id	sid	tid	token	lemma	pos
ejpam-3637	1	1	european	european	PROPN
ejpam-3637	1	2	journal	journal	PROPN
ejpam-3637	1	3	of	of	ADP
ejpam-3637	1	4	pure	pure	ADJ
ejpam-3637	1	5	and	and	CCONJ
ejpam-3637	1	6	applied	apply	VERB
ejpam-3637	1	7	mathematics	mathematic	NOUN
ejpam-3637	1	8	vol	vol	NOUN
ejpam-3637	1	9	.	.	PROPN
ejpam-3637	2	1	13	13	NUM
ejpam-3637	2	2	,	,	PUNCT
ejpam-3637	2	3	no	no	INTJ
ejpam-3637	2	4	.	.	NOUN
ejpam-3637	2	5	2	2	NUM
ejpam-3637	2	6	,	,	PUNCT
ejpam-3637	2	7	2020	2020	NUM
ejpam-3637	2	8	,	,	PUNCT
ejpam-3637	2	9	280	280	NUM
ejpam-3637	2	10	-	-	SYM
ejpam-3637	2	11	286	286	NUM
ejpam-3637	2	12	issn	issn	PROPN
ejpam-3637	2	13	1307	1307	NUM
ejpam-3637	2	14	-	-	SYM
ejpam-3637	2	15	5543	5543	NUM
ejpam-3637	2	16	–	–	PUNCT
ejpam-3637	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3637	2	18	published	publish	VERB
ejpam-3637	2	19	by	by	ADP
ejpam-3637	2	20	new	new	PROPN
ejpam-3637	2	21	york	york	PROPN
ejpam-3637	2	22	business	business	PROPN
ejpam-3637	2	23	global	global	PROPN
ejpam-3637	2	24	a	a	PROPN
ejpam-3637	2	25	-	-	PUNCT
ejpam-3637	2	26	paracompactness	paracompactness	NOUN
ejpam-3637	2	27	and	and	CCONJ
ejpam-3637	2	28	strongly	strongly	ADV
ejpam-3637	2	29	a	a	DET
ejpam-3637	2	30	-	-	PUNCT
ejpam-3637	2	31	screenability	screenability	NOUN
ejpam-3637	2	32	in	in	ADP
ejpam-3637	2	33	topological	topological	ADJ
ejpam-3637	2	34	groups	group	NOUN
ejpam-3637	2	35	muhammad	muhammad	PROPN
ejpam-3637	2	36	kashif	kashif	PROPN
ejpam-3637	2	37	maqbool1,∗	maqbool1,∗	PROPN
ejpam-3637	2	38	,	,	PUNCT
ejpam-3637	2	39	awais	awais	PROPN
ejpam-3637	2	40	yousaf1	yousaf1	PROPN
ejpam-3637	2	41	,	,	PUNCT
ejpam-3637	2	42	muhammad	muhammad	PROPN
ejpam-3637	2	43	siddique	siddique	PROPN
ejpam-3637	2	44	bosan2	bosan2	PROPN
ejpam-3637	2	45	,	,	PUNCT
ejpam-3637	2	46	saeid	saeid	PROPN
ejpam-3637	2	47	jafari3	jafari3	PROPN
ejpam-3637	2	48	1	1	NUM
ejpam-3637	2	49	department	department	NOUN
ejpam-3637	2	50	of	of	ADP
ejpam-3637	2	51	mathematics	mathematic	NOUN
ejpam-3637	2	52	,	,	PUNCT
ejpam-3637	2	53	the	the	DET
ejpam-3637	2	54	islamia	islamia	PROPN
ejpam-3637	2	55	university	university	PROPN
ejpam-3637	2	56	of	of	ADP
ejpam-3637	2	57	bahawalpur	bahawalpur	PROPN
ejpam-3637	2	58	,	,	PUNCT
ejpam-3637	2	59	bahawalpur	bahawalpur	NOUN
ejpam-3637	2	60	63100	63100	NUM
ejpam-3637	2	61	,	,	PUNCT
ejpam-3637	2	62	pakistan	pakistan	PROPN
ejpam-3637	2	63	2	2	NUM
ejpam-3637	2	64	department	department	NOUN
ejpam-3637	2	65	of	of	ADP
ejpam-3637	2	66	mathematics	mathematic	NOUN
ejpam-3637	2	67	,	,	PUNCT
ejpam-3637	2	68	comsats	comsats	PROPN
ejpam-3637	2	69	institute	institute	PROPN
ejpam-3637	2	70	of	of	ADP
ejpam-3637	2	71	information	information	NOUN
ejpam-3637	2	72	technology	technology	PROPN
ejpam-3637	2	73	,	,	PUNCT
ejpam-3637	2	74	chack	chack	PROPN
ejpam-3637	2	75	shahzad	shahzad	PROPN
ejpam-3637	2	76	,	,	PUNCT
ejpam-3637	2	77	islamabad	islamabad	PROPN
ejpam-3637	2	78	44000	44000	NUM
ejpam-3637	2	79	,	,	PUNCT
ejpam-3637	2	80	pakistan	pakistan	PROPN
ejpam-3637	2	81	3	3	NUM
ejpam-3637	2	82	college	college	NOUN
ejpam-3637	2	83	of	of	ADP
ejpam-3637	2	84	vestsjaelland	vestsjaelland	PROPN
ejpam-3637	2	85	south	south	NOUN
ejpam-3637	2	86	,	,	PUNCT
ejpam-3637	2	87	slagelse	slagelse	NOUN
ejpam-3637	2	88	4200	4200	NUM
ejpam-3637	2	89	,	,	PUNCT
ejpam-3637	2	90	denmark	denmark	NOUN
ejpam-3637	2	91	abstract	abstract	NOUN
ejpam-3637	2	92	.	.	PUNCT
ejpam-3637	3	1	a	a	DET
ejpam-3637	3	2	space	space	NOUN
ejpam-3637	3	3	is	be	AUX
ejpam-3637	3	4	said	say	VERB
ejpam-3637	3	5	to	to	PART
ejpam-3637	3	6	be	be	AUX
ejpam-3637	3	7	strongly	strongly	ADV
ejpam-3637	3	8	a	a	ADV
ejpam-3637	3	9	-	-	PUNCT
ejpam-3637	3	10	screenable	screenable	ADJ
ejpam-3637	3	11	if	if	SCONJ
ejpam-3637	3	12	there	there	PRON
ejpam-3637	3	13	exists	exist	VERB
ejpam-3637	3	14	a	a	DET
ejpam-3637	3	15	σ	σ	NOUN
ejpam-3637	3	16	-	-	PUNCT
ejpam-3637	3	17	discrete	discrete	NOUN
ejpam-3637	3	18	refinement	refinement	NOUN
ejpam-3637	3	19	for	for	ADP
ejpam-3637	3	20	each	each	DET
ejpam-3637	3	21	open	open	ADJ
ejpam-3637	3	22	cover	cover	NOUN
ejpam-3637	3	23	.	.	PUNCT
ejpam-3637	4	1	in	in	ADP
ejpam-3637	4	2	this	this	DET
ejpam-3637	4	3	article	article	NOUN
ejpam-3637	4	4	,	,	PUNCT
ejpam-3637	4	5	we	we	PRON
ejpam-3637	4	6	have	have	AUX
ejpam-3637	4	7	investigated	investigate	VERB
ejpam-3637	4	8	some	some	PRON
ejpam-3637	4	9	of	of	ADP
ejpam-3637	4	10	the	the	DET
ejpam-3637	4	11	features	feature	NOUN
ejpam-3637	4	12	of	of	ADP
ejpam-3637	4	13	a	a	DET
ejpam-3637	4	14	-	-	PUNCT
ejpam-3637	4	15	paracompact	paracompact	ADJ
ejpam-3637	4	16	and	and	CCONJ
ejpam-3637	4	17	strongly	strongly	ADV
ejpam-3637	4	18	a	a	PRON
ejpam-3637	4	19	-	-	PUNCT
ejpam-3637	4	20	screenable	screenable	ADJ
ejpam-3637	4	21	spaces	space	NOUN
ejpam-3637	4	22	in	in	ADP
ejpam-3637	4	23	topological	topological	ADJ
ejpam-3637	4	24	and	and	CCONJ
ejpam-3637	4	25	semi	semi	ADJ
ejpam-3637	4	26	topological	topological	ADJ
ejpam-3637	4	27	groups	group	NOUN
ejpam-3637	4	28	.	.	PUNCT
ejpam-3637	5	1	we	we	PRON
ejpam-3637	5	2	predominantly	predominantly	ADV
ejpam-3637	5	3	show	show	VERB
ejpam-3637	5	4	that	that	SCONJ
ejpam-3637	5	5	(	(	PUNCT
ejpam-3637	5	6	i	i	NOUN
ejpam-3637	5	7	)	)	PUNCT
ejpam-3637	5	8	topological	topological	ADJ
ejpam-3637	5	9	direct	direct	ADJ
ejpam-3637	5	10	product	product	NOUN
ejpam-3637	5	11	of	of	ADP
ejpam-3637	5	12	(	(	PUNCT
ejpam-3637	5	13	countably	countably	ADV
ejpam-3637	5	14	)	)	PUNCT
ejpam-3637	5	15	a	a	DET
ejpam-3637	5	16	-	-	PUNCT
ejpam-3637	5	17	paracompact	paracompact	ADJ
ejpam-3637	5	18	topological	topological	ADJ
ejpam-3637	5	19	group	group	NOUN
ejpam-3637	5	20	and	and	CCONJ
ejpam-3637	5	21	a	a	DET
ejpam-3637	5	22	compact	compact	ADJ
ejpam-3637	5	23	topological	topological	ADJ
ejpam-3637	5	24	group	group	NOUN
ejpam-3637	5	25	is	be	AUX
ejpam-3637	5	26	(	(	PUNCT
ejpam-3637	5	27	countably	countably	ADV
ejpam-3637	5	28	)	)	PUNCT
ejpam-3637	5	29	a	a	DET
ejpam-3637	5	30	-	-	PUNCT
ejpam-3637	5	31	paracompact	paracompact	ADJ
ejpam-3637	5	32	topological	topological	ADJ
ejpam-3637	5	33	group	group	NOUN
ejpam-3637	5	34	.	.	PUNCT
ejpam-3637	6	1	(	(	PUNCT
ejpam-3637	6	2	ii	ii	NOUN
ejpam-3637	6	3	)	)	PUNCT
ejpam-3637	6	4	all	all	DET
ejpam-3637	6	5	the	the	DET
ejpam-3637	6	6	left	left	ADJ
ejpam-3637	6	7	and	and	CCONJ
ejpam-3637	6	8	right	right	ADJ
ejpam-3637	6	9	cosets	coset	NOUN
ejpam-3637	6	10	of	of	ADP
ejpam-3637	6	11	a	a	DET
ejpam-3637	6	12	strongly	strongly	ADV
ejpam-3637	6	13	a	a	PRON
ejpam-3637	6	14	-	-	PUNCT
ejpam-3637	6	15	screenable	screenable	ADJ
ejpam-3637	6	16	subset	subset	NOUN
ejpam-3637	6	17	h	h	NOUN
ejpam-3637	6	18	of	of	ADP
ejpam-3637	6	19	a	a	DET
ejpam-3637	6	20	semi	semi	ADJ
ejpam-3637	6	21	topological	topological	ADJ
ejpam-3637	6	22	group	group	NOUN
ejpam-3637	6	23	(	(	PUNCT
ejpam-3637	6	24	g	g	PROPN
ejpam-3637	6	25	,	,	PUNCT
ejpam-3637	6	26	∗	∗	NOUN
ejpam-3637	6	27	,	,	PUNCT
ejpam-3637	6	28	τ	τ	X
ejpam-3637	6	29	)	)	PUNCT
ejpam-3637	6	30	are	be	AUX
ejpam-3637	6	31	strongly	strongly	ADV
ejpam-3637	6	32	a	a	ADV
ejpam-3637	6	33	-	-	PUNCT
ejpam-3637	6	34	screenable	screenable	ADJ
ejpam-3637	6	35	.	.	PUNCT
ejpam-3637	7	1	2020	2020	NUM
ejpam-3637	7	2	mathematics	mathematic	NOUN
ejpam-3637	7	3	subject	subject	NOUN
ejpam-3637	7	4	classifications	classification	NOUN
ejpam-3637	7	5	:	:	PUNCT
ejpam-3637	7	6	22c05	22c05	NUM
ejpam-3637	7	7	,	,	PUNCT
ejpam-3637	7	8	22a05	22a05	NUM
ejpam-3637	7	9	,	,	PUNCT
ejpam-3637	7	10	22a10	22a10	NUM
ejpam-3637	7	11	,	,	PUNCT
ejpam-3637	7	12	54c05	54c05	NUM
ejpam-3637	7	13	key	key	ADJ
ejpam-3637	7	14	words	word	NOUN
ejpam-3637	7	15	and	and	CCONJ
ejpam-3637	7	16	phrases	phrase	NOUN
ejpam-3637	7	17	:	:	PUNCT
ejpam-3637	7	18	a	a	DET
ejpam-3637	7	19	-	-	PUNCT
ejpam-3637	7	20	paracompactness	paracompactness	NOUN
ejpam-3637	7	21	,	,	PUNCT
ejpam-3637	7	22	semi	semi	ADV
ejpam-3637	7	23	δ	δ	PROPN
ejpam-3637	7	24	-	-	ADJ
ejpam-3637	7	25	topological	topological	ADJ
ejpam-3637	7	26	group	group	NOUN
ejpam-3637	7	27	,	,	PUNCT
ejpam-3637	7	28	strongly	strongly	ADV
ejpam-3637	7	29	a	a	DET
ejpam-3637	7	30	-	-	PUNCT
ejpam-3637	7	31	screenability	screenability	NOUN
ejpam-3637	7	32	,	,	PUNCT
ejpam-3637	7	33	n−capc	n−capc	PROPN
ejpam-3637	7	34	disjoint	disjoint	NOUN
ejpam-3637	7	35	set	set	NOUN
ejpam-3637	7	36	1	1	NUM
ejpam-3637	7	37	.	.	PUNCT
ejpam-3637	8	1	introduction	introduction	NOUN
ejpam-3637	8	2	and	and	CCONJ
ejpam-3637	8	3	background	background	NOUN
ejpam-3637	8	4	results	result	NOUN
ejpam-3637	8	5	it	it	PRON
ejpam-3637	8	6	is	be	AUX
ejpam-3637	8	7	always	always	ADV
ejpam-3637	8	8	captivating	captivate	VERB
ejpam-3637	8	9	to	to	PART
ejpam-3637	8	10	dig	dig	VERB
ejpam-3637	8	11	into	into	ADP
ejpam-3637	8	12	relationship	relationship	NOUN
ejpam-3637	8	13	of	of	ADP
ejpam-3637	8	14	the	the	DET
ejpam-3637	8	15	topological	topological	ADJ
ejpam-3637	8	16	spaces	space	NOUN
ejpam-3637	8	17	with	with	ADP
ejpam-3637	8	18	algebraic	algebraic	ADJ
ejpam-3637	8	19	structures	structure	NOUN
ejpam-3637	8	20	.	.	PUNCT
ejpam-3637	9	1	to	to	PART
ejpam-3637	9	2	bring	bring	VERB
ejpam-3637	9	3	out	out	ADP
ejpam-3637	9	4	some	some	DET
ejpam-3637	9	5	new	new	ADJ
ejpam-3637	9	6	results	result	NOUN
ejpam-3637	9	7	and	and	CCONJ
ejpam-3637	9	8	explore	explore	VERB
ejpam-3637	9	9	several	several	ADJ
ejpam-3637	9	10	concepts	concept	NOUN
ejpam-3637	9	11	,	,	PUNCT
ejpam-3637	9	12	many	many	ADJ
ejpam-3637	9	13	of	of	ADP
ejpam-3637	9	14	the	the	DET
ejpam-3637	9	15	mathematicians	mathematician	NOUN
ejpam-3637	9	16	make	make	VERB
ejpam-3637	9	17	a	a	DET
ejpam-3637	9	18	relationship	relationship	NOUN
ejpam-3637	9	19	between	between	ADP
ejpam-3637	9	20	these	these	DET
ejpam-3637	9	21	two	two	NUM
ejpam-3637	9	22	structures	structure	NOUN
ejpam-3637	9	23	by	by	ADP
ejpam-3637	9	24	debilitating	debilitate	VERB
ejpam-3637	9	25	or	or	CCONJ
ejpam-3637	9	26	strengthening	strengthen	VERB
ejpam-3637	9	27	different	different	ADJ
ejpam-3637	9	28	conditions	condition	NOUN
ejpam-3637	9	29	[	[	X
ejpam-3637	9	30	3	3	NUM
ejpam-3637	9	31	,	,	PUNCT
ejpam-3637	9	32	19	19	NUM
ejpam-3637	9	33	,	,	PUNCT
ejpam-3637	9	34	20	20	NUM
ejpam-3637	9	35	]	]	PUNCT
ejpam-3637	9	36	.	.	PUNCT
ejpam-3637	10	1	j.	j.	PROPN
ejpam-3637	10	2	dieudonne	dieudonne	PROPN
ejpam-3637	10	3	(	(	PUNCT
ejpam-3637	10	4	1944	1944	NUM
ejpam-3637	10	5	)	)	PUNCT
ejpam-3637	10	6	and	and	CCONJ
ejpam-3637	10	7	p.	p.	NOUN
ejpam-3637	10	8	alexandrov	alexandrov	PROPN
ejpam-3637	10	9	(	(	PUNCT
ejpam-3637	10	10	1945	1945	NUM
ejpam-3637	10	11	)	)	PUNCT
ejpam-3637	10	12	introduced	introduce	VERB
ejpam-3637	10	13	the	the	DET
ejpam-3637	10	14	terms	term	NOUN
ejpam-3637	10	15	paracompactness	paracompactness	PROPN
ejpam-3637	10	16	and	and	CCONJ
ejpam-3637	10	17	a	a	DET
ejpam-3637	10	18	-	-	PUNCT
ejpam-3637	10	19	paracompactness	paracompactness	NOUN
ejpam-3637	10	20	respectively	respectively	ADV
ejpam-3637	10	21	[	[	X
ejpam-3637	10	22	5	5	NUM
ejpam-3637	10	23	,	,	PUNCT
ejpam-3637	10	24	11	11	NUM
ejpam-3637	10	25	]	]	PUNCT
ejpam-3637	10	26	.	.	PUNCT
ejpam-3637	11	1	l.	l.	PROPN
ejpam-3637	11	2	ivanovski	ivanovski	PROPN
ejpam-3637	11	3	and	and	CCONJ
ejpam-3637	12	1	v.	v.	ADP
ejpam-3637	12	2	kusminov	kusminov	NOUN
ejpam-3637	12	3	discussed	discuss	VERB
ejpam-3637	12	4	that	that	SCONJ
ejpam-3637	12	5	each	each	DET
ejpam-3637	12	6	bicompact	bicompact	ADJ
ejpam-3637	12	7	topological	topological	PROPN
ejpam-3637	12	8	group	group	NOUN
ejpam-3637	12	9	is	be	AUX
ejpam-3637	12	10	dyadic	dyadic	ADJ
ejpam-3637	12	11	.	.	PUNCT
ejpam-3637	13	1	in	in	ADP
ejpam-3637	13	2	1962	1962	NUM
ejpam-3637	13	3	,	,	PUNCT
ejpam-3637	13	4	j.	j.	PROPN
ejpam-3637	13	5	kister	kister	PROPN
ejpam-3637	13	6	proved	prove	VERB
ejpam-3637	13	7	some	some	DET
ejpam-3637	13	8	properties	property	NOUN
ejpam-3637	13	9	of	of	ADP
ejpam-3637	13	10	compactness	compactness	NOUN
ejpam-3637	13	11	in	in	ADP
ejpam-3637	13	12	topological	topological	ADJ
ejpam-3637	13	13	groups	group	NOUN
ejpam-3637	13	14	[	[	X
ejpam-3637	13	15	17	17	NUM
ejpam-3637	13	16	]	]	PUNCT
ejpam-3637	13	17	.	.	PUNCT
ejpam-3637	14	1	in	in	ADP
ejpam-3637	14	2	1972	1972	NUM
ejpam-3637	14	3	,	,	PUNCT
ejpam-3637	14	4	o.	o.	NOUN
ejpam-3637	14	5	t.	t.	PROPN
ejpam-3637	14	6	alas	alas	PROPN
ejpam-3637	14	7	explored	explore	VERB
ejpam-3637	14	8	the	the	DET
ejpam-3637	14	9	properties	property	NOUN
ejpam-3637	14	10	of	of	ADP
ejpam-3637	14	11	paracompactness	paracompactness	NOUN
ejpam-3637	14	12	in	in	ADP
ejpam-3637	14	13	topological	topological	ADJ
ejpam-3637	14	14	groups	group	NOUN
ejpam-3637	14	15	[	[	X
ejpam-3637	14	16	4	4	NUM
ejpam-3637	14	17	]	]	PUNCT
ejpam-3637	14	18	,	,	PUNCT
ejpam-3637	14	19	and	and	CCONJ
ejpam-3637	14	20	l.	l.	PROPN
ejpam-3637	14	21	g.	g.	PROPN
ejpam-3637	14	22	brown	brown	PROPN
ejpam-3637	14	23	discussed	discuss	VERB
ejpam-3637	14	24	some	some	DET
ejpam-3637	14	25	properties	property	NOUN
ejpam-3637	14	26	in	in	ADP
ejpam-3637	14	27	topologically	topologically	ADV
ejpam-3637	14	28	complete	complete	ADJ
ejpam-3637	14	29	topological	topological	ADJ
ejpam-3637	14	30	groups	group	NOUN
ejpam-3637	15	1	[	[	X
ejpam-3637	15	2	9	9	NUM
ejpam-3637	15	3	]	]	PUNCT
ejpam-3637	15	4	.	.	PUNCT
ejpam-3637	16	1	in	in	ADP
ejpam-3637	16	2	1981	1981	NUM
ejpam-3637	16	3	,	,	PUNCT
ejpam-3637	16	4	a.	a.	NOUN
ejpam-3637	16	5	v.	v.	ADP
ejpam-3637	16	6	arhangelskii	arhangelskii	PROPN
ejpam-3637	16	7	discussed	discuss	VERB
ejpam-3637	16	8	locally	locally	ADV
ejpam-3637	16	9	subparacompact	subparacompact	ADJ
ejpam-3637	16	10	,	,	PUNCT
ejpam-3637	16	11	locally	locally	ADV
ejpam-3637	16	12	paracompact	paracompact	ADJ
ejpam-3637	16	13	,	,	PUNCT
ejpam-3637	16	14	∗corresponding	∗corresponde	VERB
ejpam-3637	16	15	author	author	NOUN
ejpam-3637	16	16	.	.	PUNCT
ejpam-3637	17	1	doi	doi	NOUN
ejpam-3637	17	2	:	:	PUNCT
ejpam-3637	17	3	https://doi.org/10.29020/nybg.ejpam.v13i2.3637	https://doi.org/10.29020/nybg.ejpam.v13i2.3637	ADJ
ejpam-3637	17	4	email	email	NOUN
ejpam-3637	17	5	addresses	address	NOUN
ejpam-3637	17	6	:	:	PUNCT
ejpam-3637	17	7	kashifmaqbool9@gmail.com	kashifmaqbool9@gmail.com	X
ejpam-3637	17	8	(	(	PUNCT
ejpam-3637	17	9	m.	m.	PROPN
ejpam-3637	17	10	k.	k.	PROPN
ejpam-3637	17	11	maqbool	maqbool	PROPN
ejpam-3637	17	12	)	)	PUNCT
ejpam-3637	17	13	,	,	PUNCT
ejpam-3637	17	14	awaisysf@gmail.com	awaisysf@gmail.com	X
ejpam-3637	17	15	(	(	PUNCT
ejpam-3637	17	16	a.	a.	PROPN
ejpam-3637	17	17	yousaf	yousaf	PROPN
ejpam-3637	17	18	)	)	PUNCT
ejpam-3637	17	19	,	,	PUNCT
ejpam-3637	17	20	siddiquebosan@hotmail.com	siddiquebosan@hotmail.com	X
ejpam-3637	17	21	(	(	PUNCT
ejpam-3637	17	22	m.	m.	PROPN
ejpam-3637	17	23	s.	s.	PROPN
ejpam-3637	17	24	bosan	bosan	PROPN
ejpam-3637	17	25	)	)	PUNCT
ejpam-3637	17	26	,	,	PUNCT
ejpam-3637	17	27	jafaripersia@gmail.com	jafaripersia@gmail.com	X
ejpam-3637	17	28	(	(	PUNCT
ejpam-3637	17	29	s.	s.	PROPN
ejpam-3637	17	30	jafari	jafari	PROPN
ejpam-3637	17	31	)	)	PUNCT
ejpam-3637	17	32	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3637	18	1	280	280	NUM
ejpam-3637	18	2	c	c	NOUN
ejpam-3637	18	3	©	©	NOUN
ejpam-3637	18	4	2020	2020	NUM
ejpam-3637	18	5	ejpam	ejpam	VERB
ejpam-3637	18	6	all	all	DET
ejpam-3637	18	7	rights	right	NOUN
ejpam-3637	18	8	reserved	reserve	VERB
ejpam-3637	18	9	.	.	PUNCT
ejpam-3637	19	1	m.	m.	NOUN
ejpam-3637	19	2	k.	k.	PROPN
ejpam-3637	20	1	maqbool	maqbool	PROPN
ejpam-3637	20	2	et	et	PROPN
ejpam-3637	21	1	al	al	PROPN
ejpam-3637	21	2	.	.	PUNCT
ejpam-3637	21	3	/	/	SYM
ejpam-3637	21	4	eur	eur	PROPN
ejpam-3637	21	5	.	.	PUNCT
ejpam-3637	22	1	j.	j.	PROPN
ejpam-3637	22	2	pure	pure	PROPN
ejpam-3637	22	3	appl	appl	PROPN
ejpam-3637	22	4	.	.	PROPN
ejpam-3637	22	5	math	math	PROPN
ejpam-3637	22	6	,	,	PUNCT
ejpam-3637	22	7	13	13	NUM
ejpam-3637	22	8	(	(	PUNCT
ejpam-3637	22	9	2	2	NUM
ejpam-3637	22	10	)	)	PUNCT
ejpam-3637	22	11	(	(	PUNCT
ejpam-3637	22	12	2020	2020	NUM
ejpam-3637	22	13	)	)	PUNCT
ejpam-3637	22	14	,	,	PUNCT
ejpam-3637	22	15	280	280	NUM
ejpam-3637	22	16	-	-	SYM
ejpam-3637	22	17	286	286	NUM
ejpam-3637	22	18	281	281	NUM
ejpam-3637	22	19	locally	locally	ADV
ejpam-3637	22	20	strongly	strongly	ADV
ejpam-3637	22	21	paracompact	paracompact	ADJ
ejpam-3637	22	22	topological	topological	ADJ
ejpam-3637	22	23	groups	group	NOUN
ejpam-3637	23	1	[	[	X
ejpam-3637	23	2	8	8	NUM
ejpam-3637	23	3	]	]	PUNCT
ejpam-3637	23	4	.	.	PUNCT
ejpam-3637	24	1	in	in	ADP
ejpam-3637	24	2	1989	1989	NUM
ejpam-3637	24	3	,	,	PUNCT
ejpam-3637	24	4	d.	d.	PROPN
ejpam-3637	24	5	b.	b.	PROPN
ejpam-3637	24	6	shakhmatov	shakhmatov	PROPN
ejpam-3637	24	7	presented	present	VERB
ejpam-3637	24	8	strongly	strongly	ADV
ejpam-3637	24	9	and	and	CCONJ
ejpam-3637	24	10	completely	completely	ADV
ejpam-3637	24	11	paracompactness	paracompactness	NOUN
ejpam-3637	24	12	in	in	ADP
ejpam-3637	24	13	topological	topological	ADJ
ejpam-3637	24	14	groups	group	NOUN
ejpam-3637	24	15	[	[	X
ejpam-3637	24	16	24	24	NUM
ejpam-3637	24	17	]	]	PUNCT
ejpam-3637	24	18	.	.	PUNCT
ejpam-3637	25	1	in	in	ADP
ejpam-3637	25	2	1996	1996	NUM
ejpam-3637	25	3	,	,	PUNCT
ejpam-3637	25	4	d.	d.	PROPN
ejpam-3637	25	5	buhagiar	buhagiar	PROPN
ejpam-3637	25	6	and	and	CCONJ
ejpam-3637	25	7	b.	b.	PROPN
ejpam-3637	25	8	pasynkov	pasynkov	PROPN
ejpam-3637	25	9	discussed	discuss	VERB
ejpam-3637	25	10	uniform	uniform	ADJ
ejpam-3637	25	11	paracompactness	paracompactness	PROPN
ejpam-3637	25	12	in	in	ADP
ejpam-3637	25	13	topological	topological	ADJ
ejpam-3637	25	14	groups	group	NOUN
ejpam-3637	25	15	[	[	X
ejpam-3637	25	16	10	10	NUM
ejpam-3637	25	17	]	]	PUNCT
ejpam-3637	25	18	.	.	PUNCT
ejpam-3637	26	1	s.	s.	PROPN
ejpam-3637	26	2	romaguera	romaguera	PROPN
ejpam-3637	26	3	and	and	CCONJ
ejpam-3637	26	4	m.	m.	NOUN
ejpam-3637	26	5	sanchis	sanchis	PROPN
ejpam-3637	26	6	in	in	ADP
ejpam-3637	26	7	2000	2000	NUM
ejpam-3637	26	8	investigated	investigate	VERB
ejpam-3637	26	9	locally	locally	ADV
ejpam-3637	26	10	compactness	compactness	NOUN
ejpam-3637	26	11	in	in	ADP
ejpam-3637	26	12	topological	topological	ADJ
ejpam-3637	26	13	groups	group	NOUN
ejpam-3637	26	14	[	[	X
ejpam-3637	26	15	23	23	NUM
ejpam-3637	26	16	]	]	PUNCT
ejpam-3637	26	17	.	.	PUNCT
ejpam-3637	27	1	in	in	ADP
ejpam-3637	27	2	2007	2007	NUM
ejpam-3637	27	3	,	,	PUNCT
ejpam-3637	27	4	a.	a.	NOUN
ejpam-3637	27	5	v.	v.	ADP
ejpam-3637	27	6	arhangelskii	arhangelskii	PROPN
ejpam-3637	27	7	discusses	discuss	VERB
ejpam-3637	27	8	some	some	DET
ejpam-3637	27	9	properties	property	NOUN
ejpam-3637	27	10	concerning	concern	VERB
ejpam-3637	27	11	paracompactness	paracompactness	NOUN
ejpam-3637	27	12	in	in	ADP
ejpam-3637	27	13	topological	topological	ADJ
ejpam-3637	27	14	groups	group	NOUN
ejpam-3637	27	15	[	[	X
ejpam-3637	27	16	6	6	NUM
ejpam-3637	27	17	]	]	PUNCT
ejpam-3637	27	18	.	.	PUNCT
ejpam-3637	28	1	strong	strong	ADJ
ejpam-3637	28	2	realcompactness	realcompactness	NOUN
ejpam-3637	28	3	is	be	AUX
ejpam-3637	28	4	discussed	discuss	VERB
ejpam-3637	28	5	in	in	ADP
ejpam-3637	28	6	2012	2012	NUM
ejpam-3637	28	7	by	by	ADP
ejpam-3637	28	8	m.	m.	NOUN
ejpam-3637	28	9	g.	g.	PROPN
ejpam-3637	28	10	tkachenko	tkachenko	PROPN
ejpam-3637	28	11	in	in	ADP
ejpam-3637	28	12	topological	topological	ADJ
ejpam-3637	28	13	groups	group	NOUN
ejpam-3637	29	1	[	[	X
ejpam-3637	29	2	26	26	NUM
ejpam-3637	29	3	]	]	PUNCT
ejpam-3637	29	4	.	.	PUNCT
ejpam-3637	30	1	in	in	ADP
ejpam-3637	30	2	2017	2017	NUM
ejpam-3637	30	3	,	,	PUNCT
ejpam-3637	30	4	h.	h.	PROPN
ejpam-3637	30	5	juarez	juarez	PROPN
ejpam-3637	30	6	-	-	PUNCT
ejpam-3637	30	7	anguiano	anguiano	PROPN
ejpam-3637	30	8	discussed	discuss	VERB
ejpam-3637	30	9	strongly	strongly	ADV
ejpam-3637	30	10	paracompactness	paracompactness	NOUN
ejpam-3637	30	11	in	in	ADP
ejpam-3637	30	12	topological	topological	ADJ
ejpam-3637	30	13	groups	group	NOUN
ejpam-3637	30	14	[	[	X
ejpam-3637	30	15	15	15	NUM
ejpam-3637	30	16	]	]	PUNCT
ejpam-3637	30	17	.	.	PUNCT
ejpam-3637	31	1	to	to	PART
ejpam-3637	31	2	extend	extend	VERB
ejpam-3637	31	3	this	this	DET
ejpam-3637	31	4	work	work	NOUN
ejpam-3637	31	5	,	,	PUNCT
ejpam-3637	31	6	we	we	PRON
ejpam-3637	31	7	have	have	AUX
ejpam-3637	31	8	discussed	discuss	VERB
ejpam-3637	31	9	a	a	DET
ejpam-3637	31	10	-	-	PUNCT
ejpam-3637	31	11	paracompactness	paracompactness	NOUN
ejpam-3637	31	12	and	and	CCONJ
ejpam-3637	31	13	strongly	strongly	ADV
ejpam-3637	31	14	a	a	DET
ejpam-3637	31	15	-	-	PUNCT
ejpam-3637	31	16	screenability	screenability	NOUN
ejpam-3637	31	17	in	in	ADP
ejpam-3637	31	18	topological	topological	ADJ
ejpam-3637	31	19	and	and	CCONJ
ejpam-3637	31	20	semi	semi	ADJ
ejpam-3637	31	21	topological	topological	ADJ
ejpam-3637	31	22	groups	group	NOUN
ejpam-3637	31	23	.	.	PUNCT
ejpam-3637	32	1	we	we	PRON
ejpam-3637	32	2	introduced	introduce	VERB
ejpam-3637	32	3	the	the	DET
ejpam-3637	32	4	term	term	NOUN
ejpam-3637	32	5	n	n	PRON
ejpam-3637	32	6	-capc	-capc	NOUN
ejpam-3637	32	7	disjoint	disjoint	NOUN
ejpam-3637	32	8	sets	set	NOUN
ejpam-3637	32	9	,	,	PUNCT
ejpam-3637	32	10	and	and	CCONJ
ejpam-3637	32	11	presented	present	VERB
ejpam-3637	32	12	the	the	DET
ejpam-3637	32	13	notion	notion	NOUN
ejpam-3637	32	14	semi	semi	ADV
ejpam-3637	32	15	δ	δ	PROPN
ejpam-3637	32	16	-	-	PUNCT
ejpam-3637	32	17	topological	topological	ADJ
ejpam-3637	32	18	group	group	NOUN
ejpam-3637	32	19	.	.	PUNCT
ejpam-3637	33	1	moreover	moreover	ADV
ejpam-3637	33	2	,	,	PUNCT
ejpam-3637	33	3	we	we	PRON
ejpam-3637	33	4	prove	prove	VERB
ejpam-3637	33	5	that	that	SCONJ
ejpam-3637	33	6	,	,	PUNCT
ejpam-3637	33	7	(	(	PUNCT
ejpam-3637	33	8	r,+	r,+	NUM
ejpam-3637	33	9	,	,	PUNCT
ejpam-3637	33	10	τ	τ	X
ejpam-3637	33	11	)	)	PUNCT
ejpam-3637	33	12	is	be	AUX
ejpam-3637	33	13	an	an	DET
ejpam-3637	33	14	ultra	ultra	ADJ
ejpam-3637	33	15	-	-	ADJ
ejpam-3637	33	16	a	a	DET
ejpam-3637	33	17	-	-	PUNCT
ejpam-3637	33	18	paracompact	paracompact	ADJ
ejpam-3637	33	19	topological	topological	ADJ
ejpam-3637	33	20	group	group	NOUN
ejpam-3637	33	21	.	.	PUNCT
ejpam-3637	34	1	2	2	X
ejpam-3637	34	2	.	.	NUM
ejpam-3637	34	3	preliminaries	preliminary	NOUN
ejpam-3637	34	4	a	a	DET
ejpam-3637	34	5	topological	topological	ADJ
ejpam-3637	34	6	space	space	NOUN
ejpam-3637	34	7	is	be	AUX
ejpam-3637	34	8	said	say	VERB
ejpam-3637	34	9	to	to	PART
ejpam-3637	34	10	be	be	AUX
ejpam-3637	34	11	compact	compact	ADJ
ejpam-3637	34	12	if	if	SCONJ
ejpam-3637	34	13	there	there	PRON
ejpam-3637	34	14	is	be	VERB
ejpam-3637	34	15	a	a	DET
ejpam-3637	34	16	finite	finite	ADJ
ejpam-3637	34	17	subcover	subcover	NOUN
ejpam-3637	34	18	for	for	ADP
ejpam-3637	34	19	each	each	DET
ejpam-3637	34	20	open	open	ADJ
ejpam-3637	34	21	cover	cover	NOUN
ejpam-3637	34	22	[	[	X
ejpam-3637	34	23	28	28	NUM
ejpam-3637	34	24	]	]	PUNCT
ejpam-3637	34	25	.	.	PUNCT
ejpam-3637	35	1	an	an	DET
ejpam-3637	35	2	a	a	PRON
ejpam-3637	35	3	-	-	PUNCT
ejpam-3637	35	4	paracompact	paracompact	ADJ
ejpam-3637	35	5	space	space	NOUN
ejpam-3637	35	6	is	be	AUX
ejpam-3637	35	7	a	a	DET
ejpam-3637	35	8	space	space	NOUN
ejpam-3637	35	9	which	which	PRON
ejpam-3637	35	10	contain	contain	VERB
ejpam-3637	35	11	a	a	DET
ejpam-3637	35	12	locally	locally	ADV
ejpam-3637	35	13	finite	finite	ADJ
ejpam-3637	35	14	refinement	refinement	NOUN
ejpam-3637	35	15	for	for	ADP
ejpam-3637	35	16	every	every	DET
ejpam-3637	35	17	open	open	ADJ
ejpam-3637	35	18	cover	cover	NOUN
ejpam-3637	35	19	.	.	PUNCT
ejpam-3637	36	1	in	in	ADP
ejpam-3637	36	2	paracompact	paracompact	ADJ
ejpam-3637	36	3	space	space	NOUN
ejpam-3637	36	4	there	there	PRON
ejpam-3637	36	5	exists	exist	VERB
ejpam-3637	36	6	a	a	DET
ejpam-3637	36	7	locally	locally	ADV
ejpam-3637	36	8	finite	finite	ADJ
ejpam-3637	36	9	open	open	ADJ
ejpam-3637	36	10	refinement	refinement	NOUN
ejpam-3637	36	11	for	for	ADP
ejpam-3637	36	12	each	each	DET
ejpam-3637	36	13	open	open	ADJ
ejpam-3637	36	14	cover	cover	NOUN
ejpam-3637	36	15	[	[	X
ejpam-3637	36	16	11	11	NUM
ejpam-3637	36	17	]	]	PUNCT
ejpam-3637	36	18	.	.	PUNCT
ejpam-3637	37	1	unlike	unlike	ADP
ejpam-3637	37	2	paracompact	paracompact	ADJ
ejpam-3637	37	3	space	space	NOUN
ejpam-3637	37	4	,	,	PUNCT
ejpam-3637	37	5	in	in	ADP
ejpam-3637	37	6	a	a	DET
ejpam-3637	37	7	-	-	PUNCT
ejpam-3637	37	8	paracompact	paracompact	ADJ
ejpam-3637	37	9	space	space	NOUN
ejpam-3637	37	10	locally	locally	ADV
ejpam-3637	37	11	finite	finite	PROPN
ejpam-3637	37	12	refinement	refinement	NOUN
ejpam-3637	37	13	need	need	AUX
ejpam-3637	37	14	not	not	PART
ejpam-3637	37	15	be	be	AUX
ejpam-3637	37	16	necessarily	necessarily	ADV
ejpam-3637	37	17	open	open	ADJ
ejpam-3637	37	18	.	.	PUNCT
ejpam-3637	38	1	every	every	DET
ejpam-3637	38	2	closed	close	VERB
ejpam-3637	38	3	subset	subset	NOUN
ejpam-3637	38	4	of	of	ADP
ejpam-3637	38	5	a	a	DET
ejpam-3637	38	6	paracompact	paracompact	ADJ
ejpam-3637	38	7	space	space	NOUN
ejpam-3637	38	8	is	be	AUX
ejpam-3637	38	9	paracompact	paracompact	ADJ
ejpam-3637	38	10	[	[	X
ejpam-3637	38	11	5	5	NUM
ejpam-3637	38	12	]	]	PUNCT
ejpam-3637	38	13	.	.	PUNCT
ejpam-3637	39	1	closed	close	VERB
ejpam-3637	39	2	continuous	continuous	ADJ
ejpam-3637	39	3	image	image	NOUN
ejpam-3637	39	4	of	of	ADP
ejpam-3637	39	5	a	a	DET
ejpam-3637	39	6	paracompact	paracompact	ADJ
ejpam-3637	39	7	space	space	NOUN
ejpam-3637	39	8	is	be	AUX
ejpam-3637	39	9	paracompact	paracompact	ADJ
ejpam-3637	39	10	[	[	X
ejpam-3637	39	11	22	22	NUM
ejpam-3637	39	12	]	]	PUNCT
ejpam-3637	39	13	.	.	PUNCT
ejpam-3637	40	1	every	every	DET
ejpam-3637	40	2	regular	regular	ADJ
ejpam-3637	40	3	strongly	strongly	ADV
ejpam-3637	40	4	screenable	screenable	ADJ
ejpam-3637	40	5	topological	topological	ADJ
ejpam-3637	40	6	space	space	NOUN
ejpam-3637	40	7	is	be	AUX
ejpam-3637	40	8	paracompact	paracompact	ADJ
ejpam-3637	40	9	[	[	X
ejpam-3637	40	10	21	21	NUM
ejpam-3637	40	11	]	]	PUNCT
ejpam-3637	40	12	.	.	PUNCT
ejpam-3637	41	1	topological	topological	ADJ
ejpam-3637	41	2	product	product	NOUN
ejpam-3637	41	3	of	of	ADP
ejpam-3637	41	4	metric	metric	ADJ
ejpam-3637	41	5	and	and	CCONJ
ejpam-3637	41	6	compact	compact	ADJ
ejpam-3637	41	7	hausdorff	hausdorff	NOUN
ejpam-3637	41	8	space	space	NOUN
ejpam-3637	41	9	is	be	AUX
ejpam-3637	41	10	paracompact	paracompact	ADJ
ejpam-3637	41	11	[	[	X
ejpam-3637	41	12	25	25	NUM
ejpam-3637	41	13	]	]	PUNCT
ejpam-3637	41	14	.	.	PUNCT
ejpam-3637	42	1	katetov	katetov	PROPN
ejpam-3637	43	1	[	[	X
ejpam-3637	43	2	16	16	NUM
ejpam-3637	43	3	]	]	PUNCT
ejpam-3637	43	4	and	and	CCONJ
ejpam-3637	43	5	dowker	dowker	NOUN
ejpam-3637	44	1	[	[	X
ejpam-3637	44	2	12	12	NUM
ejpam-3637	44	3	]	]	PUNCT
ejpam-3637	44	4	introduced	introduce	VERB
ejpam-3637	44	5	countably	countably	ADV
ejpam-3637	44	6	paracompact	paracompact	ADJ
ejpam-3637	44	7	spaces	space	NOUN
ejpam-3637	44	8	.	.	PUNCT
ejpam-3637	45	1	a	a	DET
ejpam-3637	45	2	space	space	NOUN
ejpam-3637	45	3	in	in	ADP
ejpam-3637	45	4	which	which	PRON
ejpam-3637	45	5	there	there	PRON
ejpam-3637	45	6	exists	exist	VERB
ejpam-3637	45	7	a	a	DET
ejpam-3637	45	8	locally	locally	ADV
ejpam-3637	45	9	finite	finite	ADJ
ejpam-3637	45	10	refinement	refinement	NOUN
ejpam-3637	45	11	for	for	ADP
ejpam-3637	45	12	each	each	DET
ejpam-3637	45	13	countably	countably	ADV
ejpam-3637	45	14	open	open	ADJ
ejpam-3637	45	15	cover	cover	NOUN
ejpam-3637	45	16	is	be	AUX
ejpam-3637	45	17	said	say	VERB
ejpam-3637	45	18	to	to	PART
ejpam-3637	45	19	be	be	AUX
ejpam-3637	45	20	countably	countably	ADV
ejpam-3637	45	21	a	a	DET
ejpam-3637	45	22	-	-	PUNCT
ejpam-3637	45	23	paracompact	paracompact	ADJ
ejpam-3637	45	24	space	space	NOUN
ejpam-3637	45	25	[	[	X
ejpam-3637	45	26	12	12	NUM
ejpam-3637	45	27	]	]	PUNCT
ejpam-3637	45	28	.	.	PUNCT
ejpam-3637	46	1	moreover	moreover	ADV
ejpam-3637	46	2	,	,	PUNCT
ejpam-3637	46	3	in	in	ADP
ejpam-3637	46	4	many	many	ADJ
ejpam-3637	46	5	results	result	NOUN
ejpam-3637	46	6	countable	countable	ADJ
ejpam-3637	46	7	paracompactness	paracompactness	NOUN
ejpam-3637	46	8	occur	occur	VERB
ejpam-3637	46	9	with	with	ADP
ejpam-3637	46	10	normality	normality	NOUN
ejpam-3637	46	11	[	[	X
ejpam-3637	46	12	13	13	NUM
ejpam-3637	46	13	,	,	PUNCT
ejpam-3637	46	14	14	14	NUM
ejpam-3637	46	15	]	]	PUNCT
ejpam-3637	46	16	.	.	PUNCT
ejpam-3637	47	1	let	let	VERB
ejpam-3637	47	2	k	k	PROPN
ejpam-3637	47	3	≤	≤	PROPN
ejpam-3637	47	4	g	g	NOUN
ejpam-3637	47	5	and	and	CCONJ
ejpam-3637	47	6	g	g	PROPN
ejpam-3637	47	7	∈	∈	PROPN
ejpam-3637	47	8	g	g	PROPN
ejpam-3637	47	9	,	,	PUNCT
ejpam-3637	47	10	then	then	ADV
ejpam-3637	47	11	kg	kg	PROPN
ejpam-3637	47	12	and	and	CCONJ
ejpam-3637	47	13	gk	gk	PROPN
ejpam-3637	47	14	are	be	AUX
ejpam-3637	47	15	said	say	VERB
ejpam-3637	47	16	to	to	PART
ejpam-3637	47	17	be	be	AUX
ejpam-3637	47	18	the	the	DET
ejpam-3637	47	19	right	right	NOUN
ejpam-3637	47	20	and	and	CCONJ
ejpam-3637	47	21	left	leave	VERB
ejpam-3637	47	22	cosets	coset	NOUN
ejpam-3637	47	23	of	of	ADP
ejpam-3637	47	24	k	k	PROPN
ejpam-3637	47	25	in	in	ADP
ejpam-3637	47	26	g	g	NOUN
ejpam-3637	47	27	respectively	respectively	ADV
ejpam-3637	47	28	.	.	PUNCT
ejpam-3637	48	1	left	leave	VERB
ejpam-3637	48	2	(	(	PUNCT
ejpam-3637	48	3	right	right	ADJ
ejpam-3637	48	4	)	)	PUNCT
ejpam-3637	48	5	translation	translation	NOUN
ejpam-3637	48	6	lt1	lt1	NOUN
ejpam-3637	48	7	:	:	PUNCT
ejpam-3637	48	8	g→	g→	NOUN
ejpam-3637	48	9	g	g	PROPN
ejpam-3637	48	10	(	(	PUNCT
ejpam-3637	48	11	rt1	rt1	PROPN
ejpam-3637	48	12	:	:	PUNCT
ejpam-3637	48	13	g→	g→	NOUN
ejpam-3637	48	14	g	g	NOUN
ejpam-3637	48	15	)	)	PUNCT
ejpam-3637	48	16	is	be	AUX
ejpam-3637	48	17	defined	define	VERB
ejpam-3637	48	18	as	as	ADP
ejpam-3637	48	19	lt1(t2	lt1(t2	NOUN
ejpam-3637	48	20	)	)	PUNCT
ejpam-3637	49	1	=	=	SYM
ejpam-3637	49	2	t1∗t2	t1∗t2	NOUN
ejpam-3637	49	3	(	(	PUNCT
ejpam-3637	49	4	rt1(t2	rt1(t2	ADJ
ejpam-3637	49	5	)	)	PUNCT
ejpam-3637	49	6	=	=	SYM
ejpam-3637	49	7	t2	t2	PROPN
ejpam-3637	49	8	∗	∗	NOUN
ejpam-3637	49	9	t1	t1	NOUN
ejpam-3637	49	10	)	)	PUNCT
ejpam-3637	49	11	.	.	PUNCT
ejpam-3637	50	1	for	for	ADP
ejpam-3637	50	2	a	a	DET
ejpam-3637	50	3	group	group	NOUN
ejpam-3637	50	4	(	(	PUNCT
ejpam-3637	50	5	g	g	NOUN
ejpam-3637	50	6	,	,	PUNCT
ejpam-3637	50	7	∗	∗	NOUN
ejpam-3637	50	8	)	)	PUNCT
ejpam-3637	50	9	,	,	PUNCT
ejpam-3637	50	10	the	the	DET
ejpam-3637	50	11	multiplication	multiplication	NOUN
ejpam-3637	50	12	mapping	mapping	NOUN
ejpam-3637	50	13	m	m	VERB
ejpam-3637	50	14	:	:	PUNCT
ejpam-3637	50	15	g	g	ADP
ejpam-3637	50	16	×	×	PROPN
ejpam-3637	50	17	g	g	PROPN
ejpam-3637	50	18	→	→	SYM
ejpam-3637	50	19	g	g	NOUN
ejpam-3637	50	20	is	be	AUX
ejpam-3637	50	21	defined	define	VERB
ejpam-3637	50	22	as	as	ADP
ejpam-3637	50	23	m(x	m(x	PROPN
ejpam-3637	50	24	,	,	PUNCT
ejpam-3637	50	25	y	y	NOUN
ejpam-3637	50	26	)	)	PUNCT
ejpam-3637	51	1	=	=	PUNCT
ejpam-3637	52	1	x	x	PUNCT
ejpam-3637	52	2	×	×	NOUN
ejpam-3637	52	3	y	y	PROPN
ejpam-3637	52	4	=	=	SYM
ejpam-3637	52	5	z	z	PROPN
ejpam-3637	52	6	,	,	PUNCT
ejpam-3637	52	7	for	for	ADP
ejpam-3637	52	8	x	x	SYM
ejpam-3637	52	9	,	,	PUNCT
ejpam-3637	52	10	y	y	PROPN
ejpam-3637	52	11	,	,	PUNCT
ejpam-3637	52	12	z	z	PROPN
ejpam-3637	52	13	∈	∈	PROPN
ejpam-3637	52	14	g.	g.	NOUN
ejpam-3637	52	15	a	a	DET
ejpam-3637	52	16	multiplication	multiplication	NOUN
ejpam-3637	52	17	mapping	mapping	NOUN
ejpam-3637	52	18	is	be	AUX
ejpam-3637	52	19	said	say	VERB
ejpam-3637	52	20	to	to	PART
ejpam-3637	52	21	be	be	AUX
ejpam-3637	52	22	jointly	jointly	ADV
ejpam-3637	52	23	continuous	continuous	ADJ
ejpam-3637	52	24	if	if	SCONJ
ejpam-3637	52	25	the	the	DET
ejpam-3637	52	26	defined	define	VERB
ejpam-3637	52	27	multiplication	multiplication	NOUN
ejpam-3637	52	28	mapping	mapping	NOUN
ejpam-3637	52	29	is	be	AUX
ejpam-3637	52	30	continuous	continuous	ADJ
ejpam-3637	52	31	and	and	CCONJ
ejpam-3637	52	32	is	be	AUX
ejpam-3637	52	33	separately	separately	ADV
ejpam-3637	52	34	continuous	continuous	ADJ
ejpam-3637	52	35	if	if	SCONJ
ejpam-3637	52	36	the	the	DET
ejpam-3637	52	37	left	left	NOUN
ejpam-3637	52	38	and	and	CCONJ
ejpam-3637	52	39	the	the	DET
ejpam-3637	52	40	right	right	ADJ
ejpam-3637	52	41	translations	translation	NOUN
ejpam-3637	52	42	are	be	AUX
ejpam-3637	52	43	continuous	continuous	ADJ
ejpam-3637	52	44	.	.	PUNCT
ejpam-3637	53	1	for	for	ADP
ejpam-3637	53	2	a	a	DET
ejpam-3637	53	3	space	space	NOUN
ejpam-3637	53	4	τ	τ	PROPN
ejpam-3637	53	5	and	and	CCONJ
ejpam-3637	53	6	a	a	DET
ejpam-3637	53	7	group	group	NOUN
ejpam-3637	53	8	g	g	NOUN
ejpam-3637	53	9	,	,	PUNCT
ejpam-3637	53	10	a	a	DET
ejpam-3637	53	11	triplet	triplet	NOUN
ejpam-3637	53	12	(	(	PUNCT
ejpam-3637	53	13	g	g	NOUN
ejpam-3637	53	14	,	,	PUNCT
ejpam-3637	53	15	∗	∗	NOUN
ejpam-3637	53	16	,	,	PUNCT
ejpam-3637	53	17	τ	τ	X
ejpam-3637	53	18	)	)	PUNCT
ejpam-3637	53	19	is	be	AUX
ejpam-3637	53	20	said	say	VERB
ejpam-3637	53	21	to	to	PART
ejpam-3637	53	22	be	be	AUX
ejpam-3637	53	23	a	a	DET
ejpam-3637	53	24	semi	semi	ADJ
ejpam-3637	53	25	topological	topological	ADJ
ejpam-3637	53	26	group	group	NOUN
ejpam-3637	53	27	if	if	SCONJ
ejpam-3637	53	28	multiplication	multiplication	NOUN
ejpam-3637	53	29	mapping	mapping	NOUN
ejpam-3637	53	30	is	be	AUX
ejpam-3637	53	31	separately	separately	ADV
ejpam-3637	53	32	continuous	continuous	ADJ
ejpam-3637	53	33	.	.	PUNCT
ejpam-3637	54	1	a	a	DET
ejpam-3637	54	2	quasi	quasi	PROPN
ejpam-3637	54	3	topological	topological	PROPN
ejpam-3637	54	4	group	group	NOUN
ejpam-3637	54	5	is	be	AUX
ejpam-3637	54	6	a	a	DET
ejpam-3637	54	7	semi	semi	ADJ
ejpam-3637	54	8	topological	topological	ADJ
ejpam-3637	54	9	group	group	NOUN
ejpam-3637	54	10	with	with	ADP
ejpam-3637	54	11	continuous	continuous	ADJ
ejpam-3637	54	12	inverse	inverse	NOUN
ejpam-3637	54	13	mapping	mapping	NOUN
ejpam-3637	54	14	.	.	PUNCT
ejpam-3637	55	1	in	in	ADP
ejpam-3637	55	2	a	a	DET
ejpam-3637	55	3	paratopological	paratopological	ADJ
ejpam-3637	55	4	group	group	NOUN
ejpam-3637	55	5	(	(	PUNCT
ejpam-3637	55	6	g	g	PROPN
ejpam-3637	55	7	,	,	PUNCT
ejpam-3637	55	8	∗	∗	NOUN
ejpam-3637	55	9	,	,	PUNCT
ejpam-3637	55	10	τ	τ	NOUN
ejpam-3637	55	11	)	)	PUNCT
ejpam-3637	55	12	multiplication	multiplication	NOUN
ejpam-3637	55	13	mapping	mapping	NOUN
ejpam-3637	55	14	is	be	AUX
ejpam-3637	55	15	jointly	jointly	ADV
ejpam-3637	55	16	continuous	continuous	ADJ
ejpam-3637	55	17	.	.	PUNCT
ejpam-3637	56	1	a	a	DET
ejpam-3637	56	2	paratopological	paratopological	ADJ
ejpam-3637	56	3	group	group	NOUN
ejpam-3637	56	4	having	have	VERB
ejpam-3637	56	5	continuous	continuous	ADJ
ejpam-3637	56	6	inverse	inverse	NOUN
ejpam-3637	56	7	mapping	mapping	NOUN
ejpam-3637	56	8	is	be	AUX
ejpam-3637	56	9	said	say	VERB
ejpam-3637	56	10	to	to	PART
ejpam-3637	56	11	be	be	AUX
ejpam-3637	56	12	a	a	DET
ejpam-3637	56	13	topological	topological	ADJ
ejpam-3637	56	14	group	group	NOUN
ejpam-3637	57	1	[	[	X
ejpam-3637	57	2	7	7	NUM
ejpam-3637	57	3	]	]	PUNCT
ejpam-3637	57	4	.	.	PUNCT
ejpam-3637	58	1	in	in	ADP
ejpam-3637	58	2	addition	addition	NOUN
ejpam-3637	58	3	,	,	PUNCT
ejpam-3637	58	4	many	many	ADJ
ejpam-3637	58	5	mathematicians	mathematician	NOUN
ejpam-3637	58	6	have	have	AUX
ejpam-3637	58	7	explored	explore	VERB
ejpam-3637	58	8	different	different	ADJ
ejpam-3637	58	9	properties	property	NOUN
ejpam-3637	58	10	related	relate	VERB
ejpam-3637	58	11	to	to	ADP
ejpam-3637	58	12	compactness	compactness	NOUN
ejpam-3637	58	13	[	[	X
ejpam-3637	58	14	1	1	NUM
ejpam-3637	58	15	,	,	PUNCT
ejpam-3637	58	16	2	2	NUM
ejpam-3637	58	17	,	,	PUNCT
ejpam-3637	58	18	18	18	NUM
ejpam-3637	58	19	]	]	PUNCT
ejpam-3637	58	20	.	.	PUNCT
ejpam-3637	59	1	our	our	PRON
ejpam-3637	59	2	notations	notation	NOUN
ejpam-3637	59	3	are	be	AUX
ejpam-3637	59	4	standard	standard	ADJ
ejpam-3637	59	5	as	as	SCONJ
ejpam-3637	59	6	used	use	VERB
ejpam-3637	59	7	in	in	ADP
ejpam-3637	59	8	[	[	X
ejpam-3637	59	9	13	13	NUM
ejpam-3637	59	10	,	,	PUNCT
ejpam-3637	59	11	27	27	NUM
ejpam-3637	59	12	]	]	PUNCT
ejpam-3637	59	13	.	.	PUNCT
ejpam-3637	60	1	m.	m.	NOUN
ejpam-3637	60	2	k.	k.	PROPN
ejpam-3637	61	1	maqbool	maqbool	PROPN
ejpam-3637	61	2	et	et	PROPN
ejpam-3637	62	1	al	al	PROPN
ejpam-3637	62	2	.	.	PUNCT
ejpam-3637	62	3	/	/	SYM
ejpam-3637	62	4	eur	eur	PROPN
ejpam-3637	62	5	.	.	PUNCT
ejpam-3637	63	1	j.	j.	PROPN
ejpam-3637	63	2	pure	pure	PROPN
ejpam-3637	63	3	appl	appl	PROPN
ejpam-3637	63	4	.	.	PROPN
ejpam-3637	63	5	math	math	PROPN
ejpam-3637	63	6	,	,	PUNCT
ejpam-3637	63	7	13	13	NUM
ejpam-3637	63	8	(	(	PUNCT
ejpam-3637	63	9	2	2	NUM
ejpam-3637	63	10	)	)	PUNCT
ejpam-3637	63	11	(	(	PUNCT
ejpam-3637	63	12	2020	2020	NUM
ejpam-3637	63	13	)	)	PUNCT
ejpam-3637	63	14	,	,	PUNCT
ejpam-3637	63	15	280	280	NUM
ejpam-3637	63	16	-	-	SYM
ejpam-3637	63	17	286	286	NUM
ejpam-3637	63	18	282	282	NUM
ejpam-3637	63	19	3	3	NUM
ejpam-3637	63	20	.	.	PUNCT
ejpam-3637	64	1	a	a	X
ejpam-3637	64	2	-	-	PUNCT
ejpam-3637	64	3	paracompactness	paracompactness	NOUN
ejpam-3637	64	4	and	and	CCONJ
ejpam-3637	64	5	strongly	strongly	ADV
ejpam-3637	64	6	a	a	DET
ejpam-3637	64	7	-	-	PUNCT
ejpam-3637	64	8	screenability	screenability	NOUN
ejpam-3637	64	9	definition	definition	NOUN
ejpam-3637	64	10	1	1	NUM
ejpam-3637	64	11	.	.	PUNCT
ejpam-3637	65	1	a	a	DET
ejpam-3637	65	2	space	space	NOUN
ejpam-3637	65	3	is	be	AUX
ejpam-3637	65	4	said	say	VERB
ejpam-3637	65	5	to	to	PART
ejpam-3637	65	6	be	be	AUX
ejpam-3637	65	7	strongly	strongly	ADV
ejpam-3637	65	8	a	a	ADV
ejpam-3637	65	9	-	-	PUNCT
ejpam-3637	65	10	screenable	screenable	ADJ
ejpam-3637	65	11	if	if	SCONJ
ejpam-3637	65	12	there	there	PRON
ejpam-3637	65	13	exists	exist	VERB
ejpam-3637	65	14	a	a	DET
ejpam-3637	65	15	σ	σ	NOUN
ejpam-3637	65	16	-	-	PUNCT
ejpam-3637	65	17	discrete	discrete	NOUN
ejpam-3637	65	18	refinement	refinement	NOUN
ejpam-3637	65	19	for	for	ADP
ejpam-3637	65	20	each	each	DET
ejpam-3637	65	21	open	open	ADJ
ejpam-3637	65	22	cover	cover	NOUN
ejpam-3637	65	23	.	.	PUNCT
ejpam-3637	66	1	theorem	theorem	NOUN
ejpam-3637	66	2	1	1	NUM
ejpam-3637	66	3	.	.	PUNCT
ejpam-3637	67	1	all	all	DET
ejpam-3637	67	2	the	the	DET
ejpam-3637	67	3	left	left	ADJ
ejpam-3637	67	4	and	and	CCONJ
ejpam-3637	67	5	right	right	ADJ
ejpam-3637	67	6	cosets	coset	NOUN
ejpam-3637	67	7	of	of	ADP
ejpam-3637	67	8	a	a	DET
ejpam-3637	67	9	strongly	strongly	ADV
ejpam-3637	67	10	a	a	PRON
ejpam-3637	67	11	-	-	PUNCT
ejpam-3637	67	12	screenable	screenable	ADJ
ejpam-3637	67	13	subset	subset	NOUN
ejpam-3637	67	14	h	h	NOUN
ejpam-3637	67	15	of	of	ADP
ejpam-3637	67	16	a	a	DET
ejpam-3637	67	17	semi	semi	ADJ
ejpam-3637	67	18	topological	topological	ADJ
ejpam-3637	67	19	group	group	NOUN
ejpam-3637	67	20	(	(	PUNCT
ejpam-3637	67	21	g	g	PROPN
ejpam-3637	67	22	,	,	PUNCT
ejpam-3637	67	23	∗	∗	NOUN
ejpam-3637	67	24	,	,	PUNCT
ejpam-3637	67	25	τ	τ	X
ejpam-3637	67	26	)	)	PUNCT
ejpam-3637	67	27	are	be	AUX
ejpam-3637	67	28	strongly	strongly	ADV
ejpam-3637	67	29	a	a	ADV
ejpam-3637	67	30	-	-	PUNCT
ejpam-3637	67	31	screenable	screenable	ADJ
ejpam-3637	67	32	.	.	PUNCT
ejpam-3637	68	1	proof	proof	NOUN
ejpam-3637	68	2	.	.	PUNCT
ejpam-3637	69	1	for	for	ADP
ejpam-3637	69	2	any	any	DET
ejpam-3637	69	3	a	a	DET
ejpam-3637	69	4	∈	∈	PROPN
ejpam-3637	69	5	g	g	NOUN
ejpam-3637	69	6	,	,	PUNCT
ejpam-3637	69	7	let	let	VERB
ejpam-3637	69	8	ω	ω	PRON
ejpam-3637	69	9	be	be	AUX
ejpam-3637	69	10	an	an	DET
ejpam-3637	69	11	open	open	ADJ
ejpam-3637	69	12	cover	cover	NOUN
ejpam-3637	69	13	of	of	ADP
ejpam-3637	69	14	left	left	ADJ
ejpam-3637	69	15	coset	coset	NOUN
ejpam-3637	69	16	ah	ah	INTJ
ejpam-3637	69	17	.	.	PUNCT
ejpam-3637	70	1	then	then	ADV
ejpam-3637	70	2	l−1	l−1	PROPN
ejpam-3637	70	3	a	a	DET
ejpam-3637	70	4	(	(	PUNCT
ejpam-3637	70	5	ω	ω	NOUN
ejpam-3637	70	6	)	)	PUNCT
ejpam-3637	70	7	is	be	AUX
ejpam-3637	70	8	an	an	DET
ejpam-3637	70	9	open	open	ADJ
ejpam-3637	70	10	cover	cover	NOUN
ejpam-3637	70	11	of	of	ADP
ejpam-3637	70	12	subset	subset	NOUN
ejpam-3637	70	13	h.	h.	PROPN
ejpam-3637	70	14	since	since	SCONJ
ejpam-3637	70	15	h	h	PROPN
ejpam-3637	70	16	is	be	AUX
ejpam-3637	70	17	strongly	strongly	ADV
ejpam-3637	70	18	a	a	PRON
ejpam-3637	70	19	-	-	PUNCT
ejpam-3637	70	20	screenable	screenable	ADJ
ejpam-3637	70	21	,	,	PUNCT
ejpam-3637	70	22	there	there	PRON
ejpam-3637	70	23	exists	exist	VERB
ejpam-3637	70	24	σ	σ	NOUN
ejpam-3637	70	25	-	-	PUNCT
ejpam-3637	70	26	discrete	discrete	ADJ
ejpam-3637	70	27	refinement	refinement	NOUN
ejpam-3637	70	28	u	u	NOUN
ejpam-3637	70	29	=	=	PROPN
ejpam-3637	70	30	∪∞i=1µi	∪∞i=1µi	PROPN
ejpam-3637	70	31	.	.	PUNCT
ejpam-3637	71	1	thus	thus	ADV
ejpam-3637	71	2	,	,	PUNCT
ejpam-3637	71	3	la(u	la(u	PUNCT
ejpam-3637	71	4	)	)	PUNCT
ejpam-3637	71	5	is	be	AUX
ejpam-3637	71	6	σ	σ	NOUN
ejpam-3637	71	7	-	-	PUNCT
ejpam-3637	71	8	discrete	discrete	ADJ
ejpam-3637	71	9	refinement	refinement	NOUN
ejpam-3637	71	10	of	of	ADP
ejpam-3637	71	11	open	open	ADJ
ejpam-3637	71	12	cover	cover	NOUN
ejpam-3637	71	13	ω	ω	NOUN
ejpam-3637	71	14	of	of	ADP
ejpam-3637	71	15	ah	ah	INTJ
ejpam-3637	71	16	which	which	PRON
ejpam-3637	71	17	asseverates	asseverate	VERB
ejpam-3637	71	18	that	that	SCONJ
ejpam-3637	71	19	for	for	ADP
ejpam-3637	71	20	every	every	DET
ejpam-3637	71	21	a	a	DET
ejpam-3637	71	22	∈	∈	PROPN
ejpam-3637	71	23	g	g	NOUN
ejpam-3637	71	24	,	,	PUNCT
ejpam-3637	71	25	ah	ah	INTJ
ejpam-3637	71	26	is	be	AUX
ejpam-3637	71	27	strongly	strongly	ADV
ejpam-3637	71	28	a	a	PRON
ejpam-3637	71	29	-	-	PUNCT
ejpam-3637	71	30	screenable	screenable	ADJ
ejpam-3637	71	31	.	.	PUNCT
ejpam-3637	72	1	similarly	similarly	ADV
ejpam-3637	72	2	,	,	PUNCT
ejpam-3637	72	3	all	all	DET
ejpam-3637	72	4	right	right	ADJ
ejpam-3637	72	5	cosets	coset	NOUN
ejpam-3637	72	6	are	be	AUX
ejpam-3637	72	7	strongly	strongly	ADV
ejpam-3637	72	8	a	a	ADV
ejpam-3637	72	9	-	-	PUNCT
ejpam-3637	72	10	screenable	screenable	ADJ
ejpam-3637	72	11	.	.	PUNCT
ejpam-3637	73	1	corollary	corollary	ADJ
ejpam-3637	73	2	1	1	NUM
ejpam-3637	73	3	.	.	PUNCT
ejpam-3637	74	1	a	a	DET
ejpam-3637	74	2	semi	semi	ADJ
ejpam-3637	74	3	topological	topological	ADJ
ejpam-3637	74	4	group	group	NOUN
ejpam-3637	74	5	(	(	PUNCT
ejpam-3637	74	6	g	g	PROPN
ejpam-3637	74	7	,	,	PUNCT
ejpam-3637	74	8	∗	∗	NOUN
ejpam-3637	74	9	,	,	PUNCT
ejpam-3637	74	10	τ	τ	X
ejpam-3637	74	11	)	)	PUNCT
ejpam-3637	74	12	is	be	AUX
ejpam-3637	74	13	strongly	strongly	ADV
ejpam-3637	74	14	a	a	ADV
ejpam-3637	74	15	-	-	PUNCT
ejpam-3637	74	16	screenable	screenable	ADJ
ejpam-3637	74	17	if	if	SCONJ
ejpam-3637	74	18	it	it	PRON
ejpam-3637	74	19	contains	contain	VERB
ejpam-3637	74	20	a	a	DET
ejpam-3637	74	21	strongly	strongly	ADV
ejpam-3637	74	22	a	a	PRON
ejpam-3637	74	23	-	-	PUNCT
ejpam-3637	74	24	screenable	screenable	ADJ
ejpam-3637	74	25	subset	subset	NOUN
ejpam-3637	74	26	h	h	NOUN
ejpam-3637	74	27	such	such	ADJ
ejpam-3637	74	28	that	that	SCONJ
ejpam-3637	74	29	|g|/|h|	|g|/|h|	PROPN
ejpam-3637	74	30	is	be	AUX
ejpam-3637	74	31	countable	countable	ADJ
ejpam-3637	74	32	.	.	PUNCT
ejpam-3637	75	1	theorem	theorem	NOUN
ejpam-3637	75	2	2	2	NUM
ejpam-3637	75	3	.	.	PUNCT
ejpam-3637	76	1	in	in	ADP
ejpam-3637	76	2	a	a	DET
ejpam-3637	76	3	semi	semi	ADJ
ejpam-3637	76	4	topological	topological	ADJ
ejpam-3637	76	5	group	group	NOUN
ejpam-3637	76	6	free	free	ADJ
ejpam-3637	76	7	product	product	NOUN
ejpam-3637	76	8	of	of	ADP
ejpam-3637	76	9	an	an	DET
ejpam-3637	76	10	a	a	DET
ejpam-3637	76	11	-	-	PUNCT
ejpam-3637	76	12	paracompact	paracompact	ADJ
ejpam-3637	76	13	(	(	PUNCT
ejpam-3637	76	14	countably	countably	ADV
ejpam-3637	76	15	aparacompact	aparacompact	ADJ
ejpam-3637	76	16	)	)	PUNCT
ejpam-3637	76	17	subset	subset	VERB
ejpam-3637	76	18	with	with	ADP
ejpam-3637	76	19	any	any	DET
ejpam-3637	76	20	finite	finite	NOUN
ejpam-3637	76	21	subset	subset	NOUN
ejpam-3637	76	22	is	be	AUX
ejpam-3637	76	23	a	a	DET
ejpam-3637	76	24	-	-	PUNCT
ejpam-3637	76	25	paracompact	paracompact	NOUN
ejpam-3637	76	26	(	(	PUNCT
ejpam-3637	76	27	countably	countably	ADV
ejpam-3637	76	28	a	a	DET
ejpam-3637	76	29	-	-	PUNCT
ejpam-3637	76	30	paracompact	paracompact	ADJ
ejpam-3637	76	31	)	)	PUNCT
ejpam-3637	76	32	.	.	PUNCT
ejpam-3637	77	1	proof	proof	NOUN
ejpam-3637	77	2	.	.	PUNCT
ejpam-3637	78	1	suppose	suppose	VERB
ejpam-3637	78	2	that	that	SCONJ
ejpam-3637	78	3	(	(	PUNCT
ejpam-3637	78	4	g	g	NOUN
ejpam-3637	78	5	,	,	PUNCT
ejpam-3637	78	6	∗	∗	NOUN
ejpam-3637	78	7	,	,	PUNCT
ejpam-3637	78	8	τ	τ	X
ejpam-3637	78	9	)	)	PUNCT
ejpam-3637	78	10	is	be	AUX
ejpam-3637	78	11	a	a	DET
ejpam-3637	78	12	semi	semi	ADJ
ejpam-3637	78	13	topological	topological	ADJ
ejpam-3637	78	14	group	group	NOUN
ejpam-3637	78	15	,	,	PUNCT
ejpam-3637	78	16	where	where	SCONJ
ejpam-3637	78	17	s	s	PRON
ejpam-3637	78	18	and	and	CCONJ
ejpam-3637	78	19	t	t	PROPN
ejpam-3637	78	20	are	be	AUX
ejpam-3637	78	21	respectively	respectively	ADV
ejpam-3637	78	22	a	a	DET
ejpam-3637	78	23	-	-	PUNCT
ejpam-3637	78	24	paracompact	paracompact	NOUN
ejpam-3637	78	25	(	(	PUNCT
ejpam-3637	78	26	countably	countably	ADV
ejpam-3637	78	27	a	a	DET
ejpam-3637	78	28	-	-	PUNCT
ejpam-3637	78	29	paracompact	paracompact	ADJ
ejpam-3637	78	30	)	)	PUNCT
ejpam-3637	78	31	and	and	CCONJ
ejpam-3637	78	32	finite	finite	ADJ
ejpam-3637	78	33	subsets	subset	NOUN
ejpam-3637	78	34	of	of	ADP
ejpam-3637	78	35	g.	g.	PROPN
ejpam-3637	78	36	for	for	ADP
ejpam-3637	78	37	t1	t1	PROPN
ejpam-3637	78	38	∈	∈	PROPN
ejpam-3637	78	39	t	t	PROPN
ejpam-3637	78	40	,	,	PUNCT
ejpam-3637	78	41	lt1(s	lt1(s	PROPN
ejpam-3637	78	42	)	)	PUNCT
ejpam-3637	79	1	=	=	SYM
ejpam-3637	79	2	t1	t1	NOUN
ejpam-3637	79	3	∗	∗	NOUN
ejpam-3637	79	4	s.	s.	PROPN
ejpam-3637	79	5	let	let	VERB
ejpam-3637	79	6	{	{	PUNCT
ejpam-3637	79	7	aλ	aλ	PROPN
ejpam-3637	79	8	,	,	PUNCT
ejpam-3637	79	9	λ	λ	PROPN
ejpam-3637	79	10	∈	∈	PROPN
ejpam-3637	79	11	ω	ω	PROPN
ejpam-3637	79	12	}	}	PUNCT
ejpam-3637	79	13	be	be	AUX
ejpam-3637	79	14	an	an	DET
ejpam-3637	79	15	open	open	ADJ
ejpam-3637	79	16	(	(	PUNCT
ejpam-3637	79	17	countably	countably	ADV
ejpam-3637	79	18	open	open	ADJ
ejpam-3637	79	19	)	)	PUNCT
ejpam-3637	79	20	cover	cover	NOUN
ejpam-3637	79	21	of	of	ADP
ejpam-3637	79	22	t1	t1	PROPN
ejpam-3637	79	23	∗	∗	NOUN
ejpam-3637	79	24	s.	s.	PROPN
ejpam-3637	80	1	then	then	ADV
ejpam-3637	80	2	{	{	PUNCT
ejpam-3637	80	3	lt−1	lt−1	PROPN
ejpam-3637	80	4	1	1	NUM
ejpam-3637	80	5	(	(	PUNCT
ejpam-3637	80	6	aλ	aλ	PROPN
ejpam-3637	80	7	)	)	PUNCT
ejpam-3637	80	8	,	,	PUNCT
ejpam-3637	80	9	λ	λ	PROPN
ejpam-3637	80	10	∈	∈	PROPN
ejpam-3637	80	11	ω	ω	PROPN
ejpam-3637	80	12	}	}	PUNCT
ejpam-3637	80	13	is	be	AUX
ejpam-3637	80	14	an	an	DET
ejpam-3637	80	15	open	open	ADJ
ejpam-3637	80	16	(	(	PUNCT
ejpam-3637	80	17	countably	countably	ADV
ejpam-3637	80	18	open	open	ADJ
ejpam-3637	80	19	)	)	PUNCT
ejpam-3637	80	20	cover	cover	NOUN
ejpam-3637	80	21	of	of	ADP
ejpam-3637	80	22	s.	s.	PROPN
ejpam-3637	80	23	so	so	ADV
ejpam-3637	80	24	,	,	PUNCT
ejpam-3637	80	25	there	there	PRON
ejpam-3637	80	26	is	be	VERB
ejpam-3637	80	27	a	a	DET
ejpam-3637	80	28	locally	locally	ADV
ejpam-3637	80	29	finite	finite	ADJ
ejpam-3637	80	30	refinement	refinement	NOUN
ejpam-3637	80	31	{	{	PUNCT
ejpam-3637	80	32	lt−1	lt−1	PROPN
ejpam-3637	80	33	1	1	NUM
ejpam-3637	80	34	(	(	PUNCT
ejpam-3637	80	35	a∗λ	a∗λ	NUM
ejpam-3637	80	36	)	)	PUNCT
ejpam-3637	80	37	,	,	PUNCT
ejpam-3637	80	38	λ	λ	PROPN
ejpam-3637	80	39	∈	∈	PROPN
ejpam-3637	80	40	ω∗	ω∗	NOUN
ejpam-3637	80	41	}	}	PUNCT
ejpam-3637	80	42	of	of	ADP
ejpam-3637	80	43	s.	s.	PROPN
ejpam-3637	80	44	therefore	therefore	ADV
ejpam-3637	80	45	,	,	PUNCT
ejpam-3637	80	46	{	{	PUNCT
ejpam-3637	80	47	a∗λ	a∗λ	NUM
ejpam-3637	80	48	,	,	PUNCT
ejpam-3637	80	49	λ	λ	PROPN
ejpam-3637	80	50	∈	∈	PROPN
ejpam-3637	80	51	ω∗	ω∗	NOUN
ejpam-3637	80	52	}	}	PUNCT
ejpam-3637	80	53	is	be	AUX
ejpam-3637	80	54	locally	locally	ADV
ejpam-3637	80	55	finite	finite	ADJ
ejpam-3637	80	56	refinement	refinement	NOUN
ejpam-3637	80	57	of	of	ADP
ejpam-3637	80	58	t1	t1	PROPN
ejpam-3637	80	59	∗	∗	NOUN
ejpam-3637	80	60	s.	s.	PROPN
ejpam-3637	80	61	hence	hence	ADV
ejpam-3637	80	62	,	,	PUNCT
ejpam-3637	80	63	t1	t1	PROPN
ejpam-3637	80	64	∗	∗	NOUN
ejpam-3637	80	65	s	s	PART
ejpam-3637	80	66	is	be	AUX
ejpam-3637	80	67	a	a	DET
ejpam-3637	80	68	-	-	PUNCT
ejpam-3637	80	69	paracompact	paracompact	ADJ
ejpam-3637	80	70	.	.	PUNCT
ejpam-3637	81	1	let	let	VERB
ejpam-3637	81	2	ω	ω	PRON
ejpam-3637	81	3	be	be	AUX
ejpam-3637	81	4	an	an	DET
ejpam-3637	81	5	open	open	ADJ
ejpam-3637	81	6	(	(	PUNCT
ejpam-3637	81	7	countably	countably	ADV
ejpam-3637	81	8	open	open	ADJ
ejpam-3637	81	9	)	)	PUNCT
ejpam-3637	81	10	cover	cover	NOUN
ejpam-3637	81	11	of	of	ADP
ejpam-3637	81	12	ts	ts	NOUN
ejpam-3637	81	13	=	=	PUNCT
ejpam-3637	81	14	∪ti∈t	∪ti∈t	PROPN
ejpam-3637	81	15	ti	ti	NOUN
ejpam-3637	81	16	∗	∗	X
ejpam-3637	81	17	s	s	PROPN
ejpam-3637	81	18	,	,	PUNCT
ejpam-3637	81	19	then	then	ADV
ejpam-3637	81	20	there	there	PRON
ejpam-3637	81	21	is	be	VERB
ejpam-3637	81	22	an	an	DET
ejpam-3637	81	23	open	open	ADJ
ejpam-3637	81	24	(	(	PUNCT
ejpam-3637	81	25	countably	countably	ADV
ejpam-3637	81	26	open	open	ADJ
ejpam-3637	81	27	)	)	PUNCT
ejpam-3637	81	28	cover	cover	NOUN
ejpam-3637	81	29	ω1	ω1	PROPN
ejpam-3637	81	30	⊆	⊆	NUM
ejpam-3637	81	31	ω	ω	NOUN
ejpam-3637	81	32	of	of	ADP
ejpam-3637	81	33	t1	t1	PROPN
ejpam-3637	81	34	∗	∗	NOUN
ejpam-3637	81	35	s.	s.	PROPN
ejpam-3637	82	1	so	so	ADV
ejpam-3637	82	2	,	,	PUNCT
ejpam-3637	82	3	there	there	PRON
ejpam-3637	82	4	exists	exist	VERB
ejpam-3637	82	5	a	a	DET
ejpam-3637	82	6	locally	locally	ADV
ejpam-3637	82	7	finite	finite	ADJ
ejpam-3637	82	8	refinement	refinement	NOUN
ejpam-3637	82	9	ω∗1	ω∗1	PROPN
ejpam-3637	82	10	of	of	ADP
ejpam-3637	82	11	ω1	ω1	PROPN
ejpam-3637	82	12	.	.	PUNCT
ejpam-3637	83	1	therefore	therefore	ADV
ejpam-3637	83	2	,	,	PUNCT
ejpam-3637	83	3	ω∗	ω∗	NOUN
ejpam-3637	83	4	=	=	NOUN
ejpam-3637	83	5	∪{ω∗i	∪{ω∗i	NOUN
ejpam-3637	83	6	,	,	PUNCT
ejpam-3637	83	7	i	i	PRON
ejpam-3637	83	8	=	=	NOUN
ejpam-3637	83	9	1	1	NUM
ejpam-3637	83	10	,	,	PUNCT
ejpam-3637	83	11	2	2	NUM
ejpam-3637	83	12	,	,	PUNCT
ejpam-3637	83	13	...	...	PUNCT
ejpam-3637	83	14	,	,	PUNCT
ejpam-3637	83	15	|t	|t	VERB
ejpam-3637	83	16	|	|	ADV
ejpam-3637	83	17	}	}	PUNCT
ejpam-3637	83	18	is	be	AUX
ejpam-3637	83	19	locally	locally	ADV
ejpam-3637	83	20	finite	finite	ADJ
ejpam-3637	83	21	refinement	refinement	NOUN
ejpam-3637	83	22	of	of	ADP
ejpam-3637	83	23	ts	ts	PROPN
ejpam-3637	83	24	.	.	PUNCT
ejpam-3637	83	25	theorem	theorem	NOUN
ejpam-3637	83	26	3	3	X
ejpam-3637	83	27	.	.	PUNCT
ejpam-3637	84	1	let	let	VERB
ejpam-3637	84	2	h	h	PRON
ejpam-3637	84	3	be	be	AUX
ejpam-3637	84	4	a	a	DET
ejpam-3637	84	5	hausdorff	hausdorff	NOUN
ejpam-3637	84	6	paracompact	paracompact	NOUN
ejpam-3637	84	7	subset	subset	NOUN
ejpam-3637	84	8	of	of	ADP
ejpam-3637	84	9	a	a	DET
ejpam-3637	84	10	semi	semi	ADJ
ejpam-3637	84	11	topological	topological	ADJ
ejpam-3637	84	12	group	group	NOUN
ejpam-3637	84	13	(	(	PUNCT
ejpam-3637	84	14	g	g	PROPN
ejpam-3637	84	15	,	,	PUNCT
ejpam-3637	84	16	∗	∗	NOUN
ejpam-3637	84	17	,	,	PUNCT
ejpam-3637	84	18	τ	τ	PROPN
ejpam-3637	84	19	)	)	PUNCT
ejpam-3637	84	20	,	,	PUNCT
ejpam-3637	84	21	then	then	ADV
ejpam-3637	84	22	each	each	DET
ejpam-3637	84	23	right	right	NOUN
ejpam-3637	84	24	or	or	CCONJ
ejpam-3637	84	25	left	leave	VERB
ejpam-3637	84	26	coset	coset	NOUN
ejpam-3637	84	27	of	of	ADP
ejpam-3637	84	28	h	h	NOUN
ejpam-3637	84	29	is	be	AUX
ejpam-3637	84	30	a	a	DET
ejpam-3637	84	31	normal	normal	ADJ
ejpam-3637	84	32	space	space	NOUN
ejpam-3637	84	33	if	if	SCONJ
ejpam-3637	84	34	and	and	CCONJ
ejpam-3637	84	35	only	only	ADV
ejpam-3637	84	36	if	if	SCONJ
ejpam-3637	84	37	each	each	DET
ejpam-3637	84	38	pair	pair	NOUN
ejpam-3637	84	39	of	of	ADP
ejpam-3637	84	40	closed	closed	ADJ
ejpam-3637	84	41	disjoint	disjoint	PROPN
ejpam-3637	84	42	singleton	singleton	PROPN
ejpam-3637	84	43	subsets	subset	NOUN
ejpam-3637	84	44	of	of	ADP
ejpam-3637	84	45	a	a	DET
ejpam-3637	84	46	coset	coset	NOUN
ejpam-3637	84	47	can	can	AUX
ejpam-3637	84	48	be	be	AUX
ejpam-3637	84	49	separated	separate	VERB
ejpam-3637	84	50	by	by	ADP
ejpam-3637	84	51	its	its	PRON
ejpam-3637	84	52	open	open	ADJ
ejpam-3637	84	53	sets	set	NOUN
ejpam-3637	84	54	.	.	PUNCT
ejpam-3637	85	1	proof	proof	NOUN
ejpam-3637	85	2	.	.	PUNCT
ejpam-3637	86	1	for	for	ADP
ejpam-3637	86	2	g	g	PROPN
ejpam-3637	86	3	∈	∈	PROPN
ejpam-3637	86	4	g	g	NOUN
ejpam-3637	86	5	,	,	PUNCT
ejpam-3637	86	6	let	let	VERB
ejpam-3637	86	7	f1	f1	NOUN
ejpam-3637	86	8	and	and	CCONJ
ejpam-3637	86	9	f2	f2	PROPN
ejpam-3637	86	10	be	be	VERB
ejpam-3637	86	11	a	a	DET
ejpam-3637	86	12	pair	pair	NOUN
ejpam-3637	86	13	of	of	ADP
ejpam-3637	86	14	disjoint	disjoint	PROPN
ejpam-3637	86	15	singleton	singleton	PROPN
ejpam-3637	86	16	closed	close	VERB
ejpam-3637	86	17	subsets	subset	NOUN
ejpam-3637	86	18	and	and	CCONJ
ejpam-3637	86	19	m1	m1	PROPN
ejpam-3637	86	20	is	be	AUX
ejpam-3637	86	21	an	an	DET
ejpam-3637	86	22	open	open	ADJ
ejpam-3637	86	23	set	set	NOUN
ejpam-3637	86	24	of	of	ADP
ejpam-3637	86	25	a	a	DET
ejpam-3637	86	26	coset	coset	NOUN
ejpam-3637	86	27	gh	gh	PROPN
ejpam-3637	86	28	of	of	ADP
ejpam-3637	86	29	a	a	DET
ejpam-3637	86	30	set	set	NOUN
ejpam-3637	86	31	h	h	NOUN
ejpam-3637	86	32	⊆	⊆	NUM
ejpam-3637	86	33	g.	g.	NOUN
ejpam-3637	86	34	as	as	SCONJ
ejpam-3637	86	35	the	the	DET
ejpam-3637	86	36	set	set	NOUN
ejpam-3637	86	37	u	u	NOUN
ejpam-3637	86	38	=	=	PUNCT
ejpam-3637	86	39	{	{	PUNCT
ejpam-3637	86	40	h|lg(h	h|lg(h	ADJ
ejpam-3637	86	41	)	)	PUNCT
ejpam-3637	86	42	∩	∩	ADJ
ejpam-3637	86	43	f1	f1	NOUN
ejpam-3637	86	44	⊆	⊆	NUM
ejpam-3637	86	45	m1	m1	NOUN
ejpam-3637	86	46	}	}	PUNCT
ejpam-3637	86	47	is	be	AUX
ejpam-3637	86	48	open	open	ADJ
ejpam-3637	86	49	in	in	ADP
ejpam-3637	86	50	h.	h.	PROPN
ejpam-3637	86	51	let	let	VERB
ejpam-3637	87	1	w1	w1	NOUN
ejpam-3637	87	2	=	=	PUNCT
ejpam-3637	87	3	h	h	NOUN
ejpam-3637	87	4	\	\	NOUN
ejpam-3637	88	1	l−1	l−1	PROPN
ejpam-3637	88	2	g	g	PROPN
ejpam-3637	88	3	(	(	PUNCT
ejpam-3637	88	4	f1	f1	PROPN
ejpam-3637	88	5	∩	∩	NOUN
ejpam-3637	88	6	(	(	PUNCT
ejpam-3637	88	7	gh	gh	PROPN
ejpam-3637	88	8	\m1	\m1	PROPN
ejpam-3637	88	9	)	)	PUNCT
ejpam-3637	88	10	)	)	PUNCT
ejpam-3637	88	11	and	and	CCONJ
ejpam-3637	88	12	h∗	h∗	PROPN
ejpam-3637	88	13	be	be	AUX
ejpam-3637	88	14	an	an	DET
ejpam-3637	88	15	arbitrary	arbitrary	ADJ
ejpam-3637	88	16	point	point	NOUN
ejpam-3637	88	17	such	such	ADJ
ejpam-3637	88	18	that	that	SCONJ
ejpam-3637	88	19	lg(h	lg(h	NUM
ejpam-3637	88	20	∗	∗	NOUN
ejpam-3637	88	21	)	)	PUNCT
ejpam-3637	88	22	∩	∩	ADJ
ejpam-3637	88	23	f1	f1	NOUN
ejpam-3637	88	24	⊆	⊆	NUM
ejpam-3637	88	25	m1	m1	NOUN
ejpam-3637	88	26	,	,	PUNCT
ejpam-3637	88	27	then	then	ADV
ejpam-3637	88	28	w1	w1	NOUN
ejpam-3637	88	29	is	be	AUX
ejpam-3637	88	30	open	open	ADJ
ejpam-3637	88	31	in	in	ADP
ejpam-3637	88	32	h	h	NOUN
ejpam-3637	88	33	and	and	CCONJ
ejpam-3637	88	34	h∗	h∗	PROPN
ejpam-3637	88	35	∈	∈	PROPN
ejpam-3637	88	36	w1	w1	NOUN
ejpam-3637	88	37	,	,	PUNCT
ejpam-3637	88	38	(	(	PUNCT
ejpam-3637	88	39	lg(w1	lg(w1	NOUN
ejpam-3637	88	40	)	)	PUNCT
ejpam-3637	88	41	∩	∩	ADJ
ejpam-3637	88	42	f1	f1	NOUN
ejpam-3637	88	43	)	)	PUNCT
ejpam-3637	88	44	∩	∩	NOUN
ejpam-3637	88	45	(	(	PUNCT
ejpam-3637	88	46	gh	gh	PROPN
ejpam-3637	88	47	\m1	\m1	PROPN
ejpam-3637	88	48	)	)	PUNCT
ejpam-3637	88	49	=	=	PUNCT
ejpam-3637	89	1	φ	φ	PROPN
ejpam-3637	89	2	.	.	PUNCT
ejpam-3637	90	1	hence	hence	ADV
ejpam-3637	90	2	,	,	PUNCT
ejpam-3637	90	3	lg(w1)∩f1	lg(w1)∩f1	PROPN
ejpam-3637	90	4	⊆m1	⊆m1	PRON
ejpam-3637	90	5	.	.	PUNCT
ejpam-3637	91	1	thus	thus	ADV
ejpam-3637	91	2	,	,	PUNCT
ejpam-3637	91	3	the	the	DET
ejpam-3637	91	4	set	set	NOUN
ejpam-3637	91	5	u	u	NOUN
ejpam-3637	91	6	is	be	AUX
ejpam-3637	91	7	open	open	ADJ
ejpam-3637	91	8	in	in	ADP
ejpam-3637	91	9	h.	h.	PROPN
ejpam-3637	91	10	moreover	moreover	ADV
ejpam-3637	91	11	,	,	PUNCT
ejpam-3637	91	12	um1	um1	PROPN
ejpam-3637	91	13	=	=	PRON
ejpam-3637	91	14	{	{	PUNCT
ejpam-3637	91	15	h|lg(h)∩f1	h|lg(h)∩f1	PROPN
ejpam-3637	91	16	⊆	⊆	NUM
ejpam-3637	91	17	m1	m1	NOUN
ejpam-3637	91	18	,	,	PUNCT
ejpam-3637	91	19	lg(h)∩f2	lg(h)∩f2	PROPN
ejpam-3637	91	20	⊆	⊆	NUM
ejpam-3637	91	21	gh	gh	PROPN
ejpam-3637	91	22	\cl(m1	\cl(m1	PROPN
ejpam-3637	91	23	)	)	PUNCT
ejpam-3637	91	24	}	}	PUNCT
ejpam-3637	91	25	is	be	AUX
ejpam-3637	91	26	open	open	ADJ
ejpam-3637	91	27	in	in	ADP
ejpam-3637	91	28	h.	h.	PROPN
ejpam-3637	91	29	for	for	ADP
ejpam-3637	91	30	each	each	DET
ejpam-3637	91	31	h∗	h∗	PROPN
ejpam-3637	91	32	∈	∈	PROPN
ejpam-3637	91	33	h	h	NOUN
ejpam-3637	91	34	,	,	PUNCT
ejpam-3637	91	35	lg(h	lg(h	NOUN
ejpam-3637	91	36	∗)∩f1	∗)∩f1	NUM
ejpam-3637	91	37	and	and	CCONJ
ejpam-3637	91	38	lg(h	lg(h	ADV
ejpam-3637	91	39	∗)∩f2	∗)∩f2	NOUN
ejpam-3637	91	40	are	be	AUX
ejpam-3637	91	41	closed	closed	ADJ
ejpam-3637	91	42	and	and	CCONJ
ejpam-3637	91	43	disjoint	disjoint	NOUN
ejpam-3637	91	44	sets	set	NOUN
ejpam-3637	91	45	of	of	ADP
ejpam-3637	91	46	lg(h	lg(h	NUM
ejpam-3637	91	47	∗	∗	NOUN
ejpam-3637	91	48	)	)	PUNCT
ejpam-3637	91	49	.	.	PUNCT
ejpam-3637	92	1	therefore	therefore	ADV
ejpam-3637	92	2	,	,	PUNCT
ejpam-3637	92	3	there	there	PRON
ejpam-3637	92	4	exists	exist	VERB
ejpam-3637	92	5	two	two	NUM
ejpam-3637	92	6	open	open	ADJ
ejpam-3637	92	7	sets	set	NOUN
ejpam-3637	92	8	m∗1	m∗1	ADJ
ejpam-3637	92	9	and	and	CCONJ
ejpam-3637	92	10	m∗2	m∗2	NOUN
ejpam-3637	92	11	of	of	ADP
ejpam-3637	92	12	gh	gh	PROPN
ejpam-3637	92	13	such	such	ADJ
ejpam-3637	92	14	that	that	SCONJ
ejpam-3637	92	15	lg(h	lg(h	NUM
ejpam-3637	92	16	∗)∩f1	∗)∩f1	PROPN
ejpam-3637	92	17	⊆m∗1	⊆m∗1	ADV
ejpam-3637	92	18	,	,	PUNCT
ejpam-3637	92	19	lg(h	lg(h	X
ejpam-3637	92	20	∗)∩f2	∗)∩f2	ADP
ejpam-3637	92	21	⊆m∗2	⊆m∗2	NOUN
ejpam-3637	92	22	and	and	CCONJ
ejpam-3637	92	23	m∗1	m∗1	ADJ
ejpam-3637	92	24	∩m∗2	∩m∗2	PUNCT
ejpam-3637	92	25	=	=	SYM
ejpam-3637	92	26	φ	φ	PROPN
ejpam-3637	92	27	.	.	PUNCT
ejpam-3637	93	1	as	as	ADP
ejpam-3637	93	2	cl(m∗1	cl(m∗1	NOUN
ejpam-3637	93	3	)	)	PUNCT
ejpam-3637	93	4	∩m∗2	∩m∗2	PROPN
ejpam-3637	93	5	=	=	SYM
ejpam-3637	93	6	φ	φ	PROPN
ejpam-3637	93	7	,	,	PUNCT
ejpam-3637	93	8	m∗2	m∗2	PROPN
ejpam-3637	93	9	contained	contain	VERB
ejpam-3637	93	10	in	in	ADP
ejpam-3637	93	11	complement	complement	NOUN
ejpam-3637	93	12	of	of	ADP
ejpam-3637	93	13	closure	closure	NOUN
ejpam-3637	93	14	of	of	ADP
ejpam-3637	93	15	m∗1	m∗1	PROPN
ejpam-3637	93	16	in	in	ADP
ejpam-3637	93	17	gh	gh	PROPN
ejpam-3637	93	18	,	,	PUNCT
ejpam-3637	93	19	so	so	ADV
ejpam-3637	93	20	y∗	y∗	PROPN
ejpam-3637	93	21	∈	∈	PROPN
ejpam-3637	93	22	u∗m1	u∗m1	X
ejpam-3637	93	23	.	.	PUNCT
ejpam-3637	94	1	hence	hence	ADV
ejpam-3637	94	2	,	,	PUNCT
ejpam-3637	94	3	{	{	PUNCT
ejpam-3637	94	4	um1	um1	X
ejpam-3637	94	5	}	}	PUNCT
ejpam-3637	94	6	for	for	ADP
ejpam-3637	94	7	all	all	DET
ejpam-3637	94	8	open	open	ADJ
ejpam-3637	94	9	sets	set	NOUN
ejpam-3637	94	10	m1	m1	PROPN
ejpam-3637	94	11	of	of	ADP
ejpam-3637	94	12	gh	gh	PROPN
ejpam-3637	94	13	is	be	AUX
ejpam-3637	94	14	open	open	ADJ
ejpam-3637	94	15	cover	cover	NOUN
ejpam-3637	94	16	of	of	ADP
ejpam-3637	94	17	h.	h.	PROPN
ejpam-3637	94	18	thus	thus	ADV
ejpam-3637	94	19	,	,	PUNCT
ejpam-3637	94	20	there	there	PRON
ejpam-3637	94	21	exists	exist	VERB
ejpam-3637	94	22	an	an	DET
ejpam-3637	94	23	open	open	ADJ
ejpam-3637	94	24	locally	locally	ADV
ejpam-3637	94	25	finite	finite	ADJ
ejpam-3637	94	26	refinements	refinement	NOUN
ejpam-3637	94	27	{	{	PUNCT
ejpam-3637	94	28	wm1	wm1	NOUN
ejpam-3637	94	29	|m1	|m1	NOUN
ejpam-3637	94	30	∈	∈	PROPN
ejpam-3637	94	31	ω	ω	PROPN
ejpam-3637	94	32	}	}	PUNCT
ejpam-3637	94	33	,	,	PUNCT
ejpam-3637	94	34	ω	ω	PROPN
ejpam-3637	94	35	is	be	AUX
ejpam-3637	94	36	collection	collection	NOUN
ejpam-3637	94	37	of	of	ADP
ejpam-3637	94	38	open	open	ADJ
ejpam-3637	94	39	sets	set	NOUN
ejpam-3637	94	40	of	of	ADP
ejpam-3637	94	41	gh	gh	PROPN
ejpam-3637	95	1	such	such	ADJ
ejpam-3637	95	2	that	that	SCONJ
ejpam-3637	95	3	cl(wm1	cl(wm1	NUM
ejpam-3637	95	4	)	)	PUNCT
ejpam-3637	95	5	⊆	⊆	NUM
ejpam-3637	95	6	um1	um1	PROPN
ejpam-3637	95	7	m.	m.	PROPN
ejpam-3637	95	8	k.	k.	PROPN
ejpam-3637	96	1	maqbool	maqbool	PROPN
ejpam-3637	96	2	et	et	PROPN
ejpam-3637	97	1	al	al	PROPN
ejpam-3637	97	2	.	.	PUNCT
ejpam-3637	97	3	/	/	SYM
ejpam-3637	97	4	eur	eur	PROPN
ejpam-3637	97	5	.	.	PUNCT
ejpam-3637	98	1	j.	j.	PROPN
ejpam-3637	98	2	pure	pure	PROPN
ejpam-3637	98	3	appl	appl	PROPN
ejpam-3637	98	4	.	.	PROPN
ejpam-3637	98	5	math	math	PROPN
ejpam-3637	98	6	,	,	PUNCT
ejpam-3637	98	7	13	13	NUM
ejpam-3637	98	8	(	(	PUNCT
ejpam-3637	98	9	2	2	NUM
ejpam-3637	98	10	)	)	PUNCT
ejpam-3637	98	11	(	(	PUNCT
ejpam-3637	98	12	2020	2020	NUM
ejpam-3637	98	13	)	)	PUNCT
ejpam-3637	98	14	,	,	PUNCT
ejpam-3637	98	15	280	280	NUM
ejpam-3637	98	16	-	-	SYM
ejpam-3637	98	17	286	286	NUM
ejpam-3637	98	18	283	283	NUM
ejpam-3637	98	19	for	for	ADP
ejpam-3637	98	20	each	each	DET
ejpam-3637	98	21	m1	m1	PROPN
ejpam-3637	98	22	∈	∈	PROPN
ejpam-3637	98	23	ω	ω	PROPN
ejpam-3637	98	24	.	.	PUNCT
ejpam-3637	98	25	suppose	suppose	VERB
ejpam-3637	98	26	,	,	PUNCT
ejpam-3637	98	27	m2	m2	PROPN
ejpam-3637	98	28	=	=	PUNCT
ejpam-3637	98	29	∪m1∈ω(lg(wm1	∪m1∈ω(lg(wm1	PROPN
ejpam-3637	98	30	)	)	PUNCT
ejpam-3637	98	31	∩m1	∩m1	NOUN
ejpam-3637	98	32	)	)	PUNCT
ejpam-3637	98	33	,	,	PUNCT
ejpam-3637	98	34	then	then	ADV
ejpam-3637	98	35	m2	m2	PROPN
ejpam-3637	98	36	is	be	AUX
ejpam-3637	98	37	open	open	ADJ
ejpam-3637	98	38	in	in	ADP
ejpam-3637	98	39	gh	gh	PROPN
ejpam-3637	98	40	and	and	CCONJ
ejpam-3637	98	41	{	{	PUNCT
ejpam-3637	98	42	lg((wm1	lg((wm1	NOUN
ejpam-3637	98	43	)	)	PUNCT
ejpam-3637	98	44	∩m1),m1	∩m1),m1	PROPN
ejpam-3637	98	45	∈	∈	PROPN
ejpam-3637	98	46	ω	ω	PROPN
ejpam-3637	98	47	}	}	PUNCT
ejpam-3637	98	48	is	be	AUX
ejpam-3637	98	49	locally	locally	ADV
ejpam-3637	98	50	finite	finite	ADJ
ejpam-3637	98	51	.	.	PUNCT
ejpam-3637	99	1	therefore	therefore	ADV
ejpam-3637	99	2	,	,	PUNCT
ejpam-3637	99	3	cl(m2	cl(m2	NOUN
ejpam-3637	99	4	)	)	PUNCT
ejpam-3637	99	5	=	=	SYM
ejpam-3637	99	6	∪m1∈ω(cl(lg(wm1	∪m1∈ω(cl(lg(wm1	ADJ
ejpam-3637	99	7	)	)	PUNCT
ejpam-3637	99	8	∩	∩	ADJ
ejpam-3637	99	9	m1	m1	NOUN
ejpam-3637	99	10	)	)	PUNCT
ejpam-3637	99	11	)	)	PUNCT
ejpam-3637	100	1	⊆	⊆	NUM
ejpam-3637	100	2	∪m1∈ω(lg(cl(wm1	∪m1∈ω(lg(cl(wm1	ADJ
ejpam-3637	100	3	)	)	PUNCT
ejpam-3637	100	4	)	)	PUNCT
ejpam-3637	100	5	∩	∩	NOUN
ejpam-3637	100	6	cl(m1	cl(m1	NOUN
ejpam-3637	100	7	)	)	PUNCT
ejpam-3637	100	8	)	)	PUNCT
ejpam-3637	100	9	.	.	PUNCT
ejpam-3637	101	1	also	also	ADV
ejpam-3637	101	2	,	,	PUNCT
ejpam-3637	101	3	as	as	ADP
ejpam-3637	101	4	lg(wm1	lg(wm1	ADJ
ejpam-3637	101	5	)	)	PUNCT
ejpam-3637	101	6	∩	∩	ADJ
ejpam-3637	101	7	f1	f1	NOUN
ejpam-3637	101	8	⊆	⊆	NUM
ejpam-3637	101	9	lg(um1	lg(um1	PROPN
ejpam-3637	101	10	)	)	PUNCT
ejpam-3637	101	11	∩	∩	ADJ
ejpam-3637	101	12	f1	f1	NOUN
ejpam-3637	101	13	⊆	⊆	NUM
ejpam-3637	101	14	m1	m1	NOUN
ejpam-3637	101	15	,	,	PUNCT
ejpam-3637	101	16	we	we	PRON
ejpam-3637	101	17	have	have	VERB
ejpam-3637	101	18	lg(wm1	lg(wm1	VERB
ejpam-3637	101	19	)	)	PUNCT
ejpam-3637	101	20	∩	∩	NOUN
ejpam-3637	101	21	f1	f1	NOUN
ejpam-3637	101	22	⊆	⊆	NUM
ejpam-3637	101	23	lg(wm1	lg(wm1	ADJ
ejpam-3637	101	24	)	)	PUNCT
ejpam-3637	101	25	∩m1	∩m1	PROPN
ejpam-3637	102	1	⊆	⊆	NUM
ejpam-3637	102	2	m2	m2	PROPN
ejpam-3637	102	3	.	.	PUNCT
ejpam-3637	103	1	as	as	SCONJ
ejpam-3637	103	2	{	{	PUNCT
ejpam-3637	103	3	lg(wm1)|m1	lg(wm1)|m1	PROPN
ejpam-3637	103	4	∈	∈	PROPN
ejpam-3637	103	5	ω	ω	PROPN
ejpam-3637	103	6	}	}	PUNCT
ejpam-3637	103	7	is	be	AUX
ejpam-3637	103	8	cover	cover	NOUN
ejpam-3637	103	9	of	of	ADP
ejpam-3637	103	10	gh	gh	PROPN
ejpam-3637	103	11	,	,	PUNCT
ejpam-3637	103	12	so	so	ADV
ejpam-3637	103	13	f1	f1	PROPN
ejpam-3637	103	14	⊆	⊆	NUM
ejpam-3637	103	15	m2	m2	PROPN
ejpam-3637	103	16	.	.	PUNCT
ejpam-3637	104	1	moreover	moreover	ADV
ejpam-3637	104	2	,	,	PUNCT
ejpam-3637	104	3	(	(	PUNCT
ejpam-3637	104	4	lg(cl(wm1	lg(cl(wm1	NOUN
ejpam-3637	104	5	)	)	PUNCT
ejpam-3637	104	6	)	)	PUNCT
ejpam-3637	104	7	∩	∩	NOUN
ejpam-3637	104	8	f2	f2	PROPN
ejpam-3637	104	9	)	)	PUNCT
ejpam-3637	104	10	∩	∩	NOUN
ejpam-3637	104	11	cl(m1	cl(m1	NOUN
ejpam-3637	104	12	)	)	PUNCT
ejpam-3637	104	13	⊆	⊆	NUM
ejpam-3637	104	14	(	(	PUNCT
ejpam-3637	104	15	lg(um1	lg(um1	PROPN
ejpam-3637	104	16	)	)	PUNCT
ejpam-3637	104	17	∩	∩	ADJ
ejpam-3637	104	18	f2	f2	PROPN
ejpam-3637	104	19	)	)	PUNCT
ejpam-3637	104	20	∩	∩	NOUN
ejpam-3637	104	21	cl(m1	cl(m1	NOUN
ejpam-3637	104	22	)	)	PUNCT
ejpam-3637	104	23	⊆	⊆	NUM
ejpam-3637	104	24	(	(	PUNCT
ejpam-3637	104	25	gh\cl(m1))∩cl(m1	gh\cl(m1))∩cl(m1	NOUN
ejpam-3637	104	26	)	)	PUNCT
ejpam-3637	104	27	=	=	SYM
ejpam-3637	105	1	φ	φ	PROPN
ejpam-3637	105	2	.	.	PUNCT
ejpam-3637	106	1	then	then	ADV
ejpam-3637	106	2	f2∩cl(m2	f2∩cl(m2	NOUN
ejpam-3637	106	3	)	)	PUNCT
ejpam-3637	106	4	=	=	SYM
ejpam-3637	107	1	φ	φ	PROPN
ejpam-3637	107	2	.	.	PUNCT
ejpam-3637	108	1	f2	f2	PROPN
ejpam-3637	108	2	contained	contain	VERB
ejpam-3637	108	3	in	in	ADP
ejpam-3637	108	4	open	open	ADJ
ejpam-3637	108	5	set	set	NOUN
ejpam-3637	108	6	gh\cl(m2	gh\cl(m2	PROPN
ejpam-3637	108	7	)	)	PUNCT
ejpam-3637	108	8	.	.	PUNCT
ejpam-3637	109	1	thus	thus	ADV
ejpam-3637	109	2	,	,	PUNCT
ejpam-3637	109	3	open	open	ADJ
ejpam-3637	109	4	sets	set	VERB
ejpam-3637	109	5	m2	m2	PROPN
ejpam-3637	109	6	and	and	CCONJ
ejpam-3637	109	7	gh	gh	PROPN
ejpam-3637	109	8	\	\	PROPN
ejpam-3637	109	9	cl(m2	cl(m2	NOUN
ejpam-3637	109	10	)	)	PUNCT
ejpam-3637	109	11	separates	separate	VERB
ejpam-3637	109	12	f1	f1	NOUN
ejpam-3637	109	13	and	and	CCONJ
ejpam-3637	109	14	f2	f2	PROPN
ejpam-3637	109	15	.	.	PUNCT
ejpam-3637	110	1	hence	hence	ADV
ejpam-3637	110	2	,	,	PUNCT
ejpam-3637	110	3	any	any	DET
ejpam-3637	110	4	left	left	ADJ
ejpam-3637	110	5	coset	coset	NOUN
ejpam-3637	110	6	of	of	ADP
ejpam-3637	110	7	h	h	NOUN
ejpam-3637	110	8	is	be	AUX
ejpam-3637	110	9	normal	normal	ADJ
ejpam-3637	110	10	.	.	PUNCT
ejpam-3637	111	1	similarly	similarly	ADV
ejpam-3637	111	2	,	,	PUNCT
ejpam-3637	111	3	it	it	PRON
ejpam-3637	111	4	can	can	AUX
ejpam-3637	111	5	be	be	AUX
ejpam-3637	111	6	prove	prove	VERB
ejpam-3637	111	7	that	that	SCONJ
ejpam-3637	111	8	,	,	PUNCT
ejpam-3637	111	9	any	any	DET
ejpam-3637	111	10	right	right	ADJ
ejpam-3637	111	11	coset	coset	NOUN
ejpam-3637	111	12	of	of	ADP
ejpam-3637	111	13	h	h	NOUN
ejpam-3637	111	14	is	be	AUX
ejpam-3637	111	15	normal	normal	ADJ
ejpam-3637	111	16	.	.	PUNCT
ejpam-3637	112	1	conversely	conversely	ADV
ejpam-3637	112	2	,	,	PUNCT
ejpam-3637	112	3	if	if	SCONJ
ejpam-3637	112	4	any	any	DET
ejpam-3637	112	5	left	left	ADJ
ejpam-3637	112	6	or	or	CCONJ
ejpam-3637	112	7	right	right	ADJ
ejpam-3637	112	8	coset	coset	NOUN
ejpam-3637	112	9	of	of	ADP
ejpam-3637	112	10	h	h	NOUN
ejpam-3637	112	11	is	be	AUX
ejpam-3637	112	12	a	a	DET
ejpam-3637	112	13	normal	normal	ADJ
ejpam-3637	112	14	space	space	NOUN
ejpam-3637	112	15	,	,	PUNCT
ejpam-3637	112	16	then	then	ADV
ejpam-3637	112	17	each	each	DET
ejpam-3637	112	18	pair	pair	NOUN
ejpam-3637	112	19	of	of	ADP
ejpam-3637	112	20	disjoint	disjoint	PROPN
ejpam-3637	112	21	singleton	singleton	PROPN
ejpam-3637	112	22	closed	close	VERB
ejpam-3637	112	23	subsets	subset	NOUN
ejpam-3637	112	24	of	of	ADP
ejpam-3637	112	25	coset	coset	NOUN
ejpam-3637	112	26	can	can	AUX
ejpam-3637	112	27	be	be	AUX
ejpam-3637	112	28	separated	separate	VERB
ejpam-3637	112	29	by	by	ADP
ejpam-3637	112	30	its	its	PRON
ejpam-3637	112	31	open	open	ADJ
ejpam-3637	112	32	sets	set	NOUN
ejpam-3637	112	33	.	.	PUNCT
ejpam-3637	113	1	theorem	theorem	NOUN
ejpam-3637	113	2	4	4	NUM
ejpam-3637	113	3	.	.	PUNCT
ejpam-3637	113	4	topological	topological	ADJ
ejpam-3637	113	5	direct	direct	ADJ
ejpam-3637	113	6	product	product	NOUN
ejpam-3637	113	7	of	of	ADP
ejpam-3637	113	8	(	(	PUNCT
ejpam-3637	113	9	countably	countably	ADV
ejpam-3637	113	10	)	)	PUNCT
ejpam-3637	113	11	a	a	DET
ejpam-3637	113	12	-	-	PUNCT
ejpam-3637	113	13	paracompact	paracompact	ADJ
ejpam-3637	113	14	topological	topological	ADJ
ejpam-3637	113	15	group	group	NOUN
ejpam-3637	113	16	and	and	CCONJ
ejpam-3637	113	17	a	a	DET
ejpam-3637	113	18	compact	compact	ADJ
ejpam-3637	113	19	topological	topological	ADJ
ejpam-3637	113	20	group	group	NOUN
ejpam-3637	113	21	is	be	AUX
ejpam-3637	113	22	(	(	PUNCT
ejpam-3637	113	23	countably	countably	ADV
ejpam-3637	113	24	)	)	PUNCT
ejpam-3637	113	25	a	a	DET
ejpam-3637	113	26	-	-	PUNCT
ejpam-3637	113	27	paracompact	paracompact	ADJ
ejpam-3637	113	28	topological	topological	ADJ
ejpam-3637	113	29	group	group	NOUN
ejpam-3637	113	30	.	.	PUNCT
ejpam-3637	114	1	proof	proof	NOUN
ejpam-3637	114	2	.	.	PUNCT
ejpam-3637	115	1	suppose	suppose	VERB
ejpam-3637	115	2	that	that	SCONJ
ejpam-3637	115	3	x	x	PRON
ejpam-3637	115	4	is	be	AUX
ejpam-3637	115	5	a	a	DET
ejpam-3637	115	6	(	(	PUNCT
ejpam-3637	115	7	countably	countably	NOUN
ejpam-3637	115	8	)	)	PUNCT
ejpam-3637	115	9	a	a	DET
ejpam-3637	115	10	-	-	PUNCT
ejpam-3637	115	11	paracompact	paracompact	ADJ
ejpam-3637	115	12	topological	topological	ADJ
ejpam-3637	115	13	group	group	NOUN
ejpam-3637	115	14	and	and	CCONJ
ejpam-3637	115	15	y	y	PROPN
ejpam-3637	115	16	be	be	AUX
ejpam-3637	115	17	a	a	DET
ejpam-3637	115	18	compact	compact	ADJ
ejpam-3637	115	19	topological	topological	ADJ
ejpam-3637	115	20	group	group	NOUN
ejpam-3637	115	21	.	.	PUNCT
ejpam-3637	116	1	suppose	suppose	VERB
ejpam-3637	116	2	that	that	SCONJ
ejpam-3637	116	3	{	{	PUNCT
ejpam-3637	116	4	uj}(j	uj}(j	X
ejpam-3637	116	5	=	=	SYM
ejpam-3637	116	6	1	1	NUM
ejpam-3637	116	7	,	,	PUNCT
ejpam-3637	116	8	2	2	NUM
ejpam-3637	116	9	,	,	PUNCT
ejpam-3637	116	10	3	3	NUM
ejpam-3637	116	11	,	,	PUNCT
ejpam-3637	116	12	...	...	PUNCT
ejpam-3637	116	13	)	)	PUNCT
ejpam-3637	116	14	is	be	AUX
ejpam-3637	116	15	a	a	DET
ejpam-3637	116	16	(	(	PUNCT
ejpam-3637	116	17	countable	countable	ADJ
ejpam-3637	116	18	)	)	PUNCT
ejpam-3637	116	19	covering	covering	NOUN
ejpam-3637	116	20	of	of	ADP
ejpam-3637	116	21	x	x	PUNCT
ejpam-3637	116	22	×	×	PROPN
ejpam-3637	116	23	y	y	PROPN
ejpam-3637	116	24	.	.	PUNCT
ejpam-3637	117	1	let	let	VERB
ejpam-3637	117	2	vi	vi	PROPN
ejpam-3637	117	3	consists	consist	VERB
ejpam-3637	117	4	of	of	ADP
ejpam-3637	117	5	all	all	DET
ejpam-3637	117	6	points	point	NOUN
ejpam-3637	117	7	x	x	PUNCT
ejpam-3637	117	8	of	of	ADP
ejpam-3637	117	9	x	x	SYM
ejpam-3637	117	10	satisfying	satisfy	VERB
ejpam-3637	117	11	x	x	SYM
ejpam-3637	117	12	×	×	PROPN
ejpam-3637	117	13	y	y	NOUN
ejpam-3637	117	14	⊆	⊆	NUM
ejpam-3637	117	15	∪j≤iuj	∪j≤iuj	NOUN
ejpam-3637	117	16	.	.	PUNCT
ejpam-3637	118	1	if	if	SCONJ
ejpam-3637	118	2	x	x	PROPN
ejpam-3637	118	3	∈	∈	PROPN
ejpam-3637	118	4	vi	vi	PROPN
ejpam-3637	118	5	,	,	PUNCT
ejpam-3637	118	6	then	then	ADV
ejpam-3637	118	7	each	each	PRON
ejpam-3637	118	8	(	(	PUNCT
ejpam-3637	118	9	x	x	NOUN
ejpam-3637	118	10	,	,	PUNCT
ejpam-3637	118	11	y	y	NOUN
ejpam-3637	118	12	)	)	PUNCT
ejpam-3637	118	13	of	of	ADP
ejpam-3637	118	14	x	x	SYM
ejpam-3637	118	15	×	×	PROPN
ejpam-3637	118	16	y	y	PROPN
ejpam-3637	118	17	has	have	VERB
ejpam-3637	118	18	a	a	DET
ejpam-3637	118	19	neighbourhood	neighbourhood	NOUN
ejpam-3637	118	20	n	n	PRON
ejpam-3637	118	21	×m	×m	NOUN
ejpam-3637	118	22	contained	contain	VERB
ejpam-3637	118	23	in	in	ADP
ejpam-3637	118	24	open	open	ADJ
ejpam-3637	118	25	set	set	VERB
ejpam-3637	118	26	∪j≤iuj	∪j≤iuj	NOUN
ejpam-3637	118	27	.	.	PUNCT
ejpam-3637	119	1	these	these	DET
ejpam-3637	119	2	finite	finite	PROPN
ejpam-3637	119	3	open	open	ADJ
ejpam-3637	119	4	sets	set	NOUN
ejpam-3637	119	5	m	m	VERB
ejpam-3637	119	6	cover	cover	VERB
ejpam-3637	119	7	y	y	PROPN
ejpam-3637	119	8	.	.	PUNCT
ejpam-3637	120	1	let	let	VERB
ejpam-3637	120	2	nx	nx	NOUN
ejpam-3637	120	3	be	be	AUX
ejpam-3637	120	4	the	the	DET
ejpam-3637	120	5	intersection	intersection	NOUN
ejpam-3637	120	6	of	of	ADP
ejpam-3637	120	7	corresponding	corresponding	ADJ
ejpam-3637	120	8	sets	set	NOUN
ejpam-3637	120	9	n	n	ADV
ejpam-3637	120	10	.	.	PUNCT
ejpam-3637	121	1	then	then	ADV
ejpam-3637	121	2	x	x	SYM
ejpam-3637	121	3	∈	∈	PROPN
ejpam-3637	121	4	nx	nx	PROPN
ejpam-3637	121	5	,	,	PUNCT
ejpam-3637	121	6	nx	nx	PROPN
ejpam-3637	121	7	is	be	AUX
ejpam-3637	121	8	open	open	ADJ
ejpam-3637	121	9	and	and	CCONJ
ejpam-3637	121	10	nx	nx	NUM
ejpam-3637	121	11	×	×	NOUN
ejpam-3637	121	12	y	y	PROPN
ejpam-3637	121	13	⊆	⊆	NUM
ejpam-3637	121	14	∪j≤iuj	∪j≤iuj	NOUN
ejpam-3637	121	15	,	,	PUNCT
ejpam-3637	121	16	and	and	CCONJ
ejpam-3637	121	17	hence	hence	ADV
ejpam-3637	121	18	nx	nx	PROPN
ejpam-3637	121	19	⊆	⊆	NUM
ejpam-3637	121	20	vi	vi	NOUN
ejpam-3637	121	21	.	.	PUNCT
ejpam-3637	122	1	therefore	therefore	ADV
ejpam-3637	122	2	,	,	PUNCT
ejpam-3637	122	3	vi	vi	PROPN
ejpam-3637	122	4	is	be	AUX
ejpam-3637	122	5	open	open	ADJ
ejpam-3637	122	6	.	.	PUNCT
ejpam-3637	123	1	moreover	moreover	ADV
ejpam-3637	123	2	,	,	PUNCT
ejpam-3637	123	3	for	for	ADP
ejpam-3637	123	4	an	an	DET
ejpam-3637	123	5	arbitrary	arbitrary	ADJ
ejpam-3637	123	6	x	x	SYM
ejpam-3637	123	7	∈	∈	PROPN
ejpam-3637	123	8	x	x	NOUN
ejpam-3637	123	9	,	,	PUNCT
ejpam-3637	123	10	x	x	SYM
ejpam-3637	123	11	×	×	NOUN
ejpam-3637	123	12	y	y	PROPN
ejpam-3637	123	13	is	be	AUX
ejpam-3637	123	14	contained	contain	VERB
ejpam-3637	123	15	in	in	ADP
ejpam-3637	123	16	some	some	DET
ejpam-3637	123	17	finite	finite	ADJ
ejpam-3637	123	18	sets	set	NOUN
ejpam-3637	123	19	of	of	ADP
ejpam-3637	123	20	the	the	DET
ejpam-3637	123	21	covering	covering	NOUN
ejpam-3637	123	22	{	{	PUNCT
ejpam-3637	123	23	uj	uj	PROPN
ejpam-3637	123	24	}	}	PUNCT
ejpam-3637	123	25	,	,	PUNCT
ejpam-3637	123	26	because	because	SCONJ
ejpam-3637	123	27	x×y	x×y	PROPN
ejpam-3637	123	28	is	be	AUX
ejpam-3637	123	29	compact	compact	ADJ
ejpam-3637	123	30	.	.	PUNCT
ejpam-3637	124	1	therefore	therefore	ADV
ejpam-3637	124	2	,	,	PUNCT
ejpam-3637	124	3	x	x	PUNCT
ejpam-3637	124	4	is	be	AUX
ejpam-3637	124	5	in	in	ADP
ejpam-3637	124	6	some	some	DET
ejpam-3637	124	7	vi	vi	NOUN
ejpam-3637	124	8	.	.	PUNCT
ejpam-3637	125	1	thus	thus	ADV
ejpam-3637	125	2	,	,	PUNCT
ejpam-3637	125	3	{	{	PUNCT
ejpam-3637	125	4	vi	vi	NOUN
ejpam-3637	125	5	}	}	PUNCT
ejpam-3637	125	6	is	be	AUX
ejpam-3637	125	7	a	a	DET
ejpam-3637	125	8	covering	covering	NOUN
ejpam-3637	125	9	of	of	ADP
ejpam-3637	125	10	x.	x.	NOUN
ejpam-3637	125	11	as	as	ADP
ejpam-3637	125	12	{	{	PUNCT
ejpam-3637	125	13	vi	vi	NOUN
ejpam-3637	125	14	}	}	PUNCT
ejpam-3637	125	15	is	be	AUX
ejpam-3637	125	16	(	(	PUNCT
ejpam-3637	125	17	countable	countable	ADJ
ejpam-3637	125	18	)	)	PUNCT
ejpam-3637	125	19	open	open	ADJ
ejpam-3637	125	20	covering	covering	NOUN
ejpam-3637	125	21	and	and	CCONJ
ejpam-3637	125	22	x	x	X
ejpam-3637	125	23	is	be	AUX
ejpam-3637	125	24	(	(	PUNCT
ejpam-3637	125	25	countably	countably	ADV
ejpam-3637	125	26	)	)	PUNCT
ejpam-3637	125	27	a	a	DET
ejpam-3637	125	28	-	-	PUNCT
ejpam-3637	125	29	paracompact	paracompact	ADJ
ejpam-3637	125	30	,	,	PUNCT
ejpam-3637	125	31	{	{	PUNCT
ejpam-3637	125	32	vi	vi	NOUN
ejpam-3637	125	33	}	}	PUNCT
ejpam-3637	125	34	possess	possess	VERB
ejpam-3637	125	35	a	a	DET
ejpam-3637	125	36	locally	locally	ADV
ejpam-3637	125	37	finite	finite	PROPN
ejpam-3637	125	38	refinement	refinement	PROPN
ejpam-3637	125	39	b.	b.	PROPN
ejpam-3637	125	40	for	for	ADP
ejpam-3637	125	41	every	every	DET
ejpam-3637	125	42	w	w	PROPN
ejpam-3637	125	43	∈	∈	PROPN
ejpam-3637	125	44	b	b	PROPN
ejpam-3637	125	45	,	,	PUNCT
ejpam-3637	125	46	suppose	suppose	VERB
ejpam-3637	125	47	g(w	g(w	PROPN
ejpam-3637	125	48	)	)	PUNCT
ejpam-3637	125	49	is	be	AUX
ejpam-3637	125	50	the	the	DET
ejpam-3637	125	51	first	first	ADJ
ejpam-3637	125	52	vi	vi	PROPN
ejpam-3637	125	53	that	that	PRON
ejpam-3637	125	54	contain	contain	VERB
ejpam-3637	125	55	w	w	ADV
ejpam-3637	125	56	and	and	CCONJ
ejpam-3637	125	57	let	let	VERB
ejpam-3637	125	58	gi	gi	NOUN
ejpam-3637	125	59	is	be	AUX
ejpam-3637	125	60	the	the	DET
ejpam-3637	125	61	union	union	NOUN
ejpam-3637	125	62	of	of	ADP
ejpam-3637	125	63	all	all	DET
ejpam-3637	125	64	w	w	NOUN
ejpam-3637	125	65	for	for	ADP
ejpam-3637	125	66	which	which	PRON
ejpam-3637	126	1	g(w	g(w	ADJ
ejpam-3637	126	2	)	)	PUNCT
ejpam-3637	126	3	=	=	SYM
ejpam-3637	126	4	vi	vi	PROPN
ejpam-3637	126	5	.	.	PUNCT
ejpam-3637	126	6	then	then	ADV
ejpam-3637	126	7	gi	gi	VERB
ejpam-3637	126	8	⊆	⊆	NUM
ejpam-3637	126	9	vi	vi	NOUN
ejpam-3637	126	10	and	and	CCONJ
ejpam-3637	126	11	{	{	PUNCT
ejpam-3637	126	12	gi	gi	INTJ
ejpam-3637	126	13	}	}	PUNCT
ejpam-3637	126	14	is	be	AUX
ejpam-3637	126	15	locally	locally	ADV
ejpam-3637	126	16	finite	finite	ADJ
ejpam-3637	126	17	covering	covering	NOUN
ejpam-3637	126	18	of	of	ADP
ejpam-3637	126	19	x.	x.	NOUN
ejpam-3637	126	20	let	let	VERB
ejpam-3637	126	21	gij	gij	NOUN
ejpam-3637	126	22	=	=	VERB
ejpam-3637	126	23	(	(	PUNCT
ejpam-3637	126	24	gi	gi	INTJ
ejpam-3637	126	25	×	×	PROPN
ejpam-3637	126	26	y	y	PROPN
ejpam-3637	126	27	)	)	PUNCT
ejpam-3637	126	28	∩	∩	PROPN
ejpam-3637	126	29	uj	uj	PROPN
ejpam-3637	126	30	,	,	PUNCT
ejpam-3637	126	31	for	for	ADP
ejpam-3637	126	32	j	j	PROPN
ejpam-3637	126	33	≤	≤	PROPN
ejpam-3637	126	34	i.	i.	NOUN
ejpam-3637	126	35	if	if	SCONJ
ejpam-3637	126	36	(	(	PUNCT
ejpam-3637	126	37	x	x	NOUN
ejpam-3637	126	38	,	,	PUNCT
ejpam-3637	126	39	y	y	NOUN
ejpam-3637	126	40	)	)	PUNCT
ejpam-3637	126	41	is	be	AUX
ejpam-3637	126	42	an	an	DET
ejpam-3637	126	43	arbitrary	arbitrary	ADJ
ejpam-3637	126	44	point	point	NOUN
ejpam-3637	126	45	of	of	ADP
ejpam-3637	126	46	(	(	PUNCT
ejpam-3637	126	47	x	x	X
ejpam-3637	126	48	,	,	PUNCT
ejpam-3637	126	49	y	y	PROPN
ejpam-3637	126	50	)	)	PUNCT
ejpam-3637	126	51	,	,	PUNCT
ejpam-3637	127	1	then	then	ADV
ejpam-3637	127	2	for	for	ADP
ejpam-3637	127	3	some	some	DET
ejpam-3637	127	4	i	i	PRON
ejpam-3637	127	5	,	,	PUNCT
ejpam-3637	127	6	x	x	SYM
ejpam-3637	127	7	∈	∈	PROPN
ejpam-3637	127	8	gi	gi	NOUN
ejpam-3637	127	9	,	,	PUNCT
ejpam-3637	127	10	(	(	PUNCT
ejpam-3637	127	11	x	x	X
ejpam-3637	127	12	,	,	PUNCT
ejpam-3637	127	13	y	y	NOUN
ejpam-3637	127	14	)	)	PUNCT
ejpam-3637	127	15	∈	∈	PROPN
ejpam-3637	128	1	gi	gi	VERB
ejpam-3637	128	2	×	×	PROPN
ejpam-3637	128	3	y	y	PROPN
ejpam-3637	128	4	.	.	PUNCT
ejpam-3637	129	1	also	also	ADV
ejpam-3637	129	2	since	since	SCONJ
ejpam-3637	129	3	x	x	PUNCT
ejpam-3637	129	4	∈	∈	PROPN
ejpam-3637	129	5	gi	gi	VERB
ejpam-3637	129	6	⊆	⊆	NUM
ejpam-3637	129	7	vi	vi	NOUN
ejpam-3637	129	8	,	,	PUNCT
ejpam-3637	129	9	(	(	PUNCT
ejpam-3637	129	10	x	x	X
ejpam-3637	129	11	,	,	PUNCT
ejpam-3637	129	12	y	y	NOUN
ejpam-3637	129	13	)	)	PUNCT
ejpam-3637	129	14	∈	∈	PROPN
ejpam-3637	129	15	x×	x×	PUNCT
ejpam-3637	129	16	y	y	PROPN
ejpam-3637	129	17	⊆	⊆	NUM
ejpam-3637	129	18	∪j≤iuj	∪j≤iuj	NOUN
ejpam-3637	129	19	.	.	PUNCT
ejpam-3637	130	1	hence	hence	ADV
ejpam-3637	130	2	,	,	PUNCT
ejpam-3637	130	3	for	for	ADP
ejpam-3637	130	4	some	some	DET
ejpam-3637	130	5	i	i	PRON
ejpam-3637	130	6	≥	≥	VERB
ejpam-3637	130	7	j	j	PROPN
ejpam-3637	130	8	,	,	PUNCT
ejpam-3637	130	9	(	(	PUNCT
ejpam-3637	130	10	x	x	NOUN
ejpam-3637	130	11	,	,	PUNCT
ejpam-3637	130	12	y	y	NOUN
ejpam-3637	130	13	)	)	PUNCT
ejpam-3637	130	14	∈	∈	PROPN
ejpam-3637	130	15	uj	uj	PROPN
ejpam-3637	130	16	.	.	PUNCT
ejpam-3637	131	1	it	it	PRON
ejpam-3637	131	2	follows	follow	VERB
ejpam-3637	131	3	that	that	SCONJ
ejpam-3637	131	4	,	,	PUNCT
ejpam-3637	131	5	(	(	PUNCT
ejpam-3637	131	6	x	x	X
ejpam-3637	131	7	,	,	PUNCT
ejpam-3637	131	8	y	y	NOUN
ejpam-3637	131	9	)	)	PUNCT
ejpam-3637	131	10	∈	∈	PROPN
ejpam-3637	131	11	gij	gij	NOUN
ejpam-3637	131	12	.	.	PUNCT
ejpam-3637	132	1	therefore	therefore	ADV
ejpam-3637	132	2	,	,	PUNCT
ejpam-3637	132	3	{	{	PUNCT
ejpam-3637	132	4	gij	gij	ADJ
ejpam-3637	132	5	}	}	PUNCT
ejpam-3637	132	6	is	be	AUX
ejpam-3637	132	7	covering	cover	VERB
ejpam-3637	132	8	of	of	ADP
ejpam-3637	132	9	x	x	PUNCT
ejpam-3637	132	10	×	×	PROPN
ejpam-3637	132	11	y	y	PROPN
ejpam-3637	132	12	.	.	PUNCT
ejpam-3637	133	1	since	since	SCONJ
ejpam-3637	133	2	,	,	PUNCT
ejpam-3637	133	3	gij	gij	NOUN
ejpam-3637	133	4	⊆	⊆	NUM
ejpam-3637	133	5	uj	uj	PROPN
ejpam-3637	133	6	,	,	PUNCT
ejpam-3637	133	7	then	then	ADV
ejpam-3637	133	8	{	{	PUNCT
ejpam-3637	133	9	gij	gij	NOUN
ejpam-3637	133	10	}	}	PUNCT
ejpam-3637	133	11	is	be	AUX
ejpam-3637	133	12	a	a	DET
ejpam-3637	133	13	refinement	refinement	NOUN
ejpam-3637	133	14	of	of	ADP
ejpam-3637	133	15	{	{	PUNCT
ejpam-3637	133	16	uj	uj	PROPN
ejpam-3637	133	17	}	}	PUNCT
ejpam-3637	133	18	.	.	PUNCT
ejpam-3637	134	1	also	also	ADV
ejpam-3637	134	2	if	if	SCONJ
ejpam-3637	134	3	(	(	PUNCT
ejpam-3637	134	4	x	x	NOUN
ejpam-3637	134	5	,	,	PUNCT
ejpam-3637	134	6	y	y	NOUN
ejpam-3637	134	7	)	)	PUNCT
ejpam-3637	134	8	∈	∈	PROPN
ejpam-3637	134	9	x	x	SYM
ejpam-3637	134	10	×	×	PROPN
ejpam-3637	134	11	y	y	PROPN
ejpam-3637	134	12	,	,	PUNCT
ejpam-3637	134	13	x	x	VERB
ejpam-3637	134	14	belongs	belong	VERB
ejpam-3637	134	15	to	to	ADP
ejpam-3637	134	16	an	an	DET
ejpam-3637	134	17	open	open	ADJ
ejpam-3637	134	18	set	set	NOUN
ejpam-3637	134	19	h(x	h(x	PROPN
ejpam-3637	134	20	)	)	PUNCT
ejpam-3637	134	21	which	which	PRON
ejpam-3637	134	22	meet	meet	VERB
ejpam-3637	134	23	only	only	ADV
ejpam-3637	134	24	a	a	DET
ejpam-3637	134	25	finite	finite	ADJ
ejpam-3637	134	26	sets	set	NOUN
ejpam-3637	134	27	of	of	ADP
ejpam-3637	134	28	{	{	PUNCT
ejpam-3637	134	29	gi	gi	INTJ
ejpam-3637	134	30	}	}	PUNCT
ejpam-3637	134	31	.	.	PUNCT
ejpam-3637	135	1	then	then	ADV
ejpam-3637	135	2	h(x)×	h(x)×	PROPN
ejpam-3637	135	3	y	y	PROPN
ejpam-3637	135	4	is	be	AUX
ejpam-3637	135	5	an	an	DET
ejpam-3637	135	6	open	open	ADJ
ejpam-3637	135	7	set	set	NOUN
ejpam-3637	135	8	containing	contain	VERB
ejpam-3637	135	9	(	(	PUNCT
ejpam-3637	135	10	x	x	NOUN
ejpam-3637	135	11	,	,	PUNCT
ejpam-3637	135	12	y	y	PROPN
ejpam-3637	135	13	)	)	PUNCT
ejpam-3637	135	14	which	which	PRON
ejpam-3637	135	15	can	can	AUX
ejpam-3637	135	16	meet	meet	VERB
ejpam-3637	135	17	gij	gij	NOUN
ejpam-3637	135	18	only	only	ADV
ejpam-3637	135	19	if	if	SCONJ
ejpam-3637	135	20	h(x	h(x	PROPN
ejpam-3637	135	21	)	)	PUNCT
ejpam-3637	135	22	meet	meet	VERB
ejpam-3637	135	23	gi	gi	NOUN
ejpam-3637	135	24	.	.	PUNCT
ejpam-3637	136	1	but	but	CCONJ
ejpam-3637	136	2	for	for	ADP
ejpam-3637	136	3	each	each	PRON
ejpam-3637	136	4	i	i	PRON
ejpam-3637	136	5	there	there	PRON
ejpam-3637	136	6	is	be	VERB
ejpam-3637	136	7	only	only	ADV
ejpam-3637	136	8	finite	finite	ADJ
ejpam-3637	136	9	sets	set	NOUN
ejpam-3637	136	10	gij	gij	NOUN
ejpam-3637	136	11	.	.	PUNCT
ejpam-3637	137	1	hence	hence	ADV
ejpam-3637	137	2	,	,	PUNCT
ejpam-3637	137	3	h(x)×y	h(x)×y	PROPN
ejpam-3637	137	4	meets	meet	VERB
ejpam-3637	137	5	only	only	ADV
ejpam-3637	137	6	a	a	DET
ejpam-3637	137	7	finite	finite	ADJ
ejpam-3637	137	8	sets	set	NOUN
ejpam-3637	137	9	of	of	ADP
ejpam-3637	137	10	{	{	PUNCT
ejpam-3637	137	11	gij	gij	NOUN
ejpam-3637	137	12	}	}	PUNCT
ejpam-3637	137	13	.	.	PUNCT
ejpam-3637	138	1	so	so	ADV
ejpam-3637	138	2	,	,	PUNCT
ejpam-3637	138	3	{	{	PUNCT
ejpam-3637	138	4	gij	gij	ADJ
ejpam-3637	138	5	}	}	PUNCT
ejpam-3637	138	6	is	be	AUX
ejpam-3637	138	7	locally	locally	ADV
ejpam-3637	138	8	finite	finite	ADJ
ejpam-3637	138	9	.	.	PUNCT
ejpam-3637	139	1	also	also	ADV
ejpam-3637	139	2	x×y	x×y	PROPN
ejpam-3637	139	3	is	be	AUX
ejpam-3637	139	4	a	a	DET
ejpam-3637	139	5	topological	topological	ADJ
ejpam-3637	139	6	group	group	NOUN
ejpam-3637	139	7	.	.	PUNCT
ejpam-3637	140	1	therefore	therefore	ADV
ejpam-3637	140	2	,	,	PUNCT
ejpam-3637	140	3	x×y	x×y	PROPN
ejpam-3637	140	4	is	be	AUX
ejpam-3637	140	5	(	(	PUNCT
ejpam-3637	140	6	countably	countably	ADV
ejpam-3637	140	7	)	)	PUNCT
ejpam-3637	140	8	a	a	DET
ejpam-3637	140	9	-	-	PUNCT
ejpam-3637	140	10	paracompact	paracompact	ADJ
ejpam-3637	140	11	topological	topological	ADJ
ejpam-3637	140	12	group	group	NOUN
ejpam-3637	140	13	.	.	PUNCT
ejpam-3637	141	1	definition	definition	NOUN
ejpam-3637	141	2	2	2	NUM
ejpam-3637	141	3	.	.	PUNCT
ejpam-3637	141	4	a	a	DET
ejpam-3637	141	5	triplet	triplet	NOUN
ejpam-3637	141	6	(	(	PUNCT
ejpam-3637	141	7	g	g	NOUN
ejpam-3637	141	8	,	,	PUNCT
ejpam-3637	141	9	∗	∗	NOUN
ejpam-3637	141	10	,	,	PUNCT
ejpam-3637	141	11	τ	τ	PROPN
ejpam-3637	141	12	)	)	PUNCT
ejpam-3637	141	13	,	,	PUNCT
ejpam-3637	141	14	where	where	SCONJ
ejpam-3637	141	15	τ	τ	PROPN
ejpam-3637	141	16	is	be	AUX
ejpam-3637	141	17	a	a	DET
ejpam-3637	141	18	space	space	NOUN
ejpam-3637	141	19	and	and	CCONJ
ejpam-3637	141	20	g	g	NOUN
ejpam-3637	141	21	is	be	AUX
ejpam-3637	141	22	a	a	DET
ejpam-3637	141	23	group	group	NOUN
ejpam-3637	141	24	,	,	PUNCT
ejpam-3637	141	25	is	be	AUX
ejpam-3637	141	26	called	call	VERB
ejpam-3637	141	27	semi	semi	ADV
ejpam-3637	141	28	δ	δ	PROPN
ejpam-3637	141	29	-	-	ADJ
ejpam-3637	141	30	topological	topological	ADJ
ejpam-3637	141	31	group	group	NOUN
ejpam-3637	141	32	if	if	SCONJ
ejpam-3637	141	33	multiplication	multiplication	NOUN
ejpam-3637	141	34	mapping	mapping	NOUN
ejpam-3637	141	35	is	be	AUX
ejpam-3637	141	36	separately	separately	ADV
ejpam-3637	141	37	δ	δ	NOUN
ejpam-3637	141	38	-	-	ADJ
ejpam-3637	141	39	continuous	continuous	ADJ
ejpam-3637	141	40	in	in	ADP
ejpam-3637	141	41	(	(	PUNCT
ejpam-3637	141	42	g	g	NOUN
ejpam-3637	141	43	,	,	PUNCT
ejpam-3637	141	44	∗	∗	NOUN
ejpam-3637	141	45	,	,	PUNCT
ejpam-3637	141	46	τ	τ	PROPN
ejpam-3637	141	47	)	)	PUNCT
ejpam-3637	141	48	.	.	PUNCT
ejpam-3637	142	1	definition	definition	NOUN
ejpam-3637	142	2	3	3	NUM
ejpam-3637	142	3	.	.	PUNCT
ejpam-3637	143	1	a	a	DET
ejpam-3637	143	2	space	space	NOUN
ejpam-3637	143	3	is	be	AUX
ejpam-3637	143	4	called	call	VERB
ejpam-3637	143	5	almost	almost	ADV
ejpam-3637	143	6	a	a	DET
ejpam-3637	143	7	-	-	PUNCT
ejpam-3637	143	8	paracompact	paracompact	NOUN
ejpam-3637	143	9	if	if	SCONJ
ejpam-3637	143	10	its	its	PRON
ejpam-3637	143	11	each	each	DET
ejpam-3637	143	12	open	open	ADJ
ejpam-3637	143	13	cover	cover	NOUN
ejpam-3637	143	14	has	have	VERB
ejpam-3637	143	15	a	a	DET
ejpam-3637	143	16	starfinite	starfinite	NOUN
ejpam-3637	143	17	refinement	refinement	NOUN
ejpam-3637	143	18	.	.	PUNCT
ejpam-3637	144	1	definition	definition	NOUN
ejpam-3637	144	2	4	4	NUM
ejpam-3637	144	3	.	.	PUNCT
ejpam-3637	145	1	a	a	DET
ejpam-3637	145	2	space	space	NOUN
ejpam-3637	145	3	is	be	AUX
ejpam-3637	145	4	called	call	VERB
ejpam-3637	145	5	nearly	nearly	ADV
ejpam-3637	145	6	almost	almost	ADV
ejpam-3637	145	7	a	a	DET
ejpam-3637	145	8	-	-	PUNCT
ejpam-3637	145	9	paracompact	paracompact	NOUN
ejpam-3637	145	10	if	if	SCONJ
ejpam-3637	145	11	its	its	PRON
ejpam-3637	145	12	every	every	DET
ejpam-3637	145	13	regular	regular	ADJ
ejpam-3637	145	14	open	open	ADJ
ejpam-3637	145	15	cover	cover	NOUN
ejpam-3637	145	16	has	have	VERB
ejpam-3637	145	17	a	a	DET
ejpam-3637	145	18	star	star	NOUN
ejpam-3637	145	19	-	-	PUNCT
ejpam-3637	145	20	finite	finite	PROPN
ejpam-3637	145	21	refinement	refinement	NOUN
ejpam-3637	145	22	.	.	PUNCT
ejpam-3637	146	1	references	reference	NOUN
ejpam-3637	146	2	284	284	NUM
ejpam-3637	146	3	theorem	theorem	NOUN
ejpam-3637	146	4	5	5	NUM
ejpam-3637	146	5	.	.	PUNCT
ejpam-3637	147	1	(	(	PUNCT
ejpam-3637	147	2	g	g	NOUN
ejpam-3637	147	3	,	,	PUNCT
ejpam-3637	147	4	∗	∗	NOUN
ejpam-3637	147	5	,	,	PUNCT
ejpam-3637	147	6	τs	τs	NOUN
ejpam-3637	147	7	)	)	PUNCT
ejpam-3637	147	8	is	be	AUX
ejpam-3637	147	9	almost	almost	ADV
ejpam-3637	147	10	a	a	PRON
ejpam-3637	147	11	-	-	PUNCT
ejpam-3637	147	12	paracompact	paracompact	ADJ
ejpam-3637	147	13	semi	semi	ADJ
ejpam-3637	147	14	topological	topological	ADJ
ejpam-3637	147	15	group	group	NOUN
ejpam-3637	147	16	if	if	SCONJ
ejpam-3637	147	17	and	and	CCONJ
ejpam-3637	147	18	only	only	ADV
ejpam-3637	147	19	if	if	SCONJ
ejpam-3637	147	20	(	(	PUNCT
ejpam-3637	147	21	g	g	NOUN
ejpam-3637	147	22	,	,	PUNCT
ejpam-3637	147	23	∗	∗	NOUN
ejpam-3637	147	24	,	,	PUNCT
ejpam-3637	147	25	τ	τ	X
ejpam-3637	147	26	)	)	PUNCT
ejpam-3637	147	27	is	be	AUX
ejpam-3637	147	28	nearly	nearly	ADV
ejpam-3637	147	29	almost	almost	ADV
ejpam-3637	147	30	a	a	DET
ejpam-3637	147	31	-	-	PUNCT
ejpam-3637	147	32	paracompact	paracompact	ADJ
ejpam-3637	147	33	semi	semi	ADJ
ejpam-3637	147	34	δ	δ	PROPN
ejpam-3637	147	35	-	-	ADJ
ejpam-3637	147	36	topological	topological	ADJ
ejpam-3637	147	37	group	group	NOUN
ejpam-3637	147	38	.	.	PUNCT
ejpam-3637	148	1	proof	proof	NOUN
ejpam-3637	148	2	.	.	PUNCT
ejpam-3637	149	1	separate	separate	ADJ
ejpam-3637	149	2	continuity	continuity	NOUN
ejpam-3637	149	3	of	of	ADP
ejpam-3637	149	4	multiplication	multiplication	NOUN
ejpam-3637	149	5	mapping	mapping	NOUN
ejpam-3637	149	6	in	in	ADP
ejpam-3637	149	7	(	(	PUNCT
ejpam-3637	149	8	g	g	NOUN
ejpam-3637	149	9	,	,	PUNCT
ejpam-3637	149	10	∗	∗	NOUN
ejpam-3637	149	11	,	,	PUNCT
ejpam-3637	149	12	τs	τs	NOUN
ejpam-3637	149	13	)	)	PUNCT
ejpam-3637	149	14	is	be	AUX
ejpam-3637	149	15	the	the	DET
ejpam-3637	149	16	same	same	ADJ
ejpam-3637	149	17	as	as	ADP
ejpam-3637	149	18	separate	separate	ADJ
ejpam-3637	149	19	δ	δ	NOUN
ejpam-3637	149	20	-	-	NOUN
ejpam-3637	149	21	continuity	continuity	NOUN
ejpam-3637	149	22	of	of	ADP
ejpam-3637	149	23	multiplication	multiplication	NOUN
ejpam-3637	149	24	mapping	mapping	NOUN
ejpam-3637	149	25	in	in	ADP
ejpam-3637	149	26	(	(	PUNCT
ejpam-3637	149	27	g	g	NOUN
ejpam-3637	149	28	,	,	PUNCT
ejpam-3637	149	29	∗	∗	NOUN
ejpam-3637	149	30	,	,	PUNCT
ejpam-3637	149	31	τ	τ	PROPN
ejpam-3637	149	32	)	)	PUNCT
ejpam-3637	149	33	.	.	PUNCT
ejpam-3637	150	1	let	let	VERB
ejpam-3637	150	2	ω	ω	PRON
ejpam-3637	150	3	is	be	AUX
ejpam-3637	150	4	a	a	DET
ejpam-3637	150	5	regular	regular	ADJ
ejpam-3637	150	6	open	open	ADJ
ejpam-3637	150	7	cover	cover	NOUN
ejpam-3637	150	8	of	of	ADP
ejpam-3637	150	9	(	(	PUNCT
ejpam-3637	150	10	g	g	PROPN
ejpam-3637	150	11	,	,	PUNCT
ejpam-3637	150	12	∗	∗	NOUN
ejpam-3637	150	13	,	,	PUNCT
ejpam-3637	150	14	τ	τ	PROPN
ejpam-3637	150	15	)	)	PUNCT
ejpam-3637	150	16	.	.	PUNCT
ejpam-3637	151	1	therefore	therefore	ADV
ejpam-3637	151	2	,	,	PUNCT
ejpam-3637	151	3	for	for	ADP
ejpam-3637	151	4	each	each	DET
ejpam-3637	151	5	ω	ω	PROPN
ejpam-3637	151	6	∈	∈	PROPN
ejpam-3637	151	7	ω	ω	PROPN
ejpam-3637	151	8	,	,	PUNCT
ejpam-3637	151	9	ω	ω	PROPN
ejpam-3637	151	10	=	=	SYM
ejpam-3637	151	11	int(cl(ω	int(cl(ω	NOUN
ejpam-3637	151	12	)	)	PUNCT
ejpam-3637	151	13	)	)	PUNCT
ejpam-3637	151	14	,	,	PUNCT
ejpam-3637	151	15	so	so	CCONJ
ejpam-3637	151	16	{	{	PUNCT
ejpam-3637	151	17	int(cl(ω	int(cl(ω	NOUN
ejpam-3637	151	18	)	)	PUNCT
ejpam-3637	151	19	)	)	PUNCT
ejpam-3637	151	20	,	,	PUNCT
ejpam-3637	151	21	ω	ω	PROPN
ejpam-3637	151	22	∈	∈	PROPN
ejpam-3637	151	23	ω	ω	PROPN
ejpam-3637	151	24	}	}	PUNCT
ejpam-3637	151	25	is	be	AUX
ejpam-3637	151	26	an	an	DET
ejpam-3637	151	27	open	open	ADJ
ejpam-3637	151	28	cover	cover	NOUN
ejpam-3637	151	29	of	of	ADP
ejpam-3637	151	30	(	(	PUNCT
ejpam-3637	151	31	g	g	PROPN
ejpam-3637	151	32	,	,	PUNCT
ejpam-3637	151	33	∗	∗	NOUN
ejpam-3637	151	34	,	,	PUNCT
ejpam-3637	151	35	τs	τs	NOUN
ejpam-3637	151	36	)	)	PUNCT
ejpam-3637	151	37	.	.	PUNCT
ejpam-3637	152	1	thus	thus	ADV
ejpam-3637	152	2	,	,	PUNCT
ejpam-3637	152	3	there	there	PRON
ejpam-3637	152	4	is	be	VERB
ejpam-3637	152	5	a	a	DET
ejpam-3637	152	6	star	star	NOUN
ejpam-3637	152	7	finite	finite	PROPN
ejpam-3637	152	8	refinement	refinement	PROPN
ejpam-3637	152	9	u	u	PROPN
ejpam-3637	152	10	=	=	PUNCT
ejpam-3637	152	11	{	{	PUNCT
ejpam-3637	152	12	µα	µα	ADP
ejpam-3637	152	13	,	,	PUNCT
ejpam-3637	152	14	α	α	PROPN
ejpam-3637	152	15	∈	∈	PROPN
ejpam-3637	152	16	j	j	PROPN
ejpam-3637	152	17	}	}	PUNCT
ejpam-3637	152	18	of	of	ADP
ejpam-3637	152	19	(	(	PUNCT
ejpam-3637	152	20	g	g	NOUN
ejpam-3637	152	21	,	,	PUNCT
ejpam-3637	152	22	∗	∗	NOUN
ejpam-3637	152	23	,	,	PUNCT
ejpam-3637	152	24	τs	τs	NOUN
ejpam-3637	152	25	)	)	PUNCT
ejpam-3637	152	26	.	.	PUNCT
ejpam-3637	153	1	hence	hence	ADV
ejpam-3637	153	2	,	,	PUNCT
ejpam-3637	153	3	u	u	PROPN
ejpam-3637	153	4	is	be	AUX
ejpam-3637	153	5	star	star	NOUN
ejpam-3637	153	6	finite	finite	PROPN
ejpam-3637	153	7	refinement	refinement	NOUN
ejpam-3637	153	8	of	of	ADP
ejpam-3637	153	9	ω	ω	PROPN
ejpam-3637	153	10	.	.	PUNCT
ejpam-3637	154	1	conversely	conversely	ADV
ejpam-3637	154	2	,	,	PUNCT
ejpam-3637	154	3	every	every	DET
ejpam-3637	154	4	open	open	ADJ
ejpam-3637	154	5	cover	cover	NOUN
ejpam-3637	154	6	ω	ω	PROPN
ejpam-3637	154	7	of	of	ADP
ejpam-3637	154	8	(	(	PUNCT
ejpam-3637	154	9	g	g	PROPN
ejpam-3637	154	10	,	,	PUNCT
ejpam-3637	154	11	∗	∗	NOUN
ejpam-3637	154	12	,	,	PUNCT
ejpam-3637	154	13	τs	τs	NOUN
ejpam-3637	154	14	)	)	PUNCT
ejpam-3637	154	15	is	be	AUX
ejpam-3637	154	16	regular	regular	ADJ
ejpam-3637	154	17	open	open	ADJ
ejpam-3637	154	18	cover	cover	NOUN
ejpam-3637	154	19	of	of	ADP
ejpam-3637	154	20	(	(	PUNCT
ejpam-3637	154	21	g	g	PROPN
ejpam-3637	154	22	,	,	PUNCT
ejpam-3637	154	23	∗	∗	NOUN
ejpam-3637	154	24	,	,	PUNCT
ejpam-3637	154	25	τ	τ	PROPN
ejpam-3637	154	26	)	)	PUNCT
ejpam-3637	154	27	.	.	PUNCT
ejpam-3637	155	1	so	so	ADV
ejpam-3637	155	2	,	,	PUNCT
ejpam-3637	155	3	there	there	PRON
ejpam-3637	155	4	is	be	VERB
ejpam-3637	155	5	a	a	DET
ejpam-3637	155	6	star	star	NOUN
ejpam-3637	155	7	finite	finite	PROPN
ejpam-3637	155	8	refinement	refinement	PROPN
ejpam-3637	155	9	u	u	PROPN
ejpam-3637	155	10	=	=	PUNCT
ejpam-3637	155	11	{	{	PUNCT
ejpam-3637	155	12	µα	µα	ADP
ejpam-3637	155	13	,	,	PUNCT
ejpam-3637	155	14	α	α	PROPN
ejpam-3637	155	15	∈	∈	PROPN
ejpam-3637	155	16	j	j	PROPN
ejpam-3637	155	17	}	}	PUNCT
ejpam-3637	155	18	of	of	ADP
ejpam-3637	155	19	ω	ω	PROPN
ejpam-3637	155	20	.	.	PUNCT
ejpam-3637	156	1	definition	definition	NOUN
ejpam-3637	156	2	5	5	NUM
ejpam-3637	156	3	.	.	PUNCT
ejpam-3637	157	1	in	in	ADP
ejpam-3637	157	2	semi	semi	ADJ
ejpam-3637	157	3	topological	topological	ADJ
ejpam-3637	157	4	group	group	NOUN
ejpam-3637	157	5	(	(	PUNCT
ejpam-3637	157	6	g	g	PROPN
ejpam-3637	157	7	,	,	PUNCT
ejpam-3637	157	8	∗	∗	NOUN
ejpam-3637	157	9	,	,	PUNCT
ejpam-3637	157	10	τ	τ	X
ejpam-3637	157	11	)	)	PUNCT
ejpam-3637	157	12	having	have	VERB
ejpam-3637	157	13	a	a	DET
ejpam-3637	157	14	closed	closed	ADJ
ejpam-3637	157	15	a	a	DET
ejpam-3637	157	16	-	-	PUNCT
ejpam-3637	157	17	paracompact	paracompact	NOUN
ejpam-3637	157	18	(	(	PUNCT
ejpam-3637	157	19	countably	countably	ADV
ejpam-3637	157	20	a	a	DET
ejpam-3637	157	21	-	-	PUNCT
ejpam-3637	157	22	paracompact	paracompact	ADJ
ejpam-3637	157	23	)	)	PUNCT
ejpam-3637	157	24	subset	subset	NOUN
ejpam-3637	157	25	n	n	X
ejpam-3637	157	26	.	.	PUNCT
ejpam-3637	158	1	a	a	DET
ejpam-3637	158	2	subset	subset	NOUN
ejpam-3637	158	3	s	s	X
ejpam-3637	158	4	is	be	AUX
ejpam-3637	158	5	said	say	VERB
ejpam-3637	158	6	to	to	PART
ejpam-3637	158	7	be	be	AUX
ejpam-3637	158	8	n−capc	n−capc	PROPN
ejpam-3637	158	9	disjoint	disjoint	X
ejpam-3637	158	10	(	(	PUNCT
ejpam-3637	158	11	n−ccapc	n−ccapc	X
ejpam-3637	158	12	disjoint	disjoint	NOUN
ejpam-3637	158	13	)	)	PUNCT
ejpam-3637	158	14	,	,	PUNCT
ejpam-3637	158	15	if	if	SCONJ
ejpam-3637	158	16	for	for	ADP
ejpam-3637	158	17	each	each	DET
ejpam-3637	158	18	s1	s1	NOUN
ejpam-3637	158	19	,	,	PUNCT
ejpam-3637	158	20	s2	s2	NOUN
ejpam-3637	158	21	∈	∈	PROPN
ejpam-3637	158	22	s	s	PROPN
ejpam-3637	158	23	,	,	PUNCT
ejpam-3637	158	24	s1	s1	PROPN
ejpam-3637	158	25	/∈	/∈	PUNCT
ejpam-3637	159	1	s2	s2	PROPN
ejpam-3637	159	2	∗n	∗n	PROPN
ejpam-3637	159	3	.	.	PUNCT
ejpam-3637	160	1	theorem	theorem	VERB
ejpam-3637	160	2	6	6	NUM
ejpam-3637	160	3	.	.	PUNCT
ejpam-3637	161	1	let	let	AUX
ejpam-3637	161	2	(	(	PUNCT
ejpam-3637	161	3	g	g	NOUN
ejpam-3637	161	4	,	,	PUNCT
ejpam-3637	161	5	∗	∗	NOUN
ejpam-3637	161	6	,	,	PUNCT
ejpam-3637	161	7	τ	τ	X
ejpam-3637	161	8	)	)	PUNCT
ejpam-3637	161	9	be	be	VERB
ejpam-3637	161	10	a	a	DET
ejpam-3637	161	11	semi	semi	ADJ
ejpam-3637	161	12	topological	topological	ADJ
ejpam-3637	161	13	group	group	NOUN
ejpam-3637	161	14	with	with	ADP
ejpam-3637	161	15	b	b	PROPN
ejpam-3637	161	16	⊆	⊆	NUM
ejpam-3637	161	17	g	g	NOUN
ejpam-3637	161	18	and	and	CCONJ
ejpam-3637	161	19	h	h	NOUN
ejpam-3637	161	20	is	be	AUX
ejpam-3637	161	21	closed	close	VERB
ejpam-3637	161	22	aparacompact	aparacompact	ADJ
ejpam-3637	161	23	(	(	PUNCT
ejpam-3637	161	24	countably	countably	ADV
ejpam-3637	161	25	a	a	DET
ejpam-3637	161	26	-	-	PUNCT
ejpam-3637	161	27	paracompact	paracompact	ADJ
ejpam-3637	161	28	)	)	PUNCT
ejpam-3637	161	29	subset	subset	NOUN
ejpam-3637	161	30	of	of	ADP
ejpam-3637	161	31	g.	g.	PROPN
ejpam-3637	161	32	then	then	ADV
ejpam-3637	161	33	there	there	PRON
ejpam-3637	161	34	exists	exist	VERB
ejpam-3637	161	35	a	a	DET
ejpam-3637	161	36	subset	subset	NOUN
ejpam-3637	161	37	n	n	NOUN
ejpam-3637	161	38	of	of	ADP
ejpam-3637	161	39	h	h	NOUN
ejpam-3637	161	40	such	such	ADJ
ejpam-3637	161	41	that	that	SCONJ
ejpam-3637	161	42	b	b	PROPN
ejpam-3637	161	43	is	be	AUX
ejpam-3637	161	44	n−capc	n−capc	PRON
ejpam-3637	161	45	disjoint	disjoint	X
ejpam-3637	161	46	(	(	PUNCT
ejpam-3637	161	47	n−ccapc	n−ccapc	X
ejpam-3637	161	48	disjoint	disjoint	NOUN
ejpam-3637	161	49	)	)	PUNCT
ejpam-3637	161	50	.	.	PUNCT
ejpam-3637	162	1	proof	proof	NOUN
ejpam-3637	162	2	.	.	PUNCT
ejpam-3637	163	1	since	since	SCONJ
ejpam-3637	163	2	,	,	PUNCT
ejpam-3637	163	3	h	h	NOUN
ejpam-3637	163	4	is	be	AUX
ejpam-3637	163	5	closed	close	VERB
ejpam-3637	163	6	a	a	DET
ejpam-3637	163	7	-	-	PUNCT
ejpam-3637	163	8	paracompact	paracompact	NOUN
ejpam-3637	163	9	(	(	PUNCT
ejpam-3637	163	10	countably	countably	ADV
ejpam-3637	163	11	a	a	DET
ejpam-3637	163	12	-	-	PUNCT
ejpam-3637	163	13	paracompact	paracompact	ADJ
ejpam-3637	163	14	)	)	PUNCT
ejpam-3637	163	15	therefore	therefore	ADV
ejpam-3637	163	16	lb(h	lb(h	PUNCT
ejpam-3637	163	17	)	)	PUNCT
ejpam-3637	164	1	=	=	SYM
ejpam-3637	164	2	b∗h	b∗h	NUM
ejpam-3637	164	3	for	for	ADP
ejpam-3637	164	4	every	every	DET
ejpam-3637	164	5	b	b	PROPN
ejpam-3637	164	6	∈	∈	PROPN
ejpam-3637	164	7	b	b	NOUN
ejpam-3637	164	8	is	be	AUX
ejpam-3637	164	9	a	a	DET
ejpam-3637	164	10	-	-	PUNCT
ejpam-3637	164	11	paracompact	paracompact	NOUN
ejpam-3637	164	12	(	(	PUNCT
ejpam-3637	164	13	countably	countably	ADV
ejpam-3637	164	14	a	a	DET
ejpam-3637	164	15	-	-	PUNCT
ejpam-3637	164	16	paracompact	paracompact	ADJ
ejpam-3637	164	17	)	)	PUNCT
ejpam-3637	164	18	.	.	PUNCT
ejpam-3637	165	1	moreover	moreover	ADV
ejpam-3637	165	2	,	,	PUNCT
ejpam-3637	165	3	b∗h	b∗h	PRON
ejpam-3637	165	4	being	be	AUX
ejpam-3637	165	5	inverse	inverse	ADJ
ejpam-3637	165	6	image	image	NOUN
ejpam-3637	165	7	of	of	ADP
ejpam-3637	165	8	closed	closed	ADJ
ejpam-3637	165	9	set	set	VERB
ejpam-3637	165	10	under	under	ADP
ejpam-3637	165	11	translation	translation	NOUN
ejpam-3637	165	12	lb−1(b∗h	lb−1(b∗h	PROPN
ejpam-3637	165	13	)	)	PUNCT
ejpam-3637	166	1	=	=	PRON
ejpam-3637	166	2	h	h	NOUN
ejpam-3637	166	3	is	be	AUX
ejpam-3637	166	4	closed	closed	ADJ
ejpam-3637	166	5	.	.	PUNCT
ejpam-3637	167	1	each	each	DET
ejpam-3637	167	2	ai	ai	PROPN
ejpam-3637	167	3	∈	∈	PROPN
ejpam-3637	167	4	b	b	PROPN
ejpam-3637	167	5	has	have	VERB
ejpam-3637	167	6	an	an	DET
ejpam-3637	167	7	open	open	ADJ
ejpam-3637	167	8	neighbourhood	neighbourhood	NOUN
ejpam-3637	167	9	ui	ui	NOUN
ejpam-3637	167	10	which	which	PRON
ejpam-3637	167	11	intersects	intersect	VERB
ejpam-3637	167	12	finite	finite	NOUN
ejpam-3637	167	13	sets	set	NOUN
ejpam-3637	167	14	in	in	ADP
ejpam-3637	167	15	the	the	DET
ejpam-3637	167	16	refinement	refinement	NOUN
ejpam-3637	167	17	of	of	ADP
ejpam-3637	167	18	open	open	ADJ
ejpam-3637	167	19	(	(	PUNCT
ejpam-3637	167	20	countably	countably	ADV
ejpam-3637	167	21	open	open	ADJ
ejpam-3637	167	22	)	)	PUNCT
ejpam-3637	167	23	cover	cover	NOUN
ejpam-3637	167	24	of	of	ADP
ejpam-3637	167	25	b	b	NOUN
ejpam-3637	167	26	∗h	∗h	NOUN
ejpam-3637	167	27	.	.	PUNCT
ejpam-3637	168	1	by	by	ADP
ejpam-3637	168	2	removing	remove	VERB
ejpam-3637	168	3	all	all	DET
ejpam-3637	168	4	ui	ui	NOUN
ejpam-3637	168	5	from	from	ADP
ejpam-3637	168	6	b	b	PROPN
ejpam-3637	168	7	∗h	∗h	NOUN
ejpam-3637	168	8	a	a	DET
ejpam-3637	168	9	closed	closed	ADJ
ejpam-3637	168	10	a	a	DET
ejpam-3637	168	11	-	-	PUNCT
ejpam-3637	168	12	paracompact	paracompact	NOUN
ejpam-3637	168	13	(	(	PUNCT
ejpam-3637	168	14	countably	countably	ADV
ejpam-3637	168	15	a	a	DET
ejpam-3637	168	16	-	-	PUNCT
ejpam-3637	168	17	paracompact	paracompact	ADJ
ejpam-3637	168	18	)	)	PUNCT
ejpam-3637	168	19	set	set	NOUN
ejpam-3637	168	20	n	n	NOUN
ejpam-3637	168	21	=	=	SYM
ejpam-3637	168	22	b	b	NOUN
ejpam-3637	168	23	∗h	∗h	NOUN
ejpam-3637	168	24	\ui	\ui	VERB
ejpam-3637	168	25	is	be	AUX
ejpam-3637	168	26	obtained	obtain	VERB
ejpam-3637	168	27	such	such	ADJ
ejpam-3637	168	28	that	that	PRON
ejpam-3637	168	29	b	b	NOUN
ejpam-3637	168	30	is	be	AUX
ejpam-3637	168	31	n−capc	n−capc	PRON
ejpam-3637	168	32	disjoint	disjoint	X
ejpam-3637	168	33	(	(	PUNCT
ejpam-3637	168	34	n−ccapc	n−ccapc	X
ejpam-3637	168	35	disjoint	disjoint	NOUN
ejpam-3637	168	36	)	)	PUNCT
ejpam-3637	168	37	.	.	PUNCT
ejpam-3637	169	1	definition	definition	NOUN
ejpam-3637	169	2	6	6	NUM
ejpam-3637	169	3	.	.	PUNCT
ejpam-3637	170	1	a	a	DET
ejpam-3637	170	2	hausdorff	hausdorff	NOUN
ejpam-3637	170	3	space	space	NOUN
ejpam-3637	170	4	is	be	AUX
ejpam-3637	170	5	called	call	VERB
ejpam-3637	170	6	an	an	DET
ejpam-3637	170	7	ultra	ultra	ADJ
ejpam-3637	170	8	-	-	ADJ
ejpam-3637	170	9	a	a	DET
ejpam-3637	170	10	-	-	PUNCT
ejpam-3637	170	11	paracompact	paracompact	NOUN
ejpam-3637	170	12	if	if	SCONJ
ejpam-3637	170	13	there	there	PRON
ejpam-3637	170	14	exits	exit	VERB
ejpam-3637	170	15	a	a	DET
ejpam-3637	170	16	closed	closed	ADJ
ejpam-3637	170	17	locally	locally	ADV
ejpam-3637	170	18	finite	finite	ADJ
ejpam-3637	170	19	refinement	refinement	NOUN
ejpam-3637	170	20	for	for	ADP
ejpam-3637	170	21	each	each	DET
ejpam-3637	170	22	open	open	ADJ
ejpam-3637	170	23	cover	cover	NOUN
ejpam-3637	170	24	.	.	PUNCT
ejpam-3637	170	25	example	example	NOUN
ejpam-3637	171	1	1	1	NUM
ejpam-3637	171	2	.	.	PUNCT
ejpam-3637	171	3	(	(	PUNCT
ejpam-3637	171	4	r,+	r,+	NUM
ejpam-3637	171	5	,	,	PUNCT
ejpam-3637	171	6	τ	τ	X
ejpam-3637	171	7	)	)	PUNCT
ejpam-3637	171	8	is	be	AUX
ejpam-3637	171	9	an	an	DET
ejpam-3637	171	10	ultra	ultra	ADJ
ejpam-3637	171	11	-	-	ADJ
ejpam-3637	171	12	a	a	DET
ejpam-3637	171	13	-	-	PUNCT
ejpam-3637	171	14	paracompact	paracompact	ADJ
ejpam-3637	171	15	topological	topological	ADJ
ejpam-3637	171	16	group	group	NOUN
ejpam-3637	171	17	for	for	ADP
ejpam-3637	171	18	a	a	DET
ejpam-3637	171	19	usual	usual	ADJ
ejpam-3637	171	20	topology	topology	NOUN
ejpam-3637	171	21	τ	τ	X
ejpam-3637	171	22	.	.	PUNCT
ejpam-3637	172	1	proof	proof	NOUN
ejpam-3637	172	2	.	.	PUNCT
ejpam-3637	173	1	let	let	VERB
ejpam-3637	173	2	ω	ω	PRON
ejpam-3637	173	3	be	be	AUX
ejpam-3637	173	4	an	an	DET
ejpam-3637	173	5	open	open	ADJ
ejpam-3637	173	6	cover	cover	NOUN
ejpam-3637	173	7	of	of	ADP
ejpam-3637	173	8	(	(	PUNCT
ejpam-3637	173	9	0,∞	0,∞	NUM
ejpam-3637	173	10	)	)	PUNCT
ejpam-3637	173	11	.	.	PUNCT
ejpam-3637	174	1	if	if	SCONJ
ejpam-3637	174	2	κ	κ	X
ejpam-3637	174	3	=	=	PUNCT
ejpam-3637	174	4	sup{xα	sup{xα	AUX
ejpam-3637	174	5	:	:	PUNCT
ejpam-3637	174	6	α	α	X
ejpam-3637	174	7	<	<	X
ejpam-3637	174	8	β	β	X
ejpam-3637	174	9	}	}	PUNCT
ejpam-3637	174	10	<	<	X
ejpam-3637	174	11	∞	∞	PROPN
ejpam-3637	174	12	for	for	ADP
ejpam-3637	174	13	an	an	DET
ejpam-3637	174	14	ordinal	ordinal	ADJ
ejpam-3637	174	15	β	β	NOUN
ejpam-3637	174	16	,	,	PUNCT
ejpam-3637	174	17	then	then	ADV
ejpam-3637	174	18	let	let	VERB
ejpam-3637	174	19	there	there	PRON
ejpam-3637	174	20	is	be	VERB
ejpam-3637	174	21	a	a	DET
ejpam-3637	174	22	real	real	ADJ
ejpam-3637	174	23	number	number	NOUN
ejpam-3637	174	24	xβ	xβ	NOUN
ejpam-3637	174	25	satisfying	satisfy	VERB
ejpam-3637	174	26	κ	κ	X
ejpam-3637	174	27	<	<	X
ejpam-3637	174	28	xβ	xβ	NOUN
ejpam-3637	174	29	and	and	CCONJ
ejpam-3637	174	30	[	[	X
ejpam-3637	174	31	κ	κ	X
ejpam-3637	174	32	,	,	PUNCT
ejpam-3637	174	33	xβ	xβ	PROPN
ejpam-3637	174	34	]	]	X
ejpam-3637	174	35	⊆	⊆	NUM
ejpam-3637	174	36	u	u	NOUN
ejpam-3637	174	37	for	for	ADP
ejpam-3637	174	38	u	u	PROPN
ejpam-3637	174	39	∈	∈	PROPN
ejpam-3637	174	40	ω	ω	PROPN
ejpam-3637	174	41	.	.	PUNCT
ejpam-3637	175	1	then	then	ADV
ejpam-3637	175	2	{	{	PUNCT
ejpam-3637	176	1	[	[	X
ejpam-3637	176	2	xβ	xβ	NOUN
ejpam-3637	176	3	,	,	PUNCT
ejpam-3637	176	4	xβ+1	xβ+1	PROPN
ejpam-3637	176	5	]	]	PUNCT
ejpam-3637	176	6	:	:	PUNCT
ejpam-3637	176	7	β	β	X
ejpam-3637	176	8	}	}	PUNCT
ejpam-3637	176	9	is	be	AUX
ejpam-3637	176	10	a	a	DET
ejpam-3637	176	11	partition	partition	NOUN
ejpam-3637	176	12	into	into	ADP
ejpam-3637	176	13	closed	closed	ADJ
ejpam-3637	176	14	sets	set	NOUN
ejpam-3637	176	15	of	of	ADP
ejpam-3637	176	16	(	(	PUNCT
ejpam-3637	176	17	0,∞	0,∞	NOUN
ejpam-3637	176	18	)	)	PUNCT
ejpam-3637	176	19	that	that	PRON
ejpam-3637	176	20	refines	refine	VERB
ejpam-3637	176	21	ω	ω	NOUN
ejpam-3637	176	22	.	.	PUNCT
ejpam-3637	177	1	as	as	SCONJ
ejpam-3637	177	2	r	r	NOUN
ejpam-3637	177	3	is	be	AUX
ejpam-3637	177	4	homeomorphic	homeomorphic	ADJ
ejpam-3637	177	5	to	to	ADP
ejpam-3637	177	6	(	(	PUNCT
ejpam-3637	177	7	0,∞	0,∞	NUM
ejpam-3637	177	8	)	)	PUNCT
ejpam-3637	177	9	and	and	CCONJ
ejpam-3637	177	10	(	(	PUNCT
ejpam-3637	177	11	r,+	r,+	NUM
ejpam-3637	177	12	,	,	PUNCT
ejpam-3637	177	13	τ	τ	X
ejpam-3637	177	14	)	)	PUNCT
ejpam-3637	177	15	is	be	AUX
ejpam-3637	177	16	a	a	DET
ejpam-3637	177	17	topological	topological	ADJ
ejpam-3637	177	18	group	group	NOUN
ejpam-3637	177	19	.	.	PUNCT
ejpam-3637	178	1	hence	hence	ADV
ejpam-3637	178	2	,	,	PUNCT
ejpam-3637	178	3	(	(	PUNCT
ejpam-3637	178	4	r,+	r,+	NUM
ejpam-3637	178	5	,	,	PUNCT
ejpam-3637	178	6	τ	τ	X
ejpam-3637	178	7	)	)	PUNCT
ejpam-3637	178	8	is	be	AUX
ejpam-3637	178	9	an	an	DET
ejpam-3637	178	10	ultra	ultra	ADJ
ejpam-3637	178	11	-	-	ADJ
ejpam-3637	178	12	a	a	DET
ejpam-3637	178	13	-	-	PUNCT
ejpam-3637	178	14	paracompact	paracompact	ADJ
ejpam-3637	178	15	topological	topological	ADJ
ejpam-3637	178	16	group	group	NOUN
ejpam-3637	178	17	.	.	PUNCT
ejpam-3637	179	1	references	reference	NOUN
ejpam-3637	179	2	[	[	X
ejpam-3637	179	3	1	1	NUM
ejpam-3637	179	4	]	]	PUNCT
ejpam-3637	179	5	w	w	PROPN
ejpam-3637	179	6	al	al	PROPN
ejpam-3637	179	7	-	-	PUNCT
ejpam-3637	179	8	omeri	omeri	NOUN
ejpam-3637	179	9	,	,	PUNCT
ejpam-3637	179	10	mohd	mohd	PROPN
ejpam-3637	179	11	salmi	salmi	PROPN
ejpam-3637	179	12	md	md	PROPN
ejpam-3637	179	13	noorani	noorani	PROPN
ejpam-3637	179	14	,	,	PUNCT
ejpam-3637	179	15	and	and	CCONJ
ejpam-3637	179	16	a	a	DET
ejpam-3637	179	17	al	al	PROPN
ejpam-3637	179	18	-	-	PUNCT
ejpam-3637	179	19	omari	omari	PROPN
ejpam-3637	179	20	.	.	PUNCT
ejpam-3637	180	1	on	on	ADP
ejpam-3637	180	2	e	e	PROPN
ejpam-3637	180	3	-	-	PROPN
ejpam-3637	180	4	i	i	PRON
ejpam-3637	180	5	-	-	PUNCT
ejpam-3637	180	6	open	open	ADJ
ejpam-3637	180	7	sets	set	NOUN
ejpam-3637	180	8	,	,	PUNCT
ejpam-3637	180	9	e	e	ADJ
ejpam-3637	180	10	-	-	ADJ
ejpam-3637	180	11	icontinuous	icontinuous	ADJ
ejpam-3637	180	12	functions	function	NOUN
ejpam-3637	180	13	and	and	CCONJ
ejpam-3637	180	14	decomposition	decomposition	NOUN
ejpam-3637	180	15	of	of	ADP
ejpam-3637	180	16	continuity	continuity	NOUN
ejpam-3637	180	17	.	.	PUNCT
ejpam-3637	181	1	journal	journal	NOUN
ejpam-3637	181	2	of	of	ADP
ejpam-3637	181	3	mathematics	mathematic	NOUN
ejpam-3637	181	4	and	and	CCONJ
ejpam-3637	181	5	applications	application	NOUN
ejpam-3637	181	6	,	,	PUNCT
ejpam-3637	181	7	38	38	NUM
ejpam-3637	181	8	,	,	PUNCT
ejpam-3637	181	9	2015	2015	NUM
ejpam-3637	181	10	.	.	PUNCT
ejpam-3637	182	1	[	[	X
ejpam-3637	182	2	2	2	X
ejpam-3637	182	3	]	]	PUNCT
ejpam-3637	182	4	wadei	wadei	VERB
ejpam-3637	182	5	al	al	PROPN
ejpam-3637	182	6	-	-	PUNCT
ejpam-3637	182	7	omeri	omeri	ADJ
ejpam-3637	182	8	,	,	PUNCT
ejpam-3637	182	9	mohd	mohd	PROPN
ejpam-3637	182	10	salmi	salmi	PROPN
ejpam-3637	182	11	md	md	PROPN
ejpam-3637	182	12	noorani	noorani	PROPN
ejpam-3637	182	13	,	,	PUNCT
ejpam-3637	182	14	ahmad	ahmad	PROPN
ejpam-3637	182	15	al	al	PROPN
ejpam-3637	182	16	-	-	PUNCT
ejpam-3637	182	17	omari	omari	PROPN
ejpam-3637	182	18	,	,	PUNCT
ejpam-3637	182	19	et	et	PROPN
ejpam-3637	182	20	al	al	PROPN
ejpam-3637	182	21	.	.	PUNCT
ejpam-3637	183	1	new	new	ADJ
ejpam-3637	183	2	forms	form	NOUN
ejpam-3637	183	3	of	of	ADP
ejpam-3637	183	4	contra	contra	NOUN
ejpam-3637	183	5	-	-	NOUN
ejpam-3637	183	6	continuity	continuity	NOUN
ejpam-3637	183	7	in	in	ADP
ejpam-3637	183	8	ideal	ideal	ADJ
ejpam-3637	183	9	topology	topology	NOUN
ejpam-3637	183	10	spaces	space	NOUN
ejpam-3637	183	11	.	.	PUNCT
ejpam-3637	184	1	missouri	missouri	PROPN
ejpam-3637	184	2	journal	journal	PROPN
ejpam-3637	184	3	of	of	ADP
ejpam-3637	184	4	mathematical	mathematical	ADJ
ejpam-3637	184	5	sciences	science	NOUN
ejpam-3637	184	6	,	,	PUNCT
ejpam-3637	184	7	26(1):33–47	26(1):33–47	NUM
ejpam-3637	184	8	,	,	PUNCT
ejpam-3637	184	9	2014	2014	NUM
ejpam-3637	184	10	.	.	PUNCT
ejpam-3637	185	1	references	reference	NOUN
ejpam-3637	185	2	285	285	NUM
ejpam-3637	185	3	[	[	X
ejpam-3637	185	4	3	3	NUM
ejpam-3637	185	5	]	]	PUNCT
ejpam-3637	185	6	wadei	wadei	X
ejpam-3637	185	7	faris	faris	PROPN
ejpam-3637	185	8	al	al	PROPN
ejpam-3637	185	9	-	-	PUNCT
ejpam-3637	185	10	omeri	omeri	NOUN
ejpam-3637	185	11	,	,	PUNCT
ejpam-3637	185	12	ms	ms	PROPN
ejpam-3637	185	13	md	md	PROPN
ejpam-3637	185	14	noorani	noorani	PROPN
ejpam-3637	185	15	,	,	PUNCT
ejpam-3637	185	16	ahmad	ahmad	PROPN
ejpam-3637	185	17	al	al	PROPN
ejpam-3637	185	18	-	-	PUNCT
ejpam-3637	185	19	omeri	omeri	NOUN
ejpam-3637	185	20	,	,	PUNCT
ejpam-3637	185	21	and	and	CCONJ
ejpam-3637	185	22	t	t	PROPN
ejpam-3637	185	23	noiri	noiri	PROPN
ejpam-3637	185	24	.	.	PUNCT
ejpam-3637	186	1	weak	weak	ADJ
ejpam-3637	186	2	separation	separation	NOUN
ejpam-3637	186	3	axioms	axiom	NOUN
ejpam-3637	186	4	via	via	ADP
ejpam-3637	186	5	e	e	NOUN
ejpam-3637	186	6	-	-	ADJ
ejpam-3637	186	7	i	i	NOUN
ejpam-3637	186	8	-	-	PUNCT
ejpam-3637	186	9	sets	set	NOUN
ejpam-3637	186	10	in	in	ADP
ejpam-3637	186	11	ideal	ideal	ADJ
ejpam-3637	186	12	topological	topological	ADJ
ejpam-3637	186	13	spaces	space	NOUN
ejpam-3637	186	14	.	.	PUNCT
ejpam-3637	187	1	european	european	ADJ
ejpam-3637	187	2	journal	journal	PROPN
ejpam-3637	187	3	of	of	ADP
ejpam-3637	187	4	pure	pure	ADJ
ejpam-3637	187	5	and	and	CCONJ
ejpam-3637	187	6	applied	applied	ADJ
ejpam-3637	187	7	mathematics	mathematic	NOUN
ejpam-3637	187	8	,	,	PUNCT
ejpam-3637	187	9	8(4):502–513	8(4):502–513	NUM
ejpam-3637	187	10	,	,	PUNCT
ejpam-3637	187	11	2015	2015	NUM
ejpam-3637	187	12	.	.	PUNCT
ejpam-3637	188	1	[	[	X
ejpam-3637	188	2	4	4	X
ejpam-3637	188	3	]	]	PUNCT
ejpam-3637	188	4	ot	ot	INTJ
ejpam-3637	188	5	alas	alas	INTJ
ejpam-3637	188	6	.	.	PUNCT
ejpam-3637	188	7	uniform	uniform	PROPN
ejpam-3637	188	8	continuity	continuity	NOUN
ejpam-3637	188	9	in	in	ADP
ejpam-3637	188	10	paracompact	paracompact	ADJ
ejpam-3637	188	11	spaces	space	NOUN
ejpam-3637	188	12	.	.	PUNCT
ejpam-3637	189	1	general	general	ADJ
ejpam-3637	189	2	topology	topology	NOUN
ejpam-3637	189	3	and	and	CCONJ
ejpam-3637	189	4	its	its	PRON
ejpam-3637	189	5	relations	relation	NOUN
ejpam-3637	189	6	to	to	ADP
ejpam-3637	189	7	modern	modern	ADJ
ejpam-3637	189	8	analysis	analysis	NOUN
ejpam-3637	189	9	and	and	CCONJ
ejpam-3637	189	10	algebra	algebra	NOUN
ejpam-3637	189	11	,	,	PUNCT
ejpam-3637	189	12	pages	page	NOUN
ejpam-3637	189	13	19–22	19–22	NUM
ejpam-3637	189	14	,	,	PUNCT
ejpam-3637	189	15	1972	1972	NUM
ejpam-3637	189	16	.	.	PUNCT
ejpam-3637	190	1	[	[	X
ejpam-3637	190	2	5	5	X
ejpam-3637	190	3	]	]	X
ejpam-3637	190	4	p	p	NOUN
ejpam-3637	190	5	alexandroff	alexandroff	NOUN
ejpam-3637	190	6	and	and	CCONJ
ejpam-3637	190	7	h	h	NOUN
ejpam-3637	190	8	hopf	hopf	ADJ
ejpam-3637	190	9	.	.	PUNCT
ejpam-3637	191	1	topologie	topologie	NOUN
ejpam-3637	191	2	,	,	PUNCT
ejpam-3637	191	3	berlin	berlin	PROPN
ejpam-3637	191	4	,	,	PUNCT
ejpam-3637	191	5	1935	1935	NUM
ejpam-3637	191	6	.	.	PUNCT
ejpam-3637	192	1	zentralblatt	zentralblatt	PROPN
ejpam-3637	192	2	math	math	PROPN
ejpam-3637	192	3	,	,	PUNCT
ejpam-3637	192	4	13	13	NUM
ejpam-3637	192	5	,	,	PUNCT
ejpam-3637	192	6	1945	1945	NUM
ejpam-3637	192	7	.	.	PUNCT
ejpam-3637	193	1	[	[	X
ejpam-3637	193	2	6	6	NUM
ejpam-3637	193	3	]	]	PUNCT
ejpam-3637	193	4	av	av	PROPN
ejpam-3637	193	5	arhangel’skii	arhangel’skii	PROPN
ejpam-3637	193	6	.	.	PUNCT
ejpam-3637	194	1	first	first	ADJ
ejpam-3637	194	2	countability	countability	NOUN
ejpam-3637	194	3	,	,	PUNCT
ejpam-3637	194	4	tightness	tightness	NOUN
ejpam-3637	194	5	,	,	PUNCT
ejpam-3637	194	6	and	and	CCONJ
ejpam-3637	194	7	other	other	ADJ
ejpam-3637	194	8	cardinal	cardinal	ADJ
ejpam-3637	194	9	invariants	invariant	NOUN
ejpam-3637	194	10	in	in	ADP
ejpam-3637	194	11	remainders	remainder	NOUN
ejpam-3637	194	12	of	of	ADP
ejpam-3637	194	13	topological	topological	ADJ
ejpam-3637	194	14	groups	group	NOUN
ejpam-3637	194	15	.	.	PUNCT
ejpam-3637	195	1	topology	topology	NOUN
ejpam-3637	195	2	and	and	CCONJ
ejpam-3637	195	3	its	its	PRON
ejpam-3637	195	4	applications	application	NOUN
ejpam-3637	195	5	,	,	PUNCT
ejpam-3637	195	6	154(16):2950–2961	154(16):2950–2961	NUM
ejpam-3637	195	7	,	,	PUNCT
ejpam-3637	195	8	2007	2007	NUM
ejpam-3637	195	9	.	.	PUNCT
ejpam-3637	196	1	[	[	X
ejpam-3637	196	2	7	7	X
ejpam-3637	196	3	]	]	X
ejpam-3637	196	4	alexander	alexander	NOUN
ejpam-3637	196	5	arhangelskii	arhangelskii	PROPN
ejpam-3637	196	6	and	and	CCONJ
ejpam-3637	196	7	mikhail	mikhail	PROPN
ejpam-3637	196	8	tkachenko	tkachenko	PROPN
ejpam-3637	196	9	.	.	PUNCT
ejpam-3637	197	1	topological	topological	ADJ
ejpam-3637	197	2	groups	group	NOUN
ejpam-3637	197	3	and	and	CCONJ
ejpam-3637	197	4	related	related	ADJ
ejpam-3637	197	5	structures	structure	NOUN
ejpam-3637	197	6	,	,	PUNCT
ejpam-3637	197	7	an	an	DET
ejpam-3637	197	8	introduction	introduction	NOUN
ejpam-3637	197	9	to	to	ADP
ejpam-3637	197	10	topological	topological	ADJ
ejpam-3637	197	11	algebra	algebra	PROPN
ejpam-3637	197	12	.	.	PUNCT
ejpam-3637	197	13	,	,	PUNCT
ejpam-3637	197	14	volume	volume	NOUN
ejpam-3637	197	15	1	1	NUM
ejpam-3637	197	16	.	.	PUNCT
ejpam-3637	197	17	springer	springer	PROPN
ejpam-3637	197	18	science	science	PROPN
ejpam-3637	197	19	&	&	CCONJ
ejpam-3637	197	20	business	business	NOUN
ejpam-3637	197	21	media	medium	NOUN
ejpam-3637	197	22	,	,	PUNCT
ejpam-3637	197	23	2008	2008	NUM
ejpam-3637	197	24	.	.	PUNCT
ejpam-3637	198	1	[	[	X
ejpam-3637	198	2	8	8	NUM
ejpam-3637	198	3	]	]	X
ejpam-3637	198	4	alexander	alexander	PROPN
ejpam-3637	198	5	vladimirovich	vladimirovich	PROPN
ejpam-3637	198	6	arkhangelskii	arkhangelskii	PROPN
ejpam-3637	198	7	.	.	PUNCT
ejpam-3637	199	1	classes	class	NOUN
ejpam-3637	199	2	of	of	ADP
ejpam-3637	199	3	topological	topological	ADJ
ejpam-3637	199	4	groups	group	NOUN
ejpam-3637	199	5	.	.	PUNCT
ejpam-3637	200	1	russian	russian	ADJ
ejpam-3637	200	2	mathematical	mathematical	ADJ
ejpam-3637	200	3	surveys	survey	NOUN
ejpam-3637	200	4	,	,	PUNCT
ejpam-3637	200	5	36(3):151	36(3):151	NOUN
ejpam-3637	200	6	,	,	PUNCT
ejpam-3637	200	7	1981	1981	NUM
ejpam-3637	200	8	.	.	PUNCT
ejpam-3637	201	1	[	[	X
ejpam-3637	201	2	9	9	NUM
ejpam-3637	201	3	]	]	PUNCT
ejpam-3637	201	4	lawrence	lawrence	PROPN
ejpam-3637	201	5	g	g	PROPN
ejpam-3637	201	6	brown	brown	PROPN
ejpam-3637	201	7	.	.	PUNCT
ejpam-3637	202	1	topologically	topologically	ADV
ejpam-3637	202	2	complete	complete	ADJ
ejpam-3637	202	3	groups	group	NOUN
ejpam-3637	202	4	.	.	PUNCT
ejpam-3637	203	1	proceedings	proceeding	NOUN
ejpam-3637	203	2	of	of	ADP
ejpam-3637	203	3	the	the	DET
ejpam-3637	203	4	american	american	PROPN
ejpam-3637	203	5	mathematical	mathematical	PROPN
ejpam-3637	203	6	society	society	NOUN
ejpam-3637	203	7	,	,	PUNCT
ejpam-3637	203	8	35(2):593–600	35(2):593–600	PROPN
ejpam-3637	203	9	,	,	PUNCT
ejpam-3637	203	10	1972	1972	NUM
ejpam-3637	203	11	.	.	PUNCT
ejpam-3637	204	1	[	[	X
ejpam-3637	204	2	10	10	NUM
ejpam-3637	204	3	]	]	X
ejpam-3637	204	4	david	david	PROPN
ejpam-3637	204	5	buhagiar	buhagiar	PROPN
ejpam-3637	204	6	and	and	CCONJ
ejpam-3637	204	7	b	b	NOUN
ejpam-3637	204	8	pasynkov	pasynkov	NOUN
ejpam-3637	204	9	.	.	PUNCT
ejpam-3637	205	1	on	on	ADP
ejpam-3637	205	2	uniform	uniform	ADJ
ejpam-3637	205	3	paracompactness	paracompactness	PROPN
ejpam-3637	205	4	.	.	PUNCT
ejpam-3637	206	1	czechoslovak	czechoslovak	ADJ
ejpam-3637	206	2	mathematical	mathematical	PROPN
ejpam-3637	206	3	journal	journal	PROPN
ejpam-3637	206	4	,	,	PUNCT
ejpam-3637	206	5	46(4):577–586	46(4):577–586	PROPN
ejpam-3637	206	6	,	,	PUNCT
ejpam-3637	206	7	1996	1996	NUM
ejpam-3637	206	8	.	.	PUNCT
ejpam-3637	207	1	[	[	X
ejpam-3637	207	2	11	11	NUM
ejpam-3637	207	3	]	]	PUNCT
ejpam-3637	207	4	ja	ja	PROPN
ejpam-3637	207	5	dieudonné.	dieudonné.	PROPN
ejpam-3637	207	6	une	une	PROPN
ejpam-3637	207	7	généralisation	généralisation	PROPN
ejpam-3637	207	8	des	des	PROPN
ejpam-3637	207	9	espaces	espace	NOUN
ejpam-3637	207	10	compacts	compact	NOUN
ejpam-3637	207	11	.	.	PUNCT
ejpam-3637	208	1	j.	j.	PROPN
ejpam-3637	208	2	math	math	PROPN
ejpam-3637	208	3	.	.	PUNCT
ejpam-3637	209	1	pures	pure	NOUN
ejpam-3637	209	2	.	.	PUNCT
ejpam-3637	209	3	appl	appl	PROPN
ejpam-3637	209	4	.	.	PROPN
ejpam-3637	209	5	,	,	PUNCT
ejpam-3637	209	6	23:65–76	23:65–76	NUM
ejpam-3637	209	7	,	,	PUNCT
ejpam-3637	209	8	1944	1944	NUM
ejpam-3637	209	9	.	.	PUNCT
ejpam-3637	210	1	[	[	X
ejpam-3637	210	2	12	12	NUM
ejpam-3637	210	3	]	]	X
ejpam-3637	210	4	clifford	clifford	PROPN
ejpam-3637	210	5	h	h	PROPN
ejpam-3637	210	6	dowker	dowker	PROPN
ejpam-3637	210	7	.	.	PUNCT
ejpam-3637	211	1	on	on	ADP
ejpam-3637	211	2	countably	countably	ADV
ejpam-3637	211	3	paracompact	paracompact	ADJ
ejpam-3637	211	4	spaces	space	NOUN
ejpam-3637	211	5	.	.	PUNCT
ejpam-3637	212	1	canadian	canadian	ADJ
ejpam-3637	212	2	journal	journal	PROPN
ejpam-3637	212	3	of	of	ADP
ejpam-3637	212	4	mathematics	mathematic	NOUN
ejpam-3637	212	5	,	,	PUNCT
ejpam-3637	212	6	3:219–224	3:219–224	NUM
ejpam-3637	212	7	,	,	PUNCT
ejpam-3637	212	8	1951	1951	NUM
ejpam-3637	212	9	.	.	PUNCT
ejpam-3637	213	1	[	[	X
ejpam-3637	213	2	13	13	NUM
ejpam-3637	213	3	]	]	X
ejpam-3637	213	4	r	r	NOUN
ejpam-3637	213	5	engelking	engelking	NOUN
ejpam-3637	213	6	.	.	PUNCT
ejpam-3637	214	1	general	general	ADJ
ejpam-3637	214	2	topology	topology	NOUN
ejpam-3637	214	3	,	,	PUNCT
ejpam-3637	214	4	heldermann	heldermann	NOUN
ejpam-3637	214	5	,	,	PUNCT
ejpam-3637	214	6	1989	1989	NUM
ejpam-3637	214	7	.	.	PUNCT
ejpam-3637	215	1	[	[	X
ejpam-3637	215	2	14	14	NUM
ejpam-3637	215	3	]	]	X
ejpam-3637	215	4	chris	chris	PROPN
ejpam-3637	215	5	good	good	PROPN
ejpam-3637	215	6	,	,	PUNCT
ejpam-3637	215	7	robin	robin	PROPN
ejpam-3637	215	8	knight	knight	PROPN
ejpam-3637	215	9	,	,	PUNCT
ejpam-3637	215	10	and	and	CCONJ
ejpam-3637	215	11	ian	ian	ADJ
ejpam-3637	215	12	stares	stare	VERB
ejpam-3637	215	13	.	.	PUNCT
ejpam-3637	216	1	monotone	monotone	ADJ
ejpam-3637	216	2	countable	countable	ADJ
ejpam-3637	216	3	paracompactness	paracompactness	NOUN
ejpam-3637	216	4	.	.	PUNCT
ejpam-3637	217	1	topology	topology	NOUN
ejpam-3637	217	2	and	and	CCONJ
ejpam-3637	217	3	its	its	PRON
ejpam-3637	217	4	applications	application	NOUN
ejpam-3637	217	5	,	,	PUNCT
ejpam-3637	217	6	101(3):281–298	101(3):281–298	NUM
ejpam-3637	217	7	,	,	PUNCT
ejpam-3637	217	8	2000	2000	NUM
ejpam-3637	217	9	.	.	PUNCT
ejpam-3637	218	1	[	[	X
ejpam-3637	218	2	15	15	NUM
ejpam-3637	218	3	]	]	X
ejpam-3637	218	4	hugo	hugo	PROPN
ejpam-3637	218	5	juárez	juárez	PROPN
ejpam-3637	218	6	-	-	PUNCT
ejpam-3637	218	7	anguiano	anguiano	NOUN
ejpam-3637	218	8	and	and	CCONJ
ejpam-3637	218	9	iván	iván	PROPN
ejpam-3637	218	10	sánchez	sánchez	PROPN
ejpam-3637	218	11	.	.	PUNCT
ejpam-3637	219	1	on	on	ADP
ejpam-3637	219	2	strongly	strongly	ADV
ejpam-3637	219	3	ω	ω	ADJ
ejpam-3637	219	4	-	-	PUNCT
ejpam-3637	219	5	balanced	balanced	ADJ
ejpam-3637	219	6	topological	topological	ADJ
ejpam-3637	219	7	groups	group	NOUN
ejpam-3637	219	8	.	.	PUNCT
ejpam-3637	220	1	topology	topology	NOUN
ejpam-3637	220	2	and	and	CCONJ
ejpam-3637	220	3	its	its	PRON
ejpam-3637	220	4	applications	application	NOUN
ejpam-3637	220	5	,	,	PUNCT
ejpam-3637	220	6	221:370–378	221:370–378	NUM
ejpam-3637	220	7	,	,	PUNCT
ejpam-3637	220	8	2017	2017	NUM
ejpam-3637	220	9	.	.	PUNCT
ejpam-3637	221	1	[	[	X
ejpam-3637	221	2	16	16	NUM
ejpam-3637	221	3	]	]	PUNCT
ejpam-3637	221	4	miroslav	miroslav	ADJ
ejpam-3637	221	5	katětov	katětov	PROPN
ejpam-3637	221	6	.	.	PUNCT
ejpam-3637	222	1	measures	measure	NOUN
ejpam-3637	222	2	in	in	ADP
ejpam-3637	222	3	fully	fully	ADV
ejpam-3637	222	4	normal	normal	ADJ
ejpam-3637	222	5	spaces	space	NOUN
ejpam-3637	222	6	.	.	PUNCT
ejpam-3637	223	1	fundamenta	fundamenta	PROPN
ejpam-3637	223	2	mathematicae	mathematicae	PROPN
ejpam-3637	223	3	,	,	PUNCT
ejpam-3637	223	4	38(1):73–84	38(1):73–84	NUM
ejpam-3637	223	5	,	,	PUNCT
ejpam-3637	223	6	1951	1951	NUM
ejpam-3637	223	7	.	.	PUNCT
ejpam-3637	224	1	[	[	X
ejpam-3637	224	2	17	17	NUM
ejpam-3637	224	3	]	]	PUNCT
ejpam-3637	224	4	jm	jm	PROPN
ejpam-3637	224	5	kister	kister	PROPN
ejpam-3637	224	6	.	.	PUNCT
ejpam-3637	225	1	uniform	uniform	ADJ
ejpam-3637	225	2	continuity	continuity	NOUN
ejpam-3637	225	3	and	and	CCONJ
ejpam-3637	225	4	compactness	compactness	NOUN
ejpam-3637	225	5	in	in	ADP
ejpam-3637	225	6	topological	topological	ADJ
ejpam-3637	225	7	groups	group	NOUN
ejpam-3637	225	8	.	.	PUNCT
ejpam-3637	226	1	proceedings	proceeding	NOUN
ejpam-3637	226	2	of	of	ADP
ejpam-3637	226	3	the	the	DET
ejpam-3637	226	4	american	american	PROPN
ejpam-3637	226	5	mathematical	mathematical	PROPN
ejpam-3637	226	6	society	society	NOUN
ejpam-3637	226	7	,	,	PUNCT
ejpam-3637	226	8	13(1):37–40	13(1):37–40	NUM
ejpam-3637	226	9	,	,	PUNCT
ejpam-3637	226	10	1962	1962	NUM
ejpam-3637	226	11	.	.	PUNCT
ejpam-3637	227	1	[	[	X
ejpam-3637	227	2	18	18	NUM
ejpam-3637	227	3	]	]	X
ejpam-3637	227	4	fucai	fucai	PROPN
ejpam-3637	227	5	lin	lin	PROPN
ejpam-3637	227	6	,	,	PUNCT
ejpam-3637	227	7	jing	jing	PROPN
ejpam-3637	227	8	zhang	zhang	PROPN
ejpam-3637	227	9	,	,	PUNCT
ejpam-3637	227	10	and	and	CCONJ
ejpam-3637	227	11	kexiu	kexiu	PROPN
ejpam-3637	227	12	zhang	zhang	PROPN
ejpam-3637	227	13	.	.	PUNCT
ejpam-3637	228	1	locally	locally	ADV
ejpam-3637	228	2	σ	σ	VERB
ejpam-3637	228	3	-	-	ADJ
ejpam-3637	228	4	compact	compact	ADJ
ejpam-3637	228	5	rectifiable	rectifiable	ADJ
ejpam-3637	228	6	spaces	space	NOUN
ejpam-3637	228	7	.	.	PUNCT
ejpam-3637	229	1	topology	topology	NOUN
ejpam-3637	229	2	and	and	CCONJ
ejpam-3637	229	3	its	its	PRON
ejpam-3637	229	4	applications	application	NOUN
ejpam-3637	229	5	,	,	PUNCT
ejpam-3637	229	6	193:182–191	193:182–191	NUM
ejpam-3637	229	7	,	,	PUNCT
ejpam-3637	229	8	2015	2015	NUM
ejpam-3637	229	9	.	.	PUNCT
ejpam-3637	230	1	references	reference	NOUN
ejpam-3637	230	2	286	286	NUM
ejpam-3637	230	3	[	[	SYM
ejpam-3637	230	4	19	19	NUM
ejpam-3637	230	5	]	]	PUNCT
ejpam-3637	230	6	muhammad	muhammad	PROPN
ejpam-3637	230	7	kashif	kashif	PROPN
ejpam-3637	230	8	maqbool	maqbool	PROPN
ejpam-3637	230	9	and	and	CCONJ
ejpam-3637	230	10	muhammad	muhammad	PROPN
ejpam-3637	230	11	awais	awais	PROPN
ejpam-3637	230	12	yousaf	yousaf	PROPN
ejpam-3637	230	13	.	.	PUNCT
ejpam-3637	231	1	on	on	ADP
ejpam-3637	231	2	separately	separately	ADV
ejpam-3637	231	3	irresolute	irresolute	ADJ
ejpam-3637	231	4	and	and	CCONJ
ejpam-3637	231	5	pre	pre	VERB
ejpam-3637	231	6	semi	semi	ADV
ejpam-3637	231	7	open	open	ADJ
ejpam-3637	231	8	multiplication	multiplication	NOUN
ejpam-3637	231	9	mapping	mapping	NOUN
ejpam-3637	231	10	of	of	ADP
ejpam-3637	231	11	topological	topological	ADJ
ejpam-3637	231	12	spaces	space	NOUN
ejpam-3637	231	13	defined	define	VERB
ejpam-3637	231	14	on	on	ADP
ejpam-3637	231	15	loops	loop	NOUN
ejpam-3637	231	16	.	.	PUNCT
ejpam-3637	232	1	punjab	punjab	PROPN
ejpam-3637	232	2	university	university	PROPN
ejpam-3637	232	3	journal	journal	NOUN
ejpam-3637	232	4	of	of	ADP
ejpam-3637	232	5	mathematics	mathematic	NOUN
ejpam-3637	232	6	,	,	PUNCT
ejpam-3637	232	7	51(12):37–44	51(12):37–44	NUM
ejpam-3637	232	8	,	,	PUNCT
ejpam-3637	232	9	2019	2019	NUM
ejpam-3637	232	10	.	.	PUNCT
ejpam-3637	233	1	[	[	X
ejpam-3637	233	2	20	20	NUM
ejpam-3637	233	3	]	]	PUNCT
ejpam-3637	233	4	muhammad	muhammad	PROPN
ejpam-3637	233	5	kashif	kashif	PROPN
ejpam-3637	233	6	maqbool	maqbool	PROPN
ejpam-3637	233	7	,	,	PUNCT
ejpam-3637	233	8	muhammad	muhammad	PROPN
ejpam-3637	233	9	awais	awais	PROPN
ejpam-3637	233	10	yousaf	yousaf	PROPN
ejpam-3637	233	11	,	,	PUNCT
ejpam-3637	233	12	and	and	CCONJ
ejpam-3637	233	13	abdul	abdul	PROPN
ejpam-3637	233	14	razaq	razaq	PROPN
ejpam-3637	233	15	.	.	PUNCT
ejpam-3637	234	1	on	on	ADP
ejpam-3637	234	2	generalization	generalization	NOUN
ejpam-3637	234	3	of	of	ADP
ejpam-3637	234	4	quasi	quasi	NOUN
ejpam-3637	234	5	s	s	NOUN
ejpam-3637	234	6	-	-	ADJ
ejpam-3637	234	7	topological	topological	ADJ
ejpam-3637	234	8	ip	ip	NOUN
ejpam-3637	234	9	-	-	PUNCT
ejpam-3637	234	10	loops	loop	NOUN
ejpam-3637	234	11	.	.	PUNCT
ejpam-3637	235	1	punjab	punjab	PROPN
ejpam-3637	235	2	university	university	PROPN
ejpam-3637	235	3	journal	journal	NOUN
ejpam-3637	235	4	of	of	ADP
ejpam-3637	235	5	mathematics	mathematic	NOUN
ejpam-3637	235	6	,	,	PUNCT
ejpam-3637	235	7	52(1):121–128	52(1):121–128	PROPN
ejpam-3637	235	8	,	,	PUNCT
ejpam-3637	235	9	2020	2020	NUM
ejpam-3637	235	10	.	.	PUNCT
ejpam-3637	236	1	[	[	X
ejpam-3637	236	2	21	21	NUM
ejpam-3637	236	3	]	]	X
ejpam-3637	236	4	ernest	ernest	PROPN
ejpam-3637	236	5	michael	michael	PROPN
ejpam-3637	236	6	.	.	PUNCT
ejpam-3637	237	1	a	a	DET
ejpam-3637	237	2	note	note	NOUN
ejpam-3637	237	3	on	on	ADP
ejpam-3637	237	4	paracompact	paracompact	ADJ
ejpam-3637	237	5	spaces	space	NOUN
ejpam-3637	237	6	.	.	PUNCT
ejpam-3637	238	1	proceedings	proceeding	NOUN
ejpam-3637	238	2	of	of	ADP
ejpam-3637	238	3	the	the	DET
ejpam-3637	238	4	american	american	PROPN
ejpam-3637	238	5	mathematical	mathematical	PROPN
ejpam-3637	238	6	society	society	NOUN
ejpam-3637	238	7	,	,	PUNCT
ejpam-3637	238	8	4(5):831–838	4(5):831–838	NOUN
ejpam-3637	238	9	,	,	PUNCT
ejpam-3637	238	10	1953	1953	NUM
ejpam-3637	238	11	.	.	PUNCT
ejpam-3637	239	1	[	[	X
ejpam-3637	239	2	22	22	NUM
ejpam-3637	239	3	]	]	X
ejpam-3637	239	4	ernest	ernest	PROPN
ejpam-3637	239	5	michael	michael	PROPN
ejpam-3637	239	6	.	.	PUNCT
ejpam-3637	240	1	another	another	DET
ejpam-3637	240	2	note	note	NOUN
ejpam-3637	240	3	on	on	ADP
ejpam-3637	240	4	paracompact	paracompact	ADJ
ejpam-3637	240	5	spaces	space	NOUN
ejpam-3637	240	6	.	.	PUNCT
ejpam-3637	241	1	proceedings	proceeding	NOUN
ejpam-3637	241	2	of	of	ADP
ejpam-3637	241	3	the	the	DET
ejpam-3637	241	4	american	american	PROPN
ejpam-3637	241	5	mathematical	mathematical	PROPN
ejpam-3637	241	6	society	society	NOUN
ejpam-3637	241	7	,	,	PUNCT
ejpam-3637	241	8	8(4):822–828	8(4):822–828	NUM
ejpam-3637	241	9	,	,	PUNCT
ejpam-3637	241	10	1957	1957	NUM
ejpam-3637	241	11	.	.	PUNCT
ejpam-3637	242	1	[	[	X
ejpam-3637	242	2	23	23	NUM
ejpam-3637	242	3	]	]	X
ejpam-3637	242	4	salvador	salvador	PROPN
ejpam-3637	242	5	romaguera	romaguera	PROPN
ejpam-3637	242	6	and	and	CCONJ
ejpam-3637	242	7	manuel	manuel	PROPN
ejpam-3637	242	8	sanchis	sanchis	PROPN
ejpam-3637	242	9	.	.	PUNCT
ejpam-3637	243	1	locally	locally	ADV
ejpam-3637	243	2	compact	compact	ADJ
ejpam-3637	243	3	topological	topological	ADJ
ejpam-3637	243	4	groups	group	NOUN
ejpam-3637	243	5	and	and	CCONJ
ejpam-3637	243	6	cofinal	cofinal	ADJ
ejpam-3637	243	7	completeness	completeness	NOUN
ejpam-3637	243	8	.	.	PUNCT
ejpam-3637	244	1	journal	journal	NOUN
ejpam-3637	244	2	of	of	ADP
ejpam-3637	244	3	the	the	DET
ejpam-3637	244	4	london	london	PROPN
ejpam-3637	244	5	mathematical	mathematical	ADJ
ejpam-3637	244	6	society	society	NOUN
ejpam-3637	244	7	,	,	PUNCT
ejpam-3637	244	8	62(2):451–460	62(2):451–460	PROPN
ejpam-3637	244	9	,	,	PUNCT
ejpam-3637	244	10	2000	2000	NUM
ejpam-3637	244	11	.	.	PUNCT
ejpam-3637	245	1	[	[	X
ejpam-3637	245	2	24	24	NUM
ejpam-3637	245	3	]	]	PUNCT
ejpam-3637	245	4	db	db	PROPN
ejpam-3637	245	5	shakhmatov	shakhmatov	PROPN
ejpam-3637	245	6	.	.	PUNCT
ejpam-3637	246	1	a	a	DET
ejpam-3637	246	2	problem	problem	NOUN
ejpam-3637	246	3	of	of	ADP
ejpam-3637	246	4	coincidence	coincidence	NOUN
ejpam-3637	246	5	of	of	ADP
ejpam-3637	246	6	dimensions	dimension	NOUN
ejpam-3637	246	7	in	in	ADP
ejpam-3637	246	8	topological	topological	ADJ
ejpam-3637	246	9	groups	group	NOUN
ejpam-3637	246	10	.	.	PUNCT
ejpam-3637	247	1	topology	topology	NOUN
ejpam-3637	247	2	and	and	CCONJ
ejpam-3637	247	3	its	its	PRON
ejpam-3637	247	4	applications	application	NOUN
ejpam-3637	247	5	,	,	PUNCT
ejpam-3637	247	6	33(1):105–113	33(1):105–113	PROPN
ejpam-3637	247	7	,	,	PUNCT
ejpam-3637	247	8	1989	1989	NUM
ejpam-3637	247	9	.	.	PUNCT
ejpam-3637	248	1	[	[	X
ejpam-3637	248	2	25	25	NUM
ejpam-3637	248	3	]	]	X
ejpam-3637	248	4	arthur	arthur	PROPN
ejpam-3637	248	5	h	h	PROPN
ejpam-3637	248	6	stone	stone	PROPN
ejpam-3637	248	7	.	.	PUNCT
ejpam-3637	249	1	paracompactness	paracompactness	NOUN
ejpam-3637	249	2	and	and	CCONJ
ejpam-3637	249	3	product	product	NOUN
ejpam-3637	249	4	spaces	space	NOUN
ejpam-3637	249	5	.	.	PUNCT
ejpam-3637	250	1	bulletin	bulletin	NOUN
ejpam-3637	250	2	of	of	ADP
ejpam-3637	250	3	the	the	DET
ejpam-3637	250	4	american	american	PROPN
ejpam-3637	250	5	mathematical	mathematical	PROPN
ejpam-3637	250	6	society	society	NOUN
ejpam-3637	250	7	,	,	PUNCT
ejpam-3637	250	8	54(10):977–982	54(10):977–982	NOUN
ejpam-3637	250	9	,	,	PUNCT
ejpam-3637	250	10	1948	1948	NUM
ejpam-3637	250	11	.	.	PUNCT
ejpam-3637	251	1	[	[	X
ejpam-3637	251	2	26	26	NUM
ejpam-3637	251	3	]	]	SYM
ejpam-3637	251	4	mg	mg	PROPN
ejpam-3637	251	5	tkachenko	tkachenko	PROPN
ejpam-3637	251	6	,	,	PUNCT
ejpam-3637	251	7	c	c	PROPN
ejpam-3637	251	8	hernández	hernández	PROPN
ejpam-3637	251	9	-	-	PUNCT
ejpam-3637	251	10	garćıa	garćıa	NOUN
ejpam-3637	251	11	,	,	PUNCT
ejpam-3637	251	12	and	and	CCONJ
ejpam-3637	251	13	ma	ma	PROPN
ejpam-3637	251	14	lópez	lópez	PROPN
ejpam-3637	251	15	ramı́rez	ramı́rez	PROPN
ejpam-3637	251	16	.	.	PUNCT
ejpam-3637	251	17	strong	strong	ADJ
ejpam-3637	251	18	realcompactness	realcompactness	NOUN
ejpam-3637	251	19	and	and	CCONJ
ejpam-3637	251	20	strong	strong	ADJ
ejpam-3637	251	21	dieudonné	dieudonné	NOUN
ejpam-3637	251	22	completeness	completeness	NOUN
ejpam-3637	251	23	in	in	ADP
ejpam-3637	251	24	topological	topological	ADJ
ejpam-3637	251	25	groups	group	NOUN
ejpam-3637	251	26	.	.	PUNCT
ejpam-3637	252	1	topology	topology	NOUN
ejpam-3637	252	2	and	and	CCONJ
ejpam-3637	252	3	its	its	PRON
ejpam-3637	252	4	applications	application	NOUN
ejpam-3637	252	5	,	,	PUNCT
ejpam-3637	252	6	159(7):1948–1955	159(7):1948–1955	NUM
ejpam-3637	252	7	,	,	PUNCT
ejpam-3637	252	8	2012	2012	NUM
ejpam-3637	252	9	.	.	PUNCT
ejpam-3637	253	1	[	[	X
ejpam-3637	253	2	27	27	NUM
ejpam-3637	253	3	]	]	SYM
ejpam-3637	253	4	jerry	jerry	PROPN
ejpam-3637	253	5	e	e	PROPN
ejpam-3637	253	6	vaughan	vaughan	PROPN
ejpam-3637	253	7	,	,	PUNCT
ejpam-3637	253	8	kenneth	kenneth	PROPN
ejpam-3637	253	9	kunen	kunen	PROPN
ejpam-3637	253	10	,	,	PUNCT
ejpam-3637	253	11	and	and	CCONJ
ejpam-3637	253	12	je	je	PROPN
ejpam-3637	253	13	vaughan	vaughan	PROPN
ejpam-3637	253	14	.	.	PROPN
ejpam-3637	254	1	handbook	handbook	PROPN
ejpam-3637	254	2	of	of	ADP
ejpam-3637	254	3	set	set	NOUN
ejpam-3637	254	4	-	-	PUNCT
ejpam-3637	254	5	theoretic	theoretic	NOUN
ejpam-3637	254	6	topology	topology	NOUN
ejpam-3637	254	7	.	.	PUNCT
ejpam-3637	255	1	north	north	NOUN
ejpam-3637	255	2	-	-	PUNCT
ejpam-3637	255	3	holland	holland	PROPN
ejpam-3637	255	4	,	,	PUNCT
ejpam-3637	255	5	1984	1984	NUM
ejpam-3637	255	6	.	.	PUNCT
ejpam-3637	256	1	[	[	X
ejpam-3637	256	2	28	28	NUM
ejpam-3637	256	3	]	]	X
ejpam-3637	256	4	stephen	stephen	PROPN
ejpam-3637	256	5	willard	willard	PROPN
ejpam-3637	256	6	.	.	PUNCT
ejpam-3637	256	7	general	general	ADJ
ejpam-3637	256	8	topology	topology	PROPN
ejpam-3637	256	9	,	,	PUNCT
ejpam-3637	256	10	addison	addison	PROPN
ejpam-3637	256	11	,	,	PUNCT
ejpam-3637	256	12	1970	1970	NUM
ejpam-3637	256	13	.	.	PUNCT