id	sid	tid	token	lemma	pos
ejpam-491	1	1	1_xxx_noiri.dvi	1_xxx_noiri.dvi	NUM
ejpam-491	1	2	european	european	ADJ
ejpam-491	1	3	journal	journal	NOUN
ejpam-491	1	4	of	of	ADP
ejpam-491	1	5	pure	pure	ADJ
ejpam-491	1	6	and	and	CCONJ
ejpam-491	1	7	applied	apply	VERB
ejpam-491	1	8	mathematics	mathematic	NOUN
ejpam-491	1	9	vol	vol	NOUN
ejpam-491	1	10	.	.	PROPN
ejpam-491	2	1	2	2	NUM
ejpam-491	2	2	,	,	PUNCT
ejpam-491	2	3	no	no	INTJ
ejpam-491	2	4	.	.	NOUN
ejpam-491	2	5	4	4	NUM
ejpam-491	2	6	,	,	PUNCT
ejpam-491	2	7	2009	2009	NUM
ejpam-491	2	8	,	,	PUNCT
ejpam-491	2	9	(	(	PUNCT
ejpam-491	2	10	473	473	NUM
ejpam-491	2	11	-	-	NUM
ejpam-491	2	12	493	493	NUM
ejpam-491	2	13	)	)	PUNCT
ejpam-491	2	14	issn	issn	PROPN
ejpam-491	2	15	1307	1307	NUM
ejpam-491	2	16	-	-	SYM
ejpam-491	2	17	5543	5543	NUM
ejpam-491	2	18	–	–	PUNCT
ejpam-491	2	19	www.ejpam.com	www.ejpam.com	X
ejpam-491	2	20	a	a	DET
ejpam-491	2	21	generalization	generalization	NOUN
ejpam-491	2	22	of	of	ADP
ejpam-491	2	23	some	some	DET
ejpam-491	2	24	forms	form	NOUN
ejpam-491	2	25	of	of	ADP
ejpam-491	2	26	g	g	NOUN
ejpam-491	2	27	-	-	PUNCT
ejpam-491	2	28	irresolute	irresolute	ADJ
ejpam-491	2	29	functions	function	NOUN
ejpam-491	2	30	takashi	takashi	PROPN
ejpam-491	2	31	noiri1∗	noiri1∗	PROPN
ejpam-491	2	32	and	and	CCONJ
ejpam-491	2	33	valeriu	valeriu	PROPN
ejpam-491	2	34	popa2	popa2	VERB
ejpam-491	2	35	1	1	NUM
ejpam-491	2	36	2949	2949	NUM
ejpam-491	2	37	-	-	SYM
ejpam-491	2	38	1	1	NUM
ejpam-491	2	39	shiokita	shiokita	NOUN
ejpam-491	2	40	-	-	PUNCT
ejpam-491	2	41	cho	cho	ADJ
ejpam-491	2	42	,	,	PUNCT
ejpam-491	2	43	hinagu	hinagu	ADJ
ejpam-491	2	44	,	,	PUNCT
ejpam-491	2	45	yatsushiro	yatsushiro	PROPN
ejpam-491	2	46	-	-	PUNCT
ejpam-491	2	47	shi	shi	PROPN
ejpam-491	2	48	,	,	PUNCT
ejpam-491	2	49	kumamoto	kumamoto	PROPN
ejpam-491	2	50	-	-	PUNCT
ejpam-491	2	51	ken	ken	PROPN
ejpam-491	2	52	,	,	PUNCT
ejpam-491	2	53	869	869	NUM
ejpam-491	2	54	-	-	SYM
ejpam-491	2	55	5142	5142	NUM
ejpam-491	2	56	japan	japan	PROPN
ejpam-491	2	57	2	2	NUM
ejpam-491	2	58	department	department	NOUN
ejpam-491	2	59	of	of	ADP
ejpam-491	2	60	mathematics	mathematic	NOUN
ejpam-491	2	61	,	,	PUNCT
ejpam-491	2	62	university	university	NOUN
ejpam-491	2	63	of	of	ADP
ejpam-491	2	64	bacǎu	bacǎu	PROPN
ejpam-491	2	65	,	,	PUNCT
ejpam-491	2	66	600	600	NUM
ejpam-491	2	67	114	114	NUM
ejpam-491	2	68	bacǎu	bacǎu	PROPN
ejpam-491	2	69	,	,	PUNCT
ejpam-491	2	70	romania	romania	PROPN
ejpam-491	2	71	abstract	abstract	NOUN
ejpam-491	2	72	.	.	PUNCT
ejpam-491	3	1	in	in	ADP
ejpam-491	3	2	this	this	DET
ejpam-491	3	3	paper	paper	NOUN
ejpam-491	3	4	,	,	PUNCT
ejpam-491	3	5	by	by	ADP
ejpam-491	3	6	using	use	VERB
ejpam-491	3	7	gm	gm	PROPN
ejpam-491	3	8	-	-	PUNCT
ejpam-491	3	9	closed	close	VERB
ejpam-491	3	10	sets	set	NOUN
ejpam-491	3	11	[	[	X
ejpam-491	3	12	27	27	NUM
ejpam-491	3	13	]	]	PUNCT
ejpam-491	3	14	,	,	PUNCT
ejpam-491	3	15	we	we	PRON
ejpam-491	3	16	obtain	obtain	VERB
ejpam-491	3	17	the	the	DET
ejpam-491	3	18	unified	unified	ADJ
ejpam-491	3	19	definitions	definition	NOUN
ejpam-491	3	20	and	and	CCONJ
ejpam-491	3	21	properties	property	NOUN
ejpam-491	3	22	for	for	ADP
ejpam-491	3	23	g	g	NOUN
ejpam-491	3	24	-	-	PUNCT
ejpam-491	3	25	continuity	continuity	NOUN
ejpam-491	3	26	,	,	PUNCT
ejpam-491	3	27	gs	gs	NOUN
ejpam-491	3	28	-	-	PUNCT
ejpam-491	3	29	continuity	continuity	NOUN
ejpam-491	3	30	,	,	PUNCT
ejpam-491	3	31	gp	gp	NOUN
ejpam-491	3	32	-	-	NOUN
ejpam-491	3	33	continuity	continuity	NOUN
ejpam-491	3	34	,	,	PUNCT
ejpam-491	3	35	αg	αg	NOUN
ejpam-491	3	36	-	-	PUNCT
ejpam-491	3	37	continuity	continuity	NOUN
ejpam-491	3	38	,	,	PUNCT
ejpam-491	3	39	γg	γg	ADJ
ejpam-491	3	40	-	-	PUNCT
ejpam-491	3	41	continuity	continuity	NOUN
ejpam-491	3	42	and	and	CCONJ
ejpam-491	3	43	gspcontinuity	gspcontinuity	NOUN
ejpam-491	3	44	.	.	PUNCT
ejpam-491	4	1	2000	2000	NUM
ejpam-491	4	2	mathematics	mathematic	NOUN
ejpam-491	4	3	subject	subject	NOUN
ejpam-491	4	4	classifications	classification	NOUN
ejpam-491	4	5	:	:	PUNCT
ejpam-491	4	6	54a05	54a05	NUM
ejpam-491	4	7	,	,	PUNCT
ejpam-491	4	8	54c08	54c08	NUM
ejpam-491	4	9	,	,	PUNCT
ejpam-491	4	10	54c10	54c10	NUM
ejpam-491	4	11	.	.	PUNCT
ejpam-491	5	1	key	key	ADJ
ejpam-491	5	2	words	word	NOUN
ejpam-491	5	3	and	and	CCONJ
ejpam-491	5	4	phrases	phrase	NOUN
ejpam-491	5	5	:	:	PUNCT
ejpam-491	5	6	m	m	NOUN
ejpam-491	5	7	-	-	NOUN
ejpam-491	5	8	structure	structure	NOUN
ejpam-491	5	9	,	,	PUNCT
ejpam-491	5	10	g	g	NOUN
ejpam-491	5	11	-	-	PUNCT
ejpam-491	5	12	closed	closed	ADJ
ejpam-491	5	13	,	,	PUNCT
ejpam-491	5	14	gm	gm	PROPN
ejpam-491	5	15	-	-	PUNCT
ejpam-491	5	16	closed	closed	ADJ
ejpam-491	5	17	,	,	PUNCT
ejpam-491	5	18	gm	gm	PROPN
ejpam-491	5	19	-	-	PUNCT
ejpam-491	5	20	continuous	continuous	ADJ
ejpam-491	5	21	.	.	PUNCT
ejpam-491	6	1	1	1	X
ejpam-491	6	2	.	.	X
ejpam-491	6	3	introduction	introduction	NOUN
ejpam-491	6	4	the	the	DET
ejpam-491	6	5	concept	concept	NOUN
ejpam-491	6	6	of	of	ADP
ejpam-491	6	7	generalized	generalize	VERB
ejpam-491	6	8	closed	close	VERB
ejpam-491	6	9	(	(	PUNCT
ejpam-491	6	10	briefly	briefly	NOUN
ejpam-491	6	11	g	g	NOUN
ejpam-491	6	12	-	-	PUNCT
ejpam-491	6	13	closed	closed	ADJ
ejpam-491	6	14	)	)	PUNCT
ejpam-491	6	15	sets	set	NOUN
ejpam-491	6	16	in	in	ADP
ejpam-491	6	17	topological	topological	ADJ
ejpam-491	6	18	spaces	space	NOUN
ejpam-491	6	19	was	be	AUX
ejpam-491	6	20	introduced	introduce	VERB
ejpam-491	6	21	by	by	ADP
ejpam-491	6	22	levine	levine	PROPN
ejpam-491	7	1	[	[	X
ejpam-491	7	2	20	20	NUM
ejpam-491	7	3	]	]	PUNCT
ejpam-491	7	4	in	in	ADP
ejpam-491	7	5	1970	1970	NUM
ejpam-491	7	6	.	.	PUNCT
ejpam-491	8	1	these	these	DET
ejpam-491	8	2	sets	set	NOUN
ejpam-491	8	3	were	be	AUX
ejpam-491	8	4	also	also	ADV
ejpam-491	8	5	considered	consider	VERB
ejpam-491	8	6	by	by	ADP
ejpam-491	8	7	dunham	dunham	PROPN
ejpam-491	9	1	[	[	X
ejpam-491	9	2	15	15	NUM
ejpam-491	9	3	]	]	PUNCT
ejpam-491	9	4	and	and	CCONJ
ejpam-491	9	5	dunham	dunham	PROPN
ejpam-491	9	6	and	and	CCONJ
ejpam-491	9	7	levine	levine	PROPN
ejpam-491	10	1	[	[	X
ejpam-491	10	2	16	16	NUM
ejpam-491	10	3	]	]	PUNCT
ejpam-491	10	4	.	.	PUNCT
ejpam-491	11	1	the	the	DET
ejpam-491	11	2	notion	notion	NOUN
ejpam-491	11	3	of	of	ADP
ejpam-491	11	4	αg	αg	NOUN
ejpam-491	11	5	-	-	PUNCT
ejpam-491	11	6	closed	closed	ADJ
ejpam-491	11	7	[	[	X
ejpam-491	11	8	12	12	NUM
ejpam-491	11	9	]	]	PUNCT
ejpam-491	11	10	(	(	PUNCT
ejpam-491	11	11	resp	resp	NOUN
ejpam-491	11	12	.	.	PUNCT
ejpam-491	12	1	gs	gs	NOUN
ejpam-491	12	2	-	-	PUNCT
ejpam-491	12	3	closed	close	VERB
ejpam-491	12	4	[	[	X
ejpam-491	12	5	11	11	NUM
ejpam-491	12	6	]	]	PUNCT
ejpam-491	12	7	,	,	PUNCT
ejpam-491	12	8	∗corresponding	∗corresponde	VERB
ejpam-491	12	9	author	author	NOUN
ejpam-491	12	10	.	.	PUNCT
ejpam-491	13	1	email	email	NOUN
ejpam-491	13	2	addresses	address	NOUN
ejpam-491	13	3	:	:	PUNCT
ejpam-491	13	4	t.noiri	t.noiri	X
ejpam-491	13	5	�	�	NOUN
ejpam-491	13	6	nifty	nifty	ADJ
ejpam-491	13	7	.	.	PUNCT
ejpam-491	14	1	om	om	PROPN
ejpam-491	14	2	(	(	PUNCT
ejpam-491	14	3	t.	t.	PROPN
ejpam-491	14	4	noiri	noiri	PROPN
ejpam-491	14	5	)	)	PUNCT
ejpam-491	14	6	,	,	PUNCT
ejpam-491	14	7	vpopa�ub.ro	vpopa�ub.ro	NOUN
ejpam-491	14	8	(	(	PUNCT
ejpam-491	14	9	v.	v.	ADP
ejpam-491	14	10	popa	popa	NOUN
ejpam-491	14	11	)	)	PUNCT
ejpam-491	14	12	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-491	15	1	473	473	NUM
ejpam-491	15	2	c	c	NOUN
ejpam-491	15	3	©	©	PROPN
ejpam-491	15	4	2009	2009	NUM
ejpam-491	15	5	ejpam	ejpam	NOUN
ejpam-491	15	6	all	all	DET
ejpam-491	15	7	rights	right	NOUN
ejpam-491	15	8	reserved	reserve	VERB
ejpam-491	15	9	.	.	PUNCT
ejpam-491	16	1	t.	t.	PROPN
ejpam-491	16	2	noiri	noiri	PROPN
ejpam-491	16	3	and	and	CCONJ
ejpam-491	16	4	v.	v.	ADP
ejpam-491	16	5	popa	popa	NOUN
ejpam-491	16	6	/	/	SYM
ejpam-491	16	7	eur	eur	PROPN
ejpam-491	16	8	.	.	PUNCT
ejpam-491	17	1	j.	j.	PROPN
ejpam-491	17	2	pure	pure	PROPN
ejpam-491	17	3	appl	appl	PROPN
ejpam-491	17	4	.	.	PROPN
ejpam-491	17	5	math	math	PROPN
ejpam-491	17	6	,	,	PUNCT
ejpam-491	17	7	2	2	NUM
ejpam-491	17	8	(	(	PUNCT
ejpam-491	17	9	2009	2009	NUM
ejpam-491	17	10	)	)	PUNCT
ejpam-491	17	11	,	,	PUNCT
ejpam-491	17	12	(	(	PUNCT
ejpam-491	17	13	473	473	NUM
ejpam-491	17	14	-	-	NUM
ejpam-491	17	15	493	493	NUM
ejpam-491	17	16	)	)	PUNCT
ejpam-491	17	17	474	474	NUM
ejpam-491	17	18	gp	gp	NOUN
ejpam-491	17	19	-	-	ADJ
ejpam-491	17	20	closed	closed	ADJ
ejpam-491	17	21	[	[	X
ejpam-491	17	22	6	6	NUM
ejpam-491	17	23	]	]	PUNCT
ejpam-491	17	24	,	,	PUNCT
ejpam-491	17	25	g	g	PROPN
ejpam-491	17	26	b	b	X
ejpam-491	17	27	-	-	PUNCT
ejpam-491	17	28	closed	closed	ADJ
ejpam-491	17	29	or	or	CCONJ
ejpam-491	17	30	γg	γg	ADV
ejpam-491	17	31	-	-	PUNCT
ejpam-491	17	32	closed	closed	ADJ
ejpam-491	17	33	[	[	X
ejpam-491	17	34	18	18	NUM
ejpam-491	17	35	]	]	PUNCT
ejpam-491	17	36	,	,	PUNCT
ejpam-491	17	37	gsp	gsp	NOUN
ejpam-491	17	38	-	-	PUNCT
ejpam-491	17	39	closed	close	VERB
ejpam-491	17	40	or	or	CCONJ
ejpam-491	17	41	gβ	gβ	NOUN
ejpam-491	17	42	-closed	-closed	ADJ
ejpam-491	17	43	[	[	X
ejpam-491	17	44	14	14	NUM
ejpam-491	17	45	]	]	PUNCT
ejpam-491	17	46	)	)	PUNCT
ejpam-491	17	47	sets	set	NOUN
ejpam-491	17	48	is	be	AUX
ejpam-491	17	49	introduced	introduce	VERB
ejpam-491	17	50	and	and	CCONJ
ejpam-491	17	51	investigated	investigate	VERB
ejpam-491	17	52	.	.	PUNCT
ejpam-491	18	1	in	in	ADP
ejpam-491	18	2	1981	1981	NUM
ejpam-491	18	3	,	,	PUNCT
ejpam-491	18	4	munshy	munshy	ADJ
ejpam-491	18	5	and	and	CCONJ
ejpam-491	18	6	bassan	bassan	NOUN
ejpam-491	18	7	[	[	X
ejpam-491	18	8	25	25	NUM
ejpam-491	18	9	]	]	PUNCT
ejpam-491	18	10	introduced	introduce	VERB
ejpam-491	18	11	the	the	DET
ejpam-491	18	12	notion	notion	NOUN
ejpam-491	18	13	of	of	ADP
ejpam-491	18	14	generalized	generalized	ADJ
ejpam-491	18	15	continuous	continuous	ADJ
ejpam-491	18	16	(	(	PUNCT
ejpam-491	18	17	briefly	briefly	NOUN
ejpam-491	18	18	g	g	NOUN
ejpam-491	18	19	-	-	PUNCT
ejpam-491	18	20	continuous	continuous	ADJ
ejpam-491	18	21	)	)	PUNCT
ejpam-491	18	22	functions	function	NOUN
ejpam-491	18	23	which	which	PRON
ejpam-491	18	24	are	be	AUX
ejpam-491	18	25	called	call	VERB
ejpam-491	18	26	in	in	ADP
ejpam-491	18	27	[	[	X
ejpam-491	18	28	7	7	NUM
ejpam-491	18	29	]	]	PUNCT
ejpam-491	18	30	as	as	ADP
ejpam-491	18	31	g	g	NOUN
ejpam-491	18	32	-	-	PUNCT
ejpam-491	18	33	irresolute	irresolute	ADJ
ejpam-491	18	34	functions	function	NOUN
ejpam-491	18	35	.	.	PUNCT
ejpam-491	19	1	furthermore	furthermore	ADV
ejpam-491	19	2	,	,	PUNCT
ejpam-491	19	3	the	the	DET
ejpam-491	19	4	notion	notion	NOUN
ejpam-491	19	5	of	of	ADP
ejpam-491	19	6	gs	gs	NOUN
ejpam-491	19	7	-	-	PUNCT
ejpam-491	19	8	irresolute	irresolute	ADJ
ejpam-491	19	9	[	[	X
ejpam-491	19	10	11	11	NUM
ejpam-491	19	11	]	]	PUNCT
ejpam-491	19	12	(	(	PUNCT
ejpam-491	19	13	resp	resp	NOUN
ejpam-491	19	14	.	.	PUNCT
ejpam-491	20	1	gpirresolute	gpirresolute	PROPN
ejpam-491	21	1	[	[	X
ejpam-491	21	2	6	6	NUM
ejpam-491	21	3	]	]	PUNCT
ejpam-491	21	4	,	,	PUNCT
ejpam-491	21	5	αg	αg	NOUN
ejpam-491	21	6	-	-	PUNCT
ejpam-491	21	7	irresolute	irresolute	NOUN
ejpam-491	22	1	[	[	X
ejpam-491	22	2	12	12	NUM
ejpam-491	22	3	]	]	PUNCT
ejpam-491	22	4	,	,	PUNCT
ejpam-491	22	5	g	g	PROPN
ejpam-491	22	6	b	b	X
ejpam-491	22	7	-	-	PUNCT
ejpam-491	22	8	irresolute	irresolute	ADJ
ejpam-491	23	1	[	[	X
ejpam-491	23	2	3	3	NUM
ejpam-491	23	3	]	]	PUNCT
ejpam-491	23	4	,	,	PUNCT
ejpam-491	23	5	gsp	gsp	NOUN
ejpam-491	23	6	-	-	PUNCT
ejpam-491	23	7	irresolute	irresolute	NOUN
ejpam-491	23	8	[	[	X
ejpam-491	23	9	32	32	NUM
ejpam-491	23	10	]	]	SYM
ejpam-491	23	11	)	)	PUNCT
ejpam-491	23	12	functions	function	NOUN
ejpam-491	23	13	is	be	AUX
ejpam-491	23	14	introduced	introduce	VERB
ejpam-491	23	15	.	.	PUNCT
ejpam-491	24	1	recently	recently	ADV
ejpam-491	24	2	,	,	PUNCT
ejpam-491	24	3	the	the	DET
ejpam-491	24	4	present	present	ADJ
ejpam-491	24	5	authors	author	NOUN
ejpam-491	24	6	[	[	X
ejpam-491	24	7	29	29	NUM
ejpam-491	24	8	]	]	PUNCT
ejpam-491	24	9	,	,	PUNCT
ejpam-491	24	10	[	[	X
ejpam-491	24	11	30	30	NUM
ejpam-491	24	12	]	]	PUNCT
ejpam-491	24	13	have	have	AUX
ejpam-491	24	14	introduced	introduce	VERB
ejpam-491	24	15	the	the	DET
ejpam-491	24	16	notions	notion	NOUN
ejpam-491	24	17	of	of	ADP
ejpam-491	24	18	m	m	NOUN
ejpam-491	24	19	-	-	PUNCT
ejpam-491	24	20	structures	structure	NOUN
ejpam-491	24	21	,	,	PUNCT
ejpam-491	24	22	m	m	NOUN
ejpam-491	24	23	-	-	NOUN
ejpam-491	24	24	spaces	space	NOUN
ejpam-491	24	25	and	and	CCONJ
ejpam-491	24	26	m	m	NOUN
ejpam-491	24	27	-continuity	-continuity	ADJ
ejpam-491	24	28	.	.	PUNCT
ejpam-491	25	1	in	in	ADP
ejpam-491	25	2	[	[	X
ejpam-491	25	3	27	27	NUM
ejpam-491	25	4	]	]	PUNCT
ejpam-491	25	5	,	,	PUNCT
ejpam-491	25	6	the	the	DET
ejpam-491	25	7	first	first	ADJ
ejpam-491	25	8	author	author	NOUN
ejpam-491	25	9	introduced	introduce	VERB
ejpam-491	25	10	the	the	DET
ejpam-491	25	11	notion	notion	NOUN
ejpam-491	25	12	of	of	ADP
ejpam-491	25	13	generalized	generalized	ADJ
ejpam-491	25	14	m	m	NOUN
ejpam-491	25	15	-	-	ADJ
ejpam-491	25	16	closed	closed	ADJ
ejpam-491	25	17	(	(	PUNCT
ejpam-491	25	18	briefly	briefly	NOUN
ejpam-491	25	19	gm	gm	NOUN
ejpam-491	25	20	-	-	PUNCT
ejpam-491	25	21	closed	closed	ADJ
ejpam-491	25	22	)	)	PUNCT
ejpam-491	25	23	sets	set	NOUN
ejpam-491	25	24	and	and	CCONJ
ejpam-491	25	25	tried	try	VERB
ejpam-491	25	26	to	to	PART
ejpam-491	25	27	unify	unify	VERB
ejpam-491	25	28	certain	certain	ADJ
ejpam-491	25	29	types	type	NOUN
ejpam-491	25	30	of	of	ADP
ejpam-491	25	31	modifications	modification	NOUN
ejpam-491	25	32	of	of	ADP
ejpam-491	25	33	g	g	NOUN
ejpam-491	25	34	-	-	PUNCT
ejpam-491	25	35	closed	close	VERB
ejpam-491	25	36	sets	set	NOUN
ejpam-491	25	37	such	such	ADJ
ejpam-491	25	38	as	as	SCONJ
ejpam-491	25	39	stated	state	VERB
ejpam-491	25	40	above	above	ADV
ejpam-491	25	41	.	.	PUNCT
ejpam-491	26	1	in	in	ADP
ejpam-491	26	2	this	this	DET
ejpam-491	26	3	paper	paper	NOUN
ejpam-491	26	4	,	,	PUNCT
ejpam-491	26	5	by	by	ADP
ejpam-491	26	6	using	use	VERB
ejpam-491	26	7	gm	gm	PROPN
ejpam-491	26	8	-	-	PUNCT
ejpam-491	26	9	closed	close	VERB
ejpam-491	26	10	sets	set	NOUN
ejpam-491	26	11	,	,	PUNCT
ejpam-491	26	12	we	we	PRON
ejpam-491	26	13	obtain	obtain	VERB
ejpam-491	26	14	the	the	DET
ejpam-491	26	15	unified	unified	ADJ
ejpam-491	26	16	definitions	definition	NOUN
ejpam-491	26	17	and	and	CCONJ
ejpam-491	26	18	properties	property	NOUN
ejpam-491	26	19	for	for	ADP
ejpam-491	26	20	g	g	NOUN
ejpam-491	26	21	-	-	PUNCT
ejpam-491	26	22	irresoluteness	irresoluteness	NOUN
ejpam-491	26	23	,	,	PUNCT
ejpam-491	26	24	gs	gs	NOUN
ejpam-491	26	25	-	-	PUNCT
ejpam-491	26	26	irresoluteness	irresoluteness	NOUN
ejpam-491	26	27	,	,	PUNCT
ejpam-491	26	28	gp	gp	NOUN
ejpam-491	26	29	-	-	PUNCT
ejpam-491	26	30	irresoluteness	irresoluteness	NOUN
ejpam-491	26	31	,	,	PUNCT
ejpam-491	26	32	αg	αg	NOUN
ejpam-491	26	33	-	-	PUNCT
ejpam-491	26	34	irresoluteness	irresoluteness	NOUN
ejpam-491	26	35	,	,	PUNCT
ejpam-491	26	36	g	g	PROPN
ejpam-491	26	37	b	b	PROPN
ejpam-491	26	38	-	-	PUNCT
ejpam-491	26	39	irresoluteness	irresoluteness	NOUN
ejpam-491	26	40	and	and	CCONJ
ejpam-491	26	41	gsp	gsp	NOUN
ejpam-491	26	42	-	-	PUNCT
ejpam-491	26	43	irresoluteness	irresoluteness	NOUN
ejpam-491	26	44	.	.	PUNCT
ejpam-491	27	1	2	2	X
ejpam-491	27	2	.	.	X
ejpam-491	27	3	preliminaries	preliminary	NOUN
ejpam-491	27	4	let	let	VERB
ejpam-491	27	5	(	(	PUNCT
ejpam-491	27	6	x	x	X
ejpam-491	27	7	,	,	PUNCT
ejpam-491	27	8	τ	τ	X
ejpam-491	27	9	)	)	PUNCT
ejpam-491	27	10	be	be	VERB
ejpam-491	27	11	a	a	DET
ejpam-491	27	12	topological	topological	ADJ
ejpam-491	27	13	space	space	NOUN
ejpam-491	27	14	and	and	CCONJ
ejpam-491	27	15	a	a	DET
ejpam-491	27	16	a	a	DET
ejpam-491	27	17	subset	subset	NOUN
ejpam-491	27	18	of	of	ADP
ejpam-491	27	19	x	x	PRON
ejpam-491	27	20	.	.	PUNCT
ejpam-491	28	1	the	the	DET
ejpam-491	28	2	closure	closure	NOUN
ejpam-491	28	3	of	of	ADP
ejpam-491	28	4	a	a	PRON
ejpam-491	28	5	and	and	CCONJ
ejpam-491	28	6	the	the	DET
ejpam-491	28	7	interior	interior	NOUN
ejpam-491	28	8	of	of	ADP
ejpam-491	28	9	a	a	PRON
ejpam-491	28	10	are	be	AUX
ejpam-491	28	11	denoted	denote	VERB
ejpam-491	28	12	by	by	ADP
ejpam-491	28	13	cl(a	cl(a	NOUN
ejpam-491	28	14	)	)	PUNCT
ejpam-491	28	15	and	and	CCONJ
ejpam-491	28	16	int(a	int(a	PROPN
ejpam-491	28	17	)	)	PUNCT
ejpam-491	28	18	,	,	PUNCT
ejpam-491	28	19	respectively	respectively	ADV
ejpam-491	28	20	.	.	PUNCT
ejpam-491	29	1	we	we	PRON
ejpam-491	29	2	recall	recall	VERB
ejpam-491	29	3	some	some	DET
ejpam-491	29	4	generalized	generalize	VERB
ejpam-491	29	5	open	open	ADJ
ejpam-491	29	6	sets	set	NOUN
ejpam-491	29	7	in	in	ADP
ejpam-491	29	8	topological	topological	ADJ
ejpam-491	29	9	spaces	space	NOUN
ejpam-491	29	10	.	.	PUNCT
ejpam-491	30	1	definition	definition	NOUN
ejpam-491	30	2	1	1	NUM
ejpam-491	30	3	.	.	PUNCT
ejpam-491	31	1	let	let	AUX
ejpam-491	31	2	(	(	PUNCT
ejpam-491	31	3	x	x	X
ejpam-491	31	4	,	,	PUNCT
ejpam-491	31	5	τ	τ	X
ejpam-491	31	6	)	)	PUNCT
ejpam-491	31	7	be	be	VERB
ejpam-491	31	8	a	a	DET
ejpam-491	31	9	topological	topological	ADJ
ejpam-491	31	10	space	space	NOUN
ejpam-491	31	11	.	.	PUNCT
ejpam-491	32	1	a	a	DET
ejpam-491	32	2	subset	subset	NOUN
ejpam-491	32	3	a	a	PRON
ejpam-491	32	4	of	of	ADP
ejpam-491	32	5	x	x	SYM
ejpam-491	32	6	is	be	AUX
ejpam-491	32	7	said	say	VERB
ejpam-491	32	8	to	to	PART
ejpam-491	32	9	be	be	AUX
ejpam-491	32	10	(	(	PUNCT
ejpam-491	32	11	1	1	X
ejpam-491	32	12	)	)	PUNCT
ejpam-491	32	13	α	α	NOUN
ejpam-491	32	14	-	-	ADJ
ejpam-491	32	15	open	open	ADJ
ejpam-491	33	1	[	[	X
ejpam-491	33	2	26	26	NUM
ejpam-491	33	3	]	]	X
ejpam-491	33	4	if	if	SCONJ
ejpam-491	33	5	a⊂	a⊂	ADP
ejpam-491	33	6	int(cl(int(a	int(cl(int(a	NOUN
ejpam-491	33	7	)	)	PUNCT
ejpam-491	33	8	)	)	PUNCT
ejpam-491	33	9	)	)	PUNCT
ejpam-491	33	10	,	,	PUNCT
ejpam-491	33	11	(	(	PUNCT
ejpam-491	33	12	2	2	X
ejpam-491	33	13	)	)	PUNCT
ejpam-491	33	14	semi	semi	ADJ
ejpam-491	33	15	-	-	ADJ
ejpam-491	33	16	open	open	ADJ
ejpam-491	33	17	[	[	X
ejpam-491	33	18	19	19	NUM
ejpam-491	33	19	]	]	X
ejpam-491	33	20	if	if	SCONJ
ejpam-491	33	21	a⊂	a⊂	PRON
ejpam-491	33	22	cl(int(a	cl(int(a	NOUN
ejpam-491	33	23	)	)	PUNCT
ejpam-491	33	24	)	)	PUNCT
ejpam-491	34	1	,	,	PUNCT
ejpam-491	34	2	(	(	PUNCT
ejpam-491	34	3	3	3	X
ejpam-491	34	4	)	)	PUNCT
ejpam-491	34	5	preopen	preopen	NOUN
ejpam-491	34	6	[	[	X
ejpam-491	34	7	22	22	NUM
ejpam-491	34	8	]	]	PUNCT
ejpam-491	34	9	if	if	SCONJ
ejpam-491	34	10	a⊂	a⊂	PRON
ejpam-491	34	11	int(cl(a	int(cl(a	PROPN
ejpam-491	34	12	)	)	PUNCT
ejpam-491	34	13	)	)	PUNCT
ejpam-491	34	14	,	,	PUNCT
ejpam-491	34	15	(	(	PUNCT
ejpam-491	34	16	4	4	X
ejpam-491	34	17	)	)	PUNCT
ejpam-491	34	18	β	β	X
ejpam-491	34	19	-open	-open	NOUN
ejpam-491	35	1	[	[	X
ejpam-491	35	2	1	1	NUM
ejpam-491	35	3	]	]	PUNCT
ejpam-491	35	4	or	or	CCONJ
ejpam-491	35	5	semi	semi	ADJ
ejpam-491	35	6	-	-	ADJ
ejpam-491	35	7	preopen	preopen	ADJ
ejpam-491	35	8	[	[	X
ejpam-491	35	9	4	4	NUM
ejpam-491	35	10	]	]	X
ejpam-491	35	11	if	if	SCONJ
ejpam-491	35	12	a⊂	a⊂	DET
ejpam-491	35	13	cl(int(cl(a	cl(int(cl(a	NOUN
ejpam-491	35	14	)	)	PUNCT
ejpam-491	35	15	)	)	PUNCT
ejpam-491	35	16	)	)	PUNCT
ejpam-491	35	17	,	,	PUNCT
ejpam-491	35	18	(	(	PUNCT
ejpam-491	35	19	5	5	X
ejpam-491	35	20	)	)	PUNCT
ejpam-491	35	21	γ	γ	NOUN
ejpam-491	35	22	-	-	ADJ
ejpam-491	35	23	open	open	ADJ
ejpam-491	35	24	[	[	X
ejpam-491	35	25	18	18	NUM
ejpam-491	35	26	]	]	PUNCT
ejpam-491	35	27	or	or	CCONJ
ejpam-491	35	28	b	b	X
ejpam-491	35	29	-	-	PUNCT
ejpam-491	35	30	open	open	ADJ
ejpam-491	35	31	[	[	X
ejpam-491	35	32	5	5	NUM
ejpam-491	35	33	]	]	PUNCT
ejpam-491	35	34	if	if	SCONJ
ejpam-491	35	35	a⊂	a⊂	PRON
ejpam-491	35	36	int(cl(a))∪cl(int(a	int(cl(a))∪cl(int(a	NOUN
ejpam-491	35	37	)	)	PUNCT
ejpam-491	35	38	)	)	PUNCT
ejpam-491	35	39	.	.	PUNCT
ejpam-491	36	1	the	the	DET
ejpam-491	36	2	family	family	NOUN
ejpam-491	36	3	of	of	ADP
ejpam-491	36	4	all	all	DET
ejpam-491	36	5	α	α	NOUN
ejpam-491	36	6	-	-	ADJ
ejpam-491	36	7	open	open	ADJ
ejpam-491	36	8	(	(	PUNCT
ejpam-491	36	9	resp	resp	NOUN
ejpam-491	36	10	.	.	PUNCT
ejpam-491	37	1	semi	semi	ADJ
ejpam-491	37	2	-	-	ADJ
ejpam-491	37	3	open	open	ADJ
ejpam-491	37	4	,	,	PUNCT
ejpam-491	37	5	preopen	preopen	ADJ
ejpam-491	37	6	,	,	PUNCT
ejpam-491	37	7	β	β	X
ejpam-491	37	8	-open	-open	PROPN
ejpam-491	37	9	,	,	PUNCT
ejpam-491	37	10	γ	γ	NOUN
ejpam-491	37	11	-	-	ADJ
ejpam-491	37	12	open	open	ADJ
ejpam-491	37	13	)	)	PUNCT
ejpam-491	37	14	sets	set	NOUN
ejpam-491	37	15	in	in	ADP
ejpam-491	37	16	(	(	PUNCT
ejpam-491	37	17	x	x	INTJ
ejpam-491	37	18	,	,	PUNCT
ejpam-491	37	19	τ	τ	X
ejpam-491	37	20	)	)	PUNCT
ejpam-491	37	21	is	be	AUX
ejpam-491	37	22	denoted	denote	VERB
ejpam-491	37	23	by	by	ADP
ejpam-491	37	24	α(x	α(x	PROPN
ejpam-491	37	25	)	)	PUNCT
ejpam-491	37	26	(	(	PUNCT
ejpam-491	37	27	resp	resp	NOUN
ejpam-491	37	28	.	.	PUNCT
ejpam-491	37	29	so(x	so(x	PROPN
ejpam-491	37	30	)	)	PUNCT
ejpam-491	37	31	,	,	PUNCT
ejpam-491	37	32	po(x	po(x	NUM
ejpam-491	37	33	)	)	PUNCT
ejpam-491	37	34	,	,	PUNCT
ejpam-491	37	35	β(x	β(x	NOUN
ejpam-491	37	36	)	)	PUNCT
ejpam-491	37	37	or	or	CCONJ
ejpam-491	37	38	spo(x	spo(x	PROPN
ejpam-491	37	39	)	)	PUNCT
ejpam-491	37	40	,	,	PUNCT
ejpam-491	37	41	γ(x	γ(x	NOUN
ejpam-491	37	42	)	)	PUNCT
ejpam-491	37	43	or	or	CCONJ
ejpam-491	37	44	bo(x	bo(x	NUM
ejpam-491	37	45	)	)	PUNCT
ejpam-491	37	46	)	)	PUNCT
ejpam-491	37	47	.	.	PUNCT
ejpam-491	38	1	t.	t.	PROPN
ejpam-491	38	2	noiri	noiri	PROPN
ejpam-491	38	3	and	and	CCONJ
ejpam-491	38	4	v.	v.	ADP
ejpam-491	38	5	popa	popa	NOUN
ejpam-491	38	6	/	/	SYM
ejpam-491	38	7	eur	eur	PROPN
ejpam-491	38	8	.	.	PUNCT
ejpam-491	39	1	j.	j.	PROPN
ejpam-491	39	2	pure	pure	PROPN
ejpam-491	39	3	appl	appl	PROPN
ejpam-491	39	4	.	.	PROPN
ejpam-491	39	5	math	math	PROPN
ejpam-491	39	6	,	,	PUNCT
ejpam-491	39	7	2	2	NUM
ejpam-491	39	8	(	(	PUNCT
ejpam-491	39	9	2009	2009	NUM
ejpam-491	39	10	)	)	PUNCT
ejpam-491	39	11	,	,	PUNCT
ejpam-491	39	12	(	(	PUNCT
ejpam-491	39	13	473	473	NUM
ejpam-491	39	14	-	-	NUM
ejpam-491	39	15	493	493	NUM
ejpam-491	39	16	)	)	PUNCT
ejpam-491	39	17	475	475	NUM
ejpam-491	39	18	definition	definition	NOUN
ejpam-491	39	19	2	2	NUM
ejpam-491	39	20	.	.	PUNCT
ejpam-491	40	1	let	let	AUX
ejpam-491	40	2	(	(	PUNCT
ejpam-491	40	3	x	x	X
ejpam-491	40	4	,	,	PUNCT
ejpam-491	40	5	τ	τ	X
ejpam-491	40	6	)	)	PUNCT
ejpam-491	40	7	be	be	VERB
ejpam-491	40	8	a	a	DET
ejpam-491	40	9	topological	topological	ADJ
ejpam-491	40	10	space	space	NOUN
ejpam-491	40	11	.	.	PUNCT
ejpam-491	41	1	a	a	DET
ejpam-491	41	2	subset	subset	NOUN
ejpam-491	41	3	a	a	PRON
ejpam-491	41	4	of	of	ADP
ejpam-491	41	5	x	x	SYM
ejpam-491	41	6	is	be	AUX
ejpam-491	41	7	said	say	VERB
ejpam-491	41	8	to	to	PART
ejpam-491	41	9	be	be	AUX
ejpam-491	41	10	αclosed	αclose	VERB
ejpam-491	42	1	[	[	X
ejpam-491	42	2	23	23	NUM
ejpam-491	42	3	]	]	PUNCT
ejpam-491	42	4	(	(	PUNCT
ejpam-491	42	5	resp	resp	NOUN
ejpam-491	42	6	.	.	PUNCT
ejpam-491	43	1	semi	semi	ADJ
ejpam-491	43	2	-	-	ADJ
ejpam-491	43	3	closed	closed	ADJ
ejpam-491	43	4	[	[	X
ejpam-491	43	5	10	10	NUM
ejpam-491	43	6	]	]	PUNCT
ejpam-491	43	7	,	,	PUNCT
ejpam-491	43	8	preclosed	preclose	VERB
ejpam-491	43	9	[	[	X
ejpam-491	43	10	22	22	NUM
ejpam-491	43	11	]	]	PUNCT
ejpam-491	43	12	,	,	PUNCT
ejpam-491	43	13	β	β	X
ejpam-491	43	14	-closed	-close	VERB
ejpam-491	44	1	[	[	X
ejpam-491	44	2	1	1	NUM
ejpam-491	44	3	]	]	PUNCT
ejpam-491	44	4	or	or	CCONJ
ejpam-491	44	5	semi	semi	ADV
ejpam-491	44	6	-	-	ADJ
ejpam-491	44	7	preclosed	preclosed	ADJ
ejpam-491	45	1	[	[	X
ejpam-491	45	2	4	4	NUM
ejpam-491	45	3	]	]	PUNCT
ejpam-491	45	4	,	,	PUNCT
ejpam-491	45	5	γ	γ	X
ejpam-491	45	6	-	-	ADJ
ejpam-491	45	7	closed	closed	ADJ
ejpam-491	45	8	[	[	X
ejpam-491	45	9	18	18	NUM
ejpam-491	45	10	]	]	PUNCT
ejpam-491	45	11	or	or	CCONJ
ejpam-491	45	12	b	b	X
ejpam-491	45	13	-	-	PUNCT
ejpam-491	45	14	closed	closed	ADJ
ejpam-491	45	15	[	[	X
ejpam-491	45	16	5	5	NUM
ejpam-491	45	17	]	]	PUNCT
ejpam-491	45	18	)	)	PUNCT
ejpam-491	45	19	if	if	SCONJ
ejpam-491	45	20	the	the	DET
ejpam-491	45	21	complement	complement	NOUN
ejpam-491	45	22	of	of	ADP
ejpam-491	45	23	a	a	PRON
ejpam-491	45	24	is	be	AUX
ejpam-491	45	25	α	α	NOUN
ejpam-491	45	26	-	-	ADJ
ejpam-491	45	27	open	open	ADJ
ejpam-491	45	28	(	(	PUNCT
ejpam-491	45	29	resp	resp	NOUN
ejpam-491	45	30	.	.	PUNCT
ejpam-491	46	1	semi	semi	ADJ
ejpam-491	46	2	-	-	ADJ
ejpam-491	46	3	open	open	ADJ
ejpam-491	46	4	,	,	PUNCT
ejpam-491	46	5	preopen	preopen	ADJ
ejpam-491	46	6	,	,	PUNCT
ejpam-491	46	7	β	β	X
ejpam-491	46	8	-open	-open	PROPN
ejpam-491	46	9	,	,	PUNCT
ejpam-491	46	10	γ	γ	NOUN
ejpam-491	46	11	-	-	ADJ
ejpam-491	46	12	open	open	ADJ
ejpam-491	46	13	)	)	PUNCT
ejpam-491	46	14	.	.	PUNCT
ejpam-491	47	1	definition	definition	NOUN
ejpam-491	47	2	3	3	X
ejpam-491	47	3	.	.	PUNCT
ejpam-491	48	1	let	let	AUX
ejpam-491	48	2	(	(	PUNCT
ejpam-491	48	3	x	x	X
ejpam-491	48	4	,	,	PUNCT
ejpam-491	48	5	τ	τ	X
ejpam-491	48	6	)	)	PUNCT
ejpam-491	48	7	be	be	VERB
ejpam-491	48	8	a	a	DET
ejpam-491	48	9	topological	topological	ADJ
ejpam-491	48	10	space	space	NOUN
ejpam-491	48	11	and	and	CCONJ
ejpam-491	48	12	a	a	DET
ejpam-491	48	13	a	a	DET
ejpam-491	48	14	subset	subset	NOUN
ejpam-491	48	15	of	of	ADP
ejpam-491	48	16	x	x	PRON
ejpam-491	48	17	.	.	PUNCT
ejpam-491	49	1	the	the	DET
ejpam-491	49	2	intersection	intersection	NOUN
ejpam-491	49	3	of	of	ADP
ejpam-491	49	4	all	all	DET
ejpam-491	49	5	α	α	PRON
ejpam-491	49	6	-	-	ADJ
ejpam-491	49	7	closed	closed	ADJ
ejpam-491	49	8	(	(	PUNCT
ejpam-491	49	9	resp	resp	NOUN
ejpam-491	49	10	.	.	PUNCT
ejpam-491	50	1	semi	semi	ADJ
ejpam-491	50	2	-	-	ADJ
ejpam-491	50	3	closed	closed	ADJ
ejpam-491	50	4	,	,	PUNCT
ejpam-491	50	5	preclosed	preclose	VERB
ejpam-491	50	6	,	,	PUNCT
ejpam-491	50	7	β	β	X
ejpam-491	50	8	-closed	-closed	PROPN
ejpam-491	50	9	,	,	PUNCT
ejpam-491	50	10	γ	γ	NOUN
ejpam-491	50	11	-	-	ADJ
ejpam-491	50	12	closed	closed	ADJ
ejpam-491	50	13	)	)	PUNCT
ejpam-491	50	14	sets	set	NOUN
ejpam-491	50	15	of	of	ADP
ejpam-491	50	16	x	x	PUNCT
ejpam-491	50	17	containing	contain	VERB
ejpam-491	50	18	a	a	PRON
ejpam-491	50	19	is	be	AUX
ejpam-491	50	20	called	call	VERB
ejpam-491	50	21	the	the	DET
ejpam-491	50	22	α	α	NOUN
ejpam-491	50	23	-	-	NOUN
ejpam-491	50	24	closure	closure	NOUN
ejpam-491	50	25	[	[	X
ejpam-491	50	26	23	23	NUM
ejpam-491	50	27	]	]	PUNCT
ejpam-491	50	28	(	(	PUNCT
ejpam-491	50	29	resp	resp	NOUN
ejpam-491	50	30	.	.	PUNCT
ejpam-491	50	31	semi	semi	NOUN
ejpam-491	50	32	-	-	NOUN
ejpam-491	50	33	closure	closure	ADJ
ejpam-491	50	34	[	[	X
ejpam-491	50	35	10	10	NUM
ejpam-491	50	36	]	]	PUNCT
ejpam-491	50	37	,	,	PUNCT
ejpam-491	50	38	preclosure	preclosure	ADJ
ejpam-491	50	39	[	[	X
ejpam-491	50	40	17	17	NUM
ejpam-491	50	41	]	]	PUNCT
ejpam-491	50	42	,	,	PUNCT
ejpam-491	50	43	β	β	X
ejpam-491	50	44	-closure	-closure	NOUN
ejpam-491	50	45	[	[	X
ejpam-491	50	46	2	2	NUM
ejpam-491	50	47	]	]	PUNCT
ejpam-491	50	48	or	or	CCONJ
ejpam-491	50	49	semi	semi	ADJ
ejpam-491	50	50	-	-	ADJ
ejpam-491	50	51	preclosure	preclosure	ADJ
ejpam-491	50	52	[	[	X
ejpam-491	50	53	4	4	NUM
ejpam-491	50	54	]	]	PUNCT
ejpam-491	50	55	,	,	PUNCT
ejpam-491	50	56	γ	γ	X
ejpam-491	50	57	-	-	NOUN
ejpam-491	50	58	closure	closure	NOUN
ejpam-491	50	59	[	[	X
ejpam-491	50	60	18	18	NUM
ejpam-491	50	61	]	]	PUNCT
ejpam-491	50	62	or	or	CCONJ
ejpam-491	50	63	b	b	NOUN
ejpam-491	50	64	-	-	PUNCT
ejpam-491	50	65	closure	closure	NOUN
ejpam-491	50	66	[	[	X
ejpam-491	50	67	5	5	NUM
ejpam-491	50	68	]	]	PUNCT
ejpam-491	50	69	)	)	PUNCT
ejpam-491	50	70	of	of	ADP
ejpam-491	50	71	a	a	PRON
ejpam-491	50	72	and	and	CCONJ
ejpam-491	50	73	is	be	AUX
ejpam-491	50	74	denoted	denote	VERB
ejpam-491	50	75	by	by	ADP
ejpam-491	50	76	αcl(a	αcl(a	NUM
ejpam-491	50	77	)	)	PUNCT
ejpam-491	50	78	(	(	PUNCT
ejpam-491	50	79	resp	resp	NOUN
ejpam-491	50	80	.	.	PUNCT
ejpam-491	50	81	scl(a	scl(a	PROPN
ejpam-491	50	82	)	)	PUNCT
ejpam-491	50	83	,	,	PUNCT
ejpam-491	50	84	pcl(a	pcl(a	PROPN
ejpam-491	50	85	)	)	PUNCT
ejpam-491	50	86	,	,	PUNCT
ejpam-491	50	87	βcl(a	βcl(a	PROPN
ejpam-491	50	88	)	)	PUNCT
ejpam-491	50	89	or	or	CCONJ
ejpam-491	50	90	spcl(a	spcl(a	NUM
ejpam-491	50	91	)	)	PUNCT
ejpam-491	50	92	)	)	PUNCT
ejpam-491	50	93	,	,	PUNCT
ejpam-491	50	94	clγ(a	clγ(a	PROPN
ejpam-491	50	95	)	)	PUNCT
ejpam-491	50	96	or	or	CCONJ
ejpam-491	50	97	bcl(a	bcl(a	VERB
ejpam-491	50	98	)	)	PUNCT
ejpam-491	50	99	)	)	PUNCT
ejpam-491	50	100	.	.	PUNCT
ejpam-491	51	1	definition	definition	NOUN
ejpam-491	51	2	4	4	X
ejpam-491	51	3	.	.	PUNCT
ejpam-491	52	1	let	let	AUX
ejpam-491	52	2	(	(	PUNCT
ejpam-491	52	3	x	x	X
ejpam-491	52	4	,	,	PUNCT
ejpam-491	52	5	τ	τ	X
ejpam-491	52	6	)	)	PUNCT
ejpam-491	52	7	be	be	VERB
ejpam-491	52	8	a	a	DET
ejpam-491	52	9	topological	topological	ADJ
ejpam-491	52	10	space	space	NOUN
ejpam-491	52	11	and	and	CCONJ
ejpam-491	52	12	a	a	DET
ejpam-491	52	13	a	a	DET
ejpam-491	52	14	subset	subset	NOUN
ejpam-491	52	15	of	of	ADP
ejpam-491	52	16	x	x	PRON
ejpam-491	52	17	.	.	PUNCT
ejpam-491	53	1	the	the	DET
ejpam-491	53	2	union	union	NOUN
ejpam-491	53	3	of	of	ADP
ejpam-491	53	4	all	all	DET
ejpam-491	53	5	α	α	NOUN
ejpam-491	53	6	-	-	ADJ
ejpam-491	53	7	open	open	ADJ
ejpam-491	53	8	(	(	PUNCT
ejpam-491	53	9	resp	resp	NOUN
ejpam-491	53	10	.	.	PUNCT
ejpam-491	54	1	semi	semi	ADJ
ejpam-491	54	2	-	-	ADJ
ejpam-491	54	3	open	open	ADJ
ejpam-491	54	4	,	,	PUNCT
ejpam-491	54	5	preopen	preopen	ADJ
ejpam-491	54	6	,	,	PUNCT
ejpam-491	54	7	β	β	X
ejpam-491	54	8	-open	-open	PROPN
ejpam-491	54	9	,	,	PUNCT
ejpam-491	54	10	γ	γ	NOUN
ejpam-491	54	11	-	-	ADJ
ejpam-491	54	12	open	open	ADJ
ejpam-491	54	13	)	)	PUNCT
ejpam-491	54	14	sets	set	NOUN
ejpam-491	54	15	of	of	ADP
ejpam-491	54	16	x	x	PUNCT
ejpam-491	54	17	contained	contain	VERB
ejpam-491	54	18	in	in	ADP
ejpam-491	54	19	a	a	PRON
ejpam-491	54	20	is	be	AUX
ejpam-491	54	21	called	call	VERB
ejpam-491	54	22	the	the	DET
ejpam-491	54	23	α	α	NOUN
ejpam-491	54	24	-	-	NOUN
ejpam-491	54	25	interior	interior	ADJ
ejpam-491	54	26	[	[	X
ejpam-491	54	27	23	23	NUM
ejpam-491	54	28	]	]	PUNCT
ejpam-491	54	29	(	(	PUNCT
ejpam-491	54	30	resp	resp	NOUN
ejpam-491	54	31	.	.	PUNCT
ejpam-491	54	32	semi	semi	ADJ
ejpam-491	54	33	-	-	ADJ
ejpam-491	54	34	interior	interior	ADJ
ejpam-491	54	35	[	[	X
ejpam-491	54	36	10	10	NUM
ejpam-491	54	37	]	]	PUNCT
ejpam-491	54	38	,	,	PUNCT
ejpam-491	54	39	preinterior	preinterior	PROPN
ejpam-491	54	40	[	[	X
ejpam-491	54	41	17	17	NUM
ejpam-491	54	42	]	]	PUNCT
ejpam-491	54	43	,	,	PUNCT
ejpam-491	54	44	β	β	X
ejpam-491	54	45	-interior	-interior	NOUN
ejpam-491	55	1	[	[	X
ejpam-491	55	2	2	2	NUM
ejpam-491	55	3	]	]	PUNCT
ejpam-491	55	4	or	or	CCONJ
ejpam-491	55	5	semi	semi	ADJ
ejpam-491	55	6	-	-	ADJ
ejpam-491	55	7	preinterior	preinterior	ADJ
ejpam-491	55	8	[	[	X
ejpam-491	55	9	4	4	NUM
ejpam-491	55	10	]	]	PUNCT
ejpam-491	55	11	,	,	PUNCT
ejpam-491	55	12	γ	γ	PROPN
ejpam-491	55	13	-	-	ADJ
ejpam-491	55	14	interior	interior	ADJ
ejpam-491	55	15	[	[	X
ejpam-491	55	16	18	18	NUM
ejpam-491	55	17	]	]	PUNCT
ejpam-491	55	18	or	or	CCONJ
ejpam-491	55	19	b	b	NOUN
ejpam-491	55	20	-	-	ADJ
ejpam-491	55	21	interior	interior	ADJ
ejpam-491	55	22	[	[	X
ejpam-491	55	23	5	5	NUM
ejpam-491	55	24	]	]	PUNCT
ejpam-491	55	25	)	)	PUNCT
ejpam-491	55	26	of	of	ADP
ejpam-491	55	27	a	a	PRON
ejpam-491	55	28	and	and	CCONJ
ejpam-491	55	29	is	be	AUX
ejpam-491	55	30	denoted	denote	VERB
ejpam-491	55	31	by	by	ADP
ejpam-491	55	32	αint(a	αint(a	PROPN
ejpam-491	55	33	)	)	PUNCT
ejpam-491	55	34	(	(	PUNCT
ejpam-491	55	35	resp	resp	NOUN
ejpam-491	55	36	.	.	PUNCT
ejpam-491	56	1	sint(a	sint(a	NOUN
ejpam-491	56	2	)	)	PUNCT
ejpam-491	56	3	,	,	PUNCT
ejpam-491	56	4	pint(a	pint(a	NOUN
ejpam-491	56	5	)	)	PUNCT
ejpam-491	56	6	,	,	PUNCT
ejpam-491	56	7	β	β	X
ejpam-491	56	8	int(a	int(a	PROPN
ejpam-491	56	9	)	)	PUNCT
ejpam-491	56	10	or	or	CCONJ
ejpam-491	56	11	spint(a	spint(a	NOUN
ejpam-491	56	12	)	)	PUNCT
ejpam-491	56	13	)	)	PUNCT
ejpam-491	56	14	,	,	PUNCT
ejpam-491	56	15	intγ(a	intγ(a	NOUN
ejpam-491	56	16	)	)	PUNCT
ejpam-491	56	17	or	or	CCONJ
ejpam-491	56	18	bint(a	bint(a	NUM
ejpam-491	56	19	)	)	PUNCT
ejpam-491	56	20	)	)	PUNCT
ejpam-491	56	21	.	.	PUNCT
ejpam-491	57	1	3	3	X
ejpam-491	57	2	.	.	NOUN
ejpam-491	57	3	minimal	minimal	ADJ
ejpam-491	57	4	structures	structure	NOUN
ejpam-491	57	5	and	and	CCONJ
ejpam-491	57	6	m	m	NOUN
ejpam-491	57	7	-	-	PUNCT
ejpam-491	57	8	continuity	continuity	NOUN
ejpam-491	57	9	definition	definition	NOUN
ejpam-491	57	10	5	5	NUM
ejpam-491	57	11	.	.	PUNCT
ejpam-491	58	1	let	let	VERB
ejpam-491	58	2	x	x	PRON
ejpam-491	58	3	be	be	AUX
ejpam-491	58	4	a	a	DET
ejpam-491	58	5	nonempty	nonempty	ADV
ejpam-491	58	6	set	set	VERB
ejpam-491	58	7	and	and	CCONJ
ejpam-491	58	8	p	p	X
ejpam-491	58	9	(	(	PUNCT
ejpam-491	58	10	x	x	X
ejpam-491	58	11	)	)	PUNCT
ejpam-491	58	12	the	the	DET
ejpam-491	58	13	power	power	NOUN
ejpam-491	58	14	set	set	NOUN
ejpam-491	58	15	of	of	ADP
ejpam-491	58	16	x	x	PROPN
ejpam-491	58	17	.	.	PUNCT
ejpam-491	59	1	a	a	DET
ejpam-491	59	2	subfamily	subfamily	ADV
ejpam-491	59	3	mx	mx	NOUN
ejpam-491	59	4	of	of	ADP
ejpam-491	59	5	p	p	PROPN
ejpam-491	59	6	(	(	PUNCT
ejpam-491	59	7	x	x	X
ejpam-491	59	8	)	)	PUNCT
ejpam-491	59	9	is	be	AUX
ejpam-491	59	10	called	call	VERB
ejpam-491	59	11	a	a	DET
ejpam-491	59	12	minimal	minimal	ADJ
ejpam-491	59	13	structure	structure	NOUN
ejpam-491	59	14	(	(	PUNCT
ejpam-491	59	15	briefly	briefly	NOUN
ejpam-491	59	16	m	m	NOUN
ejpam-491	59	17	-	-	NOUN
ejpam-491	59	18	structure	structure	NOUN
ejpam-491	59	19	)	)	PUNCT
ejpam-491	59	20	on	on	ADP
ejpam-491	59	21	x	x	PUNCT
ejpam-491	60	1	[	[	X
ejpam-491	60	2	29	29	NUM
ejpam-491	60	3	]	]	PUNCT
ejpam-491	60	4	,	,	PUNCT
ejpam-491	60	5	[	[	X
ejpam-491	60	6	30	30	NUM
ejpam-491	60	7	]	]	X
ejpam-491	60	8	if	if	SCONJ
ejpam-491	60	9	;	;	PUNCT
ejpam-491	60	10	∈	∈	PROPN
ejpam-491	60	11	mx	mx	PROPN
ejpam-491	60	12	and	and	CCONJ
ejpam-491	60	13	x	x	PROPN
ejpam-491	60	14	∈	∈	PROPN
ejpam-491	60	15	mx	mx	PROPN
ejpam-491	60	16	.	.	PUNCT
ejpam-491	61	1	by	by	ADP
ejpam-491	61	2	(	(	PUNCT
ejpam-491	61	3	x	x	INTJ
ejpam-491	61	4	,	,	PUNCT
ejpam-491	61	5	mx	mx	PROPN
ejpam-491	61	6	)	)	PUNCT
ejpam-491	61	7	,	,	PUNCT
ejpam-491	61	8	we	we	PRON
ejpam-491	61	9	denote	denote	VERB
ejpam-491	61	10	a	a	DET
ejpam-491	61	11	nonempty	nonempty	ADV
ejpam-491	61	12	set	set	VERB
ejpam-491	61	13	x	x	PUNCT
ejpam-491	61	14	with	with	ADP
ejpam-491	61	15	an	an	DET
ejpam-491	61	16	m	m	NOUN
ejpam-491	61	17	-	-	PUNCT
ejpam-491	61	18	structure	structure	ADJ
ejpam-491	61	19	mx	mx	NOUN
ejpam-491	61	20	on	on	ADP
ejpam-491	61	21	x	x	PUNCT
ejpam-491	61	22	and	and	CCONJ
ejpam-491	61	23	call	call	VERB
ejpam-491	61	24	it	it	PRON
ejpam-491	61	25	an	an	DET
ejpam-491	61	26	m	m	NOUN
ejpam-491	61	27	-	-	NOUN
ejpam-491	61	28	space	space	NOUN
ejpam-491	61	29	.	.	PUNCT
ejpam-491	62	1	each	each	DET
ejpam-491	62	2	member	member	NOUN
ejpam-491	62	3	of	of	ADP
ejpam-491	62	4	mx	mx	PROPN
ejpam-491	62	5	is	be	AUX
ejpam-491	62	6	said	say	VERB
ejpam-491	62	7	to	to	PART
ejpam-491	62	8	be	be	AUX
ejpam-491	62	9	mx	mx	NOUN
ejpam-491	62	10	-open	-open	ADJ
ejpam-491	62	11	and	and	CCONJ
ejpam-491	62	12	the	the	DET
ejpam-491	62	13	complement	complement	NOUN
ejpam-491	62	14	of	of	ADP
ejpam-491	62	15	an	an	DET
ejpam-491	62	16	mx	mx	PROPN
ejpam-491	62	17	-open	-open	NOUN
ejpam-491	62	18	set	set	NOUN
ejpam-491	62	19	is	be	AUX
ejpam-491	62	20	said	say	VERB
ejpam-491	62	21	to	to	PART
ejpam-491	62	22	be	be	AUX
ejpam-491	62	23	mx	mx	NOUN
ejpam-491	62	24	-closed	-close	VERB
ejpam-491	62	25	.	.	PUNCT
ejpam-491	63	1	remark	remark	PROPN
ejpam-491	63	2	1	1	NUM
ejpam-491	63	3	.	.	PUNCT
ejpam-491	64	1	let	let	AUX
ejpam-491	64	2	(	(	PUNCT
ejpam-491	64	3	x	x	X
ejpam-491	64	4	,	,	PUNCT
ejpam-491	64	5	τ	τ	X
ejpam-491	64	6	)	)	PUNCT
ejpam-491	64	7	be	be	VERB
ejpam-491	64	8	a	a	DET
ejpam-491	64	9	topological	topological	ADJ
ejpam-491	64	10	space	space	NOUN
ejpam-491	64	11	.	.	PUNCT
ejpam-491	65	1	then	then	ADV
ejpam-491	65	2	the	the	DET
ejpam-491	65	3	family	family	NOUN
ejpam-491	65	4	α(x	α(x	PROPN
ejpam-491	65	5	)	)	PUNCT
ejpam-491	65	6	is	be	AUX
ejpam-491	65	7	a	a	DET
ejpam-491	65	8	topology	topology	NOUN
ejpam-491	65	9	finer	fine	ADJ
ejpam-491	65	10	than	than	ADP
ejpam-491	65	11	τ	τ	PROPN
ejpam-491	65	12	.	.	PUNCT
ejpam-491	66	1	the	the	DET
ejpam-491	66	2	families	family	NOUN
ejpam-491	66	3	so(x	so(x	PUNCT
ejpam-491	66	4	)	)	PUNCT
ejpam-491	66	5	,	,	PUNCT
ejpam-491	66	6	po(x	po(x	NUM
ejpam-491	66	7	)	)	PUNCT
ejpam-491	66	8	,	,	PUNCT
ejpam-491	66	9	β(x	β(x	NOUN
ejpam-491	66	10	)	)	PUNCT
ejpam-491	66	11	,	,	PUNCT
ejpam-491	66	12	and	and	CCONJ
ejpam-491	66	13	γ(x	γ(x	NOUN
ejpam-491	66	14	)	)	PUNCT
ejpam-491	66	15	are	be	AUX
ejpam-491	66	16	all	all	PRON
ejpam-491	66	17	m	m	NOUN
ejpam-491	66	18	-	-	NOUN
ejpam-491	66	19	structures	structure	NOUN
ejpam-491	66	20	on	on	ADP
ejpam-491	66	21	x	x	X
ejpam-491	66	22	.	.	PUNCT
ejpam-491	67	1	t.	t.	PROPN
ejpam-491	67	2	noiri	noiri	PROPN
ejpam-491	67	3	and	and	CCONJ
ejpam-491	67	4	v.	v.	ADP
ejpam-491	67	5	popa	popa	NOUN
ejpam-491	67	6	/	/	SYM
ejpam-491	67	7	eur	eur	PROPN
ejpam-491	67	8	.	.	PUNCT
ejpam-491	68	1	j.	j.	PROPN
ejpam-491	68	2	pure	pure	PROPN
ejpam-491	68	3	appl	appl	PROPN
ejpam-491	68	4	.	.	PROPN
ejpam-491	68	5	math	math	PROPN
ejpam-491	68	6	,	,	PUNCT
ejpam-491	68	7	2	2	NUM
ejpam-491	68	8	(	(	PUNCT
ejpam-491	68	9	2009	2009	NUM
ejpam-491	68	10	)	)	PUNCT
ejpam-491	68	11	,	,	PUNCT
ejpam-491	68	12	(	(	PUNCT
ejpam-491	68	13	473	473	NUM
ejpam-491	68	14	-	-	NUM
ejpam-491	68	15	493	493	NUM
ejpam-491	68	16	)	)	PUNCT
ejpam-491	68	17	476	476	NUM
ejpam-491	68	18	definition	definition	NOUN
ejpam-491	68	19	6	6	NUM
ejpam-491	68	20	.	.	PUNCT
ejpam-491	69	1	let	let	VERB
ejpam-491	69	2	x	x	PRON
ejpam-491	69	3	be	be	AUX
ejpam-491	69	4	a	a	DET
ejpam-491	69	5	nonempty	nonempty	ADV
ejpam-491	69	6	set	set	VERB
ejpam-491	69	7	and	and	CCONJ
ejpam-491	69	8	mx	mx	X
ejpam-491	69	9	an	an	DET
ejpam-491	69	10	m	m	NOUN
ejpam-491	69	11	-	-	NOUN
ejpam-491	69	12	structure	structure	NOUN
ejpam-491	69	13	on	on	ADP
ejpam-491	69	14	x	x	X
ejpam-491	69	15	.	.	PUNCT
ejpam-491	70	1	for	for	ADP
ejpam-491	70	2	a	a	DET
ejpam-491	70	3	subset	subset	NOUN
ejpam-491	70	4	a	a	PRON
ejpam-491	70	5	of	of	ADP
ejpam-491	70	6	x	x	PRON
ejpam-491	70	7	,	,	PUNCT
ejpam-491	70	8	the	the	DET
ejpam-491	70	9	mx	mx	PROPN
ejpam-491	70	10	-closure	-closure	NOUN
ejpam-491	70	11	of	of	ADP
ejpam-491	70	12	a	a	PRON
ejpam-491	70	13	and	and	CCONJ
ejpam-491	70	14	the	the	DET
ejpam-491	70	15	mx	mx	PROPN
ejpam-491	70	16	-interior	-interior	NOUN
ejpam-491	70	17	of	of	ADP
ejpam-491	70	18	a	a	PRON
ejpam-491	70	19	are	be	AUX
ejpam-491	70	20	defined	define	VERB
ejpam-491	70	21	in	in	ADP
ejpam-491	70	22	[	[	X
ejpam-491	70	23	21	21	NUM
ejpam-491	70	24	]	]	PUNCT
ejpam-491	70	25	as	as	SCONJ
ejpam-491	70	26	follows	follow	VERB
ejpam-491	70	27	:	:	PUNCT
ejpam-491	70	28	(	(	PUNCT
ejpam-491	70	29	1	1	X
ejpam-491	70	30	)	)	PUNCT
ejpam-491	70	31	mcl(a	mcl(a	X
ejpam-491	70	32	)	)	PUNCT
ejpam-491	70	33	=	=	SYM
ejpam-491	70	34	∩{f	∩{f	NOUN
ejpam-491	70	35	:	:	PUNCT
ejpam-491	70	36	a⊂	a⊂	X
ejpam-491	70	37	f	f	X
ejpam-491	70	38	,	,	PUNCT
ejpam-491	70	39	x	x	PROPN
ejpam-491	70	40	−	−	PROPN
ejpam-491	70	41	f	f	PROPN
ejpam-491	70	42	∈	∈	PROPN
ejpam-491	70	43	mx	mx	PROPN
ejpam-491	70	44	}	}	PUNCT
ejpam-491	70	45	,	,	PUNCT
ejpam-491	70	46	(	(	PUNCT
ejpam-491	70	47	2	2	X
ejpam-491	70	48	)	)	PUNCT
ejpam-491	70	49	mint(a	mint(a	PROPN
ejpam-491	70	50	)	)	PUNCT
ejpam-491	70	51	=	=	SYM
ejpam-491	71	1	∪{u	∪{u	VERB
ejpam-491	71	2	:	:	PUNCT
ejpam-491	71	3	u	u	X
ejpam-491	71	4	⊂	⊂	PROPN
ejpam-491	71	5	a	a	X
ejpam-491	71	6	,	,	PUNCT
ejpam-491	71	7	u	u	PROPN
ejpam-491	71	8	∈	∈	PROPN
ejpam-491	71	9	mx	mx	PROPN
ejpam-491	71	10	}	}	PUNCT
ejpam-491	71	11	.	.	PUNCT
ejpam-491	72	1	remark	remark	NOUN
ejpam-491	72	2	2	2	NUM
ejpam-491	72	3	.	.	PUNCT
ejpam-491	73	1	let	let	AUX
ejpam-491	73	2	(	(	PUNCT
ejpam-491	73	3	x	x	X
ejpam-491	73	4	,	,	PUNCT
ejpam-491	73	5	τ	τ	X
ejpam-491	73	6	)	)	PUNCT
ejpam-491	73	7	be	be	VERB
ejpam-491	73	8	a	a	DET
ejpam-491	73	9	topological	topological	ADJ
ejpam-491	73	10	space	space	NOUN
ejpam-491	73	11	and	and	CCONJ
ejpam-491	73	12	a	a	DET
ejpam-491	73	13	a	a	DET
ejpam-491	73	14	subset	subset	NOUN
ejpam-491	73	15	of	of	ADP
ejpam-491	73	16	x	x	X
ejpam-491	73	17	.	.	PUNCT
ejpam-491	74	1	if	if	SCONJ
ejpam-491	74	2	mx	mx	PROPN
ejpam-491	74	3	=	=	SYM
ejpam-491	74	4	τ	τ	PROPN
ejpam-491	74	5	(	(	PUNCT
ejpam-491	74	6	resp	resp	PROPN
ejpam-491	74	7	.	.	PUNCT
ejpam-491	74	8	so(x	so(x	PROPN
ejpam-491	74	9	)	)	PUNCT
ejpam-491	74	10	,	,	PUNCT
ejpam-491	74	11	po(x	po(x	NUM
ejpam-491	74	12	)	)	PUNCT
ejpam-491	74	13	,	,	PUNCT
ejpam-491	74	14	α(x	α(x	PROPN
ejpam-491	74	15	)	)	PUNCT
ejpam-491	74	16	,	,	PUNCT
ejpam-491	74	17	β(x	β(x	NOUN
ejpam-491	74	18	)	)	PUNCT
ejpam-491	74	19	,	,	PUNCT
ejpam-491	74	20	γ(x	γ(x	NOUN
ejpam-491	74	21	)	)	PUNCT
ejpam-491	74	22	)	)	PUNCT
ejpam-491	74	23	,	,	PUNCT
ejpam-491	74	24	then	then	ADV
ejpam-491	74	25	we	we	PRON
ejpam-491	74	26	have	have	VERB
ejpam-491	74	27	(	(	PUNCT
ejpam-491	74	28	1	1	X
ejpam-491	74	29	)	)	PUNCT
ejpam-491	74	30	mcl(a	mcl(a	NOUN
ejpam-491	74	31	)	)	PUNCT
ejpam-491	74	32	=	=	SYM
ejpam-491	74	33	cl(a	cl(a	X
ejpam-491	74	34	)	)	PUNCT
ejpam-491	74	35	(	(	PUNCT
ejpam-491	74	36	resp	resp	NOUN
ejpam-491	74	37	.	.	PUNCT
ejpam-491	75	1	scl(a	scl(a	PROPN
ejpam-491	75	2	)	)	PUNCT
ejpam-491	75	3	,	,	PUNCT
ejpam-491	75	4	pcl(a	pcl(a	PROPN
ejpam-491	75	5	)	)	PUNCT
ejpam-491	75	6	,	,	PUNCT
ejpam-491	75	7	αcl(a	αcl(a	PROPN
ejpam-491	75	8	)	)	PUNCT
ejpam-491	75	9	,	,	PUNCT
ejpam-491	75	10	βcl(a	βcl(a	PROPN
ejpam-491	75	11	)	)	PUNCT
ejpam-491	75	12	,	,	PUNCT
ejpam-491	75	13	clγ(a	clγ(a	PROPN
ejpam-491	75	14	)	)	PUNCT
ejpam-491	75	15	)	)	PUNCT
ejpam-491	76	1	,	,	PUNCT
ejpam-491	76	2	(	(	PUNCT
ejpam-491	76	3	2	2	X
ejpam-491	76	4	)	)	PUNCT
ejpam-491	76	5	mint(a	mint(a	PROPN
ejpam-491	76	6	)	)	PUNCT
ejpam-491	76	7	=	=	SYM
ejpam-491	76	8	int(a	int(a	NOUN
ejpam-491	76	9	)	)	PUNCT
ejpam-491	76	10	(	(	PUNCT
ejpam-491	76	11	resp	resp	NOUN
ejpam-491	76	12	.	.	PUNCT
ejpam-491	77	1	sint(a	sint(a	NOUN
ejpam-491	77	2	)	)	PUNCT
ejpam-491	77	3	,	,	PUNCT
ejpam-491	77	4	pint(a	pint(a	NOUN
ejpam-491	77	5	)	)	PUNCT
ejpam-491	77	6	,	,	PUNCT
ejpam-491	77	7	αint(a	αint(a	NOUN
ejpam-491	77	8	)	)	PUNCT
ejpam-491	77	9	,	,	PUNCT
ejpam-491	77	10	β	β	X
ejpam-491	77	11	int(a	int(a	PROPN
ejpam-491	77	12	)	)	PUNCT
ejpam-491	77	13	,	,	PUNCT
ejpam-491	77	14	intγ(a	intγ(a	NOUN
ejpam-491	77	15	)	)	PUNCT
ejpam-491	77	16	)	)	PUNCT
ejpam-491	77	17	.	.	PUNCT
ejpam-491	78	1	lemma	lemma	PROPN
ejpam-491	78	2	1	1	NUM
ejpam-491	78	3	.	.	PUNCT
ejpam-491	79	1	(	(	PUNCT
ejpam-491	79	2	maki	maki	NOUN
ejpam-491	79	3	et	et	PROPN
ejpam-491	79	4	al	al	PROPN
ejpam-491	79	5	.	.	PUNCT
ejpam-491	80	1	[	[	X
ejpam-491	80	2	21	21	NUM
ejpam-491	80	3	]	]	PUNCT
ejpam-491	80	4	)	)	PUNCT
ejpam-491	80	5	.	.	PUNCT
ejpam-491	81	1	let	let	VERB
ejpam-491	81	2	x	x	PRON
ejpam-491	81	3	be	be	AUX
ejpam-491	81	4	a	a	DET
ejpam-491	81	5	nonempty	nonempty	ADV
ejpam-491	81	6	set	set	VERB
ejpam-491	81	7	and	and	CCONJ
ejpam-491	81	8	mx	mx	X
ejpam-491	81	9	a	a	DET
ejpam-491	81	10	minimal	minimal	ADJ
ejpam-491	81	11	structure	structure	NOUN
ejpam-491	81	12	on	on	ADP
ejpam-491	81	13	x.	x.	NOUN
ejpam-491	81	14	for	for	ADP
ejpam-491	81	15	subsets	subset	NOUN
ejpam-491	81	16	a	a	PRON
ejpam-491	81	17	and	and	CCONJ
ejpam-491	81	18	b	b	NOUN
ejpam-491	81	19	of	of	ADP
ejpam-491	81	20	x	x	PRON
ejpam-491	81	21	,	,	PUNCT
ejpam-491	81	22	the	the	DET
ejpam-491	81	23	following	follow	VERB
ejpam-491	81	24	properties	property	NOUN
ejpam-491	81	25	hold	hold	VERB
ejpam-491	81	26	:	:	PUNCT
ejpam-491	81	27	(	(	PUNCT
ejpam-491	81	28	1	1	X
ejpam-491	81	29	)	)	PUNCT
ejpam-491	81	30	mcl(x	mcl(x	PROPN
ejpam-491	82	1	−	−	NOUN
ejpam-491	82	2	a	a	NOUN
ejpam-491	82	3	)	)	PUNCT
ejpam-491	82	4	=	=	PUNCT
ejpam-491	83	1	x	x	SYM
ejpam-491	83	2	−mint(a	−mint(a	NOUN
ejpam-491	83	3	)	)	PUNCT
ejpam-491	83	4	and	and	CCONJ
ejpam-491	83	5	mint(x	mint(x	NOUN
ejpam-491	83	6	−	−	PROPN
ejpam-491	83	7	a	a	X
ejpam-491	83	8	)	)	PUNCT
ejpam-491	83	9	=	=	SYM
ejpam-491	83	10	x	x	SYM
ejpam-491	83	11	−mcl(a	−mcl(a	NOUN
ejpam-491	83	12	)	)	PUNCT
ejpam-491	83	13	,	,	PUNCT
ejpam-491	83	14	(	(	PUNCT
ejpam-491	83	15	2	2	X
ejpam-491	83	16	)	)	PUNCT
ejpam-491	83	17	if	if	SCONJ
ejpam-491	83	18	(	(	PUNCT
ejpam-491	83	19	x	x	SYM
ejpam-491	83	20	−	−	NOUN
ejpam-491	83	21	a	a	X
ejpam-491	83	22	)	)	PUNCT
ejpam-491	83	23	∈	∈	PROPN
ejpam-491	83	24	mx	mx	PROPN
ejpam-491	83	25	,	,	PUNCT
ejpam-491	83	26	then	then	ADV
ejpam-491	83	27	mcl(a	mcl(a	X
ejpam-491	83	28	)	)	PUNCT
ejpam-491	83	29	=	=	SYM
ejpam-491	84	1	a	a	PROPN
ejpam-491	85	1	and	and	CCONJ
ejpam-491	85	2	if	if	SCONJ
ejpam-491	85	3	a∈	a∈	PROPN
ejpam-491	85	4	mx	mx	PROPN
ejpam-491	85	5	,	,	PUNCT
ejpam-491	85	6	then	then	ADV
ejpam-491	85	7	mint(a	mint(a	PROPN
ejpam-491	85	8	)	)	PUNCT
ejpam-491	85	9	=	=	SYM
ejpam-491	85	10	a	a	PRON
ejpam-491	85	11	,	,	PUNCT
ejpam-491	85	12	(	(	PUNCT
ejpam-491	85	13	3	3	X
ejpam-491	85	14	)	)	PUNCT
ejpam-491	85	15	mcl	mcl	NOUN
ejpam-491	85	16	(;	(;	X
ejpam-491	85	17	)	)	PUNCT
ejpam-491	85	18	=	=	SYM
ejpam-491	85	19	;	;	PUNCT
ejpam-491	85	20	,	,	PUNCT
ejpam-491	85	21	mcl(x	mcl(x	PROPN
ejpam-491	85	22	)	)	PUNCT
ejpam-491	85	23	=	=	SYM
ejpam-491	85	24	x	x	NOUN
ejpam-491	85	25	,	,	PUNCT
ejpam-491	85	26	mint	mint	NOUN
ejpam-491	85	27	(;	(;	X
ejpam-491	85	28	)	)	PUNCT
ejpam-491	85	29	=	=	SYM
ejpam-491	85	30	;	;	PUNCT
ejpam-491	85	31	and	and	CCONJ
ejpam-491	85	32	mint(x	mint(x	NOUN
ejpam-491	85	33	)	)	PUNCT
ejpam-491	86	1	=	=	PUNCT
ejpam-491	86	2	x	x	X
ejpam-491	86	3	,	,	PUNCT
ejpam-491	86	4	(	(	PUNCT
ejpam-491	86	5	4	4	X
ejpam-491	86	6	)	)	PUNCT
ejpam-491	86	7	if	if	SCONJ
ejpam-491	86	8	a⊂	a⊂	NOUN
ejpam-491	86	9	b	b	NOUN
ejpam-491	86	10	,	,	PUNCT
ejpam-491	86	11	then	then	ADV
ejpam-491	86	12	mcl(a	mcl(a	X
ejpam-491	86	13	)	)	PUNCT
ejpam-491	86	14	⊂mcl(b	⊂mcl(b	PROPN
ejpam-491	86	15	)	)	PUNCT
ejpam-491	86	16	and	and	CCONJ
ejpam-491	86	17	mint(a)⊂mint(b	mint(a)⊂mint(b	PROPN
ejpam-491	86	18	)	)	PUNCT
ejpam-491	86	19	,	,	PUNCT
ejpam-491	86	20	(	(	PUNCT
ejpam-491	86	21	5	5	NUM
ejpam-491	86	22	)	)	PUNCT
ejpam-491	86	23	a⊂mcl(a	a⊂mcl(a	NUM
ejpam-491	86	24	)	)	PUNCT
ejpam-491	86	25	and	and	CCONJ
ejpam-491	86	26	mint(a	mint(a	PROPN
ejpam-491	86	27	)	)	PUNCT
ejpam-491	86	28	⊂	⊂	PROPN
ejpam-491	86	29	a	a	X
ejpam-491	86	30	,	,	PUNCT
ejpam-491	86	31	(	(	PUNCT
ejpam-491	86	32	6	6	NUM
ejpam-491	86	33	)	)	PUNCT
ejpam-491	86	34	mcl(mcl(a	mcl(mcl(a	ADJ
ejpam-491	86	35	)	)	PUNCT
ejpam-491	86	36	)	)	PUNCT
ejpam-491	87	1	=	=	SYM
ejpam-491	87	2	mcl(a	mcl(a	X
ejpam-491	87	3	)	)	PUNCT
ejpam-491	87	4	and	and	CCONJ
ejpam-491	87	5	mint(mint(a	mint(mint(a	NUM
ejpam-491	87	6	)	)	PUNCT
ejpam-491	87	7	)	)	PUNCT
ejpam-491	88	1	=	=	PUNCT
ejpam-491	88	2	mint(a	mint(a	PROPN
ejpam-491	88	3	)	)	PUNCT
ejpam-491	88	4	.	.	PUNCT
ejpam-491	89	1	lemma	lemma	PROPN
ejpam-491	89	2	2	2	NUM
ejpam-491	89	3	.	.	PUNCT
ejpam-491	89	4	(	(	PUNCT
ejpam-491	89	5	popa	popa	NOUN
ejpam-491	89	6	and	and	CCONJ
ejpam-491	89	7	noiri	noiri	ADV
ejpam-491	89	8	[	[	X
ejpam-491	89	9	29	29	NUM
ejpam-491	89	10	]	]	PUNCT
ejpam-491	89	11	)	)	PUNCT
ejpam-491	89	12	.	.	PUNCT
ejpam-491	90	1	let	let	VERB
ejpam-491	90	2	x	x	PRON
ejpam-491	90	3	be	be	AUX
ejpam-491	90	4	a	a	DET
ejpam-491	90	5	nonempty	nonempty	NOUN
ejpam-491	90	6	set	set	VERB
ejpam-491	90	7	with	with	ADP
ejpam-491	90	8	a	a	DET
ejpam-491	90	9	minimal	minimal	ADJ
ejpam-491	90	10	structure	structure	NOUN
ejpam-491	90	11	mx	mx	PROPN
ejpam-491	90	12	and	and	CCONJ
ejpam-491	90	13	a	a	DET
ejpam-491	90	14	a	a	DET
ejpam-491	90	15	subset	subset	NOUN
ejpam-491	90	16	of	of	ADP
ejpam-491	90	17	x.	x.	NOUN
ejpam-491	90	18	then	then	ADV
ejpam-491	90	19	x	x	PROPN
ejpam-491	90	20	∈	∈	PROPN
ejpam-491	90	21	mcl(a	mcl(a	PROPN
ejpam-491	90	22	)	)	PUNCT
ejpam-491	91	1	if	if	SCONJ
ejpam-491	91	2	and	and	CCONJ
ejpam-491	91	3	only	only	ADV
ejpam-491	91	4	if	if	SCONJ
ejpam-491	91	5	u	u	PROPN
ejpam-491	91	6	∩	∩	VERB
ejpam-491	91	7	a	a	DET
ejpam-491	91	8	6=	6=	NOUN
ejpam-491	91	9	;	;	PUNCT
ejpam-491	91	10	for	for	ADP
ejpam-491	91	11	every	every	DET
ejpam-491	91	12	u	u	PROPN
ejpam-491	91	13	∈	∈	PROPN
ejpam-491	91	14	mx	mx	NOUN
ejpam-491	91	15	containing	contain	VERB
ejpam-491	91	16	x.	x.	NOUN
ejpam-491	91	17	definition	definition	NOUN
ejpam-491	91	18	7	7	NUM
ejpam-491	91	19	.	.	PUNCT
ejpam-491	92	1	an	an	DET
ejpam-491	92	2	m	m	NOUN
ejpam-491	92	3	-	-	PUNCT
ejpam-491	92	4	structure	structure	ADJ
ejpam-491	92	5	mx	mx	NOUN
ejpam-491	92	6	on	on	ADP
ejpam-491	92	7	a	a	DET
ejpam-491	92	8	nonempty	nonempty	ADJ
ejpam-491	92	9	set	set	VERB
ejpam-491	92	10	x	x	SYM
ejpam-491	92	11	is	be	AUX
ejpam-491	92	12	said	say	VERB
ejpam-491	92	13	to	to	PART
ejpam-491	92	14	have	have	VERB
ejpam-491	92	15	propertyb	propertyb	NOUN
ejpam-491	92	16	[	[	X
ejpam-491	92	17	21	21	NUM
ejpam-491	92	18	]	]	X
ejpam-491	92	19	if	if	SCONJ
ejpam-491	92	20	the	the	DET
ejpam-491	92	21	union	union	NOUN
ejpam-491	92	22	of	of	ADP
ejpam-491	92	23	any	any	DET
ejpam-491	92	24	family	family	NOUN
ejpam-491	92	25	of	of	ADP
ejpam-491	92	26	subsets	subset	NOUN
ejpam-491	92	27	belong	belong	VERB
ejpam-491	92	28	to	to	ADP
ejpam-491	92	29	mx	mx	PROPN
ejpam-491	92	30	belongs	belong	VERB
ejpam-491	92	31	to	to	ADP
ejpam-491	92	32	mx	mx	PROPN
ejpam-491	92	33	.	.	PUNCT
ejpam-491	93	1	remark	remark	PROPN
ejpam-491	93	2	3	3	NUM
ejpam-491	93	3	.	.	PUNCT
ejpam-491	94	1	if	if	SCONJ
ejpam-491	94	2	(	(	PUNCT
ejpam-491	94	3	x	x	X
ejpam-491	94	4	,	,	PUNCT
ejpam-491	94	5	τ	τ	X
ejpam-491	94	6	)	)	PUNCT
ejpam-491	94	7	is	be	AUX
ejpam-491	94	8	a	a	DET
ejpam-491	94	9	topological	topological	ADJ
ejpam-491	94	10	space	space	NOUN
ejpam-491	94	11	,	,	PUNCT
ejpam-491	94	12	then	then	ADV
ejpam-491	94	13	so(x	so(x	PUNCT
ejpam-491	94	14	)	)	PUNCT
ejpam-491	94	15	,	,	PUNCT
ejpam-491	94	16	po(x	po(x	NUM
ejpam-491	94	17	)	)	PUNCT
ejpam-491	94	18	,	,	PUNCT
ejpam-491	94	19	α(x	α(x	PROPN
ejpam-491	94	20	)	)	PUNCT
ejpam-491	94	21	,	,	PUNCT
ejpam-491	94	22	β(x	β(x	NOUN
ejpam-491	94	23	)	)	PUNCT
ejpam-491	94	24	and	and	CCONJ
ejpam-491	94	25	γ(x	γ(x	NOUN
ejpam-491	94	26	)	)	PUNCT
ejpam-491	94	27	have	have	AUX
ejpam-491	94	28	propertyb	propertyb	NOUN
ejpam-491	94	29	,	,	PUNCT
ejpam-491	94	30	lemma	lemma	PROPN
ejpam-491	94	31	3	3	X
ejpam-491	94	32	.	.	PUNCT
ejpam-491	94	33	(	(	PUNCT
ejpam-491	94	34	popa	popa	NOUN
ejpam-491	94	35	and	and	CCONJ
ejpam-491	94	36	noiri	noiri	ADV
ejpam-491	94	37	[	[	X
ejpam-491	94	38	30	30	NUM
ejpam-491	94	39	]	]	PUNCT
ejpam-491	94	40	)	)	PUNCT
ejpam-491	94	41	.	.	PUNCT
ejpam-491	95	1	let	let	VERB
ejpam-491	95	2	x	x	PRON
ejpam-491	95	3	be	be	AUX
ejpam-491	95	4	a	a	DET
ejpam-491	95	5	nonempty	nonempty	ADV
ejpam-491	95	6	set	set	VERB
ejpam-491	95	7	and	and	CCONJ
ejpam-491	95	8	mx	mx	X
ejpam-491	95	9	an	an	DET
ejpam-491	95	10	m	m	NOUN
ejpam-491	95	11	-	-	NOUN
ejpam-491	95	12	structure	structure	NOUN
ejpam-491	95	13	on	on	ADP
ejpam-491	95	14	x	x	SYM
ejpam-491	95	15	satisfying	satisfy	VERB
ejpam-491	95	16	propertyb	propertyb	NOUN
ejpam-491	95	17	.	.	PUNCT
ejpam-491	96	1	for	for	ADP
ejpam-491	96	2	a	a	DET
ejpam-491	96	3	subset	subset	NOUN
ejpam-491	96	4	a	a	PRON
ejpam-491	96	5	of	of	ADP
ejpam-491	96	6	x	x	PRON
ejpam-491	96	7	,	,	PUNCT
ejpam-491	96	8	the	the	DET
ejpam-491	96	9	following	follow	VERB
ejpam-491	96	10	properties	property	NOUN
ejpam-491	96	11	hold	hold	VERB
ejpam-491	96	12	:	:	PUNCT
ejpam-491	96	13	t.	t.	PROPN
ejpam-491	96	14	noiri	noiri	PROPN
ejpam-491	96	15	and	and	CCONJ
ejpam-491	96	16	v.	v.	ADP
ejpam-491	96	17	popa	popa	NOUN
ejpam-491	96	18	/	/	SYM
ejpam-491	96	19	eur	eur	PROPN
ejpam-491	96	20	.	.	PUNCT
ejpam-491	97	1	j.	j.	PROPN
ejpam-491	97	2	pure	pure	PROPN
ejpam-491	97	3	appl	appl	PROPN
ejpam-491	97	4	.	.	PROPN
ejpam-491	97	5	math	math	PROPN
ejpam-491	97	6	,	,	PUNCT
ejpam-491	97	7	2	2	NUM
ejpam-491	97	8	(	(	PUNCT
ejpam-491	97	9	2009	2009	NUM
ejpam-491	97	10	)	)	PUNCT
ejpam-491	97	11	,	,	PUNCT
ejpam-491	97	12	(	(	PUNCT
ejpam-491	97	13	473	473	NUM
ejpam-491	97	14	-	-	NUM
ejpam-491	97	15	493	493	NUM
ejpam-491	97	16	)	)	PUNCT
ejpam-491	97	17	477	477	NUM
ejpam-491	97	18	(	(	PUNCT
ejpam-491	97	19	1	1	NUM
ejpam-491	97	20	)	)	PUNCT
ejpam-491	97	21	a∈	a∈	PROPN
ejpam-491	97	22	mx	mx	PROPN
ejpam-491	98	1	if	if	SCONJ
ejpam-491	98	2	and	and	CCONJ
ejpam-491	98	3	only	only	ADV
ejpam-491	98	4	if	if	SCONJ
ejpam-491	98	5	mint(a	mint(a	PROPN
ejpam-491	98	6	)	)	PUNCT
ejpam-491	98	7	=	=	SYM
ejpam-491	98	8	a	a	PRON
ejpam-491	98	9	,	,	PUNCT
ejpam-491	98	10	(	(	PUNCT
ejpam-491	98	11	2	2	X
ejpam-491	98	12	)	)	PUNCT
ejpam-491	98	13	a	a	PRON
ejpam-491	98	14	is	be	AUX
ejpam-491	98	15	mx	mx	NOUN
ejpam-491	98	16	-closed	-close	VERB
ejpam-491	98	17	if	if	SCONJ
ejpam-491	98	18	and	and	CCONJ
ejpam-491	98	19	only	only	ADV
ejpam-491	98	20	if	if	SCONJ
ejpam-491	98	21	mcl(a	mcl(a	X
ejpam-491	98	22	)	)	PUNCT
ejpam-491	98	23	=	=	SYM
ejpam-491	98	24	a	a	DET
ejpam-491	98	25	,	,	PUNCT
ejpam-491	98	26	(	(	PUNCT
ejpam-491	98	27	3	3	X
ejpam-491	98	28	)	)	PUNCT
ejpam-491	98	29	mint(a	mint(a	PROPN
ejpam-491	98	30	)	)	PUNCT
ejpam-491	98	31	∈	∈	PROPN
ejpam-491	98	32	mx	mx	PROPN
ejpam-491	98	33	and	and	CCONJ
ejpam-491	98	34	mcl(a	mcl(a	PROPN
ejpam-491	98	35	)	)	PUNCT
ejpam-491	98	36	is	be	AUX
ejpam-491	98	37	mx	mx	NOUN
ejpam-491	98	38	-closed	-closed	ADJ
ejpam-491	98	39	.	.	PUNCT
ejpam-491	99	1	definition	definition	NOUN
ejpam-491	99	2	8	8	NUM
ejpam-491	99	3	.	.	PUNCT
ejpam-491	100	1	a	a	DET
ejpam-491	100	2	function	function	NOUN
ejpam-491	100	3	f	f	NOUN
ejpam-491	100	4	:	:	PUNCT
ejpam-491	100	5	(	(	PUNCT
ejpam-491	100	6	x	x	X
ejpam-491	100	7	,	,	PUNCT
ejpam-491	100	8	mx	mx	PROPN
ejpam-491	100	9	)	)	PUNCT
ejpam-491	100	10	→	→	SYM
ejpam-491	100	11	(	(	PUNCT
ejpam-491	100	12	y	y	PROPN
ejpam-491	100	13	,	,	PUNCT
ejpam-491	100	14	my	my	INTJ
ejpam-491	100	15	)	)	PUNCT
ejpam-491	100	16	is	be	AUX
ejpam-491	100	17	said	say	VERB
ejpam-491	100	18	to	to	PART
ejpam-491	100	19	be	be	AUX
ejpam-491	100	20	m	m	NOUN
ejpam-491	100	21	-	-	ADJ
ejpam-491	100	22	continuous	continuous	ADJ
ejpam-491	100	23	at	at	ADP
ejpam-491	100	24	a	a	DET
ejpam-491	100	25	point	point	NOUN
ejpam-491	100	26	x	x	X
ejpam-491	100	27	∈	∈	NOUN
ejpam-491	100	28	x	x	PUNCT
ejpam-491	101	1	[	[	X
ejpam-491	101	2	30	30	NUM
ejpam-491	101	3	]	]	X
ejpam-491	101	4	if	if	SCONJ
ejpam-491	101	5	for	for	ADP
ejpam-491	101	6	each	each	DET
ejpam-491	101	7	x	x	SYM
ejpam-491	101	8	∈	∈	PROPN
ejpam-491	101	9	x	x	X
ejpam-491	101	10	and	and	CCONJ
ejpam-491	101	11	each	each	PRON
ejpam-491	101	12	v	v	NOUN
ejpam-491	101	13	∈	∈	PRON
ejpam-491	101	14	my	my	PRON
ejpam-491	101	15	containing	contain	VERB
ejpam-491	101	16	f	f	X
ejpam-491	101	17	(	(	PUNCT
ejpam-491	101	18	x	x	NOUN
ejpam-491	101	19	)	)	PUNCT
ejpam-491	101	20	,	,	PUNCT
ejpam-491	101	21	there	there	PRON
ejpam-491	101	22	exists	exist	VERB
ejpam-491	101	23	u	u	PROPN
ejpam-491	101	24	∈	∈	PROPN
ejpam-491	101	25	mx	mx	NOUN
ejpam-491	101	26	containing	contain	VERB
ejpam-491	101	27	x	x	PUNCT
ejpam-491	101	28	such	such	ADJ
ejpam-491	101	29	that	that	SCONJ
ejpam-491	101	30	f	f	PROPN
ejpam-491	101	31	(	(	PUNCT
ejpam-491	101	32	u	u	NOUN
ejpam-491	101	33	)	)	PUNCT
ejpam-491	101	34	⊂	⊂	PROPN
ejpam-491	101	35	v	v	NOUN
ejpam-491	101	36	.	.	PUNCT
ejpam-491	102	1	a	a	DET
ejpam-491	102	2	function	function	NOUN
ejpam-491	102	3	f	f	NOUN
ejpam-491	102	4	:	:	PUNCT
ejpam-491	102	5	(	(	PUNCT
ejpam-491	102	6	x	x	X
ejpam-491	102	7	,	,	PUNCT
ejpam-491	102	8	mx	mx	PROPN
ejpam-491	102	9	)	)	PUNCT
ejpam-491	102	10	→	→	SYM
ejpam-491	102	11	(	(	PUNCT
ejpam-491	102	12	y	y	NOUN
ejpam-491	102	13	,	,	PUNCT
ejpam-491	102	14	my	my	INTJ
ejpam-491	102	15	)	)	PUNCT
ejpam-491	102	16	is	be	AUX
ejpam-491	102	17	said	say	VERB
ejpam-491	102	18	to	to	PART
ejpam-491	102	19	be	be	AUX
ejpam-491	102	20	m	m	NOUN
ejpam-491	102	21	-	-	ADJ
ejpam-491	102	22	continuous	continuous	ADJ
ejpam-491	102	23	if	if	SCONJ
ejpam-491	102	24	it	it	PRON
ejpam-491	102	25	has	have	VERB
ejpam-491	102	26	this	this	DET
ejpam-491	102	27	property	property	NOUN
ejpam-491	102	28	at	at	ADP
ejpam-491	102	29	each	each	DET
ejpam-491	102	30	point	point	NOUN
ejpam-491	102	31	x	x	X
ejpam-491	102	32	∈	∈	PROPN
ejpam-491	102	33	x	x	X
ejpam-491	102	34	.	.	PUNCT
ejpam-491	103	1	theorem	theorem	NOUN
ejpam-491	103	2	1	1	NUM
ejpam-491	103	3	.	.	X
ejpam-491	103	4	for	for	ADP
ejpam-491	103	5	a	a	DET
ejpam-491	103	6	function	function	NOUN
ejpam-491	103	7	f	f	NOUN
ejpam-491	103	8	:	:	PUNCT
ejpam-491	103	9	(	(	PUNCT
ejpam-491	103	10	x	x	X
ejpam-491	103	11	,	,	PUNCT
ejpam-491	103	12	mx	mx	PROPN
ejpam-491	103	13	)	)	PUNCT
ejpam-491	103	14	→	→	SYM
ejpam-491	103	15	(	(	PUNCT
ejpam-491	103	16	y	y	PROPN
ejpam-491	103	17	,	,	PUNCT
ejpam-491	103	18	my	my	INTJ
ejpam-491	103	19	)	)	PUNCT
ejpam-491	103	20	,	,	PUNCT
ejpam-491	103	21	the	the	DET
ejpam-491	103	22	following	follow	VERB
ejpam-491	103	23	properties	property	NOUN
ejpam-491	103	24	are	be	AUX
ejpam-491	103	25	equivalent	equivalent	ADJ
ejpam-491	103	26	:	:	PUNCT
ejpam-491	103	27	(	(	PUNCT
ejpam-491	103	28	1	1	X
ejpam-491	103	29	)	)	PUNCT
ejpam-491	103	30	f	f	PROPN
ejpam-491	103	31	is	be	AUX
ejpam-491	103	32	m	m	NOUN
ejpam-491	103	33	-	-	ADJ
ejpam-491	103	34	continuous	continuous	ADJ
ejpam-491	103	35	at	at	ADP
ejpam-491	103	36	x	x	X
ejpam-491	103	37	∈	∈	PROPN
ejpam-491	103	38	x	x	X
ejpam-491	103	39	;	;	PUNCT
ejpam-491	103	40	(	(	PUNCT
ejpam-491	103	41	2	2	X
ejpam-491	103	42	)	)	PUNCT
ejpam-491	103	43	x	x	SYM
ejpam-491	103	44	∈mint	∈mint	PROPN
ejpam-491	103	45	(	(	PUNCT
ejpam-491	103	46	f	f	PROPN
ejpam-491	103	47	−1(v	−1(v	PROPN
ejpam-491	103	48	)	)	PUNCT
ejpam-491	103	49	)	)	PUNCT
ejpam-491	103	50	for	for	ADP
ejpam-491	103	51	every	every	DET
ejpam-491	103	52	v	v	NOUN
ejpam-491	103	53	∈	∈	PRON
ejpam-491	103	54	my	my	PRON
ejpam-491	103	55	containing	contain	VERB
ejpam-491	103	56	f(x	f(x	PROPN
ejpam-491	103	57	)	)	PUNCT
ejpam-491	103	58	;	;	PUNCT
ejpam-491	104	1	(	(	PUNCT
ejpam-491	104	2	3	3	X
ejpam-491	104	3	)	)	PUNCT
ejpam-491	104	4	x	x	SYM
ejpam-491	104	5	∈	∈	PROPN
ejpam-491	104	6	f	f	X
ejpam-491	104	7	−1(mcl	−1(mcl	X
ejpam-491	104	8	(	(	PUNCT
ejpam-491	104	9	f	f	PROPN
ejpam-491	104	10	(	(	PUNCT
ejpam-491	104	11	a	a	NOUN
ejpam-491	104	12	)	)	PUNCT
ejpam-491	104	13	)	)	PUNCT
ejpam-491	104	14	)	)	PUNCT
ejpam-491	104	15	for	for	ADP
ejpam-491	104	16	every	every	DET
ejpam-491	104	17	subset	subset	NOUN
ejpam-491	104	18	a	a	PRON
ejpam-491	104	19	of	of	ADP
ejpam-491	104	20	x	x	PUNCT
ejpam-491	104	21	with	with	ADP
ejpam-491	104	22	x	x	PROPN
ejpam-491	104	23	∈mcl(a	∈mcl(a	PROPN
ejpam-491	104	24	)	)	PUNCT
ejpam-491	104	25	;	;	PUNCT
ejpam-491	104	26	(	(	PUNCT
ejpam-491	104	27	4	4	X
ejpam-491	104	28	)	)	PUNCT
ejpam-491	104	29	x	x	SYM
ejpam-491	104	30	∈	∈	PROPN
ejpam-491	104	31	f	f	PROPN
ejpam-491	104	32	−1(mcl(b	−1(mcl(b	NOUN
ejpam-491	104	33	)	)	PUNCT
ejpam-491	104	34	)	)	PUNCT
ejpam-491	104	35	for	for	ADP
ejpam-491	104	36	every	every	DET
ejpam-491	104	37	subset	subset	NOUN
ejpam-491	104	38	b	b	PROPN
ejpam-491	104	39	of	of	ADP
ejpam-491	104	40	y	y	PROPN
ejpam-491	104	41	with	with	ADP
ejpam-491	104	42	x	x	PUNCT
ejpam-491	104	43	∈mcl	∈mcl	PROPN
ejpam-491	104	44	(	(	PUNCT
ejpam-491	104	45	f	f	PROPN
ejpam-491	104	46	−1(b	−1(b	NOUN
ejpam-491	104	47	)	)	PUNCT
ejpam-491	104	48	)	)	PUNCT
ejpam-491	104	49	;	;	PUNCT
ejpam-491	104	50	(	(	PUNCT
ejpam-491	104	51	5	5	X
ejpam-491	104	52	)	)	PUNCT
ejpam-491	104	53	x	x	SYM
ejpam-491	104	54	∈mint	∈mint	PROPN
ejpam-491	104	55	(	(	PUNCT
ejpam-491	104	56	f	f	PROPN
ejpam-491	104	57	−1(b	−1(b	NOUN
ejpam-491	104	58	)	)	PUNCT
ejpam-491	104	59	)	)	PUNCT
ejpam-491	104	60	for	for	ADP
ejpam-491	104	61	every	every	DET
ejpam-491	104	62	subset	subset	NOUN
ejpam-491	104	63	b	b	PROPN
ejpam-491	104	64	of	of	ADP
ejpam-491	104	65	y	y	PROPN
ejpam-491	104	66	with	with	ADP
ejpam-491	104	67	x	x	PROPN
ejpam-491	104	68	∈	∈	PROPN
ejpam-491	104	69	f	f	PROPN
ejpam-491	104	70	−1(mint(b	−1(mint(b	NUM
ejpam-491	104	71	)	)	PUNCT
ejpam-491	104	72	)	)	PUNCT
ejpam-491	104	73	;	;	PUNCT
ejpam-491	104	74	(	(	PUNCT
ejpam-491	104	75	6	6	X
ejpam-491	104	76	)	)	PUNCT
ejpam-491	104	77	x	x	SYM
ejpam-491	104	78	∈	∈	PROPN
ejpam-491	104	79	f	f	PROPN
ejpam-491	104	80	−1(k	−1(k	NOUN
ejpam-491	104	81	)	)	PUNCT
ejpam-491	104	82	for	for	ADP
ejpam-491	104	83	every	every	DET
ejpam-491	104	84	my	my	PRON
ejpam-491	104	85	-closed	-closed	ADJ
ejpam-491	104	86	set	set	NOUN
ejpam-491	104	87	k	k	PROPN
ejpam-491	104	88	of	of	ADP
ejpam-491	104	89	y	y	PROPN
ejpam-491	104	90	such	such	ADJ
ejpam-491	104	91	that	that	SCONJ
ejpam-491	104	92	x	x	PUNCT
ejpam-491	104	93	∈mcl	∈mcl	X
ejpam-491	104	94	(	(	PUNCT
ejpam-491	104	95	f	f	PROPN
ejpam-491	104	96	−1(k	−1(k	NOUN
ejpam-491	104	97	)	)	PUNCT
ejpam-491	104	98	)	)	PUNCT
ejpam-491	104	99	.	.	PUNCT
ejpam-491	105	1	proof	proof	NOUN
ejpam-491	105	2	.	.	PUNCT
ejpam-491	106	1	(	(	PUNCT
ejpam-491	106	2	1	1	X
ejpam-491	106	3	)	)	PUNCT
ejpam-491	106	4	⇒	⇒	NOUN
ejpam-491	106	5	(	(	PUNCT
ejpam-491	106	6	2	2	NUM
ejpam-491	106	7	):	):	PUNCT
ejpam-491	106	8	let	let	VERB
ejpam-491	106	9	v	v	AUX
ejpam-491	106	10	∈	∈	VERB
ejpam-491	106	11	my	my	PRON
ejpam-491	106	12	containing	contain	VERB
ejpam-491	106	13	f	f	X
ejpam-491	106	14	(	(	PUNCT
ejpam-491	106	15	x	x	NOUN
ejpam-491	106	16	)	)	PUNCT
ejpam-491	106	17	.	.	PUNCT
ejpam-491	107	1	then	then	ADV
ejpam-491	107	2	,	,	PUNCT
ejpam-491	107	3	there	there	PRON
ejpam-491	107	4	exists	exist	VERB
ejpam-491	107	5	u	u	PROPN
ejpam-491	107	6	∈	∈	PROPN
ejpam-491	107	7	mx	mx	NOUN
ejpam-491	107	8	containing	contain	VERB
ejpam-491	107	9	x	x	PUNCT
ejpam-491	107	10	such	such	ADJ
ejpam-491	107	11	that	that	SCONJ
ejpam-491	107	12	f	f	PROPN
ejpam-491	107	13	(	(	PUNCT
ejpam-491	107	14	u	u	NOUN
ejpam-491	107	15	)	)	PUNCT
ejpam-491	107	16	⊂	⊂	PROPN
ejpam-491	107	17	v	v	NOUN
ejpam-491	107	18	.	.	PUNCT
ejpam-491	108	1	thus	thus	ADV
ejpam-491	108	2	x	x	SYM
ejpam-491	108	3	∈	∈	X
ejpam-491	108	4	u	u	X
ejpam-491	108	5	⊂	⊂	PROPN
ejpam-491	108	6	f	f	PROPN
ejpam-491	108	7	−1(v	−1(v	PROPN
ejpam-491	108	8	)	)	PUNCT
ejpam-491	108	9	.	.	PUNCT
ejpam-491	109	1	since	since	SCONJ
ejpam-491	109	2	u	u	PROPN
ejpam-491	109	3	∈	∈	PROPN
ejpam-491	109	4	mx	mx	PROPN
ejpam-491	109	5	,	,	PUNCT
ejpam-491	109	6	we	we	PRON
ejpam-491	109	7	have	have	VERB
ejpam-491	109	8	x	x	PART
ejpam-491	109	9	∈mint	∈mint	PROPN
ejpam-491	109	10	(	(	PUNCT
ejpam-491	109	11	f	f	PROPN
ejpam-491	109	12	−1(v	−1(v	PROPN
ejpam-491	109	13	)	)	PUNCT
ejpam-491	109	14	)	)	PUNCT
ejpam-491	109	15	.	.	PUNCT
ejpam-491	110	1	(	(	PUNCT
ejpam-491	110	2	2	2	X
ejpam-491	110	3	)	)	PUNCT
ejpam-491	110	4	⇒	⇒	NOUN
ejpam-491	110	5	(	(	PUNCT
ejpam-491	110	6	3	3	NUM
ejpam-491	110	7	):	):	PUNCT
ejpam-491	110	8	let	let	VERB
ejpam-491	110	9	a	a	PRON
ejpam-491	110	10	be	be	AUX
ejpam-491	110	11	any	any	DET
ejpam-491	110	12	subset	subset	NOUN
ejpam-491	110	13	of	of	ADP
ejpam-491	110	14	x	x	X
ejpam-491	110	15	.	.	PUNCT
ejpam-491	111	1	let	let	VERB
ejpam-491	111	2	x	x	SYM
ejpam-491	111	3	∈	∈	PROPN
ejpam-491	111	4	mcl(a	mcl(a	PROPN
ejpam-491	111	5	)	)	PUNCT
ejpam-491	111	6	and	and	CCONJ
ejpam-491	111	7	v	v	ADP
ejpam-491	111	8	∈	∈	PRON
ejpam-491	111	9	my	my	PRON
ejpam-491	111	10	containing	contain	VERB
ejpam-491	111	11	f	f	X
ejpam-491	111	12	(	(	PUNCT
ejpam-491	111	13	x	x	NOUN
ejpam-491	111	14	)	)	PUNCT
ejpam-491	111	15	.	.	PUNCT
ejpam-491	112	1	then	then	ADV
ejpam-491	112	2	x	x	X
ejpam-491	112	3	∈mint	∈mint	PROPN
ejpam-491	112	4	(	(	PUNCT
ejpam-491	112	5	f	f	PROPN
ejpam-491	112	6	−1(v	−1(v	PROPN
ejpam-491	112	7	)	)	PUNCT
ejpam-491	112	8	)	)	PUNCT
ejpam-491	112	9	.	.	PUNCT
ejpam-491	113	1	there	there	PRON
ejpam-491	113	2	exists	exist	VERB
ejpam-491	113	3	u	u	PROPN
ejpam-491	113	4	∈	∈	PROPN
ejpam-491	113	5	mx	mx	PROPN
ejpam-491	113	6	such	such	ADJ
ejpam-491	113	7	that	that	SCONJ
ejpam-491	113	8	x	x	SYM
ejpam-491	113	9	∈	∈	PROPN
ejpam-491	113	10	u	u	X
ejpam-491	113	11	⊂	⊂	PROPN
ejpam-491	113	12	f	f	PROPN
ejpam-491	113	13	−1(v	−1(v	PROPN
ejpam-491	113	14	)	)	PUNCT
ejpam-491	113	15	.	.	PUNCT
ejpam-491	114	1	since	since	SCONJ
ejpam-491	114	2	x	x	PROPN
ejpam-491	114	3	∈mcl(a	∈mcl(a	NOUN
ejpam-491	114	4	)	)	PUNCT
ejpam-491	114	5	,	,	PUNCT
ejpam-491	114	6	by	by	ADP
ejpam-491	114	7	lemma	lemma	PROPN
ejpam-491	114	8	2	2	NUM
ejpam-491	114	9	,	,	PUNCT
ejpam-491	114	10	u	u	NOUN
ejpam-491	114	11	∩a	∩a	PROPN
ejpam-491	114	12	6=	6=	PROPN
ejpam-491	114	13	;	;	PUNCT
ejpam-491	114	14	and	and	CCONJ
ejpam-491	114	15	;	;	PUNCT
ejpam-491	114	16	6=	6=	NUM
ejpam-491	114	17	f	f	X
ejpam-491	114	18	(	(	PUNCT
ejpam-491	114	19	u	u	NOUN
ejpam-491	114	20	∩a	∩a	PROPN
ejpam-491	114	21	)	)	PUNCT
ejpam-491	115	1	⊂	⊂	PROPN
ejpam-491	115	2	f	f	X
ejpam-491	115	3	(	(	PUNCT
ejpam-491	115	4	u)∩	u)∩	PROPN
ejpam-491	115	5	f	f	PROPN
ejpam-491	115	6	(	(	PUNCT
ejpam-491	115	7	a)⊂	a)⊂	PROPN
ejpam-491	115	8	v	v	ADP
ejpam-491	115	9	∩	∩	ADJ
ejpam-491	115	10	f	f	X
ejpam-491	115	11	(	(	PUNCT
ejpam-491	115	12	a	a	NOUN
ejpam-491	115	13	)	)	PUNCT
ejpam-491	115	14	.	.	PUNCT
ejpam-491	116	1	since	since	SCONJ
ejpam-491	116	2	v	v	NUM
ejpam-491	116	3	∈	∈	PRON
ejpam-491	116	4	my	my	PRON
ejpam-491	116	5	containing	contain	VERB
ejpam-491	116	6	f	f	X
ejpam-491	116	7	(	(	PUNCT
ejpam-491	116	8	x	x	NOUN
ejpam-491	116	9	)	)	PUNCT
ejpam-491	116	10	,	,	PUNCT
ejpam-491	116	11	f	f	PROPN
ejpam-491	116	12	(	(	PUNCT
ejpam-491	116	13	x	x	X
ejpam-491	116	14	)	)	PUNCT
ejpam-491	116	15	∈mcl	∈mcl	PROPN
ejpam-491	116	16	(	(	PUNCT
ejpam-491	116	17	f	f	X
ejpam-491	116	18	(	(	PUNCT
ejpam-491	116	19	a	a	NOUN
ejpam-491	116	20	)	)	PUNCT
ejpam-491	116	21	)	)	PUNCT
ejpam-491	116	22	and	and	CCONJ
ejpam-491	116	23	hence	hence	ADV
ejpam-491	116	24	x	x	X
ejpam-491	116	25	∈	∈	PROPN
ejpam-491	116	26	f	f	X
ejpam-491	116	27	−1(mcl	−1(mcl	X
ejpam-491	116	28	(	(	PUNCT
ejpam-491	116	29	f	f	PROPN
ejpam-491	116	30	(	(	PUNCT
ejpam-491	116	31	a	a	NOUN
ejpam-491	116	32	)	)	PUNCT
ejpam-491	116	33	)	)	PUNCT
ejpam-491	116	34	.	.	PUNCT
ejpam-491	117	1	(	(	PUNCT
ejpam-491	117	2	3	3	X
ejpam-491	117	3	)	)	PUNCT
ejpam-491	117	4	⇒	⇒	NOUN
ejpam-491	117	5	(	(	PUNCT
ejpam-491	117	6	4	4	NUM
ejpam-491	117	7	):	):	PUNCT
ejpam-491	117	8	let	let	VERB
ejpam-491	117	9	b	b	X
ejpam-491	117	10	be	be	AUX
ejpam-491	117	11	any	any	DET
ejpam-491	117	12	subset	subset	NOUN
ejpam-491	117	13	of	of	ADP
ejpam-491	117	14	y	y	PROPN
ejpam-491	117	15	and	and	CCONJ
ejpam-491	117	16	x	x	PROPN
ejpam-491	117	17	∈	∈	PROPN
ejpam-491	117	18	mcl	mcl	PROPN
ejpam-491	117	19	(	(	PUNCT
ejpam-491	117	20	f	f	PROPN
ejpam-491	117	21	−1(b	−1(b	NOUN
ejpam-491	117	22	)	)	PUNCT
ejpam-491	117	23	)	)	PUNCT
ejpam-491	117	24	,	,	PUNCT
ejpam-491	117	25	then	then	ADV
ejpam-491	117	26	by	by	ADP
ejpam-491	117	27	(	(	PUNCT
ejpam-491	117	28	3	3	X
ejpam-491	117	29	)	)	PUNCT
ejpam-491	117	30	x	x	SYM
ejpam-491	117	31	∈	∈	PROPN
ejpam-491	117	32	f	f	X
ejpam-491	117	33	−1(mcl	−1(mcl	X
ejpam-491	117	34	(	(	PUNCT
ejpam-491	117	35	f	f	PROPN
ejpam-491	117	36	(	(	PUNCT
ejpam-491	117	37	f	f	PROPN
ejpam-491	117	38	−1(b	−1(b	NOUN
ejpam-491	117	39	)	)	PUNCT
ejpam-491	117	40	)	)	PUNCT
ejpam-491	117	41	)	)	PUNCT
ejpam-491	117	42	)	)	PUNCT
ejpam-491	118	1	⊂	⊂	PROPN
ejpam-491	118	2	f	f	X
ejpam-491	118	3	−1(mcl(b	−1(mcl(b	NOUN
ejpam-491	118	4	)	)	PUNCT
ejpam-491	118	5	)	)	PUNCT
ejpam-491	118	6	.	.	PUNCT
ejpam-491	119	1	hence	hence	ADV
ejpam-491	119	2	,	,	PUNCT
ejpam-491	119	3	we	we	PRON
ejpam-491	119	4	have	have	VERB
ejpam-491	119	5	x	x	X
ejpam-491	119	6	∈	∈	PROPN
ejpam-491	119	7	f	f	PROPN
ejpam-491	119	8	−1(mcl(b	−1(mcl(b	NOUN
ejpam-491	119	9	)	)	PUNCT
ejpam-491	119	10	)	)	PUNCT
ejpam-491	119	11	.	.	PUNCT
ejpam-491	120	1	(	(	PUNCT
ejpam-491	120	2	4	4	X
ejpam-491	120	3	)	)	PUNCT
ejpam-491	120	4	⇒	⇒	NOUN
ejpam-491	120	5	(	(	PUNCT
ejpam-491	120	6	5	5	NUM
ejpam-491	120	7	):	):	PUNCT
ejpam-491	120	8	let	let	VERB
ejpam-491	120	9	b	b	X
ejpam-491	120	10	be	be	AUX
ejpam-491	120	11	any	any	DET
ejpam-491	120	12	subset	subset	NOUN
ejpam-491	120	13	of	of	ADP
ejpam-491	120	14	y	y	PRON
ejpam-491	121	1	such	such	ADJ
ejpam-491	121	2	that	that	SCONJ
ejpam-491	121	3	x	x	SYM
ejpam-491	121	4	/∈	/∈	PUNCT
ejpam-491	121	5	mint	mint	PROPN
ejpam-491	121	6	(	(	PUNCT
ejpam-491	121	7	f	f	PROPN
ejpam-491	121	8	−1(b	−1(b	NOUN
ejpam-491	121	9	)	)	PUNCT
ejpam-491	121	10	)	)	PUNCT
ejpam-491	121	11	.	.	PUNCT
ejpam-491	122	1	then	then	ADV
ejpam-491	122	2	x	x	SYM
ejpam-491	122	3	∈	∈	PROPN
ejpam-491	122	4	x	x	PUNCT
ejpam-491	122	5	−	−	PROPN
ejpam-491	122	6	mint	mint	PROPN
ejpam-491	122	7	(	(	PUNCT
ejpam-491	122	8	f	f	PROPN
ejpam-491	122	9	−1(b	−1(b	NOUN
ejpam-491	122	10	)	)	PUNCT
ejpam-491	122	11	)	)	PUNCT
ejpam-491	123	1	=	=	NOUN
ejpam-491	124	1	mcl(x	mcl(x	PROPN
ejpam-491	124	2	−	−	NOUN
ejpam-491	124	3	f	f	PROPN
ejpam-491	124	4	−1(b	−1(b	NOUN
ejpam-491	124	5	)	)	PUNCT
ejpam-491	124	6	)	)	PUNCT
ejpam-491	125	1	=	=	SYM
ejpam-491	125	2	mcl	mcl	PROPN
ejpam-491	125	3	(	(	PUNCT
ejpam-491	125	4	f	f	PROPN
ejpam-491	125	5	−1(y	−1(y	X
ejpam-491	125	6	−	−	PROPN
ejpam-491	125	7	b	b	NOUN
ejpam-491	125	8	)	)	PUNCT
ejpam-491	125	9	)	)	PUNCT
ejpam-491	125	10	.	.	PUNCT
ejpam-491	126	1	by	by	ADP
ejpam-491	126	2	(	(	PUNCT
ejpam-491	126	3	4	4	NUM
ejpam-491	126	4	)	)	PUNCT
ejpam-491	126	5	,	,	PUNCT
ejpam-491	126	6	we	we	PRON
ejpam-491	126	7	have	have	VERB
ejpam-491	126	8	x	x	X
ejpam-491	126	9	∈	∈	PROPN
ejpam-491	126	10	t.	t.	NOUN
ejpam-491	126	11	noiri	noiri	PROPN
ejpam-491	126	12	and	and	CCONJ
ejpam-491	126	13	v.	v.	ADP
ejpam-491	126	14	popa	popa	NOUN
ejpam-491	126	15	/	/	SYM
ejpam-491	126	16	eur	eur	PROPN
ejpam-491	126	17	.	.	PUNCT
ejpam-491	127	1	j.	j.	PROPN
ejpam-491	127	2	pure	pure	PROPN
ejpam-491	127	3	appl	appl	PROPN
ejpam-491	127	4	.	.	PROPN
ejpam-491	127	5	math	math	PROPN
ejpam-491	127	6	,	,	PUNCT
ejpam-491	127	7	2	2	NUM
ejpam-491	127	8	(	(	PUNCT
ejpam-491	127	9	2009	2009	NUM
ejpam-491	127	10	)	)	PUNCT
ejpam-491	127	11	,	,	PUNCT
ejpam-491	127	12	(	(	PUNCT
ejpam-491	127	13	473	473	NUM
ejpam-491	127	14	-	-	NUM
ejpam-491	127	15	493	493	NUM
ejpam-491	127	16	)	)	PUNCT
ejpam-491	127	17	478	478	NUM
ejpam-491	127	18	f	f	PROPN
ejpam-491	127	19	−1(mcl(y	−1(mcl(y	NOUN
ejpam-491	127	20	−b	−b	NOUN
ejpam-491	127	21	)	)	PUNCT
ejpam-491	127	22	)	)	PUNCT
ejpam-491	128	1	=	=	PUNCT
ejpam-491	128	2	f	f	X
ejpam-491	128	3	−1(y	−1(y	ADV
ejpam-491	128	4	−mint(b	−mint(b	NUM
ejpam-491	128	5	)	)	PUNCT
ejpam-491	128	6	)	)	PUNCT
ejpam-491	129	1	=	=	PUNCT
ejpam-491	129	2	x	x	PUNCT
ejpam-491	130	1	−	−	PROPN
ejpam-491	130	2	f	f	X
ejpam-491	130	3	−1(mint(b	−1(mint(b	NUM
ejpam-491	130	4	)	)	PUNCT
ejpam-491	130	5	)	)	PUNCT
ejpam-491	130	6	.	.	PUNCT
ejpam-491	131	1	hence	hence	ADV
ejpam-491	131	2	,	,	PUNCT
ejpam-491	131	3	x	x	PROPN
ejpam-491	131	4	/∈	/∈	PUNCT
ejpam-491	131	5	f	f	NOUN
ejpam-491	131	6	−1(mint(b	−1(mint(b	NUM
ejpam-491	131	7	)	)	PUNCT
ejpam-491	131	8	)	)	PUNCT
ejpam-491	131	9	.	.	PUNCT
ejpam-491	132	1	(	(	PUNCT
ejpam-491	132	2	5	5	X
ejpam-491	132	3	)	)	PUNCT
ejpam-491	132	4	⇒	⇒	NOUN
ejpam-491	132	5	(	(	PUNCT
ejpam-491	132	6	6	6	NUM
ejpam-491	132	7	):	):	PUNCT
ejpam-491	132	8	let	let	VERB
ejpam-491	132	9	k	k	PRON
ejpam-491	132	10	be	be	AUX
ejpam-491	132	11	any	any	DET
ejpam-491	132	12	my	my	PRON
ejpam-491	132	13	-closed	-close	VERB
ejpam-491	132	14	set	set	NOUN
ejpam-491	132	15	of	of	ADP
ejpam-491	132	16	y	y	PRON
ejpam-491	132	17	such	such	ADJ
ejpam-491	132	18	that	that	PRON
ejpam-491	132	19	x	x	X
ejpam-491	132	20	/∈	/∈	PUNCT
ejpam-491	132	21	f	f	PROPN
ejpam-491	132	22	−1(k	−1(k	NOUN
ejpam-491	132	23	)	)	PUNCT
ejpam-491	132	24	.	.	PUNCT
ejpam-491	133	1	then	then	ADV
ejpam-491	133	2	x	x	SYM
ejpam-491	133	3	∈	∈	PROPN
ejpam-491	133	4	x	x	X
ejpam-491	133	5	−	−	PROPN
ejpam-491	133	6	f	f	PROPN
ejpam-491	133	7	−1(k	−1(k	NOUN
ejpam-491	133	8	)	)	PUNCT
ejpam-491	133	9	=	=	SYM
ejpam-491	133	10	f	f	PROPN
ejpam-491	133	11	−1(y	−1(y	ADV
ejpam-491	133	12	−k	−k	PROPN
ejpam-491	133	13	)	)	PUNCT
ejpam-491	133	14	=	=	SYM
ejpam-491	133	15	f	f	PROPN
ejpam-491	133	16	−1(mint(y	−1(mint(y	NUM
ejpam-491	133	17	−k	−k	PROPN
ejpam-491	133	18	)	)	PUNCT
ejpam-491	133	19	)	)	PUNCT
ejpam-491	134	1	because	because	SCONJ
ejpam-491	134	2	y	y	PROPN
ejpam-491	134	3	−k	−k	PROPN
ejpam-491	134	4	is	be	AUX
ejpam-491	134	5	my	my	PRON
ejpam-491	134	6	-open	-open	NOUN
ejpam-491	134	7	.	.	PUNCT
ejpam-491	135	1	by	by	ADP
ejpam-491	135	2	(	(	PUNCT
ejpam-491	135	3	5	5	NUM
ejpam-491	135	4	)	)	PUNCT
ejpam-491	135	5	,	,	PUNCT
ejpam-491	135	6	x	x	PROPN
ejpam-491	135	7	∈	∈	PROPN
ejpam-491	135	8	mint	mint	NOUN
ejpam-491	135	9	(	(	PUNCT
ejpam-491	135	10	f	f	PROPN
ejpam-491	135	11	−1(y	−1(y	ADV
ejpam-491	135	12	−k	−k	PROPN
ejpam-491	135	13	)	)	PUNCT
ejpam-491	135	14	)	)	PUNCT
ejpam-491	136	1	=	=	X
ejpam-491	136	2	mint(x	mint(x	NOUN
ejpam-491	136	3	−	−	NUM
ejpam-491	136	4	f	f	PROPN
ejpam-491	136	5	−1(k	−1(k	NOUN
ejpam-491	136	6	)	)	PUNCT
ejpam-491	136	7	)	)	PUNCT
ejpam-491	137	1	=	=	SYM
ejpam-491	137	2	x	x	SYM
ejpam-491	137	3	−mcl	−mcl	X
ejpam-491	137	4	(	(	PUNCT
ejpam-491	137	5	f	f	PROPN
ejpam-491	137	6	−1(k	−1(k	NOUN
ejpam-491	137	7	)	)	PUNCT
ejpam-491	137	8	)	)	PUNCT
ejpam-491	137	9	.	.	PUNCT
ejpam-491	138	1	hence	hence	ADV
ejpam-491	138	2	x	x	X
ejpam-491	138	3	/∈mcl	/∈mcl	X
ejpam-491	138	4	(	(	PUNCT
ejpam-491	138	5	f	f	NOUN
ejpam-491	138	6	−1(k	−1(k	NOUN
ejpam-491	138	7	)	)	PUNCT
ejpam-491	138	8	)	)	PUNCT
ejpam-491	138	9	.	.	PUNCT
ejpam-491	139	1	(	(	PUNCT
ejpam-491	139	2	6)⇒	6)⇒	NUM
ejpam-491	139	3	(	(	PUNCT
ejpam-491	139	4	2	2	NUM
ejpam-491	139	5	):	):	PUNCT
ejpam-491	139	6	let	let	VERB
ejpam-491	139	7	x	x	PUNCT
ejpam-491	139	8	∈	∈	PROPN
ejpam-491	139	9	x	x	X
ejpam-491	139	10	and	and	CCONJ
ejpam-491	139	11	v	v	ADP
ejpam-491	139	12	∈	∈	NOUN
ejpam-491	139	13	my	my	PRON
ejpam-491	139	14	containing	contain	VERB
ejpam-491	139	15	f	f	X
ejpam-491	139	16	(	(	PUNCT
ejpam-491	139	17	x	x	NOUN
ejpam-491	139	18	)	)	PUNCT
ejpam-491	139	19	.	.	PUNCT
ejpam-491	140	1	suppose	suppose	VERB
ejpam-491	140	2	that	that	SCONJ
ejpam-491	140	3	x	x	X
ejpam-491	140	4	/∈mint	/∈mint	PROPN
ejpam-491	140	5	(	(	PUNCT
ejpam-491	140	6	f	f	PROPN
ejpam-491	140	7	−1(v	−1(v	PROPN
ejpam-491	140	8	)	)	PUNCT
ejpam-491	140	9	)	)	PUNCT
ejpam-491	140	10	.	.	PUNCT
ejpam-491	141	1	then	then	ADV
ejpam-491	141	2	x	x	SYM
ejpam-491	141	3	∈	∈	PROPN
ejpam-491	141	4	x	x	SYM
ejpam-491	141	5	−mint	−mint	PROPN
ejpam-491	141	6	(	(	PUNCT
ejpam-491	141	7	f	f	PROPN
ejpam-491	141	8	−1(v	−1(v	PROPN
ejpam-491	141	9	)	)	PUNCT
ejpam-491	141	10	)	)	PUNCT
ejpam-491	142	1	=	=	NOUN
ejpam-491	143	1	mcl(x	mcl(x	PROPN
ejpam-491	143	2	−	−	PROPN
ejpam-491	143	3	f	f	PROPN
ejpam-491	143	4	−1(v	−1(v	PROPN
ejpam-491	143	5	)	)	PUNCT
ejpam-491	143	6	)	)	PUNCT
ejpam-491	144	1	=	=	SYM
ejpam-491	144	2	mcl	mcl	PROPN
ejpam-491	144	3	(	(	PUNCT
ejpam-491	144	4	f	f	PROPN
ejpam-491	144	5	−1(y	−1(y	X
ejpam-491	144	6	−	−	PROPN
ejpam-491	144	7	v	v	NOUN
ejpam-491	144	8	)	)	PUNCT
ejpam-491	144	9	)	)	PUNCT
ejpam-491	144	10	.	.	PUNCT
ejpam-491	145	1	by	by	ADP
ejpam-491	145	2	(	(	PUNCT
ejpam-491	145	3	6	6	NUM
ejpam-491	145	4	)	)	PUNCT
ejpam-491	145	5	,	,	PUNCT
ejpam-491	145	6	x	x	PUNCT
ejpam-491	145	7	∈	∈	PROPN
ejpam-491	145	8	f	f	X
ejpam-491	145	9	−1(y	−1(y	PRON
ejpam-491	145	10	−	−	PROPN
ejpam-491	145	11	v	v	NOUN
ejpam-491	145	12	)	)	PUNCT
ejpam-491	145	13	=	=	PUNCT
ejpam-491	146	1	x	x	PUNCT
ejpam-491	146	2	−	−	PROPN
ejpam-491	146	3	f	f	PROPN
ejpam-491	146	4	−1(v	−1(v	PROPN
ejpam-491	146	5	)	)	PUNCT
ejpam-491	146	6	.	.	PUNCT
ejpam-491	147	1	hence	hence	ADV
ejpam-491	147	2	x	x	X
ejpam-491	147	3	/∈	/∈	PUNCT
ejpam-491	147	4	f	f	PROPN
ejpam-491	147	5	−1(v	−1(v	PROPN
ejpam-491	147	6	)	)	PUNCT
ejpam-491	147	7	.	.	PUNCT
ejpam-491	148	1	this	this	DET
ejpam-491	148	2	contraries	contrary	NOUN
ejpam-491	148	3	to	to	ADP
ejpam-491	148	4	the	the	DET
ejpam-491	148	5	hypothesis	hypothesis	NOUN
ejpam-491	148	6	.	.	PUNCT
ejpam-491	149	1	(	(	PUNCT
ejpam-491	149	2	2	2	X
ejpam-491	149	3	)	)	PUNCT
ejpam-491	149	4	⇒	⇒	NOUN
ejpam-491	149	5	(	(	PUNCT
ejpam-491	149	6	1	1	NUM
ejpam-491	149	7	):	):	PUNCT
ejpam-491	149	8	let	let	VERB
ejpam-491	149	9	v	v	AUX
ejpam-491	149	10	∈	∈	VERB
ejpam-491	149	11	my	my	PRON
ejpam-491	149	12	containing	contain	VERB
ejpam-491	149	13	f	f	X
ejpam-491	149	14	(	(	PUNCT
ejpam-491	149	15	x	x	NOUN
ejpam-491	149	16	)	)	PUNCT
ejpam-491	149	17	.	.	PUNCT
ejpam-491	150	1	by	by	ADP
ejpam-491	150	2	(	(	PUNCT
ejpam-491	150	3	2	2	NUM
ejpam-491	150	4	)	)	PUNCT
ejpam-491	150	5	,	,	PUNCT
ejpam-491	150	6	x	x	PROPN
ejpam-491	150	7	∈	∈	PROPN
ejpam-491	150	8	mint	mint	NOUN
ejpam-491	150	9	(	(	PUNCT
ejpam-491	150	10	f	f	PROPN
ejpam-491	150	11	−1(v	−1(v	PROPN
ejpam-491	150	12	)	)	PUNCT
ejpam-491	150	13	)	)	PUNCT
ejpam-491	150	14	and	and	CCONJ
ejpam-491	150	15	hence	hence	ADV
ejpam-491	150	16	there	there	PRON
ejpam-491	150	17	exists	exist	VERB
ejpam-491	150	18	u	u	PROPN
ejpam-491	150	19	∈	∈	PROPN
ejpam-491	150	20	mx	mx	NOUN
ejpam-491	150	21	containing	contain	VERB
ejpam-491	150	22	x	x	PUNCT
ejpam-491	150	23	such	such	ADJ
ejpam-491	150	24	that	that	SCONJ
ejpam-491	150	25	x	x	SYM
ejpam-491	150	26	∈	∈	PROPN
ejpam-491	150	27	u	u	X
ejpam-491	150	28	⊂	⊂	PROPN
ejpam-491	150	29	f	f	PROPN
ejpam-491	150	30	−1(v	−1(v	PROPN
ejpam-491	150	31	)	)	PUNCT
ejpam-491	150	32	.	.	PUNCT
ejpam-491	151	1	therefore	therefore	ADV
ejpam-491	151	2	,	,	PUNCT
ejpam-491	151	3	f	f	PROPN
ejpam-491	151	4	(	(	PUNCT
ejpam-491	151	5	u	u	NOUN
ejpam-491	151	6	)	)	PUNCT
ejpam-491	151	7	⊂	⊂	PROPN
ejpam-491	151	8	v	v	PROPN
ejpam-491	151	9	and	and	CCONJ
ejpam-491	151	10	f	f	PROPN
ejpam-491	151	11	is	be	AUX
ejpam-491	151	12	m	m	PRON
ejpam-491	151	13	-continuous	-continuous	ADJ
ejpam-491	151	14	at	at	ADP
ejpam-491	151	15	x	x	X
ejpam-491	151	16	.	.	PUNCT
ejpam-491	152	1	for	for	ADP
ejpam-491	152	2	a	a	DET
ejpam-491	152	3	function	function	NOUN
ejpam-491	152	4	f	f	NOUN
ejpam-491	152	5	:	:	PUNCT
ejpam-491	152	6	(	(	PUNCT
ejpam-491	152	7	x	x	X
ejpam-491	152	8	,	,	PUNCT
ejpam-491	152	9	mx	mx	PROPN
ejpam-491	152	10	)	)	PUNCT
ejpam-491	152	11	→	→	SYM
ejpam-491	152	12	(	(	PUNCT
ejpam-491	152	13	y	y	PROPN
ejpam-491	152	14	,	,	PUNCT
ejpam-491	152	15	my	my	INTJ
ejpam-491	152	16	)	)	PUNCT
ejpam-491	152	17	,	,	PUNCT
ejpam-491	152	18	we	we	PRON
ejpam-491	152	19	define	define	VERB
ejpam-491	152	20	dm	dm	PROPN
ejpam-491	152	21	(	(	PUNCT
ejpam-491	152	22	f	f	PROPN
ejpam-491	152	23	)	)	PUNCT
ejpam-491	152	24	as	as	SCONJ
ejpam-491	152	25	follows	follow	VERB
ejpam-491	152	26	:	:	PUNCT
ejpam-491	152	27	dm	dm	PROPN
ejpam-491	152	28	(	(	PUNCT
ejpam-491	152	29	f	f	PROPN
ejpam-491	152	30	)	)	PUNCT
ejpam-491	152	31	=	=	PRON
ejpam-491	153	1	{	{	PUNCT
ejpam-491	153	2	x	x	PUNCT
ejpam-491	153	3	∈	∈	PROPN
ejpam-491	153	4	x	x	X
ejpam-491	153	5	:	:	PUNCT
ejpam-491	153	6	f	f	X
ejpam-491	153	7	is	be	AUX
ejpam-491	153	8	not	not	PART
ejpam-491	153	9	m	m	PRON
ejpam-491	153	10	-continuous	-continuous	ADJ
ejpam-491	153	11	at	at	ADP
ejpam-491	153	12	x	x	X
ejpam-491	153	13	}	}	PUNCT
ejpam-491	153	14	.	.	PUNCT
ejpam-491	154	1	theorem	theorem	NOUN
ejpam-491	154	2	2	2	NUM
ejpam-491	154	3	.	.	X
ejpam-491	154	4	for	for	ADP
ejpam-491	154	5	a	a	DET
ejpam-491	154	6	function	function	NOUN
ejpam-491	154	7	f	f	NOUN
ejpam-491	154	8	:	:	PUNCT
ejpam-491	154	9	(	(	PUNCT
ejpam-491	154	10	x	x	X
ejpam-491	154	11	,	,	PUNCT
ejpam-491	154	12	mx	mx	PROPN
ejpam-491	154	13	)	)	PUNCT
ejpam-491	154	14	→	→	SYM
ejpam-491	154	15	(	(	PUNCT
ejpam-491	154	16	y	y	PROPN
ejpam-491	154	17	,	,	PUNCT
ejpam-491	154	18	my	my	INTJ
ejpam-491	154	19	)	)	PUNCT
ejpam-491	154	20	,	,	PUNCT
ejpam-491	154	21	the	the	DET
ejpam-491	154	22	following	follow	VERB
ejpam-491	154	23	properties	property	NOUN
ejpam-491	154	24	hold	hold	VERB
ejpam-491	154	25	:	:	PUNCT
ejpam-491	154	26	dm	dm	PROPN
ejpam-491	154	27	(	(	PUNCT
ejpam-491	154	28	f	f	PROPN
ejpam-491	154	29	)	)	PUNCT
ejpam-491	155	1	=	=	PUNCT
ejpam-491	155	2	⋃	⋃	PROPN
ejpam-491	155	3	g∈my	g∈my	NOUN
ejpam-491	155	4	{	{	PUNCT
ejpam-491	155	5	f	f	NOUN
ejpam-491	155	6	−1(g)−mint	−1(g)−mint	NOUN
ejpam-491	155	7	(	(	PUNCT
ejpam-491	155	8	f	f	NOUN
ejpam-491	155	9	−1(g	−1(g	NOUN
ejpam-491	155	10	)	)	PUNCT
ejpam-491	155	11	)	)	PUNCT
ejpam-491	155	12	}	}	PUNCT
ejpam-491	156	1	=	=	SYM
ejpam-491	156	2	⋃	⋃	NOUN
ejpam-491	156	3	b∈p	b∈p	NOUN
ejpam-491	156	4	(	(	PUNCT
ejpam-491	156	5	y	y	PROPN
ejpam-491	156	6	)	)	PUNCT
ejpam-491	156	7	{	{	PUNCT
ejpam-491	156	8	f	f	PROPN
ejpam-491	156	9	−1(int(b))−mint	−1(int(b))−mint	PROPN
ejpam-491	156	10	(	(	PUNCT
ejpam-491	156	11	f	f	PROPN
ejpam-491	156	12	−1(b	−1(b	NOUN
ejpam-491	156	13	)	)	PUNCT
ejpam-491	156	14	)	)	PUNCT
ejpam-491	156	15	}	}	PUNCT
ejpam-491	157	1	=	=	SYM
ejpam-491	157	2	⋃	⋃	NOUN
ejpam-491	157	3	b∈p	b∈p	NOUN
ejpam-491	157	4	(	(	PUNCT
ejpam-491	157	5	y	y	PROPN
ejpam-491	157	6	)	)	PUNCT
ejpam-491	157	7	{	{	PUNCT
ejpam-491	157	8	mcl	mcl	PROPN
ejpam-491	157	9	(	(	PUNCT
ejpam-491	157	10	f	f	PROPN
ejpam-491	157	11	−1(b))−	−1(b))−	NUM
ejpam-491	157	12	f	f	PROPN
ejpam-491	157	13	−1(mcl(b	−1(mcl(b	NOUN
ejpam-491	157	14	)	)	PUNCT
ejpam-491	157	15	)	)	PUNCT
ejpam-491	157	16	}	}	PUNCT
ejpam-491	158	1	=	=	SYM
ejpam-491	158	2	⋃	⋃	NOUN
ejpam-491	158	3	a∈p	a∈p	NOUN
ejpam-491	158	4	(	(	PUNCT
ejpam-491	158	5	x	x	X
ejpam-491	158	6	)	)	PUNCT
ejpam-491	158	7	{	{	PUNCT
ejpam-491	158	8	mcl(a)−	mcl(a)−	NOUN
ejpam-491	158	9	f	f	PROPN
ejpam-491	158	10	−1(mcl	−1(mcl	X
ejpam-491	158	11	(	(	PUNCT
ejpam-491	158	12	f	f	PROPN
ejpam-491	158	13	(	(	PUNCT
ejpam-491	158	14	a	a	NOUN
ejpam-491	158	15	)	)	PUNCT
ejpam-491	158	16	)	)	PUNCT
ejpam-491	158	17	)	)	PUNCT
ejpam-491	158	18	}	}	PUNCT
ejpam-491	158	19	=	=	SYM
ejpam-491	158	20	⋃	⋃	NOUN
ejpam-491	158	21	k∈f	k∈f	NOUN
ejpam-491	158	22	{	{	PUNCT
ejpam-491	158	23	mcl	mcl	PROPN
ejpam-491	158	24	(	(	PUNCT
ejpam-491	158	25	f	f	PROPN
ejpam-491	158	26	−1(k))−	−1(k))−	PROPN
ejpam-491	158	27	f	f	PROPN
ejpam-491	158	28	−1(k	−1(k	NOUN
ejpam-491	158	29	)	)	PUNCT
ejpam-491	158	30	}	}	PUNCT
ejpam-491	158	31	,	,	PUNCT
ejpam-491	158	32	where	where	SCONJ
ejpam-491	158	33	f	f	PROPN
ejpam-491	158	34	is	be	AUX
ejpam-491	158	35	the	the	DET
ejpam-491	158	36	family	family	NOUN
ejpam-491	158	37	of	of	ADP
ejpam-491	158	38	my	my	PRON
ejpam-491	158	39	-closed	-close	VERB
ejpam-491	158	40	sets	set	NOUN
ejpam-491	158	41	of	of	ADP
ejpam-491	158	42	y	y	PROPN
ejpam-491	158	43	.	.	PUNCT
ejpam-491	159	1	proof	proof	NOUN
ejpam-491	159	2	.	.	PUNCT
ejpam-491	160	1	we	we	PRON
ejpam-491	160	2	show	show	VERB
ejpam-491	160	3	only	only	ADV
ejpam-491	160	4	the	the	DET
ejpam-491	160	5	first	first	ADJ
ejpam-491	160	6	equality	equality	NOUN
ejpam-491	160	7	because	because	SCONJ
ejpam-491	160	8	the	the	DET
ejpam-491	160	9	proofs	proof	NOUN
ejpam-491	160	10	of	of	ADP
ejpam-491	160	11	the	the	DET
ejpam-491	160	12	others	other	NOUN
ejpam-491	160	13	are	be	AUX
ejpam-491	160	14	similar	similar	ADJ
ejpam-491	160	15	to	to	ADP
ejpam-491	160	16	the	the	DET
ejpam-491	160	17	first	first	ADJ
ejpam-491	160	18	one	one	NUM
ejpam-491	160	19	.	.	PUNCT
ejpam-491	161	1	let	let	VERB
ejpam-491	161	2	x	x	SYM
ejpam-491	161	3	∈	∈	PROPN
ejpam-491	161	4	dm	dm	X
ejpam-491	161	5	(	(	PUNCT
ejpam-491	161	6	f	f	PROPN
ejpam-491	161	7	)	)	PUNCT
ejpam-491	161	8	.	.	PUNCT
ejpam-491	162	1	by	by	ADP
ejpam-491	162	2	theorem	theorem	NOUN
ejpam-491	162	3	1	1	NUM
ejpam-491	162	4	,	,	PUNCT
ejpam-491	162	5	there	there	PRON
ejpam-491	162	6	exists	exist	VERB
ejpam-491	162	7	v	v	ADP
ejpam-491	162	8	∈	∈	PRON
ejpam-491	162	9	my	my	PRON
ejpam-491	162	10	such	such	ADJ
ejpam-491	162	11	that	that	SCONJ
ejpam-491	162	12	f	f	PROPN
ejpam-491	162	13	(	(	PUNCT
ejpam-491	162	14	x	x	X
ejpam-491	162	15	)	)	PUNCT
ejpam-491	162	16	∈	∈	NOUN
ejpam-491	162	17	v	v	NOUN
ejpam-491	162	18	and	and	CCONJ
ejpam-491	162	19	x	x	PROPN
ejpam-491	162	20	/∈	/∈	PROPN
ejpam-491	162	21	mint	mint	PROPN
ejpam-491	162	22	(	(	PUNCT
ejpam-491	162	23	f	f	PROPN
ejpam-491	162	24	−1(v	−1(v	PROPN
ejpam-491	162	25	)	)	PUNCT
ejpam-491	162	26	)	)	PUNCT
ejpam-491	162	27	.	.	PUNCT
ejpam-491	163	1	therefore	therefore	ADV
ejpam-491	163	2	,	,	PUNCT
ejpam-491	163	3	we	we	PRON
ejpam-491	163	4	have	have	VERB
ejpam-491	163	5	x	x	X
ejpam-491	163	6	∈	∈	PROPN
ejpam-491	163	7	f	f	PROPN
ejpam-491	163	8	−1(v	−1(v	NOUN
ejpam-491	163	9	)	)	PUNCT
ejpam-491	163	10	−mint	−mint	PROPN
ejpam-491	164	1	(	(	PUNCT
ejpam-491	164	2	f	f	PROPN
ejpam-491	164	3	−1(v	−1(v	PROPN
ejpam-491	164	4	)	)	PUNCT
ejpam-491	164	5	)	)	PUNCT
ejpam-491	165	1	⊂	⊂	PROPN
ejpam-491	165	2	⋃	⋃	PROPN
ejpam-491	165	3	g∈my	g∈my	PROPN
ejpam-491	165	4	{	{	PUNCT
ejpam-491	165	5	f	f	NOUN
ejpam-491	165	6	−1(g)−mint	−1(g)−mint	NOUN
ejpam-491	165	7	(	(	PUNCT
ejpam-491	165	8	f	f	NOUN
ejpam-491	165	9	−1(g	−1(g	NOUN
ejpam-491	165	10	)	)	PUNCT
ejpam-491	165	11	)	)	PUNCT
ejpam-491	165	12	}	}	PUNCT
ejpam-491	165	13	.	.	PUNCT
ejpam-491	166	1	conversely	conversely	ADV
ejpam-491	166	2	,	,	PUNCT
ejpam-491	166	3	let	let	VERB
ejpam-491	166	4	x	x	X
ejpam-491	166	5	∈	∈	PROPN
ejpam-491	166	6	⋃	⋃	PROPN
ejpam-491	166	7	g∈my	g∈my	NOUN
ejpam-491	166	8	{	{	PUNCT
ejpam-491	166	9	f	f	NOUN
ejpam-491	166	10	−1(g)−mint	−1(g)−mint	NOUN
ejpam-491	166	11	(	(	PUNCT
ejpam-491	166	12	f	f	NOUN
ejpam-491	166	13	−1(g	−1(g	NOUN
ejpam-491	166	14	)	)	PUNCT
ejpam-491	166	15	)	)	PUNCT
ejpam-491	166	16	}	}	PUNCT
ejpam-491	166	17	.	.	PUNCT
ejpam-491	167	1	there	there	PRON
ejpam-491	167	2	exists	exist	VERB
ejpam-491	167	3	v	v	ADP
ejpam-491	167	4	∈	∈	PRON
ejpam-491	167	5	my	my	PRON
ejpam-491	167	6	such	such	ADJ
ejpam-491	167	7	that	that	SCONJ
ejpam-491	167	8	x	x	SYM
ejpam-491	167	9	∈	∈	PROPN
ejpam-491	167	10	f	f	X
ejpam-491	167	11	−1(v	−1(v	NOUN
ejpam-491	167	12	)	)	PUNCT
ejpam-491	167	13	−mint	−mint	PROPN
ejpam-491	167	14	(	(	PUNCT
ejpam-491	167	15	f	f	PROPN
ejpam-491	167	16	−1(v	−1(v	PROPN
ejpam-491	167	17	)	)	PUNCT
ejpam-491	167	18	)	)	PUNCT
ejpam-491	167	19	.	.	PUNCT
ejpam-491	168	1	by	by	ADP
ejpam-491	168	2	theorem	theorem	NOUN
ejpam-491	168	3	1	1	NUM
ejpam-491	168	4	,	,	PUNCT
ejpam-491	168	5	x	x	SYM
ejpam-491	168	6	∈	∈	NOUN
ejpam-491	168	7	dm	dm	X
ejpam-491	168	8	(	(	PUNCT
ejpam-491	168	9	f	f	PROPN
ejpam-491	168	10	)	)	PUNCT
ejpam-491	168	11	.	.	PUNCT
ejpam-491	169	1	theorem	theorem	NOUN
ejpam-491	169	2	3	3	NUM
ejpam-491	169	3	.	.	PUNCT
ejpam-491	169	4	(	(	PUNCT
ejpam-491	169	5	popa	popa	NOUN
ejpam-491	169	6	and	and	CCONJ
ejpam-491	169	7	noiri	noiri	ADV
ejpam-491	169	8	[	[	X
ejpam-491	169	9	29	29	NUM
ejpam-491	169	10	]	]	PUNCT
ejpam-491	169	11	)	)	PUNCT
ejpam-491	169	12	.	.	PUNCT
ejpam-491	170	1	for	for	ADP
ejpam-491	170	2	a	a	DET
ejpam-491	170	3	function	function	NOUN
ejpam-491	170	4	f	f	NOUN
ejpam-491	170	5	:	:	PUNCT
ejpam-491	170	6	(	(	PUNCT
ejpam-491	170	7	x	x	X
ejpam-491	170	8	,	,	PUNCT
ejpam-491	170	9	mx	mx	PROPN
ejpam-491	170	10	)	)	PUNCT
ejpam-491	170	11	→	→	SYM
ejpam-491	170	12	(	(	PUNCT
ejpam-491	170	13	y	y	PROPN
ejpam-491	170	14	,	,	PUNCT
ejpam-491	170	15	my	my	INTJ
ejpam-491	170	16	)	)	PUNCT
ejpam-491	170	17	,	,	PUNCT
ejpam-491	170	18	the	the	DET
ejpam-491	170	19	following	follow	VERB
ejpam-491	170	20	properties	property	NOUN
ejpam-491	170	21	are	be	AUX
ejpam-491	170	22	equivalent	equivalent	ADJ
ejpam-491	170	23	:	:	PUNCT
ejpam-491	170	24	t.	t.	PROPN
ejpam-491	170	25	noiri	noiri	PROPN
ejpam-491	170	26	and	and	CCONJ
ejpam-491	170	27	v.	v.	ADP
ejpam-491	170	28	popa	popa	NOUN
ejpam-491	170	29	/	/	SYM
ejpam-491	170	30	eur	eur	PROPN
ejpam-491	170	31	.	.	PUNCT
ejpam-491	171	1	j.	j.	PROPN
ejpam-491	171	2	pure	pure	PROPN
ejpam-491	171	3	appl	appl	PROPN
ejpam-491	171	4	.	.	PROPN
ejpam-491	171	5	math	math	PROPN
ejpam-491	171	6	,	,	PUNCT
ejpam-491	171	7	2	2	NUM
ejpam-491	171	8	(	(	PUNCT
ejpam-491	171	9	2009	2009	NUM
ejpam-491	171	10	)	)	PUNCT
ejpam-491	171	11	,	,	PUNCT
ejpam-491	171	12	(	(	PUNCT
ejpam-491	171	13	473	473	NUM
ejpam-491	171	14	-	-	NUM
ejpam-491	171	15	493	493	NUM
ejpam-491	171	16	)	)	PUNCT
ejpam-491	171	17	479	479	NUM
ejpam-491	171	18	(	(	PUNCT
ejpam-491	171	19	1	1	X
ejpam-491	171	20	)	)	PUNCT
ejpam-491	171	21	f	f	PROPN
ejpam-491	171	22	is	be	AUX
ejpam-491	171	23	m	m	NOUN
ejpam-491	171	24	-	-	ADJ
ejpam-491	171	25	continuous	continuous	ADJ
ejpam-491	171	26	;	;	PUNCT
ejpam-491	171	27	(	(	PUNCT
ejpam-491	171	28	2	2	X
ejpam-491	171	29	)	)	PUNCT
ejpam-491	171	30	f	f	PROPN
ejpam-491	171	31	−1(v	−1(v	PROPN
ejpam-491	171	32	)	)	PUNCT
ejpam-491	172	1	=	=	NOUN
ejpam-491	172	2	mint	mint	NOUN
ejpam-491	172	3	(	(	PUNCT
ejpam-491	172	4	f	f	PROPN
ejpam-491	172	5	−1(v	−1(v	PROPN
ejpam-491	172	6	)	)	PUNCT
ejpam-491	172	7	)	)	PUNCT
ejpam-491	172	8	for	for	ADP
ejpam-491	172	9	every	every	DET
ejpam-491	172	10	v	v	NOUN
ejpam-491	172	11	∈	∈	PRON
ejpam-491	172	12	my	my	PRON
ejpam-491	172	13	;	;	PUNCT
ejpam-491	172	14	(	(	PUNCT
ejpam-491	172	15	3	3	X
ejpam-491	172	16	)	)	PUNCT
ejpam-491	172	17	f	f	NOUN
ejpam-491	172	18	(	(	PUNCT
ejpam-491	172	19	mcl(a	mcl(a	NOUN
ejpam-491	172	20	)	)	PUNCT
ejpam-491	172	21	)	)	PUNCT
ejpam-491	173	1	⊂	⊂	PROPN
ejpam-491	173	2	cl	cl	PROPN
ejpam-491	173	3	(	(	PUNCT
ejpam-491	173	4	f	f	PROPN
ejpam-491	173	5	(	(	PUNCT
ejpam-491	173	6	a	a	NOUN
ejpam-491	173	7	)	)	PUNCT
ejpam-491	173	8	)	)	PUNCT
ejpam-491	173	9	for	for	ADP
ejpam-491	173	10	every	every	DET
ejpam-491	173	11	subset	subset	NOUN
ejpam-491	173	12	a	a	PRON
ejpam-491	173	13	of	of	ADP
ejpam-491	173	14	x	x	PRON
ejpam-491	173	15	;	;	PUNCT
ejpam-491	173	16	(	(	PUNCT
ejpam-491	173	17	4	4	X
ejpam-491	173	18	)	)	PUNCT
ejpam-491	173	19	mcl	mcl	PROPN
ejpam-491	173	20	(	(	PUNCT
ejpam-491	173	21	f	f	PROPN
ejpam-491	173	22	−1(b	−1(b	NOUN
ejpam-491	173	23	)	)	PUNCT
ejpam-491	173	24	)	)	PUNCT
ejpam-491	174	1	⊂	⊂	PROPN
ejpam-491	174	2	f	f	X
ejpam-491	174	3	−1(mcl(b	−1(mcl(b	NOUN
ejpam-491	174	4	)	)	PUNCT
ejpam-491	174	5	)	)	PUNCT
ejpam-491	175	1	for	for	ADP
ejpam-491	175	2	every	every	DET
ejpam-491	175	3	subset	subset	NOUN
ejpam-491	175	4	b	b	PROPN
ejpam-491	175	5	of	of	ADP
ejpam-491	175	6	y	y	PROPN
ejpam-491	175	7	;	;	PUNCT
ejpam-491	175	8	(	(	PUNCT
ejpam-491	175	9	5	5	X
ejpam-491	175	10	)	)	PUNCT
ejpam-491	175	11	f	f	NOUN
ejpam-491	175	12	−1(int(b	−1(int(b	NOUN
ejpam-491	175	13	)	)	PUNCT
ejpam-491	175	14	)	)	PUNCT
ejpam-491	175	15	⊂mint	⊂mint	NOUN
ejpam-491	175	16	(	(	PUNCT
ejpam-491	175	17	f	f	PROPN
ejpam-491	175	18	−1(b	−1(b	NOUN
ejpam-491	175	19	)	)	PUNCT
ejpam-491	175	20	)	)	PUNCT
ejpam-491	175	21	for	for	ADP
ejpam-491	175	22	every	every	DET
ejpam-491	175	23	subset	subset	NOUN
ejpam-491	175	24	b	b	PROPN
ejpam-491	175	25	of	of	ADP
ejpam-491	175	26	y	y	PROPN
ejpam-491	175	27	;	;	PUNCT
ejpam-491	175	28	(	(	PUNCT
ejpam-491	175	29	6	6	X
ejpam-491	175	30	)	)	PUNCT
ejpam-491	175	31	mcl	mcl	PROPN
ejpam-491	175	32	(	(	PUNCT
ejpam-491	175	33	f	f	PROPN
ejpam-491	175	34	−1(k	−1(k	NOUN
ejpam-491	175	35	)	)	PUNCT
ejpam-491	175	36	)	)	PUNCT
ejpam-491	176	1	=	=	PUNCT
ejpam-491	176	2	f	f	PROPN
ejpam-491	176	3	−1(k	−1(k	NOUN
ejpam-491	176	4	)	)	PUNCT
ejpam-491	176	5	for	for	ADP
ejpam-491	176	6	every	every	DET
ejpam-491	176	7	my	my	PRON
ejpam-491	176	8	-closed	-closed	ADJ
ejpam-491	176	9	set	set	NOUN
ejpam-491	176	10	k	k	PROPN
ejpam-491	176	11	of	of	ADP
ejpam-491	176	12	y.	y.	PROPN
ejpam-491	176	13	corollary	corollary	PROPN
ejpam-491	176	14	1	1	NUM
ejpam-491	176	15	.	.	PUNCT
ejpam-491	176	16	(	(	PUNCT
ejpam-491	176	17	popa	popa	NOUN
ejpam-491	176	18	and	and	CCONJ
ejpam-491	176	19	noiri	noiri	ADV
ejpam-491	177	1	[	[	X
ejpam-491	177	2	29	29	NUM
ejpam-491	177	3	]	]	PUNCT
ejpam-491	177	4	)	)	PUNCT
ejpam-491	177	5	.	.	PUNCT
ejpam-491	178	1	for	for	ADP
ejpam-491	178	2	a	a	DET
ejpam-491	178	3	function	function	NOUN
ejpam-491	178	4	f	f	NOUN
ejpam-491	178	5	:	:	PUNCT
ejpam-491	178	6	(	(	PUNCT
ejpam-491	178	7	x	x	X
ejpam-491	178	8	,	,	PUNCT
ejpam-491	178	9	mx	mx	PROPN
ejpam-491	178	10	)	)	PUNCT
ejpam-491	178	11	→	→	SYM
ejpam-491	178	12	(	(	PUNCT
ejpam-491	178	13	y	y	PROPN
ejpam-491	178	14	,	,	PUNCT
ejpam-491	178	15	my	my	INTJ
ejpam-491	178	16	)	)	PUNCT
ejpam-491	178	17	,	,	PUNCT
ejpam-491	178	18	where	where	SCONJ
ejpam-491	178	19	mx	mx	PROPN
ejpam-491	178	20	has	have	VERB
ejpam-491	178	21	propertyb	propertyb	NOUN
ejpam-491	178	22	,	,	PUNCT
ejpam-491	178	23	the	the	DET
ejpam-491	178	24	following	follow	VERB
ejpam-491	178	25	properties	property	NOUN
ejpam-491	178	26	are	be	AUX
ejpam-491	178	27	equivalent	equivalent	ADJ
ejpam-491	178	28	:	:	PUNCT
ejpam-491	178	29	(	(	PUNCT
ejpam-491	178	30	1	1	X
ejpam-491	178	31	)	)	PUNCT
ejpam-491	178	32	f	f	PROPN
ejpam-491	178	33	is	be	AUX
ejpam-491	178	34	m	m	NOUN
ejpam-491	178	35	-	-	ADJ
ejpam-491	178	36	continuous	continuous	ADJ
ejpam-491	178	37	;	;	PUNCT
ejpam-491	178	38	(	(	PUNCT
ejpam-491	178	39	2	2	X
ejpam-491	178	40	)	)	PUNCT
ejpam-491	178	41	f	f	PROPN
ejpam-491	178	42	−1(v	−1(v	PROPN
ejpam-491	178	43	)	)	PUNCT
ejpam-491	178	44	is	be	AUX
ejpam-491	178	45	mx	mx	NOUN
ejpam-491	178	46	-open	-open	NOUN
ejpam-491	178	47	for	for	ADP
ejpam-491	178	48	every	every	DET
ejpam-491	178	49	v	v	NOUN
ejpam-491	178	50	∈	∈	PRON
ejpam-491	178	51	my	my	PRON
ejpam-491	178	52	;	;	PUNCT
ejpam-491	178	53	(	(	PUNCT
ejpam-491	178	54	3	3	X
ejpam-491	178	55	)	)	PUNCT
ejpam-491	178	56	f	f	PROPN
ejpam-491	178	57	−1(f	−1(f	PROPN
ejpam-491	178	58	)	)	PUNCT
ejpam-491	178	59	is	be	AUX
ejpam-491	178	60	mx	mx	NOUN
ejpam-491	178	61	-closed	-close	VERB
ejpam-491	178	62	in	in	ADP
ejpam-491	178	63	x	x	PUNCT
ejpam-491	178	64	for	for	ADP
ejpam-491	178	65	every	every	DET
ejpam-491	178	66	my	my	PRON
ejpam-491	178	67	-closed	-closed	ADJ
ejpam-491	178	68	set	set	NOUN
ejpam-491	178	69	f	f	PROPN
ejpam-491	178	70	of	of	ADP
ejpam-491	178	71	y.	y.	PROPN
ejpam-491	178	72	definition	definition	NOUN
ejpam-491	178	73	9	9	NUM
ejpam-491	178	74	.	.	PUNCT
ejpam-491	179	1	a	a	DET
ejpam-491	179	2	function	function	NOUN
ejpam-491	179	3	f	f	NOUN
ejpam-491	179	4	:	:	PUNCT
ejpam-491	179	5	(	(	PUNCT
ejpam-491	179	6	x	x	X
ejpam-491	179	7	,	,	PUNCT
ejpam-491	179	8	mx	mx	PROPN
ejpam-491	179	9	)	)	PUNCT
ejpam-491	179	10	→	→	SYM
ejpam-491	179	11	(	(	PUNCT
ejpam-491	179	12	y	y	NOUN
ejpam-491	179	13	,	,	PUNCT
ejpam-491	179	14	my	my	INTJ
ejpam-491	179	15	)	)	PUNCT
ejpam-491	179	16	is	be	AUX
ejpam-491	179	17	said	say	VERB
ejpam-491	179	18	to	to	PART
ejpam-491	179	19	be	be	AUX
ejpam-491	179	20	m	m	PROPN
ejpam-491	179	21	∗-continuous	∗-continuous	ADJ
ejpam-491	179	22	[	[	X
ejpam-491	179	23	24	24	NUM
ejpam-491	179	24	]	]	PUNCT
ejpam-491	179	25	if	if	SCONJ
ejpam-491	179	26	f	f	PROPN
ejpam-491	179	27	−1(v	−1(v	PROPN
ejpam-491	179	28	)	)	PUNCT
ejpam-491	179	29	is	be	AUX
ejpam-491	179	30	mx	mx	NOUN
ejpam-491	179	31	-open	-open	NOUN
ejpam-491	179	32	for	for	ADP
ejpam-491	179	33	each	each	DET
ejpam-491	179	34	my	my	PRON
ejpam-491	179	35	-open	-open	NOUN
ejpam-491	179	36	set	set	ADJ
ejpam-491	179	37	v	v	NOUN
ejpam-491	179	38	of	of	ADP
ejpam-491	179	39	y	y	PROPN
ejpam-491	179	40	.	.	PUNCT
ejpam-491	180	1	remark	remark	PROPN
ejpam-491	180	2	4	4	NUM
ejpam-491	180	3	.	.	PUNCT
ejpam-491	181	1	(	(	PUNCT
ejpam-491	181	2	1	1	X
ejpam-491	181	3	)	)	PUNCT
ejpam-491	181	4	if	if	SCONJ
ejpam-491	181	5	f	f	PROPN
ejpam-491	181	6	:	:	PUNCT
ejpam-491	181	7	(	(	PUNCT
ejpam-491	181	8	x	x	X
ejpam-491	181	9	,	,	PUNCT
ejpam-491	181	10	mx	mx	PROPN
ejpam-491	181	11	)	)	PUNCT
ejpam-491	181	12	→	→	SYM
ejpam-491	181	13	(	(	PUNCT
ejpam-491	181	14	y	y	NOUN
ejpam-491	181	15	,	,	PUNCT
ejpam-491	181	16	my	my	INTJ
ejpam-491	181	17	)	)	PUNCT
ejpam-491	181	18	is	be	AUX
ejpam-491	181	19	m	m	VERB
ejpam-491	181	20	∗-continuous	∗-continuous	ADJ
ejpam-491	181	21	,	,	PUNCT
ejpam-491	181	22	then	then	ADV
ejpam-491	181	23	it	it	PRON
ejpam-491	181	24	is	be	AUX
ejpam-491	181	25	m	m	NOUN
ejpam-491	181	26	-continuous	-continuous	ADJ
ejpam-491	181	27	.	.	PUNCT
ejpam-491	182	1	by	by	ADP
ejpam-491	182	2	example	example	NOUN
ejpam-491	182	3	3.4	3.4	NUM
ejpam-491	182	4	of	of	ADP
ejpam-491	182	5	[	[	X
ejpam-491	182	6	24	24	NUM
ejpam-491	182	7	]	]	PUNCT
ejpam-491	182	8	,	,	PUNCT
ejpam-491	182	9	an	an	DET
ejpam-491	182	10	m	m	NOUN
ejpam-491	182	11	-continuous	-continuous	ADJ
ejpam-491	182	12	function	function	NOUN
ejpam-491	182	13	may	may	AUX
ejpam-491	182	14	not	not	PART
ejpam-491	182	15	be	be	AUX
ejpam-491	182	16	m	m	NOUN
ejpam-491	182	17	∗-continuous	∗-continuous	ADJ
ejpam-491	182	18	.	.	PUNCT
ejpam-491	183	1	(	(	PUNCT
ejpam-491	183	2	2	2	X
ejpam-491	183	3	)	)	PUNCT
ejpam-491	183	4	if	if	SCONJ
ejpam-491	183	5	mx	mx	PROPN
ejpam-491	183	6	has	have	VERB
ejpam-491	183	7	propertyb	propertyb	NOUN
ejpam-491	183	8	,	,	PUNCT
ejpam-491	183	9	then	then	ADV
ejpam-491	183	10	m	m	VERB
ejpam-491	183	11	-continuity	-continuity	ADJ
ejpam-491	183	12	and	and	CCONJ
ejpam-491	183	13	m	m	PRON
ejpam-491	183	14	∗-continuity	∗-continuity	NOUN
ejpam-491	183	15	are	be	AUX
ejpam-491	183	16	equivalent	equivalent	ADJ
ejpam-491	183	17	.	.	PUNCT
ejpam-491	184	1	4	4	X
ejpam-491	184	2	.	.	X
ejpam-491	184	3	gm	gm	ADJ
ejpam-491	184	4	-	-	PUNCT
ejpam-491	184	5	closed	close	VERB
ejpam-491	184	6	sets	set	NOUN
ejpam-491	184	7	and	and	CCONJ
ejpam-491	184	8	gm	gm	PROPN
ejpam-491	184	9	-continuity	-continuity	PROPN
ejpam-491	184	10	definition	definition	NOUN
ejpam-491	184	11	10	10	NUM
ejpam-491	184	12	.	.	PUNCT
ejpam-491	185	1	let	let	AUX
ejpam-491	185	2	(	(	PUNCT
ejpam-491	185	3	x	x	X
ejpam-491	185	4	,	,	PUNCT
ejpam-491	185	5	τ	τ	X
ejpam-491	185	6	)	)	PUNCT
ejpam-491	185	7	be	be	VERB
ejpam-491	185	8	a	a	DET
ejpam-491	185	9	topological	topological	ADJ
ejpam-491	185	10	space	space	NOUN
ejpam-491	185	11	.	.	PUNCT
ejpam-491	186	1	a	a	DET
ejpam-491	186	2	subset	subset	NOUN
ejpam-491	186	3	a	a	PRON
ejpam-491	186	4	of	of	ADP
ejpam-491	186	5	x	x	SYM
ejpam-491	186	6	is	be	AUX
ejpam-491	186	7	said	say	VERB
ejpam-491	186	8	to	to	PART
ejpam-491	186	9	be	be	AUX
ejpam-491	186	10	(	(	PUNCT
ejpam-491	186	11	1	1	X
ejpam-491	186	12	)	)	PUNCT
ejpam-491	186	13	g	g	NOUN
ejpam-491	186	14	-	-	PUNCT
ejpam-491	186	15	closed	closed	ADJ
ejpam-491	186	16	[	[	X
ejpam-491	186	17	20	20	NUM
ejpam-491	186	18	]	]	PUNCT
ejpam-491	186	19	if	if	SCONJ
ejpam-491	186	20	cl(a	cl(a	NUM
ejpam-491	186	21	)	)	PUNCT
ejpam-491	187	1	⊂	⊂	PROPN
ejpam-491	187	2	u	u	NOUN
ejpam-491	187	3	whenever	whenever	SCONJ
ejpam-491	187	4	a⊂	a⊂	PUNCT
ejpam-491	187	5	u	u	NOUN
ejpam-491	187	6	and	and	CCONJ
ejpam-491	187	7	u	u	PROPN
ejpam-491	187	8	∈	∈	PROPN
ejpam-491	187	9	τ	τ	PROPN
ejpam-491	187	10	,	,	PUNCT
ejpam-491	187	11	(	(	PUNCT
ejpam-491	187	12	2	2	NUM
ejpam-491	187	13	)	)	PUNCT
ejpam-491	187	14	αg	αg	NOUN
ejpam-491	187	15	-	-	PUNCT
ejpam-491	187	16	closed	closed	ADJ
ejpam-491	187	17	[	[	X
ejpam-491	187	18	12	12	NUM
ejpam-491	187	19	]	]	X
ejpam-491	187	20	if	if	SCONJ
ejpam-491	187	21	αcl(a)⊂	αcl(a)⊂	PROPN
ejpam-491	187	22	u	u	NOUN
ejpam-491	187	23	whenever	whenever	SCONJ
ejpam-491	187	24	a⊂	a⊂	PUNCT
ejpam-491	187	25	u	u	NOUN
ejpam-491	187	26	and	and	CCONJ
ejpam-491	187	27	u	u	PROPN
ejpam-491	187	28	∈	∈	PROPN
ejpam-491	187	29	τ	τ	PROPN
ejpam-491	187	30	,	,	PUNCT
ejpam-491	187	31	(	(	PUNCT
ejpam-491	187	32	3	3	X
ejpam-491	187	33	)	)	PUNCT
ejpam-491	187	34	gs	gs	NOUN
ejpam-491	187	35	-	-	PUNCT
ejpam-491	187	36	closed	closed	ADJ
ejpam-491	187	37	[	[	X
ejpam-491	187	38	11	11	NUM
ejpam-491	187	39	]	]	PUNCT
ejpam-491	187	40	if	if	SCONJ
ejpam-491	187	41	scl(a)⊂	scl(a)⊂	NOUN
ejpam-491	187	42	u	u	NOUN
ejpam-491	187	43	whenever	whenever	SCONJ
ejpam-491	187	44	a⊂	a⊂	PUNCT
ejpam-491	187	45	u	u	NOUN
ejpam-491	187	46	and	and	CCONJ
ejpam-491	187	47	u	u	PROPN
ejpam-491	187	48	∈	∈	PROPN
ejpam-491	187	49	τ	τ	PROPN
ejpam-491	187	50	,	,	PUNCT
ejpam-491	187	51	(	(	PUNCT
ejpam-491	187	52	4	4	X
ejpam-491	187	53	)	)	PUNCT
ejpam-491	187	54	gp	gp	NOUN
ejpam-491	187	55	-	-	PUNCT
ejpam-491	187	56	closed	closed	ADJ
ejpam-491	187	57	[	[	X
ejpam-491	187	58	6	6	NUM
ejpam-491	187	59	]	]	PUNCT
ejpam-491	187	60	if	if	SCONJ
ejpam-491	187	61	pcl(a	pcl(a	X
ejpam-491	187	62	)	)	PUNCT
ejpam-491	187	63	⊂	⊂	PROPN
ejpam-491	187	64	u	u	NOUN
ejpam-491	187	65	whenever	whenever	SCONJ
ejpam-491	187	66	a⊂	a⊂	PUNCT
ejpam-491	187	67	u	u	NOUN
ejpam-491	187	68	and	and	CCONJ
ejpam-491	187	69	u	u	PROPN
ejpam-491	187	70	∈	∈	PROPN
ejpam-491	187	71	τ	τ	PROPN
ejpam-491	187	72	,	,	PUNCT
ejpam-491	187	73	(	(	PUNCT
ejpam-491	187	74	5	5	X
ejpam-491	187	75	)	)	PUNCT
ejpam-491	187	76	gb	gb	ADV
ejpam-491	187	77	-	-	PUNCT
ejpam-491	187	78	closed	close	VERB
ejpam-491	187	79	or	or	CCONJ
ejpam-491	187	80	γg	γg	ADV
ejpam-491	187	81	-	-	PUNCT
ejpam-491	187	82	closed	closed	ADJ
ejpam-491	187	83	[	[	X
ejpam-491	187	84	18	18	NUM
ejpam-491	187	85	]	]	PUNCT
ejpam-491	187	86	if	if	SCONJ
ejpam-491	187	87	bcl(a	bcl(a	PROPN
ejpam-491	187	88	)	)	PUNCT
ejpam-491	187	89	⊂	⊂	PROPN
ejpam-491	187	90	u	u	NOUN
ejpam-491	187	91	whenever	whenever	SCONJ
ejpam-491	187	92	a⊂	a⊂	PUNCT
ejpam-491	187	93	u	u	NOUN
ejpam-491	187	94	and	and	CCONJ
ejpam-491	187	95	u	u	PROPN
ejpam-491	187	96	∈	∈	PROPN
ejpam-491	187	97	τ	τ	PROPN
ejpam-491	187	98	,	,	PUNCT
ejpam-491	187	99	(	(	PUNCT
ejpam-491	187	100	6	6	NUM
ejpam-491	187	101	)	)	PUNCT
ejpam-491	187	102	gsp	gsp	NOUN
ejpam-491	187	103	-	-	PUNCT
ejpam-491	187	104	closed	closed	ADJ
ejpam-491	187	105	[	[	X
ejpam-491	187	106	14	14	NUM
ejpam-491	187	107	]	]	PUNCT
ejpam-491	187	108	or	or	CCONJ
ejpam-491	187	109	gβ	gβ	AUX
ejpam-491	187	110	-closed	-close	VERB
ejpam-491	187	111	if	if	SCONJ
ejpam-491	187	112	spcl(a)⊂	spcl(a)⊂	X
ejpam-491	187	113	u	u	NOUN
ejpam-491	187	114	whenever	whenever	SCONJ
ejpam-491	187	115	a⊂	a⊂	PUNCT
ejpam-491	187	116	u	u	NOUN
ejpam-491	187	117	and	and	CCONJ
ejpam-491	187	118	u	u	PROPN
ejpam-491	187	119	∈	∈	PROPN
ejpam-491	187	120	τ	τ	PROPN
ejpam-491	187	121	,	,	PUNCT
ejpam-491	187	122	t.	t.	PROPN
ejpam-491	187	123	noiri	noiri	PROPN
ejpam-491	187	124	and	and	CCONJ
ejpam-491	187	125	v.	v.	ADP
ejpam-491	187	126	popa	popa	NOUN
ejpam-491	187	127	/	/	SYM
ejpam-491	187	128	eur	eur	PROPN
ejpam-491	187	129	.	.	PUNCT
ejpam-491	188	1	j.	j.	PROPN
ejpam-491	188	2	pure	pure	PROPN
ejpam-491	188	3	appl	appl	PROPN
ejpam-491	188	4	.	.	PROPN
ejpam-491	188	5	math	math	PROPN
ejpam-491	188	6	,	,	PUNCT
ejpam-491	188	7	2	2	NUM
ejpam-491	188	8	(	(	PUNCT
ejpam-491	188	9	2009	2009	NUM
ejpam-491	188	10	)	)	PUNCT
ejpam-491	188	11	,	,	PUNCT
ejpam-491	188	12	(	(	PUNCT
ejpam-491	188	13	473	473	NUM
ejpam-491	188	14	-	-	NUM
ejpam-491	188	15	493	493	NUM
ejpam-491	188	16	)	)	PUNCT
ejpam-491	188	17	480	480	NUM
ejpam-491	188	18	definition	definition	NOUN
ejpam-491	188	19	11	11	NUM
ejpam-491	188	20	.	.	PUNCT
ejpam-491	189	1	a	a	DET
ejpam-491	189	2	subset	subset	NOUN
ejpam-491	189	3	a	a	PRON
ejpam-491	189	4	of	of	ADP
ejpam-491	189	5	a	a	DET
ejpam-491	189	6	topological	topological	ADJ
ejpam-491	189	7	space	space	NOUN
ejpam-491	189	8	is	be	AUX
ejpam-491	189	9	said	say	VERB
ejpam-491	189	10	to	to	PART
ejpam-491	189	11	be	be	AUX
ejpam-491	189	12	g	g	NOUN
ejpam-491	189	13	-	-	PUNCT
ejpam-491	189	14	open	open	ADJ
ejpam-491	189	15	(	(	PUNCT
ejpam-491	189	16	resp	resp	NOUN
ejpam-491	189	17	.	.	PUNCT
ejpam-491	190	1	gs	g	VERB
ejpam-491	190	2	-	-	PUNCT
ejpam-491	190	3	open	open	ADJ
ejpam-491	190	4	,	,	PUNCT
ejpam-491	190	5	gp	gp	NOUN
ejpam-491	190	6	-	-	ADJ
ejpam-491	190	7	open	open	ADJ
ejpam-491	190	8	,	,	PUNCT
ejpam-491	190	9	αg	αg	NOUN
ejpam-491	190	10	-	-	PUNCT
ejpam-491	190	11	open	open	ADJ
ejpam-491	190	12	,	,	PUNCT
ejpam-491	190	13	g	g	PROPN
ejpam-491	190	14	b	b	X
ejpam-491	190	15	-	-	PUNCT
ejpam-491	190	16	open	open	ADJ
ejpam-491	190	17	,	,	PUNCT
ejpam-491	190	18	gsp	gsp	NOUN
ejpam-491	190	19	-	-	PUNCT
ejpam-491	190	20	open	open	ADJ
ejpam-491	190	21	)	)	PUNCT
ejpam-491	190	22	if	if	SCONJ
ejpam-491	190	23	x	x	X
ejpam-491	190	24	−	−	NOUN
ejpam-491	190	25	a	a	PRON
ejpam-491	190	26	is	be	AUX
ejpam-491	190	27	g	g	NOUN
ejpam-491	190	28	-	-	PUNCT
ejpam-491	190	29	closed	closed	ADJ
ejpam-491	190	30	(	(	PUNCT
ejpam-491	190	31	resp	resp	NOUN
ejpam-491	190	32	.	.	PUNCT
ejpam-491	191	1	gs	gs	NOUN
ejpam-491	191	2	-	-	PUNCT
ejpam-491	191	3	closed	closed	ADJ
ejpam-491	191	4	,	,	PUNCT
ejpam-491	191	5	gpclosed	gpclose	VERB
ejpam-491	191	6	αg	αg	NOUN
ejpam-491	191	7	-	-	PUNCT
ejpam-491	191	8	closed	closed	ADJ
ejpam-491	191	9	,	,	PUNCT
ejpam-491	191	10	g	g	PROPN
ejpam-491	191	11	b	b	NOUN
ejpam-491	191	12	-	-	PUNCT
ejpam-491	191	13	closed	closed	ADJ
ejpam-491	191	14	,	,	PUNCT
ejpam-491	191	15	gsp	gsp	NOUN
ejpam-491	191	16	-	-	PUNCT
ejpam-491	191	17	closed	closed	ADJ
ejpam-491	191	18	)	)	PUNCT
ejpam-491	191	19	.	.	PUNCT
ejpam-491	192	1	the	the	DET
ejpam-491	192	2	family	family	NOUN
ejpam-491	192	3	of	of	ADP
ejpam-491	192	4	all	all	DET
ejpam-491	192	5	g	g	NOUN
ejpam-491	192	6	-	-	PUNCT
ejpam-491	192	7	open	open	ADJ
ejpam-491	192	8	(	(	PUNCT
ejpam-491	192	9	resp	resp	NOUN
ejpam-491	192	10	.	.	PUNCT
ejpam-491	193	1	gs	g	VERB
ejpam-491	193	2	-	-	PUNCT
ejpam-491	193	3	open	open	ADJ
ejpam-491	193	4	,	,	PUNCT
ejpam-491	193	5	gp	gp	NOUN
ejpam-491	193	6	-	-	ADJ
ejpam-491	193	7	open	open	ADJ
ejpam-491	193	8	,	,	PUNCT
ejpam-491	193	9	αg	αg	NOUN
ejpam-491	193	10	-	-	PUNCT
ejpam-491	193	11	open	open	ADJ
ejpam-491	193	12	,	,	PUNCT
ejpam-491	193	13	g	g	PROPN
ejpam-491	193	14	b	b	X
ejpam-491	193	15	-	-	PUNCT
ejpam-491	193	16	open	open	ADJ
ejpam-491	193	17	,	,	PUNCT
ejpam-491	193	18	gsp	gsp	NOUN
ejpam-491	193	19	-	-	PUNCT
ejpam-491	193	20	open	open	ADJ
ejpam-491	193	21	)	)	PUNCT
ejpam-491	193	22	sets	set	NOUN
ejpam-491	193	23	of	of	ADP
ejpam-491	193	24	x	x	SYM
ejpam-491	193	25	is	be	AUX
ejpam-491	193	26	denoted	denote	VERB
ejpam-491	193	27	by	by	ADP
ejpam-491	193	28	go(x	go(x	PROPN
ejpam-491	193	29	)	)	PUNCT
ejpam-491	193	30	(	(	PUNCT
ejpam-491	193	31	resp	resp	NOUN
ejpam-491	193	32	.	.	PUNCT
ejpam-491	194	1	gso(x	gso(x	VERB
ejpam-491	194	2	)	)	PUNCT
ejpam-491	194	3	,	,	PUNCT
ejpam-491	194	4	gpo(x	gpo(x	NOUN
ejpam-491	194	5	)	)	PUNCT
ejpam-491	194	6	,	,	PUNCT
ejpam-491	194	7	αgo(x	αgo(x	PROPN
ejpam-491	194	8	)	)	PUNCT
ejpam-491	194	9	,	,	PUNCT
ejpam-491	194	10	gbo(x	gbo(x	PROPN
ejpam-491	194	11	)	)	PUNCT
ejpam-491	194	12	,	,	PUNCT
ejpam-491	194	13	gspo(x	gspo(x	NOUN
ejpam-491	194	14	)	)	PUNCT
ejpam-491	194	15	)	)	PUNCT
ejpam-491	194	16	.	.	PUNCT
ejpam-491	195	1	definition	definition	NOUN
ejpam-491	195	2	12	12	NUM
ejpam-491	195	3	.	.	PUNCT
ejpam-491	196	1	let	let	AUX
ejpam-491	196	2	(	(	PUNCT
ejpam-491	196	3	x	x	X
ejpam-491	196	4	,	,	PUNCT
ejpam-491	196	5	τ	τ	X
ejpam-491	196	6	)	)	PUNCT
ejpam-491	196	7	be	be	VERB
ejpam-491	196	8	a	a	DET
ejpam-491	196	9	topological	topological	ADJ
ejpam-491	196	10	space	space	NOUN
ejpam-491	196	11	and	and	CCONJ
ejpam-491	196	12	a	a	DET
ejpam-491	196	13	a	a	DET
ejpam-491	196	14	subset	subset	NOUN
ejpam-491	196	15	of	of	ADP
ejpam-491	196	16	x	x	PRON
ejpam-491	196	17	.	.	PUNCT
ejpam-491	197	1	the	the	DET
ejpam-491	197	2	intersection	intersection	NOUN
ejpam-491	197	3	of	of	ADP
ejpam-491	197	4	all	all	DET
ejpam-491	197	5	g	g	NOUN
ejpam-491	197	6	-	-	PUNCT
ejpam-491	197	7	closed	closed	ADJ
ejpam-491	197	8	(	(	PUNCT
ejpam-491	197	9	resp	resp	NOUN
ejpam-491	197	10	.	.	PUNCT
ejpam-491	198	1	αg	αg	NOUN
ejpam-491	198	2	-	-	PUNCT
ejpam-491	198	3	closed	closed	ADJ
ejpam-491	198	4	,	,	PUNCT
ejpam-491	198	5	gs	gs	NOUN
ejpam-491	198	6	-	-	PUNCT
ejpam-491	198	7	closed	closed	ADJ
ejpam-491	198	8	,	,	PUNCT
ejpam-491	198	9	gp	gp	NOUN
ejpam-491	198	10	-	-	ADJ
ejpam-491	198	11	closed	closed	ADJ
ejpam-491	198	12	,	,	PUNCT
ejpam-491	198	13	gsp	gsp	NOUN
ejpam-491	198	14	-	-	PUNCT
ejpam-491	198	15	closed	closed	ADJ
ejpam-491	198	16	,	,	PUNCT
ejpam-491	198	17	g	g	PROPN
ejpam-491	198	18	b	b	X
ejpam-491	198	19	-	-	PUNCT
ejpam-491	198	20	closed	closed	ADJ
ejpam-491	198	21	)	)	PUNCT
ejpam-491	198	22	sets	set	NOUN
ejpam-491	198	23	of	of	ADP
ejpam-491	198	24	x	x	PUNCT
ejpam-491	198	25	containing	contain	VERB
ejpam-491	198	26	a	a	PRON
ejpam-491	198	27	is	be	AUX
ejpam-491	198	28	called	call	VERB
ejpam-491	198	29	the	the	DET
ejpam-491	198	30	g	g	NOUN
ejpam-491	198	31	-	-	PUNCT
ejpam-491	198	32	closure	closure	NOUN
ejpam-491	198	33	[	[	X
ejpam-491	198	34	15	15	NUM
ejpam-491	198	35	]	]	X
ejpam-491	198	36	(	(	PUNCT
ejpam-491	198	37	resp	resp	NOUN
ejpam-491	198	38	.	.	PUNCT
ejpam-491	199	1	αg	αg	NOUN
ejpam-491	199	2	-	-	PUNCT
ejpam-491	199	3	closure	closure	NOUN
ejpam-491	199	4	,	,	PUNCT
ejpam-491	199	5	gs	gs	NOUN
ejpam-491	199	6	-	-	PUNCT
ejpam-491	199	7	closure	closure	NOUN
ejpam-491	199	8	,	,	PUNCT
ejpam-491	199	9	gp	gp	NOUN
ejpam-491	199	10	-	-	NOUN
ejpam-491	199	11	closure	closure	NOUN
ejpam-491	199	12	,	,	PUNCT
ejpam-491	199	13	gsp	gsp	NOUN
ejpam-491	199	14	-	-	PUNCT
ejpam-491	199	15	closure	closure	NOUN
ejpam-491	199	16	,	,	PUNCT
ejpam-491	199	17	gb	gb	NOUN
ejpam-491	199	18	-	-	PUNCT
ejpam-491	199	19	closure	closure	NOUN
ejpam-491	199	20	)	)	PUNCT
ejpam-491	199	21	of	of	ADP
ejpam-491	199	22	a	a	PRON
ejpam-491	199	23	and	and	CCONJ
ejpam-491	199	24	is	be	AUX
ejpam-491	199	25	denoted	denote	VERB
ejpam-491	199	26	by	by	ADP
ejpam-491	199	27	clg(a	clg(a	PROPN
ejpam-491	199	28	)	)	PUNCT
ejpam-491	199	29	(	(	PUNCT
ejpam-491	199	30	resp	resp	NOUN
ejpam-491	199	31	.	.	PUNCT
ejpam-491	200	1	αclg(a	αclg(a	NOUN
ejpam-491	200	2	)	)	PUNCT
ejpam-491	200	3	,	,	PUNCT
ejpam-491	200	4	sclg(a	sclg(a	PROPN
ejpam-491	200	5	)	)	PUNCT
ejpam-491	200	6	,	,	PUNCT
ejpam-491	200	7	pclg(a	pclg(a	PROPN
ejpam-491	200	8	)	)	PUNCT
ejpam-491	200	9	,	,	PUNCT
ejpam-491	200	10	spclg(a	spclg(a	PROPN
ejpam-491	200	11	)	)	PUNCT
ejpam-491	200	12	,	,	PUNCT
ejpam-491	200	13	bclg(a	bclg(a	NOUN
ejpam-491	200	14	)	)	PUNCT
ejpam-491	200	15	)	)	PUNCT
ejpam-491	200	16	.	.	PUNCT
ejpam-491	201	1	definition	definition	NOUN
ejpam-491	201	2	13	13	NUM
ejpam-491	201	3	.	.	PUNCT
ejpam-491	202	1	let	let	AUX
ejpam-491	202	2	(	(	PUNCT
ejpam-491	202	3	x	x	X
ejpam-491	202	4	,	,	PUNCT
ejpam-491	202	5	τ	τ	X
ejpam-491	202	6	)	)	PUNCT
ejpam-491	202	7	be	be	VERB
ejpam-491	202	8	a	a	DET
ejpam-491	202	9	topological	topological	ADJ
ejpam-491	202	10	space	space	NOUN
ejpam-491	202	11	and	and	CCONJ
ejpam-491	202	12	a	a	DET
ejpam-491	202	13	a	a	DET
ejpam-491	202	14	subset	subset	NOUN
ejpam-491	202	15	of	of	ADP
ejpam-491	202	16	x	x	PRON
ejpam-491	202	17	.	.	PUNCT
ejpam-491	203	1	the	the	DET
ejpam-491	203	2	union	union	NOUN
ejpam-491	203	3	of	of	ADP
ejpam-491	203	4	all	all	DET
ejpam-491	203	5	g	g	NOUN
ejpam-491	203	6	-	-	PUNCT
ejpam-491	203	7	open	open	ADJ
ejpam-491	203	8	(	(	PUNCT
ejpam-491	203	9	resp	resp	NOUN
ejpam-491	203	10	.	.	PUNCT
ejpam-491	204	1	αg	αg	NOUN
ejpam-491	204	2	-	-	PUNCT
ejpam-491	204	3	open	open	ADJ
ejpam-491	204	4	,	,	PUNCT
ejpam-491	204	5	gs	gs	NOUN
ejpam-491	204	6	-	-	PUNCT
ejpam-491	204	7	open	open	ADJ
ejpam-491	204	8	,	,	PUNCT
ejpam-491	204	9	gp	gp	NOUN
ejpam-491	204	10	-	-	ADJ
ejpam-491	204	11	open	open	ADJ
ejpam-491	204	12	,	,	PUNCT
ejpam-491	204	13	gsp	gsp	NOUN
ejpam-491	204	14	-	-	PUNCT
ejpam-491	204	15	open	open	ADJ
ejpam-491	204	16	,	,	PUNCT
ejpam-491	204	17	g	g	PROPN
ejpam-491	204	18	b	b	X
ejpam-491	204	19	-	-	PUNCT
ejpam-491	204	20	open	open	ADJ
ejpam-491	204	21	)	)	PUNCT
ejpam-491	204	22	sets	set	NOUN
ejpam-491	204	23	of	of	ADP
ejpam-491	204	24	x	x	PUNCT
ejpam-491	204	25	contained	contain	VERB
ejpam-491	204	26	in	in	ADP
ejpam-491	204	27	a	a	PRON
ejpam-491	204	28	is	be	AUX
ejpam-491	204	29	called	call	VERB
ejpam-491	204	30	the	the	DET
ejpam-491	204	31	g	g	NOUN
ejpam-491	204	32	-	-	NOUN
ejpam-491	204	33	interior	interior	NOUN
ejpam-491	204	34	[	[	X
ejpam-491	204	35	9	9	NUM
ejpam-491	204	36	]	]	PUNCT
ejpam-491	204	37	(	(	PUNCT
ejpam-491	204	38	resp	resp	NOUN
ejpam-491	204	39	.	.	PUNCT
ejpam-491	205	1	αg	αg	NOUN
ejpam-491	205	2	-	-	PUNCT
ejpam-491	205	3	interior	interior	ADJ
ejpam-491	205	4	,	,	PUNCT
ejpam-491	205	5	gs	gs	NOUN
ejpam-491	205	6	-	-	PUNCT
ejpam-491	205	7	interior	interior	ADJ
ejpam-491	205	8	,	,	PUNCT
ejpam-491	205	9	gp	gp	NOUN
ejpam-491	205	10	-	-	NOUN
ejpam-491	205	11	interior	interior	ADJ
ejpam-491	205	12	,	,	PUNCT
ejpam-491	205	13	gsp	gsp	NOUN
ejpam-491	205	14	-	-	PUNCT
ejpam-491	205	15	interior	interior	NOUN
ejpam-491	205	16	,	,	PUNCT
ejpam-491	205	17	gbinterior	gbinterior	NOUN
ejpam-491	205	18	)	)	PUNCT
ejpam-491	205	19	of	of	ADP
ejpam-491	205	20	a	a	PRON
ejpam-491	205	21	and	and	CCONJ
ejpam-491	205	22	is	be	AUX
ejpam-491	205	23	denoted	denote	VERB
ejpam-491	205	24	by	by	ADP
ejpam-491	205	25	intg(a	intg(a	PROPN
ejpam-491	205	26	)	)	PUNCT
ejpam-491	205	27	(	(	PUNCT
ejpam-491	205	28	resp	resp	NOUN
ejpam-491	205	29	.	.	PUNCT
ejpam-491	206	1	αintg(a	αintg(a	X
ejpam-491	206	2	)	)	PUNCT
ejpam-491	206	3	,	,	PUNCT
ejpam-491	206	4	sintg(a	sintg(a	PROPN
ejpam-491	206	5	)	)	PUNCT
ejpam-491	206	6	,	,	PUNCT
ejpam-491	206	7	pintg(a	pintg(a	PROPN
ejpam-491	206	8	)	)	PUNCT
ejpam-491	206	9	,	,	PUNCT
ejpam-491	206	10	spintg(a	spintg(a	PROPN
ejpam-491	206	11	)	)	PUNCT
ejpam-491	206	12	,	,	PUNCT
ejpam-491	206	13	bintg(a	bintg(a	NOUN
ejpam-491	206	14	)	)	PUNCT
ejpam-491	206	15	)	)	PUNCT
ejpam-491	206	16	.	.	PUNCT
ejpam-491	207	1	remark	remark	NOUN
ejpam-491	207	2	5	5	NUM
ejpam-491	207	3	.	.	PUNCT
ejpam-491	208	1	let	let	AUX
ejpam-491	208	2	(	(	PUNCT
ejpam-491	208	3	x	x	X
ejpam-491	208	4	,	,	PUNCT
ejpam-491	208	5	τ	τ	X
ejpam-491	208	6	)	)	PUNCT
ejpam-491	208	7	be	be	VERB
ejpam-491	208	8	a	a	DET
ejpam-491	208	9	topological	topological	ADJ
ejpam-491	208	10	space	space	NOUN
ejpam-491	208	11	and	and	CCONJ
ejpam-491	208	12	a	a	DET
ejpam-491	208	13	a	a	DET
ejpam-491	208	14	subset	subset	NOUN
ejpam-491	208	15	of	of	ADP
ejpam-491	208	16	x	x	X
ejpam-491	208	17	.	.	PUNCT
ejpam-491	209	1	(	(	PUNCT
ejpam-491	209	2	1	1	X
ejpam-491	209	3	)	)	PUNCT
ejpam-491	209	4	then	then	ADV
ejpam-491	209	5	,	,	PUNCT
ejpam-491	209	6	go(x	go(x	X
ejpam-491	209	7	)	)	PUNCT
ejpam-491	209	8	,	,	PUNCT
ejpam-491	209	9	gso(x	gso(x	VERB
ejpam-491	209	10	)	)	PUNCT
ejpam-491	209	11	,	,	PUNCT
ejpam-491	209	12	gpo(x	gpo(x	NOUN
ejpam-491	209	13	)	)	PUNCT
ejpam-491	209	14	,	,	PUNCT
ejpam-491	209	15	αgo(x	αgo(x	PROPN
ejpam-491	209	16	)	)	PUNCT
ejpam-491	209	17	and	and	CCONJ
ejpam-491	209	18	gspo(x	gspo(x	PROPN
ejpam-491	209	19	)	)	PUNCT
ejpam-491	209	20	are	be	AUX
ejpam-491	209	21	all	all	PRON
ejpam-491	209	22	m	m	NOUN
ejpam-491	209	23	-	-	NOUN
ejpam-491	209	24	structures	structure	NOUN
ejpam-491	209	25	on	on	ADP
ejpam-491	209	26	x	x	X
ejpam-491	209	27	.	.	PUNCT
ejpam-491	210	1	hence	hence	ADV
ejpam-491	210	2	,	,	PUNCT
ejpam-491	210	3	if	if	SCONJ
ejpam-491	210	4	we	we	PRON
ejpam-491	210	5	put	put	VERB
ejpam-491	210	6	mx	mx	NOUN
ejpam-491	210	7	=	=	NOUN
ejpam-491	210	8	go(x	go(x	PROPN
ejpam-491	210	9	)	)	PUNCT
ejpam-491	210	10	(	(	PUNCT
ejpam-491	210	11	resp	resp	NOUN
ejpam-491	210	12	.	.	PUNCT
ejpam-491	211	1	αgo(x	αgo(x	PROPN
ejpam-491	211	2	)	)	PUNCT
ejpam-491	211	3	,	,	PUNCT
ejpam-491	211	4	gso(x	gso(x	VERB
ejpam-491	211	5	)	)	PUNCT
ejpam-491	211	6	,	,	PUNCT
ejpam-491	211	7	gpo(x	gpo(x	NOUN
ejpam-491	211	8	)	)	PUNCT
ejpam-491	211	9	,	,	PUNCT
ejpam-491	211	10	gspo(x	gspo(x	NOUN
ejpam-491	211	11	)	)	PUNCT
ejpam-491	211	12	)	)	PUNCT
ejpam-491	211	13	,	,	PUNCT
ejpam-491	211	14	then	then	ADV
ejpam-491	211	15	we	we	PRON
ejpam-491	211	16	have	have	VERB
ejpam-491	211	17	(	(	PUNCT
ejpam-491	211	18	i	i	NOUN
ejpam-491	211	19	)	)	PUNCT
ejpam-491	211	20	mcl(a	mcl(a	PROPN
ejpam-491	211	21	)	)	PUNCT
ejpam-491	211	22	=	=	SYM
ejpam-491	211	23	clg(a	clg(a	NOUN
ejpam-491	211	24	)	)	PUNCT
ejpam-491	211	25	(	(	PUNCT
ejpam-491	211	26	resp	resp	NOUN
ejpam-491	211	27	.	.	PUNCT
ejpam-491	212	1	αclg(a	αclg(a	NOUN
ejpam-491	212	2	)	)	PUNCT
ejpam-491	212	3	,	,	PUNCT
ejpam-491	212	4	sclg(a	sclg(a	PROPN
ejpam-491	212	5	)	)	PUNCT
ejpam-491	212	6	,	,	PUNCT
ejpam-491	212	7	pclg(a	pclg(a	PROPN
ejpam-491	212	8	)	)	PUNCT
ejpam-491	212	9	,	,	PUNCT
ejpam-491	212	10	spclg(a	spclg(a	PROPN
ejpam-491	212	11	)	)	PUNCT
ejpam-491	212	12	)	)	PUNCT
ejpam-491	212	13	,	,	PUNCT
ejpam-491	212	14	(	(	PUNCT
ejpam-491	212	15	ii	ii	NOUN
ejpam-491	212	16	)	)	PUNCT
ejpam-491	212	17	mint(a	mint(a	PROPN
ejpam-491	212	18	)	)	PUNCT
ejpam-491	212	19	=	=	SYM
ejpam-491	212	20	intg(a	intg(a	PROPN
ejpam-491	212	21	)	)	PUNCT
ejpam-491	212	22	(	(	PUNCT
ejpam-491	212	23	resp	resp	NOUN
ejpam-491	212	24	.	.	PUNCT
ejpam-491	213	1	αintg(a	αintg(a	X
ejpam-491	213	2	)	)	PUNCT
ejpam-491	213	3	)	)	PUNCT
ejpam-491	213	4	,	,	PUNCT
ejpam-491	213	5	sintg(a	sintg(a	PROPN
ejpam-491	213	6	)	)	PUNCT
ejpam-491	213	7	,	,	PUNCT
ejpam-491	213	8	pintg(a	pintg(a	PROPN
ejpam-491	213	9	)	)	PUNCT
ejpam-491	213	10	,	,	PUNCT
ejpam-491	213	11	spintg(a	spintg(a	NOUN
ejpam-491	213	12	)	)	PUNCT
ejpam-491	213	13	)	)	PUNCT
ejpam-491	213	14	.	.	PUNCT
ejpam-491	214	1	(	(	PUNCT
ejpam-491	214	2	2	2	X
ejpam-491	214	3	)	)	PUNCT
ejpam-491	214	4	if	if	SCONJ
ejpam-491	214	5	mx	mx	PROPN
ejpam-491	214	6	=	=	SYM
ejpam-491	214	7	go(x	go(x	NUM
ejpam-491	214	8	)	)	PUNCT
ejpam-491	214	9	,	,	PUNCT
ejpam-491	214	10	then	then	ADV
ejpam-491	214	11	by	by	ADP
ejpam-491	214	12	lemma	lemma	PROPN
ejpam-491	214	13	1	1	NUM
ejpam-491	214	14	we	we	PRON
ejpam-491	214	15	obtain	obtain	VERB
ejpam-491	214	16	the	the	DET
ejpam-491	214	17	results	result	NOUN
ejpam-491	214	18	established	establish	VERB
ejpam-491	214	19	in	in	ADP
ejpam-491	214	20	theorem	theorem	ADJ
ejpam-491	214	21	2.1	2.1	NUM
ejpam-491	214	22	(	(	PUNCT
ejpam-491	214	23	4	4	NUM
ejpam-491	214	24	)	)	PUNCT
ejpam-491	214	25	,	,	PUNCT
ejpam-491	214	26	(	(	PUNCT
ejpam-491	214	27	5	5	NUM
ejpam-491	214	28	)	)	PUNCT
ejpam-491	214	29	and	and	CCONJ
ejpam-491	214	30	theorem	theorem	VERB
ejpam-491	214	31	2.8	2.8	NUM
ejpam-491	214	32	(	(	PUNCT
ejpam-491	214	33	2	2	NUM
ejpam-491	214	34	)	)	PUNCT
ejpam-491	214	35	,	,	PUNCT
ejpam-491	214	36	(	(	PUNCT
ejpam-491	214	37	3	3	NUM
ejpam-491	214	38	)	)	PUNCT
ejpam-491	214	39	,	,	PUNCT
ejpam-491	214	40	(	(	PUNCT
ejpam-491	214	41	5	5	NUM
ejpam-491	214	42	)	)	PUNCT
ejpam-491	214	43	,	,	PUNCT
ejpam-491	214	44	(	(	PUNCT
ejpam-491	214	45	6	6	NUM
ejpam-491	214	46	)	)	PUNCT
ejpam-491	214	47	in	in	ADP
ejpam-491	214	48	[	[	X
ejpam-491	214	49	9	9	NUM
ejpam-491	214	50	]	]	PUNCT
ejpam-491	214	51	.	.	PUNCT
ejpam-491	215	1	by	by	ADP
ejpam-491	215	2	lemma	lemma	PROPN
ejpam-491	215	3	2	2	NUM
ejpam-491	215	4	,	,	PUNCT
ejpam-491	215	5	we	we	PRON
ejpam-491	215	6	obtain	obtain	VERB
ejpam-491	215	7	the	the	DET
ejpam-491	215	8	result	result	NOUN
ejpam-491	215	9	established	establish	VERB
ejpam-491	215	10	in	in	ADP
ejpam-491	215	11	theorem	theorem	ADJ
ejpam-491	215	12	2.1	2.1	NUM
ejpam-491	215	13	(	(	PUNCT
ejpam-491	215	14	4	4	NUM
ejpam-491	215	15	)	)	PUNCT
ejpam-491	215	16	in	in	ADP
ejpam-491	215	17	[	[	X
ejpam-491	215	18	9	9	NUM
ejpam-491	215	19	]	]	PUNCT
ejpam-491	215	20	.	.	PUNCT
ejpam-491	216	1	(	(	PUNCT
ejpam-491	216	2	3	3	X
ejpam-491	216	3	)	)	PUNCT
ejpam-491	216	4	the	the	DET
ejpam-491	216	5	m	m	NOUN
ejpam-491	216	6	-	-	PUNCT
ejpam-491	216	7	structures	structure	NOUN
ejpam-491	216	8	go(x	go(x	PUNCT
ejpam-491	216	9	)	)	PUNCT
ejpam-491	216	10	,	,	PUNCT
ejpam-491	216	11	gso(x	gso(x	VERB
ejpam-491	216	12	)	)	PUNCT
ejpam-491	216	13	,	,	PUNCT
ejpam-491	216	14	gpo(x	gpo(x	NOUN
ejpam-491	216	15	)	)	PUNCT
ejpam-491	216	16	,	,	PUNCT
ejpam-491	216	17	αgo(x	αgo(x	PROPN
ejpam-491	216	18	)	)	PUNCT
ejpam-491	216	19	,	,	PUNCT
ejpam-491	216	20	gspo(x	gspo(x	NOUN
ejpam-491	216	21	)	)	PUNCT
ejpam-491	216	22	and	and	CCONJ
ejpam-491	216	23	gbo(x	gbo(x	PROPN
ejpam-491	216	24	)	)	PUNCT
ejpam-491	216	25	do	do	AUX
ejpam-491	216	26	not	not	PART
ejpam-491	216	27	have	have	VERB
ejpam-491	216	28	propertyb	propertyb	NOUN
ejpam-491	216	29	,	,	PUNCT
ejpam-491	216	30	in	in	ADP
ejpam-491	216	31	general	general	ADJ
ejpam-491	216	32	.	.	PUNCT
ejpam-491	217	1	t.	t.	PROPN
ejpam-491	217	2	noiri	noiri	PROPN
ejpam-491	217	3	and	and	CCONJ
ejpam-491	217	4	v.	v.	ADP
ejpam-491	217	5	popa	popa	NOUN
ejpam-491	217	6	/	/	SYM
ejpam-491	217	7	eur	eur	PROPN
ejpam-491	217	8	.	.	PUNCT
ejpam-491	218	1	j.	j.	PROPN
ejpam-491	218	2	pure	pure	PROPN
ejpam-491	218	3	appl	appl	PROPN
ejpam-491	218	4	.	.	PROPN
ejpam-491	218	5	math	math	PROPN
ejpam-491	218	6	,	,	PUNCT
ejpam-491	218	7	2	2	NUM
ejpam-491	218	8	(	(	PUNCT
ejpam-491	218	9	2009	2009	NUM
ejpam-491	218	10	)	)	PUNCT
ejpam-491	218	11	,	,	PUNCT
ejpam-491	218	12	(	(	PUNCT
ejpam-491	218	13	473	473	NUM
ejpam-491	218	14	-	-	NUM
ejpam-491	218	15	493	493	NUM
ejpam-491	218	16	)	)	PUNCT
ejpam-491	218	17	481	481	NUM
ejpam-491	218	18	definition	definition	NOUN
ejpam-491	218	19	14	14	NUM
ejpam-491	218	20	.	.	PUNCT
ejpam-491	219	1	let	let	AUX
ejpam-491	219	2	(	(	PUNCT
ejpam-491	219	3	x	x	X
ejpam-491	219	4	,	,	PUNCT
ejpam-491	219	5	τ	τ	X
ejpam-491	219	6	)	)	PUNCT
ejpam-491	219	7	be	be	VERB
ejpam-491	219	8	a	a	DET
ejpam-491	219	9	topological	topological	ADJ
ejpam-491	219	10	space	space	NOUN
ejpam-491	219	11	and	and	CCONJ
ejpam-491	219	12	mx	mx	X
ejpam-491	219	13	an	an	DET
ejpam-491	219	14	m	m	NOUN
ejpam-491	219	15	-	-	NOUN
ejpam-491	219	16	structure	structure	NOUN
ejpam-491	219	17	on	on	ADP
ejpam-491	219	18	x	x	X
ejpam-491	219	19	.	.	PUNCT
ejpam-491	220	1	a	a	DET
ejpam-491	220	2	subset	subset	NOUN
ejpam-491	220	3	a	a	PRON
ejpam-491	220	4	of	of	ADP
ejpam-491	220	5	x	x	SYM
ejpam-491	220	6	is	be	AUX
ejpam-491	220	7	said	say	VERB
ejpam-491	220	8	to	to	PART
ejpam-491	220	9	be	be	AUX
ejpam-491	220	10	generalized	generalize	VERB
ejpam-491	220	11	m	m	NOUN
ejpam-491	220	12	-	-	ADJ
ejpam-491	220	13	closed	closed	ADJ
ejpam-491	220	14	(	(	PUNCT
ejpam-491	220	15	briefly	briefly	NOUN
ejpam-491	220	16	gm	gm	NOUN
ejpam-491	220	17	-	-	PUNCT
ejpam-491	220	18	closed	closed	ADJ
ejpam-491	220	19	)	)	PUNCT
ejpam-491	221	1	[	[	X
ejpam-491	221	2	27	27	NUM
ejpam-491	221	3	]	]	X
ejpam-491	221	4	if	if	SCONJ
ejpam-491	221	5	mcl(a)⊂	mcl(a)⊂	PROPN
ejpam-491	221	6	u	u	NOUN
ejpam-491	221	7	whenever	whenever	SCONJ
ejpam-491	221	8	a⊂	a⊂	PUNCT
ejpam-491	221	9	u	u	NOUN
ejpam-491	221	10	and	and	CCONJ
ejpam-491	221	11	u	u	PROPN
ejpam-491	221	12	∈	∈	PROPN
ejpam-491	221	13	τ	τ	PROPN
ejpam-491	221	14	.	.	PUNCT
ejpam-491	222	1	the	the	DET
ejpam-491	222	2	complement	complement	NOUN
ejpam-491	222	3	of	of	ADP
ejpam-491	222	4	a	a	DET
ejpam-491	222	5	gm	gm	ADV
ejpam-491	222	6	-	-	PUNCT
ejpam-491	222	7	closed	close	VERB
ejpam-491	222	8	set	set	NOUN
ejpam-491	222	9	is	be	AUX
ejpam-491	222	10	said	say	VERB
ejpam-491	222	11	to	to	PART
ejpam-491	222	12	be	be	AUX
ejpam-491	222	13	gm	gm	NOUN
ejpam-491	222	14	-	-	PUNCT
ejpam-491	222	15	open	open	ADJ
ejpam-491	222	16	.	.	PUNCT
ejpam-491	223	1	the	the	DET
ejpam-491	223	2	family	family	NOUN
ejpam-491	223	3	of	of	ADP
ejpam-491	223	4	all	all	DET
ejpam-491	223	5	gmopen	gmopen	ADJ
ejpam-491	223	6	sets	set	NOUN
ejpam-491	223	7	of	of	ADP
ejpam-491	223	8	a	a	DET
ejpam-491	223	9	topological	topological	ADJ
ejpam-491	223	10	space	space	NOUN
ejpam-491	223	11	(	(	PUNCT
ejpam-491	223	12	x	x	X
ejpam-491	223	13	,	,	PUNCT
ejpam-491	223	14	τ	τ	X
ejpam-491	223	15	)	)	PUNCT
ejpam-491	223	16	is	be	AUX
ejpam-491	223	17	denoted	denote	VERB
ejpam-491	223	18	by	by	ADP
ejpam-491	223	19	gmo(x	gmo(x	PROPN
ejpam-491	223	20	)	)	PUNCT
ejpam-491	223	21	.	.	PUNCT
ejpam-491	224	1	obviously	obviously	ADV
ejpam-491	224	2	,	,	PUNCT
ejpam-491	224	3	gmo(x	gmo(x	PROPN
ejpam-491	224	4	)	)	PUNCT
ejpam-491	224	5	is	be	AUX
ejpam-491	224	6	an	an	DET
ejpam-491	224	7	m	m	NOUN
ejpam-491	224	8	-	-	NOUN
ejpam-491	224	9	structure	structure	NOUN
ejpam-491	224	10	on	on	ADP
ejpam-491	224	11	x	x	PUNCT
ejpam-491	224	12	and	and	CCONJ
ejpam-491	224	13	is	be	AUX
ejpam-491	224	14	called	call	VERB
ejpam-491	224	15	a	a	DET
ejpam-491	224	16	gm	gm	NOUN
ejpam-491	224	17	-	-	PUNCT
ejpam-491	224	18	structure	structure	NOUN
ejpam-491	224	19	on	on	ADP
ejpam-491	224	20	x	x	X
ejpam-491	224	21	.	.	PUNCT
ejpam-491	225	1	remark	remark	PROPN
ejpam-491	225	2	6	6	NUM
ejpam-491	225	3	.	.	PUNCT
ejpam-491	226	1	let	let	AUX
ejpam-491	226	2	(	(	PUNCT
ejpam-491	226	3	x	x	X
ejpam-491	226	4	,	,	PUNCT
ejpam-491	226	5	τ	τ	X
ejpam-491	226	6	)	)	PUNCT
ejpam-491	226	7	be	be	VERB
ejpam-491	226	8	a	a	DET
ejpam-491	226	9	topological	topological	ADJ
ejpam-491	226	10	space	space	NOUN
ejpam-491	226	11	and	and	CCONJ
ejpam-491	226	12	mx	mx	X
ejpam-491	226	13	an	an	DET
ejpam-491	226	14	m	m	NOUN
ejpam-491	226	15	-	-	NOUN
ejpam-491	226	16	structure	structure	NOUN
ejpam-491	226	17	on	on	ADP
ejpam-491	226	18	x	x	X
ejpam-491	226	19	.	.	PUNCT
ejpam-491	227	1	we	we	PRON
ejpam-491	227	2	put	put	VERB
ejpam-491	227	3	mx	mx	PROPN
ejpam-491	228	1	=	=	SYM
ejpam-491	228	2	τ	τ	PROPN
ejpam-491	228	3	(	(	PUNCT
ejpam-491	228	4	resp	resp	PROPN
ejpam-491	228	5	.	.	PUNCT
ejpam-491	228	6	so(x	so(x	PROPN
ejpam-491	228	7	)	)	PUNCT
ejpam-491	228	8	,	,	PUNCT
ejpam-491	228	9	po(x	po(x	NUM
ejpam-491	228	10	)	)	PUNCT
ejpam-491	228	11	,	,	PUNCT
ejpam-491	228	12	α(x	α(x	PROPN
ejpam-491	228	13	)	)	PUNCT
ejpam-491	228	14	,	,	PUNCT
ejpam-491	228	15	spo(x	spo(x	PROPN
ejpam-491	228	16	)	)	PUNCT
ejpam-491	228	17	,	,	PUNCT
ejpam-491	228	18	bo(x	bo(x	NUM
ejpam-491	228	19	)	)	PUNCT
ejpam-491	228	20	)	)	PUNCT
ejpam-491	228	21	.	.	PUNCT
ejpam-491	229	1	then	then	ADV
ejpam-491	229	2	,	,	PUNCT
ejpam-491	229	3	a	a	DET
ejpam-491	229	4	gm	gm	ADV
ejpam-491	229	5	-	-	PUNCT
ejpam-491	229	6	closed	close	VERB
ejpam-491	229	7	set	set	NOUN
ejpam-491	229	8	is	be	AUX
ejpam-491	229	9	a	a	DET
ejpam-491	229	10	g	g	NOUN
ejpam-491	229	11	-	-	PUNCT
ejpam-491	229	12	closed	closed	ADJ
ejpam-491	229	13	(	(	PUNCT
ejpam-491	229	14	resp	resp	NOUN
ejpam-491	229	15	.	.	PUNCT
ejpam-491	230	1	gs	gs	NOUN
ejpam-491	230	2	-	-	PUNCT
ejpam-491	230	3	closed	closed	ADJ
ejpam-491	230	4	,	,	PUNCT
ejpam-491	230	5	gp	gp	NOUN
ejpam-491	230	6	-	-	ADJ
ejpam-491	230	7	closed	closed	ADJ
ejpam-491	230	8	,	,	PUNCT
ejpam-491	230	9	αg	αg	NOUN
ejpam-491	230	10	-	-	PUNCT
ejpam-491	230	11	closed	closed	ADJ
ejpam-491	230	12	,	,	PUNCT
ejpam-491	230	13	gsp	gsp	NOUN
ejpam-491	230	14	-	-	PUNCT
ejpam-491	230	15	closed	closed	ADJ
ejpam-491	230	16	,	,	PUNCT
ejpam-491	230	17	g	g	PROPN
ejpam-491	230	18	b	b	X
ejpam-491	230	19	-	-	PUNCT
ejpam-491	230	20	closed	closed	ADJ
ejpam-491	230	21	)	)	PUNCT
ejpam-491	230	22	set	set	NOUN
ejpam-491	230	23	.	.	PUNCT
ejpam-491	231	1	definition	definition	NOUN
ejpam-491	231	2	15	15	NUM
ejpam-491	231	3	.	.	PUNCT
ejpam-491	232	1	a	a	DET
ejpam-491	232	2	function	function	NOUN
ejpam-491	232	3	f	f	NOUN
ejpam-491	232	4	:	:	PUNCT
ejpam-491	232	5	(	(	PUNCT
ejpam-491	232	6	x	x	X
ejpam-491	232	7	,	,	PUNCT
ejpam-491	232	8	τ	τ	PROPN
ejpam-491	232	9	)	)	PUNCT
ejpam-491	232	10	→	→	SYM
ejpam-491	232	11	(	(	PUNCT
ejpam-491	232	12	y	y	PROPN
ejpam-491	232	13	,	,	PUNCT
ejpam-491	232	14	σ	σ	PROPN
ejpam-491	232	15	)	)	PUNCT
ejpam-491	232	16	is	be	AUX
ejpam-491	232	17	said	say	VERB
ejpam-491	232	18	to	to	PART
ejpam-491	232	19	be	be	AUX
ejpam-491	232	20	g	g	NOUN
ejpam-491	232	21	-	-	PUNCT
ejpam-491	232	22	irresolute	irresolute	ADJ
ejpam-491	233	1	[	[	X
ejpam-491	233	2	7	7	NUM
ejpam-491	233	3	]	]	PUNCT
ejpam-491	233	4	or	or	CCONJ
ejpam-491	233	5	gcontinuous	gcontinuous	ADJ
ejpam-491	233	6	[	[	X
ejpam-491	233	7	25	25	NUM
ejpam-491	233	8	]	]	PUNCT
ejpam-491	233	9	(	(	PUNCT
ejpam-491	233	10	resp	resp	NOUN
ejpam-491	233	11	.	.	PUNCT
ejpam-491	234	1	gs	gs	NOUN
ejpam-491	234	2	-	-	PUNCT
ejpam-491	234	3	irresolute	irresolute	ADJ
ejpam-491	235	1	[	[	X
ejpam-491	235	2	11	11	NUM
ejpam-491	235	3	]	]	PUNCT
ejpam-491	235	4	,	,	PUNCT
ejpam-491	235	5	gp	gp	NOUN
ejpam-491	235	6	-	-	NOUN
ejpam-491	235	7	irresolute	irresolute	ADJ
ejpam-491	235	8	[	[	X
ejpam-491	235	9	6	6	NUM
ejpam-491	235	10	]	]	PUNCT
ejpam-491	235	11	,	,	PUNCT
ejpam-491	235	12	αg	αg	NOUN
ejpam-491	235	13	-	-	PUNCT
ejpam-491	235	14	irresolute	irresolute	NOUN
ejpam-491	236	1	[	[	X
ejpam-491	236	2	12	12	NUM
ejpam-491	236	3	]	]	PUNCT
ejpam-491	236	4	,	,	PUNCT
ejpam-491	236	5	gspirresolute	gspirresolute	NOUN
ejpam-491	236	6	[	[	X
ejpam-491	236	7	32	32	NUM
ejpam-491	236	8	]	]	PUNCT
ejpam-491	236	9	,	,	PUNCT
ejpam-491	236	10	gb	gb	NOUN
ejpam-491	236	11	-	-	PUNCT
ejpam-491	236	12	irresolute	irresolute	ADJ
ejpam-491	236	13	[	[	X
ejpam-491	236	14	3	3	NUM
ejpam-491	236	15	]	]	PUNCT
ejpam-491	236	16	)	)	PUNCT
ejpam-491	236	17	if	if	SCONJ
ejpam-491	236	18	f	f	PROPN
ejpam-491	236	19	−1(k	−1(k	NOUN
ejpam-491	236	20	)	)	PUNCT
ejpam-491	236	21	is	be	AUX
ejpam-491	236	22	a	a	DET
ejpam-491	236	23	g	g	NOUN
ejpam-491	236	24	-	-	PUNCT
ejpam-491	236	25	closed	closed	ADJ
ejpam-491	236	26	(	(	PUNCT
ejpam-491	236	27	resp	resp	NOUN
ejpam-491	236	28	.	.	PUNCT
ejpam-491	237	1	gs	gs	NOUN
ejpam-491	237	2	-	-	PUNCT
ejpam-491	237	3	closed	closed	ADJ
ejpam-491	237	4	,	,	PUNCT
ejpam-491	237	5	gp	gp	NOUN
ejpam-491	237	6	-	-	ADJ
ejpam-491	237	7	closed	closed	ADJ
ejpam-491	237	8	,	,	PUNCT
ejpam-491	237	9	αg	αg	NOUN
ejpam-491	237	10	-	-	PUNCT
ejpam-491	237	11	closed	closed	ADJ
ejpam-491	237	12	,	,	PUNCT
ejpam-491	237	13	gsp	gsp	NOUN
ejpam-491	237	14	-	-	PUNCT
ejpam-491	237	15	closed	closed	ADJ
ejpam-491	237	16	,	,	PUNCT
ejpam-491	237	17	g	g	PROPN
ejpam-491	237	18	b	b	X
ejpam-491	237	19	-	-	PUNCT
ejpam-491	237	20	closed	closed	ADJ
ejpam-491	237	21	)	)	PUNCT
ejpam-491	237	22	in	in	ADP
ejpam-491	237	23	x	x	PUNCT
ejpam-491	237	24	for	for	ADP
ejpam-491	237	25	every	every	DET
ejpam-491	237	26	g	g	NOUN
ejpam-491	237	27	-	-	PUNCT
ejpam-491	237	28	closed	closed	ADJ
ejpam-491	237	29	(	(	PUNCT
ejpam-491	237	30	resp	resp	NOUN
ejpam-491	237	31	.	.	PUNCT
ejpam-491	238	1	gs	gs	NOUN
ejpam-491	238	2	-	-	PUNCT
ejpam-491	238	3	closed	closed	ADJ
ejpam-491	238	4	,	,	PUNCT
ejpam-491	238	5	gp	gp	NOUN
ejpam-491	238	6	-	-	ADJ
ejpam-491	238	7	closed	closed	ADJ
ejpam-491	238	8	,	,	PUNCT
ejpam-491	238	9	αg	αg	NOUN
ejpam-491	238	10	-	-	PUNCT
ejpam-491	238	11	closed	closed	ADJ
ejpam-491	238	12	,	,	PUNCT
ejpam-491	238	13	gsp	gsp	NOUN
ejpam-491	238	14	-	-	PUNCT
ejpam-491	238	15	closed	closed	ADJ
ejpam-491	238	16	,	,	PUNCT
ejpam-491	238	17	g	g	PROPN
ejpam-491	238	18	b	b	X
ejpam-491	238	19	-	-	PUNCT
ejpam-491	238	20	closed	closed	ADJ
ejpam-491	238	21	)	)	PUNCT
ejpam-491	239	1	set	set	VERB
ejpam-491	239	2	k	k	PROPN
ejpam-491	239	3	of	of	ADP
ejpam-491	239	4	y	y	PROPN
ejpam-491	239	5	.	.	PUNCT
ejpam-491	240	1	definition	definition	NOUN
ejpam-491	240	2	16	16	NUM
ejpam-491	240	3	.	.	PUNCT
ejpam-491	241	1	a	a	DET
ejpam-491	241	2	function	function	NOUN
ejpam-491	241	3	f	f	NOUN
ejpam-491	241	4	:	:	PUNCT
ejpam-491	241	5	(	(	PUNCT
ejpam-491	241	6	x	x	X
ejpam-491	241	7	,	,	PUNCT
ejpam-491	241	8	τ)→	τ)→	PROPN
ejpam-491	241	9	(	(	PUNCT
ejpam-491	241	10	y	y	PROPN
ejpam-491	241	11	,	,	PUNCT
ejpam-491	241	12	σ	σ	PROPN
ejpam-491	241	13	)	)	PUNCT
ejpam-491	241	14	is	be	AUX
ejpam-491	241	15	said	say	VERB
ejpam-491	241	16	to	to	PART
ejpam-491	241	17	be	be	AUX
ejpam-491	241	18	(	(	PUNCT
ejpam-491	241	19	1	1	X
ejpam-491	241	20	)	)	PUNCT
ejpam-491	241	21	gm	gm	NOUN
ejpam-491	241	22	-	-	PUNCT
ejpam-491	241	23	continuous	continuous	ADJ
ejpam-491	241	24	at	at	ADP
ejpam-491	241	25	a	a	DET
ejpam-491	241	26	point	point	NOUN
ejpam-491	241	27	x	x	SYM
ejpam-491	241	28	∈	∈	NOUN
ejpam-491	241	29	x	x	INTJ
ejpam-491	241	30	if	if	SCONJ
ejpam-491	241	31	f	f	X
ejpam-491	241	32	:	:	PUNCT
ejpam-491	241	33	(	(	PUNCT
ejpam-491	241	34	x	x	X
ejpam-491	241	35	,	,	PUNCT
ejpam-491	241	36	gmo(x	gmo(x	PROPN
ejpam-491	241	37	)	)	PUNCT
ejpam-491	241	38	)	)	PUNCT
ejpam-491	242	1	→	→	PUNCT
ejpam-491	242	2	(	(	PUNCT
ejpam-491	242	3	y	y	NOUN
ejpam-491	242	4	,	,	PUNCT
ejpam-491	242	5	gmo(y	gmo(y	NOUN
ejpam-491	242	6	)	)	PUNCT
ejpam-491	242	7	)	)	PUNCT
ejpam-491	242	8	is	be	AUX
ejpam-491	242	9	m	m	VERB
ejpam-491	242	10	continuous	continuous	ADJ
ejpam-491	242	11	at	at	ADP
ejpam-491	242	12	a	a	DET
ejpam-491	242	13	point	point	NOUN
ejpam-491	242	14	x	x	SYM
ejpam-491	242	15	∈	∈	NOUN
ejpam-491	242	16	x	x	X
ejpam-491	242	17	.	.	PUNCT
ejpam-491	243	1	the	the	DET
ejpam-491	243	2	function	function	NOUN
ejpam-491	243	3	f	f	NOUN
ejpam-491	243	4	:	:	PUNCT
ejpam-491	243	5	(	(	PUNCT
ejpam-491	243	6	x	x	X
ejpam-491	243	7	,	,	PUNCT
ejpam-491	243	8	τ	τ	PROPN
ejpam-491	243	9	)	)	PUNCT
ejpam-491	243	10	→	→	SYM
ejpam-491	243	11	(	(	PUNCT
ejpam-491	243	12	y	y	PROPN
ejpam-491	243	13	,	,	PUNCT
ejpam-491	243	14	σ	σ	PROPN
ejpam-491	243	15	)	)	PUNCT
ejpam-491	243	16	is	be	AUX
ejpam-491	243	17	said	say	VERB
ejpam-491	243	18	to	to	PART
ejpam-491	243	19	be	be	AUX
ejpam-491	243	20	gmcontinuous	gmcontinuous	ADJ
ejpam-491	243	21	if	if	SCONJ
ejpam-491	243	22	it	it	PRON
ejpam-491	243	23	is	be	AUX
ejpam-491	243	24	gm	gm	PROPN
ejpam-491	243	25	-continuous	-continuous	ADJ
ejpam-491	243	26	at	at	ADP
ejpam-491	243	27	each	each	DET
ejpam-491	243	28	point	point	NOUN
ejpam-491	243	29	x	x	X
ejpam-491	243	30	∈	∈	NOUN
ejpam-491	243	31	x	x	X
ejpam-491	243	32	.	.	PUNCT
ejpam-491	244	1	(	(	PUNCT
ejpam-491	244	2	2	2	X
ejpam-491	244	3	)	)	PUNCT
ejpam-491	244	4	gm	gm	PROPN
ejpam-491	244	5	-	-	PUNCT
ejpam-491	244	6	irresolute	irresolute	ADJ
ejpam-491	244	7	if	if	SCONJ
ejpam-491	244	8	f	f	X
ejpam-491	244	9	:	:	PUNCT
ejpam-491	244	10	(	(	PUNCT
ejpam-491	244	11	x	x	X
ejpam-491	244	12	,	,	PUNCT
ejpam-491	244	13	gmo(x	gmo(x	PROPN
ejpam-491	244	14	)	)	PUNCT
ejpam-491	244	15	)	)	PUNCT
ejpam-491	244	16	→	→	SYM
ejpam-491	244	17	(	(	PUNCT
ejpam-491	244	18	y	y	PROPN
ejpam-491	244	19	,	,	PUNCT
ejpam-491	244	20	gmo(y	gmo(y	NOUN
ejpam-491	244	21	)	)	PUNCT
ejpam-491	244	22	)	)	PUNCT
ejpam-491	244	23	is	be	AUX
ejpam-491	244	24	m	m	VERB
ejpam-491	244	25	∗-continuous	∗-continuous	ADJ
ejpam-491	244	26	.	.	PUNCT
ejpam-491	245	1	remark	remark	PROPN
ejpam-491	245	2	7	7	NUM
ejpam-491	245	3	.	.	PUNCT
ejpam-491	246	1	(	(	PUNCT
ejpam-491	246	2	1	1	X
ejpam-491	246	3	)	)	PUNCT
ejpam-491	246	4	every	every	DET
ejpam-491	246	5	gm	gm	PROPN
ejpam-491	246	6	-irresolute	-irresolute	PROPN
ejpam-491	246	7	function	function	NOUN
ejpam-491	246	8	is	be	AUX
ejpam-491	246	9	gm	gm	PROPN
ejpam-491	246	10	-continuous	-continuous	PROPN
ejpam-491	246	11	.	.	PUNCT
ejpam-491	247	1	(	(	PUNCT
ejpam-491	247	2	2)if	2)if	NOUN
ejpam-491	247	3	mx	mx	NOUN
ejpam-491	247	4	=	=	NOUN
ejpam-491	247	5	go(x	go(x	PROPN
ejpam-491	247	6	)	)	PUNCT
ejpam-491	247	7	(	(	PUNCT
ejpam-491	247	8	resp	resp	NOUN
ejpam-491	247	9	.	.	PUNCT
ejpam-491	248	1	gso(x	gso(x	VERB
ejpam-491	248	2	)	)	PUNCT
ejpam-491	248	3	,	,	PUNCT
ejpam-491	248	4	gpo(x	gpo(x	NOUN
ejpam-491	248	5	)	)	PUNCT
ejpam-491	248	6	,	,	PUNCT
ejpam-491	248	7	αgo(x	αgo(x	PROPN
ejpam-491	248	8	)	)	PUNCT
ejpam-491	248	9	,	,	PUNCT
ejpam-491	248	10	gspo(x	gspo(x	NOUN
ejpam-491	248	11	)	)	PUNCT
ejpam-491	248	12	,	,	PUNCT
ejpam-491	248	13	bo(x	bo(x	NUM
ejpam-491	248	14	)	)	PUNCT
ejpam-491	248	15	)	)	PUNCT
ejpam-491	248	16	,	,	PUNCT
ejpam-491	248	17	my	my	PRON
ejpam-491	248	18	=	=	NOUN
ejpam-491	248	19	go(y	go(y	X
ejpam-491	248	20	)	)	PUNCT
ejpam-491	248	21	(	(	PUNCT
ejpam-491	248	22	resp	resp	NOUN
ejpam-491	248	23	.	.	PUNCT
ejpam-491	249	1	gso(y	gso(y	NOUN
ejpam-491	249	2	)	)	PUNCT
ejpam-491	249	3	,	,	PUNCT
ejpam-491	249	4	gpo(y	gpo(y	PROPN
ejpam-491	249	5	)	)	PUNCT
ejpam-491	249	6	,	,	PUNCT
ejpam-491	249	7	αgo(y	αgo(y	NOUN
ejpam-491	249	8	)	)	PUNCT
ejpam-491	249	9	,	,	PUNCT
ejpam-491	249	10	gspo(y	gspo(y	PROPN
ejpam-491	249	11	)	)	PUNCT
ejpam-491	249	12	,	,	PUNCT
ejpam-491	249	13	bo(y	bo(y	NUM
ejpam-491	249	14	)	)	PUNCT
ejpam-491	249	15	)	)	PUNCT
ejpam-491	250	1	and	and	CCONJ
ejpam-491	250	2	f	f	X
ejpam-491	250	3	:	:	PUNCT
ejpam-491	250	4	(	(	PUNCT
ejpam-491	250	5	x	x	X
ejpam-491	250	6	,	,	PUNCT
ejpam-491	250	7	τ	τ	PROPN
ejpam-491	250	8	)	)	PUNCT
ejpam-491	250	9	→	→	SYM
ejpam-491	250	10	(	(	PUNCT
ejpam-491	250	11	y	y	PROPN
ejpam-491	250	12	,	,	PUNCT
ejpam-491	250	13	σ	σ	PROPN
ejpam-491	250	14	)	)	PUNCT
ejpam-491	250	15	is	be	AUX
ejpam-491	250	16	gm	gm	PROPN
ejpam-491	250	17	-irresolute	-irresolute	PROPN
ejpam-491	250	18	,	,	PUNCT
ejpam-491	250	19	then	then	ADV
ejpam-491	250	20	f	f	PROPN
ejpam-491	250	21	is	be	AUX
ejpam-491	250	22	g	g	NOUN
ejpam-491	250	23	-	-	PUNCT
ejpam-491	250	24	irresolute	irresolute	ADJ
ejpam-491	250	25	(	(	PUNCT
ejpam-491	250	26	resp	resp	NOUN
ejpam-491	250	27	.	.	PUNCT
ejpam-491	251	1	gs	gs	NOUN
ejpam-491	251	2	-	-	PUNCT
ejpam-491	251	3	irresolute	irresolute	ADJ
ejpam-491	251	4	,	,	PUNCT
ejpam-491	251	5	gp	gp	NOUN
ejpam-491	251	6	-	-	PUNCT
ejpam-491	251	7	irresolute	irresolute	ADJ
ejpam-491	251	8	,	,	PUNCT
ejpam-491	251	9	αgirresolute	αgirresolute	NOUN
ejpam-491	251	10	,	,	PUNCT
ejpam-491	251	11	gsp	gsp	NOUN
ejpam-491	251	12	-	-	PUNCT
ejpam-491	251	13	irresolute	irresolute	PROPN
ejpam-491	251	14	,	,	PUNCT
ejpam-491	251	15	g	g	PROPN
ejpam-491	252	1	b	b	NOUN
ejpam-491	252	2	-	-	PUNCT
ejpam-491	252	3	irresolute	irresolute	ADJ
ejpam-491	252	4	)	)	PUNCT
ejpam-491	252	5	.	.	PUNCT
ejpam-491	253	1	t.	t.	PROPN
ejpam-491	253	2	noiri	noiri	PROPN
ejpam-491	253	3	and	and	CCONJ
ejpam-491	253	4	v.	v.	ADP
ejpam-491	253	5	popa	popa	NOUN
ejpam-491	253	6	/	/	SYM
ejpam-491	253	7	eur	eur	PROPN
ejpam-491	253	8	.	.	PUNCT
ejpam-491	254	1	j.	j.	PROPN
ejpam-491	254	2	pure	pure	PROPN
ejpam-491	254	3	appl	appl	PROPN
ejpam-491	254	4	.	.	PROPN
ejpam-491	254	5	math	math	PROPN
ejpam-491	254	6	,	,	PUNCT
ejpam-491	254	7	2	2	NUM
ejpam-491	254	8	(	(	PUNCT
ejpam-491	254	9	2009	2009	NUM
ejpam-491	254	10	)	)	PUNCT
ejpam-491	254	11	,	,	PUNCT
ejpam-491	254	12	(	(	PUNCT
ejpam-491	254	13	473	473	NUM
ejpam-491	254	14	-	-	NUM
ejpam-491	254	15	493	493	NUM
ejpam-491	254	16	)	)	PUNCT
ejpam-491	254	17	482	482	NUM
ejpam-491	254	18	definition	definition	NOUN
ejpam-491	254	19	17	17	NUM
ejpam-491	254	20	.	.	PUNCT
ejpam-491	255	1	let	let	AUX
ejpam-491	255	2	(	(	PUNCT
ejpam-491	255	3	x	x	X
ejpam-491	255	4	,	,	PUNCT
ejpam-491	255	5	τ	τ	X
ejpam-491	255	6	)	)	PUNCT
ejpam-491	255	7	be	be	VERB
ejpam-491	255	8	a	a	DET
ejpam-491	255	9	topological	topological	ADJ
ejpam-491	255	10	space	space	NOUN
ejpam-491	255	11	and	and	CCONJ
ejpam-491	255	12	gmo(x	gmo(x	PROPN
ejpam-491	255	13	)	)	PUNCT
ejpam-491	255	14	a	a	DET
ejpam-491	255	15	gm	gm	NOUN
ejpam-491	255	16	-	-	PUNCT
ejpam-491	255	17	structure	structure	NOUN
ejpam-491	255	18	on	on	ADP
ejpam-491	255	19	x	x	X
ejpam-491	255	20	.	.	PUNCT
ejpam-491	256	1	for	for	ADP
ejpam-491	256	2	a	a	DET
ejpam-491	256	3	subset	subset	NOUN
ejpam-491	256	4	a	a	PRON
ejpam-491	256	5	of	of	ADP
ejpam-491	256	6	x	x	SYM
ejpam-491	256	7	,	,	PUNCT
ejpam-491	256	8	the	the	DET
ejpam-491	256	9	gm	gm	NOUN
ejpam-491	256	10	-	-	PUNCT
ejpam-491	256	11	closure	closure	NOUN
ejpam-491	256	12	of	of	ADP
ejpam-491	256	13	a	a	PRON
ejpam-491	256	14	and	and	CCONJ
ejpam-491	256	15	the	the	DET
ejpam-491	256	16	gm	gm	PROPN
ejpam-491	256	17	-	-	NOUN
ejpam-491	256	18	interior	interior	NOUN
ejpam-491	256	19	of	of	ADP
ejpam-491	256	20	a	a	PRON
ejpam-491	256	21	are	be	AUX
ejpam-491	256	22	defined	define	VERB
ejpam-491	256	23	as	as	SCONJ
ejpam-491	256	24	follows	follow	VERB
ejpam-491	256	25	:	:	PUNCT
ejpam-491	256	26	(	(	PUNCT
ejpam-491	256	27	1	1	X
ejpam-491	256	28	)	)	PUNCT
ejpam-491	256	29	mclg(a	mclg(a	PROPN
ejpam-491	256	30	)	)	PUNCT
ejpam-491	256	31	=	=	PUNCT
ejpam-491	256	32	∩{f	∩{f	NOUN
ejpam-491	256	33	:	:	PUNCT
ejpam-491	256	34	a⊂	a⊂	X
ejpam-491	256	35	f	f	X
ejpam-491	256	36	,	,	PUNCT
ejpam-491	256	37	x	x	PROPN
ejpam-491	256	38	−	−	NOUN
ejpam-491	256	39	f	f	PROPN
ejpam-491	256	40	∈	∈	PROPN
ejpam-491	256	41	gmo(x	gmo(x	PROPN
ejpam-491	256	42	)	)	PUNCT
ejpam-491	256	43	}	}	PUNCT
ejpam-491	256	44	,	,	PUNCT
ejpam-491	256	45	(	(	PUNCT
ejpam-491	256	46	2	2	X
ejpam-491	256	47	)	)	PUNCT
ejpam-491	256	48	mintg(a	mintg(a	NOUN
ejpam-491	256	49	)	)	PUNCT
ejpam-491	256	50	=	=	SYM
ejpam-491	257	1	∪{u	∪{u	VERB
ejpam-491	257	2	:	:	PUNCT
ejpam-491	257	3	u	u	X
ejpam-491	257	4	⊂	⊂	PROPN
ejpam-491	257	5	a	a	X
ejpam-491	257	6	,	,	PUNCT
ejpam-491	257	7	u	u	PROPN
ejpam-491	257	8	∈	∈	PROPN
ejpam-491	257	9	gmo(x	gmo(x	PROPN
ejpam-491	257	10	)	)	PUNCT
ejpam-491	257	11	}	}	PUNCT
ejpam-491	257	12	.	.	PUNCT
ejpam-491	258	1	by	by	ADP
ejpam-491	258	2	definition	definition	NOUN
ejpam-491	258	3	16	16	NUM
ejpam-491	258	4	and	and	CCONJ
ejpam-491	258	5	theorem	theorem	VERB
ejpam-491	258	6	3	3	NUM
ejpam-491	258	7	,	,	PUNCT
ejpam-491	258	8	we	we	PRON
ejpam-491	258	9	obtain	obtain	VERB
ejpam-491	258	10	the	the	DET
ejpam-491	258	11	following	following	ADJ
ejpam-491	258	12	theorem	theorem	NOUN
ejpam-491	258	13	and	and	CCONJ
ejpam-491	258	14	corollary	corollary	ADJ
ejpam-491	258	15	.	.	PUNCT
ejpam-491	259	1	theorem	theorem	ADJ
ejpam-491	259	2	4	4	NUM
ejpam-491	259	3	.	.	X
ejpam-491	260	1	for	for	ADP
ejpam-491	260	2	a	a	DET
ejpam-491	260	3	function	function	NOUN
ejpam-491	260	4	f	f	NOUN
ejpam-491	260	5	:	:	PUNCT
ejpam-491	260	6	(	(	PUNCT
ejpam-491	260	7	x	x	X
ejpam-491	260	8	,	,	PUNCT
ejpam-491	260	9	τ)→	τ)→	PROPN
ejpam-491	260	10	(	(	PUNCT
ejpam-491	260	11	y	y	PROPN
ejpam-491	260	12	,	,	PUNCT
ejpam-491	260	13	σ	σ	PROPN
ejpam-491	260	14	)	)	PUNCT
ejpam-491	260	15	,	,	PUNCT
ejpam-491	260	16	the	the	DET
ejpam-491	260	17	following	follow	VERB
ejpam-491	260	18	properties	property	NOUN
ejpam-491	260	19	are	be	AUX
ejpam-491	260	20	equivalent	equivalent	ADJ
ejpam-491	260	21	:	:	PUNCT
ejpam-491	260	22	(	(	PUNCT
ejpam-491	260	23	1	1	X
ejpam-491	260	24	)	)	PUNCT
ejpam-491	260	25	f	f	PROPN
ejpam-491	260	26	is	be	AUX
ejpam-491	260	27	gm	gm	NOUN
ejpam-491	260	28	-	-	PUNCT
ejpam-491	260	29	continuous	continuous	ADJ
ejpam-491	260	30	;	;	PUNCT
ejpam-491	260	31	(	(	PUNCT
ejpam-491	260	32	2	2	X
ejpam-491	260	33	)	)	PUNCT
ejpam-491	260	34	f	f	PROPN
ejpam-491	260	35	−1(v	−1(v	NOUN
ejpam-491	260	36	)	)	PUNCT
ejpam-491	261	1	=	=	NOUN
ejpam-491	261	2	mintg	mintg	NOUN
ejpam-491	261	3	(	(	PUNCT
ejpam-491	261	4	f	f	PROPN
ejpam-491	261	5	−1(v	−1(v	PROPN
ejpam-491	261	6	)	)	PUNCT
ejpam-491	261	7	)	)	PUNCT
ejpam-491	262	1	for	for	ADP
ejpam-491	262	2	every	every	DET
ejpam-491	262	3	gm	gm	PROPN
ejpam-491	262	4	-	-	PUNCT
ejpam-491	262	5	open	open	NOUN
ejpam-491	262	6	set	set	NOUN
ejpam-491	262	7	v	v	NOUN
ejpam-491	262	8	of	of	ADP
ejpam-491	262	9	y	y	PROPN
ejpam-491	262	10	;	;	PUNCT
ejpam-491	262	11	(	(	PUNCT
ejpam-491	262	12	3	3	X
ejpam-491	262	13	)	)	PUNCT
ejpam-491	262	14	mclg	mclg	NOUN
ejpam-491	262	15	(	(	PUNCT
ejpam-491	262	16	f	f	PROPN
ejpam-491	262	17	−1(f	−1(f	PROPN
ejpam-491	262	18	)	)	PUNCT
ejpam-491	262	19	)	)	PUNCT
ejpam-491	263	1	=	=	PUNCT
ejpam-491	263	2	f	f	X
ejpam-491	263	3	−1(f	−1(f	PROPN
ejpam-491	263	4	)	)	PUNCT
ejpam-491	263	5	for	for	ADP
ejpam-491	263	6	every	every	DET
ejpam-491	263	7	gm	gm	PROPN
ejpam-491	263	8	-	-	PUNCT
ejpam-491	263	9	closed	close	VERB
ejpam-491	263	10	set	set	ADJ
ejpam-491	263	11	f	f	PROPN
ejpam-491	263	12	of	of	ADP
ejpam-491	263	13	y	y	PROPN
ejpam-491	263	14	;	;	PUNCT
ejpam-491	263	15	(	(	PUNCT
ejpam-491	263	16	4	4	X
ejpam-491	263	17	)	)	PUNCT
ejpam-491	263	18	mclg	mclg	NOUN
ejpam-491	263	19	(	(	PUNCT
ejpam-491	263	20	f	f	PROPN
ejpam-491	263	21	−1(b	−1(b	NOUN
ejpam-491	263	22	)	)	PUNCT
ejpam-491	263	23	)	)	PUNCT
ejpam-491	264	1	⊂	⊂	PROPN
ejpam-491	264	2	f	f	X
ejpam-491	264	3	−1(mclg(b	−1(mclg(b	NUM
ejpam-491	264	4	)	)	PUNCT
ejpam-491	264	5	)	)	PUNCT
ejpam-491	264	6	for	for	ADP
ejpam-491	264	7	every	every	DET
ejpam-491	264	8	subset	subset	NOUN
ejpam-491	264	9	b	b	PROPN
ejpam-491	264	10	of	of	ADP
ejpam-491	264	11	y	y	PROPN
ejpam-491	264	12	;	;	PUNCT
ejpam-491	264	13	(	(	PUNCT
ejpam-491	264	14	5	5	X
ejpam-491	264	15	)	)	PUNCT
ejpam-491	264	16	f	f	NOUN
ejpam-491	264	17	(	(	PUNCT
ejpam-491	264	18	mclg(a	mclg(a	PROPN
ejpam-491	264	19	)	)	PUNCT
ejpam-491	264	20	)	)	PUNCT
ejpam-491	265	1	⊂mclg	⊂mclg	PROPN
ejpam-491	265	2	(	(	PUNCT
ejpam-491	265	3	f	f	X
ejpam-491	265	4	(	(	PUNCT
ejpam-491	265	5	a	a	NOUN
ejpam-491	265	6	)	)	PUNCT
ejpam-491	265	7	)	)	PUNCT
ejpam-491	265	8	for	for	ADP
ejpam-491	265	9	every	every	DET
ejpam-491	265	10	subset	subset	NOUN
ejpam-491	265	11	a	a	PRON
ejpam-491	265	12	of	of	ADP
ejpam-491	265	13	x	x	PRON
ejpam-491	265	14	;	;	PUNCT
ejpam-491	265	15	(	(	PUNCT
ejpam-491	265	16	6	6	NUM
ejpam-491	265	17	)	)	PUNCT
ejpam-491	265	18	f	f	NOUN
ejpam-491	265	19	−1(mintg(b	−1(mintg(b	NUM
ejpam-491	265	20	)	)	PUNCT
ejpam-491	265	21	)	)	PUNCT
ejpam-491	265	22	⊂mintg	⊂mintg	NOUN
ejpam-491	265	23	(	(	PUNCT
ejpam-491	265	24	f	f	PROPN
ejpam-491	265	25	−1(b	−1(b	NOUN
ejpam-491	265	26	)	)	PUNCT
ejpam-491	265	27	)	)	PUNCT
ejpam-491	265	28	for	for	ADP
ejpam-491	265	29	every	every	DET
ejpam-491	265	30	subset	subset	NOUN
ejpam-491	265	31	b	b	PROPN
ejpam-491	265	32	of	of	ADP
ejpam-491	265	33	y.	y.	PROPN
ejpam-491	265	34	corollary	corollary	PROPN
ejpam-491	265	35	2	2	NUM
ejpam-491	265	36	.	.	PUNCT
ejpam-491	265	37	for	for	ADP
ejpam-491	265	38	a	a	DET
ejpam-491	265	39	function	function	NOUN
ejpam-491	265	40	f	f	NOUN
ejpam-491	265	41	:	:	PUNCT
ejpam-491	265	42	(	(	PUNCT
ejpam-491	265	43	x	x	X
ejpam-491	265	44	,	,	PUNCT
ejpam-491	265	45	τ	τ	PROPN
ejpam-491	265	46	)	)	PUNCT
ejpam-491	265	47	→	→	SYM
ejpam-491	265	48	(	(	PUNCT
ejpam-491	265	49	y	y	PROPN
ejpam-491	265	50	,	,	PUNCT
ejpam-491	265	51	σ	σ	PROPN
ejpam-491	265	52	)	)	PUNCT
ejpam-491	265	53	,	,	PUNCT
ejpam-491	265	54	where	where	SCONJ
ejpam-491	265	55	gmo(x	gmo(x	PROPN
ejpam-491	265	56	)	)	PUNCT
ejpam-491	265	57	has	have	VERB
ejpam-491	265	58	property	property	NOUN
ejpam-491	265	59	b	b	PROPN
ejpam-491	265	60	,	,	PUNCT
ejpam-491	265	61	the	the	DET
ejpam-491	265	62	following	follow	VERB
ejpam-491	265	63	properties	property	NOUN
ejpam-491	265	64	are	be	AUX
ejpam-491	265	65	equivalent	equivalent	ADJ
ejpam-491	265	66	:	:	PUNCT
ejpam-491	265	67	(	(	PUNCT
ejpam-491	265	68	1	1	X
ejpam-491	265	69	)	)	PUNCT
ejpam-491	265	70	f	f	PROPN
ejpam-491	265	71	is	be	AUX
ejpam-491	265	72	gm	gm	NOUN
ejpam-491	265	73	-	-	PUNCT
ejpam-491	265	74	continuous	continuous	ADJ
ejpam-491	265	75	;	;	PUNCT
ejpam-491	265	76	(	(	PUNCT
ejpam-491	265	77	2	2	X
ejpam-491	265	78	)	)	PUNCT
ejpam-491	265	79	f	f	PROPN
ejpam-491	265	80	−1(v	−1(v	PROPN
ejpam-491	265	81	)	)	PUNCT
ejpam-491	265	82	is	be	AUX
ejpam-491	265	83	gm	gm	NOUN
ejpam-491	265	84	-	-	PUNCT
ejpam-491	265	85	open	open	ADJ
ejpam-491	265	86	for	for	ADP
ejpam-491	265	87	every	every	DET
ejpam-491	265	88	gm	gm	PROPN
ejpam-491	265	89	-	-	PUNCT
ejpam-491	265	90	open	open	NOUN
ejpam-491	265	91	set	set	NOUN
ejpam-491	265	92	v	v	NOUN
ejpam-491	265	93	of	of	ADP
ejpam-491	265	94	y	y	PROPN
ejpam-491	265	95	;	;	PUNCT
ejpam-491	265	96	(	(	PUNCT
ejpam-491	265	97	3	3	X
ejpam-491	265	98	)	)	PUNCT
ejpam-491	265	99	f	f	PROPN
ejpam-491	265	100	−1(f	−1(f	PROPN
ejpam-491	265	101	)	)	PUNCT
ejpam-491	265	102	is	be	AUX
ejpam-491	265	103	gm	gm	PROPN
ejpam-491	265	104	-	-	PUNCT
ejpam-491	265	105	closed	closed	ADJ
ejpam-491	265	106	for	for	SCONJ
ejpam-491	265	107	every	every	DET
ejpam-491	265	108	gm	gm	PROPN
ejpam-491	265	109	-	-	PUNCT
ejpam-491	265	110	closed	close	VERB
ejpam-491	265	111	set	set	ADJ
ejpam-491	265	112	f	f	PROPN
ejpam-491	265	113	of	of	ADP
ejpam-491	265	114	y.	y.	PROPN
ejpam-491	265	115	let	let	VERB
ejpam-491	265	116	(	(	PUNCT
ejpam-491	265	117	x	x	X
ejpam-491	265	118	,	,	PUNCT
ejpam-491	265	119	τ	τ	X
ejpam-491	265	120	)	)	PUNCT
ejpam-491	265	121	be	be	VERB
ejpam-491	265	122	a	a	DET
ejpam-491	265	123	topological	topological	ADJ
ejpam-491	265	124	space	space	NOUN
ejpam-491	265	125	and	and	CCONJ
ejpam-491	265	126	gmo(x	gmo(x	PROPN
ejpam-491	265	127	)	)	PUNCT
ejpam-491	265	128	a	a	DET
ejpam-491	265	129	gm	gm	NOUN
ejpam-491	265	130	-	-	PUNCT
ejpam-491	265	131	structure	structure	NOUN
ejpam-491	265	132	on	on	ADP
ejpam-491	265	133	x	x	X
ejpam-491	265	134	.	.	PUNCT
ejpam-491	266	1	for	for	ADP
ejpam-491	266	2	a	a	DET
ejpam-491	266	3	function	function	NOUN
ejpam-491	266	4	f	f	NOUN
ejpam-491	266	5	:	:	PUNCT
ejpam-491	266	6	(	(	PUNCT
ejpam-491	266	7	x	x	X
ejpam-491	266	8	,	,	PUNCT
ejpam-491	266	9	τ	τ	PROPN
ejpam-491	266	10	)	)	PUNCT
ejpam-491	266	11	→	→	SYM
ejpam-491	266	12	(	(	PUNCT
ejpam-491	266	13	y	y	PROPN
ejpam-491	266	14	,	,	PUNCT
ejpam-491	266	15	σ	σ	PROPN
ejpam-491	266	16	)	)	PUNCT
ejpam-491	266	17	,	,	PUNCT
ejpam-491	266	18	we	we	PRON
ejpam-491	266	19	denote	denote	VERB
ejpam-491	266	20	by	by	ADP
ejpam-491	266	21	dgm	dgm	PROPN
ejpam-491	266	22	(	(	PUNCT
ejpam-491	266	23	f	f	PROPN
ejpam-491	266	24	)	)	PUNCT
ejpam-491	266	25	the	the	DET
ejpam-491	266	26	set	set	NOUN
ejpam-491	266	27	of	of	ADP
ejpam-491	266	28	all	all	DET
ejpam-491	266	29	points	point	NOUN
ejpam-491	266	30	of	of	ADP
ejpam-491	266	31	x	x	PUNCT
ejpam-491	266	32	at	at	ADP
ejpam-491	266	33	which	which	PRON
ejpam-491	266	34	the	the	DET
ejpam-491	266	35	function	function	NOUN
ejpam-491	266	36	f	f	PROPN
ejpam-491	266	37	is	be	AUX
ejpam-491	266	38	not	not	PART
ejpam-491	266	39	gm	gm	PROPN
ejpam-491	266	40	-continuous	-continuous	ADJ
ejpam-491	266	41	.	.	PUNCT
ejpam-491	267	1	then	then	ADV
ejpam-491	267	2	by	by	ADP
ejpam-491	267	3	definition	definition	NOUN
ejpam-491	267	4	16	16	NUM
ejpam-491	267	5	and	and	CCONJ
ejpam-491	267	6	theorem	theorem	VERB
ejpam-491	267	7	4	4	NUM
ejpam-491	267	8	,	,	PUNCT
ejpam-491	267	9	we	we	PRON
ejpam-491	267	10	obtain	obtain	VERB
ejpam-491	267	11	the	the	DET
ejpam-491	267	12	following	follow	VERB
ejpam-491	267	13	theorem	theorem	VERB
ejpam-491	267	14	.	.	PUNCT
ejpam-491	267	15	theorem	theorem	NOUN
ejpam-491	267	16	5	5	NUM
ejpam-491	267	17	.	.	X
ejpam-491	267	18	for	for	ADP
ejpam-491	267	19	a	a	DET
ejpam-491	267	20	function	function	NOUN
ejpam-491	267	21	f	f	NOUN
ejpam-491	267	22	:	:	PUNCT
ejpam-491	267	23	(	(	PUNCT
ejpam-491	267	24	x	x	X
ejpam-491	267	25	,	,	PUNCT
ejpam-491	267	26	τ)→	τ)→	PROPN
ejpam-491	267	27	(	(	PUNCT
ejpam-491	267	28	y	y	PROPN
ejpam-491	267	29	,	,	PUNCT
ejpam-491	267	30	σ	σ	PROPN
ejpam-491	267	31	)	)	PUNCT
ejpam-491	267	32	,	,	PUNCT
ejpam-491	267	33	the	the	DET
ejpam-491	267	34	following	follow	VERB
ejpam-491	267	35	properties	property	NOUN
ejpam-491	267	36	hold	hold	VERB
ejpam-491	267	37	:	:	PUNCT
ejpam-491	268	1	dgm	dgm	PROPN
ejpam-491	268	2	(	(	PUNCT
ejpam-491	268	3	f	f	PROPN
ejpam-491	268	4	)	)	PUNCT
ejpam-491	268	5	=	=	SYM
ejpam-491	268	6	⋃	⋃	NOUN
ejpam-491	268	7	g∈gmo(y	g∈gmo(y	NOUN
ejpam-491	268	8	)	)	PUNCT
ejpam-491	268	9	{	{	PUNCT
ejpam-491	268	10	f	f	PROPN
ejpam-491	268	11	−1(g)−mintg	−1(g)−mintg	PROPN
ejpam-491	268	12	(	(	PUNCT
ejpam-491	268	13	f	f	PROPN
ejpam-491	268	14	−1(g	−1(g	NOUN
ejpam-491	268	15	)	)	PUNCT
ejpam-491	268	16	)	)	PUNCT
ejpam-491	268	17	}	}	PUNCT
ejpam-491	269	1	=	=	SYM
ejpam-491	269	2	⋃	⋃	NOUN
ejpam-491	269	3	b∈p	b∈p	NOUN
ejpam-491	269	4	(	(	PUNCT
ejpam-491	269	5	y	y	PROPN
ejpam-491	269	6	)	)	PUNCT
ejpam-491	269	7	{	{	PUNCT
ejpam-491	269	8	f	f	PROPN
ejpam-491	269	9	−1(mintg(b))−mintg	−1(mintg(b))−mintg	PROPN
ejpam-491	269	10	(	(	PUNCT
ejpam-491	269	11	f	f	PROPN
ejpam-491	269	12	−1(b	−1(b	NOUN
ejpam-491	269	13	)	)	PUNCT
ejpam-491	269	14	)	)	PUNCT
ejpam-491	269	15	}	}	PUNCT
ejpam-491	270	1	=	=	SYM
ejpam-491	270	2	⋃	⋃	NOUN
ejpam-491	270	3	b∈p	b∈p	NOUN
ejpam-491	270	4	(	(	PUNCT
ejpam-491	270	5	y	y	PROPN
ejpam-491	270	6	)	)	PUNCT
ejpam-491	270	7	{	{	PUNCT
ejpam-491	270	8	mclg	mclg	PROPN
ejpam-491	270	9	(	(	PUNCT
ejpam-491	270	10	f	f	PROPN
ejpam-491	270	11	−1(b))−	−1(b))−	X
ejpam-491	270	12	f	f	PROPN
ejpam-491	270	13	−1(mclg(b	−1(mclg(b	NUM
ejpam-491	270	14	)	)	PUNCT
ejpam-491	270	15	)	)	PUNCT
ejpam-491	270	16	}	}	PUNCT
ejpam-491	270	17	t.	t.	NOUN
ejpam-491	270	18	noiri	noiri	PROPN
ejpam-491	270	19	and	and	CCONJ
ejpam-491	270	20	v.	v.	ADP
ejpam-491	270	21	popa	popa	NOUN
ejpam-491	270	22	/	/	SYM
ejpam-491	270	23	eur	eur	PROPN
ejpam-491	270	24	.	.	PUNCT
ejpam-491	271	1	j.	j.	PROPN
ejpam-491	271	2	pure	pure	PROPN
ejpam-491	271	3	appl	appl	PROPN
ejpam-491	271	4	.	.	PROPN
ejpam-491	271	5	math	math	PROPN
ejpam-491	271	6	,	,	PUNCT
ejpam-491	271	7	2	2	NUM
ejpam-491	271	8	(	(	PUNCT
ejpam-491	271	9	2009	2009	NUM
ejpam-491	271	10	)	)	PUNCT
ejpam-491	271	11	,	,	PUNCT
ejpam-491	271	12	(	(	PUNCT
ejpam-491	271	13	473	473	NUM
ejpam-491	271	14	-	-	NUM
ejpam-491	271	15	493	493	NUM
ejpam-491	271	16	)	)	PUNCT
ejpam-491	271	17	483	483	NUM
ejpam-491	271	18	=	=	SYM
ejpam-491	272	1	⋃	⋃	NOUN
ejpam-491	272	2	a∈p	a∈p	NOUN
ejpam-491	272	3	(	(	PUNCT
ejpam-491	272	4	x	x	X
ejpam-491	272	5	)	)	PUNCT
ejpam-491	272	6	{	{	PUNCT
ejpam-491	272	7	mclg(a)−	mclg(a)−	PROPN
ejpam-491	272	8	f	f	X
ejpam-491	272	9	−1(mclg	−1(mclg	X
ejpam-491	272	10	(	(	PUNCT
ejpam-491	272	11	f	f	X
ejpam-491	272	12	(	(	PUNCT
ejpam-491	272	13	a	a	NOUN
ejpam-491	272	14	)	)	PUNCT
ejpam-491	272	15	)	)	PUNCT
ejpam-491	272	16	)	)	PUNCT
ejpam-491	272	17	}	}	PUNCT
ejpam-491	273	1	=	=	PUNCT
ejpam-491	273	2	⋃	⋃	NOUN
ejpam-491	273	3	k∈f	k∈f	NOUN
ejpam-491	273	4	g	g	PROPN
ejpam-491	273	5	{	{	PUNCT
ejpam-491	273	6	mclg	mclg	PROPN
ejpam-491	273	7	(	(	PUNCT
ejpam-491	273	8	f	f	PROPN
ejpam-491	273	9	−1(k))−	−1(k))−	NOUN
ejpam-491	273	10	f	f	PROPN
ejpam-491	273	11	−1(k	−1(k	NOUN
ejpam-491	273	12	)	)	PUNCT
ejpam-491	273	13	}	}	PUNCT
ejpam-491	273	14	,	,	PUNCT
ejpam-491	273	15	where	where	SCONJ
ejpam-491	273	16	f	f	PROPN
ejpam-491	273	17	g	g	PROPN
ejpam-491	273	18	is	be	AUX
ejpam-491	273	19	the	the	DET
ejpam-491	273	20	family	family	NOUN
ejpam-491	273	21	of	of	ADP
ejpam-491	273	22	gm	gm	PROPN
ejpam-491	273	23	-	-	PUNCT
ejpam-491	273	24	closed	close	VERB
ejpam-491	273	25	sets	set	NOUN
ejpam-491	273	26	of	of	ADP
ejpam-491	273	27	y	y	PROPN
ejpam-491	273	28	.	.	PUNCT
ejpam-491	274	1	definition	definition	NOUN
ejpam-491	274	2	18	18	NUM
ejpam-491	274	3	.	.	PUNCT
ejpam-491	275	1	let	let	AUX
ejpam-491	275	2	(	(	PUNCT
ejpam-491	275	3	x	x	X
ejpam-491	275	4	,	,	PUNCT
ejpam-491	275	5	mx	mx	PROPN
ejpam-491	275	6	)	)	PUNCT
ejpam-491	275	7	be	be	AUX
ejpam-491	275	8	an	an	DET
ejpam-491	275	9	m	m	NOUN
ejpam-491	275	10	-	-	NOUN
ejpam-491	275	11	space	space	NOUN
ejpam-491	275	12	and	and	CCONJ
ejpam-491	275	13	a	a	DET
ejpam-491	275	14	a	a	DET
ejpam-491	275	15	subset	subset	NOUN
ejpam-491	275	16	of	of	ADP
ejpam-491	275	17	x	x	X
ejpam-491	275	18	.	.	PUNCT
ejpam-491	276	1	the	the	DET
ejpam-491	276	2	mx	mx	PROPN
ejpam-491	276	3	-frontier	-frontier	NOUN
ejpam-491	276	4	of	of	ADP
ejpam-491	276	5	a	a	DET
ejpam-491	276	6	,	,	PUNCT
ejpam-491	276	7	mfr(a	mfr(a	PROPN
ejpam-491	276	8	)	)	PUNCT
ejpam-491	276	9	,	,	PUNCT
ejpam-491	276	10	[	[	X
ejpam-491	276	11	30	30	NUM
ejpam-491	276	12	]	]	PUNCT
ejpam-491	276	13	is	be	AUX
ejpam-491	276	14	defined	define	VERB
ejpam-491	276	15	by	by	ADP
ejpam-491	276	16	mfr(a	mfr(a	PROPN
ejpam-491	276	17	)	)	PUNCT
ejpam-491	277	1	=	=	SYM
ejpam-491	277	2	mcl(a)∩mcl(x	mcl(a)∩mcl(x	PROPN
ejpam-491	277	3	−	−	PROPN
ejpam-491	277	4	a	a	NOUN
ejpam-491	277	5	)	)	PUNCT
ejpam-491	277	6	=	=	NOUN
ejpam-491	277	7	mcl(a)−mint(a	mcl(a)−mint(a	NOUN
ejpam-491	277	8	)	)	PUNCT
ejpam-491	277	9	.	.	PUNCT
ejpam-491	278	1	if	if	SCONJ
ejpam-491	278	2	(	(	PUNCT
ejpam-491	278	3	x	x	X
ejpam-491	278	4	,	,	PUNCT
ejpam-491	278	5	τ	τ	X
ejpam-491	278	6	)	)	PUNCT
ejpam-491	278	7	is	be	AUX
ejpam-491	278	8	a	a	DET
ejpam-491	278	9	topological	topological	ADJ
ejpam-491	278	10	space	space	NOUN
ejpam-491	278	11	and	and	CCONJ
ejpam-491	278	12	gmo(x	gmo(x	PROPN
ejpam-491	278	13	)	)	PUNCT
ejpam-491	278	14	is	be	AUX
ejpam-491	278	15	a	a	DET
ejpam-491	278	16	gm	gm	NOUN
ejpam-491	278	17	-	-	PUNCT
ejpam-491	278	18	structure	structure	NOUN
ejpam-491	278	19	on	on	ADP
ejpam-491	278	20	x	x	X
ejpam-491	278	21	,	,	PUNCT
ejpam-491	278	22	then	then	ADV
ejpam-491	278	23	gmfr(a	gmfr(a	PROPN
ejpam-491	278	24	)	)	PUNCT
ejpam-491	278	25	=	=	PUNCT
ejpam-491	278	26	mclg(a)∩mclg(x	mclg(a)∩mclg(x	NOUN
ejpam-491	278	27	−	−	PROPN
ejpam-491	278	28	a	a	NOUN
ejpam-491	278	29	)	)	PUNCT
ejpam-491	278	30	=	=	NOUN
ejpam-491	278	31	mclg(a)−mintg(a	mclg(a)−mintg(a	PROPN
ejpam-491	278	32	)	)	PUNCT
ejpam-491	278	33	.	.	PUNCT
ejpam-491	279	1	theorem	theorem	VERB
ejpam-491	279	2	6	6	NUM
ejpam-491	279	3	.	.	PUNCT
ejpam-491	280	1	the	the	DET
ejpam-491	280	2	set	set	NOUN
ejpam-491	280	3	of	of	ADP
ejpam-491	280	4	all	all	DET
ejpam-491	280	5	points	point	NOUN
ejpam-491	280	6	of	of	ADP
ejpam-491	280	7	x	x	PUNCT
ejpam-491	280	8	at	at	ADP
ejpam-491	280	9	which	which	PRON
ejpam-491	280	10	a	a	DET
ejpam-491	280	11	function	function	NOUN
ejpam-491	280	12	f	f	NOUN
ejpam-491	280	13	:	:	PUNCT
ejpam-491	280	14	(	(	PUNCT
ejpam-491	280	15	x	x	X
ejpam-491	280	16	,	,	PUNCT
ejpam-491	280	17	mx	mx	PROPN
ejpam-491	280	18	)	)	PUNCT
ejpam-491	280	19	→	→	SYM
ejpam-491	280	20	(	(	PUNCT
ejpam-491	280	21	y	y	NOUN
ejpam-491	280	22	,	,	PUNCT
ejpam-491	280	23	my	my	INTJ
ejpam-491	280	24	)	)	PUNCT
ejpam-491	280	25	is	be	AUX
ejpam-491	280	26	not	not	PART
ejpam-491	280	27	m	m	ADJ
ejpam-491	280	28	-	-	ADJ
ejpam-491	280	29	continuous	continuous	ADJ
ejpam-491	280	30	is	be	AUX
ejpam-491	280	31	identical	identical	ADJ
ejpam-491	280	32	with	with	ADP
ejpam-491	280	33	the	the	DET
ejpam-491	280	34	union	union	NOUN
ejpam-491	280	35	of	of	ADP
ejpam-491	280	36	the	the	DET
ejpam-491	280	37	m	m	NOUN
ejpam-491	280	38	-	-	NOUN
ejpam-491	280	39	frontiers	frontier	NOUN
ejpam-491	280	40	of	of	ADP
ejpam-491	280	41	the	the	DET
ejpam-491	280	42	inverse	inverse	NOUN
ejpam-491	280	43	images	image	NOUN
ejpam-491	280	44	of	of	ADP
ejpam-491	280	45	my	my	PRON
ejpam-491	280	46	-open	-open	ADJ
ejpam-491	280	47	sets	set	NOUN
ejpam-491	280	48	containing	contain	VERB
ejpam-491	280	49	f(x	f(x	PROPN
ejpam-491	280	50	)	)	PUNCT
ejpam-491	280	51	.	.	PUNCT
ejpam-491	281	1	proof	proof	NOUN
ejpam-491	281	2	.	.	PUNCT
ejpam-491	282	1	suppose	suppose	VERB
ejpam-491	282	2	that	that	SCONJ
ejpam-491	282	3	f	f	PROPN
ejpam-491	282	4	is	be	AUX
ejpam-491	282	5	not	not	PART
ejpam-491	282	6	m	m	PRON
ejpam-491	282	7	-continuous	-continuous	ADJ
ejpam-491	282	8	at	at	ADP
ejpam-491	282	9	x	x	X
ejpam-491	282	10	∈	∈	PROPN
ejpam-491	282	11	x	x	X
ejpam-491	282	12	.	.	PUNCT
ejpam-491	283	1	there	there	PRON
ejpam-491	283	2	exists	exist	VERB
ejpam-491	283	3	an	an	DET
ejpam-491	283	4	my	my	PRON
ejpam-491	283	5	-open	-open	NOUN
ejpam-491	283	6	set	set	ADJ
ejpam-491	283	7	v	v	NOUN
ejpam-491	283	8	of	of	ADP
ejpam-491	283	9	y	y	PROPN
ejpam-491	283	10	containing	contain	VERB
ejpam-491	283	11	f	f	PROPN
ejpam-491	283	12	(	(	PUNCT
ejpam-491	283	13	x	x	X
ejpam-491	283	14	)	)	PUNCT
ejpam-491	283	15	such	such	ADJ
ejpam-491	283	16	that	that	SCONJ
ejpam-491	283	17	u	u	PROPN
ejpam-491	283	18	∩	∩	NOUN
ejpam-491	283	19	(	(	PUNCT
ejpam-491	283	20	x	x	SYM
ejpam-491	283	21	−	−	PROPN
ejpam-491	283	22	f	f	PROPN
ejpam-491	283	23	−1(v	−1(v	PROPN
ejpam-491	283	24	)	)	PUNCT
ejpam-491	283	25	)	)	PUNCT
ejpam-491	284	1	6=	6=	NUM
ejpam-491	284	2	;	;	PUNCT
ejpam-491	284	3	for	for	ADP
ejpam-491	284	4	every	every	DET
ejpam-491	284	5	mx	mx	PROPN
ejpam-491	284	6	-open	-open	PROPN
ejpam-491	284	7	set	set	NOUN
ejpam-491	284	8	u	u	NOUN
ejpam-491	284	9	containing	contain	VERB
ejpam-491	284	10	x	x	X
ejpam-491	284	11	.	.	PUNCT
ejpam-491	285	1	by	by	ADP
ejpam-491	285	2	lemma	lemma	PROPN
ejpam-491	285	3	2	2	NUM
ejpam-491	285	4	,	,	PUNCT
ejpam-491	285	5	we	we	PRON
ejpam-491	285	6	have	have	VERB
ejpam-491	285	7	x	x	PART
ejpam-491	285	8	∈	∈	PROPN
ejpam-491	285	9	mcl(x	mcl(x	PROPN
ejpam-491	285	10	−	−	PROPN
ejpam-491	285	11	f	f	PROPN
ejpam-491	285	12	−1(v	−1(v	PROPN
ejpam-491	285	13	)	)	PUNCT
ejpam-491	285	14	)	)	PUNCT
ejpam-491	285	15	.	.	PUNCT
ejpam-491	286	1	on	on	ADP
ejpam-491	286	2	the	the	DET
ejpam-491	286	3	other	other	ADJ
ejpam-491	286	4	hand	hand	NOUN
ejpam-491	286	5	,	,	PUNCT
ejpam-491	286	6	we	we	PRON
ejpam-491	286	7	have	have	VERB
ejpam-491	286	8	x	x	X
ejpam-491	286	9	∈	∈	PROPN
ejpam-491	286	10	f	f	PROPN
ejpam-491	286	11	−1(v	−1(v	PROPN
ejpam-491	286	12	)	)	PUNCT
ejpam-491	286	13	and	and	CCONJ
ejpam-491	286	14	hence	hence	ADV
ejpam-491	286	15	x	x	X
ejpam-491	286	16	∈mfr	∈mfr	PROPN
ejpam-491	286	17	(	(	PUNCT
ejpam-491	286	18	f	f	PROPN
ejpam-491	286	19	−1(v	−1(v	PROPN
ejpam-491	286	20	)	)	PUNCT
ejpam-491	286	21	)	)	PUNCT
ejpam-491	286	22	.	.	PUNCT
ejpam-491	287	1	conversely	conversely	ADV
ejpam-491	287	2	,	,	PUNCT
ejpam-491	287	3	suppose	suppose	VERB
ejpam-491	287	4	that	that	SCONJ
ejpam-491	287	5	f	f	PROPN
ejpam-491	287	6	is	be	AUX
ejpam-491	287	7	m	m	PRON
ejpam-491	287	8	-continuous	-continuous	ADJ
ejpam-491	287	9	at	at	ADP
ejpam-491	287	10	x	x	X
ejpam-491	287	11	∈	∈	PROPN
ejpam-491	287	12	x	x	X
ejpam-491	287	13	.	.	PUNCT
ejpam-491	288	1	then	then	ADV
ejpam-491	288	2	,	,	PUNCT
ejpam-491	288	3	for	for	ADP
ejpam-491	288	4	any	any	DET
ejpam-491	288	5	my	my	PRON
ejpam-491	288	6	-open	-open	NOUN
ejpam-491	288	7	set	set	ADJ
ejpam-491	288	8	v	v	NOUN
ejpam-491	288	9	of	of	ADP
ejpam-491	288	10	y	y	PROPN
ejpam-491	288	11	containing	contain	VERB
ejpam-491	288	12	f	f	PROPN
ejpam-491	288	13	(	(	PUNCT
ejpam-491	288	14	x	x	NOUN
ejpam-491	288	15	)	)	PUNCT
ejpam-491	288	16	,	,	PUNCT
ejpam-491	288	17	there	there	PRON
ejpam-491	288	18	exists	exist	VERB
ejpam-491	288	19	u	u	PROPN
ejpam-491	288	20	∈	∈	PROPN
ejpam-491	288	21	mx	mx	NOUN
ejpam-491	288	22	containing	contain	VERB
ejpam-491	288	23	x	x	PUNCT
ejpam-491	288	24	such	such	ADJ
ejpam-491	288	25	that	that	SCONJ
ejpam-491	288	26	f	f	PROPN
ejpam-491	288	27	(	(	PUNCT
ejpam-491	288	28	u	u	NOUN
ejpam-491	288	29	)	)	PUNCT
ejpam-491	288	30	⊂	⊂	PROPN
ejpam-491	288	31	v	v	NOUN
ejpam-491	288	32	;	;	PUNCT
ejpam-491	288	33	hence	hence	ADV
ejpam-491	288	34	u	u	X
ejpam-491	288	35	⊂	⊂	PROPN
ejpam-491	288	36	f	f	PROPN
ejpam-491	288	37	−1(v	−1(v	PROPN
ejpam-491	288	38	)	)	PUNCT
ejpam-491	288	39	.	.	PUNCT
ejpam-491	289	1	therefore	therefore	ADV
ejpam-491	289	2	,	,	PUNCT
ejpam-491	289	3	we	we	PRON
ejpam-491	289	4	have	have	VERB
ejpam-491	289	5	x	x	X
ejpam-491	289	6	∈	∈	PROPN
ejpam-491	289	7	u	u	PROPN
ejpam-491	289	8	⊂	⊂	PROPN
ejpam-491	289	9	mint	mint	PROPN
ejpam-491	289	10	(	(	PUNCT
ejpam-491	289	11	f	f	PROPN
ejpam-491	289	12	−1(v	−1(v	PROPN
ejpam-491	289	13	)	)	PUNCT
ejpam-491	289	14	)	)	PUNCT
ejpam-491	289	15	.	.	PUNCT
ejpam-491	290	1	this	this	PRON
ejpam-491	290	2	contradicts	contradict	VERB
ejpam-491	290	3	to	to	ADP
ejpam-491	290	4	the	the	DET
ejpam-491	290	5	fact	fact	NOUN
ejpam-491	290	6	that	that	SCONJ
ejpam-491	290	7	x	x	X
ejpam-491	290	8	∈mfr	∈mfr	PROPN
ejpam-491	290	9	(	(	PUNCT
ejpam-491	290	10	f	f	PROPN
ejpam-491	290	11	−1(v	−1(v	PROPN
ejpam-491	290	12	)	)	PUNCT
ejpam-491	290	13	)	)	PUNCT
ejpam-491	290	14	.	.	PUNCT
ejpam-491	291	1	corollary	corollary	ADJ
ejpam-491	291	2	3	3	X
ejpam-491	291	3	.	.	PUNCT
ejpam-491	292	1	let	let	VERB
ejpam-491	292	2	(	(	PUNCT
ejpam-491	292	3	x	x	X
ejpam-491	292	4	,	,	PUNCT
ejpam-491	292	5	τ	τ	PROPN
ejpam-491	292	6	)	)	PUNCT
ejpam-491	292	7	(	(	PUNCT
ejpam-491	292	8	resp	resp	NOUN
ejpam-491	292	9	.	.	PUNCT
ejpam-491	293	1	(	(	PUNCT
ejpam-491	293	2	y	y	PROPN
ejpam-491	293	3	,	,	PUNCT
ejpam-491	293	4	σ	σ	PROPN
ejpam-491	293	5	)	)	PUNCT
ejpam-491	293	6	)	)	PUNCT
ejpam-491	293	7	be	be	AUX
ejpam-491	293	8	a	a	DET
ejpam-491	293	9	topological	topological	ADJ
ejpam-491	293	10	space	space	NOUN
ejpam-491	293	11	and	and	CCONJ
ejpam-491	293	12	gom(x	gom(x	PROPN
ejpam-491	293	13	)	)	PUNCT
ejpam-491	293	14	(	(	PUNCT
ejpam-491	293	15	resp	resp	NOUN
ejpam-491	293	16	.	.	PUNCT
ejpam-491	294	1	gom(y	gom(y	NOUN
ejpam-491	294	2	)	)	PUNCT
ejpam-491	294	3	)	)	PUNCT
ejpam-491	295	1	a	a	DET
ejpam-491	295	2	gm	gm	NOUN
ejpam-491	295	3	-	-	PUNCT
ejpam-491	295	4	structure	structure	NOUN
ejpam-491	295	5	on	on	ADP
ejpam-491	295	6	x	x	PROPN
ejpam-491	295	7	(	(	PUNCT
ejpam-491	295	8	resp	resp	NOUN
ejpam-491	295	9	.	.	PUNCT
ejpam-491	296	1	y	y	X
ejpam-491	296	2	)	)	PUNCT
ejpam-491	296	3	.	.	PUNCT
ejpam-491	297	1	then	then	ADV
ejpam-491	297	2	,	,	PUNCT
ejpam-491	297	3	the	the	DET
ejpam-491	297	4	set	set	NOUN
ejpam-491	297	5	of	of	ADP
ejpam-491	297	6	all	all	DET
ejpam-491	297	7	points	point	NOUN
ejpam-491	297	8	at	at	ADP
ejpam-491	297	9	x	x	X
ejpam-491	297	10	∈	∈	PROPN
ejpam-491	297	11	x	x	X
ejpam-491	297	12	which	which	PRON
ejpam-491	297	13	a	a	DET
ejpam-491	297	14	function	function	NOUN
ejpam-491	297	15	f	f	NOUN
ejpam-491	297	16	:	:	PUNCT
ejpam-491	297	17	(	(	PUNCT
ejpam-491	297	18	x	x	X
ejpam-491	297	19	,	,	PUNCT
ejpam-491	297	20	τ)→	τ)→	PROPN
ejpam-491	297	21	(	(	PUNCT
ejpam-491	297	22	y	y	PROPN
ejpam-491	297	23	,	,	PUNCT
ejpam-491	297	24	σ	σ	PROPN
ejpam-491	297	25	)	)	PUNCT
ejpam-491	297	26	is	be	AUX
ejpam-491	297	27	not	not	PART
ejpam-491	297	28	gm	gm	NOUN
ejpam-491	297	29	-	-	PUNCT
ejpam-491	297	30	continuous	continuous	ADJ
ejpam-491	297	31	is	be	AUX
ejpam-491	297	32	identical	identical	ADJ
ejpam-491	297	33	with	with	ADP
ejpam-491	297	34	the	the	DET
ejpam-491	297	35	union	union	NOUN
ejpam-491	297	36	of	of	ADP
ejpam-491	297	37	the	the	DET
ejpam-491	297	38	gm	gm	PROPN
ejpam-491	297	39	-	-	PUNCT
ejpam-491	297	40	frontiers	frontier	NOUN
ejpam-491	297	41	of	of	ADP
ejpam-491	297	42	the	the	DET
ejpam-491	297	43	inverse	inverse	NOUN
ejpam-491	297	44	images	image	NOUN
ejpam-491	297	45	of	of	ADP
ejpam-491	297	46	gm	gm	PROPN
ejpam-491	297	47	-	-	PUNCT
ejpam-491	297	48	open	open	ADJ
ejpam-491	297	49	sets	set	NOUN
ejpam-491	297	50	containing	contain	VERB
ejpam-491	297	51	f(x	f(x	PROPN
ejpam-491	297	52	)	)	PUNCT
ejpam-491	297	53	.	.	PUNCT
ejpam-491	298	1	proof	proof	NOUN
ejpam-491	298	2	.	.	PUNCT
ejpam-491	299	1	this	this	PRON
ejpam-491	299	2	follows	follow	VERB
ejpam-491	299	3	immediately	immediately	ADV
ejpam-491	299	4	from	from	ADP
ejpam-491	299	5	theorem	theorem	ADJ
ejpam-491	299	6	6	6	NUM
ejpam-491	299	7	.	.	PUNCT
ejpam-491	300	1	t.	t.	PROPN
ejpam-491	300	2	noiri	noiri	PROPN
ejpam-491	300	3	and	and	CCONJ
ejpam-491	300	4	v.	v.	ADP
ejpam-491	300	5	popa	popa	NOUN
ejpam-491	300	6	/	/	SYM
ejpam-491	300	7	eur	eur	PROPN
ejpam-491	300	8	.	.	PUNCT
ejpam-491	301	1	j.	j.	PROPN
ejpam-491	301	2	pure	pure	PROPN
ejpam-491	301	3	appl	appl	PROPN
ejpam-491	301	4	.	.	PROPN
ejpam-491	301	5	math	math	PROPN
ejpam-491	301	6	,	,	PUNCT
ejpam-491	301	7	2	2	NUM
ejpam-491	301	8	(	(	PUNCT
ejpam-491	301	9	2009	2009	NUM
ejpam-491	301	10	)	)	PUNCT
ejpam-491	301	11	,	,	PUNCT
ejpam-491	301	12	(	(	PUNCT
ejpam-491	301	13	473	473	NUM
ejpam-491	301	14	-	-	NUM
ejpam-491	301	15	493	493	NUM
ejpam-491	301	16	)	)	PUNCT
ejpam-491	301	17	484	484	NUM
ejpam-491	301	18	5	5	NUM
ejpam-491	301	19	.	.	PUNCT
ejpam-491	302	1	some	some	DET
ejpam-491	302	2	properties	property	NOUN
ejpam-491	302	3	of	of	ADP
ejpam-491	302	4	gm	gm	PROPN
ejpam-491	302	5	-continuity	-continuity	PROPN
ejpam-491	302	6	in	in	ADP
ejpam-491	302	7	this	this	DET
ejpam-491	302	8	section	section	NOUN
ejpam-491	302	9	,	,	PUNCT
ejpam-491	302	10	we	we	PRON
ejpam-491	302	11	use	use	VERB
ejpam-491	302	12	gm	gm	PROPN
ejpam-491	302	13	-	-	PUNCT
ejpam-491	302	14	open	open	ADJ
ejpam-491	302	15	sets	set	NOUN
ejpam-491	302	16	and	and	CCONJ
ejpam-491	302	17	gm	gm	NOUN
ejpam-491	302	18	-	-	PUNCT
ejpam-491	302	19	closed	close	VERB
ejpam-491	302	20	sets	set	NOUN
ejpam-491	302	21	in	in	ADP
ejpam-491	302	22	order	order	NOUN
ejpam-491	302	23	to	to	PART
ejpam-491	302	24	obtain	obtain	VERB
ejpam-491	302	25	some	some	DET
ejpam-491	302	26	properties	property	NOUN
ejpam-491	302	27	of	of	ADP
ejpam-491	302	28	gm	gm	PROPN
ejpam-491	302	29	-	-	PUNCT
ejpam-491	302	30	t2	t2	NOUN
ejpam-491	302	31	spaces	space	NOUN
ejpam-491	302	32	and	and	CCONJ
ejpam-491	302	33	the	the	DET
ejpam-491	302	34	preservation	preservation	NOUN
ejpam-491	302	35	theorems	theorem	NOUN
ejpam-491	302	36	of	of	ADP
ejpam-491	302	37	gm	gm	PROPN
ejpam-491	302	38	-	-	ADJ
ejpam-491	302	39	compact	compact	ADJ
ejpam-491	302	40	spaces	space	NOUN
ejpam-491	302	41	and	and	CCONJ
ejpam-491	302	42	gm	gm	ADV
ejpam-491	302	43	-	-	PUNCT
ejpam-491	302	44	connected	connect	VERB
ejpam-491	302	45	spaces	space	NOUN
ejpam-491	302	46	.	.	PUNCT
ejpam-491	303	1	furthermore	furthermore	ADV
ejpam-491	303	2	,	,	PUNCT
ejpam-491	303	3	we	we	PRON
ejpam-491	303	4	investigate	investigate	VERB
ejpam-491	303	5	some	some	DET
ejpam-491	303	6	properties	property	NOUN
ejpam-491	303	7	of	of	ADP
ejpam-491	303	8	strongly	strongly	ADV
ejpam-491	303	9	mclosed	mclose	VERB
ejpam-491	303	10	graphs	graph	NOUN
ejpam-491	303	11	.	.	PUNCT
ejpam-491	304	1	definition	definition	NOUN
ejpam-491	304	2	19	19	NUM
ejpam-491	304	3	.	.	PUNCT
ejpam-491	305	1	an	an	DET
ejpam-491	305	2	m	m	NOUN
ejpam-491	305	3	-	-	NOUN
ejpam-491	305	4	space	space	NOUN
ejpam-491	305	5	(	(	PUNCT
ejpam-491	305	6	x	x	X
ejpam-491	305	7	,	,	PUNCT
ejpam-491	305	8	mx	mx	PROPN
ejpam-491	305	9	)	)	PUNCT
ejpam-491	305	10	is	be	AUX
ejpam-491	305	11	said	say	VERB
ejpam-491	305	12	to	to	PART
ejpam-491	305	13	be	be	AUX
ejpam-491	305	14	m	m	NOUN
ejpam-491	305	15	-	-	NOUN
ejpam-491	305	16	t2	t2	NOUN
ejpam-491	305	17	[	[	X
ejpam-491	305	18	29	29	NUM
ejpam-491	305	19	]	]	X
ejpam-491	305	20	if	if	SCONJ
ejpam-491	305	21	for	for	ADP
ejpam-491	305	22	any	any	DET
ejpam-491	305	23	distinct	distinct	ADJ
ejpam-491	305	24	points	point	NOUN
ejpam-491	305	25	x	x	X
ejpam-491	305	26	,	,	PUNCT
ejpam-491	305	27	y	y	PROPN
ejpam-491	305	28	,	,	PUNCT
ejpam-491	305	29	there	there	PRON
ejpam-491	305	30	exist	exist	VERB
ejpam-491	305	31	u	u	NOUN
ejpam-491	305	32	,	,	PUNCT
ejpam-491	305	33	v	v	PROPN
ejpam-491	305	34	∈	∈	PROPN
ejpam-491	305	35	mx	mx	NOUN
ejpam-491	305	36	such	such	ADJ
ejpam-491	305	37	that	that	SCONJ
ejpam-491	305	38	x	x	SYM
ejpam-491	305	39	∈	∈	PROPN
ejpam-491	305	40	u	u	NOUN
ejpam-491	305	41	,	,	PUNCT
ejpam-491	305	42	y	y	PROPN
ejpam-491	305	43	∈	∈	PROPN
ejpam-491	305	44	v	v	NOUN
ejpam-491	305	45	,	,	PUNCT
ejpam-491	305	46	and	and	CCONJ
ejpam-491	305	47	u	u	NOUN
ejpam-491	305	48	∩	∩	NOUN
ejpam-491	305	49	v	v	NOUN
ejpam-491	305	50	=	=	PUNCT
ejpam-491	305	51	;	;	PUNCT
ejpam-491	305	52	.	.	PUNCT
ejpam-491	306	1	remark	remark	PROPN
ejpam-491	306	2	8	8	NUM
ejpam-491	306	3	.	.	PUNCT
ejpam-491	307	1	(	(	PUNCT
ejpam-491	307	2	1	1	X
ejpam-491	307	3	)	)	PUNCT
ejpam-491	307	4	let	let	VERB
ejpam-491	307	5	(	(	PUNCT
ejpam-491	307	6	x	x	X
ejpam-491	307	7	,	,	PUNCT
ejpam-491	307	8	τ	τ	X
ejpam-491	307	9	)	)	PUNCT
ejpam-491	307	10	be	be	VERB
ejpam-491	307	11	a	a	DET
ejpam-491	307	12	topological	topological	ADJ
ejpam-491	307	13	space	space	NOUN
ejpam-491	307	14	,	,	PUNCT
ejpam-491	307	15	then	then	ADV
ejpam-491	307	16	(	(	PUNCT
ejpam-491	307	17	x	x	X
ejpam-491	307	18	,	,	PUNCT
ejpam-491	307	19	τ	τ	X
ejpam-491	307	20	)	)	PUNCT
ejpam-491	307	21	is	be	AUX
ejpam-491	307	22	said	say	VERB
ejpam-491	307	23	to	to	PART
ejpam-491	307	24	be	be	AUX
ejpam-491	307	25	gm	gm	NOUN
ejpam-491	307	26	-	-	PUNCT
ejpam-491	307	27	t2	t2	NOUN
ejpam-491	307	28	if	if	SCONJ
ejpam-491	307	29	the	the	DET
ejpam-491	307	30	m	m	NOUN
ejpam-491	307	31	-	-	NOUN
ejpam-491	307	32	space	space	NOUN
ejpam-491	307	33	(	(	PUNCT
ejpam-491	307	34	x	x	X
ejpam-491	307	35	,	,	PUNCT
ejpam-491	307	36	gmo(x	gmo(x	PROPN
ejpam-491	307	37	)	)	PUNCT
ejpam-491	307	38	)	)	PUNCT
ejpam-491	307	39	is	be	AUX
ejpam-491	307	40	m	m	NOUN
ejpam-491	307	41	-	-	NOUN
ejpam-491	307	42	t2	t2	NOUN
ejpam-491	307	43	.	.	PUNCT
ejpam-491	308	1	(	(	PUNCT
ejpam-491	308	2	2	2	X
ejpam-491	308	3	)	)	PUNCT
ejpam-491	308	4	if	if	SCONJ
ejpam-491	308	5	gmo(x	gmo(x	X
ejpam-491	308	6	)	)	PUNCT
ejpam-491	308	7	=	=	PUNCT
ejpam-491	308	8	go(x	go(x	X
ejpam-491	308	9	)	)	PUNCT
ejpam-491	308	10	(	(	PUNCT
ejpam-491	308	11	resp	resp	NOUN
ejpam-491	308	12	.	.	PUNCT
ejpam-491	309	1	gso(x	gso(x	VERB
ejpam-491	309	2	)	)	PUNCT
ejpam-491	309	3	,	,	PUNCT
ejpam-491	309	4	gpo(x	gpo(x	NOUN
ejpam-491	309	5	)	)	PUNCT
ejpam-491	309	6	,	,	PUNCT
ejpam-491	309	7	αgo(x	αgo(x	PROPN
ejpam-491	309	8	)	)	PUNCT
ejpam-491	309	9	gbo(x	gbo(x	PROPN
ejpam-491	309	10	)	)	PUNCT
ejpam-491	309	11	,	,	PUNCT
ejpam-491	309	12	gspo(x	gspo(x	NOUN
ejpam-491	309	13	)	)	PUNCT
ejpam-491	309	14	)	)	PUNCT
ejpam-491	310	1	and	and	CCONJ
ejpam-491	310	2	(	(	PUNCT
ejpam-491	310	3	x	x	X
ejpam-491	310	4	,	,	PUNCT
ejpam-491	310	5	τ	τ	X
ejpam-491	310	6	)	)	PUNCT
ejpam-491	310	7	is	be	AUX
ejpam-491	310	8	mg	mg	PROPN
ejpam-491	310	9	-	-	PUNCT
ejpam-491	310	10	t2	t2	NOUN
ejpam-491	310	11	,	,	PUNCT
ejpam-491	310	12	then	then	ADV
ejpam-491	310	13	(	(	PUNCT
ejpam-491	310	14	x	x	X
ejpam-491	310	15	,	,	PUNCT
ejpam-491	310	16	τ	τ	X
ejpam-491	310	17	)	)	PUNCT
ejpam-491	310	18	is	be	AUX
ejpam-491	310	19	said	say	VERB
ejpam-491	310	20	to	to	PART
ejpam-491	310	21	be	be	AUX
ejpam-491	310	22	g	g	NOUN
ejpam-491	310	23	-	-	PUNCT
ejpam-491	310	24	t2	t2	NOUN
ejpam-491	310	25	[	[	X
ejpam-491	310	26	8	8	NUM
ejpam-491	310	27	]	]	PUNCT
ejpam-491	310	28	(	(	PUNCT
ejpam-491	310	29	resp	resp	NOUN
ejpam-491	310	30	.	.	PUNCT
ejpam-491	311	1	gs	gs	NOUN
ejpam-491	311	2	-	-	PUNCT
ejpam-491	311	3	t2	t2	NOUN
ejpam-491	311	4	,	,	PUNCT
ejpam-491	311	5	gp	gp	NOUN
ejpam-491	311	6	-	-	NOUN
ejpam-491	311	7	t2	t2	NOUN
ejpam-491	311	8	,	,	PUNCT
ejpam-491	311	9	αg	αg	NOUN
ejpam-491	311	10	-	-	PUNCT
ejpam-491	311	11	t2	t2	NOUN
ejpam-491	311	12	,	,	PUNCT
ejpam-491	311	13	g	g	PROPN
ejpam-491	311	14	b	b	PROPN
ejpam-491	311	15	-	-	PUNCT
ejpam-491	311	16	t2	t2	NOUN
ejpam-491	311	17	,	,	PUNCT
ejpam-491	311	18	gsp	gsp	NOUN
ejpam-491	311	19	-	-	PUNCT
ejpam-491	311	20	t2	t2	NOUN
ejpam-491	311	21	)	)	PUNCT
ejpam-491	311	22	.	.	PUNCT
ejpam-491	312	1	lemma	lemma	PROPN
ejpam-491	312	2	4	4	NUM
ejpam-491	312	3	.	.	PUNCT
ejpam-491	313	1	(	(	PUNCT
ejpam-491	313	2	popa	popa	NOUN
ejpam-491	313	3	and	and	CCONJ
ejpam-491	313	4	noiri	noiri	ADV
ejpam-491	314	1	[	[	X
ejpam-491	314	2	29	29	NUM
ejpam-491	314	3	]	]	PUNCT
ejpam-491	314	4	)	)	PUNCT
ejpam-491	314	5	.	.	PUNCT
ejpam-491	315	1	if	if	SCONJ
ejpam-491	315	2	f	f	PROPN
ejpam-491	315	3	:	:	PUNCT
ejpam-491	315	4	(	(	PUNCT
ejpam-491	315	5	x	x	X
ejpam-491	315	6	,	,	PUNCT
ejpam-491	315	7	mx	mx	PROPN
ejpam-491	315	8	)	)	PUNCT
ejpam-491	315	9	→	→	SYM
ejpam-491	315	10	(	(	PUNCT
ejpam-491	315	11	y	y	PROPN
ejpam-491	315	12	,	,	PUNCT
ejpam-491	315	13	my	my	INTJ
ejpam-491	315	14	)	)	PUNCT
ejpam-491	315	15	is	be	AUX
ejpam-491	315	16	an	an	DET
ejpam-491	315	17	m	m	ADJ
ejpam-491	315	18	-	-	ADJ
ejpam-491	315	19	continuous	continuous	ADJ
ejpam-491	315	20	injection	injection	NOUN
ejpam-491	315	21	and	and	CCONJ
ejpam-491	315	22	(	(	PUNCT
ejpam-491	315	23	y	y	PROPN
ejpam-491	315	24	,	,	PUNCT
ejpam-491	315	25	my	my	PRON
ejpam-491	315	26	)	)	PUNCT
ejpam-491	315	27	is	be	AUX
ejpam-491	315	28	m	m	NOUN
ejpam-491	315	29	-	-	NOUN
ejpam-491	315	30	t2	t2	NOUN
ejpam-491	315	31	,	,	PUNCT
ejpam-491	315	32	then	then	ADV
ejpam-491	315	33	(	(	PUNCT
ejpam-491	315	34	x	x	X
ejpam-491	315	35	,	,	PUNCT
ejpam-491	315	36	mx	mx	PROPN
ejpam-491	315	37	)	)	PUNCT
ejpam-491	315	38	is	be	AUX
ejpam-491	315	39	m	m	NOUN
ejpam-491	315	40	-	-	NOUN
ejpam-491	315	41	t2	t2	NOUN
ejpam-491	315	42	.	.	PUNCT
ejpam-491	316	1	theorem	theorem	VERB
ejpam-491	316	2	7	7	NUM
ejpam-491	316	3	.	.	PUNCT
ejpam-491	317	1	if	if	SCONJ
ejpam-491	317	2	f	f	PROPN
ejpam-491	317	3	:	:	PUNCT
ejpam-491	317	4	(	(	PUNCT
ejpam-491	317	5	x	x	X
ejpam-491	317	6	,	,	PUNCT
ejpam-491	317	7	τ)→	τ)→	PROPN
ejpam-491	317	8	(	(	PUNCT
ejpam-491	317	9	y	y	PROPN
ejpam-491	317	10	,	,	PUNCT
ejpam-491	317	11	σ	σ	PROPN
ejpam-491	317	12	)	)	PUNCT
ejpam-491	317	13	is	be	AUX
ejpam-491	317	14	a	a	DET
ejpam-491	317	15	gm	gm	ADJ
ejpam-491	317	16	-	-	PUNCT
ejpam-491	317	17	continuous	continuous	ADJ
ejpam-491	317	18	injection	injection	NOUN
ejpam-491	317	19	and	and	CCONJ
ejpam-491	317	20	(	(	PUNCT
ejpam-491	317	21	y	y	PROPN
ejpam-491	317	22	,	,	PUNCT
ejpam-491	317	23	σ	σ	PROPN
ejpam-491	317	24	)	)	PUNCT
ejpam-491	317	25	is	be	AUX
ejpam-491	317	26	a	a	DET
ejpam-491	317	27	gm	gm	PROPN
ejpam-491	317	28	-	-	PUNCT
ejpam-491	317	29	t2space	t2space	NOUN
ejpam-491	317	30	,	,	PUNCT
ejpam-491	317	31	then	then	ADV
ejpam-491	317	32	(	(	PUNCT
ejpam-491	317	33	x	x	X
ejpam-491	317	34	,	,	PUNCT
ejpam-491	317	35	τ	τ	X
ejpam-491	317	36	)	)	PUNCT
ejpam-491	317	37	is	be	AUX
ejpam-491	317	38	gm	gm	PROPN
ejpam-491	317	39	-	-	PUNCT
ejpam-491	317	40	t2	t2	NOUN
ejpam-491	317	41	.	.	PUNCT
ejpam-491	318	1	proof	proof	NOUN
ejpam-491	318	2	.	.	PUNCT
ejpam-491	319	1	the	the	DET
ejpam-491	319	2	proof	proof	NOUN
ejpam-491	319	3	follows	follow	VERB
ejpam-491	319	4	from	from	ADP
ejpam-491	319	5	remark	remark	NOUN
ejpam-491	319	6	8	8	NUM
ejpam-491	319	7	and	and	CCONJ
ejpam-491	319	8	lemma	lemma	PROPN
ejpam-491	319	9	4	4	X
ejpam-491	319	10	.	.	PUNCT
ejpam-491	319	11	corollary	corollary	ADJ
ejpam-491	319	12	4	4	NUM
ejpam-491	319	13	.	.	PUNCT
ejpam-491	320	1	if	if	SCONJ
ejpam-491	320	2	f	f	PROPN
ejpam-491	320	3	:	:	PUNCT
ejpam-491	320	4	(	(	PUNCT
ejpam-491	320	5	x	x	X
ejpam-491	320	6	,	,	PUNCT
ejpam-491	320	7	τ)→	τ)→	PROPN
ejpam-491	320	8	(	(	PUNCT
ejpam-491	320	9	y	y	PROPN
ejpam-491	320	10	,	,	PUNCT
ejpam-491	320	11	σ	σ	PROPN
ejpam-491	320	12	)	)	PUNCT
ejpam-491	320	13	is	be	AUX
ejpam-491	320	14	a	a	DET
ejpam-491	320	15	gm	gm	NOUN
ejpam-491	320	16	-	-	PUNCT
ejpam-491	320	17	irresolute	irresolute	ADJ
ejpam-491	320	18	injection	injection	NOUN
ejpam-491	320	19	and	and	CCONJ
ejpam-491	320	20	(	(	PUNCT
ejpam-491	320	21	y	y	PROPN
ejpam-491	320	22	,	,	PUNCT
ejpam-491	320	23	σ	σ	PROPN
ejpam-491	320	24	)	)	PUNCT
ejpam-491	320	25	is	be	AUX
ejpam-491	320	26	a	a	DET
ejpam-491	320	27	gm	gm	PROPN
ejpam-491	320	28	-	-	PUNCT
ejpam-491	320	29	t2space	t2space	NOUN
ejpam-491	320	30	,	,	PUNCT
ejpam-491	320	31	then	then	ADV
ejpam-491	320	32	(	(	PUNCT
ejpam-491	320	33	x	x	X
ejpam-491	320	34	,	,	PUNCT
ejpam-491	320	35	τ	τ	X
ejpam-491	320	36	)	)	PUNCT
ejpam-491	320	37	is	be	AUX
ejpam-491	320	38	gm	gm	PROPN
ejpam-491	320	39	-	-	PUNCT
ejpam-491	320	40	t2	t2	NOUN
ejpam-491	320	41	.	.	PUNCT
ejpam-491	321	1	definition	definition	NOUN
ejpam-491	321	2	20	20	NUM
ejpam-491	321	3	.	.	PUNCT
ejpam-491	322	1	an	an	DET
ejpam-491	322	2	m	m	NOUN
ejpam-491	322	3	-	-	NOUN
ejpam-491	322	4	space	space	NOUN
ejpam-491	322	5	(	(	PUNCT
ejpam-491	322	6	x	x	X
ejpam-491	322	7	,	,	PUNCT
ejpam-491	322	8	mx	mx	PROPN
ejpam-491	322	9	)	)	PUNCT
ejpam-491	322	10	is	be	AUX
ejpam-491	322	11	said	say	VERB
ejpam-491	322	12	to	to	PART
ejpam-491	322	13	be	be	AUX
ejpam-491	322	14	m	m	NOUN
ejpam-491	322	15	-	-	ADJ
ejpam-491	322	16	compact	compact	ADJ
ejpam-491	322	17	[	[	X
ejpam-491	322	18	29	29	NUM
ejpam-491	322	19	]	]	X
ejpam-491	322	20	if	if	SCONJ
ejpam-491	322	21	every	every	DET
ejpam-491	322	22	cover	cover	NOUN
ejpam-491	322	23	of	of	ADP
ejpam-491	322	24	x	x	PUNCT
ejpam-491	322	25	by	by	ADP
ejpam-491	322	26	sets	set	NOUN
ejpam-491	322	27	of	of	ADP
ejpam-491	322	28	mx	mx	NOUN
ejpam-491	322	29	has	have	VERB
ejpam-491	322	30	a	a	DET
ejpam-491	322	31	finite	finite	ADJ
ejpam-491	322	32	subcover	subcover	PROPN
ejpam-491	322	33	.	.	PUNCT
ejpam-491	323	1	a	a	DET
ejpam-491	323	2	subset	subset	NOUN
ejpam-491	323	3	k	k	PROPN
ejpam-491	323	4	of	of	ADP
ejpam-491	323	5	an	an	DET
ejpam-491	323	6	m	m	NOUN
ejpam-491	323	7	-	-	NOUN
ejpam-491	323	8	space	space	NOUN
ejpam-491	323	9	(	(	PUNCT
ejpam-491	323	10	x	x	X
ejpam-491	323	11	,	,	PUNCT
ejpam-491	323	12	mx	mx	PROPN
ejpam-491	323	13	)	)	PUNCT
ejpam-491	323	14	is	be	AUX
ejpam-491	323	15	said	say	VERB
ejpam-491	323	16	to	to	PART
ejpam-491	323	17	be	be	AUX
ejpam-491	323	18	m	m	NOUN
ejpam-491	323	19	-	-	ADJ
ejpam-491	323	20	compact	compact	ADJ
ejpam-491	323	21	[	[	X
ejpam-491	323	22	29	29	NUM
ejpam-491	323	23	]	]	X
ejpam-491	323	24	if	if	SCONJ
ejpam-491	323	25	every	every	DET
ejpam-491	323	26	cover	cover	NOUN
ejpam-491	323	27	of	of	ADP
ejpam-491	323	28	k	k	X
ejpam-491	323	29	by	by	ADP
ejpam-491	323	30	subsets	subset	NOUN
ejpam-491	323	31	of	of	ADP
ejpam-491	323	32	mx	mx	PROPN
ejpam-491	323	33	has	have	VERB
ejpam-491	323	34	a	a	DET
ejpam-491	323	35	finite	finite	ADJ
ejpam-491	323	36	subcover	subcover	PROPN
ejpam-491	323	37	.	.	PUNCT
ejpam-491	324	1	t.	t.	PROPN
ejpam-491	324	2	noiri	noiri	PROPN
ejpam-491	324	3	and	and	CCONJ
ejpam-491	324	4	v.	v.	ADP
ejpam-491	324	5	popa	popa	NOUN
ejpam-491	324	6	/	/	SYM
ejpam-491	324	7	eur	eur	PROPN
ejpam-491	324	8	.	.	PUNCT
ejpam-491	325	1	j.	j.	PROPN
ejpam-491	325	2	pure	pure	PROPN
ejpam-491	325	3	appl	appl	PROPN
ejpam-491	325	4	.	.	PROPN
ejpam-491	325	5	math	math	PROPN
ejpam-491	325	6	,	,	PUNCT
ejpam-491	325	7	2	2	NUM
ejpam-491	325	8	(	(	PUNCT
ejpam-491	325	9	2009	2009	NUM
ejpam-491	325	10	)	)	PUNCT
ejpam-491	325	11	,	,	PUNCT
ejpam-491	325	12	(	(	PUNCT
ejpam-491	325	13	473	473	NUM
ejpam-491	325	14	-	-	NUM
ejpam-491	325	15	493	493	NUM
ejpam-491	325	16	)	)	PUNCT
ejpam-491	325	17	485	485	NUM
ejpam-491	325	18	remark	remark	NOUN
ejpam-491	325	19	9	9	NUM
ejpam-491	325	20	.	.	PUNCT
ejpam-491	326	1	(	(	PUNCT
ejpam-491	326	2	1	1	X
ejpam-491	326	3	)	)	PUNCT
ejpam-491	326	4	if	if	SCONJ
ejpam-491	326	5	(	(	PUNCT
ejpam-491	326	6	x	x	X
ejpam-491	326	7	,	,	PUNCT
ejpam-491	326	8	τ	τ	X
ejpam-491	326	9	)	)	PUNCT
ejpam-491	326	10	is	be	AUX
ejpam-491	326	11	a	a	DET
ejpam-491	326	12	topological	topological	ADJ
ejpam-491	326	13	space	space	NOUN
ejpam-491	326	14	and	and	CCONJ
ejpam-491	326	15	(	(	PUNCT
ejpam-491	326	16	x	x	X
ejpam-491	326	17	,	,	PUNCT
ejpam-491	326	18	gmo(x	gmo(x	PROPN
ejpam-491	326	19	)	)	PUNCT
ejpam-491	326	20	)	)	PUNCT
ejpam-491	327	1	is	be	AUX
ejpam-491	327	2	m	m	NOUN
ejpam-491	327	3	-	-	ADJ
ejpam-491	327	4	compact	compact	ADJ
ejpam-491	327	5	,	,	PUNCT
ejpam-491	327	6	then	then	ADV
ejpam-491	327	7	(	(	PUNCT
ejpam-491	327	8	x	x	X
ejpam-491	327	9	,	,	PUNCT
ejpam-491	327	10	τ	τ	X
ejpam-491	327	11	)	)	PUNCT
ejpam-491	327	12	is	be	AUX
ejpam-491	327	13	said	say	VERB
ejpam-491	327	14	to	to	PART
ejpam-491	327	15	be	be	AUX
ejpam-491	327	16	gm	gm	NOUN
ejpam-491	327	17	-	-	PUNCT
ejpam-491	327	18	compact	compact	ADJ
ejpam-491	327	19	.	.	PUNCT
ejpam-491	328	1	(	(	PUNCT
ejpam-491	328	2	2	2	X
ejpam-491	328	3	)	)	PUNCT
ejpam-491	328	4	if	if	SCONJ
ejpam-491	328	5	gmo(x	gmo(x	X
ejpam-491	328	6	)	)	PUNCT
ejpam-491	328	7	=	=	PUNCT
ejpam-491	328	8	go(x	go(x	X
ejpam-491	328	9	)	)	PUNCT
ejpam-491	328	10	(	(	PUNCT
ejpam-491	328	11	resp	resp	NOUN
ejpam-491	328	12	.	.	PUNCT
ejpam-491	329	1	gso(x	gso(x	VERB
ejpam-491	329	2	)	)	PUNCT
ejpam-491	329	3	,	,	PUNCT
ejpam-491	329	4	gpo(x	gpo(x	NOUN
ejpam-491	329	5	)	)	PUNCT
ejpam-491	329	6	,	,	PUNCT
ejpam-491	329	7	αgo(x	αgo(x	PROPN
ejpam-491	329	8	)	)	PUNCT
ejpam-491	329	9	)	)	PUNCT
ejpam-491	329	10	,	,	PUNCT
ejpam-491	329	11	then	then	ADV
ejpam-491	329	12	we	we	PRON
ejpam-491	329	13	obtain	obtain	VERB
ejpam-491	329	14	the	the	DET
ejpam-491	329	15	definition	definition	NOUN
ejpam-491	329	16	of	of	ADP
ejpam-491	329	17	go	go	NOUN
ejpam-491	329	18	-	-	PUNCT
ejpam-491	329	19	compactness	compactness	NOUN
ejpam-491	329	20	[	[	X
ejpam-491	329	21	7	7	NUM
ejpam-491	329	22	]	]	X
ejpam-491	329	23	(	(	PUNCT
ejpam-491	329	24	resp	resp	NOUN
ejpam-491	329	25	.	.	PUNCT
ejpam-491	330	1	gso	gso	NOUN
ejpam-491	330	2	-	-	PUNCT
ejpam-491	330	3	compactness	compactness	NOUN
ejpam-491	331	1	[	[	X
ejpam-491	331	2	11	11	NUM
ejpam-491	331	3	]	]	PUNCT
ejpam-491	331	4	,	,	PUNCT
ejpam-491	331	5	gpo	gpo	NOUN
ejpam-491	331	6	-	-	PUNCT
ejpam-491	331	7	compactness	compactness	NOUN
ejpam-491	331	8	[	[	X
ejpam-491	331	9	6	6	NUM
ejpam-491	331	10	]	]	PUNCT
ejpam-491	331	11	,	,	PUNCT
ejpam-491	331	12	αgo	αgo	NOUN
ejpam-491	331	13	-	-	NOUN
ejpam-491	331	14	compactness	compactness	NOUN
ejpam-491	331	15	[	[	X
ejpam-491	331	16	12	12	NUM
ejpam-491	331	17	]	]	NUM
ejpam-491	331	18	)	)	PUNCT
ejpam-491	331	19	.	.	PUNCT
ejpam-491	332	1	lemma	lemma	PROPN
ejpam-491	332	2	5	5	NUM
ejpam-491	332	3	.	.	PUNCT
ejpam-491	332	4	(	(	PUNCT
ejpam-491	332	5	popa	popa	NOUN
ejpam-491	332	6	and	and	CCONJ
ejpam-491	332	7	noiri	noiri	ADV
ejpam-491	332	8	[	[	X
ejpam-491	332	9	29	29	NUM
ejpam-491	332	10	]	]	PUNCT
ejpam-491	332	11	)	)	PUNCT
ejpam-491	332	12	.	.	PUNCT
ejpam-491	333	1	if	if	SCONJ
ejpam-491	333	2	a	a	DET
ejpam-491	333	3	function	function	NOUN
ejpam-491	333	4	f	f	NOUN
ejpam-491	333	5	:	:	PUNCT
ejpam-491	333	6	(	(	PUNCT
ejpam-491	333	7	x	x	X
ejpam-491	333	8	,	,	PUNCT
ejpam-491	333	9	mx	mx	PROPN
ejpam-491	333	10	)	)	PUNCT
ejpam-491	333	11	→	→	SYM
ejpam-491	333	12	(	(	PUNCT
ejpam-491	333	13	y	y	PROPN
ejpam-491	333	14	,	,	PUNCT
ejpam-491	333	15	my	my	PRON
ejpam-491	333	16	)	)	PUNCT
ejpam-491	333	17	is	be	AUX
ejpam-491	333	18	m	m	NOUN
ejpam-491	333	19	-	-	ADJ
ejpam-491	333	20	continuous	continuous	ADJ
ejpam-491	333	21	and	and	CCONJ
ejpam-491	333	22	k	k	PROPN
ejpam-491	333	23	is	be	AUX
ejpam-491	333	24	an	an	DET
ejpam-491	333	25	m	m	ADJ
ejpam-491	333	26	-	-	ADJ
ejpam-491	333	27	compact	compact	ADJ
ejpam-491	333	28	set	set	NOUN
ejpam-491	333	29	of	of	ADP
ejpam-491	333	30	x	x	PRON
ejpam-491	333	31	,	,	PUNCT
ejpam-491	333	32	then	then	ADV
ejpam-491	333	33	f(k	f(k	VERB
ejpam-491	333	34	)	)	PUNCT
ejpam-491	333	35	is	be	AUX
ejpam-491	333	36	m	m	NOUN
ejpam-491	333	37	-	-	ADJ
ejpam-491	333	38	compact	compact	ADJ
ejpam-491	333	39	.	.	PUNCT
ejpam-491	334	1	theorem	theorem	VERB
ejpam-491	334	2	8	8	NUM
ejpam-491	334	3	.	.	PUNCT
ejpam-491	335	1	if	if	SCONJ
ejpam-491	335	2	f	f	PROPN
ejpam-491	335	3	:	:	PUNCT
ejpam-491	335	4	(	(	PUNCT
ejpam-491	335	5	x	x	X
ejpam-491	335	6	,	,	PUNCT
ejpam-491	335	7	τ)→	τ)→	PROPN
ejpam-491	335	8	(	(	PUNCT
ejpam-491	335	9	y	y	PROPN
ejpam-491	335	10	,	,	PUNCT
ejpam-491	335	11	σ	σ	PROPN
ejpam-491	335	12	)	)	PUNCT
ejpam-491	335	13	is	be	AUX
ejpam-491	335	14	a	a	DET
ejpam-491	335	15	gm	gm	ADJ
ejpam-491	335	16	-	-	PUNCT
ejpam-491	335	17	continuous	continuous	ADJ
ejpam-491	335	18	function	function	NOUN
ejpam-491	335	19	and	and	CCONJ
ejpam-491	335	20	k	k	PROPN
ejpam-491	335	21	is	be	AUX
ejpam-491	335	22	a	a	DET
ejpam-491	335	23	gm	gm	ADJ
ejpam-491	335	24	-	-	PUNCT
ejpam-491	335	25	compact	compact	ADJ
ejpam-491	335	26	set	set	NOUN
ejpam-491	335	27	of	of	ADP
ejpam-491	335	28	x	x	PRON
ejpam-491	335	29	,	,	PUNCT
ejpam-491	335	30	then	then	ADV
ejpam-491	335	31	f(k	f(k	VERB
ejpam-491	335	32	)	)	PUNCT
ejpam-491	335	33	is	be	AUX
ejpam-491	335	34	gm	gm	NOUN
ejpam-491	335	35	-	-	PUNCT
ejpam-491	335	36	compact	compact	ADJ
ejpam-491	335	37	.	.	PUNCT
ejpam-491	336	1	proof	proof	NOUN
ejpam-491	336	2	.	.	PUNCT
ejpam-491	337	1	the	the	DET
ejpam-491	337	2	proof	proof	NOUN
ejpam-491	337	3	follows	follow	VERB
ejpam-491	337	4	from	from	ADP
ejpam-491	337	5	definition	definition	NOUN
ejpam-491	337	6	20	20	NUM
ejpam-491	337	7	and	and	CCONJ
ejpam-491	337	8	lemma	lemma	PROPN
ejpam-491	337	9	5	5	NUM
ejpam-491	337	10	.	.	PUNCT
ejpam-491	337	11	corollary	corollary	ADJ
ejpam-491	337	12	5	5	NUM
ejpam-491	337	13	.	.	PUNCT
ejpam-491	338	1	if	if	SCONJ
ejpam-491	338	2	f	f	PROPN
ejpam-491	338	3	:	:	PUNCT
ejpam-491	338	4	(	(	PUNCT
ejpam-491	338	5	x	x	X
ejpam-491	338	6	,	,	PUNCT
ejpam-491	338	7	τ)→	τ)→	PROPN
ejpam-491	338	8	(	(	PUNCT
ejpam-491	338	9	y	y	PROPN
ejpam-491	338	10	,	,	PUNCT
ejpam-491	338	11	σ	σ	PROPN
ejpam-491	338	12	)	)	PUNCT
ejpam-491	338	13	is	be	AUX
ejpam-491	338	14	a	a	DET
ejpam-491	338	15	gm	gm	PROPN
ejpam-491	338	16	-	-	PUNCT
ejpam-491	338	17	irresolute	irresolute	ADJ
ejpam-491	338	18	function	function	NOUN
ejpam-491	338	19	and	and	CCONJ
ejpam-491	338	20	k	k	PROPN
ejpam-491	338	21	is	be	AUX
ejpam-491	338	22	a	a	DET
ejpam-491	338	23	gm	gm	ADJ
ejpam-491	338	24	-	-	PUNCT
ejpam-491	338	25	compact	compact	ADJ
ejpam-491	338	26	set	set	NOUN
ejpam-491	338	27	of	of	ADP
ejpam-491	338	28	x	x	PRON
ejpam-491	338	29	,	,	PUNCT
ejpam-491	338	30	then	then	ADV
ejpam-491	338	31	f(k	f(k	VERB
ejpam-491	338	32	)	)	PUNCT
ejpam-491	338	33	is	be	AUX
ejpam-491	338	34	gm	gm	PROPN
ejpam-491	338	35	-	-	PUNCT
ejpam-491	338	36	compact	compact	ADJ
ejpam-491	338	37	.	.	PUNCT
ejpam-491	339	1	remark	remark	NOUN
ejpam-491	339	2	10	10	NUM
ejpam-491	339	3	.	.	PUNCT
ejpam-491	340	1	if	if	SCONJ
ejpam-491	340	2	gmo(x	gmo(x	PROPN
ejpam-491	340	3	)	)	PUNCT
ejpam-491	340	4	=	=	PUNCT
ejpam-491	340	5	go(x	go(x	X
ejpam-491	340	6	)	)	PUNCT
ejpam-491	340	7	(	(	PUNCT
ejpam-491	340	8	resp	resp	NOUN
ejpam-491	340	9	.	.	PUNCT
ejpam-491	341	1	gso(x	gso(x	VERB
ejpam-491	341	2	)	)	PUNCT
ejpam-491	341	3	,	,	PUNCT
ejpam-491	341	4	gpo(x	gpo(x	NOUN
ejpam-491	341	5	)	)	PUNCT
ejpam-491	341	6	,	,	PUNCT
ejpam-491	341	7	αgo(x	αgo(x	PROPN
ejpam-491	341	8	)	)	PUNCT
ejpam-491	341	9	)	)	PUNCT
ejpam-491	341	10	and	and	CCONJ
ejpam-491	341	11	gmo(y	gmo(y	NOUN
ejpam-491	341	12	)	)	PUNCT
ejpam-491	342	1	=	=	SYM
ejpam-491	342	2	go(y	go(y	X
ejpam-491	342	3	)	)	PUNCT
ejpam-491	342	4	(	(	PUNCT
ejpam-491	342	5	resp	resp	NOUN
ejpam-491	342	6	.	.	PUNCT
ejpam-491	343	1	gso(y	gso(y	NOUN
ejpam-491	343	2	)	)	PUNCT
ejpam-491	343	3	,	,	PUNCT
ejpam-491	343	4	gpo(y	gpo(y	PROPN
ejpam-491	343	5	)	)	PUNCT
ejpam-491	343	6	,	,	PUNCT
ejpam-491	343	7	αgo(y	αgo(y	NOUN
ejpam-491	343	8	)	)	PUNCT
ejpam-491	343	9	)	)	PUNCT
ejpam-491	343	10	,	,	PUNCT
ejpam-491	343	11	then	then	ADV
ejpam-491	343	12	by	by	ADP
ejpam-491	343	13	corollary	corollary	ADJ
ejpam-491	343	14	5	5	NUM
ejpam-491	343	15	we	we	PRON
ejpam-491	343	16	obtain	obtain	VERB
ejpam-491	343	17	the	the	DET
ejpam-491	343	18	result	result	NOUN
ejpam-491	343	19	established	establish	VERB
ejpam-491	343	20	in	in	ADP
ejpam-491	343	21	proposition	proposition	NOUN
ejpam-491	343	22	9(ii	9(ii	NUM
ejpam-491	343	23	)	)	PUNCT
ejpam-491	343	24	of	of	ADP
ejpam-491	343	25	[	[	X
ejpam-491	343	26	7	7	NUM
ejpam-491	343	27	]	]	X
ejpam-491	343	28	(	(	PUNCT
ejpam-491	343	29	resp	resp	NOUN
ejpam-491	343	30	.	.	PUNCT
ejpam-491	344	1	proposition	proposition	NOUN
ejpam-491	344	2	5.5(iii	5.5(iii	NUM
ejpam-491	344	3	)	)	PUNCT
ejpam-491	344	4	of	of	ADP
ejpam-491	344	5	[	[	X
ejpam-491	344	6	11	11	NUM
ejpam-491	344	7	]	]	PUNCT
ejpam-491	344	8	,	,	PUNCT
ejpam-491	344	9	theorem	theorem	VERB
ejpam-491	344	10	5.5(iii	5.5(iii	NUM
ejpam-491	344	11	)	)	PUNCT
ejpam-491	344	12	of	of	ADP
ejpam-491	344	13	[	[	X
ejpam-491	344	14	6	6	NUM
ejpam-491	344	15	]	]	PUNCT
ejpam-491	344	16	,	,	PUNCT
ejpam-491	344	17	proposition	proposition	NOUN
ejpam-491	344	18	4.3(iii	4.3(iii	NUM
ejpam-491	344	19	)	)	PUNCT
ejpam-491	345	1	[	[	X
ejpam-491	345	2	12	12	NUM
ejpam-491	345	3	]	]	PUNCT
ejpam-491	345	4	)	)	PUNCT
ejpam-491	345	5	.	.	PUNCT
ejpam-491	346	1	definition	definition	NOUN
ejpam-491	346	2	21	21	NUM
ejpam-491	346	3	.	.	PUNCT
ejpam-491	347	1	an	an	DET
ejpam-491	347	2	m	m	NOUN
ejpam-491	347	3	-	-	NOUN
ejpam-491	347	4	space	space	NOUN
ejpam-491	347	5	(	(	PUNCT
ejpam-491	347	6	x	x	X
ejpam-491	347	7	,	,	PUNCT
ejpam-491	347	8	mx	mx	PROPN
ejpam-491	347	9	)	)	PUNCT
ejpam-491	347	10	is	be	AUX
ejpam-491	347	11	said	say	VERB
ejpam-491	347	12	to	to	PART
ejpam-491	347	13	be	be	AUX
ejpam-491	347	14	m	m	ADJ
ejpam-491	347	15	-	-	ADJ
ejpam-491	347	16	connected	connect	VERB
ejpam-491	347	17	[	[	X
ejpam-491	347	18	29	29	NUM
ejpam-491	347	19	]	]	X
ejpam-491	347	20	if	if	SCONJ
ejpam-491	347	21	x	x	PRON
ejpam-491	347	22	can	can	AUX
ejpam-491	347	23	not	not	PART
ejpam-491	347	24	be	be	AUX
ejpam-491	347	25	written	write	VERB
ejpam-491	347	26	as	as	ADP
ejpam-491	347	27	the	the	DET
ejpam-491	347	28	union	union	NOUN
ejpam-491	347	29	of	of	ADP
ejpam-491	347	30	two	two	NUM
ejpam-491	347	31	nonempty	nonempty	ADJ
ejpam-491	347	32	disjoint	disjoint	ADJ
ejpam-491	347	33	mx	mx	PROPN
ejpam-491	347	34	-open	-open	PROPN
ejpam-491	347	35	sets	set	NOUN
ejpam-491	347	36	.	.	PUNCT
ejpam-491	348	1	remark	remark	NOUN
ejpam-491	348	2	11	11	NUM
ejpam-491	348	3	.	.	PUNCT
ejpam-491	349	1	let	let	AUX
ejpam-491	349	2	(	(	PUNCT
ejpam-491	349	3	x	x	X
ejpam-491	349	4	,	,	PUNCT
ejpam-491	349	5	τ	τ	X
ejpam-491	349	6	)	)	PUNCT
ejpam-491	349	7	be	be	VERB
ejpam-491	349	8	a	a	DET
ejpam-491	349	9	topological	topological	ADJ
ejpam-491	349	10	space	space	NOUN
ejpam-491	349	11	and	and	CCONJ
ejpam-491	349	12	gmo(x	gmo(x	PROPN
ejpam-491	349	13	)	)	PUNCT
ejpam-491	349	14	a	a	DET
ejpam-491	349	15	gm	gm	NOUN
ejpam-491	349	16	-	-	PUNCT
ejpam-491	349	17	structure	structure	NOUN
ejpam-491	349	18	on	on	ADP
ejpam-491	349	19	x	x	X
ejpam-491	349	20	,	,	PUNCT
ejpam-491	349	21	then	then	ADV
ejpam-491	349	22	(	(	PUNCT
ejpam-491	349	23	1	1	X
ejpam-491	349	24	)	)	PUNCT
ejpam-491	349	25	(	(	PUNCT
ejpam-491	349	26	x	x	X
ejpam-491	349	27	,	,	PUNCT
ejpam-491	349	28	τ	τ	X
ejpam-491	349	29	)	)	PUNCT
ejpam-491	349	30	is	be	AUX
ejpam-491	349	31	said	say	VERB
ejpam-491	349	32	to	to	PART
ejpam-491	349	33	be	be	AUX
ejpam-491	349	34	gm	gm	NOUN
ejpam-491	349	35	-	-	PUNCT
ejpam-491	349	36	connected	connect	VERB
ejpam-491	349	37	if	if	SCONJ
ejpam-491	349	38	x	x	PRON
ejpam-491	349	39	can	can	AUX
ejpam-491	349	40	not	not	PART
ejpam-491	349	41	be	be	AUX
ejpam-491	349	42	written	write	VERB
ejpam-491	349	43	as	as	ADP
ejpam-491	349	44	the	the	DET
ejpam-491	349	45	union	union	NOUN
ejpam-491	349	46	of	of	ADP
ejpam-491	349	47	two	two	NUM
ejpam-491	349	48	nonempty	nonempty	ADV
ejpam-491	349	49	disjoint	disjoint	NOUN
ejpam-491	349	50	gm	gm	NOUN
ejpam-491	349	51	-	-	PUNCT
ejpam-491	349	52	open	open	ADJ
ejpam-491	349	53	sets	set	NOUN
ejpam-491	349	54	.	.	PUNCT
ejpam-491	350	1	(	(	PUNCT
ejpam-491	350	2	2	2	X
ejpam-491	350	3	)	)	PUNCT
ejpam-491	350	4	if	if	SCONJ
ejpam-491	350	5	gmo(x	gmo(x	X
ejpam-491	350	6	)	)	PUNCT
ejpam-491	350	7	=	=	PUNCT
ejpam-491	350	8	go(x	go(x	X
ejpam-491	350	9	)	)	PUNCT
ejpam-491	350	10	(	(	PUNCT
ejpam-491	350	11	resp	resp	NOUN
ejpam-491	350	12	.	.	PUNCT
ejpam-491	351	1	αgo(x	αgo(x	PROPN
ejpam-491	351	2	)	)	PUNCT
ejpam-491	351	3	)	)	PUNCT
ejpam-491	352	1	,	,	PUNCT
ejpam-491	352	2	then	then	ADV
ejpam-491	352	3	we	we	PRON
ejpam-491	352	4	obtain	obtain	VERB
ejpam-491	352	5	the	the	DET
ejpam-491	352	6	definition	definition	NOUN
ejpam-491	352	7	of	of	ADP
ejpam-491	352	8	goconnected	goconnecte	VERB
ejpam-491	352	9	spaces	space	NOUN
ejpam-491	352	10	[	[	X
ejpam-491	352	11	7	7	NUM
ejpam-491	352	12	]	]	X
ejpam-491	352	13	(	(	PUNCT
ejpam-491	352	14	resp	resp	NOUN
ejpam-491	352	15	.	.	PUNCT
ejpam-491	353	1	αgo	αgo	ADJ
ejpam-491	353	2	-	-	ADJ
ejpam-491	353	3	connected	connect	VERB
ejpam-491	353	4	spaces	space	NOUN
ejpam-491	353	5	[	[	X
ejpam-491	353	6	12	12	NUM
ejpam-491	353	7	]	]	PUNCT
ejpam-491	353	8	)	)	PUNCT
ejpam-491	353	9	.	.	PUNCT
ejpam-491	354	1	t.	t.	PROPN
ejpam-491	354	2	noiri	noiri	PROPN
ejpam-491	354	3	and	and	CCONJ
ejpam-491	354	4	v.	v.	ADP
ejpam-491	354	5	popa	popa	NOUN
ejpam-491	354	6	/	/	SYM
ejpam-491	354	7	eur	eur	PROPN
ejpam-491	354	8	.	.	PUNCT
ejpam-491	355	1	j.	j.	PROPN
ejpam-491	355	2	pure	pure	PROPN
ejpam-491	355	3	appl	appl	PROPN
ejpam-491	355	4	.	.	PROPN
ejpam-491	355	5	math	math	PROPN
ejpam-491	355	6	,	,	PUNCT
ejpam-491	355	7	2	2	NUM
ejpam-491	355	8	(	(	PUNCT
ejpam-491	355	9	2009	2009	NUM
ejpam-491	355	10	)	)	PUNCT
ejpam-491	355	11	,	,	PUNCT
ejpam-491	355	12	(	(	PUNCT
ejpam-491	355	13	473	473	NUM
ejpam-491	355	14	-	-	NUM
ejpam-491	355	15	493	493	NUM
ejpam-491	355	16	)	)	PUNCT
ejpam-491	355	17	486	486	NUM
ejpam-491	355	18	lemma	lemma	PROPN
ejpam-491	355	19	6	6	NUM
ejpam-491	355	20	.	.	PUNCT
ejpam-491	356	1	if	if	SCONJ
ejpam-491	356	2	f	f	PROPN
ejpam-491	356	3	:	:	PUNCT
ejpam-491	356	4	(	(	PUNCT
ejpam-491	356	5	x	x	X
ejpam-491	356	6	,	,	PUNCT
ejpam-491	356	7	mx	mx	PROPN
ejpam-491	356	8	)	)	PUNCT
ejpam-491	356	9	→	→	SYM
ejpam-491	356	10	(	(	PUNCT
ejpam-491	356	11	y	y	NOUN
ejpam-491	356	12	,	,	PUNCT
ejpam-491	356	13	my	my	INTJ
ejpam-491	356	14	)	)	PUNCT
ejpam-491	356	15	is	be	AUX
ejpam-491	356	16	an	an	DET
ejpam-491	356	17	m	m	NOUN
ejpam-491	356	18	∗-continuous	∗-continuous	ADJ
ejpam-491	356	19	surjection	surjection	NOUN
ejpam-491	356	20	and	and	CCONJ
ejpam-491	356	21	(	(	PUNCT
ejpam-491	356	22	x	x	X
ejpam-491	356	23	,	,	PUNCT
ejpam-491	356	24	mx	mx	PROPN
ejpam-491	356	25	)	)	PUNCT
ejpam-491	356	26	is	be	AUX
ejpam-491	356	27	m	m	NOUN
ejpam-491	356	28	-	-	PUNCT
ejpam-491	356	29	connected	connect	VERB
ejpam-491	356	30	,	,	PUNCT
ejpam-491	356	31	then	then	ADV
ejpam-491	356	32	(	(	PUNCT
ejpam-491	356	33	y	y	NOUN
ejpam-491	356	34	,	,	PUNCT
ejpam-491	356	35	my	my	PRON
ejpam-491	356	36	)	)	PUNCT
ejpam-491	356	37	is	be	AUX
ejpam-491	356	38	m	m	ADV
ejpam-491	356	39	-	-	PUNCT
ejpam-491	356	40	connected	connect	VERB
ejpam-491	356	41	.	.	PUNCT
ejpam-491	357	1	proof	proof	NOUN
ejpam-491	357	2	.	.	PUNCT
ejpam-491	358	1	suppose	suppose	VERB
ejpam-491	358	2	that	that	SCONJ
ejpam-491	358	3	(	(	PUNCT
ejpam-491	358	4	y	y	NOUN
ejpam-491	358	5	,	,	PUNCT
ejpam-491	358	6	my	my	INTJ
ejpam-491	358	7	)	)	PUNCT
ejpam-491	358	8	is	be	AUX
ejpam-491	358	9	not	not	PART
ejpam-491	358	10	m	m	ADV
ejpam-491	358	11	-	-	PUNCT
ejpam-491	358	12	connected	connect	VERB
ejpam-491	358	13	.	.	PUNCT
ejpam-491	359	1	then	then	ADV
ejpam-491	359	2	there	there	PRON
ejpam-491	359	3	exist	exist	VERB
ejpam-491	359	4	nonempty	nonempty	ADJ
ejpam-491	359	5	my	my	PRON
ejpam-491	359	6	-open	-open	NOUN
ejpam-491	359	7	sets	set	NOUN
ejpam-491	359	8	v1	v1	NOUN
ejpam-491	359	9	and	and	CCONJ
ejpam-491	359	10	v2	v2	VERB
ejpam-491	359	11	such	such	ADJ
ejpam-491	359	12	that	that	DET
ejpam-491	359	13	v1	v1	NOUN
ejpam-491	359	14	∩	∩	ADJ
ejpam-491	359	15	v2	v2	NOUN
ejpam-491	359	16	=	=	NOUN
ejpam-491	359	17	;	;	PUNCT
ejpam-491	359	18	and	and	CCONJ
ejpam-491	359	19	v1	v1	VERB
ejpam-491	359	20	∪	∪	NOUN
ejpam-491	359	21	v2	v2	NOUN
ejpam-491	359	22	=	=	SYM
ejpam-491	359	23	y	y	PROPN
ejpam-491	359	24	.	.	PUNCT
ejpam-491	360	1	hence	hence	ADV
ejpam-491	360	2	we	we	PRON
ejpam-491	360	3	have	have	VERB
ejpam-491	360	4	f	f	PROPN
ejpam-491	360	5	−1(v1	−1(v1	X
ejpam-491	360	6	)	)	PUNCT
ejpam-491	360	7	∩	∩	PROPN
ejpam-491	360	8	f	f	PROPN
ejpam-491	360	9	−1(v2	−1(v2	PROPN
ejpam-491	360	10	)	)	PUNCT
ejpam-491	360	11	=	=	SYM
ejpam-491	360	12	;	;	PUNCT
ejpam-491	360	13	and	and	CCONJ
ejpam-491	360	14	f	f	PROPN
ejpam-491	360	15	−1(v1	−1(v1	X
ejpam-491	360	16	)	)	PUNCT
ejpam-491	360	17	∪	∪	ADP
ejpam-491	360	18	f	f	PROPN
ejpam-491	360	19	−1(v2	−1(v2	PROPN
ejpam-491	360	20	)	)	PUNCT
ejpam-491	361	1	=	=	SYM
ejpam-491	361	2	x	x	X
ejpam-491	361	3	.	.	PUNCT
ejpam-491	362	1	since	since	SCONJ
ejpam-491	362	2	f	f	PROPN
ejpam-491	362	3	is	be	AUX
ejpam-491	362	4	an	an	DET
ejpam-491	362	5	m	m	NOUN
ejpam-491	362	6	∗-continuous	∗-continuous	ADJ
ejpam-491	362	7	surjection	surjection	NOUN
ejpam-491	362	8	,	,	PUNCT
ejpam-491	362	9	f	f	PROPN
ejpam-491	362	10	−1(v1	−1(v1	X
ejpam-491	362	11	)	)	PUNCT
ejpam-491	362	12	and	and	CCONJ
ejpam-491	362	13	f	f	PROPN
ejpam-491	362	14	−1(v2	−1(v2	NOUN
ejpam-491	362	15	)	)	PUNCT
ejpam-491	362	16	are	be	AUX
ejpam-491	362	17	nonempty	nonempty	X
ejpam-491	362	18	mx	mx	PROPN
ejpam-491	362	19	-open	-open	PROPN
ejpam-491	362	20	sets	set	NOUN
ejpam-491	362	21	.	.	PUNCT
ejpam-491	363	1	therefore	therefore	ADV
ejpam-491	363	2	,	,	PUNCT
ejpam-491	363	3	(	(	PUNCT
ejpam-491	363	4	x	x	X
ejpam-491	363	5	,	,	PUNCT
ejpam-491	363	6	mx	mx	PROPN
ejpam-491	363	7	)	)	PUNCT
ejpam-491	363	8	is	be	AUX
ejpam-491	363	9	not	not	PART
ejpam-491	363	10	m	m	ADV
ejpam-491	363	11	-	-	PUNCT
ejpam-491	363	12	connected	connect	VERB
ejpam-491	363	13	.	.	PUNCT
ejpam-491	364	1	this	this	PRON
ejpam-491	364	2	is	be	AUX
ejpam-491	364	3	a	a	DET
ejpam-491	364	4	contradiction	contradiction	NOUN
ejpam-491	364	5	and	and	CCONJ
ejpam-491	364	6	hence	hence	ADV
ejpam-491	364	7	(	(	PUNCT
ejpam-491	364	8	y	y	PROPN
ejpam-491	364	9	,	,	PUNCT
ejpam-491	364	10	my	my	PRON
ejpam-491	364	11	)	)	PUNCT
ejpam-491	364	12	is	be	AUX
ejpam-491	364	13	m	m	ADV
ejpam-491	364	14	-	-	PUNCT
ejpam-491	364	15	connected	connect	VERB
ejpam-491	364	16	.	.	PUNCT
ejpam-491	365	1	theorem	theorem	VERB
ejpam-491	365	2	9	9	NUM
ejpam-491	365	3	.	.	PUNCT
ejpam-491	366	1	if	if	SCONJ
ejpam-491	366	2	f	f	PROPN
ejpam-491	366	3	:	:	PUNCT
ejpam-491	366	4	(	(	PUNCT
ejpam-491	366	5	x	x	X
ejpam-491	366	6	,	,	PUNCT
ejpam-491	366	7	τ	τ	PROPN
ejpam-491	366	8	)	)	PUNCT
ejpam-491	366	9	→	→	SYM
ejpam-491	366	10	(	(	PUNCT
ejpam-491	366	11	y	y	PROPN
ejpam-491	366	12	,	,	PUNCT
ejpam-491	366	13	σ	σ	PROPN
ejpam-491	366	14	)	)	PUNCT
ejpam-491	366	15	is	be	AUX
ejpam-491	366	16	a	a	DET
ejpam-491	366	17	gm	gm	PROPN
ejpam-491	366	18	-	-	PUNCT
ejpam-491	366	19	irresolute	irresolute	ADJ
ejpam-491	366	20	surjection	surjection	NOUN
ejpam-491	366	21	and	and	CCONJ
ejpam-491	366	22	(	(	PUNCT
ejpam-491	366	23	x	x	X
ejpam-491	366	24	,	,	PUNCT
ejpam-491	366	25	τ	τ	X
ejpam-491	366	26	)	)	PUNCT
ejpam-491	366	27	is	be	AUX
ejpam-491	366	28	gmconnected	gmconnecte	VERB
ejpam-491	366	29	,	,	PUNCT
ejpam-491	366	30	then	then	ADV
ejpam-491	366	31	(	(	PUNCT
ejpam-491	366	32	y	y	PROPN
ejpam-491	366	33	,	,	PUNCT
ejpam-491	366	34	σ	σ	PROPN
ejpam-491	366	35	)	)	PUNCT
ejpam-491	366	36	is	be	AUX
ejpam-491	366	37	gm	gm	PROPN
ejpam-491	366	38	-	-	PUNCT
ejpam-491	366	39	connected	connect	VERB
ejpam-491	366	40	.	.	PUNCT
ejpam-491	367	1	proof	proof	NOUN
ejpam-491	367	2	.	.	PUNCT
ejpam-491	368	1	the	the	DET
ejpam-491	368	2	proof	proof	NOUN
ejpam-491	368	3	follows	follow	VERB
ejpam-491	368	4	from	from	ADP
ejpam-491	368	5	definition	definition	NOUN
ejpam-491	368	6	21	21	NUM
ejpam-491	368	7	,	,	PUNCT
ejpam-491	368	8	remark	remark	VERB
ejpam-491	368	9	11	11	NUM
ejpam-491	368	10	and	and	CCONJ
ejpam-491	368	11	lemma	lemma	PROPN
ejpam-491	368	12	6	6	NUM
ejpam-491	368	13	.	.	PUNCT
ejpam-491	368	14	remark	remark	PROPN
ejpam-491	368	15	12	12	NUM
ejpam-491	368	16	.	.	PUNCT
ejpam-491	369	1	if	if	SCONJ
ejpam-491	369	2	gmo(x	gmo(x	PROPN
ejpam-491	369	3	)	)	PUNCT
ejpam-491	369	4	=	=	SYM
ejpam-491	369	5	go(x	go(x	NUM
ejpam-491	369	6	)	)	PUNCT
ejpam-491	369	7	,	,	PUNCT
ejpam-491	369	8	then	then	ADV
ejpam-491	369	9	we	we	PRON
ejpam-491	369	10	obtain	obtain	VERB
ejpam-491	369	11	the	the	DET
ejpam-491	369	12	result	result	NOUN
ejpam-491	369	13	established	establish	VERB
ejpam-491	369	14	in	in	ADP
ejpam-491	369	15	proposition	proposition	NOUN
ejpam-491	369	16	13	13	NUM
ejpam-491	369	17	of	of	ADP
ejpam-491	369	18	[	[	X
ejpam-491	369	19	7	7	NUM
ejpam-491	369	20	]	]	PUNCT
ejpam-491	369	21	.	.	PUNCT
ejpam-491	370	1	definition	definition	NOUN
ejpam-491	370	2	22	22	NUM
ejpam-491	370	3	.	.	PUNCT
ejpam-491	371	1	a	a	DET
ejpam-491	371	2	function	function	NOUN
ejpam-491	371	3	f	f	NOUN
ejpam-491	371	4	:	:	PUNCT
ejpam-491	371	5	(	(	PUNCT
ejpam-491	371	6	x	x	X
ejpam-491	371	7	,	,	PUNCT
ejpam-491	371	8	mx	mx	PROPN
ejpam-491	371	9	)	)	PUNCT
ejpam-491	371	10	→	→	SYM
ejpam-491	371	11	(	(	PUNCT
ejpam-491	371	12	y	y	NOUN
ejpam-491	371	13	,	,	PUNCT
ejpam-491	371	14	my	my	INTJ
ejpam-491	371	15	)	)	PUNCT
ejpam-491	371	16	is	be	AUX
ejpam-491	371	17	said	say	VERB
ejpam-491	371	18	to	to	PART
ejpam-491	371	19	have	have	VERB
ejpam-491	371	20	a	a	DET
ejpam-491	371	21	strongly	strongly	ADV
ejpam-491	371	22	m	m	ADJ
ejpam-491	371	23	-	-	PUNCT
ejpam-491	371	24	closed	closed	ADJ
ejpam-491	371	25	graph	graph	NOUN
ejpam-491	371	26	(	(	PUNCT
ejpam-491	371	27	resp	resp	NOUN
ejpam-491	371	28	.	.	PUNCT
ejpam-491	372	1	m	m	ADJ
ejpam-491	372	2	-	-	PUNCT
ejpam-491	372	3	closed	closed	ADJ
ejpam-491	372	4	graph	graph	NOUN
ejpam-491	372	5	)	)	PUNCT
ejpam-491	373	1	[	[	X
ejpam-491	373	2	29	29	NUM
ejpam-491	373	3	]	]	X
ejpam-491	373	4	if	if	SCONJ
ejpam-491	373	5	for	for	ADP
ejpam-491	373	6	each	each	DET
ejpam-491	373	7	(	(	PUNCT
ejpam-491	373	8	x	x	PROPN
ejpam-491	373	9	,	,	PUNCT
ejpam-491	373	10	y	y	PROPN
ejpam-491	373	11	)	)	PUNCT
ejpam-491	373	12	∈	∈	PROPN
ejpam-491	373	13	(	(	PUNCT
ejpam-491	373	14	x	x	SYM
ejpam-491	373	15	×	×	PROPN
ejpam-491	373	16	y	y	PROPN
ejpam-491	373	17	)	)	PUNCT
ejpam-491	374	1	−	−	PROPN
ejpam-491	374	2	g	g	PROPN
ejpam-491	374	3	(	(	PUNCT
ejpam-491	374	4	f	f	PROPN
ejpam-491	374	5	)	)	PUNCT
ejpam-491	374	6	,	,	PUNCT
ejpam-491	374	7	there	there	PRON
ejpam-491	374	8	exist	exist	VERB
ejpam-491	374	9	u	u	PROPN
ejpam-491	374	10	∈	∈	PROPN
ejpam-491	374	11	mx	mx	NOUN
ejpam-491	374	12	containing	contain	VERB
ejpam-491	374	13	x	x	PROPN
ejpam-491	374	14	and	and	CCONJ
ejpam-491	374	15	v	v	ADP
ejpam-491	374	16	∈	∈	PRON
ejpam-491	374	17	my	my	PRON
ejpam-491	374	18	containing	contain	VERB
ejpam-491	374	19	y	y	PRON
ejpam-491	374	20	such	such	ADJ
ejpam-491	374	21	that	that	SCONJ
ejpam-491	375	1	[	[	X
ejpam-491	375	2	u	u	X
ejpam-491	375	3	×mcl(v	×mcl(v	PROPN
ejpam-491	375	4	)	)	PUNCT
ejpam-491	375	5	]	]	PUNCT
ejpam-491	375	6	∩	∩	PROPN
ejpam-491	375	7	g	g	PROPN
ejpam-491	375	8	(	(	PUNCT
ejpam-491	375	9	f	f	PROPN
ejpam-491	375	10	)	)	PUNCT
ejpam-491	375	11	=	=	SYM
ejpam-491	375	12	;	;	PUNCT
ejpam-491	375	13	(	(	PUNCT
ejpam-491	375	14	resp	resp	NOUN
ejpam-491	375	15	.	.	PUNCT
ejpam-491	376	1	[	[	X
ejpam-491	376	2	u	u	X
ejpam-491	376	3	×	×	NOUN
ejpam-491	376	4	v	v	X
ejpam-491	376	5	]	]	X
ejpam-491	376	6	∩g	∩g	PROPN
ejpam-491	376	7	(	(	PUNCT
ejpam-491	376	8	f	f	PROPN
ejpam-491	376	9	)	)	PUNCT
ejpam-491	376	10	=	=	PUNCT
ejpam-491	376	11	;)	;)	X
ejpam-491	376	12	.	.	PROPN
ejpam-491	376	13	remark	remark	PROPN
ejpam-491	376	14	13	13	NUM
ejpam-491	376	15	.	.	PUNCT
ejpam-491	377	1	let	let	VERB
ejpam-491	377	2	(	(	PUNCT
ejpam-491	377	3	x	x	X
ejpam-491	377	4	,	,	PUNCT
ejpam-491	377	5	τ	τ	PROPN
ejpam-491	377	6	)	)	PUNCT
ejpam-491	377	7	(	(	PUNCT
ejpam-491	377	8	resp	resp	NOUN
ejpam-491	377	9	.	.	PUNCT
ejpam-491	378	1	(	(	PUNCT
ejpam-491	378	2	y	y	PROPN
ejpam-491	378	3	,	,	PUNCT
ejpam-491	378	4	σ	σ	PROPN
ejpam-491	378	5	)	)	PUNCT
ejpam-491	378	6	)	)	PUNCT
ejpam-491	378	7	be	be	AUX
ejpam-491	378	8	a	a	DET
ejpam-491	378	9	topological	topological	ADJ
ejpam-491	378	10	space	space	NOUN
ejpam-491	378	11	and	and	CCONJ
ejpam-491	378	12	gmo(x	gmo(x	PROPN
ejpam-491	378	13	)	)	PUNCT
ejpam-491	378	14	(	(	PUNCT
ejpam-491	378	15	resp	resp	NOUN
ejpam-491	378	16	.	.	PUNCT
ejpam-491	379	1	gmo(y	gmo(y	NOUN
ejpam-491	379	2	)	)	PUNCT
ejpam-491	379	3	)	)	PUNCT
ejpam-491	380	1	a	a	DET
ejpam-491	380	2	gm	gm	NOUN
ejpam-491	380	3	-	-	PUNCT
ejpam-491	380	4	structure	structure	NOUN
ejpam-491	380	5	on	on	ADP
ejpam-491	380	6	x	x	PROPN
ejpam-491	380	7	(	(	PUNCT
ejpam-491	380	8	resp	resp	NOUN
ejpam-491	380	9	.	.	PUNCT
ejpam-491	381	1	y	y	PROPN
ejpam-491	381	2	)	)	PUNCT
ejpam-491	381	3	.	.	PUNCT
ejpam-491	382	1	a	a	DET
ejpam-491	382	2	function	function	NOUN
ejpam-491	382	3	f	f	NOUN
ejpam-491	382	4	:	:	PUNCT
ejpam-491	382	5	(	(	PUNCT
ejpam-491	382	6	x	x	X
ejpam-491	382	7	,	,	PUNCT
ejpam-491	382	8	τ	τ	PROPN
ejpam-491	382	9	)	)	PUNCT
ejpam-491	382	10	→	→	SYM
ejpam-491	382	11	(	(	PUNCT
ejpam-491	382	12	y	y	PROPN
ejpam-491	382	13	,	,	PUNCT
ejpam-491	382	14	σ	σ	PROPN
ejpam-491	382	15	)	)	PUNCT
ejpam-491	382	16	is	be	AUX
ejpam-491	382	17	said	say	VERB
ejpam-491	382	18	to	to	PART
ejpam-491	382	19	have	have	VERB
ejpam-491	382	20	a	a	DET
ejpam-491	382	21	strongly	strongly	ADV
ejpam-491	382	22	gm	gm	NOUN
ejpam-491	382	23	-	-	PUNCT
ejpam-491	382	24	closed	closed	ADJ
ejpam-491	382	25	graph	graph	NOUN
ejpam-491	382	26	(	(	PUNCT
ejpam-491	382	27	resp	resp	NOUN
ejpam-491	382	28	.	.	PUNCT
ejpam-491	383	1	gm	gm	ADJ
ejpam-491	383	2	-	-	PUNCT
ejpam-491	383	3	closed	closed	ADJ
ejpam-491	383	4	graph	graph	NOUN
ejpam-491	383	5	)	)	PUNCT
ejpam-491	383	6	if	if	SCONJ
ejpam-491	383	7	for	for	ADP
ejpam-491	383	8	each	each	DET
ejpam-491	383	9	(	(	PUNCT
ejpam-491	383	10	x	x	PROPN
ejpam-491	383	11	,	,	PUNCT
ejpam-491	383	12	y	y	PROPN
ejpam-491	383	13	)	)	PUNCT
ejpam-491	383	14	∈	∈	PROPN
ejpam-491	383	15	(	(	PUNCT
ejpam-491	383	16	x	x	SYM
ejpam-491	383	17	×	×	PROPN
ejpam-491	383	18	y	y	PROPN
ejpam-491	383	19	)	)	PUNCT
ejpam-491	383	20	−	−	PROPN
ejpam-491	384	1	g	g	PROPN
ejpam-491	384	2	(	(	PUNCT
ejpam-491	384	3	f	f	PROPN
ejpam-491	384	4	)	)	PUNCT
ejpam-491	384	5	,	,	PUNCT
ejpam-491	384	6	there	there	PRON
ejpam-491	384	7	exist	exist	VERB
ejpam-491	384	8	u	u	PROPN
ejpam-491	384	9	∈	∈	PROPN
ejpam-491	384	10	gmo(x	gmo(x	PROPN
ejpam-491	384	11	)	)	PUNCT
ejpam-491	384	12	containing	contain	VERB
ejpam-491	384	13	x	x	PROPN
ejpam-491	384	14	and	and	CCONJ
ejpam-491	384	15	v	v	ADP
ejpam-491	384	16	∈	∈	NOUN
ejpam-491	384	17	gmo(y	gmo(y	NOUN
ejpam-491	384	18	)	)	PUNCT
ejpam-491	384	19	containing	contain	VERB
ejpam-491	384	20	y	y	PRON
ejpam-491	384	21	such	such	ADJ
ejpam-491	384	22	that	that	SCONJ
ejpam-491	385	1	[	[	X
ejpam-491	385	2	u	u	X
ejpam-491	385	3	×mclg(v	×mclg(v	PUNCT
ejpam-491	385	4	)	)	PUNCT
ejpam-491	385	5	]	]	SYM
ejpam-491	385	6	∩g	∩g	PROPN
ejpam-491	385	7	(	(	PUNCT
ejpam-491	385	8	f	f	PROPN
ejpam-491	385	9	)	)	PUNCT
ejpam-491	385	10	=	=	SYM
ejpam-491	385	11	;	;	PUNCT
ejpam-491	385	12	(	(	PUNCT
ejpam-491	385	13	resp	resp	NOUN
ejpam-491	385	14	.	.	PUNCT
ejpam-491	386	1	[	[	X
ejpam-491	386	2	u	u	X
ejpam-491	386	3	×	×	NOUN
ejpam-491	386	4	v	v	X
ejpam-491	386	5	]	]	X
ejpam-491	386	6	∩g	∩g	PROPN
ejpam-491	386	7	(	(	PUNCT
ejpam-491	386	8	f	f	PROPN
ejpam-491	386	9	)	)	PUNCT
ejpam-491	386	10	=	=	PUNCT
ejpam-491	387	1	;)	;)	PUNCT
ejpam-491	387	2	.	.	PUNCT
ejpam-491	388	1	lemma	lemma	PROPN
ejpam-491	388	2	7	7	NUM
ejpam-491	388	3	.	.	PUNCT
ejpam-491	388	4	(	(	PUNCT
ejpam-491	388	5	popa	popa	NOUN
ejpam-491	388	6	and	and	CCONJ
ejpam-491	388	7	noiri	noiri	ADV
ejpam-491	388	8	[	[	X
ejpam-491	388	9	29	29	NUM
ejpam-491	388	10	]	]	PUNCT
ejpam-491	388	11	)	)	PUNCT
ejpam-491	388	12	.	.	PUNCT
ejpam-491	389	1	a	a	DET
ejpam-491	389	2	function	function	NOUN
ejpam-491	389	3	f	f	NOUN
ejpam-491	389	4	:	:	PUNCT
ejpam-491	389	5	(	(	PUNCT
ejpam-491	389	6	x	x	X
ejpam-491	389	7	,	,	PUNCT
ejpam-491	389	8	mx	mx	PROPN
ejpam-491	389	9	)	)	PUNCT
ejpam-491	389	10	→	→	SYM
ejpam-491	389	11	(	(	PUNCT
ejpam-491	389	12	y	y	PROPN
ejpam-491	389	13	,	,	PUNCT
ejpam-491	389	14	my	my	PRON
ejpam-491	389	15	)	)	PUNCT
ejpam-491	389	16	is	be	AUX
ejpam-491	389	17	m	m	NOUN
ejpam-491	389	18	-	-	ADJ
ejpam-491	389	19	continuous	continuous	ADJ
ejpam-491	389	20	and	and	CCONJ
ejpam-491	389	21	(	(	PUNCT
ejpam-491	389	22	y	y	PROPN
ejpam-491	389	23	,	,	PUNCT
ejpam-491	389	24	my	my	PRON
ejpam-491	389	25	)	)	PUNCT
ejpam-491	389	26	is	be	AUX
ejpam-491	389	27	m	m	NOUN
ejpam-491	389	28	-	-	NOUN
ejpam-491	389	29	t2	t2	NOUN
ejpam-491	389	30	,	,	PUNCT
ejpam-491	389	31	then	then	ADV
ejpam-491	389	32	f	f	PROPN
ejpam-491	389	33	has	have	VERB
ejpam-491	389	34	a	a	DET
ejpam-491	389	35	strongly	strongly	ADV
ejpam-491	389	36	m	m	ADJ
ejpam-491	389	37	-	-	PUNCT
ejpam-491	389	38	closed	closed	ADJ
ejpam-491	389	39	graph	graph	NOUN
ejpam-491	389	40	.	.	PUNCT
ejpam-491	390	1	t.	t.	PROPN
ejpam-491	390	2	noiri	noiri	PROPN
ejpam-491	390	3	and	and	CCONJ
ejpam-491	390	4	v.	v.	ADP
ejpam-491	390	5	popa	popa	NOUN
ejpam-491	390	6	/	/	SYM
ejpam-491	390	7	eur	eur	PROPN
ejpam-491	390	8	.	.	PUNCT
ejpam-491	391	1	j.	j.	PROPN
ejpam-491	391	2	pure	pure	PROPN
ejpam-491	391	3	appl	appl	PROPN
ejpam-491	391	4	.	.	PROPN
ejpam-491	391	5	math	math	PROPN
ejpam-491	391	6	,	,	PUNCT
ejpam-491	391	7	2	2	NUM
ejpam-491	391	8	(	(	PUNCT
ejpam-491	391	9	2009	2009	NUM
ejpam-491	391	10	)	)	PUNCT
ejpam-491	391	11	,	,	PUNCT
ejpam-491	391	12	(	(	PUNCT
ejpam-491	391	13	473	473	NUM
ejpam-491	391	14	-	-	NUM
ejpam-491	391	15	493	493	NUM
ejpam-491	391	16	)	)	PUNCT
ejpam-491	391	17	487	487	NUM
ejpam-491	391	18	theorem	theorem	VERB
ejpam-491	391	19	10	10	NUM
ejpam-491	391	20	.	.	PUNCT
ejpam-491	392	1	let	let	VERB
ejpam-491	392	2	(	(	PUNCT
ejpam-491	392	3	x	x	X
ejpam-491	392	4	,	,	PUNCT
ejpam-491	392	5	τ	τ	PROPN
ejpam-491	392	6	)	)	PUNCT
ejpam-491	392	7	(	(	PUNCT
ejpam-491	392	8	resp	resp	NOUN
ejpam-491	392	9	.	.	PUNCT
ejpam-491	393	1	(	(	PUNCT
ejpam-491	393	2	y	y	PROPN
ejpam-491	393	3	,	,	PUNCT
ejpam-491	393	4	σ	σ	PROPN
ejpam-491	393	5	)	)	PUNCT
ejpam-491	393	6	)	)	PUNCT
ejpam-491	393	7	be	be	AUX
ejpam-491	393	8	a	a	DET
ejpam-491	393	9	topological	topological	ADJ
ejpam-491	393	10	space	space	NOUN
ejpam-491	393	11	and	and	CCONJ
ejpam-491	393	12	gmo(x	gmo(x	PROPN
ejpam-491	393	13	)	)	PUNCT
ejpam-491	393	14	(	(	PUNCT
ejpam-491	393	15	resp	resp	NOUN
ejpam-491	393	16	.	.	PUNCT
ejpam-491	394	1	gmo(y	gmo(y	NOUN
ejpam-491	394	2	)	)	PUNCT
ejpam-491	394	3	)	)	PUNCT
ejpam-491	395	1	a	a	DET
ejpam-491	395	2	gm	gm	NOUN
ejpam-491	395	3	-	-	PUNCT
ejpam-491	395	4	structure	structure	NOUN
ejpam-491	395	5	on	on	ADP
ejpam-491	395	6	x	x	PROPN
ejpam-491	395	7	(	(	PUNCT
ejpam-491	395	8	resp	resp	NOUN
ejpam-491	395	9	.	.	PUNCT
ejpam-491	396	1	y	y	PROPN
ejpam-491	396	2	)	)	PUNCT
ejpam-491	396	3	.	.	PUNCT
ejpam-491	397	1	if	if	SCONJ
ejpam-491	397	2	a	a	DET
ejpam-491	397	3	function	function	NOUN
ejpam-491	397	4	f	f	NOUN
ejpam-491	397	5	:	:	PUNCT
ejpam-491	397	6	(	(	PUNCT
ejpam-491	397	7	x	x	X
ejpam-491	397	8	,	,	PUNCT
ejpam-491	397	9	τ	τ	PROPN
ejpam-491	397	10	)	)	PUNCT
ejpam-491	397	11	→	→	SYM
ejpam-491	397	12	(	(	PUNCT
ejpam-491	397	13	y	y	PROPN
ejpam-491	397	14	,	,	PUNCT
ejpam-491	397	15	σ	σ	PROPN
ejpam-491	397	16	)	)	PUNCT
ejpam-491	397	17	is	be	AUX
ejpam-491	397	18	gmcontinuous	gmcontinuous	ADJ
ejpam-491	397	19	and	and	CCONJ
ejpam-491	397	20	(	(	PUNCT
ejpam-491	397	21	y	y	PROPN
ejpam-491	397	22	,	,	PUNCT
ejpam-491	397	23	σ	σ	PROPN
ejpam-491	397	24	)	)	PUNCT
ejpam-491	397	25	is	be	AUX
ejpam-491	397	26	gm	gm	PROPN
ejpam-491	397	27	-	-	PUNCT
ejpam-491	397	28	t2	t2	NOUN
ejpam-491	397	29	,	,	PUNCT
ejpam-491	397	30	then	then	ADV
ejpam-491	397	31	f	f	PROPN
ejpam-491	397	32	has	have	VERB
ejpam-491	397	33	a	a	DET
ejpam-491	397	34	strongly	strongly	ADV
ejpam-491	397	35	gm	gm	NOUN
ejpam-491	397	36	-	-	PUNCT
ejpam-491	397	37	closed	closed	ADJ
ejpam-491	397	38	graph	graph	NOUN
ejpam-491	397	39	.	.	PUNCT
ejpam-491	398	1	proof	proof	NOUN
ejpam-491	398	2	.	.	PUNCT
ejpam-491	399	1	the	the	DET
ejpam-491	399	2	proof	proof	NOUN
ejpam-491	399	3	follows	follow	VERB
ejpam-491	399	4	from	from	ADP
ejpam-491	399	5	definition	definition	NOUN
ejpam-491	399	6	22	22	NUM
ejpam-491	399	7	,	,	PUNCT
ejpam-491	399	8	remark	remark	VERB
ejpam-491	399	9	13	13	NUM
ejpam-491	399	10	and	and	CCONJ
ejpam-491	399	11	lemma	lemma	PROPN
ejpam-491	399	12	7	7	X
ejpam-491	399	13	.	.	PUNCT
ejpam-491	399	14	corollary	corollary	ADJ
ejpam-491	399	15	6	6	NUM
ejpam-491	399	16	.	.	PUNCT
ejpam-491	400	1	if	if	SCONJ
ejpam-491	400	2	a	a	DET
ejpam-491	400	3	function	function	NOUN
ejpam-491	400	4	f	f	NOUN
ejpam-491	400	5	:	:	PUNCT
ejpam-491	400	6	(	(	PUNCT
ejpam-491	400	7	x	x	X
ejpam-491	400	8	,	,	PUNCT
ejpam-491	400	9	τ)→	τ)→	PROPN
ejpam-491	400	10	(	(	PUNCT
ejpam-491	400	11	y	y	PROPN
ejpam-491	400	12	,	,	PUNCT
ejpam-491	400	13	σ	σ	PROPN
ejpam-491	400	14	)	)	PUNCT
ejpam-491	400	15	is	be	AUX
ejpam-491	400	16	gm	gm	NOUN
ejpam-491	400	17	-	-	PUNCT
ejpam-491	400	18	irresolute	irresolute	ADJ
ejpam-491	400	19	and	and	CCONJ
ejpam-491	400	20	(	(	PUNCT
ejpam-491	400	21	y	y	PROPN
ejpam-491	400	22	,	,	PUNCT
ejpam-491	400	23	σ	σ	PROPN
ejpam-491	400	24	)	)	PUNCT
ejpam-491	400	25	is	be	AUX
ejpam-491	400	26	gm	gm	PROPN
ejpam-491	400	27	-	-	PUNCT
ejpam-491	400	28	t2	t2	NOUN
ejpam-491	400	29	,	,	PUNCT
ejpam-491	400	30	then	then	ADV
ejpam-491	400	31	f	f	PROPN
ejpam-491	400	32	has	have	VERB
ejpam-491	400	33	a	a	DET
ejpam-491	400	34	strongly	strongly	ADV
ejpam-491	400	35	gm	gm	NOUN
ejpam-491	400	36	-	-	PUNCT
ejpam-491	400	37	closed	closed	ADJ
ejpam-491	400	38	graph	graph	NOUN
ejpam-491	400	39	.	.	PUNCT
ejpam-491	401	1	remark	remark	PROPN
ejpam-491	401	2	14	14	NUM
ejpam-491	401	3	.	.	PUNCT
ejpam-491	402	1	if	if	SCONJ
ejpam-491	402	2	(	(	PUNCT
ejpam-491	402	3	y	y	PROPN
ejpam-491	402	4	,	,	PUNCT
ejpam-491	402	5	σ	σ	PROPN
ejpam-491	402	6	)	)	PUNCT
ejpam-491	402	7	is	be	AUX
ejpam-491	402	8	g	g	NOUN
ejpam-491	402	9	-	-	PUNCT
ejpam-491	402	10	t2	t2	NOUN
ejpam-491	402	11	(	(	PUNCT
ejpam-491	402	12	resp	resp	NOUN
ejpam-491	402	13	.	.	PUNCT
ejpam-491	403	1	gs	gs	NOUN
ejpam-491	403	2	-	-	PUNCT
ejpam-491	403	3	t2	t2	NOUN
ejpam-491	403	4	,	,	PUNCT
ejpam-491	403	5	gp	gp	NOUN
ejpam-491	403	6	-	-	NOUN
ejpam-491	403	7	t2	t2	NOUN
ejpam-491	403	8	,	,	PUNCT
ejpam-491	403	9	αg	αg	NOUN
ejpam-491	403	10	-	-	PUNCT
ejpam-491	403	11	t2	t2	NOUN
ejpam-491	403	12	,	,	PUNCT
ejpam-491	403	13	g	g	PROPN
ejpam-491	403	14	b	b	PROPN
ejpam-491	403	15	-	-	PUNCT
ejpam-491	403	16	t2	t2	NOUN
ejpam-491	403	17	,	,	PUNCT
ejpam-491	403	18	gsp	gsp	NOUN
ejpam-491	403	19	-	-	PUNCT
ejpam-491	403	20	t2	t2	NOUN
ejpam-491	403	21	)	)	PUNCT
ejpam-491	403	22	and	and	CCONJ
ejpam-491	403	23	f	f	X
ejpam-491	403	24	:	:	PUNCT
ejpam-491	403	25	(	(	PUNCT
ejpam-491	403	26	x	x	X
ejpam-491	403	27	,	,	PUNCT
ejpam-491	403	28	τ	τ	PROPN
ejpam-491	403	29	)	)	PUNCT
ejpam-491	403	30	→	→	SYM
ejpam-491	403	31	(	(	PUNCT
ejpam-491	403	32	y	y	PROPN
ejpam-491	403	33	,	,	PUNCT
ejpam-491	403	34	σ	σ	PROPN
ejpam-491	403	35	)	)	PUNCT
ejpam-491	403	36	is	be	AUX
ejpam-491	403	37	a	a	DET
ejpam-491	403	38	g	g	NOUN
ejpam-491	403	39	-	-	PUNCT
ejpam-491	403	40	irresolute	irresolute	ADJ
ejpam-491	403	41	(	(	PUNCT
ejpam-491	403	42	resp	resp	NOUN
ejpam-491	403	43	.	.	PUNCT
ejpam-491	404	1	gs	gs	NOUN
ejpam-491	404	2	-	-	PUNCT
ejpam-491	404	3	irresolute	irresolute	ADJ
ejpam-491	404	4	,	,	PUNCT
ejpam-491	404	5	gp	gp	NOUN
ejpam-491	404	6	-	-	PUNCT
ejpam-491	404	7	irresolute	irresolute	ADJ
ejpam-491	404	8	,	,	PUNCT
ejpam-491	404	9	αg	αg	NOUN
ejpam-491	404	10	-	-	PUNCT
ejpam-491	404	11	irresolute	irresolute	ADJ
ejpam-491	404	12	,	,	PUNCT
ejpam-491	404	13	g	g	PROPN
ejpam-491	404	14	b	b	NOUN
ejpam-491	404	15	-	-	PUNCT
ejpam-491	404	16	irresolute	irresolute	ADJ
ejpam-491	404	17	,	,	PUNCT
ejpam-491	404	18	gsp	gsp	NOUN
ejpam-491	404	19	-	-	PUNCT
ejpam-491	404	20	irresolute	irresolute	NOUN
ejpam-491	404	21	)	)	PUNCT
ejpam-491	404	22	function	function	NOUN
ejpam-491	405	1	,	,	PUNCT
ejpam-491	405	2	then	then	ADV
ejpam-491	405	3	g	g	PROPN
ejpam-491	405	4	(	(	PUNCT
ejpam-491	405	5	f	f	PROPN
ejpam-491	405	6	)	)	PUNCT
ejpam-491	405	7	is	be	AUX
ejpam-491	405	8	strongly	strongly	ADV
ejpam-491	405	9	g	g	NOUN
ejpam-491	405	10	-	-	PUNCT
ejpam-491	405	11	closed	closed	ADJ
ejpam-491	405	12	(	(	PUNCT
ejpam-491	405	13	resp	resp	NOUN
ejpam-491	405	14	.	.	PUNCT
ejpam-491	406	1	strongly	strongly	ADV
ejpam-491	406	2	gs	gs	NOUN
ejpam-491	406	3	-	-	PUNCT
ejpam-491	406	4	closed	closed	ADJ
ejpam-491	406	5	,	,	PUNCT
ejpam-491	406	6	strongly	strongly	ADV
ejpam-491	406	7	gp	gp	NOUN
ejpam-491	406	8	-	-	PUNCT
ejpam-491	406	9	closed	closed	ADJ
ejpam-491	406	10	,	,	PUNCT
ejpam-491	406	11	strongly	strongly	ADV
ejpam-491	406	12	αg	αg	NOUN
ejpam-491	406	13	-	-	PUNCT
ejpam-491	406	14	closed	closed	ADJ
ejpam-491	406	15	,	,	PUNCT
ejpam-491	406	16	strongly	strongly	ADV
ejpam-491	406	17	g	g	PROPN
ejpam-491	406	18	b	b	ADV
ejpam-491	406	19	-	-	PUNCT
ejpam-491	406	20	closed	closed	ADJ
ejpam-491	406	21	,	,	PUNCT
ejpam-491	406	22	strongly	strongly	ADV
ejpam-491	406	23	gspclosed	gspclosed	ADJ
ejpam-491	406	24	)	)	PUNCT
ejpam-491	406	25	.	.	PUNCT
ejpam-491	407	1	lemma	lemma	PROPN
ejpam-491	407	2	8	8	NUM
ejpam-491	407	3	.	.	PUNCT
ejpam-491	408	1	(	(	PUNCT
ejpam-491	408	2	popa	popa	NOUN
ejpam-491	408	3	and	and	CCONJ
ejpam-491	408	4	noiri	noiri	ADV
ejpam-491	409	1	[	[	X
ejpam-491	409	2	29	29	NUM
ejpam-491	409	3	]	]	PUNCT
ejpam-491	409	4	)	)	PUNCT
ejpam-491	409	5	.	.	PUNCT
ejpam-491	410	1	if	if	SCONJ
ejpam-491	410	2	f	f	PROPN
ejpam-491	410	3	:	:	PUNCT
ejpam-491	410	4	(	(	PUNCT
ejpam-491	410	5	x	x	X
ejpam-491	410	6	,	,	PUNCT
ejpam-491	410	7	mx	mx	PROPN
ejpam-491	410	8	)	)	PUNCT
ejpam-491	410	9	→	→	SYM
ejpam-491	410	10	(	(	PUNCT
ejpam-491	410	11	y	y	PROPN
ejpam-491	410	12	,	,	PUNCT
ejpam-491	410	13	my	my	INTJ
ejpam-491	410	14	)	)	PUNCT
ejpam-491	410	15	is	be	AUX
ejpam-491	410	16	a	a	DET
ejpam-491	410	17	surjective	surjective	ADJ
ejpam-491	410	18	function	function	NOUN
ejpam-491	410	19	with	with	ADP
ejpam-491	410	20	a	a	DET
ejpam-491	410	21	strongly	strongly	ADV
ejpam-491	410	22	m	m	ADJ
ejpam-491	410	23	-	-	PUNCT
ejpam-491	410	24	closed	closed	ADJ
ejpam-491	410	25	graph	graph	NOUN
ejpam-491	410	26	,	,	PUNCT
ejpam-491	410	27	then	then	ADV
ejpam-491	410	28	(	(	PUNCT
ejpam-491	410	29	y	y	NOUN
ejpam-491	410	30	,	,	PUNCT
ejpam-491	410	31	my	my	PRON
ejpam-491	410	32	)	)	PUNCT
ejpam-491	410	33	is	be	AUX
ejpam-491	410	34	m	m	NOUN
ejpam-491	410	35	-	-	NOUN
ejpam-491	410	36	t2	t2	NOUN
ejpam-491	410	37	.	.	PUNCT
ejpam-491	411	1	theorem	theorem	NOUN
ejpam-491	411	2	11	11	NUM
ejpam-491	411	3	.	.	PUNCT
ejpam-491	412	1	let	let	VERB
ejpam-491	412	2	(	(	PUNCT
ejpam-491	412	3	x	x	X
ejpam-491	412	4	,	,	PUNCT
ejpam-491	412	5	τ	τ	PROPN
ejpam-491	412	6	)	)	PUNCT
ejpam-491	412	7	(	(	PUNCT
ejpam-491	412	8	resp	resp	NOUN
ejpam-491	412	9	.	.	PUNCT
ejpam-491	413	1	(	(	PUNCT
ejpam-491	413	2	y	y	PROPN
ejpam-491	413	3	,	,	PUNCT
ejpam-491	413	4	σ	σ	PROPN
ejpam-491	413	5	)	)	PUNCT
ejpam-491	413	6	)	)	PUNCT
ejpam-491	413	7	be	be	AUX
ejpam-491	413	8	a	a	DET
ejpam-491	413	9	topological	topological	ADJ
ejpam-491	413	10	space	space	NOUN
ejpam-491	413	11	and	and	CCONJ
ejpam-491	413	12	gmo(x	gmo(x	PROPN
ejpam-491	413	13	)	)	PUNCT
ejpam-491	413	14	(	(	PUNCT
ejpam-491	413	15	resp	resp	NOUN
ejpam-491	413	16	.	.	PUNCT
ejpam-491	414	1	gmo(y	gmo(y	NOUN
ejpam-491	414	2	)	)	PUNCT
ejpam-491	414	3	)	)	PUNCT
ejpam-491	415	1	a	a	DET
ejpam-491	415	2	gm	gm	NOUN
ejpam-491	415	3	-	-	PUNCT
ejpam-491	415	4	structure	structure	NOUN
ejpam-491	415	5	on	on	ADP
ejpam-491	415	6	x	x	PROPN
ejpam-491	415	7	(	(	PUNCT
ejpam-491	415	8	resp	resp	NOUN
ejpam-491	415	9	.	.	PUNCT
ejpam-491	416	1	y	y	PROPN
ejpam-491	416	2	)	)	PUNCT
ejpam-491	416	3	.	.	PUNCT
ejpam-491	417	1	if	if	SCONJ
ejpam-491	417	2	f	f	PROPN
ejpam-491	417	3	:	:	PUNCT
ejpam-491	417	4	(	(	PUNCT
ejpam-491	417	5	x	x	X
ejpam-491	417	6	,	,	PUNCT
ejpam-491	417	7	τ)→	τ)→	PROPN
ejpam-491	417	8	(	(	PUNCT
ejpam-491	417	9	y	y	PROPN
ejpam-491	417	10	,	,	PUNCT
ejpam-491	417	11	σ	σ	PROPN
ejpam-491	417	12	)	)	PUNCT
ejpam-491	417	13	is	be	AUX
ejpam-491	417	14	a	a	DET
ejpam-491	417	15	surjective	surjective	ADJ
ejpam-491	417	16	function	function	NOUN
ejpam-491	417	17	with	with	ADP
ejpam-491	417	18	a	a	DET
ejpam-491	417	19	strongly	strongly	ADV
ejpam-491	417	20	gm	gm	NOUN
ejpam-491	417	21	-	-	PUNCT
ejpam-491	417	22	closed	close	VERB
ejpam-491	417	23	graph	graph	NOUN
ejpam-491	417	24	,	,	PUNCT
ejpam-491	417	25	then	then	ADV
ejpam-491	417	26	(	(	PUNCT
ejpam-491	417	27	y	y	PROPN
ejpam-491	417	28	,	,	PUNCT
ejpam-491	417	29	σ	σ	PROPN
ejpam-491	417	30	)	)	PUNCT
ejpam-491	417	31	is	be	AUX
ejpam-491	417	32	gm	gm	PROPN
ejpam-491	417	33	-	-	PUNCT
ejpam-491	417	34	t2	t2	NOUN
ejpam-491	417	35	.	.	PUNCT
ejpam-491	418	1	proof	proof	NOUN
ejpam-491	418	2	.	.	PUNCT
ejpam-491	419	1	the	the	DET
ejpam-491	419	2	proof	proof	NOUN
ejpam-491	419	3	follows	follow	VERB
ejpam-491	419	4	from	from	ADP
ejpam-491	419	5	definition	definition	NOUN
ejpam-491	419	6	22	22	NUM
ejpam-491	419	7	and	and	CCONJ
ejpam-491	419	8	lemma	lemma	PROPN
ejpam-491	419	9	8	8	NUM
ejpam-491	419	10	.	.	PUNCT
ejpam-491	419	11	remark	remark	PROPN
ejpam-491	419	12	15	15	NUM
ejpam-491	419	13	.	.	PUNCT
ejpam-491	420	1	if	if	SCONJ
ejpam-491	420	2	f	f	PROPN
ejpam-491	420	3	:	:	PUNCT
ejpam-491	420	4	(	(	PUNCT
ejpam-491	420	5	x	x	X
ejpam-491	420	6	,	,	PUNCT
ejpam-491	420	7	τ	τ	PROPN
ejpam-491	420	8	)	)	PUNCT
ejpam-491	420	9	→	→	SYM
ejpam-491	420	10	(	(	PUNCT
ejpam-491	420	11	y	y	PROPN
ejpam-491	420	12	,	,	PUNCT
ejpam-491	420	13	σ	σ	PROPN
ejpam-491	420	14	)	)	PUNCT
ejpam-491	420	15	is	be	AUX
ejpam-491	420	16	a	a	DET
ejpam-491	420	17	surjective	surjective	ADJ
ejpam-491	420	18	function	function	NOUN
ejpam-491	420	19	with	with	ADP
ejpam-491	420	20	a	a	DET
ejpam-491	420	21	strongly	strongly	ADV
ejpam-491	420	22	g	g	NOUN
ejpam-491	420	23	-	-	PUNCT
ejpam-491	420	24	closed	closed	ADJ
ejpam-491	420	25	(	(	PUNCT
ejpam-491	420	26	resp	resp	NOUN
ejpam-491	420	27	.	.	PUNCT
ejpam-491	421	1	strongly	strongly	ADV
ejpam-491	421	2	gs	gs	NOUN
ejpam-491	421	3	-	-	PUNCT
ejpam-491	421	4	closed	closed	ADJ
ejpam-491	421	5	,	,	PUNCT
ejpam-491	421	6	strongly	strongly	ADV
ejpam-491	421	7	gp	gp	NOUN
ejpam-491	421	8	-	-	PUNCT
ejpam-491	421	9	closed	closed	ADJ
ejpam-491	421	10	,	,	PUNCT
ejpam-491	421	11	strongly	strongly	ADV
ejpam-491	421	12	αg	αg	NOUN
ejpam-491	421	13	-	-	PUNCT
ejpam-491	421	14	closed	closed	ADJ
ejpam-491	421	15	,	,	PUNCT
ejpam-491	421	16	strongly	strongly	ADV
ejpam-491	421	17	g	g	PROPN
ejpam-491	421	18	b	b	ADV
ejpam-491	421	19	-	-	PUNCT
ejpam-491	421	20	closed	closed	ADJ
ejpam-491	421	21	,	,	PUNCT
ejpam-491	421	22	strongly	strongly	ADV
ejpam-491	421	23	gsp	gsp	VERB
ejpam-491	421	24	-	-	PUNCT
ejpam-491	421	25	closed	close	VERB
ejpam-491	421	26	)	)	PUNCT
ejpam-491	421	27	,	,	PUNCT
ejpam-491	421	28	then	then	ADV
ejpam-491	421	29	y	y	PROPN
ejpam-491	421	30	is	be	AUX
ejpam-491	421	31	g	g	NOUN
ejpam-491	421	32	-	-	PUNCT
ejpam-491	421	33	t2	t2	NOUN
ejpam-491	421	34	(	(	PUNCT
ejpam-491	421	35	resp	resp	NOUN
ejpam-491	421	36	.	.	PUNCT
ejpam-491	422	1	gs	gs	NOUN
ejpam-491	422	2	-	-	PUNCT
ejpam-491	422	3	t2	t2	NOUN
ejpam-491	422	4	,	,	PUNCT
ejpam-491	422	5	gp	gp	NOUN
ejpam-491	422	6	-	-	NOUN
ejpam-491	422	7	t2	t2	NOUN
ejpam-491	422	8	,	,	PUNCT
ejpam-491	422	9	αg	αg	NOUN
ejpam-491	422	10	-	-	PUNCT
ejpam-491	422	11	t2	t2	NOUN
ejpam-491	422	12	,	,	PUNCT
ejpam-491	422	13	g	g	PROPN
ejpam-491	422	14	b	b	PROPN
ejpam-491	422	15	-	-	PUNCT
ejpam-491	422	16	t2	t2	NOUN
ejpam-491	422	17	,	,	PUNCT
ejpam-491	422	18	gsp	gsp	NOUN
ejpam-491	422	19	-	-	PUNCT
ejpam-491	422	20	t2	t2	NOUN
ejpam-491	422	21	)	)	PUNCT
ejpam-491	422	22	.	.	PUNCT
ejpam-491	423	1	lemma	lemma	PROPN
ejpam-491	423	2	9	9	NUM
ejpam-491	423	3	.	.	PUNCT
ejpam-491	424	1	(	(	PUNCT
ejpam-491	424	2	popa	popa	NOUN
ejpam-491	424	3	and	and	CCONJ
ejpam-491	424	4	noiri	noiri	ADV
ejpam-491	425	1	[	[	X
ejpam-491	425	2	29	29	NUM
ejpam-491	425	3	]	]	PUNCT
ejpam-491	425	4	)	)	PUNCT
ejpam-491	425	5	.	.	PUNCT
ejpam-491	426	1	let	let	VERB
ejpam-491	426	2	f	f	NOUN
ejpam-491	426	3	:	:	PUNCT
ejpam-491	426	4	(	(	PUNCT
ejpam-491	426	5	x	x	X
ejpam-491	426	6	,	,	PUNCT
ejpam-491	426	7	mx	mx	PROPN
ejpam-491	426	8	)	)	PUNCT
ejpam-491	426	9	→	→	SYM
ejpam-491	426	10	(	(	PUNCT
ejpam-491	426	11	y	y	PROPN
ejpam-491	426	12	,	,	PUNCT
ejpam-491	426	13	my	my	PRON
ejpam-491	426	14	)	)	PUNCT
ejpam-491	426	15	be	be	AUX
ejpam-491	426	16	a	a	DET
ejpam-491	426	17	function	function	NOUN
ejpam-491	426	18	,	,	PUNCT
ejpam-491	426	19	where	where	SCONJ
ejpam-491	426	20	mx	mx	PROPN
ejpam-491	426	21	has	have	VERB
ejpam-491	426	22	propertyb	propertyb	NOUN
ejpam-491	426	23	.	.	PUNCT
ejpam-491	427	1	if	if	SCONJ
ejpam-491	427	2	f	f	PROPN
ejpam-491	427	3	is	be	AUX
ejpam-491	427	4	an	an	DET
ejpam-491	427	5	m	m	ADJ
ejpam-491	427	6	-	-	ADJ
ejpam-491	427	7	continuous	continuous	ADJ
ejpam-491	427	8	surjection	surjection	NOUN
ejpam-491	427	9	with	with	ADP
ejpam-491	427	10	an	an	DET
ejpam-491	427	11	m	m	NOUN
ejpam-491	427	12	-	-	PUNCT
ejpam-491	427	13	closed	closed	ADJ
ejpam-491	427	14	graph	graph	NOUN
ejpam-491	427	15	,	,	PUNCT
ejpam-491	427	16	then	then	ADV
ejpam-491	427	17	(	(	PUNCT
ejpam-491	427	18	x	x	X
ejpam-491	427	19	,	,	PUNCT
ejpam-491	427	20	mx	mx	PROPN
ejpam-491	427	21	)	)	PUNCT
ejpam-491	427	22	is	be	AUX
ejpam-491	427	23	m	m	NOUN
ejpam-491	427	24	-	-	NOUN
ejpam-491	427	25	t2	t2	NOUN
ejpam-491	427	26	.	.	PUNCT
ejpam-491	428	1	t.	t.	PROPN
ejpam-491	428	2	noiri	noiri	PROPN
ejpam-491	428	3	and	and	CCONJ
ejpam-491	428	4	v.	v.	ADP
ejpam-491	428	5	popa	popa	NOUN
ejpam-491	428	6	/	/	SYM
ejpam-491	428	7	eur	eur	PROPN
ejpam-491	428	8	.	.	PUNCT
ejpam-491	429	1	j.	j.	PROPN
ejpam-491	429	2	pure	pure	PROPN
ejpam-491	429	3	appl	appl	PROPN
ejpam-491	429	4	.	.	PROPN
ejpam-491	429	5	math	math	PROPN
ejpam-491	429	6	,	,	PUNCT
ejpam-491	429	7	2	2	NUM
ejpam-491	429	8	(	(	PUNCT
ejpam-491	429	9	2009	2009	NUM
ejpam-491	429	10	)	)	PUNCT
ejpam-491	429	11	,	,	PUNCT
ejpam-491	429	12	(	(	PUNCT
ejpam-491	429	13	473	473	NUM
ejpam-491	429	14	-	-	NUM
ejpam-491	429	15	493	493	NUM
ejpam-491	429	16	)	)	PUNCT
ejpam-491	429	17	488	488	NUM
ejpam-491	429	18	theorem	theorem	NOUN
ejpam-491	429	19	12	12	NUM
ejpam-491	429	20	.	.	PUNCT
ejpam-491	430	1	let	let	VERB
ejpam-491	430	2	(	(	PUNCT
ejpam-491	430	3	x	x	X
ejpam-491	430	4	,	,	PUNCT
ejpam-491	430	5	τ	τ	PROPN
ejpam-491	430	6	)	)	PUNCT
ejpam-491	430	7	(	(	PUNCT
ejpam-491	430	8	resp	resp	NOUN
ejpam-491	430	9	.	.	PUNCT
ejpam-491	431	1	(	(	PUNCT
ejpam-491	431	2	y	y	PROPN
ejpam-491	431	3	,	,	PUNCT
ejpam-491	431	4	σ	σ	PROPN
ejpam-491	431	5	)	)	PUNCT
ejpam-491	431	6	)	)	PUNCT
ejpam-491	431	7	be	be	AUX
ejpam-491	431	8	a	a	DET
ejpam-491	431	9	topological	topological	ADJ
ejpam-491	431	10	space	space	NOUN
ejpam-491	431	11	and	and	CCONJ
ejpam-491	431	12	gmo(x	gmo(x	PROPN
ejpam-491	431	13	)	)	PUNCT
ejpam-491	431	14	(	(	PUNCT
ejpam-491	431	15	resp	resp	NOUN
ejpam-491	431	16	.	.	PUNCT
ejpam-491	432	1	gmo(y	gmo(y	NOUN
ejpam-491	432	2	)	)	PUNCT
ejpam-491	432	3	)	)	PUNCT
ejpam-491	433	1	a	a	DET
ejpam-491	433	2	gm	gm	NOUN
ejpam-491	433	3	-	-	PUNCT
ejpam-491	433	4	structure	structure	NOUN
ejpam-491	433	5	on	on	ADP
ejpam-491	433	6	x	x	PROPN
ejpam-491	433	7	(	(	PUNCT
ejpam-491	433	8	resp	resp	NOUN
ejpam-491	433	9	.	.	PUNCT
ejpam-491	434	1	y	y	PROPN
ejpam-491	434	2	)	)	PUNCT
ejpam-491	434	3	and	and	CCONJ
ejpam-491	434	4	gmo(x	gmo(x	PROPN
ejpam-491	434	5	)	)	PUNCT
ejpam-491	434	6	a	a	DET
ejpam-491	434	7	gm	gm	NOUN
ejpam-491	434	8	-	-	PUNCT
ejpam-491	434	9	structure	structure	NOUN
ejpam-491	434	10	satisfying	satisfying	NOUN
ejpam-491	434	11	property	property	NOUN
ejpam-491	434	12	b	b	NOUN
ejpam-491	434	13	.	.	PUNCT
ejpam-491	435	1	if	if	SCONJ
ejpam-491	435	2	f	f	PROPN
ejpam-491	435	3	:	:	PUNCT
ejpam-491	435	4	(	(	PUNCT
ejpam-491	435	5	x	x	X
ejpam-491	435	6	,	,	PUNCT
ejpam-491	435	7	τ	τ	PROPN
ejpam-491	435	8	)	)	PUNCT
ejpam-491	435	9	→	→	SYM
ejpam-491	435	10	(	(	PUNCT
ejpam-491	435	11	y	y	PROPN
ejpam-491	435	12	,	,	PUNCT
ejpam-491	435	13	σ	σ	PROPN
ejpam-491	435	14	)	)	PUNCT
ejpam-491	435	15	is	be	AUX
ejpam-491	435	16	a	a	DET
ejpam-491	435	17	gm	gm	ADJ
ejpam-491	435	18	-	-	PUNCT
ejpam-491	435	19	continuous	continuous	ADJ
ejpam-491	435	20	surjection	surjection	NOUN
ejpam-491	435	21	with	with	ADP
ejpam-491	435	22	a	a	DET
ejpam-491	435	23	gm	gm	NOUN
ejpam-491	435	24	-	-	PUNCT
ejpam-491	435	25	closed	closed	ADJ
ejpam-491	435	26	graph	graph	NOUN
ejpam-491	435	27	,	,	PUNCT
ejpam-491	435	28	then	then	ADV
ejpam-491	435	29	x	x	PUNCT
ejpam-491	435	30	is	be	AUX
ejpam-491	435	31	gm	gm	PROPN
ejpam-491	435	32	-	-	PUNCT
ejpam-491	435	33	t2	t2	NOUN
ejpam-491	435	34	.	.	PUNCT
ejpam-491	436	1	proof	proof	NOUN
ejpam-491	436	2	.	.	PUNCT
ejpam-491	437	1	the	the	DET
ejpam-491	437	2	proof	proof	NOUN
ejpam-491	437	3	follows	follow	VERB
ejpam-491	437	4	from	from	ADP
ejpam-491	437	5	definition	definition	NOUN
ejpam-491	437	6	22	22	NUM
ejpam-491	437	7	and	and	CCONJ
ejpam-491	437	8	lemma	lemma	PROPN
ejpam-491	437	9	9	9	NUM
ejpam-491	437	10	.	.	PUNCT
ejpam-491	437	11	corollary	corollary	ADJ
ejpam-491	437	12	7	7	NUM
ejpam-491	437	13	.	.	PUNCT
ejpam-491	438	1	if	if	SCONJ
ejpam-491	438	2	a	a	DET
ejpam-491	438	3	function	function	NOUN
ejpam-491	438	4	f	f	NOUN
ejpam-491	438	5	:	:	PUNCT
ejpam-491	438	6	(	(	PUNCT
ejpam-491	438	7	x	x	X
ejpam-491	438	8	,	,	PUNCT
ejpam-491	438	9	τ	τ	PROPN
ejpam-491	438	10	)	)	PUNCT
ejpam-491	438	11	→	→	SYM
ejpam-491	438	12	(	(	PUNCT
ejpam-491	438	13	y	y	PROPN
ejpam-491	438	14	,	,	PUNCT
ejpam-491	438	15	σ	σ	PROPN
ejpam-491	438	16	)	)	PUNCT
ejpam-491	438	17	is	be	AUX
ejpam-491	438	18	a	a	DET
ejpam-491	438	19	gm	gm	PROPN
ejpam-491	438	20	-	-	PUNCT
ejpam-491	438	21	irresolute	irresolute	ADJ
ejpam-491	438	22	surjection	surjection	NOUN
ejpam-491	438	23	with	with	ADP
ejpam-491	438	24	a	a	DET
ejpam-491	438	25	gmclosed	gmclose	VERB
ejpam-491	438	26	graph	graph	NOUN
ejpam-491	438	27	and	and	CCONJ
ejpam-491	438	28	gmo(x	gmo(x	PROPN
ejpam-491	438	29	)	)	PUNCT
ejpam-491	438	30	has	have	VERB
ejpam-491	438	31	propertyb	propertyb	NOUN
ejpam-491	438	32	,	,	PUNCT
ejpam-491	438	33	then	then	ADV
ejpam-491	438	34	(	(	PUNCT
ejpam-491	438	35	x	x	X
ejpam-491	438	36	,	,	PUNCT
ejpam-491	438	37	τ	τ	X
ejpam-491	438	38	)	)	PUNCT
ejpam-491	438	39	is	be	AUX
ejpam-491	438	40	gm	gm	PROPN
ejpam-491	438	41	-	-	PUNCT
ejpam-491	438	42	t2	t2	NOUN
ejpam-491	438	43	.	.	PUNCT
ejpam-491	439	1	definition	definition	NOUN
ejpam-491	439	2	23	23	NUM
ejpam-491	439	3	.	.	PUNCT
ejpam-491	440	1	let	let	VERB
ejpam-491	440	2	a	a	DET
ejpam-491	440	3	a	a	DET
ejpam-491	440	4	subset	subset	NOUN
ejpam-491	440	5	of	of	ADP
ejpam-491	440	6	an	an	DET
ejpam-491	440	7	m	m	NOUN
ejpam-491	440	8	-	-	NOUN
ejpam-491	440	9	space	space	NOUN
ejpam-491	440	10	(	(	PUNCT
ejpam-491	440	11	x	x	NOUN
ejpam-491	440	12	,	,	PUNCT
ejpam-491	440	13	mx	mx	PROPN
ejpam-491	440	14	)	)	PUNCT
ejpam-491	440	15	.	.	PUNCT
ejpam-491	441	1	a	a	DET
ejpam-491	441	2	point	point	NOUN
ejpam-491	441	3	x	x	X
ejpam-491	441	4	∈	∈	NOUN
ejpam-491	441	5	x	x	PUNCT
ejpam-491	441	6	is	be	AUX
ejpam-491	441	7	called	call	VERB
ejpam-491	441	8	an	an	DET
ejpam-491	441	9	mθ	mθ	NOUN
ejpam-491	441	10	-adherent	-adherent	NOUN
ejpam-491	441	11	point	point	NOUN
ejpam-491	441	12	of	of	ADP
ejpam-491	441	13	a	a	DET
ejpam-491	441	14	[	[	X
ejpam-491	441	15	31	31	NUM
ejpam-491	441	16	]	]	PUNCT
ejpam-491	441	17	if	if	SCONJ
ejpam-491	441	18	mcl(u	mcl(u	PROPN
ejpam-491	441	19	)	)	PUNCT
ejpam-491	441	20	∩	∩	NOUN
ejpam-491	441	21	a	a	DET
ejpam-491	441	22	6=	6=	NOUN
ejpam-491	441	23	;	;	PUNCT
ejpam-491	441	24	for	for	ADP
ejpam-491	441	25	every	every	DET
ejpam-491	441	26	mx	mx	PROPN
ejpam-491	441	27	-open	-open	PROPN
ejpam-491	441	28	set	set	NOUN
ejpam-491	441	29	u	u	NOUN
ejpam-491	441	30	containing	contain	VERB
ejpam-491	441	31	x	x	X
ejpam-491	441	32	.	.	PUNCT
ejpam-491	442	1	the	the	DET
ejpam-491	442	2	set	set	NOUN
ejpam-491	442	3	of	of	ADP
ejpam-491	443	1	all	all	DET
ejpam-491	443	2	mθ	mθ	NOUN
ejpam-491	443	3	-adherent	-adherent	ADJ
ejpam-491	443	4	points	point	NOUN
ejpam-491	443	5	of	of	ADP
ejpam-491	443	6	a	a	PRON
ejpam-491	443	7	is	be	AUX
ejpam-491	443	8	called	call	VERB
ejpam-491	443	9	the	the	DET
ejpam-491	443	10	mθ	mθ	ADJ
ejpam-491	443	11	-closure	-closure	NOUN
ejpam-491	443	12	of	of	ADP
ejpam-491	443	13	a	a	PRON
ejpam-491	443	14	and	and	CCONJ
ejpam-491	443	15	is	be	AUX
ejpam-491	443	16	denoted	denote	VERB
ejpam-491	443	17	by	by	ADP
ejpam-491	443	18	mclθ	mclθ	NOUN
ejpam-491	443	19	(	(	PUNCT
ejpam-491	443	20	a	a	NOUN
ejpam-491	443	21	)	)	PUNCT
ejpam-491	443	22	.	.	PUNCT
ejpam-491	444	1	if	if	SCONJ
ejpam-491	444	2	a	a	DET
ejpam-491	444	3	=	=	NOUN
ejpam-491	444	4	mclθ	mclθ	NOUN
ejpam-491	444	5	(	(	PUNCT
ejpam-491	444	6	a	a	NOUN
ejpam-491	444	7	)	)	PUNCT
ejpam-491	444	8	,	,	PUNCT
ejpam-491	444	9	then	then	ADV
ejpam-491	444	10	a	a	PRON
ejpam-491	444	11	is	be	AUX
ejpam-491	444	12	said	say	VERB
ejpam-491	444	13	to	to	PART
ejpam-491	444	14	be	be	AUX
ejpam-491	444	15	mθ	mθ	ADV
ejpam-491	444	16	-closed	-close	VERB
ejpam-491	444	17	.	.	PUNCT
ejpam-491	445	1	the	the	DET
ejpam-491	445	2	complement	complement	NOUN
ejpam-491	445	3	of	of	ADP
ejpam-491	445	4	a	a	DET
ejpam-491	445	5	mθ	mθ	NOUN
ejpam-491	445	6	-closed	-close	VERB
ejpam-491	445	7	set	set	NOUN
ejpam-491	445	8	is	be	AUX
ejpam-491	445	9	said	say	VERB
ejpam-491	445	10	to	to	PART
ejpam-491	445	11	be	be	AUX
ejpam-491	445	12	mθ	mθ	NOUN
ejpam-491	445	13	-open	-open	NOUN
ejpam-491	445	14	.	.	PUNCT
ejpam-491	446	1	the	the	DET
ejpam-491	446	2	union	union	NOUN
ejpam-491	446	3	of	of	ADP
ejpam-491	446	4	all	all	DET
ejpam-491	446	5	mθ	mθ	NOUN
ejpam-491	446	6	-open	-open	ADJ
ejpam-491	446	7	sets	set	NOUN
ejpam-491	446	8	contained	contain	VERB
ejpam-491	446	9	in	in	ADP
ejpam-491	446	10	a	a	PRON
ejpam-491	446	11	is	be	AUX
ejpam-491	446	12	called	call	VERB
ejpam-491	446	13	the	the	DET
ejpam-491	446	14	mθ	mθ	ADJ
ejpam-491	446	15	-interior	-interior	NOUN
ejpam-491	446	16	of	of	ADP
ejpam-491	446	17	a	a	PRON
ejpam-491	446	18	and	and	CCONJ
ejpam-491	446	19	is	be	AUX
ejpam-491	446	20	denoted	denote	VERB
ejpam-491	446	21	by	by	ADP
ejpam-491	446	22	mintθ	mintθ	NOUN
ejpam-491	446	23	(	(	PUNCT
ejpam-491	446	24	a	a	NOUN
ejpam-491	446	25	)	)	PUNCT
ejpam-491	446	26	.	.	PUNCT
ejpam-491	447	1	remark	remark	PROPN
ejpam-491	447	2	16	16	NUM
ejpam-491	447	3	.	.	PUNCT
ejpam-491	448	1	let	let	VERB
ejpam-491	448	2	a	a	DET
ejpam-491	448	3	be	be	AUX
ejpam-491	448	4	a	a	DET
ejpam-491	448	5	subset	subset	NOUN
ejpam-491	448	6	of	of	ADP
ejpam-491	448	7	a	a	DET
ejpam-491	448	8	topological	topological	ADJ
ejpam-491	448	9	space	space	NOUN
ejpam-491	448	10	(	(	PUNCT
ejpam-491	448	11	x	x	X
ejpam-491	448	12	,	,	PUNCT
ejpam-491	448	13	τ	τ	PROPN
ejpam-491	448	14	)	)	PUNCT
ejpam-491	448	15	and	and	CCONJ
ejpam-491	448	16	mx	mx	X
ejpam-491	448	17	an	an	DET
ejpam-491	448	18	m	m	NOUN
ejpam-491	448	19	-	-	NOUN
ejpam-491	448	20	structure	structure	NOUN
ejpam-491	448	21	on	on	ADP
ejpam-491	448	22	x	x	X
ejpam-491	448	23	.	.	PUNCT
ejpam-491	449	1	if	if	SCONJ
ejpam-491	449	2	mx	mx	PROPN
ejpam-491	449	3	=	=	SYM
ejpam-491	449	4	τ	τ	PROPN
ejpam-491	449	5	(	(	PUNCT
ejpam-491	449	6	resp	resp	PROPN
ejpam-491	449	7	.	.	PUNCT
ejpam-491	449	8	so(x	so(x	PROPN
ejpam-491	449	9	)	)	PUNCT
ejpam-491	449	10	,	,	PUNCT
ejpam-491	449	11	po(x	po(x	NUM
ejpam-491	449	12	)	)	PUNCT
ejpam-491	449	13	)	)	PUNCT
ejpam-491	449	14	,	,	PUNCT
ejpam-491	449	15	then	then	ADV
ejpam-491	449	16	mclθ(a	mclθ(a	NOUN
ejpam-491	449	17	)	)	PUNCT
ejpam-491	449	18	=	=	SYM
ejpam-491	449	19	clθ	clθ	NOUN
ejpam-491	449	20	(	(	PUNCT
ejpam-491	449	21	a	a	NOUN
ejpam-491	449	22	)	)	PUNCT
ejpam-491	450	1	[	[	X
ejpam-491	450	2	33	33	NUM
ejpam-491	450	3	]	]	PUNCT
ejpam-491	450	4	(	(	PUNCT
ejpam-491	450	5	resp	resp	NOUN
ejpam-491	450	6	.	.	PUNCT
ejpam-491	451	1	sclθ(a	sclθ(a	NOUN
ejpam-491	451	2	)	)	PUNCT
ejpam-491	452	1	[	[	X
ejpam-491	452	2	13	13	NUM
ejpam-491	452	3	]	]	PUNCT
ejpam-491	452	4	,	,	PUNCT
ejpam-491	452	5	pclθ	pclθ	NOUN
ejpam-491	452	6	(	(	PUNCT
ejpam-491	452	7	a	a	X
ejpam-491	452	8	)	)	PUNCT
ejpam-491	453	1	[	[	X
ejpam-491	453	2	28	28	NUM
ejpam-491	453	3	]	]	NUM
ejpam-491	453	4	)	)	PUNCT
ejpam-491	453	5	.	.	PUNCT
ejpam-491	454	1	lemma	lemma	PROPN
ejpam-491	454	2	10	10	NUM
ejpam-491	454	3	.	.	PUNCT
ejpam-491	455	1	(	(	PUNCT
ejpam-491	455	2	popa	popa	NOUN
ejpam-491	455	3	and	and	CCONJ
ejpam-491	455	4	noiri	noiri	ADV
ejpam-491	456	1	[	[	X
ejpam-491	456	2	31	31	NUM
ejpam-491	456	3	]	]	PUNCT
ejpam-491	456	4	)	)	PUNCT
ejpam-491	456	5	.	.	PUNCT
ejpam-491	457	1	let	let	VERB
ejpam-491	457	2	a	a	DET
ejpam-491	457	3	be	be	AUX
ejpam-491	457	4	a	a	DET
ejpam-491	457	5	subset	subset	NOUN
ejpam-491	457	6	of	of	ADP
ejpam-491	457	7	an	an	DET
ejpam-491	457	8	m	m	NOUN
ejpam-491	457	9	-	-	NOUN
ejpam-491	457	10	space	space	NOUN
ejpam-491	457	11	(	(	PUNCT
ejpam-491	457	12	x	x	NOUN
ejpam-491	457	13	,	,	PUNCT
ejpam-491	457	14	mx	mx	PROPN
ejpam-491	457	15	)	)	PUNCT
ejpam-491	457	16	.	.	PUNCT
ejpam-491	458	1	then	then	ADV
ejpam-491	458	2	the	the	DET
ejpam-491	458	3	following	follow	VERB
ejpam-491	458	4	properties	property	NOUN
ejpam-491	458	5	hold	hold	VERB
ejpam-491	458	6	:	:	PUNCT
ejpam-491	458	7	(	(	PUNCT
ejpam-491	458	8	1	1	X
ejpam-491	458	9	)	)	PUNCT
ejpam-491	458	10	if	if	SCONJ
ejpam-491	458	11	a	a	PRON
ejpam-491	458	12	is	be	AUX
ejpam-491	458	13	mx	mx	NOUN
ejpam-491	458	14	-open	-open	NOUN
ejpam-491	458	15	in	in	ADP
ejpam-491	458	16	x	x	NOUN
ejpam-491	458	17	,	,	PUNCT
ejpam-491	458	18	then	then	ADV
ejpam-491	458	19	mclθ	mclθ	INTJ
ejpam-491	458	20	(	(	PUNCT
ejpam-491	458	21	a	a	NOUN
ejpam-491	458	22	)	)	PUNCT
ejpam-491	458	23	=	=	SYM
ejpam-491	458	24	mcl(a	mcl(a	NOUN
ejpam-491	458	25	)	)	PUNCT
ejpam-491	458	26	,	,	PUNCT
ejpam-491	458	27	(	(	PUNCT
ejpam-491	458	28	2	2	X
ejpam-491	458	29	)	)	PUNCT
ejpam-491	458	30	if	if	SCONJ
ejpam-491	458	31	mx	mx	PROPN
ejpam-491	458	32	has	have	VERB
ejpam-491	458	33	propertyb	propertyb	NOUN
ejpam-491	458	34	,	,	PUNCT
ejpam-491	458	35	then	then	ADV
ejpam-491	458	36	mclθ(a	mclθ(a	NOUN
ejpam-491	458	37	)	)	PUNCT
ejpam-491	458	38	is	be	AUX
ejpam-491	458	39	mx	mx	NOUN
ejpam-491	458	40	-closed	-close	VERB
ejpam-491	458	41	in	in	ADP
ejpam-491	458	42	x	x	PUNCT
ejpam-491	458	43	for	for	ADP
ejpam-491	458	44	every	every	DET
ejpam-491	458	45	subset	subset	NOUN
ejpam-491	458	46	a	a	PRON
ejpam-491	458	47	of	of	ADP
ejpam-491	458	48	x.	x.	NOUN
ejpam-491	458	49	definition	definition	NOUN
ejpam-491	458	50	24	24	NUM
ejpam-491	458	51	.	.	PUNCT
ejpam-491	459	1	an	an	DET
ejpam-491	459	2	m	m	NOUN
ejpam-491	459	3	-	-	NOUN
ejpam-491	459	4	space	space	NOUN
ejpam-491	459	5	(	(	PUNCT
ejpam-491	459	6	x	x	X
ejpam-491	459	7	,	,	PUNCT
ejpam-491	459	8	mx	mx	PROPN
ejpam-491	459	9	)	)	PUNCT
ejpam-491	459	10	is	be	AUX
ejpam-491	459	11	said	say	VERB
ejpam-491	459	12	to	to	PART
ejpam-491	459	13	be	be	AUX
ejpam-491	459	14	m	m	NOUN
ejpam-491	459	15	-	-	ADJ
ejpam-491	459	16	regular	regular	ADJ
ejpam-491	459	17	[	[	X
ejpam-491	459	18	31	31	NUM
ejpam-491	459	19	]	]	X
ejpam-491	459	20	if	if	SCONJ
ejpam-491	459	21	for	for	ADP
ejpam-491	459	22	each	each	DET
ejpam-491	459	23	mx	mx	PROPN
ejpam-491	459	24	-closed	-close	VERB
ejpam-491	460	1	set	set	VERB
ejpam-491	460	2	f	f	PROPN
ejpam-491	460	3	of	of	ADP
ejpam-491	460	4	x	x	PUNCT
ejpam-491	460	5	and	and	CCONJ
ejpam-491	460	6	each	each	DET
ejpam-491	460	7	point	point	NOUN
ejpam-491	460	8	x	x	X
ejpam-491	460	9	/∈	/∈	PUNCT
ejpam-491	461	1	f	f	PROPN
ejpam-491	461	2	,	,	PUNCT
ejpam-491	461	3	there	there	PRON
ejpam-491	461	4	exist	exist	VERB
ejpam-491	461	5	disjoint	disjoint	NOUN
ejpam-491	461	6	mx	mx	PROPN
ejpam-491	461	7	-open	-open	PROPN
ejpam-491	461	8	sets	set	VERB
ejpam-491	461	9	u	u	NOUN
ejpam-491	461	10	and	and	CCONJ
ejpam-491	461	11	v	v	ADP
ejpam-491	461	12	such	such	ADJ
ejpam-491	461	13	that	that	SCONJ
ejpam-491	461	14	x	x	SYM
ejpam-491	461	15	∈	∈	PROPN
ejpam-491	461	16	u	u	NOUN
ejpam-491	461	17	and	and	CCONJ
ejpam-491	461	18	f	f	PROPN
ejpam-491	461	19	⊂	⊂	PROPN
ejpam-491	461	20	v	v	PROPN
ejpam-491	461	21	.	.	PUNCT
ejpam-491	462	1	lemma	lemma	PROPN
ejpam-491	462	2	11	11	NUM
ejpam-491	462	3	.	.	PUNCT
ejpam-491	463	1	(	(	PUNCT
ejpam-491	463	2	popa	popa	NOUN
ejpam-491	463	3	and	and	CCONJ
ejpam-491	463	4	noiri	noiri	ADV
ejpam-491	464	1	[	[	X
ejpam-491	464	2	31	31	NUM
ejpam-491	464	3	]	]	PUNCT
ejpam-491	464	4	)	)	PUNCT
ejpam-491	464	5	.	.	PUNCT
ejpam-491	465	1	let	let	AUX
ejpam-491	465	2	(	(	PUNCT
ejpam-491	465	3	x	x	X
ejpam-491	465	4	,	,	PUNCT
ejpam-491	465	5	mx	mx	PROPN
ejpam-491	465	6	)	)	PUNCT
ejpam-491	465	7	be	be	AUX
ejpam-491	465	8	an	an	DET
ejpam-491	465	9	m	m	NOUN
ejpam-491	465	10	-	-	ADJ
ejpam-491	465	11	regular	regular	ADJ
ejpam-491	465	12	m	m	NOUN
ejpam-491	465	13	-	-	NOUN
ejpam-491	465	14	space	space	NOUN
ejpam-491	465	15	.	.	PUNCT
ejpam-491	466	1	then	then	ADV
ejpam-491	466	2	the	the	DET
ejpam-491	466	3	following	follow	VERB
ejpam-491	466	4	properties	property	NOUN
ejpam-491	466	5	hold	hold	VERB
ejpam-491	466	6	:	:	PUNCT
ejpam-491	466	7	t.	t.	PROPN
ejpam-491	466	8	noiri	noiri	PROPN
ejpam-491	466	9	and	and	CCONJ
ejpam-491	466	10	v.	v.	ADP
ejpam-491	466	11	popa	popa	NOUN
ejpam-491	466	12	/	/	SYM
ejpam-491	466	13	eur	eur	PROPN
ejpam-491	466	14	.	.	PUNCT
ejpam-491	467	1	j.	j.	PROPN
ejpam-491	467	2	pure	pure	PROPN
ejpam-491	467	3	appl	appl	PROPN
ejpam-491	467	4	.	.	PROPN
ejpam-491	467	5	math	math	PROPN
ejpam-491	467	6	,	,	PUNCT
ejpam-491	467	7	2	2	NUM
ejpam-491	467	8	(	(	PUNCT
ejpam-491	467	9	2009	2009	NUM
ejpam-491	467	10	)	)	PUNCT
ejpam-491	467	11	,	,	PUNCT
ejpam-491	467	12	(	(	PUNCT
ejpam-491	467	13	473	473	NUM
ejpam-491	467	14	-	-	NUM
ejpam-491	467	15	493	493	NUM
ejpam-491	467	16	)	)	PUNCT
ejpam-491	467	17	489	489	NUM
ejpam-491	467	18	(	(	PUNCT
ejpam-491	467	19	1	1	NUM
ejpam-491	467	20	)	)	PUNCT
ejpam-491	467	21	mclθ	mclθ	NOUN
ejpam-491	467	22	(	(	PUNCT
ejpam-491	467	23	a	a	NOUN
ejpam-491	467	24	)	)	PUNCT
ejpam-491	467	25	=	=	SYM
ejpam-491	467	26	mcl(a	mcl(a	X
ejpam-491	467	27	)	)	PUNCT
ejpam-491	467	28	for	for	ADP
ejpam-491	467	29	every	every	DET
ejpam-491	467	30	subset	subset	NOUN
ejpam-491	467	31	a	a	PRON
ejpam-491	467	32	of	of	ADP
ejpam-491	467	33	x	x	PRON
ejpam-491	467	34	,	,	PUNCT
ejpam-491	467	35	(	(	PUNCT
ejpam-491	467	36	2	2	X
ejpam-491	467	37	)	)	PUNCT
ejpam-491	467	38	every	every	DET
ejpam-491	467	39	mx	mx	PROPN
ejpam-491	467	40	-open	-open	PROPN
ejpam-491	467	41	set	set	NOUN
ejpam-491	467	42	is	be	AUX
ejpam-491	467	43	mθ	mθ	NOUN
ejpam-491	467	44	-open	-open	NOUN
ejpam-491	467	45	.	.	PUNCT
ejpam-491	468	1	theorem	theorem	NOUN
ejpam-491	468	2	13	13	NUM
ejpam-491	468	3	.	.	PUNCT
ejpam-491	469	1	let	let	AUX
ejpam-491	469	2	(	(	PUNCT
ejpam-491	469	3	y	y	NOUN
ejpam-491	469	4	,	,	PUNCT
ejpam-491	469	5	my	my	PRON
ejpam-491	469	6	)	)	PUNCT
ejpam-491	469	7	be	be	AUX
ejpam-491	469	8	an	an	DET
ejpam-491	469	9	m	m	NOUN
ejpam-491	469	10	-	-	ADJ
ejpam-491	469	11	regular	regular	ADJ
ejpam-491	469	12	m	m	NOUN
ejpam-491	469	13	-	-	NOUN
ejpam-491	469	14	space	space	NOUN
ejpam-491	469	15	and	and	CCONJ
ejpam-491	469	16	my	my	PRON
ejpam-491	469	17	have	have	VERB
ejpam-491	469	18	property	property	NOUN
ejpam-491	469	19	b	b	PROPN
ejpam-491	469	20	.	.	PUNCT
ejpam-491	470	1	for	for	ADP
ejpam-491	470	2	a	a	DET
ejpam-491	470	3	function	function	NOUN
ejpam-491	470	4	f	f	NOUN
ejpam-491	470	5	:	:	PUNCT
ejpam-491	470	6	(	(	PUNCT
ejpam-491	470	7	x	x	X
ejpam-491	470	8	,	,	PUNCT
ejpam-491	470	9	mx	mx	PROPN
ejpam-491	470	10	)	)	PUNCT
ejpam-491	470	11	→	→	SYM
ejpam-491	470	12	(	(	PUNCT
ejpam-491	470	13	y	y	PROPN
ejpam-491	470	14	,	,	PUNCT
ejpam-491	470	15	my	my	INTJ
ejpam-491	470	16	)	)	PUNCT
ejpam-491	470	17	,	,	PUNCT
ejpam-491	470	18	the	the	DET
ejpam-491	470	19	following	follow	VERB
ejpam-491	470	20	properties	property	NOUN
ejpam-491	470	21	are	be	AUX
ejpam-491	470	22	equivalent	equivalent	ADJ
ejpam-491	470	23	:	:	PUNCT
ejpam-491	470	24	(	(	PUNCT
ejpam-491	470	25	1	1	X
ejpam-491	470	26	)	)	PUNCT
ejpam-491	470	27	f	f	PROPN
ejpam-491	470	28	is	be	AUX
ejpam-491	470	29	m	m	NOUN
ejpam-491	470	30	-	-	ADJ
ejpam-491	470	31	continuous	continuous	ADJ
ejpam-491	470	32	;	;	PUNCT
ejpam-491	470	33	(	(	PUNCT
ejpam-491	470	34	2	2	X
ejpam-491	470	35	)	)	PUNCT
ejpam-491	470	36	f	f	NOUN
ejpam-491	470	37	−1(mclθ(b	−1(mclθ(b	NUM
ejpam-491	470	38	)	)	PUNCT
ejpam-491	470	39	)	)	PUNCT
ejpam-491	471	1	=	=	X
ejpam-491	471	2	mcl	mcl	PROPN
ejpam-491	471	3	(	(	PUNCT
ejpam-491	471	4	f	f	PROPN
ejpam-491	471	5	−1(mclθ	−1(mclθ	PROPN
ejpam-491	471	6	(	(	PUNCT
ejpam-491	471	7	b	b	NOUN
ejpam-491	471	8	)	)	PUNCT
ejpam-491	471	9	)	)	PUNCT
ejpam-491	471	10	)	)	PUNCT
ejpam-491	471	11	for	for	ADP
ejpam-491	471	12	every	every	DET
ejpam-491	471	13	subset	subset	NOUN
ejpam-491	471	14	b	b	PROPN
ejpam-491	471	15	of	of	ADP
ejpam-491	471	16	y	y	PROPN
ejpam-491	471	17	;	;	PUNCT
ejpam-491	471	18	(	(	PUNCT
ejpam-491	471	19	3	3	X
ejpam-491	471	20	)	)	PUNCT
ejpam-491	471	21	f	f	NOUN
ejpam-491	471	22	−1(k	−1(k	NOUN
ejpam-491	471	23	)	)	PUNCT
ejpam-491	471	24	=	=	SYM
ejpam-491	471	25	mcl	mcl	PROPN
ejpam-491	471	26	(	(	PUNCT
ejpam-491	471	27	f	f	PROPN
ejpam-491	471	28	−1(k	−1(k	NOUN
ejpam-491	471	29	)	)	PUNCT
ejpam-491	471	30	)	)	PUNCT
ejpam-491	471	31	for	for	ADP
ejpam-491	471	32	every	every	DET
ejpam-491	471	33	mθ	mθ	NOUN
ejpam-491	471	34	-closed	-close	VERB
ejpam-491	471	35	set	set	NOUN
ejpam-491	471	36	k	k	PROPN
ejpam-491	471	37	of	of	ADP
ejpam-491	471	38	y	y	PROPN
ejpam-491	471	39	;	;	PUNCT
ejpam-491	471	40	(	(	PUNCT
ejpam-491	471	41	4	4	X
ejpam-491	471	42	)	)	PUNCT
ejpam-491	471	43	f	f	PROPN
ejpam-491	471	44	−1(v	−1(v	PROPN
ejpam-491	471	45	)	)	PUNCT
ejpam-491	472	1	=	=	NOUN
ejpam-491	472	2	mint	mint	NOUN
ejpam-491	472	3	(	(	PUNCT
ejpam-491	472	4	f	f	PROPN
ejpam-491	472	5	−1(v	−1(v	PROPN
ejpam-491	472	6	)	)	PUNCT
ejpam-491	472	7	)	)	PUNCT
ejpam-491	473	1	for	for	ADP
ejpam-491	473	2	every	every	DET
ejpam-491	473	3	mθ	mθ	NOUN
ejpam-491	473	4	-open	-open	NOUN
ejpam-491	473	5	set	set	VERB
ejpam-491	473	6	v	v	NOUN
ejpam-491	473	7	of	of	ADP
ejpam-491	473	8	y.	y.	PROPN
ejpam-491	473	9	proof	proof	NOUN
ejpam-491	473	10	.	.	PUNCT
ejpam-491	474	1	(	(	PUNCT
ejpam-491	474	2	1	1	X
ejpam-491	474	3	)	)	PUNCT
ejpam-491	474	4	⇒	⇒	NOUN
ejpam-491	474	5	(	(	PUNCT
ejpam-491	474	6	2	2	NUM
ejpam-491	474	7	):	):	PUNCT
ejpam-491	474	8	let	let	VERB
ejpam-491	474	9	b	b	X
ejpam-491	474	10	be	be	AUX
ejpam-491	474	11	any	any	DET
ejpam-491	474	12	subset	subset	NOUN
ejpam-491	474	13	of	of	ADP
ejpam-491	474	14	y	y	PROPN
ejpam-491	474	15	.	.	PUNCT
ejpam-491	475	1	then	then	ADV
ejpam-491	475	2	,	,	PUNCT
ejpam-491	475	3	by	by	ADP
ejpam-491	475	4	lemma	lemma	PROPN
ejpam-491	475	5	10	10	NUM
ejpam-491	475	6	mclθ(b	mclθ(b	PROPN
ejpam-491	475	7	)	)	PUNCT
ejpam-491	475	8	is	be	AUX
ejpam-491	475	9	my	my	PRON
ejpam-491	475	10	closed	closed	NOUN
ejpam-491	475	11	in	in	ADP
ejpam-491	475	12	y	y	PROPN
ejpam-491	475	13	.	.	PUNCT
ejpam-491	476	1	by	by	ADP
ejpam-491	476	2	theorem	theorem	NOUN
ejpam-491	476	3	3	3	NUM
ejpam-491	476	4	,	,	PUNCT
ejpam-491	476	5	we	we	PRON
ejpam-491	476	6	obtain	obtain	VERB
ejpam-491	476	7	f	f	PROPN
ejpam-491	476	8	−1(mclθ	−1(mclθ	PROPN
ejpam-491	476	9	(	(	PUNCT
ejpam-491	476	10	b	b	NOUN
ejpam-491	476	11	)	)	PUNCT
ejpam-491	476	12	)	)	PUNCT
ejpam-491	477	1	=	=	SYM
ejpam-491	477	2	mcl	mcl	PROPN
ejpam-491	477	3	(	(	PUNCT
ejpam-491	477	4	f	f	PROPN
ejpam-491	477	5	−1(mclθ(b	−1(mclθ(b	NUM
ejpam-491	477	6	)	)	PUNCT
ejpam-491	477	7	)	)	PUNCT
ejpam-491	477	8	)	)	PUNCT
ejpam-491	477	9	.	.	PUNCT
ejpam-491	478	1	(	(	PUNCT
ejpam-491	478	2	2	2	X
ejpam-491	478	3	)	)	PUNCT
ejpam-491	478	4	⇒	⇒	NOUN
ejpam-491	478	5	(	(	PUNCT
ejpam-491	478	6	3	3	NUM
ejpam-491	478	7	):	):	PUNCT
ejpam-491	478	8	let	let	VERB
ejpam-491	478	9	k	k	PRON
ejpam-491	478	10	be	be	AUX
ejpam-491	478	11	an	an	DET
ejpam-491	478	12	mθ	mθ	NOUN
ejpam-491	478	13	-closed	-close	VERB
ejpam-491	478	14	set	set	NOUN
ejpam-491	478	15	of	of	ADP
ejpam-491	478	16	y	y	PROPN
ejpam-491	478	17	.	.	PUNCT
ejpam-491	479	1	then	then	ADV
ejpam-491	479	2	mclθ	mclθ	INTJ
ejpam-491	479	3	(	(	PUNCT
ejpam-491	479	4	k	k	NOUN
ejpam-491	479	5	)	)	PUNCT
ejpam-491	479	6	=	=	SYM
ejpam-491	480	1	k	k	PROPN
ejpam-491	480	2	.	.	PUNCT
ejpam-491	481	1	then	then	ADV
ejpam-491	481	2	by	by	ADP
ejpam-491	481	3	(	(	PUNCT
ejpam-491	481	4	2	2	X
ejpam-491	481	5	)	)	PUNCT
ejpam-491	481	6	we	we	PRON
ejpam-491	481	7	obtain	obtain	VERB
ejpam-491	481	8	f	f	PROPN
ejpam-491	481	9	−1(k	−1(k	NOUN
ejpam-491	481	10	)	)	PUNCT
ejpam-491	481	11	=	=	SYM
ejpam-491	481	12	mcl	mcl	PROPN
ejpam-491	481	13	(	(	PUNCT
ejpam-491	481	14	f	f	PROPN
ejpam-491	481	15	−1(k	−1(k	NOUN
ejpam-491	481	16	)	)	PUNCT
ejpam-491	481	17	)	)	PUNCT
ejpam-491	481	18	.	.	PUNCT
ejpam-491	482	1	(	(	PUNCT
ejpam-491	482	2	3	3	X
ejpam-491	482	3	)	)	PUNCT
ejpam-491	482	4	⇒	⇒	NOUN
ejpam-491	482	5	(	(	PUNCT
ejpam-491	482	6	4	4	NUM
ejpam-491	482	7	):	):	PUNCT
ejpam-491	482	8	let	let	VERB
ejpam-491	482	9	v	v	PART
ejpam-491	482	10	be	be	AUX
ejpam-491	482	11	an	an	DET
ejpam-491	482	12	mθ	mθ	NOUN
ejpam-491	482	13	-open	-open	ADJ
ejpam-491	482	14	set	set	NOUN
ejpam-491	482	15	of	of	ADP
ejpam-491	482	16	y	y	PROPN
ejpam-491	482	17	.	.	PUNCT
ejpam-491	483	1	then	then	ADV
ejpam-491	483	2	y	y	PROPN
ejpam-491	483	3	−	−	PROPN
ejpam-491	483	4	v	v	PROPN
ejpam-491	483	5	is	be	AUX
ejpam-491	483	6	mθ	mθ	NOUN
ejpam-491	483	7	-closed	-close	VERB
ejpam-491	483	8	and	and	CCONJ
ejpam-491	483	9	f	f	NOUN
ejpam-491	483	10	−1(y	−1(y	PRON
ejpam-491	483	11	−	−	PROPN
ejpam-491	483	12	v	v	NOUN
ejpam-491	483	13	)	)	PUNCT
ejpam-491	483	14	=	=	SYM
ejpam-491	483	15	mcl	mcl	PROPN
ejpam-491	483	16	(	(	PUNCT
ejpam-491	483	17	f	f	PROPN
ejpam-491	483	18	−1(y	−1(y	PROPN
ejpam-491	483	19	−v	−v	NOUN
ejpam-491	483	20	)	)	PUNCT
ejpam-491	483	21	)	)	PUNCT
ejpam-491	483	22	.	.	PUNCT
ejpam-491	484	1	therefore	therefore	ADV
ejpam-491	484	2	,	,	PUNCT
ejpam-491	484	3	x	x	PUNCT
ejpam-491	484	4	−	−	PROPN
ejpam-491	484	5	f	f	PROPN
ejpam-491	484	6	−1(v	−1(v	PROPN
ejpam-491	484	7	)	)	PUNCT
ejpam-491	485	1	=	=	PUNCT
ejpam-491	485	2	x	x	SYM
ejpam-491	485	3	−mint	−mint	PROPN
ejpam-491	485	4	(	(	PUNCT
ejpam-491	485	5	f	f	PROPN
ejpam-491	485	6	−1(v	−1(v	PROPN
ejpam-491	485	7	)	)	PUNCT
ejpam-491	485	8	)	)	PUNCT
ejpam-491	485	9	.	.	PUNCT
ejpam-491	486	1	hence	hence	ADV
ejpam-491	486	2	we	we	PRON
ejpam-491	486	3	obtain	obtain	VERB
ejpam-491	486	4	f	f	PROPN
ejpam-491	486	5	−1(v	−1(v	NOUN
ejpam-491	486	6	)	)	PUNCT
ejpam-491	487	1	=	=	NOUN
ejpam-491	487	2	mint	mint	NOUN
ejpam-491	487	3	(	(	PUNCT
ejpam-491	487	4	f	f	PROPN
ejpam-491	487	5	−1(v	−1(v	PROPN
ejpam-491	487	6	)	)	PUNCT
ejpam-491	487	7	)	)	PUNCT
ejpam-491	487	8	.	.	PUNCT
ejpam-491	488	1	(	(	PUNCT
ejpam-491	488	2	4	4	X
ejpam-491	488	3	)	)	PUNCT
ejpam-491	488	4	⇒	⇒	NOUN
ejpam-491	488	5	(	(	PUNCT
ejpam-491	488	6	1	1	NUM
ejpam-491	488	7	):	):	PUNCT
ejpam-491	488	8	let	let	VERB
ejpam-491	488	9	v	v	PART
ejpam-491	488	10	be	be	AUX
ejpam-491	488	11	any	any	DET
ejpam-491	488	12	my	my	PRON
ejpam-491	488	13	-open	-open	ADJ
ejpam-491	488	14	set	set	NOUN
ejpam-491	488	15	of	of	ADP
ejpam-491	488	16	y	y	PROPN
ejpam-491	488	17	.	.	PUNCT
ejpam-491	489	1	since	since	SCONJ
ejpam-491	489	2	y	y	PROPN
ejpam-491	489	3	is	be	AUX
ejpam-491	489	4	m	m	NOUN
ejpam-491	489	5	-	-	ADJ
ejpam-491	489	6	regular	regular	ADJ
ejpam-491	489	7	,	,	PUNCT
ejpam-491	489	8	by	by	ADP
ejpam-491	489	9	lemma	lemma	PROPN
ejpam-491	489	10	11	11	NUM
ejpam-491	489	11	v	v	NOUN
ejpam-491	489	12	is	be	AUX
ejpam-491	489	13	mθ	mθ	NOUN
ejpam-491	489	14	-open	-open	ADJ
ejpam-491	489	15	and	and	CCONJ
ejpam-491	489	16	by	by	ADP
ejpam-491	489	17	(	(	PUNCT
ejpam-491	489	18	4	4	X
ejpam-491	489	19	)	)	PUNCT
ejpam-491	489	20	we	we	PRON
ejpam-491	489	21	have	have	VERB
ejpam-491	489	22	f	f	PROPN
ejpam-491	489	23	−1(v	−1(v	PROPN
ejpam-491	489	24	)	)	PUNCT
ejpam-491	490	1	=	=	SYM
ejpam-491	490	2	mint	mint	PROPN
ejpam-491	490	3	(	(	PUNCT
ejpam-491	490	4	f	f	PROPN
ejpam-491	490	5	−1(v	−1(v	PROPN
ejpam-491	490	6	)	)	PUNCT
ejpam-491	490	7	)	)	PUNCT
ejpam-491	490	8	.	.	PUNCT
ejpam-491	491	1	by	by	ADP
ejpam-491	491	2	theorem	theorem	NOUN
ejpam-491	491	3	1	1	NUM
ejpam-491	491	4	,	,	PUNCT
ejpam-491	491	5	f	f	PROPN
ejpam-491	491	6	is	be	AUX
ejpam-491	491	7	m	m	PRON
ejpam-491	491	8	-continuous	-continuous	ADJ
ejpam-491	491	9	.	.	PUNCT
ejpam-491	492	1	theorem	theorem	NOUN
ejpam-491	492	2	14	14	NUM
ejpam-491	492	3	.	.	PUNCT
ejpam-491	493	1	let	let	VERB
ejpam-491	493	2	(	(	PUNCT
ejpam-491	493	3	y	y	NOUN
ejpam-491	493	4	,	,	PUNCT
ejpam-491	493	5	my	my	PRON
ejpam-491	493	6	)	)	PUNCT
ejpam-491	493	7	be	be	AUX
ejpam-491	493	8	m	m	NOUN
ejpam-491	493	9	-	-	ADJ
ejpam-491	493	10	regular	regular	ADJ
ejpam-491	493	11	and	and	CCONJ
ejpam-491	493	12	let	let	VERB
ejpam-491	493	13	mx	mx	PROPN
ejpam-491	493	14	and	and	CCONJ
ejpam-491	493	15	my	my	PRON
ejpam-491	493	16	have	have	VERB
ejpam-491	493	17	property	property	NOUN
ejpam-491	493	18	b	b	PROPN
ejpam-491	493	19	.	.	PUNCT
ejpam-491	494	1	for	for	ADP
ejpam-491	494	2	a	a	DET
ejpam-491	494	3	function	function	NOUN
ejpam-491	494	4	f	f	NOUN
ejpam-491	494	5	:	:	PUNCT
ejpam-491	494	6	(	(	PUNCT
ejpam-491	494	7	x	x	X
ejpam-491	494	8	,	,	PUNCT
ejpam-491	494	9	mx	mx	PROPN
ejpam-491	494	10	)	)	PUNCT
ejpam-491	494	11	→	→	SYM
ejpam-491	494	12	(	(	PUNCT
ejpam-491	494	13	y	y	PROPN
ejpam-491	494	14	,	,	PUNCT
ejpam-491	494	15	my	my	INTJ
ejpam-491	494	16	)	)	PUNCT
ejpam-491	494	17	,	,	PUNCT
ejpam-491	494	18	the	the	DET
ejpam-491	494	19	following	follow	VERB
ejpam-491	494	20	properties	property	NOUN
ejpam-491	494	21	are	be	AUX
ejpam-491	494	22	equivalent	equivalent	ADJ
ejpam-491	494	23	:	:	PUNCT
ejpam-491	494	24	(	(	PUNCT
ejpam-491	494	25	1	1	X
ejpam-491	494	26	)	)	PUNCT
ejpam-491	494	27	f	f	PROPN
ejpam-491	494	28	is	be	AUX
ejpam-491	494	29	m	m	NOUN
ejpam-491	494	30	-	-	ADJ
ejpam-491	494	31	continuous	continuous	ADJ
ejpam-491	494	32	;	;	PUNCT
ejpam-491	494	33	(	(	PUNCT
ejpam-491	494	34	2	2	X
ejpam-491	494	35	)	)	PUNCT
ejpam-491	494	36	f	f	NOUN
ejpam-491	494	37	−1(mclθ(b	−1(mclθ(b	NUM
ejpam-491	494	38	)	)	PUNCT
ejpam-491	494	39	)	)	PUNCT
ejpam-491	494	40	is	be	AUX
ejpam-491	494	41	mx	mx	PROPN
ejpam-491	494	42	-closed	-close	VERB
ejpam-491	494	43	for	for	ADP
ejpam-491	494	44	every	every	DET
ejpam-491	494	45	subset	subset	NOUN
ejpam-491	494	46	b	b	PROPN
ejpam-491	494	47	of	of	ADP
ejpam-491	494	48	y	y	PROPN
ejpam-491	494	49	;	;	PUNCT
ejpam-491	494	50	(	(	PUNCT
ejpam-491	494	51	3	3	X
ejpam-491	494	52	)	)	PUNCT
ejpam-491	494	53	f	f	NOUN
ejpam-491	494	54	−1(k	−1(k	NOUN
ejpam-491	494	55	)	)	PUNCT
ejpam-491	494	56	is	be	AUX
ejpam-491	494	57	mx	mx	NOUN
ejpam-491	494	58	-closed	-close	VERB
ejpam-491	494	59	for	for	ADP
ejpam-491	494	60	every	every	DET
ejpam-491	494	61	mθ	mθ	NOUN
ejpam-491	494	62	-closed	-close	VERB
ejpam-491	494	63	set	set	NOUN
ejpam-491	494	64	k	k	PROPN
ejpam-491	494	65	of	of	ADP
ejpam-491	494	66	y	y	PROPN
ejpam-491	494	67	;	;	PUNCT
ejpam-491	494	68	(	(	PUNCT
ejpam-491	494	69	4	4	X
ejpam-491	494	70	)	)	PUNCT
ejpam-491	494	71	f	f	PROPN
ejpam-491	494	72	−1(v	−1(v	PROPN
ejpam-491	494	73	)	)	PUNCT
ejpam-491	494	74	is	be	AUX
ejpam-491	494	75	mx	mx	NOUN
ejpam-491	494	76	-open	-open	NOUN
ejpam-491	494	77	for	for	ADP
ejpam-491	494	78	every	every	DET
ejpam-491	494	79	mθ	mθ	NOUN
ejpam-491	494	80	-open	-open	NOUN
ejpam-491	494	81	set	set	VERB
ejpam-491	494	82	v	v	NOUN
ejpam-491	494	83	of	of	ADP
ejpam-491	494	84	y.	y.	PROPN
ejpam-491	494	85	proof	proof	NOUN
ejpam-491	494	86	.	.	PUNCT
ejpam-491	495	1	the	the	DET
ejpam-491	495	2	proof	proof	NOUN
ejpam-491	495	3	follows	follow	VERB
ejpam-491	495	4	from	from	ADP
ejpam-491	495	5	theorem	theorem	ADJ
ejpam-491	495	6	13	13	NUM
ejpam-491	495	7	and	and	CCONJ
ejpam-491	495	8	lemma	lemma	PROPN
ejpam-491	495	9	3	3	X
ejpam-491	495	10	.	.	PUNCT
ejpam-491	495	11	references	reference	NOUN
ejpam-491	495	12	490	490	NUM
ejpam-491	495	13	let	let	VERB
ejpam-491	495	14	(	(	PUNCT
ejpam-491	495	15	x	x	X
ejpam-491	495	16	,	,	PUNCT
ejpam-491	495	17	τ	τ	X
ejpam-491	495	18	)	)	PUNCT
ejpam-491	495	19	be	be	VERB
ejpam-491	495	20	a	a	DET
ejpam-491	495	21	topological	topological	ADJ
ejpam-491	495	22	space	space	NOUN
ejpam-491	495	23	and	and	CCONJ
ejpam-491	495	24	gmo(x	gmo(x	PROPN
ejpam-491	495	25	)	)	PUNCT
ejpam-491	495	26	a	a	DET
ejpam-491	495	27	gm	gm	NOUN
ejpam-491	495	28	-	-	PUNCT
ejpam-491	495	29	structure	structure	NOUN
ejpam-491	495	30	on	on	ADP
ejpam-491	495	31	x	x	X
ejpam-491	495	32	.	.	PUNCT
ejpam-491	496	1	for	for	ADP
ejpam-491	496	2	a	a	DET
ejpam-491	496	3	subset	subset	NOUN
ejpam-491	496	4	a	a	PRON
ejpam-491	496	5	of	of	ADP
ejpam-491	496	6	x	x	SYM
ejpam-491	496	7	,	,	PUNCT
ejpam-491	496	8	we	we	PRON
ejpam-491	496	9	denote	denote	VERB
ejpam-491	496	10	the	the	DET
ejpam-491	496	11	gm	gm	PROPN
ejpam-491	496	12	-	-	PUNCT
ejpam-491	496	13	θ	θ	NOUN
ejpam-491	496	14	-closure	-closure	NOUN
ejpam-491	496	15	of	of	ADP
ejpam-491	496	16	a	a	PRON
ejpam-491	496	17	by	by	ADP
ejpam-491	496	18	gmclθ(a	gmclθ(a	NOUN
ejpam-491	496	19	)	)	PUNCT
ejpam-491	496	20	.	.	PUNCT
ejpam-491	497	1	if	if	SCONJ
ejpam-491	497	2	a	a	DET
ejpam-491	497	3	=	=	NOUN
ejpam-491	497	4	gmclθ(a	gmclθ(a	NOUN
ejpam-491	497	5	)	)	PUNCT
ejpam-491	497	6	,	,	PUNCT
ejpam-491	497	7	then	then	ADV
ejpam-491	497	8	a	a	PRON
ejpam-491	497	9	is	be	AUX
ejpam-491	497	10	said	say	VERB
ejpam-491	497	11	to	to	PART
ejpam-491	497	12	be	be	AUX
ejpam-491	497	13	gmθ	gmθ	NOUN
ejpam-491	497	14	-closed	-close	VERB
ejpam-491	497	15	.	.	PUNCT
ejpam-491	498	1	the	the	DET
ejpam-491	498	2	complement	complement	NOUN
ejpam-491	498	3	of	of	ADP
ejpam-491	498	4	a	a	DET
ejpam-491	498	5	gmθ	gmθ	NOUN
ejpam-491	498	6	-closed	-close	VERB
ejpam-491	498	7	set	set	NOUN
ejpam-491	498	8	is	be	AUX
ejpam-491	498	9	said	say	VERB
ejpam-491	498	10	to	to	PART
ejpam-491	498	11	be	be	AUX
ejpam-491	498	12	gmθ	gmθ	NOUN
ejpam-491	498	13	-open	-open	ADJ
ejpam-491	498	14	.	.	PUNCT
ejpam-491	499	1	by	by	ADP
ejpam-491	499	2	theorems	theorem	NOUN
ejpam-491	499	3	13	13	NUM
ejpam-491	499	4	and	and	CCONJ
ejpam-491	499	5	14	14	NUM
ejpam-491	499	6	,	,	PUNCT
ejpam-491	499	7	we	we	PRON
ejpam-491	499	8	obtain	obtain	VERB
ejpam-491	499	9	the	the	DET
ejpam-491	499	10	following	follow	VERB
ejpam-491	499	11	theorems	theorem	NOUN
ejpam-491	499	12	:	:	PUNCT
ejpam-491	499	13	theorem	theorem	NOUN
ejpam-491	499	14	15	15	NUM
ejpam-491	499	15	.	.	PUNCT
ejpam-491	500	1	let	let	VERB
ejpam-491	500	2	(	(	PUNCT
ejpam-491	500	3	x	x	X
ejpam-491	500	4	,	,	PUNCT
ejpam-491	500	5	τ	τ	PROPN
ejpam-491	500	6	)	)	PUNCT
ejpam-491	500	7	(	(	PUNCT
ejpam-491	500	8	resp	resp	NOUN
ejpam-491	500	9	.	.	PUNCT
ejpam-491	501	1	(	(	PUNCT
ejpam-491	501	2	y	y	PROPN
ejpam-491	501	3	,	,	PUNCT
ejpam-491	501	4	σ	σ	PROPN
ejpam-491	501	5	)	)	PUNCT
ejpam-491	501	6	)	)	PUNCT
ejpam-491	501	7	be	be	AUX
ejpam-491	501	8	a	a	DET
ejpam-491	501	9	topological	topological	ADJ
ejpam-491	501	10	space	space	NOUN
ejpam-491	501	11	and	and	CCONJ
ejpam-491	501	12	gmo(x	gmo(x	PROPN
ejpam-491	501	13	)	)	PUNCT
ejpam-491	501	14	(	(	PUNCT
ejpam-491	501	15	resp	resp	NOUN
ejpam-491	501	16	.	.	PUNCT
ejpam-491	502	1	gmo(y	gmo(y	NOUN
ejpam-491	502	2	)	)	PUNCT
ejpam-491	502	3	)	)	PUNCT
ejpam-491	503	1	a	a	DET
ejpam-491	503	2	gm	gm	NOUN
ejpam-491	503	3	-	-	PUNCT
ejpam-491	503	4	structure	structure	NOUN
ejpam-491	503	5	on	on	ADP
ejpam-491	503	6	x	x	PROPN
ejpam-491	503	7	(	(	PUNCT
ejpam-491	503	8	resp	resp	NOUN
ejpam-491	503	9	.	.	PUNCT
ejpam-491	504	1	y	y	PROPN
ejpam-491	504	2	)	)	PUNCT
ejpam-491	505	1	and	and	CCONJ
ejpam-491	505	2	let	let	VERB
ejpam-491	505	3	gmo(y	gmo(y	PROPN
ejpam-491	505	4	)	)	PUNCT
ejpam-491	505	5	be	be	AUX
ejpam-491	505	6	gm	gm	NOUN
ejpam-491	505	7	-	-	PUNCT
ejpam-491	505	8	regular	regular	ADJ
ejpam-491	505	9	and	and	CCONJ
ejpam-491	505	10	have	have	VERB
ejpam-491	505	11	propertyb	propertyb	NOUN
ejpam-491	505	12	.	.	PUNCT
ejpam-491	506	1	for	for	ADP
ejpam-491	506	2	a	a	DET
ejpam-491	506	3	function	function	NOUN
ejpam-491	506	4	f	f	NOUN
ejpam-491	506	5	:	:	PUNCT
ejpam-491	506	6	(	(	PUNCT
ejpam-491	506	7	x	x	X
ejpam-491	506	8	,	,	PUNCT
ejpam-491	506	9	τ)→	τ)→	PROPN
ejpam-491	506	10	(	(	PUNCT
ejpam-491	506	11	y	y	PROPN
ejpam-491	506	12	,	,	PUNCT
ejpam-491	506	13	σ	σ	PROPN
ejpam-491	506	14	)	)	PUNCT
ejpam-491	506	15	,	,	PUNCT
ejpam-491	506	16	the	the	DET
ejpam-491	506	17	following	follow	VERB
ejpam-491	506	18	properties	property	NOUN
ejpam-491	506	19	are	be	AUX
ejpam-491	506	20	equivalent	equivalent	ADJ
ejpam-491	506	21	:	:	PUNCT
ejpam-491	506	22	(	(	PUNCT
ejpam-491	506	23	1	1	X
ejpam-491	506	24	)	)	PUNCT
ejpam-491	506	25	f	f	PROPN
ejpam-491	506	26	is	be	AUX
ejpam-491	506	27	gm	gm	NOUN
ejpam-491	506	28	-	-	PUNCT
ejpam-491	506	29	continuous	continuous	ADJ
ejpam-491	506	30	;	;	PUNCT
ejpam-491	506	31	(	(	PUNCT
ejpam-491	506	32	2	2	X
ejpam-491	506	33	)	)	PUNCT
ejpam-491	506	34	f	f	NOUN
ejpam-491	506	35	−1(gmclθ(b	−1(gmclθ(b	NUM
ejpam-491	506	36	)	)	PUNCT
ejpam-491	506	37	)	)	PUNCT
ejpam-491	507	1	=	=	NOUN
ejpam-491	507	2	mclg	mclg	NOUN
ejpam-491	507	3	(	(	PUNCT
ejpam-491	507	4	f	f	PROPN
ejpam-491	507	5	−1(gmclθ(b	−1(gmclθ(b	NUM
ejpam-491	507	6	)	)	PUNCT
ejpam-491	507	7	)	)	PUNCT
ejpam-491	507	8	)	)	PUNCT
ejpam-491	507	9	for	for	ADP
ejpam-491	507	10	every	every	DET
ejpam-491	507	11	subset	subset	NOUN
ejpam-491	507	12	b	b	PROPN
ejpam-491	507	13	of	of	ADP
ejpam-491	507	14	y	y	PROPN
ejpam-491	507	15	;	;	PUNCT
ejpam-491	507	16	(	(	PUNCT
ejpam-491	507	17	3	3	X
ejpam-491	507	18	)	)	PUNCT
ejpam-491	507	19	f	f	NOUN
ejpam-491	507	20	−1(k	−1(k	NOUN
ejpam-491	507	21	)	)	PUNCT
ejpam-491	507	22	=	=	NOUN
ejpam-491	507	23	mclg	mclg	NOUN
ejpam-491	507	24	(	(	PUNCT
ejpam-491	507	25	f	f	NOUN
ejpam-491	507	26	−1(k	−1(k	NOUN
ejpam-491	507	27	)	)	PUNCT
ejpam-491	507	28	)	)	PUNCT
ejpam-491	507	29	for	for	ADP
ejpam-491	507	30	every	every	DET
ejpam-491	507	31	gmθ	gmθ	NOUN
ejpam-491	507	32	-closed	-close	VERB
ejpam-491	507	33	set	set	VERB
ejpam-491	507	34	k	k	PROPN
ejpam-491	507	35	of	of	ADP
ejpam-491	507	36	y	y	PROPN
ejpam-491	507	37	;	;	PUNCT
ejpam-491	507	38	(	(	PUNCT
ejpam-491	507	39	4	4	X
ejpam-491	507	40	)	)	PUNCT
ejpam-491	507	41	f	f	PROPN
ejpam-491	507	42	−1(v	−1(v	NOUN
ejpam-491	507	43	)	)	PUNCT
ejpam-491	508	1	=	=	NOUN
ejpam-491	508	2	mintg	mintg	NOUN
ejpam-491	508	3	(	(	PUNCT
ejpam-491	508	4	f	f	PROPN
ejpam-491	508	5	−1(v	−1(v	PROPN
ejpam-491	508	6	)	)	PUNCT
ejpam-491	508	7	)	)	PUNCT
ejpam-491	509	1	for	for	ADP
ejpam-491	509	2	every	every	DET
ejpam-491	509	3	gmθ	gmθ	NOUN
ejpam-491	509	4	-open	-open	NOUN
ejpam-491	509	5	set	set	VERB
ejpam-491	509	6	v	v	NOUN
ejpam-491	509	7	of	of	ADP
ejpam-491	509	8	y.	y.	PROPN
ejpam-491	509	9	theorem	theorem	VERB
ejpam-491	509	10	16	16	NUM
ejpam-491	509	11	.	.	PUNCT
ejpam-491	510	1	let	let	VERB
ejpam-491	510	2	(	(	PUNCT
ejpam-491	510	3	x	x	X
ejpam-491	510	4	,	,	PUNCT
ejpam-491	510	5	τ	τ	PROPN
ejpam-491	510	6	)	)	PUNCT
ejpam-491	510	7	(	(	PUNCT
ejpam-491	510	8	resp	resp	NOUN
ejpam-491	510	9	.	.	PUNCT
ejpam-491	511	1	(	(	PUNCT
ejpam-491	511	2	y	y	PROPN
ejpam-491	511	3	,	,	PUNCT
ejpam-491	511	4	σ	σ	PROPN
ejpam-491	511	5	)	)	PUNCT
ejpam-491	511	6	)	)	PUNCT
ejpam-491	511	7	be	be	AUX
ejpam-491	511	8	a	a	DET
ejpam-491	511	9	topological	topological	ADJ
ejpam-491	511	10	space	space	NOUN
ejpam-491	511	11	and	and	CCONJ
ejpam-491	511	12	gmo(x	gmo(x	PROPN
ejpam-491	511	13	)	)	PUNCT
ejpam-491	511	14	(	(	PUNCT
ejpam-491	511	15	resp	resp	NOUN
ejpam-491	511	16	.	.	PUNCT
ejpam-491	512	1	gmo(y	gmo(y	NOUN
ejpam-491	512	2	)	)	PUNCT
ejpam-491	512	3	)	)	PUNCT
ejpam-491	513	1	a	a	DET
ejpam-491	513	2	gm	gm	NOUN
ejpam-491	513	3	-	-	PUNCT
ejpam-491	513	4	structure	structure	NOUN
ejpam-491	513	5	on	on	ADP
ejpam-491	513	6	x	x	PROPN
ejpam-491	513	7	(	(	PUNCT
ejpam-491	513	8	resp	resp	NOUN
ejpam-491	513	9	.	.	PUNCT
ejpam-491	514	1	y	y	PROPN
ejpam-491	514	2	)	)	PUNCT
ejpam-491	514	3	,	,	PUNCT
ejpam-491	514	4	where	where	SCONJ
ejpam-491	514	5	gmo(x	gmo(x	PROPN
ejpam-491	514	6	)	)	PUNCT
ejpam-491	514	7	and	and	CCONJ
ejpam-491	514	8	gmo(y	gmo(y	PROPN
ejpam-491	514	9	)	)	PUNCT
ejpam-491	514	10	have	have	VERB
ejpam-491	514	11	property	property	NOUN
ejpam-491	514	12	b	b	NOUN
ejpam-491	514	13	,	,	PUNCT
ejpam-491	514	14	and	and	CCONJ
ejpam-491	514	15	let	let	VERB
ejpam-491	514	16	gmo(y	gmo(y	PROPN
ejpam-491	514	17	)	)	PUNCT
ejpam-491	514	18	be	be	AUX
ejpam-491	514	19	gm	gm	NOUN
ejpam-491	514	20	-	-	PUNCT
ejpam-491	514	21	regular	regular	ADJ
ejpam-491	514	22	.	.	PUNCT
ejpam-491	515	1	for	for	ADP
ejpam-491	515	2	a	a	DET
ejpam-491	515	3	function	function	NOUN
ejpam-491	515	4	f	f	NOUN
ejpam-491	515	5	:	:	PUNCT
ejpam-491	515	6	(	(	PUNCT
ejpam-491	515	7	x	x	X
ejpam-491	515	8	,	,	PUNCT
ejpam-491	515	9	τ	τ	PROPN
ejpam-491	515	10	)	)	PUNCT
ejpam-491	515	11	→	→	SYM
ejpam-491	515	12	(	(	PUNCT
ejpam-491	515	13	y	y	PROPN
ejpam-491	515	14	,	,	PUNCT
ejpam-491	515	15	σ	σ	PROPN
ejpam-491	515	16	)	)	PUNCT
ejpam-491	515	17	,	,	PUNCT
ejpam-491	515	18	the	the	DET
ejpam-491	515	19	following	follow	VERB
ejpam-491	515	20	properties	property	NOUN
ejpam-491	515	21	are	be	AUX
ejpam-491	515	22	equivalent	equivalent	ADJ
ejpam-491	515	23	:	:	PUNCT
ejpam-491	515	24	(	(	PUNCT
ejpam-491	515	25	1	1	X
ejpam-491	515	26	)	)	PUNCT
ejpam-491	515	27	f	f	PROPN
ejpam-491	515	28	is	be	AUX
ejpam-491	515	29	gm	gm	NOUN
ejpam-491	515	30	-	-	PUNCT
ejpam-491	515	31	continuous	continuous	ADJ
ejpam-491	515	32	;	;	PUNCT
ejpam-491	515	33	(	(	PUNCT
ejpam-491	515	34	2	2	X
ejpam-491	515	35	)	)	PUNCT
ejpam-491	515	36	f	f	NOUN
ejpam-491	515	37	−1(gmclθ(b	−1(gmclθ(b	NUM
ejpam-491	515	38	)	)	PUNCT
ejpam-491	515	39	)	)	PUNCT
ejpam-491	515	40	is	be	AUX
ejpam-491	515	41	gm	gm	PROPN
ejpam-491	515	42	-	-	PUNCT
ejpam-491	515	43	closed	closed	ADJ
ejpam-491	515	44	for	for	ADP
ejpam-491	515	45	every	every	DET
ejpam-491	515	46	subset	subset	NOUN
ejpam-491	515	47	b	b	PROPN
ejpam-491	515	48	of	of	ADP
ejpam-491	515	49	y	y	PROPN
ejpam-491	515	50	;	;	PUNCT
ejpam-491	515	51	(	(	PUNCT
ejpam-491	515	52	3	3	X
ejpam-491	515	53	)	)	PUNCT
ejpam-491	515	54	f	f	NOUN
ejpam-491	515	55	−1(k	−1(k	NOUN
ejpam-491	515	56	)	)	PUNCT
ejpam-491	515	57	is	be	AUX
ejpam-491	515	58	gm	gm	PROPN
ejpam-491	515	59	-	-	PUNCT
ejpam-491	515	60	closed	closed	ADJ
ejpam-491	515	61	for	for	SCONJ
ejpam-491	515	62	every	every	DET
ejpam-491	515	63	gmθ	gmθ	NOUN
ejpam-491	515	64	-closed	-close	VERB
ejpam-491	515	65	set	set	VERB
ejpam-491	515	66	k	k	PROPN
ejpam-491	515	67	of	of	ADP
ejpam-491	515	68	y	y	PROPN
ejpam-491	515	69	;	;	PUNCT
ejpam-491	515	70	(	(	PUNCT
ejpam-491	515	71	4	4	X
ejpam-491	515	72	)	)	PUNCT
ejpam-491	515	73	f	f	PROPN
ejpam-491	515	74	−1(v	−1(v	PROPN
ejpam-491	515	75	)	)	PUNCT
ejpam-491	515	76	is	be	AUX
ejpam-491	515	77	gm	gm	NOUN
ejpam-491	515	78	-	-	PUNCT
ejpam-491	515	79	open	open	ADJ
ejpam-491	515	80	for	for	ADP
ejpam-491	515	81	every	every	DET
ejpam-491	515	82	gmθ	gmθ	NOUN
ejpam-491	515	83	-open	-open	NOUN
ejpam-491	515	84	set	set	VERB
ejpam-491	515	85	v	v	NOUN
ejpam-491	515	86	of	of	ADP
ejpam-491	515	87	y.	y.	NOUN
ejpam-491	515	88	references	reference	NOUN
ejpam-491	515	89	[	[	X
ejpam-491	515	90	1	1	NUM
ejpam-491	515	91	]	]	PUNCT
ejpam-491	515	92	m.	m.	NOUN
ejpam-491	515	93	e.	e.	PROPN
ejpam-491	515	94	abd	abd	PROPN
ejpam-491	515	95	el	el	PROPN
ejpam-491	515	96	-	-	PROPN
ejpam-491	515	97	monsef	monsef	PROPN
ejpam-491	515	98	,	,	PUNCT
ejpam-491	515	99	s.	s.	PROPN
ejpam-491	515	100	n.	n.	PROPN
ejpam-491	515	101	el	el	PROPN
ejpam-491	515	102	-	-	PUNCT
ejpam-491	515	103	deeb	deeb	PROPN
ejpam-491	515	104	and	and	CCONJ
ejpam-491	515	105	r.	r.	PROPN
ejpam-491	515	106	a.	a.	PROPN
ejpam-491	515	107	mahmoud	mahmoud	PROPN
ejpam-491	515	108	,	,	PUNCT
ejpam-491	515	109	β	β	X
ejpam-491	515	110	-open	-open	NOUN
ejpam-491	515	111	sets	set	NOUN
ejpam-491	515	112	and	and	CCONJ
ejpam-491	515	113	β	β	PRON
ejpam-491	515	114	-continuous	-continuous	ADJ
ejpam-491	515	115	mappings	mapping	NOUN
ejpam-491	515	116	,	,	PUNCT
ejpam-491	515	117	bull	bull	NOUN
ejpam-491	515	118	.	.	PUNCT
ejpam-491	516	1	fac	fac	PROPN
ejpam-491	516	2	.	.	PUNCT
ejpam-491	517	1	sci	sci	PROPN
ejpam-491	517	2	.	.	PUNCT
ejpam-491	517	3	assiut	assiut	PROPN
ejpam-491	517	4	univ	univ	PROPN
ejpam-491	517	5	.	.	PROPN
ejpam-491	517	6	,	,	PUNCT
ejpam-491	517	7	12	12	NUM
ejpam-491	517	8	(	(	PUNCT
ejpam-491	517	9	1983	1983	NUM
ejpam-491	517	10	)	)	PUNCT
ejpam-491	517	11	,	,	PUNCT
ejpam-491	517	12	77–90	77–90	NUM
ejpam-491	517	13	.	.	PUNCT
ejpam-491	518	1	[	[	X
ejpam-491	518	2	2	2	NUM
ejpam-491	518	3	]	]	PUNCT
ejpam-491	518	4	m.	m.	NOUN
ejpam-491	518	5	e.	e.	PROPN
ejpam-491	518	6	abd	abd	PROPN
ejpam-491	519	1	el	el	PROPN
ejpam-491	519	2	-	-	PROPN
ejpam-491	519	3	monsef	monsef	PROPN
ejpam-491	519	4	,	,	PUNCT
ejpam-491	519	5	r.	r.	PROPN
ejpam-491	519	6	a.	a.	PROPN
ejpam-491	519	7	mahmoud	mahmoud	PROPN
ejpam-491	519	8	and	and	CCONJ
ejpam-491	519	9	e.	e.	PROPN
ejpam-491	519	10	r.	r.	PROPN
ejpam-491	519	11	lashin	lashin	PROPN
ejpam-491	519	12	,	,	PUNCT
ejpam-491	519	13	β	β	NOUN
ejpam-491	519	14	-closure	-closure	NOUN
ejpam-491	519	15	and	and	CCONJ
ejpam-491	519	16	β	β	X
ejpam-491	519	17	-interior	-interior	PROPN
ejpam-491	519	18	,	,	PUNCT
ejpam-491	519	19	j.	j.	PROPN
ejpam-491	519	20	fac	fac	PROPN
ejpam-491	519	21	.	.	PUNCT
ejpam-491	520	1	ed	ed	PROPN
ejpam-491	520	2	.	.	PUNCT
ejpam-491	520	3	ain	ain	PROPN
ejpam-491	520	4	shams	sham	NOUN
ejpam-491	520	5	univ	univ	PROPN
ejpam-491	520	6	.	.	PROPN
ejpam-491	520	7	,	,	PUNCT
ejpam-491	520	8	10	10	NUM
ejpam-491	520	9	(	(	PUNCT
ejpam-491	520	10	1986	1986	NUM
ejpam-491	520	11	)	)	PUNCT
ejpam-491	520	12	,	,	PUNCT
ejpam-491	520	13	235–245	235–245	NUM
ejpam-491	520	14	.	.	PUNCT
ejpam-491	521	1	references	reference	NOUN
ejpam-491	521	2	491	491	NUM
ejpam-491	522	1	[	[	X
ejpam-491	522	2	3	3	NUM
ejpam-491	522	3	]	]	PUNCT
ejpam-491	522	4	a.	a.	PROPN
ejpam-491	522	5	al	al	PROPN
ejpam-491	522	6	-	-	PUNCT
ejpam-491	522	7	omari	omari	PROPN
ejpam-491	522	8	and	and	CCONJ
ejpam-491	522	9	m.	m.	PROPN
ejpam-491	522	10	s.	s.	PROPN
ejpam-491	522	11	m.	m.	PROPN
ejpam-491	522	12	naorami	naorami	PROPN
ejpam-491	522	13	,	,	PUNCT
ejpam-491	522	14	on	on	ADP
ejpam-491	522	15	generalized	generalized	ADJ
ejpam-491	522	16	b	b	X
ejpam-491	522	17	-	-	PUNCT
ejpam-491	522	18	closed	closed	ADJ
ejpam-491	522	19	sets	set	NOUN
ejpam-491	522	20	,	,	PUNCT
ejpam-491	522	21	,	,	PUNCT
ejpam-491	522	22	bull	bull	NOUN
ejpam-491	522	23	.	.	PUNCT
ejpam-491	523	1	malays	malays	PROPN
ejpam-491	523	2	.	.	PUNCT
ejpam-491	524	1	math	math	NOUN
ejpam-491	524	2	.	.	PUNCT
ejpam-491	525	1	sci	sci	PROPN
ejpam-491	525	2	.	.	PROPN
ejpam-491	525	3	soc	soc	PROPN
ejpam-491	525	4	.	.	PUNCT
ejpam-491	526	1	(	(	PUNCT
ejpam-491	526	2	2	2	NUM
ejpam-491	526	3	)	)	PUNCT
ejpam-491	526	4	,	,	PUNCT
ejpam-491	526	5	32	32	NUM
ejpam-491	526	6	(	(	PUNCT
ejpam-491	526	7	2009	2009	NUM
ejpam-491	526	8	)	)	PUNCT
ejpam-491	526	9	,	,	PUNCT
ejpam-491	526	10	19–30	19–30	NUM
ejpam-491	526	11	.	.	PUNCT
ejpam-491	527	1	[	[	X
ejpam-491	527	2	4	4	X
ejpam-491	527	3	]	]	X
ejpam-491	527	4	d.	d.	PROPN
ejpam-491	527	5	andrijević	andrijević	PROPN
ejpam-491	527	6	,	,	PUNCT
ejpam-491	527	7	semi	semi	ADJ
ejpam-491	527	8	-	-	ADJ
ejpam-491	527	9	preopen	preopen	ADJ
ejpam-491	527	10	sets	set	NOUN
ejpam-491	527	11	,	,	PUNCT
ejpam-491	527	12	mat	mat	PROPN
ejpam-491	527	13	.	.	PROPN
ejpam-491	527	14	vesnik	vesnik	PROPN
ejpam-491	527	15	,	,	PUNCT
ejpam-491	527	16	38	38	NUM
ejpam-491	527	17	(	(	PUNCT
ejpam-491	527	18	1986	1986	NUM
ejpam-491	527	19	)	)	PUNCT
ejpam-491	527	20	,	,	PUNCT
ejpam-491	527	21	24–32	24–32	NUM
ejpam-491	527	22	.	.	PUNCT
ejpam-491	528	1	[	[	X
ejpam-491	528	2	5	5	X
ejpam-491	528	3	]	]	X
ejpam-491	528	4	d.	d.	PROPN
ejpam-491	528	5	andrijević	andrijević	PROPN
ejpam-491	528	6	,	,	PUNCT
ejpam-491	528	7	on	on	ADP
ejpam-491	528	8	b	b	X
ejpam-491	528	9	-	-	PUNCT
ejpam-491	528	10	open	open	ADJ
ejpam-491	528	11	sets	set	NOUN
ejpam-491	528	12	,	,	PUNCT
ejpam-491	528	13	mat	mat	PROPN
ejpam-491	528	14	.	.	PROPN
ejpam-491	528	15	vesnik	vesnik	PROPN
ejpam-491	528	16	,	,	PUNCT
ejpam-491	528	17	48	48	NUM
ejpam-491	528	18	(	(	PUNCT
ejpam-491	528	19	1996	1996	NUM
ejpam-491	528	20	)	)	PUNCT
ejpam-491	528	21	,	,	PUNCT
ejpam-491	528	22	59–64	59–64	NUM
ejpam-491	528	23	.	.	PUNCT
ejpam-491	529	1	[	[	X
ejpam-491	529	2	6	6	NUM
ejpam-491	529	3	]	]	PUNCT
ejpam-491	529	4	i.	i.	PROPN
ejpam-491	529	5	arokiarani	arokiarani	PROPN
ejpam-491	529	6	,	,	PUNCT
ejpam-491	529	7	k.	k.	PROPN
ejpam-491	529	8	barachandran	barachandran	PROPN
ejpam-491	529	9	and	and	CCONJ
ejpam-491	529	10	j.	j.	PROPN
ejpam-491	529	11	dontchev	dontchev	PROPN
ejpam-491	529	12	,	,	PUNCT
ejpam-491	529	13	some	some	DET
ejpam-491	529	14	characterization	characterization	NOUN
ejpam-491	529	15	of	of	ADP
ejpam-491	529	16	gp	gp	NOUN
ejpam-491	529	17	-	-	NOUN
ejpam-491	529	18	irresolute	irresolute	ADJ
ejpam-491	529	19	and	and	CCONJ
ejpam-491	529	20	gp	gp	ADJ
ejpam-491	529	21	-	-	ADJ
ejpam-491	529	22	continuous	continuous	ADJ
ejpam-491	529	23	maps	map	NOUN
ejpam-491	529	24	between	between	ADP
ejpam-491	529	25	toopological	toopological	ADJ
ejpam-491	529	26	spaces	space	NOUN
ejpam-491	529	27	,	,	PUNCT
ejpam-491	529	28	mem	mem	PROPN
ejpam-491	529	29	.	.	PUNCT
ejpam-491	530	1	fac	fac	PROPN
ejpam-491	530	2	.	.	PUNCT
ejpam-491	531	1	sci	sci	PROPN
ejpam-491	531	2	.	.	PROPN
ejpam-491	531	3	kochi	kochi	PROPN
ejpam-491	531	4	univ	univ	PROPN
ejpam-491	531	5	.	.	PUNCT
ejpam-491	532	1	ser	ser	PROPN
ejpam-491	532	2	.	.	PUNCT
ejpam-491	533	1	a	a	DET
ejpam-491	533	2	math	math	NOUN
ejpam-491	533	3	.	.	PUNCT
ejpam-491	534	1	,	,	PUNCT
ejpam-491	534	2	20	20	NUM
ejpam-491	534	3	(	(	PUNCT
ejpam-491	534	4	1999	1999	NUM
ejpam-491	534	5	)	)	PUNCT
ejpam-491	534	6	,	,	PUNCT
ejpam-491	534	7	93–104	93–104	PROPN
ejpam-491	534	8	.	.	PUNCT
ejpam-491	535	1	[	[	X
ejpam-491	535	2	7	7	X
ejpam-491	535	3	]	]	X
ejpam-491	535	4	k.	k.	PROPN
ejpam-491	535	5	balachandran	balachandran	PROPN
ejpam-491	535	6	,	,	PUNCT
ejpam-491	535	7	p.	p.	NOUN
ejpam-491	535	8	sundarm	sundarm	NOUN
ejpam-491	535	9	and	and	CCONJ
ejpam-491	535	10	h.	h.	PROPN
ejpam-491	535	11	maki	maki	PROPN
ejpam-491	535	12	,	,	PUNCT
ejpam-491	535	13	on	on	ADP
ejpam-491	535	14	generalized	generalized	ADJ
ejpam-491	535	15	continuous	continuous	ADJ
ejpam-491	535	16	maps	map	NOUN
ejpam-491	535	17	in	in	ADP
ejpam-491	535	18	topological	topological	ADJ
ejpam-491	535	19	spaces	space	NOUN
ejpam-491	535	20	,	,	PUNCT
ejpam-491	535	21	mem	mem	PROPN
ejpam-491	535	22	.	.	PUNCT
ejpam-491	536	1	fac	fac	PROPN
ejpam-491	536	2	.	.	PUNCT
ejpam-491	537	1	sci	sci	PROPN
ejpam-491	537	2	.	.	PROPN
ejpam-491	537	3	kochi	kochi	PROPN
ejpam-491	537	4	univ	univ	PROPN
ejpam-491	537	5	.	.	PUNCT
ejpam-491	538	1	ser	ser	PROPN
ejpam-491	538	2	.	.	PUNCT
ejpam-491	539	1	a	a	DET
ejpam-491	539	2	math	math	NOUN
ejpam-491	539	3	.	.	PUNCT
ejpam-491	540	1	,	,	PUNCT
ejpam-491	540	2	12	12	NUM
ejpam-491	540	3	(	(	PUNCT
ejpam-491	540	4	1991	1991	NUM
ejpam-491	540	5	)	)	PUNCT
ejpam-491	540	6	,	,	PUNCT
ejpam-491	540	7	5–13	5–13	PROPN
ejpam-491	540	8	.	.	PUNCT
ejpam-491	541	1	[	[	X
ejpam-491	541	2	8	8	NUM
ejpam-491	541	3	]	]	X
ejpam-491	541	4	c.	c.	PROPN
ejpam-491	541	5	boonpok	boonpok	PROPN
ejpam-491	541	6	,	,	PUNCT
ejpam-491	541	7	preservation	preservation	NOUN
ejpam-491	541	8	theorems	theorem	NOUN
ejpam-491	541	9	concerning	concern	VERB
ejpam-491	541	10	g	g	NOUN
ejpam-491	541	11	-	-	PUNCT
ejpam-491	541	12	hausdorff	hausdorff	NOUN
ejpam-491	541	13	and	and	CCONJ
ejpam-491	541	14	rg	rg	NOUN
ejpam-491	541	15	-	-	PUNCT
ejpam-491	541	16	hausdorff	hausdorff	NOUN
ejpam-491	541	17	spaces	space	NOUN
ejpam-491	541	18	,	,	PUNCT
ejpam-491	541	19	naresuan	naresuan	PROPN
ejpam-491	541	20	univ	univ	PROPN
ejpam-491	541	21	.	.	PUNCT
ejpam-491	542	1	j.	j.	PROPN
ejpam-491	542	2	11(3	11(3	PROPN
ejpam-491	542	3	)	)	PUNCT
ejpam-491	542	4	(	(	PUNCT
ejpam-491	542	5	2003	2003	NUM
ejpam-491	542	6	)	)	PUNCT
ejpam-491	542	7	,	,	PUNCT
ejpam-491	542	8	75–77	75–77	NUM
ejpam-491	542	9	.	.	PUNCT
ejpam-491	543	1	[	[	X
ejpam-491	543	2	9	9	NUM
ejpam-491	543	3	]	]	PUNCT
ejpam-491	543	4	m.	m.	NOUN
ejpam-491	543	5	caldas	caldas	PROPN
ejpam-491	543	6	,	,	PUNCT
ejpam-491	543	7	s.	s.	PROPN
ejpam-491	543	8	jafari	jafari	PROPN
ejpam-491	543	9	and	and	CCONJ
ejpam-491	543	10	t.	t.	PROPN
ejpam-491	543	11	noiri	noiri	PROPN
ejpam-491	543	12	,	,	PUNCT
ejpam-491	543	13	notions	notion	NOUN
ejpam-491	543	14	via	via	ADP
ejpam-491	543	15	g	g	NOUN
ejpam-491	543	16	-	-	PUNCT
ejpam-491	543	17	open	open	ADJ
ejpam-491	543	18	sets	set	NOUN
ejpam-491	543	19	,	,	PUNCT
ejpam-491	543	20	kochi	kochi	PROPN
ejpam-491	543	21	j.	j.	PROPN
ejpam-491	543	22	math	math	PROPN
ejpam-491	543	23	.	.	PUNCT
ejpam-491	543	24	,	,	PUNCT
ejpam-491	543	25	2	2	NUM
ejpam-491	543	26	(	(	PUNCT
ejpam-491	543	27	2007	2007	NUM
ejpam-491	543	28	)	)	PUNCT
ejpam-491	543	29	,	,	PUNCT
ejpam-491	543	30	45–50	45–50	NOUN
ejpam-491	543	31	.	.	PUNCT
ejpam-491	544	1	[	[	X
ejpam-491	544	2	10	10	NUM
ejpam-491	544	3	]	]	X
ejpam-491	544	4	s.	s.	PROPN
ejpam-491	544	5	g.	g.	PROPN
ejpam-491	544	6	crossley	crossley	PROPN
ejpam-491	544	7	and	and	CCONJ
ejpam-491	544	8	s.	s.	PROPN
ejpam-491	544	9	k.	k.	PROPN
ejpam-491	544	10	hildebrand	hildebrand	PROPN
ejpam-491	544	11	,	,	PUNCT
ejpam-491	544	12	semi	semi	ADJ
ejpam-491	544	13	-	-	ADJ
ejpam-491	544	14	closure	closure	ADJ
ejpam-491	544	15	,	,	PUNCT
ejpam-491	544	16	texas	texas	PROPN
ejpam-491	544	17	j.	j.	PROPN
ejpam-491	544	18	sci	sci	PROPN
ejpam-491	544	19	.	.	PROPN
ejpam-491	544	20	,	,	PUNCT
ejpam-491	544	21	22	22	NUM
ejpam-491	544	22	(	(	PUNCT
ejpam-491	544	23	1971	1971	NUM
ejpam-491	544	24	)	)	PUNCT
ejpam-491	544	25	,	,	PUNCT
ejpam-491	544	26	99–112	99–112	NUM
ejpam-491	544	27	.	.	PUNCT
ejpam-491	545	1	[	[	X
ejpam-491	545	2	11	11	NUM
ejpam-491	545	3	]	]	PUNCT
ejpam-491	545	4	r.	r.	PROPN
ejpam-491	545	5	devi	devi	PROPN
ejpam-491	545	6	,	,	PUNCT
ejpam-491	545	7	k.	k.	PROPN
ejpam-491	545	8	balachandran	balachandran	PROPN
ejpam-491	545	9	and	and	CCONJ
ejpam-491	545	10	h.	h.	PROPN
ejpam-491	545	11	maki	maki	PROPN
ejpam-491	545	12	,	,	PUNCT
ejpam-491	545	13	semi	semi	ADJ
ejpam-491	545	14	-	-	ADJ
ejpam-491	545	15	generalized	generalized	ADJ
ejpam-491	545	16	homeomorphisms	homeomorphism	NOUN
ejpam-491	545	17	and	and	CCONJ
ejpam-491	545	18	generalized	generalize	VERB
ejpam-491	545	19	semi	semi	NOUN
ejpam-491	545	20	-	-	NOUN
ejpam-491	545	21	homeomorphisms	homeomorphism	NOUN
ejpam-491	545	22	in	in	ADP
ejpam-491	545	23	topological	topological	ADJ
ejpam-491	545	24	spaces	space	NOUN
ejpam-491	545	25	,	,	PUNCT
ejpam-491	545	26	indian	indian	PROPN
ejpam-491	545	27	j.	j.	PROPN
ejpam-491	545	28	pure	pure	PROPN
ejpam-491	545	29	appl	appl	PROPN
ejpam-491	545	30	.	.	PUNCT
ejpam-491	545	31	math	math	PROPN
ejpam-491	545	32	.	.	PUNCT
ejpam-491	546	1	,	,	PUNCT
ejpam-491	546	2	26	26	NUM
ejpam-491	546	3	(	(	PUNCT
ejpam-491	546	4	1995	1995	NUM
ejpam-491	546	5	)	)	PUNCT
ejpam-491	546	6	,	,	PUNCT
ejpam-491	546	7	271–284	271–284	NUM
ejpam-491	546	8	.	.	PUNCT
ejpam-491	547	1	[	[	X
ejpam-491	547	2	12	12	NUM
ejpam-491	547	3	]	]	X
ejpam-491	547	4	r.	r.	PROPN
ejpam-491	547	5	devi	devi	PROPN
ejpam-491	547	6	,	,	PUNCT
ejpam-491	547	7	k.	k.	PROPN
ejpam-491	547	8	balachandran	balachandran	PROPN
ejpam-491	547	9	and	and	CCONJ
ejpam-491	547	10	h.	h.	PROPN
ejpam-491	547	11	maki	maki	PROPN
ejpam-491	547	12	,	,	PUNCT
ejpam-491	547	13	on	on	ADP
ejpam-491	547	14	generalized	generalized	ADJ
ejpam-491	547	15	α	α	NUM
ejpam-491	547	16	-	-	ADJ
ejpam-491	547	17	continuous	continuous	ADJ
ejpam-491	547	18	maps	map	NOUN
ejpam-491	547	19	and	and	CCONJ
ejpam-491	547	20	αgeneralized	αgeneralize	VERB
ejpam-491	547	21	continuous	continuous	ADJ
ejpam-491	547	22	maps	map	NOUN
ejpam-491	547	23	,	,	PUNCT
ejpam-491	547	24	far	far	PROPN
ejpam-491	547	25	east	east	PROPN
ejpam-491	547	26	j.	j.	PROPN
ejpam-491	547	27	math	math	PROPN
ejpam-491	547	28	.	.	PUNCT
ejpam-491	548	1	sci	sci	PROPN
ejpam-491	548	2	.	.	PROPN
ejpam-491	548	3	,	,	PUNCT
ejpam-491	548	4	special	special	ADJ
ejpam-491	548	5	volume	volume	NOUN
ejpam-491	548	6	(	(	PUNCT
ejpam-491	548	7	1997	1997	NUM
ejpam-491	548	8	)	)	PUNCT
ejpam-491	548	9	,	,	PUNCT
ejpam-491	548	10	part	part	NOUN
ejpam-491	548	11	i	i	PRON
ejpam-491	548	12	,	,	PUNCT
ejpam-491	548	13	1–15	1–15	PROPN
ejpam-491	548	14	..	..	PUNCT
ejpam-491	549	1	[	[	X
ejpam-491	549	2	13	13	NUM
ejpam-491	549	3	]	]	X
ejpam-491	549	4	g.	g.	PROPN
ejpam-491	549	5	di	di	PROPN
ejpam-491	549	6	maio	maio	PROPN
ejpam-491	549	7	and	and	CCONJ
ejpam-491	549	8	t.	t.	PROPN
ejpam-491	549	9	noiri	noiri	PROPN
ejpam-491	549	10	,	,	PUNCT
ejpam-491	549	11	on	on	ADP
ejpam-491	549	12	s	s	ADJ
ejpam-491	549	13	-	-	PUNCT
ejpam-491	549	14	closed	closed	ADJ
ejpam-491	549	15	spaces	space	NOUN
ejpam-491	549	16	,	,	PUNCT
ejpam-491	549	17	indian	indian	ADJ
ejpam-491	549	18	j.	j.	PROPN
ejpam-491	549	19	pure	pure	PROPN
ejpam-491	549	20	appl	appl	PROPN
ejpam-491	550	1	.	.	PUNCT
ejpam-491	550	2	math	math	PROPN
ejpam-491	550	3	.	.	PUNCT
ejpam-491	551	1	,	,	PUNCT
ejpam-491	551	2	18	18	NUM
ejpam-491	551	3	(	(	PUNCT
ejpam-491	551	4	1987	1987	NUM
ejpam-491	551	5	)	)	PUNCT
ejpam-491	551	6	,	,	PUNCT
ejpam-491	551	7	226–233	226–233	NUM
ejpam-491	551	8	.	.	PUNCT
ejpam-491	552	1	[	[	X
ejpam-491	552	2	14	14	NUM
ejpam-491	552	3	]	]	X
ejpam-491	552	4	j.	j.	PROPN
ejpam-491	552	5	dontchev	dontchev	PROPN
ejpam-491	552	6	,	,	PUNCT
ejpam-491	552	7	on	on	ADP
ejpam-491	552	8	generalizing	generalize	VERB
ejpam-491	552	9	semi	semi	ADJ
ejpam-491	552	10	-	-	ADJ
ejpam-491	552	11	preopen	preopen	ADJ
ejpam-491	552	12	sets	set	NOUN
ejpam-491	552	13	,	,	PUNCT
ejpam-491	552	14	mem	mem	PROPN
ejpam-491	552	15	.	.	PUNCT
ejpam-491	552	16	fac	fac	PROPN
ejpam-491	552	17	.	.	PUNCT
ejpam-491	552	18	sci	sci	PROPN
ejpam-491	552	19	.	.	PROPN
ejpam-491	552	20	kochi	kochi	PROPN
ejpam-491	552	21	univ	univ	PROPN
ejpam-491	552	22	.	.	PUNCT
ejpam-491	553	1	ser	ser	PROPN
ejpam-491	553	2	.	.	PUNCT
ejpam-491	554	1	a	a	DET
ejpam-491	554	2	,	,	PUNCT
ejpam-491	554	3	math	math	NOUN
ejpam-491	554	4	.	.	PUNCT
ejpam-491	554	5	,	,	PUNCT
ejpam-491	554	6	16	16	NUM
ejpam-491	554	7	(	(	PUNCT
ejpam-491	554	8	1995	1995	NUM
ejpam-491	554	9	)	)	PUNCT
ejpam-491	554	10	,	,	PUNCT
ejpam-491	554	11	35–48	35–48	NUM
ejpam-491	554	12	.	.	PUNCT
ejpam-491	555	1	[	[	X
ejpam-491	555	2	15	15	NUM
ejpam-491	555	3	]	]	X
ejpam-491	555	4	w.	w.	PROPN
ejpam-491	555	5	dunham	dunham	PROPN
ejpam-491	555	6	,	,	PUNCT
ejpam-491	555	7	a	a	DET
ejpam-491	555	8	new	new	ADJ
ejpam-491	555	9	closure	closure	NOUN
ejpam-491	555	10	operator	operator	NOUN
ejpam-491	555	11	for	for	ADP
ejpam-491	555	12	non	non	ADJ
ejpam-491	555	13	-	-	ADJ
ejpam-491	555	14	t1	t1	ADJ
ejpam-491	555	15	topologies	topology	NOUN
ejpam-491	555	16	,	,	PUNCT
ejpam-491	555	17	kyungpook	kyungpook	NOUN
ejpam-491	555	18	math	math	NOUN
ejpam-491	555	19	.	.	PUNCT
ejpam-491	556	1	j.	j.	PROPN
ejpam-491	556	2	,	,	PUNCT
ejpam-491	556	3	22	22	NUM
ejpam-491	556	4	(	(	PUNCT
ejpam-491	556	5	1982	1982	NUM
ejpam-491	556	6	)	)	PUNCT
ejpam-491	556	7	,	,	PUNCT
ejpam-491	556	8	55–60	55–60	NUM
ejpam-491	556	9	.	.	PUNCT
ejpam-491	557	1	[	[	X
ejpam-491	557	2	16	16	NUM
ejpam-491	557	3	]	]	X
ejpam-491	557	4	w.	w.	PROPN
ejpam-491	557	5	dunham	dunham	PROPN
ejpam-491	557	6	and	and	CCONJ
ejpam-491	557	7	n.	n.	PROPN
ejpam-491	557	8	levine	levine	PROPN
ejpam-491	557	9	,	,	PUNCT
ejpam-491	557	10	further	further	ADJ
ejpam-491	557	11	results	result	NOUN
ejpam-491	557	12	of	of	ADP
ejpam-491	557	13	generalized	generalized	ADJ
ejpam-491	557	14	closed	closed	ADJ
ejpam-491	557	15	sets	set	NOUN
ejpam-491	557	16	in	in	ADP
ejpam-491	557	17	topology	topology	NOUN
ejpam-491	557	18	,	,	PUNCT
ejpam-491	557	19	kyungpook	kyungpook	PROPN
ejpam-491	557	20	math	math	PROPN
ejpam-491	557	21	.	.	PUNCT
ejpam-491	558	1	j.	j.	PROPN
ejpam-491	558	2	,	,	PUNCT
ejpam-491	558	3	20	20	NUM
ejpam-491	558	4	(	(	PUNCT
ejpam-491	558	5	1980	1980	NUM
ejpam-491	558	6	)	)	PUNCT
ejpam-491	558	7	,	,	PUNCT
ejpam-491	558	8	169–175	169–175	NUM
ejpam-491	558	9	.	.	PUNCT
ejpam-491	559	1	[	[	X
ejpam-491	559	2	17	17	NUM
ejpam-491	559	3	]	]	PUNCT
ejpam-491	559	4	s.	s.	PROPN
ejpam-491	559	5	n.	n.	PROPN
ejpam-491	559	6	el	el	PROPN
ejpam-491	559	7	-	-	PROPN
ejpam-491	559	8	deeb	deeb	PROPN
ejpam-491	559	9	,	,	PUNCT
ejpam-491	559	10	i.	i.	PROPN
ejpam-491	559	11	a.	a.	PROPN
ejpam-491	559	12	hasanein	hasanein	PROPN
ejpam-491	559	13	,	,	PUNCT
ejpam-491	559	14	a.	a.	PROPN
ejpam-491	559	15	s.	s.	PROPN
ejpam-491	559	16	mashhour	mashhour	PROPN
ejpam-491	559	17	and	and	CCONJ
ejpam-491	559	18	t.	t.	PROPN
ejpam-491	559	19	noiri	noiri	PROPN
ejpam-491	559	20	,	,	PUNCT
ejpam-491	559	21	on	on	ADP
ejpam-491	559	22	p	p	NOUN
ejpam-491	559	23	-	-	PUNCT
ejpam-491	559	24	regular	regular	ADJ
ejpam-491	559	25	spaces	space	NOUN
ejpam-491	559	26	,	,	PUNCT
ejpam-491	559	27	bull	bull	NOUN
ejpam-491	559	28	.	.	PUNCT
ejpam-491	560	1	references	reference	NOUN
ejpam-491	560	2	492	492	NUM
ejpam-491	560	3	math	math	NOUN
ejpam-491	560	4	.	.	PUNCT
ejpam-491	561	1	soc	soc	PROPN
ejpam-491	561	2	.	.	PUNCT
ejpam-491	562	1	sci	sci	PROPN
ejpam-491	562	2	.	.	PROPN
ejpam-491	562	3	math	math	PROPN
ejpam-491	562	4	.	.	PUNCT
ejpam-491	563	1	r.	r.	PROPN
ejpam-491	563	2	s.	s.	PROPN
ejpam-491	563	3	roumanie	roumanie	PROPN
ejpam-491	563	4	,	,	PUNCT
ejpam-491	563	5	27(75	27(75	NUM
ejpam-491	563	6	)	)	PUNCT
ejpam-491	563	7	(	(	PUNCT
ejpam-491	563	8	1983	1983	NUM
ejpam-491	563	9	)	)	PUNCT
ejpam-491	563	10	,	,	PUNCT
ejpam-491	563	11	311–315	311–315	NUM
ejpam-491	563	12	.	.	PUNCT
ejpam-491	564	1	[	[	X
ejpam-491	564	2	18	18	NUM
ejpam-491	564	3	]	]	PUNCT
ejpam-491	564	4	t.	t.	NOUN
ejpam-491	564	5	fukutake	fukutake	NOUN
ejpam-491	564	6	,	,	PUNCT
ejpam-491	564	7	a.	a.	NOUN
ejpam-491	564	8	a.	a.	NOUN
ejpam-491	564	9	nasef	nasef	PROPN
ejpam-491	564	10	and	and	CCONJ
ejpam-491	564	11	a.	a.	PROPN
ejpam-491	564	12	i.	i.	PROPN
ejpam-491	564	13	el	el	PROPN
ejpam-491	564	14	-	-	PUNCT
ejpam-491	564	15	maghrabi	maghrabi	PROPN
ejpam-491	564	16	,	,	PUNCT
ejpam-491	564	17	some	some	DET
ejpam-491	564	18	topological	topological	ADJ
ejpam-491	564	19	concepts	concept	NOUN
ejpam-491	564	20	via	via	ADP
ejpam-491	564	21	γgeneralized	γgeneralize	VERB
ejpam-491	564	22	closed	closed	ADJ
ejpam-491	564	23	sets	set	NOUN
ejpam-491	564	24	,	,	PUNCT
ejpam-491	564	25	bull	bull	NOUN
ejpam-491	564	26	.	.	PUNCT
ejpam-491	565	1	fukuoka	fukuoka	PROPN
ejpam-491	565	2	univ	univ	PROPN
ejpam-491	565	3	.	.	PUNCT
ejpam-491	566	1	ed	ed	NOUN
ejpam-491	566	2	.	.	PUNCT
ejpam-491	566	3	iii	iii	PROPN
ejpam-491	566	4	,	,	PUNCT
ejpam-491	566	5	52	52	NUM
ejpam-491	566	6	(	(	PUNCT
ejpam-491	566	7	2003	2003	NUM
ejpam-491	566	8	)	)	PUNCT
ejpam-491	566	9	,	,	PUNCT
ejpam-491	566	10	1–9	1–9	NOUN
ejpam-491	566	11	.	.	PUNCT
ejpam-491	567	1	[	[	X
ejpam-491	567	2	19	19	NUM
ejpam-491	567	3	]	]	X
ejpam-491	567	4	n.	n.	PROPN
ejpam-491	567	5	levine	levine	PROPN
ejpam-491	567	6	,	,	PUNCT
ejpam-491	567	7	semi	semi	ADJ
ejpam-491	567	8	-	-	ADJ
ejpam-491	567	9	open	open	ADJ
ejpam-491	567	10	sets	set	NOUN
ejpam-491	567	11	and	and	CCONJ
ejpam-491	567	12	semi	semi	ADJ
ejpam-491	567	13	-	-	NOUN
ejpam-491	567	14	continuity	continuity	NOUN
ejpam-491	567	15	in	in	ADP
ejpam-491	567	16	topological	topological	ADJ
ejpam-491	567	17	spaces	space	NOUN
ejpam-491	567	18	,	,	PUNCT
ejpam-491	567	19	amer	amer	PROPN
ejpam-491	567	20	.	.	PROPN
ejpam-491	567	21	math	math	PROPN
ejpam-491	567	22	.	.	PUNCT
ejpam-491	568	1	monthly	monthly	ADJ
ejpam-491	568	2	,	,	PUNCT
ejpam-491	568	3	70	70	NUM
ejpam-491	568	4	(	(	PUNCT
ejpam-491	568	5	1963	1963	NUM
ejpam-491	568	6	)	)	PUNCT
ejpam-491	568	7	,	,	PUNCT
ejpam-491	568	8	36–41	36–41	NUM
ejpam-491	568	9	.	.	PUNCT
ejpam-491	569	1	[	[	X
ejpam-491	569	2	20	20	NUM
ejpam-491	569	3	]	]	X
ejpam-491	569	4	n.	n.	PROPN
ejpam-491	569	5	levine	levine	PROPN
ejpam-491	569	6	,	,	PUNCT
ejpam-491	569	7	generalized	generalize	VERB
ejpam-491	569	8	closed	closed	ADJ
ejpam-491	569	9	sets	set	NOUN
ejpam-491	569	10	in	in	ADP
ejpam-491	569	11	topology	topology	NOUN
ejpam-491	569	12	,	,	PUNCT
ejpam-491	569	13	rend	rend	VERB
ejpam-491	569	14	.	.	PUNCT
ejpam-491	570	1	circ	circ	PROPN
ejpam-491	570	2	.	.	PUNCT
ejpam-491	571	1	mat	mat	PROPN
ejpam-491	571	2	.	.	PUNCT
ejpam-491	571	3	palermo	palermo	PROPN
ejpam-491	571	4	(	(	PUNCT
ejpam-491	571	5	2	2	NUM
ejpam-491	571	6	)	)	PUNCT
ejpam-491	571	7	,	,	PUNCT
ejpam-491	571	8	19	19	NUM
ejpam-491	571	9	(	(	PUNCT
ejpam-491	571	10	1970	1970	NUM
ejpam-491	571	11	)	)	PUNCT
ejpam-491	571	12	,	,	PUNCT
ejpam-491	571	13	89–96	89–96	NUM
ejpam-491	571	14	.	.	PUNCT
ejpam-491	572	1	[	[	X
ejpam-491	572	2	21	21	NUM
ejpam-491	572	3	]	]	X
ejpam-491	572	4	h.	h.	PROPN
ejpam-491	572	5	maki	maki	PROPN
ejpam-491	572	6	,	,	PUNCT
ejpam-491	572	7	k.	k.	PROPN
ejpam-491	572	8	c.	c.	PROPN
ejpam-491	572	9	rao	rao	PROPN
ejpam-491	572	10	and	and	CCONJ
ejpam-491	572	11	a.	a.	PROPN
ejpam-491	572	12	nagoor	nagoor	PROPN
ejpam-491	572	13	gani	gani	PROPN
ejpam-491	572	14	,	,	PUNCT
ejpam-491	572	15	on	on	ADP
ejpam-491	572	16	generalizing	generalize	VERB
ejpam-491	572	17	semi	semi	ADJ
ejpam-491	572	18	-	-	ADJ
ejpam-491	572	19	open	open	ADJ
ejpam-491	572	20	and	and	CCONJ
ejpam-491	572	21	preopen	preopen	ADJ
ejpam-491	572	22	sets	set	NOUN
ejpam-491	572	23	,	,	PUNCT
ejpam-491	572	24	pure	pure	ADJ
ejpam-491	572	25	appl	appl	NOUN
ejpam-491	572	26	.	.	PUNCT
ejpam-491	572	27	math	math	PROPN
ejpam-491	572	28	.	.	PUNCT
ejpam-491	573	1	sci	sci	PROPN
ejpam-491	573	2	.	.	PROPN
ejpam-491	573	3	,	,	PUNCT
ejpam-491	573	4	49	49	NUM
ejpam-491	573	5	(	(	PUNCT
ejpam-491	573	6	1999	1999	NUM
ejpam-491	573	7	)	)	PUNCT
ejpam-491	573	8	,	,	PUNCT
ejpam-491	573	9	17–29	17–29	NUM
ejpam-491	573	10	.	.	PUNCT
ejpam-491	574	1	[	[	X
ejpam-491	574	2	22	22	NUM
ejpam-491	574	3	]	]	PUNCT
ejpam-491	574	4	a.	a.	NOUN
ejpam-491	574	5	s.	s.	PROPN
ejpam-491	574	6	mashhour	mashhour	PROPN
ejpam-491	574	7	,	,	PUNCT
ejpam-491	574	8	m.	m.	PROPN
ejpam-491	574	9	e.	e.	PROPN
ejpam-491	574	10	abd	abd	PROPN
ejpam-491	574	11	el	el	PROPN
ejpam-491	574	12	-	-	PROPN
ejpam-491	574	13	monsef	monsef	PROPN
ejpam-491	574	14	and	and	CCONJ
ejpam-491	574	15	s.	s.	PROPN
ejpam-491	574	16	n.	n.	PROPN
ejpam-491	574	17	el	el	PROPN
ejpam-491	574	18	-	-	PUNCT
ejpam-491	574	19	deep	deep	ADJ
ejpam-491	574	20	,	,	PUNCT
ejpam-491	574	21	on	on	ADP
ejpam-491	574	22	precontinuous	precontinuous	ADJ
ejpam-491	574	23	and	and	CCONJ
ejpam-491	574	24	weak	weak	ADJ
ejpam-491	574	25	precontinuous	precontinuous	ADJ
ejpam-491	574	26	mappings	mapping	NOUN
ejpam-491	574	27	,	,	PUNCT
ejpam-491	574	28	proc	proc	NOUN
ejpam-491	574	29	.	.	PUNCT
ejpam-491	574	30	math	math	NOUN
ejpam-491	574	31	.	.	PUNCT
ejpam-491	575	1	phys	phy	NOUN
ejpam-491	575	2	.	.	PUNCT
ejpam-491	576	1	soc	soc	PROPN
ejpam-491	576	2	.	.	PUNCT
ejpam-491	577	1	egypt	egypt	PROPN
ejpam-491	577	2	,	,	PUNCT
ejpam-491	577	3	53	53	NUM
ejpam-491	577	4	(	(	PUNCT
ejpam-491	577	5	1982	1982	NUM
ejpam-491	577	6	)	)	PUNCT
ejpam-491	577	7	,	,	PUNCT
ejpam-491	577	8	47–53	47–53	NUM
ejpam-491	577	9	.	.	PUNCT
ejpam-491	578	1	[	[	X
ejpam-491	578	2	23	23	NUM
ejpam-491	578	3	]	]	PUNCT
ejpam-491	578	4	a.	a.	NOUN
ejpam-491	578	5	s.	s.	PROPN
ejpam-491	578	6	mashhour	mashhour	PROPN
ejpam-491	578	7	,	,	PUNCT
ejpam-491	578	8	i.	i.	PROPN
ejpam-491	578	9	a.	a.	PROPN
ejpam-491	578	10	hasanein	hasanein	PROPN
ejpam-491	578	11	and	and	CCONJ
ejpam-491	578	12	s.	s.	PROPN
ejpam-491	578	13	n.	n.	PROPN
ejpam-491	578	14	el	el	PROPN
ejpam-491	578	15	-	-	PROPN
ejpam-491	578	16	deeb	deeb	PROPN
ejpam-491	578	17	,	,	PUNCT
ejpam-491	578	18	α	α	NOUN
ejpam-491	578	19	-	-	ADJ
ejpam-491	578	20	continuous	continuous	ADJ
ejpam-491	578	21	and	and	CCONJ
ejpam-491	578	22	α	α	NOUN
ejpam-491	578	23	-	-	ADJ
ejpam-491	578	24	open	open	ADJ
ejpam-491	578	25	mappings	mapping	NOUN
ejpam-491	578	26	,	,	PUNCT
ejpam-491	578	27	acta	acta	PROPN
ejpam-491	578	28	math	math	PROPN
ejpam-491	578	29	.	.	PUNCT
ejpam-491	579	1	hungar	hungar	PROPN
ejpam-491	579	2	.	.	PUNCT
ejpam-491	579	3	,	,	PUNCT
ejpam-491	579	4	41	41	NUM
ejpam-491	579	5	(	(	PUNCT
ejpam-491	579	6	1983	1983	NUM
ejpam-491	579	7	)	)	PUNCT
ejpam-491	579	8	,	,	PUNCT
ejpam-491	579	9	213–218	213–218	NUM
ejpam-491	579	10	.	.	PUNCT
ejpam-491	580	1	[	[	X
ejpam-491	580	2	24	24	NUM
ejpam-491	580	3	]	]	PUNCT
ejpam-491	580	4	w.	w.	PROPN
ejpam-491	580	5	k.	k.	PROPN
ejpam-491	580	6	min	min	PROPN
ejpam-491	580	7	,	,	PUNCT
ejpam-491	580	8	m∗-continuity	m∗-continuity	NOUN
ejpam-491	580	9	and	and	CCONJ
ejpam-491	580	10	product	product	NOUN
ejpam-491	580	11	minimal	minimal	ADJ
ejpam-491	580	12	structures	structure	NOUN
ejpam-491	580	13	on	on	ADP
ejpam-491	580	14	minimal	minimal	ADJ
ejpam-491	580	15	structures	structure	NOUN
ejpam-491	580	16	(	(	PUNCT
ejpam-491	580	17	submitted	submit	VERB
ejpam-491	580	18	)	)	PUNCT
ejpam-491	580	19	.	.	PUNCT
ejpam-491	581	1	[	[	X
ejpam-491	581	2	25	25	NUM
ejpam-491	581	3	]	]	X
ejpam-491	581	4	b.	b.	PROPN
ejpam-491	581	5	m.	m.	PROPN
ejpam-491	581	6	munshi	munshi	PROPN
ejpam-491	581	7	and	and	CCONJ
ejpam-491	581	8	d.	d.	PROPN
ejpam-491	581	9	s.	s.	PROPN
ejpam-491	581	10	bassan	bassan	PROPN
ejpam-491	581	11	,	,	PUNCT
ejpam-491	581	12	g	g	NOUN
ejpam-491	581	13	-	-	PUNCT
ejpam-491	581	14	continuous	continuous	ADJ
ejpam-491	581	15	mappings	mapping	NOUN
ejpam-491	581	16	,	,	PUNCT
ejpam-491	581	17	vidya	vidya	PROPN
ejpam-491	581	18	j.	j.	PROPN
ejpam-491	581	19	gujarat	gujarat	PROPN
ejpam-491	581	20	univ	univ	PROPN
ejpam-491	581	21	.	.	PUNCT
ejpam-491	582	1	b	b	PROPN
ejpam-491	582	2	sci	sci	PROPN
ejpam-491	582	3	.	.	PROPN
ejpam-491	582	4	,	,	PUNCT
ejpam-491	582	5	24	24	NUM
ejpam-491	582	6	(	(	PUNCT
ejpam-491	582	7	1981	1981	NUM
ejpam-491	582	8	)	)	PUNCT
ejpam-491	582	9	,	,	PUNCT
ejpam-491	582	10	63–68	63–68	NUM
ejpam-491	582	11	.	.	PUNCT
ejpam-491	583	1	[	[	X
ejpam-491	583	2	26	26	NUM
ejpam-491	583	3	]	]	X
ejpam-491	583	4	o.	o.	NOUN
ejpam-491	583	5	njåstad	njåstad	PROPN
ejpam-491	583	6	,	,	PUNCT
ejpam-491	583	7	on	on	ADP
ejpam-491	583	8	some	some	DET
ejpam-491	583	9	classes	class	NOUN
ejpam-491	583	10	of	of	ADP
ejpam-491	583	11	nearly	nearly	ADV
ejpam-491	583	12	open	open	ADJ
ejpam-491	583	13	sets	set	NOUN
ejpam-491	583	14	,	,	PUNCT
ejpam-491	583	15	pacific	pacific	PROPN
ejpam-491	583	16	j.	j.	PROPN
ejpam-491	583	17	math	math	PROPN
ejpam-491	583	18	.	.	PUNCT
ejpam-491	583	19	,	,	PUNCT
ejpam-491	583	20	15	15	NUM
ejpam-491	583	21	(	(	PUNCT
ejpam-491	583	22	1965	1965	NUM
ejpam-491	583	23	)	)	PUNCT
ejpam-491	583	24	,	,	PUNCT
ejpam-491	583	25	961–970	961–970	NUM
ejpam-491	583	26	.	.	PUNCT
ejpam-491	584	1	[	[	X
ejpam-491	584	2	27	27	NUM
ejpam-491	584	3	]	]	PUNCT
ejpam-491	584	4	t.	t.	PROPN
ejpam-491	584	5	noiri	noiri	PROPN
ejpam-491	584	6	,	,	PUNCT
ejpam-491	584	7	a	a	DET
ejpam-491	584	8	unified	unified	ADJ
ejpam-491	584	9	theory	theory	NOUN
ejpam-491	584	10	for	for	ADP
ejpam-491	584	11	certain	certain	ADJ
ejpam-491	584	12	modifications	modification	NOUN
ejpam-491	584	13	of	of	ADP
ejpam-491	584	14	generalized	generalized	ADJ
ejpam-491	584	15	closed	close	VERB
ejpam-491	584	16	sets	set	NOUN
ejpam-491	584	17	,	,	PUNCT
ejpam-491	584	18	internat	internat	NOUN
ejpam-491	584	19	.	.	PUNCT
ejpam-491	585	1	j.	j.	PROPN
ejpam-491	585	2	general	general	PROPN
ejpam-491	585	3	topology	topology	PROPN
ejpam-491	585	4	,	,	PUNCT
ejpam-491	585	5	1	1	NUM
ejpam-491	585	6	(	(	PUNCT
ejpam-491	585	7	2008	2008	NUM
ejpam-491	585	8	)	)	PUNCT
ejpam-491	585	9	,	,	PUNCT
ejpam-491	585	10	87–99	87–99	NUM
ejpam-491	585	11	.	.	PUNCT
ejpam-491	586	1	[	[	X
ejpam-491	586	2	28	28	NUM
ejpam-491	586	3	]	]	X
ejpam-491	586	4	m.	m.	NOUN
ejpam-491	586	5	c.	c.	PROPN
ejpam-491	586	6	pal	pal	PROPN
ejpam-491	586	7	and	and	CCONJ
ejpam-491	586	8	p.	p.	NOUN
ejpam-491	586	9	bhattacharyya	bhattacharyya	ADJ
ejpam-491	586	10	,	,	PUNCT
ejpam-491	586	11	feeble	feeble	ADJ
ejpam-491	586	12	and	and	CCONJ
ejpam-491	586	13	strong	strong	ADJ
ejpam-491	586	14	forms	form	NOUN
ejpam-491	586	15	of	of	ADP
ejpam-491	586	16	preirresolute	preirresolute	ADJ
ejpam-491	586	17	functions	function	NOUN
ejpam-491	586	18	,	,	PUNCT
ejpam-491	586	19	bull	bull	NOUN
ejpam-491	586	20	.	.	PUNCT
ejpam-491	587	1	malays	malays	PROPN
ejpam-491	587	2	.	.	PUNCT
ejpam-491	588	1	math	math	NOUN
ejpam-491	588	2	.	.	PUNCT
ejpam-491	589	1	sci	sci	PROPN
ejpam-491	589	2	.	.	PROPN
ejpam-491	589	3	soc	soc	PROPN
ejpam-491	589	4	.	.	PUNCT
ejpam-491	590	1	(	(	PUNCT
ejpam-491	590	2	2	2	NUM
ejpam-491	590	3	)	)	PUNCT
ejpam-491	590	4	,	,	PUNCT
ejpam-491	590	5	19	19	NUM
ejpam-491	590	6	(	(	PUNCT
ejpam-491	590	7	1996	1996	NUM
ejpam-491	590	8	)	)	PUNCT
ejpam-491	590	9	,	,	PUNCT
ejpam-491	590	10	63–75	63–75	NUM
ejpam-491	590	11	.	.	PUNCT
ejpam-491	591	1	[	[	X
ejpam-491	591	2	29	29	NUM
ejpam-491	591	3	]	]	PUNCT
ejpam-491	591	4	v.	v.	CCONJ
ejpam-491	591	5	popa	popa	NOUN
ejpam-491	591	6	and	and	CCONJ
ejpam-491	591	7	t.	t.	PROPN
ejpam-491	591	8	noiri	noiri	PROPN
ejpam-491	591	9	,	,	PUNCT
ejpam-491	591	10	on	on	ADP
ejpam-491	591	11	m	m	ADJ
ejpam-491	591	12	-	-	ADJ
ejpam-491	591	13	continuous	continuous	ADJ
ejpam-491	591	14	functions	function	NOUN
ejpam-491	591	15	,	,	PUNCT
ejpam-491	591	16	anal	anal	NOUN
ejpam-491	591	17	.	.	PUNCT
ejpam-491	591	18	univ	univ	PROPN
ejpam-491	591	19	.	.	PUNCT
ejpam-491	592	1	"	"	PUNCT
ejpam-491	592	2	dunǎrea	dunǎrea	X
ejpam-491	592	3	de	de	X
ejpam-491	592	4	jos	jos	PROPN
ejpam-491	592	5	"	"	PUNCT
ejpam-491	592	6	gala̧ti	gala̧ti	PROPN
ejpam-491	592	7	,	,	PUNCT
ejpam-491	592	8	ser	ser	PROPN
ejpam-491	592	9	.	.	PROPN
ejpam-491	592	10	mat	mat	PROPN
ejpam-491	592	11	.	.	PUNCT
ejpam-491	592	12	fiz	fiz	PROPN
ejpam-491	592	13	.	.	PUNCT
ejpam-491	593	1	mec	mec	PROPN
ejpam-491	593	2	.	.	PROPN
ejpam-491	593	3	teor	teor	PROPN
ejpam-491	593	4	.	.	PUNCT
ejpam-491	594	1	(	(	PUNCT
ejpam-491	594	2	2	2	NUM
ejpam-491	594	3	)	)	PUNCT
ejpam-491	594	4	,	,	PUNCT
ejpam-491	594	5	18(23	18(23	NOUN
ejpam-491	594	6	)	)	PUNCT
ejpam-491	594	7	(	(	PUNCT
ejpam-491	594	8	2000	2000	NUM
ejpam-491	594	9	)	)	PUNCT
ejpam-491	594	10	,	,	PUNCT
ejpam-491	594	11	31–41	31–41	NUM
ejpam-491	594	12	.	.	PUNCT
ejpam-491	595	1	[	[	X
ejpam-491	595	2	30	30	NUM
ejpam-491	595	3	]	]	X
ejpam-491	595	4	v.	v.	CCONJ
ejpam-491	595	5	popa	popa	NOUN
ejpam-491	595	6	and	and	CCONJ
ejpam-491	595	7	t.	t.	PROPN
ejpam-491	595	8	noiri	noiri	PROPN
ejpam-491	595	9	,	,	PUNCT
ejpam-491	595	10	on	on	ADP
ejpam-491	595	11	the	the	DET
ejpam-491	595	12	definitions	definition	NOUN
ejpam-491	595	13	of	of	ADP
ejpam-491	595	14	some	some	DET
ejpam-491	595	15	generalized	generalized	ADJ
ejpam-491	595	16	forms	form	NOUN
ejpam-491	595	17	of	of	ADP
ejpam-491	595	18	continuity	continuity	NOUN
ejpam-491	595	19	under	under	ADP
ejpam-491	595	20	minimal	minimal	ADJ
ejpam-491	595	21	conditions	condition	NOUN
ejpam-491	595	22	,	,	PUNCT
ejpam-491	595	23	mem	mem	PROPN
ejpam-491	595	24	.	.	PUNCT
ejpam-491	595	25	fac	fac	PROPN
ejpam-491	595	26	.	.	PUNCT
ejpam-491	595	27	sci	sci	PROPN
ejpam-491	595	28	.	.	PROPN
ejpam-491	595	29	kochi	kochi	PROPN
ejpam-491	595	30	univ	univ	PROPN
ejpam-491	595	31	.	.	PUNCT
ejpam-491	595	32	ser	ser	PROPN
ejpam-491	595	33	.	.	PUNCT
ejpam-491	596	1	a	a	DET
ejpam-491	596	2	math	math	NOUN
ejpam-491	596	3	.	.	PUNCT
ejpam-491	597	1	,	,	PUNCT
ejpam-491	597	2	22	22	NUM
ejpam-491	597	3	(	(	PUNCT
ejpam-491	597	4	2001	2001	NUM
ejpam-491	597	5	)	)	PUNCT
ejpam-491	597	6	,	,	PUNCT
ejpam-491	597	7	9–18	9–18	NOUN
ejpam-491	597	8	.	.	PUNCT
ejpam-491	598	1	[	[	X
ejpam-491	598	2	31	31	NUM
ejpam-491	598	3	]	]	PUNCT
ejpam-491	598	4	v.	v.	CCONJ
ejpam-491	598	5	popa	popa	NOUN
ejpam-491	598	6	and	and	CCONJ
ejpam-491	598	7	t.	t.	PROPN
ejpam-491	598	8	noiri	noiri	PROPN
ejpam-491	598	9	,	,	PUNCT
ejpam-491	598	10	a	a	DET
ejpam-491	598	11	unified	unified	ADJ
ejpam-491	598	12	theory	theory	NOUN
ejpam-491	598	13	of	of	ADP
ejpam-491	598	14	weak	weak	ADJ
ejpam-491	598	15	continuity	continuity	NOUN
ejpam-491	598	16	for	for	ADP
ejpam-491	598	17	functions	function	NOUN
ejpam-491	598	18	,	,	PUNCT
ejpam-491	598	19	rend	rend	VERB
ejpam-491	598	20	.	.	PUNCT
ejpam-491	599	1	circ	circ	PROPN
ejpam-491	599	2	.	.	PUNCT
ejpam-491	600	1	mat	mat	PROPN
ejpam-491	600	2	.	.	PUNCT
ejpam-491	600	3	palermo	palermo	PROPN
ejpam-491	600	4	(	(	PUNCT
ejpam-491	600	5	2	2	NUM
ejpam-491	600	6	)	)	PUNCT
ejpam-491	600	7	,	,	PUNCT
ejpam-491	600	8	51	51	NUM
ejpam-491	600	9	(	(	PUNCT
ejpam-491	600	10	2002	2002	NUM
ejpam-491	600	11	)	)	PUNCT
ejpam-491	600	12	,	,	PUNCT
ejpam-491	600	13	439–464	439–464	NUM
ejpam-491	600	14	.	.	PUNCT
ejpam-491	601	1	[	[	X
ejpam-491	601	2	32	32	NUM
ejpam-491	601	3	]	]	X
ejpam-491	601	4	m.k.r.s	m.k.r.s	PROPN
ejpam-491	601	5	.	.	PUNCT
ejpam-491	601	6	veera	veera	PROPN
ejpam-491	601	7	kumar	kumar	PROPN
ejpam-491	601	8	,	,	PUNCT
ejpam-491	601	9	semi	semi	ADJ
ejpam-491	601	10	-	-	ADJ
ejpam-491	601	11	pregeneralized	pregeneralized	ADJ
ejpam-491	601	12	closed	closed	ADJ
ejpam-491	601	13	sets	set	NOUN
ejpam-491	601	14	,	,	PUNCT
ejpam-491	601	15	mem	mem	PROPN
ejpam-491	601	16	.	.	PUNCT
ejpam-491	602	1	fac	fac	PROPN
ejpam-491	602	2	.	.	PUNCT
ejpam-491	603	1	sci	sci	PROPN
ejpam-491	603	2	.	.	PROPN
ejpam-491	603	3	kochi	kochi	PROPN
ejpam-491	603	4	univ	univ	PROPN
ejpam-491	603	5	.	.	PUNCT
ejpam-491	604	1	ser	ser	PROPN
ejpam-491	604	2	.	.	PUNCT
ejpam-491	605	1	a	a	DET
ejpam-491	605	2	references	reference	NOUN
ejpam-491	605	3	493	493	NUM
ejpam-491	605	4	math	math	NOUN
ejpam-491	605	5	.	.	PUNCT
ejpam-491	605	6	,	,	PUNCT
ejpam-491	605	7	19	19	NUM
ejpam-491	605	8	(	(	PUNCT
ejpam-491	605	9	1999	1999	NUM
ejpam-491	605	10	)	)	PUNCT
ejpam-491	605	11	,	,	PUNCT
ejpam-491	605	12	33–46	33–46	NUM
ejpam-491	605	13	.	.	PUNCT
ejpam-491	606	1	[	[	X
ejpam-491	606	2	33	33	NUM
ejpam-491	606	3	]	]	X
ejpam-491	606	4	n.	n.	NOUN
ejpam-491	606	5	v.	v.	PROPN
ejpam-491	606	6	veličko	veličko	PROPN
ejpam-491	606	7	,	,	PUNCT
ejpam-491	606	8	h	h	NOUN
ejpam-491	606	9	-	-	PUNCT
ejpam-491	606	10	closed	closed	ADJ
ejpam-491	606	11	topological	topological	ADJ
ejpam-491	606	12	spaces	space	NOUN
ejpam-491	606	13	,	,	PUNCT
ejpam-491	606	14	amer	amer	PROPN
ejpam-491	606	15	.	.	PROPN
ejpam-491	606	16	math	math	PROPN
ejpam-491	606	17	.	.	PUNCT
ejpam-491	607	1	soc	soc	PROPN
ejpam-491	607	2	.	.	PUNCT
ejpam-491	608	1	transl	transl	PROPN
ejpam-491	608	2	.	.	PUNCT
ejpam-491	609	1	(	(	PUNCT
ejpam-491	609	2	2	2	NUM
ejpam-491	609	3	)	)	PUNCT
ejpam-491	609	4	,	,	PUNCT
ejpam-491	609	5	78	78	NUM
ejpam-491	609	6	(	(	PUNCT
ejpam-491	609	7	1968	1968	NUM
ejpam-491	609	8	)	)	PUNCT
ejpam-491	609	9	,	,	PUNCT
ejpam-491	609	10	103–118	103–118	NUM
ejpam-491	609	11	.	.	PUNCT