id	sid	tid	token	lemma	pos
ejpam-3293	1	1	european	european	PROPN
ejpam-3293	1	2	journal	journal	PROPN
ejpam-3293	1	3	of	of	ADP
ejpam-3293	1	4	pure	pure	ADJ
ejpam-3293	1	5	and	and	CCONJ
ejpam-3293	1	6	applied	apply	VERB
ejpam-3293	1	7	mathematics	mathematic	NOUN
ejpam-3293	1	8	vol	vol	NOUN
ejpam-3293	1	9	.	.	PUNCT
ejpam-3293	2	1	11	11	NUM
ejpam-3293	2	2	,	,	PUNCT
ejpam-3293	2	3	no	no	INTJ
ejpam-3293	2	4	.	.	NOUN
ejpam-3293	2	5	3	3	NUM
ejpam-3293	2	6	,	,	PUNCT
ejpam-3293	2	7	2018	2018	NUM
ejpam-3293	3	1	,	,	PUNCT
ejpam-3293	3	2	834	834	NUM
ejpam-3293	3	3	-	-	SYM
ejpam-3293	3	4	843	843	NUM
ejpam-3293	3	5	issn	issn	PROPN
ejpam-3293	3	6	1307	1307	NUM
ejpam-3293	3	7	-	-	SYM
ejpam-3293	3	8	5543	5543	NUM
ejpam-3293	3	9	–	–	PUNCT
ejpam-3293	3	10	www.ejpam.com	www.ejpam.com	X
ejpam-3293	3	11	published	publish	VERB
ejpam-3293	3	12	by	by	ADP
ejpam-3293	3	13	new	new	PROPN
ejpam-3293	3	14	york	york	PROPN
ejpam-3293	3	15	business	business	PROPN
ejpam-3293	3	16	global	global	PROPN
ejpam-3293	3	17	on	on	ADP
ejpam-3293	3	18	ω	ω	NOUN
ejpam-3293	3	19	-	-	NOUN
ejpam-3293	3	20	connectedness	connectedness	NOUN
ejpam-3293	3	21	and	and	CCONJ
ejpam-3293	3	22	ω	ω	NOUN
ejpam-3293	3	23	-	-	NOUN
ejpam-3293	3	24	continuity	continuity	NOUN
ejpam-3293	3	25	in	in	ADP
ejpam-3293	3	26	the	the	DET
ejpam-3293	3	27	product	product	NOUN
ejpam-3293	3	28	space	space	NOUN
ejpam-3293	3	29	mhelmar	mhelmar	PROPN
ejpam-3293	3	30	a.	a.	PROPN
ejpam-3293	3	31	labendia1,∗	labendia1,∗	PROPN
ejpam-3293	3	32	,	,	PUNCT
ejpam-3293	3	33	jan	jan	PROPN
ejpam-3293	3	34	alejandro	alejandro	PROPN
ejpam-3293	3	35	c.	c.	PROPN
ejpam-3293	3	36	sasam1	sasam1	PROPN
ejpam-3293	4	1	1	1	NUM
ejpam-3293	4	2	department	department	NOUN
ejpam-3293	4	3	of	of	ADP
ejpam-3293	4	4	mathematics	mathematic	NOUN
ejpam-3293	4	5	and	and	CCONJ
ejpam-3293	4	6	statistics	statistic	NOUN
ejpam-3293	4	7	,	,	PUNCT
ejpam-3293	4	8	college	college	NOUN
ejpam-3293	4	9	of	of	ADP
ejpam-3293	4	10	science	science	NOUN
ejpam-3293	4	11	and	and	CCONJ
ejpam-3293	4	12	mathematics	mathematic	NOUN
ejpam-3293	4	13	,	,	PUNCT
ejpam-3293	4	14	mindanao	mindanao	PROPN
ejpam-3293	4	15	state	state	PROPN
ejpam-3293	4	16	university	university	PROPN
ejpam-3293	4	17	-	-	PUNCT
ejpam-3293	4	18	iligan	iligan	PROPN
ejpam-3293	4	19	institute	institute	PROPN
ejpam-3293	4	20	of	of	ADP
ejpam-3293	4	21	technology	technology	PROPN
ejpam-3293	4	22	,	,	PUNCT
ejpam-3293	4	23	9200	9200	NUM
ejpam-3293	4	24	iligan	iligan	ADJ
ejpam-3293	4	25	city	city	NOUN
ejpam-3293	4	26	,	,	PUNCT
ejpam-3293	4	27	philippines	philippine	NOUN
ejpam-3293	4	28	abstract	abstract	ADJ
ejpam-3293	4	29	.	.	PUNCT
ejpam-3293	5	1	in	in	ADP
ejpam-3293	5	2	this	this	DET
ejpam-3293	5	3	paper	paper	NOUN
ejpam-3293	5	4	,	,	PUNCT
ejpam-3293	5	5	the	the	DET
ejpam-3293	5	6	concepts	concept	NOUN
ejpam-3293	5	7	of	of	ADP
ejpam-3293	5	8	ω	ω	NOUN
ejpam-3293	5	9	-	-	ADJ
ejpam-3293	5	10	open	open	ADJ
ejpam-3293	5	11	and	and	CCONJ
ejpam-3293	5	12	ω	ω	VERB
ejpam-3293	5	13	-	-	PUNCT
ejpam-3293	5	14	closed	close	VERB
ejpam-3293	5	15	functions	function	NOUN
ejpam-3293	5	16	between	between	ADP
ejpam-3293	5	17	topological	topological	ADJ
ejpam-3293	5	18	spaces	space	NOUN
ejpam-3293	5	19	will	will	AUX
ejpam-3293	5	20	be	be	AUX
ejpam-3293	5	21	introduced	introduce	VERB
ejpam-3293	5	22	and	and	CCONJ
ejpam-3293	5	23	characterized	characterize	VERB
ejpam-3293	5	24	.	.	PUNCT
ejpam-3293	6	1	moreover	moreover	ADV
ejpam-3293	6	2	,	,	PUNCT
ejpam-3293	6	3	related	related	ADJ
ejpam-3293	6	4	concepts	concept	NOUN
ejpam-3293	6	5	such	such	ADJ
ejpam-3293	6	6	as	as	ADP
ejpam-3293	6	7	ω	ω	NOUN
ejpam-3293	6	8	-	-	NOUN
ejpam-3293	6	9	connectedness	connectedness	NOUN
ejpam-3293	6	10	and	and	CCONJ
ejpam-3293	6	11	ωcontinuity	ωcontinuity	NOUN
ejpam-3293	6	12	from	from	ADP
ejpam-3293	6	13	an	an	DET
ejpam-3293	6	14	arbitarary	arbitarary	NOUN
ejpam-3293	6	15	topological	topological	ADJ
ejpam-3293	6	16	space	space	NOUN
ejpam-3293	6	17	into	into	ADP
ejpam-3293	6	18	the	the	DET
ejpam-3293	6	19	product	product	NOUN
ejpam-3293	6	20	space	space	NOUN
ejpam-3293	6	21	will	will	AUX
ejpam-3293	6	22	also	also	ADV
ejpam-3293	6	23	be	be	AUX
ejpam-3293	6	24	characterized	characterize	VERB
ejpam-3293	6	25	.	.	PUNCT
ejpam-3293	7	1	2010	2010	NUM
ejpam-3293	7	2	mathematics	mathematic	NOUN
ejpam-3293	7	3	subject	subject	NOUN
ejpam-3293	7	4	classifications	classification	NOUN
ejpam-3293	7	5	:	:	PUNCT
ejpam-3293	7	6	54a05	54a05	NUM
ejpam-3293	7	7	key	key	ADJ
ejpam-3293	7	8	words	word	NOUN
ejpam-3293	7	9	and	and	CCONJ
ejpam-3293	7	10	phrases	phrase	NOUN
ejpam-3293	7	11	:	:	PUNCT
ejpam-3293	7	12	ω	ω	X
ejpam-3293	7	13	-	-	ADJ
ejpam-3293	7	14	open	open	ADJ
ejpam-3293	7	15	,	,	PUNCT
ejpam-3293	7	16	ω	ω	NOUN
ejpam-3293	7	17	-	-	ADJ
ejpam-3293	7	18	closed	closed	ADJ
ejpam-3293	7	19	,	,	PUNCT
ejpam-3293	7	20	ω	ω	NOUN
ejpam-3293	7	21	-	-	VERB
ejpam-3293	7	22	connected	connect	VERB
ejpam-3293	7	23	,	,	PUNCT
ejpam-3293	7	24	ω	ω	NOUN
ejpam-3293	7	25	-	-	ADJ
ejpam-3293	7	26	continuous	continuous	ADJ
ejpam-3293	7	27	1	1	NUM
ejpam-3293	7	28	.	.	PUNCT
ejpam-3293	8	1	introduction	introduction	NOUN
ejpam-3293	8	2	one	one	NUM
ejpam-3293	8	3	of	of	ADP
ejpam-3293	8	4	the	the	DET
ejpam-3293	8	5	attempts	attempt	NOUN
ejpam-3293	8	6	to	to	PART
ejpam-3293	8	7	substitute	substitute	VERB
ejpam-3293	8	8	numerous	numerous	ADJ
ejpam-3293	8	9	concepts	concept	NOUN
ejpam-3293	8	10	in	in	ADP
ejpam-3293	8	11	topology	topology	NOUN
ejpam-3293	8	12	with	with	ADP
ejpam-3293	8	13	concepts	concept	NOUN
ejpam-3293	8	14	possessing	possess	VERB
ejpam-3293	8	15	either	either	CCONJ
ejpam-3293	8	16	weaker	weak	ADJ
ejpam-3293	8	17	or	or	CCONJ
ejpam-3293	8	18	stronger	strong	ADJ
ejpam-3293	8	19	properties	property	NOUN
ejpam-3293	8	20	was	be	AUX
ejpam-3293	8	21	done	do	VERB
ejpam-3293	8	22	by	by	ADP
ejpam-3293	8	23	n.	n.	PROPN
ejpam-3293	8	24	levine	levine	PROPN
ejpam-3293	9	1	[	[	X
ejpam-3293	9	2	4	4	NUM
ejpam-3293	9	3	]	]	PUNCT
ejpam-3293	9	4	.	.	PUNCT
ejpam-3293	10	1	he	he	PRON
ejpam-3293	10	2	introduced	introduce	VERB
ejpam-3293	10	3	the	the	DET
ejpam-3293	10	4	concepts	concept	NOUN
ejpam-3293	10	5	of	of	ADP
ejpam-3293	10	6	semi	semi	ADJ
ejpam-3293	10	7	-	-	ADJ
ejpam-3293	10	8	open	open	ADJ
ejpam-3293	10	9	,	,	PUNCT
ejpam-3293	10	10	semi	semi	ADJ
ejpam-3293	10	11	-	-	ADJ
ejpam-3293	10	12	closed	closed	ADJ
ejpam-3293	10	13	set	set	ADJ
ejpam-3293	10	14	and	and	CCONJ
ejpam-3293	10	15	semi	semi	ADJ
ejpam-3293	10	16	-	-	NOUN
ejpam-3293	10	17	continuity	continuity	NOUN
ejpam-3293	10	18	of	of	ADP
ejpam-3293	10	19	a	a	DET
ejpam-3293	10	20	function	function	NOUN
ejpam-3293	10	21	,	,	PUNCT
ejpam-3293	10	22	which	which	PRON
ejpam-3293	10	23	generated	generate	VERB
ejpam-3293	10	24	new	new	ADJ
ejpam-3293	10	25	results	result	NOUN
ejpam-3293	10	26	,	,	PUNCT
ejpam-3293	10	27	some	some	PRON
ejpam-3293	10	28	of	of	ADP
ejpam-3293	10	29	which	which	PRON
ejpam-3293	10	30	are	be	AUX
ejpam-3293	10	31	generalization	generalization	NOUN
ejpam-3293	10	32	of	of	ADP
ejpam-3293	10	33	existing	exist	VERB
ejpam-3293	10	34	ones	one	NOUN
ejpam-3293	10	35	.	.	PUNCT
ejpam-3293	11	1	after	after	ADP
ejpam-3293	11	2	this	this	DET
ejpam-3293	11	3	noteworthy	noteworthy	ADJ
ejpam-3293	11	4	work	work	NOUN
ejpam-3293	11	5	of	of	ADP
ejpam-3293	11	6	levine	levine	PROPN
ejpam-3293	11	7	several	several	ADJ
ejpam-3293	11	8	mathematicians	mathematician	NOUN
ejpam-3293	11	9	became	become	VERB
ejpam-3293	11	10	attracted	attract	VERB
ejpam-3293	11	11	in	in	ADP
ejpam-3293	11	12	presenting	present	VERB
ejpam-3293	11	13	other	other	ADJ
ejpam-3293	11	14	topological	topological	ADJ
ejpam-3293	11	15	concepts	concept	NOUN
ejpam-3293	11	16	which	which	PRON
ejpam-3293	11	17	can	can	AUX
ejpam-3293	11	18	substitute	substitute	VERB
ejpam-3293	11	19	the	the	DET
ejpam-3293	11	20	concepts	concept	NOUN
ejpam-3293	11	21	of	of	ADP
ejpam-3293	11	22	open	open	ADJ
ejpam-3293	11	23	sets	set	NOUN
ejpam-3293	11	24	.	.	PUNCT
ejpam-3293	12	1	in	in	ADP
ejpam-3293	12	2	[	[	X
ejpam-3293	12	3	5	5	NUM
ejpam-3293	12	4	]	]	PUNCT
ejpam-3293	12	5	,	,	PUNCT
ejpam-3293	12	6	velicko	velicko	NOUN
ejpam-3293	12	7	introduced	introduce	VERB
ejpam-3293	12	8	the	the	DET
ejpam-3293	12	9	concepts	concept	NOUN
ejpam-3293	12	10	of	of	ADP
ejpam-3293	12	11	θ	θ	NOUN
ejpam-3293	12	12	-	-	NOUN
ejpam-3293	12	13	continuity	continuity	NOUN
ejpam-3293	12	14	between	between	ADP
ejpam-3293	12	15	topological	topological	ADJ
ejpam-3293	12	16	spaces	space	NOUN
ejpam-3293	12	17	and	and	CCONJ
ejpam-3293	12	18	subsequently	subsequently	ADV
ejpam-3293	12	19	defined	define	VERB
ejpam-3293	12	20	the	the	DET
ejpam-3293	12	21	concepts	concept	NOUN
ejpam-3293	12	22	of	of	ADP
ejpam-3293	12	23	θ	θ	NOUN
ejpam-3293	12	24	-	-	NOUN
ejpam-3293	12	25	closure	closure	NOUN
ejpam-3293	12	26	and	and	CCONJ
ejpam-3293	12	27	θ	θ	NOUN
ejpam-3293	12	28	-	-	NOUN
ejpam-3293	12	29	interior	interior	NOUN
ejpam-3293	12	30	of	of	ADP
ejpam-3293	12	31	a	a	DET
ejpam-3293	12	32	subset	subset	NOUN
ejpam-3293	12	33	of	of	ADP
ejpam-3293	12	34	topological	topological	ADJ
ejpam-3293	12	35	space	space	NOUN
ejpam-3293	12	36	.	.	PUNCT
ejpam-3293	13	1	in	in	ADP
ejpam-3293	13	2	[	[	X
ejpam-3293	13	3	1	1	NUM
ejpam-3293	13	4	]	]	PUNCT
ejpam-3293	13	5	,	,	PUNCT
ejpam-3293	13	6	al	al	PROPN
ejpam-3293	13	7	-	-	PUNCT
ejpam-3293	13	8	hawary	hawary	PROPN
ejpam-3293	13	9	characterized	characterize	VERB
ejpam-3293	13	10	θ	θ	NOUN
ejpam-3293	13	11	-	-	NOUN
ejpam-3293	13	12	continuity	continuity	NOUN
ejpam-3293	13	13	and	and	CCONJ
ejpam-3293	13	14	the	the	DET
ejpam-3293	13	15	other	other	ADJ
ejpam-3293	13	16	well	well	ADV
ejpam-3293	13	17	-	-	PUNCT
ejpam-3293	13	18	known	know	VERB
ejpam-3293	13	19	variations	variation	NOUN
ejpam-3293	13	20	of	of	ADP
ejpam-3293	13	21	continuity	continuity	NOUN
ejpam-3293	13	22	such	such	ADJ
ejpam-3293	13	23	as	as	ADP
ejpam-3293	13	24	strong	strong	ADJ
ejpam-3293	13	25	continuity	continuity	NOUN
ejpam-3293	13	26	,	,	PUNCT
ejpam-3293	13	27	semi	semi	ADJ
ejpam-3293	13	28	-	-	NOUN
ejpam-3293	13	29	continuity	continuity	NOUN
ejpam-3293	13	30	and	and	CCONJ
ejpam-3293	13	31	closure	closure	NOUN
ejpam-3293	13	32	-	-	PUNCT
ejpam-3293	13	33	continuity	continuity	NOUN
ejpam-3293	13	34	.	.	PUNCT
ejpam-3293	14	1	let	let	VERB
ejpam-3293	14	2	(	(	PUNCT
ejpam-3293	14	3	x	x	NOUN
ejpam-3293	14	4	,	,	PUNCT
ejpam-3293	14	5	t	t	PROPN
ejpam-3293	14	6	)	)	PUNCT
ejpam-3293	14	7	be	be	AUX
ejpam-3293	14	8	a	a	DET
ejpam-3293	14	9	topological	topological	ADJ
ejpam-3293	14	10	space	space	NOUN
ejpam-3293	14	11	and	and	CCONJ
ejpam-3293	14	12	a	a	DET
ejpam-3293	14	13	⊆	⊆	NUM
ejpam-3293	14	14	x.	x.	NOUN
ejpam-3293	14	15	the	the	DET
ejpam-3293	14	16	θ	θ	NOUN
ejpam-3293	14	17	-	-	PUNCT
ejpam-3293	14	18	closure	closure	NOUN
ejpam-3293	14	19	and	and	CCONJ
ejpam-3293	14	20	θ	θ	NOUN
ejpam-3293	14	21	-	-	NOUN
ejpam-3293	14	22	interior	interior	NOUN
ejpam-3293	14	23	of	of	ADP
ejpam-3293	14	24	a	a	DET
ejpam-3293	14	25	are	are	NOUN
ejpam-3293	14	26	,	,	PUNCT
ejpam-3293	14	27	respectively	respectively	ADV
ejpam-3293	14	28	,	,	PUNCT
ejpam-3293	14	29	denoted	denote	VERB
ejpam-3293	14	30	and	and	CCONJ
ejpam-3293	14	31	defined	define	VERB
ejpam-3293	14	32	by	by	ADP
ejpam-3293	14	33	cls(a	cls(a	PROPN
ejpam-3293	14	34	)	)	PUNCT
ejpam-3293	14	35	=	=	PRON
ejpam-3293	15	1	{	{	PUNCT
ejpam-3293	15	2	x	x	PUNCT
ejpam-3293	15	3	∈	∈	NOUN
ejpam-3293	15	4	x	x	X
ejpam-3293	15	5	:	:	PUNCT
ejpam-3293	15	6	cl(u	cl(u	SYM
ejpam-3293	15	7	)	)	PUNCT
ejpam-3293	15	8	∩a	∩a	PROPN
ejpam-3293	15	9	6=	6=	ADP
ejpam-3293	15	10	∅	∅	NOUN
ejpam-3293	15	11	for	for	ADP
ejpam-3293	15	12	every	every	DET
ejpam-3293	15	13	open	open	ADJ
ejpam-3293	15	14	set	set	NOUN
ejpam-3293	15	15	u	u	NOUN
ejpam-3293	15	16	containing	contain	VERB
ejpam-3293	15	17	x	x	X
ejpam-3293	15	18	}	}	PUNCT
ejpam-3293	15	19	and	and	CCONJ
ejpam-3293	15	20	ints(a	ints(a	NUM
ejpam-3293	15	21	)	)	PUNCT
ejpam-3293	15	22	=	=	PRON
ejpam-3293	15	23	{	{	PUNCT
ejpam-3293	15	24	x	x	PUNCT
ejpam-3293	15	25	∈	∈	NOUN
ejpam-3293	15	26	x	x	X
ejpam-3293	15	27	:	:	PUNCT
ejpam-3293	15	28	cl(u	cl(u	X
ejpam-3293	15	29	)	)	PUNCT
ejpam-3293	15	30	⊆	⊆	NUM
ejpam-3293	15	31	a	a	PRON
ejpam-3293	15	32	for	for	ADP
ejpam-3293	15	33	some	some	DET
ejpam-3293	15	34	open	open	ADJ
ejpam-3293	15	35	set	set	NOUN
ejpam-3293	15	36	u	u	NOUN
ejpam-3293	15	37	containing	contain	VERB
ejpam-3293	15	38	x	x	X
ejpam-3293	15	39	}	}	PUNCT
ejpam-3293	15	40	,	,	PUNCT
ejpam-3293	15	41	∗corresponding	∗corresponde	VERB
ejpam-3293	15	42	author	author	NOUN
ejpam-3293	15	43	.	.	PUNCT
ejpam-3293	16	1	doi	doi	NOUN
ejpam-3293	16	2	:	:	PUNCT
ejpam-3293	16	3	https://doi.org/10.29020/nybg.ejpam.v11i3.3293	https://doi.org/10.29020/nybg.ejpam.v11i3.3293	NOUN
ejpam-3293	16	4	email	email	NOUN
ejpam-3293	16	5	addresses	address	NOUN
ejpam-3293	16	6	:	:	PUNCT
ejpam-3293	16	7	mhelmar.labendia@g.msuiit.edu.ph	mhelmar.labendia@g.msuiit.edu.ph	PROPN
ejpam-3293	16	8	(	(	PUNCT
ejpam-3293	16	9	m.	m.	NOUN
ejpam-3293	16	10	labendia	labendia	PROPN
ejpam-3293	16	11	)	)	PUNCT
ejpam-3293	16	12	,	,	PUNCT
ejpam-3293	16	13	janalejandro.sasam@g.msuiit.edu.ph	janalejandro.sasam@g.msuiit.edu.ph	PROPN
ejpam-3293	16	14	(	(	PUNCT
ejpam-3293	16	15	j.	j.	PROPN
ejpam-3293	16	16	a.	a.	PROPN
ejpam-3293	16	17	sasam	sasam	PROPN
ejpam-3293	16	18	)	)	PUNCT
ejpam-3293	16	19	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3293	17	1	834	834	NUM
ejpam-3293	17	2	c	c	X
ejpam-3293	17	3	©	©	PROPN
ejpam-3293	17	4	2018	2018	NUM
ejpam-3293	17	5	ejpam	ejpam	VERB
ejpam-3293	17	6	all	all	DET
ejpam-3293	17	7	rights	right	NOUN
ejpam-3293	17	8	reserved	reserve	VERB
ejpam-3293	17	9	.	.	PUNCT
ejpam-3293	18	1	m.	m.	NOUN
ejpam-3293	18	2	labendia	labendia	PROPN
ejpam-3293	18	3	,	,	PUNCT
ejpam-3293	18	4	j.	j.	PROPN
ejpam-3293	18	5	a.	a.	PROPN
ejpam-3293	18	6	sasam	sasam	PROPN
ejpam-3293	18	7	/	/	SYM
ejpam-3293	18	8	eur	eur	PROPN
ejpam-3293	18	9	.	.	PUNCT
ejpam-3293	19	1	j.	j.	PROPN
ejpam-3293	19	2	pure	pure	PROPN
ejpam-3293	19	3	appl	appl	PROPN
ejpam-3293	19	4	.	.	PROPN
ejpam-3293	19	5	math	math	PROPN
ejpam-3293	19	6	,	,	PUNCT
ejpam-3293	19	7	11	11	NUM
ejpam-3293	19	8	(	(	PUNCT
ejpam-3293	19	9	3	3	NUM
ejpam-3293	19	10	)	)	PUNCT
ejpam-3293	19	11	(	(	PUNCT
ejpam-3293	19	12	2018	2018	NUM
ejpam-3293	19	13	)	)	PUNCT
ejpam-3293	19	14	,	,	PUNCT
ejpam-3293	19	15	834	834	NUM
ejpam-3293	19	16	-	-	SYM
ejpam-3293	19	17	843	843	NUM
ejpam-3293	19	18	835	835	NUM
ejpam-3293	19	19	where	where	SCONJ
ejpam-3293	19	20	cl(u	cl(u	NOUN
ejpam-3293	19	21	)	)	PUNCT
ejpam-3293	19	22	is	be	AUX
ejpam-3293	19	23	the	the	DET
ejpam-3293	19	24	closure	closure	NOUN
ejpam-3293	19	25	of	of	ADP
ejpam-3293	19	26	u	u	NOUN
ejpam-3293	19	27	in	in	ADP
ejpam-3293	19	28	x.	x.	PROPN
ejpam-3293	19	29	a	a	DET
ejpam-3293	19	30	subset	subset	NOUN
ejpam-3293	19	31	a	a	PRON
ejpam-3293	19	32	of	of	ADP
ejpam-3293	19	33	x	x	NOUN
ejpam-3293	19	34	is	be	AUX
ejpam-3293	19	35	θ	θ	NOUN
ejpam-3293	19	36	-	-	PUNCT
ejpam-3293	19	37	closed	closed	ADJ
ejpam-3293	19	38	if	if	SCONJ
ejpam-3293	19	39	cls(a	cls(a	PROPN
ejpam-3293	19	40	)	)	PUNCT
ejpam-3293	19	41	=	=	PUNCT
ejpam-3293	19	42	a	a	PRON
ejpam-3293	19	43	and	and	CCONJ
ejpam-3293	19	44	θ	θ	NOUN
ejpam-3293	19	45	-	-	VERB
ejpam-3293	19	46	open	open	ADJ
ejpam-3293	19	47	if	if	SCONJ
ejpam-3293	19	48	ints(a	ints(a	NOUN
ejpam-3293	19	49	)	)	PUNCT
ejpam-3293	19	50	=	=	PUNCT
ejpam-3293	19	51	a.	a.	NOUN
ejpam-3293	19	52	equivalently	equivalently	ADV
ejpam-3293	19	53	,	,	PUNCT
ejpam-3293	19	54	a	a	PRON
ejpam-3293	19	55	is	be	AUX
ejpam-3293	19	56	θ	θ	NOUN
ejpam-3293	19	57	-	-	ADJ
ejpam-3293	19	58	open	open	ADJ
ejpam-3293	19	59	if	if	SCONJ
ejpam-3293	19	60	and	and	CCONJ
ejpam-3293	19	61	only	only	ADV
ejpam-3293	19	62	if	if	SCONJ
ejpam-3293	19	63	x\a	x\a	PROPN
ejpam-3293	19	64	is	be	AUX
ejpam-3293	19	65	θ	θ	NOUN
ejpam-3293	19	66	-	-	PUNCT
ejpam-3293	19	67	closed	closed	ADJ
ejpam-3293	19	68	.	.	PUNCT
ejpam-3293	20	1	in	in	ADP
ejpam-3293	20	2	[	[	X
ejpam-3293	20	3	2	2	NUM
ejpam-3293	20	4	]	]	PUNCT
ejpam-3293	20	5	,	,	PUNCT
ejpam-3293	20	6	hdeib	hdeib	PROPN
ejpam-3293	20	7	introduced	introduce	VERB
ejpam-3293	20	8	the	the	DET
ejpam-3293	20	9	concepts	concept	NOUN
ejpam-3293	20	10	of	of	ADP
ejpam-3293	20	11	ω	ω	NOUN
ejpam-3293	20	12	-	-	ADJ
ejpam-3293	20	13	open	open	ADJ
ejpam-3293	20	14	and	and	CCONJ
ejpam-3293	20	15	ω	ω	VERB
ejpam-3293	20	16	-	-	PUNCT
ejpam-3293	20	17	closed	close	VERB
ejpam-3293	20	18	sets	set	NOUN
ejpam-3293	20	19	and	and	CCONJ
ejpam-3293	20	20	ω	ω	VERB
ejpam-3293	20	21	-	-	PUNCT
ejpam-3293	20	22	closed	close	VERB
ejpam-3293	20	23	mappings	mapping	NOUN
ejpam-3293	20	24	on	on	ADP
ejpam-3293	20	25	a	a	DET
ejpam-3293	20	26	topological	topological	ADJ
ejpam-3293	20	27	space	space	NOUN
ejpam-3293	20	28	.	.	PUNCT
ejpam-3293	21	1	he	he	PRON
ejpam-3293	21	2	showed	show	VERB
ejpam-3293	21	3	that	that	SCONJ
ejpam-3293	21	4	ω	ω	VERB
ejpam-3293	21	5	-	-	PUNCT
ejpam-3293	21	6	closed	close	VERB
ejpam-3293	21	7	mappings	mapping	NOUN
ejpam-3293	21	8	are	be	AUX
ejpam-3293	21	9	strictly	strictly	ADV
ejpam-3293	21	10	weaker	weak	ADJ
ejpam-3293	21	11	than	than	ADP
ejpam-3293	21	12	closed	closed	ADJ
ejpam-3293	21	13	mappings	mapping	NOUN
ejpam-3293	21	14	and	and	CCONJ
ejpam-3293	21	15	also	also	ADV
ejpam-3293	21	16	showed	show	VERB
ejpam-3293	21	17	that	that	SCONJ
ejpam-3293	21	18	the	the	DET
ejpam-3293	21	19	lindelöf	lindelöf	NOUN
ejpam-3293	21	20	property	property	NOUN
ejpam-3293	21	21	is	be	AUX
ejpam-3293	21	22	preserved	preserve	VERB
ejpam-3293	21	23	by	by	ADP
ejpam-3293	21	24	counter	counter	ADJ
ejpam-3293	21	25	images	image	NOUN
ejpam-3293	21	26	of	of	ADP
ejpam-3293	21	27	ω	ω	VERB
ejpam-3293	21	28	-	-	PUNCT
ejpam-3293	21	29	closed	close	VERB
ejpam-3293	21	30	mappings	mapping	NOUN
ejpam-3293	21	31	with	with	ADP
ejpam-3293	21	32	lindelöf	lindelöf	NOUN
ejpam-3293	21	33	counter	counter	NOUN
ejpam-3293	21	34	image	image	NOUN
ejpam-3293	21	35	of	of	ADP
ejpam-3293	21	36	points	point	NOUN
ejpam-3293	21	37	.	.	PUNCT
ejpam-3293	22	1	in	in	ADP
ejpam-3293	22	2	2010	2010	NUM
ejpam-3293	22	3	,	,	PUNCT
ejpam-3293	22	4	ekici	ekici	NOUN
ejpam-3293	22	5	et	et	PROPN
ejpam-3293	22	6	al	al	PROPN
ejpam-3293	22	7	.	.	PUNCT
ejpam-3293	23	1	[	[	X
ejpam-3293	23	2	3	3	X
ejpam-3293	23	3	]	]	PUNCT
ejpam-3293	23	4	introduced	introduce	VERB
ejpam-3293	23	5	the	the	DET
ejpam-3293	23	6	concepts	concept	NOUN
ejpam-3293	23	7	of	of	ADP
ejpam-3293	23	8	ωθ	ωθ	NOUN
ejpam-3293	23	9	-	-	PUNCT
ejpam-3293	23	10	open	open	ADJ
ejpam-3293	23	11	and	and	CCONJ
ejpam-3293	23	12	ωθ	ωθ	NUM
ejpam-3293	23	13	-	-	PUNCT
ejpam-3293	23	14	closed	close	VERB
ejpam-3293	23	15	sets	set	NOUN
ejpam-3293	23	16	on	on	ADP
ejpam-3293	23	17	a	a	DET
ejpam-3293	23	18	topological	topological	ADJ
ejpam-3293	23	19	space	space	NOUN
ejpam-3293	23	20	.	.	PUNCT
ejpam-3293	24	1	they	they	PRON
ejpam-3293	24	2	showed	show	VERB
ejpam-3293	24	3	that	that	SCONJ
ejpam-3293	24	4	the	the	DET
ejpam-3293	24	5	family	family	NOUN
ejpam-3293	24	6	of	of	ADP
ejpam-3293	24	7	all	all	DET
ejpam-3293	24	8	ωθ	ωθ	NOUN
ejpam-3293	24	9	-	-	PUNCT
ejpam-3293	24	10	open	open	ADJ
ejpam-3293	24	11	sets	set	NOUN
ejpam-3293	24	12	in	in	ADP
ejpam-3293	24	13	a	a	DET
ejpam-3293	24	14	topological	topological	ADJ
ejpam-3293	24	15	space	space	NOUN
ejpam-3293	24	16	x	x	PRON
ejpam-3293	24	17	forms	form	VERB
ejpam-3293	24	18	a	a	DET
ejpam-3293	24	19	topology	topology	NOUN
ejpam-3293	24	20	on	on	ADP
ejpam-3293	24	21	x.	x.	NOUN
ejpam-3293	24	22	they	they	PRON
ejpam-3293	24	23	also	also	ADV
ejpam-3293	24	24	introduced	introduce	VERB
ejpam-3293	24	25	the	the	DET
ejpam-3293	24	26	notions	notion	NOUN
ejpam-3293	24	27	of	of	ADP
ejpam-3293	24	28	ωθ	ωθ	NOUN
ejpam-3293	24	29	-	-	ADJ
ejpam-3293	24	30	interior	interior	ADJ
ejpam-3293	24	31	and	and	CCONJ
ejpam-3293	24	32	ωθ	ωθ	NOUN
ejpam-3293	24	33	-	-	PUNCT
ejpam-3293	24	34	closure	closure	NOUN
ejpam-3293	24	35	of	of	ADP
ejpam-3293	24	36	a	a	DET
ejpam-3293	24	37	subset	subset	NOUN
ejpam-3293	24	38	of	of	ADP
ejpam-3293	24	39	a	a	DET
ejpam-3293	24	40	topological	topological	ADJ
ejpam-3293	24	41	space	space	NOUN
ejpam-3293	24	42	.	.	PUNCT
ejpam-3293	25	1	a	a	DET
ejpam-3293	25	2	point	point	NOUN
ejpam-3293	25	3	x	x	PUNCT
ejpam-3293	25	4	of	of	ADP
ejpam-3293	25	5	a	a	DET
ejpam-3293	25	6	topological	topological	ADJ
ejpam-3293	25	7	space	space	NOUN
ejpam-3293	25	8	x	x	PRON
ejpam-3293	25	9	is	be	AUX
ejpam-3293	25	10	called	call	VERB
ejpam-3293	25	11	a	a	DET
ejpam-3293	25	12	condensation	condensation	NOUN
ejpam-3293	25	13	point	point	NOUN
ejpam-3293	25	14	of	of	ADP
ejpam-3293	25	15	a	a	DET
ejpam-3293	25	16	⊆	⊆	NUM
ejpam-3293	25	17	x	x	SYM
ejpam-3293	25	18	if	if	SCONJ
ejpam-3293	25	19	for	for	ADP
ejpam-3293	25	20	each	each	DET
ejpam-3293	25	21	open	open	ADJ
ejpam-3293	25	22	set	set	VERB
ejpam-3293	25	23	g	g	NOUN
ejpam-3293	25	24	containing	contain	VERB
ejpam-3293	25	25	x	x	PRON
ejpam-3293	25	26	,	,	PUNCT
ejpam-3293	25	27	g∩a	g∩a	PROPN
ejpam-3293	25	28	is	be	AUX
ejpam-3293	25	29	uncountable	uncountable	ADJ
ejpam-3293	25	30	.	.	PUNCT
ejpam-3293	26	1	a	a	DET
ejpam-3293	26	2	subset	subset	NOUN
ejpam-3293	26	3	b	b	NOUN
ejpam-3293	26	4	of	of	ADP
ejpam-3293	26	5	x	x	PROPN
ejpam-3293	26	6	is	be	AUX
ejpam-3293	26	7	ω	ω	NOUN
ejpam-3293	26	8	-	-	PUNCT
ejpam-3293	26	9	closed	closed	ADJ
ejpam-3293	26	10	if	if	SCONJ
ejpam-3293	26	11	it	it	PRON
ejpam-3293	26	12	contains	contain	VERB
ejpam-3293	26	13	all	all	PRON
ejpam-3293	26	14	of	of	ADP
ejpam-3293	26	15	its	its	PRON
ejpam-3293	26	16	condensation	condensation	NOUN
ejpam-3293	26	17	points	point	NOUN
ejpam-3293	26	18	.	.	PUNCT
ejpam-3293	27	1	the	the	DET
ejpam-3293	27	2	complement	complement	NOUN
ejpam-3293	27	3	of	of	ADP
ejpam-3293	27	4	b	b	PROPN
ejpam-3293	27	5	is	be	AUX
ejpam-3293	27	6	ω	ω	NOUN
ejpam-3293	27	7	-	-	NOUN
ejpam-3293	27	8	open	open	ADJ
ejpam-3293	27	9	.	.	PUNCT
ejpam-3293	28	1	equivalently	equivalently	ADV
ejpam-3293	28	2	,	,	PUNCT
ejpam-3293	28	3	a	a	DET
ejpam-3293	28	4	subset	subset	ADJ
ejpam-3293	28	5	u	u	NOUN
ejpam-3293	28	6	of	of	ADP
ejpam-3293	28	7	x	x	PROPN
ejpam-3293	28	8	is	be	AUX
ejpam-3293	28	9	ω	ω	NOUN
ejpam-3293	28	10	-	-	ADJ
ejpam-3293	28	11	open	open	ADJ
ejpam-3293	28	12	(	(	PUNCT
ejpam-3293	28	13	resp	resp	NOUN
ejpam-3293	28	14	.	.	PROPN
ejpam-3293	28	15	,	,	PUNCT
ejpam-3293	28	16	ωθ	ωθ	NOUN
ejpam-3293	28	17	-	-	PUNCT
ejpam-3293	28	18	open	open	ADJ
ejpam-3293	28	19	[	[	X
ejpam-3293	28	20	3	3	NUM
ejpam-3293	28	21	]	]	PUNCT
ejpam-3293	28	22	)	)	PUNCT
ejpam-3293	29	1	if	if	SCONJ
ejpam-3293	29	2	and	and	CCONJ
ejpam-3293	29	3	only	only	ADV
ejpam-3293	29	4	if	if	SCONJ
ejpam-3293	29	5	for	for	ADP
ejpam-3293	29	6	each	each	DET
ejpam-3293	29	7	x	x	SYM
ejpam-3293	29	8	∈	∈	PROPN
ejpam-3293	29	9	u	u	NOUN
ejpam-3293	29	10	,	,	PUNCT
ejpam-3293	29	11	there	there	PRON
ejpam-3293	29	12	exists	exist	VERB
ejpam-3293	29	13	an	an	DET
ejpam-3293	29	14	open	open	ADJ
ejpam-3293	29	15	set	set	NOUN
ejpam-3293	29	16	o	o	NOUN
ejpam-3293	29	17	containing	contain	VERB
ejpam-3293	29	18	x	x	PUNCT
ejpam-3293	29	19	such	such	ADJ
ejpam-3293	29	20	that	that	DET
ejpam-3293	29	21	o\u	o\u	NOUN
ejpam-3293	29	22	(	(	PUNCT
ejpam-3293	29	23	resp	resp	NOUN
ejpam-3293	29	24	.	.	PUNCT
ejpam-3293	29	25	,	,	PUNCT
ejpam-3293	29	26	o\ints(u	o\ints(u	PROPN
ejpam-3293	29	27	)	)	PUNCT
ejpam-3293	29	28	)	)	PUNCT
ejpam-3293	29	29	is	be	AUX
ejpam-3293	29	30	countable	countable	ADJ
ejpam-3293	29	31	.	.	PUNCT
ejpam-3293	30	1	a	a	DET
ejpam-3293	30	2	subset	subset	NOUN
ejpam-3293	30	3	b	b	NOUN
ejpam-3293	30	4	of	of	ADP
ejpam-3293	30	5	x	x	PROPN
ejpam-3293	30	6	is	be	AUX
ejpam-3293	30	7	ωθ	ωθ	NUM
ejpam-3293	30	8	-	-	PUNCT
ejpam-3293	30	9	closed	closed	ADJ
ejpam-3293	30	10	[	[	X
ejpam-3293	30	11	3	3	NUM
ejpam-3293	30	12	]	]	PUNCT
ejpam-3293	30	13	if	if	SCONJ
ejpam-3293	30	14	its	its	PRON
ejpam-3293	30	15	complement	complement	NOUN
ejpam-3293	30	16	x\b	x\b	PROPN
ejpam-3293	30	17	is	be	AUX
ejpam-3293	30	18	ωθ	ωθ	NOUN
ejpam-3293	30	19	-	-	PUNCT
ejpam-3293	30	20	open	open	ADJ
ejpam-3293	30	21	.	.	PUNCT
ejpam-3293	31	1	the	the	DET
ejpam-3293	31	2	ω	ω	NOUN
ejpam-3293	31	3	-	-	NOUN
ejpam-3293	31	4	closure	closure	NOUN
ejpam-3293	31	5	(	(	PUNCT
ejpam-3293	31	6	resp	resp	NOUN
ejpam-3293	31	7	.	.	PROPN
ejpam-3293	31	8	,	,	PUNCT
ejpam-3293	31	9	ωθ	ωθ	NOUN
ejpam-3293	31	10	-	-	PUNCT
ejpam-3293	31	11	closure	closure	NOUN
ejpam-3293	31	12	[	[	X
ejpam-3293	31	13	3	3	NUM
ejpam-3293	31	14	]	]	PUNCT
ejpam-3293	31	15	)	)	PUNCT
ejpam-3293	31	16	and	and	CCONJ
ejpam-3293	31	17	ω	ω	VERB
ejpam-3293	31	18	-	-	ADJ
ejpam-3293	31	19	interior	interior	ADJ
ejpam-3293	31	20	(	(	PUNCT
ejpam-3293	31	21	resp	resp	NOUN
ejpam-3293	31	22	.	.	PROPN
ejpam-3293	31	23	,	,	PUNCT
ejpam-3293	31	24	ωθ	ωθ	NOUN
ejpam-3293	31	25	-	-	ADJ
ejpam-3293	31	26	interior	interior	NOUN
ejpam-3293	31	27	[	[	X
ejpam-3293	31	28	3	3	NUM
ejpam-3293	31	29	]	]	PUNCT
ejpam-3293	31	30	)	)	PUNCT
ejpam-3293	31	31	of	of	ADP
ejpam-3293	31	32	a	a	DET
ejpam-3293	31	33	⊆	⊆	NUM
ejpam-3293	31	34	x	x	SYM
ejpam-3293	31	35	are	be	AUX
ejpam-3293	31	36	,	,	PUNCT
ejpam-3293	31	37	respectively	respectively	ADV
ejpam-3293	31	38	,	,	PUNCT
ejpam-3293	31	39	denoted	denote	VERB
ejpam-3293	31	40	and	and	CCONJ
ejpam-3293	31	41	defined	define	VERB
ejpam-3293	31	42	by	by	ADP
ejpam-3293	31	43	clω(a	clω(a	NOUN
ejpam-3293	31	44	)	)	PUNCT
ejpam-3293	31	45	=	=	SYM
ejpam-3293	31	46	∩{f	∩{f	NOUN
ejpam-3293	31	47	:	:	PUNCT
ejpam-3293	31	48	f	f	PROPN
ejpam-3293	31	49	is	be	AUX
ejpam-3293	31	50	an	an	DET
ejpam-3293	31	51	ω	ω	ADV
ejpam-3293	31	52	-	-	PUNCT
ejpam-3293	31	53	closed	closed	ADJ
ejpam-3293	31	54	set	set	NOUN
ejpam-3293	31	55	containing	contain	VERB
ejpam-3293	31	56	a	a	PRON
ejpam-3293	31	57	}	}	PUNCT
ejpam-3293	31	58	(	(	PUNCT
ejpam-3293	31	59	resp	resp	NOUN
ejpam-3293	31	60	.	.	PUNCT
ejpam-3293	31	61	,	,	PUNCT
ejpam-3293	31	62	clωθ(a	clωθ(a	NUM
ejpam-3293	31	63	)	)	PUNCT
ejpam-3293	32	1	=	=	SYM
ejpam-3293	32	2	∩{f	∩{f	NOUN
ejpam-3293	32	3	:	:	PUNCT
ejpam-3293	32	4	f	f	PROPN
ejpam-3293	32	5	is	be	AUX
ejpam-3293	32	6	an	an	DET
ejpam-3293	32	7	ωθ	ωθ	NOUN
ejpam-3293	32	8	-	-	PUNCT
ejpam-3293	32	9	closed	close	VERB
ejpam-3293	32	10	set	set	NOUN
ejpam-3293	32	11	containing	contain	VERB
ejpam-3293	32	12	a	a	PRON
ejpam-3293	32	13	}	}	PUNCT
ejpam-3293	32	14	)	)	PUNCT
ejpam-3293	32	15	and	and	CCONJ
ejpam-3293	32	16	intω(a	intω(a	PROPN
ejpam-3293	32	17	)	)	PUNCT
ejpam-3293	32	18	=	=	SYM
ejpam-3293	32	19	∪{g	∪{g	PROPN
ejpam-3293	32	20	:	:	PUNCT
ejpam-3293	32	21	g	g	PROPN
ejpam-3293	32	22	is	be	AUX
ejpam-3293	32	23	an	an	DET
ejpam-3293	32	24	ω	ω	ADJ
ejpam-3293	32	25	-	-	ADJ
ejpam-3293	32	26	open	open	ADJ
ejpam-3293	32	27	set	set	NOUN
ejpam-3293	32	28	contained	contain	VERB
ejpam-3293	32	29	in	in	ADP
ejpam-3293	32	30	a	a	DET
ejpam-3293	32	31	}	}	PUNCT
ejpam-3293	32	32	(	(	PUNCT
ejpam-3293	32	33	resp	resp	NOUN
ejpam-3293	32	34	.	.	NOUN
ejpam-3293	32	35	,	,	PUNCT
ejpam-3293	32	36	intωθ(a	intωθ(a	NUM
ejpam-3293	32	37	)	)	PUNCT
ejpam-3293	32	38	=	=	SYM
ejpam-3293	32	39	∪{g	∪{g	PROPN
ejpam-3293	32	40	:	:	PUNCT
ejpam-3293	32	41	g	g	PROPN
ejpam-3293	32	42	is	be	AUX
ejpam-3293	32	43	an	an	DET
ejpam-3293	32	44	ωθ	ωθ	ADV
ejpam-3293	32	45	-	-	PUNCT
ejpam-3293	32	46	open	open	ADJ
ejpam-3293	32	47	set	set	NOUN
ejpam-3293	32	48	contained	contain	VERB
ejpam-3293	32	49	in	in	ADP
ejpam-3293	32	50	a	a	PRON
ejpam-3293	32	51	}	}	PUNCT
ejpam-3293	32	52	)	)	PUNCT
ejpam-3293	32	53	.	.	PUNCT
ejpam-3293	33	1	it	it	PRON
ejpam-3293	33	2	is	be	AUX
ejpam-3293	33	3	worth	worth	ADJ
ejpam-3293	33	4	noting	note	VERB
ejpam-3293	33	5	that	that	SCONJ
ejpam-3293	33	6	a	a	DET
ejpam-3293	33	7	⊆	⊆	NUM
ejpam-3293	33	8	clω(a	clω(a	NOUN
ejpam-3293	33	9	)	)	PUNCT
ejpam-3293	33	10	(	(	PUNCT
ejpam-3293	33	11	resp	resp	NOUN
ejpam-3293	33	12	.	.	PUNCT
ejpam-3293	33	13	,	,	PUNCT
ejpam-3293	33	14	a	a	DET
ejpam-3293	33	15	⊆	⊆	NUM
ejpam-3293	33	16	clωθ(a	clωθ(a	NOUN
ejpam-3293	33	17	)	)	PUNCT
ejpam-3293	34	1	[	[	X
ejpam-3293	34	2	3	3	NUM
ejpam-3293	34	3	]	]	PUNCT
ejpam-3293	34	4	)	)	PUNCT
ejpam-3293	34	5	and	and	CCONJ
ejpam-3293	34	6	intω(a	intω(a	PROPN
ejpam-3293	34	7	)	)	PUNCT
ejpam-3293	34	8	⊆	⊆	PROPN
ejpam-3293	34	9	a	a	DET
ejpam-3293	34	10	(	(	PUNCT
ejpam-3293	34	11	resp	resp	NOUN
ejpam-3293	34	12	.	.	NOUN
ejpam-3293	34	13	,	,	PUNCT
ejpam-3293	34	14	intωθ(a	intωθ(a	NUM
ejpam-3293	34	15	)	)	PUNCT
ejpam-3293	34	16	⊆	⊆	NUM
ejpam-3293	34	17	a	a	PRON
ejpam-3293	34	18	[	[	X
ejpam-3293	34	19	3	3	NUM
ejpam-3293	34	20	]	]	NUM
ejpam-3293	34	21	)	)	PUNCT
ejpam-3293	34	22	.	.	PUNCT
ejpam-3293	35	1	let	let	VERB
ejpam-3293	35	2	tω	tω	PROPN
ejpam-3293	35	3	(	(	PUNCT
ejpam-3293	35	4	resp	resp	PROPN
ejpam-3293	35	5	.	.	PUNCT
ejpam-3293	35	6	,	,	PUNCT
ejpam-3293	35	7	tωθ	tωθ	AUX
ejpam-3293	35	8	)	)	PUNCT
ejpam-3293	35	9	be	be	AUX
ejpam-3293	35	10	the	the	DET
ejpam-3293	35	11	family	family	NOUN
ejpam-3293	35	12	of	of	ADP
ejpam-3293	35	13	all	all	DET
ejpam-3293	35	14	ω	ω	NOUN
ejpam-3293	35	15	-	-	ADJ
ejpam-3293	35	16	open	open	ADJ
ejpam-3293	35	17	(	(	PUNCT
ejpam-3293	35	18	resp	resp	NOUN
ejpam-3293	35	19	.	.	PROPN
ejpam-3293	35	20	,	,	PUNCT
ejpam-3293	35	21	ωθ	ωθ	NOUN
ejpam-3293	35	22	-	-	PUNCT
ejpam-3293	35	23	open	open	ADJ
ejpam-3293	35	24	)	)	PUNCT
ejpam-3293	35	25	subsets	subset	NOUN
ejpam-3293	35	26	of	of	ADP
ejpam-3293	35	27	a	a	DET
ejpam-3293	35	28	topological	topological	ADJ
ejpam-3293	35	29	space	space	NOUN
ejpam-3293	35	30	x.	x.	NOUN
ejpam-3293	35	31	since	since	SCONJ
ejpam-3293	35	32	tω	tω	PROPN
ejpam-3293	35	33	(	(	PUNCT
ejpam-3293	35	34	resp	resp	PROPN
ejpam-3293	35	35	.	.	PUNCT
ejpam-3293	35	36	,	,	PUNCT
ejpam-3293	35	37	tωθ	tωθ	PROPN
ejpam-3293	35	38	)	)	PUNCT
ejpam-3293	35	39	is	be	AUX
ejpam-3293	35	40	a	a	DET
ejpam-3293	35	41	topology	topology	NOUN
ejpam-3293	35	42	on	on	ADP
ejpam-3293	35	43	x	x	NOUN
ejpam-3293	35	44	,	,	PUNCT
ejpam-3293	35	45	for	for	ADP
ejpam-3293	35	46	any	any	DET
ejpam-3293	35	47	set	set	NOUN
ejpam-3293	35	48	a	a	DET
ejpam-3293	35	49	⊆	⊆	NUM
ejpam-3293	35	50	x	x	SYM
ejpam-3293	35	51	,	,	PUNCT
ejpam-3293	35	52	intω(a	intω(a	PROPN
ejpam-3293	35	53	)	)	PUNCT
ejpam-3293	35	54	(	(	PUNCT
ejpam-3293	35	55	resp	resp	NOUN
ejpam-3293	35	56	.	.	NOUN
ejpam-3293	35	57	,	,	PUNCT
ejpam-3293	35	58	intωθ(a	intωθ(a	NUM
ejpam-3293	35	59	)	)	PUNCT
ejpam-3293	35	60	)	)	PUNCT
ejpam-3293	35	61	is	be	AUX
ejpam-3293	35	62	ω	ω	NOUN
ejpam-3293	35	63	-	-	ADJ
ejpam-3293	35	64	open	open	ADJ
ejpam-3293	35	65	(	(	PUNCT
ejpam-3293	35	66	resp	resp	NOUN
ejpam-3293	35	67	.	.	PROPN
ejpam-3293	35	68	,	,	PUNCT
ejpam-3293	35	69	ωθ	ωθ	NOUN
ejpam-3293	35	70	-	-	PUNCT
ejpam-3293	35	71	open	open	ADJ
ejpam-3293	35	72	)	)	PUNCT
ejpam-3293	35	73	and	and	CCONJ
ejpam-3293	35	74	the	the	DET
ejpam-3293	35	75	largest	large	ADJ
ejpam-3293	35	76	ω	ω	NOUN
ejpam-3293	35	77	-	-	ADJ
ejpam-3293	35	78	open	open	ADJ
ejpam-3293	35	79	(	(	PUNCT
ejpam-3293	35	80	resp	resp	NOUN
ejpam-3293	35	81	.	.	PROPN
ejpam-3293	36	1	,	,	PUNCT
ejpam-3293	36	2	ωθ	ωθ	NOUN
ejpam-3293	36	3	-	-	PUNCT
ejpam-3293	36	4	open	open	ADJ
ejpam-3293	36	5	set	set	NOUN
ejpam-3293	36	6	)	)	PUNCT
ejpam-3293	36	7	contained	contain	VERB
ejpam-3293	36	8	in	in	ADP
ejpam-3293	36	9	a.	a.	NOUN
ejpam-3293	36	10	moreover	moreover	ADV
ejpam-3293	36	11	,	,	PUNCT
ejpam-3293	36	12	for	for	ADP
ejpam-3293	36	13	any	any	DET
ejpam-3293	36	14	set	set	NOUN
ejpam-3293	36	15	a	a	DET
ejpam-3293	36	16	⊆	⊆	NUM
ejpam-3293	36	17	x	x	SYM
ejpam-3293	36	18	,	,	PUNCT
ejpam-3293	36	19	clω(a	clω(a	PROPN
ejpam-3293	36	20	)	)	PUNCT
ejpam-3293	36	21	(	(	PUNCT
ejpam-3293	36	22	resp	resp	NOUN
ejpam-3293	36	23	.	.	PUNCT
ejpam-3293	36	24	,	,	PUNCT
ejpam-3293	36	25	clωθ(a	clωθ(a	NOUN
ejpam-3293	36	26	)	)	PUNCT
ejpam-3293	36	27	)	)	PUNCT
ejpam-3293	36	28	is	be	AUX
ejpam-3293	36	29	ω	ω	ADV
ejpam-3293	36	30	-	-	ADJ
ejpam-3293	36	31	closed	closed	ADJ
ejpam-3293	36	32	(	(	PUNCT
ejpam-3293	36	33	resp	resp	NOUN
ejpam-3293	36	34	.	.	PROPN
ejpam-3293	36	35	,	,	PUNCT
ejpam-3293	36	36	ωθ	ωθ	NOUN
ejpam-3293	36	37	-	-	PUNCT
ejpam-3293	36	38	closed	closed	ADJ
ejpam-3293	36	39	)	)	PUNCT
ejpam-3293	36	40	and	and	CCONJ
ejpam-3293	36	41	the	the	DET
ejpam-3293	36	42	smallest	small	ADJ
ejpam-3293	36	43	ω	ω	NOUN
ejpam-3293	36	44	-	-	ADJ
ejpam-3293	36	45	closed	closed	ADJ
ejpam-3293	36	46	(	(	PUNCT
ejpam-3293	36	47	resp	resp	NOUN
ejpam-3293	36	48	.	.	PROPN
ejpam-3293	37	1	,	,	PUNCT
ejpam-3293	37	2	ωθ	ωθ	NOUN
ejpam-3293	37	3	-	-	PUNCT
ejpam-3293	37	4	closed	closed	ADJ
ejpam-3293	37	5	)	)	PUNCT
ejpam-3293	37	6	set	set	NOUN
ejpam-3293	37	7	containing	contain	VERB
ejpam-3293	37	8	a.	a.	NOUN
ejpam-3293	37	9	a	a	DET
ejpam-3293	37	10	topological	topological	ADJ
ejpam-3293	37	11	space	space	NOUN
ejpam-3293	37	12	x	x	PRON
ejpam-3293	37	13	is	be	AUX
ejpam-3293	37	14	said	say	VERB
ejpam-3293	37	15	to	to	PART
ejpam-3293	37	16	be	be	AUX
ejpam-3293	37	17	ω	ω	VERB
ejpam-3293	37	18	-	-	VERB
ejpam-3293	37	19	connected	connected	ADJ
ejpam-3293	37	20	(	(	PUNCT
ejpam-3293	37	21	resp	resp	NOUN
ejpam-3293	37	22	.	.	PUNCT
ejpam-3293	37	23	,	,	PUNCT
ejpam-3293	37	24	θ	θ	X
ejpam-3293	37	25	-	-	PUNCT
ejpam-3293	37	26	connected	connect	VERB
ejpam-3293	37	27	,	,	PUNCT
ejpam-3293	37	28	ωθ	ωθ	NOUN
ejpam-3293	37	29	-	-	PUNCT
ejpam-3293	37	30	connected	connect	VERB
ejpam-3293	37	31	[	[	X
ejpam-3293	37	32	3	3	NUM
ejpam-3293	37	33	]	]	PUNCT
ejpam-3293	37	34	)	)	PUNCT
ejpam-3293	37	35	if	if	SCONJ
ejpam-3293	37	36	x	x	PRON
ejpam-3293	37	37	can	can	AUX
ejpam-3293	37	38	not	not	PART
ejpam-3293	37	39	be	be	AUX
ejpam-3293	37	40	written	write	VERB
ejpam-3293	37	41	as	as	ADP
ejpam-3293	37	42	the	the	DET
ejpam-3293	37	43	union	union	NOUN
ejpam-3293	37	44	of	of	ADP
ejpam-3293	37	45	two	two	NUM
ejpam-3293	37	46	nonempty	nonempty	ADJ
ejpam-3293	37	47	disjoint	disjoint	ADJ
ejpam-3293	37	48	ω	ω	NOUN
ejpam-3293	37	49	-	-	ADJ
ejpam-3293	37	50	open	open	ADJ
ejpam-3293	37	51	(	(	PUNCT
ejpam-3293	37	52	resp	resp	NOUN
ejpam-3293	37	53	.	.	PUNCT
ejpam-3293	37	54	,	,	PUNCT
ejpam-3293	37	55	θ	θ	ADJ
ejpam-3293	37	56	-	-	ADJ
ejpam-3293	37	57	open	open	ADJ
ejpam-3293	37	58	,	,	PUNCT
ejpam-3293	37	59	ωθopen	ωθopen	ADJ
ejpam-3293	37	60	)	)	PUNCT
ejpam-3293	37	61	sets	set	NOUN
ejpam-3293	37	62	.	.	PUNCT
ejpam-3293	38	1	otherwise	otherwise	ADV
ejpam-3293	38	2	,	,	PUNCT
ejpam-3293	38	3	x	x	X
ejpam-3293	38	4	is	be	AUX
ejpam-3293	38	5	ω	ω	NOUN
ejpam-3293	38	6	-	-	ADJ
ejpam-3293	38	7	disconnected	disconnected	ADJ
ejpam-3293	38	8	(	(	PUNCT
ejpam-3293	38	9	resp	resp	NOUN
ejpam-3293	38	10	.	.	PUNCT
ejpam-3293	38	11	,	,	PUNCT
ejpam-3293	38	12	θ	θ	X
ejpam-3293	38	13	-	-	PUNCT
ejpam-3293	38	14	disconnected	disconnected	ADJ
ejpam-3293	38	15	,	,	PUNCT
ejpam-3293	38	16	ωθ	ωθ	NOUN
ejpam-3293	38	17	-	-	PUNCT
ejpam-3293	38	18	disconnected	disconnected	ADJ
ejpam-3293	38	19	[	[	X
ejpam-3293	38	20	3	3	NUM
ejpam-3293	38	21	]	]	NUM
ejpam-3293	38	22	)	)	PUNCT
ejpam-3293	38	23	.	.	PUNCT
ejpam-3293	39	1	a	a	DET
ejpam-3293	39	2	subset	subset	NOUN
ejpam-3293	39	3	b	b	NOUN
ejpam-3293	39	4	of	of	ADP
ejpam-3293	39	5	x	x	PROPN
ejpam-3293	39	6	is	be	AUX
ejpam-3293	39	7	ω	ω	ADV
ejpam-3293	39	8	-	-	VERB
ejpam-3293	39	9	connected	connected	ADJ
ejpam-3293	39	10	(	(	PUNCT
ejpam-3293	39	11	resp	resp	NOUN
ejpam-3293	39	12	.	.	PUNCT
ejpam-3293	39	13	,	,	PUNCT
ejpam-3293	40	1	θ	θ	X
ejpam-3293	40	2	-	-	PUNCT
ejpam-3293	40	3	connected	connect	VERB
ejpam-3293	40	4	,	,	PUNCT
ejpam-3293	40	5	ωθ	ωθ	NOUN
ejpam-3293	40	6	-	-	PUNCT
ejpam-3293	40	7	connected	connect	VERB
ejpam-3293	40	8	)	)	PUNCT
ejpam-3293	40	9	if	if	SCONJ
ejpam-3293	40	10	it	it	PRON
ejpam-3293	40	11	is	be	AUX
ejpam-3293	40	12	ω	ω	ADV
ejpam-3293	40	13	-	-	ADJ
ejpam-3293	40	14	connected	connected	ADJ
ejpam-3293	40	15	(	(	PUNCT
ejpam-3293	40	16	resp	resp	NOUN
ejpam-3293	40	17	.	.	PUNCT
ejpam-3293	40	18	,	,	PUNCT
ejpam-3293	41	1	θ	θ	X
ejpam-3293	41	2	-	-	PUNCT
ejpam-3293	41	3	connected	connect	VERB
ejpam-3293	41	4	,	,	PUNCT
ejpam-3293	41	5	ωθ	ωθ	NOUN
ejpam-3293	41	6	-	-	PUNCT
ejpam-3293	41	7	connected	connect	VERB
ejpam-3293	41	8	)	)	PUNCT
ejpam-3293	41	9	as	as	ADP
ejpam-3293	41	10	a	a	DET
ejpam-3293	41	11	subspace	subspace	NOUN
ejpam-3293	41	12	of	of	ADP
ejpam-3293	41	13	x.	x.	NOUN
ejpam-3293	41	14	throughout	throughout	ADP
ejpam-3293	41	15	the	the	DET
ejpam-3293	41	16	paper	paper	NOUN
ejpam-3293	41	17	,	,	PUNCT
ejpam-3293	41	18	related	relate	VERB
ejpam-3293	41	19	results	result	NOUN
ejpam-3293	41	20	of	of	ADP
ejpam-3293	41	21	ωθ	ωθ	NOUN
ejpam-3293	41	22	-	-	PUNCT
ejpam-3293	41	23	open	open	ADJ
ejpam-3293	41	24	,	,	PUNCT
ejpam-3293	41	25	ωθ	ωθ	NOUN
ejpam-3293	41	26	-	-	PUNCT
ejpam-3293	41	27	closed	closed	ADJ
ejpam-3293	41	28	,	,	PUNCT
ejpam-3293	41	29	ωθ	ωθ	NOUN
ejpam-3293	41	30	-	-	PUNCT
ejpam-3293	41	31	closure	closure	NOUN
ejpam-3293	41	32	,	,	PUNCT
ejpam-3293	41	33	ωθ	ωθ	NOUN
ejpam-3293	41	34	-	-	PUNCT
ejpam-3293	41	35	interior	interior	NOUN
ejpam-3293	41	36	,	,	PUNCT
ejpam-3293	41	37	and	and	CCONJ
ejpam-3293	41	38	ωθ	ωθ	NUM
ejpam-3293	41	39	-	-	PUNCT
ejpam-3293	41	40	connectedness	connectedness	NOUN
ejpam-3293	41	41	are	be	AUX
ejpam-3293	41	42	due	due	ADJ
ejpam-3293	41	43	to	to	ADP
ejpam-3293	41	44	[	[	X
ejpam-3293	41	45	3	3	NUM
ejpam-3293	41	46	]	]	PUNCT
ejpam-3293	41	47	.	.	PUNCT
ejpam-3293	42	1	a	a	DET
ejpam-3293	42	2	function	function	NOUN
ejpam-3293	42	3	f	f	NOUN
ejpam-3293	42	4	from	from	ADP
ejpam-3293	42	5	a	a	DET
ejpam-3293	42	6	topological	topological	ADJ
ejpam-3293	42	7	space	space	NOUN
ejpam-3293	42	8	x	x	PUNCT
ejpam-3293	42	9	to	to	ADP
ejpam-3293	42	10	another	another	DET
ejpam-3293	42	11	topological	topological	ADJ
ejpam-3293	42	12	space	space	NOUN
ejpam-3293	42	13	y	y	PROPN
ejpam-3293	42	14	is	be	AUX
ejpam-3293	42	15	said	say	VERB
ejpam-3293	42	16	to	to	PART
ejpam-3293	42	17	be	be	AUX
ejpam-3293	42	18	(	(	PUNCT
ejpam-3293	42	19	i	i	NOUN
ejpam-3293	42	20	)	)	PUNCT
ejpam-3293	42	21	ω	ω	PROPN
ejpam-3293	42	22	-	-	NOUN
ejpam-3293	42	23	open	open	ADJ
ejpam-3293	42	24	(	(	PUNCT
ejpam-3293	42	25	resp	resp	NOUN
ejpam-3293	42	26	.	.	PUNCT
ejpam-3293	42	27	,	,	PUNCT
ejpam-3293	42	28	θ	θ	X
ejpam-3293	42	29	-	-	ADJ
ejpam-3293	42	30	open	open	ADJ
ejpam-3293	42	31	,	,	PUNCT
ejpam-3293	42	32	ωθ	ωθ	NOUN
ejpam-3293	42	33	-	-	PUNCT
ejpam-3293	42	34	open	open	ADJ
ejpam-3293	42	35	)	)	PUNCT
ejpam-3293	42	36	if	if	SCONJ
ejpam-3293	42	37	f(g	f(g	NOUN
ejpam-3293	42	38	)	)	PUNCT
ejpam-3293	42	39	is	be	AUX
ejpam-3293	42	40	ω	ω	NOUN
ejpam-3293	42	41	-	-	ADJ
ejpam-3293	42	42	open	open	ADJ
ejpam-3293	42	43	(	(	PUNCT
ejpam-3293	42	44	resp	resp	NOUN
ejpam-3293	42	45	.	.	PUNCT
ejpam-3293	42	46	,	,	PUNCT
ejpam-3293	43	1	θ	θ	X
ejpam-3293	43	2	-	-	ADJ
ejpam-3293	43	3	open	open	ADJ
ejpam-3293	43	4	,	,	PUNCT
ejpam-3293	43	5	ωθ	ωθ	NOUN
ejpam-3293	43	6	-	-	PUNCT
ejpam-3293	43	7	open	open	ADJ
ejpam-3293	43	8	)	)	PUNCT
ejpam-3293	43	9	in	in	ADP
ejpam-3293	43	10	y	y	PROPN
ejpam-3293	43	11	for	for	ADP
ejpam-3293	43	12	every	every	DET
ejpam-3293	43	13	open	open	ADJ
ejpam-3293	43	14	set	set	VERB
ejpam-3293	43	15	g	g	NOUN
ejpam-3293	43	16	in	in	ADP
ejpam-3293	43	17	x	x	ADP
ejpam-3293	43	18	;	;	PUNCT
ejpam-3293	43	19	(	(	PUNCT
ejpam-3293	43	20	ii	ii	NOUN
ejpam-3293	43	21	)	)	PUNCT
ejpam-3293	43	22	ω	ω	PROPN
ejpam-3293	43	23	-	-	PUNCT
ejpam-3293	43	24	closed	closed	ADJ
ejpam-3293	43	25	(	(	PUNCT
ejpam-3293	43	26	resp	resp	NOUN
ejpam-3293	43	27	.	.	PUNCT
ejpam-3293	43	28	,	,	PUNCT
ejpam-3293	43	29	θ	θ	NOUN
ejpam-3293	43	30	-	-	PUNCT
ejpam-3293	43	31	closed	closed	ADJ
ejpam-3293	43	32	,	,	PUNCT
ejpam-3293	43	33	ωθ	ωθ	NOUN
ejpam-3293	43	34	-	-	PUNCT
ejpam-3293	43	35	closed	closed	ADJ
ejpam-3293	43	36	)	)	PUNCT
ejpam-3293	43	37	if	if	SCONJ
ejpam-3293	43	38	f(g	f(g	NOUN
ejpam-3293	43	39	)	)	PUNCT
ejpam-3293	43	40	is	be	AUX
ejpam-3293	43	41	ω	ω	NOUN
ejpam-3293	43	42	-	-	ADJ
ejpam-3293	43	43	closed	closed	ADJ
ejpam-3293	43	44	(	(	PUNCT
ejpam-3293	43	45	resp	resp	NOUN
ejpam-3293	43	46	.	.	PUNCT
ejpam-3293	43	47	,	,	PUNCT
ejpam-3293	44	1	θ	θ	NOUN
ejpam-3293	44	2	-	-	PUNCT
ejpam-3293	44	3	closed	closed	ADJ
ejpam-3293	44	4	,	,	PUNCT
ejpam-3293	44	5	ωθ	ωθ	NOUN
ejpam-3293	44	6	-	-	PUNCT
ejpam-3293	44	7	closed	closed	ADJ
ejpam-3293	44	8	)	)	PUNCT
ejpam-3293	44	9	in	in	ADP
ejpam-3293	44	10	y	y	PROPN
ejpam-3293	44	11	for	for	ADP
ejpam-3293	44	12	every	every	DET
ejpam-3293	44	13	closed	close	VERB
ejpam-3293	44	14	set	set	VERB
ejpam-3293	44	15	g	g	NOUN
ejpam-3293	44	16	in	in	ADP
ejpam-3293	44	17	x	x	PROPN
ejpam-3293	44	18	;	;	PUNCT
ejpam-3293	44	19	m.	m.	NOUN
ejpam-3293	44	20	labendia	labendia	PROPN
ejpam-3293	44	21	,	,	PUNCT
ejpam-3293	44	22	j.	j.	PROPN
ejpam-3293	44	23	a.	a.	PROPN
ejpam-3293	44	24	sasam	sasam	PROPN
ejpam-3293	44	25	/	/	SYM
ejpam-3293	44	26	eur	eur	PROPN
ejpam-3293	44	27	.	.	PUNCT
ejpam-3293	45	1	j.	j.	PROPN
ejpam-3293	45	2	pure	pure	PROPN
ejpam-3293	45	3	appl	appl	PROPN
ejpam-3293	45	4	.	.	PROPN
ejpam-3293	45	5	math	math	PROPN
ejpam-3293	45	6	,	,	PUNCT
ejpam-3293	45	7	11	11	NUM
ejpam-3293	45	8	(	(	PUNCT
ejpam-3293	45	9	3	3	NUM
ejpam-3293	45	10	)	)	PUNCT
ejpam-3293	45	11	(	(	PUNCT
ejpam-3293	45	12	2018	2018	NUM
ejpam-3293	45	13	)	)	PUNCT
ejpam-3293	45	14	,	,	PUNCT
ejpam-3293	45	15	834	834	NUM
ejpam-3293	45	16	-	-	SYM
ejpam-3293	45	17	843	843	NUM
ejpam-3293	45	18	836	836	NUM
ejpam-3293	45	19	(	(	PUNCT
ejpam-3293	45	20	iii	iii	NOUN
ejpam-3293	45	21	)	)	PUNCT
ejpam-3293	45	22	ω	ω	NOUN
ejpam-3293	45	23	-	-	ADJ
ejpam-3293	45	24	continuous	continuous	ADJ
ejpam-3293	45	25	if	if	SCONJ
ejpam-3293	45	26	f−1(v	f−1(v	PROPN
ejpam-3293	45	27	)	)	PUNCT
ejpam-3293	45	28	is	be	AUX
ejpam-3293	45	29	ω	ω	NOUN
ejpam-3293	45	30	-	-	ADJ
ejpam-3293	45	31	open	open	ADJ
ejpam-3293	45	32	(	(	PUNCT
ejpam-3293	45	33	resp	resp	NOUN
ejpam-3293	45	34	.	.	PUNCT
ejpam-3293	45	35	,	,	PUNCT
ejpam-3293	45	36	θ	θ	X
ejpam-3293	45	37	-	-	ADJ
ejpam-3293	45	38	open	open	ADJ
ejpam-3293	45	39	,	,	PUNCT
ejpam-3293	45	40	ωθ	ωθ	NOUN
ejpam-3293	45	41	-	-	PUNCT
ejpam-3293	45	42	open	open	ADJ
ejpam-3293	45	43	)	)	PUNCT
ejpam-3293	45	44	in	in	ADP
ejpam-3293	45	45	x	x	PUNCT
ejpam-3293	45	46	for	for	ADP
ejpam-3293	45	47	every	every	DET
ejpam-3293	45	48	open	open	NOUN
ejpam-3293	45	49	subset	subset	NOUN
ejpam-3293	45	50	v	v	NOUN
ejpam-3293	45	51	of	of	ADP
ejpam-3293	45	52	y	y	PROPN
ejpam-3293	45	53	;	;	PUNCT
ejpam-3293	45	54	(	(	PUNCT
ejpam-3293	45	55	iv	iv	X
ejpam-3293	45	56	)	)	PUNCT
ejpam-3293	45	57	ω	ω	NOUN
ejpam-3293	45	58	-	-	NOUN
ejpam-3293	45	59	irresolute	irresolute	ADJ
ejpam-3293	45	60	if	if	SCONJ
ejpam-3293	45	61	for	for	SCONJ
ejpam-3293	45	62	every	every	DET
ejpam-3293	45	63	x	x	SYM
ejpam-3293	45	64	∈	∈	PROPN
ejpam-3293	45	65	x	x	X
ejpam-3293	45	66	and	and	CCONJ
ejpam-3293	45	67	every	every	DET
ejpam-3293	45	68	ωθ	ωθ	NOUN
ejpam-3293	45	69	-	-	PUNCT
ejpam-3293	45	70	open	open	NOUN
ejpam-3293	45	71	set	set	VERB
ejpam-3293	45	72	a	a	DET
ejpam-3293	45	73	containing	contain	VERB
ejpam-3293	45	74	f(x	f(x	PROPN
ejpam-3293	45	75	)	)	PUNCT
ejpam-3293	45	76	,	,	PUNCT
ejpam-3293	45	77	there	there	PRON
ejpam-3293	45	78	exists	exist	VERB
ejpam-3293	45	79	an	an	DET
ejpam-3293	45	80	ω	ω	ADJ
ejpam-3293	45	81	-	-	ADJ
ejpam-3293	45	82	open	open	ADJ
ejpam-3293	45	83	set	set	NOUN
ejpam-3293	45	84	u	u	NOUN
ejpam-3293	45	85	containing	contain	VERB
ejpam-3293	45	86	x	x	PUNCT
ejpam-3293	45	87	such	such	ADJ
ejpam-3293	45	88	that	that	DET
ejpam-3293	45	89	f(u	f(u	PROPN
ejpam-3293	45	90	)	)	PUNCT
ejpam-3293	45	91	⊆	⊆	NUM
ejpam-3293	45	92	a.	a.	NOUN
ejpam-3293	45	93	let	let	VERB
ejpam-3293	45	94	a	a	PRON
ejpam-3293	45	95	be	be	AUX
ejpam-3293	45	96	an	an	DET
ejpam-3293	45	97	indexing	indexing	NOUN
ejpam-3293	45	98	set	set	NOUN
ejpam-3293	45	99	and	and	CCONJ
ejpam-3293	45	100	{	{	PUNCT
ejpam-3293	45	101	yα	yα	NOUN
ejpam-3293	45	102	:	:	PUNCT
ejpam-3293	45	103	α	α	PROPN
ejpam-3293	45	104	∈	∈	PROPN
ejpam-3293	45	105	a	a	DET
ejpam-3293	45	106	}	}	PUNCT
ejpam-3293	45	107	be	be	AUX
ejpam-3293	45	108	a	a	DET
ejpam-3293	45	109	family	family	NOUN
ejpam-3293	45	110	of	of	ADP
ejpam-3293	45	111	topological	topological	ADJ
ejpam-3293	45	112	spaces	space	NOUN
ejpam-3293	45	113	.	.	PUNCT
ejpam-3293	46	1	for	for	ADP
ejpam-3293	46	2	each	each	DET
ejpam-3293	46	3	α	α	NOUN
ejpam-3293	46	4	∈	∈	PROPN
ejpam-3293	46	5	a	a	PRON
ejpam-3293	46	6	,	,	PUNCT
ejpam-3293	46	7	let	let	VERB
ejpam-3293	46	8	tα	tα	NOUN
ejpam-3293	46	9	be	be	AUX
ejpam-3293	46	10	the	the	DET
ejpam-3293	46	11	topology	topology	NOUN
ejpam-3293	46	12	on	on	ADP
ejpam-3293	46	13	yα	yα	NOUN
ejpam-3293	46	14	.	.	PUNCT
ejpam-3293	47	1	the	the	DET
ejpam-3293	47	2	tychonoff	tychonoff	NOUN
ejpam-3293	47	3	topology	topology	NOUN
ejpam-3293	47	4	on	on	ADP
ejpam-3293	47	5	π{yα	π{yα	PROPN
ejpam-3293	47	6	:	:	PUNCT
ejpam-3293	47	7	α	α	PROPN
ejpam-3293	47	8	∈	∈	PROPN
ejpam-3293	47	9	a	a	DET
ejpam-3293	47	10	}	}	PUNCT
ejpam-3293	47	11	is	be	AUX
ejpam-3293	47	12	the	the	DET
ejpam-3293	47	13	topology	topology	NOUN
ejpam-3293	47	14	generated	generate	VERB
ejpam-3293	47	15	by	by	ADP
ejpam-3293	47	16	a	a	DET
ejpam-3293	47	17	subbase	subbase	NOUN
ejpam-3293	47	18	consisting	consist	VERB
ejpam-3293	47	19	of	of	ADP
ejpam-3293	47	20	all	all	DET
ejpam-3293	47	21	sets	set	NOUN
ejpam-3293	47	22	p−1α	p−1α	NOUN
ejpam-3293	47	23	(	(	PUNCT
ejpam-3293	47	24	uα	uα	NOUN
ejpam-3293	47	25	)	)	PUNCT
ejpam-3293	47	26	,	,	PUNCT
ejpam-3293	47	27	where	where	SCONJ
ejpam-3293	47	28	the	the	DET
ejpam-3293	47	29	projection	projection	NOUN
ejpam-3293	47	30	map	map	NOUN
ejpam-3293	47	31	pα	pα	INTJ
ejpam-3293	47	32	:	:	PUNCT
ejpam-3293	47	33	π{yα	π{yα	ADP
ejpam-3293	47	34	:	:	PUNCT
ejpam-3293	47	35	α	α	PROPN
ejpam-3293	47	36	∈	∈	PROPN
ejpam-3293	47	37	a	a	PRON
ejpam-3293	47	38	}	}	PUNCT
ejpam-3293	47	39	→	→	SYM
ejpam-3293	47	40	yα	yα	NOUN
ejpam-3293	47	41	is	be	AUX
ejpam-3293	47	42	defined	define	VERB
ejpam-3293	47	43	by	by	ADP
ejpam-3293	47	44	pα(〈yβ	pα(〈yβ	PROPN
ejpam-3293	47	45	〉	〉	PROPN
ejpam-3293	47	46	)	)	PUNCT
ejpam-3293	48	1	=	=	SYM
ejpam-3293	48	2	yα	yα	NOUN
ejpam-3293	48	3	,	,	PUNCT
ejpam-3293	48	4	uα	uα	PROPN
ejpam-3293	48	5	ranges	range	VERB
ejpam-3293	48	6	over	over	ADP
ejpam-3293	48	7	all	all	DET
ejpam-3293	48	8	members	member	NOUN
ejpam-3293	48	9	of	of	ADP
ejpam-3293	48	10	tα	tα	PROPN
ejpam-3293	48	11	,	,	PUNCT
ejpam-3293	48	12	and	and	CCONJ
ejpam-3293	48	13	α	α	NOUN
ejpam-3293	48	14	ranges	range	VERB
ejpam-3293	48	15	over	over	ADP
ejpam-3293	48	16	all	all	DET
ejpam-3293	48	17	elements	element	NOUN
ejpam-3293	48	18	of	of	ADP
ejpam-3293	48	19	a.	a.	NOUN
ejpam-3293	48	20	corresponding	correspond	VERB
ejpam-3293	48	21	to	to	ADP
ejpam-3293	48	22	uα	uα	PROPN
ejpam-3293	48	23	⊆	⊆	NUM
ejpam-3293	48	24	yα	yα	NOUN
ejpam-3293	48	25	,	,	PUNCT
ejpam-3293	48	26	denote	denote	VERB
ejpam-3293	48	27	p−1α	p−1α	NOUN
ejpam-3293	48	28	(	(	PUNCT
ejpam-3293	48	29	uα	uα	NOUN
ejpam-3293	48	30	)	)	PUNCT
ejpam-3293	48	31	by	by	ADP
ejpam-3293	48	32	〈	〈	PROPN
ejpam-3293	48	33	uα	uα	PROPN
ejpam-3293	48	34	〉	〉	PROPN
ejpam-3293	48	35	.	.	PUNCT
ejpam-3293	49	1	similarly	similarly	ADV
ejpam-3293	49	2	,	,	PUNCT
ejpam-3293	49	3	for	for	ADP
ejpam-3293	49	4	finitely	finitely	ADV
ejpam-3293	49	5	many	many	ADJ
ejpam-3293	49	6	indices	index	NOUN
ejpam-3293	49	7	α1	α1	PROPN
ejpam-3293	49	8	,	,	PUNCT
ejpam-3293	49	9	α2	α2	ADJ
ejpam-3293	49	10	,	,	PUNCT
ejpam-3293	49	11	.	.	PUNCT
ejpam-3293	49	12	.	.	PUNCT
ejpam-3293	49	13	.	.	PUNCT
ejpam-3293	50	1	,	,	PUNCT
ejpam-3293	50	2	αn	αn	VERB
ejpam-3293	50	3	,	,	PUNCT
ejpam-3293	50	4	and	and	CCONJ
ejpam-3293	50	5	sets	set	VERB
ejpam-3293	50	6	uα1	uα1	NOUN
ejpam-3293	50	7	⊆	⊆	NUM
ejpam-3293	50	8	yα1	yα1	NOUN
ejpam-3293	50	9	,	,	PUNCT
ejpam-3293	50	10	uα2	uα2	ADV
ejpam-3293	50	11	⊆	⊆	NUM
ejpam-3293	50	12	yα2	yα2	NOUN
ejpam-3293	50	13	,	,	PUNCT
ejpam-3293	50	14	.	.	PUNCT
ejpam-3293	50	15	.	.	PUNCT
ejpam-3293	51	1	.	.	PUNCT
ejpam-3293	52	1	,	,	PUNCT
ejpam-3293	52	2	uαn	uαn	PROPN
ejpam-3293	52	3	⊆	⊆	NUM
ejpam-3293	52	4	yαn	yαn	PROPN
ejpam-3293	52	5	,	,	PUNCT
ejpam-3293	52	6	the	the	DET
ejpam-3293	52	7	subset	subset	NOUN
ejpam-3293	53	1	〈	〈	PROPN
ejpam-3293	53	2	uα1	uα1	ADJ
ejpam-3293	53	3	〉	〉	PROPN
ejpam-3293	53	4	∩	∩	NOUN
ejpam-3293	53	5	〈	〈	PROPN
ejpam-3293	53	6	uα2	uα2	ADJ
ejpam-3293	53	7	〉	〉	NOUN
ejpam-3293	53	8	∩	∩	NOUN
ejpam-3293	53	9	·	·	PUNCT
ejpam-3293	53	10	·	·	PUNCT
ejpam-3293	53	11	·	·	PUNCT
ejpam-3293	53	12	∩	∩	PROPN
ejpam-3293	53	13	〈	〈	PROPN
ejpam-3293	53	14	uαn	uαn	PROPN
ejpam-3293	53	15	〉	〉	PROPN
ejpam-3293	53	16	=	=	SYM
ejpam-3293	53	17	p−1α1	p−1α1	NOUN
ejpam-3293	53	18	(	(	PUNCT
ejpam-3293	53	19	uα1	uα1	NOUN
ejpam-3293	53	20	)	)	PUNCT
ejpam-3293	53	21	∩	∩	NOUN
ejpam-3293	53	22	p−1α2	p−1α2	NUM
ejpam-3293	53	23	(	(	PUNCT
ejpam-3293	53	24	uα2	uα2	ADJ
ejpam-3293	53	25	)	)	PUNCT
ejpam-3293	53	26	∩	∩	NOUN
ejpam-3293	53	27	·	·	PUNCT
ejpam-3293	53	28	·	·	PUNCT
ejpam-3293	53	29	·	·	PUNCT
ejpam-3293	53	30	∩	∩	ADJ
ejpam-3293	53	31	p−1αn	p−1αn	NOUN
ejpam-3293	53	32	(	(	PUNCT
ejpam-3293	53	33	uαn	uαn	PROPN
ejpam-3293	53	34	)	)	PUNCT
ejpam-3293	53	35	is	be	AUX
ejpam-3293	53	36	denoted	denote	VERB
ejpam-3293	53	37	by	by	ADP
ejpam-3293	53	38	〈	〈	PROPN
ejpam-3293	53	39	uα1	uα1	PROPN
ejpam-3293	53	40	,	,	PUNCT
ejpam-3293	53	41	uα2	uα2	ADV
ejpam-3293	53	42	,	,	PUNCT
ejpam-3293	53	43	.	.	PUNCT
ejpam-3293	53	44	.	.	PUNCT
ejpam-3293	54	1	.	.	PUNCT
ejpam-3293	55	1	,	,	PUNCT
ejpam-3293	55	2	uαn	uαn	PROPN
ejpam-3293	55	3	〉	〉	PROPN
ejpam-3293	55	4	.	.	PUNCT
ejpam-3293	56	1	we	we	PRON
ejpam-3293	56	2	note	note	VERB
ejpam-3293	56	3	that	that	SCONJ
ejpam-3293	56	4	for	for	ADP
ejpam-3293	56	5	each	each	DET
ejpam-3293	56	6	open	open	ADJ
ejpam-3293	56	7	set	set	NOUN
ejpam-3293	56	8	uα	uα	PROPN
ejpam-3293	56	9	subset	subset	NOUN
ejpam-3293	56	10	of	of	ADP
ejpam-3293	56	11	yα	yα	NOUN
ejpam-3293	56	12	,	,	PUNCT
ejpam-3293	56	13	〈	〈	PROPN
ejpam-3293	56	14	uα	uα	PROPN
ejpam-3293	56	15	〉	〉	NOUN
ejpam-3293	56	16	=	=	NOUN
ejpam-3293	56	17	p−1α	p−1α	NOUN
ejpam-3293	56	18	(	(	PUNCT
ejpam-3293	56	19	uα	uα	NOUN
ejpam-3293	56	20	)	)	PUNCT
ejpam-3293	56	21	=	=	SYM
ejpam-3293	57	1	uα×πβ	uα×πβ	PROPN
ejpam-3293	57	2	6	6	NUM
ejpam-3293	57	3	=	=	NOUN
ejpam-3293	57	4	αyβ	αyβ	NOUN
ejpam-3293	57	5	.	.	PUNCT
ejpam-3293	58	1	hence	hence	ADV
ejpam-3293	58	2	,	,	PUNCT
ejpam-3293	58	3	a	a	DET
ejpam-3293	58	4	basis	basis	NOUN
ejpam-3293	58	5	for	for	ADP
ejpam-3293	58	6	the	the	DET
ejpam-3293	58	7	tychonoff	tychonoff	NOUN
ejpam-3293	58	8	topology	topology	NOUN
ejpam-3293	58	9	consists	consist	VERB
ejpam-3293	58	10	of	of	ADP
ejpam-3293	58	11	sets	set	NOUN
ejpam-3293	58	12	of	of	ADP
ejpam-3293	58	13	the	the	DET
ejpam-3293	58	14	form	form	NOUN
ejpam-3293	58	15	〈	〈	PROPN
ejpam-3293	58	16	bα1	bα1	NOUN
ejpam-3293	58	17	,	,	PUNCT
ejpam-3293	58	18	bα2	bα2	NOUN
ejpam-3293	58	19	,	,	PUNCT
ejpam-3293	58	20	...	...	PUNCT
ejpam-3293	58	21	,	,	PUNCT
ejpam-3293	58	22	bαk	bαk	VERB
ejpam-3293	58	23	〉	〉	PROPN
ejpam-3293	58	24	,	,	PUNCT
ejpam-3293	58	25	where	where	SCONJ
ejpam-3293	58	26	bαi	bαi	NOUN
ejpam-3293	58	27	is	be	AUX
ejpam-3293	58	28	open	open	ADJ
ejpam-3293	58	29	in	in	ADP
ejpam-3293	58	30	yαi	yαi	PROPN
ejpam-3293	58	31	for	for	ADP
ejpam-3293	58	32	every	every	DET
ejpam-3293	58	33	i	i	NOUN
ejpam-3293	58	34	∈	∈	PROPN
ejpam-3293	58	35	k	k	NOUN
ejpam-3293	59	1	=	=	PUNCT
ejpam-3293	59	2	{	{	PUNCT
ejpam-3293	59	3	1	1	NUM
ejpam-3293	59	4	,	,	PUNCT
ejpam-3293	59	5	2	2	NUM
ejpam-3293	59	6	,	,	PUNCT
ejpam-3293	59	7	...	...	PUNCT
ejpam-3293	59	8	,	,	PUNCT
ejpam-3293	59	9	k	k	NOUN
ejpam-3293	59	10	}	}	PUNCT
ejpam-3293	59	11	.	.	PUNCT
ejpam-3293	60	1	now	now	ADV
ejpam-3293	60	2	,	,	PUNCT
ejpam-3293	60	3	the	the	DET
ejpam-3293	60	4	projection	projection	NOUN
ejpam-3293	60	5	map	map	NOUN
ejpam-3293	60	6	pα	pα	INTJ
ejpam-3293	60	7	:	:	PUNCT
ejpam-3293	60	8	π{yα	π{yα	ADP
ejpam-3293	60	9	:	:	PUNCT
ejpam-3293	60	10	α	α	PROPN
ejpam-3293	60	11	∈	∈	PROPN
ejpam-3293	60	12	a	a	PRON
ejpam-3293	60	13	}	}	PUNCT
ejpam-3293	60	14	→	→	SYM
ejpam-3293	60	15	yα	yα	NOUN
ejpam-3293	60	16	is	be	AUX
ejpam-3293	60	17	defined	define	VERB
ejpam-3293	60	18	by	by	ADP
ejpam-3293	60	19	pα(〈yβ	pα(〈yβ	PROPN
ejpam-3293	60	20	〉	〉	PROPN
ejpam-3293	60	21	)	)	PUNCT
ejpam-3293	61	1	=	=	NOUN
ejpam-3293	61	2	yα	yα	NOUN
ejpam-3293	61	3	for	for	ADP
ejpam-3293	61	4	each	each	DET
ejpam-3293	61	5	α	α	PROPN
ejpam-3293	61	6	∈	∈	NOUN
ejpam-3293	61	7	a.	a.	NOUN
ejpam-3293	62	1	it	it	PRON
ejpam-3293	62	2	is	be	AUX
ejpam-3293	62	3	known	know	VERB
ejpam-3293	62	4	that	that	SCONJ
ejpam-3293	62	5	every	every	DET
ejpam-3293	62	6	projection	projection	NOUN
ejpam-3293	62	7	map	map	NOUN
ejpam-3293	62	8	is	be	AUX
ejpam-3293	62	9	a	a	DET
ejpam-3293	62	10	continuous	continuous	ADJ
ejpam-3293	62	11	open	open	ADJ
ejpam-3293	62	12	surjection	surjection	NOUN
ejpam-3293	62	13	.	.	PUNCT
ejpam-3293	63	1	also	also	ADV
ejpam-3293	63	2	,	,	PUNCT
ejpam-3293	63	3	it	it	PRON
ejpam-3293	63	4	is	be	AUX
ejpam-3293	63	5	well	well	ADV
ejpam-3293	63	6	known	know	VERB
ejpam-3293	63	7	that	that	SCONJ
ejpam-3293	63	8	a	a	DET
ejpam-3293	63	9	function	function	NOUN
ejpam-3293	63	10	f	f	NOUN
ejpam-3293	63	11	from	from	ADP
ejpam-3293	63	12	an	an	DET
ejpam-3293	63	13	arbitrary	arbitrary	ADJ
ejpam-3293	63	14	space	space	NOUN
ejpam-3293	63	15	x	x	NOUN
ejpam-3293	63	16	into	into	ADP
ejpam-3293	63	17	the	the	DET
ejpam-3293	63	18	cartesian	cartesian	ADJ
ejpam-3293	63	19	product	product	NOUN
ejpam-3293	63	20	y	y	PROPN
ejpam-3293	63	21	of	of	ADP
ejpam-3293	63	22	the	the	DET
ejpam-3293	63	23	family	family	NOUN
ejpam-3293	63	24	of	of	ADP
ejpam-3293	63	25	spaces	space	NOUN
ejpam-3293	63	26	{	{	PUNCT
ejpam-3293	63	27	yα	yα	NOUN
ejpam-3293	63	28	:	:	PUNCT
ejpam-3293	63	29	α	α	PROPN
ejpam-3293	63	30	∈	∈	PROPN
ejpam-3293	63	31	a	a	X
ejpam-3293	63	32	}	}	PUNCT
ejpam-3293	63	33	with	with	ADP
ejpam-3293	63	34	the	the	DET
ejpam-3293	63	35	tychonoff	tychonoff	NOUN
ejpam-3293	63	36	topology	topology	NOUN
ejpam-3293	63	37	is	be	AUX
ejpam-3293	63	38	continuous	continuous	ADJ
ejpam-3293	63	39	if	if	SCONJ
ejpam-3293	63	40	and	and	CCONJ
ejpam-3293	63	41	only	only	ADV
ejpam-3293	63	42	if	if	SCONJ
ejpam-3293	63	43	each	each	DET
ejpam-3293	63	44	coordinate	coordinate	NOUN
ejpam-3293	63	45	function	function	NOUN
ejpam-3293	63	46	pα	pα	NOUN
ejpam-3293	63	47	◦	◦	NOUN
ejpam-3293	63	48	f	f	PROPN
ejpam-3293	63	49	is	be	AUX
ejpam-3293	63	50	continuous	continuous	ADJ
ejpam-3293	63	51	,	,	PUNCT
ejpam-3293	63	52	where	where	SCONJ
ejpam-3293	63	53	pα	pα	NOUN
ejpam-3293	63	54	is	be	AUX
ejpam-3293	63	55	the	the	DET
ejpam-3293	63	56	α	α	NOUN
ejpam-3293	63	57	-	-	PUNCT
ejpam-3293	63	58	th	th	VERB
ejpam-3293	63	59	coordinate	coordinate	NOUN
ejpam-3293	63	60	projection	projection	NOUN
ejpam-3293	63	61	map	map	NOUN
ejpam-3293	63	62	.	.	PUNCT
ejpam-3293	64	1	2	2	X
ejpam-3293	64	2	.	.	X
ejpam-3293	64	3	ω	ω	NOUN
ejpam-3293	64	4	-	-	ADJ
ejpam-3293	64	5	open	open	ADJ
ejpam-3293	64	6	and	and	CCONJ
ejpam-3293	64	7	ω	ω	VERB
ejpam-3293	64	8	-	-	PUNCT
ejpam-3293	64	9	closed	close	VERB
ejpam-3293	64	10	functions	function	NOUN
ejpam-3293	64	11	in	in	ADP
ejpam-3293	64	12	this	this	DET
ejpam-3293	64	13	section	section	NOUN
ejpam-3293	64	14	,	,	PUNCT
ejpam-3293	64	15	we	we	PRON
ejpam-3293	64	16	investigate	investigate	VERB
ejpam-3293	64	17	the	the	DET
ejpam-3293	64	18	connection	connection	NOUN
ejpam-3293	64	19	of	of	ADP
ejpam-3293	64	20	ω	ω	NOUN
ejpam-3293	64	21	-	-	ADJ
ejpam-3293	64	22	open	open	ADJ
ejpam-3293	64	23	(	(	PUNCT
ejpam-3293	64	24	resp	resp	NOUN
ejpam-3293	64	25	.	.	PUNCT
ejpam-3293	64	26	,	,	PUNCT
ejpam-3293	64	27	ω	ω	X
ejpam-3293	64	28	-	-	ADJ
ejpam-3293	64	29	closed	closed	ADJ
ejpam-3293	64	30	)	)	PUNCT
ejpam-3293	64	31	function	function	NOUN
ejpam-3293	64	32	to	to	ADP
ejpam-3293	64	33	the	the	DET
ejpam-3293	64	34	other	other	ADJ
ejpam-3293	64	35	well	well	ADV
ejpam-3293	64	36	-	-	PUNCT
ejpam-3293	64	37	known	know	VERB
ejpam-3293	64	38	functions	function	NOUN
ejpam-3293	64	39	such	such	ADJ
ejpam-3293	64	40	as	as	ADP
ejpam-3293	64	41	open	open	ADJ
ejpam-3293	64	42	,	,	PUNCT
ejpam-3293	64	43	θ	θ	NOUN
ejpam-3293	64	44	-	-	NOUN
ejpam-3293	64	45	open	open	ADJ
ejpam-3293	64	46	,	,	PUNCT
ejpam-3293	64	47	and	and	CCONJ
ejpam-3293	64	48	ωθ	ωθ	X
ejpam-3293	64	49	-	-	PUNCT
ejpam-3293	64	50	open	open	ADJ
ejpam-3293	64	51	(	(	PUNCT
ejpam-3293	64	52	resp	resp	NOUN
ejpam-3293	64	53	.	.	PROPN
ejpam-3293	64	54	,	,	PUNCT
ejpam-3293	64	55	closed	close	VERB
ejpam-3293	64	56	,	,	PUNCT
ejpam-3293	64	57	θ	θ	NOUN
ejpam-3293	64	58	-	-	ADJ
ejpam-3293	64	59	closed	closed	ADJ
ejpam-3293	64	60	,	,	PUNCT
ejpam-3293	64	61	ωθclosed	ωθclosed	ADJ
ejpam-3293	64	62	)	)	PUNCT
ejpam-3293	64	63	functions	function	NOUN
ejpam-3293	64	64	.	.	PUNCT
ejpam-3293	65	1	we	we	PRON
ejpam-3293	65	2	also	also	ADV
ejpam-3293	65	3	give	give	VERB
ejpam-3293	65	4	some	some	DET
ejpam-3293	65	5	characterizations	characterization	NOUN
ejpam-3293	65	6	of	of	ADP
ejpam-3293	65	7	ω	ω	NOUN
ejpam-3293	65	8	-	-	ADJ
ejpam-3293	65	9	open	open	ADJ
ejpam-3293	65	10	and	and	CCONJ
ejpam-3293	65	11	ω	ω	VERB
ejpam-3293	65	12	-	-	PUNCT
ejpam-3293	65	13	closed	close	VERB
ejpam-3293	65	14	functions	function	NOUN
ejpam-3293	65	15	.	.	PUNCT
ejpam-3293	66	1	throughout	throughout	ADP
ejpam-3293	66	2	,	,	PUNCT
ejpam-3293	66	3	if	if	SCONJ
ejpam-3293	66	4	no	no	DET
ejpam-3293	66	5	confusion	confusion	NOUN
ejpam-3293	66	6	arises	arise	VERB
ejpam-3293	66	7	,	,	PUNCT
ejpam-3293	66	8	let	let	VERB
ejpam-3293	66	9	x	x	PRON
ejpam-3293	66	10	and	and	CCONJ
ejpam-3293	66	11	y	y	PROPN
ejpam-3293	66	12	be	be	AUX
ejpam-3293	66	13	topological	topological	ADJ
ejpam-3293	66	14	spaces	space	NOUN
ejpam-3293	66	15	.	.	PUNCT
ejpam-3293	67	1	we	we	PRON
ejpam-3293	67	2	shall	shall	AUX
ejpam-3293	67	3	be	be	AUX
ejpam-3293	67	4	using	use	VERB
ejpam-3293	67	5	the	the	DET
ejpam-3293	67	6	following	follow	VERB
ejpam-3293	67	7	lemma	lemma	PROPN
ejpam-3293	67	8	later	later	ADV
ejpam-3293	67	9	.	.	PUNCT
ejpam-3293	68	1	lemma	lemma	PROPN
ejpam-3293	68	2	1	1	X
ejpam-3293	68	3	.	.	PUNCT
ejpam-3293	69	1	let	let	VERB
ejpam-3293	69	2	f	f	NOUN
ejpam-3293	69	3	:	:	PUNCT
ejpam-3293	69	4	x	x	X
ejpam-3293	69	5	→	→	SYM
ejpam-3293	69	6	y	y	X
ejpam-3293	69	7	be	be	AUX
ejpam-3293	69	8	a	a	DET
ejpam-3293	69	9	bijective	bijective	ADJ
ejpam-3293	69	10	function	function	NOUN
ejpam-3293	69	11	.	.	PUNCT
ejpam-3293	70	1	then	then	ADV
ejpam-3293	70	2	f	f	PROPN
ejpam-3293	70	3	is	be	AUX
ejpam-3293	70	4	ω	ω	NOUN
ejpam-3293	70	5	-	-	NOUN
ejpam-3293	70	6	open	open	ADJ
ejpam-3293	70	7	on	on	ADP
ejpam-3293	70	8	x	x	SYM
ejpam-3293	70	9	if	if	SCONJ
ejpam-3293	70	10	and	and	CCONJ
ejpam-3293	70	11	only	only	ADV
ejpam-3293	70	12	if	if	SCONJ
ejpam-3293	70	13	it	it	PRON
ejpam-3293	70	14	is	be	AUX
ejpam-3293	70	15	ω	ω	NOUN
ejpam-3293	70	16	-	-	ADJ
ejpam-3293	70	17	closed	closed	ADJ
ejpam-3293	70	18	on	on	ADP
ejpam-3293	70	19	x.	x.	NOUN
ejpam-3293	70	20	remark	remark	PROPN
ejpam-3293	70	21	1	1	NUM
ejpam-3293	70	22	.	.	PUNCT
ejpam-3293	71	1	[	[	X
ejpam-3293	71	2	3	3	NUM
ejpam-3293	71	3	,	,	PUNCT
ejpam-3293	71	4	remark	remark	NOUN
ejpam-3293	71	5	4	4	NUM
ejpam-3293	71	6	]	]	PUNCT
ejpam-3293	71	7	let	let	VERB
ejpam-3293	71	8	a	a	DET
ejpam-3293	71	9	⊆	⊆	NUM
ejpam-3293	71	10	x.	x.	NOUN
ejpam-3293	71	11	then	then	ADV
ejpam-3293	71	12	(	(	PUNCT
ejpam-3293	71	13	i	i	NOUN
ejpam-3293	71	14	)	)	PUNCT
ejpam-3293	71	15	if	if	SCONJ
ejpam-3293	71	16	a	a	PRON
ejpam-3293	71	17	is	be	AUX
ejpam-3293	71	18	open	open	ADJ
ejpam-3293	71	19	,	,	PUNCT
ejpam-3293	71	20	then	then	ADV
ejpam-3293	71	21	a	a	PRON
ejpam-3293	71	22	is	be	AUX
ejpam-3293	71	23	ω	ω	NOUN
ejpam-3293	71	24	-	-	NOUN
ejpam-3293	71	25	open	open	ADJ
ejpam-3293	71	26	;	;	PUNCT
ejpam-3293	71	27	(	(	PUNCT
ejpam-3293	71	28	ii	ii	NOUN
ejpam-3293	71	29	)	)	PUNCT
ejpam-3293	71	30	if	if	SCONJ
ejpam-3293	71	31	a	a	PRON
ejpam-3293	71	32	is	be	AUX
ejpam-3293	71	33	θ	θ	NOUN
ejpam-3293	71	34	-	-	ADJ
ejpam-3293	71	35	open	open	ADJ
ejpam-3293	71	36	,	,	PUNCT
ejpam-3293	71	37	then	then	ADV
ejpam-3293	71	38	a	a	PRON
ejpam-3293	71	39	is	be	AUX
ejpam-3293	71	40	open	open	ADJ
ejpam-3293	71	41	;	;	PUNCT
ejpam-3293	71	42	(	(	PUNCT
ejpam-3293	71	43	iii	iii	X
ejpam-3293	71	44	)	)	PUNCT
ejpam-3293	71	45	if	if	SCONJ
ejpam-3293	71	46	a	a	PRON
ejpam-3293	71	47	is	be	AUX
ejpam-3293	71	48	θ	θ	NOUN
ejpam-3293	71	49	-	-	ADJ
ejpam-3293	71	50	open	open	ADJ
ejpam-3293	71	51	,	,	PUNCT
ejpam-3293	71	52	then	then	ADV
ejpam-3293	71	53	a	a	PRON
ejpam-3293	71	54	is	be	AUX
ejpam-3293	71	55	ωθ	ωθ	NOUN
ejpam-3293	71	56	-	-	PUNCT
ejpam-3293	71	57	open	open	ADJ
ejpam-3293	71	58	;	;	PUNCT
ejpam-3293	71	59	and	and	CCONJ
ejpam-3293	71	60	(	(	PUNCT
ejpam-3293	71	61	iv	iv	X
ejpam-3293	71	62	)	)	PUNCT
ejpam-3293	71	63	if	if	SCONJ
ejpam-3293	71	64	a	a	PRON
ejpam-3293	71	65	is	be	AUX
ejpam-3293	71	66	ωθ	ωθ	NOUN
ejpam-3293	71	67	-	-	PUNCT
ejpam-3293	71	68	open	open	ADJ
ejpam-3293	71	69	,	,	PUNCT
ejpam-3293	71	70	then	then	ADV
ejpam-3293	71	71	a	a	PRON
ejpam-3293	71	72	is	be	AUX
ejpam-3293	71	73	ω	ω	NOUN
ejpam-3293	71	74	-	-	ADJ
ejpam-3293	71	75	open	open	ADJ
ejpam-3293	71	76	.	.	PUNCT
ejpam-3293	72	1	m.	m.	NOUN
ejpam-3293	72	2	labendia	labendia	PROPN
ejpam-3293	72	3	,	,	PUNCT
ejpam-3293	72	4	j.	j.	PROPN
ejpam-3293	72	5	a.	a.	PROPN
ejpam-3293	72	6	sasam	sasam	PROPN
ejpam-3293	72	7	/	/	SYM
ejpam-3293	72	8	eur	eur	PROPN
ejpam-3293	72	9	.	.	PUNCT
ejpam-3293	73	1	j.	j.	PROPN
ejpam-3293	73	2	pure	pure	PROPN
ejpam-3293	73	3	appl	appl	PROPN
ejpam-3293	73	4	.	.	PROPN
ejpam-3293	73	5	math	math	PROPN
ejpam-3293	73	6	,	,	PUNCT
ejpam-3293	73	7	11	11	NUM
ejpam-3293	73	8	(	(	PUNCT
ejpam-3293	73	9	3	3	NUM
ejpam-3293	73	10	)	)	PUNCT
ejpam-3293	73	11	(	(	PUNCT
ejpam-3293	73	12	2018	2018	NUM
ejpam-3293	73	13	)	)	PUNCT
ejpam-3293	73	14	,	,	PUNCT
ejpam-3293	73	15	834	834	NUM
ejpam-3293	73	16	-	-	SYM
ejpam-3293	73	17	843	843	NUM
ejpam-3293	73	18	837	837	NUM
ejpam-3293	73	19	it	it	PRON
ejpam-3293	73	20	is	be	AUX
ejpam-3293	73	21	shown	show	VERB
ejpam-3293	73	22	in	in	ADP
ejpam-3293	73	23	[	[	X
ejpam-3293	73	24	3	3	NUM
ejpam-3293	73	25	,	,	PUNCT
ejpam-3293	73	26	p.295	p.295	VERB
ejpam-3293	73	27	]	]	PUNCT
ejpam-3293	73	28	that	that	SCONJ
ejpam-3293	73	29	the	the	DET
ejpam-3293	73	30	implications	implication	NOUN
ejpam-3293	73	31	above	above	ADV
ejpam-3293	73	32	are	be	AUX
ejpam-3293	73	33	not	not	PART
ejpam-3293	73	34	reversible	reversible	ADJ
ejpam-3293	73	35	.	.	PUNCT
ejpam-3293	74	1	remark	remark	NOUN
ejpam-3293	74	2	2	2	NUM
ejpam-3293	74	3	.	.	PUNCT
ejpam-3293	75	1	let	let	VERB
ejpam-3293	75	2	f	f	NOUN
ejpam-3293	75	3	:	:	PUNCT
ejpam-3293	75	4	x	x	X
ejpam-3293	75	5	→	→	SYM
ejpam-3293	75	6	y	y	X
ejpam-3293	75	7	be	be	AUX
ejpam-3293	75	8	a	a	DET
ejpam-3293	75	9	function	function	NOUN
ejpam-3293	75	10	.	.	PUNCT
ejpam-3293	76	1	then	then	ADV
ejpam-3293	76	2	(	(	PUNCT
ejpam-3293	76	3	i	i	NOUN
ejpam-3293	76	4	)	)	PUNCT
ejpam-3293	76	5	if	if	SCONJ
ejpam-3293	76	6	f	f	PROPN
ejpam-3293	76	7	is	be	AUX
ejpam-3293	76	8	open	open	ADJ
ejpam-3293	76	9	(	(	PUNCT
ejpam-3293	76	10	resp	resp	NOUN
ejpam-3293	76	11	.	.	PROPN
ejpam-3293	76	12	,	,	PUNCT
ejpam-3293	76	13	closed	closed	ADJ
ejpam-3293	76	14	)	)	PUNCT
ejpam-3293	76	15	,	,	PUNCT
ejpam-3293	76	16	then	then	ADV
ejpam-3293	76	17	f	f	PROPN
ejpam-3293	76	18	is	be	AUX
ejpam-3293	76	19	ω	ω	NOUN
ejpam-3293	76	20	-	-	ADJ
ejpam-3293	76	21	open	open	ADJ
ejpam-3293	76	22	(	(	PUNCT
ejpam-3293	76	23	resp	resp	NOUN
ejpam-3293	76	24	.	.	PUNCT
ejpam-3293	76	25	,	,	PUNCT
ejpam-3293	77	1	ω	ω	X
ejpam-3293	77	2	-	-	PUNCT
ejpam-3293	77	3	closed	closed	ADJ
ejpam-3293	77	4	)	)	PUNCT
ejpam-3293	77	5	.	.	PUNCT
ejpam-3293	78	1	(	(	PUNCT
ejpam-3293	78	2	ii	ii	NOUN
ejpam-3293	78	3	)	)	PUNCT
ejpam-3293	78	4	if	if	SCONJ
ejpam-3293	78	5	f	f	PROPN
ejpam-3293	78	6	is	be	AUX
ejpam-3293	78	7	ωθ	ωθ	NOUN
ejpam-3293	78	8	-	-	PUNCT
ejpam-3293	78	9	open	open	ADJ
ejpam-3293	78	10	(	(	PUNCT
ejpam-3293	78	11	resp	resp	NOUN
ejpam-3293	78	12	.	.	PROPN
ejpam-3293	78	13	,	,	PUNCT
ejpam-3293	78	14	ωθ	ωθ	NOUN
ejpam-3293	78	15	-	-	PUNCT
ejpam-3293	78	16	closed	closed	ADJ
ejpam-3293	78	17	)	)	PUNCT
ejpam-3293	78	18	,	,	PUNCT
ejpam-3293	78	19	then	then	ADV
ejpam-3293	78	20	f	f	PROPN
ejpam-3293	78	21	is	be	AUX
ejpam-3293	78	22	ω	ω	NOUN
ejpam-3293	78	23	-	-	ADJ
ejpam-3293	78	24	open	open	ADJ
ejpam-3293	78	25	(	(	PUNCT
ejpam-3293	78	26	resp	resp	NOUN
ejpam-3293	78	27	.	.	PUNCT
ejpam-3293	78	28	,	,	PUNCT
ejpam-3293	79	1	ω	ω	X
ejpam-3293	79	2	-	-	PUNCT
ejpam-3293	79	3	closed	closed	ADJ
ejpam-3293	79	4	)	)	PUNCT
ejpam-3293	79	5	.	.	PUNCT
ejpam-3293	80	1	remark	remark	PROPN
ejpam-3293	80	2	3	3	NUM
ejpam-3293	80	3	.	.	PUNCT
ejpam-3293	81	1	the	the	DET
ejpam-3293	81	2	converses	converse	NOUN
ejpam-3293	81	3	of	of	ADP
ejpam-3293	81	4	remark	remark	NOUN
ejpam-3293	81	5	2	2	NUM
ejpam-3293	81	6	(	(	PUNCT
ejpam-3293	81	7	i	i	NOUN
ejpam-3293	81	8	)	)	PUNCT
ejpam-3293	81	9	and	and	CCONJ
ejpam-3293	81	10	(	(	PUNCT
ejpam-3293	81	11	ii	ii	NOUN
ejpam-3293	81	12	)	)	PUNCT
ejpam-3293	81	13	do	do	AUX
ejpam-3293	81	14	not	not	PART
ejpam-3293	81	15	necessarily	necessarily	ADV
ejpam-3293	81	16	hold	hold	VERB
ejpam-3293	81	17	.	.	PUNCT
ejpam-3293	82	1	(	(	PUNCT
ejpam-3293	82	2	i	i	NOUN
ejpam-3293	82	3	):	):	PUNCT
ejpam-3293	82	4	first	first	ADV
ejpam-3293	82	5	,	,	PUNCT
ejpam-3293	82	6	consider	consider	VERB
ejpam-3293	82	7	the	the	DET
ejpam-3293	82	8	topological	topological	ADJ
ejpam-3293	82	9	spaces	space	NOUN
ejpam-3293	82	10	x	x	PUNCT
ejpam-3293	83	1	=	=	PUNCT
ejpam-3293	83	2	z	z	NOUN
ejpam-3293	83	3	=	=	SYM
ejpam-3293	83	4	y	y	PROPN
ejpam-3293	83	5	=	=	PUNCT
ejpam-3293	83	6	{	{	PUNCT
ejpam-3293	83	7	a	a	PRON
ejpam-3293	83	8	,	,	PUNCT
ejpam-3293	83	9	b	b	NOUN
ejpam-3293	83	10	,	,	PUNCT
ejpam-3293	83	11	c	c	NOUN
ejpam-3293	83	12	,	,	PUNCT
ejpam-3293	83	13	d	d	NOUN
ejpam-3293	83	14	}	}	PUNCT
ejpam-3293	83	15	with	with	ADP
ejpam-3293	83	16	respective	respective	ADJ
ejpam-3293	83	17	topologies	topology	NOUN
ejpam-3293	83	18	tx	tx	VERB
ejpam-3293	83	19	=	=	SYM
ejpam-3293	83	20	{	{	PUNCT
ejpam-3293	83	21	∅	∅	NOUN
ejpam-3293	83	22	,	,	PUNCT
ejpam-3293	83	23	x	x	X
ejpam-3293	83	24	,	,	PUNCT
ejpam-3293	83	25	{	{	PUNCT
ejpam-3293	83	26	a	a	PRON
ejpam-3293	83	27	,	,	PUNCT
ejpam-3293	83	28	b	b	NOUN
ejpam-3293	83	29	,	,	PUNCT
ejpam-3293	83	30	c	c	NOUN
ejpam-3293	83	31	}	}	PUNCT
ejpam-3293	83	32	}	}	PUNCT
ejpam-3293	83	33	,	,	PUNCT
ejpam-3293	83	34	tz	tz	PROPN
ejpam-3293	83	35	=	=	SYM
ejpam-3293	83	36	{	{	PUNCT
ejpam-3293	83	37	∅	∅	NOUN
ejpam-3293	83	38	,	,	PUNCT
ejpam-3293	83	39	z	z	PROPN
ejpam-3293	83	40	,	,	PUNCT
ejpam-3293	83	41	{	{	PUNCT
ejpam-3293	83	42	a	a	PRON
ejpam-3293	83	43	,	,	PUNCT
ejpam-3293	83	44	b	b	NOUN
ejpam-3293	83	45	}	}	PUNCT
ejpam-3293	83	46	}	}	PUNCT
ejpam-3293	83	47	,	,	PUNCT
ejpam-3293	83	48	and	and	CCONJ
ejpam-3293	83	49	ty	ty	INTJ
ejpam-3293	83	50	=	=	SYM
ejpam-3293	83	51	{	{	PUNCT
ejpam-3293	83	52	∅	∅	NOUN
ejpam-3293	83	53	,	,	PUNCT
ejpam-3293	83	54	y	y	PROPN
ejpam-3293	83	55	,	,	PUNCT
ejpam-3293	83	56	{	{	PUNCT
ejpam-3293	83	57	a	a	X
ejpam-3293	83	58	}	}	PUNCT
ejpam-3293	83	59	,	,	PUNCT
ejpam-3293	83	60	{	{	PUNCT
ejpam-3293	83	61	d	d	NOUN
ejpam-3293	83	62	}	}	PUNCT
ejpam-3293	83	63	,	,	PUNCT
ejpam-3293	83	64	{	{	PUNCT
ejpam-3293	83	65	a	a	PRON
ejpam-3293	83	66	,	,	PUNCT
ejpam-3293	83	67	d	d	NOUN
ejpam-3293	83	68	}	}	PUNCT
ejpam-3293	83	69	,	,	PUNCT
ejpam-3293	83	70	{	{	PUNCT
ejpam-3293	83	71	a	a	DET
ejpam-3293	83	72	,	,	PUNCT
ejpam-3293	83	73	b	b	NOUN
ejpam-3293	83	74	}	}	PUNCT
ejpam-3293	83	75	,	,	PUNCT
ejpam-3293	83	76	{	{	PUNCT
ejpam-3293	83	77	a	a	PRON
ejpam-3293	83	78	,	,	PUNCT
ejpam-3293	83	79	b	b	NOUN
ejpam-3293	83	80	,	,	PUNCT
ejpam-3293	83	81	d	d	NOUN
ejpam-3293	83	82	}	}	PUNCT
ejpam-3293	83	83	}	}	PUNCT
ejpam-3293	83	84	.	.	PUNCT
ejpam-3293	84	1	define	define	VERB
ejpam-3293	84	2	f	f	NOUN
ejpam-3293	84	3	:	:	PUNCT
ejpam-3293	84	4	x	x	X
ejpam-3293	84	5	→	→	SYM
ejpam-3293	84	6	y	y	PROPN
ejpam-3293	84	7	by	by	ADP
ejpam-3293	84	8	f(a	f(a	PROPN
ejpam-3293	84	9	)	)	PUNCT
ejpam-3293	84	10	=	=	SYM
ejpam-3293	85	1	a	a	PRON
ejpam-3293	85	2	,	,	PUNCT
ejpam-3293	85	3	f(b	f(b	PROPN
ejpam-3293	85	4	)	)	PUNCT
ejpam-3293	85	5	=	=	SYM
ejpam-3293	85	6	b	b	PROPN
ejpam-3293	85	7	,	,	PUNCT
ejpam-3293	85	8	f(c	f(c	PROPN
ejpam-3293	85	9	)	)	PUNCT
ejpam-3293	85	10	=	=	SYM
ejpam-3293	85	11	c	c	NOUN
ejpam-3293	85	12	,	,	PUNCT
ejpam-3293	85	13	and	and	CCONJ
ejpam-3293	85	14	f(d	f(d	PROPN
ejpam-3293	85	15	)	)	PUNCT
ejpam-3293	85	16	=	=	NOUN
ejpam-3293	85	17	a.	a.	NOUN
ejpam-3293	85	18	define	define	VERB
ejpam-3293	85	19	g	g	PROPN
ejpam-3293	85	20	:	:	PUNCT
ejpam-3293	85	21	z	z	PROPN
ejpam-3293	85	22	→	→	SYM
ejpam-3293	85	23	y	y	PROPN
ejpam-3293	85	24	by	by	ADP
ejpam-3293	85	25	g(a	g(a	PROPN
ejpam-3293	85	26	)	)	PUNCT
ejpam-3293	85	27	=	=	PUNCT
ejpam-3293	86	1	g(b	g(b	X
ejpam-3293	86	2	)	)	PUNCT
ejpam-3293	86	3	=	=	SYM
ejpam-3293	86	4	g(c	g(c	NOUN
ejpam-3293	86	5	)	)	PUNCT
ejpam-3293	86	6	=	=	SYM
ejpam-3293	87	1	g(d	g(d	PROPN
ejpam-3293	87	2	)	)	PUNCT
ejpam-3293	87	3	=	=	SYM
ejpam-3293	88	1	d.	d.	PROPN
ejpam-3293	88	2	since	since	SCONJ
ejpam-3293	88	3	y	y	PROPN
ejpam-3293	88	4	is	be	AUX
ejpam-3293	88	5	countable	countable	ADJ
ejpam-3293	88	6	,	,	PUNCT
ejpam-3293	88	7	f(a	f(a	NOUN
ejpam-3293	88	8	)	)	PUNCT
ejpam-3293	88	9	is	be	AUX
ejpam-3293	88	10	ω	ω	NOUN
ejpam-3293	88	11	-	-	NOUN
ejpam-3293	88	12	open	open	ADJ
ejpam-3293	88	13	in	in	ADP
ejpam-3293	88	14	y	y	PROPN
ejpam-3293	88	15	for	for	ADP
ejpam-3293	88	16	every	every	DET
ejpam-3293	88	17	open	open	NOUN
ejpam-3293	88	18	set	set	NOUN
ejpam-3293	88	19	a	a	PRON
ejpam-3293	88	20	of	of	ADP
ejpam-3293	88	21	x.	x.	NOUN
ejpam-3293	88	22	however	however	ADV
ejpam-3293	88	23	,	,	PUNCT
ejpam-3293	88	24	f({a	f({a	PROPN
ejpam-3293	88	25	,	,	PUNCT
ejpam-3293	88	26	b	b	PROPN
ejpam-3293	88	27	,	,	PUNCT
ejpam-3293	88	28	c	c	NOUN
ejpam-3293	88	29	}	}	PUNCT
ejpam-3293	88	30	)	)	PUNCT
ejpam-3293	89	1	=	=	PRON
ejpam-3293	89	2	{	{	PUNCT
ejpam-3293	89	3	a	a	PRON
ejpam-3293	89	4	,	,	PUNCT
ejpam-3293	89	5	b	b	NOUN
ejpam-3293	89	6	,	,	PUNCT
ejpam-3293	89	7	c	c	NOUN
ejpam-3293	89	8	}	}	PUNCT
ejpam-3293	89	9	is	be	AUX
ejpam-3293	89	10	not	not	PART
ejpam-3293	89	11	open	open	ADJ
ejpam-3293	89	12	in	in	ADP
ejpam-3293	89	13	y	y	PROPN
ejpam-3293	89	14	.	.	PUNCT
ejpam-3293	90	1	thus	thus	ADV
ejpam-3293	90	2	,	,	PUNCT
ejpam-3293	90	3	f	f	PROPN
ejpam-3293	90	4	is	be	AUX
ejpam-3293	90	5	ω	ω	NOUN
ejpam-3293	90	6	-	-	ADJ
ejpam-3293	90	7	open	open	ADJ
ejpam-3293	90	8	but	but	CCONJ
ejpam-3293	90	9	not	not	PART
ejpam-3293	90	10	open	open	VERB
ejpam-3293	90	11	on	on	ADP
ejpam-3293	90	12	x.	x.	NOUN
ejpam-3293	90	13	since	since	SCONJ
ejpam-3293	90	14	y	y	PROPN
ejpam-3293	90	15	is	be	AUX
ejpam-3293	90	16	countable	countable	ADJ
ejpam-3293	90	17	,	,	PUNCT
ejpam-3293	90	18	g(a	g(a	PROPN
ejpam-3293	90	19	)	)	PUNCT
ejpam-3293	90	20	is	be	AUX
ejpam-3293	90	21	ω	ω	NOUN
ejpam-3293	90	22	-	-	ADJ
ejpam-3293	90	23	closed	closed	ADJ
ejpam-3293	90	24	in	in	ADP
ejpam-3293	90	25	y	y	PROPN
ejpam-3293	90	26	for	for	ADP
ejpam-3293	90	27	every	every	DET
ejpam-3293	90	28	closed	close	VERB
ejpam-3293	90	29	set	set	NOUN
ejpam-3293	90	30	a	a	PRON
ejpam-3293	90	31	in	in	ADP
ejpam-3293	90	32	x.	x.	NOUN
ejpam-3293	90	33	however	however	ADV
ejpam-3293	90	34	,	,	PUNCT
ejpam-3293	90	35	g({c	g({c	ADJ
ejpam-3293	90	36	,	,	PUNCT
ejpam-3293	90	37	d	d	NOUN
ejpam-3293	90	38	}	}	PUNCT
ejpam-3293	90	39	)	)	PUNCT
ejpam-3293	91	1	=	=	PRON
ejpam-3293	91	2	{	{	PUNCT
ejpam-3293	91	3	d	d	X
ejpam-3293	91	4	}	}	PUNCT
ejpam-3293	91	5	is	be	AUX
ejpam-3293	91	6	not	not	PART
ejpam-3293	91	7	closed	close	VERB
ejpam-3293	91	8	in	in	ADP
ejpam-3293	91	9	y	y	PROPN
ejpam-3293	91	10	.	.	PUNCT
ejpam-3293	92	1	thus	thus	ADV
ejpam-3293	92	2	,	,	PUNCT
ejpam-3293	92	3	g	g	PROPN
ejpam-3293	92	4	is	be	AUX
ejpam-3293	92	5	ω	ω	NOUN
ejpam-3293	92	6	-	-	ADJ
ejpam-3293	92	7	closed	closed	ADJ
ejpam-3293	92	8	but	but	CCONJ
ejpam-3293	92	9	not	not	PART
ejpam-3293	92	10	closed	close	VERB
ejpam-3293	92	11	on	on	ADP
ejpam-3293	92	12	z.	z.	PROPN
ejpam-3293	92	13	(	(	PUNCT
ejpam-3293	92	14	ii	ii	PROPN
ejpam-3293	92	15	):	):	PUNCT
ejpam-3293	92	16	next	next	ADV
ejpam-3293	92	17	,	,	PUNCT
ejpam-3293	92	18	consider	consider	VERB
ejpam-3293	92	19	r	r	NOUN
ejpam-3293	92	20	with	with	ADP
ejpam-3293	92	21	topologies	topology	NOUN
ejpam-3293	92	22	t1	t1	NOUN
ejpam-3293	92	23	=	=	PUNCT
ejpam-3293	92	24	{	{	PUNCT
ejpam-3293	92	25	∅,r	∅,r	PROPN
ejpam-3293	92	26	,	,	PUNCT
ejpam-3293	92	27	qc	qc	PROPN
ejpam-3293	92	28	∪	∪	X
ejpam-3293	92	29	{	{	PUNCT
ejpam-3293	92	30	0	0	NUM
ejpam-3293	92	31	}	}	PUNCT
ejpam-3293	92	32	}	}	PUNCT
ejpam-3293	92	33	and	and	CCONJ
ejpam-3293	92	34	t2	t2	PROPN
ejpam-3293	92	35	=	=	SYM
ejpam-3293	92	36	{	{	PUNCT
ejpam-3293	92	37	∅,r	∅,r	PROPN
ejpam-3293	92	38	,	,	PUNCT
ejpam-3293	92	39	qc	qc	PROPN
ejpam-3293	92	40	}	}	PUNCT
ejpam-3293	92	41	.	.	PUNCT
ejpam-3293	93	1	define	define	VERB
ejpam-3293	93	2	f	f	NOUN
ejpam-3293	93	3	:	:	PUNCT
ejpam-3293	93	4	(	(	PUNCT
ejpam-3293	93	5	r	r	NOUN
ejpam-3293	93	6	,	,	PUNCT
ejpam-3293	93	7	t1	t1	NOUN
ejpam-3293	93	8	)	)	PUNCT
ejpam-3293	93	9	→	→	SYM
ejpam-3293	93	10	(	(	PUNCT
ejpam-3293	93	11	r	r	NOUN
ejpam-3293	93	12	,	,	PUNCT
ejpam-3293	93	13	t2	t2	NOUN
ejpam-3293	93	14	)	)	PUNCT
ejpam-3293	93	15	by	by	ADP
ejpam-3293	93	16	f(x	f(x	PROPN
ejpam-3293	93	17	)	)	PUNCT
ejpam-3293	94	1	=	=	PUNCT
ejpam-3293	94	2	x	x	PUNCT
ejpam-3293	94	3	for	for	ADP
ejpam-3293	94	4	all	all	DET
ejpam-3293	94	5	x	x	SYM
ejpam-3293	94	6	∈	∈	PROPN
ejpam-3293	94	7	r.	r.	NOUN
ejpam-3293	94	8	we	we	PRON
ejpam-3293	94	9	will	will	AUX
ejpam-3293	94	10	show	show	VERB
ejpam-3293	94	11	first	first	ADV
ejpam-3293	94	12	that	that	SCONJ
ejpam-3293	94	13	qc	qc	PROPN
ejpam-3293	94	14	∪	∪	X
ejpam-3293	94	15	{	{	PUNCT
ejpam-3293	94	16	0	0	NUM
ejpam-3293	94	17	}	}	PUNCT
ejpam-3293	94	18	is	be	AUX
ejpam-3293	94	19	ω	ω	NOUN
ejpam-3293	94	20	-	-	NOUN
ejpam-3293	94	21	open	open	ADJ
ejpam-3293	94	22	in	in	ADP
ejpam-3293	94	23	t2	t2	NOUN
ejpam-3293	94	24	.	.	PUNCT
ejpam-3293	95	1	let	let	VERB
ejpam-3293	95	2	x	x	SYM
ejpam-3293	95	3	∈	∈	PROPN
ejpam-3293	95	4	qc	qc	PROPN
ejpam-3293	95	5	∪	∪	X
ejpam-3293	95	6	{	{	PUNCT
ejpam-3293	95	7	0	0	NUM
ejpam-3293	95	8	}	}	PUNCT
ejpam-3293	95	9	.	.	PUNCT
ejpam-3293	96	1	then	then	ADV
ejpam-3293	96	2	x	x	SYM
ejpam-3293	96	3	∈	∈	NOUN
ejpam-3293	96	4	r	r	NOUN
ejpam-3293	96	5	and	and	CCONJ
ejpam-3293	96	6	r\(qc	r\(qc	ADJ
ejpam-3293	96	7	∪	∪	ADJ
ejpam-3293	96	8	{	{	PUNCT
ejpam-3293	96	9	0	0	NUM
ejpam-3293	96	10	}	}	PUNCT
ejpam-3293	96	11	)	)	PUNCT
ejpam-3293	96	12	=	=	SYM
ejpam-3293	96	13	q\{0	q\{0	NOUN
ejpam-3293	96	14	}	}	PUNCT
ejpam-3293	96	15	is	be	AUX
ejpam-3293	96	16	countable	countable	ADJ
ejpam-3293	96	17	.	.	PUNCT
ejpam-3293	97	1	hence	hence	ADV
ejpam-3293	97	2	,	,	PUNCT
ejpam-3293	97	3	qc∪{0	qc∪{0	PROPN
ejpam-3293	97	4	}	}	PUNCT
ejpam-3293	97	5	is	be	AUX
ejpam-3293	97	6	ω	ω	NOUN
ejpam-3293	97	7	-	-	NOUN
ejpam-3293	97	8	open	open	ADJ
ejpam-3293	97	9	in	in	ADP
ejpam-3293	97	10	t2	t2	NOUN
ejpam-3293	97	11	.	.	PUNCT
ejpam-3293	98	1	since	since	SCONJ
ejpam-3293	98	2	f(qc∪{0	f(qc∪{0	NOUN
ejpam-3293	98	3	}	}	PUNCT
ejpam-3293	98	4	)	)	PUNCT
ejpam-3293	98	5	=	=	SYM
ejpam-3293	98	6	qc∪{0	qc∪{0	PROPN
ejpam-3293	98	7	}	}	PUNCT
ejpam-3293	98	8	,	,	PUNCT
ejpam-3293	98	9	f	f	PROPN
ejpam-3293	98	10	is	be	AUX
ejpam-3293	98	11	ω	ω	NOUN
ejpam-3293	98	12	-	-	NOUN
ejpam-3293	98	13	open	open	ADJ
ejpam-3293	98	14	on	on	ADP
ejpam-3293	98	15	(	(	PUNCT
ejpam-3293	98	16	r	r	NOUN
ejpam-3293	98	17	,	,	PUNCT
ejpam-3293	98	18	t1	t1	NOUN
ejpam-3293	98	19	)	)	PUNCT
ejpam-3293	98	20	.	.	PUNCT
ejpam-3293	99	1	next	next	ADV
ejpam-3293	99	2	we	we	PRON
ejpam-3293	99	3	show	show	VERB
ejpam-3293	99	4	that	that	SCONJ
ejpam-3293	99	5	every	every	DET
ejpam-3293	99	6	nonempty	nonempty	ADV
ejpam-3293	99	7	proper	proper	ADJ
ejpam-3293	99	8	subset	subset	NOUN
ejpam-3293	99	9	a	a	PRON
ejpam-3293	99	10	of	of	ADP
ejpam-3293	99	11	r	r	NOUN
ejpam-3293	99	12	is	be	AUX
ejpam-3293	99	13	not	not	PART
ejpam-3293	99	14	ωθ	ωθ	NOUN
ejpam-3293	99	15	-	-	PUNCT
ejpam-3293	99	16	open	open	ADJ
ejpam-3293	99	17	in	in	ADP
ejpam-3293	99	18	(	(	PUNCT
ejpam-3293	99	19	r	r	NOUN
ejpam-3293	99	20	,	,	PUNCT
ejpam-3293	99	21	t2	t2	NOUN
ejpam-3293	99	22	)	)	PUNCT
ejpam-3293	99	23	.	.	PUNCT
ejpam-3293	100	1	suppose	suppose	VERB
ejpam-3293	100	2	that	that	SCONJ
ejpam-3293	100	3	ints(a	ints(a	PROPN
ejpam-3293	100	4	)	)	PUNCT
ejpam-3293	100	5	6=	6=	ADP
ejpam-3293	100	6	∅.	∅.	PROPN
ejpam-3293	100	7	note	note	NOUN
ejpam-3293	100	8	first	first	ADV
ejpam-3293	100	9	that	that	SCONJ
ejpam-3293	100	10	the	the	DET
ejpam-3293	100	11	only	only	ADV
ejpam-3293	100	12	nonempty	nonempty	ADJ
ejpam-3293	100	13	open	open	ADJ
ejpam-3293	100	14	sets	set	NOUN
ejpam-3293	100	15	in	in	ADP
ejpam-3293	100	16	t2	t2	NOUN
ejpam-3293	100	17	are	be	AUX
ejpam-3293	100	18	r	r	NOUN
ejpam-3293	100	19	and	and	CCONJ
ejpam-3293	100	20	qc	qc	PROPN
ejpam-3293	100	21	with	with	ADP
ejpam-3293	100	22	cl(r	cl(r	NOUN
ejpam-3293	100	23	)	)	PUNCT
ejpam-3293	100	24	=	=	SYM
ejpam-3293	100	25	cl(qc	cl(qc	ADJ
ejpam-3293	100	26	)	)	PUNCT
ejpam-3293	100	27	=	=	SYM
ejpam-3293	101	1	r.	r.	NOUN
ejpam-3293	101	2	let	let	VERB
ejpam-3293	101	3	y	y	PROPN
ejpam-3293	101	4	∈	∈	PROPN
ejpam-3293	101	5	ints(a	ints(a	PROPN
ejpam-3293	101	6	)	)	PUNCT
ejpam-3293	101	7	.	.	PUNCT
ejpam-3293	102	1	then	then	ADV
ejpam-3293	102	2	there	there	PRON
ejpam-3293	102	3	exists	exist	VERB
ejpam-3293	102	4	an	an	DET
ejpam-3293	102	5	open	open	ADJ
ejpam-3293	102	6	set	set	NOUN
ejpam-3293	102	7	o	o	NOUN
ejpam-3293	102	8	containing	contain	VERB
ejpam-3293	102	9	y	y	PRON
ejpam-3293	102	10	such	such	ADJ
ejpam-3293	102	11	that	that	PRON
ejpam-3293	102	12	cl(o	cl(o	NOUN
ejpam-3293	102	13	)	)	PUNCT
ejpam-3293	102	14	=	=	PUNCT
ejpam-3293	103	1	r	r	NOUN
ejpam-3293	103	2	⊆	⊆	NUM
ejpam-3293	103	3	a	a	PRON
ejpam-3293	103	4	,	,	PUNCT
ejpam-3293	103	5	a	a	DET
ejpam-3293	103	6	contradiction	contradiction	NOUN
ejpam-3293	103	7	.	.	PUNCT
ejpam-3293	104	1	hence	hence	ADV
ejpam-3293	104	2	,	,	PUNCT
ejpam-3293	104	3	ints(a	ints(a	PROPN
ejpam-3293	104	4	)	)	PUNCT
ejpam-3293	104	5	=	=	PUNCT
ejpam-3293	105	1	∅.	∅.	NOUN
ejpam-3293	105	2	if	if	SCONJ
ejpam-3293	105	3	follows	follow	VERB
ejpam-3293	105	4	that	that	PRON
ejpam-3293	105	5	r\ints(a	r\ints(a	NOUN
ejpam-3293	105	6	)	)	PUNCT
ejpam-3293	105	7	=	=	SYM
ejpam-3293	105	8	r	r	NOUN
ejpam-3293	105	9	and	and	CCONJ
ejpam-3293	105	10	qc\ints(a	qc\ints(a	NOUN
ejpam-3293	105	11	)	)	PUNCT
ejpam-3293	105	12	=	=	SYM
ejpam-3293	105	13	qc	qc	PROPN
ejpam-3293	105	14	,	,	PUNCT
ejpam-3293	105	15	which	which	PRON
ejpam-3293	105	16	are	be	AUX
ejpam-3293	105	17	uncountable	uncountable	ADJ
ejpam-3293	105	18	.	.	PUNCT
ejpam-3293	106	1	thus	thus	ADV
ejpam-3293	106	2	,	,	PUNCT
ejpam-3293	106	3	a	a	PRON
ejpam-3293	106	4	is	be	AUX
ejpam-3293	106	5	not	not	PART
ejpam-3293	106	6	ωθ	ωθ	NOUN
ejpam-3293	106	7	-	-	PUNCT
ejpam-3293	106	8	open	open	ADJ
ejpam-3293	106	9	in	in	ADP
ejpam-3293	106	10	(	(	PUNCT
ejpam-3293	106	11	r	r	NOUN
ejpam-3293	106	12	,	,	PUNCT
ejpam-3293	106	13	t2	t2	NOUN
ejpam-3293	106	14	)	)	PUNCT
ejpam-3293	106	15	.	.	PUNCT
ejpam-3293	107	1	this	this	PRON
ejpam-3293	107	2	means	mean	VERB
ejpam-3293	107	3	that	that	SCONJ
ejpam-3293	107	4	f(qc	f(qc	NOUN
ejpam-3293	107	5	∪	∪	ADJ
ejpam-3293	107	6	{	{	PUNCT
ejpam-3293	107	7	0	0	NUM
ejpam-3293	107	8	}	}	PUNCT
ejpam-3293	107	9	)	)	PUNCT
ejpam-3293	107	10	=	=	SYM
ejpam-3293	107	11	qc	qc	PROPN
ejpam-3293	107	12	∪	∪	X
ejpam-3293	107	13	{	{	PUNCT
ejpam-3293	107	14	0	0	NUM
ejpam-3293	107	15	}	}	PUNCT
ejpam-3293	107	16	is	be	AUX
ejpam-3293	107	17	not	not	PART
ejpam-3293	107	18	ωθ	ωθ	NOUN
ejpam-3293	107	19	-	-	PUNCT
ejpam-3293	107	20	open	open	ADJ
ejpam-3293	107	21	in	in	ADP
ejpam-3293	107	22	(	(	PUNCT
ejpam-3293	107	23	r	r	NOUN
ejpam-3293	107	24	,	,	PUNCT
ejpam-3293	107	25	t2	t2	NOUN
ejpam-3293	107	26	)	)	PUNCT
ejpam-3293	107	27	.	.	PUNCT
ejpam-3293	108	1	thus	thus	ADV
ejpam-3293	108	2	,	,	PUNCT
ejpam-3293	108	3	f	f	PROPN
ejpam-3293	108	4	is	be	AUX
ejpam-3293	108	5	not	not	PART
ejpam-3293	108	6	ωθ	ωθ	NOUN
ejpam-3293	108	7	-	-	PUNCT
ejpam-3293	108	8	open	open	ADJ
ejpam-3293	108	9	on	on	ADP
ejpam-3293	108	10	(	(	PUNCT
ejpam-3293	108	11	r	r	NOUN
ejpam-3293	108	12	,	,	PUNCT
ejpam-3293	108	13	t1	t1	NOUN
ejpam-3293	108	14	)	)	PUNCT
ejpam-3293	108	15	.	.	PUNCT
ejpam-3293	109	1	since	since	SCONJ
ejpam-3293	109	2	f	f	PROPN
ejpam-3293	109	3	is	be	AUX
ejpam-3293	109	4	bijective	bijective	ADJ
ejpam-3293	109	5	,	,	PUNCT
ejpam-3293	109	6	f	f	PROPN
ejpam-3293	109	7	is	be	AUX
ejpam-3293	109	8	ω	ω	NOUN
ejpam-3293	109	9	-	-	PUNCT
ejpam-3293	109	10	closed	closed	ADJ
ejpam-3293	109	11	but	but	CCONJ
ejpam-3293	109	12	not	not	PART
ejpam-3293	109	13	ωθ	ωθ	NOUN
ejpam-3293	109	14	-	-	PUNCT
ejpam-3293	109	15	closed	closed	ADJ
ejpam-3293	109	16	on	on	ADP
ejpam-3293	109	17	(	(	PUNCT
ejpam-3293	109	18	r	r	NOUN
ejpam-3293	109	19	,	,	PUNCT
ejpam-3293	109	20	t1	t1	NOUN
ejpam-3293	109	21	)	)	PUNCT
ejpam-3293	109	22	.	.	PUNCT
ejpam-3293	110	1	lemma	lemma	PROPN
ejpam-3293	110	2	2	2	X
ejpam-3293	110	3	.	.	PUNCT
ejpam-3293	111	1	let	let	VERB
ejpam-3293	111	2	a	a	DET
ejpam-3293	111	3	⊆	⊆	NUM
ejpam-3293	111	4	x.	x.	NOUN
ejpam-3293	111	5	then	then	ADV
ejpam-3293	111	6	(	(	PUNCT
ejpam-3293	111	7	i	i	NOUN
ejpam-3293	111	8	)	)	PUNCT
ejpam-3293	111	9	x	x	SYM
ejpam-3293	111	10	∈	∈	PROPN
ejpam-3293	111	11	intω(a	intω(a	PROPN
ejpam-3293	111	12	)	)	PUNCT
ejpam-3293	112	1	if	if	SCONJ
ejpam-3293	112	2	and	and	CCONJ
ejpam-3293	112	3	only	only	ADV
ejpam-3293	112	4	if	if	SCONJ
ejpam-3293	112	5	there	there	PRON
ejpam-3293	112	6	exists	exist	VERB
ejpam-3293	112	7	an	an	DET
ejpam-3293	112	8	ω	ω	ADJ
ejpam-3293	112	9	-	-	ADJ
ejpam-3293	112	10	open	open	ADJ
ejpam-3293	112	11	set	set	NOUN
ejpam-3293	112	12	u	u	NOUN
ejpam-3293	112	13	containing	contain	VERB
ejpam-3293	112	14	x	x	PUNCT
ejpam-3293	112	15	such	such	ADJ
ejpam-3293	112	16	that	that	SCONJ
ejpam-3293	112	17	u	u	PROPN
ejpam-3293	112	18	⊆	⊆	NUM
ejpam-3293	112	19	a	a	PRON
ejpam-3293	112	20	;	;	PUNCT
ejpam-3293	112	21	(	(	PUNCT
ejpam-3293	112	22	ii	ii	NOUN
ejpam-3293	112	23	)	)	PUNCT
ejpam-3293	112	24	a	a	PRON
ejpam-3293	112	25	is	be	AUX
ejpam-3293	112	26	ω	ω	NOUN
ejpam-3293	112	27	-	-	NOUN
ejpam-3293	112	28	open	open	ADJ
ejpam-3293	112	29	if	if	SCONJ
ejpam-3293	112	30	and	and	CCONJ
ejpam-3293	112	31	only	only	ADV
ejpam-3293	112	32	if	if	SCONJ
ejpam-3293	112	33	a	a	DET
ejpam-3293	112	34	=	=	X
ejpam-3293	112	35	intω(a	intω(a	PROPN
ejpam-3293	112	36	)	)	PUNCT
ejpam-3293	112	37	;	;	PUNCT
ejpam-3293	112	38	(	(	PUNCT
ejpam-3293	112	39	iii	iii	X
ejpam-3293	112	40	)	)	PUNCT
ejpam-3293	112	41	x	x	SYM
ejpam-3293	112	42	∈	∈	PROPN
ejpam-3293	112	43	clω(a	clω(a	PROPN
ejpam-3293	112	44	)	)	PUNCT
ejpam-3293	112	45	if	if	SCONJ
ejpam-3293	112	46	and	and	CCONJ
ejpam-3293	112	47	only	only	ADV
ejpam-3293	112	48	if	if	SCONJ
ejpam-3293	112	49	for	for	ADP
ejpam-3293	112	50	every	every	DET
ejpam-3293	112	51	ω	ω	NOUN
ejpam-3293	112	52	-	-	ADJ
ejpam-3293	112	53	open	open	ADJ
ejpam-3293	112	54	set	set	NOUN
ejpam-3293	112	55	u	u	NOUN
ejpam-3293	112	56	containing	contain	VERB
ejpam-3293	112	57	x	x	X
ejpam-3293	112	58	,	,	PUNCT
ejpam-3293	112	59	u	u	PROPN
ejpam-3293	112	60	∩a	∩a	PROPN
ejpam-3293	112	61	6=	6=	NUM
ejpam-3293	112	62	∅	∅	NOUN
ejpam-3293	112	63	;	;	PUNCT
ejpam-3293	112	64	(	(	PUNCT
ejpam-3293	112	65	iv	iv	X
ejpam-3293	112	66	)	)	PUNCT
ejpam-3293	112	67	a	a	PRON
ejpam-3293	112	68	is	be	AUX
ejpam-3293	112	69	ω	ω	NOUN
ejpam-3293	112	70	-	-	PUNCT
ejpam-3293	112	71	closed	closed	ADJ
ejpam-3293	112	72	if	if	SCONJ
ejpam-3293	112	73	and	and	CCONJ
ejpam-3293	112	74	only	only	ADV
ejpam-3293	112	75	if	if	SCONJ
ejpam-3293	112	76	a	a	DET
ejpam-3293	112	77	=	=	SYM
ejpam-3293	112	78	clω(a	clω(a	NOUN
ejpam-3293	112	79	)	)	PUNCT
ejpam-3293	112	80	;	;	PUNCT
ejpam-3293	112	81	and	and	CCONJ
ejpam-3293	112	82	(	(	PUNCT
ejpam-3293	112	83	v	v	NOUN
ejpam-3293	112	84	)	)	PUNCT
ejpam-3293	112	85	clω(x	clω(x	NOUN
ejpam-3293	112	86	\a	\a	ADJ
ejpam-3293	112	87	)	)	PUNCT
ejpam-3293	113	1	=	=	PUNCT
ejpam-3293	113	2	x	x	SYM
ejpam-3293	113	3	\	\	PROPN
ejpam-3293	113	4	intω(a	intω(a	PROPN
ejpam-3293	113	5	)	)	PUNCT
ejpam-3293	113	6	.	.	PUNCT
ejpam-3293	114	1	we	we	PRON
ejpam-3293	114	2	shall	shall	AUX
ejpam-3293	114	3	now	now	ADV
ejpam-3293	114	4	give	give	VERB
ejpam-3293	114	5	some	some	DET
ejpam-3293	114	6	characterizations	characterization	NOUN
ejpam-3293	114	7	of	of	ADP
ejpam-3293	114	8	ω	ω	NOUN
ejpam-3293	114	9	-	-	ADJ
ejpam-3293	114	10	open	open	ADJ
ejpam-3293	114	11	and	and	CCONJ
ejpam-3293	114	12	ω	ω	VERB
ejpam-3293	114	13	-	-	PUNCT
ejpam-3293	114	14	closed	close	VERB
ejpam-3293	114	15	functions	function	NOUN
ejpam-3293	114	16	.	.	PUNCT
ejpam-3293	115	1	theorem	theorem	NOUN
ejpam-3293	115	2	1	1	NUM
ejpam-3293	115	3	.	.	PUNCT
ejpam-3293	116	1	let	let	VERB
ejpam-3293	116	2	f	f	NOUN
ejpam-3293	116	3	:	:	PUNCT
ejpam-3293	116	4	x	x	X
ejpam-3293	116	5	→	→	SYM
ejpam-3293	116	6	y	y	X
ejpam-3293	116	7	be	be	AUX
ejpam-3293	116	8	a	a	DET
ejpam-3293	116	9	function	function	NOUN
ejpam-3293	116	10	.	.	PUNCT
ejpam-3293	117	1	then	then	ADV
ejpam-3293	117	2	the	the	DET
ejpam-3293	117	3	following	follow	VERB
ejpam-3293	117	4	statements	statement	NOUN
ejpam-3293	117	5	are	be	AUX
ejpam-3293	117	6	equivalent	equivalent	ADJ
ejpam-3293	117	7	.	.	PUNCT
ejpam-3293	118	1	(	(	PUNCT
ejpam-3293	118	2	i	i	NOUN
ejpam-3293	118	3	)	)	PUNCT
ejpam-3293	118	4	f	f	PROPN
ejpam-3293	118	5	is	be	AUX
ejpam-3293	118	6	ω	ω	NOUN
ejpam-3293	118	7	-	-	NOUN
ejpam-3293	118	8	open	open	ADJ
ejpam-3293	118	9	on	on	ADP
ejpam-3293	118	10	x.	x.	PROPN
ejpam-3293	118	11	m.	m.	PROPN
ejpam-3293	118	12	labendia	labendia	PROPN
ejpam-3293	118	13	,	,	PUNCT
ejpam-3293	118	14	j.	j.	PROPN
ejpam-3293	118	15	a.	a.	PROPN
ejpam-3293	118	16	sasam	sasam	PROPN
ejpam-3293	118	17	/	/	SYM
ejpam-3293	118	18	eur	eur	PROPN
ejpam-3293	118	19	.	.	PUNCT
ejpam-3293	119	1	j.	j.	PROPN
ejpam-3293	119	2	pure	pure	PROPN
ejpam-3293	119	3	appl	appl	PROPN
ejpam-3293	119	4	.	.	PROPN
ejpam-3293	119	5	math	math	PROPN
ejpam-3293	119	6	,	,	PUNCT
ejpam-3293	119	7	11	11	NUM
ejpam-3293	119	8	(	(	PUNCT
ejpam-3293	119	9	3	3	NUM
ejpam-3293	119	10	)	)	PUNCT
ejpam-3293	119	11	(	(	PUNCT
ejpam-3293	119	12	2018	2018	NUM
ejpam-3293	119	13	)	)	PUNCT
ejpam-3293	119	14	,	,	PUNCT
ejpam-3293	119	15	834	834	NUM
ejpam-3293	119	16	-	-	SYM
ejpam-3293	119	17	843	843	NUM
ejpam-3293	119	18	838	838	NUM
ejpam-3293	119	19	(	(	PUNCT
ejpam-3293	119	20	ii	ii	NOUN
ejpam-3293	119	21	)	)	PUNCT
ejpam-3293	119	22	f(int(a	f(int(a	NOUN
ejpam-3293	119	23	)	)	PUNCT
ejpam-3293	119	24	)	)	PUNCT
ejpam-3293	120	1	⊆	⊆	NUM
ejpam-3293	120	2	intω(f(a	intω(f(a	NOUN
ejpam-3293	120	3	)	)	PUNCT
ejpam-3293	120	4	)	)	PUNCT
ejpam-3293	120	5	for	for	ADP
ejpam-3293	120	6	every	every	DET
ejpam-3293	120	7	a	a	DET
ejpam-3293	120	8	⊆	⊆	NUM
ejpam-3293	120	9	x.	x.	NOUN
ejpam-3293	120	10	(	(	PUNCT
ejpam-3293	120	11	iii	iii	NOUN
ejpam-3293	120	12	)	)	PUNCT
ejpam-3293	120	13	f(b	f(b	PROPN
ejpam-3293	120	14	)	)	PUNCT
ejpam-3293	120	15	is	be	AUX
ejpam-3293	120	16	ω	ω	NOUN
ejpam-3293	120	17	-	-	NOUN
ejpam-3293	120	18	open	open	ADJ
ejpam-3293	120	19	for	for	ADP
ejpam-3293	120	20	every	every	DET
ejpam-3293	120	21	basic	basic	ADJ
ejpam-3293	120	22	open	open	ADJ
ejpam-3293	120	23	set	set	NOUN
ejpam-3293	120	24	b	b	PROPN
ejpam-3293	120	25	in	in	ADP
ejpam-3293	120	26	x.	x.	PROPN
ejpam-3293	120	27	(	(	PUNCT
ejpam-3293	120	28	iv	iv	X
ejpam-3293	120	29	)	)	PUNCT
ejpam-3293	120	30	for	for	ADP
ejpam-3293	120	31	each	each	DET
ejpam-3293	120	32	p	p	NOUN
ejpam-3293	120	33	∈	∈	PROPN
ejpam-3293	120	34	x	x	X
ejpam-3293	120	35	and	and	CCONJ
ejpam-3293	120	36	every	every	DET
ejpam-3293	120	37	open	open	ADJ
ejpam-3293	120	38	set	set	VERB
ejpam-3293	120	39	o	o	NOUN
ejpam-3293	120	40	in	in	ADP
ejpam-3293	120	41	x	x	PUNCT
ejpam-3293	120	42	containing	contain	VERB
ejpam-3293	120	43	p	p	X
ejpam-3293	120	44	,	,	PUNCT
ejpam-3293	120	45	there	there	PRON
ejpam-3293	120	46	exists	exist	VERB
ejpam-3293	120	47	an	an	DET
ejpam-3293	120	48	open	open	ADJ
ejpam-3293	120	49	set	set	NOUN
ejpam-3293	120	50	u	u	NOUN
ejpam-3293	120	51	in	in	ADP
ejpam-3293	120	52	y	y	NOUN
ejpam-3293	120	53	containing	contain	VERB
ejpam-3293	120	54	f(p	f(p	NOUN
ejpam-3293	120	55	)	)	PUNCT
ejpam-3293	120	56	and	and	CCONJ
ejpam-3293	120	57	a	a	DET
ejpam-3293	120	58	countable	countable	ADJ
ejpam-3293	120	59	subset	subset	NOUN
ejpam-3293	120	60	v	v	NOUN
ejpam-3293	120	61	of	of	ADP
ejpam-3293	120	62	y	y	PRON
ejpam-3293	120	63	such	such	ADJ
ejpam-3293	120	64	that	that	SCONJ
ejpam-3293	120	65	u\v	u\v	ADP
ejpam-3293	120	66	⊆	⊆	NUM
ejpam-3293	120	67	f(o	f(o	NOUN
ejpam-3293	120	68	)	)	PUNCT
ejpam-3293	120	69	.	.	PUNCT
ejpam-3293	121	1	proof	proof	NOUN
ejpam-3293	121	2	.	.	PUNCT
ejpam-3293	122	1	(	(	PUNCT
ejpam-3293	122	2	i	i	NOUN
ejpam-3293	122	3	)	)	PUNCT
ejpam-3293	122	4	⇒	⇒	PROPN
ejpam-3293	122	5	(	(	PUNCT
ejpam-3293	122	6	ii	ii	PROPN
ejpam-3293	122	7	):	):	PUNCT
ejpam-3293	122	8	let	let	VERB
ejpam-3293	122	9	a	a	DET
ejpam-3293	122	10	⊆	⊆	NUM
ejpam-3293	122	11	x.	x.	NOUN
ejpam-3293	122	12	then	then	ADV
ejpam-3293	122	13	f(int(a	f(int(a	NOUN
ejpam-3293	122	14	)	)	PUNCT
ejpam-3293	122	15	)	)	PUNCT
ejpam-3293	123	1	⊆	⊆	NUM
ejpam-3293	123	2	f(a	f(a	NOUN
ejpam-3293	123	3	)	)	PUNCT
ejpam-3293	123	4	.	.	PUNCT
ejpam-3293	124	1	since	since	SCONJ
ejpam-3293	124	2	int(a	int(a	PROPN
ejpam-3293	124	3	)	)	PUNCT
ejpam-3293	124	4	is	be	AUX
ejpam-3293	124	5	open	open	ADJ
ejpam-3293	124	6	in	in	ADP
ejpam-3293	124	7	x	x	NOUN
ejpam-3293	124	8	,	,	PUNCT
ejpam-3293	124	9	f(int(a	f(int(a	NOUN
ejpam-3293	124	10	)	)	PUNCT
ejpam-3293	124	11	)	)	PUNCT
ejpam-3293	125	1	is	be	AUX
ejpam-3293	125	2	ω	ω	NOUN
ejpam-3293	125	3	-	-	NOUN
ejpam-3293	125	4	open	open	ADJ
ejpam-3293	125	5	in	in	ADP
ejpam-3293	125	6	y	y	PROPN
ejpam-3293	125	7	.	.	PUNCT
ejpam-3293	126	1	then	then	ADV
ejpam-3293	126	2	f(int(a	f(int(a	NOUN
ejpam-3293	126	3	)	)	PUNCT
ejpam-3293	126	4	)	)	PUNCT
ejpam-3293	127	1	⊆	⊆	NUM
ejpam-3293	127	2	intω(f(a	intω(f(a	NOUN
ejpam-3293	127	3	)	)	PUNCT
ejpam-3293	127	4	)	)	PUNCT
ejpam-3293	127	5	since	since	SCONJ
ejpam-3293	127	6	intω(f(a	intω(f(a	NOUN
ejpam-3293	127	7	)	)	PUNCT
ejpam-3293	127	8	)	)	PUNCT
ejpam-3293	127	9	is	be	AUX
ejpam-3293	127	10	the	the	DET
ejpam-3293	127	11	largest	large	ADJ
ejpam-3293	127	12	ω	ω	ADJ
ejpam-3293	127	13	-	-	ADJ
ejpam-3293	127	14	open	open	ADJ
ejpam-3293	127	15	set	set	NOUN
ejpam-3293	127	16	contained	contain	VERB
ejpam-3293	127	17	in	in	ADP
ejpam-3293	127	18	f(a	f(a	PROPN
ejpam-3293	127	19	)	)	PUNCT
ejpam-3293	127	20	.	.	PUNCT
ejpam-3293	128	1	(	(	PUNCT
ejpam-3293	128	2	ii)⇒	ii)⇒	X
ejpam-3293	128	3	(	(	PUNCT
ejpam-3293	128	4	iii	iii	NOUN
ejpam-3293	128	5	):	):	PUNCT
ejpam-3293	128	6	let	let	VERB
ejpam-3293	128	7	b	b	X
ejpam-3293	128	8	be	be	AUX
ejpam-3293	128	9	a	a	DET
ejpam-3293	128	10	basic	basic	ADJ
ejpam-3293	128	11	open	open	ADJ
ejpam-3293	128	12	set	set	NOUN
ejpam-3293	128	13	in	in	ADP
ejpam-3293	128	14	x.	x.	PROPN
ejpam-3293	128	15	then	then	ADV
ejpam-3293	128	16	f(b	f(b	PROPN
ejpam-3293	128	17	)	)	PUNCT
ejpam-3293	128	18	=	=	SYM
ejpam-3293	128	19	f(int(b	f(int(b	NOUN
ejpam-3293	128	20	)	)	PUNCT
ejpam-3293	128	21	)	)	PUNCT
ejpam-3293	128	22	.	.	PUNCT
ejpam-3293	129	1	by	by	ADP
ejpam-3293	129	2	assumption	assumption	NOUN
ejpam-3293	129	3	,	,	PUNCT
ejpam-3293	129	4	f(b	f(b	PROPN
ejpam-3293	129	5	)	)	PUNCT
ejpam-3293	129	6	=	=	SYM
ejpam-3293	129	7	f(int(b	f(int(b	NOUN
ejpam-3293	129	8	)	)	PUNCT
ejpam-3293	129	9	)	)	PUNCT
ejpam-3293	130	1	⊆	⊆	NUM
ejpam-3293	130	2	intω(f(b	intω(f(b	NUM
ejpam-3293	130	3	)	)	PUNCT
ejpam-3293	130	4	)	)	PUNCT
ejpam-3293	131	1	⊆	⊆	NUM
ejpam-3293	131	2	f(b	f(b	NOUN
ejpam-3293	131	3	)	)	PUNCT
ejpam-3293	131	4	.	.	PUNCT
ejpam-3293	132	1	hence	hence	ADV
ejpam-3293	132	2	,	,	PUNCT
ejpam-3293	132	3	f(b	f(b	PROPN
ejpam-3293	132	4	)	)	PUNCT
ejpam-3293	132	5	=	=	SYM
ejpam-3293	132	6	intω(f(b	intω(f(b	PROPN
ejpam-3293	132	7	)	)	PUNCT
ejpam-3293	132	8	)	)	PUNCT
ejpam-3293	132	9	.	.	PUNCT
ejpam-3293	133	1	thus	thus	ADV
ejpam-3293	133	2	,	,	PUNCT
ejpam-3293	133	3	f(b	f(b	PROPN
ejpam-3293	133	4	)	)	PUNCT
ejpam-3293	133	5	is	be	AUX
ejpam-3293	133	6	ω	ω	NOUN
ejpam-3293	133	7	-	-	NOUN
ejpam-3293	133	8	open	open	ADJ
ejpam-3293	133	9	in	in	ADP
ejpam-3293	133	10	y	y	PROPN
ejpam-3293	133	11	.	.	PUNCT
ejpam-3293	134	1	(	(	PUNCT
ejpam-3293	134	2	iii	iii	X
ejpam-3293	134	3	)	)	PUNCT
ejpam-3293	134	4	⇒	⇒	NOUN
ejpam-3293	134	5	(	(	PUNCT
ejpam-3293	134	6	iv	iv	NUM
ejpam-3293	134	7	):	):	PUNCT
ejpam-3293	134	8	let	let	VERB
ejpam-3293	134	9	p	p	PRON
ejpam-3293	134	10	∈	∈	PROPN
ejpam-3293	134	11	x	x	X
ejpam-3293	134	12	and	and	CCONJ
ejpam-3293	134	13	o	o	NOUN
ejpam-3293	134	14	be	be	AUX
ejpam-3293	134	15	an	an	DET
ejpam-3293	134	16	open	open	ADJ
ejpam-3293	134	17	set	set	NOUN
ejpam-3293	134	18	containing	contain	VERB
ejpam-3293	134	19	p.	p.	NOUN
ejpam-3293	134	20	then	then	ADV
ejpam-3293	134	21	there	there	PRON
ejpam-3293	134	22	exists	exist	VERB
ejpam-3293	134	23	a	a	DET
ejpam-3293	134	24	basic	basic	ADJ
ejpam-3293	134	25	open	open	ADJ
ejpam-3293	134	26	set	set	NOUN
ejpam-3293	134	27	b	b	NOUN
ejpam-3293	134	28	containing	contain	VERB
ejpam-3293	134	29	p	p	NOUN
ejpam-3293	135	1	such	such	DET
ejpam-3293	135	2	that	that	DET
ejpam-3293	135	3	b	b	NOUN
ejpam-3293	135	4	⊆	⊆	NUM
ejpam-3293	135	5	o.	o.	NOUN
ejpam-3293	135	6	this	this	PRON
ejpam-3293	135	7	implies	imply	VERB
ejpam-3293	135	8	that	that	SCONJ
ejpam-3293	135	9	f(p	f(p	NOUN
ejpam-3293	135	10	)	)	PUNCT
ejpam-3293	135	11	∈	∈	PROPN
ejpam-3293	135	12	f(b	f(b	PROPN
ejpam-3293	135	13	)	)	PUNCT
ejpam-3293	135	14	⊆	⊆	NUM
ejpam-3293	135	15	f(o	f(o	NOUN
ejpam-3293	135	16	)	)	PUNCT
ejpam-3293	135	17	.	.	PUNCT
ejpam-3293	136	1	by	by	ADP
ejpam-3293	136	2	assumption	assumption	NOUN
ejpam-3293	136	3	,	,	PUNCT
ejpam-3293	136	4	there	there	PRON
ejpam-3293	136	5	exists	exist	VERB
ejpam-3293	136	6	an	an	DET
ejpam-3293	136	7	open	open	ADJ
ejpam-3293	136	8	set	set	NOUN
ejpam-3293	136	9	u	u	NOUN
ejpam-3293	136	10	in	in	ADP
ejpam-3293	136	11	y	y	NOUN
ejpam-3293	136	12	containing	contain	VERB
ejpam-3293	136	13	f(p	f(p	NOUN
ejpam-3293	136	14	)	)	PUNCT
ejpam-3293	136	15	such	such	ADJ
ejpam-3293	136	16	that	that	DET
ejpam-3293	136	17	u\f(b	u\f(b	PROPN
ejpam-3293	136	18	)	)	PUNCT
ejpam-3293	136	19	is	be	AUX
ejpam-3293	136	20	countable	countable	ADJ
ejpam-3293	136	21	.	.	PUNCT
ejpam-3293	137	1	take	take	VERB
ejpam-3293	137	2	v	v	NOUN
ejpam-3293	137	3	=	=	SYM
ejpam-3293	137	4	u\f(b	u\f(b	PROPN
ejpam-3293	137	5	)	)	PUNCT
ejpam-3293	137	6	.	.	PUNCT
ejpam-3293	138	1	then	then	ADV
ejpam-3293	138	2	u\v	u\v	PROPN
ejpam-3293	138	3	=	=	PUNCT
ejpam-3293	138	4	u\(u\f(b	u\(u\f(b	X
ejpam-3293	138	5	)	)	PUNCT
ejpam-3293	138	6	)	)	PUNCT
ejpam-3293	139	1	=	=	SYM
ejpam-3293	139	2	u	u	NOUN
ejpam-3293	139	3	∩	∩	X
ejpam-3293	139	4	f(b	f(b	X
ejpam-3293	139	5	)	)	PUNCT
ejpam-3293	139	6	⊆	⊆	NUM
ejpam-3293	139	7	f(b	f(b	X
ejpam-3293	139	8	)	)	PUNCT
ejpam-3293	139	9	⊆	⊆	NUM
ejpam-3293	139	10	f(o	f(o	NOUN
ejpam-3293	139	11	)	)	PUNCT
ejpam-3293	139	12	.	.	PUNCT
ejpam-3293	140	1	(	(	PUNCT
ejpam-3293	140	2	iv	iv	X
ejpam-3293	140	3	)	)	PUNCT
ejpam-3293	140	4	⇒	⇒	NOUN
ejpam-3293	140	5	(	(	PUNCT
ejpam-3293	140	6	i	i	NOUN
ejpam-3293	140	7	):	):	PUNCT
ejpam-3293	140	8	let	let	VERB
ejpam-3293	140	9	o	o	NOUN
ejpam-3293	140	10	be	be	AUX
ejpam-3293	140	11	open	open	ADJ
ejpam-3293	140	12	in	in	ADP
ejpam-3293	140	13	x	x	PUNCT
ejpam-3293	140	14	and	and	CCONJ
ejpam-3293	140	15	y	y	PROPN
ejpam-3293	140	16	∈	∈	PROPN
ejpam-3293	140	17	f(o	f(o	NOUN
ejpam-3293	140	18	)	)	PUNCT
ejpam-3293	140	19	.	.	PUNCT
ejpam-3293	141	1	then	then	ADV
ejpam-3293	141	2	there	there	PRON
ejpam-3293	141	3	exists	exist	VERB
ejpam-3293	141	4	x	x	X
ejpam-3293	141	5	∈	∈	NOUN
ejpam-3293	141	6	o	o	NOUN
ejpam-3293	141	7	such	such	ADJ
ejpam-3293	141	8	that	that	SCONJ
ejpam-3293	141	9	f(x	f(x	NOUN
ejpam-3293	141	10	)	)	PUNCT
ejpam-3293	142	1	=	=	PUNCT
ejpam-3293	142	2	y.	y.	NOUN
ejpam-3293	142	3	by	by	ADP
ejpam-3293	142	4	assumption	assumption	NOUN
ejpam-3293	142	5	,	,	PUNCT
ejpam-3293	142	6	there	there	PRON
ejpam-3293	142	7	exists	exist	VERB
ejpam-3293	142	8	an	an	DET
ejpam-3293	142	9	open	open	ADJ
ejpam-3293	142	10	set	set	NOUN
ejpam-3293	142	11	u	u	NOUN
ejpam-3293	142	12	in	in	ADP
ejpam-3293	142	13	y	y	NOUN
ejpam-3293	142	14	containing	contain	VERB
ejpam-3293	142	15	y	y	PROPN
ejpam-3293	142	16	and	and	CCONJ
ejpam-3293	142	17	a	a	DET
ejpam-3293	142	18	countable	countable	ADJ
ejpam-3293	142	19	subset	subset	NOUN
ejpam-3293	142	20	v	v	NOUN
ejpam-3293	142	21	of	of	ADP
ejpam-3293	142	22	y	y	PRON
ejpam-3293	142	23	such	such	ADJ
ejpam-3293	142	24	that	that	SCONJ
ejpam-3293	142	25	u\v	u\v	ADP
ejpam-3293	142	26	⊆	⊆	NUM
ejpam-3293	142	27	f(o	f(o	NOUN
ejpam-3293	142	28	)	)	PUNCT
ejpam-3293	142	29	.	.	PUNCT
ejpam-3293	143	1	then	then	ADV
ejpam-3293	143	2	u\f(o	u\f(o	NOUN
ejpam-3293	143	3	)	)	PUNCT
ejpam-3293	143	4	⊆	⊆	NUM
ejpam-3293	143	5	u\(u\v	u\(u\v	NOUN
ejpam-3293	143	6	)	)	PUNCT
ejpam-3293	144	1	=	=	SYM
ejpam-3293	144	2	u	u	PROPN
ejpam-3293	144	3	∩	∩	NOUN
ejpam-3293	144	4	v	v	ADP
ejpam-3293	144	5	⊆	⊆	NUM
ejpam-3293	144	6	v	v	NOUN
ejpam-3293	144	7	so	so	SCONJ
ejpam-3293	144	8	that	that	SCONJ
ejpam-3293	144	9	u\f(o	u\f(o	NOUN
ejpam-3293	144	10	)	)	PUNCT
ejpam-3293	144	11	is	be	AUX
ejpam-3293	144	12	countable	countable	ADJ
ejpam-3293	144	13	.	.	PUNCT
ejpam-3293	145	1	thus	thus	ADV
ejpam-3293	145	2	,	,	PUNCT
ejpam-3293	145	3	f(o	f(o	NOUN
ejpam-3293	145	4	)	)	PUNCT
ejpam-3293	145	5	is	be	AUX
ejpam-3293	145	6	ω	ω	NOUN
ejpam-3293	145	7	-	-	NOUN
ejpam-3293	145	8	open	open	ADJ
ejpam-3293	145	9	in	in	ADP
ejpam-3293	145	10	y	y	PROPN
ejpam-3293	145	11	.	.	PUNCT
ejpam-3293	146	1	theorem	theorem	NOUN
ejpam-3293	146	2	2	2	NUM
ejpam-3293	146	3	.	.	PUNCT
ejpam-3293	147	1	the	the	DET
ejpam-3293	147	2	function	function	NOUN
ejpam-3293	147	3	f	f	NOUN
ejpam-3293	147	4	:	:	PUNCT
ejpam-3293	147	5	x	x	X
ejpam-3293	147	6	→	→	SYM
ejpam-3293	147	7	y	y	PROPN
ejpam-3293	147	8	is	be	AUX
ejpam-3293	147	9	ω	ω	NOUN
ejpam-3293	147	10	-	-	PUNCT
ejpam-3293	147	11	closed	closed	ADJ
ejpam-3293	147	12	if	if	SCONJ
ejpam-3293	147	13	and	and	CCONJ
ejpam-3293	147	14	only	only	ADV
ejpam-3293	147	15	if	if	SCONJ
ejpam-3293	147	16	clω(f(a	clω(f(a	NOUN
ejpam-3293	147	17	)	)	PUNCT
ejpam-3293	147	18	)	)	PUNCT
ejpam-3293	148	1	⊆	⊆	NUM
ejpam-3293	148	2	f(cl(a	f(cl(a	NUM
ejpam-3293	148	3	)	)	PUNCT
ejpam-3293	148	4	)	)	PUNCT
ejpam-3293	148	5	for	for	ADP
ejpam-3293	148	6	any	any	DET
ejpam-3293	148	7	a	a	DET
ejpam-3293	148	8	⊆	⊆	NUM
ejpam-3293	148	9	x.	x.	NOUN
ejpam-3293	148	10	proof	proof	NOUN
ejpam-3293	148	11	.	.	PUNCT
ejpam-3293	148	12	suppose	suppose	VERB
ejpam-3293	148	13	that	that	SCONJ
ejpam-3293	148	14	f	f	PROPN
ejpam-3293	148	15	is	be	AUX
ejpam-3293	148	16	ω	ω	NOUN
ejpam-3293	148	17	-	-	ADJ
ejpam-3293	148	18	closed	closed	ADJ
ejpam-3293	148	19	on	on	ADP
ejpam-3293	148	20	x.	x.	NOUN
ejpam-3293	148	21	now	now	ADV
ejpam-3293	148	22	,	,	PUNCT
ejpam-3293	148	23	f(a	f(a	PROPN
ejpam-3293	148	24	)	)	PUNCT
ejpam-3293	148	25	⊆	⊆	NUM
ejpam-3293	148	26	f(cl(a	f(cl(a	NOUN
ejpam-3293	148	27	)	)	PUNCT
ejpam-3293	148	28	)	)	PUNCT
ejpam-3293	148	29	.	.	PUNCT
ejpam-3293	149	1	since	since	SCONJ
ejpam-3293	149	2	cl(a	cl(a	NUM
ejpam-3293	149	3	)	)	PUNCT
ejpam-3293	149	4	is	be	AUX
ejpam-3293	149	5	closed	close	VERB
ejpam-3293	149	6	in	in	ADP
ejpam-3293	149	7	x	x	NOUN
ejpam-3293	149	8	,	,	PUNCT
ejpam-3293	149	9	f(cl(a	f(cl(a	ADJ
ejpam-3293	149	10	)	)	PUNCT
ejpam-3293	149	11	)	)	PUNCT
ejpam-3293	149	12	is	be	AUX
ejpam-3293	149	13	ω	ω	NOUN
ejpam-3293	149	14	-	-	ADJ
ejpam-3293	149	15	closed	closed	ADJ
ejpam-3293	149	16	in	in	ADP
ejpam-3293	149	17	y	y	PROPN
ejpam-3293	149	18	.	.	PUNCT
ejpam-3293	150	1	then	then	ADV
ejpam-3293	150	2	clω(f(a	clω(f(a	NOUN
ejpam-3293	150	3	)	)	PUNCT
ejpam-3293	150	4	)	)	PUNCT
ejpam-3293	151	1	⊆	⊆	NUM
ejpam-3293	151	2	f(cl(a	f(cl(a	NUM
ejpam-3293	151	3	)	)	PUNCT
ejpam-3293	151	4	)	)	PUNCT
ejpam-3293	151	5	since	since	SCONJ
ejpam-3293	151	6	clω(f(a	clω(f(a	NOUN
ejpam-3293	151	7	)	)	PUNCT
ejpam-3293	151	8	)	)	PUNCT
ejpam-3293	151	9	is	be	AUX
ejpam-3293	151	10	the	the	DET
ejpam-3293	151	11	smallest	small	ADJ
ejpam-3293	151	12	ω	ω	ADJ
ejpam-3293	151	13	-	-	ADJ
ejpam-3293	151	14	closed	closed	ADJ
ejpam-3293	151	15	set	set	NOUN
ejpam-3293	151	16	containing	contain	VERB
ejpam-3293	151	17	f(a	f(a	NOUN
ejpam-3293	151	18	)	)	PUNCT
ejpam-3293	151	19	.	.	PUNCT
ejpam-3293	152	1	conversely	conversely	ADV
ejpam-3293	152	2	,	,	PUNCT
ejpam-3293	152	3	assume	assume	VERB
ejpam-3293	152	4	that	that	SCONJ
ejpam-3293	152	5	clω(f(a	clω(f(a	NOUN
ejpam-3293	152	6	)	)	PUNCT
ejpam-3293	152	7	)	)	PUNCT
ejpam-3293	153	1	⊆	⊆	NUM
ejpam-3293	153	2	f(cl(a	f(cl(a	NUM
ejpam-3293	153	3	)	)	PUNCT
ejpam-3293	153	4	)	)	PUNCT
ejpam-3293	153	5	for	for	ADP
ejpam-3293	153	6	any	any	DET
ejpam-3293	153	7	a	a	DET
ejpam-3293	153	8	⊆	⊆	NUM
ejpam-3293	153	9	x.	x.	NOUN
ejpam-3293	153	10	let	let	VERB
ejpam-3293	153	11	b	b	NOUN
ejpam-3293	153	12	be	be	AUX
ejpam-3293	153	13	closed	close	VERB
ejpam-3293	153	14	in	in	ADP
ejpam-3293	153	15	x.	x.	NOUN
ejpam-3293	153	16	then	then	ADV
ejpam-3293	153	17	f(b	f(b	PROPN
ejpam-3293	153	18	)	)	PUNCT
ejpam-3293	153	19	=	=	SYM
ejpam-3293	153	20	f(cl(b	f(cl(b	PROPN
ejpam-3293	153	21	)	)	PUNCT
ejpam-3293	153	22	)	)	PUNCT
ejpam-3293	153	23	.	.	PUNCT
ejpam-3293	154	1	by	by	ADP
ejpam-3293	154	2	assumption	assumption	NOUN
ejpam-3293	154	3	,	,	PUNCT
ejpam-3293	154	4	f(b	f(b	PROPN
ejpam-3293	154	5	)	)	PUNCT
ejpam-3293	154	6	⊆	⊆	NUM
ejpam-3293	154	7	clω(f(b	clω(f(b	NOUN
ejpam-3293	154	8	)	)	PUNCT
ejpam-3293	154	9	)	)	PUNCT
ejpam-3293	155	1	⊆	⊆	NUM
ejpam-3293	155	2	f(cl(b	f(cl(b	NOUN
ejpam-3293	155	3	)	)	PUNCT
ejpam-3293	155	4	)	)	PUNCT
ejpam-3293	156	1	=	=	SYM
ejpam-3293	156	2	f(b	f(b	PROPN
ejpam-3293	156	3	)	)	PUNCT
ejpam-3293	156	4	.	.	PUNCT
ejpam-3293	157	1	thus	thus	ADV
ejpam-3293	157	2	,	,	PUNCT
ejpam-3293	157	3	f(b	f(b	PROPN
ejpam-3293	157	4	)	)	PUNCT
ejpam-3293	157	5	=	=	SYM
ejpam-3293	157	6	clω(f(b	clω(f(b	NOUN
ejpam-3293	157	7	)	)	PUNCT
ejpam-3293	157	8	)	)	PUNCT
ejpam-3293	157	9	.	.	PUNCT
ejpam-3293	158	1	accordingly	accordingly	ADV
ejpam-3293	158	2	,	,	PUNCT
ejpam-3293	158	3	f(b	f(b	PROPN
ejpam-3293	158	4	)	)	PUNCT
ejpam-3293	158	5	is	be	AUX
ejpam-3293	158	6	ω	ω	NOUN
ejpam-3293	158	7	-	-	ADJ
ejpam-3293	158	8	closed	closed	ADJ
ejpam-3293	158	9	in	in	ADP
ejpam-3293	158	10	y	y	PROPN
ejpam-3293	158	11	.	.	PUNCT
ejpam-3293	159	1	3	3	X
ejpam-3293	159	2	.	.	X
ejpam-3293	159	3	ω	ω	NOUN
ejpam-3293	159	4	-	-	NOUN
ejpam-3293	159	5	connectedness	connectedness	NOUN
ejpam-3293	159	6	in	in	ADP
ejpam-3293	159	7	this	this	DET
ejpam-3293	159	8	section	section	NOUN
ejpam-3293	159	9	,	,	PUNCT
ejpam-3293	159	10	we	we	PRON
ejpam-3293	159	11	study	study	VERB
ejpam-3293	159	12	the	the	DET
ejpam-3293	159	13	relationship	relationship	NOUN
ejpam-3293	159	14	of	of	ADP
ejpam-3293	159	15	ω	ω	PROPN
ejpam-3293	159	16	-	-	PUNCT
ejpam-3293	159	17	connected	connect	VERB
ejpam-3293	159	18	topological	topological	ADJ
ejpam-3293	159	19	spaces	space	NOUN
ejpam-3293	159	20	to	to	PART
ejpam-3293	159	21	connected	connect	VERB
ejpam-3293	159	22	,	,	PUNCT
ejpam-3293	159	23	θ	θ	NOUN
ejpam-3293	159	24	-	-	PUNCT
ejpam-3293	159	25	connected	connect	VERB
ejpam-3293	159	26	,	,	PUNCT
ejpam-3293	159	27	and	and	CCONJ
ejpam-3293	159	28	ωθ	ωθ	NUM
ejpam-3293	159	29	-	-	PUNCT
ejpam-3293	159	30	connected	connect	VERB
ejpam-3293	159	31	topological	topological	ADJ
ejpam-3293	159	32	spaces	space	NOUN
ejpam-3293	159	33	and	and	CCONJ
ejpam-3293	159	34	characterize	characterize	VERB
ejpam-3293	159	35	the	the	DET
ejpam-3293	159	36	concept	concept	NOUN
ejpam-3293	159	37	of	of	ADP
ejpam-3293	159	38	ω	ω	NOUN
ejpam-3293	159	39	-	-	NOUN
ejpam-3293	159	40	connectedness	connectedness	NOUN
ejpam-3293	159	41	.	.	PUNCT
ejpam-3293	160	1	denote	denote	VERB
ejpam-3293	160	2	by	by	ADP
ejpam-3293	160	3	d	d	PROPN
ejpam-3293	160	4	,	,	PUNCT
ejpam-3293	160	5	the	the	DET
ejpam-3293	160	6	topological	topological	ADJ
ejpam-3293	160	7	space	space	NOUN
ejpam-3293	160	8	{	{	PUNCT
ejpam-3293	160	9	0	0	NUM
ejpam-3293	160	10	,	,	PUNCT
ejpam-3293	160	11	1	1	NUM
ejpam-3293	160	12	}	}	PUNCT
ejpam-3293	160	13	with	with	ADP
ejpam-3293	160	14	the	the	DET
ejpam-3293	160	15	discrete	discrete	ADJ
ejpam-3293	160	16	topology	topology	NOUN
ejpam-3293	160	17	.	.	PUNCT
ejpam-3293	161	1	the	the	DET
ejpam-3293	161	2	proof	proof	NOUN
ejpam-3293	161	3	of	of	ADP
ejpam-3293	161	4	the	the	DET
ejpam-3293	161	5	following	follow	VERB
ejpam-3293	161	6	lemma	lemma	PROPN
ejpam-3293	161	7	is	be	AUX
ejpam-3293	161	8	straightforward	straightforward	ADJ
ejpam-3293	161	9	,	,	PUNCT
ejpam-3293	161	10	hence	hence	ADV
ejpam-3293	161	11	omitted	omit	VERB
ejpam-3293	161	12	.	.	PUNCT
ejpam-3293	162	1	m.	m.	NOUN
ejpam-3293	162	2	labendia	labendia	PROPN
ejpam-3293	162	3	,	,	PUNCT
ejpam-3293	162	4	j.	j.	PROPN
ejpam-3293	162	5	a.	a.	PROPN
ejpam-3293	162	6	sasam	sasam	PROPN
ejpam-3293	162	7	/	/	SYM
ejpam-3293	162	8	eur	eur	PROPN
ejpam-3293	162	9	.	.	PUNCT
ejpam-3293	163	1	j.	j.	PROPN
ejpam-3293	163	2	pure	pure	PROPN
ejpam-3293	163	3	appl	appl	PROPN
ejpam-3293	163	4	.	.	PROPN
ejpam-3293	163	5	math	math	PROPN
ejpam-3293	163	6	,	,	PUNCT
ejpam-3293	163	7	11	11	NUM
ejpam-3293	163	8	(	(	PUNCT
ejpam-3293	163	9	3	3	NUM
ejpam-3293	163	10	)	)	PUNCT
ejpam-3293	163	11	(	(	PUNCT
ejpam-3293	163	12	2018	2018	NUM
ejpam-3293	163	13	)	)	PUNCT
ejpam-3293	163	14	,	,	PUNCT
ejpam-3293	163	15	834	834	NUM
ejpam-3293	163	16	-	-	SYM
ejpam-3293	163	17	843	843	NUM
ejpam-3293	163	18	839	839	NUM
ejpam-3293	163	19	lemma	lemma	PROPN
ejpam-3293	163	20	3	3	X
ejpam-3293	163	21	.	.	PUNCT
ejpam-3293	164	1	let	let	VERB
ejpam-3293	164	2	x	x	PRON
ejpam-3293	164	3	be	be	AUX
ejpam-3293	164	4	any	any	DET
ejpam-3293	164	5	topological	topological	ADJ
ejpam-3293	164	6	space	space	NOUN
ejpam-3293	164	7	and	and	CCONJ
ejpam-3293	164	8	χa	χa	NOUN
ejpam-3293	164	9	:	:	PUNCT
ejpam-3293	164	10	x	x	X
ejpam-3293	164	11	→	→	PUNCT
ejpam-3293	164	12	d	d	X
ejpam-3293	164	13	the	the	DET
ejpam-3293	164	14	characteristic	characteristic	ADJ
ejpam-3293	164	15	function	function	NOUN
ejpam-3293	164	16	of	of	ADP
ejpam-3293	164	17	a	a	DET
ejpam-3293	164	18	subset	subset	NOUN
ejpam-3293	164	19	a	a	PRON
ejpam-3293	164	20	of	of	ADP
ejpam-3293	164	21	x.	x.	NOUN
ejpam-3293	164	22	then	then	ADV
ejpam-3293	164	23	χa	χa	PROPN
ejpam-3293	164	24	is	be	AUX
ejpam-3293	164	25	ω	ω	NOUN
ejpam-3293	164	26	-	-	ADJ
ejpam-3293	164	27	continuous	continuous	ADJ
ejpam-3293	164	28	if	if	SCONJ
ejpam-3293	165	1	and	and	CCONJ
ejpam-3293	165	2	only	only	ADV
ejpam-3293	165	3	if	if	SCONJ
ejpam-3293	165	4	a	a	PRON
ejpam-3293	165	5	is	be	AUX
ejpam-3293	165	6	both	both	PRON
ejpam-3293	165	7	ω	ω	NOUN
ejpam-3293	165	8	-	-	ADJ
ejpam-3293	165	9	open	open	ADJ
ejpam-3293	165	10	and	and	CCONJ
ejpam-3293	165	11	ω	ω	VERB
ejpam-3293	165	12	-	-	PUNCT
ejpam-3293	165	13	closed	closed	ADJ
ejpam-3293	165	14	.	.	PUNCT
ejpam-3293	166	1	theorem	theorem	NOUN
ejpam-3293	166	2	3	3	X
ejpam-3293	166	3	.	.	PUNCT
ejpam-3293	167	1	let	let	VERB
ejpam-3293	167	2	x	x	PRON
ejpam-3293	167	3	be	be	AUX
ejpam-3293	167	4	a	a	DET
ejpam-3293	167	5	topological	topological	ADJ
ejpam-3293	167	6	space	space	NOUN
ejpam-3293	167	7	.	.	PUNCT
ejpam-3293	168	1	then	then	ADV
ejpam-3293	168	2	the	the	DET
ejpam-3293	168	3	following	follow	VERB
ejpam-3293	168	4	statements	statement	NOUN
ejpam-3293	168	5	are	be	AUX
ejpam-3293	168	6	equivalent	equivalent	ADJ
ejpam-3293	168	7	:	:	PUNCT
ejpam-3293	168	8	(	(	PUNCT
ejpam-3293	168	9	i	i	NOUN
ejpam-3293	168	10	)	)	PUNCT
ejpam-3293	168	11	x	x	X
ejpam-3293	168	12	is	be	AUX
ejpam-3293	168	13	ω	ω	ADV
ejpam-3293	168	14	-	-	PUNCT
ejpam-3293	168	15	connected	connect	VERB
ejpam-3293	168	16	.	.	PUNCT
ejpam-3293	169	1	(	(	PUNCT
ejpam-3293	169	2	ii	ii	X
ejpam-3293	169	3	)	)	PUNCT
ejpam-3293	169	4	the	the	DET
ejpam-3293	169	5	only	only	ADJ
ejpam-3293	169	6	subsets	subset	NOUN
ejpam-3293	169	7	of	of	ADP
ejpam-3293	169	8	x	x	PRON
ejpam-3293	169	9	that	that	PRON
ejpam-3293	169	10	are	be	AUX
ejpam-3293	169	11	both	both	PRON
ejpam-3293	169	12	ω	ω	NOUN
ejpam-3293	169	13	-	-	ADJ
ejpam-3293	169	14	open	open	ADJ
ejpam-3293	169	15	and	and	CCONJ
ejpam-3293	169	16	ω	ω	VERB
ejpam-3293	169	17	-	-	PUNCT
ejpam-3293	169	18	closed	close	VERB
ejpam-3293	169	19	are	be	AUX
ejpam-3293	169	20	∅	∅	NOUN
ejpam-3293	169	21	and	and	CCONJ
ejpam-3293	169	22	x.	x.	NOUN
ejpam-3293	169	23	(	(	PUNCT
ejpam-3293	169	24	iii	iii	NOUN
ejpam-3293	169	25	)	)	PUNCT
ejpam-3293	169	26	no	no	DET
ejpam-3293	169	27	ω	ω	ADJ
ejpam-3293	169	28	-	-	ADJ
ejpam-3293	169	29	continuous	continuous	ADJ
ejpam-3293	169	30	function	function	NOUN
ejpam-3293	169	31	from	from	ADP
ejpam-3293	169	32	x	x	PUNCT
ejpam-3293	169	33	to	to	ADP
ejpam-3293	169	34	d	d	PROPN
ejpam-3293	169	35	is	be	AUX
ejpam-3293	169	36	surjective	surjective	ADJ
ejpam-3293	169	37	.	.	PUNCT
ejpam-3293	170	1	proof	proof	NOUN
ejpam-3293	170	2	.	.	PUNCT
ejpam-3293	171	1	(	(	PUNCT
ejpam-3293	171	2	i	i	NOUN
ejpam-3293	171	3	)	)	PUNCT
ejpam-3293	171	4	⇒	⇒	PROPN
ejpam-3293	171	5	(	(	PUNCT
ejpam-3293	171	6	ii	ii	PROPN
ejpam-3293	171	7	):	):	PUNCT
ejpam-3293	171	8	let	let	VERB
ejpam-3293	171	9	g	g	PROPN
ejpam-3293	171	10	⊆	⊆	NUM
ejpam-3293	171	11	x	x	SYM
ejpam-3293	171	12	which	which	PRON
ejpam-3293	171	13	is	be	AUX
ejpam-3293	171	14	both	both	PRON
ejpam-3293	171	15	ω	ω	NOUN
ejpam-3293	171	16	-	-	ADJ
ejpam-3293	171	17	open	open	ADJ
ejpam-3293	171	18	and	and	CCONJ
ejpam-3293	171	19	ω	ω	VERB
ejpam-3293	171	20	-	-	PUNCT
ejpam-3293	171	21	closed	closed	ADJ
ejpam-3293	171	22	.	.	PUNCT
ejpam-3293	172	1	then	then	ADV
ejpam-3293	172	2	x\g	x\g	PROPN
ejpam-3293	172	3	is	be	AUX
ejpam-3293	172	4	also	also	ADV
ejpam-3293	172	5	both	both	CCONJ
ejpam-3293	172	6	ω	ω	NOUN
ejpam-3293	172	7	-	-	ADJ
ejpam-3293	172	8	open	open	ADJ
ejpam-3293	172	9	and	and	CCONJ
ejpam-3293	172	10	ω	ω	VERB
ejpam-3293	172	11	-	-	PUNCT
ejpam-3293	172	12	closed	closed	ADJ
ejpam-3293	172	13	.	.	PUNCT
ejpam-3293	173	1	moreover	moreover	ADV
ejpam-3293	173	2	,	,	PUNCT
ejpam-3293	173	3	x	x	PUNCT
ejpam-3293	173	4	=	=	PUNCT
ejpam-3293	173	5	g	g	NOUN
ejpam-3293	173	6	∪	∪	ADV
ejpam-3293	173	7	(	(	PUNCT
ejpam-3293	173	8	x\g	x\g	NOUN
ejpam-3293	173	9	)	)	PUNCT
ejpam-3293	173	10	.	.	PUNCT
ejpam-3293	174	1	since	since	SCONJ
ejpam-3293	174	2	x	x	PROPN
ejpam-3293	174	3	is	be	AUX
ejpam-3293	174	4	ω	ω	ADV
ejpam-3293	174	5	-	-	VERB
ejpam-3293	174	6	connected	connect	VERB
ejpam-3293	174	7	,	,	PUNCT
ejpam-3293	174	8	either	either	CCONJ
ejpam-3293	174	9	g	g	PROPN
ejpam-3293	174	10	=	=	PUNCT
ejpam-3293	174	11	∅	∅	NOUN
ejpam-3293	174	12	or	or	CCONJ
ejpam-3293	174	13	g	g	NOUN
ejpam-3293	174	14	=	=	PROPN
ejpam-3293	174	15	x.	x.	NOUN
ejpam-3293	174	16	(	(	PUNCT
ejpam-3293	174	17	ii)⇒	ii)⇒	PROPN
ejpam-3293	174	18	(	(	PUNCT
ejpam-3293	174	19	iii	iii	NOUN
ejpam-3293	174	20	):	):	PUNCT
ejpam-3293	174	21	suppose	suppose	VERB
ejpam-3293	174	22	that	that	SCONJ
ejpam-3293	174	23	f	f	X
ejpam-3293	174	24	:	:	PUNCT
ejpam-3293	174	25	x	x	X
ejpam-3293	174	26	→	→	SYM
ejpam-3293	174	27	d	d	X
ejpam-3293	174	28	is	be	AUX
ejpam-3293	174	29	an	an	DET
ejpam-3293	174	30	ω	ω	ADJ
ejpam-3293	174	31	-	-	ADJ
ejpam-3293	174	32	continuous	continuous	ADJ
ejpam-3293	174	33	surjection	surjection	NOUN
ejpam-3293	174	34	.	.	PUNCT
ejpam-3293	175	1	then	then	ADV
ejpam-3293	175	2	f−1({0	f−1({0	PRON
ejpam-3293	175	3	}	}	PUNCT
ejpam-3293	175	4	)	)	PUNCT
ejpam-3293	175	5	6=	6=	ADP
ejpam-3293	175	6	∅	∅	NOUN
ejpam-3293	175	7	,	,	PUNCT
ejpam-3293	175	8	x.	x.	NOUN
ejpam-3293	175	9	since	since	SCONJ
ejpam-3293	175	10	{	{	PUNCT
ejpam-3293	175	11	0	0	NUM
ejpam-3293	175	12	}	}	PUNCT
ejpam-3293	175	13	is	be	AUX
ejpam-3293	175	14	open	open	ADJ
ejpam-3293	175	15	and	and	CCONJ
ejpam-3293	175	16	closed	close	VERB
ejpam-3293	175	17	in	in	ADP
ejpam-3293	175	18	d	d	PROPN
ejpam-3293	175	19	,	,	PUNCT
ejpam-3293	175	20	f−1({0	f−1({0	PRON
ejpam-3293	175	21	}	}	PUNCT
ejpam-3293	175	22	)	)	PUNCT
ejpam-3293	175	23	is	be	AUX
ejpam-3293	175	24	both	both	PRON
ejpam-3293	175	25	ω	ω	NOUN
ejpam-3293	175	26	-	-	ADJ
ejpam-3293	175	27	open	open	ADJ
ejpam-3293	175	28	and	and	CCONJ
ejpam-3293	175	29	ω	ω	VERB
ejpam-3293	175	30	-	-	VERB
ejpam-3293	175	31	closed	closed	ADJ
ejpam-3293	175	32	in	in	ADP
ejpam-3293	175	33	x.	x.	NOUN
ejpam-3293	175	34	this	this	PRON
ejpam-3293	175	35	is	be	AUX
ejpam-3293	175	36	a	a	DET
ejpam-3293	175	37	contradiction	contradiction	NOUN
ejpam-3293	175	38	.	.	PUNCT
ejpam-3293	176	1	(	(	PUNCT
ejpam-3293	176	2	iii)⇒	iii)⇒	PROPN
ejpam-3293	176	3	(	(	PUNCT
ejpam-3293	176	4	i	i	NOUN
ejpam-3293	176	5	):	):	PUNCT
ejpam-3293	176	6	if	if	SCONJ
ejpam-3293	176	7	x	x	X
ejpam-3293	176	8	=	=	PUNCT
ejpam-3293	176	9	a	a	PRON
ejpam-3293	176	10	∪b	∪b	NOUN
ejpam-3293	176	11	,	,	PUNCT
ejpam-3293	176	12	where	where	SCONJ
ejpam-3293	176	13	a	a	PRON
ejpam-3293	176	14	and	and	CCONJ
ejpam-3293	176	15	b	b	NOUN
ejpam-3293	176	16	are	be	AUX
ejpam-3293	176	17	disjoint	disjoint	X
ejpam-3293	176	18	nonempty	nonempty	X
ejpam-3293	176	19	ω	ω	VERB
ejpam-3293	176	20	-	-	ADJ
ejpam-3293	176	21	open	open	ADJ
ejpam-3293	176	22	sets	set	NOUN
ejpam-3293	176	23	,	,	PUNCT
ejpam-3293	176	24	then	then	ADV
ejpam-3293	176	25	a	a	PRON
ejpam-3293	176	26	and	and	CCONJ
ejpam-3293	176	27	b	b	NOUN
ejpam-3293	176	28	are	be	AUX
ejpam-3293	176	29	also	also	ADV
ejpam-3293	176	30	ω	ω	VERB
ejpam-3293	176	31	-	-	PUNCT
ejpam-3293	176	32	closed	close	VERB
ejpam-3293	176	33	sets	set	NOUN
ejpam-3293	176	34	.	.	PUNCT
ejpam-3293	177	1	consider	consider	VERB
ejpam-3293	177	2	the	the	DET
ejpam-3293	177	3	characteristic	characteristic	ADJ
ejpam-3293	177	4	function	function	NOUN
ejpam-3293	177	5	χa	χa	NOUN
ejpam-3293	177	6	:	:	PUNCT
ejpam-3293	177	7	x	x	X
ejpam-3293	177	8	→	→	SYM
ejpam-3293	177	9	d	d	NOUN
ejpam-3293	177	10	of	of	ADP
ejpam-3293	177	11	a	a	DET
ejpam-3293	177	12	⊆	⊆	NUM
ejpam-3293	177	13	x.	x.	NOUN
ejpam-3293	177	14	by	by	ADP
ejpam-3293	177	15	lemma	lemma	PROPN
ejpam-3293	177	16	3	3	NUM
ejpam-3293	177	17	,	,	PUNCT
ejpam-3293	177	18	χa	χa	PROPN
ejpam-3293	177	19	is	be	AUX
ejpam-3293	177	20	ω	ω	NOUN
ejpam-3293	177	21	-	-	ADJ
ejpam-3293	177	22	continuous	continuous	ADJ
ejpam-3293	177	23	.	.	PUNCT
ejpam-3293	178	1	this	this	PRON
ejpam-3293	178	2	is	be	AUX
ejpam-3293	178	3	a	a	DET
ejpam-3293	178	4	contradiction	contradiction	NOUN
ejpam-3293	178	5	.	.	PUNCT
ejpam-3293	179	1	thus	thus	ADV
ejpam-3293	179	2	x	x	X
ejpam-3293	179	3	is	be	AUX
ejpam-3293	179	4	ω	ω	ADV
ejpam-3293	179	5	-	-	VERB
ejpam-3293	179	6	connected	connect	VERB
ejpam-3293	179	7	.	.	PUNCT
ejpam-3293	180	1	in	in	ADP
ejpam-3293	180	2	view	view	NOUN
ejpam-3293	180	3	of	of	ADP
ejpam-3293	180	4	remark	remark	NOUN
ejpam-3293	180	5	1	1	NUM
ejpam-3293	180	6	,	,	PUNCT
ejpam-3293	180	7	we	we	PRON
ejpam-3293	180	8	have	have	VERB
ejpam-3293	180	9	the	the	DET
ejpam-3293	180	10	following	follow	VERB
ejpam-3293	180	11	consequences	consequence	NOUN
ejpam-3293	180	12	.	.	PUNCT
ejpam-3293	181	1	remark	remark	NOUN
ejpam-3293	181	2	4	4	NUM
ejpam-3293	181	3	.	.	PUNCT
ejpam-3293	182	1	let	let	VERB
ejpam-3293	182	2	x	x	PRON
ejpam-3293	182	3	be	be	AUX
ejpam-3293	182	4	a	a	DET
ejpam-3293	182	5	topological	topological	ADJ
ejpam-3293	182	6	space	space	NOUN
ejpam-3293	182	7	.	.	PUNCT
ejpam-3293	183	1	(	(	PUNCT
ejpam-3293	183	2	i	i	NOUN
ejpam-3293	183	3	)	)	PUNCT
ejpam-3293	183	4	if	if	SCONJ
ejpam-3293	183	5	x	x	PRON
ejpam-3293	183	6	is	be	AUX
ejpam-3293	183	7	ω	ω	ADV
ejpam-3293	183	8	-	-	VERB
ejpam-3293	183	9	connected	connect	VERB
ejpam-3293	183	10	,	,	PUNCT
ejpam-3293	183	11	then	then	ADV
ejpam-3293	183	12	x	x	PUNCT
ejpam-3293	183	13	is	be	AUX
ejpam-3293	183	14	ωθ	ωθ	ADV
ejpam-3293	183	15	-	-	PUNCT
ejpam-3293	183	16	connected	connect	VERB
ejpam-3293	183	17	;	;	PUNCT
ejpam-3293	183	18	(	(	PUNCT
ejpam-3293	183	19	ii	ii	NOUN
ejpam-3293	183	20	)	)	PUNCT
ejpam-3293	183	21	if	if	SCONJ
ejpam-3293	183	22	x	x	PRON
ejpam-3293	183	23	is	be	AUX
ejpam-3293	183	24	ωθ	ωθ	ADV
ejpam-3293	183	25	-	-	PUNCT
ejpam-3293	183	26	connected	connect	VERB
ejpam-3293	183	27	,	,	PUNCT
ejpam-3293	183	28	then	then	ADV
ejpam-3293	183	29	x	x	PUNCT
ejpam-3293	183	30	is	be	AUX
ejpam-3293	183	31	θ	θ	NOUN
ejpam-3293	183	32	-	-	PUNCT
ejpam-3293	183	33	connected	connect	VERB
ejpam-3293	183	34	;	;	PUNCT
ejpam-3293	183	35	and	and	CCONJ
ejpam-3293	183	36	(	(	PUNCT
ejpam-3293	183	37	iii	iii	X
ejpam-3293	183	38	)	)	PUNCT
ejpam-3293	183	39	if	if	SCONJ
ejpam-3293	183	40	x	x	PRON
ejpam-3293	183	41	is	be	AUX
ejpam-3293	183	42	ω	ω	ADV
ejpam-3293	183	43	-	-	VERB
ejpam-3293	183	44	connected	connect	VERB
ejpam-3293	183	45	,	,	PUNCT
ejpam-3293	183	46	then	then	ADV
ejpam-3293	183	47	x	x	PUNCT
ejpam-3293	183	48	is	be	AUX
ejpam-3293	183	49	connected	connect	VERB
ejpam-3293	183	50	.	.	PUNCT
ejpam-3293	184	1	remark	remark	NOUN
ejpam-3293	184	2	5	5	NUM
ejpam-3293	184	3	.	.	PUNCT
ejpam-3293	185	1	the	the	DET
ejpam-3293	185	2	converse	converse	NOUN
ejpam-3293	185	3	of	of	ADP
ejpam-3293	185	4	remark	remark	NOUN
ejpam-3293	185	5	4	4	NUM
ejpam-3293	185	6	(	(	PUNCT
ejpam-3293	185	7	i	i	NOUN
ejpam-3293	185	8	)	)	PUNCT
ejpam-3293	185	9	is	be	AUX
ejpam-3293	185	10	not	not	PART
ejpam-3293	185	11	necessarily	necessarily	ADV
ejpam-3293	185	12	true	true	ADJ
ejpam-3293	185	13	.	.	PUNCT
ejpam-3293	186	1	to	to	PART
ejpam-3293	186	2	see	see	VERB
ejpam-3293	186	3	this	this	PRON
ejpam-3293	186	4	,	,	PUNCT
ejpam-3293	186	5	consider	consider	VERB
ejpam-3293	186	6	r	r	NOUN
ejpam-3293	186	7	with	with	ADP
ejpam-3293	186	8	topology	topology	NOUN
ejpam-3293	186	9	t	t	NOUN
ejpam-3293	186	10	=	=	SYM
ejpam-3293	186	11	{	{	PUNCT
ejpam-3293	186	12	∅,r	∅,r	PROPN
ejpam-3293	186	13	,	,	PUNCT
ejpam-3293	186	14	q	q	NOUN
ejpam-3293	186	15	}	}	PUNCT
ejpam-3293	186	16	.	.	PUNCT
ejpam-3293	187	1	we	we	PRON
ejpam-3293	187	2	will	will	AUX
ejpam-3293	187	3	show	show	VERB
ejpam-3293	187	4	first	first	ADV
ejpam-3293	187	5	that	that	DET
ejpam-3293	187	6	ints(a	ints(a	NOUN
ejpam-3293	187	7	)	)	PUNCT
ejpam-3293	187	8	=	=	NOUN
ejpam-3293	187	9	∅	∅	NOUN
ejpam-3293	187	10	for	for	ADP
ejpam-3293	187	11	every	every	DET
ejpam-3293	187	12	nonempty	nonempty	ADV
ejpam-3293	187	13	proper	proper	ADJ
ejpam-3293	187	14	subset	subset	NOUN
ejpam-3293	187	15	a	a	PRON
ejpam-3293	187	16	of	of	ADP
ejpam-3293	187	17	r.	r.	PROPN
ejpam-3293	187	18	suppose	suppose	VERB
ejpam-3293	187	19	that	that	SCONJ
ejpam-3293	187	20	ints(a	ints(a	PROPN
ejpam-3293	187	21	)	)	PUNCT
ejpam-3293	187	22	6=	6=	ADP
ejpam-3293	187	23	∅.	∅.	PROPN
ejpam-3293	187	24	note	note	NOUN
ejpam-3293	187	25	first	first	ADV
ejpam-3293	187	26	that	that	SCONJ
ejpam-3293	187	27	the	the	DET
ejpam-3293	187	28	only	only	ADV
ejpam-3293	187	29	nonempty	nonempty	ADJ
ejpam-3293	187	30	open	open	ADJ
ejpam-3293	187	31	sets	set	NOUN
ejpam-3293	187	32	in	in	ADP
ejpam-3293	187	33	t	t	PROPN
ejpam-3293	187	34	are	be	AUX
ejpam-3293	187	35	r	r	NOUN
ejpam-3293	187	36	and	and	CCONJ
ejpam-3293	187	37	q	q	NOUN
ejpam-3293	187	38	with	with	ADP
ejpam-3293	187	39	cl(r	cl(r	NOUN
ejpam-3293	187	40	)	)	PUNCT
ejpam-3293	187	41	=	=	PUNCT
ejpam-3293	187	42	cl(q	cl(q	X
ejpam-3293	187	43	)	)	PUNCT
ejpam-3293	187	44	=	=	VERB
ejpam-3293	188	1	r.	r.	NOUN
ejpam-3293	188	2	let	let	VERB
ejpam-3293	188	3	y	y	PROPN
ejpam-3293	188	4	∈	∈	PROPN
ejpam-3293	188	5	ints(a	ints(a	PROPN
ejpam-3293	188	6	)	)	PUNCT
ejpam-3293	188	7	.	.	PUNCT
ejpam-3293	189	1	then	then	ADV
ejpam-3293	189	2	there	there	PRON
ejpam-3293	189	3	exists	exist	VERB
ejpam-3293	189	4	an	an	DET
ejpam-3293	189	5	open	open	ADJ
ejpam-3293	189	6	set	set	NOUN
ejpam-3293	189	7	o	o	NOUN
ejpam-3293	189	8	containing	contain	VERB
ejpam-3293	189	9	y	y	PRON
ejpam-3293	189	10	such	such	ADJ
ejpam-3293	189	11	that	that	PRON
ejpam-3293	189	12	cl(o	cl(o	NOUN
ejpam-3293	189	13	)	)	PUNCT
ejpam-3293	189	14	=	=	PUNCT
ejpam-3293	190	1	r	r	NOUN
ejpam-3293	190	2	⊆	⊆	NUM
ejpam-3293	190	3	a	a	PRON
ejpam-3293	190	4	,	,	PUNCT
ejpam-3293	190	5	a	a	DET
ejpam-3293	190	6	contradiction	contradiction	NOUN
ejpam-3293	190	7	.	.	PUNCT
ejpam-3293	191	1	hence	hence	ADV
ejpam-3293	191	2	,	,	PUNCT
ejpam-3293	191	3	ints(a	ints(a	PROPN
ejpam-3293	191	4	)	)	PUNCT
ejpam-3293	191	5	=	=	PUNCT
ejpam-3293	192	1	∅.	∅.	VERB
ejpam-3293	192	2	next	next	ADV
ejpam-3293	192	3	we	we	PRON
ejpam-3293	192	4	show	show	VERB
ejpam-3293	192	5	that	that	SCONJ
ejpam-3293	192	6	all	all	DET
ejpam-3293	192	7	a	a	DET
ejpam-3293	192	8	⊆	⊆	NUM
ejpam-3293	192	9	q	q	NOUN
ejpam-3293	192	10	are	be	AUX
ejpam-3293	192	11	the	the	DET
ejpam-3293	192	12	only	only	ADJ
ejpam-3293	192	13	ωθ	ωθ	ADV
ejpam-3293	192	14	-	-	PUNCT
ejpam-3293	192	15	open	open	ADJ
ejpam-3293	192	16	subsets	subset	NOUN
ejpam-3293	192	17	of	of	ADP
ejpam-3293	192	18	r.	r.	PROPN
ejpam-3293	192	19	let	let	VERB
ejpam-3293	192	20	a	a	DET
ejpam-3293	192	21	⊆	⊆	NUM
ejpam-3293	192	22	q.	q.	NOUN
ejpam-3293	192	23	then	then	ADV
ejpam-3293	192	24	for	for	ADP
ejpam-3293	192	25	all	all	PRON
ejpam-3293	192	26	x	x	SYM
ejpam-3293	192	27	∈	∈	PROPN
ejpam-3293	192	28	a	a	PRON
ejpam-3293	192	29	,	,	PUNCT
ejpam-3293	192	30	there	there	PRON
ejpam-3293	192	31	exists	exist	VERB
ejpam-3293	192	32	an	an	DET
ejpam-3293	192	33	open	open	ADJ
ejpam-3293	192	34	set	set	NOUN
ejpam-3293	192	35	o	o	X
ejpam-3293	192	36	=	=	PUNCT
ejpam-3293	193	1	q	q	X
ejpam-3293	193	2	containing	contain	VERB
ejpam-3293	193	3	x	x	SYM
ejpam-3293	193	4	such	such	ADJ
ejpam-3293	193	5	that	that	DET
ejpam-3293	193	6	q\ints(a	q\ints(a	NOUN
ejpam-3293	193	7	)	)	PUNCT
ejpam-3293	194	1	=	=	PUNCT
ejpam-3293	195	1	q	q	PROPN
ejpam-3293	195	2	is	be	AUX
ejpam-3293	195	3	countable	countable	ADJ
ejpam-3293	195	4	.	.	PUNCT
ejpam-3293	196	1	hence	hence	ADV
ejpam-3293	196	2	,	,	PUNCT
ejpam-3293	196	3	a	a	DET
ejpam-3293	196	4	⊆	⊆	NUM
ejpam-3293	196	5	q	q	NOUN
ejpam-3293	196	6	is	be	AUX
ejpam-3293	196	7	ωθ	ωθ	NOUN
ejpam-3293	196	8	-	-	PUNCT
ejpam-3293	196	9	open	open	ADJ
ejpam-3293	196	10	.	.	PUNCT
ejpam-3293	197	1	let	let	VERB
ejpam-3293	197	2	b	b	PROPN
ejpam-3293	197	3	6⊆	6⊆	PROPN
ejpam-3293	197	4	q.	q.	PROPN
ejpam-3293	197	5	then	then	ADV
ejpam-3293	197	6	there	there	PRON
ejpam-3293	197	7	exists	exist	VERB
ejpam-3293	197	8	y	y	PROPN
ejpam-3293	197	9	∈	∈	PROPN
ejpam-3293	197	10	b	b	PROPN
ejpam-3293	198	1	such	such	ADJ
ejpam-3293	198	2	that	that	DET
ejpam-3293	198	3	y	y	PROPN
ejpam-3293	198	4	/∈	/∈	PUNCT
ejpam-3293	198	5	q.	q.	PROPN
ejpam-3293	198	6	hence	hence	ADV
ejpam-3293	198	7	,	,	PUNCT
ejpam-3293	198	8	the	the	DET
ejpam-3293	198	9	only	only	ADJ
ejpam-3293	198	10	open	open	ADJ
ejpam-3293	198	11	set	set	NOUN
ejpam-3293	198	12	containing	contain	VERB
ejpam-3293	198	13	y	y	PROPN
ejpam-3293	198	14	is	be	AUX
ejpam-3293	198	15	r.	r.	NOUN
ejpam-3293	198	16	but	but	CCONJ
ejpam-3293	198	17	r\ints(b	r\ints(b	NOUN
ejpam-3293	198	18	)	)	PUNCT
ejpam-3293	199	1	=	=	SYM
ejpam-3293	199	2	r	r	NOUN
ejpam-3293	199	3	is	be	AUX
ejpam-3293	199	4	uncountable	uncountable	ADJ
ejpam-3293	199	5	.	.	PUNCT
ejpam-3293	200	1	thus	thus	ADV
ejpam-3293	200	2	,	,	PUNCT
ejpam-3293	200	3	b	b	PROPN
ejpam-3293	200	4	is	be	AUX
ejpam-3293	200	5	not	not	PART
ejpam-3293	200	6	ωθ	ωθ	NOUN
ejpam-3293	200	7	-	-	PUNCT
ejpam-3293	200	8	open	open	ADJ
ejpam-3293	200	9	.	.	PUNCT
ejpam-3293	201	1	accordingly	accordingly	ADV
ejpam-3293	201	2	,	,	PUNCT
ejpam-3293	201	3	(	(	PUNCT
ejpam-3293	201	4	r	r	NOUN
ejpam-3293	201	5	,	,	PUNCT
ejpam-3293	201	6	t	t	PROPN
ejpam-3293	201	7	)	)	PUNCT
ejpam-3293	201	8	is	be	AUX
ejpam-3293	201	9	ωθ	ωθ	PRON
ejpam-3293	201	10	-	-	PUNCT
ejpam-3293	201	11	connected	connect	VERB
ejpam-3293	201	12	.	.	PUNCT
ejpam-3293	202	1	using	use	VERB
ejpam-3293	202	2	the	the	DET
ejpam-3293	202	3	similar	similar	ADJ
ejpam-3293	202	4	argument	argument	NOUN
ejpam-3293	202	5	in	in	ADP
ejpam-3293	202	6	remark	remark	NOUN
ejpam-3293	202	7	3	3	NUM
ejpam-3293	202	8	,	,	PUNCT
ejpam-3293	202	9	qc	qc	PROPN
ejpam-3293	202	10	∪	∪	X
ejpam-3293	202	11	{	{	PUNCT
ejpam-3293	202	12	0	0	NUM
ejpam-3293	202	13	}	}	PUNCT
ejpam-3293	202	14	is	be	AUX
ejpam-3293	202	15	ω	ω	NOUN
ejpam-3293	202	16	-	-	NOUN
ejpam-3293	202	17	open	open	ADJ
ejpam-3293	202	18	in	in	ADP
ejpam-3293	202	19	r.	r.	PROPN
ejpam-3293	202	20	also	also	ADV
ejpam-3293	202	21	,	,	PUNCT
ejpam-3293	202	22	for	for	ADP
ejpam-3293	202	23	all	all	DET
ejpam-3293	202	24	x	x	SYM
ejpam-3293	202	25	∈	∈	PROPN
ejpam-3293	202	26	q\{0	q\{0	NOUN
ejpam-3293	202	27	}	}	PUNCT
ejpam-3293	202	28	,	,	PUNCT
ejpam-3293	202	29	there	there	PRON
ejpam-3293	202	30	exists	exist	VERB
ejpam-3293	202	31	an	an	DET
ejpam-3293	202	32	open	open	ADJ
ejpam-3293	202	33	set	set	NOUN
ejpam-3293	202	34	o	o	X
ejpam-3293	202	35	=	=	PUNCT
ejpam-3293	203	1	q	q	X
ejpam-3293	203	2	containing	contain	VERB
ejpam-3293	203	3	x	x	PUNCT
ejpam-3293	203	4	such	such	ADJ
ejpam-3293	203	5	that	that	SCONJ
ejpam-3293	203	6	q\(q\{0	q\(q\{0	NOUN
ejpam-3293	203	7	}	}	PUNCT
ejpam-3293	203	8	)	)	PUNCT
ejpam-3293	203	9	is	be	AUX
ejpam-3293	203	10	countable	countable	ADJ
ejpam-3293	203	11	.	.	PUNCT
ejpam-3293	204	1	thus	thus	ADV
ejpam-3293	204	2	,	,	PUNCT
ejpam-3293	204	3	q\{0	q\{0	NOUN
ejpam-3293	204	4	}	}	PUNCT
ejpam-3293	204	5	is	be	AUX
ejpam-3293	204	6	ω	ω	NOUN
ejpam-3293	204	7	-	-	NOUN
ejpam-3293	204	8	open	open	ADJ
ejpam-3293	204	9	in	in	ADP
ejpam-3293	204	10	r.	r.	PROPN
ejpam-3293	204	11	moreover	moreover	ADV
ejpam-3293	204	12	,	,	PUNCT
ejpam-3293	204	13	qc	qc	PROPN
ejpam-3293	204	14	∪	∪	X
ejpam-3293	204	15	{	{	PUNCT
ejpam-3293	204	16	0	0	NUM
ejpam-3293	204	17	}	}	PUNCT
ejpam-3293	204	18	and	and	CCONJ
ejpam-3293	204	19	q\{0	q\{0	PROPN
ejpam-3293	204	20	}	}	PUNCT
ejpam-3293	204	21	are	be	AUX
ejpam-3293	204	22	disjoint	disjoint	NOUN
ejpam-3293	204	23	and	and	CCONJ
ejpam-3293	204	24	r	r	NOUN
ejpam-3293	204	25	=	=	SYM
ejpam-3293	204	26	(	(	PUNCT
ejpam-3293	204	27	qc	qc	PROPN
ejpam-3293	204	28	∪	∪	X
ejpam-3293	204	29	{	{	PUNCT
ejpam-3293	204	30	0	0	NUM
ejpam-3293	204	31	}	}	PUNCT
ejpam-3293	204	32	)	)	PUNCT
ejpam-3293	204	33	∪	∪	NOUN
ejpam-3293	204	34	(	(	PUNCT
ejpam-3293	204	35	q\{0	q\{0	NOUN
ejpam-3293	204	36	}	}	PUNCT
ejpam-3293	204	37	)	)	PUNCT
ejpam-3293	204	38	.	.	PUNCT
ejpam-3293	205	1	this	this	PRON
ejpam-3293	205	2	means	mean	VERB
ejpam-3293	205	3	that	that	SCONJ
ejpam-3293	205	4	(	(	PUNCT
ejpam-3293	205	5	r	r	NOUN
ejpam-3293	205	6	,	,	PUNCT
ejpam-3293	205	7	t	t	PROPN
ejpam-3293	205	8	)	)	PUNCT
ejpam-3293	205	9	is	be	AUX
ejpam-3293	205	10	ω	ω	NOUN
ejpam-3293	205	11	-	-	ADJ
ejpam-3293	205	12	disconnected	disconnected	ADJ
ejpam-3293	205	13	.	.	PUNCT
ejpam-3293	206	1	next	next	ADV
ejpam-3293	206	2	,	,	PUNCT
ejpam-3293	206	3	we	we	PRON
ejpam-3293	206	4	show	show	VERB
ejpam-3293	206	5	that	that	SCONJ
ejpam-3293	206	6	a	a	DET
ejpam-3293	206	7	surjective	surjective	ADJ
ejpam-3293	206	8	ω	ω	ADJ
ejpam-3293	206	9	-	-	ADJ
ejpam-3293	206	10	irresolute	irresolute	ADJ
ejpam-3293	206	11	function	function	NOUN
ejpam-3293	206	12	sends	send	VERB
ejpam-3293	206	13	an	an	DET
ejpam-3293	206	14	ω	ω	ADV
ejpam-3293	206	15	-	-	PUNCT
ejpam-3293	206	16	connected	connect	VERB
ejpam-3293	206	17	space	space	NOUN
ejpam-3293	206	18	to	to	ADP
ejpam-3293	206	19	an	an	DET
ejpam-3293	206	20	ω	ω	ADV
ejpam-3293	206	21	-	-	PUNCT
ejpam-3293	206	22	connected	connect	VERB
ejpam-3293	206	23	space	space	NOUN
ejpam-3293	206	24	.	.	PUNCT
ejpam-3293	207	1	we	we	PRON
ejpam-3293	207	2	shall	shall	AUX
ejpam-3293	207	3	consider	consider	VERB
ejpam-3293	207	4	first	first	ADV
ejpam-3293	207	5	the	the	DET
ejpam-3293	207	6	following	follow	VERB
ejpam-3293	207	7	characterization	characterization	NOUN
ejpam-3293	207	8	of	of	ADP
ejpam-3293	207	9	ω	ω	ADJ
ejpam-3293	207	10	-	-	PUNCT
ejpam-3293	207	11	irresolute	irresolute	ADJ
ejpam-3293	207	12	functions	function	NOUN
ejpam-3293	207	13	.	.	PUNCT
ejpam-3293	208	1	m.	m.	NOUN
ejpam-3293	208	2	labendia	labendia	PROPN
ejpam-3293	208	3	,	,	PUNCT
ejpam-3293	208	4	j.	j.	PROPN
ejpam-3293	208	5	a.	a.	PROPN
ejpam-3293	208	6	sasam	sasam	PROPN
ejpam-3293	208	7	/	/	SYM
ejpam-3293	208	8	eur	eur	PROPN
ejpam-3293	208	9	.	.	PUNCT
ejpam-3293	209	1	j.	j.	PROPN
ejpam-3293	209	2	pure	pure	PROPN
ejpam-3293	209	3	appl	appl	PROPN
ejpam-3293	209	4	.	.	PROPN
ejpam-3293	209	5	math	math	PROPN
ejpam-3293	209	6	,	,	PUNCT
ejpam-3293	209	7	11	11	NUM
ejpam-3293	209	8	(	(	PUNCT
ejpam-3293	209	9	3	3	NUM
ejpam-3293	209	10	)	)	PUNCT
ejpam-3293	209	11	(	(	PUNCT
ejpam-3293	209	12	2018	2018	NUM
ejpam-3293	209	13	)	)	PUNCT
ejpam-3293	209	14	,	,	PUNCT
ejpam-3293	209	15	834	834	NUM
ejpam-3293	209	16	-	-	SYM
ejpam-3293	209	17	843	843	NUM
ejpam-3293	209	18	840	840	NUM
ejpam-3293	209	19	theorem	theorem	NOUN
ejpam-3293	209	20	4	4	NUM
ejpam-3293	209	21	.	.	PUNCT
ejpam-3293	210	1	let	let	VERB
ejpam-3293	210	2	f	f	NOUN
ejpam-3293	210	3	:	:	PUNCT
ejpam-3293	210	4	x	x	X
ejpam-3293	210	5	→	→	SYM
ejpam-3293	210	6	y	y	X
ejpam-3293	210	7	be	be	AUX
ejpam-3293	210	8	a	a	DET
ejpam-3293	210	9	function	function	NOUN
ejpam-3293	210	10	.	.	PUNCT
ejpam-3293	211	1	then	then	ADV
ejpam-3293	211	2	the	the	DET
ejpam-3293	211	3	following	follow	VERB
ejpam-3293	211	4	statements	statement	NOUN
ejpam-3293	211	5	are	be	AUX
ejpam-3293	211	6	equivalent	equivalent	ADJ
ejpam-3293	211	7	.	.	PUNCT
ejpam-3293	212	1	(	(	PUNCT
ejpam-3293	212	2	i	i	NOUN
ejpam-3293	212	3	)	)	PUNCT
ejpam-3293	212	4	f	f	PROPN
ejpam-3293	212	5	is	be	AUX
ejpam-3293	212	6	ω	ω	NOUN
ejpam-3293	212	7	-	-	NOUN
ejpam-3293	212	8	irresolute	irresolute	ADJ
ejpam-3293	212	9	on	on	ADP
ejpam-3293	212	10	x.	x.	PROPN
ejpam-3293	212	11	(	(	PUNCT
ejpam-3293	212	12	ii	ii	NOUN
ejpam-3293	212	13	)	)	PUNCT
ejpam-3293	212	14	f−1(a	f−1(a	PROPN
ejpam-3293	212	15	)	)	PUNCT
ejpam-3293	212	16	is	be	AUX
ejpam-3293	212	17	ω	ω	NOUN
ejpam-3293	212	18	-	-	NOUN
ejpam-3293	212	19	open	open	ADJ
ejpam-3293	212	20	in	in	ADP
ejpam-3293	212	21	x	x	PUNCT
ejpam-3293	212	22	for	for	ADP
ejpam-3293	212	23	each	each	DET
ejpam-3293	212	24	ω	ω	NOUN
ejpam-3293	212	25	-	-	ADJ
ejpam-3293	212	26	open	open	NOUN
ejpam-3293	212	27	subset	subset	VERB
ejpam-3293	212	28	a	a	PRON
ejpam-3293	212	29	of	of	ADP
ejpam-3293	212	30	y	y	PROPN
ejpam-3293	212	31	.	.	PUNCT
ejpam-3293	213	1	(	(	PUNCT
ejpam-3293	213	2	iii	iii	X
ejpam-3293	213	3	)	)	PUNCT
ejpam-3293	213	4	f−1(f	f−1(f	NOUN
ejpam-3293	213	5	)	)	PUNCT
ejpam-3293	213	6	is	be	AUX
ejpam-3293	213	7	ω	ω	NOUN
ejpam-3293	213	8	-	-	ADJ
ejpam-3293	213	9	closed	closed	ADJ
ejpam-3293	213	10	in	in	ADP
ejpam-3293	213	11	x	x	PUNCT
ejpam-3293	213	12	for	for	ADP
ejpam-3293	213	13	each	each	DET
ejpam-3293	213	14	ω	ω	NOUN
ejpam-3293	213	15	-	-	PUNCT
ejpam-3293	213	16	closed	closed	ADJ
ejpam-3293	213	17	subset	subset	NOUN
ejpam-3293	213	18	f	f	PROPN
ejpam-3293	213	19	of	of	ADP
ejpam-3293	213	20	y	y	PROPN
ejpam-3293	213	21	.	.	PUNCT
ejpam-3293	214	1	(	(	PUNCT
ejpam-3293	214	2	iv	iv	X
ejpam-3293	214	3	)	)	PUNCT
ejpam-3293	214	4	clω(f−1(a	clω(f−1(a	PROPN
ejpam-3293	214	5	)	)	PUNCT
ejpam-3293	214	6	)	)	PUNCT
ejpam-3293	215	1	⊆	⊆	NUM
ejpam-3293	215	2	f−1(clω(a	f−1(clω(a	NUM
ejpam-3293	215	3	)	)	PUNCT
ejpam-3293	215	4	)	)	PUNCT
ejpam-3293	215	5	for	for	ADP
ejpam-3293	215	6	each	each	PRON
ejpam-3293	215	7	subset	subset	VERB
ejpam-3293	215	8	a	a	PRON
ejpam-3293	215	9	of	of	ADP
ejpam-3293	215	10	y	y	PROPN
ejpam-3293	215	11	.	.	PUNCT
ejpam-3293	216	1	(	(	PUNCT
ejpam-3293	216	2	v	v	NOUN
ejpam-3293	216	3	)	)	PUNCT
ejpam-3293	216	4	f−1(intω(a	f−1(intω(a	NOUN
ejpam-3293	216	5	)	)	PUNCT
ejpam-3293	216	6	)	)	PUNCT
ejpam-3293	217	1	⊆	⊆	NUM
ejpam-3293	217	2	intω(f−1(a	intω(f−1(a	NOUN
ejpam-3293	217	3	)	)	PUNCT
ejpam-3293	217	4	)	)	PUNCT
ejpam-3293	217	5	for	for	SCONJ
ejpam-3293	217	6	each	each	PRON
ejpam-3293	217	7	subset	subset	VERB
ejpam-3293	217	8	a	a	PRON
ejpam-3293	217	9	of	of	ADP
ejpam-3293	217	10	y	y	PROPN
ejpam-3293	217	11	.	.	PUNCT
ejpam-3293	218	1	proof	proof	NOUN
ejpam-3293	218	2	.	.	PUNCT
ejpam-3293	219	1	(	(	PUNCT
ejpam-3293	219	2	i	i	NOUN
ejpam-3293	219	3	)	)	PUNCT
ejpam-3293	219	4	⇔	⇔	PROPN
ejpam-3293	219	5	(	(	PUNCT
ejpam-3293	219	6	ii	ii	PROPN
ejpam-3293	219	7	):	):	PUNCT
ejpam-3293	219	8	let	let	VERB
ejpam-3293	219	9	a	a	PRON
ejpam-3293	219	10	be	be	AUX
ejpam-3293	219	11	ω	ω	NOUN
ejpam-3293	219	12	-	-	NOUN
ejpam-3293	219	13	open	open	ADJ
ejpam-3293	219	14	in	in	ADP
ejpam-3293	219	15	y	y	PROPN
ejpam-3293	219	16	and	and	CCONJ
ejpam-3293	219	17	x	x	PROPN
ejpam-3293	219	18	∈	∈	PROPN
ejpam-3293	219	19	f−1(a	f−1(a	NOUN
ejpam-3293	219	20	)	)	PUNCT
ejpam-3293	219	21	.	.	PUNCT
ejpam-3293	220	1	by	by	ADP
ejpam-3293	220	2	(	(	PUNCT
ejpam-3293	220	3	i	i	NOUN
ejpam-3293	220	4	)	)	PUNCT
ejpam-3293	220	5	,	,	PUNCT
ejpam-3293	220	6	there	there	PRON
ejpam-3293	220	7	exists	exist	VERB
ejpam-3293	220	8	an	an	DET
ejpam-3293	220	9	ω	ω	ADJ
ejpam-3293	220	10	-	-	ADJ
ejpam-3293	220	11	open	open	ADJ
ejpam-3293	220	12	subset	subset	NOUN
ejpam-3293	220	13	u	u	NOUN
ejpam-3293	220	14	containing	contain	VERB
ejpam-3293	220	15	x	x	PUNCT
ejpam-3293	220	16	such	such	ADJ
ejpam-3293	220	17	that	that	DET
ejpam-3293	220	18	f(u	f(u	PROPN
ejpam-3293	220	19	)	)	PUNCT
ejpam-3293	220	20	⊆	⊆	NUM
ejpam-3293	220	21	a	a	PRON
ejpam-3293	220	22	,	,	PUNCT
ejpam-3293	220	23	so	so	SCONJ
ejpam-3293	220	24	that	that	SCONJ
ejpam-3293	220	25	u	u	PROPN
ejpam-3293	220	26	⊆	⊆	NUM
ejpam-3293	220	27	f−1(a	f−1(a	NOUN
ejpam-3293	220	28	)	)	PUNCT
ejpam-3293	220	29	.	.	PUNCT
ejpam-3293	221	1	thus	thus	ADV
ejpam-3293	221	2	,	,	PUNCT
ejpam-3293	221	3	f−1(a	f−1(a	PROPN
ejpam-3293	221	4	)	)	PUNCT
ejpam-3293	221	5	is	be	AUX
ejpam-3293	221	6	ω	ω	NOUN
ejpam-3293	221	7	-	-	NOUN
ejpam-3293	221	8	open	open	ADJ
ejpam-3293	221	9	in	in	ADP
ejpam-3293	221	10	x.	x.	NOUN
ejpam-3293	221	11	conversely	conversely	ADV
ejpam-3293	221	12	,	,	PUNCT
ejpam-3293	221	13	let	let	VERB
ejpam-3293	221	14	x	x	X
ejpam-3293	221	15	∈	∈	PROPN
ejpam-3293	221	16	x	x	X
ejpam-3293	221	17	and	and	CCONJ
ejpam-3293	221	18	v	v	AUX
ejpam-3293	221	19	be	be	AUX
ejpam-3293	221	20	an	an	DET
ejpam-3293	221	21	ω	ω	ADJ
ejpam-3293	221	22	-	-	ADJ
ejpam-3293	221	23	open	open	ADJ
ejpam-3293	221	24	subset	subset	NOUN
ejpam-3293	221	25	of	of	ADP
ejpam-3293	221	26	y	y	PROPN
ejpam-3293	221	27	containing	contain	VERB
ejpam-3293	221	28	f(x	f(x	PROPN
ejpam-3293	221	29	)	)	PUNCT
ejpam-3293	221	30	.	.	PUNCT
ejpam-3293	222	1	by	by	ADP
ejpam-3293	222	2	assumption	assumption	NOUN
ejpam-3293	222	3	,	,	PUNCT
ejpam-3293	222	4	f−1(v	f−1(v	PROPN
ejpam-3293	222	5	)	)	PUNCT
ejpam-3293	222	6	is	be	AUX
ejpam-3293	222	7	ω	ω	NOUN
ejpam-3293	222	8	-	-	NOUN
ejpam-3293	222	9	open	open	ADJ
ejpam-3293	222	10	in	in	ADP
ejpam-3293	222	11	x	x	PUNCT
ejpam-3293	222	12	containing	contain	VERB
ejpam-3293	222	13	x.	x.	NOUN
ejpam-3293	222	14	let	let	VERB
ejpam-3293	222	15	u	u	PRON
ejpam-3293	222	16	:	:	PUNCT
ejpam-3293	222	17	=	=	SYM
ejpam-3293	222	18	f−1(v	f−1(v	PROPN
ejpam-3293	222	19	)	)	PUNCT
ejpam-3293	222	20	.	.	PUNCT
ejpam-3293	223	1	hence	hence	ADV
ejpam-3293	223	2	,	,	PUNCT
ejpam-3293	223	3	f(u	f(u	PROPN
ejpam-3293	223	4	)	)	PUNCT
ejpam-3293	223	5	⊆	⊆	NUM
ejpam-3293	223	6	v	v	NOUN
ejpam-3293	223	7	.	.	PUNCT
ejpam-3293	224	1	(	(	PUNCT
ejpam-3293	224	2	ii)⇔	ii)⇔	X
ejpam-3293	224	3	(	(	PUNCT
ejpam-3293	224	4	iii	iii	NOUN
ejpam-3293	224	5	):	):	PUNCT
ejpam-3293	224	6	let	let	VERB
ejpam-3293	224	7	f	f	PRON
ejpam-3293	224	8	be	be	AUX
ejpam-3293	224	9	an	an	DET
ejpam-3293	224	10	ω	ω	ADV
ejpam-3293	224	11	-	-	PUNCT
ejpam-3293	224	12	closed	closed	ADJ
ejpam-3293	224	13	subset	subset	NOUN
ejpam-3293	224	14	of	of	ADP
ejpam-3293	224	15	y	y	PROPN
ejpam-3293	224	16	.	.	PUNCT
ejpam-3293	225	1	by	by	ADP
ejpam-3293	225	2	assumption	assumption	NOUN
ejpam-3293	225	3	,	,	PUNCT
ejpam-3293	225	4	f−1(y	f−1(y	NOUN
ejpam-3293	225	5	\f	\f	PUNCT
ejpam-3293	225	6	)	)	PUNCT
ejpam-3293	225	7	=	=	SYM
ejpam-3293	225	8	x\f−1(f	x\f−1(f	PROPN
ejpam-3293	225	9	)	)	PUNCT
ejpam-3293	225	10	is	be	AUX
ejpam-3293	225	11	ω	ω	NOUN
ejpam-3293	225	12	-	-	NOUN
ejpam-3293	225	13	open	open	ADJ
ejpam-3293	225	14	in	in	ADP
ejpam-3293	225	15	x.	x.	PROPN
ejpam-3293	225	16	thus	thus	ADV
ejpam-3293	225	17	,	,	PUNCT
ejpam-3293	225	18	f−1(f	f−1(f	PROPN
ejpam-3293	225	19	)	)	PUNCT
ejpam-3293	225	20	is	be	AUX
ejpam-3293	225	21	ω	ω	ADV
ejpam-3293	225	22	-	-	ADJ
ejpam-3293	225	23	closed	closed	ADJ
ejpam-3293	225	24	.	.	PUNCT
ejpam-3293	226	1	the	the	DET
ejpam-3293	226	2	converse	converse	NOUN
ejpam-3293	226	3	is	be	AUX
ejpam-3293	226	4	proved	prove	VERB
ejpam-3293	226	5	similarly	similarly	ADV
ejpam-3293	226	6	.	.	PUNCT
ejpam-3293	227	1	(	(	PUNCT
ejpam-3293	227	2	ii	ii	NOUN
ejpam-3293	227	3	)	)	PUNCT
ejpam-3293	227	4	⇒	⇒	NOUN
ejpam-3293	227	5	(	(	PUNCT
ejpam-3293	227	6	iv	iv	NUM
ejpam-3293	227	7	):	):	PUNCT
ejpam-3293	227	8	let	let	VERB
ejpam-3293	227	9	a	a	DET
ejpam-3293	227	10	⊆	⊆	NUM
ejpam-3293	227	11	y	y	NOUN
ejpam-3293	227	12	.	.	PUNCT
ejpam-3293	228	1	let	let	VERB
ejpam-3293	228	2	x	x	PUNCT
ejpam-3293	228	3	∈	∈	PROPN
ejpam-3293	228	4	x	x	SYM
ejpam-3293	228	5	\	\	PROPN
ejpam-3293	228	6	f−1(clω(a	f−1(clω(a	NUM
ejpam-3293	228	7	)	)	PUNCT
ejpam-3293	228	8	)	)	PUNCT
ejpam-3293	228	9	.	.	PUNCT
ejpam-3293	229	1	then	then	ADV
ejpam-3293	229	2	f(x	f(x	PROPN
ejpam-3293	229	3	)	)	PUNCT
ejpam-3293	229	4	∈	∈	PROPN
ejpam-3293	229	5	y	y	PROPN
ejpam-3293	229	6	\	\	PROPN
ejpam-3293	229	7	clω(a	clω(a	PROPN
ejpam-3293	229	8	)	)	PUNCT
ejpam-3293	229	9	.	.	PUNCT
ejpam-3293	230	1	then	then	ADV
ejpam-3293	230	2	there	there	PRON
ejpam-3293	230	3	exists	exist	VERB
ejpam-3293	230	4	an	an	DET
ejpam-3293	230	5	ω	ω	ADJ
ejpam-3293	230	6	-	-	ADJ
ejpam-3293	230	7	open	open	ADJ
ejpam-3293	230	8	subset	subset	NOUN
ejpam-3293	230	9	v	v	NOUN
ejpam-3293	230	10	of	of	ADP
ejpam-3293	230	11	y	y	PROPN
ejpam-3293	230	12	containing	contain	VERB
ejpam-3293	230	13	f(x	f(x	PROPN
ejpam-3293	230	14	)	)	PUNCT
ejpam-3293	230	15	such	such	ADJ
ejpam-3293	230	16	that	that	PRON
ejpam-3293	230	17	v	v	ADP
ejpam-3293	230	18	∩	∩	NOUN
ejpam-3293	230	19	a	a	DET
ejpam-3293	230	20	=	=	SYM
ejpam-3293	230	21	∅.	∅.	NOUN
ejpam-3293	230	22	by	by	ADP
ejpam-3293	230	23	assumption	assumption	NOUN
ejpam-3293	230	24	,	,	PUNCT
ejpam-3293	230	25	f−1(v	f−1(v	PROPN
ejpam-3293	230	26	)	)	PUNCT
ejpam-3293	230	27	is	be	AUX
ejpam-3293	230	28	ω	ω	NOUN
ejpam-3293	230	29	-	-	NOUN
ejpam-3293	230	30	open	open	ADJ
ejpam-3293	230	31	in	in	ADP
ejpam-3293	230	32	x	x	PUNCT
ejpam-3293	230	33	containing	contain	VERB
ejpam-3293	230	34	x	x	PUNCT
ejpam-3293	230	35	such	such	ADJ
ejpam-3293	230	36	that	that	DET
ejpam-3293	230	37	f−1(v	f−1(v	NOUN
ejpam-3293	230	38	)	)	PUNCT
ejpam-3293	230	39	∩	∩	ADJ
ejpam-3293	230	40	f−1(a	f−1(a	NOUN
ejpam-3293	230	41	)	)	PUNCT
ejpam-3293	231	1	=	=	PUNCT
ejpam-3293	231	2	∅.	∅.	VERB
ejpam-3293	231	3	hence	hence	ADV
ejpam-3293	231	4	,	,	PUNCT
ejpam-3293	231	5	x	x	PUNCT
ejpam-3293	231	6	∈	∈	NOUN
ejpam-3293	231	7	x	x	SYM
ejpam-3293	231	8	\	\	PROPN
ejpam-3293	231	9	clω(f−1(a	clω(f−1(a	PROPN
ejpam-3293	231	10	)	)	PUNCT
ejpam-3293	231	11	)	)	PUNCT
ejpam-3293	231	12	.	.	PUNCT
ejpam-3293	232	1	thus	thus	ADV
ejpam-3293	232	2	,	,	PUNCT
ejpam-3293	232	3	clω(f−1(a	clω(f−1(a	PROPN
ejpam-3293	232	4	)	)	PUNCT
ejpam-3293	232	5	)	)	PUNCT
ejpam-3293	233	1	⊆	⊆	NUM
ejpam-3293	233	2	f−1(clω(a	f−1(clω(a	NUM
ejpam-3293	233	3	)	)	PUNCT
ejpam-3293	233	4	)	)	PUNCT
ejpam-3293	233	5	.	.	PUNCT
ejpam-3293	234	1	(	(	PUNCT
ejpam-3293	234	2	iv)⇒	iv)⇒	X
ejpam-3293	234	3	(	(	PUNCT
ejpam-3293	234	4	v	v	NOUN
ejpam-3293	234	5	):	):	PUNCT
ejpam-3293	234	6	let	let	VERB
ejpam-3293	234	7	a	a	DET
ejpam-3293	234	8	⊆	⊆	NUM
ejpam-3293	234	9	y	y	NOUN
ejpam-3293	234	10	.	.	PUNCT
ejpam-3293	235	1	by	by	ADP
ejpam-3293	235	2	assumption	assumption	NOUN
ejpam-3293	235	3	and	and	CCONJ
ejpam-3293	235	4	lemma	lemma	PROPN
ejpam-3293	235	5	2	2	NUM
ejpam-3293	235	6	(	(	PUNCT
ejpam-3293	235	7	v	v	NOUN
ejpam-3293	235	8	)	)	PUNCT
ejpam-3293	235	9	,	,	PUNCT
ejpam-3293	235	10	x	x	SYM
ejpam-3293	235	11	\	\	PROPN
ejpam-3293	235	12	intω(f−1(a	intω(f−1(a	NOUN
ejpam-3293	235	13	)	)	PUNCT
ejpam-3293	235	14	)	)	PUNCT
ejpam-3293	236	1	=	=	PRON
ejpam-3293	236	2	clω(f−1(y	clω(f−1(y	ADJ
ejpam-3293	236	3	\a	\a	ADJ
ejpam-3293	236	4	)	)	PUNCT
ejpam-3293	236	5	)	)	PUNCT
ejpam-3293	237	1	⊆	⊆	NUM
ejpam-3293	237	2	f−1(clω(y	f−1(clω(y	NOUN
ejpam-3293	237	3	\a	\a	NUM
ejpam-3293	237	4	)	)	PUNCT
ejpam-3293	237	5	)	)	PUNCT
ejpam-3293	238	1	=	=	PUNCT
ejpam-3293	238	2	f−1(y	f−1(y	PROPN
ejpam-3293	238	3	\	\	PROPN
ejpam-3293	238	4	intω(a	intω(a	PROPN
ejpam-3293	238	5	)	)	PUNCT
ejpam-3293	238	6	)	)	PUNCT
ejpam-3293	239	1	=	=	PUNCT
ejpam-3293	239	2	x	x	SYM
ejpam-3293	239	3	\	\	PROPN
ejpam-3293	239	4	f−1(intω(a	f−1(intω(a	PROPN
ejpam-3293	239	5	)	)	PUNCT
ejpam-3293	239	6	)	)	PUNCT
ejpam-3293	239	7	.	.	PUNCT
ejpam-3293	240	1	(	(	PUNCT
ejpam-3293	240	2	v	v	NOUN
ejpam-3293	240	3	)	)	PUNCT
ejpam-3293	240	4	⇒	⇒	NOUN
ejpam-3293	240	5	(	(	PUNCT
ejpam-3293	240	6	i	i	NOUN
ejpam-3293	240	7	):	):	PUNCT
ejpam-3293	240	8	let	let	VERB
ejpam-3293	240	9	x	x	PUNCT
ejpam-3293	240	10	∈	∈	PROPN
ejpam-3293	240	11	x	x	X
ejpam-3293	240	12	and	and	CCONJ
ejpam-3293	240	13	a	a	DET
ejpam-3293	240	14	be	be	AUX
ejpam-3293	240	15	an	an	DET
ejpam-3293	240	16	ω	ω	ADJ
ejpam-3293	240	17	-	-	ADJ
ejpam-3293	240	18	open	open	ADJ
ejpam-3293	240	19	subset	subset	NOUN
ejpam-3293	240	20	of	of	ADP
ejpam-3293	240	21	y	y	PROPN
ejpam-3293	240	22	containing	contain	VERB
ejpam-3293	240	23	f(x	f(x	PROPN
ejpam-3293	240	24	)	)	PUNCT
ejpam-3293	240	25	.	.	PUNCT
ejpam-3293	241	1	then	then	ADV
ejpam-3293	241	2	x	x	SYM
ejpam-3293	241	3	∈	∈	PROPN
ejpam-3293	241	4	f−1(a	f−1(a	NOUN
ejpam-3293	241	5	)	)	PUNCT
ejpam-3293	242	1	=	=	SYM
ejpam-3293	242	2	f−1(intω(a	f−1(intω(a	PROPN
ejpam-3293	242	3	)	)	PUNCT
ejpam-3293	242	4	)	)	PUNCT
ejpam-3293	243	1	⊆	⊆	NUM
ejpam-3293	243	2	intω(f−1(a	intω(f−1(a	NOUN
ejpam-3293	243	3	)	)	PUNCT
ejpam-3293	243	4	)	)	PUNCT
ejpam-3293	243	5	.	.	PUNCT
ejpam-3293	244	1	this	this	PRON
ejpam-3293	244	2	means	mean	VERB
ejpam-3293	244	3	that	that	SCONJ
ejpam-3293	244	4	b	b	X
ejpam-3293	244	5	:	:	PUNCT
ejpam-3293	244	6	=	=	SYM
ejpam-3293	244	7	f−1(a	f−1(a	NOUN
ejpam-3293	244	8	)	)	PUNCT
ejpam-3293	244	9	is	be	AUX
ejpam-3293	244	10	ω	ω	NOUN
ejpam-3293	244	11	-	-	NOUN
ejpam-3293	244	12	open	open	ADJ
ejpam-3293	244	13	in	in	ADP
ejpam-3293	244	14	x	x	PUNCT
ejpam-3293	244	15	containing	contain	VERB
ejpam-3293	244	16	x	x	PUNCT
ejpam-3293	244	17	such	such	ADJ
ejpam-3293	244	18	that	that	DET
ejpam-3293	244	19	f(b	f(b	PROPN
ejpam-3293	244	20	)	)	PUNCT
ejpam-3293	244	21	⊆	⊆	NUM
ejpam-3293	244	22	a.	a.	NOUN
ejpam-3293	244	23	the	the	DET
ejpam-3293	244	24	following	follow	VERB
ejpam-3293	244	25	result	result	NOUN
ejpam-3293	244	26	shows	show	VERB
ejpam-3293	244	27	that	that	SCONJ
ejpam-3293	244	28	a	a	DET
ejpam-3293	244	29	surjective	surjective	ADJ
ejpam-3293	244	30	ω	ω	ADJ
ejpam-3293	244	31	-	-	ADJ
ejpam-3293	244	32	irresolute	irresolute	ADJ
ejpam-3293	244	33	function	function	NOUN
ejpam-3293	244	34	sends	send	VERB
ejpam-3293	244	35	an	an	DET
ejpam-3293	244	36	ω	ω	ADV
ejpam-3293	244	37	-	-	PUNCT
ejpam-3293	244	38	connected	connect	VERB
ejpam-3293	244	39	space	space	NOUN
ejpam-3293	244	40	to	to	ADP
ejpam-3293	244	41	an	an	DET
ejpam-3293	244	42	ω	ω	ADV
ejpam-3293	244	43	-	-	PUNCT
ejpam-3293	244	44	connected	connect	VERB
ejpam-3293	244	45	space	space	NOUN
ejpam-3293	244	46	.	.	PUNCT
ejpam-3293	245	1	theorem	theorem	NOUN
ejpam-3293	245	2	5	5	NUM
ejpam-3293	245	3	.	.	PUNCT
ejpam-3293	246	1	if	if	SCONJ
ejpam-3293	246	2	f	f	PROPN
ejpam-3293	246	3	:	:	PUNCT
ejpam-3293	246	4	x	x	X
ejpam-3293	246	5	→	→	SYM
ejpam-3293	246	6	y	y	PROPN
ejpam-3293	246	7	is	be	AUX
ejpam-3293	246	8	a	a	DET
ejpam-3293	246	9	surjective	surjective	ADJ
ejpam-3293	246	10	ω	ω	ADJ
ejpam-3293	246	11	-	-	ADJ
ejpam-3293	246	12	irresolute	irresolute	ADJ
ejpam-3293	246	13	function	function	NOUN
ejpam-3293	246	14	and	and	CCONJ
ejpam-3293	246	15	x	x	X
ejpam-3293	246	16	is	be	AUX
ejpam-3293	246	17	ω	ω	ADV
ejpam-3293	246	18	-	-	VERB
ejpam-3293	246	19	connected	connected	ADJ
ejpam-3293	246	20	,	,	PUNCT
ejpam-3293	246	21	then	then	ADV
ejpam-3293	246	22	y	y	PROPN
ejpam-3293	246	23	is	be	AUX
ejpam-3293	246	24	ω	ω	ADV
ejpam-3293	246	25	-	-	PUNCT
ejpam-3293	246	26	connected	connect	VERB
ejpam-3293	246	27	.	.	PUNCT
ejpam-3293	247	1	proof	proof	NOUN
ejpam-3293	247	2	.	.	PUNCT
ejpam-3293	248	1	suppose	suppose	VERB
ejpam-3293	248	2	that	that	SCONJ
ejpam-3293	248	3	y	y	PROPN
ejpam-3293	248	4	is	be	AUX
ejpam-3293	248	5	ω	ω	NOUN
ejpam-3293	248	6	-	-	ADJ
ejpam-3293	248	7	disconnected	disconnected	ADJ
ejpam-3293	248	8	.	.	PUNCT
ejpam-3293	249	1	then	then	ADV
ejpam-3293	249	2	there	there	PRON
ejpam-3293	249	3	exist	exist	VERB
ejpam-3293	249	4	disjoint	disjoint	NOUN
ejpam-3293	249	5	nonempty	nonempty	X
ejpam-3293	249	6	ω	ω	ADJ
ejpam-3293	249	7	-	-	ADJ
ejpam-3293	249	8	open	open	ADJ
ejpam-3293	249	9	sets	set	VERB
ejpam-3293	249	10	u	u	NOUN
ejpam-3293	249	11	and	and	CCONJ
ejpam-3293	249	12	v	v	ADP
ejpam-3293	249	13	such	such	ADJ
ejpam-3293	249	14	that	that	DET
ejpam-3293	249	15	y	y	NOUN
ejpam-3293	249	16	=	=	PUNCT
ejpam-3293	249	17	u∪v	u∪v	INTJ
ejpam-3293	249	18	.	.	PUNCT
ejpam-3293	250	1	since	since	SCONJ
ejpam-3293	250	2	f	f	PROPN
ejpam-3293	250	3	is	be	AUX
ejpam-3293	250	4	surjective	surjective	ADJ
ejpam-3293	250	5	,	,	PUNCT
ejpam-3293	250	6	f−1(u	f−1(u	PROPN
ejpam-3293	250	7	)	)	PUNCT
ejpam-3293	250	8	and	and	CCONJ
ejpam-3293	250	9	f−1(v	f−1(v	PROPN
ejpam-3293	250	10	)	)	PUNCT
ejpam-3293	250	11	are	be	AUX
ejpam-3293	250	12	nonempty	nonempty	ADJ
ejpam-3293	250	13	.	.	PUNCT
ejpam-3293	251	1	by	by	ADP
ejpam-3293	251	2	theorem	theorem	ADJ
ejpam-3293	251	3	4	4	NUM
ejpam-3293	251	4	,	,	PUNCT
ejpam-3293	251	5	f−1(u	f−1(u	PROPN
ejpam-3293	251	6	)	)	PUNCT
ejpam-3293	251	7	and	and	CCONJ
ejpam-3293	251	8	f−1(v	f−1(v	PROPN
ejpam-3293	251	9	)	)	PUNCT
ejpam-3293	251	10	are	be	AUX
ejpam-3293	251	11	ω	ω	ADV
ejpam-3293	251	12	-	-	ADJ
ejpam-3293	251	13	open	open	ADJ
ejpam-3293	251	14	and	and	CCONJ
ejpam-3293	251	15	x	x	X
ejpam-3293	251	16	=	=	SYM
ejpam-3293	251	17	f−1(u	f−1(u	PROPN
ejpam-3293	251	18	)	)	PUNCT
ejpam-3293	251	19	∪	∪	NOUN
ejpam-3293	251	20	f−1(v	f−1(v	PROPN
ejpam-3293	251	21	)	)	PUNCT
ejpam-3293	251	22	.	.	PUNCT
ejpam-3293	252	1	this	this	PRON
ejpam-3293	252	2	implies	imply	VERB
ejpam-3293	252	3	that	that	SCONJ
ejpam-3293	252	4	x	x	PRON
ejpam-3293	252	5	is	be	AUX
ejpam-3293	252	6	ω	ω	NOUN
ejpam-3293	252	7	-	-	ADJ
ejpam-3293	252	8	disconnected	disconnected	ADJ
ejpam-3293	252	9	,	,	PUNCT
ejpam-3293	252	10	a	a	DET
ejpam-3293	252	11	contradiction	contradiction	NOUN
ejpam-3293	252	12	.	.	PUNCT
ejpam-3293	253	1	m.	m.	NOUN
ejpam-3293	253	2	labendia	labendia	PROPN
ejpam-3293	253	3	,	,	PUNCT
ejpam-3293	253	4	j.	j.	PROPN
ejpam-3293	253	5	a.	a.	PROPN
ejpam-3293	253	6	sasam	sasam	PROPN
ejpam-3293	253	7	/	/	SYM
ejpam-3293	253	8	eur	eur	PROPN
ejpam-3293	253	9	.	.	PUNCT
ejpam-3293	254	1	j.	j.	PROPN
ejpam-3293	254	2	pure	pure	PROPN
ejpam-3293	254	3	appl	appl	PROPN
ejpam-3293	254	4	.	.	PROPN
ejpam-3293	254	5	math	math	PROPN
ejpam-3293	254	6	,	,	PUNCT
ejpam-3293	254	7	11	11	NUM
ejpam-3293	254	8	(	(	PUNCT
ejpam-3293	254	9	3	3	NUM
ejpam-3293	254	10	)	)	PUNCT
ejpam-3293	254	11	(	(	PUNCT
ejpam-3293	254	12	2018	2018	NUM
ejpam-3293	254	13	)	)	PUNCT
ejpam-3293	254	14	,	,	PUNCT
ejpam-3293	254	15	834	834	NUM
ejpam-3293	254	16	-	-	SYM
ejpam-3293	254	17	843	843	NUM
ejpam-3293	254	18	841	841	NUM
ejpam-3293	254	19	4	4	NUM
ejpam-3293	254	20	.	.	PUNCT
ejpam-3293	255	1	ω	ω	NUM
ejpam-3293	255	2	-	-	PUNCT
ejpam-3293	255	3	continuity	continuity	NOUN
ejpam-3293	255	4	of	of	ADP
ejpam-3293	255	5	functions	function	NOUN
ejpam-3293	255	6	in	in	ADP
ejpam-3293	255	7	the	the	DET
ejpam-3293	255	8	product	product	NOUN
ejpam-3293	255	9	space	space	NOUN
ejpam-3293	255	10	this	this	DET
ejpam-3293	255	11	section	section	NOUN
ejpam-3293	255	12	gives	give	VERB
ejpam-3293	255	13	a	a	DET
ejpam-3293	255	14	characterization	characterization	NOUN
ejpam-3293	255	15	of	of	ADP
ejpam-3293	255	16	an	an	DET
ejpam-3293	255	17	ω	ω	ADJ
ejpam-3293	255	18	-	-	ADJ
ejpam-3293	255	19	continuous	continuous	ADJ
ejpam-3293	255	20	function	function	NOUN
ejpam-3293	255	21	from	from	ADP
ejpam-3293	255	22	an	an	DET
ejpam-3293	255	23	arbitrary	arbitrary	ADJ
ejpam-3293	255	24	topological	topological	ADJ
ejpam-3293	255	25	space	space	NOUN
ejpam-3293	255	26	into	into	ADP
ejpam-3293	255	27	the	the	DET
ejpam-3293	255	28	product	product	NOUN
ejpam-3293	255	29	space	space	NOUN
ejpam-3293	255	30	.	.	PUNCT
ejpam-3293	256	1	we	we	PRON
ejpam-3293	256	2	shall	shall	AUX
ejpam-3293	256	3	give	give	VERB
ejpam-3293	256	4	first	first	ADV
ejpam-3293	256	5	the	the	DET
ejpam-3293	256	6	characterization	characterization	NOUN
ejpam-3293	256	7	of	of	ADP
ejpam-3293	256	8	ω	ω	ADJ
ejpam-3293	256	9	-	-	ADJ
ejpam-3293	256	10	continuous	continuous	ADJ
ejpam-3293	256	11	function	function	NOUN
ejpam-3293	256	12	.	.	PUNCT
ejpam-3293	257	1	theorem	theorem	NOUN
ejpam-3293	257	2	6	6	NUM
ejpam-3293	257	3	.	.	PUNCT
ejpam-3293	258	1	let	let	VERB
ejpam-3293	258	2	f	f	NOUN
ejpam-3293	258	3	:	:	PUNCT
ejpam-3293	258	4	x	x	X
ejpam-3293	258	5	→	→	SYM
ejpam-3293	258	6	y	y	X
ejpam-3293	258	7	be	be	AUX
ejpam-3293	258	8	a	a	DET
ejpam-3293	258	9	function	function	NOUN
ejpam-3293	258	10	.	.	PUNCT
ejpam-3293	259	1	then	then	ADV
ejpam-3293	259	2	the	the	DET
ejpam-3293	259	3	following	follow	VERB
ejpam-3293	259	4	statements	statement	NOUN
ejpam-3293	259	5	are	be	AUX
ejpam-3293	259	6	equivalent	equivalent	ADJ
ejpam-3293	259	7	.	.	PUNCT
ejpam-3293	260	1	(	(	PUNCT
ejpam-3293	260	2	i	i	NOUN
ejpam-3293	260	3	)	)	PUNCT
ejpam-3293	260	4	f	f	PROPN
ejpam-3293	260	5	is	be	AUX
ejpam-3293	260	6	ω	ω	NOUN
ejpam-3293	260	7	-	-	ADJ
ejpam-3293	260	8	continuous	continuous	ADJ
ejpam-3293	260	9	on	on	ADP
ejpam-3293	260	10	x.	x.	PROPN
ejpam-3293	260	11	(	(	PUNCT
ejpam-3293	260	12	ii	ii	PROPN
ejpam-3293	260	13	)	)	PUNCT
ejpam-3293	260	14	f−1(f	f−1(f	PROPN
ejpam-3293	260	15	)	)	PUNCT
ejpam-3293	260	16	is	be	AUX
ejpam-3293	260	17	ω	ω	NOUN
ejpam-3293	260	18	-	-	ADJ
ejpam-3293	260	19	closed	closed	ADJ
ejpam-3293	260	20	in	in	ADP
ejpam-3293	260	21	x	x	PUNCT
ejpam-3293	260	22	for	for	ADP
ejpam-3293	260	23	each	each	DET
ejpam-3293	260	24	closed	close	VERB
ejpam-3293	260	25	subset	subset	VERB
ejpam-3293	260	26	f	f	PROPN
ejpam-3293	260	27	of	of	ADP
ejpam-3293	260	28	y	y	PROPN
ejpam-3293	260	29	.	.	PUNCT
ejpam-3293	261	1	(	(	PUNCT
ejpam-3293	261	2	iii	iii	NOUN
ejpam-3293	261	3	)	)	PUNCT
ejpam-3293	261	4	f−1(b	f−1(b	PROPN
ejpam-3293	261	5	)	)	PUNCT
ejpam-3293	261	6	is	be	AUX
ejpam-3293	261	7	ω	ω	NOUN
ejpam-3293	261	8	-	-	NOUN
ejpam-3293	261	9	open	open	ADJ
ejpam-3293	261	10	in	in	ADP
ejpam-3293	261	11	x	x	PUNCT
ejpam-3293	261	12	for	for	ADP
ejpam-3293	261	13	each	each	DET
ejpam-3293	261	14	(	(	PUNCT
ejpam-3293	261	15	subbasic	subbasic	NOUN
ejpam-3293	261	16	)	)	PUNCT
ejpam-3293	261	17	basic	basic	ADJ
ejpam-3293	261	18	open	open	ADJ
ejpam-3293	261	19	set	set	NOUN
ejpam-3293	261	20	b	b	PROPN
ejpam-3293	261	21	in	in	ADP
ejpam-3293	261	22	y	y	PROPN
ejpam-3293	261	23	.	.	PUNCT
ejpam-3293	262	1	(	(	PUNCT
ejpam-3293	262	2	iv	iv	X
ejpam-3293	262	3	)	)	PUNCT
ejpam-3293	262	4	for	for	ADP
ejpam-3293	262	5	every	every	DET
ejpam-3293	262	6	p	p	NOUN
ejpam-3293	262	7	∈	∈	PROPN
ejpam-3293	262	8	x	x	X
ejpam-3293	262	9	and	and	CCONJ
ejpam-3293	262	10	every	every	DET
ejpam-3293	262	11	open	open	ADJ
ejpam-3293	262	12	set	set	VERB
ejpam-3293	262	13	v	v	NOUN
ejpam-3293	262	14	of	of	ADP
ejpam-3293	262	15	y	y	PROPN
ejpam-3293	262	16	containing	contain	VERB
ejpam-3293	262	17	f(p	f(p	PROPN
ejpam-3293	262	18	)	)	PUNCT
ejpam-3293	262	19	,	,	PUNCT
ejpam-3293	262	20	then	then	ADV
ejpam-3293	262	21	exists	exist	VERB
ejpam-3293	262	22	an	an	DET
ejpam-3293	262	23	ω	ω	ADJ
ejpam-3293	262	24	-	-	ADJ
ejpam-3293	262	25	open	open	ADJ
ejpam-3293	262	26	set	set	NOUN
ejpam-3293	262	27	u	u	NOUN
ejpam-3293	262	28	containing	contain	VERB
ejpam-3293	262	29	p	p	NOUN
ejpam-3293	262	30	such	such	ADJ
ejpam-3293	262	31	that	that	DET
ejpam-3293	262	32	f(u	f(u	PROPN
ejpam-3293	262	33	)	)	PUNCT
ejpam-3293	262	34	⊆	⊆	NUM
ejpam-3293	262	35	v	v	NOUN
ejpam-3293	262	36	.	.	PUNCT
ejpam-3293	263	1	(	(	PUNCT
ejpam-3293	263	2	v	v	NOUN
ejpam-3293	263	3	)	)	PUNCT
ejpam-3293	263	4	f(clω(a	f(clω(a	NOUN
ejpam-3293	263	5	)	)	PUNCT
ejpam-3293	263	6	)	)	PUNCT
ejpam-3293	264	1	⊆	⊆	NUM
ejpam-3293	264	2	cl(f(a	cl(f(a	NOUN
ejpam-3293	264	3	)	)	PUNCT
ejpam-3293	264	4	)	)	PUNCT
ejpam-3293	264	5	for	for	ADP
ejpam-3293	264	6	each	each	DET
ejpam-3293	264	7	a	a	DET
ejpam-3293	264	8	⊆	⊆	NUM
ejpam-3293	264	9	x.	x.	NOUN
ejpam-3293	264	10	(	(	PUNCT
ejpam-3293	264	11	vi	vi	NOUN
ejpam-3293	264	12	)	)	PUNCT
ejpam-3293	264	13	clω(f−1(b	clω(f−1(b	PROPN
ejpam-3293	264	14	)	)	PUNCT
ejpam-3293	264	15	)	)	PUNCT
ejpam-3293	264	16	⊆	⊆	NUM
ejpam-3293	264	17	f−1(cl(b	f−1(cl(b	NOUN
ejpam-3293	264	18	)	)	PUNCT
ejpam-3293	264	19	)	)	PUNCT
ejpam-3293	264	20	for	for	ADP
ejpam-3293	264	21	each	each	DET
ejpam-3293	264	22	b	b	PROPN
ejpam-3293	264	23	⊆	⊆	NUM
ejpam-3293	264	24	y	y	PROPN
ejpam-3293	264	25	.	.	PUNCT
ejpam-3293	265	1	proof	proof	NOUN
ejpam-3293	265	2	.	.	PUNCT
ejpam-3293	266	1	(	(	PUNCT
ejpam-3293	266	2	i	i	NOUN
ejpam-3293	266	3	)	)	PUNCT
ejpam-3293	266	4	⇔	⇔	PROPN
ejpam-3293	266	5	(	(	PUNCT
ejpam-3293	266	6	ii	ii	PROPN
ejpam-3293	266	7	):	):	PUNCT
ejpam-3293	266	8	let	let	VERB
ejpam-3293	266	9	f	f	PRON
ejpam-3293	266	10	be	be	AUX
ejpam-3293	266	11	closed	close	VERB
ejpam-3293	266	12	in	in	ADP
ejpam-3293	266	13	y	y	PROPN
ejpam-3293	266	14	.	.	PUNCT
ejpam-3293	267	1	then	then	ADV
ejpam-3293	267	2	f−1(y	f−1(y	PROPN
ejpam-3293	267	3	\f	\f	X
ejpam-3293	267	4	)	)	PUNCT
ejpam-3293	268	1	=	=	SYM
ejpam-3293	268	2	x\f−1(f	x\f−1(f	PROPN
ejpam-3293	268	3	)	)	PUNCT
ejpam-3293	268	4	is	be	AUX
ejpam-3293	268	5	ω	ω	NOUN
ejpam-3293	268	6	-	-	NOUN
ejpam-3293	268	7	open	open	ADJ
ejpam-3293	268	8	in	in	ADP
ejpam-3293	268	9	x.	x.	PROPN
ejpam-3293	268	10	thus	thus	ADV
ejpam-3293	268	11	,	,	PUNCT
ejpam-3293	268	12	f−1(f	f−1(f	PROPN
ejpam-3293	268	13	)	)	PUNCT
ejpam-3293	268	14	is	be	AUX
ejpam-3293	268	15	ω	ω	NOUN
ejpam-3293	268	16	-	-	ADJ
ejpam-3293	268	17	closed	closed	ADJ
ejpam-3293	268	18	in	in	ADP
ejpam-3293	268	19	x.	x.	NOUN
ejpam-3293	268	20	the	the	DET
ejpam-3293	268	21	converse	converse	NOUN
ejpam-3293	268	22	is	be	AUX
ejpam-3293	268	23	proved	prove	VERB
ejpam-3293	268	24	similarly	similarly	ADV
ejpam-3293	268	25	.	.	PUNCT
ejpam-3293	269	1	(	(	PUNCT
ejpam-3293	269	2	i)⇔	i)⇔	PROPN
ejpam-3293	269	3	(	(	PUNCT
ejpam-3293	269	4	iii	iii	NOUN
ejpam-3293	269	5	):	):	PUNCT
ejpam-3293	269	6	(	(	PUNCT
ejpam-3293	269	7	i	i	NOUN
ejpam-3293	269	8	)	)	PUNCT
ejpam-3293	269	9	implies	imply	VERB
ejpam-3293	269	10	(	(	PUNCT
ejpam-3293	269	11	iii	iii	X
ejpam-3293	269	12	)	)	PUNCT
ejpam-3293	269	13	holds	hold	VERB
ejpam-3293	269	14	since	since	ADV
ejpam-3293	269	15	(	(	PUNCT
ejpam-3293	269	16	subbasic	subbasic	ADJ
ejpam-3293	269	17	)	)	PUNCT
ejpam-3293	269	18	basic	basic	ADJ
ejpam-3293	269	19	open	open	ADJ
ejpam-3293	269	20	sets	set	NOUN
ejpam-3293	269	21	are	be	AUX
ejpam-3293	269	22	open	open	ADJ
ejpam-3293	269	23	sets	set	NOUN
ejpam-3293	269	24	.	.	PUNCT
ejpam-3293	270	1	conversely	conversely	ADV
ejpam-3293	270	2	,	,	PUNCT
ejpam-3293	270	3	suppose	suppose	VERB
ejpam-3293	270	4	that	that	SCONJ
ejpam-3293	270	5	f−1(b	f−1(b	PROPN
ejpam-3293	270	6	)	)	PUNCT
ejpam-3293	270	7	is	be	AUX
ejpam-3293	270	8	ω	ω	NOUN
ejpam-3293	270	9	-	-	NOUN
ejpam-3293	270	10	open	open	ADJ
ejpam-3293	270	11	in	in	ADP
ejpam-3293	270	12	x	x	PUNCT
ejpam-3293	270	13	for	for	ADP
ejpam-3293	270	14	each	each	DET
ejpam-3293	270	15	b	b	PROPN
ejpam-3293	270	16	∈	∈	PROPN
ejpam-3293	270	17	b	b	PROPN
ejpam-3293	270	18	where	where	SCONJ
ejpam-3293	270	19	b	b	NOUN
ejpam-3293	270	20	is	be	AUX
ejpam-3293	270	21	a	a	DET
ejpam-3293	270	22	basis	basis	NOUN
ejpam-3293	270	23	for	for	ADP
ejpam-3293	270	24	the	the	DET
ejpam-3293	270	25	topology	topology	NOUN
ejpam-3293	270	26	in	in	ADP
ejpam-3293	270	27	y	y	PROPN
ejpam-3293	270	28	.	.	PUNCT
ejpam-3293	271	1	let	let	VERB
ejpam-3293	271	2	g	g	PRON
ejpam-3293	271	3	be	be	AUX
ejpam-3293	271	4	an	an	DET
ejpam-3293	271	5	open	open	ADJ
ejpam-3293	271	6	set	set	NOUN
ejpam-3293	271	7	in	in	ADP
ejpam-3293	271	8	y	y	PROPN
ejpam-3293	271	9	.	.	PUNCT
ejpam-3293	272	1	then	then	ADV
ejpam-3293	272	2	g	g	PROPN
ejpam-3293	272	3	=	=	PUNCT
ejpam-3293	272	4	∪{b	∪{b	NOUN
ejpam-3293	272	5	:	:	PUNCT
ejpam-3293	272	6	b	b	X
ejpam-3293	272	7	∈	∈	PROPN
ejpam-3293	272	8	b∗	b∗	ADJ
ejpam-3293	272	9	}	}	PUNCT
ejpam-3293	272	10	,	,	PUNCT
ejpam-3293	272	11	where	where	SCONJ
ejpam-3293	272	12	b∗	b∗	ADJ
ejpam-3293	272	13	⊆	⊆	NUM
ejpam-3293	272	14	b.	b.	NOUN
ejpam-3293	272	15	it	it	PRON
ejpam-3293	272	16	follows	follow	VERB
ejpam-3293	272	17	that	that	DET
ejpam-3293	272	18	f−1(g	f−1(g	PROPN
ejpam-3293	272	19	)	)	PUNCT
ejpam-3293	272	20	=	=	SYM
ejpam-3293	272	21	∪	∪	X
ejpam-3293	272	22	{	{	PUNCT
ejpam-3293	272	23	f−1(b	f−1(b	PROPN
ejpam-3293	272	24	)	)	PUNCT
ejpam-3293	272	25	:	:	PUNCT
ejpam-3293	273	1	b	b	X
ejpam-3293	273	2	∈	∈	NOUN
ejpam-3293	273	3	b∗	b∗	ADJ
ejpam-3293	273	4	}	}	PUNCT
ejpam-3293	273	5	.	.	PUNCT
ejpam-3293	274	1	since	since	SCONJ
ejpam-3293	274	2	the	the	DET
ejpam-3293	274	3	collection	collection	NOUN
ejpam-3293	274	4	of	of	ADP
ejpam-3293	274	5	all	all	DET
ejpam-3293	274	6	ω	ω	ADJ
ejpam-3293	274	7	-	-	ADJ
ejpam-3293	274	8	open	open	ADJ
ejpam-3293	274	9	sets	set	NOUN
ejpam-3293	274	10	forms	form	VERB
ejpam-3293	274	11	a	a	DET
ejpam-3293	274	12	topology	topology	NOUN
ejpam-3293	274	13	,	,	PUNCT
ejpam-3293	274	14	f−1(g	f−1(g	PROPN
ejpam-3293	274	15	)	)	PUNCT
ejpam-3293	274	16	is	be	AUX
ejpam-3293	274	17	ω	ω	NOUN
ejpam-3293	274	18	-	-	NOUN
ejpam-3293	274	19	open	open	ADJ
ejpam-3293	274	20	in	in	ADP
ejpam-3293	274	21	x.	x.	PROPN
ejpam-3293	274	22	(	(	PUNCT
ejpam-3293	274	23	i)⇒	i)⇒	PROPN
ejpam-3293	274	24	(	(	PUNCT
ejpam-3293	274	25	iv	iv	NUM
ejpam-3293	274	26	):	):	PUNCT
ejpam-3293	274	27	let	let	VERB
ejpam-3293	274	28	p	p	PRON
ejpam-3293	274	29	∈	∈	PROPN
ejpam-3293	274	30	x	x	X
ejpam-3293	274	31	and	and	CCONJ
ejpam-3293	274	32	v	v	AUX
ejpam-3293	274	33	be	be	AUX
ejpam-3293	274	34	an	an	DET
ejpam-3293	274	35	open	open	ADJ
ejpam-3293	274	36	set	set	NOUN
ejpam-3293	274	37	in	in	ADP
ejpam-3293	274	38	y	y	NOUN
ejpam-3293	274	39	containing	contain	VERB
ejpam-3293	274	40	f(p	f(p	NOUN
ejpam-3293	274	41	)	)	PUNCT
ejpam-3293	274	42	.	.	PUNCT
ejpam-3293	275	1	since	since	SCONJ
ejpam-3293	275	2	f	f	PROPN
ejpam-3293	275	3	is	be	AUX
ejpam-3293	275	4	ω	ω	NOUN
ejpam-3293	275	5	-	-	ADJ
ejpam-3293	275	6	open	open	ADJ
ejpam-3293	275	7	,	,	PUNCT
ejpam-3293	275	8	u	u	NOUN
ejpam-3293	275	9	:	:	PUNCT
ejpam-3293	275	10	=	=	SYM
ejpam-3293	275	11	f−1(v	f−1(v	PROPN
ejpam-3293	275	12	)	)	PUNCT
ejpam-3293	275	13	is	be	AUX
ejpam-3293	275	14	ω	ω	NOUN
ejpam-3293	275	15	-	-	NOUN
ejpam-3293	275	16	open	open	ADJ
ejpam-3293	275	17	in	in	ADP
ejpam-3293	275	18	x	x	PUNCT
ejpam-3293	275	19	containing	contain	VERB
ejpam-3293	275	20	p.	p.	NOUN
ejpam-3293	275	21	also	also	ADV
ejpam-3293	275	22	,	,	PUNCT
ejpam-3293	275	23	f(u	f(u	PROPN
ejpam-3293	275	24	)	)	PUNCT
ejpam-3293	275	25	=	=	PUNCT
ejpam-3293	275	26	f(f−1(v	f(f−1(v	PROPN
ejpam-3293	275	27	)	)	PUNCT
ejpam-3293	275	28	)	)	PUNCT
ejpam-3293	276	1	⊆	⊆	NUM
ejpam-3293	276	2	v	v	NOUN
ejpam-3293	276	3	.	.	PUNCT
ejpam-3293	277	1	(	(	PUNCT
ejpam-3293	277	2	iv)⇒	iv)⇒	X
ejpam-3293	277	3	(	(	PUNCT
ejpam-3293	277	4	v	v	NOUN
ejpam-3293	277	5	):	):	PUNCT
ejpam-3293	277	6	let	let	VERB
ejpam-3293	277	7	a	a	DET
ejpam-3293	277	8	⊆	⊆	NUM
ejpam-3293	277	9	x	x	NOUN
ejpam-3293	277	10	and	and	CCONJ
ejpam-3293	277	11	p	p	NOUN
ejpam-3293	277	12	∈	∈	PROPN
ejpam-3293	277	13	clω(a	clω(a	PROPN
ejpam-3293	277	14	)	)	PUNCT
ejpam-3293	277	15	.	.	PUNCT
ejpam-3293	278	1	let	let	VERB
ejpam-3293	278	2	g	g	PRON
ejpam-3293	278	3	be	be	AUX
ejpam-3293	278	4	an	an	DET
ejpam-3293	278	5	open	open	ADJ
ejpam-3293	278	6	subset	subset	NOUN
ejpam-3293	278	7	of	of	ADP
ejpam-3293	278	8	y	y	PROPN
ejpam-3293	278	9	containing	contain	VERB
ejpam-3293	278	10	f(p	f(p	PROPN
ejpam-3293	278	11	)	)	PUNCT
ejpam-3293	278	12	.	.	PUNCT
ejpam-3293	279	1	since	since	SCONJ
ejpam-3293	279	2	f	f	PROPN
ejpam-3293	279	3	is	be	AUX
ejpam-3293	279	4	ω	ω	NOUN
ejpam-3293	279	5	-	-	ADJ
ejpam-3293	279	6	continuous	continuous	ADJ
ejpam-3293	279	7	on	on	ADP
ejpam-3293	279	8	x	x	NOUN
ejpam-3293	279	9	,	,	PUNCT
ejpam-3293	279	10	there	there	PRON
ejpam-3293	279	11	exists	exist	VERB
ejpam-3293	279	12	an	an	DET
ejpam-3293	279	13	ω	ω	ADJ
ejpam-3293	279	14	-	-	ADJ
ejpam-3293	279	15	open	open	ADJ
ejpam-3293	279	16	subset	subset	NOUN
ejpam-3293	279	17	o	o	NOUN
ejpam-3293	279	18	of	of	ADP
ejpam-3293	279	19	x	x	SYM
ejpam-3293	279	20	containing	contain	VERB
ejpam-3293	279	21	p	p	NOUN
ejpam-3293	279	22	such	such	ADJ
ejpam-3293	279	23	that	that	SCONJ
ejpam-3293	279	24	f(o	f(o	NOUN
ejpam-3293	279	25	)	)	PUNCT
ejpam-3293	279	26	⊆	⊆	NUM
ejpam-3293	279	27	g.	g.	NOUN
ejpam-3293	279	28	since	since	SCONJ
ejpam-3293	279	29	p	p	PROPN
ejpam-3293	279	30	∈	∈	PROPN
ejpam-3293	279	31	clω(a	clω(a	PROPN
ejpam-3293	279	32	)	)	PUNCT
ejpam-3293	279	33	,	,	PUNCT
ejpam-3293	280	1	o	o	NOUN
ejpam-3293	280	2	∩a	∩a	PROPN
ejpam-3293	280	3	6=	6=	ADP
ejpam-3293	280	4	∅.	∅.	PROPN
ejpam-3293	280	5	it	it	PRON
ejpam-3293	280	6	follows	follow	VERB
ejpam-3293	280	7	that	that	DET
ejpam-3293	280	8	∅	∅	NOUN
ejpam-3293	280	9	6=	6=	ADP
ejpam-3293	280	10	f(o	f(o	ADP
ejpam-3293	280	11	∩a	∩a	NOUN
ejpam-3293	280	12	)	)	PUNCT
ejpam-3293	280	13	⊆	⊆	NUM
ejpam-3293	280	14	f(o	f(o	NOUN
ejpam-3293	280	15	)	)	PUNCT
ejpam-3293	280	16	∩	∩	NOUN
ejpam-3293	280	17	f(a	f(a	NOUN
ejpam-3293	280	18	)	)	PUNCT
ejpam-3293	280	19	⊆	⊆	NUM
ejpam-3293	280	20	g	g	PROPN
ejpam-3293	280	21	∩	∩	ADJ
ejpam-3293	280	22	f(a	f(a	NOUN
ejpam-3293	280	23	)	)	PUNCT
ejpam-3293	280	24	.	.	PUNCT
ejpam-3293	281	1	this	this	PRON
ejpam-3293	281	2	implies	imply	VERB
ejpam-3293	281	3	that	that	SCONJ
ejpam-3293	281	4	f(p	f(p	NOUN
ejpam-3293	281	5	)	)	PUNCT
ejpam-3293	281	6	∈	∈	PROPN
ejpam-3293	281	7	cl(f(a	cl(f(a	NOUN
ejpam-3293	281	8	)	)	PUNCT
ejpam-3293	281	9	)	)	PUNCT
ejpam-3293	281	10	.	.	PUNCT
ejpam-3293	282	1	hence	hence	ADV
ejpam-3293	282	2	,	,	PUNCT
ejpam-3293	282	3	f(clω(a	f(clω(a	NOUN
ejpam-3293	282	4	)	)	PUNCT
ejpam-3293	282	5	)	)	PUNCT
ejpam-3293	283	1	⊆	⊆	NUM
ejpam-3293	283	2	cl(f(a	cl(f(a	NOUN
ejpam-3293	283	3	)	)	PUNCT
ejpam-3293	283	4	)	)	PUNCT
ejpam-3293	283	5	.	.	PUNCT
ejpam-3293	284	1	(	(	PUNCT
ejpam-3293	284	2	v	v	NOUN
ejpam-3293	284	3	)	)	PUNCT
ejpam-3293	284	4	⇒	⇒	NOUN
ejpam-3293	284	5	(	(	PUNCT
ejpam-3293	284	6	vi	vi	ADJ
ejpam-3293	284	7	):	):	PUNCT
ejpam-3293	284	8	let	let	VERB
ejpam-3293	284	9	b	b	NOUN
ejpam-3293	284	10	⊆	⊆	NUM
ejpam-3293	284	11	y	y	PROPN
ejpam-3293	284	12	and	and	CCONJ
ejpam-3293	284	13	let	let	VERB
ejpam-3293	284	14	a	a	DET
ejpam-3293	284	15	=	=	SYM
ejpam-3293	284	16	f−1(b	f−1(b	PROPN
ejpam-3293	284	17	)	)	PUNCT
ejpam-3293	284	18	⊆	⊆	NUM
ejpam-3293	284	19	x.	x.	NOUN
ejpam-3293	284	20	by	by	ADP
ejpam-3293	284	21	assumption	assumption	NOUN
ejpam-3293	284	22	,	,	PUNCT
ejpam-3293	284	23	f(clω(a	f(clω(a	NOUN
ejpam-3293	284	24	)	)	PUNCT
ejpam-3293	284	25	)	)	PUNCT
ejpam-3293	285	1	⊆	⊆	NUM
ejpam-3293	285	2	cl(f(a	cl(f(a	NOUN
ejpam-3293	285	3	)	)	PUNCT
ejpam-3293	285	4	)	)	PUNCT
ejpam-3293	285	5	.	.	PUNCT
ejpam-3293	286	1	hence	hence	ADV
ejpam-3293	286	2	,	,	PUNCT
ejpam-3293	286	3	clω(f−1(b	clω(f−1(b	PROPN
ejpam-3293	286	4	)	)	PUNCT
ejpam-3293	286	5	)	)	PUNCT
ejpam-3293	287	1	⊆	⊆	NUM
ejpam-3293	287	2	f−1(f(clω(a	f−1(f(clω(a	NOUN
ejpam-3293	287	3	)	)	PUNCT
ejpam-3293	287	4	)	)	PUNCT
ejpam-3293	287	5	)	)	PUNCT
ejpam-3293	288	1	⊆	⊆	NUM
ejpam-3293	288	2	f−1(cl(f(a	f−1(cl(f(a	NOUN
ejpam-3293	288	3	)	)	PUNCT
ejpam-3293	288	4	)	)	PUNCT
ejpam-3293	288	5	)	)	PUNCT
ejpam-3293	288	6	⊆	⊆	NUM
ejpam-3293	288	7	f−1(cl(b	f−1(cl(b	NOUN
ejpam-3293	288	8	)	)	PUNCT
ejpam-3293	288	9	)	)	PUNCT
ejpam-3293	288	10	.	.	PUNCT
ejpam-3293	289	1	(	(	PUNCT
ejpam-3293	289	2	vi)⇒	vi)⇒	NUM
ejpam-3293	289	3	(	(	PUNCT
ejpam-3293	289	4	ii	ii	NOUN
ejpam-3293	289	5	):	):	PUNCT
ejpam-3293	289	6	let	let	VERB
ejpam-3293	289	7	f	f	PRON
ejpam-3293	289	8	be	be	AUX
ejpam-3293	289	9	a	a	DET
ejpam-3293	289	10	closed	closed	ADJ
ejpam-3293	289	11	subset	subset	NOUN
ejpam-3293	289	12	of	of	ADP
ejpam-3293	289	13	y	y	PROPN
ejpam-3293	289	14	.	.	PUNCT
ejpam-3293	290	1	by	by	ADP
ejpam-3293	290	2	assumption	assumption	NOUN
ejpam-3293	290	3	,	,	PUNCT
ejpam-3293	290	4	clω(f−1(f	clω(f−1(f	PROPN
ejpam-3293	290	5	)	)	PUNCT
ejpam-3293	290	6	)	)	PUNCT
ejpam-3293	291	1	⊆	⊆	NUM
ejpam-3293	291	2	f−1(cl(f	f−1(cl(f	NOUN
ejpam-3293	291	3	)	)	PUNCT
ejpam-3293	291	4	)	)	PUNCT
ejpam-3293	292	1	=	=	SYM
ejpam-3293	292	2	f−1(f	f−1(f	PROPN
ejpam-3293	292	3	)	)	PUNCT
ejpam-3293	292	4	.	.	PUNCT
ejpam-3293	293	1	hence	hence	ADV
ejpam-3293	293	2	,	,	PUNCT
ejpam-3293	293	3	f−1(f	f−1(f	PROPN
ejpam-3293	293	4	)	)	PUNCT
ejpam-3293	293	5	⊆	⊆	NUM
ejpam-3293	293	6	clω(f−1(f	clω(f−1(f	NOUN
ejpam-3293	293	7	)	)	PUNCT
ejpam-3293	293	8	)	)	PUNCT
ejpam-3293	293	9	.	.	PUNCT
ejpam-3293	294	1	then	then	ADV
ejpam-3293	294	2	clω(f−1(f	clω(f−1(f	PROPN
ejpam-3293	294	3	)	)	PUNCT
ejpam-3293	294	4	)	)	PUNCT
ejpam-3293	295	1	=	=	SYM
ejpam-3293	295	2	f−1(f	f−1(f	PROPN
ejpam-3293	295	3	)	)	PUNCT
ejpam-3293	295	4	,	,	PUNCT
ejpam-3293	295	5	which	which	PRON
ejpam-3293	295	6	means	mean	VERB
ejpam-3293	295	7	that	that	SCONJ
ejpam-3293	295	8	f−1(f	f−1(f	PROPN
ejpam-3293	295	9	)	)	PUNCT
ejpam-3293	295	10	is	be	AUX
ejpam-3293	295	11	ω	ω	ADV
ejpam-3293	295	12	-	-	PUNCT
ejpam-3293	295	13	closed	closed	ADJ
ejpam-3293	295	14	.	.	PUNCT
ejpam-3293	296	1	theorem	theorem	VERB
ejpam-3293	296	2	7	7	NUM
ejpam-3293	296	3	.	.	PUNCT
ejpam-3293	297	1	let	let	VERB
ejpam-3293	297	2	x	x	PRON
ejpam-3293	297	3	be	be	AUX
ejpam-3293	297	4	a	a	DET
ejpam-3293	297	5	topological	topological	ADJ
ejpam-3293	297	6	space	space	NOUN
ejpam-3293	297	7	and	and	CCONJ
ejpam-3293	297	8	y	y	PROPN
ejpam-3293	297	9	=	=	SYM
ejpam-3293	297	10	∏	∏	PROPN
ejpam-3293	297	11	{	{	PUNCT
ejpam-3293	297	12	yα	yα	NOUN
ejpam-3293	297	13	:	:	PUNCT
ejpam-3293	297	14	α	α	PROPN
ejpam-3293	297	15	∈	∈	PROPN
ejpam-3293	297	16	a	a	DET
ejpam-3293	297	17	}	}	PUNCT
ejpam-3293	297	18	a	a	DET
ejpam-3293	297	19	product	product	NOUN
ejpam-3293	297	20	space	space	NOUN
ejpam-3293	297	21	.	.	PUNCT
ejpam-3293	298	1	a	a	DET
ejpam-3293	298	2	function	function	NOUN
ejpam-3293	298	3	f	f	NOUN
ejpam-3293	298	4	:	:	PUNCT
ejpam-3293	298	5	x	x	X
ejpam-3293	298	6	→	→	SYM
ejpam-3293	298	7	y	y	PROPN
ejpam-3293	298	8	is	be	AUX
ejpam-3293	298	9	ω	ω	NOUN
ejpam-3293	298	10	-	-	ADJ
ejpam-3293	298	11	continuous	continuous	ADJ
ejpam-3293	298	12	on	on	ADP
ejpam-3293	298	13	x	x	PUNCT
ejpam-3293	298	14	if	if	SCONJ
ejpam-3293	298	15	and	and	CCONJ
ejpam-3293	298	16	only	only	ADV
ejpam-3293	298	17	if	if	SCONJ
ejpam-3293	298	18	each	each	DET
ejpam-3293	298	19	coordinate	coordinate	NOUN
ejpam-3293	298	20	function	function	NOUN
ejpam-3293	298	21	pα	pα	INTJ
ejpam-3293	298	22	◦	◦	NOUN
ejpam-3293	298	23	f	f	PROPN
ejpam-3293	298	24	is	be	AUX
ejpam-3293	298	25	ω	ω	NOUN
ejpam-3293	298	26	-	-	ADJ
ejpam-3293	298	27	continuous	continuous	ADJ
ejpam-3293	298	28	on	on	ADP
ejpam-3293	298	29	x.	x.	PROPN
ejpam-3293	298	30	m.	m.	PROPN
ejpam-3293	298	31	labendia	labendia	PROPN
ejpam-3293	298	32	,	,	PUNCT
ejpam-3293	298	33	j.	j.	PROPN
ejpam-3293	298	34	a.	a.	PROPN
ejpam-3293	298	35	sasam	sasam	PROPN
ejpam-3293	298	36	/	/	SYM
ejpam-3293	298	37	eur	eur	PROPN
ejpam-3293	298	38	.	.	PUNCT
ejpam-3293	299	1	j.	j.	PROPN
ejpam-3293	299	2	pure	pure	PROPN
ejpam-3293	299	3	appl	appl	PROPN
ejpam-3293	299	4	.	.	PROPN
ejpam-3293	299	5	math	math	PROPN
ejpam-3293	299	6	,	,	PUNCT
ejpam-3293	299	7	11	11	NUM
ejpam-3293	299	8	(	(	PUNCT
ejpam-3293	299	9	3	3	NUM
ejpam-3293	299	10	)	)	PUNCT
ejpam-3293	299	11	(	(	PUNCT
ejpam-3293	299	12	2018	2018	NUM
ejpam-3293	299	13	)	)	PUNCT
ejpam-3293	299	14	,	,	PUNCT
ejpam-3293	299	15	834	834	NUM
ejpam-3293	299	16	-	-	SYM
ejpam-3293	299	17	843	843	NUM
ejpam-3293	299	18	842	842	NUM
ejpam-3293	299	19	proof	proof	NOUN
ejpam-3293	299	20	.	.	PUNCT
ejpam-3293	299	21	suppose	suppose	VERB
ejpam-3293	299	22	that	that	SCONJ
ejpam-3293	299	23	f	f	PROPN
ejpam-3293	299	24	is	be	AUX
ejpam-3293	299	25	ω	ω	NOUN
ejpam-3293	299	26	-	-	ADJ
ejpam-3293	299	27	continuous	continuous	ADJ
ejpam-3293	299	28	on	on	ADP
ejpam-3293	299	29	x.	x.	NOUN
ejpam-3293	299	30	let	let	VERB
ejpam-3293	299	31	α	α	PROPN
ejpam-3293	299	32	∈	∈	PROPN
ejpam-3293	299	33	a	a	PRON
ejpam-3293	299	34	,	,	PUNCT
ejpam-3293	299	35	and	and	CCONJ
ejpam-3293	299	36	uα	uα	PROPN
ejpam-3293	299	37	be	be	AUX
ejpam-3293	299	38	open	open	ADJ
ejpam-3293	299	39	in	in	ADP
ejpam-3293	299	40	yα	yα	NOUN
ejpam-3293	299	41	.	.	PUNCT
ejpam-3293	300	1	since	since	SCONJ
ejpam-3293	300	2	pα	pα	NOUN
ejpam-3293	300	3	is	be	AUX
ejpam-3293	300	4	continuous	continuous	ADJ
ejpam-3293	300	5	,	,	PUNCT
ejpam-3293	300	6	p−1α	p−1α	NOUN
ejpam-3293	300	7	(	(	PUNCT
ejpam-3293	300	8	uα	uα	NOUN
ejpam-3293	300	9	)	)	PUNCT
ejpam-3293	300	10	is	be	AUX
ejpam-3293	300	11	open	open	ADJ
ejpam-3293	300	12	in	in	ADP
ejpam-3293	300	13	y	y	PROPN
ejpam-3293	300	14	.	.	PUNCT
ejpam-3293	301	1	hence	hence	ADV
ejpam-3293	301	2	,	,	PUNCT
ejpam-3293	301	3	f−1(p−1α	f−1(p−1α	NOUN
ejpam-3293	301	4	(	(	PUNCT
ejpam-3293	301	5	uα	uα	NOUN
ejpam-3293	301	6	)	)	PUNCT
ejpam-3293	301	7	)	)	PUNCT
ejpam-3293	302	1	=	=	PUNCT
ejpam-3293	302	2	(	(	PUNCT
ejpam-3293	302	3	pα	pα	INTJ
ejpam-3293	302	4	◦	◦	NOUN
ejpam-3293	302	5	f)−1(uα	f)−1(uα	NOUN
ejpam-3293	302	6	)	)	PUNCT
ejpam-3293	302	7	is	be	AUX
ejpam-3293	302	8	an	an	DET
ejpam-3293	302	9	ω	ω	ADJ
ejpam-3293	302	10	-	-	ADJ
ejpam-3293	302	11	open	open	ADJ
ejpam-3293	302	12	set	set	NOUN
ejpam-3293	302	13	in	in	ADP
ejpam-3293	302	14	x.	x.	NOUN
ejpam-3293	302	15	thus	thus	ADV
ejpam-3293	302	16	,	,	PUNCT
ejpam-3293	302	17	pα	pα	ADP
ejpam-3293	302	18	◦	◦	NOUN
ejpam-3293	302	19	f	f	PROPN
ejpam-3293	302	20	is	be	AUX
ejpam-3293	302	21	ω	ω	NOUN
ejpam-3293	302	22	-	-	ADJ
ejpam-3293	302	23	continuous	continuous	ADJ
ejpam-3293	302	24	for	for	ADP
ejpam-3293	302	25	every	every	DET
ejpam-3293	302	26	α	α	PROPN
ejpam-3293	302	27	∈	∈	PROPN
ejpam-3293	302	28	a.	a.	NOUN
ejpam-3293	302	29	conversely	conversely	ADV
ejpam-3293	302	30	,	,	PUNCT
ejpam-3293	302	31	suppose	suppose	VERB
ejpam-3293	302	32	that	that	SCONJ
ejpam-3293	302	33	each	each	DET
ejpam-3293	302	34	coordinate	coordinate	NOUN
ejpam-3293	302	35	function	function	NOUN
ejpam-3293	302	36	pα	pα	INTJ
ejpam-3293	302	37	◦	◦	NOUN
ejpam-3293	302	38	f	f	PROPN
ejpam-3293	302	39	is	be	AUX
ejpam-3293	302	40	ω	ω	NOUN
ejpam-3293	302	41	-	-	ADJ
ejpam-3293	302	42	continuous	continuous	ADJ
ejpam-3293	302	43	.	.	PUNCT
ejpam-3293	303	1	let	let	AUX
ejpam-3293	303	2	gα	gα	ADV
ejpam-3293	303	3	be	be	AUX
ejpam-3293	303	4	open	open	ADJ
ejpam-3293	303	5	in	in	ADP
ejpam-3293	303	6	yα	yα	NOUN
ejpam-3293	303	7	.	.	PUNCT
ejpam-3293	304	1	then	then	ADV
ejpam-3293	304	2	〈	〈	PROPN
ejpam-3293	304	3	gα	gα	PROPN
ejpam-3293	304	4	〉	〉	PROPN
ejpam-3293	304	5	is	be	AUX
ejpam-3293	304	6	a	a	DET
ejpam-3293	304	7	subbasic	subbasic	ADJ
ejpam-3293	304	8	open	open	NOUN
ejpam-3293	304	9	set	set	NOUN
ejpam-3293	304	10	in	in	ADP
ejpam-3293	304	11	y	y	PROPN
ejpam-3293	304	12	and	and	CCONJ
ejpam-3293	304	13	(	(	PUNCT
ejpam-3293	304	14	pα	pα	INTJ
ejpam-3293	304	15	◦	◦	NOUN
ejpam-3293	304	16	f)−1(gα	f)−1(gα	NUM
ejpam-3293	304	17	)	)	PUNCT
ejpam-3293	304	18	=	=	NOUN
ejpam-3293	304	19	f−1(p−1α	f−1(p−1α	NOUN
ejpam-3293	304	20	(	(	PUNCT
ejpam-3293	304	21	gα	gα	NOUN
ejpam-3293	304	22	)	)	PUNCT
ejpam-3293	304	23	)	)	PUNCT
ejpam-3293	305	1	=	=	PUNCT
ejpam-3293	305	2	f−1(〈gα	f−1(〈gα	PROPN
ejpam-3293	305	3	〉	〉	NUM
ejpam-3293	305	4	)	)	PUNCT
ejpam-3293	305	5	is	be	AUX
ejpam-3293	305	6	an	an	DET
ejpam-3293	305	7	ω	ω	ADJ
ejpam-3293	305	8	-	-	ADJ
ejpam-3293	305	9	open	open	ADJ
ejpam-3293	305	10	set	set	NOUN
ejpam-3293	305	11	in	in	ADP
ejpam-3293	305	12	x.	x.	NOUN
ejpam-3293	305	13	therefore	therefore	ADV
ejpam-3293	305	14	,	,	PUNCT
ejpam-3293	305	15	f	f	PROPN
ejpam-3293	305	16	is	be	AUX
ejpam-3293	305	17	ω	ω	NOUN
ejpam-3293	305	18	-	-	ADJ
ejpam-3293	305	19	continuous	continuous	ADJ
ejpam-3293	305	20	on	on	ADP
ejpam-3293	305	21	x.	x.	PROPN
ejpam-3293	305	22	corollary	corollary	NOUN
ejpam-3293	305	23	1	1	X
ejpam-3293	305	24	.	.	PUNCT
ejpam-3293	306	1	let	let	VERB
ejpam-3293	306	2	x	x	PRON
ejpam-3293	306	3	be	be	AUX
ejpam-3293	306	4	a	a	DET
ejpam-3293	306	5	topological	topological	ADJ
ejpam-3293	306	6	space	space	NOUN
ejpam-3293	306	7	,	,	PUNCT
ejpam-3293	306	8	y	y	PROPN
ejpam-3293	306	9	=	=	SYM
ejpam-3293	306	10	∏	∏	PROPN
ejpam-3293	306	11	{	{	PUNCT
ejpam-3293	306	12	yα	yα	NOUN
ejpam-3293	306	13	:	:	PUNCT
ejpam-3293	307	1	α	α	PROPN
ejpam-3293	307	2	∈	∈	PROPN
ejpam-3293	307	3	a	a	DET
ejpam-3293	307	4	}	}	PUNCT
ejpam-3293	307	5	a	a	DET
ejpam-3293	307	6	product	product	NOUN
ejpam-3293	307	7	space	space	NOUN
ejpam-3293	307	8	,	,	PUNCT
ejpam-3293	307	9	and	and	CCONJ
ejpam-3293	307	10	fα	fα	SCONJ
ejpam-3293	307	11	:	:	PUNCT
ejpam-3293	307	12	x	x	X
ejpam-3293	307	13	→	→	SYM
ejpam-3293	307	14	yα	yα	VERB
ejpam-3293	307	15	a	a	DET
ejpam-3293	307	16	function	function	NOUN
ejpam-3293	307	17	for	for	ADP
ejpam-3293	307	18	each	each	DET
ejpam-3293	307	19	α	α	PROPN
ejpam-3293	307	20	∈	∈	NOUN
ejpam-3293	307	21	a.	a.	NOUN
ejpam-3293	307	22	let	let	VERB
ejpam-3293	307	23	f	f	NOUN
ejpam-3293	307	24	:	:	PUNCT
ejpam-3293	307	25	x	x	X
ejpam-3293	307	26	→	→	SYM
ejpam-3293	307	27	y	y	PROPN
ejpam-3293	307	28	be	be	AUX
ejpam-3293	307	29	the	the	DET
ejpam-3293	307	30	function	function	NOUN
ejpam-3293	307	31	defined	define	VERB
ejpam-3293	307	32	by	by	ADP
ejpam-3293	307	33	f(x	f(x	PROPN
ejpam-3293	307	34	)	)	PUNCT
ejpam-3293	308	1	=	=	PUNCT
ejpam-3293	308	2	〈	〈	PROPN
ejpam-3293	308	3	fα(x	fα(x	NOUN
ejpam-3293	308	4	)	)	PUNCT
ejpam-3293	308	5	〉	〉	PROPN
ejpam-3293	308	6	.	.	PUNCT
ejpam-3293	309	1	then	then	ADV
ejpam-3293	309	2	f	f	PROPN
ejpam-3293	309	3	is	be	AUX
ejpam-3293	309	4	ω	ω	NOUN
ejpam-3293	309	5	-	-	ADJ
ejpam-3293	309	6	continuous	continuous	ADJ
ejpam-3293	309	7	on	on	ADP
ejpam-3293	309	8	x	x	PUNCT
ejpam-3293	309	9	if	if	SCONJ
ejpam-3293	309	10	and	and	CCONJ
ejpam-3293	309	11	only	only	ADV
ejpam-3293	309	12	if	if	SCONJ
ejpam-3293	309	13	each	each	DET
ejpam-3293	309	14	fα	fα	NOUN
ejpam-3293	309	15	is	be	AUX
ejpam-3293	309	16	ω	ω	NOUN
ejpam-3293	309	17	-	-	ADJ
ejpam-3293	309	18	continuous	continuous	ADJ
ejpam-3293	309	19	for	for	ADP
ejpam-3293	309	20	each	each	DET
ejpam-3293	309	21	α	α	NOUN
ejpam-3293	309	22	∈	∈	NOUN
ejpam-3293	309	23	a.	a.	NOUN
ejpam-3293	309	24	proof	proof	NOUN
ejpam-3293	309	25	.	.	PUNCT
ejpam-3293	310	1	for	for	ADP
ejpam-3293	310	2	each	each	DET
ejpam-3293	310	3	α	α	NOUN
ejpam-3293	310	4	∈	∈	PROPN
ejpam-3293	310	5	a	a	PRON
ejpam-3293	310	6	and	and	CCONJ
ejpam-3293	310	7	each	each	DET
ejpam-3293	310	8	x	x	SYM
ejpam-3293	310	9	∈	∈	PROPN
ejpam-3293	310	10	x	x	X
ejpam-3293	310	11	,	,	PUNCT
ejpam-3293	310	12	we	we	PRON
ejpam-3293	310	13	have	have	AUX
ejpam-3293	310	14	(	(	PUNCT
ejpam-3293	310	15	pα	pα	INTJ
ejpam-3293	310	16	◦	◦	VERB
ejpam-3293	310	17	f)(x	f)(x	NOUN
ejpam-3293	310	18	)	)	PUNCT
ejpam-3293	310	19	=	=	SYM
ejpam-3293	310	20	pα(f(x	pα(f(x	NOUN
ejpam-3293	310	21	)	)	PUNCT
ejpam-3293	310	22	)	)	PUNCT
ejpam-3293	311	1	=	=	PUNCT
ejpam-3293	311	2	pα(〈fβ(x	pα(〈fβ(x	NOUN
ejpam-3293	311	3	)	)	PUNCT
ejpam-3293	311	4	〉	〉	NOUN
ejpam-3293	311	5	)	)	PUNCT
ejpam-3293	311	6	=	=	SYM
ejpam-3293	311	7	fα(x	fα(x	NOUN
ejpam-3293	311	8	)	)	PUNCT
ejpam-3293	311	9	.	.	PUNCT
ejpam-3293	312	1	thus	thus	ADV
ejpam-3293	312	2	,	,	PUNCT
ejpam-3293	312	3	pα	pα	INTJ
ejpam-3293	312	4	◦	◦	NOUN
ejpam-3293	312	5	f	f	NOUN
ejpam-3293	312	6	=	=	PUNCT
ejpam-3293	312	7	fα	fα	NOUN
ejpam-3293	312	8	for	for	ADP
ejpam-3293	312	9	every	every	DET
ejpam-3293	312	10	α	α	PROPN
ejpam-3293	312	11	∈	∈	PROPN
ejpam-3293	312	12	a.	a.	NOUN
ejpam-3293	312	13	the	the	DET
ejpam-3293	312	14	result	result	NOUN
ejpam-3293	312	15	now	now	ADV
ejpam-3293	312	16	follows	follow	VERB
ejpam-3293	312	17	from	from	ADP
ejpam-3293	312	18	theorem	theorem	ADJ
ejpam-3293	312	19	7	7	NUM
ejpam-3293	312	20	.	.	PUNCT
ejpam-3293	312	21	theorem	theorem	NOUN
ejpam-3293	312	22	8	8	NUM
ejpam-3293	312	23	.	.	PUNCT
ejpam-3293	313	1	let	let	VERB
ejpam-3293	313	2	y	y	PROPN
ejpam-3293	313	3	=	=	SYM
ejpam-3293	313	4	∏	∏	PROPN
ejpam-3293	313	5	{	{	PUNCT
ejpam-3293	313	6	yαi	yαi	NOUN
ejpam-3293	313	7	:	:	PUNCT
ejpam-3293	313	8	1	1	NUM
ejpam-3293	313	9	≤	≤	NUM
ejpam-3293	313	10	i	i	PRON
ejpam-3293	313	11	≤	≤	PROPN
ejpam-3293	313	12	n	n	CCONJ
ejpam-3293	313	13	}	}	PUNCT
ejpam-3293	313	14	be	be	AUX
ejpam-3293	313	15	a	a	DET
ejpam-3293	313	16	product	product	NOUN
ejpam-3293	313	17	space	space	NOUN
ejpam-3293	313	18	and	and	CCONJ
ejpam-3293	313	19	∅	∅	NOUN
ejpam-3293	313	20	6=	6=	NUM
ejpam-3293	313	21	oαi	oαi	ADP
ejpam-3293	313	22	⊆	⊆	NUM
ejpam-3293	313	23	yαi	yαi	NOUN
ejpam-3293	313	24	for	for	ADP
ejpam-3293	313	25	each	each	DET
ejpam-3293	313	26	i	i	PRON
ejpam-3293	313	27	∈	∈	PROPN
ejpam-3293	313	28	{	{	PUNCT
ejpam-3293	313	29	1	1	NUM
ejpam-3293	313	30	,	,	PUNCT
ejpam-3293	313	31	2	2	NUM
ejpam-3293	313	32	,	,	PUNCT
ejpam-3293	313	33	.	.	PUNCT
ejpam-3293	313	34	.	.	PUNCT
ejpam-3293	314	1	.	.	PUNCT
ejpam-3293	314	2	,	,	PUNCT
ejpam-3293	314	3	n	n	CCONJ
ejpam-3293	314	4	}	}	PUNCT
ejpam-3293	314	5	.	.	PUNCT
ejpam-3293	315	1	if	if	SCONJ
ejpam-3293	315	2	o	o	NOUN
ejpam-3293	315	3	=	=	PUNCT
ejpam-3293	316	1	〈	〈	PROPN
ejpam-3293	316	2	oα1	oα1	NOUN
ejpam-3293	316	3	,	,	PUNCT
ejpam-3293	316	4	.	.	PUNCT
ejpam-3293	316	5	.	.	PUNCT
ejpam-3293	317	1	.	.	PUNCT
ejpam-3293	318	1	,	,	PUNCT
ejpam-3293	318	2	oαn	oαn	PROPN
ejpam-3293	318	3	〉	〉	PROPN
ejpam-3293	318	4	is	be	AUX
ejpam-3293	318	5	ω	ω	NOUN
ejpam-3293	318	6	-	-	NOUN
ejpam-3293	318	7	open	open	ADJ
ejpam-3293	318	8	in	in	ADP
ejpam-3293	318	9	y	y	PROPN
ejpam-3293	318	10	,	,	PUNCT
ejpam-3293	318	11	then	then	ADV
ejpam-3293	318	12	each	each	DET
ejpam-3293	318	13	oαi	oαi	NOUN
ejpam-3293	318	14	is	be	AUX
ejpam-3293	318	15	ω	ω	NOUN
ejpam-3293	318	16	-	-	NOUN
ejpam-3293	318	17	open	open	ADJ
ejpam-3293	318	18	in	in	ADP
ejpam-3293	318	19	yαi	yαi	PROPN
ejpam-3293	318	20	.	.	PUNCT
ejpam-3293	319	1	proof	proof	NOUN
ejpam-3293	319	2	.	.	PUNCT
ejpam-3293	320	1	suppose	suppose	VERB
ejpam-3293	320	2	that	that	SCONJ
ejpam-3293	320	3	o	o	NOUN
ejpam-3293	321	1	=	=	PUNCT
ejpam-3293	321	2	〈	〈	PROPN
ejpam-3293	321	3	oα1	oα1	NOUN
ejpam-3293	321	4	,	,	PUNCT
ejpam-3293	321	5	.	.	PUNCT
ejpam-3293	321	6	.	.	PUNCT
ejpam-3293	322	1	.	.	PUNCT
ejpam-3293	323	1	,	,	PUNCT
ejpam-3293	323	2	oαn	oαn	PROPN
ejpam-3293	323	3	〉	〉	PROPN
ejpam-3293	323	4	is	be	AUX
ejpam-3293	323	5	ω	ω	NOUN
ejpam-3293	323	6	-	-	NOUN
ejpam-3293	323	7	open	open	ADJ
ejpam-3293	323	8	in	in	ADP
ejpam-3293	323	9	y	y	PROPN
ejpam-3293	323	10	.	.	PUNCT
ejpam-3293	324	1	let	let	VERB
ejpam-3293	324	2	aαi	aαi	INTJ
ejpam-3293	324	3	∈	∈	PROPN
ejpam-3293	324	4	oαi	oαi	NOUN
ejpam-3293	325	1	=	=	SYM
ejpam-3293	325	2	pαi(o	pαi(o	NOUN
ejpam-3293	325	3	)	)	PUNCT
ejpam-3293	326	1	for	for	ADP
ejpam-3293	326	2	each	each	DET
ejpam-3293	326	3	i	i	PRON
ejpam-3293	326	4	∈	∈	PROPN
ejpam-3293	326	5	{	{	PUNCT
ejpam-3293	326	6	1	1	NUM
ejpam-3293	326	7	,	,	PUNCT
ejpam-3293	326	8	2	2	NUM
ejpam-3293	326	9	,	,	PUNCT
ejpam-3293	326	10	.	.	PUNCT
ejpam-3293	326	11	.	.	PUNCT
ejpam-3293	326	12	.	.	PUNCT
ejpam-3293	326	13	,	,	PUNCT
ejpam-3293	326	14	n	n	CCONJ
ejpam-3293	326	15	}	}	PUNCT
ejpam-3293	326	16	.	.	PUNCT
ejpam-3293	327	1	then	then	ADV
ejpam-3293	327	2	there	there	PRON
ejpam-3293	327	3	exists	exist	VERB
ejpam-3293	327	4	x	x	X
ejpam-3293	327	5	=	=	SYM
ejpam-3293	327	6	〈	〈	PROPN
ejpam-3293	327	7	aαi	aαi	ADJ
ejpam-3293	327	8	〉	〉	PROPN
ejpam-3293	327	9	∈	∈	PROPN
ejpam-3293	327	10	o	o	NOUN
ejpam-3293	327	11	such	such	ADJ
ejpam-3293	327	12	that	that	DET
ejpam-3293	327	13	pαi(x	pαi(x	PROPN
ejpam-3293	327	14	)	)	PUNCT
ejpam-3293	327	15	=	=	PRON
ejpam-3293	328	1	aαi	aαi	INTJ
ejpam-3293	328	2	.	.	PUNCT
ejpam-3293	329	1	since	since	SCONJ
ejpam-3293	329	2	o	o	PROPN
ejpam-3293	329	3	is	be	AUX
ejpam-3293	329	4	ω	ω	NOUN
ejpam-3293	329	5	-	-	ADJ
ejpam-3293	329	6	open	open	ADJ
ejpam-3293	329	7	,	,	PUNCT
ejpam-3293	329	8	there	there	PRON
ejpam-3293	329	9	exists	exist	VERB
ejpam-3293	329	10	a	a	DET
ejpam-3293	329	11	basic	basic	ADJ
ejpam-3293	329	12	open	open	ADJ
ejpam-3293	329	13	set	set	VERB
ejpam-3293	329	14	u	u	NOUN
ejpam-3293	329	15	=	=	SYM
ejpam-3293	329	16	〈	〈	PROPN
ejpam-3293	329	17	uα1	uα1	NOUN
ejpam-3293	329	18	,	,	PUNCT
ejpam-3293	329	19	.	.	PUNCT
ejpam-3293	329	20	.	.	PUNCT
ejpam-3293	330	1	.	.	PUNCT
ejpam-3293	331	1	,	,	PUNCT
ejpam-3293	331	2	uαn	uαn	PROPN
ejpam-3293	331	3	〉	〉	PROPN
ejpam-3293	331	4	containing	contain	VERB
ejpam-3293	331	5	x	x	PUNCT
ejpam-3293	331	6	such	such	ADJ
ejpam-3293	331	7	that	that	SCONJ
ejpam-3293	331	8	u\o	u\o	PROPN
ejpam-3293	331	9	is	be	AUX
ejpam-3293	331	10	countable	countable	ADJ
ejpam-3293	331	11	.	.	PUNCT
ejpam-3293	332	1	note	note	VERB
ejpam-3293	332	2	that	that	SCONJ
ejpam-3293	332	3	pαi(u)\pαi(o	pαi(u)\pαi(o	VERB
ejpam-3293	332	4	)	)	PUNCT
ejpam-3293	332	5	=	=	SYM
ejpam-3293	332	6	uαi\oαi	uαi\oαi	ADP
ejpam-3293	332	7	⊆	⊆	NUM
ejpam-3293	332	8	pαi(u\o	pαi(u\o	NOUN
ejpam-3293	332	9	)	)	PUNCT
ejpam-3293	332	10	and	and	CCONJ
ejpam-3293	332	11	since	since	SCONJ
ejpam-3293	332	12	u\o	u\o	PROPN
ejpam-3293	332	13	is	be	AUX
ejpam-3293	332	14	countable	countable	ADJ
ejpam-3293	332	15	,	,	PUNCT
ejpam-3293	332	16	pαi(u\o	pαi(u\o	NOUN
ejpam-3293	332	17	)	)	PUNCT
ejpam-3293	332	18	is	be	AUX
ejpam-3293	332	19	countable	countable	ADJ
ejpam-3293	332	20	.	.	PUNCT
ejpam-3293	333	1	it	it	PRON
ejpam-3293	333	2	follows	follow	VERB
ejpam-3293	333	3	that	that	SCONJ
ejpam-3293	333	4	uαi\oαi	uαi\oαi	ADP
ejpam-3293	333	5	is	be	AUX
ejpam-3293	333	6	also	also	ADV
ejpam-3293	333	7	countable	countable	ADJ
ejpam-3293	333	8	.	.	PUNCT
ejpam-3293	334	1	thus	thus	ADV
ejpam-3293	334	2	,	,	PUNCT
ejpam-3293	334	3	each	each	DET
ejpam-3293	334	4	oαi	oαi	NOUN
ejpam-3293	334	5	is	be	AUX
ejpam-3293	334	6	ω	ω	NOUN
ejpam-3293	334	7	-	-	NOUN
ejpam-3293	334	8	open	open	ADJ
ejpam-3293	334	9	in	in	ADP
ejpam-3293	334	10	yαi	yαi	PROPN
ejpam-3293	334	11	.	.	PUNCT
ejpam-3293	335	1	theorem	theorem	ADJ
ejpam-3293	335	2	9	9	NUM
ejpam-3293	335	3	.	.	PUNCT
ejpam-3293	336	1	let	let	VERB
ejpam-3293	336	2	x	x	SYM
ejpam-3293	336	3	=	=	SYM
ejpam-3293	336	4	∏	∏	X
ejpam-3293	336	5	{	{	PUNCT
ejpam-3293	336	6	xαi	xαi	NOUN
ejpam-3293	336	7	:	:	PUNCT
ejpam-3293	336	8	1	1	NUM
ejpam-3293	336	9	≤	≤	NUM
ejpam-3293	336	10	i	i	PRON
ejpam-3293	336	11	≤	≤	NOUN
ejpam-3293	336	12	n	n	CCONJ
ejpam-3293	336	13	}	}	PUNCT
ejpam-3293	336	14	and	and	CCONJ
ejpam-3293	336	15	y	y	PROPN
ejpam-3293	336	16	=	=	SYM
ejpam-3293	336	17	∏	∏	PROPN
ejpam-3293	336	18	{	{	PUNCT
ejpam-3293	336	19	yαi	yαi	NOUN
ejpam-3293	336	20	:	:	PUNCT
ejpam-3293	336	21	1	1	NUM
ejpam-3293	336	22	≤	≤	NUM
ejpam-3293	336	23	i	i	PRON
ejpam-3293	336	24	≤	≤	PROPN
ejpam-3293	336	25	n	n	CCONJ
ejpam-3293	336	26	}	}	PUNCT
ejpam-3293	336	27	be	be	AUX
ejpam-3293	336	28	product	product	NOUN
ejpam-3293	336	29	spaces	space	NOUN
ejpam-3293	336	30	,	,	PUNCT
ejpam-3293	336	31	and	and	CCONJ
ejpam-3293	336	32	for	for	ADP
ejpam-3293	336	33	each	each	DET
ejpam-3293	336	34	i	i	PRON
ejpam-3293	336	35	∈	∈	PROPN
ejpam-3293	336	36	{	{	PUNCT
ejpam-3293	336	37	1	1	NUM
ejpam-3293	336	38	,	,	PUNCT
ejpam-3293	336	39	2	2	NUM
ejpam-3293	336	40	,	,	PUNCT
ejpam-3293	336	41	.	.	PUNCT
ejpam-3293	336	42	.	.	PUNCT
ejpam-3293	337	1	.	.	PUNCT
ejpam-3293	338	1	,	,	PUNCT
ejpam-3293	338	2	n	n	CCONJ
ejpam-3293	338	3	}	}	PUNCT
ejpam-3293	338	4	,	,	PUNCT
ejpam-3293	338	5	let	let	VERB
ejpam-3293	338	6	fαi	fαi	ADJ
ejpam-3293	338	7	:	:	PUNCT
ejpam-3293	338	8	xαi	xαi	PROPN
ejpam-3293	338	9	→	→	SYM
ejpam-3293	338	10	yαi	yαi	X
ejpam-3293	338	11	be	be	AUX
ejpam-3293	338	12	a	a	DET
ejpam-3293	338	13	function	function	NOUN
ejpam-3293	338	14	.	.	PUNCT
ejpam-3293	339	1	if	if	SCONJ
ejpam-3293	339	2	f	f	PROPN
ejpam-3293	339	3	:	:	PUNCT
ejpam-3293	339	4	x	x	X
ejpam-3293	339	5	→	→	SYM
ejpam-3293	339	6	y	y	PROPN
ejpam-3293	339	7	defined	define	VERB
ejpam-3293	339	8	by	by	ADP
ejpam-3293	339	9	f(〈xαi	f(〈xαi	NOUN
ejpam-3293	339	10	〉	〉	NOUN
ejpam-3293	339	11	)	)	PUNCT
ejpam-3293	340	1	=	=	PUNCT
ejpam-3293	340	2	〈	〈	PROPN
ejpam-3293	340	3	fαi(xαi	fαi(xαi	NOUN
ejpam-3293	340	4	)	)	PUNCT
ejpam-3293	340	5	〉	〉	PROPN
ejpam-3293	340	6	,	,	PUNCT
ejpam-3293	340	7	is	be	AUX
ejpam-3293	340	8	ω	ω	NOUN
ejpam-3293	340	9	-	-	ADJ
ejpam-3293	340	10	continuous	continuous	ADJ
ejpam-3293	340	11	on	on	ADP
ejpam-3293	340	12	x	x	X
ejpam-3293	340	13	,	,	PUNCT
ejpam-3293	340	14	then	then	ADV
ejpam-3293	340	15	each	each	DET
ejpam-3293	340	16	fαi	fαi	NOUN
ejpam-3293	340	17	is	be	AUX
ejpam-3293	340	18	ω	ω	NOUN
ejpam-3293	340	19	-	-	ADJ
ejpam-3293	340	20	continuous	continuous	ADJ
ejpam-3293	340	21	on	on	ADP
ejpam-3293	340	22	xαi	xαi	PROPN
ejpam-3293	340	23	.	.	PUNCT
ejpam-3293	341	1	proof	proof	NOUN
ejpam-3293	341	2	.	.	PUNCT
ejpam-3293	342	1	assume	assume	VERB
ejpam-3293	342	2	that	that	SCONJ
ejpam-3293	342	3	f	f	X
ejpam-3293	342	4	:	:	PUNCT
ejpam-3293	342	5	x	x	X
ejpam-3293	342	6	→	→	SYM
ejpam-3293	342	7	y	y	PROPN
ejpam-3293	342	8	is	be	AUX
ejpam-3293	342	9	ω	ω	NOUN
ejpam-3293	342	10	-	-	ADJ
ejpam-3293	342	11	continuous	continuous	ADJ
ejpam-3293	342	12	.	.	PUNCT
ejpam-3293	343	1	let	let	VERB
ejpam-3293	343	2	oαi	oαi	INTJ
ejpam-3293	343	3	be	be	AUX
ejpam-3293	343	4	an	an	DET
ejpam-3293	343	5	open	open	ADJ
ejpam-3293	343	6	set	set	NOUN
ejpam-3293	343	7	in	in	ADP
ejpam-3293	343	8	yαi	yαi	PROPN
ejpam-3293	343	9	.	.	PUNCT
ejpam-3293	344	1	for	for	ADP
ejpam-3293	344	2	each	each	DET
ejpam-3293	344	3	i	i	PRON
ejpam-3293	344	4	∈	∈	PROPN
ejpam-3293	344	5	{	{	PUNCT
ejpam-3293	344	6	1	1	NUM
ejpam-3293	344	7	,	,	PUNCT
ejpam-3293	344	8	2	2	NUM
ejpam-3293	344	9	,	,	PUNCT
ejpam-3293	344	10	.	.	PUNCT
ejpam-3293	344	11	.	.	PUNCT
ejpam-3293	344	12	.	.	PUNCT
ejpam-3293	344	13	,	,	PUNCT
ejpam-3293	344	14	n	n	CCONJ
ejpam-3293	344	15	}	}	PUNCT
ejpam-3293	344	16	,	,	PUNCT
ejpam-3293	344	17	let	let	VERB
ejpam-3293	344	18	aαi	aαi	PROPN
ejpam-3293	344	19	∈	∈	PROPN
ejpam-3293	344	20	f−1αi	f−1αi	NOUN
ejpam-3293	344	21	(	(	PUNCT
ejpam-3293	344	22	oαi	oαi	PROPN
ejpam-3293	344	23	)	)	PUNCT
ejpam-3293	344	24	:	:	PUNCT
ejpam-3293	344	25	=	=	PUNCT
ejpam-3293	344	26	gαi	gαi	PROPN
ejpam-3293	344	27	.	.	PUNCT
ejpam-3293	345	1	then	then	ADV
ejpam-3293	345	2	x	x	X
ejpam-3293	345	3	:	:	PUNCT
ejpam-3293	345	4	=	=	PUNCT
ejpam-3293	345	5	〈	〈	NOUN
ejpam-3293	345	6	aα1	aα1	PRON
ejpam-3293	345	7	,	,	PUNCT
ejpam-3293	345	8	.	.	PUNCT
ejpam-3293	345	9	.	.	PUNCT
ejpam-3293	345	10	.	.	PUNCT
ejpam-3293	346	1	,	,	PUNCT
ejpam-3293	346	2	aαn	aαn	VERB
ejpam-3293	346	3	〉	〉	PROPN
ejpam-3293	346	4	∈	∈	NOUN
ejpam-3293	346	5	〈	〈	NOUN
ejpam-3293	346	6	gα1	gα1	NOUN
ejpam-3293	346	7	,	,	PUNCT
ejpam-3293	346	8	.	.	PUNCT
ejpam-3293	346	9	.	.	PUNCT
ejpam-3293	347	1	.	.	PUNCT
ejpam-3293	348	1	,	,	PUNCT
ejpam-3293	348	2	gαn	gαn	PROPN
ejpam-3293	348	3	〉	〉	NOUN
ejpam-3293	348	4	=	=	SYM
ejpam-3293	348	5	〈	〈	NOUN
ejpam-3293	348	6	f−1α1	f−1α1	NOUN
ejpam-3293	348	7	(	(	PUNCT
ejpam-3293	348	8	oα1	oα1	NOUN
ejpam-3293	348	9	)	)	PUNCT
ejpam-3293	348	10	,	,	PUNCT
ejpam-3293	348	11	.	.	PUNCT
ejpam-3293	348	12	.	.	PUNCT
ejpam-3293	348	13	.	.	PUNCT
ejpam-3293	349	1	,	,	PUNCT
ejpam-3293	349	2	f−1αn	f−1αn	PROPN
ejpam-3293	349	3	(	(	PUNCT
ejpam-3293	349	4	oαn	oαn	NOUN
ejpam-3293	349	5	)	)	PUNCT
ejpam-3293	349	6	〉	〉	NOUN
ejpam-3293	349	7	=	=	NOUN
ejpam-3293	349	8	f−1(〈oα1	f−1(〈oα1	PROPN
ejpam-3293	349	9	,	,	PUNCT
ejpam-3293	349	10	.	.	PUNCT
ejpam-3293	349	11	.	.	PUNCT
ejpam-3293	350	1	.	.	PUNCT
ejpam-3293	351	1	,	,	PUNCT
ejpam-3293	351	2	oαn	oαn	PROPN
ejpam-3293	351	3	〉	〉	PROPN
ejpam-3293	351	4	)	)	PUNCT
ejpam-3293	351	5	.	.	PUNCT
ejpam-3293	352	1	since	since	SCONJ
ejpam-3293	352	2	each	each	DET
ejpam-3293	352	3	oαi	oαi	NOUN
ejpam-3293	352	4	is	be	AUX
ejpam-3293	352	5	open	open	ADJ
ejpam-3293	352	6	in	in	ADP
ejpam-3293	352	7	yαi	yαi	PROPN
ejpam-3293	352	8	,	,	PUNCT
ejpam-3293	352	9	o	o	X
ejpam-3293	352	10	:	:	PUNCT
ejpam-3293	352	11	=	=	PUNCT
ejpam-3293	353	1	〈	〈	ADJ
ejpam-3293	353	2	oα1	oα1	NOUN
ejpam-3293	353	3	,	,	PUNCT
ejpam-3293	353	4	.	.	PUNCT
ejpam-3293	353	5	.	.	PUNCT
ejpam-3293	353	6	.	.	PUNCT
ejpam-3293	354	1	,	,	PUNCT
ejpam-3293	354	2	oαn	oαn	PROPN
ejpam-3293	354	3	〉	〉	PROPN
ejpam-3293	354	4	is	be	AUX
ejpam-3293	354	5	open	open	ADJ
ejpam-3293	354	6	in	in	ADP
ejpam-3293	354	7	y	y	PROPN
ejpam-3293	354	8	.	.	PUNCT
ejpam-3293	355	1	since	since	SCONJ
ejpam-3293	355	2	f	f	PROPN
ejpam-3293	355	3	is	be	AUX
ejpam-3293	355	4	ω	ω	ADJ
ejpam-3293	355	5	-	-	ADJ
ejpam-3293	355	6	continuous	continuous	ADJ
ejpam-3293	355	7	,	,	PUNCT
ejpam-3293	355	8	f−1(o	f−1(o	PROPN
ejpam-3293	355	9	)	)	PUNCT
ejpam-3293	355	10	=	=	PUNCT
ejpam-3293	356	1	〈	〈	NOUN
ejpam-3293	356	2	gα1	gα1	NOUN
ejpam-3293	356	3	,	,	PUNCT
ejpam-3293	356	4	.	.	PUNCT
ejpam-3293	356	5	.	.	PUNCT
ejpam-3293	356	6	.	.	PUNCT
ejpam-3293	357	1	gαn	gαn	PROPN
ejpam-3293	357	2	〉	〉	PROPN
ejpam-3293	357	3	is	be	AUX
ejpam-3293	357	4	ω	ω	NOUN
ejpam-3293	357	5	-	-	NOUN
ejpam-3293	357	6	open	open	ADJ
ejpam-3293	357	7	in	in	ADP
ejpam-3293	357	8	x.	x.	NOUN
ejpam-3293	357	9	then	then	ADV
ejpam-3293	357	10	there	there	PRON
ejpam-3293	357	11	exists	exist	VERB
ejpam-3293	357	12	a	a	DET
ejpam-3293	357	13	basic	basic	ADJ
ejpam-3293	357	14	open	open	ADJ
ejpam-3293	357	15	set	set	VERB
ejpam-3293	357	16	u	u	NOUN
ejpam-3293	357	17	=	=	SYM
ejpam-3293	357	18	〈	〈	PROPN
ejpam-3293	357	19	uα1	uα1	NOUN
ejpam-3293	357	20	,	,	PUNCT
ejpam-3293	357	21	.	.	PUNCT
ejpam-3293	357	22	.	.	PUNCT
ejpam-3293	357	23	.	.	PUNCT
ejpam-3293	358	1	uαn	uαn	PROPN
ejpam-3293	358	2	〉	〉	PROPN
ejpam-3293	358	3	containing	contain	VERB
ejpam-3293	358	4	x	x	PUNCT
ejpam-3293	358	5	such	such	ADJ
ejpam-3293	358	6	that	that	SCONJ
ejpam-3293	358	7	u	u	NOUN
ejpam-3293	358	8	\	\	NOUN
ejpam-3293	358	9	〈	〈	PROPN
ejpam-3293	358	10	gα1	gα1	NOUN
ejpam-3293	358	11	,	,	PUNCT
ejpam-3293	358	12	.	.	PUNCT
ejpam-3293	358	13	.	.	PUNCT
ejpam-3293	358	14	.	.	PUNCT
ejpam-3293	359	1	,	,	PUNCT
ejpam-3293	359	2	gαn	gαn	PROPN
ejpam-3293	359	3	〉	〉	PROPN
ejpam-3293	359	4	is	be	AUX
ejpam-3293	359	5	countable	countable	ADJ
ejpam-3293	359	6	.	.	PUNCT
ejpam-3293	360	1	note	note	VERB
ejpam-3293	360	2	that	that	SCONJ
ejpam-3293	360	3	pαi(u	pαi(u	NOUN
ejpam-3293	360	4	)	)	PUNCT
ejpam-3293	360	5	\	\	PUNCT
ejpam-3293	361	1	pαi(〈gα1	pαi(〈gα1	NOUN
ejpam-3293	361	2	,	,	PUNCT
ejpam-3293	361	3	.	.	PUNCT
ejpam-3293	361	4	.	.	PUNCT
ejpam-3293	361	5	.	.	PUNCT
ejpam-3293	362	1	,	,	PUNCT
ejpam-3293	362	2	gαn	gαn	PROPN
ejpam-3293	362	3	〉	〉	NUM
ejpam-3293	362	4	)	)	PUNCT
ejpam-3293	362	5	=	=	PUNCT
ejpam-3293	363	1	uαi	uαi	ADJ
ejpam-3293	363	2	\gαi	\gαi	NOUN
ejpam-3293	363	3	⊆	⊆	NUM
ejpam-3293	363	4	pαi(u	pαi(u	PROPN
ejpam-3293	363	5	\	\	NOUN
ejpam-3293	363	6	〈	〈	PROPN
ejpam-3293	363	7	gα1	gα1	NOUN
ejpam-3293	363	8	,	,	PUNCT
ejpam-3293	363	9	.	.	PUNCT
ejpam-3293	363	10	.	.	PUNCT
ejpam-3293	363	11	.	.	PUNCT
ejpam-3293	364	1	,	,	PUNCT
ejpam-3293	364	2	gαn	gαn	PROPN
ejpam-3293	364	3	〉	〉	PROPN
ejpam-3293	364	4	)	)	PUNCT
ejpam-3293	364	5	.	.	PUNCT
ejpam-3293	365	1	references	reference	NOUN
ejpam-3293	365	2	843	843	NUM
ejpam-3293	365	3	since	since	SCONJ
ejpam-3293	365	4	u	u	NOUN
ejpam-3293	365	5	\	\	NOUN
ejpam-3293	365	6	〈	〈	PROPN
ejpam-3293	365	7	gα1	gα1	NOUN
ejpam-3293	365	8	,	,	PUNCT
ejpam-3293	365	9	.	.	PUNCT
ejpam-3293	365	10	.	.	PUNCT
ejpam-3293	365	11	.	.	PUNCT
ejpam-3293	366	1	,	,	PUNCT
ejpam-3293	366	2	gαn	gαn	PROPN
ejpam-3293	366	3	〉	〉	PROPN
ejpam-3293	366	4	is	be	AUX
ejpam-3293	366	5	countable	countable	ADJ
ejpam-3293	366	6	,	,	PUNCT
ejpam-3293	366	7	pαi(u	pαi(u	PROPN
ejpam-3293	366	8	\	\	NOUN
ejpam-3293	366	9	〈	〈	PROPN
ejpam-3293	366	10	gα1	gα1	NOUN
ejpam-3293	366	11	,	,	PUNCT
ejpam-3293	366	12	.	.	PUNCT
ejpam-3293	366	13	.	.	PUNCT
ejpam-3293	367	1	.	.	PUNCT
ejpam-3293	368	1	,	,	PUNCT
ejpam-3293	368	2	gαn	gαn	PROPN
ejpam-3293	368	3	〉	〉	NOUN
ejpam-3293	368	4	)	)	PUNCT
ejpam-3293	368	5	is	be	AUX
ejpam-3293	368	6	also	also	ADV
ejpam-3293	368	7	countable	countable	ADJ
ejpam-3293	368	8	.	.	PUNCT
ejpam-3293	369	1	it	it	PRON
ejpam-3293	369	2	follows	follow	VERB
ejpam-3293	369	3	that	that	SCONJ
ejpam-3293	369	4	uαi\gαi	uαi\gαi	PROPN
ejpam-3293	369	5	is	be	AUX
ejpam-3293	369	6	countable	countable	ADJ
ejpam-3293	369	7	.	.	PUNCT
ejpam-3293	370	1	this	this	PRON
ejpam-3293	370	2	means	mean	VERB
ejpam-3293	370	3	that	that	SCONJ
ejpam-3293	370	4	each	each	DET
ejpam-3293	370	5	gαi	gαi	PROPN
ejpam-3293	370	6	=	=	SYM
ejpam-3293	370	7	f−1αi	f−1αi	PROPN
ejpam-3293	370	8	(	(	PUNCT
ejpam-3293	370	9	oαi	oαi	PROPN
ejpam-3293	370	10	)	)	PUNCT
ejpam-3293	370	11	is	be	AUX
ejpam-3293	370	12	ω	ω	NOUN
ejpam-3293	370	13	-	-	NOUN
ejpam-3293	370	14	open	open	ADJ
ejpam-3293	370	15	in	in	ADP
ejpam-3293	370	16	xαi	xαi	PROPN
ejpam-3293	370	17	.	.	PUNCT
ejpam-3293	371	1	thus	thus	ADV
ejpam-3293	371	2	,	,	PUNCT
ejpam-3293	371	3	each	each	DET
ejpam-3293	371	4	fαi	fαi	NOUN
ejpam-3293	371	5	is	be	AUX
ejpam-3293	371	6	ω	ω	NOUN
ejpam-3293	371	7	-	-	ADJ
ejpam-3293	371	8	continuous	continuous	ADJ
ejpam-3293	371	9	on	on	ADP
ejpam-3293	371	10	xαi	xαi	PROPN
ejpam-3293	371	11	.	.	PUNCT
ejpam-3293	372	1	5	5	X
ejpam-3293	372	2	.	.	X
ejpam-3293	372	3	conclusion	conclusion	NOUN
ejpam-3293	372	4	the	the	DET
ejpam-3293	372	5	paper	paper	NOUN
ejpam-3293	372	6	has	have	AUX
ejpam-3293	372	7	studied	study	VERB
ejpam-3293	372	8	the	the	DET
ejpam-3293	372	9	relationships	relationship	NOUN
ejpam-3293	372	10	between	between	ADP
ejpam-3293	372	11	connected	connected	ADJ
ejpam-3293	372	12	,	,	PUNCT
ejpam-3293	372	13	ωθ	ωθ	NOUN
ejpam-3293	372	14	-	-	PUNCT
ejpam-3293	372	15	connected	connect	VERB
ejpam-3293	372	16	and	and	CCONJ
ejpam-3293	372	17	ωconnected	ωconnecte	VERB
ejpam-3293	372	18	topological	topological	ADJ
ejpam-3293	372	19	spaces	space	NOUN
ejpam-3293	372	20	and	and	CCONJ
ejpam-3293	372	21	gave	give	VERB
ejpam-3293	372	22	a	a	DET
ejpam-3293	372	23	characterization	characterization	NOUN
ejpam-3293	372	24	of	of	ADP
ejpam-3293	372	25	an	an	DET
ejpam-3293	372	26	ω	ω	ADJ
ejpam-3293	372	27	-	-	ADJ
ejpam-3293	372	28	continuous	continuous	ADJ
ejpam-3293	372	29	function	function	NOUN
ejpam-3293	372	30	from	from	ADP
ejpam-3293	372	31	an	an	DET
ejpam-3293	372	32	arbitrary	arbitrary	ADJ
ejpam-3293	372	33	topological	topological	ADJ
ejpam-3293	372	34	space	space	NOUN
ejpam-3293	372	35	into	into	ADP
ejpam-3293	372	36	the	the	DET
ejpam-3293	372	37	product	product	NOUN
ejpam-3293	372	38	space	space	NOUN
ejpam-3293	372	39	via	via	ADP
ejpam-3293	372	40	ω	ω	VERB
ejpam-3293	372	41	-	-	ADJ
ejpam-3293	372	42	open	open	ADJ
ejpam-3293	372	43	sets	set	NOUN
ejpam-3293	372	44	and	and	CCONJ
ejpam-3293	372	45	ωθ	ωθ	NUM
ejpam-3293	372	46	-	-	PUNCT
ejpam-3293	372	47	open	open	ADJ
ejpam-3293	372	48	sets	set	NOUN
ejpam-3293	372	49	.	.	PUNCT
ejpam-3293	373	1	the	the	DET
ejpam-3293	373	2	present	present	ADJ
ejpam-3293	373	3	paper	paper	NOUN
ejpam-3293	373	4	is	be	AUX
ejpam-3293	373	5	related	relate	VERB
ejpam-3293	373	6	to	to	ADP
ejpam-3293	373	7	some	some	DET
ejpam-3293	373	8	good	good	ADJ
ejpam-3293	373	9	papers	paper	NOUN
ejpam-3293	373	10	.	.	PUNCT
ejpam-3293	374	1	acknowledgements	acknowledgement	VERB
ejpam-3293	374	2	the	the	DET
ejpam-3293	374	3	main	main	ADJ
ejpam-3293	374	4	author	author	NOUN
ejpam-3293	374	5	would	would	AUX
ejpam-3293	374	6	like	like	VERB
ejpam-3293	374	7	to	to	PART
ejpam-3293	374	8	express	express	VERB
ejpam-3293	374	9	his	his	PRON
ejpam-3293	374	10	sincerest	sincere	ADJ
ejpam-3293	374	11	gratitude	gratitude	NOUN
ejpam-3293	374	12	to	to	ADP
ejpam-3293	374	13	his	his	PRON
ejpam-3293	374	14	wife	wife	NOUN
ejpam-3293	374	15	for	for	ADP
ejpam-3293	374	16	the	the	DET
ejpam-3293	374	17	inspiration	inspiration	NOUN
ejpam-3293	374	18	in	in	ADP
ejpam-3293	374	19	completing	complete	VERB
ejpam-3293	374	20	this	this	DET
ejpam-3293	374	21	paper	paper	NOUN
ejpam-3293	374	22	.	.	PUNCT
ejpam-3293	375	1	also	also	ADV
ejpam-3293	375	2	,	,	PUNCT
ejpam-3293	375	3	the	the	DET
ejpam-3293	375	4	authors	author	NOUN
ejpam-3293	375	5	would	would	AUX
ejpam-3293	375	6	like	like	VERB
ejpam-3293	375	7	to	to	PART
ejpam-3293	375	8	thank	thank	VERB
ejpam-3293	375	9	the	the	DET
ejpam-3293	375	10	referees	referee	NOUN
ejpam-3293	375	11	for	for	ADP
ejpam-3293	375	12	their	their	PRON
ejpam-3293	375	13	helpful	helpful	ADJ
ejpam-3293	375	14	comments	comment	NOUN
ejpam-3293	375	15	for	for	ADP
ejpam-3293	375	16	the	the	DET
ejpam-3293	375	17	improvement	improvement	NOUN
ejpam-3293	375	18	of	of	ADP
ejpam-3293	375	19	this	this	DET
ejpam-3293	375	20	paper	paper	NOUN
ejpam-3293	375	21	.	.	PUNCT
ejpam-3293	376	1	references	reference	NOUN
ejpam-3293	376	2	[	[	X
ejpam-3293	376	3	1	1	X
ejpam-3293	376	4	]	]	X
ejpam-3293	376	5	t.a	t.a	PROPN
ejpam-3293	376	6	.	.	PROPN
ejpam-3293	376	7	al	al	PROPN
ejpam-3293	376	8	-	-	PUNCT
ejpam-3293	376	9	hawary	hawary	PROPN
ejpam-3293	376	10	.	.	PUNCT
ejpam-3293	377	1	on	on	ADP
ejpam-3293	377	2	supper	supper	NOUN
ejpam-3293	377	3	continuity	continuity	NOUN
ejpam-3293	377	4	of	of	ADP
ejpam-3293	377	5	topological	topological	ADJ
ejpam-3293	377	6	spaces	space	NOUN
ejpam-3293	377	7	.	.	PUNCT
ejpam-3293	378	1	matematika	matematika	PROPN
ejpam-3293	378	2	,	,	PUNCT
ejpam-3293	378	3	21:43	21:43	NUM
ejpam-3293	378	4	–	–	PUNCT
ejpam-3293	378	5	49	49	NUM
ejpam-3293	378	6	,	,	PUNCT
ejpam-3293	378	7	2005	2005	NUM
ejpam-3293	378	8	.	.	PUNCT
ejpam-3293	379	1	[	[	X
ejpam-3293	379	2	2	2	NUM
ejpam-3293	379	3	]	]	X
ejpam-3293	379	4	h.z	h.z	PROPN
ejpam-3293	379	5	.	.	PROPN
ejpam-3293	379	6	hdeib	hdeib	PROPN
ejpam-3293	379	7	.	.	PUNCT
ejpam-3293	380	1	ω	ω	VERB
ejpam-3293	380	2	-	-	PUNCT
ejpam-3293	380	3	closed	close	VERB
ejpam-3293	380	4	mappings	mapping	NOUN
ejpam-3293	380	5	.	.	PUNCT
ejpam-3293	381	1	rev	rev	PROPN
ejpam-3293	381	2	.	.	PUNCT
ejpam-3293	382	1	colombiana	colombiana	PROPN
ejpam-3293	382	2	mat	mat	PROPN
ejpam-3293	382	3	.	.	PROPN
ejpam-3293	382	4	,	,	PUNCT
ejpam-3293	382	5	1	1	NUM
ejpam-3293	382	6	-	-	SYM
ejpam-3293	382	7	2:65–78	2:65–78	NUM
ejpam-3293	382	8	,	,	PUNCT
ejpam-3293	382	9	1982	1982	NUM
ejpam-3293	382	10	.	.	PUNCT
ejpam-3293	383	1	[	[	X
ejpam-3293	383	2	3	3	X
ejpam-3293	383	3	]	]	X
ejpam-3293	383	4	e.	e.	PROPN
ejpam-3293	383	5	ekici	ekici	PROPN
ejpam-3293	383	6	s.	s.	PROPN
ejpam-3293	383	7	jafari	jafari	PROPN
ejpam-3293	383	8	and	and	CCONJ
ejpam-3293	383	9	r.m	r.m	PROPN
ejpam-3293	383	10	.	.	PROPN
ejpam-3293	383	11	latif	latif	PROPN
ejpam-3293	383	12	.	.	PUNCT
ejpam-3293	384	1	on	on	ADP
ejpam-3293	384	2	a	a	DET
ejpam-3293	384	3	finer	fine	ADJ
ejpam-3293	384	4	topological	topological	ADJ
ejpam-3293	384	5	space	space	NOUN
ejpam-3293	384	6	than	than	ADP
ejpam-3293	384	7	τθ	τθ	NOUN
ejpam-3293	384	8	and	and	CCONJ
ejpam-3293	384	9	some	some	DET
ejpam-3293	384	10	maps	map	NOUN
ejpam-3293	384	11	.	.	PUNCT
ejpam-3293	385	1	italian	italian	ADJ
ejpam-3293	385	2	journal	journal	NOUN
ejpam-3293	385	3	of	of	ADP
ejpam-3293	385	4	pure	pure	ADJ
ejpam-3293	385	5	and	and	CCONJ
ejpam-3293	385	6	applied	applied	ADJ
ejpam-3293	385	7	mathematics	mathematic	NOUN
ejpam-3293	385	8	,	,	PUNCT
ejpam-3293	385	9	27:293–304	27:293–304	PROPN
ejpam-3293	385	10	,	,	PUNCT
ejpam-3293	385	11	2010	2010	NUM
ejpam-3293	385	12	.	.	PUNCT
ejpam-3293	386	1	[	[	X
ejpam-3293	386	2	4	4	NUM
ejpam-3293	386	3	]	]	X
ejpam-3293	386	4	n.	n.	PROPN
ejpam-3293	386	5	levine	levine	PROPN
ejpam-3293	386	6	.	.	PUNCT
ejpam-3293	387	1	semi	semi	ADJ
ejpam-3293	387	2	-	-	ADJ
ejpam-3293	387	3	open	open	ADJ
ejpam-3293	387	4	sets	set	NOUN
ejpam-3293	387	5	and	and	CCONJ
ejpam-3293	387	6	semi	semi	ADJ
ejpam-3293	387	7	-	-	NOUN
ejpam-3293	387	8	continuity	continuity	NOUN
ejpam-3293	387	9	in	in	ADP
ejpam-3293	387	10	topological	topological	ADJ
ejpam-3293	387	11	spaces	space	NOUN
ejpam-3293	387	12	.	.	PUNCT
ejpam-3293	388	1	amer	amer	PROPN
ejpam-3293	388	2	.	.	PUNCT
ejpam-3293	388	3	math	math	PROPN
ejpam-3293	388	4	.	.	PUNCT
ejpam-3293	389	1	month	month	NOUN
ejpam-3293	389	2	.	.	PUNCT
ejpam-3293	390	1	,	,	PUNCT
ejpam-3293	390	2	70:36–41	70:36–41	NUM
ejpam-3293	390	3	,	,	PUNCT
ejpam-3293	390	4	1963	1963	NUM
ejpam-3293	390	5	.	.	PUNCT
ejpam-3293	391	1	[	[	X
ejpam-3293	391	2	5	5	X
ejpam-3293	391	3	]	]	PUNCT
ejpam-3293	391	4	n.	n.	NOUN
ejpam-3293	391	5	velicko	velicko	NOUN
ejpam-3293	391	6	.	.	PUNCT
ejpam-3293	392	1	h	h	NOUN
ejpam-3293	392	2	-	-	PUNCT
ejpam-3293	392	3	closed	close	VERB
ejpam-3293	392	4	topological	topological	ADJ
ejpam-3293	392	5	spaces	space	NOUN
ejpam-3293	392	6	.	.	PUNCT
ejpam-3293	393	1	trans	trans	PROPN
ejpam-3293	393	2	.	.	PUNCT
ejpam-3293	394	1	ams	am	NOUN
ejpam-3293	394	2	.	.	PUNCT
ejpam-3293	394	3	,	,	PUNCT
ejpam-3293	395	1	78:103–118	78:103–118	PROPN
ejpam-3293	395	2	,	,	PUNCT
ejpam-3293	395	3	1968	1968	NUM
ejpam-3293	395	4	.	.	PUNCT