id	sid	tid	token	lemma	pos
ejpam-5426	1	1	european	european	PROPN
ejpam-5426	1	2	journal	journal	PROPN
ejpam-5426	1	3	of	of	ADP
ejpam-5426	1	4	pure	pure	ADJ
ejpam-5426	1	5	and	and	CCONJ
ejpam-5426	1	6	applied	apply	VERB
ejpam-5426	1	7	mathematics	mathematic	NOUN
ejpam-5426	1	8	vol	vol	NOUN
ejpam-5426	1	9	.	.	PROPN
ejpam-5426	2	1	17	17	NUM
ejpam-5426	2	2	,	,	PUNCT
ejpam-5426	2	3	no	no	INTJ
ejpam-5426	2	4	.	.	NOUN
ejpam-5426	2	5	4	4	NUM
ejpam-5426	2	6	,	,	PUNCT
ejpam-5426	2	7	2024	2024	NUM
ejpam-5426	2	8	,	,	PUNCT
ejpam-5426	2	9	2990	2990	NUM
ejpam-5426	2	10	-	-	SYM
ejpam-5426	2	11	3003	3003	NUM
ejpam-5426	2	12	issn	issn	PROPN
ejpam-5426	2	13	1307	1307	NUM
ejpam-5426	2	14	-	-	SYM
ejpam-5426	2	15	5543	5543	NUM
ejpam-5426	2	16	–	–	PUNCT
ejpam-5426	3	1	ejpam.com	ejpam.com	X
ejpam-5426	3	2	published	publish	VERB
ejpam-5426	3	3	by	by	ADP
ejpam-5426	3	4	new	new	PROPN
ejpam-5426	3	5	york	york	PROPN
ejpam-5426	3	6	business	business	PROPN
ejpam-5426	3	7	global	global	ADJ
ejpam-5426	3	8	new	new	ADJ
ejpam-5426	3	9	results	result	NOUN
ejpam-5426	3	10	on	on	ADP
ejpam-5426	3	11	difference	difference	NOUN
ejpam-5426	3	12	paracompactness	paracompactness	NOUN
ejpam-5426	3	13	in	in	ADP
ejpam-5426	3	14	topological	topological	ADJ
ejpam-5426	3	15	spaces	space	NOUN
ejpam-5426	3	16	rahmeh	rahmeh	NOUN
ejpam-5426	3	17	alrababah1	alrababah1	PROPN
ejpam-5426	3	18	,	,	PUNCT
ejpam-5426	3	19	ala	ala	PROPN
ejpam-5426	3	20	amourah2,3,∗	amourah2,3,∗	PROPN
ejpam-5426	3	21	,	,	PUNCT
ejpam-5426	3	22	jamal	jamal	PROPN
ejpam-5426	3	23	salah4,∗	salah4,∗	PROPN
ejpam-5426	3	24	,	,	PUNCT
ejpam-5426	3	25	reyaz	reyaz	PROPN
ejpam-5426	3	26	ahmad5	ahmad5	PROPN
ejpam-5426	3	27	,	,	PUNCT
ejpam-5426	3	28	ali	ali	PROPN
ejpam-5426	3	29	a.	a.	PROPN
ejpam-5426	3	30	atoom1	atoom1	PROPN
ejpam-5426	3	31	1	1	NUM
ejpam-5426	3	32	ajloun	ajloun	PROPN
ejpam-5426	3	33	national	national	PROPN
ejpam-5426	3	34	previate	previate	PROPN
ejpam-5426	3	35	university	university	PROPN
ejpam-5426	3	36	,	,	PUNCT
ejpam-5426	3	37	college	college	NOUN
ejpam-5426	3	38	of	of	ADP
ejpam-5426	3	39	science	science	NOUN
ejpam-5426	3	40	,	,	PUNCT
ejpam-5426	3	41	department	department	NOUN
ejpam-5426	3	42	of	of	ADP
ejpam-5426	3	43	mathematics	mathematics	PROPN
ejpam-5426	3	44	,	,	PUNCT
ejpam-5426	3	45	jordan	jordan	PROPN
ejpam-5426	3	46	2	2	NUM
ejpam-5426	3	47	mathematics	mathematics	PROPN
ejpam-5426	3	48	education	education	NOUN
ejpam-5426	3	49	program	program	NOUN
ejpam-5426	3	50	,	,	PUNCT
ejpam-5426	3	51	faculty	faculty	NOUN
ejpam-5426	3	52	of	of	ADP
ejpam-5426	3	53	education	education	NOUN
ejpam-5426	3	54	and	and	CCONJ
ejpam-5426	3	55	arts	art	NOUN
ejpam-5426	3	56	,	,	PUNCT
ejpam-5426	3	57	sohar	sohar	PROPN
ejpam-5426	3	58	university	university	PROPN
ejpam-5426	3	59	,	,	PUNCT
ejpam-5426	3	60	sohar	sohar	PROPN
ejpam-5426	3	61	3111	3111	PROPN
ejpam-5426	3	62	,	,	PUNCT
ejpam-5426	3	63	oman	oman	NOUN
ejpam-5426	3	64	3	3	NUM
ejpam-5426	3	65	applied	apply	VERB
ejpam-5426	3	66	science	science	NOUN
ejpam-5426	3	67	research	research	NOUN
ejpam-5426	3	68	center	center	NOUN
ejpam-5426	3	69	,	,	PUNCT
ejpam-5426	3	70	applied	apply	VERB
ejpam-5426	3	71	science	science	NOUN
ejpam-5426	3	72	private	private	ADJ
ejpam-5426	3	73	university	university	NOUN
ejpam-5426	3	74	,	,	PUNCT
ejpam-5426	3	75	amman	amman	PROPN
ejpam-5426	3	76	,	,	PUNCT
ejpam-5426	3	77	jordan	jordan	PROPN
ejpam-5426	3	78	4	4	NUM
ejpam-5426	3	79	college	college	NOUN
ejpam-5426	3	80	of	of	ADP
ejpam-5426	3	81	applied	apply	VERB
ejpam-5426	3	82	and	and	CCONJ
ejpam-5426	3	83	health	health	NOUN
ejpam-5426	3	84	sciences	science	NOUN
ejpam-5426	3	85	,	,	PUNCT
ejpam-5426	3	86	a’sharqiyah	a’sharqiyah	PROPN
ejpam-5426	3	87	university	university	NOUN
ejpam-5426	3	88	,	,	PUNCT
ejpam-5426	4	1	post	post	PROPN
ejpam-5426	4	2	box	box	PROPN
ejpam-5426	4	3	no	no	INTJ
ejpam-5426	4	4	.	.	PROPN
ejpam-5426	4	5	42	42	NUM
ejpam-5426	4	6	,	,	PUNCT
ejpam-5426	4	7	post	post	VERB
ejpam-5426	4	8	code	code	NOUN
ejpam-5426	4	9	no	no	INTJ
ejpam-5426	4	10	.	.	NOUN
ejpam-5426	4	11	400	400	NUM
ejpam-5426	4	12	ibra	ibra	NOUN
ejpam-5426	4	13	,	,	PUNCT
ejpam-5426	4	14	sultanate	sultanate	NOUN
ejpam-5426	4	15	of	of	ADP
ejpam-5426	4	16	oman	oman	PROPN
ejpam-5426	4	17	5	5	NUM
ejpam-5426	4	18	skyline	skyline	PROPN
ejpam-5426	4	19	university	university	PROPN
ejpam-5426	4	20	college	college	PROPN
ejpam-5426	4	21	of	of	ADP
ejpam-5426	4	22	sharjah	sharjah	PROPN
ejpam-5426	4	23	,	,	PUNCT
ejpam-5426	4	24	department	department	PROPN
ejpam-5426	4	25	of	of	ADP
ejpam-5426	4	26	general	general	ADJ
ejpam-5426	4	27	education	education	PROPN
ejpam-5426	4	28	,	,	PUNCT
ejpam-5426	4	29	united	united	PROPN
ejpam-5426	4	30	arab	arab	PROPN
ejpam-5426	4	31	emirates	emirates	PROPN
ejpam-5426	4	32	abstract	abstract	PROPN
ejpam-5426	4	33	.	.	PUNCT
ejpam-5426	5	1	an	an	DET
ejpam-5426	5	2	interesting	interesting	ADJ
ejpam-5426	5	3	area	area	NOUN
ejpam-5426	5	4	of	of	ADP
ejpam-5426	5	5	research	research	NOUN
ejpam-5426	5	6	in	in	ADP
ejpam-5426	5	7	topology	topology	NOUN
ejpam-5426	5	8	is	be	AUX
ejpam-5426	5	9	d−paracompact	d−paracompact	PROPN
ejpam-5426	5	10	spaces	space	NOUN
ejpam-5426	5	11	.	.	PUNCT
ejpam-5426	6	1	it	it	PRON
ejpam-5426	6	2	is	be	AUX
ejpam-5426	6	3	a	a	DET
ejpam-5426	6	4	significant	significant	ADJ
ejpam-5426	6	5	type	type	NOUN
ejpam-5426	6	6	of	of	ADP
ejpam-5426	6	7	topological	topological	ADJ
ejpam-5426	6	8	spaces	space	NOUN
ejpam-5426	6	9	that	that	PRON
ejpam-5426	6	10	retain	retain	VERB
ejpam-5426	6	11	compactness	compactness	NOUN
ejpam-5426	6	12	while	while	SCONJ
ejpam-5426	6	13	benefiting	benefit	VERB
ejpam-5426	6	14	from	from	ADP
ejpam-5426	6	15	paracompactness	paracompactness	NOUN
ejpam-5426	6	16	,	,	PUNCT
ejpam-5426	6	17	which	which	PRON
ejpam-5426	6	18	is	be	AUX
ejpam-5426	6	19	considered	consider	VERB
ejpam-5426	6	20	a	a	DET
ejpam-5426	6	21	generalisation	generalisation	NOUN
ejpam-5426	6	22	of	of	ADP
ejpam-5426	6	23	compact	compact	ADJ
ejpam-5426	6	24	spaces	space	NOUN
ejpam-5426	6	25	.	.	PUNCT
ejpam-5426	7	1	the	the	DET
ejpam-5426	7	2	concept	concept	NOUN
ejpam-5426	7	3	ofd−paracompactness	ofd−paracompactnes	VERB
ejpam-5426	7	4	was	be	AUX
ejpam-5426	7	5	introduced	introduce	VERB
ejpam-5426	7	6	,	,	PUNCT
ejpam-5426	7	7	and	and	CCONJ
ejpam-5426	7	8	its	its	PRON
ejpam-5426	7	9	basic	basic	ADJ
ejpam-5426	7	10	characteristics	characteristic	NOUN
ejpam-5426	7	11	were	be	AUX
ejpam-5426	7	12	examined	examine	VERB
ejpam-5426	7	13	by	by	ADP
ejpam-5426	7	14	the	the	DET
ejpam-5426	7	15	author	author	NOUN
ejpam-5426	7	16	in	in	ADP
ejpam-5426	7	17	[	[	X
ejpam-5426	7	18	18	18	NUM
ejpam-5426	7	19	]	]	PUNCT
ejpam-5426	7	20	.	.	PUNCT
ejpam-5426	8	1	in	in	ADP
ejpam-5426	8	2	this	this	DET
ejpam-5426	8	3	research	research	NOUN
ejpam-5426	8	4	,	,	PUNCT
ejpam-5426	8	5	we	we	PRON
ejpam-5426	8	6	introduce	introduce	VERB
ejpam-5426	8	7	and	and	CCONJ
ejpam-5426	8	8	improve	improve	VERB
ejpam-5426	8	9	this	this	DET
ejpam-5426	8	10	concept	concept	NOUN
ejpam-5426	8	11	further	far	ADV
ejpam-5426	8	12	by	by	ADP
ejpam-5426	8	13	using	use	VERB
ejpam-5426	8	14	a	a	DET
ejpam-5426	8	15	special	special	ADJ
ejpam-5426	8	16	type	type	NOUN
ejpam-5426	8	17	of	of	ADP
ejpam-5426	8	18	covering	covering	NOUN
ejpam-5426	8	19	and	and	CCONJ
ejpam-5426	8	20	the	the	DET
ejpam-5426	8	21	difference	difference	NOUN
ejpam-5426	8	22	sets	set	NOUN
ejpam-5426	8	23	(	(	PUNCT
ejpam-5426	8	24	called	call	VERB
ejpam-5426	8	25	d−sets	d−set	NOUN
ejpam-5426	8	26	)	)	PUNCT
ejpam-5426	8	27	,	,	PUNCT
ejpam-5426	8	28	which	which	PRON
ejpam-5426	8	29	contain	contain	VERB
ejpam-5426	8	30	new	new	ADJ
ejpam-5426	8	31	and	and	CCONJ
ejpam-5426	8	32	impact	impact	NOUN
ejpam-5426	8	33	properties	property	NOUN
ejpam-5426	8	34	.	.	PUNCT
ejpam-5426	9	1	as	as	ADP
ejpam-5426	9	2	a	a	DET
ejpam-5426	9	3	result	result	NOUN
ejpam-5426	9	4	,	,	PUNCT
ejpam-5426	9	5	we	we	PRON
ejpam-5426	9	6	obtained	obtain	VERB
ejpam-5426	9	7	several	several	ADJ
ejpam-5426	9	8	new	new	ADJ
ejpam-5426	9	9	properties	property	NOUN
ejpam-5426	9	10	and	and	CCONJ
ejpam-5426	9	11	results	result	NOUN
ejpam-5426	9	12	.	.	PUNCT
ejpam-5426	10	1	we	we	PRON
ejpam-5426	10	2	discuss	discuss	VERB
ejpam-5426	10	3	the	the	DET
ejpam-5426	10	4	concept	concept	NOUN
ejpam-5426	10	5	,	,	PUNCT
ejpam-5426	10	6	characteristics	characteristic	NOUN
ejpam-5426	10	7	,	,	PUNCT
ejpam-5426	10	8	and	and	CCONJ
ejpam-5426	10	9	theorems	theorem	NOUN
ejpam-5426	10	10	that	that	SCONJ
ejpam-5426	10	11	related	relate	VERB
ejpam-5426	10	12	of	of	ADP
ejpam-5426	10	13	d−paracompact	d−paracompact	PROPN
ejpam-5426	10	14	space	space	NOUN
ejpam-5426	10	15	.	.	PUNCT
ejpam-5426	11	1	we	we	PRON
ejpam-5426	11	2	also	also	ADV
ejpam-5426	11	3	studied	study	VERB
ejpam-5426	11	4	different	different	ADJ
ejpam-5426	11	5	characterizations	characterization	NOUN
ejpam-5426	11	6	of	of	ADP
ejpam-5426	11	7	d−paracompact	d−paracompact	PROPN
ejpam-5426	11	8	spaces	space	NOUN
ejpam-5426	11	9	and	and	CCONJ
ejpam-5426	11	10	discussed	discuss	VERB
ejpam-5426	11	11	how	how	SCONJ
ejpam-5426	11	12	they	they	PRON
ejpam-5426	11	13	relate	relate	VERB
ejpam-5426	11	14	to	to	ADP
ejpam-5426	11	15	other	other	ADJ
ejpam-5426	11	16	topological	topological	ADJ
ejpam-5426	11	17	characteristics	characteristic	NOUN
ejpam-5426	11	18	.	.	PUNCT
ejpam-5426	12	1	we	we	PRON
ejpam-5426	12	2	also	also	ADV
ejpam-5426	12	3	give	give	VERB
ejpam-5426	12	4	numerous	numerous	ADJ
ejpam-5426	12	5	instances	instance	NOUN
ejpam-5426	12	6	ofd−paracompact	ofd−paracompact	NOUN
ejpam-5426	12	7	spaces	space	NOUN
ejpam-5426	12	8	along	along	ADP
ejpam-5426	12	9	with	with	ADP
ejpam-5426	12	10	highlighting	highlight	VERB
ejpam-5426	12	11	their	their	PRON
ejpam-5426	12	12	applicability	applicability	NOUN
ejpam-5426	12	13	in	in	ADP
ejpam-5426	12	14	different	different	ADJ
ejpam-5426	12	15	topological	topological	ADJ
ejpam-5426	12	16	spaces	space	NOUN
ejpam-5426	12	17	.	.	PUNCT
ejpam-5426	13	1	2020	2020	NUM
ejpam-5426	13	2	mathematics	mathematic	NOUN
ejpam-5426	13	3	subject	subject	NOUN
ejpam-5426	13	4	classifications	classification	NOUN
ejpam-5426	13	5	:	:	PUNCT
ejpam-5426	13	6	54b05	54b05	NUM
ejpam-5426	13	7	,	,	PUNCT
ejpam-5426	13	8	54b10	54b10	NUM
ejpam-5426	13	9	,	,	PUNCT
ejpam-5426	13	10	54c05	54c05	NUM
ejpam-5426	13	11	,	,	PUNCT
ejpam-5426	13	12	54d05	54d05	NUM
ejpam-5426	13	13	,	,	PUNCT
ejpam-5426	13	14	54d10	54d10	NUM
ejpam-5426	13	15	,	,	PUNCT
ejpam-5426	13	16	54d30	54d30	NUM
ejpam-5426	13	17	,	,	PUNCT
ejpam-5426	13	18	54e55	54e55	NUM
ejpam-5426	13	19	key	key	ADJ
ejpam-5426	13	20	words	word	NOUN
ejpam-5426	13	21	and	and	CCONJ
ejpam-5426	13	22	phrases	phrase	NOUN
ejpam-5426	13	23	:	:	PUNCT
ejpam-5426	13	24	topological	topological	ADJ
ejpam-5426	13	25	spaces	space	NOUN
ejpam-5426	13	26	,	,	PUNCT
ejpam-5426	13	27	paracompact	paracompact	ADJ
ejpam-5426	13	28	spaces	space	NOUN
ejpam-5426	13	29	,	,	PUNCT
ejpam-5426	13	30	d−paracompact	d−paracompact	PROPN
ejpam-5426	13	31	spaces	space	NOUN
ejpam-5426	13	32	,	,	PUNCT
ejpam-5426	13	33	countably	countably	ADV
ejpam-5426	13	34	d−paracompact	d−paracompact	AUX
ejpam-5426	13	35	spaces	space	NOUN
ejpam-5426	13	36	∗corresponding	∗corresponde	VERB
ejpam-5426	13	37	author	author	NOUN
ejpam-5426	13	38	.	.	PUNCT
ejpam-5426	14	1	∗corresponding	∗corresponde	VERB
ejpam-5426	14	2	author	author	NOUN
ejpam-5426	14	3	.	.	PUNCT
ejpam-5426	15	1	doi	doi	NOUN
ejpam-5426	15	2	:	:	PUNCT
ejpam-5426	15	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5426	https://doi.org/10.29020/nybg.ejpam.v17i4.5426	NUM
ejpam-5426	15	4	email	email	NOUN
ejpam-5426	15	5	addresses	address	NOUN
ejpam-5426	15	6	:	:	PUNCT
ejpam-5426	15	7	rrr.ra2020r@gmail.com	rrr.ra2020r@gmail.com	X
ejpam-5426	15	8	(	(	PUNCT
ejpam-5426	15	9	r.	r.	PROPN
ejpam-5426	15	10	alrababah	alrababah	PROPN
ejpam-5426	15	11	)	)	PUNCT
ejpam-5426	15	12	,	,	PUNCT
ejpam-5426	15	13	aamourah@su.edu.om	aamourah@su.edu.om	NOUN
ejpam-5426	15	14	(	(	PUNCT
ejpam-5426	15	15	a.	a.	NOUN
ejpam-5426	15	16	amourah	amourah	PROPN
ejpam-5426	15	17	)	)	PUNCT
ejpam-5426	15	18	,	,	PUNCT
ejpam-5426	15	19	damous73@yahoo.com	damous73@yahoo.com	X
ejpam-5426	15	20	(	(	PUNCT
ejpam-5426	15	21	j.	j.	PROPN
ejpam-5426	15	22	salah	salah	PROPN
ejpam-5426	15	23	)	)	PUNCT
ejpam-5426	15	24	,	,	PUNCT
ejpam-5426	15	25	aliatoom@anu.edu.jo	aliatoom@anu.edu.jo	NOUN
ejpam-5426	15	26	(	(	PUNCT
ejpam-5426	15	27	a.	a.	NOUN
ejpam-5426	15	28	atoom	atoom	PROPN
ejpam-5426	15	29	)	)	PUNCT
ejpam-5426	15	30	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5426	16	1	2990	2990	NUM
ejpam-5426	17	1	copyright	copyright	NOUN
ejpam-5426	17	2	:	:	PUNCT
ejpam-5426	17	3	©	©	PROPN
ejpam-5426	17	4	2024	2024	NUM
ejpam-5426	17	5	the	the	DET
ejpam-5426	17	6	author(s	author(s	NOUN
ejpam-5426	17	7	)	)	PUNCT
ejpam-5426	17	8	.	.	PUNCT
ejpam-5426	18	1	(	(	PUNCT
ejpam-5426	18	2	cc	cc	NOUN
ejpam-5426	18	3	by	by	ADP
ejpam-5426	18	4	-	-	PUNCT
ejpam-5426	18	5	nc	nc	PROPN
ejpam-5426	18	6	4.0	4.0	NUM
ejpam-5426	18	7	)	)	PUNCT
ejpam-5426	18	8	a.	a.	NOUN
ejpam-5426	18	9	amourah	amourah	PROPN
ejpam-5426	18	10	et	et	PROPN
ejpam-5426	18	11	al	al	PROPN
ejpam-5426	18	12	.	.	PUNCT
ejpam-5426	18	13	/	/	SYM
ejpam-5426	18	14	eur	eur	PROPN
ejpam-5426	18	15	.	.	PUNCT
ejpam-5426	19	1	j.	j.	PROPN
ejpam-5426	19	2	pure	pure	PROPN
ejpam-5426	19	3	appl	appl	PROPN
ejpam-5426	19	4	.	.	PROPN
ejpam-5426	19	5	math	math	PROPN
ejpam-5426	19	6	,	,	PUNCT
ejpam-5426	19	7	17	17	NUM
ejpam-5426	19	8	(	(	PUNCT
ejpam-5426	19	9	4	4	NUM
ejpam-5426	19	10	)	)	PUNCT
ejpam-5426	19	11	(	(	PUNCT
ejpam-5426	19	12	2024	2024	NUM
ejpam-5426	19	13	)	)	PUNCT
ejpam-5426	19	14	,	,	PUNCT
ejpam-5426	19	15	2990	2990	NUM
ejpam-5426	19	16	-	-	SYM
ejpam-5426	19	17	3003	3003	NUM
ejpam-5426	19	18	2991	2991	NUM
ejpam-5426	19	19	1	1	NUM
ejpam-5426	19	20	.	.	PUNCT
ejpam-5426	20	1	overview	overview	NOUN
ejpam-5426	20	2	of	of	ADP
ejpam-5426	20	3	the	the	DET
ejpam-5426	20	4	historical	historical	ADJ
ejpam-5426	20	5	developments	development	NOUN
ejpam-5426	20	6	and	and	CCONJ
ejpam-5426	20	7	progress	progress	NOUN
ejpam-5426	20	8	soon	soon	ADV
ejpam-5426	20	9	after	after	ADP
ejpam-5426	20	10	the	the	DET
ejpam-5426	20	11	notion	notion	NOUN
ejpam-5426	20	12	of	of	ADP
ejpam-5426	20	13	paracompact	paracompact	ADJ
ejpam-5426	20	14	spaces	space	NOUN
ejpam-5426	20	15	was	be	AUX
ejpam-5426	20	16	introduced	introduce	VERB
ejpam-5426	20	17	,	,	PUNCT
ejpam-5426	20	18	several	several	ADJ
ejpam-5426	20	19	articles	article	NOUN
ejpam-5426	20	20	were	be	AUX
ejpam-5426	20	21	published	publish	VERB
ejpam-5426	20	22	that	that	PRON
ejpam-5426	20	23	examine	examine	VERB
ejpam-5426	20	24	the	the	DET
ejpam-5426	20	25	idea	idea	NOUN
ejpam-5426	20	26	from	from	ADP
ejpam-5426	20	27	various	various	ADJ
ejpam-5426	20	28	angles	angle	NOUN
ejpam-5426	20	29	and	and	CCONJ
ejpam-5426	20	30	tools	tool	NOUN
ejpam-5426	20	31	.	.	PUNCT
ejpam-5426	21	1	in	in	ADP
ejpam-5426	21	2	the	the	DET
ejpam-5426	21	3	year	year	NOUN
ejpam-5426	21	4	1944	1944	NUM
ejpam-5426	21	5	,	,	PUNCT
ejpam-5426	21	6	dieudonnè	dieudonnè	PROPN
ejpam-5426	21	7	[	[	X
ejpam-5426	21	8	7	7	X
ejpam-5426	21	9	]	]	PUNCT
ejpam-5426	21	10	first	first	ADV
ejpam-5426	21	11	suggested	suggest	VERB
ejpam-5426	21	12	the	the	DET
ejpam-5426	21	13	notion	notion	NOUN
ejpam-5426	21	14	of	of	ADP
ejpam-5426	21	15	paracompact	paracompact	ADJ
ejpam-5426	21	16	space	space	NOUN
ejpam-5426	21	17	as	as	ADP
ejpam-5426	21	18	a	a	DET
ejpam-5426	21	19	concept	concept	NOUN
ejpam-5426	21	20	that	that	PRON
ejpam-5426	21	21	is	be	AUX
ejpam-5426	21	22	the	the	DET
ejpam-5426	21	23	extension	extension	NOUN
ejpam-5426	21	24	of	of	ADP
ejpam-5426	21	25	compactness	compactness	NOUN
ejpam-5426	21	26	.	.	PUNCT
ejpam-5426	22	1	later	later	ADV
ejpam-5426	22	2	,	,	PUNCT
ejpam-5426	22	3	in	in	ADP
ejpam-5426	22	4	1969	1969	NUM
ejpam-5426	22	5	,	,	PUNCT
ejpam-5426	22	6	singal	singal	NOUN
ejpam-5426	22	7	and	and	CCONJ
ejpam-5426	22	8	arya	arya	NOUN
ejpam-5426	23	1	[	[	X
ejpam-5426	23	2	20	20	NUM
ejpam-5426	23	3	]	]	PUNCT
ejpam-5426	23	4	provided	provide	VERB
ejpam-5426	23	5	concept	concept	NOUN
ejpam-5426	23	6	a	a	DET
ejpam-5426	23	7	new	new	ADJ
ejpam-5426	23	8	type	type	NOUN
ejpam-5426	23	9	of	of	ADP
ejpam-5426	23	10	paracompactness	paracompactness	NOUN
ejpam-5426	23	11	named	name	VERB
ejpam-5426	23	12	nearly	nearly	ADV
ejpam-5426	23	13	paracompactness	paracompactness	NOUN
ejpam-5426	23	14	,	,	PUNCT
ejpam-5426	23	15	weaker	weak	ADJ
ejpam-5426	23	16	than	than	ADP
ejpam-5426	23	17	the	the	DET
ejpam-5426	23	18	usual	usual	ADJ
ejpam-5426	23	19	paracompactness	paracompactness	NOUN
ejpam-5426	23	20	,	,	PUNCT
ejpam-5426	23	21	that	that	PRON
ejpam-5426	23	22	determines	determine	VERB
ejpam-5426	23	23	its	its	PRON
ejpam-5426	23	24	basic	basic	ADJ
ejpam-5426	23	25	topological	topological	ADJ
ejpam-5426	23	26	properties	property	NOUN
ejpam-5426	23	27	.	.	PUNCT
ejpam-5426	24	1	based	base	VERB
ejpam-5426	24	2	on	on	ADP
ejpam-5426	24	3	that	that	PRON
ejpam-5426	24	4	,	,	PUNCT
ejpam-5426	24	5	in	in	ADP
ejpam-5426	24	6	1978	1978	NUM
ejpam-5426	24	7	,	,	PUNCT
ejpam-5426	24	8	steen	steen	PROPN
ejpam-5426	24	9	and	and	CCONJ
ejpam-5426	24	10	seebach	seebach	NOUN
ejpam-5426	25	1	[	[	X
ejpam-5426	25	2	21	21	NUM
ejpam-5426	25	3	]	]	PUNCT
ejpam-5426	25	4	introduced	introduce	VERB
ejpam-5426	25	5	the	the	DET
ejpam-5426	25	6	notion	notion	NOUN
ejpam-5426	25	7	of	of	ADP
ejpam-5426	25	8	metacompact	metacompact	NOUN
ejpam-5426	25	9	in	in	ADP
ejpam-5426	25	10	the	the	DET
ejpam-5426	25	11	topological	topological	ADJ
ejpam-5426	25	12	space	space	NOUN
ejpam-5426	25	13	(	(	PUNCT
ejpam-5426	25	14	x	x	X
ejpam-5426	25	15	,	,	PUNCT
ejpam-5426	25	16	τ	τ	PROPN
ejpam-5426	25	17	)	)	PUNCT
ejpam-5426	25	18	.	.	PUNCT
ejpam-5426	26	1	in	in	ADP
ejpam-5426	26	2	1982	1982	NUM
ejpam-5426	26	3	,	,	PUNCT
ejpam-5426	26	4	tong	tong	PROPN
ejpam-5426	26	5	[	[	X
ejpam-5426	26	6	22	22	NUM
ejpam-5426	26	7	]	]	PUNCT
ejpam-5426	26	8	introduced	introduce	VERB
ejpam-5426	26	9	the	the	DET
ejpam-5426	26	10	notion	notion	NOUN
ejpam-5426	26	11	of	of	ADP
ejpam-5426	26	12	difference	difference	NOUN
ejpam-5426	26	13	sets	set	NOUN
ejpam-5426	26	14	,	,	PUNCT
ejpam-5426	26	15	often	often	ADV
ejpam-5426	26	16	known	know	VERB
ejpam-5426	26	17	as	as	ADP
ejpam-5426	26	18	d−sets	d−set	NOUN
ejpam-5426	26	19	.	.	PUNCT
ejpam-5426	27	1	also	also	ADV
ejpam-5426	27	2	,	,	PUNCT
ejpam-5426	27	3	in	in	ADP
ejpam-5426	27	4	1984	1984	NUM
ejpam-5426	27	5	,	,	PUNCT
ejpam-5426	27	6	pareek	pareek	NOUN
ejpam-5426	27	7	[	[	X
ejpam-5426	27	8	16	16	NUM
ejpam-5426	27	9	]	]	PUNCT
ejpam-5426	27	10	,	,	PUNCT
ejpam-5426	27	11	contributed	contribute	VERB
ejpam-5426	27	12	the	the	DET
ejpam-5426	27	13	concept	concept	NOUN
ejpam-5426	27	14	ofd−paracompact	ofd−paracompact	PROPN
ejpam-5426	27	15	and	and	CCONJ
ejpam-5426	27	16	studied	study	VERB
ejpam-5426	27	17	their	their	PRON
ejpam-5426	27	18	properties	property	NOUN
ejpam-5426	27	19	and	and	CCONJ
ejpam-5426	27	20	relations	relation	NOUN
ejpam-5426	27	21	with	with	ADP
ejpam-5426	27	22	other	other	ADJ
ejpam-5426	27	23	topological	topological	ADJ
ejpam-5426	27	24	spaces	space	NOUN
ejpam-5426	27	25	.	.	PUNCT
ejpam-5426	28	1	in	in	ADP
ejpam-5426	28	2	1998	1998	NUM
ejpam-5426	28	3	,	,	PUNCT
ejpam-5426	28	4	mukherjee	mukherjee	NOUN
ejpam-5426	28	5	and	and	CCONJ
ejpam-5426	28	6	debray	debray	VERB
ejpam-5426	28	7	[	[	X
ejpam-5426	28	8	15	15	NUM
ejpam-5426	28	9	]	]	PUNCT
ejpam-5426	28	10	used	use	VERB
ejpam-5426	28	11	paracompact	paracompact	NOUN
ejpam-5426	28	12	to	to	PART
ejpam-5426	28	13	give	give	VERB
ejpam-5426	28	14	,	,	PUNCT
ejpam-5426	28	15	the	the	DET
ejpam-5426	28	16	same	same	ADJ
ejpam-5426	28	17	definition	definition	NOUN
ejpam-5426	28	18	.	.	PUNCT
ejpam-5426	29	1	it	it	PRON
ejpam-5426	29	2	has	have	AUX
ejpam-5426	29	3	been	be	AUX
ejpam-5426	29	4	investigated	investigate	VERB
ejpam-5426	29	5	in	in	ADP
ejpam-5426	29	6	terms	term	NOUN
ejpam-5426	29	7	of	of	ADP
ejpam-5426	29	8	a	a	DET
ejpam-5426	29	9	certain	certain	ADJ
ejpam-5426	29	10	type	type	NOUN
ejpam-5426	29	11	of	of	ADP
ejpam-5426	29	12	cover	cover	NOUN
ejpam-5426	29	13	,	,	PUNCT
ejpam-5426	29	14	called	call	VERB
ejpam-5426	29	15	regular	regular	ADV
ejpam-5426	29	16	even	even	ADV
ejpam-5426	29	17	cover	cover	NOUN
ejpam-5426	29	18	.	.	PUNCT
ejpam-5426	30	1	while	while	SCONJ
ejpam-5426	30	2	,	,	PUNCT
ejpam-5426	30	3	in	in	ADP
ejpam-5426	30	4	2006	2006	NUM
ejpam-5426	30	5	,	,	PUNCT
ejpam-5426	30	6	the	the	DET
ejpam-5426	30	7	topologists	topologist	NOUN
ejpam-5426	30	8	al	al	PROPN
ejpam-5426	30	9	-	-	PROPN
ejpam-5426	30	10	ghour	ghour	PROPN
ejpam-5426	31	1	[	[	X
ejpam-5426	31	2	13	13	NUM
ejpam-5426	31	3	]	]	PUNCT
ejpam-5426	31	4	defined	define	VERB
ejpam-5426	31	5	the	the	DET
ejpam-5426	31	6	concepts	concept	NOUN
ejpam-5426	31	7	of	of	ADP
ejpam-5426	31	8	ω−paracompactness	ω−paracompactness	NUM
ejpam-5426	31	9	and	and	CCONJ
ejpam-5426	31	10	countable	countable	ADJ
ejpam-5426	31	11	ω−paracompactness	ω−paracompactness	NOUN
ejpam-5426	31	12	as	as	ADP
ejpam-5426	31	13	generalizations	generalization	NOUN
ejpam-5426	31	14	of	of	ADP
ejpam-5426	31	15	paracompactness	paracompactness	NOUN
ejpam-5426	31	16	.	.	PUNCT
ejpam-5426	32	1	he	he	PRON
ejpam-5426	32	2	explained	explain	VERB
ejpam-5426	32	3	characterized	characterize	VERB
ejpam-5426	32	4	each	each	PRON
ejpam-5426	32	5	of	of	ADP
ejpam-5426	32	6	them	they	PRON
ejpam-5426	32	7	,	,	PUNCT
ejpam-5426	32	8	which	which	PRON
ejpam-5426	32	9	he	he	PRON
ejpam-5426	32	10	studied	study	VERB
ejpam-5426	32	11	dealt	deal	VERB
ejpam-5426	32	12	with	with	ADP
ejpam-5426	32	13	subspaces	subspace	NOUN
ejpam-5426	32	14	,	,	PUNCT
ejpam-5426	32	15	products	product	NOUN
ejpam-5426	32	16	,	,	PUNCT
ejpam-5426	32	17	and	and	CCONJ
ejpam-5426	32	18	mappings	mapping	NOUN
ejpam-5426	32	19	of	of	ADP
ejpam-5426	32	20	each	each	PRON
ejpam-5426	32	21	.	.	PUNCT
ejpam-5426	33	1	also	also	ADV
ejpam-5426	33	2	,	,	PUNCT
ejpam-5426	33	3	in	in	ADP
ejpam-5426	33	4	2006	2006	NUM
ejpam-5426	33	5	,	,	PUNCT
ejpam-5426	33	6	al	al	PROPN
ejpam-5426	33	7	-	-	PROPN
ejpam-5426	33	8	zoubi	zoubi	PROPN
ejpam-5426	34	1	[	[	X
ejpam-5426	34	2	2	2	NUM
ejpam-5426	34	3	]	]	PUNCT
ejpam-5426	34	4	as	as	ADP
ejpam-5426	34	5	a	a	DET
ejpam-5426	34	6	generalization	generalization	NOUN
ejpam-5426	34	7	of	of	ADP
ejpam-5426	34	8	paracompact	paracompact	ADJ
ejpam-5426	34	9	spaces	space	NOUN
ejpam-5426	34	10	,	,	PUNCT
ejpam-5426	34	11	he	he	PRON
ejpam-5426	34	12	uses	use	VERB
ejpam-5426	34	13	the	the	DET
ejpam-5426	34	14	semi−open	semi−open	ADJ
ejpam-5426	34	15	sets	set	NOUN
ejpam-5426	34	16	to	to	PART
ejpam-5426	34	17	developed	developed	VERB
ejpam-5426	34	18	the	the	DET
ejpam-5426	34	19	class	class	NOUN
ejpam-5426	34	20	of	of	ADP
ejpam-5426	34	21	s−paracompact	s−paracompact	NOUN
ejpam-5426	34	22	space	space	NOUN
ejpam-5426	34	23	and	and	CCONJ
ejpam-5426	34	24	define	define	VERB
ejpam-5426	34	25	s−paracompact	s−paracompact	ADP
ejpam-5426	34	26	spaces	space	NOUN
ejpam-5426	34	27	,	,	PUNCT
ejpam-5426	34	28	he	he	PRON
ejpam-5426	34	29	also	also	ADV
ejpam-5426	34	30	investigated	investigate	VERB
ejpam-5426	34	31	their	their	PRON
ejpam-5426	34	32	fundamental	fundamental	ADJ
ejpam-5426	34	33	characteristics	characteristic	NOUN
ejpam-5426	34	34	.	.	PUNCT
ejpam-5426	35	1	the	the	DET
ejpam-5426	35	2	investigations	investigation	NOUN
ejpam-5426	35	3	are	be	AUX
ejpam-5426	35	4	made	make	VERB
ejpam-5426	35	5	into	into	ADP
ejpam-5426	35	6	the	the	DET
ejpam-5426	35	7	connections	connection	NOUN
ejpam-5426	35	8	between	between	ADP
ejpam-5426	35	9	s−paracompact	s−paracompact	ADP
ejpam-5426	35	10	spaces	space	NOUN
ejpam-5426	35	11	and	and	CCONJ
ejpam-5426	35	12	other	other	ADJ
ejpam-5426	35	13	well	well	ADV
ejpam-5426	35	14	-	-	PUNCT
ejpam-5426	35	15	known	know	VERB
ejpam-5426	35	16	spaces	space	NOUN
ejpam-5426	35	17	.	.	PUNCT
ejpam-5426	36	1	later	later	ADV
ejpam-5426	36	2	,	,	PUNCT
ejpam-5426	36	3	in	in	ADP
ejpam-5426	36	4	2007	2007	NUM
ejpam-5426	36	5	,	,	PUNCT
ejpam-5426	36	6	al	al	PROPN
ejpam-5426	36	7	-	-	PUNCT
ejpam-5426	36	8	zoubi	zoubi	PROPN
ejpam-5426	36	9	and	and	CCONJ
ejpam-5426	36	10	al	al	PROPN
ejpam-5426	36	11	-	-	PROPN
ejpam-5426	36	12	ghour	ghour	PROPN
ejpam-5426	37	1	[	[	X
ejpam-5426	37	2	1	1	NUM
ejpam-5426	37	3	]	]	PUNCT
ejpam-5426	37	4	provided	provide	VERB
ejpam-5426	37	5	and	and	CCONJ
ejpam-5426	37	6	studied	study	VERB
ejpam-5426	37	7	p3−paracompact	p3−paracompact	PROPN
ejpam-5426	37	8	,	,	PUNCT
ejpam-5426	37	9	a	a	DET
ejpam-5426	37	10	weaker	weak	ADJ
ejpam-5426	37	11	variant	variant	NOUN
ejpam-5426	37	12	of	of	ADP
ejpam-5426	37	13	paracompactness	paracompactness	NOUN
ejpam-5426	37	14	.	.	PUNCT
ejpam-5426	38	1	with	with	ADP
ejpam-5426	38	2	it	it	PRON
ejpam-5426	38	3	and	and	CCONJ
ejpam-5426	38	4	its	its	PRON
ejpam-5426	38	5	interactions	interaction	NOUN
ejpam-5426	38	6	with	with	ADP
ejpam-5426	38	7	other	other	ADJ
ejpam-5426	38	8	spaces	space	NOUN
ejpam-5426	38	9	,	,	PUNCT
ejpam-5426	38	10	they	they	PRON
ejpam-5426	38	11	obtained	obtain	VERB
ejpam-5426	38	12	a	a	DET
ejpam-5426	38	13	variety	variety	NOUN
ejpam-5426	38	14	of	of	ADP
ejpam-5426	38	15	characterizations	characterization	NOUN
ejpam-5426	38	16	,	,	PUNCT
ejpam-5426	38	17	properties	property	NOUN
ejpam-5426	38	18	,	,	PUNCT
ejpam-5426	38	19	instances	instance	NOUN
ejpam-5426	38	20	,	,	PUNCT
ejpam-5426	38	21	and	and	CCONJ
ejpam-5426	38	22	counterexamples	counterexample	NOUN
ejpam-5426	38	23	.	.	PUNCT
ejpam-5426	39	1	in	in	ADP
ejpam-5426	39	2	2013	2013	NUM
ejpam-5426	39	3	,	,	PUNCT
ejpam-5426	39	4	demir	demir	PROPN
ejpam-5426	39	5	and	and	CCONJ
ejpam-5426	39	6	ozbakir	ozbakir	VERB
ejpam-5426	39	7	[	[	X
ejpam-5426	39	8	6	6	NUM
ejpam-5426	39	9	]	]	PUNCT
ejpam-5426	39	10	defined	define	VERB
ejpam-5426	39	11	the	the	DET
ejpam-5426	39	12	concepts	concept	NOUN
ejpam-5426	39	13	β−paracompact	β−paracompact	PUNCT
ejpam-5426	39	14	spaces	space	NOUN
ejpam-5426	39	15	and	and	CCONJ
ejpam-5426	39	16	β−expandable	β−expandable	PUNCT
ejpam-5426	39	17	spaces	space	NOUN
ejpam-5426	39	18	as	as	ADP
ejpam-5426	39	19	a	a	DET
ejpam-5426	39	20	weak	weak	ADJ
ejpam-5426	39	21	variant	variant	NOUN
ejpam-5426	39	22	of	of	ADP
ejpam-5426	39	23	paracompact	paracompact	ADJ
ejpam-5426	39	24	and	and	CCONJ
ejpam-5426	39	25	expandable	expandable	ADJ
ejpam-5426	39	26	spaces	space	NOUN
ejpam-5426	39	27	,	,	PUNCT
ejpam-5426	39	28	respectively	respectively	ADV
ejpam-5426	39	29	.	.	PUNCT
ejpam-5426	40	1	these	these	DET
ejpam-5426	40	2	spaces	space	NOUN
ejpam-5426	40	3	’	'	PUNCT
ejpam-5426	40	4	basic	basic	ADJ
ejpam-5426	40	5	characteristics	characteristic	NOUN
ejpam-5426	40	6	were	be	AUX
ejpam-5426	40	7	also	also	ADV
ejpam-5426	40	8	provided	provide	VERB
ejpam-5426	40	9	.	.	PUNCT
ejpam-5426	41	1	additionally	additionally	ADV
ejpam-5426	41	2	,	,	PUNCT
ejpam-5426	41	3	it	it	PRON
ejpam-5426	41	4	is	be	AUX
ejpam-5426	41	5	established	establish	VERB
ejpam-5426	41	6	that	that	SCONJ
ejpam-5426	41	7	every	every	DET
ejpam-5426	41	8	β−paracompact	β−paracompact	NOUN
ejpam-5426	41	9	space	space	NOUN
ejpam-5426	41	10	is	be	AUX
ejpam-5426	41	11	a	a	DET
ejpam-5426	41	12	β−expandable	β−expandable	ADJ
ejpam-5426	41	13	space	space	NOUN
ejpam-5426	41	14	,	,	PUNCT
ejpam-5426	41	15	and	and	CCONJ
ejpam-5426	41	16	the	the	DET
ejpam-5426	41	17	connections	connection	NOUN
ejpam-5426	41	18	between	between	ADP
ejpam-5426	41	19	these	these	DET
ejpam-5426	41	20	spaces	space	NOUN
ejpam-5426	41	21	and	and	CCONJ
ejpam-5426	41	22	a	a	DET
ejpam-5426	41	23	few	few	ADJ
ejpam-5426	41	24	previously	previously	ADV
ejpam-5426	41	25	researched	research	VERB
ejpam-5426	41	26	spaces	space	NOUN
ejpam-5426	41	27	are	be	AUX
ejpam-5426	41	28	investigated	investigate	VERB
ejpam-5426	41	29	.	.	PUNCT
ejpam-5426	42	1	in	in	ADP
ejpam-5426	42	2	2019	2019	NUM
ejpam-5426	42	3	,	,	PUNCT
ejpam-5426	42	4	turanli	turanli	NOUN
ejpam-5426	42	5	and	and	CCONJ
ejpam-5426	42	6	ozbakir	ozbakir	NOUN
ejpam-5426	42	7	[	[	X
ejpam-5426	42	8	23	23	NUM
ejpam-5426	42	9	]	]	PUNCT
ejpam-5426	42	10	,	,	PUNCT
ejpam-5426	42	11	introduced	introduce	VERB
ejpam-5426	42	12	and	and	CCONJ
ejpam-5426	42	13	investigated	investigate	VERB
ejpam-5426	42	14	β1	β1	PROPN
ejpam-5426	42	15	−	−	PROPN
ejpam-5426	42	16	l−paracompact	l−paracompact	PROPN
ejpam-5426	42	17	space	space	NOUN
ejpam-5426	42	18	,	,	PUNCT
ejpam-5426	42	19	which	which	PRON
ejpam-5426	42	20	is	be	AUX
ejpam-5426	42	21	a	a	DET
ejpam-5426	42	22	stronger	strong	ADJ
ejpam-5426	42	23	variant	variant	NOUN
ejpam-5426	42	24	of	of	ADP
ejpam-5426	42	25	l−paracompact	l−paracompact	PROPN
ejpam-5426	42	26	space	space	NOUN
ejpam-5426	42	27	established	establish	VERB
ejpam-5426	42	28	on	on	ADP
ejpam-5426	42	29	an	an	DET
ejpam-5426	42	30	ideal	ideal	ADJ
ejpam-5426	42	31	space	space	NOUN
ejpam-5426	42	32	.	.	PUNCT
ejpam-5426	43	1	after	after	ADP
ejpam-5426	43	2	that	that	PRON
ejpam-5426	43	3	,	,	PUNCT
ejpam-5426	43	4	they	they	PRON
ejpam-5426	43	5	looked	look	VERB
ejpam-5426	43	6	into	into	ADP
ejpam-5426	43	7	connections	connection	NOUN
ejpam-5426	43	8	between	between	ADP
ejpam-5426	43	9	β1−l−paracompact	β1−l−paracompact	NUM
ejpam-5426	43	10	spaces	space	NOUN
ejpam-5426	43	11	and	and	CCONJ
ejpam-5426	43	12	other	other	ADJ
ejpam-5426	43	13	paracompactnesses	paracompactnesse	NOUN
ejpam-5426	43	14	.	.	PUNCT
ejpam-5426	44	1	additionally	additionally	ADV
ejpam-5426	44	2	,	,	PUNCT
ejpam-5426	44	3	they	they	PRON
ejpam-5426	44	4	discovered	discover	VERB
ejpam-5426	44	5	numerous	numerous	ADJ
ejpam-5426	44	6	characteristics	characteristic	NOUN
ejpam-5426	44	7	,	,	PUNCT
ejpam-5426	44	8	instances	instance	NOUN
ejpam-5426	44	9	,	,	PUNCT
ejpam-5426	44	10	and	and	CCONJ
ejpam-5426	44	11	counterexamples	counterexample	NOUN
ejpam-5426	44	12	of	of	ADP
ejpam-5426	44	13	β1	β1	PROPN
ejpam-5426	44	14	−	−	PROPN
ejpam-5426	44	15	l−paracompactness	l−paracompactness	NOUN
ejpam-5426	44	16	.	.	PUNCT
ejpam-5426	45	1	in	in	ADP
ejpam-5426	45	2	2021	2021	NUM
ejpam-5426	45	3	,	,	PUNCT
ejpam-5426	45	4	al	al	PROPN
ejpam-5426	45	5	ghour	ghour	PROPN
ejpam-5426	46	1	[	[	X
ejpam-5426	46	2	12	12	NUM
ejpam-5426	46	3	]	]	PUNCT
ejpam-5426	46	4	,	,	PUNCT
ejpam-5426	46	5	introduced	introduce	VERB
ejpam-5426	46	6	both	both	DET
ejpam-5426	46	7	concepts	concept	NOUN
ejpam-5426	46	8	of	of	ADP
ejpam-5426	46	9	σ	σ	PROPN
ejpam-5426	46	10	−	−	PROPN
ejpam-5426	46	11	ω−paracompactness	ω−paracompactness	NUM
ejpam-5426	46	12	and	and	CCONJ
ejpam-5426	46	13	feebly	feebly	ADJ
ejpam-5426	46	14	ω−paracompactness	ω−paracompactness	NUM
ejpam-5426	46	15	,	,	PUNCT
ejpam-5426	46	16	with	with	ADP
ejpam-5426	46	17	ω−paracompactness	ω−paracompactness	NUM
ejpam-5426	46	18	being	be	AUX
ejpam-5426	46	19	a	a	DET
ejpam-5426	46	20	weaker	weak	ADJ
ejpam-5426	46	21	version	version	NOUN
ejpam-5426	46	22	of	of	ADP
ejpam-5426	46	23	σ−ω−paracompactness	σ−ω−paracompactness	NOUN
ejpam-5426	46	24	.	.	PUNCT
ejpam-5426	47	1	furthermore	furthermore	ADV
ejpam-5426	47	2	,	,	PUNCT
ejpam-5426	47	3	in	in	ADP
ejpam-5426	47	4	2021	2021	NUM
ejpam-5426	47	5	,	,	PUNCT
ejpam-5426	47	6	oudetallah	oudetallah	PROPN
ejpam-5426	47	7	,	,	PUNCT
ejpam-5426	47	8	et	et	PROPN
ejpam-5426	47	9	al	al	PROPN
ejpam-5426	47	10	.	.	PUNCT
ejpam-5426	48	1	[	[	X
ejpam-5426	48	2	16	16	NUM
ejpam-5426	48	3	]	]	PUNCT
ejpam-5426	48	4	introduced	introduce	VERB
ejpam-5426	48	5	the	the	DET
ejpam-5426	48	6	notions	notion	NOUN
ejpam-5426	48	7	of	of	ADP
ejpam-5426	48	8	d−metacompact	d−metacompact	ADJ
ejpam-5426	48	9	spaces	space	NOUN
ejpam-5426	48	10	and	and	CCONJ
ejpam-5426	48	11	studied	study	VERB
ejpam-5426	48	12	their	their	PRON
ejpam-5426	48	13	properties	property	NOUN
ejpam-5426	48	14	.	.	PUNCT
ejpam-5426	49	1	however	however	ADV
ejpam-5426	49	2	,	,	PUNCT
ejpam-5426	49	3	for	for	ADP
ejpam-5426	49	4	more	more	ADJ
ejpam-5426	49	5	studies	study	NOUN
ejpam-5426	49	6	,	,	PUNCT
ejpam-5426	49	7	you	you	PRON
ejpam-5426	49	8	can	can	AUX
ejpam-5426	49	9	see	see	VERB
ejpam-5426	49	10	[	[	X
ejpam-5426	49	11	14	14	NUM
ejpam-5426	49	12	]	]	PUNCT
ejpam-5426	49	13	,	,	PUNCT
ejpam-5426	49	14	[	[	X
ejpam-5426	49	15	3	3	NUM
ejpam-5426	49	16	]	]	PUNCT
ejpam-5426	49	17	,	,	PUNCT
ejpam-5426	49	18	and	and	CCONJ
ejpam-5426	49	19	[	[	X
ejpam-5426	49	20	10	10	NUM
ejpam-5426	49	21	]	]	PUNCT
ejpam-5426	49	22	.	.	PUNCT
ejpam-5426	50	1	the	the	DET
ejpam-5426	50	2	present	present	ADJ
ejpam-5426	50	3	research	research	NOUN
ejpam-5426	50	4	is	be	AUX
ejpam-5426	50	5	mainly	mainly	ADV
ejpam-5426	50	6	a	a	DET
ejpam-5426	50	7	continuation	continuation	NOUN
ejpam-5426	50	8	of	of	ADP
ejpam-5426	50	9	the	the	DET
ejpam-5426	50	10	study	study	NOUN
ejpam-5426	50	11	of	of	ADP
ejpam-5426	50	12	d−paracompact	d−paracompact	PROPN
ejpam-5426	50	13	spaces	space	NOUN
ejpam-5426	50	14	from	from	ADP
ejpam-5426	50	15	new	new	ADJ
ejpam-5426	50	16	viewpoints	viewpoint	NOUN
ejpam-5426	50	17	.	.	PUNCT
ejpam-5426	51	1	we	we	PRON
ejpam-5426	51	2	have	have	AUX
ejpam-5426	51	3	aimed	aim	VERB
ejpam-5426	51	4	to	to	PART
ejpam-5426	51	5	eventually	eventually	ADV
ejpam-5426	51	6	arrive	arrive	VERB
ejpam-5426	51	7	at	at	ADP
ejpam-5426	51	8	new	new	ADJ
ejpam-5426	51	9	concepts	concept	NOUN
ejpam-5426	51	10	as	as	ADV
ejpam-5426	51	11	well	well	ADV
ejpam-5426	51	12	as	as	ADP
ejpam-5426	51	13	a	a	DET
ejpam-5426	51	14	develop	develop	VERB
ejpam-5426	51	15	several	several	ADJ
ejpam-5426	51	16	characteristic	characteristic	ADJ
ejpam-5426	51	17	theorems	theorem	NOUN
ejpam-5426	51	18	and	and	CCONJ
ejpam-5426	51	19	instances	instance	NOUN
ejpam-5426	51	20	,	,	PUNCT
ejpam-5426	51	21	all	all	PRON
ejpam-5426	51	22	of	of	ADP
ejpam-5426	51	23	which	which	PRON
ejpam-5426	51	24	we	we	PRON
ejpam-5426	51	25	present	present	VERB
ejpam-5426	51	26	in	in	ADP
ejpam-5426	51	27	this	this	DET
ejpam-5426	51	28	research	research	NOUN
ejpam-5426	51	29	.	.	PUNCT
ejpam-5426	52	1	a.	a.	PROPN
ejpam-5426	52	2	amourah	amourah	PROPN
ejpam-5426	52	3	et	et	PROPN
ejpam-5426	52	4	al	al	PROPN
ejpam-5426	52	5	.	.	PUNCT
ejpam-5426	52	6	/	/	SYM
ejpam-5426	52	7	eur	eur	PROPN
ejpam-5426	52	8	.	.	PUNCT
ejpam-5426	53	1	j.	j.	PROPN
ejpam-5426	53	2	pure	pure	PROPN
ejpam-5426	53	3	appl	appl	PROPN
ejpam-5426	53	4	.	.	PROPN
ejpam-5426	53	5	math	math	PROPN
ejpam-5426	53	6	,	,	PUNCT
ejpam-5426	53	7	17	17	NUM
ejpam-5426	53	8	(	(	PUNCT
ejpam-5426	53	9	4	4	NUM
ejpam-5426	53	10	)	)	PUNCT
ejpam-5426	53	11	(	(	PUNCT
ejpam-5426	53	12	2024	2024	NUM
ejpam-5426	53	13	)	)	PUNCT
ejpam-5426	53	14	,	,	PUNCT
ejpam-5426	53	15	2990	2990	NUM
ejpam-5426	53	16	-	-	SYM
ejpam-5426	53	17	3003	3003	NUM
ejpam-5426	53	18	2992	2992	NUM
ejpam-5426	53	19	2	2	NUM
ejpam-5426	53	20	.	.	PUNCT
ejpam-5426	53	21	preliminary	preliminary	ADJ
ejpam-5426	53	22	and	and	CCONJ
ejpam-5426	53	23	basic	basic	ADJ
ejpam-5426	53	24	notions	notion	NOUN
ejpam-5426	53	25	within	within	ADP
ejpam-5426	53	26	this	this	DET
ejpam-5426	53	27	section	section	NOUN
ejpam-5426	54	1	,	,	PUNCT
ejpam-5426	54	2	we	we	PRON
ejpam-5426	54	3	include	include	VERB
ejpam-5426	54	4	some	some	DET
ejpam-5426	54	5	essential	essential	ADJ
ejpam-5426	54	6	symbols	symbol	NOUN
ejpam-5426	54	7	,	,	PUNCT
ejpam-5426	54	8	such	such	ADJ
ejpam-5426	54	9	as	as	ADP
ejpam-5426	54	10	r	r	NOUN
ejpam-5426	54	11	to	to	PART
ejpam-5426	54	12	denote	denote	VERB
ejpam-5426	54	13	the	the	DET
ejpam-5426	54	14	collection	collection	NOUN
ejpam-5426	54	15	of	of	ADP
ejpam-5426	54	16	real	real	ADJ
ejpam-5426	54	17	numbers	number	NOUN
ejpam-5426	54	18	.	.	PUNCT
ejpam-5426	55	1	also	also	ADV
ejpam-5426	55	2	,	,	PUNCT
ejpam-5426	55	3	ϑu	ϑu	PROPN
ejpam-5426	55	4	,	,	PUNCT
ejpam-5426	55	5	ϑcof	ϑcof	NOUN
ejpam-5426	55	6	,	,	PUNCT
ejpam-5426	55	7	ϑl.r	ϑl.r	ADV
ejpam-5426	55	8	,	,	PUNCT
ejpam-5426	55	9	ϑind	ϑind	NOUN
ejpam-5426	55	10	,	,	PUNCT
ejpam-5426	55	11	and	and	CCONJ
ejpam-5426	55	12	ϑdis	ϑdi	NOUN
ejpam-5426	55	13	will	will	AUX
ejpam-5426	55	14	denote	denote	VERB
ejpam-5426	55	15	the	the	DET
ejpam-5426	55	16	standard	standard	NOUN
ejpam-5426	55	17	,	,	PUNCT
ejpam-5426	55	18	co	co	NOUN
ejpam-5426	55	19	-	-	NOUN
ejpam-5426	55	20	finite	finite	ADJ
ejpam-5426	55	21	,	,	PUNCT
ejpam-5426	55	22	left	left	ADJ
ejpam-5426	55	23	-	-	PUNCT
ejpam-5426	55	24	ray	ray	NOUN
ejpam-5426	55	25	,	,	PUNCT
ejpam-5426	55	26	indiscreet	indiscreet	ADJ
ejpam-5426	55	27	,	,	PUNCT
ejpam-5426	55	28	and	and	CCONJ
ejpam-5426	55	29	discrete	discrete	ADJ
ejpam-5426	55	30	topologies	topology	NOUN
ejpam-5426	55	31	,	,	PUNCT
ejpam-5426	55	32	respectively	respectively	ADV
ejpam-5426	55	33	.	.	PUNCT
ejpam-5426	56	1	now	now	ADV
ejpam-5426	56	2	,	,	PUNCT
ejpam-5426	56	3	we	we	PRON
ejpam-5426	56	4	provide	provide	VERB
ejpam-5426	56	5	some	some	DET
ejpam-5426	56	6	basic	basic	ADJ
ejpam-5426	56	7	definitions	definition	NOUN
ejpam-5426	56	8	as	as	ADV
ejpam-5426	56	9	well	well	ADV
ejpam-5426	56	10	as	as	ADP
ejpam-5426	56	11	the	the	DET
ejpam-5426	56	12	major	major	ADJ
ejpam-5426	56	13	results	result	NOUN
ejpam-5426	56	14	that	that	PRON
ejpam-5426	56	15	are	be	AUX
ejpam-5426	56	16	required	require	VERB
ejpam-5426	56	17	.	.	PUNCT
ejpam-5426	57	1	definition	definition	NOUN
ejpam-5426	57	2	1	1	NUM
ejpam-5426	57	3	.	.	PUNCT
ejpam-5426	58	1	[	[	X
ejpam-5426	58	2	7	7	X
ejpam-5426	58	3	]	]	X
ejpam-5426	58	4	if	if	SCONJ
ejpam-5426	58	5	any	any	DET
ejpam-5426	58	6	open	open	ADJ
ejpam-5426	58	7	cover	cover	NOUN
ejpam-5426	58	8	of	of	ADP
ejpam-5426	58	9	the	the	DET
ejpam-5426	58	10	topological	topological	ADJ
ejpam-5426	58	11	space	space	NOUN
ejpam-5426	58	12	(	(	PUNCT
ejpam-5426	58	13	w,ϑ	w,ϑ	PROPN
ejpam-5426	58	14	)	)	PUNCT
ejpam-5426	58	15	has	have	VERB
ejpam-5426	58	16	an	an	DET
ejpam-5426	58	17	open	open	ADJ
ejpam-5426	58	18	locally−finite	locally−finite	NOUN
ejpam-5426	58	19	refinement	refinement	NOUN
ejpam-5426	58	20	,	,	PUNCT
ejpam-5426	58	21	then	then	ADV
ejpam-5426	58	22	the	the	DET
ejpam-5426	58	23	space	space	NOUN
ejpam-5426	58	24	is	be	AUX
ejpam-5426	58	25	called	call	VERB
ejpam-5426	58	26	paracompact	paracompact	ADJ
ejpam-5426	58	27	space	space	NOUN
ejpam-5426	58	28	.	.	PUNCT
ejpam-5426	59	1	definition	definition	NOUN
ejpam-5426	59	2	2	2	NUM
ejpam-5426	59	3	.	.	PUNCT
ejpam-5426	60	1	[	[	X
ejpam-5426	60	2	8	8	NUM
ejpam-5426	60	3	]	]	X
ejpam-5426	60	4	if	if	SCONJ
ejpam-5426	60	5	any	any	DET
ejpam-5426	60	6	countable	countable	ADJ
ejpam-5426	60	7	open	open	ADJ
ejpam-5426	60	8	cover	cover	NOUN
ejpam-5426	60	9	of	of	ADP
ejpam-5426	60	10	the	the	DET
ejpam-5426	60	11	topological	topological	ADJ
ejpam-5426	60	12	space	space	NOUN
ejpam-5426	60	13	(	(	PUNCT
ejpam-5426	60	14	w,ϑ	w,ϑ	PROPN
ejpam-5426	60	15	)	)	PUNCT
ejpam-5426	60	16	has	have	VERB
ejpam-5426	60	17	an	an	DET
ejpam-5426	60	18	open	open	ADJ
ejpam-5426	60	19	locally−finite	locally−finite	NOUN
ejpam-5426	60	20	refinement	refinement	NOUN
ejpam-5426	60	21	,	,	PUNCT
ejpam-5426	60	22	then	then	ADV
ejpam-5426	60	23	the	the	DET
ejpam-5426	60	24	space	space	NOUN
ejpam-5426	60	25	is	be	AUX
ejpam-5426	60	26	called	call	VERB
ejpam-5426	60	27	countably	countably	ADV
ejpam-5426	60	28	paracompact	paracompact	ADJ
ejpam-5426	60	29	.	.	PUNCT
ejpam-5426	61	1	definition	definition	NOUN
ejpam-5426	61	2	3	3	NUM
ejpam-5426	61	3	.	.	PUNCT
ejpam-5426	62	1	[	[	X
ejpam-5426	62	2	23	23	NUM
ejpam-5426	62	3	]	]	X
ejpam-5426	62	4	if	if	SCONJ
ejpam-5426	62	5	any	any	DET
ejpam-5426	62	6	open	open	ADJ
ejpam-5426	62	7	cover	cover	NOUN
ejpam-5426	62	8	of	of	ADP
ejpam-5426	62	9	the	the	DET
ejpam-5426	62	10	topological	topological	ADJ
ejpam-5426	62	11	space	space	NOUN
ejpam-5426	62	12	(	(	PUNCT
ejpam-5426	62	13	w,ϑ	w,ϑ	PROPN
ejpam-5426	62	14	)	)	PUNCT
ejpam-5426	62	15	has	have	VERB
ejpam-5426	62	16	an	an	DET
ejpam-5426	62	17	open	open	ADJ
ejpam-5426	62	18	locallycountable	locallycountable	ADJ
ejpam-5426	62	19	refinement	refinement	NOUN
ejpam-5426	62	20	,	,	PUNCT
ejpam-5426	62	21	then	then	ADV
ejpam-5426	62	22	the	the	DET
ejpam-5426	62	23	space	space	NOUN
ejpam-5426	62	24	is	be	AUX
ejpam-5426	62	25	called	call	VERB
ejpam-5426	62	26	paralindelöf	paralindelöf	NOUN
ejpam-5426	62	27	space	space	NOUN
ejpam-5426	62	28	.	.	PUNCT
ejpam-5426	63	1	definition	definition	NOUN
ejpam-5426	63	2	4	4	NUM
ejpam-5426	63	3	.	.	PUNCT
ejpam-5426	64	1	[	[	X
ejpam-5426	64	2	22	22	NUM
ejpam-5426	64	3	]	]	PUNCT
ejpam-5426	64	4	a	a	DET
ejpam-5426	64	5	subset	subset	NOUN
ejpam-5426	64	6	w1	w1	NOUN
ejpam-5426	64	7	⊆	⊆	NUM
ejpam-5426	64	8	(	(	PUNCT
ejpam-5426	64	9	w,ϑ	w,ϑ	PROPN
ejpam-5426	64	10	)	)	PUNCT
ejpam-5426	64	11	is	be	AUX
ejpam-5426	64	12	d−set	d−set	VERB
ejpam-5426	64	13	if	if	SCONJ
ejpam-5426	64	14	there	there	PRON
ejpam-5426	64	15	are	be	VERB
ejpam-5426	64	16	open	open	ADJ
ejpam-5426	64	17	sets	set	NOUN
ejpam-5426	64	18	a	a	PRON
ejpam-5426	64	19	and	and	CCONJ
ejpam-5426	64	20	b	b	NOUN
ejpam-5426	64	21	such	such	ADJ
ejpam-5426	64	22	that	that	SCONJ
ejpam-5426	64	23	a	a	DET
ejpam-5426	64	24	̸=	̸=	PROPN
ejpam-5426	64	25	w	w	NOUN
ejpam-5426	64	26	and	and	CCONJ
ejpam-5426	64	27	w1	w1	NOUN
ejpam-5426	64	28	=	=	PUNCT
ejpam-5426	64	29	a−b	a−b	PROPN
ejpam-5426	64	30	.	.	PUNCT
ejpam-5426	65	1	furthermore	furthermore	ADV
ejpam-5426	65	2	,	,	PUNCT
ejpam-5426	65	3	the	the	DET
ejpam-5426	65	4	subset	subset	NOUN
ejpam-5426	65	5	w1	w1	NOUN
ejpam-5426	65	6	is	be	AUX
ejpam-5426	65	7	d−set	d−set	VERB
ejpam-5426	65	8	that	that	PRON
ejpam-5426	65	9	generated	generate	VERB
ejpam-5426	65	10	by	by	ADP
ejpam-5426	65	11	a	a	DET
ejpam-5426	65	12	and	and	CCONJ
ejpam-5426	65	13	b.	b.	PROPN
ejpam-5426	65	14	definition	definition	NOUN
ejpam-5426	65	15	5	5	NUM
ejpam-5426	65	16	.	.	PUNCT
ejpam-5426	66	1	[	[	X
ejpam-5426	66	2	19	19	NUM
ejpam-5426	66	3	]	]	PUNCT
ejpam-5426	66	4	a	a	DET
ejpam-5426	66	5	cover	cover	NOUN
ejpam-5426	66	6	ẽ	ẽ	NOUN
ejpam-5426	66	7	=	=	SYM
ejpam-5426	66	8	{	{	PUNCT
ejpam-5426	66	9	eρ	eρ	NOUN
ejpam-5426	66	10	:	:	PUNCT
ejpam-5426	66	11	ρ	ρ	PROPN
ejpam-5426	66	12	∈	∈	PROPN
ejpam-5426	66	13	λ	λ	NOUN
ejpam-5426	66	14	}	}	PUNCT
ejpam-5426	66	15	of	of	ADP
ejpam-5426	66	16	the	the	DET
ejpam-5426	66	17	space	space	NOUN
ejpam-5426	66	18	(	(	PUNCT
ejpam-5426	66	19	w,ϑ	w,ϑ	PROPN
ejpam-5426	66	20	)	)	PUNCT
ejpam-5426	66	21	is	be	AUX
ejpam-5426	66	22	called	call	VERB
ejpam-5426	66	23	d−cover	d−cover	PROPN
ejpam-5426	66	24	if	if	SCONJ
ejpam-5426	66	25	any	any	DET
ejpam-5426	66	26	eρ	eρ	NOUN
ejpam-5426	66	27	is	be	AUX
ejpam-5426	66	28	d−set	d−set	VERB
ejpam-5426	66	29	,	,	PUNCT
ejpam-5426	66	30	for	for	ADP
ejpam-5426	66	31	every	every	DET
ejpam-5426	66	32	ρ	ρ	PROPN
ejpam-5426	66	33	∈	∈	PROPN
ejpam-5426	66	34	λ	λ	PROPN
ejpam-5426	66	35	.	.	PROPN
ejpam-5426	66	36	definition	definition	NOUN
ejpam-5426	66	37	6	6	NUM
ejpam-5426	66	38	.	.	PUNCT
ejpam-5426	67	1	if	if	SCONJ
ejpam-5426	67	2	any	any	DET
ejpam-5426	67	3	d−cover	d−cover	PROPN
ejpam-5426	67	4	of	of	ADP
ejpam-5426	67	5	the	the	DET
ejpam-5426	67	6	topological	topological	ADJ
ejpam-5426	67	7	space	space	NOUN
ejpam-5426	67	8	(	(	PUNCT
ejpam-5426	67	9	w,ϑ	w,ϑ	PROPN
ejpam-5426	67	10	)	)	PUNCT
ejpam-5426	67	11	has	have	VERB
ejpam-5426	67	12	an	an	DET
ejpam-5426	67	13	open	open	ADJ
ejpam-5426	67	14	locally−countable	locally−countable	ADJ
ejpam-5426	67	15	refinement	refinement	NOUN
ejpam-5426	67	16	,	,	PUNCT
ejpam-5426	67	17	then	then	ADV
ejpam-5426	67	18	the	the	DET
ejpam-5426	67	19	space	space	NOUN
ejpam-5426	67	20	is	be	AUX
ejpam-5426	67	21	called	call	VERB
ejpam-5426	67	22	d−paralindelöf	d−paralindelöf	NOUN
ejpam-5426	67	23	space	space	NOUN
ejpam-5426	67	24	.	.	PUNCT
ejpam-5426	68	1	definition	definition	NOUN
ejpam-5426	68	2	7	7	NUM
ejpam-5426	68	3	.	.	PUNCT
ejpam-5426	69	1	[	[	X
ejpam-5426	69	2	19	19	NUM
ejpam-5426	69	3	]	]	X
ejpam-5426	69	4	if	if	SCONJ
ejpam-5426	69	5	any	any	DET
ejpam-5426	69	6	d−cover	d−cover	PROPN
ejpam-5426	69	7	of	of	ADP
ejpam-5426	69	8	the	the	DET
ejpam-5426	69	9	topological	topological	ADJ
ejpam-5426	69	10	space	space	NOUN
ejpam-5426	69	11	(	(	PUNCT
ejpam-5426	69	12	w,ϑ	w,ϑ	PROPN
ejpam-5426	69	13	)	)	PUNCT
ejpam-5426	69	14	has	have	VERB
ejpam-5426	69	15	a	a	DET
ejpam-5426	69	16	countable	countable	ADJ
ejpam-5426	69	17	subcover	subcover	NOUN
ejpam-5426	69	18	,	,	PUNCT
ejpam-5426	69	19	then	then	ADV
ejpam-5426	69	20	the	the	DET
ejpam-5426	69	21	space	space	NOUN
ejpam-5426	69	22	is	be	AUX
ejpam-5426	69	23	called	call	VERB
ejpam-5426	69	24	d−lindelöf	d−lindelöf	PROPN
ejpam-5426	69	25	.	.	PUNCT
ejpam-5426	70	1	definition	definition	NOUN
ejpam-5426	70	2	8	8	NUM
ejpam-5426	70	3	.	.	PUNCT
ejpam-5426	71	1	[	[	X
ejpam-5426	71	2	19	19	NUM
ejpam-5426	71	3	]	]	X
ejpam-5426	71	4	if	if	SCONJ
ejpam-5426	71	5	any	any	DET
ejpam-5426	71	6	d−cover	d−cover	PROPN
ejpam-5426	71	7	of	of	ADP
ejpam-5426	71	8	the	the	DET
ejpam-5426	71	9	topological	topological	ADJ
ejpam-5426	71	10	space	space	NOUN
ejpam-5426	71	11	(	(	PUNCT
ejpam-5426	71	12	w,ϑ	w,ϑ	PROPN
ejpam-5426	71	13	)	)	PUNCT
ejpam-5426	71	14	has	have	VERB
ejpam-5426	71	15	a	a	DET
ejpam-5426	71	16	finite−subcover	finite−subcover	ADJ
ejpam-5426	71	17	,	,	PUNCT
ejpam-5426	71	18	then	then	ADV
ejpam-5426	71	19	the	the	DET
ejpam-5426	71	20	space	space	NOUN
ejpam-5426	71	21	is	be	AUX
ejpam-5426	71	22	called	call	VERB
ejpam-5426	71	23	d−compact	d−compact	PROPN
ejpam-5426	71	24	.	.	PUNCT
ejpam-5426	71	25	definition	definition	NOUN
ejpam-5426	71	26	9	9	NUM
ejpam-5426	71	27	.	.	PUNCT
ejpam-5426	72	1	[	[	X
ejpam-5426	72	2	11	11	NUM
ejpam-5426	72	3	]	]	PUNCT
ejpam-5426	72	4	a	a	DET
ejpam-5426	72	5	subset	subset	NOUN
ejpam-5426	72	6	w1	w1	NOUN
ejpam-5426	72	7	⊆	⊆	NUM
ejpam-5426	72	8	(	(	PUNCT
ejpam-5426	72	9	w,ϑ	w,ϑ	NOUN
ejpam-5426	72	10	)	)	PUNCT
ejpam-5426	72	11	is	be	AUX
ejpam-5426	72	12	called	call	VERB
ejpam-5426	72	13	d−dense	d−dense	ADP
ejpam-5426	72	14	set	set	NOUN
ejpam-5426	72	15	,	,	PUNCT
ejpam-5426	72	16	if	if	SCONJ
ejpam-5426	72	17	for	for	ADP
ejpam-5426	72	18	any	any	DET
ejpam-5426	72	19	y	y	PROPN
ejpam-5426	72	20	∈	∈	PROPN
ejpam-5426	72	21	w	w	NOUN
ejpam-5426	72	22	,	,	PUNCT
ejpam-5426	72	23	we	we	PRON
ejpam-5426	72	24	have	have	AUX
ejpam-5426	72	25	dy	dy	NOUN
ejpam-5426	72	26	∩w1	∩w1	NOUN
ejpam-5426	73	1	̸=	̸=	PROPN
ejpam-5426	73	2	ϕ	ϕ	NOUN
ejpam-5426	73	3	,	,	PUNCT
ejpam-5426	73	4	and	and	CCONJ
ejpam-5426	73	5	each	each	DET
ejpam-5426	73	6	d−set	d−set	NOUN
ejpam-5426	73	7	containing	contain	VERB
ejpam-5426	73	8	y.	y.	PROPN
ejpam-5426	73	9	definition	definition	NOUN
ejpam-5426	73	10	10	10	NUM
ejpam-5426	73	11	.	.	PUNCT
ejpam-5426	74	1	[	[	X
ejpam-5426	74	2	11	11	NUM
ejpam-5426	74	3	]	]	PUNCT
ejpam-5426	74	4	the	the	DET
ejpam-5426	74	5	space	space	NOUN
ejpam-5426	74	6	(	(	PUNCT
ejpam-5426	74	7	w,ϑ	w,ϑ	PROPN
ejpam-5426	74	8	)	)	PUNCT
ejpam-5426	74	9	is	be	AUX
ejpam-5426	74	10	called	call	VERB
ejpam-5426	74	11	d−separable	d−separable	ADJ
ejpam-5426	74	12	,	,	PUNCT
ejpam-5426	74	13	if	if	SCONJ
ejpam-5426	74	14	the	the	DET
ejpam-5426	74	15	space	space	NOUN
ejpam-5426	74	16	has	have	VERB
ejpam-5426	74	17	a	a	DET
ejpam-5426	74	18	subset	subset	ADJ
ejpam-5426	74	19	h	h	NOUN
ejpam-5426	74	20	,	,	PUNCT
ejpam-5426	74	21	which	which	PRON
ejpam-5426	74	22	is	be	AUX
ejpam-5426	74	23	d−dense	d−dense	PRON
ejpam-5426	74	24	countable	countable	ADJ
ejpam-5426	74	25	.	.	PUNCT
ejpam-5426	75	1	definition	definition	NOUN
ejpam-5426	75	2	11	11	NUM
ejpam-5426	75	3	.	.	PUNCT
ejpam-5426	76	1	[	[	X
ejpam-5426	76	2	17	17	NUM
ejpam-5426	76	3	]	]	PUNCT
ejpam-5426	76	4	the	the	DET
ejpam-5426	76	5	space	space	NOUN
ejpam-5426	76	6	(	(	PUNCT
ejpam-5426	76	7	w,ϑ	w,ϑ	PROPN
ejpam-5426	76	8	)	)	PUNCT
ejpam-5426	76	9	is	be	AUX
ejpam-5426	76	10	called	call	VERB
ejpam-5426	76	11	locally−indiscreet	locally−indiscreet	NOUN
ejpam-5426	76	12	if	if	SCONJ
ejpam-5426	76	13	any	any	DET
ejpam-5426	76	14	set	set	NOUN
ejpam-5426	76	15	ϑn−open	ϑn−open	NOUN
ejpam-5426	76	16	is	be	AUX
ejpam-5426	76	17	ϑn−clopen	ϑn−clopen	ADJ
ejpam-5426	76	18	,	,	PUNCT
ejpam-5426	76	19	where	where	SCONJ
ejpam-5426	76	20	n	n	NOUN
ejpam-5426	76	21	=	=	SYM
ejpam-5426	76	22	1	1	NUM
ejpam-5426	76	23	,	,	PUNCT
ejpam-5426	76	24	2	2	NUM
ejpam-5426	76	25	.	.	PUNCT
ejpam-5426	76	26	definition	definition	NOUN
ejpam-5426	76	27	12	12	NUM
ejpam-5426	76	28	.	.	PUNCT
ejpam-5426	77	1	[	[	X
ejpam-5426	77	2	9	9	NUM
ejpam-5426	77	3	]	]	X
ejpam-5426	77	4	if	if	SCONJ
ejpam-5426	77	5	any	any	DET
ejpam-5426	77	6	cover	cover	NOUN
ejpam-5426	77	7	of	of	ADP
ejpam-5426	77	8	the	the	DET
ejpam-5426	77	9	topological	topological	ADJ
ejpam-5426	77	10	space	space	NOUN
ejpam-5426	77	11	(	(	PUNCT
ejpam-5426	77	12	w,ϑ	w,ϑ	PROPN
ejpam-5426	77	13	)	)	PUNCT
ejpam-5426	77	14	has	have	VERB
ejpam-5426	77	15	a	a	DET
ejpam-5426	77	16	countable	countable	ADJ
ejpam-5426	77	17	subcover	subcover	NOUN
ejpam-5426	77	18	,	,	PUNCT
ejpam-5426	77	19	then	then	ADV
ejpam-5426	77	20	the	the	DET
ejpam-5426	77	21	space	space	NOUN
ejpam-5426	77	22	is	be	AUX
ejpam-5426	77	23	called	call	VERB
ejpam-5426	77	24	lindelöf	lindelöf	NOUN
ejpam-5426	77	25	space	space	NOUN
ejpam-5426	77	26	.	.	PUNCT
ejpam-5426	78	1	definition	definition	NOUN
ejpam-5426	78	2	13	13	NUM
ejpam-5426	78	3	.	.	PUNCT
ejpam-5426	79	1	[	[	X
ejpam-5426	79	2	11	11	NUM
ejpam-5426	79	3	]	]	X
ejpam-5426	79	4	let	let	ADJ
ejpam-5426	79	5	(	(	PUNCT
ejpam-5426	79	6	w,ϑ	w,ϑ	PROPN
ejpam-5426	79	7	)	)	PUNCT
ejpam-5426	79	8	and	and	CCONJ
ejpam-5426	79	9	(	(	PUNCT
ejpam-5426	79	10	q	q	ADJ
ejpam-5426	79	11	,	,	PUNCT
ejpam-5426	79	12	ι	ι	AUX
ejpam-5426	79	13	)	)	PUNCT
ejpam-5426	79	14	be	be	VERB
ejpam-5426	79	15	any	any	DET
ejpam-5426	79	16	topological	topological	ADJ
ejpam-5426	79	17	spaces	space	NOUN
ejpam-5426	79	18	.	.	PUNCT
ejpam-5426	80	1	if	if	SCONJ
ejpam-5426	80	2	the	the	DET
ejpam-5426	80	3	inverse	inverse	ADJ
ejpam-5426	80	4	image	image	NOUN
ejpam-5426	80	5	of	of	ADP
ejpam-5426	80	6	any	any	DET
ejpam-5426	80	7	open	open	ADJ
ejpam-5426	80	8	subset	subset	NOUN
ejpam-5426	80	9	in	in	ADP
ejpam-5426	80	10	q	q	PROPN
ejpam-5426	80	11	of	of	ADP
ejpam-5426	80	12	φ	φ	PROPN
ejpam-5426	80	13	:	:	PUNCT
ejpam-5426	80	14	w	w	X
ejpam-5426	80	15	−→	−→	NOUN
ejpam-5426	80	16	q	q	NOUN
ejpam-5426	80	17	is	be	AUX
ejpam-5426	80	18	open	open	ADJ
ejpam-5426	80	19	in	in	ADP
ejpam-5426	80	20	w	w	PROPN
ejpam-5426	80	21	,	,	PUNCT
ejpam-5426	80	22	then	then	ADV
ejpam-5426	80	23	the	the	DET
ejpam-5426	80	24	function	function	NOUN
ejpam-5426	80	25	φ	φ	PROPN
ejpam-5426	80	26	is	be	AUX
ejpam-5426	80	27	called	call	VERB
ejpam-5426	80	28	continuous	continuous	ADJ
ejpam-5426	80	29	function	function	NOUN
ejpam-5426	80	30	.	.	PUNCT
ejpam-5426	81	1	that	that	PRON
ejpam-5426	81	2	is	be	AUX
ejpam-5426	81	3	,	,	PUNCT
ejpam-5426	81	4	if	if	SCONJ
ejpam-5426	81	5	x	x	PROPN
ejpam-5426	81	6	∈	∈	PROPN
ejpam-5426	81	7	ι	ι	PROPN
ejpam-5426	81	8	,	,	PUNCT
ejpam-5426	81	9	then	then	ADV
ejpam-5426	81	10	φ−1(x	φ−1(x	PROPN
ejpam-5426	81	11	)	)	PUNCT
ejpam-5426	81	12	∈	∈	PROPN
ejpam-5426	81	13	ϑ	ϑ	X
ejpam-5426	81	14	is	be	AUX
ejpam-5426	81	15	its	its	PRON
ejpam-5426	81	16	inverse	inverse	NOUN
ejpam-5426	81	17	image	image	NOUN
ejpam-5426	81	18	.	.	PUNCT
ejpam-5426	82	1	a.	a.	PROPN
ejpam-5426	82	2	amourah	amourah	PROPN
ejpam-5426	82	3	et	et	PROPN
ejpam-5426	82	4	al	al	PROPN
ejpam-5426	82	5	.	.	PUNCT
ejpam-5426	82	6	/	/	SYM
ejpam-5426	82	7	eur	eur	PROPN
ejpam-5426	82	8	.	.	PUNCT
ejpam-5426	83	1	j.	j.	PROPN
ejpam-5426	83	2	pure	pure	PROPN
ejpam-5426	83	3	appl	appl	PROPN
ejpam-5426	83	4	.	.	PROPN
ejpam-5426	83	5	math	math	PROPN
ejpam-5426	83	6	,	,	PUNCT
ejpam-5426	83	7	17	17	NUM
ejpam-5426	83	8	(	(	PUNCT
ejpam-5426	83	9	4	4	NUM
ejpam-5426	83	10	)	)	PUNCT
ejpam-5426	83	11	(	(	PUNCT
ejpam-5426	83	12	2024	2024	NUM
ejpam-5426	83	13	)	)	PUNCT
ejpam-5426	83	14	,	,	PUNCT
ejpam-5426	83	15	2990	2990	NUM
ejpam-5426	83	16	-	-	SYM
ejpam-5426	83	17	3003	3003	NUM
ejpam-5426	83	18	2993	2993	NUM
ejpam-5426	83	19	definition	definition	NOUN
ejpam-5426	83	20	14	14	NUM
ejpam-5426	83	21	.	.	PUNCT
ejpam-5426	84	1	[	[	X
ejpam-5426	84	2	5	5	NUM
ejpam-5426	84	3	]	]	X
ejpam-5426	84	4	let	let	ADJ
ejpam-5426	84	5	(	(	PUNCT
ejpam-5426	84	6	w,ϑ	w,ϑ	PROPN
ejpam-5426	84	7	)	)	PUNCT
ejpam-5426	84	8	and	and	CCONJ
ejpam-5426	84	9	(	(	PUNCT
ejpam-5426	84	10	q	q	ADJ
ejpam-5426	84	11	,	,	PUNCT
ejpam-5426	84	12	ι	ι	AUX
ejpam-5426	84	13	)	)	PUNCT
ejpam-5426	84	14	be	be	VERB
ejpam-5426	84	15	any	any	DET
ejpam-5426	84	16	topological	topological	ADJ
ejpam-5426	84	17	spaces	space	NOUN
ejpam-5426	84	18	.	.	PUNCT
ejpam-5426	85	1	if	if	SCONJ
ejpam-5426	85	2	the	the	DET
ejpam-5426	85	3	image	image	NOUN
ejpam-5426	85	4	φ(a	φ(a	ADJ
ejpam-5426	85	5	)	)	PUNCT
ejpam-5426	85	6	is	be	AUX
ejpam-5426	85	7	open	open	ADJ
ejpam-5426	85	8	in	in	ADP
ejpam-5426	85	9	q	q	NOUN
ejpam-5426	85	10	for	for	SCONJ
ejpam-5426	85	11	each	each	DET
ejpam-5426	85	12	open	open	ADJ
ejpam-5426	85	13	set	set	VERB
ejpam-5426	85	14	a	a	PRON
ejpam-5426	85	15	in	in	ADP
ejpam-5426	85	16	w	w	PROPN
ejpam-5426	85	17	,	,	PUNCT
ejpam-5426	85	18	then	then	ADV
ejpam-5426	85	19	the	the	DET
ejpam-5426	85	20	function	function	NOUN
ejpam-5426	85	21	φ	φ	NOUN
ejpam-5426	85	22	:	:	PUNCT
ejpam-5426	85	23	w	w	X
ejpam-5426	85	24	−→	−→	NOUN
ejpam-5426	85	25	q	q	NOUN
ejpam-5426	85	26	is	be	AUX
ejpam-5426	85	27	called	call	VERB
ejpam-5426	85	28	open	open	ADJ
ejpam-5426	85	29	.	.	PUNCT
ejpam-5426	86	1	definition	definition	NOUN
ejpam-5426	86	2	15	15	NUM
ejpam-5426	86	3	.	.	PUNCT
ejpam-5426	87	1	[	[	X
ejpam-5426	87	2	9	9	NUM
ejpam-5426	87	3	]	]	X
ejpam-5426	87	4	let	let	ADJ
ejpam-5426	87	5	(	(	PUNCT
ejpam-5426	87	6	w,ϑ	w,ϑ	PROPN
ejpam-5426	87	7	)	)	PUNCT
ejpam-5426	87	8	and	and	CCONJ
ejpam-5426	87	9	(	(	PUNCT
ejpam-5426	87	10	q	q	ADJ
ejpam-5426	87	11	,	,	PUNCT
ejpam-5426	87	12	ι	ι	AUX
ejpam-5426	87	13	)	)	PUNCT
ejpam-5426	87	14	be	be	VERB
ejpam-5426	87	15	any	any	DET
ejpam-5426	87	16	topological	topological	ADJ
ejpam-5426	87	17	spaces	space	NOUN
ejpam-5426	87	18	.	.	PUNCT
ejpam-5426	88	1	if	if	SCONJ
ejpam-5426	88	2	the	the	DET
ejpam-5426	88	3	image	image	NOUN
ejpam-5426	88	4	φ(f	φ(f	PROPN
ejpam-5426	88	5	)	)	PUNCT
ejpam-5426	88	6	is	be	AUX
ejpam-5426	88	7	closed	close	VERB
ejpam-5426	88	8	in	in	ADP
ejpam-5426	88	9	q	q	NOUN
ejpam-5426	88	10	for	for	ADP
ejpam-5426	88	11	each	each	DET
ejpam-5426	88	12	closed	close	VERB
ejpam-5426	88	13	set	set	VERB
ejpam-5426	88	14	f	f	PROPN
ejpam-5426	88	15	in	in	ADP
ejpam-5426	88	16	w	w	PROPN
ejpam-5426	88	17	,	,	PUNCT
ejpam-5426	88	18	then	then	ADV
ejpam-5426	88	19	the	the	DET
ejpam-5426	88	20	function	function	NOUN
ejpam-5426	88	21	φ	φ	NOUN
ejpam-5426	88	22	:	:	PUNCT
ejpam-5426	88	23	w	w	X
ejpam-5426	88	24	−→	−→	NOUN
ejpam-5426	88	25	q	q	NOUN
ejpam-5426	88	26	is	be	AUX
ejpam-5426	88	27	called	call	VERB
ejpam-5426	88	28	closed	closed	ADJ
ejpam-5426	88	29	.	.	PUNCT
ejpam-5426	89	1	definition	definition	NOUN
ejpam-5426	89	2	16	16	NUM
ejpam-5426	89	3	.	.	PUNCT
ejpam-5426	90	1	[	[	X
ejpam-5426	90	2	4	4	X
ejpam-5426	90	3	]	]	X
ejpam-5426	90	4	if	if	SCONJ
ejpam-5426	90	5	the	the	DET
ejpam-5426	90	6	function	function	NOUN
ejpam-5426	90	7	φ	φ	X
ejpam-5426	90	8	:	:	PUNCT
ejpam-5426	90	9	(	(	PUNCT
ejpam-5426	90	10	w,ϑ	w,ϑ	ADJ
ejpam-5426	90	11	)	)	PUNCT
ejpam-5426	90	12	−→	−→	NOUN
ejpam-5426	90	13	(	(	PUNCT
ejpam-5426	90	14	q	q	NOUN
ejpam-5426	90	15	,	,	PUNCT
ejpam-5426	90	16	ι	ι	X
ejpam-5426	90	17	)	)	PUNCT
ejpam-5426	90	18	is	be	AUX
ejpam-5426	90	19	continuous	continuous	ADJ
ejpam-5426	90	20	,	,	PUNCT
ejpam-5426	90	21	d−compact	d−compact	PUNCT
ejpam-5426	90	22	and	and	CCONJ
ejpam-5426	90	23	closed	close	VERB
ejpam-5426	90	24	for	for	ADP
ejpam-5426	90	25	each	each	DET
ejpam-5426	90	26	q	q	PROPN
ejpam-5426	90	27	∈	∈	PROPN
ejpam-5426	90	28	q	q	NOUN
ejpam-5426	90	29	,	,	PUNCT
ejpam-5426	90	30	then	then	ADV
ejpam-5426	90	31	the	the	DET
ejpam-5426	90	32	function	function	NOUN
ejpam-5426	90	33	φ	φ	PROPN
ejpam-5426	90	34	is	be	AUX
ejpam-5426	90	35	called	call	VERB
ejpam-5426	90	36	d−perfect	d−perfect	PROPN
ejpam-5426	90	37	.	.	PUNCT
ejpam-5426	91	1	theorem	theorem	NOUN
ejpam-5426	91	2	1	1	NUM
ejpam-5426	91	3	.	.	PUNCT
ejpam-5426	92	1	[	[	X
ejpam-5426	92	2	19	19	NUM
ejpam-5426	92	3	]	]	X
ejpam-5426	92	4	any	any	DET
ejpam-5426	92	5	open	open	ADJ
ejpam-5426	92	6	cover	cover	NOUN
ejpam-5426	92	7	is	be	AUX
ejpam-5426	92	8	d−cover	d−cover	PROPN
ejpam-5426	92	9	.	.	PUNCT
ejpam-5426	93	1	3	3	X
ejpam-5426	93	2	.	.	X
ejpam-5426	93	3	new	new	ADJ
ejpam-5426	93	4	results	result	NOUN
ejpam-5426	93	5	of	of	ADP
ejpam-5426	93	6	d−paracompact	d−paracompact	PROPN
ejpam-5426	93	7	spaces	space	VERB
ejpam-5426	93	8	this	this	DET
ejpam-5426	93	9	section	section	NOUN
ejpam-5426	93	10	presents	present	VERB
ejpam-5426	93	11	the	the	DET
ejpam-5426	93	12	new	new	ADJ
ejpam-5426	93	13	notion	notion	NOUN
ejpam-5426	93	14	of	of	ADP
ejpam-5426	93	15	d−paracompact	d−paracompact	PROPN
ejpam-5426	93	16	spaces	space	NOUN
ejpam-5426	93	17	,	,	PUNCT
ejpam-5426	93	18	and	and	CCONJ
ejpam-5426	93	19	explores	explore	VERB
ejpam-5426	93	20	their	their	PRON
ejpam-5426	93	21	connections	connection	NOUN
ejpam-5426	93	22	to	to	ADP
ejpam-5426	93	23	other	other	ADJ
ejpam-5426	93	24	spaces	space	NOUN
ejpam-5426	93	25	,	,	PUNCT
ejpam-5426	93	26	and	and	CCONJ
ejpam-5426	93	27	introduces	introduce	VERB
ejpam-5426	93	28	a	a	DET
ejpam-5426	93	29	new	new	ADJ
ejpam-5426	93	30	set	set	NOUN
ejpam-5426	93	31	of	of	ADP
ejpam-5426	93	32	properties	property	NOUN
ejpam-5426	93	33	.	.	PUNCT
ejpam-5426	94	1	definition	definition	NOUN
ejpam-5426	94	2	17	17	NUM
ejpam-5426	94	3	.	.	PUNCT
ejpam-5426	95	1	a	a	DET
ejpam-5426	95	2	topological	topological	ADJ
ejpam-5426	95	3	space	space	NOUN
ejpam-5426	95	4	(	(	PUNCT
ejpam-5426	95	5	w,ϑ	w,ϑ	PROPN
ejpam-5426	95	6	)	)	PUNCT
ejpam-5426	95	7	is	be	AUX
ejpam-5426	95	8	called	call	VERB
ejpam-5426	95	9	d−paracompact	d−paracompact	PROPN
ejpam-5426	95	10	if	if	SCONJ
ejpam-5426	95	11	every	every	DET
ejpam-5426	95	12	d−cover	d−cover	PROPN
ejpam-5426	95	13	of	of	ADP
ejpam-5426	95	14	the	the	DET
ejpam-5426	95	15	space	space	NOUN
ejpam-5426	95	16	(	(	PUNCT
ejpam-5426	95	17	w,ϑ	w,ϑ	PROPN
ejpam-5426	95	18	)	)	PUNCT
ejpam-5426	95	19	has	have	VERB
ejpam-5426	95	20	an	an	DET
ejpam-5426	95	21	open	open	ADJ
ejpam-5426	95	22	locally	locally	ADV
ejpam-5426	95	23	-	-	PUNCT
ejpam-5426	95	24	finite	finite	NOUN
ejpam-5426	95	25	refinement	refinement	NOUN
ejpam-5426	95	26	.	.	PUNCT
ejpam-5426	96	1	figure	figure	NOUN
ejpam-5426	96	2	1	1	NUM
ejpam-5426	96	3	:	:	PUNCT
ejpam-5426	96	4	the	the	DET
ejpam-5426	96	5	space	space	NOUN
ejpam-5426	96	6	of	of	ADP
ejpam-5426	96	7	difference	difference	NOUN
ejpam-5426	96	8	paracompact	paracompact	NOUN
ejpam-5426	96	9	.	.	PUNCT
ejpam-5426	97	1	figure	figure	NOUN
ejpam-5426	97	2	1	1	NUM
ejpam-5426	97	3	illustrates	illustrate	VERB
ejpam-5426	97	4	the	the	DET
ejpam-5426	97	5	space	space	NOUN
ejpam-5426	97	6	of	of	ADP
ejpam-5426	97	7	d−paracompact	d−paracompact	PROPN
ejpam-5426	97	8	such	such	ADJ
ejpam-5426	97	9	that	that	SCONJ
ejpam-5426	97	10	ẽ	ẽ	PROPN
ejpam-5426	97	11	=	=	PUNCT
ejpam-5426	97	12	{	{	PUNCT
ejpam-5426	97	13	eρ	eρ	NOUN
ejpam-5426	97	14	:	:	PUNCT
ejpam-5426	97	15	ρ	ρ	PROPN
ejpam-5426	97	16	∈	∈	PROPN
ejpam-5426	97	17	λ	λ	PROPN
ejpam-5426	97	18	}	}	PUNCT
ejpam-5426	97	19	is	be	AUX
ejpam-5426	97	20	d−cover	d−cover	PROPN
ejpam-5426	97	21	of	of	ADP
ejpam-5426	97	22	the	the	DET
ejpam-5426	97	23	topological	topological	ADJ
ejpam-5426	97	24	space	space	NOUN
ejpam-5426	97	25	(	(	PUNCT
ejpam-5426	97	26	w,ϑ	w,ϑ	PROPN
ejpam-5426	97	27	)	)	PUNCT
ejpam-5426	97	28	has	have	VERB
ejpam-5426	97	29	an	an	DET
ejpam-5426	97	30	open	open	ADJ
ejpam-5426	97	31	locally−finite	locally−finite	NOUN
ejpam-5426	97	32	refinement	refinement	NOUN
ejpam-5426	97	33	k̃	k̃	PROPN
ejpam-5426	98	1	=	=	PROPN
ejpam-5426	98	2	{	{	PUNCT
ejpam-5426	98	3	kω	kω	X
ejpam-5426	98	4	:	:	PUNCT
ejpam-5426	98	5	ω	ω	PROPN
ejpam-5426	98	6	∈	∈	PROPN
ejpam-5426	98	7	ω	ω	NOUN
ejpam-5426	98	8	}	}	PUNCT
ejpam-5426	98	9	.	.	PUNCT
ejpam-5426	99	1	i.e.	i.e.	X
ejpam-5426	99	2	each	each	DET
ejpam-5426	99	3	eρ	eρ	NOUN
ejpam-5426	99	4	is	be	AUX
ejpam-5426	99	5	a	a	DET
ejpam-5426	99	6	d−set	d−set	NOUN
ejpam-5426	99	7	for	for	ADP
ejpam-5426	99	8	all	all	DET
ejpam-5426	99	9	ρ	ρ	NOUN
ejpam-5426	99	10	∈	∈	PROPN
ejpam-5426	99	11	λ	λ	NOUN
ejpam-5426	99	12	such	such	ADJ
ejpam-5426	99	13	that	that	SCONJ
ejpam-5426	99	14	w	w	PROPN
ejpam-5426	99	15	=	=	SYM
ejpam-5426	99	16	∪ρ∈λeρ	∪ρ∈λeρ	NOUN
ejpam-5426	99	17	has	have	VERB
ejpam-5426	99	18	an	an	DET
ejpam-5426	99	19	open	open	ADJ
ejpam-5426	99	20	locally−finite	locally−finite	NOUN
ejpam-5426	99	21	refinement	refinement	NOUN
ejpam-5426	99	22	k̃	k̃	PROPN
ejpam-5426	99	23	,	,	PUNCT
ejpam-5426	99	24	which	which	PRON
ejpam-5426	99	25	the	the	DET
ejpam-5426	99	26	open	open	ADJ
ejpam-5426	99	27	refinement	refinement	NOUN
ejpam-5426	99	28	k̃	k̃	PROPN
ejpam-5426	99	29	is	be	AUX
ejpam-5426	99	30	a	a	DET
ejpam-5426	99	31	locally−finite	locally−finite	NOUN
ejpam-5426	99	32	if	if	SCONJ
ejpam-5426	99	33	every	every	DET
ejpam-5426	99	34	point	point	NOUN
ejpam-5426	99	35	xi	xi	INTJ
ejpam-5426	99	36	of	of	ADP
ejpam-5426	99	37	the	the	DET
ejpam-5426	99	38	space	space	NOUN
ejpam-5426	99	39	w	w	NOUN
ejpam-5426	99	40	has	have	VERB
ejpam-5426	99	41	a	a	DET
ejpam-5426	99	42	neighborhood	neighborhood	NOUN
ejpam-5426	99	43	ni	ni	NOUN
ejpam-5426	99	44	such	such	ADJ
ejpam-5426	99	45	that	that	SCONJ
ejpam-5426	99	46	eρ	eρ	PROPN
ejpam-5426	99	47	∩ni	∩ni	PROPN
ejpam-5426	99	48	̸=	̸=	PROPN
ejpam-5426	99	49	ϕ	ϕ	PROPN
ejpam-5426	99	50	is	be	AUX
ejpam-5426	99	51	finite	finite	ADJ
ejpam-5426	99	52	for	for	ADP
ejpam-5426	99	53	all	all	DET
ejpam-5426	99	54	ρ	ρ	NOUN
ejpam-5426	99	55	,	,	PUNCT
ejpam-5426	99	56	i	i	PROPN
ejpam-5426	99	57	∈	∈	PROPN
ejpam-5426	99	58	λ	λ	PROPN
ejpam-5426	99	59	.	.	PUNCT
ejpam-5426	99	60	theorem	theorem	PROPN
ejpam-5426	99	61	2	2	NUM
ejpam-5426	99	62	.	.	PUNCT
ejpam-5426	100	1	every	every	DET
ejpam-5426	100	2	d−paracompact	d−paracompact	NOUN
ejpam-5426	100	3	space	space	NOUN
ejpam-5426	100	4	(	(	PUNCT
ejpam-5426	100	5	w,ϑ	w,ϑ	PROPN
ejpam-5426	100	6	)	)	PUNCT
ejpam-5426	100	7	is	be	AUX
ejpam-5426	100	8	paracompact	paracompact	ADJ
ejpam-5426	100	9	.	.	PUNCT
ejpam-5426	101	1	proof	proof	NOUN
ejpam-5426	101	2	.	.	PUNCT
ejpam-5426	102	1	suppose	suppose	VERB
ejpam-5426	102	2	that	that	SCONJ
ejpam-5426	102	3	(	(	PUNCT
ejpam-5426	102	4	w,ϑ	w,ϑ	PROPN
ejpam-5426	102	5	)	)	PUNCT
ejpam-5426	102	6	is	be	AUX
ejpam-5426	102	7	a	a	DET
ejpam-5426	102	8	d−paracompact	d−paracompact	NOUN
ejpam-5426	102	9	space	space	NOUN
ejpam-5426	102	10	and	and	CCONJ
ejpam-5426	102	11	ẽ	ẽ	PROPN
ejpam-5426	102	12	=	=	SYM
ejpam-5426	102	13	{	{	PUNCT
ejpam-5426	102	14	eρ	eρ	NOUN
ejpam-5426	102	15	:	:	PUNCT
ejpam-5426	102	16	ρ	ρ	PROPN
ejpam-5426	102	17	∈	∈	PROPN
ejpam-5426	102	18	λ	λ	PROPN
ejpam-5426	102	19	}	}	PUNCT
ejpam-5426	102	20	is	be	AUX
ejpam-5426	102	21	an	an	DET
ejpam-5426	102	22	open	open	ADJ
ejpam-5426	102	23	-	-	PUNCT
ejpam-5426	102	24	cover	cover	NOUN
ejpam-5426	102	25	of	of	ADP
ejpam-5426	102	26	(	(	PUNCT
ejpam-5426	102	27	w,ϑ	w,ϑ	PROPN
ejpam-5426	102	28	)	)	PUNCT
ejpam-5426	102	29	.	.	PUNCT
ejpam-5426	103	1	by	by	ADP
ejpam-5426	103	2	theorem	theorem	NOUN
ejpam-5426	103	3	1	1	NUM
ejpam-5426	103	4	,	,	PUNCT
ejpam-5426	103	5	the	the	DET
ejpam-5426	103	6	cover	cover	NOUN
ejpam-5426	103	7	ẽ	ẽ	PROPN
ejpam-5426	103	8	is	be	AUX
ejpam-5426	103	9	a	a	DET
ejpam-5426	103	10	d−cover	d−cover	PROPN
ejpam-5426	103	11	,	,	PUNCT
ejpam-5426	103	12	and	and	CCONJ
ejpam-5426	103	13	it	it	PRON
ejpam-5426	103	14	has	have	VERB
ejpam-5426	103	15	an	an	DET
ejpam-5426	103	16	open	open	ADJ
ejpam-5426	103	17	locally−finite	locally−finite	NOUN
ejpam-5426	103	18	refinement	refinement	NOUN
ejpam-5426	103	19	.	.	PUNCT
ejpam-5426	104	1	a.	a.	PROPN
ejpam-5426	104	2	amourah	amourah	PROPN
ejpam-5426	104	3	et	et	PROPN
ejpam-5426	104	4	al	al	PROPN
ejpam-5426	104	5	.	.	PUNCT
ejpam-5426	104	6	/	/	SYM
ejpam-5426	104	7	eur	eur	PROPN
ejpam-5426	104	8	.	.	PUNCT
ejpam-5426	105	1	j.	j.	PROPN
ejpam-5426	105	2	pure	pure	PROPN
ejpam-5426	105	3	appl	appl	PROPN
ejpam-5426	105	4	.	.	PROPN
ejpam-5426	105	5	math	math	PROPN
ejpam-5426	105	6	,	,	PUNCT
ejpam-5426	105	7	17	17	NUM
ejpam-5426	105	8	(	(	PUNCT
ejpam-5426	105	9	4	4	NUM
ejpam-5426	105	10	)	)	PUNCT
ejpam-5426	105	11	(	(	PUNCT
ejpam-5426	105	12	2024	2024	NUM
ejpam-5426	105	13	)	)	PUNCT
ejpam-5426	105	14	,	,	PUNCT
ejpam-5426	105	15	2990	2990	NUM
ejpam-5426	105	16	-	-	SYM
ejpam-5426	105	17	3003	3003	NUM
ejpam-5426	105	18	2994	2994	NUM
ejpam-5426	105	19	figure	figure	NOUN
ejpam-5426	105	20	2	2	NUM
ejpam-5426	105	21	:	:	PUNCT
ejpam-5426	105	22	the	the	DET
ejpam-5426	105	23	relation	relation	NOUN
ejpam-5426	105	24	of	of	ADP
ejpam-5426	105	25	d−paracompact	d−paracompact	PROPN
ejpam-5426	105	26	with	with	ADP
ejpam-5426	105	27	paracompact	paracompact	ADJ
ejpam-5426	105	28	spaces	space	NOUN
ejpam-5426	105	29	.	.	PUNCT
ejpam-5426	106	1	figure	figure	VERB
ejpam-5426	106	2	2	2	NUM
ejpam-5426	106	3	presents	present	VERB
ejpam-5426	106	4	the	the	DET
ejpam-5426	106	5	basic	basic	ADJ
ejpam-5426	106	6	relation	relation	NOUN
ejpam-5426	106	7	between	between	ADP
ejpam-5426	106	8	d−paracompact	d−paracompact	PROPN
ejpam-5426	106	9	and	and	CCONJ
ejpam-5426	106	10	paracompact	paracompact	ADJ
ejpam-5426	106	11	spaces	space	NOUN
ejpam-5426	106	12	,	,	PUNCT
ejpam-5426	106	13	which	which	PRON
ejpam-5426	106	14	represents	represent	VERB
ejpam-5426	106	15	a	a	DET
ejpam-5426	106	16	crucial	crucial	ADJ
ejpam-5426	106	17	fact	fact	NOUN
ejpam-5426	106	18	that	that	SCONJ
ejpam-5426	106	19	every	every	DET
ejpam-5426	106	20	d−paracompact	d−paracompact	NOUN
ejpam-5426	106	21	space	space	NOUN
ejpam-5426	106	22	must	must	AUX
ejpam-5426	106	23	be	be	AUX
ejpam-5426	106	24	paracompact	paracompact	ADJ
ejpam-5426	106	25	such	such	ADJ
ejpam-5426	106	26	that	that	SCONJ
ejpam-5426	106	27	ẽ	ẽ	PROPN
ejpam-5426	106	28	=	=	PUNCT
ejpam-5426	106	29	{	{	PUNCT
ejpam-5426	106	30	eρ	eρ	NOUN
ejpam-5426	106	31	:	:	PUNCT
ejpam-5426	106	32	ρ	ρ	PROPN
ejpam-5426	106	33	∈	∈	PROPN
ejpam-5426	106	34	λ	λ	PROPN
ejpam-5426	106	35	}	}	PUNCT
ejpam-5426	106	36	is	be	AUX
ejpam-5426	106	37	d−cover	d−cover	PROPN
ejpam-5426	106	38	of	of	ADP
ejpam-5426	106	39	the	the	DET
ejpam-5426	106	40	topological	topological	ADJ
ejpam-5426	106	41	space	space	NOUN
ejpam-5426	106	42	(	(	PUNCT
ejpam-5426	106	43	w,ϑ	w,ϑ	PROPN
ejpam-5426	106	44	)	)	PUNCT
ejpam-5426	106	45	has	have	VERB
ejpam-5426	106	46	an	an	DET
ejpam-5426	106	47	open	open	ADJ
ejpam-5426	106	48	locally−finite	locally−finite	NOUN
ejpam-5426	106	49	refinement	refinement	NOUN
ejpam-5426	107	1	and	and	CCONJ
ejpam-5426	107	2	we	we	PRON
ejpam-5426	107	3	have	have	VERB
ejpam-5426	107	4	g̃	g̃	PROPN
ejpam-5426	107	5	=	=	SYM
ejpam-5426	107	6	{	{	PUNCT
ejpam-5426	107	7	gω	gω	X
ejpam-5426	107	8	:	:	PUNCT
ejpam-5426	107	9	ω	ω	PROPN
ejpam-5426	107	10	∈	∈	PROPN
ejpam-5426	107	11	ω	ω	PROPN
ejpam-5426	107	12	}	}	PUNCT
ejpam-5426	107	13	is	be	AUX
ejpam-5426	107	14	cover	cover	NOUN
ejpam-5426	107	15	of	of	ADP
ejpam-5426	107	16	the	the	DET
ejpam-5426	107	17	topological	topological	ADJ
ejpam-5426	107	18	space	space	NOUN
ejpam-5426	107	19	(	(	PUNCT
ejpam-5426	107	20	q	q	NOUN
ejpam-5426	107	21	,	,	PUNCT
ejpam-5426	107	22	ι	ι	PROPN
ejpam-5426	107	23	)	)	PUNCT
ejpam-5426	107	24	has	have	AUX
ejpam-5426	107	25	an	an	DET
ejpam-5426	107	26	open	open	ADJ
ejpam-5426	107	27	locally−finite	locally−finite	NOUN
ejpam-5426	107	28	refinement	refinement	NOUN
ejpam-5426	107	29	.	.	PUNCT
ejpam-5426	108	1	example	example	NOUN
ejpam-5426	109	1	1	1	NUM
ejpam-5426	109	2	.	.	PUNCT
ejpam-5426	110	1	let	let	AUX
ejpam-5426	110	2	(	(	PUNCT
ejpam-5426	110	3	r	r	NOUN
ejpam-5426	110	4	,	,	PUNCT
ejpam-5426	110	5	ϑu	ϑu	NOUN
ejpam-5426	110	6	)	)	PUNCT
ejpam-5426	110	7	be	be	VERB
ejpam-5426	110	8	a	a	DET
ejpam-5426	110	9	d−paracompact	d−paracompact	NOUN
ejpam-5426	110	10	topological	topological	ADJ
ejpam-5426	110	11	space	space	NOUN
ejpam-5426	110	12	.	.	PUNCT
ejpam-5426	111	1	then	then	ADV
ejpam-5426	111	2	by	by	ADP
ejpam-5426	111	3	using	use	VERB
ejpam-5426	111	4	the	the	DET
ejpam-5426	111	5	theorem	theorem	ADJ
ejpam-5426	111	6	2	2	NUM
ejpam-5426	111	7	we	we	PRON
ejpam-5426	111	8	get	get	VERB
ejpam-5426	111	9	that	that	SCONJ
ejpam-5426	111	10	the	the	DET
ejpam-5426	111	11	space	space	NOUN
ejpam-5426	111	12	(	(	PUNCT
ejpam-5426	111	13	r	r	NOUN
ejpam-5426	111	14	,	,	PUNCT
ejpam-5426	111	15	ϑu	ϑu	NOUN
ejpam-5426	111	16	)	)	PUNCT
ejpam-5426	111	17	is	be	AUX
ejpam-5426	111	18	paracompact	paracompact	ADJ
ejpam-5426	111	19	.	.	PUNCT
ejpam-5426	112	1	the	the	DET
ejpam-5426	112	2	explanation	explanation	NOUN
ejpam-5426	112	3	for	for	ADP
ejpam-5426	112	4	why	why	SCONJ
ejpam-5426	112	5	the	the	DET
ejpam-5426	112	6	previous	previous	ADJ
ejpam-5426	112	7	theorem	theorem	NOUN
ejpam-5426	112	8	’s	’s	PART
ejpam-5426	112	9	converse	converse	NOUN
ejpam-5426	112	10	may	may	AUX
ejpam-5426	112	11	not	not	PART
ejpam-5426	112	12	be	be	AUX
ejpam-5426	112	13	true	true	ADJ
ejpam-5426	112	14	is	be	AUX
ejpam-5426	112	15	illustrated	illustrate	VERB
ejpam-5426	112	16	by	by	ADP
ejpam-5426	112	17	the	the	DET
ejpam-5426	112	18	example	example	NOUN
ejpam-5426	112	19	that	that	PRON
ejpam-5426	112	20	follows	follow	VERB
ejpam-5426	112	21	.	.	PUNCT
ejpam-5426	113	1	example	example	NOUN
ejpam-5426	114	1	2	2	NUM
ejpam-5426	114	2	.	.	PUNCT
ejpam-5426	115	1	the	the	DET
ejpam-5426	115	2	topological	topological	ADJ
ejpam-5426	115	3	space	space	NOUN
ejpam-5426	115	4	(	(	PUNCT
ejpam-5426	115	5	r	r	NOUN
ejpam-5426	115	6	,	,	PUNCT
ejpam-5426	115	7	ϑcof	ϑcof	NOUN
ejpam-5426	115	8	)	)	PUNCT
ejpam-5426	115	9	is	be	AUX
ejpam-5426	115	10	paracompact	paracompact	ADJ
ejpam-5426	115	11	but	but	CCONJ
ejpam-5426	115	12	not	not	PART
ejpam-5426	115	13	a	a	DET
ejpam-5426	115	14	d	d	NOUN
ejpam-5426	115	15	-	-	NOUN
ejpam-5426	115	16	paracompact	paracompact	ADJ
ejpam-5426	115	17	.	.	PUNCT
ejpam-5426	116	1	this	this	PRON
ejpam-5426	116	2	is	be	AUX
ejpam-5426	116	3	because	because	SCONJ
ejpam-5426	116	4	for	for	SCONJ
ejpam-5426	116	5	all	all	DET
ejpam-5426	116	6	x	x	SYM
ejpam-5426	116	7	∈	∈	PROPN
ejpam-5426	116	8	r	r	NOUN
ejpam-5426	116	9	,	,	PUNCT
ejpam-5426	116	10	each	each	DET
ejpam-5426	116	11	set	set	NOUN
ejpam-5426	116	12	of	of	ADP
ejpam-5426	116	13	the	the	DET
ejpam-5426	116	14	form	form	NOUN
ejpam-5426	116	15	r	r	NOUN
ejpam-5426	116	16	−	−	NOUN
ejpam-5426	116	17	x	x	PUNCT
ejpam-5426	116	18	is	be	AUX
ejpam-5426	116	19	open	open	ADJ
ejpam-5426	116	20	in	in	ADP
ejpam-5426	116	21	a	a	DET
ejpam-5426	116	22	topological	topological	ADJ
ejpam-5426	116	23	space	space	NOUN
ejpam-5426	116	24	(	(	PUNCT
ejpam-5426	116	25	r	r	NOUN
ejpam-5426	116	26	,	,	PUNCT
ejpam-5426	116	27	ϑcof	ϑcof	NOUN
ejpam-5426	116	28	)	)	PUNCT
ejpam-5426	116	29	.	.	PUNCT
ejpam-5426	117	1	now	now	ADV
ejpam-5426	117	2	,	,	PUNCT
ejpam-5426	117	3	for	for	ADP
ejpam-5426	117	4	all	all	DET
ejpam-5426	117	5	a	a	DET
ejpam-5426	117	6	,	,	PUNCT
ejpam-5426	117	7	b	b	X
ejpam-5426	117	8	∈	∈	PROPN
ejpam-5426	117	9	r	r	NOUN
ejpam-5426	117	10	,	,	PUNCT
ejpam-5426	117	11	if	if	SCONJ
ejpam-5426	117	12	a	a	PRON
ejpam-5426	117	13	=	=	NOUN
ejpam-5426	117	14	r	r	NOUN
ejpam-5426	117	15	−	−	PROPN
ejpam-5426	117	16	{	{	PUNCT
ejpam-5426	117	17	a	a	NOUN
ejpam-5426	117	18	}	}	PUNCT
ejpam-5426	117	19	and	and	CCONJ
ejpam-5426	117	20	b	b	X
ejpam-5426	117	21	=	=	SYM
ejpam-5426	117	22	r	r	NOUN
ejpam-5426	117	23	−	−	PROPN
ejpam-5426	117	24	{	{	PUNCT
ejpam-5426	117	25	b	b	NOUN
ejpam-5426	117	26	}	}	PUNCT
ejpam-5426	117	27	be	be	AUX
ejpam-5426	117	28	any	any	DET
ejpam-5426	117	29	two	two	NUM
ejpam-5426	117	30	open	open	ADJ
ejpam-5426	117	31	sets	set	NOUN
ejpam-5426	117	32	in	in	ADP
ejpam-5426	117	33	(	(	PUNCT
ejpam-5426	117	34	r	r	NOUN
ejpam-5426	117	35	,	,	PUNCT
ejpam-5426	117	36	ϑcof	ϑcof	NOUN
ejpam-5426	117	37	)	)	PUNCT
ejpam-5426	117	38	,	,	PUNCT
ejpam-5426	117	39	then	then	ADV
ejpam-5426	117	40	d	d	X
ejpam-5426	117	41	=	=	PUNCT
ejpam-5426	117	42	a	a	DET
ejpam-5426	117	43	−	−	PROPN
ejpam-5426	117	44	b	b	NOUN
ejpam-5426	117	45	=	=	PRON
ejpam-5426	117	46	{	{	PUNCT
ejpam-5426	117	47	b	b	NOUN
ejpam-5426	117	48	}	}	PUNCT
ejpam-5426	117	49	is	be	AUX
ejpam-5426	117	50	a	a	DET
ejpam-5426	117	51	d−set	d−set	NOUN
ejpam-5426	117	52	but	but	CCONJ
ejpam-5426	117	53	not	not	PART
ejpam-5426	117	54	an	an	DET
ejpam-5426	117	55	open	open	ADJ
ejpam-5426	117	56	set	set	NOUN
ejpam-5426	117	57	.	.	PUNCT
ejpam-5426	118	1	this	this	PRON
ejpam-5426	118	2	is	be	AUX
ejpam-5426	118	3	because	because	SCONJ
ejpam-5426	118	4	a	a	DET
ejpam-5426	118	5	d−cover	d−cover	PROPN
ejpam-5426	118	6	d̃	d̃	PROPN
ejpam-5426	118	7	=	=	SYM
ejpam-5426	118	8	{	{	PUNCT
ejpam-5426	118	9	{	{	PUNCT
ejpam-5426	118	10	b	b	NOUN
ejpam-5426	118	11	}	}	PUNCT
ejpam-5426	118	12	:	:	PUNCT
ejpam-5426	118	13	b	b	X
ejpam-5426	118	14	∈	∈	ADP
ejpam-5426	118	15	r	r	NOUN
ejpam-5426	118	16	}	}	PUNCT
ejpam-5426	118	17	has	have	VERB
ejpam-5426	118	18	not	not	PART
ejpam-5426	118	19	an	an	DET
ejpam-5426	118	20	open	open	ADJ
ejpam-5426	118	21	locally	locally	ADV
ejpam-5426	118	22	-	-	PUNCT
ejpam-5426	118	23	finite	finite	NOUN
ejpam-5426	118	24	refinement	refinement	NOUN
ejpam-5426	118	25	.	.	PUNCT
ejpam-5426	119	1	because	because	SCONJ
ejpam-5426	119	2	,	,	PUNCT
ejpam-5426	119	3	if	if	SCONJ
ejpam-5426	119	4	d̃	d̃	PROPN
ejpam-5426	119	5	has	have	VERB
ejpam-5426	119	6	an	an	DET
ejpam-5426	119	7	open	open	ADJ
ejpam-5426	119	8	locally	locally	ADV
ejpam-5426	119	9	-	-	PUNCT
ejpam-5426	119	10	finite	finite	ADJ
ejpam-5426	119	11	refinement	refinement	NOUN
ejpam-5426	119	12	{	{	PUNCT
ejpam-5426	119	13	{	{	PUNCT
ejpam-5426	119	14	b1	b1	PROPN
ejpam-5426	119	15	,	,	PUNCT
ejpam-5426	119	16	b2	b2	NOUN
ejpam-5426	119	17	,	,	PUNCT
ejpam-5426	119	18	.	.	PUNCT
ejpam-5426	119	19	.	.	PUNCT
ejpam-5426	119	20	.	.	PUNCT
ejpam-5426	119	21	,	,	PUNCT
ejpam-5426	119	22	bn	bn	PROPN
ejpam-5426	119	23	}	}	PUNCT
ejpam-5426	119	24	,	,	PUNCT
ejpam-5426	119	25	then	then	ADV
ejpam-5426	119	26	we	we	PRON
ejpam-5426	119	27	have	have	VERB
ejpam-5426	119	28	r	r	NOUN
ejpam-5426	119	29	⊆	⊆	NUM
ejpam-5426	119	30	∪n	∪n	X
ejpam-5426	119	31	i=1bi	i=1bi	NUM
ejpam-5426	119	32	,	,	PUNCT
ejpam-5426	119	33	which	which	PRON
ejpam-5426	119	34	implies	imply	VERB
ejpam-5426	119	35	that	that	SCONJ
ejpam-5426	119	36	r	r	NOUN
ejpam-5426	119	37	is	be	AUX
ejpam-5426	119	38	a	a	DET
ejpam-5426	119	39	finite	finite	ADJ
ejpam-5426	119	40	set	set	NOUN
ejpam-5426	119	41	.	.	PUNCT
ejpam-5426	120	1	which	which	PRON
ejpam-5426	120	2	is	be	AUX
ejpam-5426	120	3	a	a	DET
ejpam-5426	120	4	contradiction	contradiction	NOUN
ejpam-5426	120	5	.	.	PUNCT
ejpam-5426	121	1	the	the	DET
ejpam-5426	121	2	following	follow	VERB
ejpam-5426	121	3	example	example	NOUN
ejpam-5426	121	4	illustrates	illustrate	VERB
ejpam-5426	121	5	the	the	DET
ejpam-5426	121	6	contrapositive	contrapositive	NOUN
ejpam-5426	121	7	of	of	ADP
ejpam-5426	121	8	the	the	DET
ejpam-5426	121	9	above	above	ADJ
ejpam-5426	121	10	theorem	theorem	PROPN
ejpam-5426	121	11	.	.	PROPN
ejpam-5426	121	12	example	example	NOUN
ejpam-5426	122	1	3	3	NUM
ejpam-5426	122	2	.	.	PUNCT
ejpam-5426	123	1	the	the	DET
ejpam-5426	123	2	space	space	NOUN
ejpam-5426	123	3	(	(	PUNCT
ejpam-5426	123	4	r	r	NOUN
ejpam-5426	123	5	,	,	PUNCT
ejpam-5426	123	6	ϑl.r	ϑl.r	ADJ
ejpam-5426	123	7	)	)	PUNCT
ejpam-5426	123	8	is	be	AUX
ejpam-5426	123	9	not	not	PART
ejpam-5426	123	10	paracompact	paracompact	ADJ
ejpam-5426	123	11	,	,	PUNCT
ejpam-5426	123	12	which	which	PRON
ejpam-5426	123	13	is	be	AUX
ejpam-5426	123	14	not	not	PART
ejpam-5426	123	15	d−paracompact	d−paracompact	PROPN
ejpam-5426	123	16	space	space	NOUN
ejpam-5426	123	17	.	.	PUNCT
ejpam-5426	124	1	the	the	DET
ejpam-5426	124	2	next	next	ADJ
ejpam-5426	124	3	theorem	theorem	NOUN
ejpam-5426	124	4	has	have	VERB
ejpam-5426	124	5	the	the	DET
ejpam-5426	124	6	purpose	purpose	NOUN
ejpam-5426	124	7	to	to	PART
ejpam-5426	124	8	indicate	indicate	VERB
ejpam-5426	124	9	that	that	SCONJ
ejpam-5426	124	10	,	,	PUNCT
ejpam-5426	124	11	in	in	ADP
ejpam-5426	124	12	under	under	ADP
ejpam-5426	124	13	conditions	condition	NOUN
ejpam-5426	124	14	,	,	PUNCT
ejpam-5426	124	15	the	the	DET
ejpam-5426	124	16	converses	converse	NOUN
ejpam-5426	124	17	of	of	ADP
ejpam-5426	124	18	the	the	DET
ejpam-5426	124	19	theorem	theorem	NOUN
ejpam-5426	124	20	above	above	ADV
ejpam-5426	124	21	could	could	AUX
ejpam-5426	124	22	be	be	AUX
ejpam-5426	124	23	held	hold	VERB
ejpam-5426	124	24	.	.	PUNCT
ejpam-5426	125	1	theorem	theorem	NOUN
ejpam-5426	125	2	3	3	NUM
ejpam-5426	125	3	.	.	PUNCT
ejpam-5426	126	1	every	every	DET
ejpam-5426	126	2	topological	topological	ADJ
ejpam-5426	126	3	space	space	NOUN
ejpam-5426	126	4	(	(	PUNCT
ejpam-5426	126	5	w,ϑ	w,ϑ	PROPN
ejpam-5426	126	6	)	)	PUNCT
ejpam-5426	126	7	that	that	PRON
ejpam-5426	126	8	is	be	AUX
ejpam-5426	126	9	a	a	DET
ejpam-5426	126	10	locally	locally	ADV
ejpam-5426	126	11	-	-	PUNCT
ejpam-5426	126	12	indiscreet	indiscreet	ADJ
ejpam-5426	126	13	paracompact	paracompact	NOUN
ejpam-5426	126	14	is	be	AUX
ejpam-5426	126	15	d−paracompact	d−paracompact	NOUN
ejpam-5426	126	16	.	.	PUNCT
ejpam-5426	127	1	proof	proof	NOUN
ejpam-5426	127	2	.	.	PUNCT
ejpam-5426	128	1	let	let	VERB
ejpam-5426	128	2	ẽ	ẽ	NOUN
ejpam-5426	128	3	=	=	PRON
ejpam-5426	128	4	{	{	PUNCT
ejpam-5426	128	5	eρ	eρ	NOUN
ejpam-5426	128	6	:	:	PUNCT
ejpam-5426	128	7	ρ	ρ	PROPN
ejpam-5426	128	8	∈	∈	PROPN
ejpam-5426	128	9	λ	λ	NOUN
ejpam-5426	128	10	}	}	PUNCT
ejpam-5426	128	11	be	be	VERB
ejpam-5426	128	12	any	any	DET
ejpam-5426	128	13	d−cover	d−cover	PROPN
ejpam-5426	128	14	of	of	ADP
ejpam-5426	128	15	(	(	PUNCT
ejpam-5426	128	16	w,ϑ	w,ϑ	PROPN
ejpam-5426	128	17	)	)	PUNCT
ejpam-5426	128	18	.	.	PUNCT
ejpam-5426	129	1	then	then	ADV
ejpam-5426	129	2	ẽ	ẽ	PROPN
ejpam-5426	129	3	=	=	PUNCT
ejpam-5426	129	4	{	{	PUNCT
ejpam-5426	129	5	eρ	eρ	NOUN
ejpam-5426	129	6	:	:	PUNCT
ejpam-5426	129	7	ρ	ρ	PROPN
ejpam-5426	129	8	∈	∈	PROPN
ejpam-5426	129	9	λ	λ	NOUN
ejpam-5426	129	10	}	}	PUNCT
ejpam-5426	129	11	is	be	AUX
ejpam-5426	129	12	open	open	ADJ
ejpam-5426	129	13	cover	cover	NOUN
ejpam-5426	129	14	,	,	PUNCT
ejpam-5426	129	15	which	which	PRON
ejpam-5426	129	16	has	have	VERB
ejpam-5426	129	17	an	an	DET
ejpam-5426	129	18	open	open	ADJ
ejpam-5426	129	19	locally	locally	ADV
ejpam-5426	129	20	-	-	PUNCT
ejpam-5426	129	21	finite	finite	ADJ
ejpam-5426	129	22	refinement	refinement	NOUN
ejpam-5426	129	23	.	.	PUNCT
ejpam-5426	130	1	hence	hence	ADV
ejpam-5426	130	2	,	,	PUNCT
ejpam-5426	130	3	the	the	DET
ejpam-5426	130	4	result	result	NOUN
ejpam-5426	130	5	.	.	PUNCT
ejpam-5426	131	1	a.	a.	PROPN
ejpam-5426	131	2	amourah	amourah	PROPN
ejpam-5426	131	3	et	et	PROPN
ejpam-5426	131	4	al	al	PROPN
ejpam-5426	131	5	.	.	PUNCT
ejpam-5426	131	6	/	/	SYM
ejpam-5426	131	7	eur	eur	PROPN
ejpam-5426	131	8	.	.	PUNCT
ejpam-5426	132	1	j.	j.	PROPN
ejpam-5426	132	2	pure	pure	PROPN
ejpam-5426	132	3	appl	appl	PROPN
ejpam-5426	132	4	.	.	PROPN
ejpam-5426	132	5	math	math	PROPN
ejpam-5426	132	6	,	,	PUNCT
ejpam-5426	132	7	17	17	NUM
ejpam-5426	132	8	(	(	PUNCT
ejpam-5426	132	9	4	4	NUM
ejpam-5426	132	10	)	)	PUNCT
ejpam-5426	132	11	(	(	PUNCT
ejpam-5426	132	12	2024	2024	NUM
ejpam-5426	132	13	)	)	PUNCT
ejpam-5426	132	14	,	,	PUNCT
ejpam-5426	132	15	2990	2990	NUM
ejpam-5426	132	16	-	-	SYM
ejpam-5426	132	17	3003	3003	NUM
ejpam-5426	132	18	2995	2995	NUM
ejpam-5426	132	19	figure	figure	NOUN
ejpam-5426	132	20	3	3	NUM
ejpam-5426	132	21	:	:	PUNCT
ejpam-5426	132	22	the	the	DET
ejpam-5426	132	23	relation	relation	NOUN
ejpam-5426	132	24	of	of	ADP
ejpam-5426	132	25	d−paracompact	d−paracompact	PROPN
ejpam-5426	132	26	and	and	CCONJ
ejpam-5426	132	27	paracompact	paracompact	ADJ
ejpam-5426	132	28	spaces	space	NOUN
ejpam-5426	132	29	with	with	ADP
ejpam-5426	132	30	locally	locally	ADV
ejpam-5426	132	31	indiscreet	indiscreet	ADJ
ejpam-5426	132	32	condition	condition	NOUN
ejpam-5426	132	33	.	.	PUNCT
ejpam-5426	133	1	figure	figure	VERB
ejpam-5426	133	2	3	3	NUM
ejpam-5426	133	3	presents	present	VERB
ejpam-5426	133	4	the	the	DET
ejpam-5426	133	5	complex	complex	ADJ
ejpam-5426	133	6	relation	relation	NOUN
ejpam-5426	133	7	between	between	ADP
ejpam-5426	133	8	d−paracompact	d−paracompact	PROPN
ejpam-5426	133	9	and	and	CCONJ
ejpam-5426	133	10	paracompact	paracompact	ADJ
ejpam-5426	133	11	spaces	space	NOUN
ejpam-5426	133	12	under	under	ADP
ejpam-5426	133	13	extra	extra	ADJ
ejpam-5426	133	14	condition	condition	NOUN
ejpam-5426	133	15	,	,	PUNCT
ejpam-5426	133	16	which	which	PRON
ejpam-5426	133	17	represents	represent	VERB
ejpam-5426	133	18	a	a	DET
ejpam-5426	133	19	significant	significant	ADJ
ejpam-5426	133	20	fact	fact	NOUN
ejpam-5426	133	21	that	that	SCONJ
ejpam-5426	133	22	everyd−paracompact	everyd−paracompact	NOUN
ejpam-5426	133	23	space	space	NOUN
ejpam-5426	133	24	must	must	AUX
ejpam-5426	133	25	be	be	AUX
ejpam-5426	133	26	paracompact	paracompact	ADJ
ejpam-5426	133	27	,	,	PUNCT
ejpam-5426	133	28	while	while	SCONJ
ejpam-5426	133	29	the	the	DET
ejpam-5426	133	30	converse	converse	NOUN
ejpam-5426	133	31	is	be	AUX
ejpam-5426	133	32	true	true	ADJ
ejpam-5426	133	33	if	if	SCONJ
ejpam-5426	133	34	the	the	DET
ejpam-5426	133	35	paracompact	paracompact	ADJ
ejpam-5426	133	36	space	space	NOUN
ejpam-5426	133	37	is	be	AUX
ejpam-5426	133	38	locally	locally	ADV
ejpam-5426	133	39	indiscreet	indiscreet	ADJ
ejpam-5426	133	40	such	such	ADJ
ejpam-5426	133	41	that	that	SCONJ
ejpam-5426	133	42	ẽ	ẽ	PROPN
ejpam-5426	133	43	=	=	PUNCT
ejpam-5426	133	44	{	{	PUNCT
ejpam-5426	133	45	eρ	eρ	NOUN
ejpam-5426	133	46	:	:	PUNCT
ejpam-5426	133	47	ρ	ρ	PROPN
ejpam-5426	133	48	∈	∈	PROPN
ejpam-5426	133	49	λ	λ	PROPN
ejpam-5426	133	50	}	}	PUNCT
ejpam-5426	133	51	is	be	AUX
ejpam-5426	133	52	d−cover	d−cover	PROPN
ejpam-5426	133	53	of	of	ADP
ejpam-5426	133	54	the	the	DET
ejpam-5426	133	55	topological	topological	ADJ
ejpam-5426	133	56	space	space	NOUN
ejpam-5426	133	57	(	(	PUNCT
ejpam-5426	133	58	w,ϑ	w,ϑ	PROPN
ejpam-5426	133	59	)	)	PUNCT
ejpam-5426	133	60	has	have	VERB
ejpam-5426	133	61	an	an	DET
ejpam-5426	133	62	open	open	ADJ
ejpam-5426	133	63	locally−finite	locally−finite	NOUN
ejpam-5426	133	64	refinement	refinement	NOUN
ejpam-5426	133	65	and	and	CCONJ
ejpam-5426	133	66	we	we	PRON
ejpam-5426	133	67	have	have	VERB
ejpam-5426	133	68	g̃	g̃	PROPN
ejpam-5426	133	69	=	=	SYM
ejpam-5426	133	70	{	{	PUNCT
ejpam-5426	133	71	gω	gω	X
ejpam-5426	133	72	:	:	PUNCT
ejpam-5426	133	73	ω	ω	PROPN
ejpam-5426	133	74	∈	∈	PROPN
ejpam-5426	133	75	ω	ω	PROPN
ejpam-5426	133	76	}	}	PUNCT
ejpam-5426	133	77	is	be	AUX
ejpam-5426	133	78	cover	cover	NOUN
ejpam-5426	133	79	of	of	ADP
ejpam-5426	133	80	the	the	DET
ejpam-5426	133	81	topological	topological	ADJ
ejpam-5426	133	82	space	space	NOUN
ejpam-5426	133	83	(	(	PUNCT
ejpam-5426	133	84	q	q	NOUN
ejpam-5426	133	85	,	,	PUNCT
ejpam-5426	133	86	ι	ι	PROPN
ejpam-5426	133	87	)	)	PUNCT
ejpam-5426	133	88	has	have	AUX
ejpam-5426	133	89	an	an	DET
ejpam-5426	133	90	open	open	ADJ
ejpam-5426	133	91	locally−finite	locally−finite	NOUN
ejpam-5426	133	92	refinement	refinement	NOUN
ejpam-5426	133	93	.	.	PUNCT
ejpam-5426	134	1	example	example	NOUN
ejpam-5426	135	1	4	4	NUM
ejpam-5426	135	2	.	.	PUNCT
ejpam-5426	136	1	(	(	PUNCT
ejpam-5426	136	2	i	i	NOUN
ejpam-5426	136	3	)	)	PUNCT
ejpam-5426	136	4	notice	notice	VERB
ejpam-5426	136	5	that	that	SCONJ
ejpam-5426	136	6	the	the	DET
ejpam-5426	136	7	space	space	NOUN
ejpam-5426	136	8	(	(	PUNCT
ejpam-5426	136	9	r	r	NOUN
ejpam-5426	136	10	,	,	PUNCT
ejpam-5426	136	11	ϑind	ϑind	NOUN
ejpam-5426	136	12	)	)	PUNCT
ejpam-5426	136	13	is	be	AUX
ejpam-5426	136	14	locally	locally	ADV
ejpam-5426	136	15	-	-	PUNCT
ejpam-5426	136	16	indiscreet	indiscreet	ADJ
ejpam-5426	136	17	and	and	CCONJ
ejpam-5426	136	18	paracompact	paracompact	ADJ
ejpam-5426	136	19	,	,	PUNCT
ejpam-5426	136	20	then	then	ADV
ejpam-5426	136	21	it	it	PRON
ejpam-5426	136	22	is	be	AUX
ejpam-5426	136	23	d−paracompact	d−paracompact	PROPN
ejpam-5426	136	24	space	space	NOUN
ejpam-5426	136	25	.	.	PUNCT
ejpam-5426	137	1	(	(	PUNCT
ejpam-5426	137	2	ii	ii	NOUN
ejpam-5426	137	3	)	)	PUNCT
ejpam-5426	137	4	let	let	VERB
ejpam-5426	137	5	w	w	NOUN
ejpam-5426	137	6	=	=	SYM
ejpam-5426	137	7	r	r	NOUN
ejpam-5426	137	8	and	and	CCONJ
ejpam-5426	137	9	ϑ	ϑ	X
ejpam-5426	137	10	=	=	SYM
ejpam-5426	137	11	{	{	PUNCT
ejpam-5426	137	12	ϕ,r	ϕ,r	NOUN
ejpam-5426	137	13	,	,	PUNCT
ejpam-5426	137	14	r−{5	r−{5	NOUN
ejpam-5426	137	15	}	}	PUNCT
ejpam-5426	137	16	,	,	PUNCT
ejpam-5426	137	17	{	{	PUNCT
ejpam-5426	137	18	5	5	NUM
ejpam-5426	137	19	}	}	PUNCT
ejpam-5426	137	20	}	}	PUNCT
ejpam-5426	137	21	.	.	PUNCT
ejpam-5426	138	1	then	then	ADV
ejpam-5426	138	2	(	(	PUNCT
ejpam-5426	138	3	w,ϑ	w,ϑ	PROPN
ejpam-5426	138	4	)	)	PUNCT
ejpam-5426	138	5	is	be	AUX
ejpam-5426	138	6	locally	locally	ADV
ejpam-5426	138	7	-	-	PUNCT
ejpam-5426	138	8	indiscreet	indiscreet	ADJ
ejpam-5426	138	9	paracompact	paracompact	ADJ
ejpam-5426	138	10	space	space	NOUN
ejpam-5426	138	11	.	.	PUNCT
ejpam-5426	139	1	thus	thus	ADV
ejpam-5426	139	2	,	,	PUNCT
ejpam-5426	139	3	it	it	PRON
ejpam-5426	139	4	must	must	AUX
ejpam-5426	139	5	be	be	AUX
ejpam-5426	139	6	d−paracompact	d−paracompact	PROPN
ejpam-5426	139	7	.	.	PUNCT
ejpam-5426	140	1	theorem	theorem	NOUN
ejpam-5426	140	2	4	4	NUM
ejpam-5426	140	3	.	.	PUNCT
ejpam-5426	141	1	given	give	VERB
ejpam-5426	141	2	that	that	SCONJ
ejpam-5426	141	3	a	a	DET
ejpam-5426	141	4	⊆	⊆	NUM
ejpam-5426	141	5	w	w	NOUN
ejpam-5426	141	6	of	of	ADP
ejpam-5426	141	7	the	the	DET
ejpam-5426	141	8	topological	topological	ADJ
ejpam-5426	141	9	space	space	NOUN
ejpam-5426	141	10	(	(	PUNCT
ejpam-5426	141	11	w,ϑ	w,ϑ	PROPN
ejpam-5426	141	12	)	)	PUNCT
ejpam-5426	141	13	,	,	PUNCT
ejpam-5426	141	14	then	then	ADV
ejpam-5426	141	15	(	(	PUNCT
ejpam-5426	141	16	a	a	DET
ejpam-5426	141	17	,	,	PUNCT
ejpam-5426	141	18	ϑa	ϑa	PROPN
ejpam-5426	141	19	)	)	PUNCT
ejpam-5426	141	20	is	be	AUX
ejpam-5426	141	21	d−paracompact	d−paracompact	PUNCT
ejpam-5426	141	22	if	if	SCONJ
ejpam-5426	141	23	and	and	CCONJ
ejpam-5426	141	24	only	only	ADV
ejpam-5426	141	25	if	if	SCONJ
ejpam-5426	141	26	any	any	DET
ejpam-5426	141	27	d−cover	d−cover	PROPN
ejpam-5426	141	28	of	of	ADP
ejpam-5426	141	29	a	a	PRON
ejpam-5426	141	30	by	by	ADP
ejpam-5426	141	31	d−sets	d−set	NOUN
ejpam-5426	141	32	in	in	ADP
ejpam-5426	141	33	w	w	NOUN
ejpam-5426	141	34	has	have	VERB
ejpam-5426	141	35	an	an	DET
ejpam-5426	141	36	open	open	ADJ
ejpam-5426	141	37	locally	locally	ADV
ejpam-5426	141	38	-	-	PUNCT
ejpam-5426	141	39	finite	finite	NOUN
ejpam-5426	141	40	refinement	refinement	NOUN
ejpam-5426	141	41	.	.	PUNCT
ejpam-5426	142	1	proof	proof	NOUN
ejpam-5426	142	2	.	.	PUNCT
ejpam-5426	143	1	⇒	⇒	NOUN
ejpam-5426	143	2	)	)	PUNCT
ejpam-5426	143	3	let	let	VERB
ejpam-5426	143	4	(	(	PUNCT
ejpam-5426	143	5	a	a	DET
ejpam-5426	143	6	,	,	PUNCT
ejpam-5426	143	7	ϑa	ϑa	PROPN
ejpam-5426	143	8	)	)	PUNCT
ejpam-5426	143	9	be	be	AUX
ejpam-5426	143	10	d−paracompact	d−paracompact	PROPN
ejpam-5426	143	11	and	and	CCONJ
ejpam-5426	143	12	ẽ	ẽ	PROPN
ejpam-5426	143	13	=	=	SYM
ejpam-5426	143	14	{	{	PUNCT
ejpam-5426	143	15	eρ	eρ	NOUN
ejpam-5426	143	16	:	:	PUNCT
ejpam-5426	143	17	ρ	ρ	PROPN
ejpam-5426	143	18	∈	∈	PROPN
ejpam-5426	143	19	λ	λ	NOUN
ejpam-5426	143	20	}	}	PUNCT
ejpam-5426	143	21	be	be	VERB
ejpam-5426	143	22	any	any	DET
ejpam-5426	143	23	d−cover	d−cover	PROPN
ejpam-5426	143	24	of	of	ADP
ejpam-5426	143	25	a	a	PRON
ejpam-5426	143	26	in	in	ADP
ejpam-5426	143	27	w	w	PROPN
ejpam-5426	143	28	.	.	PUNCT
ejpam-5426	144	1	let	let	VERB
ejpam-5426	144	2	e∗	e∗	PROPN
ejpam-5426	144	3	ρ	ρ	PROPN
ejpam-5426	144	4	=	=	PROPN
ejpam-5426	144	5	eρ	eρ	ADP
ejpam-5426	144	6	∩a	∩a	PROPN
ejpam-5426	144	7	,	,	PUNCT
ejpam-5426	144	8	for	for	SCONJ
ejpam-5426	144	9	all	all	DET
ejpam-5426	144	10	ρ	ρ	NOUN
ejpam-5426	144	11	∈	∈	PROPN
ejpam-5426	144	12	λ	λ	NOUN
ejpam-5426	144	13	is	be	AUX
ejpam-5426	144	14	a	a	DET
ejpam-5426	144	15	d−set	d−set	NOUN
ejpam-5426	144	16	in	in	ADP
ejpam-5426	144	17	a.	a.	NOUN
ejpam-5426	144	18	then	then	ADV
ejpam-5426	144	19	,	,	PUNCT
ejpam-5426	144	20	ẽ∗	ẽ∗	PROPN
ejpam-5426	144	21	=	=	X
ejpam-5426	144	22	{	{	PUNCT
ejpam-5426	144	23	e∗	e∗	PROPN
ejpam-5426	144	24	ρ	ρ	PROPN
ejpam-5426	144	25	:	:	PUNCT
ejpam-5426	144	26	ρ	ρ	PROPN
ejpam-5426	144	27	∈	∈	PROPN
ejpam-5426	144	28	λ	λ	PROPN
ejpam-5426	144	29	}	}	PUNCT
ejpam-5426	144	30	must	must	AUX
ejpam-5426	144	31	be	be	AUX
ejpam-5426	144	32	d−cover	d−cover	PROPN
ejpam-5426	144	33	of	of	ADP
ejpam-5426	144	34	a	a	PRON
ejpam-5426	144	35	by	by	ADP
ejpam-5426	144	36	d−sets	d−set	NOUN
ejpam-5426	144	37	in	in	ADP
ejpam-5426	144	38	a.	a.	NOUN
ejpam-5426	144	39	since	since	SCONJ
ejpam-5426	144	40	(	(	PUNCT
ejpam-5426	144	41	a	a	DET
ejpam-5426	144	42	,	,	PUNCT
ejpam-5426	144	43	ϑa	ϑa	PROPN
ejpam-5426	144	44	)	)	PUNCT
ejpam-5426	144	45	is	be	AUX
ejpam-5426	144	46	d−paracompact	d−paracompact	PROPN
ejpam-5426	144	47	space	space	NOUN
ejpam-5426	144	48	,	,	PUNCT
ejpam-5426	144	49	then	then	ADV
ejpam-5426	144	50	ẽ∗	ẽ∗	PROPN
ejpam-5426	144	51	has	have	VERB
ejpam-5426	144	52	an	an	DET
ejpam-5426	144	53	open	open	ADJ
ejpam-5426	144	54	locally	locally	ADV
ejpam-5426	144	55	-	-	PUNCT
ejpam-5426	144	56	finite	finite	ADJ
ejpam-5426	144	57	refinement	refinement	NOUN
ejpam-5426	144	58	{	{	PUNCT
ejpam-5426	144	59	e∗	e∗	PROPN
ejpam-5426	144	60	ρ1	ρ1	PROPN
ejpam-5426	144	61	,	,	PUNCT
ejpam-5426	144	62	e	e	NOUN
ejpam-5426	144	63	∗	∗	NOUN
ejpam-5426	144	64	ρ2	ρ2	NOUN
ejpam-5426	144	65	,	,	PUNCT
ejpam-5426	144	66	.	.	PUNCT
ejpam-5426	144	67	.	.	PUNCT
ejpam-5426	145	1	.	.	PUNCT
ejpam-5426	146	1	,	,	PUNCT
ejpam-5426	146	2	e	e	X
ejpam-5426	146	3	∗	∗	NOUN
ejpam-5426	146	4	ρn	ρn	INTJ
ejpam-5426	146	5	}	}	PUNCT
ejpam-5426	146	6	.	.	PUNCT
ejpam-5426	147	1	thus	thus	ADV
ejpam-5426	147	2	,	,	PUNCT
ejpam-5426	147	3	the	the	DET
ejpam-5426	147	4	family	family	NOUN
ejpam-5426	147	5	{	{	PUNCT
ejpam-5426	147	6	eρ1	eρ1	PROPN
ejpam-5426	147	7	,	,	PUNCT
ejpam-5426	147	8	eρ2	eρ2	ADV
ejpam-5426	147	9	,	,	PUNCT
ejpam-5426	147	10	.	.	PUNCT
ejpam-5426	147	11	.	.	PUNCT
ejpam-5426	147	12	.	.	PUNCT
ejpam-5426	148	1	,	,	PUNCT
ejpam-5426	148	2	eρn	eρn	PROPN
ejpam-5426	148	3	}	}	PUNCT
ejpam-5426	148	4	must	must	AUX
ejpam-5426	148	5	be	be	AUX
ejpam-5426	148	6	an	an	DET
ejpam-5426	148	7	open	open	ADJ
ejpam-5426	148	8	locally	locally	ADV
ejpam-5426	148	9	-	-	PUNCT
ejpam-5426	148	10	finite	finite	ADJ
ejpam-5426	148	11	refinement	refinement	NOUN
ejpam-5426	148	12	of	of	ADP
ejpam-5426	148	13	ẽ	ẽ	PROPN
ejpam-5426	148	14	in	in	ADP
ejpam-5426	148	15	w	w	NOUN
ejpam-5426	148	16	for	for	ADP
ejpam-5426	148	17	a	a	PRON
ejpam-5426	148	18	,	,	PUNCT
ejpam-5426	148	19	which	which	DET
ejpam-5426	148	20	e∗	e∗	NOUN
ejpam-5426	148	21	=	=	SYM
ejpam-5426	148	22	e	e	PROPN
ejpam-5426	148	23	∩a	∩a	PROPN
ejpam-5426	148	24	.	.	PUNCT
ejpam-5426	149	1	hence	hence	ADV
ejpam-5426	149	2	,	,	PUNCT
ejpam-5426	149	3	the	the	DET
ejpam-5426	149	4	result	result	NOUN
ejpam-5426	149	5	.	.	PUNCT
ejpam-5426	150	1	⇐	⇐	ADJ
ejpam-5426	150	2	)	)	PUNCT
ejpam-5426	150	3	suppose	suppose	VERB
ejpam-5426	150	4	that	that	SCONJ
ejpam-5426	150	5	any	any	DET
ejpam-5426	150	6	d−cover	d−cover	PROPN
ejpam-5426	150	7	of	of	ADP
ejpam-5426	150	8	a	a	PRON
ejpam-5426	150	9	by	by	ADP
ejpam-5426	150	10	d−sets	d−set	NOUN
ejpam-5426	150	11	in	in	ADP
ejpam-5426	150	12	w	w	NOUN
ejpam-5426	150	13	has	have	VERB
ejpam-5426	150	14	an	an	DET
ejpam-5426	150	15	open	open	ADJ
ejpam-5426	150	16	locally	locally	ADV
ejpam-5426	150	17	-	-	PUNCT
ejpam-5426	150	18	finite	finite	NOUN
ejpam-5426	150	19	refinement	refinement	NOUN
ejpam-5426	150	20	.	.	PUNCT
ejpam-5426	151	1	let	let	VERB
ejpam-5426	151	2	ã	ã	PROPN
ejpam-5426	151	3	=	=	PRON
ejpam-5426	151	4	{	{	PUNCT
ejpam-5426	151	5	aρ	aρ	X
ejpam-5426	151	6	:	:	PUNCT
ejpam-5426	151	7	ρ	ρ	PROPN
ejpam-5426	151	8	∈	∈	PROPN
ejpam-5426	151	9	λ	λ	NOUN
ejpam-5426	151	10	}	}	PUNCT
ejpam-5426	151	11	be	be	VERB
ejpam-5426	151	12	a	a	DET
ejpam-5426	151	13	d−cover	d−cover	PROPN
ejpam-5426	151	14	of	of	ADP
ejpam-5426	151	15	a	a	PRON
ejpam-5426	151	16	by	by	ADP
ejpam-5426	151	17	d−sets	d−set	NOUN
ejpam-5426	151	18	in	in	ADP
ejpam-5426	151	19	w	w	NOUN
ejpam-5426	151	20	.	.	PUNCT
ejpam-5426	152	1	in	in	ADP
ejpam-5426	152	2	consequence	consequence	NOUN
ejpam-5426	152	3	,	,	PUNCT
ejpam-5426	152	4	there	there	PRON
ejpam-5426	152	5	is	be	VERB
ejpam-5426	152	6	d−set	d−set	VERB
ejpam-5426	152	7	of	of	ADP
ejpam-5426	152	8	eρ	eρ	NOUN
ejpam-5426	152	9	in	in	ADP
ejpam-5426	152	10	w	w	NOUN
ejpam-5426	152	11	such	such	ADJ
ejpam-5426	152	12	as	as	ADP
ejpam-5426	152	13	aρ	aρ	ADP
ejpam-5426	152	14	=	=	PUNCT
ejpam-5426	152	15	eρ	eρ	PROPN
ejpam-5426	152	16	∩	∩	NOUN
ejpam-5426	152	17	a	a	PRON
ejpam-5426	152	18	for	for	ADP
ejpam-5426	152	19	all	all	DET
ejpam-5426	152	20	ρ	ρ	NUM
ejpam-5426	152	21	∈	∈	PROPN
ejpam-5426	152	22	λ	λ	NOUN
ejpam-5426	152	23	.	.	PUNCT
ejpam-5426	153	1	so	so	ADV
ejpam-5426	153	2	,	,	PUNCT
ejpam-5426	153	3	ẽ	ẽ	PROPN
ejpam-5426	153	4	=	=	SYM
ejpam-5426	153	5	{	{	PUNCT
ejpam-5426	153	6	eρ	eρ	NOUN
ejpam-5426	153	7	:	:	PUNCT
ejpam-5426	153	8	ρ	ρ	PROPN
ejpam-5426	153	9	∈	∈	PROPN
ejpam-5426	153	10	λ	λ	NOUN
ejpam-5426	153	11	}	}	PUNCT
ejpam-5426	153	12	where	where	SCONJ
ejpam-5426	153	13	ẽ	ẽ	PROPN
ejpam-5426	153	14	is	be	AUX
ejpam-5426	153	15	a	a	DET
ejpam-5426	153	16	d−cover	d−cover	PROPN
ejpam-5426	153	17	of	of	ADP
ejpam-5426	153	18	a	a	PRON
ejpam-5426	153	19	by	by	ADP
ejpam-5426	153	20	d−sets	d−set	NOUN
ejpam-5426	153	21	in	in	ADP
ejpam-5426	153	22	w	w	PROPN
ejpam-5426	153	23	.	.	PUNCT
ejpam-5426	153	24	based	base	VERB
ejpam-5426	153	25	on	on	ADP
ejpam-5426	153	26	the	the	DET
ejpam-5426	153	27	assumption	assumption	NOUN
ejpam-5426	153	28	that	that	SCONJ
ejpam-5426	153	29	ẽ	ẽ	PROPN
ejpam-5426	153	30	has	have	AUX
ejpam-5426	153	31	an	an	DET
ejpam-5426	153	32	open	open	ADJ
ejpam-5426	153	33	locally	locally	ADV
ejpam-5426	153	34	-	-	PUNCT
ejpam-5426	153	35	finite	finite	ADJ
ejpam-5426	153	36	refinement	refinement	NOUN
ejpam-5426	153	37	{	{	PUNCT
ejpam-5426	153	38	eρ1	eρ1	PROPN
ejpam-5426	153	39	,	,	PUNCT
ejpam-5426	153	40	eρ2	eρ2	ADV
ejpam-5426	153	41	,	,	PUNCT
ejpam-5426	153	42	.	.	PUNCT
ejpam-5426	153	43	.	.	PUNCT
ejpam-5426	153	44	.	.	PUNCT
ejpam-5426	154	1	,	,	PUNCT
ejpam-5426	154	2	eρn	eρn	ADV
ejpam-5426	154	3	}	}	PUNCT
ejpam-5426	154	4	.	.	PUNCT
ejpam-5426	155	1	since	since	SCONJ
ejpam-5426	155	2	aρ	aρ	ADP
ejpam-5426	155	3	⊆	⊆	NUM
ejpam-5426	155	4	eρ	eρ	NOUN
ejpam-5426	155	5	,	,	PUNCT
ejpam-5426	155	6	for	for	ADP
ejpam-5426	155	7	all	all	DET
ejpam-5426	155	8	ρ	ρ	NUM
ejpam-5426	155	9	∈	∈	PROPN
ejpam-5426	155	10	λ	λ	NOUN
ejpam-5426	155	11	,	,	PUNCT
ejpam-5426	155	12	then	then	ADV
ejpam-5426	155	13	the	the	DET
ejpam-5426	155	14	family	family	NOUN
ejpam-5426	155	15	{	{	PUNCT
ejpam-5426	155	16	eρ1	eρ1	PROPN
ejpam-5426	155	17	,	,	PUNCT
ejpam-5426	155	18	eρ2	eρ2	ADV
ejpam-5426	155	19	,	,	PUNCT
ejpam-5426	155	20	.	.	PUNCT
ejpam-5426	155	21	.	.	PUNCT
ejpam-5426	155	22	.	.	PUNCT
ejpam-5426	155	23	,	,	PUNCT
ejpam-5426	155	24	eρn	eρn	PROPN
ejpam-5426	155	25	}	}	PUNCT
ejpam-5426	155	26	must	must	AUX
ejpam-5426	155	27	be	be	AUX
ejpam-5426	155	28	an	an	DET
ejpam-5426	155	29	open	open	ADJ
ejpam-5426	155	30	locally	locally	ADV
ejpam-5426	155	31	-	-	PUNCT
ejpam-5426	155	32	finite	finite	ADJ
ejpam-5426	155	33	refinement	refinement	NOUN
ejpam-5426	155	34	of	of	ADP
ejpam-5426	155	35	ã	ã	PROPN
ejpam-5426	155	36	for	for	ADP
ejpam-5426	155	37	a.	a.	NOUN
ejpam-5426	155	38	hence	hence	ADV
ejpam-5426	155	39	,	,	PUNCT
ejpam-5426	155	40	the	the	DET
ejpam-5426	155	41	result	result	NOUN
ejpam-5426	155	42	.	.	PUNCT
ejpam-5426	156	1	a.	a.	PROPN
ejpam-5426	156	2	amourah	amourah	PROPN
ejpam-5426	156	3	et	et	PROPN
ejpam-5426	156	4	al	al	PROPN
ejpam-5426	156	5	.	.	PUNCT
ejpam-5426	156	6	/	/	SYM
ejpam-5426	156	7	eur	eur	PROPN
ejpam-5426	156	8	.	.	PUNCT
ejpam-5426	157	1	j.	j.	PROPN
ejpam-5426	157	2	pure	pure	PROPN
ejpam-5426	157	3	appl	appl	PROPN
ejpam-5426	157	4	.	.	PROPN
ejpam-5426	157	5	math	math	PROPN
ejpam-5426	157	6	,	,	PUNCT
ejpam-5426	157	7	17	17	NUM
ejpam-5426	157	8	(	(	PUNCT
ejpam-5426	157	9	4	4	NUM
ejpam-5426	157	10	)	)	PUNCT
ejpam-5426	157	11	(	(	PUNCT
ejpam-5426	157	12	2024	2024	NUM
ejpam-5426	157	13	)	)	PUNCT
ejpam-5426	157	14	,	,	PUNCT
ejpam-5426	157	15	2990	2990	NUM
ejpam-5426	157	16	-	-	SYM
ejpam-5426	157	17	3003	3003	NUM
ejpam-5426	157	18	2996	2996	NUM
ejpam-5426	157	19	figure	figure	NOUN
ejpam-5426	157	20	4	4	NUM
ejpam-5426	157	21	:	:	PUNCT
ejpam-5426	157	22	the	the	DET
ejpam-5426	157	23	subspace	subspace	NOUN
ejpam-5426	157	24	topology	topology	NOUN
ejpam-5426	157	25	of	of	ADP
ejpam-5426	157	26	d−paracompact	d−paracompact	PROPN
ejpam-5426	157	27	space	space	NOUN
ejpam-5426	157	28	.	.	PUNCT
ejpam-5426	158	1	figure	figure	NOUN
ejpam-5426	158	2	4	4	NUM
ejpam-5426	158	3	demonstrates	demonstrate	VERB
ejpam-5426	158	4	a	a	DET
ejpam-5426	158	5	significant	significant	ADJ
ejpam-5426	158	6	fact	fact	NOUN
ejpam-5426	158	7	between	between	ADP
ejpam-5426	158	8	the	the	DET
ejpam-5426	158	9	topological	topological	ADJ
ejpam-5426	158	10	space	space	NOUN
ejpam-5426	158	11	and	and	CCONJ
ejpam-5426	158	12	its	its	PRON
ejpam-5426	158	13	subspace	subspace	NOUN
ejpam-5426	158	14	,	,	PUNCT
ejpam-5426	158	15	where	where	SCONJ
ejpam-5426	158	16	the	the	DET
ejpam-5426	158	17	topological	topological	ADJ
ejpam-5426	158	18	subspace	subspace	NOUN
ejpam-5426	158	19	(	(	PUNCT
ejpam-5426	158	20	a	a	PRON
ejpam-5426	158	21	,	,	PUNCT
ejpam-5426	158	22	ϑa	ϑa	PROPN
ejpam-5426	158	23	)	)	PUNCT
ejpam-5426	158	24	of	of	ADP
ejpam-5426	158	25	the	the	DET
ejpam-5426	158	26	d−paracompact	d−paracompact	PROPN
ejpam-5426	158	27	space	space	NOUN
ejpam-5426	158	28	(	(	PUNCT
ejpam-5426	158	29	w,ϑ	w,ϑ	PROPN
ejpam-5426	158	30	)	)	PUNCT
ejpam-5426	158	31	must	must	AUX
ejpam-5426	158	32	be	be	AUX
ejpam-5426	158	33	d−paracompact	d−paracompact	NOUN
ejpam-5426	158	34	space	space	NOUN
ejpam-5426	158	35	such	such	ADJ
ejpam-5426	158	36	that	that	SCONJ
ejpam-5426	158	37	ẽ	ẽ	PROPN
ejpam-5426	158	38	=	=	PUNCT
ejpam-5426	158	39	{	{	PUNCT
ejpam-5426	158	40	eρ	eρ	NOUN
ejpam-5426	158	41	:	:	PUNCT
ejpam-5426	158	42	ρ	ρ	PROPN
ejpam-5426	158	43	∈	∈	PROPN
ejpam-5426	158	44	λ	λ	PROPN
ejpam-5426	158	45	}	}	PUNCT
ejpam-5426	158	46	is	be	AUX
ejpam-5426	158	47	d−cover	d−cover	PROPN
ejpam-5426	158	48	of	of	ADP
ejpam-5426	158	49	the	the	DET
ejpam-5426	158	50	topological	topological	ADJ
ejpam-5426	158	51	subspace	subspace	NOUN
ejpam-5426	158	52	(	(	PUNCT
ejpam-5426	158	53	a	a	DET
ejpam-5426	158	54	,	,	PUNCT
ejpam-5426	158	55	ϑa	ϑa	PROPN
ejpam-5426	158	56	)	)	PUNCT
ejpam-5426	158	57	has	have	VERB
ejpam-5426	158	58	an	an	DET
ejpam-5426	158	59	open	open	ADJ
ejpam-5426	158	60	locally−finite	locally−finite	NOUN
ejpam-5426	158	61	refinement	refinement	NOUN
ejpam-5426	158	62	,	,	PUNCT
ejpam-5426	158	63	for	for	ADP
ejpam-5426	158	64	all	all	DET
ejpam-5426	158	65	d−sets	d−set	NOUN
ejpam-5426	158	66	in	in	ADP
ejpam-5426	158	67	the	the	DET
ejpam-5426	158	68	space	space	NOUN
ejpam-5426	158	69	(	(	PUNCT
ejpam-5426	158	70	w,ϑ	w,ϑ	PROPN
ejpam-5426	158	71	)	)	PUNCT
ejpam-5426	158	72	.	.	PUNCT
ejpam-5426	159	1	observe	observe	VERB
ejpam-5426	159	2	the	the	DET
ejpam-5426	159	3	next	next	ADJ
ejpam-5426	159	4	corollaries	corollary	NOUN
ejpam-5426	159	5	such	such	ADJ
ejpam-5426	159	6	that	that	SCONJ
ejpam-5426	159	7	each	each	DET
ejpam-5426	159	8	open	open	ADJ
ejpam-5426	159	9	cover	cover	NOUN
ejpam-5426	159	10	is	be	AUX
ejpam-5426	159	11	a	a	DET
ejpam-5426	159	12	d−cover	d−cover	PROPN
ejpam-5426	159	13	.	.	PUNCT
ejpam-5426	160	1	corollary	corollary	ADJ
ejpam-5426	160	2	1	1	NUM
ejpam-5426	160	3	.	.	PUNCT
ejpam-5426	161	1	if	if	SCONJ
ejpam-5426	161	2	the	the	DET
ejpam-5426	161	3	space	space	NOUN
ejpam-5426	161	4	(	(	PUNCT
ejpam-5426	161	5	a	a	DET
ejpam-5426	161	6	,	,	PUNCT
ejpam-5426	161	7	ϑa	ϑa	PROPN
ejpam-5426	161	8	)	)	PUNCT
ejpam-5426	161	9	is	be	AUX
ejpam-5426	161	10	d−paracompact	d−paracompact	PROPN
ejpam-5426	161	11	,	,	PUNCT
ejpam-5426	161	12	then	then	ADV
ejpam-5426	161	13	any	any	DET
ejpam-5426	161	14	open	open	ADJ
ejpam-5426	161	15	cover	cover	NOUN
ejpam-5426	161	16	of	of	ADP
ejpam-5426	161	17	a	a	PRON
ejpam-5426	161	18	by	by	ADP
ejpam-5426	161	19	open	open	ADJ
ejpam-5426	161	20	sets	set	NOUN
ejpam-5426	161	21	in	in	ADP
ejpam-5426	161	22	w	w	PROPN
ejpam-5426	161	23	has	have	VERB
ejpam-5426	161	24	an	an	DET
ejpam-5426	161	25	open	open	ADJ
ejpam-5426	161	26	locally	locally	ADV
ejpam-5426	161	27	-	-	PUNCT
ejpam-5426	161	28	finite	finite	ADJ
ejpam-5426	161	29	refinement	refinement	NOUN
ejpam-5426	161	30	.	.	PUNCT
ejpam-5426	162	1	corollary	corollary	ADJ
ejpam-5426	162	2	2	2	NUM
ejpam-5426	162	3	.	.	PUNCT
ejpam-5426	163	1	a	a	DET
ejpam-5426	163	2	space	space	NOUN
ejpam-5426	163	3	(	(	PUNCT
ejpam-5426	163	4	a	a	DET
ejpam-5426	163	5	,	,	PUNCT
ejpam-5426	163	6	ϑa	ϑa	PROPN
ejpam-5426	163	7	)	)	PUNCT
ejpam-5426	163	8	is	be	AUX
ejpam-5426	163	9	paracompact	paracompact	ADJ
ejpam-5426	163	10	if	if	SCONJ
ejpam-5426	163	11	any	any	DET
ejpam-5426	163	12	d−cover	d−cover	PROPN
ejpam-5426	163	13	of	of	ADP
ejpam-5426	163	14	a	a	PRON
ejpam-5426	163	15	by	by	ADP
ejpam-5426	163	16	d−sets	d−set	NOUN
ejpam-5426	163	17	in	in	ADP
ejpam-5426	163	18	w	w	NOUN
ejpam-5426	163	19	has	have	VERB
ejpam-5426	163	20	an	an	DET
ejpam-5426	163	21	open	open	ADJ
ejpam-5426	163	22	locally	locally	ADV
ejpam-5426	163	23	-	-	PUNCT
ejpam-5426	163	24	finite	finite	NOUN
ejpam-5426	163	25	refinement	refinement	NOUN
ejpam-5426	163	26	.	.	PUNCT
ejpam-5426	164	1	proof	proof	NOUN
ejpam-5426	164	2	.	.	PUNCT
ejpam-5426	165	1	since	since	SCONJ
ejpam-5426	165	2	each	each	DET
ejpam-5426	165	3	d−paracompact	d−paracompact	PROPN
ejpam-5426	165	4	space	space	NOUN
ejpam-5426	165	5	is	be	AUX
ejpam-5426	165	6	paracompact	paracompact	ADJ
ejpam-5426	165	7	,	,	PUNCT
ejpam-5426	165	8	then	then	ADV
ejpam-5426	165	9	the	the	DET
ejpam-5426	165	10	second	second	ADJ
ejpam-5426	165	11	part	part	NOUN
ejpam-5426	165	12	of	of	ADP
ejpam-5426	165	13	theorem	theorem	ADJ
ejpam-5426	165	14	4	4	NUM
ejpam-5426	165	15	is	be	AUX
ejpam-5426	165	16	this	this	DET
ejpam-5426	165	17	corollary	corollary	NOUN
ejpam-5426	165	18	’s	’s	NOUN
ejpam-5426	165	19	direct	direct	ADJ
ejpam-5426	165	20	cause	cause	NOUN
ejpam-5426	165	21	.	.	PUNCT
ejpam-5426	166	1	theorem	theorem	NOUN
ejpam-5426	166	2	5	5	NUM
ejpam-5426	166	3	.	.	PUNCT
ejpam-5426	167	1	let	let	VERB
ejpam-5426	167	2	(	(	PUNCT
ejpam-5426	167	3	w,ϑ1	w,ϑ1	PROPN
ejpam-5426	167	4	)	)	PUNCT
ejpam-5426	167	5	and	and	CCONJ
ejpam-5426	167	6	(	(	PUNCT
ejpam-5426	167	7	w,ϑ2	w,ϑ2	PROPN
ejpam-5426	167	8	)	)	PUNCT
ejpam-5426	167	9	be	be	VERB
ejpam-5426	167	10	any	any	DET
ejpam-5426	167	11	topological	topological	ADJ
ejpam-5426	167	12	spaces	space	NOUN
ejpam-5426	167	13	.	.	PUNCT
ejpam-5426	168	1	if	if	SCONJ
ejpam-5426	168	2	ϑ1	ϑ1	PROPN
ejpam-5426	168	3	⊆	⊆	NUM
ejpam-5426	168	4	ϑ2	ϑ2	PROPN
ejpam-5426	168	5	and	and	CCONJ
ejpam-5426	168	6	(	(	PUNCT
ejpam-5426	168	7	w,ϑ2	w,ϑ2	PROPN
ejpam-5426	168	8	)	)	PUNCT
ejpam-5426	168	9	is	be	AUX
ejpam-5426	168	10	d−paracompact	d−paracompact	PROPN
ejpam-5426	168	11	,	,	PUNCT
ejpam-5426	168	12	then	then	ADV
ejpam-5426	168	13	(	(	PUNCT
ejpam-5426	168	14	w,ϑ1	w,ϑ1	PROPN
ejpam-5426	168	15	)	)	PUNCT
ejpam-5426	168	16	is	be	AUX
ejpam-5426	168	17	a	a	DET
ejpam-5426	168	18	d−paracompact	d−paracompact	NOUN
ejpam-5426	168	19	.	.	PUNCT
ejpam-5426	169	1	proof	proof	NOUN
ejpam-5426	169	2	.	.	PUNCT
ejpam-5426	170	1	let	let	VERB
ejpam-5426	170	2	ẽ	ẽ	NOUN
ejpam-5426	170	3	=	=	PRON
ejpam-5426	170	4	{	{	PUNCT
ejpam-5426	170	5	eρ	eρ	NOUN
ejpam-5426	170	6	:	:	PUNCT
ejpam-5426	170	7	ρ	ρ	PROPN
ejpam-5426	170	8	∈	∈	PROPN
ejpam-5426	170	9	λ	λ	NOUN
ejpam-5426	170	10	}	}	PUNCT
ejpam-5426	170	11	be	be	VERB
ejpam-5426	170	12	any	any	DET
ejpam-5426	170	13	d−cover	d−cover	PROPN
ejpam-5426	170	14	of	of	ADP
ejpam-5426	170	15	(	(	PUNCT
ejpam-5426	170	16	w,ϑ1	w,ϑ1	PROPN
ejpam-5426	170	17	)	)	PUNCT
ejpam-5426	170	18	.	.	PUNCT
ejpam-5426	171	1	since	since	SCONJ
ejpam-5426	171	2	ϑ1	ϑ1	NOUN
ejpam-5426	171	3	⊆	⊆	NUM
ejpam-5426	171	4	ϑ2	ϑ2	NOUN
ejpam-5426	171	5	,	,	PUNCT
ejpam-5426	171	6	we	we	PRON
ejpam-5426	171	7	have	have	VERB
ejpam-5426	171	8	ẽ	ẽ	PROPN
ejpam-5426	171	9	is	be	AUX
ejpam-5426	171	10	d−cover	d−cover	PROPN
ejpam-5426	171	11	of	of	ADP
ejpam-5426	171	12	(	(	PUNCT
ejpam-5426	171	13	w,ϑ2	w,ϑ2	PROPN
ejpam-5426	171	14	)	)	PUNCT
ejpam-5426	171	15	,	,	PUNCT
ejpam-5426	171	16	which	which	PRON
ejpam-5426	171	17	it	it	PRON
ejpam-5426	171	18	is	be	AUX
ejpam-5426	171	19	has	have	VERB
ejpam-5426	171	20	an	an	DET
ejpam-5426	171	21	open	open	ADJ
ejpam-5426	171	22	locally	locally	ADV
ejpam-5426	171	23	-	-	PUNCT
ejpam-5426	171	24	finite	finite	ADJ
ejpam-5426	171	25	refinement	refinement	NOUN
ejpam-5426	171	26	.	.	PUNCT
ejpam-5426	172	1	hence	hence	ADV
ejpam-5426	172	2	,	,	PUNCT
ejpam-5426	172	3	the	the	DET
ejpam-5426	172	4	result	result	NOUN
ejpam-5426	172	5	.	.	PUNCT
ejpam-5426	173	1	theorem	theorem	VERB
ejpam-5426	173	2	6	6	NUM
ejpam-5426	173	3	.	.	PUNCT
ejpam-5426	174	1	if	if	SCONJ
ejpam-5426	174	2	the	the	DET
ejpam-5426	174	3	topological	topological	ADJ
ejpam-5426	174	4	space	space	NOUN
ejpam-5426	174	5	(	(	PUNCT
ejpam-5426	174	6	w,ϑ	w,ϑ	PROPN
ejpam-5426	174	7	)	)	PUNCT
ejpam-5426	174	8	is	be	AUX
ejpam-5426	174	9	d−paracompact	d−paracompact	PROPN
ejpam-5426	174	10	,	,	PUNCT
ejpam-5426	174	11	then	then	ADV
ejpam-5426	174	12	there	there	PRON
ejpam-5426	174	13	are	be	VERB
ejpam-5426	174	14	closed	closed	ADJ
ejpam-5426	174	15	,	,	PUNCT
ejpam-5426	174	16	paracompact	paracompact	ADJ
ejpam-5426	174	17	subspaces	subspace	NOUN
ejpam-5426	174	18	in	in	ADP
ejpam-5426	174	19	(	(	PUNCT
ejpam-5426	174	20	w,ϑ	w,ϑ	PROPN
ejpam-5426	174	21	)	)	PUNCT
ejpam-5426	174	22	.	.	PUNCT
ejpam-5426	175	1	proof	proof	NOUN
ejpam-5426	175	2	.	.	PUNCT
ejpam-5426	176	1	let	let	VERB
ejpam-5426	176	2	a	a	DET
ejpam-5426	176	3	be	be	AUX
ejpam-5426	176	4	any	any	DET
ejpam-5426	176	5	closed	closed	ADJ
ejpam-5426	176	6	subset	subset	NOUN
ejpam-5426	176	7	of	of	ADP
ejpam-5426	176	8	w	w	PROPN
ejpam-5426	176	9	and	and	CCONJ
ejpam-5426	176	10	w	w	PROPN
ejpam-5426	176	11	be	be	AUX
ejpam-5426	176	12	d−paracompact	d−paracompact	PROPN
ejpam-5426	176	13	space	space	NOUN
ejpam-5426	176	14	.	.	PUNCT
ejpam-5426	177	1	if	if	SCONJ
ejpam-5426	177	2	ẽ	ẽ	PROPN
ejpam-5426	177	3	=	=	SYM
ejpam-5426	177	4	{	{	PUNCT
ejpam-5426	177	5	eρ	eρ	NOUN
ejpam-5426	177	6	:	:	PUNCT
ejpam-5426	177	7	ρ	ρ	PROPN
ejpam-5426	177	8	∈	∈	PROPN
ejpam-5426	177	9	λ	λ	PROPN
ejpam-5426	177	10	}	}	PUNCT
ejpam-5426	177	11	is	be	AUX
ejpam-5426	177	12	an	an	DET
ejpam-5426	177	13	open	open	ADJ
ejpam-5426	177	14	cover	cover	NOUN
ejpam-5426	177	15	of	of	ADP
ejpam-5426	177	16	a	a	PRON
ejpam-5426	177	17	by	by	ADP
ejpam-5426	177	18	open	open	ADJ
ejpam-5426	177	19	sets	set	NOUN
ejpam-5426	177	20	in	in	ADP
ejpam-5426	177	21	w	w	NOUN
ejpam-5426	177	22	,	,	PUNCT
ejpam-5426	177	23	so	so	ADV
ejpam-5426	177	24	ẽ	ẽ	PROPN
ejpam-5426	177	25	∪	∪	NOUN
ejpam-5426	177	26	{	{	PUNCT
ejpam-5426	177	27	w	w	NOUN
ejpam-5426	177	28	−	−	PROPN
ejpam-5426	177	29	a	a	PRON
ejpam-5426	177	30	}	}	PUNCT
ejpam-5426	177	31	must	must	AUX
ejpam-5426	177	32	be	be	AUX
ejpam-5426	177	33	open	open	ADJ
ejpam-5426	177	34	cover	cover	NOUN
ejpam-5426	177	35	of	of	ADP
ejpam-5426	177	36	w	w	PROPN
ejpam-5426	177	37	.	.	PUNCT
ejpam-5426	178	1	since	since	SCONJ
ejpam-5426	178	2	w	w	PROPN
ejpam-5426	178	3	is	be	AUX
ejpam-5426	178	4	a	a	DET
ejpam-5426	178	5	d−paracompact	d−paracompact	PROPN
ejpam-5426	178	6	space	space	NOUN
ejpam-5426	178	7	,	,	PUNCT
ejpam-5426	178	8	it	it	PRON
ejpam-5426	178	9	has	have	VERB
ejpam-5426	178	10	an	an	DET
ejpam-5426	178	11	open	open	ADJ
ejpam-5426	178	12	locally	locally	ADV
ejpam-5426	178	13	-	-	PUNCT
ejpam-5426	178	14	finite	finite	ADJ
ejpam-5426	178	15	refinement	refinement	NOUN
ejpam-5426	178	16	of	of	ADP
ejpam-5426	178	17	ẽ∗.	ẽ∗.	PROPN
ejpam-5426	178	18	moreover	moreover	ADV
ejpam-5426	178	19	,	,	PUNCT
ejpam-5426	178	20	ẽ∗	ẽ∗	PROPN
ejpam-5426	178	21	−	−	PROPN
ejpam-5426	178	22	{	{	PUNCT
ejpam-5426	178	23	w	w	NOUN
ejpam-5426	178	24	−	−	PROPN
ejpam-5426	178	25	a	a	PRON
ejpam-5426	178	26	}	}	PUNCT
ejpam-5426	178	27	is	be	AUX
ejpam-5426	178	28	an	an	DET
ejpam-5426	178	29	open	open	ADJ
ejpam-5426	178	30	locally	locally	ADV
ejpam-5426	178	31	-	-	PUNCT
ejpam-5426	178	32	finite	finite	ADJ
ejpam-5426	178	33	refinement	refinement	NOUN
ejpam-5426	178	34	of	of	ADP
ejpam-5426	178	35	ẽ	ẽ	PROPN
ejpam-5426	178	36	for	for	ADP
ejpam-5426	178	37	a.	a.	NOUN
ejpam-5426	178	38	hence	hence	ADV
ejpam-5426	178	39	,	,	PUNCT
ejpam-5426	178	40	we	we	PRON
ejpam-5426	178	41	get	get	VERB
ejpam-5426	178	42	the	the	DET
ejpam-5426	178	43	result	result	NOUN
ejpam-5426	178	44	.	.	PUNCT
ejpam-5426	179	1	theorem	theorem	ADJ
ejpam-5426	179	2	7	7	NUM
ejpam-5426	179	3	.	.	PUNCT
ejpam-5426	180	1	any	any	DET
ejpam-5426	180	2	d−separable	d−separable	ADJ
ejpam-5426	180	3	,	,	PUNCT
ejpam-5426	180	4	d−paracompact	d−paracompact	PROPN
ejpam-5426	180	5	(	(	PUNCT
ejpam-5426	180	6	w,ϑ	w,ϑ	PROPN
ejpam-5426	180	7	)	)	PUNCT
ejpam-5426	180	8	must	must	AUX
ejpam-5426	180	9	be	be	AUX
ejpam-5426	180	10	d−lindelöf	d−lindelöf	PROPN
ejpam-5426	180	11	.	.	PUNCT
ejpam-5426	181	1	a.	a.	PROPN
ejpam-5426	181	2	amourah	amourah	PROPN
ejpam-5426	181	3	et	et	PROPN
ejpam-5426	181	4	al	al	PROPN
ejpam-5426	181	5	.	.	PUNCT
ejpam-5426	181	6	/	/	SYM
ejpam-5426	181	7	eur	eur	PROPN
ejpam-5426	181	8	.	.	PUNCT
ejpam-5426	182	1	j.	j.	PROPN
ejpam-5426	182	2	pure	pure	PROPN
ejpam-5426	182	3	appl	appl	PROPN
ejpam-5426	182	4	.	.	PROPN
ejpam-5426	182	5	math	math	PROPN
ejpam-5426	182	6	,	,	PUNCT
ejpam-5426	182	7	17	17	NUM
ejpam-5426	182	8	(	(	PUNCT
ejpam-5426	182	9	4	4	NUM
ejpam-5426	182	10	)	)	PUNCT
ejpam-5426	182	11	(	(	PUNCT
ejpam-5426	182	12	2024	2024	NUM
ejpam-5426	182	13	)	)	PUNCT
ejpam-5426	182	14	,	,	PUNCT
ejpam-5426	182	15	2990	2990	NUM
ejpam-5426	182	16	-	-	SYM
ejpam-5426	182	17	3003	3003	NUM
ejpam-5426	182	18	2997	2997	NUM
ejpam-5426	182	19	proof	proof	NOUN
ejpam-5426	182	20	.	.	PUNCT
ejpam-5426	183	1	let	let	VERB
ejpam-5426	183	2	ẽ	ẽ	NOUN
ejpam-5426	183	3	=	=	PRON
ejpam-5426	183	4	{	{	PUNCT
ejpam-5426	183	5	eρ	eρ	NOUN
ejpam-5426	183	6	:	:	PUNCT
ejpam-5426	183	7	ρ	ρ	PROPN
ejpam-5426	183	8	∈	∈	PROPN
ejpam-5426	183	9	λ	λ	NOUN
ejpam-5426	183	10	}	}	PUNCT
ejpam-5426	183	11	be	be	VERB
ejpam-5426	183	12	any	any	DET
ejpam-5426	183	13	d−cover	d−cover	PROPN
ejpam-5426	183	14	of	of	ADP
ejpam-5426	183	15	w	w	PROPN
ejpam-5426	183	16	.	.	PUNCT
ejpam-5426	184	1	believe	believe	VERB
ejpam-5426	184	2	that	that	SCONJ
ejpam-5426	184	3	ẽ	ẽ	PROPN
ejpam-5426	184	4	has	have	VERB
ejpam-5426	184	5	no	no	DET
ejpam-5426	184	6	a	a	DET
ejpam-5426	184	7	countable	countable	ADJ
ejpam-5426	184	8	subcover	subcover	NOUN
ejpam-5426	184	9	.	.	PUNCT
ejpam-5426	185	1	let	let	VERB
ejpam-5426	185	2	k̃	k̃	PROPN
ejpam-5426	185	3	=	=	PRON
ejpam-5426	185	4	{	{	PUNCT
ejpam-5426	185	5	kε	kε	X
ejpam-5426	185	6	:	:	PUNCT
ejpam-5426	185	7	ε	ε	PROPN
ejpam-5426	185	8	∈	∈	PROPN
ejpam-5426	185	9	υ	υ	PROPN
ejpam-5426	185	10	}	}	PUNCT
ejpam-5426	185	11	is	be	AUX
ejpam-5426	185	12	an	an	DET
ejpam-5426	185	13	open	open	ADJ
ejpam-5426	185	14	uncountable	uncountable	ADJ
ejpam-5426	185	15	locally	locally	ADV
ejpam-5426	185	16	-	-	PUNCT
ejpam-5426	185	17	finite	finite	ADJ
ejpam-5426	185	18	refinement	refinement	NOUN
ejpam-5426	185	19	subcover	subcover	PROPN
ejpam-5426	185	20	of	of	ADP
ejpam-5426	185	21	ẽ.	ẽ.	PROPN
ejpam-5426	185	22	now	now	ADV
ejpam-5426	185	23	,	,	PUNCT
ejpam-5426	185	24	if	if	SCONJ
ejpam-5426	185	25	d	d	NOUN
ejpam-5426	185	26	is	be	AUX
ejpam-5426	185	27	a	a	DET
ejpam-5426	185	28	countable	countable	ADJ
ejpam-5426	185	29	d−dense	d−dense	NOUN
ejpam-5426	185	30	subsets	subset	NOUN
ejpam-5426	185	31	of	of	ADP
ejpam-5426	185	32	w	w	NOUN
ejpam-5426	185	33	,	,	PUNCT
ejpam-5426	185	34	then	then	ADV
ejpam-5426	185	35	kε	kε	PROPN
ejpam-5426	185	36	∩d	∩d	PROPN
ejpam-5426	185	37	̸=	̸=	PROPN
ejpam-5426	185	38	ϕ	ϕ	PROPN
ejpam-5426	185	39	,	,	PUNCT
ejpam-5426	185	40	for	for	ADP
ejpam-5426	185	41	all	all	DET
ejpam-5426	185	42	ε	ε	PROPN
ejpam-5426	185	43	∈	∈	PROPN
ejpam-5426	185	44	υ	υ	NOUN
ejpam-5426	185	45	.	.	PUNCT
ejpam-5426	186	1	thus	thus	ADV
ejpam-5426	186	2	,	,	PUNCT
ejpam-5426	186	3	the	the	DET
ejpam-5426	186	4	set	set	NOUN
ejpam-5426	186	5	d	d	NOUN
ejpam-5426	186	6	is	be	AUX
ejpam-5426	186	7	uncountable	uncountable	ADJ
ejpam-5426	186	8	because	because	SCONJ
ejpam-5426	186	9	k̃	k̃	PROPN
ejpam-5426	186	10	is	be	AUX
ejpam-5426	186	11	uncountable	uncountable	ADJ
ejpam-5426	186	12	,	,	PUNCT
ejpam-5426	186	13	that	that	PRON
ejpam-5426	186	14	is	be	AUX
ejpam-5426	186	15	a	a	DET
ejpam-5426	186	16	contradiction	contradiction	NOUN
ejpam-5426	186	17	.	.	PUNCT
ejpam-5426	187	1	hence	hence	ADV
ejpam-5426	187	2	,	,	PUNCT
ejpam-5426	187	3	the	the	DET
ejpam-5426	187	4	result	result	NOUN
ejpam-5426	187	5	.	.	PUNCT
ejpam-5426	188	1	figure	figure	VERB
ejpam-5426	188	2	5	5	NUM
ejpam-5426	188	3	:	:	PUNCT
ejpam-5426	188	4	the	the	DET
ejpam-5426	188	5	relation	relation	NOUN
ejpam-5426	188	6	of	of	ADP
ejpam-5426	188	7	d−paracompact	d−paracompact	PROPN
ejpam-5426	188	8	and	and	CCONJ
ejpam-5426	188	9	d−lindelöf	d−lindelöf	PROPN
ejpam-5426	188	10	spaces	space	VERB
ejpam-5426	188	11	with	with	ADP
ejpam-5426	188	12	d−separable	d−separable	ADJ
ejpam-5426	188	13	condition	condition	NOUN
ejpam-5426	188	14	.	.	PUNCT
ejpam-5426	189	1	figure	figure	NOUN
ejpam-5426	189	2	5	5	NUM
ejpam-5426	189	3	presents	present	VERB
ejpam-5426	189	4	the	the	DET
ejpam-5426	189	5	basic	basic	ADJ
ejpam-5426	189	6	relation	relation	NOUN
ejpam-5426	189	7	between	between	ADP
ejpam-5426	189	8	d−paracompact	d−paracompact	PROPN
ejpam-5426	189	9	and	and	CCONJ
ejpam-5426	189	10	d−lindelöf	d−lindelöf	PROPN
ejpam-5426	189	11	spaces	space	VERB
ejpam-5426	189	12	under	under	ADP
ejpam-5426	189	13	extra	extra	ADJ
ejpam-5426	189	14	condition	condition	NOUN
ejpam-5426	189	15	,	,	PUNCT
ejpam-5426	189	16	which	which	PRON
ejpam-5426	189	17	represents	represent	VERB
ejpam-5426	189	18	a	a	DET
ejpam-5426	189	19	significant	significant	ADJ
ejpam-5426	189	20	fact	fact	NOUN
ejpam-5426	189	21	that	that	SCONJ
ejpam-5426	189	22	if	if	SCONJ
ejpam-5426	189	23	the	the	DET
ejpam-5426	189	24	space	space	NOUN
ejpam-5426	189	25	ofd−paracompact	ofd−paracompact	NOUN
ejpam-5426	189	26	is	be	AUX
ejpam-5426	189	27	d−separable	d−separable	ADJ
ejpam-5426	189	28	then	then	ADV
ejpam-5426	189	29	must	must	AUX
ejpam-5426	189	30	be	be	AUX
ejpam-5426	189	31	d−lindelöf	d−lindelöf	PRON
ejpam-5426	189	32	such	such	ADJ
ejpam-5426	189	33	that	that	SCONJ
ejpam-5426	189	34	ẽ	ẽ	PROPN
ejpam-5426	189	35	=	=	PUNCT
ejpam-5426	189	36	{	{	PUNCT
ejpam-5426	189	37	eρ	eρ	NOUN
ejpam-5426	189	38	:	:	PUNCT
ejpam-5426	189	39	ρ	ρ	PROPN
ejpam-5426	189	40	∈	∈	PROPN
ejpam-5426	189	41	λ	λ	PROPN
ejpam-5426	189	42	}	}	PUNCT
ejpam-5426	189	43	is	be	AUX
ejpam-5426	189	44	d−cover	d−cover	PROPN
ejpam-5426	189	45	of	of	ADP
ejpam-5426	189	46	the	the	DET
ejpam-5426	189	47	topological	topological	ADJ
ejpam-5426	189	48	space	space	NOUN
ejpam-5426	189	49	(	(	PUNCT
ejpam-5426	189	50	w,ϑ	w,ϑ	PROPN
ejpam-5426	189	51	)	)	PUNCT
ejpam-5426	189	52	has	have	AUX
ejpam-5426	189	53	an	an	DET
ejpam-5426	189	54	open	open	ADJ
ejpam-5426	189	55	locally−finite	locally−finite	NOUN
ejpam-5426	189	56	refinement	refinement	NOUN
ejpam-5426	189	57	and	and	CCONJ
ejpam-5426	189	58	we	we	PRON
ejpam-5426	189	59	have	have	VERB
ejpam-5426	189	60	g̃	g̃	PROPN
ejpam-5426	189	61	=	=	SYM
ejpam-5426	189	62	{	{	PUNCT
ejpam-5426	189	63	gω	gω	X
ejpam-5426	189	64	:	:	PUNCT
ejpam-5426	189	65	ω	ω	PROPN
ejpam-5426	189	66	∈	∈	PROPN
ejpam-5426	189	67	ω	ω	PROPN
ejpam-5426	189	68	}	}	PUNCT
ejpam-5426	189	69	is	be	AUX
ejpam-5426	189	70	cover	cover	NOUN
ejpam-5426	189	71	of	of	ADP
ejpam-5426	189	72	the	the	DET
ejpam-5426	189	73	topological	topological	ADJ
ejpam-5426	189	74	space	space	NOUN
ejpam-5426	189	75	(	(	PUNCT
ejpam-5426	189	76	q	q	NOUN
ejpam-5426	189	77	,	,	PUNCT
ejpam-5426	189	78	ι	ι	PROPN
ejpam-5426	189	79	)	)	PUNCT
ejpam-5426	189	80	has	have	VERB
ejpam-5426	189	81	an	an	DET
ejpam-5426	189	82	open	open	ADJ
ejpam-5426	189	83	locally−finite	locally−finite	NOUN
ejpam-5426	189	84	refinement	refinement	NOUN
ejpam-5426	189	85	.	.	PUNCT
ejpam-5426	190	1	with	with	ADP
ejpam-5426	190	2	the	the	DET
ejpam-5426	190	3	same	same	ADJ
ejpam-5426	190	4	work	work	NOUN
ejpam-5426	190	5	,	,	PUNCT
ejpam-5426	190	6	we	we	PRON
ejpam-5426	190	7	can	can	AUX
ejpam-5426	190	8	achieve	achieve	VERB
ejpam-5426	190	9	the	the	DET
ejpam-5426	190	10	next	next	ADJ
ejpam-5426	190	11	corollary	corollary	NOUN
ejpam-5426	190	12	.	.	PUNCT
ejpam-5426	191	1	corollary	corollary	ADJ
ejpam-5426	191	2	3	3	NUM
ejpam-5426	191	3	.	.	PUNCT
ejpam-5426	192	1	any	any	DET
ejpam-5426	192	2	d−separable	d−separable	ADJ
ejpam-5426	192	3	,	,	PUNCT
ejpam-5426	192	4	d−paracompact	d−paracompact	PROPN
ejpam-5426	192	5	(	(	PUNCT
ejpam-5426	192	6	w,ϑ	w,ϑ	PROPN
ejpam-5426	192	7	)	)	PUNCT
ejpam-5426	192	8	must	must	AUX
ejpam-5426	192	9	be	be	AUX
ejpam-5426	192	10	lindelöf	lindelöf	NOUN
ejpam-5426	192	11	.	.	PUNCT
ejpam-5426	193	1	definition	definition	NOUN
ejpam-5426	193	2	18	18	NUM
ejpam-5426	193	3	.	.	PUNCT
ejpam-5426	194	1	the	the	DET
ejpam-5426	194	2	topological	topological	ADJ
ejpam-5426	194	3	space	space	NOUN
ejpam-5426	194	4	(	(	PUNCT
ejpam-5426	194	5	w,ϑ	w,ϑ	PROPN
ejpam-5426	194	6	)	)	PUNCT
ejpam-5426	194	7	is	be	AUX
ejpam-5426	194	8	called	call	VERB
ejpam-5426	194	9	countably	countably	ADV
ejpam-5426	194	10	d−paracompact	d−paracompact	NOUN
ejpam-5426	194	11	if	if	SCONJ
ejpam-5426	194	12	every	every	DET
ejpam-5426	194	13	countably	countably	ADV
ejpam-5426	194	14	d−cover	d−cover	PROPN
ejpam-5426	194	15	of	of	ADP
ejpam-5426	194	16	(	(	PUNCT
ejpam-5426	194	17	w,ϑ	w,ϑ	PROPN
ejpam-5426	194	18	)	)	PUNCT
ejpam-5426	194	19	has	have	VERB
ejpam-5426	194	20	an	an	DET
ejpam-5426	194	21	open	open	ADJ
ejpam-5426	194	22	locally	locally	ADV
ejpam-5426	194	23	-	-	PUNCT
ejpam-5426	194	24	finite	finite	NOUN
ejpam-5426	194	25	refinement	refinement	NOUN
ejpam-5426	194	26	.	.	PUNCT
ejpam-5426	195	1	figure	figure	VERB
ejpam-5426	195	2	6	6	NUM
ejpam-5426	195	3	:	:	PUNCT
ejpam-5426	195	4	the	the	DET
ejpam-5426	195	5	space	space	NOUN
ejpam-5426	195	6	of	of	ADP
ejpam-5426	195	7	countably	countably	ADV
ejpam-5426	195	8	d−paracompact	d−paracompact	NOUN
ejpam-5426	195	9	.	.	PUNCT
ejpam-5426	196	1	figure	figure	NOUN
ejpam-5426	196	2	6	6	NUM
ejpam-5426	196	3	illustrates	illustrate	VERB
ejpam-5426	196	4	the	the	DET
ejpam-5426	196	5	space	space	NOUN
ejpam-5426	196	6	of	of	ADP
ejpam-5426	196	7	countablyd−paracompact	countablyd−paracompact	ADV
ejpam-5426	196	8	such	such	ADJ
ejpam-5426	196	9	that	that	SCONJ
ejpam-5426	196	10	ẽ	ẽ	NOUN
ejpam-5426	196	11	=	=	PUNCT
ejpam-5426	196	12	{	{	PUNCT
ejpam-5426	196	13	eρ	eρ	NOUN
ejpam-5426	196	14	:	:	PUNCT
ejpam-5426	196	15	ρ	ρ	PROPN
ejpam-5426	196	16	∈	∈	PROPN
ejpam-5426	196	17	λ	λ	PROPN
ejpam-5426	196	18	}	}	PUNCT
ejpam-5426	196	19	is	be	AUX
ejpam-5426	196	20	countably	countably	ADV
ejpam-5426	196	21	d−cover	d−cover	PROPN
ejpam-5426	196	22	of	of	ADP
ejpam-5426	196	23	the	the	DET
ejpam-5426	196	24	topological	topological	ADJ
ejpam-5426	196	25	space	space	NOUN
ejpam-5426	196	26	(	(	PUNCT
ejpam-5426	196	27	w,ϑ	w,ϑ	PROPN
ejpam-5426	196	28	)	)	PUNCT
ejpam-5426	196	29	has	have	VERB
ejpam-5426	196	30	an	an	DET
ejpam-5426	196	31	open	open	ADJ
ejpam-5426	196	32	locally−finite	locally−finite	NOUN
ejpam-5426	196	33	refinement	refinement	NOUN
ejpam-5426	196	34	k̃	k̃	PROPN
ejpam-5426	196	35	=	=	PROPN
ejpam-5426	196	36	{	{	PUNCT
ejpam-5426	196	37	kω	kω	X
ejpam-5426	196	38	:	:	PUNCT
ejpam-5426	196	39	ω	ω	PROPN
ejpam-5426	196	40	∈	∈	PROPN
ejpam-5426	196	41	ω	ω	NOUN
ejpam-5426	196	42	}	}	PUNCT
ejpam-5426	196	43	.	.	PUNCT
ejpam-5426	197	1	i.e.	i.e.	X
ejpam-5426	197	2	each	each	DET
ejpam-5426	197	3	countably	countably	ADV
ejpam-5426	197	4	of	of	ADP
ejpam-5426	197	5	eρ	eρ	NOUN
ejpam-5426	197	6	isd−set	isd−set	VERB
ejpam-5426	197	7	for	for	ADP
ejpam-5426	197	8	all	all	DET
ejpam-5426	197	9	ρ	ρ	NUM
ejpam-5426	197	10	∈	∈	PROPN
ejpam-5426	197	11	λ	λ	NOUN
ejpam-5426	197	12	such	such	ADJ
ejpam-5426	197	13	thatw	thatw	PROPN
ejpam-5426	197	14	=	=	SYM
ejpam-5426	197	15	∪ρ∈λeρ	∪ρ∈λeρ	PROPN
ejpam-5426	197	16	has	have	VERB
ejpam-5426	197	17	an	an	DET
ejpam-5426	197	18	open	open	ADJ
ejpam-5426	197	19	locally−finite	locally−finite	NOUN
ejpam-5426	197	20	refinement	refinement	NOUN
ejpam-5426	197	21	k̃	k̃	PROPN
ejpam-5426	197	22	,	,	PUNCT
ejpam-5426	197	23	which	which	PRON
ejpam-5426	197	24	the	the	DET
ejpam-5426	197	25	open	open	ADJ
ejpam-5426	197	26	refinement	refinement	NOUN
ejpam-5426	197	27	k̃	k̃	PROPN
ejpam-5426	197	28	is	be	AUX
ejpam-5426	197	29	a	a	DET
ejpam-5426	197	30	locally−finite	locally−finite	NOUN
ejpam-5426	197	31	if	if	SCONJ
ejpam-5426	197	32	every	every	DET
ejpam-5426	197	33	point	point	NOUN
ejpam-5426	197	34	xi	xi	INTJ
ejpam-5426	197	35	of	of	ADP
ejpam-5426	197	36	the	the	DET
ejpam-5426	197	37	space	space	NOUN
ejpam-5426	197	38	w	w	NOUN
ejpam-5426	197	39	has	have	VERB
ejpam-5426	197	40	a	a	DET
ejpam-5426	197	41	neighborhood	neighborhood	NOUN
ejpam-5426	197	42	ni	ni	NOUN
ejpam-5426	197	43	such	such	ADJ
ejpam-5426	197	44	that	that	SCONJ
ejpam-5426	197	45	eρ	eρ	PROPN
ejpam-5426	197	46	∩ni	∩ni	PROPN
ejpam-5426	197	47	̸=	̸=	PROPN
ejpam-5426	197	48	ϕ	ϕ	PROPN
ejpam-5426	197	49	is	be	AUX
ejpam-5426	197	50	finite	finite	ADJ
ejpam-5426	197	51	for	for	ADP
ejpam-5426	197	52	all	all	DET
ejpam-5426	197	53	ρ	ρ	NOUN
ejpam-5426	197	54	,	,	PUNCT
ejpam-5426	198	1	i	i	PROPN
ejpam-5426	198	2	∈	∈	PROPN
ejpam-5426	198	3	λ	λ	PROPN
ejpam-5426	198	4	.	.	PUNCT
ejpam-5426	198	5	a.	a.	PROPN
ejpam-5426	198	6	amourah	amourah	PROPN
ejpam-5426	198	7	et	et	PROPN
ejpam-5426	198	8	al	al	PROPN
ejpam-5426	198	9	.	.	PUNCT
ejpam-5426	198	10	/	/	SYM
ejpam-5426	198	11	eur	eur	PROPN
ejpam-5426	198	12	.	.	PUNCT
ejpam-5426	199	1	j.	j.	PROPN
ejpam-5426	199	2	pure	pure	PROPN
ejpam-5426	199	3	appl	appl	PROPN
ejpam-5426	199	4	.	.	PROPN
ejpam-5426	199	5	math	math	PROPN
ejpam-5426	199	6	,	,	PUNCT
ejpam-5426	199	7	17	17	NUM
ejpam-5426	199	8	(	(	PUNCT
ejpam-5426	199	9	4	4	NUM
ejpam-5426	199	10	)	)	PUNCT
ejpam-5426	199	11	(	(	PUNCT
ejpam-5426	199	12	2024	2024	NUM
ejpam-5426	199	13	)	)	PUNCT
ejpam-5426	199	14	,	,	PUNCT
ejpam-5426	199	15	2990	2990	NUM
ejpam-5426	199	16	-	-	SYM
ejpam-5426	199	17	3003	3003	NUM
ejpam-5426	199	18	2998	2998	NUM
ejpam-5426	199	19	theorem	theorem	VERB
ejpam-5426	199	20	8	8	NUM
ejpam-5426	199	21	.	.	PUNCT
ejpam-5426	200	1	if	if	SCONJ
ejpam-5426	200	2	any	any	DET
ejpam-5426	200	3	topological	topological	ADJ
ejpam-5426	200	4	space	space	NOUN
ejpam-5426	200	5	(	(	PUNCT
ejpam-5426	200	6	w,ϑ	w,ϑ	PROPN
ejpam-5426	200	7	)	)	PUNCT
ejpam-5426	200	8	is	be	AUX
ejpam-5426	200	9	d−lindelöf	d−lindelöf	PROPN
ejpam-5426	200	10	and	and	CCONJ
ejpam-5426	200	11	countably	countably	ADV
ejpam-5426	200	12	d−paracompact	d−paracompact	PROPN
ejpam-5426	200	13	,	,	PUNCT
ejpam-5426	200	14	then	then	ADV
ejpam-5426	200	15	it	it	PRON
ejpam-5426	200	16	must	must	AUX
ejpam-5426	200	17	be	be	AUX
ejpam-5426	200	18	d−paracompact	d−paracompact	NOUN
ejpam-5426	200	19	.	.	PUNCT
ejpam-5426	201	1	proof	proof	NOUN
ejpam-5426	201	2	.	.	PUNCT
ejpam-5426	202	1	let	let	VERB
ejpam-5426	202	2	ẽ	ẽ	NOUN
ejpam-5426	202	3	=	=	PRON
ejpam-5426	202	4	{	{	PUNCT
ejpam-5426	202	5	eρ	eρ	NOUN
ejpam-5426	202	6	:	:	PUNCT
ejpam-5426	202	7	ρ	ρ	PROPN
ejpam-5426	202	8	∈	∈	PROPN
ejpam-5426	202	9	λ	λ	NOUN
ejpam-5426	202	10	}	}	PUNCT
ejpam-5426	202	11	be	be	VERB
ejpam-5426	202	12	a	a	DET
ejpam-5426	202	13	d−cover	d−cover	PROPN
ejpam-5426	202	14	for	for	ADP
ejpam-5426	202	15	w	w	PROPN
ejpam-5426	202	16	and	and	CCONJ
ejpam-5426	202	17	let	let	VERB
ejpam-5426	202	18	w	w	NOUN
ejpam-5426	202	19	is	be	AUX
ejpam-5426	202	20	a	a	DET
ejpam-5426	202	21	d−lindelöf	d−lindelöf	PROPN
ejpam-5426	202	22	.	.	PUNCT
ejpam-5426	203	1	then	then	ADV
ejpam-5426	203	2	ẽ	ẽ	PROPN
ejpam-5426	203	3	has	have	VERB
ejpam-5426	203	4	a	a	DET
ejpam-5426	203	5	countable	countable	ADJ
ejpam-5426	203	6	subcover	subcover	NOUN
ejpam-5426	203	7	k̃	k̃	PROPN
ejpam-5426	203	8	=	=	PROPN
ejpam-5426	203	9	{	{	PUNCT
ejpam-5426	203	10	k}∞i=1	k}∞i=1	PROPN
ejpam-5426	203	11	.	.	PUNCT
ejpam-5426	204	1	since	since	SCONJ
ejpam-5426	204	2	w	w	PROPN
ejpam-5426	204	3	is	be	AUX
ejpam-5426	204	4	countably	countably	ADV
ejpam-5426	204	5	d−paracompact	d−paracompact	NOUN
ejpam-5426	204	6	,	,	PUNCT
ejpam-5426	204	7	then	then	ADV
ejpam-5426	204	8	k̃	k̃	PROPN
ejpam-5426	204	9	has	have	VERB
ejpam-5426	204	10	an	an	DET
ejpam-5426	204	11	open	open	ADJ
ejpam-5426	204	12	locally	locally	ADV
ejpam-5426	204	13	-	-	PUNCT
ejpam-5426	204	14	finite	finite	NOUN
ejpam-5426	204	15	refinement	refinement	NOUN
ejpam-5426	204	16	s̃	s̃	PROPN
ejpam-5426	204	17	of	of	ADP
ejpam-5426	204	18	ẽ.thus	ẽ.thus	PROPN
ejpam-5426	204	19	,	,	PUNCT
ejpam-5426	204	20	the	the	DET
ejpam-5426	204	21	space	space	NOUN
ejpam-5426	204	22	(	(	PUNCT
ejpam-5426	204	23	w,ϑ	w,ϑ	PROPN
ejpam-5426	204	24	)	)	PUNCT
ejpam-5426	204	25	must	must	AUX
ejpam-5426	204	26	be	be	AUX
ejpam-5426	204	27	d−paracompact	d−paracompact	PROPN
ejpam-5426	204	28	.	.	PUNCT
ejpam-5426	205	1	figure	figure	VERB
ejpam-5426	205	2	7	7	NUM
ejpam-5426	205	3	:	:	PUNCT
ejpam-5426	205	4	the	the	DET
ejpam-5426	205	5	relation	relation	NOUN
ejpam-5426	205	6	of	of	ADP
ejpam-5426	205	7	d−paracompact	d−paracompact	PROPN
ejpam-5426	205	8	and	and	CCONJ
ejpam-5426	205	9	countably	countably	ADV
ejpam-5426	205	10	d−paracompact	d−paracompact	AUX
ejpam-5426	205	11	spaces	space	NOUN
ejpam-5426	205	12	with	with	ADP
ejpam-5426	205	13	d−lindelöf	d−lindelöf	PROPN
ejpam-5426	205	14	condition	condition	NOUN
ejpam-5426	205	15	.	.	PUNCT
ejpam-5426	206	1	figure	figure	VERB
ejpam-5426	206	2	7	7	NUM
ejpam-5426	206	3	presents	present	VERB
ejpam-5426	206	4	the	the	DET
ejpam-5426	206	5	relation	relation	NOUN
ejpam-5426	206	6	betweend−paracompact	betweend−paracompact	NOUN
ejpam-5426	206	7	spaces	space	NOUN
ejpam-5426	206	8	countablyd−paracompact	countablyd−paracompact	VERB
ejpam-5426	206	9	under	under	ADP
ejpam-5426	206	10	extra	extra	ADJ
ejpam-5426	206	11	condition	condition	NOUN
ejpam-5426	206	12	,	,	PUNCT
ejpam-5426	206	13	which	which	PRON
ejpam-5426	206	14	represents	represent	VERB
ejpam-5426	206	15	a	a	DET
ejpam-5426	206	16	significant	significant	ADJ
ejpam-5426	206	17	fact	fact	NOUN
ejpam-5426	206	18	that	that	SCONJ
ejpam-5426	206	19	if	if	SCONJ
ejpam-5426	206	20	the	the	DET
ejpam-5426	206	21	space	space	NOUN
ejpam-5426	206	22	of	of	ADP
ejpam-5426	206	23	countably	countably	ADV
ejpam-5426	206	24	d−paracompact	d−paracompact	NOUN
ejpam-5426	206	25	is	be	AUX
ejpam-5426	206	26	d−lindelöf	d−lindelöf	PROPN
ejpam-5426	206	27	then	then	ADV
ejpam-5426	206	28	must	must	AUX
ejpam-5426	206	29	be	be	AUX
ejpam-5426	206	30	d−paracompact	d−paracompact	NOUN
ejpam-5426	206	31	such	such	ADJ
ejpam-5426	206	32	that	that	SCONJ
ejpam-5426	206	33	ẽ	ẽ	PROPN
ejpam-5426	206	34	=	=	PUNCT
ejpam-5426	206	35	{	{	PUNCT
ejpam-5426	206	36	eρ	eρ	NOUN
ejpam-5426	206	37	:	:	PUNCT
ejpam-5426	206	38	ρ	ρ	PROPN
ejpam-5426	206	39	∈	∈	PROPN
ejpam-5426	206	40	λ	λ	PROPN
ejpam-5426	206	41	}	}	PUNCT
ejpam-5426	206	42	is	be	AUX
ejpam-5426	206	43	the	the	DET
ejpam-5426	206	44	countably	countably	ADJ
ejpam-5426	206	45	d−cover	d−cover	PROPN
ejpam-5426	206	46	of	of	ADP
ejpam-5426	206	47	the	the	DET
ejpam-5426	206	48	topological	topological	ADJ
ejpam-5426	206	49	space	space	NOUN
ejpam-5426	206	50	(	(	PUNCT
ejpam-5426	206	51	w,ϑ	w,ϑ	PROPN
ejpam-5426	206	52	)	)	PUNCT
ejpam-5426	206	53	has	have	VERB
ejpam-5426	206	54	an	an	DET
ejpam-5426	206	55	open	open	ADJ
ejpam-5426	206	56	locally−finite	locally−finite	NOUN
ejpam-5426	206	57	refinement	refinement	NOUN
ejpam-5426	206	58	and	and	CCONJ
ejpam-5426	206	59	we	we	PRON
ejpam-5426	206	60	have	have	VERB
ejpam-5426	206	61	g̃	g̃	PROPN
ejpam-5426	206	62	=	=	SYM
ejpam-5426	206	63	{	{	PUNCT
ejpam-5426	206	64	gω	gω	X
ejpam-5426	206	65	:	:	PUNCT
ejpam-5426	206	66	ω	ω	PROPN
ejpam-5426	206	67	∈	∈	PROPN
ejpam-5426	206	68	ω	ω	PROPN
ejpam-5426	206	69	}	}	PUNCT
ejpam-5426	206	70	is	be	AUX
ejpam-5426	206	71	d−cover	d−cover	PROPN
ejpam-5426	206	72	of	of	ADP
ejpam-5426	206	73	the	the	DET
ejpam-5426	206	74	topological	topological	ADJ
ejpam-5426	206	75	space	space	NOUN
ejpam-5426	206	76	(	(	PUNCT
ejpam-5426	206	77	q	q	NOUN
ejpam-5426	206	78	,	,	PUNCT
ejpam-5426	206	79	ι	ι	PROPN
ejpam-5426	206	80	)	)	PUNCT
ejpam-5426	206	81	has	have	AUX
ejpam-5426	206	82	an	an	DET
ejpam-5426	206	83	open	open	ADJ
ejpam-5426	206	84	locally−finite	locally−finite	NOUN
ejpam-5426	206	85	refinement	refinement	NOUN
ejpam-5426	206	86	.	.	PUNCT
ejpam-5426	207	1	with	with	ADP
ejpam-5426	207	2	the	the	DET
ejpam-5426	207	3	same	same	ADJ
ejpam-5426	207	4	work	work	NOUN
ejpam-5426	207	5	,	,	PUNCT
ejpam-5426	207	6	we	we	PRON
ejpam-5426	207	7	can	can	AUX
ejpam-5426	207	8	achieve	achieve	VERB
ejpam-5426	207	9	the	the	DET
ejpam-5426	207	10	next	next	ADJ
ejpam-5426	207	11	corollaries	corollary	NOUN
ejpam-5426	207	12	.	.	PUNCT
ejpam-5426	208	1	corollary	corollary	ADJ
ejpam-5426	208	2	4	4	NUM
ejpam-5426	208	3	.	.	PUNCT
ejpam-5426	209	1	if	if	SCONJ
ejpam-5426	209	2	any	any	DET
ejpam-5426	209	3	topological	topological	ADJ
ejpam-5426	209	4	space	space	NOUN
ejpam-5426	209	5	(	(	PUNCT
ejpam-5426	209	6	w,ϑ	w,ϑ	PROPN
ejpam-5426	209	7	)	)	PUNCT
ejpam-5426	209	8	is	be	AUX
ejpam-5426	209	9	d−lindelöf	d−lindelöf	PROPN
ejpam-5426	209	10	and	and	CCONJ
ejpam-5426	209	11	countably	countably	ADV
ejpam-5426	209	12	d−paracompact	d−paracompact	PROPN
ejpam-5426	209	13	,	,	PUNCT
ejpam-5426	209	14	then	then	ADV
ejpam-5426	209	15	it	it	PRON
ejpam-5426	209	16	must	must	AUX
ejpam-5426	209	17	be	be	AUX
ejpam-5426	209	18	paracompact	paracompact	ADJ
ejpam-5426	209	19	.	.	PUNCT
ejpam-5426	210	1	corollary	corollary	ADJ
ejpam-5426	210	2	5	5	NUM
ejpam-5426	210	3	.	.	PUNCT
ejpam-5426	211	1	if	if	SCONJ
ejpam-5426	211	2	any	any	DET
ejpam-5426	211	3	topological	topological	ADJ
ejpam-5426	211	4	space	space	NOUN
ejpam-5426	211	5	(	(	PUNCT
ejpam-5426	211	6	w,ϑ	w,ϑ	PROPN
ejpam-5426	211	7	)	)	PUNCT
ejpam-5426	211	8	is	be	AUX
ejpam-5426	211	9	lindelöf	lindelöf	PUNCT
ejpam-5426	211	10	and	and	CCONJ
ejpam-5426	211	11	countably	countably	ADV
ejpam-5426	211	12	d−paracompact	d−paracompact	PROPN
ejpam-5426	211	13	,	,	PUNCT
ejpam-5426	211	14	then	then	ADV
ejpam-5426	211	15	it	it	PRON
ejpam-5426	211	16	must	must	AUX
ejpam-5426	211	17	be	be	AUX
ejpam-5426	211	18	paracompact	paracompact	ADJ
ejpam-5426	211	19	.	.	PUNCT
ejpam-5426	211	20	example	example	NOUN
ejpam-5426	212	1	5	5	NUM
ejpam-5426	212	2	.	.	PUNCT
ejpam-5426	213	1	let	let	VERB
ejpam-5426	213	2	the	the	DET
ejpam-5426	213	3	space	space	NOUN
ejpam-5426	213	4	(	(	PUNCT
ejpam-5426	213	5	w,ϑdis	w,ϑdi	NOUN
ejpam-5426	213	6	)	)	PUNCT
ejpam-5426	213	7	be	be	VERB
ejpam-5426	213	8	a	a	DET
ejpam-5426	213	9	d−lindelöf	d−lindelöf	PROPN
ejpam-5426	213	10	and	and	CCONJ
ejpam-5426	213	11	a	a	DET
ejpam-5426	213	12	countably	countably	ADJ
ejpam-5426	213	13	d−paracompact	d−paracompact	NOUN
ejpam-5426	213	14	space	space	NOUN
ejpam-5426	213	15	.	.	PUNCT
ejpam-5426	214	1	then	then	ADV
ejpam-5426	214	2	by	by	ADP
ejpam-5426	214	3	using	use	VERB
ejpam-5426	214	4	the	the	DET
ejpam-5426	214	5	theorem	theorem	NOUN
ejpam-5426	214	6	3.16	3.16	NUM
ejpam-5426	214	7	,	,	PUNCT
ejpam-5426	214	8	we	we	PRON
ejpam-5426	214	9	get	get	VERB
ejpam-5426	214	10	that	that	PRON
ejpam-5426	214	11	(	(	PUNCT
ejpam-5426	214	12	w,ϑdis	w,ϑdi	NOUN
ejpam-5426	214	13	)	)	PUNCT
ejpam-5426	214	14	must	must	AUX
ejpam-5426	214	15	be	be	AUX
ejpam-5426	214	16	d−paracompact	d−paracompact	PROPN
ejpam-5426	214	17	.	.	PUNCT
ejpam-5426	215	1	theorem	theorem	NOUN
ejpam-5426	215	2	9	9	NUM
ejpam-5426	215	3	.	.	PUNCT
ejpam-5426	216	1	if	if	SCONJ
ejpam-5426	216	2	any	any	DET
ejpam-5426	216	3	topological	topological	ADJ
ejpam-5426	216	4	space	space	NOUN
ejpam-5426	216	5	(	(	PUNCT
ejpam-5426	216	6	w,ϑ	w,ϑ	PROPN
ejpam-5426	216	7	)	)	PUNCT
ejpam-5426	216	8	is	be	AUX
ejpam-5426	216	9	d−paralindelöf	d−paralindelöf	PROPN
ejpam-5426	216	10	and	and	CCONJ
ejpam-5426	216	11	countably	countably	ADV
ejpam-5426	216	12	d−paracompact	d−paracompact	PROPN
ejpam-5426	216	13	,	,	PUNCT
ejpam-5426	216	14	then	then	ADV
ejpam-5426	216	15	it	it	PRON
ejpam-5426	216	16	must	must	AUX
ejpam-5426	216	17	be	be	AUX
ejpam-5426	216	18	a	a	DET
ejpam-5426	216	19	d−paracompact	d−paracompact	NOUN
ejpam-5426	216	20	space	space	NOUN
ejpam-5426	216	21	.	.	PUNCT
ejpam-5426	217	1	proof	proof	NOUN
ejpam-5426	217	2	.	.	PUNCT
ejpam-5426	218	1	let	let	VERB
ejpam-5426	218	2	ẽ	ẽ	NOUN
ejpam-5426	218	3	=	=	PRON
ejpam-5426	218	4	{	{	PUNCT
ejpam-5426	218	5	eρ	eρ	NOUN
ejpam-5426	218	6	:	:	PUNCT
ejpam-5426	218	7	ρ	ρ	PROPN
ejpam-5426	218	8	∈	∈	PROPN
ejpam-5426	218	9	λ	λ	NOUN
ejpam-5426	218	10	}	}	PUNCT
ejpam-5426	218	11	be	be	VERB
ejpam-5426	218	12	any	any	DET
ejpam-5426	218	13	d−cover	d−cover	PROPN
ejpam-5426	218	14	for	for	ADP
ejpam-5426	218	15	w	w	PROPN
ejpam-5426	218	16	and	and	CCONJ
ejpam-5426	218	17	let	let	VERB
ejpam-5426	218	18	w	w	NOUN
ejpam-5426	218	19	is	be	AUX
ejpam-5426	218	20	d−paralindelöf	d−paralindelöf	NOUN
ejpam-5426	218	21	space	space	NOUN
ejpam-5426	218	22	.	.	PUNCT
ejpam-5426	219	1	then	then	ADV
ejpam-5426	219	2	ẽ	ẽ	PROPN
ejpam-5426	219	3	has	have	VERB
ejpam-5426	219	4	an	an	DET
ejpam-5426	219	5	open	open	ADJ
ejpam-5426	219	6	locally	locally	ADV
ejpam-5426	219	7	-	-	PUNCT
ejpam-5426	219	8	countable	countable	ADJ
ejpam-5426	219	9	refinement	refinement	NOUN
ejpam-5426	219	10	k̃	k̃	PROPN
ejpam-5426	219	11	=	=	PROPN
ejpam-5426	219	12	{	{	PUNCT
ejpam-5426	219	13	kρi}∞i=1	kρi}∞i=1	PROPN
ejpam-5426	219	14	,	,	PUNCT
ejpam-5426	219	15	where	where	SCONJ
ejpam-5426	219	16	is	be	AUX
ejpam-5426	219	17	also	also	ADV
ejpam-5426	219	18	a	a	DET
ejpam-5426	219	19	d−cover	d−cover	PROPN
ejpam-5426	219	20	of	of	ADP
ejpam-5426	219	21	(	(	PUNCT
ejpam-5426	219	22	w,ϑ	w,ϑ	PROPN
ejpam-5426	219	23	)	)	PUNCT
ejpam-5426	219	24	.	.	PUNCT
ejpam-5426	220	1	now	now	ADV
ejpam-5426	220	2	,	,	PUNCT
ejpam-5426	220	3	since	since	SCONJ
ejpam-5426	220	4	w	w	NOUN
ejpam-5426	220	5	is	be	AUX
ejpam-5426	220	6	countably	countably	ADV
ejpam-5426	220	7	d−paracompact	d−paracompact	NOUN
ejpam-5426	220	8	,	,	PUNCT
ejpam-5426	220	9	then	then	ADV
ejpam-5426	220	10	k̃	k̃	PROPN
ejpam-5426	220	11	has	have	VERB
ejpam-5426	220	12	an	an	DET
ejpam-5426	220	13	open	open	ADJ
ejpam-5426	220	14	locally	locally	ADV
ejpam-5426	220	15	-	-	PUNCT
ejpam-5426	220	16	finite	finite	NOUN
ejpam-5426	220	17	refinement	refinement	NOUN
ejpam-5426	220	18	s̃	s̃	PROPN
ejpam-5426	220	19	of	of	ADP
ejpam-5426	220	20	ẽ.	ẽ.	PROPN
ejpam-5426	220	21	thus	thus	ADV
ejpam-5426	220	22	,	,	PUNCT
ejpam-5426	220	23	the	the	DET
ejpam-5426	220	24	space	space	NOUN
ejpam-5426	220	25	(	(	PUNCT
ejpam-5426	220	26	w,ϑ	w,ϑ	PROPN
ejpam-5426	220	27	)	)	PUNCT
ejpam-5426	220	28	must	must	AUX
ejpam-5426	220	29	be	be	AUX
ejpam-5426	220	30	d−paracompact	d−paracompact	PROPN
ejpam-5426	220	31	.	.	PUNCT
ejpam-5426	221	1	a.	a.	PROPN
ejpam-5426	221	2	amourah	amourah	PROPN
ejpam-5426	221	3	et	et	PROPN
ejpam-5426	221	4	al	al	PROPN
ejpam-5426	221	5	.	.	PUNCT
ejpam-5426	221	6	/	/	SYM
ejpam-5426	221	7	eur	eur	PROPN
ejpam-5426	221	8	.	.	PUNCT
ejpam-5426	222	1	j.	j.	PROPN
ejpam-5426	222	2	pure	pure	PROPN
ejpam-5426	222	3	appl	appl	PROPN
ejpam-5426	222	4	.	.	PROPN
ejpam-5426	222	5	math	math	PROPN
ejpam-5426	222	6	,	,	PUNCT
ejpam-5426	222	7	17	17	NUM
ejpam-5426	222	8	(	(	PUNCT
ejpam-5426	222	9	4	4	NUM
ejpam-5426	222	10	)	)	PUNCT
ejpam-5426	222	11	(	(	PUNCT
ejpam-5426	222	12	2024	2024	NUM
ejpam-5426	222	13	)	)	PUNCT
ejpam-5426	222	14	,	,	PUNCT
ejpam-5426	222	15	2990	2990	NUM
ejpam-5426	222	16	-	-	SYM
ejpam-5426	222	17	3003	3003	NUM
ejpam-5426	222	18	2999	2999	NUM
ejpam-5426	222	19	figure	figure	NOUN
ejpam-5426	222	20	8	8	NUM
ejpam-5426	222	21	:	:	PUNCT
ejpam-5426	222	22	the	the	DET
ejpam-5426	222	23	relation	relation	NOUN
ejpam-5426	222	24	of	of	ADP
ejpam-5426	222	25	d−paracompact	d−paracompact	PROPN
ejpam-5426	222	26	and	and	CCONJ
ejpam-5426	222	27	countably	countably	ADV
ejpam-5426	222	28	d−paracompact	d−paracompact	AUX
ejpam-5426	222	29	spaces	space	NOUN
ejpam-5426	222	30	with	with	ADP
ejpam-5426	222	31	d−paralindelöf	d−paralindelöf	NOUN
ejpam-5426	222	32	condition	condition	NOUN
ejpam-5426	222	33	.	.	PUNCT
ejpam-5426	223	1	figure	figure	NOUN
ejpam-5426	223	2	8	8	NUM
ejpam-5426	223	3	presents	present	VERB
ejpam-5426	223	4	the	the	DET
ejpam-5426	223	5	relation	relation	NOUN
ejpam-5426	223	6	betweend−paracompact	betweend−paracompact	NOUN
ejpam-5426	223	7	spaces	space	NOUN
ejpam-5426	223	8	countablyd−paracompact	countablyd−paracompact	VERB
ejpam-5426	223	9	under	under	ADP
ejpam-5426	223	10	extra	extra	ADJ
ejpam-5426	223	11	condition	condition	NOUN
ejpam-5426	223	12	,	,	PUNCT
ejpam-5426	223	13	which	which	PRON
ejpam-5426	223	14	represents	represent	VERB
ejpam-5426	223	15	a	a	DET
ejpam-5426	223	16	significant	significant	ADJ
ejpam-5426	223	17	fact	fact	NOUN
ejpam-5426	223	18	that	that	SCONJ
ejpam-5426	223	19	if	if	SCONJ
ejpam-5426	223	20	the	the	DET
ejpam-5426	223	21	space	space	NOUN
ejpam-5426	223	22	of	of	ADP
ejpam-5426	223	23	countably	countably	ADV
ejpam-5426	223	24	d−paracompact	d−paracompact	NOUN
ejpam-5426	223	25	is	be	AUX
ejpam-5426	223	26	d−paralindelöf	d−paralindelöf	PROPN
ejpam-5426	223	27	then	then	ADV
ejpam-5426	223	28	must	must	AUX
ejpam-5426	223	29	be	be	AUX
ejpam-5426	223	30	d−paracompact	d−paracompact	NOUN
ejpam-5426	223	31	such	such	ADJ
ejpam-5426	223	32	that	that	SCONJ
ejpam-5426	223	33	ẽ	ẽ	PROPN
ejpam-5426	223	34	=	=	PUNCT
ejpam-5426	223	35	{	{	PUNCT
ejpam-5426	223	36	eρ	eρ	NOUN
ejpam-5426	223	37	:	:	PUNCT
ejpam-5426	223	38	ρ	ρ	PROPN
ejpam-5426	223	39	∈	∈	PROPN
ejpam-5426	223	40	λ	λ	PROPN
ejpam-5426	223	41	}	}	PUNCT
ejpam-5426	223	42	is	be	AUX
ejpam-5426	223	43	the	the	DET
ejpam-5426	223	44	countably	countably	ADJ
ejpam-5426	223	45	d−cover	d−cover	PROPN
ejpam-5426	223	46	of	of	ADP
ejpam-5426	223	47	the	the	DET
ejpam-5426	223	48	topological	topological	ADJ
ejpam-5426	223	49	space	space	NOUN
ejpam-5426	223	50	(	(	PUNCT
ejpam-5426	223	51	w,ϑ	w,ϑ	PROPN
ejpam-5426	223	52	)	)	PUNCT
ejpam-5426	223	53	has	have	VERB
ejpam-5426	223	54	an	an	DET
ejpam-5426	223	55	open	open	ADJ
ejpam-5426	223	56	locally−finite	locally−finite	NOUN
ejpam-5426	223	57	refinement	refinement	NOUN
ejpam-5426	223	58	and	and	CCONJ
ejpam-5426	223	59	we	we	PRON
ejpam-5426	223	60	have	have	VERB
ejpam-5426	223	61	g̃	g̃	PROPN
ejpam-5426	223	62	=	=	SYM
ejpam-5426	223	63	{	{	PUNCT
ejpam-5426	223	64	gω	gω	X
ejpam-5426	223	65	:	:	PUNCT
ejpam-5426	223	66	ω	ω	PROPN
ejpam-5426	223	67	∈	∈	PROPN
ejpam-5426	223	68	ω	ω	PROPN
ejpam-5426	223	69	}	}	PUNCT
ejpam-5426	223	70	is	be	AUX
ejpam-5426	223	71	d−cover	d−cover	PROPN
ejpam-5426	223	72	of	of	ADP
ejpam-5426	223	73	the	the	DET
ejpam-5426	223	74	topological	topological	ADJ
ejpam-5426	223	75	space	space	NOUN
ejpam-5426	223	76	(	(	PUNCT
ejpam-5426	223	77	q	q	NOUN
ejpam-5426	223	78	,	,	PUNCT
ejpam-5426	223	79	ι	ι	PROPN
ejpam-5426	223	80	)	)	PUNCT
ejpam-5426	223	81	has	have	AUX
ejpam-5426	223	82	an	an	DET
ejpam-5426	223	83	open	open	ADJ
ejpam-5426	223	84	locally−finite	locally−finite	ADJ
ejpam-5426	223	85	refinement	refinement	NOUN
ejpam-5426	223	86	.	.	PUNCT
ejpam-5426	224	1	the	the	DET
ejpam-5426	224	2	following	follow	VERB
ejpam-5426	224	3	corollaries	corollary	NOUN
ejpam-5426	224	4	can	can	AUX
ejpam-5426	224	5	be	be	AUX
ejpam-5426	224	6	obtained	obtain	VERB
ejpam-5426	224	7	with	with	ADP
ejpam-5426	224	8	the	the	DET
ejpam-5426	224	9	same	same	ADJ
ejpam-5426	224	10	work	work	NOUN
ejpam-5426	224	11	.	.	PUNCT
ejpam-5426	225	1	corollary	corollary	ADJ
ejpam-5426	225	2	6	6	NUM
ejpam-5426	225	3	.	.	PUNCT
ejpam-5426	226	1	if	if	SCONJ
ejpam-5426	226	2	any	any	DET
ejpam-5426	226	3	topological	topological	ADJ
ejpam-5426	226	4	space	space	NOUN
ejpam-5426	226	5	(	(	PUNCT
ejpam-5426	226	6	w,ϑ	w,ϑ	PROPN
ejpam-5426	226	7	)	)	PUNCT
ejpam-5426	226	8	is	be	AUX
ejpam-5426	226	9	d−paralindelöf	d−paralindelöf	PROPN
ejpam-5426	226	10	and	and	CCONJ
ejpam-5426	226	11	countably	countably	ADV
ejpam-5426	226	12	d−paracompact	d−paracompact	PROPN
ejpam-5426	226	13	,	,	PUNCT
ejpam-5426	226	14	then	then	ADV
ejpam-5426	226	15	it	it	PRON
ejpam-5426	226	16	must	must	AUX
ejpam-5426	226	17	be	be	AUX
ejpam-5426	226	18	a	a	DET
ejpam-5426	226	19	paracompact	paracompact	ADJ
ejpam-5426	226	20	space	space	NOUN
ejpam-5426	226	21	.	.	PUNCT
ejpam-5426	227	1	corollary	corollary	ADJ
ejpam-5426	227	2	7	7	NUM
ejpam-5426	227	3	.	.	PUNCT
ejpam-5426	228	1	if	if	SCONJ
ejpam-5426	228	2	any	any	DET
ejpam-5426	228	3	topological	topological	ADJ
ejpam-5426	228	4	space	space	NOUN
ejpam-5426	228	5	(	(	PUNCT
ejpam-5426	228	6	w,ϑ	w,ϑ	PROPN
ejpam-5426	228	7	)	)	PUNCT
ejpam-5426	228	8	is	be	AUX
ejpam-5426	228	9	paralindelöf	paralindelöf	NOUN
ejpam-5426	228	10	and	and	CCONJ
ejpam-5426	228	11	countably	countably	ADV
ejpam-5426	228	12	d−paracompact	d−paracompact	PROPN
ejpam-5426	228	13	,	,	PUNCT
ejpam-5426	228	14	then	then	ADV
ejpam-5426	228	15	it	it	PRON
ejpam-5426	228	16	must	must	AUX
ejpam-5426	228	17	be	be	AUX
ejpam-5426	228	18	a	a	DET
ejpam-5426	228	19	paracompact	paracompact	ADJ
ejpam-5426	228	20	space	space	NOUN
ejpam-5426	228	21	.	.	PUNCT
ejpam-5426	229	1	figure	figure	NOUN
ejpam-5426	229	2	9	9	NUM
ejpam-5426	229	3	:	:	PUNCT
ejpam-5426	229	4	the	the	DET
ejpam-5426	229	5	flow	flow	NOUN
ejpam-5426	229	6	chart	chart	NOUN
ejpam-5426	229	7	of	of	ADP
ejpam-5426	229	8	d−paracompact	d−paracompact	PROPN
ejpam-5426	229	9	with	with	ADP
ejpam-5426	229	10	some	some	DET
ejpam-5426	229	11	spaces	space	NOUN
ejpam-5426	229	12	.	.	PUNCT
ejpam-5426	230	1	figure	figure	VERB
ejpam-5426	230	2	9	9	NUM
ejpam-5426	230	3	presents	present	NOUN
ejpam-5426	230	4	the	the	DET
ejpam-5426	230	5	study	study	NOUN
ejpam-5426	230	6	’s	’s	PART
ejpam-5426	230	7	results	result	NOUN
ejpam-5426	230	8	flow	flow	VERB
ejpam-5426	230	9	chart	chart	NOUN
ejpam-5426	230	10	,	,	PUNCT
ejpam-5426	230	11	which	which	PRON
ejpam-5426	230	12	represents	represent	VERB
ejpam-5426	230	13	the	the	DET
ejpam-5426	230	14	relation	relation	NOUN
ejpam-5426	230	15	of	of	ADP
ejpam-5426	230	16	difference	difference	NOUN
ejpam-5426	230	17	paracompact	paracompact	NOUN
ejpam-5426	230	18	spaces	space	NOUN
ejpam-5426	230	19	with	with	ADP
ejpam-5426	230	20	common	common	ADJ
ejpam-5426	230	21	topological	topological	ADJ
ejpam-5426	230	22	spaces	space	NOUN
ejpam-5426	230	23	,	,	PUNCT
ejpam-5426	230	24	in	in	ADP
ejpam-5426	230	25	which	which	PRON
ejpam-5426	230	26	the	the	DET
ejpam-5426	230	27	space	space	NOUN
ejpam-5426	230	28	of	of	ADP
ejpam-5426	230	29	difference	difference	NOUN
ejpam-5426	230	30	paracompact	paracompact	NOUN
ejpam-5426	230	31	represents	represent	VERB
ejpam-5426	230	32	a	a	DET
ejpam-5426	230	33	basic	basic	ADJ
ejpam-5426	230	34	class	class	NOUN
ejpam-5426	230	35	characterized	characterize	VERB
ejpam-5426	230	36	by	by	ADP
ejpam-5426	230	37	special	special	ADJ
ejpam-5426	230	38	coverings	covering	NOUN
ejpam-5426	230	39	.	.	PUNCT
ejpam-5426	231	1	a.	a.	PROPN
ejpam-5426	231	2	amourah	amourah	PROPN
ejpam-5426	231	3	et	et	PROPN
ejpam-5426	231	4	al	al	PROPN
ejpam-5426	231	5	.	.	PUNCT
ejpam-5426	231	6	/	/	SYM
ejpam-5426	231	7	eur	eur	PROPN
ejpam-5426	231	8	.	.	PUNCT
ejpam-5426	232	1	j.	j.	PROPN
ejpam-5426	232	2	pure	pure	PROPN
ejpam-5426	232	3	appl	appl	PROPN
ejpam-5426	232	4	.	.	PROPN
ejpam-5426	232	5	math	math	PROPN
ejpam-5426	232	6	,	,	PUNCT
ejpam-5426	232	7	17	17	NUM
ejpam-5426	232	8	(	(	PUNCT
ejpam-5426	232	9	4	4	NUM
ejpam-5426	232	10	)	)	PUNCT
ejpam-5426	232	11	(	(	PUNCT
ejpam-5426	232	12	2024	2024	NUM
ejpam-5426	232	13	)	)	PUNCT
ejpam-5426	232	14	,	,	PUNCT
ejpam-5426	232	15	2990	2990	NUM
ejpam-5426	232	16	-	-	SYM
ejpam-5426	232	17	3003	3003	NUM
ejpam-5426	232	18	3000	3000	NUM
ejpam-5426	232	19	4	4	NUM
ejpam-5426	232	20	.	.	PUNCT
ejpam-5426	232	21	product	product	NOUN
ejpam-5426	232	22	of	of	ADP
ejpam-5426	232	23	d	d	ADJ
ejpam-5426	232	24	-	-	ADJ
ejpam-5426	232	25	paracompact	paracompact	ADJ
ejpam-5426	232	26	topological	topological	ADJ
ejpam-5426	232	27	spaces	space	NOUN
ejpam-5426	232	28	this	this	DET
ejpam-5426	232	29	section	section	NOUN
ejpam-5426	232	30	presents	present	VERB
ejpam-5426	232	31	several	several	ADJ
ejpam-5426	232	32	main	main	ADJ
ejpam-5426	232	33	theoretical	theoretical	ADJ
ejpam-5426	232	34	results	result	NOUN
ejpam-5426	232	35	the	the	DET
ejpam-5426	232	36	concepts	concept	NOUN
ejpam-5426	232	37	of	of	ADP
ejpam-5426	232	38	maps	map	NOUN
ejpam-5426	232	39	with	with	ADP
ejpam-5426	232	40	the	the	DET
ejpam-5426	232	41	product	product	NOUN
ejpam-5426	232	42	for	for	ADP
ejpam-5426	232	43	two	two	NUM
ejpam-5426	232	44	d−paracompact	d−paracompact	NOUN
ejpam-5426	232	45	spaces	space	NOUN
ejpam-5426	232	46	.	.	PUNCT
ejpam-5426	233	1	theorem	theorem	ADJ
ejpam-5426	233	2	10	10	NUM
ejpam-5426	233	3	.	.	PUNCT
ejpam-5426	234	1	let	let	VERB
ejpam-5426	234	2	(	(	PUNCT
ejpam-5426	234	3	w,ϑ	w,ϑ	VERB
ejpam-5426	234	4	)	)	PUNCT
ejpam-5426	234	5	and	and	CCONJ
ejpam-5426	234	6	(	(	PUNCT
ejpam-5426	234	7	q	q	ADJ
ejpam-5426	234	8	,	,	PUNCT
ejpam-5426	234	9	ι	ι	AUX
ejpam-5426	234	10	)	)	PUNCT
ejpam-5426	234	11	be	be	VERB
ejpam-5426	234	12	any	any	DET
ejpam-5426	234	13	topological	topological	ADJ
ejpam-5426	234	14	spaces	space	NOUN
ejpam-5426	234	15	.	.	PUNCT
ejpam-5426	235	1	if	if	SCONJ
ejpam-5426	235	2	φ	φ	PROPN
ejpam-5426	235	3	:	:	PUNCT
ejpam-5426	235	4	w	w	X
ejpam-5426	235	5	−→	−→	NOUN
ejpam-5426	235	6	q	q	NOUN
ejpam-5426	235	7	is	be	AUX
ejpam-5426	235	8	a	a	DET
ejpam-5426	235	9	d−perfect	d−perfect	NOUN
ejpam-5426	235	10	function	function	NOUN
ejpam-5426	235	11	,	,	PUNCT
ejpam-5426	235	12	and	and	CCONJ
ejpam-5426	235	13	w	w	NOUN
ejpam-5426	235	14	is	be	AUX
ejpam-5426	235	15	locally	locally	ADV
ejpam-5426	235	16	-	-	PUNCT
ejpam-5426	235	17	indiscreet	indiscreet	ADJ
ejpam-5426	235	18	space	space	NOUN
ejpam-5426	235	19	,	,	PUNCT
ejpam-5426	235	20	then	then	ADV
ejpam-5426	235	21	w	w	PROPN
ejpam-5426	235	22	must	must	AUX
ejpam-5426	235	23	be	be	AUX
ejpam-5426	235	24	d−paracompact	d−paracompact	PROPN
ejpam-5426	235	25	if	if	SCONJ
ejpam-5426	235	26	the	the	DET
ejpam-5426	235	27	space	space	NOUN
ejpam-5426	235	28	q	q	NOUN
ejpam-5426	235	29	is	be	AUX
ejpam-5426	235	30	so	so	ADV
ejpam-5426	235	31	proof	proof	ADJ
ejpam-5426	235	32	.	.	PUNCT
ejpam-5426	236	1	let	let	VERB
ejpam-5426	236	2	ẽ	ẽ	NOUN
ejpam-5426	236	3	=	=	PRON
ejpam-5426	236	4	{	{	PUNCT
ejpam-5426	236	5	eρ	eρ	NOUN
ejpam-5426	236	6	:	:	PUNCT
ejpam-5426	236	7	ρ	ρ	PROPN
ejpam-5426	236	8	∈	∈	PROPN
ejpam-5426	236	9	λ	λ	NOUN
ejpam-5426	236	10	}	}	PUNCT
ejpam-5426	236	11	be	be	VERB
ejpam-5426	236	12	any	any	DET
ejpam-5426	236	13	d−cover	d−cover	PROPN
ejpam-5426	236	14	of	of	ADP
ejpam-5426	236	15	w	w	PROPN
ejpam-5426	236	16	.	.	PUNCT
ejpam-5426	237	1	since	since	SCONJ
ejpam-5426	237	2	φ	φ	PROPN
ejpam-5426	237	3	is	be	AUX
ejpam-5426	237	4	d−perfect	d−perfect	NOUN
ejpam-5426	237	5	,	,	PUNCT
ejpam-5426	237	6	then	then	ADV
ejpam-5426	237	7	for	for	ADP
ejpam-5426	237	8	any	any	DET
ejpam-5426	237	9	q	q	PROPN
ejpam-5426	237	10	∈	∈	PROPN
ejpam-5426	237	11	q	q	NOUN
ejpam-5426	237	12	,	,	PUNCT
ejpam-5426	237	13	we	we	PRON
ejpam-5426	237	14	have	have	AUX
ejpam-5426	237	15	φ−1(q	φ−1(q	NOUN
ejpam-5426	237	16	)	)	PUNCT
ejpam-5426	237	17	is	be	AUX
ejpam-5426	237	18	d−compact	d−compact	PROPN
ejpam-5426	237	19	subsets	subset	NOUN
ejpam-5426	237	20	of	of	ADP
ejpam-5426	237	21	w	w	PROPN
ejpam-5426	237	22	.	.	PUNCT
ejpam-5426	238	1	so	so	ADV
ejpam-5426	238	2	,	,	PUNCT
ejpam-5426	238	3	there	there	PRON
ejpam-5426	238	4	is	be	VERB
ejpam-5426	238	5	a	a	DET
ejpam-5426	238	6	finite	finite	NOUN
ejpam-5426	238	7	subset	subset	NOUN
ejpam-5426	238	8	ιq	ιq	NOUN
ejpam-5426	238	9	of	of	ADP
ejpam-5426	238	10	λ	λ	PROPN
ejpam-5426	238	11	,	,	PUNCT
ejpam-5426	238	12	such	such	ADJ
ejpam-5426	238	13	that	that	SCONJ
ejpam-5426	238	14	φ−1(q	φ−1(q	NOUN
ejpam-5426	238	15	)	)	PUNCT
ejpam-5426	238	16	⊆	⊆	NUM
ejpam-5426	238	17	∪ρ∈ιqhρ	∪ρ∈ιqhρ	PROPN
ejpam-5426	238	18	,	,	PUNCT
ejpam-5426	238	19	and	and	CCONJ
ejpam-5426	238	20	ẽ	ẽ	PROPN
ejpam-5426	238	21	is	be	AUX
ejpam-5426	238	22	an	an	DET
ejpam-5426	238	23	open	open	ADJ
ejpam-5426	238	24	cover	cover	NOUN
ejpam-5426	238	25	of	of	ADP
ejpam-5426	238	26	w	w	PROPN
ejpam-5426	238	27	.	.	PUNCT
ejpam-5426	239	1	that	that	PRON
ejpam-5426	239	2	is	be	AUX
ejpam-5426	239	3	,	,	PUNCT
ejpam-5426	239	4	pq	pq	INTJ
ejpam-5426	239	5	=	=	SYM
ejpam-5426	239	6	q−φ(w	q−φ(w	NOUN
ejpam-5426	239	7	−∪ρ∈ιqhρ	−∪ρ∈ιqhρ	NOUN
ejpam-5426	239	8	)	)	PUNCT
ejpam-5426	239	9	is	be	AUX
ejpam-5426	239	10	d−open	d−open	ADJ
ejpam-5426	239	11	subsets	subset	NOUN
ejpam-5426	239	12	of	of	ADP
ejpam-5426	239	13	q	q	PROPN
ejpam-5426	239	14	and	and	CCONJ
ejpam-5426	239	15	φ−1(pq)∪ρ∈ιq	φ−1(pq)∪ρ∈ιq	PROPN
ejpam-5426	239	16	hρ	hρ	PROPN
ejpam-5426	239	17	,	,	PUNCT
ejpam-5426	239	18	for	for	ADP
ejpam-5426	239	19	any	any	DET
ejpam-5426	239	20	q	q	PROPN
ejpam-5426	239	21	∈	∈	PROPN
ejpam-5426	239	22	pq	pq	NOUN
ejpam-5426	239	23	,	,	PUNCT
ejpam-5426	239	24	therefore	therefore	ADV
ejpam-5426	239	25	p̃	p̃	PROPN
ejpam-5426	239	26	=	=	PUNCT
ejpam-5426	239	27	{	{	PUNCT
ejpam-5426	239	28	pq	pq	NOUN
ejpam-5426	239	29	:	:	PUNCT
ejpam-5426	239	30	q	q	PROPN
ejpam-5426	239	31	∈	∈	PROPN
ejpam-5426	239	32	q	q	NOUN
ejpam-5426	239	33	}	}	PUNCT
ejpam-5426	239	34	is	be	AUX
ejpam-5426	239	35	open	open	ADJ
ejpam-5426	239	36	d−cover	d−cover	PROPN
ejpam-5426	239	37	of	of	ADP
ejpam-5426	239	38	q.	q.	PROPN
ejpam-5426	239	39	since	since	SCONJ
ejpam-5426	239	40	q	q	PROPN
ejpam-5426	239	41	is	be	AUX
ejpam-5426	239	42	d−paracompact	d−paracompact	PROPN
ejpam-5426	239	43	,	,	PUNCT
ejpam-5426	239	44	then	then	ADV
ejpam-5426	239	45	we	we	PRON
ejpam-5426	239	46	get	get	VERB
ejpam-5426	239	47	that	that	PRON
ejpam-5426	239	48	p̃	p̃	PROPN
ejpam-5426	239	49	has	have	VERB
ejpam-5426	239	50	an	an	DET
ejpam-5426	239	51	open	open	ADJ
ejpam-5426	239	52	locallyfinite	locallyfinite	ADJ
ejpam-5426	239	53	refinement	refinement	NOUN
ejpam-5426	239	54	p̃	p̃	PROPN
ejpam-5426	239	55	∗	∗	NOUN
ejpam-5426	239	56	=	=	PUNCT
ejpam-5426	239	57	{	{	PUNCT
ejpam-5426	239	58	p	p	X
ejpam-5426	239	59	∗	∗	X
ejpam-5426	239	60	q	q	NOUN
ejpam-5426	239	61	:	:	PUNCT
ejpam-5426	239	62	q	q	PUNCT
ejpam-5426	239	63	∈	∈	PROPN
ejpam-5426	239	64	q	q	X
ejpam-5426	239	65	}	}	PUNCT
ejpam-5426	239	66	.	.	PUNCT
ejpam-5426	240	1	thus	thus	ADV
ejpam-5426	240	2	,	,	PUNCT
ejpam-5426	240	3	the	the	DET
ejpam-5426	240	4	set	set	NOUN
ejpam-5426	240	5	p	p	NOUN
ejpam-5426	240	6	∗	∗	X
ejpam-5426	240	7	q	q	PUNCT
ejpam-5426	240	8	is	be	AUX
ejpam-5426	240	9	d−open	d−open	ADJ
ejpam-5426	240	10	subsets	subset	NOUN
ejpam-5426	240	11	of	of	ADP
ejpam-5426	240	12	w	w	PROPN
ejpam-5426	240	13	.	.	PUNCT
ejpam-5426	241	1	since	since	SCONJ
ejpam-5426	241	2	the	the	DET
ejpam-5426	241	3	function	function	NOUN
ejpam-5426	241	4	φ	φ	PROPN
ejpam-5426	241	5	is	be	AUX
ejpam-5426	241	6	d−perfect	d−perfect	PROPN
ejpam-5426	241	7	,	,	PUNCT
ejpam-5426	241	8	that	that	PRON
ejpam-5426	241	9	is	be	AUX
ejpam-5426	241	10	means	mean	VERB
ejpam-5426	241	11	{	{	PUNCT
ejpam-5426	241	12	φ−1(p	φ−1(p	NOUN
ejpam-5426	241	13	∗	∗	X
ejpam-5426	241	14	q	q	NOUN
ejpam-5426	241	15	)	)	PUNCT
ejpam-5426	241	16	:	:	PUNCT
ejpam-5426	241	17	q	q	PUNCT
ejpam-5426	242	1	∈	∈	PROPN
ejpam-5426	242	2	q	q	X
ejpam-5426	242	3	}	}	PUNCT
ejpam-5426	242	4	is	be	AUX
ejpam-5426	242	5	an	an	DET
ejpam-5426	242	6	open	open	ADJ
ejpam-5426	242	7	locally	locally	ADV
ejpam-5426	242	8	-	-	PUNCT
ejpam-5426	242	9	finite	finite	ADJ
ejpam-5426	242	10	refinement	refinement	NOUN
ejpam-5426	242	11	of	of	ADP
ejpam-5426	242	12	w	w	PROPN
ejpam-5426	242	13	.	.	PUNCT
ejpam-5426	243	1	hence	hence	ADV
ejpam-5426	243	2	,	,	PUNCT
ejpam-5426	243	3	the	the	DET
ejpam-5426	243	4	space	space	NOUN
ejpam-5426	243	5	w	w	NOUN
ejpam-5426	243	6	is	be	AUX
ejpam-5426	243	7	d−paracompact	d−paracompact	PROPN
ejpam-5426	243	8	space	space	NOUN
ejpam-5426	243	9	.	.	PUNCT
ejpam-5426	244	1	theorem	theorem	VERB
ejpam-5426	244	2	11	11	NUM
ejpam-5426	244	3	.	.	PUNCT
ejpam-5426	245	1	let	let	VERB
ejpam-5426	245	2	φ	φ	NOUN
ejpam-5426	245	3	:	:	PUNCT
ejpam-5426	245	4	w	w	X
ejpam-5426	245	5	−→	−→	ADJ
ejpam-5426	245	6	q	q	PUNCT
ejpam-5426	245	7	as	as	ADP
ejpam-5426	245	8	d−perfect	d−perfect	NOUN
ejpam-5426	245	9	function	function	NOUN
ejpam-5426	245	10	.	.	PUNCT
ejpam-5426	246	1	then	then	ADV
ejpam-5426	246	2	,	,	PUNCT
ejpam-5426	246	3	w	w	NOUN
ejpam-5426	246	4	is	be	AUX
ejpam-5426	246	5	paracompact	paracompact	ADJ
ejpam-5426	246	6	space	space	NOUN
ejpam-5426	246	7	if	if	SCONJ
ejpam-5426	246	8	the	the	DET
ejpam-5426	246	9	space	space	NOUN
ejpam-5426	246	10	q	q	NOUN
ejpam-5426	246	11	is	be	AUX
ejpam-5426	246	12	d−paracompact	d−paracompact	PROPN
ejpam-5426	246	13	proof	proof	NOUN
ejpam-5426	246	14	.	.	PUNCT
ejpam-5426	247	1	as	as	ADP
ejpam-5426	247	2	the	the	DET
ejpam-5426	247	3	proof	proof	NOUN
ejpam-5426	247	4	of	of	ADP
ejpam-5426	247	5	the	the	DET
ejpam-5426	247	6	above	above	ADJ
ejpam-5426	247	7	theorem	theorem	NOUN
ejpam-5426	247	8	10	10	NUM
ejpam-5426	247	9	,	,	PUNCT
ejpam-5426	247	10	this	this	DET
ejpam-5426	247	11	theory	theory	NOUN
ejpam-5426	247	12	is	be	AUX
ejpam-5426	247	13	also	also	ADV
ejpam-5426	247	14	simply	simply	ADV
ejpam-5426	247	15	to	to	PART
ejpam-5426	247	16	prove	prove	VERB
ejpam-5426	247	17	.	.	PUNCT
ejpam-5426	248	1	theorem	theorem	NOUN
ejpam-5426	248	2	12	12	NUM
ejpam-5426	248	3	.	.	PUNCT
ejpam-5426	249	1	if	if	SCONJ
ejpam-5426	249	2	φ	φ	PROPN
ejpam-5426	249	3	:	:	PUNCT
ejpam-5426	249	4	w	w	X
ejpam-5426	249	5	−→	−→	NOUN
ejpam-5426	249	6	q	q	PUNCT
ejpam-5426	249	7	be	be	AUX
ejpam-5426	249	8	d−perfect	d−perfect	NOUN
ejpam-5426	249	9	,	,	PUNCT
ejpam-5426	249	10	where	where	SCONJ
ejpam-5426	249	11	q	q	NOUN
ejpam-5426	249	12	is	be	AUX
ejpam-5426	249	13	a	a	DET
ejpam-5426	249	14	countable	countable	ADJ
ejpam-5426	249	15	and	and	CCONJ
ejpam-5426	249	16	w	w	NOUN
ejpam-5426	249	17	is	be	AUX
ejpam-5426	249	18	locallyindiscreet	locallyindiscreet	ADJ
ejpam-5426	249	19	,	,	PUNCT
ejpam-5426	249	20	then	then	ADV
ejpam-5426	249	21	w	w	PROPN
ejpam-5426	249	22	must	must	AUX
ejpam-5426	249	23	be	be	AUX
ejpam-5426	249	24	countably	countably	ADV
ejpam-5426	249	25	d−paracompact	d−paracompact	NOUN
ejpam-5426	249	26	,	,	PUNCT
ejpam-5426	249	27	if	if	SCONJ
ejpam-5426	249	28	the	the	DET
ejpam-5426	249	29	space	space	NOUN
ejpam-5426	249	30	q	q	NOUN
ejpam-5426	249	31	is	be	AUX
ejpam-5426	249	32	so	so	ADV
ejpam-5426	249	33	.	.	PUNCT
ejpam-5426	250	1	proof	proof	NOUN
ejpam-5426	250	2	.	.	PUNCT
ejpam-5426	251	1	let	let	VERB
ejpam-5426	251	2	ẽ	ẽ	NOUN
ejpam-5426	251	3	=	=	PRON
ejpam-5426	251	4	{	{	PUNCT
ejpam-5426	251	5	eρ	eρ	NOUN
ejpam-5426	251	6	:	:	PUNCT
ejpam-5426	251	7	ρ	ρ	PROPN
ejpam-5426	251	8	∈	∈	PROPN
ejpam-5426	251	9	λ	λ	NOUN
ejpam-5426	251	10	}	}	PUNCT
ejpam-5426	251	11	be	be	AUX
ejpam-5426	251	12	countable	countable	ADJ
ejpam-5426	251	13	d−cover	d−cover	PROPN
ejpam-5426	251	14	of	of	ADP
ejpam-5426	251	15	w	w	PROPN
ejpam-5426	251	16	and	and	CCONJ
ejpam-5426	251	17	φ	φ	PROPN
ejpam-5426	251	18	is	be	AUX
ejpam-5426	251	19	d−perfect	d−perfect	NOUN
ejpam-5426	251	20	function	function	NOUN
ejpam-5426	251	21	.	.	PUNCT
ejpam-5426	252	1	then	then	ADV
ejpam-5426	252	2	for	for	ADP
ejpam-5426	252	3	any	any	DET
ejpam-5426	252	4	q	q	PROPN
ejpam-5426	252	5	∈	∈	PROPN
ejpam-5426	252	6	q	q	NOUN
ejpam-5426	252	7	,	,	PUNCT
ejpam-5426	252	8	φ−1(q	φ−1(q	NOUN
ejpam-5426	252	9	)	)	PUNCT
ejpam-5426	252	10	is	be	AUX
ejpam-5426	252	11	d−compact	d−compact	NOUN
ejpam-5426	252	12	space	space	NOUN
ejpam-5426	252	13	subsets	subset	NOUN
ejpam-5426	252	14	of	of	ADP
ejpam-5426	252	15	w	w	PROPN
ejpam-5426	252	16	.	.	PUNCT
ejpam-5426	253	1	it	it	PRON
ejpam-5426	253	2	therefore	therefore	ADV
ejpam-5426	253	3	obtains	obtain	VERB
ejpam-5426	253	4	in	in	ADP
ejpam-5426	253	5	a	a	DET
ejpam-5426	253	6	finite	finite	NOUN
ejpam-5426	253	7	subset	subset	NOUN
ejpam-5426	253	8	of	of	ADP
ejpam-5426	253	9	λ	λ	NOUN
ejpam-5426	253	10	such	such	ADJ
ejpam-5426	253	11	as	as	ADP
ejpam-5426	253	12	φ−1(q	φ−1(q	PROPN
ejpam-5426	253	13	)	)	PUNCT
ejpam-5426	253	14	⊆	⊆	NUM
ejpam-5426	253	15	∪n	∪n	NUM
ejpam-5426	253	16	i=1ai	i=1ai	NUM
ejpam-5426	253	17	.	.	PUNCT
ejpam-5426	254	1	since	since	SCONJ
ejpam-5426	254	2	w	w	PROPN
ejpam-5426	254	3	is	be	AUX
ejpam-5426	254	4	locally	locally	ADV
ejpam-5426	254	5	indiscreet	indiscreet	ADJ
ejpam-5426	254	6	,	,	PUNCT
ejpam-5426	254	7	then	then	ADV
ejpam-5426	254	8	ai	ai	VERB
ejpam-5426	254	9	is	be	AUX
ejpam-5426	254	10	d−open	d−open	PROPN
ejpam-5426	254	11	subset	subset	NOUN
ejpam-5426	254	12	of	of	ADP
ejpam-5426	254	13	w	w	PROPN
ejpam-5426	254	14	,	,	PUNCT
ejpam-5426	254	15	for	for	ADP
ejpam-5426	254	16	any	any	DET
ejpam-5426	254	17	i	i	PROPN
ejpam-5426	254	18	∈	∈	PROPN
ejpam-5426	254	19	λ	λ	X
ejpam-5426	254	20	.	.	PUNCT
ejpam-5426	254	21	presently	presently	ADV
ejpam-5426	254	22	,	,	PUNCT
ejpam-5426	254	23	bq	bq	INTJ
ejpam-5426	254	24	=	=	PUNCT
ejpam-5426	254	25	q	q	NOUN
ejpam-5426	255	1	−	−	PROPN
ejpam-5426	255	2	φ(w	φ(w	PROPN
ejpam-5426	255	3	−	−	PROPN
ejpam-5426	255	4	∪n	∪n	NUM
ejpam-5426	255	5	i=1ai	i=1ai	NUM
ejpam-5426	255	6	)	)	PUNCT
ejpam-5426	255	7	is	be	AUX
ejpam-5426	255	8	d−set	d−set	VERB
ejpam-5426	255	9	containing	contain	VERB
ejpam-5426	255	10	q.	q.	PROPN
ejpam-5426	255	11	moreover	moreover	ADV
ejpam-5426	255	12	,	,	PUNCT
ejpam-5426	255	13	φ−1(bq	φ−1(bq	PROPN
ejpam-5426	255	14	)	)	PUNCT
ejpam-5426	255	15	⊆	⊆	NUM
ejpam-5426	255	16	∪n	∪n	NUM
ejpam-5426	255	17	i=1ai	i=1ai	NUM
ejpam-5426	255	18	.	.	PUNCT
ejpam-5426	256	1	thus	thus	ADV
ejpam-5426	256	2	,	,	PUNCT
ejpam-5426	256	3	b̃	b̃	PROPN
ejpam-5426	256	4	=	=	PROPN
ejpam-5426	256	5	{	{	PUNCT
ejpam-5426	256	6	bq	bq	INTJ
ejpam-5426	256	7	:	:	PUNCT
ejpam-5426	256	8	q	q	PROPN
ejpam-5426	256	9	∈	∈	PROPN
ejpam-5426	256	10	q	q	X
ejpam-5426	256	11	}	}	PUNCT
ejpam-5426	256	12	presents	present	VERB
ejpam-5426	256	13	countable	countable	ADJ
ejpam-5426	256	14	d−cover	d−cover	PROPN
ejpam-5426	256	15	for	for	ADP
ejpam-5426	256	16	q.	q.	PROPN
ejpam-5426	256	17	now	now	ADV
ejpam-5426	256	18	,	,	PUNCT
ejpam-5426	256	19	since	since	SCONJ
ejpam-5426	256	20	q	q	NOUN
ejpam-5426	256	21	is	be	AUX
ejpam-5426	256	22	countably	countably	ADV
ejpam-5426	256	23	d−paracompact	d−paracompact	NOUN
ejpam-5426	256	24	,	,	PUNCT
ejpam-5426	256	25	then	then	ADV
ejpam-5426	256	26	b̃	b̃	PROPN
ejpam-5426	256	27	has	have	VERB
ejpam-5426	256	28	an	an	DET
ejpam-5426	256	29	open	open	ADJ
ejpam-5426	256	30	locallyfinite	locallyfinite	ADJ
ejpam-5426	256	31	refinement	refinement	NOUN
ejpam-5426	256	32	b̃∗	b̃∗	PROPN
ejpam-5426	257	1	=	=	PRON
ejpam-5426	257	2	{	{	PUNCT
ejpam-5426	257	3	bq1	bq1	PROPN
ejpam-5426	257	4	,	,	PUNCT
ejpam-5426	257	5	bq2	bq2	NOUN
ejpam-5426	257	6	,	,	PUNCT
ejpam-5426	257	7	.	.	PUNCT
ejpam-5426	257	8	.	.	PUNCT
ejpam-5426	257	9	.	.	PUNCT
ejpam-5426	258	1	,	,	PUNCT
ejpam-5426	258	2	bqn	bqn	NOUN
ejpam-5426	258	3	}	}	PUNCT
ejpam-5426	258	4	and	and	CCONJ
ejpam-5426	258	5	so	so	ADV
ejpam-5426	258	6	b∗	b∗	ADJ
ejpam-5426	258	7	q	q	NOUN
ejpam-5426	258	8	is	be	AUX
ejpam-5426	258	9	d−open	d−open	PROPN
ejpam-5426	258	10	subset	subset	NOUN
ejpam-5426	258	11	of	of	ADP
ejpam-5426	258	12	w	w	PROPN
ejpam-5426	258	13	.	.	PUNCT
ejpam-5426	259	1	also	also	ADV
ejpam-5426	259	2	,	,	PUNCT
ejpam-5426	259	3	since	since	SCONJ
ejpam-5426	259	4	φ	φ	PROPN
ejpam-5426	259	5	is	be	AUX
ejpam-5426	259	6	d−perfect	d−perfect	NOUN
ejpam-5426	259	7	,	,	PUNCT
ejpam-5426	259	8	so	so	CCONJ
ejpam-5426	259	9	{	{	PUNCT
ejpam-5426	259	10	φ−1(b∗	φ−1(b∗	PROPN
ejpam-5426	259	11	q	q	PROPN
ejpam-5426	259	12	)	)	PUNCT
ejpam-5426	260	1	:	:	PUNCT
ejpam-5426	260	2	q	q	PUNCT
ejpam-5426	261	1	∈	∈	PROPN
ejpam-5426	261	2	q	q	X
ejpam-5426	261	3	}	}	PUNCT
ejpam-5426	261	4	is	be	AUX
ejpam-5426	261	5	an	an	DET
ejpam-5426	261	6	open	open	ADJ
ejpam-5426	261	7	locally	locally	ADV
ejpam-5426	261	8	-	-	PUNCT
ejpam-5426	261	9	finite	finite	ADJ
ejpam-5426	261	10	refinement	refinement	NOUN
ejpam-5426	261	11	of	of	ADP
ejpam-5426	261	12	w	w	PROPN
ejpam-5426	261	13	.	.	PUNCT
ejpam-5426	262	1	thus	thus	ADV
ejpam-5426	262	2	,	,	PUNCT
ejpam-5426	262	3	the	the	DET
ejpam-5426	262	4	space	space	NOUN
ejpam-5426	262	5	w	w	NOUN
ejpam-5426	262	6	must	must	AUX
ejpam-5426	262	7	be	be	AUX
ejpam-5426	262	8	countably	countably	ADV
ejpam-5426	262	9	d−paracompact	d−paracompact	NOUN
ejpam-5426	262	10	.	.	PUNCT
ejpam-5426	263	1	theorem	theorem	NOUN
ejpam-5426	263	2	13	13	NUM
ejpam-5426	263	3	.	.	PUNCT
ejpam-5426	264	1	let	let	VERB
ejpam-5426	264	2	(	(	PUNCT
ejpam-5426	264	3	w,ϑ	w,ϑ	VERB
ejpam-5426	264	4	)	)	PUNCT
ejpam-5426	264	5	and	and	CCONJ
ejpam-5426	264	6	(	(	PUNCT
ejpam-5426	264	7	q	q	ADJ
ejpam-5426	264	8	,	,	PUNCT
ejpam-5426	264	9	ι	ι	AUX
ejpam-5426	264	10	)	)	PUNCT
ejpam-5426	264	11	be	be	VERB
ejpam-5426	264	12	topological	topological	ADJ
ejpam-5426	264	13	spaces	space	NOUN
ejpam-5426	264	14	,	,	PUNCT
ejpam-5426	264	15	such	such	ADJ
ejpam-5426	264	16	that	that	SCONJ
ejpam-5426	264	17	w	w	NOUN
ejpam-5426	264	18	is	be	AUX
ejpam-5426	264	19	d	d	ADJ
ejpam-5426	264	20	-	-	ADJ
ejpam-5426	264	21	compact	compact	ADJ
ejpam-5426	264	22	and	and	CCONJ
ejpam-5426	264	23	q	q	NOUN
ejpam-5426	264	24	is	be	AUX
ejpam-5426	264	25	d−paracompact	d−paracompact	PROPN
ejpam-5426	264	26	spaces	space	NOUN
ejpam-5426	264	27	.	.	PUNCT
ejpam-5426	265	1	then	then	ADV
ejpam-5426	265	2	w	w	NOUN
ejpam-5426	265	3	×q	×q	NOUN
ejpam-5426	265	4	must	must	AUX
ejpam-5426	265	5	be	be	AUX
ejpam-5426	265	6	d−paracompact	d−paracompact	PROPN
ejpam-5426	265	7	space	space	NOUN
ejpam-5426	265	8	.	.	PUNCT
ejpam-5426	266	1	proof	proof	NOUN
ejpam-5426	266	2	.	.	PUNCT
ejpam-5426	267	1	given	give	VERB
ejpam-5426	267	2	the	the	DET
ejpam-5426	267	3	truth	truth	NOUN
ejpam-5426	267	4	that	that	PRON
ejpam-5426	267	5	the	the	DET
ejpam-5426	267	6	projection	projection	NOUN
ejpam-5426	267	7	function	function	NOUN
ejpam-5426	267	8	t	t	NOUN
ejpam-5426	267	9	:	:	PUNCT
ejpam-5426	267	10	w	w	PROPN
ejpam-5426	267	11	×	×	NOUN
ejpam-5426	267	12	q	q	NOUN
ejpam-5426	267	13	−→	−→	NOUN
ejpam-5426	267	14	q	q	NOUN
ejpam-5426	267	15	is	be	AUX
ejpam-5426	267	16	continuous	continuous	ADJ
ejpam-5426	267	17	and	and	CCONJ
ejpam-5426	267	18	t−1{q	t−1{q	ADJ
ejpam-5426	267	19	}	}	PUNCT
ejpam-5426	267	20	=	=	SYM
ejpam-5426	267	21	w	w	PROPN
ejpam-5426	267	22	×	×	PROPN
ejpam-5426	267	23	{	{	PUNCT
ejpam-5426	267	24	q	q	NOUN
ejpam-5426	267	25	}	}	PUNCT
ejpam-5426	267	26	≃	≃	NOUN
ejpam-5426	267	27	w	w	PROPN
ejpam-5426	267	28	is	be	AUX
ejpam-5426	267	29	d−compact	d−compact	PROPN
ejpam-5426	267	30	,	,	PUNCT
ejpam-5426	267	31	for	for	ADP
ejpam-5426	267	32	any	any	DET
ejpam-5426	267	33	q	q	PROPN
ejpam-5426	267	34	∈	∈	PROPN
ejpam-5426	267	35	q.	q.	NOUN
ejpam-5426	267	36	then	then	ADV
ejpam-5426	267	37	t	t	X
ejpam-5426	267	38	:	:	PUNCT
ejpam-5426	267	39	w	w	PROPN
ejpam-5426	267	40	×	×	NOUN
ejpam-5426	267	41	q	q	NOUN
ejpam-5426	267	42	−→	−→	NOUN
ejpam-5426	267	43	q	q	NOUN
ejpam-5426	267	44	is	be	AUX
ejpam-5426	267	45	d−perfect	d−perfect	NOUN
ejpam-5426	267	46	function	function	NOUN
ejpam-5426	267	47	.	.	PUNCT
ejpam-5426	268	1	so	so	ADV
ejpam-5426	268	2	,	,	PUNCT
ejpam-5426	268	3	since	since	SCONJ
ejpam-5426	268	4	q	q	NOUN
ejpam-5426	268	5	is	be	AUX
ejpam-5426	268	6	d−paracompact	d−paracompact	PROPN
ejpam-5426	268	7	space	space	NOUN
ejpam-5426	268	8	,	,	PUNCT
ejpam-5426	268	9	then	then	ADV
ejpam-5426	268	10	w	w	PROPN
ejpam-5426	268	11	×	×	PROPN
ejpam-5426	268	12	q	q	NOUN
ejpam-5426	268	13	must	must	AUX
ejpam-5426	268	14	be	be	AUX
ejpam-5426	268	15	also	also	ADV
ejpam-5426	268	16	d−paracompact	d−paracompact	PROPN
ejpam-5426	268	17	.	.	PUNCT
ejpam-5426	269	1	a.	a.	PROPN
ejpam-5426	269	2	amourah	amourah	PROPN
ejpam-5426	269	3	et	et	PROPN
ejpam-5426	269	4	al	al	PROPN
ejpam-5426	269	5	.	.	PUNCT
ejpam-5426	269	6	/	/	SYM
ejpam-5426	269	7	eur	eur	PROPN
ejpam-5426	269	8	.	.	PUNCT
ejpam-5426	270	1	j.	j.	PROPN
ejpam-5426	270	2	pure	pure	PROPN
ejpam-5426	270	3	appl	appl	PROPN
ejpam-5426	270	4	.	.	PROPN
ejpam-5426	270	5	math	math	PROPN
ejpam-5426	270	6	,	,	PUNCT
ejpam-5426	270	7	17	17	NUM
ejpam-5426	270	8	(	(	PUNCT
ejpam-5426	270	9	4	4	NUM
ejpam-5426	270	10	)	)	PUNCT
ejpam-5426	270	11	(	(	PUNCT
ejpam-5426	270	12	2024	2024	NUM
ejpam-5426	270	13	)	)	PUNCT
ejpam-5426	270	14	,	,	PUNCT
ejpam-5426	270	15	2990	2990	NUM
ejpam-5426	270	16	-	-	SYM
ejpam-5426	270	17	3003	3003	NUM
ejpam-5426	270	18	3001	3001	NUM
ejpam-5426	270	19	theorem	theorem	VERB
ejpam-5426	270	20	14	14	NUM
ejpam-5426	270	21	.	.	PUNCT
ejpam-5426	271	1	let	let	VERB
ejpam-5426	271	2	(	(	PUNCT
ejpam-5426	271	3	w,ϑ	w,ϑ	VERB
ejpam-5426	271	4	)	)	PUNCT
ejpam-5426	271	5	and	and	CCONJ
ejpam-5426	271	6	(	(	PUNCT
ejpam-5426	271	7	q	q	ADJ
ejpam-5426	271	8	,	,	PUNCT
ejpam-5426	271	9	ι	ι	AUX
ejpam-5426	271	10	)	)	PUNCT
ejpam-5426	271	11	be	be	AUX
ejpam-5426	271	12	topological	topological	ADJ
ejpam-5426	271	13	spaces	space	NOUN
ejpam-5426	271	14	.	.	PUNCT
ejpam-5426	272	1	if	if	SCONJ
ejpam-5426	272	2	w	w	NOUN
ejpam-5426	272	3	is	be	AUX
ejpam-5426	272	4	paracompact	paracompact	ADJ
ejpam-5426	272	5	,	,	PUNCT
ejpam-5426	272	6	and	and	CCONJ
ejpam-5426	272	7	q	q	NOUN
ejpam-5426	272	8	is	be	AUX
ejpam-5426	272	9	d−paracompact	d−paracompact	PROPN
ejpam-5426	272	10	spaces	space	NOUN
ejpam-5426	272	11	,	,	PUNCT
ejpam-5426	272	12	then	then	ADV
ejpam-5426	272	13	the	the	DET
ejpam-5426	272	14	projection	projection	NOUN
ejpam-5426	272	15	function	function	NOUN
ejpam-5426	272	16	t	t	NOUN
ejpam-5426	272	17	:	:	PUNCT
ejpam-5426	272	18	(	(	PUNCT
ejpam-5426	272	19	w	w	PROPN
ejpam-5426	272	20	×q,ϑ×	×q,ϑ×	NOUN
ejpam-5426	272	21	ι	ι	NOUN
ejpam-5426	272	22	)	)	PUNCT
ejpam-5426	272	23	−→	−→	NOUN
ejpam-5426	272	24	(	(	PUNCT
ejpam-5426	272	25	q	q	NOUN
ejpam-5426	272	26	,	,	PUNCT
ejpam-5426	272	27	ι	ι	X
ejpam-5426	272	28	)	)	PUNCT
ejpam-5426	272	29	must	must	AUX
ejpam-5426	272	30	be	be	AUX
ejpam-5426	272	31	closed	close	VERB
ejpam-5426	272	32	.	.	PUNCT
ejpam-5426	273	1	proof	proof	NOUN
ejpam-5426	273	2	.	.	PUNCT
ejpam-5426	274	1	let	let	AUX
ejpam-5426	274	2	(	(	PUNCT
ejpam-5426	274	3	w,ϑ	w,ϑ	VERB
ejpam-5426	274	4	)	)	PUNCT
ejpam-5426	274	5	be	be	AUX
ejpam-5426	274	6	paracompact	paracompact	ADJ
ejpam-5426	274	7	and	and	CCONJ
ejpam-5426	274	8	(	(	PUNCT
ejpam-5426	274	9	q	q	ADJ
ejpam-5426	274	10	,	,	PUNCT
ejpam-5426	274	11	ι	ι	AUX
ejpam-5426	274	12	)	)	PUNCT
ejpam-5426	274	13	be	be	AUX
ejpam-5426	274	14	a	a	DET
ejpam-5426	274	15	d−paracompact	d−paracompact	NOUN
ejpam-5426	274	16	.	.	PUNCT
ejpam-5426	275	1	then	then	ADV
ejpam-5426	275	2	(	(	PUNCT
ejpam-5426	275	3	w	w	NOUN
ejpam-5426	275	4	×q,ϑ×ι	×q,ϑ×ι	PROPN
ejpam-5426	275	5	)	)	PUNCT
ejpam-5426	275	6	is	be	AUX
ejpam-5426	275	7	d−paracompact	d−paracompact	PROPN
ejpam-5426	275	8	,	,	PUNCT
ejpam-5426	275	9	therefore	therefore	ADV
ejpam-5426	275	10	the	the	DET
ejpam-5426	275	11	projection	projection	NOUN
ejpam-5426	275	12	function	function	NOUN
ejpam-5426	275	13	t	t	NOUN
ejpam-5426	275	14	:	:	PUNCT
ejpam-5426	275	15	(	(	PUNCT
ejpam-5426	275	16	w	w	PROPN
ejpam-5426	275	17	×q,ϑ×	×q,ϑ×	NOUN
ejpam-5426	275	18	ι	ι	NOUN
ejpam-5426	275	19	)	)	PUNCT
ejpam-5426	275	20	−→	−→	NOUN
ejpam-5426	275	21	(	(	PUNCT
ejpam-5426	275	22	q	q	NOUN
ejpam-5426	275	23	,	,	PUNCT
ejpam-5426	275	24	ι	ι	X
ejpam-5426	275	25	)	)	PUNCT
ejpam-5426	275	26	must	must	AUX
ejpam-5426	275	27	be	be	AUX
ejpam-5426	275	28	closed	close	VERB
ejpam-5426	275	29	function	function	NOUN
ejpam-5426	275	30	.	.	PUNCT
ejpam-5426	276	1	theorem	theorem	NOUN
ejpam-5426	276	2	15	15	NUM
ejpam-5426	276	3	.	.	PUNCT
ejpam-5426	277	1	let	let	VERB
ejpam-5426	277	2	φ	φ	PROPN
ejpam-5426	277	3	:	:	PUNCT
ejpam-5426	277	4	(	(	PUNCT
ejpam-5426	277	5	w,ϑ	w,ϑ	ADJ
ejpam-5426	277	6	)	)	PUNCT
ejpam-5426	277	7	−→	−→	NOUN
ejpam-5426	277	8	(	(	PUNCT
ejpam-5426	277	9	q	q	NOUN
ejpam-5426	277	10	,	,	PUNCT
ejpam-5426	277	11	ι	ι	X
ejpam-5426	277	12	)	)	PUNCT
ejpam-5426	277	13	be	be	AUX
ejpam-5426	277	14	a	a	DET
ejpam-5426	277	15	closed	closed	ADJ
ejpam-5426	277	16	,	,	PUNCT
ejpam-5426	277	17	continuous	continuous	ADJ
ejpam-5426	277	18	,	,	PUNCT
ejpam-5426	277	19	onto	onto	ADP
ejpam-5426	277	20	function	function	NOUN
ejpam-5426	277	21	such	such	DET
ejpam-5426	277	22	that	that	DET
ejpam-5426	277	23	q	q	NOUN
ejpam-5426	277	24	is	be	AUX
ejpam-5426	277	25	locally	locally	ADV
ejpam-5426	277	26	-	-	PUNCT
ejpam-5426	277	27	indiscreet	indiscreet	ADJ
ejpam-5426	277	28	space	space	NOUN
ejpam-5426	277	29	.	.	PUNCT
ejpam-5426	278	1	then	then	ADV
ejpam-5426	278	2	q	q	X
ejpam-5426	278	3	is	be	AUX
ejpam-5426	278	4	d−paracompact	d−paracompact	PROPN
ejpam-5426	278	5	,	,	PUNCT
ejpam-5426	278	6	if	if	SCONJ
ejpam-5426	278	7	the	the	DET
ejpam-5426	278	8	space	space	NOUN
ejpam-5426	278	9	w	w	NOUN
ejpam-5426	278	10	is	be	AUX
ejpam-5426	278	11	so	so	ADV
ejpam-5426	278	12	.	.	PUNCT
ejpam-5426	279	1	proof	proof	NOUN
ejpam-5426	279	2	.	.	PUNCT
ejpam-5426	280	1	let	let	VERB
ejpam-5426	280	2	ẽ	ẽ	NOUN
ejpam-5426	280	3	=	=	PRON
ejpam-5426	280	4	{	{	PUNCT
ejpam-5426	280	5	eρ	eρ	NOUN
ejpam-5426	280	6	:	:	PUNCT
ejpam-5426	280	7	ρ	ρ	PROPN
ejpam-5426	280	8	∈	∈	PROPN
ejpam-5426	280	9	λ	λ	NOUN
ejpam-5426	280	10	}	}	PUNCT
ejpam-5426	280	11	be	be	VERB
ejpam-5426	280	12	any	any	DET
ejpam-5426	280	13	d−cover	d−cover	PROPN
ejpam-5426	280	14	of	of	ADP
ejpam-5426	280	15	q.	q.	PROPN
ejpam-5426	280	16	since	since	SCONJ
ejpam-5426	280	17	φ	φ	PROPN
ejpam-5426	280	18	is	be	AUX
ejpam-5426	280	19	onto	onto	ADP
ejpam-5426	280	20	function	function	NOUN
ejpam-5426	280	21	and	and	CCONJ
ejpam-5426	280	22	continuous	continuous	ADJ
ejpam-5426	280	23	,	,	PUNCT
ejpam-5426	280	24	that	that	PRON
ejpam-5426	280	25	means	mean	VERB
ejpam-5426	280	26	ẽ	ẽ	PROPN
ejpam-5426	280	27	=	=	SYM
ejpam-5426	280	28	{	{	PUNCT
ejpam-5426	280	29	φ−1(eρ	φ−1(eρ	PROPN
ejpam-5426	280	30	)	)	PUNCT
ejpam-5426	280	31	:	:	PUNCT
ejpam-5426	280	32	ρ	ρ	PROPN
ejpam-5426	280	33	∈	∈	PROPN
ejpam-5426	280	34	λ	λ	PROPN
ejpam-5426	280	35	}	}	PUNCT
ejpam-5426	280	36	is	be	AUX
ejpam-5426	280	37	an	an	DET
ejpam-5426	280	38	open	open	ADJ
ejpam-5426	280	39	cover	cover	NOUN
ejpam-5426	280	40	of	of	ADP
ejpam-5426	280	41	w	w	PROPN
ejpam-5426	280	42	.	.	PUNCT
ejpam-5426	281	1	since	since	SCONJ
ejpam-5426	281	2	w	w	PROPN
ejpam-5426	281	3	is	be	AUX
ejpam-5426	281	4	d−paracompact	d−paracompact	PROPN
ejpam-5426	281	5	,	,	PUNCT
ejpam-5426	281	6	then	then	ADV
ejpam-5426	281	7	there	there	PRON
ejpam-5426	281	8	is	be	VERB
ejpam-5426	281	9	an	an	DET
ejpam-5426	281	10	open	open	ADJ
ejpam-5426	281	11	locally	locally	ADV
ejpam-5426	281	12	-	-	PUNCT
ejpam-5426	281	13	finite	finite	ADJ
ejpam-5426	281	14	refinement	refinement	NOUN
ejpam-5426	281	15	of	of	ADP
ejpam-5426	281	16	ẽ	ẽ	PROPN
ejpam-5426	281	17	as	as	ADP
ejpam-5426	281	18	ẽ∗	ẽ∗	PROPN
ejpam-5426	281	19	=	=	SYM
ejpam-5426	281	20	{	{	PUNCT
ejpam-5426	281	21	φ−1(e∗	φ−1(e∗	PROPN
ejpam-5426	281	22	ρ	ρ	PROPN
ejpam-5426	281	23	)	)	PUNCT
ejpam-5426	281	24	:	:	PUNCT
ejpam-5426	282	1	ρ	ρ	PROPN
ejpam-5426	282	2	∈	∈	PROPN
ejpam-5426	282	3	λ	λ	NOUN
ejpam-5426	282	4	}	}	PUNCT
ejpam-5426	282	5	.	.	PUNCT
ejpam-5426	283	1	thus	thus	ADV
ejpam-5426	283	2	,	,	PUNCT
ejpam-5426	283	3	q	q	PROPN
ejpam-5426	283	4	must	must	AUX
ejpam-5426	283	5	be	be	AUX
ejpam-5426	283	6	a	a	DET
ejpam-5426	283	7	d−paracompact	d−paracompact	NOUN
ejpam-5426	283	8	space	space	NOUN
ejpam-5426	283	9	.	.	PUNCT
ejpam-5426	284	1	with	with	ADP
ejpam-5426	284	2	the	the	DET
ejpam-5426	284	3	same	same	ADJ
ejpam-5426	284	4	work	work	NOUN
ejpam-5426	284	5	,	,	PUNCT
ejpam-5426	284	6	the	the	DET
ejpam-5426	284	7	corollary	corollary	NOUN
ejpam-5426	284	8	that	that	PRON
ejpam-5426	284	9	follows	follow	VERB
ejpam-5426	284	10	can	can	AUX
ejpam-5426	284	11	be	be	AUX
ejpam-5426	284	12	achieved	achieve	VERB
ejpam-5426	284	13	.	.	PUNCT
ejpam-5426	285	1	corollary	corollary	ADJ
ejpam-5426	285	2	8	8	NUM
ejpam-5426	285	3	.	.	PUNCT
ejpam-5426	286	1	let	let	VERB
ejpam-5426	286	2	φ	φ	PROPN
ejpam-5426	286	3	:	:	PUNCT
ejpam-5426	286	4	(	(	PUNCT
ejpam-5426	286	5	w,ϑ	w,ϑ	ADJ
ejpam-5426	286	6	)	)	PUNCT
ejpam-5426	286	7	−→	−→	NOUN
ejpam-5426	286	8	(	(	PUNCT
ejpam-5426	286	9	q	q	NOUN
ejpam-5426	286	10	,	,	PUNCT
ejpam-5426	286	11	ι	ι	X
ejpam-5426	286	12	)	)	PUNCT
ejpam-5426	286	13	be	be	AUX
ejpam-5426	286	14	a	a	DET
ejpam-5426	286	15	closed	closed	ADJ
ejpam-5426	286	16	,	,	PUNCT
ejpam-5426	286	17	onto	onto	ADP
ejpam-5426	286	18	,	,	PUNCT
ejpam-5426	286	19	continuous	continuous	ADJ
ejpam-5426	286	20	function	function	NOUN
ejpam-5426	286	21	such	such	DET
ejpam-5426	286	22	that	that	SCONJ
ejpam-5426	286	23	q	q	NOUN
ejpam-5426	286	24	is	be	AUX
ejpam-5426	286	25	locally	locally	ADV
ejpam-5426	286	26	-	-	PUNCT
ejpam-5426	286	27	indiscreet	indiscreet	ADJ
ejpam-5426	286	28	space	space	NOUN
ejpam-5426	286	29	.	.	PUNCT
ejpam-5426	287	1	then	then	ADV
ejpam-5426	287	2	,	,	PUNCT
ejpam-5426	287	3	q	q	PROPN
ejpam-5426	287	4	is	be	AUX
ejpam-5426	287	5	d−paracompact	d−paracompact	PROPN
ejpam-5426	287	6	,	,	PUNCT
ejpam-5426	287	7	if	if	SCONJ
ejpam-5426	287	8	the	the	DET
ejpam-5426	287	9	space	space	NOUN
ejpam-5426	287	10	w	w	NOUN
ejpam-5426	287	11	is	be	AUX
ejpam-5426	287	12	paracompact	paracompact	ADJ
ejpam-5426	287	13	.	.	PUNCT
ejpam-5426	288	1	5	5	X
ejpam-5426	288	2	.	.	X
ejpam-5426	288	3	conclusions	conclusion	NOUN
ejpam-5426	288	4	this	this	DET
ejpam-5426	288	5	research	research	NOUN
ejpam-5426	288	6	highlights	highlight	NOUN
ejpam-5426	288	7	that	that	PRON
ejpam-5426	288	8	d−paracompact	d−paracompact	VERB
ejpam-5426	288	9	topological	topological	ADJ
ejpam-5426	288	10	spaces	space	NOUN
ejpam-5426	288	11	have	have	VERB
ejpam-5426	288	12	a	a	DET
ejpam-5426	288	13	key	key	ADJ
ejpam-5426	288	14	topological	topological	ADJ
ejpam-5426	288	15	characteristic	characteristic	NOUN
ejpam-5426	288	16	.	.	PUNCT
ejpam-5426	289	1	their	their	PRON
ejpam-5426	289	2	flexibility	flexibility	NOUN
ejpam-5426	289	3	to	to	PART
ejpam-5426	289	4	provide	provide	VERB
ejpam-5426	289	5	d−covers	d−cover	NOUN
ejpam-5426	289	6	with	with	ADP
ejpam-5426	289	7	locally	locally	ADV
ejpam-5426	289	8	-	-	PUNCT
ejpam-5426	289	9	finite	finite	ADJ
ejpam-5426	289	10	refinements	refinement	NOUN
ejpam-5426	289	11	is	be	AUX
ejpam-5426	289	12	demonstrated	demonstrate	VERB
ejpam-5426	289	13	by	by	ADP
ejpam-5426	289	14	their	their	PRON
ejpam-5426	289	15	conclusion	conclusion	NOUN
ejpam-5426	289	16	.	.	PUNCT
ejpam-5426	290	1	the	the	DET
ejpam-5426	290	2	research	research	NOUN
ejpam-5426	290	3	introduced	introduce	VERB
ejpam-5426	290	4	several	several	ADJ
ejpam-5426	290	5	new	new	ADJ
ejpam-5426	290	6	properties	property	NOUN
ejpam-5426	290	7	and	and	CCONJ
ejpam-5426	290	8	explained	explain	VERB
ejpam-5426	290	9	examples	example	NOUN
ejpam-5426	290	10	that	that	PRON
ejpam-5426	290	11	relate	relate	VERB
ejpam-5426	290	12	to	to	ADP
ejpam-5426	290	13	such	such	ADJ
ejpam-5426	290	14	superimposed	superimpose	VERB
ejpam-5426	290	15	spaces	space	NOUN
ejpam-5426	290	16	.	.	PUNCT
ejpam-5426	291	1	the	the	DET
ejpam-5426	291	2	study	study	NOUN
ejpam-5426	291	3	’s	’s	PART
ejpam-5426	291	4	additional	additional	ADJ
ejpam-5426	291	5	objective	objective	NOUN
ejpam-5426	291	6	was	be	AUX
ejpam-5426	291	7	to	to	PART
ejpam-5426	291	8	draw	draw	VERB
ejpam-5426	291	9	attention	attention	NOUN
ejpam-5426	291	10	to	to	ADP
ejpam-5426	291	11	some	some	PRON
ejpam-5426	291	12	of	of	ADP
ejpam-5426	291	13	the	the	DET
ejpam-5426	291	14	new	new	ADJ
ejpam-5426	291	15	notions	notion	NOUN
ejpam-5426	291	16	and	and	CCONJ
ejpam-5426	291	17	characteristics	characteristic	NOUN
ejpam-5426	291	18	of	of	ADP
ejpam-5426	291	19	d−paracompact	d−paracompact	PROPN
ejpam-5426	291	20	spaces	space	NOUN
ejpam-5426	291	21	,	,	PUNCT
ejpam-5426	291	22	as	as	ADV
ejpam-5426	291	23	well	well	ADV
ejpam-5426	291	24	as	as	ADP
ejpam-5426	291	25	some	some	DET
ejpam-5426	291	26	properties	property	NOUN
ejpam-5426	291	27	of	of	ADP
ejpam-5426	291	28	the	the	DET
ejpam-5426	291	29	cartesian	cartesian	ADJ
ejpam-5426	291	30	multiplication	multiplication	NOUN
ejpam-5426	291	31	of	of	ADP
ejpam-5426	291	32	such	such	ADJ
ejpam-5426	291	33	spaces	space	NOUN
ejpam-5426	291	34	under	under	ADP
ejpam-5426	291	35	special	special	ADJ
ejpam-5426	291	36	conditions	condition	NOUN
ejpam-5426	291	37	.	.	PUNCT
ejpam-5426	292	1	furthermore	furthermore	ADV
ejpam-5426	292	2	,	,	PUNCT
ejpam-5426	292	3	certain	certain	ADJ
ejpam-5426	292	4	illustrative	illustrative	ADJ
ejpam-5426	292	5	examples	example	NOUN
ejpam-5426	292	6	and	and	CCONJ
ejpam-5426	292	7	the	the	DET
ejpam-5426	292	8	main	main	ADJ
ejpam-5426	292	9	characteristics	characteristic	NOUN
ejpam-5426	292	10	of	of	ADP
ejpam-5426	292	11	these	these	DET
ejpam-5426	292	12	concepts	concept	NOUN
ejpam-5426	292	13	were	be	AUX
ejpam-5426	292	14	carefully	carefully	ADV
ejpam-5426	292	15	studied	study	VERB
ejpam-5426	292	16	.	.	PUNCT
ejpam-5426	293	1	we	we	PRON
ejpam-5426	293	2	identified	identify	VERB
ejpam-5426	293	3	their	their	PRON
ejpam-5426	293	4	principal	principal	ADJ
ejpam-5426	293	5	characteristics	characteristic	NOUN
ejpam-5426	293	6	along	along	ADP
ejpam-5426	293	7	with	with	ADP
ejpam-5426	293	8	illustrated	illustrate	VERB
ejpam-5426	293	9	figures	figure	NOUN
ejpam-5426	293	10	.	.	PUNCT
ejpam-5426	294	1	we	we	PRON
ejpam-5426	294	2	talked	talk	VERB
ejpam-5426	294	3	about	about	ADP
ejpam-5426	294	4	their	their	PRON
ejpam-5426	294	5	main	main	ADJ
ejpam-5426	294	6	traits	trait	NOUN
ejpam-5426	294	7	and	and	CCONJ
ejpam-5426	294	8	demonstrated	demonstrate	VERB
ejpam-5426	294	9	how	how	SCONJ
ejpam-5426	294	10	they	they	PRON
ejpam-5426	294	11	work	work	VERB
ejpam-5426	294	12	together	together	ADV
ejpam-5426	294	13	.	.	PUNCT
ejpam-5426	295	1	the	the	DET
ejpam-5426	295	2	study	study	NOUN
ejpam-5426	295	3	lies	lie	VERB
ejpam-5426	295	4	at	at	ADP
ejpam-5426	295	5	the	the	DET
ejpam-5426	295	6	interface	interface	NOUN
ejpam-5426	295	7	of	of	ADP
ejpam-5426	295	8	topology	topology	NOUN
ejpam-5426	295	9	and	and	CCONJ
ejpam-5426	295	10	other	other	ADJ
ejpam-5426	295	11	branches	branch	NOUN
ejpam-5426	295	12	of	of	ADP
ejpam-5426	295	13	mathematics	mathematic	NOUN
ejpam-5426	295	14	.	.	PUNCT
ejpam-5426	296	1	as	as	ADP
ejpam-5426	296	2	in	in	ADP
ejpam-5426	296	3	fuzzy	fuzzy	ADJ
ejpam-5426	296	4	sets	set	NOUN
ejpam-5426	296	5	,	,	PUNCT
ejpam-5426	296	6	researchers	researcher	NOUN
ejpam-5426	296	7	can	can	AUX
ejpam-5426	296	8	generalize	generalize	VERB
ejpam-5426	296	9	the	the	DET
ejpam-5426	296	10	fuzzy	fuzzy	ADJ
ejpam-5426	296	11	paracompact	paracompact	NOUN
ejpam-5426	296	12	spaces	space	NOUN
ejpam-5426	296	13	to	to	PART
ejpam-5426	296	14	be	be	AUX
ejpam-5426	296	15	fuzzy	fuzzy	ADJ
ejpam-5426	296	16	d−paracompact	d−paracompact	NOUN
ejpam-5426	296	17	spaces	space	NOUN
ejpam-5426	296	18	.	.	PUNCT
ejpam-5426	297	1	also	also	ADV
ejpam-5426	297	2	,	,	PUNCT
ejpam-5426	297	3	in	in	ADP
ejpam-5426	297	4	the	the	DET
ejpam-5426	297	5	algebra	algebra	NOUN
ejpam-5426	297	6	field	field	NOUN
ejpam-5426	297	7	,	,	PUNCT
ejpam-5426	297	8	there	there	PRON
ejpam-5426	297	9	is	be	VERB
ejpam-5426	297	10	a	a	DET
ejpam-5426	297	11	compact	compact	ADJ
ejpam-5426	297	12	(	(	PUNCT
ejpam-5426	297	13	topological	topological	ADJ
ejpam-5426	297	14	)	)	PUNCT
ejpam-5426	297	15	group	group	NOUN
ejpam-5426	297	16	,	,	PUNCT
ejpam-5426	297	17	which	which	PRON
ejpam-5426	297	18	we	we	PRON
ejpam-5426	297	19	can	can	AUX
ejpam-5426	297	20	generalize	generalize	VERB
ejpam-5426	297	21	to	to	ADP
ejpam-5426	297	22	a	a	DET
ejpam-5426	297	23	d−paracompact	d−paracompact	NOUN
ejpam-5426	297	24	group	group	NOUN
ejpam-5426	297	25	and	and	CCONJ
ejpam-5426	297	26	provide	provide	VERB
ejpam-5426	297	27	mathematicians	mathematician	NOUN
ejpam-5426	297	28	with	with	ADP
ejpam-5426	297	29	a	a	DET
ejpam-5426	297	30	way	way	NOUN
ejpam-5426	297	31	to	to	PART
ejpam-5426	297	32	expand	expand	VERB
ejpam-5426	297	33	their	their	PRON
ejpam-5426	297	34	knowledge	knowledge	NOUN
ejpam-5426	297	35	about	about	ADP
ejpam-5426	297	36	both	both	CCONJ
ejpam-5426	297	37	topological	topological	ADJ
ejpam-5426	297	38	and	and	CCONJ
ejpam-5426	297	39	group	group	NOUN
ejpam-5426	297	40	algebra	algebra	NOUN
ejpam-5426	297	41	.	.	PUNCT
ejpam-5426	298	1	this	this	PRON
ejpam-5426	298	2	also	also	ADV
ejpam-5426	298	3	acts	act	VERB
ejpam-5426	298	4	as	as	ADP
ejpam-5426	298	5	an	an	DET
ejpam-5426	298	6	effective	effective	ADJ
ejpam-5426	298	7	basis	basis	NOUN
ejpam-5426	298	8	for	for	ADP
ejpam-5426	298	9	future	future	ADJ
ejpam-5426	298	10	research	research	NOUN
ejpam-5426	298	11	.	.	PUNCT
ejpam-5426	299	1	in	in	ADP
ejpam-5426	299	2	general	general	ADJ
ejpam-5426	299	3	topology	topology	NOUN
ejpam-5426	299	4	,	,	PUNCT
ejpam-5426	299	5	these	these	DET
ejpam-5426	299	6	spaces	space	NOUN
ejpam-5426	299	7	might	might	AUX
ejpam-5426	299	8	be	be	AUX
ejpam-5426	299	9	generalized	generalize	VERB
ejpam-5426	299	10	to	to	ADP
ejpam-5426	299	11	bitopological	bitopological	ADJ
ejpam-5426	299	12	and	and	CCONJ
ejpam-5426	299	13	tritopological	tritopological	ADJ
ejpam-5426	299	14	spaces	space	NOUN
ejpam-5426	299	15	.	.	PUNCT
ejpam-5426	300	1	acknowledgments	acknowledgment	NOUN
ejpam-5426	300	2	we	we	PRON
ejpam-5426	300	3	very	very	ADV
ejpam-5426	300	4	much	much	ADV
ejpam-5426	300	5	appreciate	appreciate	VERB
ejpam-5426	300	6	everyone	everyone	PRON
ejpam-5426	300	7	who	who	PRON
ejpam-5426	300	8	made	make	VERB
ejpam-5426	300	9	a	a	DET
ejpam-5426	300	10	contribution	contribution	NOUN
ejpam-5426	300	11	to	to	ADP
ejpam-5426	300	12	this	this	DET
ejpam-5426	300	13	research	research	NOUN
ejpam-5426	300	14	project	project	NOUN
ejpam-5426	300	15	.	.	PUNCT
ejpam-5426	301	1	their	their	PRON
ejpam-5426	301	2	help	help	NOUN
ejpam-5426	301	3	,	,	PUNCT
ejpam-5426	301	4	guidance	guidance	NOUN
ejpam-5426	301	5	,	,	PUNCT
ejpam-5426	301	6	and	and	CCONJ
ejpam-5426	301	7	teamwork	teamwork	NOUN
ejpam-5426	301	8	have	have	AUX
ejpam-5426	301	9	been	be	AUX
ejpam-5426	301	10	key	key	ADJ
ejpam-5426	301	11	to	to	ADP
ejpam-5426	301	12	the	the	DET
ejpam-5426	301	13	completion	completion	NOUN
ejpam-5426	301	14	of	of	ADP
ejpam-5426	301	15	this	this	DET
ejpam-5426	301	16	research	research	NOUN
ejpam-5426	301	17	.	.	PUNCT
ejpam-5426	302	1	references	reference	NOUN
ejpam-5426	302	2	3002	3002	NUM
ejpam-5426	302	3	references	reference	NOUN
ejpam-5426	302	4	[	[	X
ejpam-5426	302	5	1	1	NUM
ejpam-5426	302	6	]	]	PUNCT
ejpam-5426	302	7	k.	k.	PROPN
ejpam-5426	303	1	al	al	PROPN
ejpam-5426	303	2	-	-	PROPN
ejpam-5426	303	3	zoubi	zoubi	PROPN
ejpam-5426	303	4	and	and	CCONJ
ejpam-5426	303	5	s.	s.	PROPN
ejpam-5426	303	6	al	al	PROPN
ejpam-5426	303	7	-	-	PROPN
ejpam-5426	303	8	ghour	ghour	PROPN
ejpam-5426	303	9	.	.	PUNCT
ejpam-5426	304	1	on	on	ADP
ejpam-5426	304	2	p3−paracompact	p3−paracompact	PROPN
ejpam-5426	304	3	spaces	space	NOUN
ejpam-5426	304	4	.	.	PUNCT
ejpam-5426	305	1	international	international	ADJ
ejpam-5426	305	2	journal	journal	PROPN
ejpam-5426	305	3	of	of	ADP
ejpam-5426	305	4	mathematics	mathematics	PROPN
ejpam-5426	305	5	and	and	CCONJ
ejpam-5426	305	6	mathematical	mathematical	ADJ
ejpam-5426	305	7	sciences	science	NOUN
ejpam-5426	305	8	,	,	PUNCT
ejpam-5426	305	9	2007(1):080697	2007(1):080697	NOUN
ejpam-5426	305	10	,	,	PUNCT
ejpam-5426	305	11	2007	2007	NUM
ejpam-5426	305	12	.	.	PUNCT
ejpam-5426	306	1	[	[	X
ejpam-5426	306	2	2	2	NUM
ejpam-5426	306	3	]	]	PUNCT
ejpam-5426	306	4	k.	k.	PROPN
ejpam-5426	307	1	y.	y.	PROPN
ejpam-5426	307	2	al	al	PROPN
ejpam-5426	307	3	-	-	PROPN
ejpam-5426	307	4	zoubi	zoubi	PROPN
ejpam-5426	307	5	.	.	PUNCT
ejpam-5426	308	1	s	s	X
ejpam-5426	308	2	-	-	PUNCT
ejpam-5426	308	3	paracompact	paracompact	ADJ
ejpam-5426	308	4	spaces	space	NOUN
ejpam-5426	308	5	.	.	PUNCT
ejpam-5426	309	1	acta	acta	PROPN
ejpam-5426	309	2	mathematica	mathematica	PROPN
ejpam-5426	309	3	hungarica	hungarica	PROPN
ejpam-5426	309	4	,	,	PUNCT
ejpam-5426	309	5	110(1	110(1	NUM
ejpam-5426	309	6	-	-	SYM
ejpam-5426	309	7	2):165	2):165	NUM
ejpam-5426	309	8	–	–	PUNCT
ejpam-5426	309	9	174	174	NUM
ejpam-5426	309	10	,	,	PUNCT
ejpam-5426	309	11	2006	2006	NUM
ejpam-5426	309	12	.	.	PUNCT
ejpam-5426	310	1	[	[	X
ejpam-5426	310	2	3	3	NUM
ejpam-5426	310	3	]	]	X
ejpam-5426	310	4	n.	n.	PROPN
ejpam-5426	310	5	c.	c.	PROPN
ejpam-5426	310	6	açıkgöz	açıkgöz	PROPN
ejpam-5426	310	7	.	.	PUNCT
ejpam-5426	311	1	on	on	ADP
ejpam-5426	311	2	γ	γ	NOUN
ejpam-5426	311	3	-	-	ADJ
ejpam-5426	311	4	paracompact	paracompact	ADJ
ejpam-5426	311	5	spaces	space	NOUN
ejpam-5426	311	6	.	.	PUNCT
ejpam-5426	312	1	konuralp	konuralp	PROPN
ejpam-5426	312	2	journal	journal	PROPN
ejpam-5426	312	3	of	of	ADP
ejpam-5426	312	4	mathematics	mathematic	NOUN
ejpam-5426	312	5	,	,	PUNCT
ejpam-5426	312	6	11(1):77–81	11(1):77–81	NUM
ejpam-5426	312	7	,	,	PUNCT
ejpam-5426	312	8	2023	2023	NUM
ejpam-5426	312	9	.	.	PUNCT
ejpam-5426	313	1	[	[	X
ejpam-5426	313	2	4	4	NUM
ejpam-5426	313	3	]	]	X
ejpam-5426	313	4	f.	f.	PROPN
ejpam-5426	313	5	bani	bani	PROPN
ejpam-5426	313	6	-	-	PUNCT
ejpam-5426	313	7	ahmad	ahmad	PROPN
ejpam-5426	313	8	,	,	PUNCT
ejpam-5426	313	9	o.	o.	PROPN
ejpam-5426	313	10	alsayyed	alsayye	VERB
ejpam-5426	313	11	,	,	PUNCT
ejpam-5426	313	12	,	,	PUNCT
ejpam-5426	313	13	and	and	CCONJ
ejpam-5426	313	14	a.	a.	NOUN
ejpam-5426	313	15	a.	a.	NOUN
ejpam-5426	313	16	atoom	atoom	PROPN
ejpam-5426	313	17	.	.	PUNCT
ejpam-5426	314	1	some	some	DET
ejpam-5426	314	2	new	new	ADJ
ejpam-5426	314	3	results	result	NOUN
ejpam-5426	314	4	of	of	ADP
ejpam-5426	314	5	difference	difference	NOUN
ejpam-5426	314	6	perfect	perfect	ADJ
ejpam-5426	314	7	functions	function	NOUN
ejpam-5426	314	8	in	in	ADP
ejpam-5426	314	9	topological	topological	ADJ
ejpam-5426	314	10	spaces	space	NOUN
ejpam-5426	314	11	.	.	PUNCT
ejpam-5426	315	1	aims	aim	VERB
ejpam-5426	315	2	mathematics	mathematic	NOUN
ejpam-5426	315	3	,	,	PUNCT
ejpam-5426	315	4	7(11):20058–20065	7(11):20058–20065	NOUN
ejpam-5426	315	5	,	,	PUNCT
ejpam-5426	315	6	2022	2022	NUM
ejpam-5426	315	7	.	.	PUNCT
ejpam-5426	316	1	[	[	X
ejpam-5426	316	2	5	5	NUM
ejpam-5426	316	3	]	]	PUNCT
ejpam-5426	316	4	m.	m.	NOUN
ejpam-5426	316	5	caldas	caldas	PROPN
ejpam-5426	316	6	.	.	PUNCT
ejpam-5426	317	1	a	a	DET
ejpam-5426	317	2	separation	separation	NOUN
ejpam-5426	317	3	axiom	axiom	NOUN
ejpam-5426	317	4	between	between	ADP
ejpam-5426	317	5	semi−t0	semi−t0	NUM
ejpam-5426	317	6	and	and	CCONJ
ejpam-5426	317	7	semi−t1	semi−t1	NOUN
ejpam-5426	317	8	.	.	PUNCT
ejpam-5426	318	1	mem	mem	PROPN
ejpam-5426	318	2	.	.	PUNCT
ejpam-5426	319	1	fac	fac	PROPN
ejpam-5426	319	2	.	.	PUNCT
ejpam-5426	320	1	sci	sci	PROPN
ejpam-5426	320	2	.	.	PROPN
ejpam-5426	320	3	kochi	kochi	PROPN
ejpam-5426	320	4	univ	univ	PROPN
ejpam-5426	320	5	.	.	PUNCT
ejpam-5426	321	1	ser	ser	PROPN
ejpam-5426	321	2	.	.	PUNCT
ejpam-5426	322	1	a	a	DET
ejpam-5426	322	2	math	math	NOUN
ejpam-5426	322	3	,	,	PUNCT
ejpam-5426	322	4	181:37–42	181:37–42	NUM
ejpam-5426	322	5	,	,	PUNCT
ejpam-5426	322	6	1997	1997	NUM
ejpam-5426	322	7	.	.	PUNCT
ejpam-5426	323	1	[	[	X
ejpam-5426	323	2	6	6	NUM
ejpam-5426	323	3	]	]	X
ejpam-5426	323	4	i.	i.	PROPN
ejpam-5426	323	5	demir	demir	PROPN
ejpam-5426	323	6	and	and	CCONJ
ejpam-5426	323	7	o.	o.	PROPN
ejpam-5426	323	8	b.	b.	PROPN
ejpam-5426	323	9	ozbakir	ozbakir	PROPN
ejpam-5426	323	10	.	.	PUNCT
ejpam-5426	324	1	on	on	ADP
ejpam-5426	324	2	β	β	ADJ
ejpam-5426	324	3	-	-	ADJ
ejpam-5426	324	4	paracompact	paracompact	ADJ
ejpam-5426	324	5	spaces	space	NOUN
ejpam-5426	324	6	.	.	PUNCT
ejpam-5426	325	1	filomat	filomat	NOUN
ejpam-5426	325	2	,	,	PUNCT
ejpam-5426	325	3	27(6):971–976	27(6):971–976	PROPN
ejpam-5426	325	4	,	,	PUNCT
ejpam-5426	325	5	2013	2013	NUM
ejpam-5426	325	6	.	.	PUNCT
ejpam-5426	326	1	[	[	X
ejpam-5426	326	2	7	7	X
ejpam-5426	326	3	]	]	PUNCT
ejpam-5426	326	4	j.	j.	PROPN
ejpam-5426	326	5	dieudonné.	dieudonné.	PROPN
ejpam-5426	326	6	une	une	PROPN
ejpam-5426	326	7	généralisation	généralisation	PROPN
ejpam-5426	326	8	des	des	PROPN
ejpam-5426	326	9	espaces	espace	NOUN
ejpam-5426	326	10	compacts	compact	NOUN
ejpam-5426	326	11	.	.	PUNCT
ejpam-5426	327	1	journal	journal	PROPN
ejpam-5426	327	2	de	de	PROPN
ejpam-5426	327	3	mathématiques	mathématiques	PROPN
ejpam-5426	327	4	pures	pure	NOUN
ejpam-5426	327	5	et	et	NOUN
ejpam-5426	327	6	appliquées	appliquée	NOUN
ejpam-5426	327	7	,	,	PUNCT
ejpam-5426	327	8	23:65–76	23:65–76	NUM
ejpam-5426	327	9	,	,	PUNCT
ejpam-5426	327	10	1944	1944	NUM
ejpam-5426	327	11	.	.	PUNCT
ejpam-5426	328	1	[	[	X
ejpam-5426	328	2	8	8	NUM
ejpam-5426	328	3	]	]	X
ejpam-5426	328	4	c.	c.	PROPN
ejpam-5426	328	5	h.	h.	PROPN
ejpam-5426	328	6	dowker	dowker	PROPN
ejpam-5426	328	7	.	.	PUNCT
ejpam-5426	329	1	on	on	ADP
ejpam-5426	329	2	countably	countably	ADV
ejpam-5426	329	3	paracompact	paracompact	ADJ
ejpam-5426	329	4	spaces	space	NOUN
ejpam-5426	329	5	.	.	PUNCT
ejpam-5426	330	1	canadian	canadian	ADJ
ejpam-5426	330	2	journal	journal	PROPN
ejpam-5426	330	3	of	of	ADP
ejpam-5426	330	4	mathematics	mathematic	NOUN
ejpam-5426	330	5	,	,	PUNCT
ejpam-5426	330	6	3:219–224	3:219–224	NUM
ejpam-5426	330	7	,	,	PUNCT
ejpam-5426	330	8	1951	1951	NUM
ejpam-5426	330	9	.	.	PUNCT
ejpam-5426	331	1	[	[	X
ejpam-5426	331	2	9	9	NUM
ejpam-5426	331	3	]	]	X
ejpam-5426	331	4	r.	r.	PROPN
ejpam-5426	331	5	engelking	engelke	VERB
ejpam-5426	331	6	.	.	PUNCT
ejpam-5426	332	1	general	general	ADJ
ejpam-5426	332	2	topology	topology	PROPN
ejpam-5426	332	3	.	.	PUNCT
ejpam-5426	333	1	pwn	pwn	PROPN
ejpam-5426	333	2	,	,	PUNCT
ejpam-5426	333	3	warszawa	warszawa	PROPN
ejpam-5426	333	4	,	,	PUNCT
ejpam-5426	333	5	2nd	2nd	PROPN
ejpam-5426	333	6	edition	edition	PROPN
ejpam-5426	333	7	edition	edition	PROPN
ejpam-5426	333	8	,	,	PUNCT
ejpam-5426	333	9	1989	1989	NUM
ejpam-5426	333	10	.	.	PUNCT
ejpam-5426	334	1	[	[	X
ejpam-5426	334	2	10	10	NUM
ejpam-5426	334	3	]	]	X
ejpam-5426	334	4	w.	w.	PROPN
ejpam-5426	334	5	g.	g.	PROPN
ejpam-5426	334	6	fleissner	fleissner	PROPN
ejpam-5426	334	7	.	.	PUNCT
ejpam-5426	335	1	normal	normal	ADJ
ejpam-5426	335	2	,	,	PUNCT
ejpam-5426	335	3	not	not	PART
ejpam-5426	335	4	paracompact	paracompact	ADJ
ejpam-5426	335	5	spaces	space	NOUN
ejpam-5426	335	6	.	.	PUNCT
ejpam-5426	336	1	american	american	ADJ
ejpam-5426	336	2	math	math	PROPN
ejpam-5426	336	3	.	.	PUNCT
ejpam-5426	337	1	soc	soc	PROPN
ejpam-5426	337	2	.	.	PUNCT
ejpam-5426	337	3	,	,	PUNCT
ejpam-5426	337	4	1(7):233	1(7):233	NUM
ejpam-5426	337	5	–	–	PUNCT
ejpam-5426	337	6	236	236	NUM
ejpam-5426	337	7	,	,	PUNCT
ejpam-5426	337	8	1982	1982	NUM
ejpam-5426	337	9	.	.	PUNCT
ejpam-5426	338	1	[	[	X
ejpam-5426	338	2	11	11	NUM
ejpam-5426	338	3	]	]	PUNCT
ejpam-5426	338	4	p.	p.	NOUN
ejpam-5426	338	5	fletcher	fletcher	PROPN
ejpam-5426	338	6	,	,	PUNCT
ejpam-5426	338	7	h.	h.	PROPN
ejpam-5426	338	8	b.	b.	PROPN
ejpam-5426	338	9	holy	holy	PROPN
ejpam-5426	338	10	iii	iii	PROPN
ejpam-5426	338	11	,	,	PUNCT
ejpam-5426	338	12	and	and	CCONJ
ejpam-5426	338	13	c.	c.	PROPN
ejpam-5426	338	14	w.	w.	PROPN
ejpam-5426	338	15	patty	patty	PROPN
ejpam-5426	338	16	.	.	PUNCT
ejpam-5426	339	1	the	the	DET
ejpam-5426	339	2	comparison	comparison	NOUN
ejpam-5426	339	3	of	of	ADP
ejpam-5426	339	4	topologies	topology	NOUN
ejpam-5426	339	5	.	.	PUNCT
ejpam-5426	340	1	duke	duke	PROPN
ejpam-5426	340	2	math	math	PROPN
ejpam-5426	340	3	.	.	PUNCT
ejpam-5426	341	1	j	j	PROPN
ejpam-5426	341	2	,	,	PUNCT
ejpam-5426	341	3	36:325–331	36:325–331	PROPN
ejpam-5426	341	4	,	,	PUNCT
ejpam-5426	341	5	1969	1969	NUM
ejpam-5426	341	6	.	.	PUNCT
ejpam-5426	342	1	[	[	X
ejpam-5426	342	2	12	12	NUM
ejpam-5426	342	3	]	]	PUNCT
ejpam-5426	342	4	s.	s.	PROPN
ejpam-5426	342	5	al	al	PROPN
ejpam-5426	342	6	ghour	ghour	PROPN
ejpam-5426	342	7	.	.	PUNCT
ejpam-5426	343	1	decomposition	decomposition	NOUN
ejpam-5426	343	2	,	,	PUNCT
ejpam-5426	343	3	mapping	mapping	NOUN
ejpam-5426	343	4	,	,	PUNCT
ejpam-5426	343	5	and	and	CCONJ
ejpam-5426	343	6	sum	sum	VERB
ejpam-5426	343	7	theorems	theorem	NOUN
ejpam-5426	343	8	of	of	ADP
ejpam-5426	343	9	ω	ω	ADJ
ejpam-5426	343	10	-	-	ADJ
ejpam-5426	343	11	paracompact	paracompact	ADJ
ejpam-5426	343	12	topological	topological	ADJ
ejpam-5426	343	13	spaces	space	NOUN
ejpam-5426	343	14	.	.	PUNCT
ejpam-5426	344	1	axioms	axiom	NOUN
ejpam-5426	344	2	,	,	PUNCT
ejpam-5426	344	3	10(4):339	10(4):339	NUM
ejpam-5426	344	4	,	,	PUNCT
ejpam-5426	344	5	2021	2021	NUM
ejpam-5426	344	6	.	.	PUNCT
ejpam-5426	345	1	[	[	X
ejpam-5426	345	2	13	13	NUM
ejpam-5426	345	3	]	]	PUNCT
ejpam-5426	345	4	s.	s.	PROPN
ejpam-5426	345	5	h.	h.	PROPN
ejpam-5426	345	6	al	al	PROPN
ejpam-5426	345	7	ghour	ghour	PROPN
ejpam-5426	345	8	.	.	PUNCT
ejpam-5426	346	1	some	some	DET
ejpam-5426	346	2	generalizations	generalization	NOUN
ejpam-5426	346	3	of	of	ADP
ejpam-5426	346	4	paracompactness	paracompactness	NOUN
ejpam-5426	346	5	.	.	PUNCT
ejpam-5426	347	1	missouri	missouri	PROPN
ejpam-5426	347	2	journal	journal	PROPN
ejpam-5426	347	3	of	of	ADP
ejpam-5426	347	4	mathematical	mathematical	ADJ
ejpam-5426	347	5	sciences	science	NOUN
ejpam-5426	347	6	,	,	PUNCT
ejpam-5426	347	7	18(1):64–77	18(1):64–77	NUM
ejpam-5426	347	8	,	,	PUNCT
ejpam-5426	347	9	2006	2006	NUM
ejpam-5426	347	10	.	.	PUNCT
ejpam-5426	348	1	[	[	X
ejpam-5426	348	2	14	14	NUM
ejpam-5426	348	3	]	]	X
ejpam-5426	348	4	j.	j.	PROPN
ejpam-5426	348	5	g.	g.	PROPN
ejpam-5426	348	6	lee	lee	PROPN
ejpam-5426	348	7	,	,	PUNCT
ejpam-5426	348	8	g.	g.	PROPN
ejpam-5426	348	9	senel	senel	PROPN
ejpam-5426	348	10	,	,	PUNCT
ejpam-5426	348	11	y.	y.	PROPN
ejpam-5426	348	12	b.jun	b.jun	PROPN
ejpam-5426	348	13	,	,	PUNCT
ejpam-5426	348	14	f.	f.	PROPN
ejpam-5426	348	15	abbas	abbas	PROPN
ejpam-5426	348	16	,	,	PUNCT
ejpam-5426	348	17	and	and	CCONJ
ejpam-5426	348	18	k.	k.	PROPN
ejpam-5426	348	19	hur	hur	PROPN
ejpam-5426	348	20	.	.	PUNCT
ejpam-5426	348	21	topological	topological	ADJ
ejpam-5426	348	22	structures	structure	NOUN
ejpam-5426	348	23	via	via	ADP
ejpam-5426	348	24	interval	interval	NOUN
ejpam-5426	348	25	-	-	PUNCT
ejpam-5426	348	26	valued	value	VERB
ejpam-5426	348	27	soft	soft	ADJ
ejpam-5426	348	28	sets	set	NOUN
ejpam-5426	348	29	.	.	PUNCT
ejpam-5426	349	1	ann	ann	PROPN
ejpam-5426	349	2	.	.	PUNCT
ejpam-5426	349	3	fuzzy	fuzzy	ADJ
ejpam-5426	349	4	math	math	PROPN
ejpam-5426	349	5	.	.	PUNCT
ejpam-5426	350	1	inform	inform	NOUN
ejpam-5426	350	2	,	,	PUNCT
ejpam-5426	350	3	22(2):133–169	22(2):133–169	NUM
ejpam-5426	350	4	,	,	PUNCT
ejpam-5426	350	5	2021	2021	NUM
ejpam-5426	350	6	.	.	PUNCT
ejpam-5426	351	1	[	[	X
ejpam-5426	351	2	15	15	NUM
ejpam-5426	351	3	]	]	X
ejpam-5426	351	4	m.	m.	NOUN
ejpam-5426	351	5	n.	n.	PROPN
ejpam-5426	351	6	mukherjee	mukherjee	PROPN
ejpam-5426	351	7	and	and	CCONJ
ejpam-5426	351	8	a.	a.	PROPN
ejpam-5426	351	9	debray	debray	PROPN
ejpam-5426	351	10	.	.	PUNCT
ejpam-5426	352	1	on	on	ADP
ejpam-5426	352	2	nearly	nearly	ADV
ejpam-5426	352	3	paracompact	paracompact	ADJ
ejpam-5426	352	4	spaces	space	NOUN
ejpam-5426	352	5	via	via	ADP
ejpam-5426	352	6	regular	regular	ADJ
ejpam-5426	352	7	even	even	ADV
ejpam-5426	352	8	covers	cover	NOUN
ejpam-5426	352	9	.	.	PUNCT
ejpam-5426	353	1	matematicki	matematicki	NOUN
ejpam-5426	353	2	vesnik	vesnik	PROPN
ejpam-5426	353	3	-	-	PUNCT
ejpam-5426	353	4	beograd	beograd	PROPN
ejpam-5426	353	5	,	,	PUNCT
ejpam-5426	353	6	50:23–29	50:23–29	NUM
ejpam-5426	353	7	,	,	PUNCT
ejpam-5426	353	8	1998	1998	NUM
ejpam-5426	353	9	.	.	PUNCT
ejpam-5426	354	1	[	[	X
ejpam-5426	354	2	16	16	NUM
ejpam-5426	354	3	]	]	X
ejpam-5426	354	4	j.	j.	PROPN
ejpam-5426	354	5	oudetallah	oudetallah	PROPN
ejpam-5426	354	6	,	,	PUNCT
ejpam-5426	354	7	m.	m.	NOUN
ejpam-5426	354	8	m.	m.	NOUN
ejpam-5426	354	9	rousan	rousan	PROPN
ejpam-5426	354	10	,	,	PUNCT
ejpam-5426	354	11	and	and	CCONJ
ejpam-5426	354	12	i.	i.	PROPN
ejpam-5426	354	13	m.	m.	PROPN
ejpam-5426	354	14	batiha	batiha	PROPN
ejpam-5426	354	15	.	.	PUNCT
ejpam-5426	355	1	on	on	ADP
ejpam-5426	355	2	d−metacompactness	d−metacompactness	PROPN
ejpam-5426	355	3	in	in	ADP
ejpam-5426	355	4	topological	topological	ADJ
ejpam-5426	355	5	spaces	space	NOUN
ejpam-5426	355	6	.	.	PUNCT
ejpam-5426	356	1	j.	j.	PROPN
ejpam-5426	356	2	appl	appl	PROPN
ejpam-5426	356	3	.	.	PROPN
ejpam-5426	356	4	math	math	PROPN
ejpam-5426	356	5	.	.	PUNCT
ejpam-5426	357	1	inform	inform	NOUN
ejpam-5426	357	2	,	,	PUNCT
ejpam-5426	357	3	39:919–926	39:919–926	NUM
ejpam-5426	357	4	,	,	PUNCT
ejpam-5426	357	5	2021	2021	NUM
ejpam-5426	357	6	.	.	PUNCT
ejpam-5426	358	1	references	reference	NOUN
ejpam-5426	358	2	3003	3003	NUM
ejpam-5426	358	3	[	[	X
ejpam-5426	358	4	17	17	NUM
ejpam-5426	358	5	]	]	PUNCT
ejpam-5426	358	6	j.	j.	PROPN
ejpam-5426	358	7	oudetallah	oudetallah	PROPN
ejpam-5426	358	8	,	,	PUNCT
ejpam-5426	358	9	m.	m.	NOUN
ejpam-5426	358	10	m.	m.	NOUN
ejpam-5426	358	11	rousan	rousan	PROPN
ejpam-5426	358	12	,	,	PUNCT
ejpam-5426	358	13	and	and	CCONJ
ejpam-5426	358	14	i.	i.	PROPN
ejpam-5426	358	15	m.	m.	PROPN
ejpam-5426	358	16	batiha	batiha	PROPN
ejpam-5426	358	17	.	.	PUNCT
ejpam-5426	359	1	on	on	ADP
ejpam-5426	359	2	d−metacompactness	d−metacompactness	PROPN
ejpam-5426	359	3	in	in	ADP
ejpam-5426	359	4	topological	topological	ADJ
ejpam-5426	359	5	spaces	space	NOUN
ejpam-5426	359	6	.	.	PUNCT
ejpam-5426	360	1	j.	j.	PROPN
ejpam-5426	360	2	appl	appl	PROPN
ejpam-5426	360	3	.	.	PROPN
ejpam-5426	360	4	math	math	PROPN
ejpam-5426	360	5	.	.	PUNCT
ejpam-5426	361	1	inform	inform	NOUN
ejpam-5426	361	2	,	,	PUNCT
ejpam-5426	361	3	39:919–926	39:919–926	NUM
ejpam-5426	361	4	,	,	PUNCT
ejpam-5426	361	5	2021	2021	NUM
ejpam-5426	361	6	.	.	PUNCT
ejpam-5426	362	1	[	[	X
ejpam-5426	362	2	18	18	NUM
ejpam-5426	362	3	]	]	X
ejpam-5426	362	4	c.	c.	PROPN
ejpam-5426	362	5	m.	m.	PROPN
ejpam-5426	362	6	pareek	pareek	PROPN
ejpam-5426	362	7	.	.	PUNCT
ejpam-5426	363	1	moore	moore	PROPN
ejpam-5426	363	2	spaces	space	NOUN
ejpam-5426	363	3	,	,	PUNCT
ejpam-5426	363	4	semi	semi	ADJ
ejpam-5426	363	5	-	-	ADJ
ejpam-5426	363	6	metric	metric	ADJ
ejpam-5426	363	7	spaces	space	NOUN
ejpam-5426	363	8	and	and	CCONJ
ejpam-5426	363	9	continuous	continuous	ADJ
ejpam-5426	363	10	mappings	mapping	NOUN
ejpam-5426	363	11	connected	connect	VERB
ejpam-5426	363	12	with	with	ADP
ejpam-5426	363	13	them	they	PRON
ejpam-5426	363	14	.	.	PUNCT
ejpam-5426	364	1	canadian	canadian	ADJ
ejpam-5426	364	2	journal	journal	PROPN
ejpam-5426	364	3	of	of	ADP
ejpam-5426	364	4	mathematics	mathematic	NOUN
ejpam-5426	364	5	,	,	PUNCT
ejpam-5426	364	6	24(6):1033–1042	24(6):1033–1042	NUM
ejpam-5426	364	7	,	,	PUNCT
ejpam-5426	364	8	1972	1972	NUM
ejpam-5426	364	9	.	.	PUNCT
ejpam-5426	365	1	[	[	X
ejpam-5426	365	2	19	19	NUM
ejpam-5426	365	3	]	]	X
ejpam-5426	365	4	h.	h.	PROPN
ejpam-5426	365	5	qoqazeh	qoqazeh	PROPN
ejpam-5426	365	6	,	,	PUNCT
ejpam-5426	365	7	y.	y.	PROPN
ejpam-5426	365	8	al	al	PROPN
ejpam-5426	365	9	-	-	PUNCT
ejpam-5426	365	10	qudah	qudah	PROPN
ejpam-5426	365	11	,	,	PUNCT
ejpam-5426	365	12	m.	m.	NOUN
ejpam-5426	365	13	almousa	almousa	NOUN
ejpam-5426	365	14	,	,	PUNCT
ejpam-5426	365	15	and	and	CCONJ
ejpam-5426	365	16	a.	a.	NOUN
ejpam-5426	365	17	jaradat	jaradat	PROPN
ejpam-5426	365	18	.	.	PUNCT
ejpam-5426	366	1	on	on	ADP
ejpam-5426	366	2	d−compact	d−compact	PRON
ejpam-5426	366	3	topological	topological	ADJ
ejpam-5426	366	4	spaces	space	NOUN
ejpam-5426	366	5	.	.	PUNCT
ejpam-5426	367	1	journal	journal	NOUN
ejpam-5426	367	2	of	of	ADP
ejpam-5426	367	3	applied	apply	VERB
ejpam-5426	367	4	mathematics	mathematics	PROPN
ejpam-5426	367	5	&	&	CCONJ
ejpam-5426	367	6	informatics	informatic	NOUN
ejpam-5426	367	7	,	,	PUNCT
ejpam-5426	367	8	39(5	39(5	NUM
ejpam-5426	367	9	6):883–894	6):883–894	NUM
ejpam-5426	367	10	,	,	PUNCT
ejpam-5426	367	11	2021	2021	NUM
ejpam-5426	367	12	.	.	PUNCT
ejpam-5426	368	1	[	[	X
ejpam-5426	368	2	20	20	NUM
ejpam-5426	368	3	]	]	PUNCT
ejpam-5426	368	4	m.	m.	NOUN
ejpam-5426	368	5	k.	k.	PROPN
ejpam-5426	368	6	singal	singal	PROPN
ejpam-5426	368	7	and	and	CCONJ
ejpam-5426	368	8	s.	s.	PROPN
ejpam-5426	368	9	p.	p.	PROPN
ejpam-5426	368	10	arya	arya	PROPN
ejpam-5426	368	11	.	.	PUNCT
ejpam-5426	369	1	on	on	ADP
ejpam-5426	369	2	nearly	nearly	ADV
ejpam-5426	369	3	paracompact	paracompact	ADJ
ejpam-5426	369	4	spaces	space	NOUN
ejpam-5426	369	5	.	.	PUNCT
ejpam-5426	370	1	matematički	matematički	PROPN
ejpam-5426	370	2	vesnik	vesnik	PROPN
ejpam-5426	370	3	,	,	PUNCT
ejpam-5426	370	4	6(47):3–16	6(47):3–16	NOUN
ejpam-5426	370	5	,	,	PUNCT
ejpam-5426	370	6	1969	1969	NUM
ejpam-5426	370	7	.	.	PUNCT
ejpam-5426	371	1	[	[	X
ejpam-5426	371	2	21	21	NUM
ejpam-5426	371	3	]	]	X
ejpam-5426	371	4	l.	l.	PROPN
ejpam-5426	371	5	a.	a.	PROPN
ejpam-5426	371	6	steen	steen	PROPN
ejpam-5426	371	7	.	.	PUNCT
ejpam-5426	372	1	counterexamples	counterexample	NOUN
ejpam-5426	372	2	in	in	ADP
ejpam-5426	372	3	topology	topology	NOUN
ejpam-5426	372	4	.	.	PUNCT
ejpam-5426	373	1	springer	springer	NOUN
ejpam-5426	373	2	-	-	PUNCT
ejpam-5426	373	3	verlag	verlag	PROPN
ejpam-5426	373	4	,	,	PUNCT
ejpam-5426	373	5	1978	1978	NUM
ejpam-5426	373	6	.	.	PUNCT
ejpam-5426	374	1	[	[	X
ejpam-5426	374	2	22	22	NUM
ejpam-5426	374	3	]	]	PUNCT
ejpam-5426	374	4	j.	j.	PROPN
ejpam-5426	374	5	c.	c.	PROPN
ejpam-5426	374	6	tong	tong	PROPN
ejpam-5426	374	7	.	.	PUNCT
ejpam-5426	375	1	a	a	DET
ejpam-5426	375	2	separation	separation	NOUN
ejpam-5426	375	3	axiom	axiom	NOUN
ejpam-5426	375	4	between	between	ADP
ejpam-5426	375	5	t0	t0	PROPN
ejpam-5426	375	6	and	and	CCONJ
ejpam-5426	375	7	t1	t1	NOUN
ejpam-5426	375	8	.	.	PUNCT
ejpam-5426	376	1	annales	annales	PROPN
ejpam-5426	376	2	de	de	ADP
ejpam-5426	376	3	la	la	PROPN
ejpam-5426	376	4	société	société	PROPN
ejpam-5426	376	5	scientifique	scientifique	PROPN
ejpam-5426	376	6	de	de	PROPN
ejpam-5426	376	7	bruxelles	bruxelles	PROPN
ejpam-5426	376	8	series	series	PROPN
ejpam-5426	376	9	1	1	NUM
ejpam-5426	376	10	-	-	PUNCT
ejpam-5426	376	11	sciences	science	NOUN
ejpam-5426	376	12	mathématiques	mathématiques	PROPN
ejpam-5426	376	13	astronomiques	astronomique	NOUN
ejpam-5426	376	14	et	et	NOUN
ejpam-5426	376	15	physiques	physique	NOUN
ejpam-5426	376	16	,	,	PUNCT
ejpam-5426	376	17	96(2):85	96(2):85	NUM
ejpam-5426	376	18	–	–	PUNCT
ejpam-5426	376	19	90	90	NUM
ejpam-5426	376	20	,	,	PUNCT
ejpam-5426	376	21	1982	1982	NUM
ejpam-5426	376	22	.	.	PUNCT
ejpam-5426	377	1	[	[	X
ejpam-5426	377	2	23	23	NUM
ejpam-5426	377	3	]	]	X
ejpam-5426	377	4	e.	e.	PROPN
ejpam-5426	377	5	turanlıand	turanlıand	PROPN
ejpam-5426	377	6	o.	o.	PROPN
ejpam-5426	377	7	b.	b.	PROPN
ejpam-5426	378	1	özbak	özbak	PROPN
ejpam-5426	378	2	.	.	PUNCT
ejpam-5426	379	1	on	on	ADP
ejpam-5426	379	2	β1	β1	PROPN
ejpam-5426	379	3	−	−	PROPN
ejpam-5426	379	4	i	i	NOUN
ejpam-5426	379	5	-	-	PUNCT
ejpam-5426	379	6	paracompact	paracompact	ADJ
ejpam-5426	379	7	spaces	space	NOUN
ejpam-5426	379	8	.	.	PUNCT
ejpam-5426	380	1	konuralp	konuralp	PROPN
ejpam-5426	380	2	journal	journal	PROPN
ejpam-5426	380	3	of	of	ADP
ejpam-5426	380	4	mathematics	mathematic	NOUN
ejpam-5426	380	5	,	,	PUNCT
ejpam-5426	380	6	7(1):73–78	7(1):73–78	NUM
ejpam-5426	380	7	,	,	PUNCT
ejpam-5426	380	8	2019	2019	NUM
ejpam-5426	380	9	.	.	PUNCT