id	sid	tid	token	lemma	pos
ejpam-3401	1	1	european	european	PROPN
ejpam-3401	1	2	journal	journal	PROPN
ejpam-3401	1	3	of	of	ADP
ejpam-3401	1	4	pure	pure	ADJ
ejpam-3401	1	5	and	and	CCONJ
ejpam-3401	1	6	applied	apply	VERB
ejpam-3401	1	7	mathematics	mathematic	NOUN
ejpam-3401	1	8	vol	vol	NOUN
ejpam-3401	1	9	.	.	PROPN
ejpam-3401	2	1	12	12	NUM
ejpam-3401	2	2	,	,	PUNCT
ejpam-3401	2	3	no	no	INTJ
ejpam-3401	2	4	.	.	NOUN
ejpam-3401	2	5	2	2	NUM
ejpam-3401	2	6	,	,	PUNCT
ejpam-3401	2	7	2019	2019	NUM
ejpam-3401	2	8	,	,	PUNCT
ejpam-3401	2	9	358	358	NUM
ejpam-3401	2	10	-	-	SYM
ejpam-3401	2	11	369	369	NUM
ejpam-3401	2	12	issn	issn	PROPN
ejpam-3401	2	13	1307	1307	NUM
ejpam-3401	2	14	-	-	SYM
ejpam-3401	2	15	5543	5543	NUM
ejpam-3401	2	16	–	–	PUNCT
ejpam-3401	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3401	2	18	published	publish	VERB
ejpam-3401	2	19	by	by	ADP
ejpam-3401	2	20	new	new	PROPN
ejpam-3401	2	21	york	york	PROPN
ejpam-3401	2	22	business	business	PROPN
ejpam-3401	2	23	global	global	PROPN
ejpam-3401	2	24	on	on	ADP
ejpam-3401	2	25	b	b	X
ejpam-3401	2	26	-	-	PUNCT
ejpam-3401	2	27	open	open	ADJ
ejpam-3401	2	28	sets	set	NOUN
ejpam-3401	2	29	layth	layth	PROPN
ejpam-3401	2	30	m.	m.	PROPN
ejpam-3401	2	31	alabdulsada	alabdulsada	PROPN
ejpam-3401	2	32	institute	institute	PROPN
ejpam-3401	2	33	of	of	ADP
ejpam-3401	2	34	mathematics	mathematics	PROPN
ejpam-3401	2	35	,	,	PUNCT
ejpam-3401	2	36	university	university	PROPN
ejpam-3401	2	37	of	of	ADP
ejpam-3401	2	38	debrecen	debrecen	PROPN
ejpam-3401	2	39	,	,	PUNCT
ejpam-3401	2	40	h-4002	h-4002	PROPN
ejpam-3401	2	41	debrecen	debrecen	PROPN
ejpam-3401	2	42	,	,	PUNCT
ejpam-3401	2	43	p.o	p.o	PROPN
ejpam-3401	2	44	.	.	PROPN
ejpam-3401	2	45	box	box	PROPN
ejpam-3401	2	46	400	400	NUM
ejpam-3401	2	47	,	,	PUNCT
ejpam-3401	2	48	hungary	hungary	PROPN
ejpam-3401	2	49	abstract	abstract	NOUN
ejpam-3401	2	50	.	.	PUNCT
ejpam-3401	3	1	the	the	DET
ejpam-3401	3	2	aim	aim	NOUN
ejpam-3401	3	3	of	of	ADP
ejpam-3401	3	4	this	this	DET
ejpam-3401	3	5	paper	paper	NOUN
ejpam-3401	3	6	is	be	AUX
ejpam-3401	3	7	to	to	PART
ejpam-3401	3	8	define	define	VERB
ejpam-3401	3	9	and	and	CCONJ
ejpam-3401	3	10	study	study	VERB
ejpam-3401	3	11	b	b	X
ejpam-3401	3	12	-	-	PUNCT
ejpam-3401	3	13	open	open	ADJ
ejpam-3401	3	14	sets	set	NOUN
ejpam-3401	3	15	and	and	CCONJ
ejpam-3401	3	16	related	related	ADJ
ejpam-3401	3	17	properties	property	NOUN
ejpam-3401	3	18	.	.	PUNCT
ejpam-3401	4	1	a	a	DET
ejpam-3401	4	2	b	b	X
ejpam-3401	4	3	-	-	PUNCT
ejpam-3401	4	4	open	open	ADJ
ejpam-3401	4	5	set	set	NOUN
ejpam-3401	4	6	is	be	AUX
ejpam-3401	4	7	,	,	PUNCT
ejpam-3401	4	8	roughly	roughly	ADV
ejpam-3401	4	9	speaking	speak	VERB
ejpam-3401	4	10	,	,	PUNCT
ejpam-3401	4	11	a	a	DET
ejpam-3401	4	12	generalization	generalization	NOUN
ejpam-3401	4	13	of	of	ADP
ejpam-3401	4	14	a	a	DET
ejpam-3401	4	15	b	b	NOUN
ejpam-3401	4	16	-	-	PUNCT
ejpam-3401	4	17	open	open	ADJ
ejpam-3401	4	18	set	set	NOUN
ejpam-3401	4	19	,	,	PUNCT
ejpam-3401	4	20	which	which	PRON
ejpam-3401	4	21	is	be	AUX
ejpam-3401	4	22	in	in	ADP
ejpam-3401	4	23	turn	turn	NOUN
ejpam-3401	4	24	a	a	DET
ejpam-3401	4	25	generalization	generalization	NOUN
ejpam-3401	4	26	of	of	ADP
ejpam-3401	4	27	a	a	DET
ejpam-3401	4	28	pre	pre	ADJ
ejpam-3401	4	29	-	-	ADJ
ejpam-3401	4	30	open	open	ADJ
ejpam-3401	4	31	set	set	NOUN
ejpam-3401	4	32	and	and	CCONJ
ejpam-3401	4	33	a	a	DET
ejpam-3401	4	34	semi	semi	ADJ
ejpam-3401	4	35	-	-	ADJ
ejpam-3401	4	36	open	open	ADJ
ejpam-3401	4	37	set	set	NOUN
ejpam-3401	4	38	.	.	PUNCT
ejpam-3401	5	1	using	use	VERB
ejpam-3401	5	2	b	b	X
ejpam-3401	5	3	-	-	PUNCT
ejpam-3401	5	4	open	open	ADJ
ejpam-3401	5	5	sets	set	NOUN
ejpam-3401	5	6	,	,	PUNCT
ejpam-3401	5	7	we	we	PRON
ejpam-3401	5	8	introduce	introduce	VERB
ejpam-3401	5	9	a	a	DET
ejpam-3401	5	10	number	number	NOUN
ejpam-3401	5	11	of	of	ADP
ejpam-3401	5	12	concepts	concept	NOUN
ejpam-3401	5	13	such	such	ADJ
ejpam-3401	5	14	as	as	ADP
ejpam-3401	5	15	b	b	NOUN
ejpam-3401	5	16	-	-	PUNCT
ejpam-3401	5	17	dense	dense	ADJ
ejpam-3401	5	18	,	,	PUNCT
ejpam-3401	5	19	b	b	X
ejpam-3401	5	20	-	-	PUNCT
ejpam-3401	5	21	frechet	frechet	NOUN
ejpam-3401	5	22	,	,	PUNCT
ejpam-3401	5	23	contra	contra	PROPN
ejpam-3401	5	24	-	-	PUNCT
ejpam-3401	5	25	b	b	NOUN
ejpam-3401	5	26	-	-	PUNCT
ejpam-3401	5	27	closed	closed	ADJ
ejpam-3401	5	28	graph	graph	NOUN
ejpam-3401	5	29	and	and	CCONJ
ejpam-3401	5	30	contra	contra	PROPN
ejpam-3401	5	31	-	-	PUNCT
ejpam-3401	5	32	b	b	NOUN
ejpam-3401	5	33	-	-	PUNCT
ejpam-3401	5	34	continuity	continuity	NOUN
ejpam-3401	5	35	.	.	PUNCT
ejpam-3401	6	1	also	also	ADV
ejpam-3401	6	2	,	,	PUNCT
ejpam-3401	6	3	we	we	PRON
ejpam-3401	6	4	define	define	VERB
ejpam-3401	6	5	a	a	DET
ejpam-3401	6	6	bi	bi	ADJ
ejpam-3401	6	7	-	-	NOUN
ejpam-3401	6	8	operator	operator	NOUN
ejpam-3401	6	9	topological	topological	ADJ
ejpam-3401	6	10	space	space	NOUN
ejpam-3401	6	11	(	(	PUNCT
ejpam-3401	6	12	x	x	X
ejpam-3401	6	13	,	,	PUNCT
ejpam-3401	6	14	τ	τ	PROPN
ejpam-3401	6	15	,	,	PUNCT
ejpam-3401	6	16	t1	t1	NOUN
ejpam-3401	6	17	,	,	PUNCT
ejpam-3401	6	18	t2	t2	PROPN
ejpam-3401	6	19	)	)	PUNCT
ejpam-3401	6	20	which	which	PRON
ejpam-3401	6	21	involves	involve	VERB
ejpam-3401	6	22	two	two	NUM
ejpam-3401	6	23	operators	operator	NOUN
ejpam-3401	6	24	t1	t1	VERB
ejpam-3401	6	25	and	and	CCONJ
ejpam-3401	6	26	t2	t2	PROPN
ejpam-3401	6	27	,	,	PUNCT
ejpam-3401	6	28	which	which	PRON
ejpam-3401	6	29	are	be	AUX
ejpam-3401	6	30	used	use	VERB
ejpam-3401	6	31	to	to	PART
ejpam-3401	6	32	define	define	VERB
ejpam-3401	6	33	b	b	X
ejpam-3401	6	34	-	-	PUNCT
ejpam-3401	6	35	open	open	ADJ
ejpam-3401	6	36	sets	set	NOUN
ejpam-3401	6	37	.	.	PUNCT
ejpam-3401	7	1	2010	2010	NUM
ejpam-3401	7	2	mathematics	mathematic	NOUN
ejpam-3401	7	3	subject	subject	NOUN
ejpam-3401	7	4	classifications	classification	NOUN
ejpam-3401	7	5	:	:	PUNCT
ejpam-3401	7	6	54c05	54c05	NUM
ejpam-3401	7	7	,	,	PUNCT
ejpam-3401	7	8	54c08	54c08	NUM
ejpam-3401	7	9	,	,	PUNCT
ejpam-3401	7	10	54c10	54c10	NUM
ejpam-3401	7	11	key	key	ADJ
ejpam-3401	7	12	words	word	NOUN
ejpam-3401	7	13	and	and	CCONJ
ejpam-3401	7	14	phrases	phrase	NOUN
ejpam-3401	7	15	:	:	PUNCT
ejpam-3401	7	16	operator	operator	NOUN
ejpam-3401	7	17	topological	topological	ADJ
ejpam-3401	7	18	space	space	NOUN
ejpam-3401	7	19	,	,	PUNCT
ejpam-3401	7	20	bi	bi	ADJ
ejpam-3401	7	21	-	-	NOUN
ejpam-3401	7	22	operator	operator	NOUN
ejpam-3401	7	23	topological	topological	ADJ
ejpam-3401	7	24	space	space	NOUN
ejpam-3401	7	25	,	,	PUNCT
ejpam-3401	7	26	b	b	X
ejpam-3401	7	27	-	-	PUNCT
ejpam-3401	7	28	open	open	ADJ
ejpam-3401	7	29	sets	set	NOUN
ejpam-3401	7	30	,	,	PUNCT
ejpam-3401	7	31	t	t	NOUN
ejpam-3401	7	32	∗-open	∗-open	NOUN
ejpam-3401	7	33	sets	set	NOUN
ejpam-3401	7	34	,	,	PUNCT
ejpam-3401	7	35	contra	contra	PROPN
ejpam-3401	7	36	-	-	ADJ
ejpam-3401	7	37	b	b	NOUN
ejpam-3401	7	38	-	-	PUNCT
ejpam-3401	7	39	continuous	continuous	ADJ
ejpam-3401	7	40	,	,	PUNCT
ejpam-3401	7	41	urysohn	urysohn	PROPN
ejpam-3401	7	42	space	space	NOUN
ejpam-3401	7	43	,	,	PUNCT
ejpam-3401	7	44	weakly	weakly	ADJ
ejpam-3401	7	45	hausdorff	hausdorff	NOUN
ejpam-3401	7	46	space	space	NOUN
ejpam-3401	7	47	1	1	NUM
ejpam-3401	7	48	.	.	PUNCT
ejpam-3401	8	1	introduction	introduction	NOUN
ejpam-3401	8	2	over	over	ADP
ejpam-3401	8	3	the	the	DET
ejpam-3401	8	4	past	past	ADJ
ejpam-3401	8	5	years	year	NOUN
ejpam-3401	8	6	,	,	PUNCT
ejpam-3401	8	7	an	an	DET
ejpam-3401	8	8	amount	amount	NOUN
ejpam-3401	8	9	of	of	ADP
ejpam-3401	8	10	generalizations	generalization	NOUN
ejpam-3401	8	11	of	of	ADP
ejpam-3401	8	12	open	open	ADJ
ejpam-3401	8	13	sets	set	NOUN
ejpam-3401	8	14	has	have	AUX
ejpam-3401	8	15	been	be	AUX
ejpam-3401	8	16	considered	consider	VERB
ejpam-3401	8	17	.	.	PUNCT
ejpam-3401	9	1	the	the	DET
ejpam-3401	9	2	first	first	ADJ
ejpam-3401	9	3	notion	notion	NOUN
ejpam-3401	9	4	due	due	ADP
ejpam-3401	9	5	to	to	ADP
ejpam-3401	9	6	levine	levine	PROPN
ejpam-3401	9	7	[	[	X
ejpam-3401	9	8	12	12	NUM
ejpam-3401	9	9	]	]	PUNCT
ejpam-3401	9	10	in	in	ADP
ejpam-3401	9	11	1963	1963	NUM
ejpam-3401	9	12	was	be	AUX
ejpam-3401	9	13	semi	semi	ADJ
ejpam-3401	9	14	-	-	ADJ
ejpam-3401	9	15	open	open	ADJ
ejpam-3401	9	16	sets	set	NOUN
ejpam-3401	9	17	,	,	PUNCT
ejpam-3401	9	18	while	while	SCONJ
ejpam-3401	9	19	in	in	ADP
ejpam-3401	9	20	1965	1965	NUM
ejpam-3401	9	21	nj̊astad	nj̊astad	NOUN
ejpam-3401	10	1	[	[	X
ejpam-3401	10	2	15	15	NUM
ejpam-3401	10	3	]	]	PUNCT
ejpam-3401	10	4	introduced	introduce	VERB
ejpam-3401	10	5	some	some	DET
ejpam-3401	10	6	classes	class	NOUN
ejpam-3401	10	7	of	of	ADP
ejpam-3401	10	8	nearly	nearly	ADV
ejpam-3401	10	9	open	open	ADJ
ejpam-3401	10	10	sets	set	NOUN
ejpam-3401	10	11	,	,	PUNCT
ejpam-3401	10	12	more	more	ADV
ejpam-3401	10	13	precisely	precisely	ADV
ejpam-3401	10	14	,	,	PUNCT
ejpam-3401	10	15	they	they	PRON
ejpam-3401	10	16	investigated	investigate	VERB
ejpam-3401	10	17	the	the	DET
ejpam-3401	10	18	structure	structure	NOUN
ejpam-3401	10	19	of	of	ADP
ejpam-3401	10	20	α	α	NOUN
ejpam-3401	10	21	-	-	ADJ
ejpam-3401	10	22	open	open	ADJ
ejpam-3401	10	23	set	set	NOUN
ejpam-3401	10	24	and	and	CCONJ
ejpam-3401	10	25	gave	give	VERB
ejpam-3401	10	26	some	some	DET
ejpam-3401	10	27	applications	application	NOUN
ejpam-3401	10	28	.	.	PUNCT
ejpam-3401	11	1	mashhour	mashhour	INTJ
ejpam-3401	11	2	et	et	PROPN
ejpam-3401	11	3	al	al	PROPN
ejpam-3401	11	4	.	.	PROPN
ejpam-3401	12	1	in	in	ADP
ejpam-3401	12	2	1982	1982	NUM
ejpam-3401	12	3	[	[	X
ejpam-3401	12	4	5	5	NUM
ejpam-3401	12	5	]	]	PUNCT
ejpam-3401	12	6	introduced	introduce	VERB
ejpam-3401	12	7	and	and	CCONJ
ejpam-3401	12	8	studied	study	VERB
ejpam-3401	12	9	pre	pre	ADJ
ejpam-3401	12	10	-	-	ADJ
ejpam-3401	12	11	open	open	ADJ
ejpam-3401	12	12	sets	set	NOUN
ejpam-3401	12	13	and	and	CCONJ
ejpam-3401	12	14	pre	pre	ADJ
ejpam-3401	12	15	-	-	ADJ
ejpam-3401	12	16	continuous	continuous	ADJ
ejpam-3401	12	17	functions	function	NOUN
ejpam-3401	12	18	.	.	PUNCT
ejpam-3401	13	1	in	in	ADP
ejpam-3401	13	2	1983	1983	NUM
ejpam-3401	13	3	abd	abd	PROPN
ejpam-3401	13	4	el	el	PROPN
ejpam-3401	13	5	-	-	PROPN
ejpam-3401	13	6	monsef	monsef	PROPN
ejpam-3401	13	7	et	et	PROPN
ejpam-3401	13	8	al	al	PROPN
ejpam-3401	13	9	.	.	PUNCT
ejpam-3401	14	1	[	[	X
ejpam-3401	14	2	13	13	NUM
ejpam-3401	14	3	]	]	PUNCT
ejpam-3401	14	4	introduced	introduce	VERB
ejpam-3401	14	5	the	the	DET
ejpam-3401	14	6	new	new	ADJ
ejpam-3401	14	7	topological	topological	ADJ
ejpam-3401	14	8	notions	notion	NOUN
ejpam-3401	14	9	,	,	PUNCT
ejpam-3401	14	10	β	β	X
ejpam-3401	14	11	-	-	ADJ
ejpam-3401	14	12	open	open	ADJ
ejpam-3401	14	13	sets	set	NOUN
ejpam-3401	14	14	,	,	PUNCT
ejpam-3401	14	15	β	β	ADJ
ejpam-3401	14	16	-	-	ADJ
ejpam-3401	14	17	continuous	continuous	ADJ
ejpam-3401	14	18	mappings	mapping	NOUN
ejpam-3401	14	19	and	and	CCONJ
ejpam-3401	14	20	β	β	NOUN
ejpam-3401	14	21	-	-	ADJ
ejpam-3401	14	22	open	open	ADJ
ejpam-3401	14	23	mappings	mapping	NOUN
ejpam-3401	14	24	.	.	PUNCT
ejpam-3401	15	1	in	in	ADP
ejpam-3401	15	2	1996	1996	NUM
ejpam-3401	15	3	[	[	X
ejpam-3401	15	4	3	3	NUM
ejpam-3401	15	5	]	]	PUNCT
ejpam-3401	15	6	,	,	PUNCT
ejpam-3401	15	7	andrijević	andrijević	AUX
ejpam-3401	15	8	introduced	introduce	VERB
ejpam-3401	15	9	and	and	CCONJ
ejpam-3401	15	10	studied	study	VERB
ejpam-3401	15	11	a	a	DET
ejpam-3401	15	12	new	new	ADJ
ejpam-3401	15	13	class	class	NOUN
ejpam-3401	15	14	of	of	ADP
ejpam-3401	15	15	generalized	generalized	ADJ
ejpam-3401	15	16	open	open	ADJ
ejpam-3401	15	17	sets	set	NOUN
ejpam-3401	15	18	in	in	ADP
ejpam-3401	15	19	a	a	DET
ejpam-3401	15	20	topological	topological	ADJ
ejpam-3401	15	21	space	space	NOUN
ejpam-3401	15	22	,	,	PUNCT
ejpam-3401	15	23	called	call	VERB
ejpam-3401	15	24	b	b	X
ejpam-3401	15	25	-	-	PUNCT
ejpam-3401	15	26	open	open	ADJ
ejpam-3401	15	27	sets	set	NOUN
ejpam-3401	15	28	.	.	PUNCT
ejpam-3401	16	1	all	all	PRON
ejpam-3401	16	2	of	of	ADP
ejpam-3401	16	3	these	these	PRON
ejpam-3401	16	4	above	above	ADJ
ejpam-3401	16	5	concepts	concept	NOUN
ejpam-3401	16	6	were	be	AUX
ejpam-3401	16	7	defined	define	VERB
ejpam-3401	16	8	similarly	similarly	ADV
ejpam-3401	16	9	using	use	VERB
ejpam-3401	16	10	the	the	DET
ejpam-3401	16	11	closure	closure	NOUN
ejpam-3401	16	12	operator	operator	NOUN
ejpam-3401	16	13	cl	cl	NOUN
ejpam-3401	16	14	and	and	CCONJ
ejpam-3401	16	15	the	the	DET
ejpam-3401	16	16	interior	interior	ADJ
ejpam-3401	16	17	operator	operator	NOUN
ejpam-3401	16	18	int	int	NOUN
ejpam-3401	16	19	.	.	PUNCT
ejpam-3401	17	1	this	this	DET
ejpam-3401	17	2	research	research	NOUN
ejpam-3401	17	3	area	area	NOUN
ejpam-3401	17	4	(	(	PUNCT
ejpam-3401	17	5	which	which	PRON
ejpam-3401	17	6	is	be	AUX
ejpam-3401	17	7	fertile	fertile	ADJ
ejpam-3401	17	8	in	in	ADP
ejpam-3401	17	9	information	information	NOUN
ejpam-3401	17	10	)	)	PUNCT
ejpam-3401	17	11	still	still	ADV
ejpam-3401	17	12	takes	take	VERB
ejpam-3401	17	13	a	a	DET
ejpam-3401	17	14	significant	significant	ADJ
ejpam-3401	17	15	part	part	NOUN
ejpam-3401	17	16	of	of	ADP
ejpam-3401	17	17	the	the	DET
ejpam-3401	17	18	investigations	investigation	NOUN
ejpam-3401	17	19	because	because	SCONJ
ejpam-3401	17	20	it	it	PRON
ejpam-3401	17	21	has	have	VERB
ejpam-3401	17	22	a	a	DET
ejpam-3401	17	23	clear	clear	ADJ
ejpam-3401	17	24	effect	effect	NOUN
ejpam-3401	17	25	on	on	ADP
ejpam-3401	17	26	the	the	DET
ejpam-3401	17	27	development	development	NOUN
ejpam-3401	17	28	of	of	ADP
ejpam-3401	17	29	the	the	DET
ejpam-3401	17	30	topological	topological	ADJ
ejpam-3401	17	31	space	space	NOUN
ejpam-3401	17	32	through	through	ADP
ejpam-3401	17	33	the	the	DET
ejpam-3401	17	34	experience	experience	NOUN
ejpam-3401	17	35	of	of	ADP
ejpam-3401	17	36	many	many	ADJ
ejpam-3401	17	37	theories	theory	NOUN
ejpam-3401	17	38	and	and	CCONJ
ejpam-3401	17	39	characteristics	characteristic	NOUN
ejpam-3401	17	40	of	of	ADP
ejpam-3401	17	41	different	different	ADJ
ejpam-3401	17	42	types	type	NOUN
ejpam-3401	17	43	of	of	ADP
ejpam-3401	17	44	open	open	ADJ
ejpam-3401	17	45	sets	set	NOUN
ejpam-3401	17	46	,	,	PUNCT
ejpam-3401	17	47	for	for	ADP
ejpam-3401	17	48	instance	instance	NOUN
ejpam-3401	17	49	see	see	VERB
ejpam-3401	17	50	(	(	PUNCT
ejpam-3401	17	51	[	[	X
ejpam-3401	17	52	1	1	NUM
ejpam-3401	17	53	]	]	PUNCT
ejpam-3401	17	54	,	,	PUNCT
ejpam-3401	17	55	[	[	X
ejpam-3401	17	56	17	17	NUM
ejpam-3401	17	57	]	]	PUNCT
ejpam-3401	17	58	,	,	PUNCT
ejpam-3401	17	59	[	[	X
ejpam-3401	17	60	7	7	NUM
ejpam-3401	17	61	]	]	PUNCT
ejpam-3401	17	62	,	,	PUNCT
ejpam-3401	17	63	[	[	X
ejpam-3401	17	64	8	8	NUM
ejpam-3401	17	65	]	]	PUNCT
ejpam-3401	17	66	,	,	PUNCT
ejpam-3401	17	67	[	[	X
ejpam-3401	17	68	10	10	NUM
ejpam-3401	17	69	]	]	PUNCT
ejpam-3401	17	70	,	,	PUNCT
ejpam-3401	17	71	[	[	X
ejpam-3401	17	72	9	9	NUM
ejpam-3401	17	73	]	]	PUNCT
ejpam-3401	17	74	and	and	CCONJ
ejpam-3401	17	75	[	[	X
ejpam-3401	17	76	21	21	NUM
ejpam-3401	17	77	]	]	PUNCT
ejpam-3401	17	78	)	)	PUNCT
ejpam-3401	17	79	.	.	PUNCT
ejpam-3401	18	1	we	we	PRON
ejpam-3401	18	2	work	work	VERB
ejpam-3401	18	3	on	on	ADP
ejpam-3401	18	4	circulating	circulate	VERB
ejpam-3401	18	5	the	the	DET
ejpam-3401	18	6	b	b	NOUN
ejpam-3401	18	7	-	-	NOUN
ejpam-3401	18	8	openness	openness	NOUN
ejpam-3401	18	9	from	from	ADP
ejpam-3401	18	10	a	a	DET
ejpam-3401	18	11	different	different	ADJ
ejpam-3401	18	12	point	point	NOUN
ejpam-3401	18	13	of	of	ADP
ejpam-3401	18	14	view	view	NOUN
ejpam-3401	18	15	than	than	SCONJ
ejpam-3401	18	16	previously	previously	ADV
ejpam-3401	18	17	stated	state	VERB
ejpam-3401	18	18	since	since	SCONJ
ejpam-3401	18	19	our	our	PRON
ejpam-3401	18	20	generalization	generalization	NOUN
ejpam-3401	18	21	depends	depend	VERB
ejpam-3401	18	22	entirely	entirely	ADV
ejpam-3401	18	23	on	on	ADP
ejpam-3401	18	24	operators	operator	NOUN
ejpam-3401	18	25	attached	attach	VERB
ejpam-3401	18	26	with	with	ADP
ejpam-3401	18	27	topology	topology	NOUN
ejpam-3401	18	28	τ	τ	PROPN
ejpam-3401	18	29	on	on	ADP
ejpam-3401	18	30	x	x	INTJ
ejpam-3401	18	31	to	to	PART
ejpam-3401	18	32	define	define	VERB
ejpam-3401	18	33	the	the	DET
ejpam-3401	18	34	b	b	NOUN
ejpam-3401	18	35	-	-	PUNCT
ejpam-3401	18	36	open	open	ADJ
ejpam-3401	18	37	sets	set	NOUN
ejpam-3401	18	38	.	.	PUNCT
ejpam-3401	19	1	more	more	ADV
ejpam-3401	19	2	accurately	accurately	ADV
ejpam-3401	19	3	,	,	PUNCT
ejpam-3401	19	4	let	let	VERB
ejpam-3401	19	5	p	p	NOUN
ejpam-3401	19	6	(	(	PUNCT
ejpam-3401	19	7	x	x	NOUN
ejpam-3401	19	8	)	)	PUNCT
ejpam-3401	19	9	be	be	VERB
ejpam-3401	19	10	the	the	DET
ejpam-3401	19	11	power	power	NOUN
ejpam-3401	19	12	set	set	NOUN
ejpam-3401	19	13	of	of	ADP
ejpam-3401	19	14	x	x	PUNCT
ejpam-3401	19	15	and	and	CCONJ
ejpam-3401	19	16	functions	function	NOUN
ejpam-3401	19	17	t1	t1	VERB
ejpam-3401	19	18	,	,	PUNCT
ejpam-3401	19	19	t2	t2	NOUN
ejpam-3401	19	20	:	:	PUNCT
ejpam-3401	19	21	p	p	X
ejpam-3401	19	22	(	(	PUNCT
ejpam-3401	19	23	x)→	x)→	PROPN
ejpam-3401	19	24	p	p	X
ejpam-3401	19	25	(	(	PUNCT
ejpam-3401	19	26	x	x	NOUN
ejpam-3401	19	27	)	)	PUNCT
ejpam-3401	19	28	are	be	AUX
ejpam-3401	19	29	operators	operator	NOUN
ejpam-3401	19	30	associated	associate	VERB
ejpam-3401	19	31	with	with	ADP
ejpam-3401	19	32	topology	topology	NOUN
ejpam-3401	19	33	τ	τ	PROPN
ejpam-3401	19	34	on	on	ADP
ejpam-3401	19	35	x.	x.	PROPN
ejpam-3401	19	36	then	then	ADV
ejpam-3401	19	37	the	the	DET
ejpam-3401	19	38	quadruple	quadruple	NOUN
ejpam-3401	19	39	doi	doi	NOUN
ejpam-3401	19	40	:	:	PUNCT
ejpam-3401	19	41	https://doi.org/10.29020/nybg.ejpam.v12i2.3401	https://doi.org/10.29020/nybg.ejpam.v12i2.3401	NOUN
ejpam-3401	19	42	email	email	NOUN
ejpam-3401	19	43	address	address	NOUN
ejpam-3401	19	44	:	:	PUNCT
ejpam-3401	19	45	layth.muhsin@science.unideb.hu	layth.muhsin@science.unideb.hu	PROPN
ejpam-3401	19	46	(	(	PUNCT
ejpam-3401	19	47	l.	l.	PROPN
ejpam-3401	19	48	m.	m.	PROPN
ejpam-3401	19	49	alabdulsada	alabdulsada	PROPN
ejpam-3401	19	50	)	)	PUNCT
ejpam-3401	19	51	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3401	20	1	358	358	NUM
ejpam-3401	20	2	c	c	X
ejpam-3401	20	3	©	©	PROPN
ejpam-3401	20	4	2019	2019	NUM
ejpam-3401	20	5	ejpam	ejpam	NOUN
ejpam-3401	20	6	all	all	DET
ejpam-3401	20	7	rights	right	NOUN
ejpam-3401	20	8	reserved	reserve	VERB
ejpam-3401	20	9	.	.	PUNCT
ejpam-3401	21	1	l.	l.	PROPN
ejpam-3401	21	2	m.	m.	PROPN
ejpam-3401	21	3	alabdulsada	alabdulsada	PROPN
ejpam-3401	21	4	/	/	SYM
ejpam-3401	21	5	eur	eur	PROPN
ejpam-3401	21	6	.	.	PUNCT
ejpam-3401	22	1	j.	j.	PROPN
ejpam-3401	22	2	pure	pure	PROPN
ejpam-3401	22	3	appl	appl	PROPN
ejpam-3401	22	4	.	.	PROPN
ejpam-3401	22	5	math	math	PROPN
ejpam-3401	22	6	,	,	PUNCT
ejpam-3401	22	7	12	12	NUM
ejpam-3401	22	8	(	(	PUNCT
ejpam-3401	22	9	2	2	NUM
ejpam-3401	22	10	)	)	PUNCT
ejpam-3401	22	11	(	(	PUNCT
ejpam-3401	22	12	2019	2019	NUM
ejpam-3401	22	13	)	)	PUNCT
ejpam-3401	22	14	,	,	PUNCT
ejpam-3401	22	15	358	358	NUM
ejpam-3401	22	16	-	-	SYM
ejpam-3401	22	17	369	369	NUM
ejpam-3401	22	18	359	359	NUM
ejpam-3401	22	19	(	(	PUNCT
ejpam-3401	22	20	x	x	X
ejpam-3401	22	21	,	,	PUNCT
ejpam-3401	22	22	τ	τ	PROPN
ejpam-3401	22	23	,	,	PUNCT
ejpam-3401	22	24	t1	t1	NOUN
ejpam-3401	22	25	,	,	PUNCT
ejpam-3401	22	26	t2	t2	NOUN
ejpam-3401	22	27	)	)	PUNCT
ejpam-3401	22	28	is	be	AUX
ejpam-3401	22	29	called	call	VERB
ejpam-3401	22	30	a	a	DET
ejpam-3401	22	31	bi	bi	ADJ
ejpam-3401	22	32	-	-	ADJ
ejpam-3401	22	33	operator	operator	NOUN
ejpam-3401	22	34	topological	topological	ADJ
ejpam-3401	22	35	space	space	NOUN
ejpam-3401	22	36	.	.	PUNCT
ejpam-3401	23	1	however	however	ADV
ejpam-3401	23	2	,	,	PUNCT
ejpam-3401	23	3	if	if	SCONJ
ejpam-3401	23	4	t1(s	t1(s	ADP
ejpam-3401	23	5	)	)	PUNCT
ejpam-3401	23	6	=	=	SYM
ejpam-3401	23	7	cl(int(s	cl(int(s	NOUN
ejpam-3401	23	8	)	)	PUNCT
ejpam-3401	23	9	)	)	PUNCT
ejpam-3401	23	10	and	and	CCONJ
ejpam-3401	23	11	t2(s	t2(s	NOUN
ejpam-3401	23	12	)	)	PUNCT
ejpam-3401	23	13	=	=	SYM
ejpam-3401	23	14	int(cl(s	int(cl(s	PROPN
ejpam-3401	23	15	)	)	PUNCT
ejpam-3401	23	16	)	)	PUNCT
ejpam-3401	24	1	,	,	PUNCT
ejpam-3401	24	2	then	then	ADV
ejpam-3401	24	3	the	the	DET
ejpam-3401	24	4	notion	notion	NOUN
ejpam-3401	24	5	of	of	ADP
ejpam-3401	24	6	b	b	NOUN
ejpam-3401	24	7	-	-	PUNCT
ejpam-3401	24	8	open	open	ADJ
ejpam-3401	24	9	sets	set	NOUN
ejpam-3401	24	10	became	become	VERB
ejpam-3401	24	11	exactly	exactly	ADV
ejpam-3401	24	12	the	the	DET
ejpam-3401	24	13	same	same	ADJ
ejpam-3401	24	14	as	as	ADP
ejpam-3401	24	15	the	the	DET
ejpam-3401	24	16	definition	definition	NOUN
ejpam-3401	24	17	of	of	ADP
ejpam-3401	24	18	the	the	DET
ejpam-3401	24	19	b	b	NOUN
ejpam-3401	24	20	-	-	PUNCT
ejpam-3401	24	21	open	open	ADJ
ejpam-3401	24	22	sets	set	NOUN
ejpam-3401	24	23	.	.	PUNCT
ejpam-3401	25	1	the	the	DET
ejpam-3401	25	2	use	use	NOUN
ejpam-3401	25	3	of	of	ADP
ejpam-3401	25	4	the	the	DET
ejpam-3401	25	5	operator	operator	NOUN
ejpam-3401	25	6	topological	topological	ADJ
ejpam-3401	25	7	spaces	space	NOUN
ejpam-3401	25	8	for	for	ADP
ejpam-3401	25	9	the	the	DET
ejpam-3401	25	10	first	first	ADJ
ejpam-3401	25	11	time	time	NOUN
ejpam-3401	25	12	goes	go	VERB
ejpam-3401	25	13	back	back	ADV
ejpam-3401	25	14	to	to	ADP
ejpam-3401	25	15	h.	h.	PROPN
ejpam-3401	25	16	j.	j.	PROPN
ejpam-3401	25	17	mustafa	mustafa	PROPN
ejpam-3401	25	18	et	et	PROPN
ejpam-3401	25	19	al	al	PROPN
ejpam-3401	25	20	.	.	PUNCT
ejpam-3401	26	1	[	[	X
ejpam-3401	26	2	11	11	NUM
ejpam-3401	26	3	]	]	PUNCT
ejpam-3401	26	4	,	,	PUNCT
ejpam-3401	26	5	[	[	X
ejpam-3401	26	6	14	14	NUM
ejpam-3401	26	7	]	]	PUNCT
ejpam-3401	26	8	,	,	PUNCT
ejpam-3401	26	9	and	and	CCONJ
ejpam-3401	26	10	recently	recently	ADV
ejpam-3401	26	11	alabdulsada	alabdulsada	NOUN
ejpam-3401	27	1	[	[	X
ejpam-3401	27	2	2	2	NUM
ejpam-3401	27	3	]	]	PUNCT
ejpam-3401	27	4	.	.	PUNCT
ejpam-3401	28	1	in	in	ADP
ejpam-3401	28	2	this	this	DET
ejpam-3401	28	3	paper	paper	NOUN
ejpam-3401	28	4	,	,	PUNCT
ejpam-3401	28	5	first	first	ADV
ejpam-3401	28	6	we	we	PRON
ejpam-3401	28	7	introduce	introduce	VERB
ejpam-3401	28	8	and	and	CCONJ
ejpam-3401	28	9	study	study	VERB
ejpam-3401	28	10	the	the	DET
ejpam-3401	28	11	new	new	ADJ
ejpam-3401	28	12	notion	notion	NOUN
ejpam-3401	28	13	of	of	ADP
ejpam-3401	28	14	bi	bi	ADJ
ejpam-3401	28	15	-	-	NOUN
ejpam-3401	28	16	operator	operator	NOUN
ejpam-3401	28	17	topological	topological	ADJ
ejpam-3401	28	18	spaces	space	NOUN
ejpam-3401	28	19	and	and	CCONJ
ejpam-3401	28	20	its	its	PRON
ejpam-3401	28	21	related	related	ADJ
ejpam-3401	28	22	properties	property	NOUN
ejpam-3401	28	23	.	.	PUNCT
ejpam-3401	29	1	our	our	PRON
ejpam-3401	29	2	generalization	generalization	NOUN
ejpam-3401	29	3	of	of	ADP
ejpam-3401	29	4	open	open	ADJ
ejpam-3401	29	5	sets	set	NOUN
ejpam-3401	29	6	in	in	ADP
ejpam-3401	29	7	topological	topological	ADJ
ejpam-3401	29	8	space	space	NOUN
ejpam-3401	29	9	is	be	AUX
ejpam-3401	29	10	called	call	VERB
ejpam-3401	29	11	b	b	NOUN
ejpam-3401	29	12	-	-	PUNCT
ejpam-3401	29	13	open	open	ADJ
ejpam-3401	29	14	sets	set	NOUN
ejpam-3401	29	15	,	,	PUNCT
ejpam-3401	29	16	which	which	PRON
ejpam-3401	29	17	linked	link	VERB
ejpam-3401	29	18	to	to	ADP
ejpam-3401	29	19	bi	bi	ADJ
ejpam-3401	29	20	-	-	NOUN
ejpam-3401	29	21	operator	operator	NOUN
ejpam-3401	29	22	topological	topological	ADJ
ejpam-3401	29	23	spaces	space	NOUN
ejpam-3401	29	24	.	.	PUNCT
ejpam-3401	30	1	first	first	ADV
ejpam-3401	30	2	we	we	PRON
ejpam-3401	30	3	recall	recall	VERB
ejpam-3401	30	4	several	several	ADJ
ejpam-3401	30	5	concepts	concept	NOUN
ejpam-3401	30	6	and	and	CCONJ
ejpam-3401	30	7	definitions	definition	NOUN
ejpam-3401	30	8	that	that	PRON
ejpam-3401	30	9	contributed	contribute	VERB
ejpam-3401	30	10	to	to	ADP
ejpam-3401	30	11	constructing	construct	VERB
ejpam-3401	30	12	our	our	PRON
ejpam-3401	30	13	definition	definition	NOUN
ejpam-3401	30	14	,	,	PUNCT
ejpam-3401	30	15	namely	namely	ADV
ejpam-3401	30	16	b	b	X
ejpam-3401	30	17	-	-	PUNCT
ejpam-3401	30	18	open	open	ADJ
ejpam-3401	30	19	which	which	PRON
ejpam-3401	30	20	generalizes	generalize	VERB
ejpam-3401	30	21	b	b	X
ejpam-3401	30	22	-	-	PUNCT
ejpam-3401	30	23	open	open	ADJ
ejpam-3401	30	24	sets	set	NOUN
ejpam-3401	30	25	in	in	ADP
ejpam-3401	30	26	a	a	DET
ejpam-3401	30	27	topological	topological	ADJ
ejpam-3401	30	28	space	space	NOUN
ejpam-3401	30	29	.	.	PUNCT
ejpam-3401	31	1	afterwards	afterwards	ADV
ejpam-3401	31	2	,	,	PUNCT
ejpam-3401	31	3	we	we	PRON
ejpam-3401	31	4	apply	apply	VERB
ejpam-3401	31	5	b	b	X
ejpam-3401	31	6	-	-	PUNCT
ejpam-3401	31	7	open	open	ADJ
ejpam-3401	31	8	sets	set	NOUN
ejpam-3401	31	9	to	to	PART
ejpam-3401	31	10	define	define	VERB
ejpam-3401	31	11	some	some	DET
ejpam-3401	31	12	further	further	ADJ
ejpam-3401	31	13	new	new	ADJ
ejpam-3401	31	14	concepts	concept	NOUN
ejpam-3401	31	15	,	,	PUNCT
ejpam-3401	31	16	and	and	CCONJ
ejpam-3401	31	17	show	show	VERB
ejpam-3401	31	18	some	some	DET
ejpam-3401	31	19	remarks	remark	NOUN
ejpam-3401	31	20	and	and	CCONJ
ejpam-3401	31	21	examples	example	NOUN
ejpam-3401	31	22	for	for	ADP
ejpam-3401	31	23	b	b	NOUN
ejpam-3401	31	24	-	-	PUNCT
ejpam-3401	31	25	open	open	ADJ
ejpam-3401	31	26	sets	set	NOUN
ejpam-3401	31	27	.	.	PUNCT
ejpam-3401	32	1	our	our	PRON
ejpam-3401	32	2	main	main	ADJ
ejpam-3401	32	3	results	result	NOUN
ejpam-3401	32	4	are	be	AUX
ejpam-3401	32	5	given	give	VERB
ejpam-3401	32	6	in	in	ADP
ejpam-3401	32	7	section	section	NOUN
ejpam-3401	32	8	3	3	NUM
ejpam-3401	32	9	,	,	PUNCT
ejpam-3401	32	10	where	where	SCONJ
ejpam-3401	32	11	we	we	PRON
ejpam-3401	32	12	present	present	VERB
ejpam-3401	32	13	and	and	CCONJ
ejpam-3401	32	14	study	study	VERB
ejpam-3401	32	15	several	several	ADJ
ejpam-3401	32	16	different	different	ADJ
ejpam-3401	32	17	spaces	space	NOUN
ejpam-3401	32	18	as	as	ADV
ejpam-3401	32	19	well	well	ADV
ejpam-3401	32	20	as	as	ADP
ejpam-3401	32	21	functions	function	NOUN
ejpam-3401	32	22	which	which	PRON
ejpam-3401	32	23	are	be	AUX
ejpam-3401	32	24	based	base	VERB
ejpam-3401	32	25	on	on	ADP
ejpam-3401	32	26	b	b	NOUN
ejpam-3401	32	27	-	-	PUNCT
ejpam-3401	32	28	open	open	ADJ
ejpam-3401	32	29	sets	set	NOUN
ejpam-3401	32	30	.	.	PUNCT
ejpam-3401	33	1	also	also	ADV
ejpam-3401	33	2	,	,	PUNCT
ejpam-3401	33	3	we	we	PRON
ejpam-3401	33	4	investigate	investigate	VERB
ejpam-3401	33	5	the	the	DET
ejpam-3401	33	6	relationships	relationship	NOUN
ejpam-3401	33	7	between	between	ADP
ejpam-3401	33	8	these	these	DET
ejpam-3401	33	9	types	type	NOUN
ejpam-3401	33	10	of	of	ADP
ejpam-3401	33	11	functions	function	NOUN
ejpam-3401	33	12	,	,	PUNCT
ejpam-3401	33	13	besides	besides	SCONJ
ejpam-3401	33	14	we	we	PRON
ejpam-3401	33	15	check	check	VERB
ejpam-3401	33	16	the	the	DET
ejpam-3401	33	17	relationships	relationship	NOUN
ejpam-3401	33	18	with	with	ADP
ejpam-3401	33	19	some	some	DET
ejpam-3401	33	20	special	special	ADJ
ejpam-3401	33	21	spaces	space	NOUN
ejpam-3401	33	22	such	such	ADJ
ejpam-3401	33	23	as	as	ADP
ejpam-3401	33	24	urysohn	urysohn	PROPN
ejpam-3401	33	25	space	space	NOUN
ejpam-3401	33	26	or	or	CCONJ
ejpam-3401	33	27	weakly	weakly	ADJ
ejpam-3401	33	28	hausdorff	hausdorff	NOUN
ejpam-3401	33	29	space	space	NOUN
ejpam-3401	33	30	.	.	PUNCT
ejpam-3401	34	1	to	to	PART
ejpam-3401	34	2	be	be	AUX
ejpam-3401	34	3	precise	precise	ADJ
ejpam-3401	34	4	,	,	PUNCT
ejpam-3401	34	5	we	we	PRON
ejpam-3401	34	6	prove	prove	VERB
ejpam-3401	34	7	that	that	SCONJ
ejpam-3401	34	8	,	,	PUNCT
ejpam-3401	34	9	among	among	ADP
ejpam-3401	34	10	others	other	NOUN
ejpam-3401	34	11	,	,	PUNCT
ejpam-3401	34	12	if	if	SCONJ
ejpam-3401	34	13	the	the	DET
ejpam-3401	34	14	function	function	NOUN
ejpam-3401	34	15	f	f	X
ejpam-3401	34	16	:	:	PUNCT
ejpam-3401	34	17	(	(	PUNCT
ejpam-3401	34	18	x	x	X
ejpam-3401	34	19	,	,	PUNCT
ejpam-3401	34	20	τ	τ	PROPN
ejpam-3401	34	21	,	,	PUNCT
ejpam-3401	34	22	t1	t1	PROPN
ejpam-3401	34	23	,	,	PUNCT
ejpam-3401	34	24	t2)→	t2)→	X
ejpam-3401	34	25	(	(	PUNCT
ejpam-3401	34	26	y	y	PROPN
ejpam-3401	34	27	,	,	PUNCT
ejpam-3401	34	28	σ	σ	PROPN
ejpam-3401	34	29	)	)	PUNCT
ejpam-3401	34	30	has	have	VERB
ejpam-3401	34	31	a	a	DET
ejpam-3401	34	32	contra	contra	PROPN
ejpam-3401	34	33	-	-	PUNCT
ejpam-3401	34	34	b	b	NOUN
ejpam-3401	34	35	-	-	PUNCT
ejpam-3401	34	36	closed	closed	ADJ
ejpam-3401	34	37	graph	graph	NOUN
ejpam-3401	34	38	,	,	PUNCT
ejpam-3401	34	39	then	then	ADV
ejpam-3401	34	40	the	the	DET
ejpam-3401	34	41	inverse	inverse	ADJ
ejpam-3401	34	42	image	image	NOUN
ejpam-3401	34	43	of	of	ADP
ejpam-3401	34	44	a	a	DET
ejpam-3401	34	45	contra	contra	ADJ
ejpam-3401	34	46	-	-	ADJ
ejpam-3401	34	47	compact	compact	ADJ
ejpam-3401	34	48	set	set	NOUN
ejpam-3401	34	49	s	s	PRON
ejpam-3401	34	50	of	of	ADP
ejpam-3401	34	51	y	y	PROPN
ejpam-3401	34	52	is	be	AUX
ejpam-3401	34	53	b	b	NOUN
ejpam-3401	34	54	-	-	PUNCT
ejpam-3401	34	55	closed	closed	ADJ
ejpam-3401	34	56	in	in	ADP
ejpam-3401	34	57	x.	x.	NOUN
ejpam-3401	34	58	in	in	ADP
ejpam-3401	34	59	addition	addition	NOUN
ejpam-3401	34	60	,	,	PUNCT
ejpam-3401	34	61	if	if	SCONJ
ejpam-3401	34	62	f	f	X
ejpam-3401	34	63	:	:	PUNCT
ejpam-3401	34	64	(	(	PUNCT
ejpam-3401	34	65	x	x	X
ejpam-3401	34	66	,	,	PUNCT
ejpam-3401	34	67	τ	τ	PROPN
ejpam-3401	34	68	,	,	PUNCT
ejpam-3401	34	69	t1	t1	PROPN
ejpam-3401	34	70	,	,	PUNCT
ejpam-3401	34	71	t2)→	t2)→	X
ejpam-3401	34	72	(	(	PUNCT
ejpam-3401	34	73	y	y	PROPN
ejpam-3401	34	74	,	,	PUNCT
ejpam-3401	34	75	σ	σ	PROPN
ejpam-3401	34	76	)	)	PUNCT
ejpam-3401	34	77	is	be	AUX
ejpam-3401	34	78	contra	contra	PROPN
ejpam-3401	34	79	-	-	PUNCT
ejpam-3401	34	80	b	b	NOUN
ejpam-3401	34	81	-	-	PUNCT
ejpam-3401	34	82	continuous	continuous	ADJ
ejpam-3401	34	83	from	from	ADP
ejpam-3401	34	84	a	a	DET
ejpam-3401	34	85	b	b	NOUN
ejpam-3401	34	86	-	-	PUNCT
ejpam-3401	34	87	connected	connect	VERB
ejpam-3401	34	88	space	space	NOUN
ejpam-3401	34	89	onto	onto	ADP
ejpam-3401	34	90	y	y	PROPN
ejpam-3401	34	91	,	,	PUNCT
ejpam-3401	34	92	then	then	ADV
ejpam-3401	34	93	y	y	PROPN
ejpam-3401	34	94	is	be	AUX
ejpam-3401	34	95	not	not	PART
ejpam-3401	34	96	a	a	DET
ejpam-3401	34	97	discrete	discrete	ADJ
ejpam-3401	34	98	space	space	NOUN
ejpam-3401	34	99	.	.	PUNCT
ejpam-3401	35	1	another	another	DET
ejpam-3401	35	2	new	new	ADJ
ejpam-3401	35	3	result	result	NOUN
ejpam-3401	35	4	says	say	VERB
ejpam-3401	35	5	if	if	SCONJ
ejpam-3401	35	6	f	f	PROPN
ejpam-3401	35	7	:	:	PUNCT
ejpam-3401	35	8	(	(	PUNCT
ejpam-3401	35	9	x	x	X
ejpam-3401	35	10	,	,	PUNCT
ejpam-3401	35	11	τ	τ	PROPN
ejpam-3401	35	12	,	,	PUNCT
ejpam-3401	35	13	t1	t1	NOUN
ejpam-3401	35	14	,	,	PUNCT
ejpam-3401	35	15	t2	t2	NOUN
ejpam-3401	35	16	)	)	PUNCT
ejpam-3401	35	17	→	→	SYM
ejpam-3401	35	18	(	(	PUNCT
ejpam-3401	35	19	y	y	PROPN
ejpam-3401	35	20	,	,	PUNCT
ejpam-3401	35	21	σ	σ	PROPN
ejpam-3401	35	22	)	)	PUNCT
ejpam-3401	35	23	is	be	AUX
ejpam-3401	35	24	a	a	DET
ejpam-3401	35	25	contra	contra	PROPN
ejpam-3401	35	26	-	-	PUNCT
ejpam-3401	35	27	b	b	NOUN
ejpam-3401	35	28	-	-	PUNCT
ejpam-3401	35	29	continuous	continuous	ADJ
ejpam-3401	35	30	surjective	surjective	ADJ
ejpam-3401	35	31	function	function	NOUN
ejpam-3401	35	32	and	and	CCONJ
ejpam-3401	35	33	x	x	ADJ
ejpam-3401	35	34	is	be	AUX
ejpam-3401	35	35	b	b	NOUN
ejpam-3401	35	36	-	-	ADJ
ejpam-3401	35	37	compact	compact	ADJ
ejpam-3401	35	38	,	,	PUNCT
ejpam-3401	35	39	then	then	ADV
ejpam-3401	35	40	y	y	PROPN
ejpam-3401	35	41	is	be	AUX
ejpam-3401	35	42	contra	contra	ADJ
ejpam-3401	35	43	-	-	ADJ
ejpam-3401	35	44	compact	compact	ADJ
ejpam-3401	35	45	.	.	PUNCT
ejpam-3401	36	1	furthermore	furthermore	ADV
ejpam-3401	36	2	,	,	PUNCT
ejpam-3401	36	3	a	a	DET
ejpam-3401	36	4	number	number	NOUN
ejpam-3401	36	5	of	of	ADP
ejpam-3401	36	6	important	important	ADJ
ejpam-3401	36	7	related	related	ADJ
ejpam-3401	36	8	properties	property	NOUN
ejpam-3401	36	9	are	be	AUX
ejpam-3401	36	10	stated	state	VERB
ejpam-3401	36	11	and	and	CCONJ
ejpam-3401	36	12	proved	prove	VERB
ejpam-3401	36	13	.	.	PUNCT
ejpam-3401	37	1	2	2	X
ejpam-3401	37	2	.	.	X
ejpam-3401	37	3	background	background	NOUN
ejpam-3401	37	4	in	in	ADP
ejpam-3401	37	5	this	this	DET
ejpam-3401	37	6	section	section	NOUN
ejpam-3401	37	7	,	,	PUNCT
ejpam-3401	37	8	we	we	PRON
ejpam-3401	37	9	recall	recall	VERB
ejpam-3401	37	10	and	and	CCONJ
ejpam-3401	37	11	introduce	introduce	VERB
ejpam-3401	37	12	some	some	PRON
ejpam-3401	37	13	of	of	ADP
ejpam-3401	37	14	the	the	DET
ejpam-3401	37	15	definitions	definition	NOUN
ejpam-3401	37	16	and	and	CCONJ
ejpam-3401	37	17	the	the	DET
ejpam-3401	37	18	fundamental	fundamental	ADJ
ejpam-3401	37	19	notions	notion	NOUN
ejpam-3401	37	20	that	that	PRON
ejpam-3401	37	21	play	play	VERB
ejpam-3401	37	22	a	a	DET
ejpam-3401	37	23	key	key	ADJ
ejpam-3401	37	24	role	role	NOUN
ejpam-3401	37	25	in	in	ADP
ejpam-3401	37	26	this	this	DET
ejpam-3401	37	27	paper	paper	NOUN
ejpam-3401	37	28	.	.	PUNCT
ejpam-3401	38	1	throughout	throughout	ADP
ejpam-3401	38	2	,	,	PUNCT
ejpam-3401	38	3	(	(	PUNCT
ejpam-3401	38	4	x	x	X
ejpam-3401	38	5	,	,	PUNCT
ejpam-3401	38	6	τ	τ	PROPN
ejpam-3401	38	7	)	)	PUNCT
ejpam-3401	38	8	,	,	PUNCT
ejpam-3401	38	9	(	(	PUNCT
ejpam-3401	38	10	y	y	PROPN
ejpam-3401	38	11	,	,	PUNCT
ejpam-3401	38	12	σ	σ	PROPN
ejpam-3401	38	13	)	)	PUNCT
ejpam-3401	38	14	are	be	AUX
ejpam-3401	38	15	arbitrary	arbitrary	ADJ
ejpam-3401	38	16	topological	topological	ADJ
ejpam-3401	38	17	spaces	space	NOUN
ejpam-3401	38	18	and	and	CCONJ
ejpam-3401	38	19	s	s	VERB
ejpam-3401	38	20	⊆	⊆	NUM
ejpam-3401	38	21	x.	x.	NOUN
ejpam-3401	38	22	the	the	DET
ejpam-3401	38	23	closure	closure	NOUN
ejpam-3401	38	24	of	of	ADP
ejpam-3401	38	25	s	s	PRON
ejpam-3401	38	26	will	will	AUX
ejpam-3401	38	27	be	be	AUX
ejpam-3401	38	28	denoted	denote	VERB
ejpam-3401	38	29	by	by	ADP
ejpam-3401	38	30	cl(s	cl(	NOUN
ejpam-3401	38	31	)	)	PUNCT
ejpam-3401	38	32	.	.	PUNCT
ejpam-3401	39	1	the	the	DET
ejpam-3401	39	2	interior	interior	NOUN
ejpam-3401	39	3	of	of	ADP
ejpam-3401	39	4	s	s	PRON
ejpam-3401	39	5	will	will	AUX
ejpam-3401	39	6	be	be	AUX
ejpam-3401	39	7	denoted	denote	VERB
ejpam-3401	39	8	by	by	ADP
ejpam-3401	39	9	int(s	int(s	PROPN
ejpam-3401	39	10	)	)	PUNCT
ejpam-3401	39	11	.	.	PUNCT
ejpam-3401	40	1	definition	definition	NOUN
ejpam-3401	40	2	1	1	NUM
ejpam-3401	40	3	.	.	PUNCT
ejpam-3401	41	1	a	a	DET
ejpam-3401	41	2	subset	subset	NOUN
ejpam-3401	41	3	s	s	NOUN
ejpam-3401	41	4	of	of	ADP
ejpam-3401	41	5	a	a	DET
ejpam-3401	41	6	topological	topological	ADJ
ejpam-3401	41	7	space	space	NOUN
ejpam-3401	41	8	(	(	PUNCT
ejpam-3401	41	9	x	x	X
ejpam-3401	41	10	,	,	PUNCT
ejpam-3401	41	11	τ	τ	X
ejpam-3401	41	12	)	)	PUNCT
ejpam-3401	41	13	is	be	AUX
ejpam-3401	41	14	said	say	VERB
ejpam-3401	41	15	to	to	PART
ejpam-3401	41	16	be	be	AUX
ejpam-3401	41	17	:	:	PUNCT
ejpam-3401	41	18	(	(	PUNCT
ejpam-3401	41	19	i	i	NOUN
ejpam-3401	41	20	)	)	PUNCT
ejpam-3401	41	21	regular	regular	ADJ
ejpam-3401	41	22	open	open	ADJ
ejpam-3401	41	23	,	,	PUNCT
ejpam-3401	41	24	if	if	SCONJ
ejpam-3401	41	25	s	s	PART
ejpam-3401	41	26	=	=	ADJ
ejpam-3401	41	27	int(cl(s	int(cl(s	PROPN
ejpam-3401	41	28	)	)	PUNCT
ejpam-3401	41	29	)	)	PUNCT
ejpam-3401	41	30	,	,	PUNCT
ejpam-3401	41	31	regular	regular	PROPN
ejpam-3401	41	32	closed	close	VERB
ejpam-3401	41	33	if	if	SCONJ
ejpam-3401	41	34	s	s	NOUN
ejpam-3401	41	35	=	=	NOUN
ejpam-3401	41	36	cl(int(s	cl(int(s	NOUN
ejpam-3401	41	37	)	)	PUNCT
ejpam-3401	41	38	)	)	PUNCT
ejpam-3401	42	1	[	[	X
ejpam-3401	42	2	20	20	NUM
ejpam-3401	42	3	]	]	PUNCT
ejpam-3401	42	4	.	.	PUNCT
ejpam-3401	43	1	(	(	PUNCT
ejpam-3401	43	2	ii	ii	NOUN
ejpam-3401	43	3	)	)	PUNCT
ejpam-3401	43	4	pre	pre	ADJ
ejpam-3401	43	5	-	-	ADJ
ejpam-3401	43	6	open	open	ADJ
ejpam-3401	43	7	,	,	PUNCT
ejpam-3401	43	8	if	if	SCONJ
ejpam-3401	43	9	s	s	VERB
ejpam-3401	43	10	⊆	⊆	NUM
ejpam-3401	43	11	int(cl(s	int(cl(s	PROPN
ejpam-3401	43	12	)	)	PUNCT
ejpam-3401	43	13	)	)	PUNCT
ejpam-3401	43	14	,	,	PUNCT
ejpam-3401	43	15	the	the	DET
ejpam-3401	43	16	complement	complement	NOUN
ejpam-3401	43	17	of	of	ADP
ejpam-3401	43	18	a	a	DET
ejpam-3401	43	19	pre	pre	NOUN
ejpam-3401	43	20	-	-	ADJ
ejpam-3401	43	21	open	open	ADJ
ejpam-3401	43	22	is	be	AUX
ejpam-3401	43	23	pre	pre	ADJ
ejpam-3401	43	24	-	-	ADJ
ejpam-3401	43	25	closed	closed	ADJ
ejpam-3401	43	26	[	[	X
ejpam-3401	43	27	5	5	NUM
ejpam-3401	43	28	]	]	PUNCT
ejpam-3401	43	29	.	.	PUNCT
ejpam-3401	44	1	(	(	PUNCT
ejpam-3401	44	2	iii	iii	NOUN
ejpam-3401	44	3	)	)	PUNCT
ejpam-3401	44	4	semi	semi	ADJ
ejpam-3401	44	5	-	-	ADJ
ejpam-3401	44	6	open	open	ADJ
ejpam-3401	44	7	,	,	PUNCT
ejpam-3401	44	8	if	if	SCONJ
ejpam-3401	44	9	s	s	VERB
ejpam-3401	44	10	⊆	⊆	NUM
ejpam-3401	44	11	cl(int(s	cl(int(s	NOUN
ejpam-3401	44	12	)	)	PUNCT
ejpam-3401	44	13	)	)	PUNCT
ejpam-3401	44	14	,	,	PUNCT
ejpam-3401	44	15	the	the	DET
ejpam-3401	44	16	complement	complement	NOUN
ejpam-3401	44	17	of	of	ADP
ejpam-3401	44	18	a	a	DET
ejpam-3401	44	19	semi	semi	ADJ
ejpam-3401	44	20	-	-	ADJ
ejpam-3401	44	21	open	open	ADJ
ejpam-3401	44	22	is	be	AUX
ejpam-3401	44	23	semi	semi	ADJ
ejpam-3401	44	24	-	-	ADJ
ejpam-3401	44	25	closed	closed	ADJ
ejpam-3401	44	26	[	[	X
ejpam-3401	44	27	12	12	NUM
ejpam-3401	44	28	]	]	PUNCT
ejpam-3401	44	29	.	.	PUNCT
ejpam-3401	45	1	(	(	PUNCT
ejpam-3401	45	2	iv	iv	X
ejpam-3401	45	3	)	)	PUNCT
ejpam-3401	45	4	α	α	NOUN
ejpam-3401	45	5	-	-	ADJ
ejpam-3401	45	6	open	open	ADJ
ejpam-3401	45	7	,	,	PUNCT
ejpam-3401	45	8	if	if	SCONJ
ejpam-3401	45	9	s	s	VERB
ejpam-3401	45	10	⊆	⊆	NUM
ejpam-3401	45	11	int(cl(int(s	int(cl(int(s	PROPN
ejpam-3401	45	12	)	)	PUNCT
ejpam-3401	45	13	)	)	PUNCT
ejpam-3401	45	14	)	)	PUNCT
ejpam-3401	45	15	,	,	PUNCT
ejpam-3401	45	16	the	the	DET
ejpam-3401	45	17	complement	complement	NOUN
ejpam-3401	45	18	of	of	ADP
ejpam-3401	45	19	an	an	DET
ejpam-3401	45	20	α	α	NOUN
ejpam-3401	45	21	-	-	ADJ
ejpam-3401	45	22	open	open	ADJ
ejpam-3401	45	23	is	be	AUX
ejpam-3401	45	24	α	α	NOUN
ejpam-3401	45	25	-	-	ADJ
ejpam-3401	45	26	closed	closed	ADJ
ejpam-3401	45	27	[	[	X
ejpam-3401	45	28	15	15	NUM
ejpam-3401	45	29	]	]	PUNCT
ejpam-3401	45	30	.	.	PUNCT
ejpam-3401	46	1	(	(	PUNCT
ejpam-3401	46	2	v	v	NOUN
ejpam-3401	46	3	)	)	PUNCT
ejpam-3401	46	4	β	β	NOUN
ejpam-3401	46	5	-	-	ADJ
ejpam-3401	46	6	open	open	ADJ
ejpam-3401	46	7	,	,	PUNCT
ejpam-3401	46	8	if	if	SCONJ
ejpam-3401	46	9	s	s	VERB
ejpam-3401	46	10	⊆	⊆	NUM
ejpam-3401	46	11	cl(int(cl(s	cl(int(cl(s	NOUN
ejpam-3401	46	12	)	)	PUNCT
ejpam-3401	46	13	)	)	PUNCT
ejpam-3401	46	14	)	)	PUNCT
ejpam-3401	46	15	,	,	PUNCT
ejpam-3401	46	16	the	the	DET
ejpam-3401	46	17	complement	complement	NOUN
ejpam-3401	46	18	of	of	ADP
ejpam-3401	46	19	a	a	DET
ejpam-3401	46	20	β	β	X
ejpam-3401	46	21	-	-	ADJ
ejpam-3401	46	22	open	open	ADJ
ejpam-3401	46	23	is	be	AUX
ejpam-3401	46	24	β	β	X
ejpam-3401	46	25	-	-	ADJ
ejpam-3401	46	26	closed	closed	ADJ
ejpam-3401	46	27	[	[	X
ejpam-3401	46	28	13	13	NUM
ejpam-3401	46	29	]	]	PUNCT
ejpam-3401	46	30	.	.	PUNCT
ejpam-3401	47	1	(	(	PUNCT
ejpam-3401	47	2	vi	vi	NOUN
ejpam-3401	47	3	)	)	PUNCT
ejpam-3401	47	4	b	b	NOUN
ejpam-3401	47	5	-	-	PUNCT
ejpam-3401	47	6	open	open	ADJ
ejpam-3401	47	7	,	,	PUNCT
ejpam-3401	47	8	if	if	SCONJ
ejpam-3401	47	9	s	s	VERB
ejpam-3401	47	10	⊆	⊆	NUM
ejpam-3401	47	11	cl(int(s	cl(int(s	NOUN
ejpam-3401	47	12	)	)	PUNCT
ejpam-3401	47	13	)	)	PUNCT
ejpam-3401	47	14	∪	∪	ADP
ejpam-3401	47	15	int(cl(s	int(cl(s	PROPN
ejpam-3401	47	16	)	)	PUNCT
ejpam-3401	47	17	)	)	PUNCT
ejpam-3401	48	1	,	,	PUNCT
ejpam-3401	48	2	the	the	DET
ejpam-3401	48	3	complement	complement	NOUN
ejpam-3401	48	4	of	of	ADP
ejpam-3401	48	5	a	a	DET
ejpam-3401	48	6	b	b	NOUN
ejpam-3401	48	7	-	-	PUNCT
ejpam-3401	48	8	open	open	ADJ
ejpam-3401	48	9	is	be	AUX
ejpam-3401	48	10	b	b	NOUN
ejpam-3401	48	11	-	-	PUNCT
ejpam-3401	48	12	closed	closed	ADJ
ejpam-3401	48	13	[	[	X
ejpam-3401	48	14	3	3	NUM
ejpam-3401	48	15	]	]	PUNCT
ejpam-3401	48	16	.	.	PUNCT
ejpam-3401	49	1	in	in	ADP
ejpam-3401	49	2	particular	particular	ADJ
ejpam-3401	49	3	,	,	PUNCT
ejpam-3401	49	4	the	the	DET
ejpam-3401	49	5	β	β	NOUN
ejpam-3401	49	6	-	-	NOUN
ejpam-3401	49	7	closure	closure	NOUN
ejpam-3401	49	8	of	of	ADP
ejpam-3401	49	9	a	a	DET
ejpam-3401	49	10	set	set	NOUN
ejpam-3401	49	11	s	s	AUX
ejpam-3401	49	12	denoted	denote	VERB
ejpam-3401	49	13	by	by	ADP
ejpam-3401	49	14	βcl(s	βcl(s	PROPN
ejpam-3401	49	15	)	)	PUNCT
ejpam-3401	49	16	,	,	PUNCT
ejpam-3401	49	17	is	be	AUX
ejpam-3401	49	18	the	the	DET
ejpam-3401	49	19	intersection	intersection	NOUN
ejpam-3401	49	20	of	of	ADP
ejpam-3401	49	21	all	all	DET
ejpam-3401	49	22	βclosed	βclose	VERB
ejpam-3401	49	23	sets	set	NOUN
ejpam-3401	49	24	containing	contain	VERB
ejpam-3401	49	25	s.	s.	PROPN
ejpam-3401	49	26	the	the	DET
ejpam-3401	49	27	β	β	NOUN
ejpam-3401	49	28	-	-	NOUN
ejpam-3401	49	29	interior	interior	ADJ
ejpam-3401	49	30	of	of	ADP
ejpam-3401	49	31	a	a	DET
ejpam-3401	49	32	set	set	NOUN
ejpam-3401	49	33	s	s	AUX
ejpam-3401	49	34	denoted	denote	VERB
ejpam-3401	49	35	by	by	ADP
ejpam-3401	49	36	βint(s	βint(	NOUN
ejpam-3401	49	37	)	)	PUNCT
ejpam-3401	49	38	,	,	PUNCT
ejpam-3401	49	39	is	be	AUX
ejpam-3401	49	40	the	the	DET
ejpam-3401	49	41	union	union	NOUN
ejpam-3401	49	42	of	of	ADP
ejpam-3401	49	43	all	all	DET
ejpam-3401	49	44	β	β	ADJ
ejpam-3401	49	45	-	-	ADJ
ejpam-3401	49	46	open	open	ADJ
ejpam-3401	49	47	sets	set	NOUN
ejpam-3401	49	48	contained	contain	VERB
ejpam-3401	49	49	in	in	ADP
ejpam-3401	49	50	s.	s.	PROPN
ejpam-3401	49	51	the	the	DET
ejpam-3401	49	52	preclosure	preclosure	ADJ
ejpam-3401	49	53	,	,	PUNCT
ejpam-3401	49	54	preinterior	preinterior	ADJ
ejpam-3401	49	55	,	,	PUNCT
ejpam-3401	49	56	semiclosure	semiclosure	NOUN
ejpam-3401	49	57	,	,	PUNCT
ejpam-3401	49	58	semiinterior	semiinterior	NOUN
ejpam-3401	49	59	,	,	PUNCT
ejpam-3401	49	60	b	b	NOUN
ejpam-3401	49	61	-	-	PUNCT
ejpam-3401	49	62	closure	closure	NOUN
ejpam-3401	49	63	and	and	CCONJ
ejpam-3401	49	64	b	b	NOUN
ejpam-3401	49	65	-	-	NOUN
ejpam-3401	49	66	interior	interior	NOUN
ejpam-3401	49	67	of	of	ADP
ejpam-3401	49	68	a	a	DET
ejpam-3401	49	69	set	set	NOUN
ejpam-3401	49	70	s	s	VERB
ejpam-3401	49	71	denoted	denote	VERB
ejpam-3401	49	72	by	by	ADP
ejpam-3401	49	73	pcl(s),pint(s	pcl(s),pint(s	PROPN
ejpam-3401	49	74	)	)	PUNCT
ejpam-3401	49	75	,	,	PUNCT
ejpam-3401	49	76	scl(s	scl(s	PROPN
ejpam-3401	49	77	)	)	PUNCT
ejpam-3401	49	78	,	,	PUNCT
ejpam-3401	49	79	sint(s	sint(s	PROPN
ejpam-3401	49	80	)	)	PUNCT
ejpam-3401	49	81	,	,	PUNCT
ejpam-3401	49	82	bcl(s	bcl(s	PROPN
ejpam-3401	49	83	)	)	PUNCT
ejpam-3401	49	84	and	and	CCONJ
ejpam-3401	49	85	bint(s	bint(s	PROPN
ejpam-3401	49	86	)	)	PUNCT
ejpam-3401	49	87	,	,	PUNCT
ejpam-3401	49	88	respectively	respectively	ADV
ejpam-3401	49	89	,	,	PUNCT
ejpam-3401	49	90	are	be	AUX
ejpam-3401	49	91	defined	define	VERB
ejpam-3401	49	92	analogously	analogously	ADV
ejpam-3401	49	93	.	.	PUNCT
ejpam-3401	50	1	l.	l.	PROPN
ejpam-3401	50	2	m.	m.	PROPN
ejpam-3401	50	3	alabdulsada	alabdulsada	PROPN
ejpam-3401	50	4	/	/	SYM
ejpam-3401	50	5	eur	eur	PROPN
ejpam-3401	50	6	.	.	PUNCT
ejpam-3401	51	1	j.	j.	PROPN
ejpam-3401	51	2	pure	pure	PROPN
ejpam-3401	51	3	appl	appl	PROPN
ejpam-3401	51	4	.	.	PROPN
ejpam-3401	51	5	math	math	PROPN
ejpam-3401	51	6	,	,	PUNCT
ejpam-3401	51	7	12	12	NUM
ejpam-3401	51	8	(	(	PUNCT
ejpam-3401	51	9	2	2	NUM
ejpam-3401	51	10	)	)	PUNCT
ejpam-3401	51	11	(	(	PUNCT
ejpam-3401	51	12	2019	2019	NUM
ejpam-3401	51	13	)	)	PUNCT
ejpam-3401	51	14	,	,	PUNCT
ejpam-3401	51	15	358	358	NUM
ejpam-3401	51	16	-	-	SYM
ejpam-3401	51	17	369	369	NUM
ejpam-3401	51	18	360	360	NUM
ejpam-3401	51	19	proposition	proposition	NOUN
ejpam-3401	51	20	1	1	NUM
ejpam-3401	51	21	.	.	PUNCT
ejpam-3401	52	1	[	[	X
ejpam-3401	52	2	3	3	X
ejpam-3401	52	3	]	]	PUNCT
ejpam-3401	52	4	let	let	VERB
ejpam-3401	52	5	s	s	PRON
ejpam-3401	52	6	be	be	AUX
ejpam-3401	52	7	a	a	DET
ejpam-3401	52	8	subset	subset	NOUN
ejpam-3401	52	9	of	of	ADP
ejpam-3401	52	10	a	a	DET
ejpam-3401	52	11	space	space	NOUN
ejpam-3401	52	12	x.	x.	NOUN
ejpam-3401	52	13	then	then	ADV
ejpam-3401	52	14	:	:	PUNCT
ejpam-3401	52	15	(	(	PUNCT
ejpam-3401	52	16	i	i	NOUN
ejpam-3401	52	17	)	)	PUNCT
ejpam-3401	52	18	pint(s	pint(s	NOUN
ejpam-3401	52	19	)	)	PUNCT
ejpam-3401	52	20	=	=	SYM
ejpam-3401	52	21	s	s	PROPN
ejpam-3401	52	22	∩	∩	ADJ
ejpam-3401	52	23	int(cl(s	int(cl(s	PROPN
ejpam-3401	52	24	)	)	PUNCT
ejpam-3401	52	25	)	)	PUNCT
ejpam-3401	52	26	,	,	PUNCT
ejpam-3401	52	27	(	(	PUNCT
ejpam-3401	52	28	ii	ii	NOUN
ejpam-3401	52	29	)	)	PUNCT
ejpam-3401	52	30	pcl(s	pcl(s	PROPN
ejpam-3401	52	31	)	)	PUNCT
ejpam-3401	52	32	=	=	SYM
ejpam-3401	52	33	s	s	NOUN
ejpam-3401	52	34	∪	∪	ADJ
ejpam-3401	52	35	cl(int(s	cl(int(s	NOUN
ejpam-3401	52	36	)	)	PUNCT
ejpam-3401	52	37	)	)	PUNCT
ejpam-3401	52	38	,	,	PUNCT
ejpam-3401	52	39	(	(	PUNCT
ejpam-3401	52	40	iii	iii	X
ejpam-3401	52	41	)	)	PUNCT
ejpam-3401	52	42	sint(s	sint(s	PROPN
ejpam-3401	52	43	)	)	PUNCT
ejpam-3401	52	44	=	=	SYM
ejpam-3401	52	45	s	s	PART
ejpam-3401	52	46	∩	∩	ADJ
ejpam-3401	52	47	cl(int(s	cl(int(s	NOUN
ejpam-3401	52	48	)	)	PUNCT
ejpam-3401	52	49	)	)	PUNCT
ejpam-3401	52	50	,	,	PUNCT
ejpam-3401	52	51	(	(	PUNCT
ejpam-3401	52	52	iv	iv	X
ejpam-3401	52	53	)	)	PUNCT
ejpam-3401	52	54	scl(s	scl(s	PROPN
ejpam-3401	52	55	)	)	PUNCT
ejpam-3401	52	56	=	=	SYM
ejpam-3401	52	57	s	s	PART
ejpam-3401	52	58	∪	∪	ADJ
ejpam-3401	52	59	int(cl(s	int(cl(s	PROPN
ejpam-3401	52	60	)	)	PUNCT
ejpam-3401	52	61	)	)	PUNCT
ejpam-3401	52	62	.	.	PUNCT
ejpam-3401	53	1	definition	definition	NOUN
ejpam-3401	53	2	2	2	NUM
ejpam-3401	53	3	.	.	PUNCT
ejpam-3401	54	1	[	[	X
ejpam-3401	54	2	11	11	NUM
ejpam-3401	54	3	]	]	X
ejpam-3401	54	4	let	let	VERB
ejpam-3401	54	5	(	(	PUNCT
ejpam-3401	54	6	x	x	NOUN
ejpam-3401	54	7	,	,	PUNCT
ejpam-3401	54	8	τ	τ	X
ejpam-3401	54	9	)	)	PUNCT
ejpam-3401	54	10	be	be	VERB
ejpam-3401	54	11	a	a	DET
ejpam-3401	54	12	topological	topological	ADJ
ejpam-3401	54	13	space	space	NOUN
ejpam-3401	54	14	and	and	CCONJ
ejpam-3401	54	15	p	p	X
ejpam-3401	54	16	(	(	PUNCT
ejpam-3401	54	17	x	x	X
ejpam-3401	54	18	)	)	PUNCT
ejpam-3401	54	19	be	be	VERB
ejpam-3401	54	20	the	the	DET
ejpam-3401	54	21	power	power	NOUN
ejpam-3401	54	22	set	set	NOUN
ejpam-3401	54	23	of	of	ADP
ejpam-3401	54	24	x.	x.	NOUN
ejpam-3401	54	25	a	a	DET
ejpam-3401	54	26	function	function	NOUN
ejpam-3401	54	27	t	t	NOUN
ejpam-3401	54	28	:	:	PUNCT
ejpam-3401	54	29	p	p	X
ejpam-3401	54	30	(	(	PUNCT
ejpam-3401	54	31	x)→	x)→	PROPN
ejpam-3401	54	32	p	p	X
ejpam-3401	54	33	(	(	PUNCT
ejpam-3401	54	34	x	x	X
ejpam-3401	54	35	)	)	PUNCT
ejpam-3401	54	36	is	be	AUX
ejpam-3401	54	37	said	say	VERB
ejpam-3401	54	38	to	to	PART
ejpam-3401	54	39	be	be	AUX
ejpam-3401	54	40	an	an	DET
ejpam-3401	54	41	operator	operator	NOUN
ejpam-3401	54	42	associated	associate	VERB
ejpam-3401	54	43	with	with	ADP
ejpam-3401	54	44	topology	topology	NOUN
ejpam-3401	54	45	τ	τ	PROPN
ejpam-3401	54	46	on	on	ADP
ejpam-3401	54	47	x	x	SYM
ejpam-3401	54	48	if	if	SCONJ
ejpam-3401	54	49	u	u	PROPN
ejpam-3401	54	50	⊆	⊆	NUM
ejpam-3401	54	51	t	t	PROPN
ejpam-3401	54	52	(	(	PUNCT
ejpam-3401	54	53	u	u	NOUN
ejpam-3401	54	54	)	)	PUNCT
ejpam-3401	54	55	for	for	ADP
ejpam-3401	54	56	all	all	PRON
ejpam-3401	54	57	u	u	PROPN
ejpam-3401	54	58	∈	∈	PROPN
ejpam-3401	54	59	τ	τ	X
ejpam-3401	54	60	and	and	CCONJ
ejpam-3401	54	61	the	the	DET
ejpam-3401	54	62	triple	triple	ADJ
ejpam-3401	54	63	(	(	PUNCT
ejpam-3401	54	64	x	x	NOUN
ejpam-3401	54	65	,	,	PUNCT
ejpam-3401	54	66	τ	τ	PROPN
ejpam-3401	54	67	,	,	PUNCT
ejpam-3401	54	68	t	t	PROPN
ejpam-3401	54	69	)	)	PUNCT
ejpam-3401	54	70	is	be	AUX
ejpam-3401	54	71	called	call	VERB
ejpam-3401	54	72	an	an	DET
ejpam-3401	54	73	operator	operator	NOUN
ejpam-3401	54	74	topological	topological	ADJ
ejpam-3401	54	75	space	space	NOUN
ejpam-3401	54	76	.	.	PUNCT
ejpam-3401	55	1	definition	definition	NOUN
ejpam-3401	55	2	3	3	X
ejpam-3401	55	3	.	.	PUNCT
ejpam-3401	56	1	let	let	VERB
ejpam-3401	56	2	(	(	PUNCT
ejpam-3401	56	3	x	x	NOUN
ejpam-3401	56	4	,	,	PUNCT
ejpam-3401	56	5	τ	τ	PROPN
ejpam-3401	56	6	,	,	PUNCT
ejpam-3401	56	7	t	t	PROPN
ejpam-3401	56	8	)	)	PUNCT
ejpam-3401	56	9	be	be	AUX
ejpam-3401	56	10	an	an	DET
ejpam-3401	56	11	operator	operator	NOUN
ejpam-3401	56	12	topological	topological	ADJ
ejpam-3401	56	13	space	space	NOUN
ejpam-3401	56	14	and	and	CCONJ
ejpam-3401	56	15	s	s	VERB
ejpam-3401	56	16	⊆	⊆	NUM
ejpam-3401	56	17	x	x	NOUN
ejpam-3401	56	18	,	,	PUNCT
ejpam-3401	56	19	then	then	ADV
ejpam-3401	56	20	(	(	PUNCT
ejpam-3401	56	21	i	i	NOUN
ejpam-3401	56	22	)	)	PUNCT
ejpam-3401	57	1	s	s	VERB
ejpam-3401	57	2	is	be	AUX
ejpam-3401	57	3	said	say	VERB
ejpam-3401	57	4	to	to	PART
ejpam-3401	57	5	be	be	AUX
ejpam-3401	57	6	t	t	PROPN
ejpam-3401	57	7	-open	-open	PROPN
ejpam-3401	57	8	[	[	X
ejpam-3401	57	9	11	11	NUM
ejpam-3401	57	10	]	]	PUNCT
ejpam-3401	57	11	,	,	PUNCT
ejpam-3401	57	12	if	if	SCONJ
ejpam-3401	57	13	for	for	ADP
ejpam-3401	57	14	each	each	DET
ejpam-3401	57	15	x	x	SYM
ejpam-3401	57	16	∈	∈	PROPN
ejpam-3401	57	17	s	s	VERB
ejpam-3401	57	18	there	there	PRON
ejpam-3401	57	19	exists	exist	VERB
ejpam-3401	57	20	u	u	PROPN
ejpam-3401	57	21	∈	∈	PROPN
ejpam-3401	57	22	τ	τ	X
ejpam-3401	57	23	such	such	ADJ
ejpam-3401	57	24	that	that	SCONJ
ejpam-3401	57	25	x	x	SYM
ejpam-3401	57	26	∈	∈	PROPN
ejpam-3401	57	27	u	u	NOUN
ejpam-3401	57	28	⊆	⊆	NUM
ejpam-3401	57	29	t	t	PROPN
ejpam-3401	57	30	(	(	PUNCT
ejpam-3401	57	31	u	u	NOUN
ejpam-3401	57	32	)	)	PUNCT
ejpam-3401	57	33	⊆	⊆	NUM
ejpam-3401	57	34	s.	s.	PROPN
ejpam-3401	57	35	the	the	DET
ejpam-3401	57	36	complement	complement	NOUN
ejpam-3401	57	37	of	of	ADP
ejpam-3401	57	38	t	t	PROPN
ejpam-3401	57	39	-open	-open	PROPN
ejpam-3401	57	40	is	be	AUX
ejpam-3401	57	41	called	call	VERB
ejpam-3401	57	42	t	t	PROPN
ejpam-3401	57	43	-closed	-close	VERB
ejpam-3401	57	44	.	.	PUNCT
ejpam-3401	58	1	(	(	PUNCT
ejpam-3401	58	2	ii	ii	NOUN
ejpam-3401	58	3	)	)	PUNCT
ejpam-3401	58	4	s	s	VERB
ejpam-3401	58	5	is	be	AUX
ejpam-3401	58	6	said	say	VERB
ejpam-3401	58	7	to	to	PART
ejpam-3401	58	8	be	be	AUX
ejpam-3401	58	9	t	t	X
ejpam-3401	58	10	∗-open	∗-open	X
ejpam-3401	59	1	[	[	X
ejpam-3401	59	2	14	14	NUM
ejpam-3401	59	3	]	]	X
ejpam-3401	59	4	,	,	PUNCT
ejpam-3401	59	5	if	if	SCONJ
ejpam-3401	59	6	s	s	VERB
ejpam-3401	59	7	⊆	⊆	NUM
ejpam-3401	59	8	t	t	NOUN
ejpam-3401	59	9	(	(	PUNCT
ejpam-3401	59	10	s	s	NOUN
ejpam-3401	59	11	)	)	PUNCT
ejpam-3401	59	12	(	(	PUNCT
ejpam-3401	59	13	observe	observe	VERB
ejpam-3401	59	14	that	that	PRON
ejpam-3401	59	15	s	s	VERB
ejpam-3401	59	16	not	not	PART
ejpam-3401	59	17	necessarily	necessarily	ADV
ejpam-3401	59	18	open	open	ADJ
ejpam-3401	59	19	)	)	PUNCT
ejpam-3401	59	20	.	.	PUNCT
ejpam-3401	60	1	the	the	DET
ejpam-3401	60	2	complement	complement	NOUN
ejpam-3401	60	3	of	of	ADP
ejpam-3401	60	4	t	t	PROPN
ejpam-3401	60	5	∗-open	∗-open	X
ejpam-3401	60	6	is	be	AUX
ejpam-3401	60	7	called	call	VERB
ejpam-3401	60	8	t	t	PROPN
ejpam-3401	60	9	∗-closed	∗-closed	PROPN
ejpam-3401	60	10	.	.	PUNCT
ejpam-3401	61	1	remark	remark	PROPN
ejpam-3401	61	2	1	1	NUM
ejpam-3401	61	3	.	.	PUNCT
ejpam-3401	62	1	t1cl(s	t1cl(	NOUN
ejpam-3401	62	2	)	)	PUNCT
ejpam-3401	62	3	,	,	PUNCT
ejpam-3401	62	4	t2cl(s	t2cl(s	PROPN
ejpam-3401	62	5	)	)	PUNCT
ejpam-3401	62	6	are	be	AUX
ejpam-3401	62	7	the	the	DET
ejpam-3401	62	8	intersection	intersection	NOUN
ejpam-3401	62	9	of	of	ADP
ejpam-3401	62	10	all	all	DET
ejpam-3401	62	11	t1	t1	NOUN
ejpam-3401	62	12	-	-	PUNCT
ejpam-3401	62	13	closed	closed	ADJ
ejpam-3401	62	14	,	,	PUNCT
ejpam-3401	62	15	t2	t2	NOUN
ejpam-3401	62	16	-	-	PUNCT
ejpam-3401	62	17	closed	close	VERB
ejpam-3401	62	18	sets	set	NOUN
ejpam-3401	62	19	,	,	PUNCT
ejpam-3401	62	20	resp	resp	NOUN
ejpam-3401	62	21	.	.	PUNCT
ejpam-3401	62	22	,	,	PUNCT
ejpam-3401	62	23	in	in	ADP
ejpam-3401	62	24	x	x	SYM
ejpam-3401	62	25	containing	contain	VERB
ejpam-3401	62	26	s.	s.	PROPN
ejpam-3401	62	27	now	now	ADV
ejpam-3401	62	28	,	,	PUNCT
ejpam-3401	62	29	if	if	SCONJ
ejpam-3401	62	30	t1(s	t1(s	ADP
ejpam-3401	62	31	)	)	PUNCT
ejpam-3401	62	32	=	=	SYM
ejpam-3401	62	33	int(cl(s	int(cl(s	PROPN
ejpam-3401	62	34	)	)	PUNCT
ejpam-3401	62	35	)	)	PUNCT
ejpam-3401	62	36	and	and	CCONJ
ejpam-3401	62	37	t2(s	t2(s	NOUN
ejpam-3401	62	38	)	)	PUNCT
ejpam-3401	62	39	=	=	SYM
ejpam-3401	62	40	cl(int(s	cl(int(s	NOUN
ejpam-3401	62	41	)	)	PUNCT
ejpam-3401	62	42	)	)	PUNCT
ejpam-3401	63	1	where	where	SCONJ
ejpam-3401	63	2	s	s	VERB
ejpam-3401	63	3	⊆	⊆	NUM
ejpam-3401	63	4	x	x	NOUN
ejpam-3401	63	5	,	,	PUNCT
ejpam-3401	63	6	then	then	ADV
ejpam-3401	63	7	t1	t1	NOUN
ejpam-3401	63	8	-	-	PUNCT
ejpam-3401	63	9	open	open	ADJ
ejpam-3401	63	10	set	set	NOUN
ejpam-3401	63	11	is	be	AUX
ejpam-3401	63	12	exactly	exactly	ADV
ejpam-3401	63	13	the	the	DET
ejpam-3401	63	14	pre	pre	ADJ
ejpam-3401	63	15	-	-	ADJ
ejpam-3401	63	16	open	open	ADJ
ejpam-3401	63	17	set	set	NOUN
ejpam-3401	63	18	and	and	CCONJ
ejpam-3401	63	19	t2	t2	NOUN
ejpam-3401	63	20	-	-	PUNCT
ejpam-3401	63	21	open	open	ADJ
ejpam-3401	63	22	set	set	NOUN
ejpam-3401	63	23	is	be	AUX
ejpam-3401	63	24	exactly	exactly	ADV
ejpam-3401	63	25	the	the	DET
ejpam-3401	63	26	semi	semi	ADJ
ejpam-3401	63	27	-	-	ADJ
ejpam-3401	63	28	open	open	ADJ
ejpam-3401	63	29	set	set	NOUN
ejpam-3401	63	30	.	.	PUNCT
ejpam-3401	64	1	in	in	ADP
ejpam-3401	64	2	addition	addition	NOUN
ejpam-3401	64	3	,	,	PUNCT
ejpam-3401	64	4	we	we	PRON
ejpam-3401	64	5	have	have	VERB
ejpam-3401	64	6	that	that	DET
ejpam-3401	64	7	t1cl(s	t1cl(s	PROPN
ejpam-3401	64	8	)	)	PUNCT
ejpam-3401	64	9	≡	≡	PROPN
ejpam-3401	64	10	pcl(s	pcl(s	PROPN
ejpam-3401	64	11	)	)	PUNCT
ejpam-3401	64	12	and	and	CCONJ
ejpam-3401	64	13	t2cl(s	t2cl(s	PROPN
ejpam-3401	64	14	)	)	PUNCT
ejpam-3401	64	15	≡	≡	PROPN
ejpam-3401	64	16	sint(s	sint(s	PROPN
ejpam-3401	64	17	)	)	PUNCT
ejpam-3401	64	18	.	.	PUNCT
ejpam-3401	65	1	definition	definition	NOUN
ejpam-3401	65	2	4	4	X
ejpam-3401	65	3	.	.	PUNCT
ejpam-3401	66	1	let	let	AUX
ejpam-3401	66	2	(	(	PUNCT
ejpam-3401	66	3	x	x	NOUN
ejpam-3401	66	4	,	,	PUNCT
ejpam-3401	66	5	τ	τ	X
ejpam-3401	66	6	)	)	PUNCT
ejpam-3401	66	7	be	be	VERB
ejpam-3401	66	8	a	a	DET
ejpam-3401	66	9	topological	topological	ADJ
ejpam-3401	66	10	space	space	NOUN
ejpam-3401	66	11	and	and	CCONJ
ejpam-3401	66	12	t1	t1	NOUN
ejpam-3401	66	13	,	,	PUNCT
ejpam-3401	66	14	t2	t2	PROPN
ejpam-3401	66	15	be	be	VERB
ejpam-3401	66	16	two	two	NUM
ejpam-3401	66	17	operators	operator	NOUN
ejpam-3401	66	18	associated	associate	VERB
ejpam-3401	66	19	with	with	ADP
ejpam-3401	66	20	the	the	DET
ejpam-3401	66	21	topology	topology	NOUN
ejpam-3401	66	22	τ	τ	PROPN
ejpam-3401	66	23	on	on	ADP
ejpam-3401	66	24	x	x	SYM
ejpam-3401	66	25	that	that	PRON
ejpam-3401	66	26	is	be	AUX
ejpam-3401	66	27	u	u	NOUN
ejpam-3401	66	28	⊆	⊆	NUM
ejpam-3401	66	29	t1(u	t1(u	NUM
ejpam-3401	66	30	)	)	PUNCT
ejpam-3401	66	31	and	and	CCONJ
ejpam-3401	66	32	u	u	NOUN
ejpam-3401	66	33	⊆	⊆	NUM
ejpam-3401	66	34	t2(u	t2(u	NUM
ejpam-3401	66	35	)	)	PUNCT
ejpam-3401	66	36	for	for	ADP
ejpam-3401	66	37	each	each	DET
ejpam-3401	66	38	u	u	PROPN
ejpam-3401	66	39	∈	∈	PROPN
ejpam-3401	66	40	τ	τ	X
ejpam-3401	66	41	.	.	PUNCT
ejpam-3401	67	1	the	the	DET
ejpam-3401	67	2	quadruple	quadruple	NOUN
ejpam-3401	67	3	(	(	PUNCT
ejpam-3401	67	4	x	x	X
ejpam-3401	67	5	,	,	PUNCT
ejpam-3401	67	6	τ	τ	PROPN
ejpam-3401	67	7	,	,	PUNCT
ejpam-3401	67	8	t1	t1	NOUN
ejpam-3401	67	9	,	,	PUNCT
ejpam-3401	67	10	t2	t2	NOUN
ejpam-3401	67	11	)	)	PUNCT
ejpam-3401	67	12	is	be	AUX
ejpam-3401	67	13	called	call	VERB
ejpam-3401	67	14	a	a	DET
ejpam-3401	67	15	bi	bi	ADJ
ejpam-3401	67	16	-	-	ADJ
ejpam-3401	67	17	operator	operator	NOUN
ejpam-3401	67	18	topological	topological	ADJ
ejpam-3401	67	19	space	space	NOUN
ejpam-3401	67	20	.	.	PUNCT
ejpam-3401	67	21	example	example	NOUN
ejpam-3401	68	1	1	1	NUM
ejpam-3401	68	2	.	.	PUNCT
ejpam-3401	69	1	(	(	PUNCT
ejpam-3401	69	2	i	i	NOUN
ejpam-3401	69	3	)	)	PUNCT
ejpam-3401	69	4	if	if	SCONJ
ejpam-3401	69	5	t1	t1	PROPN
ejpam-3401	69	6	,	,	PUNCT
ejpam-3401	69	7	t2	t2	PROPN
ejpam-3401	69	8	are	be	AUX
ejpam-3401	69	9	the	the	DET
ejpam-3401	69	10	identity	identity	NOUN
ejpam-3401	69	11	operators	operator	NOUN
ejpam-3401	69	12	,	,	PUNCT
ejpam-3401	69	13	i.e.	i.e.	X
ejpam-3401	69	14	t1(s	t1(s	X
ejpam-3401	69	15	)	)	PUNCT
ejpam-3401	69	16	=	=	SYM
ejpam-3401	69	17	s	s	PROPN
ejpam-3401	69	18	and	and	CCONJ
ejpam-3401	69	19	t2(s	t2(s	NUM
ejpam-3401	69	20	)	)	PUNCT
ejpam-3401	70	1	=	=	SYM
ejpam-3401	70	2	s	s	PROPN
ejpam-3401	70	3	,	,	PUNCT
ejpam-3401	70	4	then	then	ADV
ejpam-3401	70	5	the	the	DET
ejpam-3401	70	6	quadruple	quadruple	NOUN
ejpam-3401	70	7	(	(	PUNCT
ejpam-3401	70	8	x	x	X
ejpam-3401	70	9	,	,	PUNCT
ejpam-3401	70	10	τ	τ	PROPN
ejpam-3401	70	11	,	,	PUNCT
ejpam-3401	70	12	t1	t1	NOUN
ejpam-3401	70	13	,	,	PUNCT
ejpam-3401	70	14	t2	t2	NOUN
ejpam-3401	70	15	)	)	PUNCT
ejpam-3401	70	16	will	will	AUX
ejpam-3401	70	17	reduces	reduce	VERB
ejpam-3401	70	18	to	to	ADP
ejpam-3401	70	19	(	(	PUNCT
ejpam-3401	70	20	x	x	NOUN
ejpam-3401	70	21	,	,	PUNCT
ejpam-3401	70	22	τ	τ	PROPN
ejpam-3401	70	23	)	)	PUNCT
ejpam-3401	70	24	,	,	PUNCT
ejpam-3401	70	25	thus	thus	ADV
ejpam-3401	70	26	the	the	DET
ejpam-3401	70	27	bi	bi	ADJ
ejpam-3401	70	28	-	-	NOUN
ejpam-3401	70	29	operator	operator	NOUN
ejpam-3401	70	30	topological	topological	ADJ
ejpam-3401	70	31	space	space	NOUN
ejpam-3401	70	32	is	be	AUX
ejpam-3401	70	33	the	the	DET
ejpam-3401	70	34	ordinary	ordinary	ADJ
ejpam-3401	70	35	topological	topological	ADJ
ejpam-3401	70	36	space	space	NOUN
ejpam-3401	70	37	.	.	PUNCT
ejpam-3401	71	1	(	(	PUNCT
ejpam-3401	71	2	ii	ii	NOUN
ejpam-3401	71	3	)	)	PUNCT
ejpam-3401	71	4	let	let	VERB
ejpam-3401	71	5	(	(	PUNCT
ejpam-3401	71	6	x	x	NOUN
ejpam-3401	71	7	,	,	PUNCT
ejpam-3401	71	8	τ	τ	X
ejpam-3401	71	9	)	)	PUNCT
ejpam-3401	71	10	be	be	VERB
ejpam-3401	71	11	any	any	DET
ejpam-3401	71	12	topological	topological	ADJ
ejpam-3401	71	13	space	space	NOUN
ejpam-3401	71	14	and	and	CCONJ
ejpam-3401	71	15	t1	t1	NOUN
ejpam-3401	71	16	,	,	PUNCT
ejpam-3401	71	17	t2	t2	NOUN
ejpam-3401	71	18	:	:	PUNCT
ejpam-3401	71	19	p	p	X
ejpam-3401	71	20	(	(	PUNCT
ejpam-3401	71	21	x)→	x)→	PROPN
ejpam-3401	71	22	p	p	X
ejpam-3401	71	23	(	(	PUNCT
ejpam-3401	71	24	x	x	NOUN
ejpam-3401	71	25	)	)	PUNCT
ejpam-3401	71	26	be	be	AUX
ejpam-3401	71	27	functions	function	NOUN
ejpam-3401	71	28	such	such	ADJ
ejpam-3401	71	29	that	that	PRON
ejpam-3401	71	30	t1(s	t1(s	PROPN
ejpam-3401	71	31	)	)	PUNCT
ejpam-3401	71	32	:	:	PUNCT
ejpam-3401	71	33	=	=	SYM
ejpam-3401	71	34	int(cl(s	int(cl(s	PROPN
ejpam-3401	71	35	)	)	PUNCT
ejpam-3401	71	36	)	)	PUNCT
ejpam-3401	71	37	and	and	CCONJ
ejpam-3401	71	38	t2(s	t2(s	NOUN
ejpam-3401	71	39	)	)	PUNCT
ejpam-3401	71	40	:	:	PUNCT
ejpam-3401	71	41	=	=	SYM
ejpam-3401	71	42	cl(int(s	cl(int(s	PROPN
ejpam-3401	71	43	)	)	PUNCT
ejpam-3401	71	44	)	)	PUNCT
ejpam-3401	72	1	for	for	ADP
ejpam-3401	72	2	any	any	DET
ejpam-3401	72	3	s	s	NOUN
ejpam-3401	72	4	⊆	⊆	NUM
ejpam-3401	72	5	x.	x.	NOUN
ejpam-3401	72	6	notice	notice	VERB
ejpam-3401	72	7	that	that	SCONJ
ejpam-3401	72	8	if	if	SCONJ
ejpam-3401	72	9	u	u	NOUN
ejpam-3401	72	10	is	be	AUX
ejpam-3401	72	11	open	open	ADJ
ejpam-3401	72	12	in	in	ADP
ejpam-3401	72	13	x	x	NOUN
ejpam-3401	72	14	,	,	PUNCT
ejpam-3401	72	15	then	then	ADV
ejpam-3401	72	16	u	u	NOUN
ejpam-3401	72	17	⊆	⊆	PROPN
ejpam-3401	72	18	int(cl(u	int(cl(u	PROPN
ejpam-3401	72	19	)	)	PUNCT
ejpam-3401	72	20	)	)	PUNCT
ejpam-3401	73	1	=	=	SYM
ejpam-3401	73	2	t1(u	t1(u	NOUN
ejpam-3401	73	3	)	)	PUNCT
ejpam-3401	73	4	and	and	CCONJ
ejpam-3401	73	5	u	u	NOUN
ejpam-3401	73	6	⊆	⊆	NUM
ejpam-3401	73	7	cl(int(u	cl(int(u	NUM
ejpam-3401	73	8	)	)	PUNCT
ejpam-3401	73	9	)	)	PUNCT
ejpam-3401	74	1	=	=	PUNCT
ejpam-3401	74	2	t2(u	t2(u	NOUN
ejpam-3401	74	3	)	)	PUNCT
ejpam-3401	74	4	.	.	PUNCT
ejpam-3401	75	1	thus	thus	ADV
ejpam-3401	75	2	,	,	PUNCT
ejpam-3401	75	3	t1	t1	PROPN
ejpam-3401	75	4	,	,	PUNCT
ejpam-3401	75	5	t2	t2	PROPN
ejpam-3401	75	6	are	be	AUX
ejpam-3401	75	7	operators	operator	NOUN
ejpam-3401	75	8	associated	associate	VERB
ejpam-3401	75	9	with	with	ADP
ejpam-3401	75	10	the	the	DET
ejpam-3401	75	11	topology	topology	NOUN
ejpam-3401	75	12	τ	τ	PROPN
ejpam-3401	75	13	on	on	ADP
ejpam-3401	75	14	x	x	X
ejpam-3401	75	15	and	and	CCONJ
ejpam-3401	75	16	the	the	DET
ejpam-3401	75	17	quadruple	quadruple	NOUN
ejpam-3401	75	18	(	(	PUNCT
ejpam-3401	75	19	x	x	X
ejpam-3401	75	20	,	,	PUNCT
ejpam-3401	75	21	τ	τ	PROPN
ejpam-3401	75	22	,	,	PUNCT
ejpam-3401	75	23	t1	t1	NOUN
ejpam-3401	75	24	,	,	PUNCT
ejpam-3401	75	25	t2	t2	NOUN
ejpam-3401	75	26	)	)	PUNCT
ejpam-3401	75	27	is	be	AUX
ejpam-3401	75	28	a	a	DET
ejpam-3401	75	29	bi	bi	ADJ
ejpam-3401	75	30	-	-	ADJ
ejpam-3401	75	31	operator	operator	NOUN
ejpam-3401	75	32	topological	topological	ADJ
ejpam-3401	75	33	space	space	NOUN
ejpam-3401	75	34	.	.	PUNCT
ejpam-3401	76	1	definition	definition	NOUN
ejpam-3401	76	2	5	5	NUM
ejpam-3401	76	3	.	.	PUNCT
ejpam-3401	77	1	let	let	AUX
ejpam-3401	77	2	(	(	PUNCT
ejpam-3401	77	3	x	x	NOUN
ejpam-3401	77	4	,	,	PUNCT
ejpam-3401	77	5	τ	τ	PROPN
ejpam-3401	77	6	,	,	PUNCT
ejpam-3401	77	7	t1	t1	NOUN
ejpam-3401	77	8	,	,	PUNCT
ejpam-3401	77	9	t2	t2	NOUN
ejpam-3401	77	10	)	)	PUNCT
ejpam-3401	77	11	be	be	AUX
ejpam-3401	77	12	a	a	DET
ejpam-3401	77	13	bi	bi	ADJ
ejpam-3401	77	14	-	-	ADJ
ejpam-3401	77	15	operator	operator	NOUN
ejpam-3401	77	16	topological	topological	ADJ
ejpam-3401	77	17	space	space	NOUN
ejpam-3401	77	18	and	and	CCONJ
ejpam-3401	77	19	s	s	VERB
ejpam-3401	77	20	⊆	⊆	NUM
ejpam-3401	77	21	x.	x.	NOUN
ejpam-3401	77	22	the	the	DET
ejpam-3401	77	23	set	set	NOUN
ejpam-3401	77	24	s	s	NOUN
ejpam-3401	77	25	is	be	AUX
ejpam-3401	77	26	said	say	VERB
ejpam-3401	77	27	to	to	PART
ejpam-3401	77	28	be	be	AUX
ejpam-3401	77	29	a	a	DET
ejpam-3401	77	30	b	b	NOUN
ejpam-3401	77	31	-	-	PUNCT
ejpam-3401	77	32	open	open	ADJ
ejpam-3401	77	33	set	set	NOUN
ejpam-3401	77	34	if	if	SCONJ
ejpam-3401	77	35	s	s	VERB
ejpam-3401	77	36	⊆	⊆	NUM
ejpam-3401	77	37	t1(s	t1(s	SYM
ejpam-3401	77	38	)	)	PUNCT
ejpam-3401	77	39	∪	∪	ADP
ejpam-3401	77	40	t2(s	t2(s	PROPN
ejpam-3401	77	41	)	)	PUNCT
ejpam-3401	77	42	.	.	PUNCT
ejpam-3401	78	1	l.	l.	PROPN
ejpam-3401	78	2	m.	m.	PROPN
ejpam-3401	78	3	alabdulsada	alabdulsada	PROPN
ejpam-3401	78	4	/	/	SYM
ejpam-3401	78	5	eur	eur	PROPN
ejpam-3401	78	6	.	.	PUNCT
ejpam-3401	79	1	j.	j.	PROPN
ejpam-3401	79	2	pure	pure	PROPN
ejpam-3401	79	3	appl	appl	PROPN
ejpam-3401	79	4	.	.	PROPN
ejpam-3401	79	5	math	math	PROPN
ejpam-3401	79	6	,	,	PUNCT
ejpam-3401	79	7	12	12	NUM
ejpam-3401	79	8	(	(	PUNCT
ejpam-3401	79	9	2	2	NUM
ejpam-3401	79	10	)	)	PUNCT
ejpam-3401	79	11	(	(	PUNCT
ejpam-3401	79	12	2019	2019	NUM
ejpam-3401	79	13	)	)	PUNCT
ejpam-3401	79	14	,	,	PUNCT
ejpam-3401	79	15	358	358	NUM
ejpam-3401	79	16	-	-	SYM
ejpam-3401	79	17	369	369	NUM
ejpam-3401	79	18	361	361	NUM
ejpam-3401	79	19	the	the	DET
ejpam-3401	79	20	complement	complement	NOUN
ejpam-3401	79	21	of	of	ADP
ejpam-3401	79	22	a	a	DET
ejpam-3401	79	23	b	b	NOUN
ejpam-3401	79	24	-	-	PUNCT
ejpam-3401	79	25	open	open	ADJ
ejpam-3401	79	26	set	set	NOUN
ejpam-3401	79	27	is	be	AUX
ejpam-3401	79	28	b	b	NOUN
ejpam-3401	79	29	-	-	PUNCT
ejpam-3401	79	30	closed	closed	ADJ
ejpam-3401	79	31	.	.	PUNCT
ejpam-3401	80	1	moreover	moreover	ADV
ejpam-3401	80	2	,	,	PUNCT
ejpam-3401	80	3	if	if	SCONJ
ejpam-3401	80	4	t1(s	t1(s	ADP
ejpam-3401	80	5	)	)	PUNCT
ejpam-3401	80	6	=	=	SYM
ejpam-3401	80	7	cl(int(s	cl(int(s	NOUN
ejpam-3401	80	8	)	)	PUNCT
ejpam-3401	80	9	)	)	PUNCT
ejpam-3401	80	10	and	and	CCONJ
ejpam-3401	80	11	t2(s	t2(s	NOUN
ejpam-3401	80	12	)	)	PUNCT
ejpam-3401	80	13	=	=	SYM
ejpam-3401	80	14	int(cl(s	int(cl(s	PROPN
ejpam-3401	80	15	)	)	PUNCT
ejpam-3401	80	16	)	)	PUNCT
ejpam-3401	80	17	,	,	PUNCT
ejpam-3401	80	18	then	then	ADV
ejpam-3401	80	19	s	s	VERB
ejpam-3401	80	20	is	be	AUX
ejpam-3401	80	21	b	b	NOUN
ejpam-3401	80	22	-	-	PUNCT
ejpam-3401	80	23	open	open	ADJ
ejpam-3401	80	24	if	if	SCONJ
ejpam-3401	80	25	and	and	CCONJ
ejpam-3401	80	26	only	only	ADV
ejpam-3401	80	27	if	if	SCONJ
ejpam-3401	80	28	s	s	NOUN
ejpam-3401	80	29	is	be	AUX
ejpam-3401	80	30	b	b	NOUN
ejpam-3401	80	31	-	-	ADJ
ejpam-3401	80	32	open	open	ADJ
ejpam-3401	80	33	,	,	PUNCT
ejpam-3401	80	34	so	so	SCONJ
ejpam-3401	80	35	the	the	DET
ejpam-3401	80	36	concepts	concept	NOUN
ejpam-3401	80	37	of	of	ADP
ejpam-3401	80	38	bopenness	bopenness	NOUN
ejpam-3401	80	39	reduces	reduce	VERB
ejpam-3401	80	40	to	to	ADP
ejpam-3401	80	41	the	the	DET
ejpam-3401	80	42	concepts	concept	NOUN
ejpam-3401	80	43	of	of	ADP
ejpam-3401	80	44	b	b	NOUN
ejpam-3401	80	45	-	-	NOUN
ejpam-3401	80	46	openness	openness	NOUN
ejpam-3401	80	47	in	in	ADP
ejpam-3401	80	48	this	this	DET
ejpam-3401	80	49	case	case	NOUN
ejpam-3401	80	50	.	.	PUNCT
ejpam-3401	81	1	cf	cf	NOUN
ejpam-3401	81	2	.	.	PUNCT
ejpam-3401	82	1	definition	definition	NOUN
ejpam-3401	82	2	1	1	NUM
ejpam-3401	82	3	.	.	PUNCT
ejpam-3401	82	4	remark	remark	PROPN
ejpam-3401	82	5	2	2	NUM
ejpam-3401	82	6	.	.	PUNCT
ejpam-3401	83	1	(	(	PUNCT
ejpam-3401	83	2	i	i	NOUN
ejpam-3401	83	3	)	)	PUNCT
ejpam-3401	83	4	as	as	ADP
ejpam-3401	83	5	an	an	DET
ejpam-3401	83	6	example	example	NOUN
ejpam-3401	83	7	of	of	ADP
ejpam-3401	83	8	b	b	NOUN
ejpam-3401	83	9	-	-	PUNCT
ejpam-3401	83	10	open	open	ADJ
ejpam-3401	83	11	set	set	NOUN
ejpam-3401	83	12	,	,	PUNCT
ejpam-3401	83	13	one	one	PRON
ejpam-3401	83	14	can	can	AUX
ejpam-3401	83	15	consider	consider	VERB
ejpam-3401	83	16	a	a	DET
ejpam-3401	83	17	bi	bi	ADJ
ejpam-3401	83	18	-	-	ADJ
ejpam-3401	83	19	operator	operator	NOUN
ejpam-3401	83	20	topological	topological	ADJ
ejpam-3401	83	21	space	space	NOUN
ejpam-3401	83	22	(	(	PUNCT
ejpam-3401	83	23	r	r	NOUN
ejpam-3401	83	24	,	,	PUNCT
ejpam-3401	83	25	τu	τu	ADP
ejpam-3401	83	26	,	,	PUNCT
ejpam-3401	83	27	t1	t1	NOUN
ejpam-3401	83	28	,	,	PUNCT
ejpam-3401	83	29	t2	t2	NOUN
ejpam-3401	83	30	)	)	PUNCT
ejpam-3401	83	31	such	such	ADJ
ejpam-3401	83	32	that	that	SCONJ
ejpam-3401	83	33	r	r	NOUN
ejpam-3401	83	34	stands	stand	VERB
ejpam-3401	83	35	for	for	ADP
ejpam-3401	83	36	the	the	DET
ejpam-3401	83	37	set	set	NOUN
ejpam-3401	83	38	of	of	ADP
ejpam-3401	83	39	real	real	ADJ
ejpam-3401	83	40	numbers	number	NOUN
ejpam-3401	83	41	and	and	CCONJ
ejpam-3401	83	42	τu	τu	ADP
ejpam-3401	83	43	for	for	ADP
ejpam-3401	83	44	the	the	DET
ejpam-3401	83	45	usual	usual	ADJ
ejpam-3401	83	46	topology	topology	NOUN
ejpam-3401	83	47	.	.	PUNCT
ejpam-3401	84	1	let	let	VERB
ejpam-3401	84	2	s	s	PRON
ejpam-3401	84	3	⊆	⊆	NUM
ejpam-3401	84	4	r	r	NOUN
ejpam-3401	84	5	and	and	CCONJ
ejpam-3401	84	6	t1(s	t1(s	PROPN
ejpam-3401	84	7	)	)	PUNCT
ejpam-3401	84	8	=	=	SYM
ejpam-3401	84	9	int(cl(s	int(cl(s	PROPN
ejpam-3401	84	10	)	)	PUNCT
ejpam-3401	84	11	)	)	PUNCT
ejpam-3401	84	12	and	and	CCONJ
ejpam-3401	84	13	t2(s	t2(s	NOUN
ejpam-3401	84	14	)	)	PUNCT
ejpam-3401	84	15	=	=	SYM
ejpam-3401	84	16	cl(int(s	cl(int(s	NOUN
ejpam-3401	84	17	)	)	PUNCT
ejpam-3401	84	18	)	)	PUNCT
ejpam-3401	84	19	.	.	PUNCT
ejpam-3401	85	1	if	if	SCONJ
ejpam-3401	85	2	s	s	VERB
ejpam-3401	85	3	=	=	PUNCT
ejpam-3401	86	1	[	[	X
ejpam-3401	86	2	0	0	NUM
ejpam-3401	86	3	,	,	PUNCT
ejpam-3401	86	4	1]∪	1]∪	NUM
ejpam-3401	86	5	(	(	PUNCT
ejpam-3401	86	6	(	(	PUNCT
ejpam-3401	86	7	1	1	NUM
ejpam-3401	86	8	,	,	PUNCT
ejpam-3401	86	9	2)∩q	2)∩q	NUM
ejpam-3401	86	10	)	)	PUNCT
ejpam-3401	86	11	,	,	PUNCT
ejpam-3401	86	12	q	q	PROPN
ejpam-3401	86	13	denotes	denote	VERB
ejpam-3401	86	14	the	the	DET
ejpam-3401	86	15	set	set	NOUN
ejpam-3401	86	16	of	of	ADP
ejpam-3401	86	17	the	the	DET
ejpam-3401	86	18	rational	rational	ADJ
ejpam-3401	86	19	numbers	number	NOUN
ejpam-3401	86	20	then	then	ADV
ejpam-3401	86	21	s	s	VERB
ejpam-3401	86	22	is	be	AUX
ejpam-3401	86	23	b	b	NOUN
ejpam-3401	86	24	-	-	PUNCT
ejpam-3401	86	25	open	open	ADJ
ejpam-3401	86	26	but	but	CCONJ
ejpam-3401	86	27	neither	neither	CCONJ
ejpam-3401	86	28	t	t	NOUN
ejpam-3401	86	29	∗1	∗1	NOUN
ejpam-3401	86	30	-open	-open	PROPN
ejpam-3401	86	31	nor	nor	CCONJ
ejpam-3401	86	32	t	t	NOUN
ejpam-3401	86	33	∗2	∗2	NOUN
ejpam-3401	86	34	-open	-open	VERB
ejpam-3401	86	35	set	set	NOUN
ejpam-3401	86	36	.	.	PUNCT
ejpam-3401	87	1	on	on	ADP
ejpam-3401	87	2	other	other	ADJ
ejpam-3401	87	3	hand	hand	NOUN
ejpam-3401	87	4	,	,	PUNCT
ejpam-3401	87	5	if	if	SCONJ
ejpam-3401	87	6	e	e	NOUN
ejpam-3401	87	7	=	=	PUNCT
ejpam-3401	87	8	[	[	X
ejpam-3401	87	9	0	0	NUM
ejpam-3401	87	10	,	,	PUNCT
ejpam-3401	87	11	1	1	NUM
ejpam-3401	87	12	)	)	PUNCT
ejpam-3401	87	13	∪	∪	ADP
ejpam-3401	87	14	q	q	NOUN
ejpam-3401	87	15	,	,	PUNCT
ejpam-3401	87	16	then	then	ADV
ejpam-3401	87	17	e	e	PROPN
ejpam-3401	87	18	is	be	AUX
ejpam-3401	87	19	t	t	NOUN
ejpam-3401	87	20	∗1	∗1	PROPN
ejpam-3401	87	21	-open	-open	PROPN
ejpam-3401	87	22	but	but	CCONJ
ejpam-3401	87	23	not	not	PART
ejpam-3401	87	24	t	t	NOUN
ejpam-3401	87	25	∗2	∗2	NOUN
ejpam-3401	87	26	-open	-open	VERB
ejpam-3401	87	27	while	while	SCONJ
ejpam-3401	87	28	e	e	NOUN
ejpam-3401	87	29	is	be	AUX
ejpam-3401	87	30	b	b	NOUN
ejpam-3401	87	31	-	-	ADV
ejpam-3401	87	32	open	open	ADJ
ejpam-3401	87	33	.	.	PUNCT
ejpam-3401	88	1	(	(	PUNCT
ejpam-3401	88	2	ii	ii	X
ejpam-3401	88	3	)	)	PUNCT
ejpam-3401	88	4	the	the	DET
ejpam-3401	88	5	intersection	intersection	NOUN
ejpam-3401	88	6	of	of	ADP
ejpam-3401	88	7	two	two	NUM
ejpam-3401	88	8	b	b	X
ejpam-3401	88	9	-	-	PUNCT
ejpam-3401	88	10	open	open	ADJ
ejpam-3401	88	11	sets	set	NOUN
ejpam-3401	88	12	is	be	AUX
ejpam-3401	88	13	not	not	PART
ejpam-3401	88	14	necessarily	necessarily	ADV
ejpam-3401	88	15	b	b	NOUN
ejpam-3401	88	16	-	-	PUNCT
ejpam-3401	88	17	open	open	ADJ
ejpam-3401	88	18	.	.	PUNCT
ejpam-3401	89	1	so	so	ADV
ejpam-3401	89	2	,	,	PUNCT
ejpam-3401	89	3	the	the	DET
ejpam-3401	89	4	collection	collection	NOUN
ejpam-3401	89	5	of	of	ADP
ejpam-3401	89	6	all	all	DET
ejpam-3401	89	7	b	b	NOUN
ejpam-3401	89	8	-	-	PUNCT
ejpam-3401	89	9	open	open	ADJ
ejpam-3401	89	10	sets	set	NOUN
ejpam-3401	89	11	is	be	AUX
ejpam-3401	89	12	not	not	PART
ejpam-3401	89	13	necessarily	necessarily	ADV
ejpam-3401	89	14	a	a	DET
ejpam-3401	89	15	topology	topology	NOUN
ejpam-3401	89	16	on	on	ADP
ejpam-3401	89	17	x.	x.	PROPN
ejpam-3401	89	18	(	(	PUNCT
ejpam-3401	89	19	iii	iii	X
ejpam-3401	89	20	)	)	PUNCT
ejpam-3401	89	21	the	the	DET
ejpam-3401	89	22	intersection	intersection	NOUN
ejpam-3401	89	23	of	of	ADP
ejpam-3401	89	24	any	any	DET
ejpam-3401	89	25	collection	collection	NOUN
ejpam-3401	89	26	of	of	ADP
ejpam-3401	89	27	b	b	NOUN
ejpam-3401	89	28	-	-	PUNCT
ejpam-3401	89	29	closed	closed	ADJ
ejpam-3401	89	30	sets	set	NOUN
ejpam-3401	89	31	is	be	AUX
ejpam-3401	89	32	b	b	NOUN
ejpam-3401	89	33	-	-	PUNCT
ejpam-3401	89	34	closed	closed	ADJ
ejpam-3401	89	35	.	.	PUNCT
ejpam-3401	90	1	bcl(s	bcl(	NOUN
ejpam-3401	90	2	)	)	PUNCT
ejpam-3401	90	3	is	be	AUX
ejpam-3401	90	4	the	the	DET
ejpam-3401	90	5	intersection	intersection	NOUN
ejpam-3401	90	6	of	of	ADP
ejpam-3401	90	7	all	all	DET
ejpam-3401	90	8	b	b	NOUN
ejpam-3401	90	9	-	-	PUNCT
ejpam-3401	90	10	closed	closed	ADJ
ejpam-3401	90	11	sets	set	NOUN
ejpam-3401	90	12	containing	contain	VERB
ejpam-3401	90	13	s	s	NOUN
ejpam-3401	90	14	,	,	PUNCT
ejpam-3401	90	15	i.e.	i.e.	X
ejpam-3401	90	16	bcl(s	bcl(s	PROPN
ejpam-3401	90	17	)	)	PUNCT
ejpam-3401	90	18	:	:	PUNCT
ejpam-3401	90	19	=	=	NOUN
ejpam-3401	90	20	∩	∩	X
ejpam-3401	90	21	{	{	PUNCT
ejpam-3401	90	22	u	u	NOUN
ejpam-3401	90	23	|	|	ADV
ejpam-3401	90	24	u	u	NOUN
ejpam-3401	90	25	is	be	AUX
ejpam-3401	90	26	b	b	NOUN
ejpam-3401	90	27	-	-	PUNCT
ejpam-3401	90	28	closed	closed	ADJ
ejpam-3401	90	29	,	,	PUNCT
ejpam-3401	90	30	u	u	PROPN
ejpam-3401	90	31	⊇	⊇	NOUN
ejpam-3401	90	32	s	s	PART
ejpam-3401	90	33	}	}	PUNCT
ejpam-3401	90	34	.	.	PUNCT
ejpam-3401	91	1	(	(	PUNCT
ejpam-3401	91	2	iv	iv	X
ejpam-3401	91	3	)	)	PUNCT
ejpam-3401	91	4	bint(s	bint(s	PROPN
ejpam-3401	91	5	)	)	PUNCT
ejpam-3401	91	6	is	be	AUX
ejpam-3401	91	7	the	the	DET
ejpam-3401	91	8	union	union	NOUN
ejpam-3401	91	9	of	of	ADP
ejpam-3401	91	10	all	all	DET
ejpam-3401	91	11	b	b	NOUN
ejpam-3401	91	12	-	-	PUNCT
ejpam-3401	91	13	open	open	ADJ
ejpam-3401	91	14	sets	set	NOUN
ejpam-3401	91	15	contained	contain	VERB
ejpam-3401	91	16	in	in	ADP
ejpam-3401	91	17	s	s	PROPN
ejpam-3401	91	18	,	,	PUNCT
ejpam-3401	91	19	i.e.	i.e.	X
ejpam-3401	91	20	bint(s	bint(s	PROPN
ejpam-3401	91	21	)	)	PUNCT
ejpam-3401	91	22	:	:	PUNCT
ejpam-3401	92	1	=	=	SYM
ejpam-3401	92	2	∪	∪	X
ejpam-3401	92	3	{	{	PUNCT
ejpam-3401	92	4	u	u	NOUN
ejpam-3401	92	5	|	|	ADV
ejpam-3401	92	6	u	u	NOUN
ejpam-3401	92	7	is	be	AUX
ejpam-3401	92	8	b	b	NOUN
ejpam-3401	92	9	-	-	ADJ
ejpam-3401	92	10	open	open	ADJ
ejpam-3401	92	11	,	,	PUNCT
ejpam-3401	92	12	u	u	NOUN
ejpam-3401	92	13	⊆	⊆	NUM
ejpam-3401	92	14	s	s	NOUN
ejpam-3401	92	15	}	}	PUNCT
ejpam-3401	92	16	.	.	PUNCT
ejpam-3401	93	1	(	(	PUNCT
ejpam-3401	93	2	v	v	NOUN
ejpam-3401	93	3	)	)	PUNCT
ejpam-3401	93	4	every	every	DET
ejpam-3401	93	5	t	t	NOUN
ejpam-3401	93	6	∗1	∗1	PROPN
ejpam-3401	93	7	-open	-open	PROPN
ejpam-3401	93	8	(	(	PUNCT
ejpam-3401	93	9	t	t	NOUN
ejpam-3401	93	10	∗2	∗2	PUNCT
ejpam-3401	93	11	-open	-open	NOUN
ejpam-3401	93	12	)	)	PUNCT
ejpam-3401	93	13	set	set	NOUN
ejpam-3401	93	14	is	be	AUX
ejpam-3401	93	15	b	b	NOUN
ejpam-3401	93	16	-	-	PUNCT
ejpam-3401	93	17	open	open	ADJ
ejpam-3401	93	18	because	because	SCONJ
ejpam-3401	93	19	if	if	SCONJ
ejpam-3401	93	20	we	we	PRON
ejpam-3401	93	21	assume	assume	VERB
ejpam-3401	93	22	that	that	SCONJ
ejpam-3401	93	23	s	s	VERB
ejpam-3401	93	24	is	be	AUX
ejpam-3401	93	25	t	t	NOUN
ejpam-3401	93	26	∗1	∗1	PROPN
ejpam-3401	93	27	-open	-open	PROPN
ejpam-3401	93	28	then	then	ADV
ejpam-3401	93	29	s	s	VERB
ejpam-3401	93	30	⊆	⊆	NUM
ejpam-3401	93	31	t1(s	t1(	NOUN
ejpam-3401	93	32	)	)	PUNCT
ejpam-3401	93	33	⊆	⊆	NUM
ejpam-3401	93	34	t1(s	t1(s	PROPN
ejpam-3401	93	35	)	)	PUNCT
ejpam-3401	93	36	∪	∪	ADP
ejpam-3401	93	37	t2(s	t2(s	PROPN
ejpam-3401	93	38	)	)	PUNCT
ejpam-3401	93	39	,	,	PUNCT
ejpam-3401	93	40	therefore	therefore	ADV
ejpam-3401	93	41	,	,	PUNCT
ejpam-3401	93	42	s	s	X
ejpam-3401	93	43	is	be	AUX
ejpam-3401	93	44	b	b	NOUN
ejpam-3401	93	45	-	-	PUNCT
ejpam-3401	93	46	open	open	ADJ
ejpam-3401	93	47	and	and	CCONJ
ejpam-3401	93	48	the	the	DET
ejpam-3401	93	49	same	same	ADJ
ejpam-3401	93	50	for	for	ADP
ejpam-3401	93	51	the	the	DET
ejpam-3401	93	52	t	t	NOUN
ejpam-3401	93	53	∗2	∗2	SYM
ejpam-3401	93	54	-open	-open	VERB
ejpam-3401	93	55	.	.	PUNCT
ejpam-3401	94	1	more	more	ADV
ejpam-3401	94	2	precisely	precisely	ADV
ejpam-3401	94	3	,	,	PUNCT
ejpam-3401	94	4	if	if	SCONJ
ejpam-3401	94	5	we	we	PRON
ejpam-3401	94	6	put	put	VERB
ejpam-3401	94	7	t	t	PROPN
ejpam-3401	94	8	∗12	∗12	PROPN
ejpam-3401	94	9	-	-	ADJ
ejpam-3401	94	10	open	open	ADJ
ejpam-3401	94	11	instead	instead	ADV
ejpam-3401	94	12	of	of	ADP
ejpam-3401	94	13	b	b	NOUN
ejpam-3401	94	14	-	-	PUNCT
ejpam-3401	94	15	open	open	ADJ
ejpam-3401	94	16	,	,	PUNCT
ejpam-3401	94	17	then	then	ADV
ejpam-3401	94	18	we	we	PRON
ejpam-3401	94	19	have	have	VERB
ejpam-3401	94	20	t1	t1	NOUN
ejpam-3401	94	21	-	-	PUNCT
ejpam-3401	94	22	open	open	ADJ
ejpam-3401	94	23	→	→	SYM
ejpam-3401	94	24	open	open	ADJ
ejpam-3401	94	25	→	→	SYM
ejpam-3401	94	26	t	t	NOUN
ejpam-3401	94	27	∗1	∗1	PROPN
ejpam-3401	94	28	-open	-open	PROPN
ejpam-3401	94	29	→	→	SYM
ejpam-3401	94	30	t	t	PROPN
ejpam-3401	94	31	∗12	∗12	PROPN
ejpam-3401	94	32	-	-	ADJ
ejpam-3401	94	33	open	open	ADJ
ejpam-3401	94	34	→	→	SYM
ejpam-3401	94	35	t	t	NOUN
ejpam-3401	94	36	∗123	∗123	NOUN
ejpam-3401	94	37	-	-	PUNCT
ejpam-3401	94	38	open	open	ADJ
ejpam-3401	94	39	→	→	SYM
ejpam-3401	94	40	...	...	PUNCT
ejpam-3401	94	41	t	t	PROPN
ejpam-3401	94	42	∗123	∗123	PROPN
ejpam-3401	94	43	...	...	PUNCT
ejpam-3401	94	44	n	n	CCONJ
ejpam-3401	94	45	-	-	ADV
ejpam-3401	94	46	open	open	ADJ
ejpam-3401	94	47	.	.	PUNCT
ejpam-3401	95	1	similarly	similarly	ADV
ejpam-3401	95	2	,	,	PUNCT
ejpam-3401	95	3	t2	t2	NOUN
ejpam-3401	95	4	-	-	PUNCT
ejpam-3401	95	5	open	open	ADJ
ejpam-3401	95	6	→	→	SYM
ejpam-3401	95	7	open	open	ADJ
ejpam-3401	95	8	→	→	SYM
ejpam-3401	95	9	t	t	NOUN
ejpam-3401	95	10	∗2	∗2	NOUN
ejpam-3401	95	11	-open	-open	PROPN
ejpam-3401	95	12	→	→	SYM
ejpam-3401	95	13	t	t	PROPN
ejpam-3401	95	14	∗12	∗12	PROPN
ejpam-3401	95	15	-	-	ADJ
ejpam-3401	95	16	open	open	ADJ
ejpam-3401	95	17	→	→	SYM
ejpam-3401	95	18	t	t	NOUN
ejpam-3401	95	19	∗123	∗123	NOUN
ejpam-3401	95	20	-	-	PUNCT
ejpam-3401	95	21	open	open	ADJ
ejpam-3401	95	22	→	→	SYM
ejpam-3401	95	23	...	...	PUNCT
ejpam-3401	95	24	t	t	PROPN
ejpam-3401	95	25	∗123	∗123	PROPN
ejpam-3401	95	26	...	...	PUNCT
ejpam-3401	95	27	n	n	CCONJ
ejpam-3401	95	28	-	-	PUNCT
ejpam-3401	95	29	open	open	ADJ
ejpam-3401	95	30	,	,	PUNCT
ejpam-3401	95	31	means	mean	VERB
ejpam-3401	95	32	that	that	SCONJ
ejpam-3401	95	33	s	s	VERB
ejpam-3401	95	34	is	be	AUX
ejpam-3401	95	35	t	t	NOUN
ejpam-3401	95	36	∗123	∗123	NOUN
ejpam-3401	95	37	-	-	PUNCT
ejpam-3401	95	38	open	open	ADJ
ejpam-3401	95	39	if	if	SCONJ
ejpam-3401	95	40	s	s	VERB
ejpam-3401	95	41	⊆	⊆	NUM
ejpam-3401	95	42	t1(s	t1(s	SYM
ejpam-3401	95	43	)	)	PUNCT
ejpam-3401	95	44	∪	∪	ADP
ejpam-3401	95	45	t2(s	t2(s	NOUN
ejpam-3401	95	46	)	)	PUNCT
ejpam-3401	95	47	∪	∪	ADP
ejpam-3401	95	48	t3(s	t3(	NOUN
ejpam-3401	95	49	)	)	PUNCT
ejpam-3401	95	50	,	,	PUNCT
ejpam-3401	95	51	and	and	CCONJ
ejpam-3401	95	52	t	t	PROPN
ejpam-3401	95	53	∗123	∗123	NOUN
ejpam-3401	95	54	...	...	PUNCT
ejpam-3401	95	55	n	n	CCONJ
ejpam-3401	95	56	-	-	PUNCT
ejpam-3401	95	57	open	open	ADJ
ejpam-3401	95	58	means	mean	VERB
ejpam-3401	95	59	analogously	analogously	ADV
ejpam-3401	95	60	s	s	VERB
ejpam-3401	95	61	⊆	⊆	NUM
ejpam-3401	95	62	t1(s	t1(s	SYM
ejpam-3401	95	63	)	)	PUNCT
ejpam-3401	95	64	∪	∪	ADP
ejpam-3401	95	65	t2(s	t2(s	NOUN
ejpam-3401	95	66	)	)	PUNCT
ejpam-3401	95	67	∪	∪	ADP
ejpam-3401	95	68	t3(s	t3(	NOUN
ejpam-3401	95	69	)	)	PUNCT
ejpam-3401	95	70	∪	∪	NOUN
ejpam-3401	95	71	...	...	PUNCT
ejpam-3401	95	72	∪	∪	X
ejpam-3401	95	73	tn(s	tn(s	NUM
ejpam-3401	95	74	)	)	PUNCT
ejpam-3401	95	75	.	.	PUNCT
ejpam-3401	96	1	definition	definition	NOUN
ejpam-3401	96	2	6	6	NUM
ejpam-3401	96	3	.	.	PUNCT
ejpam-3401	97	1	the	the	DET
ejpam-3401	97	2	graph	graph	NOUN
ejpam-3401	97	3	g(f	g(f	PROPN
ejpam-3401	97	4	)	)	PUNCT
ejpam-3401	97	5	of	of	ADP
ejpam-3401	97	6	a	a	DET
ejpam-3401	97	7	function	function	NOUN
ejpam-3401	97	8	from	from	ADP
ejpam-3401	97	9	a	a	DET
ejpam-3401	97	10	bi	bi	ADJ
ejpam-3401	97	11	-	-	NOUN
ejpam-3401	97	12	operator	operator	NOUN
ejpam-3401	97	13	topological	topological	ADJ
ejpam-3401	97	14	space	space	NOUN
ejpam-3401	97	15	(	(	PUNCT
ejpam-3401	97	16	x	x	X
ejpam-3401	97	17	,	,	PUNCT
ejpam-3401	97	18	τ	τ	PROPN
ejpam-3401	97	19	,	,	PUNCT
ejpam-3401	97	20	t1	t1	NOUN
ejpam-3401	97	21	,	,	PUNCT
ejpam-3401	97	22	t2	t2	NOUN
ejpam-3401	97	23	)	)	PUNCT
ejpam-3401	97	24	into	into	ADP
ejpam-3401	97	25	a	a	DET
ejpam-3401	97	26	topological	topological	ADJ
ejpam-3401	97	27	space	space	NOUN
ejpam-3401	97	28	(	(	PUNCT
ejpam-3401	97	29	y	y	PROPN
ejpam-3401	97	30	,	,	PUNCT
ejpam-3401	97	31	σ	σ	PROPN
ejpam-3401	97	32	)	)	PUNCT
ejpam-3401	97	33	is	be	AUX
ejpam-3401	97	34	said	say	VERB
ejpam-3401	97	35	to	to	PART
ejpam-3401	97	36	be	be	AUX
ejpam-3401	97	37	(	(	PUNCT
ejpam-3401	97	38	i	i	NOUN
ejpam-3401	97	39	)	)	PUNCT
ejpam-3401	97	40	b	b	X
ejpam-3401	97	41	-	-	PUNCT
ejpam-3401	97	42	regular	regular	ADJ
ejpam-3401	97	43	graph	graph	NOUN
ejpam-3401	97	44	,	,	PUNCT
ejpam-3401	97	45	if	if	SCONJ
ejpam-3401	97	46	for	for	ADP
ejpam-3401	97	47	every	every	DET
ejpam-3401	97	48	(	(	PUNCT
ejpam-3401	97	49	x	x	NOUN
ejpam-3401	97	50	,	,	PUNCT
ejpam-3401	97	51	y	y	NOUN
ejpam-3401	97	52	)	)	PUNCT
ejpam-3401	97	53	∈	∈	PROPN
ejpam-3401	98	1	x	x	SYM
ejpam-3401	98	2	×	×	PROPN
ejpam-3401	98	3	y	y	PROPN
ejpam-3401	98	4	\	\	PROPN
ejpam-3401	98	5	g(f	g(f	PROPN
ejpam-3401	98	6	)	)	PUNCT
ejpam-3401	99	1	,	,	PUNCT
ejpam-3401	99	2	there	there	PRON
ejpam-3401	99	3	exists	exist	VERB
ejpam-3401	99	4	u	u	NOUN
ejpam-3401	99	5	which	which	PRON
ejpam-3401	99	6	is	be	AUX
ejpam-3401	99	7	bclosed	bclose	VERB
ejpam-3401	99	8	in	in	ADP
ejpam-3401	99	9	x	x	PUNCT
ejpam-3401	99	10	containing	contain	VERB
ejpam-3401	99	11	x	x	X
ejpam-3401	99	12	and	and	CCONJ
ejpam-3401	99	13	a	a	DET
ejpam-3401	99	14	regular	regular	ADJ
ejpam-3401	99	15	open	open	NOUN
ejpam-3401	99	16	set	set	VERB
ejpam-3401	99	17	v	v	NOUN
ejpam-3401	99	18	in	in	ADP
ejpam-3401	99	19	y	y	NOUN
ejpam-3401	99	20	containing	contain	VERB
ejpam-3401	99	21	y	y	PRON
ejpam-3401	99	22	such	such	ADJ
ejpam-3401	99	23	that	that	PRON
ejpam-3401	99	24	(	(	PUNCT
ejpam-3401	99	25	u	u	NOUN
ejpam-3401	99	26	×	×	PROPN
ejpam-3401	99	27	v	v	NOUN
ejpam-3401	99	28	)	)	PUNCT
ejpam-3401	99	29	∩g(f	∩g(f	PROPN
ejpam-3401	99	30	)	)	PUNCT
ejpam-3401	100	1	=	=	PUNCT
ejpam-3401	100	2	∅.	∅.	PRON
ejpam-3401	100	3	(	(	PUNCT
ejpam-3401	100	4	ii	ii	NOUN
ejpam-3401	100	5	)	)	PUNCT
ejpam-3401	100	6	contra	contra	PROPN
ejpam-3401	100	7	-	-	PUNCT
ejpam-3401	100	8	b	b	NOUN
ejpam-3401	100	9	-	-	PUNCT
ejpam-3401	100	10	closed	closed	ADJ
ejpam-3401	100	11	graph	graph	NOUN
ejpam-3401	100	12	,	,	PUNCT
ejpam-3401	100	13	if	if	SCONJ
ejpam-3401	100	14	for	for	ADP
ejpam-3401	100	15	each	each	DET
ejpam-3401	100	16	(	(	PUNCT
ejpam-3401	100	17	x	x	NOUN
ejpam-3401	100	18	,	,	PUNCT
ejpam-3401	100	19	y	y	NOUN
ejpam-3401	100	20	)	)	PUNCT
ejpam-3401	100	21	∈	∈	PROPN
ejpam-3401	100	22	x	x	SYM
ejpam-3401	100	23	×	×	PROPN
ejpam-3401	100	24	y	y	PROPN
ejpam-3401	100	25	\	\	PROPN
ejpam-3401	100	26	g(f	g(f	PROPN
ejpam-3401	100	27	)	)	PUNCT
ejpam-3401	100	28	,	,	PUNCT
ejpam-3401	100	29	there	there	PRON
ejpam-3401	100	30	exists	exist	VERB
ejpam-3401	100	31	a	a	DET
ejpam-3401	100	32	b	b	NOUN
ejpam-3401	100	33	-	-	PUNCT
ejpam-3401	100	34	closed	closed	ADJ
ejpam-3401	100	35	set	set	NOUN
ejpam-3401	100	36	u	u	NOUN
ejpam-3401	100	37	in	in	ADP
ejpam-3401	100	38	x	x	SYM
ejpam-3401	100	39	containing	contain	VERB
ejpam-3401	100	40	x	x	X
ejpam-3401	100	41	and	and	CCONJ
ejpam-3401	100	42	a	a	DET
ejpam-3401	100	43	regular	regular	ADJ
ejpam-3401	100	44	closed	closed	ADJ
ejpam-3401	100	45	set	set	VERB
ejpam-3401	100	46	v	v	NOUN
ejpam-3401	100	47	in	in	ADP
ejpam-3401	100	48	y	y	NOUN
ejpam-3401	100	49	containing	contain	VERB
ejpam-3401	100	50	y	y	PRON
ejpam-3401	100	51	such	such	ADJ
ejpam-3401	100	52	that	that	DET
ejpam-3401	100	53	f(u	f(u	PROPN
ejpam-3401	100	54	)	)	PUNCT
ejpam-3401	100	55	∩	∩	PROPN
ejpam-3401	100	56	v	v	NOUN
ejpam-3401	100	57	=	=	PUNCT
ejpam-3401	100	58	∅.	∅.	PROPN
ejpam-3401	100	59	l.	l.	PROPN
ejpam-3401	100	60	m.	m.	PROPN
ejpam-3401	100	61	alabdulsada	alabdulsada	PROPN
ejpam-3401	100	62	/	/	SYM
ejpam-3401	100	63	eur	eur	PROPN
ejpam-3401	100	64	.	.	PUNCT
ejpam-3401	101	1	j.	j.	PROPN
ejpam-3401	101	2	pure	pure	PROPN
ejpam-3401	101	3	appl	appl	PROPN
ejpam-3401	101	4	.	.	PROPN
ejpam-3401	101	5	math	math	PROPN
ejpam-3401	101	6	,	,	PUNCT
ejpam-3401	101	7	12	12	NUM
ejpam-3401	101	8	(	(	PUNCT
ejpam-3401	101	9	2	2	NUM
ejpam-3401	101	10	)	)	PUNCT
ejpam-3401	101	11	(	(	PUNCT
ejpam-3401	101	12	2019	2019	NUM
ejpam-3401	101	13	)	)	PUNCT
ejpam-3401	101	14	,	,	PUNCT
ejpam-3401	101	15	358	358	NUM
ejpam-3401	101	16	-	-	SYM
ejpam-3401	101	17	369	369	NUM
ejpam-3401	101	18	362	362	NUM
ejpam-3401	101	19	definition	definition	NOUN
ejpam-3401	101	20	7	7	NUM
ejpam-3401	101	21	.	.	PUNCT
ejpam-3401	102	1	[	[	X
ejpam-3401	102	2	6	6	NUM
ejpam-3401	102	3	]	]	PUNCT
ejpam-3401	102	4	a	a	DET
ejpam-3401	102	5	function	function	NOUN
ejpam-3401	102	6	f	f	NOUN
ejpam-3401	102	7	:	:	PUNCT
ejpam-3401	102	8	(	(	PUNCT
ejpam-3401	102	9	x	x	X
ejpam-3401	102	10	,	,	PUNCT
ejpam-3401	102	11	τ)→	τ)→	PROPN
ejpam-3401	102	12	(	(	PUNCT
ejpam-3401	102	13	y	y	PROPN
ejpam-3401	102	14	,	,	PUNCT
ejpam-3401	102	15	σ	σ	PROPN
ejpam-3401	102	16	)	)	PUNCT
ejpam-3401	102	17	is	be	AUX
ejpam-3401	102	18	said	say	VERB
ejpam-3401	102	19	to	to	PART
ejpam-3401	102	20	be	be	AUX
ejpam-3401	102	21	contra	contra	ADJ
ejpam-3401	102	22	-	-	ADJ
ejpam-3401	102	23	continuous	continuous	ADJ
ejpam-3401	102	24	,	,	PUNCT
ejpam-3401	102	25	if	if	SCONJ
ejpam-3401	102	26	f−1(v	f−1(v	PROPN
ejpam-3401	102	27	)	)	PUNCT
ejpam-3401	102	28	is	be	AUX
ejpam-3401	102	29	closed	close	VERB
ejpam-3401	102	30	in	in	ADP
ejpam-3401	102	31	x	x	PUNCT
ejpam-3401	102	32	for	for	SCONJ
ejpam-3401	102	33	each	each	DET
ejpam-3401	102	34	open	open	ADJ
ejpam-3401	102	35	subset	subset	VERB
ejpam-3401	102	36	v	v	NOUN
ejpam-3401	102	37	of	of	ADP
ejpam-3401	102	38	y	y	PROPN
ejpam-3401	102	39	.	.	PUNCT
ejpam-3401	103	1	definition	definition	NOUN
ejpam-3401	103	2	8	8	NUM
ejpam-3401	103	3	.	.	PUNCT
ejpam-3401	104	1	a	a	DET
ejpam-3401	104	2	function	function	NOUN
ejpam-3401	104	3	f	f	NOUN
ejpam-3401	104	4	:	:	PUNCT
ejpam-3401	104	5	(	(	PUNCT
ejpam-3401	104	6	x	x	X
ejpam-3401	104	7	,	,	PUNCT
ejpam-3401	104	8	τ	τ	PROPN
ejpam-3401	104	9	,	,	PUNCT
ejpam-3401	104	10	t1	t1	NOUN
ejpam-3401	104	11	,	,	PUNCT
ejpam-3401	104	12	t2	t2	NOUN
ejpam-3401	104	13	)	)	PUNCT
ejpam-3401	104	14	→	→	SYM
ejpam-3401	104	15	(	(	PUNCT
ejpam-3401	104	16	y	y	PROPN
ejpam-3401	104	17	,	,	PUNCT
ejpam-3401	104	18	σ	σ	PROPN
ejpam-3401	104	19	)	)	PUNCT
ejpam-3401	104	20	is	be	AUX
ejpam-3401	104	21	said	say	VERB
ejpam-3401	104	22	to	to	PART
ejpam-3401	104	23	be	be	AUX
ejpam-3401	104	24	contra	contra	PROPN
ejpam-3401	104	25	-	-	PUNCT
ejpam-3401	104	26	b	b	NOUN
ejpam-3401	104	27	-	-	PUNCT
ejpam-3401	104	28	continuous	continuous	ADJ
ejpam-3401	104	29	,	,	PUNCT
ejpam-3401	104	30	if	if	SCONJ
ejpam-3401	104	31	f−1(v	f−1(v	PROPN
ejpam-3401	104	32	)	)	PUNCT
ejpam-3401	104	33	is	be	AUX
ejpam-3401	104	34	b	b	NOUN
ejpam-3401	104	35	-	-	PUNCT
ejpam-3401	104	36	closed	closed	ADJ
ejpam-3401	104	37	in	in	ADP
ejpam-3401	104	38	x	x	PUNCT
ejpam-3401	104	39	for	for	SCONJ
ejpam-3401	104	40	each	each	DET
ejpam-3401	104	41	open	open	ADJ
ejpam-3401	104	42	subset	subset	VERB
ejpam-3401	104	43	v	v	NOUN
ejpam-3401	104	44	of	of	ADP
ejpam-3401	104	45	y	y	PROPN
ejpam-3401	104	46	.	.	PUNCT
ejpam-3401	105	1	definition	definition	NOUN
ejpam-3401	105	2	9	9	NUM
ejpam-3401	105	3	.	.	PUNCT
ejpam-3401	106	1	let	let	AUX
ejpam-3401	106	2	(	(	PUNCT
ejpam-3401	106	3	x	x	NOUN
ejpam-3401	106	4	,	,	PUNCT
ejpam-3401	106	5	τ	τ	PROPN
ejpam-3401	106	6	,	,	PUNCT
ejpam-3401	106	7	t1	t1	NOUN
ejpam-3401	106	8	,	,	PUNCT
ejpam-3401	106	9	t2	t2	NOUN
ejpam-3401	106	10	)	)	PUNCT
ejpam-3401	106	11	be	be	AUX
ejpam-3401	106	12	a	a	DET
ejpam-3401	106	13	bi	bi	ADJ
ejpam-3401	106	14	-	-	ADJ
ejpam-3401	106	15	operator	operator	NOUN
ejpam-3401	106	16	topological	topological	ADJ
ejpam-3401	106	17	space	space	NOUN
ejpam-3401	106	18	,	,	PUNCT
ejpam-3401	106	19	then	then	ADV
ejpam-3401	106	20	x	x	PUNCT
ejpam-3401	106	21	is	be	AUX
ejpam-3401	106	22	called	call	VERB
ejpam-3401	106	23	a	a	DET
ejpam-3401	106	24	bfrechet	bfrechet	NOUN
ejpam-3401	106	25	,	,	PUNCT
ejpam-3401	106	26	if	if	SCONJ
ejpam-3401	106	27	for	for	ADP
ejpam-3401	106	28	each	each	DET
ejpam-3401	106	29	pair	pair	NOUN
ejpam-3401	106	30	of	of	ADP
ejpam-3401	106	31	distinct	distinct	ADJ
ejpam-3401	106	32	points	point	NOUN
ejpam-3401	106	33	x1	x1	PROPN
ejpam-3401	106	34	,	,	PUNCT
ejpam-3401	106	35	x2	x2	PROPN
ejpam-3401	106	36	of	of	ADP
ejpam-3401	106	37	x	x	PRON
ejpam-3401	106	38	,	,	PUNCT
ejpam-3401	106	39	there	there	PRON
ejpam-3401	106	40	exists	exist	VERB
ejpam-3401	106	41	b	b	X
ejpam-3401	106	42	-	-	PUNCT
ejpam-3401	106	43	open	open	ADJ
ejpam-3401	106	44	sets	set	NOUN
ejpam-3401	106	45	u	u	NOUN
ejpam-3401	106	46	and	and	CCONJ
ejpam-3401	106	47	v	v	ADP
ejpam-3401	106	48	containing	contain	VERB
ejpam-3401	106	49	x1	x1	PROPN
ejpam-3401	106	50	and	and	CCONJ
ejpam-3401	106	51	x2	x2	NUM
ejpam-3401	106	52	,	,	PUNCT
ejpam-3401	106	53	respectively	respectively	ADV
ejpam-3401	106	54	where	where	SCONJ
ejpam-3401	106	55	x2	x2	PROPN
ejpam-3401	106	56	/∈	/∈	PUNCT
ejpam-3401	106	57	u	u	PROPN
ejpam-3401	106	58	and	and	CCONJ
ejpam-3401	106	59	x1	x1	NUM
ejpam-3401	106	60	/∈	/∈	PUNCT
ejpam-3401	107	1	v.	v.	CCONJ
ejpam-3401	107	2	this	this	PRON
ejpam-3401	107	3	is	be	AUX
ejpam-3401	107	4	equivalent	equivalent	ADJ
ejpam-3401	107	5	to	to	ADP
ejpam-3401	107	6	saying	say	VERB
ejpam-3401	107	7	that	that	SCONJ
ejpam-3401	107	8	each	each	PRON
ejpam-3401	107	9	single	single	ADJ
ejpam-3401	107	10	{	{	PUNCT
ejpam-3401	107	11	x	x	NOUN
ejpam-3401	107	12	}	}	PUNCT
ejpam-3401	107	13	is	be	AUX
ejpam-3401	107	14	b	b	NOUN
ejpam-3401	107	15	-	-	PUNCT
ejpam-3401	107	16	closed	closed	ADJ
ejpam-3401	107	17	.	.	PUNCT
ejpam-3401	108	1	definition	definition	NOUN
ejpam-3401	108	2	10	10	NUM
ejpam-3401	108	3	.	.	PUNCT
ejpam-3401	109	1	a	a	DET
ejpam-3401	109	2	topological	topological	ADJ
ejpam-3401	109	3	space	space	NOUN
ejpam-3401	109	4	(	(	PUNCT
ejpam-3401	109	5	x	x	X
ejpam-3401	109	6	,	,	PUNCT
ejpam-3401	109	7	τ	τ	X
ejpam-3401	109	8	)	)	PUNCT
ejpam-3401	109	9	is	be	AUX
ejpam-3401	109	10	said	say	VERB
ejpam-3401	109	11	to	to	PART
ejpam-3401	109	12	be	be	AUX
ejpam-3401	109	13	(	(	PUNCT
ejpam-3401	109	14	see	see	VERB
ejpam-3401	109	15	[	[	X
ejpam-3401	109	16	1	1	NUM
ejpam-3401	109	17	]	]	PUNCT
ejpam-3401	109	18	,	,	PUNCT
ejpam-3401	109	19	[	[	X
ejpam-3401	109	20	7	7	NUM
ejpam-3401	109	21	]	]	PUNCT
ejpam-3401	109	22	,	,	PUNCT
ejpam-3401	109	23	[	[	X
ejpam-3401	109	24	21	21	NUM
ejpam-3401	109	25	]	]	X
ejpam-3401	110	1	[	[	X
ejpam-3401	110	2	22	22	NUM
ejpam-3401	110	3	]	]	PUNCT
ejpam-3401	110	4	and	and	CCONJ
ejpam-3401	110	5	[	[	X
ejpam-3401	110	6	18	18	NUM
ejpam-3401	110	7	]	]	SYM
ejpam-3401	110	8	):	):	PUNCT
ejpam-3401	110	9	(	(	PUNCT
ejpam-3401	110	10	i	i	NOUN
ejpam-3401	110	11	)	)	PUNCT
ejpam-3401	110	12	compact	compact	ADJ
ejpam-3401	110	13	,	,	PUNCT
ejpam-3401	110	14	if	if	SCONJ
ejpam-3401	110	15	for	for	ADP
ejpam-3401	110	16	every	every	DET
ejpam-3401	110	17	open	open	ADJ
ejpam-3401	110	18	cover	cover	NOUN
ejpam-3401	110	19	of	of	ADP
ejpam-3401	110	20	x	x	PUNCT
ejpam-3401	110	21	has	have	VERB
ejpam-3401	110	22	finite	finite	PROPN
ejpam-3401	110	23	subcover	subcover	PROPN
ejpam-3401	110	24	.	.	PUNCT
ejpam-3401	111	1	(	(	PUNCT
ejpam-3401	111	2	ii	ii	NOUN
ejpam-3401	111	3	)	)	PUNCT
ejpam-3401	111	4	contra	contra	PROPN
ejpam-3401	111	5	-	-	ADJ
ejpam-3401	111	6	compact	compact	ADJ
ejpam-3401	111	7	,	,	PUNCT
ejpam-3401	111	8	if	if	SCONJ
ejpam-3401	111	9	for	for	ADP
ejpam-3401	111	10	every	every	DET
ejpam-3401	111	11	closed	closed	ADJ
ejpam-3401	111	12	cover	cover	NOUN
ejpam-3401	111	13	of	of	ADP
ejpam-3401	111	14	x	x	PUNCT
ejpam-3401	111	15	has	have	VERB
ejpam-3401	111	16	finite	finite	PROPN
ejpam-3401	111	17	subcover	subcover	PROPN
ejpam-3401	111	18	.	.	PUNCT
ejpam-3401	112	1	(	(	PUNCT
ejpam-3401	112	2	iii	iii	NOUN
ejpam-3401	112	3	)	)	PUNCT
ejpam-3401	112	4	r	r	NOUN
ejpam-3401	112	5	-	-	ADJ
ejpam-3401	112	6	compact	compact	ADJ
ejpam-3401	112	7	,	,	PUNCT
ejpam-3401	112	8	if	if	SCONJ
ejpam-3401	112	9	for	for	ADP
ejpam-3401	112	10	every	every	DET
ejpam-3401	112	11	regular	regular	ADJ
ejpam-3401	112	12	open	open	ADJ
ejpam-3401	112	13	cover	cover	NOUN
ejpam-3401	112	14	of	of	ADP
ejpam-3401	112	15	x	x	PUNCT
ejpam-3401	112	16	has	have	VERB
ejpam-3401	112	17	finite	finite	PROPN
ejpam-3401	112	18	subcover	subcover	PROPN
ejpam-3401	112	19	.	.	PUNCT
ejpam-3401	113	1	(	(	PUNCT
ejpam-3401	113	2	iv	iv	X
ejpam-3401	113	3	)	)	PUNCT
ejpam-3401	113	4	contra	contra	PROPN
ejpam-3401	113	5	-	-	PUNCT
ejpam-3401	113	6	r	r	NOUN
ejpam-3401	113	7	-	-	ADJ
ejpam-3401	113	8	compact	compact	ADJ
ejpam-3401	113	9	,	,	PUNCT
ejpam-3401	113	10	if	if	SCONJ
ejpam-3401	113	11	for	for	ADP
ejpam-3401	113	12	every	every	DET
ejpam-3401	113	13	regular	regular	ADJ
ejpam-3401	113	14	closed	closed	ADJ
ejpam-3401	113	15	cover	cover	NOUN
ejpam-3401	113	16	of	of	ADP
ejpam-3401	113	17	x	x	PUNCT
ejpam-3401	113	18	has	have	VERB
ejpam-3401	113	19	finite	finite	PROPN
ejpam-3401	113	20	subcover	subcover	PROPN
ejpam-3401	113	21	.	.	PUNCT
ejpam-3401	114	1	(	(	PUNCT
ejpam-3401	114	2	v	v	NOUN
ejpam-3401	114	3	)	)	PUNCT
ejpam-3401	114	4	r	r	NOUN
ejpam-3401	114	5	-	-	PUNCT
ejpam-3401	114	6	lindelöf	lindelöf	NOUN
ejpam-3401	114	7	,	,	PUNCT
ejpam-3401	114	8	if	if	SCONJ
ejpam-3401	114	9	for	for	ADP
ejpam-3401	114	10	every	every	DET
ejpam-3401	114	11	regular	regular	ADJ
ejpam-3401	114	12	open	open	ADJ
ejpam-3401	114	13	cover	cover	NOUN
ejpam-3401	114	14	of	of	ADP
ejpam-3401	114	15	x	x	PUNCT
ejpam-3401	114	16	has	have	AUX
ejpam-3401	114	17	countable	countable	ADJ
ejpam-3401	114	18	subcover	subcover	PROPN
ejpam-3401	114	19	.	.	PUNCT
ejpam-3401	115	1	(	(	PUNCT
ejpam-3401	115	2	vi	vi	NOUN
ejpam-3401	115	3	)	)	PUNCT
ejpam-3401	115	4	contra	contra	PROPN
ejpam-3401	115	5	-	-	PUNCT
ejpam-3401	115	6	r	r	NOUN
ejpam-3401	115	7	-	-	PUNCT
ejpam-3401	115	8	lindelöf	lindelöf	NOUN
ejpam-3401	115	9	,	,	PUNCT
ejpam-3401	115	10	if	if	SCONJ
ejpam-3401	115	11	for	for	ADP
ejpam-3401	115	12	every	every	DET
ejpam-3401	115	13	regular	regular	ADJ
ejpam-3401	115	14	closed	closed	ADJ
ejpam-3401	115	15	cover	cover	NOUN
ejpam-3401	115	16	of	of	ADP
ejpam-3401	115	17	x	x	PUNCT
ejpam-3401	115	18	has	have	AUX
ejpam-3401	115	19	countable	countable	ADJ
ejpam-3401	115	20	subcover	subcover	PROPN
ejpam-3401	115	21	.	.	PUNCT
ejpam-3401	116	1	(	(	PUNCT
ejpam-3401	116	2	vii	vii	PROPN
ejpam-3401	116	3	)	)	PUNCT
ejpam-3401	116	4	countable	countable	ADJ
ejpam-3401	116	5	-	-	PUNCT
ejpam-3401	116	6	r	r	NOUN
ejpam-3401	116	7	-	-	PUNCT
ejpam-3401	116	8	compact	compact	ADJ
ejpam-3401	116	9	,	,	PUNCT
ejpam-3401	116	10	if	if	SCONJ
ejpam-3401	116	11	for	for	ADP
ejpam-3401	116	12	every	every	DET
ejpam-3401	116	13	countable	countable	ADJ
ejpam-3401	116	14	regular	regular	ADJ
ejpam-3401	116	15	open	open	ADJ
ejpam-3401	116	16	cover	cover	NOUN
ejpam-3401	116	17	of	of	ADP
ejpam-3401	116	18	x	x	PUNCT
ejpam-3401	116	19	has	have	VERB
ejpam-3401	116	20	finite	finite	PROPN
ejpam-3401	116	21	subcover	subcover	PROPN
ejpam-3401	116	22	.	.	PUNCT
ejpam-3401	117	1	(	(	PUNCT
ejpam-3401	117	2	viii	viii	NOUN
ejpam-3401	117	3	)	)	PUNCT
ejpam-3401	117	4	contra	contra	PROPN
ejpam-3401	117	5	countable	countable	ADJ
ejpam-3401	117	6	-	-	PUNCT
ejpam-3401	117	7	r	r	NOUN
ejpam-3401	117	8	-	-	PUNCT
ejpam-3401	117	9	compact	compact	ADJ
ejpam-3401	117	10	,	,	PUNCT
ejpam-3401	117	11	if	if	SCONJ
ejpam-3401	117	12	for	for	ADP
ejpam-3401	117	13	every	every	DET
ejpam-3401	117	14	countable	countable	ADJ
ejpam-3401	117	15	regular	regular	ADJ
ejpam-3401	117	16	closed	closed	ADJ
ejpam-3401	117	17	cover	cover	NOUN
ejpam-3401	117	18	of	of	ADP
ejpam-3401	117	19	x	x	PUNCT
ejpam-3401	117	20	has	have	VERB
ejpam-3401	117	21	finite	finite	PROPN
ejpam-3401	117	22	subcover	subcover	PROPN
ejpam-3401	117	23	.	.	PUNCT
ejpam-3401	118	1	definition	definition	NOUN
ejpam-3401	118	2	11	11	NUM
ejpam-3401	118	3	.	.	PUNCT
ejpam-3401	119	1	we	we	PRON
ejpam-3401	119	2	call	call	VERB
ejpam-3401	119	3	the	the	DET
ejpam-3401	119	4	bi	bi	NOUN
ejpam-3401	119	5	-	-	NOUN
ejpam-3401	119	6	operator	operator	NOUN
ejpam-3401	119	7	topological	topological	ADJ
ejpam-3401	119	8	space	space	NOUN
ejpam-3401	119	9	(	(	PUNCT
ejpam-3401	119	10	x	x	X
ejpam-3401	119	11	,	,	PUNCT
ejpam-3401	119	12	τ	τ	PROPN
ejpam-3401	119	13	,	,	PUNCT
ejpam-3401	119	14	t1	t1	NOUN
ejpam-3401	119	15	,	,	PUNCT
ejpam-3401	119	16	t2	t2	PROPN
ejpam-3401	119	17	):	):	PUNCT
ejpam-3401	119	18	(	(	PUNCT
ejpam-3401	119	19	i	i	NOUN
ejpam-3401	119	20	)	)	PUNCT
ejpam-3401	119	21	b	b	X
ejpam-3401	119	22	-	-	PUNCT
ejpam-3401	119	23	compact	compact	ADJ
ejpam-3401	119	24	,	,	PUNCT
ejpam-3401	119	25	if	if	SCONJ
ejpam-3401	119	26	for	for	ADP
ejpam-3401	119	27	every	every	DET
ejpam-3401	119	28	b	b	NOUN
ejpam-3401	119	29	-	-	PUNCT
ejpam-3401	119	30	open	open	ADJ
ejpam-3401	119	31	cover	cover	NOUN
ejpam-3401	119	32	of	of	ADP
ejpam-3401	119	33	x	x	PUNCT
ejpam-3401	119	34	has	have	VERB
ejpam-3401	119	35	finite	finite	PROPN
ejpam-3401	119	36	subcover	subcover	PROPN
ejpam-3401	119	37	.	.	PUNCT
ejpam-3401	120	1	(	(	PUNCT
ejpam-3401	120	2	ii	ii	NOUN
ejpam-3401	120	3	)	)	PUNCT
ejpam-3401	120	4	b	b	X
ejpam-3401	120	5	-	-	PUNCT
ejpam-3401	120	6	lindelöf	lindelöf	NOUN
ejpam-3401	120	7	,	,	PUNCT
ejpam-3401	120	8	if	if	SCONJ
ejpam-3401	120	9	for	for	ADP
ejpam-3401	120	10	every	every	DET
ejpam-3401	120	11	b	b	NOUN
ejpam-3401	120	12	-	-	PUNCT
ejpam-3401	120	13	open	open	ADJ
ejpam-3401	120	14	cover	cover	NOUN
ejpam-3401	120	15	of	of	ADP
ejpam-3401	120	16	x	x	PUNCT
ejpam-3401	120	17	has	have	AUX
ejpam-3401	120	18	countable	countable	ADJ
ejpam-3401	120	19	subcover	subcover	PROPN
ejpam-3401	120	20	.	.	PUNCT
ejpam-3401	121	1	(	(	PUNCT
ejpam-3401	121	2	iii	iii	NOUN
ejpam-3401	121	3	)	)	PUNCT
ejpam-3401	121	4	countable	countable	ADJ
ejpam-3401	121	5	-	-	PUNCT
ejpam-3401	121	6	b	b	NOUN
ejpam-3401	121	7	-	-	PUNCT
ejpam-3401	121	8	compact	compact	ADJ
ejpam-3401	121	9	,	,	PUNCT
ejpam-3401	121	10	if	if	SCONJ
ejpam-3401	121	11	for	for	ADP
ejpam-3401	121	12	every	every	DET
ejpam-3401	121	13	countable	countable	ADJ
ejpam-3401	121	14	-	-	PUNCT
ejpam-3401	121	15	b	b	NOUN
ejpam-3401	121	16	-	-	PUNCT
ejpam-3401	121	17	open	open	ADJ
ejpam-3401	121	18	cover	cover	NOUN
ejpam-3401	121	19	of	of	ADP
ejpam-3401	121	20	x	x	PUNCT
ejpam-3401	121	21	has	have	VERB
ejpam-3401	121	22	finite	finite	PROPN
ejpam-3401	121	23	subcover	subcover	PROPN
ejpam-3401	121	24	.	.	PUNCT
ejpam-3401	122	1	definition	definition	NOUN
ejpam-3401	122	2	12	12	NUM
ejpam-3401	122	3	.	.	PUNCT
ejpam-3401	123	1	a	a	DET
ejpam-3401	123	2	subset	subset	NOUN
ejpam-3401	123	3	s	s	NOUN
ejpam-3401	123	4	of	of	ADP
ejpam-3401	123	5	a	a	DET
ejpam-3401	123	6	bi	bi	ADJ
ejpam-3401	123	7	-	-	ADJ
ejpam-3401	123	8	operator	operator	NOUN
ejpam-3401	123	9	topological	topological	ADJ
ejpam-3401	123	10	space	space	NOUN
ejpam-3401	123	11	(	(	PUNCT
ejpam-3401	123	12	x	x	X
ejpam-3401	123	13	,	,	PUNCT
ejpam-3401	123	14	τ	τ	PROPN
ejpam-3401	123	15	,	,	PUNCT
ejpam-3401	123	16	t1	t1	NOUN
ejpam-3401	123	17	,	,	PUNCT
ejpam-3401	123	18	t2	t2	NOUN
ejpam-3401	123	19	)	)	PUNCT
ejpam-3401	123	20	is	be	AUX
ejpam-3401	123	21	said	say	VERB
ejpam-3401	123	22	to	to	PART
ejpam-3401	123	23	be	be	AUX
ejpam-3401	123	24	b	b	NOUN
ejpam-3401	123	25	-	-	PUNCT
ejpam-3401	123	26	dense	dense	ADJ
ejpam-3401	123	27	,	,	PUNCT
ejpam-3401	123	28	if	if	SCONJ
ejpam-3401	123	29	bcl(s	bcl(s	PROPN
ejpam-3401	123	30	)	)	PUNCT
ejpam-3401	123	31	=	=	SYM
ejpam-3401	123	32	x.	x.	NOUN
ejpam-3401	123	33	remark	remark	VERB
ejpam-3401	123	34	3	3	NUM
ejpam-3401	123	35	.	.	PUNCT
ejpam-3401	124	1	if	if	SCONJ
ejpam-3401	124	2	t1(s	t1(s	PROPN
ejpam-3401	124	3	)	)	PUNCT
ejpam-3401	124	4	=	=	SYM
ejpam-3401	124	5	int(cl(s	int(cl(s	PROPN
ejpam-3401	124	6	)	)	PUNCT
ejpam-3401	124	7	)	)	PUNCT
ejpam-3401	124	8	,	,	PUNCT
ejpam-3401	124	9	t2(s	t2(s	NOUN
ejpam-3401	124	10	)	)	PUNCT
ejpam-3401	124	11	=	=	SYM
ejpam-3401	124	12	cl(int(s	cl(int(s	NOUN
ejpam-3401	124	13	)	)	PUNCT
ejpam-3401	124	14	)	)	PUNCT
ejpam-3401	124	15	,	,	PUNCT
ejpam-3401	124	16	then	then	ADV
ejpam-3401	124	17	b	b	X
ejpam-3401	124	18	-	-	PUNCT
ejpam-3401	124	19	dense	dense	ADJ
ejpam-3401	124	20	will	will	AUX
ejpam-3401	124	21	be	be	AUX
ejpam-3401	124	22	b	b	NOUN
ejpam-3401	124	23	-	-	PUNCT
ejpam-3401	124	24	dense	dense	ADJ
ejpam-3401	124	25	and	and	CCONJ
ejpam-3401	124	26	bcl(s	bcl(	NOUN
ejpam-3401	124	27	)	)	PUNCT
ejpam-3401	124	28	will	will	AUX
ejpam-3401	124	29	be	be	AUX
ejpam-3401	124	30	bcl(s	bcl(s	PROPN
ejpam-3401	124	31	)	)	PUNCT
ejpam-3401	124	32	such	such	ADJ
ejpam-3401	124	33	that	that	SCONJ
ejpam-3401	124	34	b	b	X
ejpam-3401	124	35	-	-	PUNCT
ejpam-3401	124	36	dense	dense	ADJ
ejpam-3401	124	37	is	be	AUX
ejpam-3401	124	38	a	a	DET
ejpam-3401	124	39	set	set	NOUN
ejpam-3401	124	40	in	in	ADP
ejpam-3401	124	41	x	x	PUNCT
ejpam-3401	124	42	if	if	SCONJ
ejpam-3401	124	43	bcl(s	bcl(s	PROPN
ejpam-3401	124	44	)	)	PUNCT
ejpam-3401	124	45	=	=	PUNCT
ejpam-3401	125	1	x.	x.	NOUN
ejpam-3401	125	2	definition	definition	NOUN
ejpam-3401	125	3	13	13	NUM
ejpam-3401	125	4	.	.	PUNCT
ejpam-3401	126	1	a	a	DET
ejpam-3401	126	2	bi	bi	ADJ
ejpam-3401	126	3	-	-	ADJ
ejpam-3401	126	4	operator	operator	NOUN
ejpam-3401	126	5	topological	topological	ADJ
ejpam-3401	126	6	space	space	NOUN
ejpam-3401	126	7	(	(	PUNCT
ejpam-3401	126	8	x	x	X
ejpam-3401	126	9	,	,	PUNCT
ejpam-3401	126	10	τ	τ	PROPN
ejpam-3401	126	11	,	,	PUNCT
ejpam-3401	126	12	t1	t1	NOUN
ejpam-3401	126	13	,	,	PUNCT
ejpam-3401	126	14	t2	t2	NOUN
ejpam-3401	126	15	)	)	PUNCT
ejpam-3401	126	16	is	be	AUX
ejpam-3401	126	17	called	call	VERB
ejpam-3401	126	18	a	a	DET
ejpam-3401	126	19	b	b	NOUN
ejpam-3401	126	20	-	-	PUNCT
ejpam-3401	126	21	connected	connect	VERB
ejpam-3401	126	22	provided	provide	VERB
ejpam-3401	126	23	x	x	VERB
ejpam-3401	126	24	is	be	AUX
ejpam-3401	126	25	not	not	PART
ejpam-3401	126	26	a	a	DET
ejpam-3401	126	27	union	union	NOUN
ejpam-3401	126	28	of	of	ADP
ejpam-3401	126	29	two	two	NUM
ejpam-3401	126	30	nonempty	nonempty	ADJ
ejpam-3401	126	31	b	b	X
ejpam-3401	126	32	-	-	PUNCT
ejpam-3401	126	33	open	open	ADJ
ejpam-3401	126	34	sets	set	NOUN
ejpam-3401	126	35	.	.	PUNCT
ejpam-3401	127	1	definition	definition	NOUN
ejpam-3401	127	2	14	14	NUM
ejpam-3401	127	3	.	.	PUNCT
ejpam-3401	128	1	a	a	DET
ejpam-3401	128	2	topological	topological	ADJ
ejpam-3401	128	3	space	space	NOUN
ejpam-3401	128	4	(	(	PUNCT
ejpam-3401	128	5	x	x	X
ejpam-3401	128	6	,	,	PUNCT
ejpam-3401	128	7	τ	τ	X
ejpam-3401	128	8	)	)	PUNCT
ejpam-3401	128	9	is	be	AUX
ejpam-3401	128	10	said	say	VERB
ejpam-3401	128	11	to	to	PART
ejpam-3401	128	12	be	be	AUX
ejpam-3401	128	13	a	a	DET
ejpam-3401	128	14	weakly	weakly	ADJ
ejpam-3401	128	15	hausdorff	hausdorff	NOUN
ejpam-3401	128	16	space	space	NOUN
ejpam-3401	128	17	[	[	X
ejpam-3401	128	18	19	19	NUM
ejpam-3401	128	19	]	]	X
ejpam-3401	128	20	,	,	PUNCT
ejpam-3401	128	21	if	if	SCONJ
ejpam-3401	128	22	each	each	DET
ejpam-3401	128	23	element	element	NOUN
ejpam-3401	128	24	of	of	ADP
ejpam-3401	128	25	x	x	PUNCT
ejpam-3401	128	26	is	be	AUX
ejpam-3401	128	27	an	an	DET
ejpam-3401	128	28	intersection	intersection	NOUN
ejpam-3401	128	29	of	of	ADP
ejpam-3401	128	30	regular	regular	ADJ
ejpam-3401	128	31	closed	closed	ADJ
ejpam-3401	128	32	sets	set	NOUN
ejpam-3401	128	33	.	.	PUNCT
ejpam-3401	129	1	definition	definition	NOUN
ejpam-3401	129	2	15	15	NUM
ejpam-3401	129	3	.	.	PUNCT
ejpam-3401	130	1	a	a	DET
ejpam-3401	130	2	topological	topological	ADJ
ejpam-3401	130	3	space	space	NOUN
ejpam-3401	130	4	(	(	PUNCT
ejpam-3401	130	5	x	x	X
ejpam-3401	130	6	,	,	PUNCT
ejpam-3401	130	7	τ	τ	X
ejpam-3401	130	8	)	)	PUNCT
ejpam-3401	130	9	is	be	AUX
ejpam-3401	130	10	an	an	DET
ejpam-3401	130	11	urysohn	urysohn	ADJ
ejpam-3401	130	12	space	space	NOUN
ejpam-3401	130	13	[	[	X
ejpam-3401	130	14	4	4	NUM
ejpam-3401	130	15	]	]	PUNCT
ejpam-3401	130	16	,	,	PUNCT
ejpam-3401	130	17	if	if	SCONJ
ejpam-3401	130	18	for	for	ADP
ejpam-3401	130	19	every	every	DET
ejpam-3401	130	20	pair	pair	NOUN
ejpam-3401	130	21	of	of	ADP
ejpam-3401	130	22	distinct	distinct	ADJ
ejpam-3401	130	23	points	point	NOUN
ejpam-3401	130	24	x	x	PUNCT
ejpam-3401	130	25	and	and	CCONJ
ejpam-3401	130	26	y	y	PROPN
ejpam-3401	130	27	in	in	ADP
ejpam-3401	130	28	x	x	SYM
ejpam-3401	130	29	,	,	PUNCT
ejpam-3401	130	30	there	there	PRON
ejpam-3401	130	31	exist	exist	VERB
ejpam-3401	130	32	open	open	ADJ
ejpam-3401	130	33	sets	set	NOUN
ejpam-3401	130	34	u	u	NOUN
ejpam-3401	130	35	and	and	CCONJ
ejpam-3401	130	36	v	v	ADP
ejpam-3401	130	37	such	such	ADJ
ejpam-3401	130	38	that	that	SCONJ
ejpam-3401	130	39	x	x	SYM
ejpam-3401	130	40	∈	∈	PROPN
ejpam-3401	130	41	u	u	NOUN
ejpam-3401	130	42	,	,	PUNCT
ejpam-3401	130	43	y	y	PROPN
ejpam-3401	130	44	∈	∈	PROPN
ejpam-3401	130	45	v	v	NOUN
ejpam-3401	130	46	and	and	CCONJ
ejpam-3401	130	47	cl(u	cl(u	NOUN
ejpam-3401	130	48	)	)	PUNCT
ejpam-3401	130	49	∩	∩	NOUN
ejpam-3401	130	50	cl(v	cl(v	NOUN
ejpam-3401	130	51	)	)	PUNCT
ejpam-3401	130	52	=	=	PUNCT
ejpam-3401	130	53	∅.	∅.	PROPN
ejpam-3401	130	54	l.	l.	PROPN
ejpam-3401	130	55	m.	m.	PROPN
ejpam-3401	130	56	alabdulsada	alabdulsada	PROPN
ejpam-3401	130	57	/	/	SYM
ejpam-3401	130	58	eur	eur	PROPN
ejpam-3401	130	59	.	.	PUNCT
ejpam-3401	131	1	j.	j.	PROPN
ejpam-3401	131	2	pure	pure	PROPN
ejpam-3401	131	3	appl	appl	PROPN
ejpam-3401	131	4	.	.	PROPN
ejpam-3401	131	5	math	math	PROPN
ejpam-3401	131	6	,	,	PUNCT
ejpam-3401	131	7	12	12	NUM
ejpam-3401	131	8	(	(	PUNCT
ejpam-3401	131	9	2	2	NUM
ejpam-3401	131	10	)	)	PUNCT
ejpam-3401	131	11	(	(	PUNCT
ejpam-3401	131	12	2019	2019	NUM
ejpam-3401	131	13	)	)	PUNCT
ejpam-3401	131	14	,	,	PUNCT
ejpam-3401	131	15	358	358	NUM
ejpam-3401	131	16	-	-	SYM
ejpam-3401	131	17	369	369	NUM
ejpam-3401	131	18	363	363	NUM
ejpam-3401	131	19	3	3	NUM
ejpam-3401	131	20	.	.	PUNCT
ejpam-3401	132	1	some	some	DET
ejpam-3401	132	2	properties	property	NOUN
ejpam-3401	132	3	of	of	ADP
ejpam-3401	132	4	b	b	NOUN
ejpam-3401	132	5	-	-	PUNCT
ejpam-3401	132	6	open	open	ADJ
ejpam-3401	132	7	sets	set	NOUN
ejpam-3401	132	8	lemma	lemma	PROPN
ejpam-3401	132	9	1	1	X
ejpam-3401	132	10	.	.	PUNCT
ejpam-3401	133	1	let	let	AUX
ejpam-3401	133	2	(	(	PUNCT
ejpam-3401	133	3	x	x	NOUN
ejpam-3401	133	4	,	,	PUNCT
ejpam-3401	133	5	τ	τ	PROPN
ejpam-3401	133	6	,	,	PUNCT
ejpam-3401	133	7	t1	t1	NOUN
ejpam-3401	133	8	,	,	PUNCT
ejpam-3401	133	9	t2	t2	NOUN
ejpam-3401	133	10	)	)	PUNCT
ejpam-3401	133	11	be	be	AUX
ejpam-3401	133	12	a	a	DET
ejpam-3401	133	13	bi	bi	ADJ
ejpam-3401	133	14	-	-	ADJ
ejpam-3401	133	15	operator	operator	NOUN
ejpam-3401	133	16	topological	topological	ADJ
ejpam-3401	133	17	space	space	NOUN
ejpam-3401	133	18	given	give	VERB
ejpam-3401	133	19	by	by	ADP
ejpam-3401	133	20	t1(s	t1(s	PROPN
ejpam-3401	133	21	)	)	PUNCT
ejpam-3401	133	22	=	=	SYM
ejpam-3401	133	23	int(cl(s	int(cl(s	PROPN
ejpam-3401	133	24	)	)	PUNCT
ejpam-3401	133	25	)	)	PUNCT
ejpam-3401	133	26	,	,	PUNCT
ejpam-3401	133	27	t2(s	t2(s	NOUN
ejpam-3401	133	28	)	)	PUNCT
ejpam-3401	133	29	=	=	SYM
ejpam-3401	133	30	cl(int(s	cl(int(s	NOUN
ejpam-3401	133	31	)	)	PUNCT
ejpam-3401	133	32	)	)	PUNCT
ejpam-3401	133	33	.	.	PUNCT
ejpam-3401	134	1	then	then	ADV
ejpam-3401	134	2	(	(	PUNCT
ejpam-3401	134	3	i	i	NOUN
ejpam-3401	134	4	)	)	PUNCT
ejpam-3401	134	5	bint(s	bint(s	PROPN
ejpam-3401	134	6	)	)	PUNCT
ejpam-3401	134	7	=	=	SYM
ejpam-3401	134	8	sint(s	sint(s	NOUN
ejpam-3401	134	9	)	)	PUNCT
ejpam-3401	134	10	∪	∪	ADP
ejpam-3401	134	11	pint(s	pint(s	NOUN
ejpam-3401	134	12	)	)	PUNCT
ejpam-3401	134	13	.	.	PUNCT
ejpam-3401	135	1	(	(	PUNCT
ejpam-3401	135	2	ii	ii	X
ejpam-3401	135	3	)	)	PUNCT
ejpam-3401	135	4	bcl(s	bcl(s	PROPN
ejpam-3401	135	5	)	)	PUNCT
ejpam-3401	135	6	=	=	SYM
ejpam-3401	135	7	scl(s	scl(s	PROPN
ejpam-3401	135	8	)	)	PUNCT
ejpam-3401	135	9	∩	∩	NOUN
ejpam-3401	135	10	pcl(s	pcl(s	PROPN
ejpam-3401	135	11	)	)	PUNCT
ejpam-3401	135	12	.	.	PUNCT
ejpam-3401	136	1	proof	proof	NOUN
ejpam-3401	136	2	.	.	PUNCT
ejpam-3401	137	1	it	it	PRON
ejpam-3401	137	2	is	be	AUX
ejpam-3401	137	3	sufficient	sufficient	ADJ
ejpam-3401	137	4	to	to	PART
ejpam-3401	137	5	prove	prove	VERB
ejpam-3401	137	6	only	only	ADV
ejpam-3401	137	7	the	the	DET
ejpam-3401	137	8	first	first	ADJ
ejpam-3401	137	9	assertion	assertion	NOUN
ejpam-3401	137	10	.	.	PUNCT
ejpam-3401	138	1	as	as	SCONJ
ejpam-3401	138	2	we	we	PRON
ejpam-3401	138	3	have	have	AUX
ejpam-3401	138	4	stated	state	VERB
ejpam-3401	138	5	in	in	ADP
ejpam-3401	138	6	remark	remark	NOUN
ejpam-3401	138	7	2	2	NUM
ejpam-3401	138	8	(	(	PUNCT
ejpam-3401	138	9	iv	iv	X
ejpam-3401	138	10	)	)	PUNCT
ejpam-3401	138	11	that	that	DET
ejpam-3401	138	12	bint(s	bint(s	PROPN
ejpam-3401	138	13	)	)	PUNCT
ejpam-3401	138	14	is	be	AUX
ejpam-3401	138	15	the	the	DET
ejpam-3401	138	16	union	union	NOUN
ejpam-3401	138	17	of	of	ADP
ejpam-3401	138	18	all	all	DET
ejpam-3401	138	19	b	b	NOUN
ejpam-3401	138	20	-	-	PUNCT
ejpam-3401	138	21	open	open	ADJ
ejpam-3401	138	22	sets	set	NOUN
ejpam-3401	138	23	contained	contain	VERB
ejpam-3401	138	24	in	in	ADP
ejpam-3401	138	25	s	s	PROPN
ejpam-3401	138	26	,	,	PUNCT
ejpam-3401	138	27	therefore	therefore	ADV
ejpam-3401	138	28	bint(s	bint(s	PROPN
ejpam-3401	138	29	)	)	PUNCT
ejpam-3401	138	30	⊃	⊃	PROPN
ejpam-3401	138	31	cl(int(bint(s	cl(int(bint(s	PROPN
ejpam-3401	138	32	)	)	PUNCT
ejpam-3401	138	33	)	)	PUNCT
ejpam-3401	138	34	)	)	PUNCT
ejpam-3401	138	35	∪	∪	ADP
ejpam-3401	138	36	int(cl(bint(s	int(cl(bint(s	PRON
ejpam-3401	138	37	)	)	PUNCT
ejpam-3401	138	38	)	)	PUNCT
ejpam-3401	138	39	)	)	PUNCT
ejpam-3401	139	1	⊃	⊃	PROPN
ejpam-3401	139	2	cl(int(s	cl(int(s	PROPN
ejpam-3401	139	3	)	)	PUNCT
ejpam-3401	139	4	)	)	PUNCT
ejpam-3401	139	5	∪	∪	ADP
ejpam-3401	139	6	int(cl(s	int(cl(s	PROPN
ejpam-3401	139	7	)	)	PUNCT
ejpam-3401	139	8	)	)	PUNCT
ejpam-3401	139	9	)	)	PUNCT
ejpam-3401	139	10	.	.	PUNCT
ejpam-3401	140	1	thus	thus	ADV
ejpam-3401	140	2	,	,	PUNCT
ejpam-3401	140	3	with	with	ADP
ejpam-3401	140	4	the	the	DET
ejpam-3401	140	5	help	help	NOUN
ejpam-3401	140	6	of	of	ADP
ejpam-3401	140	7	proposition	proposition	NOUN
ejpam-3401	140	8	1	1	NUM
ejpam-3401	140	9	,	,	PUNCT
ejpam-3401	140	10	we	we	PRON
ejpam-3401	140	11	obtain	obtain	VERB
ejpam-3401	140	12	bint(s	bint(s	PROPN
ejpam-3401	140	13	)	)	PUNCT
ejpam-3401	140	14	=	=	SYM
ejpam-3401	140	15	s	s	PART
ejpam-3401	140	16	∩	∩	ADJ
ejpam-3401	140	17	[	[	X
ejpam-3401	140	18	cl(int(s	cl(int(s	NOUN
ejpam-3401	140	19	)	)	PUNCT
ejpam-3401	140	20	)	)	PUNCT
ejpam-3401	140	21	∪	∪	ADP
ejpam-3401	140	22	int(cl(s	int(cl(s	PROPN
ejpam-3401	140	23	)	)	PUNCT
ejpam-3401	140	24	)	)	PUNCT
ejpam-3401	140	25	]	]	PUNCT
ejpam-3401	141	1	=	=	PUNCT
ejpam-3401	142	1	[	[	X
ejpam-3401	142	2	s	s	X
ejpam-3401	142	3	∩	∩	ADJ
ejpam-3401	142	4	cl(int(s	cl(int(s	NOUN
ejpam-3401	142	5	)	)	PUNCT
ejpam-3401	142	6	)	)	PUNCT
ejpam-3401	142	7	]	]	PUNCT
ejpam-3401	143	1	∪	∪	ADP
ejpam-3401	143	2	[	[	X
ejpam-3401	143	3	s	s	X
ejpam-3401	143	4	∩	∩	ADJ
ejpam-3401	143	5	int(cl(s	int(cl(s	PROPN
ejpam-3401	143	6	)	)	PUNCT
ejpam-3401	143	7	)	)	PUNCT
ejpam-3401	143	8	]	]	PUNCT
ejpam-3401	143	9	=	=	PUNCT
ejpam-3401	143	10	sint(s	sint(s	NOUN
ejpam-3401	143	11	)	)	PUNCT
ejpam-3401	143	12	∪	∪	ADP
ejpam-3401	143	13	pint(s	pint(s	NOUN
ejpam-3401	143	14	)	)	PUNCT
ejpam-3401	143	15	.	.	PUNCT
ejpam-3401	144	1	the	the	DET
ejpam-3401	144	2	opposite	opposite	ADJ
ejpam-3401	144	3	direction	direction	NOUN
ejpam-3401	144	4	is	be	AUX
ejpam-3401	144	5	evident	evident	ADJ
ejpam-3401	144	6	.	.	PUNCT
ejpam-3401	145	1	one	one	PRON
ejpam-3401	145	2	can	can	AUX
ejpam-3401	145	3	prove	prove	VERB
ejpam-3401	145	4	the	the	DET
ejpam-3401	145	5	second	second	ADJ
ejpam-3401	145	6	statement	statement	NOUN
ejpam-3401	145	7	in	in	ADP
ejpam-3401	145	8	a	a	DET
ejpam-3401	145	9	similar	similar	ADJ
ejpam-3401	145	10	way	way	NOUN
ejpam-3401	145	11	.	.	PUNCT
ejpam-3401	146	1	lemma	lemma	PROPN
ejpam-3401	146	2	2	2	X
ejpam-3401	146	3	.	.	PUNCT
ejpam-3401	147	1	let	let	AUX
ejpam-3401	147	2	(	(	PUNCT
ejpam-3401	147	3	x	x	NOUN
ejpam-3401	147	4	,	,	PUNCT
ejpam-3401	147	5	τ	τ	PROPN
ejpam-3401	147	6	,	,	PUNCT
ejpam-3401	147	7	t1	t1	NOUN
ejpam-3401	147	8	,	,	PUNCT
ejpam-3401	147	9	t2	t2	NOUN
ejpam-3401	147	10	)	)	PUNCT
ejpam-3401	147	11	be	be	AUX
ejpam-3401	147	12	a	a	DET
ejpam-3401	147	13	bi	bi	ADJ
ejpam-3401	147	14	-	-	ADJ
ejpam-3401	147	15	operator	operator	NOUN
ejpam-3401	147	16	topological	topological	ADJ
ejpam-3401	147	17	space	space	NOUN
ejpam-3401	147	18	,	,	PUNCT
ejpam-3401	147	19	suppose	suppose	VERB
ejpam-3401	147	20	that	that	SCONJ
ejpam-3401	147	21	t1(w	t1(w	ADP
ejpam-3401	147	22	∩	∩	ADJ
ejpam-3401	147	23	z	z	NOUN
ejpam-3401	147	24	)	)	PUNCT
ejpam-3401	147	25	=	=	SYM
ejpam-3401	147	26	t1(w	t1(w	X
ejpam-3401	147	27	)	)	PUNCT
ejpam-3401	147	28	∩	∩	NOUN
ejpam-3401	147	29	t1(z	t1(z	NUM
ejpam-3401	147	30	)	)	PUNCT
ejpam-3401	147	31	and	and	CCONJ
ejpam-3401	147	32	t2(w	t2(w	X
ejpam-3401	147	33	∩	∩	ADJ
ejpam-3401	147	34	z	z	X
ejpam-3401	147	35	)	)	PUNCT
ejpam-3401	147	36	=	=	SYM
ejpam-3401	147	37	t2(w	t2(w	NUM
ejpam-3401	147	38	)	)	PUNCT
ejpam-3401	147	39	∩	∩	NOUN
ejpam-3401	147	40	t2(z	t2(z	NOUN
ejpam-3401	147	41	)	)	PUNCT
ejpam-3401	147	42	,	,	PUNCT
ejpam-3401	147	43	for	for	ADP
ejpam-3401	147	44	all	all	DET
ejpam-3401	147	45	w	w	PROPN
ejpam-3401	147	46	∈	∈	PROPN
ejpam-3401	147	47	τ	τ	NOUN
ejpam-3401	147	48	,	,	PUNCT
ejpam-3401	147	49	z	z	PROPN
ejpam-3401	147	50	⊆	⊆	NUM
ejpam-3401	147	51	x	x	X
ejpam-3401	147	52	then	then	ADV
ejpam-3401	147	53	the	the	DET
ejpam-3401	147	54	following	follow	VERB
ejpam-3401	147	55	assertions	assertion	NOUN
ejpam-3401	147	56	are	be	AUX
ejpam-3401	147	57	satisfied	satisfied	ADJ
ejpam-3401	147	58	:	:	PUNCT
ejpam-3401	147	59	(	(	PUNCT
ejpam-3401	147	60	i	i	NOUN
ejpam-3401	147	61	)	)	PUNCT
ejpam-3401	147	62	the	the	DET
ejpam-3401	147	63	intersection	intersection	NOUN
ejpam-3401	147	64	of	of	ADP
ejpam-3401	147	65	an	an	DET
ejpam-3401	147	66	open	open	ADJ
ejpam-3401	147	67	set	set	NOUN
ejpam-3401	147	68	with	with	ADP
ejpam-3401	147	69	a	a	DET
ejpam-3401	147	70	b	b	NOUN
ejpam-3401	147	71	-	-	PUNCT
ejpam-3401	147	72	open	open	ADJ
ejpam-3401	147	73	set	set	NOUN
ejpam-3401	147	74	is	be	AUX
ejpam-3401	147	75	a	a	DET
ejpam-3401	147	76	b	b	NOUN
ejpam-3401	147	77	-	-	PUNCT
ejpam-3401	147	78	open	open	ADJ
ejpam-3401	147	79	set	set	NOUN
ejpam-3401	147	80	.	.	PUNCT
ejpam-3401	148	1	(	(	PUNCT
ejpam-3401	148	2	ii	ii	NOUN
ejpam-3401	148	3	)	)	PUNCT
ejpam-3401	148	4	the	the	DET
ejpam-3401	148	5	union	union	NOUN
ejpam-3401	148	6	of	of	ADP
ejpam-3401	148	7	any	any	DET
ejpam-3401	148	8	family	family	NOUN
ejpam-3401	148	9	of	of	ADP
ejpam-3401	148	10	b	b	NOUN
ejpam-3401	148	11	-	-	PUNCT
ejpam-3401	148	12	open	open	ADJ
ejpam-3401	148	13	sets	set	NOUN
ejpam-3401	148	14	is	be	AUX
ejpam-3401	148	15	a	a	DET
ejpam-3401	148	16	b	b	NOUN
ejpam-3401	148	17	-	-	PUNCT
ejpam-3401	148	18	open	open	ADJ
ejpam-3401	148	19	set	set	NOUN
ejpam-3401	148	20	.	.	PUNCT
ejpam-3401	149	1	proof	proof	NOUN
ejpam-3401	149	2	.	.	PUNCT
ejpam-3401	150	1	(	(	PUNCT
ejpam-3401	150	2	i	i	NOUN
ejpam-3401	150	3	)	)	PUNCT
ejpam-3401	150	4	assume	assume	VERB
ejpam-3401	150	5	that	that	SCONJ
ejpam-3401	150	6	there	there	PRON
ejpam-3401	150	7	exists	exist	VERB
ejpam-3401	150	8	u	u	PROPN
ejpam-3401	150	9	∈	∈	PROPN
ejpam-3401	150	10	τ	τ	X
ejpam-3401	150	11	,	,	PUNCT
ejpam-3401	150	12	which	which	PRON
ejpam-3401	150	13	is	be	AUX
ejpam-3401	150	14	an	an	DET
ejpam-3401	150	15	open	open	ADJ
ejpam-3401	150	16	set	set	NOUN
ejpam-3401	150	17	,	,	PUNCT
ejpam-3401	150	18	and	and	CCONJ
ejpam-3401	150	19	v	v	NOUN
ejpam-3401	150	20	is	be	AUX
ejpam-3401	150	21	a	a	DET
ejpam-3401	150	22	b	b	NOUN
ejpam-3401	150	23	-	-	PUNCT
ejpam-3401	150	24	open	open	ADJ
ejpam-3401	150	25	set	set	NOUN
ejpam-3401	150	26	.	.	PUNCT
ejpam-3401	151	1	we	we	PRON
ejpam-3401	151	2	are	be	AUX
ejpam-3401	151	3	going	go	VERB
ejpam-3401	151	4	to	to	PART
ejpam-3401	151	5	show	show	VERB
ejpam-3401	151	6	that	that	SCONJ
ejpam-3401	151	7	u	u	PROPN
ejpam-3401	151	8	∩	∩	NOUN
ejpam-3401	151	9	v	v	NOUN
ejpam-3401	151	10	is	be	AUX
ejpam-3401	151	11	also	also	ADV
ejpam-3401	151	12	a	a	DET
ejpam-3401	151	13	b	b	NOUN
ejpam-3401	151	14	-	-	PUNCT
ejpam-3401	151	15	open	open	ADJ
ejpam-3401	151	16	set	set	NOUN
ejpam-3401	151	17	.	.	PUNCT
ejpam-3401	152	1	since	since	SCONJ
ejpam-3401	152	2	u	u	NOUN
ejpam-3401	152	3	is	be	AUX
ejpam-3401	152	4	open	open	ADJ
ejpam-3401	152	5	,	,	PUNCT
ejpam-3401	152	6	then	then	ADV
ejpam-3401	152	7	u	u	NOUN
ejpam-3401	152	8	⊆	⊆	NUM
ejpam-3401	152	9	t1(u	t1(u	NUM
ejpam-3401	152	10	)	)	PUNCT
ejpam-3401	152	11	,	,	PUNCT
ejpam-3401	152	12	u	u	NOUN
ejpam-3401	152	13	⊆	⊆	NUM
ejpam-3401	152	14	t2(u	t2(u	PROPN
ejpam-3401	152	15	.	.	NOUN
ejpam-3401	152	16	by	by	ADP
ejpam-3401	152	17	the	the	DET
ejpam-3401	152	18	definition	definition	NOUN
ejpam-3401	152	19	of	of	ADP
ejpam-3401	152	20	the	the	DET
ejpam-3401	152	21	b	b	NOUN
ejpam-3401	152	22	-	-	PUNCT
ejpam-3401	152	23	open	open	ADJ
ejpam-3401	152	24	set	set	NOUN
ejpam-3401	152	25	:	:	PUNCT
ejpam-3401	152	26	v	v	ADP
ejpam-3401	152	27	⊆	⊆	NUM
ejpam-3401	152	28	t1(v	t1(v	NOUN
ejpam-3401	152	29	)	)	PUNCT
ejpam-3401	152	30	∪	∪	ADP
ejpam-3401	152	31	t2(v	t2(v	PRON
ejpam-3401	152	32	)	)	PUNCT
ejpam-3401	152	33	.	.	PUNCT
ejpam-3401	153	1	now	now	ADV
ejpam-3401	153	2	,	,	PUNCT
ejpam-3401	153	3	u	u	PROPN
ejpam-3401	153	4	∩	∩	NOUN
ejpam-3401	153	5	v	v	ADP
ejpam-3401	153	6	⊆	⊆	NUM
ejpam-3401	153	7	u	u	NOUN
ejpam-3401	153	8	∩	∩	NOUN
ejpam-3401	153	9	[	[	X
ejpam-3401	153	10	t1(v	t1(v	X
ejpam-3401	153	11	)	)	PUNCT
ejpam-3401	153	12	∪	∪	ADP
ejpam-3401	153	13	t2(v	t2(v	PROPN
ejpam-3401	153	14	)	)	PUNCT
ejpam-3401	153	15	]	]	PUNCT
ejpam-3401	153	16	l.	l.	PROPN
ejpam-3401	153	17	m.	m.	PROPN
ejpam-3401	153	18	alabdulsada	alabdulsada	PROPN
ejpam-3401	153	19	/	/	SYM
ejpam-3401	153	20	eur	eur	PROPN
ejpam-3401	153	21	.	.	PUNCT
ejpam-3401	154	1	j.	j.	PROPN
ejpam-3401	154	2	pure	pure	PROPN
ejpam-3401	154	3	appl	appl	PROPN
ejpam-3401	154	4	.	.	PROPN
ejpam-3401	154	5	math	math	PROPN
ejpam-3401	154	6	,	,	PUNCT
ejpam-3401	154	7	12	12	NUM
ejpam-3401	154	8	(	(	PUNCT
ejpam-3401	154	9	2	2	NUM
ejpam-3401	154	10	)	)	PUNCT
ejpam-3401	154	11	(	(	PUNCT
ejpam-3401	154	12	2019	2019	NUM
ejpam-3401	154	13	)	)	PUNCT
ejpam-3401	154	14	,	,	PUNCT
ejpam-3401	154	15	358	358	NUM
ejpam-3401	154	16	-	-	SYM
ejpam-3401	154	17	369	369	NUM
ejpam-3401	154	18	364	364	NUM
ejpam-3401	154	19	=	=	SYM
ejpam-3401	155	1	[	[	X
ejpam-3401	155	2	u	u	NOUN
ejpam-3401	155	3	∩	∩	X
ejpam-3401	155	4	t1(v	t1(v	NOUN
ejpam-3401	155	5	)	)	PUNCT
ejpam-3401	155	6	]	]	PUNCT
ejpam-3401	155	7	∪	∪	PUNCT
ejpam-3401	155	8	[	[	X
ejpam-3401	155	9	u	u	NOUN
ejpam-3401	155	10	∩	∩	NOUN
ejpam-3401	155	11	t2(v	t2(v	X
ejpam-3401	155	12	)	)	PUNCT
ejpam-3401	155	13	]	]	PUNCT
ejpam-3401	156	1	⊆	⊆	NUM
ejpam-3401	156	2	[	[	X
ejpam-3401	156	3	t1(u	t1(u	NOUN
ejpam-3401	156	4	)	)	PUNCT
ejpam-3401	156	5	∩	∩	NOUN
ejpam-3401	156	6	t1(v	t1(v	NOUN
ejpam-3401	156	7	)	)	PUNCT
ejpam-3401	156	8	]	]	PUNCT
ejpam-3401	156	9	∪	∪	ADP
ejpam-3401	156	10	[	[	X
ejpam-3401	156	11	t2(u	t2(u	ADJ
ejpam-3401	156	12	)	)	PUNCT
ejpam-3401	156	13	∩	∩	NOUN
ejpam-3401	156	14	t2(v	t2(v	PRON
ejpam-3401	156	15	)	)	PUNCT
ejpam-3401	156	16	]	]	PUNCT
ejpam-3401	157	1	=	=	PUNCT
ejpam-3401	158	1	[	[	X
ejpam-3401	158	2	t1(u	t1(u	X
ejpam-3401	158	3	∩	∩	ADJ
ejpam-3401	158	4	v	v	NOUN
ejpam-3401	158	5	)	)	PUNCT
ejpam-3401	158	6	]	]	PUNCT
ejpam-3401	158	7	∪	∪	PUNCT
ejpam-3401	158	8	[	[	X
ejpam-3401	158	9	t2(u	t2(u	X
ejpam-3401	158	10	∩	∩	NOUN
ejpam-3401	158	11	v	v	NOUN
ejpam-3401	158	12	)	)	PUNCT
ejpam-3401	158	13	]	]	PUNCT
ejpam-3401	158	14	,	,	PUNCT
ejpam-3401	158	15	as	as	SCONJ
ejpam-3401	158	16	wanted	want	VERB
ejpam-3401	158	17	to	to	PART
ejpam-3401	158	18	be	be	AUX
ejpam-3401	158	19	shown	show	VERB
ejpam-3401	158	20	.	.	PUNCT
ejpam-3401	159	1	(	(	PUNCT
ejpam-3401	159	2	ii	ii	NOUN
ejpam-3401	159	3	)	)	PUNCT
ejpam-3401	159	4	suppose	suppose	VERB
ejpam-3401	159	5	that	that	SCONJ
ejpam-3401	159	6	f	f	PROPN
ejpam-3401	159	7	=	=	X
ejpam-3401	159	8	{	{	PUNCT
ejpam-3401	159	9	va|	va|	NOUN
ejpam-3401	159	10	a	a	PRON
ejpam-3401	159	11	∈	∈	PROPN
ejpam-3401	159	12	λ	λ	PROPN
ejpam-3401	159	13	}	}	PUNCT
ejpam-3401	159	14	is	be	AUX
ejpam-3401	159	15	a	a	DET
ejpam-3401	159	16	family	family	NOUN
ejpam-3401	159	17	of	of	ADP
ejpam-3401	159	18	b	b	NOUN
ejpam-3401	159	19	-	-	PUNCT
ejpam-3401	159	20	open	open	ADJ
ejpam-3401	159	21	set	set	NOUN
ejpam-3401	159	22	,	,	PUNCT
ejpam-3401	159	23	va	va	PROPN
ejpam-3401	159	24	⊆	⊆	NUM
ejpam-3401	159	25	t1(va	t1(va	NUM
ejpam-3401	159	26	)	)	PUNCT
ejpam-3401	159	27	∪	∪	ADP
ejpam-3401	159	28	t2(va	t2(va	PROPN
ejpam-3401	159	29	)	)	PUNCT
ejpam-3401	159	30	.	.	PUNCT
ejpam-3401	160	1	then	then	ADV
ejpam-3401	160	2	we	we	PRON
ejpam-3401	160	3	have	have	VERB
ejpam-3401	160	4	,	,	PUNCT
ejpam-3401	160	5	⋃	⋃	ADP
ejpam-3401	160	6	a	a	DET
ejpam-3401	160	7	va	va	NOUN
ejpam-3401	160	8	⊆	⊆	NUM
ejpam-3401	160	9	⋃	⋃	NOUN
ejpam-3401	160	10	a	a	DET
ejpam-3401	160	11	(	(	PUNCT
ejpam-3401	160	12	t1(va	t1(va	NUM
ejpam-3401	160	13	)	)	PUNCT
ejpam-3401	160	14	∪	∪	ADP
ejpam-3401	160	15	t2(va	t2(va	PROPN
ejpam-3401	160	16	)	)	PUNCT
ejpam-3401	160	17	)	)	PUNCT
ejpam-3401	161	1	=	=	SYM
ejpam-3401	161	2	⋃	⋃	VERB
ejpam-3401	161	3	a	a	DET
ejpam-3401	161	4	t1(va	t1(va	NUM
ejpam-3401	161	5	)	)	PUNCT
ejpam-3401	161	6	∪	∪	NOUN
ejpam-3401	161	7	⋃	⋃	PROPN
ejpam-3401	161	8	a	a	DET
ejpam-3401	161	9	t2(va	t2(va	PROPN
ejpam-3401	161	10	)	)	PUNCT
ejpam-3401	161	11	.	.	PUNCT
ejpam-3401	162	1	it	it	PRON
ejpam-3401	162	2	is	be	AUX
ejpam-3401	162	3	clear	clear	ADJ
ejpam-3401	162	4	that	that	SCONJ
ejpam-3401	162	5	⋃	⋃	PUNCT
ejpam-3401	162	6	a	a	DET
ejpam-3401	162	7	t1(va	t1(va	NUM
ejpam-3401	162	8	)	)	PUNCT
ejpam-3401	162	9	=	=	SYM
ejpam-3401	162	10	t1	t1	PROPN
ejpam-3401	162	11	(	(	PUNCT
ejpam-3401	162	12	⋃	⋃	PROPN
ejpam-3401	162	13	a	a	DET
ejpam-3401	162	14	va	va	NOUN
ejpam-3401	162	15	)	)	PUNCT
ejpam-3401	162	16	and	and	CCONJ
ejpam-3401	162	17	⋃	⋃	ADP
ejpam-3401	162	18	a	a	DET
ejpam-3401	162	19	t2(va	t2(va	PROPN
ejpam-3401	162	20	)	)	PUNCT
ejpam-3401	162	21	=	=	SYM
ejpam-3401	162	22	t2	t2	NOUN
ejpam-3401	162	23	(	(	PUNCT
ejpam-3401	162	24	⋃	⋃	PROPN
ejpam-3401	162	25	a	a	DET
ejpam-3401	162	26	va	va	NOUN
ejpam-3401	162	27	)	)	PUNCT
ejpam-3401	162	28	,	,	PUNCT
ejpam-3401	162	29	therefore⋃	therefore⋃	VERB
ejpam-3401	162	30	a	a	DET
ejpam-3401	162	31	va	va	NOUN
ejpam-3401	162	32	⊆	⊆	NUM
ejpam-3401	162	33	t1	t1	PROPN
ejpam-3401	162	34	(	(	PUNCT
ejpam-3401	162	35	⋃	⋃	PROPN
ejpam-3401	162	36	a	a	DET
ejpam-3401	162	37	va	va	NOUN
ejpam-3401	162	38	)	)	PUNCT
ejpam-3401	162	39	∪	∪	NOUN
ejpam-3401	162	40	t2	t2	NOUN
ejpam-3401	162	41	(	(	PUNCT
ejpam-3401	162	42	⋃	⋃	NOUN
ejpam-3401	162	43	a	a	DET
ejpam-3401	162	44	va	va	NOUN
ejpam-3401	162	45	)	)	PUNCT
ejpam-3401	162	46	.	.	PUNCT
ejpam-3401	163	1	thus	thus	ADV
ejpam-3401	163	2	,	,	PUNCT
ejpam-3401	163	3	⋃	⋃	SCONJ
ejpam-3401	163	4	a	a	DET
ejpam-3401	163	5	va	va	PROPN
ejpam-3401	163	6	is	be	AUX
ejpam-3401	163	7	a	a	DET
ejpam-3401	163	8	b	b	NOUN
ejpam-3401	163	9	-	-	PUNCT
ejpam-3401	163	10	open	open	ADJ
ejpam-3401	163	11	set	set	NOUN
ejpam-3401	163	12	,	,	PUNCT
ejpam-3401	163	13	which	which	PRON
ejpam-3401	163	14	completes	complete	VERB
ejpam-3401	163	15	the	the	DET
ejpam-3401	163	16	proof	proof	NOUN
ejpam-3401	163	17	.	.	PUNCT
ejpam-3401	164	1	proposition	proposition	NOUN
ejpam-3401	164	2	2	2	NUM
ejpam-3401	164	3	.	.	PUNCT
ejpam-3401	165	1	let	let	AUX
ejpam-3401	165	2	(	(	PUNCT
ejpam-3401	165	3	x	x	NOUN
ejpam-3401	165	4	,	,	PUNCT
ejpam-3401	165	5	τ	τ	PROPN
ejpam-3401	165	6	,	,	PUNCT
ejpam-3401	165	7	t1	t1	NOUN
ejpam-3401	165	8	,	,	PUNCT
ejpam-3401	165	9	t2	t2	NOUN
ejpam-3401	165	10	)	)	PUNCT
ejpam-3401	165	11	be	be	AUX
ejpam-3401	165	12	a	a	DET
ejpam-3401	165	13	bi	bi	ADJ
ejpam-3401	165	14	-	-	ADJ
ejpam-3401	165	15	operator	operator	NOUN
ejpam-3401	165	16	topological	topological	ADJ
ejpam-3401	165	17	space	space	NOUN
ejpam-3401	165	18	.	.	PUNCT
ejpam-3401	166	1	if	if	SCONJ
ejpam-3401	166	2	the	the	DET
ejpam-3401	166	3	function	function	NOUN
ejpam-3401	166	4	f	f	X
ejpam-3401	166	5	:	:	PUNCT
ejpam-3401	166	6	(	(	PUNCT
ejpam-3401	166	7	x	x	X
ejpam-3401	166	8	,	,	PUNCT
ejpam-3401	166	9	τ	τ	PROPN
ejpam-3401	166	10	,	,	PUNCT
ejpam-3401	166	11	t1	t1	PROPN
ejpam-3401	166	12	,	,	PUNCT
ejpam-3401	166	13	t2)→	t2)→	X
ejpam-3401	166	14	(	(	PUNCT
ejpam-3401	166	15	y	y	PROPN
ejpam-3401	166	16	,	,	PUNCT
ejpam-3401	166	17	σ	σ	PROPN
ejpam-3401	166	18	)	)	PUNCT
ejpam-3401	166	19	has	have	VERB
ejpam-3401	166	20	a	a	DET
ejpam-3401	166	21	contra	contra	PROPN
ejpam-3401	166	22	-	-	PUNCT
ejpam-3401	166	23	b	b	NOUN
ejpam-3401	166	24	-	-	PUNCT
ejpam-3401	166	25	closed	closed	ADJ
ejpam-3401	166	26	graph	graph	NOUN
ejpam-3401	166	27	,	,	PUNCT
ejpam-3401	166	28	then	then	ADV
ejpam-3401	166	29	the	the	DET
ejpam-3401	166	30	inverse	inverse	ADJ
ejpam-3401	166	31	image	image	NOUN
ejpam-3401	166	32	of	of	ADP
ejpam-3401	166	33	a	a	DET
ejpam-3401	166	34	contracompact	contracompact	NOUN
ejpam-3401	166	35	set	set	NOUN
ejpam-3401	166	36	s	s	PRON
ejpam-3401	166	37	of	of	ADP
ejpam-3401	166	38	y	y	PROPN
ejpam-3401	166	39	is	be	AUX
ejpam-3401	166	40	b	b	NOUN
ejpam-3401	166	41	-	-	PUNCT
ejpam-3401	166	42	closed	closed	ADJ
ejpam-3401	166	43	in	in	ADP
ejpam-3401	166	44	x.	x.	NOUN
ejpam-3401	166	45	proof	proof	NOUN
ejpam-3401	166	46	.	.	PUNCT
ejpam-3401	167	1	assume	assume	VERB
ejpam-3401	167	2	that	that	SCONJ
ejpam-3401	167	3	s	s	VERB
ejpam-3401	167	4	is	be	AUX
ejpam-3401	167	5	a	a	DET
ejpam-3401	167	6	contra	contra	ADJ
ejpam-3401	167	7	-	-	ADJ
ejpam-3401	167	8	compact	compact	ADJ
ejpam-3401	167	9	set	set	NOUN
ejpam-3401	167	10	of	of	ADP
ejpam-3401	167	11	y	y	PROPN
ejpam-3401	167	12	and	and	CCONJ
ejpam-3401	167	13	x	x	PROPN
ejpam-3401	167	14	/∈	/∈	PROPN
ejpam-3401	167	15	f−1(s	f−1(s	PROPN
ejpam-3401	167	16	)	)	PUNCT
ejpam-3401	167	17	,	,	PUNCT
ejpam-3401	167	18	i.e.	i.e.	X
ejpam-3401	167	19	for	for	ADP
ejpam-3401	167	20	all	all	DET
ejpam-3401	167	21	a	a	DET
ejpam-3401	167	22	∈	∈	ADJ
ejpam-3401	167	23	s	s	NOUN
ejpam-3401	167	24	,	,	PUNCT
ejpam-3401	167	25	(	(	PUNCT
ejpam-3401	167	26	x	x	X
ejpam-3401	167	27	,	,	PUNCT
ejpam-3401	167	28	a	a	PRON
ejpam-3401	167	29	)	)	PUNCT
ejpam-3401	167	30	/∈	/∈	PUNCT
ejpam-3401	168	1	g(f	g(f	PROPN
ejpam-3401	168	2	)	)	PUNCT
ejpam-3401	168	3	.	.	PUNCT
ejpam-3401	169	1	then	then	ADV
ejpam-3401	169	2	there	there	PRON
ejpam-3401	169	3	exist	exist	VERB
ejpam-3401	169	4	ua	ua	PRON
ejpam-3401	169	5	which	which	PRON
ejpam-3401	169	6	is	be	AUX
ejpam-3401	169	7	b	b	NOUN
ejpam-3401	169	8	-	-	PUNCT
ejpam-3401	169	9	closed	closed	ADJ
ejpam-3401	169	10	containing	contain	VERB
ejpam-3401	169	11	x	x	PROPN
ejpam-3401	169	12	and	and	CCONJ
ejpam-3401	169	13	va	va	NOUN
ejpam-3401	169	14	which	which	PRON
ejpam-3401	169	15	is	be	AUX
ejpam-3401	169	16	closed	close	VERB
ejpam-3401	169	17	in	in	ADP
ejpam-3401	169	18	y	y	NOUN
ejpam-3401	169	19	containing	contain	VERB
ejpam-3401	169	20	a	a	DET
ejpam-3401	169	21	such	such	ADJ
ejpam-3401	169	22	that	that	SCONJ
ejpam-3401	169	23	f(ua	f(ua	NOUN
ejpam-3401	169	24	)	)	PUNCT
ejpam-3401	169	25	∩	∩	PROPN
ejpam-3401	169	26	va	va	NOUN
ejpam-3401	169	27	=	=	PUNCT
ejpam-3401	169	28	∅.	∅.	X
ejpam-3401	169	29	on	on	ADP
ejpam-3401	169	30	the	the	DET
ejpam-3401	169	31	other	other	ADJ
ejpam-3401	169	32	hand	hand	NOUN
ejpam-3401	169	33	one	one	NUM
ejpam-3401	169	34	can	can	AUX
ejpam-3401	169	35	consider	consider	VERB
ejpam-3401	169	36	f	f	NOUN
ejpam-3401	169	37	=	=	PRON
ejpam-3401	169	38	{	{	PUNCT
ejpam-3401	169	39	s	s	NOUN
ejpam-3401	169	40	∩	∩	X
ejpam-3401	169	41	va|	va|	NUM
ejpam-3401	169	42	a	a	DET
ejpam-3401	169	43	∈	∈	PROPN
ejpam-3401	169	44	s	s	PART
ejpam-3401	169	45	}	}	PUNCT
ejpam-3401	169	46	and	and	CCONJ
ejpam-3401	169	47	f	f	PROPN
ejpam-3401	169	48	is	be	AUX
ejpam-3401	169	49	closed	close	VERB
ejpam-3401	169	50	cover	cover	NOUN
ejpam-3401	169	51	of	of	ADP
ejpam-3401	169	52	the	the	DET
ejpam-3401	169	53	subspace	subspace	NOUN
ejpam-3401	169	54	s.	s.	PROPN
ejpam-3401	169	55	we	we	PRON
ejpam-3401	169	56	have	have	VERB
ejpam-3401	169	57	that	that	DET
ejpam-3401	169	58	s	s	NOUN
ejpam-3401	169	59	is	be	AUX
ejpam-3401	169	60	contra	contra	ADJ
ejpam-3401	169	61	-	-	ADJ
ejpam-3401	169	62	compact	compact	ADJ
ejpam-3401	169	63	,	,	PUNCT
ejpam-3401	169	64	then	then	ADV
ejpam-3401	169	65	there	there	PRON
ejpam-3401	169	66	exists	exist	VERB
ejpam-3401	169	67	a1	a1	PROPN
ejpam-3401	169	68	,	,	PUNCT
ejpam-3401	169	69	a2	a2	PROPN
ejpam-3401	169	70	,	,	PUNCT
ejpam-3401	169	71	...	...	PUNCT
ejpam-3401	169	72	,	,	PUNCT
ejpam-3401	169	73	an	an	DET
ejpam-3401	169	74	such	such	ADJ
ejpam-3401	169	75	that	that	PRON
ejpam-3401	169	76	s	s	ADV
ejpam-3401	169	77	⊆	⊆	NUM
ejpam-3401	169	78	∪ni=1vai	∪ni=1vai	NUM
ejpam-3401	169	79	.	.	PUNCT
ejpam-3401	170	1	now	now	ADV
ejpam-3401	170	2	,	,	PUNCT
ejpam-3401	170	3	if	if	SCONJ
ejpam-3401	170	4	u	u	NOUN
ejpam-3401	170	5	=	=	NOUN
ejpam-3401	170	6	∩ni=1uai	∩ni=1uai	X
ejpam-3401	170	7	,	,	PUNCT
ejpam-3401	170	8	then	then	ADV
ejpam-3401	170	9	u	u	NOUN
ejpam-3401	170	10	is	be	AUX
ejpam-3401	170	11	b	b	NOUN
ejpam-3401	170	12	-	-	PUNCT
ejpam-3401	170	13	closed	closed	ADJ
ejpam-3401	170	14	containing	contain	VERB
ejpam-3401	170	15	x	x	PROPN
ejpam-3401	170	16	and	and	CCONJ
ejpam-3401	170	17	f(u	f(u	PROPN
ejpam-3401	170	18	)	)	PUNCT
ejpam-3401	170	19	∩	∩	NOUN
ejpam-3401	170	20	s	s	PART
ejpam-3401	170	21	=	=	SYM
ejpam-3401	170	22	∅	∅	NOUN
ejpam-3401	170	23	,	,	PUNCT
ejpam-3401	170	24	therefore	therefore	ADV
ejpam-3401	170	25	u	u	PROPN
ejpam-3401	170	26	∩	∩	NOUN
ejpam-3401	170	27	f−1(s	f−1(s	PROPN
ejpam-3401	170	28	)	)	PUNCT
ejpam-3401	170	29	=	=	PUNCT
ejpam-3401	170	30	∅.	∅.	VERB
ejpam-3401	170	31	hence	hence	ADV
ejpam-3401	170	32	x	x	NOUN
ejpam-3401	170	33	/∈	/∈	PUNCT
ejpam-3401	170	34	bcl(f−1(s	bcl(f−1(	NOUN
ejpam-3401	170	35	)	)	PUNCT
ejpam-3401	170	36	)	)	PUNCT
ejpam-3401	170	37	,	,	PUNCT
ejpam-3401	170	38	this	this	PRON
ejpam-3401	170	39	shows	show	VERB
ejpam-3401	170	40	that	that	SCONJ
ejpam-3401	170	41	f−1(s	f−1(s	PROPN
ejpam-3401	170	42	)	)	PUNCT
ejpam-3401	170	43	is	be	AUX
ejpam-3401	170	44	b	b	NOUN
ejpam-3401	170	45	-	-	PUNCT
ejpam-3401	170	46	closed	closed	ADJ
ejpam-3401	170	47	.	.	PUNCT
ejpam-3401	171	1	proposition	proposition	NOUN
ejpam-3401	171	2	3	3	X
ejpam-3401	171	3	.	.	PUNCT
ejpam-3401	172	1	let	let	VERB
ejpam-3401	172	2	f	f	NOUN
ejpam-3401	172	3	:	:	PUNCT
ejpam-3401	172	4	(	(	PUNCT
ejpam-3401	172	5	x	x	X
ejpam-3401	172	6	,	,	PUNCT
ejpam-3401	172	7	τ	τ	PROPN
ejpam-3401	172	8	,	,	PUNCT
ejpam-3401	172	9	t1	t1	NOUN
ejpam-3401	172	10	,	,	PUNCT
ejpam-3401	172	11	t2	t2	NOUN
ejpam-3401	172	12	)	)	PUNCT
ejpam-3401	172	13	→	→	SYM
ejpam-3401	172	14	(	(	PUNCT
ejpam-3401	172	15	y	y	PROPN
ejpam-3401	172	16	,	,	PUNCT
ejpam-3401	172	17	σ	σ	PROPN
ejpam-3401	172	18	)	)	PUNCT
ejpam-3401	172	19	from	from	ADP
ejpam-3401	172	20	a	a	DET
ejpam-3401	172	21	bi	bi	ADJ
ejpam-3401	172	22	-	-	NOUN
ejpam-3401	172	23	operator	operator	NOUN
ejpam-3401	172	24	topological	topological	ADJ
ejpam-3401	172	25	space	space	NOUN
ejpam-3401	172	26	to	to	ADP
ejpam-3401	172	27	a	a	DET
ejpam-3401	172	28	contra	contra	ADJ
ejpam-3401	172	29	-	-	ADJ
ejpam-3401	172	30	compact	compact	ADJ
ejpam-3401	172	31	space	space	NOUN
ejpam-3401	172	32	which	which	PRON
ejpam-3401	172	33	has	have	VERB
ejpam-3401	172	34	a	a	DET
ejpam-3401	172	35	contra	contra	PROPN
ejpam-3401	172	36	-	-	PUNCT
ejpam-3401	172	37	b	b	NOUN
ejpam-3401	172	38	-	-	PUNCT
ejpam-3401	172	39	closed	closed	ADJ
ejpam-3401	172	40	graph	graph	NOUN
ejpam-3401	172	41	,	,	PUNCT
ejpam-3401	172	42	then	then	ADV
ejpam-3401	172	43	f	f	PROPN
ejpam-3401	172	44	is	be	AUX
ejpam-3401	172	45	a	a	DET
ejpam-3401	172	46	contra	contra	PROPN
ejpam-3401	172	47	-	-	PUNCT
ejpam-3401	172	48	b	b	ADJ
ejpam-3401	172	49	-	-	PUNCT
ejpam-3401	172	50	continuous	continuous	ADJ
ejpam-3401	172	51	function	function	NOUN
ejpam-3401	172	52	.	.	PUNCT
ejpam-3401	173	1	proof	proof	NOUN
ejpam-3401	173	2	.	.	PUNCT
ejpam-3401	174	1	let	let	VERB
ejpam-3401	174	2	f	f	PROPN
ejpam-3401	174	3	=	=	PRON
ejpam-3401	174	4	{	{	PUNCT
ejpam-3401	174	5	va|	va|	NOUN
ejpam-3401	174	6	a	a	DET
ejpam-3401	174	7	∈	∈	PROPN
ejpam-3401	174	8	λ	λ	NOUN
ejpam-3401	174	9	}	}	PUNCT
ejpam-3401	174	10	be	be	VERB
ejpam-3401	174	11	a	a	DET
ejpam-3401	174	12	cover	cover	NOUN
ejpam-3401	174	13	of	of	ADP
ejpam-3401	174	14	an	an	DET
ejpam-3401	174	15	open	open	ADJ
ejpam-3401	174	16	set	set	NOUN
ejpam-3401	174	17	u	u	PROPN
ejpam-3401	174	18	⊂	⊂	PROPN
ejpam-3401	174	19	y	y	PROPN
ejpam-3401	174	20	by	by	ADP
ejpam-3401	174	21	the	the	DET
ejpam-3401	174	22	closed	close	VERB
ejpam-3401	174	23	subsets	subset	NOUN
ejpam-3401	174	24	va	va	PROPN
ejpam-3401	174	25	of	of	ADP
ejpam-3401	174	26	u	u	PROPN
ejpam-3401	174	27	for	for	ADP
ejpam-3401	174	28	each	each	DET
ejpam-3401	174	29	a	a	DET
ejpam-3401	174	30	∈	∈	PROPN
ejpam-3401	174	31	λ	λ	NOUN
ejpam-3401	174	32	.	.	PUNCT
ejpam-3401	175	1	thus	thus	ADV
ejpam-3401	175	2	,	,	PUNCT
ejpam-3401	175	3	there	there	PRON
ejpam-3401	175	4	exists	exist	VERB
ejpam-3401	175	5	a	a	DET
ejpam-3401	175	6	closed	closed	ADJ
ejpam-3401	175	7	set	set	VERB
ejpam-3401	175	8	wa	wa	NOUN
ejpam-3401	175	9	of	of	ADP
ejpam-3401	175	10	y	y	PROPN
ejpam-3401	175	11	where	where	SCONJ
ejpam-3401	175	12	va	va	PROPN
ejpam-3401	175	13	=	=	PUNCT
ejpam-3401	175	14	wa	wa	PROPN
ejpam-3401	175	15	∩	∩	PROPN
ejpam-3401	175	16	u	u	PROPN
ejpam-3401	175	17	,	,	PUNCT
ejpam-3401	175	18	i.e.	i.e.	X
ejpam-3401	175	19	{	{	PUNCT
ejpam-3401	175	20	wa|	wa|	NOUN
ejpam-3401	175	21	a	a	DET
ejpam-3401	175	22	∈	∈	NOUN
ejpam-3401	175	23	λ}∪{u	λ}∪{u	X
ejpam-3401	176	1	c	c	AUX
ejpam-3401	176	2	}	}	PUNCT
ejpam-3401	176	3	is	be	AUX
ejpam-3401	176	4	a	a	DET
ejpam-3401	176	5	closed	closed	ADJ
ejpam-3401	176	6	cover	cover	NOUN
ejpam-3401	176	7	of	of	ADP
ejpam-3401	176	8	y	y	PROPN
ejpam-3401	176	9	.	.	PUNCT
ejpam-3401	177	1	but	but	CCONJ
ejpam-3401	177	2	y	y	PROPN
ejpam-3401	177	3	is	be	AUX
ejpam-3401	177	4	a	a	DET
ejpam-3401	177	5	contra	contra	ADJ
ejpam-3401	177	6	-	-	ADJ
ejpam-3401	177	7	compact	compact	ADJ
ejpam-3401	177	8	space	space	NOUN
ejpam-3401	177	9	,	,	PUNCT
ejpam-3401	177	10	namely	namely	ADV
ejpam-3401	177	11	,	,	PUNCT
ejpam-3401	177	12	there	there	PRON
ejpam-3401	177	13	exist	exist	VERB
ejpam-3401	177	14	a1	a1	NOUN
ejpam-3401	177	15	,	,	PUNCT
ejpam-3401	177	16	a2	a2	PROPN
ejpam-3401	177	17	,	,	PUNCT
ejpam-3401	177	18	...	...	PUNCT
ejpam-3401	177	19	,	,	PUNCT
ejpam-3401	177	20	an	an	DET
ejpam-3401	177	21	such	such	ADJ
ejpam-3401	177	22	that	that	DET
ejpam-3401	177	23	y	y	PROPN
ejpam-3401	177	24	=	=	PUNCT
ejpam-3401	177	25	∪ni=1wai	∪ni=1wai	NOUN
ejpam-3401	177	26	∪	∪	PROPN
ejpam-3401	177	27	u	u	PROPN
ejpam-3401	177	28	c.	c.	NOUN
ejpam-3401	177	29	hence	hence	ADV
ejpam-3401	177	30	u	u	PROPN
ejpam-3401	177	31	=	=	PUNCT
ejpam-3401	177	32	∪ni=1vai	∪ni=1vai	NUM
ejpam-3401	177	33	,	,	PUNCT
ejpam-3401	177	34	and	and	CCONJ
ejpam-3401	177	35	consequently	consequently	ADV
ejpam-3401	177	36	u	u	PROPN
ejpam-3401	177	37	l.	l.	PROPN
ejpam-3401	177	38	m.	m.	PROPN
ejpam-3401	177	39	alabdulsada	alabdulsada	PROPN
ejpam-3401	177	40	/	/	SYM
ejpam-3401	177	41	eur	eur	PROPN
ejpam-3401	177	42	.	.	PUNCT
ejpam-3401	178	1	j.	j.	PROPN
ejpam-3401	178	2	pure	pure	PROPN
ejpam-3401	178	3	appl	appl	PROPN
ejpam-3401	178	4	.	.	PROPN
ejpam-3401	178	5	math	math	PROPN
ejpam-3401	178	6	,	,	PUNCT
ejpam-3401	178	7	12	12	NUM
ejpam-3401	178	8	(	(	PUNCT
ejpam-3401	178	9	2	2	NUM
ejpam-3401	178	10	)	)	PUNCT
ejpam-3401	178	11	(	(	PUNCT
ejpam-3401	178	12	2019	2019	NUM
ejpam-3401	178	13	)	)	PUNCT
ejpam-3401	178	14	,	,	PUNCT
ejpam-3401	178	15	358	358	NUM
ejpam-3401	178	16	-	-	SYM
ejpam-3401	178	17	369	369	NUM
ejpam-3401	178	18	365	365	NUM
ejpam-3401	178	19	is	be	AUX
ejpam-3401	178	20	contra	contra	ADJ
ejpam-3401	178	21	-	-	ADJ
ejpam-3401	178	22	compact	compact	ADJ
ejpam-3401	178	23	.	.	PUNCT
ejpam-3401	179	1	from	from	ADP
ejpam-3401	179	2	previous	previous	ADJ
ejpam-3401	179	3	proposition	proposition	NOUN
ejpam-3401	179	4	f−1(u	f−1(u	NOUN
ejpam-3401	179	5	)	)	PUNCT
ejpam-3401	179	6	is	be	AUX
ejpam-3401	179	7	b	b	NOUN
ejpam-3401	179	8	-	-	PUNCT
ejpam-3401	179	9	closed	closed	ADJ
ejpam-3401	179	10	in	in	ADP
ejpam-3401	179	11	x	x	NOUN
ejpam-3401	179	12	,	,	PUNCT
ejpam-3401	179	13	thus	thus	ADV
ejpam-3401	179	14	f	f	PROPN
ejpam-3401	179	15	is	be	AUX
ejpam-3401	179	16	contrab	contrab	NOUN
ejpam-3401	179	17	-	-	PUNCT
ejpam-3401	179	18	continuous	continuous	ADJ
ejpam-3401	179	19	.	.	PUNCT
ejpam-3401	180	1	the	the	DET
ejpam-3401	180	2	proof	proof	NOUN
ejpam-3401	180	3	of	of	ADP
ejpam-3401	180	4	the	the	DET
ejpam-3401	180	5	next	next	ADJ
ejpam-3401	180	6	lemma	lemma	PROPN
ejpam-3401	180	7	is	be	AUX
ejpam-3401	180	8	immediate	immediate	ADJ
ejpam-3401	180	9	,	,	PUNCT
ejpam-3401	180	10	since	since	SCONJ
ejpam-3401	180	11	g	g	PROPN
ejpam-3401	180	12	is	be	AUX
ejpam-3401	180	13	contra	contra	PROPN
ejpam-3401	180	14	-	-	PUNCT
ejpam-3401	180	15	b	b	NOUN
ejpam-3401	180	16	-	-	PUNCT
ejpam-3401	180	17	continuous	continuous	ADJ
ejpam-3401	180	18	,	,	PUNCT
ejpam-3401	180	19	so	so	ADV
ejpam-3401	180	20	f−1(u	f−1(u	PROPN
ejpam-3401	180	21	)	)	PUNCT
ejpam-3401	180	22	=	=	PUNCT
ejpam-3401	181	1	g−1(x	g−1(x	NOUN
ejpam-3401	181	2	×	×	PROPN
ejpam-3401	181	3	u	u	NOUN
ejpam-3401	181	4	)	)	PUNCT
ejpam-3401	181	5	is	be	AUX
ejpam-3401	181	6	b	b	NOUN
ejpam-3401	181	7	-	-	PUNCT
ejpam-3401	181	8	closed	closed	ADJ
ejpam-3401	181	9	in	in	ADP
ejpam-3401	181	10	x	x	NOUN
ejpam-3401	181	11	,	,	PUNCT
ejpam-3401	181	12	then	then	ADV
ejpam-3401	181	13	f	f	PROPN
ejpam-3401	181	14	is	be	AUX
ejpam-3401	181	15	contra	contra	PROPN
ejpam-3401	181	16	-	-	PUNCT
ejpam-3401	181	17	b	b	NOUN
ejpam-3401	181	18	-	-	PUNCT
ejpam-3401	181	19	continuous	continuous	ADJ
ejpam-3401	181	20	.	.	PUNCT
ejpam-3401	182	1	lemma	lemma	PROPN
ejpam-3401	182	2	3	3	X
ejpam-3401	182	3	.	.	PUNCT
ejpam-3401	183	1	let	let	VERB
ejpam-3401	183	2	f	f	NOUN
ejpam-3401	183	3	:	:	PUNCT
ejpam-3401	183	4	(	(	PUNCT
ejpam-3401	183	5	x	x	X
ejpam-3401	183	6	,	,	PUNCT
ejpam-3401	183	7	τ	τ	PROPN
ejpam-3401	183	8	,	,	PUNCT
ejpam-3401	183	9	t1	t1	PROPN
ejpam-3401	183	10	,	,	PUNCT
ejpam-3401	183	11	t2)→	t2)→	X
ejpam-3401	183	12	(	(	PUNCT
ejpam-3401	183	13	y	y	PROPN
ejpam-3401	183	14	,	,	PUNCT
ejpam-3401	183	15	σ	σ	PROPN
ejpam-3401	183	16	)	)	PUNCT
ejpam-3401	183	17	be	be	AUX
ejpam-3401	183	18	a	a	DET
ejpam-3401	183	19	function	function	NOUN
ejpam-3401	183	20	and	and	CCONJ
ejpam-3401	183	21	g	g	NOUN
ejpam-3401	183	22	:	:	PUNCT
ejpam-3401	183	23	(	(	PUNCT
ejpam-3401	183	24	x	x	X
ejpam-3401	183	25	,	,	PUNCT
ejpam-3401	183	26	τ	τ	PROPN
ejpam-3401	183	27	,	,	PUNCT
ejpam-3401	183	28	t1	t1	NOUN
ejpam-3401	183	29	,	,	PUNCT
ejpam-3401	183	30	t2	t2	NOUN
ejpam-3401	183	31	)	)	PUNCT
ejpam-3401	183	32	→	→	SYM
ejpam-3401	183	33	(	(	PUNCT
ejpam-3401	183	34	x	x	SYM
ejpam-3401	183	35	×	×	PROPN
ejpam-3401	183	36	y	y	PROPN
ejpam-3401	183	37	)	)	PUNCT
ejpam-3401	183	38	be	be	AUX
ejpam-3401	183	39	a	a	DET
ejpam-3401	183	40	graph	graph	NOUN
ejpam-3401	183	41	function	function	NOUN
ejpam-3401	183	42	of	of	ADP
ejpam-3401	183	43	f	f	PROPN
ejpam-3401	183	44	defined	define	VERB
ejpam-3401	183	45	by	by	ADP
ejpam-3401	183	46	g(x	g(x	NOUN
ejpam-3401	183	47	)	)	PUNCT
ejpam-3401	184	1	=	=	SYM
ejpam-3401	184	2	(	(	PUNCT
ejpam-3401	184	3	x	x	X
ejpam-3401	184	4	,	,	PUNCT
ejpam-3401	184	5	f(x	f(x	PROPN
ejpam-3401	184	6	)	)	PUNCT
ejpam-3401	184	7	)	)	PUNCT
ejpam-3401	185	1	for	for	ADP
ejpam-3401	185	2	every	every	DET
ejpam-3401	185	3	x	x	SYM
ejpam-3401	185	4	∈	∈	PROPN
ejpam-3401	185	5	x.	x.	NOUN
ejpam-3401	185	6	if	if	SCONJ
ejpam-3401	185	7	g	g	PROPN
ejpam-3401	185	8	is	be	AUX
ejpam-3401	185	9	contra	contra	ADJ
ejpam-3401	185	10	-	-	ADJ
ejpam-3401	185	11	bcontinuous	bcontinuous	ADJ
ejpam-3401	185	12	then	then	ADV
ejpam-3401	185	13	f	f	PROPN
ejpam-3401	185	14	is	be	AUX
ejpam-3401	185	15	contra	contra	PROPN
ejpam-3401	185	16	-	-	PUNCT
ejpam-3401	185	17	b	b	NOUN
ejpam-3401	185	18	-	-	PUNCT
ejpam-3401	185	19	continuous	continuous	ADJ
ejpam-3401	185	20	.	.	PUNCT
ejpam-3401	186	1	proposition	proposition	NOUN
ejpam-3401	186	2	4	4	NUM
ejpam-3401	186	3	.	.	PUNCT
ejpam-3401	187	1	let	let	VERB
ejpam-3401	187	2	f	f	NOUN
ejpam-3401	187	3	:	:	PUNCT
ejpam-3401	187	4	(	(	PUNCT
ejpam-3401	187	5	x	x	X
ejpam-3401	187	6	,	,	PUNCT
ejpam-3401	187	7	τ	τ	PROPN
ejpam-3401	187	8	,	,	PUNCT
ejpam-3401	187	9	t1	t1	NOUN
ejpam-3401	187	10	,	,	PUNCT
ejpam-3401	187	11	t2	t2	NOUN
ejpam-3401	187	12	)	)	PUNCT
ejpam-3401	187	13	→	→	SYM
ejpam-3401	187	14	(	(	PUNCT
ejpam-3401	187	15	y	y	PROPN
ejpam-3401	187	16	,	,	PUNCT
ejpam-3401	187	17	σ	σ	PROPN
ejpam-3401	187	18	)	)	PUNCT
ejpam-3401	187	19	be	be	AUX
ejpam-3401	187	20	contra	contra	PROPN
ejpam-3401	187	21	-	-	PUNCT
ejpam-3401	187	22	b	b	NOUN
ejpam-3401	187	23	-	-	PUNCT
ejpam-3401	187	24	continuous	continuous	ADJ
ejpam-3401	187	25	and	and	CCONJ
ejpam-3401	187	26	g	g	NOUN
ejpam-3401	187	27	:	:	PUNCT
ejpam-3401	187	28	(	(	PUNCT
ejpam-3401	187	29	x	x	X
ejpam-3401	187	30	,	,	PUNCT
ejpam-3401	187	31	τ	τ	X
ejpam-3401	187	32	)	)	PUNCT
ejpam-3401	187	33	→	→	SYM
ejpam-3401	187	34	(	(	PUNCT
ejpam-3401	187	35	y	y	PROPN
ejpam-3401	187	36	,	,	PUNCT
ejpam-3401	187	37	σ	σ	PROPN
ejpam-3401	187	38	)	)	PUNCT
ejpam-3401	187	39	is	be	AUX
ejpam-3401	187	40	contra	contra	ADJ
ejpam-3401	187	41	-	-	ADJ
ejpam-3401	187	42	continuous	continuous	ADJ
ejpam-3401	187	43	.	.	PUNCT
ejpam-3401	188	1	if	if	SCONJ
ejpam-3401	188	2	y	y	PROPN
ejpam-3401	188	3	is	be	AUX
ejpam-3401	188	4	an	an	DET
ejpam-3401	188	5	urysohn	urysohn	PROPN
ejpam-3401	188	6	space	space	NOUN
ejpam-3401	188	7	,	,	PUNCT
ejpam-3401	188	8	then	then	ADV
ejpam-3401	188	9	e	e	X
ejpam-3401	188	10	=	=	PRON
ejpam-3401	188	11	{	{	PUNCT
ejpam-3401	188	12	x	x	PUNCT
ejpam-3401	188	13	∈	∈	PROPN
ejpam-3401	188	14	x|	x|	X
ejpam-3401	188	15	f(x	f(x	PROPN
ejpam-3401	188	16	)	)	PUNCT
ejpam-3401	188	17	=	=	PUNCT
ejpam-3401	189	1	g(x	g(x	NOUN
ejpam-3401	189	2	)	)	PUNCT
ejpam-3401	189	3	}	}	PUNCT
ejpam-3401	189	4	is	be	AUX
ejpam-3401	189	5	b	b	NOUN
ejpam-3401	189	6	-	-	PUNCT
ejpam-3401	189	7	closed	closed	ADJ
ejpam-3401	189	8	in	in	ADP
ejpam-3401	189	9	x.	x.	NOUN
ejpam-3401	189	10	proof	proof	NOUN
ejpam-3401	189	11	.	.	PUNCT
ejpam-3401	190	1	suppose	suppose	VERB
ejpam-3401	190	2	that	that	SCONJ
ejpam-3401	190	3	x	x	PROPN
ejpam-3401	190	4	∈	∈	PROPN
ejpam-3401	190	5	ec	ec	PROPN
ejpam-3401	190	6	,	,	PUNCT
ejpam-3401	190	7	this	this	PRON
ejpam-3401	190	8	implies	imply	VERB
ejpam-3401	190	9	that	that	SCONJ
ejpam-3401	190	10	f(x	f(x	PROPN
ejpam-3401	190	11	)	)	PUNCT
ejpam-3401	190	12	6=	6=	ADP
ejpam-3401	190	13	g(x	g(x	NOUN
ejpam-3401	190	14	)	)	PUNCT
ejpam-3401	190	15	.	.	PUNCT
ejpam-3401	191	1	since	since	SCONJ
ejpam-3401	191	2	y	y	PROPN
ejpam-3401	191	3	is	be	AUX
ejpam-3401	191	4	an	an	DET
ejpam-3401	191	5	urysohn	urysohn	NOUN
ejpam-3401	191	6	space	space	NOUN
ejpam-3401	191	7	,	,	PUNCT
ejpam-3401	191	8	then	then	ADV
ejpam-3401	191	9	there	there	PRON
ejpam-3401	191	10	exist	exist	VERB
ejpam-3401	191	11	open	open	ADJ
ejpam-3401	191	12	sets	set	NOUN
ejpam-3401	191	13	u	u	NOUN
ejpam-3401	191	14	and	and	CCONJ
ejpam-3401	191	15	v	v	ADP
ejpam-3401	191	16	such	such	ADJ
ejpam-3401	191	17	that	that	DET
ejpam-3401	191	18	f(x	f(x	PROPN
ejpam-3401	191	19	)	)	PUNCT
ejpam-3401	191	20	∈	∈	PROPN
ejpam-3401	191	21	u	u	NOUN
ejpam-3401	191	22	,	,	PUNCT
ejpam-3401	191	23	g(x	g(x	NOUN
ejpam-3401	191	24	)	)	PUNCT
ejpam-3401	191	25	∈	∈	PROPN
ejpam-3401	191	26	v	v	NOUN
ejpam-3401	191	27	and	and	CCONJ
ejpam-3401	191	28	cl(u	cl(u	NOUN
ejpam-3401	191	29	)	)	PUNCT
ejpam-3401	191	30	∩	∩	NOUN
ejpam-3401	191	31	cl(v	cl(v	NOUN
ejpam-3401	191	32	)	)	PUNCT
ejpam-3401	192	1	=	=	PUNCT
ejpam-3401	192	2	∅.	∅.	ADV
ejpam-3401	192	3	since	since	SCONJ
ejpam-3401	192	4	the	the	DET
ejpam-3401	192	5	function	function	NOUN
ejpam-3401	192	6	f	f	PROPN
ejpam-3401	192	7	is	be	AUX
ejpam-3401	192	8	contra	contra	PROPN
ejpam-3401	192	9	-	-	PUNCT
ejpam-3401	192	10	b	b	NOUN
ejpam-3401	192	11	-	-	PUNCT
ejpam-3401	192	12	continuous	continuous	ADJ
ejpam-3401	192	13	,	,	PUNCT
ejpam-3401	192	14	f−1(cl(u	f−1(cl(u	NUM
ejpam-3401	192	15	)	)	PUNCT
ejpam-3401	192	16	)	)	PUNCT
ejpam-3401	192	17	is	be	AUX
ejpam-3401	192	18	b	b	NOUN
ejpam-3401	192	19	-	-	PUNCT
ejpam-3401	192	20	open	open	ADJ
ejpam-3401	192	21	in	in	ADP
ejpam-3401	192	22	x	x	PUNCT
ejpam-3401	192	23	and	and	CCONJ
ejpam-3401	192	24	g	g	PROPN
ejpam-3401	192	25	is	be	AUX
ejpam-3401	192	26	contra	contra	ADJ
ejpam-3401	192	27	-	-	ADJ
ejpam-3401	192	28	continuous	continuous	ADJ
ejpam-3401	192	29	,	,	PUNCT
ejpam-3401	192	30	therefore	therefore	ADV
ejpam-3401	192	31	g−1(cl(v	g−1(cl(v	ADJ
ejpam-3401	192	32	)	)	PUNCT
ejpam-3401	192	33	)	)	PUNCT
ejpam-3401	193	1	is	be	AUX
ejpam-3401	193	2	open	open	ADJ
ejpam-3401	193	3	in	in	ADP
ejpam-3401	193	4	x.	x.	NOUN
ejpam-3401	193	5	if	if	SCONJ
ejpam-3401	193	6	we	we	PRON
ejpam-3401	193	7	consider	consider	VERB
ejpam-3401	193	8	w	w	NOUN
ejpam-3401	193	9	=	=	PUNCT
ejpam-3401	193	10	f−1(cl(u	f−1(cl(u	NOUN
ejpam-3401	193	11	)	)	PUNCT
ejpam-3401	193	12	)	)	PUNCT
ejpam-3401	193	13	,	,	PUNCT
ejpam-3401	193	14	z	z	NOUN
ejpam-3401	193	15	=	=	NOUN
ejpam-3401	193	16	g−1(cl(v	g−1(cl(v	ADJ
ejpam-3401	193	17	)	)	PUNCT
ejpam-3401	193	18	)	)	PUNCT
ejpam-3401	193	19	,	,	PUNCT
ejpam-3401	193	20	then	then	ADV
ejpam-3401	193	21	x	x	X
ejpam-3401	193	22	∈	∈	PROPN
ejpam-3401	193	23	w	w	PROPN
ejpam-3401	193	24	∩	∩	PROPN
ejpam-3401	193	25	z	z	NOUN
ejpam-3401	193	26	=	=	SYM
ejpam-3401	193	27	s	s	VERB
ejpam-3401	193	28	where	where	SCONJ
ejpam-3401	193	29	s	s	NOUN
ejpam-3401	193	30	is	be	AUX
ejpam-3401	193	31	b	b	NOUN
ejpam-3401	193	32	-	-	PUNCT
ejpam-3401	193	33	open	open	ADJ
ejpam-3401	193	34	in	in	ADP
ejpam-3401	193	35	x	x	X
ejpam-3401	193	36	and	and	CCONJ
ejpam-3401	193	37	f(s	f(	NOUN
ejpam-3401	193	38	)	)	PUNCT
ejpam-3401	193	39	∩	∩	ADJ
ejpam-3401	193	40	g(s	g(s	NOUN
ejpam-3401	193	41	)	)	PUNCT
ejpam-3401	193	42	⊆	⊆	NUM
ejpam-3401	193	43	f(w	f(w	PROPN
ejpam-3401	193	44	)	)	PUNCT
ejpam-3401	193	45	∩	∩	NOUN
ejpam-3401	193	46	g(z	g(z	ADJ
ejpam-3401	193	47	)	)	PUNCT
ejpam-3401	193	48	⊆	⊆	NUM
ejpam-3401	193	49	cl(u	cl(u	NOUN
ejpam-3401	193	50	)	)	PUNCT
ejpam-3401	193	51	∩	∩	NOUN
ejpam-3401	193	52	cl(v	cl(v	NOUN
ejpam-3401	193	53	)	)	PUNCT
ejpam-3401	194	1	=	=	PUNCT
ejpam-3401	194	2	∅.	∅.	VERB
ejpam-3401	194	3	hence	hence	ADV
ejpam-3401	194	4	f(s	f(	NOUN
ejpam-3401	194	5	)	)	PUNCT
ejpam-3401	194	6	∩	∩	ADJ
ejpam-3401	194	7	g(s	g(s	NOUN
ejpam-3401	194	8	)	)	PUNCT
ejpam-3401	194	9	=	=	SYM
ejpam-3401	194	10	∅	∅	NOUN
ejpam-3401	194	11	and	and	CCONJ
ejpam-3401	194	12	s	s	X
ejpam-3401	194	13	∩	∩	ADJ
ejpam-3401	194	14	e	e	NOUN
ejpam-3401	194	15	=	=	SYM
ejpam-3401	194	16	∅	∅	NOUN
ejpam-3401	194	17	,	,	PUNCT
ejpam-3401	194	18	s	s	VERB
ejpam-3401	194	19	⊆	⊆	NUM
ejpam-3401	194	20	ec	ec	NOUN
ejpam-3401	194	21	where	where	SCONJ
ejpam-3401	194	22	s	s	VERB
ejpam-3401	194	23	is	be	AUX
ejpam-3401	194	24	b	b	NOUN
ejpam-3401	194	25	-	-	ADV
ejpam-3401	194	26	open	open	ADJ
ejpam-3401	194	27	.	.	PUNCT
ejpam-3401	195	1	we	we	PRON
ejpam-3401	195	2	conclude	conclude	VERB
ejpam-3401	195	3	that	that	PRON
ejpam-3401	195	4	x	x	X
ejpam-3401	195	5	/∈	/∈	PUNCT
ejpam-3401	195	6	bcl(e	bcl(e	PROPN
ejpam-3401	195	7	)	)	PUNCT
ejpam-3401	195	8	,	,	PUNCT
ejpam-3401	195	9	and	and	CCONJ
ejpam-3401	195	10	so	so	ADV
ejpam-3401	195	11	e	e	NOUN
ejpam-3401	195	12	is	be	AUX
ejpam-3401	195	13	b	b	NOUN
ejpam-3401	195	14	-	-	PUNCT
ejpam-3401	195	15	closed	closed	ADJ
ejpam-3401	195	16	in	in	ADP
ejpam-3401	195	17	x.	x.	NOUN
ejpam-3401	195	18	corollary	corollary	NOUN
ejpam-3401	195	19	1	1	X
ejpam-3401	195	20	.	.	PUNCT
ejpam-3401	196	1	let	let	VERB
ejpam-3401	196	2	f	f	NOUN
ejpam-3401	196	3	:	:	PUNCT
ejpam-3401	196	4	(	(	PUNCT
ejpam-3401	196	5	x	x	X
ejpam-3401	196	6	,	,	PUNCT
ejpam-3401	196	7	τ	τ	PROPN
ejpam-3401	196	8	,	,	PUNCT
ejpam-3401	196	9	t1	t1	NOUN
ejpam-3401	196	10	,	,	PUNCT
ejpam-3401	196	11	t2	t2	NOUN
ejpam-3401	196	12	)	)	PUNCT
ejpam-3401	196	13	→	→	SYM
ejpam-3401	196	14	(	(	PUNCT
ejpam-3401	196	15	y	y	PROPN
ejpam-3401	196	16	,	,	PUNCT
ejpam-3401	196	17	σ	σ	PROPN
ejpam-3401	196	18	)	)	PUNCT
ejpam-3401	196	19	be	be	AUX
ejpam-3401	196	20	contra	contra	PROPN
ejpam-3401	196	21	-	-	PUNCT
ejpam-3401	196	22	b	b	NOUN
ejpam-3401	196	23	-	-	PUNCT
ejpam-3401	196	24	continuous	continuous	ADJ
ejpam-3401	196	25	and	and	CCONJ
ejpam-3401	196	26	let	let	VERB
ejpam-3401	196	27	g	g	NOUN
ejpam-3401	196	28	:	:	PUNCT
ejpam-3401	196	29	(	(	PUNCT
ejpam-3401	196	30	x	x	X
ejpam-3401	196	31	,	,	PUNCT
ejpam-3401	196	32	τ	τ	X
ejpam-3401	196	33	)	)	PUNCT
ejpam-3401	196	34	→	→	SYM
ejpam-3401	196	35	(	(	PUNCT
ejpam-3401	196	36	y	y	PROPN
ejpam-3401	196	37	,	,	PUNCT
ejpam-3401	196	38	σ	σ	PROPN
ejpam-3401	196	39	)	)	PUNCT
ejpam-3401	196	40	be	be	AUX
ejpam-3401	196	41	contra	contra	ADJ
ejpam-3401	196	42	-	-	ADJ
ejpam-3401	196	43	continuous	continuous	ADJ
ejpam-3401	196	44	.	.	PUNCT
ejpam-3401	197	1	if	if	SCONJ
ejpam-3401	197	2	y	y	PROPN
ejpam-3401	197	3	is	be	AUX
ejpam-3401	197	4	an	an	DET
ejpam-3401	197	5	urysohn	urysohn	NOUN
ejpam-3401	197	6	space	space	NOUN
ejpam-3401	197	7	and	and	CCONJ
ejpam-3401	197	8	f	f	NOUN
ejpam-3401	197	9	=	=	SYM
ejpam-3401	197	10	g	g	PROPN
ejpam-3401	197	11	on	on	ADP
ejpam-3401	197	12	a	a	DET
ejpam-3401	197	13	b	b	NOUN
ejpam-3401	197	14	-	-	PUNCT
ejpam-3401	197	15	dense	dense	ADJ
ejpam-3401	197	16	set	set	NOUN
ejpam-3401	197	17	s	s	NOUN
ejpam-3401	197	18	⊆	⊆	NUM
ejpam-3401	197	19	x	x	NOUN
ejpam-3401	197	20	,	,	PUNCT
ejpam-3401	197	21	then	then	ADV
ejpam-3401	197	22	f	f	PROPN
ejpam-3401	197	23	=	=	SYM
ejpam-3401	197	24	g	g	PROPN
ejpam-3401	197	25	on	on	ADP
ejpam-3401	197	26	x.	x.	NOUN
ejpam-3401	197	27	proof	proof	NOUN
ejpam-3401	197	28	.	.	PUNCT
ejpam-3401	198	1	from	from	ADP
ejpam-3401	198	2	the	the	DET
ejpam-3401	198	3	previous	previous	ADJ
ejpam-3401	198	4	result	result	NOUN
ejpam-3401	198	5	e	e	X
ejpam-3401	198	6	=	=	PRON
ejpam-3401	198	7	{	{	PUNCT
ejpam-3401	198	8	x	x	PROPN
ejpam-3401	198	9	∈	∈	PROPN
ejpam-3401	198	10	x|f(x	x|f(x	PROPN
ejpam-3401	198	11	)	)	PUNCT
ejpam-3401	198	12	=	=	SYM
ejpam-3401	198	13	g(x	g(x	NOUN
ejpam-3401	198	14	)	)	PUNCT
ejpam-3401	198	15	}	}	PUNCT
ejpam-3401	198	16	is	be	AUX
ejpam-3401	198	17	b	b	NOUN
ejpam-3401	198	18	-	-	PUNCT
ejpam-3401	198	19	closed	closed	ADJ
ejpam-3401	198	20	in	in	ADP
ejpam-3401	198	21	x.	x.	NOUN
ejpam-3401	198	22	now	now	ADV
ejpam-3401	198	23	we	we	PRON
ejpam-3401	198	24	assumed	assume	VERB
ejpam-3401	198	25	that	that	SCONJ
ejpam-3401	198	26	f	f	PROPN
ejpam-3401	198	27	=	=	SYM
ejpam-3401	198	28	g	g	PROPN
ejpam-3401	198	29	on	on	ADP
ejpam-3401	198	30	b	b	NOUN
ejpam-3401	198	31	-	-	PUNCT
ejpam-3401	198	32	dense	dense	ADJ
ejpam-3401	198	33	set	set	NOUN
ejpam-3401	198	34	and	and	CCONJ
ejpam-3401	198	35	s	s	NOUN
ejpam-3401	198	36	⊆	⊆	NUM
ejpam-3401	198	37	e.	e.	NOUN
ejpam-3401	198	38	since	since	SCONJ
ejpam-3401	198	39	f	f	PROPN
ejpam-3401	198	40	is	be	AUX
ejpam-3401	198	41	contra	contra	PROPN
ejpam-3401	198	42	-	-	PUNCT
ejpam-3401	198	43	b	b	NOUN
ejpam-3401	198	44	-	-	PUNCT
ejpam-3401	198	45	continuous	continuous	ADJ
ejpam-3401	198	46	and	and	CCONJ
ejpam-3401	198	47	g	g	NOUN
ejpam-3401	198	48	is	be	AUX
ejpam-3401	198	49	contra	contra	ADJ
ejpam-3401	198	50	-	-	ADJ
ejpam-3401	198	51	continuous	continuous	ADJ
ejpam-3401	198	52	,	,	PUNCT
ejpam-3401	198	53	then	then	ADV
ejpam-3401	198	54	x	x	PROPN
ejpam-3401	198	55	=	=	SYM
ejpam-3401	198	56	bcl(s	bcl(s	PROPN
ejpam-3401	198	57	)	)	PUNCT
ejpam-3401	198	58	⊆	⊆	NUM
ejpam-3401	198	59	bcl(e	bcl(e	PROPN
ejpam-3401	198	60	)	)	PUNCT
ejpam-3401	198	61	=	=	PUNCT
ejpam-3401	199	1	s.	s.	PROPN
ejpam-3401	199	2	therefore	therefore	ADV
ejpam-3401	199	3	,	,	PUNCT
ejpam-3401	199	4	f	f	PROPN
ejpam-3401	199	5	=	=	SYM
ejpam-3401	199	6	g	g	PROPN
ejpam-3401	199	7	on	on	ADP
ejpam-3401	199	8	x.	x.	NOUN
ejpam-3401	199	9	proposition	proposition	NOUN
ejpam-3401	199	10	5	5	NUM
ejpam-3401	199	11	.	.	PUNCT
ejpam-3401	200	1	if	if	SCONJ
ejpam-3401	200	2	f	f	PROPN
ejpam-3401	200	3	:	:	PUNCT
ejpam-3401	200	4	(	(	PUNCT
ejpam-3401	200	5	x	x	X
ejpam-3401	200	6	,	,	PUNCT
ejpam-3401	200	7	τ	τ	PROPN
ejpam-3401	200	8	,	,	PUNCT
ejpam-3401	200	9	t1	t1	NOUN
ejpam-3401	200	10	,	,	PUNCT
ejpam-3401	200	11	t2	t2	NOUN
ejpam-3401	200	12	)	)	PUNCT
ejpam-3401	200	13	→	→	SYM
ejpam-3401	200	14	(	(	PUNCT
ejpam-3401	200	15	y	y	PROPN
ejpam-3401	200	16	,	,	PUNCT
ejpam-3401	200	17	σ	σ	PROPN
ejpam-3401	200	18	)	)	PUNCT
ejpam-3401	200	19	is	be	AUX
ejpam-3401	200	20	contra	contra	PROPN
ejpam-3401	200	21	-	-	PUNCT
ejpam-3401	200	22	b	b	NOUN
ejpam-3401	200	23	-	-	PUNCT
ejpam-3401	200	24	continuous	continuous	ADJ
ejpam-3401	200	25	from	from	ADP
ejpam-3401	200	26	a	a	DET
ejpam-3401	200	27	b	b	NOUN
ejpam-3401	200	28	-	-	PUNCT
ejpam-3401	200	29	connected	connect	VERB
ejpam-3401	200	30	space	space	NOUN
ejpam-3401	200	31	onto	onto	ADP
ejpam-3401	200	32	y	y	PROPN
ejpam-3401	200	33	,	,	PUNCT
ejpam-3401	200	34	then	then	ADV
ejpam-3401	200	35	y	y	PROPN
ejpam-3401	200	36	is	be	AUX
ejpam-3401	200	37	not	not	PART
ejpam-3401	200	38	a	a	DET
ejpam-3401	200	39	discrete	discrete	ADJ
ejpam-3401	200	40	space	space	NOUN
ejpam-3401	200	41	.	.	PUNCT
ejpam-3401	201	1	proof	proof	NOUN
ejpam-3401	201	2	.	.	PUNCT
ejpam-3401	202	1	let	let	VERB
ejpam-3401	202	2	y	y	PRON
ejpam-3401	202	3	be	be	AUX
ejpam-3401	202	4	a	a	DET
ejpam-3401	202	5	discrete	discrete	ADJ
ejpam-3401	202	6	space	space	NOUN
ejpam-3401	202	7	and	and	CCONJ
ejpam-3401	202	8	∅	∅	NOUN
ejpam-3401	202	9	6=	6=	ADP
ejpam-3401	202	10	s	s	PROPN
ejpam-3401	202	11	⊂	⊂	PROPN
ejpam-3401	202	12	y	y	PROPN
ejpam-3401	202	13	,	,	PUNCT
ejpam-3401	202	14	then	then	ADV
ejpam-3401	202	15	s	s	VERB
ejpam-3401	202	16	is	be	AUX
ejpam-3401	202	17	a	a	DET
ejpam-3401	202	18	proper	proper	ADJ
ejpam-3401	202	19	nonempty	nonempty	ADV
ejpam-3401	202	20	open	open	ADJ
ejpam-3401	202	21	and	and	CCONJ
ejpam-3401	202	22	closed	closed	ADJ
ejpam-3401	202	23	subset	subset	NOUN
ejpam-3401	202	24	of	of	ADP
ejpam-3401	202	25	y	y	PROPN
ejpam-3401	202	26	.	.	PUNCT
ejpam-3401	203	1	then	then	ADV
ejpam-3401	203	2	f−1(s	f−1(s	PROPN
ejpam-3401	203	3	)	)	PUNCT
ejpam-3401	203	4	is	be	AUX
ejpam-3401	203	5	a	a	DET
ejpam-3401	203	6	proper	proper	ADJ
ejpam-3401	203	7	nonempty	nonempty	X
ejpam-3401	203	8	b	b	NOUN
ejpam-3401	203	9	-	-	PUNCT
ejpam-3401	203	10	open	open	ADJ
ejpam-3401	203	11	and	and	CCONJ
ejpam-3401	203	12	b	b	X
ejpam-3401	203	13	-	-	PUNCT
ejpam-3401	203	14	closed	closed	ADJ
ejpam-3401	203	15	subset	subset	NOUN
ejpam-3401	203	16	of	of	ADP
ejpam-3401	203	17	x	x	SYM
ejpam-3401	203	18	such	such	ADJ
ejpam-3401	203	19	that	that	SCONJ
ejpam-3401	203	20	x	x	X
ejpam-3401	203	21	=	=	PUNCT
ejpam-3401	203	22	f−1(s)∪	f−1(s)∪	PROPN
ejpam-3401	203	23	(	(	PUNCT
ejpam-3401	203	24	f−1(s))c	f−1(s))c	PROPN
ejpam-3401	203	25	which	which	PRON
ejpam-3401	203	26	means	mean	VERB
ejpam-3401	203	27	that	that	SCONJ
ejpam-3401	203	28	x	x	PRON
ejpam-3401	203	29	is	be	AUX
ejpam-3401	203	30	b	b	NUM
ejpam-3401	203	31	-	-	PUNCT
ejpam-3401	203	32	disconnected	disconnected	ADJ
ejpam-3401	203	33	space	space	NOUN
ejpam-3401	203	34	and	and	CCONJ
ejpam-3401	203	35	this	this	PRON
ejpam-3401	203	36	contradicts	contradict	VERB
ejpam-3401	203	37	our	our	PRON
ejpam-3401	203	38	assumption	assumption	NOUN
ejpam-3401	203	39	.	.	PUNCT
ejpam-3401	204	1	thus	thus	ADV
ejpam-3401	204	2	,	,	PUNCT
ejpam-3401	204	3	y	y	PROPN
ejpam-3401	204	4	is	be	AUX
ejpam-3401	204	5	not	not	PART
ejpam-3401	204	6	discrete	discrete	ADJ
ejpam-3401	204	7	.	.	PUNCT
ejpam-3401	205	1	definition	definition	NOUN
ejpam-3401	205	2	16	16	NUM
ejpam-3401	205	3	.	.	PUNCT
ejpam-3401	206	1	a	a	DET
ejpam-3401	206	2	function	function	NOUN
ejpam-3401	206	3	f	f	NOUN
ejpam-3401	206	4	:	:	PUNCT
ejpam-3401	206	5	(	(	PUNCT
ejpam-3401	206	6	x	x	X
ejpam-3401	206	7	,	,	PUNCT
ejpam-3401	206	8	τ	τ	PROPN
ejpam-3401	206	9	,	,	PUNCT
ejpam-3401	206	10	t1	t1	NOUN
ejpam-3401	206	11	,	,	PUNCT
ejpam-3401	206	12	t2	t2	NOUN
ejpam-3401	206	13	)	)	PUNCT
ejpam-3401	206	14	→	→	SYM
ejpam-3401	206	15	(	(	PUNCT
ejpam-3401	206	16	y	y	PROPN
ejpam-3401	206	17	,	,	PUNCT
ejpam-3401	206	18	σ	σ	PROPN
ejpam-3401	206	19	)	)	PUNCT
ejpam-3401	206	20	is	be	AUX
ejpam-3401	206	21	called	call	VERB
ejpam-3401	206	22	an	an	DET
ejpam-3401	206	23	almost	almost	ADV
ejpam-3401	206	24	contra	contra	ADJ
ejpam-3401	206	25	-	-	ADJ
ejpam-3401	206	26	bcontinuous	bcontinuous	ADJ
ejpam-3401	206	27	function	function	NOUN
ejpam-3401	206	28	,	,	PUNCT
ejpam-3401	206	29	if	if	SCONJ
ejpam-3401	206	30	f−1(v	f−1(v	PROPN
ejpam-3401	206	31	)	)	PUNCT
ejpam-3401	206	32	is	be	AUX
ejpam-3401	206	33	a	a	DET
ejpam-3401	206	34	b	b	NOUN
ejpam-3401	206	35	-	-	PUNCT
ejpam-3401	206	36	closed	closed	ADJ
ejpam-3401	206	37	for	for	ADP
ejpam-3401	206	38	every	every	DET
ejpam-3401	206	39	regular	regular	ADJ
ejpam-3401	206	40	open	open	NOUN
ejpam-3401	206	41	set	set	VERB
ejpam-3401	206	42	v	v	NOUN
ejpam-3401	206	43	in	in	ADP
ejpam-3401	206	44	y.	y.	PROPN
ejpam-3401	206	45	proposition	proposition	NOUN
ejpam-3401	206	46	6	6	NUM
ejpam-3401	206	47	.	.	PUNCT
ejpam-3401	207	1	let	let	VERB
ejpam-3401	207	2	f	f	NOUN
ejpam-3401	207	3	:	:	PUNCT
ejpam-3401	207	4	(	(	PUNCT
ejpam-3401	207	5	x	x	X
ejpam-3401	207	6	,	,	PUNCT
ejpam-3401	207	7	τ	τ	PROPN
ejpam-3401	207	8	,	,	PUNCT
ejpam-3401	207	9	t1	t1	PROPN
ejpam-3401	207	10	,	,	PUNCT
ejpam-3401	207	11	t2)→	t2)→	X
ejpam-3401	207	12	(	(	PUNCT
ejpam-3401	207	13	y	y	PROPN
ejpam-3401	207	14	,	,	PUNCT
ejpam-3401	207	15	σ	σ	PROPN
ejpam-3401	207	16	)	)	PUNCT
ejpam-3401	207	17	be	be	VERB
ejpam-3401	207	18	a	a	DET
ejpam-3401	207	19	surjective	surjective	ADJ
ejpam-3401	207	20	almost	almost	ADV
ejpam-3401	207	21	contra	contra	PROPN
ejpam-3401	207	22	-	-	PUNCT
ejpam-3401	207	23	b	b	ADJ
ejpam-3401	207	24	-	-	PUNCT
ejpam-3401	207	25	continuous	continuous	ADJ
ejpam-3401	207	26	function	function	NOUN
ejpam-3401	207	27	,	,	PUNCT
ejpam-3401	207	28	then	then	ADV
ejpam-3401	207	29	:	:	PUNCT
ejpam-3401	207	30	(	(	PUNCT
ejpam-3401	207	31	i	i	NOUN
ejpam-3401	207	32	)	)	PUNCT
ejpam-3401	207	33	if	if	SCONJ
ejpam-3401	207	34	x	x	PRON
ejpam-3401	207	35	is	be	AUX
ejpam-3401	207	36	b	b	NOUN
ejpam-3401	207	37	-	-	PUNCT
ejpam-3401	207	38	lindelöf	lindelöf	NOUN
ejpam-3401	207	39	,	,	PUNCT
ejpam-3401	207	40	then	then	ADV
ejpam-3401	207	41	y	y	PROPN
ejpam-3401	207	42	is	be	AUX
ejpam-3401	207	43	contra	contra	PROPN
ejpam-3401	207	44	-	-	PUNCT
ejpam-3401	207	45	r	r	NOUN
ejpam-3401	207	46	-	-	PUNCT
ejpam-3401	207	47	lindelöf	lindelöf	NOUN
ejpam-3401	207	48	.	.	PUNCT
ejpam-3401	208	1	(	(	PUNCT
ejpam-3401	208	2	ii	ii	NOUN
ejpam-3401	208	3	)	)	PUNCT
ejpam-3401	208	4	if	if	SCONJ
ejpam-3401	208	5	x	x	PRON
ejpam-3401	208	6	is	be	AUX
ejpam-3401	208	7	b	b	NOUN
ejpam-3401	208	8	-	-	ADJ
ejpam-3401	208	9	compact	compact	ADJ
ejpam-3401	208	10	,	,	PUNCT
ejpam-3401	208	11	then	then	ADV
ejpam-3401	208	12	y	y	PROPN
ejpam-3401	208	13	is	be	AUX
ejpam-3401	208	14	contra	contra	PROPN
ejpam-3401	208	15	-	-	PUNCT
ejpam-3401	208	16	r	r	NOUN
ejpam-3401	208	17	-	-	PUNCT
ejpam-3401	208	18	compact	compact	ADJ
ejpam-3401	208	19	.	.	PUNCT
ejpam-3401	209	1	l.	l.	PROPN
ejpam-3401	209	2	m.	m.	PROPN
ejpam-3401	209	3	alabdulsada	alabdulsada	PROPN
ejpam-3401	209	4	/	/	SYM
ejpam-3401	209	5	eur	eur	PROPN
ejpam-3401	209	6	.	.	PUNCT
ejpam-3401	210	1	j.	j.	PROPN
ejpam-3401	210	2	pure	pure	PROPN
ejpam-3401	210	3	appl	appl	PROPN
ejpam-3401	210	4	.	.	PROPN
ejpam-3401	210	5	math	math	PROPN
ejpam-3401	210	6	,	,	PUNCT
ejpam-3401	210	7	12	12	NUM
ejpam-3401	210	8	(	(	PUNCT
ejpam-3401	210	9	2	2	NUM
ejpam-3401	210	10	)	)	PUNCT
ejpam-3401	210	11	(	(	PUNCT
ejpam-3401	210	12	2019	2019	NUM
ejpam-3401	210	13	)	)	PUNCT
ejpam-3401	210	14	,	,	PUNCT
ejpam-3401	210	15	358	358	NUM
ejpam-3401	210	16	-	-	SYM
ejpam-3401	210	17	369	369	NUM
ejpam-3401	210	18	366	366	NUM
ejpam-3401	210	19	(	(	PUNCT
ejpam-3401	210	20	iii	iii	NOUN
ejpam-3401	210	21	)	)	PUNCT
ejpam-3401	210	22	if	if	SCONJ
ejpam-3401	210	23	x	x	PRON
ejpam-3401	210	24	is	be	AUX
ejpam-3401	210	25	countable	countable	ADJ
ejpam-3401	210	26	-	-	PUNCT
ejpam-3401	210	27	b	b	NOUN
ejpam-3401	210	28	-	-	PUNCT
ejpam-3401	210	29	compact	compact	ADJ
ejpam-3401	210	30	,	,	PUNCT
ejpam-3401	210	31	then	then	ADV
ejpam-3401	210	32	y	y	PROPN
ejpam-3401	210	33	is	be	AUX
ejpam-3401	210	34	countable	countable	ADJ
ejpam-3401	210	35	contra	contra	PROPN
ejpam-3401	210	36	-	-	PUNCT
ejpam-3401	210	37	r	r	NOUN
ejpam-3401	210	38	-	-	PUNCT
ejpam-3401	210	39	compact	compact	ADJ
ejpam-3401	210	40	.	.	PUNCT
ejpam-3401	211	1	proof	proof	NOUN
ejpam-3401	211	2	.	.	PUNCT
ejpam-3401	212	1	we	we	PRON
ejpam-3401	212	2	are	be	AUX
ejpam-3401	212	3	going	go	VERB
ejpam-3401	212	4	to	to	PART
ejpam-3401	212	5	prove	prove	VERB
ejpam-3401	212	6	(	(	PUNCT
ejpam-3401	212	7	i	i	NOUN
ejpam-3401	212	8	)	)	PUNCT
ejpam-3401	212	9	and	and	CCONJ
ejpam-3401	212	10	(	(	PUNCT
ejpam-3401	212	11	ii	ii	NOUN
ejpam-3401	212	12	)	)	PUNCT
ejpam-3401	212	13	and	and	CCONJ
ejpam-3401	212	14	one	one	PRON
ejpam-3401	212	15	can	can	AUX
ejpam-3401	212	16	prove	prove	VERB
ejpam-3401	212	17	(	(	PUNCT
ejpam-3401	212	18	iii	iii	NOUN
ejpam-3401	212	19	)	)	PUNCT
ejpam-3401	212	20	in	in	ADP
ejpam-3401	212	21	a	a	DET
ejpam-3401	212	22	similar	similar	ADJ
ejpam-3401	212	23	way	way	NOUN
ejpam-3401	212	24	.	.	PUNCT
ejpam-3401	213	1	(	(	PUNCT
ejpam-3401	213	2	i	i	NOUN
ejpam-3401	213	3	)	)	PUNCT
ejpam-3401	213	4	consider	consider	VERB
ejpam-3401	213	5	a	a	DET
ejpam-3401	213	6	family	family	NOUN
ejpam-3401	213	7	s	s	PART
ejpam-3401	213	8	=	=	PUNCT
ejpam-3401	213	9	{	{	PUNCT
ejpam-3401	213	10	va|	va|	NOUN
ejpam-3401	213	11	a	a	DET
ejpam-3401	213	12	∈	∈	PROPN
ejpam-3401	213	13	λ	λ	NOUN
ejpam-3401	213	14	}	}	PUNCT
ejpam-3401	213	15	to	to	PART
ejpam-3401	213	16	be	be	AUX
ejpam-3401	213	17	a	a	DET
ejpam-3401	213	18	regular	regular	ADJ
ejpam-3401	213	19	closed	closed	ADJ
ejpam-3401	213	20	cover	cover	NOUN
ejpam-3401	213	21	of	of	ADP
ejpam-3401	213	22	y	y	PROPN
ejpam-3401	213	23	,	,	PUNCT
ejpam-3401	213	24	at	at	ADP
ejpam-3401	213	25	the	the	DET
ejpam-3401	213	26	same	same	ADJ
ejpam-3401	213	27	time	time	NOUN
ejpam-3401	213	28	let	let	VERB
ejpam-3401	213	29	s∗	s∗	PROPN
ejpam-3401	213	30	=	=	PRON
ejpam-3401	213	31	{	{	PUNCT
ejpam-3401	213	32	f−1(va)|	f−1(va)|	NOUN
ejpam-3401	213	33	a	a	PRON
ejpam-3401	213	34	∈	∈	PROPN
ejpam-3401	213	35	λ	λ	NOUN
ejpam-3401	213	36	}	}	PUNCT
ejpam-3401	213	37	be	be	VERB
ejpam-3401	213	38	a	a	DET
ejpam-3401	213	39	b	b	NOUN
ejpam-3401	213	40	-	-	PUNCT
ejpam-3401	213	41	open	open	ADJ
ejpam-3401	213	42	cover	cover	NOUN
ejpam-3401	213	43	of	of	ADP
ejpam-3401	213	44	x.	x.	NOUN
ejpam-3401	214	1	but	but	CCONJ
ejpam-3401	214	2	x	x	X
ejpam-3401	214	3	is	be	AUX
ejpam-3401	214	4	b	b	NOUN
ejpam-3401	214	5	-	-	PUNCT
ejpam-3401	214	6	lindelöf	lindelöf	NOUN
ejpam-3401	214	7	,	,	PUNCT
ejpam-3401	214	8	then	then	ADV
ejpam-3401	214	9	there	there	PRON
ejpam-3401	214	10	exist	exist	VERB
ejpam-3401	214	11	a1	a1	NOUN
ejpam-3401	214	12	,	,	PUNCT
ejpam-3401	214	13	a2	a2	PROPN
ejpam-3401	214	14	,	,	PUNCT
ejpam-3401	214	15	...	...	PUNCT
ejpam-3401	214	16	,	,	PUNCT
ejpam-3401	214	17	an	an	DET
ejpam-3401	214	18	such	such	ADJ
ejpam-3401	214	19	that	that	SCONJ
ejpam-3401	214	20	x	x	X
ejpam-3401	214	21	=	=	SYM
ejpam-3401	214	22	∪∞i=1f	∪∞i=1f	PROPN
ejpam-3401	214	23	−1(vai	−1(vai	PROPN
ejpam-3401	214	24	)	)	PUNCT
ejpam-3401	214	25	,	,	PUNCT
ejpam-3401	214	26	we	we	PRON
ejpam-3401	214	27	have	have	VERB
ejpam-3401	214	28	y	y	PROPN
ejpam-3401	214	29	=	=	SYM
ejpam-3401	214	30	f(x	f(x	PROPN
ejpam-3401	214	31	)	)	PUNCT
ejpam-3401	214	32	=	=	SYM
ejpam-3401	214	33	f(∪∞i=1f	f(∪∞i=1f	PROPN
ejpam-3401	214	34	−1(vai	−1(vai	PROPN
ejpam-3401	214	35	)	)	PUNCT
ejpam-3401	214	36	)	)	PUNCT
ejpam-3401	214	37	.	.	PUNCT
ejpam-3401	215	1	then	then	ADV
ejpam-3401	215	2	y	y	PROPN
ejpam-3401	215	3	=	=	PUNCT
ejpam-3401	215	4	∪∞i=1(vai	∪∞i=1(vai	PRON
ejpam-3401	215	5	)	)	PUNCT
ejpam-3401	215	6	is	be	AUX
ejpam-3401	215	7	contra	contra	PROPN
ejpam-3401	215	8	-	-	PUNCT
ejpam-3401	215	9	r	r	NOUN
ejpam-3401	215	10	-	-	PUNCT
ejpam-3401	215	11	lindelöf	lindelöf	NOUN
ejpam-3401	215	12	.	.	PUNCT
ejpam-3401	216	1	(	(	PUNCT
ejpam-3401	216	2	ii	ii	NOUN
ejpam-3401	216	3	)	)	PUNCT
ejpam-3401	216	4	using	use	VERB
ejpam-3401	216	5	the	the	DET
ejpam-3401	216	6	same	same	ADJ
ejpam-3401	216	7	technique	technique	NOUN
ejpam-3401	216	8	as	as	ADP
ejpam-3401	216	9	above	above	ADV
ejpam-3401	216	10	,	,	PUNCT
ejpam-3401	216	11	let	let	VERB
ejpam-3401	216	12	f	f	PROPN
ejpam-3401	216	13	=	=	PRON
ejpam-3401	216	14	{	{	PUNCT
ejpam-3401	216	15	ua|	ua|	PROPN
ejpam-3401	216	16	a	a	PRON
ejpam-3401	216	17	∈	∈	PROPN
ejpam-3401	216	18	λ	λ	NOUN
ejpam-3401	216	19	}	}	PUNCT
ejpam-3401	216	20	be	be	VERB
ejpam-3401	216	21	a	a	DET
ejpam-3401	216	22	regular	regular	ADJ
ejpam-3401	216	23	closed	closed	ADJ
ejpam-3401	216	24	cover	cover	NOUN
ejpam-3401	216	25	of	of	ADP
ejpam-3401	216	26	y	y	PROPN
ejpam-3401	216	27	since	since	SCONJ
ejpam-3401	216	28	f	f	PROPN
ejpam-3401	216	29	is	be	AUX
ejpam-3401	216	30	a	a	DET
ejpam-3401	216	31	surjective	surjective	ADJ
ejpam-3401	216	32	almost	almost	ADV
ejpam-3401	216	33	contra	contra	PROPN
ejpam-3401	216	34	-	-	PUNCT
ejpam-3401	216	35	b	b	ADJ
ejpam-3401	216	36	-	-	PUNCT
ejpam-3401	216	37	continuous	continuous	ADJ
ejpam-3401	216	38	function	function	NOUN
ejpam-3401	216	39	.	.	PUNCT
ejpam-3401	217	1	so	so	ADV
ejpam-3401	217	2	f∗	f∗	NOUN
ejpam-3401	217	3	=	=	SYM
ejpam-3401	217	4	{	{	PUNCT
ejpam-3401	217	5	f−1(ua)|	f−1(ua)|	NOUN
ejpam-3401	217	6	a	a	DET
ejpam-3401	217	7	∈	∈	PROPN
ejpam-3401	217	8	λ	λ	PROPN
ejpam-3401	217	9	}	}	PUNCT
ejpam-3401	217	10	is	be	AUX
ejpam-3401	217	11	a	a	DET
ejpam-3401	217	12	b	b	NOUN
ejpam-3401	217	13	-	-	PUNCT
ejpam-3401	217	14	open	open	ADJ
ejpam-3401	217	15	cover	cover	NOUN
ejpam-3401	217	16	of	of	ADP
ejpam-3401	217	17	x	x	X
ejpam-3401	218	1	but	but	CCONJ
ejpam-3401	218	2	x	x	X
ejpam-3401	218	3	is	be	AUX
ejpam-3401	218	4	b	b	NOUN
ejpam-3401	218	5	-	-	ADJ
ejpam-3401	218	6	compact	compact	ADJ
ejpam-3401	218	7	,	,	PUNCT
ejpam-3401	218	8	then	then	ADV
ejpam-3401	218	9	there	there	PRON
ejpam-3401	218	10	exists	exist	VERB
ejpam-3401	218	11	a1	a1	PROPN
ejpam-3401	218	12	,	,	PUNCT
ejpam-3401	218	13	a2	a2	PROPN
ejpam-3401	218	14	,	,	PUNCT
ejpam-3401	218	15	...	...	PUNCT
ejpam-3401	218	16	,	,	PUNCT
ejpam-3401	218	17	an	an	DET
ejpam-3401	218	18	where	where	SCONJ
ejpam-3401	218	19	x	x	SYM
ejpam-3401	218	20	=	=	SYM
ejpam-3401	218	21	∪ni=1f	∪ni=1f	NOUN
ejpam-3401	218	22	−1(uai	−1(uai	NOUN
ejpam-3401	218	23	)	)	PUNCT
ejpam-3401	218	24	.	.	PUNCT
ejpam-3401	219	1	consequently	consequently	ADV
ejpam-3401	219	2	,	,	PUNCT
ejpam-3401	219	3	y	y	PROPN
ejpam-3401	219	4	=	=	SYM
ejpam-3401	219	5	f(x	f(x	PROPN
ejpam-3401	219	6	)	)	PUNCT
ejpam-3401	219	7	=	=	SYM
ejpam-3401	220	1	f(∪ni=1f	f(∪ni=1f	PROPN
ejpam-3401	220	2	−1(uai	−1(uai	PROPN
ejpam-3401	220	3	)	)	PUNCT
ejpam-3401	220	4	)	)	PUNCT
ejpam-3401	221	1	=	=	SYM
ejpam-3401	221	2	∪ni=1(uai	∪ni=1(uai	X
ejpam-3401	221	3	)	)	PUNCT
ejpam-3401	221	4	.	.	PUNCT
ejpam-3401	222	1	this	this	PRON
ejpam-3401	222	2	clearly	clearly	ADV
ejpam-3401	222	3	forces	force	VERB
ejpam-3401	222	4	y	y	PRON
ejpam-3401	222	5	to	to	PART
ejpam-3401	222	6	be	be	AUX
ejpam-3401	222	7	contra	contra	ADJ
ejpam-3401	222	8	-	-	PUNCT
ejpam-3401	222	9	r	r	NOUN
ejpam-3401	222	10	-	-	PUNCT
ejpam-3401	222	11	compact	compact	ADJ
ejpam-3401	222	12	.	.	PUNCT
ejpam-3401	223	1	definition	definition	NOUN
ejpam-3401	223	2	17	17	NUM
ejpam-3401	223	3	.	.	PUNCT
ejpam-3401	224	1	[	[	X
ejpam-3401	224	2	16	16	NUM
ejpam-3401	224	3	]	]	PUNCT
ejpam-3401	224	4	a	a	DET
ejpam-3401	224	5	function	function	NOUN
ejpam-3401	224	6	f	f	NOUN
ejpam-3401	224	7	:	:	PUNCT
ejpam-3401	224	8	x	x	X
ejpam-3401	224	9	→	→	SYM
ejpam-3401	224	10	y	y	PROPN
ejpam-3401	224	11	is	be	AUX
ejpam-3401	224	12	called	call	VERB
ejpam-3401	224	13	:	:	PUNCT
ejpam-3401	224	14	•	•	NUM
ejpam-3401	224	15	almost	almost	ADV
ejpam-3401	224	16	continuous	continuous	ADJ
ejpam-3401	224	17	,	,	PUNCT
ejpam-3401	224	18	if	if	SCONJ
ejpam-3401	224	19	f−1(v	f−1(v	PROPN
ejpam-3401	224	20	)	)	PUNCT
ejpam-3401	225	1	is	be	AUX
ejpam-3401	225	2	open	open	ADJ
ejpam-3401	225	3	in	in	ADP
ejpam-3401	225	4	x	x	PUNCT
ejpam-3401	225	5	for	for	ADP
ejpam-3401	225	6	every	every	DET
ejpam-3401	225	7	regular	regular	ADJ
ejpam-3401	225	8	open	open	NOUN
ejpam-3401	225	9	set	set	VERB
ejpam-3401	225	10	v	v	NOUN
ejpam-3401	225	11	in	in	ADP
ejpam-3401	225	12	y	y	PROPN
ejpam-3401	225	13	.	.	PUNCT
ejpam-3401	226	1	•	•	ADV
ejpam-3401	226	2	r	r	NOUN
ejpam-3401	226	3	-	-	NOUN
ejpam-3401	226	4	continuous	continuous	ADJ
ejpam-3401	226	5	,	,	PUNCT
ejpam-3401	226	6	if	if	SCONJ
ejpam-3401	226	7	f−1(v	f−1(v	PROPN
ejpam-3401	226	8	)	)	PUNCT
ejpam-3401	226	9	is	be	AUX
ejpam-3401	226	10	a	a	DET
ejpam-3401	226	11	regular	regular	ADJ
ejpam-3401	226	12	open	open	ADJ
ejpam-3401	226	13	set	set	NOUN
ejpam-3401	226	14	of	of	ADP
ejpam-3401	226	15	x	x	PUNCT
ejpam-3401	226	16	for	for	ADP
ejpam-3401	226	17	each	each	DET
ejpam-3401	226	18	regular	regular	ADJ
ejpam-3401	226	19	closed	close	VERB
ejpam-3401	226	20	set	set	VERB
ejpam-3401	226	21	v	v	NOUN
ejpam-3401	226	22	in	in	ADP
ejpam-3401	226	23	y	y	PROPN
ejpam-3401	226	24	.	.	PUNCT
ejpam-3401	227	1	lemma	lemma	PROPN
ejpam-3401	227	2	4	4	NUM
ejpam-3401	227	3	.	.	PUNCT
ejpam-3401	228	1	[	[	X
ejpam-3401	228	2	16	16	NUM
ejpam-3401	228	3	]	]	X
ejpam-3401	228	4	if	if	SCONJ
ejpam-3401	228	5	a	a	DET
ejpam-3401	228	6	function	function	NOUN
ejpam-3401	228	7	f	f	NOUN
ejpam-3401	228	8	:	:	PUNCT
ejpam-3401	228	9	x	x	X
ejpam-3401	228	10	→	→	SYM
ejpam-3401	228	11	y	y	PROPN
ejpam-3401	228	12	is	be	AUX
ejpam-3401	228	13	almost	almost	ADV
ejpam-3401	228	14	contra	contra	PROPN
ejpam-3401	228	15	-	-	PUNCT
ejpam-3401	228	16	b	b	NOUN
ejpam-3401	228	17	-	-	PUNCT
ejpam-3401	228	18	continuous	continuous	ADJ
ejpam-3401	228	19	and	and	CCONJ
ejpam-3401	228	20	almost	almost	ADV
ejpam-3401	228	21	continuous	continuous	ADJ
ejpam-3401	228	22	,	,	PUNCT
ejpam-3401	228	23	then	then	ADV
ejpam-3401	228	24	f	f	PROPN
ejpam-3401	228	25	is	be	AUX
ejpam-3401	228	26	a	a	DET
ejpam-3401	228	27	r	r	NOUN
ejpam-3401	228	28	-	-	PUNCT
ejpam-3401	228	29	continuous	continuous	ADJ
ejpam-3401	228	30	function	function	NOUN
ejpam-3401	228	31	.	.	PUNCT
ejpam-3401	229	1	proposition	proposition	NOUN
ejpam-3401	229	2	7	7	NUM
ejpam-3401	229	3	.	.	PUNCT
ejpam-3401	230	1	let	let	VERB
ejpam-3401	230	2	f	f	NOUN
ejpam-3401	230	3	:	:	PUNCT
ejpam-3401	230	4	(	(	PUNCT
ejpam-3401	230	5	x	x	X
ejpam-3401	230	6	,	,	PUNCT
ejpam-3401	230	7	τ	τ	PROPN
ejpam-3401	230	8	,	,	PUNCT
ejpam-3401	230	9	t1	t1	PROPN
ejpam-3401	230	10	,	,	PUNCT
ejpam-3401	230	11	t2)→	t2)→	X
ejpam-3401	230	12	(	(	PUNCT
ejpam-3401	230	13	y	y	PROPN
ejpam-3401	230	14	,	,	PUNCT
ejpam-3401	230	15	σ	σ	PROPN
ejpam-3401	230	16	)	)	PUNCT
ejpam-3401	230	17	be	be	AUX
ejpam-3401	230	18	an	an	DET
ejpam-3401	230	19	almost	almost	ADV
ejpam-3401	230	20	contra	contra	ADJ
ejpam-3401	230	21	-	-	PUNCT
ejpam-3401	230	22	b	b	NOUN
ejpam-3401	230	23	-	-	PUNCT
ejpam-3401	230	24	continuous	continuous	ADJ
ejpam-3401	230	25	and	and	CCONJ
ejpam-3401	230	26	surjective	surjective	ADJ
ejpam-3401	230	27	almost	almost	ADV
ejpam-3401	230	28	-	-	PUNCT
ejpam-3401	230	29	continuous	continuous	ADJ
ejpam-3401	230	30	function	function	NOUN
ejpam-3401	230	31	,	,	PUNCT
ejpam-3401	230	32	suppose	suppose	VERB
ejpam-3401	230	33	t1(s	t1(	NOUN
ejpam-3401	230	34	)	)	PUNCT
ejpam-3401	230	35	=	=	SYM
ejpam-3401	230	36	int(cl(s	int(cl(s	PROPN
ejpam-3401	230	37	)	)	PUNCT
ejpam-3401	230	38	)	)	PUNCT
ejpam-3401	230	39	and	and	CCONJ
ejpam-3401	230	40	t2(s	t2(s	NOUN
ejpam-3401	230	41	)	)	PUNCT
ejpam-3401	230	42	=	=	SYM
ejpam-3401	230	43	cl(int(s	cl(int(s	NOUN
ejpam-3401	230	44	)	)	PUNCT
ejpam-3401	230	45	)	)	PUNCT
ejpam-3401	230	46	,	,	PUNCT
ejpam-3401	230	47	then	then	ADV
ejpam-3401	230	48	y	y	PROPN
ejpam-3401	230	49	is	be	AUX
ejpam-3401	230	50	:	:	PUNCT
ejpam-3401	230	51	(	(	PUNCT
ejpam-3401	230	52	i	i	NOUN
ejpam-3401	230	53	)	)	PUNCT
ejpam-3401	230	54	contra	contra	PROPN
ejpam-3401	230	55	-	-	PUNCT
ejpam-3401	230	56	r	r	NOUN
ejpam-3401	230	57	-	-	ADJ
ejpam-3401	230	58	compact	compact	ADJ
ejpam-3401	230	59	,	,	PUNCT
ejpam-3401	230	60	if	if	SCONJ
ejpam-3401	230	61	x	x	PRON
ejpam-3401	230	62	is	be	AUX
ejpam-3401	230	63	contra	contra	PROPN
ejpam-3401	230	64	-	-	PUNCT
ejpam-3401	230	65	r	r	NOUN
ejpam-3401	230	66	-	-	ADJ
ejpam-3401	230	67	compact	compact	ADJ
ejpam-3401	230	68	.	.	PUNCT
ejpam-3401	231	1	(	(	PUNCT
ejpam-3401	231	2	ii	ii	NOUN
ejpam-3401	231	3	)	)	PUNCT
ejpam-3401	231	4	r	r	NOUN
ejpam-3401	231	5	-	-	PUNCT
ejpam-3401	231	6	compact	compact	ADJ
ejpam-3401	231	7	,	,	PUNCT
ejpam-3401	231	8	if	if	SCONJ
ejpam-3401	231	9	x	x	PRON
ejpam-3401	231	10	is	be	AUX
ejpam-3401	231	11	r	r	NOUN
ejpam-3401	231	12	-	-	ADJ
ejpam-3401	231	13	compact	compact	ADJ
ejpam-3401	231	14	.	.	PUNCT
ejpam-3401	232	1	(	(	PUNCT
ejpam-3401	232	2	iii	iii	NOUN
ejpam-3401	232	3	)	)	PUNCT
ejpam-3401	232	4	r	r	NOUN
ejpam-3401	232	5	-	-	PUNCT
ejpam-3401	232	6	lindelöf	lindelöf	NOUN
ejpam-3401	232	7	,	,	PUNCT
ejpam-3401	232	8	if	if	SCONJ
ejpam-3401	232	9	x	x	PRON
ejpam-3401	232	10	is	be	AUX
ejpam-3401	232	11	r	r	NOUN
ejpam-3401	232	12	-	-	PUNCT
ejpam-3401	232	13	lindelöf	lindelöf	NOUN
ejpam-3401	232	14	.	.	PUNCT
ejpam-3401	233	1	(	(	PUNCT
ejpam-3401	233	2	iv	iv	X
ejpam-3401	233	3	)	)	PUNCT
ejpam-3401	233	4	countable	countable	ADJ
ejpam-3401	233	5	-	-	PUNCT
ejpam-3401	233	6	r	r	NOUN
ejpam-3401	233	7	-	-	ADJ
ejpam-3401	233	8	compact	compact	ADJ
ejpam-3401	233	9	,	,	PUNCT
ejpam-3401	233	10	if	if	SCONJ
ejpam-3401	233	11	x	x	PRON
ejpam-3401	233	12	is	be	AUX
ejpam-3401	233	13	countabler	countabler	NOUN
ejpam-3401	233	14	-	-	PUNCT
ejpam-3401	233	15	compact	compact	ADJ
ejpam-3401	233	16	.	.	PUNCT
ejpam-3401	234	1	(	(	PUNCT
ejpam-3401	234	2	v	v	NOUN
ejpam-3401	234	3	)	)	PUNCT
ejpam-3401	234	4	countable	countable	ADJ
ejpam-3401	234	5	contra	contra	PROPN
ejpam-3401	234	6	-	-	PUNCT
ejpam-3401	234	7	r	r	NOUN
ejpam-3401	234	8	-	-	ADJ
ejpam-3401	234	9	compact	compact	ADJ
ejpam-3401	234	10	,	,	PUNCT
ejpam-3401	234	11	if	if	SCONJ
ejpam-3401	234	12	x	x	PRON
ejpam-3401	234	13	is	be	AUX
ejpam-3401	234	14	countable	countable	ADJ
ejpam-3401	234	15	contra	contra	PROPN
ejpam-3401	234	16	-	-	PUNCT
ejpam-3401	234	17	r	r	NOUN
ejpam-3401	234	18	-	-	ADJ
ejpam-3401	234	19	compact	compact	ADJ
ejpam-3401	234	20	.	.	PUNCT
ejpam-3401	235	1	(	(	PUNCT
ejpam-3401	235	2	vi	vi	NOUN
ejpam-3401	235	3	)	)	PUNCT
ejpam-3401	235	4	contra	contra	PROPN
ejpam-3401	235	5	-	-	PUNCT
ejpam-3401	235	6	r	r	NOUN
ejpam-3401	235	7	-	-	PUNCT
ejpam-3401	235	8	lindelöf	lindelöf	NOUN
ejpam-3401	235	9	,	,	PUNCT
ejpam-3401	235	10	if	if	SCONJ
ejpam-3401	235	11	x	x	PRON
ejpam-3401	235	12	is	be	AUX
ejpam-3401	235	13	contra	contra	PROPN
ejpam-3401	235	14	-	-	PUNCT
ejpam-3401	235	15	r	r	NOUN
ejpam-3401	235	16	-	-	PUNCT
ejpam-3401	235	17	lindelöf	lindelöf	NOUN
ejpam-3401	235	18	.	.	PUNCT
ejpam-3401	236	1	proof	proof	NOUN
ejpam-3401	236	2	.	.	PUNCT
ejpam-3401	237	1	it	it	PRON
ejpam-3401	237	2	is	be	AUX
ejpam-3401	237	3	enough	enough	ADJ
ejpam-3401	237	4	to	to	PART
ejpam-3401	237	5	prove	prove	VERB
ejpam-3401	237	6	(	(	PUNCT
ejpam-3401	237	7	i	i	NOUN
ejpam-3401	237	8	)	)	PUNCT
ejpam-3401	237	9	and	and	CCONJ
ejpam-3401	237	10	for	for	ADP
ejpam-3401	237	11	the	the	DET
ejpam-3401	237	12	rest	rest	NOUN
ejpam-3401	237	13	one	one	NUM
ejpam-3401	237	14	can	can	AUX
ejpam-3401	237	15	use	use	VERB
ejpam-3401	237	16	the	the	DET
ejpam-3401	237	17	same	same	ADJ
ejpam-3401	237	18	methods	method	NOUN
ejpam-3401	237	19	to	to	PART
ejpam-3401	237	20	prove	prove	VERB
ejpam-3401	237	21	them	they	PRON
ejpam-3401	237	22	.	.	PUNCT
ejpam-3401	238	1	(	(	PUNCT
ejpam-3401	238	2	i	i	NOUN
ejpam-3401	238	3	)	)	PUNCT
ejpam-3401	238	4	t1(s	t1(s	PROPN
ejpam-3401	238	5	)	)	PUNCT
ejpam-3401	238	6	=	=	SYM
ejpam-3401	238	7	int(cl(s	int(cl(s	PROPN
ejpam-3401	238	8	)	)	PUNCT
ejpam-3401	238	9	)	)	PUNCT
ejpam-3401	238	10	and	and	CCONJ
ejpam-3401	238	11	t2(s	t2(s	NOUN
ejpam-3401	238	12	)	)	PUNCT
ejpam-3401	238	13	=	=	SYM
ejpam-3401	238	14	cl(int(s	cl(int(s	NOUN
ejpam-3401	238	15	)	)	PUNCT
ejpam-3401	238	16	)	)	PUNCT
ejpam-3401	238	17	are	be	AUX
ejpam-3401	238	18	given	give	VERB
ejpam-3401	238	19	.	.	PUNCT
ejpam-3401	239	1	so	so	ADV
ejpam-3401	239	2	f	f	PROPN
ejpam-3401	239	3	is	be	AUX
ejpam-3401	239	4	almost	almost	ADV
ejpam-3401	239	5	contra	contra	ADJ
ejpam-3401	239	6	-	-	ADJ
ejpam-3401	239	7	bcontinuous	bcontinuous	ADJ
ejpam-3401	239	8	and	and	CCONJ
ejpam-3401	239	9	surjective	surjective	ADJ
ejpam-3401	239	10	almost	almost	ADV
ejpam-3401	239	11	-	-	PUNCT
ejpam-3401	239	12	continuous	continuous	ADJ
ejpam-3401	239	13	,	,	PUNCT
ejpam-3401	239	14	by	by	ADP
ejpam-3401	239	15	the	the	DET
ejpam-3401	239	16	above	above	ADJ
ejpam-3401	239	17	lemma	lemma	PROPN
ejpam-3401	239	18	,	,	PUNCT
ejpam-3401	239	19	f	f	PROPN
ejpam-3401	239	20	is	be	AUX
ejpam-3401	239	21	r	r	NOUN
ejpam-3401	239	22	-	-	PUNCT
ejpam-3401	239	23	continuous	continuous	ADJ
ejpam-3401	239	24	,	,	PUNCT
ejpam-3401	239	25	that	that	PRON
ejpam-3401	239	26	is	be	AUX
ejpam-3401	239	27	the	the	DET
ejpam-3401	239	28	inverse	inverse	NOUN
ejpam-3401	239	29	of	of	ADP
ejpam-3401	239	30	each	each	DET
ejpam-3401	239	31	regular	regular	ADJ
ejpam-3401	239	32	closed	close	VERB
ejpam-3401	239	33	set	set	NOUN
ejpam-3401	239	34	in	in	ADP
ejpam-3401	239	35	y	y	PROPN
ejpam-3401	239	36	is	be	AUX
ejpam-3401	239	37	regular	regular	ADJ
ejpam-3401	239	38	in	in	ADP
ejpam-3401	239	39	x.	x.	NOUN
ejpam-3401	239	40	assume	assume	VERB
ejpam-3401	239	41	that	that	SCONJ
ejpam-3401	239	42	s	s	VERB
ejpam-3401	239	43	=	=	X
ejpam-3401	239	44	{	{	PUNCT
ejpam-3401	239	45	va|	va|	NOUN
ejpam-3401	239	46	a	a	DET
ejpam-3401	239	47	∈	∈	PROPN
ejpam-3401	239	48	λ	λ	PROPN
ejpam-3401	239	49	}	}	PUNCT
ejpam-3401	239	50	is	be	AUX
ejpam-3401	239	51	a	a	DET
ejpam-3401	239	52	regular	regular	ADJ
ejpam-3401	239	53	closed	closed	ADJ
ejpam-3401	239	54	cover	cover	NOUN
ejpam-3401	239	55	of	of	ADP
ejpam-3401	239	56	y.	y.	PROPN
ejpam-3401	239	57	consequently	consequently	ADV
ejpam-3401	239	58	,	,	PUNCT
ejpam-3401	239	59	s∗	s∗	PROPN
ejpam-3401	239	60	=	=	SYM
ejpam-3401	239	61	{	{	PUNCT
ejpam-3401	239	62	f−1(va)|	f−1(va)|	VERB
ejpam-3401	239	63	a	a	PRON
ejpam-3401	239	64	∈	∈	PROPN
ejpam-3401	239	65	λ	λ	PROPN
ejpam-3401	239	66	}	}	PUNCT
ejpam-3401	239	67	is	be	AUX
ejpam-3401	239	68	a	a	DET
ejpam-3401	239	69	regular	regular	ADJ
ejpam-3401	239	70	closed	closed	ADJ
ejpam-3401	239	71	cover	cover	NOUN
ejpam-3401	239	72	of	of	ADP
ejpam-3401	239	73	x	x	NOUN
ejpam-3401	239	74	,	,	PUNCT
ejpam-3401	239	75	but	but	CCONJ
ejpam-3401	239	76	x	x	X
ejpam-3401	239	77	is	be	AUX
ejpam-3401	239	78	contra	contra	PROPN
ejpam-3401	239	79	-	-	PUNCT
ejpam-3401	239	80	r	r	NOUN
ejpam-3401	239	81	-	-	PUNCT
ejpam-3401	239	82	compact	compact	ADJ
ejpam-3401	239	83	,	,	PUNCT
ejpam-3401	239	84	therefore	therefore	ADV
ejpam-3401	239	85	there	there	PRON
ejpam-3401	239	86	exists	exist	VERB
ejpam-3401	239	87	a1	a1	PROPN
ejpam-3401	239	88	,	,	PUNCT
ejpam-3401	239	89	a2	a2	PROPN
ejpam-3401	239	90	,	,	PUNCT
ejpam-3401	239	91	...	...	PUNCT
ejpam-3401	239	92	,	,	PUNCT
ejpam-3401	239	93	an	an	DET
ejpam-3401	239	94	such	such	ADJ
ejpam-3401	239	95	that	that	SCONJ
ejpam-3401	239	96	x	x	X
ejpam-3401	239	97	=	=	SYM
ejpam-3401	239	98	∪ni=1f	∪ni=1f	X
ejpam-3401	239	99	−1(vai	−1(vai	ADJ
ejpam-3401	239	100	)	)	PUNCT
ejpam-3401	239	101	and	and	CCONJ
ejpam-3401	239	102	y	y	PROPN
ejpam-3401	239	103	=	=	SYM
ejpam-3401	239	104	f(x	f(x	PROPN
ejpam-3401	239	105	)	)	PUNCT
ejpam-3401	239	106	=	=	SYM
ejpam-3401	239	107	f(∪ni=1f	f(∪ni=1f	PROPN
ejpam-3401	239	108	−1(vai	−1(vai	PROPN
ejpam-3401	239	109	)	)	PUNCT
ejpam-3401	239	110	)	)	PUNCT
ejpam-3401	239	111	,	,	PUNCT
ejpam-3401	239	112	which	which	PRON
ejpam-3401	239	113	shows	show	VERB
ejpam-3401	239	114	that	that	SCONJ
ejpam-3401	239	115	y	y	PROPN
ejpam-3401	239	116	is	be	AUX
ejpam-3401	239	117	contra	contra	PROPN
ejpam-3401	239	118	-	-	PUNCT
ejpam-3401	239	119	r	r	NOUN
ejpam-3401	239	120	-	-	PUNCT
ejpam-3401	239	121	compact	compact	ADJ
ejpam-3401	239	122	.	.	PUNCT
ejpam-3401	240	1	l.	l.	PROPN
ejpam-3401	240	2	m.	m.	PROPN
ejpam-3401	240	3	alabdulsada	alabdulsada	PROPN
ejpam-3401	240	4	/	/	SYM
ejpam-3401	240	5	eur	eur	PROPN
ejpam-3401	240	6	.	.	PUNCT
ejpam-3401	241	1	j.	j.	PROPN
ejpam-3401	241	2	pure	pure	PROPN
ejpam-3401	241	3	appl	appl	PROPN
ejpam-3401	241	4	.	.	PROPN
ejpam-3401	241	5	math	math	PROPN
ejpam-3401	241	6	,	,	PUNCT
ejpam-3401	241	7	12	12	NUM
ejpam-3401	241	8	(	(	PUNCT
ejpam-3401	241	9	2	2	NUM
ejpam-3401	241	10	)	)	PUNCT
ejpam-3401	241	11	(	(	PUNCT
ejpam-3401	241	12	2019	2019	NUM
ejpam-3401	241	13	)	)	PUNCT
ejpam-3401	241	14	,	,	PUNCT
ejpam-3401	241	15	358	358	NUM
ejpam-3401	241	16	-	-	SYM
ejpam-3401	241	17	369	369	NUM
ejpam-3401	241	18	367	367	NUM
ejpam-3401	241	19	proposition	proposition	NOUN
ejpam-3401	241	20	8	8	NUM
ejpam-3401	241	21	.	.	PUNCT
ejpam-3401	242	1	if	if	SCONJ
ejpam-3401	242	2	f	f	PROPN
ejpam-3401	242	3	:	:	PUNCT
ejpam-3401	242	4	(	(	PUNCT
ejpam-3401	242	5	x	x	X
ejpam-3401	242	6	,	,	PUNCT
ejpam-3401	242	7	τ	τ	PROPN
ejpam-3401	242	8	,	,	PUNCT
ejpam-3401	242	9	t1	t1	NOUN
ejpam-3401	242	10	,	,	PUNCT
ejpam-3401	242	11	t2	t2	NOUN
ejpam-3401	242	12	)	)	PUNCT
ejpam-3401	242	13	→	→	SYM
ejpam-3401	242	14	(	(	PUNCT
ejpam-3401	242	15	y	y	PROPN
ejpam-3401	242	16	,	,	PUNCT
ejpam-3401	242	17	σ	σ	PROPN
ejpam-3401	242	18	)	)	PUNCT
ejpam-3401	242	19	is	be	AUX
ejpam-3401	242	20	a	a	DET
ejpam-3401	242	21	contra	contra	PROPN
ejpam-3401	242	22	-	-	PUNCT
ejpam-3401	242	23	b	b	ADJ
ejpam-3401	242	24	-	-	PUNCT
ejpam-3401	242	25	continuous	continuous	ADJ
ejpam-3401	242	26	function	function	NOUN
ejpam-3401	242	27	and	and	CCONJ
ejpam-3401	242	28	s	s	NOUN
ejpam-3401	242	29	is	be	AUX
ejpam-3401	242	30	b	b	ADJ
ejpam-3401	242	31	-	-	ADJ
ejpam-3401	242	32	compact	compact	ADJ
ejpam-3401	242	33	relative	relative	NOUN
ejpam-3401	242	34	to	to	ADP
ejpam-3401	242	35	x	x	PRON
ejpam-3401	242	36	,	,	PUNCT
ejpam-3401	242	37	then	then	ADV
ejpam-3401	242	38	f(x	f(x	PROPN
ejpam-3401	242	39	)	)	PUNCT
ejpam-3401	243	1	is	be	AUX
ejpam-3401	243	2	contra	contra	ADJ
ejpam-3401	243	3	-	-	ADJ
ejpam-3401	243	4	compact	compact	ADJ
ejpam-3401	243	5	in	in	ADP
ejpam-3401	243	6	y.	y.	PROPN
ejpam-3401	243	7	proof	proof	NOUN
ejpam-3401	243	8	.	.	PUNCT
ejpam-3401	244	1	let	let	VERB
ejpam-3401	244	2	f	f	PROPN
ejpam-3401	244	3	=	=	PRON
ejpam-3401	244	4	{	{	PUNCT
ejpam-3401	244	5	va|	va|	NOUN
ejpam-3401	244	6	a	a	DET
ejpam-3401	244	7	∈	∈	PROPN
ejpam-3401	244	8	λ	λ	NOUN
ejpam-3401	244	9	}	}	PUNCT
ejpam-3401	244	10	be	be	VERB
ejpam-3401	244	11	any	any	DET
ejpam-3401	244	12	cover	cover	NOUN
ejpam-3401	244	13	of	of	ADP
ejpam-3401	244	14	f(s	f(	NOUN
ejpam-3401	244	15	)	)	PUNCT
ejpam-3401	244	16	.	.	PUNCT
ejpam-3401	245	1	it	it	PRON
ejpam-3401	245	2	follows	follow	VERB
ejpam-3401	245	3	from	from	ADP
ejpam-3401	245	4	the	the	DET
ejpam-3401	245	5	closed	closed	ADJ
ejpam-3401	245	6	set	set	NOUN
ejpam-3401	245	7	of	of	ADP
ejpam-3401	245	8	the	the	DET
ejpam-3401	245	9	subspace	subspace	NOUN
ejpam-3401	245	10	of	of	ADP
ejpam-3401	245	11	f(s	f(	NOUN
ejpam-3401	245	12	)	)	PUNCT
ejpam-3401	245	13	for	for	ADP
ejpam-3401	245	14	all	all	DET
ejpam-3401	245	15	a	a	DET
ejpam-3401	245	16	∈	∈	ADJ
ejpam-3401	245	17	λ	λ	NOUN
ejpam-3401	245	18	that	that	SCONJ
ejpam-3401	245	19	there	there	PRON
ejpam-3401	245	20	exists	exist	VERB
ejpam-3401	245	21	a	a	DET
ejpam-3401	245	22	closed	closed	ADJ
ejpam-3401	245	23	set	set	VERB
ejpam-3401	245	24	sa	sa	NOUN
ejpam-3401	245	25	of	of	ADP
ejpam-3401	245	26	y	y	PRON
ejpam-3401	245	27	such	such	ADJ
ejpam-3401	245	28	that	that	SCONJ
ejpam-3401	245	29	sa∩f(s	sa∩f(s	NOUN
ejpam-3401	245	30	)	)	PUNCT
ejpam-3401	245	31	=	=	SYM
ejpam-3401	245	32	va	va	NOUN
ejpam-3401	245	33	and	and	CCONJ
ejpam-3401	245	34	for	for	ADP
ejpam-3401	245	35	each	each	DET
ejpam-3401	245	36	x	x	SYM
ejpam-3401	245	37	∈	∈	PROPN
ejpam-3401	245	38	s	s	X
ejpam-3401	245	39	,	,	PUNCT
ejpam-3401	245	40	there	there	PRON
ejpam-3401	245	41	exists	exist	VERB
ejpam-3401	245	42	a(x	a(x	NOUN
ejpam-3401	245	43	)	)	PUNCT
ejpam-3401	245	44	∈	∈	PROPN
ejpam-3401	245	45	λ	λ	X
ejpam-3401	245	46	where	where	SCONJ
ejpam-3401	245	47	f(s	f(	NOUN
ejpam-3401	245	48	)	)	PUNCT
ejpam-3401	245	49	∈	∈	PROPN
ejpam-3401	245	50	sa(x	sa(x	NOUN
ejpam-3401	245	51	)	)	PUNCT
ejpam-3401	245	52	.	.	PUNCT
ejpam-3401	246	1	then	then	ADV
ejpam-3401	246	2	there	there	PRON
ejpam-3401	246	3	exists	exist	VERB
ejpam-3401	246	4	ux	ux	PROPN
ejpam-3401	246	5	which	which	PRON
ejpam-3401	246	6	is	be	AUX
ejpam-3401	246	7	b	b	NOUN
ejpam-3401	246	8	-	-	ADJ
ejpam-3401	246	9	open	open	ADJ
ejpam-3401	246	10	,	,	PUNCT
ejpam-3401	246	11	this	this	PRON
ejpam-3401	246	12	implies	imply	VERB
ejpam-3401	246	13	that	that	SCONJ
ejpam-3401	246	14	f(ux	f(ux	NOUN
ejpam-3401	246	15	)	)	PUNCT
ejpam-3401	246	16	∈	∈	NOUN
ejpam-3401	246	17	sa(x	sa(x	NOUN
ejpam-3401	246	18	)	)	PUNCT
ejpam-3401	246	19	such	such	ADJ
ejpam-3401	246	20	that	that	SCONJ
ejpam-3401	246	21	the	the	DET
ejpam-3401	246	22	family	family	NOUN
ejpam-3401	246	23	f∗	f∗	NOUN
ejpam-3401	246	24	=	=	PUNCT
ejpam-3401	246	25	{	{	PUNCT
ejpam-3401	246	26	ux|	ux|	NOUN
ejpam-3401	246	27	x	x	SYM
ejpam-3401	246	28	∈	∈	PROPN
ejpam-3401	246	29	s	s	PART
ejpam-3401	246	30	}	}	PUNCT
ejpam-3401	246	31	is	be	AUX
ejpam-3401	246	32	a	a	DET
ejpam-3401	246	33	cover	cover	NOUN
ejpam-3401	246	34	of	of	ADP
ejpam-3401	246	35	s	s	NOUN
ejpam-3401	246	36	by	by	ADP
ejpam-3401	246	37	b	b	NOUN
ejpam-3401	246	38	-	-	PUNCT
ejpam-3401	246	39	open	open	ADJ
ejpam-3401	246	40	of	of	ADP
ejpam-3401	246	41	x.	x.	NOUN
ejpam-3401	246	42	but	but	CCONJ
ejpam-3401	246	43	s	s	NOUN
ejpam-3401	246	44	is	be	AUX
ejpam-3401	246	45	b	b	NOUN
ejpam-3401	246	46	-	-	ADJ
ejpam-3401	246	47	compact	compact	ADJ
ejpam-3401	246	48	relative	relative	NOUN
ejpam-3401	246	49	to	to	ADP
ejpam-3401	246	50	x	x	PRON
ejpam-3401	246	51	,	,	PUNCT
ejpam-3401	246	52	so	so	SCONJ
ejpam-3401	246	53	there	there	PRON
ejpam-3401	246	54	exist	exist	VERB
ejpam-3401	246	55	x1	x1	PROPN
ejpam-3401	246	56	,	,	PUNCT
ejpam-3401	246	57	...	...	PUNCT
ejpam-3401	246	58	,	,	PUNCT
ejpam-3401	246	59	xn	xn	PROPN
ejpam-3401	246	60	∈	∈	PROPN
ejpam-3401	246	61	s	s	PART
ejpam-3401	246	62	and	and	CCONJ
ejpam-3401	246	63	s	s	NOUN
ejpam-3401	246	64	⊆	⊆	NUM
ejpam-3401	246	65	∪ni=1f	∪ni=1f	NOUN
ejpam-3401	246	66	−1uxi	−1uxi	NOUN
ejpam-3401	246	67	.	.	PUNCT
ejpam-3401	247	1	hence	hence	ADV
ejpam-3401	247	2	f(s	f(	VERB
ejpam-3401	247	3	)	)	PUNCT
ejpam-3401	247	4	⊆	⊆	NUM
ejpam-3401	247	5	f(∪ni=1f	f(∪ni=1f	PROPN
ejpam-3401	247	6	−1uxi	−1uxi	NOUN
ejpam-3401	247	7	)	)	PUNCT
ejpam-3401	248	1	=	=	SYM
ejpam-3401	249	1	∪ni=1uxi	∪ni=1uxi	PROPN
ejpam-3401	249	2	,	,	PUNCT
ejpam-3401	249	3	therefore	therefore	ADV
ejpam-3401	249	4	,	,	PUNCT
ejpam-3401	249	5	f(s	f(s	ADV
ejpam-3401	249	6	)	)	PUNCT
ejpam-3401	249	7	=	=	SYM
ejpam-3401	249	8	∪ni=1va(xi	∪ni=1va(xi	PROPN
ejpam-3401	249	9	)	)	PUNCT
ejpam-3401	249	10	.	.	PUNCT
ejpam-3401	250	1	corollary	corollary	ADJ
ejpam-3401	250	2	2	2	NUM
ejpam-3401	250	3	.	.	PUNCT
ejpam-3401	251	1	if	if	SCONJ
ejpam-3401	251	2	f	f	PROPN
ejpam-3401	251	3	:	:	PUNCT
ejpam-3401	251	4	(	(	PUNCT
ejpam-3401	251	5	x	x	X
ejpam-3401	251	6	,	,	PUNCT
ejpam-3401	251	7	τ	τ	PROPN
ejpam-3401	251	8	,	,	PUNCT
ejpam-3401	251	9	t1	t1	NOUN
ejpam-3401	251	10	,	,	PUNCT
ejpam-3401	251	11	t2	t2	NOUN
ejpam-3401	251	12	)	)	PUNCT
ejpam-3401	251	13	→	→	SYM
ejpam-3401	251	14	(	(	PUNCT
ejpam-3401	251	15	y	y	PROPN
ejpam-3401	251	16	,	,	PUNCT
ejpam-3401	251	17	σ	σ	PROPN
ejpam-3401	251	18	)	)	PUNCT
ejpam-3401	251	19	is	be	AUX
ejpam-3401	251	20	a	a	DET
ejpam-3401	251	21	contra	contra	PROPN
ejpam-3401	251	22	-	-	PUNCT
ejpam-3401	251	23	b	b	NOUN
ejpam-3401	251	24	-	-	PUNCT
ejpam-3401	251	25	continuous	continuous	ADJ
ejpam-3401	251	26	surjective	surjective	ADJ
ejpam-3401	251	27	function	function	NOUN
ejpam-3401	251	28	and	and	CCONJ
ejpam-3401	251	29	x	x	ADJ
ejpam-3401	251	30	is	be	AUX
ejpam-3401	251	31	b	b	NOUN
ejpam-3401	251	32	-	-	ADJ
ejpam-3401	251	33	compact	compact	ADJ
ejpam-3401	251	34	,	,	PUNCT
ejpam-3401	251	35	then	then	ADV
ejpam-3401	251	36	y	y	PROPN
ejpam-3401	251	37	is	be	AUX
ejpam-3401	251	38	contra	contra	ADJ
ejpam-3401	251	39	-	-	ADJ
ejpam-3401	251	40	compact	compact	ADJ
ejpam-3401	251	41	.	.	PUNCT
ejpam-3401	252	1	definition	definition	NOUN
ejpam-3401	252	2	18	18	NUM
ejpam-3401	252	3	.	.	PUNCT
ejpam-3401	253	1	a	a	DET
ejpam-3401	253	2	function	function	NOUN
ejpam-3401	253	3	f	f	NOUN
ejpam-3401	253	4	:	:	PUNCT
ejpam-3401	253	5	(	(	PUNCT
ejpam-3401	253	6	x	x	X
ejpam-3401	253	7	,	,	PUNCT
ejpam-3401	253	8	τ	τ	PROPN
ejpam-3401	253	9	,	,	PUNCT
ejpam-3401	253	10	t1	t1	PROPN
ejpam-3401	253	11	,	,	PUNCT
ejpam-3401	253	12	t2)→	t2)→	X
ejpam-3401	253	13	(	(	PUNCT
ejpam-3401	253	14	y	y	PROPN
ejpam-3401	253	15	,	,	PUNCT
ejpam-3401	253	16	σ	σ	PROPN
ejpam-3401	253	17	)	)	PUNCT
ejpam-3401	253	18	is	be	AUX
ejpam-3401	253	19	called	call	VERB
ejpam-3401	253	20	almost	almost	ADV
ejpam-3401	253	21	weakly	weakly	ADJ
ejpam-3401	253	22	-	-	PUNCT
ejpam-3401	253	23	b	b	NOUN
ejpam-3401	253	24	-	-	PUNCT
ejpam-3401	253	25	continuous	continuous	ADJ
ejpam-3401	253	26	,	,	PUNCT
ejpam-3401	253	27	if	if	SCONJ
ejpam-3401	253	28	for	for	ADP
ejpam-3401	253	29	each	each	DET
ejpam-3401	253	30	x	x	SYM
ejpam-3401	253	31	∈	∈	PROPN
ejpam-3401	253	32	x	x	X
ejpam-3401	253	33	and	and	CCONJ
ejpam-3401	253	34	regular	regular	ADJ
ejpam-3401	253	35	set	set	VERB
ejpam-3401	253	36	v	v	NOUN
ejpam-3401	253	37	containing	contain	VERB
ejpam-3401	253	38	f(x	f(x	PROPN
ejpam-3401	253	39	)	)	PUNCT
ejpam-3401	253	40	there	there	PRON
ejpam-3401	253	41	exist	exist	VERB
ejpam-3401	253	42	u	u	NOUN
ejpam-3401	253	43	which	which	PRON
ejpam-3401	253	44	is	be	AUX
ejpam-3401	253	45	a	a	DET
ejpam-3401	253	46	b	b	NOUN
ejpam-3401	253	47	-	-	PUNCT
ejpam-3401	253	48	open	open	ADJ
ejpam-3401	253	49	set	set	NOUN
ejpam-3401	253	50	in	in	ADP
ejpam-3401	253	51	x	x	PUNCT
ejpam-3401	253	52	containing	contain	VERB
ejpam-3401	253	53	x	x	PUNCT
ejpam-3401	253	54	such	such	ADJ
ejpam-3401	253	55	that	that	DET
ejpam-3401	253	56	f(u	f(u	PROPN
ejpam-3401	253	57	)	)	PUNCT
ejpam-3401	253	58	⊆	⊆	NUM
ejpam-3401	253	59	cl(v	cl(v	NOUN
ejpam-3401	253	60	)	)	PUNCT
ejpam-3401	253	61	.	.	PUNCT
ejpam-3401	254	1	proposition	proposition	NOUN
ejpam-3401	254	2	9	9	NUM
ejpam-3401	254	3	.	.	PUNCT
ejpam-3401	255	1	let	let	VERB
ejpam-3401	255	2	a	a	DET
ejpam-3401	255	3	function	function	NOUN
ejpam-3401	255	4	f	f	NOUN
ejpam-3401	255	5	:	:	PUNCT
ejpam-3401	255	6	(	(	PUNCT
ejpam-3401	255	7	x	x	X
ejpam-3401	255	8	,	,	PUNCT
ejpam-3401	255	9	τ	τ	PROPN
ejpam-3401	255	10	,	,	PUNCT
ejpam-3401	255	11	t1	t1	PROPN
ejpam-3401	255	12	,	,	PUNCT
ejpam-3401	255	13	t2)→	t2)→	X
ejpam-3401	255	14	(	(	PUNCT
ejpam-3401	255	15	y	y	PROPN
ejpam-3401	255	16	,	,	PUNCT
ejpam-3401	255	17	σ	σ	PROPN
ejpam-3401	255	18	)	)	PUNCT
ejpam-3401	255	19	be	be	AUX
ejpam-3401	255	20	an	an	DET
ejpam-3401	255	21	almost	almost	ADV
ejpam-3401	255	22	contra	contra	ADJ
ejpam-3401	255	23	-	-	PUNCT
ejpam-3401	255	24	b	b	NOUN
ejpam-3401	255	25	-	-	PUNCT
ejpam-3401	255	26	continuous	continuous	ADJ
ejpam-3401	255	27	and	and	CCONJ
ejpam-3401	255	28	y	y	PROPN
ejpam-3401	255	29	be	be	AUX
ejpam-3401	255	30	an	an	DET
ejpam-3401	255	31	urysohn	urysohn	NOUN
ejpam-3401	255	32	space	space	NOUN
ejpam-3401	255	33	,	,	PUNCT
ejpam-3401	255	34	then	then	ADV
ejpam-3401	255	35	g(f	g(f	PROPN
ejpam-3401	255	36	)	)	PUNCT
ejpam-3401	255	37	is	be	AUX
ejpam-3401	255	38	regular	regular	ADJ
ejpam-3401	255	39	in	in	ADP
ejpam-3401	255	40	x	x	SYM
ejpam-3401	255	41	×	×	PROPN
ejpam-3401	255	42	y.	y.	NOUN
ejpam-3401	255	43	proof	proof	NOUN
ejpam-3401	255	44	.	.	PUNCT
ejpam-3401	256	1	let	let	VERB
ejpam-3401	256	2	(	(	PUNCT
ejpam-3401	256	3	x	x	NOUN
ejpam-3401	256	4	,	,	PUNCT
ejpam-3401	256	5	y	y	NOUN
ejpam-3401	256	6	)	)	PUNCT
ejpam-3401	256	7	∈	∈	PROPN
ejpam-3401	256	8	x×y	x×y	PROPN
ejpam-3401	256	9	\g(f	\g(f	PROPN
ejpam-3401	256	10	)	)	PUNCT
ejpam-3401	256	11	,	,	PUNCT
ejpam-3401	256	12	it	it	PRON
ejpam-3401	256	13	follows	follow	VERB
ejpam-3401	256	14	that	that	SCONJ
ejpam-3401	256	15	y	y	PROPN
ejpam-3401	256	16	6=	6=	PROPN
ejpam-3401	256	17	f(x	f(x	PROPN
ejpam-3401	256	18	)	)	PUNCT
ejpam-3401	256	19	,	,	PUNCT
ejpam-3401	256	20	since	since	SCONJ
ejpam-3401	256	21	y	y	PROPN
ejpam-3401	256	22	is	be	AUX
ejpam-3401	256	23	an	an	DET
ejpam-3401	256	24	urysohn	urysohn	NOUN
ejpam-3401	256	25	,	,	PUNCT
ejpam-3401	256	26	then	then	ADV
ejpam-3401	256	27	there	there	PRON
ejpam-3401	256	28	exist	exist	VERB
ejpam-3401	256	29	open	open	ADJ
ejpam-3401	256	30	sets	set	NOUN
ejpam-3401	256	31	u	u	NOUN
ejpam-3401	256	32	and	and	CCONJ
ejpam-3401	256	33	v	v	ADP
ejpam-3401	256	34	containing	contain	VERB
ejpam-3401	256	35	f(x	f(x	PROPN
ejpam-3401	256	36	)	)	PUNCT
ejpam-3401	256	37	and	and	CCONJ
ejpam-3401	256	38	y	y	PROPN
ejpam-3401	256	39	,	,	PUNCT
ejpam-3401	256	40	respectively	respectively	ADV
ejpam-3401	256	41	where	where	SCONJ
ejpam-3401	256	42	u	u	NOUN
ejpam-3401	256	43	∩v	∩v	NOUN
ejpam-3401	256	44	=	=	PUNCT
ejpam-3401	256	45	∅.	∅.	NOUN
ejpam-3401	256	46	then	then	ADV
ejpam-3401	256	47	int(cl(u	int(cl(u	PROPN
ejpam-3401	256	48	)	)	PUNCT
ejpam-3401	256	49	)	)	PUNCT
ejpam-3401	256	50	∩	∩	NOUN
ejpam-3401	256	51	cl(int(v	cl(int(v	NOUN
ejpam-3401	256	52	)	)	PUNCT
ejpam-3401	256	53	)	)	PUNCT
ejpam-3401	257	1	=	=	PUNCT
ejpam-3401	257	2	∅.	∅.	NOUN
ejpam-3401	257	3	since	since	SCONJ
ejpam-3401	257	4	f	f	PROPN
ejpam-3401	257	5	is	be	AUX
ejpam-3401	257	6	almost	almost	ADV
ejpam-3401	257	7	contra	contra	PROPN
ejpam-3401	257	8	-	-	PUNCT
ejpam-3401	257	9	b	b	NOUN
ejpam-3401	257	10	-	-	PUNCT
ejpam-3401	257	11	continuous	continuous	ADJ
ejpam-3401	257	12	,	,	PUNCT
ejpam-3401	257	13	we	we	PRON
ejpam-3401	257	14	have	have	VERB
ejpam-3401	257	15	that	that	DET
ejpam-3401	257	16	f−1(int(cl(u	f−1(int(cl(u	PROPN
ejpam-3401	257	17	)	)	PUNCT
ejpam-3401	257	18	)	)	PUNCT
ejpam-3401	257	19	)	)	PUNCT
ejpam-3401	257	20	is	be	AUX
ejpam-3401	257	21	b	b	NOUN
ejpam-3401	257	22	-	-	PUNCT
ejpam-3401	257	23	closed	closed	ADJ
ejpam-3401	257	24	in	in	ADP
ejpam-3401	257	25	x	x	PUNCT
ejpam-3401	257	26	containing	contain	VERB
ejpam-3401	257	27	x.	x.	NOUN
ejpam-3401	257	28	if	if	SCONJ
ejpam-3401	257	29	w	w	PROPN
ejpam-3401	257	30	=	=	SYM
ejpam-3401	257	31	f−1(int(cl(u	f−1(int(cl(u	PROPN
ejpam-3401	257	32	)	)	PUNCT
ejpam-3401	257	33	)	)	PUNCT
ejpam-3401	257	34	)	)	PUNCT
ejpam-3401	257	35	,	,	PUNCT
ejpam-3401	257	36	then	then	ADV
ejpam-3401	257	37	f(w	f(w	PROPN
ejpam-3401	257	38	)	)	PUNCT
ejpam-3401	257	39	⊆	⊆	NUM
ejpam-3401	257	40	int(cl(u	int(cl(u	PROPN
ejpam-3401	257	41	)	)	PUNCT
ejpam-3401	257	42	)	)	PUNCT
ejpam-3401	257	43	such	such	ADJ
ejpam-3401	257	44	that	that	SCONJ
ejpam-3401	257	45	f(w	f(w	PROPN
ejpam-3401	257	46	)	)	PUNCT
ejpam-3401	257	47	∩	∩	NOUN
ejpam-3401	257	48	int(cl(v	int(cl(v	NOUN
ejpam-3401	257	49	)	)	PUNCT
ejpam-3401	257	50	)	)	PUNCT
ejpam-3401	258	1	=	=	NOUN
ejpam-3401	258	2	∅	∅	NOUN
ejpam-3401	258	3	and	and	CCONJ
ejpam-3401	258	4	int(cl(v	int(cl(v	NOUN
ejpam-3401	258	5	)	)	PUNCT
ejpam-3401	258	6	is	be	AUX
ejpam-3401	258	7	regular	regular	ADJ
ejpam-3401	258	8	in	in	ADP
ejpam-3401	258	9	y	y	PROPN
ejpam-3401	258	10	.	.	PUNCT
ejpam-3401	259	1	hence	hence	ADV
ejpam-3401	259	2	g(f	g(f	PROPN
ejpam-3401	259	3	)	)	PUNCT
ejpam-3401	259	4	is	be	AUX
ejpam-3401	259	5	b	b	NOUN
ejpam-3401	259	6	-	-	ADJ
ejpam-3401	259	7	regular	regular	ADJ
ejpam-3401	259	8	in	in	ADP
ejpam-3401	259	9	x	x	SYM
ejpam-3401	259	10	×	×	PROPN
ejpam-3401	259	11	y.	y.	NOUN
ejpam-3401	259	12	proposition	proposition	NOUN
ejpam-3401	259	13	10	10	NUM
ejpam-3401	259	14	.	.	PUNCT
ejpam-3401	260	1	suppose	suppose	VERB
ejpam-3401	260	2	that	that	SCONJ
ejpam-3401	260	3	f	f	X
ejpam-3401	260	4	:	:	PUNCT
ejpam-3401	260	5	(	(	PUNCT
ejpam-3401	260	6	x	x	X
ejpam-3401	260	7	,	,	PUNCT
ejpam-3401	260	8	τ	τ	PROPN
ejpam-3401	260	9	,	,	PUNCT
ejpam-3401	260	10	t1	t1	PROPN
ejpam-3401	260	11	,	,	PUNCT
ejpam-3401	260	12	t2)→	t2)→	X
ejpam-3401	260	13	(	(	PUNCT
ejpam-3401	260	14	y	y	PROPN
ejpam-3401	260	15	,	,	PUNCT
ejpam-3401	260	16	σ	σ	PROPN
ejpam-3401	260	17	)	)	PUNCT
ejpam-3401	260	18	has	have	VERB
ejpam-3401	260	19	a	a	DET
ejpam-3401	260	20	b	b	NOUN
ejpam-3401	260	21	-	-	PUNCT
ejpam-3401	260	22	regular	regular	ADJ
ejpam-3401	260	23	graph	graph	NOUN
ejpam-3401	260	24	.	.	PUNCT
ejpam-3401	261	1	if	if	SCONJ
ejpam-3401	261	2	f	f	PROPN
ejpam-3401	261	3	is	be	AUX
ejpam-3401	261	4	a	a	DET
ejpam-3401	261	5	surjective	surjective	ADJ
ejpam-3401	261	6	function	function	NOUN
ejpam-3401	261	7	,	,	PUNCT
ejpam-3401	261	8	then	then	ADV
ejpam-3401	261	9	y	y	PROPN
ejpam-3401	261	10	is	be	AUX
ejpam-3401	261	11	weakly	weakly	ADJ
ejpam-3401	261	12	hausdorff	hausdorff	NOUN
ejpam-3401	261	13	.	.	PUNCT
ejpam-3401	262	1	proof	proof	NOUN
ejpam-3401	262	2	.	.	PUNCT
ejpam-3401	263	1	let	let	VERB
ejpam-3401	263	2	y	y	PRON
ejpam-3401	263	3	,	,	PUNCT
ejpam-3401	263	4	ȳ	ȳ	PROPN
ejpam-3401	263	5	be	be	AUX
ejpam-3401	263	6	any	any	DET
ejpam-3401	263	7	two	two	NUM
ejpam-3401	263	8	distinct	distinct	ADJ
ejpam-3401	263	9	points	point	NOUN
ejpam-3401	263	10	of	of	ADP
ejpam-3401	263	11	y	y	PROPN
ejpam-3401	263	12	.	.	PUNCT
ejpam-3401	264	1	since	since	SCONJ
ejpam-3401	264	2	f	f	PROPN
ejpam-3401	264	3	is	be	AUX
ejpam-3401	264	4	surjective	surjective	ADJ
ejpam-3401	264	5	,	,	PUNCT
ejpam-3401	264	6	then	then	ADV
ejpam-3401	264	7	there	there	PRON
ejpam-3401	264	8	exists	exist	VERB
ejpam-3401	264	9	x	x	X
ejpam-3401	264	10	∈	∈	PROPN
ejpam-3401	264	11	x	x	PUNCT
ejpam-3401	264	12	where	where	SCONJ
ejpam-3401	264	13	f(x	f(x	NOUN
ejpam-3401	264	14	)	)	PUNCT
ejpam-3401	265	1	=	=	PUNCT
ejpam-3401	266	1	y.	y.	NOUN
ejpam-3401	266	2	notice	notice	VERB
ejpam-3401	266	3	(	(	PUNCT
ejpam-3401	266	4	x	x	NOUN
ejpam-3401	266	5	,	,	PUNCT
ejpam-3401	266	6	ȳ	ȳ	NUM
ejpam-3401	266	7	)	)	PUNCT
ejpam-3401	266	8	∈	∈	PROPN
ejpam-3401	266	9	(	(	PUNCT
ejpam-3401	266	10	x×y	x×y	PROPN
ejpam-3401	266	11	)	)	PUNCT
ejpam-3401	266	12	\g(f	\g(f	PROPN
ejpam-3401	266	13	)	)	PUNCT
ejpam-3401	266	14	,	,	PUNCT
ejpam-3401	266	15	by	by	ADP
ejpam-3401	266	16	the	the	DET
ejpam-3401	266	17	definition	definition	NOUN
ejpam-3401	266	18	of	of	ADP
ejpam-3401	266	19	b	b	NOUN
ejpam-3401	266	20	-	-	PUNCT
ejpam-3401	266	21	regular	regular	ADJ
ejpam-3401	266	22	graph	graph	NOUN
ejpam-3401	266	23	,	,	PUNCT
ejpam-3401	266	24	there	there	PRON
ejpam-3401	266	25	exists	exist	VERB
ejpam-3401	266	26	b	b	NOUN
ejpam-3401	266	27	-	-	PUNCT
ejpam-3401	266	28	closed	closed	ADJ
ejpam-3401	266	29	set	set	ADJ
ejpam-3401	266	30	u	u	NOUN
ejpam-3401	266	31	of	of	ADP
ejpam-3401	266	32	x	x	X
ejpam-3401	266	33	and	and	CCONJ
ejpam-3401	266	34	a	a	DET
ejpam-3401	266	35	regular	regular	ADJ
ejpam-3401	266	36	open	open	ADJ
ejpam-3401	266	37	fȳ	fȳ	NOUN
ejpam-3401	266	38	in	in	ADP
ejpam-3401	266	39	y	y	PROPN
ejpam-3401	266	40	such	such	ADJ
ejpam-3401	266	41	that	that	SCONJ
ejpam-3401	266	42	(	(	PUNCT
ejpam-3401	266	43	x	x	NOUN
ejpam-3401	266	44	,	,	PUNCT
ejpam-3401	266	45	ȳ	ȳ	NUM
ejpam-3401	266	46	)	)	PUNCT
ejpam-3401	266	47	∈	∈	PROPN
ejpam-3401	266	48	u	u	NOUN
ejpam-3401	266	49	×fȳ	×fȳ	PROPN
ejpam-3401	266	50	and	and	CCONJ
ejpam-3401	266	51	f(u)∩	f(u)∩	ADJ
ejpam-3401	266	52	fȳ	fȳ	NOUN
ejpam-3401	266	53	=	=	PUNCT
ejpam-3401	266	54	∅.	∅.	NOUN
ejpam-3401	266	55	since	since	SCONJ
ejpam-3401	266	56	f(x	f(x	PROPN
ejpam-3401	266	57	)	)	PUNCT
ejpam-3401	266	58	∈	∈	PROPN
ejpam-3401	266	59	f(u	f(u	PROPN
ejpam-3401	266	60	)	)	PUNCT
ejpam-3401	266	61	and	and	CCONJ
ejpam-3401	266	62	y	y	PROPN
ejpam-3401	266	63	/∈	/∈	PUNCT
ejpam-3401	266	64	fȳ	fȳ	NOUN
ejpam-3401	266	65	,	,	PUNCT
ejpam-3401	266	66	ȳ	ȳ	PROPN
ejpam-3401	266	67	/∈	/∈	PUNCT
ejpam-3401	267	1	f	f	PROPN
ejpam-3401	267	2	c	c	NOUN
ejpam-3401	267	3	ȳ	ȳ	PROPN
ejpam-3401	267	4	which	which	PRON
ejpam-3401	267	5	is	be	AUX
ejpam-3401	267	6	regular	regular	ADV
ejpam-3401	267	7	closed	closed	ADJ
ejpam-3401	267	8	in	in	ADP
ejpam-3401	267	9	y	y	PROPN
ejpam-3401	267	10	,	,	PUNCT
ejpam-3401	267	11	we	we	PRON
ejpam-3401	267	12	get	get	VERB
ejpam-3401	267	13	y	y	NOUN
ejpam-3401	267	14	=	=	PRON
ejpam-3401	267	15	∩	∩	ADJ
ejpam-3401	267	16	ȳ	ȳ	PROPN
ejpam-3401	267	17	6	6	NUM
ejpam-3401	267	18	=	=	SYM
ejpam-3401	267	19	y	y	NOUN
ejpam-3401	267	20	f	f	NOUN
ejpam-3401	267	21	c	c	PROPN
ejpam-3401	267	22	ȳ	ȳ	PROPN
ejpam-3401	267	23	.	.	PUNCT
ejpam-3401	268	1	thus	thus	ADV
ejpam-3401	268	2	,	,	PUNCT
ejpam-3401	268	3	y	y	PROPN
ejpam-3401	268	4	is	be	AUX
ejpam-3401	268	5	weakly	weakly	ADJ
ejpam-3401	268	6	hausdorff	hausdorff	NOUN
ejpam-3401	268	7	.	.	PUNCT
ejpam-3401	269	1	proposition	proposition	NOUN
ejpam-3401	269	2	11	11	NUM
ejpam-3401	269	3	.	.	PUNCT
ejpam-3401	270	1	let	let	VERB
ejpam-3401	270	2	f	f	NOUN
ejpam-3401	270	3	:	:	PUNCT
ejpam-3401	270	4	(	(	PUNCT
ejpam-3401	270	5	x	x	X
ejpam-3401	270	6	,	,	PUNCT
ejpam-3401	270	7	τ	τ	PROPN
ejpam-3401	270	8	,	,	PUNCT
ejpam-3401	270	9	t1	t1	PROPN
ejpam-3401	270	10	,	,	PUNCT
ejpam-3401	270	11	t2)→	t2)→	X
ejpam-3401	270	12	(	(	PUNCT
ejpam-3401	270	13	y	y	PROPN
ejpam-3401	270	14	,	,	PUNCT
ejpam-3401	270	15	σ	σ	PROPN
ejpam-3401	270	16	)	)	PUNCT
ejpam-3401	270	17	be	be	VERB
ejpam-3401	270	18	a	a	DET
ejpam-3401	270	19	function	function	NOUN
ejpam-3401	270	20	which	which	PRON
ejpam-3401	270	21	has	have	VERB
ejpam-3401	270	22	a	a	DET
ejpam-3401	270	23	b	b	NOUN
ejpam-3401	270	24	-	-	PUNCT
ejpam-3401	270	25	regular	regular	ADJ
ejpam-3401	270	26	graph	graph	NOUN
ejpam-3401	270	27	.	.	PUNCT
ejpam-3401	271	1	if	if	SCONJ
ejpam-3401	271	2	f	f	PROPN
ejpam-3401	271	3	is	be	AUX
ejpam-3401	271	4	an	an	DET
ejpam-3401	271	5	injective	injective	ADJ
ejpam-3401	271	6	function	function	NOUN
ejpam-3401	271	7	,	,	PUNCT
ejpam-3401	271	8	then	then	ADV
ejpam-3401	271	9	x	x	PUNCT
ejpam-3401	271	10	is	be	AUX
ejpam-3401	271	11	b	b	NOUN
ejpam-3401	271	12	-	-	PUNCT
ejpam-3401	271	13	frechet	frechet	NOUN
ejpam-3401	271	14	.	.	PUNCT
ejpam-3401	272	1	proof	proof	NOUN
ejpam-3401	272	2	.	.	PUNCT
ejpam-3401	273	1	assume	assume	VERB
ejpam-3401	273	2	that	that	SCONJ
ejpam-3401	273	3	x1	x1	PROPN
ejpam-3401	273	4	,	,	PUNCT
ejpam-3401	273	5	x2	x2	PRON
ejpam-3401	273	6	are	be	AUX
ejpam-3401	273	7	any	any	DET
ejpam-3401	273	8	two	two	NUM
ejpam-3401	273	9	distinct	distinct	ADJ
ejpam-3401	273	10	points	point	NOUN
ejpam-3401	273	11	of	of	ADP
ejpam-3401	273	12	x.	x.	NOUN
ejpam-3401	273	13	since	since	SCONJ
ejpam-3401	273	14	f	f	PROPN
ejpam-3401	273	15	is	be	AUX
ejpam-3401	273	16	injective	injective	ADJ
ejpam-3401	273	17	,	,	PUNCT
ejpam-3401	273	18	it	it	PRON
ejpam-3401	273	19	follows	follow	VERB
ejpam-3401	273	20	that	that	SCONJ
ejpam-3401	273	21	(	(	PUNCT
ejpam-3401	273	22	x1	x1	ADJ
ejpam-3401	273	23	,	,	PUNCT
ejpam-3401	273	24	f(x2	f(x2	NOUN
ejpam-3401	273	25	)	)	PUNCT
ejpam-3401	273	26	)	)	PUNCT
ejpam-3401	274	1	∈	∈	PROPN
ejpam-3401	274	2	(	(	PUNCT
ejpam-3401	274	3	x×y	x×y	PROPN
ejpam-3401	274	4	)	)	PUNCT
ejpam-3401	274	5	\g(f	\g(f	PROPN
ejpam-3401	274	6	)	)	PUNCT
ejpam-3401	274	7	,	,	PUNCT
ejpam-3401	274	8	by	by	ADP
ejpam-3401	274	9	the	the	DET
ejpam-3401	274	10	definition	definition	NOUN
ejpam-3401	274	11	of	of	ADP
ejpam-3401	274	12	b	b	NOUN
ejpam-3401	274	13	-	-	PUNCT
ejpam-3401	274	14	regular	regular	ADJ
ejpam-3401	274	15	graph	graph	NOUN
ejpam-3401	274	16	.	.	PUNCT
ejpam-3401	275	1	then	then	ADV
ejpam-3401	275	2	there	there	PRON
ejpam-3401	275	3	exist	exist	VERB
ejpam-3401	275	4	a	a	DET
ejpam-3401	275	5	b	b	NOUN
ejpam-3401	275	6	-	-	PUNCT
ejpam-3401	275	7	closed	closed	ADJ
ejpam-3401	275	8	set	set	ADJ
ejpam-3401	275	9	u	u	NOUN
ejpam-3401	275	10	of	of	ADP
ejpam-3401	275	11	x	x	X
ejpam-3401	275	12	and	and	CCONJ
ejpam-3401	275	13	a	a	DET
ejpam-3401	275	14	regular	regular	ADJ
ejpam-3401	275	15	open	open	NOUN
ejpam-3401	275	16	set	set	VERB
ejpam-3401	275	17	v	v	NOUN
ejpam-3401	275	18	in	in	ADP
ejpam-3401	275	19	y	y	PROPN
ejpam-3401	275	20	such	such	ADJ
ejpam-3401	275	21	that	that	PRON
ejpam-3401	275	22	(	(	PUNCT
ejpam-3401	275	23	x1	x1	ADJ
ejpam-3401	275	24	,	,	PUNCT
ejpam-3401	275	25	f(x2	f(x2	NOUN
ejpam-3401	275	26	)	)	PUNCT
ejpam-3401	275	27	)	)	PUNCT
ejpam-3401	276	1	⊂	⊂	PROPN
ejpam-3401	276	2	u	u	X
ejpam-3401	276	3	×	×	PROPN
ejpam-3401	276	4	v	v	NOUN
ejpam-3401	276	5	and	and	CCONJ
ejpam-3401	276	6	f(u)∩	f(u)∩	PROPN
ejpam-3401	276	7	v	v	X
ejpam-3401	276	8	=	=	SYM
ejpam-3401	276	9	∅	∅	NOUN
ejpam-3401	276	10	,	,	PUNCT
ejpam-3401	276	11	therefore	therefore	ADV
ejpam-3401	276	12	u	u	NOUN
ejpam-3401	276	13	∩	∩	ADJ
ejpam-3401	276	14	f−1(v	f−1(v	NOUN
ejpam-3401	276	15	)	)	PUNCT
ejpam-3401	277	1	=	=	NOUN
ejpam-3401	277	2	∅	∅	NOUN
ejpam-3401	278	1	and	and	CCONJ
ejpam-3401	278	2	x2	x2	NOUN
ejpam-3401	278	3	/∈	/∈	PUNCT
ejpam-3401	279	1	u	u	INTJ
ejpam-3401	279	2	.	.	PUNCT
ejpam-3401	280	1	thus	thus	ADV
ejpam-3401	280	2	x1	x1	NUM
ejpam-3401	280	3	/∈	/∈	PUNCT
ejpam-3401	281	1	u	u	NOUN
ejpam-3401	281	2	c	c	NOUN
ejpam-3401	281	3	,	,	PUNCT
ejpam-3401	281	4	x2	x2	PROPN
ejpam-3401	281	5	∈	∈	PROPN
ejpam-3401	281	6	u	u	NOUN
ejpam-3401	281	7	c	c	NOUN
ejpam-3401	281	8	and	and	CCONJ
ejpam-3401	281	9	u	u	PROPN
ejpam-3401	281	10	c	c	PROPN
ejpam-3401	281	11	is	be	AUX
ejpam-3401	281	12	b	b	NOUN
ejpam-3401	281	13	-	-	PUNCT
ejpam-3401	281	14	open	open	ADJ
ejpam-3401	281	15	which	which	PRON
ejpam-3401	281	16	means	mean	VERB
ejpam-3401	281	17	that	that	SCONJ
ejpam-3401	281	18	{	{	PUNCT
ejpam-3401	281	19	x1}c	x1}c	PROPN
ejpam-3401	281	20	is	be	AUX
ejpam-3401	281	21	b	b	NOUN
ejpam-3401	281	22	-	-	ADJ
ejpam-3401	281	23	open	open	ADJ
ejpam-3401	281	24	,	,	PUNCT
ejpam-3401	281	25	that	that	ADV
ejpam-3401	281	26	is	is	ADV
ejpam-3401	281	27	{	{	PUNCT
ejpam-3401	281	28	x1	x1	PROPN
ejpam-3401	281	29	}	}	PUNCT
ejpam-3401	281	30	is	be	AUX
ejpam-3401	281	31	b	b	NOUN
ejpam-3401	281	32	-	-	PUNCT
ejpam-3401	281	33	closed	closed	ADJ
ejpam-3401	281	34	.	.	PUNCT
ejpam-3401	282	1	so	so	ADV
ejpam-3401	282	2	x	x	X
ejpam-3401	282	3	is	be	AUX
ejpam-3401	282	4	is	be	AUX
ejpam-3401	282	5	b	b	NOUN
ejpam-3401	282	6	-	-	PUNCT
ejpam-3401	282	7	frechet	frechet	NOUN
ejpam-3401	282	8	.	.	PUNCT
ejpam-3401	283	1	references	reference	NOUN
ejpam-3401	283	2	368	368	NUM
ejpam-3401	283	3	proposition	proposition	NOUN
ejpam-3401	283	4	12	12	NUM
ejpam-3401	283	5	.	.	PUNCT
ejpam-3401	284	1	let	let	VERB
ejpam-3401	284	2	f	f	NOUN
ejpam-3401	284	3	:	:	PUNCT
ejpam-3401	284	4	(	(	PUNCT
ejpam-3401	284	5	x	x	X
ejpam-3401	284	6	,	,	PUNCT
ejpam-3401	284	7	τ	τ	PROPN
ejpam-3401	284	8	,	,	PUNCT
ejpam-3401	284	9	t1	t1	PROPN
ejpam-3401	284	10	,	,	PUNCT
ejpam-3401	284	11	t2)→	t2)→	X
ejpam-3401	284	12	(	(	PUNCT
ejpam-3401	284	13	y	y	PROPN
ejpam-3401	284	14	,	,	PUNCT
ejpam-3401	284	15	σ	σ	PROPN
ejpam-3401	284	16	)	)	PUNCT
ejpam-3401	284	17	be	be	AUX
ejpam-3401	284	18	a	a	DET
ejpam-3401	284	19	weakly	weakly	ADJ
ejpam-3401	284	20	-	-	PUNCT
ejpam-3401	284	21	b	b	NOUN
ejpam-3401	284	22	-	-	PUNCT
ejpam-3401	284	23	continuous	continuous	ADJ
ejpam-3401	284	24	function	function	NOUN
ejpam-3401	284	25	and	and	CCONJ
ejpam-3401	284	26	y	y	PROPN
ejpam-3401	284	27	be	be	AUX
ejpam-3401	284	28	an	an	DET
ejpam-3401	284	29	urysohn	urysohn	NOUN
ejpam-3401	284	30	space	space	NOUN
ejpam-3401	284	31	.	.	PUNCT
ejpam-3401	285	1	then	then	ADV
ejpam-3401	285	2	g(f	g(f	PROPN
ejpam-3401	285	3	)	)	PUNCT
ejpam-3401	285	4	is	be	AUX
ejpam-3401	285	5	contra	contra	PROPN
ejpam-3401	285	6	b	b	PROPN
ejpam-3401	285	7	-	-	PUNCT
ejpam-3401	285	8	regular	regular	ADJ
ejpam-3401	285	9	in	in	ADP
ejpam-3401	285	10	x	x	SYM
ejpam-3401	285	11	×	×	PROPN
ejpam-3401	285	12	y.	y.	NOUN
ejpam-3401	285	13	proof	proof	NOUN
ejpam-3401	285	14	.	.	PUNCT
ejpam-3401	286	1	let	let	VERB
ejpam-3401	286	2	us	we	PRON
ejpam-3401	286	3	consider	consider	VERB
ejpam-3401	286	4	(	(	PUNCT
ejpam-3401	286	5	x	x	NOUN
ejpam-3401	286	6	,	,	PUNCT
ejpam-3401	286	7	y	y	NOUN
ejpam-3401	286	8	)	)	PUNCT
ejpam-3401	286	9	∈	∈	PROPN
ejpam-3401	286	10	(	(	PUNCT
ejpam-3401	286	11	x	x	SYM
ejpam-3401	286	12	×	×	PROPN
ejpam-3401	286	13	y	y	PROPN
ejpam-3401	286	14	)	)	PUNCT
ejpam-3401	286	15	\	\	PROPN
ejpam-3401	286	16	g(f	g(f	PROPN
ejpam-3401	286	17	)	)	PUNCT
ejpam-3401	286	18	,	,	PUNCT
ejpam-3401	286	19	therefore	therefore	ADV
ejpam-3401	286	20	y	y	PROPN
ejpam-3401	286	21	6=	6=	PROPN
ejpam-3401	286	22	f(x	f(x	PROPN
ejpam-3401	286	23	)	)	PUNCT
ejpam-3401	286	24	.	.	PUNCT
ejpam-3401	287	1	since	since	SCONJ
ejpam-3401	287	2	y	y	PROPN
ejpam-3401	287	3	is	be	AUX
ejpam-3401	287	4	an	an	DET
ejpam-3401	287	5	urysohn	urysohn	NOUN
ejpam-3401	287	6	space	space	NOUN
ejpam-3401	287	7	,	,	PUNCT
ejpam-3401	287	8	then	then	ADV
ejpam-3401	287	9	there	there	PRON
ejpam-3401	287	10	exist	exist	VERB
ejpam-3401	287	11	two	two	NUM
ejpam-3401	287	12	open	open	ADJ
ejpam-3401	287	13	sets	set	NOUN
ejpam-3401	287	14	u	u	NOUN
ejpam-3401	287	15	and	and	CCONJ
ejpam-3401	287	16	v	v	NOUN
ejpam-3401	287	17	in	in	ADP
ejpam-3401	287	18	y	y	NOUN
ejpam-3401	287	19	containing	contain	VERB
ejpam-3401	287	20	y	y	PROPN
ejpam-3401	287	21	and	and	CCONJ
ejpam-3401	287	22	f(x	f(x	PROPN
ejpam-3401	287	23	)	)	PUNCT
ejpam-3401	287	24	,	,	PUNCT
ejpam-3401	287	25	respectively	respectively	ADV
ejpam-3401	287	26	.	.	PUNCT
ejpam-3401	288	1	consider	consider	VERB
ejpam-3401	288	2	that	that	PRON
ejpam-3401	288	3	w	w	NOUN
ejpam-3401	288	4	is	be	AUX
ejpam-3401	288	5	a	a	DET
ejpam-3401	288	6	b	b	NOUN
ejpam-3401	288	7	-	-	PUNCT
ejpam-3401	288	8	open	open	ADJ
ejpam-3401	288	9	set	set	NOUN
ejpam-3401	288	10	containing	contain	VERB
ejpam-3401	288	11	x	x	NOUN
ejpam-3401	288	12	and	and	CCONJ
ejpam-3401	288	13	cl(u)∩cl(w	cl(u)∩cl(w	NOUN
ejpam-3401	288	14	)	)	PUNCT
ejpam-3401	289	1	=	=	PUNCT
ejpam-3401	289	2	∅.	∅.	NOUN
ejpam-3401	289	3	since	since	SCONJ
ejpam-3401	289	4	we	we	PRON
ejpam-3401	289	5	are	be	AUX
ejpam-3401	289	6	working	work	VERB
ejpam-3401	289	7	under	under	ADP
ejpam-3401	289	8	the	the	DET
ejpam-3401	289	9	assumption	assumption	NOUN
ejpam-3401	289	10	that	that	SCONJ
ejpam-3401	289	11	f	f	PROPN
ejpam-3401	289	12	is	be	AUX
ejpam-3401	289	13	weakly	weakly	ADJ
ejpam-3401	289	14	-	-	PUNCT
ejpam-3401	289	15	b	b	NOUN
ejpam-3401	289	16	-	-	PUNCT
ejpam-3401	289	17	continuous	continuous	ADJ
ejpam-3401	289	18	,	,	PUNCT
ejpam-3401	289	19	then	then	ADV
ejpam-3401	289	20	f(x	f(x	PROPN
ejpam-3401	289	21	)	)	PUNCT
ejpam-3401	289	22	⊆	⊆	NUM
ejpam-3401	289	23	cl(v	cl(v	NOUN
ejpam-3401	289	24	)	)	PUNCT
ejpam-3401	289	25	which	which	PRON
ejpam-3401	289	26	implies	imply	VERB
ejpam-3401	289	27	that	that	SCONJ
ejpam-3401	289	28	f(w	f(w	PROPN
ejpam-3401	289	29	)	)	PUNCT
ejpam-3401	289	30	∩	∩	NOUN
ejpam-3401	289	31	cl(u	cl(u	X
ejpam-3401	289	32	)	)	PUNCT
ejpam-3401	289	33	=	=	SYM
ejpam-3401	289	34	f(w	f(w	PROPN
ejpam-3401	289	35	)	)	PUNCT
ejpam-3401	289	36	∩	∩	NOUN
ejpam-3401	289	37	cl(int(u	cl(int(u	NOUN
ejpam-3401	289	38	)	)	PUNCT
ejpam-3401	289	39	)	)	PUNCT
ejpam-3401	290	1	=	=	PUNCT
ejpam-3401	290	2	∅	∅	NOUN
ejpam-3401	290	3	and	and	CCONJ
ejpam-3401	290	4	cl(int(u	cl(int(u	NUM
ejpam-3401	290	5	)	)	PUNCT
ejpam-3401	290	6	)	)	PUNCT
ejpam-3401	290	7	is	be	AUX
ejpam-3401	290	8	regular	regular	ADJ
ejpam-3401	290	9	closed	closed	ADJ
ejpam-3401	290	10	containing	contain	VERB
ejpam-3401	290	11	y.	y.	NOUN
ejpam-3401	290	12	hence	hence	ADV
ejpam-3401	290	13	g(f	g(f	PROPN
ejpam-3401	290	14	)	)	PUNCT
ejpam-3401	290	15	is	be	AUX
ejpam-3401	290	16	a	a	DET
ejpam-3401	290	17	contra	contra	PROPN
ejpam-3401	290	18	b	b	PROPN
ejpam-3401	290	19	-	-	PUNCT
ejpam-3401	290	20	regular	regular	ADJ
ejpam-3401	290	21	graph	graph	NOUN
ejpam-3401	290	22	in	in	ADP
ejpam-3401	290	23	x	x	PROPN
ejpam-3401	290	24	×	×	PROPN
ejpam-3401	290	25	y	y	PROPN
ejpam-3401	290	26	,	,	PUNCT
ejpam-3401	290	27	which	which	PRON
ejpam-3401	290	28	completes	complete	VERB
ejpam-3401	290	29	the	the	DET
ejpam-3401	290	30	proof	proof	NOUN
ejpam-3401	290	31	.	.	PUNCT
ejpam-3401	291	1	acknowledgements	acknowledgement	NOUN
ejpam-3401	291	2	i	i	PRON
ejpam-3401	291	3	would	would	AUX
ejpam-3401	291	4	like	like	VERB
ejpam-3401	291	5	to	to	PART
ejpam-3401	291	6	express	express	VERB
ejpam-3401	291	7	my	my	PRON
ejpam-3401	291	8	sincere	sincere	ADJ
ejpam-3401	291	9	gratitude	gratitude	NOUN
ejpam-3401	291	10	to	to	ADP
ejpam-3401	291	11	my	my	PRON
ejpam-3401	291	12	supervisor	supervisor	NOUN
ejpam-3401	291	13	dr	dr	PROPN
ejpam-3401	291	14	.	.	PROPN
ejpam-3401	292	1	lászló	lászló	PROPN
ejpam-3401	292	2	kozma	kozma	NOUN
ejpam-3401	292	3	,	,	PUNCT
ejpam-3401	292	4	for	for	ADP
ejpam-3401	292	5	carefully	carefully	ADV
ejpam-3401	292	6	reviewing	review	VERB
ejpam-3401	292	7	this	this	DET
ejpam-3401	292	8	paper	paper	NOUN
ejpam-3401	292	9	,	,	PUNCT
ejpam-3401	292	10	providing	provide	VERB
ejpam-3401	292	11	beneficial	beneficial	ADJ
ejpam-3401	292	12	suggestions	suggestion	NOUN
ejpam-3401	292	13	.	.	PUNCT
ejpam-3401	293	1	references	reference	NOUN
ejpam-3401	293	2	[	[	X
ejpam-3401	293	3	1	1	NUM
ejpam-3401	293	4	]	]	PUNCT
ejpam-3401	293	5	a.	a.	PROPN
ejpam-3401	293	6	al	al	PROPN
ejpam-3401	293	7	-	-	PUNCT
ejpam-3401	293	8	omari	omari	PROPN
ejpam-3401	293	9	and	and	CCONJ
ejpam-3401	293	10	m.s.m	m.s.m	PROPN
ejpam-3401	293	11	.	.	PUNCT
ejpam-3401	293	12	noorani	noorani	PROPN
ejpam-3401	293	13	.	.	PUNCT
ejpam-3401	294	1	some	some	DET
ejpam-3401	294	2	properties	property	NOUN
ejpam-3401	294	3	of	of	ADP
ejpam-3401	294	4	contra	contra	PROPN
ejpam-3401	294	5	-	-	PUNCT
ejpam-3401	294	6	b	b	NOUN
ejpam-3401	294	7	-	-	PUNCT
ejpam-3401	294	8	continuous	continuous	ADJ
ejpam-3401	294	9	and	and	CCONJ
ejpam-3401	294	10	almost	almost	ADV
ejpam-3401	294	11	contra	contra	ADJ
ejpam-3401	294	12	-	-	PUNCT
ejpam-3401	294	13	b	b	ADJ
ejpam-3401	294	14	-	-	PUNCT
ejpam-3401	294	15	continuous	continuous	ADJ
ejpam-3401	294	16	functions	function	NOUN
ejpam-3401	294	17	.	.	PUNCT
ejpam-3401	295	1	eur	eur	PROPN
ejpam-3401	295	2	.	.	PUNCT
ejpam-3401	296	1	j.	j.	PROPN
ejpam-3401	296	2	pure	pure	PROPN
ejpam-3401	296	3	appl	appl	PROPN
ejpam-3401	296	4	.	.	PUNCT
ejpam-3401	296	5	math	math	PROPN
ejpam-3401	296	6	.	.	PUNCT
ejpam-3401	296	7	,	,	PUNCT
ejpam-3401	296	8	2(2):213–230	2(2):213–230	NUM
ejpam-3401	296	9	,	,	PUNCT
ejpam-3401	296	10	2009	2009	NUM
ejpam-3401	296	11	.	.	PUNCT
ejpam-3401	297	1	[	[	X
ejpam-3401	297	2	2	2	NUM
ejpam-3401	297	3	]	]	X
ejpam-3401	297	4	l.	l.	PROPN
ejpam-3401	297	5	m.	m.	PROPN
ejpam-3401	297	6	alabdulsada	alabdulsada	PROPN
ejpam-3401	297	7	.	.	PUNCT
ejpam-3401	298	1	on	on	ADP
ejpam-3401	298	2	the	the	DET
ejpam-3401	298	3	class	class	NOUN
ejpam-3401	298	4	of	of	ADP
ejpam-3401	298	5	weakly	weakly	ADJ
ejpam-3401	298	6	almost	almost	ADV
ejpam-3401	298	7	contra	contra	PROPN
ejpam-3401	298	8	-	-	ADJ
ejpam-3401	298	9	t	t	ADJ
ejpam-3401	298	10	∗-continuous	∗-continuous	ADJ
ejpam-3401	298	11	functions	function	NOUN
ejpam-3401	298	12	.	.	PUNCT
ejpam-3401	299	1	to	to	PART
ejpam-3401	299	2	appear	appear	VERB
ejpam-3401	299	3	in	in	ADP
ejpam-3401	299	4	publ	publ	NOUN
ejpam-3401	299	5	.	.	PUNCT
ejpam-3401	300	1	math	math	NOUN
ejpam-3401	300	2	.	.	PUNCT
ejpam-3401	301	1	debrecen	debrecen	PROPN
ejpam-3401	301	2	,	,	PUNCT
ejpam-3401	301	3	2019	2019	NUM
ejpam-3401	301	4	.	.	PUNCT
ejpam-3401	302	1	[	[	X
ejpam-3401	302	2	3	3	X
ejpam-3401	302	3	]	]	X
ejpam-3401	302	4	d.	d.	PROPN
ejpam-3401	302	5	andrijević.	andrijević.	PROPN
ejpam-3401	302	6	on	on	ADP
ejpam-3401	302	7	b	b	X
ejpam-3401	302	8	-	-	PUNCT
ejpam-3401	302	9	open	open	ADJ
ejpam-3401	302	10	sets	set	NOUN
ejpam-3401	302	11	.	.	PUNCT
ejpam-3401	303	1	mat	mat	X
ejpam-3401	303	2	.	.	PROPN
ejpam-3401	303	3	vesnik	vesnik	PROPN
ejpam-3401	303	4	,	,	PUNCT
ejpam-3401	303	5	48(1	48(1	NOUN
ejpam-3401	303	6	-	-	PUNCT
ejpam-3401	303	7	2):59–64	2):59–64	NUM
ejpam-3401	303	8	,	,	PUNCT
ejpam-3401	303	9	1996	1996	NUM
ejpam-3401	303	10	.	.	PUNCT
ejpam-3401	304	1	[	[	X
ejpam-3401	304	2	4	4	X
ejpam-3401	304	3	]	]	PUNCT
ejpam-3401	304	4	s.	s.	PROPN
ejpam-3401	304	5	p.	p.	PROPN
ejpam-3401	304	6	arya	arya	PROPN
ejpam-3401	304	7	and	and	CCONJ
ejpam-3401	304	8	m.	m.	PROPN
ejpam-3401	304	9	p.	p.	PROPN
ejpam-3401	304	10	bhamini	bhamini	PROPN
ejpam-3401	304	11	.	.	PUNCT
ejpam-3401	305	1	some	some	DET
ejpam-3401	305	2	generalizations	generalization	NOUN
ejpam-3401	305	3	of	of	ADP
ejpam-3401	305	4	pairwise	pairwise	NOUN
ejpam-3401	305	5	urysohn	urysohn	NOUN
ejpam-3401	305	6	spaces	space	VERB
ejpam-3401	305	7	.	.	PUNCT
ejpam-3401	306	1	indian	indian	PROPN
ejpam-3401	306	2	j.	j.	PROPN
ejpam-3401	306	3	pure	pure	PROPN
ejpam-3401	306	4	appl	appl	PROPN
ejpam-3401	306	5	.	.	PUNCT
ejpam-3401	306	6	math	math	PROPN
ejpam-3401	306	7	.	.	PUNCT
ejpam-3401	306	8	,	,	PUNCT
ejpam-3401	306	9	18(12):1088–1093	18(12):1088–1093	NUM
ejpam-3401	306	10	,	,	PUNCT
ejpam-3401	306	11	1987	1987	NUM
ejpam-3401	306	12	.	.	PUNCT
ejpam-3401	307	1	[	[	X
ejpam-3401	307	2	5	5	NUM
ejpam-3401	307	3	]	]	X
ejpam-3401	307	4	m.e	m.e	PROPN
ejpam-3401	307	5	.	.	PROPN
ejpam-3401	307	6	abd	abd	PROPN
ejpam-3401	307	7	el	el	PROPN
ejpam-3401	307	8	-	-	PUNCT
ejpam-3401	307	9	monsef	monsef	PROPN
ejpam-3401	307	10	a.s	a.s	PROPN
ejpam-3401	307	11	.	.	PROPN
ejpam-3401	307	12	mashhour	mashhour	PROPN
ejpam-3401	307	13	and	and	CCONJ
ejpam-3401	307	14	s.n	s.n	PROPN
ejpam-3401	307	15	.	.	PROPN
ejpam-3401	307	16	el	el	PROPN
ejpam-3401	307	17	-	-	PUNCT
ejpam-3401	307	18	deeb	deeb	PROPN
ejpam-3401	307	19	.	.	PUNCT
ejpam-3401	308	1	on	on	ADP
ejpam-3401	308	2	precontinuous	precontinuous	ADJ
ejpam-3401	308	3	and	and	CCONJ
ejpam-3401	308	4	weak	weak	ADJ
ejpam-3401	308	5	precontinuous	precontinuous	ADJ
ejpam-3401	308	6	mappings	mapping	NOUN
ejpam-3401	308	7	.	.	PUNCT
ejpam-3401	309	1	proc	proc	NOUN
ejpam-3401	309	2	.	.	PUNCT
ejpam-3401	310	1	math	math	NOUN
ejpam-3401	310	2	.	.	PUNCT
ejpam-3401	311	1	phys	phy	NOUN
ejpam-3401	311	2	.	.	PUNCT
ejpam-3401	312	1	soc	soc	PROPN
ejpam-3401	312	2	.	.	PUNCT
ejpam-3401	313	1	egypt	egypt	PROPN
ejpam-3401	313	2	.	.	PROPN
ejpam-3401	313	3	,	,	PUNCT
ejpam-3401	313	4	53:47–53	53:47–53	NUM
ejpam-3401	313	5	,	,	PUNCT
ejpam-3401	313	6	1982	1982	NUM
ejpam-3401	313	7	.	.	PUNCT
ejpam-3401	314	1	[	[	X
ejpam-3401	314	2	6	6	NUM
ejpam-3401	314	3	]	]	PUNCT
ejpam-3401	314	4	j.	j.	PROPN
ejpam-3401	314	5	dontchev	dontchev	PROPN
ejpam-3401	314	6	.	.	PUNCT
ejpam-3401	315	1	contra	contra	ADJ
ejpam-3401	315	2	-	-	ADJ
ejpam-3401	315	3	continuous	continuous	ADJ
ejpam-3401	315	4	functions	function	NOUN
ejpam-3401	315	5	and	and	CCONJ
ejpam-3401	315	6	strongly	strongly	ADV
ejpam-3401	315	7	s	s	NOUN
ejpam-3401	315	8	-	-	PUNCT
ejpam-3401	315	9	closed	closed	ADJ
ejpam-3401	315	10	spaces	space	NOUN
ejpam-3401	315	11	.	.	PUNCT
ejpam-3401	316	1	internat.j	internat.j	PROPN
ejpam-3401	316	2	.	.	PUNCT
ejpam-3401	317	1	math	math	PROPN
ejpam-3401	317	2	.	.	PUNCT
ejpam-3401	318	1	math	math	NOUN
ejpam-3401	318	2	.	.	PUNCT
ejpam-3401	319	1	sci	sci	PROPN
ejpam-3401	319	2	.	.	PROPN
ejpam-3401	319	3	,	,	PUNCT
ejpam-3401	319	4	19(2):303–310	19(2):303–310	NUM
ejpam-3401	319	5	,	,	PUNCT
ejpam-3401	319	6	1996	1996	NUM
ejpam-3401	319	7	.	.	PUNCT
ejpam-3401	320	1	[	[	X
ejpam-3401	320	2	7	7	X
ejpam-3401	320	3	]	]	X
ejpam-3401	320	4	e.	e.	PROPN
ejpam-3401	320	5	ekici	ekici	PROPN
ejpam-3401	320	6	.	.	PUNCT
ejpam-3401	321	1	almost	almost	ADV
ejpam-3401	321	2	contra	contra	ADJ
ejpam-3401	321	3	-	-	ADJ
ejpam-3401	321	4	precontinuous	precontinuous	ADJ
ejpam-3401	321	5	functions	function	NOUN
ejpam-3401	321	6	.	.	PUNCT
ejpam-3401	322	1	bull	bull	NOUN
ejpam-3401	322	2	.	.	PUNCT
ejpam-3401	323	1	malays	malays	PROPN
ejpam-3401	323	2	.	.	PUNCT
ejpam-3401	324	1	math	math	NOUN
ejpam-3401	324	2	.	.	PUNCT
ejpam-3401	325	1	sci	sci	PROPN
ejpam-3401	325	2	.	.	PUNCT
ejpam-3401	326	1	soc.(2	soc.(2	PROPN
ejpam-3401	326	2	)	)	PUNCT
ejpam-3401	326	3	,	,	PUNCT
ejpam-3401	326	4	27(1):53–65	27(1):53–65	NUM
ejpam-3401	326	5	,	,	PUNCT
ejpam-3401	326	6	2004	2004	NUM
ejpam-3401	326	7	.	.	PUNCT
ejpam-3401	327	1	[	[	X
ejpam-3401	327	2	8	8	NUM
ejpam-3401	327	3	]	]	X
ejpam-3401	327	4	e.	e.	PROPN
ejpam-3401	327	5	ekici	ekici	PROPN
ejpam-3401	327	6	.	.	PUNCT
ejpam-3401	328	1	on	on	ADP
ejpam-3401	328	2	the	the	DET
ejpam-3401	328	3	notion	notion	NOUN
ejpam-3401	328	4	of	of	ADP
ejpam-3401	328	5	(	(	PUNCT
ejpam-3401	328	6	γ	γ	PROPN
ejpam-3401	328	7	,	,	PUNCT
ejpam-3401	328	8	s)-continuous	s)-continuous	ADJ
ejpam-3401	328	9	functions	function	NOUN
ejpam-3401	328	10	.	.	PUNCT
ejpam-3401	329	1	demonstratio	demonstratio	PROPN
ejpam-3401	329	2	math	math	PROPN
ejpam-3401	329	3	.	.	PUNCT
ejpam-3401	329	4	,	,	PUNCT
ejpam-3401	329	5	38(3):715	38(3):715	PROPN
ejpam-3401	329	6	–	–	PUNCT
ejpam-3401	329	7	727	727	NUM
ejpam-3401	329	8	,	,	PUNCT
ejpam-3401	329	9	2005	2005	NUM
ejpam-3401	329	10	.	.	PUNCT
ejpam-3401	330	1	[	[	X
ejpam-3401	330	2	9	9	NUM
ejpam-3401	330	3	]	]	PUNCT
ejpam-3401	330	4	e.	e.	PROPN
ejpam-3401	330	5	ekici	ekici	PROPN
ejpam-3401	330	6	.	.	PUNCT
ejpam-3401	331	1	new	new	ADJ
ejpam-3401	331	2	forms	form	NOUN
ejpam-3401	331	3	of	of	ADP
ejpam-3401	331	4	contra	contra	NOUN
ejpam-3401	331	5	-	-	NOUN
ejpam-3401	331	6	continuity	continuity	NOUN
ejpam-3401	331	7	.	.	PUNCT
ejpam-3401	332	1	carpathian	carpathian	PROPN
ejpam-3401	332	2	j.	j.	PROPN
ejpam-3401	332	3	math	math	PROPN
ejpam-3401	332	4	.	.	PUNCT
ejpam-3401	332	5	,	,	PUNCT
ejpam-3401	332	6	24(1):37–45	24(1):37–45	NUM
ejpam-3401	332	7	,	,	PUNCT
ejpam-3401	332	8	2008	2008	NUM
ejpam-3401	332	9	.	.	PUNCT
ejpam-3401	333	1	[	[	X
ejpam-3401	333	2	10	10	NUM
ejpam-3401	333	3	]	]	X
ejpam-3401	333	4	e.	e.	PROPN
ejpam-3401	333	5	ekici	ekici	PROPN
ejpam-3401	333	6	.	.	PUNCT
ejpam-3401	334	1	on	on	ADP
ejpam-3401	334	2	contra	contra	PROPN
ejpam-3401	334	3	πg	πg	ADP
ejpam-3401	334	4	-	-	PUNCT
ejpam-3401	334	5	continuous	continuous	ADJ
ejpam-3401	334	6	functions	function	NOUN
ejpam-3401	334	7	.	.	PUNCT
ejpam-3401	335	1	chaos	chaos	NOUN
ejpam-3401	335	2	solitons	soliton	NOUN
ejpam-3401	335	3	fractals	fractal	NOUN
ejpam-3401	335	4	.	.	PUNCT
ejpam-3401	335	5	,	,	PUNCT
ejpam-3401	335	6	35(1):71–81	35(1):71–81	NUM
ejpam-3401	335	7	,	,	PUNCT
ejpam-3401	335	8	2008	2008	NUM
ejpam-3401	335	9	.	.	PUNCT
ejpam-3401	336	1	references	reference	NOUN
ejpam-3401	336	2	369	369	NUM
ejpam-3401	337	1	[	[	X
ejpam-3401	337	2	11	11	NUM
ejpam-3401	337	3	]	]	PUNCT
ejpam-3401	337	4	a.	a.	NOUN
ejpam-3401	337	5	l.	l.	PROPN
ejpam-3401	337	6	moussa	moussa	PROPN
ejpam-3401	337	7	h.	h.	PROPN
ejpam-3401	337	8	j.	j.	PROPN
ejpam-3401	337	9	mustafa	mustafa	PROPN
ejpam-3401	337	10	and	and	CCONJ
ejpam-3401	337	11	a.	a.	PROPN
ejpam-3401	337	12	k.	k.	PROPN
ejpam-3401	337	13	mazal	mazal	PROPN
ejpam-3401	337	14	.	.	PUNCT
ejpam-3401	338	1	operator	operator	NOUN
ejpam-3401	338	2	topological	topological	ADJ
ejpam-3401	338	3	spaces	space	NOUN
ejpam-3401	338	4	.	.	PUNCT
ejpam-3401	339	1	journal	journal	NOUN
ejpam-3401	339	2	of	of	ADP
ejpam-3401	339	3	the	the	DET
ejpam-3401	339	4	college	college	NOUN
ejpam-3401	339	5	of	of	ADP
ejpam-3401	339	6	education	education	NOUN
ejpam-3401	339	7	,	,	PUNCT
ejpam-3401	339	8	1:213–221	1:213–221	NUM
ejpam-3401	339	9	,	,	PUNCT
ejpam-3401	339	10	2011	2011	NUM
ejpam-3401	339	11	.	.	PUNCT
ejpam-3401	340	1	[	[	X
ejpam-3401	340	2	12	12	NUM
ejpam-3401	340	3	]	]	X
ejpam-3401	340	4	n.	n.	PROPN
ejpam-3401	340	5	levine	levine	PROPN
ejpam-3401	340	6	.	.	PUNCT
ejpam-3401	341	1	semi	semi	ADJ
ejpam-3401	341	2	-	-	ADJ
ejpam-3401	341	3	open	open	ADJ
ejpam-3401	341	4	sets	set	NOUN
ejpam-3401	341	5	and	and	CCONJ
ejpam-3401	341	6	semi	semi	ADJ
ejpam-3401	341	7	-	-	NOUN
ejpam-3401	341	8	continuity	continuity	NOUN
ejpam-3401	341	9	in	in	ADP
ejpam-3401	341	10	topological	topological	ADJ
ejpam-3401	341	11	spaces	space	NOUN
ejpam-3401	341	12	.	.	PUNCT
ejpam-3401	342	1	amer	amer	PROPN
ejpam-3401	342	2	.	.	PUNCT
ejpam-3401	342	3	math	math	PROPN
ejpam-3401	342	4	.	.	PUNCT
ejpam-3401	343	1	monthly	monthly	ADV
ejpam-3401	343	2	.	.	PUNCT
ejpam-3401	344	1	,	,	PUNCT
ejpam-3401	345	1	70:36–41	70:36–41	NUM
ejpam-3401	345	2	,	,	PUNCT
ejpam-3401	345	3	1963	1963	NUM
ejpam-3401	345	4	.	.	PUNCT
ejpam-3401	346	1	[	[	X
ejpam-3401	346	2	13	13	NUM
ejpam-3401	346	3	]	]	SYM
ejpam-3401	346	4	s.n	s.n	PROPN
ejpam-3401	346	5	.	.	PROPN
ejpam-3401	346	6	el	el	PROPN
ejpam-3401	346	7	-	-	PUNCT
ejpam-3401	346	8	deeb	deeb	PROPN
ejpam-3401	346	9	m.e	m.e	PROPN
ejpam-3401	346	10	.	.	PROPN
ejpam-3401	346	11	abd	abd	PROPN
ejpam-3401	346	12	el	el	PROPN
ejpam-3401	346	13	-	-	PROPN
ejpam-3401	346	14	monsef	monsef	PROPN
ejpam-3401	346	15	and	and	CCONJ
ejpam-3401	346	16	r.a	r.a	PROPN
ejpam-3401	346	17	.	.	PROPN
ejpam-3401	346	18	mahmoud	mahmoud	PROPN
ejpam-3401	346	19	.	.	PUNCT
ejpam-3401	347	1	β	β	X
ejpam-3401	347	2	-	-	ADJ
ejpam-3401	347	3	open	open	ADJ
ejpam-3401	347	4	sets	set	NOUN
ejpam-3401	347	5	and	and	CCONJ
ejpam-3401	347	6	β	β	NOUN
ejpam-3401	347	7	-	-	ADJ
ejpam-3401	347	8	continuous	continuous	ADJ
ejpam-3401	347	9	mapping	mapping	NOUN
ejpam-3401	347	10	.	.	PUNCT
ejpam-3401	348	1	bull	bull	NOUN
ejpam-3401	348	2	.	.	PUNCT
ejpam-3401	349	1	fac	fac	PROPN
ejpam-3401	349	2	.	.	PUNCT
ejpam-3401	350	1	sci	sci	PROPN
ejpam-3401	350	2	.	.	PUNCT
ejpam-3401	350	3	assiut	assiut	PROPN
ejpam-3401	350	4	univ	univ	PROPN
ejpam-3401	350	5	.	.	PUNCT
ejpam-3401	351	1	a	a	DET
ejpam-3401	351	2	,	,	PUNCT
ejpam-3401	351	3	12(1):77–90	12(1):77–90	NUM
ejpam-3401	351	4	,	,	PUNCT
ejpam-3401	351	5	1983	1983	NUM
ejpam-3401	351	6	.	.	PUNCT
ejpam-3401	352	1	[	[	X
ejpam-3401	352	2	14	14	NUM
ejpam-3401	352	3	]	]	X
ejpam-3401	352	4	h.	h.	PROPN
ejpam-3401	352	5	j.	j.	PROPN
ejpam-3401	352	6	mustafa	mustafa	PROPN
ejpam-3401	352	7	and	and	CCONJ
ejpam-3401	352	8	l.	l.	PROPN
ejpam-3401	352	9	m.	m.	PROPN
ejpam-3401	352	10	alabdulsada	alabdulsada	PROPN
ejpam-3401	352	11	.	.	PUNCT
ejpam-3401	353	1	on	on	ADP
ejpam-3401	353	2	almost	almost	ADV
ejpam-3401	353	3	contra	contra	PROPN
ejpam-3401	353	4	t	t	PROPN
ejpam-3401	353	5	∗-continuous	∗-continuous	ADJ
ejpam-3401	353	6	functions	function	NOUN
ejpam-3401	353	7	.	.	PUNCT
ejpam-3401	354	1	j.	j.	PROPN
ejpam-3401	354	2	of	of	ADP
ejpam-3401	354	3	kufa	kufa	PROPN
ejpam-3401	354	4	for	for	ADP
ejpam-3401	354	5	math	math	NOUN
ejpam-3401	354	6	.	.	PUNCT
ejpam-3401	355	1	and	and	CCONJ
ejpam-3401	355	2	comp	comp	PROPN
ejpam-3401	355	3	.	.	PUNCT
ejpam-3401	355	4	,	,	PUNCT
ejpam-3401	355	5	1(6):1–6	1(6):1–6	NUM
ejpam-3401	355	6	,	,	PUNCT
ejpam-3401	355	7	2012	2012	NUM
ejpam-3401	355	8	.	.	PUNCT
ejpam-3401	356	1	[	[	X
ejpam-3401	356	2	15	15	NUM
ejpam-3401	356	3	]	]	X
ejpam-3401	356	4	o.	o.	NOUN
ejpam-3401	356	5	nj̊astad	nj̊astad	NOUN
ejpam-3401	356	6	.	.	PUNCT
ejpam-3401	357	1	on	on	ADP
ejpam-3401	357	2	some	some	DET
ejpam-3401	357	3	classes	class	NOUN
ejpam-3401	357	4	of	of	ADP
ejpam-3401	357	5	nearly	nearly	ADV
ejpam-3401	357	6	open	open	ADJ
ejpam-3401	357	7	sets	set	NOUN
ejpam-3401	357	8	.	.	PUNCT
ejpam-3401	358	1	pacific	pacific	PROPN
ejpam-3401	358	2	j.	j.	PROPN
ejpam-3401	358	3	math	math	PROPN
ejpam-3401	358	4	.	.	PUNCT
ejpam-3401	358	5	,	,	PUNCT
ejpam-3401	358	6	15:961–970	15:961–970	PROPN
ejpam-3401	358	7	,	,	PUNCT
ejpam-3401	358	8	1965	1965	NUM
ejpam-3401	358	9	.	.	PUNCT
ejpam-3401	359	1	[	[	X
ejpam-3401	359	2	16	16	NUM
ejpam-3401	359	3	]	]	PUNCT
ejpam-3401	359	4	t.	t.	PROPN
ejpam-3401	359	5	noiri	noiri	PROPN
ejpam-3401	359	6	.	.	PUNCT
ejpam-3401	360	1	on	on	ADP
ejpam-3401	360	2	almost	almost	ADV
ejpam-3401	360	3	continuous	continuous	ADJ
ejpam-3401	360	4	functions	function	NOUN
ejpam-3401	360	5	.	.	PUNCT
ejpam-3401	361	1	indian	indian	PROPN
ejpam-3401	361	2	j.	j.	PROPN
ejpam-3401	361	3	pure	pure	PROPN
ejpam-3401	361	4	appl	appl	PROPN
ejpam-3401	361	5	.	.	PUNCT
ejpam-3401	361	6	math	math	PROPN
ejpam-3401	361	7	.	.	PUNCT
ejpam-3401	361	8	,	,	PUNCT
ejpam-3401	361	9	20(6):571–576	20(6):571–576	PROPN
ejpam-3401	361	10	,	,	PUNCT
ejpam-3401	361	11	1989	1989	NUM
ejpam-3401	361	12	.	.	PUNCT
ejpam-3401	362	1	[	[	X
ejpam-3401	362	2	17	17	NUM
ejpam-3401	362	3	]	]	PUNCT
ejpam-3401	362	4	j.	j.	PROPN
ejpam-3401	362	5	b.	b.	PROPN
ejpam-3401	362	6	toranagatti	toranagatti	PROPN
ejpam-3401	362	7	s.	s.	PROPN
ejpam-3401	362	8	s.	s.	PROPN
ejpam-3401	362	9	benchalli	benchalli	PROPN
ejpam-3401	362	10	,	,	PUNCT
ejpam-3401	362	11	p.	p.	PROPN
ejpam-3401	362	12	g.	g.	PROPN
ejpam-3401	362	13	patil	patil	PROPN
ejpam-3401	362	14	and	and	CCONJ
ejpam-3401	362	15	s.	s.	PROPN
ejpam-3401	362	16	r.	r.	PROPN
ejpam-3401	362	17	vighneshi	vighneshi	PROPN
ejpam-3401	362	18	.	.	PUNCT
ejpam-3401	363	1	contra	contra	PROPN
ejpam-3401	363	2	δgbcontinuous	δgbcontinuous	ADJ
ejpam-3401	363	3	functions	function	NOUN
ejpam-3401	363	4	in	in	ADP
ejpam-3401	363	5	topological	topological	ADJ
ejpam-3401	363	6	spaces	space	NOUN
ejpam-3401	363	7	.	.	PUNCT
ejpam-3401	364	1	eur	eur	PROPN
ejpam-3401	364	2	.	.	PUNCT
ejpam-3401	365	1	j.	j.	PROPN
ejpam-3401	365	2	pure	pure	PROPN
ejpam-3401	365	3	appl	appl	PROPN
ejpam-3401	365	4	.	.	PUNCT
ejpam-3401	365	5	math	math	PROPN
ejpam-3401	365	6	.	.	PUNCT
ejpam-3401	365	7	,	,	PUNCT
ejpam-3401	365	8	10(2):312–322	10(2):312–322	PROPN
ejpam-3401	365	9	,	,	PUNCT
ejpam-3401	365	10	2017	2017	NUM
ejpam-3401	365	11	.	.	PUNCT
ejpam-3401	366	1	[	[	X
ejpam-3401	366	2	18	18	NUM
ejpam-3401	366	3	]	]	X
ejpam-3401	366	4	m.k	m.k	PROPN
ejpam-3401	366	5	.	.	PROPN
ejpam-3401	366	6	singal	singal	PROPN
ejpam-3401	366	7	and	and	CCONJ
ejpam-3401	366	8	a.	a.	PROPN
ejpam-3401	366	9	mathur	mathur	PROPN
ejpam-3401	366	10	.	.	PUNCT
ejpam-3401	367	1	on	on	ADP
ejpam-3401	367	2	nearly	nearly	ADV
ejpam-3401	367	3	-	-	PUNCT
ejpam-3401	367	4	compact	compact	ADJ
ejpam-3401	367	5	spaces	space	NOUN
ejpam-3401	367	6	.	.	PUNCT
ejpam-3401	368	1	boll	boll	NOUN
ejpam-3401	368	2	.	.	PUNCT
ejpam-3401	369	1	un	un	PROPN
ejpam-3401	369	2	.	.	PROPN
ejpam-3401	369	3	mat	mat	PROPN
ejpam-3401	369	4	.	.	PUNCT
ejpam-3401	369	5	ital	ital	PROPN
ejpam-3401	369	6	.	.	PUNCT
ejpam-3401	370	1	(	(	PUNCT
ejpam-3401	370	2	4	4	NUM
ejpam-3401	370	3	)	)	PUNCT
ejpam-3401	370	4	,	,	PUNCT
ejpam-3401	370	5	2:702–710	2:702–710	NUM
ejpam-3401	370	6	,	,	PUNCT
ejpam-3401	370	7	1969	1969	NUM
ejpam-3401	370	8	.	.	PUNCT
ejpam-3401	371	1	[	[	X
ejpam-3401	371	2	19	19	NUM
ejpam-3401	371	3	]	]	X
ejpam-3401	371	4	t.	t.	PROPN
ejpam-3401	371	5	soundararajan	soundararajan	PROPN
ejpam-3401	371	6	.	.	PUNCT
ejpam-3401	372	1	weakly	weakly	ADJ
ejpam-3401	372	2	hausdorff	hausdorff	NOUN
ejpam-3401	372	3	spaces	space	NOUN
ejpam-3401	372	4	and	and	CCONJ
ejpam-3401	372	5	the	the	DET
ejpam-3401	372	6	cardinality	cardinality	NOUN
ejpam-3401	372	7	of	of	ADP
ejpam-3401	372	8	topological	topological	ADJ
ejpam-3401	372	9	spaces	space	NOUN
ejpam-3401	372	10	.	.	PUNCT
ejpam-3401	373	1	pages	page	NOUN
ejpam-3401	373	2	301–306	301–306	NUM
ejpam-3401	373	3	,	,	PUNCT
ejpam-3401	373	4	1971	1971	NUM
ejpam-3401	373	5	.	.	PUNCT
ejpam-3401	374	1	[	[	X
ejpam-3401	374	2	20	20	NUM
ejpam-3401	374	3	]	]	X
ejpam-3401	374	4	m.h	m.h	PROPN
ejpam-3401	374	5	.	.	PROPN
ejpam-3401	374	6	stone	stone	PROPN
ejpam-3401	374	7	.	.	PUNCT
ejpam-3401	375	1	applications	application	NOUN
ejpam-3401	375	2	of	of	ADP
ejpam-3401	375	3	the	the	DET
ejpam-3401	375	4	theory	theory	NOUN
ejpam-3401	375	5	of	of	ADP
ejpam-3401	375	6	boolean	boolean	ADJ
ejpam-3401	375	7	rings	ring	NOUN
ejpam-3401	375	8	to	to	ADP
ejpam-3401	375	9	general	general	ADJ
ejpam-3401	375	10	topology	topology	NOUN
ejpam-3401	375	11	.	.	PUNCT
ejpam-3401	376	1	trans	trans	PROPN
ejpam-3401	376	2	.	.	PUNCT
ejpam-3401	377	1	amer	amer	PROPN
ejpam-3401	377	2	.	.	PUNCT
ejpam-3401	377	3	math	math	PROPN
ejpam-3401	377	4	.	.	PUNCT
ejpam-3401	378	1	soc	soc	PROPN
ejpam-3401	378	2	.	.	PUNCT
ejpam-3401	378	3	,	,	PUNCT
ejpam-3401	378	4	41(3):375–481	41(3):375–481	PROPN
ejpam-3401	378	5	,	,	PUNCT
ejpam-3401	378	6	1937	1937	NUM
ejpam-3401	378	7	.	.	PUNCT
ejpam-3401	379	1	[	[	X
ejpam-3401	379	2	21	21	NUM
ejpam-3401	379	3	]	]	PUNCT
ejpam-3401	379	4	a.	a.	PROPN
ejpam-3401	379	5	al	al	PROPN
ejpam-3401	379	6	-	-	PUNCT
ejpam-3401	379	7	omari	omari	PROPN
ejpam-3401	379	8	t.	t.	PROPN
ejpam-3401	379	9	noiri	noiri	PROPN
ejpam-3401	379	10	and	and	CCONJ
ejpam-3401	379	11	m.s.m	m.s.m	PROPN
ejpam-3401	379	12	.	.	PUNCT
ejpam-3401	379	13	noorani	noorani	PROPN
ejpam-3401	379	14	.	.	PUNCT
ejpam-3401	380	1	weakly	weakly	ADJ
ejpam-3401	380	2	b	b	X
ejpam-3401	380	3	-	-	PUNCT
ejpam-3401	380	4	open	open	ADJ
ejpam-3401	380	5	functions	function	NOUN
ejpam-3401	380	6	.	.	PUNCT
ejpam-3401	381	1	math	math	NOUN
ejpam-3401	381	2	.	.	PUNCT
ejpam-3401	382	1	balkanica	balkanica	PROPN
ejpam-3401	382	2	(	(	PUNCT
ejpam-3401	382	3	n.s	n.s	PROPN
ejpam-3401	382	4	.	.	PROPN
ejpam-3401	382	5	)	)	PUNCT
ejpam-3401	382	6	,	,	PUNCT
ejpam-3401	382	7	23(1	23(1	PROPN
ejpam-3401	382	8	-	-	PUNCT
ejpam-3401	382	9	2):1–13	2):1–13	PROPN
ejpam-3401	382	10	,	,	PUNCT
ejpam-3401	382	11	2009	2009	NUM
ejpam-3401	382	12	.	.	PUNCT
ejpam-3401	383	1	[	[	X
ejpam-3401	383	2	22	22	NUM
ejpam-3401	383	3	]	]	PUNCT
ejpam-3401	383	4	s.	s.	PROPN
ejpam-3401	383	5	willard	willard	PROPN
ejpam-3401	383	6	.	.	PUNCT
ejpam-3401	384	1	general	general	ADJ
ejpam-3401	384	2	topology	topology	NOUN
ejpam-3401	384	3	spaces	space	VERB
ejpam-3401	384	4	.	.	PUNCT
ejpam-3401	385	1	addison	addison	PROPN
ejpam-3401	385	2	wesley	wesley	PROPN
ejpam-3401	385	3	.	.	PUNCT
ejpam-3401	385	4	,	,	PUNCT
ejpam-3401	385	5	1970	1970	NUM
ejpam-3401	385	6	.	.	PUNCT