id	sid	tid	token	lemma	pos
ejpam-3029	1	1	european	european	PROPN
ejpam-3029	1	2	journal	journal	PROPN
ejpam-3029	1	3	of	of	ADP
ejpam-3029	1	4	pure	pure	ADJ
ejpam-3029	1	5	and	and	CCONJ
ejpam-3029	1	6	applied	apply	VERB
ejpam-3029	1	7	mathematics	mathematic	NOUN
ejpam-3029	1	8	vol	vol	NOUN
ejpam-3029	1	9	.	.	PROPN
ejpam-3029	2	1	10	10	NUM
ejpam-3029	2	2	,	,	PUNCT
ejpam-3029	2	3	no	no	INTJ
ejpam-3029	2	4	.	.	NOUN
ejpam-3029	2	5	3	3	NUM
ejpam-3029	2	6	,	,	PUNCT
ejpam-3029	2	7	2017	2017	NUM
ejpam-3029	2	8	,	,	PUNCT
ejpam-3029	2	9	410	410	NUM
ejpam-3029	2	10	-	-	SYM
ejpam-3029	2	11	418	418	NUM
ejpam-3029	2	12	issn	issn	PROPN
ejpam-3029	2	13	1307	1307	NUM
ejpam-3029	2	14	-	-	SYM
ejpam-3029	2	15	5543	5543	NUM
ejpam-3029	2	16	–	–	PUNCT
ejpam-3029	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3029	2	18	published	publish	VERB
ejpam-3029	2	19	by	by	ADP
ejpam-3029	2	20	new	new	PROPN
ejpam-3029	2	21	york	york	PROPN
ejpam-3029	2	22	business	business	PROPN
ejpam-3029	2	23	global	global	PROPN
ejpam-3029	2	24	invited	invite	VERB
ejpam-3029	2	25	paper	paper	NOUN
ejpam-3029	2	26	functions	function	NOUN
ejpam-3029	2	27	and	and	CCONJ
ejpam-3029	2	28	weakly	weakly	ADJ
ejpam-3029	2	29	µh	µh	ADJ
ejpam-3029	2	30	-	-	ADJ
ejpam-3029	2	31	compact	compact	ADJ
ejpam-3029	2	32	spaces	space	NOUN
ejpam-3029	2	33	abdo	abdo	PROPN
ejpam-3029	2	34	qahis1,∗	qahis1,∗	PROPN
ejpam-3029	2	35	,	,	PUNCT
ejpam-3029	2	36	takashi	takashi	PROPN
ejpam-3029	2	37	noiri2	noiri2	PROPN
ejpam-3029	2	38	1	1	NUM
ejpam-3029	2	39	department	department	NOUN
ejpam-3029	2	40	of	of	ADP
ejpam-3029	2	41	mathematics	mathematic	NOUN
ejpam-3029	2	42	,	,	PUNCT
ejpam-3029	2	43	faculty	faculty	NOUN
ejpam-3029	2	44	of	of	ADP
ejpam-3029	2	45	science	science	NOUN
ejpam-3029	2	46	and	and	CCONJ
ejpam-3029	2	47	arts	art	NOUN
ejpam-3029	2	48	,	,	PUNCT
ejpam-3029	2	49	nagran	nagran	ADJ
ejpam-3029	2	50	university	university	NOUN
ejpam-3029	2	51	,	,	PUNCT
ejpam-3029	2	52	saudi	saudi	PROPN
ejpam-3029	2	53	arabia	arabia	PROPN
ejpam-3029	2	54	.	.	PUNCT
ejpam-3029	3	1	2	2	NUM
ejpam-3029	3	2	shiokita	shiokita	NOUN
ejpam-3029	3	3	-	-	PUNCT
ejpam-3029	3	4	cho	cho	ADJ
ejpam-3029	3	5	,	,	PUNCT
ejpam-3029	3	6	hinagu	hinagu	ADJ
ejpam-3029	3	7	,	,	PUNCT
ejpam-3029	3	8	yatsushiro	yatsushiro	PROPN
ejpam-3029	3	9	-	-	PUNCT
ejpam-3029	3	10	shi	shi	PROPN
ejpam-3029	3	11	,	,	PUNCT
ejpam-3029	3	12	kumamoto	kumamoto	PROPN
ejpam-3029	3	13	-	-	PUNCT
ejpam-3029	3	14	ken	ken	PROPN
ejpam-3029	3	15	,	,	PUNCT
ejpam-3029	3	16	japan	japan	PROPN
ejpam-3029	3	17	.	.	PUNCT
ejpam-3029	4	1	abstract	abstract	PROPN
ejpam-3029	4	2	.	.	PUNCT
ejpam-3029	5	1	a	a	DET
ejpam-3029	5	2	gts	gts	NOUN
ejpam-3029	5	3	(	(	PUNCT
ejpam-3029	5	4	x,µ	x,µ	NOUN
ejpam-3029	5	5	)	)	PUNCT
ejpam-3029	5	6	is	be	AUX
ejpam-3029	5	7	said	say	VERB
ejpam-3029	5	8	to	to	PART
ejpam-3029	5	9	be	be	AUX
ejpam-3029	5	10	weakly	weakly	ADJ
ejpam-3029	5	11	µh	µh	NOUN
ejpam-3029	5	12	-	-	ADJ
ejpam-3029	5	13	compact	compact	ADJ
ejpam-3029	5	14	if	if	SCONJ
ejpam-3029	5	15	for	for	ADP
ejpam-3029	5	16	every	every	DET
ejpam-3029	5	17	µ-open	µ-open	NOUN
ejpam-3029	5	18	cover	cover	NOUN
ejpam-3029	5	19	{	{	PUNCT
ejpam-3029	5	20	vα	vα	X
ejpam-3029	5	21	:	:	PUNCT
ejpam-3029	5	22	α	α	PROPN
ejpam-3029	5	23	∈	∈	PROPN
ejpam-3029	5	24	∆	∆	PROPN
ejpam-3029	5	25	}	}	PUNCT
ejpam-3029	5	26	of	of	ADP
ejpam-3029	5	27	x	x	SYM
ejpam-3029	5	28	there	there	PRON
ejpam-3029	5	29	exists	exist	VERB
ejpam-3029	5	30	a	a	DET
ejpam-3029	5	31	finite	finite	NOUN
ejpam-3029	5	32	subset	subset	VERB
ejpam-3029	5	33	∆0	∆0	NUM
ejpam-3029	5	34	of	of	ADP
ejpam-3029	5	35	∆	∆	PROPN
ejpam-3029	5	36	such	such	ADJ
ejpam-3029	5	37	that	that	SCONJ
ejpam-3029	5	38	x	x	X
ejpam-3029	5	39	\	\	PROPN
ejpam-3029	5	40	∪{cµ(vα	∪{cµ(vα	PROPN
ejpam-3029	5	41	)	)	PUNCT
ejpam-3029	5	42	:	:	PUNCT
ejpam-3029	5	43	α	α	PROPN
ejpam-3029	5	44	∈	∈	PROPN
ejpam-3029	5	45	∆0	∆0	PRON
ejpam-3029	5	46	}	}	PUNCT
ejpam-3029	5	47	∈	∈	PROPN
ejpam-3029	5	48	h.	h.	NOUN
ejpam-3029	5	49	in	in	ADP
ejpam-3029	5	50	this	this	DET
ejpam-3029	5	51	paper	paper	NOUN
ejpam-3029	5	52	we	we	PRON
ejpam-3029	5	53	study	study	VERB
ejpam-3029	5	54	the	the	DET
ejpam-3029	5	55	effect	effect	NOUN
ejpam-3029	5	56	of	of	ADP
ejpam-3029	5	57	functions	function	NOUN
ejpam-3029	5	58	on	on	ADP
ejpam-3029	5	59	weakly	weakly	ADJ
ejpam-3029	5	60	µh	µh	ADJ
ejpam-3029	5	61	-	-	ADJ
ejpam-3029	5	62	compact	compact	ADJ
ejpam-3029	5	63	spaces	space	NOUN
ejpam-3029	5	64	.	.	PUNCT
ejpam-3029	6	1	the	the	DET
ejpam-3029	6	2	main	main	ADJ
ejpam-3029	6	3	result	result	NOUN
ejpam-3029	6	4	is	be	AUX
ejpam-3029	6	5	that	that	SCONJ
ejpam-3029	6	6	the	the	DET
ejpam-3029	6	7	θ(µ	θ(µ	PROPN
ejpam-3029	6	8	,	,	PUNCT
ejpam-3029	6	9	ν)-continuous	ν)-continuous	ADJ
ejpam-3029	6	10	image	image	NOUN
ejpam-3029	6	11	of	of	ADP
ejpam-3029	6	12	a	a	DET
ejpam-3029	6	13	weakly	weakly	ADJ
ejpam-3029	6	14	µh	µh	ADJ
ejpam-3029	6	15	-	-	ADJ
ejpam-3029	6	16	compact	compact	ADJ
ejpam-3029	6	17	space	space	NOUN
ejpam-3029	6	18	is	be	AUX
ejpam-3029	6	19	weakly	weakly	ADJ
ejpam-3029	6	20	νf(h)-compact	νf(h)-compact	PROPN
ejpam-3029	6	21	.	.	PUNCT
ejpam-3029	7	1	2010	2010	NUM
ejpam-3029	7	2	mathematics	mathematic	NOUN
ejpam-3029	7	3	subject	subject	NOUN
ejpam-3029	7	4	classifications	classification	NOUN
ejpam-3029	7	5	:	:	PUNCT
ejpam-3029	7	6	54a05	54a05	NUM
ejpam-3029	7	7	,	,	PUNCT
ejpam-3029	7	8	54a08	54a08	NUM
ejpam-3029	7	9	,	,	PUNCT
ejpam-3029	7	10	54d10	54d10	NUM
ejpam-3029	7	11	key	key	ADJ
ejpam-3029	7	12	words	word	NOUN
ejpam-3029	7	13	and	and	CCONJ
ejpam-3029	7	14	phrases	phrase	NOUN
ejpam-3029	7	15	:	:	PUNCT
ejpam-3029	7	16	generalized	generalized	ADJ
ejpam-3029	7	17	topology	topology	NOUN
ejpam-3029	7	18	,	,	PUNCT
ejpam-3029	7	19	hereditary	hereditary	ADJ
ejpam-3029	7	20	class	class	NOUN
ejpam-3029	7	21	,	,	PUNCT
ejpam-3029	7	22	µh	µh	NOUN
ejpam-3029	7	23	-	-	ADJ
ejpam-3029	7	24	compact	compact	ADJ
ejpam-3029	7	25	,	,	PUNCT
ejpam-3029	7	26	weakly	weakly	ADJ
ejpam-3029	7	27	µhcompact	µhcompact	NOUN
ejpam-3029	7	28	,	,	PUNCT
ejpam-3029	7	29	θ(µ	θ(µ	PROPN
ejpam-3029	7	30	,	,	PUNCT
ejpam-3029	7	31	ν)-continuity	ν)-continuity	NOUN
ejpam-3029	7	32	.	.	NOUN
ejpam-3029	8	1	1	1	X
ejpam-3029	8	2	.	.	X
ejpam-3029	8	3	introduction	introduction	NOUN
ejpam-3029	8	4	the	the	DET
ejpam-3029	8	5	ideas	idea	NOUN
ejpam-3029	8	6	of	of	ADP
ejpam-3029	8	7	generalized	generalized	ADJ
ejpam-3029	8	8	topology	topology	NOUN
ejpam-3029	8	9	and	and	CCONJ
ejpam-3029	8	10	hereditary	hereditary	ADJ
ejpam-3029	8	11	classes	class	NOUN
ejpam-3029	8	12	were	be	AUX
ejpam-3029	8	13	introduced	introduce	VERB
ejpam-3029	8	14	and	and	CCONJ
ejpam-3029	8	15	studied	study	VERB
ejpam-3029	8	16	by	by	ADP
ejpam-3029	8	17	császár	császár	NOUN
ejpam-3029	8	18	in	in	ADP
ejpam-3029	8	19	[	[	X
ejpam-3029	8	20	3	3	NUM
ejpam-3029	8	21	]	]	PUNCT
ejpam-3029	8	22	and	and	CCONJ
ejpam-3029	8	23	[	[	X
ejpam-3029	8	24	5	5	NUM
ejpam-3029	8	25	]	]	PUNCT
ejpam-3029	8	26	,	,	PUNCT
ejpam-3029	8	27	respectively	respectively	ADV
ejpam-3029	8	28	.	.	PUNCT
ejpam-3029	9	1	the	the	DET
ejpam-3029	9	2	strategy	strategy	NOUN
ejpam-3029	9	3	of	of	ADP
ejpam-3029	9	4	using	use	VERB
ejpam-3029	9	5	generalized	generalized	ADJ
ejpam-3029	9	6	topologies	topology	NOUN
ejpam-3029	9	7	and	and	CCONJ
ejpam-3029	9	8	hereditary	hereditary	ADJ
ejpam-3029	9	9	classes	class	NOUN
ejpam-3029	9	10	to	to	PART
ejpam-3029	9	11	extend	extend	VERB
ejpam-3029	9	12	classical	classical	ADJ
ejpam-3029	9	13	topological	topological	ADJ
ejpam-3029	9	14	concepts	concept	NOUN
ejpam-3029	9	15	have	have	AUX
ejpam-3029	9	16	been	be	AUX
ejpam-3029	9	17	used	use	VERB
ejpam-3029	9	18	by	by	ADP
ejpam-3029	9	19	many	many	ADJ
ejpam-3029	9	20	authors	author	NOUN
ejpam-3029	9	21	such	such	ADJ
ejpam-3029	9	22	as	as	ADP
ejpam-3029	9	23	[	[	X
ejpam-3029	9	24	5	5	NUM
ejpam-3029	9	25	]	]	PUNCT
ejpam-3029	9	26	,	,	PUNCT
ejpam-3029	9	27	[	[	X
ejpam-3029	9	28	8	8	NUM
ejpam-3029	9	29	]	]	PUNCT
ejpam-3029	9	30	,	,	PUNCT
ejpam-3029	9	31	[	[	X
ejpam-3029	9	32	15	15	NUM
ejpam-3029	9	33	]	]	PUNCT
ejpam-3029	9	34	,	,	PUNCT
ejpam-3029	9	35	and	and	CCONJ
ejpam-3029	9	36	[	[	X
ejpam-3029	9	37	18	18	NUM
ejpam-3029	9	38	]	]	PUNCT
ejpam-3029	9	39	.	.	PUNCT
ejpam-3029	10	1	moreover	moreover	ADV
ejpam-3029	10	2	,	,	PUNCT
ejpam-3029	10	3	investigations	investigation	NOUN
ejpam-3029	10	4	of	of	ADP
ejpam-3029	10	5	continuity	continuity	NOUN
ejpam-3029	10	6	on	on	ADP
ejpam-3029	10	7	generalized	generalized	ADJ
ejpam-3029	10	8	topological	topological	ADJ
ejpam-3029	10	9	spaces	space	NOUN
ejpam-3029	10	10	have	have	AUX
ejpam-3029	10	11	been	be	AUX
ejpam-3029	10	12	recently	recently	ADV
ejpam-3029	10	13	of	of	ADP
ejpam-3029	10	14	major	major	ADJ
ejpam-3029	10	15	interest	interest	NOUN
ejpam-3029	10	16	among	among	ADP
ejpam-3029	10	17	general	general	ADJ
ejpam-3029	10	18	topologists	topologist	NOUN
ejpam-3029	10	19	.	.	PUNCT
ejpam-3029	11	1	they	they	PRON
ejpam-3029	11	2	are	be	AUX
ejpam-3029	11	3	studied	study	VERB
ejpam-3029	11	4	by	by	ADP
ejpam-3029	11	5	many	many	ADJ
ejpam-3029	11	6	authors	author	NOUN
ejpam-3029	11	7	,	,	PUNCT
ejpam-3029	11	8	including	include	VERB
ejpam-3029	11	9	min	min	NOUN
ejpam-3029	11	10	[	[	X
ejpam-3029	11	11	10	10	NUM
ejpam-3029	11	12	]	]	PUNCT
ejpam-3029	11	13	,	,	PUNCT
ejpam-3029	11	14	al	al	PROPN
ejpam-3029	11	15	-	-	PUNCT
ejpam-3029	11	16	omari	omari	PROPN
ejpam-3029	11	17	and	and	CCONJ
ejpam-3029	11	18	noiri	noiri	ADV
ejpam-3029	12	1	[	[	X
ejpam-3029	12	2	1	1	NUM
ejpam-3029	12	3	]	]	PUNCT
ejpam-3029	12	4	,	,	PUNCT
ejpam-3029	12	5	császár	császár	PROPN
ejpam-3029	13	1	[	[	X
ejpam-3029	13	2	3	3	NUM
ejpam-3029	13	3	]	]	PUNCT
ejpam-3029	13	4	,	,	PUNCT
ejpam-3029	13	5	and	and	CCONJ
ejpam-3029	13	6	jayanthi	jayanthi	PROPN
ejpam-3029	14	1	[	[	X
ejpam-3029	14	2	6	6	NUM
ejpam-3029	14	3	]	]	PUNCT
ejpam-3029	14	4	.	.	PUNCT
ejpam-3029	15	1	in	in	ADP
ejpam-3029	15	2	fact	fact	NOUN
ejpam-3029	15	3	,	,	PUNCT
ejpam-3029	15	4	mathematicians	mathematician	NOUN
ejpam-3029	15	5	introduced	introduce	VERB
ejpam-3029	15	6	in	in	ADP
ejpam-3029	15	7	several	several	ADJ
ejpam-3029	15	8	papers	paper	NOUN
ejpam-3029	15	9	different	different	ADJ
ejpam-3029	15	10	and	and	CCONJ
ejpam-3029	15	11	interesting	interesting	ADJ
ejpam-3029	15	12	new	new	ADJ
ejpam-3029	15	13	types	type	NOUN
ejpam-3029	15	14	of	of	ADP
ejpam-3029	15	15	functions	function	NOUN
ejpam-3029	15	16	as	as	ADV
ejpam-3029	15	17	well	well	ADV
ejpam-3029	15	18	as	as	ADP
ejpam-3029	15	19	generalized	generalize	VERB
ejpam-3029	15	20	continuous	continuous	ADJ
ejpam-3029	15	21	functions	function	NOUN
ejpam-3029	15	22	in	in	ADP
ejpam-3029	15	23	generalized	generalized	ADJ
ejpam-3029	15	24	topological	topological	ADJ
ejpam-3029	15	25	spaces	space	NOUN
ejpam-3029	15	26	.	.	PUNCT
ejpam-3029	16	1	the	the	DET
ejpam-3029	16	2	purpose	purpose	NOUN
ejpam-3029	16	3	of	of	ADP
ejpam-3029	16	4	this	this	DET
ejpam-3029	16	5	paper	paper	NOUN
ejpam-3029	16	6	is	be	AUX
ejpam-3029	16	7	to	to	PART
ejpam-3029	16	8	study	study	VERB
ejpam-3029	16	9	the	the	DET
ejpam-3029	16	10	effect	effect	NOUN
ejpam-3029	16	11	of	of	ADP
ejpam-3029	16	12	functions	function	NOUN
ejpam-3029	16	13	on	on	ADP
ejpam-3029	16	14	weakly	weakly	ADJ
ejpam-3029	16	15	µh	µh	ADJ
ejpam-3029	16	16	-	-	ADJ
ejpam-3029	16	17	compact	compact	ADJ
ejpam-3029	16	18	spaces	space	NOUN
ejpam-3029	16	19	.	.	PUNCT
ejpam-3029	17	1	we	we	PRON
ejpam-3029	17	2	also	also	ADV
ejpam-3029	17	3	show	show	VERB
ejpam-3029	17	4	that	that	SCONJ
ejpam-3029	17	5	some	some	DET
ejpam-3029	17	6	functions	function	NOUN
ejpam-3029	17	7	preserve	preserve	VERB
ejpam-3029	17	8	this	this	DET
ejpam-3029	17	9	property	property	NOUN
ejpam-3029	17	10	.	.	PUNCT
ejpam-3029	18	1	the	the	DET
ejpam-3029	18	2	main	main	ADJ
ejpam-3029	18	3	result	result	NOUN
ejpam-3029	18	4	is	be	AUX
ejpam-3029	18	5	that	that	SCONJ
ejpam-3029	18	6	the	the	DET
ejpam-3029	18	7	image	image	NOUN
ejpam-3029	18	8	of	of	ADP
ejpam-3029	18	9	a	a	DET
ejpam-3029	18	10	weakly	weakly	ADJ
ejpam-3029	18	11	µh	µh	ADJ
ejpam-3029	18	12	-	-	ADJ
ejpam-3029	18	13	compact	compact	ADJ
ejpam-3029	18	14	space	space	NOUN
ejpam-3029	18	15	under	under	ADP
ejpam-3029	18	16	a	a	DET
ejpam-3029	18	17	θ(µ	θ(µ	PROPN
ejpam-3029	18	18	,	,	PUNCT
ejpam-3029	18	19	ν)-continuous	ν)-continuous	ADJ
ejpam-3029	18	20	function	function	NOUN
ejpam-3029	18	21	is	be	AUX
ejpam-3029	18	22	weakly	weakly	ADJ
ejpam-3029	18	23	µh	µh	NOUN
ejpam-3029	18	24	-	-	ADJ
ejpam-3029	18	25	compact	compact	ADJ
ejpam-3029	18	26	.	.	PUNCT
ejpam-3029	19	1	∗corresponding	∗corresponde	VERB
ejpam-3029	19	2	author	author	NOUN
ejpam-3029	19	3	.	.	PUNCT
ejpam-3029	20	1	email	email	NOUN
ejpam-3029	20	2	addresses	address	NOUN
ejpam-3029	20	3	:	:	PUNCT
ejpam-3029	20	4	cahis82@gmail.com	cahis82@gmail.com	X
ejpam-3029	20	5	(	(	PUNCT
ejpam-3029	20	6	a.	a.	NOUN
ejpam-3029	20	7	qahis	qahis	PROPN
ejpam-3029	20	8	)	)	PUNCT
ejpam-3029	20	9	,	,	PUNCT
ejpam-3029	20	10	t.noiri@nifty.com	t.noiri@nifty.com	X
ejpam-3029	20	11	(	(	PUNCT
ejpam-3029	20	12	t.	t.	PROPN
ejpam-3029	20	13	noiri	noiri	PROPN
ejpam-3029	20	14	)	)	PUNCT
ejpam-3029	20	15	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3029	21	1	410	410	NUM
ejpam-3029	21	2	c	c	NOUN
ejpam-3029	21	3	©	©	PROPN
ejpam-3029	21	4	2017	2017	NUM
ejpam-3029	21	5	ejpam	ejpam	NOUN
ejpam-3029	21	6	all	all	DET
ejpam-3029	21	7	rights	right	NOUN
ejpam-3029	21	8	reserved	reserve	VERB
ejpam-3029	21	9	.	.	PUNCT
ejpam-3029	22	1	a.	a.	NOUN
ejpam-3029	22	2	qahis	qahis	PROPN
ejpam-3029	22	3	,	,	PUNCT
ejpam-3029	22	4	t.	t.	PROPN
ejpam-3029	22	5	noiri	noiri	PROPN
ejpam-3029	22	6	/	/	SYM
ejpam-3029	22	7	eur	eur	PROPN
ejpam-3029	22	8	.	.	PUNCT
ejpam-3029	23	1	j.	j.	PROPN
ejpam-3029	23	2	pure	pure	PROPN
ejpam-3029	23	3	appl	appl	PROPN
ejpam-3029	23	4	.	.	PROPN
ejpam-3029	23	5	math	math	PROPN
ejpam-3029	23	6	,	,	PUNCT
ejpam-3029	23	7	10	10	NUM
ejpam-3029	23	8	(	(	PUNCT
ejpam-3029	23	9	3	3	NUM
ejpam-3029	23	10	)	)	PUNCT
ejpam-3029	23	11	(	(	PUNCT
ejpam-3029	23	12	2017	2017	NUM
ejpam-3029	23	13	)	)	PUNCT
ejpam-3029	23	14	,	,	PUNCT
ejpam-3029	23	15	410	410	NUM
ejpam-3029	23	16	-	-	SYM
ejpam-3029	23	17	418	418	NUM
ejpam-3029	23	18	411	411	NUM
ejpam-3029	23	19	2	2	NUM
ejpam-3029	23	20	.	.	PUNCT
ejpam-3029	24	1	preliminaries	preliminary	NOUN
ejpam-3029	24	2	let	let	VERB
ejpam-3029	24	3	x	x	PRON
ejpam-3029	24	4	be	be	AUX
ejpam-3029	24	5	a	a	DET
ejpam-3029	24	6	nonempty	nonempty	ADV
ejpam-3029	24	7	set	set	VERB
ejpam-3029	24	8	and	and	CCONJ
ejpam-3029	24	9	p(x	p(x	PROPN
ejpam-3029	24	10	)	)	PUNCT
ejpam-3029	24	11	the	the	DET
ejpam-3029	24	12	power	power	NOUN
ejpam-3029	24	13	set	set	NOUN
ejpam-3029	24	14	of	of	ADP
ejpam-3029	24	15	x.	x.	NOUN
ejpam-3029	24	16	a	a	DET
ejpam-3029	24	17	subfamily	subfamily	ADV
ejpam-3029	24	18	µ	µ	NOUN
ejpam-3029	24	19	of	of	ADP
ejpam-3029	24	20	p(x	p(x	PROPN
ejpam-3029	24	21	)	)	PUNCT
ejpam-3029	24	22	is	be	AUX
ejpam-3029	24	23	called	call	VERB
ejpam-3029	24	24	a	a	DET
ejpam-3029	24	25	generalized	generalized	ADJ
ejpam-3029	24	26	topology	topology	NOUN
ejpam-3029	24	27	[	[	X
ejpam-3029	24	28	3	3	X
ejpam-3029	24	29	]	]	PUNCT
ejpam-3029	24	30	if	if	SCONJ
ejpam-3029	24	31	∅	∅	NOUN
ejpam-3029	24	32	∈	∈	PROPN
ejpam-3029	24	33	µ	µ	X
ejpam-3029	24	34	and	and	CCONJ
ejpam-3029	24	35	the	the	DET
ejpam-3029	24	36	arbitrary	arbitrary	ADJ
ejpam-3029	24	37	union	union	NOUN
ejpam-3029	24	38	of	of	ADP
ejpam-3029	24	39	members	member	NOUN
ejpam-3029	24	40	of	of	ADP
ejpam-3029	24	41	µ	µ	NOUN
ejpam-3029	24	42	is	be	AUX
ejpam-3029	24	43	again	again	ADV
ejpam-3029	24	44	in	in	ADP
ejpam-3029	24	45	µ.	µ.	NOUN
ejpam-3029	24	46	the	the	DET
ejpam-3029	24	47	pair	pair	NOUN
ejpam-3029	24	48	(	(	PUNCT
ejpam-3029	24	49	x,µ	x,µ	NOUN
ejpam-3029	24	50	)	)	PUNCT
ejpam-3029	24	51	is	be	AUX
ejpam-3029	24	52	called	call	VERB
ejpam-3029	24	53	a	a	DET
ejpam-3029	24	54	generalized	generalized	ADJ
ejpam-3029	24	55	topological	topological	ADJ
ejpam-3029	24	56	space	space	NOUN
ejpam-3029	24	57	(	(	PUNCT
ejpam-3029	24	58	briefly	briefly	NOUN
ejpam-3029	24	59	gts	gts	NOUN
ejpam-3029	24	60	)	)	PUNCT
ejpam-3029	24	61	.	.	PUNCT
ejpam-3029	25	1	the	the	DET
ejpam-3029	25	2	elements	element	NOUN
ejpam-3029	25	3	of	of	ADP
ejpam-3029	25	4	µ	µ	NOUN
ejpam-3029	25	5	are	be	AUX
ejpam-3029	25	6	called	call	VERB
ejpam-3029	25	7	µ-open	µ-open	NOUN
ejpam-3029	25	8	sets	set	NOUN
ejpam-3029	25	9	and	and	CCONJ
ejpam-3029	25	10	the	the	DET
ejpam-3029	25	11	complement	complement	NOUN
ejpam-3029	25	12	of	of	ADP
ejpam-3029	25	13	µ-open	µ-open	PROPN
ejpam-3029	25	14	sets	set	NOUN
ejpam-3029	25	15	are	be	AUX
ejpam-3029	25	16	called	call	VERB
ejpam-3029	25	17	µ-closed	µ-close	VERB
ejpam-3029	25	18	sets	set	NOUN
ejpam-3029	25	19	.	.	PUNCT
ejpam-3029	26	1	for	for	ADP
ejpam-3029	26	2	a	a	DET
ejpam-3029	26	3	⊆	⊆	NUM
ejpam-3029	26	4	x	x	SYM
ejpam-3029	26	5	,	,	PUNCT
ejpam-3029	26	6	we	we	PRON
ejpam-3029	26	7	denote	denote	VERB
ejpam-3029	26	8	by	by	ADP
ejpam-3029	26	9	cµ(a	cµ(a	PROPN
ejpam-3029	26	10	)	)	PUNCT
ejpam-3029	26	11	the	the	DET
ejpam-3029	26	12	intersection	intersection	NOUN
ejpam-3029	26	13	of	of	ADP
ejpam-3029	26	14	all	all	DET
ejpam-3029	26	15	µ-closed	µ-close	VERB
ejpam-3029	26	16	sets	set	NOUN
ejpam-3029	26	17	containing	contain	VERB
ejpam-3029	26	18	a	a	DET
ejpam-3029	26	19	,	,	PUNCT
ejpam-3029	26	20	i.e.	i.e.	X
ejpam-3029	26	21	,	,	PUNCT
ejpam-3029	26	22	the	the	DET
ejpam-3029	26	23	smallest	small	ADJ
ejpam-3029	26	24	µ-closed	µ-close	VERB
ejpam-3029	26	25	set	set	NOUN
ejpam-3029	26	26	containing	contain	VERB
ejpam-3029	26	27	a	a	PRON
ejpam-3029	26	28	and	and	CCONJ
ejpam-3029	26	29	by	by	ADP
ejpam-3029	26	30	iµ(a	iµ(a	PROPN
ejpam-3029	26	31	)	)	PUNCT
ejpam-3029	26	32	the	the	DET
ejpam-3029	26	33	union	union	NOUN
ejpam-3029	26	34	of	of	ADP
ejpam-3029	26	35	all	all	DET
ejpam-3029	26	36	µ-open	µ-open	NOUN
ejpam-3029	26	37	sets	set	NOUN
ejpam-3029	26	38	contained	contain	VERB
ejpam-3029	26	39	in	in	ADP
ejpam-3029	26	40	a	a	PRON
ejpam-3029	26	41	,	,	PUNCT
ejpam-3029	26	42	i.e.	i.e.	X
ejpam-3029	26	43	,	,	PUNCT
ejpam-3029	26	44	the	the	DET
ejpam-3029	26	45	largest	large	ADJ
ejpam-3029	26	46	µ-open	µ-open	NOUN
ejpam-3029	26	47	set	set	NOUN
ejpam-3029	26	48	contained	contain	VERB
ejpam-3029	26	49	in	in	ADP
ejpam-3029	26	50	a	a	DET
ejpam-3029	26	51	(	(	PUNCT
ejpam-3029	26	52	see	see	VERB
ejpam-3029	26	53	[	[	X
ejpam-3029	26	54	3	3	NUM
ejpam-3029	26	55	]	]	PUNCT
ejpam-3029	26	56	,	,	PUNCT
ejpam-3029	26	57	[	[	X
ejpam-3029	26	58	4	4	NUM
ejpam-3029	26	59	]	]	NUM
ejpam-3029	26	60	)	)	PUNCT
ejpam-3029	26	61	.	.	PUNCT
ejpam-3029	27	1	a	a	DET
ejpam-3029	27	2	nonempty	nonempty	ADJ
ejpam-3029	27	3	subcollection	subcollection	NOUN
ejpam-3029	27	4	h	h	NOUN
ejpam-3029	27	5	of	of	ADP
ejpam-3029	27	6	p(x	p(x	PROPN
ejpam-3029	27	7	)	)	PUNCT
ejpam-3029	27	8	is	be	AUX
ejpam-3029	27	9	called	call	VERB
ejpam-3029	27	10	a	a	DET
ejpam-3029	27	11	hereditary	hereditary	ADJ
ejpam-3029	27	12	class	class	NOUN
ejpam-3029	27	13	(	(	PUNCT
ejpam-3029	27	14	briefly	briefly	NOUN
ejpam-3029	27	15	hc	hc	X
ejpam-3029	27	16	)	)	PUNCT
ejpam-3029	28	1	[	[	X
ejpam-3029	28	2	5	5	X
ejpam-3029	28	3	]	]	PUNCT
ejpam-3029	28	4	if	if	SCONJ
ejpam-3029	28	5	a	a	DET
ejpam-3029	28	6	⊂	⊂	PROPN
ejpam-3029	28	7	b	b	PROPN
ejpam-3029	28	8	,	,	PUNCT
ejpam-3029	28	9	b	b	X
ejpam-3029	28	10	∈	∈	PROPN
ejpam-3029	28	11	h	h	NOUN
ejpam-3029	28	12	implies	imply	VERB
ejpam-3029	28	13	a	a	DET
ejpam-3029	28	14	∈	∈	PROPN
ejpam-3029	28	15	h.	h.	NOUN
ejpam-3029	28	16	an	an	DET
ejpam-3029	28	17	hc	hc	PROPN
ejpam-3029	28	18	h	h	NOUN
ejpam-3029	28	19	is	be	AUX
ejpam-3029	28	20	called	call	VERB
ejpam-3029	28	21	an	an	DET
ejpam-3029	28	22	ideal	ideal	NOUN
ejpam-3029	28	23	if	if	SCONJ
ejpam-3029	28	24	h	h	NOUN
ejpam-3029	28	25	satisfies	satisfy	VERB
ejpam-3029	28	26	the	the	DET
ejpam-3029	28	27	additional	additional	ADJ
ejpam-3029	28	28	condition	condition	NOUN
ejpam-3029	28	29	:	:	PUNCT
ejpam-3029	28	30	a	a	X
ejpam-3029	28	31	,	,	PUNCT
ejpam-3029	28	32	b	b	X
ejpam-3029	28	33	∈	∈	PROPN
ejpam-3029	28	34	h	h	NOUN
ejpam-3029	28	35	implies	imply	VERB
ejpam-3029	28	36	a	a	DET
ejpam-3029	28	37	∪	∪	X
ejpam-3029	28	38	b	b	NOUN
ejpam-3029	28	39	∈	∈	ADJ
ejpam-3029	28	40	h	h	NOUN
ejpam-3029	29	1	[	[	X
ejpam-3029	29	2	9	9	NUM
ejpam-3029	29	3	]	]	PUNCT
ejpam-3029	29	4	.	.	PUNCT
ejpam-3029	30	1	some	some	DET
ejpam-3029	30	2	useful	useful	ADJ
ejpam-3029	30	3	hereditary	hereditary	ADJ
ejpam-3029	30	4	classes	class	NOUN
ejpam-3029	30	5	in	in	ADP
ejpam-3029	30	6	x	x	SYM
ejpam-3029	30	7	are	be	AUX
ejpam-3029	30	8	:	:	PUNCT
ejpam-3029	30	9	p(a	p(a	PROPN
ejpam-3029	30	10	)	)	PUNCT
ejpam-3029	30	11	,	,	PUNCT
ejpam-3029	30	12	where	where	SCONJ
ejpam-3029	30	13	a	a	DET
ejpam-3029	30	14	⊆	⊆	NUM
ejpam-3029	30	15	x	x	NOUN
ejpam-3029	30	16	and	and	CCONJ
ejpam-3029	30	17	hf	hf	INTJ
ejpam-3029	30	18	,	,	PUNCT
ejpam-3029	30	19	the	the	DET
ejpam-3029	30	20	hc	hc	PROPN
ejpam-3029	30	21	of	of	ADP
ejpam-3029	30	22	all	all	DET
ejpam-3029	30	23	finite	finite	ADJ
ejpam-3029	30	24	subsets	subset	NOUN
ejpam-3029	30	25	of	of	ADP
ejpam-3029	30	26	x.	x.	PROPN
ejpam-3029	30	27	a	a	DET
ejpam-3029	30	28	subset	subset	NOUN
ejpam-3029	30	29	a	a	PRON
ejpam-3029	30	30	of	of	ADP
ejpam-3029	30	31	a	a	DET
ejpam-3029	30	32	gts	gts	NOUN
ejpam-3029	30	33	(	(	PUNCT
ejpam-3029	30	34	x,µ	x,µ	NOUN
ejpam-3029	30	35	)	)	PUNCT
ejpam-3029	30	36	is	be	AUX
ejpam-3029	30	37	said	say	VERB
ejpam-3029	30	38	to	to	PART
ejpam-3029	30	39	be	be	AUX
ejpam-3029	30	40	weakly	weakly	ADJ
ejpam-3029	30	41	µ-compact	µ-compact	PROPN
ejpam-3029	31	1	[	[	X
ejpam-3029	31	2	17	17	NUM
ejpam-3029	31	3	]	]	PUNCT
ejpam-3029	31	4	if	if	SCONJ
ejpam-3029	31	5	any	any	DET
ejpam-3029	31	6	cover	cover	NOUN
ejpam-3029	31	7	of	of	ADP
ejpam-3029	31	8	a	a	PRON
ejpam-3029	31	9	by	by	ADP
ejpam-3029	31	10	µ-open	µ-open	NOUN
ejpam-3029	31	11	sets	set	NOUN
ejpam-3029	31	12	of	of	ADP
ejpam-3029	31	13	x	x	PUNCT
ejpam-3029	31	14	has	have	VERB
ejpam-3029	31	15	a	a	DET
ejpam-3029	31	16	finite	finite	NOUN
ejpam-3029	31	17	subfamily	subfamily	ADV
ejpam-3029	31	18	,	,	PUNCT
ejpam-3029	31	19	the	the	DET
ejpam-3029	31	20	union	union	NOUN
ejpam-3029	31	21	of	of	ADP
ejpam-3029	31	22	the	the	DET
ejpam-3029	31	23	µ-closures	µ-closure	NOUN
ejpam-3029	31	24	of	of	ADP
ejpam-3029	31	25	whose	whose	DET
ejpam-3029	31	26	members	member	NOUN
ejpam-3029	31	27	covers	cover	VERB
ejpam-3029	31	28	a.	a.	NOUN
ejpam-3029	31	29	if	if	SCONJ
ejpam-3029	31	30	a	a	DET
ejpam-3029	31	31	=	=	SYM
ejpam-3029	31	32	x	x	NOUN
ejpam-3029	31	33	,	,	PUNCT
ejpam-3029	31	34	then	then	ADV
ejpam-3029	31	35	(	(	PUNCT
ejpam-3029	31	36	x,µ	x,µ	NOUN
ejpam-3029	31	37	)	)	PUNCT
ejpam-3029	31	38	is	be	AUX
ejpam-3029	31	39	called	call	VERB
ejpam-3029	31	40	a	a	DET
ejpam-3029	31	41	weakly	weakly	ADJ
ejpam-3029	31	42	µ-compact	µ-compact	NOUN
ejpam-3029	31	43	space	space	NOUN
ejpam-3029	31	44	.	.	PUNCT
ejpam-3029	32	1	given	give	VERB
ejpam-3029	32	2	a	a	DET
ejpam-3029	32	3	generalized	generalized	ADJ
ejpam-3029	32	4	topological	topological	ADJ
ejpam-3029	32	5	space	space	NOUN
ejpam-3029	32	6	(	(	PUNCT
ejpam-3029	32	7	x,µ	x,µ	NOUN
ejpam-3029	32	8	)	)	PUNCT
ejpam-3029	32	9	with	with	ADP
ejpam-3029	32	10	an	an	DET
ejpam-3029	32	11	hc	hc	NOUN
ejpam-3029	32	12	h	h	NOUN
ejpam-3029	32	13	,	,	PUNCT
ejpam-3029	32	14	for	for	ADP
ejpam-3029	32	15	a	a	DET
ejpam-3029	32	16	subset	subset	NOUN
ejpam-3029	32	17	a	a	PRON
ejpam-3029	32	18	of	of	ADP
ejpam-3029	32	19	x	x	PRON
ejpam-3029	32	20	,	,	PUNCT
ejpam-3029	32	21	the	the	DET
ejpam-3029	32	22	generalized	generalized	ADJ
ejpam-3029	32	23	local	local	ADJ
ejpam-3029	32	24	function	function	NOUN
ejpam-3029	32	25	of	of	ADP
ejpam-3029	32	26	a	a	PRON
ejpam-3029	32	27	with	with	ADP
ejpam-3029	32	28	respect	respect	NOUN
ejpam-3029	32	29	to	to	ADP
ejpam-3029	32	30	h	h	NOUN
ejpam-3029	32	31	and	and	CCONJ
ejpam-3029	32	32	µ	µ	X
ejpam-3029	32	33	[	[	X
ejpam-3029	32	34	5	5	NUM
ejpam-3029	32	35	]	]	PUNCT
ejpam-3029	32	36	is	be	AUX
ejpam-3029	32	37	defined	define	VERB
ejpam-3029	32	38	as	as	SCONJ
ejpam-3029	32	39	follows	follow	VERB
ejpam-3029	32	40	:	:	PUNCT
ejpam-3029	32	41	a∗(h	a∗(h	PROPN
ejpam-3029	32	42	,	,	PUNCT
ejpam-3029	32	43	µ	µ	NOUN
ejpam-3029	32	44	)	)	PUNCT
ejpam-3029	32	45	=	=	AUX
ejpam-3029	32	46	{	{	PUNCT
ejpam-3029	32	47	x	x	PUNCT
ejpam-3029	32	48	∈	∈	PROPN
ejpam-3029	32	49	x	x	X
ejpam-3029	32	50	:	:	PUNCT
ejpam-3029	32	51	u	u	NOUN
ejpam-3029	32	52	∩	∩	NOUN
ejpam-3029	32	53	a	a	DET
ejpam-3029	32	54	/∈	/∈	NOUN
ejpam-3029	32	55	h	h	NOUN
ejpam-3029	32	56	for	for	ADP
ejpam-3029	32	57	all	all	DET
ejpam-3029	32	58	u	u	NOUN
ejpam-3029	32	59	∈	∈	NOUN
ejpam-3029	32	60	µx	µx	VERB
ejpam-3029	32	61	}	}	PUNCT
ejpam-3029	32	62	,	,	PUNCT
ejpam-3029	32	63	where	where	SCONJ
ejpam-3029	32	64	µx	µx	ADV
ejpam-3029	32	65	=	=	PRON
ejpam-3029	32	66	{	{	PUNCT
ejpam-3029	32	67	u	u	NOUN
ejpam-3029	32	68	:	:	PUNCT
ejpam-3029	32	69	x	x	SYM
ejpam-3029	32	70	∈	∈	PROPN
ejpam-3029	32	71	u	u	NOUN
ejpam-3029	32	72	and	and	CCONJ
ejpam-3029	32	73	u	u	PROPN
ejpam-3029	32	74	∈	∈	PROPN
ejpam-3029	32	75	µ	µ	X
ejpam-3029	32	76	}	}	PUNCT
ejpam-3029	32	77	.	.	PUNCT
ejpam-3029	33	1	if	if	SCONJ
ejpam-3029	33	2	there	there	PRON
ejpam-3029	33	3	is	be	VERB
ejpam-3029	33	4	no	no	DET
ejpam-3029	33	5	confusion	confusion	NOUN
ejpam-3029	33	6	,	,	PUNCT
ejpam-3029	33	7	we	we	PRON
ejpam-3029	33	8	simply	simply	ADV
ejpam-3029	33	9	write	write	VERB
ejpam-3029	33	10	a∗	a∗	PROPN
ejpam-3029	33	11	instead	instead	ADV
ejpam-3029	33	12	of	of	ADP
ejpam-3029	33	13	a∗(h	a∗(h	PROPN
ejpam-3029	33	14	,	,	PUNCT
ejpam-3029	33	15	µ	µ	NOUN
ejpam-3029	33	16	)	)	PUNCT
ejpam-3029	33	17	.	.	PUNCT
ejpam-3029	34	1	h	h	PROPN
ejpam-3029	34	2	is	be	AUX
ejpam-3029	34	3	said	say	VERB
ejpam-3029	34	4	to	to	PART
ejpam-3029	34	5	be	be	AUX
ejpam-3029	34	6	µ-codense	µ-codense	NOUN
ejpam-3029	34	7	if	if	SCONJ
ejpam-3029	34	8	µ	µ	PRON
ejpam-3029	34	9	∩	∩	ADJ
ejpam-3029	34	10	h	h	NOUN
ejpam-3029	34	11	=	=	PUNCT
ejpam-3029	34	12	∅	∅	NOUN
ejpam-3029	34	13	[	[	X
ejpam-3029	34	14	5	5	NUM
ejpam-3029	34	15	]	]	PUNCT
ejpam-3029	34	16	.	.	PUNCT
ejpam-3029	35	1	and	and	CCONJ
ejpam-3029	35	2	for	for	ADP
ejpam-3029	35	3	a	a	DET
ejpam-3029	35	4	subset	subset	NOUN
ejpam-3029	35	5	a	a	PRON
ejpam-3029	35	6	of	of	ADP
ejpam-3029	35	7	x	x	PRON
ejpam-3029	35	8	,	,	PUNCT
ejpam-3029	35	9	c∗µ(a	c∗µ(a	PROPN
ejpam-3029	35	10	)	)	PUNCT
ejpam-3029	35	11	is	be	AUX
ejpam-3029	35	12	defined	define	VERB
ejpam-3029	35	13	by	by	ADP
ejpam-3029	35	14	c∗µ(a	c∗µ(a	PROPN
ejpam-3029	35	15	)	)	PUNCT
ejpam-3029	36	1	=	=	VERB
ejpam-3029	36	2	a∪a∗.	a∪a∗.	NOUN
ejpam-3029	36	3	the	the	DET
ejpam-3029	36	4	family	family	NOUN
ejpam-3029	36	5	µ∗	µ∗	VERB
ejpam-3029	36	6	=	=	PRON
ejpam-3029	36	7	{	{	PUNCT
ejpam-3029	36	8	a	a	DET
ejpam-3029	36	9	⊂	⊂	X
ejpam-3029	36	10	x	x	X
ejpam-3029	36	11	:	:	PUNCT
ejpam-3029	36	12	x	x	X
ejpam-3029	36	13	\a	\a	ADJ
ejpam-3029	36	14	=	=	SYM
ejpam-3029	36	15	c∗µ(x	c∗µ(x	NOUN
ejpam-3029	36	16	\a	\a	ADJ
ejpam-3029	36	17	)	)	PUNCT
ejpam-3029	36	18	}	}	PUNCT
ejpam-3029	36	19	is	be	AUX
ejpam-3029	36	20	a	a	DET
ejpam-3029	36	21	gt	gt	PROPN
ejpam-3029	36	22	on	on	ADP
ejpam-3029	36	23	x	x	PUNCT
ejpam-3029	36	24	which	which	PRON
ejpam-3029	36	25	is	be	AUX
ejpam-3029	36	26	finer	fine	ADJ
ejpam-3029	36	27	than	than	ADP
ejpam-3029	36	28	µ	µ	NOUN
ejpam-3029	36	29	[	[	X
ejpam-3029	36	30	5	5	NUM
ejpam-3029	36	31	]	]	PUNCT
ejpam-3029	36	32	.	.	PUNCT
ejpam-3029	37	1	the	the	DET
ejpam-3029	37	2	elements	element	NOUN
ejpam-3029	37	3	of	of	ADP
ejpam-3029	37	4	µ∗	µ∗	PROPN
ejpam-3029	37	5	are	be	AUX
ejpam-3029	37	6	said	say	VERB
ejpam-3029	37	7	to	to	PART
ejpam-3029	37	8	be	be	AUX
ejpam-3029	37	9	µ∗-open	µ∗-open	ADJ
ejpam-3029	37	10	and	and	CCONJ
ejpam-3029	37	11	the	the	DET
ejpam-3029	37	12	complement	complement	NOUN
ejpam-3029	37	13	of	of	ADP
ejpam-3029	37	14	a	a	DET
ejpam-3029	37	15	µ∗-open	µ∗-open	PROPN
ejpam-3029	37	16	set	set	NOUN
ejpam-3029	37	17	is	be	AUX
ejpam-3029	37	18	called	call	VERB
ejpam-3029	37	19	a	a	DET
ejpam-3029	37	20	µ∗-closed	µ∗-close	VERB
ejpam-3029	37	21	set	set	NOUN
ejpam-3029	37	22	.	.	PUNCT
ejpam-3029	38	1	it	it	PRON
ejpam-3029	38	2	is	be	AUX
ejpam-3029	38	3	clear	clear	ADJ
ejpam-3029	38	4	that	that	SCONJ
ejpam-3029	38	5	a	a	DET
ejpam-3029	38	6	subset	subset	NOUN
ejpam-3029	38	7	a	a	PRON
ejpam-3029	38	8	is	be	AUX
ejpam-3029	38	9	µ∗-closed	µ∗-close	VERB
ejpam-3029	38	10	if	if	SCONJ
ejpam-3029	38	11	and	and	CCONJ
ejpam-3029	38	12	only	only	ADV
ejpam-3029	38	13	if	if	SCONJ
ejpam-3029	38	14	a∗	a∗	PROPN
ejpam-3029	38	15	⊂	⊂	PROPN
ejpam-3029	38	16	a.	a.	NOUN
ejpam-3029	38	17	we	we	PRON
ejpam-3029	38	18	call	call	VERB
ejpam-3029	38	19	(	(	PUNCT
ejpam-3029	38	20	x,µ,h	x,µ,h	PROPN
ejpam-3029	38	21	)	)	PUNCT
ejpam-3029	38	22	a	a	DET
ejpam-3029	38	23	hereditary	hereditary	ADJ
ejpam-3029	38	24	generalized	generalize	VERB
ejpam-3029	38	25	topological	topological	ADJ
ejpam-3029	38	26	space	space	NOUN
ejpam-3029	38	27	and	and	CCONJ
ejpam-3029	38	28	briefly	briefly	ADV
ejpam-3029	38	29	we	we	PRON
ejpam-3029	38	30	denote	denote	VERB
ejpam-3029	38	31	it	it	PRON
ejpam-3029	38	32	by	by	ADP
ejpam-3029	38	33	hgts	hgts	NOUN
ejpam-3029	38	34	.	.	PUNCT
ejpam-3029	39	1	next	next	ADV
ejpam-3029	39	2	we	we	PRON
ejpam-3029	39	3	recall	recall	VERB
ejpam-3029	39	4	some	some	DET
ejpam-3029	39	5	known	known	ADJ
ejpam-3029	39	6	definitions	definition	NOUN
ejpam-3029	39	7	,	,	PUNCT
ejpam-3029	39	8	corollaries	corollary	NOUN
ejpam-3029	39	9	and	and	CCONJ
ejpam-3029	39	10	theorems	theorem	NOUN
ejpam-3029	39	11	which	which	PRON
ejpam-3029	39	12	will	will	AUX
ejpam-3029	39	13	be	be	AUX
ejpam-3029	39	14	used	use	VERB
ejpam-3029	39	15	in	in	ADP
ejpam-3029	39	16	the	the	DET
ejpam-3029	39	17	work	work	NOUN
ejpam-3029	39	18	.	.	PUNCT
ejpam-3029	40	1	theorem	theorem	NOUN
ejpam-3029	40	2	1	1	NUM
ejpam-3029	40	3	.	.	PUNCT
ejpam-3029	41	1	[	[	X
ejpam-3029	41	2	5	5	NUM
ejpam-3029	41	3	]	]	X
ejpam-3029	41	4	let	let	VERB
ejpam-3029	41	5	(	(	PUNCT
ejpam-3029	41	6	x,µ	x,µ	NOUN
ejpam-3029	41	7	)	)	PUNCT
ejpam-3029	41	8	be	be	VERB
ejpam-3029	41	9	a	a	DET
ejpam-3029	41	10	gts	gts	NOUN
ejpam-3029	41	11	,	,	PUNCT
ejpam-3029	41	12	h	h	NOUN
ejpam-3029	41	13	a	a	DET
ejpam-3029	41	14	hereditary	hereditary	ADJ
ejpam-3029	41	15	class	class	NOUN
ejpam-3029	41	16	on	on	ADP
ejpam-3029	41	17	x	x	PUNCT
ejpam-3029	41	18	and	and	CCONJ
ejpam-3029	41	19	a	a	DET
ejpam-3029	41	20	be	be	AUX
ejpam-3029	41	21	a	a	DET
ejpam-3029	41	22	subset	subset	NOUN
ejpam-3029	41	23	of	of	ADP
ejpam-3029	41	24	x.	x.	NOUN
ejpam-3029	41	25	if	if	SCONJ
ejpam-3029	41	26	a	a	PRON
ejpam-3029	41	27	is	be	AUX
ejpam-3029	41	28	µ∗-open	µ∗-open	ADJ
ejpam-3029	41	29	,	,	PUNCT
ejpam-3029	41	30	then	then	ADV
ejpam-3029	41	31	for	for	ADP
ejpam-3029	41	32	each	each	DET
ejpam-3029	41	33	x	x	SYM
ejpam-3029	41	34	∈	∈	PROPN
ejpam-3029	41	35	a	a	PRON
ejpam-3029	41	36	there	there	PRON
ejpam-3029	41	37	exist	exist	VERB
ejpam-3029	41	38	u	u	NOUN
ejpam-3029	41	39	∈	∈	NOUN
ejpam-3029	41	40	µx	µx	ADJ
ejpam-3029	41	41	and	and	CCONJ
ejpam-3029	41	42	h	h	NOUN
ejpam-3029	41	43	∈	∈	PROPN
ejpam-3029	41	44	h	h	NOUN
ejpam-3029	41	45	such	such	ADJ
ejpam-3029	41	46	that	that	SCONJ
ejpam-3029	41	47	x	x	SYM
ejpam-3029	41	48	∈	∈	PROPN
ejpam-3029	41	49	u	u	NOUN
ejpam-3029	41	50	\h	\h	PROPN
ejpam-3029	41	51	⊂	⊂	PROPN
ejpam-3029	41	52	a.	a.	NOUN
ejpam-3029	41	53	definition	definition	NOUN
ejpam-3029	41	54	1	1	NUM
ejpam-3029	41	55	.	.	PUNCT
ejpam-3029	42	1	[	[	X
ejpam-3029	42	2	17	17	NUM
ejpam-3029	42	3	]	]	PUNCT
ejpam-3029	42	4	let	let	VERB
ejpam-3029	42	5	a	a	PRON
ejpam-3029	42	6	be	be	AUX
ejpam-3029	42	7	a	a	DET
ejpam-3029	42	8	subset	subset	NOUN
ejpam-3029	42	9	of	of	ADP
ejpam-3029	42	10	a	a	DET
ejpam-3029	42	11	space	space	NOUN
ejpam-3029	42	12	(	(	PUNCT
ejpam-3029	42	13	x,µ	x,µ	NOUN
ejpam-3029	42	14	)	)	PUNCT
ejpam-3029	42	15	.	.	PUNCT
ejpam-3029	43	1	then	then	ADV
ejpam-3029	43	2	a	a	PRON
ejpam-3029	43	3	is	be	AUX
ejpam-3029	43	4	said	say	VERB
ejpam-3029	43	5	to	to	PART
ejpam-3029	43	6	be	be	AUX
ejpam-3029	43	7	:	:	PUNCT
ejpam-3029	43	8	(	(	PUNCT
ejpam-3029	43	9	1	1	X
ejpam-3029	43	10	)	)	PUNCT
ejpam-3029	43	11	µ-regular	µ-regular	PROPN
ejpam-3029	43	12	closed	close	VERB
ejpam-3029	43	13	if	if	SCONJ
ejpam-3029	43	14	a	a	DET
ejpam-3029	43	15	=	=	X
ejpam-3029	43	16	cµ(iµ(a	cµ(iµ(a	NOUN
ejpam-3029	43	17	)	)	PUNCT
ejpam-3029	43	18	)	)	PUNCT
ejpam-3029	43	19	;	;	PUNCT
ejpam-3029	43	20	(	(	PUNCT
ejpam-3029	43	21	2	2	X
ejpam-3029	43	22	)	)	PUNCT
ejpam-3029	43	23	µ-regular	µ-regular	NOUN
ejpam-3029	43	24	open	open	VERB
ejpam-3029	43	25	if	if	SCONJ
ejpam-3029	43	26	x	x	SYM
ejpam-3029	43	27	\a	\a	ADJ
ejpam-3029	43	28	is	be	AUX
ejpam-3029	43	29	µ-regular	µ-regular	PROPN
ejpam-3029	43	30	closed	closed	ADJ
ejpam-3029	43	31	.	.	PUNCT
ejpam-3029	44	1	corollary	corollary	ADJ
ejpam-3029	44	2	1	1	NUM
ejpam-3029	44	3	.	.	PUNCT
ejpam-3029	45	1	[	[	X
ejpam-3029	45	2	14	14	NUM
ejpam-3029	45	3	]	]	PUNCT
ejpam-3029	45	4	let	let	VERB
ejpam-3029	45	5	f	f	PRON
ejpam-3029	45	6	:	:	PUNCT
ejpam-3029	45	7	(	(	PUNCT
ejpam-3029	45	8	x,µ,h)→	x,µ,h)→	X
ejpam-3029	45	9	(	(	PUNCT
ejpam-3029	45	10	y	y	PROPN
ejpam-3029	45	11	,	,	PUNCT
ejpam-3029	45	12	ν	ν	NOUN
ejpam-3029	45	13	)	)	PUNCT
ejpam-3029	45	14	be	be	VERB
ejpam-3029	45	15	a	a	DET
ejpam-3029	45	16	(	(	PUNCT
ejpam-3029	45	17	µ	µ	NUM
ejpam-3029	45	18	,	,	PUNCT
ejpam-3029	45	19	ν)-continuous	ν)-continuous	ADJ
ejpam-3029	45	20	surjection	surjection	NOUN
ejpam-3029	45	21	.	.	PUNCT
ejpam-3029	46	1	if	if	SCONJ
ejpam-3029	46	2	(	(	PUNCT
ejpam-3029	46	3	x,µ,h	x,µ,h	PROPN
ejpam-3029	46	4	)	)	PUNCT
ejpam-3029	46	5	is	be	AUX
ejpam-3029	46	6	weakly	weakly	ADJ
ejpam-3029	46	7	µh	µh	NOUN
ejpam-3029	46	8	-	-	ADJ
ejpam-3029	46	9	compact	compact	ADJ
ejpam-3029	46	10	,	,	PUNCT
ejpam-3029	46	11	then	then	ADV
ejpam-3029	46	12	(	(	PUNCT
ejpam-3029	46	13	y	y	PROPN
ejpam-3029	46	14	,	,	PUNCT
ejpam-3029	46	15	ν	ν	NOUN
ejpam-3029	46	16	)	)	PUNCT
ejpam-3029	46	17	is	be	AUX
ejpam-3029	46	18	weakly	weakly	ADJ
ejpam-3029	46	19	νf(h)-compact	νf(h)-compact	NOUN
ejpam-3029	46	20	.	.	PUNCT
ejpam-3029	47	1	definition	definition	NOUN
ejpam-3029	47	2	2	2	NUM
ejpam-3029	47	3	.	.	PUNCT
ejpam-3029	48	1	a	a	DET
ejpam-3029	48	2	subset	subset	NOUN
ejpam-3029	48	3	a	a	PRON
ejpam-3029	48	4	of	of	ADP
ejpam-3029	48	5	x	x	SYM
ejpam-3029	48	6	is	be	AUX
ejpam-3029	48	7	said	say	VERB
ejpam-3029	48	8	to	to	PART
ejpam-3029	48	9	be	be	AUX
ejpam-3029	48	10	µh	µh	NOUN
ejpam-3029	48	11	-	-	ADJ
ejpam-3029	48	12	compact	compact	ADJ
ejpam-3029	48	13	[	[	X
ejpam-3029	48	14	2	2	NUM
ejpam-3029	48	15	]	]	PUNCT
ejpam-3029	48	16	(	(	PUNCT
ejpam-3029	48	17	resp	resp	NOUN
ejpam-3029	48	18	.	.	PUNCT
ejpam-3029	49	1	µ-compact	µ-compact	PROPN
ejpam-3029	50	1	[	[	X
ejpam-3029	50	2	7	7	NUM
ejpam-3029	50	3	,	,	PUNCT
ejpam-3029	50	4	16	16	NUM
ejpam-3029	50	5	]	]	PUNCT
ejpam-3029	50	6	)	)	PUNCT
ejpam-3029	50	7	if	if	SCONJ
ejpam-3029	50	8	for	for	ADP
ejpam-3029	50	9	every	every	DET
ejpam-3029	50	10	cover	cover	NOUN
ejpam-3029	50	11	{	{	PUNCT
ejpam-3029	50	12	uα	uα	X
ejpam-3029	50	13	:	:	PUNCT
ejpam-3029	50	14	α	α	PROPN
ejpam-3029	50	15	∈	∈	PROPN
ejpam-3029	50	16	∆	∆	PROPN
ejpam-3029	50	17	}	}	PUNCT
ejpam-3029	50	18	of	of	ADP
ejpam-3029	50	19	a	a	PRON
ejpam-3029	50	20	by	by	ADP
ejpam-3029	50	21	µ-open	µ-open	NOUN
ejpam-3029	50	22	sets	set	NOUN
ejpam-3029	50	23	of	of	ADP
ejpam-3029	50	24	(	(	PUNCT
ejpam-3029	50	25	x,µ	x,µ	NOUN
ejpam-3029	50	26	)	)	PUNCT
ejpam-3029	50	27	there	there	PRON
ejpam-3029	50	28	exists	exist	VERB
ejpam-3029	50	29	a	a	DET
ejpam-3029	50	30	finite	finite	NOUN
ejpam-3029	50	31	subset	subset	NOUN
ejpam-3029	50	32	λ0	λ0	NOUN
ejpam-3029	50	33	of	of	ADP
ejpam-3029	50	34	λ	λ	PROPN
ejpam-3029	50	35	such	such	ADJ
ejpam-3029	50	36	that	that	SCONJ
ejpam-3029	50	37	a	a	DET
ejpam-3029	50	38	\	\	NOUN
ejpam-3029	50	39	∪{uα	∪{uα	PROPN
ejpam-3029	50	40	:	:	PUNCT
ejpam-3029	50	41	α	α	NUM
ejpam-3029	50	42	∈	∈	PROPN
ejpam-3029	50	43	λ0	λ0	NOUN
ejpam-3029	50	44	}	}	PUNCT
ejpam-3029	50	45	∈	∈	PROPN
ejpam-3029	50	46	h	h	NOUN
ejpam-3029	50	47	(	(	PUNCT
ejpam-3029	50	48	resp	resp	PROPN
ejpam-3029	50	49	.	.	PUNCT
ejpam-3029	51	1	a	a	DET
ejpam-3029	51	2	⊆	⊆	NUM
ejpam-3029	51	3	∪{uα	∪{uα	PROPN
ejpam-3029	51	4	:	:	PUNCT
ejpam-3029	51	5	α	α	PROPN
ejpam-3029	51	6	∈	∈	PROPN
ejpam-3029	51	7	∆0	∆0	NOUN
ejpam-3029	51	8	}	}	PUNCT
ejpam-3029	51	9	)	)	PUNCT
ejpam-3029	51	10	.	.	PUNCT
ejpam-3029	52	1	if	if	SCONJ
ejpam-3029	52	2	a	a	DET
ejpam-3029	52	3	=	=	SYM
ejpam-3029	52	4	x	x	NOUN
ejpam-3029	52	5	,	,	PUNCT
ejpam-3029	52	6	then	then	ADV
ejpam-3029	52	7	(	(	PUNCT
ejpam-3029	52	8	x,µ	x,µ	NOUN
ejpam-3029	52	9	)	)	PUNCT
ejpam-3029	52	10	is	be	AUX
ejpam-3029	52	11	called	call	VERB
ejpam-3029	52	12	a	a	DET
ejpam-3029	52	13	µh	µh	NOUN
ejpam-3029	52	14	-	-	ADJ
ejpam-3029	52	15	compact	compact	ADJ
ejpam-3029	52	16	(	(	PUNCT
ejpam-3029	52	17	resp	resp	NOUN
ejpam-3029	52	18	.	.	PUNCT
ejpam-3029	53	1	µ-compact	µ-compact	ADJ
ejpam-3029	53	2	)	)	PUNCT
ejpam-3029	53	3	space	space	NOUN
ejpam-3029	53	4	.	.	PUNCT
ejpam-3029	54	1	definition	definition	NOUN
ejpam-3029	54	2	3	3	X
ejpam-3029	54	3	.	.	PUNCT
ejpam-3029	55	1	let	let	VERB
ejpam-3029	55	2	(	(	PUNCT
ejpam-3029	55	3	x,µ	x,µ	NOUN
ejpam-3029	55	4	)	)	PUNCT
ejpam-3029	55	5	and	and	CCONJ
ejpam-3029	55	6	(	(	PUNCT
ejpam-3029	55	7	y	y	PROPN
ejpam-3029	55	8	,	,	PUNCT
ejpam-3029	55	9	ν	ν	NOUN
ejpam-3029	55	10	)	)	PUNCT
ejpam-3029	55	11	be	be	VERB
ejpam-3029	55	12	two	two	NUM
ejpam-3029	55	13	gtss	gtss	NOUN
ejpam-3029	55	14	,	,	PUNCT
ejpam-3029	55	15	then	then	ADV
ejpam-3029	55	16	a	a	DET
ejpam-3029	55	17	function	function	NOUN
ejpam-3029	55	18	f	f	NOUN
ejpam-3029	55	19	:	:	PUNCT
ejpam-3029	55	20	(	(	PUNCT
ejpam-3029	55	21	x,µ	x,µ	NOUN
ejpam-3029	55	22	)	)	PUNCT
ejpam-3029	55	23	→	→	SYM
ejpam-3029	55	24	(	(	PUNCT
ejpam-3029	55	25	y	y	PROPN
ejpam-3029	55	26	,	,	PUNCT
ejpam-3029	55	27	ν	ν	NOUN
ejpam-3029	55	28	)	)	PUNCT
ejpam-3029	55	29	is	be	AUX
ejpam-3029	55	30	said	say	VERB
ejpam-3029	55	31	to	to	PART
ejpam-3029	55	32	be	be	AUX
ejpam-3029	55	33	.	.	PUNCT
ejpam-3029	56	1	a.	a.	NOUN
ejpam-3029	56	2	qahis	qahis	PROPN
ejpam-3029	56	3	,	,	PUNCT
ejpam-3029	56	4	t.	t.	PROPN
ejpam-3029	56	5	noiri	noiri	PROPN
ejpam-3029	56	6	/	/	SYM
ejpam-3029	56	7	eur	eur	PROPN
ejpam-3029	56	8	.	.	PUNCT
ejpam-3029	57	1	j.	j.	PROPN
ejpam-3029	57	2	pure	pure	PROPN
ejpam-3029	57	3	appl	appl	PROPN
ejpam-3029	57	4	.	.	PROPN
ejpam-3029	57	5	math	math	PROPN
ejpam-3029	57	6	,	,	PUNCT
ejpam-3029	57	7	10	10	NUM
ejpam-3029	57	8	(	(	PUNCT
ejpam-3029	57	9	3	3	NUM
ejpam-3029	57	10	)	)	PUNCT
ejpam-3029	57	11	(	(	PUNCT
ejpam-3029	57	12	2017	2017	NUM
ejpam-3029	57	13	)	)	PUNCT
ejpam-3029	57	14	,	,	PUNCT
ejpam-3029	57	15	410	410	NUM
ejpam-3029	57	16	-	-	SYM
ejpam-3029	57	17	418	418	NUM
ejpam-3029	57	18	412	412	NUM
ejpam-3029	57	19	(	(	PUNCT
ejpam-3029	57	20	1	1	NUM
ejpam-3029	57	21	)	)	PUNCT
ejpam-3029	57	22	(	(	PUNCT
ejpam-3029	57	23	µ	µ	NUM
ejpam-3029	57	24	,	,	PUNCT
ejpam-3029	57	25	ν)-continuous	ν)-continuous	ADJ
ejpam-3029	57	26	[	[	X
ejpam-3029	57	27	3	3	NUM
ejpam-3029	57	28	]	]	PUNCT
ejpam-3029	57	29	if	if	SCONJ
ejpam-3029	57	30	u	u	PROPN
ejpam-3029	57	31	∈	∈	NOUN
ejpam-3029	57	32	ν	ν	NOUN
ejpam-3029	57	33	implies	imply	VERB
ejpam-3029	57	34	f−1(u	f−1(u	PROPN
ejpam-3029	57	35	)	)	PUNCT
ejpam-3029	57	36	∈	∈	PROPN
ejpam-3029	57	37	µ.	µ.	NOUN
ejpam-3029	57	38	(	(	PUNCT
ejpam-3029	57	39	2	2	NUM
ejpam-3029	57	40	)	)	PUNCT
ejpam-3029	57	41	almost	almost	ADV
ejpam-3029	57	42	(	(	PUNCT
ejpam-3029	57	43	µ	µ	NUM
ejpam-3029	57	44	,	,	PUNCT
ejpam-3029	57	45	ν)-continuous	ν)-continuous	ADJ
ejpam-3029	57	46	[	[	X
ejpam-3029	57	47	13	13	NUM
ejpam-3029	57	48	]	]	X
ejpam-3029	57	49	if	if	SCONJ
ejpam-3029	57	50	for	for	ADP
ejpam-3029	57	51	each	each	DET
ejpam-3029	57	52	x	x	SYM
ejpam-3029	57	53	∈	∈	PROPN
ejpam-3029	57	54	x	x	X
ejpam-3029	57	55	and	and	CCONJ
ejpam-3029	57	56	each	each	DET
ejpam-3029	57	57	ν	ν	NOUN
ejpam-3029	57	58	-	-	ADJ
ejpam-3029	57	59	open	open	ADJ
ejpam-3029	57	60	set	set	NOUN
ejpam-3029	57	61	v	v	NOUN
ejpam-3029	57	62	containing	contain	VERB
ejpam-3029	57	63	f(x	f(x	PROPN
ejpam-3029	57	64	)	)	PUNCT
ejpam-3029	57	65	,	,	PUNCT
ejpam-3029	57	66	there	there	PRON
ejpam-3029	57	67	exists	exist	VERB
ejpam-3029	57	68	a	a	DET
ejpam-3029	57	69	µ-open	µ-open	NOUN
ejpam-3029	57	70	set	set	VERB
ejpam-3029	57	71	u	u	PRON
ejpam-3029	57	72	containing	contain	VERB
ejpam-3029	57	73	x	x	PUNCT
ejpam-3029	57	74	such	such	ADJ
ejpam-3029	57	75	that	that	DET
ejpam-3029	57	76	f(u	f(u	PROPN
ejpam-3029	57	77	)	)	PUNCT
ejpam-3029	57	78	⊆	⊆	NUM
ejpam-3029	57	79	iν(cν(v	iν(cν(v	NOUN
ejpam-3029	57	80	)	)	PUNCT
ejpam-3029	57	81	)	)	PUNCT
ejpam-3029	57	82	.	.	PUNCT
ejpam-3029	58	1	(	(	PUNCT
ejpam-3029	58	2	3	3	X
ejpam-3029	58	3	)	)	PUNCT
ejpam-3029	58	4	(	(	PUNCT
ejpam-3029	58	5	µ	µ	NOUN
ejpam-3029	58	6	,	,	PUNCT
ejpam-3029	58	7	ν)-precontinuous	ν)-precontinuous	ADJ
ejpam-3029	59	1	[	[	X
ejpam-3029	59	2	11	11	NUM
ejpam-3029	59	3	]	]	PUNCT
ejpam-3029	59	4	if	if	SCONJ
ejpam-3029	59	5	f−1(v	f−1(v	PROPN
ejpam-3029	59	6	)	)	PUNCT
ejpam-3029	60	1	⊆	⊆	NUM
ejpam-3029	60	2	iν(cν(f−1(v	iν(cν(f−1(v	NUM
ejpam-3029	60	3	)	)	PUNCT
ejpam-3029	60	4	)	)	PUNCT
ejpam-3029	60	5	)	)	PUNCT
ejpam-3029	60	6	for	for	ADP
ejpam-3029	60	7	every	every	DET
ejpam-3029	60	8	ν	ν	NOUN
ejpam-3029	60	9	-	-	ADJ
ejpam-3029	60	10	open	open	ADJ
ejpam-3029	60	11	set	set	VERB
ejpam-3029	60	12	v	v	NOUN
ejpam-3029	60	13	in	in	ADP
ejpam-3029	60	14	y	y	PROPN
ejpam-3029	60	15	.	.	PUNCT
ejpam-3029	61	1	(	(	PUNCT
ejpam-3029	61	2	4	4	X
ejpam-3029	61	3	)	)	PUNCT
ejpam-3029	61	4	δ(µ	δ(µ	NOUN
ejpam-3029	61	5	,	,	PUNCT
ejpam-3029	61	6	ν)-continuous	ν)-continuous	ADJ
ejpam-3029	61	7	[	[	X
ejpam-3029	61	8	10	10	NUM
ejpam-3029	61	9	]	]	X
ejpam-3029	61	10	(	(	PUNCT
ejpam-3029	61	11	resp	resp	NOUN
ejpam-3029	61	12	.	.	PUNCT
ejpam-3029	62	1	almost	almost	ADV
ejpam-3029	62	2	δ(µ	δ(µ	NOUN
ejpam-3029	62	3	,	,	PUNCT
ejpam-3029	62	4	ν)-continuous	ν)-continuous	ADJ
ejpam-3029	62	5	)	)	PUNCT
ejpam-3029	62	6	if	if	SCONJ
ejpam-3029	62	7	for	for	ADP
ejpam-3029	62	8	each	each	DET
ejpam-3029	62	9	x	x	SYM
ejpam-3029	62	10	∈	∈	PROPN
ejpam-3029	62	11	x	x	X
ejpam-3029	62	12	and	and	CCONJ
ejpam-3029	62	13	each	each	DET
ejpam-3029	62	14	ν	ν	NOUN
ejpam-3029	62	15	-	-	ADJ
ejpam-3029	62	16	open	open	ADJ
ejpam-3029	62	17	set	set	NOUN
ejpam-3029	62	18	v	v	NOUN
ejpam-3029	62	19	of	of	ADP
ejpam-3029	62	20	y	y	NOUN
ejpam-3029	62	21	containing	contain	VERB
ejpam-3029	62	22	f(x	f(x	PROPN
ejpam-3029	62	23	)	)	PUNCT
ejpam-3029	62	24	,	,	PUNCT
ejpam-3029	62	25	there	there	PRON
ejpam-3029	62	26	exists	exist	VERB
ejpam-3029	62	27	a	a	DET
ejpam-3029	62	28	µ-open	µ-open	NOUN
ejpam-3029	62	29	set	set	VERB
ejpam-3029	62	30	u	u	NOUN
ejpam-3029	62	31	of	of	ADP
ejpam-3029	62	32	x	x	PUNCT
ejpam-3029	62	33	containing	contain	VERB
ejpam-3029	62	34	x	x	PUNCT
ejpam-3029	62	35	such	such	ADJ
ejpam-3029	62	36	that	that	DET
ejpam-3029	62	37	f(iµ(cµ(u	f(iµ(cµ(u	NOUN
ejpam-3029	62	38	)	)	PUNCT
ejpam-3029	62	39	)	)	PUNCT
ejpam-3029	62	40	)	)	PUNCT
ejpam-3029	63	1	⊆	⊆	NUM
ejpam-3029	63	2	iν(cν(v	iν(cν(v	NOUN
ejpam-3029	63	3	)	)	PUNCT
ejpam-3029	63	4	)	)	PUNCT
ejpam-3029	63	5	(	(	PUNCT
ejpam-3029	63	6	resp	resp	NOUN
ejpam-3029	63	7	.	.	PUNCT
ejpam-3029	63	8	f(iµ(cµ(u	f(iµ(cµ(u	NOUN
ejpam-3029	63	9	)	)	PUNCT
ejpam-3029	63	10	)	)	PUNCT
ejpam-3029	63	11	)	)	PUNCT
ejpam-3029	64	1	⊆	⊆	NUM
ejpam-3029	64	2	cν(v	cν(v	NUM
ejpam-3029	64	3	)	)	PUNCT
ejpam-3029	64	4	)	)	PUNCT
ejpam-3029	64	5	.	.	PUNCT
ejpam-3029	65	1	(	(	PUNCT
ejpam-3029	65	2	5	5	X
ejpam-3029	65	3	)	)	PUNCT
ejpam-3029	65	4	θ(µ	θ(µ	NOUN
ejpam-3029	65	5	,	,	PUNCT
ejpam-3029	65	6	ν)-continuous	ν)-continuous	ADJ
ejpam-3029	65	7	[	[	X
ejpam-3029	65	8	3	3	NUM
ejpam-3029	65	9	]	]	PUNCT
ejpam-3029	65	10	(	(	PUNCT
ejpam-3029	65	11	resp	resp	NOUN
ejpam-3029	65	12	.	.	PUNCT
ejpam-3029	66	1	strongly	strongly	ADV
ejpam-3029	66	2	θ(µ	θ(µ	PROPN
ejpam-3029	66	3	,	,	PUNCT
ejpam-3029	66	4	ν)-continuous	ν)-continuous	ADJ
ejpam-3029	66	5	[	[	X
ejpam-3029	66	6	12	12	NUM
ejpam-3029	66	7	]	]	SYM
ejpam-3029	66	8	)	)	PUNCT
ejpam-3029	66	9	if	if	SCONJ
ejpam-3029	66	10	for	for	ADP
ejpam-3029	66	11	every	every	DET
ejpam-3029	66	12	x	x	SYM
ejpam-3029	66	13	∈	∈	PROPN
ejpam-3029	66	14	x	x	X
ejpam-3029	66	15	and	and	CCONJ
ejpam-3029	66	16	every	every	DET
ejpam-3029	66	17	ν	ν	NOUN
ejpam-3029	66	18	-	-	ADJ
ejpam-3029	66	19	open	open	ADJ
ejpam-3029	66	20	subset	subset	NOUN
ejpam-3029	66	21	v	v	NOUN
ejpam-3029	66	22	of	of	ADP
ejpam-3029	66	23	y	y	PROPN
ejpam-3029	66	24	containing	contain	VERB
ejpam-3029	66	25	f(x	f(x	PROPN
ejpam-3029	66	26	)	)	PUNCT
ejpam-3029	66	27	,	,	PUNCT
ejpam-3029	66	28	there	there	PRON
ejpam-3029	66	29	exists	exist	VERB
ejpam-3029	66	30	a	a	DET
ejpam-3029	66	31	µ-open	µ-open	NOUN
ejpam-3029	66	32	subset	subset	VERB
ejpam-3029	66	33	u	u	NOUN
ejpam-3029	66	34	in	in	ADP
ejpam-3029	66	35	x	x	SYM
ejpam-3029	66	36	containing	contain	VERB
ejpam-3029	66	37	x	x	PUNCT
ejpam-3029	66	38	such	such	ADJ
ejpam-3029	66	39	that	that	SCONJ
ejpam-3029	66	40	f(cµ(u	f(cµ(u	NOUN
ejpam-3029	66	41	)	)	PUNCT
ejpam-3029	66	42	)	)	PUNCT
ejpam-3029	67	1	⊆	⊆	NUM
ejpam-3029	67	2	cν(v	cν(v	NUM
ejpam-3029	67	3	)	)	PUNCT
ejpam-3029	67	4	(	(	PUNCT
ejpam-3029	67	5	resp	resp	NOUN
ejpam-3029	67	6	.	.	PUNCT
ejpam-3029	68	1	f(cµ(u	f(cµ(u	NOUN
ejpam-3029	68	2	)	)	PUNCT
ejpam-3029	68	3	)	)	PUNCT
ejpam-3029	69	1	⊆	⊆	NUM
ejpam-3029	69	2	v	v	NOUN
ejpam-3029	69	3	)	)	PUNCT
ejpam-3029	69	4	.	.	PUNCT
ejpam-3029	70	1	(	(	PUNCT
ejpam-3029	70	2	6	6	X
ejpam-3029	70	3	)	)	PUNCT
ejpam-3029	70	4	contra-(µ	contra-(µ	PROPN
ejpam-3029	70	5	,	,	PUNCT
ejpam-3029	70	6	ν)-continuous	ν)-continuous	ADJ
ejpam-3029	70	7	[	[	X
ejpam-3029	70	8	1	1	NUM
ejpam-3029	70	9	]	]	PUNCT
ejpam-3029	70	10	if	if	SCONJ
ejpam-3029	70	11	f−1(v	f−1(v	PROPN
ejpam-3029	70	12	)	)	PUNCT
ejpam-3029	70	13	is	be	AUX
ejpam-3029	70	14	µ-closed	µ-close	VERB
ejpam-3029	70	15	in	in	ADP
ejpam-3029	70	16	x	x	PUNCT
ejpam-3029	70	17	for	for	ADP
ejpam-3029	70	18	every	every	DET
ejpam-3029	70	19	ν	ν	NOUN
ejpam-3029	70	20	-	-	ADJ
ejpam-3029	70	21	open	open	ADJ
ejpam-3029	70	22	set	set	VERB
ejpam-3029	70	23	v	v	NOUN
ejpam-3029	70	24	in	in	ADP
ejpam-3029	70	25	y	y	PROPN
ejpam-3029	70	26	.	.	PUNCT
ejpam-3029	71	1	3	3	X
ejpam-3029	71	2	.	.	X
ejpam-3029	71	3	weakly	weakly	ADJ
ejpam-3029	71	4	µh	µh	ADJ
ejpam-3029	71	5	-	-	ADJ
ejpam-3029	71	6	compact	compact	ADJ
ejpam-3029	71	7	spaces	space	NOUN
ejpam-3029	71	8	firstly	firstly	ADV
ejpam-3029	71	9	,	,	PUNCT
ejpam-3029	71	10	we	we	PRON
ejpam-3029	71	11	show	show	VERB
ejpam-3029	71	12	some	some	DET
ejpam-3029	71	13	basic	basic	ADJ
ejpam-3029	71	14	properties	property	NOUN
ejpam-3029	71	15	for	for	ADP
ejpam-3029	71	16	weakly	weakly	ADJ
ejpam-3029	71	17	µh	µh	ADJ
ejpam-3029	71	18	-	-	ADJ
ejpam-3029	71	19	compact	compact	ADJ
ejpam-3029	71	20	spaces	space	NOUN
ejpam-3029	71	21	.	.	PUNCT
ejpam-3029	72	1	definition	definition	NOUN
ejpam-3029	72	2	4	4	NUM
ejpam-3029	72	3	.	.	PUNCT
ejpam-3029	73	1	[	[	X
ejpam-3029	73	2	14	14	NUM
ejpam-3029	73	3	]	]	X
ejpam-3029	73	4	let	let	VERB
ejpam-3029	73	5	(	(	PUNCT
ejpam-3029	73	6	x,µ	x,µ	NOUN
ejpam-3029	73	7	)	)	PUNCT
ejpam-3029	73	8	be	be	VERB
ejpam-3029	73	9	a	a	DET
ejpam-3029	73	10	gts	gts	NOUN
ejpam-3029	73	11	with	with	ADP
ejpam-3029	73	12	hc	hc	PROPN
ejpam-3029	73	13	.	.	PUNCT
ejpam-3029	74	1	an	an	DET
ejpam-3029	74	2	hgts	hgts	NOUN
ejpam-3029	74	3	(	(	PUNCT
ejpam-3029	74	4	x,µ,h	x,µ,h	PROPN
ejpam-3029	74	5	)	)	PUNCT
ejpam-3029	74	6	is	be	AUX
ejpam-3029	74	7	said	say	VERB
ejpam-3029	74	8	to	to	PART
ejpam-3029	74	9	be	be	AUX
ejpam-3029	74	10	weakly	weakly	ADJ
ejpam-3029	74	11	µh	µh	NOUN
ejpam-3029	74	12	-	-	ADJ
ejpam-3029	74	13	compact	compact	ADJ
ejpam-3029	74	14	if	if	SCONJ
ejpam-3029	74	15	for	for	ADP
ejpam-3029	74	16	every	every	DET
ejpam-3029	74	17	cover	cover	NOUN
ejpam-3029	74	18	{	{	PUNCT
ejpam-3029	74	19	vα	vα	X
ejpam-3029	74	20	:	:	PUNCT
ejpam-3029	74	21	α	α	PROPN
ejpam-3029	74	22	∈	∈	PROPN
ejpam-3029	74	23	∆	∆	PROPN
ejpam-3029	74	24	}	}	PUNCT
ejpam-3029	74	25	of	of	ADP
ejpam-3029	74	26	x	x	PUNCT
ejpam-3029	74	27	by	by	ADP
ejpam-3029	74	28	µ-open	µ-open	NOUN
ejpam-3029	74	29	sets	set	NOUN
ejpam-3029	74	30	in	in	ADP
ejpam-3029	74	31	x	x	NOUN
ejpam-3029	74	32	,	,	PUNCT
ejpam-3029	74	33	there	there	PRON
ejpam-3029	74	34	exists	exist	VERB
ejpam-3029	74	35	a	a	DET
ejpam-3029	74	36	finite	finite	NOUN
ejpam-3029	74	37	subset	subset	VERB
ejpam-3029	74	38	∆0	∆0	NUM
ejpam-3029	74	39	of	of	ADP
ejpam-3029	74	40	∆	∆	PROPN
ejpam-3029	74	41	such	such	ADJ
ejpam-3029	74	42	that	that	SCONJ
ejpam-3029	74	43	x	x	X
ejpam-3029	74	44	\	\	PROPN
ejpam-3029	74	45	∪{cµ(vα	∪{cµ(vα	PROPN
ejpam-3029	74	46	)	)	PUNCT
ejpam-3029	74	47	:	:	PUNCT
ejpam-3029	74	48	α	α	PROPN
ejpam-3029	74	49	∈	∈	PROPN
ejpam-3029	74	50	∆0	∆0	PRON
ejpam-3029	74	51	}	}	PUNCT
ejpam-3029	74	52	∈	∈	PROPN
ejpam-3029	74	53	h.	h.	NOUN
ejpam-3029	74	54	the	the	DET
ejpam-3029	74	55	following	follow	VERB
ejpam-3029	74	56	lemma	lemma	PROPN
ejpam-3029	74	57	is	be	AUX
ejpam-3029	74	58	used	use	VERB
ejpam-3029	74	59	in	in	ADP
ejpam-3029	74	60	the	the	DET
ejpam-3029	74	61	proof	proof	NOUN
ejpam-3029	74	62	of	of	ADP
ejpam-3029	74	63	the	the	DET
ejpam-3029	74	64	corollary	corollary	NOUN
ejpam-3029	74	65	stated	state	VERB
ejpam-3029	74	66	below	below	ADV
ejpam-3029	74	67	.	.	PUNCT
ejpam-3029	75	1	lemma	lemma	PROPN
ejpam-3029	75	2	1	1	NUM
ejpam-3029	75	3	.	.	PUNCT
ejpam-3029	76	1	an	an	DET
ejpam-3029	76	2	hgts	hgts	NOUN
ejpam-3029	76	3	(	(	PUNCT
ejpam-3029	76	4	x,µ,hf	x,µ,hf	PROPN
ejpam-3029	76	5	)	)	PUNCT
ejpam-3029	76	6	is	be	AUX
ejpam-3029	76	7	weakly	weakly	ADJ
ejpam-3029	76	8	µ-compact	µ-compact	NOUN
ejpam-3029	76	9	if	if	SCONJ
ejpam-3029	76	10	and	and	CCONJ
ejpam-3029	76	11	only	only	ADV
ejpam-3029	76	12	if	if	SCONJ
ejpam-3029	76	13	(	(	PUNCT
ejpam-3029	76	14	x,µ,hf	x,µ,hf	PROPN
ejpam-3029	76	15	)	)	PUNCT
ejpam-3029	76	16	is	be	AUX
ejpam-3029	76	17	weakly	weakly	ADJ
ejpam-3029	76	18	µhf	µhf	INTJ
ejpam-3029	76	19	-compact	-compact	NOUN
ejpam-3029	76	20	.	.	PUNCT
ejpam-3029	77	1	proof	proof	NOUN
ejpam-3029	77	2	.	.	PUNCT
ejpam-3029	78	1	the	the	DET
ejpam-3029	78	2	necessity	necessity	NOUN
ejpam-3029	78	3	is	be	AUX
ejpam-3029	78	4	clear	clear	ADJ
ejpam-3029	78	5	and	and	CCONJ
ejpam-3029	78	6	we	we	PRON
ejpam-3029	78	7	prove	prove	VERB
ejpam-3029	78	8	the	the	DET
ejpam-3029	78	9	sufficiency	sufficiency	NOUN
ejpam-3029	78	10	.	.	PUNCT
ejpam-3029	79	1	assume	assume	VERB
ejpam-3029	79	2	that	that	SCONJ
ejpam-3029	79	3	(	(	PUNCT
ejpam-3029	79	4	x,µ,hf	x,µ,hf	PROPN
ejpam-3029	79	5	)	)	PUNCT
ejpam-3029	79	6	is	be	AUX
ejpam-3029	79	7	weakly	weakly	ADJ
ejpam-3029	79	8	µhf	µhf	INTJ
ejpam-3029	79	9	-compact	-compact	PROPN
ejpam-3029	79	10	.	.	PUNCT
ejpam-3029	80	1	let	let	VERB
ejpam-3029	80	2	{	{	PUNCT
ejpam-3029	80	3	vα	vα	X
ejpam-3029	80	4	:	:	PUNCT
ejpam-3029	80	5	α	α	PROPN
ejpam-3029	80	6	∈	∈	PROPN
ejpam-3029	80	7	∆	∆	PROPN
ejpam-3029	80	8	}	}	PUNCT
ejpam-3029	80	9	be	be	AUX
ejpam-3029	80	10	a	a	DET
ejpam-3029	80	11	cover	cover	NOUN
ejpam-3029	80	12	of	of	ADP
ejpam-3029	80	13	x	x	PUNCT
ejpam-3029	80	14	by	by	ADP
ejpam-3029	80	15	µ-open	µ-open	NOUN
ejpam-3029	80	16	subsets	subset	NOUN
ejpam-3029	80	17	of	of	ADP
ejpam-3029	80	18	x.	x.	NOUN
ejpam-3029	80	19	then	then	ADV
ejpam-3029	80	20	by	by	ADP
ejpam-3029	80	21	hypothesis	hypothesis	NOUN
ejpam-3029	80	22	,	,	PUNCT
ejpam-3029	80	23	there	there	PRON
ejpam-3029	80	24	exists	exist	VERB
ejpam-3029	80	25	a	a	DET
ejpam-3029	80	26	fnite	fnite	NOUN
ejpam-3029	80	27	subset	subset	VERB
ejpam-3029	80	28	∆0	∆0	NUM
ejpam-3029	80	29	of	of	ADP
ejpam-3029	80	30	∆	∆	PROPN
ejpam-3029	80	31	such	such	ADJ
ejpam-3029	80	32	that	that	SCONJ
ejpam-3029	80	33	x	x	SYM
ejpam-3029	80	34	\	\	PROPN
ejpam-3029	80	35	⋃	⋃	PUNCT
ejpam-3029	80	36	α∈∆0	α∈∆0	NUM
ejpam-3029	80	37	cµ(vα	cµ(vα	NOUN
ejpam-3029	80	38	)	)	PUNCT
ejpam-3029	80	39	∈	∈	PROPN
ejpam-3029	80	40	hf	hf	NOUN
ejpam-3029	80	41	.	.	PUNCT
ejpam-3029	81	1	let	let	VERB
ejpam-3029	81	2	x	x	SYM
ejpam-3029	81	3	\	\	PROPN
ejpam-3029	81	4	⋃	⋃	PUNCT
ejpam-3029	81	5	α∈∆0	α∈∆0	NUM
ejpam-3029	81	6	cµ(vα	cµ(vα	NOUN
ejpam-3029	81	7	)	)	PUNCT
ejpam-3029	81	8	=	=	PRON
ejpam-3029	81	9	{	{	PUNCT
ejpam-3029	81	10	x1	x1	PROPN
ejpam-3029	81	11	,	,	PUNCT
ejpam-3029	81	12	x2	x2	PROPN
ejpam-3029	81	13	,	,	PUNCT
ejpam-3029	81	14	...	...	PUNCT
ejpam-3029	81	15	,	,	PUNCT
ejpam-3029	81	16	xn	xn	PROPN
ejpam-3029	81	17	}	}	PUNCT
ejpam-3029	81	18	.	.	PUNCT
ejpam-3029	82	1	for	for	ADP
ejpam-3029	82	2	each	each	DET
ejpam-3029	82	3	1	1	NUM
ejpam-3029	82	4	≤	≤	NUM
ejpam-3029	82	5	j	j	PROPN
ejpam-3029	82	6	≤	≤	PROPN
ejpam-3029	82	7	n	n	CCONJ
ejpam-3029	82	8	,	,	PUNCT
ejpam-3029	82	9	choose	choose	VERB
ejpam-3029	82	10	vαj	vαj	ADJ
ejpam-3029	82	11	such	such	ADJ
ejpam-3029	82	12	that	that	SCONJ
ejpam-3029	82	13	xj	xj	PROPN
ejpam-3029	82	14	∈	∈	PROPN
ejpam-3029	82	15	vαj	vαj	NOUN
ejpam-3029	82	16	.	.	PUNCT
ejpam-3029	83	1	hence	hence	ADV
ejpam-3029	83	2	x	x	X
ejpam-3029	83	3	=	=	PRON
ejpam-3029	83	4	(	(	PUNCT
ejpam-3029	83	5	⋃	⋃	NOUN
ejpam-3029	83	6	α∈∆0	α∈∆0	NUM
ejpam-3029	83	7	cµ(vα))∪	cµ(vα))∪	NOUN
ejpam-3029	83	8	(	(	PUNCT
ejpam-3029	83	9	⋃	⋃	PROPN
ejpam-3029	83	10	1≤j≤n	1≤j≤n	NUM
ejpam-3029	83	11	cµ(vαi	cµ(vαi	NOUN
ejpam-3029	83	12	)	)	PUNCT
ejpam-3029	83	13	)	)	PUNCT
ejpam-3029	83	14	.	.	PUNCT
ejpam-3029	84	1	this	this	PRON
ejpam-3029	84	2	implies	imply	VERB
ejpam-3029	84	3	that	that	SCONJ
ejpam-3029	84	4	(	(	PUNCT
ejpam-3029	84	5	x,µ	x,µ	NOUN
ejpam-3029	84	6	)	)	PUNCT
ejpam-3029	84	7	is	be	AUX
ejpam-3029	84	8	weakly	weakly	ADJ
ejpam-3029	84	9	µ-compact	µ-compact	NOUN
ejpam-3029	84	10	.	.	PUNCT
ejpam-3029	85	1	corollary	corollary	ADJ
ejpam-3029	85	2	2	2	NUM
ejpam-3029	85	3	.	.	PUNCT
ejpam-3029	86	1	let	let	VERB
ejpam-3029	86	2	f	f	PROPN
ejpam-3029	86	3	:	:	PUNCT
ejpam-3029	86	4	(	(	PUNCT
ejpam-3029	86	5	x,µ,h)→	x,µ,h)→	X
ejpam-3029	86	6	(	(	PUNCT
ejpam-3029	86	7	y	y	PROPN
ejpam-3029	86	8	,	,	PUNCT
ejpam-3029	86	9	ν	ν	NOUN
ejpam-3029	86	10	)	)	PUNCT
ejpam-3029	86	11	be	be	VERB
ejpam-3029	86	12	a	a	DET
ejpam-3029	86	13	(	(	PUNCT
ejpam-3029	86	14	µ	µ	NUM
ejpam-3029	86	15	,	,	PUNCT
ejpam-3029	86	16	ν)-continuous	ν)-continuous	ADJ
ejpam-3029	86	17	surjection	surjection	NOUN
ejpam-3029	86	18	.	.	PUNCT
ejpam-3029	87	1	if	if	SCONJ
ejpam-3029	87	2	(	(	PUNCT
ejpam-3029	87	3	x,µ,h	x,µ,h	PROPN
ejpam-3029	87	4	)	)	PUNCT
ejpam-3029	87	5	is	be	AUX
ejpam-3029	87	6	weakly	weakly	ADJ
ejpam-3029	87	7	µh	µh	NOUN
ejpam-3029	87	8	-	-	ADJ
ejpam-3029	87	9	compact	compact	ADJ
ejpam-3029	87	10	and	and	CCONJ
ejpam-3029	87	11	y	y	PROPN
ejpam-3029	87	12	is	be	AUX
ejpam-3029	87	13	a	a	DET
ejpam-3029	87	14	finite	finite	ADJ
ejpam-3029	87	15	space	space	NOUN
ejpam-3029	87	16	,	,	PUNCT
ejpam-3029	87	17	then	then	ADV
ejpam-3029	87	18	(	(	PUNCT
ejpam-3029	87	19	y	y	PROPN
ejpam-3029	87	20	,	,	PUNCT
ejpam-3029	87	21	ν	ν	NOUN
ejpam-3029	87	22	)	)	PUNCT
ejpam-3029	87	23	is	be	AUX
ejpam-3029	87	24	weakly	weakly	ADJ
ejpam-3029	87	25	ν	ν	NOUN
ejpam-3029	87	26	-	-	ADJ
ejpam-3029	87	27	compact	compact	ADJ
ejpam-3029	87	28	.	.	PUNCT
ejpam-3029	88	1	proof	proof	NOUN
ejpam-3029	88	2	.	.	PUNCT
ejpam-3029	89	1	let	let	VERB
ejpam-3029	89	2	f	f	PRON
ejpam-3029	89	3	be	be	AUX
ejpam-3029	89	4	a	a	DET
ejpam-3029	89	5	(	(	PUNCT
ejpam-3029	89	6	µ	µ	NUM
ejpam-3029	89	7	,	,	PUNCT
ejpam-3029	89	8	ν)-continuous	ν)-continuous	ADJ
ejpam-3029	89	9	surjection	surjection	NOUN
ejpam-3029	89	10	.	.	PUNCT
ejpam-3029	90	1	by	by	ADP
ejpam-3029	90	2	corollary	corollary	ADJ
ejpam-3029	90	3	1	1	NUM
ejpam-3029	90	4	,	,	PUNCT
ejpam-3029	90	5	(	(	PUNCT
ejpam-3029	90	6	y	y	NOUN
ejpam-3029	90	7	,	,	PUNCT
ejpam-3029	90	8	ν	ν	NOUN
ejpam-3029	90	9	)	)	PUNCT
ejpam-3029	90	10	is	be	AUX
ejpam-3029	90	11	weakly	weakly	ADJ
ejpam-3029	90	12	νf(h)compact	νf(h)compact	NOUN
ejpam-3029	90	13	.	.	PUNCT
ejpam-3029	91	1	since	since	SCONJ
ejpam-3029	91	2	y	y	PROPN
ejpam-3029	91	3	is	be	AUX
ejpam-3029	91	4	a	a	DET
ejpam-3029	91	5	finite	finite	ADJ
ejpam-3029	91	6	space	space	NOUN
ejpam-3029	91	7	,	,	PUNCT
ejpam-3029	91	8	then	then	ADV
ejpam-3029	91	9	the	the	DET
ejpam-3029	91	10	hc	hc	PROPN
ejpam-3029	91	11	f(h	f(h	PROPN
ejpam-3029	91	12	)	)	PUNCT
ejpam-3029	91	13	of	of	ADP
ejpam-3029	91	14	finite	finite	ADJ
ejpam-3029	91	15	subsets	subset	NOUN
ejpam-3029	91	16	and	and	CCONJ
ejpam-3029	91	17	and	and	CCONJ
ejpam-3029	91	18	apply	apply	VERB
ejpam-3029	91	19	the	the	DET
ejpam-3029	91	20	lemma	lemma	PROPN
ejpam-3029	91	21	1	1	NUM
ejpam-3029	91	22	.	.	PUNCT
ejpam-3029	92	1	a	a	DET
ejpam-3029	92	2	subset	subset	NOUN
ejpam-3029	92	3	a	a	PRON
ejpam-3029	92	4	of	of	ADP
ejpam-3029	92	5	a	a	DET
ejpam-3029	92	6	gts	gts	NOUN
ejpam-3029	92	7	(	(	PUNCT
ejpam-3029	92	8	x,µ	x,µ	NOUN
ejpam-3029	92	9	)	)	PUNCT
ejpam-3029	92	10	is	be	AUX
ejpam-3029	92	11	said	say	VERB
ejpam-3029	92	12	to	to	PART
ejpam-3029	92	13	be	be	AUX
ejpam-3029	92	14	µ-nowhere	µ-nowhere	ADV
ejpam-3029	92	15	dense	dense	ADJ
ejpam-3029	92	16	if	if	SCONJ
ejpam-3029	92	17	iµ(cµ(a	iµ(cµ(a	PROPN
ejpam-3029	92	18	)	)	PUNCT
ejpam-3029	92	19	)	)	PUNCT
ejpam-3029	93	1	=	=	NOUN
ejpam-3029	93	2	∅	∅	NOUN
ejpam-3029	93	3	,	,	PUNCT
ejpam-3029	93	4	and	and	CCONJ
ejpam-3029	93	5	we	we	PRON
ejpam-3029	93	6	denote	denote	VERB
ejpam-3029	93	7	the	the	DET
ejpam-3029	93	8	hc	hc	NOUN
ejpam-3029	93	9	of	of	ADP
ejpam-3029	93	10	µ-nowhere	µ-nowhere	ADP
ejpam-3029	93	11	dense	dense	ADJ
ejpam-3029	93	12	sets	set	NOUN
ejpam-3029	93	13	by	by	ADP
ejpam-3029	93	14	n	n	PROPN
ejpam-3029	93	15	(	(	PUNCT
ejpam-3029	93	16	µ	µ	NOUN
ejpam-3029	93	17	)	)	PUNCT
ejpam-3029	93	18	.	.	PUNCT
ejpam-3029	94	1	proposition	proposition	NOUN
ejpam-3029	94	2	1	1	NUM
ejpam-3029	94	3	.	.	PUNCT
ejpam-3029	95	1	if	if	SCONJ
ejpam-3029	95	2	(	(	PUNCT
ejpam-3029	95	3	x,µ,h	x,µ,h	PROPN
ejpam-3029	95	4	)	)	PUNCT
ejpam-3029	95	5	is	be	AUX
ejpam-3029	95	6	weakly	weakly	ADJ
ejpam-3029	95	7	µh	µh	NOUN
ejpam-3029	95	8	-	-	ADJ
ejpam-3029	95	9	compact	compact	ADJ
ejpam-3029	96	1	and	and	CCONJ
ejpam-3029	96	2	h	h	NOUN
ejpam-3029	96	3	is	be	AUX
ejpam-3029	96	4	µ-condense	µ-condense	PROPN
ejpam-3029	96	5	,	,	PUNCT
ejpam-3029	96	6	then	then	ADV
ejpam-3029	96	7	(	(	PUNCT
ejpam-3029	96	8	x,µ	x,µ	NOUN
ejpam-3029	96	9	)	)	PUNCT
ejpam-3029	96	10	is	be	AUX
ejpam-3029	96	11	weakly	weakly	ADJ
ejpam-3029	96	12	µ-compact	µ-compact	NOUN
ejpam-3029	96	13	.	.	PUNCT
ejpam-3029	97	1	a.	a.	NOUN
ejpam-3029	97	2	qahis	qahis	PROPN
ejpam-3029	97	3	,	,	PUNCT
ejpam-3029	97	4	t.	t.	PROPN
ejpam-3029	97	5	noiri	noiri	PROPN
ejpam-3029	97	6	/	/	SYM
ejpam-3029	97	7	eur	eur	PROPN
ejpam-3029	97	8	.	.	PUNCT
ejpam-3029	98	1	j.	j.	PROPN
ejpam-3029	98	2	pure	pure	PROPN
ejpam-3029	98	3	appl	appl	PROPN
ejpam-3029	98	4	.	.	PROPN
ejpam-3029	98	5	math	math	PROPN
ejpam-3029	98	6	,	,	PUNCT
ejpam-3029	98	7	10	10	NUM
ejpam-3029	98	8	(	(	PUNCT
ejpam-3029	98	9	3	3	NUM
ejpam-3029	98	10	)	)	PUNCT
ejpam-3029	98	11	(	(	PUNCT
ejpam-3029	98	12	2017	2017	NUM
ejpam-3029	98	13	)	)	PUNCT
ejpam-3029	98	14	,	,	PUNCT
ejpam-3029	98	15	410	410	NUM
ejpam-3029	98	16	-	-	SYM
ejpam-3029	98	17	418	418	NUM
ejpam-3029	98	18	413	413	NUM
ejpam-3029	98	19	proof	proof	NOUN
ejpam-3029	98	20	.	.	PUNCT
ejpam-3029	98	21	suppose	suppose	VERB
ejpam-3029	98	22	that	that	SCONJ
ejpam-3029	98	23	(	(	PUNCT
ejpam-3029	98	24	x,µ,h	x,µ,h	PROPN
ejpam-3029	98	25	)	)	PUNCT
ejpam-3029	98	26	is	be	AUX
ejpam-3029	98	27	weakly	weakly	ADJ
ejpam-3029	98	28	µh	µh	NOUN
ejpam-3029	98	29	-	-	ADJ
ejpam-3029	98	30	compact	compact	ADJ
ejpam-3029	98	31	and	and	CCONJ
ejpam-3029	98	32	let	let	VERB
ejpam-3029	98	33	{	{	PUNCT
ejpam-3029	98	34	vα	vα	X
ejpam-3029	98	35	:	:	PUNCT
ejpam-3029	98	36	α	α	PROPN
ejpam-3029	98	37	∈	∈	PROPN
ejpam-3029	98	38	∆	∆	PROPN
ejpam-3029	98	39	}	}	PUNCT
ejpam-3029	98	40	be	be	AUX
ejpam-3029	98	41	a	a	DET
ejpam-3029	98	42	cover	cover	NOUN
ejpam-3029	98	43	of	of	ADP
ejpam-3029	98	44	x	x	PUNCT
ejpam-3029	98	45	by	by	ADP
ejpam-3029	98	46	µ-open	µ-open	NOUN
ejpam-3029	98	47	subsets	subset	NOUN
ejpam-3029	98	48	of	of	ADP
ejpam-3029	98	49	x.	x.	NOUN
ejpam-3029	98	50	there	there	PRON
ejpam-3029	98	51	exists	exist	VERB
ejpam-3029	98	52	a	a	DET
ejpam-3029	98	53	finite	finite	NOUN
ejpam-3029	98	54	subset	subset	VERB
ejpam-3029	98	55	∆0	∆0	NUM
ejpam-3029	98	56	of	of	ADP
ejpam-3029	98	57	∆	∆	PROPN
ejpam-3029	98	58	such	such	ADJ
ejpam-3029	98	59	that	that	SCONJ
ejpam-3029	98	60	x	x	SYM
ejpam-3029	98	61	\	\	PROPN
ejpam-3029	98	62	⋃	⋃	PUNCT
ejpam-3029	98	63	α∈∆0	α∈∆0	NUM
ejpam-3029	98	64	cµ(vα	cµ(vα	NOUN
ejpam-3029	98	65	)	)	PUNCT
ejpam-3029	98	66	∈	∈	PROPN
ejpam-3029	98	67	h.	h.	PROPN
ejpam-3029	98	68	since	since	SCONJ
ejpam-3029	98	69	h	h	PROPN
ejpam-3029	98	70	is	be	AUX
ejpam-3029	98	71	µ-codense	µ-codense	NOUN
ejpam-3029	98	72	,	,	PUNCT
ejpam-3029	98	73	then	then	ADV
ejpam-3029	98	74	iµ(x	iµ(x	VERB
ejpam-3029	98	75	\	\	NOUN
ejpam-3029	98	76	⋃	⋃	PUNCT
ejpam-3029	98	77	α∈∆0	α∈∆0	NUM
ejpam-3029	98	78	cµ(vα	cµ(vα	NOUN
ejpam-3029	98	79	)	)	PUNCT
ejpam-3029	98	80	)	)	PUNCT
ejpam-3029	99	1	=	=	PUNCT
ejpam-3029	99	2	∅	∅	NOUN
ejpam-3029	99	3	which	which	PRON
ejpam-3029	99	4	implies	imply	VERB
ejpam-3029	99	5	x	x	PUNCT
ejpam-3029	99	6	−	−	NOUN
ejpam-3029	99	7	iµ(x	iµ(x	VERB
ejpam-3029	99	8	\	\	VERB
ejpam-3029	99	9	⋃	⋃	PUNCT
ejpam-3029	99	10	α∈∆0	α∈∆0	NUM
ejpam-3029	99	11	cµ(vα	cµ(vα	NOUN
ejpam-3029	99	12	)	)	PUNCT
ejpam-3029	99	13	)	)	PUNCT
ejpam-3029	100	1	=	=	SYM
ejpam-3029	100	2	cµ	cµ	NOUN
ejpam-3029	100	3	(	(	PUNCT
ejpam-3029	100	4	⋃	⋃	PROPN
ejpam-3029	100	5	α∈∆0	α∈∆0	NUM
ejpam-3029	100	6	cµ(vα	cµ(vα	NOUN
ejpam-3029	100	7	)	)	PUNCT
ejpam-3029	100	8	=	=	SYM
ejpam-3029	101	1	⋃	⋃	NOUN
ejpam-3029	101	2	α∈∆0	α∈∆0	NUM
ejpam-3029	101	3	cµ(vα	cµ(vα	NOUN
ejpam-3029	101	4	)	)	PUNCT
ejpam-3029	101	5	=	=	PUNCT
ejpam-3029	102	1	x.	x.	NOUN
ejpam-3029	102	2	hence	hence	ADV
ejpam-3029	102	3	(	(	PUNCT
ejpam-3029	102	4	x,µ	x,µ	NOUN
ejpam-3029	102	5	)	)	PUNCT
ejpam-3029	102	6	is	be	AUX
ejpam-3029	102	7	weakly	weakly	ADJ
ejpam-3029	102	8	µ-compact	µ-compact	NOUN
ejpam-3029	102	9	.	.	PUNCT
ejpam-3029	103	1	theorem	theorem	VERB
ejpam-3029	103	2	2	2	NUM
ejpam-3029	103	3	.	.	X
ejpam-3029	103	4	for	for	ADP
ejpam-3029	103	5	a	a	DET
ejpam-3029	103	6	gts	gts	NOUN
ejpam-3029	103	7	(	(	PUNCT
ejpam-3029	103	8	x,µ	x,µ	NOUN
ejpam-3029	103	9	)	)	PUNCT
ejpam-3029	103	10	,	,	PUNCT
ejpam-3029	103	11	the	the	DET
ejpam-3029	103	12	following	follow	VERB
ejpam-3029	103	13	properties	property	NOUN
ejpam-3029	103	14	hold	hold	VERB
ejpam-3029	103	15	.	.	PUNCT
ejpam-3029	104	1	(	(	PUNCT
ejpam-3029	104	2	1	1	X
ejpam-3029	104	3	)	)	PUNCT
ejpam-3029	104	4	(	(	PUNCT
ejpam-3029	104	5	x,µ	x,µ	NOUN
ejpam-3029	104	6	)	)	PUNCT
ejpam-3029	104	7	is	be	AUX
ejpam-3029	104	8	weakly	weakly	ADJ
ejpam-3029	104	9	µ-compact	µ-compact	NOUN
ejpam-3029	104	10	if	if	SCONJ
ejpam-3029	104	11	and	and	CCONJ
ejpam-3029	104	12	only	only	ADV
ejpam-3029	104	13	if	if	SCONJ
ejpam-3029	104	14	(	(	PUNCT
ejpam-3029	104	15	x,µ,n	x,µ,n	PROPN
ejpam-3029	104	16	(	(	PUNCT
ejpam-3029	104	17	µ	µ	NOUN
ejpam-3029	104	18	)	)	PUNCT
ejpam-3029	104	19	)	)	PUNCT
ejpam-3029	104	20	is	be	AUX
ejpam-3029	104	21	µn	µn	PROPN
ejpam-3029	104	22	(	(	PUNCT
ejpam-3029	104	23	µ)-compact	µ)-compact	PROPN
ejpam-3029	104	24	.	.	PUNCT
ejpam-3029	105	1	(	(	PUNCT
ejpam-3029	105	2	2	2	NUM
ejpam-3029	105	3	)	)	PUNCT
ejpam-3029	105	4	(	(	PUNCT
ejpam-3029	105	5	x,µ	x,µ	NOUN
ejpam-3029	105	6	)	)	PUNCT
ejpam-3029	105	7	is	be	AUX
ejpam-3029	105	8	weakly	weakly	ADJ
ejpam-3029	105	9	µ-compact	µ-compact	NOUN
ejpam-3029	105	10	if	if	SCONJ
ejpam-3029	105	11	and	and	CCONJ
ejpam-3029	105	12	only	only	ADV
ejpam-3029	105	13	if	if	SCONJ
ejpam-3029	105	14	(	(	PUNCT
ejpam-3029	105	15	x,µ,h	x,µ,h	PROPN
ejpam-3029	105	16	)	)	PUNCT
ejpam-3029	105	17	is	be	AUX
ejpam-3029	105	18	µh	µh	NOUN
ejpam-3029	105	19	-	-	ADJ
ejpam-3029	105	20	compact	compact	ADJ
ejpam-3029	105	21	with	with	ADP
ejpam-3029	105	22	respect	respect	NOUN
ejpam-3029	105	23	to	to	ADP
ejpam-3029	105	24	some	some	DET
ejpam-3029	105	25	µ-codense	µ-codense	PROPN
ejpam-3029	105	26	hc	hc	PROPN
ejpam-3029	105	27	.	.	PROPN
ejpam-3029	105	28	proof	proof	NOUN
ejpam-3029	105	29	.	.	PUNCT
ejpam-3029	106	1	(	(	PUNCT
ejpam-3029	106	2	1	1	X
ejpam-3029	106	3	)	)	PUNCT
ejpam-3029	106	4	necessity	necessity	NOUN
ejpam-3029	106	5	.	.	PUNCT
ejpam-3029	107	1	assume	assume	VERB
ejpam-3029	107	2	(	(	PUNCT
ejpam-3029	107	3	x,µ	x,µ	NOUN
ejpam-3029	107	4	)	)	PUNCT
ejpam-3029	107	5	is	be	AUX
ejpam-3029	107	6	weakly	weakly	ADJ
ejpam-3029	107	7	µ-compact	µ-compact	NOUN
ejpam-3029	107	8	and	and	CCONJ
ejpam-3029	107	9	let	let	VERB
ejpam-3029	107	10	{	{	PUNCT
ejpam-3029	107	11	vα	vα	X
ejpam-3029	107	12	:	:	PUNCT
ejpam-3029	107	13	α	α	PROPN
ejpam-3029	107	14	∈	∈	PROPN
ejpam-3029	107	15	∆	∆	PROPN
ejpam-3029	107	16	}	}	PUNCT
ejpam-3029	107	17	be	be	AUX
ejpam-3029	107	18	a	a	DET
ejpam-3029	107	19	µ-open	µ-open	NOUN
ejpam-3029	107	20	cover	cover	NOUN
ejpam-3029	107	21	of	of	ADP
ejpam-3029	107	22	x.	x.	NOUN
ejpam-3029	107	23	then	then	ADV
ejpam-3029	107	24	by	by	ADP
ejpam-3029	107	25	assumption	assumption	NOUN
ejpam-3029	107	26	there	there	PRON
ejpam-3029	107	27	exists	exist	VERB
ejpam-3029	107	28	a	a	DET
ejpam-3029	107	29	finite	finite	NOUN
ejpam-3029	107	30	subset	subset	VERB
ejpam-3029	107	31	∆0	∆0	NUM
ejpam-3029	107	32	of	of	ADP
ejpam-3029	107	33	∆	∆	PROPN
ejpam-3029	107	34	such	such	ADJ
ejpam-3029	107	35	that	that	SCONJ
ejpam-3029	107	36	x	x	X
ejpam-3029	107	37	=	=	PUNCT
ejpam-3029	107	38	⋃	⋃	NOUN
ejpam-3029	107	39	α∈∆0	α∈∆0	NUM
ejpam-3029	107	40	cµ(vα	cµ(vα	NOUN
ejpam-3029	107	41	)	)	PUNCT
ejpam-3029	108	1	=	=	SYM
ejpam-3029	108	2	cµ	cµ	NOUN
ejpam-3029	108	3	(	(	PUNCT
ejpam-3029	108	4	⋃	⋃	NOUN
ejpam-3029	108	5	α∈∆0	α∈∆0	NUM
ejpam-3029	108	6	vα	vα	NOUN
ejpam-3029	108	7	)	)	PUNCT
ejpam-3029	108	8	.	.	PUNCT
ejpam-3029	109	1	since	since	SCONJ
ejpam-3029	109	2	x	x	SYM
ejpam-3029	109	3	\	\	PROPN
ejpam-3029	109	4	cµ	cµ	PROPN
ejpam-3029	109	5	(	(	PUNCT
ejpam-3029	109	6	⋃	⋃	NOUN
ejpam-3029	109	7	α∈∆0	α∈∆0	NUM
ejpam-3029	109	8	vα	vα	NOUN
ejpam-3029	109	9	)	)	PUNCT
ejpam-3029	109	10	=	=	NOUN
ejpam-3029	109	11	∅	∅	NOUN
ejpam-3029	109	12	and	and	CCONJ
ejpam-3029	109	13	x	x	SYM
ejpam-3029	109	14	\	\	PROPN
ejpam-3029	109	15	⋃	⋃	ADV
ejpam-3029	109	16	α∈∆0	α∈∆0	NOUN
ejpam-3029	109	17	vα	vα	NOUN
ejpam-3029	109	18	is	be	AUX
ejpam-3029	109	19	a	a	DET
ejpam-3029	109	20	µ-closed	µ-close	VERB
ejpam-3029	109	21	,	,	PUNCT
ejpam-3029	109	22	then	then	ADV
ejpam-3029	109	23	iµ(x	iµ(x	VERB
ejpam-3029	109	24	\	\	NOUN
ejpam-3029	109	25	⋃	⋃	SCONJ
ejpam-3029	109	26	α∈∆0	α∈∆0	NUM
ejpam-3029	109	27	vα	vα	NOUN
ejpam-3029	109	28	)	)	PUNCT
ejpam-3029	109	29	=	=	PUNCT
ejpam-3029	109	30	∅.	∅.	ADP
ejpam-3029	109	31	this	this	PRON
ejpam-3029	109	32	implies	imply	VERB
ejpam-3029	109	33	x	x	SYM
ejpam-3029	109	34	\	\	NOUN
ejpam-3029	110	1	⋃	⋃	SCONJ
ejpam-3029	110	2	α∈∆0	α∈∆0	VERB
ejpam-3029	110	3	vα	vα	ADP
ejpam-3029	110	4	∈	∈	PROPN
ejpam-3029	110	5	n	n	CCONJ
ejpam-3029	110	6	(	(	PUNCT
ejpam-3029	110	7	µ	µ	NOUN
ejpam-3029	110	8	)	)	PUNCT
ejpam-3029	110	9	.	.	PUNCT
ejpam-3029	111	1	thus	thus	ADV
ejpam-3029	111	2	(	(	PUNCT
ejpam-3029	111	3	x,µ,h	x,µ,h	PROPN
ejpam-3029	111	4	)	)	PUNCT
ejpam-3029	111	5	is	be	AUX
ejpam-3029	111	6	µn	µn	NOUN
ejpam-3029	111	7	(	(	PUNCT
ejpam-3029	111	8	µ)compact	µ)compact	PROPN
ejpam-3029	111	9	.	.	PUNCT
ejpam-3029	112	1	sufficiency	sufficiency	PROPN
ejpam-3029	112	2	.	.	PUNCT
ejpam-3029	113	1	assume	assume	VERB
ejpam-3029	113	2	(	(	PUNCT
ejpam-3029	113	3	x,µ,n	x,µ,n	PROPN
ejpam-3029	113	4	(	(	PUNCT
ejpam-3029	113	5	µ	µ	NOUN
ejpam-3029	113	6	)	)	PUNCT
ejpam-3029	113	7	)	)	PUNCT
ejpam-3029	113	8	is	be	AUX
ejpam-3029	113	9	µn	µn	PROPN
ejpam-3029	113	10	(	(	PUNCT
ejpam-3029	113	11	µ)-compact	µ)-compact	PUNCT
ejpam-3029	113	12	and	and	CCONJ
ejpam-3029	113	13	let	let	VERB
ejpam-3029	113	14	{	{	PUNCT
ejpam-3029	113	15	vα	vα	X
ejpam-3029	113	16	:	:	PUNCT
ejpam-3029	113	17	α	α	PROPN
ejpam-3029	113	18	∈	∈	PROPN
ejpam-3029	113	19	∆	∆	PROPN
ejpam-3029	113	20	}	}	PUNCT
ejpam-3029	113	21	be	be	AUX
ejpam-3029	113	22	a	a	DET
ejpam-3029	113	23	µ-open	µ-open	NOUN
ejpam-3029	113	24	cover	cover	NOUN
ejpam-3029	113	25	of	of	ADP
ejpam-3029	113	26	x.	x.	NOUN
ejpam-3029	113	27	by	by	ADP
ejpam-3029	113	28	assumption	assumption	NOUN
ejpam-3029	113	29	,	,	PUNCT
ejpam-3029	113	30	there	there	PRON
ejpam-3029	113	31	exists	exist	VERB
ejpam-3029	113	32	a	a	DET
ejpam-3029	113	33	finite	finite	NOUN
ejpam-3029	113	34	subset	subset	VERB
ejpam-3029	113	35	∆0	∆0	NUM
ejpam-3029	113	36	of	of	ADP
ejpam-3029	113	37	∆	∆	PROPN
ejpam-3029	113	38	such	such	ADJ
ejpam-3029	113	39	that	that	SCONJ
ejpam-3029	113	40	x	x	SYM
ejpam-3029	113	41	\	\	NOUN
ejpam-3029	113	42	⋃	⋃	SCONJ
ejpam-3029	113	43	α∈∆	α∈∆	PRON
ejpam-3029	113	44	vα	vα	ADP
ejpam-3029	113	45	∈	∈	PROPN
ejpam-3029	113	46	n	n	CCONJ
ejpam-3029	113	47	(	(	PUNCT
ejpam-3029	113	48	µ	µ	NOUN
ejpam-3029	113	49	)	)	PUNCT
ejpam-3029	113	50	.	.	PUNCT
ejpam-3029	114	1	this	this	PRON
ejpam-3029	114	2	implies	imply	VERB
ejpam-3029	114	3	that	that	SCONJ
ejpam-3029	114	4	iµ(x	iµ(x	VERB
ejpam-3029	114	5	\	\	NOUN
ejpam-3029	114	6	⋃	⋃	SCONJ
ejpam-3029	114	7	α∈∆	α∈∆	PRON
ejpam-3029	114	8	vα	vα	NOUN
ejpam-3029	114	9	)	)	PUNCT
ejpam-3029	114	10	=	=	NOUN
ejpam-3029	114	11	∅	∅	NOUN
ejpam-3029	114	12	and	and	CCONJ
ejpam-3029	114	13	hence	hence	ADV
ejpam-3029	114	14	x	x	X
ejpam-3029	114	15	=	=	SYM
ejpam-3029	114	16	cµ	cµ	NOUN
ejpam-3029	114	17	(	(	PUNCT
ejpam-3029	114	18	⋃	⋃	NOUN
ejpam-3029	114	19	α∈∆0	α∈∆0	NUM
ejpam-3029	114	20	vα	vα	NOUN
ejpam-3029	114	21	)	)	PUNCT
ejpam-3029	114	22	=	=	PUNCT
ejpam-3029	114	23	⋃	⋃	NOUN
ejpam-3029	114	24	α∈∆0	α∈∆0	NUM
ejpam-3029	114	25	cµ(vα	cµ(vα	NOUN
ejpam-3029	114	26	)	)	PUNCT
ejpam-3029	114	27	.	.	PUNCT
ejpam-3029	115	1	(	(	PUNCT
ejpam-3029	115	2	2	2	X
ejpam-3029	115	3	)	)	PUNCT
ejpam-3029	115	4	necessity	necessity	NOUN
ejpam-3029	115	5	.	.	PUNCT
ejpam-3029	116	1	from	from	ADP
ejpam-3029	116	2	(	(	PUNCT
ejpam-3029	116	3	1	1	X
ejpam-3029	116	4	)	)	PUNCT
ejpam-3029	116	5	h	h	NOUN
ejpam-3029	116	6	is	be	AUX
ejpam-3029	116	7	a	a	DET
ejpam-3029	116	8	µ-codense	µ-codense	NOUN
ejpam-3029	116	9	.	.	PUNCT
ejpam-3029	117	1	sufficiency	sufficiency	NOUN
ejpam-3029	117	2	.	.	PUNCT
ejpam-3029	118	1	the	the	DET
ejpam-3029	118	2	proof	proof	NOUN
ejpam-3029	118	3	is	be	AUX
ejpam-3029	118	4	obvious	obvious	ADJ
ejpam-3029	118	5	by	by	ADP
ejpam-3029	118	6	proposition	proposition	NOUN
ejpam-3029	118	7	1	1	NUM
ejpam-3029	118	8	.	.	PUNCT
ejpam-3029	118	9	theorem	theorem	NOUN
ejpam-3029	118	10	3	3	X
ejpam-3029	118	11	.	.	PUNCT
ejpam-3029	119	1	let	let	VERB
ejpam-3029	119	2	f	f	NOUN
ejpam-3029	119	3	:	:	PUNCT
ejpam-3029	119	4	(	(	PUNCT
ejpam-3029	119	5	x,µ)→	x,µ)→	X
ejpam-3029	119	6	(	(	PUNCT
ejpam-3029	119	7	y	y	PROPN
ejpam-3029	119	8	,	,	PUNCT
ejpam-3029	119	9	ν	ν	PROPN
ejpam-3029	119	10	,	,	PUNCT
ejpam-3029	119	11	g	g	NOUN
ejpam-3029	119	12	)	)	PUNCT
ejpam-3029	119	13	be	be	AUX
ejpam-3029	119	14	a	a	DET
ejpam-3029	119	15	surjection	surjection	NOUN
ejpam-3029	119	16	onto	onto	ADP
ejpam-3029	119	17	a	a	DET
ejpam-3029	119	18	νg	νg	NOUN
ejpam-3029	119	19	-	-	ADJ
ejpam-3029	119	20	compact	compact	ADJ
ejpam-3029	119	21	.	.	PUNCT
ejpam-3029	120	1	if	if	SCONJ
ejpam-3029	120	2	µ	µ	X
ejpam-3029	120	3	=	=	SYM
ejpam-3029	120	4	f−1(ν	f−1(ν	PROPN
ejpam-3029	120	5	)	)	PUNCT
ejpam-3029	120	6	is	be	AUX
ejpam-3029	120	7	the	the	DET
ejpam-3029	120	8	weak	weak	ADJ
ejpam-3029	120	9	generalized	generalized	ADJ
ejpam-3029	120	10	topology	topology	NOUN
ejpam-3029	120	11	on	on	ADP
ejpam-3029	120	12	x	x	PUNCT
ejpam-3029	120	13	induced	induce	VERB
ejpam-3029	120	14	by	by	ADP
ejpam-3029	120	15	f	f	PROPN
ejpam-3029	120	16	and	and	CCONJ
ejpam-3029	120	17	ν	ν	PROPN
ejpam-3029	120	18	,	,	PUNCT
ejpam-3029	120	19	then	then	ADV
ejpam-3029	120	20	(	(	PUNCT
ejpam-3029	120	21	x,µ	x,µ	NOUN
ejpam-3029	120	22	)	)	PUNCT
ejpam-3029	120	23	is	be	AUX
ejpam-3029	120	24	µf−1(g)-compact	µf−1(g)-compact	ADJ
ejpam-3029	120	25	.	.	PUNCT
ejpam-3029	121	1	proof	proof	NOUN
ejpam-3029	121	2	.	.	PUNCT
ejpam-3029	122	1	let	let	VERB
ejpam-3029	122	2	{	{	PUNCT
ejpam-3029	122	3	f−1(vα	f−1(vα	VERB
ejpam-3029	122	4	)	)	PUNCT
ejpam-3029	122	5	:	:	PUNCT
ejpam-3029	123	1	α	α	PROPN
ejpam-3029	123	2	∈	∈	PROPN
ejpam-3029	123	3	∆	∆	PROPN
ejpam-3029	123	4	}	}	PUNCT
ejpam-3029	123	5	be	be	AUX
ejpam-3029	123	6	a	a	DET
ejpam-3029	123	7	µ-open	µ-open	NOUN
ejpam-3029	123	8	cover	cover	NOUN
ejpam-3029	123	9	of	of	ADP
ejpam-3029	123	10	x.	x.	NOUN
ejpam-3029	123	11	then	then	ADV
ejpam-3029	123	12	{	{	PUNCT
ejpam-3029	123	13	vα	vα	X
ejpam-3029	123	14	:	:	PUNCT
ejpam-3029	123	15	α	α	PROPN
ejpam-3029	123	16	∈	∈	PROPN
ejpam-3029	123	17	∆	∆	X
ejpam-3029	123	18	}	}	PUNCT
ejpam-3029	123	19	is	be	AUX
ejpam-3029	123	20	a	a	DET
ejpam-3029	123	21	ν	ν	NOUN
ejpam-3029	123	22	-	-	ADJ
ejpam-3029	123	23	open	open	ADJ
ejpam-3029	123	24	cover	cover	NOUN
ejpam-3029	123	25	of	of	ADP
ejpam-3029	123	26	y	y	PROPN
ejpam-3029	123	27	and	and	CCONJ
ejpam-3029	123	28	hence	hence	ADV
ejpam-3029	123	29	there	there	PRON
ejpam-3029	123	30	exists	exist	VERB
ejpam-3029	123	31	a	a	DET
ejpam-3029	123	32	finite	finite	NOUN
ejpam-3029	123	33	subset	subset	VERB
ejpam-3029	123	34	∆0	∆0	NUM
ejpam-3029	123	35	of	of	ADP
ejpam-3029	123	36	∆	∆	PROPN
ejpam-3029	123	37	such	such	ADJ
ejpam-3029	123	38	that	that	SCONJ
ejpam-3029	123	39	y	y	PROPN
ejpam-3029	123	40	\	\	PUNCT
ejpam-3029	123	41	⋃	⋃	SCONJ
ejpam-3029	123	42	α∈∆	α∈∆	PRON
ejpam-3029	123	43	vα	vα	ADP
ejpam-3029	123	44	∈	∈	PROPN
ejpam-3029	123	45	g.	g.	NOUN
ejpam-3029	123	46	now	now	ADV
ejpam-3029	123	47	we	we	PRON
ejpam-3029	123	48	have	have	VERB
ejpam-3029	123	49	f−1	f−1	PROPN
ejpam-3029	123	50	y	y	PUNCT
ejpam-3029	123	51	\	\	NOUN
ejpam-3029	124	1	⋃	⋃	SCONJ
ejpam-3029	124	2	α∈∆0	α∈∆0	NOUN
ejpam-3029	124	3	vα	vα	ADP
ejpam-3029	124	4			PROPN
ejpam-3029	124	5	=	=	PUNCT
ejpam-3029	124	6	x	x	SYM
ejpam-3029	124	7	\	\	PROPN
ejpam-3029	124	8	⋃	⋃	ADV
ejpam-3029	124	9	α∈∆0	α∈∆0	NUM
ejpam-3029	124	10	f−1	f−1	PROPN
ejpam-3029	124	11	(	(	PUNCT
ejpam-3029	124	12	vα	vα	PROPN
ejpam-3029	124	13	)	)	PUNCT
ejpam-3029	124	14	∈	∈	PROPN
ejpam-3029	124	15	f−1(g	f−1(g	PROPN
ejpam-3029	124	16	)	)	PUNCT
ejpam-3029	124	17	.	.	PUNCT
ejpam-3029	125	1	hence	hence	ADV
ejpam-3029	125	2	(	(	PUNCT
ejpam-3029	125	3	x,µ	x,µ	NOUN
ejpam-3029	125	4	)	)	PUNCT
ejpam-3029	125	5	is	be	AUX
ejpam-3029	125	6	µf−1(g)-compact	µf−1(g)-compact	ADJ
ejpam-3029	125	7	.	.	PUNCT
ejpam-3029	126	1	the	the	DET
ejpam-3029	126	2	following	follow	VERB
ejpam-3029	126	3	lemma	lemma	PROPN
ejpam-3029	126	4	is	be	AUX
ejpam-3029	126	5	used	use	VERB
ejpam-3029	126	6	to	to	PART
ejpam-3029	126	7	prove	prove	VERB
ejpam-3029	126	8	the	the	DET
ejpam-3029	126	9	corollary	corollary	NOUN
ejpam-3029	126	10	which	which	PRON
ejpam-3029	126	11	is	be	AUX
ejpam-3029	126	12	stated	state	VERB
ejpam-3029	126	13	below	below	ADV
ejpam-3029	126	14	.	.	PUNCT
ejpam-3029	127	1	lemma	lemma	PROPN
ejpam-3029	127	2	2	2	X
ejpam-3029	127	3	.	.	PUNCT
ejpam-3029	128	1	if	if	SCONJ
ejpam-3029	128	2	f	f	PROPN
ejpam-3029	128	3	:	:	PUNCT
ejpam-3029	128	4	(	(	PUNCT
ejpam-3029	128	5	x,µ	x,µ	NOUN
ejpam-3029	128	6	)	)	PUNCT
ejpam-3029	128	7	→	→	SYM
ejpam-3029	128	8	(	(	PUNCT
ejpam-3029	128	9	y	y	PROPN
ejpam-3029	128	10	,	,	PUNCT
ejpam-3029	128	11	ν	ν	PROPN
ejpam-3029	128	12	,	,	PUNCT
ejpam-3029	128	13	g	g	NOUN
ejpam-3029	128	14	)	)	PUNCT
ejpam-3029	128	15	is	be	AUX
ejpam-3029	128	16	a	a	DET
ejpam-3029	128	17	surjection	surjection	NOUN
ejpam-3029	128	18	and	and	CCONJ
ejpam-3029	128	19	g	g	NOUN
ejpam-3029	128	20	is	be	AUX
ejpam-3029	128	21	ν	ν	NOUN
ejpam-3029	128	22	-	-	NOUN
ejpam-3029	128	23	codense	codense	NOUN
ejpam-3029	128	24	,	,	PUNCT
ejpam-3029	128	25	then	then	ADV
ejpam-3029	128	26	f−1(g	f−1(g	PROPN
ejpam-3029	128	27	)	)	PUNCT
ejpam-3029	128	28	is	be	AUX
ejpam-3029	128	29	f−1(ν)-codense	f−1(ν)-codense	PROPN
ejpam-3029	128	30	,	,	PUNCT
ejpam-3029	128	31	where	where	SCONJ
ejpam-3029	128	32	µ	µ	X
ejpam-3029	128	33	=	=	SYM
ejpam-3029	128	34	f−1(ν	f−1(ν	PROPN
ejpam-3029	128	35	)	)	PUNCT
ejpam-3029	128	36	.	.	PUNCT
ejpam-3029	129	1	a.	a.	NOUN
ejpam-3029	129	2	qahis	qahis	PROPN
ejpam-3029	129	3	,	,	PUNCT
ejpam-3029	129	4	t.	t.	PROPN
ejpam-3029	129	5	noiri	noiri	PROPN
ejpam-3029	129	6	/	/	SYM
ejpam-3029	129	7	eur	eur	PROPN
ejpam-3029	129	8	.	.	PUNCT
ejpam-3029	130	1	j.	j.	PROPN
ejpam-3029	130	2	pure	pure	PROPN
ejpam-3029	130	3	appl	appl	PROPN
ejpam-3029	130	4	.	.	PROPN
ejpam-3029	130	5	math	math	PROPN
ejpam-3029	130	6	,	,	PUNCT
ejpam-3029	130	7	10	10	NUM
ejpam-3029	130	8	(	(	PUNCT
ejpam-3029	130	9	3	3	NUM
ejpam-3029	130	10	)	)	PUNCT
ejpam-3029	130	11	(	(	PUNCT
ejpam-3029	130	12	2017	2017	NUM
ejpam-3029	130	13	)	)	PUNCT
ejpam-3029	130	14	,	,	PUNCT
ejpam-3029	130	15	410	410	NUM
ejpam-3029	130	16	-	-	SYM
ejpam-3029	130	17	418	418	NUM
ejpam-3029	130	18	414	414	NUM
ejpam-3029	130	19	proof	proof	NOUN
ejpam-3029	130	20	.	.	PUNCT
ejpam-3029	131	1	assume	assume	VERB
ejpam-3029	131	2	f	f	X
ejpam-3029	131	3	:	:	PUNCT
ejpam-3029	131	4	(	(	PUNCT
ejpam-3029	131	5	x	x	X
ejpam-3029	131	6	,	,	PUNCT
ejpam-3029	131	7	µ)→	µ)→	X
ejpam-3029	131	8	(	(	PUNCT
ejpam-3029	131	9	y	y	PROPN
ejpam-3029	131	10	,	,	PUNCT
ejpam-3029	131	11	ν	ν	PROPN
ejpam-3029	131	12	,	,	PUNCT
ejpam-3029	131	13	g	g	NOUN
ejpam-3029	131	14	)	)	PUNCT
ejpam-3029	131	15	is	be	AUX
ejpam-3029	131	16	a	a	DET
ejpam-3029	131	17	surjection	surjection	NOUN
ejpam-3029	131	18	and	and	CCONJ
ejpam-3029	131	19	f−1(g	f−1(g	PROPN
ejpam-3029	131	20	)	)	PUNCT
ejpam-3029	131	21	is	be	AUX
ejpam-3029	131	22	not	not	PART
ejpam-3029	131	23	f−1(ν)-codense	f−1(ν)-codense	ADJ
ejpam-3029	131	24	,	,	PUNCT
ejpam-3029	131	25	then	then	ADV
ejpam-3029	131	26	there	there	PRON
ejpam-3029	131	27	exists	exist	VERB
ejpam-3029	131	28	g	g	PROPN
ejpam-3029	131	29	∈	∈	PROPN
ejpam-3029	131	30	g	g	PROPN
ejpam-3029	131	31	such	such	ADJ
ejpam-3029	131	32	that	that	DET
ejpam-3029	131	33	f−1(g	f−1(g	PROPN
ejpam-3029	131	34	)	)	PUNCT
ejpam-3029	131	35	∈	∈	PROPN
ejpam-3029	131	36	f−1(ν	f−1(ν	PROPN
ejpam-3029	131	37	)	)	PUNCT
ejpam-3029	131	38	\	\	NOUN
ejpam-3029	132	1	{	{	PUNCT
ejpam-3029	132	2	∅	∅	NOUN
ejpam-3029	132	3	}	}	PUNCT
ejpam-3029	132	4	,	,	PUNCT
ejpam-3029	132	5	say	say	VERB
ejpam-3029	132	6	f−1(g	f−1(g	X
ejpam-3029	132	7	)	)	PUNCT
ejpam-3029	132	8	=	=	SYM
ejpam-3029	132	9	f−1(v	f−1(v	PROPN
ejpam-3029	132	10	)	)	PUNCT
ejpam-3029	133	1	where	where	SCONJ
ejpam-3029	133	2	v	v	X
ejpam-3029	133	3	∈	∈	NOUN
ejpam-3029	133	4	ν	ν	X
ejpam-3029	133	5	\	\	X
ejpam-3029	133	6	{	{	PUNCT
ejpam-3029	133	7	∅	∅	NOUN
ejpam-3029	133	8	}	}	PUNCT
ejpam-3029	133	9	.	.	PUNCT
ejpam-3029	134	1	then	then	ADV
ejpam-3029	134	2	g	g	PROPN
ejpam-3029	134	3	=	=	SYM
ejpam-3029	134	4	v	v	PROPN
ejpam-3029	134	5	∈	∈	PROPN
ejpam-3029	134	6	ν	ν	X
ejpam-3029	134	7	\	\	X
ejpam-3029	134	8	{	{	PUNCT
ejpam-3029	134	9	∅	∅	NOUN
ejpam-3029	134	10	}	}	PUNCT
ejpam-3029	134	11	and	and	CCONJ
ejpam-3029	134	12	g	g	PROPN
ejpam-3029	134	13	is	be	AUX
ejpam-3029	134	14	not	not	PART
ejpam-3029	134	15	ν	ν	NOUN
ejpam-3029	134	16	-	-	NOUN
ejpam-3029	134	17	codense	codense	NOUN
ejpam-3029	134	18	.	.	PUNCT
ejpam-3029	135	1	then	then	ADV
ejpam-3029	135	2	this	this	PRON
ejpam-3029	135	3	contradicts	contradict	VERB
ejpam-3029	135	4	to	to	ADP
ejpam-3029	135	5	our	our	PRON
ejpam-3029	135	6	assumption	assumption	NOUN
ejpam-3029	135	7	.	.	PUNCT
ejpam-3029	136	1	corollary	corollary	ADJ
ejpam-3029	136	2	3	3	X
ejpam-3029	136	3	.	.	PUNCT
ejpam-3029	137	1	let	let	VERB
ejpam-3029	137	2	f	f	NOUN
ejpam-3029	137	3	:	:	PUNCT
ejpam-3029	137	4	(	(	PUNCT
ejpam-3029	137	5	x,µ	x,µ	NOUN
ejpam-3029	137	6	)	)	PUNCT
ejpam-3029	137	7	→	→	SYM
ejpam-3029	137	8	(	(	PUNCT
ejpam-3029	137	9	y	y	PROPN
ejpam-3029	137	10	,	,	PUNCT
ejpam-3029	137	11	ν	ν	PROPN
ejpam-3029	137	12	,	,	PUNCT
ejpam-3029	137	13	g	g	NOUN
ejpam-3029	137	14	)	)	PUNCT
ejpam-3029	137	15	be	be	AUX
ejpam-3029	137	16	a	a	DET
ejpam-3029	137	17	surjection	surjection	NOUN
ejpam-3029	137	18	and	and	CCONJ
ejpam-3029	137	19	let	let	VERB
ejpam-3029	137	20	µ	µ	PRON
ejpam-3029	137	21	denote	denote	VERB
ejpam-3029	137	22	the	the	DET
ejpam-3029	137	23	weak	weak	ADJ
ejpam-3029	137	24	generalized	generalized	ADJ
ejpam-3029	137	25	topology	topology	NOUN
ejpam-3029	137	26	on	on	ADP
ejpam-3029	137	27	x	x	PUNCT
ejpam-3029	137	28	induced	induce	VERB
ejpam-3029	137	29	by	by	ADP
ejpam-3029	137	30	f	f	PROPN
ejpam-3029	137	31	and	and	CCONJ
ejpam-3029	137	32	ν	ν	NOUN
ejpam-3029	137	33	.	.	PUNCT
ejpam-3029	138	1	if	if	SCONJ
ejpam-3029	138	2	g	g	PROPN
ejpam-3029	138	3	is	be	AUX
ejpam-3029	138	4	ν	ν	NOUN
ejpam-3029	138	5	-	-	NOUN
ejpam-3029	138	6	codense	codense	NOUN
ejpam-3029	138	7	and	and	CCONJ
ejpam-3029	138	8	(	(	PUNCT
ejpam-3029	138	9	y	y	PROPN
ejpam-3029	138	10	,	,	PUNCT
ejpam-3029	138	11	ν	ν	PROPN
ejpam-3029	138	12	,	,	PUNCT
ejpam-3029	138	13	g	g	NOUN
ejpam-3029	138	14	)	)	PUNCT
ejpam-3029	138	15	is	be	AUX
ejpam-3029	138	16	νg	νg	NOUN
ejpam-3029	138	17	-	-	ADJ
ejpam-3029	138	18	compact	compact	ADJ
ejpam-3029	138	19	,	,	PUNCT
ejpam-3029	138	20	then	then	ADV
ejpam-3029	138	21	(	(	PUNCT
ejpam-3029	138	22	x,µ	x,µ	NOUN
ejpam-3029	138	23	)	)	PUNCT
ejpam-3029	138	24	is	be	AUX
ejpam-3029	138	25	weakly	weakly	ADJ
ejpam-3029	138	26	µ-compact	µ-compact	NOUN
ejpam-3029	138	27	proof	proof	NOUN
ejpam-3029	138	28	.	.	PUNCT
ejpam-3029	139	1	if	if	SCONJ
ejpam-3029	139	2	g	g	PROPN
ejpam-3029	139	3	is	be	AUX
ejpam-3029	139	4	ν	ν	NOUN
ejpam-3029	139	5	-	-	NOUN
ejpam-3029	139	6	codense	codense	NOUN
ejpam-3029	139	7	and	and	CCONJ
ejpam-3029	139	8	(	(	PUNCT
ejpam-3029	139	9	y	y	PROPN
ejpam-3029	139	10	,	,	PUNCT
ejpam-3029	139	11	ν	ν	NOUN
ejpam-3029	139	12	)	)	PUNCT
ejpam-3029	139	13	is	be	AUX
ejpam-3029	139	14	νg	νg	NOUN
ejpam-3029	139	15	-	-	ADJ
ejpam-3029	139	16	compact	compact	ADJ
ejpam-3029	139	17	,	,	PUNCT
ejpam-3029	139	18	then	then	ADV
ejpam-3029	139	19	by	by	ADP
ejpam-3029	139	20	theorem	theorem	NOUN
ejpam-3029	139	21	3	3	NUM
ejpam-3029	139	22	,	,	PUNCT
ejpam-3029	139	23	(	(	PUNCT
ejpam-3029	139	24	x,µ	x,µ	NOUN
ejpam-3029	139	25	)	)	PUNCT
ejpam-3029	139	26	is	be	AUX
ejpam-3029	139	27	µf−1(g)-compact	µf−1(g)-compact	ADJ
ejpam-3029	139	28	.	.	PUNCT
ejpam-3029	140	1	since	since	SCONJ
ejpam-3029	140	2	g	g	PROPN
ejpam-3029	140	3	is	be	AUX
ejpam-3029	140	4	ν	ν	NOUN
ejpam-3029	140	5	-	-	NOUN
ejpam-3029	140	6	codense	codense	NOUN
ejpam-3029	140	7	.	.	PUNCT
ejpam-3029	141	1	then	then	ADV
ejpam-3029	141	2	by	by	ADP
ejpam-3029	141	3	lemma	lemma	PROPN
ejpam-3029	141	4	2	2	NUM
ejpam-3029	141	5	,	,	PUNCT
ejpam-3029	141	6	f−1(g	f−1(g	PROPN
ejpam-3029	141	7	)	)	PUNCT
ejpam-3029	141	8	is	be	AUX
ejpam-3029	141	9	µ	µ	NOUN
ejpam-3029	141	10	=	=	SYM
ejpam-3029	141	11	f−1(ν)codense	f−1(ν)codense	NOUN
ejpam-3029	141	12	.	.	PUNCT
ejpam-3029	142	1	by	by	ADP
ejpam-3029	142	2	theorem	theorem	NOUN
ejpam-3029	142	3	2(2	2(2	NUM
ejpam-3029	142	4	)	)	PUNCT
ejpam-3029	142	5	,	,	PUNCT
ejpam-3029	142	6	(	(	PUNCT
ejpam-3029	142	7	x,µ	x,µ	NOUN
ejpam-3029	142	8	)	)	PUNCT
ejpam-3029	142	9	is	be	AUX
ejpam-3029	142	10	weakly	weakly	ADJ
ejpam-3029	142	11	µ-compact	µ-compact	NOUN
ejpam-3029	142	12	.	.	PUNCT
ejpam-3029	143	1	next	next	ADV
ejpam-3029	143	2	we	we	PRON
ejpam-3029	143	3	introduce	introduce	VERB
ejpam-3029	143	4	the	the	DET
ejpam-3029	143	5	main	main	ADJ
ejpam-3029	143	6	result	result	NOUN
ejpam-3029	143	7	and	and	CCONJ
ejpam-3029	143	8	prove	prove	VERB
ejpam-3029	143	9	that	that	SCONJ
ejpam-3029	143	10	the	the	DET
ejpam-3029	143	11	θ(µ	θ(µ	PROPN
ejpam-3029	143	12	,	,	PUNCT
ejpam-3029	143	13	ν)-continuous	ν)-continuous	ADJ
ejpam-3029	143	14	image	image	NOUN
ejpam-3029	143	15	of	of	ADP
ejpam-3029	143	16	a	a	DET
ejpam-3029	143	17	weakly	weakly	ADJ
ejpam-3029	143	18	µh	µh	ADJ
ejpam-3029	143	19	-	-	ADJ
ejpam-3029	143	20	compact	compact	ADJ
ejpam-3029	143	21	space	space	NOUN
ejpam-3029	143	22	is	be	AUX
ejpam-3029	143	23	weakly	weakly	ADJ
ejpam-3029	143	24	νf(h)-compact	νf(h)-compact	NOUN
ejpam-3029	143	25	.	.	PUNCT
ejpam-3029	144	1	note	note	VERB
ejpam-3029	144	2	that	that	SCONJ
ejpam-3029	144	3	if	if	SCONJ
ejpam-3029	144	4	h	h	NOUN
ejpam-3029	144	5	is	be	AUX
ejpam-3029	144	6	a	a	DET
ejpam-3029	144	7	hereditary	hereditary	ADJ
ejpam-3029	144	8	class	class	NOUN
ejpam-3029	144	9	on	on	ADP
ejpam-3029	144	10	a	a	DET
ejpam-3029	144	11	set	set	NOUN
ejpam-3029	144	12	x	x	PUNCT
ejpam-3029	144	13	and	and	CCONJ
ejpam-3029	144	14	f	f	X
ejpam-3029	144	15	:	:	PUNCT
ejpam-3029	144	16	(	(	PUNCT
ejpam-3029	144	17	x,µ	x,µ	NOUN
ejpam-3029	144	18	)	)	PUNCT
ejpam-3029	144	19	→	→	SYM
ejpam-3029	144	20	(	(	PUNCT
ejpam-3029	144	21	y	y	PROPN
ejpam-3029	144	22	,	,	PUNCT
ejpam-3029	144	23	ν	ν	NOUN
ejpam-3029	144	24	)	)	PUNCT
ejpam-3029	144	25	is	be	AUX
ejpam-3029	144	26	a	a	DET
ejpam-3029	144	27	function	function	NOUN
ejpam-3029	144	28	,	,	PUNCT
ejpam-3029	144	29	then	then	ADV
ejpam-3029	144	30	f(h	f(h	PROPN
ejpam-3029	144	31	)	)	PUNCT
ejpam-3029	145	1	=	=	PRON
ejpam-3029	145	2	{	{	PUNCT
ejpam-3029	145	3	f(h	f(h	PROPN
ejpam-3029	145	4	)	)	PUNCT
ejpam-3029	145	5	:	:	PUNCT
ejpam-3029	146	1	h	h	PROPN
ejpam-3029	146	2	∈	∈	PROPN
ejpam-3029	146	3	h	h	NOUN
ejpam-3029	146	4	}	}	PUNCT
ejpam-3029	146	5	is	be	AUX
ejpam-3029	146	6	a	a	DET
ejpam-3029	146	7	hc	hc	NOUN
ejpam-3029	146	8	on	on	ADP
ejpam-3029	146	9	y	y	PROPN
ejpam-3029	147	1	[	[	X
ejpam-3029	147	2	2	2	NUM
ejpam-3029	147	3	]	]	PUNCT
ejpam-3029	147	4	.	.	PUNCT
ejpam-3029	148	1	theorem	theorem	ADJ
ejpam-3029	148	2	4	4	NUM
ejpam-3029	148	3	.	.	PUNCT
ejpam-3029	149	1	let	let	VERB
ejpam-3029	149	2	f	f	PROPN
ejpam-3029	149	3	:	:	PUNCT
ejpam-3029	149	4	(	(	PUNCT
ejpam-3029	149	5	x,µ,h)→	x,µ,h)→	X
ejpam-3029	149	6	(	(	PUNCT
ejpam-3029	149	7	y	y	PROPN
ejpam-3029	149	8	,	,	PUNCT
ejpam-3029	149	9	ν	ν	NOUN
ejpam-3029	149	10	)	)	PUNCT
ejpam-3029	149	11	be	be	AUX
ejpam-3029	149	12	a	a	DET
ejpam-3029	149	13	θ(µ	θ(µ	PROPN
ejpam-3029	149	14	,	,	PUNCT
ejpam-3029	149	15	ν)-continuous	ν)-continuous	ADJ
ejpam-3029	149	16	function	function	NOUN
ejpam-3029	149	17	.	.	PUNCT
ejpam-3029	150	1	if	if	SCONJ
ejpam-3029	150	2	a	a	PRON
ejpam-3029	150	3	is	be	AUX
ejpam-3029	150	4	a	a	DET
ejpam-3029	150	5	weakly	weakly	ADJ
ejpam-3029	150	6	µh	µh	NOUN
ejpam-3029	150	7	-	-	ADJ
ejpam-3029	150	8	compact	compact	ADJ
ejpam-3029	150	9	subset	subset	NOUN
ejpam-3029	150	10	of	of	ADP
ejpam-3029	150	11	x	x	PRON
ejpam-3029	150	12	,	,	PUNCT
ejpam-3029	150	13	then	then	ADV
ejpam-3029	150	14	f(a	f(a	PROPN
ejpam-3029	150	15	)	)	PUNCT
ejpam-3029	150	16	is	be	AUX
ejpam-3029	150	17	weakly	weakly	ADJ
ejpam-3029	150	18	νf(h)-compact	νf(h)-compact	NOUN
ejpam-3029	150	19	.	.	PUNCT
ejpam-3029	151	1	proof	proof	NOUN
ejpam-3029	151	2	.	.	PUNCT
ejpam-3029	152	1	let	let	VERB
ejpam-3029	152	2	v	v	VERB
ejpam-3029	152	3	=	=	PUNCT
ejpam-3029	152	4	{	{	PUNCT
ejpam-3029	152	5	vα	vα	X
ejpam-3029	152	6	:	:	PUNCT
ejpam-3029	152	7	α	α	PROPN
ejpam-3029	152	8	∈	∈	PROPN
ejpam-3029	152	9	∆	∆	PROPN
ejpam-3029	152	10	}	}	PUNCT
ejpam-3029	152	11	be	be	AUX
ejpam-3029	152	12	a	a	DET
ejpam-3029	152	13	cover	cover	NOUN
ejpam-3029	152	14	of	of	ADP
ejpam-3029	152	15	f(a	f(a	NOUN
ejpam-3029	152	16	)	)	PUNCT
ejpam-3029	152	17	by	by	ADP
ejpam-3029	152	18	ν	ν	NOUN
ejpam-3029	152	19	-	-	ADJ
ejpam-3029	152	20	open	open	ADJ
ejpam-3029	152	21	subsets	subset	NOUN
ejpam-3029	152	22	of	of	ADP
ejpam-3029	152	23	y	y	PROPN
ejpam-3029	152	24	.	.	PUNCT
ejpam-3029	153	1	let	let	VERB
ejpam-3029	153	2	x	x	SYM
ejpam-3029	153	3	∈	∈	VERB
ejpam-3029	153	4	a	a	PRON
ejpam-3029	153	5	and	and	CCONJ
ejpam-3029	153	6	vα(x	vα(x	NUM
ejpam-3029	153	7	)	)	PUNCT
ejpam-3029	153	8	be	be	AUX
ejpam-3029	153	9	a	a	DET
ejpam-3029	153	10	ν	ν	NOUN
ejpam-3029	153	11	-	-	ADJ
ejpam-3029	153	12	open	open	ADJ
ejpam-3029	153	13	set	set	NOUN
ejpam-3029	153	14	in	in	ADP
ejpam-3029	153	15	y	y	PROPN
ejpam-3029	153	16	such	such	ADJ
ejpam-3029	153	17	that	that	SCONJ
ejpam-3029	153	18	f(x	f(x	PROPN
ejpam-3029	153	19	)	)	PUNCT
ejpam-3029	153	20	∈	∈	PROPN
ejpam-3029	153	21	vα(x	vα(x	NOUN
ejpam-3029	153	22	)	)	PUNCT
ejpam-3029	153	23	.	.	PUNCT
ejpam-3029	154	1	since	since	SCONJ
ejpam-3029	154	2	f	f	PROPN
ejpam-3029	154	3	is	be	AUX
ejpam-3029	154	4	θ(µ	θ(µ	PROPN
ejpam-3029	154	5	,	,	PUNCT
ejpam-3029	154	6	ν)-continuous	ν)-continuous	ADJ
ejpam-3029	154	7	,	,	PUNCT
ejpam-3029	154	8	there	there	PRON
ejpam-3029	154	9	exists	exist	VERB
ejpam-3029	154	10	a	a	DET
ejpam-3029	154	11	µ-open	µ-open	NOUN
ejpam-3029	154	12	set	set	VERB
ejpam-3029	154	13	uα(x	uα(x	NOUN
ejpam-3029	154	14	)	)	PUNCT
ejpam-3029	154	15	of	of	ADP
ejpam-3029	154	16	x	x	SYM
ejpam-3029	154	17	containing	contain	VERB
ejpam-3029	154	18	x	x	PUNCT
ejpam-3029	154	19	such	such	ADJ
ejpam-3029	154	20	that	that	DET
ejpam-3029	154	21	f(cµ(uα(x	f(cµ(uα(x	NOUN
ejpam-3029	154	22	)	)	PUNCT
ejpam-3029	154	23	)	)	PUNCT
ejpam-3029	154	24	)	)	PUNCT
ejpam-3029	155	1	⊆	⊆	NUM
ejpam-3029	155	2	cν(vα(x	cν(vα(x	NOUN
ejpam-3029	155	3	)	)	PUNCT
ejpam-3029	155	4	)	)	PUNCT
ejpam-3029	155	5	.	.	PUNCT
ejpam-3029	156	1	now	now	ADV
ejpam-3029	156	2	{	{	PUNCT
ejpam-3029	156	3	uα(x	uα(x	NOUN
ejpam-3029	156	4	)	)	PUNCT
ejpam-3029	156	5	:	:	PUNCT
ejpam-3029	156	6	x	x	X
ejpam-3029	156	7	∈	∈	PROPN
ejpam-3029	156	8	a	a	PRON
ejpam-3029	156	9	}	}	PUNCT
ejpam-3029	156	10	is	be	AUX
ejpam-3029	156	11	a	a	DET
ejpam-3029	156	12	cover	cover	NOUN
ejpam-3029	156	13	of	of	ADP
ejpam-3029	156	14	a	a	PRON
ejpam-3029	156	15	by	by	ADP
ejpam-3029	156	16	µ-open	µ-open	PROPN
ejpam-3029	156	17	subsets	subset	NOUN
ejpam-3029	156	18	of	of	ADP
ejpam-3029	156	19	x.	x.	NOUN
ejpam-3029	156	20	since	since	SCONJ
ejpam-3029	156	21	a	a	PRON
ejpam-3029	156	22	is	be	AUX
ejpam-3029	156	23	weakly	weakly	ADJ
ejpam-3029	156	24	µhcompact	µhcompact	NOUN
ejpam-3029	156	25	,	,	PUNCT
ejpam-3029	156	26	there	there	PRON
ejpam-3029	156	27	exists	exist	VERB
ejpam-3029	156	28	a	a	DET
ejpam-3029	156	29	finite	finite	NOUN
ejpam-3029	156	30	subset	subset	VERB
ejpam-3029	156	31	a0	a0	NOUN
ejpam-3029	156	32	of	of	ADP
ejpam-3029	156	33	a	a	DET
ejpam-3029	156	34	such	such	ADJ
ejpam-3029	156	35	that	that	SCONJ
ejpam-3029	156	36	a	a	DET
ejpam-3029	156	37	\	\	PROPN
ejpam-3029	156	38	⋃	⋃	PROPN
ejpam-3029	156	39	x∈a0	x∈a0	PROPN
ejpam-3029	156	40	cµ(uα(x	cµ(uα(x	PROPN
ejpam-3029	156	41	)	)	PUNCT
ejpam-3029	156	42	)	)	PUNCT
ejpam-3029	157	1	∈	∈	PROPN
ejpam-3029	157	2	h.	h.	PROPN
ejpam-3029	157	3	now	now	ADV
ejpam-3029	157	4	f(a	f(a	X
ejpam-3029	157	5	\	\	X
ejpam-3029	158	1	⋃	⋃	PUNCT
ejpam-3029	158	2	x∈a0	x∈a0	PROPN
ejpam-3029	158	3	cµ(uα(x	cµ(uα(x	PROPN
ejpam-3029	158	4	)	)	PUNCT
ejpam-3029	158	5	)	)	PUNCT
ejpam-3029	158	6	)	)	PUNCT
ejpam-3029	159	1	∈	∈	PROPN
ejpam-3029	159	2	f(h	f(h	PROPN
ejpam-3029	159	3	)	)	PUNCT
ejpam-3029	159	4	.	.	PUNCT
ejpam-3029	160	1	we	we	PRON
ejpam-3029	160	2	know	know	VERB
ejpam-3029	160	3	f(a	f(a	NOUN
ejpam-3029	160	4	)	)	PUNCT
ejpam-3029	160	5	\	\	X
ejpam-3029	161	1	f	f	X
ejpam-3029	161	2	(	(	PUNCT
ejpam-3029	161	3	⋃	⋃	PROPN
ejpam-3029	161	4	x∈a0	x∈a0	PROPN
ejpam-3029	161	5	cµ(uα(x	cµ(uα(x	PROPN
ejpam-3029	161	6	)	)	PUNCT
ejpam-3029	161	7	)	)	PUNCT
ejpam-3029	161	8	)	)	PUNCT
ejpam-3029	162	1	⊆	⊆	NUM
ejpam-3029	162	2	f(a	f(a	X
ejpam-3029	162	3	\	\	X
ejpam-3029	162	4	⋃	⋃	PUNCT
ejpam-3029	162	5	x∈a0	x∈a0	PROPN
ejpam-3029	162	6	cµ(uα(x	cµ(uα(x	PROPN
ejpam-3029	162	7	)	)	PUNCT
ejpam-3029	162	8	)	)	PUNCT
ejpam-3029	162	9	)	)	PUNCT
ejpam-3029	162	10	.	.	PUNCT
ejpam-3029	163	1	this	this	PRON
ejpam-3029	163	2	implies	imply	VERB
ejpam-3029	163	3	f(a	f(a	NOUN
ejpam-3029	163	4	)	)	PUNCT
ejpam-3029	163	5	\	\	X
ejpam-3029	164	1	f	f	X
ejpam-3029	164	2	(	(	PUNCT
ejpam-3029	164	3	⋃	⋃	PROPN
ejpam-3029	164	4	x∈a0	x∈a0	PROPN
ejpam-3029	164	5	cµ(uα(x	cµ(uα(x	PROPN
ejpam-3029	164	6	)	)	PUNCT
ejpam-3029	164	7	)	)	PUNCT
ejpam-3029	164	8	)	)	PUNCT
ejpam-3029	165	1	=	=	SYM
ejpam-3029	165	2	f(a	f(a	X
ejpam-3029	165	3	)	)	PUNCT
ejpam-3029	165	4	\	\	PUNCT
ejpam-3029	166	1	⋃	⋃	PUNCT
ejpam-3029	166	2	x∈a0	x∈a0	PROPN
ejpam-3029	166	3	f(cµ(uα(x	f(cµ(uα(x	NOUN
ejpam-3029	166	4	)	)	PUNCT
ejpam-3029	166	5	)	)	PUNCT
ejpam-3029	166	6	)	)	PUNCT
ejpam-3029	167	1	∈	∈	PROPN
ejpam-3029	167	2	f(h	f(h	PROPN
ejpam-3029	167	3	)	)	PUNCT
ejpam-3029	167	4	.	.	PUNCT
ejpam-3029	168	1	since	since	SCONJ
ejpam-3029	168	2	f(cµ(uα(x	f(cµ(uα(x	NOUN
ejpam-3029	168	3	)	)	PUNCT
ejpam-3029	168	4	)	)	PUNCT
ejpam-3029	168	5	)	)	PUNCT
ejpam-3029	169	1	⊆	⊆	NUM
ejpam-3029	169	2	cν(vα(x	cν(vα(x	NOUN
ejpam-3029	169	3	)	)	PUNCT
ejpam-3029	169	4	)	)	PUNCT
ejpam-3029	169	5	for	for	ADP
ejpam-3029	169	6	each	each	DET
ejpam-3029	169	7	α(x	α(x	NOUN
ejpam-3029	169	8	)	)	PUNCT
ejpam-3029	169	9	,	,	PUNCT
ejpam-3029	169	10	f(a)\	f(a)\	ADP
ejpam-3029	169	11	⋃	⋃	PROPN
ejpam-3029	169	12	x∈a0	x∈a0	NOUN
ejpam-3029	169	13	cν(vα(x	cν(vα(x	NOUN
ejpam-3029	169	14	)	)	PUNCT
ejpam-3029	169	15	)	)	PUNCT
ejpam-3029	170	1	⊆	⊆	NUM
ejpam-3029	170	2	f(a)\	f(a)\	ADP
ejpam-3029	170	3	⋃	⋃	NOUN
ejpam-3029	170	4	x∈a0	x∈a0	PROPN
ejpam-3029	170	5	f(cµ(uα(x	f(cµ(uα(x	NOUN
ejpam-3029	170	6	)	)	PUNCT
ejpam-3029	170	7	)	)	PUNCT
ejpam-3029	170	8	)	)	PUNCT
ejpam-3029	170	9	.	.	PUNCT
ejpam-3029	171	1	thus	thus	ADV
ejpam-3029	171	2	f(a	f(a	X
ejpam-3029	171	3	)	)	PUNCT
ejpam-3029	171	4	\	\	PUNCT
ejpam-3029	172	1	⋃	⋃	PUNCT
ejpam-3029	172	2	x∈a0	x∈a0	NOUN
ejpam-3029	172	3	cν(vα(x	cν(vα(x	NOUN
ejpam-3029	172	4	)	)	PUNCT
ejpam-3029	172	5	)	)	PUNCT
ejpam-3029	172	6	∈	∈	PROPN
ejpam-3029	172	7	f(h	f(h	PROPN
ejpam-3029	172	8	)	)	PUNCT
ejpam-3029	172	9	.	.	PUNCT
ejpam-3029	173	1	this	this	PRON
ejpam-3029	173	2	implies	imply	VERB
ejpam-3029	173	3	that	that	SCONJ
ejpam-3029	173	4	f(a	f(a	NOUN
ejpam-3029	173	5	)	)	PUNCT
ejpam-3029	173	6	is	be	AUX
ejpam-3029	173	7	weakly	weakly	ADJ
ejpam-3029	173	8	νf(h)-compact	νf(h)-compact	NOUN
ejpam-3029	173	9	.	.	PUNCT
ejpam-3029	174	1	corollary	corollary	ADJ
ejpam-3029	174	2	4	4	NUM
ejpam-3029	174	3	.	.	PUNCT
ejpam-3029	175	1	let	let	VERB
ejpam-3029	175	2	f	f	NOUN
ejpam-3029	175	3	:	:	PUNCT
ejpam-3029	175	4	(	(	PUNCT
ejpam-3029	175	5	x,µ	x,µ	NOUN
ejpam-3029	175	6	)	)	PUNCT
ejpam-3029	175	7	→	→	SYM
ejpam-3029	175	8	(	(	PUNCT
ejpam-3029	175	9	y	y	PROPN
ejpam-3029	175	10	,	,	PUNCT
ejpam-3029	175	11	ν	ν	NOUN
ejpam-3029	175	12	)	)	PUNCT
ejpam-3029	175	13	be	be	AUX
ejpam-3029	175	14	a	a	DET
ejpam-3029	175	15	θ(µ	θ(µ	PROPN
ejpam-3029	175	16	,	,	PUNCT
ejpam-3029	175	17	ν)-continuous	ν)-continuous	ADJ
ejpam-3029	175	18	surjection	surjection	NOUN
ejpam-3029	175	19	.	.	PUNCT
ejpam-3029	176	1	if	if	SCONJ
ejpam-3029	176	2	(	(	PUNCT
ejpam-3029	176	3	x,µ,h	x,µ,h	PROPN
ejpam-3029	176	4	)	)	PUNCT
ejpam-3029	176	5	is	be	AUX
ejpam-3029	176	6	weakly	weakly	ADJ
ejpam-3029	176	7	µh	µh	NOUN
ejpam-3029	176	8	-	-	ADJ
ejpam-3029	176	9	compact	compact	ADJ
ejpam-3029	176	10	,	,	PUNCT
ejpam-3029	176	11	then	then	ADV
ejpam-3029	176	12	(	(	PUNCT
ejpam-3029	176	13	y	y	PROPN
ejpam-3029	176	14	,	,	PUNCT
ejpam-3029	176	15	ν	ν	PROPN
ejpam-3029	176	16	,	,	PUNCT
ejpam-3029	176	17	f(h	f(h	PROPN
ejpam-3029	176	18	)	)	PUNCT
ejpam-3029	176	19	)	)	PUNCT
ejpam-3029	176	20	is	be	AUX
ejpam-3029	176	21	weakly	weakly	ADJ
ejpam-3029	176	22	νf(h)-compact	νf(h)-compact	PROPN
ejpam-3029	176	23	.	.	PUNCT
ejpam-3029	177	1	the	the	DET
ejpam-3029	177	2	following	follow	VERB
ejpam-3029	177	3	lemma	lemma	PROPN
ejpam-3029	177	4	is	be	AUX
ejpam-3029	177	5	used	use	VERB
ejpam-3029	177	6	in	in	ADP
ejpam-3029	177	7	the	the	DET
ejpam-3029	177	8	proofs	proof	NOUN
ejpam-3029	177	9	of	of	ADP
ejpam-3029	177	10	corollaries	corollary	NOUN
ejpam-3029	177	11	stated	state	VERB
ejpam-3029	177	12	below	below	ADV
ejpam-3029	177	13	.	.	PUNCT
ejpam-3029	178	1	a.	a.	NOUN
ejpam-3029	178	2	qahis	qahis	PROPN
ejpam-3029	178	3	,	,	PUNCT
ejpam-3029	178	4	t.	t.	PROPN
ejpam-3029	178	5	noiri	noiri	PROPN
ejpam-3029	178	6	/	/	SYM
ejpam-3029	178	7	eur	eur	PROPN
ejpam-3029	178	8	.	.	PUNCT
ejpam-3029	179	1	j.	j.	PROPN
ejpam-3029	179	2	pure	pure	PROPN
ejpam-3029	179	3	appl	appl	PROPN
ejpam-3029	179	4	.	.	PROPN
ejpam-3029	179	5	math	math	PROPN
ejpam-3029	179	6	,	,	PUNCT
ejpam-3029	179	7	10	10	NUM
ejpam-3029	179	8	(	(	PUNCT
ejpam-3029	179	9	3	3	NUM
ejpam-3029	179	10	)	)	PUNCT
ejpam-3029	179	11	(	(	PUNCT
ejpam-3029	179	12	2017	2017	NUM
ejpam-3029	179	13	)	)	PUNCT
ejpam-3029	179	14	,	,	PUNCT
ejpam-3029	179	15	410	410	NUM
ejpam-3029	179	16	-	-	SYM
ejpam-3029	179	17	418	418	NUM
ejpam-3029	179	18	415	415	NUM
ejpam-3029	179	19	lemma	lemma	PROPN
ejpam-3029	179	20	3	3	X
ejpam-3029	179	21	.	.	PUNCT
ejpam-3029	180	1	if	if	SCONJ
ejpam-3029	180	2	f	f	PROPN
ejpam-3029	180	3	:	:	PUNCT
ejpam-3029	180	4	(	(	PUNCT
ejpam-3029	180	5	x,µ)→	x,µ)→	X
ejpam-3029	180	6	(	(	PUNCT
ejpam-3029	180	7	y	y	PROPN
ejpam-3029	180	8	,	,	PUNCT
ejpam-3029	180	9	ν	ν	NOUN
ejpam-3029	180	10	)	)	PUNCT
ejpam-3029	180	11	is	be	AUX
ejpam-3029	180	12	almost	almost	ADV
ejpam-3029	180	13	(	(	PUNCT
ejpam-3029	180	14	µ	µ	NUM
ejpam-3029	180	15	,	,	PUNCT
ejpam-3029	180	16	ν)-continuous	ν)-continuous	ADJ
ejpam-3029	180	17	,	,	PUNCT
ejpam-3029	180	18	then	then	ADV
ejpam-3029	180	19	f	f	PROPN
ejpam-3029	180	20	is	be	AUX
ejpam-3029	180	21	θ(µ	θ(µ	NOUN
ejpam-3029	180	22	,	,	PUNCT
ejpam-3029	180	23	ν)-continuous	ν)-continuous	ADJ
ejpam-3029	180	24	.	.	PUNCT
ejpam-3029	181	1	proof	proof	NOUN
ejpam-3029	181	2	.	.	PUNCT
ejpam-3029	182	1	let	let	VERB
ejpam-3029	182	2	f	f	PRON
ejpam-3029	182	3	be	be	AUX
ejpam-3029	182	4	almost	almost	ADV
ejpam-3029	182	5	(	(	PUNCT
ejpam-3029	182	6	µ	µ	NOUN
ejpam-3029	182	7	,	,	PUNCT
ejpam-3029	182	8	ν)-continuous	ν)-continuous	ADJ
ejpam-3029	182	9	.	.	PUNCT
ejpam-3029	183	1	let	let	VERB
ejpam-3029	183	2	x	x	PUNCT
ejpam-3029	183	3	∈	∈	PROPN
ejpam-3029	183	4	x	x	X
ejpam-3029	183	5	and	and	CCONJ
ejpam-3029	183	6	v	v	AUX
ejpam-3029	183	7	be	be	AUX
ejpam-3029	183	8	a	a	DET
ejpam-3029	183	9	ν	ν	NOUN
ejpam-3029	183	10	-	-	ADJ
ejpam-3029	183	11	open	open	ADJ
ejpam-3029	183	12	set	set	NOUN
ejpam-3029	183	13	in	in	ADP
ejpam-3029	183	14	y	y	PROPN
ejpam-3029	183	15	such	such	ADJ
ejpam-3029	183	16	that	that	SCONJ
ejpam-3029	183	17	f(x	f(x	PROPN
ejpam-3029	183	18	)	)	PUNCT
ejpam-3029	183	19	∈	∈	PROPN
ejpam-3029	183	20	v	v	NOUN
ejpam-3029	183	21	.	.	PUNCT
ejpam-3029	184	1	since	since	SCONJ
ejpam-3029	184	2	f	f	PROPN
ejpam-3029	184	3	is	be	AUX
ejpam-3029	184	4	almost	almost	ADV
ejpam-3029	184	5	(	(	PUNCT
ejpam-3029	184	6	µ	µ	NUM
ejpam-3029	184	7	,	,	PUNCT
ejpam-3029	184	8	ν)-continuous	ν)-continuous	ADJ
ejpam-3029	184	9	,	,	PUNCT
ejpam-3029	184	10	there	there	PRON
ejpam-3029	184	11	exists	exist	VERB
ejpam-3029	184	12	a	a	DET
ejpam-3029	184	13	µ-open	µ-open	NOUN
ejpam-3029	184	14	set	set	VERB
ejpam-3029	184	15	u	u	NOUN
ejpam-3029	184	16	of	of	ADP
ejpam-3029	184	17	x	x	PUNCT
ejpam-3029	184	18	containing	contain	VERB
ejpam-3029	184	19	x	x	PUNCT
ejpam-3029	184	20	such	such	ADJ
ejpam-3029	184	21	that	that	DET
ejpam-3029	184	22	f(u	f(u	PROPN
ejpam-3029	184	23	)	)	PUNCT
ejpam-3029	184	24	⊆	⊆	NUM
ejpam-3029	184	25	iν(cν(v	iν(cν(v	NOUN
ejpam-3029	184	26	)	)	PUNCT
ejpam-3029	184	27	)	)	PUNCT
ejpam-3029	184	28	.	.	PUNCT
ejpam-3029	185	1	this	this	PRON
ejpam-3029	185	2	implies	imply	VERB
ejpam-3029	185	3	f(u	f(u	PROPN
ejpam-3029	185	4	)	)	PUNCT
ejpam-3029	185	5	⊆	⊆	NUM
ejpam-3029	185	6	iν(cν(v	iν(cν(v	NOUN
ejpam-3029	185	7	)	)	PUNCT
ejpam-3029	185	8	)	)	PUNCT
ejpam-3029	186	1	⊆	⊆	NUM
ejpam-3029	186	2	cν(v	cν(v	NUM
ejpam-3029	186	3	)	)	PUNCT
ejpam-3029	186	4	.	.	PUNCT
ejpam-3029	187	1	we	we	PRON
ejpam-3029	187	2	have	have	VERB
ejpam-3029	187	3	to	to	PART
ejpam-3029	187	4	show	show	VERB
ejpam-3029	187	5	that	that	SCONJ
ejpam-3029	187	6	f(cµ(u	f(cµ(u	NOUN
ejpam-3029	187	7	)	)	PUNCT
ejpam-3029	187	8	)	)	PUNCT
ejpam-3029	187	9	⊆	⊆	NUM
ejpam-3029	187	10	cν(v	cν(v	NUM
ejpam-3029	187	11	)	)	PUNCT
ejpam-3029	187	12	.	.	PUNCT
ejpam-3029	188	1	for	for	ADP
ejpam-3029	188	2	some	some	DET
ejpam-3029	188	3	x0	x0	PROPN
ejpam-3029	188	4	∈	∈	PROPN
ejpam-3029	188	5	cµ(u	cµ(u	NOUN
ejpam-3029	188	6	)	)	PUNCT
ejpam-3029	188	7	let	let	VERB
ejpam-3029	188	8	f(x0	f(x0	NOUN
ejpam-3029	188	9	)	)	PUNCT
ejpam-3029	188	10	∈	∈	PROPN
ejpam-3029	188	11	y	y	PROPN
ejpam-3029	188	12	\	\	PROPN
ejpam-3029	188	13	cν(v	cν(v	PUNCT
ejpam-3029	188	14	)	)	PUNCT
ejpam-3029	188	15	.	.	PUNCT
ejpam-3029	189	1	then	then	ADV
ejpam-3029	189	2	by	by	ADP
ejpam-3029	189	3	the	the	DET
ejpam-3029	189	4	almost	almost	ADV
ejpam-3029	189	5	(	(	PUNCT
ejpam-3029	189	6	µ	µ	NOUN
ejpam-3029	189	7	,	,	PUNCT
ejpam-3029	189	8	ν)-continuity	ν)-continuity	NOUN
ejpam-3029	189	9	of	of	ADP
ejpam-3029	189	10	f	f	PROPN
ejpam-3029	189	11	there	there	PRON
ejpam-3029	189	12	exists	exist	VERB
ejpam-3029	189	13	a	a	DET
ejpam-3029	189	14	µ-open	µ-open	NOUN
ejpam-3029	189	15	set	set	VERB
ejpam-3029	189	16	w	w	PROPN
ejpam-3029	189	17	of	of	ADP
ejpam-3029	189	18	x	x	PUNCT
ejpam-3029	189	19	containing	contain	VERB
ejpam-3029	189	20	x0	x0	PROPN
ejpam-3029	189	21	such	such	ADJ
ejpam-3029	189	22	that	that	SCONJ
ejpam-3029	189	23	f(w	f(w	PROPN
ejpam-3029	189	24	)	)	PUNCT
ejpam-3029	189	25	⊆	⊆	NUM
ejpam-3029	189	26	iν(cν(y	iν(cν(y	NOUN
ejpam-3029	189	27	\	\	NOUN
ejpam-3029	189	28	cν(v	cν(v	NUM
ejpam-3029	189	29	)	)	PUNCT
ejpam-3029	189	30	)	)	PUNCT
ejpam-3029	189	31	)	)	PUNCT
ejpam-3029	189	32	.	.	PUNCT
ejpam-3029	190	1	but	but	CCONJ
ejpam-3029	190	2	w	w	PROPN
ejpam-3029	190	3	∩	∩	ADJ
ejpam-3029	190	4	u	u	PROPN
ejpam-3029	190	5	6=	6=	NOUN
ejpam-3029	190	6	∅	∅	NOUN
ejpam-3029	190	7	and	and	CCONJ
ejpam-3029	190	8	hence	hence	ADV
ejpam-3029	190	9	f(u	f(u	PROPN
ejpam-3029	190	10	)	)	PUNCT
ejpam-3029	190	11	∩	∩	ADJ
ejpam-3029	190	12	iν(cν(y	iν(cν(y	NOUN
ejpam-3029	190	13	\	\	NOUN
ejpam-3029	190	14	cν(v	cν(v	NUM
ejpam-3029	190	15	)	)	PUNCT
ejpam-3029	190	16	)	)	PUNCT
ejpam-3029	190	17	)	)	PUNCT
ejpam-3029	191	1	6=	6=	ADP
ejpam-3029	191	2	∅.	∅.	ADP
ejpam-3029	191	3	hence	hence	ADV
ejpam-3029	191	4	,	,	PUNCT
ejpam-3029	191	5	we	we	PRON
ejpam-3029	191	6	get	get	VERB
ejpam-3029	191	7	a	a	DET
ejpam-3029	191	8	contradiction	contradiction	NOUN
ejpam-3029	191	9	to	to	ADP
ejpam-3029	191	10	the	the	DET
ejpam-3029	191	11	fact	fact	NOUN
ejpam-3029	191	12	that	that	SCONJ
ejpam-3029	191	13	f(u	f(u	PROPN
ejpam-3029	191	14	)	)	PUNCT
ejpam-3029	191	15	⊆	⊆	NUM
ejpam-3029	191	16	iν(cν(v	iν(cν(v	NOUN
ejpam-3029	191	17	)	)	PUNCT
ejpam-3029	191	18	)	)	PUNCT
ejpam-3029	192	1	⊆	⊆	NUM
ejpam-3029	192	2	cν(iν(cν(v	cν(iν(cν(v	ADV
ejpam-3029	192	3	)	)	PUNCT
ejpam-3029	192	4	)	)	PUNCT
ejpam-3029	192	5	)	)	PUNCT
ejpam-3029	193	1	⊆	⊆	NUM
ejpam-3029	193	2	cν(v	cν(v	NUM
ejpam-3029	193	3	)	)	PUNCT
ejpam-3029	193	4	.	.	PUNCT
ejpam-3029	194	1	thus	thus	ADV
ejpam-3029	194	2	f(cµ(u	f(cµ(u	NOUN
ejpam-3029	194	3	)	)	PUNCT
ejpam-3029	194	4	)	)	PUNCT
ejpam-3029	195	1	⊆	⊆	NUM
ejpam-3029	195	2	cν(v	cν(v	NUM
ejpam-3029	195	3	)	)	PUNCT
ejpam-3029	195	4	.	.	PUNCT
ejpam-3029	196	1	this	this	PRON
ejpam-3029	196	2	implies	imply	VERB
ejpam-3029	196	3	that	that	SCONJ
ejpam-3029	196	4	f	f	PROPN
ejpam-3029	196	5	is	be	AUX
ejpam-3029	196	6	θ(µ	θ(µ	NOUN
ejpam-3029	196	7	,	,	PUNCT
ejpam-3029	196	8	ν)-continuous	ν)-continuous	ADJ
ejpam-3029	196	9	.	.	PUNCT
ejpam-3029	196	10	corollary	corollary	ADJ
ejpam-3029	196	11	5	5	NUM
ejpam-3029	196	12	.	.	PUNCT
ejpam-3029	197	1	let	let	VERB
ejpam-3029	197	2	f	f	NOUN
ejpam-3029	197	3	:	:	PUNCT
ejpam-3029	197	4	(	(	PUNCT
ejpam-3029	197	5	x,µ	x,µ	NOUN
ejpam-3029	197	6	)	)	PUNCT
ejpam-3029	197	7	→	→	SYM
ejpam-3029	197	8	(	(	PUNCT
ejpam-3029	197	9	y	y	PROPN
ejpam-3029	197	10	,	,	PUNCT
ejpam-3029	197	11	ν	ν	NOUN
ejpam-3029	197	12	)	)	PUNCT
ejpam-3029	197	13	be	be	AUX
ejpam-3029	197	14	an	an	DET
ejpam-3029	197	15	almost	almost	ADV
ejpam-3029	197	16	(	(	PUNCT
ejpam-3029	197	17	µ	µ	NUM
ejpam-3029	197	18	,	,	PUNCT
ejpam-3029	197	19	ν)-continuous	ν)-continuous	ADJ
ejpam-3029	197	20	surjection	surjection	NOUN
ejpam-3029	197	21	.	.	PUNCT
ejpam-3029	198	1	if	if	SCONJ
ejpam-3029	198	2	(	(	PUNCT
ejpam-3029	198	3	x,µ,h	x,µ,h	PROPN
ejpam-3029	198	4	)	)	PUNCT
ejpam-3029	198	5	is	be	AUX
ejpam-3029	198	6	weakly	weakly	ADJ
ejpam-3029	198	7	µh	µh	NOUN
ejpam-3029	198	8	-	-	ADJ
ejpam-3029	198	9	compact	compact	ADJ
ejpam-3029	198	10	,	,	PUNCT
ejpam-3029	198	11	then	then	ADV
ejpam-3029	198	12	(	(	PUNCT
ejpam-3029	198	13	y	y	PROPN
ejpam-3029	198	14	,	,	PUNCT
ejpam-3029	198	15	ν	ν	PROPN
ejpam-3029	198	16	,	,	PUNCT
ejpam-3029	198	17	f(h	f(h	PROPN
ejpam-3029	198	18	)	)	PUNCT
ejpam-3029	198	19	)	)	PUNCT
ejpam-3029	198	20	is	be	AUX
ejpam-3029	198	21	weakly	weakly	ADJ
ejpam-3029	198	22	νf(h)-compact	νf(h)-compact	PROPN
ejpam-3029	198	23	.	.	PUNCT
ejpam-3029	199	1	since	since	SCONJ
ejpam-3029	199	2	every	every	DET
ejpam-3029	199	3	(	(	PUNCT
ejpam-3029	199	4	µ	µ	NUM
ejpam-3029	199	5	,	,	PUNCT
ejpam-3029	199	6	ν)-continuous	ν)-continuous	ADJ
ejpam-3029	199	7	function	function	NOUN
ejpam-3029	199	8	is	be	AUX
ejpam-3029	199	9	almost	almost	ADV
ejpam-3029	199	10	(	(	PUNCT
ejpam-3029	199	11	µ	µ	NUM
ejpam-3029	199	12	,	,	PUNCT
ejpam-3029	199	13	ν)-continuous	ν)-continuous	ADJ
ejpam-3029	199	14	and	and	CCONJ
ejpam-3029	199	15	by	by	ADP
ejpam-3029	199	16	lemma	lemma	PROPN
ejpam-3029	199	17	3	3	NUM
ejpam-3029	199	18	,	,	PUNCT
ejpam-3029	199	19	we	we	PRON
ejpam-3029	199	20	conclude	conclude	VERB
ejpam-3029	199	21	the	the	DET
ejpam-3029	199	22	following	follow	VERB
ejpam-3029	199	23	corollary	corollary	NOUN
ejpam-3029	199	24	.	.	PUNCT
ejpam-3029	200	1	corollary	corollary	ADJ
ejpam-3029	200	2	6	6	NUM
ejpam-3029	200	3	.	.	PUNCT
ejpam-3029	201	1	weakly	weakly	ADJ
ejpam-3029	201	2	µh	µh	ADJ
ejpam-3029	201	3	-	-	ADJ
ejpam-3029	201	4	compact	compact	ADJ
ejpam-3029	201	5	property	property	NOUN
ejpam-3029	201	6	is	be	AUX
ejpam-3029	201	7	a	a	DET
ejpam-3029	201	8	gt	gt	PROPN
ejpam-3029	201	9	property	property	NOUN
ejpam-3029	201	10	.	.	PUNCT
ejpam-3029	202	1	by	by	ADP
ejpam-3029	202	2	taking	take	VERB
ejpam-3029	202	3	h	h	NOUN
ejpam-3029	202	4	=	=	PUNCT
ejpam-3029	202	5	{	{	PUNCT
ejpam-3029	202	6	∅	∅	NOUN
ejpam-3029	202	7	}	}	PUNCT
ejpam-3029	202	8	,	,	PUNCT
ejpam-3029	202	9	we	we	PRON
ejpam-3029	202	10	get	get	VERB
ejpam-3029	202	11	the	the	DET
ejpam-3029	202	12	following	follow	VERB
ejpam-3029	202	13	corollary	corollary	ADJ
ejpam-3029	202	14	corollary	corollary	ADJ
ejpam-3029	202	15	7	7	NUM
ejpam-3029	202	16	.	.	PUNCT
ejpam-3029	203	1	let	let	VERB
ejpam-3029	203	2	f	f	NOUN
ejpam-3029	203	3	:	:	PUNCT
ejpam-3029	203	4	(	(	PUNCT
ejpam-3029	203	5	x,µ	x,µ	NOUN
ejpam-3029	203	6	)	)	PUNCT
ejpam-3029	203	7	→	→	SYM
ejpam-3029	203	8	(	(	PUNCT
ejpam-3029	203	9	y	y	PROPN
ejpam-3029	203	10	,	,	PUNCT
ejpam-3029	203	11	ν	ν	NOUN
ejpam-3029	203	12	)	)	PUNCT
ejpam-3029	203	13	be	be	AUX
ejpam-3029	203	14	a	a	DET
ejpam-3029	203	15	θ(µ	θ(µ	PROPN
ejpam-3029	203	16	,	,	PUNCT
ejpam-3029	203	17	ν)-continuous	ν)-continuous	ADJ
ejpam-3029	203	18	function	function	NOUN
ejpam-3029	203	19	.	.	PUNCT
ejpam-3029	204	1	if	if	SCONJ
ejpam-3029	204	2	a	a	PRON
ejpam-3029	204	3	is	be	AUX
ejpam-3029	204	4	a	a	DET
ejpam-3029	204	5	weakly	weakly	ADJ
ejpam-3029	204	6	µ-compact	µ-compact	NOUN
ejpam-3029	204	7	subset	subset	NOUN
ejpam-3029	204	8	of	of	ADP
ejpam-3029	204	9	x	x	PRON
ejpam-3029	204	10	,	,	PUNCT
ejpam-3029	204	11	then	then	ADV
ejpam-3029	204	12	f(a	f(a	PROPN
ejpam-3029	204	13	)	)	PUNCT
ejpam-3029	204	14	is	be	AUX
ejpam-3029	204	15	weakly	weakly	ADJ
ejpam-3029	204	16	ν	ν	NOUN
ejpam-3029	204	17	-	-	ADJ
ejpam-3029	204	18	compact	compact	ADJ
ejpam-3029	204	19	.	.	PUNCT
ejpam-3029	205	1	proposition	proposition	NOUN
ejpam-3029	205	2	2	2	NUM
ejpam-3029	205	3	.	.	PUNCT
ejpam-3029	206	1	let	let	AUX
ejpam-3029	206	2	f	f	PROPN
ejpam-3029	206	3	:	:	PUNCT
ejpam-3029	206	4	(	(	PUNCT
ejpam-3029	206	5	x,µ,h	x,µ,h	PROPN
ejpam-3029	206	6	)	)	PUNCT
ejpam-3029	206	7	→	→	SYM
ejpam-3029	206	8	(	(	PUNCT
ejpam-3029	206	9	y	y	PROPN
ejpam-3029	206	10	,	,	PUNCT
ejpam-3029	206	11	ν	ν	NOUN
ejpam-3029	206	12	)	)	PUNCT
ejpam-3029	206	13	be	be	AUX
ejpam-3029	206	14	a	a	DET
ejpam-3029	206	15	strongly	strongly	ADV
ejpam-3029	206	16	θ(µ	θ(µ	NOUN
ejpam-3029	206	17	,	,	PUNCT
ejpam-3029	206	18	ν)-continuous	ν)-continuous	ADJ
ejpam-3029	206	19	function	function	NOUN
ejpam-3029	206	20	.	.	PUNCT
ejpam-3029	207	1	if	if	SCONJ
ejpam-3029	207	2	a	a	PRON
ejpam-3029	207	3	is	be	AUX
ejpam-3029	207	4	a	a	DET
ejpam-3029	207	5	weakly	weakly	ADJ
ejpam-3029	207	6	µh	µh	NOUN
ejpam-3029	207	7	-	-	ADJ
ejpam-3029	207	8	compact	compact	ADJ
ejpam-3029	207	9	subset	subset	NOUN
ejpam-3029	207	10	of	of	ADP
ejpam-3029	207	11	x	x	PRON
ejpam-3029	207	12	,	,	PUNCT
ejpam-3029	207	13	then	then	ADV
ejpam-3029	207	14	f(a	f(a	PROPN
ejpam-3029	207	15	)	)	PUNCT
ejpam-3029	207	16	is	be	AUX
ejpam-3029	207	17	νf(h)-compact	νf(h)-compact	PROPN
ejpam-3029	207	18	.	.	PUNCT
ejpam-3029	208	1	proof	proof	NOUN
ejpam-3029	208	2	.	.	PUNCT
ejpam-3029	209	1	let	let	VERB
ejpam-3029	209	2	{	{	PUNCT
ejpam-3029	209	3	vα	vα	X
ejpam-3029	209	4	:	:	PUNCT
ejpam-3029	209	5	α	α	PROPN
ejpam-3029	209	6	∈	∈	PROPN
ejpam-3029	209	7	∆	∆	PROPN
ejpam-3029	209	8	}	}	PUNCT
ejpam-3029	209	9	be	be	AUX
ejpam-3029	209	10	a	a	DET
ejpam-3029	209	11	cover	cover	NOUN
ejpam-3029	209	12	of	of	ADP
ejpam-3029	209	13	f(a	f(a	NOUN
ejpam-3029	209	14	)	)	PUNCT
ejpam-3029	209	15	by	by	ADP
ejpam-3029	209	16	ν	ν	NOUN
ejpam-3029	209	17	-	-	ADJ
ejpam-3029	209	18	open	open	ADJ
ejpam-3029	209	19	subsets	subset	NOUN
ejpam-3029	209	20	of	of	ADP
ejpam-3029	209	21	y	y	PROPN
ejpam-3029	209	22	.	.	PUNCT
ejpam-3029	210	1	let	let	VERB
ejpam-3029	210	2	x	x	SYM
ejpam-3029	210	3	∈	∈	VERB
ejpam-3029	210	4	a	a	PRON
ejpam-3029	210	5	and	and	CCONJ
ejpam-3029	210	6	vα(x	vα(x	NUM
ejpam-3029	210	7	)	)	PUNCT
ejpam-3029	210	8	be	be	AUX
ejpam-3029	210	9	a	a	DET
ejpam-3029	210	10	ν	ν	NOUN
ejpam-3029	210	11	-	-	ADJ
ejpam-3029	210	12	open	open	ADJ
ejpam-3029	210	13	set	set	NOUN
ejpam-3029	210	14	in	in	ADP
ejpam-3029	210	15	y	y	PROPN
ejpam-3029	210	16	such	such	ADJ
ejpam-3029	210	17	that	that	SCONJ
ejpam-3029	210	18	f(x	f(x	PROPN
ejpam-3029	210	19	)	)	PUNCT
ejpam-3029	210	20	∈	∈	PROPN
ejpam-3029	210	21	vα(x	vα(x	NOUN
ejpam-3029	210	22	)	)	PUNCT
ejpam-3029	210	23	.	.	PUNCT
ejpam-3029	211	1	since	since	SCONJ
ejpam-3029	211	2	f	f	PROPN
ejpam-3029	211	3	is	be	AUX
ejpam-3029	211	4	strongly	strongly	ADV
ejpam-3029	211	5	θ(µ	θ(µ	NOUN
ejpam-3029	211	6	,	,	PUNCT
ejpam-3029	211	7	ν)-continuous	ν)-continuous	ADJ
ejpam-3029	211	8	,	,	PUNCT
ejpam-3029	211	9	there	there	PRON
ejpam-3029	211	10	exists	exist	VERB
ejpam-3029	211	11	a	a	DET
ejpam-3029	211	12	µ-open	µ-open	NOUN
ejpam-3029	211	13	set	set	VERB
ejpam-3029	211	14	uα(x	uα(x	NOUN
ejpam-3029	211	15	)	)	PUNCT
ejpam-3029	211	16	of	of	ADP
ejpam-3029	211	17	x	x	SYM
ejpam-3029	211	18	containing	contain	VERB
ejpam-3029	211	19	x	x	PUNCT
ejpam-3029	211	20	such	such	ADJ
ejpam-3029	211	21	that	that	DET
ejpam-3029	211	22	f(cµ(uα(x	f(cµ(uα(x	NOUN
ejpam-3029	211	23	)	)	PUNCT
ejpam-3029	211	24	)	)	PUNCT
ejpam-3029	211	25	)	)	PUNCT
ejpam-3029	212	1	⊆	⊆	NUM
ejpam-3029	212	2	vα(x	vα(x	NOUN
ejpam-3029	212	3	)	)	PUNCT
ejpam-3029	212	4	.	.	PUNCT
ejpam-3029	213	1	now	now	ADV
ejpam-3029	213	2	{	{	PUNCT
ejpam-3029	213	3	uα(x	uα(x	NOUN
ejpam-3029	213	4	)	)	PUNCT
ejpam-3029	213	5	:	:	PUNCT
ejpam-3029	213	6	x	x	X
ejpam-3029	213	7	∈	∈	PROPN
ejpam-3029	213	8	a	a	PRON
ejpam-3029	213	9	}	}	PUNCT
ejpam-3029	213	10	is	be	AUX
ejpam-3029	213	11	a	a	DET
ejpam-3029	213	12	µ-open	µ-open	NOUN
ejpam-3029	213	13	cover	cover	NOUN
ejpam-3029	213	14	of	of	ADP
ejpam-3029	213	15	the	the	DET
ejpam-3029	213	16	weakly	weakly	ADJ
ejpam-3029	213	17	µh	µh	ADJ
ejpam-3029	213	18	-	-	ADJ
ejpam-3029	213	19	compact	compact	ADJ
ejpam-3029	213	20	set	set	NOUN
ejpam-3029	213	21	a.	a.	NOUN
ejpam-3029	214	1	so	so	ADV
ejpam-3029	214	2	there	there	PRON
ejpam-3029	214	3	exists	exist	VERB
ejpam-3029	214	4	a	a	DET
ejpam-3029	214	5	finite	finite	NOUN
ejpam-3029	214	6	subset	subset	VERB
ejpam-3029	214	7	a0	a0	NOUN
ejpam-3029	214	8	of	of	ADP
ejpam-3029	214	9	a	a	DET
ejpam-3029	214	10	such	such	ADJ
ejpam-3029	214	11	that	that	SCONJ
ejpam-3029	214	12	a	a	DET
ejpam-3029	214	13	\	\	PROPN
ejpam-3029	214	14	⋃	⋃	PROPN
ejpam-3029	214	15	x∈a0	x∈a0	PROPN
ejpam-3029	214	16	cµ(uα(x	cµ(uα(x	PROPN
ejpam-3029	214	17	)	)	PUNCT
ejpam-3029	214	18	)	)	PUNCT
ejpam-3029	215	1	∈	∈	PROPN
ejpam-3029	215	2	h.	h.	PROPN
ejpam-3029	215	3	now	now	ADV
ejpam-3029	215	4	f(a	f(a	X
ejpam-3029	215	5	\	\	X
ejpam-3029	216	1	⋃	⋃	PUNCT
ejpam-3029	216	2	x∈a0	x∈a0	PROPN
ejpam-3029	216	3	cµ(uα(x	cµ(uα(x	PROPN
ejpam-3029	216	4	)	)	PUNCT
ejpam-3029	216	5	)	)	PUNCT
ejpam-3029	216	6	)	)	PUNCT
ejpam-3029	217	1	∈	∈	PROPN
ejpam-3029	217	2	f(h	f(h	PROPN
ejpam-3029	217	3	)	)	PUNCT
ejpam-3029	217	4	.	.	PUNCT
ejpam-3029	218	1	we	we	PRON
ejpam-3029	218	2	know	know	VERB
ejpam-3029	218	3	f(a	f(a	NOUN
ejpam-3029	218	4	)	)	PUNCT
ejpam-3029	218	5	\	\	X
ejpam-3029	219	1	f	f	X
ejpam-3029	219	2	(	(	PUNCT
ejpam-3029	219	3	⋃	⋃	PROPN
ejpam-3029	219	4	x∈a0	x∈a0	PROPN
ejpam-3029	219	5	cµ(uα(x	cµ(uα(x	PROPN
ejpam-3029	219	6	)	)	PUNCT
ejpam-3029	219	7	)	)	PUNCT
ejpam-3029	219	8	)	)	PUNCT
ejpam-3029	220	1	⊆	⊆	NUM
ejpam-3029	220	2	f(a	f(a	X
ejpam-3029	220	3	\	\	X
ejpam-3029	220	4	⋃	⋃	PUNCT
ejpam-3029	220	5	x∈a0	x∈a0	PROPN
ejpam-3029	220	6	cµ(uα(x	cµ(uα(x	PROPN
ejpam-3029	220	7	)	)	PUNCT
ejpam-3029	220	8	)	)	PUNCT
ejpam-3029	220	9	)	)	PUNCT
ejpam-3029	220	10	.	.	PUNCT
ejpam-3029	221	1	this	this	PRON
ejpam-3029	221	2	implies	imply	VERB
ejpam-3029	221	3	f(a	f(a	NOUN
ejpam-3029	221	4	)	)	PUNCT
ejpam-3029	221	5	\	\	X
ejpam-3029	222	1	f	f	X
ejpam-3029	222	2	(	(	PUNCT
ejpam-3029	222	3	⋃	⋃	PROPN
ejpam-3029	222	4	x∈a0	x∈a0	PROPN
ejpam-3029	222	5	cµ(uα(x	cµ(uα(x	PROPN
ejpam-3029	222	6	)	)	PUNCT
ejpam-3029	222	7	)	)	PUNCT
ejpam-3029	222	8	)	)	PUNCT
ejpam-3029	223	1	=	=	SYM
ejpam-3029	223	2	f(a	f(a	X
ejpam-3029	223	3	)	)	PUNCT
ejpam-3029	223	4	\	\	PUNCT
ejpam-3029	224	1	⋃	⋃	PUNCT
ejpam-3029	224	2	x∈a0	x∈a0	PROPN
ejpam-3029	224	3	f(cµ(uα(x	f(cµ(uα(x	NOUN
ejpam-3029	224	4	)	)	PUNCT
ejpam-3029	224	5	)	)	PUNCT
ejpam-3029	224	6	)	)	PUNCT
ejpam-3029	225	1	∈	∈	PROPN
ejpam-3029	225	2	f(h	f(h	PROPN
ejpam-3029	225	3	)	)	PUNCT
ejpam-3029	225	4	.	.	PUNCT
ejpam-3029	226	1	since	since	SCONJ
ejpam-3029	226	2	f(cµ(uα(x	f(cµ(uα(x	NOUN
ejpam-3029	226	3	)	)	PUNCT
ejpam-3029	226	4	)	)	PUNCT
ejpam-3029	226	5	)	)	PUNCT
ejpam-3029	227	1	⊆	⊆	NUM
ejpam-3029	227	2	vα(x	vα(x	NOUN
ejpam-3029	227	3	)	)	PUNCT
ejpam-3029	227	4	for	for	ADP
ejpam-3029	227	5	each	each	DET
ejpam-3029	227	6	α(x	α(x	NOUN
ejpam-3029	227	7	)	)	PUNCT
ejpam-3029	227	8	,	,	PUNCT
ejpam-3029	227	9	f(a	f(a	NOUN
ejpam-3029	227	10	)	)	PUNCT
ejpam-3029	227	11	\	\	PUNCT
ejpam-3029	228	1	⋃	⋃	SCONJ
ejpam-3029	228	2	x∈a0	x∈a0	PROPN
ejpam-3029	228	3	vα(x	vα(x	NOUN
ejpam-3029	228	4	)	)	PUNCT
ejpam-3029	228	5	⊆	⊆	NUM
ejpam-3029	228	6	f(a	f(a	NOUN
ejpam-3029	228	7	)	)	PUNCT
ejpam-3029	228	8	\	\	PUNCT
ejpam-3029	228	9	⋃	⋃	PUNCT
ejpam-3029	228	10	x∈a0	x∈a0	PROPN
ejpam-3029	228	11	f(cµ(uα(x	f(cµ(uα(x	NOUN
ejpam-3029	228	12	)	)	PUNCT
ejpam-3029	228	13	)	)	PUNCT
ejpam-3029	228	14	)	)	PUNCT
ejpam-3029	228	15	.	.	PUNCT
ejpam-3029	229	1	thus	thus	ADV
ejpam-3029	229	2	f(a	f(a	X
ejpam-3029	229	3	)	)	PUNCT
ejpam-3029	229	4	\	\	PUNCT
ejpam-3029	230	1	⋃	⋃	SCONJ
ejpam-3029	230	2	x∈a0	x∈a0	PROPN
ejpam-3029	230	3	vα(x	vα(x	NOUN
ejpam-3029	230	4	)	)	PUNCT
ejpam-3029	230	5	∈	∈	PROPN
ejpam-3029	230	6	f(h	f(h	PROPN
ejpam-3029	230	7	)	)	PUNCT
ejpam-3029	230	8	.	.	PUNCT
ejpam-3029	231	1	hence	hence	ADV
ejpam-3029	231	2	f(a	f(a	PROPN
ejpam-3029	231	3	)	)	PUNCT
ejpam-3029	231	4	is	be	AUX
ejpam-3029	231	5	νf(h)-compact	νf(h)-compact	PROPN
ejpam-3029	231	6	.	.	PUNCT
ejpam-3029	232	1	a.	a.	NOUN
ejpam-3029	232	2	qahis	qahis	PROPN
ejpam-3029	232	3	,	,	PUNCT
ejpam-3029	232	4	t.	t.	PROPN
ejpam-3029	232	5	noiri	noiri	PROPN
ejpam-3029	232	6	/	/	SYM
ejpam-3029	232	7	eur	eur	PROPN
ejpam-3029	232	8	.	.	PUNCT
ejpam-3029	233	1	j.	j.	PROPN
ejpam-3029	233	2	pure	pure	PROPN
ejpam-3029	233	3	appl	appl	PROPN
ejpam-3029	233	4	.	.	PROPN
ejpam-3029	233	5	math	math	PROPN
ejpam-3029	233	6	,	,	PUNCT
ejpam-3029	233	7	10	10	NUM
ejpam-3029	233	8	(	(	PUNCT
ejpam-3029	233	9	3	3	NUM
ejpam-3029	233	10	)	)	PUNCT
ejpam-3029	233	11	(	(	PUNCT
ejpam-3029	233	12	2017	2017	NUM
ejpam-3029	233	13	)	)	PUNCT
ejpam-3029	233	14	,	,	PUNCT
ejpam-3029	233	15	410	410	NUM
ejpam-3029	233	16	-	-	SYM
ejpam-3029	233	17	418	418	NUM
ejpam-3029	233	18	416	416	NUM
ejpam-3029	233	19	corollary	corollary	ADJ
ejpam-3029	233	20	8	8	NUM
ejpam-3029	233	21	.	.	PUNCT
ejpam-3029	234	1	let	let	VERB
ejpam-3029	234	2	f	f	NOUN
ejpam-3029	234	3	:	:	PUNCT
ejpam-3029	234	4	(	(	PUNCT
ejpam-3029	234	5	x,µ	x,µ	NOUN
ejpam-3029	234	6	)	)	PUNCT
ejpam-3029	234	7	→	→	SYM
ejpam-3029	234	8	(	(	PUNCT
ejpam-3029	234	9	x	x	X
ejpam-3029	234	10	,	,	PUNCT
ejpam-3029	234	11	ν	ν	NOUN
ejpam-3029	234	12	)	)	PUNCT
ejpam-3029	234	13	be	be	AUX
ejpam-3029	234	14	a	a	DET
ejpam-3029	234	15	strongly	strongly	ADV
ejpam-3029	234	16	θ(µ	θ(µ	NOUN
ejpam-3029	234	17	,	,	PUNCT
ejpam-3029	234	18	ν)-continuous	ν)-continuous	ADJ
ejpam-3029	234	19	surjection	surjection	NOUN
ejpam-3029	234	20	.	.	PUNCT
ejpam-3029	235	1	if	if	SCONJ
ejpam-3029	235	2	(	(	PUNCT
ejpam-3029	235	3	x,µ,h	x,µ,h	PROPN
ejpam-3029	235	4	)	)	PUNCT
ejpam-3029	235	5	is	be	AUX
ejpam-3029	235	6	weakly	weakly	ADJ
ejpam-3029	235	7	µh	µh	NOUN
ejpam-3029	235	8	-	-	ADJ
ejpam-3029	235	9	compact	compact	ADJ
ejpam-3029	235	10	,	,	PUNCT
ejpam-3029	235	11	then	then	ADV
ejpam-3029	235	12	(	(	PUNCT
ejpam-3029	235	13	y	y	PROPN
ejpam-3029	235	14	,	,	PUNCT
ejpam-3029	235	15	ν	ν	PROPN
ejpam-3029	235	16	,	,	PUNCT
ejpam-3029	235	17	f(h	f(h	PROPN
ejpam-3029	235	18	)	)	PUNCT
ejpam-3029	235	19	)	)	PUNCT
ejpam-3029	235	20	is	be	AUX
ejpam-3029	235	21	νf(h)-compact	νf(h)-compact	PROPN
ejpam-3029	235	22	.	.	PUNCT
ejpam-3029	236	1	by	by	ADP
ejpam-3029	236	2	taking	take	VERB
ejpam-3029	236	3	h	h	NOUN
ejpam-3029	236	4	=	=	PUNCT
ejpam-3029	236	5	{	{	PUNCT
ejpam-3029	236	6	∅	∅	NOUN
ejpam-3029	236	7	}	}	PUNCT
ejpam-3029	236	8	,	,	PUNCT
ejpam-3029	236	9	we	we	PRON
ejpam-3029	236	10	get	get	VERB
ejpam-3029	236	11	the	the	DET
ejpam-3029	236	12	following	follow	VERB
ejpam-3029	236	13	corollary	corollary	NOUN
ejpam-3029	236	14	.	.	PUNCT
ejpam-3029	237	1	corollary	corollary	ADJ
ejpam-3029	237	2	9	9	NUM
ejpam-3029	237	3	.	.	PUNCT
ejpam-3029	238	1	let	let	VERB
ejpam-3029	238	2	f	f	NOUN
ejpam-3029	238	3	:	:	PUNCT
ejpam-3029	238	4	(	(	PUNCT
ejpam-3029	238	5	x,µ)→	x,µ)→	X
ejpam-3029	238	6	(	(	PUNCT
ejpam-3029	238	7	x	x	NOUN
ejpam-3029	238	8	,	,	PUNCT
ejpam-3029	238	9	ν	ν	NOUN
ejpam-3029	238	10	)	)	PUNCT
ejpam-3029	238	11	be	be	AUX
ejpam-3029	238	12	a	a	DET
ejpam-3029	238	13	strongly	strongly	ADV
ejpam-3029	238	14	θ(µ	θ(µ	NOUN
ejpam-3029	238	15	,	,	PUNCT
ejpam-3029	238	16	ν)-continuous	ν)-continuous	ADJ
ejpam-3029	238	17	function	function	NOUN
ejpam-3029	238	18	.	.	PUNCT
ejpam-3029	239	1	if	if	SCONJ
ejpam-3029	239	2	a	a	PRON
ejpam-3029	239	3	is	be	AUX
ejpam-3029	239	4	a	a	DET
ejpam-3029	239	5	weakly	weakly	ADJ
ejpam-3029	239	6	µ-compact	µ-compact	NOUN
ejpam-3029	239	7	subset	subset	NOUN
ejpam-3029	239	8	of	of	ADP
ejpam-3029	239	9	x	x	PRON
ejpam-3029	239	10	,	,	PUNCT
ejpam-3029	239	11	then	then	ADV
ejpam-3029	239	12	f(a	f(a	PROPN
ejpam-3029	239	13	)	)	PUNCT
ejpam-3029	239	14	is	be	AUX
ejpam-3029	239	15	ν	ν	NOUN
ejpam-3029	239	16	-	-	ADJ
ejpam-3029	239	17	compact	compact	ADJ
ejpam-3029	239	18	.	.	PUNCT
ejpam-3029	240	1	proposition	proposition	NOUN
ejpam-3029	240	2	3	3	X
ejpam-3029	240	3	.	.	PUNCT
ejpam-3029	241	1	let	let	VERB
ejpam-3029	241	2	f	f	PROPN
ejpam-3029	241	3	:	:	PUNCT
ejpam-3029	241	4	(	(	PUNCT
ejpam-3029	241	5	x,µ,h	x,µ,h	PROPN
ejpam-3029	241	6	)	)	PUNCT
ejpam-3029	241	7	→	→	SYM
ejpam-3029	241	8	(	(	PUNCT
ejpam-3029	241	9	y	y	PROPN
ejpam-3029	241	10	,	,	PUNCT
ejpam-3029	241	11	ν	ν	NOUN
ejpam-3029	241	12	)	)	PUNCT
ejpam-3029	241	13	be	be	AUX
ejpam-3029	241	14	a	a	DET
ejpam-3029	241	15	contra	contra	PROPN
ejpam-3029	241	16	(	(	PUNCT
ejpam-3029	241	17	µ	µ	NOUN
ejpam-3029	241	18	,	,	PUNCT
ejpam-3029	241	19	ν)-continuous	ν)-continuous	ADJ
ejpam-3029	241	20	and	and	CCONJ
ejpam-3029	241	21	(	(	PUNCT
ejpam-3029	241	22	µ	µ	NUM
ejpam-3029	241	23	,	,	PUNCT
ejpam-3029	241	24	ν)precontinuous	ν)precontinuous	ADJ
ejpam-3029	241	25	function	function	NOUN
ejpam-3029	241	26	.	.	PUNCT
ejpam-3029	242	1	if	if	SCONJ
ejpam-3029	242	2	a	a	PRON
ejpam-3029	242	3	is	be	AUX
ejpam-3029	242	4	weakly	weakly	ADJ
ejpam-3029	242	5	µh	µh	NOUN
ejpam-3029	242	6	-	-	ADJ
ejpam-3029	242	7	compact	compact	ADJ
ejpam-3029	242	8	,	,	PUNCT
ejpam-3029	242	9	then	then	ADV
ejpam-3029	242	10	f(a	f(a	PROPN
ejpam-3029	242	11	)	)	PUNCT
ejpam-3029	242	12	is	be	AUX
ejpam-3029	242	13	νf(h)-compact	νf(h)-compact	PROPN
ejpam-3029	242	14	.	.	PUNCT
ejpam-3029	243	1	proof	proof	NOUN
ejpam-3029	243	2	.	.	PUNCT
ejpam-3029	244	1	let	let	VERB
ejpam-3029	244	2	v	v	VERB
ejpam-3029	244	3	=	=	PUNCT
ejpam-3029	244	4	{	{	PUNCT
ejpam-3029	244	5	vα	vα	X
ejpam-3029	244	6	:	:	PUNCT
ejpam-3029	244	7	α	α	PROPN
ejpam-3029	244	8	∈	∈	PROPN
ejpam-3029	244	9	∆	∆	PROPN
ejpam-3029	244	10	}	}	PUNCT
ejpam-3029	244	11	be	be	AUX
ejpam-3029	244	12	a	a	DET
ejpam-3029	244	13	cover	cover	NOUN
ejpam-3029	244	14	of	of	ADP
ejpam-3029	244	15	f(a	f(a	NOUN
ejpam-3029	244	16	)	)	PUNCT
ejpam-3029	244	17	by	by	ADP
ejpam-3029	244	18	ν	ν	NOUN
ejpam-3029	244	19	-	-	ADJ
ejpam-3029	244	20	open	open	ADJ
ejpam-3029	244	21	sets	set	NOUN
ejpam-3029	244	22	of	of	ADP
ejpam-3029	244	23	(	(	PUNCT
ejpam-3029	244	24	y	y	PROPN
ejpam-3029	244	25	,	,	PUNCT
ejpam-3029	244	26	ν	ν	NOUN
ejpam-3029	244	27	)	)	PUNCT
ejpam-3029	244	28	.	.	PUNCT
ejpam-3029	245	1	for	for	ADP
ejpam-3029	245	2	each	each	DET
ejpam-3029	245	3	x	x	SYM
ejpam-3029	245	4	∈	∈	PROPN
ejpam-3029	245	5	a	a	DET
ejpam-3029	245	6	,	,	PUNCT
ejpam-3029	245	7	let	let	VERB
ejpam-3029	245	8	vα(x	vα(x	NOUN
ejpam-3029	245	9	)	)	PUNCT
ejpam-3029	245	10	∈	∈	NOUN
ejpam-3029	245	11	v	v	ADP
ejpam-3029	245	12	such	such	ADJ
ejpam-3029	245	13	that	that	DET
ejpam-3029	245	14	f(x	f(x	PROPN
ejpam-3029	245	15	)	)	PUNCT
ejpam-3029	245	16	∈	∈	PROPN
ejpam-3029	245	17	vα(x	vα(x	NOUN
ejpam-3029	245	18	)	)	PUNCT
ejpam-3029	245	19	.	.	PUNCT
ejpam-3029	246	1	since	since	SCONJ
ejpam-3029	246	2	f	f	PROPN
ejpam-3029	246	3	is	be	AUX
ejpam-3029	246	4	contra	contra	PROPN
ejpam-3029	246	5	(	(	PUNCT
ejpam-3029	246	6	µ	µ	NUM
ejpam-3029	246	7	,	,	PUNCT
ejpam-3029	246	8	ν)-continuous	ν)-continuous	ADJ
ejpam-3029	246	9	and	and	CCONJ
ejpam-3029	246	10	(	(	PUNCT
ejpam-3029	246	11	µ	µ	NUM
ejpam-3029	246	12	,	,	PUNCT
ejpam-3029	246	13	ν)-precontinuous	ν)-precontinuous	ADJ
ejpam-3029	246	14	,	,	PUNCT
ejpam-3029	246	15	f−1(vα(x	f−1(vα(x	NOUN
ejpam-3029	246	16	)	)	PUNCT
ejpam-3029	246	17	)	)	PUNCT
ejpam-3029	246	18	is	be	AUX
ejpam-3029	246	19	µ-closed	µ-close	VERB
ejpam-3029	246	20	in	in	ADP
ejpam-3029	246	21	x	x	NOUN
ejpam-3029	246	22	and	and	CCONJ
ejpam-3029	246	23	f−1(vα(x	f−1(vα(x	NOUN
ejpam-3029	246	24	)	)	PUNCT
ejpam-3029	246	25	)	)	PUNCT
ejpam-3029	247	1	⊆	⊆	NUM
ejpam-3029	247	2	iµ(cµ(f−1(vα(x	iµ(cµ(f−1(vα(x	NOUN
ejpam-3029	247	3	)	)	PUNCT
ejpam-3029	247	4	)	)	PUNCT
ejpam-3029	247	5	)	)	PUNCT
ejpam-3029	247	6	)	)	PUNCT
ejpam-3029	248	1	=	=	SYM
ejpam-3029	248	2	iµ(f−1(vα(x	iµ(f−1(vα(x	PROPN
ejpam-3029	248	3	)	)	PUNCT
ejpam-3029	248	4	)	)	PUNCT
ejpam-3029	248	5	)	)	PUNCT
ejpam-3029	248	6	.	.	PUNCT
ejpam-3029	249	1	so	so	ADV
ejpam-3029	249	2	f−1(vα(x	f−1(vα(x	ADJ
ejpam-3029	249	3	)	)	PUNCT
ejpam-3029	249	4	)	)	PUNCT
ejpam-3029	250	1	=	=	SYM
ejpam-3029	250	2	iµ(f−1(vα(x	iµ(f−1(vα(x	PROPN
ejpam-3029	250	3	)	)	PUNCT
ejpam-3029	250	4	)	)	PUNCT
ejpam-3029	250	5	)	)	PUNCT
ejpam-3029	250	6	.	.	PUNCT
ejpam-3029	251	1	this	this	PRON
ejpam-3029	251	2	implies	imply	VERB
ejpam-3029	251	3	f−1(vα(x	f−1(vα(x	NOUN
ejpam-3029	251	4	)	)	PUNCT
ejpam-3029	251	5	)	)	PUNCT
ejpam-3029	251	6	is	be	AUX
ejpam-3029	251	7	µ-clopen	µ-clopen	VERB
ejpam-3029	251	8	and	and	CCONJ
ejpam-3029	251	9	hence	hence	ADV
ejpam-3029	251	10	{	{	PUNCT
ejpam-3029	251	11	f−1(vα(x	f−1(vα(x	NOUN
ejpam-3029	251	12	)	)	PUNCT
ejpam-3029	251	13	)	)	PUNCT
ejpam-3029	251	14	:	:	PUNCT
ejpam-3029	252	1	x	x	X
ejpam-3029	252	2	∈	∈	PROPN
ejpam-3029	252	3	a	a	PRON
ejpam-3029	252	4	}	}	PUNCT
ejpam-3029	252	5	is	be	AUX
ejpam-3029	252	6	a	a	DET
ejpam-3029	252	7	µ-clopen	µ-clopen	NOUN
ejpam-3029	252	8	cover	cover	NOUN
ejpam-3029	252	9	of	of	ADP
ejpam-3029	252	10	the	the	DET
ejpam-3029	252	11	weakly	weakly	ADJ
ejpam-3029	252	12	µh	µh	ADJ
ejpam-3029	252	13	-	-	ADJ
ejpam-3029	252	14	compact	compact	ADJ
ejpam-3029	252	15	subset	subset	NOUN
ejpam-3029	252	16	a.	a.	NOUN
ejpam-3029	252	17	there	there	PRON
ejpam-3029	252	18	exists	exist	VERB
ejpam-3029	252	19	a	a	DET
ejpam-3029	252	20	finite	finite	NOUN
ejpam-3029	252	21	subset	subset	VERB
ejpam-3029	252	22	a0	a0	NOUN
ejpam-3029	252	23	of	of	ADP
ejpam-3029	252	24	a	a	DET
ejpam-3029	252	25	such	such	ADJ
ejpam-3029	252	26	that	that	SCONJ
ejpam-3029	252	27	a	a	DET
ejpam-3029	252	28	\	\	PROPN
ejpam-3029	252	29	⋃	⋃	PROPN
ejpam-3029	252	30	x∈a0	x∈a0	PROPN
ejpam-3029	252	31	cµ(f−1(vα(x	cµ(f−1(vα(x	PROPN
ejpam-3029	252	32	)	)	PUNCT
ejpam-3029	252	33	)	)	PUNCT
ejpam-3029	252	34	)	)	PUNCT
ejpam-3029	253	1	=	=	PUNCT
ejpam-3029	253	2	a	a	DET
ejpam-3029	253	3	\	\	PROPN
ejpam-3029	253	4	⋃	⋃	PUNCT
ejpam-3029	253	5	x∈a0	x∈a0	PROPN
ejpam-3029	253	6	f−1(vα(x	f−1(vα(x	NOUN
ejpam-3029	253	7	)	)	PUNCT
ejpam-3029	253	8	)	)	PUNCT
ejpam-3029	254	1	∈	∈	PROPN
ejpam-3029	254	2	h.	h.	NOUN
ejpam-3029	254	3	now	now	ADV
ejpam-3029	254	4	we	we	PRON
ejpam-3029	254	5	have	have	VERB
ejpam-3029	254	6	f(a	f(a	NOUN
ejpam-3029	254	7	)	)	PUNCT
ejpam-3029	254	8	\	\	PUNCT
ejpam-3029	255	1	⋃	⋃	SCONJ
ejpam-3029	255	2	x∈a0	x∈a0	PROPN
ejpam-3029	255	3	vα(x	vα(x	NOUN
ejpam-3029	255	4	)	)	PUNCT
ejpam-3029	255	5	⊂	⊂	PROPN
ejpam-3029	255	6	f(a	f(a	PROPN
ejpam-3029	255	7	)	)	PUNCT
ejpam-3029	255	8	\	\	X
ejpam-3029	256	1	f	f	X
ejpam-3029	256	2	(	(	PUNCT
ejpam-3029	256	3	⋃	⋃	PROPN
ejpam-3029	256	4	x∈a0	x∈a0	PROPN
ejpam-3029	256	5	f−1(vα(x	f−1(vα(x	NOUN
ejpam-3029	256	6	)	)	PUNCT
ejpam-3029	256	7	)	)	PUNCT
ejpam-3029	256	8	)	)	PUNCT
ejpam-3029	257	1	⊂	⊂	PROPN
ejpam-3029	258	1	f(a	f(a	X
ejpam-3029	258	2	\	\	X
ejpam-3029	259	1	⋃	⋃	PUNCT
ejpam-3029	259	2	x∈a0	x∈a0	PROPN
ejpam-3029	259	3	f−1(vα(x	f−1(vα(x	NOUN
ejpam-3029	259	4	)	)	PUNCT
ejpam-3029	259	5	)	)	PUNCT
ejpam-3029	259	6	)	)	PUNCT
ejpam-3029	260	1	∈	∈	PROPN
ejpam-3029	260	2	f(h	f(h	PROPN
ejpam-3029	260	3	)	)	PUNCT
ejpam-3029	260	4	.	.	PUNCT
ejpam-3029	261	1	this	this	PRON
ejpam-3029	261	2	implies	imply	VERB
ejpam-3029	261	3	f(a	f(a	NOUN
ejpam-3029	261	4	)	)	PUNCT
ejpam-3029	261	5	\	\	PUNCT
ejpam-3029	262	1	⋃	⋃	SCONJ
ejpam-3029	262	2	x∈a0	x∈a0	PROPN
ejpam-3029	262	3	vα(x	vα(x	NOUN
ejpam-3029	262	4	)	)	PUNCT
ejpam-3029	262	5	∈	∈	PROPN
ejpam-3029	262	6	f(h	f(h	PROPN
ejpam-3029	262	7	)	)	PUNCT
ejpam-3029	262	8	.	.	PUNCT
ejpam-3029	263	1	hence	hence	ADV
ejpam-3029	263	2	f(a	f(a	PROPN
ejpam-3029	263	3	)	)	PUNCT
ejpam-3029	263	4	is	be	AUX
ejpam-3029	263	5	νf(h)-compact	νf(h)-compact	PROPN
ejpam-3029	263	6	.	.	PUNCT
ejpam-3029	264	1	corollary	corollary	ADJ
ejpam-3029	264	2	10	10	NUM
ejpam-3029	264	3	.	.	PUNCT
ejpam-3029	265	1	let	let	VERB
ejpam-3029	265	2	f	f	NOUN
ejpam-3029	265	3	:	:	PUNCT
ejpam-3029	265	4	(	(	PUNCT
ejpam-3029	265	5	x,µ)→	x,µ)→	X
ejpam-3029	265	6	(	(	PUNCT
ejpam-3029	265	7	y	y	PROPN
ejpam-3029	265	8	,	,	PUNCT
ejpam-3029	265	9	ν	ν	NOUN
ejpam-3029	265	10	)	)	PUNCT
ejpam-3029	265	11	be	be	AUX
ejpam-3029	265	12	a	a	DET
ejpam-3029	265	13	contra	contra	PROPN
ejpam-3029	265	14	(	(	PUNCT
ejpam-3029	265	15	µ	µ	NOUN
ejpam-3029	265	16	,	,	PUNCT
ejpam-3029	265	17	ν)-continuous	ν)-continuous	ADJ
ejpam-3029	265	18	and	and	CCONJ
ejpam-3029	265	19	(	(	PUNCT
ejpam-3029	265	20	µ	µ	NUM
ejpam-3029	265	21	,	,	PUNCT
ejpam-3029	265	22	ν)-precontinuous	ν)-precontinuous	ADJ
ejpam-3029	265	23	surjection	surjection	NOUN
ejpam-3029	265	24	.	.	PUNCT
ejpam-3029	266	1	if	if	SCONJ
ejpam-3029	266	2	(	(	PUNCT
ejpam-3029	266	3	x,µ,h	x,µ,h	PROPN
ejpam-3029	266	4	)	)	PUNCT
ejpam-3029	266	5	is	be	AUX
ejpam-3029	266	6	weakly	weakly	ADJ
ejpam-3029	266	7	µh	µh	NOUN
ejpam-3029	266	8	-	-	ADJ
ejpam-3029	266	9	compact	compact	ADJ
ejpam-3029	266	10	,	,	PUNCT
ejpam-3029	266	11	then	then	ADV
ejpam-3029	266	12	(	(	PUNCT
ejpam-3029	266	13	y	y	PROPN
ejpam-3029	266	14	,	,	PUNCT
ejpam-3029	266	15	ν	ν	PROPN
ejpam-3029	266	16	,	,	PUNCT
ejpam-3029	266	17	f(h	f(h	PROPN
ejpam-3029	266	18	)	)	PUNCT
ejpam-3029	266	19	)	)	PUNCT
ejpam-3029	266	20	is	be	AUX
ejpam-3029	266	21	νf(h)-compact	νf(h)-compact	PROPN
ejpam-3029	266	22	.	.	PUNCT
ejpam-3029	267	1	by	by	ADP
ejpam-3029	267	2	taking	take	VERB
ejpam-3029	267	3	h	h	NOUN
ejpam-3029	267	4	=	=	PUNCT
ejpam-3029	267	5	{	{	PUNCT
ejpam-3029	267	6	∅	∅	NOUN
ejpam-3029	267	7	}	}	PUNCT
ejpam-3029	267	8	,	,	PUNCT
ejpam-3029	267	9	we	we	PRON
ejpam-3029	267	10	get	get	VERB
ejpam-3029	267	11	the	the	DET
ejpam-3029	267	12	following	follow	VERB
ejpam-3029	267	13	corollary	corollary	NOUN
ejpam-3029	267	14	.	.	PUNCT
ejpam-3029	268	1	corollary	corollary	ADJ
ejpam-3029	268	2	11	11	NUM
ejpam-3029	268	3	.	.	PUNCT
ejpam-3029	269	1	let	let	VERB
ejpam-3029	269	2	f	f	NOUN
ejpam-3029	269	3	:	:	PUNCT
ejpam-3029	269	4	(	(	PUNCT
ejpam-3029	269	5	x,µ)→	x,µ)→	X
ejpam-3029	269	6	(	(	PUNCT
ejpam-3029	269	7	y	y	PROPN
ejpam-3029	269	8	,	,	PUNCT
ejpam-3029	269	9	ν	ν	NOUN
ejpam-3029	269	10	)	)	PUNCT
ejpam-3029	269	11	be	be	AUX
ejpam-3029	269	12	a	a	DET
ejpam-3029	269	13	contra	contra	PROPN
ejpam-3029	269	14	(	(	PUNCT
ejpam-3029	269	15	µ	µ	NOUN
ejpam-3029	269	16	,	,	PUNCT
ejpam-3029	269	17	ν)-continuous	ν)-continuous	ADJ
ejpam-3029	269	18	and	and	CCONJ
ejpam-3029	269	19	(	(	PUNCT
ejpam-3029	269	20	µ	µ	NUM
ejpam-3029	269	21	,	,	PUNCT
ejpam-3029	269	22	ν)-precontinuous	ν)-precontinuous	ADJ
ejpam-3029	269	23	function	function	NOUN
ejpam-3029	269	24	.	.	PUNCT
ejpam-3029	270	1	if	if	SCONJ
ejpam-3029	270	2	a	a	PRON
ejpam-3029	270	3	is	be	AUX
ejpam-3029	270	4	weakly	weakly	ADJ
ejpam-3029	270	5	µ-compact	µ-compact	NOUN
ejpam-3029	270	6	,	,	PUNCT
ejpam-3029	270	7	then	then	ADV
ejpam-3029	270	8	f(a	f(a	PROPN
ejpam-3029	270	9	)	)	PUNCT
ejpam-3029	270	10	is	be	AUX
ejpam-3029	270	11	ν	ν	NOUN
ejpam-3029	270	12	-	-	ADJ
ejpam-3029	270	13	compact	compact	ADJ
ejpam-3029	270	14	.	.	PUNCT
ejpam-3029	271	1	theorem	theorem	NOUN
ejpam-3029	271	2	5	5	NUM
ejpam-3029	271	3	.	.	PUNCT
ejpam-3029	272	1	let	let	AUX
ejpam-3029	272	2	f	f	PROPN
ejpam-3029	272	3	:	:	PUNCT
ejpam-3029	272	4	(	(	PUNCT
ejpam-3029	272	5	x,µ,h	x,µ,h	PROPN
ejpam-3029	272	6	)	)	PUNCT
ejpam-3029	272	7	→	→	SYM
ejpam-3029	272	8	(	(	PUNCT
ejpam-3029	272	9	y	y	PROPN
ejpam-3029	272	10	,	,	PUNCT
ejpam-3029	272	11	ν	ν	NOUN
ejpam-3029	272	12	)	)	PUNCT
ejpam-3029	272	13	be	be	AUX
ejpam-3029	272	14	an	an	DET
ejpam-3029	272	15	almost	almost	ADV
ejpam-3029	272	16	δ(µ	δ(µ	NOUN
ejpam-3029	272	17	,	,	PUNCT
ejpam-3029	272	18	ν)-continuous	ν)-continuous	ADJ
ejpam-3029	272	19	function	function	NOUN
ejpam-3029	272	20	.	.	PUNCT
ejpam-3029	273	1	if	if	SCONJ
ejpam-3029	273	2	for	for	ADP
ejpam-3029	273	3	every	every	DET
ejpam-3029	273	4	cover	cover	NOUN
ejpam-3029	273	5	{	{	PUNCT
ejpam-3029	273	6	uα	uα	X
ejpam-3029	273	7	:	:	PUNCT
ejpam-3029	273	8	α	α	PROPN
ejpam-3029	273	9	∈	∈	PROPN
ejpam-3029	273	10	∆	∆	PROPN
ejpam-3029	273	11	}	}	PUNCT
ejpam-3029	273	12	of	of	ADP
ejpam-3029	273	13	a	a	DET
ejpam-3029	273	14	⊆	⊆	NUM
ejpam-3029	273	15	x	x	SYM
ejpam-3029	273	16	by	by	ADP
ejpam-3029	273	17	µ-regular	µ-regular	PROPN
ejpam-3029	273	18	open	open	ADJ
ejpam-3029	273	19	sets	set	NOUN
ejpam-3029	273	20	in	in	ADP
ejpam-3029	273	21	x	x	SYM
ejpam-3029	273	22	there	there	PRON
ejpam-3029	273	23	exists	exist	VERB
ejpam-3029	273	24	a	a	DET
ejpam-3029	273	25	finite	finite	NOUN
ejpam-3029	273	26	subset	subset	VERB
ejpam-3029	273	27	∆0	∆0	NUM
ejpam-3029	273	28	of	of	ADP
ejpam-3029	273	29	∆	∆	PROPN
ejpam-3029	273	30	such	such	ADJ
ejpam-3029	273	31	that	that	SCONJ
ejpam-3029	273	32	a	a	DET
ejpam-3029	273	33	\	\	NOUN
ejpam-3029	273	34	⋃	⋃	SCONJ
ejpam-3029	273	35	α∈∆0	α∈∆0	NOUN
ejpam-3029	273	36	uα	uα	PROPN
ejpam-3029	273	37	∈	∈	PROPN
ejpam-3029	273	38	h	h	NOUN
ejpam-3029	273	39	,	,	PUNCT
ejpam-3029	273	40	then	then	ADV
ejpam-3029	273	41	f(a	f(a	PROPN
ejpam-3029	273	42	)	)	PUNCT
ejpam-3029	273	43	is	be	AUX
ejpam-3029	273	44	weakly	weakly	ADJ
ejpam-3029	273	45	νf(h)-compact	νf(h)-compact	NOUN
ejpam-3029	273	46	.	.	PUNCT
ejpam-3029	274	1	proof	proof	NOUN
ejpam-3029	274	2	.	.	PUNCT
ejpam-3029	275	1	let	let	VERB
ejpam-3029	275	2	v	v	VERB
ejpam-3029	275	3	=	=	PUNCT
ejpam-3029	275	4	{	{	PUNCT
ejpam-3029	275	5	vα	vα	X
ejpam-3029	275	6	:	:	PUNCT
ejpam-3029	275	7	α	α	PROPN
ejpam-3029	275	8	∈	∈	PROPN
ejpam-3029	275	9	∆	∆	PROPN
ejpam-3029	275	10	}	}	PUNCT
ejpam-3029	275	11	be	be	AUX
ejpam-3029	275	12	a	a	DET
ejpam-3029	275	13	cover	cover	NOUN
ejpam-3029	275	14	of	of	ADP
ejpam-3029	275	15	f(a	f(a	NOUN
ejpam-3029	275	16	)	)	PUNCT
ejpam-3029	275	17	by	by	ADP
ejpam-3029	275	18	ν	ν	NOUN
ejpam-3029	275	19	-	-	ADJ
ejpam-3029	275	20	open	open	ADJ
ejpam-3029	275	21	sets	set	NOUN
ejpam-3029	275	22	of	of	ADP
ejpam-3029	275	23	y	y	PROPN
ejpam-3029	275	24	.	.	PUNCT
ejpam-3029	276	1	let	let	VERB
ejpam-3029	276	2	x	x	SYM
ejpam-3029	276	3	∈	∈	VERB
ejpam-3029	276	4	a	a	PRON
ejpam-3029	276	5	and	and	CCONJ
ejpam-3029	276	6	vα(x	vα(x	NUM
ejpam-3029	276	7	)	)	PUNCT
ejpam-3029	276	8	∈	∈	NOUN
ejpam-3029	276	9	v	v	ADP
ejpam-3029	276	10	such	such	ADJ
ejpam-3029	276	11	that	that	DET
ejpam-3029	276	12	f(x	f(x	PROPN
ejpam-3029	276	13	)	)	PUNCT
ejpam-3029	276	14	∈	∈	PROPN
ejpam-3029	276	15	vα(x	vα(x	NOUN
ejpam-3029	276	16	)	)	PUNCT
ejpam-3029	276	17	.	.	PUNCT
ejpam-3029	277	1	then	then	ADV
ejpam-3029	277	2	iµ(cµ(vα(x	iµ(cµ(vα(x	NOUN
ejpam-3029	277	3	)	)	PUNCT
ejpam-3029	277	4	)	)	PUNCT
ejpam-3029	277	5	)	)	PUNCT
ejpam-3029	277	6	is	be	AUX
ejpam-3029	277	7	a	a	DET
ejpam-3029	277	8	µ-regularly	µ-regularly	ADV
ejpam-3029	277	9	open	open	ADJ
ejpam-3029	277	10	set	set	VERB
ejpam-3029	277	11	in	in	ADP
ejpam-3029	277	12	y	y	NOUN
ejpam-3029	277	13	containing	contain	VERB
ejpam-3029	277	14	f(x	f(x	PROPN
ejpam-3029	277	15	)	)	PUNCT
ejpam-3029	277	16	.	.	PUNCT
ejpam-3029	278	1	since	since	SCONJ
ejpam-3029	278	2	f	f	PROPN
ejpam-3029	278	3	is	be	AUX
ejpam-3029	278	4	almost	almost	ADV
ejpam-3029	278	5	δ(µ	δ(µ	NOUN
ejpam-3029	278	6	,	,	PUNCT
ejpam-3029	278	7	ν)-continuous	ν)-continuous	ADJ
ejpam-3029	278	8	,	,	PUNCT
ejpam-3029	278	9	then	then	ADV
ejpam-3029	278	10	for	for	ADP
ejpam-3029	278	11	every	every	DET
ejpam-3029	278	12	x	x	PROPN
ejpam-3029	278	13	∈	∈	PROPN
ejpam-3029	278	14	a	a	PRON
ejpam-3029	278	15	,	,	PUNCT
ejpam-3029	278	16	there	there	PRON
ejpam-3029	278	17	exists	exist	VERB
ejpam-3029	278	18	a	a	DET
ejpam-3029	278	19	µ-open	µ-open	NOUN
ejpam-3029	278	20	subset	subset	NOUN
ejpam-3029	278	21	uα(x	uα(x	NOUN
ejpam-3029	278	22	)	)	PUNCT
ejpam-3029	278	23	of	of	ADP
ejpam-3029	278	24	x	x	SYM
ejpam-3029	278	25	containing	contain	VERB
ejpam-3029	278	26	x	x	PUNCT
ejpam-3029	278	27	such	such	ADJ
ejpam-3029	278	28	that	that	DET
ejpam-3029	278	29	f(iµ(cµ(uα(x	f(iµ(cµ(uα(x	NOUN
ejpam-3029	278	30	)	)	PUNCT
ejpam-3029	278	31	)	)	PUNCT
ejpam-3029	278	32	)	)	PUNCT
ejpam-3029	278	33	)	)	PUNCT
ejpam-3029	279	1	⊆	⊆	NUM
ejpam-3029	279	2	cν(vα(x	cν(vα(x	NOUN
ejpam-3029	279	3	)	)	PUNCT
ejpam-3029	279	4	)	)	PUNCT
ejpam-3029	279	5	.	.	PUNCT
ejpam-3029	280	1	then	then	ADV
ejpam-3029	280	2	references	reference	VERB
ejpam-3029	280	3	417	417	NUM
ejpam-3029	280	4	{	{	PUNCT
ejpam-3029	280	5	iµ(cµ(uα(x	iµ(cµ(uα(x	PROPN
ejpam-3029	280	6	)	)	PUNCT
ejpam-3029	280	7	)	)	PUNCT
ejpam-3029	280	8	)	)	PUNCT
ejpam-3029	280	9	:	:	PUNCT
ejpam-3029	280	10	x	x	X
ejpam-3029	280	11	∈	∈	PROPN
ejpam-3029	280	12	a	a	PRON
ejpam-3029	280	13	}	}	PUNCT
ejpam-3029	280	14	is	be	AUX
ejpam-3029	280	15	a	a	DET
ejpam-3029	280	16	µ-regularly	µ-regularly	ADV
ejpam-3029	280	17	open	open	ADJ
ejpam-3029	280	18	cover	cover	NOUN
ejpam-3029	280	19	of	of	ADP
ejpam-3029	280	20	a.	a.	NOUN
ejpam-3029	280	21	it	it	PRON
ejpam-3029	280	22	follows	follow	VERB
ejpam-3029	280	23	that	that	SCONJ
ejpam-3029	280	24	there	there	PRON
ejpam-3029	280	25	exists	exist	VERB
ejpam-3029	280	26	a	a	DET
ejpam-3029	280	27	finite	finite	NOUN
ejpam-3029	280	28	subset	subset	VERB
ejpam-3029	280	29	a0	a0	NOUN
ejpam-3029	280	30	of	of	ADP
ejpam-3029	280	31	a	a	DET
ejpam-3029	280	32	such	such	ADJ
ejpam-3029	281	1	that	that	SCONJ
ejpam-3029	281	2	a	a	PRON
ejpam-3029	281	3	\	\	PROPN
ejpam-3029	281	4	⋃	⋃	PROPN
ejpam-3029	281	5	x∈a0	x∈a0	PROPN
ejpam-3029	281	6	iµ(cµ(uα(x	iµ(cµ(uα(x	NOUN
ejpam-3029	281	7	)	)	PUNCT
ejpam-3029	281	8	)	)	PUNCT
ejpam-3029	281	9	)	)	PUNCT
ejpam-3029	282	1	∈	∈	PROPN
ejpam-3029	282	2	h.	h.	PROPN
ejpam-3029	282	3	now	now	ADV
ejpam-3029	282	4	f(a	f(a	PROPN
ejpam-3029	282	5	)	)	PUNCT
ejpam-3029	282	6	\	\	X
ejpam-3029	283	1	f	f	X
ejpam-3029	283	2	(	(	PUNCT
ejpam-3029	283	3	⋃	⋃	PROPN
ejpam-3029	283	4	x∈a0	x∈a0	PROPN
ejpam-3029	283	5	iµ(cµ(uα(x	iµ(cµ(uα(x	NOUN
ejpam-3029	283	6	)	)	PUNCT
ejpam-3029	283	7	)	)	PUNCT
ejpam-3029	283	8	)	)	PUNCT
ejpam-3029	283	9	)	)	PUNCT
ejpam-3029	284	1	⊆	⊆	NUM
ejpam-3029	284	2	f(a	f(a	X
ejpam-3029	284	3	\	\	X
ejpam-3029	284	4	⋃	⋃	PUNCT
ejpam-3029	284	5	x∈a0	x∈a0	PROPN
ejpam-3029	284	6	iµ(cµ(uα(x	iµ(cµ(uα(x	NOUN
ejpam-3029	284	7	)	)	PUNCT
ejpam-3029	284	8	)	)	PUNCT
ejpam-3029	284	9	)	)	PUNCT
ejpam-3029	284	10	)	)	PUNCT
ejpam-3029	285	1	∈	∈	PROPN
ejpam-3029	285	2	f(h	f(h	PROPN
ejpam-3029	285	3	)	)	PUNCT
ejpam-3029	285	4	.	.	PUNCT
ejpam-3029	286	1	this	this	PRON
ejpam-3029	286	2	implies	imply	VERB
ejpam-3029	286	3	f(a	f(a	NOUN
ejpam-3029	286	4	)	)	PUNCT
ejpam-3029	286	5	\	\	PUNCT
ejpam-3029	287	1	⋃	⋃	NOUN
ejpam-3029	287	2	x∈a0	x∈a0	NOUN
ejpam-3029	287	3	f(iµ(cµ(uα(x	f(iµ(cµ(uα(x	NOUN
ejpam-3029	287	4	)	)	PUNCT
ejpam-3029	287	5	)	)	PUNCT
ejpam-3029	287	6	)	)	PUNCT
ejpam-3029	287	7	)	)	PUNCT
ejpam-3029	288	1	∈	∈	PROPN
ejpam-3029	288	2	f(h	f(h	PROPN
ejpam-3029	288	3	)	)	PUNCT
ejpam-3029	288	4	.	.	PUNCT
ejpam-3029	289	1	therefore	therefore	ADV
ejpam-3029	289	2	,	,	PUNCT
ejpam-3029	289	3	we	we	PRON
ejpam-3029	289	4	obtain	obtain	VERB
ejpam-3029	289	5	f(a	f(a	NOUN
ejpam-3029	289	6	)	)	PUNCT
ejpam-3029	289	7	\	\	PUNCT
ejpam-3029	290	1	⋃	⋃	PUNCT
ejpam-3029	290	2	x∈a0	x∈a0	NOUN
ejpam-3029	290	3	cν(vα(x	cν(vα(x	NOUN
ejpam-3029	290	4	)	)	PUNCT
ejpam-3029	290	5	)	)	PUNCT
ejpam-3029	290	6	⊆	⊆	NUM
ejpam-3029	290	7	f(a	f(a	NOUN
ejpam-3029	290	8	)	)	PUNCT
ejpam-3029	290	9	\	\	PUNCT
ejpam-3029	290	10	⋃	⋃	NOUN
ejpam-3029	290	11	x∈a0	x∈a0	NOUN
ejpam-3029	290	12	f(iµ(cµ(uα(x	f(iµ(cµ(uα(x	NOUN
ejpam-3029	290	13	)	)	PUNCT
ejpam-3029	290	14	)	)	PUNCT
ejpam-3029	290	15	)	)	PUNCT
ejpam-3029	290	16	)	)	PUNCT
ejpam-3029	290	17	.	.	PUNCT
ejpam-3029	291	1	this	this	PRON
ejpam-3029	291	2	implies	imply	VERB
ejpam-3029	291	3	f(a)\	f(a)\	X
ejpam-3029	291	4	⋃	⋃	PROPN
ejpam-3029	291	5	x∈a0	x∈a0	NOUN
ejpam-3029	291	6	cν(vα(x	cν(vα(x	NOUN
ejpam-3029	291	7	)	)	PUNCT
ejpam-3029	291	8	)	)	PUNCT
ejpam-3029	292	1	∈	∈	PROPN
ejpam-3029	292	2	f(h	f(h	PROPN
ejpam-3029	292	3	)	)	PUNCT
ejpam-3029	292	4	.	.	PUNCT
ejpam-3029	293	1	this	this	PRON
ejpam-3029	293	2	shows	show	VERB
ejpam-3029	293	3	that	that	SCONJ
ejpam-3029	293	4	f(a	f(a	NOUN
ejpam-3029	293	5	)	)	PUNCT
ejpam-3029	293	6	is	be	AUX
ejpam-3029	293	7	weakly	weakly	ADJ
ejpam-3029	293	8	νf(h)-compact	νf(h)-compact	NOUN
ejpam-3029	293	9	.	.	PUNCT
ejpam-3029	294	1	corollary	corollary	ADJ
ejpam-3029	294	2	12	12	NUM
ejpam-3029	294	3	.	.	PUNCT
ejpam-3029	295	1	let	let	AUX
ejpam-3029	295	2	f	f	NOUN
ejpam-3029	295	3	:	:	PUNCT
ejpam-3029	295	4	(	(	PUNCT
ejpam-3029	295	5	x,µ,h	x,µ,h	PROPN
ejpam-3029	295	6	)	)	PUNCT
ejpam-3029	295	7	→	→	SYM
ejpam-3029	295	8	(	(	PUNCT
ejpam-3029	295	9	y	y	PROPN
ejpam-3029	295	10	,	,	PUNCT
ejpam-3029	295	11	ν	ν	NOUN
ejpam-3029	295	12	)	)	PUNCT
ejpam-3029	295	13	be	be	AUX
ejpam-3029	295	14	an	an	DET
ejpam-3029	295	15	almost	almost	ADV
ejpam-3029	295	16	δ(µ	δ(µ	NOUN
ejpam-3029	295	17	,	,	PUNCT
ejpam-3029	295	18	ν)-continuous	ν)-continuous	ADJ
ejpam-3029	295	19	surjection	surjection	NOUN
ejpam-3029	295	20	.	.	PUNCT
ejpam-3029	296	1	if	if	SCONJ
ejpam-3029	296	2	for	for	ADP
ejpam-3029	296	3	every	every	DET
ejpam-3029	296	4	cover	cover	NOUN
ejpam-3029	296	5	{	{	PUNCT
ejpam-3029	296	6	uα	uα	X
ejpam-3029	296	7	:	:	PUNCT
ejpam-3029	296	8	α	α	PROPN
ejpam-3029	296	9	∈	∈	PROPN
ejpam-3029	296	10	∆	∆	PROPN
ejpam-3029	296	11	}	}	PUNCT
ejpam-3029	296	12	of	of	ADP
ejpam-3029	296	13	x	x	PUNCT
ejpam-3029	296	14	by	by	ADP
ejpam-3029	296	15	µ-regular	µ-regular	PROPN
ejpam-3029	296	16	open	open	ADJ
ejpam-3029	296	17	sets	set	NOUN
ejpam-3029	296	18	of	of	ADP
ejpam-3029	296	19	x	x	SYM
ejpam-3029	296	20	there	there	PRON
ejpam-3029	296	21	exists	exist	VERB
ejpam-3029	296	22	a	a	DET
ejpam-3029	296	23	finite	finite	NOUN
ejpam-3029	296	24	subset	subset	VERB
ejpam-3029	296	25	∆0	∆0	NUM
ejpam-3029	296	26	of	of	ADP
ejpam-3029	296	27	∆	∆	PROPN
ejpam-3029	296	28	such	such	ADJ
ejpam-3029	296	29	that	that	SCONJ
ejpam-3029	296	30	x	x	SYM
ejpam-3029	296	31	\	\	PROPN
ejpam-3029	296	32	⋃	⋃	ADV
ejpam-3029	296	33	α∈∆0	α∈∆0	VERB
ejpam-3029	296	34	uα	uα	PROPN
ejpam-3029	296	35	∈	∈	PROPN
ejpam-3029	296	36	h	h	NOUN
ejpam-3029	296	37	,	,	PUNCT
ejpam-3029	296	38	then	then	ADV
ejpam-3029	296	39	(	(	PUNCT
ejpam-3029	296	40	y	y	PROPN
ejpam-3029	296	41	,	,	PUNCT
ejpam-3029	296	42	ν	ν	PROPN
ejpam-3029	296	43	,	,	PUNCT
ejpam-3029	296	44	f(h	f(h	PROPN
ejpam-3029	296	45	)	)	PUNCT
ejpam-3029	296	46	)	)	PUNCT
ejpam-3029	296	47	is	be	AUX
ejpam-3029	296	48	weakly	weakly	ADJ
ejpam-3029	296	49	νf(h)-compact	νf(h)-compact	PROPN
ejpam-3029	296	50	.	.	PUNCT
ejpam-3029	297	1	by	by	ADP
ejpam-3029	297	2	taking	take	VERB
ejpam-3029	297	3	h	h	NOUN
ejpam-3029	297	4	=	=	PUNCT
ejpam-3029	297	5	{	{	PUNCT
ejpam-3029	297	6	∅	∅	NOUN
ejpam-3029	297	7	}	}	PUNCT
ejpam-3029	297	8	,	,	PUNCT
ejpam-3029	297	9	we	we	PRON
ejpam-3029	297	10	get	get	VERB
ejpam-3029	297	11	the	the	DET
ejpam-3029	297	12	following	follow	VERB
ejpam-3029	297	13	corollary	corollary	NOUN
ejpam-3029	297	14	.	.	PUNCT
ejpam-3029	298	1	corollary	corollary	ADJ
ejpam-3029	298	2	13	13	NUM
ejpam-3029	298	3	.	.	PUNCT
ejpam-3029	299	1	let	let	VERB
ejpam-3029	299	2	f	f	NOUN
ejpam-3029	299	3	:	:	PUNCT
ejpam-3029	299	4	(	(	PUNCT
ejpam-3029	299	5	x,µ	x,µ	NOUN
ejpam-3029	299	6	)	)	PUNCT
ejpam-3029	299	7	→	→	SYM
ejpam-3029	299	8	(	(	PUNCT
ejpam-3029	299	9	y	y	PROPN
ejpam-3029	299	10	,	,	PUNCT
ejpam-3029	299	11	ν	ν	NOUN
ejpam-3029	299	12	)	)	PUNCT
ejpam-3029	299	13	be	be	AUX
ejpam-3029	299	14	an	an	DET
ejpam-3029	299	15	almost	almost	ADV
ejpam-3029	299	16	δ(µ	δ(µ	NOUN
ejpam-3029	299	17	,	,	PUNCT
ejpam-3029	299	18	ν)-continuous	ν)-continuous	ADJ
ejpam-3029	299	19	function	function	NOUN
ejpam-3029	299	20	.	.	PUNCT
ejpam-3029	300	1	if	if	SCONJ
ejpam-3029	300	2	for	for	ADP
ejpam-3029	300	3	every	every	DET
ejpam-3029	300	4	cover	cover	NOUN
ejpam-3029	300	5	{	{	PUNCT
ejpam-3029	300	6	uα	uα	X
ejpam-3029	300	7	:	:	PUNCT
ejpam-3029	300	8	α	α	PROPN
ejpam-3029	300	9	∈	∈	PROPN
ejpam-3029	300	10	∆	∆	PROPN
ejpam-3029	300	11	}	}	PUNCT
ejpam-3029	300	12	of	of	ADP
ejpam-3029	300	13	a	a	DET
ejpam-3029	300	14	⊆	⊆	NUM
ejpam-3029	300	15	x	x	SYM
ejpam-3029	300	16	by	by	ADP
ejpam-3029	300	17	µ-regular	µ-regular	PROPN
ejpam-3029	300	18	open	open	ADJ
ejpam-3029	300	19	sets	set	NOUN
ejpam-3029	300	20	in	in	ADP
ejpam-3029	300	21	x	x	SYM
ejpam-3029	300	22	there	there	PRON
ejpam-3029	300	23	exists	exist	VERB
ejpam-3029	300	24	a	a	DET
ejpam-3029	300	25	finite	finite	NOUN
ejpam-3029	300	26	subset	subset	VERB
ejpam-3029	300	27	∆0	∆0	NUM
ejpam-3029	300	28	of	of	ADP
ejpam-3029	300	29	∆	∆	PROPN
ejpam-3029	300	30	such	such	ADJ
ejpam-3029	300	31	that	that	SCONJ
ejpam-3029	300	32	a	a	DET
ejpam-3029	300	33	⊆	⊆	NUM
ejpam-3029	300	34	⋃	⋃	NOUN
ejpam-3029	300	35	α∈∆0	α∈∆0	X
ejpam-3029	300	36	uα	uα	PROPN
ejpam-3029	300	37	,	,	PUNCT
ejpam-3029	300	38	then	then	ADV
ejpam-3029	300	39	f(a	f(a	PROPN
ejpam-3029	300	40	)	)	PUNCT
ejpam-3029	300	41	is	be	AUX
ejpam-3029	300	42	weakly	weakly	ADJ
ejpam-3029	300	43	ν	ν	NOUN
ejpam-3029	300	44	-	-	ADJ
ejpam-3029	300	45	compact	compact	ADJ
ejpam-3029	300	46	.	.	PUNCT
ejpam-3029	301	1	references	reference	NOUN
ejpam-3029	301	2	[	[	X
ejpam-3029	301	3	1	1	NUM
ejpam-3029	301	4	]	]	PUNCT
ejpam-3029	301	5	a.	a.	PROPN
ejpam-3029	301	6	al	al	PROPN
ejpam-3029	301	7	-	-	PUNCT
ejpam-3029	301	8	omari	omari	PROPN
ejpam-3029	301	9	and	and	CCONJ
ejpam-3029	301	10	t.	t.	PROPN
ejpam-3029	301	11	noiri	noiri	PROPN
ejpam-3029	301	12	.	.	PUNCT
ejpam-3029	302	1	a	a	DET
ejpam-3029	302	2	unified	unified	ADJ
ejpam-3029	302	3	theory	theory	NOUN
ejpam-3029	302	4	of	of	ADP
ejpam-3029	302	5	contra-(µ	contra-(µ	PROPN
ejpam-3029	302	6	,	,	PUNCT
ejpam-3029	302	7	ν)-continuous	ν)-continuous	ADJ
ejpam-3029	302	8	functions	function	NOUN
ejpam-3029	302	9	in	in	ADP
ejpam-3029	302	10	generalized	generalized	ADJ
ejpam-3029	302	11	topological	topological	ADJ
ejpam-3029	302	12	spaces	space	NOUN
ejpam-3029	302	13	.	.	PUNCT
ejpam-3029	303	1	acta	acta	PROPN
ejpam-3029	303	2	math	math	PROPN
ejpam-3029	303	3	.	.	PUNCT
ejpam-3029	304	1	hungar	hungar	NOUN
ejpam-3029	304	2	,	,	PUNCT
ejpam-3029	304	3	135:31–41	135:31–41	NUM
ejpam-3029	304	4	,	,	PUNCT
ejpam-3029	304	5	2012	2012	NUM
ejpam-3029	304	6	.	.	PUNCT
ejpam-3029	305	1	[	[	X
ejpam-3029	305	2	2	2	NUM
ejpam-3029	305	3	]	]	PUNCT
ejpam-3029	305	4	c.	c.	PROPN
ejpam-3029	305	5	carpintero	carpintero	PROPN
ejpam-3029	305	6	,	,	PUNCT
ejpam-3029	305	7	e.	e.	PROPN
ejpam-3029	305	8	rosas	rosas	PROPN
ejpam-3029	305	9	,	,	PUNCT
ejpam-3029	305	10	m.	m.	NOUN
ejpam-3029	305	11	salas	salas	PROPN
ejpam-3029	305	12	-	-	PUNCT
ejpam-3029	305	13	brown	brown	PROPN
ejpam-3029	305	14	,	,	PUNCT
ejpam-3029	305	15	and	and	CCONJ
ejpam-3029	305	16	j.	j.	PROPN
ejpam-3029	305	17	sanabria	sanabria	PROPN
ejpam-3029	305	18	.	.	PUNCT
ejpam-3029	306	1	µ-compactness	µ-compactness	NOUN
ejpam-3029	306	2	with	with	ADP
ejpam-3029	306	3	respect	respect	NOUN
ejpam-3029	306	4	to	to	ADP
ejpam-3029	306	5	a	a	DET
ejpam-3029	306	6	hereditary	hereditary	ADJ
ejpam-3029	306	7	class	class	NOUN
ejpam-3029	306	8	.	.	PUNCT
ejpam-3029	307	1	bol	bol	NOUN
ejpam-3029	307	2	.	.	PUNCT
ejpam-3029	308	1	soc	soc	PROPN
ejpam-3029	308	2	.	.	PUNCT
ejpam-3029	309	1	paran	paran	PROPN
ejpam-3029	309	2	.	.	PUNCT
ejpam-3029	310	1	mat	mat	PROPN
ejpam-3029	310	2	,	,	PUNCT
ejpam-3029	310	3	34(2):231–236	34(2):231–236	PROPN
ejpam-3029	310	4	,	,	PUNCT
ejpam-3029	310	5	2016	2016	NUM
ejpam-3029	310	6	.	.	PUNCT
ejpam-3029	311	1	[	[	X
ejpam-3029	311	2	3	3	NUM
ejpam-3029	311	3	]	]	X
ejpam-3029	311	4	á.	á.	NOUN
ejpam-3029	311	5	császár	császár	PROPN
ejpam-3029	311	6	.	.	PUNCT
ejpam-3029	312	1	generalized	generalize	VERB
ejpam-3029	312	2	topology	topology	NOUN
ejpam-3029	312	3	,	,	PUNCT
ejpam-3029	312	4	generalized	generalize	VERB
ejpam-3029	312	5	continuity	continuity	NOUN
ejpam-3029	312	6	.	.	PUNCT
ejpam-3029	313	1	acta	acta	PROPN
ejpam-3029	313	2	math	math	PROPN
ejpam-3029	313	3	.	.	PUNCT
ejpam-3029	314	1	hungar	hungar	NOUN
ejpam-3029	314	2	,	,	PUNCT
ejpam-3029	314	3	96:351	96:351	NOUN
ejpam-3029	314	4	–	–	PUNCT
ejpam-3029	314	5	357	357	NUM
ejpam-3029	314	6	,	,	PUNCT
ejpam-3029	314	7	2002	2002	NUM
ejpam-3029	314	8	.	.	PUNCT
ejpam-3029	315	1	[	[	X
ejpam-3029	315	2	4	4	NUM
ejpam-3029	315	3	]	]	PUNCT
ejpam-3029	315	4	á.	á.	PRON
ejpam-3029	315	5	császár	császár	PROPN
ejpam-3029	315	6	.	.	PUNCT
ejpam-3029	316	1	generalized	generalize	VERB
ejpam-3029	316	2	open	open	ADJ
ejpam-3029	316	3	sets	set	NOUN
ejpam-3029	316	4	in	in	ADP
ejpam-3029	316	5	generalized	generalized	ADJ
ejpam-3029	316	6	topologies	topology	NOUN
ejpam-3029	316	7	.	.	PUNCT
ejpam-3029	317	1	acta	acta	PROPN
ejpam-3029	317	2	math	math	PROPN
ejpam-3029	317	3	.	.	PUNCT
ejpam-3029	318	1	hungar	hungar	NOUN
ejpam-3029	318	2	,	,	PUNCT
ejpam-3029	318	3	106(3):53–66	106(3):53–66	NUM
ejpam-3029	318	4	,	,	PUNCT
ejpam-3029	318	5	2005	2005	NUM
ejpam-3029	318	6	.	.	PUNCT
ejpam-3029	319	1	[	[	X
ejpam-3029	319	2	5	5	NUM
ejpam-3029	319	3	]	]	PUNCT
ejpam-3029	319	4	á.	á.	NOUN
ejpam-3029	319	5	császár	császár	NOUN
ejpam-3029	319	6	.	.	PUNCT
ejpam-3029	320	1	modification	modification	NOUN
ejpam-3029	320	2	of	of	ADP
ejpam-3029	320	3	generalized	generalized	ADJ
ejpam-3029	320	4	topologies	topology	NOUN
ejpam-3029	320	5	via	via	ADP
ejpam-3029	320	6	hereditary	hereditary	ADJ
ejpam-3029	320	7	classes	class	NOUN
ejpam-3029	320	8	.	.	PUNCT
ejpam-3029	321	1	acta	acta	PROPN
ejpam-3029	321	2	math	math	PROPN
ejpam-3029	321	3	.	.	PUNCT
ejpam-3029	322	1	hungar	hungar	NOUN
ejpam-3029	322	2	,	,	PUNCT
ejpam-3029	322	3	115:29–36	115:29–36	NUM
ejpam-3029	322	4	,	,	PUNCT
ejpam-3029	322	5	2007	2007	NUM
ejpam-3029	322	6	.	.	PUNCT
ejpam-3029	323	1	[	[	X
ejpam-3029	323	2	6	6	NUM
ejpam-3029	323	3	]	]	X
ejpam-3029	323	4	d.	d.	PROPN
ejpam-3029	323	5	jayanthi	jayanthi	PROPN
ejpam-3029	323	6	.	.	PUNCT
ejpam-3029	324	1	contra	contra	PROPN
ejpam-3029	324	2	continuity	continuity	NOUN
ejpam-3029	324	3	on	on	ADP
ejpam-3029	324	4	generalized	generalized	ADJ
ejpam-3029	324	5	topological	topological	ADJ
ejpam-3029	324	6	spaces	space	NOUN
ejpam-3029	324	7	.	.	PUNCT
ejpam-3029	325	1	acta	acta	PROPN
ejpam-3029	325	2	math	math	PROPN
ejpam-3029	325	3	.	.	PUNCT
ejpam-3029	326	1	hungar	hungar	NOUN
ejpam-3029	326	2	,	,	PUNCT
ejpam-3029	326	3	137(4):263–271	137(4):263–271	NUM
ejpam-3029	326	4	,	,	PUNCT
ejpam-3029	326	5	2012	2012	NUM
ejpam-3029	326	6	.	.	PUNCT
ejpam-3029	327	1	[	[	X
ejpam-3029	327	2	7	7	X
ejpam-3029	327	3	]	]	PUNCT
ejpam-3029	327	4	t.	t.	PROPN
ejpam-3029	327	5	jyothis	jyothis	PROPN
ejpam-3029	327	6	and	and	CCONJ
ejpam-3029	327	7	j.	j.	PROPN
ejpam-3029	327	8	sunil	sunil	PROPN
ejpam-3029	327	9	.	.	PUNCT
ejpam-3029	328	1	µ-compactness	µ-compactness	NOUN
ejpam-3029	328	2	in	in	ADP
ejpam-3029	328	3	generalized	generalized	ADJ
ejpam-3029	328	4	topological	topological	ADJ
ejpam-3029	328	5	spaces	space	NOUN
ejpam-3029	328	6	.	.	PUNCT
ejpam-3029	329	1	j.	j.	PROPN
ejpam-3029	329	2	adv	adv	PROPN
ejpam-3029	329	3	.	.	PUNCT
ejpam-3029	329	4	stud	stud	PROPN
ejpam-3029	329	5	.	.	PUNCT
ejpam-3029	330	1	top	top	ADJ
ejpam-3029	330	2	,	,	PUNCT
ejpam-3029	330	3	3(3):18–22	3(3):18–22	NUM
ejpam-3029	330	4	,	,	PUNCT
ejpam-3029	330	5	2012	2012	NUM
ejpam-3029	330	6	.	.	PUNCT
ejpam-3029	331	1	references	reference	NOUN
ejpam-3029	331	2	418	418	NUM
ejpam-3029	332	1	[	[	X
ejpam-3029	332	2	8	8	NUM
ejpam-3029	332	3	]	]	X
ejpam-3029	332	4	y.	y.	PROPN
ejpam-3029	332	5	k.	k.	PROPN
ejpam-3029	332	6	kim	kim	PROPN
ejpam-3029	332	7	and	and	CCONJ
ejpam-3029	332	8	w.	w.	PROPN
ejpam-3029	332	9	k.	k.	PROPN
ejpam-3029	332	10	min	min	PROPN
ejpam-3029	332	11	.	.	PROPN
ejpam-3029	333	1	on	on	ADP
ejpam-3029	333	2	operations	operation	NOUN
ejpam-3029	333	3	induced	induce	VERB
ejpam-3029	333	4	by	by	ADP
ejpam-3029	333	5	hereditary	hereditary	ADJ
ejpam-3029	333	6	classes	class	NOUN
ejpam-3029	333	7	on	on	ADP
ejpam-3029	333	8	generalized	generalized	ADJ
ejpam-3029	333	9	topological	topological	ADJ
ejpam-3029	333	10	spaces	space	NOUN
ejpam-3029	333	11	.	.	PUNCT
ejpam-3029	334	1	acta	acta	PROPN
ejpam-3029	334	2	math	math	PROPN
ejpam-3029	334	3	.	.	PUNCT
ejpam-3029	335	1	hungar	hungar	NOUN
ejpam-3029	335	2	,	,	PUNCT
ejpam-3029	335	3	137(1	137(1	NUM
ejpam-3029	335	4	-	-	SYM
ejpam-3029	335	5	2):130–138	2):130–138	NUM
ejpam-3029	335	6	,	,	PUNCT
ejpam-3029	335	7	2012	2012	NUM
ejpam-3029	335	8	.	.	PUNCT
ejpam-3029	336	1	[	[	X
ejpam-3029	336	2	9	9	NUM
ejpam-3029	336	3	]	]	PUNCT
ejpam-3029	336	4	k.	k.	PROPN
ejpam-3029	336	5	kuratowski	kuratowski	PROPN
ejpam-3029	336	6	.	.	PUNCT
ejpam-3029	337	1	topologies	topology	NOUN
ejpam-3029	337	2	i.	i.	PROPN
ejpam-3029	337	3	warszawa	warszawa	PROPN
ejpam-3029	337	4	,	,	PUNCT
ejpam-3029	337	5	1933	1933	NUM
ejpam-3029	337	6	.	.	PUNCT
ejpam-3029	338	1	[	[	X
ejpam-3029	338	2	10	10	NUM
ejpam-3029	338	3	]	]	X
ejpam-3029	338	4	w.	w.	PROPN
ejpam-3029	338	5	k.	k.	PROPN
ejpam-3029	338	6	min	min	PROPN
ejpam-3029	338	7	.	.	PROPN
ejpam-3029	338	8	(	(	PUNCT
ejpam-3029	338	9	δ	δ	PROPN
ejpam-3029	338	10	,	,	PUNCT
ejpam-3029	338	11	δ′)-continuity	δ′)-continuity	NOUN
ejpam-3029	338	12	on	on	ADP
ejpam-3029	338	13	generalized	generalized	ADJ
ejpam-3029	338	14	topological	topological	ADJ
ejpam-3029	338	15	spaces	space	NOUN
ejpam-3029	338	16	.	.	PUNCT
ejpam-3029	339	1	acta	acta	PROPN
ejpam-3029	339	2	math	math	PROPN
ejpam-3029	339	3	.	.	PUNCT
ejpam-3029	340	1	hungar	hungar	PROPN
ejpam-3029	340	2	,	,	PUNCT
ejpam-3029	340	3	131297(4):350–356	131297(4):350–356	NUM
ejpam-3029	340	4	,	,	PUNCT
ejpam-3029	340	5	2010	2010	NUM
ejpam-3029	340	6	.	.	PUNCT
ejpam-3029	341	1	[	[	X
ejpam-3029	341	2	11	11	NUM
ejpam-3029	341	3	]	]	PUNCT
ejpam-3029	341	4	w.	w.	PROPN
ejpam-3029	341	5	k.	k.	PROPN
ejpam-3029	341	6	min	min	PROPN
ejpam-3029	341	7	.	.	PROPN
ejpam-3029	341	8	generalized	generalize	VERB
ejpam-3029	341	9	continuous	continuous	ADJ
ejpam-3029	341	10	functions	function	NOUN
ejpam-3029	341	11	defined	define	VERB
ejpam-3029	341	12	by	by	ADP
ejpam-3029	341	13	generalized	generalized	ADJ
ejpam-3029	341	14	open	open	ADJ
ejpam-3029	341	15	sets	set	NOUN
ejpam-3029	341	16	on	on	ADP
ejpam-3029	341	17	generalized	generalized	ADJ
ejpam-3029	341	18	topological	topological	ADJ
ejpam-3029	341	19	spaces	space	NOUN
ejpam-3029	341	20	.	.	PUNCT
ejpam-3029	342	1	acta	acta	PROPN
ejpam-3029	342	2	math	math	PROPN
ejpam-3029	342	3	.	.	PUNCT
ejpam-3029	343	1	hungar	hungar	NOUN
ejpam-3029	343	2	,	,	PUNCT
ejpam-3029	343	3	128:299–306	128:299–306	NUM
ejpam-3029	343	4	,	,	PUNCT
ejpam-3029	343	5	2010	2010	NUM
ejpam-3029	343	6	.	.	PUNCT
ejpam-3029	344	1	[	[	X
ejpam-3029	344	2	12	12	NUM
ejpam-3029	344	3	]	]	PUNCT
ejpam-3029	344	4	w.	w.	PROPN
ejpam-3029	344	5	k.	k.	PROPN
ejpam-3029	344	6	min	min	PROPN
ejpam-3029	345	1	and	and	CCONJ
ejpam-3029	346	1	y.	y.	PROPN
ejpam-3029	346	2	k.	k.	PROPN
ejpam-3029	346	3	kim	kim	PROPN
ejpam-3029	346	4	.	.	PUNCT
ejpam-3029	347	1	some	some	DET
ejpam-3029	347	2	strong	strong	ADJ
ejpam-3029	347	3	forms	form	NOUN
ejpam-3029	347	4	of	of	ADP
ejpam-3029	347	5	(	(	PUNCT
ejpam-3029	347	6	g	g	PROPN
ejpam-3029	347	7	,	,	PUNCT
ejpam-3029	347	8	g)-continuity	g)-continuity	NOUN
ejpam-3029	347	9	on	on	ADP
ejpam-3029	347	10	generalized	generalized	ADJ
ejpam-3029	347	11	topological	topological	ADJ
ejpam-3029	347	12	spaces	space	NOUN
ejpam-3029	347	13	.	.	PUNCT
ejpam-3029	348	1	honam	honam	PROPN
ejpam-3029	348	2	math	math	PROPN
ejpam-3029	348	3	.	.	PUNCT
ejpam-3029	349	1	j	j	NOUN
ejpam-3029	349	2	,	,	PUNCT
ejpam-3029	349	3	33(1):85–91	33(1):85–91	NUM
ejpam-3029	349	4	,	,	PUNCT
ejpam-3029	349	5	2011	2011	NUM
ejpam-3029	349	6	.	.	PUNCT
ejpam-3029	350	1	[	[	X
ejpam-3029	350	2	13	13	NUM
ejpam-3029	350	3	]	]	SYM
ejpam-3029	350	4	w.k	w.k	PROPN
ejpam-3029	350	5	.	.	PROPN
ejpam-3029	350	6	min	min	PROPN
ejpam-3029	350	7	.	.	PROPN
ejpam-3029	350	8	almost	almost	ADV
ejpam-3029	350	9	continuity	continuity	NOUN
ejpam-3029	350	10	on	on	ADP
ejpam-3029	350	11	generalized	generalized	ADJ
ejpam-3029	350	12	topological	topological	ADJ
ejpam-3029	350	13	spaces	space	NOUN
ejpam-3029	350	14	.	.	PUNCT
ejpam-3029	351	1	acta	acta	PROPN
ejpam-3029	351	2	math	math	PROPN
ejpam-3029	351	3	.	.	PUNCT
ejpam-3029	352	1	hungar	hungar	NOUN
ejpam-3029	352	2	,	,	PUNCT
ejpam-3029	352	3	125:121–125	125:121–125	NUM
ejpam-3029	352	4	,	,	PUNCT
ejpam-3029	352	5	2009	2009	NUM
ejpam-3029	352	6	.	.	PUNCT
ejpam-3029	353	1	[	[	X
ejpam-3029	353	2	14	14	NUM
ejpam-3029	353	3	]	]	PUNCT
ejpam-3029	353	4	a.	a.	NOUN
ejpam-3029	353	5	qahis	qahis	PROPN
ejpam-3029	353	6	,	,	PUNCT
ejpam-3029	353	7	h.h	h.h	PROPN
ejpam-3029	353	8	.	.	PROPN
ejpam-3029	353	9	aljarrah	aljarrah	PROPN
ejpam-3029	353	10	,	,	PUNCT
ejpam-3029	353	11	and	and	CCONJ
ejpam-3029	353	12	t.	t.	PROPN
ejpam-3029	353	13	noiri	noiri	PROPN
ejpam-3029	353	14	.	.	PUNCT
ejpam-3029	354	1	weakly	weakly	ADJ
ejpam-3029	354	2	µ-compact	µ-compact	NOUN
ejpam-3029	354	3	via	via	ADP
ejpam-3029	354	4	a	a	DET
ejpam-3029	354	5	herediatary	herediatary	ADJ
ejpam-3029	354	6	class	class	NOUN
ejpam-3029	354	7	.	.	PUNCT
ejpam-3029	355	1	submitted	submit	VERB
ejpam-3029	355	2	.	.	PUNCT
ejpam-3029	356	1	[	[	X
ejpam-3029	356	2	15	15	NUM
ejpam-3029	356	3	]	]	X
ejpam-3029	356	4	m.	m.	NOUN
ejpam-3029	356	5	rajamani	rajamani	NOUN
ejpam-3029	356	6	and	and	CCONJ
ejpam-3029	356	7	w.	w.	PROPN
ejpam-3029	356	8	v.	v.	PROPN
ejpam-3029	356	9	ramesh	ramesh	PROPN
ejpam-3029	356	10	.	.	PUNCT
ejpam-3029	357	1	some	some	DET
ejpam-3029	357	2	new	new	ADJ
ejpam-3029	357	3	generalized	generalized	ADJ
ejpam-3029	357	4	topologies	topology	NOUN
ejpam-3029	357	5	via	via	ADP
ejpam-3029	357	6	hereditary	hereditary	ADJ
ejpam-3029	357	7	classes	class	NOUN
ejpam-3029	357	8	.	.	PUNCT
ejpam-3029	358	1	bol	bol	NOUN
ejpam-3029	358	2	.	.	PUNCT
ejpam-3029	359	1	soc	soc	PROPN
ejpam-3029	359	2	.	.	PUNCT
ejpam-3029	360	1	paran	paran	PROPN
ejpam-3029	360	2	.	.	PUNCT
ejpam-3029	361	1	mat	mat	PROPN
ejpam-3029	361	2	,	,	PUNCT
ejpam-3029	361	3	30(2):71–77	30(2):71–77	NUM
ejpam-3029	361	4	,	,	PUNCT
ejpam-3029	361	5	2012	2012	NUM
ejpam-3029	361	6	.	.	PUNCT
ejpam-3029	362	1	[	[	X
ejpam-3029	362	2	16	16	NUM
ejpam-3029	362	3	]	]	PUNCT
ejpam-3029	362	4	m.	m.	NOUN
ejpam-3029	362	5	s.	s.	PROPN
ejpam-3029	362	6	sarsak	sarsak	PROPN
ejpam-3029	362	7	.	.	PUNCT
ejpam-3029	363	1	on	on	ADP
ejpam-3029	363	2	µ-compact	µ-compact	PROPN
ejpam-3029	363	3	sets	set	NOUN
ejpam-3029	363	4	in	in	ADP
ejpam-3029	363	5	µ-spaces	µ-space	NOUN
ejpam-3029	363	6	.	.	PUNCT
ejpam-3029	364	1	questions	question	NOUN
ejpam-3029	364	2	answers	answer	VERB
ejpam-3029	364	3	general	general	ADJ
ejpam-3029	364	4	topology	topology	NOUN
ejpam-3029	364	5	,	,	PUNCT
ejpam-3029	364	6	31:49–57	31:49–57	NUM
ejpam-3029	364	7	,	,	PUNCT
ejpam-3029	364	8	2013	2013	NUM
ejpam-3029	364	9	.	.	PUNCT
ejpam-3029	365	1	[	[	X
ejpam-3029	365	2	17	17	NUM
ejpam-3029	365	3	]	]	X
ejpam-3029	365	4	m.s	m.s	PROPN
ejpam-3029	365	5	.	.	PROPN
ejpam-3029	365	6	sarsak	sarsak	PROPN
ejpam-3029	365	7	.	.	PUNCT
ejpam-3029	366	1	weakly	weakly	ADJ
ejpam-3029	366	2	µ-compact	µ-compact	PROPN
ejpam-3029	366	3	spaces	space	NOUN
ejpam-3029	366	4	.	.	PUNCT
ejpam-3029	367	1	demonstratio	demonstratio	PROPN
ejpam-3029	367	2	math	math	PROPN
ejpam-3029	367	3	,	,	PUNCT
ejpam-3029	367	4	45(2):929–938	45(2):929–938	PROPN
ejpam-3029	367	5	,	,	PUNCT
ejpam-3029	367	6	2012	2012	NUM
ejpam-3029	367	7	.	.	PUNCT
ejpam-3029	368	1	[	[	X
ejpam-3029	368	2	18	18	NUM
ejpam-3029	368	3	]	]	PUNCT
ejpam-3029	368	4	a.	a.	NOUN
ejpam-3029	368	5	m.	m.	PROPN
ejpam-3029	368	6	zahram	zahram	PROPN
ejpam-3029	368	7	,	,	PUNCT
ejpam-3029	368	8	k.	k.	PROPN
ejpam-3029	368	9	el	el	PROPN
ejpam-3029	368	10	-	-	PUNCT
ejpam-3029	368	11	saady	saady	NOUN
ejpam-3029	368	12	,	,	PUNCT
ejpam-3029	368	13	and	and	CCONJ
ejpam-3029	368	14	a.	a.	NOUN
ejpam-3029	368	15	ghareeb	ghareeb	NOUN
ejpam-3029	368	16	.	.	PUNCT
ejpam-3029	369	1	modification	modification	NOUN
ejpam-3029	369	2	of	of	ADP
ejpam-3029	369	3	weak	weak	ADJ
ejpam-3029	369	4	structures	structure	NOUN
ejpam-3029	369	5	via	via	ADP
ejpam-3029	369	6	hereditary	hereditary	ADJ
ejpam-3029	369	7	classes	class	NOUN
ejpam-3029	369	8	.	.	PUNCT
ejpam-3029	370	1	appl	appl	PROPN
ejpam-3029	370	2	.	.	PROPN
ejpam-3029	370	3	math	math	PROPN
ejpam-3029	370	4	.	.	PUNCT
ejpam-3029	371	1	letters	letter	NOUN
ejpam-3029	371	2	,	,	PUNCT
ejpam-3029	371	3	25(2):869–872	25(2):869–872	NUM
ejpam-3029	371	4	,	,	PUNCT
ejpam-3029	371	5	2012	2012	NUM
ejpam-3029	371	6	.	.	PUNCT