id	sid	tid	token	lemma	pos
ejpam-3394	1	1	compile	compile	NOUN
ejpam-3394	1	2	/	/	SYM
ejpam-3394	1	3	output.dvi	output.dvi	NOUN
ejpam-3394	1	4	european	european	ADJ
ejpam-3394	1	5	journal	journal	NOUN
ejpam-3394	1	6	of	of	ADP
ejpam-3394	1	7	pure	pure	ADJ
ejpam-3394	1	8	and	and	CCONJ
ejpam-3394	1	9	applied	apply	VERB
ejpam-3394	1	10	mathematics	mathematic	NOUN
ejpam-3394	1	11	vol	vol	NOUN
ejpam-3394	1	12	.	.	PROPN
ejpam-3394	2	1	12	12	NUM
ejpam-3394	2	2	,	,	PUNCT
ejpam-3394	2	3	no	no	INTJ
ejpam-3394	2	4	.	.	NOUN
ejpam-3394	2	5	2	2	NUM
ejpam-3394	2	6	,	,	PUNCT
ejpam-3394	2	7	2019	2019	NUM
ejpam-3394	2	8	,	,	PUNCT
ejpam-3394	2	9	270	270	NUM
ejpam-3394	2	10	-	-	SYM
ejpam-3394	2	11	278	278	NUM
ejpam-3394	2	12	issn	issn	PROPN
ejpam-3394	2	13	1307	1307	NUM
ejpam-3394	2	14	-	-	SYM
ejpam-3394	2	15	5543	5543	NUM
ejpam-3394	2	16	–	–	PUNCT
ejpam-3394	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3394	2	18	published	publish	VERB
ejpam-3394	2	19	by	by	ADP
ejpam-3394	2	20	new	new	PROPN
ejpam-3394	2	21	york	york	PROPN
ejpam-3394	2	22	business	business	NOUN
ejpam-3394	2	23	global	global	VERB
ejpam-3394	2	24	some	some	DET
ejpam-3394	2	25	characterizations	characterization	NOUN
ejpam-3394	2	26	of	of	ADP
ejpam-3394	2	27	β	β	NOUN
ejpam-3394	2	28	-	-	NOUN
ejpam-3394	2	29	paracompactness	paracompactness	NOUN
ejpam-3394	2	30	in	in	ADP
ejpam-3394	2	31	ideal	ideal	ADJ
ejpam-3394	2	32	topological	topological	ADJ
ejpam-3394	2	33	space	space	NOUN
ejpam-3394	2	34	e.	e.	PROPN
ejpam-3394	2	35	d.	d.	PROPN
ejpam-3394	2	36	yıldırım1	yıldırım1	PROPN
ejpam-3394	2	37	,	,	PUNCT
ejpam-3394	2	38	o.	o.	PROPN
ejpam-3394	2	39	b.	b.	PROPN
ejpam-3394	2	40	özbakır2,∗and	özbakır2,∗and	PROPN
ejpam-3394	2	41	a.c	a.c	PROPN
ejpam-3394	2	42	.	.	PROPN
ejpam-3394	2	43	.	.	PUNCT
ejpam-3394	3	1	güler2	güler2	PROPN
ejpam-3394	3	2	1	1	NUM
ejpam-3394	3	3	department	department	NOUN
ejpam-3394	3	4	of	of	ADP
ejpam-3394	3	5	mathematics	mathematic	NOUN
ejpam-3394	3	6	,	,	PUNCT
ejpam-3394	3	7	faculty	faculty	NOUN
ejpam-3394	3	8	of	of	ADP
ejpam-3394	3	9	science	science	NOUN
ejpam-3394	3	10	and	and	CCONJ
ejpam-3394	3	11	letters	letter	NOUN
ejpam-3394	3	12	,	,	PUNCT
ejpam-3394	3	13	yaşar	yaşar	PROPN
ejpam-3394	3	14	university	university	PROPN
ejpam-3394	3	15	,	,	PUNCT
ejpam-3394	3	16	i̇zmir	i̇zmir	NOUN
ejpam-3394	3	17	,	,	PUNCT
ejpam-3394	3	18	turkey	turkey	PROPN
ejpam-3394	3	19	2	2	NUM
ejpam-3394	3	20	department	department	NOUN
ejpam-3394	3	21	of	of	ADP
ejpam-3394	3	22	mathematics	mathematic	NOUN
ejpam-3394	3	23	,	,	PUNCT
ejpam-3394	3	24	faculty	faculty	NOUN
ejpam-3394	3	25	of	of	ADP
ejpam-3394	3	26	science	science	NOUN
ejpam-3394	3	27	,	,	PUNCT
ejpam-3394	3	28	ege	ege	PROPN
ejpam-3394	3	29	university	university	NOUN
ejpam-3394	3	30	,	,	PUNCT
ejpam-3394	3	31	i̇zmir	i̇zmir	NOUN
ejpam-3394	3	32	,	,	PUNCT
ejpam-3394	3	33	turkey	turkey	NOUN
ejpam-3394	3	34	abstract	abstract	NOUN
ejpam-3394	3	35	.	.	PUNCT
ejpam-3394	4	1	in	in	ADP
ejpam-3394	4	2	this	this	DET
ejpam-3394	4	3	paper	paper	NOUN
ejpam-3394	4	4	,	,	PUNCT
ejpam-3394	4	5	we	we	PRON
ejpam-3394	4	6	introduce	introduce	VERB
ejpam-3394	4	7	β	β	NOUN
ejpam-3394	4	8	-	-	NOUN
ejpam-3394	4	9	paracompactness	paracompactness	NOUN
ejpam-3394	4	10	with	with	ADP
ejpam-3394	4	11	respect	respect	NOUN
ejpam-3394	4	12	to	to	ADP
ejpam-3394	4	13	an	an	DET
ejpam-3394	4	14	ideal	ideal	NOUN
ejpam-3394	4	15	(	(	PUNCT
ejpam-3394	4	16	i	i	NOUN
ejpam-3394	4	17	-	-	PUNCT
ejpam-3394	4	18	β	β	NOUN
ejpam-3394	4	19	-	-	NOUN
ejpam-3394	4	20	paracompactness	paracompactness	NOUN
ejpam-3394	4	21	)	)	PUNCT
ejpam-3394	4	22	as	as	ADP
ejpam-3394	4	23	a	a	DET
ejpam-3394	4	24	weak	weak	ADJ
ejpam-3394	4	25	form	form	NOUN
ejpam-3394	4	26	of	of	ADP
ejpam-3394	4	27	β	β	NOUN
ejpam-3394	4	28	-	-	NOUN
ejpam-3394	4	29	paracompactness	paracompactness	NOUN
ejpam-3394	4	30	and	and	CCONJ
ejpam-3394	4	31	i	i	PROPN
ejpam-3394	4	32	-	-	NOUN
ejpam-3394	4	33	paracompactness	paracompactness	NOUN
ejpam-3394	4	34	.	.	PUNCT
ejpam-3394	5	1	we	we	PRON
ejpam-3394	5	2	give	give	VERB
ejpam-3394	5	3	some	some	DET
ejpam-3394	5	4	relations	relation	NOUN
ejpam-3394	5	5	between	between	ADP
ejpam-3394	5	6	this	this	DET
ejpam-3394	5	7	concept	concept	NOUN
ejpam-3394	5	8	and	and	CCONJ
ejpam-3394	5	9	some	some	DET
ejpam-3394	5	10	other	other	ADJ
ejpam-3394	5	11	types	type	NOUN
ejpam-3394	5	12	of	of	ADP
ejpam-3394	5	13	paracompactness	paracompactness	NOUN
ejpam-3394	5	14	,	,	PUNCT
ejpam-3394	5	15	and	and	CCONJ
ejpam-3394	5	16	also	also	ADV
ejpam-3394	5	17	we	we	PRON
ejpam-3394	5	18	study	study	VERB
ejpam-3394	5	19	some	some	PRON
ejpam-3394	5	20	of	of	ADP
ejpam-3394	5	21	its	its	PRON
ejpam-3394	5	22	fundamental	fundamental	ADJ
ejpam-3394	5	23	properties	property	NOUN
ejpam-3394	5	24	.	.	PUNCT
ejpam-3394	6	1	2010	2010	NUM
ejpam-3394	6	2	mathematics	mathematic	NOUN
ejpam-3394	6	3	subject	subject	NOUN
ejpam-3394	6	4	classifications	classification	NOUN
ejpam-3394	6	5	:	:	PUNCT
ejpam-3394	6	6	54d20	54d20	NUM
ejpam-3394	6	7	,	,	PUNCT
ejpam-3394	6	8	54a05	54a05	NUM
ejpam-3394	6	9	,	,	PUNCT
ejpam-3394	6	10	54c10	54c10	NUM
ejpam-3394	6	11	,	,	PUNCT
ejpam-3394	6	12	54g05	54g05	NUM
ejpam-3394	6	13	key	key	ADJ
ejpam-3394	6	14	words	word	NOUN
ejpam-3394	6	15	and	and	CCONJ
ejpam-3394	6	16	phrases	phrase	NOUN
ejpam-3394	6	17	:	:	PUNCT
ejpam-3394	6	18	β	β	X
ejpam-3394	6	19	-	-	ADJ
ejpam-3394	6	20	paracompact	paracompact	ADJ
ejpam-3394	6	21	,	,	PUNCT
ejpam-3394	6	22	ideal	ideal	ADJ
ejpam-3394	6	23	,	,	PUNCT
ejpam-3394	6	24	i	i	PROPN
ejpam-3394	6	25	-	-	PUNCT
ejpam-3394	6	26	β	β	NOUN
ejpam-3394	6	27	-	-	NOUN
ejpam-3394	6	28	paracompact	paracompact	ADJ
ejpam-3394	6	29	,	,	PUNCT
ejpam-3394	6	30	σ	σ	PROPN
ejpam-3394	6	31	-	-	PUNCT
ejpam-3394	6	32	β	β	NOUN
ejpam-3394	6	33	-	-	ADJ
ejpam-3394	6	34	locally	locally	ADV
ejpam-3394	6	35	finite	finite	ADJ
ejpam-3394	6	36	1	1	NUM
ejpam-3394	6	37	.	.	PUNCT
ejpam-3394	7	1	introduction	introduction	NOUN
ejpam-3394	7	2	paracompactness	paracompactness	NOUN
ejpam-3394	7	3	is	be	AUX
ejpam-3394	7	4	one	one	NUM
ejpam-3394	7	5	of	of	ADP
ejpam-3394	7	6	the	the	DET
ejpam-3394	7	7	important	important	ADJ
ejpam-3394	7	8	concepts	concept	NOUN
ejpam-3394	7	9	of	of	ADP
ejpam-3394	7	10	general	general	ADJ
ejpam-3394	7	11	topology	topology	NOUN
ejpam-3394	7	12	.	.	PUNCT
ejpam-3394	8	1	in	in	ADP
ejpam-3394	8	2	literature	literature	NOUN
ejpam-3394	8	3	,	,	PUNCT
ejpam-3394	8	4	different	different	ADJ
ejpam-3394	8	5	kinds	kind	NOUN
ejpam-3394	8	6	of	of	ADP
ejpam-3394	8	7	generalized	generalized	ADJ
ejpam-3394	8	8	paracompactness	paracompactness	NOUN
ejpam-3394	8	9	such	such	ADJ
ejpam-3394	8	10	as	as	ADP
ejpam-3394	8	11	s	s	NOUN
ejpam-3394	8	12	-	-	NOUN
ejpam-3394	8	13	paracompactness	paracompactness	NOUN
ejpam-3394	8	14	[	[	X
ejpam-3394	8	15	5	5	NUM
ejpam-3394	8	16	]	]	PUNCT
ejpam-3394	8	17	,	,	PUNCT
ejpam-3394	8	18	p3paracompactness	p3paracompactness	NOUN
ejpam-3394	8	19	[	[	X
ejpam-3394	8	20	6	6	NUM
ejpam-3394	8	21	]	]	PUNCT
ejpam-3394	8	22	and	and	CCONJ
ejpam-3394	8	23	β	β	NOUN
ejpam-3394	8	24	-	-	NOUN
ejpam-3394	8	25	paracompactness	paracompactness	NOUN
ejpam-3394	8	26	[	[	X
ejpam-3394	8	27	11	11	NUM
ejpam-3394	8	28	]	]	PUNCT
ejpam-3394	8	29	are	be	AUX
ejpam-3394	8	30	studied	study	VERB
ejpam-3394	8	31	.	.	PUNCT
ejpam-3394	9	1	the	the	DET
ejpam-3394	9	2	concept	concept	NOUN
ejpam-3394	9	3	of	of	ADP
ejpam-3394	9	4	i	i	PROPN
ejpam-3394	9	5	-	-	PUNCT
ejpam-3394	9	6	paracompactness	paracompactness	NOUN
ejpam-3394	9	7	as	as	ADP
ejpam-3394	9	8	generalization	generalization	NOUN
ejpam-3394	9	9	of	of	ADP
ejpam-3394	9	10	paracompactness	paracompactness	NOUN
ejpam-3394	9	11	was	be	AUX
ejpam-3394	9	12	given	give	VERB
ejpam-3394	9	13	by	by	ADP
ejpam-3394	9	14	zahid	zahid	PROPN
ejpam-3394	9	15	[	[	X
ejpam-3394	9	16	24	24	NUM
ejpam-3394	9	17	]	]	PUNCT
ejpam-3394	9	18	.	.	PUNCT
ejpam-3394	10	1	furthermore	furthermore	ADV
ejpam-3394	10	2	,	,	PUNCT
ejpam-3394	10	3	this	this	DET
ejpam-3394	10	4	concept	concept	NOUN
ejpam-3394	10	5	was	be	AUX
ejpam-3394	10	6	studied	study	VERB
ejpam-3394	10	7	by	by	ADP
ejpam-3394	10	8	hamlet	hamlet	PROPN
ejpam-3394	10	9	et	et	PROPN
ejpam-3394	10	10	al	al	PROPN
ejpam-3394	10	11	.	.	PUNCT
ejpam-3394	11	1	[	[	X
ejpam-3394	11	2	13	13	NUM
ejpam-3394	11	3	]	]	PUNCT
ejpam-3394	11	4	and	and	CCONJ
ejpam-3394	11	5	sathiyasundari	sathiyasundari	PROPN
ejpam-3394	11	6	and	and	CCONJ
ejpam-3394	11	7	renukadevi	renukadevi	NOUN
ejpam-3394	11	8	[	[	X
ejpam-3394	11	9	22	22	NUM
ejpam-3394	11	10	]	]	PUNCT
ejpam-3394	11	11	.	.	PUNCT
ejpam-3394	12	1	recently	recently	ADV
ejpam-3394	12	2	,	,	PUNCT
ejpam-3394	12	3	s	s	NOUN
ejpam-3394	12	4	-	-	NOUN
ejpam-3394	12	5	paracompactness	paracompactness	NOUN
ejpam-3394	12	6	with	with	ADP
ejpam-3394	12	7	respect	respect	NOUN
ejpam-3394	12	8	to	to	ADP
ejpam-3394	12	9	an	an	DET
ejpam-3394	12	10	ideal	ideal	NOUN
ejpam-3394	12	11	which	which	PRON
ejpam-3394	12	12	is	be	AUX
ejpam-3394	12	13	weaker	weak	ADJ
ejpam-3394	12	14	form	form	NOUN
ejpam-3394	12	15	of	of	ADP
ejpam-3394	12	16	i	i	PROPN
ejpam-3394	12	17	-	-	PUNCT
ejpam-3394	12	18	paracompactness	paracompactness	PROPN
ejpam-3394	12	19	was	be	AUX
ejpam-3394	12	20	studied	study	VERB
ejpam-3394	12	21	by	by	ADP
ejpam-3394	12	22	j.	j.	PROPN
ejpam-3394	12	23	sanabria	sanabria	PROPN
ejpam-3394	12	24	et	et	PROPN
ejpam-3394	12	25	al	al	PROPN
ejpam-3394	12	26	.	.	PUNCT
ejpam-3394	13	1	[	[	X
ejpam-3394	13	2	21	21	NUM
ejpam-3394	13	3	]	]	PUNCT
ejpam-3394	13	4	.	.	PUNCT
ejpam-3394	14	1	here	here	ADV
ejpam-3394	14	2	,	,	PUNCT
ejpam-3394	14	3	we	we	PRON
ejpam-3394	14	4	introduce	introduce	VERB
ejpam-3394	14	5	i	i	PRON
ejpam-3394	14	6	-	-	PUNCT
ejpam-3394	14	7	β	β	NOUN
ejpam-3394	14	8	-	-	NOUN
ejpam-3394	14	9	paracompactness	paracompactness	NOUN
ejpam-3394	14	10	and	and	CCONJ
ejpam-3394	14	11	we	we	PRON
ejpam-3394	14	12	compare	compare	VERB
ejpam-3394	14	13	this	this	DET
ejpam-3394	14	14	concept	concept	NOUN
ejpam-3394	14	15	with	with	ADP
ejpam-3394	14	16	the	the	DET
ejpam-3394	14	17	other	other	ADJ
ejpam-3394	14	18	types	type	NOUN
ejpam-3394	14	19	of	of	ADP
ejpam-3394	14	20	paracompactness	paracompactness	NOUN
ejpam-3394	14	21	.	.	PUNCT
ejpam-3394	15	1	then	then	ADV
ejpam-3394	15	2	,	,	PUNCT
ejpam-3394	15	3	we	we	PRON
ejpam-3394	15	4	give	give	VERB
ejpam-3394	15	5	counterexamples	counterexample	NOUN
ejpam-3394	15	6	showing	show	VERB
ejpam-3394	15	7	that	that	SCONJ
ejpam-3394	15	8	the	the	DET
ejpam-3394	15	9	opposite	opposite	ADJ
ejpam-3394	15	10	directions	direction	NOUN
ejpam-3394	15	11	of	of	ADP
ejpam-3394	15	12	proposition	proposition	NOUN
ejpam-3394	15	13	1	1	NUM
ejpam-3394	15	14	and	and	CCONJ
ejpam-3394	15	15	2	2	NUM
ejpam-3394	15	16	do	do	AUX
ejpam-3394	15	17	not	not	PART
ejpam-3394	15	18	hold	hold	VERB
ejpam-3394	15	19	.	.	PUNCT
ejpam-3394	16	1	furthermore	furthermore	ADV
ejpam-3394	16	2	,	,	PUNCT
ejpam-3394	16	3	adding	add	VERB
ejpam-3394	16	4	some	some	DET
ejpam-3394	16	5	conditions	condition	NOUN
ejpam-3394	16	6	,	,	PUNCT
ejpam-3394	16	7	we	we	PRON
ejpam-3394	16	8	find	find	VERB
ejpam-3394	16	9	that	that	SCONJ
ejpam-3394	16	10	the	the	DET
ejpam-3394	16	11	reverse	reverse	ADJ
ejpam-3394	16	12	directions	direction	NOUN
ejpam-3394	16	13	may	may	AUX
ejpam-3394	16	14	happen	happen	VERB
ejpam-3394	16	15	to	to	PART
ejpam-3394	16	16	be	be	AUX
ejpam-3394	16	17	true	true	ADJ
ejpam-3394	16	18	.	.	PUNCT
ejpam-3394	17	1	besides	besides	ADV
ejpam-3394	17	2	,	,	PUNCT
ejpam-3394	17	3	we	we	PRON
ejpam-3394	17	4	investigate	investigate	VERB
ejpam-3394	17	5	some	some	PRON
ejpam-3394	17	6	of	of	ADP
ejpam-3394	17	7	its	its	PRON
ejpam-3394	17	8	essential	essential	ADJ
ejpam-3394	17	9	properties	property	NOUN
ejpam-3394	17	10	.	.	PUNCT
ejpam-3394	18	1	finally	finally	ADV
ejpam-3394	18	2	,	,	PUNCT
ejpam-3394	18	3	we	we	PRON
ejpam-3394	18	4	examine	examine	VERB
ejpam-3394	18	5	i	i	PROPN
ejpam-3394	18	6	-	-	PUNCT
ejpam-3394	18	7	β	β	NOUN
ejpam-3394	18	8	-	-	NOUN
ejpam-3394	18	9	paracompactness	paracompactness	NOUN
ejpam-3394	18	10	under	under	ADP
ejpam-3394	18	11	some	some	DET
ejpam-3394	18	12	functions	function	NOUN
ejpam-3394	18	13	.	.	PUNCT
ejpam-3394	19	1	∗corresponding	∗corresponde	VERB
ejpam-3394	19	2	author	author	NOUN
ejpam-3394	19	3	.	.	PUNCT
ejpam-3394	20	1	doi	doi	NOUN
ejpam-3394	20	2	:	:	PUNCT
ejpam-3394	20	3	https://doi.org/10.29020/nybg.ejpam.v12i2.3394	https://doi.org/10.29020/nybg.ejpam.v12i2.3394	NOUN
ejpam-3394	20	4	email	email	NOUN
ejpam-3394	20	5	addresses	address	VERB
ejpam-3394	20	6	:	:	PUNCT
ejpam-3394	20	7	esra.dalan@yasar.edu.tr	esra.dalan@yasar.edu.tr	PROPN
ejpam-3394	20	8	(	(	PUNCT
ejpam-3394	20	9	e.	e.	PROPN
ejpam-3394	20	10	d.	d.	PROPN
ejpam-3394	20	11	yıldırım	yıldırım	PROPN
ejpam-3394	20	12	)	)	PUNCT
ejpam-3394	20	13	,	,	PUNCT
ejpam-3394	20	14	oya.ozbakir@ege.edu.tr	oya.ozbakir@ege.edu.tr	INTJ
ejpam-3394	20	15	(	(	PUNCT
ejpam-3394	20	16	o.	o.	PROPN
ejpam-3394	20	17	b.	b.	PROPN
ejpam-3394	20	18	özbakır	özbakır	PROPN
ejpam-3394	20	19	)	)	PUNCT
ejpam-3394	20	20	,	,	PUNCT
ejpam-3394	20	21	aysegul.caksu.guler@ege.edu.tr	aysegul.caksu.guler@ege.edu.tr	PROPN
ejpam-3394	20	22	(	(	PUNCT
ejpam-3394	20	23	a.c	a.c	PROPN
ejpam-3394	20	24	.	.	PROPN
ejpam-3394	20	25	.	.	PUNCT
ejpam-3394	21	1	güler	güler	NOUN
ejpam-3394	21	2	)	)	PUNCT
ejpam-3394	21	3	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3394	22	1	270	270	NUM
ejpam-3394	22	2	c	c	X
ejpam-3394	22	3	©	©	PROPN
ejpam-3394	22	4	2019	2019	NUM
ejpam-3394	22	5	ejpam	ejpam	NOUN
ejpam-3394	22	6	all	all	DET
ejpam-3394	22	7	rights	right	NOUN
ejpam-3394	22	8	reserved	reserve	VERB
ejpam-3394	22	9	.	.	PUNCT
ejpam-3394	23	1	e.	e.	PROPN
ejpam-3394	23	2	d.	d.	PROPN
ejpam-3394	23	3	yıldırım	yıldırım	PROPN
ejpam-3394	23	4	,	,	PUNCT
ejpam-3394	23	5	o.	o.	PROPN
ejpam-3394	23	6	b.	b.	PROPN
ejpam-3394	23	7	özbakır	özbakır	PROPN
ejpam-3394	23	8	,	,	PUNCT
ejpam-3394	23	9	a.	a.	PROPN
ejpam-3394	23	10	c.	c.	PROPN
ejpam-3394	23	11	.	.	PUNCT
ejpam-3394	24	1	güler	güler	PROPN
ejpam-3394	24	2	/	/	SYM
ejpam-3394	24	3	eur	eur	PROPN
ejpam-3394	24	4	.	.	PUNCT
ejpam-3394	25	1	j.	j.	PROPN
ejpam-3394	25	2	pure	pure	PROPN
ejpam-3394	25	3	appl	appl	PROPN
ejpam-3394	25	4	.	.	PROPN
ejpam-3394	25	5	math	math	PROPN
ejpam-3394	25	6	,	,	PUNCT
ejpam-3394	25	7	12	12	NUM
ejpam-3394	25	8	(	(	PUNCT
ejpam-3394	25	9	2	2	NUM
ejpam-3394	25	10	)	)	PUNCT
ejpam-3394	25	11	(	(	PUNCT
ejpam-3394	25	12	2019	2019	NUM
ejpam-3394	25	13	)	)	PUNCT
ejpam-3394	25	14	,	,	PUNCT
ejpam-3394	25	15	270	270	NUM
ejpam-3394	25	16	-	-	SYM
ejpam-3394	25	17	278	278	NUM
ejpam-3394	25	18	271	271	NUM
ejpam-3394	25	19	2	2	NUM
ejpam-3394	25	20	.	.	PUNCT
ejpam-3394	25	21	preliminaries	preliminary	NOUN
ejpam-3394	25	22	throughout	throughout	ADP
ejpam-3394	25	23	this	this	DET
ejpam-3394	25	24	work	work	NOUN
ejpam-3394	25	25	,	,	PUNCT
ejpam-3394	25	26	(	(	PUNCT
ejpam-3394	25	27	x	x	X
ejpam-3394	25	28	,	,	PUNCT
ejpam-3394	25	29	τ	τ	X
ejpam-3394	25	30	)	)	PUNCT
ejpam-3394	25	31	denotes	denote	VERB
ejpam-3394	25	32	a	a	DET
ejpam-3394	25	33	topological	topological	ADJ
ejpam-3394	25	34	space	space	NOUN
ejpam-3394	25	35	on	on	ADP
ejpam-3394	25	36	which	which	PRON
ejpam-3394	25	37	no	no	DET
ejpam-3394	25	38	separation	separation	NOUN
ejpam-3394	25	39	axioms	axiom	NOUN
ejpam-3394	25	40	are	be	AUX
ejpam-3394	25	41	assumed	assume	VERB
ejpam-3394	25	42	unless	unless	SCONJ
ejpam-3394	25	43	clearly	clearly	ADV
ejpam-3394	25	44	indicated	indicate	VERB
ejpam-3394	25	45	.	.	PUNCT
ejpam-3394	26	1	if	if	SCONJ
ejpam-3394	26	2	a	a	PRON
ejpam-3394	26	3	is	be	AUX
ejpam-3394	26	4	a	a	DET
ejpam-3394	26	5	subset	subset	NOUN
ejpam-3394	26	6	of	of	ADP
ejpam-3394	26	7	(	(	PUNCT
ejpam-3394	26	8	x	x	PROPN
ejpam-3394	26	9	,	,	PUNCT
ejpam-3394	26	10	τ	τ	PROPN
ejpam-3394	26	11	)	)	PUNCT
ejpam-3394	26	12	,	,	PUNCT
ejpam-3394	26	13	then	then	ADV
ejpam-3394	26	14	the	the	DET
ejpam-3394	26	15	closure	closure	NOUN
ejpam-3394	26	16	of	of	ADP
ejpam-3394	26	17	a	a	PRON
ejpam-3394	26	18	and	and	CCONJ
ejpam-3394	26	19	the	the	DET
ejpam-3394	26	20	interior	interior	NOUN
ejpam-3394	26	21	of	of	ADP
ejpam-3394	26	22	a	a	PRON
ejpam-3394	26	23	will	will	AUX
ejpam-3394	26	24	be	be	AUX
ejpam-3394	26	25	denoted	denote	VERB
ejpam-3394	26	26	by	by	ADP
ejpam-3394	26	27	cl(a	cl(a	NOUN
ejpam-3394	26	28	)	)	PUNCT
ejpam-3394	26	29	and	and	CCONJ
ejpam-3394	26	30	int(a	int(a	PROPN
ejpam-3394	26	31	)	)	PUNCT
ejpam-3394	26	32	,	,	PUNCT
ejpam-3394	26	33	respectively	respectively	ADV
ejpam-3394	26	34	.	.	PUNCT
ejpam-3394	27	1	also	also	ADV
ejpam-3394	27	2	,	,	PUNCT
ejpam-3394	27	3	the	the	DET
ejpam-3394	27	4	class	class	NOUN
ejpam-3394	27	5	of	of	ADP
ejpam-3394	27	6	all	all	DET
ejpam-3394	27	7	subsets	subset	NOUN
ejpam-3394	27	8	of	of	ADP
ejpam-3394	27	9	x	x	PRON
ejpam-3394	27	10	will	will	AUX
ejpam-3394	27	11	be	be	AUX
ejpam-3394	27	12	denoted	denote	VERB
ejpam-3394	27	13	by	by	ADP
ejpam-3394	27	14	p(x	p(x	PROPN
ejpam-3394	27	15	)	)	PUNCT
ejpam-3394	27	16	.	.	PUNCT
ejpam-3394	28	1	a	a	DET
ejpam-3394	28	2	subset	subset	NOUN
ejpam-3394	28	3	a	a	PRON
ejpam-3394	28	4	of	of	ADP
ejpam-3394	28	5	(	(	PUNCT
ejpam-3394	28	6	x	x	PROPN
ejpam-3394	28	7	,	,	PUNCT
ejpam-3394	28	8	τ	τ	X
ejpam-3394	28	9	)	)	PUNCT
ejpam-3394	28	10	is	be	AUX
ejpam-3394	28	11	said	say	VERB
ejpam-3394	28	12	to	to	PART
ejpam-3394	28	13	be	be	AUX
ejpam-3394	28	14	semi	semi	ADJ
ejpam-3394	28	15	-	-	ADJ
ejpam-3394	28	16	open	open	ADJ
ejpam-3394	29	1	[	[	X
ejpam-3394	29	2	16	16	NUM
ejpam-3394	29	3	]	]	X
ejpam-3394	29	4	if	if	SCONJ
ejpam-3394	29	5	there	there	PRON
ejpam-3394	29	6	exists	exist	VERB
ejpam-3394	29	7	u	u	PROPN
ejpam-3394	29	8	∈	∈	PROPN
ejpam-3394	29	9	τ	τ	X
ejpam-3394	29	10	such	such	ADJ
ejpam-3394	29	11	that	that	SCONJ
ejpam-3394	29	12	u	u	PROPN
ejpam-3394	29	13	⊆	⊆	NUM
ejpam-3394	29	14	a	a	DET
ejpam-3394	29	15	⊆	⊆	NUM
ejpam-3394	29	16	cl(u	cl(u	NUM
ejpam-3394	29	17	)	)	PUNCT
ejpam-3394	29	18	.	.	PUNCT
ejpam-3394	30	1	this	this	PRON
ejpam-3394	30	2	is	be	AUX
ejpam-3394	30	3	equivalent	equivalent	ADJ
ejpam-3394	30	4	to	to	PART
ejpam-3394	30	5	say	say	VERB
ejpam-3394	30	6	that	that	SCONJ
ejpam-3394	30	7	a	a	DET
ejpam-3394	30	8	⊆	⊆	NUM
ejpam-3394	30	9	cl(int(a	cl(int(a	NOUN
ejpam-3394	30	10	)	)	PUNCT
ejpam-3394	30	11	)	)	PUNCT
ejpam-3394	30	12	.	.	PUNCT
ejpam-3394	31	1	also	also	ADV
ejpam-3394	31	2	,	,	PUNCT
ejpam-3394	31	3	a	a	PRON
ejpam-3394	31	4	is	be	AUX
ejpam-3394	31	5	said	say	VERB
ejpam-3394	31	6	to	to	PART
ejpam-3394	31	7	be	be	AUX
ejpam-3394	31	8	β	β	X
ejpam-3394	31	9	-	-	ADJ
ejpam-3394	31	10	open	open	ADJ
ejpam-3394	31	11	[	[	X
ejpam-3394	31	12	1	1	NUM
ejpam-3394	31	13	]	]	PUNCT
ejpam-3394	31	14	(	(	PUNCT
ejpam-3394	31	15	preopen	preopen	ADJ
ejpam-3394	31	16	[	[	X
ejpam-3394	31	17	18	18	NUM
ejpam-3394	31	18	]	]	SYM
ejpam-3394	31	19	)	)	PUNCT
ejpam-3394	31	20	if	if	SCONJ
ejpam-3394	31	21	a	a	DET
ejpam-3394	31	22	⊆	⊆	NUM
ejpam-3394	31	23	cl(int(cl(a)))(a	cl(int(cl(a)))(a	NOUN
ejpam-3394	31	24	⊆	⊆	NUM
ejpam-3394	31	25	int(cl(a	int(cl(a	PROPN
ejpam-3394	31	26	)	)	PUNCT
ejpam-3394	31	27	)	)	PUNCT
ejpam-3394	31	28	)	)	PUNCT
ejpam-3394	31	29	.	.	PUNCT
ejpam-3394	32	1	the	the	DET
ejpam-3394	32	2	concept	concept	NOUN
ejpam-3394	32	3	of	of	ADP
ejpam-3394	32	4	β	β	ADJ
ejpam-3394	32	5	-	-	ADJ
ejpam-3394	32	6	open	open	ADJ
ejpam-3394	32	7	sets	set	NOUN
ejpam-3394	32	8	is	be	AUX
ejpam-3394	32	9	equal	equal	ADJ
ejpam-3394	32	10	to	to	ADP
ejpam-3394	32	11	that	that	PRON
ejpam-3394	32	12	of	of	ADP
ejpam-3394	32	13	semi	semi	ADJ
ejpam-3394	32	14	-	-	ADJ
ejpam-3394	32	15	preopen	preopen	ADJ
ejpam-3394	32	16	sets	set	NOUN
ejpam-3394	32	17	in	in	ADP
ejpam-3394	32	18	[	[	X
ejpam-3394	32	19	7	7	NUM
ejpam-3394	32	20	]	]	PUNCT
ejpam-3394	32	21	.	.	PUNCT
ejpam-3394	33	1	the	the	DET
ejpam-3394	33	2	family	family	NOUN
ejpam-3394	33	3	of	of	ADP
ejpam-3394	33	4	all	all	PRON
ejpam-3394	33	5	semiopen	semiopen	ADJ
ejpam-3394	33	6	(	(	PUNCT
ejpam-3394	33	7	resp	resp	NOUN
ejpam-3394	33	8	.	.	PUNCT
ejpam-3394	34	1	β	β	X
ejpam-3394	34	2	-	-	PUNCT
ejpam-3394	34	3	open	open	ADJ
ejpam-3394	34	4	and	and	CCONJ
ejpam-3394	34	5	preopen	preopen	ADJ
ejpam-3394	34	6	)	)	PUNCT
ejpam-3394	34	7	sets	set	NOUN
ejpam-3394	34	8	of	of	ADP
ejpam-3394	34	9	(	(	PUNCT
ejpam-3394	34	10	x	x	NOUN
ejpam-3394	34	11	,	,	PUNCT
ejpam-3394	34	12	τ	τ	X
ejpam-3394	34	13	)	)	PUNCT
ejpam-3394	34	14	is	be	AUX
ejpam-3394	34	15	denoted	denote	VERB
ejpam-3394	34	16	by	by	ADP
ejpam-3394	34	17	so(x	so(x	NOUN
ejpam-3394	34	18	,	,	PUNCT
ejpam-3394	34	19	τ	τ	X
ejpam-3394	34	20	)	)	PUNCT
ejpam-3394	34	21	(	(	PUNCT
ejpam-3394	34	22	resp	resp	NOUN
ejpam-3394	34	23	.	.	PUNCT
ejpam-3394	35	1	βo(x	βo(x	PROPN
ejpam-3394	35	2	,	,	PUNCT
ejpam-3394	35	3	τ	τ	X
ejpam-3394	35	4	)	)	PUNCT
ejpam-3394	35	5	and	and	CCONJ
ejpam-3394	35	6	po(x	po(x	NUM
ejpam-3394	35	7	,	,	PUNCT
ejpam-3394	35	8	τ	τ	PROPN
ejpam-3394	35	9	)	)	PUNCT
ejpam-3394	35	10	)	)	PUNCT
ejpam-3394	35	11	.	.	PUNCT
ejpam-3394	36	1	the	the	DET
ejpam-3394	36	2	complement	complement	NOUN
ejpam-3394	36	3	of	of	ADP
ejpam-3394	36	4	a	a	DET
ejpam-3394	36	5	semi	semi	ADJ
ejpam-3394	36	6	-	-	ADJ
ejpam-3394	36	7	open	open	ADJ
ejpam-3394	36	8	(	(	PUNCT
ejpam-3394	36	9	resp	resp	NOUN
ejpam-3394	36	10	.	.	PUNCT
ejpam-3394	37	1	β	β	X
ejpam-3394	37	2	-	-	PUNCT
ejpam-3394	37	3	open	open	ADJ
ejpam-3394	37	4	and	and	CCONJ
ejpam-3394	37	5	preopen	preopen	ADJ
ejpam-3394	37	6	)	)	PUNCT
ejpam-3394	37	7	set	set	NOUN
ejpam-3394	37	8	is	be	AUX
ejpam-3394	37	9	said	say	VERB
ejpam-3394	37	10	to	to	PART
ejpam-3394	37	11	be	be	AUX
ejpam-3394	37	12	semi	semi	ADJ
ejpam-3394	37	13	-	-	ADJ
ejpam-3394	37	14	closed	closed	ADJ
ejpam-3394	37	15	[	[	X
ejpam-3394	37	16	10	10	NUM
ejpam-3394	37	17	]	]	PUNCT
ejpam-3394	37	18	(	(	PUNCT
ejpam-3394	37	19	resp	resp	NOUN
ejpam-3394	37	20	.	.	PUNCT
ejpam-3394	38	1	β	β	X
ejpam-3394	38	2	-	-	PUNCT
ejpam-3394	38	3	closed	closed	ADJ
ejpam-3394	38	4	[	[	X
ejpam-3394	38	5	1	1	NUM
ejpam-3394	38	6	,	,	PUNCT
ejpam-3394	38	7	7	7	NUM
ejpam-3394	38	8	]	]	PUNCT
ejpam-3394	38	9	and	and	CCONJ
ejpam-3394	38	10	preclosed	preclose	VERB
ejpam-3394	38	11	[	[	X
ejpam-3394	38	12	18	18	NUM
ejpam-3394	38	13	]	]	NUM
ejpam-3394	38	14	)	)	PUNCT
ejpam-3394	38	15	.	.	PUNCT
ejpam-3394	39	1	the	the	DET
ejpam-3394	39	2	semi	semi	NOUN
ejpam-3394	39	3	-	-	NOUN
ejpam-3394	39	4	closure	closure	ADJ
ejpam-3394	39	5	[	[	X
ejpam-3394	39	6	10	10	NUM
ejpam-3394	39	7	]	]	X
ejpam-3394	39	8	(	(	PUNCT
ejpam-3394	39	9	resp	resp	NOUN
ejpam-3394	39	10	.	.	PUNCT
ejpam-3394	40	1	β	β	X
ejpam-3394	40	2	-	-	PUNCT
ejpam-3394	40	3	closure	closure	NOUN
ejpam-3394	40	4	[	[	X
ejpam-3394	40	5	3	3	NUM
ejpam-3394	40	6	,	,	PUNCT
ejpam-3394	40	7	7	7	NUM
ejpam-3394	40	8	]	]	PUNCT
ejpam-3394	40	9	and	and	CCONJ
ejpam-3394	40	10	preclosure[18	preclosure[18	NOUN
ejpam-3394	40	11	]	]	PUNCT
ejpam-3394	40	12	)	)	PUNCT
ejpam-3394	40	13	of	of	ADP
ejpam-3394	40	14	a	a	PRON
ejpam-3394	40	15	,	,	PUNCT
ejpam-3394	40	16	denoted	denote	VERB
ejpam-3394	40	17	by	by	ADP
ejpam-3394	40	18	scl(a	scl(a	PROPN
ejpam-3394	40	19	)	)	PUNCT
ejpam-3394	40	20	(	(	PUNCT
ejpam-3394	40	21	resp	resp	NOUN
ejpam-3394	40	22	.	.	PUNCT
ejpam-3394	41	1	βcl(a	βcl(a	VERB
ejpam-3394	41	2	)	)	PUNCT
ejpam-3394	41	3	and	and	CCONJ
ejpam-3394	41	4	pcl(a	pcl(a	NUM
ejpam-3394	41	5	)	)	PUNCT
ejpam-3394	41	6	)	)	PUNCT
ejpam-3394	41	7	,	,	PUNCT
ejpam-3394	41	8	is	be	AUX
ejpam-3394	41	9	the	the	DET
ejpam-3394	41	10	intersection	intersection	NOUN
ejpam-3394	41	11	of	of	ADP
ejpam-3394	41	12	all	all	PRON
ejpam-3394	41	13	semi	semi	ADJ
ejpam-3394	41	14	-	-	ADJ
ejpam-3394	41	15	closed	closed	ADJ
ejpam-3394	41	16	(	(	PUNCT
ejpam-3394	41	17	resp	resp	NOUN
ejpam-3394	41	18	.	.	PUNCT
ejpam-3394	42	1	β	β	X
ejpam-3394	42	2	-	-	PUNCT
ejpam-3394	42	3	closed	closed	ADJ
ejpam-3394	42	4	and	and	CCONJ
ejpam-3394	42	5	preclosed	preclose	VERB
ejpam-3394	42	6	)	)	PUNCT
ejpam-3394	42	7	sets	set	NOUN
ejpam-3394	42	8	containing	contain	VERB
ejpam-3394	42	9	a.	a.	NOUN
ejpam-3394	42	10	note	note	NOUN
ejpam-3394	43	1	that	that	SCONJ
ejpam-3394	43	2	,	,	PUNCT
ejpam-3394	43	3	βcl(a	βcl(a	PROPN
ejpam-3394	43	4	)	)	PUNCT
ejpam-3394	43	5	is	be	AUX
ejpam-3394	43	6	β	β	X
ejpam-3394	43	7	-	-	ADJ
ejpam-3394	43	8	closed	closed	ADJ
ejpam-3394	43	9	[	[	X
ejpam-3394	43	10	3	3	NUM
ejpam-3394	43	11	,	,	PUNCT
ejpam-3394	43	12	7	7	NUM
ejpam-3394	43	13	]	]	PUNCT
ejpam-3394	43	14	.	.	PUNCT
ejpam-3394	44	1	lemma	lemma	PROPN
ejpam-3394	44	2	1	1	NUM
ejpam-3394	44	3	.	.	PUNCT
ejpam-3394	45	1	[	[	X
ejpam-3394	45	2	3	3	NUM
ejpam-3394	45	3	,	,	PUNCT
ejpam-3394	45	4	7	7	NUM
ejpam-3394	45	5	]	]	PUNCT
ejpam-3394	45	6	for	for	ADP
ejpam-3394	45	7	a	a	DET
ejpam-3394	45	8	subset	subset	NOUN
ejpam-3394	45	9	a	a	PRON
ejpam-3394	45	10	of	of	ADP
ejpam-3394	45	11	a	a	DET
ejpam-3394	45	12	topological	topological	ADJ
ejpam-3394	45	13	space	space	NOUN
ejpam-3394	45	14	(	(	PUNCT
ejpam-3394	45	15	x	x	X
ejpam-3394	45	16	,	,	PUNCT
ejpam-3394	45	17	τ	τ	PROPN
ejpam-3394	45	18	)	)	PUNCT
ejpam-3394	45	19	,	,	PUNCT
ejpam-3394	45	20	the	the	DET
ejpam-3394	45	21	following	follow	VERB
ejpam-3394	45	22	conditions	condition	NOUN
ejpam-3394	45	23	hold	hold	VERB
ejpam-3394	45	24	:	:	PUNCT
ejpam-3394	45	25	(	(	PUNCT
ejpam-3394	45	26	i	i	NOUN
ejpam-3394	45	27	)	)	PUNCT
ejpam-3394	45	28	x	x	SYM
ejpam-3394	45	29	∈	∈	NOUN
ejpam-3394	45	30	βcl(a	βcl(a	PROPN
ejpam-3394	45	31	)	)	PUNCT
ejpam-3394	45	32	if	if	SCONJ
ejpam-3394	45	33	and	and	CCONJ
ejpam-3394	45	34	only	only	ADV
ejpam-3394	45	35	if	if	SCONJ
ejpam-3394	45	36	a	a	DET
ejpam-3394	45	37	∩	∩	ADJ
ejpam-3394	45	38	u	u	NOUN
ejpam-3394	45	39	6=	6=	NOUN
ejpam-3394	45	40	∅	∅	NOUN
ejpam-3394	45	41	for	for	ADP
ejpam-3394	45	42	every	every	DET
ejpam-3394	45	43	u	u	PROPN
ejpam-3394	45	44	∈	∈	PROPN
ejpam-3394	45	45	βo(x	βo(x	PUNCT
ejpam-3394	45	46	,	,	PUNCT
ejpam-3394	45	47	τ	τ	X
ejpam-3394	45	48	)	)	PUNCT
ejpam-3394	45	49	containing	contain	VERB
ejpam-3394	45	50	x	x	SYM
ejpam-3394	45	51	,	,	PUNCT
ejpam-3394	45	52	(	(	PUNCT
ejpam-3394	45	53	ii	ii	NOUN
ejpam-3394	45	54	)	)	PUNCT
ejpam-3394	45	55	a	a	PRON
ejpam-3394	45	56	is	be	AUX
ejpam-3394	45	57	β	β	NOUN
ejpam-3394	45	58	-	-	VERB
ejpam-3394	45	59	closed	closed	ADJ
ejpam-3394	45	60	if	if	SCONJ
ejpam-3394	45	61	and	and	CCONJ
ejpam-3394	45	62	only	only	ADV
ejpam-3394	45	63	if	if	SCONJ
ejpam-3394	45	64	a	a	DET
ejpam-3394	45	65	=	=	SYM
ejpam-3394	45	66	βcl(a	βcl(a	NOUN
ejpam-3394	45	67	)	)	PUNCT
ejpam-3394	45	68	.	.	PUNCT
ejpam-3394	46	1	theorem	theorem	NOUN
ejpam-3394	46	2	1	1	NUM
ejpam-3394	46	3	.	.	PUNCT
ejpam-3394	47	1	[	[	X
ejpam-3394	47	2	19	19	NUM
ejpam-3394	47	3	]	]	X
ejpam-3394	47	4	let	let	VERB
ejpam-3394	47	5	(	(	PUNCT
ejpam-3394	47	6	x	x	NOUN
ejpam-3394	47	7	,	,	PUNCT
ejpam-3394	47	8	τ	τ	X
ejpam-3394	47	9	)	)	PUNCT
ejpam-3394	47	10	be	be	VERB
ejpam-3394	47	11	a	a	DET
ejpam-3394	47	12	space	space	NOUN
ejpam-3394	47	13	,	,	PUNCT
ejpam-3394	47	14	a	a	DET
ejpam-3394	47	15	⊆	⊆	NUM
ejpam-3394	47	16	y	y	SYM
ejpam-3394	47	17	⊆	⊆	NUM
ejpam-3394	47	18	x	x	PUNCT
ejpam-3394	47	19	and	and	CCONJ
ejpam-3394	47	20	y	y	PROPN
ejpam-3394	47	21	be	be	AUX
ejpam-3394	47	22	β	β	X
ejpam-3394	47	23	-	-	VERB
ejpam-3394	47	24	open	open	ADJ
ejpam-3394	47	25	in	in	ADP
ejpam-3394	47	26	(	(	PUNCT
ejpam-3394	47	27	x	x	NOUN
ejpam-3394	47	28	,	,	PUNCT
ejpam-3394	47	29	τ	τ	PROPN
ejpam-3394	47	30	)	)	PUNCT
ejpam-3394	47	31	.	.	PUNCT
ejpam-3394	48	1	then	then	ADV
ejpam-3394	48	2	a	a	PRON
ejpam-3394	48	3	is	be	AUX
ejpam-3394	48	4	β	β	X
ejpam-3394	48	5	-	-	ADJ
ejpam-3394	48	6	open	open	ADJ
ejpam-3394	48	7	in	in	ADP
ejpam-3394	48	8	(	(	PUNCT
ejpam-3394	48	9	x	x	NOUN
ejpam-3394	48	10	,	,	PUNCT
ejpam-3394	48	11	τ	τ	X
ejpam-3394	48	12	)	)	PUNCT
ejpam-3394	49	1	if	if	SCONJ
ejpam-3394	49	2	and	and	CCONJ
ejpam-3394	49	3	only	only	ADV
ejpam-3394	49	4	if	if	SCONJ
ejpam-3394	49	5	a	a	PRON
ejpam-3394	49	6	is	be	AUX
ejpam-3394	49	7	β	β	X
ejpam-3394	49	8	-	-	ADJ
ejpam-3394	49	9	open	open	ADJ
ejpam-3394	49	10	in	in	ADP
ejpam-3394	49	11	the	the	DET
ejpam-3394	49	12	subspace	subspace	NOUN
ejpam-3394	49	13	(	(	PUNCT
ejpam-3394	49	14	y	y	PROPN
ejpam-3394	49	15	,	,	PUNCT
ejpam-3394	49	16	τy	τy	PRON
ejpam-3394	49	17	)	)	PUNCT
ejpam-3394	49	18	.	.	PUNCT
ejpam-3394	50	1	a	a	DET
ejpam-3394	50	2	function	function	NOUN
ejpam-3394	50	3	f	f	NOUN
ejpam-3394	50	4	:	:	PUNCT
ejpam-3394	50	5	(	(	PUNCT
ejpam-3394	50	6	x	x	X
ejpam-3394	50	7	,	,	PUNCT
ejpam-3394	50	8	τ	τ	X
ejpam-3394	50	9	)	)	PUNCT
ejpam-3394	50	10	→	→	SYM
ejpam-3394	50	11	(	(	PUNCT
ejpam-3394	50	12	y	y	PROPN
ejpam-3394	50	13	,	,	PUNCT
ejpam-3394	50	14	σ	σ	PROPN
ejpam-3394	50	15	)	)	PUNCT
ejpam-3394	50	16	is	be	AUX
ejpam-3394	50	17	said	say	VERB
ejpam-3394	50	18	to	to	PART
ejpam-3394	50	19	be	be	AUX
ejpam-3394	50	20	pre	pre	VERB
ejpam-3394	50	21	β	β	X
ejpam-3394	50	22	-	-	ADJ
ejpam-3394	50	23	closed	closed	ADJ
ejpam-3394	50	24	[	[	X
ejpam-3394	50	25	17	17	NUM
ejpam-3394	50	26	]	]	PUNCT
ejpam-3394	50	27	(	(	PUNCT
ejpam-3394	50	28	pre	pre	X
ejpam-3394	50	29	β	β	X
ejpam-3394	50	30	-	-	ADJ
ejpam-3394	50	31	open	open	ADJ
ejpam-3394	50	32	[	[	X
ejpam-3394	50	33	17	17	NUM
ejpam-3394	50	34	]	]	SYM
ejpam-3394	50	35	)	)	PUNCT
ejpam-3394	50	36	if	if	SCONJ
ejpam-3394	50	37	for	for	ADP
ejpam-3394	50	38	every	every	DET
ejpam-3394	50	39	β	β	NOUN
ejpam-3394	50	40	-	-	VERB
ejpam-3394	50	41	closed	closed	ADJ
ejpam-3394	50	42	(	(	PUNCT
ejpam-3394	50	43	β	β	NOUN
ejpam-3394	50	44	-	-	NOUN
ejpam-3394	50	45	open)set	open)set	VERB
ejpam-3394	50	46	a	a	PRON
ejpam-3394	50	47	of	of	ADP
ejpam-3394	50	48	(	(	PUNCT
ejpam-3394	50	49	x	x	PROPN
ejpam-3394	50	50	,	,	PUNCT
ejpam-3394	50	51	τ	τ	PROPN
ejpam-3394	50	52	)	)	PUNCT
ejpam-3394	50	53	,	,	PUNCT
ejpam-3394	50	54	f(a	f(a	PROPN
ejpam-3394	50	55	)	)	PUNCT
ejpam-3394	50	56	is	be	AUX
ejpam-3394	50	57	β	β	X
ejpam-3394	51	1	-	-	VERB
ejpam-3394	51	2	closed	closed	ADJ
ejpam-3394	51	3	(	(	PUNCT
ejpam-3394	51	4	β	β	NOUN
ejpam-3394	51	5	-	-	ADJ
ejpam-3394	51	6	open	open	ADJ
ejpam-3394	51	7	)	)	PUNCT
ejpam-3394	51	8	in	in	ADP
ejpam-3394	51	9	(	(	PUNCT
ejpam-3394	51	10	y	y	PROPN
ejpam-3394	51	11	,	,	PUNCT
ejpam-3394	51	12	σ	σ	PROPN
ejpam-3394	51	13	)	)	PUNCT
ejpam-3394	51	14	and	and	CCONJ
ejpam-3394	51	15	f	f	NOUN
ejpam-3394	51	16	:	:	PUNCT
ejpam-3394	51	17	(	(	PUNCT
ejpam-3394	51	18	x	x	X
ejpam-3394	51	19	,	,	PUNCT
ejpam-3394	51	20	τ	τ	X
ejpam-3394	51	21	)	)	PUNCT
ejpam-3394	51	22	→	→	SYM
ejpam-3394	51	23	(	(	PUNCT
ejpam-3394	51	24	y	y	PROPN
ejpam-3394	51	25	,	,	PUNCT
ejpam-3394	51	26	σ	σ	PROPN
ejpam-3394	51	27	)	)	PUNCT
ejpam-3394	51	28	is	be	AUX
ejpam-3394	51	29	said	say	VERB
ejpam-3394	51	30	to	to	PART
ejpam-3394	51	31	be	be	AUX
ejpam-3394	51	32	β	β	X
ejpam-3394	51	33	-	-	NOUN
ejpam-3394	51	34	irresolute	irresolute	ADJ
ejpam-3394	51	35	[	[	X
ejpam-3394	51	36	17	17	NUM
ejpam-3394	51	37	]	]	X
ejpam-3394	51	38	if	if	SCONJ
ejpam-3394	51	39	for	for	ADP
ejpam-3394	51	40	every	every	DET
ejpam-3394	51	41	β	β	NOUN
ejpam-3394	51	42	-	-	ADJ
ejpam-3394	51	43	open	open	ADJ
ejpam-3394	51	44	set	set	ADJ
ejpam-3394	51	45	b	b	PROPN
ejpam-3394	51	46	of	of	ADP
ejpam-3394	51	47	(	(	PUNCT
ejpam-3394	51	48	y	y	PROPN
ejpam-3394	51	49	,	,	PUNCT
ejpam-3394	51	50	σ	σ	PROPN
ejpam-3394	51	51	)	)	PUNCT
ejpam-3394	51	52	,	,	PUNCT
ejpam-3394	51	53	f−1(b	f−1(b	PROPN
ejpam-3394	51	54	)	)	PUNCT
ejpam-3394	51	55	is	be	AUX
ejpam-3394	51	56	β	β	NOUN
ejpam-3394	51	57	-	-	VERB
ejpam-3394	51	58	open	open	ADJ
ejpam-3394	51	59	in	in	ADP
ejpam-3394	51	60	(	(	PUNCT
ejpam-3394	51	61	x	x	NOUN
ejpam-3394	51	62	,	,	PUNCT
ejpam-3394	51	63	τ	τ	PROPN
ejpam-3394	51	64	)	)	PUNCT
ejpam-3394	51	65	.	.	PUNCT
ejpam-3394	52	1	if	if	SCONJ
ejpam-3394	52	2	f	f	PROPN
ejpam-3394	52	3	:	:	PUNCT
ejpam-3394	52	4	(	(	PUNCT
ejpam-3394	52	5	x	x	X
ejpam-3394	52	6	,	,	PUNCT
ejpam-3394	52	7	τ	τ	X
ejpam-3394	52	8	)	)	PUNCT
ejpam-3394	52	9	→	→	SYM
ejpam-3394	52	10	(	(	PUNCT
ejpam-3394	52	11	y	y	PROPN
ejpam-3394	52	12	,	,	PUNCT
ejpam-3394	52	13	σ	σ	PROPN
ejpam-3394	52	14	)	)	PUNCT
ejpam-3394	52	15	is	be	AUX
ejpam-3394	52	16	continuous	continuous	ADJ
ejpam-3394	52	17	and	and	CCONJ
ejpam-3394	52	18	open	open	ADJ
ejpam-3394	52	19	,	,	PUNCT
ejpam-3394	52	20	then	then	ADV
ejpam-3394	52	21	f	f	PROPN
ejpam-3394	52	22	is	be	AUX
ejpam-3394	52	23	β	β	NOUN
ejpam-3394	52	24	-	-	NOUN
ejpam-3394	52	25	irresolute	irresolute	ADJ
ejpam-3394	52	26	and	and	CCONJ
ejpam-3394	52	27	pre	pre	VERB
ejpam-3394	52	28	β	β	X
ejpam-3394	52	29	-	-	ADJ
ejpam-3394	52	30	open	open	ADJ
ejpam-3394	52	31	.	.	PUNCT
ejpam-3394	53	1	lemma	lemma	PROPN
ejpam-3394	53	2	2	2	NUM
ejpam-3394	53	3	.	.	PUNCT
ejpam-3394	54	1	[	[	X
ejpam-3394	54	2	11	11	NUM
ejpam-3394	54	3	]	]	PUNCT
ejpam-3394	54	4	let	let	VERB
ejpam-3394	54	5	f	f	PRON
ejpam-3394	54	6	:	:	PUNCT
ejpam-3394	54	7	(	(	PUNCT
ejpam-3394	54	8	x	x	X
ejpam-3394	54	9	,	,	PUNCT
ejpam-3394	54	10	τ	τ	X
ejpam-3394	54	11	)	)	PUNCT
ejpam-3394	54	12	→	→	SYM
ejpam-3394	54	13	(	(	PUNCT
ejpam-3394	54	14	y	y	PROPN
ejpam-3394	54	15	,	,	PUNCT
ejpam-3394	54	16	σ	σ	PROPN
ejpam-3394	54	17	)	)	PUNCT
ejpam-3394	54	18	be	be	AUX
ejpam-3394	54	19	a	a	DET
ejpam-3394	54	20	surjective	surjective	ADJ
ejpam-3394	54	21	function	function	NOUN
ejpam-3394	54	22	.	.	PUNCT
ejpam-3394	55	1	then	then	ADV
ejpam-3394	55	2	f	f	PROPN
ejpam-3394	55	3	is	be	AUX
ejpam-3394	55	4	pre	pre	ADJ
ejpam-3394	55	5	β	β	X
ejpam-3394	55	6	-	-	ADJ
ejpam-3394	55	7	closed	closed	ADJ
ejpam-3394	55	8	if	if	SCONJ
ejpam-3394	55	9	and	and	CCONJ
ejpam-3394	55	10	only	only	ADV
ejpam-3394	55	11	if	if	SCONJ
ejpam-3394	55	12	for	for	ADP
ejpam-3394	55	13	every	every	DET
ejpam-3394	55	14	y	y	PROPN
ejpam-3394	55	15	∈	∈	PROPN
ejpam-3394	55	16	y	y	PROPN
ejpam-3394	55	17	and	and	CCONJ
ejpam-3394	55	18	every	every	DET
ejpam-3394	55	19	β	β	NOUN
ejpam-3394	55	20	-	-	ADJ
ejpam-3394	55	21	open	open	ADJ
ejpam-3394	55	22	set	set	NOUN
ejpam-3394	55	23	u	u	NOUN
ejpam-3394	55	24	in	in	ADP
ejpam-3394	55	25	(	(	PUNCT
ejpam-3394	55	26	x	x	NOUN
ejpam-3394	55	27	,	,	PUNCT
ejpam-3394	55	28	τ	τ	X
ejpam-3394	55	29	)	)	PUNCT
ejpam-3394	55	30	which	which	PRON
ejpam-3394	55	31	contains	contain	VERB
ejpam-3394	55	32	f−1(y	f−1(y	PROPN
ejpam-3394	55	33	)	)	PUNCT
ejpam-3394	55	34	,	,	PUNCT
ejpam-3394	55	35	there	there	PRON
ejpam-3394	55	36	exists	exist	VERB
ejpam-3394	55	37	a	a	DET
ejpam-3394	55	38	v	v	NOUN
ejpam-3394	55	39	∈	∈	NOUN
ejpam-3394	55	40	βo(y	βo(y	PUNCT
ejpam-3394	55	41	,	,	PUNCT
ejpam-3394	55	42	σ	σ	PROPN
ejpam-3394	55	43	)	)	PUNCT
ejpam-3394	55	44	such	such	ADJ
ejpam-3394	55	45	that	that	SCONJ
ejpam-3394	55	46	y	y	PROPN
ejpam-3394	55	47	∈	∈	PROPN
ejpam-3394	55	48	v	v	NOUN
ejpam-3394	55	49	and	and	CCONJ
ejpam-3394	55	50	f−1(v	f−1(v	NOUN
ejpam-3394	55	51	)	)	PUNCT
ejpam-3394	56	1	⊆	⊆	NUM
ejpam-3394	56	2	u	u	NOUN
ejpam-3394	56	3	.	.	PUNCT
ejpam-3394	57	1	a	a	DET
ejpam-3394	57	2	space	space	NOUN
ejpam-3394	57	3	(	(	PUNCT
ejpam-3394	57	4	x	x	X
ejpam-3394	57	5	,	,	PUNCT
ejpam-3394	57	6	τ	τ	X
ejpam-3394	57	7	)	)	PUNCT
ejpam-3394	57	8	is	be	AUX
ejpam-3394	57	9	called	call	VERB
ejpam-3394	57	10	extremally	extremally	ADV
ejpam-3394	57	11	disconnected[23](briefly	disconnected[23](briefly	ADJ
ejpam-3394	57	12	,	,	PUNCT
ejpam-3394	57	13	e.	e.	PROPN
ejpam-3394	57	14	d.	d.	PROPN
ejpam-3394	57	15	)	)	PUNCT
ejpam-3394	58	1	if	if	SCONJ
ejpam-3394	58	2	the	the	DET
ejpam-3394	58	3	closure	closure	NOUN
ejpam-3394	58	4	of	of	ADP
ejpam-3394	58	5	every	every	DET
ejpam-3394	58	6	open	open	ADJ
ejpam-3394	58	7	set	set	NOUN
ejpam-3394	58	8	in	in	ADP
ejpam-3394	58	9	x	x	VERB
ejpam-3394	58	10	is	be	AUX
ejpam-3394	58	11	open	open	ADJ
ejpam-3394	58	12	and	and	CCONJ
ejpam-3394	58	13	called	call	VERB
ejpam-3394	58	14	submaximal	submaximal	ADJ
ejpam-3394	58	15	[	[	X
ejpam-3394	58	16	8	8	NUM
ejpam-3394	58	17	]	]	X
ejpam-3394	58	18	if	if	SCONJ
ejpam-3394	58	19	each	each	DET
ejpam-3394	58	20	dense	dense	ADJ
ejpam-3394	58	21	subset	subset	NOUN
ejpam-3394	58	22	of	of	ADP
ejpam-3394	58	23	x	x	PUNCT
ejpam-3394	58	24	is	be	AUX
ejpam-3394	58	25	open	open	ADJ
ejpam-3394	58	26	in	in	ADP
ejpam-3394	58	27	x.	x.	PROPN
ejpam-3394	58	28	lemma	lemma	PROPN
ejpam-3394	59	1	3	3	X
ejpam-3394	59	2	.	.	PUNCT
ejpam-3394	60	1	[	[	X
ejpam-3394	60	2	20	20	NUM
ejpam-3394	60	3	]	]	PUNCT
ejpam-3394	60	4	(	(	PUNCT
ejpam-3394	60	5	x	x	X
ejpam-3394	60	6	,	,	PUNCT
ejpam-3394	60	7	τ	τ	X
ejpam-3394	60	8	)	)	PUNCT
ejpam-3394	60	9	is	be	AUX
ejpam-3394	60	10	submaximal	submaximal	ADJ
ejpam-3394	60	11	if	if	SCONJ
ejpam-3394	60	12	and	and	CCONJ
ejpam-3394	60	13	only	only	ADV
ejpam-3394	60	14	if	if	SCONJ
ejpam-3394	60	15	every	every	DET
ejpam-3394	60	16	pre	pre	ADJ
ejpam-3394	60	17	-	-	ADJ
ejpam-3394	60	18	open	open	ADJ
ejpam-3394	60	19	set	set	NOUN
ejpam-3394	60	20	is	be	AUX
ejpam-3394	60	21	open	open	ADJ
ejpam-3394	60	22	.	.	PUNCT
ejpam-3394	61	1	lemma	lemma	PROPN
ejpam-3394	61	2	4	4	NUM
ejpam-3394	61	3	.	.	PUNCT
ejpam-3394	62	1	[	[	X
ejpam-3394	62	2	9	9	NUM
ejpam-3394	62	3	]	]	SYM
ejpam-3394	62	4	(	(	PUNCT
ejpam-3394	62	5	x	x	X
ejpam-3394	62	6	,	,	PUNCT
ejpam-3394	62	7	τ	τ	X
ejpam-3394	62	8	)	)	PUNCT
ejpam-3394	62	9	is	be	AUX
ejpam-3394	62	10	e.d	e.d	PROPN
ejpam-3394	62	11	.	.	PUNCT
ejpam-3394	63	1	if	if	SCONJ
ejpam-3394	63	2	and	and	CCONJ
ejpam-3394	63	3	only	only	ADV
ejpam-3394	63	4	if	if	SCONJ
ejpam-3394	63	5	every	every	DET
ejpam-3394	63	6	β	β	NOUN
ejpam-3394	63	7	-	-	ADJ
ejpam-3394	63	8	open	open	ADJ
ejpam-3394	63	9	set	set	NOUN
ejpam-3394	63	10	is	be	AUX
ejpam-3394	63	11	pre	pre	ADJ
ejpam-3394	63	12	-	-	ADJ
ejpam-3394	63	13	open	open	ADJ
ejpam-3394	63	14	.	.	PUNCT
ejpam-3394	64	1	a	a	DET
ejpam-3394	64	2	collection	collection	NOUN
ejpam-3394	64	3	v	v	NOUN
ejpam-3394	64	4	of	of	ADP
ejpam-3394	64	5	subsets	subset	NOUN
ejpam-3394	64	6	of	of	ADP
ejpam-3394	64	7	a	a	DET
ejpam-3394	64	8	space	space	NOUN
ejpam-3394	64	9	(	(	PUNCT
ejpam-3394	64	10	x	x	X
ejpam-3394	64	11	,	,	PUNCT
ejpam-3394	64	12	τ	τ	X
ejpam-3394	64	13	)	)	PUNCT
ejpam-3394	64	14	is	be	AUX
ejpam-3394	64	15	said	say	VERB
ejpam-3394	64	16	to	to	PART
ejpam-3394	64	17	be	be	AUX
ejpam-3394	64	18	locally	locally	ADV
ejpam-3394	64	19	finite	finite	ADJ
ejpam-3394	64	20	[	[	X
ejpam-3394	64	21	23](resp	23](resp	NUM
ejpam-3394	64	22	.	.	PUNCT
ejpam-3394	65	1	s	s	X
ejpam-3394	65	2	-	-	PUNCT
ejpam-3394	65	3	locally	locally	ADV
ejpam-3394	65	4	finite	finite	NOUN
ejpam-3394	65	5	[	[	X
ejpam-3394	65	6	4	4	NUM
ejpam-3394	65	7	]	]	PUNCT
ejpam-3394	65	8	,	,	PUNCT
ejpam-3394	65	9	β	β	X
ejpam-3394	65	10	-	-	PUNCT
ejpam-3394	65	11	locally	locally	ADV
ejpam-3394	65	12	finite	finite	NOUN
ejpam-3394	66	1	[	[	X
ejpam-3394	66	2	11	11	NUM
ejpam-3394	66	3	]	]	PUNCT
ejpam-3394	66	4	and	and	CCONJ
ejpam-3394	66	5	p	p	NOUN
ejpam-3394	66	6	-	-	PUNCT
ejpam-3394	66	7	locally	locally	ADV
ejpam-3394	66	8	finite[6	finite[6	NOUN
ejpam-3394	66	9	]	]	NUM
ejpam-3394	66	10	)	)	PUNCT
ejpam-3394	66	11	,	,	PUNCT
ejpam-3394	66	12	if	if	SCONJ
ejpam-3394	66	13	for	for	ADP
ejpam-3394	66	14	each	each	DET
ejpam-3394	66	15	x	x	SYM
ejpam-3394	66	16	∈	∈	PROPN
ejpam-3394	66	17	x	x	PUNCT
ejpam-3394	66	18	there	there	PRON
ejpam-3394	66	19	exists	exist	VERB
ejpam-3394	66	20	ux	ux	PROPN
ejpam-3394	66	21	∈	∈	PROPN
ejpam-3394	66	22	τ	τ	X
ejpam-3394	66	23	(	(	PUNCT
ejpam-3394	66	24	resp	resp	NOUN
ejpam-3394	66	25	.	.	PUNCT
ejpam-3394	67	1	ux	ux	PROPN
ejpam-3394	67	2	∈	∈	PROPN
ejpam-3394	67	3	so(x	so(x	NOUN
ejpam-3394	67	4	,	,	PUNCT
ejpam-3394	67	5	τ	τ	PROPN
ejpam-3394	67	6	)	)	PUNCT
ejpam-3394	67	7	,	,	PUNCT
ejpam-3394	67	8	ux	ux	PROPN
ejpam-3394	67	9	∈	∈	PROPN
ejpam-3394	67	10	βo(x	βo(x	PUNCT
ejpam-3394	67	11	,	,	PUNCT
ejpam-3394	67	12	τ	τ	X
ejpam-3394	67	13	)	)	PUNCT
ejpam-3394	67	14	and	and	CCONJ
ejpam-3394	67	15	ux	ux	PROPN
ejpam-3394	67	16	∈	∈	PROPN
ejpam-3394	67	17	po(x	po(x	NOUN
ejpam-3394	67	18	,	,	PUNCT
ejpam-3394	67	19	τ	τ	NOUN
ejpam-3394	67	20	)	)	PUNCT
ejpam-3394	67	21	)	)	PUNCT
ejpam-3394	68	1	containing	contain	VERB
ejpam-3394	68	2	x	x	PROPN
ejpam-3394	68	3	and	and	CCONJ
ejpam-3394	68	4	ux	ux	PROPN
ejpam-3394	68	5	intersects	intersect	NOUN
ejpam-3394	68	6	at	at	ADV
ejpam-3394	68	7	most	most	ADV
ejpam-3394	68	8	finitely	finitely	ADV
ejpam-3394	68	9	many	many	ADJ
ejpam-3394	68	10	members	member	NOUN
ejpam-3394	68	11	of	of	ADP
ejpam-3394	68	12	v	v	NOUN
ejpam-3394	68	13	.	.	PUNCT
ejpam-3394	69	1	every	every	DET
ejpam-3394	69	2	locally	locally	ADV
ejpam-3394	69	3	finite	finite	ADJ
ejpam-3394	69	4	collection	collection	NOUN
ejpam-3394	69	5	of	of	ADP
ejpam-3394	69	6	subsets	subset	NOUN
ejpam-3394	69	7	of	of	ADP
ejpam-3394	69	8	a	a	DET
ejpam-3394	69	9	space	space	NOUN
ejpam-3394	69	10	e.	e.	PROPN
ejpam-3394	69	11	d.	d.	PROPN
ejpam-3394	69	12	yıldırım	yıldırım	PROPN
ejpam-3394	69	13	,	,	PUNCT
ejpam-3394	69	14	o.	o.	PROPN
ejpam-3394	69	15	b.	b.	PROPN
ejpam-3394	69	16	özbakır	özbakır	PROPN
ejpam-3394	69	17	,	,	PUNCT
ejpam-3394	69	18	a.	a.	PROPN
ejpam-3394	69	19	c.	c.	PROPN
ejpam-3394	69	20	.	.	PUNCT
ejpam-3394	70	1	güler	güler	PROPN
ejpam-3394	70	2	/	/	SYM
ejpam-3394	70	3	eur	eur	PROPN
ejpam-3394	70	4	.	.	PUNCT
ejpam-3394	71	1	j.	j.	PROPN
ejpam-3394	71	2	pure	pure	PROPN
ejpam-3394	71	3	appl	appl	PROPN
ejpam-3394	71	4	.	.	PROPN
ejpam-3394	71	5	math	math	PROPN
ejpam-3394	71	6	,	,	PUNCT
ejpam-3394	71	7	12	12	NUM
ejpam-3394	71	8	(	(	PUNCT
ejpam-3394	71	9	2	2	NUM
ejpam-3394	71	10	)	)	PUNCT
ejpam-3394	71	11	(	(	PUNCT
ejpam-3394	71	12	2019	2019	NUM
ejpam-3394	71	13	)	)	PUNCT
ejpam-3394	71	14	,	,	PUNCT
ejpam-3394	71	15	270	270	NUM
ejpam-3394	71	16	-	-	SYM
ejpam-3394	71	17	278	278	NUM
ejpam-3394	71	18	272	272	NUM
ejpam-3394	71	19	(	(	PUNCT
ejpam-3394	71	20	x	x	X
ejpam-3394	71	21	,	,	PUNCT
ejpam-3394	71	22	τ	τ	X
ejpam-3394	71	23	)	)	PUNCT
ejpam-3394	71	24	is	be	AUX
ejpam-3394	71	25	β	β	X
ejpam-3394	71	26	-	-	ADJ
ejpam-3394	71	27	locally	locally	ADV
ejpam-3394	71	28	finite[11	finite[11	NOUN
ejpam-3394	71	29	]	]	PUNCT
ejpam-3394	71	30	and	and	CCONJ
ejpam-3394	71	31	p	p	NOUN
ejpam-3394	71	32	-	-	PUNCT
ejpam-3394	71	33	locally	locally	ADV
ejpam-3394	71	34	finite[6	finite[6	NOUN
ejpam-3394	71	35	]	]	X
ejpam-3394	71	36	.	.	PUNCT
ejpam-3394	72	1	also	also	ADV
ejpam-3394	72	2	,	,	PUNCT
ejpam-3394	72	3	a	a	DET
ejpam-3394	72	4	collection	collection	NOUN
ejpam-3394	72	5	a	a	PRON
ejpam-3394	72	6	of	of	ADP
ejpam-3394	72	7	subsets	subset	NOUN
ejpam-3394	72	8	of	of	ADP
ejpam-3394	72	9	a	a	DET
ejpam-3394	72	10	space	space	NOUN
ejpam-3394	72	11	(	(	PUNCT
ejpam-3394	72	12	x	x	X
ejpam-3394	72	13	,	,	PUNCT
ejpam-3394	72	14	τ	τ	X
ejpam-3394	72	15	)	)	PUNCT
ejpam-3394	72	16	is	be	AUX
ejpam-3394	72	17	said	say	VERB
ejpam-3394	72	18	to	to	PART
ejpam-3394	72	19	be	be	AUX
ejpam-3394	72	20	σ	σ	NOUN
ejpam-3394	72	21	-	-	PUNCT
ejpam-3394	72	22	locally	locally	ADV
ejpam-3394	72	23	finite	finite	NOUN
ejpam-3394	72	24	if	if	SCONJ
ejpam-3394	72	25	a	a	DET
ejpam-3394	72	26	=	=	ADJ
ejpam-3394	72	27	∞⋃	∞⋃	NOUN
ejpam-3394	72	28	n=1	n=1	PROPN
ejpam-3394	72	29	an	an	PRON
ejpam-3394	72	30	where	where	SCONJ
ejpam-3394	72	31	each	each	DET
ejpam-3394	72	32	an	an	PRON
ejpam-3394	72	33	is	be	AUX
ejpam-3394	72	34	locally	locally	ADV
ejpam-3394	72	35	finite	finite	ADJ
ejpam-3394	72	36	family	family	NOUN
ejpam-3394	72	37	[	[	X
ejpam-3394	72	38	13	13	NUM
ejpam-3394	72	39	]	]	PUNCT
ejpam-3394	72	40	.	.	PUNCT
ejpam-3394	73	1	theorem	theorem	NOUN
ejpam-3394	73	2	2	2	NUM
ejpam-3394	73	3	.	.	PUNCT
ejpam-3394	74	1	[	[	X
ejpam-3394	74	2	11	11	NUM
ejpam-3394	74	3	]	]	X
ejpam-3394	74	4	let	let	AUX
ejpam-3394	74	5	(	(	PUNCT
ejpam-3394	74	6	x	x	NOUN
ejpam-3394	74	7	,	,	PUNCT
ejpam-3394	74	8	τ	τ	X
ejpam-3394	74	9	)	)	PUNCT
ejpam-3394	74	10	be	be	VERB
ejpam-3394	74	11	an	an	DET
ejpam-3394	74	12	e.d	e.d	PROPN
ejpam-3394	74	13	.	.	PROPN
ejpam-3394	74	14	submaximal	submaximal	ADJ
ejpam-3394	74	15	space	space	NOUN
ejpam-3394	74	16	.	.	PUNCT
ejpam-3394	75	1	then	then	ADV
ejpam-3394	75	2	every	every	DET
ejpam-3394	75	3	β	β	X
ejpam-3394	75	4	-	-	ADJ
ejpam-3394	75	5	locally	locally	ADV
ejpam-3394	75	6	finite	finite	ADJ
ejpam-3394	75	7	collection	collection	NOUN
ejpam-3394	75	8	of	of	ADP
ejpam-3394	75	9	subsets	subset	NOUN
ejpam-3394	75	10	of	of	ADP
ejpam-3394	75	11	x	x	SYM
ejpam-3394	75	12	is	be	AUX
ejpam-3394	75	13	locally	locally	ADV
ejpam-3394	75	14	finite	finite	ADJ
ejpam-3394	75	15	.	.	PUNCT
ejpam-3394	76	1	a	a	DET
ejpam-3394	76	2	space	space	NOUN
ejpam-3394	76	3	(	(	PUNCT
ejpam-3394	76	4	x	x	X
ejpam-3394	76	5	,	,	PUNCT
ejpam-3394	76	6	τ	τ	X
ejpam-3394	76	7	)	)	PUNCT
ejpam-3394	76	8	is	be	AUX
ejpam-3394	76	9	said	say	VERB
ejpam-3394	76	10	to	to	PART
ejpam-3394	76	11	be	be	AUX
ejpam-3394	76	12	β	β	X
ejpam-3394	76	13	-	-	ADJ
ejpam-3394	76	14	compact	compact	ADJ
ejpam-3394	76	15	[	[	X
ejpam-3394	76	16	2	2	X
ejpam-3394	76	17	]	]	PUNCT
ejpam-3394	76	18	if	if	SCONJ
ejpam-3394	76	19	every	every	DET
ejpam-3394	76	20	cover	cover	NOUN
ejpam-3394	76	21	of	of	ADP
ejpam-3394	76	22	x	x	PUNCT
ejpam-3394	76	23	by	by	ADP
ejpam-3394	76	24	β	β	ADJ
ejpam-3394	76	25	-	-	ADJ
ejpam-3394	76	26	open	open	ADJ
ejpam-3394	76	27	sets	set	NOUN
ejpam-3394	76	28	has	have	VERB
ejpam-3394	76	29	a	a	DET
ejpam-3394	76	30	finite	finite	ADJ
ejpam-3394	76	31	subcover	subcover	PROPN
ejpam-3394	76	32	.	.	PUNCT
ejpam-3394	77	1	also	also	ADV
ejpam-3394	77	2	a	a	DET
ejpam-3394	77	3	space	space	NOUN
ejpam-3394	77	4	(	(	PUNCT
ejpam-3394	77	5	x	x	X
ejpam-3394	77	6	,	,	PUNCT
ejpam-3394	77	7	τ	τ	X
ejpam-3394	77	8	)	)	PUNCT
ejpam-3394	77	9	is	be	AUX
ejpam-3394	77	10	said	say	VERB
ejpam-3394	77	11	to	to	PART
ejpam-3394	77	12	be	be	AUX
ejpam-3394	77	13	paracompact	paracompact	ADJ
ejpam-3394	77	14	[	[	X
ejpam-3394	77	15	23	23	NUM
ejpam-3394	77	16	]	]	PUNCT
ejpam-3394	77	17	(	(	PUNCT
ejpam-3394	77	18	resp	resp	NOUN
ejpam-3394	77	19	.	.	PUNCT
ejpam-3394	78	1	s	s	X
ejpam-3394	78	2	-	-	NOUN
ejpam-3394	78	3	paracompact	paracompact	ADJ
ejpam-3394	79	1	[	[	X
ejpam-3394	79	2	5	5	NUM
ejpam-3394	79	3	]	]	PUNCT
ejpam-3394	79	4	,	,	PUNCT
ejpam-3394	79	5	β	β	NOUN
ejpam-3394	79	6	-	-	NOUN
ejpam-3394	79	7	paracompact	paracompact	ADJ
ejpam-3394	80	1	[	[	X
ejpam-3394	80	2	11	11	NUM
ejpam-3394	80	3	]	]	PUNCT
ejpam-3394	80	4	and	and	CCONJ
ejpam-3394	80	5	p3	p3	NOUN
ejpam-3394	80	6	-	-	NOUN
ejpam-3394	80	7	paracompact	paracompact	NOUN
ejpam-3394	81	1	[	[	X
ejpam-3394	81	2	6	6	NUM
ejpam-3394	81	3	]	]	NUM
ejpam-3394	81	4	)	)	PUNCT
ejpam-3394	81	5	,	,	PUNCT
ejpam-3394	81	6	if	if	SCONJ
ejpam-3394	81	7	every	every	DET
ejpam-3394	81	8	open	open	ADJ
ejpam-3394	81	9	cover	cover	NOUN
ejpam-3394	81	10	of	of	ADP
ejpam-3394	81	11	x	x	PUNCT
ejpam-3394	81	12	has	have	VERB
ejpam-3394	81	13	a	a	DET
ejpam-3394	81	14	locally	locally	ADV
ejpam-3394	81	15	finite	finite	ADJ
ejpam-3394	81	16	open	open	ADJ
ejpam-3394	81	17	(	(	PUNCT
ejpam-3394	81	18	resp	resp	NOUN
ejpam-3394	81	19	.	.	PUNCT
ejpam-3394	82	1	locally	locally	ADV
ejpam-3394	82	2	finite	finite	VERB
ejpam-3394	82	3	semi	semi	ADJ
ejpam-3394	82	4	-	-	ADJ
ejpam-3394	82	5	open	open	ADJ
ejpam-3394	82	6	,	,	PUNCT
ejpam-3394	82	7	β	β	X
ejpam-3394	82	8	-	-	PUNCT
ejpam-3394	82	9	locally	locally	ADV
ejpam-3394	82	10	finite	finite	ADJ
ejpam-3394	82	11	β	β	NOUN
ejpam-3394	82	12	-	-	ADJ
ejpam-3394	82	13	open	open	ADJ
ejpam-3394	82	14	and	and	CCONJ
ejpam-3394	82	15	p	p	NOUN
ejpam-3394	82	16	-	-	PUNCT
ejpam-3394	82	17	locally	locally	ADV
ejpam-3394	82	18	finite	finite	ADJ
ejpam-3394	82	19	preopen	preopen	NOUN
ejpam-3394	82	20	)	)	PUNCT
ejpam-3394	82	21	refinement	refinement	NOUN
ejpam-3394	82	22	which	which	PRON
ejpam-3394	82	23	covers	cover	VERB
ejpam-3394	82	24	to	to	PART
ejpam-3394	82	25	x.	x.	VERB
ejpam-3394	82	26	an	an	DET
ejpam-3394	82	27	ideal	ideal	NOUN
ejpam-3394	82	28	is	be	AUX
ejpam-3394	82	29	defined	define	VERB
ejpam-3394	82	30	as	as	ADP
ejpam-3394	82	31	a	a	DET
ejpam-3394	82	32	nonempty	nonempty	ADJ
ejpam-3394	82	33	collection	collection	NOUN
ejpam-3394	82	34	i	i	PRON
ejpam-3394	82	35	of	of	ADP
ejpam-3394	82	36	subsets	subset	NOUN
ejpam-3394	82	37	of	of	ADP
ejpam-3394	82	38	x	x	PUNCT
ejpam-3394	82	39	satisfying	satisfy	VERB
ejpam-3394	82	40	the	the	DET
ejpam-3394	82	41	following	follow	VERB
ejpam-3394	82	42	two	two	NUM
ejpam-3394	82	43	conditions	condition	NOUN
ejpam-3394	82	44	:	:	PUNCT
ejpam-3394	82	45	(	(	PUNCT
ejpam-3394	82	46	1	1	X
ejpam-3394	82	47	)	)	PUNCT
ejpam-3394	82	48	if	if	SCONJ
ejpam-3394	82	49	a	a	DET
ejpam-3394	82	50	∈	∈	X
ejpam-3394	82	51	i	i	PRON
ejpam-3394	82	52	and	and	CCONJ
ejpam-3394	82	53	b	b	X
ejpam-3394	82	54	⊆	⊆	NUM
ejpam-3394	82	55	a	a	PRON
ejpam-3394	82	56	,	,	PUNCT
ejpam-3394	82	57	then	then	ADV
ejpam-3394	82	58	b	b	X
ejpam-3394	82	59	∈	∈	PROPN
ejpam-3394	82	60	i	i	PRON
ejpam-3394	82	61	,	,	PUNCT
ejpam-3394	82	62	(	(	PUNCT
ejpam-3394	82	63	2	2	X
ejpam-3394	82	64	)	)	PUNCT
ejpam-3394	82	65	if	if	SCONJ
ejpam-3394	82	66	a	a	DET
ejpam-3394	82	67	∈	∈	X
ejpam-3394	82	68	i	i	PRON
ejpam-3394	82	69	and	and	CCONJ
ejpam-3394	82	70	b	b	X
ejpam-3394	82	71	∈	∈	PROPN
ejpam-3394	82	72	i	i	PRON
ejpam-3394	82	73	,	,	PUNCT
ejpam-3394	82	74	then	then	ADV
ejpam-3394	82	75	a	a	DET
ejpam-3394	82	76	∪b	∪b	PUNCT
ejpam-3394	82	77	∈	∈	PROPN
ejpam-3394	82	78	i.	i.	NOUN
ejpam-3394	82	79	given	give	VERB
ejpam-3394	82	80	a	a	DET
ejpam-3394	82	81	topological	topological	ADJ
ejpam-3394	82	82	space	space	NOUN
ejpam-3394	82	83	(	(	PUNCT
ejpam-3394	82	84	x	x	X
ejpam-3394	82	85	,	,	PUNCT
ejpam-3394	82	86	τ	τ	X
ejpam-3394	82	87	)	)	PUNCT
ejpam-3394	82	88	with	with	ADP
ejpam-3394	82	89	an	an	DET
ejpam-3394	82	90	ideal	ideal	ADJ
ejpam-3394	82	91	i	i	PRON
ejpam-3394	82	92	on	on	ADP
ejpam-3394	82	93	x	x	X
ejpam-3394	82	94	and	and	CCONJ
ejpam-3394	82	95	if	if	SCONJ
ejpam-3394	82	96	p(x	p(x	PROPN
ejpam-3394	82	97	)	)	PUNCT
ejpam-3394	82	98	is	be	AUX
ejpam-3394	82	99	the	the	DET
ejpam-3394	82	100	set	set	NOUN
ejpam-3394	82	101	of	of	ADP
ejpam-3394	82	102	all	all	DET
ejpam-3394	82	103	subsets	subset	NOUN
ejpam-3394	82	104	of	of	ADP
ejpam-3394	82	105	x	x	PRON
ejpam-3394	82	106	,	,	PUNCT
ejpam-3394	82	107	a	a	DET
ejpam-3394	82	108	set	set	NOUN
ejpam-3394	82	109	operator	operator	NOUN
ejpam-3394	82	110	(	(	PUNCT
ejpam-3394	83	1	.)∗	.)∗	X
ejpam-3394	83	2	:	:	PUNCT
ejpam-3394	83	3	p(x	p(x	PROPN
ejpam-3394	83	4	)	)	PUNCT
ejpam-3394	83	5	→	→	SYM
ejpam-3394	83	6	p(x	p(x	PROPN
ejpam-3394	83	7	)	)	PUNCT
ejpam-3394	83	8	,	,	PUNCT
ejpam-3394	83	9	called	call	VERB
ejpam-3394	83	10	a	a	DET
ejpam-3394	83	11	local	local	ADJ
ejpam-3394	83	12	function	function	NOUN
ejpam-3394	83	13	[	[	X
ejpam-3394	83	14	15	15	NUM
ejpam-3394	83	15	]	]	PUNCT
ejpam-3394	83	16	of	of	ADP
ejpam-3394	83	17	a	a	PRON
ejpam-3394	83	18	with	with	ADP
ejpam-3394	83	19	respect	respect	NOUN
ejpam-3394	83	20	to	to	ADP
ejpam-3394	83	21	τ	τ	PROPN
ejpam-3394	83	22	and	and	CCONJ
ejpam-3394	83	23	i	i	PRON
ejpam-3394	83	24	is	be	AUX
ejpam-3394	83	25	defined	define	VERB
ejpam-3394	83	26	as	as	SCONJ
ejpam-3394	83	27	follows	follow	VERB
ejpam-3394	83	28	:	:	PUNCT
ejpam-3394	83	29	for	for	ADP
ejpam-3394	83	30	a	a	DET
ejpam-3394	83	31	⊆	⊆	NUM
ejpam-3394	83	32	x	x	SYM
ejpam-3394	83	33	,	,	PUNCT
ejpam-3394	83	34	a∗(i	a∗(i	PROPN
ejpam-3394	83	35	,	,	PUNCT
ejpam-3394	83	36	τ	τ	X
ejpam-3394	83	37	)	)	PUNCT
ejpam-3394	83	38	=	=	PRON
ejpam-3394	84	1	{	{	PUNCT
ejpam-3394	84	2	x	x	PUNCT
ejpam-3394	84	3	∈	∈	PROPN
ejpam-3394	84	4	x	x	X
ejpam-3394	84	5	:	:	PUNCT
ejpam-3394	84	6	v	v	NUM
ejpam-3394	84	7	∩	∩	PROPN
ejpam-3394	84	8	a	a	X
ejpam-3394	84	9	/∈	/∈	PUNCT
ejpam-3394	85	1	i	i	PRON
ejpam-3394	85	2	for	for	ADP
ejpam-3394	85	3	every	every	DET
ejpam-3394	85	4	v	v	ADP
ejpam-3394	85	5	∈	∈	NOUN
ejpam-3394	85	6	τ(x	τ(x	NOUN
ejpam-3394	85	7	)	)	PUNCT
ejpam-3394	85	8	}	}	PUNCT
ejpam-3394	85	9	where	where	SCONJ
ejpam-3394	85	10	τ(x	τ(x	NOUN
ejpam-3394	85	11	)	)	PUNCT
ejpam-3394	85	12	=	=	PRON
ejpam-3394	85	13	{	{	PUNCT
ejpam-3394	85	14	v	v	NUM
ejpam-3394	85	15	∈	∈	NOUN
ejpam-3394	85	16	τ	τ	X
ejpam-3394	85	17	:	:	PUNCT
ejpam-3394	85	18	x	x	SYM
ejpam-3394	85	19	∈	∈	NOUN
ejpam-3394	85	20	v	v	ADP
ejpam-3394	85	21	}	}	PUNCT
ejpam-3394	85	22	.	.	PUNCT
ejpam-3394	86	1	a	a	DET
ejpam-3394	86	2	kuratowski	kuratowski	ADJ
ejpam-3394	86	3	closure	closure	NOUN
ejpam-3394	86	4	operator	operator	NOUN
ejpam-3394	86	5	cl∗	cl∗	PROPN
ejpam-3394	86	6	(	(	PUNCT
ejpam-3394	86	7	.	.	PUNCT
ejpam-3394	86	8	)	)	PUNCT
ejpam-3394	87	1	for	for	ADP
ejpam-3394	87	2	a	a	DET
ejpam-3394	87	3	topology	topology	NOUN
ejpam-3394	87	4	τ∗(i	τ∗(i	PROPN
ejpam-3394	87	5	,	,	PUNCT
ejpam-3394	87	6	τ	τ	PROPN
ejpam-3394	87	7	)	)	PUNCT
ejpam-3394	87	8	,	,	PUNCT
ejpam-3394	87	9	called	call	VERB
ejpam-3394	87	10	the	the	DET
ejpam-3394	87	11	*	*	PUNCT
ejpam-3394	87	12	-topology	-topology	NOUN
ejpam-3394	87	13	,	,	PUNCT
ejpam-3394	87	14	finer	fine	ADJ
ejpam-3394	87	15	than	than	ADP
ejpam-3394	87	16	τ	τ	PROPN
ejpam-3394	87	17	,	,	PUNCT
ejpam-3394	87	18	is	be	AUX
ejpam-3394	87	19	defined	define	VERB
ejpam-3394	87	20	by	by	ADP
ejpam-3394	87	21	cl∗(a	cl∗(a	NOUN
ejpam-3394	87	22	)	)	PUNCT
ejpam-3394	87	23	=	=	SYM
ejpam-3394	87	24	a∪a∗(i	a∪a∗(i	PROPN
ejpam-3394	87	25	,	,	PUNCT
ejpam-3394	87	26	τ	τ	X
ejpam-3394	87	27	)	)	PUNCT
ejpam-3394	88	1	[	[	X
ejpam-3394	88	2	14	14	NUM
ejpam-3394	88	3	]	]	PUNCT
ejpam-3394	88	4	.	.	PUNCT
ejpam-3394	89	1	a	a	DET
ejpam-3394	89	2	basis	basis	NOUN
ejpam-3394	89	3	β(i	β(i	NOUN
ejpam-3394	89	4	,	,	PUNCT
ejpam-3394	89	5	τ	τ	X
ejpam-3394	89	6	)	)	PUNCT
ejpam-3394	89	7	for	for	ADP
ejpam-3394	89	8	τ∗(i	τ∗(i	PROPN
ejpam-3394	89	9	,	,	PUNCT
ejpam-3394	89	10	τ	τ	X
ejpam-3394	89	11	)	)	PUNCT
ejpam-3394	89	12	can	can	AUX
ejpam-3394	89	13	be	be	AUX
ejpam-3394	89	14	described	describe	VERB
ejpam-3394	89	15	as	as	ADP
ejpam-3394	89	16	follows	follow	VERB
ejpam-3394	89	17	:	:	PUNCT
ejpam-3394	89	18	β(i	β(i	NUM
ejpam-3394	89	19	,	,	PUNCT
ejpam-3394	89	20	τ	τ	X
ejpam-3394	89	21	)	)	PUNCT
ejpam-3394	89	22	=	=	PRON
ejpam-3394	89	23	{	{	PUNCT
ejpam-3394	90	1	v	v	NOUN
ejpam-3394	90	2	−	−	PROPN
ejpam-3394	90	3	j	j	NOUN
ejpam-3394	90	4	:	:	PUNCT
ejpam-3394	90	5	v	v	NUM
ejpam-3394	90	6	∈	∈	X
ejpam-3394	90	7	τ	τ	X
ejpam-3394	90	8	and	and	CCONJ
ejpam-3394	90	9	j	j	PROPN
ejpam-3394	90	10	∈	∈	PROPN
ejpam-3394	90	11	i}[14	i}[14	PROPN
ejpam-3394	90	12	]	]	PUNCT
ejpam-3394	90	13	.	.	PUNCT
ejpam-3394	91	1	we	we	PRON
ejpam-3394	91	2	will	will	AUX
ejpam-3394	91	3	simply	simply	ADV
ejpam-3394	91	4	write	write	VERB
ejpam-3394	91	5	a∗	a∗	NOUN
ejpam-3394	91	6	for	for	ADP
ejpam-3394	91	7	a∗(i	a∗(i	PROPN
ejpam-3394	91	8	,	,	PUNCT
ejpam-3394	91	9	τ	τ	PROPN
ejpam-3394	91	10	)	)	PUNCT
ejpam-3394	91	11	,	,	PUNCT
ejpam-3394	91	12	τ∗	τ∗	NOUN
ejpam-3394	91	13	or	or	CCONJ
ejpam-3394	91	14	τ∗(i	τ∗(i	PROPN
ejpam-3394	91	15	)	)	PUNCT
ejpam-3394	91	16	for	for	ADP
ejpam-3394	91	17	τ∗(i	τ∗(i	PROPN
ejpam-3394	91	18	,	,	PUNCT
ejpam-3394	91	19	τ	τ	PROPN
ejpam-3394	91	20	)	)	PUNCT
ejpam-3394	91	21	and	and	CCONJ
ejpam-3394	91	22	β	β	X
ejpam-3394	91	23	for	for	ADP
ejpam-3394	91	24	β(i	β(i	PRON
ejpam-3394	91	25	,	,	PUNCT
ejpam-3394	91	26	τ	τ	PROPN
ejpam-3394	91	27	)	)	PUNCT
ejpam-3394	91	28	.	.	PUNCT
ejpam-3394	92	1	if	if	SCONJ
ejpam-3394	92	2	i	i	PRON
ejpam-3394	92	3	is	be	AUX
ejpam-3394	92	4	an	an	DET
ejpam-3394	92	5	ideal	ideal	NOUN
ejpam-3394	92	6	on	on	ADP
ejpam-3394	92	7	x	x	NOUN
ejpam-3394	92	8	,	,	PUNCT
ejpam-3394	92	9	then	then	ADV
ejpam-3394	92	10	(	(	PUNCT
ejpam-3394	92	11	x	x	X
ejpam-3394	92	12	,	,	PUNCT
ejpam-3394	92	13	τ	τ	PROPN
ejpam-3394	92	14	,	,	PUNCT
ejpam-3394	92	15	i	i	PROPN
ejpam-3394	92	16	)	)	PUNCT
ejpam-3394	92	17	is	be	AUX
ejpam-3394	92	18	called	call	VERB
ejpam-3394	92	19	an	an	DET
ejpam-3394	92	20	ideal	ideal	ADJ
ejpam-3394	92	21	topological	topological	ADJ
ejpam-3394	92	22	space	space	NOUN
ejpam-3394	92	23	.	.	PUNCT
ejpam-3394	93	1	a	a	DET
ejpam-3394	93	2	space	space	NOUN
ejpam-3394	93	3	(	(	PUNCT
ejpam-3394	93	4	x	x	X
ejpam-3394	93	5	,	,	PUNCT
ejpam-3394	93	6	τ	τ	PROPN
ejpam-3394	93	7	,	,	PUNCT
ejpam-3394	93	8	i	i	PROPN
ejpam-3394	93	9	)	)	PUNCT
ejpam-3394	93	10	is	be	AUX
ejpam-3394	93	11	said	say	VERB
ejpam-3394	93	12	to	to	PART
ejpam-3394	93	13	be	be	AUX
ejpam-3394	93	14	i	i	NOUN
ejpam-3394	93	15	-	-	NOUN
ejpam-3394	93	16	paracompact	paracompact	NOUN
ejpam-3394	93	17	[	[	X
ejpam-3394	93	18	24	24	NUM
ejpam-3394	93	19	]	]	PUNCT
ejpam-3394	93	20	(	(	PUNCT
ejpam-3394	93	21	i	i	PROPN
ejpam-3394	93	22	-	-	PUNCT
ejpam-3394	93	23	s	s	NOUN
ejpam-3394	93	24	-	-	PUNCT
ejpam-3394	93	25	paracompact	paracompact	NOUN
ejpam-3394	93	26	[	[	X
ejpam-3394	93	27	21	21	NUM
ejpam-3394	93	28	]	]	PUNCT
ejpam-3394	93	29	)	)	PUNCT
ejpam-3394	93	30	if	if	SCONJ
ejpam-3394	93	31	every	every	DET
ejpam-3394	93	32	open	open	ADJ
ejpam-3394	93	33	cover	cover	VERB
ejpam-3394	93	34	u	u	NOUN
ejpam-3394	93	35	of	of	ADP
ejpam-3394	93	36	x	x	PUNCT
ejpam-3394	93	37	has	have	VERB
ejpam-3394	93	38	a	a	DET
ejpam-3394	93	39	locally	locally	ADV
ejpam-3394	93	40	finite	finite	ADJ
ejpam-3394	93	41	open	open	ADJ
ejpam-3394	93	42	(	(	PUNCT
ejpam-3394	93	43	semi	semi	ADJ
ejpam-3394	93	44	-	-	ADJ
ejpam-3394	93	45	open	open	ADJ
ejpam-3394	93	46	)	)	PUNCT
ejpam-3394	93	47	refinement	refinement	NOUN
ejpam-3394	93	48	v	v	NOUN
ejpam-3394	93	49	,	,	PUNCT
ejpam-3394	93	50	not	not	PART
ejpam-3394	93	51	necessarily	necessarily	ADV
ejpam-3394	93	52	a	a	DET
ejpam-3394	93	53	cover	cover	NOUN
ejpam-3394	93	54	,	,	PUNCT
ejpam-3394	94	1	such	such	ADJ
ejpam-3394	94	2	that	that	SCONJ
ejpam-3394	94	3	x	x	PART
ejpam-3394	94	4	−	−	X
ejpam-3394	94	5	⋃	⋃	NOUN
ejpam-3394	94	6	{	{	PUNCT
ejpam-3394	94	7	v	v	NOUN
ejpam-3394	94	8	:	:	PUNCT
ejpam-3394	94	9	v	v	NUM
ejpam-3394	94	10	∈	∈	PROPN
ejpam-3394	94	11	v	v	NOUN
ejpam-3394	94	12	}	}	PUNCT
ejpam-3394	94	13	∈	∈	PROPN
ejpam-3394	94	14	i.	i.	NOUN
ejpam-3394	94	15	a	a	DET
ejpam-3394	94	16	collection	collection	NOUN
ejpam-3394	94	17	v	v	NOUN
ejpam-3394	94	18	of	of	ADP
ejpam-3394	94	19	subsets	subset	NOUN
ejpam-3394	94	20	of	of	ADP
ejpam-3394	94	21	x	x	PUNCT
ejpam-3394	94	22	such	such	ADJ
ejpam-3394	94	23	that	that	SCONJ
ejpam-3394	94	24	x	x	PRON
ejpam-3394	95	1	−	−	NOUN
ejpam-3394	95	2	⋃	⋃	NOUN
ejpam-3394	95	3	{	{	PUNCT
ejpam-3394	95	4	v	v	NOUN
ejpam-3394	95	5	:	:	PUNCT
ejpam-3394	95	6	v	v	NUM
ejpam-3394	95	7	∈	∈	PROPN
ejpam-3394	95	8	v	v	NOUN
ejpam-3394	95	9	}	}	PUNCT
ejpam-3394	95	10	∈	∈	NOUN
ejpam-3394	95	11	i	i	PRON
ejpam-3394	95	12	is	be	AUX
ejpam-3394	95	13	called	call	VERB
ejpam-3394	95	14	an	an	DET
ejpam-3394	95	15	i	i	NOUN
ejpam-3394	95	16	-	-	PUNCT
ejpam-3394	95	17	cover	cover	NOUN
ejpam-3394	95	18	[	[	X
ejpam-3394	95	19	24	24	NUM
ejpam-3394	95	20	]	]	PUNCT
ejpam-3394	95	21	of	of	ADP
ejpam-3394	95	22	x.	x.	NOUN
ejpam-3394	95	23	a	a	DET
ejpam-3394	95	24	space	space	NOUN
ejpam-3394	95	25	(	(	PUNCT
ejpam-3394	95	26	x	x	X
ejpam-3394	95	27	,	,	PUNCT
ejpam-3394	95	28	τ	τ	PROPN
ejpam-3394	95	29	,	,	PUNCT
ejpam-3394	95	30	i	i	PROPN
ejpam-3394	95	31	)	)	PUNCT
ejpam-3394	95	32	is	be	AUX
ejpam-3394	95	33	said	say	VERB
ejpam-3394	95	34	to	to	PART
ejpam-3394	95	35	be	be	AUX
ejpam-3394	95	36	i	i	NOUN
ejpam-3394	95	37	-	-	PUNCT
ejpam-3394	95	38	regular[12	regular[12	NOUN
ejpam-3394	95	39	]	]	X
ejpam-3394	95	40	if	if	SCONJ
ejpam-3394	95	41	for	for	ADP
ejpam-3394	95	42	each	each	DET
ejpam-3394	95	43	closed	close	VERB
ejpam-3394	95	44	set	set	VERB
ejpam-3394	95	45	f	f	PROPN
ejpam-3394	95	46	and	and	CCONJ
ejpam-3394	95	47	a	a	DET
ejpam-3394	95	48	point	point	NOUN
ejpam-3394	95	49	p	p	NOUN
ejpam-3394	95	50	/∈	/∈	PUNCT
ejpam-3394	96	1	f	f	PROPN
ejpam-3394	96	2	,	,	PUNCT
ejpam-3394	96	3	there	there	PRON
ejpam-3394	96	4	exist	exist	VERB
ejpam-3394	96	5	disjoint	disjoint	ADJ
ejpam-3394	96	6	open	open	ADJ
ejpam-3394	96	7	sets	set	NOUN
ejpam-3394	96	8	u	u	NOUN
ejpam-3394	96	9	and	and	CCONJ
ejpam-3394	96	10	v	v	ADP
ejpam-3394	96	11	such	such	ADJ
ejpam-3394	96	12	that	that	SCONJ
ejpam-3394	96	13	p	p	PROPN
ejpam-3394	96	14	∈	∈	PROPN
ejpam-3394	96	15	u	u	NOUN
ejpam-3394	96	16	and	and	CCONJ
ejpam-3394	96	17	f	f	PROPN
ejpam-3394	96	18	−	−	PROPN
ejpam-3394	96	19	v	v	PROPN
ejpam-3394	96	20	∈	∈	PROPN
ejpam-3394	96	21	i.	i.	NOUN
ejpam-3394	96	22	3	3	NUM
ejpam-3394	96	23	.	.	PUNCT
ejpam-3394	97	1	i	i	PRON
ejpam-3394	97	2	-	-	PUNCT
ejpam-3394	97	3	β	β	NOUN
ejpam-3394	97	4	-	-	ADJ
ejpam-3394	97	5	paracompactness	paracompactness	NOUN
ejpam-3394	97	6	definition	definition	NOUN
ejpam-3394	97	7	1	1	NUM
ejpam-3394	97	8	.	.	PUNCT
ejpam-3394	98	1	a	a	DET
ejpam-3394	98	2	space	space	NOUN
ejpam-3394	98	3	(	(	PUNCT
ejpam-3394	98	4	x	x	X
ejpam-3394	98	5	,	,	PUNCT
ejpam-3394	98	6	τ	τ	PROPN
ejpam-3394	98	7	,	,	PUNCT
ejpam-3394	98	8	i	i	PROPN
ejpam-3394	98	9	)	)	PUNCT
ejpam-3394	98	10	is	be	AUX
ejpam-3394	98	11	said	say	VERB
ejpam-3394	98	12	to	to	PART
ejpam-3394	98	13	be	be	AUX
ejpam-3394	98	14	i	i	NOUN
ejpam-3394	98	15	-	-	PUNCT
ejpam-3394	98	16	β	β	NOUN
ejpam-3394	98	17	-	-	NOUN
ejpam-3394	98	18	paracompact	paracompact	ADJ
ejpam-3394	98	19	or	or	CCONJ
ejpam-3394	98	20	β	β	NOUN
ejpam-3394	98	21	-	-	NOUN
ejpam-3394	98	22	paracompact	paracompact	ADJ
ejpam-3394	98	23	with	with	ADP
ejpam-3394	98	24	respect	respect	NOUN
ejpam-3394	98	25	to	to	ADP
ejpam-3394	98	26	i	i	PRON
ejpam-3394	98	27	if	if	SCONJ
ejpam-3394	98	28	every	every	DET
ejpam-3394	98	29	open	open	ADJ
ejpam-3394	98	30	cover	cover	VERB
ejpam-3394	98	31	u	u	NOUN
ejpam-3394	98	32	of	of	ADP
ejpam-3394	98	33	x	x	PUNCT
ejpam-3394	98	34	has	have	VERB
ejpam-3394	98	35	a	a	DET
ejpam-3394	98	36	β	β	NOUN
ejpam-3394	98	37	-	-	ADJ
ejpam-3394	98	38	locally	locally	ADV
ejpam-3394	98	39	finite	finite	ADJ
ejpam-3394	98	40	β	β	NOUN
ejpam-3394	98	41	-	-	ADJ
ejpam-3394	98	42	open	open	ADJ
ejpam-3394	98	43	refinement	refinement	NOUN
ejpam-3394	98	44	v	v	NOUN
ejpam-3394	98	45	(	(	PUNCT
ejpam-3394	98	46	not	not	PART
ejpam-3394	98	47	necessarily	necessarily	ADV
ejpam-3394	98	48	a	a	DET
ejpam-3394	98	49	cover	cover	NOUN
ejpam-3394	98	50	)	)	PUNCT
ejpam-3394	98	51	such	such	ADJ
ejpam-3394	98	52	that	that	SCONJ
ejpam-3394	98	53	x	x	X
ejpam-3394	98	54	−	−	X
ejpam-3394	98	55	⋃	⋃	NOUN
ejpam-3394	98	56	{	{	PUNCT
ejpam-3394	98	57	v	v	NOUN
ejpam-3394	98	58	:	:	PUNCT
ejpam-3394	98	59	v	v	NUM
ejpam-3394	98	60	∈	∈	PROPN
ejpam-3394	98	61	v	v	NOUN
ejpam-3394	98	62	}	}	PUNCT
ejpam-3394	98	63	∈	∈	PROPN
ejpam-3394	98	64	i.	i.	NOUN
ejpam-3394	98	65	a	a	PRON
ejpam-3394	98	66	subset	subset	VERB
ejpam-3394	98	67	a	a	PRON
ejpam-3394	98	68	of	of	ADP
ejpam-3394	98	69	a	a	DET
ejpam-3394	98	70	space	space	NOUN
ejpam-3394	98	71	(	(	PUNCT
ejpam-3394	98	72	x	x	X
ejpam-3394	98	73	,	,	PUNCT
ejpam-3394	98	74	τ	τ	PROPN
ejpam-3394	98	75	,	,	PUNCT
ejpam-3394	98	76	i	i	PROPN
ejpam-3394	98	77	)	)	PUNCT
ejpam-3394	98	78	is	be	AUX
ejpam-3394	98	79	called	call	VERB
ejpam-3394	98	80	an	an	DET
ejpam-3394	98	81	i	i	PROPN
ejpam-3394	98	82	-	-	PUNCT
ejpam-3394	98	83	β	β	NOUN
ejpam-3394	98	84	-	-	ADJ
ejpam-3394	98	85	paracompact	paracompact	ADJ
ejpam-3394	98	86	set	set	NOUN
ejpam-3394	98	87	in	in	ADP
ejpam-3394	98	88	(	(	PUNCT
ejpam-3394	98	89	x	x	NOUN
ejpam-3394	98	90	,	,	PUNCT
ejpam-3394	98	91	τ	τ	PROPN
ejpam-3394	98	92	,	,	PUNCT
ejpam-3394	98	93	i	i	PROPN
ejpam-3394	98	94	)	)	PUNCT
ejpam-3394	98	95	if	if	SCONJ
ejpam-3394	98	96	every	every	DET
ejpam-3394	98	97	open	open	ADJ
ejpam-3394	98	98	cover	cover	VERB
ejpam-3394	98	99	u	u	NOUN
ejpam-3394	98	100	of	of	ADP
ejpam-3394	98	101	a	a	PRON
ejpam-3394	98	102	has	have	VERB
ejpam-3394	98	103	a	a	DET
ejpam-3394	98	104	β	β	NOUN
ejpam-3394	98	105	-	-	ADJ
ejpam-3394	98	106	locally	locally	ADV
ejpam-3394	98	107	finite	finite	NOUN
ejpam-3394	98	108	(	(	PUNCT
ejpam-3394	98	109	with	with	ADP
ejpam-3394	98	110	respect	respect	NOUN
ejpam-3394	98	111	to	to	ADP
ejpam-3394	98	112	τ	τ	PROPN
ejpam-3394	98	113	)	)	PUNCT
ejpam-3394	98	114	β	β	X
ejpam-3394	98	115	-	-	PUNCT
ejpam-3394	98	116	open	open	ADJ
ejpam-3394	98	117	refinement	refinement	NOUN
ejpam-3394	98	118	v	v	ADP
ejpam-3394	98	119	such	such	ADJ
ejpam-3394	98	120	that	that	DET
ejpam-3394	98	121	a−	a−	PROPN
ejpam-3394	98	122	⋃	⋃	PROPN
ejpam-3394	98	123	{	{	PUNCT
ejpam-3394	98	124	v	v	NOUN
ejpam-3394	98	125	:	:	PUNCT
ejpam-3394	98	126	v	v	NUM
ejpam-3394	98	127	∈	∈	PROPN
ejpam-3394	98	128	v	v	NOUN
ejpam-3394	98	129	}	}	PUNCT
ejpam-3394	98	130	∈	∈	PROPN
ejpam-3394	98	131	i.	i.	NOUN
ejpam-3394	98	132	proposition	proposition	NOUN
ejpam-3394	98	133	1	1	X
ejpam-3394	98	134	.	.	PUNCT
ejpam-3394	99	1	if	if	SCONJ
ejpam-3394	99	2	(	(	PUNCT
ejpam-3394	99	3	x	x	NOUN
ejpam-3394	99	4	,	,	PUNCT
ejpam-3394	99	5	τ	τ	X
ejpam-3394	99	6	)	)	PUNCT
ejpam-3394	99	7	is	be	AUX
ejpam-3394	99	8	β	β	NOUN
ejpam-3394	99	9	-	-	NOUN
ejpam-3394	99	10	paracompact	paracompact	ADJ
ejpam-3394	99	11	,	,	PUNCT
ejpam-3394	99	12	then	then	ADV
ejpam-3394	99	13	(	(	PUNCT
ejpam-3394	99	14	x	x	X
ejpam-3394	99	15	,	,	PUNCT
ejpam-3394	99	16	τ	τ	PROPN
ejpam-3394	99	17	,	,	PUNCT
ejpam-3394	99	18	i	i	PROPN
ejpam-3394	99	19	)	)	PUNCT
ejpam-3394	99	20	is	be	AUX
ejpam-3394	99	21	i	i	PROPN
ejpam-3394	99	22	-	-	PUNCT
ejpam-3394	99	23	β	β	NOUN
ejpam-3394	99	24	-	-	NOUN
ejpam-3394	99	25	paracompact	paracompact	ADJ
ejpam-3394	99	26	.	.	PUNCT
ejpam-3394	100	1	proof	proof	NOUN
ejpam-3394	100	2	.	.	PUNCT
ejpam-3394	101	1	it	it	PRON
ejpam-3394	101	2	is	be	AUX
ejpam-3394	101	3	obvious	obvious	ADJ
ejpam-3394	101	4	since	since	SCONJ
ejpam-3394	101	5	∅	∅	NOUN
ejpam-3394	101	6	∈	∈	PROPN
ejpam-3394	101	7	i.	i.	PROPN
ejpam-3394	101	8	e.	e.	PROPN
ejpam-3394	101	9	d.	d.	PROPN
ejpam-3394	101	10	yıldırım	yıldırım	PROPN
ejpam-3394	101	11	,	,	PUNCT
ejpam-3394	101	12	o.	o.	PROPN
ejpam-3394	101	13	b.	b.	PROPN
ejpam-3394	101	14	özbakır	özbakır	PROPN
ejpam-3394	101	15	,	,	PUNCT
ejpam-3394	101	16	a.	a.	PROPN
ejpam-3394	101	17	c.	c.	PROPN
ejpam-3394	101	18	.	.	PUNCT
ejpam-3394	102	1	güler	güler	PROPN
ejpam-3394	102	2	/	/	SYM
ejpam-3394	102	3	eur	eur	PROPN
ejpam-3394	102	4	.	.	PUNCT
ejpam-3394	103	1	j.	j.	PROPN
ejpam-3394	103	2	pure	pure	PROPN
ejpam-3394	103	3	appl	appl	PROPN
ejpam-3394	103	4	.	.	PROPN
ejpam-3394	103	5	math	math	PROPN
ejpam-3394	103	6	,	,	PUNCT
ejpam-3394	103	7	12	12	NUM
ejpam-3394	103	8	(	(	PUNCT
ejpam-3394	103	9	2	2	NUM
ejpam-3394	103	10	)	)	PUNCT
ejpam-3394	103	11	(	(	PUNCT
ejpam-3394	103	12	2019	2019	NUM
ejpam-3394	103	13	)	)	PUNCT
ejpam-3394	103	14	,	,	PUNCT
ejpam-3394	103	15	270	270	NUM
ejpam-3394	103	16	-	-	SYM
ejpam-3394	103	17	278	278	NUM
ejpam-3394	103	18	273	273	NUM
ejpam-3394	103	19	obviously	obviously	ADV
ejpam-3394	103	20	,	,	PUNCT
ejpam-3394	103	21	every	every	DET
ejpam-3394	103	22	compact	compact	ADJ
ejpam-3394	103	23	space	space	NOUN
ejpam-3394	103	24	is	be	AUX
ejpam-3394	103	25	i	i	PROPN
ejpam-3394	103	26	-	-	PUNCT
ejpam-3394	103	27	β	β	NOUN
ejpam-3394	103	28	-	-	NOUN
ejpam-3394	103	29	paracompact	paracompact	NOUN
ejpam-3394	103	30	since	since	SCONJ
ejpam-3394	103	31	every	every	DET
ejpam-3394	103	32	compact	compact	ADJ
ejpam-3394	103	33	space	space	NOUN
ejpam-3394	103	34	is	be	AUX
ejpam-3394	103	35	βparacompact	βparacompact	ADJ
ejpam-3394	103	36	[	[	X
ejpam-3394	103	37	11	11	NUM
ejpam-3394	103	38	]	]	PUNCT
ejpam-3394	103	39	.	.	PUNCT
ejpam-3394	104	1	the	the	DET
ejpam-3394	104	2	following	follow	VERB
ejpam-3394	104	3	example	example	NOUN
ejpam-3394	104	4	shows	show	VERB
ejpam-3394	104	5	that	that	SCONJ
ejpam-3394	104	6	the	the	DET
ejpam-3394	104	7	converse	converse	NOUN
ejpam-3394	104	8	of	of	ADP
ejpam-3394	104	9	proposition	proposition	NOUN
ejpam-3394	104	10	1	1	NUM
ejpam-3394	104	11	may	may	AUX
ejpam-3394	104	12	not	not	PART
ejpam-3394	104	13	be	be	AUX
ejpam-3394	104	14	true	true	ADJ
ejpam-3394	104	15	,	,	PUNCT
ejpam-3394	104	16	in	in	ADP
ejpam-3394	104	17	general	general	ADJ
ejpam-3394	104	18	.	.	PUNCT
ejpam-3394	104	19	example	example	NOUN
ejpam-3394	105	1	1	1	NUM
ejpam-3394	105	2	.	.	PUNCT
ejpam-3394	105	3	let	let	VERB
ejpam-3394	105	4	x	x	PUNCT
ejpam-3394	105	5	=	=	PRON
ejpam-3394	105	6	n	n	CCONJ
ejpam-3394	105	7	be	be	VERB
ejpam-3394	105	8	the	the	DET
ejpam-3394	105	9	set	set	NOUN
ejpam-3394	105	10	of	of	ADP
ejpam-3394	105	11	natural	natural	ADJ
ejpam-3394	105	12	numbers	number	NOUN
ejpam-3394	105	13	with	with	ADP
ejpam-3394	105	14	the	the	DET
ejpam-3394	105	15	topology	topology	NOUN
ejpam-3394	105	16	τ	τ	X
ejpam-3394	105	17	=	=	PUNCT
ejpam-3394	105	18	{	{	PUNCT
ejpam-3394	105	19	g	g	PROPN
ejpam-3394	105	20	⊆	⊆	NUM
ejpam-3394	105	21	n	n	NUM
ejpam-3394	105	22	:	:	PUNCT
ejpam-3394	105	23	5	5	NUM
ejpam-3394	105	24	∈	∈	NOUN
ejpam-3394	105	25	g	g	NOUN
ejpam-3394	105	26	}	}	PUNCT
ejpam-3394	105	27	∪	∪	ADJ
ejpam-3394	105	28	{	{	PUNCT
ejpam-3394	105	29	∅	∅	NOUN
ejpam-3394	105	30	}	}	PUNCT
ejpam-3394	105	31	and	and	CCONJ
ejpam-3394	105	32	the	the	DET
ejpam-3394	105	33	ideal	ideal	NOUN
ejpam-3394	106	1	i	i	X
ejpam-3394	106	2	=	=	PUNCT
ejpam-3394	106	3	{	{	PUNCT
ejpam-3394	106	4	u	u	NOUN
ejpam-3394	106	5	⊆	⊆	NUM
ejpam-3394	106	6	n	n	NUM
ejpam-3394	106	7	:	:	PUNCT
ejpam-3394	106	8	5	5	NUM
ejpam-3394	106	9	/∈	/∈	SYM
ejpam-3394	106	10	u	u	NOUN
ejpam-3394	106	11	}	}	PUNCT
ejpam-3394	106	12	.	.	PUNCT
ejpam-3394	107	1	observe	observe	VERB
ejpam-3394	107	2	that	that	SCONJ
ejpam-3394	107	3	(	(	PUNCT
ejpam-3394	107	4	x	x	X
ejpam-3394	107	5	,	,	PUNCT
ejpam-3394	107	6	τ	τ	PROPN
ejpam-3394	107	7	,	,	PUNCT
ejpam-3394	107	8	i	i	PROPN
ejpam-3394	107	9	)	)	PUNCT
ejpam-3394	107	10	is	be	AUX
ejpam-3394	107	11	i	i	PROPN
ejpam-3394	107	12	-	-	PUNCT
ejpam-3394	107	13	β	β	NOUN
ejpam-3394	107	14	-	-	ADJ
ejpam-3394	107	15	paracompact	paracompact	ADJ
ejpam-3394	107	16	space	space	NOUN
ejpam-3394	107	17	but	but	CCONJ
ejpam-3394	107	18	(	(	PUNCT
ejpam-3394	107	19	x	x	X
ejpam-3394	107	20	,	,	PUNCT
ejpam-3394	107	21	τ	τ	X
ejpam-3394	107	22	)	)	PUNCT
ejpam-3394	107	23	is	be	AUX
ejpam-3394	107	24	not	not	PART
ejpam-3394	107	25	β	β	NOUN
ejpam-3394	107	26	-	-	NOUN
ejpam-3394	107	27	paracompact	paracompact	ADJ
ejpam-3394	107	28	since	since	SCONJ
ejpam-3394	107	29	the	the	DET
ejpam-3394	107	30	collection	collection	NOUN
ejpam-3394	107	31	{	{	PUNCT
ejpam-3394	107	32	{	{	PUNCT
ejpam-3394	107	33	5	5	NUM
ejpam-3394	107	34	,	,	PUNCT
ejpam-3394	107	35	x	x	NOUN
ejpam-3394	107	36	}	}	PUNCT
ejpam-3394	107	37	:	:	PUNCT
ejpam-3394	107	38	x	x	SYM
ejpam-3394	107	39	∈	∈	PROPN
ejpam-3394	107	40	n	n	CCONJ
ejpam-3394	107	41	}	}	PUNCT
ejpam-3394	107	42	is	be	AUX
ejpam-3394	107	43	an	an	DET
ejpam-3394	107	44	open	open	ADJ
ejpam-3394	107	45	cover	cover	NOUN
ejpam-3394	107	46	of	of	ADP
ejpam-3394	107	47	x	x	PUNCT
ejpam-3394	107	48	which	which	PRON
ejpam-3394	107	49	admits	admit	VERB
ejpam-3394	107	50	no	no	DET
ejpam-3394	107	51	β	β	NOUN
ejpam-3394	107	52	-	-	ADJ
ejpam-3394	107	53	locally	locally	ADV
ejpam-3394	107	54	finite	finite	ADJ
ejpam-3394	107	55	β	β	ADJ
ejpam-3394	107	56	-	-	ADJ
ejpam-3394	107	57	open	open	ADJ
ejpam-3394	107	58	refinement	refinement	NOUN
ejpam-3394	107	59	in	in	ADP
ejpam-3394	107	60	x.	x.	PROPN
ejpam-3394	107	61	remark	remark	PROPN
ejpam-3394	107	62	1	1	NUM
ejpam-3394	107	63	.	.	PUNCT
ejpam-3394	108	1	(	(	PUNCT
ejpam-3394	108	2	1	1	X
ejpam-3394	108	3	)	)	PUNCT
ejpam-3394	108	4	if	if	SCONJ
ejpam-3394	108	5	i	i	PRON
ejpam-3394	108	6	=	=	SYM
ejpam-3394	108	7	{	{	PUNCT
ejpam-3394	108	8	∅	∅	NOUN
ejpam-3394	108	9	}	}	PUNCT
ejpam-3394	108	10	,	,	PUNCT
ejpam-3394	108	11	then	then	ADV
ejpam-3394	108	12	(	(	PUNCT
ejpam-3394	108	13	x	x	X
ejpam-3394	108	14	,	,	PUNCT
ejpam-3394	108	15	τ	τ	PROPN
ejpam-3394	108	16	,	,	PUNCT
ejpam-3394	108	17	i	i	PROPN
ejpam-3394	108	18	)	)	PUNCT
ejpam-3394	108	19	is	be	AUX
ejpam-3394	108	20	i	i	PROPN
ejpam-3394	108	21	-	-	PUNCT
ejpam-3394	108	22	β	β	NOUN
ejpam-3394	108	23	-	-	NOUN
ejpam-3394	108	24	paracompact	paracompact	ADJ
ejpam-3394	108	25	if	if	SCONJ
ejpam-3394	108	26	and	and	CCONJ
ejpam-3394	108	27	only	only	ADV
ejpam-3394	108	28	if	if	SCONJ
ejpam-3394	108	29	(	(	PUNCT
ejpam-3394	108	30	x	x	NOUN
ejpam-3394	108	31	,	,	PUNCT
ejpam-3394	108	32	τ	τ	X
ejpam-3394	108	33	)	)	PUNCT
ejpam-3394	108	34	is	be	AUX
ejpam-3394	108	35	β	β	X
ejpam-3394	108	36	-	-	NOUN
ejpam-3394	108	37	paracompact	paracompact	ADJ
ejpam-3394	108	38	.	.	PUNCT
ejpam-3394	109	1	(	(	PUNCT
ejpam-3394	109	2	2	2	X
ejpam-3394	109	3	)	)	PUNCT
ejpam-3394	109	4	if	if	SCONJ
ejpam-3394	109	5	i	i	PRON
ejpam-3394	109	6	=	=	SYM
ejpam-3394	109	7	{	{	PUNCT
ejpam-3394	109	8	∅	∅	NOUN
ejpam-3394	109	9	}	}	PUNCT
ejpam-3394	109	10	and	and	CCONJ
ejpam-3394	109	11	(	(	PUNCT
ejpam-3394	109	12	x	x	X
ejpam-3394	109	13	,	,	PUNCT
ejpam-3394	109	14	τ	τ	PROPN
ejpam-3394	109	15	,	,	PUNCT
ejpam-3394	109	16	i	i	PROPN
ejpam-3394	109	17	)	)	PUNCT
ejpam-3394	109	18	is	be	AUX
ejpam-3394	109	19	an	an	DET
ejpam-3394	109	20	e.d	e.d	PROPN
ejpam-3394	109	21	.	.	PROPN
ejpam-3394	109	22	space	space	NOUN
ejpam-3394	109	23	,	,	PUNCT
ejpam-3394	109	24	then	then	ADV
ejpam-3394	109	25	(	(	PUNCT
ejpam-3394	109	26	x	x	X
ejpam-3394	109	27	,	,	PUNCT
ejpam-3394	109	28	τ	τ	PROPN
ejpam-3394	109	29	,	,	PUNCT
ejpam-3394	109	30	i	i	PROPN
ejpam-3394	109	31	)	)	PUNCT
ejpam-3394	109	32	is	be	AUX
ejpam-3394	109	33	i	i	PROPN
ejpam-3394	109	34	-	-	PUNCT
ejpam-3394	109	35	β	β	NOUN
ejpam-3394	109	36	-	-	NOUN
ejpam-3394	109	37	paracompact	paracompact	ADJ
ejpam-3394	110	1	if	if	SCONJ
ejpam-3394	110	2	and	and	CCONJ
ejpam-3394	110	3	only	only	ADV
ejpam-3394	110	4	if	if	SCONJ
ejpam-3394	110	5	(	(	PUNCT
ejpam-3394	110	6	x	x	NOUN
ejpam-3394	110	7	,	,	PUNCT
ejpam-3394	110	8	τ	τ	X
ejpam-3394	110	9	)	)	PUNCT
ejpam-3394	110	10	is	be	AUX
ejpam-3394	110	11	p3	p3	NOUN
ejpam-3394	110	12	-	-	PUNCT
ejpam-3394	110	13	paracompact	paracompact	ADJ
ejpam-3394	110	14	.	.	PUNCT
ejpam-3394	111	1	proposition	proposition	NOUN
ejpam-3394	111	2	2	2	NUM
ejpam-3394	111	3	.	.	PUNCT
ejpam-3394	112	1	if	if	SCONJ
ejpam-3394	112	2	(	(	PUNCT
ejpam-3394	112	3	x	x	X
ejpam-3394	112	4	,	,	PUNCT
ejpam-3394	112	5	τ	τ	PROPN
ejpam-3394	112	6	,	,	PUNCT
ejpam-3394	112	7	i	i	PROPN
ejpam-3394	112	8	)	)	PUNCT
ejpam-3394	112	9	is	be	AUX
ejpam-3394	112	10	i	i	PROPN
ejpam-3394	112	11	-	-	PUNCT
ejpam-3394	112	12	s	s	NOUN
ejpam-3394	112	13	-	-	PUNCT
ejpam-3394	112	14	paracompact	paracompact	NOUN
ejpam-3394	112	15	then	then	ADV
ejpam-3394	112	16	it	it	PRON
ejpam-3394	112	17	is	be	AUX
ejpam-3394	112	18	i	i	PROPN
ejpam-3394	112	19	-	-	PUNCT
ejpam-3394	112	20	β	β	NOUN
ejpam-3394	112	21	-	-	NOUN
ejpam-3394	112	22	paracompact	paracompact	ADJ
ejpam-3394	112	23	.	.	PUNCT
ejpam-3394	113	1	proof	proof	NOUN
ejpam-3394	113	2	.	.	PUNCT
ejpam-3394	114	1	since	since	SCONJ
ejpam-3394	114	2	every	every	DET
ejpam-3394	114	3	locally	locally	ADV
ejpam-3394	114	4	finite	finite	ADJ
ejpam-3394	114	5	collection	collection	NOUN
ejpam-3394	114	6	of	of	ADP
ejpam-3394	114	7	subsets	subset	NOUN
ejpam-3394	114	8	of	of	ADP
ejpam-3394	114	9	x	x	PUNCT
ejpam-3394	114	10	is	be	AUX
ejpam-3394	114	11	β	β	X
ejpam-3394	114	12	-	-	ADJ
ejpam-3394	114	13	locally	locally	ADV
ejpam-3394	114	14	finite	finite	NOUN
ejpam-3394	114	15	and	and	CCONJ
ejpam-3394	114	16	every	every	DET
ejpam-3394	114	17	semi	semi	ADJ
ejpam-3394	114	18	-	-	ADJ
ejpam-3394	114	19	open	open	ADJ
ejpam-3394	114	20	set	set	NOUN
ejpam-3394	114	21	is	be	AUX
ejpam-3394	114	22	β	β	NOUN
ejpam-3394	114	23	-	-	ADJ
ejpam-3394	114	24	open	open	ADJ
ejpam-3394	114	25	,	,	PUNCT
ejpam-3394	114	26	it	it	PRON
ejpam-3394	114	27	is	be	AUX
ejpam-3394	114	28	clear	clear	ADJ
ejpam-3394	114	29	.	.	PUNCT
ejpam-3394	115	1	clearly	clearly	ADV
ejpam-3394	115	2	,	,	PUNCT
ejpam-3394	115	3	every	every	DET
ejpam-3394	115	4	s	s	NOUN
ejpam-3394	115	5	-	-	PUNCT
ejpam-3394	115	6	paracompact	paracompact	ADJ
ejpam-3394	115	7	space	space	NOUN
ejpam-3394	115	8	is	be	AUX
ejpam-3394	115	9	i	i	PROPN
ejpam-3394	115	10	-	-	PUNCT
ejpam-3394	115	11	β	β	NOUN
ejpam-3394	115	12	-	-	NOUN
ejpam-3394	115	13	paracompact	paracompact	NOUN
ejpam-3394	115	14	since	since	SCONJ
ejpam-3394	115	15	every	every	DET
ejpam-3394	115	16	s	s	NOUN
ejpam-3394	115	17	-	-	PUNCT
ejpam-3394	115	18	paracompact	paracompact	ADJ
ejpam-3394	115	19	space	space	NOUN
ejpam-3394	115	20	is	be	AUX
ejpam-3394	115	21	i	i	PROPN
ejpam-3394	115	22	-	-	PUNCT
ejpam-3394	115	23	s	s	PROPN
ejpam-3394	115	24	-	-	NOUN
ejpam-3394	115	25	paracompact[21	paracompact[21	X
ejpam-3394	115	26	]	]	X
ejpam-3394	115	27	.	.	PUNCT
ejpam-3394	116	1	also	also	ADV
ejpam-3394	116	2	,	,	PUNCT
ejpam-3394	116	3	every	every	DET
ejpam-3394	116	4	i	i	NOUN
ejpam-3394	116	5	-	-	PUNCT
ejpam-3394	116	6	paracompact	paracompact	ADJ
ejpam-3394	116	7	space	space	NOUN
ejpam-3394	116	8	is	be	AUX
ejpam-3394	116	9	i	i	PROPN
ejpam-3394	116	10	-	-	PUNCT
ejpam-3394	116	11	β	β	NOUN
ejpam-3394	116	12	-	-	NOUN
ejpam-3394	116	13	paracompact	paracompact	NOUN
ejpam-3394	116	14	since	since	SCONJ
ejpam-3394	116	15	every	every	DET
ejpam-3394	116	16	i	i	NOUN
ejpam-3394	116	17	-	-	PUNCT
ejpam-3394	116	18	paracompact	paracompact	ADJ
ejpam-3394	116	19	space	space	NOUN
ejpam-3394	116	20	is	be	AUX
ejpam-3394	116	21	i	i	PROPN
ejpam-3394	116	22	-	-	PUNCT
ejpam-3394	116	23	s	s	PROPN
ejpam-3394	116	24	-	-	NOUN
ejpam-3394	116	25	paracompact[21	paracompact[21	X
ejpam-3394	116	26	]	]	X
ejpam-3394	116	27	.	.	PUNCT
ejpam-3394	117	1	the	the	DET
ejpam-3394	117	2	following	follow	VERB
ejpam-3394	117	3	example	example	NOUN
ejpam-3394	117	4	shows	show	VERB
ejpam-3394	117	5	that	that	SCONJ
ejpam-3394	117	6	the	the	DET
ejpam-3394	117	7	converse	converse	NOUN
ejpam-3394	117	8	of	of	ADP
ejpam-3394	117	9	proposition	proposition	NOUN
ejpam-3394	117	10	2	2	NUM
ejpam-3394	117	11	may	may	AUX
ejpam-3394	117	12	not	not	PART
ejpam-3394	117	13	be	be	AUX
ejpam-3394	117	14	true	true	ADJ
ejpam-3394	117	15	,	,	PUNCT
ejpam-3394	117	16	in	in	ADP
ejpam-3394	117	17	general	general	ADJ
ejpam-3394	117	18	.	.	PUNCT
ejpam-3394	117	19	example	example	NOUN
ejpam-3394	118	1	2	2	NUM
ejpam-3394	118	2	.	.	PUNCT
ejpam-3394	118	3	let	let	VERB
ejpam-3394	118	4	x	x	PUNCT
ejpam-3394	118	5	=	=	PUNCT
ejpam-3394	119	1	[	[	X
ejpam-3394	119	2	0	0	NUM
ejpam-3394	119	3	,	,	PUNCT
ejpam-3394	119	4	2]∪[3	2]∪[3	NUM
ejpam-3394	119	5	,	,	PUNCT
ejpam-3394	119	6	10	10	NUM
ejpam-3394	119	7	]	]	PUNCT
ejpam-3394	119	8	with	with	ADP
ejpam-3394	119	9	the	the	DET
ejpam-3394	119	10	topology	topology	NOUN
ejpam-3394	119	11	τ	τ	X
ejpam-3394	119	12	=	=	PUNCT
ejpam-3394	119	13	{	{	PUNCT
ejpam-3394	119	14	u	u	NOUN
ejpam-3394	119	15	⊆	⊆	NUM
ejpam-3394	119	16	x	x	SYM
ejpam-3394	119	17	:	:	PUNCT
ejpam-3394	120	1	[	[	X
ejpam-3394	120	2	0	0	NUM
ejpam-3394	120	3	,	,	PUNCT
ejpam-3394	120	4	2	2	NUM
ejpam-3394	120	5	]	]	SYM
ejpam-3394	120	6	⊆	⊆	NUM
ejpam-3394	120	7	u}∪{∅	u}∪{∅	NUM
ejpam-3394	120	8	}	}	PUNCT
ejpam-3394	120	9	and	and	CCONJ
ejpam-3394	120	10	the	the	DET
ejpam-3394	120	11	ideal	ideal	NOUN
ejpam-3394	120	12	i	i	PRON
ejpam-3394	120	13	=	=	PUNCT
ejpam-3394	120	14	{	{	PUNCT
ejpam-3394	120	15	a	a	X
ejpam-3394	120	16	:	:	PUNCT
ejpam-3394	120	17	a	a	DET
ejpam-3394	120	18	⊆	⊆	NUM
ejpam-3394	120	19	[	[	X
ejpam-3394	120	20	0	0	NUM
ejpam-3394	120	21	,	,	PUNCT
ejpam-3394	120	22	2	2	NUM
ejpam-3394	120	23	]	]	PUNCT
ejpam-3394	120	24	}	}	PUNCT
ejpam-3394	120	25	.	.	PUNCT
ejpam-3394	121	1	then	then	ADV
ejpam-3394	121	2	(	(	PUNCT
ejpam-3394	121	3	x	x	X
ejpam-3394	121	4	,	,	PUNCT
ejpam-3394	121	5	τ	τ	PROPN
ejpam-3394	121	6	,	,	PUNCT
ejpam-3394	121	7	i	i	PROPN
ejpam-3394	121	8	)	)	PUNCT
ejpam-3394	121	9	is	be	AUX
ejpam-3394	121	10	i	i	PROPN
ejpam-3394	121	11	-	-	PUNCT
ejpam-3394	121	12	β	β	NOUN
ejpam-3394	121	13	-	-	NOUN
ejpam-3394	121	14	paracompact	paracompact	NOUN
ejpam-3394	121	15	since	since	SCONJ
ejpam-3394	121	16	every	every	DET
ejpam-3394	121	17	open	open	ADJ
ejpam-3394	121	18	cover	cover	NOUN
ejpam-3394	121	19	of	of	ADP
ejpam-3394	121	20	x	x	PUNCT
ejpam-3394	121	21	has	have	VERB
ejpam-3394	121	22	β	β	X
ejpam-3394	121	23	-	-	ADJ
ejpam-3394	121	24	locally	locally	ADV
ejpam-3394	121	25	finite	finite	ADJ
ejpam-3394	121	26	β	β	NOUN
ejpam-3394	121	27	-	-	ADJ
ejpam-3394	121	28	open	open	ADJ
ejpam-3394	121	29	refinement	refinement	NOUN
ejpam-3394	121	30	v	v	NOUN
ejpam-3394	121	31	=	=	SYM
ejpam-3394	121	32	{	{	PUNCT
ejpam-3394	121	33	{	{	PUNCT
ejpam-3394	121	34	x	x	NOUN
ejpam-3394	121	35	}	}	PUNCT
ejpam-3394	121	36	:	:	PUNCT
ejpam-3394	121	37	x	x	X
ejpam-3394	121	38	∈	∈	PROPN
ejpam-3394	122	1	[	[	X
ejpam-3394	122	2	0	0	NUM
ejpam-3394	122	3	,	,	PUNCT
ejpam-3394	122	4	2]}∪{{y	2]}∪{{y	NUM
ejpam-3394	122	5	,	,	PUNCT
ejpam-3394	122	6	z	z	NOUN
ejpam-3394	122	7	}	}	PUNCT
ejpam-3394	122	8	:	:	PUNCT
ejpam-3394	122	9	y	y	PROPN
ejpam-3394	122	10	∈	∈	PROPN
ejpam-3394	123	1	[	[	X
ejpam-3394	123	2	0	0	NUM
ejpam-3394	123	3	,	,	PUNCT
ejpam-3394	123	4	2	2	NUM
ejpam-3394	123	5	]	]	PUNCT
ejpam-3394	123	6	,	,	PUNCT
ejpam-3394	123	7	z	z	PROPN
ejpam-3394	123	8	∈	∈	PROPN
ejpam-3394	124	1	[	[	X
ejpam-3394	124	2	3	3	NUM
ejpam-3394	124	3	,	,	PUNCT
ejpam-3394	124	4	10	10	NUM
ejpam-3394	124	5	]	]	PUNCT
ejpam-3394	124	6	}	}	PUNCT
ejpam-3394	124	7	such	such	ADJ
ejpam-3394	124	8	that	that	SCONJ
ejpam-3394	124	9	x	x	PUNCT
ejpam-3394	124	10	−	−	X
ejpam-3394	124	11	⋃	⋃	NOUN
ejpam-3394	124	12	{	{	PUNCT
ejpam-3394	124	13	v	v	NOUN
ejpam-3394	124	14	:	:	PUNCT
ejpam-3394	124	15	v	v	NUM
ejpam-3394	124	16	∈	∈	PROPN
ejpam-3394	124	17	v	v	NOUN
ejpam-3394	124	18	}	}	PUNCT
ejpam-3394	124	19	∈	∈	PROPN
ejpam-3394	124	20	i.	i.	NOUN
ejpam-3394	125	1	but	but	CCONJ
ejpam-3394	125	2	it	it	PRON
ejpam-3394	125	3	is	be	AUX
ejpam-3394	125	4	not	not	PART
ejpam-3394	125	5	i	i	PROPN
ejpam-3394	125	6	-	-	PUNCT
ejpam-3394	125	7	s	s	NOUN
ejpam-3394	125	8	-	-	NOUN
ejpam-3394	125	9	paracompact	paracompact	NOUN
ejpam-3394	125	10	since	since	SCONJ
ejpam-3394	125	11	τ	τ	PROPN
ejpam-3394	125	12	=	=	SYM
ejpam-3394	125	13	so(x	so(x	NUM
ejpam-3394	125	14	)	)	PUNCT
ejpam-3394	125	15	.	.	PUNCT
ejpam-3394	126	1	theorem	theorem	NOUN
ejpam-3394	126	2	3	3	NUM
ejpam-3394	126	3	.	.	PUNCT
ejpam-3394	127	1	if	if	SCONJ
ejpam-3394	127	2	(	(	PUNCT
ejpam-3394	127	3	x	x	X
ejpam-3394	127	4	,	,	PUNCT
ejpam-3394	127	5	τ	τ	PROPN
ejpam-3394	127	6	,	,	PUNCT
ejpam-3394	127	7	i	i	PROPN
ejpam-3394	127	8	)	)	PUNCT
ejpam-3394	127	9	is	be	AUX
ejpam-3394	127	10	an	an	DET
ejpam-3394	127	11	e.d	e.d	PROPN
ejpam-3394	127	12	.	.	PROPN
ejpam-3394	127	13	submaximal	submaximal	PROPN
ejpam-3394	127	14	i	i	PROPN
ejpam-3394	127	15	-	-	PUNCT
ejpam-3394	127	16	β	β	NOUN
ejpam-3394	127	17	-	-	ADJ
ejpam-3394	127	18	paracompact	paracompact	ADJ
ejpam-3394	127	19	space	space	NOUN
ejpam-3394	127	20	,	,	PUNCT
ejpam-3394	127	21	then	then	ADV
ejpam-3394	127	22	it	it	PRON
ejpam-3394	127	23	is	be	AUX
ejpam-3394	127	24	i	i	NOUN
ejpam-3394	127	25	-	-	PUNCT
ejpam-3394	127	26	sparacompact	sparacompact	ADJ
ejpam-3394	127	27	.	.	PUNCT
ejpam-3394	128	1	proof	proof	NOUN
ejpam-3394	128	2	.	.	PUNCT
ejpam-3394	129	1	it	it	PRON
ejpam-3394	129	2	is	be	AUX
ejpam-3394	129	3	obvious	obvious	ADJ
ejpam-3394	129	4	from	from	ADP
ejpam-3394	129	5	lemma	lemma	PROPN
ejpam-3394	129	6	3	3	NUM
ejpam-3394	129	7	,	,	PUNCT
ejpam-3394	129	8	lemma	lemma	PROPN
ejpam-3394	129	9	4	4	NUM
ejpam-3394	129	10	and	and	CCONJ
ejpam-3394	129	11	theorem	theorem	VERB
ejpam-3394	129	12	2	2	NUM
ejpam-3394	129	13	.	.	PUNCT
ejpam-3394	129	14	theorem	theorem	NOUN
ejpam-3394	129	15	4	4	NUM
ejpam-3394	129	16	.	.	PUNCT
ejpam-3394	130	1	if	if	SCONJ
ejpam-3394	130	2	(	(	PUNCT
ejpam-3394	130	3	x	x	X
ejpam-3394	130	4	,	,	PUNCT
ejpam-3394	130	5	τ	τ	PROPN
ejpam-3394	130	6	,	,	PUNCT
ejpam-3394	130	7	i	i	PROPN
ejpam-3394	130	8	)	)	PUNCT
ejpam-3394	130	9	is	be	AUX
ejpam-3394	130	10	i	i	PROPN
ejpam-3394	130	11	-	-	PUNCT
ejpam-3394	130	12	β	β	NOUN
ejpam-3394	130	13	-	-	NOUN
ejpam-3394	130	14	paracompact	paracompact	NOUN
ejpam-3394	130	15	and	and	CCONJ
ejpam-3394	130	16	j	j	PROPN
ejpam-3394	130	17	is	be	AUX
ejpam-3394	130	18	an	an	DET
ejpam-3394	130	19	ideal	ideal	NOUN
ejpam-3394	130	20	on	on	ADP
ejpam-3394	130	21	x	x	PUNCT
ejpam-3394	130	22	with	with	ADP
ejpam-3394	130	23	i	i	PRON
ejpam-3394	130	24	⊆	⊆	NUM
ejpam-3394	130	25	j	j	PROPN
ejpam-3394	130	26	,	,	PUNCT
ejpam-3394	130	27	then	then	ADV
ejpam-3394	130	28	(	(	PUNCT
ejpam-3394	130	29	x	x	X
ejpam-3394	130	30	,	,	PUNCT
ejpam-3394	130	31	τ	τ	PROPN
ejpam-3394	130	32	,	,	PUNCT
ejpam-3394	130	33	j	j	PROPN
ejpam-3394	130	34	)	)	PUNCT
ejpam-3394	130	35	is	be	AUX
ejpam-3394	130	36	j	j	PROPN
ejpam-3394	130	37	-	-	PUNCT
ejpam-3394	130	38	β	β	NOUN
ejpam-3394	130	39	-	-	ADJ
ejpam-3394	130	40	paracompact	paracompact	ADJ
ejpam-3394	130	41	.	.	PUNCT
ejpam-3394	131	1	proof	proof	NOUN
ejpam-3394	131	2	.	.	PUNCT
ejpam-3394	132	1	let	let	VERB
ejpam-3394	132	2	(	(	PUNCT
ejpam-3394	132	3	x	x	X
ejpam-3394	132	4	,	,	PUNCT
ejpam-3394	132	5	τ	τ	PROPN
ejpam-3394	132	6	,	,	PUNCT
ejpam-3394	132	7	i	i	PRON
ejpam-3394	132	8	)	)	PUNCT
ejpam-3394	132	9	be	be	VERB
ejpam-3394	132	10	i	i	PROPN
ejpam-3394	132	11	-	-	PUNCT
ejpam-3394	132	12	β	β	NOUN
ejpam-3394	132	13	-	-	NOUN
ejpam-3394	132	14	paracompact	paracompact	NOUN
ejpam-3394	132	15	and	and	CCONJ
ejpam-3394	132	16	i	i	PRON
ejpam-3394	132	17	⊆	⊆	NUM
ejpam-3394	132	18	j	j	PROPN
ejpam-3394	132	19	.	.	PUNCT
ejpam-3394	133	1	and	and	CCONJ
ejpam-3394	133	2	let	let	VERB
ejpam-3394	133	3	u	u	PRON
ejpam-3394	133	4	=	=	PUNCT
ejpam-3394	133	5	{	{	PUNCT
ejpam-3394	133	6	uλ	uλ	X
ejpam-3394	133	7	:	:	PUNCT
ejpam-3394	133	8	λ	λ	X
ejpam-3394	133	9	∈	∈	PROPN
ejpam-3394	133	10	λ	λ	PROPN
ejpam-3394	133	11	}	}	PUNCT
ejpam-3394	133	12	be	be	VERB
ejpam-3394	133	13	an	an	DET
ejpam-3394	133	14	open	open	ADJ
ejpam-3394	133	15	cover	cover	NOUN
ejpam-3394	133	16	of	of	ADP
ejpam-3394	133	17	x.	x.	NOUN
ejpam-3394	133	18	since	since	SCONJ
ejpam-3394	133	19	(	(	PUNCT
ejpam-3394	133	20	x	x	X
ejpam-3394	133	21	,	,	PUNCT
ejpam-3394	133	22	τ	τ	PROPN
ejpam-3394	133	23	,	,	PUNCT
ejpam-3394	133	24	i	i	PROPN
ejpam-3394	133	25	)	)	PUNCT
ejpam-3394	133	26	is	be	AUX
ejpam-3394	133	27	i	i	PROPN
ejpam-3394	133	28	-	-	PUNCT
ejpam-3394	133	29	β	β	NOUN
ejpam-3394	133	30	-	-	NOUN
ejpam-3394	133	31	paracompact	paracompact	ADJ
ejpam-3394	133	32	,	,	PUNCT
ejpam-3394	133	33	u	u	NOUN
ejpam-3394	133	34	has	have	VERB
ejpam-3394	133	35	a	a	DET
ejpam-3394	133	36	β	β	NOUN
ejpam-3394	133	37	-	-	ADJ
ejpam-3394	133	38	locally	locally	ADV
ejpam-3394	133	39	finite	finite	ADJ
ejpam-3394	133	40	β	β	NOUN
ejpam-3394	133	41	-	-	ADJ
ejpam-3394	133	42	open	open	ADJ
ejpam-3394	133	43	refinement	refinement	NOUN
ejpam-3394	133	44	v	v	ADP
ejpam-3394	133	45	such	such	ADJ
ejpam-3394	133	46	that	that	SCONJ
ejpam-3394	133	47	x	x	PART
ejpam-3394	133	48	−	−	NOUN
ejpam-3394	133	49	⋃	⋃	NOUN
ejpam-3394	133	50	{	{	PUNCT
ejpam-3394	133	51	v	v	NOUN
ejpam-3394	133	52	:	:	PUNCT
ejpam-3394	133	53	v	v	NUM
ejpam-3394	133	54	∈	∈	PROPN
ejpam-3394	133	55	v	v	NOUN
ejpam-3394	133	56	}	}	PUNCT
ejpam-3394	133	57	∈	∈	PROPN
ejpam-3394	133	58	i.	i.	NOUN
ejpam-3394	133	59	since	since	SCONJ
ejpam-3394	133	60	i	i	PROPN
ejpam-3394	133	61	⊆	⊆	NUM
ejpam-3394	133	62	j	j	PROPN
ejpam-3394	133	63	,	,	PUNCT
ejpam-3394	133	64	x	x	X
ejpam-3394	134	1	−	−	PROPN
ejpam-3394	134	2	⋃	⋃	NOUN
ejpam-3394	134	3	{	{	PUNCT
ejpam-3394	134	4	v	v	NOUN
ejpam-3394	134	5	:	:	PUNCT
ejpam-3394	134	6	v	v	NUM
ejpam-3394	134	7	∈	∈	PROPN
ejpam-3394	134	8	v	v	ADP
ejpam-3394	134	9	}	}	PUNCT
ejpam-3394	134	10	∈	∈	PROPN
ejpam-3394	134	11	j	j	PROPN
ejpam-3394	134	12	.	.	PUNCT
ejpam-3394	135	1	thus	thus	ADV
ejpam-3394	135	2	,	,	PUNCT
ejpam-3394	135	3	(	(	PUNCT
ejpam-3394	135	4	x	x	X
ejpam-3394	135	5	,	,	PUNCT
ejpam-3394	135	6	τ	τ	PROPN
ejpam-3394	135	7	,	,	PUNCT
ejpam-3394	135	8	j	j	PROPN
ejpam-3394	135	9	)	)	PUNCT
ejpam-3394	135	10	is	be	AUX
ejpam-3394	135	11	j	j	PROPN
ejpam-3394	135	12	-	-	PUNCT
ejpam-3394	135	13	β	β	NOUN
ejpam-3394	135	14	-	-	NOUN
ejpam-3394	135	15	paracompact	paracompact	ADJ
ejpam-3394	135	16	.	.	PUNCT
ejpam-3394	136	1	lemma	lemma	PROPN
ejpam-3394	136	2	5	5	NUM
ejpam-3394	136	3	.	.	PUNCT
ejpam-3394	137	1	[	[	X
ejpam-3394	137	2	11]let	11]let	NUM
ejpam-3394	137	3	v	v	X
ejpam-3394	137	4	=	=	PUNCT
ejpam-3394	137	5	{	{	PUNCT
ejpam-3394	137	6	vλ	vλ	INTJ
ejpam-3394	137	7	:	:	PUNCT
ejpam-3394	137	8	λ	λ	PROPN
ejpam-3394	137	9	∈	∈	PROPN
ejpam-3394	137	10	λ	λ	PROPN
ejpam-3394	137	11	}	}	PUNCT
ejpam-3394	137	12	be	be	VERB
ejpam-3394	137	13	a	a	DET
ejpam-3394	137	14	collection	collection	NOUN
ejpam-3394	137	15	of	of	ADP
ejpam-3394	137	16	subsets	subset	NOUN
ejpam-3394	137	17	of	of	ADP
ejpam-3394	137	18	a	a	DET
ejpam-3394	137	19	space	space	NOUN
ejpam-3394	137	20	(	(	PUNCT
ejpam-3394	137	21	x	x	X
ejpam-3394	137	22	,	,	PUNCT
ejpam-3394	137	23	τ	τ	PROPN
ejpam-3394	137	24	)	)	PUNCT
ejpam-3394	137	25	.	.	PUNCT
ejpam-3394	138	1	v	v	NOUN
ejpam-3394	138	2	is	be	AUX
ejpam-3394	138	3	β	β	X
ejpam-3394	138	4	-	-	ADJ
ejpam-3394	138	5	locally	locally	ADV
ejpam-3394	138	6	finite	finite	NOUN
ejpam-3394	138	7	if	if	SCONJ
ejpam-3394	138	8	and	and	CCONJ
ejpam-3394	138	9	only	only	ADV
ejpam-3394	138	10	if	if	SCONJ
ejpam-3394	138	11	{	{	PUNCT
ejpam-3394	138	12	βcl(vλ	βcl(vλ	NOUN
ejpam-3394	138	13	)	)	PUNCT
ejpam-3394	138	14	:	:	PUNCT
ejpam-3394	139	1	λ	λ	X
ejpam-3394	139	2	∈	∈	PROPN
ejpam-3394	139	3	λ	λ	PROPN
ejpam-3394	139	4	}	}	PUNCT
ejpam-3394	139	5	is	be	AUX
ejpam-3394	139	6	β	β	X
ejpam-3394	139	7	-	-	ADJ
ejpam-3394	139	8	locally	locally	ADV
ejpam-3394	139	9	finite	finite	NOUN
ejpam-3394	139	10	.	.	PUNCT
ejpam-3394	140	1	e.	e.	PROPN
ejpam-3394	140	2	d.	d.	PROPN
ejpam-3394	140	3	yıldırım	yıldırım	PROPN
ejpam-3394	140	4	,	,	PUNCT
ejpam-3394	140	5	o.	o.	PROPN
ejpam-3394	140	6	b.	b.	PROPN
ejpam-3394	140	7	özbakır	özbakır	PROPN
ejpam-3394	140	8	,	,	PUNCT
ejpam-3394	140	9	a.	a.	PROPN
ejpam-3394	140	10	c.	c.	PROPN
ejpam-3394	140	11	.	.	PUNCT
ejpam-3394	141	1	güler	güler	PROPN
ejpam-3394	141	2	/	/	SYM
ejpam-3394	141	3	eur	eur	PROPN
ejpam-3394	141	4	.	.	PUNCT
ejpam-3394	142	1	j.	j.	PROPN
ejpam-3394	142	2	pure	pure	PROPN
ejpam-3394	142	3	appl	appl	PROPN
ejpam-3394	142	4	.	.	PROPN
ejpam-3394	142	5	math	math	PROPN
ejpam-3394	142	6	,	,	PUNCT
ejpam-3394	142	7	12	12	NUM
ejpam-3394	142	8	(	(	PUNCT
ejpam-3394	142	9	2	2	NUM
ejpam-3394	142	10	)	)	PUNCT
ejpam-3394	142	11	(	(	PUNCT
ejpam-3394	142	12	2019	2019	NUM
ejpam-3394	142	13	)	)	PUNCT
ejpam-3394	142	14	,	,	PUNCT
ejpam-3394	142	15	270	270	NUM
ejpam-3394	142	16	-	-	SYM
ejpam-3394	142	17	278	278	NUM
ejpam-3394	142	18	274	274	NUM
ejpam-3394	142	19	lemma	lemma	PROPN
ejpam-3394	142	20	6	6	NUM
ejpam-3394	142	21	.	.	PUNCT
ejpam-3394	143	1	if	if	SCONJ
ejpam-3394	143	2	a	a	DET
ejpam-3394	143	3	cover	cover	NOUN
ejpam-3394	143	4	u	u	NOUN
ejpam-3394	143	5	=	=	PUNCT
ejpam-3394	143	6	{	{	PUNCT
ejpam-3394	143	7	uλ	uλ	X
ejpam-3394	143	8	:	:	PUNCT
ejpam-3394	143	9	λ	λ	X
ejpam-3394	143	10	∈	∈	PROPN
ejpam-3394	143	11	λ	λ	NOUN
ejpam-3394	143	12	}	}	PUNCT
ejpam-3394	143	13	of	of	ADP
ejpam-3394	143	14	a	a	DET
ejpam-3394	143	15	space	space	NOUN
ejpam-3394	143	16	(	(	PUNCT
ejpam-3394	143	17	x	x	X
ejpam-3394	143	18	,	,	PUNCT
ejpam-3394	143	19	τ	τ	PROPN
ejpam-3394	143	20	,	,	PUNCT
ejpam-3394	143	21	i	i	NOUN
ejpam-3394	143	22	)	)	PUNCT
ejpam-3394	143	23	has	have	VERB
ejpam-3394	143	24	a	a	DET
ejpam-3394	143	25	βlocally	βlocally	ADJ
ejpam-3394	143	26	finite	finite	ADJ
ejpam-3394	143	27	β	β	NOUN
ejpam-3394	143	28	-	-	ADJ
ejpam-3394	143	29	open	open	ADJ
ejpam-3394	143	30	refinement	refinement	NOUN
ejpam-3394	143	31	v	v	ADP
ejpam-3394	143	32	such	such	ADJ
ejpam-3394	143	33	that	that	SCONJ
ejpam-3394	143	34	x	x	PART
ejpam-3394	143	35	−	−	NOUN
ejpam-3394	143	36	⋃	⋃	NOUN
ejpam-3394	143	37	{	{	PUNCT
ejpam-3394	143	38	v	v	NOUN
ejpam-3394	143	39	:	:	PUNCT
ejpam-3394	143	40	v	v	NUM
ejpam-3394	143	41	∈	∈	PROPN
ejpam-3394	143	42	v	v	NOUN
ejpam-3394	143	43	}	}	PUNCT
ejpam-3394	143	44	∈	∈	PROPN
ejpam-3394	144	1	i	i	PRON
ejpam-3394	144	2	then	then	ADV
ejpam-3394	144	3	there	there	PRON
ejpam-3394	144	4	exists	exist	VERB
ejpam-3394	144	5	a	a	DET
ejpam-3394	144	6	β	β	X
ejpam-3394	144	7	-	-	ADJ
ejpam-3394	144	8	locally	locally	ADV
ejpam-3394	144	9	finite	finite	ADJ
ejpam-3394	144	10	precise	precise	ADJ
ejpam-3394	144	11	βopen	βopen	ADJ
ejpam-3394	144	12	refinement	refinement	NOUN
ejpam-3394	144	13	h	h	NOUN
ejpam-3394	144	14	=	=	PRON
ejpam-3394	144	15	{	{	PUNCT
ejpam-3394	144	16	hλ	hλ	X
ejpam-3394	144	17	:	:	PUNCT
ejpam-3394	144	18	λ	λ	PROPN
ejpam-3394	144	19	∈	∈	PROPN
ejpam-3394	144	20	λ	λ	PROPN
ejpam-3394	144	21	}	}	PUNCT
ejpam-3394	144	22	of	of	ADP
ejpam-3394	144	23	u	u	PRON
ejpam-3394	144	24	such	such	ADJ
ejpam-3394	144	25	that	that	SCONJ
ejpam-3394	144	26	x	x	PRON
ejpam-3394	144	27	−	−	NOUN
ejpam-3394	144	28	⋃	⋃	NOUN
ejpam-3394	144	29	{	{	PUNCT
ejpam-3394	144	30	hλ	hλ	X
ejpam-3394	144	31	:	:	PUNCT
ejpam-3394	144	32	hλ	hλ	PART
ejpam-3394	144	33	∈	∈	PROPN
ejpam-3394	144	34	h	h	NOUN
ejpam-3394	144	35	}	}	PUNCT
ejpam-3394	144	36	∈	∈	PROPN
ejpam-3394	144	37	i.	i.	NOUN
ejpam-3394	144	38	proof	proof	NOUN
ejpam-3394	144	39	.	.	PUNCT
ejpam-3394	145	1	the	the	DET
ejpam-3394	145	2	proof	proof	NOUN
ejpam-3394	145	3	is	be	AUX
ejpam-3394	145	4	similar	similar	ADJ
ejpam-3394	145	5	to	to	ADP
ejpam-3394	145	6	that	that	PRON
ejpam-3394	145	7	of	of	ADP
ejpam-3394	145	8	lemma	lemma	PROPN
ejpam-3394	145	9	1.3	1.3	NUM
ejpam-3394	145	10	in	in	ADP
ejpam-3394	145	11	[	[	X
ejpam-3394	145	12	21	21	NUM
ejpam-3394	145	13	]	]	PUNCT
ejpam-3394	145	14	.	.	PUNCT
ejpam-3394	146	1	definition	definition	NOUN
ejpam-3394	146	2	2	2	NUM
ejpam-3394	146	3	.	.	PUNCT
ejpam-3394	147	1	a	a	DET
ejpam-3394	147	2	collection	collection	NOUN
ejpam-3394	147	3	a	a	PRON
ejpam-3394	147	4	of	of	ADP
ejpam-3394	147	5	subsets	subset	NOUN
ejpam-3394	147	6	of	of	ADP
ejpam-3394	147	7	a	a	DET
ejpam-3394	147	8	space	space	NOUN
ejpam-3394	147	9	(	(	PUNCT
ejpam-3394	147	10	x	x	X
ejpam-3394	147	11	,	,	PUNCT
ejpam-3394	147	12	τ	τ	X
ejpam-3394	147	13	)	)	PUNCT
ejpam-3394	147	14	is	be	AUX
ejpam-3394	147	15	said	say	VERB
ejpam-3394	147	16	to	to	PART
ejpam-3394	147	17	be	be	AUX
ejpam-3394	147	18	σ	σ	PROPN
ejpam-3394	147	19	-	-	PUNCT
ejpam-3394	147	20	β	β	NOUN
ejpam-3394	147	21	-	-	ADJ
ejpam-3394	147	22	locally	locally	ADV
ejpam-3394	147	23	finite	finite	NOUN
ejpam-3394	147	24	if	if	SCONJ
ejpam-3394	147	25	a	a	DET
ejpam-3394	147	26	=	=	ADJ
ejpam-3394	147	27	∞⋃	∞⋃	NOUN
ejpam-3394	147	28	n=1	n=1	PROPN
ejpam-3394	147	29	an	an	PRON
ejpam-3394	147	30	where	where	SCONJ
ejpam-3394	147	31	each	each	DET
ejpam-3394	147	32	collection	collection	NOUN
ejpam-3394	147	33	an	an	PRON
ejpam-3394	147	34	is	be	AUX
ejpam-3394	147	35	a	a	DET
ejpam-3394	147	36	βlocally	βlocally	ADJ
ejpam-3394	147	37	finite	finite	ADJ
ejpam-3394	147	38	family	family	NOUN
ejpam-3394	147	39	.	.	PUNCT
ejpam-3394	148	1	lemma	lemma	PROPN
ejpam-3394	148	2	7	7	NUM
ejpam-3394	148	3	.	.	PUNCT
ejpam-3394	149	1	every	every	DET
ejpam-3394	149	2	β	β	X
ejpam-3394	149	3	-	-	ADJ
ejpam-3394	149	4	locally	locally	ADV
ejpam-3394	149	5	finite	finite	ADJ
ejpam-3394	149	6	collection	collection	NOUN
ejpam-3394	149	7	of	of	ADP
ejpam-3394	149	8	subsets	subset	NOUN
ejpam-3394	149	9	of	of	ADP
ejpam-3394	149	10	a	a	DET
ejpam-3394	149	11	space	space	NOUN
ejpam-3394	149	12	(	(	PUNCT
ejpam-3394	149	13	x	x	X
ejpam-3394	149	14	,	,	PUNCT
ejpam-3394	149	15	τ	τ	X
ejpam-3394	149	16	)	)	PUNCT
ejpam-3394	149	17	is	be	AUX
ejpam-3394	149	18	σ	σ	PROPN
ejpam-3394	149	19	-	-	PUNCT
ejpam-3394	149	20	β	β	NOUN
ejpam-3394	149	21	-	-	ADJ
ejpam-3394	149	22	locally	locally	ADV
ejpam-3394	149	23	finite	finite	NOUN
ejpam-3394	149	24	.	.	PUNCT
ejpam-3394	150	1	proof	proof	NOUN
ejpam-3394	150	2	.	.	PUNCT
ejpam-3394	151	1	it	it	PRON
ejpam-3394	151	2	is	be	AUX
ejpam-3394	151	3	obvious	obvious	ADJ
ejpam-3394	151	4	.	.	PUNCT
ejpam-3394	152	1	theorem	theorem	NOUN
ejpam-3394	152	2	5	5	NUM
ejpam-3394	152	3	.	.	PUNCT
ejpam-3394	153	1	let	let	AUX
ejpam-3394	153	2	(	(	PUNCT
ejpam-3394	153	3	x	x	NOUN
ejpam-3394	153	4	,	,	PUNCT
ejpam-3394	153	5	τ	τ	X
ejpam-3394	153	6	)	)	PUNCT
ejpam-3394	153	7	be	be	AUX
ejpam-3394	153	8	a	a	DET
ejpam-3394	153	9	regular	regular	ADJ
ejpam-3394	153	10	space	space	NOUN
ejpam-3394	153	11	.	.	PUNCT
ejpam-3394	154	1	if	if	SCONJ
ejpam-3394	154	2	(	(	PUNCT
ejpam-3394	154	3	x	x	X
ejpam-3394	154	4	,	,	PUNCT
ejpam-3394	154	5	τ	τ	PROPN
ejpam-3394	154	6	,	,	PUNCT
ejpam-3394	154	7	i	i	PROPN
ejpam-3394	154	8	)	)	PUNCT
ejpam-3394	154	9	is	be	AUX
ejpam-3394	154	10	i	i	PROPN
ejpam-3394	154	11	-	-	PUNCT
ejpam-3394	154	12	β	β	NOUN
ejpam-3394	154	13	-	-	NOUN
ejpam-3394	154	14	paracompact	paracompact	ADJ
ejpam-3394	154	15	,	,	PUNCT
ejpam-3394	154	16	then	then	ADV
ejpam-3394	154	17	every	every	DET
ejpam-3394	154	18	open	open	ADJ
ejpam-3394	154	19	cover	cover	NOUN
ejpam-3394	154	20	of	of	ADP
ejpam-3394	154	21	x	x	PUNCT
ejpam-3394	154	22	has	have	VERB
ejpam-3394	154	23	a	a	DET
ejpam-3394	154	24	β	β	NOUN
ejpam-3394	154	25	-	-	VERB
ejpam-3394	154	26	closed	closed	ADJ
ejpam-3394	154	27	β	β	NOUN
ejpam-3394	154	28	-	-	ADJ
ejpam-3394	154	29	locally	locally	ADV
ejpam-3394	154	30	finite	finite	NOUN
ejpam-3394	154	31	i	i	NOUN
ejpam-3394	154	32	-	-	PUNCT
ejpam-3394	154	33	cover	cover	NOUN
ejpam-3394	154	34	refinement	refinement	NOUN
ejpam-3394	154	35	.	.	PUNCT
ejpam-3394	155	1	proof	proof	NOUN
ejpam-3394	155	2	.	.	PUNCT
ejpam-3394	156	1	let	let	VERB
ejpam-3394	156	2	u	u	PRON
ejpam-3394	156	3	be	be	AUX
ejpam-3394	156	4	an	an	DET
ejpam-3394	156	5	open	open	ADJ
ejpam-3394	156	6	cover	cover	NOUN
ejpam-3394	156	7	of	of	ADP
ejpam-3394	156	8	x.	x.	NOUN
ejpam-3394	156	9	by	by	ADP
ejpam-3394	156	10	regularity	regularity	NOUN
ejpam-3394	156	11	of	of	ADP
ejpam-3394	156	12	x	x	PRON
ejpam-3394	156	13	,	,	PUNCT
ejpam-3394	156	14	for	for	ADP
ejpam-3394	156	15	each	each	DET
ejpam-3394	156	16	x	x	SYM
ejpam-3394	156	17	∈	∈	PROPN
ejpam-3394	156	18	x	x	X
ejpam-3394	156	19	and	and	CCONJ
ejpam-3394	156	20	ux	ux	PROPN
ejpam-3394	157	1	∈	∈	PROPN
ejpam-3394	157	2	u	u	NOUN
ejpam-3394	157	3	containing	contain	VERB
ejpam-3394	157	4	x	x	PRON
ejpam-3394	157	5	,	,	PUNCT
ejpam-3394	157	6	there	there	PRON
ejpam-3394	157	7	exists	exist	VERB
ejpam-3394	157	8	an	an	DET
ejpam-3394	157	9	open	open	ADJ
ejpam-3394	157	10	set	set	NOUN
ejpam-3394	157	11	gx	gx	PROPN
ejpam-3394	157	12	of	of	ADP
ejpam-3394	157	13	x	x	INTJ
ejpam-3394	157	14	such	such	ADJ
ejpam-3394	157	15	that	that	DET
ejpam-3394	157	16	cl(gx	cl(gx	NOUN
ejpam-3394	157	17	)	)	PUNCT
ejpam-3394	157	18	⊆	⊆	NUM
ejpam-3394	157	19	ux	ux	PROPN
ejpam-3394	157	20	.	.	PUNCT
ejpam-3394	157	21	then	then	ADV
ejpam-3394	157	22	u1	u1	PROPN
ejpam-3394	157	23	=	=	SYM
ejpam-3394	157	24	{	{	PUNCT
ejpam-3394	157	25	gx	gx	PROPN
ejpam-3394	157	26	:	:	PUNCT
ejpam-3394	157	27	x	x	SYM
ejpam-3394	157	28	∈	∈	PROPN
ejpam-3394	157	29	x	x	PRON
ejpam-3394	157	30	}	}	PUNCT
ejpam-3394	157	31	is	be	AUX
ejpam-3394	157	32	an	an	DET
ejpam-3394	157	33	open	open	ADJ
ejpam-3394	157	34	cover	cover	NOUN
ejpam-3394	157	35	of	of	ADP
ejpam-3394	157	36	x.	x.	NOUN
ejpam-3394	157	37	since	since	SCONJ
ejpam-3394	157	38	x	x	PROPN
ejpam-3394	157	39	is	be	AUX
ejpam-3394	157	40	i	i	PROPN
ejpam-3394	157	41	-	-	PUNCT
ejpam-3394	157	42	β	β	NOUN
ejpam-3394	157	43	-	-	ADJ
ejpam-3394	157	44	paracompact	paracompact	ADJ
ejpam-3394	157	45	,	,	PUNCT
ejpam-3394	157	46	u1	u1	NOUN
ejpam-3394	157	47	has	have	AUX
ejpam-3394	157	48	βlocally	βlocally	ADV
ejpam-3394	157	49	finite	finite	VERB
ejpam-3394	157	50	β	β	ADJ
ejpam-3394	157	51	-	-	ADJ
ejpam-3394	157	52	open	open	ADJ
ejpam-3394	157	53	refinement	refinement	NOUN
ejpam-3394	157	54	v1	v1	NOUN
ejpam-3394	157	55	=	=	SYM
ejpam-3394	157	56	{	{	PUNCT
ejpam-3394	157	57	vλ	vλ	INTJ
ejpam-3394	157	58	:	:	PUNCT
ejpam-3394	157	59	λ	λ	PROPN
ejpam-3394	157	60	∈	∈	PROPN
ejpam-3394	157	61	λ	λ	NOUN
ejpam-3394	157	62	}	}	PUNCT
ejpam-3394	157	63	such	such	ADJ
ejpam-3394	157	64	that	that	SCONJ
ejpam-3394	157	65	x	x	PUNCT
ejpam-3394	157	66	−	−	PROPN
ejpam-3394	157	67	⋃	⋃	NOUN
ejpam-3394	157	68	{	{	PUNCT
ejpam-3394	157	69	vλ	vλ	INTJ
ejpam-3394	157	70	:	:	PUNCT
ejpam-3394	157	71	λ	λ	PROPN
ejpam-3394	157	72	∈	∈	PROPN
ejpam-3394	157	73	λ	λ	PROPN
ejpam-3394	157	74	}	}	PUNCT
ejpam-3394	157	75	∈	∈	PROPN
ejpam-3394	157	76	i.	i.	NOUN
ejpam-3394	157	77	then	then	ADV
ejpam-3394	157	78	x	x	PUNCT
ejpam-3394	157	79	−	−	PROPN
ejpam-3394	157	80	⋃	⋃	NOUN
ejpam-3394	157	81	{	{	PUNCT
ejpam-3394	157	82	βcl(vλ	βcl(vλ	NOUN
ejpam-3394	157	83	)	)	PUNCT
ejpam-3394	157	84	:	:	PUNCT
ejpam-3394	158	1	λ	λ	X
ejpam-3394	158	2	∈	∈	PROPN
ejpam-3394	158	3	λ	λ	PROPN
ejpam-3394	158	4	}	}	PUNCT
ejpam-3394	158	5	∈	∈	PROPN
ejpam-3394	158	6	i.	i.	NOUN
ejpam-3394	158	7	by	by	ADP
ejpam-3394	158	8	lemma	lemma	PROPN
ejpam-3394	158	9	5	5	NUM
ejpam-3394	158	10	,	,	PUNCT
ejpam-3394	158	11	v	v	NOUN
ejpam-3394	158	12	=	=	SYM
ejpam-3394	158	13	{	{	PUNCT
ejpam-3394	158	14	βcl(vλ	βcl(vλ	NOUN
ejpam-3394	158	15	)	)	PUNCT
ejpam-3394	158	16	:	:	PUNCT
ejpam-3394	158	17	vλ	vλ	ADP
ejpam-3394	158	18	∈	∈	PROPN
ejpam-3394	158	19	v1	v1	NOUN
ejpam-3394	158	20	}	}	PUNCT
ejpam-3394	158	21	is	be	AUX
ejpam-3394	158	22	βlocally	βlocally	ADV
ejpam-3394	158	23	finite	finite	ADJ
ejpam-3394	158	24	.	.	PUNCT
ejpam-3394	159	1	since	since	SCONJ
ejpam-3394	159	2	v1	v1	NOUN
ejpam-3394	159	3	refines	refine	NOUN
ejpam-3394	159	4	u1	u1	NOUN
ejpam-3394	159	5	,	,	PUNCT
ejpam-3394	159	6	for	for	ADP
ejpam-3394	159	7	every	every	DET
ejpam-3394	159	8	λ	λ	PROPN
ejpam-3394	159	9	∈	∈	PROPN
ejpam-3394	159	10	λ	λ	PROPN
ejpam-3394	159	11	,	,	PUNCT
ejpam-3394	159	12	there	there	PRON
ejpam-3394	159	13	is	be	VERB
ejpam-3394	159	14	some	some	DET
ejpam-3394	159	15	gx	gx	PROPN
ejpam-3394	159	16	∈	∈	PROPN
ejpam-3394	159	17	u1	u1	NOUN
ejpam-3394	159	18	such	such	ADJ
ejpam-3394	159	19	that	that	SCONJ
ejpam-3394	159	20	vλ⊆	vλ⊆	PROPN
ejpam-3394	159	21	gx	gx	PROPN
ejpam-3394	159	22	.	.	PUNCT
ejpam-3394	160	1	then	then	ADV
ejpam-3394	160	2	βcl(vλ)⊆	βcl(vλ)⊆	PROPN
ejpam-3394	160	3	cl(vλ)⊆	cl(vλ)⊆	PROPN
ejpam-3394	160	4	cl(gx	cl(gx	PROPN
ejpam-3394	160	5	)	)	PUNCT
ejpam-3394	160	6	implies	imply	VERB
ejpam-3394	160	7	βcl(vλ)⊂	βcl(vλ)⊂	PROPN
ejpam-3394	160	8	ux	ux	PROPN
ejpam-3394	160	9	.	.	PUNCT
ejpam-3394	161	1	hence	hence	ADV
ejpam-3394	161	2	v	v	NOUN
ejpam-3394	161	3	refines	refine	VERB
ejpam-3394	161	4	u	u	PRON
ejpam-3394	161	5	.	.	PUNCT
ejpam-3394	162	1	so	so	ADV
ejpam-3394	162	2	,	,	PUNCT
ejpam-3394	162	3	v	v	NOUN
ejpam-3394	162	4	=	=	SYM
ejpam-3394	162	5	{	{	PUNCT
ejpam-3394	162	6	βcl(vλ	βcl(vλ	NOUN
ejpam-3394	162	7	)	)	PUNCT
ejpam-3394	162	8	:	:	PUNCT
ejpam-3394	163	1	vλ	vλ	ADP
ejpam-3394	163	2	∈	∈	PROPN
ejpam-3394	163	3	v1	v1	NOUN
ejpam-3394	163	4	}	}	PUNCT
ejpam-3394	163	5	is	be	AUX
ejpam-3394	163	6	β	β	X
ejpam-3394	163	7	-	-	VERB
ejpam-3394	163	8	closed	closed	ADJ
ejpam-3394	163	9	β	β	NOUN
ejpam-3394	163	10	-	-	ADJ
ejpam-3394	163	11	locally	locally	ADV
ejpam-3394	163	12	finite	finite	NOUN
ejpam-3394	163	13	i	i	NOUN
ejpam-3394	163	14	-	-	PUNCT
ejpam-3394	163	15	cover	cover	NOUN
ejpam-3394	163	16	refinement	refinement	NOUN
ejpam-3394	163	17	.	.	PUNCT
ejpam-3394	164	1	remark	remark	NOUN
ejpam-3394	164	2	2	2	NUM
ejpam-3394	164	3	.	.	PUNCT
ejpam-3394	165	1	if	if	SCONJ
ejpam-3394	165	2	(	(	PUNCT
ejpam-3394	165	3	x	x	X
ejpam-3394	165	4	,	,	PUNCT
ejpam-3394	165	5	τ	τ	PROPN
ejpam-3394	165	6	,	,	PUNCT
ejpam-3394	165	7	i	i	PROPN
ejpam-3394	165	8	)	)	PUNCT
ejpam-3394	165	9	is	be	AUX
ejpam-3394	165	10	considered	consider	VERB
ejpam-3394	165	11	to	to	PART
ejpam-3394	165	12	be	be	AUX
ejpam-3394	165	13	e.d	e.d	PROPN
ejpam-3394	165	14	.	.	PROPN
ejpam-3394	165	15	submaximal	submaximal	ADJ
ejpam-3394	165	16	regular	regular	ADJ
ejpam-3394	165	17	space	space	NOUN
ejpam-3394	165	18	,	,	PUNCT
ejpam-3394	165	19	then	then	ADV
ejpam-3394	165	20	the	the	DET
ejpam-3394	165	21	theorem	theorem	NOUN
ejpam-3394	165	22	5	5	NUM
ejpam-3394	165	23	becomes	become	VERB
ejpam-3394	165	24	the	the	DET
ejpam-3394	165	25	theorem	theorem	NOUN
ejpam-3394	165	26	2.20	2.20	NUM
ejpam-3394	165	27	in	in	ADP
ejpam-3394	165	28	[	[	PUNCT
ejpam-3394	165	29	22	22	NUM
ejpam-3394	165	30	]	]	PUNCT
ejpam-3394	165	31	.	.	PUNCT
ejpam-3394	166	1	theorem	theorem	VERB
ejpam-3394	166	2	6	6	NUM
ejpam-3394	166	3	.	.	PUNCT
ejpam-3394	167	1	if	if	SCONJ
ejpam-3394	167	2	(	(	PUNCT
ejpam-3394	167	3	x	x	X
ejpam-3394	167	4	,	,	PUNCT
ejpam-3394	167	5	τ	τ	PROPN
ejpam-3394	167	6	,	,	PUNCT
ejpam-3394	167	7	i	i	PROPN
ejpam-3394	167	8	)	)	PUNCT
ejpam-3394	167	9	is	be	AUX
ejpam-3394	167	10	i	i	PROPN
ejpam-3394	167	11	-	-	PUNCT
ejpam-3394	167	12	β	β	NOUN
ejpam-3394	167	13	-	-	NOUN
ejpam-3394	167	14	paracompact	paracompact	ADJ
ejpam-3394	167	15	,	,	PUNCT
ejpam-3394	167	16	then	then	ADV
ejpam-3394	167	17	every	every	DET
ejpam-3394	167	18	open	open	ADJ
ejpam-3394	167	19	cover	cover	NOUN
ejpam-3394	167	20	of	of	ADP
ejpam-3394	167	21	x	x	PUNCT
ejpam-3394	167	22	has	have	VERB
ejpam-3394	167	23	a	a	DET
ejpam-3394	167	24	β	β	NOUN
ejpam-3394	167	25	-	-	ADJ
ejpam-3394	167	26	open	open	ADJ
ejpam-3394	167	27	σ	σ	PROPN
ejpam-3394	167	28	-	-	PUNCT
ejpam-3394	167	29	β	β	NOUN
ejpam-3394	167	30	-	-	ADJ
ejpam-3394	167	31	locally	locally	ADV
ejpam-3394	167	32	finite	finite	NOUN
ejpam-3394	167	33	i	i	NOUN
ejpam-3394	167	34	-	-	PUNCT
ejpam-3394	167	35	cover	cover	NOUN
ejpam-3394	167	36	refinement	refinement	NOUN
ejpam-3394	167	37	.	.	PUNCT
ejpam-3394	168	1	proof	proof	NOUN
ejpam-3394	168	2	.	.	PUNCT
ejpam-3394	169	1	it	it	PRON
ejpam-3394	169	2	is	be	AUX
ejpam-3394	169	3	obvious	obvious	ADJ
ejpam-3394	169	4	by	by	ADP
ejpam-3394	169	5	lemma	lemma	PROPN
ejpam-3394	169	6	7	7	NUM
ejpam-3394	169	7	.	.	PUNCT
ejpam-3394	169	8	theorem	theorem	NOUN
ejpam-3394	169	9	7	7	NUM
ejpam-3394	169	10	.	.	PUNCT
ejpam-3394	170	1	let	let	VERB
ejpam-3394	170	2	(	(	PUNCT
ejpam-3394	170	3	x	x	X
ejpam-3394	170	4	,	,	PUNCT
ejpam-3394	170	5	τ	τ	PROPN
ejpam-3394	170	6	,	,	PUNCT
ejpam-3394	170	7	i	i	PRON
ejpam-3394	170	8	)	)	PUNCT
ejpam-3394	170	9	be	be	VERB
ejpam-3394	170	10	a	a	DET
ejpam-3394	170	11	regular	regular	ADJ
ejpam-3394	170	12	space	space	NOUN
ejpam-3394	170	13	and	and	CCONJ
ejpam-3394	170	14	βo(x	βo(x	NUM
ejpam-3394	170	15	,	,	PUNCT
ejpam-3394	170	16	τ	τ	X
ejpam-3394	170	17	)	)	PUNCT
ejpam-3394	170	18	be	be	AUX
ejpam-3394	170	19	closed	close	VERB
ejpam-3394	170	20	under	under	ADP
ejpam-3394	170	21	finite	finite	ADJ
ejpam-3394	170	22	intersection	intersection	NOUN
ejpam-3394	170	23	.	.	PUNCT
ejpam-3394	171	1	then	then	ADV
ejpam-3394	171	2	,	,	PUNCT
ejpam-3394	171	3	(	(	PUNCT
ejpam-3394	171	4	x	x	X
ejpam-3394	171	5	,	,	PUNCT
ejpam-3394	171	6	τ	τ	PROPN
ejpam-3394	171	7	,	,	PUNCT
ejpam-3394	171	8	i	i	PROPN
ejpam-3394	171	9	)	)	PUNCT
ejpam-3394	171	10	is	be	AUX
ejpam-3394	171	11	i	i	PROPN
ejpam-3394	171	12	-	-	PUNCT
ejpam-3394	171	13	β	β	NOUN
ejpam-3394	171	14	-	-	NOUN
ejpam-3394	171	15	paracompact	paracompact	ADJ
ejpam-3394	171	16	if	if	SCONJ
ejpam-3394	171	17	and	and	CCONJ
ejpam-3394	171	18	only	only	ADV
ejpam-3394	171	19	if	if	SCONJ
ejpam-3394	171	20	every	every	DET
ejpam-3394	171	21	open	open	ADJ
ejpam-3394	171	22	cover	cover	NOUN
ejpam-3394	171	23	of	of	ADP
ejpam-3394	171	24	x	x	PUNCT
ejpam-3394	171	25	has	have	VERB
ejpam-3394	171	26	a	a	DET
ejpam-3394	171	27	β	β	NOUN
ejpam-3394	171	28	-	-	ADJ
ejpam-3394	171	29	open	open	ADJ
ejpam-3394	171	30	σ	σ	PROPN
ejpam-3394	171	31	-	-	PUNCT
ejpam-3394	171	32	β	β	NOUN
ejpam-3394	171	33	-	-	ADJ
ejpam-3394	171	34	locally	locally	ADV
ejpam-3394	171	35	finite	finite	NOUN
ejpam-3394	171	36	i	i	NOUN
ejpam-3394	171	37	-	-	PUNCT
ejpam-3394	171	38	cover	cover	NOUN
ejpam-3394	171	39	refinement	refinement	NOUN
ejpam-3394	171	40	.	.	PUNCT
ejpam-3394	172	1	proof	proof	NOUN
ejpam-3394	172	2	.	.	PUNCT
ejpam-3394	173	1	to	to	PART
ejpam-3394	173	2	show	show	VERB
ejpam-3394	173	3	sufficiency	sufficiency	NOUN
ejpam-3394	173	4	,	,	PUNCT
ejpam-3394	173	5	let	let	VERB
ejpam-3394	173	6	u	u	PRON
ejpam-3394	173	7	be	be	AUX
ejpam-3394	173	8	an	an	DET
ejpam-3394	173	9	open	open	ADJ
ejpam-3394	173	10	cover	cover	NOUN
ejpam-3394	173	11	of	of	ADP
ejpam-3394	173	12	x.	x.	NOUN
ejpam-3394	173	13	by	by	ADP
ejpam-3394	173	14	hypothesis	hypothesis	NOUN
ejpam-3394	173	15	,	,	PUNCT
ejpam-3394	173	16	there	there	PRON
ejpam-3394	173	17	exists	exist	VERB
ejpam-3394	173	18	a	a	DET
ejpam-3394	173	19	σ	σ	PROPN
ejpam-3394	173	20	-	-	PUNCT
ejpam-3394	173	21	β	β	NOUN
ejpam-3394	173	22	-	-	ADJ
ejpam-3394	173	23	locally	locally	ADV
ejpam-3394	173	24	finite	finite	ADJ
ejpam-3394	173	25	β	β	NOUN
ejpam-3394	173	26	-	-	ADJ
ejpam-3394	173	27	open	open	ADJ
ejpam-3394	173	28	refinement	refinement	NOUN
ejpam-3394	173	29	v	v	NOUN
ejpam-3394	173	30	of	of	ADP
ejpam-3394	173	31	u	u	PRON
ejpam-3394	173	32	such	such	ADJ
ejpam-3394	173	33	that	that	SCONJ
ejpam-3394	173	34	x	x	PRON
ejpam-3394	173	35	−	−	NOUN
ejpam-3394	173	36	⋃	⋃	NOUN
ejpam-3394	173	37	{	{	PUNCT
ejpam-3394	173	38	v	v	NOUN
ejpam-3394	173	39	:	:	PUNCT
ejpam-3394	173	40	v	v	NUM
ejpam-3394	173	41	∈	∈	PROPN
ejpam-3394	173	42	v	v	NOUN
ejpam-3394	173	43	}	}	PUNCT
ejpam-3394	173	44	∈	∈	PROPN
ejpam-3394	173	45	i.	i.	NOUN
ejpam-3394	173	46	also	also	ADV
ejpam-3394	173	47	,	,	PUNCT
ejpam-3394	173	48	v	v	X
ejpam-3394	173	49	=	=	SYM
ejpam-3394	173	50	∞⋃	∞⋃	PROPN
ejpam-3394	173	51	n=1	n=1	PROPN
ejpam-3394	173	52	vn	vn	VERB
ejpam-3394	173	53	where	where	SCONJ
ejpam-3394	173	54	each	each	DET
ejpam-3394	173	55	collection	collection	NOUN
ejpam-3394	173	56	vn	vn	PROPN
ejpam-3394	173	57	is	be	AUX
ejpam-3394	173	58	a	a	DET
ejpam-3394	173	59	βlocally	βlocally	ADV
ejpam-3394	173	60	finite	finite	NOUN
ejpam-3394	173	61	.	.	PUNCT
ejpam-3394	174	1	for	for	ADP
ejpam-3394	174	2	each	each	DET
ejpam-3394	174	3	n	n	PRON
ejpam-3394	174	4	∈	∈	PROPN
ejpam-3394	174	5	n	n	CCONJ
ejpam-3394	174	6	,	,	PUNCT
ejpam-3394	174	7	let	let	VERB
ejpam-3394	174	8	hn	hn	PROPN
ejpam-3394	174	9	=	=	PUNCT
ejpam-3394	174	10	⋃	⋃	NOUN
ejpam-3394	174	11	{	{	PUNCT
ejpam-3394	174	12	v	v	NOUN
ejpam-3394	174	13	:	:	PUNCT
ejpam-3394	174	14	v	v	NUM
ejpam-3394	174	15	∈	∈	PROPN
ejpam-3394	174	16	vn	vn	NOUN
ejpam-3394	174	17	}	}	PUNCT
ejpam-3394	174	18	so	so	SCONJ
ejpam-3394	174	19	that	that	SCONJ
ejpam-3394	174	20	x	x	X
ejpam-3394	174	21	−	−	X
ejpam-3394	174	22	⋃	⋃	PROPN
ejpam-3394	174	23	{	{	PUNCT
ejpam-3394	174	24	hn	hn	NOUN
ejpam-3394	174	25	:	:	PUNCT
ejpam-3394	174	26	n	n	CCONJ
ejpam-3394	174	27	∈	∈	PROPN
ejpam-3394	174	28	n	n	CCONJ
ejpam-3394	174	29	}	}	PUNCT
ejpam-3394	174	30	∈	∈	PROPN
ejpam-3394	174	31	i.	i.	NOUN
ejpam-3394	174	32	for	for	ADP
ejpam-3394	174	33	each	each	DET
ejpam-3394	174	34	n	n	PRON
ejpam-3394	174	35	∈	∈	PROPN
ejpam-3394	174	36	n	n	CCONJ
ejpam-3394	174	37	,	,	PUNCT
ejpam-3394	174	38	let	let	VERB
ejpam-3394	174	39	gn=	gn=	VERB
ejpam-3394	174	40	hn	hn	PRON
ejpam-3394	174	41	−	−	PROPN
ejpam-3394	174	42	n−1⋃	n−1⋃	NOUN
ejpam-3394	174	43	i=1	i=1	PROPN
ejpam-3394	175	1	hi	hi	INTJ
ejpam-3394	175	2	.	.	PUNCT
ejpam-3394	176	1	then	then	ADV
ejpam-3394	176	2	{	{	PUNCT
ejpam-3394	176	3	gn	gn	INTJ
ejpam-3394	176	4	:	:	PUNCT
ejpam-3394	176	5	n	n	CCONJ
ejpam-3394	176	6	∈	∈	PROPN
ejpam-3394	176	7	n	n	CCONJ
ejpam-3394	176	8	}	}	PUNCT
ejpam-3394	176	9	refines	refine	VERB
ejpam-3394	176	10	{	{	PUNCT
ejpam-3394	176	11	hn	hn	NOUN
ejpam-3394	176	12	:	:	PUNCT
ejpam-3394	176	13	n	n	CCONJ
ejpam-3394	176	14	∈	∈	PROPN
ejpam-3394	176	15	n	n	CCONJ
ejpam-3394	176	16	}	}	PUNCT
ejpam-3394	176	17	.	.	PUNCT
ejpam-3394	177	1	let	let	VERB
ejpam-3394	177	2	x	x	PUNCT
ejpam-3394	177	3	∈	∈	PROPN
ejpam-3394	177	4	x	x	NOUN
ejpam-3394	177	5	,	,	PUNCT
ejpam-3394	177	6	and	and	CCONJ
ejpam-3394	177	7	let	let	VERB
ejpam-3394	177	8	n	n	PRON
ejpam-3394	177	9	be	be	AUX
ejpam-3394	177	10	the	the	DET
ejpam-3394	177	11	smallest	small	ADJ
ejpam-3394	177	12	member	member	NOUN
ejpam-3394	177	13	of	of	ADP
ejpam-3394	177	14	{	{	PUNCT
ejpam-3394	177	15	n	n	X
ejpam-3394	177	16	∈	∈	PROPN
ejpam-3394	177	17	n	n	NOUN
ejpam-3394	177	18	:	:	PUNCT
ejpam-3394	177	19	x	x	X
ejpam-3394	177	20	∈	∈	PROPN
ejpam-3394	177	21	hn	hn	NOUN
ejpam-3394	177	22	}	}	PUNCT
ejpam-3394	177	23	.	.	PUNCT
ejpam-3394	178	1	then	then	ADV
ejpam-3394	178	2	x	x	SYM
ejpam-3394	178	3	∈	∈	PROPN
ejpam-3394	178	4	gn	gn	PROPN
ejpam-3394	178	5	and	and	CCONJ
ejpam-3394	178	6	x	x	X
ejpam-3394	178	7	−	−	PROPN
ejpam-3394	178	8	⋃	⋃	PROPN
ejpam-3394	178	9	{	{	PUNCT
ejpam-3394	178	10	gn	gn	NOUN
ejpam-3394	178	11	:	:	PUNCT
ejpam-3394	178	12	n	n	CCONJ
ejpam-3394	178	13	∈	∈	PROPN
ejpam-3394	178	14	n	n	CCONJ
ejpam-3394	178	15	}	}	PUNCT
ejpam-3394	178	16	∈	∈	PROPN
ejpam-3394	178	17	i.	i.	NOUN
ejpam-3394	178	18	also	also	ADV
ejpam-3394	178	19	,	,	PUNCT
ejpam-3394	178	20	gnx	gnx	PROPN
ejpam-3394	178	21	is	be	AUX
ejpam-3394	178	22	a	a	DET
ejpam-3394	178	23	β	β	NOUN
ejpam-3394	178	24	-	-	ADJ
ejpam-3394	178	25	open	open	ADJ
ejpam-3394	178	26	set	set	NOUN
ejpam-3394	178	27	containing	contain	VERB
ejpam-3394	178	28	x	x	PUNCT
ejpam-3394	178	29	that	that	DET
ejpam-3394	178	30	intersects	intersect	VERB
ejpam-3394	178	31	only	only	ADV
ejpam-3394	178	32	finite	finite	VERB
ejpam-3394	178	33	family	family	NOUN
ejpam-3394	178	34	number	number	NOUN
ejpam-3394	178	35	of	of	ADP
ejpam-3394	178	36	members	member	NOUN
ejpam-3394	178	37	of	of	ADP
ejpam-3394	178	38	gn	gn	PROPN
ejpam-3394	178	39	so	so	ADV
ejpam-3394	178	40	e.	e.	PROPN
ejpam-3394	178	41	d.	d.	PROPN
ejpam-3394	178	42	yıldırım	yıldırım	PROPN
ejpam-3394	178	43	,	,	PUNCT
ejpam-3394	178	44	o.	o.	PROPN
ejpam-3394	178	45	b.	b.	PROPN
ejpam-3394	178	46	özbakır	özbakır	PROPN
ejpam-3394	178	47	,	,	PUNCT
ejpam-3394	178	48	a.	a.	PROPN
ejpam-3394	178	49	c.	c.	PROPN
ejpam-3394	178	50	.	.	PUNCT
ejpam-3394	179	1	güler	güler	PROPN
ejpam-3394	179	2	/	/	SYM
ejpam-3394	179	3	eur	eur	PROPN
ejpam-3394	179	4	.	.	PUNCT
ejpam-3394	180	1	j.	j.	PROPN
ejpam-3394	180	2	pure	pure	PROPN
ejpam-3394	180	3	appl	appl	PROPN
ejpam-3394	180	4	.	.	PROPN
ejpam-3394	180	5	math	math	PROPN
ejpam-3394	180	6	,	,	PUNCT
ejpam-3394	180	7	12	12	NUM
ejpam-3394	180	8	(	(	PUNCT
ejpam-3394	180	9	2	2	NUM
ejpam-3394	180	10	)	)	PUNCT
ejpam-3394	180	11	(	(	PUNCT
ejpam-3394	180	12	2019	2019	NUM
ejpam-3394	180	13	)	)	PUNCT
ejpam-3394	180	14	,	,	PUNCT
ejpam-3394	180	15	270	270	NUM
ejpam-3394	180	16	-	-	SYM
ejpam-3394	180	17	278	278	NUM
ejpam-3394	180	18	275	275	NUM
ejpam-3394	180	19	that	that	PRON
ejpam-3394	180	20	{	{	PUNCT
ejpam-3394	180	21	gn	gn	INTJ
ejpam-3394	180	22	:	:	PUNCT
ejpam-3394	180	23	n	n	CCONJ
ejpam-3394	180	24	∈	∈	PROPN
ejpam-3394	180	25	n	n	CCONJ
ejpam-3394	180	26	}	}	PUNCT
ejpam-3394	180	27	is	be	AUX
ejpam-3394	180	28	β	β	X
ejpam-3394	180	29	-	-	ADJ
ejpam-3394	180	30	locally	locally	ADV
ejpam-3394	180	31	finite	finite	NOUN
ejpam-3394	180	32	.	.	PUNCT
ejpam-3394	181	1	let	let	VERB
ejpam-3394	181	2	o=	o=	NUM
ejpam-3394	181	3	{	{	PUNCT
ejpam-3394	181	4	v	v	NOUN
ejpam-3394	181	5	∩	∩	ADJ
ejpam-3394	181	6	gn	gn	NOUN
ejpam-3394	181	7	:	:	PUNCT
ejpam-3394	181	8	v	v	NUM
ejpam-3394	181	9	∈	∈	PROPN
ejpam-3394	181	10	vn	vn	NOUN
ejpam-3394	181	11	and	and	CCONJ
ejpam-3394	181	12	n	n	CCONJ
ejpam-3394	181	13	∈	∈	PROPN
ejpam-3394	181	14	n	n	CCONJ
ejpam-3394	181	15	}	}	PUNCT
ejpam-3394	181	16	.	.	PUNCT
ejpam-3394	182	1	since	since	SCONJ
ejpam-3394	182	2	{	{	PUNCT
ejpam-3394	182	3	gn	gn	INTJ
ejpam-3394	182	4	:	:	PUNCT
ejpam-3394	182	5	n	n	CCONJ
ejpam-3394	182	6	∈	∈	PROPN
ejpam-3394	182	7	n	n	CCONJ
ejpam-3394	182	8	}	}	PUNCT
ejpam-3394	182	9	is	be	AUX
ejpam-3394	182	10	β	β	NOUN
ejpam-3394	182	11	-	-	ADJ
ejpam-3394	182	12	locally	locally	ADV
ejpam-3394	182	13	finite	finite	NOUN
ejpam-3394	182	14	,	,	PUNCT
ejpam-3394	182	15	o	o	PROPN
ejpam-3394	182	16	is	be	AUX
ejpam-3394	182	17	β	β	X
ejpam-3394	182	18	-	-	ADJ
ejpam-3394	182	19	locally	locally	ADV
ejpam-3394	182	20	finite	finite	NOUN
ejpam-3394	182	21	.	.	PUNCT
ejpam-3394	183	1	also	also	ADV
ejpam-3394	183	2	,	,	PUNCT
ejpam-3394	183	3	since	since	SCONJ
ejpam-3394	183	4	βo(x	βo(x	NUM
ejpam-3394	183	5	,	,	PUNCT
ejpam-3394	183	6	τ	τ	X
ejpam-3394	183	7	)	)	PUNCT
ejpam-3394	183	8	is	be	AUX
ejpam-3394	183	9	closed	close	VERB
ejpam-3394	183	10	under	under	ADP
ejpam-3394	183	11	finite	finite	ADJ
ejpam-3394	183	12	intersection	intersection	NOUN
ejpam-3394	183	13	and	and	CCONJ
ejpam-3394	183	14	v	v	NOUN
ejpam-3394	183	15	is	be	AUX
ejpam-3394	183	16	β	β	X
ejpam-3394	183	17	-	-	ADJ
ejpam-3394	183	18	open	open	ADJ
ejpam-3394	183	19	refinement	refinement	NOUN
ejpam-3394	183	20	of	of	ADP
ejpam-3394	183	21	u	u	PROPN
ejpam-3394	183	22	,	,	PUNCT
ejpam-3394	183	23	o	o	PROPN
ejpam-3394	183	24	is	be	AUX
ejpam-3394	183	25	β	β	X
ejpam-3394	183	26	-	-	ADJ
ejpam-3394	183	27	open	open	ADJ
ejpam-3394	183	28	refinement	refinement	NOUN
ejpam-3394	183	29	of	of	ADP
ejpam-3394	183	30	u	u	PROPN
ejpam-3394	183	31	.	.	PUNCT
ejpam-3394	184	1	then	then	ADV
ejpam-3394	184	2	,	,	PUNCT
ejpam-3394	184	3	x	x	PUNCT
ejpam-3394	184	4	−	−	X
ejpam-3394	184	5	⋃	⋃	NOUN
ejpam-3394	184	6	{	{	PUNCT
ejpam-3394	184	7	v	v	NOUN
ejpam-3394	184	8	∩	∩	X
ejpam-3394	184	9	gn	gn	NOUN
ejpam-3394	184	10	:	:	PUNCT
ejpam-3394	184	11	n	n	CCONJ
ejpam-3394	184	12	∈	∈	PROPN
ejpam-3394	184	13	n	n	CCONJ
ejpam-3394	184	14	}	}	PUNCT
ejpam-3394	184	15	∈	∈	PROPN
ejpam-3394	184	16	i	i	PRON
ejpam-3394	184	17	because	because	SCONJ
ejpam-3394	184	18	x	x	X
ejpam-3394	184	19	−	−	PROPN
ejpam-3394	184	20	⋃	⋃	PROPN
ejpam-3394	184	21	{	{	PUNCT
ejpam-3394	184	22	gn	gn	NOUN
ejpam-3394	184	23	:	:	PUNCT
ejpam-3394	184	24	n	n	CCONJ
ejpam-3394	184	25	∈	∈	PROPN
ejpam-3394	184	26	n	n	CCONJ
ejpam-3394	184	27	}	}	PUNCT
ejpam-3394	184	28	∈	∈	PROPN
ejpam-3394	184	29	i.	i.	NOUN
ejpam-3394	184	30	thus	thus	ADV
ejpam-3394	184	31	,	,	PUNCT
ejpam-3394	184	32	(	(	PUNCT
ejpam-3394	184	33	x	x	X
ejpam-3394	184	34	,	,	PUNCT
ejpam-3394	184	35	τ	τ	PROPN
ejpam-3394	184	36	,	,	PUNCT
ejpam-3394	184	37	i	i	PROPN
ejpam-3394	184	38	)	)	PUNCT
ejpam-3394	184	39	is	be	AUX
ejpam-3394	184	40	i	i	PROPN
ejpam-3394	184	41	-	-	PUNCT
ejpam-3394	184	42	β	β	NOUN
ejpam-3394	184	43	-	-	ADJ
ejpam-3394	184	44	paracompact	paracompact	ADJ
ejpam-3394	184	45	.	.	PUNCT
ejpam-3394	185	1	remark	remark	NOUN
ejpam-3394	185	2	3	3	NUM
ejpam-3394	185	3	.	.	PUNCT
ejpam-3394	186	1	if	if	SCONJ
ejpam-3394	186	2	(	(	PUNCT
ejpam-3394	186	3	x	x	X
ejpam-3394	186	4	,	,	PUNCT
ejpam-3394	186	5	τ	τ	PROPN
ejpam-3394	186	6	,	,	PUNCT
ejpam-3394	186	7	i	i	PROPN
ejpam-3394	186	8	)	)	PUNCT
ejpam-3394	186	9	is	be	AUX
ejpam-3394	186	10	considered	consider	VERB
ejpam-3394	186	11	to	to	PART
ejpam-3394	186	12	be	be	AUX
ejpam-3394	186	13	e.d	e.d	PROPN
ejpam-3394	186	14	.	.	PROPN
ejpam-3394	186	15	submaximal	submaximal	ADJ
ejpam-3394	186	16	regular	regular	ADJ
ejpam-3394	186	17	space	space	NOUN
ejpam-3394	186	18	,	,	PUNCT
ejpam-3394	186	19	then	then	ADV
ejpam-3394	186	20	theorem	theorem	VERB
ejpam-3394	186	21	7	7	NUM
ejpam-3394	186	22	becomes	become	NOUN
ejpam-3394	186	23	theorem	theorem	ADJ
ejpam-3394	186	24	2.22	2.22	NUM
ejpam-3394	186	25	in	in	ADP
ejpam-3394	186	26	[	[	X
ejpam-3394	186	27	22	22	NUM
ejpam-3394	186	28	]	]	PUNCT
ejpam-3394	186	29	.	.	PUNCT
ejpam-3394	187	1	theorem	theorem	ADJ
ejpam-3394	187	2	8	8	NUM
ejpam-3394	187	3	.	.	PUNCT
ejpam-3394	188	1	for	for	ADP
ejpam-3394	188	2	any	any	DET
ejpam-3394	188	3	ideal	ideal	ADJ
ejpam-3394	188	4	topological	topological	ADJ
ejpam-3394	188	5	space	space	NOUN
ejpam-3394	188	6	(	(	PUNCT
ejpam-3394	188	7	x	x	X
ejpam-3394	188	8	,	,	PUNCT
ejpam-3394	188	9	τ	τ	PROPN
ejpam-3394	188	10	,	,	PUNCT
ejpam-3394	188	11	i	i	PROPN
ejpam-3394	188	12	)	)	PUNCT
ejpam-3394	188	13	,	,	PUNCT
ejpam-3394	188	14	the	the	DET
ejpam-3394	188	15	following	follow	VERB
ejpam-3394	188	16	are	be	AUX
ejpam-3394	188	17	equivalent	equivalent	ADJ
ejpam-3394	188	18	:	:	PUNCT
ejpam-3394	188	19	(	(	PUNCT
ejpam-3394	188	20	i	i	NOUN
ejpam-3394	188	21	)	)	PUNCT
ejpam-3394	188	22	for	for	ADP
ejpam-3394	188	23	every	every	DET
ejpam-3394	188	24	closed	closed	NOUN
ejpam-3394	188	25	subset	subset	VERB
ejpam-3394	188	26	a	a	PRON
ejpam-3394	188	27	of	of	ADP
ejpam-3394	188	28	x	x	X
ejpam-3394	188	29	and	and	CCONJ
ejpam-3394	189	1	every	every	DET
ejpam-3394	189	2	x	x	PROPN
ejpam-3394	189	3	/∈	/∈	PUNCT
ejpam-3394	190	1	a	a	INTJ
ejpam-3394	190	2	,	,	PUNCT
ejpam-3394	190	3	there	there	PRON
ejpam-3394	190	4	exist	exist	VERB
ejpam-3394	190	5	disjoint	disjoint	NOUN
ejpam-3394	190	6	β	β	NOUN
ejpam-3394	190	7	-	-	ADJ
ejpam-3394	190	8	open	open	ADJ
ejpam-3394	190	9	sets	set	VERB
ejpam-3394	190	10	u	u	NOUN
ejpam-3394	190	11	and	and	CCONJ
ejpam-3394	190	12	v	v	ADP
ejpam-3394	190	13	such	such	ADJ
ejpam-3394	190	14	that	that	SCONJ
ejpam-3394	190	15	x	x	SYM
ejpam-3394	190	16	∈	∈	PROPN
ejpam-3394	190	17	u	u	NOUN
ejpam-3394	190	18	and	and	CCONJ
ejpam-3394	190	19	a−	a−	PROPN
ejpam-3394	190	20	v	v	ADP
ejpam-3394	190	21	∈	∈	PROPN
ejpam-3394	190	22	i.	i.	NOUN
ejpam-3394	190	23	(	(	PUNCT
ejpam-3394	190	24	ii	ii	PROPN
ejpam-3394	190	25	)	)	PUNCT
ejpam-3394	190	26	for	for	ADP
ejpam-3394	190	27	every	every	DET
ejpam-3394	190	28	open	open	NOUN
ejpam-3394	190	29	subset	subset	NOUN
ejpam-3394	190	30	g	g	NOUN
ejpam-3394	190	31	of	of	ADP
ejpam-3394	190	32	x	x	PUNCT
ejpam-3394	190	33	and	and	CCONJ
ejpam-3394	190	34	every	every	DET
ejpam-3394	190	35	x	x	PROPN
ejpam-3394	190	36	∈	∈	PROPN
ejpam-3394	190	37	g	g	NOUN
ejpam-3394	190	38	,	,	PUNCT
ejpam-3394	190	39	there	there	PRON
ejpam-3394	190	40	exists	exist	VERB
ejpam-3394	190	41	a	a	DET
ejpam-3394	190	42	β	β	NOUN
ejpam-3394	190	43	-	-	ADJ
ejpam-3394	190	44	open	open	ADJ
ejpam-3394	190	45	set	set	NOUN
ejpam-3394	190	46	u	u	PRON
ejpam-3394	190	47	such	such	ADJ
ejpam-3394	190	48	that	that	SCONJ
ejpam-3394	190	49	x	x	SYM
ejpam-3394	190	50	∈	∈	NOUN
ejpam-3394	190	51	u	u	NOUN
ejpam-3394	190	52	and	and	CCONJ
ejpam-3394	190	53	βcl(u)−g	βcl(u)−g	PUNCT
ejpam-3394	190	54	∈	∈	PROPN
ejpam-3394	190	55	i.	i.	NOUN
ejpam-3394	190	56	proof	proof	NOUN
ejpam-3394	190	57	.	.	PUNCT
ejpam-3394	191	1	(	(	PUNCT
ejpam-3394	191	2	i	i	NOUN
ejpam-3394	191	3	)	)	PUNCT
ejpam-3394	191	4	⇒	⇒	PROPN
ejpam-3394	191	5	(	(	PUNCT
ejpam-3394	191	6	ii	ii	NOUN
ejpam-3394	191	7	)	)	PUNCT
ejpam-3394	191	8	let	let	VERB
ejpam-3394	191	9	g	g	PROPN
ejpam-3394	191	10	⊆	⊆	NUM
ejpam-3394	191	11	x	x	AUX
ejpam-3394	191	12	be	be	AUX
ejpam-3394	191	13	open	open	ADJ
ejpam-3394	191	14	and	and	CCONJ
ejpam-3394	191	15	x	x	SYM
ejpam-3394	191	16	∈	∈	PROPN
ejpam-3394	191	17	g.	g.	NOUN
ejpam-3394	192	1	then	then	ADV
ejpam-3394	192	2	x	x	X
ejpam-3394	192	3	−	−	NOUN
ejpam-3394	192	4	g	g	NOUN
ejpam-3394	192	5	=	=	PUNCT
ejpam-3394	192	6	a	a	PRON
ejpam-3394	192	7	is	be	AUX
ejpam-3394	192	8	closed	closed	ADJ
ejpam-3394	192	9	and	and	CCONJ
ejpam-3394	192	10	x	x	PUNCT
ejpam-3394	192	11	/∈	/∈	PUNCT
ejpam-3394	192	12	a.	a.	NOUN
ejpam-3394	192	13	from	from	ADP
ejpam-3394	192	14	(	(	PUNCT
ejpam-3394	192	15	i	i	NOUN
ejpam-3394	192	16	)	)	PUNCT
ejpam-3394	192	17	,	,	PUNCT
ejpam-3394	192	18	there	there	PRON
ejpam-3394	192	19	exist	exist	VERB
ejpam-3394	192	20	disjoint	disjoint	NOUN
ejpam-3394	192	21	β	β	NOUN
ejpam-3394	192	22	-	-	ADJ
ejpam-3394	192	23	open	open	ADJ
ejpam-3394	192	24	sets	set	VERB
ejpam-3394	192	25	u	u	NOUN
ejpam-3394	192	26	and	and	CCONJ
ejpam-3394	192	27	v	v	ADP
ejpam-3394	192	28	such	such	ADJ
ejpam-3394	192	29	that	that	SCONJ
ejpam-3394	192	30	x	x	SYM
ejpam-3394	192	31	∈	∈	NOUN
ejpam-3394	192	32	u	u	NOUN
ejpam-3394	192	33	and	and	CCONJ
ejpam-3394	192	34	a−v	a−v	ADV
ejpam-3394	192	35	∈	∈	PROPN
ejpam-3394	192	36	i.	i.	NOUN
ejpam-3394	192	37	since	since	SCONJ
ejpam-3394	192	38	u	u	PROPN
ejpam-3394	192	39	and	and	CCONJ
ejpam-3394	192	40	v	v	NOUN
ejpam-3394	192	41	are	be	AUX
ejpam-3394	192	42	disjoint	disjoint	ADJ
ejpam-3394	192	43	,	,	PUNCT
ejpam-3394	192	44	we	we	PRON
ejpam-3394	192	45	have	have	VERB
ejpam-3394	192	46	βcl(u	βcl(u	PROPN
ejpam-3394	192	47	)	)	PUNCT
ejpam-3394	192	48	⊆	⊆	NUM
ejpam-3394	192	49	x	x	SYM
ejpam-3394	192	50	−	−	NUM
ejpam-3394	192	51	v	v	NOUN
ejpam-3394	192	52	.	.	PUNCT
ejpam-3394	193	1	thus	thus	ADV
ejpam-3394	193	2	,	,	PUNCT
ejpam-3394	193	3	a∩	a∩	PROPN
ejpam-3394	193	4	βcl(u	βcl(u	PROPN
ejpam-3394	193	5	)	)	PUNCT
ejpam-3394	193	6	⊆	⊆	NUM
ejpam-3394	193	7	a−	a−	PROPN
ejpam-3394	193	8	v	v	NOUN
ejpam-3394	193	9	.	.	PUNCT
ejpam-3394	194	1	then	then	ADV
ejpam-3394	194	2	,	,	PUNCT
ejpam-3394	194	3	βcl(u	βcl(u	PROPN
ejpam-3394	194	4	)	)	PUNCT
ejpam-3394	194	5	∩	∩	NOUN
ejpam-3394	194	6	(	(	PUNCT
ejpam-3394	194	7	x	x	NOUN
ejpam-3394	194	8	−g	−g	NOUN
ejpam-3394	194	9	)	)	PUNCT
ejpam-3394	194	10	∈	∈	PROPN
ejpam-3394	194	11	i.	i.	NOUN
ejpam-3394	194	12	therefore	therefore	ADV
ejpam-3394	194	13	,	,	PUNCT
ejpam-3394	194	14	βcl(u)−g	βcl(u)−g	PROPN
ejpam-3394	194	15	∈	∈	PROPN
ejpam-3394	194	16	i.	i.	NOUN
ejpam-3394	194	17	(	(	PUNCT
ejpam-3394	194	18	ii	ii	NOUN
ejpam-3394	194	19	)	)	PUNCT
ejpam-3394	194	20	⇒	⇒	NOUN
ejpam-3394	194	21	(	(	PUNCT
ejpam-3394	194	22	i	i	NOUN
ejpam-3394	194	23	)	)	PUNCT
ejpam-3394	194	24	let	let	VERB
ejpam-3394	194	25	a	a	DET
ejpam-3394	194	26	⊆	⊆	NUM
ejpam-3394	194	27	x	x	AUX
ejpam-3394	194	28	be	be	AUX
ejpam-3394	194	29	closed	close	VERB
ejpam-3394	194	30	and	and	CCONJ
ejpam-3394	195	1	x	x	PUNCT
ejpam-3394	195	2	/∈	/∈	PUNCT
ejpam-3394	195	3	a.	a.	NOUN
ejpam-3394	195	4	then	then	ADV
ejpam-3394	195	5	,	,	PUNCT
ejpam-3394	195	6	x	x	PUNCT
ejpam-3394	195	7	−	−	NOUN
ejpam-3394	195	8	a	a	DET
ejpam-3394	195	9	=	=	X
ejpam-3394	195	10	g	g	NOUN
ejpam-3394	195	11	is	be	AUX
ejpam-3394	195	12	open	open	ADJ
ejpam-3394	195	13	and	and	CCONJ
ejpam-3394	195	14	x	x	SYM
ejpam-3394	195	15	∈	∈	PROPN
ejpam-3394	195	16	g.	g.	NOUN
ejpam-3394	195	17	from	from	ADP
ejpam-3394	195	18	(	(	PUNCT
ejpam-3394	195	19	ii	ii	NOUN
ejpam-3394	195	20	)	)	PUNCT
ejpam-3394	195	21	,	,	PUNCT
ejpam-3394	195	22	there	there	PRON
ejpam-3394	195	23	exists	exist	VERB
ejpam-3394	195	24	a	a	DET
ejpam-3394	195	25	β	β	NOUN
ejpam-3394	195	26	-	-	ADJ
ejpam-3394	195	27	open	open	ADJ
ejpam-3394	195	28	set	set	NOUN
ejpam-3394	195	29	u	u	PRON
ejpam-3394	196	1	such	such	ADJ
ejpam-3394	196	2	that	that	SCONJ
ejpam-3394	196	3	x	x	SYM
ejpam-3394	196	4	∈	∈	PROPN
ejpam-3394	196	5	u	u	NOUN
ejpam-3394	196	6	and	and	CCONJ
ejpam-3394	196	7	βcl(u	βcl(u	PROPN
ejpam-3394	196	8	)	)	PUNCT
ejpam-3394	196	9	−	−	PROPN
ejpam-3394	196	10	g	g	PROPN
ejpam-3394	196	11	∈	∈	PROPN
ejpam-3394	196	12	i.	i.	NOUN
ejpam-3394	196	13	thus	thus	ADV
ejpam-3394	196	14	,	,	PUNCT
ejpam-3394	196	15	x−βcl(u	x−βcl(u	X
ejpam-3394	196	16	)	)	PUNCT
ejpam-3394	196	17	=	=	SYM
ejpam-3394	196	18	v	v	NUM
ejpam-3394	196	19	∈	∈	NOUN
ejpam-3394	196	20	βo(x	βo(x	PUNCT
ejpam-3394	196	21	)	)	PUNCT
ejpam-3394	196	22	and	and	CCONJ
ejpam-3394	196	23	u∩v	u∩v	NOUN
ejpam-3394	196	24	=	=	X
ejpam-3394	196	25	∅.	∅.	VERB
ejpam-3394	196	26	furthermore	furthermore	ADV
ejpam-3394	196	27	,	,	PUNCT
ejpam-3394	196	28	a−v	a−v	ADV
ejpam-3394	196	29	=	=	SYM
ejpam-3394	196	30	(	(	PUNCT
ejpam-3394	196	31	x−g)−(x−βcl(u	x−g)−(x−βcl(u	PROPN
ejpam-3394	196	32	)	)	PUNCT
ejpam-3394	196	33	)	)	PUNCT
ejpam-3394	197	1	=	=	SYM
ejpam-3394	198	1	βcl(u)−g	βcl(u)−g	PUNCT
ejpam-3394	198	2	∈	∈	PROPN
ejpam-3394	198	3	i.	i.	NOUN
ejpam-3394	198	4	the	the	DET
ejpam-3394	198	5	following	follow	VERB
ejpam-3394	198	6	example	example	NOUN
ejpam-3394	198	7	reveals	reveal	VERB
ejpam-3394	198	8	that	that	SCONJ
ejpam-3394	198	9	for	for	ADP
ejpam-3394	198	10	a	a	DET
ejpam-3394	198	11	locally	locally	ADV
ejpam-3394	198	12	finite	finite	ADJ
ejpam-3394	198	13	collection	collection	NOUN
ejpam-3394	198	14	of	of	ADP
ejpam-3394	198	15	subsets	subset	NOUN
ejpam-3394	198	16	of	of	ADP
ejpam-3394	198	17	v	v	NOUN
ejpam-3394	198	18	=	=	PUNCT
ejpam-3394	198	19	{	{	PUNCT
ejpam-3394	198	20	vλ	vλ	INTJ
ejpam-3394	198	21	:	:	PUNCT
ejpam-3394	198	22	λ	λ	PROPN
ejpam-3394	198	23	∈	∈	PROPN
ejpam-3394	198	24	λ	λ	NOUN
ejpam-3394	198	25	}	}	PUNCT
ejpam-3394	198	26	of	of	ADP
ejpam-3394	198	27	a	a	DET
ejpam-3394	198	28	space	space	NOUN
ejpam-3394	198	29	(	(	PUNCT
ejpam-3394	198	30	x	x	X
ejpam-3394	198	31	,	,	PUNCT
ejpam-3394	198	32	τ	τ	PROPN
ejpam-3394	198	33	)	)	PUNCT
ejpam-3394	198	34	,	,	PUNCT
ejpam-3394	198	35	the	the	DET
ejpam-3394	198	36	equality	equality	NOUN
ejpam-3394	198	37	cl	cl	NOUN
ejpam-3394	198	38	(	(	PUNCT
ejpam-3394	198	39	⋃	⋃	X
ejpam-3394	198	40	{	{	PUNCT
ejpam-3394	198	41	vλ	vλ	INTJ
ejpam-3394	198	42	:	:	PUNCT
ejpam-3394	198	43	λ	λ	PROPN
ejpam-3394	198	44	∈	∈	PROPN
ejpam-3394	198	45	λ	λ	NOUN
ejpam-3394	198	46	}	}	PUNCT
ejpam-3394	198	47	)	)	PUNCT
ejpam-3394	198	48	=	=	SYM
ejpam-3394	198	49	⋃	⋃	NOUN
ejpam-3394	198	50	{	{	PUNCT
ejpam-3394	198	51	cl(vλ	cl(vλ	NOUN
ejpam-3394	198	52	)	)	PUNCT
ejpam-3394	198	53	:	:	PUNCT
ejpam-3394	198	54	λ	λ	X
ejpam-3394	198	55	∈	∈	PROPN
ejpam-3394	198	56	λ	λ	NOUN
ejpam-3394	198	57	}	}	PUNCT
ejpam-3394	198	58	always	always	ADV
ejpam-3394	198	59	holds	hold	VERB
ejpam-3394	198	60	whereas	whereas	SCONJ
ejpam-3394	198	61	for	for	ADP
ejpam-3394	198	62	β	β	X
ejpam-3394	198	63	-	-	ADJ
ejpam-3394	198	64	locally	locally	ADV
ejpam-3394	198	65	finite	finite	ADJ
ejpam-3394	198	66	collection	collection	NOUN
ejpam-3394	198	67	of	of	ADP
ejpam-3394	198	68	subsets	subset	NOUN
ejpam-3394	198	69	u	u	NOUN
ejpam-3394	198	70	=	=	PUNCT
ejpam-3394	198	71	{	{	PUNCT
ejpam-3394	198	72	uλ	uλ	X
ejpam-3394	198	73	:	:	PUNCT
ejpam-3394	198	74	λ	λ	X
ejpam-3394	198	75	∈	∈	PROPN
ejpam-3394	198	76	λ	λ	NOUN
ejpam-3394	198	77	}	}	PUNCT
ejpam-3394	198	78	of	of	ADP
ejpam-3394	198	79	a	a	DET
ejpam-3394	198	80	space	space	NOUN
ejpam-3394	198	81	(	(	PUNCT
ejpam-3394	198	82	x	x	X
ejpam-3394	198	83	,	,	PUNCT
ejpam-3394	198	84	τ	τ	PROPN
ejpam-3394	198	85	)	)	PUNCT
ejpam-3394	198	86	,	,	PUNCT
ejpam-3394	198	87	the	the	DET
ejpam-3394	198	88	equality	equality	NOUN
ejpam-3394	198	89	βcl	βcl	ADJ
ejpam-3394	198	90	(	(	PUNCT
ejpam-3394	198	91	⋃	⋃	X
ejpam-3394	198	92	{	{	PUNCT
ejpam-3394	198	93	uλ	uλ	NOUN
ejpam-3394	198	94	:	:	PUNCT
ejpam-3394	198	95	λ	λ	X
ejpam-3394	198	96	∈	∈	PROPN
ejpam-3394	198	97	λ	λ	NOUN
ejpam-3394	198	98	}	}	PUNCT
ejpam-3394	198	99	)	)	PUNCT
ejpam-3394	199	1	=	=	SYM
ejpam-3394	199	2	⋃	⋃	NOUN
ejpam-3394	199	3	{	{	PUNCT
ejpam-3394	199	4	βcl(uλ	βcl(uλ	NUM
ejpam-3394	199	5	)	)	PUNCT
ejpam-3394	199	6	:	:	PUNCT
ejpam-3394	200	1	λ	λ	X
ejpam-3394	200	2	∈	∈	PROPN
ejpam-3394	200	3	λ	λ	PROPN
ejpam-3394	200	4	}	}	PUNCT
ejpam-3394	200	5	does	do	AUX
ejpam-3394	200	6	not	not	PART
ejpam-3394	200	7	hold	hold	VERB
ejpam-3394	200	8	in	in	ADP
ejpam-3394	200	9	general	general	ADJ
ejpam-3394	200	10	.	.	PUNCT
ejpam-3394	201	1	example	example	NOUN
ejpam-3394	202	1	3	3	X
ejpam-3394	202	2	.	.	X
ejpam-3394	202	3	consider	consider	VERB
ejpam-3394	202	4	the	the	DET
ejpam-3394	202	5	real	real	ADJ
ejpam-3394	202	6	number	number	NOUN
ejpam-3394	202	7	r	r	NOUN
ejpam-3394	202	8	with	with	ADP
ejpam-3394	202	9	usual	usual	ADJ
ejpam-3394	202	10	topology	topology	NOUN
ejpam-3394	202	11	τ	τ	X
ejpam-3394	202	12	.	.	PUNCT
ejpam-3394	203	1	let	let	VERB
ejpam-3394	203	2	v	v	VERB
ejpam-3394	203	3	=	=	SYM
ejpam-3394	203	4	{	{	PUNCT
ejpam-3394	204	1	[	[	X
ejpam-3394	204	2	0	0	NUM
ejpam-3394	204	3	,	,	PUNCT
ejpam-3394	204	4	1	1	NUM
ejpam-3394	204	5	)	)	PUNCT
ejpam-3394	205	1	,	,	PUNCT
ejpam-3394	205	2	(	(	PUNCT
ejpam-3394	205	3	1	1	NUM
ejpam-3394	205	4	,	,	PUNCT
ejpam-3394	205	5	2	2	NUM
ejpam-3394	205	6	]	]	PUNCT
ejpam-3394	205	7	}	}	PUNCT
ejpam-3394	205	8	.	.	PUNCT
ejpam-3394	206	1	then	then	ADV
ejpam-3394	206	2	v	v	NOUN
ejpam-3394	206	3	is	be	AUX
ejpam-3394	206	4	β	β	X
ejpam-3394	206	5	-	-	ADJ
ejpam-3394	206	6	locally	locally	ADV
ejpam-3394	206	7	finite	finite	NOUN
ejpam-3394	206	8	in	in	ADP
ejpam-3394	206	9	(	(	PUNCT
ejpam-3394	206	10	r	r	NOUN
ejpam-3394	206	11	,	,	PUNCT
ejpam-3394	206	12	τ	τ	PROPN
ejpam-3394	206	13	)	)	PUNCT
ejpam-3394	206	14	since	since	SCONJ
ejpam-3394	206	15	it	it	PRON
ejpam-3394	206	16	is	be	AUX
ejpam-3394	206	17	finite	finite	ADJ
ejpam-3394	206	18	.	.	PUNCT
ejpam-3394	207	1	but	but	CCONJ
ejpam-3394	207	2	βcl([0	βcl([0	NOUN
ejpam-3394	207	3	,	,	PUNCT
ejpam-3394	207	4	1	1	X
ejpam-3394	207	5	)	)	PUNCT
ejpam-3394	207	6	∪	∪	NOUN
ejpam-3394	207	7	(	(	PUNCT
ejpam-3394	207	8	1	1	NUM
ejpam-3394	207	9	,	,	PUNCT
ejpam-3394	207	10	2	2	NUM
ejpam-3394	207	11	]	]	NUM
ejpam-3394	207	12	)	)	PUNCT
ejpam-3394	207	13	6=	6=	ADP
ejpam-3394	207	14	βcl([0	βcl([0	NOUN
ejpam-3394	207	15	,	,	PUNCT
ejpam-3394	207	16	1	1	NUM
ejpam-3394	207	17	)	)	PUNCT
ejpam-3394	207	18	)	)	PUNCT
ejpam-3394	207	19	∪	∪	ADP
ejpam-3394	207	20	βcl((1	βcl((1	PRON
ejpam-3394	207	21	,	,	PUNCT
ejpam-3394	207	22	2	2	NUM
ejpam-3394	207	23	]	]	NUM
ejpam-3394	207	24	)	)	PUNCT
ejpam-3394	207	25	.	.	PUNCT
ejpam-3394	208	1	theorem	theorem	NOUN
ejpam-3394	208	2	9	9	NUM
ejpam-3394	208	3	.	.	PUNCT
ejpam-3394	208	4	suppose	suppose	VERB
ejpam-3394	208	5	that	that	SCONJ
ejpam-3394	208	6	for	for	ADP
ejpam-3394	208	7	a	a	DET
ejpam-3394	208	8	β	β	X
ejpam-3394	208	9	-	-	ADJ
ejpam-3394	208	10	locally	locally	ADV
ejpam-3394	208	11	finite	finite	ADJ
ejpam-3394	208	12	collection	collection	NOUN
ejpam-3394	208	13	of	of	ADP
ejpam-3394	208	14	subsets	subset	NOUN
ejpam-3394	208	15	v	v	X
ejpam-3394	208	16	=	=	PUNCT
ejpam-3394	208	17	{	{	PUNCT
ejpam-3394	208	18	vλ	vλ	INTJ
ejpam-3394	208	19	:	:	PUNCT
ejpam-3394	208	20	λ	λ	PROPN
ejpam-3394	208	21	∈	∈	PROPN
ejpam-3394	208	22	λ	λ	NOUN
ejpam-3394	208	23	}	}	PUNCT
ejpam-3394	208	24	of	of	ADP
ejpam-3394	208	25	a	a	DET
ejpam-3394	208	26	space	space	NOUN
ejpam-3394	208	27	(	(	PUNCT
ejpam-3394	208	28	x	x	X
ejpam-3394	208	29	,	,	PUNCT
ejpam-3394	208	30	τ	τ	PROPN
ejpam-3394	208	31	,	,	PUNCT
ejpam-3394	208	32	i	i	PROPN
ejpam-3394	208	33	)	)	PUNCT
ejpam-3394	208	34	,	,	PUNCT
ejpam-3394	208	35	the	the	DET
ejpam-3394	208	36	equality	equality	NOUN
ejpam-3394	208	37	βcl	βcl	ADJ
ejpam-3394	208	38	(	(	PUNCT
ejpam-3394	208	39	⋃	⋃	X
ejpam-3394	208	40	{	{	PUNCT
ejpam-3394	208	41	vλ	vλ	INTJ
ejpam-3394	208	42	:	:	PUNCT
ejpam-3394	208	43	λ	λ	PROPN
ejpam-3394	208	44	∈	∈	PROPN
ejpam-3394	208	45	λ	λ	NOUN
ejpam-3394	208	46	}	}	PUNCT
ejpam-3394	208	47	)	)	PUNCT
ejpam-3394	208	48	=	=	SYM
ejpam-3394	208	49	⋃	⋃	NOUN
ejpam-3394	208	50	{	{	PUNCT
ejpam-3394	208	51	βcl(vλ	βcl(vλ	NOUN
ejpam-3394	208	52	)	)	PUNCT
ejpam-3394	208	53	:	:	PUNCT
ejpam-3394	209	1	λ	λ	X
ejpam-3394	209	2	∈	∈	PROPN
ejpam-3394	209	3	λ	λ	PROPN
ejpam-3394	209	4	}	}	PUNCT
ejpam-3394	209	5	holds	hold	VERB
ejpam-3394	209	6	.	.	PUNCT
ejpam-3394	210	1	if	if	SCONJ
ejpam-3394	210	2	(	(	PUNCT
ejpam-3394	210	3	x	x	X
ejpam-3394	210	4	,	,	PUNCT
ejpam-3394	210	5	τ	τ	PROPN
ejpam-3394	210	6	,	,	PUNCT
ejpam-3394	210	7	i	i	PROPN
ejpam-3394	210	8	)	)	PUNCT
ejpam-3394	210	9	is	be	AUX
ejpam-3394	210	10	hausdorff	hausdorff	NOUN
ejpam-3394	210	11	i	i	PROPN
ejpam-3394	210	12	-	-	PUNCT
ejpam-3394	210	13	β	β	NOUN
ejpam-3394	210	14	-	-	NOUN
ejpam-3394	210	15	paracompact	paracompact	ADJ
ejpam-3394	210	16	,	,	PUNCT
ejpam-3394	210	17	then	then	ADV
ejpam-3394	210	18	for	for	ADP
ejpam-3394	210	19	every	every	DET
ejpam-3394	210	20	closed	closed	NOUN
ejpam-3394	210	21	subset	subset	VERB
ejpam-3394	210	22	a	a	PRON
ejpam-3394	210	23	of	of	ADP
ejpam-3394	210	24	x	x	X
ejpam-3394	210	25	and	and	CCONJ
ejpam-3394	210	26	every	every	DET
ejpam-3394	210	27	x	x	PROPN
ejpam-3394	210	28	/∈	/∈	PUNCT
ejpam-3394	211	1	a	a	INTJ
ejpam-3394	211	2	,	,	PUNCT
ejpam-3394	211	3	there	there	PRON
ejpam-3394	211	4	exist	exist	VERB
ejpam-3394	211	5	disjoint	disjoint	NOUN
ejpam-3394	211	6	β	β	NOUN
ejpam-3394	211	7	-	-	ADJ
ejpam-3394	211	8	open	open	ADJ
ejpam-3394	211	9	sets	set	VERB
ejpam-3394	211	10	u	u	NOUN
ejpam-3394	211	11	and	and	CCONJ
ejpam-3394	211	12	v	v	ADP
ejpam-3394	211	13	such	such	ADJ
ejpam-3394	211	14	that	that	SCONJ
ejpam-3394	211	15	x	x	SYM
ejpam-3394	211	16	∈	∈	PROPN
ejpam-3394	211	17	u	u	NOUN
ejpam-3394	211	18	and	and	CCONJ
ejpam-3394	211	19	a−	a−	PROPN
ejpam-3394	211	20	v	v	ADP
ejpam-3394	211	21	∈	∈	PROPN
ejpam-3394	211	22	i.	i.	NOUN
ejpam-3394	211	23	proof	proof	NOUN
ejpam-3394	211	24	.	.	PUNCT
ejpam-3394	212	1	let	let	VERB
ejpam-3394	212	2	a	a	DET
ejpam-3394	212	3	⊆	⊆	NUM
ejpam-3394	212	4	x	x	SYM
ejpam-3394	212	5	closed	closed	ADJ
ejpam-3394	212	6	and	and	CCONJ
ejpam-3394	212	7	x	x	PUNCT
ejpam-3394	212	8	/∈	/∈	PUNCT
ejpam-3394	212	9	a.	a.	NOUN
ejpam-3394	212	10	since	since	SCONJ
ejpam-3394	212	11	x	x	PROPN
ejpam-3394	212	12	is	be	AUX
ejpam-3394	212	13	hausdorff	hausdorff	NOUN
ejpam-3394	212	14	space	space	NOUN
ejpam-3394	212	15	,	,	PUNCT
ejpam-3394	212	16	there	there	PRON
ejpam-3394	212	17	exists	exist	VERB
ejpam-3394	212	18	an	an	DET
ejpam-3394	212	19	open	open	ADJ
ejpam-3394	212	20	set	set	NOUN
ejpam-3394	212	21	hy	hy	NOUN
ejpam-3394	212	22	containing	contain	VERB
ejpam-3394	212	23	y	y	PRON
ejpam-3394	212	24	for	for	ADP
ejpam-3394	212	25	each	each	DET
ejpam-3394	212	26	y	y	PROPN
ejpam-3394	212	27	∈	∈	PROPN
ejpam-3394	212	28	a	a	DET
ejpam-3394	212	29	such	such	ADJ
ejpam-3394	212	30	that	that	PRON
ejpam-3394	212	31	x	x	SYM
ejpam-3394	212	32	/∈	/∈	PROPN
ejpam-3394	212	33	cl(hy	cl(hy	PROPN
ejpam-3394	212	34	)	)	PUNCT
ejpam-3394	212	35	.	.	PUNCT
ejpam-3394	213	1	thus	thus	ADV
ejpam-3394	213	2	,	,	PUNCT
ejpam-3394	213	3	h	h	NOUN
ejpam-3394	213	4	=	=	PRON
ejpam-3394	213	5	{	{	PUNCT
ejpam-3394	213	6	hy	hy	NOUN
ejpam-3394	213	7	:	:	PUNCT
ejpam-3394	213	8	y	y	PROPN
ejpam-3394	213	9	∈	∈	PROPN
ejpam-3394	213	10	a}∪{x−a	a}∪{x−a	PROPN
ejpam-3394	213	11	}	}	PUNCT
ejpam-3394	213	12	is	be	AUX
ejpam-3394	213	13	an	an	DET
ejpam-3394	213	14	open	open	ADJ
ejpam-3394	213	15	cover	cover	NOUN
ejpam-3394	213	16	of	of	ADP
ejpam-3394	213	17	x.	x.	NOUN
ejpam-3394	213	18	by	by	ADP
ejpam-3394	213	19	hypothesis	hypothesis	NOUN
ejpam-3394	213	20	and	and	CCONJ
ejpam-3394	213	21	lemma	lemma	PROPN
ejpam-3394	213	22	6	6	NUM
ejpam-3394	213	23	,	,	PUNCT
ejpam-3394	213	24	h	h	NOUN
ejpam-3394	213	25	has	have	VERB
ejpam-3394	213	26	a	a	DET
ejpam-3394	213	27	β	β	X
ejpam-3394	213	28	-	-	ADJ
ejpam-3394	213	29	locally	locally	ADV
ejpam-3394	213	30	finite	finite	NOUN
ejpam-3394	213	31	precise	precise	ADJ
ejpam-3394	213	32	β	β	X
ejpam-3394	213	33	-	-	ADJ
ejpam-3394	213	34	open	open	ADJ
ejpam-3394	213	35	refinement	refinement	NOUN
ejpam-3394	213	36	w	w	PROPN
ejpam-3394	213	37	=	=	PUNCT
ejpam-3394	213	38	{	{	PUNCT
ejpam-3394	213	39	wy	wy	PROPN
ejpam-3394	213	40	:	:	PUNCT
ejpam-3394	213	41	y	y	PROPN
ejpam-3394	213	42	∈	∈	PROPN
ejpam-3394	213	43	a	a	DET
ejpam-3394	213	44	}	}	PUNCT
ejpam-3394	213	45	∪	∪	ADJ
ejpam-3394	213	46	{	{	PUNCT
ejpam-3394	213	47	g	g	NOUN
ejpam-3394	213	48	}	}	PUNCT
ejpam-3394	213	49	such	such	ADJ
ejpam-3394	213	50	that	that	SCONJ
ejpam-3394	213	51	wy	wy	PROPN
ejpam-3394	213	52	⊆	⊆	NUM
ejpam-3394	213	53	hy	hy	NOUN
ejpam-3394	213	54	for	for	ADP
ejpam-3394	213	55	each	each	DET
ejpam-3394	213	56	y	y	PROPN
ejpam-3394	213	57	∈	∈	PROPN
ejpam-3394	213	58	a	a	PRON
ejpam-3394	213	59	,	,	PUNCT
ejpam-3394	213	60	g	g	PROPN
ejpam-3394	213	61	⊆	⊆	NUM
ejpam-3394	213	62	x−a	x−a	NOUN
ejpam-3394	213	63	and	and	CCONJ
ejpam-3394	213	64	x−	x−	PROPN
ejpam-3394	213	65	(	(	PUNCT
ejpam-3394	213	66	⋃	⋃	PROPN
ejpam-3394	213	67	{	{	PUNCT
ejpam-3394	213	68	wy	wy	PROPN
ejpam-3394	213	69	:	:	PUNCT
ejpam-3394	213	70	y	y	PROPN
ejpam-3394	213	71	∈	∈	PROPN
ejpam-3394	213	72	a}∪{g	a}∪{g	NOUN
ejpam-3394	213	73	}	}	PUNCT
ejpam-3394	213	74	)	)	PUNCT
ejpam-3394	213	75	∈	∈	PROPN
ejpam-3394	213	76	i.	i.	NOUN
ejpam-3394	213	77	since	since	SCONJ
ejpam-3394	213	78	a−	a−	PROPN
ejpam-3394	213	79	(	(	PUNCT
ejpam-3394	213	80	⋃	⋃	PROPN
ejpam-3394	213	81	{	{	PUNCT
ejpam-3394	213	82	wy	wy	PROPN
ejpam-3394	213	83	:	:	PUNCT
ejpam-3394	213	84	y	y	PROPN
ejpam-3394	213	85	∈	∈	PROPN
ejpam-3394	213	86	a	a	PRON
ejpam-3394	213	87	}	}	PUNCT
ejpam-3394	213	88	)	)	PUNCT
ejpam-3394	213	89	=	=	SYM
ejpam-3394	213	90	a−	a−	PROPN
ejpam-3394	213	91	(	(	PUNCT
ejpam-3394	213	92	⋃	⋃	PROPN
ejpam-3394	213	93	{	{	PUNCT
ejpam-3394	213	94	wy	wy	PROPN
ejpam-3394	213	95	:	:	PUNCT
ejpam-3394	213	96	y	y	PROPN
ejpam-3394	213	97	∈	∈	PROPN
ejpam-3394	213	98	a	a	DET
ejpam-3394	213	99	}	}	PUNCT
ejpam-3394	213	100	∪	∪	NOUN
ejpam-3394	213	101	{	{	PUNCT
ejpam-3394	213	102	g	g	NOUN
ejpam-3394	213	103	}	}	PUNCT
ejpam-3394	213	104	)	)	PUNCT
ejpam-3394	214	1	⊆	⊆	NUM
ejpam-3394	214	2	x	x	SYM
ejpam-3394	214	3	−	−	PROPN
ejpam-3394	214	4	(	(	PUNCT
ejpam-3394	214	5	⋃	⋃	X
ejpam-3394	214	6	{	{	PUNCT
ejpam-3394	214	7	wy	wy	PROPN
ejpam-3394	214	8	:	:	PUNCT
ejpam-3394	214	9	y	y	PROPN
ejpam-3394	214	10	∈	∈	PROPN
ejpam-3394	214	11	a	a	DET
ejpam-3394	214	12	}	}	PUNCT
ejpam-3394	214	13	∪	∪	NOUN
ejpam-3394	214	14	{	{	PUNCT
ejpam-3394	214	15	g	g	NOUN
ejpam-3394	214	16	}	}	PUNCT
ejpam-3394	214	17	)	)	PUNCT
ejpam-3394	214	18	,	,	PUNCT
ejpam-3394	214	19	we	we	PRON
ejpam-3394	214	20	have	have	VERB
ejpam-3394	214	21	a	a	DET
ejpam-3394	214	22	−	−	PROPN
ejpam-3394	214	23	(	(	PUNCT
ejpam-3394	214	24	⋃	⋃	PROPN
ejpam-3394	214	25	{	{	PUNCT
ejpam-3394	214	26	wy	wy	PROPN
ejpam-3394	214	27	:	:	PUNCT
ejpam-3394	214	28	y	y	PROPN
ejpam-3394	214	29	∈	∈	PROPN
ejpam-3394	214	30	a	a	DET
ejpam-3394	214	31	}	}	PUNCT
ejpam-3394	214	32	)	)	PUNCT
ejpam-3394	214	33	∈	∈	PROPN
ejpam-3394	214	34	i.	i.	NOUN
ejpam-3394	214	35	let	let	VERB
ejpam-3394	214	36	e.	e.	PROPN
ejpam-3394	214	37	d.	d.	PROPN
ejpam-3394	214	38	yıldırım	yıldırım	PROPN
ejpam-3394	214	39	,	,	PUNCT
ejpam-3394	214	40	o.	o.	PROPN
ejpam-3394	214	41	b.	b.	PROPN
ejpam-3394	214	42	özbakır	özbakır	PROPN
ejpam-3394	214	43	,	,	PUNCT
ejpam-3394	214	44	a.	a.	PROPN
ejpam-3394	214	45	c.	c.	PROPN
ejpam-3394	214	46	.	.	PUNCT
ejpam-3394	215	1	güler	güler	PROPN
ejpam-3394	215	2	/	/	SYM
ejpam-3394	215	3	eur	eur	PROPN
ejpam-3394	215	4	.	.	PUNCT
ejpam-3394	216	1	j.	j.	PROPN
ejpam-3394	216	2	pure	pure	PROPN
ejpam-3394	216	3	appl	appl	PROPN
ejpam-3394	216	4	.	.	PROPN
ejpam-3394	216	5	math	math	PROPN
ejpam-3394	216	6	,	,	PUNCT
ejpam-3394	216	7	12	12	NUM
ejpam-3394	216	8	(	(	PUNCT
ejpam-3394	216	9	2	2	NUM
ejpam-3394	216	10	)	)	PUNCT
ejpam-3394	216	11	(	(	PUNCT
ejpam-3394	216	12	2019	2019	NUM
ejpam-3394	216	13	)	)	PUNCT
ejpam-3394	216	14	,	,	PUNCT
ejpam-3394	216	15	270	270	NUM
ejpam-3394	216	16	-	-	SYM
ejpam-3394	216	17	278	278	NUM
ejpam-3394	216	18	276	276	NUM
ejpam-3394	216	19	we	we	PRON
ejpam-3394	216	20	say	say	VERB
ejpam-3394	216	21	v	v	ADP
ejpam-3394	216	22	=	=	SYM
ejpam-3394	216	23	⋃	⋃	PROPN
ejpam-3394	216	24	{	{	PUNCT
ejpam-3394	216	25	wy	wy	PROPN
ejpam-3394	216	26	:	:	PUNCT
ejpam-3394	216	27	y	y	PROPN
ejpam-3394	216	28	∈	∈	PROPN
ejpam-3394	216	29	a	a	PRON
ejpam-3394	216	30	}	}	PUNCT
ejpam-3394	216	31	.	.	PUNCT
ejpam-3394	217	1	then	then	ADV
ejpam-3394	217	2	,	,	PUNCT
ejpam-3394	217	3	v	v	NOUN
ejpam-3394	217	4	is	be	AUX
ejpam-3394	217	5	β	β	X
ejpam-3394	217	6	-	-	ADJ
ejpam-3394	217	7	open	open	ADJ
ejpam-3394	217	8	set	set	NOUN
ejpam-3394	217	9	in	in	ADP
ejpam-3394	217	10	x	x	PUNCT
ejpam-3394	217	11	and	and	CCONJ
ejpam-3394	217	12	a	a	DET
ejpam-3394	217	13	−	−	PROPN
ejpam-3394	217	14	v	v	PROPN
ejpam-3394	217	15	∈	∈	PROPN
ejpam-3394	217	16	i.	i.	NOUN
ejpam-3394	217	17	since	since	SCONJ
ejpam-3394	217	18	x	x	PROPN
ejpam-3394	217	19	/∈	/∈	PROPN
ejpam-3394	217	20	cl(hy	cl(hy	PROPN
ejpam-3394	217	21	)	)	PUNCT
ejpam-3394	217	22	,	,	PUNCT
ejpam-3394	217	23	we	we	PRON
ejpam-3394	217	24	have	have	VERB
ejpam-3394	217	25	x	x	X
ejpam-3394	217	26	/∈	/∈	PUNCT
ejpam-3394	217	27	cl(wy	cl(wy	PROPN
ejpam-3394	217	28	)	)	PUNCT
ejpam-3394	217	29	.	.	PUNCT
ejpam-3394	218	1	this	this	PRON
ejpam-3394	218	2	implies	imply	VERB
ejpam-3394	218	3	that	that	SCONJ
ejpam-3394	218	4	x	x	SYM
ejpam-3394	218	5	/∈	/∈	NUM
ejpam-3394	218	6	βcl(wy	βcl(wy	NUM
ejpam-3394	218	7	)	)	PUNCT
ejpam-3394	218	8	.	.	PUNCT
ejpam-3394	219	1	since	since	SCONJ
ejpam-3394	219	2	w	w	PROPN
ejpam-3394	219	3	is	be	AUX
ejpam-3394	219	4	β	β	X
ejpam-3394	219	5	-	-	ADJ
ejpam-3394	219	6	locally	locally	ADV
ejpam-3394	219	7	finite	finite	NOUN
ejpam-3394	219	8	,	,	PUNCT
ejpam-3394	219	9	βcl(v	βcl(v	X
ejpam-3394	219	10	)	)	PUNCT
ejpam-3394	219	11	=	=	SYM
ejpam-3394	219	12	βcl	βcl	ADJ
ejpam-3394	219	13	(	(	PUNCT
ejpam-3394	219	14	⋃	⋃	PROPN
ejpam-3394	219	15	{	{	PUNCT
ejpam-3394	219	16	wy	wy	PROPN
ejpam-3394	219	17	:	:	PUNCT
ejpam-3394	219	18	y	y	PROPN
ejpam-3394	219	19	∈	∈	PROPN
ejpam-3394	219	20	a	a	PRON
ejpam-3394	219	21	}	}	PUNCT
ejpam-3394	219	22	)	)	PUNCT
ejpam-3394	220	1	=	=	SYM
ejpam-3394	220	2	⋃	⋃	NOUN
ejpam-3394	220	3	{	{	PUNCT
ejpam-3394	220	4	βcl(wy	βcl(wy	NUM
ejpam-3394	220	5	)	)	PUNCT
ejpam-3394	220	6	:	:	PUNCT
ejpam-3394	221	1	y	y	PROPN
ejpam-3394	221	2	∈	∈	PROPN
ejpam-3394	221	3	a	a	PRON
ejpam-3394	221	4	}	}	PUNCT
ejpam-3394	221	5	by	by	ADP
ejpam-3394	221	6	hypothesis	hypothesis	NOUN
ejpam-3394	221	7	.	.	PUNCT
ejpam-3394	222	1	thus	thus	ADV
ejpam-3394	222	2	,	,	PUNCT
ejpam-3394	222	3	for	for	ADP
ejpam-3394	222	4	a	a	DET
ejpam-3394	222	5	β	β	NOUN
ejpam-3394	222	6	-	-	ADJ
ejpam-3394	222	7	open	open	ADJ
ejpam-3394	222	8	set	set	NOUN
ejpam-3394	222	9	u	u	NOUN
ejpam-3394	222	10	=	=	NOUN
ejpam-3394	222	11	x	x	X
ejpam-3394	222	12	−	−	PROPN
ejpam-3394	222	13	βcl(v	βcl(v	PROPN
ejpam-3394	222	14	)	)	PUNCT
ejpam-3394	222	15	,	,	PUNCT
ejpam-3394	222	16	we	we	PRON
ejpam-3394	222	17	have	have	VERB
ejpam-3394	222	18	u	u	NOUN
ejpam-3394	222	19	∩	∩	NOUN
ejpam-3394	222	20	v	v	NOUN
ejpam-3394	222	21	=	=	NOUN
ejpam-3394	222	22	∅	∅	NOUN
ejpam-3394	222	23	such	such	ADJ
ejpam-3394	222	24	that	that	SCONJ
ejpam-3394	222	25	x	x	SYM
ejpam-3394	222	26	∈	∈	PROPN
ejpam-3394	222	27	u	u	NOUN
ejpam-3394	222	28	.	.	PUNCT
ejpam-3394	223	1	from	from	ADP
ejpam-3394	223	2	theorem	theorem	ADJ
ejpam-3394	223	3	8	8	NUM
ejpam-3394	223	4	and	and	CCONJ
ejpam-3394	223	5	theorem	theorem	VERB
ejpam-3394	223	6	9	9	NUM
ejpam-3394	223	7	,	,	PUNCT
ejpam-3394	223	8	we	we	PRON
ejpam-3394	223	9	have	have	VERB
ejpam-3394	223	10	the	the	DET
ejpam-3394	223	11	following	follow	VERB
ejpam-3394	223	12	corollary	corollary	NOUN
ejpam-3394	223	13	.	.	PUNCT
ejpam-3394	224	1	corollary	corollary	ADJ
ejpam-3394	224	2	1	1	NUM
ejpam-3394	224	3	.	.	PUNCT
ejpam-3394	225	1	if	if	SCONJ
ejpam-3394	225	2	(	(	PUNCT
ejpam-3394	225	3	x	x	X
ejpam-3394	225	4	,	,	PUNCT
ejpam-3394	225	5	τ	τ	PROPN
ejpam-3394	225	6	,	,	PUNCT
ejpam-3394	225	7	i	i	PROPN
ejpam-3394	225	8	)	)	PUNCT
ejpam-3394	225	9	is	be	AUX
ejpam-3394	225	10	an	an	DET
ejpam-3394	225	11	e.d	e.d	PROPN
ejpam-3394	225	12	.	.	PROPN
ejpam-3394	225	13	submaximal	submaximal	ADJ
ejpam-3394	225	14	hausdorff	hausdorff	NOUN
ejpam-3394	225	15	i	i	PROPN
ejpam-3394	225	16	-	-	PUNCT
ejpam-3394	225	17	β	β	NOUN
ejpam-3394	225	18	-	-	ADJ
ejpam-3394	225	19	paracompact	paracompact	ADJ
ejpam-3394	225	20	space	space	NOUN
ejpam-3394	225	21	,	,	PUNCT
ejpam-3394	225	22	then	then	ADV
ejpam-3394	225	23	(	(	PUNCT
ejpam-3394	225	24	x	x	X
ejpam-3394	225	25	,	,	PUNCT
ejpam-3394	225	26	τ	τ	PROPN
ejpam-3394	225	27	,	,	PUNCT
ejpam-3394	225	28	i	i	PROPN
ejpam-3394	225	29	)	)	PUNCT
ejpam-3394	225	30	is	be	AUX
ejpam-3394	225	31	i	i	NOUN
ejpam-3394	225	32	-	-	PUNCT
ejpam-3394	225	33	regular	regular	ADJ
ejpam-3394	225	34	.	.	PUNCT
ejpam-3394	226	1	theorem	theorem	NOUN
ejpam-3394	226	2	10	10	NUM
ejpam-3394	226	3	.	.	PUNCT
ejpam-3394	227	1	let	let	VERB
ejpam-3394	227	2	a	a	PRON
ejpam-3394	227	3	and	and	CCONJ
ejpam-3394	227	4	b	b	NOUN
ejpam-3394	227	5	be	be	AUX
ejpam-3394	227	6	subsets	subset	NOUN
ejpam-3394	227	7	in	in	ADP
ejpam-3394	227	8	ideal	ideal	ADJ
ejpam-3394	227	9	topological	topological	ADJ
ejpam-3394	227	10	space	space	NOUN
ejpam-3394	227	11	(	(	PUNCT
ejpam-3394	227	12	x	x	X
ejpam-3394	227	13	,	,	PUNCT
ejpam-3394	227	14	τ	τ	PROPN
ejpam-3394	227	15	,	,	PUNCT
ejpam-3394	227	16	i	i	PROPN
ejpam-3394	227	17	)	)	PUNCT
ejpam-3394	227	18	.	.	PUNCT
ejpam-3394	228	1	if	if	SCONJ
ejpam-3394	228	2	a	a	PRON
ejpam-3394	228	3	is	be	AUX
ejpam-3394	228	4	i	i	PRON
ejpam-3394	228	5	-	-	PUNCT
ejpam-3394	228	6	βparacompact	βparacompact	NOUN
ejpam-3394	228	7	set	set	VERB
ejpam-3394	228	8	in	in	ADP
ejpam-3394	228	9	x	x	PROPN
ejpam-3394	228	10	and	and	CCONJ
ejpam-3394	228	11	b	b	PROPN
ejpam-3394	228	12	is	be	AUX
ejpam-3394	228	13	closed	close	VERB
ejpam-3394	228	14	in	in	ADP
ejpam-3394	228	15	x	x	NOUN
ejpam-3394	228	16	,	,	PUNCT
ejpam-3394	228	17	then	then	ADV
ejpam-3394	228	18	a	a	DET
ejpam-3394	228	19	∩b	∩b	NOUN
ejpam-3394	228	20	is	be	AUX
ejpam-3394	228	21	i	i	PROPN
ejpam-3394	228	22	-	-	PUNCT
ejpam-3394	228	23	β	β	NOUN
ejpam-3394	228	24	-	-	ADJ
ejpam-3394	228	25	paracompact	paracompact	ADJ
ejpam-3394	228	26	set	set	NOUN
ejpam-3394	228	27	in	in	ADP
ejpam-3394	228	28	x.	x.	NOUN
ejpam-3394	228	29	proof	proof	NOUN
ejpam-3394	228	30	.	.	PUNCT
ejpam-3394	229	1	let	let	VERB
ejpam-3394	229	2	u	u	PRON
ejpam-3394	229	3	=	=	PUNCT
ejpam-3394	229	4	{	{	PUNCT
ejpam-3394	229	5	uλ	uλ	X
ejpam-3394	229	6	:	:	PUNCT
ejpam-3394	229	7	λ	λ	X
ejpam-3394	229	8	∈	∈	PROPN
ejpam-3394	229	9	λ	λ	PROPN
ejpam-3394	229	10	}	}	PUNCT
ejpam-3394	229	11	be	be	VERB
ejpam-3394	229	12	an	an	DET
ejpam-3394	229	13	open	open	ADJ
ejpam-3394	229	14	cover	cover	NOUN
ejpam-3394	229	15	of	of	ADP
ejpam-3394	229	16	a	a	DET
ejpam-3394	229	17	∩	∩	ADJ
ejpam-3394	229	18	b.	b.	NOUN
ejpam-3394	229	19	since	since	SCONJ
ejpam-3394	229	20	x	x	PROPN
ejpam-3394	229	21	−	−	PROPN
ejpam-3394	229	22	b	b	NOUN
ejpam-3394	229	23	is	be	AUX
ejpam-3394	229	24	open	open	ADJ
ejpam-3394	229	25	in	in	ADP
ejpam-3394	229	26	x	x	X
ejpam-3394	229	27	,	,	PUNCT
ejpam-3394	229	28	u	u	NOUN
ejpam-3394	229	29	′	′	NOUN
ejpam-3394	229	30	=	=	PUNCT
ejpam-3394	229	31	{	{	PUNCT
ejpam-3394	229	32	uλ	uλ	X
ejpam-3394	229	33	:	:	PUNCT
ejpam-3394	229	34	λ	λ	X
ejpam-3394	229	35	∈	∈	PROPN
ejpam-3394	229	36	λ	λ	PROPN
ejpam-3394	229	37	}	}	PUNCT
ejpam-3394	229	38	∪	∪	NOUN
ejpam-3394	229	39	{	{	PUNCT
ejpam-3394	229	40	x	x	NOUN
ejpam-3394	229	41	−	−	PROPN
ejpam-3394	229	42	b	b	X
ejpam-3394	229	43	}	}	PUNCT
ejpam-3394	229	44	is	be	AUX
ejpam-3394	229	45	open	open	ADJ
ejpam-3394	229	46	cover	cover	NOUN
ejpam-3394	229	47	of	of	ADP
ejpam-3394	229	48	a.	a.	NOUN
ejpam-3394	229	49	by	by	ADP
ejpam-3394	229	50	hypothesis	hypothesis	NOUN
ejpam-3394	229	51	and	and	CCONJ
ejpam-3394	229	52	lemma	lemma	PROPN
ejpam-3394	229	53	6	6	NUM
ejpam-3394	229	54	,	,	PUNCT
ejpam-3394	229	55	u	u	NOUN
ejpam-3394	229	56	′	′	NOUN
ejpam-3394	229	57	has	have	VERB
ejpam-3394	229	58	a	a	DET
ejpam-3394	229	59	βlocally	βlocally	ADJ
ejpam-3394	229	60	finite	finite	NOUN
ejpam-3394	229	61	precise	precise	ADJ
ejpam-3394	229	62	β	β	X
ejpam-3394	229	63	-	-	ADJ
ejpam-3394	229	64	open	open	ADJ
ejpam-3394	229	65	refinement	refinement	NOUN
ejpam-3394	229	66	{	{	PUNCT
ejpam-3394	229	67	vλ	vλ	INTJ
ejpam-3394	229	68	:	:	PUNCT
ejpam-3394	229	69	λ	λ	PROPN
ejpam-3394	229	70	∈	∈	PROPN
ejpam-3394	229	71	λ	λ	PROPN
ejpam-3394	229	72	}	}	PUNCT
ejpam-3394	229	73	∪	∪	ADJ
ejpam-3394	229	74	{	{	PUNCT
ejpam-3394	229	75	v	v	NOUN
ejpam-3394	229	76	}	}	PUNCT
ejpam-3394	229	77	such	such	ADJ
ejpam-3394	229	78	that	that	SCONJ
ejpam-3394	229	79	vλ	vλ	ADV
ejpam-3394	229	80	⊆	⊆	NUM
ejpam-3394	229	81	uλ	uλ	NOUN
ejpam-3394	229	82	for	for	ADP
ejpam-3394	229	83	each	each	DET
ejpam-3394	229	84	λ	λ	PROPN
ejpam-3394	229	85	∈	∈	PROPN
ejpam-3394	229	86	λ	λ	PROPN
ejpam-3394	229	87	,	,	PUNCT
ejpam-3394	229	88	v	v	ADP
ejpam-3394	229	89	⊆	⊆	NUM
ejpam-3394	229	90	x	x	SYM
ejpam-3394	229	91	−	−	PROPN
ejpam-3394	229	92	b	b	NOUN
ejpam-3394	229	93	and	and	CCONJ
ejpam-3394	229	94	a	a	DET
ejpam-3394	229	95	−	−	PROPN
ejpam-3394	229	96	(	(	PUNCT
ejpam-3394	229	97	⋃	⋃	X
ejpam-3394	229	98	{	{	PUNCT
ejpam-3394	229	99	vλ	vλ	INTJ
ejpam-3394	229	100	:	:	PUNCT
ejpam-3394	229	101	λ	λ	PROPN
ejpam-3394	229	102	∈	∈	PROPN
ejpam-3394	229	103	λ	λ	PROPN
ejpam-3394	229	104	}	}	PUNCT
ejpam-3394	229	105	∪	∪	ADJ
ejpam-3394	229	106	{	{	PUNCT
ejpam-3394	229	107	v	v	NOUN
ejpam-3394	229	108	}	}	PUNCT
ejpam-3394	229	109	)	)	PUNCT
ejpam-3394	230	1	∈	∈	PROPN
ejpam-3394	230	2	i.	i.	NOUN
ejpam-3394	230	3	since	since	SCONJ
ejpam-3394	230	4	(	(	PUNCT
ejpam-3394	230	5	a∩b)−	a∩b)−	NOUN
ejpam-3394	230	6	(	(	PUNCT
ejpam-3394	230	7	⋃	⋃	X
ejpam-3394	230	8	{	{	PUNCT
ejpam-3394	230	9	vλ	vλ	INTJ
ejpam-3394	230	10	:	:	PUNCT
ejpam-3394	230	11	λ	λ	PROPN
ejpam-3394	230	12	∈	∈	PROPN
ejpam-3394	230	13	λ	λ	NOUN
ejpam-3394	230	14	}	}	PUNCT
ejpam-3394	230	15	)	)	PUNCT
ejpam-3394	230	16	=	=	SYM
ejpam-3394	230	17	(	(	PUNCT
ejpam-3394	230	18	a∩b)−	a∩b)−	NOUN
ejpam-3394	230	19	(	(	PUNCT
ejpam-3394	230	20	⋃	⋃	X
ejpam-3394	230	21	{	{	PUNCT
ejpam-3394	230	22	vλ	vλ	INTJ
ejpam-3394	230	23	:	:	PUNCT
ejpam-3394	230	24	λ	λ	PROPN
ejpam-3394	230	25	∈	∈	PROPN
ejpam-3394	230	26	λ}∪{v	λ}∪{v	NOUN
ejpam-3394	230	27	}	}	PUNCT
ejpam-3394	230	28	)	)	PUNCT
ejpam-3394	230	29	⊆	⊆	NUM
ejpam-3394	230	30	a−	a−	NOUN
ejpam-3394	230	31	(	(	PUNCT
ejpam-3394	230	32	⋃	⋃	X
ejpam-3394	230	33	{	{	PUNCT
ejpam-3394	230	34	vλ	vλ	INTJ
ejpam-3394	230	35	:	:	PUNCT
ejpam-3394	230	36	λ	λ	PROPN
ejpam-3394	230	37	∈	∈	PROPN
ejpam-3394	230	38	λ}∪{v	λ}∪{v	NOUN
ejpam-3394	230	39	}	}	PUNCT
ejpam-3394	230	40	)	)	PUNCT
ejpam-3394	230	41	,	,	PUNCT
ejpam-3394	230	42	we	we	PRON
ejpam-3394	230	43	have	have	VERB
ejpam-3394	230	44	(	(	PUNCT
ejpam-3394	230	45	a	a	DET
ejpam-3394	230	46	∩b)−	∩b)−	NOUN
ejpam-3394	230	47	(	(	PUNCT
ejpam-3394	230	48	⋃	⋃	X
ejpam-3394	230	49	{	{	PUNCT
ejpam-3394	230	50	vλ	vλ	INTJ
ejpam-3394	230	51	:	:	PUNCT
ejpam-3394	230	52	λ	λ	PROPN
ejpam-3394	230	53	∈	∈	PROPN
ejpam-3394	230	54	λ	λ	NOUN
ejpam-3394	230	55	}	}	PUNCT
ejpam-3394	230	56	)	)	PUNCT
ejpam-3394	230	57	∈	∈	PROPN
ejpam-3394	230	58	i.	i.	NOUN
ejpam-3394	230	59	hence	hence	ADV
ejpam-3394	230	60	,	,	PUNCT
ejpam-3394	230	61	a	a	DET
ejpam-3394	230	62	∩b	∩b	NOUN
ejpam-3394	230	63	is	be	AUX
ejpam-3394	230	64	i	i	PROPN
ejpam-3394	230	65	-	-	PUNCT
ejpam-3394	230	66	β	β	NOUN
ejpam-3394	230	67	-	-	ADJ
ejpam-3394	230	68	paracompact	paracompact	ADJ
ejpam-3394	230	69	set	set	NOUN
ejpam-3394	230	70	in	in	ADP
ejpam-3394	230	71	x.	x.	NOUN
ejpam-3394	230	72	corollary	corollary	NOUN
ejpam-3394	230	73	2	2	X
ejpam-3394	230	74	.	.	PUNCT
ejpam-3394	231	1	let	let	VERB
ejpam-3394	231	2	(	(	PUNCT
ejpam-3394	231	3	x	x	X
ejpam-3394	231	4	,	,	PUNCT
ejpam-3394	231	5	τ	τ	PROPN
ejpam-3394	231	6	,	,	PUNCT
ejpam-3394	231	7	i	i	PRON
ejpam-3394	231	8	)	)	PUNCT
ejpam-3394	231	9	be	be	VERB
ejpam-3394	231	10	an	an	DET
ejpam-3394	231	11	i	i	PROPN
ejpam-3394	231	12	-	-	PUNCT
ejpam-3394	231	13	β	β	NOUN
ejpam-3394	231	14	-	-	ADJ
ejpam-3394	231	15	paracompact	paracompact	ADJ
ejpam-3394	231	16	space	space	NOUN
ejpam-3394	231	17	and	and	CCONJ
ejpam-3394	231	18	a	a	DET
ejpam-3394	231	19	⊆	⊆	NUM
ejpam-3394	231	20	x.	x.	NOUN
ejpam-3394	231	21	if	if	SCONJ
ejpam-3394	231	22	a	a	PRON
ejpam-3394	231	23	is	be	AUX
ejpam-3394	231	24	closed	close	VERB
ejpam-3394	231	25	in	in	ADP
ejpam-3394	231	26	x	x	NOUN
ejpam-3394	231	27	,	,	PUNCT
ejpam-3394	231	28	then	then	ADV
ejpam-3394	231	29	a	a	PRON
ejpam-3394	231	30	is	be	AUX
ejpam-3394	231	31	an	an	DET
ejpam-3394	231	32	i	i	PROPN
ejpam-3394	231	33	-	-	PUNCT
ejpam-3394	231	34	β	β	NOUN
ejpam-3394	231	35	-	-	ADJ
ejpam-3394	231	36	paracompact	paracompact	ADJ
ejpam-3394	231	37	set	set	NOUN
ejpam-3394	231	38	in	in	ADP
ejpam-3394	231	39	x.	x.	PROPN
ejpam-3394	231	40	lemma	lemma	PROPN
ejpam-3394	231	41	8	8	NUM
ejpam-3394	231	42	.	.	PUNCT
ejpam-3394	232	1	[	[	X
ejpam-3394	232	2	13	13	NUM
ejpam-3394	232	3	]	]	PUNCT
ejpam-3394	232	4	if	if	SCONJ
ejpam-3394	232	5	i	i	PRON
ejpam-3394	232	6	6=	6=	NOUN
ejpam-3394	232	7	∅	∅	NOUN
ejpam-3394	232	8	is	be	AUX
ejpam-3394	232	9	an	an	DET
ejpam-3394	232	10	ideal	ideal	NOUN
ejpam-3394	232	11	on	on	ADP
ejpam-3394	232	12	x	x	PUNCT
ejpam-3394	232	13	and	and	CCONJ
ejpam-3394	232	14	y	y	PROPN
ejpam-3394	232	15	is	be	AUX
ejpam-3394	232	16	a	a	DET
ejpam-3394	232	17	subset	subset	NOUN
ejpam-3394	232	18	of	of	ADP
ejpam-3394	232	19	x	x	PRON
ejpam-3394	232	20	,	,	PUNCT
ejpam-3394	232	21	then	then	ADV
ejpam-3394	232	22	iy	iy	INTJ
ejpam-3394	233	1	=	=	PUNCT
ejpam-3394	233	2	{	{	PUNCT
ejpam-3394	233	3	y	y	PROPN
ejpam-3394	233	4	∩g|g	∩g|g	PROPN
ejpam-3394	233	5	∈	∈	PROPN
ejpam-3394	233	6	i	i	X
ejpam-3394	233	7	}	}	PUNCT
ejpam-3394	233	8	=	=	SYM
ejpam-3394	233	9	{	{	PUNCT
ejpam-3394	233	10	g	g	NOUN
ejpam-3394	233	11	∈	∈	PROPN
ejpam-3394	233	12	i|g	i|g	VERB
ejpam-3394	233	13	⊆	⊆	NUM
ejpam-3394	233	14	y	y	PROPN
ejpam-3394	233	15	}	}	PUNCT
ejpam-3394	233	16	is	be	AUX
ejpam-3394	233	17	an	an	DET
ejpam-3394	233	18	ideal	ideal	NOUN
ejpam-3394	233	19	on	on	ADP
ejpam-3394	233	20	y.	y.	PROPN
ejpam-3394	233	21	theorem	theorem	VERB
ejpam-3394	233	22	11	11	NUM
ejpam-3394	233	23	.	.	PUNCT
ejpam-3394	234	1	let	let	VERB
ejpam-3394	234	2	a	a	PRON
ejpam-3394	234	3	and	and	CCONJ
ejpam-3394	234	4	b	b	NOUN
ejpam-3394	234	5	be	be	AUX
ejpam-3394	234	6	subsets	subset	NOUN
ejpam-3394	234	7	in	in	ADP
ejpam-3394	234	8	ideal	ideal	ADJ
ejpam-3394	234	9	topological	topological	ADJ
ejpam-3394	234	10	space	space	NOUN
ejpam-3394	234	11	(	(	PUNCT
ejpam-3394	234	12	x	x	X
ejpam-3394	234	13	,	,	PUNCT
ejpam-3394	234	14	τ	τ	PROPN
ejpam-3394	234	15	,	,	PUNCT
ejpam-3394	234	16	i	i	NOUN
ejpam-3394	234	17	)	)	PUNCT
ejpam-3394	235	1	such	such	ADJ
ejpam-3394	235	2	that	that	PRON
ejpam-3394	235	3	b	b	NOUN
ejpam-3394	235	4	⊆	⊆	NUM
ejpam-3394	235	5	a.	a.	NOUN
ejpam-3394	235	6	if	if	SCONJ
ejpam-3394	235	7	a	a	PRON
ejpam-3394	235	8	is	be	AUX
ejpam-3394	235	9	β	β	NOUN
ejpam-3394	235	10	-	-	ADJ
ejpam-3394	235	11	open	open	ADJ
ejpam-3394	235	12	in	in	ADP
ejpam-3394	235	13	x	x	PROPN
ejpam-3394	235	14	and	and	CCONJ
ejpam-3394	235	15	b	b	PROPN
ejpam-3394	235	16	is	be	AUX
ejpam-3394	235	17	an	an	DET
ejpam-3394	235	18	ia	ia	PROPN
ejpam-3394	235	19	-	-	ADJ
ejpam-3394	235	20	β	β	NOUN
ejpam-3394	235	21	-	-	ADJ
ejpam-3394	235	22	paracompact	paracompact	ADJ
ejpam-3394	235	23	set	set	NOUN
ejpam-3394	235	24	in	in	ADP
ejpam-3394	235	25	a	a	DET
ejpam-3394	235	26	then	then	ADV
ejpam-3394	235	27	b	b	NOUN
ejpam-3394	235	28	is	be	AUX
ejpam-3394	235	29	an	an	DET
ejpam-3394	235	30	i	i	PROPN
ejpam-3394	235	31	-	-	PUNCT
ejpam-3394	235	32	β	β	NOUN
ejpam-3394	235	33	-	-	ADJ
ejpam-3394	235	34	paracompact	paracompact	ADJ
ejpam-3394	235	35	set	set	NOUN
ejpam-3394	235	36	in	in	ADP
ejpam-3394	235	37	x.	x.	NOUN
ejpam-3394	235	38	proof	proof	NOUN
ejpam-3394	235	39	.	.	PUNCT
ejpam-3394	236	1	let	let	VERB
ejpam-3394	236	2	u	u	PRON
ejpam-3394	236	3	=	=	PUNCT
ejpam-3394	236	4	{	{	PUNCT
ejpam-3394	236	5	uλ	uλ	X
ejpam-3394	236	6	:	:	PUNCT
ejpam-3394	236	7	λ	λ	X
ejpam-3394	236	8	∈	∈	PROPN
ejpam-3394	236	9	λ	λ	PROPN
ejpam-3394	236	10	}	}	PUNCT
ejpam-3394	236	11	be	be	VERB
ejpam-3394	236	12	an	an	DET
ejpam-3394	236	13	open	open	ADJ
ejpam-3394	236	14	cover	cover	NOUN
ejpam-3394	236	15	of	of	ADP
ejpam-3394	236	16	b	b	NOUN
ejpam-3394	236	17	in	in	ADP
ejpam-3394	236	18	x.	x.	NOUN
ejpam-3394	236	19	then	then	ADV
ejpam-3394	236	20	,	,	PUNCT
ejpam-3394	236	21	ub	ub	ADV
ejpam-3394	236	22	=	=	SYM
ejpam-3394	236	23	{	{	PUNCT
ejpam-3394	236	24	uλ∩a	uλ∩a	PROPN
ejpam-3394	236	25	:	:	PUNCT
ejpam-3394	236	26	λ	λ	X
ejpam-3394	236	27	∈	∈	PROPN
ejpam-3394	236	28	λ	λ	PROPN
ejpam-3394	236	29	}	}	PUNCT
ejpam-3394	236	30	is	be	AUX
ejpam-3394	236	31	an	an	DET
ejpam-3394	236	32	open	open	ADJ
ejpam-3394	236	33	cover	cover	NOUN
ejpam-3394	236	34	of	of	ADP
ejpam-3394	236	35	b	b	NOUN
ejpam-3394	236	36	in	in	ADP
ejpam-3394	236	37	a.	a.	NOUN
ejpam-3394	236	38	since	since	SCONJ
ejpam-3394	236	39	b	b	PROPN
ejpam-3394	236	40	is	be	AUX
ejpam-3394	236	41	an	an	DET
ejpam-3394	236	42	ia	ia	PROPN
ejpam-3394	236	43	-	-	ADJ
ejpam-3394	236	44	β	β	NOUN
ejpam-3394	236	45	-	-	ADJ
ejpam-3394	236	46	paracompact	paracompact	ADJ
ejpam-3394	236	47	set	set	NOUN
ejpam-3394	236	48	in	in	ADP
ejpam-3394	236	49	a	a	PRON
ejpam-3394	236	50	,	,	PUNCT
ejpam-3394	237	1	ub	ub	AUX
ejpam-3394	237	2	has	have	VERB
ejpam-3394	237	3	a	a	DET
ejpam-3394	237	4	β	β	X
ejpam-3394	237	5	-	-	ADJ
ejpam-3394	237	6	locally	locally	ADV
ejpam-3394	237	7	finite	finite	NOUN
ejpam-3394	237	8	precise	precise	ADJ
ejpam-3394	237	9	β	β	X
ejpam-3394	237	10	-	-	ADJ
ejpam-3394	237	11	open	open	ADJ
ejpam-3394	237	12	refinement	refinement	NOUN
ejpam-3394	237	13	vb	vb	NOUN
ejpam-3394	237	14	in	in	ADP
ejpam-3394	237	15	a	a	DET
ejpam-3394	237	16	such	such	ADJ
ejpam-3394	237	17	that	that	DET
ejpam-3394	237	18	b	b	NOUN
ejpam-3394	237	19	−	−	NOUN
ejpam-3394	237	20	⋃	⋃	PROPN
ejpam-3394	237	21	{	{	PUNCT
ejpam-3394	237	22	vλ	vλ	ADV
ejpam-3394	237	23	:	:	PUNCT
ejpam-3394	237	24	vλ	vλ	INTJ
ejpam-3394	237	25	∈	∈	PROPN
ejpam-3394	237	26	vb	vb	NOUN
ejpam-3394	237	27	}	}	PUNCT
ejpam-3394	237	28	∈	∈	PROPN
ejpam-3394	237	29	ia	ia	PROPN
ejpam-3394	237	30	.	.	PUNCT
ejpam-3394	238	1	thus	thus	ADV
ejpam-3394	238	2	,	,	PUNCT
ejpam-3394	238	3	vb	vb	NOUN
ejpam-3394	238	4	is	be	AUX
ejpam-3394	238	5	a	a	DET
ejpam-3394	238	6	β	β	NOUN
ejpam-3394	238	7	-	-	ADJ
ejpam-3394	238	8	locally	locally	ADV
ejpam-3394	238	9	finite	finite	NOUN
ejpam-3394	238	10	precise	precise	ADJ
ejpam-3394	238	11	β	β	X
ejpam-3394	238	12	-	-	ADJ
ejpam-3394	238	13	open	open	ADJ
ejpam-3394	238	14	refinement	refinement	NOUN
ejpam-3394	238	15	in	in	ADP
ejpam-3394	238	16	x	x	PUNCT
ejpam-3394	238	17	by	by	ADP
ejpam-3394	238	18	theorem	theorem	NOUN
ejpam-3394	238	19	1	1	NUM
ejpam-3394	238	20	.	.	PUNCT
ejpam-3394	239	1	also	also	ADV
ejpam-3394	239	2	,	,	PUNCT
ejpam-3394	239	3	b	b	X
ejpam-3394	239	4	−	−	PROPN
ejpam-3394	239	5	⋃	⋃	PROPN
ejpam-3394	239	6	{	{	PUNCT
ejpam-3394	239	7	vλ	vλ	ADV
ejpam-3394	239	8	:	:	PUNCT
ejpam-3394	239	9	vλ	vλ	INTJ
ejpam-3394	239	10	∈	∈	PROPN
ejpam-3394	239	11	vb	vb	NOUN
ejpam-3394	239	12	}	}	PUNCT
ejpam-3394	239	13	∈	∈	PROPN
ejpam-3394	239	14	i.	i.	NOUN
ejpam-3394	239	15	hence	hence	ADV
ejpam-3394	239	16	,	,	PUNCT
ejpam-3394	239	17	b	b	PROPN
ejpam-3394	239	18	is	be	AUX
ejpam-3394	239	19	an	an	DET
ejpam-3394	239	20	i	i	PROPN
ejpam-3394	239	21	-	-	PUNCT
ejpam-3394	239	22	β	β	NOUN
ejpam-3394	239	23	-	-	ADJ
ejpam-3394	239	24	paracompact	paracompact	ADJ
ejpam-3394	239	25	set	set	NOUN
ejpam-3394	239	26	in	in	ADP
ejpam-3394	239	27	x.	x.	NOUN
ejpam-3394	239	28	theorem	theorem	VERB
ejpam-3394	239	29	12	12	NUM
ejpam-3394	239	30	.	.	PUNCT
ejpam-3394	240	1	let	let	VERB
ejpam-3394	240	2	f	f	NOUN
ejpam-3394	240	3	:	:	PUNCT
ejpam-3394	240	4	(	(	PUNCT
ejpam-3394	240	5	x	x	X
ejpam-3394	240	6	,	,	PUNCT
ejpam-3394	240	7	τ	τ	PROPN
ejpam-3394	240	8	,	,	PUNCT
ejpam-3394	240	9	i	i	NOUN
ejpam-3394	240	10	)	)	PUNCT
ejpam-3394	240	11	→	→	SYM
ejpam-3394	240	12	(	(	PUNCT
ejpam-3394	240	13	y	y	PROPN
ejpam-3394	240	14	,	,	PUNCT
ejpam-3394	240	15	σ	σ	PROPN
ejpam-3394	240	16	,	,	PUNCT
ejpam-3394	240	17	j	j	PROPN
ejpam-3394	240	18	)	)	PUNCT
ejpam-3394	240	19	be	be	VERB
ejpam-3394	240	20	a	a	DET
ejpam-3394	240	21	continuous	continuous	ADJ
ejpam-3394	240	22	,	,	PUNCT
ejpam-3394	240	23	open	open	ADJ
ejpam-3394	240	24	and	and	CCONJ
ejpam-3394	240	25	pre	pre	VERB
ejpam-3394	240	26	β	β	X
ejpam-3394	240	27	-	-	ADJ
ejpam-3394	240	28	closed	closed	ADJ
ejpam-3394	240	29	surjection	surjection	NOUN
ejpam-3394	240	30	with	with	ADP
ejpam-3394	240	31	f−1(y	f−1(y	PROPN
ejpam-3394	240	32	)	)	PUNCT
ejpam-3394	240	33	β	β	NOUN
ejpam-3394	240	34	-	-	NOUN
ejpam-3394	240	35	compact	compact	ADJ
ejpam-3394	240	36	for	for	ADP
ejpam-3394	240	37	every	every	DET
ejpam-3394	240	38	y	y	PROPN
ejpam-3394	240	39	∈	∈	PROPN
ejpam-3394	240	40	y	y	PROPN
ejpam-3394	240	41	and	and	CCONJ
ejpam-3394	240	42	f(i	f(i	NUM
ejpam-3394	240	43	)	)	PUNCT
ejpam-3394	241	1	⊆	⊆	NUM
ejpam-3394	241	2	j	j	NOUN
ejpam-3394	241	3	.	.	PUNCT
ejpam-3394	242	1	if	if	SCONJ
ejpam-3394	242	2	(	(	PUNCT
ejpam-3394	242	3	x	x	X
ejpam-3394	242	4	,	,	PUNCT
ejpam-3394	242	5	τ	τ	PROPN
ejpam-3394	242	6	,	,	PUNCT
ejpam-3394	242	7	i	i	PROPN
ejpam-3394	242	8	)	)	PUNCT
ejpam-3394	242	9	is	be	AUX
ejpam-3394	242	10	i	i	PROPN
ejpam-3394	242	11	-	-	PUNCT
ejpam-3394	242	12	β	β	NOUN
ejpam-3394	242	13	-	-	NOUN
ejpam-3394	242	14	paracompact	paracompact	ADJ
ejpam-3394	242	15	,	,	PUNCT
ejpam-3394	242	16	then	then	ADV
ejpam-3394	242	17	(	(	PUNCT
ejpam-3394	242	18	y	y	PROPN
ejpam-3394	242	19	,	,	PUNCT
ejpam-3394	242	20	σ	σ	PROPN
ejpam-3394	242	21	,	,	PUNCT
ejpam-3394	242	22	j	j	PROPN
ejpam-3394	242	23	)	)	PUNCT
ejpam-3394	242	24	is	be	AUX
ejpam-3394	242	25	j	j	PROPN
ejpam-3394	242	26	-	-	PUNCT
ejpam-3394	242	27	β	β	NOUN
ejpam-3394	242	28	-	-	ADJ
ejpam-3394	242	29	paracompact	paracompact	ADJ
ejpam-3394	242	30	.	.	PUNCT
ejpam-3394	243	1	proof	proof	NOUN
ejpam-3394	243	2	.	.	PUNCT
ejpam-3394	244	1	let	let	VERB
ejpam-3394	244	2	u	u	PRON
ejpam-3394	244	3	=	=	PUNCT
ejpam-3394	244	4	{	{	PUNCT
ejpam-3394	244	5	uλ	uλ	X
ejpam-3394	244	6	:	:	PUNCT
ejpam-3394	244	7	λ	λ	X
ejpam-3394	244	8	∈	∈	PROPN
ejpam-3394	244	9	λ	λ	PROPN
ejpam-3394	244	10	}	}	PUNCT
ejpam-3394	244	11	be	be	VERB
ejpam-3394	244	12	an	an	DET
ejpam-3394	244	13	open	open	ADJ
ejpam-3394	244	14	cover	cover	NOUN
ejpam-3394	244	15	of	of	ADP
ejpam-3394	244	16	y	y	PROPN
ejpam-3394	244	17	.	.	PUNCT
ejpam-3394	245	1	then	then	ADV
ejpam-3394	245	2	,	,	PUNCT
ejpam-3394	245	3	{	{	PUNCT
ejpam-3394	245	4	f−1(uλ	f−1(uλ	PROPN
ejpam-3394	245	5	)	)	PUNCT
ejpam-3394	245	6	:	:	PUNCT
ejpam-3394	246	1	λ	λ	X
ejpam-3394	246	2	∈	∈	PROPN
ejpam-3394	246	3	λ	λ	PROPN
ejpam-3394	246	4	}	}	PUNCT
ejpam-3394	246	5	is	be	AUX
ejpam-3394	246	6	an	an	DET
ejpam-3394	246	7	open	open	ADJ
ejpam-3394	246	8	cover	cover	NOUN
ejpam-3394	246	9	of	of	ADP
ejpam-3394	246	10	x.	x.	NOUN
ejpam-3394	246	11	since	since	SCONJ
ejpam-3394	246	12	(	(	PUNCT
ejpam-3394	246	13	x	x	X
ejpam-3394	246	14	,	,	PUNCT
ejpam-3394	246	15	τ	τ	PROPN
ejpam-3394	246	16	,	,	PUNCT
ejpam-3394	246	17	i	i	PROPN
ejpam-3394	246	18	)	)	PUNCT
ejpam-3394	246	19	is	be	AUX
ejpam-3394	246	20	i	i	PROPN
ejpam-3394	246	21	-	-	PUNCT
ejpam-3394	246	22	β	β	NOUN
ejpam-3394	246	23	-	-	NOUN
ejpam-3394	246	24	paracompact	paracompact	ADJ
ejpam-3394	246	25	,	,	PUNCT
ejpam-3394	246	26	this	this	DET
ejpam-3394	246	27	open	open	ADJ
ejpam-3394	246	28	cover	cover	NOUN
ejpam-3394	246	29	has	have	VERB
ejpam-3394	246	30	a	a	DET
ejpam-3394	246	31	β	β	X
ejpam-3394	246	32	-	-	ADJ
ejpam-3394	246	33	locally	locally	ADV
ejpam-3394	246	34	finite	finite	NOUN
ejpam-3394	246	35	precise	precise	ADJ
ejpam-3394	246	36	β	β	X
ejpam-3394	246	37	-	-	ADJ
ejpam-3394	246	38	open	open	ADJ
ejpam-3394	246	39	refinement	refinement	NOUN
ejpam-3394	246	40	v	v	NOUN
ejpam-3394	246	41	=	=	PUNCT
ejpam-3394	246	42	{	{	PUNCT
ejpam-3394	246	43	vλ	vλ	INTJ
ejpam-3394	246	44	:	:	PUNCT
ejpam-3394	246	45	λ	λ	PROPN
ejpam-3394	246	46	∈	∈	PROPN
ejpam-3394	246	47	λ	λ	NOUN
ejpam-3394	246	48	}	}	PUNCT
ejpam-3394	246	49	such	such	ADJ
ejpam-3394	246	50	that	that	SCONJ
ejpam-3394	246	51	x	x	PUNCT
ejpam-3394	246	52	−	−	PROPN
ejpam-3394	246	53	⋃	⋃	NOUN
ejpam-3394	246	54	{	{	PUNCT
ejpam-3394	246	55	vλ	vλ	INTJ
ejpam-3394	246	56	:	:	PUNCT
ejpam-3394	246	57	vλ	vλ	INTJ
ejpam-3394	246	58	∈	∈	PROPN
ejpam-3394	246	59	v	v	NOUN
ejpam-3394	246	60	}	}	PUNCT
ejpam-3394	246	61	∈	∈	PROPN
ejpam-3394	246	62	i.	i.	NOUN
ejpam-3394	246	63	since	since	SCONJ
ejpam-3394	246	64	f	f	PROPN
ejpam-3394	246	65	is	be	AUX
ejpam-3394	246	66	pre	pre	VERB
ejpam-3394	246	67	β	β	X
ejpam-3394	246	68	-	-	ADJ
ejpam-3394	246	69	open	open	ADJ
ejpam-3394	246	70	,	,	PUNCT
ejpam-3394	246	71	f(v	f(v	NOUN
ejpam-3394	246	72	)	)	PUNCT
ejpam-3394	246	73	=	=	SYM
ejpam-3394	246	74	{	{	PUNCT
ejpam-3394	246	75	f(vλ	f(vλ	NOUN
ejpam-3394	246	76	)	)	PUNCT
ejpam-3394	246	77	:	:	PUNCT
ejpam-3394	247	1	λ	λ	X
ejpam-3394	247	2	∈	∈	PROPN
ejpam-3394	247	3	λ	λ	PROPN
ejpam-3394	247	4	}	}	PUNCT
ejpam-3394	247	5	is	be	AUX
ejpam-3394	247	6	a	a	DET
ejpam-3394	247	7	precise	precise	ADJ
ejpam-3394	247	8	β	β	NOUN
ejpam-3394	247	9	-	-	ADJ
ejpam-3394	247	10	open	open	ADJ
ejpam-3394	247	11	refinement	refinement	NOUN
ejpam-3394	247	12	of	of	ADP
ejpam-3394	247	13	u	u	PROPN
ejpam-3394	247	14	.	.	PUNCT
ejpam-3394	248	1	also	also	ADV
ejpam-3394	248	2	,	,	PUNCT
ejpam-3394	248	3	y	y	PROPN
ejpam-3394	248	4	−	−	PROPN
ejpam-3394	248	5	⋃	⋃	NOUN
ejpam-3394	248	6	{	{	PUNCT
ejpam-3394	248	7	f(vλ	f(vλ	NOUN
ejpam-3394	248	8	)	)	PUNCT
ejpam-3394	248	9	:	:	PUNCT
ejpam-3394	249	1	λ	λ	X
ejpam-3394	249	2	∈	∈	PROPN
ejpam-3394	249	3	λ	λ	PROPN
ejpam-3394	249	4	}	}	PUNCT
ejpam-3394	249	5	∈	∈	PROPN
ejpam-3394	249	6	j	j	PROPN
ejpam-3394	249	7	.	.	PUNCT
ejpam-3394	250	1	now	now	ADV
ejpam-3394	250	2	,	,	PUNCT
ejpam-3394	250	3	let	let	VERB
ejpam-3394	250	4	we	we	PRON
ejpam-3394	250	5	prove	prove	VERB
ejpam-3394	250	6	that	that	SCONJ
ejpam-3394	250	7	f(v	f(v	NOUN
ejpam-3394	250	8	)	)	PUNCT
ejpam-3394	250	9	is	be	AUX
ejpam-3394	250	10	β	β	X
ejpam-3394	250	11	-	-	ADJ
ejpam-3394	250	12	locally	locally	ADV
ejpam-3394	250	13	finite	finite	NOUN
ejpam-3394	250	14	.	.	PUNCT
ejpam-3394	251	1	let	let	VERB
ejpam-3394	251	2	y	y	PROPN
ejpam-3394	251	3	∈	∈	PROPN
ejpam-3394	251	4	y	y	PROPN
ejpam-3394	251	5	.	.	PUNCT
ejpam-3394	252	1	since	since	SCONJ
ejpam-3394	252	2	v	v	NOUN
ejpam-3394	252	3	is	be	AUX
ejpam-3394	252	4	β	β	X
ejpam-3394	252	5	-	-	ADJ
ejpam-3394	252	6	locally	locally	ADV
ejpam-3394	252	7	finite	finite	NOUN
ejpam-3394	252	8	,	,	PUNCT
ejpam-3394	252	9	for	for	ADP
ejpam-3394	252	10	x	x	PROPN
ejpam-3394	252	11	∈	∈	PROPN
ejpam-3394	252	12	f−1(y	f−1(y	PROPN
ejpam-3394	252	13	)	)	PUNCT
ejpam-3394	252	14	,	,	PUNCT
ejpam-3394	252	15	there	there	PRON
ejpam-3394	252	16	exists	exist	VERB
ejpam-3394	252	17	a	a	DET
ejpam-3394	252	18	β	β	NOUN
ejpam-3394	252	19	-	-	ADJ
ejpam-3394	252	20	open	open	ADJ
ejpam-3394	252	21	set	set	ADJ
ejpam-3394	252	22	gx	gx	PROPN
ejpam-3394	252	23	containing	contain	VERB
ejpam-3394	252	24	x	x	PUNCT
ejpam-3394	252	25	such	such	ADJ
ejpam-3394	252	26	that	that	SCONJ
ejpam-3394	252	27	gx	gx	PROPN
ejpam-3394	252	28	intersects	intersect	NOUN
ejpam-3394	252	29	at	at	ADP
ejpam-3394	252	30	most	most	ADV
ejpam-3394	252	31	finitely	finitely	ADJ
ejpam-3394	252	32	members	member	NOUN
ejpam-3394	252	33	of	of	ADP
ejpam-3394	252	34	v.	v.	ADV
ejpam-3394	252	35	since	since	SCONJ
ejpam-3394	252	36	f−1(y	f−1(y	PROPN
ejpam-3394	252	37	)	)	PUNCT
ejpam-3394	252	38	is	be	AUX
ejpam-3394	252	39	β	β	NOUN
ejpam-3394	252	40	-	-	ADJ
ejpam-3394	252	41	compact	compact	ADJ
ejpam-3394	252	42	,	,	PUNCT
ejpam-3394	252	43	{	{	PUNCT
ejpam-3394	252	44	gx	gx	PROPN
ejpam-3394	252	45	:	:	PUNCT
ejpam-3394	252	46	x	x	X
ejpam-3394	252	47	∈	∈	NOUN
ejpam-3394	252	48	references	reference	VERB
ejpam-3394	252	49	277	277	NUM
ejpam-3394	252	50	f−1(y	f−1(y	PROPN
ejpam-3394	252	51	)	)	PUNCT
ejpam-3394	252	52	}	}	PUNCT
ejpam-3394	252	53	has	have	VERB
ejpam-3394	252	54	a	a	DET
ejpam-3394	252	55	finite	finite	ADJ
ejpam-3394	252	56	subcollection	subcollection	NOUN
ejpam-3394	252	57	hy	hy	NOUN
ejpam-3394	252	58	such	such	ADJ
ejpam-3394	252	59	that	that	DET
ejpam-3394	252	60	f−1(y	f−1(y	PROPN
ejpam-3394	252	61	)	)	PUNCT
ejpam-3394	252	62	⊆	⊆	NUM
ejpam-3394	252	63	⋃	⋃	NOUN
ejpam-3394	252	64	hy	hy	NOUN
ejpam-3394	252	65	and	and	CCONJ
ejpam-3394	252	66	⋃	⋃	NOUN
ejpam-3394	252	67	hy	hy	NOUN
ejpam-3394	252	68	intersects	intersect	NOUN
ejpam-3394	252	69	at	at	ADP
ejpam-3394	252	70	most	most	ADV
ejpam-3394	252	71	finitely	finitely	ADJ
ejpam-3394	252	72	members	member	NOUN
ejpam-3394	252	73	of	of	ADP
ejpam-3394	252	74	v.	v.	INTJ
ejpam-3394	252	75	by	by	ADP
ejpam-3394	252	76	lemma	lemma	PROPN
ejpam-3394	252	77	2	2	NUM
ejpam-3394	252	78	,	,	PUNCT
ejpam-3394	252	79	there	there	PRON
ejpam-3394	252	80	exists	exist	VERB
ejpam-3394	252	81	a	a	DET
ejpam-3394	252	82	β	β	NOUN
ejpam-3394	252	83	-	-	ADJ
ejpam-3394	252	84	open	open	ADJ
ejpam-3394	252	85	set	set	VERB
ejpam-3394	252	86	wy	wy	PROPN
ejpam-3394	252	87	containing	contain	VERB
ejpam-3394	252	88	y	y	PRON
ejpam-3394	252	89	such	such	ADJ
ejpam-3394	252	90	that	that	SCONJ
ejpam-3394	252	91	f−1(wy	f−1(wy	PROPN
ejpam-3394	252	92	)	)	PUNCT
ejpam-3394	252	93	⊆	⊆	NUM
ejpam-3394	252	94	⋃	⋃	NOUN
ejpam-3394	252	95	hy	hy	NOUN
ejpam-3394	252	96	.	.	PUNCT
ejpam-3394	253	1	then	then	ADV
ejpam-3394	253	2	,	,	PUNCT
ejpam-3394	253	3	f−1(wy	f−1(wy	PROPN
ejpam-3394	253	4	)	)	PUNCT
ejpam-3394	253	5	intersects	intersect	NOUN
ejpam-3394	253	6	at	at	ADP
ejpam-3394	253	7	most	most	ADV
ejpam-3394	253	8	finitely	finitely	ADJ
ejpam-3394	253	9	members	member	NOUN
ejpam-3394	253	10	of	of	ADP
ejpam-3394	253	11	v.	v.	ADP
ejpam-3394	253	12	this	this	PRON
ejpam-3394	253	13	implies	imply	VERB
ejpam-3394	253	14	that	that	SCONJ
ejpam-3394	253	15	wy	wy	PROPN
ejpam-3394	253	16	intersects	intersect	NOUN
ejpam-3394	253	17	at	at	ADP
ejpam-3394	253	18	most	most	ADV
ejpam-3394	253	19	finitely	finitely	ADJ
ejpam-3394	253	20	members	member	NOUN
ejpam-3394	253	21	of	of	ADP
ejpam-3394	253	22	f(v	f(v	NOUN
ejpam-3394	253	23	)	)	PUNCT
ejpam-3394	253	24	.	.	PUNCT
ejpam-3394	254	1	hence	hence	ADV
ejpam-3394	254	2	,	,	PUNCT
ejpam-3394	254	3	f(v	f(v	PROPN
ejpam-3394	254	4	)	)	PUNCT
ejpam-3394	254	5	is	be	AUX
ejpam-3394	254	6	β	β	X
ejpam-3394	254	7	-	-	ADJ
ejpam-3394	254	8	locally	locally	ADV
ejpam-3394	254	9	finite	finite	NOUN
ejpam-3394	254	10	in	in	ADP
ejpam-3394	254	11	y	y	PROPN
ejpam-3394	254	12	.	.	PUNCT
ejpam-3394	255	1	so	so	ADV
ejpam-3394	255	2	,	,	PUNCT
ejpam-3394	255	3	(	(	PUNCT
ejpam-3394	255	4	y	y	PROPN
ejpam-3394	255	5	,	,	PUNCT
ejpam-3394	255	6	σ	σ	PROPN
ejpam-3394	255	7	,	,	PUNCT
ejpam-3394	255	8	j	j	PROPN
ejpam-3394	255	9	)	)	PUNCT
ejpam-3394	255	10	is	be	AUX
ejpam-3394	255	11	j	j	PROPN
ejpam-3394	255	12	-	-	PUNCT
ejpam-3394	255	13	β	β	NOUN
ejpam-3394	255	14	-	-	ADJ
ejpam-3394	255	15	paracompact	paracompact	ADJ
ejpam-3394	255	16	.	.	PUNCT
ejpam-3394	256	1	theorem	theorem	NOUN
ejpam-3394	256	2	13	13	NUM
ejpam-3394	256	3	.	.	PUNCT
ejpam-3394	257	1	let	let	VERB
ejpam-3394	257	2	f	f	NOUN
ejpam-3394	257	3	:	:	PUNCT
ejpam-3394	257	4	(	(	PUNCT
ejpam-3394	257	5	x	x	X
ejpam-3394	257	6	,	,	PUNCT
ejpam-3394	257	7	τ	τ	PROPN
ejpam-3394	257	8	,	,	PUNCT
ejpam-3394	257	9	i	i	NOUN
ejpam-3394	257	10	)	)	PUNCT
ejpam-3394	257	11	→	→	SYM
ejpam-3394	257	12	(	(	PUNCT
ejpam-3394	257	13	y	y	PROPN
ejpam-3394	257	14	,	,	PUNCT
ejpam-3394	257	15	σ	σ	PROPN
ejpam-3394	257	16	,	,	PUNCT
ejpam-3394	257	17	j	j	PROPN
ejpam-3394	257	18	)	)	PUNCT
ejpam-3394	257	19	be	be	VERB
ejpam-3394	257	20	an	an	DET
ejpam-3394	257	21	open	open	ADJ
ejpam-3394	257	22	,	,	PUNCT
ejpam-3394	257	23	βirresolute	βirresolute	NOUN
ejpam-3394	257	24	bijective	bijective	ADJ
ejpam-3394	257	25	mapping	mapping	NOUN
ejpam-3394	257	26	and	and	CCONJ
ejpam-3394	257	27	i	i	NOUN
ejpam-3394	257	28	=	=	SYM
ejpam-3394	257	29	f−1(j	f−1(j	PROPN
ejpam-3394	257	30	)	)	PUNCT
ejpam-3394	257	31	.	.	PUNCT
ejpam-3394	258	1	if	if	SCONJ
ejpam-3394	258	2	a	a	PRON
ejpam-3394	258	3	is	be	AUX
ejpam-3394	258	4	j	j	PROPN
ejpam-3394	258	5	-	-	PUNCT
ejpam-3394	258	6	β	β	NOUN
ejpam-3394	258	7	-	-	NOUN
ejpam-3394	258	8	paracompact	paracompact	NOUN
ejpam-3394	258	9	in	in	ADP
ejpam-3394	258	10	y	y	PROPN
ejpam-3394	258	11	,	,	PUNCT
ejpam-3394	258	12	then	then	ADV
ejpam-3394	258	13	f−1(a	f−1(a	PROPN
ejpam-3394	258	14	)	)	PUNCT
ejpam-3394	258	15	is	be	AUX
ejpam-3394	258	16	i	i	PROPN
ejpam-3394	258	17	-	-	PUNCT
ejpam-3394	258	18	β	β	NOUN
ejpam-3394	258	19	-	-	NOUN
ejpam-3394	258	20	paracompact	paracompact	NOUN
ejpam-3394	258	21	in	in	ADP
ejpam-3394	258	22	x.	x.	NOUN
ejpam-3394	258	23	proof	proof	NOUN
ejpam-3394	258	24	.	.	PUNCT
ejpam-3394	259	1	let	let	VERB
ejpam-3394	259	2	u	u	PRON
ejpam-3394	259	3	=	=	PUNCT
ejpam-3394	259	4	{	{	PUNCT
ejpam-3394	259	5	uλ	uλ	X
ejpam-3394	259	6	:	:	PUNCT
ejpam-3394	259	7	λ	λ	X
ejpam-3394	259	8	∈	∈	PROPN
ejpam-3394	259	9	λ	λ	PROPN
ejpam-3394	259	10	}	}	PUNCT
ejpam-3394	259	11	be	be	VERB
ejpam-3394	259	12	an	an	DET
ejpam-3394	259	13	open	open	ADJ
ejpam-3394	259	14	cover	cover	NOUN
ejpam-3394	259	15	of	of	ADP
ejpam-3394	259	16	f−1(a	f−1(a	NOUN
ejpam-3394	259	17	)	)	PUNCT
ejpam-3394	259	18	.	.	PUNCT
ejpam-3394	260	1	since	since	SCONJ
ejpam-3394	260	2	f	f	PROPN
ejpam-3394	260	3	is	be	AUX
ejpam-3394	260	4	open	open	ADJ
ejpam-3394	260	5	,	,	PUNCT
ejpam-3394	260	6	u1	u1	NOUN
ejpam-3394	260	7	=	=	SYM
ejpam-3394	260	8	{	{	PUNCT
ejpam-3394	260	9	f(uλ	f(uλ	PROPN
ejpam-3394	260	10	)	)	PUNCT
ejpam-3394	260	11	:	:	PUNCT
ejpam-3394	261	1	λ	λ	X
ejpam-3394	261	2	∈	∈	PROPN
ejpam-3394	261	3	λ	λ	PROPN
ejpam-3394	261	4	}	}	PUNCT
ejpam-3394	261	5	is	be	AUX
ejpam-3394	261	6	an	an	DET
ejpam-3394	261	7	open	open	ADJ
ejpam-3394	261	8	cover	cover	NOUN
ejpam-3394	261	9	of	of	ADP
ejpam-3394	261	10	a.	a.	NOUN
ejpam-3394	261	11	by	by	ADP
ejpam-3394	261	12	hypothesis	hypothesis	NOUN
ejpam-3394	261	13	,	,	PUNCT
ejpam-3394	261	14	this	this	DET
ejpam-3394	261	15	open	open	ADJ
ejpam-3394	261	16	cover	cover	NOUN
ejpam-3394	261	17	has	have	VERB
ejpam-3394	261	18	a	a	DET
ejpam-3394	261	19	β	β	X
ejpam-3394	261	20	-	-	ADJ
ejpam-3394	261	21	locally	locally	ADV
ejpam-3394	261	22	finite	finite	NOUN
ejpam-3394	261	23	precise	precise	ADJ
ejpam-3394	261	24	β	β	X
ejpam-3394	261	25	-	-	ADJ
ejpam-3394	261	26	open	open	ADJ
ejpam-3394	261	27	refinement	refinement	NOUN
ejpam-3394	261	28	v1	v1	NOUN
ejpam-3394	261	29	=	=	SYM
ejpam-3394	261	30	{	{	PUNCT
ejpam-3394	261	31	vλ	vλ	INTJ
ejpam-3394	261	32	:	:	PUNCT
ejpam-3394	261	33	λ	λ	PROPN
ejpam-3394	261	34	∈	∈	PROPN
ejpam-3394	261	35	λ	λ	NOUN
ejpam-3394	261	36	}	}	PUNCT
ejpam-3394	261	37	such	such	ADJ
ejpam-3394	261	38	that	that	DET
ejpam-3394	261	39	a−	a−	PROPN
ejpam-3394	261	40	⋃	⋃	PROPN
ejpam-3394	261	41	{	{	PUNCT
ejpam-3394	261	42	vλ	vλ	INTJ
ejpam-3394	261	43	:	:	PUNCT
ejpam-3394	261	44	λ	λ	PROPN
ejpam-3394	261	45	∈	∈	PROPN
ejpam-3394	261	46	λ	λ	PROPN
ejpam-3394	261	47	}	}	PUNCT
ejpam-3394	261	48	∈	∈	PROPN
ejpam-3394	261	49	j	j	PROPN
ejpam-3394	261	50	.	.	PUNCT
ejpam-3394	262	1	then	then	ADV
ejpam-3394	262	2	,	,	PUNCT
ejpam-3394	262	3	f−1(a	f−1(a	PROPN
ejpam-3394	262	4	)	)	PUNCT
ejpam-3394	263	1	−	−	ADP
ejpam-3394	263	2	⋃	⋃	NOUN
ejpam-3394	263	3	{	{	PUNCT
ejpam-3394	263	4	f−1(vλ	f−1(vλ	NOUN
ejpam-3394	263	5	)	)	PUNCT
ejpam-3394	263	6	:	:	PUNCT
ejpam-3394	264	1	λ	λ	X
ejpam-3394	264	2	∈	∈	PROPN
ejpam-3394	264	3	λ	λ	PROPN
ejpam-3394	264	4	}	}	PUNCT
ejpam-3394	264	5	∈	∈	PROPN
ejpam-3394	264	6	f−1(j	f−1(j	NOUN
ejpam-3394	264	7	)	)	PUNCT
ejpam-3394	264	8	=	=	SYM
ejpam-3394	264	9	i.	i.	NOUN
ejpam-3394	264	10	since	since	SCONJ
ejpam-3394	264	11	f	f	PROPN
ejpam-3394	264	12	is	be	AUX
ejpam-3394	264	13	β	β	NOUN
ejpam-3394	264	14	-	-	NOUN
ejpam-3394	264	15	irresolute	irresolute	ADJ
ejpam-3394	264	16	,	,	PUNCT
ejpam-3394	264	17	v	v	NOUN
ejpam-3394	264	18	=	=	SYM
ejpam-3394	264	19	{	{	PUNCT
ejpam-3394	264	20	f−1(vλ	f−1(vλ	X
ejpam-3394	264	21	)	)	PUNCT
ejpam-3394	264	22	:	:	PUNCT
ejpam-3394	265	1	λ	λ	X
ejpam-3394	265	2	∈	∈	PROPN
ejpam-3394	265	3	λ	λ	PROPN
ejpam-3394	265	4	}	}	PUNCT
ejpam-3394	265	5	is	be	AUX
ejpam-3394	265	6	β	β	X
ejpam-3394	265	7	-	-	ADJ
ejpam-3394	265	8	locally	locally	ADV
ejpam-3394	265	9	finite	finite	ADJ
ejpam-3394	265	10	β	β	NOUN
ejpam-3394	265	11	-	-	ADJ
ejpam-3394	265	12	open	open	ADJ
ejpam-3394	265	13	.	.	PUNCT
ejpam-3394	266	1	let	let	VERB
ejpam-3394	266	2	f−1(vλ	f−1(vλ	PRON
ejpam-3394	266	3	)	)	PUNCT
ejpam-3394	266	4	∈	∈	PROPN
ejpam-3394	266	5	v.	v.	CCONJ
ejpam-3394	266	6	since	since	SCONJ
ejpam-3394	266	7	v1	v1	NOUN
ejpam-3394	266	8	refines	refine	NOUN
ejpam-3394	266	9	u1	u1	NOUN
ejpam-3394	266	10	,	,	PUNCT
ejpam-3394	266	11	there	there	PRON
ejpam-3394	266	12	exists	exist	VERB
ejpam-3394	266	13	f(uλ	f(uλ	PROPN
ejpam-3394	266	14	)	)	PUNCT
ejpam-3394	266	15	∈	∈	PROPN
ejpam-3394	266	16	u1	u1	NOUN
ejpam-3394	267	1	such	such	ADJ
ejpam-3394	267	2	that	that	SCONJ
ejpam-3394	267	3	vλ	vλ	ADP
ejpam-3394	267	4	⊆	⊆	NUM
ejpam-3394	267	5	f(uλ	f(uλ	NOUN
ejpam-3394	267	6	)	)	PUNCT
ejpam-3394	267	7	.	.	PUNCT
ejpam-3394	268	1	then	then	ADV
ejpam-3394	268	2	f−1(vλ	f−1(vλ	X
ejpam-3394	268	3	)	)	PUNCT
ejpam-3394	268	4	⊆	⊆	NUM
ejpam-3394	268	5	f−1(f(uλ	f−1(f(uλ	NOUN
ejpam-3394	268	6	)	)	PUNCT
ejpam-3394	268	7	)	)	PUNCT
ejpam-3394	269	1	=	=	SYM
ejpam-3394	269	2	uλ	uλ	PROPN
ejpam-3394	269	3	.	.	PUNCT
ejpam-3394	270	1	hence	hence	ADV
ejpam-3394	270	2	v	v	NOUN
ejpam-3394	270	3	refines	refine	VERB
ejpam-3394	270	4	u	u	PRON
ejpam-3394	270	5	.	.	PUNCT
ejpam-3394	271	1	therefore	therefore	ADV
ejpam-3394	271	2	f−1(a	f−1(a	PROPN
ejpam-3394	271	3	)	)	PUNCT
ejpam-3394	271	4	is	be	AUX
ejpam-3394	271	5	i	i	PROPN
ejpam-3394	271	6	-	-	PUNCT
ejpam-3394	271	7	β	β	NOUN
ejpam-3394	271	8	-	-	NOUN
ejpam-3394	271	9	paracompact	paracompact	NOUN
ejpam-3394	271	10	in	in	ADP
ejpam-3394	271	11	x.	x.	NOUN
ejpam-3394	271	12	acknowledgements	acknowledgement	VERB
ejpam-3394	271	13	the	the	DET
ejpam-3394	271	14	author	author	NOUN
ejpam-3394	271	15	would	would	AUX
ejpam-3394	271	16	like	like	VERB
ejpam-3394	271	17	to	to	PART
ejpam-3394	271	18	thank	thank	VERB
ejpam-3394	271	19	the	the	DET
ejpam-3394	271	20	referees	referee	NOUN
ejpam-3394	271	21	for	for	ADP
ejpam-3394	271	22	their	their	PRON
ejpam-3394	271	23	helpful	helpful	ADJ
ejpam-3394	271	24	suggestions	suggestion	NOUN
ejpam-3394	271	25	.	.	PUNCT
ejpam-3394	272	1	references	reference	NOUN
ejpam-3394	272	2	[	[	X
ejpam-3394	272	3	1	1	NUM
ejpam-3394	272	4	]	]	X
ejpam-3394	272	5	abd	abd	PROPN
ejpam-3394	272	6	el	el	PROPN
ejpam-3394	272	7	-	-	PUNCT
ejpam-3394	272	8	monsef	monsef	ADJ
ejpam-3394	272	9	,	,	PUNCT
ejpam-3394	272	10	m.	m.	PROPN
ejpam-3394	272	11	e.	e.	PROPN
ejpam-3394	272	12	,	,	PUNCT
ejpam-3394	272	13	el	el	PROPN
ejpam-3394	272	14	-	-	PUNCT
ejpam-3394	272	15	deeb	deeb	PROPN
ejpam-3394	272	16	,	,	PUNCT
ejpam-3394	272	17	s.	s.	PROPN
ejpam-3394	272	18	n.	n.	PROPN
ejpam-3394	272	19	and	and	CCONJ
ejpam-3394	272	20	mahmoud	mahmoud	PROPN
ejpam-3394	272	21	,	,	PUNCT
ejpam-3394	272	22	r.	r.	PROPN
ejpam-3394	272	23	a.	a.	NOUN
ejpam-3394	272	24	β	β	X
ejpam-3394	272	25	-	-	ADJ
ejpam-3394	272	26	open	open	ADJ
ejpam-3394	272	27	sets	set	NOUN
ejpam-3394	272	28	and	and	CCONJ
ejpam-3394	272	29	βcontinuous	βcontinuous	ADJ
ejpam-3394	272	30	mapping	mapping	NOUN
ejpam-3394	272	31	,	,	PUNCT
ejpam-3394	272	32	bull	bull	NOUN
ejpam-3394	272	33	.	.	PUNCT
ejpam-3394	273	1	fac	fac	PROPN
ejpam-3394	273	2	.	.	PUNCT
ejpam-3394	274	1	sci	sci	PROPN
ejpam-3394	274	2	.	.	PUNCT
ejpam-3394	274	3	assiut	assiut	PROPN
ejpam-3394	274	4	univ	univ	PROPN
ejpam-3394	274	5	.	.	PROPN
ejpam-3394	275	1	12	12	NUM
ejpam-3394	275	2	,	,	PUNCT
ejpam-3394	275	3	77	77	NUM
ejpam-3394	275	4	-	-	SYM
ejpam-3394	275	5	90	90	NUM
ejpam-3394	275	6	,	,	PUNCT
ejpam-3394	275	7	1983	1983	NUM
ejpam-3394	275	8	.	.	PUNCT
ejpam-3394	276	1	[	[	X
ejpam-3394	276	2	2	2	NUM
ejpam-3394	276	3	]	]	X
ejpam-3394	276	4	abd	abd	PROPN
ejpam-3394	276	5	el	el	PROPN
ejpam-3394	276	6	-	-	PUNCT
ejpam-3394	276	7	monsef	monsef	ADJ
ejpam-3394	276	8	,	,	PUNCT
ejpam-3394	276	9	m.	m.	PROPN
ejpam-3394	276	10	e.	e.	PROPN
ejpam-3394	276	11	and	and	CCONJ
ejpam-3394	276	12	kozae	kozae	PROPN
ejpam-3394	276	13	,	,	PUNCT
ejpam-3394	276	14	a.	a.	NOUN
ejpam-3394	276	15	m.	m.	NOUN
ejpam-3394	276	16	some	some	DET
ejpam-3394	276	17	generalized	generalized	ADJ
ejpam-3394	276	18	forms	form	NOUN
ejpam-3394	276	19	of	of	ADP
ejpam-3394	276	20	compactness	compactness	NOUN
ejpam-3394	276	21	and	and	CCONJ
ejpam-3394	276	22	closedness	closedness	NOUN
ejpam-3394	276	23	,	,	PUNCT
ejpam-3394	276	24	delta	delta	PROPN
ejpam-3394	276	25	j.	j.	PROPN
ejpam-3394	276	26	sci	sci	PROPN
ejpam-3394	276	27	.	.	PROPN
ejpam-3394	276	28	9	9	NUM
ejpam-3394	276	29	,	,	PUNCT
ejpam-3394	276	30	257	257	NUM
ejpam-3394	276	31	-	-	SYM
ejpam-3394	276	32	269	269	NUM
ejpam-3394	276	33	,	,	PUNCT
ejpam-3394	276	34	1985	1985	NUM
ejpam-3394	276	35	.	.	PUNCT
ejpam-3394	277	1	[	[	X
ejpam-3394	277	2	3	3	X
ejpam-3394	277	3	]	]	X
ejpam-3394	277	4	abd	abd	PROPN
ejpam-3394	277	5	el	el	PROPN
ejpam-3394	277	6	-	-	PUNCT
ejpam-3394	277	7	monsef	monsef	ADJ
ejpam-3394	277	8	,	,	PUNCT
ejpam-3394	277	9	m.	m.	PROPN
ejpam-3394	277	10	e.	e.	PROPN
ejpam-3394	277	11	,	,	PUNCT
ejpam-3394	277	12	mahmoud	mahmoud	PROPN
ejpam-3394	277	13	,	,	PUNCT
ejpam-3394	277	14	r.	r.	PROPN
ejpam-3394	277	15	a.	a.	PROPN
ejpam-3394	277	16	and	and	CCONJ
ejpam-3394	277	17	lashin	lashin	PROPN
ejpam-3394	277	18	,	,	PUNCT
ejpam-3394	277	19	e.	e.	PROPN
ejpam-3394	277	20	r.	r.	PROPN
ejpam-3394	277	21	β	β	PROPN
ejpam-3394	277	22	-	-	PUNCT
ejpam-3394	277	23	closure	closure	NOUN
ejpam-3394	277	24	and	and	CCONJ
ejpam-3394	277	25	β	β	NOUN
ejpam-3394	277	26	-	-	NOUN
ejpam-3394	277	27	interior	interior	ADJ
ejpam-3394	277	28	,	,	PUNCT
ejpam-3394	277	29	j.	j.	PROPN
ejpam-3394	277	30	fac	fac	PROPN
ejpam-3394	277	31	.	.	PUNCT
ejpam-3394	278	1	ed	ed	PROPN
ejpam-3394	278	2	.	.	PUNCT
ejpam-3394	278	3	ain	ain	PROPN
ejpam-3394	278	4	shams	sham	NOUN
ejpam-3394	278	5	univ	univ	PROPN
ejpam-3394	278	6	.	.	PUNCT
ejpam-3394	279	1	10	10	NUM
ejpam-3394	279	2	,	,	PUNCT
ejpam-3394	279	3	235	235	NUM
ejpam-3394	279	4	-	-	SYM
ejpam-3394	279	5	245	245	NUM
ejpam-3394	279	6	,	,	PUNCT
ejpam-3394	279	7	1986	1986	NUM
ejpam-3394	279	8	.	.	PUNCT
ejpam-3394	280	1	[	[	X
ejpam-3394	280	2	4	4	NUM
ejpam-3394	280	3	]	]	X
ejpam-3394	280	4	al	al	PROPN
ejpam-3394	280	5	-	-	PUNCT
ejpam-3394	280	6	zoubi	zoubi	PROPN
ejpam-3394	280	7	,	,	PUNCT
ejpam-3394	280	8	k.	k.	PROPN
ejpam-3394	280	9	y.	y.	PROPN
ejpam-3394	280	10	s	s	PROPN
ejpam-3394	280	11	-	-	PUNCT
ejpam-3394	280	12	expandable	expandable	ADJ
ejpam-3394	280	13	spaces	space	NOUN
ejpam-3394	280	14	,	,	PUNCT
ejpam-3394	280	15	acta	acta	PROPN
ejpam-3394	280	16	math	math	PROPN
ejpam-3394	280	17	.	.	PUNCT
ejpam-3394	281	1	hungar	hungar	PROPN
ejpam-3394	281	2	102(3	102(3	NUM
ejpam-3394	281	3	)	)	PUNCT
ejpam-3394	281	4	,	,	PUNCT
ejpam-3394	281	5	203	203	NUM
ejpam-3394	281	6	-	-	SYM
ejpam-3394	281	7	212	212	NUM
ejpam-3394	281	8	,	,	PUNCT
ejpam-3394	281	9	2004	2004	NUM
ejpam-3394	281	10	.	.	PUNCT
ejpam-3394	282	1	[	[	X
ejpam-3394	282	2	5	5	NUM
ejpam-3394	282	3	]	]	X
ejpam-3394	282	4	al	al	PROPN
ejpam-3394	282	5	-	-	PUNCT
ejpam-3394	282	6	zoubi	zoubi	PROPN
ejpam-3394	282	7	,	,	PUNCT
ejpam-3394	282	8	k.	k.	PROPN
ejpam-3394	282	9	y.	y.	PROPN
ejpam-3394	282	10	s	s	PROPN
ejpam-3394	282	11	-	-	PUNCT
ejpam-3394	282	12	paracompact	paracompact	ADJ
ejpam-3394	282	13	spaces	space	NOUN
ejpam-3394	282	14	,	,	PUNCT
ejpam-3394	282	15	acta	acta	PROPN
ejpam-3394	282	16	math	math	PROPN
ejpam-3394	282	17	.	.	PUNCT
ejpam-3394	283	1	hungar	hungar	PROPN
ejpam-3394	283	2	110(1	110(1	NUM
ejpam-3394	283	3	-	-	SYM
ejpam-3394	283	4	2	2	NUM
ejpam-3394	283	5	)	)	PUNCT
ejpam-3394	283	6	,	,	PUNCT
ejpam-3394	283	7	165	165	NUM
ejpam-3394	283	8	-	-	SYM
ejpam-3394	283	9	174	174	NUM
ejpam-3394	283	10	,	,	PUNCT
ejpam-3394	283	11	2006	2006	NUM
ejpam-3394	283	12	.	.	PUNCT
ejpam-3394	284	1	[	[	X
ejpam-3394	284	2	6	6	NUM
ejpam-3394	284	3	]	]	X
ejpam-3394	284	4	al	al	PROPN
ejpam-3394	284	5	-	-	PUNCT
ejpam-3394	284	6	zoubi	zoubi	PROPN
ejpam-3394	284	7	,	,	PUNCT
ejpam-3394	284	8	k.	k.	PROPN
ejpam-3394	284	9	and	and	CCONJ
ejpam-3394	284	10	al	al	PROPN
ejpam-3394	284	11	-	-	PUNCT
ejpam-3394	284	12	ghour	ghour	PROPN
ejpam-3394	284	13	,	,	PUNCT
ejpam-3394	284	14	s.	s.	PROPN
ejpam-3394	284	15	on	on	ADP
ejpam-3394	284	16	p3	p3	PROPN
ejpam-3394	284	17	-	-	PUNCT
ejpam-3394	284	18	paracompact	paracompact	ADJ
ejpam-3394	284	19	spaces	space	NOUN
ejpam-3394	284	20	,	,	PUNCT
ejpam-3394	284	21	int	int	NOUN
ejpam-3394	284	22	.	.	PUNCT
ejpam-3394	285	1	j.	j.	PROPN
ejpam-3394	285	2	math	math	PROPN
ejpam-3394	285	3	.	.	PUNCT
ejpam-3394	286	1	math	math	NOUN
ejpam-3394	286	2	.	.	PUNCT
ejpam-3394	287	1	sci	sci	PROPN
ejpam-3394	287	2	.	.	PROPN
ejpam-3394	287	3	2007	2007	NUM
ejpam-3394	287	4	,	,	PUNCT
ejpam-3394	287	5	1	1	NUM
ejpam-3394	287	6	-	-	SYM
ejpam-3394	287	7	16	16	NUM
ejpam-3394	287	8	,	,	PUNCT
ejpam-3394	287	9	2007	2007	NUM
ejpam-3394	287	10	.	.	PUNCT
ejpam-3394	288	1	[	[	X
ejpam-3394	288	2	7	7	X
ejpam-3394	288	3	]	]	PUNCT
ejpam-3394	288	4	andrijević	andrijević	NOUN
ejpam-3394	288	5	,	,	PUNCT
ejpam-3394	288	6	d.	d.	PROPN
ejpam-3394	288	7	semipreopen	semipreopen	PROPN
ejpam-3394	288	8	sets	set	NOUN
ejpam-3394	288	9	,	,	PUNCT
ejpam-3394	288	10	mat	mat	PROPN
ejpam-3394	288	11	.	.	PROPN
ejpam-3394	288	12	vesnik	vesnik	PROPN
ejpam-3394	288	13	38	38	NUM
ejpam-3394	288	14	,	,	PUNCT
ejpam-3394	288	15	24	24	NUM
ejpam-3394	288	16	-	-	SYM
ejpam-3394	288	17	32	32	NUM
ejpam-3394	288	18	,	,	PUNCT
ejpam-3394	288	19	1986	1986	NUM
ejpam-3394	288	20	.	.	PUNCT
ejpam-3394	289	1	[	[	X
ejpam-3394	289	2	8	8	NUM
ejpam-3394	289	3	]	]	X
ejpam-3394	289	4	bourbaki	bourbaki	VERB
ejpam-3394	289	5	,	,	PUNCT
ejpam-3394	289	6	n.	n.	PROPN
ejpam-3394	289	7	general	general	ADJ
ejpam-3394	289	8	topology	topology	NOUN
ejpam-3394	289	9	,	,	PUNCT
ejpam-3394	289	10	part	part	NOUN
ejpam-3394	289	11	i.	i.	PROPN
ejpam-3394	289	12	,	,	PUNCT
ejpam-3394	289	13	addison	addison	PROPN
ejpam-3394	289	14	-	-	PUNCT
ejpam-3394	289	15	wesley	wesley	PROPN
ejpam-3394	289	16	,	,	PUNCT
ejpam-3394	289	17	reading	reading	NOUN
ejpam-3394	289	18	,	,	PUNCT
ejpam-3394	289	19	mass	mass	PROPN
ejpam-3394	289	20	.	.	PROPN
ejpam-3394	289	21	1966	1966	NUM
ejpam-3394	289	22	.	.	PUNCT
ejpam-3394	290	1	[	[	X
ejpam-3394	290	2	9	9	NUM
ejpam-3394	290	3	]	]	SYM
ejpam-3394	290	4	cao	cao	PROPN
ejpam-3394	290	5	,	,	PUNCT
ejpam-3394	290	6	j.	j.	PROPN
ejpam-3394	290	7	,	,	PUNCT
ejpam-3394	290	8	ganster	ganster	NOUN
ejpam-3394	290	9	,	,	PUNCT
ejpam-3394	290	10	m.	m.	NOUN
ejpam-3394	290	11	and	and	CCONJ
ejpam-3394	290	12	reilly	reilly	PROPN
ejpam-3394	290	13	,	,	PUNCT
ejpam-3394	290	14	i.	i.	PROPN
ejpam-3394	290	15	submaximality	submaximality	PROPN
ejpam-3394	290	16	,	,	PUNCT
ejpam-3394	290	17	extremal	extremal	ADJ
ejpam-3394	290	18	disconnectedness	disconnectedness	NOUN
ejpam-3394	290	19	and	and	CCONJ
ejpam-3394	290	20	generalized	generalized	ADJ
ejpam-3394	290	21	closed	closed	ADJ
ejpam-3394	290	22	sets	set	NOUN
ejpam-3394	290	23	,	,	PUNCT
ejpam-3394	290	24	houston	houston	PROPN
ejpam-3394	290	25	journal	journal	NOUN
ejpam-3394	290	26	of	of	ADP
ejpam-3394	290	27	mathematics	mathematics	PROPN
ejpam-3394	290	28	24(4	24(4	NUM
ejpam-3394	290	29	)	)	PUNCT
ejpam-3394	290	30	,	,	PUNCT
ejpam-3394	290	31	681	681	NUM
ejpam-3394	290	32	-	-	SYM
ejpam-3394	290	33	688	688	NUM
ejpam-3394	290	34	,	,	PUNCT
ejpam-3394	290	35	1998	1998	NUM
ejpam-3394	290	36	.	.	PUNCT
ejpam-3394	290	37	references	reference	NOUN
ejpam-3394	290	38	278	278	NUM
ejpam-3394	291	1	[	[	X
ejpam-3394	291	2	10	10	NUM
ejpam-3394	291	3	]	]	PUNCT
ejpam-3394	291	4	crossely	crossely	ADV
ejpam-3394	291	5	,	,	PUNCT
ejpam-3394	291	6	s.	s.	PROPN
ejpam-3394	291	7	g.	g.	PROPN
ejpam-3394	292	1	semi	semi	ADV
ejpam-3394	292	2	-	-	ADJ
ejpam-3394	292	3	closed	closed	ADJ
ejpam-3394	292	4	and	and	CCONJ
ejpam-3394	292	5	semi	semi	ADJ
ejpam-3394	292	6	-	-	NOUN
ejpam-3394	292	7	continuity	continuity	NOUN
ejpam-3394	292	8	in	in	ADP
ejpam-3394	292	9	topological	topological	ADJ
ejpam-3394	292	10	spaces	space	NOUN
ejpam-3394	292	11	,	,	PUNCT
ejpam-3394	292	12	texas	texas	PROPN
ejpam-3394	292	13	j.	j.	PROPN
ejpam-3394	292	14	sci	sci	PROPN
ejpam-3394	292	15	.	.	PROPN
ejpam-3394	293	1	22	22	NUM
ejpam-3394	293	2	,	,	PUNCT
ejpam-3394	293	3	123	123	NUM
ejpam-3394	293	4	-	-	SYM
ejpam-3394	293	5	126	126	NUM
ejpam-3394	293	6	,	,	PUNCT
ejpam-3394	293	7	1971	1971	NUM
ejpam-3394	293	8	.	.	PUNCT
ejpam-3394	294	1	[	[	X
ejpam-3394	294	2	11	11	NUM
ejpam-3394	294	3	]	]	X
ejpam-3394	294	4	demir	demir	PROPN
ejpam-3394	294	5	,	,	PUNCT
ejpam-3394	294	6	i.	i.	PROPN
ejpam-3394	294	7	and	and	CCONJ
ejpam-3394	294	8	ozbakir	ozbakir	NOUN
ejpam-3394	294	9	,	,	PUNCT
ejpam-3394	294	10	o.	o.	PROPN
ejpam-3394	294	11	b.	b.	PROPN
ejpam-3394	294	12	on	on	ADP
ejpam-3394	294	13	β	β	ADJ
ejpam-3394	294	14	-	-	ADJ
ejpam-3394	294	15	paracompact	paracompact	ADJ
ejpam-3394	294	16	spaces	space	NOUN
ejpam-3394	294	17	,	,	PUNCT
ejpam-3394	294	18	filomat	filomat	PROPN
ejpam-3394	294	19	27:6	27:6	NUM
ejpam-3394	294	20	,	,	PUNCT
ejpam-3394	294	21	971	971	NUM
ejpam-3394	294	22	-	-	SYM
ejpam-3394	294	23	976	976	NUM
ejpam-3394	294	24	,	,	PUNCT
ejpam-3394	294	25	2013	2013	NUM
ejpam-3394	294	26	.	.	PUNCT
ejpam-3394	295	1	[	[	X
ejpam-3394	295	2	12	12	NUM
ejpam-3394	295	3	]	]	PUNCT
ejpam-3394	295	4	hamlet	hamlet	NOUN
ejpam-3394	295	5	,	,	PUNCT
ejpam-3394	295	6	t.	t.	PROPN
ejpam-3394	295	7	r.	r.	PROPN
ejpam-3394	295	8	and	and	CCONJ
ejpam-3394	295	9	janković	janković	PROPN
ejpam-3394	295	10	,	,	PUNCT
ejpam-3394	295	11	d.	d.	PROPN
ejpam-3394	295	12	on	on	ADP
ejpam-3394	295	13	weaker	weak	ADJ
ejpam-3394	295	14	forms	form	NOUN
ejpam-3394	295	15	of	of	ADP
ejpam-3394	295	16	paracompactness	paracompactness	NOUN
ejpam-3394	295	17	,	,	PUNCT
ejpam-3394	295	18	countable	countable	ADJ
ejpam-3394	295	19	compactness	compactness	NOUN
ejpam-3394	295	20	,	,	PUNCT
ejpam-3394	295	21	and	and	CCONJ
ejpam-3394	295	22	lindelöfness	lindelöfness	NOUN
ejpam-3394	295	23	,	,	PUNCT
ejpam-3394	295	24	ann	ann	PROPN
ejpam-3394	295	25	.	.	PUNCT
ejpam-3394	296	1	new	new	PROPN
ejpam-3394	296	2	york	york	PROPN
ejpam-3394	296	3	acad	acad	PROPN
ejpam-3394	296	4	.	.	PUNCT
ejpam-3394	297	1	sci	sci	PROPN
ejpam-3394	297	2	.	.	PROPN
ejpam-3394	297	3	,	,	PUNCT
ejpam-3394	297	4	728	728	NUM
ejpam-3394	297	5	,	,	PUNCT
ejpam-3394	297	6	4149	4149	NUM
ejpam-3394	297	7	,	,	PUNCT
ejpam-3394	297	8	1994	1994	NUM
ejpam-3394	297	9	.	.	PUNCT
ejpam-3394	298	1	[	[	X
ejpam-3394	298	2	13	13	NUM
ejpam-3394	298	3	]	]	SYM
ejpam-3394	298	4	hamlet	hamlet	NOUN
ejpam-3394	298	5	,	,	PUNCT
ejpam-3394	298	6	t.	t.	PROPN
ejpam-3394	298	7	r.	r.	PROPN
ejpam-3394	298	8	,	,	PUNCT
ejpam-3394	298	9	rose	rise	VERB
ejpam-3394	298	10	,	,	PUNCT
ejpam-3394	298	11	d.	d.	NOUN
ejpam-3394	298	12	and	and	CCONJ
ejpam-3394	298	13	janković	janković	PROPN
ejpam-3394	298	14	,	,	PUNCT
ejpam-3394	298	15	d.	d.	PROPN
ejpam-3394	298	16	paracompactness	paracompactness	PROPN
ejpam-3394	298	17	with	with	ADP
ejpam-3394	298	18	respect	respect	NOUN
ejpam-3394	298	19	to	to	ADP
ejpam-3394	298	20	an	an	DET
ejpam-3394	298	21	ideal	ideal	ADJ
ejpam-3394	298	22	,	,	PUNCT
ejpam-3394	298	23	internat	internat	PROPN
ejpam-3394	298	24	.	.	PUNCT
ejpam-3394	299	1	j.	j.	PROPN
ejpam-3394	299	2	math	math	PROPN
ejpam-3394	299	3	.	.	PUNCT
ejpam-3394	300	1	and	and	CCONJ
ejpam-3394	300	2	math	math	NOUN
ejpam-3394	300	3	.	.	PUNCT
ejpam-3394	301	1	sci	sci	PROPN
ejpam-3394	301	2	.	.	PUNCT
ejpam-3394	302	1	20(3	20(3	NOUN
ejpam-3394	302	2	)	)	PUNCT
ejpam-3394	302	3	,	,	PUNCT
ejpam-3394	302	4	433	433	NUM
ejpam-3394	302	5	-	-	SYM
ejpam-3394	302	6	442	442	NUM
ejpam-3394	302	7	,	,	PUNCT
ejpam-3394	302	8	1997	1997	NUM
ejpam-3394	302	9	.	.	PUNCT
ejpam-3394	303	1	[	[	X
ejpam-3394	303	2	14	14	NUM
ejpam-3394	303	3	]	]	PUNCT
ejpam-3394	303	4	janković	janković	PROPN
ejpam-3394	303	5	,	,	PUNCT
ejpam-3394	303	6	d.	d.	PROPN
ejpam-3394	303	7	and	and	CCONJ
ejpam-3394	303	8	hamlett	hamlett	PROPN
ejpam-3394	303	9	,	,	PUNCT
ejpam-3394	303	10	t.	t.	PROPN
ejpam-3394	303	11	r.	r.	PROPN
ejpam-3394	303	12	new	new	PROPN
ejpam-3394	303	13	topologies	topology	NOUN
ejpam-3394	303	14	from	from	ADP
ejpam-3394	303	15	old	old	ADJ
ejpam-3394	303	16	via	via	ADP
ejpam-3394	303	17	ideals	ideal	NOUN
ejpam-3394	303	18	,	,	PUNCT
ejpam-3394	303	19	amer	amer	PROPN
ejpam-3394	303	20	.	.	PROPN
ejpam-3394	303	21	math	math	PROPN
ejpam-3394	303	22	.	.	PUNCT
ejpam-3394	304	1	montly	montly	ADV
ejpam-3394	304	2	97	97	NUM
ejpam-3394	304	3	,	,	PUNCT
ejpam-3394	304	4	295	295	NUM
ejpam-3394	304	5	-	-	SYM
ejpam-3394	304	6	310	310	NUM
ejpam-3394	304	7	,	,	PUNCT
ejpam-3394	304	8	1990	1990	NUM
ejpam-3394	304	9	.	.	PUNCT
ejpam-3394	305	1	[	[	X
ejpam-3394	305	2	15	15	NUM
ejpam-3394	305	3	]	]	X
ejpam-3394	305	4	kuratowski	kuratowski	PROPN
ejpam-3394	305	5	,	,	PUNCT
ejpam-3394	305	6	k.	k.	PROPN
ejpam-3394	305	7	topologie	topologie	PROPN
ejpam-3394	306	1	i	i	PROPN
ejpam-3394	306	2	,	,	PUNCT
ejpam-3394	306	3	warszawa	warszawa	PROPN
ejpam-3394	306	4	1933	1933	NUM
ejpam-3394	306	5	.	.	PUNCT
ejpam-3394	307	1	[	[	X
ejpam-3394	307	2	16	16	NUM
ejpam-3394	307	3	]	]	X
ejpam-3394	307	4	levine	levine	PROPN
ejpam-3394	307	5	,	,	PUNCT
ejpam-3394	307	6	n.	n.	PROPN
ejpam-3394	307	7	semi	semi	ADJ
ejpam-3394	307	8	-	-	ADJ
ejpam-3394	307	9	open	open	ADJ
ejpam-3394	307	10	sets	set	NOUN
ejpam-3394	307	11	and	and	CCONJ
ejpam-3394	307	12	semi	semi	ADJ
ejpam-3394	307	13	-	-	NOUN
ejpam-3394	307	14	continuity	continuity	NOUN
ejpam-3394	307	15	in	in	ADP
ejpam-3394	307	16	topological	topological	ADJ
ejpam-3394	307	17	spaces	space	NOUN
ejpam-3394	307	18	,	,	PUNCT
ejpam-3394	307	19	amer	amer	PROPN
ejpam-3394	307	20	.	.	PROPN
ejpam-3394	307	21	math	math	PROPN
ejpam-3394	307	22	.	.	PUNCT
ejpam-3394	308	1	monthly	monthly	ADJ
ejpam-3394	308	2	70	70	NUM
ejpam-3394	308	3	,	,	PUNCT
ejpam-3394	308	4	36	36	NUM
ejpam-3394	308	5	-	-	SYM
ejpam-3394	308	6	41	41	NUM
ejpam-3394	308	7	,	,	PUNCT
ejpam-3394	308	8	1963	1963	NUM
ejpam-3394	308	9	.	.	PUNCT
ejpam-3394	309	1	[	[	X
ejpam-3394	309	2	17	17	NUM
ejpam-3394	309	3	]	]	X
ejpam-3394	309	4	mahmoud	mahmoud	PROPN
ejpam-3394	309	5	,	,	PUNCT
ejpam-3394	309	6	r.	r.	PROPN
ejpam-3394	309	7	a.	a.	PROPN
ejpam-3394	309	8	and	and	CCONJ
ejpam-3394	309	9	abd	abd	PROPN
ejpam-3394	309	10	el	el	PROPN
ejpam-3394	309	11	-	-	PUNCT
ejpam-3394	309	12	monsef	monsef	ADJ
ejpam-3394	309	13	,	,	PUNCT
ejpam-3394	309	14	m.	m.	PROPN
ejpam-3394	309	15	e.	e.	PROPN
ejpam-3394	309	16	β	β	PROPN
ejpam-3394	309	17	-	-	NOUN
ejpam-3394	309	18	irresolute	irresolute	ADJ
ejpam-3394	309	19	and	and	CCONJ
ejpam-3394	309	20	β	β	NOUN
ejpam-3394	309	21	-	-	ADJ
ejpam-3394	309	22	topological	topological	ADJ
ejpam-3394	309	23	invariant	invariant	ADJ
ejpam-3394	309	24	,	,	PUNCT
ejpam-3394	309	25	proc	proc	NOUN
ejpam-3394	309	26	.	.	PUNCT
ejpam-3394	310	1	pakistan	pakistan	PROPN
ejpam-3394	310	2	acad	acad	PROPN
ejpam-3394	310	3	.	.	PUNCT
ejpam-3394	311	1	sci	sci	PROPN
ejpam-3394	311	2	.	.	PROPN
ejpam-3394	311	3	27	27	NUM
ejpam-3394	311	4	,	,	PUNCT
ejpam-3394	311	5	285296	285296	NUM
ejpam-3394	311	6	,	,	PUNCT
ejpam-3394	311	7	1990	1990	NUM
ejpam-3394	311	8	.	.	PUNCT
ejpam-3394	312	1	[	[	X
ejpam-3394	312	2	18	18	NUM
ejpam-3394	312	3	]	]	X
ejpam-3394	312	4	mashhour	mashhour	PROPN
ejpam-3394	312	5	,	,	PUNCT
ejpam-3394	312	6	a.s	a.s	PROPN
ejpam-3394	312	7	.	.	PROPN
ejpam-3394	312	8	,	,	PUNCT
ejpam-3394	312	9	abd	abd	PROPN
ejpam-3394	312	10	el	el	PROPN
ejpam-3394	312	11	-	-	PUNCT
ejpam-3394	312	12	monsef	monsef	ADJ
ejpam-3394	312	13	,	,	PUNCT
ejpam-3394	312	14	m.	m.	PROPN
ejpam-3394	312	15	e.	e.	PROPN
ejpam-3394	312	16	and	and	CCONJ
ejpam-3394	312	17	el	el	PROPN
ejpam-3394	312	18	-	-	PUNCT
ejpam-3394	312	19	deeb	deeb	PROPN
ejpam-3394	312	20	,	,	PUNCT
ejpam-3394	312	21	s.	s.	PROPN
ejpam-3394	312	22	n.	n.	PROPN
ejpam-3394	312	23	on	on	ADP
ejpam-3394	312	24	precontinuous	precontinuous	ADJ
ejpam-3394	312	25	and	and	CCONJ
ejpam-3394	312	26	weak	weak	ADJ
ejpam-3394	312	27	precontinuous	precontinuous	ADJ
ejpam-3394	312	28	mappings	mapping	NOUN
ejpam-3394	312	29	,	,	PUNCT
ejpam-3394	312	30	proc	proc	NOUN
ejpam-3394	312	31	.	.	PUNCT
ejpam-3394	313	1	math	math	NOUN
ejpam-3394	313	2	.	.	PUNCT
ejpam-3394	314	1	and	and	CCONJ
ejpam-3394	314	2	phys	phy	NOUN
ejpam-3394	314	3	.	.	PUNCT
ejpam-3394	315	1	soc	soc	PROPN
ejpam-3394	315	2	.	.	PUNCT
ejpam-3394	316	1	egypt	egypt	PROPN
ejpam-3394	316	2	51	51	NUM
ejpam-3394	316	3	,	,	PUNCT
ejpam-3394	316	4	47	47	NUM
ejpam-3394	316	5	-	-	SYM
ejpam-3394	316	6	53	53	NUM
ejpam-3394	316	7	,	,	PUNCT
ejpam-3394	316	8	1981	1981	NUM
ejpam-3394	316	9	.	.	PUNCT
ejpam-3394	317	1	[	[	X
ejpam-3394	317	2	19	19	NUM
ejpam-3394	317	3	]	]	SYM
ejpam-3394	317	4	navalagi	navalagi	PROPN
ejpam-3394	317	5	,	,	PUNCT
ejpam-3394	317	6	g.	g.	PROPN
ejpam-3394	317	7	b.	b.	PROPN
ejpam-3394	317	8	semi	semi	ADJ
ejpam-3394	317	9	-	-	ADJ
ejpam-3394	317	10	precontinuous	precontinuous	ADJ
ejpam-3394	317	11	functions	function	NOUN
ejpam-3394	317	12	and	and	CCONJ
ejpam-3394	317	13	properties	property	NOUN
ejpam-3394	317	14	of	of	ADP
ejpam-3394	317	15	generalized	generalized	ADJ
ejpam-3394	317	16	preclosed	preclose	VERB
ejpam-3394	317	17	sets	set	NOUN
ejpam-3394	317	18	in	in	ADP
ejpam-3394	317	19	topological	topological	ADJ
ejpam-3394	317	20	spaces	space	NOUN
ejpam-3394	317	21	,	,	PUNCT
ejpam-3394	317	22	int	int	NOUN
ejpam-3394	317	23	.	.	PUNCT
ejpam-3394	318	1	j.	j.	PROPN
ejpam-3394	318	2	math	math	PROPN
ejpam-3394	318	3	.	.	PUNCT
ejpam-3394	319	1	math	math	NOUN
ejpam-3394	319	2	.	.	PUNCT
ejpam-3394	320	1	sci	sci	PROPN
ejpam-3394	320	2	.	.	PROPN
ejpam-3394	320	3	29	29	NUM
ejpam-3394	320	4	,	,	PUNCT
ejpam-3394	320	5	85	85	NUM
ejpam-3394	320	6	-	-	SYM
ejpam-3394	320	7	98	98	NUM
ejpam-3394	320	8	,	,	PUNCT
ejpam-3394	320	9	2002	2002	NUM
ejpam-3394	320	10	.	.	PUNCT
ejpam-3394	321	1	[	[	X
ejpam-3394	321	2	20	20	NUM
ejpam-3394	321	3	]	]	X
ejpam-3394	321	4	reilly	reilly	PROPN
ejpam-3394	321	5	,	,	PUNCT
ejpam-3394	321	6	i.	i.	PROPN
ejpam-3394	321	7	l.	l.	PROPN
ejpam-3394	321	8	and	and	CCONJ
ejpam-3394	321	9	vamanamurthy	vamanamurthy	NOUN
ejpam-3394	321	10	,	,	PUNCT
ejpam-3394	321	11	m.	m.	NOUN
ejpam-3394	321	12	k.	k.	PROPN
ejpam-3394	322	1	on	on	ADP
ejpam-3394	322	2	some	some	DET
ejpam-3394	322	3	questions	question	NOUN
ejpam-3394	322	4	concerning	concern	VERB
ejpam-3394	322	5	preopen	preopen	ADJ
ejpam-3394	322	6	sets	set	NOUN
ejpam-3394	322	7	,	,	PUNCT
ejpam-3394	322	8	kyungpook	kyungpook	NOUN
ejpam-3394	322	9	math	math	NOUN
ejpam-3394	322	10	.	.	PUNCT
ejpam-3394	323	1	j.	j.	PROPN
ejpam-3394	323	2	30	30	PROPN
ejpam-3394	323	3	,	,	PUNCT
ejpam-3394	323	4	87	87	NUM
ejpam-3394	323	5	-	-	SYM
ejpam-3394	323	6	93	93	NUM
ejpam-3394	323	7	,	,	PUNCT
ejpam-3394	323	8	1990	1990	NUM
ejpam-3394	323	9	.	.	PUNCT
ejpam-3394	324	1	[	[	X
ejpam-3394	324	2	21	21	NUM
ejpam-3394	324	3	]	]	X
ejpam-3394	324	4	sanabria	sanabria	PROPN
ejpam-3394	324	5	,	,	PUNCT
ejpam-3394	324	6	j.	j.	PROPN
ejpam-3394	324	7	,	,	PUNCT
ejpam-3394	324	8	rosas	rosas	PROPN
ejpam-3394	324	9	,	,	PUNCT
ejpam-3394	324	10	e.	e.	PROPN
ejpam-3394	324	11	,	,	PUNCT
ejpam-3394	324	12	carpintero	carpintero	PROPN
ejpam-3394	324	13	,	,	PUNCT
ejpam-3394	324	14	c.	c.	PROPN
ejpam-3394	324	15	,	,	PUNCT
ejpam-3394	324	16	salas	salas	NOUN
ejpam-3394	324	17	-	-	PUNCT
ejpam-3394	324	18	brown	brown	ADJ
ejpam-3394	324	19	,	,	PUNCT
ejpam-3394	324	20	m.	m.	NOUN
ejpam-3394	324	21	and	and	CCONJ
ejpam-3394	324	22	garćıa	garćıa	NOUN
ejpam-3394	324	23	,	,	PUNCT
ejpam-3394	324	24	o.	o.	NOUN
ejpam-3394	324	25	sparacompactness	sparacompactness	ADJ
ejpam-3394	324	26	in	in	ADP
ejpam-3394	324	27	ideal	ideal	ADJ
ejpam-3394	324	28	topological	topological	ADJ
ejpam-3394	324	29	spaces	space	NOUN
ejpam-3394	324	30	,	,	PUNCT
ejpam-3394	324	31	mat	mat	PROPN
ejpam-3394	324	32	.	.	PROPN
ejpam-3394	324	33	vesnik	vesnik	PROPN
ejpam-3394	324	34	68(3	68(3	NUM
ejpam-3394	324	35	)	)	PUNCT
ejpam-3394	324	36	,	,	PUNCT
ejpam-3394	324	37	192203	192203	NUM
ejpam-3394	324	38	,	,	PUNCT
ejpam-3394	324	39	2016	2016	NUM
ejpam-3394	324	40	.	.	PUNCT
ejpam-3394	325	1	[	[	X
ejpam-3394	325	2	22	22	NUM
ejpam-3394	325	3	]	]	PUNCT
ejpam-3394	325	4	sathiyasundari	sathiyasundari	PROPN
ejpam-3394	325	5	,	,	PUNCT
ejpam-3394	325	6	n.	n.	NOUN
ejpam-3394	325	7	and	and	CCONJ
ejpam-3394	325	8	renukadevi	renukadevi	NOUN
ejpam-3394	325	9	,	,	PUNCT
ejpam-3394	325	10	v.	v.	CCONJ
ejpam-3394	325	11	paracompactness	paracompactness	NOUN
ejpam-3394	325	12	with	with	ADP
ejpam-3394	325	13	respect	respect	NOUN
ejpam-3394	325	14	to	to	ADP
ejpam-3394	325	15	an	an	DET
ejpam-3394	325	16	ideal	ideal	NOUN
ejpam-3394	325	17	,	,	PUNCT
ejpam-3394	325	18	filomat	filomat	PROPN
ejpam-3394	325	19	27(2	27(2	NUM
ejpam-3394	325	20	)	)	PUNCT
ejpam-3394	325	21	,	,	PUNCT
ejpam-3394	325	22	333	333	NUM
ejpam-3394	325	23	-	-	SYM
ejpam-3394	325	24	339	339	NUM
ejpam-3394	325	25	,	,	PUNCT
ejpam-3394	325	26	2013	2013	NUM
ejpam-3394	325	27	.	.	PUNCT
ejpam-3394	326	1	[	[	X
ejpam-3394	326	2	23	23	NUM
ejpam-3394	326	3	]	]	X
ejpam-3394	326	4	willard	willard	NOUN
ejpam-3394	326	5	,	,	PUNCT
ejpam-3394	326	6	s.	s.	PROPN
ejpam-3394	326	7	general	general	PROPN
ejpam-3394	326	8	topology	topology	PROPN
ejpam-3394	326	9	,	,	PUNCT
ejpam-3394	326	10	addison	addison	PROPN
ejpam-3394	326	11	-	-	PUNCT
ejpam-3394	326	12	wesley	wesley	PROPN
ejpam-3394	326	13	publishing	publishing	PROPN
ejpam-3394	326	14	company	company	NOUN
ejpam-3394	326	15	1970	1970	NUM
ejpam-3394	326	16	.	.	PUNCT
ejpam-3394	327	1	[	[	X
ejpam-3394	327	2	24	24	NUM
ejpam-3394	327	3	]	]	X
ejpam-3394	327	4	zahid	zahid	PROPN
ejpam-3394	327	5	,	,	PUNCT
ejpam-3394	327	6	m.	m.	NOUN
ejpam-3394	327	7	i.	i.	PROPN
ejpam-3394	327	8	para	para	PROPN
ejpam-3394	327	9	h	h	PROPN
ejpam-3394	327	10	-	-	PUNCT
ejpam-3394	327	11	closed	closed	ADJ
ejpam-3394	327	12	spaces	space	NOUN
ejpam-3394	327	13	,	,	PUNCT
ejpam-3394	327	14	locally	locally	ADV
ejpam-3394	327	15	para	para	ADJ
ejpam-3394	327	16	h	h	NOUN
ejpam-3394	327	17	-	-	PUNCT
ejpam-3394	327	18	closed	closed	ADJ
ejpam-3394	327	19	spaces	space	NOUN
ejpam-3394	327	20	and	and	CCONJ
ejpam-3394	327	21	their	their	PRON
ejpam-3394	327	22	minimal	minimal	ADJ
ejpam-3394	327	23	topologies	topology	NOUN
ejpam-3394	327	24	,	,	PUNCT
ejpam-3394	327	25	ph	ph	PROPN
ejpam-3394	327	26	.	.	PROPN
ejpam-3394	327	27	d.	d.	PROPN
ejpam-3394	327	28	dissertation	dissertation	PROPN
ejpam-3394	327	29	,	,	PUNCT
ejpam-3394	327	30	univ	univ	PROPN
ejpam-3394	327	31	.	.	PROPN
ejpam-3394	327	32	of	of	ADP
ejpam-3394	327	33	pittsburgh	pittsburgh	PROPN
ejpam-3394	327	34	1981	1981	NUM
ejpam-3394	327	35	.	.	PUNCT