id	sid	tid	token	lemma	pos
ejpam-5899	1	1	european	european	PROPN
ejpam-5899	1	2	journal	journal	PROPN
ejpam-5899	1	3	of	of	ADP
ejpam-5899	1	4	pure	pure	ADJ
ejpam-5899	1	5	and	and	CCONJ
ejpam-5899	1	6	applied	applied	ADJ
ejpam-5899	1	7	mathematics	mathematic	NOUN
ejpam-5899	1	8	2025	2025	NUM
ejpam-5899	1	9	,	,	PUNCT
ejpam-5899	1	10	vol	vol	NOUN
ejpam-5899	1	11	.	.	PROPN
ejpam-5899	1	12	18	18	NUM
ejpam-5899	1	13	,	,	PUNCT
ejpam-5899	1	14	issue	issue	NOUN
ejpam-5899	1	15	2	2	NUM
ejpam-5899	1	16	,	,	PUNCT
ejpam-5899	1	17	article	article	NOUN
ejpam-5899	1	18	number	number	NOUN
ejpam-5899	1	19	5899	5899	NUM
ejpam-5899	1	20	issn	issn	VERB
ejpam-5899	1	21	1307	1307	NUM
ejpam-5899	1	22	-	-	SYM
ejpam-5899	1	23	5543	5543	NUM
ejpam-5899	1	24	–	–	PUNCT
ejpam-5899	1	25	ejpam.com	ejpam.com	X
ejpam-5899	1	26	published	publish	VERB
ejpam-5899	1	27	by	by	ADP
ejpam-5899	1	28	new	new	PROPN
ejpam-5899	1	29	york	york	PROPN
ejpam-5899	1	30	business	business	PROPN
ejpam-5899	1	31	global	global	ADJ
ejpam-5899	1	32	on	on	ADP
ejpam-5899	1	33	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	1	34	sets	set	NOUN
ejpam-5899	1	35	heyam	heyam	PROPN
ejpam-5899	1	36	h.	h.	PROPN
ejpam-5899	1	37	al	al	PROPN
ejpam-5899	1	38	-	-	PUNCT
ejpam-5899	1	39	jarrah1	jarrah1	PROPN
ejpam-5899	1	40	,	,	PUNCT
ejpam-5899	1	41	amani	amani	PROPN
ejpam-5899	1	42	rawshdeh2,∗	rawshdeh2,∗	PROPN
ejpam-5899	1	43	,	,	PUNCT
ejpam-5899	1	44	khalid	khalid	PROPN
ejpam-5899	1	45	y.	y.	PROPN
ejpam-5899	1	46	al	al	PROPN
ejpam-5899	1	47	-	-	PUNCT
ejpam-5899	1	48	zoubi1	zoubi1	PROPN
ejpam-5899	1	49	,	,	PUNCT
ejpam-5899	1	50	shefa	shefa	PROPN
ejpam-5899	1	51	a.	a.	PROPN
ejpam-5899	1	52	bani	bani	PROPN
ejpam-5899	1	53	melhem1	melhem1	PROPN
ejpam-5899	2	1	1	1	NUM
ejpam-5899	2	2	department	department	NOUN
ejpam-5899	2	3	of	of	ADP
ejpam-5899	2	4	mathematics	mathematic	NOUN
ejpam-5899	2	5	,	,	PUNCT
ejpam-5899	2	6	faculty	faculty	NOUN
ejpam-5899	2	7	of	of	ADP
ejpam-5899	2	8	science	science	NOUN
ejpam-5899	2	9	,	,	PUNCT
ejpam-5899	2	10	yarmouk	yarmouk	CCONJ
ejpam-5899	2	11	university	university	NOUN
ejpam-5899	2	12	,	,	PUNCT
ejpam-5899	2	13	irbid	irbid	PROPN
ejpam-5899	2	14	,	,	PUNCT
ejpam-5899	2	15	jordan	jordan	PROPN
ejpam-5899	2	16	2	2	NUM
ejpam-5899	2	17	department	department	NOUN
ejpam-5899	2	18	of	of	ADP
ejpam-5899	2	19	mathematics	mathematic	NOUN
ejpam-5899	2	20	,	,	PUNCT
ejpam-5899	2	21	faculty	faculty	NOUN
ejpam-5899	2	22	of	of	ADP
ejpam-5899	2	23	science	science	NOUN
ejpam-5899	2	24	,	,	PUNCT
ejpam-5899	2	25	al	al	PROPN
ejpam-5899	2	26	-	-	PUNCT
ejpam-5899	2	27	balqa	balqa	NOUN
ejpam-5899	2	28	applied	apply	VERB
ejpam-5899	2	29	university	university	NOUN
ejpam-5899	2	30	,	,	PUNCT
ejpam-5899	2	31	alsalt	alsalt	NOUN
ejpam-5899	2	32	,	,	PUNCT
ejpam-5899	2	33	jordan	jordan	PROPN
ejpam-5899	2	34	abstract	abstract	PROPN
ejpam-5899	2	35	.	.	PUNCT
ejpam-5899	3	1	in	in	ADP
ejpam-5899	3	2	this	this	DET
ejpam-5899	3	3	work	work	NOUN
ejpam-5899	3	4	,	,	PUNCT
ejpam-5899	3	5	we	we	PRON
ejpam-5899	3	6	use	use	VERB
ejpam-5899	3	7	the	the	DET
ejpam-5899	3	8	notion	notion	NOUN
ejpam-5899	3	9	of	of	ADP
ejpam-5899	3	10	the	the	DET
ejpam-5899	3	11	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	3	12	space	space	NOUN
ejpam-5899	4	1	[	[	X
ejpam-5899	4	2	6	6	NUM
ejpam-5899	4	3	]	]	PUNCT
ejpam-5899	4	4	to	to	PART
ejpam-5899	4	5	introduce	introduce	VERB
ejpam-5899	4	6	two	two	NUM
ejpam-5899	4	7	types	type	NOUN
ejpam-5899	4	8	of	of	ADP
ejpam-5899	4	9	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	4	10	sets	set	NOUN
ejpam-5899	4	11	called	call	VERB
ejpam-5899	4	12	α	α	NOUN
ejpam-5899	4	13	-	-	PUNCT
ejpam-5899	4	14	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	4	15	and	and	CCONJ
ejpam-5899	4	16	β	β	NOUN
ejpam-5899	4	17	-	-	NOUN
ejpam-5899	4	18	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	4	19	.	.	PUNCT
ejpam-5899	5	1	we	we	PRON
ejpam-5899	5	2	show	show	VERB
ejpam-5899	5	3	that	that	SCONJ
ejpam-5899	5	4	every	every	DET
ejpam-5899	5	5	α	α	X
ejpam-5899	5	6	-	-	PUNCT
ejpam-5899	5	7	gµ-paracompact	gµ-paracompact	ADJ
ejpam-5899	5	8	set	set	NOUN
ejpam-5899	5	9	is	be	AUX
ejpam-5899	5	10	β	β	NOUN
ejpam-5899	5	11	-	-	NOUN
ejpam-5899	5	12	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	5	13	and	and	CCONJ
ejpam-5899	5	14	if	if	SCONJ
ejpam-5899	5	15	a	a	DET
ejpam-5899	5	16	generalized	generalized	ADJ
ejpam-5899	5	17	topological	topological	ADJ
ejpam-5899	5	18	space	space	NOUN
ejpam-5899	5	19	(	(	PUNCT
ejpam-5899	5	20	s	s	X
ejpam-5899	5	21	,	,	PUNCT
ejpam-5899	5	22	µ	µ	NOUN
ejpam-5899	5	23	)	)	PUNCT
ejpam-5899	5	24	is	be	AUX
ejpam-5899	5	25	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	5	26	,	,	PUNCT
ejpam-5899	5	27	then	then	ADV
ejpam-5899	5	28	every	every	DET
ejpam-5899	5	29	µ-closed	µ-close	VERB
ejpam-5899	5	30	subset	subset	VERB
ejpam-5899	5	31	in	in	ADP
ejpam-5899	5	32	(	(	PUNCT
ejpam-5899	5	33	s	s	PROPN
ejpam-5899	5	34	,	,	PUNCT
ejpam-5899	5	35	µ	µ	NOUN
ejpam-5899	5	36	)	)	PUNCT
ejpam-5899	5	37	is	be	AUX
ejpam-5899	5	38	α	α	NOUN
ejpam-5899	5	39	-	-	PUNCT
ejpam-5899	5	40	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	5	41	while	while	SCONJ
ejpam-5899	5	42	every	every	DET
ejpam-5899	5	43	µg	µg	ADJ
ejpam-5899	5	44	-	-	PUNCT
ejpam-5899	5	45	closed	closed	ADJ
ejpam-5899	5	46	subset	subset	NOUN
ejpam-5899	5	47	in	in	ADP
ejpam-5899	5	48	(	(	PUNCT
ejpam-5899	5	49	s	s	PROPN
ejpam-5899	5	50	,	,	PUNCT
ejpam-5899	5	51	µ	µ	NOUN
ejpam-5899	5	52	)	)	PUNCT
ejpam-5899	5	53	is	be	AUX
ejpam-5899	5	54	β	β	NOUN
ejpam-5899	5	55	-	-	NOUN
ejpam-5899	5	56	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	5	57	.	.	PUNCT
ejpam-5899	6	1	finally	finally	ADV
ejpam-5899	6	2	,	,	PUNCT
ejpam-5899	6	3	we	we	PRON
ejpam-5899	6	4	introduce	introduce	VERB
ejpam-5899	6	5	the	the	DET
ejpam-5899	6	6	notion	notion	NOUN
ejpam-5899	6	7	of	of	ADP
ejpam-5899	6	8	co	co	ADJ
ejpam-5899	6	9	-	-	ADJ
ejpam-5899	6	10	α	α	PRON
ejpam-5899	6	11	-	-	PUNCT
ejpam-5899	6	12	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	6	13	set	set	NOUN
ejpam-5899	6	14	as	as	ADP
ejpam-5899	6	15	an	an	DET
ejpam-5899	6	16	application	application	NOUN
ejpam-5899	6	17	of	of	ADP
ejpam-5899	6	18	α	α	NOUN
ejpam-5899	6	19	-	-	PUNCT
ejpam-5899	6	20	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	6	21	and	and	CCONJ
ejpam-5899	6	22	study	study	VERB
ejpam-5899	6	23	some	some	PRON
ejpam-5899	6	24	of	of	ADP
ejpam-5899	6	25	its	its	PRON
ejpam-5899	6	26	features	feature	NOUN
ejpam-5899	6	27	.	.	PUNCT
ejpam-5899	7	1	2020	2020	NUM
ejpam-5899	7	2	mathematics	mathematic	NOUN
ejpam-5899	7	3	subject	subject	NOUN
ejpam-5899	7	4	classifications	classification	NOUN
ejpam-5899	7	5	:	:	PUNCT
ejpam-5899	7	6	54a05	54a05	NUM
ejpam-5899	7	7	,	,	PUNCT
ejpam-5899	7	8	54c08	54c08	NUM
ejpam-5899	7	9	,	,	PUNCT
ejpam-5899	7	10	54d10	54d10	NUM
ejpam-5899	7	11	.	.	PUNCT
ejpam-5899	8	1	key	key	ADJ
ejpam-5899	8	2	words	word	NOUN
ejpam-5899	8	3	and	and	CCONJ
ejpam-5899	8	4	phrases	phrase	NOUN
ejpam-5899	8	5	:	:	PUNCT
ejpam-5899	8	6	generalized	generalized	ADJ
ejpam-5899	8	7	topological	topological	ADJ
ejpam-5899	8	8	space	space	NOUN
ejpam-5899	8	9	,	,	PUNCT
ejpam-5899	8	10	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	8	11	,	,	PUNCT
ejpam-5899	8	12	α	α	NOUN
ejpam-5899	8	13	-	-	NOUN
ejpam-5899	8	14	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	8	15	,	,	PUNCT
ejpam-5899	8	16	β	β	NOUN
ejpam-5899	8	17	-	-	NOUN
ejpam-5899	8	18	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	8	19	.	.	PUNCT
ejpam-5899	9	1	1	1	X
ejpam-5899	9	2	.	.	X
ejpam-5899	9	3	introduction	introduction	NOUN
ejpam-5899	9	4	in	in	ADP
ejpam-5899	9	5	1944	1944	NUM
ejpam-5899	9	6	,	,	PUNCT
ejpam-5899	9	7	dieudonné	dieudonné	NOUN
ejpam-5899	10	1	[	[	X
ejpam-5899	10	2	7	7	NUM
ejpam-5899	10	3	]	]	PUNCT
ejpam-5899	10	4	introduced	introduce	VERB
ejpam-5899	10	5	a	a	DET
ejpam-5899	10	6	broader	broad	ADJ
ejpam-5899	10	7	class	class	NOUN
ejpam-5899	10	8	of	of	ADP
ejpam-5899	10	9	compact	compact	ADJ
ejpam-5899	10	10	spaces	space	NOUN
ejpam-5899	10	11	,	,	PUNCT
ejpam-5899	10	12	namely	namely	ADV
ejpam-5899	10	13	paracompact	paracompact	ADJ
ejpam-5899	10	14	spaces	space	NOUN
ejpam-5899	10	15	.	.	PUNCT
ejpam-5899	11	1	sorgenfrey	sorgenfrey	PROPN
ejpam-5899	12	1	[	[	X
ejpam-5899	12	2	15	15	NUM
ejpam-5899	12	3	]	]	PUNCT
ejpam-5899	12	4	and	and	CCONJ
ejpam-5899	12	5	stone	stone	NOUN
ejpam-5899	12	6	[	[	X
ejpam-5899	12	7	16	16	NUM
ejpam-5899	12	8	]	]	PUNCT
ejpam-5899	12	9	investigated	investigate	VERB
ejpam-5899	12	10	the	the	DET
ejpam-5899	12	11	behavior	behavior	NOUN
ejpam-5899	12	12	of	of	ADP
ejpam-5899	12	13	paracompact	paracompact	ADJ
ejpam-5899	12	14	spaces	space	NOUN
ejpam-5899	12	15	within	within	ADP
ejpam-5899	12	16	the	the	DET
ejpam-5899	12	17	product	product	NOUN
ejpam-5899	12	18	space	space	NOUN
ejpam-5899	12	19	.	.	PUNCT
ejpam-5899	13	1	michail	michail	NOUN
ejpam-5899	13	2	[	[	X
ejpam-5899	13	3	10	10	NUM
ejpam-5899	13	4	]	]	SYM
ejpam-5899	13	5	defined	define	VERB
ejpam-5899	13	6	paracompactness	paracompactness	NOUN
ejpam-5899	13	7	in	in	ADP
ejpam-5899	13	8	the	the	DET
ejpam-5899	13	9	sense	sense	NOUN
ejpam-5899	13	10	of	of	ADP
ejpam-5899	13	11	regular	regular	ADJ
ejpam-5899	13	12	topological	topological	ADJ
ejpam-5899	13	13	spaces	space	NOUN
ejpam-5899	13	14	and	and	CCONJ
ejpam-5899	13	15	demonstrated	demonstrate	VERB
ejpam-5899	13	16	how	how	SCONJ
ejpam-5899	13	17	metrizability	metrizability	NOUN
ejpam-5899	13	18	implies	imply	VERB
ejpam-5899	13	19	paracompactness	paracompactness	NOUN
ejpam-5899	13	20	.	.	PUNCT
ejpam-5899	14	1	therefore	therefore	ADV
ejpam-5899	14	2	,	,	PUNCT
ejpam-5899	14	3	paracompactness	paracompactness	NOUN
ejpam-5899	14	4	is	be	AUX
ejpam-5899	14	5	one	one	NUM
ejpam-5899	14	6	of	of	ADP
ejpam-5899	14	7	the	the	DET
ejpam-5899	14	8	most	most	ADV
ejpam-5899	14	9	essential	essential	ADJ
ejpam-5899	14	10	concepts	concept	NOUN
ejpam-5899	14	11	and	and	CCONJ
ejpam-5899	14	12	possibly	possibly	ADV
ejpam-5899	14	13	the	the	DET
ejpam-5899	14	14	most	most	ADV
ejpam-5899	14	15	successful	successful	ADJ
ejpam-5899	14	16	generalization	generalization	NOUN
ejpam-5899	14	17	of	of	ADP
ejpam-5899	14	18	compactness	compactness	NOUN
ejpam-5899	14	19	,	,	PUNCT
ejpam-5899	14	20	which	which	PRON
ejpam-5899	14	21	is	be	AUX
ejpam-5899	14	22	introduced	introduce	VERB
ejpam-5899	14	23	not	not	PART
ejpam-5899	14	24	only	only	ADV
ejpam-5899	14	25	in	in	ADP
ejpam-5899	14	26	general	general	ADJ
ejpam-5899	14	27	topology	topology	NOUN
ejpam-5899	14	28	but	but	CCONJ
ejpam-5899	14	29	also	also	ADV
ejpam-5899	14	30	in	in	ADP
ejpam-5899	14	31	other	other	ADJ
ejpam-5899	14	32	structures	structure	NOUN
ejpam-5899	14	33	,	,	PUNCT
ejpam-5899	14	34	such	such	ADJ
ejpam-5899	14	35	as	as	ADP
ejpam-5899	14	36	generalized	generalized	ADJ
ejpam-5899	14	37	topological	topological	ADJ
ejpam-5899	14	38	spaces	space	NOUN
ejpam-5899	14	39	(	(	PUNCT
ejpam-5899	14	40	see	see	VERB
ejpam-5899	14	41	[	[	X
ejpam-5899	14	42	6	6	NUM
ejpam-5899	14	43	,	,	PUNCT
ejpam-5899	14	44	9	9	NUM
ejpam-5899	14	45	]	]	PUNCT
ejpam-5899	14	46	)	)	PUNCT
ejpam-5899	14	47	.	.	PUNCT
ejpam-5899	15	1	the	the	DET
ejpam-5899	15	2	study	study	NOUN
ejpam-5899	15	3	of	of	ADP
ejpam-5899	15	4	generalized	generalized	ADJ
ejpam-5899	15	5	topological	topological	ADJ
ejpam-5899	15	6	spaces	space	NOUN
ejpam-5899	15	7	(	(	PUNCT
ejpam-5899	15	8	briefly	briefly	ADV
ejpam-5899	15	9	,	,	PUNCT
ejpam-5899	15	10	gts	gts	NOUN
ejpam-5899	15	11	)	)	PUNCT
ejpam-5899	15	12	was	be	AUX
ejpam-5899	15	13	first	first	ADV
ejpam-5899	15	14	initiated	initiate	VERB
ejpam-5899	15	15	by	by	ADP
ejpam-5899	15	16	császár	császár	NOUN
ejpam-5899	15	17	[	[	X
ejpam-5899	15	18	4	4	NUM
ejpam-5899	15	19	]	]	PUNCT
ejpam-5899	15	20	.	.	PUNCT
ejpam-5899	16	1	the	the	DET
ejpam-5899	16	2	pair	pair	NOUN
ejpam-5899	16	3	(	(	PUNCT
ejpam-5899	16	4	s	s	X
ejpam-5899	16	5	,	,	PUNCT
ejpam-5899	16	6	µ	µ	NOUN
ejpam-5899	16	7	)	)	PUNCT
ejpam-5899	16	8	is	be	AUX
ejpam-5899	16	9	called	call	VERB
ejpam-5899	16	10	gts	gts	NOUN
ejpam-5899	16	11	if	if	SCONJ
ejpam-5899	16	12	µ	µ	PRON
ejpam-5899	16	13	⊆	⊆	NUM
ejpam-5899	16	14	p	p	X
ejpam-5899	16	15	(	(	PUNCT
ejpam-5899	16	16	s	s	NOUN
ejpam-5899	16	17	)	)	PUNCT
ejpam-5899	16	18	with	with	ADP
ejpam-5899	16	19	ϕ	ϕ	PROPN
ejpam-5899	16	20	∈	∈	PROPN
ejpam-5899	16	21	µ	µ	X
ejpam-5899	16	22	and	and	CCONJ
ejpam-5899	16	23	µ	µ	NOUN
ejpam-5899	16	24	is	be	AUX
ejpam-5899	16	25	closed	close	VERB
ejpam-5899	16	26	under	under	ADP
ejpam-5899	16	27	the	the	DET
ejpam-5899	16	28	arbitrary	arbitrary	ADJ
ejpam-5899	16	29	union	union	NOUN
ejpam-5899	16	30	where	where	SCONJ
ejpam-5899	16	31	p	p	PROPN
ejpam-5899	16	32	(	(	PUNCT
ejpam-5899	16	33	s	s	NOUN
ejpam-5899	16	34	)	)	PUNCT
ejpam-5899	16	35	denotes	denote	VERB
ejpam-5899	16	36	the	the	DET
ejpam-5899	16	37	power	power	NOUN
ejpam-5899	16	38	set	set	NOUN
ejpam-5899	16	39	of	of	ADP
ejpam-5899	16	40	s.	s.	PROPN
ejpam-5899	16	41	a	a	DET
ejpam-5899	16	42	gts	gts	NOUN
ejpam-5899	16	43	in	in	ADP
ejpam-5899	16	44	turn	turn	NOUN
ejpam-5899	16	45	motivated	motivate	VERB
ejpam-5899	16	46	other	other	ADJ
ejpam-5899	16	47	researchers	researcher	NOUN
ejpam-5899	16	48	to	to	PART
ejpam-5899	16	49	generalize	generalize	VERB
ejpam-5899	16	50	the	the	DET
ejpam-5899	16	51	topological	topological	ADJ
ejpam-5899	16	52	concepts	concept	NOUN
ejpam-5899	16	53	including	include	VERB
ejpam-5899	16	54	covering	cover	VERB
ejpam-5899	16	55	properties	property	NOUN
ejpam-5899	16	56	of	of	ADP
ejpam-5899	16	57	generalized	generalized	ADJ
ejpam-5899	16	58	topology	topology	NOUN
ejpam-5899	16	59	.	.	PUNCT
ejpam-5899	17	1	for	for	ADP
ejpam-5899	17	2	instance	instance	NOUN
ejpam-5899	17	3	,	,	PUNCT
ejpam-5899	17	4	in	in	ADP
ejpam-5899	17	5	[	[	X
ejpam-5899	17	6	6	6	NUM
ejpam-5899	17	7	]	]	PUNCT
ejpam-5899	17	8	the	the	DET
ejpam-5899	17	9	authors	author	NOUN
ejpam-5899	17	10	defined	define	VERB
ejpam-5899	17	11	µ-paracompact	µ-paracompact	PROPN
ejpam-5899	17	12	spaces	space	NOUN
ejpam-5899	17	13	and	and	CCONJ
ejpam-5899	17	14	gµparacompact	gµparacompact	NOUN
ejpam-5899	17	15	which	which	PRON
ejpam-5899	17	16	are	be	AUX
ejpam-5899	17	17	a	a	DET
ejpam-5899	17	18	generalization	generalization	NOUN
ejpam-5899	17	19	of	of	ADP
ejpam-5899	17	20	paracompactness	paracompactness	PROPN
ejpam-5899	17	21	in	in	ADP
ejpam-5899	17	22	gts	gts	NOUN
ejpam-5899	17	23	,	,	PUNCT
ejpam-5899	17	24	where	where	SCONJ
ejpam-5899	17	25	a	a	DET
ejpam-5899	17	26	gts	gts	NOUN
ejpam-5899	17	27	(	(	PUNCT
ejpam-5899	17	28	s	s	PROPN
ejpam-5899	17	29	,	,	PUNCT
ejpam-5899	17	30	µ	µ	NOUN
ejpam-5899	17	31	)	)	PUNCT
ejpam-5899	17	32	∗corresponding	∗corresponde	VERB
ejpam-5899	17	33	author	author	NOUN
ejpam-5899	17	34	.	.	PUNCT
ejpam-5899	18	1	doi	doi	NOUN
ejpam-5899	18	2	:	:	PUNCT
ejpam-5899	18	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5899	https://doi.org/10.29020/nybg.ejpam.v18i2.5899	PROPN
ejpam-5899	18	4	email	email	NOUN
ejpam-5899	18	5	addresses	address	NOUN
ejpam-5899	18	6	:	:	PUNCT
ejpam-5899	18	7	heyam@yu.edu.jo	heyam@yu.edu.jo	PROPN
ejpam-5899	18	8	(	(	PUNCT
ejpam-5899	18	9	h.	h.	PROPN
ejpam-5899	18	10	h.	h.	PROPN
ejpam-5899	18	11	al	al	PROPN
ejpam-5899	18	12	-	-	PUNCT
ejpam-5899	18	13	jarrah	jarrah	PROPN
ejpam-5899	18	14	)	)	PUNCT
ejpam-5899	18	15	,	,	PUNCT
ejpam-5899	18	16	amanirawshdeh@bau.edu.jo	amanirawshdeh@bau.edu.jo	ADJ
ejpam-5899	18	17	(	(	PUNCT
ejpam-5899	18	18	a.	a.	NOUN
ejpam-5899	18	19	rawshdeh	rawshdeh	PROPN
ejpam-5899	18	20	)	)	PUNCT
ejpam-5899	18	21	,	,	PUNCT
ejpam-5899	18	22	khalidz@yu.edu.jo	khalidz@yu.edu.jo	PROPN
ejpam-5899	18	23	(	(	PUNCT
ejpam-5899	18	24	k.	k.	PROPN
ejpam-5899	18	25	y.	y.	PROPN
ejpam-5899	18	26	al	al	PROPN
ejpam-5899	18	27	-	-	PROPN
ejpam-5899	18	28	zoubi	zoubi	NUM
ejpam-5899	18	29	)	)	PUNCT
ejpam-5899	18	30	,	,	PUNCT
ejpam-5899	18	31	shefa.bm@yu.edu.jo	shefa.bm@yu.edu.jo	PROPN
ejpam-5899	18	32	(	(	PUNCT
ejpam-5899	18	33	sh	sh	PROPN
ejpam-5899	18	34	.	.	PROPN
ejpam-5899	18	35	a.	a.	PROPN
ejpam-5899	18	36	bani	bani	PROPN
ejpam-5899	18	37	melhem	melhem	PROPN
ejpam-5899	18	38	)	)	PUNCT
ejpam-5899	18	39	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5899	19	1	1	1	NUM
ejpam-5899	19	2	copyright	copyright	NOUN
ejpam-5899	19	3	:	:	PUNCT
ejpam-5899	19	4	©	©	PROPN
ejpam-5899	19	5	2025	2025	NUM
ejpam-5899	19	6	the	the	DET
ejpam-5899	19	7	author(s	author(s	NOUN
ejpam-5899	19	8	)	)	PUNCT
ejpam-5899	19	9	.	.	PUNCT
ejpam-5899	20	1	(	(	PUNCT
ejpam-5899	20	2	cc	cc	NOUN
ejpam-5899	20	3	by	by	ADP
ejpam-5899	20	4	-	-	PUNCT
ejpam-5899	20	5	nc	nc	PROPN
ejpam-5899	20	6	4.0	4.0	NUM
ejpam-5899	20	7	)	)	PUNCT
ejpam-5899	20	8	h.	h.	PROPN
ejpam-5899	20	9	h.	h.	PROPN
ejpam-5899	20	10	al	al	PROPN
ejpam-5899	20	11	-	-	PUNCT
ejpam-5899	20	12	jarrah	jarrah	PROPN
ejpam-5899	20	13	et	et	PROPN
ejpam-5899	20	14	al	al	PROPN
ejpam-5899	20	15	.	.	PUNCT
ejpam-5899	20	16	/	/	SYM
ejpam-5899	20	17	eur	eur	PROPN
ejpam-5899	20	18	.	.	PUNCT
ejpam-5899	21	1	j.	j.	PROPN
ejpam-5899	21	2	pure	pure	PROPN
ejpam-5899	21	3	appl	appl	PROPN
ejpam-5899	21	4	.	.	PROPN
ejpam-5899	21	5	math	math	PROPN
ejpam-5899	21	6	,	,	PUNCT
ejpam-5899	21	7	18	18	NUM
ejpam-5899	21	8	(	(	PUNCT
ejpam-5899	21	9	2	2	NUM
ejpam-5899	21	10	)	)	PUNCT
ejpam-5899	21	11	(	(	PUNCT
ejpam-5899	21	12	2025	2025	NUM
ejpam-5899	21	13	)	)	PUNCT
ejpam-5899	21	14	,	,	PUNCT
ejpam-5899	21	15	5899	5899	NUM
ejpam-5899	21	16	2	2	NUM
ejpam-5899	21	17	of	of	ADP
ejpam-5899	21	18	11	11	NUM
ejpam-5899	21	19	is	be	AUX
ejpam-5899	21	20	called	call	VERB
ejpam-5899	21	21	µ-paracompact	µ-paracompact	PROPN
ejpam-5899	21	22	(	(	PUNCT
ejpam-5899	21	23	resp	resp	NOUN
ejpam-5899	21	24	.	.	PUNCT
ejpam-5899	22	1	gµ-paracompact	gµ-paracompact	PROPN
ejpam-5899	22	2	)	)	PUNCT
ejpam-5899	23	1	if	if	SCONJ
ejpam-5899	23	2	every	every	PRON
ejpam-5899	23	3	(	(	PUNCT
ejpam-5899	23	4	s	s	X
ejpam-5899	23	5	,	,	PUNCT
ejpam-5899	23	6	µ)-cover	µ)-cover	PUNCT
ejpam-5899	23	7	of	of	ADP
ejpam-5899	23	8	s	s	PROPN
ejpam-5899	23	9	has	have	VERB
ejpam-5899	23	10	a	a	DET
ejpam-5899	23	11	µ−lf(s,µ	µ−lf(s,µ	NOUN
ejpam-5899	23	12	)	)	PUNCT
ejpam-5899	23	13	(	(	PUNCT
ejpam-5899	23	14	resp	resp	NOUN
ejpam-5899	23	15	.	.	PUNCT
ejpam-5899	24	1	gµ−lf(s,µ	gµ−lf(s,µ	PROPN
ejpam-5899	24	2	)	)	PUNCT
ejpam-5899	24	3	)	)	PUNCT
ejpam-5899	25	1	(	(	PUNCT
ejpam-5899	25	2	s	s	X
ejpam-5899	25	3	,	,	PUNCT
ejpam-5899	25	4	µ)-refinement	µ)-refinement	PROPN
ejpam-5899	25	5	.	.	PUNCT
ejpam-5899	26	1	in	in	ADP
ejpam-5899	26	2	[	[	X
ejpam-5899	26	3	11	11	NUM
ejpam-5899	26	4	]	]	PUNCT
ejpam-5899	26	5	,	,	PUNCT
ejpam-5899	26	6	qahis	qahis	PROPN
ejpam-5899	26	7	and	and	CCONJ
ejpam-5899	26	8	noiri	noiri	PROPN
ejpam-5899	26	9	investigated	investigate	VERB
ejpam-5899	26	10	the	the	DET
ejpam-5899	26	11	concept	concept	NOUN
ejpam-5899	26	12	of	of	ADP
ejpam-5899	26	13	µ−paracompact	µ−paracompact	PROPN
ejpam-5899	26	14	spaces	space	NOUN
ejpam-5899	26	15	with	with	ADP
ejpam-5899	26	16	respect	respect	NOUN
ejpam-5899	26	17	to	to	ADP
ejpam-5899	26	18	hereditary	hereditary	ADJ
ejpam-5899	26	19	class	class	NOUN
ejpam-5899	26	20	h	h	NOUN
ejpam-5899	26	21	,	,	PUNCT
ejpam-5899	26	22	which	which	PRON
ejpam-5899	26	23	is	be	AUX
ejpam-5899	26	24	a	a	DET
ejpam-5899	26	25	generalization	generalization	NOUN
ejpam-5899	26	26	for	for	ADP
ejpam-5899	26	27	a	a	DET
ejpam-5899	26	28	µ-paracompact	µ-paracompact	PROPN
ejpam-5899	26	29	space	space	NOUN
ejpam-5899	26	30	.	.	PUNCT
ejpam-5899	27	1	in	in	ADP
ejpam-5899	27	2	classical	classical	ADJ
ejpam-5899	27	3	topology	topology	NOUN
ejpam-5899	27	4	,	,	PUNCT
ejpam-5899	27	5	studying	study	VERB
ejpam-5899	27	6	the	the	DET
ejpam-5899	27	7	covering	covering	NOUN
ejpam-5899	27	8	definitions	definition	NOUN
ejpam-5899	27	9	for	for	ADP
ejpam-5899	27	10	sets	set	NOUN
ejpam-5899	27	11	after	after	ADP
ejpam-5899	27	12	studying	study	VERB
ejpam-5899	27	13	the	the	DET
ejpam-5899	27	14	concept	concept	NOUN
ejpam-5899	27	15	of	of	ADP
ejpam-5899	27	16	space	space	NOUN
ejpam-5899	27	17	is	be	AUX
ejpam-5899	27	18	an	an	DET
ejpam-5899	27	19	area	area	NOUN
ejpam-5899	27	20	that	that	PRON
ejpam-5899	27	21	has	have	AUX
ejpam-5899	27	22	found	find	VERB
ejpam-5899	27	23	interest	interest	NOUN
ejpam-5899	27	24	among	among	ADP
ejpam-5899	27	25	some	some	DET
ejpam-5899	27	26	authors	author	NOUN
ejpam-5899	27	27	,	,	PUNCT
ejpam-5899	27	28	such	such	ADJ
ejpam-5899	27	29	as	as	ADP
ejpam-5899	27	30	:	:	PUNCT
ejpam-5899	27	31	based	base	VERB
ejpam-5899	27	32	on	on	ADP
ejpam-5899	27	33	the	the	DET
ejpam-5899	27	34	definition	definition	NOUN
ejpam-5899	27	35	of	of	ADP
ejpam-5899	27	36	i	i	PROPN
ejpam-5899	27	37	-	-	PUNCT
ejpam-5899	27	38	lindelöf	lindelöf	NOUN
ejpam-5899	27	39	space	space	NOUN
ejpam-5899	27	40	[	[	X
ejpam-5899	27	41	1	1	X
ejpam-5899	27	42	]	]	PUNCT
ejpam-5899	27	43	the	the	DET
ejpam-5899	27	44	author	author	NOUN
ejpam-5899	27	45	presented	present	VERB
ejpam-5899	27	46	the	the	DET
ejpam-5899	27	47	definition	definition	NOUN
ejpam-5899	27	48	of	of	ADP
ejpam-5899	27	49	i	i	PROPN
ejpam-5899	27	50	-	-	PUNCT
ejpam-5899	27	51	lindelöf	lindelöf	NOUN
ejpam-5899	27	52	sets	set	VERB
ejpam-5899	27	53	[	[	X
ejpam-5899	27	54	2	2	NUM
ejpam-5899	27	55	]	]	PUNCT
ejpam-5899	27	56	.	.	PUNCT
ejpam-5899	28	1	in	in	ADP
ejpam-5899	28	2	addition	addition	NOUN
ejpam-5899	28	3	,	,	PUNCT
ejpam-5899	28	4	the	the	DET
ejpam-5899	28	5	authors	author	NOUN
ejpam-5899	28	6	used	use	VERB
ejpam-5899	28	7	the	the	DET
ejpam-5899	28	8	concept	concept	NOUN
ejpam-5899	28	9	of	of	ADP
ejpam-5899	28	10	paracompactness	paracompactness	NOUN
ejpam-5899	28	11	to	to	PART
ejpam-5899	28	12	study	study	VERB
ejpam-5899	28	13	and	and	CCONJ
ejpam-5899	28	14	introduce	introduce	VERB
ejpam-5899	28	15	different	different	ADJ
ejpam-5899	28	16	notions	notion	NOUN
ejpam-5899	28	17	of	of	ADP
ejpam-5899	28	18	paracompact	paracompact	ADJ
ejpam-5899	28	19	sets	set	NOUN
ejpam-5899	28	20	such	such	ADJ
ejpam-5899	28	21	as	as	ADP
ejpam-5899	28	22	α	α	NOUN
ejpam-5899	28	23	-	-	NOUN
ejpam-5899	28	24	paracompact	paracompact	ADJ
ejpam-5899	28	25	and	and	CCONJ
ejpam-5899	28	26	β	β	NOUN
ejpam-5899	28	27	-	-	NOUN
ejpam-5899	28	28	paracompact	paracompact	NOUN
ejpam-5899	28	29	[	[	AUX
ejpam-5899	28	30	see	see	VERB
ejpam-5899	28	31	[	[	X
ejpam-5899	28	32	3	3	NUM
ejpam-5899	28	33	]	]	X
ejpam-5899	28	34	]	]	PUNCT
ejpam-5899	28	35	.	.	PUNCT
ejpam-5899	29	1	therefore	therefore	ADV
ejpam-5899	29	2	,	,	PUNCT
ejpam-5899	29	3	in	in	ADP
ejpam-5899	29	4	this	this	DET
ejpam-5899	29	5	work	work	NOUN
ejpam-5899	29	6	,	,	PUNCT
ejpam-5899	29	7	we	we	PRON
ejpam-5899	29	8	employ	employ	VERB
ejpam-5899	29	9	the	the	DET
ejpam-5899	29	10	definition	definition	NOUN
ejpam-5899	29	11	of	of	ADP
ejpam-5899	29	12	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	29	13	spaces	space	NOUN
ejpam-5899	29	14	that	that	PRON
ejpam-5899	29	15	are	be	AUX
ejpam-5899	29	16	defined	define	VERB
ejpam-5899	29	17	in	in	ADP
ejpam-5899	29	18	[	[	X
ejpam-5899	29	19	6	6	NUM
ejpam-5899	29	20	]	]	PUNCT
ejpam-5899	29	21	to	to	PART
ejpam-5899	29	22	introduce	introduce	VERB
ejpam-5899	29	23	the	the	DET
ejpam-5899	29	24	notions	notion	NOUN
ejpam-5899	29	25	of	of	ADP
ejpam-5899	29	26	α	α	NOUN
ejpam-5899	29	27	-	-	PUNCT
ejpam-5899	29	28	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	29	29	and	and	CCONJ
ejpam-5899	29	30	β	β	NOUN
ejpam-5899	29	31	-	-	ADJ
ejpam-5899	29	32	gµ-paracompact	gµ-paracompact	ADJ
ejpam-5899	29	33	subsets	subset	NOUN
ejpam-5899	29	34	and	and	CCONJ
ejpam-5899	29	35	provide	provide	VERB
ejpam-5899	29	36	some	some	DET
ejpam-5899	29	37	illustrative	illustrative	ADJ
ejpam-5899	29	38	examples	example	NOUN
ejpam-5899	29	39	to	to	PART
ejpam-5899	29	40	elucidate	elucidate	VERB
ejpam-5899	29	41	the	the	DET
ejpam-5899	29	42	relationship	relationship	NOUN
ejpam-5899	29	43	between	between	ADP
ejpam-5899	29	44	them	they	PRON
ejpam-5899	29	45	and	and	CCONJ
ejpam-5899	29	46	demonstrate	demonstrate	VERB
ejpam-5899	29	47	the	the	DET
ejpam-5899	29	48	results	result	NOUN
ejpam-5899	29	49	that	that	PRON
ejpam-5899	29	50	were	be	AUX
ejpam-5899	29	51	achieved	achieve	VERB
ejpam-5899	29	52	.	.	PUNCT
ejpam-5899	30	1	for	for	ADP
ejpam-5899	30	2	a	a	DET
ejpam-5899	30	3	gts	gts	NOUN
ejpam-5899	30	4	(	(	PUNCT
ejpam-5899	30	5	s	s	PROPN
ejpam-5899	30	6	,	,	PUNCT
ejpam-5899	30	7	µ	µ	NOUN
ejpam-5899	30	8	)	)	PUNCT
ejpam-5899	30	9	the	the	DET
ejpam-5899	30	10	elements	element	NOUN
ejpam-5899	30	11	of	of	ADP
ejpam-5899	30	12	µ	µ	NOUN
ejpam-5899	30	13	are	be	AUX
ejpam-5899	30	14	called	call	VERB
ejpam-5899	30	15	µ-open	µ-open	NOUN
ejpam-5899	30	16	sets	set	NOUN
ejpam-5899	30	17	and	and	CCONJ
ejpam-5899	30	18	the	the	DET
ejpam-5899	30	19	collection	collection	NOUN
ejpam-5899	30	20	of	of	ADP
ejpam-5899	30	21	all	all	DET
ejpam-5899	30	22	µ-open	µ-open	NOUN
ejpam-5899	30	23	sets	set	NOUN
ejpam-5899	30	24	containing	contain	VERB
ejpam-5899	30	25	s	s	PRON
ejpam-5899	30	26	∈	∈	NOUN
ejpam-5899	30	27	s	s	NOUN
ejpam-5899	30	28	will	will	AUX
ejpam-5899	30	29	be	be	AUX
ejpam-5899	30	30	denoted	denote	VERB
ejpam-5899	30	31	by	by	ADP
ejpam-5899	30	32	µ(s	µ(	NOUN
ejpam-5899	30	33	)	)	PUNCT
ejpam-5899	30	34	.	.	PUNCT
ejpam-5899	31	1	the	the	DET
ejpam-5899	31	2	complement	complement	NOUN
ejpam-5899	31	3	of	of	ADP
ejpam-5899	31	4	a	a	DET
ejpam-5899	31	5	µ-open	µ-open	NOUN
ejpam-5899	31	6	set	set	NOUN
ejpam-5899	31	7	is	be	AUX
ejpam-5899	31	8	called	call	VERB
ejpam-5899	31	9	a	a	DET
ejpam-5899	31	10	µ−closed	µ−closed	ADJ
ejpam-5899	31	11	set	set	NOUN
ejpam-5899	31	12	,	,	PUNCT
ejpam-5899	31	13	and	and	CCONJ
ejpam-5899	31	14	the	the	DET
ejpam-5899	31	15	intersection	intersection	NOUN
ejpam-5899	31	16	of	of	ADP
ejpam-5899	31	17	all	all	DET
ejpam-5899	31	18	µ-closed	µ-close	VERB
ejpam-5899	31	19	sets	set	NOUN
ejpam-5899	31	20	containing	contain	VERB
ejpam-5899	31	21	e	e	NOUN
ejpam-5899	31	22	will	will	AUX
ejpam-5899	31	23	be	be	AUX
ejpam-5899	31	24	denoted	denote	VERB
ejpam-5899	31	25	by	by	ADP
ejpam-5899	31	26	cµ(e	cµ(e	NOUN
ejpam-5899	31	27	)	)	PUNCT
ejpam-5899	31	28	.	.	PUNCT
ejpam-5899	32	1	a	a	DET
ejpam-5899	32	2	subset	subset	ADJ
ejpam-5899	32	3	e	e	NOUN
ejpam-5899	32	4	of	of	ADP
ejpam-5899	32	5	gts	gts	NOUN
ejpam-5899	32	6	(	(	PUNCT
ejpam-5899	32	7	s	s	PROPN
ejpam-5899	32	8	,	,	PUNCT
ejpam-5899	32	9	µ	µ	NOUN
ejpam-5899	32	10	)	)	PUNCT
ejpam-5899	32	11	is	be	AUX
ejpam-5899	32	12	called	call	VERB
ejpam-5899	32	13	a	a	DET
ejpam-5899	32	14	generalized	generalize	VERB
ejpam-5899	32	15	closed	close	VERB
ejpam-5899	32	16	set	set	NOUN
ejpam-5899	32	17	[	[	X
ejpam-5899	32	18	13	13	NUM
ejpam-5899	32	19	]	]	PUNCT
ejpam-5899	32	20	,	,	PUNCT
ejpam-5899	32	21	denoted	denote	VERB
ejpam-5899	32	22	by	by	ADP
ejpam-5899	32	23	µg	µg	ADV
ejpam-5899	32	24	-	-	PUNCT
ejpam-5899	32	25	closed	closed	ADJ
ejpam-5899	32	26	set	set	NOUN
ejpam-5899	32	27	,	,	PUNCT
ejpam-5899	32	28	if	if	SCONJ
ejpam-5899	32	29	cµ(e	cµ(e	NOUN
ejpam-5899	32	30	)	)	PUNCT
ejpam-5899	32	31	⊆	⊆	NUM
ejpam-5899	32	32	g	g	NOUN
ejpam-5899	32	33	whenever	whenever	SCONJ
ejpam-5899	32	34	e	e	PROPN
ejpam-5899	32	35	⊆	⊆	NUM
ejpam-5899	32	36	g	g	NOUN
ejpam-5899	32	37	and	and	CCONJ
ejpam-5899	32	38	g	g	PROPN
ejpam-5899	32	39	is	be	AUX
ejpam-5899	32	40	µ-open	µ-open	VERB
ejpam-5899	32	41	.	.	PUNCT
ejpam-5899	33	1	a	a	DET
ejpam-5899	33	2	gts	gts	NOUN
ejpam-5899	33	3	(	(	PUNCT
ejpam-5899	33	4	s	s	PROPN
ejpam-5899	33	5	,	,	PUNCT
ejpam-5899	33	6	µ	µ	NOUN
ejpam-5899	33	7	)	)	PUNCT
ejpam-5899	33	8	is	be	AUX
ejpam-5899	33	9	called	call	VERB
ejpam-5899	33	10	µ-t2	µ-t2	ADJ
ejpam-5899	33	11	-	-	PUNCT
ejpam-5899	33	12	space	space	NOUN
ejpam-5899	33	13	[	[	X
ejpam-5899	33	14	14	14	NUM
ejpam-5899	33	15	]	]	X
ejpam-5899	33	16	if	if	SCONJ
ejpam-5899	33	17	for	for	ADP
ejpam-5899	33	18	each	each	DET
ejpam-5899	33	19	s	s	NOUN
ejpam-5899	33	20	,	,	PUNCT
ejpam-5899	33	21	e	e	PROPN
ejpam-5899	33	22	∈	∈	PROPN
ejpam-5899	33	23	s	s	VERB
ejpam-5899	33	24	with	with	ADP
ejpam-5899	33	25	s	s	PRON
ejpam-5899	33	26	̸=	̸=	PROPN
ejpam-5899	33	27	e	e	NOUN
ejpam-5899	33	28	,	,	PUNCT
ejpam-5899	33	29	there	there	PRON
ejpam-5899	33	30	are	be	VERB
ejpam-5899	33	31	g	g	PROPN
ejpam-5899	33	32	∈	∈	PROPN
ejpam-5899	33	33	µ(s	µ(	NOUN
ejpam-5899	33	34	)	)	PUNCT
ejpam-5899	33	35	and	and	CCONJ
ejpam-5899	33	36	h	h	NOUN
ejpam-5899	33	37	∈	∈	PROPN
ejpam-5899	33	38	µ(e	µ(e	PROPN
ejpam-5899	33	39	)	)	PUNCT
ejpam-5899	33	40	with	with	ADP
ejpam-5899	33	41	g	g	PROPN
ejpam-5899	33	42	∩h	∩h	PROPN
ejpam-5899	33	43	=	=	PUNCT
ejpam-5899	33	44	ϕ.	ϕ.	PROPN
ejpam-5899	33	45	for	for	ADP
ejpam-5899	33	46	e	e	PROPN
ejpam-5899	33	47	⊆	⊆	NUM
ejpam-5899	33	48	s	s	NOUN
ejpam-5899	33	49	,	,	PUNCT
ejpam-5899	33	50	the	the	DET
ejpam-5899	33	51	subspace	subspace	NOUN
ejpam-5899	33	52	of	of	ADP
ejpam-5899	33	53	(	(	PUNCT
ejpam-5899	33	54	s	s	PROPN
ejpam-5899	33	55	,	,	PUNCT
ejpam-5899	33	56	µ	µ	NOUN
ejpam-5899	33	57	)	)	PUNCT
ejpam-5899	33	58	in	in	ADP
ejpam-5899	33	59	e	e	PROPN
ejpam-5899	33	60	is	be	AUX
ejpam-5899	33	61	denoted	denote	VERB
ejpam-5899	33	62	by	by	ADP
ejpam-5899	33	63	(	(	PUNCT
ejpam-5899	33	64	e,µe	e,µe	NOUN
ejpam-5899	33	65	)	)	PUNCT
ejpam-5899	33	66	.	.	PUNCT
ejpam-5899	34	1	2	2	X
ejpam-5899	34	2	.	.	X
ejpam-5899	34	3	preliminaries	preliminary	NOUN
ejpam-5899	34	4	in	in	ADP
ejpam-5899	34	5	this	this	DET
ejpam-5899	34	6	section	section	NOUN
ejpam-5899	34	7	,	,	PUNCT
ejpam-5899	34	8	we	we	PRON
ejpam-5899	34	9	recall	recall	VERB
ejpam-5899	34	10	the	the	DET
ejpam-5899	34	11	main	main	ADJ
ejpam-5899	34	12	concepts	concept	NOUN
ejpam-5899	34	13	and	and	CCONJ
ejpam-5899	34	14	properties	property	NOUN
ejpam-5899	34	15	which	which	PRON
ejpam-5899	34	16	will	will	AUX
ejpam-5899	34	17	be	be	AUX
ejpam-5899	34	18	needed	need	VERB
ejpam-5899	34	19	in	in	ADP
ejpam-5899	34	20	this	this	DET
ejpam-5899	34	21	work	work	NOUN
ejpam-5899	34	22	.	.	PUNCT
ejpam-5899	35	1	definition	definition	NOUN
ejpam-5899	35	2	1	1	NUM
ejpam-5899	35	3	.	.	PUNCT
ejpam-5899	36	1	[	[	X
ejpam-5899	36	2	6	6	NUM
ejpam-5899	36	3	]	]	PUNCT
ejpam-5899	36	4	let	let	VERB
ejpam-5899	36	5	(	(	PUNCT
ejpam-5899	36	6	s	s	X
ejpam-5899	36	7	,	,	PUNCT
ejpam-5899	36	8	µ	µ	NOUN
ejpam-5899	36	9	)	)	PUNCT
ejpam-5899	36	10	be	be	AUX
ejpam-5899	36	11	a	a	DET
ejpam-5899	36	12	gts	gts	NOUN
ejpam-5899	36	13	.	.	PUNCT
ejpam-5899	37	1	then	then	ADV
ejpam-5899	37	2	:	:	PUNCT
ejpam-5899	37	3	(	(	PUNCT
ejpam-5899	37	4	i	i	NOUN
ejpam-5899	37	5	)	)	PUNCT
ejpam-5899	37	6	µ∗(s	µ∗(s	PROPN
ejpam-5899	37	7	)	)	PUNCT
ejpam-5899	37	8	=	=	PRON
ejpam-5899	37	9	{	{	PUNCT
ejpam-5899	37	10	∩n	∩n	NOUN
ejpam-5899	37	11	i=1gi	i=1gi	PUNCT
ejpam-5899	37	12	:	:	PUNCT
ejpam-5899	37	13	gi	gi	VERB
ejpam-5899	37	14	∈	∈	PROPN
ejpam-5899	37	15	µ(s	µ(	NOUN
ejpam-5899	37	16	)	)	PUNCT
ejpam-5899	37	17	,	,	PUNCT
ejpam-5899	37	18	∀i	∀i	NOUN
ejpam-5899	37	19	=	=	SYM
ejpam-5899	37	20	1	1	NUM
ejpam-5899	37	21	,	,	PUNCT
ejpam-5899	37	22	...	...	PUNCT
ejpam-5899	37	23	,	,	PUNCT
ejpam-5899	37	24	n	n	PROPN
ejpam-5899	37	25	∈	∈	PROPN
ejpam-5899	37	26	n	n	CCONJ
ejpam-5899	37	27	}	}	PUNCT
ejpam-5899	37	28	for	for	ADP
ejpam-5899	37	29	each	each	DET
ejpam-5899	37	30	s	s	PROPN
ejpam-5899	37	31	∈	∈	PROPN
ejpam-5899	37	32	s.	s.	PROPN
ejpam-5899	37	33	(	(	PUNCT
ejpam-5899	37	34	ii	ii	PROPN
ejpam-5899	37	35	)	)	PUNCT
ejpam-5899	37	36	γµ(e	γµ(e	PUNCT
ejpam-5899	37	37	)	)	PUNCT
ejpam-5899	37	38	=	=	PRON
ejpam-5899	38	1	{	{	PUNCT
ejpam-5899	38	2	s	s	X
ejpam-5899	38	3	∈	∈	NOUN
ejpam-5899	38	4	s	s	PART
ejpam-5899	38	5	:	:	PUNCT
ejpam-5899	38	6	h	h	NOUN
ejpam-5899	38	7	∩	∩	NOUN
ejpam-5899	38	8	e	e	PROPN
ejpam-5899	38	9	̸=	̸=	PROPN
ejpam-5899	38	10	ϕ	ϕ	NOUN
ejpam-5899	38	11	for	for	ADP
ejpam-5899	38	12	all	all	DET
ejpam-5899	38	13	h	h	NOUN
ejpam-5899	38	14	∈	∈	PROPN
ejpam-5899	38	15	µ∗(s	µ∗(s	PROPN
ejpam-5899	38	16	)	)	PUNCT
ejpam-5899	38	17	}	}	PUNCT
ejpam-5899	38	18	for	for	ADP
ejpam-5899	38	19	each	each	DET
ejpam-5899	38	20	e	e	NOUN
ejpam-5899	38	21	⊆	⊆	NUM
ejpam-5899	38	22	s.	s.	PROPN
ejpam-5899	38	23	in	in	ADP
ejpam-5899	38	24	[	[	X
ejpam-5899	38	25	6	6	NUM
ejpam-5899	38	26	]	]	PUNCT
ejpam-5899	38	27	,	,	PUNCT
ejpam-5899	38	28	the	the	DET
ejpam-5899	38	29	authors	author	NOUN
ejpam-5899	38	30	show	show	VERB
ejpam-5899	38	31	that	that	SCONJ
ejpam-5899	38	32	the	the	DET
ejpam-5899	38	33	operator	operator	NOUN
ejpam-5899	38	34	γµ(s	γµ(	VERB
ejpam-5899	38	35	)	)	PUNCT
ejpam-5899	38	36	created	create	VERB
ejpam-5899	38	37	a	a	DET
ejpam-5899	38	38	topology	topology	NOUN
ejpam-5899	38	39	on	on	ADP
ejpam-5899	38	40	s	s	PRON
ejpam-5899	38	41	defined	define	VERB
ejpam-5899	38	42	by	by	ADP
ejpam-5899	38	43	µ∗	µ∗	PROPN
ejpam-5899	38	44	=	=	SYM
ejpam-5899	38	45	{	{	PUNCT
ejpam-5899	38	46	e	e	X
ejpam-5899	38	47	⊆	⊆	NUM
ejpam-5899	38	48	s	s	NOUN
ejpam-5899	38	49	:	:	PUNCT
ejpam-5899	38	50	γµ(s	γµ(s	NUM
ejpam-5899	38	51	−	−	PROPN
ejpam-5899	38	52	e	e	X
ejpam-5899	38	53	)	)	PUNCT
ejpam-5899	38	54	=	=	SYM
ejpam-5899	38	55	s	s	PART
ejpam-5899	38	56	−	−	X
ejpam-5899	38	57	e	e	NOUN
ejpam-5899	38	58	}	}	PUNCT
ejpam-5899	38	59	that	that	PRON
ejpam-5899	38	60	is	be	AUX
ejpam-5899	38	61	finer	fine	ADJ
ejpam-5899	38	62	than	than	ADP
ejpam-5899	38	63	µ	µ	NOUN
ejpam-5899	38	64	,	,	PUNCT
ejpam-5899	38	65	and	and	CCONJ
ejpam-5899	38	66	if	if	SCONJ
ejpam-5899	38	67	µ	µ	PRON
ejpam-5899	38	68	is	be	AUX
ejpam-5899	38	69	a	a	DET
ejpam-5899	38	70	topology	topology	NOUN
ejpam-5899	38	71	on	on	ADP
ejpam-5899	38	72	s	s	PROPN
ejpam-5899	38	73	then	then	ADV
ejpam-5899	38	74	µ	µ	X
ejpam-5899	38	75	=	=	SYM
ejpam-5899	38	76	µ∗.	µ∗.	NOUN
ejpam-5899	38	77	the	the	DET
ejpam-5899	38	78	elements	element	NOUN
ejpam-5899	38	79	of	of	ADP
ejpam-5899	38	80	µ∗	µ∗	PROPN
ejpam-5899	38	81	are	be	AUX
ejpam-5899	38	82	called	call	VERB
ejpam-5899	38	83	µ∗-open	µ∗-open	PROPN
ejpam-5899	38	84	sets	set	NOUN
ejpam-5899	38	85	and	and	CCONJ
ejpam-5899	38	86	their	their	PRON
ejpam-5899	38	87	complements	complement	NOUN
ejpam-5899	38	88	are	be	AUX
ejpam-5899	38	89	called	call	VERB
ejpam-5899	38	90	µ∗-closed	µ∗-close	VERB
ejpam-5899	38	91	sets	set	NOUN
ejpam-5899	38	92	.	.	PUNCT
ejpam-5899	39	1	for	for	ADP
ejpam-5899	39	2	each	each	DET
ejpam-5899	39	3	e	e	NOUN
ejpam-5899	39	4	⊆	⊆	NUM
ejpam-5899	39	5	s	s	VERB
ejpam-5899	39	6	the	the	DET
ejpam-5899	39	7	subspace	subspace	NOUN
ejpam-5899	39	8	of	of	ADP
ejpam-5899	39	9	(	(	PUNCT
ejpam-5899	39	10	s	s	X
ejpam-5899	39	11	,	,	PUNCT
ejpam-5899	39	12	µ∗	µ∗	ADJ
ejpam-5899	39	13	)	)	PUNCT
ejpam-5899	39	14	on	on	ADP
ejpam-5899	39	15	e	e	PROPN
ejpam-5899	39	16	is	be	AUX
ejpam-5899	39	17	denoted	denote	VERB
ejpam-5899	39	18	by	by	ADP
ejpam-5899	39	19	(	(	PUNCT
ejpam-5899	39	20	e,µ∗e	e,µ∗e	PROPN
ejpam-5899	39	21	)	)	PUNCT
ejpam-5899	39	22	.	.	PUNCT
ejpam-5899	40	1	definition	definition	NOUN
ejpam-5899	40	2	2	2	NUM
ejpam-5899	40	3	.	.	PUNCT
ejpam-5899	41	1	[	[	X
ejpam-5899	41	2	6	6	NUM
ejpam-5899	41	3	]	]	PUNCT
ejpam-5899	41	4	a	a	DET
ejpam-5899	41	5	gts	gts	NOUN
ejpam-5899	41	6	(	(	PUNCT
ejpam-5899	41	7	s	s	PROPN
ejpam-5899	41	8	,	,	PUNCT
ejpam-5899	41	9	µ	µ	NOUN
ejpam-5899	41	10	)	)	PUNCT
ejpam-5899	41	11	is	be	AUX
ejpam-5899	41	12	called	call	VERB
ejpam-5899	41	13	γµ-regular	γµ-regular	ADJ
ejpam-5899	41	14	if	if	SCONJ
ejpam-5899	41	15	for	for	ADP
ejpam-5899	41	16	each	each	DET
ejpam-5899	41	17	s	s	X
ejpam-5899	41	18	∈	∈	PROPN
ejpam-5899	41	19	s	s	NOUN
ejpam-5899	41	20	and	and	CCONJ
ejpam-5899	41	21	g	g	PROPN
ejpam-5899	41	22	∈	∈	PROPN
ejpam-5899	41	23	µ(s	µ(	NOUN
ejpam-5899	41	24	)	)	PUNCT
ejpam-5899	41	25	,	,	PUNCT
ejpam-5899	41	26	there	there	PRON
ejpam-5899	41	27	is	be	VERB
ejpam-5899	41	28	h	h	PRON
ejpam-5899	41	29	∈	∈	NOUN
ejpam-5899	41	30	µ(s	µ(	NOUN
ejpam-5899	41	31	)	)	PUNCT
ejpam-5899	41	32	with	with	ADP
ejpam-5899	41	33	γµ(h	γµ(h	NOUN
ejpam-5899	41	34	)	)	PUNCT
ejpam-5899	41	35	⊆	⊆	NUM
ejpam-5899	41	36	g.	g.	NOUN
ejpam-5899	41	37	definition	definition	NOUN
ejpam-5899	41	38	3	3	NUM
ejpam-5899	41	39	.	.	PUNCT
ejpam-5899	42	1	[	[	X
ejpam-5899	42	2	6	6	NUM
ejpam-5899	42	3	]	]	PUNCT
ejpam-5899	42	4	let	let	VERB
ejpam-5899	42	5	(	(	PUNCT
ejpam-5899	42	6	s	s	X
ejpam-5899	42	7	,	,	PUNCT
ejpam-5899	42	8	µ	µ	NOUN
ejpam-5899	42	9	)	)	PUNCT
ejpam-5899	42	10	be	be	AUX
ejpam-5899	42	11	a	a	DET
ejpam-5899	42	12	gts	gts	NOUN
ejpam-5899	42	13	.	.	PUNCT
ejpam-5899	43	1	then	then	ADV
ejpam-5899	43	2	a	a	DET
ejpam-5899	43	3	collection	collection	NOUN
ejpam-5899	43	4	g	g	NOUN
ejpam-5899	43	5	=	=	PUNCT
ejpam-5899	43	6	{	{	PUNCT
ejpam-5899	43	7	gα	gα	NOUN
ejpam-5899	43	8	:	:	PUNCT
ejpam-5899	43	9	α	α	PROPN
ejpam-5899	43	10	∈	∈	PROPN
ejpam-5899	43	11	∆	∆	X
ejpam-5899	43	12	}	}	PUNCT
ejpam-5899	43	13	is	be	AUX
ejpam-5899	43	14	called	call	VERB
ejpam-5899	43	15	:	:	PUNCT
ejpam-5899	43	16	(	(	PUNCT
ejpam-5899	43	17	i	i	NOUN
ejpam-5899	43	18	)	)	PUNCT
ejpam-5899	43	19	µ-locally	µ-locally	ADV
ejpam-5899	43	20	finite	finite	VERB
ejpam-5899	43	21	in	in	ADP
ejpam-5899	43	22	(	(	PUNCT
ejpam-5899	43	23	s	s	PROPN
ejpam-5899	43	24	,	,	PUNCT
ejpam-5899	43	25	µ	µ	NOUN
ejpam-5899	43	26	)	)	PUNCT
ejpam-5899	43	27	(	(	PUNCT
ejpam-5899	43	28	resp	resp	NOUN
ejpam-5899	43	29	.	.	PUNCT
ejpam-5899	44	1	(	(	PUNCT
ejpam-5899	44	2	e,µe	e,µe	NUM
ejpam-5899	44	3	)	)	PUNCT
ejpam-5899	44	4	)	)	PUNCT
ejpam-5899	44	5	,	,	PUNCT
ejpam-5899	44	6	denoted	denote	VERB
ejpam-5899	44	7	by	by	ADP
ejpam-5899	44	8	µ−lf(s,µ	µ−lf(s,µ	NOUN
ejpam-5899	44	9	)	)	PUNCT
ejpam-5899	44	10	(	(	PUNCT
ejpam-5899	44	11	resp	resp	NOUN
ejpam-5899	44	12	.	.	PUNCT
ejpam-5899	45	1	µ−lf(e,µe	µ−lf(e,µe	NOUN
ejpam-5899	45	2	)	)	PUNCT
ejpam-5899	45	3	)	)	PUNCT
ejpam-5899	46	1	,	,	PUNCT
ejpam-5899	46	2	if	if	SCONJ
ejpam-5899	46	3	for	for	ADP
ejpam-5899	46	4	each	each	DET
ejpam-5899	46	5	s	s	X
ejpam-5899	46	6	∈	∈	PROPN
ejpam-5899	46	7	s	s	X
ejpam-5899	46	8	(	(	PUNCT
ejpam-5899	46	9	resp	resp	NOUN
ejpam-5899	46	10	.	.	PUNCT
ejpam-5899	46	11	s	s	PART
ejpam-5899	46	12	∈	∈	PROPN
ejpam-5899	46	13	e	e	X
ejpam-5899	46	14	)	)	PUNCT
ejpam-5899	46	15	there	there	PRON
ejpam-5899	46	16	is	be	VERB
ejpam-5899	46	17	h	h	PRON
ejpam-5899	46	18	∈	∈	NOUN
ejpam-5899	46	19	µ(s	µ(s	X
ejpam-5899	46	20	)	)	PUNCT
ejpam-5899	46	21	(	(	PUNCT
ejpam-5899	46	22	resp	resp	NOUN
ejpam-5899	46	23	.	.	PUNCT
ejpam-5899	47	1	h	h	PROPN
ejpam-5899	47	2	∈	∈	PROPN
ejpam-5899	47	3	µe(s	µe(s	NUM
ejpam-5899	47	4	)	)	PUNCT
ejpam-5899	47	5	)	)	PUNCT
ejpam-5899	47	6	with	with	ADP
ejpam-5899	47	7	the	the	DET
ejpam-5899	47	8	set	set	NOUN
ejpam-5899	47	9	{	{	PUNCT
ejpam-5899	47	10	η	η	NOUN
ejpam-5899	47	11	:	:	PUNCT
ejpam-5899	47	12	h	h	PROPN
ejpam-5899	47	13	∩gη	∩gη	PROPN
ejpam-5899	47	14	̸=	̸=	PROPN
ejpam-5899	47	15	ϕ	ϕ	PROPN
ejpam-5899	47	16	}	}	PUNCT
ejpam-5899	47	17	is	be	AUX
ejpam-5899	47	18	finite	finite	ADJ
ejpam-5899	47	19	.	.	PUNCT
ejpam-5899	48	1	h.	h.	PROPN
ejpam-5899	48	2	h.	h.	PROPN
ejpam-5899	48	3	al	al	PROPN
ejpam-5899	48	4	-	-	PUNCT
ejpam-5899	48	5	jarrah	jarrah	PROPN
ejpam-5899	48	6	et	et	PROPN
ejpam-5899	48	7	al	al	PROPN
ejpam-5899	48	8	.	.	PUNCT
ejpam-5899	48	9	/	/	SYM
ejpam-5899	48	10	eur	eur	PROPN
ejpam-5899	48	11	.	.	PUNCT
ejpam-5899	49	1	j.	j.	PROPN
ejpam-5899	49	2	pure	pure	PROPN
ejpam-5899	49	3	appl	appl	PROPN
ejpam-5899	49	4	.	.	PROPN
ejpam-5899	49	5	math	math	PROPN
ejpam-5899	49	6	,	,	PUNCT
ejpam-5899	49	7	18	18	NUM
ejpam-5899	49	8	(	(	PUNCT
ejpam-5899	49	9	2	2	NUM
ejpam-5899	49	10	)	)	PUNCT
ejpam-5899	49	11	(	(	PUNCT
ejpam-5899	49	12	2025	2025	NUM
ejpam-5899	49	13	)	)	PUNCT
ejpam-5899	49	14	,	,	PUNCT
ejpam-5899	49	15	5899	5899	NUM
ejpam-5899	49	16	3	3	NUM
ejpam-5899	49	17	of	of	ADP
ejpam-5899	49	18	11	11	NUM
ejpam-5899	49	19	(	(	PUNCT
ejpam-5899	49	20	ii	ii	NOUN
ejpam-5899	49	21	)	)	PUNCT
ejpam-5899	49	22	gµ-locally	gµ-locally	ADV
ejpam-5899	49	23	finite	finite	VERB
ejpam-5899	49	24	in	in	ADP
ejpam-5899	49	25	(	(	PUNCT
ejpam-5899	49	26	s	s	PROPN
ejpam-5899	49	27	,	,	PUNCT
ejpam-5899	49	28	µ	µ	NOUN
ejpam-5899	49	29	)	)	PUNCT
ejpam-5899	49	30	(	(	PUNCT
ejpam-5899	49	31	resp	resp	NOUN
ejpam-5899	49	32	.	.	PUNCT
ejpam-5899	50	1	(	(	PUNCT
ejpam-5899	50	2	e,µe	e,µe	NUM
ejpam-5899	50	3	)	)	PUNCT
ejpam-5899	50	4	)	)	PUNCT
ejpam-5899	50	5	,	,	PUNCT
ejpam-5899	50	6	denoted	denote	VERB
ejpam-5899	50	7	by	by	ADP
ejpam-5899	50	8	gµ−lf(s,µ	gµ−lf(s,µ	PROPN
ejpam-5899	50	9	)	)	PUNCT
ejpam-5899	50	10	(	(	PUNCT
ejpam-5899	50	11	resp	resp	NOUN
ejpam-5899	50	12	.	.	PUNCT
ejpam-5899	51	1	gµ−lf(e,µe	gµ−lf(e,µe	NOUN
ejpam-5899	51	2	)	)	PUNCT
ejpam-5899	51	3	)	)	PUNCT
ejpam-5899	51	4	,	,	PUNCT
ejpam-5899	51	5	if	if	SCONJ
ejpam-5899	51	6	for	for	ADP
ejpam-5899	51	7	each	each	DET
ejpam-5899	51	8	s	s	X
ejpam-5899	51	9	∈	∈	PROPN
ejpam-5899	51	10	s	s	X
ejpam-5899	51	11	(	(	PUNCT
ejpam-5899	51	12	resp	resp	NOUN
ejpam-5899	51	13	.	.	PUNCT
ejpam-5899	52	1	s	s	PART
ejpam-5899	52	2	∈	∈	PROPN
ejpam-5899	52	3	e	e	X
ejpam-5899	52	4	)	)	PUNCT
ejpam-5899	52	5	there	there	PRON
ejpam-5899	52	6	is	be	VERB
ejpam-5899	52	7	h	h	PRON
ejpam-5899	52	8	∈	∈	PROPN
ejpam-5899	52	9	µ∗(s	µ∗(s	PROPN
ejpam-5899	52	10	)	)	PUNCT
ejpam-5899	52	11	(	(	PUNCT
ejpam-5899	52	12	resp	resp	NOUN
ejpam-5899	52	13	.	.	PUNCT
ejpam-5899	53	1	h	h	PROPN
ejpam-5899	53	2	∈	∈	PROPN
ejpam-5899	53	3	µ∗e(s	µ∗e(s	PROPN
ejpam-5899	53	4	)	)	PUNCT
ejpam-5899	53	5	)	)	PUNCT
ejpam-5899	53	6	with	with	ADP
ejpam-5899	53	7	the	the	DET
ejpam-5899	53	8	set	set	NOUN
ejpam-5899	53	9	{	{	PUNCT
ejpam-5899	53	10	η	η	NOUN
ejpam-5899	53	11	:	:	PUNCT
ejpam-5899	53	12	h	h	PROPN
ejpam-5899	53	13	∩gη	∩gη	PROPN
ejpam-5899	53	14	̸=	̸=	PROPN
ejpam-5899	53	15	ϕ	ϕ	PROPN
ejpam-5899	53	16	}	}	PUNCT
ejpam-5899	53	17	is	be	AUX
ejpam-5899	53	18	finite	finite	ADJ
ejpam-5899	53	19	.	.	PUNCT
ejpam-5899	54	1	it	it	PRON
ejpam-5899	54	2	follows	follow	VERB
ejpam-5899	54	3	from	from	ADP
ejpam-5899	54	4	the	the	DET
ejpam-5899	54	5	above	above	ADJ
ejpam-5899	54	6	definition	definition	NOUN
ejpam-5899	54	7	that	that	SCONJ
ejpam-5899	54	8	each	each	DET
ejpam-5899	54	9	µ−lf(s,µ	µ−lf(s,µ	NOUN
ejpam-5899	54	10	)	)	PUNCT
ejpam-5899	54	11	is	be	AUX
ejpam-5899	54	12	gµ−lf(s,µ	gµ−lf(s,µ	ADJ
ejpam-5899	54	13	)	)	PUNCT
ejpam-5899	54	14	but	but	CCONJ
ejpam-5899	54	15	the	the	DET
ejpam-5899	54	16	converse	converse	NOUN
ejpam-5899	54	17	need	need	AUX
ejpam-5899	54	18	not	not	PART
ejpam-5899	54	19	be	be	AUX
ejpam-5899	54	20	true	true	ADJ
ejpam-5899	54	21	in	in	ADP
ejpam-5899	54	22	general	general	ADJ
ejpam-5899	54	23	(	(	PUNCT
ejpam-5899	54	24	see	see	VERB
ejpam-5899	54	25	example	example	NOUN
ejpam-5899	54	26	2.2	2.2	NUM
ejpam-5899	54	27	of	of	ADP
ejpam-5899	54	28	[	[	X
ejpam-5899	54	29	6	6	NUM
ejpam-5899	54	30	]	]	NUM
ejpam-5899	54	31	)	)	PUNCT
ejpam-5899	54	32	.	.	PUNCT
ejpam-5899	55	1	theorem	theorem	NOUN
ejpam-5899	55	2	1	1	NUM
ejpam-5899	55	3	.	.	PUNCT
ejpam-5899	56	1	[	[	X
ejpam-5899	56	2	6	6	NUM
ejpam-5899	56	3	]	]	PUNCT
ejpam-5899	56	4	if	if	SCONJ
ejpam-5899	56	5	g	g	PROPN
ejpam-5899	56	6	=	=	PUNCT
ejpam-5899	56	7	{	{	PUNCT
ejpam-5899	56	8	gα	gα	NOUN
ejpam-5899	56	9	:	:	PUNCT
ejpam-5899	56	10	α	α	PROPN
ejpam-5899	56	11	∈	∈	PROPN
ejpam-5899	56	12	∆	∆	X
ejpam-5899	56	13	}	}	PUNCT
ejpam-5899	56	14	is	be	AUX
ejpam-5899	56	15	a	a	DET
ejpam-5899	56	16	gµ−lf(s,µ	gµ−lf(s,µ	ADJ
ejpam-5899	56	17	)	)	PUNCT
ejpam-5899	56	18	.	.	PUNCT
ejpam-5899	57	1	then	then	ADV
ejpam-5899	57	2	:	:	PUNCT
ejpam-5899	57	3	(	(	PUNCT
ejpam-5899	57	4	i	i	NOUN
ejpam-5899	57	5	)	)	PUNCT
ejpam-5899	57	6	γµ(g	γµ(g	NUM
ejpam-5899	57	7	)	)	PUNCT
ejpam-5899	57	8	=	=	SYM
ejpam-5899	57	9	{	{	PUNCT
ejpam-5899	57	10	γµ(gα	γµ(gα	PROPN
ejpam-5899	57	11	)	)	PUNCT
ejpam-5899	57	12	:	:	PUNCT
ejpam-5899	57	13	α	α	PROPN
ejpam-5899	57	14	∈	∈	PROPN
ejpam-5899	57	15	∆	∆	X
ejpam-5899	57	16	}	}	PUNCT
ejpam-5899	57	17	is	be	AUX
ejpam-5899	57	18	gµ−lf(s,µ	gµ−lf(s,µ	ADJ
ejpam-5899	57	19	)	)	PUNCT
ejpam-5899	57	20	.	.	PUNCT
ejpam-5899	58	1	(	(	PUNCT
ejpam-5899	58	2	ii	ii	NOUN
ejpam-5899	58	3	)	)	PUNCT
ejpam-5899	58	4	g	g	NOUN
ejpam-5899	58	5	is	be	AUX
ejpam-5899	58	6	γµ-closure	γµ-closure	NOUN
ejpam-5899	58	7	preserving	preserve	VERB
ejpam-5899	58	8	,	,	PUNCT
ejpam-5899	58	9	i.e.	i.e.	X
ejpam-5899	58	10	γµ(∪α∈∆gα	γµ(∪α∈∆gα	NUM
ejpam-5899	58	11	)	)	PUNCT
ejpam-5899	58	12	=	=	SYM
ejpam-5899	58	13	∪α∈∆γµ(gα	∪α∈∆γµ(gα	X
ejpam-5899	58	14	)	)	PUNCT
ejpam-5899	58	15	.	.	PUNCT
ejpam-5899	59	1	definition	definition	NOUN
ejpam-5899	59	2	4	4	NUM
ejpam-5899	59	3	.	.	PUNCT
ejpam-5899	60	1	[	[	X
ejpam-5899	60	2	11	11	NUM
ejpam-5899	60	3	]	]	X
ejpam-5899	60	4	let	let	VERB
ejpam-5899	60	5	(	(	PUNCT
ejpam-5899	60	6	s	s	X
ejpam-5899	60	7	,	,	PUNCT
ejpam-5899	60	8	µ	µ	NOUN
ejpam-5899	60	9	)	)	PUNCT
ejpam-5899	60	10	be	be	AUX
ejpam-5899	60	11	a	a	DET
ejpam-5899	60	12	gts	gts	NOUN
ejpam-5899	60	13	and	and	CCONJ
ejpam-5899	60	14	e	e	NOUN
ejpam-5899	61	1	⊆	⊆	PROPN
ejpam-5899	61	2	z	z	PROPN
ejpam-5899	61	3	⊆	⊆	NUM
ejpam-5899	61	4	s.	s.	PROPN
ejpam-5899	61	5	then	then	ADV
ejpam-5899	61	6	:	:	PUNCT
ejpam-5899	61	7	(	(	PUNCT
ejpam-5899	61	8	i	i	NOUN
ejpam-5899	61	9	)	)	PUNCT
ejpam-5899	61	10	a	a	DET
ejpam-5899	61	11	collection	collection	NOUN
ejpam-5899	61	12	g	g	NOUN
ejpam-5899	61	13	=	=	PUNCT
ejpam-5899	61	14	{	{	PUNCT
ejpam-5899	61	15	gα	gα	NOUN
ejpam-5899	61	16	:	:	PUNCT
ejpam-5899	61	17	α	α	PROPN
ejpam-5899	61	18	∈	∈	PROPN
ejpam-5899	61	19	∆	∆	X
ejpam-5899	61	20	}	}	PUNCT
ejpam-5899	61	21	is	be	AUX
ejpam-5899	61	22	cover	cover	NOUN
ejpam-5899	61	23	of	of	ADP
ejpam-5899	61	24	e	e	PRON
ejpam-5899	61	25	if	if	SCONJ
ejpam-5899	61	26	e	e	PROPN
ejpam-5899	61	27	⊆	⊆	NUM
ejpam-5899	61	28	∪α∈∆gα	∪α∈∆gα	NOUN
ejpam-5899	61	29	and	and	CCONJ
ejpam-5899	61	30	if	if	SCONJ
ejpam-5899	61	31	gα	gα	ADP
ejpam-5899	61	32	∈	∈	PROPN
ejpam-5899	61	33	µ	µ	X
ejpam-5899	61	34	(	(	PUNCT
ejpam-5899	61	35	resp	resp	NOUN
ejpam-5899	61	36	.	.	PUNCT
ejpam-5899	61	37	,	,	PUNCT
ejpam-5899	61	38	gα	gα	ADP
ejpam-5899	61	39	∈	∈	PROPN
ejpam-5899	61	40	µz	µz	PROPN
ejpam-5899	61	41	)	)	PUNCT
ejpam-5899	61	42	for	for	ADP
ejpam-5899	61	43	each	each	DET
ejpam-5899	61	44	α	α	PROPN
ejpam-5899	61	45	∈	∈	PROPN
ejpam-5899	61	46	∆	∆	PROPN
ejpam-5899	61	47	,	,	PUNCT
ejpam-5899	61	48	then	then	ADV
ejpam-5899	61	49	g	g	PROPN
ejpam-5899	61	50	is	be	AUX
ejpam-5899	61	51	called	call	VERB
ejpam-5899	61	52	(	(	PUNCT
ejpam-5899	61	53	s	s	X
ejpam-5899	61	54	,	,	PUNCT
ejpam-5899	61	55	µ)-cover	µ)-cover	X
ejpam-5899	61	56	(	(	PUNCT
ejpam-5899	61	57	resp	resp	NOUN
ejpam-5899	61	58	.	.	PUNCT
ejpam-5899	61	59	,	,	PUNCT
ejpam-5899	61	60	(	(	PUNCT
ejpam-5899	61	61	z	z	X
ejpam-5899	61	62	,	,	PUNCT
ejpam-5899	61	63	µz)-cover	µz)-cover	ADV
ejpam-5899	61	64	)	)	PUNCT
ejpam-5899	61	65	of	of	ADP
ejpam-5899	61	66	e.	e.	PROPN
ejpam-5899	61	67	(	(	PUNCT
ejpam-5899	61	68	ii	ii	PROPN
ejpam-5899	61	69	)	)	PUNCT
ejpam-5899	61	70	if	if	SCONJ
ejpam-5899	61	71	g	g	PROPN
ejpam-5899	61	72	and	and	CCONJ
ejpam-5899	61	73	h	h	NOUN
ejpam-5899	61	74	are	be	AUX
ejpam-5899	61	75	covers	cover	NOUN
ejpam-5899	61	76	of	of	ADP
ejpam-5899	61	77	e	e	NOUN
ejpam-5899	61	78	,	,	PUNCT
ejpam-5899	61	79	then	then	ADV
ejpam-5899	61	80	h	h	PROPN
ejpam-5899	61	81	is	be	AUX
ejpam-5899	61	82	called	call	VERB
ejpam-5899	61	83	a	a	DET
ejpam-5899	61	84	refinement	refinement	NOUN
ejpam-5899	61	85	of	of	ADP
ejpam-5899	61	86	g	g	PROPN
ejpam-5899	61	87	if	if	SCONJ
ejpam-5899	61	88	there	there	PRON
ejpam-5899	61	89	is	be	VERB
ejpam-5899	61	90	g	g	PROPN
ejpam-5899	61	91	∈	∈	PROPN
ejpam-5899	61	92	g	g	NOUN
ejpam-5899	61	93	with	with	ADP
ejpam-5899	61	94	h	h	PROPN
ejpam-5899	61	95	⊆	⊆	NUM
ejpam-5899	61	96	g	g	NOUN
ejpam-5899	61	97	for	for	ADP
ejpam-5899	61	98	each	each	DET
ejpam-5899	61	99	h	h	NOUN
ejpam-5899	61	100	∈	∈	PROPN
ejpam-5899	61	101	h.	h.	PROPN
ejpam-5899	62	1	moreover	moreover	ADV
ejpam-5899	62	2	,	,	PUNCT
ejpam-5899	62	3	if	if	SCONJ
ejpam-5899	62	4	h	h	NOUN
ejpam-5899	62	5	is	be	AUX
ejpam-5899	62	6	a	a	DET
ejpam-5899	62	7	refinement	refinement	NOUN
ejpam-5899	62	8	of	of	ADP
ejpam-5899	62	9	g	g	NOUN
ejpam-5899	62	10	with	with	ADP
ejpam-5899	62	11	h	h	PROPN
ejpam-5899	62	12	∈	∈	PROPN
ejpam-5899	62	13	µ	µ	X
ejpam-5899	62	14	(	(	PUNCT
ejpam-5899	62	15	resp	resp	NOUN
ejpam-5899	62	16	.	.	PUNCT
ejpam-5899	62	17	,	,	PUNCT
ejpam-5899	62	18	h	h	PROPN
ejpam-5899	62	19	∈	∈	PROPN
ejpam-5899	62	20	µz	µz	PROPN
ejpam-5899	62	21	)	)	PUNCT
ejpam-5899	62	22	,	,	PUNCT
ejpam-5899	62	23	then	then	ADV
ejpam-5899	62	24	h	h	PROPN
ejpam-5899	62	25	is	be	AUX
ejpam-5899	62	26	called	call	VERB
ejpam-5899	62	27	(	(	PUNCT
ejpam-5899	62	28	s	s	PROPN
ejpam-5899	62	29	,	,	PUNCT
ejpam-5899	62	30	µ)-refinement	µ)-refinement	PUNCT
ejpam-5899	62	31	(	(	PUNCT
ejpam-5899	62	32	resp	resp	NOUN
ejpam-5899	62	33	.	.	PUNCT
ejpam-5899	62	34	,	,	PUNCT
ejpam-5899	63	1	(	(	PUNCT
ejpam-5899	63	2	z	z	X
ejpam-5899	63	3	,	,	PUNCT
ejpam-5899	63	4	µz)-refinement	µz)-refinement	NOUN
ejpam-5899	63	5	)	)	PUNCT
ejpam-5899	63	6	of	of	ADP
ejpam-5899	63	7	g.	g.	PROPN
ejpam-5899	63	8	(	(	PUNCT
ejpam-5899	63	9	iii	iii	PROPN
ejpam-5899	63	10	)	)	PUNCT
ejpam-5899	63	11	a	a	DET
ejpam-5899	63	12	subset	subset	NOUN
ejpam-5899	63	13	e	e	NOUN
ejpam-5899	63	14	is	be	AUX
ejpam-5899	63	15	called	call	VERB
ejpam-5899	63	16	µ-paracompact	µ-paracompact	PROPN
ejpam-5899	63	17	relative	relative	ADJ
ejpam-5899	63	18	to	to	ADP
ejpam-5899	63	19	s	s	PRON
ejpam-5899	63	20	(	(	PUNCT
ejpam-5899	63	21	or	or	CCONJ
ejpam-5899	63	22	µ-paracompact	µ-paracompact	PROPN
ejpam-5899	63	23	subset	subset	NOUN
ejpam-5899	63	24	)	)	PUNCT
ejpam-5899	63	25	if	if	SCONJ
ejpam-5899	63	26	each	each	DET
ejpam-5899	63	27	(	(	PUNCT
ejpam-5899	63	28	s	s	X
ejpam-5899	63	29	,	,	PUNCT
ejpam-5899	63	30	µ)-cover	µ)-cover	NOUN
ejpam-5899	63	31	of	of	ADP
ejpam-5899	63	32	e	e	PROPN
ejpam-5899	63	33	has	have	VERB
ejpam-5899	63	34	µ−lf(s,µ	µ−lf(s,µ	NOUN
ejpam-5899	63	35	)	)	PUNCT
ejpam-5899	63	36	(	(	PUNCT
ejpam-5899	63	37	s	s	X
ejpam-5899	63	38	,	,	PUNCT
ejpam-5899	63	39	µ)-refinement	µ)-refinement	PUNCT
ejpam-5899	63	40	and	and	CCONJ
ejpam-5899	63	41	e	e	NOUN
ejpam-5899	63	42	is	be	AUX
ejpam-5899	63	43	called	call	VERB
ejpam-5899	63	44	µe	µe	ADV
ejpam-5899	63	45	-	-	PUNCT
ejpam-5899	63	46	paracompact	paracompact	ADJ
ejpam-5899	63	47	(	(	PUNCT
ejpam-5899	63	48	or	or	CCONJ
ejpam-5899	63	49	µe	µe	ADV
ejpam-5899	63	50	-	-	PUNCT
ejpam-5899	63	51	paracompact	paracompact	ADJ
ejpam-5899	63	52	subspace	subspace	NOUN
ejpam-5899	63	53	)	)	PUNCT
ejpam-5899	63	54	if	if	SCONJ
ejpam-5899	63	55	(	(	PUNCT
ejpam-5899	63	56	e,µe	e,µe	NOUN
ejpam-5899	63	57	)	)	PUNCT
ejpam-5899	63	58	is	be	AUX
ejpam-5899	63	59	µe	µe	ADV
ejpam-5899	63	60	-	-	PUNCT
ejpam-5899	63	61	paracompact	paracompact	NOUN
ejpam-5899	63	62	as	as	ADP
ejpam-5899	63	63	a	a	DET
ejpam-5899	63	64	subspace	subspace	NOUN
ejpam-5899	63	65	.	.	PUNCT
ejpam-5899	64	1	definition	definition	NOUN
ejpam-5899	64	2	5	5	NUM
ejpam-5899	64	3	.	.	PUNCT
ejpam-5899	65	1	let	let	AUX
ejpam-5899	65	2	(	(	PUNCT
ejpam-5899	65	3	s1	s1	NOUN
ejpam-5899	65	4	,	,	PUNCT
ejpam-5899	65	5	µ1	µ1	PROPN
ejpam-5899	65	6	)	)	PUNCT
ejpam-5899	65	7	and	and	CCONJ
ejpam-5899	65	8	(	(	PUNCT
ejpam-5899	65	9	s2	s2	PROPN
ejpam-5899	65	10	,	,	PUNCT
ejpam-5899	65	11	µ2	µ2	PROPN
ejpam-5899	65	12	)	)	PUNCT
ejpam-5899	65	13	be	be	VERB
ejpam-5899	65	14	gts	gts	ADJ
ejpam-5899	65	15	.	.	PUNCT
ejpam-5899	66	1	a	a	DET
ejpam-5899	66	2	mapping	mapping	NOUN
ejpam-5899	66	3	ψ	ψ	X
ejpam-5899	66	4	:	:	PUNCT
ejpam-5899	66	5	(	(	PUNCT
ejpam-5899	66	6	s1	s1	NOUN
ejpam-5899	66	7	,	,	PUNCT
ejpam-5899	66	8	µ1	µ1	PROPN
ejpam-5899	66	9	)	)	PUNCT
ejpam-5899	66	10	→	→	SYM
ejpam-5899	66	11	(	(	PUNCT
ejpam-5899	66	12	s2	s2	PROPN
ejpam-5899	66	13	,	,	PUNCT
ejpam-5899	66	14	µ2	µ2	PROPN
ejpam-5899	66	15	)	)	PUNCT
ejpam-5899	66	16	is	be	AUX
ejpam-5899	66	17	called	call	VERB
ejpam-5899	66	18	:	:	PUNCT
ejpam-5899	66	19	(	(	PUNCT
ejpam-5899	66	20	i	i	NOUN
ejpam-5899	66	21	)	)	PUNCT
ejpam-5899	66	22	(	(	PUNCT
ejpam-5899	66	23	µ1	µ1	ADJ
ejpam-5899	66	24	,	,	PUNCT
ejpam-5899	66	25	µ2)-continuous	µ2)-continuous	ADJ
ejpam-5899	66	26	[	[	X
ejpam-5899	66	27	4	4	NUM
ejpam-5899	66	28	]	]	X
ejpam-5899	66	29	if	if	SCONJ
ejpam-5899	66	30	ψ−1(h	ψ−1(h	PROPN
ejpam-5899	66	31	)	)	PUNCT
ejpam-5899	66	32	∈	∈	PROPN
ejpam-5899	66	33	µ1	µ1	NOUN
ejpam-5899	66	34	for	for	ADP
ejpam-5899	66	35	each	each	DET
ejpam-5899	66	36	h	h	NOUN
ejpam-5899	66	37	∈	∈	PROPN
ejpam-5899	66	38	µ2	µ2	PROPN
ejpam-5899	66	39	.	.	PUNCT
ejpam-5899	67	1	(	(	PUNCT
ejpam-5899	67	2	ii	ii	NOUN
ejpam-5899	67	3	)	)	PUNCT
ejpam-5899	67	4	(	(	PUNCT
ejpam-5899	67	5	µ1	µ1	PROPN
ejpam-5899	67	6	,	,	PUNCT
ejpam-5899	67	7	µ2)-open	µ2)-open	X
ejpam-5899	68	1	[	[	X
ejpam-5899	68	2	12	12	NUM
ejpam-5899	68	3	]	]	X
ejpam-5899	68	4	if	if	SCONJ
ejpam-5899	68	5	ψ(g	ψ(g	NOUN
ejpam-5899	68	6	)	)	PUNCT
ejpam-5899	69	1	∈	∈	PROPN
ejpam-5899	69	2	µ2	µ2	PROPN
ejpam-5899	69	3	for	for	ADP
ejpam-5899	69	4	each	each	DET
ejpam-5899	69	5	g	g	PROPN
ejpam-5899	69	6	∈	∈	PROPN
ejpam-5899	69	7	µ1	µ1	PROPN
ejpam-5899	69	8	.	.	PUNCT
ejpam-5899	70	1	(	(	PUNCT
ejpam-5899	70	2	iii	iii	X
ejpam-5899	70	3	)	)	PUNCT
ejpam-5899	70	4	(	(	PUNCT
ejpam-5899	70	5	µ1	µ1	PROPN
ejpam-5899	70	6	,	,	PUNCT
ejpam-5899	70	7	µ2)-closed	µ2)-close	VERB
ejpam-5899	70	8	[	[	PUNCT
ejpam-5899	70	9	13	13	NUM
ejpam-5899	70	10	]	]	PUNCT
ejpam-5899	70	11	if	if	SCONJ
ejpam-5899	70	12	ψ(m	ψ(m	NOUN
ejpam-5899	70	13	)	)	PUNCT
ejpam-5899	70	14	is	be	AUX
ejpam-5899	70	15	µ2	µ2	ADJ
ejpam-5899	70	16	-	-	PUNCT
ejpam-5899	70	17	closed	close	VERB
ejpam-5899	70	18	in	in	ADP
ejpam-5899	70	19	s2	s2	NOUN
ejpam-5899	70	20	for	for	ADP
ejpam-5899	70	21	each	each	DET
ejpam-5899	70	22	µ-closed	µ-close	VERB
ejpam-5899	70	23	set	set	VERB
ejpam-5899	70	24	m	m	PROPN
ejpam-5899	70	25	of	of	ADP
ejpam-5899	70	26	s1	s1	PROPN
ejpam-5899	70	27	.	.	PUNCT
ejpam-5899	71	1	proposition	proposition	NOUN
ejpam-5899	71	2	1	1	NUM
ejpam-5899	71	3	.	.	PUNCT
ejpam-5899	72	1	[	[	X
ejpam-5899	72	2	8	8	NUM
ejpam-5899	72	3	]	]	PUNCT
ejpam-5899	72	4	a	a	DET
ejpam-5899	72	5	function	function	NOUN
ejpam-5899	72	6	ψ	ψ	X
ejpam-5899	72	7	:	:	PUNCT
ejpam-5899	72	8	(	(	PUNCT
ejpam-5899	72	9	s1	s1	NOUN
ejpam-5899	72	10	,	,	PUNCT
ejpam-5899	72	11	µ1	µ1	PROPN
ejpam-5899	72	12	)	)	PUNCT
ejpam-5899	72	13	→	→	SYM
ejpam-5899	72	14	(	(	PUNCT
ejpam-5899	72	15	s2	s2	PROPN
ejpam-5899	72	16	,	,	PUNCT
ejpam-5899	72	17	µ2	µ2	PROPN
ejpam-5899	72	18	)	)	PUNCT
ejpam-5899	72	19	is	be	AUX
ejpam-5899	72	20	(	(	PUNCT
ejpam-5899	72	21	µ1	µ1	PROPN
ejpam-5899	72	22	,	,	PUNCT
ejpam-5899	72	23	µ2)-closed	µ2)-close	VERB
ejpam-5899	72	24	iff	iff	PROPN
ejpam-5899	72	25	for	for	ADP
ejpam-5899	72	26	each	each	DET
ejpam-5899	72	27	e	e	PROPN
ejpam-5899	72	28	∈	∈	PROPN
ejpam-5899	72	29	s2	s2	NOUN
ejpam-5899	72	30	and	and	CCONJ
ejpam-5899	72	31	g	g	PROPN
ejpam-5899	72	32	∈	∈	PROPN
ejpam-5899	72	33	µ1	µ1	PROPN
ejpam-5899	72	34	with	with	ADP
ejpam-5899	72	35	ψ−1(e	ψ−1(e	PROPN
ejpam-5899	72	36	)	)	PUNCT
ejpam-5899	73	1	⊆	⊆	NUM
ejpam-5899	73	2	g	g	NOUN
ejpam-5899	73	3	,	,	PUNCT
ejpam-5899	73	4	there	there	PRON
ejpam-5899	73	5	is	be	VERB
ejpam-5899	73	6	h	h	PRON
ejpam-5899	73	7	∈	∈	NOUN
ejpam-5899	73	8	µ2(e	µ2(e	NOUN
ejpam-5899	73	9	)	)	PUNCT
ejpam-5899	73	10	with	with	ADP
ejpam-5899	73	11	ψ	ψ	NOUN
ejpam-5899	73	12	−1(h	−1(h	NOUN
ejpam-5899	73	13	)	)	PUNCT
ejpam-5899	73	14	⊆	⊆	NUM
ejpam-5899	73	15	g.	g.	NOUN
ejpam-5899	73	16	3	3	NUM
ejpam-5899	73	17	.	.	PUNCT
ejpam-5899	74	1	α	α	X
ejpam-5899	74	2	-	-	PUNCT
ejpam-5899	74	3	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	74	4	and	and	CCONJ
ejpam-5899	74	5	β	β	NOUN
ejpam-5899	74	6	-	-	ADJ
ejpam-5899	74	7	gµ-paracompact	gµ-paracompact	ADJ
ejpam-5899	74	8	sets	set	NOUN
ejpam-5899	74	9	in	in	ADP
ejpam-5899	74	10	this	this	DET
ejpam-5899	74	11	section	section	NOUN
ejpam-5899	74	12	,	,	PUNCT
ejpam-5899	74	13	the	the	DET
ejpam-5899	74	14	concepts	concept	NOUN
ejpam-5899	74	15	of	of	ADP
ejpam-5899	74	16	α	α	NOUN
ejpam-5899	74	17	-	-	PUNCT
ejpam-5899	74	18	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	74	19	and	and	CCONJ
ejpam-5899	74	20	β	β	NOUN
ejpam-5899	74	21	-	-	ADJ
ejpam-5899	74	22	gµ-paracompact	gµ-paracompact	ADJ
ejpam-5899	74	23	subsets	subset	NOUN
ejpam-5899	74	24	are	be	AUX
ejpam-5899	74	25	illustrated	illustrate	VERB
ejpam-5899	74	26	and	and	CCONJ
ejpam-5899	74	27	the	the	DET
ejpam-5899	74	28	relationship	relationship	NOUN
ejpam-5899	74	29	between	between	ADP
ejpam-5899	74	30	them	they	PRON
ejpam-5899	74	31	with	with	ADP
ejpam-5899	74	32	some	some	PRON
ejpam-5899	74	33	of	of	ADP
ejpam-5899	74	34	their	their	PRON
ejpam-5899	74	35	properties	property	NOUN
ejpam-5899	74	36	are	be	AUX
ejpam-5899	74	37	investigated	investigate	VERB
ejpam-5899	74	38	.	.	PUNCT
ejpam-5899	75	1	proposition	proposition	NOUN
ejpam-5899	75	2	2	2	NUM
ejpam-5899	75	3	.	.	PUNCT
ejpam-5899	76	1	let	let	AUX
ejpam-5899	76	2	(	(	PUNCT
ejpam-5899	76	3	s	s	X
ejpam-5899	76	4	,	,	PUNCT
ejpam-5899	76	5	µ	µ	NOUN
ejpam-5899	76	6	)	)	PUNCT
ejpam-5899	76	7	be	be	AUX
ejpam-5899	76	8	a	a	DET
ejpam-5899	76	9	gts	gts	NOUN
ejpam-5899	76	10	with	with	ADP
ejpam-5899	76	11	e	e	PROPN
ejpam-5899	76	12	⊆	⊆	NUM
ejpam-5899	76	13	s	s	NOUN
ejpam-5899	76	14	and	and	CCONJ
ejpam-5899	76	15	g	g	NOUN
ejpam-5899	76	16	=	=	PUNCT
ejpam-5899	76	17	{	{	PUNCT
ejpam-5899	76	18	gα	gα	NOUN
ejpam-5899	76	19	:	:	PUNCT
ejpam-5899	76	20	α	α	PROPN
ejpam-5899	76	21	∈	∈	NOUN
ejpam-5899	76	22	∆	∆	NOUN
ejpam-5899	76	23	,	,	PUNCT
ejpam-5899	76	24	gα	gα	ADP
ejpam-5899	76	25	⊆	⊆	NUM
ejpam-5899	76	26	e	e	NOUN
ejpam-5899	76	27	}	}	PUNCT
ejpam-5899	76	28	.	.	PUNCT
ejpam-5899	77	1	then	then	ADV
ejpam-5899	77	2	:	:	PUNCT
ejpam-5899	77	3	(	(	PUNCT
ejpam-5899	77	4	i	i	NOUN
ejpam-5899	77	5	)	)	PUNCT
ejpam-5899	77	6	g	g	PROPN
ejpam-5899	77	7	is	be	AUX
ejpam-5899	77	8	gµ−lf(e,µe	gµ−lf(e,µe	NOUN
ejpam-5899	77	9	)	)	PUNCT
ejpam-5899	77	10	if	if	SCONJ
ejpam-5899	77	11	it	it	PRON
ejpam-5899	77	12	is	be	AUX
ejpam-5899	77	13	gµ−lf(s,µ	gµ−lf(s,µ	ADJ
ejpam-5899	77	14	)	)	PUNCT
ejpam-5899	77	15	.	.	PUNCT
ejpam-5899	78	1	(	(	PUNCT
ejpam-5899	78	2	ii	ii	NOUN
ejpam-5899	78	3	)	)	PUNCT
ejpam-5899	78	4	g	g	NOUN
ejpam-5899	78	5	is	be	AUX
ejpam-5899	78	6	gµ−lf(s,µ	gµ−lf(s,µ	ADJ
ejpam-5899	78	7	)	)	PUNCT
ejpam-5899	78	8	if	if	SCONJ
ejpam-5899	78	9	it	it	PRON
ejpam-5899	78	10	is	be	AUX
ejpam-5899	78	11	gµ−lf(e,µe	gµ−lf(e,µe	NOUN
ejpam-5899	78	12	)	)	PUNCT
ejpam-5899	78	13	provided	provide	VERB
ejpam-5899	78	14	that	that	SCONJ
ejpam-5899	78	15	e	e	PROPN
ejpam-5899	78	16	is	be	AUX
ejpam-5899	78	17	µ-closed	µ-close	VERB
ejpam-5899	78	18	.	.	PUNCT
ejpam-5899	79	1	h.	h.	PROPN
ejpam-5899	79	2	h.	h.	PROPN
ejpam-5899	79	3	al	al	PROPN
ejpam-5899	79	4	-	-	PUNCT
ejpam-5899	79	5	jarrah	jarrah	PROPN
ejpam-5899	79	6	et	et	PROPN
ejpam-5899	79	7	al	al	PROPN
ejpam-5899	79	8	.	.	PUNCT
ejpam-5899	79	9	/	/	SYM
ejpam-5899	79	10	eur	eur	PROPN
ejpam-5899	79	11	.	.	PUNCT
ejpam-5899	80	1	j.	j.	PROPN
ejpam-5899	80	2	pure	pure	PROPN
ejpam-5899	80	3	appl	appl	PROPN
ejpam-5899	80	4	.	.	PROPN
ejpam-5899	80	5	math	math	PROPN
ejpam-5899	80	6	,	,	PUNCT
ejpam-5899	80	7	18	18	NUM
ejpam-5899	80	8	(	(	PUNCT
ejpam-5899	80	9	2	2	NUM
ejpam-5899	80	10	)	)	PUNCT
ejpam-5899	80	11	(	(	PUNCT
ejpam-5899	80	12	2025	2025	NUM
ejpam-5899	80	13	)	)	PUNCT
ejpam-5899	80	14	,	,	PUNCT
ejpam-5899	80	15	5899	5899	NUM
ejpam-5899	80	16	4	4	NUM
ejpam-5899	80	17	of	of	ADP
ejpam-5899	80	18	11	11	NUM
ejpam-5899	80	19	proof	proof	NOUN
ejpam-5899	80	20	.	.	PUNCT
ejpam-5899	81	1	(	(	PUNCT
ejpam-5899	81	2	i	i	NOUN
ejpam-5899	81	3	)	)	PUNCT
ejpam-5899	81	4	it	it	PRON
ejpam-5899	81	5	follows	follow	VERB
ejpam-5899	81	6	from	from	ADP
ejpam-5899	81	7	definition	definition	NOUN
ejpam-5899	81	8	3	3	NUM
ejpam-5899	81	9	.	.	PUNCT
ejpam-5899	81	10	(	(	PUNCT
ejpam-5899	81	11	ii	ii	NOUN
ejpam-5899	81	12	)	)	PUNCT
ejpam-5899	81	13	let	let	VERB
ejpam-5899	81	14	g	g	NOUN
ejpam-5899	81	15	be	be	AUX
ejpam-5899	81	16	gµ−lf(e,µe	gµ−lf(e,µe	NOUN
ejpam-5899	81	17	)	)	PUNCT
ejpam-5899	81	18	.	.	PUNCT
ejpam-5899	82	1	if	if	SCONJ
ejpam-5899	82	2	s	s	VERB
ejpam-5899	82	3	∈	∈	PROPN
ejpam-5899	82	4	s	s	NOUN
ejpam-5899	82	5	,	,	PUNCT
ejpam-5899	82	6	then	then	ADV
ejpam-5899	82	7	either	either	CCONJ
ejpam-5899	82	8	s	s	VERB
ejpam-5899	82	9	∈	∈	PROPN
ejpam-5899	82	10	e	e	NOUN
ejpam-5899	82	11	or	or	CCONJ
ejpam-5899	82	12	s	s	PROPN
ejpam-5899	82	13	/∈	/∈	PROPN
ejpam-5899	82	14	e.	e.	PROPN
ejpam-5899	83	1	if	if	SCONJ
ejpam-5899	83	2	s	s	VERB
ejpam-5899	83	3	∈	∈	PROPN
ejpam-5899	83	4	e	e	NOUN
ejpam-5899	83	5	,	,	PUNCT
ejpam-5899	83	6	then	then	ADV
ejpam-5899	83	7	there	there	PRON
ejpam-5899	83	8	is	be	VERB
ejpam-5899	83	9	h	h	PRON
ejpam-5899	83	10	∈	∈	PROPN
ejpam-5899	83	11	µ∗e(s	µ∗e(s	PROPN
ejpam-5899	83	12	)	)	PUNCT
ejpam-5899	83	13	with	with	ADP
ejpam-5899	83	14	the	the	DET
ejpam-5899	83	15	set	set	NOUN
ejpam-5899	83	16	{	{	PUNCT
ejpam-5899	83	17	η	η	NOUN
ejpam-5899	83	18	:	:	PUNCT
ejpam-5899	83	19	h	h	PROPN
ejpam-5899	83	20	∩gη	∩gη	PROPN
ejpam-5899	83	21	̸=	̸=	PROPN
ejpam-5899	83	22	ϕ	ϕ	PROPN
ejpam-5899	83	23	}	}	PUNCT
ejpam-5899	83	24	is	be	AUX
ejpam-5899	83	25	finite	finite	ADJ
ejpam-5899	83	26	.	.	PUNCT
ejpam-5899	84	1	now	now	ADV
ejpam-5899	84	2	h	h	X
ejpam-5899	85	1	=	=	NOUN
ejpam-5899	85	2	w	w	NOUN
ejpam-5899	85	3	∩e	∩e	NOUN
ejpam-5899	85	4	for	for	ADP
ejpam-5899	85	5	some	some	DET
ejpam-5899	85	6	w	w	PROPN
ejpam-5899	85	7	∈	∈	PROPN
ejpam-5899	85	8	µ∗(s	µ∗(s	PROPN
ejpam-5899	85	9	)	)	PUNCT
ejpam-5899	85	10	.	.	PUNCT
ejpam-5899	86	1	since	since	SCONJ
ejpam-5899	86	2	g	g	PROPN
ejpam-5899	86	3	is	be	AUX
ejpam-5899	86	4	a	a	DET
ejpam-5899	86	5	collection	collection	NOUN
ejpam-5899	86	6	of	of	ADP
ejpam-5899	86	7	subsets	subset	NOUN
ejpam-5899	86	8	of	of	ADP
ejpam-5899	86	9	e	e	NOUN
ejpam-5899	86	10	,	,	PUNCT
ejpam-5899	86	11	then	then	ADV
ejpam-5899	86	12	{	{	PUNCT
ejpam-5899	86	13	η	η	PROPN
ejpam-5899	86	14	:	:	PUNCT
ejpam-5899	86	15	w	w	NOUN
ejpam-5899	86	16	∩	∩	NOUN
ejpam-5899	86	17	gη	gη	ADP
ejpam-5899	86	18	̸=	̸=	PROPN
ejpam-5899	86	19	ϕ	ϕ	NOUN
ejpam-5899	86	20	}	}	PUNCT
ejpam-5899	86	21	is	be	AUX
ejpam-5899	86	22	finite	finite	ADJ
ejpam-5899	86	23	.	.	PUNCT
ejpam-5899	87	1	if	if	SCONJ
ejpam-5899	87	2	s	s	PART
ejpam-5899	87	3	/∈	/∈	PUNCT
ejpam-5899	88	1	e	e	NOUN
ejpam-5899	88	2	then	then	ADV
ejpam-5899	88	3	s	s	VERB
ejpam-5899	88	4	−	−	PROPN
ejpam-5899	88	5	e	e	PROPN
ejpam-5899	88	6	∈	∈	PROPN
ejpam-5899	88	7	µ∗(s	µ∗(s	PROPN
ejpam-5899	88	8	)	)	PUNCT
ejpam-5899	88	9	which	which	PRON
ejpam-5899	88	10	intersects	intersect	VERB
ejpam-5899	88	11	no	no	DET
ejpam-5899	88	12	member	member	NOUN
ejpam-5899	88	13	of	of	ADP
ejpam-5899	88	14	g.	g.	PROPN
ejpam-5899	88	15	example	example	NOUN
ejpam-5899	89	1	1	1	X
ejpam-5899	89	2	.	.	PUNCT
ejpam-5899	90	1	let	let	AUX
ejpam-5899	90	2	(	(	PUNCT
ejpam-5899	90	3	s	s	X
ejpam-5899	90	4	,	,	PUNCT
ejpam-5899	90	5	µ	µ	NOUN
ejpam-5899	90	6	)	)	PUNCT
ejpam-5899	90	7	be	be	AUX
ejpam-5899	90	8	a	a	DET
ejpam-5899	90	9	gts	gts	NOUN
ejpam-5899	90	10	where	where	SCONJ
ejpam-5899	90	11	s	s	VERB
ejpam-5899	90	12	=	=	SYM
ejpam-5899	90	13	r	r	NOUN
ejpam-5899	90	14	and	and	CCONJ
ejpam-5899	90	15	µ	µ	X
ejpam-5899	90	16	=	=	PUNCT
ejpam-5899	90	17	{	{	PUNCT
ejpam-5899	90	18	g	g	NOUN
ejpam-5899	90	19	:	:	PUNCT
ejpam-5899	90	20	0	0	NUM
ejpam-5899	90	21	/∈	/∈	PUNCT
ejpam-5899	91	1	g	g	NOUN
ejpam-5899	91	2	}	}	PUNCT
ejpam-5899	91	3	.	.	PUNCT
ejpam-5899	92	1	put	put	VERB
ejpam-5899	92	2	e	e	NOUN
ejpam-5899	92	3	=	=	NOUN
ejpam-5899	92	4	q−	q−	PROPN
ejpam-5899	92	5	{	{	PUNCT
ejpam-5899	92	6	0	0	NUM
ejpam-5899	92	7	}	}	PUNCT
ejpam-5899	92	8	.	.	PUNCT
ejpam-5899	93	1	then	then	ADV
ejpam-5899	93	2	the	the	DET
ejpam-5899	93	3	collection	collection	NOUN
ejpam-5899	93	4	{	{	PUNCT
ejpam-5899	93	5	{	{	PUNCT
ejpam-5899	93	6	e	e	NOUN
ejpam-5899	93	7	}	}	PUNCT
ejpam-5899	93	8	:	:	PUNCT
ejpam-5899	93	9	e	e	X
ejpam-5899	93	10	∈	∈	PROPN
ejpam-5899	93	11	e	e	X
ejpam-5899	93	12	}	}	PUNCT
ejpam-5899	93	13	is	be	AUX
ejpam-5899	93	14	gµ−lf(e,µe	gµ−lf(e,µe	NOUN
ejpam-5899	93	15	)	)	PUNCT
ejpam-5899	93	16	while	while	SCONJ
ejpam-5899	93	17	it	it	PRON
ejpam-5899	93	18	is	be	AUX
ejpam-5899	93	19	not	not	PART
ejpam-5899	93	20	gµ−lf(s,µ	gµ−lf(s,µ	ADJ
ejpam-5899	93	21	)	)	PUNCT
ejpam-5899	93	22	.	.	PUNCT
ejpam-5899	94	1	definition	definition	NOUN
ejpam-5899	94	2	6	6	NUM
ejpam-5899	94	3	.	.	PUNCT
ejpam-5899	95	1	let	let	AUX
ejpam-5899	95	2	(	(	PUNCT
ejpam-5899	95	3	s	s	X
ejpam-5899	95	4	,	,	PUNCT
ejpam-5899	95	5	µ	µ	NOUN
ejpam-5899	95	6	)	)	PUNCT
ejpam-5899	95	7	be	be	AUX
ejpam-5899	95	8	a	a	DET
ejpam-5899	95	9	gts	gts	NOUN
ejpam-5899	95	10	and	and	CCONJ
ejpam-5899	95	11	e	e	NOUN
ejpam-5899	95	12	⊆	⊆	NUM
ejpam-5899	95	13	s.	s.	PROPN
ejpam-5899	95	14	then	then	ADV
ejpam-5899	95	15	:	:	PUNCT
ejpam-5899	95	16	(	(	PUNCT
ejpam-5899	95	17	i	i	NOUN
ejpam-5899	95	18	)	)	PUNCT
ejpam-5899	95	19	e	e	NOUN
ejpam-5899	95	20	is	be	AUX
ejpam-5899	95	21	called	call	VERB
ejpam-5899	95	22	α	α	PRON
ejpam-5899	95	23	-	-	NOUN
ejpam-5899	95	24	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	95	25	in	in	ADP
ejpam-5899	95	26	(	(	PUNCT
ejpam-5899	95	27	s	s	PROPN
ejpam-5899	95	28	,	,	PUNCT
ejpam-5899	95	29	µ	µ	NOUN
ejpam-5899	95	30	)	)	PUNCT
ejpam-5899	95	31	(	(	PUNCT
ejpam-5899	95	32	simply	simply	ADV
ejpam-5899	95	33	,	,	PUNCT
ejpam-5899	95	34	α	α	PRON
ejpam-5899	95	35	-	-	NOUN
ejpam-5899	95	36	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	95	37	)	)	PUNCT
ejpam-5899	95	38	if	if	SCONJ
ejpam-5899	95	39	each	each	PRON
ejpam-5899	95	40	(	(	PUNCT
ejpam-5899	95	41	s	s	PROPN
ejpam-5899	95	42	,	,	PUNCT
ejpam-5899	95	43	µ)cover	µ)cover	PROPN
ejpam-5899	95	44	of	of	ADP
ejpam-5899	95	45	e	e	PROPN
ejpam-5899	95	46	has	have	VERB
ejpam-5899	95	47	a	a	DET
ejpam-5899	95	48	gµ−lf(s,µ	gµ−lf(s,µ	ADJ
ejpam-5899	95	49	)	)	PUNCT
ejpam-5899	95	50	(	(	PUNCT
ejpam-5899	95	51	s	s	NOUN
ejpam-5899	95	52	,	,	PUNCT
ejpam-5899	95	53	µ)-refinement	µ)-refinement	PROPN
ejpam-5899	95	54	.	.	PUNCT
ejpam-5899	96	1	(	(	PUNCT
ejpam-5899	96	2	ii	ii	NOUN
ejpam-5899	96	3	)	)	PUNCT
ejpam-5899	96	4	e	e	NOUN
ejpam-5899	96	5	is	be	AUX
ejpam-5899	96	6	called	call	VERB
ejpam-5899	96	7	β	β	NOUN
ejpam-5899	96	8	-	-	PUNCT
ejpam-5899	96	9	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	96	10	in	in	ADP
ejpam-5899	96	11	(	(	PUNCT
ejpam-5899	96	12	s	s	PROPN
ejpam-5899	96	13	,	,	PUNCT
ejpam-5899	96	14	µ	µ	NOUN
ejpam-5899	96	15	)	)	PUNCT
ejpam-5899	96	16	(	(	PUNCT
ejpam-5899	96	17	simply	simply	ADV
ejpam-5899	96	18	β	β	X
ejpam-5899	96	19	-	-	NOUN
ejpam-5899	96	20	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	96	21	)	)	PUNCT
ejpam-5899	97	1	if	if	SCONJ
ejpam-5899	97	2	each	each	PRON
ejpam-5899	97	3	(	(	PUNCT
ejpam-5899	97	4	e,µe)cover	e,µe)cover	PROPN
ejpam-5899	97	5	of	of	ADP
ejpam-5899	97	6	e	e	PROPN
ejpam-5899	97	7	has	have	VERB
ejpam-5899	97	8	a	a	DET
ejpam-5899	97	9	gµ−lf(e,µe	gµ−lf(e,µe	NOUN
ejpam-5899	97	10	)	)	PUNCT
ejpam-5899	97	11	(	(	PUNCT
ejpam-5899	97	12	e,µe)-refinement	e,µe)-refinement	X
ejpam-5899	97	13	.	.	PUNCT
ejpam-5899	98	1	proposition	proposition	NOUN
ejpam-5899	98	2	3	3	NUM
ejpam-5899	98	3	.	.	PUNCT
ejpam-5899	99	1	each	each	PRON
ejpam-5899	99	2	α	α	NOUN
ejpam-5899	99	3	-	-	PUNCT
ejpam-5899	99	4	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	99	5	is	be	AUX
ejpam-5899	99	6	β	β	NOUN
ejpam-5899	99	7	-	-	NOUN
ejpam-5899	99	8	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	99	9	.	.	PUNCT
ejpam-5899	100	1	proof	proof	NOUN
ejpam-5899	100	2	.	.	PUNCT
ejpam-5899	101	1	it	it	PRON
ejpam-5899	101	2	follows	follow	VERB
ejpam-5899	101	3	from	from	ADP
ejpam-5899	101	4	definition	definition	NOUN
ejpam-5899	101	5	3	3	NUM
ejpam-5899	101	6	and	and	CCONJ
ejpam-5899	101	7	proposition	proposition	NOUN
ejpam-5899	101	8	2	2	NUM
ejpam-5899	101	9	.	.	X
ejpam-5899	101	10	note	note	VERB
ejpam-5899	101	11	that	that	SCONJ
ejpam-5899	101	12	the	the	DET
ejpam-5899	101	13	converse	converse	NOUN
ejpam-5899	101	14	of	of	ADP
ejpam-5899	101	15	proposition	proposition	NOUN
ejpam-5899	101	16	3	3	NUM
ejpam-5899	101	17	is	be	AUX
ejpam-5899	101	18	not	not	PART
ejpam-5899	101	19	true	true	ADJ
ejpam-5899	101	20	in	in	ADP
ejpam-5899	101	21	general	general	ADJ
ejpam-5899	101	22	.	.	PUNCT
ejpam-5899	102	1	in	in	ADP
ejpam-5899	102	2	example	example	NOUN
ejpam-5899	102	3	1	1	NUM
ejpam-5899	102	4	,	,	PUNCT
ejpam-5899	102	5	e	e	X
ejpam-5899	102	6	is	be	AUX
ejpam-5899	102	7	β	β	NOUN
ejpam-5899	102	8	-	-	NOUN
ejpam-5899	102	9	gµparacompact	gµparacompact	NOUN
ejpam-5899	102	10	,	,	PUNCT
ejpam-5899	102	11	since	since	SCONJ
ejpam-5899	102	12	each	each	PRON
ejpam-5899	102	13	(	(	PUNCT
ejpam-5899	102	14	e,µe)-cover	e,µe)-cover	PUNCT
ejpam-5899	102	15	of	of	ADP
ejpam-5899	102	16	e	e	PROPN
ejpam-5899	102	17	has	have	VERB
ejpam-5899	102	18	a	a	DET
ejpam-5899	102	19	gµ−lf(e,µe	gµ−lf(e,µe	NOUN
ejpam-5899	102	20	)	)	PUNCT
ejpam-5899	102	21	(	(	PUNCT
ejpam-5899	102	22	e,µe)-refinement	e,µe)-refinement	X
ejpam-5899	102	23	(	(	PUNCT
ejpam-5899	102	24	that	that	ADV
ejpam-5899	102	25	is	is	ADV
ejpam-5899	102	26	{	{	PUNCT
ejpam-5899	102	27	{	{	PUNCT
ejpam-5899	102	28	e	e	NOUN
ejpam-5899	102	29	}	}	PUNCT
ejpam-5899	102	30	:	:	PUNCT
ejpam-5899	102	31	e	e	X
ejpam-5899	102	32	∈	∈	PROPN
ejpam-5899	102	33	e	e	NOUN
ejpam-5899	102	34	}	}	PUNCT
ejpam-5899	102	35	)	)	PUNCT
ejpam-5899	102	36	.	.	PUNCT
ejpam-5899	103	1	on	on	ADP
ejpam-5899	103	2	the	the	DET
ejpam-5899	103	3	other	other	ADJ
ejpam-5899	103	4	hand	hand	NOUN
ejpam-5899	103	5	,	,	PUNCT
ejpam-5899	103	6	g	g	PROPN
ejpam-5899	103	7	=	=	PRON
ejpam-5899	103	8	{	{	PUNCT
ejpam-5899	103	9	{	{	PUNCT
ejpam-5899	103	10	e	e	NOUN
ejpam-5899	103	11	}	}	PUNCT
ejpam-5899	103	12	:	:	PUNCT
ejpam-5899	103	13	e	e	X
ejpam-5899	103	14	∈	∈	PROPN
ejpam-5899	103	15	e	e	X
ejpam-5899	103	16	}	}	PUNCT
ejpam-5899	103	17	is	be	AUX
ejpam-5899	103	18	an	an	DET
ejpam-5899	103	19	(	(	PUNCT
ejpam-5899	103	20	s	s	X
ejpam-5899	103	21	,	,	PUNCT
ejpam-5899	103	22	µ)-cover	µ)-cover	NOUN
ejpam-5899	103	23	of	of	ADP
ejpam-5899	103	24	e	e	NOUN
ejpam-5899	103	25	and	and	CCONJ
ejpam-5899	103	26	it	it	PRON
ejpam-5899	103	27	has	have	VERB
ejpam-5899	103	28	no	no	DET
ejpam-5899	103	29	gµ−lf(s,µ)(s	gµ−lf(s,µ)(s	NOUN
ejpam-5899	103	30	,	,	PUNCT
ejpam-5899	103	31	µ)-refinement	µ)-refinement	PUNCT
ejpam-5899	103	32	since	since	SCONJ
ejpam-5899	103	33	µ∗(0	µ∗(0	NOUN
ejpam-5899	103	34	)	)	PUNCT
ejpam-5899	104	1	=	=	SYM
ejpam-5899	104	2	ϕ.	ϕ.	PROPN
ejpam-5899	104	3	therefore	therefore	ADV
ejpam-5899	104	4	,	,	PUNCT
ejpam-5899	104	5	e	e	X
ejpam-5899	104	6	is	be	AUX
ejpam-5899	104	7	not	not	PART
ejpam-5899	104	8	α	α	NOUN
ejpam-5899	104	9	-	-	NOUN
ejpam-5899	104	10	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	104	11	.	.	PUNCT
ejpam-5899	105	1	theorem	theorem	NOUN
ejpam-5899	105	2	2	2	NUM
ejpam-5899	105	3	.	.	PUNCT
ejpam-5899	106	1	let	let	AUX
ejpam-5899	106	2	(	(	PUNCT
ejpam-5899	106	3	s	s	X
ejpam-5899	106	4	,	,	PUNCT
ejpam-5899	106	5	µ	µ	NOUN
ejpam-5899	106	6	)	)	PUNCT
ejpam-5899	106	7	be	be	AUX
ejpam-5899	106	8	a	a	DET
ejpam-5899	106	9	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	106	10	gts	gts	NOUN
ejpam-5899	106	11	and	and	CCONJ
ejpam-5899	106	12	e	e	NOUN
ejpam-5899	106	13	⊆	⊆	NUM
ejpam-5899	106	14	s.	s.	PROPN
ejpam-5899	106	15	then	then	ADV
ejpam-5899	106	16	e	e	PROPN
ejpam-5899	106	17	is	be	AUX
ejpam-5899	106	18	α	α	NOUN
ejpam-5899	106	19	-	-	PUNCT
ejpam-5899	106	20	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	106	21	if	if	SCONJ
ejpam-5899	106	22	one	one	NUM
ejpam-5899	106	23	of	of	ADP
ejpam-5899	106	24	the	the	DET
ejpam-5899	106	25	following	follow	VERB
ejpam-5899	106	26	holds	hold	VERB
ejpam-5899	106	27	:	:	PUNCT
ejpam-5899	106	28	(	(	PUNCT
ejpam-5899	106	29	i	i	NOUN
ejpam-5899	106	30	)	)	PUNCT
ejpam-5899	106	31	e	e	NOUN
ejpam-5899	106	32	is	be	AUX
ejpam-5899	106	33	µg	µg	ADV
ejpam-5899	106	34	-	-	PUNCT
ejpam-5899	106	35	closed	closed	ADJ
ejpam-5899	106	36	in	in	ADP
ejpam-5899	106	37	(	(	PUNCT
ejpam-5899	106	38	s	s	PROPN
ejpam-5899	106	39	,	,	PUNCT
ejpam-5899	106	40	µ	µ	NOUN
ejpam-5899	106	41	)	)	PUNCT
ejpam-5899	106	42	.	.	PUNCT
ejpam-5899	107	1	(	(	PUNCT
ejpam-5899	107	2	ii	ii	NOUN
ejpam-5899	107	3	)	)	PUNCT
ejpam-5899	107	4	e	e	NOUN
ejpam-5899	107	5	is	be	AUX
ejpam-5899	107	6	µ-closed	µ-close	VERB
ejpam-5899	107	7	in	in	ADP
ejpam-5899	107	8	(	(	PUNCT
ejpam-5899	107	9	s	s	PROPN
ejpam-5899	107	10	,	,	PUNCT
ejpam-5899	107	11	µ	µ	NOUN
ejpam-5899	107	12	)	)	PUNCT
ejpam-5899	107	13	.	.	PUNCT
ejpam-5899	108	1	proof	proof	NOUN
ejpam-5899	108	2	.	.	PUNCT
ejpam-5899	109	1	(	(	PUNCT
ejpam-5899	109	2	i	i	NOUN
ejpam-5899	109	3	)	)	PUNCT
ejpam-5899	109	4	let	let	VERB
ejpam-5899	109	5	g	g	NOUN
ejpam-5899	109	6	=	=	PUNCT
ejpam-5899	109	7	{	{	PUNCT
ejpam-5899	109	8	gα	gα	NOUN
ejpam-5899	109	9	:	:	PUNCT
ejpam-5899	109	10	α	α	PROPN
ejpam-5899	109	11	∈	∈	PROPN
ejpam-5899	109	12	∆	∆	PROPN
ejpam-5899	109	13	}	}	PUNCT
ejpam-5899	109	14	be	be	AUX
ejpam-5899	109	15	an	an	DET
ejpam-5899	109	16	(	(	PUNCT
ejpam-5899	109	17	s	s	X
ejpam-5899	109	18	,	,	PUNCT
ejpam-5899	109	19	µ)-cover	µ)-cover	PUNCT
ejpam-5899	109	20	of	of	ADP
ejpam-5899	109	21	e.	e.	PROPN
ejpam-5899	109	22	since	since	PROPN
ejpam-5899	109	23	cµ(e	cµ(e	NOUN
ejpam-5899	109	24	)	)	PUNCT
ejpam-5899	109	25	⊆	⊆	NUM
ejpam-5899	109	26	∪α∈∆gα	∪α∈∆gα	NOUN
ejpam-5899	109	27	,	,	PUNCT
ejpam-5899	109	28	then	then	ADV
ejpam-5899	109	29	g1	g1	VERB
ejpam-5899	109	30	=	=	PUNCT
ejpam-5899	109	31	g	g	PROPN
ejpam-5899	109	32	∪	∪	X
ejpam-5899	109	33	{	{	PUNCT
ejpam-5899	109	34	s	s	NOUN
ejpam-5899	109	35	−	−	NOUN
ejpam-5899	109	36	cµ(e	cµ(e	PUNCT
ejpam-5899	109	37	)	)	PUNCT
ejpam-5899	109	38	}	}	PUNCT
ejpam-5899	109	39	is	be	AUX
ejpam-5899	109	40	an	an	DET
ejpam-5899	109	41	(	(	PUNCT
ejpam-5899	109	42	s	s	X
ejpam-5899	109	43	,	,	PUNCT
ejpam-5899	109	44	µ)-cover	µ)-cover	PUNCT
ejpam-5899	109	45	of	of	ADP
ejpam-5899	109	46	s.	s.	PROPN
ejpam-5899	109	47	so	so	PROPN
ejpam-5899	109	48	g1	g1	PROPN
ejpam-5899	109	49	has	have	VERB
ejpam-5899	109	50	a	a	DET
ejpam-5899	109	51	gµ−lf(s,µ	gµ−lf(s,µ	ADJ
ejpam-5899	109	52	)	)	PUNCT
ejpam-5899	109	53	(	(	PUNCT
ejpam-5899	109	54	s	s	X
ejpam-5899	109	55	,	,	PUNCT
ejpam-5899	109	56	µ)-refinement	µ)-refinement	PUNCT
ejpam-5899	109	57	,	,	PUNCT
ejpam-5899	109	58	say	say	VERB
ejpam-5899	109	59	h	h	NOUN
ejpam-5899	109	60	=	=	PRON
ejpam-5899	109	61	{	{	PUNCT
ejpam-5899	109	62	hβ	hβ	INTJ
ejpam-5899	109	63	:	:	PUNCT
ejpam-5899	109	64	β	β	X
ejpam-5899	109	65	∈	∈	PROPN
ejpam-5899	109	66	λ	λ	NOUN
ejpam-5899	109	67	}	}	PUNCT
ejpam-5899	109	68	.	.	PUNCT
ejpam-5899	110	1	therefore	therefore	ADV
ejpam-5899	110	2	,	,	PUNCT
ejpam-5899	110	3	the	the	DET
ejpam-5899	110	4	collection	collection	NOUN
ejpam-5899	110	5	h1	h1	NOUN
ejpam-5899	110	6	=	=	PUNCT
ejpam-5899	110	7	{	{	PUNCT
ejpam-5899	110	8	hβ	hβ	PROPN
ejpam-5899	110	9	∈	∈	PROPN
ejpam-5899	110	10	h	h	NOUN
ejpam-5899	110	11	:	:	PUNCT
ejpam-5899	110	12	hβ	hβ	PROPN
ejpam-5899	110	13	⊆	⊆	NUM
ejpam-5899	110	14	gα	gα	NOUN
ejpam-5899	110	15	for	for	ADP
ejpam-5899	110	16	some	some	PRON
ejpam-5899	110	17	gα	gα	ADP
ejpam-5899	110	18	∈	∈	PROPN
ejpam-5899	110	19	g	g	NOUN
ejpam-5899	110	20	,	,	PUNCT
ejpam-5899	110	21	α	α	PROPN
ejpam-5899	110	22	∈	∈	PROPN
ejpam-5899	110	23	∆	∆	PROPN
ejpam-5899	110	24	and	and	CCONJ
ejpam-5899	110	25	β	β	X
ejpam-5899	110	26	∈	∈	PROPN
ejpam-5899	110	27	λ	λ	PROPN
ejpam-5899	110	28	}	}	PUNCT
ejpam-5899	110	29	is	be	AUX
ejpam-5899	110	30	gµ−lf(s,µ	gµ−lf(s,µ	ADJ
ejpam-5899	110	31	)	)	PUNCT
ejpam-5899	110	32	(	(	PUNCT
ejpam-5899	110	33	s	s	X
ejpam-5899	110	34	,	,	PUNCT
ejpam-5899	110	35	µ)-refinement	µ)-refinement	PUNCT
ejpam-5899	110	36	for	for	ADP
ejpam-5899	110	37	g.	g.	PROPN
ejpam-5899	110	38	(	(	PUNCT
ejpam-5899	110	39	ii	ii	PROPN
ejpam-5899	110	40	)	)	PUNCT
ejpam-5899	110	41	the	the	DET
ejpam-5899	110	42	proof	proof	NOUN
ejpam-5899	110	43	is	be	AUX
ejpam-5899	110	44	obvious	obvious	ADJ
ejpam-5899	110	45	since	since	SCONJ
ejpam-5899	110	46	every	every	DET
ejpam-5899	110	47	µ-closed	µ-close	VERB
ejpam-5899	110	48	set	set	NOUN
ejpam-5899	110	49	is	be	AUX
ejpam-5899	110	50	µg	µg	ADV
ejpam-5899	110	51	-	-	PUNCT
ejpam-5899	110	52	closed	closed	ADJ
ejpam-5899	110	53	.	.	PUNCT
ejpam-5899	111	1	corollary	corollary	ADJ
ejpam-5899	111	2	1	1	NUM
ejpam-5899	111	3	.	.	PUNCT
ejpam-5899	112	1	let	let	AUX
ejpam-5899	112	2	(	(	PUNCT
ejpam-5899	112	3	s	s	X
ejpam-5899	112	4	,	,	PUNCT
ejpam-5899	112	5	µ	µ	NOUN
ejpam-5899	112	6	)	)	PUNCT
ejpam-5899	112	7	be	be	AUX
ejpam-5899	112	8	a	a	DET
ejpam-5899	112	9	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	112	10	gts	gts	NOUN
ejpam-5899	112	11	and	and	CCONJ
ejpam-5899	112	12	e	e	NOUN
ejpam-5899	112	13	⊆	⊆	NUM
ejpam-5899	112	14	s.	s.	PROPN
ejpam-5899	112	15	then	then	ADV
ejpam-5899	112	16	e	e	PROPN
ejpam-5899	112	17	is	be	AUX
ejpam-5899	112	18	β	β	NOUN
ejpam-5899	112	19	-	-	NOUN
ejpam-5899	112	20	gµparacompact	gµparacompact	NOUN
ejpam-5899	112	21	if	if	SCONJ
ejpam-5899	112	22	one	one	NUM
ejpam-5899	112	23	of	of	ADP
ejpam-5899	112	24	the	the	DET
ejpam-5899	112	25	following	follow	VERB
ejpam-5899	112	26	holds	hold	VERB
ejpam-5899	112	27	:	:	PUNCT
ejpam-5899	112	28	(	(	PUNCT
ejpam-5899	112	29	i	i	NOUN
ejpam-5899	112	30	)	)	PUNCT
ejpam-5899	112	31	e	e	NOUN
ejpam-5899	112	32	is	be	AUX
ejpam-5899	112	33	µg	µg	ADV
ejpam-5899	112	34	-	-	PUNCT
ejpam-5899	112	35	closed	closed	ADJ
ejpam-5899	112	36	in	in	ADP
ejpam-5899	112	37	(	(	PUNCT
ejpam-5899	112	38	s	s	PROPN
ejpam-5899	112	39	,	,	PUNCT
ejpam-5899	112	40	µ	µ	NOUN
ejpam-5899	112	41	)	)	PUNCT
ejpam-5899	112	42	.	.	PUNCT
ejpam-5899	113	1	(	(	PUNCT
ejpam-5899	113	2	ii	ii	NOUN
ejpam-5899	113	3	)	)	PUNCT
ejpam-5899	113	4	e	e	NOUN
ejpam-5899	113	5	is	be	AUX
ejpam-5899	113	6	µ-closed	µ-close	VERB
ejpam-5899	113	7	in	in	ADP
ejpam-5899	113	8	(	(	PUNCT
ejpam-5899	113	9	s	s	PROPN
ejpam-5899	113	10	,	,	PUNCT
ejpam-5899	113	11	µ	µ	NOUN
ejpam-5899	113	12	)	)	PUNCT
ejpam-5899	113	13	.	.	PUNCT
ejpam-5899	114	1	proof	proof	NOUN
ejpam-5899	114	2	.	.	PUNCT
ejpam-5899	115	1	it	it	PRON
ejpam-5899	115	2	follows	follow	VERB
ejpam-5899	115	3	from	from	ADP
ejpam-5899	115	4	proposition	proposition	NOUN
ejpam-5899	115	5	3	3	NUM
ejpam-5899	115	6	and	and	CCONJ
ejpam-5899	115	7	theorem	theorem	VERB
ejpam-5899	115	8	2	2	NUM
ejpam-5899	115	9	.	.	PUNCT
ejpam-5899	116	1	h.	h.	PROPN
ejpam-5899	116	2	h.	h.	PROPN
ejpam-5899	116	3	al	al	PROPN
ejpam-5899	116	4	-	-	PUNCT
ejpam-5899	116	5	jarrah	jarrah	PROPN
ejpam-5899	116	6	et	et	PROPN
ejpam-5899	116	7	al	al	PROPN
ejpam-5899	116	8	.	.	PUNCT
ejpam-5899	116	9	/	/	SYM
ejpam-5899	116	10	eur	eur	PROPN
ejpam-5899	116	11	.	.	PUNCT
ejpam-5899	117	1	j.	j.	PROPN
ejpam-5899	117	2	pure	pure	PROPN
ejpam-5899	117	3	appl	appl	PROPN
ejpam-5899	117	4	.	.	PROPN
ejpam-5899	117	5	math	math	PROPN
ejpam-5899	117	6	,	,	PUNCT
ejpam-5899	117	7	18	18	NUM
ejpam-5899	117	8	(	(	PUNCT
ejpam-5899	117	9	2	2	NUM
ejpam-5899	117	10	)	)	PUNCT
ejpam-5899	117	11	(	(	PUNCT
ejpam-5899	117	12	2025	2025	NUM
ejpam-5899	117	13	)	)	PUNCT
ejpam-5899	117	14	,	,	PUNCT
ejpam-5899	117	15	5899	5899	NUM
ejpam-5899	117	16	5	5	NUM
ejpam-5899	117	17	of	of	ADP
ejpam-5899	117	18	11	11	NUM
ejpam-5899	117	19	theorem	theorem	NOUN
ejpam-5899	117	20	3	3	X
ejpam-5899	117	21	.	.	PUNCT
ejpam-5899	118	1	let	let	AUX
ejpam-5899	118	2	(	(	PUNCT
ejpam-5899	118	3	s	s	X
ejpam-5899	118	4	,	,	PUNCT
ejpam-5899	118	5	µ	µ	NOUN
ejpam-5899	118	6	)	)	PUNCT
ejpam-5899	118	7	be	be	AUX
ejpam-5899	118	8	a	a	DET
ejpam-5899	118	9	gts	gts	NOUN
ejpam-5899	118	10	.	.	PUNCT
ejpam-5899	119	1	if	if	SCONJ
ejpam-5899	119	2	each	each	DET
ejpam-5899	119	3	µ-open	µ-open	NOUN
ejpam-5899	119	4	subset	subset	VERB
ejpam-5899	119	5	of	of	ADP
ejpam-5899	119	6	(	(	PUNCT
ejpam-5899	119	7	s	s	PROPN
ejpam-5899	119	8	,	,	PUNCT
ejpam-5899	119	9	µ	µ	NOUN
ejpam-5899	119	10	)	)	PUNCT
ejpam-5899	119	11	is	be	AUX
ejpam-5899	119	12	α	α	NOUN
ejpam-5899	119	13	-	-	NOUN
ejpam-5899	119	14	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	119	15	,	,	PUNCT
ejpam-5899	119	16	then	then	ADV
ejpam-5899	119	17	each	each	DET
ejpam-5899	119	18	subset	subset	NOUN
ejpam-5899	119	19	e	e	NOUN
ejpam-5899	119	20	of	of	ADP
ejpam-5899	119	21	s	s	PROPN
ejpam-5899	119	22	is	be	AUX
ejpam-5899	119	23	β	β	NOUN
ejpam-5899	119	24	-	-	NOUN
ejpam-5899	119	25	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	119	26	.	.	PUNCT
ejpam-5899	120	1	proof	proof	NOUN
ejpam-5899	120	2	.	.	PUNCT
ejpam-5899	121	1	let	let	VERB
ejpam-5899	121	2	ge	ge	PROPN
ejpam-5899	121	3	=	=	PUNCT
ejpam-5899	121	4	{	{	PUNCT
ejpam-5899	121	5	gα	gα	ADP
ejpam-5899	121	6	∩	∩	ADJ
ejpam-5899	121	7	e	e	NOUN
ejpam-5899	121	8	:	:	PUNCT
ejpam-5899	121	9	gα	gα	ADP
ejpam-5899	121	10	∈	∈	PROPN
ejpam-5899	121	11	µ	µ	NUM
ejpam-5899	121	12	,	,	PUNCT
ejpam-5899	121	13	α	α	PROPN
ejpam-5899	121	14	∈	∈	NOUN
ejpam-5899	121	15	∆	∆	PROPN
ejpam-5899	121	16	}	}	PUNCT
ejpam-5899	121	17	be	be	AUX
ejpam-5899	121	18	(	(	PUNCT
ejpam-5899	121	19	e,µe)-cover	e,µe)-cover	X
ejpam-5899	121	20	of	of	ADP
ejpam-5899	121	21	e.	e.	PROPN
ejpam-5899	121	22	then	then	ADV
ejpam-5899	121	23	g	g	PROPN
ejpam-5899	121	24	=	=	PUNCT
ejpam-5899	121	25	{	{	PUNCT
ejpam-5899	121	26	gα	gα	NOUN
ejpam-5899	121	27	:	:	PUNCT
ejpam-5899	121	28	α	α	PROPN
ejpam-5899	121	29	∈	∈	PROPN
ejpam-5899	121	30	∆	∆	X
ejpam-5899	121	31	}	}	PUNCT
ejpam-5899	121	32	is	be	AUX
ejpam-5899	121	33	an	an	DET
ejpam-5899	121	34	(	(	PUNCT
ejpam-5899	121	35	s	s	X
ejpam-5899	121	36	,	,	PUNCT
ejpam-5899	121	37	µ)-cover	µ)-cover	NOUN
ejpam-5899	121	38	of	of	ADP
ejpam-5899	121	39	∪α∈∆gα	∪α∈∆gα	NOUN
ejpam-5899	121	40	and	and	CCONJ
ejpam-5899	121	41	so	so	ADV
ejpam-5899	121	42	g	g	PROPN
ejpam-5899	121	43	has	have	VERB
ejpam-5899	121	44	a	a	DET
ejpam-5899	121	45	gµ−lf(s,µ	gµ−lf(s,µ	ADJ
ejpam-5899	121	46	)	)	PUNCT
ejpam-5899	121	47	(	(	PUNCT
ejpam-5899	121	48	s	s	X
ejpam-5899	121	49	,	,	PUNCT
ejpam-5899	121	50	µ)-refinement	µ)-refinement	PUNCT
ejpam-5899	121	51	,	,	PUNCT
ejpam-5899	121	52	say	say	VERB
ejpam-5899	121	53	h	h	NOUN
ejpam-5899	121	54	=	=	PRON
ejpam-5899	121	55	{	{	PUNCT
ejpam-5899	121	56	hβ	hβ	INTJ
ejpam-5899	121	57	:	:	PUNCT
ejpam-5899	121	58	β	β	X
ejpam-5899	121	59	∈	∈	PROPN
ejpam-5899	121	60	λ	λ	NOUN
ejpam-5899	121	61	}	}	PUNCT
ejpam-5899	121	62	.	.	PUNCT
ejpam-5899	122	1	define	define	VERB
ejpam-5899	122	2	he	he	PRON
ejpam-5899	122	3	=	=	PUNCT
ejpam-5899	122	4	{	{	PUNCT
ejpam-5899	122	5	hβ	hβ	INTJ
ejpam-5899	122	6	∩	∩	ADJ
ejpam-5899	122	7	e	e	NOUN
ejpam-5899	122	8	:	:	PUNCT
ejpam-5899	122	9	β	β	X
ejpam-5899	122	10	∈	∈	PROPN
ejpam-5899	122	11	λ	λ	NOUN
ejpam-5899	122	12	}	}	PUNCT
ejpam-5899	122	13	.	.	PUNCT
ejpam-5899	123	1	then	then	ADV
ejpam-5899	123	2	he	he	PRON
ejpam-5899	123	3	is	be	AUX
ejpam-5899	123	4	gµ−lf(e,µe)(e,µe)refinement	gµ−lf(e,µe)(e,µe)refinement	NOUN
ejpam-5899	123	5	for	for	ADP
ejpam-5899	123	6	ge	ge	PROPN
ejpam-5899	123	7	.	.	PUNCT
ejpam-5899	124	1	note	note	VERB
ejpam-5899	124	2	that	that	SCONJ
ejpam-5899	124	3	if	if	SCONJ
ejpam-5899	124	4	s	s	X
ejpam-5899	124	5	∈	∈	NOUN
ejpam-5899	124	6	e	e	NOUN
ejpam-5899	124	7	there	there	PRON
ejpam-5899	124	8	is	be	VERB
ejpam-5899	124	9	g	g	PROPN
ejpam-5899	124	10	∈	∈	PROPN
ejpam-5899	124	11	µ∗(s	µ∗(s	PROPN
ejpam-5899	124	12	)	)	PUNCT
ejpam-5899	124	13	with	with	ADP
ejpam-5899	124	14	the	the	DET
ejpam-5899	124	15	set	set	NOUN
ejpam-5899	124	16	{	{	PUNCT
ejpam-5899	124	17	η	η	NOUN
ejpam-5899	124	18	:	:	PUNCT
ejpam-5899	124	19	g	g	PROPN
ejpam-5899	124	20	∩hη	∩hη	PROPN
ejpam-5899	124	21	̸=	̸=	PROPN
ejpam-5899	124	22	ϕ	ϕ	PROPN
ejpam-5899	124	23	}	}	PUNCT
ejpam-5899	124	24	is	be	AUX
ejpam-5899	124	25	finite	finite	NOUN
ejpam-5899	124	26	which	which	PRON
ejpam-5899	124	27	implies	imply	VERB
ejpam-5899	124	28	that	that	SCONJ
ejpam-5899	124	29	the	the	DET
ejpam-5899	124	30	set	set	NOUN
ejpam-5899	124	31	{	{	PUNCT
ejpam-5899	124	32	η	η	NOUN
ejpam-5899	124	33	:	:	PUNCT
ejpam-5899	124	34	(	(	PUNCT
ejpam-5899	124	35	g	g	PROPN
ejpam-5899	124	36	∩	∩	ADJ
ejpam-5899	124	37	e	e	NOUN
ejpam-5899	124	38	)	)	PUNCT
ejpam-5899	124	39	∩	∩	NOUN
ejpam-5899	124	40	(	(	PUNCT
ejpam-5899	124	41	hη	hη	PROPN
ejpam-5899	124	42	∩	∩	ADJ
ejpam-5899	124	43	e	e	NOUN
ejpam-5899	124	44	)	)	PUNCT
ejpam-5899	124	45	̸=	̸=	PROPN
ejpam-5899	124	46	ϕ	ϕ	PROPN
ejpam-5899	124	47	}	}	PUNCT
ejpam-5899	124	48	is	be	AUX
ejpam-5899	124	49	finite	finite	ADJ
ejpam-5899	124	50	.	.	PUNCT
ejpam-5899	125	1	finally	finally	ADV
ejpam-5899	125	2	,	,	PUNCT
ejpam-5899	125	3	since	since	SCONJ
ejpam-5899	125	4	for	for	ADP
ejpam-5899	125	5	each	each	PRON
ejpam-5899	125	6	hβ	hβ	INTJ
ejpam-5899	125	7	∩e	∩e	PUNCT
ejpam-5899	126	1	∈	∈	PROPN
ejpam-5899	127	1	he	he	PRON
ejpam-5899	127	2	,	,	PUNCT
ejpam-5899	127	3	there	there	PRON
ejpam-5899	127	4	is	be	VERB
ejpam-5899	127	5	some	some	PRON
ejpam-5899	127	6	gα	gα	ADP
ejpam-5899	127	7	∈	∈	PROPN
ejpam-5899	127	8	g	g	NOUN
ejpam-5899	127	9	with	with	ADP
ejpam-5899	127	10	hβ	hβ	PROPN
ejpam-5899	127	11	⊆	⊆	NUM
ejpam-5899	127	12	gα	gα	NOUN
ejpam-5899	128	1	so	so	ADV
ejpam-5899	128	2	we	we	PRON
ejpam-5899	128	3	obtain	obtain	VERB
ejpam-5899	128	4	hβ	hβ	NOUN
ejpam-5899	128	5	∩e	∩e	NOUN
ejpam-5899	129	1	⊆	⊆	X
ejpam-5899	129	2	gα	gα	ADP
ejpam-5899	129	3	∩e	∩e	PROPN
ejpam-5899	129	4	.	.	PUNCT
ejpam-5899	130	1	therefore	therefore	ADV
ejpam-5899	130	2	,	,	PUNCT
ejpam-5899	130	3	e	e	PROPN
ejpam-5899	130	4	is	be	AUX
ejpam-5899	130	5	β	β	NOUN
ejpam-5899	130	6	-	-	NOUN
ejpam-5899	130	7	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	130	8	.	.	PUNCT
ejpam-5899	131	1	theorem	theorem	VERB
ejpam-5899	131	2	4	4	NUM
ejpam-5899	131	3	.	.	PUNCT
ejpam-5899	132	1	let	let	AUX
ejpam-5899	132	2	(	(	PUNCT
ejpam-5899	132	3	s	s	X
ejpam-5899	132	4	,	,	PUNCT
ejpam-5899	132	5	µ	µ	NOUN
ejpam-5899	132	6	)	)	PUNCT
ejpam-5899	132	7	be	be	AUX
ejpam-5899	132	8	a	a	DET
ejpam-5899	132	9	gts	gts	NOUN
ejpam-5899	132	10	and	and	CCONJ
ejpam-5899	132	11	e	e	NOUN
ejpam-5899	132	12	⊆	⊆	NUM
ejpam-5899	132	13	s.	s.	PROPN
ejpam-5899	132	14	if	if	SCONJ
ejpam-5899	132	15	for	for	SCONJ
ejpam-5899	132	16	each	each	DET
ejpam-5899	132	17	µ-open	µ-open	NOUN
ejpam-5899	132	18	set	set	VERB
ejpam-5899	132	19	g	g	NOUN
ejpam-5899	132	20	containing	contain	VERB
ejpam-5899	132	21	e	e	NOUN
ejpam-5899	132	22	,	,	PUNCT
ejpam-5899	132	23	there	there	PRON
ejpam-5899	132	24	is	be	VERB
ejpam-5899	132	25	β	β	NOUN
ejpam-5899	132	26	-	-	ADJ
ejpam-5899	132	27	gµ-paracompact	gµ-paracompact	ADJ
ejpam-5899	132	28	z	z	NOUN
ejpam-5899	132	29	with	with	ADP
ejpam-5899	132	30	e	e	PROPN
ejpam-5899	132	31	⊆	⊆	X
ejpam-5899	132	32	z	z	NOUN
ejpam-5899	132	33	⊆	⊆	NUM
ejpam-5899	132	34	g	g	NOUN
ejpam-5899	132	35	,	,	PUNCT
ejpam-5899	132	36	then	then	ADV
ejpam-5899	132	37	e	e	PROPN
ejpam-5899	132	38	is	be	AUX
ejpam-5899	132	39	β	β	NOUN
ejpam-5899	132	40	-	-	NOUN
ejpam-5899	132	41	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	132	42	.	.	PUNCT
ejpam-5899	133	1	proof	proof	NOUN
ejpam-5899	133	2	.	.	PUNCT
ejpam-5899	134	1	let	let	VERB
ejpam-5899	134	2	ge	ge	PROPN
ejpam-5899	134	3	=	=	PRON
ejpam-5899	134	4	{	{	PUNCT
ejpam-5899	134	5	e∩hα	e∩hα	PROPN
ejpam-5899	134	6	:	:	PUNCT
ejpam-5899	134	7	hα	hα	ADP
ejpam-5899	134	8	∈	∈	PROPN
ejpam-5899	134	9	µ	µ	NUM
ejpam-5899	134	10	,	,	PUNCT
ejpam-5899	134	11	α	α	PROPN
ejpam-5899	134	12	∈	∈	NOUN
ejpam-5899	134	13	∆	∆	PROPN
ejpam-5899	134	14	}	}	PUNCT
ejpam-5899	134	15	be	be	AUX
ejpam-5899	134	16	an	an	DET
ejpam-5899	134	17	(	(	PUNCT
ejpam-5899	134	18	e,µe)-cover	e,µe)-cover	X
ejpam-5899	134	19	of	of	ADP
ejpam-5899	134	20	e.	e.	PROPN
ejpam-5899	134	21	then	then	ADV
ejpam-5899	134	22	there	there	PRON
ejpam-5899	134	23	is	be	VERB
ejpam-5899	134	24	βgµ-paracompact	βgµ-paracompact	ADJ
ejpam-5899	134	25	z	z	NOUN
ejpam-5899	134	26	with	with	ADP
ejpam-5899	134	27	e	e	PROPN
ejpam-5899	134	28	⊂	⊂	PROPN
ejpam-5899	134	29	z	z	PROPN
ejpam-5899	134	30	⊂	⊂	PROPN
ejpam-5899	134	31	∪α∈∆hα	∪α∈∆hα	PROPN
ejpam-5899	134	32	.	.	PUNCT
ejpam-5899	135	1	since	since	SCONJ
ejpam-5899	135	2	gz	gz	PROPN
ejpam-5899	135	3	=	=	SYM
ejpam-5899	135	4	{	{	PUNCT
ejpam-5899	135	5	hα∩z	hα∩z	NOUN
ejpam-5899	135	6	:	:	PUNCT
ejpam-5899	135	7	α	α	PROPN
ejpam-5899	135	8	∈	∈	NOUN
ejpam-5899	135	9	∆	∆	X
ejpam-5899	135	10	}	}	PUNCT
ejpam-5899	135	11	is	be	AUX
ejpam-5899	135	12	a	a	DET
ejpam-5899	135	13	(	(	PUNCT
ejpam-5899	135	14	z	z	NOUN
ejpam-5899	135	15	,	,	PUNCT
ejpam-5899	135	16	µz)-cover	µz)-cover	ADV
ejpam-5899	135	17	of	of	ADP
ejpam-5899	135	18	z	z	NOUN
ejpam-5899	135	19	,	,	PUNCT
ejpam-5899	135	20	then	then	ADV
ejpam-5899	135	21	gz	gz	PROPN
ejpam-5899	135	22	has	have	VERB
ejpam-5899	135	23	a	a	DET
ejpam-5899	135	24	gµ−lf(z,µz	gµ−lf(z,µz	PROPN
ejpam-5899	135	25	)	)	PUNCT
ejpam-5899	135	26	(	(	PUNCT
ejpam-5899	135	27	z	z	NOUN
ejpam-5899	135	28	,	,	PUNCT
ejpam-5899	135	29	µz)-refinement	µz)-refinement	ADJ
ejpam-5899	135	30	,	,	PUNCT
ejpam-5899	135	31	say	say	VERB
ejpam-5899	135	32	hz	hz	X
ejpam-5899	135	33	=	=	PUNCT
ejpam-5899	135	34	{	{	PUNCT
ejpam-5899	135	35	hβ	hβ	PROPN
ejpam-5899	135	36	∩z	∩z	VERB
ejpam-5899	135	37	:	:	PUNCT
ejpam-5899	135	38	hβ	hβ	PROPN
ejpam-5899	135	39	∈	∈	PROPN
ejpam-5899	135	40	µ	µ	PROPN
ejpam-5899	135	41	,	,	PUNCT
ejpam-5899	135	42	β	β	X
ejpam-5899	135	43	∈	∈	PROPN
ejpam-5899	135	44	λ	λ	NOUN
ejpam-5899	135	45	}	}	PUNCT
ejpam-5899	135	46	.	.	PUNCT
ejpam-5899	136	1	put	put	VERB
ejpam-5899	136	2	he	he	PRON
ejpam-5899	136	3	=	=	PUNCT
ejpam-5899	136	4	{	{	PUNCT
ejpam-5899	136	5	hβ∩e	hβ∩e	PROPN
ejpam-5899	136	6	:	:	PUNCT
ejpam-5899	136	7	β	β	X
ejpam-5899	136	8	∈	∈	PROPN
ejpam-5899	136	9	λ	λ	NOUN
ejpam-5899	136	10	}	}	PUNCT
ejpam-5899	136	11	.	.	PUNCT
ejpam-5899	137	1	then	then	ADV
ejpam-5899	137	2	he	he	PRON
ejpam-5899	137	3	is	be	AUX
ejpam-5899	137	4	gµ−lf(e,µe)(e,µe)-refinement	gµ−lf(e,µe)(e,µe)-refinement	PROPN
ejpam-5899	137	5	for	for	ADP
ejpam-5899	137	6	ge	ge	PROPN
ejpam-5899	137	7	,	,	PUNCT
ejpam-5899	137	8	since	since	SCONJ
ejpam-5899	137	9	for	for	ADP
ejpam-5899	137	10	s	s	NOUN
ejpam-5899	137	11	∈	∈	PROPN
ejpam-5899	137	12	e	e	NOUN
ejpam-5899	137	13	there	there	ADV
ejpam-5899	137	14	ish∩z	ish∩z	PROPN
ejpam-5899	137	15	∈	∈	PROPN
ejpam-5899	137	16	µ∗z(s	µ∗z(s	PROPN
ejpam-5899	137	17	)	)	PUNCT
ejpam-5899	137	18	withh	withh	PROPN
ejpam-5899	137	19	∈	∈	PROPN
ejpam-5899	137	20	µ∗(s	µ∗(s	PROPN
ejpam-5899	137	21	)	)	PUNCT
ejpam-5899	137	22	and	and	CCONJ
ejpam-5899	137	23	the	the	DET
ejpam-5899	137	24	set	set	NOUN
ejpam-5899	137	25	{	{	PUNCT
ejpam-5899	137	26	η	η	NOUN
ejpam-5899	137	27	:(	:(	PROPN
ejpam-5899	137	28	h∩z)∩(hη∩z	h∩z)∩(hη∩z	PROPN
ejpam-5899	137	29	)	)	PUNCT
ejpam-5899	137	30	̸=	̸=	PROPN
ejpam-5899	137	31	ϕ	ϕ	PROPN
ejpam-5899	137	32	}	}	PUNCT
ejpam-5899	137	33	is	be	AUX
ejpam-5899	137	34	finite	finite	NOUN
ejpam-5899	137	35	which	which	PRON
ejpam-5899	137	36	implies	imply	VERB
ejpam-5899	137	37	that	that	SCONJ
ejpam-5899	137	38	the	the	DET
ejpam-5899	137	39	set	set	NOUN
ejpam-5899	137	40	{	{	PUNCT
ejpam-5899	137	41	η	η	X
ejpam-5899	137	42	:	:	PUNCT
ejpam-5899	137	43	[	[	X
ejpam-5899	137	44	(	(	PUNCT
ejpam-5899	137	45	h∩z)∩(hη∩z)]∩e	h∩z)∩(hη∩z)]∩e	PROPN
ejpam-5899	137	46	̸=	̸=	PROPN
ejpam-5899	137	47	ϕ	ϕ	NOUN
ejpam-5899	137	48	}	}	PUNCT
ejpam-5899	137	49	=	=	SYM
ejpam-5899	137	50	{	{	PUNCT
ejpam-5899	137	51	η	η	NOUN
ejpam-5899	137	52	:	:	PUNCT
ejpam-5899	137	53	(	(	PUNCT
ejpam-5899	137	54	h∩e)∩(hη∩e	h∩e)∩(hη∩e	NOUN
ejpam-5899	137	55	)	)	PUNCT
ejpam-5899	137	56	̸=	̸=	PROPN
ejpam-5899	137	57	ϕ	ϕ	PROPN
ejpam-5899	137	58	}	}	PUNCT
ejpam-5899	137	59	is	be	AUX
ejpam-5899	137	60	finite	finite	ADJ
ejpam-5899	137	61	.	.	PUNCT
ejpam-5899	138	1	now	now	ADV
ejpam-5899	138	2	,	,	PUNCT
ejpam-5899	138	3	for	for	ADP
ejpam-5899	138	4	each	each	PRON
ejpam-5899	138	5	hβ	hβ	INTJ
ejpam-5899	138	6	∩e	∩e	PUNCT
ejpam-5899	139	1	∈	∈	PROPN
ejpam-5899	139	2	he	he	PRON
ejpam-5899	139	3	there	there	PRON
ejpam-5899	139	4	is	be	VERB
ejpam-5899	139	5	hα	hα	ADP
ejpam-5899	139	6	∩z	∩z	VERB
ejpam-5899	139	7	∈	∈	PROPN
ejpam-5899	139	8	gz	gz	NOUN
ejpam-5899	139	9	with	with	SCONJ
ejpam-5899	139	10	hβ	hβ	NOUN
ejpam-5899	139	11	∩z	∩z	VERB
ejpam-5899	139	12	⊆	⊆	NUM
ejpam-5899	139	13	hα	hα	ADP
ejpam-5899	139	14	∩z	∩z	VERB
ejpam-5899	139	15	and	and	CCONJ
ejpam-5899	139	16	so	so	ADV
ejpam-5899	139	17	hβ	hβ	ADP
ejpam-5899	139	18	∩	∩	NOUN
ejpam-5899	139	19	e	e	ADJ
ejpam-5899	139	20	⊆	⊆	NUM
ejpam-5899	139	21	hα	hα	ADP
ejpam-5899	139	22	∩	∩	PROPN
ejpam-5899	139	23	e.	e.	PROPN
ejpam-5899	139	24	therefore	therefore	ADV
ejpam-5899	139	25	,	,	PUNCT
ejpam-5899	139	26	e	e	PROPN
ejpam-5899	139	27	is	be	AUX
ejpam-5899	139	28	β	β	NOUN
ejpam-5899	139	29	-	-	NOUN
ejpam-5899	139	30	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	139	31	.	.	PUNCT
ejpam-5899	140	1	theorem	theorem	NOUN
ejpam-5899	140	2	5	5	NUM
ejpam-5899	140	3	.	.	PUNCT
ejpam-5899	141	1	let	let	AUX
ejpam-5899	141	2	(	(	PUNCT
ejpam-5899	141	3	s	s	X
ejpam-5899	141	4	,	,	PUNCT
ejpam-5899	141	5	µ	µ	NOUN
ejpam-5899	141	6	)	)	PUNCT
ejpam-5899	141	7	be	be	AUX
ejpam-5899	141	8	a	a	DET
ejpam-5899	141	9	gts	gts	NOUN
ejpam-5899	141	10	and	and	CCONJ
ejpam-5899	141	11	e	e	NOUN
ejpam-5899	142	1	⊆	⊆	NUM
ejpam-5899	142	2	z	z	PROPN
ejpam-5899	142	3	⊆	⊆	NUM
ejpam-5899	142	4	s.	s.	PROPN
ejpam-5899	142	5	if	if	SCONJ
ejpam-5899	142	6	e	e	PROPN
ejpam-5899	142	7	is	be	AUX
ejpam-5899	142	8	α	α	NOUN
ejpam-5899	142	9	-	-	NOUN
ejpam-5899	142	10	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	142	11	in	in	ADP
ejpam-5899	142	12	(	(	PUNCT
ejpam-5899	142	13	s	s	PROPN
ejpam-5899	142	14	,	,	PUNCT
ejpam-5899	142	15	µ	µ	NOUN
ejpam-5899	142	16	)	)	PUNCT
ejpam-5899	142	17	,	,	PUNCT
ejpam-5899	142	18	then	then	ADV
ejpam-5899	142	19	e	e	PROPN
ejpam-5899	142	20	is	be	AUX
ejpam-5899	142	21	α	α	NOUN
ejpam-5899	142	22	-	-	NOUN
ejpam-5899	142	23	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	142	24	in	in	ADP
ejpam-5899	142	25	(	(	PUNCT
ejpam-5899	142	26	z	z	PROPN
ejpam-5899	142	27	,	,	PUNCT
ejpam-5899	142	28	µz	µz	PROPN
ejpam-5899	142	29	)	)	PUNCT
ejpam-5899	142	30	.	.	PUNCT
ejpam-5899	143	1	proof	proof	NOUN
ejpam-5899	143	2	.	.	PUNCT
ejpam-5899	144	1	let	let	VERB
ejpam-5899	144	2	gz	gz	VERB
ejpam-5899	144	3	=	=	VERB
ejpam-5899	144	4	{	{	PUNCT
ejpam-5899	144	5	z	z	NOUN
ejpam-5899	144	6	∩	∩	NOUN
ejpam-5899	144	7	hα	hα	ADP
ejpam-5899	144	8	:	:	PUNCT
ejpam-5899	144	9	hα	hα	ADP
ejpam-5899	144	10	∈	∈	PROPN
ejpam-5899	144	11	µ	µ	NUM
ejpam-5899	144	12	,	,	PUNCT
ejpam-5899	144	13	α	α	PROPN
ejpam-5899	144	14	∈	∈	NOUN
ejpam-5899	144	15	∆	∆	PROPN
ejpam-5899	144	16	}	}	PUNCT
ejpam-5899	144	17	be	be	AUX
ejpam-5899	144	18	a	a	DET
ejpam-5899	144	19	(	(	PUNCT
ejpam-5899	144	20	z	z	NOUN
ejpam-5899	144	21	,	,	PUNCT
ejpam-5899	144	22	µz)-cover	µz)-cover	ADV
ejpam-5899	144	23	of	of	ADP
ejpam-5899	144	24	e.	e.	PROPN
ejpam-5899	144	25	then	then	ADV
ejpam-5899	144	26	g1	g1	PROPN
ejpam-5899	144	27	=	=	PRON
ejpam-5899	144	28	{	{	PUNCT
ejpam-5899	144	29	hα	hα	X
ejpam-5899	144	30	:	:	PUNCT
ejpam-5899	144	31	α	α	PROPN
ejpam-5899	144	32	∈	∈	PROPN
ejpam-5899	144	33	∆	∆	X
ejpam-5899	144	34	}	}	PUNCT
ejpam-5899	144	35	is	be	AUX
ejpam-5899	144	36	an	an	DET
ejpam-5899	144	37	(	(	PUNCT
ejpam-5899	144	38	s	s	X
ejpam-5899	144	39	,	,	PUNCT
ejpam-5899	144	40	µ)-cover	µ)-cover	NOUN
ejpam-5899	144	41	of	of	ADP
ejpam-5899	144	42	e	e	NOUN
ejpam-5899	145	1	and	and	CCONJ
ejpam-5899	145	2	so	so	ADV
ejpam-5899	145	3	it	it	PRON
ejpam-5899	145	4	has	have	VERB
ejpam-5899	145	5	a	a	DET
ejpam-5899	145	6	gµ−lf(s,µ	gµ−lf(s,µ	ADJ
ejpam-5899	145	7	)	)	PUNCT
ejpam-5899	145	8	(	(	PUNCT
ejpam-5899	145	9	s	s	X
ejpam-5899	145	10	,	,	PUNCT
ejpam-5899	145	11	µ)-refinement	µ)-refinement	PUNCT
ejpam-5899	145	12	,	,	PUNCT
ejpam-5899	145	13	say	say	VERB
ejpam-5899	145	14	h	h	NOUN
ejpam-5899	145	15	=	=	PRON
ejpam-5899	145	16	{	{	PUNCT
ejpam-5899	145	17	hβ	hβ	INTJ
ejpam-5899	145	18	:	:	PUNCT
ejpam-5899	145	19	β	β	X
ejpam-5899	145	20	∈	∈	PROPN
ejpam-5899	145	21	λ	λ	NOUN
ejpam-5899	145	22	}	}	PUNCT
ejpam-5899	145	23	.	.	PUNCT
ejpam-5899	146	1	put	put	VERB
ejpam-5899	146	2	h1	h1	NOUN
ejpam-5899	146	3	=	=	PUNCT
ejpam-5899	146	4	{	{	PUNCT
ejpam-5899	146	5	hβ	hβ	PROPN
ejpam-5899	146	6	∩	∩	ADJ
ejpam-5899	146	7	z	z	NOUN
ejpam-5899	146	8	:	:	PUNCT
ejpam-5899	146	9	β	β	X
ejpam-5899	146	10	∈	∈	PROPN
ejpam-5899	146	11	λ	λ	NOUN
ejpam-5899	146	12	}	}	PUNCT
ejpam-5899	146	13	.	.	PUNCT
ejpam-5899	147	1	as	as	ADP
ejpam-5899	147	2	in	in	ADP
ejpam-5899	147	3	the	the	DET
ejpam-5899	147	4	proof	proof	NOUN
ejpam-5899	147	5	of	of	ADP
ejpam-5899	147	6	theorem	theorem	NOUN
ejpam-5899	147	7	3	3	NUM
ejpam-5899	147	8	,	,	PUNCT
ejpam-5899	147	9	we	we	PRON
ejpam-5899	147	10	can	can	AUX
ejpam-5899	147	11	show	show	VERB
ejpam-5899	147	12	h1	h1	PROPN
ejpam-5899	147	13	is	be	AUX
ejpam-5899	147	14	a	a	DET
ejpam-5899	147	15	gµ−lf(z,µz)(z	gµ−lf(z,µz)(z	NOUN
ejpam-5899	147	16	,	,	PUNCT
ejpam-5899	147	17	µz)-refinement	µz)-refinement	NOUN
ejpam-5899	147	18	of	of	ADP
ejpam-5899	147	19	gz	gz	PROPN
ejpam-5899	147	20	.	.	PUNCT
ejpam-5899	148	1	therefore	therefore	ADV
ejpam-5899	148	2	,	,	PUNCT
ejpam-5899	148	3	e	e	PROPN
ejpam-5899	148	4	is	be	AUX
ejpam-5899	148	5	α	α	NOUN
ejpam-5899	148	6	-	-	NOUN
ejpam-5899	148	7	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	148	8	in	in	ADP
ejpam-5899	148	9	(	(	PUNCT
ejpam-5899	148	10	z	z	PROPN
ejpam-5899	148	11	,	,	PUNCT
ejpam-5899	148	12	µz	µz	PROPN
ejpam-5899	148	13	)	)	PUNCT
ejpam-5899	148	14	.	.	PUNCT
ejpam-5899	149	1	example	example	NOUN
ejpam-5899	150	1	2	2	NUM
ejpam-5899	150	2	.	.	X
ejpam-5899	150	3	let	let	AUX
ejpam-5899	150	4	(	(	PUNCT
ejpam-5899	150	5	s	s	X
ejpam-5899	150	6	,	,	PUNCT
ejpam-5899	150	7	µ	µ	NOUN
ejpam-5899	150	8	)	)	PUNCT
ejpam-5899	150	9	be	be	AUX
ejpam-5899	150	10	a	a	DET
ejpam-5899	150	11	gts	gts	NOUN
ejpam-5899	150	12	where	where	SCONJ
ejpam-5899	150	13	s	s	VERB
ejpam-5899	150	14	=	=	SYM
ejpam-5899	150	15	r	r	NOUN
ejpam-5899	150	16	and	and	CCONJ
ejpam-5899	150	17	µ	µ	X
ejpam-5899	150	18	=	=	PUNCT
ejpam-5899	150	19	{	{	PUNCT
ejpam-5899	150	20	g	g	NOUN
ejpam-5899	150	21	:	:	PUNCT
ejpam-5899	150	22	q	q	NOUN
ejpam-5899	150	23	⊆	⊆	NUM
ejpam-5899	150	24	g	g	NOUN
ejpam-5899	150	25	}	}	PUNCT
ejpam-5899	150	26	∪	∪	ADJ
ejpam-5899	150	27	{	{	PUNCT
ejpam-5899	150	28	ϕ	ϕ	NOUN
ejpam-5899	150	29	}	}	PUNCT
ejpam-5899	150	30	.	.	PUNCT
ejpam-5899	151	1	put	put	VERB
ejpam-5899	151	2	e	e	NOUN
ejpam-5899	151	3	=	=	NOUN
ejpam-5899	151	4	z	z	NOUN
ejpam-5899	151	5	=	=	PUNCT
ejpam-5899	151	6	r−q	r−q	NOUN
ejpam-5899	151	7	.	.	PUNCT
ejpam-5899	152	1	then	then	ADV
ejpam-5899	152	2	µz	µz	PROPN
ejpam-5899	152	3	=	=	SYM
ejpam-5899	152	4	p(z	p(z	PROPN
ejpam-5899	152	5	)	)	PUNCT
ejpam-5899	152	6	and	and	CCONJ
ejpam-5899	152	7	z	z	NOUN
ejpam-5899	152	8	is	be	AUX
ejpam-5899	152	9	µ-closed	µ-close	VERB
ejpam-5899	152	10	in	in	ADP
ejpam-5899	152	11	(	(	PUNCT
ejpam-5899	152	12	s	s	PROPN
ejpam-5899	152	13	,	,	PUNCT
ejpam-5899	152	14	µ	µ	NOUN
ejpam-5899	152	15	)	)	PUNCT
ejpam-5899	152	16	.	.	PUNCT
ejpam-5899	153	1	note	note	VERB
ejpam-5899	153	2	that	that	SCONJ
ejpam-5899	153	3	,	,	PUNCT
ejpam-5899	153	4	e	e	PROPN
ejpam-5899	153	5	is	be	AUX
ejpam-5899	153	6	α	α	NOUN
ejpam-5899	153	7	-	-	NOUN
ejpam-5899	153	8	gµparacompact	gµparacompact	NOUN
ejpam-5899	153	9	in	in	ADP
ejpam-5899	153	10	(	(	PUNCT
ejpam-5899	153	11	z	z	PROPN
ejpam-5899	153	12	,	,	PUNCT
ejpam-5899	153	13	µz	µz	PROPN
ejpam-5899	153	14	)	)	PUNCT
ejpam-5899	153	15	.	.	PUNCT
ejpam-5899	154	1	on	on	ADP
ejpam-5899	154	2	the	the	DET
ejpam-5899	154	3	other	other	ADJ
ejpam-5899	154	4	hand	hand	NOUN
ejpam-5899	154	5	,	,	PUNCT
ejpam-5899	154	6	e	e	NOUN
ejpam-5899	154	7	is	be	AUX
ejpam-5899	154	8	not	not	PART
ejpam-5899	154	9	α	α	NOUN
ejpam-5899	154	10	-	-	NOUN
ejpam-5899	154	11	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	154	12	in	in	ADP
ejpam-5899	154	13	(	(	PUNCT
ejpam-5899	154	14	s	s	PROPN
ejpam-5899	154	15	,	,	PUNCT
ejpam-5899	154	16	µ	µ	NOUN
ejpam-5899	154	17	)	)	PUNCT
ejpam-5899	154	18	since	since	SCONJ
ejpam-5899	154	19	{	{	PUNCT
ejpam-5899	154	20	q	q	NOUN
ejpam-5899	154	21	∪	∪	X
ejpam-5899	154	22	{	{	PUNCT
ejpam-5899	154	23	x	x	NOUN
ejpam-5899	154	24	}	}	PUNCT
ejpam-5899	154	25	:	:	PUNCT
ejpam-5899	154	26	x	x	X
ejpam-5899	154	27	∈	∈	PROPN
ejpam-5899	154	28	e	e	X
ejpam-5899	154	29	}	}	PUNCT
ejpam-5899	154	30	is	be	AUX
ejpam-5899	154	31	(	(	PUNCT
ejpam-5899	154	32	s	s	X
ejpam-5899	154	33	,	,	PUNCT
ejpam-5899	154	34	µ)-cover	µ)-cover	NOUN
ejpam-5899	154	35	of	of	ADP
ejpam-5899	154	36	e	e	NOUN
ejpam-5899	154	37	has	have	VERB
ejpam-5899	154	38	no	no	DET
ejpam-5899	154	39	gµ−lf(s,µ	gµ−lf(s,µ	ADJ
ejpam-5899	154	40	)	)	PUNCT
ejpam-5899	154	41	(	(	PUNCT
ejpam-5899	154	42	s	s	X
ejpam-5899	154	43	,	,	PUNCT
ejpam-5899	154	44	µ)-refinement	µ)-refinement	PUNCT
ejpam-5899	154	45	.	.	PUNCT
ejpam-5899	155	1	theorem	theorem	VERB
ejpam-5899	155	2	6	6	NUM
ejpam-5899	155	3	.	.	PUNCT
ejpam-5899	156	1	let	let	AUX
ejpam-5899	156	2	(	(	PUNCT
ejpam-5899	156	3	s	s	X
ejpam-5899	156	4	,	,	PUNCT
ejpam-5899	156	5	µ	µ	NOUN
ejpam-5899	156	6	)	)	PUNCT
ejpam-5899	156	7	be	be	AUX
ejpam-5899	156	8	a	a	DET
ejpam-5899	156	9	gts	gts	NOUN
ejpam-5899	156	10	and	and	CCONJ
ejpam-5899	156	11	e	e	NOUN
ejpam-5899	156	12	⊆	⊆	NUM
ejpam-5899	156	13	s	s	NOUN
ejpam-5899	156	14	with	with	ADP
ejpam-5899	156	15	e	e	PROPN
ejpam-5899	156	16	is	be	AUX
ejpam-5899	156	17	α	α	NOUN
ejpam-5899	156	18	-	-	NOUN
ejpam-5899	156	19	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	156	20	in	in	ADP
ejpam-5899	156	21	a	a	DET
ejpam-5899	156	22	µ-closed	µ-close	VERB
ejpam-5899	156	23	subspace	subspace	NOUN
ejpam-5899	156	24	(	(	PUNCT
ejpam-5899	156	25	z	z	NOUN
ejpam-5899	156	26	,	,	PUNCT
ejpam-5899	156	27	µz	µz	PROPN
ejpam-5899	156	28	)	)	PUNCT
ejpam-5899	156	29	.	.	PUNCT
ejpam-5899	157	1	if	if	SCONJ
ejpam-5899	157	2	there	there	PRON
ejpam-5899	157	3	is	be	VERB
ejpam-5899	157	4	a	a	DET
ejpam-5899	157	5	µ∗-open	µ∗-open	PROPN
ejpam-5899	157	6	set	set	VERB
ejpam-5899	157	7	g	g	NOUN
ejpam-5899	157	8	with	with	ADP
ejpam-5899	157	9	e	e	PROPN
ejpam-5899	157	10	⊆	⊆	NUM
ejpam-5899	157	11	g	g	PROPN
ejpam-5899	157	12	⊆	⊆	NUM
ejpam-5899	157	13	z	z	PROPN
ejpam-5899	157	14	,	,	PUNCT
ejpam-5899	157	15	then	then	ADV
ejpam-5899	157	16	each	each	PRON
ejpam-5899	157	17	(	(	PUNCT
ejpam-5899	157	18	s	s	X
ejpam-5899	157	19	,	,	PUNCT
ejpam-5899	157	20	µ)-cover	µ)-cover	NOUN
ejpam-5899	157	21	of	of	ADP
ejpam-5899	157	22	e	e	NOUN
ejpam-5899	157	23	has	have	VERB
ejpam-5899	157	24	a	a	DET
ejpam-5899	157	25	gµ−lf(s,µ	gµ−lf(s,µ	ADJ
ejpam-5899	157	26	)	)	PUNCT
ejpam-5899	157	27	(	(	PUNCT
ejpam-5899	157	28	s	s	X
ejpam-5899	157	29	,	,	PUNCT
ejpam-5899	157	30	µ	µ	X
ejpam-5899	157	31	∗)-refinement	∗)-refinement	NOUN
ejpam-5899	157	32	.	.	PUNCT
ejpam-5899	158	1	proof	proof	NOUN
ejpam-5899	158	2	.	.	PUNCT
ejpam-5899	159	1	let	let	VERB
ejpam-5899	159	2	g	g	NOUN
ejpam-5899	159	3	=	=	PUNCT
ejpam-5899	159	4	{	{	PUNCT
ejpam-5899	159	5	gα	gα	NOUN
ejpam-5899	159	6	:	:	PUNCT
ejpam-5899	159	7	α	α	PROPN
ejpam-5899	159	8	∈	∈	PROPN
ejpam-5899	159	9	∆	∆	PROPN
ejpam-5899	159	10	}	}	PUNCT
ejpam-5899	159	11	be	be	AUX
ejpam-5899	159	12	an	an	DET
ejpam-5899	159	13	(	(	PUNCT
ejpam-5899	159	14	s	s	X
ejpam-5899	159	15	,	,	PUNCT
ejpam-5899	159	16	µ)-cover	µ)-cover	PUNCT
ejpam-5899	159	17	of	of	ADP
ejpam-5899	159	18	e.	e.	PROPN
ejpam-5899	159	19	then	then	ADV
ejpam-5899	159	20	,	,	PUNCT
ejpam-5899	159	21	the	the	DET
ejpam-5899	159	22	collection	collection	NOUN
ejpam-5899	159	23	{	{	PUNCT
ejpam-5899	159	24	z	z	NOUN
ejpam-5899	159	25	∩gα	∩gα	NOUN
ejpam-5899	159	26	:	:	PUNCT
ejpam-5899	160	1	α	α	PROPN
ejpam-5899	160	2	∈	∈	PROPN
ejpam-5899	160	3	∆	∆	X
ejpam-5899	160	4	}	}	PUNCT
ejpam-5899	160	5	is	be	AUX
ejpam-5899	160	6	a	a	DET
ejpam-5899	160	7	(	(	PUNCT
ejpam-5899	160	8	z	z	NOUN
ejpam-5899	160	9	,	,	PUNCT
ejpam-5899	160	10	µz)-cover	µz)-cover	ADV
ejpam-5899	160	11	of	of	ADP
ejpam-5899	160	12	e	e	NOUN
ejpam-5899	160	13	and	and	CCONJ
ejpam-5899	160	14	so	so	ADV
ejpam-5899	160	15	it	it	PRON
ejpam-5899	160	16	has	have	VERB
ejpam-5899	160	17	a	a	DET
ejpam-5899	160	18	gµ	gµ	NOUN
ejpam-5899	160	19	−	−	PROPN
ejpam-5899	160	20	lf(z,µz	lf(z,µz	NUM
ejpam-5899	160	21	)	)	PUNCT
ejpam-5899	160	22	(	(	PUNCT
ejpam-5899	160	23	z	z	NOUN
ejpam-5899	160	24	,	,	PUNCT
ejpam-5899	160	25	µz)-refinement	µz)-refinement	ADJ
ejpam-5899	160	26	,	,	PUNCT
ejpam-5899	160	27	say	say	VERB
ejpam-5899	160	28	h.	h.	PROPN
ejpam-5899	160	29	now	now	ADV
ejpam-5899	160	30	,	,	PUNCT
ejpam-5899	160	31	for	for	ADP
ejpam-5899	160	32	each	each	DET
ejpam-5899	160	33	s	s	X
ejpam-5899	160	34	∈	∈	NOUN
ejpam-5899	160	35	e	e	NOUN
ejpam-5899	160	36	there	there	PRON
ejpam-5899	160	37	is	be	VERB
ejpam-5899	160	38	hs	hs	PROPN
ejpam-5899	160	39	∈	∈	PROPN
ejpam-5899	160	40	h	h	NOUN
ejpam-5899	160	41	and	and	CCONJ
ejpam-5899	160	42	ws	ws	PROPN
ejpam-5899	160	43	∈	∈	PROPN
ejpam-5899	160	44	µ∗(s	µ∗(s	PROPN
ejpam-5899	160	45	)	)	PUNCT
ejpam-5899	160	46	with	with	ADP
ejpam-5899	160	47	s	s	PROPN
ejpam-5899	160	48	∈	∈	PROPN
ejpam-5899	160	49	hs	hs	PROPN
ejpam-5899	160	50	=	=	PROPN
ejpam-5899	160	51	ws	ws	PROPN
ejpam-5899	160	52	∩	∩	PROPN
ejpam-5899	160	53	z.	z.	PROPN
ejpam-5899	160	54	since	since	SCONJ
ejpam-5899	160	55	g	g	PROPN
ejpam-5899	160	56	is	be	AUX
ejpam-5899	160	57	µ∗-open	µ∗-open	ADJ
ejpam-5899	160	58	,	,	PUNCT
ejpam-5899	160	59	then	then	ADV
ejpam-5899	160	60	we	we	PRON
ejpam-5899	160	61	=	=	PUNCT
ejpam-5899	160	62	{	{	PUNCT
ejpam-5899	160	63	ws	ws	NOUN
ejpam-5899	160	64	∩	∩	PROPN
ejpam-5899	160	65	g	g	PROPN
ejpam-5899	160	66	:	:	PUNCT
ejpam-5899	160	67	s	s	AUX
ejpam-5899	160	68	∈	∈	PROPN
ejpam-5899	160	69	e	e	NOUN
ejpam-5899	160	70	}	}	PUNCT
ejpam-5899	160	71	is	be	AUX
ejpam-5899	160	72	a	a	DET
ejpam-5899	160	73	gµ-lf(s,µ	gµ-lf(s,µ	PROPN
ejpam-5899	160	74	)	)	PUNCT
ejpam-5899	160	75	(	(	PUNCT
ejpam-5899	160	76	s	s	NOUN
ejpam-5899	160	77	,	,	PUNCT
ejpam-5899	160	78	µ∗)-refinement	µ∗)-refinement	NOUN
ejpam-5899	160	79	of	of	ADP
ejpam-5899	160	80	g.	g.	PROPN
ejpam-5899	160	81	at	at	ADP
ejpam-5899	160	82	h.	h.	PROPN
ejpam-5899	160	83	h.	h.	PROPN
ejpam-5899	160	84	al	al	PROPN
ejpam-5899	160	85	-	-	PUNCT
ejpam-5899	160	86	jarrah	jarrah	PROPN
ejpam-5899	160	87	et	et	PROPN
ejpam-5899	160	88	al	al	PROPN
ejpam-5899	160	89	.	.	PUNCT
ejpam-5899	160	90	/	/	SYM
ejpam-5899	160	91	eur	eur	PROPN
ejpam-5899	160	92	.	.	PUNCT
ejpam-5899	161	1	j.	j.	PROPN
ejpam-5899	161	2	pure	pure	PROPN
ejpam-5899	161	3	appl	appl	PROPN
ejpam-5899	161	4	.	.	PROPN
ejpam-5899	161	5	math	math	PROPN
ejpam-5899	161	6	,	,	PUNCT
ejpam-5899	161	7	18	18	NUM
ejpam-5899	161	8	(	(	PUNCT
ejpam-5899	161	9	2	2	NUM
ejpam-5899	161	10	)	)	PUNCT
ejpam-5899	161	11	(	(	PUNCT
ejpam-5899	161	12	2025	2025	NUM
ejpam-5899	161	13	)	)	PUNCT
ejpam-5899	161	14	,	,	PUNCT
ejpam-5899	161	15	5899	5899	NUM
ejpam-5899	161	16	6	6	NUM
ejpam-5899	161	17	of	of	ADP
ejpam-5899	161	18	11	11	NUM
ejpam-5899	161	19	first	first	ADV
ejpam-5899	161	20	,	,	PUNCT
ejpam-5899	161	21	since	since	SCONJ
ejpam-5899	161	22	z	z	NOUN
ejpam-5899	161	23	is	be	AUX
ejpam-5899	161	24	µ-closed	µ-close	VERB
ejpam-5899	161	25	and	and	CCONJ
ejpam-5899	161	26	for	for	ADP
ejpam-5899	161	27	all	all	DET
ejpam-5899	161	28	s	s	PART
ejpam-5899	161	29	∈	∈	PROPN
ejpam-5899	161	30	e	e	NOUN
ejpam-5899	161	31	,	,	PUNCT
ejpam-5899	161	32	ws	ws	PROPN
ejpam-5899	161	33	∩	∩	NOUN
ejpam-5899	161	34	g	g	PROPN
ejpam-5899	161	35	⊆	⊆	NUM
ejpam-5899	161	36	ws	ws	NOUN
ejpam-5899	161	37	∩	∩	NOUN
ejpam-5899	161	38	z	z	PROPN
ejpam-5899	161	39	=	=	SYM
ejpam-5899	161	40	hs	hs	PROPN
ejpam-5899	161	41	and	and	CCONJ
ejpam-5899	161	42	the	the	DET
ejpam-5899	161	43	collection	collection	NOUN
ejpam-5899	161	44	{	{	PUNCT
ejpam-5899	161	45	ws∩z	ws∩z	NOUN
ejpam-5899	161	46	:	:	PUNCT
ejpam-5899	161	47	s	s	X
ejpam-5899	161	48	∈	∈	PROPN
ejpam-5899	161	49	e	e	NOUN
ejpam-5899	161	50	}	}	PUNCT
ejpam-5899	161	51	is	be	AUX
ejpam-5899	161	52	gµ−lf(z,µz	gµ−lf(z,µz	PROPN
ejpam-5899	161	53	)	)	PUNCT
ejpam-5899	161	54	and	and	CCONJ
ejpam-5899	161	55	so	so	ADV
ejpam-5899	161	56	,	,	PUNCT
ejpam-5899	161	57	by	by	ADP
ejpam-5899	161	58	proposition	proposition	NOUN
ejpam-5899	161	59	2	2	NUM
ejpam-5899	161	60	,	,	PUNCT
ejpam-5899	161	61	we	we	PRON
ejpam-5899	161	62	is	be	AUX
ejpam-5899	161	63	gµ−lf(s,µ	gµ−lf(s,µ	ADJ
ejpam-5899	161	64	)	)	PUNCT
ejpam-5899	161	65	.	.	PUNCT
ejpam-5899	162	1	moreover	moreover	ADV
ejpam-5899	162	2	,	,	PUNCT
ejpam-5899	162	3	for	for	ADP
ejpam-5899	162	4	each	each	DET
ejpam-5899	162	5	s	s	X
ejpam-5899	162	6	∈	∈	ADJ
ejpam-5899	162	7	e	e	NOUN
ejpam-5899	162	8	,	,	PUNCT
ejpam-5899	162	9	there	there	PRON
ejpam-5899	162	10	is	be	VERB
ejpam-5899	162	11	gα(s	gα(	NOUN
ejpam-5899	162	12	)	)	PUNCT
ejpam-5899	163	1	∈	∈	PROPN
ejpam-5899	163	2	g	g	NOUN
ejpam-5899	163	3	with	with	ADP
ejpam-5899	163	4	s	s	PROPN
ejpam-5899	163	5	∈	∈	PROPN
ejpam-5899	163	6	ws	ws	NOUN
ejpam-5899	163	7	∩	∩	NOUN
ejpam-5899	163	8	g	g	PROPN
ejpam-5899	163	9	⊆	⊆	NUM
ejpam-5899	163	10	ws	ws	NOUN
ejpam-5899	163	11	∩	∩	NOUN
ejpam-5899	163	12	z	z	PROPN
ejpam-5899	163	13	⊆	⊆	NUM
ejpam-5899	163	14	gα(s	gα(s	NUM
ejpam-5899	163	15	)	)	PUNCT
ejpam-5899	163	16	∩	∩	PROPN
ejpam-5899	163	17	z	z	NOUN
ejpam-5899	163	18	⊆	⊆	NUM
ejpam-5899	163	19	gα(s	gα(s	NUM
ejpam-5899	163	20	)	)	PUNCT
ejpam-5899	163	21	and	and	CCONJ
ejpam-5899	163	22	hence	hence	ADV
ejpam-5899	163	23	we	we	PRON
ejpam-5899	163	24	is	be	AUX
ejpam-5899	163	25	(	(	PUNCT
ejpam-5899	163	26	s	s	X
ejpam-5899	163	27	,	,	PUNCT
ejpam-5899	163	28	µ∗)-refinement	µ∗)-refinement	NOUN
ejpam-5899	163	29	of	of	ADP
ejpam-5899	163	30	g.	g.	PROPN
ejpam-5899	163	31	proposition	proposition	PROPN
ejpam-5899	163	32	4	4	NUM
ejpam-5899	163	33	.	.	PUNCT
ejpam-5899	164	1	let	let	AUX
ejpam-5899	164	2	(	(	PUNCT
ejpam-5899	164	3	s	s	X
ejpam-5899	164	4	,	,	PUNCT
ejpam-5899	164	5	µ	µ	NOUN
ejpam-5899	164	6	)	)	PUNCT
ejpam-5899	164	7	be	be	AUX
ejpam-5899	164	8	a	a	DET
ejpam-5899	164	9	gts	gts	NOUN
ejpam-5899	164	10	and	and	CCONJ
ejpam-5899	164	11	e	e	NOUN
ejpam-5899	165	1	⊆	⊆	PROPN
ejpam-5899	165	2	z	z	PROPN
ejpam-5899	165	3	⊆	⊆	NUM
ejpam-5899	165	4	s.	s.	PROPN
ejpam-5899	165	5	then	then	ADV
ejpam-5899	165	6	e	e	PROPN
ejpam-5899	165	7	is	be	AUX
ejpam-5899	165	8	β	β	NOUN
ejpam-5899	165	9	-	-	NOUN
ejpam-5899	165	10	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	165	11	in	in	ADP
ejpam-5899	165	12	(	(	PUNCT
ejpam-5899	165	13	s	s	PROPN
ejpam-5899	165	14	,	,	PUNCT
ejpam-5899	165	15	µ	µ	NOUN
ejpam-5899	165	16	)	)	PUNCT
ejpam-5899	165	17	iff	iff	PROPN
ejpam-5899	165	18	e	e	PROPN
ejpam-5899	165	19	is	be	AUX
ejpam-5899	165	20	β	β	NOUN
ejpam-5899	165	21	-	-	NOUN
ejpam-5899	165	22	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	165	23	in	in	ADP
ejpam-5899	165	24	(	(	PUNCT
ejpam-5899	165	25	z	z	PROPN
ejpam-5899	165	26	,	,	PUNCT
ejpam-5899	165	27	µz	µz	PROPN
ejpam-5899	165	28	)	)	PUNCT
ejpam-5899	165	29	.	.	PUNCT
ejpam-5899	166	1	proof	proof	NOUN
ejpam-5899	166	2	.	.	PUNCT
ejpam-5899	167	1	note	note	VERB
ejpam-5899	167	2	that	that	SCONJ
ejpam-5899	167	3	,	,	PUNCT
ejpam-5899	167	4	(	(	PUNCT
ejpam-5899	167	5	µz)e	µz)e	NOUN
ejpam-5899	167	6	=	=	SYM
ejpam-5899	167	7	{	{	PUNCT
ejpam-5899	167	8	e	e	NOUN
ejpam-5899	167	9	∩g	∩g	NOUN
ejpam-5899	167	10	:	:	PUNCT
ejpam-5899	167	11	g	g	PROPN
ejpam-5899	167	12	∈	∈	PROPN
ejpam-5899	167	13	µz	µz	PROPN
ejpam-5899	167	14	}	}	PUNCT
ejpam-5899	167	15	=	=	PUNCT
ejpam-5899	167	16	{	{	PUNCT
ejpam-5899	167	17	e	e	NOUN
ejpam-5899	167	18	∩z	∩z	VERB
ejpam-5899	167	19	∩h	∩h	PROPN
ejpam-5899	167	20	:	:	PUNCT
ejpam-5899	168	1	h	h	PROPN
ejpam-5899	168	2	∈	∈	PROPN
ejpam-5899	168	3	µ	µ	X
ejpam-5899	168	4	}	}	PUNCT
ejpam-5899	168	5	=	=	PUNCT
ejpam-5899	168	6	{	{	PUNCT
ejpam-5899	168	7	e	e	NOUN
ejpam-5899	168	8	∩h	∩h	PROPN
ejpam-5899	168	9	:	:	PUNCT
ejpam-5899	168	10	h	h	PROPN
ejpam-5899	168	11	∈	∈	PROPN
ejpam-5899	168	12	µ	µ	X
ejpam-5899	168	13	}	}	PUNCT
ejpam-5899	168	14	=	=	SYM
ejpam-5899	168	15	µe	µe	NOUN
ejpam-5899	168	16	.	.	PUNCT
ejpam-5899	169	1	also	also	ADV
ejpam-5899	169	2	,	,	PUNCT
ejpam-5899	169	3	for	for	ADP
ejpam-5899	169	4	each	each	DET
ejpam-5899	169	5	s	s	X
ejpam-5899	169	6	∈	∈	PROPN
ejpam-5899	169	7	e	e	NOUN
ejpam-5899	169	8	,	,	PUNCT
ejpam-5899	169	9	(	(	PUNCT
ejpam-5899	169	10	µz	µz	NOUN
ejpam-5899	169	11	)	)	PUNCT
ejpam-5899	169	12	∗	∗	NOUN
ejpam-5899	169	13	e(s	e(s	PROPN
ejpam-5899	169	14	)	)	PUNCT
ejpam-5899	169	15	=	=	SYM
ejpam-5899	169	16	µ∗e(s	µ∗e(s	PROPN
ejpam-5899	169	17	)	)	PUNCT
ejpam-5899	169	18	.	.	PUNCT
ejpam-5899	170	1	then	then	ADV
ejpam-5899	170	2	,	,	PUNCT
ejpam-5899	170	3	the	the	DET
ejpam-5899	170	4	result	result	NOUN
ejpam-5899	170	5	becomes	become	VERB
ejpam-5899	170	6	obvious	obvious	ADJ
ejpam-5899	170	7	.	.	PUNCT
ejpam-5899	171	1	lemma	lemma	PROPN
ejpam-5899	171	2	1	1	X
ejpam-5899	171	3	.	.	PUNCT
ejpam-5899	172	1	let	let	AUX
ejpam-5899	172	2	(	(	PUNCT
ejpam-5899	172	3	s	s	X
ejpam-5899	172	4	,	,	PUNCT
ejpam-5899	172	5	µ	µ	NOUN
ejpam-5899	172	6	)	)	PUNCT
ejpam-5899	172	7	be	be	AUX
ejpam-5899	172	8	a	a	DET
ejpam-5899	172	9	gts	gts	NOUN
ejpam-5899	172	10	and	and	CCONJ
ejpam-5899	172	11	e	e	NOUN
ejpam-5899	172	12	⊆	⊆	NUM
ejpam-5899	172	13	s.	s.	PROPN
ejpam-5899	172	14	if	if	SCONJ
ejpam-5899	172	15	e	e	PRON
ejpam-5899	172	16	is	be	AUX
ejpam-5899	172	17	a	a	DET
ejpam-5899	172	18	µ∗-open	µ∗-open	PROPN
ejpam-5899	172	19	set	set	NOUN
ejpam-5899	172	20	,	,	PUNCT
ejpam-5899	172	21	then	then	ADV
ejpam-5899	172	22	there	there	PRON
ejpam-5899	172	23	is	be	VERB
ejpam-5899	172	24	h	h	PROPN
ejpam-5899	172	25	∈	∈	PROPN
ejpam-5899	172	26	µ	µ	NOUN
ejpam-5899	172	27	with	with	ADP
ejpam-5899	172	28	e	e	PROPN
ejpam-5899	172	29	⊆	⊆	NUM
ejpam-5899	172	30	h.	h.	NOUN
ejpam-5899	172	31	proof	proof	NOUN
ejpam-5899	172	32	.	.	PUNCT
ejpam-5899	173	1	for	for	ADP
ejpam-5899	173	2	each	each	DET
ejpam-5899	173	3	s	s	X
ejpam-5899	173	4	∈	∈	ADJ
ejpam-5899	173	5	e	e	NOUN
ejpam-5899	173	6	,	,	PUNCT
ejpam-5899	173	7	there	there	PRON
ejpam-5899	173	8	is	be	VERB
ejpam-5899	173	9	gs	gs	PROPN
ejpam-5899	173	10	∈	∈	PROPN
ejpam-5899	173	11	µ∗(s	µ∗(s	PROPN
ejpam-5899	173	12	)	)	PUNCT
ejpam-5899	173	13	with	with	ADP
ejpam-5899	173	14	e	e	NOUN
ejpam-5899	173	15	=	=	SYM
ejpam-5899	173	16	∪	∪	PROPN
ejpam-5899	173	17	s∈e	s∈e	NOUN
ejpam-5899	173	18	gs	gs	NOUN
ejpam-5899	173	19	.	.	PUNCT
ejpam-5899	174	1	now	now	ADV
ejpam-5899	174	2	gs	gs	X
ejpam-5899	175	1	=	=	PUNCT
ejpam-5899	175	2	ns∩	ns∩	PROPN
ejpam-5899	175	3	i=1	i=1	PRON
ejpam-5899	175	4	hi(s	hi(s	NUM
ejpam-5899	175	5	)	)	PUNCT
ejpam-5899	175	6	where	where	SCONJ
ejpam-5899	175	7	hi(s	hi(s	NUM
ejpam-5899	175	8	)	)	PUNCT
ejpam-5899	175	9	∈	∈	PROPN
ejpam-5899	175	10	µ(s	µ(	NOUN
ejpam-5899	175	11	)	)	PUNCT
ejpam-5899	175	12	for	for	ADP
ejpam-5899	175	13	each	each	DET
ejpam-5899	175	14	1	1	NUM
ejpam-5899	175	15	≤	≤	NUM
ejpam-5899	175	16	i	i	PRON
ejpam-5899	175	17	≤	≤	NUM
ejpam-5899	175	18	ns	ns	X
ejpam-5899	175	19	.	.	PUNCT
ejpam-5899	176	1	finally	finally	ADV
ejpam-5899	176	2	,	,	PUNCT
ejpam-5899	176	3	for	for	ADP
ejpam-5899	176	4	each	each	DET
ejpam-5899	176	5	s	s	X
ejpam-5899	176	6	∈	∈	PROPN
ejpam-5899	176	7	e	e	NOUN
ejpam-5899	176	8	,	,	PUNCT
ejpam-5899	176	9	choose	choose	VERB
ejpam-5899	176	10	1	1	NUM
ejpam-5899	176	11	≤	≤	NUM
ejpam-5899	176	12	i	i	PRON
ejpam-5899	176	13	≤	≤	NUM
ejpam-5899	176	14	ns	ns	NUM
ejpam-5899	176	15	with	with	ADP
ejpam-5899	176	16	s	s	PROPN
ejpam-5899	176	17	∈	∈	PROPN
ejpam-5899	176	18	hi(s	hi(s	NUM
ejpam-5899	176	19	)	)	PUNCT
ejpam-5899	176	20	.	.	PUNCT
ejpam-5899	177	1	therefore	therefore	ADV
ejpam-5899	177	2	,	,	PUNCT
ejpam-5899	177	3	e	e	PROPN
ejpam-5899	177	4	⊆	⊆	NUM
ejpam-5899	177	5	ns∪	ns∪	NUM
ejpam-5899	177	6	i=1	i=1	PRON
ejpam-5899	177	7	hi(s	hi(s	NUM
ejpam-5899	177	8	)	)	PUNCT
ejpam-5899	177	9	=	=	SYM
ejpam-5899	177	10	h	h	NOUN
ejpam-5899	177	11	and	and	CCONJ
ejpam-5899	177	12	h	h	NOUN
ejpam-5899	177	13	∈	∈	PROPN
ejpam-5899	177	14	µ.	µ.	NOUN
ejpam-5899	177	15	theorem	theorem	VERB
ejpam-5899	177	16	7	7	NUM
ejpam-5899	177	17	.	.	PUNCT
ejpam-5899	178	1	let	let	AUX
ejpam-5899	178	2	(	(	PUNCT
ejpam-5899	178	3	s	s	X
ejpam-5899	178	4	,	,	PUNCT
ejpam-5899	178	5	µ	µ	NOUN
ejpam-5899	178	6	)	)	PUNCT
ejpam-5899	178	7	be	be	AUX
ejpam-5899	178	8	an	an	DET
ejpam-5899	178	9	gts	gts	NOUN
ejpam-5899	178	10	and	and	CCONJ
ejpam-5899	178	11	e	e	NOUN
ejpam-5899	178	12	,	,	PUNCT
ejpam-5899	178	13	z	z	PROPN
ejpam-5899	178	14	⊆	⊆	NUM
ejpam-5899	178	15	s.	s.	PROPN
ejpam-5899	178	16	then	then	ADV
ejpam-5899	178	17	:	:	PUNCT
ejpam-5899	178	18	(	(	PUNCT
ejpam-5899	178	19	i	i	NOUN
ejpam-5899	178	20	)	)	PUNCT
ejpam-5899	178	21	e	e	NOUN
ejpam-5899	178	22	∩	∩	NOUN
ejpam-5899	178	23	z	z	PROPN
ejpam-5899	178	24	is	be	AUX
ejpam-5899	178	25	α	α	NOUN
ejpam-5899	178	26	-	-	NOUN
ejpam-5899	178	27	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	178	28	if	if	SCONJ
ejpam-5899	178	29	e	e	PRON
ejpam-5899	178	30	is	be	AUX
ejpam-5899	178	31	µ∗-closed	µ∗-close	VERB
ejpam-5899	178	32	in	in	ADP
ejpam-5899	178	33	(	(	PUNCT
ejpam-5899	178	34	s	s	PROPN
ejpam-5899	178	35	,	,	PUNCT
ejpam-5899	178	36	µ	µ	NOUN
ejpam-5899	178	37	)	)	PUNCT
ejpam-5899	178	38	and	and	CCONJ
ejpam-5899	178	39	z	z	PROPN
ejpam-5899	178	40	is	be	AUX
ejpam-5899	178	41	α	α	NOUN
ejpam-5899	178	42	-	-	NOUN
ejpam-5899	178	43	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	178	44	.	.	PUNCT
ejpam-5899	179	1	(	(	PUNCT
ejpam-5899	179	2	ii	ii	NOUN
ejpam-5899	179	3	)	)	PUNCT
ejpam-5899	179	4	e	e	NOUN
ejpam-5899	179	5	∩	∩	NOUN
ejpam-5899	179	6	z	z	PROPN
ejpam-5899	179	7	is	be	AUX
ejpam-5899	179	8	β	β	NOUN
ejpam-5899	179	9	-	-	NOUN
ejpam-5899	179	10	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	179	11	if	if	SCONJ
ejpam-5899	179	12	e	e	PRON
ejpam-5899	179	13	is	be	AUX
ejpam-5899	179	14	µ∗-closed	µ∗-close	VERB
ejpam-5899	179	15	in	in	ADP
ejpam-5899	179	16	(	(	PUNCT
ejpam-5899	179	17	s	s	PROPN
ejpam-5899	179	18	,	,	PUNCT
ejpam-5899	179	19	µ	µ	NOUN
ejpam-5899	179	20	)	)	PUNCT
ejpam-5899	179	21	and	and	CCONJ
ejpam-5899	179	22	z	z	PROPN
ejpam-5899	179	23	is	be	AUX
ejpam-5899	179	24	β	β	NOUN
ejpam-5899	179	25	-	-	NOUN
ejpam-5899	179	26	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	179	27	.	.	PUNCT
ejpam-5899	180	1	(	(	PUNCT
ejpam-5899	180	2	iii	iii	X
ejpam-5899	180	3	)	)	PUNCT
ejpam-5899	180	4	e	e	NOUN
ejpam-5899	180	5	∩z	∩z	VERB
ejpam-5899	180	6	is	be	AUX
ejpam-5899	180	7	α	α	NOUN
ejpam-5899	180	8	-	-	PUNCT
ejpam-5899	180	9	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	180	10	(	(	PUNCT
ejpam-5899	180	11	resp	resp	NOUN
ejpam-5899	180	12	.	.	PUNCT
ejpam-5899	180	13	,	,	PUNCT
ejpam-5899	180	14	β	β	X
ejpam-5899	180	15	-	-	NOUN
ejpam-5899	180	16	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	180	17	)	)	PUNCT
ejpam-5899	181	1	if	if	SCONJ
ejpam-5899	181	2	e	e	PROPN
ejpam-5899	181	3	is	be	AUX
ejpam-5899	181	4	µ-closed	µ-close	VERB
ejpam-5899	181	5	in	in	ADP
ejpam-5899	181	6	(	(	PUNCT
ejpam-5899	181	7	s	s	PROPN
ejpam-5899	181	8	,	,	PUNCT
ejpam-5899	181	9	µ	µ	NOUN
ejpam-5899	181	10	)	)	PUNCT
ejpam-5899	181	11	and	and	CCONJ
ejpam-5899	181	12	z	z	PROPN
ejpam-5899	181	13	is	be	AUX
ejpam-5899	181	14	α	α	NOUN
ejpam-5899	181	15	-	-	PUNCT
ejpam-5899	181	16	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	181	17	(	(	PUNCT
ejpam-5899	181	18	resp	resp	NOUN
ejpam-5899	181	19	.	.	PUNCT
ejpam-5899	181	20	,	,	PUNCT
ejpam-5899	181	21	β	β	X
ejpam-5899	181	22	-	-	NOUN
ejpam-5899	181	23	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	181	24	)	)	PUNCT
ejpam-5899	181	25	.	.	PUNCT
ejpam-5899	182	1	proof	proof	NOUN
ejpam-5899	182	2	.	.	PUNCT
ejpam-5899	183	1	(	(	PUNCT
ejpam-5899	183	2	i	i	NOUN
ejpam-5899	183	3	)	)	PUNCT
ejpam-5899	183	4	let	let	VERB
ejpam-5899	183	5	g	g	NOUN
ejpam-5899	183	6	=	=	PUNCT
ejpam-5899	183	7	{	{	PUNCT
ejpam-5899	183	8	gα	gα	NOUN
ejpam-5899	183	9	:	:	PUNCT
ejpam-5899	183	10	α	α	PROPN
ejpam-5899	183	11	∈	∈	PROPN
ejpam-5899	183	12	∆	∆	PROPN
ejpam-5899	183	13	}	}	PUNCT
ejpam-5899	183	14	be	be	AUX
ejpam-5899	183	15	an	an	DET
ejpam-5899	183	16	(	(	PUNCT
ejpam-5899	183	17	s	s	X
ejpam-5899	183	18	,	,	PUNCT
ejpam-5899	183	19	µ)-cover	µ)-cover	NOUN
ejpam-5899	183	20	of	of	ADP
ejpam-5899	183	21	e	e	PROPN
ejpam-5899	183	22	∩	∩	PROPN
ejpam-5899	183	23	z.	z.	PROPN
ejpam-5899	183	24	since	since	SCONJ
ejpam-5899	183	25	s	s	PRON
ejpam-5899	183	26	−e	−e	NOUN
ejpam-5899	183	27	is	be	AUX
ejpam-5899	183	28	µ∗-open	µ∗-open	ADJ
ejpam-5899	183	29	,	,	PUNCT
ejpam-5899	183	30	by	by	ADP
ejpam-5899	183	31	lemma	lemma	PROPN
ejpam-5899	183	32	1	1	NUM
ejpam-5899	183	33	,	,	PUNCT
ejpam-5899	183	34	there	there	PRON
ejpam-5899	183	35	is	be	VERB
ejpam-5899	183	36	w	w	PROPN
ejpam-5899	183	37	∈	∈	PROPN
ejpam-5899	183	38	µ	µ	X
ejpam-5899	183	39	with	with	ADP
ejpam-5899	183	40	s	s	NOUN
ejpam-5899	184	1	−	−	PROPN
ejpam-5899	184	2	e	e	NOUN
ejpam-5899	184	3	⊆	⊆	NUM
ejpam-5899	184	4	wand	wand	NOUN
ejpam-5899	184	5	hence	hence	ADV
ejpam-5899	184	6	g1	g1	PROPN
ejpam-5899	184	7	=	=	SYM
ejpam-5899	184	8	{	{	PUNCT
ejpam-5899	184	9	gα	gα	SCONJ
ejpam-5899	184	10	:	:	PUNCT
ejpam-5899	184	11	α	α	PROPN
ejpam-5899	184	12	∈	∈	PROPN
ejpam-5899	184	13	∆	∆	X
ejpam-5899	184	14	}	}	PUNCT
ejpam-5899	184	15	∪	∪	X
ejpam-5899	184	16	{	{	PUNCT
ejpam-5899	184	17	w	w	NOUN
ejpam-5899	184	18	}	}	PUNCT
ejpam-5899	184	19	is	be	AUX
ejpam-5899	184	20	an	an	DET
ejpam-5899	184	21	(	(	PUNCT
ejpam-5899	184	22	s	s	X
ejpam-5899	184	23	,	,	PUNCT
ejpam-5899	184	24	µ)-cover	µ)-cover	NOUN
ejpam-5899	184	25	of	of	ADP
ejpam-5899	184	26	z.	z.	PROPN
ejpam-5899	184	27	so	so	ADV
ejpam-5899	184	28	g1	g1	PROPN
ejpam-5899	184	29	has	have	VERB
ejpam-5899	184	30	a	a	DET
ejpam-5899	184	31	gµ−lf(s,µ	gµ−lf(s,µ	ADJ
ejpam-5899	184	32	)	)	PUNCT
ejpam-5899	184	33	(	(	PUNCT
ejpam-5899	184	34	s	s	X
ejpam-5899	184	35	,	,	PUNCT
ejpam-5899	184	36	µ)-refinement	µ)-refinement	PUNCT
ejpam-5899	184	37	,	,	PUNCT
ejpam-5899	184	38	say	say	VERB
ejpam-5899	184	39	h	h	NOUN
ejpam-5899	184	40	=	=	PRON
ejpam-5899	184	41	{	{	PUNCT
ejpam-5899	184	42	hβ	hβ	INTJ
ejpam-5899	184	43	:	:	PUNCT
ejpam-5899	184	44	β	β	X
ejpam-5899	184	45	∈	∈	PROPN
ejpam-5899	184	46	λ	λ	NOUN
ejpam-5899	184	47	}	}	PUNCT
ejpam-5899	184	48	.	.	PUNCT
ejpam-5899	185	1	hence	hence	ADV
ejpam-5899	185	2	the	the	DET
ejpam-5899	185	3	family	family	NOUN
ejpam-5899	185	4	h1	h1	NOUN
ejpam-5899	185	5	=	=	PUNCT
ejpam-5899	185	6	{	{	PUNCT
ejpam-5899	185	7	hβ	hβ	PROPN
ejpam-5899	185	8	∈	∈	PROPN
ejpam-5899	185	9	h	h	NOUN
ejpam-5899	185	10	:	:	PUNCT
ejpam-5899	185	11	hβ	hβ	PROPN
ejpam-5899	185	12	⊆	⊆	NUM
ejpam-5899	185	13	gα	gα	NOUN
ejpam-5899	185	14	for	for	ADP
ejpam-5899	185	15	some	some	PRON
ejpam-5899	185	16	gα	gα	ADP
ejpam-5899	185	17	∈	∈	PROPN
ejpam-5899	185	18	g	g	NOUN
ejpam-5899	185	19	,	,	PUNCT
ejpam-5899	185	20	α	α	PROPN
ejpam-5899	185	21	∈	∈	PROPN
ejpam-5899	185	22	∆	∆	PROPN
ejpam-5899	185	23	and	and	CCONJ
ejpam-5899	185	24	β	β	X
ejpam-5899	185	25	∈	∈	PROPN
ejpam-5899	185	26	λ	λ	PROPN
ejpam-5899	185	27	}	}	PUNCT
ejpam-5899	185	28	is	be	AUX
ejpam-5899	185	29	gµ−lf(s,µ	gµ−lf(s,µ	ADJ
ejpam-5899	185	30	)	)	PUNCT
ejpam-5899	185	31	(	(	PUNCT
ejpam-5899	185	32	s	s	X
ejpam-5899	185	33	,	,	PUNCT
ejpam-5899	185	34	µ)-refinement	µ)-refinement	PUNCT
ejpam-5899	185	35	of	of	ADP
ejpam-5899	185	36	g.	g.	PROPN
ejpam-5899	185	37	therefore	therefore	ADV
ejpam-5899	185	38	,	,	PUNCT
ejpam-5899	185	39	e	e	PROPN
ejpam-5899	185	40	∩	∩	NOUN
ejpam-5899	185	41	z	z	PROPN
ejpam-5899	185	42	is	be	AUX
ejpam-5899	185	43	α	α	NOUN
ejpam-5899	185	44	-	-	NOUN
ejpam-5899	185	45	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	185	46	.	.	PUNCT
ejpam-5899	186	1	(	(	PUNCT
ejpam-5899	186	2	ii	ii	NOUN
ejpam-5899	186	3	)	)	PUNCT
ejpam-5899	186	4	let	let	VERB
ejpam-5899	186	5	g	g	NOUN
ejpam-5899	186	6	=	=	PUNCT
ejpam-5899	186	7	{	{	PUNCT
ejpam-5899	186	8	gα	gα	ADP
ejpam-5899	186	9	∩	∩	NOUN
ejpam-5899	186	10	(	(	PUNCT
ejpam-5899	186	11	e	e	X
ejpam-5899	186	12	∩	∩	X
ejpam-5899	186	13	z	z	NOUN
ejpam-5899	186	14	)	)	PUNCT
ejpam-5899	186	15	:	:	PUNCT
ejpam-5899	186	16	gα	gα	SCONJ
ejpam-5899	186	17	∈	∈	PROPN
ejpam-5899	186	18	µ	µ	NUM
ejpam-5899	186	19	,	,	PUNCT
ejpam-5899	186	20	α	α	PROPN
ejpam-5899	186	21	∈	∈	NOUN
ejpam-5899	186	22	∆	∆	PROPN
ejpam-5899	186	23	}	}	PUNCT
ejpam-5899	186	24	be	be	AUX
ejpam-5899	186	25	an	an	DET
ejpam-5899	186	26	(	(	PUNCT
ejpam-5899	186	27	e	e	NOUN
ejpam-5899	186	28	∩	∩	PROPN
ejpam-5899	186	29	z	z	PROPN
ejpam-5899	186	30	,	,	PUNCT
ejpam-5899	186	31	µe∩z)-cover	µe∩z)-cover	ADV
ejpam-5899	186	32	of	of	ADP
ejpam-5899	186	33	e	e	NOUN
ejpam-5899	186	34	∩	∩	PROPN
ejpam-5899	186	35	z.	z.	PROPN
ejpam-5899	186	36	then	then	ADV
ejpam-5899	186	37	g1	g1	PROPN
ejpam-5899	186	38	=	=	PUNCT
ejpam-5899	186	39	g∗	g∗	VERB
ejpam-5899	186	40	∪	∪	ADJ
ejpam-5899	186	41	{	{	PUNCT
ejpam-5899	186	42	w	w	NOUN
ejpam-5899	186	43	∩	∩	PROPN
ejpam-5899	186	44	z	z	NOUN
ejpam-5899	186	45	}	}	PUNCT
ejpam-5899	186	46	is	be	AUX
ejpam-5899	186	47	a	a	DET
ejpam-5899	186	48	(	(	PUNCT
ejpam-5899	186	49	z	z	NOUN
ejpam-5899	186	50	,	,	PUNCT
ejpam-5899	186	51	µz)-cover	µz)-cover	ADV
ejpam-5899	186	52	of	of	ADP
ejpam-5899	186	53	z	z	NOUN
ejpam-5899	186	54	,	,	PUNCT
ejpam-5899	186	55	where	where	SCONJ
ejpam-5899	186	56	g∗	g∗	VERB
ejpam-5899	186	57	=	=	SYM
ejpam-5899	186	58	{	{	PUNCT
ejpam-5899	186	59	gα	gα	ADP
ejpam-5899	186	60	∩	∩	ADJ
ejpam-5899	186	61	z	z	NOUN
ejpam-5899	186	62	:	:	PUNCT
ejpam-5899	186	63	α	α	PROPN
ejpam-5899	186	64	∈	∈	NOUN
ejpam-5899	186	65	∆	∆	X
ejpam-5899	186	66	}	}	PUNCT
ejpam-5899	186	67	and	and	CCONJ
ejpam-5899	186	68	w	w	PROPN
ejpam-5899	186	69	is	be	AUX
ejpam-5899	186	70	an	an	DET
ejpam-5899	186	71	µ-open	µ-open	NOUN
ejpam-5899	186	72	set	set	VERB
ejpam-5899	186	73	with	with	ADP
ejpam-5899	186	74	s	s	PRON
ejpam-5899	186	75	−	−	PROPN
ejpam-5899	186	76	e	e	NOUN
ejpam-5899	186	77	⊆	⊆	NUM
ejpam-5899	186	78	w	w	NOUN
ejpam-5899	186	79	.	.	PUNCT
ejpam-5899	187	1	so	so	ADV
ejpam-5899	187	2	g1	g1	PROPN
ejpam-5899	187	3	has	have	VERB
ejpam-5899	187	4	a	a	DET
ejpam-5899	187	5	gµ−lf(z,µz	gµ−lf(z,µz	PROPN
ejpam-5899	187	6	)	)	PUNCT
ejpam-5899	187	7	(	(	PUNCT
ejpam-5899	187	8	z	z	NOUN
ejpam-5899	187	9	,	,	PUNCT
ejpam-5899	187	10	µz)-refinement	µz)-refinement	ADJ
ejpam-5899	187	11	,	,	PUNCT
ejpam-5899	187	12	say	say	VERB
ejpam-5899	187	13	h	h	NOUN
ejpam-5899	187	14	=	=	PRON
ejpam-5899	187	15	{	{	PUNCT
ejpam-5899	187	16	hβ	hβ	PROPN
ejpam-5899	187	17	∩z	∩z	VERB
ejpam-5899	187	18	:	:	PUNCT
ejpam-5899	187	19	hβ	hβ	PROPN
ejpam-5899	187	20	∈	∈	PROPN
ejpam-5899	187	21	µ	µ	PROPN
ejpam-5899	187	22	,	,	PUNCT
ejpam-5899	187	23	β	β	X
ejpam-5899	187	24	∈	∈	PROPN
ejpam-5899	187	25	λ	λ	NOUN
ejpam-5899	187	26	}	}	PUNCT
ejpam-5899	187	27	.	.	PUNCT
ejpam-5899	188	1	hence	hence	ADV
ejpam-5899	188	2	,	,	PUNCT
ejpam-5899	188	3	the	the	DET
ejpam-5899	188	4	family	family	NOUN
ejpam-5899	188	5	h1	h1	PROPN
ejpam-5899	188	6	=	=	SYM
ejpam-5899	188	7	{	{	PUNCT
ejpam-5899	188	8	hβ	hβ	INTJ
ejpam-5899	188	9	∩	∩	NOUN
ejpam-5899	188	10	(	(	PUNCT
ejpam-5899	188	11	e	e	NOUN
ejpam-5899	188	12	∩z	∩z	NOUN
ejpam-5899	188	13	)	)	PUNCT
ejpam-5899	188	14	:	:	PUNCT
ejpam-5899	188	15	hβ	hβ	PROPN
ejpam-5899	188	16	∩z	∩z	VERB
ejpam-5899	188	17	⊆	⊆	NUM
ejpam-5899	188	18	gα	gα	ADP
ejpam-5899	188	19	∩z	∩z	VERB
ejpam-5899	188	20	for	for	SCONJ
ejpam-5899	188	21	some	some	PRON
ejpam-5899	188	22	gα	gα	ADP
ejpam-5899	188	23	∩	∩	PROPN
ejpam-5899	188	24	z	z	PROPN
ejpam-5899	188	25	∈	∈	PROPN
ejpam-5899	188	26	g∗	g∗	PROPN
ejpam-5899	188	27	,	,	PUNCT
ejpam-5899	188	28	α	α	PROPN
ejpam-5899	188	29	∈	∈	PROPN
ejpam-5899	188	30	∆	∆	PROPN
ejpam-5899	188	31	and	and	CCONJ
ejpam-5899	188	32	β	β	X
ejpam-5899	188	33	∈	∈	PROPN
ejpam-5899	188	34	λ	λ	PROPN
ejpam-5899	188	35	}	}	PUNCT
ejpam-5899	188	36	is	be	AUX
ejpam-5899	188	37	gµ−lf(e∩z,µe∩z	gµ−lf(e∩z,µe∩z	PROPN
ejpam-5899	188	38	)	)	PUNCT
ejpam-5899	188	39	(	(	PUNCT
ejpam-5899	188	40	e	e	X
ejpam-5899	188	41	∩	∩	PROPN
ejpam-5899	188	42	z	z	PROPN
ejpam-5899	188	43	,	,	PUNCT
ejpam-5899	188	44	µe∩z)-refinement	µe∩z)-refinement	NOUN
ejpam-5899	188	45	of	of	ADP
ejpam-5899	188	46	g.	g.	PROPN
ejpam-5899	188	47	therefore	therefore	ADV
ejpam-5899	188	48	,	,	PUNCT
ejpam-5899	188	49	e	e	PROPN
ejpam-5899	188	50	∩	∩	NOUN
ejpam-5899	188	51	z	z	PROPN
ejpam-5899	188	52	is	be	AUX
ejpam-5899	188	53	β	β	NOUN
ejpam-5899	188	54	-	-	NOUN
ejpam-5899	188	55	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	188	56	.	.	PUNCT
ejpam-5899	189	1	(	(	PUNCT
ejpam-5899	189	2	iii	iii	NOUN
ejpam-5899	189	3	)	)	PUNCT
ejpam-5899	189	4	follows	follow	VERB
ejpam-5899	189	5	from	from	ADP
ejpam-5899	189	6	(	(	PUNCT
ejpam-5899	189	7	i	i	NOUN
ejpam-5899	189	8	)	)	PUNCT
ejpam-5899	189	9	and	and	CCONJ
ejpam-5899	189	10	(	(	PUNCT
ejpam-5899	189	11	ii	ii	NOUN
ejpam-5899	189	12	)	)	PUNCT
ejpam-5899	189	13	.	.	PUNCT
ejpam-5899	190	1	theorem	theorem	ADJ
ejpam-5899	190	2	8	8	NUM
ejpam-5899	190	3	.	.	PUNCT
ejpam-5899	191	1	let	let	AUX
ejpam-5899	191	2	(	(	PUNCT
ejpam-5899	191	3	s	s	X
ejpam-5899	191	4	,	,	PUNCT
ejpam-5899	191	5	µ	µ	NOUN
ejpam-5899	191	6	)	)	PUNCT
ejpam-5899	191	7	be	be	AUX
ejpam-5899	191	8	γµ-regular	γµ-regular	ADJ
ejpam-5899	191	9	gts	gts	NOUN
ejpam-5899	191	10	and	and	CCONJ
ejpam-5899	191	11	e	e	NOUN
ejpam-5899	191	12	⊆	⊆	NUM
ejpam-5899	191	13	s.	s.	PROPN
ejpam-5899	191	14	if	if	SCONJ
ejpam-5899	191	15	e	e	PROPN
ejpam-5899	191	16	is	be	AUX
ejpam-5899	191	17	α	α	NOUN
ejpam-5899	191	18	-	-	NOUN
ejpam-5899	191	19	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	191	20	,	,	PUNCT
ejpam-5899	191	21	then	then	ADV
ejpam-5899	191	22	γµ(e	γµ(e	PUNCT
ejpam-5899	191	23	)	)	PUNCT
ejpam-5899	191	24	is	be	AUX
ejpam-5899	191	25	α	α	NOUN
ejpam-5899	191	26	-	-	NOUN
ejpam-5899	191	27	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	191	28	.	.	PUNCT
ejpam-5899	192	1	h.	h.	PROPN
ejpam-5899	192	2	h.	h.	PROPN
ejpam-5899	192	3	al	al	PROPN
ejpam-5899	192	4	-	-	PUNCT
ejpam-5899	192	5	jarrah	jarrah	PROPN
ejpam-5899	192	6	et	et	PROPN
ejpam-5899	192	7	al	al	PROPN
ejpam-5899	192	8	.	.	PUNCT
ejpam-5899	192	9	/	/	SYM
ejpam-5899	192	10	eur	eur	PROPN
ejpam-5899	192	11	.	.	PUNCT
ejpam-5899	193	1	j.	j.	PROPN
ejpam-5899	193	2	pure	pure	PROPN
ejpam-5899	193	3	appl	appl	PROPN
ejpam-5899	193	4	.	.	PROPN
ejpam-5899	193	5	math	math	PROPN
ejpam-5899	193	6	,	,	PUNCT
ejpam-5899	193	7	18	18	NUM
ejpam-5899	193	8	(	(	PUNCT
ejpam-5899	193	9	2	2	NUM
ejpam-5899	193	10	)	)	PUNCT
ejpam-5899	193	11	(	(	PUNCT
ejpam-5899	193	12	2025	2025	NUM
ejpam-5899	193	13	)	)	PUNCT
ejpam-5899	193	14	,	,	PUNCT
ejpam-5899	193	15	5899	5899	NUM
ejpam-5899	193	16	7	7	NUM
ejpam-5899	193	17	of	of	ADP
ejpam-5899	193	18	11	11	NUM
ejpam-5899	193	19	proof	proof	NOUN
ejpam-5899	193	20	.	.	PUNCT
ejpam-5899	194	1	let	let	VERB
ejpam-5899	194	2	g	g	NOUN
ejpam-5899	194	3	=	=	PUNCT
ejpam-5899	194	4	{	{	PUNCT
ejpam-5899	194	5	gα	gα	NOUN
ejpam-5899	194	6	:	:	PUNCT
ejpam-5899	194	7	α	α	PROPN
ejpam-5899	194	8	∈	∈	PROPN
ejpam-5899	194	9	∆	∆	PROPN
ejpam-5899	194	10	}	}	PUNCT
ejpam-5899	194	11	be	be	AUX
ejpam-5899	194	12	(	(	PUNCT
ejpam-5899	194	13	s	s	X
ejpam-5899	194	14	,	,	PUNCT
ejpam-5899	194	15	µ)-cover	µ)-cover	NOUN
ejpam-5899	194	16	of	of	ADP
ejpam-5899	194	17	γµ(e	γµ(e	PUNCT
ejpam-5899	194	18	)	)	PUNCT
ejpam-5899	194	19	.	.	PUNCT
ejpam-5899	195	1	since	since	SCONJ
ejpam-5899	195	2	g	g	PROPN
ejpam-5899	195	3	is	be	AUX
ejpam-5899	195	4	(	(	PUNCT
ejpam-5899	195	5	s	s	X
ejpam-5899	195	6	,	,	PUNCT
ejpam-5899	195	7	µ)-cover	µ)-cover	NOUN
ejpam-5899	195	8	of	of	ADP
ejpam-5899	195	9	e	e	NOUN
ejpam-5899	195	10	,	,	PUNCT
ejpam-5899	195	11	then	then	ADV
ejpam-5899	195	12	g	g	PROPN
ejpam-5899	195	13	has	have	VERB
ejpam-5899	195	14	a	a	DET
ejpam-5899	195	15	gµ-lf(s,µ)(s	gµ-lf(s,µ)(s	NOUN
ejpam-5899	195	16	,	,	PUNCT
ejpam-5899	195	17	µ)-refinement	µ)-refinement	NUM
ejpam-5899	195	18	,	,	PUNCT
ejpam-5899	195	19	say	say	VERB
ejpam-5899	195	20	h	h	NOUN
ejpam-5899	195	21	=	=	PRON
ejpam-5899	195	22	{	{	PUNCT
ejpam-5899	195	23	hβ	hβ	INTJ
ejpam-5899	195	24	:	:	PUNCT
ejpam-5899	195	25	β	β	X
ejpam-5899	195	26	∈	∈	PROPN
ejpam-5899	195	27	λ	λ	NOUN
ejpam-5899	195	28	}	}	PUNCT
ejpam-5899	195	29	.	.	PUNCT
ejpam-5899	196	1	to	to	PART
ejpam-5899	196	2	show	show	VERB
ejpam-5899	196	3	that	that	SCONJ
ejpam-5899	196	4	h	h	NOUN
ejpam-5899	196	5	is	be	AUX
ejpam-5899	196	6	a	a	DET
ejpam-5899	196	7	cover	cover	NOUN
ejpam-5899	196	8	for	for	ADP
ejpam-5899	196	9	γµ(e	γµ(e	NOUN
ejpam-5899	196	10	)	)	PUNCT
ejpam-5899	196	11	,	,	PUNCT
ejpam-5899	196	12	let	let	VERB
ejpam-5899	196	13	hβ	hβ	PRON
ejpam-5899	196	14	∈	∈	PROPN
ejpam-5899	196	15	h.	h.	PROPN
ejpam-5899	196	16	since	since	SCONJ
ejpam-5899	196	17	(	(	PUNCT
ejpam-5899	196	18	s	s	PROPN
ejpam-5899	196	19	,	,	PUNCT
ejpam-5899	196	20	µ	µ	NOUN
ejpam-5899	196	21	)	)	PUNCT
ejpam-5899	196	22	is	be	AUX
ejpam-5899	196	23	a	a	DET
ejpam-5899	196	24	γµ-regular	γµ-regular	ADJ
ejpam-5899	196	25	gts	gts	NOUN
ejpam-5899	196	26	,	,	PUNCT
ejpam-5899	196	27	then	then	ADV
ejpam-5899	196	28	for	for	ADP
ejpam-5899	196	29	each	each	DET
ejpam-5899	196	30	s	s	X
ejpam-5899	196	31	∈	∈	NOUN
ejpam-5899	196	32	hβ	hβ	INTJ
ejpam-5899	196	33	there	there	PRON
ejpam-5899	196	34	is	be	VERB
ejpam-5899	196	35	wβs	wβs	PROPN
ejpam-5899	196	36	∈	∈	PROPN
ejpam-5899	196	37	µ(s	µ(	NOUN
ejpam-5899	196	38	)	)	PUNCT
ejpam-5899	196	39	with	with	ADP
ejpam-5899	196	40	γµ(wβs	γµ(wβs	NOUN
ejpam-5899	196	41	)	)	PUNCT
ejpam-5899	196	42	⊆	⊆	NUM
ejpam-5899	196	43	hβ	hβ	NOUN
ejpam-5899	196	44	.	.	PUNCT
ejpam-5899	197	1	now	now	ADV
ejpam-5899	197	2	,	,	PUNCT
ejpam-5899	197	3	w	w	PROPN
ejpam-5899	197	4	=	=	SYM
ejpam-5899	197	5	{	{	PUNCT
ejpam-5899	197	6	wβs	wβs	NOUN
ejpam-5899	197	7	:	:	PUNCT
ejpam-5899	197	8	β	β	PROPN
ejpam-5899	197	9	∈	∈	PROPN
ejpam-5899	197	10	λ	λ	PROPN
ejpam-5899	197	11	,	,	PUNCT
ejpam-5899	197	12	s	s	PART
ejpam-5899	197	13	∈	∈	PROPN
ejpam-5899	197	14	hβ	hβ	PROPN
ejpam-5899	197	15	}	}	PUNCT
ejpam-5899	197	16	is	be	AUX
ejpam-5899	197	17	an	an	DET
ejpam-5899	197	18	(	(	PUNCT
ejpam-5899	197	19	s	s	X
ejpam-5899	197	20	,	,	PUNCT
ejpam-5899	197	21	µ)-cover	µ)-cover	NOUN
ejpam-5899	197	22	of	of	ADP
ejpam-5899	197	23	e	e	NOUN
ejpam-5899	198	1	and	and	CCONJ
ejpam-5899	198	2	so	so	ADV
ejpam-5899	198	3	it	it	PRON
ejpam-5899	198	4	has	have	VERB
ejpam-5899	198	5	a	a	DET
ejpam-5899	198	6	gµ-lf(s,µ)(s	gµ-lf(s,µ)(s	NOUN
ejpam-5899	198	7	,	,	PUNCT
ejpam-5899	198	8	µ)-refinement	µ)-refinement	NUM
ejpam-5899	198	9	,	,	PUNCT
ejpam-5899	198	10	say	say	VERB
ejpam-5899	198	11	t	t	NOUN
ejpam-5899	198	12	=	=	PRON
ejpam-5899	198	13	{	{	PUNCT
ejpam-5899	198	14	tλ	tλ	ADP
ejpam-5899	198	15	:	:	PUNCT
ejpam-5899	198	16	λ	λ	X
ejpam-5899	198	17	∈	∈	NOUN
ejpam-5899	198	18	θ	θ	NOUN
ejpam-5899	198	19	}	}	PUNCT
ejpam-5899	198	20	.	.	PUNCT
ejpam-5899	199	1	by	by	ADP
ejpam-5899	199	2	theorem	theorem	NOUN
ejpam-5899	199	3	1	1	NUM
ejpam-5899	199	4	,	,	PUNCT
ejpam-5899	199	5	we	we	PRON
ejpam-5899	199	6	have	have	VERB
ejpam-5899	199	7	γµ(e	γµ(e	PUNCT
ejpam-5899	199	8	)	)	PUNCT
ejpam-5899	200	1	⊆	⊆	NUM
ejpam-5899	200	2	γµ(∪tλ	γµ(∪tλ	NOUN
ejpam-5899	200	3	)	)	PUNCT
ejpam-5899	200	4	=	=	SYM
ejpam-5899	200	5	∪γµ(tλ	∪γµ(tλ	PROPN
ejpam-5899	200	6	)	)	PUNCT
ejpam-5899	200	7	⊆	⊆	NUM
ejpam-5899	200	8	∪γµ(wβs	∪γµ(wβs	PROPN
ejpam-5899	200	9	)	)	PUNCT
ejpam-5899	200	10	⊆	⊆	NUM
ejpam-5899	200	11	∪hβ	∪hβ	PROPN
ejpam-5899	200	12	.	.	PROPN
ejpam-5899	200	13	therefore	therefore	ADV
ejpam-5899	200	14	,	,	PUNCT
ejpam-5899	200	15	γµ(e	γµ(e	PUNCT
ejpam-5899	200	16	)	)	PUNCT
ejpam-5899	200	17	is	be	AUX
ejpam-5899	200	18	α	α	NOUN
ejpam-5899	200	19	-	-	NOUN
ejpam-5899	200	20	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	200	21	.	.	PUNCT
ejpam-5899	201	1	theorem	theorem	VERB
ejpam-5899	201	2	9	9	NUM
ejpam-5899	201	3	.	.	PUNCT
ejpam-5899	202	1	let	let	AUX
ejpam-5899	202	2	(	(	PUNCT
ejpam-5899	202	3	s	s	X
ejpam-5899	202	4	,	,	PUNCT
ejpam-5899	202	5	µ	µ	NOUN
ejpam-5899	202	6	)	)	PUNCT
ejpam-5899	202	7	be	be	AUX
ejpam-5899	202	8	γµ-regular	γµ-regular	ADJ
ejpam-5899	202	9	gts	gts	NOUN
ejpam-5899	202	10	and	and	CCONJ
ejpam-5899	202	11	e	e	NOUN
ejpam-5899	202	12	⊆	⊆	NUM
ejpam-5899	202	13	s.	s.	PROPN
ejpam-5899	202	14	if	if	SCONJ
ejpam-5899	202	15	e	e	PROPN
ejpam-5899	202	16	is	be	AUX
ejpam-5899	202	17	α	α	NOUN
ejpam-5899	202	18	-	-	NOUN
ejpam-5899	202	19	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	202	20	,	,	PUNCT
ejpam-5899	202	21	then	then	ADV
ejpam-5899	202	22	each	each	DET
ejpam-5899	202	23	(	(	PUNCT
ejpam-5899	202	24	s	s	X
ejpam-5899	202	25	,	,	PUNCT
ejpam-5899	202	26	µ)-cover	µ)-cover	NOUN
ejpam-5899	202	27	of	of	ADP
ejpam-5899	202	28	e	e	NOUN
ejpam-5899	202	29	has	have	VERB
ejpam-5899	202	30	a	a	DET
ejpam-5899	202	31	µ∗-closed	µ∗-close	VERB
ejpam-5899	202	32	gµ-lf(s,µ	gµ-lf(s,µ	PROPN
ejpam-5899	202	33	)	)	PUNCT
ejpam-5899	202	34	refinement	refinement	NOUN
ejpam-5899	202	35	.	.	PUNCT
ejpam-5899	203	1	proof	proof	NOUN
ejpam-5899	203	2	.	.	PUNCT
ejpam-5899	204	1	let	let	VERB
ejpam-5899	204	2	g	g	NOUN
ejpam-5899	204	3	=	=	PUNCT
ejpam-5899	204	4	{	{	PUNCT
ejpam-5899	204	5	gα	gα	NOUN
ejpam-5899	204	6	:	:	PUNCT
ejpam-5899	204	7	α	α	PROPN
ejpam-5899	204	8	∈	∈	PROPN
ejpam-5899	204	9	∆	∆	PROPN
ejpam-5899	204	10	}	}	PUNCT
ejpam-5899	204	11	be	be	AUX
ejpam-5899	204	12	(	(	PUNCT
ejpam-5899	204	13	s	s	X
ejpam-5899	204	14	,	,	PUNCT
ejpam-5899	204	15	µ)-cover	µ)-cover	PUNCT
ejpam-5899	204	16	of	of	ADP
ejpam-5899	204	17	e.	e.	PROPN
ejpam-5899	204	18	for	for	SCONJ
ejpam-5899	204	19	each	each	PRON
ejpam-5899	204	20	s	s	X
ejpam-5899	204	21	∈	∈	NOUN
ejpam-5899	204	22	e	e	NOUN
ejpam-5899	204	23	pick	pick	VERB
ejpam-5899	204	24	gs	gs	PROPN
ejpam-5899	204	25	∈	∈	PROPN
ejpam-5899	204	26	g	g	PROPN
ejpam-5899	204	27	with	with	ADP
ejpam-5899	204	28	gs	gs	PROPN
ejpam-5899	204	29	∈	∈	PROPN
ejpam-5899	204	30	µ(s	µ(	NOUN
ejpam-5899	204	31	)	)	PUNCT
ejpam-5899	204	32	.	.	PUNCT
ejpam-5899	205	1	since	since	SCONJ
ejpam-5899	205	2	(	(	PUNCT
ejpam-5899	205	3	s	s	PROPN
ejpam-5899	205	4	,	,	PUNCT
ejpam-5899	205	5	µ	µ	NOUN
ejpam-5899	205	6	)	)	PUNCT
ejpam-5899	205	7	is	be	AUX
ejpam-5899	205	8	γµ-regular	γµ-regular	ADJ
ejpam-5899	205	9	,	,	PUNCT
ejpam-5899	205	10	then	then	ADV
ejpam-5899	205	11	there	there	PRON
ejpam-5899	205	12	is	be	VERB
ejpam-5899	205	13	hs	hs	PROPN
ejpam-5899	205	14	∈	∈	PROPN
ejpam-5899	205	15	µ(s	µ(s	PROPN
ejpam-5899	205	16	)	)	PUNCT
ejpam-5899	205	17	with	with	ADP
ejpam-5899	205	18	s	s	PROPN
ejpam-5899	205	19	∈	∈	PROPN
ejpam-5899	205	20	hs	hs	PROPN
ejpam-5899	205	21	⊆	⊆	NUM
ejpam-5899	205	22	γµ(hs	γµ(hs	PROPN
ejpam-5899	205	23	)	)	PUNCT
ejpam-5899	205	24	⊆	⊆	NUM
ejpam-5899	205	25	gs	gs	NOUN
ejpam-5899	205	26	.	.	PUNCT
ejpam-5899	206	1	then	then	ADV
ejpam-5899	206	2	,	,	PUNCT
ejpam-5899	206	3	the	the	DET
ejpam-5899	206	4	collection	collection	NOUN
ejpam-5899	206	5	h	h	NOUN
ejpam-5899	206	6	=	=	PRON
ejpam-5899	206	7	{	{	PUNCT
ejpam-5899	206	8	hs	hs	X
ejpam-5899	206	9	:	:	PUNCT
ejpam-5899	206	10	s	s	PART
ejpam-5899	206	11	∈	∈	PROPN
ejpam-5899	206	12	e	e	NOUN
ejpam-5899	206	13	}	}	PUNCT
ejpam-5899	206	14	is	be	AUX
ejpam-5899	206	15	(	(	PUNCT
ejpam-5899	206	16	s	s	X
ejpam-5899	206	17	,	,	PUNCT
ejpam-5899	206	18	µ)-cover	µ)-cover	NOUN
ejpam-5899	206	19	of	of	ADP
ejpam-5899	206	20	e	e	NOUN
ejpam-5899	206	21	and	and	CCONJ
ejpam-5899	206	22	so	so	ADV
ejpam-5899	206	23	it	it	PRON
ejpam-5899	206	24	has	have	VERB
ejpam-5899	206	25	a	a	DET
ejpam-5899	206	26	gµ-lf(s,µ)(s	gµ-lf(s,µ)(s	NOUN
ejpam-5899	206	27	,	,	PUNCT
ejpam-5899	206	28	µ)refinement	µ)refinement	NUM
ejpam-5899	206	29	,	,	PUNCT
ejpam-5899	206	30	say	say	VERB
ejpam-5899	206	31	w	w	NOUN
ejpam-5899	206	32	=	=	PRON
ejpam-5899	206	33	{	{	PUNCT
ejpam-5899	206	34	wβ	wβ	ADP
ejpam-5899	206	35	:	:	PUNCT
ejpam-5899	206	36	β	β	X
ejpam-5899	206	37	∈	∈	PROPN
ejpam-5899	206	38	λ	λ	NOUN
ejpam-5899	206	39	}	}	PUNCT
ejpam-5899	206	40	.	.	PUNCT
ejpam-5899	207	1	therefore	therefore	ADV
ejpam-5899	207	2	,	,	PUNCT
ejpam-5899	207	3	by	by	ADP
ejpam-5899	207	4	theorem	theorem	NOUN
ejpam-5899	207	5	1	1	NUM
ejpam-5899	207	6	,	,	PUNCT
ejpam-5899	207	7	γµ(w	γµ(w	PUNCT
ejpam-5899	207	8	)	)	PUNCT
ejpam-5899	207	9	=	=	PRON
ejpam-5899	207	10	{	{	PUNCT
ejpam-5899	207	11	γµ(wβ	γµ(wβ	PROPN
ejpam-5899	207	12	)	)	PUNCT
ejpam-5899	207	13	:	:	PUNCT
ejpam-5899	207	14	β	β	X
ejpam-5899	207	15	∈	∈	PROPN
ejpam-5899	207	16	λ	λ	PROPN
ejpam-5899	207	17	}	}	PUNCT
ejpam-5899	207	18	is	be	AUX
ejpam-5899	207	19	µ∗-closed	µ∗-close	VERB
ejpam-5899	207	20	gµ-lf(s,µ	gµ-lf(s,µ	PROPN
ejpam-5899	207	21	)	)	PUNCT
ejpam-5899	207	22	refinement	refinement	NOUN
ejpam-5899	207	23	.	.	PUNCT
ejpam-5899	208	1	theorem	theorem	VERB
ejpam-5899	208	2	10	10	NUM
ejpam-5899	208	3	.	.	PUNCT
ejpam-5899	209	1	let	let	AUX
ejpam-5899	209	2	(	(	PUNCT
ejpam-5899	209	3	s	s	X
ejpam-5899	209	4	,	,	PUNCT
ejpam-5899	209	5	µ	µ	NOUN
ejpam-5899	209	6	)	)	PUNCT
ejpam-5899	209	7	be	be	AUX
ejpam-5899	209	8	a	a	DET
ejpam-5899	209	9	gts	gts	NOUN
ejpam-5899	209	10	and	and	CCONJ
ejpam-5899	209	11	e	e	NOUN
ejpam-5899	209	12	⊆	⊆	NUM
ejpam-5899	209	13	s.	s.	PROPN
ejpam-5899	209	14	if	if	SCONJ
ejpam-5899	209	15	e	e	PROPN
ejpam-5899	209	16	is	be	AUX
ejpam-5899	209	17	α	α	NOUN
ejpam-5899	209	18	-	-	PUNCT
ejpam-5899	209	19	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	209	20	subset	subset	NOUN
ejpam-5899	209	21	of	of	ADP
ejpam-5899	209	22	a	a	DET
ejpam-5899	209	23	µ-t2	µ-t2	ADJ
ejpam-5899	209	24	-	-	PUNCT
ejpam-5899	209	25	space	space	NOUN
ejpam-5899	209	26	,	,	PUNCT
ejpam-5899	209	27	then	then	ADV
ejpam-5899	209	28	e	e	NOUN
ejpam-5899	209	29	is	be	AUX
ejpam-5899	209	30	µ∗-closed	µ∗-close	VERB
ejpam-5899	209	31	.	.	PUNCT
ejpam-5899	210	1	proof	proof	NOUN
ejpam-5899	210	2	.	.	PUNCT
ejpam-5899	211	1	let	let	VERB
ejpam-5899	211	2	s	s	PRON
ejpam-5899	211	3	/∈	/∈	VERB
ejpam-5899	211	4	e.	e.	PROPN
ejpam-5899	211	5	since	since	SCONJ
ejpam-5899	211	6	(	(	PUNCT
ejpam-5899	211	7	s	s	PROPN
ejpam-5899	211	8	,	,	PUNCT
ejpam-5899	211	9	µ	µ	NOUN
ejpam-5899	211	10	)	)	PUNCT
ejpam-5899	211	11	is	be	AUX
ejpam-5899	211	12	µ-t2	µ-t2	ADJ
ejpam-5899	211	13	-	-	PUNCT
ejpam-5899	211	14	space	space	NOUN
ejpam-5899	211	15	,	,	PUNCT
ejpam-5899	211	16	then	then	ADV
ejpam-5899	211	17	for	for	ADP
ejpam-5899	211	18	each	each	DET
ejpam-5899	211	19	e	e	NOUN
ejpam-5899	211	20	∈	∈	PROPN
ejpam-5899	211	21	e	e	NOUN
ejpam-5899	211	22	there	there	PRON
ejpam-5899	211	23	is	be	VERB
ejpam-5899	211	24	ge	ge	PROPN
ejpam-5899	211	25	∈	∈	PROPN
ejpam-5899	211	26	µ(e	µ(e	PROPN
ejpam-5899	211	27	)	)	PUNCT
ejpam-5899	211	28	and	and	CCONJ
ejpam-5899	211	29	s	s	NOUN
ejpam-5899	211	30	/∈	/∈	NOUN
ejpam-5899	211	31	cµ(ge	cµ(ge	PROPN
ejpam-5899	211	32	)	)	PUNCT
ejpam-5899	211	33	.	.	PUNCT
ejpam-5899	212	1	therefore	therefore	ADV
ejpam-5899	212	2	,	,	PUNCT
ejpam-5899	212	3	g	g	PROPN
ejpam-5899	212	4	=	=	PRON
ejpam-5899	212	5	{	{	PUNCT
ejpam-5899	212	6	ge	ge	NOUN
ejpam-5899	212	7	:	:	PUNCT
ejpam-5899	212	8	e	e	X
ejpam-5899	212	9	∈	∈	PROPN
ejpam-5899	212	10	e	e	X
ejpam-5899	212	11	}	}	PUNCT
ejpam-5899	212	12	is	be	AUX
ejpam-5899	212	13	an	an	DET
ejpam-5899	212	14	(	(	PUNCT
ejpam-5899	212	15	s	s	X
ejpam-5899	212	16	,	,	PUNCT
ejpam-5899	212	17	µ)-cover	µ)-cover	NOUN
ejpam-5899	212	18	of	of	ADP
ejpam-5899	212	19	e	e	NOUN
ejpam-5899	212	20	and	and	CCONJ
ejpam-5899	212	21	hence	hence	ADV
ejpam-5899	212	22	it	it	PRON
ejpam-5899	212	23	has	have	VERB
ejpam-5899	212	24	a	a	DET
ejpam-5899	212	25	gµ−lf(s,µs	gµ−lf(s,µs	PROPN
ejpam-5899	212	26	)	)	PUNCT
ejpam-5899	212	27	(	(	PUNCT
ejpam-5899	212	28	s	s	X
ejpam-5899	212	29	,	,	PUNCT
ejpam-5899	212	30	µ)-refinement	µ)-refinement	PROPN
ejpam-5899	212	31	,	,	PUNCT
ejpam-5899	212	32	say	say	VERB
ejpam-5899	212	33	w.	w.	PROPN
ejpam-5899	212	34	put	put	VERB
ejpam-5899	212	35	h	h	NOUN
ejpam-5899	212	36	=	=	PUNCT
ejpam-5899	212	37	∪{w	∪{w	PROPN
ejpam-5899	212	38	:	:	PUNCT
ejpam-5899	213	1	w	w	PROPN
ejpam-5899	213	2	∈	∈	PROPN
ejpam-5899	213	3	w	w	PROPN
ejpam-5899	213	4	}	}	PUNCT
ejpam-5899	213	5	,	,	PUNCT
ejpam-5899	213	6	then	then	ADV
ejpam-5899	213	7	γµ(h	γµ(h	PUNCT
ejpam-5899	213	8	)	)	PUNCT
ejpam-5899	213	9	=	=	SYM
ejpam-5899	213	10	∪{γµ(w	∪{γµ(w	NOUN
ejpam-5899	213	11	)	)	PUNCT
ejpam-5899	213	12	:	:	PUNCT
ejpam-5899	213	13	w	w	X
ejpam-5899	213	14	∈	∈	PROPN
ejpam-5899	213	15	w	w	PROPN
ejpam-5899	213	16	}	}	PUNCT
ejpam-5899	213	17	.	.	PUNCT
ejpam-5899	214	1	finally	finally	ADV
ejpam-5899	214	2	,	,	PUNCT
ejpam-5899	214	3	take	take	VERB
ejpam-5899	214	4	h∗	h∗	NOUN
ejpam-5899	214	5	=	=	PROPN
ejpam-5899	214	6	s	s	PART
ejpam-5899	214	7	−	−	NOUN
ejpam-5899	214	8	γµ(h	γµ(h	NOUN
ejpam-5899	214	9	)	)	PUNCT
ejpam-5899	214	10	.	.	PUNCT
ejpam-5899	215	1	since	since	SCONJ
ejpam-5899	215	2	h∗	h∗	PROPN
ejpam-5899	215	3	is	be	AUX
ejpam-5899	215	4	µ∗-open	µ∗-open	ADJ
ejpam-5899	215	5	with	with	ADP
ejpam-5899	215	6	s	s	PROPN
ejpam-5899	215	7	∈	∈	PROPN
ejpam-5899	215	8	h∗	h∗	PROPN
ejpam-5899	215	9	and	and	CCONJ
ejpam-5899	215	10	h∗	h∗	PROPN
ejpam-5899	215	11	∩	∩	NOUN
ejpam-5899	215	12	e	e	PROPN
ejpam-5899	215	13	=	=	SYM
ejpam-5899	215	14	ϕ	ϕ	PROPN
ejpam-5899	215	15	,	,	PUNCT
ejpam-5899	215	16	then	then	ADV
ejpam-5899	215	17	s	s	VERB
ejpam-5899	215	18	/∈	/∈	PROPN
ejpam-5899	215	19	γµ(e	γµ(e	PUNCT
ejpam-5899	215	20	)	)	PUNCT
ejpam-5899	215	21	and	and	CCONJ
ejpam-5899	215	22	hence	hence	ADV
ejpam-5899	215	23	e	e	X
ejpam-5899	215	24	is	be	AUX
ejpam-5899	215	25	µ∗-closed	µ∗-close	VERB
ejpam-5899	215	26	.	.	PUNCT
ejpam-5899	216	1	the	the	DET
ejpam-5899	216	2	converse	converse	NOUN
ejpam-5899	216	3	of	of	ADP
ejpam-5899	216	4	theorem	theorem	NOUN
ejpam-5899	216	5	10	10	NUM
ejpam-5899	216	6	is	be	AUX
ejpam-5899	216	7	not	not	PART
ejpam-5899	216	8	true	true	ADJ
ejpam-5899	216	9	in	in	ADP
ejpam-5899	216	10	general	general	ADJ
ejpam-5899	216	11	(	(	PUNCT
ejpam-5899	216	12	see	see	VERB
ejpam-5899	216	13	example	example	NOUN
ejpam-5899	216	14	20.11	20.11	NUM
ejpam-5899	216	15	,	,	PUNCT
ejpam-5899	216	16	page	page	NOUN
ejpam-5899	216	17	148	148	NUM
ejpam-5899	216	18	of	of	ADP
ejpam-5899	216	19	[	[	X
ejpam-5899	216	20	17	17	NUM
ejpam-5899	216	21	]	]	NUM
ejpam-5899	216	22	)	)	PUNCT
ejpam-5899	216	23	.	.	PUNCT
ejpam-5899	217	1	then	then	ADV
ejpam-5899	217	2	(	(	PUNCT
ejpam-5899	217	3	s	s	PROPN
ejpam-5899	217	4	,	,	PUNCT
ejpam-5899	217	5	τ	τ	X
ejpam-5899	217	6	)	)	PUNCT
ejpam-5899	217	7	is	be	AUX
ejpam-5899	217	8	a	a	DET
ejpam-5899	217	9	t2	t2	NOUN
ejpam-5899	217	10	-	-	PUNCT
ejpam-5899	217	11	space	space	NOUN
ejpam-5899	217	12	such	such	ADJ
ejpam-5899	217	13	that	that	SCONJ
ejpam-5899	217	14	(	(	PUNCT
ejpam-5899	217	15	s	s	PROPN
ejpam-5899	217	16	,	,	PUNCT
ejpam-5899	217	17	τ	τ	X
ejpam-5899	217	18	)	)	PUNCT
ejpam-5899	217	19	is	be	AUX
ejpam-5899	217	20	not	not	PART
ejpam-5899	217	21	paracompact	paracompact	ADJ
ejpam-5899	217	22	and	and	CCONJ
ejpam-5899	217	23	s	s	VERB
ejpam-5899	217	24	is	be	AUX
ejpam-5899	217	25	µ∗-closed	µ∗-close	VERB
ejpam-5899	217	26	(	(	PUNCT
ejpam-5899	217	27	µ	µ	X
ejpam-5899	217	28	=	=	SYM
ejpam-5899	217	29	τ	τ	PROPN
ejpam-5899	217	30	)	)	PUNCT
ejpam-5899	217	31	while	while	SCONJ
ejpam-5899	217	32	s	s	VERB
ejpam-5899	217	33	it	it	PRON
ejpam-5899	217	34	is	be	AUX
ejpam-5899	217	35	not	not	PART
ejpam-5899	217	36	α	α	NOUN
ejpam-5899	217	37	-	-	NOUN
ejpam-5899	217	38	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	217	39	.	.	PUNCT
ejpam-5899	218	1	theorem	theorem	VERB
ejpam-5899	218	2	11	11	NUM
ejpam-5899	218	3	.	.	PUNCT
ejpam-5899	219	1	let	let	AUX
ejpam-5899	219	2	(	(	PUNCT
ejpam-5899	219	3	s	s	X
ejpam-5899	219	4	,	,	PUNCT
ejpam-5899	219	5	µ	µ	NOUN
ejpam-5899	219	6	)	)	PUNCT
ejpam-5899	219	7	be	be	AUX
ejpam-5899	219	8	a	a	DET
ejpam-5899	219	9	gts	gts	NOUN
ejpam-5899	219	10	.	.	PUNCT
ejpam-5899	220	1	if	if	SCONJ
ejpam-5899	220	2	{	{	PUNCT
ejpam-5899	220	3	eα	eα	NOUN
ejpam-5899	220	4	:	:	PUNCT
ejpam-5899	220	5	α	α	PROPN
ejpam-5899	220	6	∈	∈	PROPN
ejpam-5899	220	7	∆	∆	X
ejpam-5899	220	8	}	}	PUNCT
ejpam-5899	220	9	is	be	AUX
ejpam-5899	220	10	a	a	DET
ejpam-5899	220	11	gµ-lf(s,µ	gµ-lf(s,µ	PROPN
ejpam-5899	220	12	)	)	PUNCT
ejpam-5899	220	13	collection	collection	NOUN
ejpam-5899	220	14	such	such	ADJ
ejpam-5899	220	15	that	that	SCONJ
ejpam-5899	220	16	eα	eα	NOUN
ejpam-5899	220	17	is	be	AUX
ejpam-5899	220	18	α	α	NOUN
ejpam-5899	220	19	-	-	PUNCT
ejpam-5899	220	20	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	220	21	of	of	ADP
ejpam-5899	220	22	(	(	PUNCT
ejpam-5899	220	23	s	s	PROPN
ejpam-5899	220	24	,	,	PUNCT
ejpam-5899	220	25	µ	µ	NOUN
ejpam-5899	220	26	)	)	PUNCT
ejpam-5899	220	27	for	for	ADP
ejpam-5899	220	28	each	each	DET
ejpam-5899	220	29	α	α	PROPN
ejpam-5899	220	30	∈	∈	PROPN
ejpam-5899	220	31	∆	∆	PROPN
ejpam-5899	220	32	,	,	PUNCT
ejpam-5899	220	33	then	then	ADV
ejpam-5899	220	34	e	e	PROPN
ejpam-5899	220	35	=	=	PUNCT
ejpam-5899	220	36	∪α∈∆eα	∪α∈∆eα	PROPN
ejpam-5899	220	37	is	be	AUX
ejpam-5899	220	38	α	α	NOUN
ejpam-5899	220	39	-	-	PUNCT
ejpam-5899	220	40	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	220	41	of	of	ADP
ejpam-5899	220	42	(	(	PUNCT
ejpam-5899	220	43	s	s	PROPN
ejpam-5899	220	44	,	,	PUNCT
ejpam-5899	220	45	µ	µ	NOUN
ejpam-5899	220	46	)	)	PUNCT
ejpam-5899	220	47	.	.	PUNCT
ejpam-5899	221	1	proof	proof	NOUN
ejpam-5899	221	2	.	.	PUNCT
ejpam-5899	222	1	let	let	VERB
ejpam-5899	222	2	g	g	PRON
ejpam-5899	222	3	be	be	AUX
ejpam-5899	222	4	an	an	DET
ejpam-5899	222	5	(	(	PUNCT
ejpam-5899	222	6	s	s	X
ejpam-5899	222	7	,	,	PUNCT
ejpam-5899	222	8	µ)-cover	µ)-cover	PUNCT
ejpam-5899	222	9	of	of	ADP
ejpam-5899	222	10	e.	e.	PROPN
ejpam-5899	222	11	for	for	ADP
ejpam-5899	222	12	each	each	DET
ejpam-5899	222	13	α	α	PROPN
ejpam-5899	222	14	∈	∈	PROPN
ejpam-5899	222	15	∆	∆	PROPN
ejpam-5899	222	16	,	,	PUNCT
ejpam-5899	222	17	g	g	PROPN
ejpam-5899	222	18	is	be	AUX
ejpam-5899	222	19	an	an	DET
ejpam-5899	222	20	(	(	PUNCT
ejpam-5899	222	21	s	s	X
ejpam-5899	222	22	,	,	PUNCT
ejpam-5899	222	23	µ)-cover	µ)-cover	NOUN
ejpam-5899	222	24	of	of	ADP
ejpam-5899	222	25	eα	eα	NOUN
ejpam-5899	222	26	and	and	CCONJ
ejpam-5899	222	27	hence	hence	ADV
ejpam-5899	222	28	it	it	PRON
ejpam-5899	222	29	has	have	VERB
ejpam-5899	222	30	a	a	DET
ejpam-5899	222	31	gµ-lf(s,µ	gµ-lf(s,µ	PROPN
ejpam-5899	222	32	)	)	PUNCT
ejpam-5899	222	33	(	(	PUNCT
ejpam-5899	222	34	s	s	X
ejpam-5899	222	35	,	,	PUNCT
ejpam-5899	222	36	µ)-refinement	µ)-refinement	PUNCT
ejpam-5899	222	37	,	,	PUNCT
ejpam-5899	222	38	say	say	VERB
ejpam-5899	222	39	hα	hα	ADP
ejpam-5899	222	40	=	=	PUNCT
ejpam-5899	222	41	{	{	PUNCT
ejpam-5899	222	42	hβ	hβ	INTJ
ejpam-5899	222	43	:	:	PUNCT
ejpam-5899	222	44	β	β	X
ejpam-5899	222	45	∈	∈	PROPN
ejpam-5899	222	46	λα	λα	X
ejpam-5899	222	47	}	}	PUNCT
ejpam-5899	222	48	.	.	PUNCT
ejpam-5899	223	1	it	it	PRON
ejpam-5899	223	2	is	be	AUX
ejpam-5899	223	3	clear	clear	ADJ
ejpam-5899	223	4	that	that	SCONJ
ejpam-5899	223	5	the	the	DET
ejpam-5899	223	6	collection	collection	NOUN
ejpam-5899	223	7	h={hβ	h={hβ	NOUN
ejpam-5899	223	8	:	:	PUNCT
ejpam-5899	223	9	β	β	X
ejpam-5899	223	10	∈	∈	PROPN
ejpam-5899	223	11	λα	λα	PROPN
ejpam-5899	223	12	,	,	PUNCT
ejpam-5899	223	13	α	α	PROPN
ejpam-5899	223	14	∈	∈	NOUN
ejpam-5899	223	15	∆	∆	X
ejpam-5899	223	16	}	}	PUNCT
ejpam-5899	223	17	is	be	AUX
ejpam-5899	223	18	an	an	DET
ejpam-5899	223	19	(	(	PUNCT
ejpam-5899	223	20	s	s	NOUN
ejpam-5899	223	21	,	,	PUNCT
ejpam-5899	223	22	µ)-refinement	µ)-refinement	PUNCT
ejpam-5899	223	23	of	of	ADP
ejpam-5899	223	24	g.	g.	PROPN
ejpam-5899	223	25	to	to	PART
ejpam-5899	223	26	show	show	VERB
ejpam-5899	223	27	that	that	SCONJ
ejpam-5899	223	28	h	h	NOUN
ejpam-5899	223	29	is	be	AUX
ejpam-5899	223	30	gµ-lf(s,µ	gµ-lf(s,µ	PROPN
ejpam-5899	223	31	)	)	PUNCT
ejpam-5899	223	32	,	,	PUNCT
ejpam-5899	223	33	let	let	VERB
ejpam-5899	223	34	s	s	PRON
ejpam-5899	223	35	∈	∈	VERB
ejpam-5899	223	36	s.	s.	PROPN
ejpam-5899	223	37	then	then	ADV
ejpam-5899	223	38	there	there	PRON
ejpam-5899	223	39	is	be	VERB
ejpam-5899	223	40	gs	gs	PROPN
ejpam-5899	223	41	∈	∈	PROPN
ejpam-5899	223	42	µ∗(s	µ∗(s	PROPN
ejpam-5899	223	43	)	)	PUNCT
ejpam-5899	223	44	and	and	CCONJ
ejpam-5899	223	45	a	a	DET
ejpam-5899	223	46	finite	finite	NOUN
ejpam-5899	223	47	subset	subset	VERB
ejpam-5899	223	48	∆s	∆s	NOUN
ejpam-5899	223	49	of	of	ADP
ejpam-5899	223	50	∆	∆	PROPN
ejpam-5899	223	51	with	with	ADP
ejpam-5899	223	52	gs	gs	PROPN
ejpam-5899	223	53	∩	∩	NOUN
ejpam-5899	223	54	eα	eα	NOUN
ejpam-5899	223	55	=	=	SYM
ejpam-5899	223	56	ϕ	ϕ	PROPN
ejpam-5899	223	57	for	for	ADP
ejpam-5899	223	58	each	each	DET
ejpam-5899	223	59	α	α	NOUN
ejpam-5899	223	60	∈	∈	PROPN
ejpam-5899	223	61	∆	∆	PROPN
ejpam-5899	223	62	−	−	NOUN
ejpam-5899	223	63	∆s	∆s	PROPN
ejpam-5899	223	64	.	.	PUNCT
ejpam-5899	224	1	now	now	ADV
ejpam-5899	224	2	,	,	PUNCT
ejpam-5899	224	3	for	for	ADP
ejpam-5899	224	4	each	each	DET
ejpam-5899	224	5	α	α	PROPN
ejpam-5899	224	6	∈	∈	PROPN
ejpam-5899	224	7	∆s	∆s	NOUN
ejpam-5899	224	8	,	,	PUNCT
ejpam-5899	224	9	there	there	PRON
ejpam-5899	224	10	is	be	VERB
ejpam-5899	224	11	wα(s	wα(s	X
ejpam-5899	224	12	)	)	PUNCT
ejpam-5899	225	1	∈	∈	PROPN
ejpam-5899	225	2	µ∗(s	µ∗(s	PROPN
ejpam-5899	225	3	)	)	PUNCT
ejpam-5899	225	4	that	that	PRON
ejpam-5899	225	5	intersects	intersect	VERB
ejpam-5899	225	6	at	at	ADV
ejpam-5899	225	7	most	most	ADV
ejpam-5899	225	8	finitely	finitely	ADV
ejpam-5899	225	9	many	many	ADJ
ejpam-5899	225	10	members	member	NOUN
ejpam-5899	225	11	of	of	ADP
ejpam-5899	225	12	hα	hα	PROPN
ejpam-5899	225	13	.	.	PUNCT
ejpam-5899	225	14	define	define	VERB
ejpam-5899	225	15	ts	ts	ADP
ejpam-5899	225	16	=	=	PUNCT
ejpam-5899	225	17	gs	gs	PROPN
ejpam-5899	225	18	∩	∩	NOUN
ejpam-5899	225	19	(	(	PUNCT
ejpam-5899	225	20	∩α∈∆swα(s	∩α∈∆swα(s	PUNCT
ejpam-5899	225	21	)	)	PUNCT
ejpam-5899	225	22	)	)	PUNCT
ejpam-5899	225	23	.	.	PUNCT
ejpam-5899	226	1	then	then	ADV
ejpam-5899	226	2	ts	ts	ADP
ejpam-5899	226	3	∈	∈	PROPN
ejpam-5899	226	4	µ∗(s	µ∗(s	PROPN
ejpam-5899	226	5	)	)	PUNCT
ejpam-5899	226	6	which	which	PRON
ejpam-5899	226	7	intersects	intersect	VERB
ejpam-5899	226	8	at	at	ADP
ejpam-5899	226	9	most	most	ADV
ejpam-5899	226	10	finitely	finitely	ADV
ejpam-5899	226	11	many	many	ADJ
ejpam-5899	226	12	members	member	NOUN
ejpam-5899	226	13	of	of	ADP
ejpam-5899	226	14	h.	h.	PROPN
ejpam-5899	226	15	definition	definition	NOUN
ejpam-5899	226	16	7	7	NUM
ejpam-5899	226	17	.	.	PUNCT
ejpam-5899	227	1	let	let	AUX
ejpam-5899	227	2	(	(	PUNCT
ejpam-5899	227	3	s	s	X
ejpam-5899	227	4	,	,	PUNCT
ejpam-5899	227	5	µ	µ	NOUN
ejpam-5899	227	6	)	)	PUNCT
ejpam-5899	227	7	be	be	AUX
ejpam-5899	227	8	a	a	DET
ejpam-5899	227	9	gts	gts	NOUN
ejpam-5899	227	10	.	.	PUNCT
ejpam-5899	228	1	if	if	SCONJ
ejpam-5899	228	2	each	each	DET
ejpam-5899	228	3	µ∗-open	µ∗-open	ADJ
ejpam-5899	228	4	cover	cover	NOUN
ejpam-5899	228	5	of	of	ADP
ejpam-5899	228	6	s	s	PROPN
ejpam-5899	228	7	has	have	VERB
ejpam-5899	228	8	a	a	DET
ejpam-5899	228	9	finite	finite	ADJ
ejpam-5899	228	10	subcover	subcover	NOUN
ejpam-5899	228	11	,	,	PUNCT
ejpam-5899	228	12	then	then	ADV
ejpam-5899	228	13	(	(	PUNCT
ejpam-5899	228	14	s	s	X
ejpam-5899	228	15	,	,	PUNCT
ejpam-5899	228	16	µ	µ	NOUN
ejpam-5899	228	17	)	)	PUNCT
ejpam-5899	228	18	is	be	AUX
ejpam-5899	228	19	called	call	VERB
ejpam-5899	228	20	µ∗-compact	µ∗-compact	PROPN
ejpam-5899	228	21	.	.	PUNCT
ejpam-5899	229	1	h.	h.	PROPN
ejpam-5899	229	2	h.	h.	PROPN
ejpam-5899	229	3	al	al	PROPN
ejpam-5899	229	4	-	-	PUNCT
ejpam-5899	229	5	jarrah	jarrah	PROPN
ejpam-5899	229	6	et	et	PROPN
ejpam-5899	229	7	al	al	PROPN
ejpam-5899	229	8	.	.	PUNCT
ejpam-5899	229	9	/	/	SYM
ejpam-5899	229	10	eur	eur	PROPN
ejpam-5899	229	11	.	.	PUNCT
ejpam-5899	230	1	j.	j.	PROPN
ejpam-5899	230	2	pure	pure	PROPN
ejpam-5899	230	3	appl	appl	PROPN
ejpam-5899	230	4	.	.	PROPN
ejpam-5899	230	5	math	math	PROPN
ejpam-5899	230	6	,	,	PUNCT
ejpam-5899	230	7	18	18	NUM
ejpam-5899	230	8	(	(	PUNCT
ejpam-5899	230	9	2	2	NUM
ejpam-5899	230	10	)	)	PUNCT
ejpam-5899	230	11	(	(	PUNCT
ejpam-5899	230	12	2025	2025	NUM
ejpam-5899	230	13	)	)	PUNCT
ejpam-5899	230	14	,	,	PUNCT
ejpam-5899	230	15	5899	5899	NUM
ejpam-5899	230	16	8	8	NUM
ejpam-5899	230	17	of	of	ADP
ejpam-5899	230	18	11	11	NUM
ejpam-5899	230	19	lemma	lemma	PROPN
ejpam-5899	230	20	2	2	NUM
ejpam-5899	230	21	.	.	PUNCT
ejpam-5899	231	1	let	let	VERB
ejpam-5899	231	2	ψ	ψ	X
ejpam-5899	231	3	:	:	PUNCT
ejpam-5899	231	4	(	(	PUNCT
ejpam-5899	231	5	s1	s1	NOUN
ejpam-5899	231	6	,	,	PUNCT
ejpam-5899	231	7	µ1	µ1	PROPN
ejpam-5899	231	8	)	)	PUNCT
ejpam-5899	231	9	→	→	SYM
ejpam-5899	231	10	(	(	PUNCT
ejpam-5899	231	11	s2	s2	PROPN
ejpam-5899	231	12	,	,	PUNCT
ejpam-5899	231	13	µ2	µ2	PROPN
ejpam-5899	231	14	)	)	PUNCT
ejpam-5899	231	15	be	be	VERB
ejpam-5899	231	16	a	a	DET
ejpam-5899	231	17	(	(	PUNCT
ejpam-5899	231	18	µ1	µ1	ADJ
ejpam-5899	231	19	,	,	PUNCT
ejpam-5899	231	20	µ2)-continuous	µ2)-continuous	ADJ
ejpam-5899	231	21	function	function	NOUN
ejpam-5899	231	22	.	.	PUNCT
ejpam-5899	232	1	if	if	SCONJ
ejpam-5899	232	2	g	g	NOUN
ejpam-5899	232	3	=	=	PUNCT
ejpam-5899	232	4	{	{	PUNCT
ejpam-5899	232	5	gα	gα	NOUN
ejpam-5899	232	6	:	:	PUNCT
ejpam-5899	232	7	α	α	PROPN
ejpam-5899	232	8	∈	∈	PROPN
ejpam-5899	232	9	∆	∆	X
ejpam-5899	232	10	}	}	PUNCT
ejpam-5899	232	11	is	be	AUX
ejpam-5899	232	12	a	a	DET
ejpam-5899	232	13	gµ−lf(s2,µ2	gµ−lf(s2,µ2	NOUN
ejpam-5899	232	14	)	)	PUNCT
ejpam-5899	232	15	,	,	PUNCT
ejpam-5899	232	16	then	then	ADV
ejpam-5899	232	17	ψ	ψ	X
ejpam-5899	232	18	−1(g	−1(g	NOUN
ejpam-5899	232	19	)	)	PUNCT
ejpam-5899	232	20	=	=	SYM
ejpam-5899	232	21	{	{	PUNCT
ejpam-5899	232	22	ψ−1(gα	ψ−1(gα	NOUN
ejpam-5899	232	23	)	)	PUNCT
ejpam-5899	232	24	:	:	PUNCT
ejpam-5899	233	1	α	α	PROPN
ejpam-5899	233	2	∈	∈	PROPN
ejpam-5899	233	3	∆	∆	X
ejpam-5899	233	4	}	}	PUNCT
ejpam-5899	233	5	is	be	AUX
ejpam-5899	233	6	gµ−lf(s1,µ1	gµ−lf(s1,µ1	NOUN
ejpam-5899	233	7	)	)	PUNCT
ejpam-5899	233	8	.	.	PUNCT
ejpam-5899	234	1	proof	proof	NOUN
ejpam-5899	234	2	.	.	PUNCT
ejpam-5899	235	1	let	let	VERB
ejpam-5899	235	2	s	s	PRON
ejpam-5899	235	3	∈	∈	PROPN
ejpam-5899	235	4	s1	s1	NOUN
ejpam-5899	235	5	with	with	ADP
ejpam-5899	235	6	e	e	X
ejpam-5899	235	7	=	=	PUNCT
ejpam-5899	235	8	ψ(s	ψ(s	PROPN
ejpam-5899	235	9	)	)	PUNCT
ejpam-5899	235	10	.	.	PUNCT
ejpam-5899	236	1	then	then	ADV
ejpam-5899	236	2	there	there	PRON
ejpam-5899	236	3	ish	ish	VERB
ejpam-5899	236	4	∈	∈	PROPN
ejpam-5899	236	5	µ∗2(e	µ∗2(e	PROPN
ejpam-5899	236	6	)	)	PUNCT
ejpam-5899	236	7	with	with	ADP
ejpam-5899	236	8	the	the	DET
ejpam-5899	236	9	set	set	NOUN
ejpam-5899	236	10	{	{	PUNCT
ejpam-5899	236	11	η	η	NOUN
ejpam-5899	236	12	:	:	PUNCT
ejpam-5899	236	13	h∩gη	h∩gη	PROPN
ejpam-5899	236	14	̸=	̸=	PROPN
ejpam-5899	236	15	ϕ	ϕ	PROPN
ejpam-5899	236	16	}	}	PUNCT
ejpam-5899	236	17	is	be	AUX
ejpam-5899	236	18	finite	finite	ADJ
ejpam-5899	236	19	.	.	PUNCT
ejpam-5899	237	1	since	since	SCONJ
ejpam-5899	237	2	h	h	NOUN
ejpam-5899	237	3	=	=	PROPN
ejpam-5899	237	4	∩n	∩n	PROPN
ejpam-5899	237	5	i=1wi	i=1wi	PROPN
ejpam-5899	237	6	where	where	SCONJ
ejpam-5899	237	7	wi	wi	PROPN
ejpam-5899	237	8	∈	∈	PROPN
ejpam-5899	237	9	µ2(e	µ2(e	NOUN
ejpam-5899	237	10	)	)	PUNCT
ejpam-5899	237	11	,	,	PUNCT
ejpam-5899	237	12	then	then	ADV
ejpam-5899	237	13	ψ−1(h	ψ−1(h	PROPN
ejpam-5899	237	14	)	)	PUNCT
ejpam-5899	237	15	=	=	SYM
ejpam-5899	237	16	∩n	∩n	NOUN
ejpam-5899	237	17	i=1ψ	i=1ψ	NOUN
ejpam-5899	237	18	−1(wi	−1(wi	NOUN
ejpam-5899	237	19	)	)	PUNCT
ejpam-5899	237	20	where	where	SCONJ
ejpam-5899	237	21	ψ−1(wi	ψ−1(wi	NOUN
ejpam-5899	237	22	)	)	PUNCT
ejpam-5899	237	23	∈	∈	PROPN
ejpam-5899	237	24	µ1(s	µ1(s	PROPN
ejpam-5899	237	25	)	)	PUNCT
ejpam-5899	237	26	.	.	PUNCT
ejpam-5899	238	1	therefore	therefore	ADV
ejpam-5899	238	2	,	,	PUNCT
ejpam-5899	238	3	ψ	ψ	X
ejpam-5899	238	4	−1(h	−1(h	NOUN
ejpam-5899	238	5	)	)	PUNCT
ejpam-5899	238	6	∈	∈	PROPN
ejpam-5899	238	7	µ∗1(s	µ∗1(s	PROPN
ejpam-5899	238	8	)	)	PUNCT
ejpam-5899	238	9	with	with	ADP
ejpam-5899	238	10	the	the	DET
ejpam-5899	238	11	set	set	NOUN
ejpam-5899	238	12	{	{	PUNCT
ejpam-5899	238	13	η	η	NOUN
ejpam-5899	238	14	:	:	PUNCT
ejpam-5899	238	15	ψ−1(h)∩ψ−1(gη	ψ−1(h)∩ψ−1(gη	X
ejpam-5899	238	16	)	)	PUNCT
ejpam-5899	238	17	̸=	̸=	PROPN
ejpam-5899	238	18	ϕ	ϕ	PROPN
ejpam-5899	238	19	}	}	PUNCT
ejpam-5899	238	20	is	be	AUX
ejpam-5899	238	21	finite	finite	ADJ
ejpam-5899	238	22	.	.	PUNCT
ejpam-5899	239	1	hence	hence	ADV
ejpam-5899	239	2	ψ−1(g	ψ−1(g	PROPN
ejpam-5899	239	3	)	)	PUNCT
ejpam-5899	239	4	is	be	AUX
ejpam-5899	239	5	gµ−lf(s1,µ1	gµ−lf(s1,µ1	NOUN
ejpam-5899	239	6	)	)	PUNCT
ejpam-5899	239	7	.	.	PUNCT
ejpam-5899	240	1	lemma	lemma	PROPN
ejpam-5899	240	2	3	3	X
ejpam-5899	240	3	.	.	PUNCT
ejpam-5899	241	1	let	let	VERB
ejpam-5899	241	2	ψ	ψ	X
ejpam-5899	241	3	:	:	PUNCT
ejpam-5899	241	4	(	(	PUNCT
ejpam-5899	241	5	s1	s1	NOUN
ejpam-5899	241	6	,	,	PUNCT
ejpam-5899	241	7	µ1	µ1	PROPN
ejpam-5899	241	8	)	)	PUNCT
ejpam-5899	241	9	→	→	SYM
ejpam-5899	241	10	(	(	PUNCT
ejpam-5899	241	11	s2	s2	PROPN
ejpam-5899	241	12	,	,	PUNCT
ejpam-5899	241	13	µ2	µ2	PROPN
ejpam-5899	241	14	)	)	PUNCT
ejpam-5899	241	15	be	be	VERB
ejpam-5899	241	16	a	a	DET
ejpam-5899	241	17	surjection	surjection	NOUN
ejpam-5899	241	18	(	(	PUNCT
ejpam-5899	241	19	µ1	µ1	PROPN
ejpam-5899	241	20	,	,	PUNCT
ejpam-5899	241	21	µ2)-closed	µ2)-close	VERB
ejpam-5899	241	22	function	function	NOUN
ejpam-5899	241	23	with	with	ADP
ejpam-5899	241	24	ψ−1(e	ψ−1(e	PROPN
ejpam-5899	241	25	)	)	PUNCT
ejpam-5899	241	26	is	be	AUX
ejpam-5899	241	27	µ∗1	µ∗1	NOUN
ejpam-5899	241	28	-	-	ADJ
ejpam-5899	241	29	compact	compact	ADJ
ejpam-5899	241	30	for	for	ADP
ejpam-5899	241	31	each	each	DET
ejpam-5899	241	32	e	e	PROPN
ejpam-5899	241	33	∈	∈	PROPN
ejpam-5899	241	34	s2	s2	PROPN
ejpam-5899	241	35	.	.	PUNCT
ejpam-5899	242	1	if	if	SCONJ
ejpam-5899	242	2	g	g	NOUN
ejpam-5899	242	3	=	=	PUNCT
ejpam-5899	242	4	{	{	PUNCT
ejpam-5899	242	5	gα	gα	NOUN
ejpam-5899	242	6	:	:	PUNCT
ejpam-5899	242	7	α	α	PROPN
ejpam-5899	242	8	∈	∈	PROPN
ejpam-5899	242	9	∆	∆	X
ejpam-5899	242	10	}	}	PUNCT
ejpam-5899	242	11	is	be	AUX
ejpam-5899	242	12	a	a	DET
ejpam-5899	242	13	gµ−lf(s1,µ1	gµ−lf(s1,µ1	NOUN
ejpam-5899	242	14	)	)	PUNCT
ejpam-5899	242	15	,	,	PUNCT
ejpam-5899	242	16	then	then	ADV
ejpam-5899	242	17	ψ(g	ψ(g	VERB
ejpam-5899	242	18	)	)	PUNCT
ejpam-5899	242	19	=	=	PUNCT
ejpam-5899	242	20	{	{	PUNCT
ejpam-5899	242	21	ψ(gα	ψ(gα	PROPN
ejpam-5899	242	22	)	)	PUNCT
ejpam-5899	242	23	:	:	PUNCT
ejpam-5899	242	24	α	α	PROPN
ejpam-5899	242	25	∈	∈	PROPN
ejpam-5899	242	26	∆	∆	X
ejpam-5899	242	27	}	}	PUNCT
ejpam-5899	242	28	is	be	AUX
ejpam-5899	242	29	gµ−lf(s2,µ2	gµ−lf(s2,µ2	PROPN
ejpam-5899	242	30	)	)	PUNCT
ejpam-5899	242	31	.	.	PUNCT
ejpam-5899	243	1	proof	proof	NOUN
ejpam-5899	243	2	.	.	PUNCT
ejpam-5899	244	1	let	let	VERB
ejpam-5899	244	2	e	e	PROPN
ejpam-5899	244	3	∈	∈	PROPN
ejpam-5899	244	4	s2	s2	PROPN
ejpam-5899	244	5	.	.	PUNCT
ejpam-5899	245	1	for	for	ADP
ejpam-5899	245	2	each	each	DET
ejpam-5899	245	3	s	s	PROPN
ejpam-5899	245	4	∈	∈	PROPN
ejpam-5899	245	5	ψ−1(e	ψ−1(e	PROPN
ejpam-5899	245	6	)	)	PUNCT
ejpam-5899	245	7	choose	choose	VERB
ejpam-5899	245	8	hs	hs	PROPN
ejpam-5899	245	9	∈	∈	PROPN
ejpam-5899	245	10	µ∗1(s	µ∗1(s	PROPN
ejpam-5899	245	11	)	)	PUNCT
ejpam-5899	245	12	with	with	ADP
ejpam-5899	245	13	the	the	DET
ejpam-5899	245	14	set	set	NOUN
ejpam-5899	245	15	{	{	PUNCT
ejpam-5899	245	16	η	η	PROPN
ejpam-5899	245	17	:	:	PUNCT
ejpam-5899	245	18	hs	hs	PROPN
ejpam-5899	245	19	∩gη	∩gη	PROPN
ejpam-5899	245	20	̸=	̸=	PROPN
ejpam-5899	245	21	ϕ	ϕ	PROPN
ejpam-5899	245	22	}	}	PUNCT
ejpam-5899	245	23	is	be	AUX
ejpam-5899	245	24	finite	finite	ADJ
ejpam-5899	245	25	.	.	PUNCT
ejpam-5899	246	1	therefore	therefore	ADV
ejpam-5899	246	2	,	,	PUNCT
ejpam-5899	246	3	the	the	DET
ejpam-5899	246	4	collection	collection	NOUN
ejpam-5899	246	5	{	{	PUNCT
ejpam-5899	246	6	hs	hs	X
ejpam-5899	246	7	:	:	PUNCT
ejpam-5899	246	8	s	s	PART
ejpam-5899	246	9	∈	∈	PROPN
ejpam-5899	246	10	ψ−1(e	ψ−1(e	PROPN
ejpam-5899	246	11	)	)	PUNCT
ejpam-5899	246	12	}	}	PUNCT
ejpam-5899	246	13	is	be	AUX
ejpam-5899	246	14	a	a	DET
ejpam-5899	246	15	µ∗1	µ∗1	ADJ
ejpam-5899	246	16	-	-	PUNCT
ejpam-5899	246	17	open	open	ADJ
ejpam-5899	246	18	cover	cover	NOUN
ejpam-5899	246	19	of	of	ADP
ejpam-5899	246	20	the	the	DET
ejpam-5899	246	21	µ∗1compact	µ∗1compact	PUNCT
ejpam-5899	246	22	subset	subset	NOUN
ejpam-5899	246	23	ψ−1(e	ψ−1(e	PROPN
ejpam-5899	246	24	)	)	PUNCT
ejpam-5899	246	25	and	and	CCONJ
ejpam-5899	246	26	so	so	ADV
ejpam-5899	246	27	there	there	PRON
ejpam-5899	246	28	is	be	VERB
ejpam-5899	246	29	a	a	DET
ejpam-5899	246	30	finite	finite	ADJ
ejpam-5899	246	31	number	number	NOUN
ejpam-5899	246	32	of	of	ADP
ejpam-5899	246	33	points	point	NOUN
ejpam-5899	246	34	s1	s1	NOUN
ejpam-5899	246	35	,	,	PUNCT
ejpam-5899	246	36	s2	s2	PROPN
ejpam-5899	246	37	,	,	PUNCT
ejpam-5899	246	38	...	...	PUNCT
ejpam-5899	246	39	sn	sn	PROPN
ejpam-5899	246	40	in	in	ADP
ejpam-5899	246	41	ψ−1(e	ψ−1(e	PROPN
ejpam-5899	246	42	)	)	PUNCT
ejpam-5899	246	43	with	with	ADP
ejpam-5899	246	44	ψ−1(e	ψ−1(e	PROPN
ejpam-5899	246	45	)	)	PUNCT
ejpam-5899	246	46	⊆	⊆	NUM
ejpam-5899	246	47	∪n	∪n	PROPN
ejpam-5899	246	48	i=1hsi	i=1hsi	NOUN
ejpam-5899	246	49	.	.	PUNCT
ejpam-5899	247	1	note	note	VERB
ejpam-5899	247	2	that	that	SCONJ
ejpam-5899	247	3	,	,	PUNCT
ejpam-5899	247	4	for	for	ADP
ejpam-5899	247	5	each	each	DET
ejpam-5899	247	6	1	1	NUM
ejpam-5899	247	7	≤	≤	NUM
ejpam-5899	247	8	i	i	PRON
ejpam-5899	247	9	≤	≤	PROPN
ejpam-5899	247	10	n	n	CCONJ
ejpam-5899	247	11	,	,	PUNCT
ejpam-5899	247	12	hsi	hsi	PROPN
ejpam-5899	247	13	is	be	AUX
ejpam-5899	247	14	a	a	DET
ejpam-5899	247	15	finite	finite	ADJ
ejpam-5899	247	16	intersection	intersection	NOUN
ejpam-5899	247	17	of	of	ADP
ejpam-5899	247	18	members	member	NOUN
ejpam-5899	247	19	of	of	ADP
ejpam-5899	247	20	µ1(si	µ1(si	PROPN
ejpam-5899	247	21	)	)	PUNCT
ejpam-5899	247	22	.	.	PUNCT
ejpam-5899	248	1	therefore	therefore	ADV
ejpam-5899	248	2	,	,	PUNCT
ejpam-5899	248	3	∪n	∪n	PROPN
ejpam-5899	248	4	i=1hsi	i=1hsi	NOUN
ejpam-5899	248	5	=	=	PUNCT
ejpam-5899	249	1	∩m	∩m	PROPN
ejpam-5899	249	2	j=1kj	j=1kj	PRON
ejpam-5899	249	3	where	where	SCONJ
ejpam-5899	249	4	kj	kj	PROPN
ejpam-5899	249	5	is	be	AUX
ejpam-5899	249	6	a	a	DET
ejpam-5899	249	7	finite	finite	ADJ
ejpam-5899	249	8	union	union	NOUN
ejpam-5899	249	9	of	of	ADP
ejpam-5899	249	10	µ1	µ1	NOUN
ejpam-5899	249	11	-	-	PUNCT
ejpam-5899	249	12	open	open	ADJ
ejpam-5899	249	13	sets	set	NOUN
ejpam-5899	250	1	and	and	CCONJ
ejpam-5899	250	2	so	so	ADV
ejpam-5899	250	3	kj	kj	PROPN
ejpam-5899	250	4	is	be	AUX
ejpam-5899	250	5	µ1	µ1	NOUN
ejpam-5899	250	6	-	-	PUNCT
ejpam-5899	250	7	open	open	ADJ
ejpam-5899	250	8	for	for	ADP
ejpam-5899	250	9	each	each	DET
ejpam-5899	250	10	1	1	NUM
ejpam-5899	250	11	≤	≤	NUM
ejpam-5899	250	12	j	j	PROPN
ejpam-5899	250	13	≤	≤	PROPN
ejpam-5899	250	14	m.	m.	NOUN
ejpam-5899	250	15	by	by	ADP
ejpam-5899	250	16	proposition	proposition	NOUN
ejpam-5899	250	17	1	1	NUM
ejpam-5899	250	18	,	,	PUNCT
ejpam-5899	250	19	there	there	PRON
ejpam-5899	250	20	is	be	VERB
ejpam-5899	250	21	we(j	we(j	NOUN
ejpam-5899	250	22	)	)	PUNCT
ejpam-5899	250	23	∈	∈	NOUN
ejpam-5899	250	24	µ2(e	µ2(e	NOUN
ejpam-5899	250	25	)	)	PUNCT
ejpam-5899	250	26	with	with	ADP
ejpam-5899	250	27	ψ−1(we(j	ψ−1(we(j	NOUN
ejpam-5899	250	28	)	)	PUNCT
ejpam-5899	250	29	)	)	PUNCT
ejpam-5899	251	1	⊆	⊆	NUM
ejpam-5899	251	2	kj	kj	NOUN
ejpam-5899	251	3	.	.	PUNCT
ejpam-5899	252	1	put	put	VERB
ejpam-5899	252	2	w	w	NOUN
ejpam-5899	252	3	=	=	NOUN
ejpam-5899	252	4	m	m	NOUN
ejpam-5899	252	5	∩	∩	ADJ
ejpam-5899	252	6	j=1	j=1	NOUN
ejpam-5899	252	7	we(j	we(j	X
ejpam-5899	252	8	)	)	PUNCT
ejpam-5899	252	9	.	.	PUNCT
ejpam-5899	253	1	then	then	ADV
ejpam-5899	253	2	w	w	PROPN
ejpam-5899	253	3	∈	∈	PROPN
ejpam-5899	253	4	µ∗2(e	µ∗2(e	PROPN
ejpam-5899	253	5	)	)	PUNCT
ejpam-5899	253	6	with	with	ADP
ejpam-5899	253	7	the	the	DET
ejpam-5899	253	8	set	set	NOUN
ejpam-5899	253	9	{	{	PUNCT
ejpam-5899	253	10	η	η	NOUN
ejpam-5899	253	11	:	:	PUNCT
ejpam-5899	253	12	w	w	NOUN
ejpam-5899	253	13	∩ψ(gη	∩ψ(gη	NOUN
ejpam-5899	253	14	)	)	PUNCT
ejpam-5899	253	15	̸=	̸=	PROPN
ejpam-5899	253	16	ϕ	ϕ	PROPN
ejpam-5899	253	17	}	}	PUNCT
ejpam-5899	253	18	is	be	AUX
ejpam-5899	253	19	finite	finite	ADJ
ejpam-5899	253	20	.	.	PUNCT
ejpam-5899	254	1	since	since	SCONJ
ejpam-5899	254	2	if	if	SCONJ
ejpam-5899	254	3	t	t	PROPN
ejpam-5899	254	4	∈	∈	PROPN
ejpam-5899	254	5	w	w	PROPN
ejpam-5899	254	6	∩	∩	PROPN
ejpam-5899	254	7	ψ(gα	ψ(gα	PROPN
ejpam-5899	254	8	)	)	PUNCT
ejpam-5899	254	9	then	then	ADV
ejpam-5899	254	10	there	there	PRON
ejpam-5899	254	11	is	be	VERB
ejpam-5899	254	12	r	r	NOUN
ejpam-5899	254	13	∈	∈	NOUN
ejpam-5899	254	14	s1	s1	NOUN
ejpam-5899	254	15	with	with	ADP
ejpam-5899	254	16	r	r	PROPN
ejpam-5899	254	17	∈	∈	PROPN
ejpam-5899	254	18	ψ−1(t	ψ−1(t	PROPN
ejpam-5899	254	19	)	)	PUNCT
ejpam-5899	254	20	⊆	⊆	NUM
ejpam-5899	254	21	ψ−1(w	ψ−1(w	NOUN
ejpam-5899	254	22	)	)	PUNCT
ejpam-5899	255	1	=	=	PUNCT
ejpam-5899	256	1	∩m	∩m	PROPN
ejpam-5899	256	2	j=1ψ	j=1ψ	PROPN
ejpam-5899	256	3	−1(we(j	−1(we(j	PROPN
ejpam-5899	256	4	)	)	PUNCT
ejpam-5899	256	5	)	)	PUNCT
ejpam-5899	257	1	⊆	⊆	NUM
ejpam-5899	257	2	∩m	∩m	NOUN
ejpam-5899	257	3	j=1kj	j=1kj	X
ejpam-5899	258	1	=	=	SYM
ejpam-5899	259	1	ks	k	NOUN
ejpam-5899	259	2	,	,	PUNCT
ejpam-5899	259	3	this	this	PRON
ejpam-5899	259	4	means	mean	VERB
ejpam-5899	259	5	hsi	hsi	PROPN
ejpam-5899	259	6	∩gα	∩gα	NOUN
ejpam-5899	259	7	̸=	̸=	PROPN
ejpam-5899	259	8	ϕ	ϕ	NOUN
ejpam-5899	259	9	for	for	ADP
ejpam-5899	259	10	some	some	DET
ejpam-5899	259	11	i.	i.	NOUN
ejpam-5899	259	12	theorem	theorem	NOUN
ejpam-5899	259	13	12	12	NUM
ejpam-5899	259	14	.	.	PUNCT
ejpam-5899	260	1	let	let	VERB
ejpam-5899	260	2	ψ	ψ	X
ejpam-5899	260	3	:	:	PUNCT
ejpam-5899	260	4	(	(	PUNCT
ejpam-5899	260	5	s1	s1	NOUN
ejpam-5899	260	6	,	,	PUNCT
ejpam-5899	260	7	µ1	µ1	PROPN
ejpam-5899	260	8	)	)	PUNCT
ejpam-5899	260	9	→	→	SYM
ejpam-5899	260	10	(	(	PUNCT
ejpam-5899	260	11	s2	s2	PROPN
ejpam-5899	260	12	,	,	PUNCT
ejpam-5899	260	13	µ2	µ2	PROPN
ejpam-5899	260	14	)	)	PUNCT
ejpam-5899	260	15	be	be	VERB
ejpam-5899	260	16	a	a	DET
ejpam-5899	260	17	(	(	PUNCT
ejpam-5899	260	18	µ1	µ1	ADJ
ejpam-5899	260	19	,	,	PUNCT
ejpam-5899	260	20	µ2)-continuous	µ2)-continuous	ADJ
ejpam-5899	260	21	mapping	mapping	NOUN
ejpam-5899	260	22	,	,	PUNCT
ejpam-5899	260	23	(	(	PUNCT
ejpam-5899	260	24	µ1	µ1	PROPN
ejpam-5899	260	25	,	,	PUNCT
ejpam-5899	260	26	µ2)open	µ2)open	ADJ
ejpam-5899	260	27	and	and	CCONJ
ejpam-5899	260	28	(	(	PUNCT
ejpam-5899	260	29	µ1	µ1	PROPN
ejpam-5899	260	30	,	,	PUNCT
ejpam-5899	260	31	µ2)-closed	µ2)-close	VERB
ejpam-5899	260	32	surjective	surjective	ADJ
ejpam-5899	260	33	with	with	ADP
ejpam-5899	260	34	ψ−1(e	ψ−1(e	PROPN
ejpam-5899	260	35	)	)	PUNCT
ejpam-5899	260	36	is	be	AUX
ejpam-5899	260	37	µ∗1	µ∗1	NOUN
ejpam-5899	260	38	-	-	ADJ
ejpam-5899	260	39	compact	compact	ADJ
ejpam-5899	260	40	for	for	ADP
ejpam-5899	260	41	each	each	DET
ejpam-5899	260	42	e	e	PROPN
ejpam-5899	260	43	∈	∈	PROPN
ejpam-5899	260	44	s2	s2	PROPN
ejpam-5899	260	45	.	.	PUNCT
ejpam-5899	261	1	if	if	SCONJ
ejpam-5899	261	2	e	e	PROPN
ejpam-5899	261	3	is	be	AUX
ejpam-5899	261	4	α	α	NOUN
ejpam-5899	261	5	-	-	NOUN
ejpam-5899	261	6	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	261	7	in	in	ADP
ejpam-5899	261	8	(	(	PUNCT
ejpam-5899	261	9	s1	s1	NOUN
ejpam-5899	261	10	,	,	PUNCT
ejpam-5899	261	11	µ1	µ1	PROPN
ejpam-5899	261	12	)	)	PUNCT
ejpam-5899	261	13	,	,	PUNCT
ejpam-5899	261	14	then	then	ADV
ejpam-5899	261	15	ψ(e	ψ(e	PROPN
ejpam-5899	261	16	)	)	PUNCT
ejpam-5899	261	17	is	be	AUX
ejpam-5899	261	18	α	α	NOUN
ejpam-5899	261	19	-	-	PUNCT
ejpam-5899	261	20	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	261	21	in	in	ADP
ejpam-5899	261	22	(	(	PUNCT
ejpam-5899	261	23	s2	s2	PROPN
ejpam-5899	261	24	,	,	PUNCT
ejpam-5899	261	25	µ2	µ2	PROPN
ejpam-5899	261	26	)	)	PUNCT
ejpam-5899	261	27	.	.	PUNCT
ejpam-5899	262	1	proof	proof	NOUN
ejpam-5899	262	2	.	.	PUNCT
ejpam-5899	263	1	let	let	VERB
ejpam-5899	263	2	h	h	NOUN
ejpam-5899	263	3	=	=	PRON
ejpam-5899	263	4	{	{	PUNCT
ejpam-5899	263	5	hα	hα	X
ejpam-5899	263	6	:	:	PUNCT
ejpam-5899	263	7	α	α	PROPN
ejpam-5899	263	8	∈	∈	PROPN
ejpam-5899	263	9	∆	∆	PROPN
ejpam-5899	263	10	}	}	PUNCT
ejpam-5899	263	11	be	be	AUX
ejpam-5899	263	12	(	(	PUNCT
ejpam-5899	263	13	s2	s2	PROPN
ejpam-5899	263	14	,	,	PUNCT
ejpam-5899	263	15	µ2)-cover	µ2)-cover	PROPN
ejpam-5899	263	16	of	of	ADP
ejpam-5899	263	17	ψ(e	ψ(e	PROPN
ejpam-5899	263	18	)	)	PUNCT
ejpam-5899	263	19	.	.	PUNCT
ejpam-5899	264	1	since	since	SCONJ
ejpam-5899	264	2	ψ	ψ	NOUN
ejpam-5899	264	3	is	be	AUX
ejpam-5899	264	4	a	a	DET
ejpam-5899	264	5	(	(	PUNCT
ejpam-5899	264	6	µ1	µ1	PROPN
ejpam-5899	264	7	,	,	PUNCT
ejpam-5899	264	8	µ2)continuous	µ2)continuous	ADJ
ejpam-5899	264	9	mapping	mapping	NOUN
ejpam-5899	264	10	,	,	PUNCT
ejpam-5899	264	11	then	then	ADV
ejpam-5899	264	12	the	the	DET
ejpam-5899	264	13	collection	collection	NOUN
ejpam-5899	264	14	g	g	NOUN
ejpam-5899	264	15	=	=	PUNCT
ejpam-5899	264	16	{	{	PUNCT
ejpam-5899	264	17	ψ−1(hα	ψ−1(hα	PROPN
ejpam-5899	264	18	)	)	PUNCT
ejpam-5899	264	19	:	:	PUNCT
ejpam-5899	264	20	α	α	PROPN
ejpam-5899	264	21	∈	∈	PROPN
ejpam-5899	264	22	∆	∆	X
ejpam-5899	264	23	}	}	PUNCT
ejpam-5899	264	24	is	be	AUX
ejpam-5899	264	25	an	an	DET
ejpam-5899	264	26	(	(	PUNCT
ejpam-5899	264	27	s1	s1	NOUN
ejpam-5899	264	28	,	,	PUNCT
ejpam-5899	264	29	µ1)-cover	µ1)-cover	PROPN
ejpam-5899	264	30	of	of	ADP
ejpam-5899	264	31	e	e	NOUN
ejpam-5899	264	32	and	and	CCONJ
ejpam-5899	264	33	so	so	ADV
ejpam-5899	264	34	g	g	PROPN
ejpam-5899	264	35	has	have	VERB
ejpam-5899	264	36	a	a	DET
ejpam-5899	264	37	gµ−lf(s1,µ1	gµ−lf(s1,µ1	NOUN
ejpam-5899	264	38	)	)	PUNCT
ejpam-5899	264	39	(	(	PUNCT
ejpam-5899	264	40	s1	s1	NOUN
ejpam-5899	264	41	,	,	PUNCT
ejpam-5899	264	42	µ1)-refinement	µ1)-refinement	ADJ
ejpam-5899	264	43	,	,	PUNCT
ejpam-5899	264	44	say	say	VERB
ejpam-5899	264	45	w	w	NOUN
ejpam-5899	264	46	=	=	PRON
ejpam-5899	264	47	{	{	PUNCT
ejpam-5899	264	48	wβ	wβ	ADP
ejpam-5899	264	49	:	:	PUNCT
ejpam-5899	264	50	β	β	X
ejpam-5899	264	51	∈	∈	PROPN
ejpam-5899	264	52	λ	λ	NOUN
ejpam-5899	264	53	}	}	PUNCT
ejpam-5899	264	54	.	.	PUNCT
ejpam-5899	265	1	therefore	therefore	ADV
ejpam-5899	265	2	,	,	PUNCT
ejpam-5899	265	3	by	by	ADP
ejpam-5899	265	4	lemma	lemma	PROPN
ejpam-5899	265	5	3	3	NUM
ejpam-5899	265	6	,	,	PUNCT
ejpam-5899	265	7	ψ(w	ψ(w	NUM
ejpam-5899	265	8	)	)	PUNCT
ejpam-5899	265	9	=	=	PRON
ejpam-5899	265	10	{	{	PUNCT
ejpam-5899	265	11	ψ(wβ	ψ(wβ	PROPN
ejpam-5899	265	12	)	)	PUNCT
ejpam-5899	265	13	:	:	PUNCT
ejpam-5899	265	14	β	β	X
ejpam-5899	265	15	∈	∈	PROPN
ejpam-5899	265	16	λ	λ	PROPN
ejpam-5899	265	17	}	}	PUNCT
ejpam-5899	265	18	is	be	AUX
ejpam-5899	265	19	gµ−lf(s2,µ2	gµ−lf(s2,µ2	PROPN
ejpam-5899	265	20	)	)	PUNCT
ejpam-5899	265	21	(	(	PUNCT
ejpam-5899	265	22	s2	s2	PROPN
ejpam-5899	265	23	,	,	PUNCT
ejpam-5899	265	24	µ2)-refinement	µ2)-refinement	NOUN
ejpam-5899	265	25	of	of	ADP
ejpam-5899	265	26	h	h	NOUN
ejpam-5899	265	27	in	in	ADP
ejpam-5899	265	28	(	(	PUNCT
ejpam-5899	265	29	s2	s2	PROPN
ejpam-5899	265	30	,	,	PUNCT
ejpam-5899	265	31	µ2	µ2	PROPN
ejpam-5899	265	32	)	)	PUNCT
ejpam-5899	265	33	.	.	PUNCT
ejpam-5899	266	1	4	4	X
ejpam-5899	266	2	.	.	X
ejpam-5899	267	1	some	some	DET
ejpam-5899	267	2	application	application	NOUN
ejpam-5899	267	3	on	on	ADP
ejpam-5899	267	4	α	α	NOUN
ejpam-5899	267	5	-	-	PUNCT
ejpam-5899	267	6	gµ-paracompact	gµ-paracompact	ADJ
ejpam-5899	267	7	sets	set	NOUN
ejpam-5899	267	8	in	in	ADP
ejpam-5899	267	9	this	this	DET
ejpam-5899	267	10	section	section	NOUN
ejpam-5899	267	11	,	,	PUNCT
ejpam-5899	267	12	we	we	PRON
ejpam-5899	267	13	introduce	introduce	VERB
ejpam-5899	267	14	the	the	DET
ejpam-5899	267	15	notion	notion	NOUN
ejpam-5899	267	16	of	of	ADP
ejpam-5899	267	17	co	co	ADJ
ejpam-5899	267	18	-	-	ADJ
ejpam-5899	267	19	α	α	PRON
ejpam-5899	267	20	-	-	PUNCT
ejpam-5899	267	21	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	267	22	set	set	NOUN
ejpam-5899	267	23	as	as	ADP
ejpam-5899	267	24	an	an	DET
ejpam-5899	267	25	application	application	NOUN
ejpam-5899	267	26	of	of	ADP
ejpam-5899	267	27	α	α	NOUN
ejpam-5899	267	28	-	-	PUNCT
ejpam-5899	267	29	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	267	30	and	and	CCONJ
ejpam-5899	267	31	study	study	VERB
ejpam-5899	267	32	some	some	PRON
ejpam-5899	267	33	of	of	ADP
ejpam-5899	267	34	its	its	PRON
ejpam-5899	267	35	properties	property	NOUN
ejpam-5899	267	36	.	.	PUNCT
ejpam-5899	268	1	definition	definition	NOUN
ejpam-5899	268	2	8	8	NUM
ejpam-5899	268	3	.	.	PUNCT
ejpam-5899	269	1	let	let	AUX
ejpam-5899	269	2	(	(	PUNCT
ejpam-5899	269	3	s	s	X
ejpam-5899	269	4	,	,	PUNCT
ejpam-5899	269	5	µ	µ	NOUN
ejpam-5899	269	6	)	)	PUNCT
ejpam-5899	269	7	be	be	AUX
ejpam-5899	269	8	a	a	DET
ejpam-5899	269	9	gts	gts	NOUN
ejpam-5899	269	10	.	.	PUNCT
ejpam-5899	270	1	a	a	DET
ejpam-5899	270	2	subset	subset	NOUN
ejpam-5899	270	3	e	e	X
ejpam-5899	270	4	⊆	⊆	NUM
ejpam-5899	270	5	s	s	PART
ejpam-5899	270	6	is	be	AUX
ejpam-5899	270	7	called	call	VERB
ejpam-5899	270	8	co	co	NOUN
ejpam-5899	270	9	-	-	NOUN
ejpam-5899	270	10	α	α	PRON
ejpam-5899	270	11	-gµ-paracompact	-gµ-paracompact	NOUN
ejpam-5899	270	12	if	if	SCONJ
ejpam-5899	270	13	for	for	ADP
ejpam-5899	270	14	each	each	DET
ejpam-5899	270	15	s	s	X
ejpam-5899	270	16	∈	∈	NOUN
ejpam-5899	270	17	e	e	NOUN
ejpam-5899	270	18	there	there	PRON
ejpam-5899	270	19	is	be	VERB
ejpam-5899	270	20	a	a	DET
ejpam-5899	270	21	pair	pair	NOUN
ejpam-5899	270	22	(	(	PUNCT
ejpam-5899	270	23	h	h	NOUN
ejpam-5899	270	24	,	,	PUNCT
ejpam-5899	270	25	g	g	NOUN
ejpam-5899	270	26	)	)	PUNCT
ejpam-5899	270	27	with	with	ADP
ejpam-5899	270	28	h	h	PROPN
ejpam-5899	270	29	∈	∈	PROPN
ejpam-5899	270	30	µ	µ	PROPN
ejpam-5899	270	31	and	and	CCONJ
ejpam-5899	270	32	g	g	PROPN
ejpam-5899	270	33	is	be	AUX
ejpam-5899	270	34	α	α	NOUN
ejpam-5899	270	35	-	-	NOUN
ejpam-5899	270	36	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	270	37	such	such	ADJ
ejpam-5899	270	38	that	that	DET
ejpam-5899	270	39	s	s	VERB
ejpam-5899	270	40	∈	∈	NOUN
ejpam-5899	270	41	h	h	NOUN
ejpam-5899	270	42	−g	−g	NOUN
ejpam-5899	270	43	⊆	⊆	NUM
ejpam-5899	270	44	e.	e.	PROPN
ejpam-5899	270	45	the	the	DET
ejpam-5899	270	46	collection	collection	NOUN
ejpam-5899	270	47	of	of	ADP
ejpam-5899	270	48	all	all	DET
ejpam-5899	270	49	co	co	ADJ
ejpam-5899	270	50	-	-	ADJ
ejpam-5899	270	51	α	α	PRON
ejpam-5899	270	52	-	-	PUNCT
ejpam-5899	270	53	gµ-paracompact	gµ-paracompact	ADJ
ejpam-5899	270	54	sets	set	NOUN
ejpam-5899	270	55	will	will	AUX
ejpam-5899	270	56	be	be	AUX
ejpam-5899	270	57	denoted	denote	VERB
ejpam-5899	270	58	by	by	ADP
ejpam-5899	270	59	µαgµ.	µαgµ.	NOUN
ejpam-5899	270	60	theorem	theorem	VERB
ejpam-5899	270	61	13	13	NUM
ejpam-5899	270	62	.	.	PUNCT
ejpam-5899	271	1	let	let	AUX
ejpam-5899	271	2	(	(	PUNCT
ejpam-5899	271	3	s	s	X
ejpam-5899	271	4	,	,	PUNCT
ejpam-5899	271	5	µ	µ	NOUN
ejpam-5899	271	6	)	)	PUNCT
ejpam-5899	271	7	be	be	AUX
ejpam-5899	271	8	a	a	DET
ejpam-5899	271	9	gts	gts	NOUN
ejpam-5899	271	10	.	.	PUNCT
ejpam-5899	272	1	then	then	ADV
ejpam-5899	272	2	:	:	PUNCT
ejpam-5899	272	3	(	(	PUNCT
ejpam-5899	272	4	i	i	NOUN
ejpam-5899	272	5	)	)	PUNCT
ejpam-5899	272	6	(	(	PUNCT
ejpam-5899	272	7	s	s	X
ejpam-5899	272	8	,	,	PUNCT
ejpam-5899	272	9	µαgµ	µαgµ	NOUN
ejpam-5899	272	10	)	)	PUNCT
ejpam-5899	272	11	is	be	AUX
ejpam-5899	272	12	a	a	DET
ejpam-5899	272	13	gts	gts	NOUN
ejpam-5899	272	14	with	with	ADP
ejpam-5899	272	15	µ	µ	PRON
ejpam-5899	272	16	⊆	⊆	NUM
ejpam-5899	272	17	µαgµ.	µαgµ.	NOUN
ejpam-5899	272	18	(	(	PUNCT
ejpam-5899	272	19	ii	ii	NOUN
ejpam-5899	272	20	)	)	PUNCT
ejpam-5899	272	21	b(µαgµ	b(µαgµ	NOUN
ejpam-5899	272	22	)	)	PUNCT
ejpam-5899	273	1	=	=	PRON
ejpam-5899	273	2	{	{	PUNCT
ejpam-5899	273	3	h	h	NOUN
ejpam-5899	273	4	−g	−g	NOUN
ejpam-5899	273	5	:	:	PUNCT
ejpam-5899	273	6	h	h	PROPN
ejpam-5899	273	7	∈	∈	PROPN
ejpam-5899	273	8	µ	µ	PROPN
ejpam-5899	273	9	and	and	CCONJ
ejpam-5899	273	10	g	g	PROPN
ejpam-5899	273	11	is	be	AUX
ejpam-5899	273	12	α	α	NOUN
ejpam-5899	273	13	-	-	PUNCT
ejpam-5899	273	14	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	273	15	}	}	PUNCT
ejpam-5899	273	16	generate	generate	VERB
ejpam-5899	273	17	a	a	DET
ejpam-5899	273	18	base	base	NOUN
ejpam-5899	273	19	for	for	ADP
ejpam-5899	273	20	µαgµ.	µαgµ.	PROPN
ejpam-5899	273	21	h.	h.	PROPN
ejpam-5899	274	1	h.	h.	PROPN
ejpam-5899	274	2	al	al	PROPN
ejpam-5899	274	3	-	-	PUNCT
ejpam-5899	274	4	jarrah	jarrah	PROPN
ejpam-5899	274	5	et	et	PROPN
ejpam-5899	274	6	al	al	PROPN
ejpam-5899	274	7	.	.	PUNCT
ejpam-5899	274	8	/	/	SYM
ejpam-5899	274	9	eur	eur	PROPN
ejpam-5899	274	10	.	.	PUNCT
ejpam-5899	275	1	j.	j.	PROPN
ejpam-5899	275	2	pure	pure	PROPN
ejpam-5899	275	3	appl	appl	PROPN
ejpam-5899	275	4	.	.	PROPN
ejpam-5899	275	5	math	math	PROPN
ejpam-5899	275	6	,	,	PUNCT
ejpam-5899	275	7	18	18	NUM
ejpam-5899	275	8	(	(	PUNCT
ejpam-5899	275	9	2	2	NUM
ejpam-5899	275	10	)	)	PUNCT
ejpam-5899	275	11	(	(	PUNCT
ejpam-5899	275	12	2025	2025	NUM
ejpam-5899	275	13	)	)	PUNCT
ejpam-5899	275	14	,	,	PUNCT
ejpam-5899	275	15	5899	5899	NUM
ejpam-5899	275	16	9	9	NUM
ejpam-5899	275	17	of	of	ADP
ejpam-5899	275	18	11	11	NUM
ejpam-5899	275	19	proof	proof	NOUN
ejpam-5899	275	20	.	.	PUNCT
ejpam-5899	276	1	(	(	PUNCT
ejpam-5899	276	2	i	i	NOUN
ejpam-5899	276	3	)	)	PUNCT
ejpam-5899	276	4	let	let	VERB
ejpam-5899	276	5	e	e	NOUN
ejpam-5899	276	6	=	=	PRON
ejpam-5899	276	7	{	{	PUNCT
ejpam-5899	276	8	eα	eα	NOUN
ejpam-5899	276	9	:	:	PUNCT
ejpam-5899	276	10	α	α	PROPN
ejpam-5899	276	11	∈	∈	PROPN
ejpam-5899	276	12	∆	∆	PROPN
ejpam-5899	276	13	}	}	PUNCT
ejpam-5899	276	14	be	be	AUX
ejpam-5899	276	15	a	a	DET
ejpam-5899	276	16	collection	collection	NOUN
ejpam-5899	276	17	of	of	ADP
ejpam-5899	276	18	µαgµ	µαgµ	NOUN
ejpam-5899	276	19	subset	subset	VERB
ejpam-5899	276	20	.	.	PUNCT
ejpam-5899	277	1	if	if	SCONJ
ejpam-5899	277	2	s	s	VERB
ejpam-5899	277	3	∈	∈	PROPN
ejpam-5899	277	4	∪	∪	ADP
ejpam-5899	277	5	α∈∆	α∈∆	PROPN
ejpam-5899	277	6	eα	eα	NOUN
ejpam-5899	277	7	,	,	PUNCT
ejpam-5899	277	8	then	then	ADV
ejpam-5899	277	9	there	there	PRON
ejpam-5899	277	10	is	be	VERB
ejpam-5899	277	11	α	α	NUM
ejpam-5899	277	12	◦	◦	NOUN
ejpam-5899	277	13	∈	∈	NOUN
ejpam-5899	277	14	∆	∆	PROPN
ejpam-5899	277	15	and	and	CCONJ
ejpam-5899	277	16	a	a	DET
ejpam-5899	277	17	pair	pair	NOUN
ejpam-5899	277	18	(	(	PUNCT
ejpam-5899	277	19	h	h	NOUN
ejpam-5899	277	20	,	,	PUNCT
ejpam-5899	277	21	g	g	NOUN
ejpam-5899	277	22	)	)	PUNCT
ejpam-5899	277	23	with	with	ADP
ejpam-5899	277	24	h	h	PROPN
ejpam-5899	277	25	∈	∈	PROPN
ejpam-5899	277	26	µ	µ	PROPN
ejpam-5899	277	27	and	and	CCONJ
ejpam-5899	277	28	g	g	PROPN
ejpam-5899	277	29	is	be	AUX
ejpam-5899	277	30	α	α	PRON
ejpam-5899	277	31	-gµ-paracompact	-gµ-paracompact	ADJ
ejpam-5899	277	32	such	such	ADJ
ejpam-5899	277	33	that	that	DET
ejpam-5899	277	34	s	s	VERB
ejpam-5899	277	35	∈	∈	NOUN
ejpam-5899	277	36	h	h	NOUN
ejpam-5899	277	37	−	−	NOUN
ejpam-5899	277	38	g	g	NOUN
ejpam-5899	277	39	⊆	⊆	NUM
ejpam-5899	277	40	eα	eα	NOUN
ejpam-5899	277	41	◦	◦	NOUN
ejpam-5899	277	42	⊆	⊆	NUM
ejpam-5899	277	43	∪	∪	ADP
ejpam-5899	277	44	α∈∆	α∈∆	NUM
ejpam-5899	277	45	eα	eα	NOUN
ejpam-5899	277	46	.	.	NOUN
ejpam-5899	278	1	since	since	SCONJ
ejpam-5899	278	2	ϕ	ϕ	PROPN
ejpam-5899	278	3	is	be	AUX
ejpam-5899	278	4	α	α	PRON
ejpam-5899	278	5	-gµ-paracompact	-gµ-paracompact	NOUN
ejpam-5899	278	6	then	then	ADV
ejpam-5899	278	7	µαgm	µαgm	PROPN
ejpam-5899	278	8	is	be	AUX
ejpam-5899	278	9	a	a	DET
ejpam-5899	278	10	gts	gts	NOUN
ejpam-5899	278	11	on	on	ADP
ejpam-5899	278	12	s.	s.	PROPN
ejpam-5899	278	13	moreover	moreover	ADV
ejpam-5899	278	14	,	,	PUNCT
ejpam-5899	278	15	if	if	SCONJ
ejpam-5899	278	16	h	h	PROPN
ejpam-5899	278	17	∈	∈	PROPN
ejpam-5899	278	18	µ	µ	X
ejpam-5899	278	19	then	then	ADV
ejpam-5899	278	20	h	h	NOUN
ejpam-5899	278	21	=	=	NOUN
ejpam-5899	278	22	h	h	PROPN
ejpam-5899	278	23	−	−	PROPN
ejpam-5899	278	24	ϕ	ϕ	PROPN
ejpam-5899	278	25	∈	∈	PROPN
ejpam-5899	278	26	µαgm	µαgm	NOUN
ejpam-5899	278	27	.	.	PUNCT
ejpam-5899	279	1	(	(	PUNCT
ejpam-5899	279	2	ii	ii	X
ejpam-5899	279	3	)	)	PUNCT
ejpam-5899	279	4	it	it	PRON
ejpam-5899	279	5	follows	follow	VERB
ejpam-5899	279	6	from	from	ADP
ejpam-5899	279	7	definition	definition	NOUN
ejpam-5899	279	8	8	8	NUM
ejpam-5899	279	9	.	.	PUNCT
ejpam-5899	280	1	the	the	DET
ejpam-5899	280	2	following	follow	VERB
ejpam-5899	280	3	example	example	NOUN
ejpam-5899	280	4	will	will	AUX
ejpam-5899	280	5	show	show	VERB
ejpam-5899	280	6	that	that	SCONJ
ejpam-5899	280	7	the	the	DET
ejpam-5899	280	8	reverse	reverse	ADJ
ejpam-5899	280	9	inclusion	inclusion	NOUN
ejpam-5899	280	10	of	of	ADP
ejpam-5899	280	11	theorem	theorem	ADJ
ejpam-5899	280	12	13	13	NUM
ejpam-5899	280	13	is	be	AUX
ejpam-5899	280	14	not	not	PART
ejpam-5899	280	15	true	true	ADJ
ejpam-5899	280	16	in	in	ADP
ejpam-5899	280	17	general	general	ADJ
ejpam-5899	280	18	.	.	PUNCT
ejpam-5899	281	1	example	example	NOUN
ejpam-5899	282	1	3	3	X
ejpam-5899	282	2	.	.	X
ejpam-5899	283	1	consider	consider	VERB
ejpam-5899	283	2	s	s	PRON
ejpam-5899	283	3	=	=	X
ejpam-5899	283	4	(	(	PUNCT
ejpam-5899	283	5	0	0	NUM
ejpam-5899	283	6	,	,	PUNCT
ejpam-5899	283	7	1	1	NUM
ejpam-5899	283	8	)	)	PUNCT
ejpam-5899	283	9	and	and	CCONJ
ejpam-5899	283	10	b	b	X
ejpam-5899	283	11	=	=	PRON
ejpam-5899	283	12	{	{	PUNCT
ejpam-5899	283	13	ϕ	ϕ	NOUN
ejpam-5899	283	14	}	}	PUNCT
ejpam-5899	283	15	∪	∪	X
ejpam-5899	283	16	{	{	PUNCT
ejpam-5899	283	17	(	(	PUNCT
ejpam-5899	283	18	0	0	NUM
ejpam-5899	283	19	,	,	PUNCT
ejpam-5899	283	20	a	a	PRON
ejpam-5899	283	21	)	)	PUNCT
ejpam-5899	283	22	,	,	PUNCT
ejpam-5899	283	23	(	(	PUNCT
ejpam-5899	283	24	a	a	PRON
ejpam-5899	283	25	,	,	PUNCT
ejpam-5899	283	26	1	1	NUM
ejpam-5899	283	27	)	)	PUNCT
ejpam-5899	283	28	:	:	PUNCT
ejpam-5899	283	29	a	a	DET
ejpam-5899	283	30	∈	∈	PROPN
ejpam-5899	283	31	(	(	PUNCT
ejpam-5899	283	32	0	0	NUM
ejpam-5899	283	33	,	,	PUNCT
ejpam-5899	283	34	1	1	NUM
ejpam-5899	283	35	)	)	PUNCT
ejpam-5899	283	36	}	}	PUNCT
ejpam-5899	283	37	.	.	PUNCT
ejpam-5899	284	1	assume	assume	VERB
ejpam-5899	284	2	that	that	SCONJ
ejpam-5899	284	3	(	(	PUNCT
ejpam-5899	284	4	s	s	X
ejpam-5899	284	5	,	,	PUNCT
ejpam-5899	284	6	µ(b	µ(b	NOUN
ejpam-5899	284	7	)	)	PUNCT
ejpam-5899	284	8	)	)	PUNCT
ejpam-5899	284	9	is	be	AUX
ejpam-5899	284	10	the	the	DET
ejpam-5899	284	11	gts	gts	NOUN
ejpam-5899	284	12	generated	generate	VERB
ejpam-5899	284	13	on	on	ADP
ejpam-5899	284	14	s	s	PRON
ejpam-5899	284	15	by	by	ADP
ejpam-5899	284	16	the	the	DET
ejpam-5899	284	17	base	base	PROPN
ejpam-5899	284	18	b.	b.	PROPN
ejpam-5899	284	19	then	then	ADV
ejpam-5899	284	20	s	s	VERB
ejpam-5899	284	21	∈	∈	PROPN
ejpam-5899	284	22	µ(b	µ(b	NOUN
ejpam-5899	284	23	)	)	PUNCT
ejpam-5899	284	24	and	and	CCONJ
ejpam-5899	284	25	hence	hence	ADV
ejpam-5899	284	26	s−{1	s−{1	NOUN
ejpam-5899	284	27	3	3	NUM
ejpam-5899	284	28	,	,	PUNCT
ejpam-5899	284	29	1	1	NUM
ejpam-5899	284	30	2	2	NUM
ejpam-5899	284	31	}	}	PUNCT
ejpam-5899	284	32	∈	∈	PROPN
ejpam-5899	284	33	µαgm	µαgm	NOUN
ejpam-5899	284	34	−	−	PROPN
ejpam-5899	284	35	µ(b	µ(b	NOUN
ejpam-5899	284	36	)	)	PUNCT
ejpam-5899	284	37	.	.	PUNCT
ejpam-5899	285	1	theorem	theorem	NOUN
ejpam-5899	285	2	14	14	NUM
ejpam-5899	285	3	.	.	PUNCT
ejpam-5899	286	1	let	let	AUX
ejpam-5899	286	2	(	(	PUNCT
ejpam-5899	286	3	s	s	X
ejpam-5899	286	4	,	,	PUNCT
ejpam-5899	286	5	µ	µ	NOUN
ejpam-5899	286	6	)	)	PUNCT
ejpam-5899	286	7	be	be	AUX
ejpam-5899	286	8	a	a	DET
ejpam-5899	286	9	gts	gts	NOUN
ejpam-5899	286	10	.	.	PUNCT
ejpam-5899	287	1	then	then	ADV
ejpam-5899	287	2	the	the	DET
ejpam-5899	287	3	following	follow	VERB
ejpam-5899	287	4	are	be	AUX
ejpam-5899	287	5	equivalent	equivalent	ADJ
ejpam-5899	287	6	:	:	PUNCT
ejpam-5899	287	7	(	(	PUNCT
ejpam-5899	287	8	i	i	NOUN
ejpam-5899	287	9	)	)	PUNCT
ejpam-5899	287	10	µ	µ	X
ejpam-5899	287	11	=	=	PUNCT
ejpam-5899	287	12	{	{	PUNCT
ejpam-5899	287	13	h	h	NOUN
ejpam-5899	287	14	−g	−g	NOUN
ejpam-5899	287	15	:	:	PUNCT
ejpam-5899	287	16	h	h	PROPN
ejpam-5899	287	17	∈	∈	PROPN
ejpam-5899	287	18	µ	µ	PROPN
ejpam-5899	287	19	and	and	CCONJ
ejpam-5899	287	20	g	g	PROPN
ejpam-5899	287	21	is	be	AUX
ejpam-5899	287	22	α	α	NOUN
ejpam-5899	287	23	-	-	NOUN
ejpam-5899	287	24	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	287	25	}	}	PUNCT
ejpam-5899	287	26	;	;	PUNCT
ejpam-5899	287	27	(	(	PUNCT
ejpam-5899	287	28	ii	ii	NOUN
ejpam-5899	287	29	)	)	PUNCT
ejpam-5899	287	30	µec	µec	PROPN
ejpam-5899	287	31	⊆	⊆	NUM
ejpam-5899	287	32	µ	µ	NOUN
ejpam-5899	287	33	for	for	ADP
ejpam-5899	287	34	each	each	DET
ejpam-5899	287	35	e	e	NOUN
ejpam-5899	287	36	is	be	AUX
ejpam-5899	287	37	α	α	NOUN
ejpam-5899	287	38	-	-	NOUN
ejpam-5899	287	39	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	287	40	;	;	PUNCT
ejpam-5899	287	41	(	(	PUNCT
ejpam-5899	287	42	iii	iii	X
ejpam-5899	287	43	)	)	PUNCT
ejpam-5899	287	44	µ	µ	X
ejpam-5899	287	45	=	=	SYM
ejpam-5899	287	46	µαgµ.	µαgµ.	NOUN
ejpam-5899	287	47	proof	proof	NOUN
ejpam-5899	287	48	.	.	PUNCT
ejpam-5899	288	1	(	(	PUNCT
ejpam-5899	288	2	i	i	PRON
ejpam-5899	288	3	⇒	⇒	VERB
ejpam-5899	288	4	ii	ii	PROPN
ejpam-5899	288	5	)	)	PUNCT
ejpam-5899	288	6	let	let	VERB
ejpam-5899	288	7	h	h	NOUN
ejpam-5899	288	8	∈	∈	PROPN
ejpam-5899	288	9	µec	µec	PROPN
ejpam-5899	288	10	.	.	PUNCT
ejpam-5899	289	1	then	then	ADV
ejpam-5899	289	2	h	h	NOUN
ejpam-5899	289	3	=	=	SYM
ejpam-5899	289	4	g	g	PROPN
ejpam-5899	289	5	∩	∩	X
ejpam-5899	289	6	ec	ec	PROPN
ejpam-5899	289	7	=	=	PUNCT
ejpam-5899	289	8	g	g	PROPN
ejpam-5899	289	9	−	−	PROPN
ejpam-5899	289	10	e	e	NOUN
ejpam-5899	289	11	with	with	ADP
ejpam-5899	289	12	g	g	PROPN
ejpam-5899	289	13	∈	∈	PROPN
ejpam-5899	289	14	µ	µ	X
ejpam-5899	289	15	and	and	CCONJ
ejpam-5899	289	16	e	e	PROPN
ejpam-5899	289	17	is	be	AUX
ejpam-5899	289	18	α	α	NOUN
ejpam-5899	289	19	-	-	NOUN
ejpam-5899	289	20	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	289	21	.	.	PUNCT
ejpam-5899	290	1	by	by	ADP
ejpam-5899	290	2	part	part	NOUN
ejpam-5899	290	3	(	(	PUNCT
ejpam-5899	290	4	i	i	NOUN
ejpam-5899	290	5	)	)	PUNCT
ejpam-5899	290	6	,	,	PUNCT
ejpam-5899	290	7	h	h	PROPN
ejpam-5899	290	8	∈	∈	PROPN
ejpam-5899	290	9	µ.	µ.	NOUN
ejpam-5899	290	10	(	(	PUNCT
ejpam-5899	290	11	ii	ii	PROPN
ejpam-5899	290	12	⇒	⇒	PROPN
ejpam-5899	290	13	iii	iii	PROPN
ejpam-5899	290	14	)	)	PUNCT
ejpam-5899	290	15	let	let	VERB
ejpam-5899	290	16	e	e	X
ejpam-5899	290	17	∈	∈	PROPN
ejpam-5899	290	18	µαgµ.	µαgµ.	NOUN
ejpam-5899	290	19	then	then	ADV
ejpam-5899	290	20	,	,	PUNCT
ejpam-5899	290	21	for	for	ADP
ejpam-5899	290	22	each	each	DET
ejpam-5899	290	23	s	s	X
ejpam-5899	290	24	∈	∈	NOUN
ejpam-5899	290	25	e	e	NOUN
ejpam-5899	290	26	there	there	PRON
ejpam-5899	290	27	is	be	VERB
ejpam-5899	290	28	a	a	DET
ejpam-5899	290	29	pair	pair	NOUN
ejpam-5899	290	30	(	(	PUNCT
ejpam-5899	290	31	h	h	NOUN
ejpam-5899	290	32	,	,	PUNCT
ejpam-5899	290	33	g	g	NOUN
ejpam-5899	290	34	)	)	PUNCT
ejpam-5899	290	35	with	with	ADP
ejpam-5899	290	36	h	h	PROPN
ejpam-5899	290	37	∈	∈	PROPN
ejpam-5899	290	38	µ	µ	PROPN
ejpam-5899	290	39	and	and	CCONJ
ejpam-5899	290	40	g	g	PROPN
ejpam-5899	290	41	is	be	AUX
ejpam-5899	290	42	α	α	NOUN
ejpam-5899	290	43	-	-	NOUN
ejpam-5899	290	44	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	290	45	such	such	ADJ
ejpam-5899	290	46	that	that	DET
ejpam-5899	290	47	s	s	VERB
ejpam-5899	290	48	∈	∈	NOUN
ejpam-5899	290	49	h	h	NOUN
ejpam-5899	290	50	−g	−g	NOUN
ejpam-5899	290	51	⊆	⊆	NUM
ejpam-5899	290	52	e.	e.	PROPN
ejpam-5899	290	53	since	since	SCONJ
ejpam-5899	290	54	h	h	PROPN
ejpam-5899	290	55	−g	−g	NOUN
ejpam-5899	290	56	∈	∈	PROPN
ejpam-5899	290	57	µgc	µgc	NUM
ejpam-5899	290	58	⊆	⊆	NUM
ejpam-5899	290	59	µ	µ	NOUN
ejpam-5899	290	60	,	,	PUNCT
ejpam-5899	290	61	then	then	ADV
ejpam-5899	290	62	e	e	PROPN
ejpam-5899	290	63	∈	∈	PROPN
ejpam-5899	290	64	µ.	µ.	NOUN
ejpam-5899	290	65	(	(	PUNCT
ejpam-5899	290	66	iii⇒	iii⇒	NOUN
ejpam-5899	290	67	i	i	PROPN
ejpam-5899	290	68	)	)	PUNCT
ejpam-5899	290	69	from	from	ADP
ejpam-5899	290	70	definition	definition	NOUN
ejpam-5899	290	71	8	8	NUM
ejpam-5899	290	72	,	,	PUNCT
ejpam-5899	290	73	the	the	DET
ejpam-5899	290	74	collection	collection	NOUN
ejpam-5899	290	75	{	{	PUNCT
ejpam-5899	290	76	h−g	h−g	NOUN
ejpam-5899	290	77	:	:	PUNCT
ejpam-5899	290	78	h	h	PROPN
ejpam-5899	290	79	∈	∈	PROPN
ejpam-5899	290	80	µ	µ	DET
ejpam-5899	290	81	andg	andg	NOUN
ejpam-5899	290	82	is	be	AUX
ejpam-5899	290	83	α	α	PRON
ejpam-5899	290	84	-	-	PUNCT
ejpam-5899	290	85	gµ-paracompact}⊆	gµ-paracompact}⊆	NOUN
ejpam-5899	290	86	µαgµ	µαgµ	NOUN
ejpam-5899	290	87	=	=	SYM
ejpam-5899	290	88	µ.	µ.	NOUN
ejpam-5899	290	89	now	now	ADV
ejpam-5899	290	90	,	,	PUNCT
ejpam-5899	290	91	let	let	VERB
ejpam-5899	290	92	e	e	PROPN
ejpam-5899	290	93	∈	∈	PROPN
ejpam-5899	290	94	µ	µ	NOUN
ejpam-5899	290	95	,	,	PUNCT
ejpam-5899	290	96	then	then	ADV
ejpam-5899	290	97	e	e	X
ejpam-5899	290	98	−	−	PROPN
ejpam-5899	290	99	ϕ	ϕ	PROPN
ejpam-5899	290	100	∈	∈	PROPN
ejpam-5899	290	101	{	{	PUNCT
ejpam-5899	290	102	h	h	NOUN
ejpam-5899	290	103	−	−	PROPN
ejpam-5899	290	104	g	g	PROPN
ejpam-5899	290	105	:	:	PUNCT
ejpam-5899	290	106	h	h	PROPN
ejpam-5899	290	107	∈	∈	PROPN
ejpam-5899	290	108	µ	µ	PROPN
ejpam-5899	290	109	and	and	CCONJ
ejpam-5899	290	110	g	g	PROPN
ejpam-5899	290	111	is	be	AUX
ejpam-5899	290	112	α	α	NOUN
ejpam-5899	290	113	-	-	NOUN
ejpam-5899	290	114	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	290	115	}	}	PUNCT
ejpam-5899	290	116	and	and	CCONJ
ejpam-5899	290	117	hence	hence	ADV
ejpam-5899	290	118	the	the	DET
ejpam-5899	290	119	result	result	NOUN
ejpam-5899	290	120	follows	follow	VERB
ejpam-5899	290	121	.	.	PUNCT
ejpam-5899	291	1	theorem	theorem	ADJ
ejpam-5899	291	2	15	15	NUM
ejpam-5899	291	3	.	.	PUNCT
ejpam-5899	292	1	let	let	AUX
ejpam-5899	292	2	(	(	PUNCT
ejpam-5899	292	3	s	s	X
ejpam-5899	292	4	,	,	PUNCT
ejpam-5899	292	5	µ	µ	NOUN
ejpam-5899	292	6	)	)	PUNCT
ejpam-5899	292	7	be	be	AUX
ejpam-5899	292	8	a	a	DET
ejpam-5899	292	9	gts	gts	NOUN
ejpam-5899	292	10	.	.	PUNCT
ejpam-5899	293	1	if	if	SCONJ
ejpam-5899	293	2	e	e	PROPN
ejpam-5899	293	3	is	be	AUX
ejpam-5899	293	4	µ∗	µ∗	PROPN
ejpam-5899	293	5	closed	close	VERB
ejpam-5899	293	6	,	,	PUNCT
ejpam-5899	293	7	then	then	ADV
ejpam-5899	293	8	(	(	PUNCT
ejpam-5899	293	9	µαgµ)e	µαgµ)e	NOUN
ejpam-5899	293	10	⊆	⊆	NUM
ejpam-5899	293	11	(	(	PUNCT
ejpam-5899	293	12	µe	µe	NOUN
ejpam-5899	293	13	)	)	PUNCT
ejpam-5899	293	14	αgµ.	αgµ.	NOUN
ejpam-5899	293	15	proof	proof	NOUN
ejpam-5899	293	16	.	.	PUNCT
ejpam-5899	294	1	let	let	VERB
ejpam-5899	294	2	h	h	PRON
ejpam-5899	294	3	∈	∈	PROPN
ejpam-5899	294	4	(	(	PUNCT
ejpam-5899	294	5	µαgµ)e	µαgµ)e	VERB
ejpam-5899	294	6	with	with	ADP
ejpam-5899	294	7	s	s	PROPN
ejpam-5899	294	8	∈	∈	PROPN
ejpam-5899	294	9	h.	h.	NOUN
ejpam-5899	294	10	then	then	ADV
ejpam-5899	294	11	h	h	NOUN
ejpam-5899	295	1	=	=	SYM
ejpam-5899	295	2	g	g	PROPN
ejpam-5899	295	3	∩	∩	X
ejpam-5899	295	4	e	e	NOUN
ejpam-5899	295	5	with	with	ADP
ejpam-5899	295	6	g	g	PROPN
ejpam-5899	295	7	∈	∈	PROPN
ejpam-5899	295	8	µαgµ.	µαgµ.	NOUN
ejpam-5899	295	9	since	since	SCONJ
ejpam-5899	295	10	there	there	PRON
ejpam-5899	295	11	is	be	VERB
ejpam-5899	295	12	a	a	DET
ejpam-5899	295	13	pair	pair	NOUN
ejpam-5899	295	14	(	(	PUNCT
ejpam-5899	295	15	z	z	NOUN
ejpam-5899	295	16	,	,	PUNCT
ejpam-5899	295	17	w	w	NOUN
ejpam-5899	295	18	)	)	PUNCT
ejpam-5899	295	19	with	with	ADP
ejpam-5899	295	20	z	z	PROPN
ejpam-5899	295	21	∈	∈	PROPN
ejpam-5899	295	22	µ	µ	PROPN
ejpam-5899	295	23	and	and	CCONJ
ejpam-5899	295	24	w	w	PROPN
ejpam-5899	295	25	is	be	AUX
ejpam-5899	295	26	α	α	NOUN
ejpam-5899	295	27	-	-	NOUN
ejpam-5899	295	28	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	295	29	such	such	ADJ
ejpam-5899	295	30	that	that	DET
ejpam-5899	295	31	s	s	VERB
ejpam-5899	295	32	∈	∈	PROPN
ejpam-5899	295	33	z	z	NOUN
ejpam-5899	295	34	−w	−w	ADV
ejpam-5899	295	35	⊆	⊆	NUM
ejpam-5899	295	36	g	g	NOUN
ejpam-5899	295	37	,	,	PUNCT
ejpam-5899	295	38	then	then	ADV
ejpam-5899	295	39	s	s	VERB
ejpam-5899	295	40	∈	∈	PROPN
ejpam-5899	295	41	(	(	PUNCT
ejpam-5899	295	42	z	z	NOUN
ejpam-5899	295	43	∩	∩	X
ejpam-5899	295	44	e	e	NOUN
ejpam-5899	295	45	)	)	PUNCT
ejpam-5899	295	46	−	−	PROPN
ejpam-5899	295	47	(	(	PUNCT
ejpam-5899	295	48	w	w	NOUN
ejpam-5899	295	49	∩	∩	ADJ
ejpam-5899	295	50	e	e	NOUN
ejpam-5899	295	51	)	)	PUNCT
ejpam-5899	295	52	⊆	⊆	PROPN
ejpam-5899	295	53	h.	h.	PROPN
ejpam-5899	295	54	now	now	ADV
ejpam-5899	295	55	z	z	X
ejpam-5899	295	56	∩	∩	NOUN
ejpam-5899	295	57	e	e	X
ejpam-5899	295	58	∈	∈	NOUN
ejpam-5899	295	59	µe	µe	ADV
ejpam-5899	295	60	and	and	CCONJ
ejpam-5899	295	61	by	by	ADP
ejpam-5899	295	62	theorems	theorem	NOUN
ejpam-5899	295	63	5	5	NUM
ejpam-5899	295	64	and	and	CCONJ
ejpam-5899	295	65	7	7	NUM
ejpam-5899	295	66	,	,	PUNCT
ejpam-5899	295	67	w	w	NOUN
ejpam-5899	295	68	∩	∩	NOUN
ejpam-5899	295	69	e	e	NOUN
ejpam-5899	295	70	is	be	AUX
ejpam-5899	295	71	α	α	PRON
ejpam-5899	295	72	-gµ-paracompact	-gµ-paracompact	NOUN
ejpam-5899	295	73	in	in	ADP
ejpam-5899	295	74	(	(	PUNCT
ejpam-5899	295	75	e,µe	e,µe	NOUN
ejpam-5899	295	76	)	)	PUNCT
ejpam-5899	295	77	.	.	PUNCT
ejpam-5899	296	1	therefore	therefore	ADV
ejpam-5899	296	2	,	,	PUNCT
ejpam-5899	296	3	h	h	NOUN
ejpam-5899	296	4	∈	∈	PROPN
ejpam-5899	296	5	(	(	PUNCT
ejpam-5899	296	6	µe	µe	NOUN
ejpam-5899	296	7	)	)	PUNCT
ejpam-5899	296	8	αgµ.	αgµ.	NOUN
ejpam-5899	296	9	proposition	proposition	NOUN
ejpam-5899	296	10	5	5	NUM
ejpam-5899	296	11	.	.	PUNCT
ejpam-5899	297	1	let	let	VERB
ejpam-5899	297	2	ψ	ψ	X
ejpam-5899	297	3	:	:	PUNCT
ejpam-5899	297	4	(	(	PUNCT
ejpam-5899	297	5	s1	s1	NOUN
ejpam-5899	297	6	,	,	PUNCT
ejpam-5899	297	7	µ1	µ1	PROPN
ejpam-5899	297	8	)	)	PUNCT
ejpam-5899	297	9	→	→	SYM
ejpam-5899	297	10	(	(	PUNCT
ejpam-5899	297	11	s2	s2	PROPN
ejpam-5899	297	12	,	,	PUNCT
ejpam-5899	297	13	µ2	µ2	PROPN
ejpam-5899	297	14	)	)	PUNCT
ejpam-5899	297	15	be	be	AUX
ejpam-5899	297	16	(	(	PUNCT
ejpam-5899	297	17	µ1	µ1	ADJ
ejpam-5899	297	18	,	,	PUNCT
ejpam-5899	297	19	µ2)-homeomorphism	µ2)-homeomorphism	NOUN
ejpam-5899	297	20	with	with	ADP
ejpam-5899	297	21	ψ−1(e	ψ−1(e	PROPN
ejpam-5899	297	22	)	)	PUNCT
ejpam-5899	297	23	is	be	AUX
ejpam-5899	297	24	µ∗-compact	µ∗-compact	PROPN
ejpam-5899	297	25	for	for	ADP
ejpam-5899	297	26	each	each	DET
ejpam-5899	297	27	e	e	PROPN
ejpam-5899	297	28	∈	∈	PROPN
ejpam-5899	297	29	s2	s2	PROPN
ejpam-5899	297	30	.	.	PUNCT
ejpam-5899	298	1	then	then	ADV
ejpam-5899	298	2	ψ	ψ	X
ejpam-5899	298	3	:	:	PUNCT
ejpam-5899	298	4	(	(	PUNCT
ejpam-5899	298	5	s1	s1	NOUN
ejpam-5899	298	6	,	,	PUNCT
ejpam-5899	298	7	µ	µ	X
ejpam-5899	298	8	αgµ1	αgµ1	NOUN
ejpam-5899	298	9	1	1	NUM
ejpam-5899	298	10	)	)	PUNCT
ejpam-5899	298	11	→	→	SYM
ejpam-5899	298	12	(	(	PUNCT
ejpam-5899	298	13	s2	s2	PROPN
ejpam-5899	298	14	,	,	PUNCT
ejpam-5899	298	15	µ	µ	X
ejpam-5899	298	16	αgµ2	αgµ2	NOUN
ejpam-5899	298	17	2	2	NUM
ejpam-5899	298	18	)	)	PUNCT
ejpam-5899	298	19	is	be	AUX
ejpam-5899	298	20	open	open	ADJ
ejpam-5899	298	21	mapping	mapping	NOUN
ejpam-5899	298	22	.	.	PUNCT
ejpam-5899	299	1	proof	proof	NOUN
ejpam-5899	299	2	.	.	PUNCT
ejpam-5899	300	1	let	let	VERB
ejpam-5899	300	2	e	e	X
ejpam-5899	300	3	∈	∈	PROPN
ejpam-5899	300	4	b(µαgµ1	b(µαgµ1	NOUN
ejpam-5899	300	5	1	1	NUM
ejpam-5899	300	6	)	)	PUNCT
ejpam-5899	300	7	.	.	PUNCT
ejpam-5899	301	1	then	then	ADV
ejpam-5899	301	2	by	by	ADP
ejpam-5899	301	3	theorem	theorem	NOUN
ejpam-5899	301	4	12	12	NUM
ejpam-5899	301	5	,	,	PUNCT
ejpam-5899	301	6	ψ(e	ψ(e	PROPN
ejpam-5899	301	7	)	)	PUNCT
ejpam-5899	301	8	∈	∈	PROPN
ejpam-5899	301	9	µαgµ2	µαgµ2	NOUN
ejpam-5899	301	10	2	2	NUM
ejpam-5899	301	11	and	and	CCONJ
ejpam-5899	301	12	hence	hence	ADV
ejpam-5899	301	13	ψ	ψ	NOUN
ejpam-5899	301	14	is	be	AUX
ejpam-5899	301	15	open	open	ADJ
ejpam-5899	301	16	.	.	PUNCT
ejpam-5899	302	1	question	question	NOUN
ejpam-5899	302	2	:	:	PUNCT
ejpam-5899	302	3	let	let	VERB
ejpam-5899	302	4	(	(	PUNCT
ejpam-5899	302	5	s	s	X
ejpam-5899	302	6	,	,	PUNCT
ejpam-5899	302	7	µ	µ	NOUN
ejpam-5899	302	8	)	)	PUNCT
ejpam-5899	302	9	be	be	AUX
ejpam-5899	302	10	agts	agt	VERB
ejpam-5899	302	11	.	.	PUNCT
ejpam-5899	303	1	what	what	PRON
ejpam-5899	303	2	are	be	AUX
ejpam-5899	303	3	the	the	DET
ejpam-5899	303	4	conditions	condition	NOUN
ejpam-5899	303	5	to	to	PART
ejpam-5899	303	6	become	become	VERB
ejpam-5899	303	7	µαgµ	µαgµ	NOUN
ejpam-5899	303	8	=	=	SYM
ejpam-5899	303	9	(	(	PUNCT
ejpam-5899	303	10	µαgµ)αgµ	µαgµ)αgµ	PROPN
ejpam-5899	303	11	?	?	PUNCT
ejpam-5899	304	1	the	the	DET
ejpam-5899	304	2	following	follow	VERB
ejpam-5899	304	3	consequence	consequence	NOUN
ejpam-5899	304	4	is	be	AUX
ejpam-5899	304	5	a	a	DET
ejpam-5899	304	6	partial	partial	ADJ
ejpam-5899	304	7	answer	answer	NOUN
ejpam-5899	304	8	to	to	ADP
ejpam-5899	304	9	this	this	DET
ejpam-5899	304	10	question	question	NOUN
ejpam-5899	304	11	.	.	PUNCT
ejpam-5899	305	1	recall	recall	VERB
ejpam-5899	305	2	that	that	SCONJ
ejpam-5899	305	3	a	a	DET
ejpam-5899	305	4	subset	subset	NOUN
ejpam-5899	305	5	e	e	NOUN
ejpam-5899	305	6	is	be	AUX
ejpam-5899	305	7	called	call	VERB
ejpam-5899	305	8	α	α	PRON
ejpam-5899	305	9	-	-	NOUN
ejpam-5899	305	10	paracompact	paracompact	NOUN
ejpam-5899	305	11	of	of	ADP
ejpam-5899	305	12	(	(	PUNCT
ejpam-5899	305	13	s	s	PROPN
ejpam-5899	305	14	,	,	PUNCT
ejpam-5899	305	15	µ	µ	NOUN
ejpam-5899	305	16	)	)	PUNCT
ejpam-5899	305	17	[	[	X
ejpam-5899	305	18	3	3	X
ejpam-5899	305	19	]	]	PUNCT
ejpam-5899	305	20	if	if	SCONJ
ejpam-5899	305	21	each	each	DET
ejpam-5899	305	22	(	(	PUNCT
ejpam-5899	305	23	s	s	X
ejpam-5899	305	24	,	,	PUNCT
ejpam-5899	305	25	µ)-cover	µ)-cover	NOUN
ejpam-5899	305	26	of	of	ADP
ejpam-5899	305	27	e	e	NOUN
ejpam-5899	305	28	has	have	AUX
ejpam-5899	305	29	a	a	DET
ejpam-5899	305	30	µ−lf(s,µ	µ−lf(s,µ	NOUN
ejpam-5899	305	31	)	)	PUNCT
ejpam-5899	305	32	(	(	PUNCT
ejpam-5899	305	33	s	s	PROPN
ejpam-5899	305	34	,	,	PUNCT
ejpam-5899	305	35	µ)-refinement	µ)-refinement	PUNCT
ejpam-5899	305	36	.	.	PUNCT
ejpam-5899	306	1	h.	h.	PROPN
ejpam-5899	306	2	h.	h.	PROPN
ejpam-5899	306	3	al	al	PROPN
ejpam-5899	306	4	-	-	PUNCT
ejpam-5899	306	5	jarrah	jarrah	PROPN
ejpam-5899	306	6	et	et	PROPN
ejpam-5899	306	7	al	al	PROPN
ejpam-5899	306	8	.	.	PUNCT
ejpam-5899	306	9	/	/	SYM
ejpam-5899	306	10	eur	eur	PROPN
ejpam-5899	306	11	.	.	PUNCT
ejpam-5899	307	1	j.	j.	PROPN
ejpam-5899	307	2	pure	pure	PROPN
ejpam-5899	307	3	appl	appl	PROPN
ejpam-5899	307	4	.	.	PROPN
ejpam-5899	307	5	math	math	PROPN
ejpam-5899	307	6	,	,	PUNCT
ejpam-5899	307	7	18	18	NUM
ejpam-5899	307	8	(	(	PUNCT
ejpam-5899	307	9	2	2	NUM
ejpam-5899	307	10	)	)	PUNCT
ejpam-5899	307	11	(	(	PUNCT
ejpam-5899	307	12	2025	2025	NUM
ejpam-5899	307	13	)	)	PUNCT
ejpam-5899	307	14	,	,	PUNCT
ejpam-5899	307	15	5899	5899	NUM
ejpam-5899	307	16	10	10	NUM
ejpam-5899	307	17	of	of	ADP
ejpam-5899	307	18	11	11	NUM
ejpam-5899	307	19	theorem	theorem	NOUN
ejpam-5899	307	20	16	16	NUM
ejpam-5899	307	21	.	.	PUNCT
ejpam-5899	308	1	let	let	AUX
ejpam-5899	308	2	(	(	PUNCT
ejpam-5899	308	3	s	s	X
ejpam-5899	308	4	,	,	PUNCT
ejpam-5899	308	5	µ	µ	NOUN
ejpam-5899	308	6	)	)	PUNCT
ejpam-5899	308	7	be	be	AUX
ejpam-5899	308	8	a	a	DET
ejpam-5899	308	9	t2	t2	NOUN
ejpam-5899	308	10	-	-	PUNCT
ejpam-5899	308	11	topological	topological	ADJ
ejpam-5899	308	12	space	space	NOUN
ejpam-5899	308	13	.	.	PUNCT
ejpam-5899	309	1	then	then	ADV
ejpam-5899	309	2	µαgµ	µαgµ	PROPN
ejpam-5899	309	3	=	=	SYM
ejpam-5899	309	4	(	(	PUNCT
ejpam-5899	309	5	µαgµ)αgµ.	µαgµ)αgµ.	ADP
ejpam-5899	309	6	proof	proof	NOUN
ejpam-5899	309	7	.	.	PUNCT
ejpam-5899	310	1	at	at	ADP
ejpam-5899	310	2	first	first	ADV
ejpam-5899	310	3	,	,	PUNCT
ejpam-5899	310	4	note	note	VERB
ejpam-5899	310	5	that	that	SCONJ
ejpam-5899	310	6	a	a	DET
ejpam-5899	310	7	subset	subset	NOUN
ejpam-5899	310	8	e	e	X
ejpam-5899	310	9	of	of	ADP
ejpam-5899	310	10	(	(	PUNCT
ejpam-5899	310	11	s	s	PROPN
ejpam-5899	310	12	,	,	PUNCT
ejpam-5899	310	13	µ	µ	NOUN
ejpam-5899	310	14	)	)	PUNCT
ejpam-5899	310	15	is	be	AUX
ejpam-5899	310	16	α	α	DET
ejpam-5899	310	17	-	-	PUNCT
ejpam-5899	310	18	gµ-paracompact	gµ-paracompact	ADJ
ejpam-5899	310	19	iff	iff	NOUN
ejpam-5899	310	20	it	it	PRON
ejpam-5899	310	21	is	be	AUX
ejpam-5899	310	22	α	α	NOUN
ejpam-5899	310	23	-	-	NOUN
ejpam-5899	310	24	paracompact	paracompact	NOUN
ejpam-5899	310	25	in	in	ADP
ejpam-5899	310	26	(	(	PUNCT
ejpam-5899	310	27	s	s	PROPN
ejpam-5899	310	28	,	,	PUNCT
ejpam-5899	310	29	µ	µ	NOUN
ejpam-5899	310	30	)	)	PUNCT
ejpam-5899	310	31	since	since	SCONJ
ejpam-5899	310	32	µ	µ	NOUN
ejpam-5899	310	33	=	=	SYM
ejpam-5899	310	34	µ∗.	µ∗.	NOUN
ejpam-5899	310	35	as	as	ADP
ejpam-5899	310	36	in	in	ADP
ejpam-5899	310	37	the	the	DET
ejpam-5899	310	38	proof	proof	NOUN
ejpam-5899	310	39	of	of	ADP
ejpam-5899	310	40	theorem	theorem	NOUN
ejpam-5899	310	41	10	10	NUM
ejpam-5899	310	42	each	each	DET
ejpam-5899	310	43	α	α	NOUN
ejpam-5899	310	44	-	-	PUNCT
ejpam-5899	310	45	paracompact	paracompact	ADJ
ejpam-5899	310	46	set	set	NOUN
ejpam-5899	310	47	in	in	ADP
ejpam-5899	310	48	(	(	PUNCT
ejpam-5899	310	49	s	s	PROPN
ejpam-5899	310	50	,	,	PUNCT
ejpam-5899	310	51	µ	µ	NOUN
ejpam-5899	310	52	)	)	PUNCT
ejpam-5899	310	53	is	be	AUX
ejpam-5899	310	54	closed	close	VERB
ejpam-5899	310	55	and	and	CCONJ
ejpam-5899	310	56	so	so	ADV
ejpam-5899	310	57	by	by	ADP
ejpam-5899	310	58	theorem	theorem	NOUN
ejpam-5899	310	59	14	14	NUM
ejpam-5899	310	60	,	,	PUNCT
ejpam-5899	310	61	µ	µ	X
ejpam-5899	310	62	=	=	SYM
ejpam-5899	310	63	µαgµ.	µαgµ.	NOUN
ejpam-5899	310	64	therefore	therefore	ADV
ejpam-5899	310	65	,	,	PUNCT
ejpam-5899	310	66	(	(	PUNCT
ejpam-5899	310	67	µαgµ)αgµ	µαgµ)αgµ	NOUN
ejpam-5899	310	68	=	=	SYM
ejpam-5899	310	69	µαgµ	µαgµ	NOUN
ejpam-5899	310	70	=	=	SYM
ejpam-5899	310	71	µ.	µ.	NOUN
ejpam-5899	310	72	5	5	X
ejpam-5899	310	73	.	.	X
ejpam-5899	310	74	conclusion	conclusion	NOUN
ejpam-5899	310	75	one	one	NUM
ejpam-5899	310	76	major	major	ADJ
ejpam-5899	310	77	area	area	NOUN
ejpam-5899	310	78	of	of	ADP
ejpam-5899	310	79	study	study	NOUN
ejpam-5899	310	80	in	in	ADP
ejpam-5899	310	81	topological	topological	ADJ
ejpam-5899	310	82	studies	study	NOUN
ejpam-5899	310	83	is	be	AUX
ejpam-5899	310	84	the	the	DET
ejpam-5899	310	85	exploration	exploration	NOUN
ejpam-5899	310	86	of	of	ADP
ejpam-5899	310	87	topological	topological	ADJ
ejpam-5899	310	88	notions	notion	NOUN
ejpam-5899	310	89	and	and	CCONJ
ejpam-5899	310	90	topics	topic	NOUN
ejpam-5899	310	91	through	through	ADP
ejpam-5899	310	92	extensions	extension	NOUN
ejpam-5899	310	93	of	of	ADP
ejpam-5899	310	94	classical	classical	ADJ
ejpam-5899	310	95	topology	topology	NOUN
ejpam-5899	310	96	.	.	PUNCT
ejpam-5899	311	1	generalized	generalized	ADJ
ejpam-5899	311	2	topology	topology	NOUN
ejpam-5899	311	3	is	be	AUX
ejpam-5899	311	4	one	one	NUM
ejpam-5899	311	5	of	of	ADP
ejpam-5899	311	6	the	the	DET
ejpam-5899	311	7	recent	recent	ADJ
ejpam-5899	311	8	extensions	extension	NOUN
ejpam-5899	311	9	of	of	ADP
ejpam-5899	311	10	topology	topology	NOUN
ejpam-5899	311	11	and	and	CCONJ
ejpam-5899	311	12	hence	hence	ADV
ejpam-5899	311	13	we	we	PRON
ejpam-5899	311	14	investigate	investigate	VERB
ejpam-5899	311	15	the	the	DET
ejpam-5899	311	16	definition	definition	NOUN
ejpam-5899	311	17	of	of	ADP
ejpam-5899	311	18	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	311	19	space	space	NOUN
ejpam-5899	311	20	that	that	PRON
ejpam-5899	311	21	is	be	AUX
ejpam-5899	311	22	defined	define	VERB
ejpam-5899	311	23	in	in	ADP
ejpam-5899	311	24	[	[	X
ejpam-5899	311	25	6	6	NUM
ejpam-5899	311	26	]	]	PUNCT
ejpam-5899	311	27	,	,	PUNCT
ejpam-5899	311	28	to	to	PART
ejpam-5899	311	29	study	study	VERB
ejpam-5899	311	30	the	the	DET
ejpam-5899	311	31	main	main	ADJ
ejpam-5899	311	32	characteristics	characteristic	NOUN
ejpam-5899	311	33	of	of	ADP
ejpam-5899	311	34	two	two	NUM
ejpam-5899	311	35	types	type	NOUN
ejpam-5899	311	36	of	of	ADP
ejpam-5899	311	37	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	311	38	subsets	subset	NOUN
ejpam-5899	311	39	,	,	PUNCT
ejpam-5899	311	40	namely	namely	ADV
ejpam-5899	311	41	,	,	PUNCT
ejpam-5899	311	42	α	α	X
ejpam-5899	311	43	-	-	PUNCT
ejpam-5899	311	44	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	311	45	and	and	CCONJ
ejpam-5899	311	46	β	β	NOUN
ejpam-5899	311	47	-	-	NOUN
ejpam-5899	311	48	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	311	49	and	and	CCONJ
ejpam-5899	311	50	we	we	PRON
ejpam-5899	311	51	examine	examine	VERB
ejpam-5899	311	52	the	the	DET
ejpam-5899	311	53	relationship	relationship	NOUN
ejpam-5899	311	54	between	between	ADP
ejpam-5899	311	55	them	they	PRON
ejpam-5899	311	56	.	.	PUNCT
ejpam-5899	312	1	in	in	ADP
ejpam-5899	312	2	future	future	ADJ
ejpam-5899	312	3	work	work	NOUN
ejpam-5899	312	4	,	,	PUNCT
ejpam-5899	312	5	we	we	PRON
ejpam-5899	312	6	intend	intend	VERB
ejpam-5899	312	7	to	to	PART
ejpam-5899	312	8	study	study	VERB
ejpam-5899	312	9	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	312	10	spaces	space	NOUN
ejpam-5899	312	11	in	in	ADP
ejpam-5899	312	12	other	other	ADJ
ejpam-5899	312	13	structures	structure	NOUN
ejpam-5899	312	14	such	such	ADJ
ejpam-5899	312	15	as	as	ADP
ejpam-5899	312	16	supra	supra	NOUN
ejpam-5899	312	17	and	and	CCONJ
ejpam-5899	312	18	infra	infra	NOUN
ejpam-5899	312	19	-	-	PUNCT
ejpam-5899	312	20	topological	topological	ADJ
ejpam-5899	312	21	spaces	space	NOUN
ejpam-5899	312	22	.	.	PUNCT
ejpam-5899	313	1	furthermore	furthermore	ADV
ejpam-5899	313	2	,	,	PUNCT
ejpam-5899	313	3	we	we	PRON
ejpam-5899	313	4	can	can	AUX
ejpam-5899	313	5	study	study	VERB
ejpam-5899	313	6	and	and	CCONJ
ejpam-5899	313	7	define	define	VERB
ejpam-5899	313	8	other	other	ADJ
ejpam-5899	313	9	forms	form	NOUN
ejpam-5899	313	10	of	of	ADP
ejpam-5899	313	11	gµ-paracompact	gµ-paracompact	NOUN
ejpam-5899	313	12	spaces	space	NOUN
ejpam-5899	313	13	by	by	ADP
ejpam-5899	313	14	using	use	VERB
ejpam-5899	313	15	µ-semi	µ-semi	NOUN
ejpam-5899	313	16	-	-	ADJ
ejpam-5899	313	17	open	open	ADJ
ejpam-5899	313	18	or	or	CCONJ
ejpam-5899	313	19	µ-preopen	µ-preopen	PROPN
ejpam-5899	313	20	sets	set	NOUN
ejpam-5899	313	21	which	which	PRON
ejpam-5899	313	22	are	be	AUX
ejpam-5899	313	23	defined	define	VERB
ejpam-5899	313	24	in	in	ADP
ejpam-5899	313	25	[	[	X
ejpam-5899	313	26	5	5	NUM
ejpam-5899	313	27	]	]	PUNCT
ejpam-5899	313	28	.	.	PUNCT
ejpam-5899	314	1	acknowledgements	acknowledgement	VERB
ejpam-5899	314	2	the	the	DET
ejpam-5899	314	3	publication	publication	NOUN
ejpam-5899	314	4	of	of	ADP
ejpam-5899	314	5	this	this	DET
ejpam-5899	314	6	paper	paper	NOUN
ejpam-5899	314	7	was	be	AUX
ejpam-5899	314	8	supported	support	VERB
ejpam-5899	314	9	by	by	ADP
ejpam-5899	314	10	the	the	DET
ejpam-5899	314	11	yarmouk	yarmouk	PROPN
ejpam-5899	314	12	university	university	NOUN
ejpam-5899	314	13	research	research	NOUN
ejpam-5899	314	14	council	council	PROPN
ejpam-5899	314	15	.	.	PUNCT
ejpam-5899	315	1	availability	availability	NOUN
ejpam-5899	315	2	of	of	ADP
ejpam-5899	315	3	data	datum	NOUN
ejpam-5899	315	4	and	and	CCONJ
ejpam-5899	315	5	material	material	NOUN
ejpam-5899	315	6	:	:	PUNCT
ejpam-5899	315	7	no	no	DET
ejpam-5899	315	8	data	datum	NOUN
ejpam-5899	315	9	were	be	AUX
ejpam-5899	315	10	used	use	VERB
ejpam-5899	315	11	to	to	PART
ejpam-5899	315	12	support	support	VERB
ejpam-5899	315	13	this	this	DET
ejpam-5899	315	14	study	study	NOUN
ejpam-5899	315	15	.	.	PUNCT
ejpam-5899	316	1	conflicts	conflict	NOUN
ejpam-5899	316	2	of	of	ADP
ejpam-5899	316	3	interest	interest	NOUN
ejpam-5899	316	4	:	:	PUNCT
ejpam-5899	316	5	the	the	DET
ejpam-5899	316	6	authors	author	NOUN
ejpam-5899	316	7	declare	declare	VERB
ejpam-5899	316	8	no	no	DET
ejpam-5899	316	9	conflict	conflict	NOUN
ejpam-5899	316	10	of	of	ADP
ejpam-5899	316	11	interest	interest	NOUN
ejpam-5899	316	12	.	.	PUNCT
ejpam-5899	317	1	references	reference	NOUN
ejpam-5899	317	2	[	[	X
ejpam-5899	317	3	1	1	NUM
ejpam-5899	317	4	]	]	PUNCT
ejpam-5899	317	5	k.	k.	PROPN
ejpam-5899	317	6	y.	y.	PROPN
ejpam-5899	317	7	al	al	PROPN
ejpam-5899	317	8	-	-	PROPN
ejpam-5899	317	9	zoubi	zoubi	PROPN
ejpam-5899	317	10	,	,	PUNCT
ejpam-5899	317	11	b.	b.	PROPN
ejpam-5899	317	12	al	al	PROPN
ejpam-5899	317	13	-	-	PUNCT
ejpam-5899	317	14	nashef	nashef	PROPN
ejpam-5899	317	15	,	,	PUNCT
ejpam-5899	317	16	i	i	PROPN
ejpam-5899	317	17	-	-	PUNCT
ejpam-5899	317	18	lindelöf	lindelöf	NOUN
ejpam-5899	317	19	spaces	space	NOUN
ejpam-5899	317	20	,	,	PUNCT
ejpam-5899	317	21	int	int	PROPN
ejpam-5899	317	22	.	.	PUNCT
ejpam-5899	318	1	j.	j.	PROPN
ejpam-5899	318	2	math	math	PROPN
ejpam-5899	318	3	.	.	PUNCT
ejpam-5899	319	1	math	math	NOUN
ejpam-5899	319	2	.	.	PUNCT
ejpam-5899	320	1	sci	sci	PROPN
ejpam-5899	320	2	.	.	PROPN
ejpam-5899	320	3	,	,	PUNCT
ejpam-5899	320	4	vol	vol	NOUN
ejpam-5899	320	5	.	.	PROPN
ejpam-5899	320	6	2004	2004	NUM
ejpam-5899	320	7	,	,	PUNCT
ejpam-5899	320	8	article	article	NOUN
ejpam-5899	320	9	i	i	PROPN
ejpam-5899	320	10	d	d	PROPN
ejpam-5899	320	11	173213	173213	NUM
ejpam-5899	320	12	,	,	PUNCT
ejpam-5899	320	13	7	7	NUM
ejpam-5899	320	14	pages	page	NOUN
ejpam-5899	320	15	,	,	PUNCT
ejpam-5899	320	16	2004	2004	NUM
ejpam-5899	320	17	.	.	PUNCT
ejpam-5899	321	1	[	[	X
ejpam-5899	321	2	2	2	NUM
ejpam-5899	321	3	]	]	X
ejpam-5899	321	4	k.y	k.y	PROPN
ejpam-5899	321	5	.	.	PROPN
ejpam-5899	321	6	al	al	PROPN
ejpam-5899	321	7	-	-	PROPN
ejpam-5899	321	8	zoubi	zoubi	PROPN
ejpam-5899	321	9	,	,	PUNCT
ejpam-5899	321	10	on	on	ADP
ejpam-5899	321	11	i	i	PROPN
ejpam-5899	321	12	-	-	PUNCT
ejpam-5899	321	13	lindelöf	lindelöf	NOUN
ejpam-5899	321	14	sets	set	NOUN
ejpam-5899	321	15	,	,	PUNCT
ejpam-5899	321	16	acta	acta	PROPN
ejpam-5899	321	17	math	math	PROPN
ejpam-5899	321	18	.	.	PUNCT
ejpam-5899	322	1	hungar	hungar	PROPN
ejpam-5899	322	2	.	.	PUNCT
ejpam-5899	323	1	,	,	PUNCT
ejpam-5899	323	2	118	118	NUM
ejpam-5899	323	3	(	(	PUNCT
ejpam-5899	323	4	2008	2008	NUM
ejpam-5899	323	5	)	)	PUNCT
ejpam-5899	323	6	,	,	PUNCT
ejpam-5899	323	7	75	75	NUM
ejpam-5899	323	8	-	-	SYM
ejpam-5899	323	9	83	83	NUM
ejpam-5899	323	10	.	.	PUNCT
ejpam-5899	324	1	[	[	X
ejpam-5899	324	2	3	3	X
ejpam-5899	324	3	]	]	X
ejpam-5899	324	4	c.	c.	PROPN
ejpam-5899	324	5	e.	e.	PROPN
ejpam-5899	324	6	aull	aull	PROPN
ejpam-5899	324	7	,	,	PUNCT
ejpam-5899	324	8	paracompact	paracompact	ADJ
ejpam-5899	324	9	subsets	subset	NOUN
ejpam-5899	324	10	,	,	PUNCT
ejpam-5899	324	11	proc	proc	NOUN
ejpam-5899	324	12	.	.	PUNCT
ejpam-5899	325	1	of	of	ADP
ejpam-5899	325	2	the	the	DET
ejpam-5899	325	3	second	second	ADJ
ejpam-5899	325	4	prague	prague	PROPN
ejpam-5899	325	5	topological	topological	PROPN
ejpam-5899	325	6	symposium	symposium	NOUN
ejpam-5899	325	7	,	,	PUNCT
ejpam-5899	325	8	prague	prague	NOUN
ejpam-5899	325	9	(	(	PUNCT
ejpam-5899	325	10	1966	1966	NUM
ejpam-5899	325	11	)	)	PUNCT
ejpam-5899	325	12	,	,	PUNCT
ejpam-5899	325	13	45	45	NUM
ejpam-5899	325	14	-	-	SYM
ejpam-5899	325	15	51	51	NUM
ejpam-5899	325	16	.	.	PUNCT
ejpam-5899	326	1	[	[	X
ejpam-5899	326	2	4	4	X
ejpam-5899	326	3	]	]	PUNCT
ejpam-5899	326	4	á.	á.	PRON
ejpam-5899	326	5	császár	császár	PROPN
ejpam-5899	326	6	,	,	PUNCT
ejpam-5899	326	7	generalized	generalized	ADJ
ejpam-5899	326	8	topology	topology	NOUN
ejpam-5899	326	9	,	,	PUNCT
ejpam-5899	326	10	generalized	generalized	ADJ
ejpam-5899	326	11	continuity	continuity	NOUN
ejpam-5899	326	12	,	,	PUNCT
ejpam-5899	326	13	acta	acta	PROPN
ejpam-5899	326	14	math	math	PROPN
ejpam-5899	326	15	.	.	PUNCT
ejpam-5899	327	1	hungar	hungar	PROPN
ejpam-5899	327	2	.	.	PUNCT
ejpam-5899	328	1	,	,	PUNCT
ejpam-5899	328	2	96	96	NUM
ejpam-5899	328	3	(	(	PUNCT
ejpam-5899	328	4	2002	2002	NUM
ejpam-5899	328	5	)	)	PUNCT
ejpam-5899	328	6	,	,	PUNCT
ejpam-5899	328	7	351	351	NUM
ejpam-5899	328	8	-	-	SYM
ejpam-5899	328	9	357	357	NUM
ejpam-5899	328	10	.	.	PUNCT
ejpam-5899	329	1	[	[	X
ejpam-5899	329	2	5	5	NUM
ejpam-5899	329	3	]	]	PUNCT
ejpam-5899	329	4	á.	á.	PROPN
ejpam-5899	329	5	császár	császár	NOUN
ejpam-5899	329	6	,	,	PUNCT
ejpam-5899	329	7	generalized	generalize	VERB
ejpam-5899	329	8	open	open	ADJ
ejpam-5899	329	9	sets	set	NOUN
ejpam-5899	329	10	in	in	ADP
ejpam-5899	329	11	generalized	generalized	ADJ
ejpam-5899	329	12	topologies	topology	NOUN
ejpam-5899	329	13	,	,	PUNCT
ejpam-5899	329	14	acta	acta	PROPN
ejpam-5899	329	15	math	math	PROPN
ejpam-5899	329	16	.	.	PUNCT
ejpam-5899	330	1	hungar	hungar	PROPN
ejpam-5899	330	2	.	.	PUNCT
ejpam-5899	331	1	,	,	PUNCT
ejpam-5899	331	2	106	106	NUM
ejpam-5899	331	3	(	(	PUNCT
ejpam-5899	331	4	1	1	NUM
ejpam-5899	331	5	-	-	SYM
ejpam-5899	331	6	2	2	NUM
ejpam-5899	331	7	)	)	PUNCT
ejpam-5899	331	8	(	(	PUNCT
ejpam-5899	331	9	2005	2005	NUM
ejpam-5899	331	10	)	)	PUNCT
ejpam-5899	331	11	,	,	PUNCT
ejpam-5899	331	12	53	53	NUM
ejpam-5899	331	13	-	-	SYM
ejpam-5899	331	14	66	66	NUM
ejpam-5899	331	15	.	.	PUNCT
ejpam-5899	332	1	[	[	X
ejpam-5899	332	2	6	6	NUM
ejpam-5899	332	3	]	]	PUNCT
ejpam-5899	332	4	a.	a.	NOUN
ejpam-5899	332	5	deb	deb	PROPN
ejpam-5899	332	6	ray	ray	PROPN
ejpam-5899	332	7	and	and	CCONJ
ejpam-5899	332	8	r.	r.	PROPN
ejpam-5899	332	9	bhowmick	bhowmick	PROPN
ejpam-5899	332	10	,	,	PUNCT
ejpam-5899	332	11	µ-paracompact	µ-paracompact	PROPN
ejpam-5899	332	12	and	and	CCONJ
ejpam-5899	332	13	gµ-paracompact	gµ-paracompact	VERB
ejpam-5899	332	14	generalized	generalize	VERB
ejpam-5899	332	15	topological	topological	ADJ
ejpam-5899	332	16	spaces	space	NOUN
ejpam-5899	332	17	,	,	PUNCT
ejpam-5899	332	18	hacettepe	hacettepe	PROPN
ejpam-5899	332	19	j.	j.	PROPN
ejpam-5899	332	20	math	math	PROPN
ejpam-5899	332	21	.	.	PUNCT
ejpam-5899	333	1	stat	stat	PROPN
ejpam-5899	333	2	.	.	PUNCT
ejpam-5899	333	3	,	,	PUNCT
ejpam-5899	333	4	45(2	45(2	NOUN
ejpam-5899	333	5	)	)	PUNCT
ejpam-5899	333	6	(	(	PUNCT
ejpam-5899	333	7	2016	2016	NUM
ejpam-5899	333	8	)	)	PUNCT
ejpam-5899	333	9	,	,	PUNCT
ejpam-5899	333	10	447	447	NUM
ejpam-5899	333	11	-	-	SYM
ejpam-5899	333	12	453	453	NUM
ejpam-5899	333	13	.	.	PUNCT
ejpam-5899	334	1	[	[	X
ejpam-5899	334	2	7	7	X
ejpam-5899	334	3	]	]	X
ejpam-5899	334	4	j.	j.	PROPN
ejpam-5899	334	5	dieudonné	dieudonné	PROPN
ejpam-5899	334	6	,	,	PUNCT
ejpam-5899	334	7	une	une	PROPN
ejpam-5899	334	8	generalization	generalization	NOUN
ejpam-5899	334	9	des	des	PROPN
ejpam-5899	334	10	espaces	espaces	PROPN
ejpam-5899	334	11	compacts	compact	NOUN
ejpam-5899	334	12	,	,	PUNCT
ejpam-5899	334	13	j.	j.	PROPN
ejpam-5899	334	14	math	math	PROPN
ejpam-5899	334	15	.	.	PUNCT
ejpam-5899	335	1	pures	pure	NOUN
ejpam-5899	335	2	appl	appl	PROPN
ejpam-5899	335	3	.	.	PROPN
ejpam-5899	335	4	,	,	PUNCT
ejpam-5899	335	5	23	23	NUM
ejpam-5899	335	6	(	(	PUNCT
ejpam-5899	335	7	1944	1944	NUM
ejpam-5899	335	8	)	)	PUNCT
ejpam-5899	335	9	,	,	PUNCT
ejpam-5899	335	10	65	65	NUM
ejpam-5899	335	11	-	-	SYM
ejpam-5899	335	12	76	76	NUM
ejpam-5899	335	13	.	.	PUNCT
ejpam-5899	336	1	[	[	X
ejpam-5899	336	2	8	8	NUM
ejpam-5899	336	3	]	]	PUNCT
ejpam-5899	336	4	x.	x.	NOUN
ejpam-5899	336	5	ge	ge	PROPN
ejpam-5899	336	6	,	,	PUNCT
ejpam-5899	336	7	j.	j.	PROPN
ejpam-5899	336	8	gong	gong	PROPN
ejpam-5899	336	9	and	and	CCONJ
ejpam-5899	336	10	i.	i.	PROPN
ejpam-5899	336	11	reilly	reilly	PROPN
ejpam-5899	336	12	,	,	PUNCT
ejpam-5899	336	13	some	some	DET
ejpam-5899	336	14	characterizations	characterization	NOUN
ejpam-5899	336	15	of	of	ADP
ejpam-5899	336	16	mappings	mapping	NOUN
ejpam-5899	336	17	on	on	ADP
ejpam-5899	336	18	generalized	generalized	ADJ
ejpam-5899	336	19	topological	topological	ADJ
ejpam-5899	336	20	spaces	space	NOUN
ejpam-5899	336	21	,	,	PUNCT
ejpam-5899	336	22	new	new	PROPN
ejpam-5899	336	23	zealand	zealand	PROPN
ejpam-5899	336	24	j.	j.	PROPN
ejpam-5899	336	25	math	math	PROPN
ejpam-5899	336	26	.	.	PUNCT
ejpam-5899	336	27	,	,	PUNCT
ejpam-5899	336	28	46	46	NUM
ejpam-5899	336	29	(	(	PUNCT
ejpam-5899	336	30	2016	2016	NUM
ejpam-5899	336	31	)	)	PUNCT
ejpam-5899	336	32	,	,	PUNCT
ejpam-5899	336	33	73	73	NUM
ejpam-5899	336	34	-	-	SYM
ejpam-5899	336	35	81	81	NUM
ejpam-5899	336	36	.	.	PUNCT
ejpam-5899	337	1	h.	h.	PROPN
ejpam-5899	337	2	h.	h.	PROPN
ejpam-5899	337	3	al	al	PROPN
ejpam-5899	337	4	-	-	PUNCT
ejpam-5899	337	5	jarrah	jarrah	PROPN
ejpam-5899	337	6	et	et	PROPN
ejpam-5899	337	7	al	al	PROPN
ejpam-5899	337	8	.	.	PUNCT
ejpam-5899	337	9	/	/	SYM
ejpam-5899	337	10	eur	eur	PROPN
ejpam-5899	337	11	.	.	PUNCT
ejpam-5899	338	1	j.	j.	PROPN
ejpam-5899	338	2	pure	pure	PROPN
ejpam-5899	338	3	appl	appl	PROPN
ejpam-5899	338	4	.	.	PROPN
ejpam-5899	338	5	math	math	PROPN
ejpam-5899	338	6	,	,	PUNCT
ejpam-5899	338	7	18	18	NUM
ejpam-5899	338	8	(	(	PUNCT
ejpam-5899	338	9	2	2	NUM
ejpam-5899	338	10	)	)	PUNCT
ejpam-5899	338	11	(	(	PUNCT
ejpam-5899	338	12	2025	2025	NUM
ejpam-5899	338	13	)	)	PUNCT
ejpam-5899	338	14	,	,	PUNCT
ejpam-5899	338	15	5899	5899	NUM
ejpam-5899	338	16	11	11	NUM
ejpam-5899	338	17	of	of	ADP
ejpam-5899	338	18	11	11	NUM
ejpam-5899	339	1	[	[	X
ejpam-5899	339	2	9	9	NUM
ejpam-5899	339	3	]	]	PUNCT
ejpam-5899	339	4	s.	s.	PROPN
ejpam-5899	339	5	kowalczyk	kowalczyk	PROPN
ejpam-5899	339	6	,	,	PUNCT
ejpam-5899	339	7	m.	m.	NOUN
ejpam-5899	339	8	turowska	turowska	PROPN
ejpam-5899	339	9	,	,	PUNCT
ejpam-5899	339	10	on	on	ADP
ejpam-5899	339	11	continuity	continuity	NOUN
ejpam-5899	339	12	in	in	ADP
ejpam-5899	339	13	generalized	generalized	ADJ
ejpam-5899	339	14	topology	topology	NOUN
ejpam-5899	339	15	,	,	PUNCT
ejpam-5899	339	16	topol	topol	PROPN
ejpam-5899	339	17	.	.	PUNCT
ejpam-5899	340	1	appl	appl	PROPN
ejpam-5899	340	2	.	.	PROPN
ejpam-5899	340	3	,	,	PUNCT
ejpam-5899	340	4	297	297	NUM
ejpam-5899	340	5	(	(	PUNCT
ejpam-5899	340	6	2021	2021	NUM
ejpam-5899	340	7	)	)	PUNCT
ejpam-5899	340	8	,	,	PUNCT
ejpam-5899	340	9	107702	107702	NUM
ejpam-5899	340	10	.	.	PUNCT
ejpam-5899	341	1	doi	doi	NOUN
ejpam-5899	341	2	:	:	PUNCT
ejpam-5899	341	3	10.1016	10.1016	NUM
ejpam-5899	341	4	/	/	SYM
ejpam-5899	341	5	j.topol.2021.107702	j.topol.2021.107702	PROPN
ejpam-5899	341	6	.	.	PUNCT
ejpam-5899	342	1	[	[	X
ejpam-5899	342	2	10	10	NUM
ejpam-5899	342	3	]	]	X
ejpam-5899	342	4	e.	e.	PROPN
ejpam-5899	342	5	michael	michael	PROPN
ejpam-5899	342	6	,	,	PUNCT
ejpam-5899	342	7	a	a	DET
ejpam-5899	342	8	note	note	NOUN
ejpam-5899	342	9	on	on	ADP
ejpam-5899	342	10	paracompact	paracompact	ADJ
ejpam-5899	342	11	spaces	space	NOUN
ejpam-5899	342	12	,	,	PUNCT
ejpam-5899	342	13	proc	proc	NOUN
ejpam-5899	342	14	.	.	PUNCT
ejpam-5899	343	1	amer	amer	PROPN
ejpam-5899	343	2	.	.	PUNCT
ejpam-5899	343	3	math	math	PROPN
ejpam-5899	343	4	.	.	PUNCT
ejpam-5899	344	1	soc	soc	PROPN
ejpam-5899	344	2	.	.	PROPN
ejpam-5899	344	3	,	,	PUNCT
ejpam-5899	344	4	4(5	4(5	PROPN
ejpam-5899	344	5	)	)	PUNCT
ejpam-5899	344	6	(	(	PUNCT
ejpam-5899	344	7	1953	1953	NUM
ejpam-5899	344	8	)	)	PUNCT
ejpam-5899	344	9	,	,	PUNCT
ejpam-5899	344	10	831	831	NUM
ejpam-5899	344	11	-	-	SYM
ejpam-5899	344	12	838	838	NUM
ejpam-5899	344	13	.	.	PUNCT
ejpam-5899	345	1	[	[	X
ejpam-5899	345	2	11	11	NUM
ejpam-5899	345	3	]	]	PUNCT
ejpam-5899	345	4	a.	a.	NOUN
ejpam-5899	345	5	qahis	qahis	PROPN
ejpam-5899	345	6	and	and	CCONJ
ejpam-5899	345	7	t.	t.	PROPN
ejpam-5899	345	8	noiri	noiri	PROPN
ejpam-5899	345	9	,	,	PUNCT
ejpam-5899	345	10	µ-paracompactness	µ-paracompactness	NOUN
ejpam-5899	345	11	via	via	ADP
ejpam-5899	345	12	hereditary	hereditary	ADJ
ejpam-5899	345	13	classes	class	NOUN
ejpam-5899	345	14	,	,	PUNCT
ejpam-5899	345	15	missouri	missouri	PROPN
ejpam-5899	345	16	j.	j.	PROPN
ejpam-5899	345	17	of	of	ADP
ejpam-5899	345	18	math	math	PROPN
ejpam-5899	345	19	.	.	PUNCT
ejpam-5899	346	1	sci	sci	PROPN
ejpam-5899	346	2	.	.	PROPN
ejpam-5899	346	3	,	,	PUNCT
ejpam-5899	346	4	32(1	32(1	NUM
ejpam-5899	346	5	)	)	PUNCT
ejpam-5899	346	6	(	(	PUNCT
ejpam-5899	346	7	2020	2020	NUM
ejpam-5899	346	8	)	)	PUNCT
ejpam-5899	346	9	,	,	PUNCT
ejpam-5899	346	10	21	21	NUM
ejpam-5899	346	11	-	-	SYM
ejpam-5899	346	12	31	31	NUM
ejpam-5899	346	13	.	.	PUNCT
ejpam-5899	347	1	[	[	X
ejpam-5899	347	2	12	12	NUM
ejpam-5899	347	3	]	]	X
ejpam-5899	347	4	b.	b.	PROPN
ejpam-5899	347	5	roy	roy	PROPN
ejpam-5899	347	6	,	,	PUNCT
ejpam-5899	347	7	a	a	DET
ejpam-5899	347	8	note	note	NOUN
ejpam-5899	347	9	on	on	ADP
ejpam-5899	347	10	weakly	weakly	ADJ
ejpam-5899	347	11	(	(	PUNCT
ejpam-5899	347	12	µ	µ	NUM
ejpam-5899	347	13	,	,	PUNCT
ejpam-5899	347	14	λ)-closed	λ)-close	VERB
ejpam-5899	347	15	function	function	NOUN
ejpam-5899	347	16	,	,	PUNCT
ejpam-5899	347	17	math	math	NOUN
ejpam-5899	347	18	.	.	PUNCT
ejpam-5899	348	1	bohemica	bohemica	PROPN
ejpam-5899	348	2	,	,	PUNCT
ejpam-5899	348	3	138(4	138(4	NUM
ejpam-5899	348	4	)	)	PUNCT
ejpam-5899	348	5	(	(	PUNCT
ejpam-5899	348	6	2013	2013	NUM
ejpam-5899	348	7	)	)	PUNCT
ejpam-5899	348	8	,	,	PUNCT
ejpam-5899	348	9	397	397	NUM
ejpam-5899	348	10	-	-	SYM
ejpam-5899	348	11	405	405	NUM
ejpam-5899	348	12	.	.	PUNCT
ejpam-5899	349	1	[	[	X
ejpam-5899	349	2	13	13	NUM
ejpam-5899	349	3	]	]	X
ejpam-5899	349	4	b.	b.	PROPN
ejpam-5899	349	5	roy	roy	PROPN
ejpam-5899	349	6	,	,	PUNCT
ejpam-5899	349	7	on	on	ADP
ejpam-5899	349	8	a	a	DET
ejpam-5899	349	9	type	type	NOUN
ejpam-5899	349	10	of	of	ADP
ejpam-5899	349	11	generalized	generalized	ADJ
ejpam-5899	349	12	open	open	ADJ
ejpam-5899	349	13	sets	set	NOUN
ejpam-5899	349	14	,	,	PUNCT
ejpam-5899	349	15	appl	appl	PROPN
ejpam-5899	349	16	.	.	PUNCT
ejpam-5899	350	1	gen	gen	PROPN
ejpam-5899	350	2	.	.	PROPN
ejpam-5899	350	3	topology	topology	PROPN
ejpam-5899	350	4	,	,	PUNCT
ejpam-5899	350	5	12	12	NUM
ejpam-5899	350	6	(	(	PUNCT
ejpam-5899	350	7	2011	2011	NUM
ejpam-5899	350	8	)	)	PUNCT
ejpam-5899	350	9	,	,	PUNCT
ejpam-5899	350	10	163	163	NUM
ejpam-5899	350	11	-	-	SYM
ejpam-5899	350	12	173	173	NUM
ejpam-5899	350	13	.	.	PUNCT
ejpam-5899	351	1	[	[	X
ejpam-5899	351	2	14	14	NUM
ejpam-5899	351	3	]	]	PUNCT
ejpam-5899	351	4	m.	m.	NOUN
ejpam-5899	351	5	s.	s.	PROPN
ejpam-5899	351	6	sarsak	sarsak	PROPN
ejpam-5899	351	7	,	,	PUNCT
ejpam-5899	351	8	weak	weak	ADJ
ejpam-5899	351	9	separation	separation	NOUN
ejpam-5899	351	10	axioms	axiom	NOUN
ejpam-5899	351	11	in	in	ADP
ejpam-5899	351	12	generalized	generalized	ADJ
ejpam-5899	351	13	topological	topological	ADJ
ejpam-5899	351	14	spaces	space	NOUN
ejpam-5899	351	15	,	,	PUNCT
ejpam-5899	351	16	acta	acta	PROPN
ejpam-5899	351	17	math	math	PROPN
ejpam-5899	351	18	.	.	PUNCT
ejpam-5899	352	1	hungar	hungar	PROPN
ejpam-5899	352	2	.	.	PUNCT
ejpam-5899	353	1	,	,	PUNCT
ejpam-5899	353	2	131	131	NUM
ejpam-5899	353	3	(	(	PUNCT
ejpam-5899	353	4	2011	2011	NUM
ejpam-5899	353	5	)	)	PUNCT
ejpam-5899	353	6	,	,	PUNCT
ejpam-5899	353	7	110	110	NUM
ejpam-5899	353	8	-	-	SYM
ejpam-5899	353	9	121	121	NUM
ejpam-5899	353	10	.	.	PUNCT
ejpam-5899	354	1	[	[	X
ejpam-5899	354	2	15	15	NUM
ejpam-5899	354	3	]	]	X
ejpam-5899	354	4	r.	r.	PROPN
ejpam-5899	354	5	h.	h.	PROPN
ejpam-5899	354	6	sorgenfrey	sorgenfrey	PROPN
ejpam-5899	354	7	,	,	PUNCT
ejpam-5899	354	8	on	on	ADP
ejpam-5899	354	9	the	the	DET
ejpam-5899	354	10	topological	topological	ADJ
ejpam-5899	354	11	product	product	NOUN
ejpam-5899	354	12	of	of	ADP
ejpam-5899	354	13	paracompact	paracompact	ADJ
ejpam-5899	354	14	spaces	space	NOUN
ejpam-5899	354	15	,	,	PUNCT
ejpam-5899	354	16	bull	bull	NOUN
ejpam-5899	354	17	.	.	PUNCT
ejpam-5899	355	1	amer	amer	PROPN
ejpam-5899	355	2	.	.	PUNCT
ejpam-5899	355	3	math	math	PROPN
ejpam-5899	355	4	.	.	PUNCT
ejpam-5899	356	1	soc	soc	PROPN
ejpam-5899	356	2	.	.	PUNCT
ejpam-5899	356	3	,	,	PUNCT
ejpam-5899	356	4	53	53	NUM
ejpam-5899	356	5	(	(	PUNCT
ejpam-5899	356	6	1947	1947	NUM
ejpam-5899	356	7	)	)	PUNCT
ejpam-5899	356	8	,	,	PUNCT
ejpam-5899	356	9	631	631	NUM
ejpam-5899	356	10	-	-	SYM
ejpam-5899	356	11	632	632	NUM
ejpam-5899	356	12	.	.	PUNCT
ejpam-5899	357	1	[	[	X
ejpam-5899	357	2	16	16	NUM
ejpam-5899	357	3	]	]	PUNCT
ejpam-5899	357	4	a.	a.	NOUN
ejpam-5899	357	5	h.	h.	PROPN
ejpam-5899	357	6	stone	stone	PROPN
ejpam-5899	357	7	,	,	PUNCT
ejpam-5899	357	8	paracompactness	paracompactness	NOUN
ejpam-5899	357	9	and	and	CCONJ
ejpam-5899	357	10	product	product	NOUN
ejpam-5899	357	11	spaces	space	NOUN
ejpam-5899	357	12	,	,	PUNCT
ejpam-5899	357	13	bull	bull	NOUN
ejpam-5899	357	14	.	.	PUNCT
ejpam-5899	358	1	amer	amer	PROPN
ejpam-5899	358	2	.	.	PUNCT
ejpam-5899	358	3	math	math	PROPN
ejpam-5899	358	4	.	.	PUNCT
ejpam-5899	359	1	soc	soc	PROPN
ejpam-5899	359	2	.	.	PROPN
ejpam-5899	359	3	,	,	PUNCT
ejpam-5899	359	4	54	54	NUM
ejpam-5899	359	5	(	(	PUNCT
ejpam-5899	359	6	1948	1948	NUM
ejpam-5899	359	7	)	)	PUNCT
ejpam-5899	359	8	,	,	PUNCT
ejpam-5899	359	9	977	977	NUM
ejpam-5899	359	10	-	-	SYM
ejpam-5899	359	11	982	982	NUM
ejpam-5899	359	12	.	.	PUNCT
ejpam-5899	360	1	[	[	X
ejpam-5899	360	2	17	17	NUM
ejpam-5899	360	3	]	]	X
ejpam-5899	360	4	s.	s.	PROPN
ejpam-5899	360	5	willard	willard	PROPN
ejpam-5899	360	6	,	,	PUNCT
ejpam-5899	360	7	general	general	ADJ
ejpam-5899	360	8	topology	topology	NOUN
ejpam-5899	360	9	,	,	PUNCT
ejpam-5899	360	10	addition	addition	NOUN
ejpam-5899	360	11	wesley	wesley	NOUN
ejpam-5899	360	12	(	(	PUNCT
ejpam-5899	360	13	1970	1970	NUM
ejpam-5899	360	14	)	)	PUNCT
ejpam-5899	360	15	.	.	PUNCT