id	sid	tid	token	lemma	pos
ejpam-721	1	1	european	european	PROPN
ejpam-721	1	2	journal	journal	PROPN
ejpam-721	1	3	of	of	ADP
ejpam-721	1	4	pure	pure	ADJ
ejpam-721	1	5	and	and	CCONJ
ejpam-721	1	6	applied	apply	VERB
ejpam-721	1	7	mathematics	mathematic	NOUN
ejpam-721	1	8	vol	vol	NOUN
ejpam-721	1	9	.	.	PUNCT
ejpam-721	2	1	3	3	NUM
ejpam-721	2	2	,	,	PUNCT
ejpam-721	2	3	no	no	INTJ
ejpam-721	2	4	.	.	NOUN
ejpam-721	2	5	2	2	NUM
ejpam-721	2	6	,	,	PUNCT
ejpam-721	2	7	2010	2010	NUM
ejpam-721	2	8	,	,	PUNCT
ejpam-721	2	9	295	295	NUM
ejpam-721	2	10	-	-	SYM
ejpam-721	2	11	302	302	NUM
ejpam-721	2	12	issn	issn	PROPN
ejpam-721	2	13	1307	1307	NUM
ejpam-721	2	14	-	-	SYM
ejpam-721	2	15	5543	5543	NUM
ejpam-721	2	16	–	–	PUNCT
ejpam-721	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-721	2	18	on	on	ADP
ejpam-721	2	19	supra	supra	PROPN
ejpam-721	2	20	b−open	b−open	PROPN
ejpam-721	2	21	sets	set	NOUN
ejpam-721	2	22	and	and	CCONJ
ejpam-721	2	23	supra	supra	PROPN
ejpam-721	2	24	b	b	NOUN
ejpam-721	2	25	-	-	PUNCT
ejpam-721	2	26	continuity	continuity	NOUN
ejpam-721	2	27	on	on	ADP
ejpam-721	2	28	topological	topological	ADJ
ejpam-721	2	29	spaces	space	NOUN
ejpam-721	2	30	o.	o.	PROPN
ejpam-721	2	31	r.	r.	PROPN
ejpam-721	2	32	sayed1∗	sayed1∗	PROPN
ejpam-721	2	33	and	and	CCONJ
ejpam-721	2	34	takashi	takashi	PROPN
ejpam-721	2	35	noiri2	noiri2	PROPN
ejpam-721	2	36	1	1	NUM
ejpam-721	2	37	department	department	NOUN
ejpam-721	2	38	of	of	ADP
ejpam-721	2	39	mathematics	mathematic	NOUN
ejpam-721	2	40	,	,	PUNCT
ejpam-721	2	41	faculty	faculty	NOUN
ejpam-721	2	42	of	of	ADP
ejpam-721	2	43	science	science	NOUN
ejpam-721	2	44	,	,	PUNCT
ejpam-721	2	45	assiut	assiut	PROPN
ejpam-721	2	46	university	university	PROPN
ejpam-721	2	47	,	,	PUNCT
ejpam-721	2	48	assiut	assiut	NOUN
ejpam-721	2	49	71516	71516	NUM
ejpam-721	2	50	,	,	PUNCT
ejpam-721	2	51	egypt	egypt	PROPN
ejpam-721	2	52	&	&	CCONJ
ejpam-721	2	53	department	department	PROPN
ejpam-721	2	54	of	of	ADP
ejpam-721	2	55	mathematics	mathematics	PROPN
ejpam-721	2	56	,	,	PUNCT
ejpam-721	2	57	university	university	NOUN
ejpam-721	2	58	’s	’s	PART
ejpam-721	2	59	college	college	NOUN
ejpam-721	2	60	,	,	PUNCT
ejpam-721	2	61	umm	umm	INTJ
ejpam-721	2	62	-	-	PUNCT
ejpam-721	2	63	al	al	PROPN
ejpam-721	2	64	-	-	PUNCT
ejpam-721	2	65	qurah	qurah	PROPN
ejpam-721	2	66	university	university	PROPN
ejpam-721	2	67	,	,	PUNCT
ejpam-721	2	68	makkah	makkah	PROPN
ejpam-721	2	69	,	,	PUNCT
ejpam-721	2	70	saudi	saudi	PROPN
ejpam-721	2	71	arabia	arabia	PROPN
ejpam-721	2	72	2	2	NUM
ejpam-721	2	73	2949	2949	NUM
ejpam-721	2	74	-	-	SYM
ejpam-721	2	75	1	1	NUM
ejpam-721	2	76	shiokita	shiokita	NOUN
ejpam-721	2	77	-	-	PUNCT
ejpam-721	2	78	cho	cho	ADJ
ejpam-721	2	79	,	,	PUNCT
ejpam-721	2	80	hinagu	hinagu	ADJ
ejpam-721	2	81	,	,	PUNCT
ejpam-721	2	82	yatsushiri	yatsushiri	PROPN
ejpam-721	2	83	-	-	PUNCT
ejpam-721	2	84	shi	shi	PROPN
ejpam-721	2	85	,	,	PUNCT
ejpam-721	2	86	kumamoto	kumamoto	PROPN
ejpam-721	2	87	-	-	PUNCT
ejpam-721	2	88	ken	ken	PROPN
ejpam-721	2	89	,	,	PUNCT
ejpam-721	2	90	869	869	NUM
ejpam-721	2	91	-	-	SYM
ejpam-721	2	92	5142	5142	NUM
ejpam-721	2	93	japan	japan	PROPN
ejpam-721	2	94	abstract	abstract	NOUN
ejpam-721	2	95	.	.	PUNCT
ejpam-721	3	1	in	in	ADP
ejpam-721	3	2	this	this	DET
ejpam-721	3	3	paper	paper	NOUN
ejpam-721	3	4	,	,	PUNCT
ejpam-721	3	5	we	we	PRON
ejpam-721	3	6	introduce	introduce	VERB
ejpam-721	3	7	and	and	CCONJ
ejpam-721	3	8	investigate	investigate	VERB
ejpam-721	3	9	a	a	DET
ejpam-721	3	10	new	new	ADJ
ejpam-721	3	11	class	class	NOUN
ejpam-721	3	12	of	of	ADP
ejpam-721	3	13	sets	set	NOUN
ejpam-721	3	14	and	and	CCONJ
ejpam-721	3	15	maps	map	NOUN
ejpam-721	3	16	between	between	ADP
ejpam-721	3	17	topological	topological	ADJ
ejpam-721	3	18	spaces	space	NOUN
ejpam-721	3	19	called	call	VERB
ejpam-721	3	20	supra	supra	PROPN
ejpam-721	3	21	b−open	b−open	PROPN
ejpam-721	3	22	sets	set	NOUN
ejpam-721	3	23	and	and	CCONJ
ejpam-721	3	24	supra	supra	ADJ
ejpam-721	3	25	b−continuous	b−continuous	ADJ
ejpam-721	3	26	maps	map	NOUN
ejpam-721	3	27	,	,	PUNCT
ejpam-721	3	28	respectively	respectively	ADV
ejpam-721	3	29	.	.	PUNCT
ejpam-721	4	1	furthermore	furthermore	ADV
ejpam-721	4	2	,	,	PUNCT
ejpam-721	4	3	we	we	PRON
ejpam-721	4	4	introduce	introduce	VERB
ejpam-721	4	5	the	the	DET
ejpam-721	4	6	concepts	concept	NOUN
ejpam-721	4	7	of	of	ADP
ejpam-721	4	8	supra	supra	PROPN
ejpam-721	4	9	b	b	NOUN
ejpam-721	4	10	-	-	PUNCT
ejpam-721	4	11	open	open	ADJ
ejpam-721	4	12	maps	map	NOUN
ejpam-721	4	13	and	and	CCONJ
ejpam-721	4	14	supra	supra	PROPN
ejpam-721	4	15	b	b	PROPN
ejpam-721	4	16	-	-	PUNCT
ejpam-721	4	17	closed	close	VERB
ejpam-721	4	18	maps	map	NOUN
ejpam-721	4	19	and	and	CCONJ
ejpam-721	4	20	investigate	investigate	VERB
ejpam-721	4	21	several	several	ADJ
ejpam-721	4	22	properties	property	NOUN
ejpam-721	4	23	of	of	ADP
ejpam-721	4	24	them	they	PRON
ejpam-721	4	25	.	.	PUNCT
ejpam-721	5	1	2000	2000	NUM
ejpam-721	5	2	mathematics	mathematic	NOUN
ejpam-721	5	3	subject	subject	NOUN
ejpam-721	5	4	classifications	classification	NOUN
ejpam-721	5	5	:	:	PUNCT
ejpam-721	5	6	54a10	54a10	NUM
ejpam-721	5	7	,	,	PUNCT
ejpam-721	5	8	54a20	54a20	NUM
ejpam-721	5	9	key	key	ADJ
ejpam-721	5	10	words	word	NOUN
ejpam-721	5	11	and	and	CCONJ
ejpam-721	5	12	phrases	phrase	NOUN
ejpam-721	5	13	:	:	PUNCT
ejpam-721	5	14	supra	supra	PROPN
ejpam-721	5	15	b−open	b−open	PROPN
ejpam-721	5	16	set	set	NOUN
ejpam-721	5	17	,	,	PUNCT
ejpam-721	5	18	supra	supra	PROPN
ejpam-721	5	19	b−continuity	b−continuity	PROPN
ejpam-721	5	20	,	,	PUNCT
ejpam-721	5	21	supra	supra	PROPN
ejpam-721	5	22	b	b	PROPN
ejpam-721	5	23	-	-	PUNCT
ejpam-721	5	24	open	open	ADJ
ejpam-721	5	25	map	map	NOUN
ejpam-721	5	26	,	,	PUNCT
ejpam-721	5	27	supra	supra	PROPN
ejpam-721	5	28	b	b	PROPN
ejpam-721	5	29	-	-	PUNCT
ejpam-721	5	30	closed	closed	ADJ
ejpam-721	5	31	map	map	NOUN
ejpam-721	5	32	and	and	CCONJ
ejpam-721	5	33	supra	supra	ADJ
ejpam-721	5	34	topological	topological	ADJ
ejpam-721	5	35	space	space	NOUN
ejpam-721	5	36	1	1	NUM
ejpam-721	5	37	.	.	PUNCT
ejpam-721	5	38	introduction	introduction	NOUN
ejpam-721	5	39	in	in	ADP
ejpam-721	5	40	1983	1983	NUM
ejpam-721	5	41	,	,	PUNCT
ejpam-721	5	42	a.	a.	PROPN
ejpam-721	5	43	s.	s.	PROPN
ejpam-721	5	44	mashhour	mashhour	PROPN
ejpam-721	5	45	et	et	PROPN
ejpam-721	5	46	al	al	PROPN
ejpam-721	5	47	.	.	PUNCT
ejpam-721	6	1	[	[	X
ejpam-721	6	2	6	6	NUM
ejpam-721	6	3	]	]	PUNCT
ejpam-721	6	4	introduced	introduce	VERB
ejpam-721	6	5	the	the	DET
ejpam-721	6	6	supra	supra	PROPN
ejpam-721	6	7	topological	topological	ADJ
ejpam-721	6	8	spaces	space	NOUN
ejpam-721	6	9	and	and	CCONJ
ejpam-721	6	10	studied	study	VERB
ejpam-721	6	11	s	s	NOUN
ejpam-721	6	12	-	-	ADJ
ejpam-721	6	13	continuous	continuous	ADJ
ejpam-721	6	14	maps	map	NOUN
ejpam-721	6	15	and	and	CCONJ
ejpam-721	6	16	s?−continuous	s?−continuous	ADJ
ejpam-721	6	17	maps	map	NOUN
ejpam-721	6	18	.	.	PUNCT
ejpam-721	7	1	in	in	ADP
ejpam-721	7	2	1996	1996	NUM
ejpam-721	7	3	,	,	PUNCT
ejpam-721	7	4	d.	d.	PROPN
ejpam-721	7	5	andrijevic	andrijevic	PROPN
ejpam-721	7	6	’	'	PUNCT
ejpam-721	8	1	[	[	X
ejpam-721	8	2	2	2	NUM
ejpam-721	8	3	]	]	PUNCT
ejpam-721	8	4	introduced	introduce	VERB
ejpam-721	8	5	and	and	CCONJ
ejpam-721	8	6	studied	study	VERB
ejpam-721	8	7	a	a	DET
ejpam-721	8	8	class	class	NOUN
ejpam-721	8	9	of	of	ADP
ejpam-721	8	10	generalized	generalized	ADJ
ejpam-721	8	11	open	open	ADJ
ejpam-721	8	12	sets	set	NOUN
ejpam-721	8	13	in	in	ADP
ejpam-721	8	14	a	a	DET
ejpam-721	8	15	topological	topological	ADJ
ejpam-721	8	16	space	space	NOUN
ejpam-721	8	17	called	call	VERB
ejpam-721	8	18	b	b	NOUN
ejpam-721	8	19	-	-	PUNCT
ejpam-721	8	20	open	open	ADJ
ejpam-721	8	21	sets	set	NOUN
ejpam-721	8	22	.	.	PUNCT
ejpam-721	9	1	this	this	DET
ejpam-721	9	2	class	class	NOUN
ejpam-721	9	3	of	of	ADP
ejpam-721	9	4	sets	set	NOUN
ejpam-721	9	5	contained	contain	VERB
ejpam-721	9	6	in	in	ADP
ejpam-721	9	7	the	the	DET
ejpam-721	9	8	class	class	NOUN
ejpam-721	9	9	of	of	ADP
ejpam-721	9	10	β	β	X
ejpam-721	9	11	-open	-open	NOUN
ejpam-721	9	12	sets	set	NOUN
ejpam-721	9	13	[	[	X
ejpam-721	9	14	1	1	NUM
ejpam-721	9	15	]	]	PUNCT
ejpam-721	9	16	and	and	CCONJ
ejpam-721	9	17	contains	contain	VERB
ejpam-721	9	18	all	all	DET
ejpam-721	9	19	semi	semi	ADJ
ejpam-721	9	20	-	-	ADJ
ejpam-721	9	21	open	open	ADJ
ejpam-721	9	22	sets	set	NOUN
ejpam-721	9	23	[	[	X
ejpam-721	9	24	4	4	NUM
ejpam-721	9	25	]	]	PUNCT
ejpam-721	9	26	and	and	CCONJ
ejpam-721	9	27	all	all	DET
ejpam-721	9	28	pre	pre	ADJ
ejpam-721	9	29	-	-	ADJ
ejpam-721	9	30	open	open	ADJ
ejpam-721	9	31	sets	set	NOUN
ejpam-721	9	32	[	[	X
ejpam-721	9	33	5	5	NUM
ejpam-721	9	34	]	]	PUNCT
ejpam-721	9	35	.	.	PUNCT
ejpam-721	10	1	in	in	ADP
ejpam-721	10	2	2008	2008	NUM
ejpam-721	10	3	,	,	PUNCT
ejpam-721	10	4	r.	r.	PROPN
ejpam-721	10	5	devi	devi	PROPN
ejpam-721	10	6	et	et	PROPN
ejpam-721	10	7	al	al	PROPN
ejpam-721	10	8	.	.	PUNCT
ejpam-721	11	1	[	[	X
ejpam-721	11	2	3	3	NUM
ejpam-721	11	3	]	]	PUNCT
ejpam-721	11	4	introduced	introduce	VERB
ejpam-721	11	5	and	and	CCONJ
ejpam-721	11	6	studied	study	VERB
ejpam-721	11	7	a	a	DET
ejpam-721	11	8	class	class	NOUN
ejpam-721	11	9	of	of	ADP
ejpam-721	11	10	sets	set	NOUN
ejpam-721	11	11	and	and	CCONJ
ejpam-721	11	12	maps	map	NOUN
ejpam-721	11	13	between	between	ADP
ejpam-721	11	14	topological	topological	ADJ
ejpam-721	11	15	spaces	space	NOUN
ejpam-721	11	16	called	call	VERB
ejpam-721	11	17	supra	supra	PROPN
ejpam-721	11	18	α−open	α−open	NOUN
ejpam-721	11	19	sets	set	NOUN
ejpam-721	11	20	and	and	CCONJ
ejpam-721	11	21	supra	supra	PROPN
ejpam-721	11	22	α−continuous	α−continuous	ADJ
ejpam-721	11	23	maps	map	NOUN
ejpam-721	11	24	,	,	PUNCT
ejpam-721	11	25	respectively	respectively	ADV
ejpam-721	11	26	.	.	PUNCT
ejpam-721	12	1	now	now	ADV
ejpam-721	12	2	,	,	PUNCT
ejpam-721	12	3	we	we	PRON
ejpam-721	12	4	introduce	introduce	VERB
ejpam-721	12	5	the	the	DET
ejpam-721	12	6	concept	concept	NOUN
ejpam-721	12	7	of	of	ADP
ejpam-721	12	8	supra	supra	ADJ
ejpam-721	12	9	b−open	b−open	PROPN
ejpam-721	12	10	sets	set	NOUN
ejpam-721	12	11	and	and	CCONJ
ejpam-721	12	12	study	study	VERB
ejpam-721	12	13	some	some	DET
ejpam-721	12	14	basic	basic	ADJ
ejpam-721	12	15	properties	property	NOUN
ejpam-721	12	16	of	of	ADP
ejpam-721	12	17	it	it	PRON
ejpam-721	12	18	.	.	PUNCT
ejpam-721	13	1	also	also	ADV
ejpam-721	13	2	,	,	PUNCT
ejpam-721	13	3	we	we	PRON
ejpam-721	13	4	introduce	introduce	VERB
ejpam-721	13	5	the	the	DET
ejpam-721	13	6	concepts	concept	NOUN
ejpam-721	13	7	of	of	ADP
ejpam-721	13	8	supra	supra	ADJ
ejpam-721	13	9	b−continuous	b−continuous	ADJ
ejpam-721	13	10	maps	map	NOUN
ejpam-721	13	11	,	,	PUNCT
ejpam-721	13	12	supra	supra	PROPN
ejpam-721	13	13	b	b	PROPN
ejpam-721	13	14	-	-	PUNCT
ejpam-721	13	15	open	open	ADJ
ejpam-721	13	16	maps	map	NOUN
ejpam-721	13	17	and	and	CCONJ
ejpam-721	13	18	supra	supra	PROPN
ejpam-721	13	19	b	b	PROPN
ejpam-721	13	20	-	-	PUNCT
ejpam-721	13	21	closed	close	VERB
ejpam-721	13	22	maps	map	NOUN
ejpam-721	13	23	and	and	CCONJ
ejpam-721	13	24	investigate	investigate	VERB
ejpam-721	13	25	several	several	ADJ
ejpam-721	13	26	properties	property	NOUN
ejpam-721	13	27	for	for	ADP
ejpam-721	13	28	these	these	DET
ejpam-721	13	29	classes	class	NOUN
ejpam-721	13	30	of	of	ADP
ejpam-721	13	31	maps	map	NOUN
ejpam-721	13	32	.	.	PUNCT
ejpam-721	14	1	in	in	ADP
ejpam-721	14	2	particular	particular	ADJ
ejpam-721	14	3	,	,	PUNCT
ejpam-721	14	4	we	we	PRON
ejpam-721	14	5	study	study	VERB
ejpam-721	14	6	the	the	DET
ejpam-721	14	7	relation	relation	NOUN
ejpam-721	14	8	between	between	ADP
ejpam-721	14	9	supra	supra	PROPN
ejpam-721	14	10	b	b	PROPN
ejpam-721	14	11	-	-	PUNCT
ejpam-721	14	12	continuous	continuous	ADJ
ejpam-721	14	13	maps	map	NOUN
ejpam-721	14	14	and	and	CCONJ
ejpam-721	14	15	supra	supra	PROPN
ejpam-721	14	16	b	b	X
ejpam-721	14	17	-	-	PUNCT
ejpam-721	14	18	open	open	ADJ
ejpam-721	14	19	maps	map	NOUN
ejpam-721	14	20	(	(	PUNCT
ejpam-721	14	21	supra	supra	PROPN
ejpam-721	14	22	b	b	PROPN
ejpam-721	14	23	-	-	PUNCT
ejpam-721	14	24	closed	closed	ADJ
ejpam-721	14	25	maps	map	NOUN
ejpam-721	14	26	)	)	PUNCT
ejpam-721	14	27	.	.	PUNCT
ejpam-721	15	1	throughout	throughout	ADP
ejpam-721	15	2	this	this	DET
ejpam-721	15	3	paper	paper	NOUN
ejpam-721	15	4	,	,	PUNCT
ejpam-721	15	5	(	(	PUNCT
ejpam-721	15	6	x	x	X
ejpam-721	15	7	,	,	PUNCT
ejpam-721	15	8	τ	τ	PROPN
ejpam-721	15	9	)	)	PUNCT
ejpam-721	15	10	,	,	PUNCT
ejpam-721	15	11	(	(	PUNCT
ejpam-721	15	12	y	y	PROPN
ejpam-721	15	13	,	,	PUNCT
ejpam-721	15	14	σ	σ	PROPN
ejpam-721	15	15	)	)	PUNCT
ejpam-721	15	16	and	and	CCONJ
ejpam-721	15	17	(	(	PUNCT
ejpam-721	15	18	z	z	NOUN
ejpam-721	15	19	,	,	PUNCT
ejpam-721	15	20	υ	υ	NOUN
ejpam-721	15	21	)	)	PUNCT
ejpam-721	15	22	(	(	PUNCT
ejpam-721	15	23	or	or	CCONJ
ejpam-721	15	24	simply	simply	ADV
ejpam-721	15	25	,	,	PUNCT
ejpam-721	15	26	x	x	INTJ
ejpam-721	15	27	,	,	PUNCT
ejpam-721	15	28	y	y	PROPN
ejpam-721	15	29	and	and	CCONJ
ejpam-721	15	30	z	z	PROPN
ejpam-721	15	31	)	)	PUNCT
ejpam-721	15	32	denote	denote	VERB
ejpam-721	15	33	topological	topological	ADJ
ejpam-721	15	34	spaces	space	NOUN
ejpam-721	15	35	on	on	ADP
ejpam-721	15	36	which	which	PRON
ejpam-721	15	37	no	no	DET
ejpam-721	15	38	separation	separation	NOUN
ejpam-721	15	39	axioms	axiom	NOUN
ejpam-721	15	40	are	be	AUX
ejpam-721	15	41	assumed	assume	VERB
ejpam-721	15	42	unless	unless	SCONJ
ejpam-721	15	43	explicitly	explicitly	ADV
ejpam-721	15	44	stated	state	VERB
ejpam-721	15	45	.	.	PUNCT
ejpam-721	16	1	for	for	ADP
ejpam-721	16	2	a	a	DET
ejpam-721	16	3	subset	subset	NOUN
ejpam-721	16	4	∗corresponding	∗corresponde	VERB
ejpam-721	16	5	author	author	NOUN
ejpam-721	16	6	.	.	PUNCT
ejpam-721	17	1	email	email	NOUN
ejpam-721	17	2	addresses	address	NOUN
ejpam-721	17	3	:	:	PUNCT
ejpam-721	17	4	o_r_sayed@yahoo.com	o_r_sayed@yahoo.com	X
ejpam-721	17	5	(	(	PUNCT
ejpam-721	17	6	o.	o.	PROPN
ejpam-721	17	7	r.	r.	PROPN
ejpam-721	17	8	sayed	say	VERB
ejpam-721	17	9	)	)	PUNCT
ejpam-721	17	10	,	,	PUNCT
ejpam-721	17	11	t.noiri@nifty.com	t.noiri@nifty.com	X
ejpam-721	17	12	(	(	PUNCT
ejpam-721	17	13	t.	t.	PROPN
ejpam-721	17	14	noiri	noiri	PROPN
ejpam-721	17	15	)	)	PUNCT
ejpam-721	17	16	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-721	18	1	295	295	NUM
ejpam-721	19	1	c	c	X
ejpam-721	19	2	©	©	PROPN
ejpam-721	19	3	2010	2010	NUM
ejpam-721	19	4	ejpam	ejpam	NOUN
ejpam-721	19	5	all	all	DET
ejpam-721	19	6	rights	right	NOUN
ejpam-721	19	7	reserved	reserve	VERB
ejpam-721	19	8	.	.	PUNCT
ejpam-721	20	1	o.	o.	PROPN
ejpam-721	20	2	r.	r.	PROPN
ejpam-721	20	3	sayed	say	VERB
ejpam-721	20	4	,	,	PUNCT
ejpam-721	20	5	t.	t.	PROPN
ejpam-721	20	6	noiri	noiri	PROPN
ejpam-721	20	7	/	/	SYM
ejpam-721	20	8	eur	eur	PROPN
ejpam-721	20	9	.	.	PUNCT
ejpam-721	21	1	j.	j.	PROPN
ejpam-721	21	2	pure	pure	PROPN
ejpam-721	21	3	appl	appl	PROPN
ejpam-721	21	4	.	.	PROPN
ejpam-721	21	5	math	math	PROPN
ejpam-721	21	6	,	,	PUNCT
ejpam-721	21	7	3	3	NUM
ejpam-721	21	8	(	(	PUNCT
ejpam-721	21	9	2010	2010	NUM
ejpam-721	21	10	)	)	PUNCT
ejpam-721	21	11	,	,	PUNCT
ejpam-721	21	12	295	295	NUM
ejpam-721	21	13	-	-	SYM
ejpam-721	21	14	302	302	NUM
ejpam-721	21	15	296	296	NUM
ejpam-721	21	16	a	a	PRON
ejpam-721	21	17	of	of	ADP
ejpam-721	21	18	(	(	PUNCT
ejpam-721	21	19	x	x	PROPN
ejpam-721	21	20	,	,	PUNCT
ejpam-721	21	21	τ	τ	PROPN
ejpam-721	21	22	)	)	PUNCT
ejpam-721	21	23	,	,	PUNCT
ejpam-721	21	24	the	the	DET
ejpam-721	21	25	closure	closure	NOUN
ejpam-721	21	26	and	and	CCONJ
ejpam-721	21	27	the	the	DET
ejpam-721	21	28	interior	interior	NOUN
ejpam-721	21	29	of	of	ADP
ejpam-721	21	30	a	a	DET
ejpam-721	21	31	in	in	NOUN
ejpam-721	21	32	x	x	X
ejpam-721	21	33	are	be	AUX
ejpam-721	21	34	denoted	denote	VERB
ejpam-721	21	35	by	by	ADP
ejpam-721	21	36	cl(a	cl(a	NOUN
ejpam-721	21	37	)	)	PUNCT
ejpam-721	21	38	and	and	CCONJ
ejpam-721	21	39	int(a	int(a	PROPN
ejpam-721	21	40	)	)	PUNCT
ejpam-721	21	41	,	,	PUNCT
ejpam-721	21	42	respectively	respectively	ADV
ejpam-721	21	43	.	.	PUNCT
ejpam-721	22	1	the	the	DET
ejpam-721	22	2	complement	complement	NOUN
ejpam-721	22	3	of	of	ADP
ejpam-721	22	4	a	a	PRON
ejpam-721	22	5	is	be	AUX
ejpam-721	22	6	denoted	denote	VERB
ejpam-721	22	7	by	by	ADP
ejpam-721	22	8	x	x	SYM
ejpam-721	22	9	−	−	PROPN
ejpam-721	22	10	a.	a.	NOUN
ejpam-721	22	11	in	in	ADP
ejpam-721	22	12	the	the	DET
ejpam-721	22	13	space	space	NOUN
ejpam-721	22	14	(	(	PUNCT
ejpam-721	22	15	x	x	X
ejpam-721	22	16	,	,	PUNCT
ejpam-721	22	17	τ	τ	PROPN
ejpam-721	22	18	)	)	PUNCT
ejpam-721	22	19	,	,	PUNCT
ejpam-721	22	20	a	a	DET
ejpam-721	22	21	subset	subset	NOUN
ejpam-721	22	22	a	a	PRON
ejpam-721	22	23	is	be	AUX
ejpam-721	22	24	said	say	VERB
ejpam-721	22	25	to	to	PART
ejpam-721	22	26	be	be	AUX
ejpam-721	22	27	β	β	X
ejpam-721	22	28	-open	-open	X
ejpam-721	22	29	(	(	PUNCT
ejpam-721	22	30	resp	resp	NOUN
ejpam-721	22	31	.	.	PUNCT
ejpam-721	23	1	b	b	X
ejpam-721	23	2	-	-	PUNCT
ejpam-721	23	3	open	open	ADJ
ejpam-721	23	4	,	,	PUNCT
ejpam-721	23	5	semi	semi	ADJ
ejpam-721	23	6	-	-	ADJ
ejpam-721	23	7	open	open	ADJ
ejpam-721	23	8	,	,	PUNCT
ejpam-721	23	9	pre	pre	ADJ
ejpam-721	23	10	-	-	ADJ
ejpam-721	23	11	open	open	ADJ
ejpam-721	23	12	,	,	PUNCT
ejpam-721	23	13	α	α	NOUN
ejpam-721	23	14	-	-	ADJ
ejpam-721	23	15	open	open	ADJ
ejpam-721	24	1	[	[	X
ejpam-721	24	2	7	7	NUM
ejpam-721	24	3	]	]	PUNCT
ejpam-721	24	4	)	)	PUNCT
ejpam-721	24	5	if	if	SCONJ
ejpam-721	24	6	a	a	DET
ejpam-721	24	7	⊆	⊆	NUM
ejpam-721	24	8	cl(int(cl(a	cl(int(cl(a	NOUN
ejpam-721	24	9	)	)	PUNCT
ejpam-721	24	10	)	)	PUNCT
ejpam-721	24	11	)	)	PUNCT
ejpam-721	24	12	(	(	PUNCT
ejpam-721	24	13	resp	resp	NOUN
ejpam-721	24	14	.	.	PUNCT
ejpam-721	25	1	a	a	DET
ejpam-721	25	2	⊆	⊆	NUM
ejpam-721	25	3	cl(int(a	cl(int(a	NOUN
ejpam-721	25	4	)	)	PUNCT
ejpam-721	25	5	)	)	PUNCT
ejpam-721	25	6	∪	∪	ADP
ejpam-721	25	7	int(cl(a	int(cl(a	PROPN
ejpam-721	25	8	)	)	PUNCT
ejpam-721	25	9	)	)	PUNCT
ejpam-721	25	10	,	,	PUNCT
ejpam-721	25	11	a	a	DET
ejpam-721	25	12	⊆	⊆	NUM
ejpam-721	25	13	cl(int(a	cl(int(a	NOUN
ejpam-721	25	14	)	)	PUNCT
ejpam-721	25	15	)	)	PUNCT
ejpam-721	25	16	,	,	PUNCT
ejpam-721	25	17	a	a	DET
ejpam-721	25	18	⊆	⊆	NUM
ejpam-721	25	19	int(cl(a	int(cl(a	PROPN
ejpam-721	25	20	)	)	PUNCT
ejpam-721	25	21	)	)	PUNCT
ejpam-721	25	22	,	,	PUNCT
ejpam-721	25	23	a	a	DET
ejpam-721	25	24	⊆	⊆	NUM
ejpam-721	25	25	int(cl(int(a	int(cl(int(a	NOUN
ejpam-721	25	26	)	)	PUNCT
ejpam-721	25	27	)	)	PUNCT
ejpam-721	25	28	)	)	PUNCT
ejpam-721	25	29	.	.	PUNCT
ejpam-721	26	1	the	the	DET
ejpam-721	26	2	family	family	NOUN
ejpam-721	26	3	of	of	ADP
ejpam-721	26	4	all	all	DET
ejpam-721	26	5	β	β	NOUN
ejpam-721	26	6	-	-	ADJ
ejpam-721	26	7	open	open	ADJ
ejpam-721	26	8	(	(	PUNCT
ejpam-721	26	9	resp	resp	NOUN
ejpam-721	26	10	.	.	PUNCT
ejpam-721	27	1	b	b	X
ejpam-721	27	2	-	-	PUNCT
ejpam-721	27	3	open	open	ADJ
ejpam-721	27	4	,	,	PUNCT
ejpam-721	27	5	semi	semi	ADJ
ejpam-721	27	6	-	-	ADJ
ejpam-721	27	7	open	open	ADJ
ejpam-721	27	8	,	,	PUNCT
ejpam-721	27	9	preopen	preopen	ADJ
ejpam-721	27	10	,	,	PUNCT
ejpam-721	27	11	α	α	NOUN
ejpam-721	27	12	-	-	ADJ
ejpam-721	27	13	open	open	ADJ
ejpam-721	27	14	)	)	PUNCT
ejpam-721	27	15	sets	set	NOUN
ejpam-721	27	16	of	of	ADP
ejpam-721	27	17	(	(	PUNCT
ejpam-721	27	18	x	x	INTJ
ejpam-721	27	19	,	,	PUNCT
ejpam-721	27	20	τ	τ	X
ejpam-721	27	21	)	)	PUNCT
ejpam-721	27	22	is	be	AUX
ejpam-721	27	23	denoted	denote	VERB
ejpam-721	27	24	by	by	ADP
ejpam-721	27	25	β	β	X
ejpam-721	27	26	(	(	PUNCT
ejpam-721	27	27	x	x	PROPN
ejpam-721	27	28	)	)	PUNCT
ejpam-721	27	29	(	(	PUNCT
ejpam-721	27	30	resp	resp	NOUN
ejpam-721	27	31	.	.	PUNCT
ejpam-721	28	1	b	b	X
ejpam-721	28	2	(	(	PUNCT
ejpam-721	28	3	x	x	PROPN
ejpam-721	28	4	)	)	PUNCT
ejpam-721	28	5	,	,	PUNCT
ejpam-721	28	6	so(x	so(x	NOUN
ejpam-721	28	7	)	)	PUNCT
ejpam-721	28	8	,	,	PUNCT
ejpam-721	28	9	po(x	po(x	NUM
ejpam-721	28	10	)	)	PUNCT
ejpam-721	28	11	,	,	PUNCT
ejpam-721	28	12	α	α	PROPN
ejpam-721	28	13	(	(	PUNCT
ejpam-721	28	14	x	x	NOUN
ejpam-721	28	15	)	)	PUNCT
ejpam-721	28	16	)	)	PUNCT
ejpam-721	28	17	.	.	PUNCT
ejpam-721	29	1	a	a	DET
ejpam-721	29	2	subcollection	subcollection	NOUN
ejpam-721	29	3	µ	µ	X
ejpam-721	29	4	⊂	⊂	X
ejpam-721	29	5	2x	2x	NUM
ejpam-721	29	6	is	be	AUX
ejpam-721	29	7	called	call	VERB
ejpam-721	29	8	a	a	DET
ejpam-721	29	9	supra	supra	ADJ
ejpam-721	29	10	topology	topology	NOUN
ejpam-721	29	11	[	[	X
ejpam-721	29	12	6	6	NUM
ejpam-721	29	13	]	]	PUNCT
ejpam-721	29	14	on	on	ADP
ejpam-721	29	15	x	x	SYM
ejpam-721	29	16	if	if	SCONJ
ejpam-721	29	17	x	x	PROPN
ejpam-721	29	18	∈	∈	PROPN
ejpam-721	29	19	µ	µ	X
ejpam-721	29	20	and	and	CCONJ
ejpam-721	29	21	µ	µ	NOUN
ejpam-721	29	22	is	be	AUX
ejpam-721	29	23	closed	close	VERB
ejpam-721	29	24	under	under	ADP
ejpam-721	29	25	arbitrary	arbitrary	ADJ
ejpam-721	29	26	union	union	NOUN
ejpam-721	29	27	.	.	PUNCT
ejpam-721	30	1	(	(	PUNCT
ejpam-721	30	2	x	x	X
ejpam-721	30	3	,	,	PUNCT
ejpam-721	30	4	µ	µ	X
ejpam-721	30	5	)	)	PUNCT
ejpam-721	30	6	is	be	AUX
ejpam-721	30	7	called	call	VERB
ejpam-721	30	8	a	a	DET
ejpam-721	30	9	supra	supra	ADJ
ejpam-721	30	10	topological	topological	ADJ
ejpam-721	30	11	space	space	NOUN
ejpam-721	30	12	.	.	PUNCT
ejpam-721	31	1	the	the	DET
ejpam-721	31	2	elements	element	NOUN
ejpam-721	31	3	of	of	ADP
ejpam-721	31	4	µ	µ	NOUN
ejpam-721	31	5	are	be	AUX
ejpam-721	31	6	said	say	VERB
ejpam-721	31	7	to	to	PART
ejpam-721	31	8	be	be	AUX
ejpam-721	31	9	supra	supra	ADJ
ejpam-721	31	10	open	open	ADJ
ejpam-721	31	11	in	in	ADP
ejpam-721	31	12	(	(	PUNCT
ejpam-721	31	13	x	x	INTJ
ejpam-721	31	14	,	,	PUNCT
ejpam-721	31	15	µ	µ	NOUN
ejpam-721	31	16	)	)	PUNCT
ejpam-721	31	17	and	and	CCONJ
ejpam-721	31	18	the	the	DET
ejpam-721	31	19	complement	complement	NOUN
ejpam-721	31	20	of	of	ADP
ejpam-721	31	21	a	a	DET
ejpam-721	31	22	supra	supra	ADJ
ejpam-721	31	23	open	open	ADJ
ejpam-721	31	24	set	set	NOUN
ejpam-721	31	25	is	be	AUX
ejpam-721	31	26	called	call	VERB
ejpam-721	31	27	a	a	DET
ejpam-721	31	28	supra	supra	NOUN
ejpam-721	31	29	closed	close	VERB
ejpam-721	31	30	set	set	NOUN
ejpam-721	31	31	.	.	PUNCT
ejpam-721	32	1	the	the	DET
ejpam-721	32	2	supra	supra	PROPN
ejpam-721	32	3	closure	closure	NOUN
ejpam-721	32	4	of	of	ADP
ejpam-721	32	5	a	a	DET
ejpam-721	32	6	set	set	NOUN
ejpam-721	32	7	a	a	PRON
ejpam-721	32	8	,	,	PUNCT
ejpam-721	32	9	denoted	denote	VERB
ejpam-721	32	10	by	by	ADP
ejpam-721	32	11	clµ(a	clµ(a	PROPN
ejpam-721	32	12	)	)	PUNCT
ejpam-721	32	13	,	,	PUNCT
ejpam-721	32	14	is	be	AUX
ejpam-721	32	15	the	the	DET
ejpam-721	32	16	intersection	intersection	NOUN
ejpam-721	32	17	of	of	ADP
ejpam-721	32	18	supra	supra	PROPN
ejpam-721	32	19	closed	closed	ADJ
ejpam-721	32	20	sets	set	NOUN
ejpam-721	32	21	including	include	VERB
ejpam-721	32	22	a.	a.	NOUN
ejpam-721	32	23	the	the	DET
ejpam-721	32	24	supra	supra	PROPN
ejpam-721	32	25	interior	interior	NOUN
ejpam-721	32	26	of	of	ADP
ejpam-721	32	27	a	a	DET
ejpam-721	32	28	set	set	NOUN
ejpam-721	32	29	a	a	PRON
ejpam-721	32	30	,	,	PUNCT
ejpam-721	32	31	denoted	denote	VERB
ejpam-721	32	32	by	by	ADP
ejpam-721	32	33	intµ(a	intµ(a	PROPN
ejpam-721	32	34	)	)	PUNCT
ejpam-721	32	35	,	,	PUNCT
ejpam-721	32	36	is	be	AUX
ejpam-721	32	37	the	the	DET
ejpam-721	32	38	union	union	NOUN
ejpam-721	32	39	of	of	ADP
ejpam-721	32	40	supra	supra	PROPN
ejpam-721	32	41	open	open	ADJ
ejpam-721	32	42	sets	set	NOUN
ejpam-721	32	43	included	include	VERB
ejpam-721	32	44	in	in	ADP
ejpam-721	32	45	a.	a.	NOUN
ejpam-721	32	46	the	the	DET
ejpam-721	32	47	supra	supra	PROPN
ejpam-721	32	48	topology	topology	PROPN
ejpam-721	32	49	µ	µ	X
ejpam-721	32	50	on	on	ADV
ejpam-721	32	51	x	x	VERB
ejpam-721	32	52	is	be	AUX
ejpam-721	32	53	associated	associate	VERB
ejpam-721	32	54	with	with	ADP
ejpam-721	32	55	the	the	DET
ejpam-721	32	56	topology	topology	NOUN
ejpam-721	32	57	τ	τ	PROPN
ejpam-721	32	58	if	if	SCONJ
ejpam-721	32	59	τ	τ	PROPN
ejpam-721	32	60	⊂	⊂	PROPN
ejpam-721	32	61	µ.	µ.	VERB
ejpam-721	32	62	a	a	DET
ejpam-721	32	63	set	set	NOUN
ejpam-721	32	64	a	a	PRON
ejpam-721	32	65	is	be	AUX
ejpam-721	32	66	called	call	VERB
ejpam-721	32	67	a	a	DET
ejpam-721	32	68	supra	supra	ADJ
ejpam-721	32	69	α	α	NOUN
ejpam-721	32	70	-	-	ADJ
ejpam-721	32	71	open	open	ADJ
ejpam-721	32	72	set	set	NOUN
ejpam-721	32	73	[	[	X
ejpam-721	32	74	3	3	NUM
ejpam-721	32	75	]	]	PUNCT
ejpam-721	32	76	(	(	PUNCT
ejpam-721	32	77	resp	resp	NOUN
ejpam-721	32	78	.	.	PUNCT
ejpam-721	33	1	supra	supra	PROPN
ejpam-721	33	2	semi	semi	ADJ
ejpam-721	33	3	-	-	ADJ
ejpam-721	33	4	open	open	ADJ
ejpam-721	33	5	set	set	NOUN
ejpam-721	33	6	[	[	X
ejpam-721	33	7	6	6	NUM
ejpam-721	33	8	]	]	PUNCT
ejpam-721	33	9	)	)	PUNCT
ejpam-721	33	10	if	if	SCONJ
ejpam-721	33	11	a⊆	a⊆	NOUN
ejpam-721	33	12	intµ(clµ(intµ(a	intµ(clµ(intµ(a	NOUN
ejpam-721	33	13	)	)	PUNCT
ejpam-721	33	14	)	)	PUNCT
ejpam-721	33	15	)	)	PUNCT
ejpam-721	34	1	(	(	PUNCT
ejpam-721	34	2	resp	resp	NOUN
ejpam-721	34	3	.	.	PUNCT
ejpam-721	35	1	a⊆	a⊆	PROPN
ejpam-721	35	2	clµ(intµ(a	clµ(intµ(a	ADJ
ejpam-721	35	3	)	)	PUNCT
ejpam-721	35	4	)	)	PUNCT
ejpam-721	35	5	)	)	PUNCT
ejpam-721	35	6	.	.	PUNCT
ejpam-721	36	1	before	before	SCONJ
ejpam-721	36	2	we	we	PRON
ejpam-721	36	3	study	study	VERB
ejpam-721	36	4	the	the	DET
ejpam-721	36	5	basic	basic	ADJ
ejpam-721	36	6	properties	property	NOUN
ejpam-721	36	7	of	of	ADP
ejpam-721	36	8	supra	supra	PROPN
ejpam-721	36	9	b	b	NOUN
ejpam-721	36	10	-	-	PUNCT
ejpam-721	36	11	open	open	ADJ
ejpam-721	36	12	sets	set	NOUN
ejpam-721	36	13	we	we	PRON
ejpam-721	36	14	have	have	VERB
ejpam-721	36	15	the	the	DET
ejpam-721	36	16	following	follow	VERB
ejpam-721	36	17	correction	correction	NOUN
ejpam-721	36	18	in	in	ADP
ejpam-721	36	19	[	[	X
ejpam-721	36	20	3	3	NUM
ejpam-721	36	21	]	]	PUNCT
ejpam-721	36	22	.	.	PUNCT
ejpam-721	37	1	(	(	PUNCT
ejpam-721	37	2	1	1	X
ejpam-721	37	3	)	)	PUNCT
ejpam-721	37	4	definition	definition	NOUN
ejpam-721	37	5	6	6	NUM
ejpam-721	37	6	should	should	AUX
ejpam-721	37	7	be	be	AUX
ejpam-721	37	8	written	write	VERB
ejpam-721	37	9	as	as	SCONJ
ejpam-721	37	10	we	we	PRON
ejpam-721	37	11	stated	state	VERB
ejpam-721	37	12	before	before	ADV
ejpam-721	37	13	.	.	PUNCT
ejpam-721	38	1	(	(	PUNCT
ejpam-721	38	2	2	2	X
ejpam-721	38	3	)	)	PUNCT
ejpam-721	38	4	example	example	NOUN
ejpam-721	38	5	3.2	3.2	NUM
ejpam-721	38	6	is	be	AUX
ejpam-721	38	7	not	not	PART
ejpam-721	38	8	correct	correct	ADJ
ejpam-721	38	9	and	and	CCONJ
ejpam-721	38	10	we	we	PRON
ejpam-721	38	11	will	will	AUX
ejpam-721	38	12	state	state	VERB
ejpam-721	38	13	instead	instead	ADV
ejpam-721	38	14	of	of	ADP
ejpam-721	38	15	it	it	PRON
ejpam-721	38	16	.	.	PUNCT
ejpam-721	39	1	(	(	PUNCT
ejpam-721	39	2	3	3	X
ejpam-721	39	3	)	)	PUNCT
ejpam-721	39	4	the	the	DET
ejpam-721	39	5	proof	proof	NOUN
ejpam-721	39	6	of	of	ADP
ejpam-721	39	7	theorem	theorem	ADJ
ejpam-721	39	8	3.3	3.3	NUM
ejpam-721	39	9	(	(	PUNCT
ejpam-721	39	10	ii	ii	NOUN
ejpam-721	39	11	)	)	PUNCT
ejpam-721	39	12	is	be	AUX
ejpam-721	39	13	not	not	PART
ejpam-721	39	14	correct	correct	ADJ
ejpam-721	39	15	as	as	SCONJ
ejpam-721	39	16	τ∗	τ∗	NOUN
ejpam-721	39	17	is	be	AUX
ejpam-721	39	18	not	not	PART
ejpam-721	39	19	supa	supa	NOUN
ejpam-721	39	20	-	-	PUNCT
ejpam-721	39	21	topology	topology	NOUN
ejpam-721	39	22	as	as	ADV
ejpam-721	39	23	well	well	ADV
ejpam-721	39	24	as	as	ADP
ejpam-721	39	25	theorem	theorem	VERB
ejpam-721	39	26	3.4	3.4	NUM
ejpam-721	39	27	(	(	PUNCT
ejpam-721	39	28	ii	ii	NOUN
ejpam-721	39	29	)	)	PUNCT
ejpam-721	39	30	.	.	PUNCT
ejpam-721	40	1	2	2	X
ejpam-721	40	2	.	.	X
ejpam-721	40	3	supra	supra	PROPN
ejpam-721	40	4	b	b	X
ejpam-721	40	5	-	-	PUNCT
ejpam-721	40	6	open	open	ADJ
ejpam-721	40	7	sets	set	NOUN
ejpam-721	40	8	in	in	ADP
ejpam-721	40	9	this	this	DET
ejpam-721	40	10	section	section	NOUN
ejpam-721	40	11	,	,	PUNCT
ejpam-721	40	12	we	we	PRON
ejpam-721	40	13	introduce	introduce	VERB
ejpam-721	40	14	a	a	DET
ejpam-721	40	15	new	new	ADJ
ejpam-721	40	16	class	class	NOUN
ejpam-721	40	17	of	of	ADP
ejpam-721	40	18	generalized	generalized	ADJ
ejpam-721	40	19	open	open	ADJ
ejpam-721	40	20	sets	set	NOUN
ejpam-721	40	21	called	call	VERB
ejpam-721	40	22	supra	supra	PROPN
ejpam-721	40	23	b	b	NOUN
ejpam-721	40	24	-	-	PUNCT
ejpam-721	40	25	open	open	ADJ
ejpam-721	40	26	sets	set	NOUN
ejpam-721	40	27	and	and	CCONJ
ejpam-721	40	28	study	study	VERB
ejpam-721	40	29	some	some	PRON
ejpam-721	40	30	of	of	ADP
ejpam-721	40	31	their	their	PRON
ejpam-721	40	32	properties	property	NOUN
ejpam-721	40	33	.	.	PUNCT
ejpam-721	41	1	definition	definition	NOUN
ejpam-721	41	2	1	1	NUM
ejpam-721	41	3	.	.	PUNCT
ejpam-721	42	1	let	let	AUX
ejpam-721	42	2	(	(	PUNCT
ejpam-721	42	3	x	x	X
ejpam-721	42	4	,	,	PUNCT
ejpam-721	42	5	µ	µ	X
ejpam-721	42	6	)	)	PUNCT
ejpam-721	42	7	be	be	AUX
ejpam-721	42	8	a	a	DET
ejpam-721	42	9	supra	supra	ADJ
ejpam-721	42	10	topological	topological	ADJ
ejpam-721	42	11	space	space	NOUN
ejpam-721	42	12	.	.	PUNCT
ejpam-721	43	1	a	a	DET
ejpam-721	43	2	set	set	NOUN
ejpam-721	43	3	a	a	PRON
ejpam-721	43	4	is	be	AUX
ejpam-721	43	5	called	call	VERB
ejpam-721	43	6	a	a	DET
ejpam-721	43	7	supra	supra	PROPN
ejpam-721	43	8	b	b	PROPN
ejpam-721	43	9	-open	-open	NOUN
ejpam-721	43	10	set	set	VERB
ejpam-721	43	11	if	if	SCONJ
ejpam-721	43	12	a	a	DET
ejpam-721	43	13	⊆	⊆	NUM
ejpam-721	43	14	clµ(intµ(a	clµ(intµ(a	NOUN
ejpam-721	43	15	)	)	PUNCT
ejpam-721	43	16	)	)	PUNCT
ejpam-721	44	1	⋃	⋃	NOUN
ejpam-721	44	2	intµ(clµ(a	intµ(clµ(a	NOUN
ejpam-721	44	3	)	)	PUNCT
ejpam-721	44	4	)	)	PUNCT
ejpam-721	44	5	.	.	PUNCT
ejpam-721	45	1	the	the	DET
ejpam-721	45	2	complement	complement	NOUN
ejpam-721	45	3	of	of	ADP
ejpam-721	45	4	a	a	DET
ejpam-721	45	5	supra	supra	PROPN
ejpam-721	45	6	b	b	NOUN
ejpam-721	45	7	-	-	PUNCT
ejpam-721	45	8	open	open	ADJ
ejpam-721	45	9	set	set	NOUN
ejpam-721	45	10	is	be	AUX
ejpam-721	45	11	called	call	VERB
ejpam-721	45	12	a	a	DET
ejpam-721	45	13	supra	supra	PROPN
ejpam-721	45	14	b	b	PROPN
ejpam-721	45	15	-	-	PUNCT
ejpam-721	45	16	closed	closed	ADJ
ejpam-721	45	17	set	set	NOUN
ejpam-721	45	18	.	.	PUNCT
ejpam-721	46	1	theorem	theorem	NOUN
ejpam-721	46	2	1	1	NUM
ejpam-721	46	3	.	.	PUNCT
ejpam-721	47	1	every	every	DET
ejpam-721	47	2	supra	supra	NOUN
ejpam-721	47	3	semi	semi	ADJ
ejpam-721	47	4	-	-	ADJ
ejpam-721	47	5	open	open	ADJ
ejpam-721	47	6	set	set	NOUN
ejpam-721	47	7	is	be	AUX
ejpam-721	47	8	supra	supra	ADJ
ejpam-721	47	9	b	b	NOUN
ejpam-721	47	10	-	-	PUNCT
ejpam-721	47	11	open	open	ADJ
ejpam-721	47	12	.	.	PUNCT
ejpam-721	48	1	proof	proof	NOUN
ejpam-721	48	2	.	.	PUNCT
ejpam-721	49	1	let	let	VERB
ejpam-721	49	2	a	a	PRON
ejpam-721	49	3	be	be	AUX
ejpam-721	49	4	a	a	DET
ejpam-721	49	5	supra	supra	NOUN
ejpam-721	49	6	semi	semi	ADJ
ejpam-721	49	7	-	-	ADJ
ejpam-721	49	8	open	open	ADJ
ejpam-721	49	9	set	set	NOUN
ejpam-721	49	10	in	in	ADP
ejpam-721	49	11	(	(	PUNCT
ejpam-721	49	12	x	x	INTJ
ejpam-721	49	13	,	,	PUNCT
ejpam-721	49	14	µ	µ	NOUN
ejpam-721	49	15	)	)	PUNCT
ejpam-721	49	16	.	.	PUNCT
ejpam-721	50	1	then	then	ADV
ejpam-721	50	2	a	a	DET
ejpam-721	50	3	⊆	⊆	NUM
ejpam-721	50	4	clµ(intµ(a	clµ(intµ(a	NOUN
ejpam-721	50	5	)	)	PUNCT
ejpam-721	50	6	)	)	PUNCT
ejpam-721	50	7	.	.	PUNCT
ejpam-721	51	1	hence	hence	ADV
ejpam-721	51	2	,	,	PUNCT
ejpam-721	51	3	a	a	DET
ejpam-721	51	4	⊆	⊆	NUM
ejpam-721	51	5	clµ(intµ(a	clµ(intµ(a	NOUN
ejpam-721	51	6	)	)	PUNCT
ejpam-721	51	7	)	)	PUNCT
ejpam-721	52	1	⋃	⋃	NOUN
ejpam-721	52	2	intµ(clµ(a	intµ(clµ(a	NOUN
ejpam-721	52	3	)	)	PUNCT
ejpam-721	52	4	)	)	PUNCT
ejpam-721	52	5	and	and	CCONJ
ejpam-721	52	6	a	a	PRON
ejpam-721	52	7	is	be	AUX
ejpam-721	52	8	supra	supra	ADJ
ejpam-721	52	9	b	b	NOUN
ejpam-721	52	10	-	-	PUNCT
ejpam-721	52	11	open	open	ADJ
ejpam-721	52	12	in	in	ADP
ejpam-721	52	13	(	(	PUNCT
ejpam-721	52	14	x	x	INTJ
ejpam-721	52	15	,	,	PUNCT
ejpam-721	52	16	µ	µ	NOUN
ejpam-721	52	17	)	)	PUNCT
ejpam-721	52	18	.	.	PUNCT
ejpam-721	53	1	the	the	DET
ejpam-721	53	2	converse	converse	NOUN
ejpam-721	53	3	of	of	ADP
ejpam-721	53	4	the	the	DET
ejpam-721	53	5	above	above	ADJ
ejpam-721	53	6	theorem	theorem	NOUN
ejpam-721	53	7	need	need	AUX
ejpam-721	53	8	not	not	PART
ejpam-721	53	9	be	be	AUX
ejpam-721	53	10	true	true	ADJ
ejpam-721	53	11	as	as	SCONJ
ejpam-721	53	12	shown	show	VERB
ejpam-721	53	13	by	by	ADP
ejpam-721	53	14	the	the	DET
ejpam-721	53	15	following	follow	VERB
ejpam-721	53	16	example	example	NOUN
ejpam-721	53	17	.	.	PUNCT
ejpam-721	54	1	example	example	NOUN
ejpam-721	55	1	1	1	NUM
ejpam-721	55	2	.	.	PUNCT
ejpam-721	56	1	let	let	AUX
ejpam-721	56	2	(	(	PUNCT
ejpam-721	56	3	x	x	X
ejpam-721	56	4	,	,	PUNCT
ejpam-721	56	5	µ	µ	X
ejpam-721	56	6	)	)	PUNCT
ejpam-721	56	7	be	be	AUX
ejpam-721	56	8	a	a	DET
ejpam-721	56	9	supra	supra	ADJ
ejpam-721	56	10	topological	topological	ADJ
ejpam-721	56	11	space	space	NOUN
ejpam-721	56	12	,	,	PUNCT
ejpam-721	56	13	where	where	SCONJ
ejpam-721	56	14	x	x	X
ejpam-721	56	15	=	=	PRON
ejpam-721	56	16	{	{	PUNCT
ejpam-721	56	17	a	a	PRON
ejpam-721	56	18	,	,	PUNCT
ejpam-721	56	19	b	b	NOUN
ejpam-721	56	20	,	,	PUNCT
ejpam-721	56	21	c	c	NOUN
ejpam-721	56	22	}	}	PUNCT
ejpam-721	56	23	and	and	CCONJ
ejpam-721	56	24	µ=	µ=	VERB
ejpam-721	56	25	{	{	PUNCT
ejpam-721	56	26	x	x	PROPN
ejpam-721	56	27	,	,	PUNCT
ejpam-721	56	28	φ	φ	PROPN
ejpam-721	56	29	,	,	PUNCT
ejpam-721	56	30	{	{	PUNCT
ejpam-721	56	31	a	a	X
ejpam-721	56	32	}	}	PUNCT
ejpam-721	56	33	,	,	PUNCT
ejpam-721	56	34	{	{	PUNCT
ejpam-721	56	35	a	a	DET
ejpam-721	56	36	,	,	PUNCT
ejpam-721	56	37	b	b	NOUN
ejpam-721	56	38	}	}	PUNCT
ejpam-721	56	39	,	,	PUNCT
ejpam-721	56	40	{	{	PUNCT
ejpam-721	56	41	b	b	X
ejpam-721	56	42	,	,	PUNCT
ejpam-721	56	43	c	c	NOUN
ejpam-721	56	44	}	}	PUNCT
ejpam-721	56	45	}	}	PUNCT
ejpam-721	56	46	.	.	PUNCT
ejpam-721	57	1	here	here	ADV
ejpam-721	57	2	{	{	PUNCT
ejpam-721	57	3	a	a	PRON
ejpam-721	57	4	,	,	PUNCT
ejpam-721	57	5	c	c	NOUN
ejpam-721	57	6	}	}	PUNCT
ejpam-721	57	7	is	be	AUX
ejpam-721	57	8	a	a	DET
ejpam-721	57	9	supra	supra	PROPN
ejpam-721	57	10	b	b	NOUN
ejpam-721	57	11	-	-	PUNCT
ejpam-721	57	12	open	open	ADJ
ejpam-721	57	13	set	set	NOUN
ejpam-721	57	14	,	,	PUNCT
ejpam-721	57	15	but	but	CCONJ
ejpam-721	57	16	it	it	PRON
ejpam-721	57	17	is	be	AUX
ejpam-721	57	18	not	not	PART
ejpam-721	57	19	supra	supra	ADJ
ejpam-721	57	20	semi	semi	ADJ
ejpam-721	57	21	-	-	ADJ
ejpam-721	57	22	open	open	ADJ
ejpam-721	57	23	.	.	PUNCT
ejpam-721	58	1	in	in	ADP
ejpam-721	58	2	[	[	X
ejpam-721	58	3	3	3	NUM
ejpam-721	58	4	]	]	PUNCT
ejpam-721	58	5	,	,	PUNCT
ejpam-721	58	6	the	the	DET
ejpam-721	58	7	author	author	NOUN
ejpam-721	58	8	proved	prove	VERB
ejpam-721	58	9	that	that	SCONJ
ejpam-721	58	10	every	every	DET
ejpam-721	58	11	supra	supra	PROPN
ejpam-721	58	12	α	α	NOUN
ejpam-721	58	13	-	-	ADJ
ejpam-721	58	14	open	open	ADJ
ejpam-721	58	15	set	set	NOUN
ejpam-721	58	16	is	be	AUX
ejpam-721	58	17	supra	supra	ADJ
ejpam-721	58	18	semi	semi	ADJ
ejpam-721	58	19	-	-	ADJ
ejpam-721	58	20	open	open	ADJ
ejpam-721	58	21	.	.	PUNCT
ejpam-721	59	1	the	the	DET
ejpam-721	59	2	following	follow	VERB
ejpam-721	59	3	example	example	NOUN
ejpam-721	59	4	(	(	PUNCT
ejpam-721	59	5	instead	instead	ADV
ejpam-721	59	6	of	of	ADP
ejpam-721	59	7	example	example	NOUN
ejpam-721	59	8	3.2	3.2	NUM
ejpam-721	60	1	[	[	X
ejpam-721	60	2	3	3	NUM
ejpam-721	60	3	]	]	PUNCT
ejpam-721	60	4	)	)	PUNCT
ejpam-721	60	5	shows	show	VERB
ejpam-721	60	6	the	the	DET
ejpam-721	60	7	converse	converse	NOUN
ejpam-721	60	8	need	need	AUX
ejpam-721	60	9	not	not	PART
ejpam-721	60	10	be	be	AUX
ejpam-721	60	11	true	true	ADJ
ejpam-721	60	12	.	.	PUNCT
ejpam-721	61	1	example	example	NOUN
ejpam-721	62	1	2	2	NUM
ejpam-721	62	2	.	.	X
ejpam-721	62	3	let	let	AUX
ejpam-721	62	4	(	(	PUNCT
ejpam-721	62	5	x	x	X
ejpam-721	62	6	,	,	PUNCT
ejpam-721	62	7	µ	µ	X
ejpam-721	62	8	)	)	PUNCT
ejpam-721	62	9	be	be	AUX
ejpam-721	62	10	a	a	DET
ejpam-721	62	11	supra	supra	ADJ
ejpam-721	62	12	topological	topological	ADJ
ejpam-721	62	13	space	space	NOUN
ejpam-721	62	14	,	,	PUNCT
ejpam-721	62	15	where	where	SCONJ
ejpam-721	62	16	x	x	X
ejpam-721	62	17	=	=	PRON
ejpam-721	62	18	{	{	PUNCT
ejpam-721	62	19	a	a	PRON
ejpam-721	62	20	,	,	PUNCT
ejpam-721	62	21	b	b	NOUN
ejpam-721	62	22	,	,	PUNCT
ejpam-721	62	23	c	c	NOUN
ejpam-721	62	24	,	,	PUNCT
ejpam-721	62	25	d	d	NOUN
ejpam-721	62	26	}	}	PUNCT
ejpam-721	62	27	and	and	CCONJ
ejpam-721	62	28	µ=	µ=	NOUN
ejpam-721	62	29	{	{	PUNCT
ejpam-721	62	30	x	x	PROPN
ejpam-721	62	31	,	,	PUNCT
ejpam-721	62	32	φ	φ	PROPN
ejpam-721	62	33	,	,	PUNCT
ejpam-721	62	34	{	{	PUNCT
ejpam-721	62	35	a	a	X
ejpam-721	62	36	}	}	PUNCT
ejpam-721	62	37	,	,	PUNCT
ejpam-721	62	38	{	{	PUNCT
ejpam-721	62	39	b	b	NOUN
ejpam-721	62	40	}	}	PUNCT
ejpam-721	62	41	,	,	PUNCT
ejpam-721	62	42	{	{	PUNCT
ejpam-721	62	43	a	a	PRON
ejpam-721	62	44	,	,	PUNCT
ejpam-721	62	45	b	b	NOUN
ejpam-721	62	46	}	}	PUNCT
ejpam-721	62	47	}	}	PUNCT
ejpam-721	62	48	.	.	PUNCT
ejpam-721	63	1	here	here	ADV
ejpam-721	63	2	{	{	PUNCT
ejpam-721	63	3	b	b	X
ejpam-721	63	4	,	,	PUNCT
ejpam-721	63	5	c	c	NOUN
ejpam-721	63	6	}	}	PUNCT
ejpam-721	63	7	is	be	AUX
ejpam-721	63	8	a	a	DET
ejpam-721	63	9	supra	supra	ADJ
ejpam-721	63	10	semi	semi	ADJ
ejpam-721	63	11	-	-	ADJ
ejpam-721	63	12	open	open	ADJ
ejpam-721	63	13	set	set	NOUN
ejpam-721	63	14	,	,	PUNCT
ejpam-721	63	15	but	but	CCONJ
ejpam-721	63	16	it	it	PRON
ejpam-721	63	17	is	be	AUX
ejpam-721	63	18	not	not	PART
ejpam-721	63	19	supra	supra	ADJ
ejpam-721	63	20	α	α	NOUN
ejpam-721	63	21	-	-	NOUN
ejpam-721	63	22	open	open	ADJ
ejpam-721	63	23	.	.	PUNCT
ejpam-721	64	1	o.	o.	PROPN
ejpam-721	64	2	r.	r.	PROPN
ejpam-721	64	3	sayed	say	VERB
ejpam-721	64	4	,	,	PUNCT
ejpam-721	64	5	t.	t.	PROPN
ejpam-721	64	6	noiri	noiri	PROPN
ejpam-721	64	7	/	/	SYM
ejpam-721	64	8	eur	eur	PROPN
ejpam-721	64	9	.	.	PUNCT
ejpam-721	65	1	j.	j.	PROPN
ejpam-721	65	2	pure	pure	PROPN
ejpam-721	65	3	appl	appl	PROPN
ejpam-721	65	4	.	.	PROPN
ejpam-721	65	5	math	math	PROPN
ejpam-721	65	6	,	,	PUNCT
ejpam-721	65	7	3	3	NUM
ejpam-721	65	8	(	(	PUNCT
ejpam-721	65	9	2010	2010	NUM
ejpam-721	65	10	)	)	PUNCT
ejpam-721	65	11	,	,	PUNCT
ejpam-721	65	12	295	295	NUM
ejpam-721	65	13	-	-	SYM
ejpam-721	65	14	302	302	NUM
ejpam-721	65	15	297	297	NUM
ejpam-721	65	16	from	from	ADP
ejpam-721	65	17	theorems	theorem	NOUN
ejpam-721	65	18	3.1	3.1	NUM
ejpam-721	65	19	and	and	CCONJ
ejpam-721	65	20	3.2	3.2	NUM
ejpam-721	65	21	in	in	ADP
ejpam-721	65	22	[	[	X
ejpam-721	65	23	3	3	NUM
ejpam-721	65	24	]	]	PUNCT
ejpam-721	65	25	,	,	PUNCT
ejpam-721	65	26	the	the	DET
ejpam-721	65	27	above	above	ADJ
ejpam-721	65	28	theorem	theorem	NOUN
ejpam-721	65	29	,	,	PUNCT
ejpam-721	65	30	example	example	NOUN
ejpam-721	65	31	3.1	3.1	NUM
ejpam-721	66	1	[	[	X
ejpam-721	66	2	3	3	NUM
ejpam-721	66	3	]	]	PUNCT
ejpam-721	66	4	,	,	PUNCT
ejpam-721	66	5	and	and	CCONJ
ejpam-721	66	6	the	the	DET
ejpam-721	66	7	above	above	ADJ
ejpam-721	66	8	two	two	NUM
ejpam-721	66	9	examples	example	NOUN
ejpam-721	66	10	,	,	PUNCT
ejpam-721	66	11	we	we	PRON
ejpam-721	66	12	have	have	VERB
ejpam-721	66	13	the	the	DET
ejpam-721	66	14	following	follow	VERB
ejpam-721	66	15	diagram	diagram	NOUN
ejpam-721	66	16	in	in	ADP
ejpam-721	66	17	which	which	PRON
ejpam-721	66	18	the	the	DET
ejpam-721	66	19	converses	converse	NOUN
ejpam-721	66	20	of	of	ADP
ejpam-721	66	21	the	the	DET
ejpam-721	66	22	implications	implication	NOUN
ejpam-721	66	23	need	need	AUX
ejpam-721	66	24	not	not	PART
ejpam-721	66	25	be	be	AUX
ejpam-721	66	26	true	true	ADJ
ejpam-721	66	27	:	:	PUNCT
ejpam-721	66	28	(	(	PUNCT
ejpam-721	66	29	diagram	diagram	NOUN
ejpam-721	66	30	1	1	NUM
ejpam-721	66	31	)	)	PUNCT
ejpam-721	66	32	supra−	supra−	NOUN
ejpam-721	66	33	open→	open→	PROPN
ejpam-721	66	34	supra	supra	PROPN
ejpam-721	66	35	α−	α−	ADP
ejpam-721	66	36	open→	open→	PROPN
ejpam-721	66	37	supra	supra	PROPN
ejpam-721	66	38	semi−	semi−	PRON
ejpam-721	66	39	open	open	VERB
ejpam-721	66	40	→	→	SYM
ejpam-721	66	41	supra	supra	PROPN
ejpam-721	66	42	b−	b−	PROPN
ejpam-721	66	43	open	open	ADJ
ejpam-721	66	44	theorem	theorem	ADJ
ejpam-721	66	45	2	2	NUM
ejpam-721	66	46	.	.	PUNCT
ejpam-721	67	1	(	(	PUNCT
ejpam-721	67	2	i	i	NOUN
ejpam-721	67	3	)	)	PUNCT
ejpam-721	67	4	arbitrary	arbitrary	ADJ
ejpam-721	67	5	union	union	NOUN
ejpam-721	67	6	of	of	ADP
ejpam-721	67	7	supra	supra	PROPN
ejpam-721	67	8	b	b	PROPN
ejpam-721	67	9	-	-	PUNCT
ejpam-721	67	10	open	open	ADJ
ejpam-721	67	11	sets	set	NOUN
ejpam-721	67	12	is	be	AUX
ejpam-721	67	13	always	always	ADV
ejpam-721	67	14	supra	supra	PROPN
ejpam-721	67	15	b	b	NOUN
ejpam-721	67	16	-	-	PUNCT
ejpam-721	67	17	open	open	ADJ
ejpam-721	67	18	.	.	PUNCT
ejpam-721	68	1	(	(	PUNCT
ejpam-721	68	2	ii	ii	NOUN
ejpam-721	68	3	)	)	PUNCT
ejpam-721	68	4	finite	finite	ADJ
ejpam-721	68	5	intersection	intersection	NOUN
ejpam-721	68	6	of	of	ADP
ejpam-721	68	7	supra	supra	PROPN
ejpam-721	68	8	b	b	NOUN
ejpam-721	68	9	-	-	PUNCT
ejpam-721	68	10	open	open	ADJ
ejpam-721	68	11	sets	set	NOUN
ejpam-721	68	12	may	may	AUX
ejpam-721	68	13	fail	fail	VERB
ejpam-721	68	14	to	to	PART
ejpam-721	68	15	be	be	AUX
ejpam-721	68	16	supra	supra	ADJ
ejpam-721	68	17	b	b	NOUN
ejpam-721	68	18	-	-	PUNCT
ejpam-721	68	19	open	open	ADJ
ejpam-721	68	20	.	.	PUNCT
ejpam-721	69	1	(	(	PUNCT
ejpam-721	69	2	iii	iii	X
ejpam-721	69	3	)	)	PUNCT
ejpam-721	69	4	x	x	X
ejpam-721	69	5	is	be	AUX
ejpam-721	69	6	a	a	DET
ejpam-721	69	7	supra	supra	PROPN
ejpam-721	69	8	b	b	NOUN
ejpam-721	69	9	-	-	PUNCT
ejpam-721	69	10	open	open	ADJ
ejpam-721	69	11	set	set	NOUN
ejpam-721	69	12	.	.	PUNCT
ejpam-721	70	1	proof	proof	NOUN
ejpam-721	70	2	.	.	PUNCT
ejpam-721	71	1	(	(	PUNCT
ejpam-721	71	2	i	i	NOUN
ejpam-721	71	3	)	)	PUNCT
ejpam-721	71	4	let	let	VERB
ejpam-721	71	5	a	a	PRON
ejpam-721	71	6	and	and	CCONJ
ejpam-721	71	7	b	b	NOUN
ejpam-721	71	8	be	be	AUX
ejpam-721	71	9	two	two	NUM
ejpam-721	71	10	supra	supra	ADJ
ejpam-721	71	11	b	b	NOUN
ejpam-721	71	12	-	-	PUNCT
ejpam-721	71	13	open	open	ADJ
ejpam-721	71	14	sets	set	NOUN
ejpam-721	71	15	.	.	PUNCT
ejpam-721	72	1	then	then	ADV
ejpam-721	72	2	,	,	PUNCT
ejpam-721	72	3	a	a	DET
ejpam-721	72	4	⊆	⊆	NUM
ejpam-721	72	5	clµ(intµ(a	clµ(intµ(a	NOUN
ejpam-721	72	6	)	)	PUNCT
ejpam-721	72	7	)	)	PUNCT
ejpam-721	73	1	⋃	⋃	NOUN
ejpam-721	73	2	intµ(clµ(a	intµ(clµ(a	NOUN
ejpam-721	73	3	)	)	PUNCT
ejpam-721	73	4	)	)	PUNCT
ejpam-721	73	5	and	and	CCONJ
ejpam-721	73	6	b	b	NOUN
ejpam-721	73	7	⊆	⊆	NUM
ejpam-721	73	8	clµ(intµ(b	clµ(intµ(b	NOUN
ejpam-721	73	9	)	)	PUNCT
ejpam-721	73	10	)	)	PUNCT
ejpam-721	73	11	⋃	⋃	NOUN
ejpam-721	73	12	intµ(clµ(b	intµ(clµ(b	NOUN
ejpam-721	73	13	)	)	PUNCT
ejpam-721	73	14	)	)	PUNCT
ejpam-721	73	15	.	.	PUNCT
ejpam-721	74	1	then	then	ADV
ejpam-721	74	2	,	,	PUNCT
ejpam-721	74	3	a∪b	a∪b	ADJ
ejpam-721	74	4	⊆	⊆	NUM
ejpam-721	74	5	clµ(intµ(a∪b	clµ(intµ(a∪b	PROPN
ejpam-721	74	6	)	)	PUNCT
ejpam-721	74	7	)	)	PUNCT
ejpam-721	75	1	⋃	⋃	VERB
ejpam-721	75	2	intµ(clµ(a∪b	intµ(clµ(a∪b	NOUN
ejpam-721	75	3	)	)	PUNCT
ejpam-721	75	4	)	)	PUNCT
ejpam-721	75	5	.	.	PUNCT
ejpam-721	76	1	therefore	therefore	ADV
ejpam-721	76	2	,	,	PUNCT
ejpam-721	76	3	a∪	a∪	PROPN
ejpam-721	76	4	b	b	PROPN
ejpam-721	76	5	is	be	AUX
ejpam-721	76	6	supra	supra	ADJ
ejpam-721	76	7	b	b	NOUN
ejpam-721	76	8	-	-	PUNCT
ejpam-721	76	9	open	open	ADJ
ejpam-721	76	10	set	set	NOUN
ejpam-721	76	11	.	.	PUNCT
ejpam-721	77	1	(	(	PUNCT
ejpam-721	77	2	ii	ii	NOUN
ejpam-721	77	3	)	)	PUNCT
ejpam-721	77	4	in	in	ADP
ejpam-721	77	5	example	example	NOUN
ejpam-721	77	6	1	1	NUM
ejpam-721	77	7	,	,	PUNCT
ejpam-721	77	8	both	both	DET
ejpam-721	77	9	{	{	PUNCT
ejpam-721	77	10	a	a	PROPN
ejpam-721	77	11	,	,	PUNCT
ejpam-721	77	12	c	c	NOUN
ejpam-721	77	13	}	}	PUNCT
ejpam-721	77	14	and	and	CCONJ
ejpam-721	77	15	{	{	PUNCT
ejpam-721	77	16	b	b	NOUN
ejpam-721	77	17	,	,	PUNCT
ejpam-721	77	18	c	c	NOUN
ejpam-721	77	19	}	}	PUNCT
ejpam-721	77	20	are	be	AUX
ejpam-721	77	21	supra	supra	PROPN
ejpam-721	77	22	b	b	NOUN
ejpam-721	77	23	-	-	PUNCT
ejpam-721	77	24	open	open	ADJ
ejpam-721	77	25	sets	set	NOUN
ejpam-721	77	26	,	,	PUNCT
ejpam-721	77	27	but	but	CCONJ
ejpam-721	77	28	their	their	PRON
ejpam-721	77	29	intersection	intersection	NOUN
ejpam-721	77	30	{	{	PUNCT
ejpam-721	77	31	c	c	NOUN
ejpam-721	77	32	}	}	PUNCT
ejpam-721	77	33	is	be	AUX
ejpam-721	77	34	not	not	PART
ejpam-721	77	35	supra	supra	ADJ
ejpam-721	77	36	b	b	NOUN
ejpam-721	77	37	-	-	PUNCT
ejpam-721	77	38	open	open	ADJ
ejpam-721	77	39	.	.	PUNCT
ejpam-721	78	1	theorem	theorem	NOUN
ejpam-721	78	2	3	3	NUM
ejpam-721	78	3	.	.	PUNCT
ejpam-721	78	4	(	(	PUNCT
ejpam-721	78	5	i	i	NOUN
ejpam-721	78	6	)	)	PUNCT
ejpam-721	78	7	arbitrary	arbitrary	ADJ
ejpam-721	78	8	intersection	intersection	NOUN
ejpam-721	78	9	of	of	ADP
ejpam-721	78	10	supra	supra	PROPN
ejpam-721	78	11	b	b	PROPN
ejpam-721	78	12	-	-	PUNCT
ejpam-721	78	13	closed	closed	ADJ
ejpam-721	78	14	sets	set	NOUN
ejpam-721	78	15	is	be	AUX
ejpam-721	78	16	always	always	ADV
ejpam-721	78	17	supra	supra	PROPN
ejpam-721	78	18	b	b	PROPN
ejpam-721	78	19	-	-	PUNCT
ejpam-721	78	20	closed	closed	ADJ
ejpam-721	78	21	.	.	PUNCT
ejpam-721	79	1	(	(	PUNCT
ejpam-721	79	2	ii	ii	NOUN
ejpam-721	79	3	)	)	PUNCT
ejpam-721	79	4	finite	finite	PROPN
ejpam-721	79	5	union	union	PROPN
ejpam-721	79	6	of	of	ADP
ejpam-721	79	7	supra	supra	PROPN
ejpam-721	79	8	b	b	PROPN
ejpam-721	79	9	-	-	PUNCT
ejpam-721	79	10	closed	closed	ADJ
ejpam-721	79	11	sets	set	NOUN
ejpam-721	79	12	may	may	AUX
ejpam-721	79	13	fail	fail	VERB
ejpam-721	79	14	to	to	PART
ejpam-721	79	15	be	be	AUX
ejpam-721	79	16	supra	supra	ADJ
ejpam-721	79	17	b	b	NOUN
ejpam-721	79	18	-	-	PUNCT
ejpam-721	79	19	closed	closed	ADJ
ejpam-721	79	20	.	.	PUNCT
ejpam-721	80	1	proof	proof	NOUN
ejpam-721	80	2	.	.	PUNCT
ejpam-721	81	1	(	(	PUNCT
ejpam-721	81	2	i	i	NOUN
ejpam-721	81	3	)	)	PUNCT
ejpam-721	81	4	this	this	PRON
ejpam-721	81	5	follows	follow	VERB
ejpam-721	81	6	immediately	immediately	ADV
ejpam-721	81	7	from	from	ADP
ejpam-721	81	8	theorem	theorem	ADJ
ejpam-721	81	9	2	2	NUM
ejpam-721	81	10	.	.	PUNCT
ejpam-721	81	11	(	(	PUNCT
ejpam-721	81	12	ii	ii	NOUN
ejpam-721	81	13	)	)	PUNCT
ejpam-721	81	14	in	in	ADP
ejpam-721	81	15	example	example	NOUN
ejpam-721	81	16	1	1	NUM
ejpam-721	81	17	,	,	PUNCT
ejpam-721	81	18	both	both	PRON
ejpam-721	81	19	{	{	PUNCT
ejpam-721	81	20	a	a	NOUN
ejpam-721	81	21	}	}	PUNCT
ejpam-721	81	22	and	and	CCONJ
ejpam-721	81	23	{	{	PUNCT
ejpam-721	81	24	b	b	NOUN
ejpam-721	81	25	}	}	PUNCT
ejpam-721	81	26	are	be	AUX
ejpam-721	81	27	supra	supra	PROPN
ejpam-721	81	28	b	b	NOUN
ejpam-721	81	29	-	-	PUNCT
ejpam-721	81	30	closed	closed	ADJ
ejpam-721	81	31	sets	set	NOUN
ejpam-721	81	32	,	,	PUNCT
ejpam-721	81	33	but	but	CCONJ
ejpam-721	81	34	their	their	PRON
ejpam-721	81	35	union	union	NOUN
ejpam-721	81	36	{	{	PUNCT
ejpam-721	81	37	a	a	PROPN
ejpam-721	81	38	,	,	PUNCT
ejpam-721	81	39	b	b	NOUN
ejpam-721	81	40	}	}	PUNCT
ejpam-721	81	41	is	be	AUX
ejpam-721	81	42	not	not	PART
ejpam-721	81	43	supra	supra	ADJ
ejpam-721	81	44	b	b	NOUN
ejpam-721	81	45	-	-	PUNCT
ejpam-721	81	46	closed	closed	ADJ
ejpam-721	81	47	.	.	PUNCT
ejpam-721	82	1	definition	definition	NOUN
ejpam-721	82	2	2	2	NUM
ejpam-721	82	3	.	.	PUNCT
ejpam-721	83	1	the	the	DET
ejpam-721	83	2	supra	supra	PROPN
ejpam-721	83	3	b−closure	b−closure	NOUN
ejpam-721	83	4	of	of	ADP
ejpam-721	83	5	a	a	DET
ejpam-721	83	6	set	set	NOUN
ejpam-721	83	7	a	a	PRON
ejpam-721	83	8	,	,	PUNCT
ejpam-721	83	9	denoted	denote	VERB
ejpam-721	83	10	by	by	ADP
ejpam-721	83	11	clµb	clµb	NOUN
ejpam-721	83	12	(	(	PUNCT
ejpam-721	83	13	a	a	NOUN
ejpam-721	83	14	)	)	PUNCT
ejpam-721	83	15	,	,	PUNCT
ejpam-721	83	16	is	be	AUX
ejpam-721	83	17	the	the	DET
ejpam-721	83	18	intersection	intersection	NOUN
ejpam-721	83	19	of	of	ADP
ejpam-721	83	20	supra	supra	PROPN
ejpam-721	83	21	b−closed	b−close	VERB
ejpam-721	83	22	sets	set	NOUN
ejpam-721	83	23	including	include	VERB
ejpam-721	83	24	a.	a.	NOUN
ejpam-721	83	25	the	the	DET
ejpam-721	83	26	supra	supra	PROPN
ejpam-721	83	27	b−interior	b−interior	PROPN
ejpam-721	83	28	of	of	ADP
ejpam-721	83	29	a	a	DET
ejpam-721	83	30	set	set	NOUN
ejpam-721	83	31	a	a	PRON
ejpam-721	83	32	,	,	PUNCT
ejpam-721	83	33	denoted	denote	VERB
ejpam-721	83	34	by	by	ADP
ejpam-721	83	35	intµb	intµb	NOUN
ejpam-721	83	36	(	(	PUNCT
ejpam-721	83	37	a	a	X
ejpam-721	83	38	)	)	PUNCT
ejpam-721	83	39	,	,	PUNCT
ejpam-721	83	40	is	be	AUX
ejpam-721	83	41	the	the	DET
ejpam-721	83	42	union	union	NOUN
ejpam-721	83	43	of	of	ADP
ejpam-721	83	44	supra	supra	PROPN
ejpam-721	83	45	b−open	b−open	PROPN
ejpam-721	83	46	sets	set	NOUN
ejpam-721	83	47	included	include	VERB
ejpam-721	83	48	in	in	ADP
ejpam-721	83	49	a.	a.	NOUN
ejpam-721	83	50	remark	remark	NOUN
ejpam-721	83	51	1	1	NUM
ejpam-721	83	52	.	.	PUNCT
ejpam-721	84	1	it	it	PRON
ejpam-721	84	2	is	be	AUX
ejpam-721	84	3	clear	clear	ADJ
ejpam-721	84	4	that	that	SCONJ
ejpam-721	84	5	intµb	intµb	NOUN
ejpam-721	84	6	(	(	PUNCT
ejpam-721	84	7	a	a	X
ejpam-721	84	8	)	)	PUNCT
ejpam-721	84	9	is	be	AUX
ejpam-721	84	10	a	a	DET
ejpam-721	84	11	supra	supra	PROPN
ejpam-721	84	12	b	b	NOUN
ejpam-721	84	13	-	-	PUNCT
ejpam-721	84	14	open	open	ADJ
ejpam-721	84	15	set	set	NOUN
ejpam-721	84	16	and	and	CCONJ
ejpam-721	84	17	clµb	clµb	NOUN
ejpam-721	84	18	(	(	PUNCT
ejpam-721	84	19	a	a	NOUN
ejpam-721	84	20	)	)	PUNCT
ejpam-721	84	21	,	,	PUNCT
ejpam-721	84	22	is	be	AUX
ejpam-721	84	23	a	a	DET
ejpam-721	84	24	supra	supra	PROPN
ejpam-721	84	25	b−closed	b−close	VERB
ejpam-721	84	26	set	set	PROPN
ejpam-721	84	27	.	.	PUNCT
ejpam-721	85	1	theorem	theorem	VERB
ejpam-721	85	2	4	4	NUM
ejpam-721	85	3	.	.	PUNCT
ejpam-721	86	1	(	(	PUNCT
ejpam-721	86	2	i	i	NOUN
ejpam-721	86	3	)	)	PUNCT
ejpam-721	86	4	a⊆	a⊆	VERB
ejpam-721	86	5	clµb	clµb	NOUN
ejpam-721	86	6	(	(	PUNCT
ejpam-721	86	7	a	a	NOUN
ejpam-721	86	8	)	)	PUNCT
ejpam-721	86	9	;	;	PUNCT
ejpam-721	86	10	and	and	CCONJ
ejpam-721	86	11	a=	a=	ADV
ejpam-721	86	12	clµb	clµb	NOUN
ejpam-721	86	13	(	(	PUNCT
ejpam-721	86	14	a	a	X
ejpam-721	86	15	)	)	PUNCT
ejpam-721	86	16	iff	iff	NOUN
ejpam-721	86	17	a	a	PRON
ejpam-721	86	18	is	be	AUX
ejpam-721	86	19	a	a	DET
ejpam-721	86	20	supra	supra	PROPN
ejpam-721	86	21	b	b	NOUN
ejpam-721	86	22	-	-	PUNCT
ejpam-721	86	23	closed	closed	ADJ
ejpam-721	86	24	set	set	NOUN
ejpam-721	86	25	;	;	PUNCT
ejpam-721	86	26	(	(	PUNCT
ejpam-721	86	27	ii	ii	NOUN
ejpam-721	86	28	)	)	PUNCT
ejpam-721	86	29	intµb	intµb	NOUN
ejpam-721	86	30	(	(	PUNCT
ejpam-721	86	31	a)⊆	a)⊆	X
ejpam-721	86	32	a	a	X
ejpam-721	86	33	;	;	PUNCT
ejpam-721	86	34	and	and	CCONJ
ejpam-721	86	35	intµb	intµb	NOUN
ejpam-721	86	36	(	(	PUNCT
ejpam-721	86	37	a	a	X
ejpam-721	86	38	)	)	PUNCT
ejpam-721	86	39	=	=	PUNCT
ejpam-721	87	1	a	a	DET
ejpam-721	87	2	iff	iff	PROPN
ejpam-721	87	3	a	a	PRON
ejpam-721	87	4	is	be	AUX
ejpam-721	87	5	a	a	DET
ejpam-721	87	6	supra	supra	PROPN
ejpam-721	87	7	b	b	NOUN
ejpam-721	87	8	-	-	PUNCT
ejpam-721	87	9	open	open	ADJ
ejpam-721	87	10	set	set	NOUN
ejpam-721	87	11	;	;	PUNCT
ejpam-721	87	12	o.	o.	PROPN
ejpam-721	87	13	r.	r.	PROPN
ejpam-721	87	14	sayed	say	VERB
ejpam-721	87	15	,	,	PUNCT
ejpam-721	87	16	t.	t.	PROPN
ejpam-721	87	17	noiri	noiri	PROPN
ejpam-721	87	18	/	/	SYM
ejpam-721	87	19	eur	eur	PROPN
ejpam-721	87	20	.	.	PUNCT
ejpam-721	88	1	j.	j.	PROPN
ejpam-721	88	2	pure	pure	PROPN
ejpam-721	88	3	appl	appl	PROPN
ejpam-721	88	4	.	.	PROPN
ejpam-721	88	5	math	math	PROPN
ejpam-721	88	6	,	,	PUNCT
ejpam-721	88	7	3	3	NUM
ejpam-721	88	8	(	(	PUNCT
ejpam-721	88	9	2010	2010	NUM
ejpam-721	88	10	)	)	PUNCT
ejpam-721	88	11	,	,	PUNCT
ejpam-721	88	12	295	295	NUM
ejpam-721	88	13	-	-	SYM
ejpam-721	88	14	302	302	NUM
ejpam-721	88	15	298	298	NUM
ejpam-721	88	16	(	(	PUNCT
ejpam-721	88	17	iii	iii	NOUN
ejpam-721	88	18	)	)	PUNCT
ejpam-721	88	19	x	x	SYM
ejpam-721	88	20	−	−	PROPN
ejpam-721	88	21	intµb	intµb	NOUN
ejpam-721	88	22	(	(	PUNCT
ejpam-721	88	23	a	a	X
ejpam-721	88	24	)	)	PUNCT
ejpam-721	88	25	=	=	NOUN
ejpam-721	88	26	clµb	clµb	NOUN
ejpam-721	88	27	(	(	PUNCT
ejpam-721	88	28	x	x	X
ejpam-721	88	29	−	−	NOUN
ejpam-721	88	30	a	a	NOUN
ejpam-721	88	31	)	)	PUNCT
ejpam-721	88	32	;	;	PUNCT
ejpam-721	88	33	(	(	PUNCT
ejpam-721	88	34	iv	iv	X
ejpam-721	88	35	)	)	PUNCT
ejpam-721	88	36	x	x	PUNCT
ejpam-721	89	1	−	−	PROPN
ejpam-721	89	2	clµb	clµb	NOUN
ejpam-721	89	3	(	(	PUNCT
ejpam-721	89	4	a	a	NOUN
ejpam-721	89	5	)	)	PUNCT
ejpam-721	89	6	=	=	SYM
ejpam-721	89	7	intµb	intµb	NOUN
ejpam-721	89	8	(	(	PUNCT
ejpam-721	89	9	x	x	X
ejpam-721	89	10	−	−	NOUN
ejpam-721	89	11	a	a	NOUN
ejpam-721	89	12	)	)	PUNCT
ejpam-721	89	13	.	.	PUNCT
ejpam-721	90	1	proof	proof	NOUN
ejpam-721	90	2	.	.	PUNCT
ejpam-721	91	1	obvious	obvious	ADJ
ejpam-721	91	2	.	.	PUNCT
ejpam-721	92	1	theorem	theorem	NOUN
ejpam-721	92	2	5	5	NUM
ejpam-721	92	3	.	.	PUNCT
ejpam-721	93	1	(	(	PUNCT
ejpam-721	93	2	a	a	X
ejpam-721	93	3	)	)	PUNCT
ejpam-721	93	4	intµb	intµb	NOUN
ejpam-721	93	5	(	(	PUNCT
ejpam-721	93	6	a)∪	a)∪	ADV
ejpam-721	93	7	intµb	intµb	PROPN
ejpam-721	93	8	(	(	PUNCT
ejpam-721	93	9	b)⊆	b)⊆	PROPN
ejpam-721	93	10	intµb	intµb	PROPN
ejpam-721	93	11	(	(	PUNCT
ejpam-721	93	12	a∪	a∪	NOUN
ejpam-721	93	13	b	b	NOUN
ejpam-721	93	14	)	)	PUNCT
ejpam-721	93	15	;	;	PUNCT
ejpam-721	93	16	(	(	PUNCT
ejpam-721	93	17	b	b	X
ejpam-721	93	18	)	)	PUNCT
ejpam-721	93	19	clµb	clµb	NOUN
ejpam-721	93	20	(	(	PUNCT
ejpam-721	93	21	a∩	a∩	PROPN
ejpam-721	93	22	b)⊆	b)⊆	PROPN
ejpam-721	93	23	clµb	clµb	PROPN
ejpam-721	93	24	(	(	PUNCT
ejpam-721	93	25	a)∩	a)∩	PROPN
ejpam-721	93	26	clµb	clµb	PROPN
ejpam-721	93	27	(	(	PUNCT
ejpam-721	93	28	b	b	NOUN
ejpam-721	93	29	)	)	PUNCT
ejpam-721	93	30	.	.	PUNCT
ejpam-721	94	1	proof	proof	NOUN
ejpam-721	94	2	.	.	PUNCT
ejpam-721	95	1	obvious	obvious	ADJ
ejpam-721	95	2	.	.	PUNCT
ejpam-721	96	1	proposition	proposition	NOUN
ejpam-721	96	2	1	1	NUM
ejpam-721	96	3	.	.	PUNCT
ejpam-721	97	1	the	the	DET
ejpam-721	97	2	intersection	intersection	NOUN
ejpam-721	97	3	of	of	ADP
ejpam-721	97	4	a	a	DET
ejpam-721	97	5	supra	supra	PROPN
ejpam-721	97	6	α	α	NOUN
ejpam-721	97	7	-	-	ADJ
ejpam-721	97	8	open	open	ADJ
ejpam-721	97	9	set	set	NOUN
ejpam-721	97	10	and	and	CCONJ
ejpam-721	97	11	a	a	DET
ejpam-721	97	12	supra	supra	PROPN
ejpam-721	97	13	b	b	NOUN
ejpam-721	97	14	-	-	PUNCT
ejpam-721	97	15	open	open	ADJ
ejpam-721	97	16	set	set	NOUN
ejpam-721	97	17	is	be	AUX
ejpam-721	97	18	a	a	DET
ejpam-721	97	19	supra	supra	PROPN
ejpam-721	97	20	b	b	NOUN
ejpam-721	97	21	-	-	PUNCT
ejpam-721	97	22	open	open	ADJ
ejpam-721	97	23	set	set	NOUN
ejpam-721	97	24	.	.	PUNCT
ejpam-721	98	1	3	3	X
ejpam-721	98	2	.	.	X
ejpam-721	98	3	supra	supra	PROPN
ejpam-721	98	4	b	b	X
ejpam-721	98	5	-	-	PUNCT
ejpam-721	98	6	continuous	continuous	ADJ
ejpam-721	98	7	maps	map	NOUN
ejpam-721	98	8	in	in	ADP
ejpam-721	98	9	this	this	DET
ejpam-721	98	10	section	section	NOUN
ejpam-721	98	11	,	,	PUNCT
ejpam-721	98	12	we	we	PRON
ejpam-721	98	13	introduce	introduce	VERB
ejpam-721	98	14	a	a	DET
ejpam-721	98	15	new	new	ADJ
ejpam-721	98	16	type	type	NOUN
ejpam-721	98	17	of	of	ADP
ejpam-721	98	18	continuous	continuous	ADJ
ejpam-721	98	19	maps	map	NOUN
ejpam-721	98	20	called	call	VERB
ejpam-721	98	21	a	a	DET
ejpam-721	98	22	supra	supra	PROPN
ejpam-721	98	23	b	b	NOUN
ejpam-721	98	24	-	-	PUNCT
ejpam-721	98	25	continuous	continuous	ADJ
ejpam-721	98	26	map	map	NOUN
ejpam-721	98	27	and	and	CCONJ
ejpam-721	98	28	obtain	obtain	VERB
ejpam-721	98	29	some	some	PRON
ejpam-721	98	30	of	of	ADP
ejpam-721	98	31	their	their	PRON
ejpam-721	98	32	properties	property	NOUN
ejpam-721	98	33	and	and	CCONJ
ejpam-721	98	34	characterizations	characterization	NOUN
ejpam-721	98	35	.	.	PUNCT
ejpam-721	99	1	definition	definition	NOUN
ejpam-721	99	2	3	3	X
ejpam-721	99	3	.	.	PUNCT
ejpam-721	100	1	let	let	VERB
ejpam-721	100	2	(	(	PUNCT
ejpam-721	100	3	x	x	X
ejpam-721	100	4	,	,	PUNCT
ejpam-721	100	5	τ	τ	PROPN
ejpam-721	100	6	)	)	PUNCT
ejpam-721	100	7	and	and	CCONJ
ejpam-721	100	8	(	(	PUNCT
ejpam-721	100	9	y	y	PROPN
ejpam-721	100	10	,	,	PUNCT
ejpam-721	100	11	σ	σ	PROPN
ejpam-721	100	12	)	)	PUNCT
ejpam-721	100	13	be	be	VERB
ejpam-721	100	14	two	two	NUM
ejpam-721	100	15	topological	topological	ADJ
ejpam-721	100	16	spaces	space	NOUN
ejpam-721	100	17	and	and	CCONJ
ejpam-721	100	18	µ	µ	PRON
ejpam-721	100	19	be	be	AUX
ejpam-721	100	20	an	an	DET
ejpam-721	100	21	associated	associated	ADJ
ejpam-721	100	22	supra	supra	NOUN
ejpam-721	100	23	topology	topology	NOUN
ejpam-721	100	24	with	with	ADP
ejpam-721	100	25	τ	τ	PROPN
ejpam-721	100	26	.	.	PUNCT
ejpam-721	101	1	a	a	DET
ejpam-721	101	2	map	map	NOUN
ejpam-721	101	3	f	f	X
ejpam-721	101	4	:	:	PUNCT
ejpam-721	101	5	(	(	PUNCT
ejpam-721	101	6	x	x	X
ejpam-721	101	7	,	,	PUNCT
ejpam-721	101	8	τ	τ	PROPN
ejpam-721	101	9	)	)	PUNCT
ejpam-721	101	10	→	→	SYM
ejpam-721	101	11	(	(	PUNCT
ejpam-721	101	12	y	y	PROPN
ejpam-721	101	13	,	,	PUNCT
ejpam-721	101	14	σ	σ	PROPN
ejpam-721	101	15	)	)	PUNCT
ejpam-721	101	16	is	be	AUX
ejpam-721	101	17	called	call	VERB
ejpam-721	101	18	a	a	DET
ejpam-721	101	19	supra	supra	PROPN
ejpam-721	101	20	b	b	NOUN
ejpam-721	101	21	-	-	PUNCT
ejpam-721	101	22	continuous	continuous	ADJ
ejpam-721	101	23	map	map	NOUN
ejpam-721	101	24	if	if	SCONJ
ejpam-721	101	25	the	the	DET
ejpam-721	101	26	inverse	inverse	ADJ
ejpam-721	101	27	image	image	NOUN
ejpam-721	101	28	of	of	ADP
ejpam-721	101	29	each	each	DET
ejpam-721	101	30	open	open	ADJ
ejpam-721	101	31	set	set	NOUN
ejpam-721	101	32	in	in	ADP
ejpam-721	101	33	y	y	PROPN
ejpam-721	101	34	is	be	AUX
ejpam-721	101	35	a	a	DET
ejpam-721	101	36	supra	supra	PROPN
ejpam-721	101	37	b	b	NOUN
ejpam-721	101	38	-	-	PUNCT
ejpam-721	101	39	open	open	ADJ
ejpam-721	101	40	set	set	NOUN
ejpam-721	101	41	in	in	ADP
ejpam-721	101	42	x	x	X
ejpam-721	101	43	.	.	PUNCT
ejpam-721	102	1	theorem	theorem	ADJ
ejpam-721	102	2	6	6	NUM
ejpam-721	102	3	.	.	PUNCT
ejpam-721	103	1	every	every	DET
ejpam-721	103	2	continuous	continuous	ADJ
ejpam-721	103	3	map	map	NOUN
ejpam-721	103	4	is	be	AUX
ejpam-721	103	5	supra	supra	ADJ
ejpam-721	103	6	b	b	NOUN
ejpam-721	103	7	-	-	PUNCT
ejpam-721	103	8	continuous	continuous	ADJ
ejpam-721	103	9	.	.	PUNCT
ejpam-721	104	1	proof	proof	NOUN
ejpam-721	104	2	.	.	PUNCT
ejpam-721	105	1	let	let	VERB
ejpam-721	105	2	f	f	NOUN
ejpam-721	105	3	:	:	PUNCT
ejpam-721	105	4	(	(	PUNCT
ejpam-721	105	5	x	x	X
ejpam-721	105	6	,	,	PUNCT
ejpam-721	105	7	τ)→	τ)→	PROPN
ejpam-721	105	8	(	(	PUNCT
ejpam-721	105	9	y	y	PROPN
ejpam-721	105	10	,	,	PUNCT
ejpam-721	105	11	σ	σ	PROPN
ejpam-721	105	12	)	)	PUNCT
ejpam-721	105	13	be	be	VERB
ejpam-721	105	14	a	a	DET
ejpam-721	105	15	continuous	continuous	ADJ
ejpam-721	105	16	map	map	NOUN
ejpam-721	105	17	and	and	CCONJ
ejpam-721	105	18	a	a	PRON
ejpam-721	105	19	is	be	AUX
ejpam-721	105	20	open	open	ADJ
ejpam-721	105	21	in	in	ADP
ejpam-721	105	22	y	y	PROPN
ejpam-721	105	23	.	.	PUNCT
ejpam-721	106	1	then	then	ADV
ejpam-721	106	2	f	f	PROPN
ejpam-721	106	3	−1(a	−1(a	CCONJ
ejpam-721	106	4	)	)	PUNCT
ejpam-721	106	5	is	be	AUX
ejpam-721	106	6	an	an	DET
ejpam-721	106	7	open	open	ADJ
ejpam-721	106	8	set	set	NOUN
ejpam-721	106	9	in	in	ADP
ejpam-721	106	10	x	x	X
ejpam-721	106	11	.	.	PUNCT
ejpam-721	107	1	since	since	SCONJ
ejpam-721	107	2	µ	µ	NOUN
ejpam-721	107	3	is	be	AUX
ejpam-721	107	4	associated	associate	VERB
ejpam-721	107	5	with	with	ADP
ejpam-721	107	6	τ	τ	PROPN
ejpam-721	107	7	,	,	PUNCT
ejpam-721	107	8	then	then	ADV
ejpam-721	107	9	τ	τ	PROPN
ejpam-721	107	10	⊆	⊆	NUM
ejpam-721	107	11	µ.	µ.	NOUN
ejpam-721	107	12	therefore	therefore	ADV
ejpam-721	107	13	,	,	PUNCT
ejpam-721	107	14	f	f	PROPN
ejpam-721	107	15	−1(a	−1(a	CCONJ
ejpam-721	107	16	)	)	PUNCT
ejpam-721	107	17	is	be	AUX
ejpam-721	107	18	supra	supra	ADJ
ejpam-721	107	19	open	open	ADJ
ejpam-721	107	20	in	in	ADP
ejpam-721	107	21	x	x	PUNCT
ejpam-721	108	1	and	and	CCONJ
ejpam-721	108	2	it	it	PRON
ejpam-721	108	3	is	be	AUX
ejpam-721	108	4	supra	supra	ADJ
ejpam-721	108	5	b	b	NOUN
ejpam-721	108	6	-	-	PUNCT
ejpam-721	108	7	open	open	ADJ
ejpam-721	108	8	in	in	ADP
ejpam-721	108	9	x	x	X
ejpam-721	108	10	.	.	PUNCT
ejpam-721	109	1	hence	hence	ADV
ejpam-721	109	2	f	f	PROPN
ejpam-721	109	3	is	be	AUX
ejpam-721	109	4	supra	supra	ADJ
ejpam-721	109	5	b	b	NOUN
ejpam-721	109	6	-	-	PUNCT
ejpam-721	109	7	continuous	continuous	ADJ
ejpam-721	109	8	.	.	PUNCT
ejpam-721	110	1	the	the	DET
ejpam-721	110	2	converse	converse	NOUN
ejpam-721	110	3	of	of	ADP
ejpam-721	110	4	the	the	DET
ejpam-721	110	5	above	above	ADJ
ejpam-721	110	6	theorem	theorem	NOUN
ejpam-721	110	7	is	be	AUX
ejpam-721	110	8	not	not	PART
ejpam-721	110	9	true	true	ADJ
ejpam-721	110	10	as	as	SCONJ
ejpam-721	110	11	shown	show	VERB
ejpam-721	110	12	in	in	ADP
ejpam-721	110	13	the	the	DET
ejpam-721	110	14	following	follow	VERB
ejpam-721	110	15	example	example	NOUN
ejpam-721	110	16	.	.	PUNCT
ejpam-721	111	1	example	example	NOUN
ejpam-721	112	1	3	3	X
ejpam-721	112	2	.	.	PUNCT
ejpam-721	112	3	let	let	VERB
ejpam-721	112	4	x	x	PUNCT
ejpam-721	112	5	=	=	PRON
ejpam-721	112	6	{	{	PUNCT
ejpam-721	112	7	a	a	PRON
ejpam-721	112	8	,	,	PUNCT
ejpam-721	112	9	b	b	NOUN
ejpam-721	112	10	,	,	PUNCT
ejpam-721	112	11	c	c	NOUN
ejpam-721	112	12	}	}	PUNCT
ejpam-721	112	13	and	and	CCONJ
ejpam-721	112	14	τ	τ	PROPN
ejpam-721	112	15	=	=	SYM
ejpam-721	112	16	�	�	PROPN
ejpam-721	112	17	x	x	SYM
ejpam-721	112	18	,	,	PUNCT
ejpam-721	112	19	φ	φ	PROPN
ejpam-721	112	20	,	,	PUNCT
ejpam-721	112	21	{	{	PUNCT
ejpam-721	112	22	a	a	PRON
ejpam-721	112	23	,	,	PUNCT
ejpam-721	112	24	b	b	AUX
ejpam-721	112	25	}	}	PUNCT
ejpam-721	112	26	be	be	AUX
ejpam-721	112	27	a	a	DET
ejpam-721	112	28	topology	topology	NOUN
ejpam-721	112	29	on	on	ADP
ejpam-721	112	30	x	x	X
ejpam-721	112	31	.	.	PUNCT
ejpam-721	113	1	the	the	DET
ejpam-721	113	2	supra	supra	PROPN
ejpam-721	113	3	topology	topology	PROPN
ejpam-721	113	4	µ	µ	NOUN
ejpam-721	113	5	is	be	AUX
ejpam-721	113	6	defined	define	VERB
ejpam-721	113	7	as	as	SCONJ
ejpam-721	113	8	follows	follow	VERB
ejpam-721	113	9	:	:	PUNCT
ejpam-721	113	10	µ	µ	X
ejpam-721	113	11	=	=	SYM
ejpam-721	113	12	�	�	PROPN
ejpam-721	113	13	x	x	SYM
ejpam-721	113	14	,	,	PUNCT
ejpam-721	113	15	φ	φ	PROPN
ejpam-721	113	16	,	,	PUNCT
ejpam-721	113	17	{	{	PUNCT
ejpam-721	113	18	a	a	X
ejpam-721	113	19	}	}	PUNCT
ejpam-721	113	20	,	,	PUNCT
ejpam-721	113	21	{	{	PUNCT
ejpam-721	113	22	a	a	DET
ejpam-721	113	23	,	,	PUNCT
ejpam-721	113	24	b	b	NOUN
ejpam-721	113	25	}	}	PUNCT
ejpam-721	113	26	.	.	PUNCT
ejpam-721	114	1	let	let	VERB
ejpam-721	114	2	f	f	NOUN
ejpam-721	114	3	:	:	PUNCT
ejpam-721	114	4	(	(	PUNCT
ejpam-721	114	5	x	x	X
ejpam-721	114	6	,	,	PUNCT
ejpam-721	114	7	τ	τ	PROPN
ejpam-721	114	8	)	)	PUNCT
ejpam-721	114	9	→	→	SYM
ejpam-721	114	10	(	(	PUNCT
ejpam-721	114	11	x	x	X
ejpam-721	114	12	,	,	PUNCT
ejpam-721	114	13	τ	τ	X
ejpam-721	114	14	)	)	PUNCT
ejpam-721	114	15	be	be	VERB
ejpam-721	114	16	a	a	DET
ejpam-721	114	17	map	map	NOUN
ejpam-721	114	18	defined	define	VERB
ejpam-721	114	19	as	as	SCONJ
ejpam-721	114	20	follows	follow	VERB
ejpam-721	114	21	:	:	PUNCT
ejpam-721	114	22	f	f	X
ejpam-721	114	23	(	(	PUNCT
ejpam-721	114	24	a	a	X
ejpam-721	114	25	)	)	PUNCT
ejpam-721	114	26	=	=	SYM
ejpam-721	115	1	a	a	PROPN
ejpam-721	115	2	,	,	PUNCT
ejpam-721	115	3	f	f	PROPN
ejpam-721	115	4	(	(	PUNCT
ejpam-721	115	5	b	b	NOUN
ejpam-721	115	6	)	)	PUNCT
ejpam-721	115	7	=	=	SYM
ejpam-721	115	8	c	c	X
ejpam-721	115	9	,	,	PUNCT
ejpam-721	115	10	f	f	PROPN
ejpam-721	115	11	(	(	PUNCT
ejpam-721	115	12	c	c	NOUN
ejpam-721	115	13	)	)	PUNCT
ejpam-721	115	14	=	=	SYM
ejpam-721	115	15	b.	b.	PROPN
ejpam-721	116	1	the	the	DET
ejpam-721	116	2	inverse	inverse	ADJ
ejpam-721	116	3	image	image	NOUN
ejpam-721	116	4	of	of	ADP
ejpam-721	116	5	the	the	DET
ejpam-721	116	6	open	open	ADJ
ejpam-721	116	7	set	set	NOUN
ejpam-721	116	8	{	{	PUNCT
ejpam-721	116	9	a	a	PRON
ejpam-721	116	10	,	,	PUNCT
ejpam-721	116	11	b	b	NOUN
ejpam-721	116	12	}	}	PUNCT
ejpam-721	116	13	is	be	AUX
ejpam-721	116	14	{	{	PUNCT
ejpam-721	116	15	a	a	PRON
ejpam-721	116	16	,	,	PUNCT
ejpam-721	116	17	c	c	NOUN
ejpam-721	116	18	}	}	PUNCT
ejpam-721	116	19	which	which	PRON
ejpam-721	116	20	is	be	AUX
ejpam-721	116	21	not	not	PART
ejpam-721	116	22	an	an	DET
ejpam-721	116	23	open	open	ADJ
ejpam-721	116	24	set	set	NOUN
ejpam-721	116	25	but	but	CCONJ
ejpam-721	116	26	it	it	PRON
ejpam-721	116	27	is	be	AUX
ejpam-721	116	28	a	a	DET
ejpam-721	116	29	supra	supra	NOUN
ejpam-721	116	30	b-open.then	b-open.then	ADP
ejpam-721	116	31	f	f	PROPN
ejpam-721	116	32	is	be	AUX
ejpam-721	116	33	supra	supra	ADJ
ejpam-721	116	34	b	b	NOUN
ejpam-721	116	35	-	-	PUNCT
ejpam-721	116	36	continuous	continuous	ADJ
ejpam-721	116	37	but	but	CCONJ
ejpam-721	116	38	it	it	PRON
ejpam-721	116	39	is	be	AUX
ejpam-721	116	40	not	not	PART
ejpam-721	116	41	continuous	continuous	ADJ
ejpam-721	116	42	.	.	PUNCT
ejpam-721	117	1	the	the	DET
ejpam-721	117	2	following	follow	VERB
ejpam-721	117	3	example	example	NOUN
ejpam-721	117	4	shows	show	VERB
ejpam-721	117	5	that	that	SCONJ
ejpam-721	117	6	supra	supra	PROPN
ejpam-721	117	7	b	b	NOUN
ejpam-721	117	8	-	-	PUNCT
ejpam-721	117	9	continuous	continuous	ADJ
ejpam-721	117	10	maps	map	NOUN
ejpam-721	117	11	need	need	AUX
ejpam-721	117	12	not	not	PART
ejpam-721	117	13	be	be	AUX
ejpam-721	117	14	supra	supra	ADJ
ejpam-721	117	15	semicontinuous	semicontinuous	ADJ
ejpam-721	117	16	.	.	PUNCT
ejpam-721	118	1	example	example	NOUN
ejpam-721	118	2	4	4	NUM
ejpam-721	118	3	.	.	PUNCT
ejpam-721	119	1	consider	consider	VERB
ejpam-721	119	2	the	the	DET
ejpam-721	119	3	set	set	NOUN
ejpam-721	119	4	x	x	PUNCT
ejpam-721	119	5	=	=	X
ejpam-721	119	6	{	{	PUNCT
ejpam-721	119	7	a	a	PRON
ejpam-721	119	8	,	,	PUNCT
ejpam-721	119	9	b	b	NOUN
ejpam-721	119	10	,	,	PUNCT
ejpam-721	119	11	c	c	NOUN
ejpam-721	119	12	,	,	PUNCT
ejpam-721	119	13	d	d	NOUN
ejpam-721	119	14	}	}	PUNCT
ejpam-721	119	15	with	with	ADP
ejpam-721	119	16	the	the	DET
ejpam-721	119	17	topology	topology	NOUN
ejpam-721	119	18	τ	τ	NOUN
ejpam-721	119	19	=	=	PUNCT
ejpam-721	119	20	{	{	PUNCT
ejpam-721	119	21	x	x	PROPN
ejpam-721	119	22	,	,	PUNCT
ejpam-721	119	23	φ	φ	PROPN
ejpam-721	119	24	,	,	PUNCT
ejpam-721	119	25	{	{	PUNCT
ejpam-721	119	26	a	a	X
ejpam-721	119	27	,	,	PUNCT
ejpam-721	119	28	c	c	NOUN
ejpam-721	119	29	}	}	PUNCT
ejpam-721	119	30	,	,	PUNCT
ejpam-721	119	31	{	{	PUNCT
ejpam-721	119	32	b	b	X
ejpam-721	119	33	,	,	PUNCT
ejpam-721	119	34	d	d	NOUN
ejpam-721	119	35	}	}	PUNCT
ejpam-721	119	36	}	}	PUNCT
ejpam-721	119	37	and	and	CCONJ
ejpam-721	119	38	the	the	DET
ejpam-721	119	39	supra	supra	PROPN
ejpam-721	119	40	topology	topology	PROPN
ejpam-721	119	41	µ	µ	X
ejpam-721	119	42	=	=	SYM
ejpam-721	119	43	�	�	PROPN
ejpam-721	119	44	x	x	SYM
ejpam-721	119	45	,	,	PUNCT
ejpam-721	119	46	φ	φ	PROPN
ejpam-721	119	47	,	,	PUNCT
ejpam-721	119	48	{	{	PUNCT
ejpam-721	119	49	a	a	X
ejpam-721	119	50	,	,	PUNCT
ejpam-721	119	51	c	c	NOUN
ejpam-721	119	52	}	}	PUNCT
ejpam-721	119	53	,	,	PUNCT
ejpam-721	119	54	{	{	PUNCT
ejpam-721	119	55	b	b	X
ejpam-721	119	56	,	,	PUNCT
ejpam-721	119	57	d	d	NOUN
ejpam-721	119	58	}	}	PUNCT
ejpam-721	119	59	,	,	PUNCT
ejpam-721	119	60	{	{	PUNCT
ejpam-721	119	61	a	a	PRON
ejpam-721	119	62	,	,	PUNCT
ejpam-721	119	63	c	c	NOUN
ejpam-721	119	64	,	,	PUNCT
ejpam-721	119	65	d	d	NOUN
ejpam-721	119	66	}	}	PUNCT
ejpam-721	119	67	.	.	PUNCT
ejpam-721	120	1	also	also	ADV
ejpam-721	120	2	,	,	PUNCT
ejpam-721	120	3	suppose	suppose	VERB
ejpam-721	120	4	y	y	PROPN
ejpam-721	120	5	=	=	PRON
ejpam-721	120	6	{	{	PUNCT
ejpam-721	120	7	x	x	X
ejpam-721	120	8	,	,	PUNCT
ejpam-721	120	9	y	y	PROPN
ejpam-721	120	10	,	,	PUNCT
ejpam-721	120	11	z	z	NOUN
ejpam-721	120	12	}	}	PUNCT
ejpam-721	120	13	with	with	ADP
ejpam-721	120	14	the	the	DET
ejpam-721	120	15	topology	topology	NOUN
ejpam-721	120	16	σ	σ	NOUN
ejpam-721	120	17	=	=	SYM
ejpam-721	120	18	{	{	PUNCT
ejpam-721	120	19	y	y	PROPN
ejpam-721	120	20	,	,	PUNCT
ejpam-721	120	21	φ	φ	PROPN
ejpam-721	120	22	,	,	PUNCT
ejpam-721	120	23	{	{	PUNCT
ejpam-721	120	24	z	z	NOUN
ejpam-721	120	25	}	}	PUNCT
ejpam-721	120	26	}	}	PUNCT
ejpam-721	120	27	.	.	PUNCT
ejpam-721	121	1	define	define	VERB
ejpam-721	121	2	the	the	DET
ejpam-721	121	3	map	map	NOUN
ejpam-721	122	1	f	f	X
ejpam-721	122	2	:	:	PUNCT
ejpam-721	122	3	(	(	PUNCT
ejpam-721	122	4	x	x	X
ejpam-721	122	5	,	,	PUNCT
ejpam-721	122	6	τ)→	τ)→	PROPN
ejpam-721	122	7	(	(	PUNCT
ejpam-721	122	8	y	y	PROPN
ejpam-721	122	9	,	,	PUNCT
ejpam-721	122	10	σ	σ	PROPN
ejpam-721	122	11	)	)	PUNCT
ejpam-721	122	12	by	by	ADP
ejpam-721	122	13	:	:	PUNCT
ejpam-721	122	14	f	f	X
ejpam-721	122	15	(	(	PUNCT
ejpam-721	122	16	a	a	X
ejpam-721	122	17	)	)	PUNCT
ejpam-721	122	18	=	=	SYM
ejpam-721	122	19	y	y	PROPN
ejpam-721	122	20	,	,	PUNCT
ejpam-721	122	21	f	f	PROPN
ejpam-721	122	22	(	(	PUNCT
ejpam-721	122	23	b	b	NOUN
ejpam-721	122	24	)	)	PUNCT
ejpam-721	122	25	=	=	SYM
ejpam-721	122	26	f	f	X
ejpam-721	122	27	(	(	PUNCT
ejpam-721	122	28	c	c	NOUN
ejpam-721	122	29	)	)	PUNCT
ejpam-721	123	1	=	=	SYM
ejpam-721	123	2	z	z	X
ejpam-721	123	3	,	,	PUNCT
ejpam-721	123	4	f	f	PROPN
ejpam-721	123	5	(	(	PUNCT
ejpam-721	123	6	d	d	NOUN
ejpam-721	123	7	)	)	PUNCT
ejpam-721	123	8	=	=	VERB
ejpam-721	123	9	x.	x.	NOUN
ejpam-721	124	1	the	the	DET
ejpam-721	124	2	inverse	inverse	ADJ
ejpam-721	124	3	image	image	NOUN
ejpam-721	124	4	of	of	ADP
ejpam-721	124	5	the	the	DET
ejpam-721	124	6	open	open	ADJ
ejpam-721	124	7	set	set	NOUN
ejpam-721	124	8	{	{	PUNCT
ejpam-721	124	9	z	z	NOUN
ejpam-721	124	10	}	}	PUNCT
ejpam-721	124	11	is	be	AUX
ejpam-721	124	12	{	{	PUNCT
ejpam-721	124	13	b	b	NOUN
ejpam-721	124	14	,	,	PUNCT
ejpam-721	124	15	c	c	NOUN
ejpam-721	124	16	}	}	PUNCT
ejpam-721	124	17	which	which	PRON
ejpam-721	124	18	is	be	AUX
ejpam-721	124	19	a	a	DET
ejpam-721	124	20	supra	supra	PROPN
ejpam-721	124	21	b	b	NOUN
ejpam-721	124	22	-	-	PUNCT
ejpam-721	124	23	open	open	ADJ
ejpam-721	124	24	set	set	NOUN
ejpam-721	124	25	but	but	CCONJ
ejpam-721	124	26	it	it	PRON
ejpam-721	124	27	is	be	AUX
ejpam-721	124	28	not	not	PART
ejpam-721	124	29	a	a	DET
ejpam-721	124	30	supra	supra	NOUN
ejpam-721	124	31	semi	semi	ADJ
ejpam-721	124	32	-	-	ADJ
ejpam-721	124	33	open	open	ADJ
ejpam-721	124	34	set.then	set.then	X
ejpam-721	125	1	f	f	PROPN
ejpam-721	125	2	is	be	AUX
ejpam-721	125	3	supra	supra	ADJ
ejpam-721	125	4	b	b	NOUN
ejpam-721	125	5	-	-	PUNCT
ejpam-721	125	6	continuous	continuous	ADJ
ejpam-721	125	7	but	but	CCONJ
ejpam-721	125	8	it	it	PRON
ejpam-721	125	9	is	be	AUX
ejpam-721	125	10	not	not	PART
ejpam-721	125	11	supra	supra	ADJ
ejpam-721	125	12	semi	semi	ADJ
ejpam-721	125	13	-	-	ADJ
ejpam-721	125	14	continuous	continuous	ADJ
ejpam-721	125	15	map	map	NOUN
ejpam-721	125	16	.	.	PUNCT
ejpam-721	126	1	o.	o.	PROPN
ejpam-721	126	2	r.	r.	PROPN
ejpam-721	126	3	sayed	say	VERB
ejpam-721	126	4	,	,	PUNCT
ejpam-721	126	5	t.	t.	PROPN
ejpam-721	126	6	noiri	noiri	PROPN
ejpam-721	126	7	/	/	SYM
ejpam-721	126	8	eur	eur	PROPN
ejpam-721	126	9	.	.	PUNCT
ejpam-721	127	1	j.	j.	PROPN
ejpam-721	127	2	pure	pure	PROPN
ejpam-721	127	3	appl	appl	PROPN
ejpam-721	127	4	.	.	PROPN
ejpam-721	127	5	math	math	PROPN
ejpam-721	127	6	,	,	PUNCT
ejpam-721	127	7	3	3	NUM
ejpam-721	127	8	(	(	PUNCT
ejpam-721	127	9	2010	2010	NUM
ejpam-721	127	10	)	)	PUNCT
ejpam-721	127	11	,	,	PUNCT
ejpam-721	127	12	295	295	NUM
ejpam-721	127	13	-	-	SYM
ejpam-721	127	14	302	302	NUM
ejpam-721	127	15	299	299	NUM
ejpam-721	127	16	therefore	therefore	ADV
ejpam-721	127	17	,	,	PUNCT
ejpam-721	127	18	from	from	ADP
ejpam-721	127	19	diagram	diagram	NOUN
ejpam-721	127	20	1	1	NUM
ejpam-721	127	21	we	we	PRON
ejpam-721	127	22	have	have	VERB
ejpam-721	127	23	the	the	DET
ejpam-721	127	24	following	follow	VERB
ejpam-721	127	25	diagram	diagram	NOUN
ejpam-721	127	26	in	in	ADP
ejpam-721	127	27	which	which	PRON
ejpam-721	127	28	the	the	DET
ejpam-721	127	29	converses	converse	NOUN
ejpam-721	127	30	of	of	ADP
ejpam-721	127	31	the	the	DET
ejpam-721	127	32	implications	implication	NOUN
ejpam-721	127	33	need	need	AUX
ejpam-721	127	34	not	not	PART
ejpam-721	127	35	be	be	AUX
ejpam-721	127	36	true	true	ADJ
ejpam-721	127	37	by	by	ADP
ejpam-721	127	38	the	the	DET
ejpam-721	127	39	above	above	ADJ
ejpam-721	127	40	discussion	discussion	NOUN
ejpam-721	127	41	.	.	PUNCT
ejpam-721	128	1	(	(	PUNCT
ejpam-721	128	2	diagram	diagram	NOUN
ejpam-721	128	3	2	2	NUM
ejpam-721	128	4	)	)	PUNCT
ejpam-721	128	5	supra	supra	NOUN
ejpam-721	128	6	-	-	PUNCT
ejpam-721	128	7	continui	continui	PROPN
ejpam-721	128	8	t	t	PROPN
ejpam-721	128	9	y	y	PROPN
ejpam-721	128	10	→	→	SYM
ejpam-721	128	11	supra	supra	PROPN
ejpam-721	128	12	α	α	PROPN
ejpam-721	128	13	-	-	PUNCT
ejpam-721	128	14	continui	continui	PROPN
ejpam-721	128	15	t	t	PROPN
ejpam-721	128	16	y	y	PROPN
ejpam-721	128	17	→	→	SYM
ejpam-721	128	18	supra	supra	PROPN
ejpam-721	128	19	semicontinui	semicontinui	PROPN
ejpam-721	128	20	t	t	PROPN
ejpam-721	128	21	y	y	PROPN
ejpam-721	128	22	→	→	SYM
ejpam-721	128	23	supra	supra	PROPN
ejpam-721	128	24	b	b	X
ejpam-721	128	25	-	-	PUNCT
ejpam-721	128	26	continui	continui	PROPN
ejpam-721	128	27	t	t	PROPN
ejpam-721	128	28	y	y	PROPN
ejpam-721	128	29	theorem	theorem	VERB
ejpam-721	128	30	7	7	NUM
ejpam-721	128	31	.	.	PUNCT
ejpam-721	129	1	let	let	VERB
ejpam-721	129	2	(	(	PUNCT
ejpam-721	129	3	x	x	X
ejpam-721	129	4	,	,	PUNCT
ejpam-721	129	5	τ	τ	PROPN
ejpam-721	129	6	)	)	PUNCT
ejpam-721	129	7	and	and	CCONJ
ejpam-721	129	8	(	(	PUNCT
ejpam-721	129	9	y	y	PROPN
ejpam-721	129	10	,	,	PUNCT
ejpam-721	129	11	σ	σ	PROPN
ejpam-721	129	12	)	)	PUNCT
ejpam-721	129	13	be	be	VERB
ejpam-721	129	14	two	two	NUM
ejpam-721	129	15	topological	topological	ADJ
ejpam-721	129	16	spaces	space	NOUN
ejpam-721	129	17	and	and	CCONJ
ejpam-721	129	18	µ	µ	PRON
ejpam-721	129	19	be	be	AUX
ejpam-721	129	20	an	an	DET
ejpam-721	129	21	associated	associated	ADJ
ejpam-721	129	22	supra	supra	NOUN
ejpam-721	129	23	topology	topology	NOUN
ejpam-721	129	24	with	with	ADP
ejpam-721	129	25	τ	τ	PROPN
ejpam-721	129	26	.	.	PUNCT
ejpam-721	130	1	let	let	VERB
ejpam-721	130	2	f	f	PRON
ejpam-721	130	3	be	be	AUX
ejpam-721	130	4	a	a	DET
ejpam-721	130	5	map	map	NOUN
ejpam-721	130	6	from	from	ADP
ejpam-721	130	7	x	x	PUNCT
ejpam-721	130	8	into	into	ADP
ejpam-721	130	9	y	y	PROPN
ejpam-721	130	10	.	.	PUNCT
ejpam-721	131	1	then	then	ADV
ejpam-721	131	2	the	the	DET
ejpam-721	131	3	following	follow	VERB
ejpam-721	131	4	are	be	AUX
ejpam-721	131	5	equivalent	equivalent	ADJ
ejpam-721	131	6	:	:	PUNCT
ejpam-721	131	7	(	(	PUNCT
ejpam-721	131	8	1	1	X
ejpam-721	131	9	)	)	PUNCT
ejpam-721	131	10	f	f	PROPN
ejpam-721	131	11	is	be	AUX
ejpam-721	131	12	a	a	DET
ejpam-721	131	13	supra	supra	PROPN
ejpam-721	131	14	b	b	NOUN
ejpam-721	131	15	-	-	PUNCT
ejpam-721	131	16	continuous	continuous	ADJ
ejpam-721	131	17	map	map	NOUN
ejpam-721	131	18	;	;	PUNCT
ejpam-721	131	19	(	(	PUNCT
ejpam-721	131	20	2	2	X
ejpam-721	131	21	)	)	PUNCT
ejpam-721	131	22	the	the	DET
ejpam-721	131	23	inverse	inverse	ADJ
ejpam-721	131	24	image	image	NOUN
ejpam-721	131	25	of	of	ADP
ejpam-721	131	26	a	a	DET
ejpam-721	131	27	closed	closed	ADJ
ejpam-721	131	28	set	set	NOUN
ejpam-721	131	29	in	in	ADP
ejpam-721	131	30	y	y	PROPN
ejpam-721	131	31	is	be	AUX
ejpam-721	131	32	a	a	DET
ejpam-721	131	33	supra	supra	PROPN
ejpam-721	131	34	b	b	NOUN
ejpam-721	131	35	-	-	PUNCT
ejpam-721	131	36	closed	closed	ADJ
ejpam-721	131	37	set	set	NOUN
ejpam-721	131	38	in	in	ADP
ejpam-721	131	39	x	x	SYM
ejpam-721	131	40	;	;	PUNCT
ejpam-721	131	41	(	(	PUNCT
ejpam-721	131	42	3	3	X
ejpam-721	131	43	)	)	PUNCT
ejpam-721	131	44	clµb	clµb	NOUN
ejpam-721	131	45	(	(	PUNCT
ejpam-721	131	46	f	f	PROPN
ejpam-721	131	47	−1(a))⊆	−1(a))⊆	PROPN
ejpam-721	131	48	f	f	PROPN
ejpam-721	131	49	−1(cl(a	−1(cl(a	PROPN
ejpam-721	131	50	)	)	PUNCT
ejpam-721	131	51	)	)	PUNCT
ejpam-721	131	52	for	for	ADP
ejpam-721	131	53	every	every	DET
ejpam-721	131	54	set	set	NOUN
ejpam-721	131	55	a	a	PRON
ejpam-721	131	56	in	in	ADP
ejpam-721	131	57	y	y	PROPN
ejpam-721	131	58	;	;	PUNCT
ejpam-721	131	59	(	(	PUNCT
ejpam-721	131	60	4	4	X
ejpam-721	131	61	)	)	PUNCT
ejpam-721	131	62	f	f	NOUN
ejpam-721	131	63	(	(	PUNCT
ejpam-721	131	64	clµb	clµb	PROPN
ejpam-721	131	65	(	(	PUNCT
ejpam-721	131	66	a))⊆	a))⊆	PROPN
ejpam-721	131	67	cl	cl	NOUN
ejpam-721	131	68	(	(	PUNCT
ejpam-721	131	69	f	f	X
ejpam-721	131	70	(	(	PUNCT
ejpam-721	131	71	a	a	NOUN
ejpam-721	131	72	)	)	PUNCT
ejpam-721	131	73	)	)	PUNCT
ejpam-721	131	74	for	for	ADP
ejpam-721	131	75	every	every	DET
ejpam-721	131	76	set	set	NOUN
ejpam-721	131	77	a	a	PRON
ejpam-721	131	78	in	in	NOUN
ejpam-721	131	79	x	x	SYM
ejpam-721	131	80	;	;	PUNCT
ejpam-721	131	81	(	(	PUNCT
ejpam-721	131	82	5	5	X
ejpam-721	131	83	)	)	PUNCT
ejpam-721	131	84	f	f	NOUN
ejpam-721	131	85	−1(int(b))⊆	−1(int(b))⊆	NOUN
ejpam-721	131	86	intµb	intµb	PROPN
ejpam-721	131	87	(	(	PUNCT
ejpam-721	131	88	f	f	PROPN
ejpam-721	131	89	−1(b	−1(b	NOUN
ejpam-721	131	90	)	)	PUNCT
ejpam-721	131	91	)	)	PUNCT
ejpam-721	131	92	for	for	ADP
ejpam-721	131	93	every	every	DET
ejpam-721	131	94	b	b	NOUN
ejpam-721	131	95	in	in	ADP
ejpam-721	131	96	y	y	PROPN
ejpam-721	131	97	.	.	PUNCT
ejpam-721	132	1	proof	proof	NOUN
ejpam-721	132	2	.	.	PUNCT
ejpam-721	133	1	•	•	NUM
ejpam-721	133	2	(	(	PUNCT
ejpam-721	133	3	1)⇒(2	1)⇒(2	NUM
ejpam-721	133	4	):	):	PUNCT
ejpam-721	133	5	let	let	VERB
ejpam-721	133	6	a	a	PRON
ejpam-721	133	7	be	be	AUX
ejpam-721	133	8	a	a	DET
ejpam-721	133	9	closed	closed	ADJ
ejpam-721	133	10	set	set	NOUN
ejpam-721	133	11	in	in	ADP
ejpam-721	133	12	y	y	PROPN
ejpam-721	133	13	,	,	PUNCT
ejpam-721	133	14	then	then	ADV
ejpam-721	133	15	y	y	PROPN
ejpam-721	133	16	−a	−a	NOUN
ejpam-721	133	17	is	be	AUX
ejpam-721	133	18	an	an	DET
ejpam-721	133	19	open	open	ADJ
ejpam-721	133	20	set	set	NOUN
ejpam-721	133	21	in	in	ADP
ejpam-721	133	22	y	y	PROPN
ejpam-721	133	23	.	.	PUNCT
ejpam-721	134	1	then	then	ADV
ejpam-721	134	2	f	f	PROPN
ejpam-721	134	3	−1(y	−1(y	PUNCT
ejpam-721	134	4	−a	−a	NOUN
ejpam-721	134	5	)	)	PUNCT
ejpam-721	134	6	=	=	PUNCT
ejpam-721	135	1	x	x	PUNCT
ejpam-721	135	2	−	−	PROPN
ejpam-721	135	3	f	f	PROPN
ejpam-721	135	4	−1(a	−1(a	VERB
ejpam-721	135	5	)	)	PUNCT
ejpam-721	135	6	is	be	AUX
ejpam-721	135	7	a	a	DET
ejpam-721	135	8	supra	supra	PROPN
ejpam-721	135	9	b	b	NOUN
ejpam-721	135	10	-	-	PUNCT
ejpam-721	135	11	open	open	ADJ
ejpam-721	135	12	set	set	NOUN
ejpam-721	135	13	in	in	ADP
ejpam-721	135	14	x	x	X
ejpam-721	135	15	.	.	PUNCT
ejpam-721	136	1	it	it	PRON
ejpam-721	136	2	follows	follow	VERB
ejpam-721	136	3	that	that	SCONJ
ejpam-721	136	4	f	f	PROPN
ejpam-721	136	5	−1(a	−1(a	CCONJ
ejpam-721	136	6	)	)	PUNCT
ejpam-721	136	7	is	be	AUX
ejpam-721	136	8	a	a	DET
ejpam-721	136	9	supra	supra	PROPN
ejpam-721	136	10	b	b	NOUN
ejpam-721	136	11	-	-	PUNCT
ejpam-721	136	12	closed	closed	ADJ
ejpam-721	136	13	subset	subset	NOUN
ejpam-721	136	14	of	of	ADP
ejpam-721	136	15	x	x	PROPN
ejpam-721	136	16	.	.	PUNCT
ejpam-721	136	17	•	•	NUM
ejpam-721	136	18	(	(	PUNCT
ejpam-721	136	19	2)⇒(3	2)⇒(3	NUM
ejpam-721	136	20	):	):	PUNCT
ejpam-721	136	21	let	let	VERB
ejpam-721	136	22	a	a	PRON
ejpam-721	136	23	be	be	AUX
ejpam-721	136	24	any	any	DET
ejpam-721	136	25	subset	subset	NOUN
ejpam-721	136	26	of	of	ADP
ejpam-721	136	27	y	y	PROPN
ejpam-721	136	28	.	.	PUNCT
ejpam-721	137	1	since	since	SCONJ
ejpam-721	137	2	cl(a	cl(a	NUM
ejpam-721	137	3	)	)	PUNCT
ejpam-721	137	4	is	be	AUX
ejpam-721	137	5	closed	close	VERB
ejpam-721	137	6	in	in	ADP
ejpam-721	137	7	y	y	PROPN
ejpam-721	137	8	,	,	PUNCT
ejpam-721	137	9	then	then	ADV
ejpam-721	137	10	f	f	PROPN
ejpam-721	137	11	−1(cl(a	−1(cl(a	PROPN
ejpam-721	137	12	)	)	PUNCT
ejpam-721	137	13	)	)	PUNCT
ejpam-721	137	14	is	be	AUX
ejpam-721	137	15	supra	supra	PROPN
ejpam-721	137	16	b	b	NOUN
ejpam-721	137	17	-	-	PUNCT
ejpam-721	137	18	closed	closed	ADJ
ejpam-721	137	19	in	in	ADP
ejpam-721	137	20	x	x	X
ejpam-721	137	21	.	.	PUNCT
ejpam-721	138	1	therefore	therefore	ADV
ejpam-721	138	2	,	,	PUNCT
ejpam-721	138	3	clµb	clµb	PROPN
ejpam-721	138	4	(	(	PUNCT
ejpam-721	138	5	f	f	PROPN
ejpam-721	138	6	−1(a))⊆	−1(a))⊆	PROPN
ejpam-721	138	7	clµb	clµb	PROPN
ejpam-721	138	8	(	(	PUNCT
ejpam-721	138	9	f	f	PROPN
ejpam-721	138	10	−1(cl(a	−1(cl(a	PROPN
ejpam-721	138	11	)	)	PUNCT
ejpam-721	138	12	)	)	PUNCT
ejpam-721	138	13	)	)	PUNCT
ejpam-721	139	1	=	=	SYM
ejpam-721	139	2	f	f	PROPN
ejpam-721	139	3	−1(cl(a	−1(cl(a	PROPN
ejpam-721	139	4	)	)	PUNCT
ejpam-721	139	5	)	)	PUNCT
ejpam-721	139	6	.	.	PUNCT
ejpam-721	140	1	•	•	NUM
ejpam-721	140	2	(	(	PUNCT
ejpam-721	140	3	3)⇒(4	3)⇒(4	NOUN
ejpam-721	140	4	):	):	PUNCT
ejpam-721	140	5	let	let	VERB
ejpam-721	140	6	a	a	PRON
ejpam-721	140	7	be	be	AUX
ejpam-721	140	8	any	any	DET
ejpam-721	140	9	subset	subset	NOUN
ejpam-721	140	10	of	of	ADP
ejpam-721	140	11	x	x	X
ejpam-721	140	12	.	.	PUNCT
ejpam-721	141	1	by	by	ADP
ejpam-721	141	2	(	(	PUNCT
ejpam-721	141	3	3	3	X
ejpam-721	141	4	)	)	PUNCT
ejpam-721	141	5	we	we	PRON
ejpam-721	141	6	have	have	VERB
ejpam-721	141	7	f	f	PROPN
ejpam-721	141	8	−1(cl	−1(cl	PROPN
ejpam-721	141	9	(	(	PUNCT
ejpam-721	141	10	f	f	PROPN
ejpam-721	141	11	(	(	PUNCT
ejpam-721	141	12	a)))⊇	a)))⊇	PROPN
ejpam-721	141	13	clµb	clµb	PROPN
ejpam-721	141	14	(	(	PUNCT
ejpam-721	141	15	f	f	PROPN
ejpam-721	141	16	−1	−1	PROPN
ejpam-721	141	17	(	(	PUNCT
ejpam-721	141	18	f	f	PROPN
ejpam-721	141	19	(	(	PUNCT
ejpam-721	141	20	a)))⊇	a)))⊇	NOUN
ejpam-721	141	21	clµb	clµb	PROPN
ejpam-721	141	22	(	(	PUNCT
ejpam-721	141	23	a).therefore	a).therefore	PROPN
ejpam-721	141	24	,	,	PUNCT
ejpam-721	141	25	f	f	PROPN
ejpam-721	141	26	(	(	PUNCT
ejpam-721	141	27	clµb	clµb	PROPN
ejpam-721	141	28	(	(	PUNCT
ejpam-721	141	29	a))⊆	a))⊆	PROPN
ejpam-721	141	30	cl	cl	NOUN
ejpam-721	141	31	(	(	PUNCT
ejpam-721	141	32	f	f	X
ejpam-721	141	33	(	(	PUNCT
ejpam-721	141	34	a	a	NOUN
ejpam-721	141	35	)	)	PUNCT
ejpam-721	141	36	)	)	PUNCT
ejpam-721	141	37	.	.	PUNCT
ejpam-721	142	1	•	•	NUM
ejpam-721	142	2	(	(	PUNCT
ejpam-721	142	3	4)⇒	4)⇒	NUM
ejpam-721	142	4	(	(	PUNCT
ejpam-721	142	5	5):let	5):let	NUM
ejpam-721	142	6	b	b	NOUN
ejpam-721	142	7	be	be	AUX
ejpam-721	142	8	any	any	DET
ejpam-721	142	9	subset	subset	NOUN
ejpam-721	142	10	of	of	ADP
ejpam-721	142	11	y	y	PROPN
ejpam-721	142	12	.	.	PUNCT
ejpam-721	143	1	by	by	ADP
ejpam-721	143	2	(	(	PUNCT
ejpam-721	143	3	4	4	NUM
ejpam-721	143	4	)	)	PUNCT
ejpam-721	143	5	,	,	PUNCT
ejpam-721	143	6	f	f	PROPN
ejpam-721	143	7	(	(	PUNCT
ejpam-721	143	8	clµb	clµb	PROPN
ejpam-721	143	9	(	(	PUNCT
ejpam-721	143	10	x	x	PROPN
ejpam-721	143	11	−	−	PROPN
ejpam-721	143	12	f	f	PROPN
ejpam-721	143	13	−1(b	−1(b	NOUN
ejpam-721	143	14	)	)	PUNCT
ejpam-721	143	15	)	)	PUNCT
ejpam-721	143	16	)	)	PUNCT
ejpam-721	144	1	⊂	⊂	PROPN
ejpam-721	144	2	cl	cl	PROPN
ejpam-721	144	3	(	(	PUNCT
ejpam-721	144	4	f	f	X
ejpam-721	144	5	(	(	PUNCT
ejpam-721	144	6	x	x	PROPN
ejpam-721	144	7	−	−	PROPN
ejpam-721	144	8	f	f	PROPN
ejpam-721	144	9	−1(b	−1(b	NOUN
ejpam-721	144	10	)	)	PUNCT
ejpam-721	144	11	)	)	PUNCT
ejpam-721	144	12	)	)	PUNCT
ejpam-721	144	13	and	and	CCONJ
ejpam-721	144	14	f	f	PROPN
ejpam-721	144	15	(	(	PUNCT
ejpam-721	144	16	x−intµb	x−intµb	PROPN
ejpam-721	144	17	(	(	PUNCT
ejpam-721	144	18	f	f	X
ejpam-721	144	19	−1(b)))⊂	−1(b)))⊂	NOUN
ejpam-721	144	20	cl(y−b	cl(y−b	ADP
ejpam-721	144	21	)	)	PUNCT
ejpam-721	144	22	=	=	SYM
ejpam-721	144	23	y−int(b	y−int(b	NUM
ejpam-721	144	24	)	)	PUNCT
ejpam-721	144	25	.	.	PUNCT
ejpam-721	145	1	therefore	therefore	ADV
ejpam-721	145	2	,	,	PUNCT
ejpam-721	145	3	we	we	PRON
ejpam-721	145	4	have	have	VERB
ejpam-721	145	5	x−intµb	x−intµb	PROPN
ejpam-721	146	1	(	(	PUNCT
ejpam-721	146	2	f	f	X
ejpam-721	146	3	−1(b))⊂	−1(b))⊂	PROPN
ejpam-721	146	4	f	f	PROPN
ejpam-721	146	5	−1(y	−1(y	X
ejpam-721	146	6	−	−	PROPN
ejpam-721	146	7	int(b	int(b	NOUN
ejpam-721	146	8	)	)	PUNCT
ejpam-721	146	9	)	)	PUNCT
ejpam-721	146	10	and	and	CCONJ
ejpam-721	146	11	f	f	PROPN
ejpam-721	146	12	−1(int(b))⊂	−1(int(b))⊂	PRON
ejpam-721	146	13	intµb	intµb	NOUN
ejpam-721	146	14	(	(	PUNCT
ejpam-721	146	15	f	f	PROPN
ejpam-721	146	16	−1(b	−1(b	NOUN
ejpam-721	146	17	)	)	PUNCT
ejpam-721	146	18	)	)	PUNCT
ejpam-721	146	19	.	.	PUNCT
ejpam-721	147	1	•	•	NUM
ejpam-721	147	2	(	(	PUNCT
ejpam-721	147	3	5)⇒(1	5)⇒(1	NUM
ejpam-721	147	4	):	):	PUNCT
ejpam-721	147	5	let	let	VERB
ejpam-721	147	6	b	b	X
ejpam-721	147	7	be	be	AUX
ejpam-721	147	8	an	an	DET
ejpam-721	147	9	open	open	ADJ
ejpam-721	147	10	set	set	NOUN
ejpam-721	147	11	in	in	ADP
ejpam-721	147	12	y	y	PROPN
ejpam-721	147	13	and	and	CCONJ
ejpam-721	147	14	f	f	PROPN
ejpam-721	147	15	−1(int(b	−1(int(b	NOUN
ejpam-721	147	16	)	)	PUNCT
ejpam-721	147	17	)	)	PUNCT
ejpam-721	148	1	⊆	⊆	NUM
ejpam-721	148	2	intµb	intµb	NOUN
ejpam-721	148	3	(	(	PUNCT
ejpam-721	148	4	f	f	PROPN
ejpam-721	148	5	−1(b	−1(b	NOUN
ejpam-721	148	6	)	)	PUNCT
ejpam-721	148	7	)	)	PUNCT
ejpam-721	148	8	.	.	PUNCT
ejpam-721	149	1	then	then	ADV
ejpam-721	149	2	,	,	PUNCT
ejpam-721	149	3	f	f	PROPN
ejpam-721	149	4	−1(b	−1(b	ADJ
ejpam-721	149	5	)	)	PUNCT
ejpam-721	149	6	⊆	⊆	NUM
ejpam-721	149	7	intµb	intµb	NOUN
ejpam-721	149	8	(	(	PUNCT
ejpam-721	149	9	f	f	PROPN
ejpam-721	149	10	−1(b	−1(b	NOUN
ejpam-721	149	11	)	)	PUNCT
ejpam-721	149	12	)	)	PUNCT
ejpam-721	149	13	.	.	PUNCT
ejpam-721	150	1	but	but	CCONJ
ejpam-721	150	2	,	,	PUNCT
ejpam-721	150	3	intµb	intµb	PROPN
ejpam-721	150	4	(	(	PUNCT
ejpam-721	150	5	f	f	X
ejpam-721	150	6	−1(b))⊆	−1(b))⊆	NOUN
ejpam-721	150	7	f	f	X
ejpam-721	150	8	−1(b	−1(b	NOUN
ejpam-721	150	9	)	)	PUNCT
ejpam-721	150	10	.	.	PUNCT
ejpam-721	151	1	hence	hence	ADV
ejpam-721	151	2	,	,	PUNCT
ejpam-721	151	3	f	f	PROPN
ejpam-721	151	4	−1(b	−1(b	NOUN
ejpam-721	151	5	)	)	PUNCT
ejpam-721	152	1	=	=	SYM
ejpam-721	152	2	intµb	intµb	NOUN
ejpam-721	152	3	(	(	PUNCT
ejpam-721	152	4	f	f	PROPN
ejpam-721	152	5	−1(b	−1(b	NOUN
ejpam-721	152	6	)	)	PUNCT
ejpam-721	152	7	)	)	PUNCT
ejpam-721	152	8	.	.	PUNCT
ejpam-721	153	1	therefore	therefore	ADV
ejpam-721	153	2	,	,	PUNCT
ejpam-721	153	3	f	f	PROPN
ejpam-721	153	4	−1(b	−1(b	NOUN
ejpam-721	153	5	)	)	PUNCT
ejpam-721	153	6	is	be	AUX
ejpam-721	153	7	supra	supra	ADJ
ejpam-721	153	8	b	b	NOUN
ejpam-721	153	9	-	-	PUNCT
ejpam-721	153	10	open	open	ADJ
ejpam-721	153	11	in	in	ADP
ejpam-721	153	12	x	x	X
ejpam-721	153	13	.	.	PUNCT
ejpam-721	153	14	theorem	theorem	ADJ
ejpam-721	153	15	8	8	NUM
ejpam-721	153	16	.	.	PUNCT
ejpam-721	154	1	let	let	VERB
ejpam-721	154	2	(	(	PUNCT
ejpam-721	154	3	x	x	X
ejpam-721	154	4	,	,	PUNCT
ejpam-721	154	5	τ	τ	PROPN
ejpam-721	154	6	)	)	PUNCT
ejpam-721	154	7	,	,	PUNCT
ejpam-721	154	8	(	(	PUNCT
ejpam-721	154	9	y	y	PROPN
ejpam-721	154	10	,	,	PUNCT
ejpam-721	154	11	σ	σ	PROPN
ejpam-721	154	12	)	)	PUNCT
ejpam-721	154	13	and	and	CCONJ
ejpam-721	154	14	(	(	PUNCT
ejpam-721	154	15	z	z	NOUN
ejpam-721	154	16	,	,	PUNCT
ejpam-721	154	17	υ	υ	PROPN
ejpam-721	154	18	)	)	PUNCT
ejpam-721	154	19	be	be	VERB
ejpam-721	154	20	three	three	NUM
ejpam-721	154	21	topological	topological	ADJ
ejpam-721	154	22	spaces	space	NOUN
ejpam-721	154	23	.	.	PUNCT
ejpam-721	155	1	if	if	SCONJ
ejpam-721	155	2	a	a	DET
ejpam-721	155	3	map	map	NOUN
ejpam-721	155	4	f	f	X
ejpam-721	155	5	:	:	PUNCT
ejpam-721	155	6	(	(	PUNCT
ejpam-721	155	7	x	x	X
ejpam-721	155	8	,	,	PUNCT
ejpam-721	155	9	τ	τ	PROPN
ejpam-721	155	10	)	)	PUNCT
ejpam-721	155	11	→	→	SYM
ejpam-721	155	12	(	(	PUNCT
ejpam-721	155	13	y	y	PROPN
ejpam-721	155	14	,	,	PUNCT
ejpam-721	155	15	σ	σ	PROPN
ejpam-721	155	16	)	)	PUNCT
ejpam-721	155	17	is	be	AUX
ejpam-721	155	18	supra	supra	ADJ
ejpam-721	155	19	b	b	NOUN
ejpam-721	155	20	-	-	PUNCT
ejpam-721	155	21	continuous	continuous	ADJ
ejpam-721	155	22	and	and	CCONJ
ejpam-721	155	23	g	g	NOUN
ejpam-721	155	24	:	:	PUNCT
ejpam-721	155	25	(	(	PUNCT
ejpam-721	155	26	y	y	NOUN
ejpam-721	155	27	,	,	PUNCT
ejpam-721	155	28	σ)→	σ)→	PROPN
ejpam-721	155	29	(	(	PUNCT
ejpam-721	155	30	z	z	NOUN
ejpam-721	155	31	,	,	PUNCT
ejpam-721	155	32	υ	υ	PROPN
ejpam-721	155	33	)	)	PUNCT
ejpam-721	155	34	is	be	AUX
ejpam-721	155	35	a	a	DET
ejpam-721	155	36	continuous	continuous	ADJ
ejpam-721	155	37	map	map	NOUN
ejpam-721	155	38	,	,	PUNCT
ejpam-721	155	39	then	then	ADV
ejpam-721	155	40	g	g	PROPN
ejpam-721	155	41	◦	◦	NOUN
ejpam-721	155	42	f	f	X
ejpam-721	155	43	:	:	PUNCT
ejpam-721	155	44	(	(	PUNCT
ejpam-721	155	45	x	x	X
ejpam-721	155	46	,	,	PUNCT
ejpam-721	155	47	τ)→	τ)→	PROPN
ejpam-721	155	48	(	(	PUNCT
ejpam-721	155	49	z	z	NOUN
ejpam-721	155	50	,	,	PUNCT
ejpam-721	155	51	υ	υ	NOUN
ejpam-721	155	52	)	)	PUNCT
ejpam-721	155	53	is	be	AUX
ejpam-721	155	54	supra	supra	ADJ
ejpam-721	155	55	b	b	NOUN
ejpam-721	155	56	-	-	PUNCT
ejpam-721	155	57	continuous	continuous	ADJ
ejpam-721	155	58	.	.	PUNCT
ejpam-721	156	1	proof	proof	NOUN
ejpam-721	156	2	.	.	PUNCT
ejpam-721	157	1	obvious	obvious	ADJ
ejpam-721	157	2	.	.	PUNCT
ejpam-721	158	1	theorem	theorem	VERB
ejpam-721	158	2	9	9	NUM
ejpam-721	158	3	.	.	PUNCT
ejpam-721	159	1	let	let	VERB
ejpam-721	159	2	(	(	PUNCT
ejpam-721	159	3	x	x	X
ejpam-721	159	4	,	,	PUNCT
ejpam-721	159	5	τ	τ	PROPN
ejpam-721	159	6	)	)	PUNCT
ejpam-721	159	7	and	and	CCONJ
ejpam-721	159	8	(	(	PUNCT
ejpam-721	159	9	y	y	PROPN
ejpam-721	159	10	,	,	PUNCT
ejpam-721	159	11	σ	σ	PROPN
ejpam-721	159	12	)	)	PUNCT
ejpam-721	159	13	be	be	VERB
ejpam-721	159	14	two	two	NUM
ejpam-721	159	15	topological	topological	ADJ
ejpam-721	159	16	spaces	space	NOUN
ejpam-721	159	17	and	and	CCONJ
ejpam-721	159	18	µ	µ	NOUN
ejpam-721	159	19	and	and	CCONJ
ejpam-721	159	20	ν	ν	PROPN
ejpam-721	159	21	be	be	AUX
ejpam-721	159	22	the	the	DET
ejpam-721	159	23	associated	associated	ADJ
ejpam-721	159	24	supra	supra	NOUN
ejpam-721	159	25	topologies	topology	NOUN
ejpam-721	159	26	with	with	ADP
ejpam-721	159	27	τ	τ	PROPN
ejpam-721	159	28	and	and	CCONJ
ejpam-721	159	29	σ	σ	PROPN
ejpam-721	159	30	,	,	PUNCT
ejpam-721	159	31	respectively	respectively	ADV
ejpam-721	159	32	.	.	PUNCT
ejpam-721	160	1	then	then	ADV
ejpam-721	160	2	f	f	X
ejpam-721	160	3	:	:	PUNCT
ejpam-721	160	4	(	(	PUNCT
ejpam-721	160	5	x	x	X
ejpam-721	160	6	,	,	PUNCT
ejpam-721	160	7	τ)→	τ)→	PROPN
ejpam-721	160	8	(	(	PUNCT
ejpam-721	160	9	y	y	PROPN
ejpam-721	160	10	,	,	PUNCT
ejpam-721	160	11	σ	σ	PROPN
ejpam-721	160	12	)	)	PUNCT
ejpam-721	160	13	is	be	AUX
ejpam-721	160	14	a	a	DET
ejpam-721	160	15	supra	supra	PROPN
ejpam-721	160	16	b	b	NOUN
ejpam-721	160	17	-	-	PUNCT
ejpam-721	160	18	continuous	continuous	ADJ
ejpam-721	160	19	map	map	NOUN
ejpam-721	160	20	,	,	PUNCT
ejpam-721	160	21	if	if	SCONJ
ejpam-721	160	22	one	one	NUM
ejpam-721	160	23	of	of	ADP
ejpam-721	160	24	the	the	DET
ejpam-721	160	25	following	follow	VERB
ejpam-721	160	26	holds	hold	NOUN
ejpam-721	160	27	:	:	PUNCT
ejpam-721	160	28	o.	o.	PROPN
ejpam-721	160	29	r.	r.	PROPN
ejpam-721	160	30	sayed	say	VERB
ejpam-721	160	31	,	,	PUNCT
ejpam-721	160	32	t.	t.	PROPN
ejpam-721	160	33	noiri	noiri	PROPN
ejpam-721	160	34	/	/	SYM
ejpam-721	160	35	eur	eur	PROPN
ejpam-721	160	36	.	.	PUNCT
ejpam-721	161	1	j.	j.	PROPN
ejpam-721	161	2	pure	pure	PROPN
ejpam-721	161	3	appl	appl	PROPN
ejpam-721	161	4	.	.	PROPN
ejpam-721	161	5	math	math	PROPN
ejpam-721	161	6	,	,	PUNCT
ejpam-721	161	7	3	3	NUM
ejpam-721	161	8	(	(	PUNCT
ejpam-721	161	9	2010	2010	NUM
ejpam-721	161	10	)	)	PUNCT
ejpam-721	161	11	,	,	PUNCT
ejpam-721	161	12	295	295	NUM
ejpam-721	161	13	-	-	SYM
ejpam-721	161	14	302	302	NUM
ejpam-721	161	15	300	300	NUM
ejpam-721	161	16	(	(	PUNCT
ejpam-721	161	17	1	1	NUM
ejpam-721	161	18	)	)	PUNCT
ejpam-721	161	19	f	f	PROPN
ejpam-721	162	1	−1(intνb(b))⊆	−1(intνb(b))⊆	PROPN
ejpam-721	162	2	int	int	PROPN
ejpam-721	162	3	(	(	PUNCT
ejpam-721	162	4	f	f	PROPN
ejpam-721	162	5	−1(b	−1(b	NOUN
ejpam-721	162	6	)	)	PUNCT
ejpam-721	162	7	)	)	PUNCT
ejpam-721	162	8	for	for	ADP
ejpam-721	162	9	every	every	DET
ejpam-721	162	10	set	set	NOUN
ejpam-721	162	11	b	b	PROPN
ejpam-721	162	12	in	in	ADP
ejpam-721	162	13	y.	y.	PROPN
ejpam-721	162	14	(	(	PUNCT
ejpam-721	162	15	2	2	NUM
ejpam-721	162	16	)	)	PUNCT
ejpam-721	162	17	cl	cl	NOUN
ejpam-721	162	18	(	(	PUNCT
ejpam-721	162	19	f	f	NOUN
ejpam-721	162	20	−1(b))⊆	−1(b))⊆	NOUN
ejpam-721	162	21	f	f	X
ejpam-721	162	22	−1(clνb	−1(clνb	PROPN
ejpam-721	162	23	(	(	PUNCT
ejpam-721	162	24	b	b	NOUN
ejpam-721	162	25	)	)	PUNCT
ejpam-721	162	26	)	)	PUNCT
ejpam-721	162	27	for	for	ADP
ejpam-721	162	28	every	every	DET
ejpam-721	162	29	set	set	NOUN
ejpam-721	162	30	b	b	PROPN
ejpam-721	162	31	in	in	ADP
ejpam-721	162	32	y	y	PROPN
ejpam-721	162	33	.	.	PUNCT
ejpam-721	163	1	(	(	PUNCT
ejpam-721	163	2	3	3	X
ejpam-721	163	3	)	)	PUNCT
ejpam-721	163	4	f	f	NOUN
ejpam-721	163	5	(	(	PUNCT
ejpam-721	163	6	cl(a))⊆	cl(a))⊆	PROPN
ejpam-721	163	7	clµb	clµb	NOUN
ejpam-721	163	8	(	(	PUNCT
ejpam-721	163	9	f	f	X
ejpam-721	163	10	(	(	PUNCT
ejpam-721	163	11	a	a	NOUN
ejpam-721	163	12	)	)	PUNCT
ejpam-721	163	13	)	)	PUNCT
ejpam-721	163	14	for	for	ADP
ejpam-721	163	15	every	every	DET
ejpam-721	163	16	set	set	NOUN
ejpam-721	163	17	a	a	PRON
ejpam-721	163	18	in	in	ADP
ejpam-721	163	19	x	x	X
ejpam-721	163	20	.	.	PUNCT
ejpam-721	164	1	proof	proof	NOUN
ejpam-721	164	2	.	.	PUNCT
ejpam-721	165	1	let	let	VERB
ejpam-721	165	2	b	b	X
ejpam-721	165	3	be	be	AUX
ejpam-721	165	4	any	any	DET
ejpam-721	165	5	open	open	ADJ
ejpam-721	165	6	set	set	NOUN
ejpam-721	165	7	of	of	ADP
ejpam-721	165	8	y	y	PROPN
ejpam-721	165	9	.	.	PUNCT
ejpam-721	166	1	if	if	SCONJ
ejpam-721	166	2	condition	condition	NOUN
ejpam-721	166	3	(	(	PUNCT
ejpam-721	166	4	1	1	X
ejpam-721	166	5	)	)	PUNCT
ejpam-721	166	6	is	be	AUX
ejpam-721	166	7	satisfied	satisfied	ADJ
ejpam-721	166	8	,	,	PUNCT
ejpam-721	166	9	then	then	ADV
ejpam-721	166	10	f	f	PROPN
ejpam-721	166	11	−1(intνb(b	−1(intνb(b	NUM
ejpam-721	166	12	)	)	PUNCT
ejpam-721	166	13	)	)	PUNCT
ejpam-721	167	1	⊆	⊆	NUM
ejpam-721	167	2	int	int	NOUN
ejpam-721	167	3	(	(	PUNCT
ejpam-721	167	4	f	f	PROPN
ejpam-721	167	5	−1(b	−1(b	NOUN
ejpam-721	167	6	)	)	PUNCT
ejpam-721	167	7	)	)	PUNCT
ejpam-721	167	8	.	.	PUNCT
ejpam-721	168	1	we	we	PRON
ejpam-721	168	2	get	get	VERB
ejpam-721	168	3	f	f	PROPN
ejpam-721	168	4	−1(b	−1(b	NOUN
ejpam-721	168	5	)	)	PUNCT
ejpam-721	168	6	⊆	⊆	NUM
ejpam-721	168	7	int	int	NOUN
ejpam-721	168	8	(	(	PUNCT
ejpam-721	168	9	f	f	PROPN
ejpam-721	168	10	−1(b	−1(b	NOUN
ejpam-721	168	11	)	)	PUNCT
ejpam-721	168	12	)	)	PUNCT
ejpam-721	168	13	.	.	PUNCT
ejpam-721	169	1	therefore	therefore	ADV
ejpam-721	169	2	,	,	PUNCT
ejpam-721	169	3	f	f	PROPN
ejpam-721	169	4	−1(b	−1(b	NOUN
ejpam-721	169	5	)	)	PUNCT
ejpam-721	169	6	is	be	AUX
ejpam-721	169	7	an	an	DET
ejpam-721	169	8	open	open	ADJ
ejpam-721	169	9	set	set	NOUN
ejpam-721	169	10	.	.	PUNCT
ejpam-721	170	1	every	every	DET
ejpam-721	170	2	open	open	ADJ
ejpam-721	170	3	set	set	NOUN
ejpam-721	170	4	is	be	AUX
ejpam-721	170	5	supra	supra	ADJ
ejpam-721	170	6	b	b	NOUN
ejpam-721	170	7	-	-	PUNCT
ejpam-721	170	8	open	open	ADJ
ejpam-721	170	9	.	.	PUNCT
ejpam-721	171	1	hence	hence	ADV
ejpam-721	171	2	,	,	PUNCT
ejpam-721	171	3	f	f	PROPN
ejpam-721	171	4	is	be	AUX
ejpam-721	171	5	a	a	DET
ejpam-721	171	6	supra	supra	PROPN
ejpam-721	171	7	b	b	NOUN
ejpam-721	171	8	-	-	PUNCT
ejpam-721	171	9	continuous	continuous	ADJ
ejpam-721	171	10	map	map	NOUN
ejpam-721	171	11	.	.	PUNCT
ejpam-721	172	1	if	if	SCONJ
ejpam-721	172	2	condition	condition	NOUN
ejpam-721	172	3	(	(	PUNCT
ejpam-721	172	4	2	2	X
ejpam-721	172	5	)	)	PUNCT
ejpam-721	172	6	is	be	AUX
ejpam-721	172	7	satisfied	satisfied	ADJ
ejpam-721	172	8	,	,	PUNCT
ejpam-721	172	9	then	then	ADV
ejpam-721	172	10	we	we	PRON
ejpam-721	172	11	can	can	AUX
ejpam-721	172	12	easily	easily	ADV
ejpam-721	172	13	prove	prove	VERB
ejpam-721	172	14	that	that	SCONJ
ejpam-721	172	15	f	f	PROPN
ejpam-721	172	16	is	be	AUX
ejpam-721	172	17	a	a	DET
ejpam-721	172	18	supra	supra	PROPN
ejpam-721	172	19	b	b	NOUN
ejpam-721	172	20	-	-	PUNCT
ejpam-721	172	21	continuous	continuous	ADJ
ejpam-721	172	22	map	map	NOUN
ejpam-721	172	23	.	.	PUNCT
ejpam-721	173	1	let	let	VERB
ejpam-721	173	2	condition	condition	NOUN
ejpam-721	173	3	(	(	PUNCT
ejpam-721	173	4	3	3	X
ejpam-721	173	5	)	)	PUNCT
ejpam-721	173	6	be	be	AUX
ejpam-721	173	7	satisfied	satisfied	ADJ
ejpam-721	173	8	and	and	CCONJ
ejpam-721	173	9	b	b	NOUN
ejpam-721	173	10	be	be	AUX
ejpam-721	173	11	any	any	DET
ejpam-721	173	12	open	open	ADJ
ejpam-721	173	13	set	set	NOUN
ejpam-721	173	14	of	of	ADP
ejpam-721	173	15	y.	y.	PROPN
ejpam-721	173	16	then	then	ADV
ejpam-721	173	17	f	f	PROPN
ejpam-721	173	18	−1(b	−1(b	NOUN
ejpam-721	173	19	)	)	PUNCT
ejpam-721	173	20	is	be	AUX
ejpam-721	173	21	a	a	DET
ejpam-721	173	22	set	set	NOUN
ejpam-721	173	23	in	in	ADP
ejpam-721	173	24	x	x	PROPN
ejpam-721	173	25	and	and	CCONJ
ejpam-721	173	26	f	f	PROPN
ejpam-721	173	27	(	(	PUNCT
ejpam-721	173	28	cl	cl	NOUN
ejpam-721	173	29	(	(	PUNCT
ejpam-721	173	30	f	f	PROPN
ejpam-721	173	31	−1(b	−1(b	NOUN
ejpam-721	173	32	)	)	PUNCT
ejpam-721	173	33	)	)	PUNCT
ejpam-721	173	34	)	)	PUNCT
ejpam-721	174	1	⊆	⊆	NUM
ejpam-721	174	2	clµb	clµb	NOUN
ejpam-721	174	3	(	(	PUNCT
ejpam-721	174	4	f	f	PROPN
ejpam-721	174	5	(	(	PUNCT
ejpam-721	174	6	f	f	PROPN
ejpam-721	174	7	−1(b	−1(b	NOUN
ejpam-721	174	8	)	)	PUNCT
ejpam-721	174	9	)	)	PUNCT
ejpam-721	174	10	)	)	PUNCT
ejpam-721	174	11	.	.	PUNCT
ejpam-721	175	1	this	this	PRON
ejpam-721	175	2	implies	imply	VERB
ejpam-721	175	3	f	f	PROPN
ejpam-721	175	4	(	(	PUNCT
ejpam-721	175	5	cl	cl	PROPN
ejpam-721	175	6	(	(	PUNCT
ejpam-721	175	7	f	f	PROPN
ejpam-721	175	8	−1(b	−1(b	NOUN
ejpam-721	175	9	)	)	PUNCT
ejpam-721	175	10	)	)	PUNCT
ejpam-721	175	11	)	)	PUNCT
ejpam-721	176	1	⊆	⊆	NUM
ejpam-721	176	2	clµb	clµb	NOUN
ejpam-721	176	3	(	(	PUNCT
ejpam-721	176	4	b	b	NOUN
ejpam-721	176	5	)	)	PUNCT
ejpam-721	176	6	.	.	PUNCT
ejpam-721	177	1	this	this	PRON
ejpam-721	177	2	is	be	AUX
ejpam-721	177	3	nothing	nothing	PRON
ejpam-721	177	4	but	but	SCONJ
ejpam-721	177	5	condition	condition	NOUN
ejpam-721	177	6	(	(	PUNCT
ejpam-721	177	7	2	2	NUM
ejpam-721	177	8	)	)	PUNCT
ejpam-721	177	9	.	.	PUNCT
ejpam-721	178	1	hence	hence	ADV
ejpam-721	178	2	f	f	PROPN
ejpam-721	178	3	is	be	AUX
ejpam-721	178	4	a	a	DET
ejpam-721	178	5	supra	supra	PROPN
ejpam-721	178	6	b	b	NOUN
ejpam-721	178	7	-	-	PUNCT
ejpam-721	178	8	continuous	continuous	ADJ
ejpam-721	178	9	map	map	NOUN
ejpam-721	178	10	.	.	PUNCT
ejpam-721	179	1	4	4	X
ejpam-721	179	2	.	.	X
ejpam-721	179	3	supra	supra	PROPN
ejpam-721	179	4	b	b	X
ejpam-721	179	5	-	-	PUNCT
ejpam-721	179	6	open	open	ADJ
ejpam-721	179	7	maps	map	NOUN
ejpam-721	179	8	and	and	CCONJ
ejpam-721	179	9	supra	supra	PROPN
ejpam-721	179	10	b	b	PROPN
ejpam-721	179	11	-	-	PUNCT
ejpam-721	179	12	closed	close	VERB
ejpam-721	179	13	maps	map	NOUN
ejpam-721	179	14	definition	definition	NOUN
ejpam-721	179	15	4	4	NUM
ejpam-721	179	16	.	.	PUNCT
ejpam-721	180	1	a	a	DET
ejpam-721	180	2	map	map	NOUN
ejpam-721	180	3	f	f	X
ejpam-721	180	4	:	:	PUNCT
ejpam-721	180	5	(	(	PUNCT
ejpam-721	180	6	x	x	X
ejpam-721	180	7	,	,	PUNCT
ejpam-721	180	8	τ	τ	PROPN
ejpam-721	180	9	)	)	PUNCT
ejpam-721	180	10	→	→	SYM
ejpam-721	180	11	(	(	PUNCT
ejpam-721	180	12	y	y	PROPN
ejpam-721	180	13	,	,	PUNCT
ejpam-721	180	14	σ	σ	PROPN
ejpam-721	180	15	)	)	PUNCT
ejpam-721	180	16	is	be	AUX
ejpam-721	180	17	called	call	VERB
ejpam-721	180	18	a	a	DET
ejpam-721	180	19	supra	supra	PROPN
ejpam-721	180	20	b	b	NOUN
ejpam-721	180	21	-	-	PUNCT
ejpam-721	180	22	open	open	ADJ
ejpam-721	180	23	(	(	PUNCT
ejpam-721	180	24	resp	resp	NOUN
ejpam-721	180	25	.	.	PUNCT
ejpam-721	181	1	supra	supra	PROPN
ejpam-721	181	2	b	b	PROPN
ejpam-721	181	3	-	-	PUNCT
ejpam-721	181	4	closed	closed	ADJ
ejpam-721	181	5	)	)	PUNCT
ejpam-721	181	6	if	if	SCONJ
ejpam-721	181	7	the	the	DET
ejpam-721	181	8	image	image	NOUN
ejpam-721	181	9	of	of	ADP
ejpam-721	181	10	each	each	PRON
ejpam-721	181	11	open	open	ADJ
ejpam-721	181	12	(	(	PUNCT
ejpam-721	181	13	resp	resp	NOUN
ejpam-721	181	14	.	.	PUNCT
ejpam-721	182	1	closed	close	VERB
ejpam-721	182	2	)	)	PUNCT
ejpam-721	182	3	set	set	VERB
ejpam-721	182	4	in	in	ADP
ejpam-721	182	5	x	x	PROPN
ejpam-721	182	6	is	be	AUX
ejpam-721	182	7	supra	supra	ADJ
ejpam-721	182	8	b	b	NOUN
ejpam-721	182	9	-	-	PUNCT
ejpam-721	182	10	open	open	ADJ
ejpam-721	182	11	(	(	PUNCT
ejpam-721	182	12	resp	resp	NOUN
ejpam-721	182	13	.	.	PUNCT
ejpam-721	183	1	supra	supra	PROPN
ejpam-721	183	2	b	b	PROPN
ejpam-721	183	3	-	-	PUNCT
ejpam-721	183	4	closed	closed	ADJ
ejpam-721	183	5	)	)	PUNCT
ejpam-721	183	6	in	in	ADP
ejpam-721	183	7	(	(	PUNCT
ejpam-721	183	8	y	y	NOUN
ejpam-721	183	9	,	,	PUNCT
ejpam-721	183	10	ν	ν	NOUN
ejpam-721	183	11	)	)	PUNCT
ejpam-721	183	12	.	.	PUNCT
ejpam-721	184	1	theorem	theorem	ADJ
ejpam-721	184	2	10	10	NUM
ejpam-721	184	3	.	.	PUNCT
ejpam-721	185	1	a	a	DET
ejpam-721	185	2	map	map	NOUN
ejpam-721	185	3	f	f	X
ejpam-721	185	4	:	:	PUNCT
ejpam-721	185	5	(	(	PUNCT
ejpam-721	185	6	x	x	X
ejpam-721	185	7	,	,	PUNCT
ejpam-721	185	8	τ)→	τ)→	PROPN
ejpam-721	185	9	(	(	PUNCT
ejpam-721	185	10	y	y	PROPN
ejpam-721	185	11	,	,	PUNCT
ejpam-721	185	12	σ	σ	PROPN
ejpam-721	185	13	)	)	PUNCT
ejpam-721	185	14	is	be	AUX
ejpam-721	185	15	supra	supra	ADJ
ejpam-721	185	16	b	b	NOUN
ejpam-721	185	17	-	-	PUNCT
ejpam-721	185	18	open	open	ADJ
ejpam-721	185	19	if	if	SCONJ
ejpam-721	185	20	and	and	CCONJ
ejpam-721	185	21	only	only	ADV
ejpam-721	185	22	if	if	SCONJ
ejpam-721	185	23	f	f	PROPN
ejpam-721	185	24	(	(	PUNCT
ejpam-721	185	25	int(a))⊆	int(a))⊆	X
ejpam-721	185	26	intνb	intνb	VERB
ejpam-721	185	27	(	(	PUNCT
ejpam-721	185	28	f	f	X
ejpam-721	185	29	(	(	PUNCT
ejpam-721	185	30	a	a	NOUN
ejpam-721	185	31	)	)	PUNCT
ejpam-721	185	32	)	)	PUNCT
ejpam-721	185	33	for	for	SCONJ
ejpam-721	185	34	each	each	DET
ejpam-721	185	35	set	set	VERB
ejpam-721	185	36	a	a	PRON
ejpam-721	185	37	in	in	ADP
ejpam-721	185	38	x.	x.	NOUN
ejpam-721	185	39	proof	proof	NOUN
ejpam-721	185	40	.	.	PUNCT
ejpam-721	186	1	suppose	suppose	VERB
ejpam-721	186	2	that	that	SCONJ
ejpam-721	186	3	f	f	PROPN
ejpam-721	186	4	is	be	AUX
ejpam-721	186	5	a	a	DET
ejpam-721	186	6	supra	supra	PROPN
ejpam-721	186	7	b	b	NOUN
ejpam-721	186	8	-	-	PUNCT
ejpam-721	186	9	open	open	ADJ
ejpam-721	186	10	map	map	NOUN
ejpam-721	186	11	.	.	PUNCT
ejpam-721	187	1	since	since	SCONJ
ejpam-721	187	2	int(a	int(a	PROPN
ejpam-721	187	3	)	)	PUNCT
ejpam-721	187	4	⊆	⊆	PROPN
ejpam-721	187	5	a	a	PRON
ejpam-721	187	6	,	,	PUNCT
ejpam-721	187	7	then	then	ADV
ejpam-721	187	8	f	f	X
ejpam-721	187	9	(	(	PUNCT
ejpam-721	187	10	int(a	int(a	PROPN
ejpam-721	187	11	)	)	PUNCT
ejpam-721	187	12	)	)	PUNCT
ejpam-721	188	1	⊆	⊆	NUM
ejpam-721	188	2	f	f	X
ejpam-721	188	3	(	(	PUNCT
ejpam-721	188	4	a	a	NOUN
ejpam-721	188	5	)	)	PUNCT
ejpam-721	188	6	.	.	PUNCT
ejpam-721	189	1	by	by	ADP
ejpam-721	189	2	hypothesis	hypothesis	NOUN
ejpam-721	189	3	,	,	PUNCT
ejpam-721	189	4	f	f	PROPN
ejpam-721	189	5	(	(	PUNCT
ejpam-721	189	6	int(a	int(a	PROPN
ejpam-721	189	7	)	)	PUNCT
ejpam-721	189	8	)	)	PUNCT
ejpam-721	189	9	is	be	AUX
ejpam-721	189	10	a	a	DET
ejpam-721	189	11	supra	supra	PROPN
ejpam-721	189	12	b	b	NOUN
ejpam-721	189	13	-	-	PUNCT
ejpam-721	189	14	open	open	ADJ
ejpam-721	189	15	set	set	NOUN
ejpam-721	189	16	and	and	CCONJ
ejpam-721	189	17	intνb	intνb	NOUN
ejpam-721	189	18	(	(	PUNCT
ejpam-721	189	19	f	f	X
ejpam-721	189	20	(	(	PUNCT
ejpam-721	189	21	a	a	NOUN
ejpam-721	189	22	)	)	PUNCT
ejpam-721	189	23	)	)	PUNCT
ejpam-721	189	24	is	be	AUX
ejpam-721	189	25	the	the	DET
ejpam-721	189	26	largest	large	ADJ
ejpam-721	189	27	supra	supra	ADJ
ejpam-721	189	28	b	b	NOUN
ejpam-721	189	29	-	-	PUNCT
ejpam-721	189	30	open	open	ADJ
ejpam-721	189	31	set	set	NOUN
ejpam-721	189	32	contained	contain	VERB
ejpam-721	189	33	in	in	ADP
ejpam-721	189	34	f	f	PROPN
ejpam-721	189	35	(	(	PUNCT
ejpam-721	189	36	a	a	NOUN
ejpam-721	189	37	)	)	PUNCT
ejpam-721	189	38	.	.	PUNCT
ejpam-721	190	1	hence	hence	ADV
ejpam-721	190	2	f	f	PROPN
ejpam-721	190	3	(	(	PUNCT
ejpam-721	190	4	int(a))⊆	int(a))⊆	X
ejpam-721	190	5	intνb	intνb	VERB
ejpam-721	190	6	(	(	PUNCT
ejpam-721	190	7	f	f	X
ejpam-721	190	8	(	(	PUNCT
ejpam-721	190	9	a	a	NOUN
ejpam-721	190	10	)	)	PUNCT
ejpam-721	190	11	)	)	PUNCT
ejpam-721	190	12	.	.	PUNCT
ejpam-721	191	1	conversely	conversely	ADV
ejpam-721	191	2	,	,	PUNCT
ejpam-721	191	3	suppose	suppose	VERB
ejpam-721	191	4	a	a	PRON
ejpam-721	191	5	is	be	AUX
ejpam-721	191	6	an	an	DET
ejpam-721	191	7	open	open	ADJ
ejpam-721	191	8	set	set	NOUN
ejpam-721	191	9	in	in	ADP
ejpam-721	191	10	x	x	X
ejpam-721	191	11	.	.	PUNCT
ejpam-721	192	1	then	then	ADV
ejpam-721	192	2	,	,	PUNCT
ejpam-721	192	3	f	f	PROPN
ejpam-721	192	4	(	(	PUNCT
ejpam-721	192	5	int(a	int(a	PROPN
ejpam-721	192	6	)	)	PUNCT
ejpam-721	192	7	)	)	PUNCT
ejpam-721	192	8	⊆	⊆	NUM
ejpam-721	192	9	intνb	intνb	NOUN
ejpam-721	192	10	(	(	PUNCT
ejpam-721	192	11	f	f	X
ejpam-721	192	12	(	(	PUNCT
ejpam-721	192	13	a	a	NOUN
ejpam-721	192	14	)	)	PUNCT
ejpam-721	192	15	)	)	PUNCT
ejpam-721	192	16	.	.	PUNCT
ejpam-721	193	1	since	since	SCONJ
ejpam-721	193	2	int(a	int(a	PROPN
ejpam-721	193	3	)	)	PUNCT
ejpam-721	193	4	=	=	SYM
ejpam-721	193	5	a	a	PRON
ejpam-721	193	6	,	,	PUNCT
ejpam-721	193	7	then	then	ADV
ejpam-721	193	8	f	f	X
ejpam-721	193	9	(	(	PUNCT
ejpam-721	193	10	a	a	X
ejpam-721	193	11	)	)	PUNCT
ejpam-721	193	12	⊆	⊆	NUM
ejpam-721	193	13	intνb	intνb	NOUN
ejpam-721	193	14	(	(	PUNCT
ejpam-721	193	15	f	f	X
ejpam-721	193	16	(	(	PUNCT
ejpam-721	193	17	a	a	NOUN
ejpam-721	193	18	)	)	PUNCT
ejpam-721	193	19	)	)	PUNCT
ejpam-721	193	20	.	.	PUNCT
ejpam-721	194	1	therefore	therefore	ADV
ejpam-721	194	2	f	f	X
ejpam-721	194	3	(	(	PUNCT
ejpam-721	194	4	a	a	PRON
ejpam-721	194	5	)	)	PUNCT
ejpam-721	194	6	is	be	AUX
ejpam-721	194	7	a	a	DET
ejpam-721	194	8	supra	supra	PROPN
ejpam-721	194	9	b	b	NOUN
ejpam-721	194	10	-	-	PUNCT
ejpam-721	194	11	open	open	ADJ
ejpam-721	194	12	set	set	NOUN
ejpam-721	194	13	in	in	ADP
ejpam-721	194	14	(	(	PUNCT
ejpam-721	194	15	y	y	PROPN
ejpam-721	194	16	,	,	PUNCT
ejpam-721	194	17	ν	ν	NOUN
ejpam-721	194	18	)	)	PUNCT
ejpam-721	194	19	and	and	CCONJ
ejpam-721	194	20	f	f	PROPN
ejpam-721	194	21	is	be	AUX
ejpam-721	194	22	a	a	DET
ejpam-721	194	23	supra	supra	PROPN
ejpam-721	194	24	b	b	NOUN
ejpam-721	194	25	-	-	PUNCT
ejpam-721	194	26	open	open	ADJ
ejpam-721	194	27	map	map	NOUN
ejpam-721	194	28	.	.	PUNCT
ejpam-721	195	1	theorem	theorem	VERB
ejpam-721	195	2	11	11	NUM
ejpam-721	195	3	.	.	PUNCT
ejpam-721	196	1	a	a	DET
ejpam-721	196	2	map	map	NOUN
ejpam-721	196	3	f	f	X
ejpam-721	196	4	:	:	PUNCT
ejpam-721	196	5	(	(	PUNCT
ejpam-721	196	6	x	x	X
ejpam-721	196	7	,	,	PUNCT
ejpam-721	196	8	τ)→	τ)→	PROPN
ejpam-721	196	9	(	(	PUNCT
ejpam-721	196	10	y	y	PROPN
ejpam-721	196	11	,	,	PUNCT
ejpam-721	196	12	σ	σ	PROPN
ejpam-721	196	13	)	)	PUNCT
ejpam-721	196	14	is	be	AUX
ejpam-721	196	15	supra	supra	PROPN
ejpam-721	196	16	b	b	NOUN
ejpam-721	196	17	-	-	PUNCT
ejpam-721	196	18	closed	closed	ADJ
ejpam-721	196	19	if	if	SCONJ
ejpam-721	197	1	and	and	CCONJ
ejpam-721	197	2	only	only	ADV
ejpam-721	197	3	if	if	SCONJ
ejpam-721	197	4	c	c	PROPN
ejpam-721	197	5	lνb	lνb	VERB
ejpam-721	197	6	(	(	PUNCT
ejpam-721	197	7	f	f	X
ejpam-721	197	8	(	(	PUNCT
ejpam-721	197	9	a	a	NOUN
ejpam-721	197	10	)	)	PUNCT
ejpam-721	197	11	)	)	PUNCT
ejpam-721	198	1	⊆	⊆	NUM
ejpam-721	198	2	f	f	NOUN
ejpam-721	198	3	(	(	PUNCT
ejpam-721	198	4	cl(a	cl(a	NUM
ejpam-721	198	5	)	)	PUNCT
ejpam-721	198	6	)	)	PUNCT
ejpam-721	198	7	for	for	SCONJ
ejpam-721	198	8	each	each	DET
ejpam-721	198	9	set	set	VERB
ejpam-721	198	10	a	a	PRON
ejpam-721	198	11	in	in	ADP
ejpam-721	198	12	x.	x.	NOUN
ejpam-721	198	13	proof	proof	NOUN
ejpam-721	198	14	.	.	PUNCT
ejpam-721	199	1	suppose	suppose	VERB
ejpam-721	199	2	f	f	PROPN
ejpam-721	199	3	is	be	AUX
ejpam-721	199	4	a	a	DET
ejpam-721	199	5	supra	supra	PROPN
ejpam-721	199	6	b	b	PROPN
ejpam-721	199	7	-	-	PUNCT
ejpam-721	199	8	closed	closed	ADJ
ejpam-721	199	9	map	map	NOUN
ejpam-721	199	10	.	.	PUNCT
ejpam-721	200	1	since	since	SCONJ
ejpam-721	200	2	for	for	ADP
ejpam-721	200	3	each	each	DET
ejpam-721	200	4	set	set	VERB
ejpam-721	200	5	a	a	PRON
ejpam-721	200	6	in	in	ADP
ejpam-721	200	7	x	x	X
ejpam-721	200	8	,	,	PUNCT
ejpam-721	200	9	cl(a	cl(a	NUM
ejpam-721	200	10	)	)	PUNCT
ejpam-721	200	11	is	be	AUX
ejpam-721	200	12	closed	close	VERB
ejpam-721	200	13	set	set	VERB
ejpam-721	200	14	in	in	ADP
ejpam-721	200	15	x	x	SYM
ejpam-721	200	16	,	,	PUNCT
ejpam-721	200	17	then	then	ADV
ejpam-721	200	18	f	f	X
ejpam-721	200	19	(	(	PUNCT
ejpam-721	200	20	cl(a	cl(a	NUM
ejpam-721	200	21	)	)	PUNCT
ejpam-721	200	22	)	)	PUNCT
ejpam-721	200	23	is	be	AUX
ejpam-721	200	24	a	a	DET
ejpam-721	200	25	supra	supra	PROPN
ejpam-721	200	26	b	b	NOUN
ejpam-721	200	27	-	-	PUNCT
ejpam-721	200	28	closed	closed	ADJ
ejpam-721	200	29	set	set	NOUN
ejpam-721	200	30	in	in	ADP
ejpam-721	200	31	y	y	PROPN
ejpam-721	200	32	.	.	PUNCT
ejpam-721	201	1	also	also	ADV
ejpam-721	201	2	,	,	PUNCT
ejpam-721	201	3	since	since	SCONJ
ejpam-721	201	4	f	f	PROPN
ejpam-721	201	5	(	(	PUNCT
ejpam-721	201	6	a	a	NOUN
ejpam-721	201	7	)	)	PUNCT
ejpam-721	201	8	⊆	⊆	NUM
ejpam-721	201	9	f	f	NOUN
ejpam-721	201	10	(	(	PUNCT
ejpam-721	201	11	cl(a	cl(a	NUM
ejpam-721	201	12	)	)	PUNCT
ejpam-721	201	13	)	)	PUNCT
ejpam-721	201	14	,	,	PUNCT
ejpam-721	201	15	then	then	ADV
ejpam-721	201	16	clνb	clνb	ADV
ejpam-721	201	17	(	(	PUNCT
ejpam-721	201	18	f	f	PROPN
ejpam-721	201	19	(	(	PUNCT
ejpam-721	201	20	a))⊆	a))⊆	PROPN
ejpam-721	201	21	f	f	X
ejpam-721	201	22	(	(	PUNCT
ejpam-721	201	23	cl(a	cl(a	NUM
ejpam-721	201	24	)	)	PUNCT
ejpam-721	201	25	)	)	PUNCT
ejpam-721	201	26	.	.	PUNCT
ejpam-721	202	1	conversely	conversely	ADV
ejpam-721	202	2	,	,	PUNCT
ejpam-721	202	3	let	let	VERB
ejpam-721	202	4	a	a	PRON
ejpam-721	202	5	be	be	AUX
ejpam-721	202	6	a	a	DET
ejpam-721	202	7	closed	closed	ADJ
ejpam-721	202	8	set	set	NOUN
ejpam-721	202	9	in	in	ADP
ejpam-721	202	10	x	x	X
ejpam-721	202	11	.	.	PUNCT
ejpam-721	203	1	since	since	SCONJ
ejpam-721	203	2	clνb	clνb	PROPN
ejpam-721	203	3	(	(	PUNCT
ejpam-721	203	4	f	f	X
ejpam-721	203	5	(	(	PUNCT
ejpam-721	203	6	a	a	NOUN
ejpam-721	203	7	)	)	PUNCT
ejpam-721	203	8	)	)	PUNCT
ejpam-721	203	9	is	be	AUX
ejpam-721	203	10	the	the	DET
ejpam-721	203	11	smallest	small	ADJ
ejpam-721	203	12	supra	supra	ADJ
ejpam-721	203	13	b	b	NOUN
ejpam-721	203	14	-	-	PUNCT
ejpam-721	203	15	closed	closed	ADJ
ejpam-721	203	16	set	set	NOUN
ejpam-721	203	17	containing	contain	VERB
ejpam-721	203	18	f	f	X
ejpam-721	203	19	(	(	PUNCT
ejpam-721	203	20	a	a	PROPN
ejpam-721	203	21	)	)	PUNCT
ejpam-721	203	22	,	,	PUNCT
ejpam-721	203	23	then	then	ADV
ejpam-721	203	24	f	f	X
ejpam-721	203	25	(	(	PUNCT
ejpam-721	203	26	a	a	NOUN
ejpam-721	203	27	)	)	PUNCT
ejpam-721	203	28	⊆	⊆	NUM
ejpam-721	203	29	clνb	clνb	NOUN
ejpam-721	203	30	(	(	PUNCT
ejpam-721	203	31	f	f	X
ejpam-721	203	32	(	(	PUNCT
ejpam-721	203	33	a	a	NOUN
ejpam-721	203	34	)	)	PUNCT
ejpam-721	203	35	)	)	PUNCT
ejpam-721	204	1	⊆	⊆	NUM
ejpam-721	204	2	f	f	NOUN
ejpam-721	204	3	(	(	PUNCT
ejpam-721	204	4	cl(a	cl(a	NUM
ejpam-721	204	5	)	)	PUNCT
ejpam-721	204	6	)	)	PUNCT
ejpam-721	205	1	=	=	SYM
ejpam-721	205	2	f	f	X
ejpam-721	205	3	(	(	PUNCT
ejpam-721	205	4	a	a	NOUN
ejpam-721	205	5	)	)	PUNCT
ejpam-721	205	6	.	.	PUNCT
ejpam-721	206	1	thus	thus	ADV
ejpam-721	206	2	,	,	PUNCT
ejpam-721	206	3	f	f	PROPN
ejpam-721	206	4	(	(	PUNCT
ejpam-721	206	5	a	a	X
ejpam-721	206	6	)	)	PUNCT
ejpam-721	206	7	=	=	SYM
ejpam-721	206	8	clνb	clνb	ADV
ejpam-721	206	9	(	(	PUNCT
ejpam-721	206	10	f	f	X
ejpam-721	206	11	(	(	PUNCT
ejpam-721	206	12	a	a	NOUN
ejpam-721	206	13	)	)	PUNCT
ejpam-721	206	14	)	)	PUNCT
ejpam-721	206	15	.	.	PUNCT
ejpam-721	207	1	hence	hence	ADV
ejpam-721	207	2	,	,	PUNCT
ejpam-721	207	3	f	f	PROPN
ejpam-721	207	4	(	(	PUNCT
ejpam-721	207	5	a	a	NOUN
ejpam-721	207	6	)	)	PUNCT
ejpam-721	207	7	is	be	AUX
ejpam-721	207	8	a	a	DET
ejpam-721	207	9	supra	supra	PROPN
ejpam-721	207	10	b	b	NOUN
ejpam-721	207	11	-	-	PUNCT
ejpam-721	207	12	closed	closed	ADJ
ejpam-721	207	13	set	set	NOUN
ejpam-721	207	14	in	in	ADP
ejpam-721	207	15	y	y	PROPN
ejpam-721	207	16	.	.	PUNCT
ejpam-721	208	1	therefore	therefore	ADV
ejpam-721	208	2	,	,	PUNCT
ejpam-721	208	3	f	f	PROPN
ejpam-721	208	4	is	be	AUX
ejpam-721	208	5	a	a	DET
ejpam-721	208	6	supra	supra	PROPN
ejpam-721	208	7	b	b	PROPN
ejpam-721	208	8	-	-	PUNCT
ejpam-721	208	9	closed	closed	ADJ
ejpam-721	208	10	map	map	NOUN
ejpam-721	208	11	.	.	PUNCT
ejpam-721	209	1	theorem	theorem	NOUN
ejpam-721	209	2	12	12	NUM
ejpam-721	209	3	.	.	PUNCT
ejpam-721	210	1	let	let	VERB
ejpam-721	210	2	(	(	PUNCT
ejpam-721	210	3	x	x	X
ejpam-721	210	4	,	,	PUNCT
ejpam-721	210	5	τ	τ	PROPN
ejpam-721	210	6	)	)	PUNCT
ejpam-721	210	7	,	,	PUNCT
ejpam-721	210	8	(	(	PUNCT
ejpam-721	210	9	y	y	PROPN
ejpam-721	210	10	,	,	PUNCT
ejpam-721	210	11	σ	σ	PROPN
ejpam-721	210	12	)	)	PUNCT
ejpam-721	210	13	and	and	CCONJ
ejpam-721	210	14	(	(	PUNCT
ejpam-721	210	15	z	z	NOUN
ejpam-721	210	16	,	,	PUNCT
ejpam-721	210	17	υ	υ	PROPN
ejpam-721	210	18	)	)	PUNCT
ejpam-721	210	19	be	be	VERB
ejpam-721	210	20	three	three	NUM
ejpam-721	210	21	topological	topological	ADJ
ejpam-721	210	22	spaces	space	NOUN
ejpam-721	210	23	and	and	CCONJ
ejpam-721	210	24	f	f	X
ejpam-721	210	25	:	:	PUNCT
ejpam-721	210	26	(	(	PUNCT
ejpam-721	210	27	x	x	X
ejpam-721	210	28	,	,	PUNCT
ejpam-721	210	29	τ)→	τ)→	PROPN
ejpam-721	210	30	(	(	PUNCT
ejpam-721	210	31	y	y	PROPN
ejpam-721	210	32	,	,	PUNCT
ejpam-721	210	33	σ	σ	PROPN
ejpam-721	210	34	)	)	PUNCT
ejpam-721	210	35	and	and	CCONJ
ejpam-721	210	36	g	g	NOUN
ejpam-721	210	37	:	:	PUNCT
ejpam-721	210	38	(	(	PUNCT
ejpam-721	210	39	y	y	NOUN
ejpam-721	210	40	,	,	PUNCT
ejpam-721	210	41	σ)→	σ)→	PROPN
ejpam-721	210	42	(	(	PUNCT
ejpam-721	210	43	z	z	NOUN
ejpam-721	210	44	,	,	PUNCT
ejpam-721	210	45	υ	υ	PROPN
ejpam-721	210	46	)	)	PUNCT
ejpam-721	210	47	be	be	VERB
ejpam-721	210	48	two	two	NUM
ejpam-721	210	49	maps	map	NOUN
ejpam-721	210	50	.	.	PUNCT
ejpam-721	211	1	then	then	ADV
ejpam-721	211	2	,	,	PUNCT
ejpam-721	211	3	(	(	PUNCT
ejpam-721	211	4	1	1	X
ejpam-721	211	5	)	)	PUNCT
ejpam-721	211	6	if	if	SCONJ
ejpam-721	211	7	g	g	PROPN
ejpam-721	211	8	◦	◦	NOUN
ejpam-721	211	9	f	f	PROPN
ejpam-721	211	10	is	be	AUX
ejpam-721	211	11	supra	supra	ADJ
ejpam-721	211	12	b	b	NOUN
ejpam-721	211	13	-	-	PUNCT
ejpam-721	211	14	open	open	ADJ
ejpam-721	211	15	and	and	CCONJ
ejpam-721	211	16	f	f	PROPN
ejpam-721	211	17	is	be	AUX
ejpam-721	211	18	continuous	continuous	ADJ
ejpam-721	211	19	surjective	surjective	ADJ
ejpam-721	211	20	,	,	PUNCT
ejpam-721	211	21	then	then	ADV
ejpam-721	211	22	g	g	PROPN
ejpam-721	211	23	is	be	AUX
ejpam-721	211	24	a	a	DET
ejpam-721	211	25	supra	supra	PROPN
ejpam-721	211	26	b	b	NOUN
ejpam-721	211	27	-	-	PUNCT
ejpam-721	211	28	open	open	ADJ
ejpam-721	211	29	map	map	NOUN
ejpam-721	211	30	.	.	PUNCT
ejpam-721	212	1	references	reference	NOUN
ejpam-721	212	2	301	301	NUM
ejpam-721	212	3	(	(	PUNCT
ejpam-721	212	4	2	2	NUM
ejpam-721	212	5	)	)	PUNCT
ejpam-721	212	6	if	if	SCONJ
ejpam-721	212	7	g	g	PROPN
ejpam-721	212	8	◦	◦	NOUN
ejpam-721	212	9	f	f	PROPN
ejpam-721	212	10	is	be	AUX
ejpam-721	212	11	open	open	ADJ
ejpam-721	212	12	and	and	CCONJ
ejpam-721	212	13	g	g	NOUN
ejpam-721	212	14	is	be	AUX
ejpam-721	212	15	supra	supra	ADJ
ejpam-721	212	16	b	b	NOUN
ejpam-721	212	17	-	-	PUNCT
ejpam-721	212	18	continuous	continuous	ADJ
ejpam-721	212	19	injective	injective	NOUN
ejpam-721	212	20	,	,	PUNCT
ejpam-721	212	21	then	then	ADV
ejpam-721	212	22	f	f	PROPN
ejpam-721	212	23	is	be	AUX
ejpam-721	212	24	a	a	DET
ejpam-721	212	25	supra	supra	PROPN
ejpam-721	212	26	b	b	NOUN
ejpam-721	212	27	-	-	PUNCT
ejpam-721	212	28	open	open	ADJ
ejpam-721	212	29	map	map	NOUN
ejpam-721	212	30	.	.	PUNCT
ejpam-721	213	1	proof	proof	NOUN
ejpam-721	213	2	.	.	PUNCT
ejpam-721	214	1	(	(	PUNCT
ejpam-721	214	2	1	1	X
ejpam-721	214	3	)	)	PUNCT
ejpam-721	214	4	let	let	VERB
ejpam-721	214	5	a	a	PRON
ejpam-721	214	6	be	be	AUX
ejpam-721	214	7	an	an	DET
ejpam-721	214	8	open	open	ADJ
ejpam-721	214	9	set	set	NOUN
ejpam-721	214	10	in	in	ADP
ejpam-721	214	11	y	y	PROPN
ejpam-721	214	12	.	.	PUNCT
ejpam-721	215	1	then	then	ADV
ejpam-721	215	2	,	,	PUNCT
ejpam-721	215	3	f	f	PROPN
ejpam-721	215	4	−1(a	−1(a	CCONJ
ejpam-721	215	5	)	)	PUNCT
ejpam-721	215	6	is	be	AUX
ejpam-721	215	7	an	an	DET
ejpam-721	215	8	open	open	ADJ
ejpam-721	215	9	set	set	NOUN
ejpam-721	215	10	in	in	ADP
ejpam-721	215	11	x	x	X
ejpam-721	215	12	.	.	PUNCT
ejpam-721	216	1	since	since	SCONJ
ejpam-721	216	2	g	g	PROPN
ejpam-721	216	3	◦	◦	PROPN
ejpam-721	216	4	f	f	PROPN
ejpam-721	216	5	is	be	AUX
ejpam-721	216	6	a	a	DET
ejpam-721	216	7	supra	supra	PROPN
ejpam-721	216	8	b	b	NOUN
ejpam-721	216	9	-	-	PUNCT
ejpam-721	216	10	open	open	ADJ
ejpam-721	216	11	map	map	NOUN
ejpam-721	216	12	,	,	PUNCT
ejpam-721	216	13	then	then	ADV
ejpam-721	216	14	(	(	PUNCT
ejpam-721	216	15	g	g	PROPN
ejpam-721	216	16	◦	◦	NOUN
ejpam-721	216	17	f	f	PROPN
ejpam-721	216	18	)	)	PUNCT
ejpam-721	216	19	(	(	PUNCT
ejpam-721	216	20	f	f	PROPN
ejpam-721	216	21	−1(a	−1(a	ADP
ejpam-721	216	22	)	)	PUNCT
ejpam-721	216	23	)	)	PUNCT
ejpam-721	217	1	=	=	SYM
ejpam-721	217	2	g	g	NOUN
ejpam-721	217	3	(	(	PUNCT
ejpam-721	217	4	f	f	PROPN
ejpam-721	217	5	(	(	PUNCT
ejpam-721	217	6	f	f	PROPN
ejpam-721	217	7	−1(a	−1(a	ADP
ejpam-721	217	8	)	)	PUNCT
ejpam-721	217	9	)	)	PUNCT
ejpam-721	217	10	)	)	PUNCT
ejpam-721	218	1	=	=	SYM
ejpam-721	218	2	g(a	g(a	PROPN
ejpam-721	218	3	)	)	PUNCT
ejpam-721	218	4	(	(	PUNCT
ejpam-721	218	5	because	because	SCONJ
ejpam-721	218	6	f	f	PROPN
ejpam-721	218	7	is	be	AUX
ejpam-721	218	8	surjective	surjective	ADJ
ejpam-721	218	9	)	)	PUNCT
ejpam-721	218	10	is	be	AUX
ejpam-721	218	11	a	a	DET
ejpam-721	218	12	supra	supra	PROPN
ejpam-721	218	13	b	b	NOUN
ejpam-721	218	14	-	-	PUNCT
ejpam-721	218	15	open	open	ADJ
ejpam-721	218	16	set	set	NOUN
ejpam-721	218	17	in	in	ADP
ejpam-721	218	18	z	z	PROPN
ejpam-721	218	19	.	.	PUNCT
ejpam-721	219	1	therefore	therefore	ADV
ejpam-721	219	2	,	,	PUNCT
ejpam-721	219	3	g	g	PROPN
ejpam-721	219	4	is	be	AUX
ejpam-721	219	5	a	a	DET
ejpam-721	219	6	supra	supra	PROPN
ejpam-721	219	7	b	b	NOUN
ejpam-721	219	8	-	-	PUNCT
ejpam-721	219	9	open	open	ADJ
ejpam-721	219	10	map	map	NOUN
ejpam-721	219	11	.	.	PUNCT
ejpam-721	220	1	(	(	PUNCT
ejpam-721	220	2	2	2	X
ejpam-721	220	3	)	)	PUNCT
ejpam-721	220	4	let	let	VERB
ejpam-721	220	5	a	a	PRON
ejpam-721	220	6	be	be	AUX
ejpam-721	220	7	an	an	DET
ejpam-721	220	8	open	open	ADJ
ejpam-721	220	9	set	set	NOUN
ejpam-721	220	10	in	in	ADP
ejpam-721	220	11	x	x	X
ejpam-721	220	12	.	.	PUNCT
ejpam-721	221	1	then	then	ADV
ejpam-721	221	2	,	,	PUNCT
ejpam-721	221	3	g	g	PROPN
ejpam-721	221	4	(	(	PUNCT
ejpam-721	221	5	f	f	X
ejpam-721	221	6	(	(	PUNCT
ejpam-721	221	7	a	a	NOUN
ejpam-721	221	8	)	)	PUNCT
ejpam-721	221	9	)	)	PUNCT
ejpam-721	221	10	is	be	AUX
ejpam-721	221	11	an	an	DET
ejpam-721	221	12	open	open	ADJ
ejpam-721	221	13	set	set	NOUN
ejpam-721	221	14	in	in	ADP
ejpam-721	221	15	z	z	PROPN
ejpam-721	221	16	.	.	PUNCT
ejpam-721	222	1	therefore	therefore	ADV
ejpam-721	222	2	,	,	PUNCT
ejpam-721	222	3	g−1(g	g−1(g	PROPN
ejpam-721	222	4	(	(	PUNCT
ejpam-721	222	5	f	f	PROPN
ejpam-721	222	6	(	(	PUNCT
ejpam-721	222	7	a	a	NOUN
ejpam-721	222	8	)	)	PUNCT
ejpam-721	222	9	)	)	PUNCT
ejpam-721	222	10	)	)	PUNCT
ejpam-721	223	1	=	=	SYM
ejpam-721	223	2	f	f	X
ejpam-721	223	3	(	(	PUNCT
ejpam-721	223	4	a	a	NOUN
ejpam-721	223	5	)	)	PUNCT
ejpam-721	223	6	(	(	PUNCT
ejpam-721	223	7	because	because	SCONJ
ejpam-721	223	8	g	g	PROPN
ejpam-721	223	9	is	be	AUX
ejpam-721	223	10	injective	injective	ADJ
ejpam-721	223	11	)	)	PUNCT
ejpam-721	223	12	is	be	AUX
ejpam-721	223	13	a	a	DET
ejpam-721	223	14	supra	supra	PROPN
ejpam-721	223	15	b	b	NOUN
ejpam-721	223	16	-	-	PUNCT
ejpam-721	223	17	open	open	ADJ
ejpam-721	223	18	set	set	NOUN
ejpam-721	223	19	in	in	ADP
ejpam-721	223	20	y	y	PROPN
ejpam-721	223	21	.	.	PUNCT
ejpam-721	224	1	hence	hence	ADV
ejpam-721	224	2	,	,	PUNCT
ejpam-721	224	3	f	f	PROPN
ejpam-721	224	4	is	be	AUX
ejpam-721	224	5	a	a	DET
ejpam-721	224	6	supra	supra	PROPN
ejpam-721	224	7	b	b	NOUN
ejpam-721	224	8	-	-	PUNCT
ejpam-721	224	9	open	open	ADJ
ejpam-721	224	10	map	map	NOUN
ejpam-721	224	11	.	.	PUNCT
ejpam-721	225	1	theorem	theorem	VERB
ejpam-721	225	2	13	13	NUM
ejpam-721	225	3	.	.	PUNCT
ejpam-721	226	1	let	let	VERB
ejpam-721	226	2	(	(	PUNCT
ejpam-721	226	3	x	x	X
ejpam-721	226	4	,	,	PUNCT
ejpam-721	226	5	τ	τ	PROPN
ejpam-721	226	6	)	)	PUNCT
ejpam-721	226	7	and	and	CCONJ
ejpam-721	226	8	(	(	PUNCT
ejpam-721	226	9	y	y	PROPN
ejpam-721	226	10	,	,	PUNCT
ejpam-721	226	11	σ	σ	PROPN
ejpam-721	226	12	)	)	PUNCT
ejpam-721	226	13	be	be	VERB
ejpam-721	226	14	two	two	NUM
ejpam-721	226	15	topological	topological	ADJ
ejpam-721	226	16	spaces	space	NOUN
ejpam-721	226	17	and	and	CCONJ
ejpam-721	226	18	f	f	X
ejpam-721	226	19	:	:	PUNCT
ejpam-721	226	20	(	(	PUNCT
ejpam-721	226	21	x	x	X
ejpam-721	226	22	,	,	PUNCT
ejpam-721	226	23	τ	τ	PROPN
ejpam-721	226	24	)	)	PUNCT
ejpam-721	226	25	→	→	SYM
ejpam-721	226	26	(	(	PUNCT
ejpam-721	226	27	y	y	PROPN
ejpam-721	226	28	,	,	PUNCT
ejpam-721	226	29	σ	σ	PROPN
ejpam-721	226	30	)	)	PUNCT
ejpam-721	226	31	be	be	VERB
ejpam-721	226	32	a	a	DET
ejpam-721	226	33	bijective	bijective	ADJ
ejpam-721	226	34	map	map	NOUN
ejpam-721	226	35	.	.	PUNCT
ejpam-721	227	1	then	then	ADV
ejpam-721	227	2	the	the	DET
ejpam-721	227	3	following	follow	VERB
ejpam-721	227	4	are	be	AUX
ejpam-721	227	5	equivalent	equivalent	ADJ
ejpam-721	227	6	:	:	PUNCT
ejpam-721	227	7	(	(	PUNCT
ejpam-721	227	8	1	1	X
ejpam-721	227	9	)	)	PUNCT
ejpam-721	227	10	f	f	PROPN
ejpam-721	227	11	is	be	AUX
ejpam-721	227	12	a	a	DET
ejpam-721	227	13	supra	supra	PROPN
ejpam-721	227	14	b	b	NOUN
ejpam-721	227	15	-	-	PUNCT
ejpam-721	227	16	open	open	ADJ
ejpam-721	227	17	map	map	NOUN
ejpam-721	227	18	;	;	PUNCT
ejpam-721	227	19	(	(	PUNCT
ejpam-721	227	20	2	2	X
ejpam-721	227	21	)	)	PUNCT
ejpam-721	227	22	f	f	PROPN
ejpam-721	227	23	is	be	AUX
ejpam-721	227	24	a	a	DET
ejpam-721	227	25	supra	supra	PROPN
ejpam-721	227	26	b	b	PROPN
ejpam-721	227	27	-	-	PUNCT
ejpam-721	227	28	closed	closed	ADJ
ejpam-721	227	29	map	map	NOUN
ejpam-721	227	30	;	;	PUNCT
ejpam-721	227	31	(	(	PUNCT
ejpam-721	227	32	3	3	X
ejpam-721	227	33	)	)	PUNCT
ejpam-721	227	34	f	f	NOUN
ejpam-721	228	1	−1	−1	NOUN
ejpam-721	228	2	is	be	AUX
ejpam-721	228	3	a	a	DET
ejpam-721	228	4	supra	supra	PROPN
ejpam-721	228	5	b	b	NOUN
ejpam-721	228	6	-	-	PUNCT
ejpam-721	228	7	continuous	continuous	ADJ
ejpam-721	228	8	map	map	NOUN
ejpam-721	228	9	.	.	PUNCT
ejpam-721	229	1	proof	proof	NOUN
ejpam-721	229	2	.	.	PUNCT
ejpam-721	230	1	•	•	NUM
ejpam-721	230	2	(	(	PUNCT
ejpam-721	230	3	1	1	X
ejpam-721	230	4	)	)	PUNCT
ejpam-721	230	5	=	=	NOUN
ejpam-721	230	6	⇒	⇒	NOUN
ejpam-721	230	7	(	(	PUNCT
ejpam-721	230	8	2	2	NUM
ejpam-721	230	9	):	):	PUNCT
ejpam-721	230	10	suppose	suppose	VERB
ejpam-721	230	11	b	b	X
ejpam-721	230	12	is	be	AUX
ejpam-721	230	13	a	a	DET
ejpam-721	230	14	closed	closed	ADJ
ejpam-721	230	15	set	set	NOUN
ejpam-721	230	16	in	in	ADP
ejpam-721	230	17	x	x	X
ejpam-721	230	18	.	.	PUNCT
ejpam-721	231	1	then	then	ADV
ejpam-721	231	2	x	x	X
ejpam-721	231	3	−	−	PROPN
ejpam-721	231	4	b	b	PROPN
ejpam-721	231	5	is	be	AUX
ejpam-721	231	6	an	an	DET
ejpam-721	231	7	open	open	ADJ
ejpam-721	231	8	set	set	NOUN
ejpam-721	231	9	in	in	ADP
ejpam-721	231	10	x	x	PUNCT
ejpam-721	231	11	and	and	CCONJ
ejpam-721	231	12	by	by	ADP
ejpam-721	231	13	(	(	PUNCT
ejpam-721	231	14	1	1	NUM
ejpam-721	231	15	)	)	PUNCT
ejpam-721	231	16	,	,	PUNCT
ejpam-721	231	17	f	f	PROPN
ejpam-721	231	18	(	(	PUNCT
ejpam-721	231	19	x−b	x−b	NOUN
ejpam-721	231	20	)	)	PUNCT
ejpam-721	231	21	is	be	AUX
ejpam-721	231	22	a	a	DET
ejpam-721	231	23	supra	supra	PROPN
ejpam-721	231	24	b	b	NOUN
ejpam-721	231	25	-	-	PUNCT
ejpam-721	231	26	open	open	ADJ
ejpam-721	231	27	set	set	NOUN
ejpam-721	231	28	in	in	ADP
ejpam-721	231	29	y	y	PROPN
ejpam-721	231	30	.	.	PUNCT
ejpam-721	232	1	since	since	SCONJ
ejpam-721	232	2	f	f	PROPN
ejpam-721	232	3	is	be	AUX
ejpam-721	232	4	bijective	bijective	ADJ
ejpam-721	232	5	,	,	PUNCT
ejpam-721	232	6	then	then	ADV
ejpam-721	232	7	f	f	X
ejpam-721	232	8	(	(	PUNCT
ejpam-721	232	9	x−b	x−b	NOUN
ejpam-721	232	10	)	)	PUNCT
ejpam-721	233	1	=	=	SYM
ejpam-721	233	2	y−	y−	X
ejpam-721	233	3	f	f	PROPN
ejpam-721	233	4	(	(	PUNCT
ejpam-721	233	5	b).hence	b).hence	PROPN
ejpam-721	233	6	,	,	PUNCT
ejpam-721	233	7	f	f	PROPN
ejpam-721	233	8	(	(	PUNCT
ejpam-721	233	9	b	b	NOUN
ejpam-721	233	10	)	)	PUNCT
ejpam-721	233	11	is	be	AUX
ejpam-721	233	12	a	a	DET
ejpam-721	233	13	supra	supra	PROPN
ejpam-721	233	14	b	b	NOUN
ejpam-721	233	15	-	-	PUNCT
ejpam-721	233	16	closed	closed	ADJ
ejpam-721	233	17	set	set	NOUN
ejpam-721	233	18	in	in	ADP
ejpam-721	233	19	y	y	PROPN
ejpam-721	233	20	.	.	PUNCT
ejpam-721	234	1	therefore	therefore	ADV
ejpam-721	234	2	,	,	PUNCT
ejpam-721	234	3	f	f	PROPN
ejpam-721	234	4	is	be	AUX
ejpam-721	234	5	a	a	DET
ejpam-721	234	6	supra	supra	PROPN
ejpam-721	234	7	b	b	PROPN
ejpam-721	234	8	-	-	PUNCT
ejpam-721	234	9	closed	close	VERB
ejpam-721	234	10	map	map	NOUN
ejpam-721	234	11	.	.	PUNCT
ejpam-721	235	1	•	•	NUM
ejpam-721	235	2	(	(	PUNCT
ejpam-721	235	3	2	2	X
ejpam-721	235	4	)	)	PUNCT
ejpam-721	236	1	=	=	NOUN
ejpam-721	236	2	⇒	⇒	NOUN
ejpam-721	236	3	(	(	PUNCT
ejpam-721	236	4	3	3	NUM
ejpam-721	236	5	):	):	PUNCT
ejpam-721	236	6	let	let	VERB
ejpam-721	236	7	f	f	PROPN
ejpam-721	236	8	is	be	AUX
ejpam-721	236	9	a	a	DET
ejpam-721	236	10	supra	supra	PROPN
ejpam-721	236	11	b	b	NOUN
ejpam-721	236	12	-	-	PUNCT
ejpam-721	236	13	closed	closed	ADJ
ejpam-721	236	14	map	map	NOUN
ejpam-721	236	15	and	and	CCONJ
ejpam-721	236	16	b	b	NOUN
ejpam-721	236	17	be	be	AUX
ejpam-721	236	18	closed	close	VERB
ejpam-721	236	19	set	set	VERB
ejpam-721	236	20	in	in	ADP
ejpam-721	236	21	x	x	X
ejpam-721	236	22	.	.	PUNCT
ejpam-721	237	1	since	since	SCONJ
ejpam-721	237	2	f	f	PROPN
ejpam-721	237	3	is	be	AUX
ejpam-721	237	4	bijective	bijective	ADJ
ejpam-721	237	5	,	,	PUNCT
ejpam-721	237	6	then	then	ADV
ejpam-721	237	7	(	(	PUNCT
ejpam-721	237	8	f	f	PROPN
ejpam-721	237	9	−1)−1(b	−1)−1(b	PROPN
ejpam-721	237	10	)	)	PUNCT
ejpam-721	238	1	=	=	SYM
ejpam-721	238	2	f	f	X
ejpam-721	238	3	(	(	PUNCT
ejpam-721	238	4	b	b	NOUN
ejpam-721	238	5	)	)	PUNCT
ejpam-721	238	6	which	which	PRON
ejpam-721	238	7	is	be	AUX
ejpam-721	238	8	a	a	DET
ejpam-721	238	9	supra	supra	PROPN
ejpam-721	238	10	b	b	NOUN
ejpam-721	238	11	-	-	PUNCT
ejpam-721	238	12	closed	closed	ADJ
ejpam-721	238	13	set	set	NOUN
ejpam-721	238	14	in	in	ADP
ejpam-721	238	15	y	y	PROPN
ejpam-721	238	16	.	.	PUNCT
ejpam-721	239	1	therefore	therefore	ADV
ejpam-721	239	2	,	,	PUNCT
ejpam-721	239	3	by	by	ADP
ejpam-721	239	4	theorem	theorem	NOUN
ejpam-721	239	5	7	7	NUM
ejpam-721	239	6	,	,	PUNCT
ejpam-721	239	7	f	f	PROPN
ejpam-721	239	8	is	be	AUX
ejpam-721	239	9	a	a	DET
ejpam-721	239	10	supra	supra	PROPN
ejpam-721	239	11	b	b	NOUN
ejpam-721	239	12	-	-	PUNCT
ejpam-721	239	13	continuous	continuous	ADJ
ejpam-721	239	14	map	map	NOUN
ejpam-721	239	15	.	.	PUNCT
ejpam-721	240	1	•	•	NUM
ejpam-721	240	2	(	(	PUNCT
ejpam-721	240	3	3	3	X
ejpam-721	240	4	)	)	PUNCT
ejpam-721	241	1	=	=	NOUN
ejpam-721	241	2	⇒	⇒	NOUN
ejpam-721	241	3	(	(	PUNCT
ejpam-721	241	4	1	1	NUM
ejpam-721	241	5	):	):	PUNCT
ejpam-721	241	6	let	let	VERB
ejpam-721	241	7	a	a	PRON
ejpam-721	241	8	be	be	AUX
ejpam-721	241	9	an	an	DET
ejpam-721	241	10	open	open	ADJ
ejpam-721	241	11	set	set	NOUN
ejpam-721	241	12	in	in	ADP
ejpam-721	241	13	x	x	X
ejpam-721	241	14	.	.	PUNCT
ejpam-721	242	1	since	since	SCONJ
ejpam-721	242	2	f	f	PROPN
ejpam-721	242	3	−1	−1	NOUN
ejpam-721	242	4	is	be	AUX
ejpam-721	242	5	a	a	DET
ejpam-721	242	6	supra	supra	PROPN
ejpam-721	242	7	b	b	NOUN
ejpam-721	242	8	-	-	PUNCT
ejpam-721	242	9	continuous	continuous	ADJ
ejpam-721	242	10	map	map	NOUN
ejpam-721	242	11	,	,	PUNCT
ejpam-721	242	12	then	then	ADV
ejpam-721	242	13	(	(	PUNCT
ejpam-721	242	14	f	f	NOUN
ejpam-721	242	15	−1)−1(a	−1)−1(a	PROPN
ejpam-721	242	16	)	)	PUNCT
ejpam-721	243	1	=	=	SYM
ejpam-721	243	2	f	f	X
ejpam-721	243	3	(	(	PUNCT
ejpam-721	243	4	a	a	NOUN
ejpam-721	243	5	)	)	PUNCT
ejpam-721	243	6	is	be	AUX
ejpam-721	243	7	a	a	DET
ejpam-721	243	8	supra	supra	PROPN
ejpam-721	243	9	b	b	NOUN
ejpam-721	243	10	-	-	PUNCT
ejpam-721	243	11	open	open	ADJ
ejpam-721	243	12	set	set	NOUN
ejpam-721	243	13	in	in	ADP
ejpam-721	243	14	y	y	PROPN
ejpam-721	243	15	.	.	PUNCT
ejpam-721	244	1	hence	hence	ADV
ejpam-721	244	2	,	,	PUNCT
ejpam-721	244	3	f	f	PROPN
ejpam-721	244	4	is	be	AUX
ejpam-721	244	5	a	a	DET
ejpam-721	244	6	supra	supra	PROPN
ejpam-721	244	7	b	b	NOUN
ejpam-721	244	8	-	-	PUNCT
ejpam-721	244	9	open	open	ADJ
ejpam-721	244	10	map	map	NOUN
ejpam-721	244	11	.	.	PUNCT
ejpam-721	245	1	references	reference	NOUN
ejpam-721	245	2	[	[	X
ejpam-721	245	3	1	1	NUM
ejpam-721	245	4	]	]	PUNCT
ejpam-721	245	5	m.	m.	NOUN
ejpam-721	245	6	e.	e.	PROPN
ejpam-721	245	7	abd	abd	PROPN
ejpam-721	245	8	el	el	PROPN
ejpam-721	245	9	-	-	PROPN
ejpam-721	245	10	monsef	monsef	PROPN
ejpam-721	245	11	,	,	PUNCT
ejpam-721	245	12	s.	s.	PROPN
ejpam-721	245	13	n.	n.	PROPN
ejpam-721	245	14	el	el	PROPN
ejpam-721	245	15	-	-	PUNCT
ejpam-721	245	16	deeb	deeb	PROPN
ejpam-721	245	17	and	and	CCONJ
ejpam-721	245	18	r.	r.	PROPN
ejpam-721	245	19	a.	a.	PROPN
ejpam-721	245	20	mahmoud	mahmoud	PROPN
ejpam-721	245	21	,	,	PUNCT
ejpam-721	245	22	β	β	X
ejpam-721	245	23	-open	-open	NOUN
ejpam-721	245	24	sets	set	NOUN
ejpam-721	245	25	and	and	CCONJ
ejpam-721	245	26	β	β	ADJ
ejpam-721	245	27	-	-	ADJ
ejpam-721	245	28	continuous	continuous	ADJ
ejpam-721	245	29	mappings	mapping	NOUN
ejpam-721	245	30	,	,	PUNCT
ejpam-721	245	31	bull	bull	NOUN
ejpam-721	245	32	.	.	PUNCT
ejpam-721	246	1	fac	fac	PROPN
ejpam-721	246	2	.	.	PUNCT
ejpam-721	247	1	sci	sci	PROPN
ejpam-721	247	2	.	.	PUNCT
ejpam-721	247	3	assiut	assiut	PROPN
ejpam-721	247	4	univ	univ	PROPN
ejpam-721	247	5	.	.	PROPN
ejpam-721	247	6	,	,	PUNCT
ejpam-721	247	7	12	12	NUM
ejpam-721	247	8	(	(	PUNCT
ejpam-721	247	9	1983	1983	NUM
ejpam-721	247	10	)	)	PUNCT
ejpam-721	247	11	,	,	PUNCT
ejpam-721	247	12	7790	7790	NUM
ejpam-721	247	13	.	.	PUNCT
ejpam-721	248	1	[	[	X
ejpam-721	248	2	2	2	NUM
ejpam-721	248	3	]	]	PUNCT
ejpam-721	248	4	d.	d.	PROPN
ejpam-721	248	5	andrijevic	andrijevic	PROPN
ejpam-721	248	6	’	'	PUNCT
ejpam-721	248	7	,	,	PUNCT
ejpam-721	248	8	on	on	ADP
ejpam-721	248	9	b	b	X
ejpam-721	248	10	-	-	PUNCT
ejpam-721	248	11	open	open	ADJ
ejpam-721	248	12	sets	set	NOUN
ejpam-721	248	13	,	,	PUNCT
ejpam-721	248	14	mat	mat	PROPN
ejpam-721	248	15	.	.	PROPN
ejpam-721	248	16	vesnik	vesnik	PROPN
ejpam-721	248	17	,	,	PUNCT
ejpam-721	248	18	48	48	NUM
ejpam-721	248	19	(	(	PUNCT
ejpam-721	248	20	1996	1996	NUM
ejpam-721	248	21	)	)	PUNCT
ejpam-721	248	22	,	,	PUNCT
ejpam-721	248	23	5964	5964	NUM
ejpam-721	248	24	.	.	PUNCT
ejpam-721	249	1	[	[	X
ejpam-721	249	2	3	3	X
ejpam-721	249	3	]	]	X
ejpam-721	249	4	r.	r.	PROPN
ejpam-721	249	5	devi	devi	PROPN
ejpam-721	249	6	,	,	PUNCT
ejpam-721	249	7	s.	s.	PROPN
ejpam-721	249	8	sampathkumar	sampathkumar	PROPN
ejpam-721	249	9	and	and	CCONJ
ejpam-721	249	10	m.	m.	PROPN
ejpam-721	249	11	caldas	caldas	PROPN
ejpam-721	249	12	,	,	PUNCT
ejpam-721	249	13	on	on	ADP
ejpam-721	249	14	supra	supra	PROPN
ejpam-721	249	15	α	α	PROPN
ejpam-721	249	16	-	-	ADJ
ejpam-721	249	17	open	open	ADJ
ejpam-721	249	18	sets	set	NOUN
ejpam-721	249	19	and	and	CCONJ
ejpam-721	249	20	sα	sα	ADJ
ejpam-721	249	21	-	-	ADJ
ejpam-721	249	22	continuous	continuous	ADJ
ejpam-721	249	23	maps	map	NOUN
ejpam-721	249	24	,	,	PUNCT
ejpam-721	249	25	general	general	ADJ
ejpam-721	249	26	mathematics	mathematic	NOUN
ejpam-721	249	27	,	,	PUNCT
ejpam-721	249	28	16	16	NUM
ejpam-721	249	29	(	(	PUNCT
ejpam-721	249	30	2	2	NUM
ejpam-721	249	31	)	)	PUNCT
ejpam-721	249	32	(	(	PUNCT
ejpam-721	249	33	2008	2008	NUM
ejpam-721	249	34	)	)	PUNCT
ejpam-721	249	35	,	,	PUNCT
ejpam-721	249	36	77	77	NUM
ejpam-721	249	37	84	84	NUM
ejpam-721	249	38	.	.	PUNCT
ejpam-721	250	1	[	[	X
ejpam-721	250	2	4	4	NUM
ejpam-721	250	3	]	]	X
ejpam-721	250	4	n.	n.	PROPN
ejpam-721	250	5	levine	levine	PROPN
ejpam-721	250	6	,	,	PUNCT
ejpam-721	250	7	semi	semi	ADJ
ejpam-721	250	8	-	-	ADJ
ejpam-721	250	9	open	open	ADJ
ejpam-721	250	10	sets	set	NOUN
ejpam-721	250	11	and	and	CCONJ
ejpam-721	250	12	semi	semi	ADJ
ejpam-721	250	13	-	-	NOUN
ejpam-721	250	14	continuity	continuity	NOUN
ejpam-721	250	15	in	in	ADP
ejpam-721	250	16	topological	topological	ADJ
ejpam-721	250	17	spaces	space	NOUN
ejpam-721	250	18	,	,	PUNCT
ejpam-721	250	19	amer	amer	PROPN
ejpam-721	250	20	.	.	PROPN
ejpam-721	250	21	math	math	PROPN
ejpam-721	250	22	.	.	PUNCT
ejpam-721	251	1	monthly	monthly	ADJ
ejpam-721	251	2	,	,	PUNCT
ejpam-721	251	3	70	70	NUM
ejpam-721	251	4	(	(	PUNCT
ejpam-721	251	5	1963	1963	NUM
ejpam-721	251	6	)	)	PUNCT
ejpam-721	251	7	,	,	PUNCT
ejpam-721	251	8	3641	3641	NUM
ejpam-721	251	9	.	.	PUNCT
ejpam-721	252	1	references	reference	NOUN
ejpam-721	252	2	302	302	NUM
ejpam-721	253	1	[	[	X
ejpam-721	253	2	5	5	NUM
ejpam-721	253	3	]	]	PUNCT
ejpam-721	253	4	a.	a.	NOUN
ejpam-721	253	5	s.	s.	PROPN
ejpam-721	253	6	mashhour	mashhour	PROPN
ejpam-721	253	7	,	,	PUNCT
ejpam-721	253	8	m.	m.	PROPN
ejpam-721	253	9	e.	e.	PROPN
ejpam-721	253	10	abd	abd	PROPN
ejpam-721	254	1	el	el	PROPN
ejpam-721	254	2	-	-	PROPN
ejpam-721	254	3	monsef	monsef	PROPN
ejpam-721	254	4	and	and	CCONJ
ejpam-721	254	5	s.	s.	PROPN
ejpam-721	254	6	n.	n.	PROPN
ejpam-721	254	7	el	el	PROPN
ejpam-721	254	8	-	-	PROPN
ejpam-721	254	9	deeb	deeb	PROPN
ejpam-721	254	10	,	,	PUNCT
ejpam-721	254	11	on	on	ADP
ejpam-721	254	12	precontinuous	precontinuous	ADJ
ejpam-721	254	13	and	and	CCONJ
ejpam-721	254	14	weak	weak	ADJ
ejpam-721	254	15	precontinuous	precontinuous	ADJ
ejpam-721	254	16	mapping	mapping	NOUN
ejpam-721	254	17	,	,	PUNCT
ejpam-721	254	18	proc	proc	NOUN
ejpam-721	254	19	.	.	PUNCT
ejpam-721	255	1	math	math	NOUN
ejpam-721	255	2	.	.	PUNCT
ejpam-721	256	1	phys	phy	NOUN
ejpam-721	256	2	.	.	PUNCT
ejpam-721	257	1	soc	soc	PROPN
ejpam-721	257	2	.	.	PUNCT
ejpam-721	258	1	egypt	egypt	PROPN
ejpam-721	258	2	,	,	PUNCT
ejpam-721	258	3	53	53	NUM
ejpam-721	258	4	(	(	PUNCT
ejpam-721	258	5	1982	1982	NUM
ejpam-721	258	6	)	)	PUNCT
ejpam-721	258	7	,	,	PUNCT
ejpam-721	258	8	47	47	NUM
ejpam-721	258	9	-	-	SYM
ejpam-721	258	10	53	53	NUM
ejpam-721	258	11	.	.	PUNCT
ejpam-721	259	1	[	[	X
ejpam-721	259	2	6	6	NUM
ejpam-721	259	3	]	]	PUNCT
ejpam-721	259	4	a.	a.	NOUN
ejpam-721	259	5	s.	s.	PROPN
ejpam-721	259	6	mashhour	mashhour	PROPN
ejpam-721	259	7	,	,	PUNCT
ejpam-721	259	8	a.	a.	PROPN
ejpam-721	259	9	a.	a.	PROPN
ejpam-721	259	10	allam	allam	PROPN
ejpam-721	259	11	,	,	PUNCT
ejpam-721	259	12	f.	f.	PROPN
ejpam-721	259	13	s.	s.	PROPN
ejpam-721	259	14	mahmoud	mahmoud	PROPN
ejpam-721	259	15	and	and	CCONJ
ejpam-721	259	16	f.	f.	PROPN
ejpam-721	259	17	h.	h.	PROPN
ejpam-721	259	18	khedr	khedr	PROPN
ejpam-721	259	19	,	,	PUNCT
ejpam-721	259	20	on	on	ADP
ejpam-721	259	21	supra	supra	PROPN
ejpam-721	259	22	topological	topological	ADJ
ejpam-721	259	23	spaces	space	NOUN
ejpam-721	259	24	,	,	PUNCT
ejpam-721	259	25	indian	indian	PROPN
ejpam-721	259	26	j.	j.	PROPN
ejpam-721	259	27	pure	pure	PROPN
ejpam-721	259	28	and	and	CCONJ
ejpam-721	259	29	appl	appl	PROPN
ejpam-721	259	30	.	.	PROPN
ejpam-721	259	31	math	math	PROPN
ejpam-721	259	32	.	.	PUNCT
ejpam-721	259	33	,	,	PUNCT
ejpam-721	259	34	14	14	NUM
ejpam-721	259	35	(	(	PUNCT
ejpam-721	259	36	4	4	NUM
ejpam-721	259	37	)	)	PUNCT
ejpam-721	259	38	(	(	PUNCT
ejpam-721	259	39	1983	1983	NUM
ejpam-721	259	40	)	)	PUNCT
ejpam-721	259	41	,	,	PUNCT
ejpam-721	259	42	502	502	NUM
ejpam-721	259	43	-	-	SYM
ejpam-721	259	44	510	510	NUM
ejpam-721	259	45	.	.	PUNCT
ejpam-721	260	1	[	[	X
ejpam-721	260	2	7	7	X
ejpam-721	260	3	]	]	X
ejpam-721	260	4	o.	o.	PROPN
ejpam-721	260	5	njastad	njastad	PROPN
ejpam-721	260	6	,	,	PUNCT
ejpam-721	260	7	on	on	ADP
ejpam-721	260	8	some	some	DET
ejpam-721	260	9	classes	class	NOUN
ejpam-721	260	10	of	of	ADP
ejpam-721	260	11	nearly	nearly	ADV
ejpam-721	260	12	open	open	ADJ
ejpam-721	260	13	sets	set	NOUN
ejpam-721	260	14	,	,	PUNCT
ejpam-721	260	15	pacific	pacific	PROPN
ejpam-721	260	16	j.	j.	PROPN
ejpam-721	260	17	math	math	PROPN
ejpam-721	260	18	.	.	PUNCT
ejpam-721	260	19	,	,	PUNCT
ejpam-721	260	20	15	15	NUM
ejpam-721	260	21	(	(	PUNCT
ejpam-721	260	22	1965	1965	NUM
ejpam-721	260	23	)	)	PUNCT
ejpam-721	260	24	,	,	PUNCT
ejpam-721	260	25	961	961	NUM
ejpam-721	260	26	-	-	SYM
ejpam-721	260	27	970	970	NUM
ejpam-721	260	28	.	.	PUNCT