam-146	498	28	.	.	PUNCT
ejpam-146	499	1	so	so	ADV
ejpam-146	499	2	d(ψ	d(ψ	PROPN
ejpam-146	499	3	)	)	PUNCT
ejpam-146	499	4	is	be	AUX
ejpam-146	499	5	not	not	PART
ejpam-146	499	6	closed	close	VERB
ejpam-146	499	7	.	.	PUNCT
ejpam-146	500	1	to	to	PART
ejpam-146	500	2	show	show	VERB
ejpam-146	500	3	ψ	ψ	NOUN
ejpam-146	500	4	has	have	VERB
ejpam-146	500	5	a	a	DET
ejpam-146	500	6	β	β	NOUN
ejpam-146	500	7	-	-	PUNCT
ejpam-146	500	8	θ	θ	NOUN
ejpam-146	500	9	-subclosed	-subclose	VERB
ejpam-146	500	10	graph	graph	NOUN
ejpam-146	500	11	,	,	PUNCT
ejpam-146	500	12	let	let	VERB
ejpam-146	500	13	n	n	X
ejpam-146	500	14	=	=	SYM
ejpam-146	500	15	(	(	PUNCT
ejpam-146	500	16	zβ)β∈j	zβ)β∈j	NUM
ejpam-146	500	17	be	be	VERB
ejpam-146	500	18	a	a	DET
ejpam-146	500	19	net	net	NOUN
ejpam-146	500	20	in	in	ADP
ejpam-146	500	21	z	z	PROPN
ejpam-146	500	22	−	−	PROPN
ejpam-146	500	23	{	{	PUNCT
ejpam-146	500	24	z	z	AUX
ejpam-146	500	25	}	}	PUNCT
ejpam-146	500	26	converging	converge	VERB
ejpam-146	500	27	to	to	ADP
ejpam-146	500	28	z.	z.	PROPN
ejpam-146	500	29	obviously	obviously	ADV
ejpam-146	500	30	z	z	PROPN
ejpam-146	501	1	=	=	SYM
ejpam-146	501	2	x0	x0	PROPN
ejpam-146	501	3	or	or	CCONJ
ejpam-146	501	4	x1	x1	NUM
ejpam-146	501	5	,	,	PUNCT
ejpam-146	501	6	otherwise	otherwise	ADV
ejpam-146	501	7	{	{	PUNCT
ejpam-146	501	8	z	z	NOUN
ejpam-146	501	9	}	}	PUNCT
ejpam-146	501	10	would	would	AUX
ejpam-146	501	11	be	be	AUX
ejpam-146	501	12	an	an	DET
ejpam-146	501	13	open	open	ADJ
ejpam-146	501	14	set	set	NOUN
ejpam-146	501	15	containing	contain	VERB
ejpam-146	501	16	z	z	NOUN
ejpam-146	501	17	and	and	CCONJ
ejpam-146	501	18	hence	hence	ADV
ejpam-146	501	19	the	the	DET
ejpam-146	501	20	net	net	NOUN
ejpam-146	501	21	(	(	PUNCT
ejpam-146	501	22	zβ)β∈j	zβ)β∈j	NOUN
ejpam-146	501	23	could	could	AUX
ejpam-146	501	24	not	not	PART
ejpam-146	501	25	converge	converge	VERB
ejpam-146	501	26	to	to	ADP
ejpam-146	501	27	z.	z.	PROPN
ejpam-146	501	28	suppose	suppose	VERB
ejpam-146	501	29	z	z	NOUN
ejpam-146	501	30	=	=	SYM
ejpam-146	501	31	x0	x0	PROPN
ejpam-146	501	32	(	(	PUNCT
ejpam-146	501	33	say	say	INTJ
ejpam-146	501	34	)	)	PUNCT
ejpam-146	501	35	.	.	PUNCT
ejpam-146	502	1	if	if	SCONJ
ejpam-146	502	2	possible	possible	ADJ
ejpam-146	502	3	,	,	PUNCT
ejpam-146	502	4	let	let	VERB
ejpam-146	502	5	ψ(n	ψ(n	NOUN
ejpam-146	502	6	)	)	PUNCT
ejpam-146	502	7	β	β	X
ejpam-146	502	8	-	-	PUNCT
ejpam-146	502	9	θ	θ	NOUN
ejpam-146	502	10	-adheres	-adhere	NOUN
ejpam-146	502	11	to	to	ADP
ejpam-146	502	12	some	some	DET
ejpam-146	502	13	point	point	NOUN
ejpam-146	502	14	x	x	X
ejpam-146	502	15	∈	∈	NOUN
ejpam-146	502	16	x	x	X
ejpam-146	502	17	.	.	PUNCT
ejpam-146	503	1	but	but	CCONJ
ejpam-146	503	2	as	as	ADP
ejpam-146	503	3	the	the	DET
ejpam-146	503	4	net	net	NOUN
ejpam-146	503	5	ψ((xλ)λ∈i	ψ((xλ)λ∈i	NUM
ejpam-146	503	6	)	)	PUNCT
ejpam-146	503	7	=	=	SYM
ejpam-146	503	8	(	(	PUNCT
ejpam-146	503	9	xλ)λ∈i	xλ)λ∈i	PROPN
ejpam-146	503	10	has	have	VERB
ejpam-146	503	11	no	no	DET
ejpam-146	503	12	β	β	NOUN
ejpam-146	503	13	-	-	PUNCT
ejpam-146	503	14	θ	θ	NOUN
ejpam-146	503	15	-adherent	-adherent	NOUN
ejpam-146	503	16	point	point	NOUN
ejpam-146	503	17	,	,	PUNCT
ejpam-146	503	18	there	there	PRON
ejpam-146	503	19	exists	exist	VERB
ejpam-146	503	20	v	v	ADP
ejpam-146	503	21	∈	∈	PROPN
ejpam-146	503	22	βr(x	βr(x	PUNCT
ejpam-146	503	23	,	,	PUNCT
ejpam-146	503	24	x	x	X
ejpam-146	503	25	)	)	PUNCT
ejpam-146	503	26	and	and	CCONJ
ejpam-146	503	27	a	a	DET
ejpam-146	503	28	λ0	λ0	NOUN
ejpam-146	503	29	∈	∈	NOUN
ejpam-146	503	30	i	i	PRON
ejpam-146	503	31	such	such	ADJ
ejpam-146	503	32	that	that	DET
ejpam-146	503	33	sλ	sλ	NOUN
ejpam-146	503	34	=	=	SYM
ejpam-146	503	35	{	{	PUNCT
ejpam-146	503	36	xλ	xλ	NOUN
ejpam-146	503	37	:	:	PUNCT
ejpam-146	503	38	λ≥	λ≥	ADJ
ejpam-146	503	39	λ0	λ0	NOUN
ejpam-146	503	40	}	}	PUNCT
ejpam-146	503	41	⊂	⊂	SYM
ejpam-146	503	42	x	x	SYM
ejpam-146	503	43	−v	−v	NOUN
ejpam-146	503	44	,	,	PUNCT
ejpam-146	503	45	for	for	ADP
ejpam-146	503	46	all	all	DET
ejpam-146	503	47	λ≥	λ≥	ADJ
ejpam-146	503	48	λ0	λ0	NOUN
ejpam-146	503	49	.	.	PUNCT
ejpam-146	504	1	since	since	SCONJ
ejpam-146	504	2	the	the	DET
ejpam-146	504	3	net	net	NOUN
ejpam-146	504	4	n	n	X
ejpam-146	504	5	=	=	PUNCT
ejpam-146	504	6	(	(	PUNCT
ejpam-146	504	7	zβ)β∈j	zβ)β∈j	PROPN
ejpam-146	504	8	is	be	AUX
ejpam-146	504	9	converging	converge	VERB
ejpam-146	504	10	to	to	ADP
ejpam-146	504	11	x0	x0	PROPN
ejpam-146	504	12	,	,	PUNCT
ejpam-146	504	13	{	{	PUNCT
ejpam-146	504	14	zβ	zβ	NOUN
ejpam-146	504	15	:	:	PUNCT
ejpam-146	504	16	β	β	X
ejpam-146	504	17	≥	≥	NOUN
ejpam-146	504	18	β0	β0	PROPN
ejpam-146	504	19	}	}	PUNCT
ejpam-146	504	20	⊂	⊂	PROPN
ejpam-146	504	21	sλ∪{x0	sλ∪{x0	PROPN
ejpam-146	504	22	}	}	PUNCT
ejpam-146	504	23	for	for	ADP
ejpam-146	504	24	some	some	DET
ejpam-146	504	25	β0	β0	PROPN
ejpam-146	504	26	∈	∈	PROPN
ejpam-146	504	27	j	j	PROPN
ejpam-146	504	28	.	.	PUNCT
ejpam-146	505	1	obviously	obviously	ADV
ejpam-146	505	2	,	,	PUNCT
ejpam-146	505	3	no	no	INTJ
ejpam-146	505	4	zβ	zβ	PROPN
ejpam-146	505	5	can	can	AUX
ejpam-146	505	6	be	be	AUX
ejpam-146	505	7	x0	x0	PROPN
ejpam-146	505	8	and	and	CCONJ
ejpam-146	505	9	x1	x1	NUM
ejpam-146	505	10	as	as	ADV
ejpam-146	505	11	well	well	ADV
ejpam-146	505	12	for	for	ADP
ejpam-146	505	13	β	β	X
ejpam-146	505	14	≥	≥	NOUN
ejpam-146	505	15	β0	β0	PROPN
ejpam-146	505	16	.	.	PUNCT
ejpam-146	506	1	so	so	ADV
ejpam-146	506	2	,	,	PUNCT
ejpam-146	506	3	{	{	PUNCT
ejpam-146	506	4	ψ(zβ	ψ(zβ	NOUN
ejpam-146	506	5	)	)	PUNCT
ejpam-146	506	6	:	:	PUNCT
ejpam-146	507	1	β	β	X
ejpam-146	507	2	≥	≥	NOUN
ejpam-146	507	3	β0}=	β0}=	X
ejpam-146	507	4	{	{	PUNCT
ejpam-146	507	5	zβ	zβ	NOUN
ejpam-146	507	6	:	:	PUNCT
ejpam-146	507	7	β	β	X
ejpam-146	507	8	≥	≥	NOUN
ejpam-146	507	9	β0	β0	NOUN
ejpam-146	507	10	}	}	PUNCT
ejpam-146	507	11	⊆	⊆	NUM
ejpam-146	507	12	sλ	sλ	NOUN
ejpam-146	507	13	⊂	⊂	X
ejpam-146	507	14	x	x	X
ejpam-146	507	15	−v	−v	NOUN
ejpam-146	507	16	.	.	PUNCT
ejpam-146	508	1	hence	hence	ADV
ejpam-146	508	2	ψ(n	ψ(n	NUM
ejpam-146	508	3	)	)	PUNCT
ejpam-146	508	4	can	can	AUX
ejpam-146	508	5	not	not	PART
ejpam-146	508	6	β	β	VERB
ejpam-146	508	7	-	-	PUNCT
ejpam-146	508	8	θ	θ	NOUN
ejpam-146	508	9	-adhere	-adhere	PROPN
ejpam-146	508	10	to	to	ADP
ejpam-146	508	11	x	x	PROPN
ejpam-146	508	12	.	.	PUNCT
ejpam-146	509	1	so	so	ADV
ejpam-146	509	2	ψ	ψ	PRON
ejpam-146	509	3	has	have	VERB
ejpam-146	509	4	a	a	DET
ejpam-146	509	5	β	β	NOUN
ejpam-146	509	6	-	-	PUNCT
ejpam-146	509	7	θ	θ	NOUN
ejpam-146	509	8	-subclosed	-subclose	VERB
ejpam-146	509	9	graph	graph	NOUN
ejpam-146	509	10	.	.	PUNCT
ejpam-146	510	1	therefore	therefore	ADV
ejpam-146	510	2	x	x	X
ejpam-146	510	3	is	be	AUX
ejpam-146	510	4	β	β	NOUN
ejpam-146	510	5	-	-	VERB
ejpam-146	510	6	closed	closed	ADJ
ejpam-146	510	7	.	.	PUNCT
ejpam-146	511	1	theorem	theorem	VERB
ejpam-146	511	2	4.14	4.14	NUM
ejpam-146	511	3	.	.	PUNCT
ejpam-146	512	1	a	a	DET
ejpam-146	512	2	space	space	NOUN
ejpam-146	512	3	(	(	PUNCT
ejpam-146	512	4	x	x	X
ejpam-146	512	5	,	,	PUNCT
ejpam-146	512	6	τ	τ	X
ejpam-146	512	7	)	)	PUNCT
ejpam-146	512	8	is	be	AUX
ejpam-146	512	9	β	β	NOUN
ejpam-146	512	10	-	-	VERB
ejpam-146	512	11	closed	closed	ADJ
ejpam-146	512	12	if	if	SCONJ
ejpam-146	512	13	and	and	CCONJ
ejpam-146	512	14	only	only	ADV
ejpam-146	512	15	if	if	SCONJ
ejpam-146	512	16	for	for	ADP
ejpam-146	512	17	any	any	DET
ejpam-146	512	18	space	space	NOUN
ejpam-146	512	19	z	z	NOUN
ejpam-146	512	20	and	and	CCONJ
ejpam-146	512	21	any	any	DET
ejpam-146	512	22	functions	function	NOUN
ejpam-146	512	23	φ	φ	NOUN
ejpam-146	512	24	,	,	PUNCT
ejpam-146	512	25	ψ	ψ	X
ejpam-146	512	26	:	:	PUNCT
ejpam-146	512	27	z	z	X
ejpam-146	512	28	→	→	SYM
ejpam-146	512	29	x	x	X
ejpam-146	512	30	with	with	ADP
ejpam-146	512	31	β	β	X
ejpam-146	512	32	-	-	PUNCT
ejpam-146	512	33	θ	θ	NOUN
ejpam-146	512	34	-subclosed	-subclose	VERB
ejpam-146	512	35	graphs	graph	NOUN
ejpam-146	512	36	,	,	PUNCT
ejpam-146	512	37	∆=	∆=	ADJ
ejpam-146	512	38	{	{	PUNCT
ejpam-146	512	39	z	z	NOUN
ejpam-146	512	40	∈	∈	PROPN
ejpam-146	512	41	z	z	NOUN
ejpam-146	512	42	:	:	PUNCT
ejpam-146	512	43	φ(z	φ(z	ADJ
ejpam-146	512	44	)	)	PUNCT
ejpam-146	512	45	=	=	SYM
ejpam-146	512	46	ψ(z	ψ(z	PROPN
ejpam-146	512	47	)	)	PUNCT
ejpam-146	512	48	}	}	PUNCT
ejpam-146	512	49	is	be	AUX
ejpam-146	512	50	closed	close	VERB
ejpam-146	512	51	in	in	ADP
ejpam-146	512	52	z	z	NOUN
ejpam-146	512	53	.	.	PUNCT
ejpam-146	513	1	proof	proof	NOUN
ejpam-146	513	2	.	.	PUNCT
ejpam-146	514	1	suppose	suppose	VERB
ejpam-146	514	2	x	x	PRON
ejpam-146	514	3	is	be	AUX
ejpam-146	514	4	not	not	PART
ejpam-146	514	5	β	β	NOUN
ejpam-146	514	6	-	-	VERB
ejpam-146	514	7	closed	closed	ADJ
ejpam-146	514	8	.	.	PUNCT
ejpam-146	515	1	then	then	ADV
ejpam-146	515	2	by	by	ADP
ejpam-146	515	3	remark	remark	NOUN
ejpam-146	515	4	3.6	3.6	NUM
ejpam-146	515	5	,	,	PUNCT
ejpam-146	515	6	there	there	PRON
ejpam-146	515	7	exists	exist	VERB
ejpam-146	515	8	a	a	DET
ejpam-146	515	9	net	net	NOUN
ejpam-146	515	10	s	s	PART
ejpam-146	515	11	=	=	PUNCT
ejpam-146	515	12	(	(	PUNCT
ejpam-146	515	13	xλ)λ∈i	xλ)λ∈i	X
ejpam-146	515	14	in	in	ADP
ejpam-146	515	15	x	x	PUNCT
ejpam-146	515	16	having	have	VERB
ejpam-146	515	17	no	no	DET
ejpam-146	515	18	β	β	NOUN
ejpam-146	515	19	-	-	ADJ
ejpam-146	515	20	θ	θ	ADJ
ejpam-146	515	21	-adherent	-adherent	NOUN
ejpam-146	515	22	point	point	NOUN
ejpam-146	515	23	in	in	ADP
ejpam-146	515	24	x	x	X
ejpam-146	515	25	.	.	PUNCT
ejpam-146	516	1	consider	consider	VERB
ejpam-146	516	2	two	two	NUM
ejpam-146	516	3	points	point	NOUN
ejpam-146	516	4	xo	xo	PROPN
ejpam-146	516	5	,	,	PUNCT
ejpam-146	516	6	x1	x1	PROPN
ejpam-146	516	7	in	in	ADP
ejpam-146	516	8	x	x	PUNCT
ejpam-146	516	9	with	with	ADP
ejpam-146	516	10	xo	xo	PROPN
ejpam-146	516	11	6=	6=	NUM
ejpam-146	516	12	x1	x1	PROPN
ejpam-146	516	13	and	and	CCONJ
ejpam-146	516	14	put	put	VERB
ejpam-146	516	15	z	z	NOUN
ejpam-146	516	16	=	=	SYM
ejpam-146	516	17	x	x	PUNCT
ejpam-146	516	18	and	and	CCONJ
ejpam-146	516	19	assume	assume	VERB
ejpam-146	516	20	without	without	ADP
ejpam-146	516	21	loss	loss	NOUN
ejpam-146	516	22	of	of	ADP
ejpam-146	516	23	generality	generality	NOUN
ejpam-146	516	24	that	that	PRON
ejpam-146	516	25	s	s	VERB
ejpam-146	516	26	=	=	X
ejpam-146	516	27	(	(	PUNCT
ejpam-146	516	28	xλ)λ∈i	xλ)λ∈i	PROPN
ejpam-146	516	29	is	be	AUX
ejpam-146	516	30	a	a	DET
ejpam-146	516	31	net	net	NOUN
ejpam-146	516	32	x	x	INTJ
ejpam-146	516	33	−	−	PROPN
ejpam-146	516	34	{	{	PUNCT
ejpam-146	516	35	x1	x1	PROPN
ejpam-146	516	36	}	}	PUNCT
ejpam-146	516	37	.	.	PUNCT
ejpam-146	517	1	let	let	VERB
ejpam-146	517	2	τ	τ	X
ejpam-146	517	3	?	?	PUNCT
ejpam-146	518	1	=	=	PRON
ejpam-146	518	2	{	{	PUNCT
ejpam-146	518	3	u	u	X
ejpam-146	518	4	⊂	⊂	PROPN
ejpam-146	518	5	z	z	NOUN
ejpam-146	518	6	:	:	PUNCT
ejpam-146	518	7	x1	x1	NUM
ejpam-146	518	8	6∈	6∈	NUM
ejpam-146	518	9	u	u	NOUN
ejpam-146	518	10	}	}	PUNCT
ejpam-146	518	11	∪	∪	VERB
ejpam-146	518	12	{	{	PUNCT
ejpam-146	518	13	u	u	NOUN
ejpam-146	518	14	⊂	⊂	PROPN
ejpam-146	518	15	z	z	NOUN
ejpam-146	518	16	:	:	PUNCT
ejpam-146	518	17	tλ0	tλ0	PROPN
ejpam-146	518	18	=	=	PUNCT
ejpam-146	518	19	{	{	PUNCT
ejpam-146	518	20	xλ	xλ	NOUN
ejpam-146	518	21	:	:	PUNCT
ejpam-146	518	22	λ	λ	X
ejpam-146	518	23	≥	≥	NOUN
ejpam-146	518	24	λ0	λ0	NOUN
ejpam-146	518	25	}	}	PUNCT
ejpam-146	518	26	⊂	⊂	PROPN
ejpam-146	518	27	u	u	NOUN
ejpam-146	518	28	for	for	ADP
ejpam-146	518	29	some	some	DET
ejpam-146	518	30	λ0	λ0	NOUN
ejpam-146	518	31	∈	∈	NOUN
ejpam-146	518	32	i	i	X
ejpam-146	518	33	}	}	PUNCT
ejpam-146	518	34	.	.	PUNCT
ejpam-146	519	1	then	then	ADV
ejpam-146	519	2	τ	τ	PROPN
ejpam-146	519	3	?	?	PROPN
ejpam-146	519	4	is	be	AUX
ejpam-146	519	5	a	a	DET
ejpam-146	519	6	topology	topology	NOUN
ejpam-146	519	7	on	on	ADP
ejpam-146	519	8	z	z	PROPN
ejpam-146	519	9	.	.	PUNCT
ejpam-146	520	1	we	we	PRON
ejpam-146	520	2	now	now	ADV
ejpam-146	520	3	define	define	VERB
ejpam-146	520	4	two	two	NUM
ejpam-146	520	5	functions	function	NOUN
ejpam-146	520	6	φ	φ	NUM
ejpam-146	520	7	,	,	PUNCT
ejpam-146	520	8	ψ	ψ	X
ejpam-146	520	9	:	:	PUNCT
ejpam-146	520	10	(	(	PUNCT
ejpam-146	520	11	z	z	NOUN
ejpam-146	520	12	,	,	PUNCT
ejpam-146	520	13	τ?)→	τ?)→	X
ejpam-146	520	14	(	(	PUNCT
ejpam-146	520	15	x	x	X
ejpam-146	520	16	,	,	PUNCT
ejpam-146	520	17	τ	τ	PROPN
ejpam-146	520	18	)	)	PUNCT
ejpam-146	520	19	as	as	SCONJ
ejpam-146	520	20	follows	follow	VERB
ejpam-146	520	21	:	:	PUNCT
ejpam-146	520	22	φ(z	φ(z	ADJ
ejpam-146	520	23	)	)	PUNCT
ejpam-146	520	24	=	=	SYM
ejpam-146	520	25	z	z	NOUN
ejpam-146	520	26	for	for	ADP
ejpam-146	520	27	z	z	PROPN
ejpam-146	520	28	∈	∈	PROPN
ejpam-146	520	29	z	z	PROPN
ejpam-146	520	30	and	and	CCONJ
ejpam-146	520	31	ψ(z	ψ(z	PROPN
ejpam-146	520	32	)	)	PUNCT
ejpam-146	520	33	=	=	SYM
ejpam-146	520	34	z	z	NOUN
ejpam-146	520	35	for	for	ADP
ejpam-146	520	36	z	z	PROPN
ejpam-146	520	37	∈	∈	PROPN
ejpam-146	521	1	z	z	NOUN
ejpam-146	521	2	−	−	PROPN
ejpam-146	521	3	{	{	PUNCT
ejpam-146	521	4	x1	x1	PROPN
ejpam-146	521	5	}	}	PUNCT
ejpam-146	521	6	and	and	CCONJ
ejpam-146	521	7	ψ(x1	ψ(x1	NOUN
ejpam-146	521	8	)	)	PUNCT
ejpam-146	521	9	=	=	SYM
ejpam-146	522	1	x0	x0	PROPN
ejpam-146	522	2	.	.	PUNCT
ejpam-146	523	1	we	we	PRON
ejpam-146	523	2	now	now	ADV
ejpam-146	523	3	claim	claim	VERB
ejpam-146	523	4	that	that	SCONJ
ejpam-146	523	5	φ	φ	PROPN
ejpam-146	523	6	and	and	CCONJ
ejpam-146	523	7	ψ	ψ	PROPN
ejpam-146	523	8	has	have	VERB
ejpam-146	523	9	β	β	NOUN
ejpam-146	523	10	-	-	PUNCT
ejpam-146	523	11	θ	θ	NOUN
ejpam-146	523	12	-subclosed	-subclose	VERB
ejpam-146	523	13	graphs	graph	NOUN
ejpam-146	523	14	.	.	PUNCT
ejpam-146	524	1	let	let	VERB
ejpam-146	524	2	n	n	NOUN
ejpam-146	524	3	=	=	SYM
ejpam-146	524	4	(	(	PUNCT
ejpam-146	524	5	zµ)µ∈j	zµ)µ∈j	NUM
ejpam-146	524	6	be	be	AUX
ejpam-146	524	7	a	a	DET
ejpam-146	524	8	net	net	NOUN
ejpam-146	524	9	on	on	ADP
ejpam-146	524	10	z	z	PROPN
ejpam-146	524	11	−	−	PROPN
ejpam-146	524	12	{	{	PUNCT
ejpam-146	524	13	z	z	AUX
ejpam-146	524	14	}	}	PUNCT
ejpam-146	524	15	converging	converge	VERB
ejpam-146	524	16	z.	z.	NOUN
ejpam-146	524	17	if	if	SCONJ
ejpam-146	524	18	z	z	PROPN
ejpam-146	524	19	6=	6=	NUM
ejpam-146	525	1	x1	x1	PRON
ejpam-146	525	2	then	then	ADV
ejpam-146	525	3	n	n	NOUN
ejpam-146	525	4	=	=	SYM
ejpam-146	525	5	(	(	PUNCT
ejpam-146	525	6	zµ)µ∈j	zµ)µ∈j	NOUN
ejpam-146	525	7	can	can	AUX
ejpam-146	525	8	not	not	PART
ejpam-146	525	9	converge	converge	VERB
ejpam-146	525	10	to	to	ADP
ejpam-146	525	11	z	z	NOUN
ejpam-146	525	12	as	as	SCONJ
ejpam-146	525	13	{	{	PUNCT
ejpam-146	525	14	x1	x1	PROPN
ejpam-146	525	15	}	}	PUNCT
ejpam-146	525	16	is	be	AUX
ejpam-146	525	17	an	an	DET
ejpam-146	525	18	open	open	ADJ
ejpam-146	525	19	set	set	NOUN
ejpam-146	525	20	in	in	ADP
ejpam-146	525	21	(	(	PUNCT
ejpam-146	525	22	z	z	PROPN
ejpam-146	525	23	,	,	PUNCT
ejpam-146	525	24	τ	τ	PROPN
ejpam-146	525	25	?	?	PUNCT
ejpam-146	525	26	)	)	PUNCT
ejpam-146	525	27	—	—	PUNCT
ejpam-146	525	28	a	a	DET
ejpam-146	525	29	contradiction	contradiction	NOUN
ejpam-146	525	30	.	.	PUNCT
ejpam-146	526	1	so	so	ADV
ejpam-146	526	2	z	z	NOUN
ejpam-146	526	3	=	=	SYM
ejpam-146	526	4	x1	x1	PROPN
ejpam-146	526	5	.	.	PUNCT
ejpam-146	527	1	if	if	SCONJ
ejpam-146	527	2	possible	possible	ADJ
ejpam-146	527	3	,	,	PUNCT
ejpam-146	527	4	let	let	VERB
ejpam-146	527	5	ψ(n	ψ(n	NOUN
ejpam-146	527	6	)	)	PUNCT
ejpam-146	527	7	β	β	X
ejpam-146	527	8	-	-	PUNCT
ejpam-146	527	9	θ	θ	NOUN
ejpam-146	527	10	-adheres	-adhere	NOUN
ejpam-146	527	11	to	to	ADP
ejpam-146	527	12	some	some	DET
ejpam-146	527	13	point	point	NOUN
ejpam-146	527	14	,	,	PUNCT
ejpam-146	527	15	say	say	VERB
ejpam-146	527	16	z0	z0	PROPN
ejpam-146	527	17	∈	∈	PROPN
ejpam-146	527	18	z	z	NOUN
ejpam-146	528	1	=	=	PUNCT
ejpam-146	528	2	x	x	X
ejpam-146	528	3	.	.	PUNCT
ejpam-146	529	1	since	since	SCONJ
ejpam-146	529	2	ψ(s	ψ(s	PROPN
ejpam-146	529	3	)	)	PUNCT
ejpam-146	530	1	=	=	PUNCT
ejpam-146	530	2	s	s	PROPN
ejpam-146	530	3	has	have	VERB
ejpam-146	530	4	no	no	DET
ejpam-146	530	5	β	β	NOUN
ejpam-146	530	6	-	-	ADJ
ejpam-146	530	7	θ	θ	ADJ
ejpam-146	530	8	-adherent	-adherent	NOUN
ejpam-146	530	9	point	point	NOUN
ejpam-146	530	10	in	in	ADP
ejpam-146	530	11	x	x	SYM
ejpam-146	530	12	,	,	PUNCT
ejpam-146	530	13	there	there	PRON
ejpam-146	530	14	is	be	VERB
ejpam-146	530	15	a	a	DET
ejpam-146	530	16	r	r	NOUN
ejpam-146	530	17	∈	∈	PROPN
ejpam-146	530	18	βr(x	βr(x	NUM
ejpam-146	530	19	,	,	PUNCT
ejpam-146	530	20	z0	z0	PROPN
ejpam-146	530	21	)	)	PUNCT
ejpam-146	530	22	such	such	ADJ
ejpam-146	530	23	that	that	PRON
ejpam-146	530	24	tλ0	tλ0	PROPN
ejpam-146	530	25	=	=	PUNCT
ejpam-146	530	26	{	{	PUNCT
ejpam-146	530	27	xλ	xλ	NOUN
ejpam-146	530	28	:	:	PUNCT
ejpam-146	530	29	λ	λ	X
ejpam-146	530	30	≥	≥	NOUN
ejpam-146	530	31	λ0	λ0	NOUN
ejpam-146	530	32	}	}	PUNCT
ejpam-146	530	33	∩	∩	NOUN
ejpam-146	530	34	r	r	NOUN
ejpam-146	530	35	=	=	PUNCT
ejpam-146	530	36	;	;	PUNCT
ejpam-146	530	37	for	for	ADP
ejpam-146	530	38	some	some	DET
ejpam-146	530	39	λ0	λ0	NOUN
ejpam-146	530	40	∈	∈	NOUN
ejpam-146	530	41	i	i	PRON
ejpam-146	530	42	.	.	PUNCT
ejpam-146	531	1	since	since	SCONJ
ejpam-146	531	2	n	n	PRON
ejpam-146	531	3	converge	converge	VERB
ejpam-146	531	4	to	to	ADP
ejpam-146	531	5	x1	x1	PROPN
ejpam-146	531	6	and	and	CCONJ
ejpam-146	531	7	ψ(n	ψ(n	NUM
ejpam-146	531	8	)	)	PUNCT
ejpam-146	532	1	=	=	SYM
ejpam-146	532	2	n	n	X
ejpam-146	532	3	,	,	PUNCT
ejpam-146	532	4	then	then	ADV
ejpam-146	532	5	{	{	PUNCT
ejpam-146	532	6	zµ	zµ	X
ejpam-146	532	7	:	:	PUNCT
ejpam-146	532	8	µ	µ	DET
ejpam-146	532	9	≥	≥	NOUN
ejpam-146	532	10	µ1	µ1	PROPN
ejpam-146	532	11	}	}	PUNCT
ejpam-146	532	12	⊂	⊂	PROPN
ejpam-146	532	13	tλ0	tλ0	X
ejpam-146	532	14	∪	∪	X
ejpam-146	532	15	{	{	PUNCT
ejpam-146	532	16	x1	x1	PROPN
ejpam-146	532	17	}	}	PUNCT
ejpam-146	532	18	for	for	ADP
ejpam-146	532	19	some	some	DET
ejpam-146	532	20	µ1	µ1	PROPN
ejpam-146	532	21	∈	∈	PROPN
ejpam-146	532	22	j	j	PROPN
ejpam-146	532	23	.	.	PUNCT
ejpam-146	533	1	but	but	CCONJ
ejpam-146	533	2	as	as	SCONJ
ejpam-146	533	3	zβ	zβ	PROPN
ejpam-146	533	4	can	can	AUX
ejpam-146	533	5	not	not	PART
ejpam-146	533	6	be	be	AUX
ejpam-146	533	7	x1	x1	PROPN
ejpam-146	533	8	for	for	ADP
ejpam-146	533	9	any	any	DET
ejpam-146	533	10	µ	µ	PRON
ejpam-146	533	11	≥	≥	NOUN
ejpam-146	533	12	µ1	µ1	NOUN
ejpam-146	533	13	,	,	PUNCT
ejpam-146	533	14	so	so	CCONJ
ejpam-146	533	15	{	{	PUNCT
ejpam-146	533	16	ψ(zµ	ψ(zµ	X
ejpam-146	533	17	)	)	PUNCT
ejpam-146	533	18	:	:	PUNCT
ejpam-146	533	19	µ	µ	X
ejpam-146	533	20	≥	≥	NOUN
ejpam-146	533	21	µ1	µ1	PROPN
ejpam-146	533	22	}	}	PUNCT
ejpam-146	533	23	=	=	SYM
ejpam-146	533	24	{	{	PUNCT
ejpam-146	533	25	zµ	zµ	X
ejpam-146	533	26	:	:	PUNCT
ejpam-146	533	27	µ	µ	DET
ejpam-146	533	28	≥	≥	NOUN
ejpam-146	533	29	µ1	µ1	PROPN
ejpam-146	533	30	}	}	PUNCT
ejpam-146	533	31	⊂	⊂	PROPN
ejpam-146	533	32	tλ0	tλ0	PROPN
ejpam-146	533	33	⊂	⊂	X
ejpam-146	533	34	x	x	PUNCT
ejpam-146	533	35	−	−	PROPN
ejpam-146	533	36	r.	r.	NOUN
ejpam-146	533	37	so	so	ADV
ejpam-146	533	38	for	for	ADP
ejpam-146	533	39	this	this	DET
ejpam-146	533	40	r	r	NOUN
ejpam-146	533	41	∈	∈	PROPN
ejpam-146	533	42	βr(z	βr(z	PUNCT
ejpam-146	533	43	,	,	PUNCT
ejpam-146	533	44	z0	z0	PROPN
ejpam-146	533	45	)	)	PUNCT
ejpam-146	533	46	and	and	CCONJ
ejpam-146	533	47	for	for	ADP
ejpam-146	533	48	µ1	µ1	PROPN
ejpam-146	533	49	∈	∈	PROPN
ejpam-146	533	50	j	j	PROPN
ejpam-146	533	51	,	,	PUNCT
ejpam-146	533	52	there	there	PRON
ejpam-146	533	53	does	do	AUX
ejpam-146	533	54	not	not	PART
ejpam-146	533	55	exist	exist	VERB
ejpam-146	533	56	any	any	DET
ejpam-146	533	57	µ	µ	PROPN
ejpam-146	533	58	∈	∈	NOUN
ejpam-146	533	59	j	j	NOUN
ejpam-146	533	60	such	such	ADJ
ejpam-146	533	61	that	that	SCONJ
ejpam-146	533	62	µ	µ	PROPN
ejpam-146	533	63	>	>	X
ejpam-146	533	64	µ1	µ1	PROPN
ejpam-146	533	65	and	and	CCONJ
ejpam-146	533	66	zµ	zµ	ADP
ejpam-146	533	67	∈	∈	NOUN
ejpam-146	533	68	r	r	NOUN
ejpam-146	533	69	—	—	PUNCT
ejpam-146	533	70	a	a	DET
ejpam-146	533	71	contradiction	contradiction	NOUN
ejpam-146	533	72	.	.	PUNCT
ejpam-146	534	1	so	so	ADV
ejpam-146	534	2	ψ(n	ψ(n	PROPN
ejpam-146	534	3	)	)	PUNCT
ejpam-146	534	4	can	can	AUX
ejpam-146	534	5	not	not	PART
ejpam-146	534	6	β	β	VERB
ejpam-146	534	7	-	-	PUNCT
ejpam-146	534	8	θ	θ	NOUN
ejpam-146	534	9	-adhere	-adhere	NOUN
ejpam-146	534	10	to	to	ADP
ejpam-146	534	11	any	any	DET
ejpam-146	534	12	point	point	NOUN
ejpam-146	534	13	in	in	ADP
ejpam-146	534	14	x	x	X
ejpam-146	534	15	.	.	PUNCT
ejpam-146	535	1	hence	hence	ADV
ejpam-146	535	2	ψ	ψ	PRON
ejpam-146	535	3	has	have	VERB
ejpam-146	535	4	a	a	DET
ejpam-146	535	5	β	β	NOUN
ejpam-146	535	6	-	-	PUNCT
ejpam-146	535	7	θ	θ	NOUN
ejpam-146	535	8	-subclosed	-subclose	VERB
ejpam-146	535	9	graph	graph	NOUN
ejpam-146	535	10	.	.	PUNCT
ejpam-146	536	1	similarly	similarly	ADV
ejpam-146	536	2	,	,	PUNCT
ejpam-146	536	3	φ	φ	PROPN
ejpam-146	536	4	has	have	VERB
ejpam-146	536	5	also	also	ADV
ejpam-146	536	6	a	a	DET
ejpam-146	536	7	β	β	NOUN
ejpam-146	536	8	-	-	PUNCT
ejpam-146	536	9	θ	θ	NOUN
ejpam-146	536	10	-subclosed	-subclose	VERB
ejpam-146	536	11	graph	graph	NOUN
ejpam-146	536	12	.	.	PUNCT
ejpam-146	537	1	clearly	clearly	ADV
ejpam-146	537	2	,	,	PUNCT
ejpam-146	537	3	∆	∆	PROPN
ejpam-146	537	4	=	=	PUNCT
ejpam-146	537	5	x	x	SYM
ejpam-146	537	6	−	−	PROPN
ejpam-146	537	7	{	{	PUNCT
ejpam-146	537	8	x1	x1	PROPN
ejpam-146	537	9	}	}	PUNCT
ejpam-146	537	10	as	as	ADP
ejpam-146	537	11	φ(x1	φ(x1	NOUN
ejpam-146	537	12	)	)	PUNCT
ejpam-146	537	13	=	=	SYM
ejpam-146	538	1	x1	x1	PROPN
ejpam-146	538	2	6=	6=	NUM
ejpam-146	538	3	x0	x0	PROPN
ejpam-146	538	4	=	=	SYM
ejpam-146	538	5	ψ(x1	ψ(x1	PROPN
ejpam-146	538	6	)	)	PUNCT
ejpam-146	538	7	.	.	PUNCT
ejpam-146	539	1	but	but	CCONJ
ejpam-146	539	2	x1	x1	PROPN
ejpam-146	539	3	is	be	AUX
ejpam-146	539	4	a	a	DET
ejpam-146	539	5	limit	limit	NOUN
ejpam-146	539	6	point	point	NOUN
ejpam-146	539	7	of	of	ADP
ejpam-146	539	8	∆	∆	PROPN
ejpam-146	539	9	in	in	ADP
ejpam-146	539	10	z	z	PROPN
ejpam-146	539	11	.	.	PUNCT
ejpam-146	540	1	so	so	ADV
ejpam-146	540	2	,	,	PUNCT
ejpam-146	540	3	∆	∆	PROPN
ejpam-146	540	4	is	be	AUX
ejpam-146	540	5	not	not	PART
ejpam-146	540	6	closed	close	VERB
ejpam-146	540	7	in	in	ADP
ejpam-146	540	8	z	z	NOUN
ejpam-146	540	9	—	—	PUNCT
ejpam-146	540	10	a	a	DET
ejpam-146	540	11	contradiction	contradiction	NOUN
ejpam-146	540	12	.	.	PUNCT
ejpam-146	541	1	hence	hence	ADV
ejpam-146	541	2	x	x	PUNCT
ejpam-146	541	3	is	be	AUX
ejpam-146	541	4	β	β	NOUN
ejpam-146	541	5	-	-	VERB
ejpam-146	541	6	closed	closed	ADJ
ejpam-146	541	7	.	.	PUNCT
ejpam-146	542	1	conversely	conversely	ADV
ejpam-146	542	2	,	,	PUNCT
ejpam-146	542	3	let	let	VERB
ejpam-146	542	4	x	x	PRON
ejpam-146	542	5	be	be	AUX
ejpam-146	542	6	β	β	X
ejpam-146	542	7	-	-	VERB
ejpam-146	542	8	closed	closed	ADJ
ejpam-146	542	9	.	.	PUNCT
ejpam-146	543	1	then	then	ADV
ejpam-146	543	2	by	by	ADP
ejpam-146	543	3	the	the	DET
ejpam-146	543	4	theorem	theorem	NOUN
ejpam-146	543	5	4.13	4.13	NUM
ejpam-146	543	6	,	,	PUNCT
ejpam-146	543	7	for	for	ADP
ejpam-146	543	8	any	any	DET
ejpam-146	543	9	space	space	NOUN
ejpam-146	543	10	z	z	NOUN
ejpam-146	543	11	and	and	CCONJ
ejpam-146	543	12	any	any	DET
ejpam-146	543	13	funcreferences	funcreference	NOUN
ejpam-146	543	14	50	50	NUM
ejpam-146	543	15	tions	tion	NOUN
ejpam-146	543	16	φ	φ	PROPN
ejpam-146	543	17	,	,	PUNCT
ejpam-146	543	18	ψ	ψ	X
ejpam-146	543	19	:	:	PUNCT
ejpam-146	543	20	z	z	X
ejpam-146	543	21	→	→	SYM
ejpam-146	543	22	x	x	X
ejpam-146	543	23	with	with	ADP
ejpam-146	543	24	β	β	X
ejpam-146	543	25	-	-	PUNCT
ejpam-146	543	26	θ	θ	NOUN
ejpam-146	543	27	-subclosed	-subclose	VERB
ejpam-146	543	28	graphs	graph	NOUN
ejpam-146	543	29	,	,	PUNCT
ejpam-146	543	30	the	the	DET
ejpam-146	543	31	set	set	ADJ
ejpam-146	543	32	d(φ	d(φ	PROPN
ejpam-146	543	33	,	,	PUNCT
ejpam-146	543	34	ψ	ψ	NOUN
ejpam-146	543	35	)	)	PUNCT
ejpam-146	543	36	=	=	SYM
ejpam-146	543	37	{	{	PUNCT
ejpam-146	543	38	(	(	PUNCT
ejpam-146	543	39	z1	z1	PROPN
ejpam-146	543	40	,	,	PUNCT
ejpam-146	543	41	z2	z2	NUM
ejpam-146	543	42	)	)	PUNCT
ejpam-146	543	43	∈	∈	PROPN
ejpam-146	543	44	z	z	NOUN
ejpam-146	543	45	×	×	PROPN
ejpam-146	543	46	z	z	NOUN
ejpam-146	543	47	:	:	PUNCT
ejpam-146	543	48	φ(z1	φ(z1	ADJ
ejpam-146	543	49	)	)	PUNCT
ejpam-146	543	50	=	=	SYM
ejpam-146	543	51	φ(z2	φ(z2	NOUN
ejpam-146	543	52	)	)	PUNCT
ejpam-146	543	53	}	}	PUNCT
ejpam-146	543	54	is	be	AUX
ejpam-146	543	55	closed	close	VERB
ejpam-146	543	56	in	in	ADP
ejpam-146	543	57	z	z	PROPN
ejpam-146	543	58	×	×	PROPN
ejpam-146	543	59	z	z	NOUN
ejpam-146	543	60	.	.	PUNCT
ejpam-146	544	1	let	let	VERB
ejpam-146	544	2	π1	π1	NOUN
ejpam-146	544	3	:	:	PUNCT
ejpam-146	544	4	z	z	NOUN
ejpam-146	544	5	×	×	NOUN
ejpam-146	544	6	z	z	PROPN
ejpam-146	544	7	→	→	SYM
ejpam-146	544	8	z	z	X
ejpam-146	544	9	be	be	AUX
ejpam-146	544	10	the	the	DET
ejpam-146	544	11	first	first	ADJ
ejpam-146	544	12	projection	projection	NOUN
ejpam-146	544	13	and	and	CCONJ
ejpam-146	544	14	∆z	∆z	NOUN
ejpam-146	544	15	be	be	VERB
ejpam-146	544	16	the	the	DET
ejpam-146	544	17	diagonal	diagonal	ADJ
ejpam-146	544	18	in	in	ADP
ejpam-146	544	19	z	z	PROPN
ejpam-146	544	20	×	×	PROPN
ejpam-146	544	21	z	z	NOUN
ejpam-146	544	22	.	.	PUNCT
ejpam-146	545	1	since	since	SCONJ
ejpam-146	545	2	π1/∆z	π1/∆z	PROPN
ejpam-146	545	3	is	be	AUX
ejpam-146	545	4	a	a	DET
ejpam-146	545	5	homeomorphism	homeomorphism	NOUN
ejpam-146	545	6	,	,	PUNCT
ejpam-146	545	7	then	then	ADV
ejpam-146	545	8	∆=	∆=	VERB
ejpam-146	545	9	π1[d(φ	π1[d(φ	NUM
ejpam-146	545	10	,	,	PUNCT
ejpam-146	545	11	ψ)∩∆z	ψ)∩∆z	NOUN
ejpam-146	545	12	]	]	PUNCT
ejpam-146	545	13	is	be	AUX
ejpam-146	545	14	closed	close	VERB
ejpam-146	545	15	in	in	ADP
ejpam-146	545	16	z	z	PROPN
ejpam-146	545	17	.	.	PUNCT
ejpam-146	546	1	acknowledgement	acknowledgement	NOUN
ejpam-146	546	2	the	the	DET
ejpam-146	546	3	authors	author	NOUN
ejpam-146	546	4	gratefully	gratefully	ADV
ejpam-146	546	5	acknowledge	acknowledge	VERB
ejpam-146	546	6	the	the	DET
ejpam-146	546	7	suggestions	suggestion	NOUN
ejpam-146	546	8	of	of	ADP
ejpam-146	546	9	the	the	DET
ejpam-146	546	10	learned	learn	VERB
ejpam-146	546	11	referee	referee	NOUN
ejpam-146	546	12	towards	towards	ADP
ejpam-146	546	13	the	the	DET
ejpam-146	546	14	improvement	improvement	NOUN
ejpam-146	546	15	of	of	ADP
ejpam-146	546	16	the	the	DET
ejpam-146	546	17	paper	paper	NOUN
ejpam-146	546	18	.	.	PUNCT
ejpam-146	547	1	references	reference	NOUN
ejpam-146	547	2	[	[	X
ejpam-146	547	3	1	1	NUM
ejpam-146	547	4	]	]	PUNCT
ejpam-146	547	5	m.	m.	PROPN
ejpam-146	547	6	e.	e.	PROPN
ejpam-146	547	7	abd	abd	PROPN
ejpam-146	547	8	.	.	PUNCT
ejpam-146	548	1	el	el	PROPN
ejpam-146	548	2	.	.	PROPN
ejpam-146	548	3	monsef	monsef	PROPN
ejpam-146	548	4	,	,	PUNCT
ejpam-146	548	5	s.	s.	PROPN
ejpam-146	548	6	n.	n.	PROPN
ejpam-146	548	7	el	el	PROPN
ejpam-146	548	8	-	-	PUNCT
ejpam-146	548	9	deeb	deeb	PROPN
ejpam-146	548	10	and	and	CCONJ
ejpam-146	548	11	r.	r.	PROPN
ejpam-146	548	12	a.	a.	PROPN
ejpam-146	548	13	mahmoud	mahmoud	PROPN
ejpam-146	548	14	,	,	PUNCT
ejpam-146	548	15	β	β	ADJ
ejpam-146	548	16	-	-	ADJ
ejpam-146	548	17	open	open	ADJ
ejpam-146	548	18	sets	set	NOUN
ejpam-146	548	19	and	and	CCONJ
ejpam-146	548	20	β	β	NOUN
ejpam-146	548	21	-	-	ADJ
ejpam-146	548	22	contnuous	contnuous	ADJ
ejpam-146	548	23	mappings	mapping	NOUN
ejpam-146	548	24	,	,	PUNCT
ejpam-146	548	25	bull	bull	NOUN
ejpam-146	548	26	.	.	PUNCT
ejpam-146	549	1	fac	fac	PROPN
ejpam-146	549	2	.	.	PUNCT
ejpam-146	550	1	sci	sci	PROPN
ejpam-146	550	2	.	.	PUNCT
ejpam-146	550	3	assiut	assiut	PROPN
ejpam-146	550	4	univ	univ	PROPN
ejpam-146	550	5	.	.	PROPN
ejpam-146	550	6	,	,	PUNCT
ejpam-146	550	7	12(1	12(1	NUM
ejpam-146	550	8	)	)	PUNCT
ejpam-146	550	9	(	(	PUNCT
ejpam-146	550	10	1983	1983	NUM
ejpam-146	550	11	)	)	PUNCT
ejpam-146	550	12	,	,	PUNCT
ejpam-146	550	13	77	77	NUM
ejpam-146	550	14	-	-	SYM
ejpam-146	550	15	90	90	NUM
ejpam-146	550	16	.	.	PUNCT
ejpam-146	551	1	[	[	X
ejpam-146	551	2	2	2	NUM
ejpam-146	551	3	]	]	PUNCT
ejpam-146	551	4	m.	m.	PROPN
ejpam-146	551	5	e.	e.	PROPN
ejpam-146	551	6	abd	abd	PROPN
ejpam-146	551	7	.	.	PUNCT
ejpam-146	552	1	el	el	PROPN
ejpam-146	552	2	.	.	PROPN
ejpam-146	552	3	monsef	monsef	PROPN
ejpam-146	552	4	,	,	PUNCT
ejpam-146	552	5	a.	a.	NOUN
ejpam-146	552	6	m.	m.	NOUN
ejpam-146	552	7	kozae	kozae	PROPN
ejpam-146	552	8	,	,	PUNCT
ejpam-146	552	9	some	some	DET
ejpam-146	552	10	generalized	generalized	ADJ
ejpam-146	552	11	forms	form	NOUN
ejpam-146	552	12	of	of	ADP
ejpam-146	552	13	compactness	compactness	NOUN
ejpam-146	552	14	and	and	CCONJ
ejpam-146	552	15	closedness	closedness	NOUN
ejpam-146	552	16	,	,	PUNCT
ejpam-146	552	17	delta	delta	PROPN
ejpam-146	552	18	j.	j.	PROPN
ejpam-146	552	19	sci	sci	PROPN
ejpam-146	552	20	.	.	PUNCT
ejpam-146	553	1	9(2	9(2	NUM
ejpam-146	553	2	)	)	PUNCT
ejpam-146	553	3	,	,	PUNCT
ejpam-146	553	4	1985	1985	NUM
ejpam-146	553	5	,	,	PUNCT
ejpam-146	553	6	257	257	NUM
ejpam-146	553	7	-	-	SYM
ejpam-146	553	8	269	269	NUM
ejpam-146	553	9	.	.	PUNCT
ejpam-146	554	1	[	[	X
ejpam-146	554	2	3	3	X
ejpam-146	554	3	]	]	PUNCT
ejpam-146	554	4	t.	t.	PROPN
ejpam-146	554	5	aho	aho	PROPN
ejpam-146	554	6	and	and	CCONJ
ejpam-146	554	7	t.	t.	PROPN
ejpam-146	554	8	nieminen	nieminen	PROPN
ejpam-146	554	9	,	,	PUNCT
ejpam-146	554	10	spaces	space	VERB
ejpam-146	554	11	in	in	ADP
ejpam-146	554	12	which	which	PRON
ejpam-146	554	13	preopen	preopen	ADJ
ejpam-146	554	14	subsets	subset	NOUN
ejpam-146	554	15	are	be	AUX
ejpam-146	554	16	semiopen	semiopen	ADJ
ejpam-146	554	17	,	,	PUNCT
ejpam-146	554	18	ricerche	ricerche	X
ejpam-146	554	19	mat	mat	PROPN
ejpam-146	554	20	.	.	PROPN
ejpam-146	554	21	,	,	PUNCT
ejpam-146	554	22	43	43	NUM
ejpam-146	554	23	(	(	PUNCT
ejpam-146	554	24	1994	1994	NUM
ejpam-146	554	25	)	)	PUNCT
ejpam-146	554	26	,	,	PUNCT
ejpam-146	554	27	45	45	NUM
ejpam-146	554	28	-	-	SYM
ejpam-146	554	29	59	59	NUM
ejpam-146	554	30	.	.	PUNCT
ejpam-146	555	1	[	[	X
ejpam-146	555	2	4	4	X
ejpam-146	555	3	]	]	X
ejpam-146	555	4	d.	d.	PROPN
ejpam-146	555	5	andrijević	andrijević	PROPN
ejpam-146	555	6	,	,	PUNCT
ejpam-146	555	7	semi	semi	ADJ
ejpam-146	555	8	-	-	ADJ
ejpam-146	555	9	preopen	preopen	ADJ
ejpam-146	555	10	sets	set	NOUN
ejpam-146	555	11	,	,	PUNCT
ejpam-146	555	12	math	math	NOUN
ejpam-146	555	13	.	.	PUNCT
ejpam-146	556	1	vesnik	vesnik	PROPN
ejpam-146	556	2	,	,	PUNCT
ejpam-146	556	3	38	38	NUM
ejpam-146	556	4	(	(	PUNCT
ejpam-146	556	5	1986	1986	NUM
ejpam-146	556	6	)	)	PUNCT
ejpam-146	556	7	,	,	PUNCT
ejpam-146	556	8	24	24	NUM
ejpam-146	556	9	-	-	SYM
ejpam-146	556	10	32	32	NUM
ejpam-146	556	11	.	.	PUNCT
ejpam-146	557	1	[	[	X
ejpam-146	557	2	5	5	X
ejpam-146	557	3	]	]	X
ejpam-146	557	4	d.	d.	PROPN
ejpam-146	557	5	andrijević	andrijević	PROPN
ejpam-146	557	6	,	,	PUNCT
ejpam-146	557	7	on	on	ADP
ejpam-146	557	8	b	b	X
ejpam-146	557	9	-	-	PUNCT
ejpam-146	557	10	open	open	ADJ
ejpam-146	557	11	sets	set	NOUN
ejpam-146	557	12	,	,	PUNCT
ejpam-146	557	13	math	math	NOUN
ejpam-146	557	14	.	.	PUNCT
ejpam-146	558	1	vesnik	vesnik	PROPN
ejpam-146	558	2	,	,	PUNCT
ejpam-146	558	3	48	48	NUM
ejpam-146	558	4	(	(	PUNCT
ejpam-146	558	5	1996	1996	NUM
ejpam-146	558	6	)	)	PUNCT
ejpam-146	558	7	,	,	PUNCT
ejpam-146	558	8	59	59	NUM
ejpam-146	558	9	-	-	SYM
ejpam-146	558	10	64	64	NUM
ejpam-146	558	11	.	.	PUNCT
ejpam-146	559	1	[	[	X
ejpam-146	559	2	6	6	NUM
ejpam-146	559	3	]	]	X
ejpam-146	559	4	y.	y.	NOUN
ejpam-146	559	5	beceren	beceren	PROPN
ejpam-146	559	6	and	and	CCONJ
ejpam-146	559	7	t.	t.	PROPN
ejpam-146	559	8	noiri	noiri	PROPN
ejpam-146	559	9	,	,	PUNCT
ejpam-146	559	10	some	some	DET
ejpam-146	559	11	functions	function	NOUN
ejpam-146	559	12	defined	define	VERB
ejpam-146	559	13	by	by	ADP
ejpam-146	559	14	semi	semi	ADJ
ejpam-146	559	15	-	-	ADJ
ejpam-146	559	16	open	open	ADJ
ejpam-146	559	17	and	and	CCONJ
ejpam-146	559	18	β	β	ADJ
ejpam-146	559	19	-	-	ADJ
ejpam-146	559	20	open	open	ADJ
ejpam-146	559	21	sets	set	NOUN
ejpam-146	559	22	,	,	PUNCT
ejpam-146	559	23	chaos	chaos	NOUN
ejpam-146	559	24	solitons	soliton	NOUN
ejpam-146	559	25	and	and	CCONJ
ejpam-146	559	26	fractals	fractal	NOUN
ejpam-146	559	27	,	,	PUNCT
ejpam-146	559	28	36	36	NUM
ejpam-146	559	29	(	(	PUNCT
ejpam-146	559	30	2008	2008	NUM
ejpam-146	559	31	)	)	PUNCT
ejpam-146	559	32	,	,	PUNCT
ejpam-146	559	33	1225	1225	NUM
ejpam-146	559	34	-	-	SYM
ejpam-146	559	35	1231	1231	NUM
ejpam-146	559	36	.	.	PUNCT
ejpam-146	560	1	[	[	X
ejpam-146	560	2	7	7	X
ejpam-146	560	3	]	]	X
ejpam-146	560	4	n.	n.	NOUN
ejpam-146	560	5	bourbaki	bourbaki	PROPN
ejpam-146	560	6	,	,	PUNCT
ejpam-146	560	7	elements	element	NOUN
ejpam-146	560	8	of	of	ADP
ejpam-146	560	9	mathemtics	mathemtic	NOUN
ejpam-146	560	10	,	,	PUNCT
ejpam-146	560	11	general	general	ADJ
ejpam-146	560	12	topology	topology	NOUN
ejpam-146	560	13	reading	reading	NOUN
ejpam-146	560	14	,	,	PUNCT
ejpam-146	560	15	ma	ma	PROPN
ejpam-146	560	16	,	,	PUNCT
ejpam-146	560	17	paris	paris	PROPN
ejpam-146	560	18	:	:	PUNCT
ejpam-146	560	19	hermann	hermann	PROPN
ejpam-146	560	20	,	,	PUNCT
ejpam-146	560	21	addition	addition	NOUN
ejpam-146	560	22	-	-	PUNCT
ejpam-146	560	23	wesley	wesley	PROPN
ejpam-146	560	24	publishing	publishing	PROPN
ejpam-146	560	25	co.	co.	PROPN
ejpam-146	560	26	,	,	PUNCT
ejpam-146	560	27	1961	1961	NUM
ejpam-146	560	28	,	,	PUNCT
ejpam-146	560	29	part	part	NOUN
ejpam-146	560	30	-	-	PUNCT
ejpam-146	560	31	i.	i.	NOUN
ejpam-146	560	32	[	[	X
ejpam-146	560	33	8	8	NUM
ejpam-146	560	34	]	]	PUNCT
ejpam-146	560	35	j.	j.	PROPN
ejpam-146	560	36	dontchev	dontchev	PROPN
ejpam-146	560	37	,	,	PUNCT
ejpam-146	560	38	m.	m.	NOUN
ejpam-146	560	39	ganster	ganster	NOUN
ejpam-146	560	40	and	and	CCONJ
ejpam-146	560	41	t.	t.	PROPN
ejpam-146	560	42	noiri	noiri	PROPN
ejpam-146	560	43	,	,	PUNCT
ejpam-146	560	44	on	on	ADP
ejpam-146	560	45	p	p	NOUN
ejpam-146	560	46	-	-	PUNCT
ejpam-146	560	47	closed	closed	ADJ
ejpam-146	560	48	spaces	space	NOUN
ejpam-146	560	49	,	,	PUNCT
ejpam-146	560	50	internat	internat	PROPN
ejpam-146	560	51	.	.	PUNCT
ejpam-146	561	1	jour	jour	PROPN
ejpam-146	561	2	.	.	PUNCT
ejpam-146	561	3	math	math	PROPN
ejpam-146	561	4	.	.	PUNCT
ejpam-146	562	1	math	math	NOUN
ejpam-146	562	2	.	.	PUNCT
ejpam-146	563	1	sci	sci	PROPN
ejpam-146	563	2	.	.	PROPN
ejpam-146	563	3	24	24	NUM
ejpam-146	563	4	(	(	PUNCT
ejpam-146	563	5	2000	2000	NUM
ejpam-146	563	6	)	)	PUNCT
ejpam-146	563	7	,	,	PUNCT
ejpam-146	563	8	203	203	NUM
ejpam-146	563	9	-	-	SYM
ejpam-146	563	10	212	212	NUM
ejpam-146	563	11	.	.	PUNCT
ejpam-146	564	1	[	[	X
ejpam-146	564	2	9	9	NUM
ejpam-146	564	3	]	]	PUNCT
ejpam-146	564	4	z.	z.	PROPN
ejpam-146	564	5	duszynski	duszynski	PROPN
ejpam-146	564	6	,	,	PUNCT
ejpam-146	564	7	on	on	ADP
ejpam-146	564	8	some	some	DET
ejpam-146	564	9	concepts	concept	NOUN
ejpam-146	564	10	of	of	ADP
ejpam-146	564	11	weak	weak	ADJ
ejpam-146	564	12	connectedness	connectedness	NOUN
ejpam-146	564	13	of	of	ADP
ejpam-146	564	14	topological	topological	ADJ
ejpam-146	564	15	spaces	space	NOUN
ejpam-146	564	16	,	,	PUNCT
ejpam-146	564	17	acta	acta	PROPN
ejpam-146	564	18	.	.	PUNCT
ejpam-146	564	19	math	math	NOUN
ejpam-146	564	20	.	.	PUNCT
ejpam-146	565	1	hungar	hungar	PROPN
ejpam-146	565	2	.	.	PUNCT
ejpam-146	565	3	,	,	PUNCT
ejpam-146	565	4	110(1	110(1	NUM
ejpam-146	565	5	-	-	SYM
ejpam-146	565	6	2	2	NUM
ejpam-146	565	7	)	)	PUNCT
ejpam-146	565	8	,	,	PUNCT
ejpam-146	565	9	2006	2006	NUM
ejpam-146	565	10	,	,	PUNCT
ejpam-146	565	11	81	81	NUM
ejpam-146	565	12	-	-	SYM
ejpam-146	565	13	90	90	NUM
ejpam-146	565	14	.	.	PUNCT
ejpam-146	566	1	[	[	X
ejpam-146	566	2	10	10	NUM
ejpam-146	566	3	]	]	X
ejpam-146	566	4	s.	s.	PROPN
ejpam-146	566	5	jafari	jafari	PROPN
ejpam-146	566	6	and	and	CCONJ
ejpam-146	566	7	t.	t.	PROPN
ejpam-146	566	8	noiri	noiri	PROPN
ejpam-146	566	9	,	,	PUNCT
ejpam-146	566	10	properties	property	NOUN
ejpam-146	566	11	of	of	ADP
ejpam-146	566	12	β	β	NOUN
ejpam-146	566	13	-	-	ADJ
ejpam-146	566	14	connected	connected	ADJ
ejpam-146	566	15	spaces	space	NOUN
ejpam-146	566	16	,	,	PUNCT
ejpam-146	566	17	acta	acta	PROPN
ejpam-146	566	18	math	math	PROPN
ejpam-146	566	19	.	.	PUNCT
ejpam-146	567	1	hungar	hungar	PROPN
ejpam-146	567	2	.	.	PUNCT
ejpam-146	567	3	,	,	PUNCT
ejpam-146	567	4	101	101	NUM
ejpam-146	567	5	(	(	PUNCT
ejpam-146	567	6	3)(2003	3)(2003	NUM
ejpam-146	567	7	)	)	PUNCT
ejpam-146	567	8	,	,	PUNCT
ejpam-146	567	9	227	227	NUM
ejpam-146	567	10	-	-	SYM
ejpam-146	567	11	236	236	NUM
ejpam-146	567	12	.	.	PUNCT
ejpam-146	568	1	[	[	X
ejpam-146	568	2	11	11	NUM
ejpam-146	568	3	]	]	PUNCT
ejpam-146	568	4	j.	j.	PROPN
ejpam-146	568	5	e.	e.	PROPN
ejpam-146	568	6	joseph	joseph	PROPN
ejpam-146	568	7	and	and	CCONJ
ejpam-146	568	8	m.	m.	PROPN
ejpam-146	568	9	h.	h.	PROPN
ejpam-146	568	10	kwack	kwack	PROPN
ejpam-146	568	11	,	,	PUNCT
ejpam-146	568	12	on	on	ADP
ejpam-146	568	13	s	s	ADJ
ejpam-146	568	14	-	-	PUNCT
ejpam-146	568	15	closed	closed	ADJ
ejpam-146	568	16	spaces	space	NOUN
ejpam-146	568	17	,	,	PUNCT
ejpam-146	568	18	proc	proc	NOUN
ejpam-146	568	19	.	.	PUNCT
ejpam-146	569	1	amer	amer	PROPN
ejpam-146	569	2	.	.	PUNCT
ejpam-146	569	3	math	math	PROPN
ejpam-146	569	4	.	.	PUNCT
ejpam-146	570	1	soc	soc	PROPN
ejpam-146	570	2	.	.	PUNCT
ejpam-146	571	1	,	,	PUNCT
ejpam-146	571	2	80	80	NUM
ejpam-146	571	3	(	(	PUNCT
ejpam-146	571	4	1980	1980	NUM
ejpam-146	571	5	)	)	PUNCT
ejpam-146	571	6	,	,	PUNCT
ejpam-146	571	7	341	341	NUM
ejpam-146	571	8	-	-	SYM
ejpam-146	571	9	348	348	NUM
ejpam-146	571	10	.	.	PUNCT
ejpam-146	572	1	[	[	X
ejpam-146	572	2	12	12	NUM
ejpam-146	572	3	]	]	X
ejpam-146	572	4	n.	n.	PROPN
ejpam-146	572	5	levine	levine	PROPN
ejpam-146	572	6	,	,	PUNCT
ejpam-146	572	7	semi	semi	ADJ
ejpam-146	572	8	-	-	ADJ
ejpam-146	572	9	open	open	ADJ
ejpam-146	572	10	sets	set	NOUN
ejpam-146	572	11	and	and	CCONJ
ejpam-146	572	12	semi	semi	ADJ
ejpam-146	572	13	-	-	NOUN
ejpam-146	572	14	continuity	continuity	NOUN
ejpam-146	572	15	in	in	ADP
ejpam-146	572	16	topological	topological	ADJ
ejpam-146	572	17	spaces	space	NOUN
ejpam-146	572	18	,	,	PUNCT
ejpam-146	572	19	amer	amer	PROPN
ejpam-146	572	20	.	.	PROPN
ejpam-146	572	21	math	math	PROPN
ejpam-146	572	22	.	.	PUNCT
ejpam-146	573	1	monthly	monthly	ADJ
ejpam-146	573	2	70	70	NUM
ejpam-146	573	3	(	(	PUNCT
ejpam-146	573	4	1963	1963	NUM
ejpam-146	573	5	)	)	PUNCT
ejpam-146	573	6	,	,	PUNCT
ejpam-146	573	7	36	36	NUM
ejpam-146	573	8	-	-	SYM
ejpam-146	573	9	41	41	NUM
ejpam-146	573	10	.	.	PUNCT
ejpam-146	574	1	[	[	X
ejpam-146	574	2	13	13	NUM
ejpam-146	574	3	]	]	X
ejpam-146	574	4	g.	g.	PROPN
ejpam-146	574	5	di	di	PROPN
ejpam-146	574	6	maio	maio	PROPN
ejpam-146	574	7	and	and	CCONJ
ejpam-146	574	8	t.	t.	PROPN
ejpam-146	574	9	noiri	noiri	PROPN
ejpam-146	574	10	,	,	PUNCT
ejpam-146	574	11	on	on	ADP
ejpam-146	574	12	s	s	ADJ
ejpam-146	574	13	-	-	PUNCT
ejpam-146	574	14	closed	closed	ADJ
ejpam-146	574	15	spaces	space	NOUN
ejpam-146	574	16	,	,	PUNCT
ejpam-146	574	17	ind	ind	PROPN
ejpam-146	574	18	.	.	PUNCT
ejpam-146	575	1	j.	j.	PROPN
ejpam-146	575	2	pure	pure	PROPN
ejpam-146	575	3	appl	appl	PROPN
ejpam-146	575	4	.	.	PUNCT
ejpam-146	575	5	math	math	NOUN
ejpam-146	575	6	.	.	PUNCT
ejpam-146	576	1	18	18	NUM
ejpam-146	576	2	(	(	PUNCT
ejpam-146	576	3	3	3	NUM
ejpam-146	576	4	)	)	PUNCT
ejpam-146	576	5	(	(	PUNCT
ejpam-146	576	6	1987	1987	NUM
ejpam-146	576	7	)	)	PUNCT
ejpam-146	576	8	,	,	PUNCT
ejpam-146	576	9	226	226	NUM
ejpam-146	576	10	-	-	SYM
ejpam-146	576	11	233	233	NUM
ejpam-146	576	12	.	.	PUNCT
ejpam-146	577	1	[	[	X
ejpam-146	577	2	14	14	NUM
ejpam-146	577	3	]	]	PUNCT
ejpam-146	577	4	a.	a.	NOUN
ejpam-146	577	5	s.	s.	PROPN
ejpam-146	577	6	mashhour	mashhour	PROPN
ejpam-146	577	7	,	,	PUNCT
ejpam-146	577	8	m.	m.	PROPN
ejpam-146	577	9	e.	e.	PROPN
ejpam-146	577	10	abd	abd	PROPN
ejpam-146	577	11	el	el	PROPN
ejpam-146	577	12	-	-	PROPN
ejpam-146	577	13	monsef	monsef	PROPN
ejpam-146	577	14	and	and	CCONJ
ejpam-146	577	15	s.	s.	PROPN
ejpam-146	577	16	n.	n.	PROPN
ejpam-146	577	17	el	el	PROPN
ejpam-146	577	18	-	-	PROPN
ejpam-146	577	19	deeb	deeb	PROPN
ejpam-146	577	20	,	,	PUNCT
ejpam-146	577	21	on	on	ADP
ejpam-146	577	22	precontinuous	precontinuous	ADJ
ejpam-146	577	23	and	and	CCONJ
ejpam-146	577	24	weak	weak	ADJ
ejpam-146	577	25	precontinuous	precontinuous	ADJ
ejpam-146	577	26	mappings	mapping	NOUN
ejpam-146	577	27	,	,	PUNCT
ejpam-146	577	28	proc	proc	NOUN
ejpam-146	577	29	.	.	PUNCT
ejpam-146	578	1	math	math	NOUN
ejpam-146	578	2	.	.	PUNCT
ejpam-146	579	1	phys	phy	NOUN
ejpam-146	579	2	.	.	PUNCT
ejpam-146	580	1	soc	soc	PROPN
ejpam-146	580	2	.	.	PUNCT
ejpam-146	581	1	egypt	egypt	PROPN
ejpam-146	581	2	,	,	PUNCT
ejpam-146	581	3	53	53	NUM
ejpam-146	581	4	(	(	PUNCT
ejpam-146	581	5	1982	1982	NUM
ejpam-146	581	6	)	)	PUNCT
ejpam-146	581	7	,	,	PUNCT
ejpam-146	581	8	47	47	NUM
ejpam-146	581	9	-	-	SYM
ejpam-146	581	10	53	53	NUM
ejpam-146	581	11	.	.	PUNCT
ejpam-146	582	1	[	[	X
ejpam-146	582	2	15	15	NUM
ejpam-146	582	3	]	]	X
ejpam-146	582	4	o.	o.	PROPN
ejpam-146	582	5	njastad	njastad	PROPN
ejpam-146	582	6	,	,	PUNCT
ejpam-146	582	7	on	on	ADP
ejpam-146	582	8	some	some	DET
ejpam-146	582	9	classes	class	NOUN
ejpam-146	582	10	of	of	ADP
ejpam-146	582	11	nearly	nearly	ADV
ejpam-146	582	12	open	open	ADJ
ejpam-146	582	13	sets	set	NOUN
ejpam-146	582	14	,	,	PUNCT
ejpam-146	582	15	pacific	pacific	PROPN
ejpam-146	582	16	jour	jour	PROPN
ejpam-146	582	17	.	.	PUNCT
ejpam-146	582	18	math	math	PROPN
ejpam-146	582	19	.	.	PUNCT
ejpam-146	582	20	,	,	PUNCT
ejpam-146	582	21	15	15	NUM
ejpam-146	582	22	(	(	PUNCT
ejpam-146	582	23	1965	1965	NUM
ejpam-146	582	24	)	)	PUNCT
ejpam-146	582	25	,	,	PUNCT
ejpam-146	582	26	961	961	NUM
ejpam-146	582	27	-	-	SYM
ejpam-146	582	28	970	970	NUM
ejpam-146	582	29	.	.	PUNCT
ejpam-146	583	1	[	[	X
ejpam-146	583	2	16	16	NUM
ejpam-146	583	3	]	]	PUNCT
ejpam-146	583	4	t.	t.	PROPN
ejpam-146	583	5	noiri	noiri	PROPN
ejpam-146	583	6	,	,	PUNCT
ejpam-146	583	7	weak	weak	ADJ
ejpam-146	583	8	and	and	CCONJ
ejpam-146	583	9	strong	strong	ADJ
ejpam-146	583	10	forms	form	NOUN
ejpam-146	583	11	of	of	ADP
ejpam-146	583	12	β	β	NOUN
ejpam-146	583	13	-	-	PUNCT
ejpam-146	583	14	irresolute	irresolute	ADJ
ejpam-146	583	15	functions	function	NOUN
ejpam-146	583	16	,	,	PUNCT
ejpam-146	583	17	acta	acta	PROPN
ejpam-146	583	18	math	math	PROPN
ejpam-146	583	19	.	.	PUNCT
ejpam-146	584	1	hungar	hungar	PROPN
ejpam-146	584	2	.	.	PUNCT
ejpam-146	585	1	,	,	PUNCT
ejpam-146	585	2	99	99	NUM
ejpam-146	585	3	,	,	PUNCT
ejpam-146	585	4	no	no	INTJ
ejpam-146	585	5	.	.	NOUN
ejpam-146	585	6	4	4	NUM
ejpam-146	585	7	,	,	PUNCT
ejpam-146	585	8	315328	315328	NUM
ejpam-146	585	9	(	(	PUNCT
ejpam-146	585	10	2003	2003	NUM
ejpam-146	585	11	)	)	PUNCT
ejpam-146	585	12	.	.	PUNCT
ejpam-146	586	1	[	[	X
ejpam-146	586	2	17	17	NUM
ejpam-146	586	3	]	]	PUNCT
ejpam-146	586	4	t.	t.	PROPN
ejpam-146	586	5	thompson	thompson	PROPN
ejpam-146	586	6	,	,	PUNCT
ejpam-146	586	7	s	s	NOUN
ejpam-146	586	8	-	-	PUNCT
ejpam-146	586	9	closed	closed	ADJ
ejpam-146	586	10	spaces	space	NOUN
ejpam-146	586	11	,	,	PUNCT
ejpam-146	586	12	proc	proc	NOUN
ejpam-146	586	13	.	.	PUNCT
ejpam-146	587	1	amer	amer	PROPN
ejpam-146	587	2	.	.	PUNCT
ejpam-146	587	3	math	math	PROPN
ejpam-146	587	4	.	.	PUNCT
ejpam-146	588	1	soc	soc	PROPN
ejpam-146	588	2	.	.	PUNCT
ejpam-146	588	3	,	,	PUNCT
ejpam-146	588	4	60	60	NUM
ejpam-146	588	5	(	(	PUNCT
ejpam-146	588	6	1976	1976	NUM
ejpam-146	588	7	)	)	PUNCT
ejpam-146	588	8	,	,	PUNCT
ejpam-146	588	9	335	335	NUM
ejpam-146	588	10	-	-	SYM
ejpam-146	588	11	338	338	NUM
ejpam-146	588	12	.	.	PUNCT