id	sid	tid	token	lemma	pos
ejpam-108	1	1	4_al-omari.dvi	4_al-omari.dvi	NUM
ejpam-108	1	2	european	european	PROPN
ejpam-108	1	3	journal	journal	PROPN
ejpam-108	1	4	of	of	ADP
ejpam-108	1	5	pure	pure	ADJ
ejpam-108	1	6	and	and	CCONJ
ejpam-108	1	7	applied	apply	VERB
ejpam-108	1	8	mathematics	mathematic	NOUN
ejpam-108	1	9	vol	vol	NOUN
ejpam-108	1	10	.	.	PROPN
ejpam-108	1	11	2	2	NUM
ejpam-108	1	12	,	,	PUNCT
ejpam-108	1	13	no	no	INTJ
ejpam-108	1	14	.	.	NOUN
ejpam-108	1	15	2	2	NUM
ejpam-108	1	16	,	,	PUNCT
ejpam-108	1	17	2009	2009	NUM
ejpam-108	1	18	,	,	PUNCT
ejpam-108	1	19	(	(	PUNCT
ejpam-108	1	20	213	213	NUM
ejpam-108	1	21	-	-	SYM
ejpam-108	1	22	230	230	NUM
ejpam-108	1	23	)	)	PUNCT
ejpam-108	1	24	issn	issn	PROPN
ejpam-108	1	25	1307	1307	NUM
ejpam-108	1	26	-	-	SYM
ejpam-108	1	27	5543	5543	NUM
ejpam-108	1	28	–	–	PUNCT
ejpam-108	1	29	www.ejpam.com	www.ejpam.com	X
ejpam-108	1	30	some	some	DET
ejpam-108	1	31	properties	property	NOUN
ejpam-108	1	32	of	of	ADP
ejpam-108	1	33	contra	contra	PROPN
ejpam-108	1	34	-	-	PUNCT
ejpam-108	1	35	b	b	NOUN
ejpam-108	1	36	-	-	PUNCT
ejpam-108	1	37	continuous	continuous	ADJ
ejpam-108	1	38	and	and	CCONJ
ejpam-108	1	39	almost	almost	ADV
ejpam-108	1	40	contra	contra	ADJ
ejpam-108	1	41	-	-	PUNCT
ejpam-108	1	42	b	b	ADJ
ejpam-108	1	43	-	-	PUNCT
ejpam-108	1	44	continuous	continuous	ADJ
ejpam-108	1	45	functions	function	NOUN
ejpam-108	1	46	ahmad	ahmad	PROPN
ejpam-108	1	47	al	al	PROPN
ejpam-108	1	48	-	-	PUNCT
ejpam-108	1	49	omari1∗	omari1∗	PROPN
ejpam-108	1	50	and	and	CCONJ
ejpam-108	1	51	mohd	mohd	PROPN
ejpam-108	1	52	.	.	PUNCT
ejpam-108	2	1	salmi	salmi	PROPN
ejpam-108	2	2	md	md	PROPN
ejpam-108	2	3	.	.	PUNCT
ejpam-108	3	1	noorani2	noorani2	PROPN
ejpam-108	3	2	1	1	NUM
ejpam-108	3	3	department	department	NOUN
ejpam-108	3	4	of	of	ADP
ejpam-108	3	5	mathematics	mathematic	NOUN
ejpam-108	3	6	and	and	CCONJ
ejpam-108	3	7	statistics	statistic	NOUN
ejpam-108	3	8	,	,	PUNCT
ejpam-108	3	9	faculty	faculty	NOUN
ejpam-108	3	10	of	of	ADP
ejpam-108	3	11	science	science	NOUN
ejpam-108	3	12	mu’tah	mu’tah	PROPN
ejpam-108	3	13	university	university	NOUN
ejpam-108	3	14	,	,	PUNCT
ejpam-108	3	15	p.o.box	p.o.box	PROPN
ejpam-108	3	16	7	7	NUM
ejpam-108	3	17	,	,	PUNCT
ejpam-108	3	18	karak	karak	PROPN
ejpam-108	3	19	-	-	PUNCT
ejpam-108	3	20	jordan	jordan	PROPN
ejpam-108	3	21	.	.	PUNCT
ejpam-108	4	1	2	2	NUM
ejpam-108	4	2	school	school	NOUN
ejpam-108	4	3	of	of	ADP
ejpam-108	4	4	mathematical	mathematical	ADJ
ejpam-108	4	5	sciences	science	NOUN
ejpam-108	4	6	,	,	PUNCT
ejpam-108	4	7	faculty	faculty	NOUN
ejpam-108	4	8	of	of	ADP
ejpam-108	4	9	science	science	NOUN
ejpam-108	4	10	and	and	CCONJ
ejpam-108	4	11	technology	technology	NOUN
ejpam-108	4	12	,	,	PUNCT
ejpam-108	4	13	universiti	universiti	PROPN
ejpam-108	4	14	kebangsaan	kebangsaan	PROPN
ejpam-108	4	15	malaysia	malaysia	PROPN
ejpam-108	4	16	43600	43600	NUM
ejpam-108	4	17	ukm	ukm	PROPN
ejpam-108	4	18	bangi	bangi	PROPN
ejpam-108	4	19	,	,	PUNCT
ejpam-108	4	20	selangor	selangor	PROPN
ejpam-108	4	21	,	,	PUNCT
ejpam-108	4	22	malaysia	malaysia	PROPN
ejpam-108	4	23	.	.	PUNCT
ejpam-108	5	1	abstract	abstract	PROPN
ejpam-108	5	2	.	.	PUNCT
ejpam-108	6	1	the	the	DET
ejpam-108	6	2	notion	notion	NOUN
ejpam-108	6	3	of	of	ADP
ejpam-108	6	4	contra	contra	ADJ
ejpam-108	6	5	-	-	ADJ
ejpam-108	6	6	continuous	continuous	ADJ
ejpam-108	6	7	functions	function	NOUN
ejpam-108	6	8	was	be	AUX
ejpam-108	6	9	introduced	introduce	VERB
ejpam-108	6	10	and	and	CCONJ
ejpam-108	6	11	investigated	investigate	VERB
ejpam-108	6	12	by	by	ADP
ejpam-108	6	13	dontchev	dontchev	NOUN
ejpam-108	6	14	[	[	X
ejpam-108	6	15	5	5	NUM
ejpam-108	6	16	]	]	PUNCT
ejpam-108	6	17	.	.	PUNCT
ejpam-108	7	1	in	in	ADP
ejpam-108	7	2	this	this	DET
ejpam-108	7	3	paper	paper	NOUN
ejpam-108	7	4	we	we	PRON
ejpam-108	7	5	apply	apply	VERB
ejpam-108	7	6	the	the	DET
ejpam-108	7	7	notion	notion	NOUN
ejpam-108	7	8	of	of	ADP
ejpam-108	7	9	b	b	NOUN
ejpam-108	7	10	-	-	PUNCT
ejpam-108	7	11	open	open	ADJ
ejpam-108	7	12	sets	set	NOUN
ejpam-108	7	13	in	in	ADP
ejpam-108	7	14	topological	topological	ADJ
ejpam-108	7	15	space	space	NOUN
ejpam-108	7	16	to	to	PART
ejpam-108	7	17	present	present	VERB
ejpam-108	7	18	and	and	CCONJ
ejpam-108	7	19	study	study	VERB
ejpam-108	7	20	a	a	DET
ejpam-108	7	21	new	new	ADJ
ejpam-108	7	22	class	class	NOUN
ejpam-108	7	23	of	of	ADP
ejpam-108	7	24	function	function	NOUN
ejpam-108	7	25	called	call	VERB
ejpam-108	7	26	almost	almost	ADV
ejpam-108	7	27	contra	contra	PROPN
ejpam-108	7	28	-	-	PUNCT
ejpam-108	7	29	b	b	ADJ
ejpam-108	7	30	-	-	PUNCT
ejpam-108	7	31	continuous	continuous	ADJ
ejpam-108	7	32	functions	function	NOUN
ejpam-108	7	33	as	as	ADP
ejpam-108	7	34	a	a	DET
ejpam-108	7	35	new	new	ADJ
ejpam-108	7	36	generalization	generalization	NOUN
ejpam-108	7	37	of	of	ADP
ejpam-108	7	38	contra	contra	PROPN
ejpam-108	7	39	-	-	NOUN
ejpam-108	7	40	continuity	continuity	NOUN
ejpam-108	7	41	.	.	PUNCT
ejpam-108	8	1	ams	am	NOUN
ejpam-108	8	2	subject	subject	ADJ
ejpam-108	8	3	classifications	classification	NOUN
ejpam-108	8	4	:	:	PUNCT
ejpam-108	8	5	54c05	54c05	NUM
ejpam-108	8	6	,	,	PUNCT
ejpam-108	8	7	54c08	54c08	NUM
ejpam-108	8	8	,	,	PUNCT
ejpam-108	8	9	54c10	54c10	NUM
ejpam-108	8	10	key	key	ADJ
ejpam-108	8	11	words	word	NOUN
ejpam-108	8	12	:	:	PUNCT
ejpam-108	8	13	contra	contra	ADJ
ejpam-108	8	14	-	-	ADJ
ejpam-108	8	15	continuous	continuous	ADJ
ejpam-108	8	16	,	,	PUNCT
ejpam-108	8	17	b	b	NOUN
ejpam-108	8	18	-	-	PUNCT
ejpam-108	8	19	continuous	continuous	ADJ
ejpam-108	8	20	,	,	PUNCT
ejpam-108	8	21	contra	contra	PROPN
ejpam-108	8	22	-	-	ADJ
ejpam-108	8	23	b	b	NOUN
ejpam-108	8	24	-	-	PUNCT
ejpam-108	8	25	continuous	continuous	ADJ
ejpam-108	8	26	,	,	PUNCT
ejpam-108	8	27	b	b	X
ejpam-108	8	28	-	-	PUNCT
ejpam-108	8	29	regular	regular	ADJ
ejpam-108	8	30	graph	graph	NOUN
ejpam-108	8	31	,	,	PUNCT
ejpam-108	8	32	almost	almost	ADV
ejpam-108	8	33	contra	contra	PROPN
ejpam-108	8	34	-	-	PUNCT
ejpam-108	8	35	b	b	NOUN
ejpam-108	8	36	-	-	PUNCT
ejpam-108	8	37	continuous	continuous	ADJ
ejpam-108	8	38	,	,	PUNCT
ejpam-108	8	39	strong	strong	ADJ
ejpam-108	8	40	s	s	NOUN
ejpam-108	8	41	-	-	PUNCT
ejpam-108	8	42	closed	closed	ADJ
ejpam-108	8	43	∗corresponding	∗corresponding	NOUN
ejpam-108	8	44	author	author	NOUN
ejpam-108	8	45	.	.	PUNCT
ejpam-108	9	1	email	email	NOUN
ejpam-108	9	2	addresses	address	NOUN
ejpam-108	9	3	:	:	PUNCT
ejpam-108	9	4	omarimutah1	omarimutah1	PROPN
ejpam-108	9	5	�	�	PROPN
ejpam-108	9	6	yahoo	yahoo	PROPN
ejpam-108	9	7	.	.	PUNCT
ejpam-108	9	8	om	om	PROPN
ejpam-108	9	9	(	(	PUNCT
ejpam-108	9	10	a.	a.	PROPN
ejpam-108	9	11	al	al	PROPN
ejpam-108	9	12	-	-	PUNCT
ejpam-108	9	13	omari	omari	PROPN
ejpam-108	9	14	)	)	PUNCT
ejpam-108	9	15	,	,	PUNCT
ejpam-108	9	16	msn	msn	PROPN
ejpam-108	9	17	�	�	PROPN
ejpam-108	9	18	pkris	pkris	NOUN
ejpam-108	9	19	.	.	PUNCT
ejpam-108	10	1	.ukm.my	.ukm.my	PROPN
ejpam-108	10	2	(	(	PUNCT
ejpam-108	10	3	s.	s.	PROPN
ejpam-108	10	4	noorani	noorani	PROPN
ejpam-108	10	5	)	)	PUNCT
ejpam-108	10	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-108	11	1	213	213	NUM
ejpam-108	11	2	c	c	NOUN
ejpam-108	11	3	©	©	PROPN
ejpam-108	11	4	2009	2009	NUM
ejpam-108	11	5	ejpam	ejpam	NOUN
ejpam-108	11	6	all	all	DET
ejpam-108	11	7	rights	right	NOUN
ejpam-108	11	8	reserved	reserve	VERB
ejpam-108	11	9	.	.	PUNCT
ejpam-108	12	1	a.	a.	PROPN
ejpam-108	12	2	al	al	PROPN
ejpam-108	12	3	-	-	PUNCT
ejpam-108	12	4	omari	omari	PROPN
ejpam-108	12	5	and	and	CCONJ
ejpam-108	12	6	s.	s.	PROPN
ejpam-108	12	7	noorani	noorani	PROPN
ejpam-108	12	8	/	/	SYM
ejpam-108	12	9	eur	eur	PROPN
ejpam-108	12	10	.	.	PUNCT
ejpam-108	13	1	j.	j.	PROPN
ejpam-108	13	2	pure	pure	PROPN
ejpam-108	13	3	appl	appl	PROPN
ejpam-108	13	4	.	.	PROPN
ejpam-108	13	5	math	math	PROPN
ejpam-108	13	6	,	,	PUNCT
ejpam-108	13	7	2	2	NUM
ejpam-108	13	8	(	(	PUNCT
ejpam-108	13	9	2009	2009	NUM
ejpam-108	13	10	)	)	PUNCT
ejpam-108	13	11	,	,	PUNCT
ejpam-108	13	12	(	(	PUNCT
ejpam-108	13	13	213	213	NUM
ejpam-108	13	14	-	-	SYM
ejpam-108	13	15	230	230	NUM
ejpam-108	13	16	)	)	PUNCT
ejpam-108	13	17	214	214	NUM
ejpam-108	13	18	1	1	NUM
ejpam-108	13	19	.	.	PUNCT
ejpam-108	14	1	introduction	introduction	NOUN
ejpam-108	14	2	and	and	CCONJ
ejpam-108	14	3	preliminaries	preliminary	NOUN
ejpam-108	14	4	in	in	ADP
ejpam-108	14	5	1996	1996	NUM
ejpam-108	14	6	,	,	PUNCT
ejpam-108	14	7	dontchev	dontchev	ADJ
ejpam-108	14	8	[	[	X
ejpam-108	14	9	5	5	NUM
ejpam-108	14	10	]	]	PUNCT
ejpam-108	14	11	introduced	introduce	VERB
ejpam-108	14	12	contra	contra	ADJ
ejpam-108	14	13	-	-	ADJ
ejpam-108	14	14	continuous	continuous	ADJ
ejpam-108	14	15	functions	function	NOUN
ejpam-108	14	16	.	.	PUNCT
ejpam-108	15	1	jafari	jafari	PROPN
ejpam-108	15	2	and	and	CCONJ
ejpam-108	15	3	noiri	noiri	ADV
ejpam-108	16	1	[	[	X
ejpam-108	16	2	8	8	NUM
ejpam-108	16	3	]	]	PUNCT
ejpam-108	16	4	introduced	introduce	VERB
ejpam-108	16	5	and	and	CCONJ
ejpam-108	16	6	studied	study	VERB
ejpam-108	16	7	contra	contra	ADJ
ejpam-108	16	8	-	-	ADJ
ejpam-108	16	9	precontinuous	precontinuous	ADJ
ejpam-108	16	10	functions	function	NOUN
ejpam-108	16	11	.	.	PUNCT
ejpam-108	17	1	ekici	ekici	NOUN
ejpam-108	18	1	[	[	X
ejpam-108	18	2	10	10	NUM
ejpam-108	18	3	]	]	PUNCT
ejpam-108	18	4	introduced	introduce	VERB
ejpam-108	18	5	and	and	CCONJ
ejpam-108	18	6	studied	study	VERB
ejpam-108	18	7	almost	almost	ADV
ejpam-108	18	8	contra	contra	ADJ
ejpam-108	18	9	-	-	ADJ
ejpam-108	18	10	precontinuous	precontinuous	ADJ
ejpam-108	18	11	functions	function	NOUN
ejpam-108	18	12	.	.	PUNCT
ejpam-108	19	1	recently	recently	ADV
ejpam-108	19	2	[	[	X
ejpam-108	19	3	13	13	NUM
ejpam-108	19	4	]	]	PUNCT
ejpam-108	19	5	introduced	introduce	VERB
ejpam-108	19	6	and	and	CCONJ
ejpam-108	19	7	studied	study	VERB
ejpam-108	19	8	contra	contra	PROPN
ejpam-108	19	9	b	b	PROPN
ejpam-108	19	10	-	-	PUNCT
ejpam-108	19	11	continuous	continuous	ADJ
ejpam-108	19	12	functions	function	NOUN
ejpam-108	19	13	.	.	PUNCT
ejpam-108	20	1	in	in	ADP
ejpam-108	20	2	this	this	DET
ejpam-108	20	3	paper	paper	NOUN
ejpam-108	20	4	,	,	PUNCT
ejpam-108	20	5	we	we	PRON
ejpam-108	20	6	introduce	introduce	VERB
ejpam-108	20	7	a	a	DET
ejpam-108	20	8	new	new	ADJ
ejpam-108	20	9	class	class	NOUN
ejpam-108	20	10	of	of	ADP
ejpam-108	20	11	functions	function	NOUN
ejpam-108	20	12	called	call	VERB
ejpam-108	20	13	almost	almost	ADV
ejpam-108	20	14	contra	contra	PROPN
ejpam-108	20	15	-	-	PUNCT
ejpam-108	20	16	b	b	ADJ
ejpam-108	20	17	-	-	PUNCT
ejpam-108	20	18	continuous	continuous	ADJ
ejpam-108	20	19	function	function	NOUN
ejpam-108	20	20	.	.	PUNCT
ejpam-108	21	1	moreover	moreover	ADV
ejpam-108	21	2	,	,	PUNCT
ejpam-108	21	3	we	we	PRON
ejpam-108	21	4	obtain	obtain	VERB
ejpam-108	21	5	basic	basic	ADJ
ejpam-108	21	6	properties	property	NOUN
ejpam-108	21	7	and	and	CCONJ
ejpam-108	21	8	preservation	preservation	NOUN
ejpam-108	21	9	theorem	theorem	NOUN
ejpam-108	21	10	of	of	ADP
ejpam-108	21	11	almost	almost	ADV
ejpam-108	21	12	contra	contra	PROPN
ejpam-108	21	13	-	-	PUNCT
ejpam-108	21	14	b	b	ADJ
ejpam-108	21	15	-	-	PUNCT
ejpam-108	21	16	continuous	continuous	ADJ
ejpam-108	21	17	function	function	NOUN
ejpam-108	21	18	,	,	PUNCT
ejpam-108	21	19	contra	contra	PROPN
ejpam-108	21	20	-	-	ADJ
ejpam-108	21	21	bcontinuous	bcontinuous	ADJ
ejpam-108	21	22	function	function	NOUN
ejpam-108	21	23	and	and	CCONJ
ejpam-108	21	24	relationships	relationship	NOUN
ejpam-108	21	25	between	between	ADP
ejpam-108	21	26	almost	almost	ADV
ejpam-108	21	27	contra	contra	PROPN
ejpam-108	21	28	-	-	PUNCT
ejpam-108	21	29	b	b	ADJ
ejpam-108	21	30	-	-	PUNCT
ejpam-108	21	31	continuous	continuous	ADJ
ejpam-108	21	32	function	function	NOUN
ejpam-108	21	33	and	and	CCONJ
ejpam-108	21	34	b	b	NOUN
ejpam-108	21	35	-	-	PUNCT
ejpam-108	21	36	regular	regular	ADJ
ejpam-108	21	37	graphs	graph	NOUN
ejpam-108	21	38	.	.	PUNCT
ejpam-108	22	1	throughout	throughout	ADP
ejpam-108	22	2	the	the	DET
ejpam-108	22	3	paper	paper	NOUN
ejpam-108	22	4	,	,	PUNCT
ejpam-108	22	5	the	the	DET
ejpam-108	22	6	space	space	NOUN
ejpam-108	22	7	x	x	PUNCT
ejpam-108	22	8	and	and	CCONJ
ejpam-108	22	9	y	y	PROPN
ejpam-108	22	10	(	(	PUNCT
ejpam-108	22	11	or	or	CCONJ
ejpam-108	22	12	(	(	PUNCT
ejpam-108	22	13	x	x	X
ejpam-108	22	14	,	,	PUNCT
ejpam-108	22	15	τ	τ	PROPN
ejpam-108	22	16	)	)	PUNCT
ejpam-108	22	17	and	and	CCONJ
ejpam-108	22	18	(	(	PUNCT
ejpam-108	22	19	y	y	PROPN
ejpam-108	22	20	,	,	PUNCT
ejpam-108	22	21	σ	σ	PROPN
ejpam-108	22	22	)	)	PUNCT
ejpam-108	22	23	)	)	PUNCT
ejpam-108	22	24	stand	stand	VERB
ejpam-108	22	25	for	for	ADP
ejpam-108	22	26	topological	topological	ADJ
ejpam-108	22	27	spaces	space	NOUN
ejpam-108	22	28	with	with	ADP
ejpam-108	22	29	no	no	DET
ejpam-108	22	30	separation	separation	NOUN
ejpam-108	22	31	axioms	axiom	NOUN
ejpam-108	22	32	assumed	assume	VERB
ejpam-108	22	33	unless	unless	SCONJ
ejpam-108	22	34	otherwise	otherwise	ADV
ejpam-108	22	35	stated	state	VERB
ejpam-108	22	36	.	.	PUNCT
ejpam-108	23	1	let	let	VERB
ejpam-108	23	2	a	a	DET
ejpam-108	23	3	be	be	AUX
ejpam-108	23	4	a	a	DET
ejpam-108	23	5	subset	subset	NOUN
ejpam-108	23	6	of	of	ADP
ejpam-108	23	7	x	x	PRON
ejpam-108	23	8	.	.	PUNCT
ejpam-108	24	1	the	the	DET
ejpam-108	24	2	closure	closure	NOUN
ejpam-108	24	3	of	of	ADP
ejpam-108	24	4	a	a	PRON
ejpam-108	24	5	and	and	CCONJ
ejpam-108	24	6	the	the	DET
ejpam-108	24	7	interior	interior	NOUN
ejpam-108	24	8	of	of	ADP
ejpam-108	24	9	a	a	PRON
ejpam-108	24	10	will	will	AUX
ejpam-108	24	11	be	be	AUX
ejpam-108	24	12	denoted	denote	VERB
ejpam-108	24	13	by	by	ADP
ejpam-108	24	14	cl(a	cl(a	NOUN
ejpam-108	24	15	)	)	PUNCT
ejpam-108	24	16	and	and	CCONJ
ejpam-108	24	17	int(a	int(a	PROPN
ejpam-108	24	18	)	)	PUNCT
ejpam-108	24	19	,	,	PUNCT
ejpam-108	24	20	respectively	respectively	ADV
ejpam-108	24	21	.	.	PUNCT
ejpam-108	25	1	definition	definition	NOUN
ejpam-108	25	2	1.1	1.1	NUM
ejpam-108	25	3	.	.	PUNCT
ejpam-108	26	1	a	a	DET
ejpam-108	26	2	subset	subset	NOUN
ejpam-108	26	3	a	a	PRON
ejpam-108	26	4	of	of	ADP
ejpam-108	26	5	a	a	DET
ejpam-108	26	6	space	space	NOUN
ejpam-108	26	7	x	x	PUNCT
ejpam-108	26	8	is	be	AUX
ejpam-108	26	9	said	say	VERB
ejpam-108	26	10	to	to	PART
ejpam-108	26	11	be	be	AUX
ejpam-108	26	12	1	1	NUM
ejpam-108	26	13	.	.	PUNCT
ejpam-108	26	14	regular	regular	ADJ
ejpam-108	26	15	open	open	ADJ
ejpam-108	27	1	[	[	X
ejpam-108	27	2	27	27	NUM
ejpam-108	27	3	]	]	X
ejpam-108	27	4	if	if	SCONJ
ejpam-108	27	5	a=	a=	ADV
ejpam-108	27	6	int(cl(a	int(cl(a	PROPN
ejpam-108	27	7	)	)	PUNCT
ejpam-108	27	8	)	)	PUNCT
ejpam-108	27	9	;	;	PUNCT
ejpam-108	28	1	2	2	X
ejpam-108	28	2	.	.	X
ejpam-108	28	3	α	α	X
ejpam-108	28	4	-	-	ADJ
ejpam-108	28	5	open	open	ADJ
ejpam-108	28	6	[	[	X
ejpam-108	28	7	20	20	NUM
ejpam-108	28	8	]	]	PUNCT
ejpam-108	28	9	if	if	SCONJ
ejpam-108	28	10	a⊆	a⊆	ADP
ejpam-108	28	11	int(cl(int(a	int(cl(int(a	PROPN
ejpam-108	28	12	)	)	PUNCT
ejpam-108	28	13	)	)	PUNCT
ejpam-108	28	14	)	)	PUNCT
ejpam-108	28	15	;	;	PUNCT
ejpam-108	28	16	3	3	X
ejpam-108	28	17	.	.	X
ejpam-108	28	18	semi	semi	ADJ
ejpam-108	28	19	-	-	ADJ
ejpam-108	28	20	open	open	ADJ
ejpam-108	28	21	[	[	X
ejpam-108	28	22	24	24	NUM
ejpam-108	28	23	]	]	X
ejpam-108	28	24	if	if	SCONJ
ejpam-108	28	25	a⊆	a⊆	PROPN
ejpam-108	28	26	cl(int(a	cl(int(a	NOUN
ejpam-108	28	27	)	)	PUNCT
ejpam-108	28	28	)	)	PUNCT
ejpam-108	29	1	;	;	PUNCT
ejpam-108	30	1	4	4	X
ejpam-108	30	2	.	.	X
ejpam-108	30	3	pre	pre	VERB
ejpam-108	30	4	-	-	ADJ
ejpam-108	30	5	open	open	ADJ
ejpam-108	30	6	[	[	X
ejpam-108	30	7	25	25	NUM
ejpam-108	30	8	]	]	X
ejpam-108	30	9	if	if	SCONJ
ejpam-108	30	10	a⊆	a⊆	ADP
ejpam-108	30	11	int(cl(a	int(cl(a	PROPN
ejpam-108	30	12	)	)	PUNCT
ejpam-108	30	13	)	)	PUNCT
ejpam-108	30	14	;	;	PUNCT
ejpam-108	30	15	5	5	X
ejpam-108	30	16	.	.	X
ejpam-108	30	17	β	β	X
ejpam-108	30	18	-open	-open	PROPN
ejpam-108	31	1	[	[	X
ejpam-108	31	2	2	2	NUM
ejpam-108	31	3	]	]	X
ejpam-108	31	4	if	if	SCONJ
ejpam-108	31	5	a⊆	a⊆	NOUN
ejpam-108	31	6	cl(int(cl(a	cl(int(cl(a	NOUN
ejpam-108	31	7	)	)	PUNCT
ejpam-108	31	8	)	)	PUNCT
ejpam-108	31	9	)	)	PUNCT
ejpam-108	31	10	;	;	PUNCT
ejpam-108	32	1	6	6	NUM
ejpam-108	32	2	.	.	X
ejpam-108	32	3	b	b	X
ejpam-108	32	4	-	-	PUNCT
ejpam-108	32	5	open	open	ADJ
ejpam-108	32	6	[	[	X
ejpam-108	32	7	3	3	NUM
ejpam-108	32	8	]	]	X
ejpam-108	32	9	if	if	SCONJ
ejpam-108	32	10	a⊆	a⊆	PROPN
ejpam-108	32	11	cl(int(a))∪	cl(int(a))∪	VERB
ejpam-108	32	12	int(cl(a	int(cl(a	PROPN
ejpam-108	32	13	)	)	PUNCT
ejpam-108	32	14	)	)	PUNCT
ejpam-108	32	15	.	.	PUNCT
ejpam-108	33	1	the	the	DET
ejpam-108	33	2	complement	complement	NOUN
ejpam-108	33	3	of	of	ADP
ejpam-108	33	4	a	a	DET
ejpam-108	33	5	b	b	NOUN
ejpam-108	33	6	-	-	PUNCT
ejpam-108	33	7	open	open	ADJ
ejpam-108	33	8	set	set	NOUN
ejpam-108	33	9	is	be	AUX
ejpam-108	33	10	said	say	VERB
ejpam-108	33	11	to	to	PART
ejpam-108	33	12	be	be	AUX
ejpam-108	33	13	b	b	NOUN
ejpam-108	33	14	-	-	PUNCT
ejpam-108	33	15	closed	closed	ADJ
ejpam-108	33	16	[	[	X
ejpam-108	33	17	3	3	NUM
ejpam-108	33	18	]	]	PUNCT
ejpam-108	33	19	.	.	PUNCT
ejpam-108	34	1	the	the	DET
ejpam-108	34	2	intersection	intersection	NOUN
ejpam-108	34	3	of	of	ADP
ejpam-108	34	4	all	all	DET
ejpam-108	34	5	b	b	NOUN
ejpam-108	34	6	-	-	PUNCT
ejpam-108	34	7	closed	closed	ADJ
ejpam-108	34	8	sets	set	NOUN
ejpam-108	34	9	of	of	ADP
ejpam-108	34	10	x	x	PUNCT
ejpam-108	34	11	containing	contain	VERB
ejpam-108	34	12	a	a	PRON
ejpam-108	34	13	is	be	AUX
ejpam-108	34	14	called	call	VERB
ejpam-108	34	15	the	the	DET
ejpam-108	34	16	b	b	NOUN
ejpam-108	34	17	-	-	PUNCT
ejpam-108	34	18	closure	closure	NOUN
ejpam-108	34	19	of	of	ADP
ejpam-108	34	20	a	a	PRON
ejpam-108	34	21	and	and	CCONJ
ejpam-108	34	22	is	be	AUX
ejpam-108	34	23	denoted	denote	VERB
ejpam-108	34	24	by	by	ADP
ejpam-108	34	25	bcl(a	bcl(a	PROPN
ejpam-108	34	26	)	)	PUNCT
ejpam-108	34	27	.	.	PUNCT
ejpam-108	35	1	the	the	DET
ejpam-108	35	2	union	union	NOUN
ejpam-108	35	3	of	of	ADP
ejpam-108	35	4	all	all	DET
ejpam-108	35	5	b	b	NOUN
ejpam-108	35	6	-	-	PUNCT
ejpam-108	35	7	open	open	ADJ
ejpam-108	35	8	sets	set	NOUN
ejpam-108	35	9	of	of	ADP
ejpam-108	35	10	x	x	PUNCT
ejpam-108	35	11	contained	contain	VERB
ejpam-108	35	12	a	a	PRON
ejpam-108	35	13	is	be	AUX
ejpam-108	35	14	called	call	VERB
ejpam-108	35	15	b	b	NOUN
ejpam-108	35	16	-	-	NOUN
ejpam-108	35	17	interior	interior	NOUN
ejpam-108	35	18	of	of	ADP
ejpam-108	35	19	a	a	PRON
ejpam-108	35	20	and	and	CCONJ
ejpam-108	35	21	a.	a.	PROPN
ejpam-108	35	22	al	al	PROPN
ejpam-108	35	23	-	-	PUNCT
ejpam-108	35	24	omari	omari	PROPN
ejpam-108	35	25	and	and	CCONJ
ejpam-108	35	26	s.	s.	PROPN
ejpam-108	35	27	noorani	noorani	PROPN
ejpam-108	35	28	/	/	SYM
ejpam-108	35	29	eur	eur	PROPN
ejpam-108	35	30	.	.	PUNCT
ejpam-108	36	1	j.	j.	PROPN
ejpam-108	36	2	pure	pure	PROPN
ejpam-108	36	3	appl	appl	PROPN
ejpam-108	36	4	.	.	PROPN
ejpam-108	36	5	math	math	PROPN
ejpam-108	36	6	,	,	PUNCT
ejpam-108	36	7	2	2	NUM
ejpam-108	36	8	(	(	PUNCT
ejpam-108	36	9	2009	2009	NUM
ejpam-108	36	10	)	)	PUNCT
ejpam-108	36	11	,	,	PUNCT
ejpam-108	36	12	(	(	PUNCT
ejpam-108	36	13	213	213	NUM
ejpam-108	36	14	-	-	SYM
ejpam-108	36	15	230	230	NUM
ejpam-108	36	16	)	)	PUNCT
ejpam-108	36	17	215	215	NUM
ejpam-108	36	18	is	be	AUX
ejpam-108	36	19	denoted	denote	VERB
ejpam-108	36	20	by	by	ADP
ejpam-108	36	21	bint(a	bint(a	PROPN
ejpam-108	36	22	)	)	PUNCT
ejpam-108	36	23	.	.	PUNCT
ejpam-108	37	1	the	the	DET
ejpam-108	37	2	family	family	NOUN
ejpam-108	37	3	of	of	ADP
ejpam-108	37	4	all	all	DET
ejpam-108	37	5	b	b	NOUN
ejpam-108	37	6	-	-	PUNCT
ejpam-108	37	7	open	open	ADJ
ejpam-108	37	8	(	(	PUNCT
ejpam-108	37	9	resp	resp	NOUN
ejpam-108	37	10	.	.	PUNCT
ejpam-108	38	1	α	α	X
ejpam-108	38	2	-	-	ADJ
ejpam-108	38	3	open	open	ADJ
ejpam-108	38	4	,	,	PUNCT
ejpam-108	38	5	semi	semi	ADJ
ejpam-108	38	6	-	-	ADJ
ejpam-108	38	7	open	open	ADJ
ejpam-108	38	8	,	,	PUNCT
ejpam-108	38	9	preopen	preopen	ADJ
ejpam-108	38	10	,	,	PUNCT
ejpam-108	38	11	β	β	X
ejpam-108	38	12	-open	-open	NOUN
ejpam-108	38	13	,	,	PUNCT
ejpam-108	38	14	regular	regular	ADJ
ejpam-108	38	15	open	open	ADJ
ejpam-108	38	16	,	,	PUNCT
ejpam-108	38	17	b	b	X
ejpam-108	38	18	-	-	PUNCT
ejpam-108	38	19	closed	closed	ADJ
ejpam-108	38	20	,	,	PUNCT
ejpam-108	38	21	preclosed	preclose	VERB
ejpam-108	38	22	,	,	PUNCT
ejpam-108	38	23	β	β	X
ejpam-108	38	24	-closed	-close	VERB
ejpam-108	38	25	,	,	PUNCT
ejpam-108	38	26	regular	regular	ADJ
ejpam-108	38	27	closed	closed	ADJ
ejpam-108	38	28	,	,	PUNCT
ejpam-108	38	29	closed	closed	ADJ
ejpam-108	38	30	)	)	PUNCT
ejpam-108	38	31	subsets	subset	NOUN
ejpam-108	38	32	of	of	ADP
ejpam-108	38	33	a	a	DET
ejpam-108	38	34	space	space	NOUN
ejpam-108	38	35	x	x	PUNCT
ejpam-108	38	36	is	be	AUX
ejpam-108	38	37	denoted	denote	VERB
ejpam-108	38	38	by	by	ADP
ejpam-108	38	39	bo(x	bo(x	NUM
ejpam-108	38	40	)	)	PUNCT
ejpam-108	38	41	(	(	PUNCT
ejpam-108	38	42	resp	resp	NOUN
ejpam-108	38	43	.	.	PUNCT
ejpam-108	38	44	αo(x	αo(x	NUM
ejpam-108	38	45	)	)	PUNCT
ejpam-108	38	46	,	,	PUNCT
ejpam-108	38	47	so(x	so(x	X
ejpam-108	38	48	)	)	PUNCT
ejpam-108	38	49	,	,	PUNCT
ejpam-108	38	50	po(x	po(x	NUM
ejpam-108	38	51	)	)	PUNCT
ejpam-108	38	52	,	,	PUNCT
ejpam-108	38	53	βo(x	βo(x	PUNCT
ejpam-108	38	54	)	)	PUNCT
ejpam-108	38	55	,	,	PUNCT
ejpam-108	38	56	ro(x	ro(x	X
ejpam-108	38	57	)	)	PUNCT
ejpam-108	38	58	,	,	PUNCT
ejpam-108	38	59	bc(x	bc(x	PUNCT
ejpam-108	38	60	)	)	PUNCT
ejpam-108	38	61	,	,	PUNCT
ejpam-108	38	62	pc(x	pc(x	NOUN
ejpam-108	38	63	)	)	PUNCT
ejpam-108	38	64	,	,	PUNCT
ejpam-108	38	65	βc(x	βc(x	PUNCT
ejpam-108	38	66	)	)	PUNCT
ejpam-108	38	67	,	,	PUNCT
ejpam-108	38	68	rc(x	rc(x	NOUN
ejpam-108	38	69	)	)	PUNCT
ejpam-108	38	70	,	,	PUNCT
ejpam-108	38	71	c(x	c(x	NOUN
ejpam-108	38	72	)	)	PUNCT
ejpam-108	38	73	respectively	respectively	ADV
ejpam-108	38	74	)	)	PUNCT
ejpam-108	38	75	and	and	CCONJ
ejpam-108	38	76	the	the	DET
ejpam-108	38	77	collection	collection	NOUN
ejpam-108	38	78	of	of	ADP
ejpam-108	38	79	all	all	DET
ejpam-108	38	80	b	b	NOUN
ejpam-108	38	81	-	-	PUNCT
ejpam-108	38	82	open	open	ADJ
ejpam-108	38	83	subsets	subset	NOUN
ejpam-108	38	84	of	of	ADP
ejpam-108	38	85	x	x	PUNCT
ejpam-108	38	86	containing	contain	VERB
ejpam-108	38	87	a	a	DET
ejpam-108	38	88	fixed	fix	VERB
ejpam-108	38	89	point	point	NOUN
ejpam-108	38	90	x	x	VERB
ejpam-108	38	91	is	be	AUX
ejpam-108	38	92	denoted	denote	VERB
ejpam-108	38	93	by	by	ADP
ejpam-108	38	94	bo(x	bo(x	NUM
ejpam-108	38	95	,	,	PUNCT
ejpam-108	38	96	x	x	NOUN
ejpam-108	38	97	)	)	PUNCT
ejpam-108	38	98	.	.	PUNCT
ejpam-108	39	1	the	the	DET
ejpam-108	39	2	sets	set	NOUN
ejpam-108	39	3	αo(x	αo(x	NUM
ejpam-108	39	4	,	,	PUNCT
ejpam-108	39	5	x	x	X
ejpam-108	39	6	)	)	PUNCT
ejpam-108	39	7	,	,	PUNCT
ejpam-108	39	8	so(x	so(x	NOUN
ejpam-108	39	9	,	,	PUNCT
ejpam-108	39	10	x	x	NOUN
ejpam-108	39	11	)	)	PUNCT
ejpam-108	39	12	,	,	PUNCT
ejpam-108	39	13	po(x	po(x	PUNCT
ejpam-108	39	14	,	,	PUNCT
ejpam-108	39	15	x	x	X
ejpam-108	39	16	)	)	PUNCT
ejpam-108	39	17	,	,	PUNCT
ejpam-108	39	18	βo(x	βo(x	PUNCT
ejpam-108	39	19	,	,	PUNCT
ejpam-108	39	20	x	x	X
ejpam-108	39	21	)	)	PUNCT
ejpam-108	39	22	,	,	PUNCT
ejpam-108	39	23	ro(x	ro(x	PUNCT
ejpam-108	39	24	,	,	PUNCT
ejpam-108	39	25	x	x	X
ejpam-108	39	26	)	)	PUNCT
ejpam-108	39	27	and	and	CCONJ
ejpam-108	39	28	c(x	c(x	NOUN
ejpam-108	39	29	,	,	PUNCT
ejpam-108	39	30	x	x	X
ejpam-108	39	31	)	)	PUNCT
ejpam-108	39	32	are	be	AUX
ejpam-108	39	33	defined	define	VERB
ejpam-108	39	34	analogously	analogously	ADV
ejpam-108	39	35	.	.	PUNCT
ejpam-108	40	1	definition	definition	NOUN
ejpam-108	40	2	1.2	1.2	NUM
ejpam-108	40	3	.	.	PUNCT
ejpam-108	41	1	a	a	DET
ejpam-108	41	2	function	function	NOUN
ejpam-108	41	3	f	f	NOUN
ejpam-108	41	4	:	:	PUNCT
ejpam-108	41	5	x	x	X
ejpam-108	41	6	→	→	SYM
ejpam-108	41	7	y	y	PROPN
ejpam-108	41	8	is	be	AUX
ejpam-108	41	9	called	call	VERB
ejpam-108	41	10	b	b	NOUN
ejpam-108	41	11	-	-	ADJ
ejpam-108	41	12	continuous	continuous	ADJ
ejpam-108	41	13	[	[	X
ejpam-108	41	14	11	11	NUM
ejpam-108	41	15	]	]	X
ejpam-108	41	16	if	if	SCONJ
ejpam-108	41	17	for	for	ADP
ejpam-108	41	18	each	each	DET
ejpam-108	41	19	x	x	SYM
ejpam-108	41	20	∈	∈	PROPN
ejpam-108	41	21	x	x	X
ejpam-108	41	22	and	and	CCONJ
ejpam-108	41	23	each	each	DET
ejpam-108	41	24	open	open	ADJ
ejpam-108	41	25	set	set	VERB
ejpam-108	41	26	v	v	NOUN
ejpam-108	41	27	of	of	ADP
ejpam-108	41	28	y	y	PROPN
ejpam-108	41	29	containing	contain	VERB
ejpam-108	41	30	f	f	PROPN
ejpam-108	41	31	(	(	PUNCT
ejpam-108	41	32	x	x	NOUN
ejpam-108	41	33	)	)	PUNCT
ejpam-108	41	34	,	,	PUNCT
ejpam-108	41	35	there	there	PRON
ejpam-108	41	36	exists	exist	VERB
ejpam-108	41	37	u	u	PROPN
ejpam-108	41	38	∈	∈	PROPN
ejpam-108	41	39	bo(x	bo(x	NUM
ejpam-108	41	40	,	,	PUNCT
ejpam-108	41	41	x	x	X
ejpam-108	41	42	)	)	PUNCT
ejpam-108	41	43	such	such	ADJ
ejpam-108	41	44	that	that	SCONJ
ejpam-108	41	45	f	f	PROPN
ejpam-108	41	46	(	(	PUNCT
ejpam-108	41	47	u)⊆	u)⊆	PROPN
ejpam-108	41	48	v	v	NOUN
ejpam-108	41	49	.	.	PUNCT
ejpam-108	42	1	definition	definition	NOUN
ejpam-108	42	2	1.3	1.3	NUM
ejpam-108	42	3	.	.	PUNCT
ejpam-108	43	1	a	a	DET
ejpam-108	43	2	function	function	NOUN
ejpam-108	43	3	f	f	NOUN
ejpam-108	43	4	:	:	PUNCT
ejpam-108	43	5	x	x	X
ejpam-108	43	6	→	→	SYM
ejpam-108	43	7	y	y	PROPN
ejpam-108	43	8	is	be	AUX
ejpam-108	43	9	called	call	VERB
ejpam-108	43	10	contra	contra	ADJ
ejpam-108	43	11	-	-	ADJ
ejpam-108	43	12	continuous	continuous	ADJ
ejpam-108	43	13	[	[	X
ejpam-108	43	14	5	5	NUM
ejpam-108	43	15	]	]	PUNCT
ejpam-108	43	16	(	(	PUNCT
ejpam-108	43	17	resp	resp	NOUN
ejpam-108	43	18	.	.	PUNCT
ejpam-108	44	1	contra	contra	PROPN
ejpam-108	44	2	-	-	NOUN
ejpam-108	44	3	precontinuous	precontinuous	ADJ
ejpam-108	45	1	[	[	X
ejpam-108	45	2	8	8	NUM
ejpam-108	45	3	]	]	PUNCT
ejpam-108	45	4	,	,	PUNCT
ejpam-108	45	5	contra	contra	PROPN
ejpam-108	45	6	-	-	PROPN
ejpam-108	45	7	β	β	X
ejpam-108	45	8	-continuous	-continuous	ADJ
ejpam-108	45	9	[	[	X
ejpam-108	45	10	4	4	NUM
ejpam-108	45	11	]	]	PUNCT
ejpam-108	45	12	,	,	PUNCT
ejpam-108	45	13	contra	contra	PROPN
ejpam-108	45	14	-	-	PUNCT
ejpam-108	45	15	b	b	NOUN
ejpam-108	45	16	-	-	PUNCT
ejpam-108	45	17	continuous	continuous	ADJ
ejpam-108	45	18	[	[	X
ejpam-108	45	19	13	13	NUM
ejpam-108	45	20	]	]	SYM
ejpam-108	45	21	)	)	PUNCT
ejpam-108	45	22	if	if	SCONJ
ejpam-108	45	23	f	f	PROPN
ejpam-108	45	24	−1(v	−1(v	PROPN
ejpam-108	45	25	)	)	PUNCT
ejpam-108	45	26	closed	close	VERB
ejpam-108	45	27	(	(	PUNCT
ejpam-108	45	28	resp	resp	NOUN
ejpam-108	45	29	.	.	PUNCT
ejpam-108	46	1	preclosed	preclose	VERB
ejpam-108	46	2	,	,	PUNCT
ejpam-108	46	3	β	β	X
ejpam-108	46	4	-closed	-close	VERB
ejpam-108	46	5	,	,	PUNCT
ejpam-108	46	6	b	b	NOUN
ejpam-108	46	7	-	-	PUNCT
ejpam-108	46	8	closed	closed	ADJ
ejpam-108	46	9	)	)	PUNCT
ejpam-108	46	10	in	in	ADP
ejpam-108	46	11	x	x	PUNCT
ejpam-108	46	12	for	for	SCONJ
ejpam-108	46	13	each	each	DET
ejpam-108	46	14	open	open	ADJ
ejpam-108	46	15	set	set	VERB
ejpam-108	46	16	v	v	NOUN
ejpam-108	46	17	of	of	ADP
ejpam-108	46	18	y	y	PROPN
ejpam-108	46	19	.	.	PUNCT
ejpam-108	47	1	2	2	X
ejpam-108	47	2	.	.	X
ejpam-108	47	3	contra	contra	PROPN
ejpam-108	47	4	-	-	PUNCT
ejpam-108	47	5	b	b	ADJ
ejpam-108	47	6	-	-	PUNCT
ejpam-108	47	7	continuous	continuous	ADJ
ejpam-108	47	8	functions	function	NOUN
ejpam-108	47	9	in	in	ADP
ejpam-108	47	10	this	this	DET
ejpam-108	47	11	section	section	NOUN
ejpam-108	47	12	,	,	PUNCT
ejpam-108	47	13	we	we	PRON
ejpam-108	47	14	obtain	obtain	VERB
ejpam-108	47	15	some	some	DET
ejpam-108	47	16	properties	property	NOUN
ejpam-108	47	17	of	of	ADP
ejpam-108	47	18	contra	contra	PROPN
ejpam-108	47	19	-	-	PUNCT
ejpam-108	47	20	b	b	ADJ
ejpam-108	47	21	-	-	PUNCT
ejpam-108	47	22	continuous	continuous	ADJ
ejpam-108	47	23	functions	function	NOUN
ejpam-108	47	24	,	,	PUNCT
ejpam-108	47	25	(	(	PUNCT
ejpam-108	47	26	for	for	ADP
ejpam-108	47	27	more	more	ADJ
ejpam-108	47	28	properties	property	NOUN
ejpam-108	47	29	the	the	DET
ejpam-108	47	30	reader	reader	NOUN
ejpam-108	47	31	should	should	AUX
ejpam-108	47	32	refer	refer	VERB
ejpam-108	47	33	to	to	ADP
ejpam-108	47	34	[	[	X
ejpam-108	47	35	1,13,17,20	1,13,17,20	NUM
ejpam-108	47	36	]	]	PUNCT
ejpam-108	47	37	)	)	PUNCT
ejpam-108	47	38	.	.	PUNCT
ejpam-108	48	1	lemma	lemma	PROPN
ejpam-108	48	2	2.1	2.1	NUM
ejpam-108	48	3	.	.	PUNCT
ejpam-108	49	1	[	[	X
ejpam-108	49	2	3	3	X
ejpam-108	49	3	]	]	X
ejpam-108	49	4	let	let	VERB
ejpam-108	49	5	(	(	PUNCT
ejpam-108	49	6	x	x	X
ejpam-108	49	7	,	,	PUNCT
ejpam-108	49	8	τ	τ	X
ejpam-108	49	9	)	)	PUNCT
ejpam-108	49	10	be	be	VERB
ejpam-108	49	11	a	a	DET
ejpam-108	49	12	topological	topological	ADJ
ejpam-108	49	13	space	space	NOUN
ejpam-108	49	14	.	.	PUNCT
ejpam-108	50	1	1	1	X
ejpam-108	50	2	.	.	X
ejpam-108	50	3	the	the	DET
ejpam-108	50	4	intersection	intersection	NOUN
ejpam-108	50	5	of	of	ADP
ejpam-108	50	6	an	an	DET
ejpam-108	50	7	open	open	ADJ
ejpam-108	50	8	set	set	NOUN
ejpam-108	50	9	and	and	CCONJ
ejpam-108	50	10	a	a	DET
ejpam-108	50	11	b	b	NOUN
ejpam-108	50	12	-	-	PUNCT
ejpam-108	50	13	open	open	ADJ
ejpam-108	50	14	set	set	NOUN
ejpam-108	50	15	is	be	AUX
ejpam-108	50	16	a	a	DET
ejpam-108	50	17	b	b	NOUN
ejpam-108	50	18	-	-	PUNCT
ejpam-108	50	19	open	open	ADJ
ejpam-108	50	20	set	set	NOUN
ejpam-108	50	21	.	.	PUNCT
ejpam-108	51	1	2	2	X
ejpam-108	51	2	.	.	X
ejpam-108	51	3	the	the	DET
ejpam-108	51	4	union	union	NOUN
ejpam-108	51	5	of	of	ADP
ejpam-108	51	6	any	any	DET
ejpam-108	51	7	family	family	NOUN
ejpam-108	51	8	of	of	ADP
ejpam-108	51	9	b	b	NOUN
ejpam-108	51	10	-	-	PUNCT
ejpam-108	51	11	open	open	ADJ
ejpam-108	51	12	sets	set	NOUN
ejpam-108	51	13	is	be	AUX
ejpam-108	51	14	a	a	DET
ejpam-108	51	15	b	b	NOUN
ejpam-108	51	16	-	-	PUNCT
ejpam-108	51	17	open	open	ADJ
ejpam-108	51	18	set	set	NOUN
ejpam-108	51	19	.	.	PUNCT
ejpam-108	52	1	recall	recall	VERB
ejpam-108	52	2	that	that	PRON
ejpam-108	52	3	for	for	ADP
ejpam-108	52	4	a	a	DET
ejpam-108	52	5	function	function	NOUN
ejpam-108	52	6	f	f	NOUN
ejpam-108	52	7	:	:	PUNCT
ejpam-108	52	8	x	x	X
ejpam-108	52	9	→	→	SYM
ejpam-108	52	10	y	y	PROPN
ejpam-108	52	11	,	,	PUNCT
ejpam-108	52	12	the	the	DET
ejpam-108	52	13	subset	subset	NOUN
ejpam-108	52	14	{	{	PUNCT
ejpam-108	52	15	(	(	PUNCT
ejpam-108	52	16	x	x	INTJ
ejpam-108	52	17	,	,	PUNCT
ejpam-108	52	18	f	f	PROPN
ejpam-108	52	19	(	(	PUNCT
ejpam-108	52	20	x	x	NOUN
ejpam-108	52	21	)	)	PUNCT
ejpam-108	52	22	)	)	PUNCT
ejpam-108	52	23	:	:	PUNCT
ejpam-108	53	1	x	x	X
ejpam-108	53	2	∈	∈	NOUN
ejpam-108	53	3	x	x	X
ejpam-108	53	4	}	}	PUNCT
ejpam-108	53	5	⊆	⊆	NUM
ejpam-108	53	6	x	x	SYM
ejpam-108	53	7	×	×	PROPN
ejpam-108	53	8	y	y	PROPN
ejpam-108	53	9	is	be	AUX
ejpam-108	53	10	called	call	VERB
ejpam-108	53	11	the	the	DET
ejpam-108	53	12	graph	graph	NOUN
ejpam-108	53	13	of	of	ADP
ejpam-108	53	14	f	f	PROPN
ejpam-108	53	15	and	and	CCONJ
ejpam-108	53	16	is	be	AUX
ejpam-108	53	17	denoted	denote	VERB
ejpam-108	53	18	by	by	ADP
ejpam-108	53	19	g	g	PROPN
ejpam-108	53	20	(	(	PUNCT
ejpam-108	53	21	f	f	PROPN
ejpam-108	53	22	)	)	PUNCT
ejpam-108	53	23	.	.	PUNCT
ejpam-108	54	1	definition	definition	NOUN
ejpam-108	54	2	2.2	2.2	NUM
ejpam-108	54	3	.	.	PUNCT
ejpam-108	55	1	[	[	X
ejpam-108	55	2	13	13	NUM
ejpam-108	55	3	]	]	PUNCT
ejpam-108	55	4	the	the	DET
ejpam-108	55	5	graph	graph	NOUN
ejpam-108	55	6	g	g	PROPN
ejpam-108	55	7	(	(	PUNCT
ejpam-108	55	8	f	f	PROPN
ejpam-108	55	9	)	)	PUNCT
ejpam-108	55	10	of	of	ADP
ejpam-108	55	11	a	a	DET
ejpam-108	55	12	function	function	NOUN
ejpam-108	55	13	f	f	NOUN
ejpam-108	55	14	:	:	PUNCT
ejpam-108	55	15	x	x	X
ejpam-108	55	16	→	→	SYM
ejpam-108	55	17	y	y	PROPN
ejpam-108	55	18	is	be	AUX
ejpam-108	55	19	said	say	VERB
ejpam-108	55	20	to	to	PART
ejpam-108	55	21	be	be	AUX
ejpam-108	55	22	contra	contra	ADJ
ejpam-108	55	23	-	-	ADJ
ejpam-108	55	24	bclosed	bclosed	ADJ
ejpam-108	55	25	graph	graph	NOUN
ejpam-108	55	26	if	if	SCONJ
ejpam-108	55	27	for	for	ADP
ejpam-108	55	28	each	each	DET
ejpam-108	55	29	(	(	PUNCT
ejpam-108	55	30	x	x	PROPN
ejpam-108	55	31	,	,	PUNCT
ejpam-108	55	32	y	y	PROPN
ejpam-108	55	33	)	)	PUNCT
ejpam-108	55	34	∈	∈	PROPN
ejpam-108	55	35	(	(	PUNCT
ejpam-108	55	36	x	x	NOUN
ejpam-108	55	37	,	,	PUNCT
ejpam-108	55	38	y	y	PROPN
ejpam-108	55	39	)	)	PUNCT
ejpam-108	55	40	−	−	PROPN
ejpam-108	56	1	g	g	PROPN
ejpam-108	56	2	(	(	PUNCT
ejpam-108	56	3	f	f	PROPN
ejpam-108	56	4	)	)	PUNCT
ejpam-108	56	5	,	,	PUNCT
ejpam-108	56	6	there	there	PRON
ejpam-108	56	7	exist	exist	VERB
ejpam-108	56	8	u	u	NOUN
ejpam-108	56	9	∈bo(x	∈bo(x	NOUN
ejpam-108	56	10	,	,	PUNCT
ejpam-108	56	11	x	x	X
ejpam-108	56	12	)	)	PUNCT
ejpam-108	56	13	and	and	CCONJ
ejpam-108	56	14	a	a	DET
ejpam-108	56	15	closed	closed	ADJ
ejpam-108	56	16	set	set	VERB
ejpam-108	56	17	v	v	NOUN
ejpam-108	56	18	of	of	ADP
ejpam-108	56	19	y	y	PROPN
ejpam-108	56	20	containing	contain	VERB
ejpam-108	56	21	y	y	PRON
ejpam-108	56	22	such	such	ADJ
ejpam-108	56	23	that	that	PRON
ejpam-108	56	24	(	(	PUNCT
ejpam-108	56	25	u	u	NOUN
ejpam-108	56	26	×	×	PROPN
ejpam-108	56	27	v	v	NOUN
ejpam-108	56	28	)	)	PUNCT
ejpam-108	56	29	∩	∩	ADJ
ejpam-108	56	30	g	g	PROPN
ejpam-108	56	31	(	(	PUNCT
ejpam-108	56	32	f	f	PROPN
ejpam-108	56	33	)	)	PUNCT
ejpam-108	57	1	=	=	SYM
ejpam-108	57	2	φ	φ	PROPN
ejpam-108	57	3	.	.	PUNCT
ejpam-108	57	4	a.	a.	PROPN
ejpam-108	57	5	al	al	PROPN
ejpam-108	57	6	-	-	PUNCT
ejpam-108	57	7	omari	omari	PROPN
ejpam-108	57	8	and	and	CCONJ
ejpam-108	57	9	s.	s.	PROPN
ejpam-108	57	10	noorani	noorani	PROPN
ejpam-108	57	11	/	/	SYM
ejpam-108	57	12	eur	eur	PROPN
ejpam-108	57	13	.	.	PUNCT
ejpam-108	58	1	j.	j.	PROPN
ejpam-108	58	2	pure	pure	PROPN
ejpam-108	58	3	appl	appl	PROPN
ejpam-108	58	4	.	.	PROPN
ejpam-108	58	5	math	math	PROPN
ejpam-108	58	6	,	,	PUNCT
ejpam-108	58	7	2	2	NUM
ejpam-108	58	8	(	(	PUNCT
ejpam-108	58	9	2009	2009	NUM
ejpam-108	58	10	)	)	PUNCT
ejpam-108	58	11	,	,	PUNCT
ejpam-108	58	12	(	(	PUNCT
ejpam-108	58	13	213	213	NUM
ejpam-108	58	14	-	-	SYM
ejpam-108	58	15	230	230	NUM
ejpam-108	58	16	)	)	PUNCT
ejpam-108	58	17	216	216	NUM
ejpam-108	58	18	definition	definition	NOUN
ejpam-108	58	19	2.3	2.3	NUM
ejpam-108	58	20	.	.	PUNCT
ejpam-108	59	1	[	[	X
ejpam-108	59	2	5	5	NUM
ejpam-108	59	3	]	]	PUNCT
ejpam-108	59	4	a	a	DET
ejpam-108	59	5	space	space	NOUN
ejpam-108	59	6	x	x	PUNCT
ejpam-108	59	7	is	be	AUX
ejpam-108	59	8	said	say	VERB
ejpam-108	59	9	to	to	PART
ejpam-108	59	10	be	be	AUX
ejpam-108	59	11	strongly	strongly	ADV
ejpam-108	59	12	s	s	NOUN
ejpam-108	59	13	-	-	PUNCT
ejpam-108	59	14	closed	closed	ADJ
ejpam-108	59	15	if	if	SCONJ
ejpam-108	59	16	every	every	DET
ejpam-108	59	17	closed	closed	ADJ
ejpam-108	59	18	cover	cover	NOUN
ejpam-108	59	19	of	of	ADP
ejpam-108	59	20	x	x	PUNCT
ejpam-108	59	21	has	have	VERB
ejpam-108	59	22	a	a	DET
ejpam-108	59	23	finite	finite	ADJ
ejpam-108	59	24	subcover	subcover	NOUN
ejpam-108	59	25	theorem	theorem	VERB
ejpam-108	59	26	2.4	2.4	NUM
ejpam-108	59	27	.	.	PUNCT
ejpam-108	60	1	if	if	SCONJ
ejpam-108	60	2	(	(	PUNCT
ejpam-108	60	3	x	x	INTJ
ejpam-108	60	4	,	,	PUNCT
ejpam-108	60	5	τb	τb	VERB
ejpam-108	60	6	)	)	PUNCT
ejpam-108	60	7	is	be	AUX
ejpam-108	60	8	a	a	DET
ejpam-108	60	9	topological	topological	ADJ
ejpam-108	60	10	space	space	NOUN
ejpam-108	60	11	and	and	CCONJ
ejpam-108	60	12	f	f	NOUN
ejpam-108	60	13	:	:	PUNCT
ejpam-108	60	14	x	x	X
ejpam-108	60	15	→	→	SYM
ejpam-108	60	16	y	y	PROPN
ejpam-108	60	17	has	have	VERB
ejpam-108	60	18	a	a	DET
ejpam-108	60	19	contra	contra	PROPN
ejpam-108	60	20	b	b	PROPN
ejpam-108	60	21	-	-	PUNCT
ejpam-108	60	22	closed	closed	ADJ
ejpam-108	60	23	graph	graph	NOUN
ejpam-108	60	24	,	,	PUNCT
ejpam-108	60	25	then	then	ADV
ejpam-108	60	26	the	the	DET
ejpam-108	60	27	inverse	inverse	ADJ
ejpam-108	60	28	image	image	NOUN
ejpam-108	60	29	of	of	ADP
ejpam-108	60	30	a	a	DET
ejpam-108	60	31	strongly	strongly	ADV
ejpam-108	60	32	s	s	NOUN
ejpam-108	60	33	-	-	PUNCT
ejpam-108	60	34	closed	closed	ADJ
ejpam-108	60	35	set	set	NOUN
ejpam-108	60	36	a	a	PRON
ejpam-108	60	37	of	of	ADP
ejpam-108	60	38	y	y	PROPN
ejpam-108	60	39	is	be	AUX
ejpam-108	60	40	b	b	NOUN
ejpam-108	60	41	-	-	PUNCT
ejpam-108	60	42	closed	closed	ADJ
ejpam-108	60	43	in	in	ADP
ejpam-108	60	44	x	x	X
ejpam-108	60	45	.	.	PUNCT
ejpam-108	61	1	proof	proof	NOUN
ejpam-108	61	2	.	.	PUNCT
ejpam-108	62	1	assume	assume	VERB
ejpam-108	62	2	that	that	SCONJ
ejpam-108	62	3	a	a	PRON
ejpam-108	62	4	is	be	AUX
ejpam-108	62	5	a	a	DET
ejpam-108	62	6	strongly	strongly	ADV
ejpam-108	62	7	s	s	NOUN
ejpam-108	62	8	-	-	PUNCT
ejpam-108	62	9	closed	closed	ADJ
ejpam-108	62	10	set	set	NOUN
ejpam-108	62	11	of	of	ADP
ejpam-108	62	12	y	y	PROPN
ejpam-108	62	13	and	and	CCONJ
ejpam-108	62	14	x	x	PROPN
ejpam-108	62	15	/∈	/∈	PROPN
ejpam-108	62	16	f	f	PROPN
ejpam-108	62	17	−1(a	−1(a	ADP
ejpam-108	62	18	)	)	PUNCT
ejpam-108	62	19	.	.	PUNCT
ejpam-108	63	1	for	for	ADP
ejpam-108	63	2	each	each	DET
ejpam-108	63	3	a	a	DET
ejpam-108	63	4	∈	∈	PROPN
ejpam-108	63	5	a	a	PRON
ejpam-108	63	6	,	,	PUNCT
ejpam-108	63	7	(	(	PUNCT
ejpam-108	63	8	x	x	X
ejpam-108	63	9	,	,	PUNCT
ejpam-108	63	10	a	a	PROPN
ejpam-108	63	11	)	)	PUNCT
ejpam-108	63	12	/∈	/∈	PUNCT
ejpam-108	64	1	g	g	NOUN
ejpam-108	64	2	(	(	PUNCT
ejpam-108	64	3	f	f	PROPN
ejpam-108	64	4	)	)	PUNCT
ejpam-108	64	5	.	.	PUNCT
ejpam-108	65	1	by	by	ADP
ejpam-108	65	2	lemma	lemma	PROPN
ejpam-108	65	3	3.3	3.3	NUM
ejpam-108	65	4	in	in	ADP
ejpam-108	65	5	[	[	PUNCT
ejpam-108	65	6	13	13	NUM
ejpam-108	65	7	]	]	PUNCT
ejpam-108	65	8	there	there	PRON
ejpam-108	65	9	exist	exist	VERB
ejpam-108	65	10	ua	ua	PROPN
ejpam-108	65	11	∈	∈	PROPN
ejpam-108	65	12	bo(x	bo(x	NUM
ejpam-108	65	13	,	,	PUNCT
ejpam-108	65	14	x	x	X
ejpam-108	65	15	)	)	PUNCT
ejpam-108	65	16	and	and	CCONJ
ejpam-108	65	17	va	va	PROPN
ejpam-108	65	18	∈	∈	PROPN
ejpam-108	65	19	c(y	c(y	PROPN
ejpam-108	65	20	,	,	PUNCT
ejpam-108	65	21	a	a	PRON
ejpam-108	65	22	)	)	PUNCT
ejpam-108	66	1	such	such	ADJ
ejpam-108	66	2	that	that	SCONJ
ejpam-108	66	3	f	f	PROPN
ejpam-108	66	4	(	(	PUNCT
ejpam-108	66	5	ua)∩	ua)∩	PROPN
ejpam-108	66	6	va	va	PROPN
ejpam-108	66	7	=	=	PROPN
ejpam-108	66	8	φ	φ	PROPN
ejpam-108	66	9	.	.	PUNCT
ejpam-108	67	1	since	since	SCONJ
ejpam-108	67	2	{	{	PUNCT
ejpam-108	67	3	a∩	a∩	PROPN
ejpam-108	67	4	va	va	PROPN
ejpam-108	67	5	:	:	PUNCT
ejpam-108	67	6	a	a	DET
ejpam-108	67	7	∈	∈	PROPN
ejpam-108	67	8	a	a	PRON
ejpam-108	67	9	}	}	PUNCT
ejpam-108	67	10	is	be	AUX
ejpam-108	67	11	a	a	DET
ejpam-108	67	12	closed	closed	ADJ
ejpam-108	67	13	cover	cover	NOUN
ejpam-108	67	14	of	of	ADP
ejpam-108	67	15	the	the	DET
ejpam-108	67	16	subspace	subspace	NOUN
ejpam-108	67	17	a	a	PRON
ejpam-108	67	18	,	,	PUNCT
ejpam-108	67	19	since	since	SCONJ
ejpam-108	67	20	a	a	DET
ejpam-108	67	21	is	be	AUX
ejpam-108	67	22	s	s	NOUN
ejpam-108	67	23	-	-	PUNCT
ejpam-108	67	24	closed	closed	ADJ
ejpam-108	67	25	,	,	PUNCT
ejpam-108	67	26	then	then	ADV
ejpam-108	67	27	there	there	PRON
ejpam-108	67	28	exists	exist	VERB
ejpam-108	67	29	a	a	DET
ejpam-108	67	30	finite	finite	NOUN
ejpam-108	67	31	subset	subset	NOUN
ejpam-108	67	32	a0	a0	NOUN
ejpam-108	67	33	⊆	⊆	NUM
ejpam-108	67	34	a	a	DET
ejpam-108	67	35	such	such	ADJ
ejpam-108	67	36	that	that	SCONJ
ejpam-108	67	37	a	a	DET
ejpam-108	67	38	⊆	⊆	NUM
ejpam-108	67	39	∪{va	∪{va	NOUN
ejpam-108	67	40	:	:	PUNCT
ejpam-108	67	41	a	a	DET
ejpam-108	67	42	∈	∈	PROPN
ejpam-108	67	43	a0	a0	NOUN
ejpam-108	67	44	}	}	PUNCT
ejpam-108	67	45	.	.	PUNCT
ejpam-108	68	1	set	set	VERB
ejpam-108	68	2	u	u	NOUN
ejpam-108	68	3	=	=	NOUN
ejpam-108	68	4	∩{ua	∩{ua	NUM
ejpam-108	68	5	:	:	PUNCT
ejpam-108	68	6	a	a	DET
ejpam-108	68	7	∈	∈	PROPN
ejpam-108	68	8	a0	a0	NOUN
ejpam-108	68	9	}	}	PUNCT
ejpam-108	68	10	,	,	PUNCT
ejpam-108	68	11	but	but	CCONJ
ejpam-108	68	12	(	(	PUNCT
ejpam-108	68	13	x	x	X
ejpam-108	68	14	,	,	PUNCT
ejpam-108	68	15	τb	τb	VERB
ejpam-108	68	16	)	)	PUNCT
ejpam-108	68	17	is	be	AUX
ejpam-108	68	18	a	a	DET
ejpam-108	68	19	topological	topological	ADJ
ejpam-108	68	20	space	space	NOUN
ejpam-108	68	21	,	,	PUNCT
ejpam-108	68	22	then	then	ADV
ejpam-108	68	23	u	u	PROPN
ejpam-108	68	24	∈	∈	PROPN
ejpam-108	68	25	bo(x	bo(x	NUM
ejpam-108	68	26	,	,	PUNCT
ejpam-108	68	27	x	x	X
ejpam-108	68	28	)	)	PUNCT
ejpam-108	68	29	and	and	CCONJ
ejpam-108	68	30	f	f	PROPN
ejpam-108	68	31	(	(	PUNCT
ejpam-108	68	32	u	u	NOUN
ejpam-108	68	33	)	)	PUNCT
ejpam-108	68	34	∩	∩	NOUN
ejpam-108	68	35	a⊆	a⊆	PROPN
ejpam-108	68	36	f	f	X
ejpam-108	68	37	(	(	PUNCT
ejpam-108	68	38	ua)∩	ua)∩	X
ejpam-108	69	1	[	[	X
ejpam-108	69	2	∪(va	∪(va	NOUN
ejpam-108	69	3	:	:	PUNCT
ejpam-108	69	4	a	a	DET
ejpam-108	69	5	∈	∈	PROPN
ejpam-108	69	6	a0	a0	NOUN
ejpam-108	69	7	)	)	PUNCT
ejpam-108	69	8	]	]	PUNCT
ejpam-108	69	9	=	=	SYM
ejpam-108	69	10	φ	φ	PROPN
ejpam-108	69	11	.	.	PUNCT
ejpam-108	69	12	therefore	therefore	ADV
ejpam-108	69	13	u	u	PROPN
ejpam-108	69	14	∩	∩	NOUN
ejpam-108	69	15	f	f	PROPN
ejpam-108	69	16	−1(a	−1(a	ADP
ejpam-108	69	17	)	)	PUNCT
ejpam-108	70	1	=	=	PUNCT
ejpam-108	70	2	φ	φ	PROPN
ejpam-108	70	3	and	and	CCONJ
ejpam-108	70	4	hence	hence	ADV
ejpam-108	70	5	and	and	CCONJ
ejpam-108	70	6	hence	hence	ADV
ejpam-108	70	7	x	x	NOUN
ejpam-108	70	8	/∈	/∈	PUNCT
ejpam-108	71	1	bcl	bcl	NOUN
ejpam-108	71	2	(	(	PUNCT
ejpam-108	71	3	f	f	NOUN
ejpam-108	71	4	−1(a	−1(a	ADP
ejpam-108	71	5	)	)	PUNCT
ejpam-108	71	6	)	)	PUNCT
ejpam-108	71	7	.	.	PUNCT
ejpam-108	72	1	this	this	PRON
ejpam-108	72	2	show	show	VERB
ejpam-108	72	3	that	that	SCONJ
ejpam-108	72	4	f	f	PROPN
ejpam-108	72	5	−1(a	−1(a	VERB
ejpam-108	72	6	)	)	PUNCT
ejpam-108	72	7	is	be	AUX
ejpam-108	72	8	b	b	NOUN
ejpam-108	72	9	-	-	PUNCT
ejpam-108	72	10	closed	closed	ADJ
ejpam-108	72	11	.	.	PUNCT
ejpam-108	73	1	theorem	theorem	VERB
ejpam-108	73	2	2.5	2.5	NUM
ejpam-108	73	3	.	.	PUNCT
ejpam-108	74	1	let	let	VERB
ejpam-108	74	2	y	y	PRON
ejpam-108	74	3	be	be	AUX
ejpam-108	74	4	a	a	DET
ejpam-108	74	5	strongly	strongly	ADV
ejpam-108	74	6	s	s	NOUN
ejpam-108	74	7	-	-	PUNCT
ejpam-108	74	8	closed	closed	ADJ
ejpam-108	74	9	space	space	NOUN
ejpam-108	74	10	.	.	PUNCT
ejpam-108	75	1	if	if	SCONJ
ejpam-108	75	2	(	(	PUNCT
ejpam-108	75	3	x	x	INTJ
ejpam-108	75	4	,	,	PUNCT
ejpam-108	75	5	τb	τb	VERB
ejpam-108	75	6	)	)	PUNCT
ejpam-108	75	7	is	be	AUX
ejpam-108	75	8	a	a	DET
ejpam-108	75	9	topological	topological	ADJ
ejpam-108	75	10	space	space	NOUN
ejpam-108	75	11	and	and	CCONJ
ejpam-108	75	12	a	a	DET
ejpam-108	75	13	function	function	NOUN
ejpam-108	75	14	f	f	NOUN
ejpam-108	75	15	:	:	PUNCT
ejpam-108	75	16	x	x	X
ejpam-108	75	17	→	→	SYM
ejpam-108	75	18	y	y	PROPN
ejpam-108	75	19	has	have	VERB
ejpam-108	75	20	a	a	DET
ejpam-108	75	21	contra	contra	PROPN
ejpam-108	75	22	b	b	PROPN
ejpam-108	75	23	-	-	PUNCT
ejpam-108	75	24	closed	closed	ADJ
ejpam-108	75	25	graph	graph	NOUN
ejpam-108	75	26	,	,	PUNCT
ejpam-108	75	27	then	then	ADV
ejpam-108	75	28	f	f	PROPN
ejpam-108	75	29	is	be	AUX
ejpam-108	75	30	contra	contra	PROPN
ejpam-108	75	31	b	b	PROPN
ejpam-108	75	32	-	-	PUNCT
ejpam-108	75	33	continuous	continuous	ADJ
ejpam-108	75	34	.	.	PUNCT
ejpam-108	76	1	proof	proof	NOUN
ejpam-108	76	2	.	.	PUNCT
ejpam-108	77	1	suppose	suppose	VERB
ejpam-108	77	2	that	that	SCONJ
ejpam-108	77	3	y	y	PROPN
ejpam-108	77	4	is	be	AUX
ejpam-108	77	5	strongly	strongly	ADV
ejpam-108	77	6	s	s	NOUN
ejpam-108	77	7	-	-	PUNCT
ejpam-108	77	8	closed	closed	ADJ
ejpam-108	77	9	and	and	CCONJ
ejpam-108	77	10	g	g	PROPN
ejpam-108	77	11	(	(	PUNCT
ejpam-108	77	12	f	f	PROPN
ejpam-108	77	13	)	)	PUNCT
ejpam-108	77	14	is	be	AUX
ejpam-108	77	15	contra	contra	PROPN
ejpam-108	77	16	b	b	PROPN
ejpam-108	77	17	-	-	PUNCT
ejpam-108	77	18	closed	closed	ADJ
ejpam-108	77	19	.	.	PUNCT
ejpam-108	78	1	first	first	ADV
ejpam-108	78	2	we	we	PRON
ejpam-108	78	3	show	show	VERB
ejpam-108	78	4	that	that	SCONJ
ejpam-108	78	5	an	an	DET
ejpam-108	78	6	open	open	ADJ
ejpam-108	78	7	set	set	NOUN
ejpam-108	78	8	of	of	ADP
ejpam-108	78	9	y	y	PROPN
ejpam-108	78	10	is	be	AUX
ejpam-108	78	11	strongly	strongly	ADV
ejpam-108	78	12	s	s	NOUN
ejpam-108	78	13	-	-	PUNCT
ejpam-108	78	14	closed	closed	ADJ
ejpam-108	78	15	.	.	PUNCT
ejpam-108	79	1	let	let	VERB
ejpam-108	79	2	u	u	PRON
ejpam-108	79	3	be	be	AUX
ejpam-108	79	4	an	an	DET
ejpam-108	79	5	open	open	ADJ
ejpam-108	79	6	set	set	NOUN
ejpam-108	79	7	of	of	ADP
ejpam-108	79	8	y	y	PROPN
ejpam-108	79	9	and	and	CCONJ
ejpam-108	79	10	{	{	PUNCT
ejpam-108	79	11	vi	vi	NOUN
ejpam-108	79	12	:	:	PUNCT
ejpam-108	80	1	i	i	PRON
ejpam-108	80	2	∈	∈	PROPN
ejpam-108	80	3	i	i	PRON
ejpam-108	80	4	}	}	PUNCT
ejpam-108	80	5	be	be	VERB
ejpam-108	80	6	a	a	DET
ejpam-108	80	7	cover	cover	NOUN
ejpam-108	80	8	of	of	ADP
ejpam-108	80	9	u	u	NOUN
ejpam-108	80	10	by	by	ADP
ejpam-108	80	11	closed	closed	ADJ
ejpam-108	80	12	sets	set	NOUN
ejpam-108	80	13	vi	vi	VERB
ejpam-108	80	14	of	of	ADP
ejpam-108	80	15	u	u	PROPN
ejpam-108	80	16	.	.	PUNCT
ejpam-108	81	1	for	for	ADP
ejpam-108	81	2	each	each	DET
ejpam-108	81	3	i	i	PRON
ejpam-108	81	4	∈	∈	PROPN
ejpam-108	81	5	i	i	PRON
ejpam-108	81	6	,	,	PUNCT
ejpam-108	81	7	there	there	PRON
ejpam-108	81	8	exists	exist	VERB
ejpam-108	81	9	a	a	DET
ejpam-108	81	10	closed	closed	ADJ
ejpam-108	81	11	set	set	NOUN
ejpam-108	81	12	ki	ki	PROPN
ejpam-108	81	13	of	of	ADP
ejpam-108	81	14	x	x	INTJ
ejpam-108	81	15	such	such	ADJ
ejpam-108	81	16	that	that	DET
ejpam-108	81	17	vi	vi	PROPN
ejpam-108	81	18	=	=	SYM
ejpam-108	81	19	ki	ki	PROPN
ejpam-108	81	20	∩	∩	PROPN
ejpam-108	81	21	u	u	PROPN
ejpam-108	81	22	.	.	PUNCT
ejpam-108	82	1	then	then	ADV
ejpam-108	82	2	the	the	DET
ejpam-108	82	3	family	family	NOUN
ejpam-108	82	4	{	{	PUNCT
ejpam-108	82	5	ki	ki	PROPN
ejpam-108	82	6	:	:	PUNCT
ejpam-108	82	7	i	i	PRON
ejpam-108	82	8	∈	∈	VERB
ejpam-108	82	9	i	i	PRON
ejpam-108	82	10	}	}	PUNCT
ejpam-108	82	11	∪	∪	VERB
ejpam-108	82	12	(	(	PUNCT
ejpam-108	82	13	y	y	PROPN
ejpam-108	82	14	−	−	PROPN
ejpam-108	82	15	u	u	NOUN
ejpam-108	82	16	)	)	PUNCT
ejpam-108	82	17	is	be	AUX
ejpam-108	82	18	a	a	DET
ejpam-108	82	19	closed	closed	ADJ
ejpam-108	82	20	cover	cover	NOUN
ejpam-108	82	21	of	of	ADP
ejpam-108	82	22	y	y	PROPN
ejpam-108	82	23	.	.	PUNCT
ejpam-108	83	1	since	since	SCONJ
ejpam-108	83	2	y	y	PROPN
ejpam-108	83	3	is	be	AUX
ejpam-108	83	4	strongly	strongly	ADV
ejpam-108	83	5	s	s	NOUN
ejpam-108	83	6	-	-	PUNCT
ejpam-108	83	7	closed	closed	ADJ
ejpam-108	83	8	,	,	PUNCT
ejpam-108	83	9	there	there	PRON
ejpam-108	83	10	exists	exist	VERB
ejpam-108	83	11	a	a	DET
ejpam-108	83	12	finite	finite	NOUN
ejpam-108	83	13	subset	subset	VERB
ejpam-108	83	14	i0	i0	PROPN
ejpam-108	83	15	⊆	⊆	NUM
ejpam-108	83	16	i	i	PRON
ejpam-108	83	17	such	such	ADJ
ejpam-108	83	18	that	that	SCONJ
ejpam-108	83	19	y	y	NOUN
ejpam-108	83	20	=	=	PUNCT
ejpam-108	83	21	∪{ki	∪{ki	X
ejpam-108	83	22	:	:	PUNCT
ejpam-108	83	23	i	i	PRON
ejpam-108	83	24	∈	∈	PROPN
ejpam-108	83	25	i0	i0	PROPN
ejpam-108	83	26	}	}	PUNCT
ejpam-108	83	27	∪	∪	NOUN
ejpam-108	83	28	(	(	PUNCT
ejpam-108	83	29	y	y	PROPN
ejpam-108	83	30	−	−	PROPN
ejpam-108	83	31	u	u	PROPN
ejpam-108	83	32	)	)	PUNCT
ejpam-108	83	33	.	.	PUNCT
ejpam-108	84	1	therefore	therefore	ADV
ejpam-108	84	2	we	we	PRON
ejpam-108	84	3	obtain	obtain	VERB
ejpam-108	84	4	u	u	NOUN
ejpam-108	84	5	=	=	X
ejpam-108	84	6	∪{vi	∪{vi	NUM
ejpam-108	84	7	:	:	PUNCT
ejpam-108	84	8	i	i	PROPN
ejpam-108	84	9	∈	∈	PROPN
ejpam-108	84	10	i0	i0	PROPN
ejpam-108	84	11	}	}	PUNCT
ejpam-108	84	12	.	.	PUNCT
ejpam-108	85	1	this	this	PRON
ejpam-108	85	2	shows	show	VERB
ejpam-108	85	3	that	that	SCONJ
ejpam-108	85	4	u	u	NOUN
ejpam-108	85	5	is	be	AUX
ejpam-108	85	6	strongly	strongly	ADV
ejpam-108	85	7	s	s	NOUN
ejpam-108	85	8	-	-	PUNCT
ejpam-108	85	9	closed	closed	ADJ
ejpam-108	85	10	.	.	PUNCT
ejpam-108	86	1	by	by	ADP
ejpam-108	86	2	theorem	theorem	VERB
ejpam-108	86	3	2.4	2.4	NUM
ejpam-108	86	4	f	f	NOUN
ejpam-108	86	5	−1(u	−1(u	NOUN
ejpam-108	86	6	)	)	PUNCT
ejpam-108	86	7	is	be	AUX
ejpam-108	86	8	b	b	NOUN
ejpam-108	86	9	-	-	PUNCT
ejpam-108	86	10	closed	closed	ADJ
ejpam-108	86	11	in	in	ADP
ejpam-108	86	12	x	x	PUNCT
ejpam-108	86	13	for	for	ADP
ejpam-108	86	14	every	every	DET
ejpam-108	86	15	open	open	ADJ
ejpam-108	86	16	u	u	NOUN
ejpam-108	86	17	in	in	ADP
ejpam-108	86	18	y	y	PROPN
ejpam-108	86	19	.	.	PUNCT
ejpam-108	87	1	therefore	therefore	ADV
ejpam-108	87	2	,	,	PUNCT
ejpam-108	87	3	f	f	PROPN
ejpam-108	87	4	is	be	AUX
ejpam-108	87	5	contra	contra	PROPN
ejpam-108	87	6	b	b	PROPN
ejpam-108	87	7	-	-	PUNCT
ejpam-108	87	8	continuous	continuous	ADJ
ejpam-108	87	9	.	.	PUNCT
ejpam-108	88	1	theorem	theorem	VERB
ejpam-108	88	2	2.6	2.6	NUM
ejpam-108	88	3	.	.	PUNCT
ejpam-108	89	1	let	let	VERB
ejpam-108	89	2	f	f	NOUN
ejpam-108	89	3	:	:	PUNCT
ejpam-108	89	4	x	x	X
ejpam-108	89	5	→	→	SYM
ejpam-108	89	6	y	y	X
ejpam-108	89	7	be	be	AUX
ejpam-108	89	8	a	a	DET
ejpam-108	89	9	function	function	NOUN
ejpam-108	89	10	and	and	CCONJ
ejpam-108	89	11	g	g	NOUN
ejpam-108	89	12	:	:	PUNCT
ejpam-108	89	13	x	x	SYM
ejpam-108	89	14	→	→	SYM
ejpam-108	89	15	x	x	SYM
ejpam-108	89	16	×	×	NOUN
ejpam-108	89	17	y	y	PROPN
ejpam-108	89	18	the	the	DET
ejpam-108	89	19	graph	graph	NOUN
ejpam-108	89	20	function	function	NOUN
ejpam-108	89	21	of	of	ADP
ejpam-108	89	22	f	f	PROPN
ejpam-108	89	23	,	,	PUNCT
ejpam-108	89	24	defined	define	VERB
ejpam-108	89	25	by	by	ADP
ejpam-108	89	26	g(x	g(x	NOUN
ejpam-108	89	27	)	)	PUNCT
ejpam-108	90	1	=	=	SYM
ejpam-108	90	2	(	(	PUNCT
ejpam-108	90	3	x	x	INTJ
ejpam-108	90	4	,	,	PUNCT
ejpam-108	90	5	f	f	PROPN
ejpam-108	90	6	(	(	PUNCT
ejpam-108	90	7	x	x	NOUN
ejpam-108	90	8	)	)	PUNCT
ejpam-108	90	9	)	)	PUNCT
ejpam-108	90	10	for	for	ADP
ejpam-108	90	11	every	every	DET
ejpam-108	90	12	x	x	SYM
ejpam-108	90	13	∈	∈	PROPN
ejpam-108	90	14	x	x	X
ejpam-108	90	15	.	.	PUNCT
ejpam-108	91	1	if	if	SCONJ
ejpam-108	91	2	g	g	PROPN
ejpam-108	91	3	is	be	AUX
ejpam-108	91	4	contra	contra	PROPN
ejpam-108	91	5	b	b	PROPN
ejpam-108	91	6	-	-	PUNCT
ejpam-108	91	7	continuous	continuous	ADJ
ejpam-108	91	8	,	,	PUNCT
ejpam-108	91	9	then	then	ADV
ejpam-108	91	10	f	f	PROPN
ejpam-108	91	11	is	be	AUX
ejpam-108	91	12	contra	contra	PROPN
ejpam-108	91	13	b	b	PROPN
ejpam-108	91	14	-	-	PUNCT
ejpam-108	91	15	continuous	continuous	ADJ
ejpam-108	91	16	.	.	PUNCT
ejpam-108	92	1	a.	a.	PROPN
ejpam-108	92	2	al	al	PROPN
ejpam-108	92	3	-	-	PUNCT
ejpam-108	92	4	omari	omari	PROPN
ejpam-108	92	5	and	and	CCONJ
ejpam-108	92	6	s.	s.	PROPN
ejpam-108	92	7	noorani	noorani	PROPN
ejpam-108	92	8	/	/	SYM
ejpam-108	92	9	eur	eur	PROPN
ejpam-108	92	10	.	.	PUNCT
ejpam-108	93	1	j.	j.	PROPN
ejpam-108	93	2	pure	pure	PROPN
ejpam-108	93	3	appl	appl	PROPN
ejpam-108	93	4	.	.	PROPN
ejpam-108	93	5	math	math	PROPN
ejpam-108	93	6	,	,	PUNCT
ejpam-108	93	7	2	2	NUM
ejpam-108	93	8	(	(	PUNCT
ejpam-108	93	9	2009	2009	NUM
ejpam-108	93	10	)	)	PUNCT
ejpam-108	93	11	,	,	PUNCT
ejpam-108	93	12	(	(	PUNCT
ejpam-108	93	13	213	213	NUM
ejpam-108	93	14	-	-	SYM
ejpam-108	93	15	230	230	NUM
ejpam-108	93	16	)	)	PUNCT
ejpam-108	93	17	217	217	NUM
ejpam-108	93	18	proof	proof	NOUN
ejpam-108	93	19	.	.	PUNCT
ejpam-108	94	1	let	let	VERB
ejpam-108	94	2	u	u	PRON
ejpam-108	94	3	be	be	AUX
ejpam-108	94	4	an	an	DET
ejpam-108	94	5	open	open	ADJ
ejpam-108	94	6	set	set	NOUN
ejpam-108	94	7	in	in	ADP
ejpam-108	94	8	y	y	PROPN
ejpam-108	94	9	,	,	PUNCT
ejpam-108	94	10	then	then	ADV
ejpam-108	94	11	x	x	SYM
ejpam-108	94	12	×	×	NOUN
ejpam-108	94	13	u	u	NOUN
ejpam-108	94	14	is	be	AUX
ejpam-108	94	15	an	an	DET
ejpam-108	94	16	open	open	ADJ
ejpam-108	94	17	set	set	NOUN
ejpam-108	94	18	in	in	ADP
ejpam-108	94	19	x	x	PUNCT
ejpam-108	94	20	×	×	PROPN
ejpam-108	94	21	y	y	PROPN
ejpam-108	94	22	.	.	PUNCT
ejpam-108	95	1	since	since	SCONJ
ejpam-108	95	2	g	g	PROPN
ejpam-108	95	3	is	be	AUX
ejpam-108	95	4	contra	contra	PROPN
ejpam-108	95	5	b	b	PROPN
ejpam-108	95	6	-	-	PUNCT
ejpam-108	95	7	continuous	continuous	ADJ
ejpam-108	95	8	.	.	PUNCT
ejpam-108	96	1	it	it	PRON
ejpam-108	96	2	follows	follow	VERB
ejpam-108	96	3	that	that	SCONJ
ejpam-108	96	4	f	f	PROPN
ejpam-108	96	5	−1(u	−1(u	X
ejpam-108	96	6	)	)	PUNCT
ejpam-108	96	7	=	=	SYM
ejpam-108	96	8	g−1(x	g−1(x	NOUN
ejpam-108	96	9	×	×	PROPN
ejpam-108	96	10	u	u	NOUN
ejpam-108	96	11	)	)	PUNCT
ejpam-108	96	12	is	be	AUX
ejpam-108	96	13	an	an	DET
ejpam-108	96	14	b	b	NOUN
ejpam-108	96	15	-	-	PUNCT
ejpam-108	96	16	closed	closed	ADJ
ejpam-108	96	17	in	in	ADP
ejpam-108	96	18	x	x	X
ejpam-108	96	19	.	.	PUNCT
ejpam-108	97	1	thus	thus	ADV
ejpam-108	97	2	,	,	PUNCT
ejpam-108	97	3	f	f	PROPN
ejpam-108	97	4	is	be	AUX
ejpam-108	97	5	contra	contra	PROPN
ejpam-108	97	6	b	b	PROPN
ejpam-108	97	7	-	-	PUNCT
ejpam-108	97	8	continuous	continuous	ADJ
ejpam-108	97	9	.	.	PUNCT
ejpam-108	98	1	theorem	theorem	ADJ
ejpam-108	98	2	2.7	2.7	NUM
ejpam-108	98	3	.	.	PUNCT
ejpam-108	99	1	if	if	SCONJ
ejpam-108	99	2	f	f	PROPN
ejpam-108	99	3	:	:	PUNCT
ejpam-108	99	4	x	x	X
ejpam-108	99	5	→	→	SYM
ejpam-108	99	6	y	y	PROPN
ejpam-108	99	7	is	be	AUX
ejpam-108	99	8	contra	contra	PROPN
ejpam-108	99	9	b	b	PROPN
ejpam-108	99	10	-	-	PUNCT
ejpam-108	99	11	continuous	continuous	ADJ
ejpam-108	99	12	,	,	PUNCT
ejpam-108	99	13	g	g	NOUN
ejpam-108	99	14	:	:	PUNCT
ejpam-108	99	15	x	x	X
ejpam-108	99	16	→	→	SYM
ejpam-108	99	17	y	y	PROPN
ejpam-108	99	18	is	be	AUX
ejpam-108	99	19	contra	contra	PROPN
ejpam-108	99	20	continuous	continuous	ADJ
ejpam-108	99	21	,	,	PUNCT
ejpam-108	99	22	and	and	CCONJ
ejpam-108	99	23	y	y	PROPN
ejpam-108	99	24	is	be	AUX
ejpam-108	99	25	urysohn	urysohn	ADJ
ejpam-108	99	26	,	,	PUNCT
ejpam-108	99	27	then	then	ADV
ejpam-108	99	28	e	e	X
ejpam-108	99	29	=	=	PRON
ejpam-108	99	30	{	{	PUNCT
ejpam-108	99	31	x	x	SYM
ejpam-108	99	32	∈	∈	PROPN
ejpam-108	99	33	x	x	X
ejpam-108	99	34	:	:	PUNCT
ejpam-108	99	35	f	f	X
ejpam-108	99	36	(	(	PUNCT
ejpam-108	99	37	x	x	X
ejpam-108	99	38	)	)	PUNCT
ejpam-108	99	39	=	=	SYM
ejpam-108	99	40	g(x	g(x	NOUN
ejpam-108	99	41	)	)	PUNCT
ejpam-108	99	42	}	}	PUNCT
ejpam-108	99	43	is	be	AUX
ejpam-108	99	44	b	b	NOUN
ejpam-108	99	45	-	-	PUNCT
ejpam-108	99	46	closed	closed	ADJ
ejpam-108	99	47	in	in	ADP
ejpam-108	99	48	x	x	X
ejpam-108	99	49	.	.	PUNCT
ejpam-108	100	1	proof	proof	NOUN
ejpam-108	100	2	.	.	PUNCT
ejpam-108	101	1	let	let	VERB
ejpam-108	101	2	x	x	SYM
ejpam-108	101	3	∈	∈	PROPN
ejpam-108	101	4	x	x	X
ejpam-108	101	5	−	−	PROPN
ejpam-108	102	1	e.	e.	PROPN
ejpam-108	102	2	then	then	ADV
ejpam-108	102	3	f	f	PROPN
ejpam-108	102	4	(	(	PUNCT
ejpam-108	102	5	x	x	X
ejpam-108	102	6	)	)	PUNCT
ejpam-108	102	7	6=	6=	ADP
ejpam-108	102	8	g(x	g(x	NOUN
ejpam-108	102	9	)	)	PUNCT
ejpam-108	102	10	.	.	PUNCT
ejpam-108	103	1	since	since	SCONJ
ejpam-108	103	2	y	y	PROPN
ejpam-108	103	3	is	be	AUX
ejpam-108	103	4	urysohn	urysohn	ADJ
ejpam-108	103	5	,	,	PUNCT
ejpam-108	103	6	there	there	PRON
ejpam-108	103	7	exist	exist	VERB
ejpam-108	103	8	open	open	ADJ
ejpam-108	103	9	sets	set	NOUN
ejpam-108	103	10	v	v	ADP
ejpam-108	103	11	and	and	CCONJ
ejpam-108	103	12	w	w	ADP
ejpam-108	103	13	such	such	ADJ
ejpam-108	103	14	that	that	SCONJ
ejpam-108	103	15	f	f	PROPN
ejpam-108	103	16	(	(	PUNCT
ejpam-108	103	17	x	x	X
ejpam-108	103	18	)	)	PUNCT
ejpam-108	103	19	∈	∈	PROPN
ejpam-108	103	20	v	v	NOUN
ejpam-108	103	21	,	,	PUNCT
ejpam-108	103	22	g(x	g(x	NOUN
ejpam-108	103	23	)	)	PUNCT
ejpam-108	103	24	∈	∈	PROPN
ejpam-108	103	25	w	w	NOUN
ejpam-108	103	26	and	and	CCONJ
ejpam-108	103	27	cl(v	cl(v	NOUN
ejpam-108	103	28	)	)	PUNCT
ejpam-108	103	29	∩	∩	NOUN
ejpam-108	103	30	cl(w	cl(w	NOUN
ejpam-108	103	31	)	)	PUNCT
ejpam-108	103	32	=	=	SYM
ejpam-108	104	1	φ	φ	PROPN
ejpam-108	104	2	.	.	PUNCT
ejpam-108	105	1	since	since	SCONJ
ejpam-108	105	2	f	f	PROPN
ejpam-108	105	3	is	be	AUX
ejpam-108	105	4	contra	contra	PROPN
ejpam-108	105	5	b	b	PROPN
ejpam-108	105	6	-	-	PUNCT
ejpam-108	105	7	continuous	continuous	ADJ
ejpam-108	105	8	,	,	PUNCT
ejpam-108	105	9	then	then	ADV
ejpam-108	105	10	f	f	PROPN
ejpam-108	105	11	−1(cl(v	−1(cl(v	PROPN
ejpam-108	105	12	)	)	PUNCT
ejpam-108	105	13	)	)	PUNCT
ejpam-108	105	14	is	be	AUX
ejpam-108	105	15	b	b	NOUN
ejpam-108	105	16	-	-	PUNCT
ejpam-108	105	17	open	open	ADJ
ejpam-108	105	18	in	in	ADP
ejpam-108	105	19	x	x	PUNCT
ejpam-108	105	20	and	and	CCONJ
ejpam-108	105	21	g	g	PROPN
ejpam-108	105	22	is	be	AUX
ejpam-108	105	23	contra	contra	PROPN
ejpam-108	105	24	continuous	continuous	ADJ
ejpam-108	105	25	,	,	PUNCT
ejpam-108	105	26	then	then	ADV
ejpam-108	105	27	g−1(cl(w	g−1(cl(w	NOUN
ejpam-108	105	28	)	)	PUNCT
ejpam-108	105	29	)	)	PUNCT
ejpam-108	105	30	is	be	AUX
ejpam-108	105	31	open	open	ADJ
ejpam-108	105	32	set	set	VERB
ejpam-108	105	33	in	in	ADP
ejpam-108	105	34	x	x	X
ejpam-108	105	35	.	.	PUNCT
ejpam-108	106	1	let	let	VERB
ejpam-108	106	2	u	u	PRON
ejpam-108	106	3	=	=	NOUN
ejpam-108	106	4	f	f	X
ejpam-108	106	5	−1(cl(v	−1(cl(v	PROPN
ejpam-108	106	6	)	)	PUNCT
ejpam-108	106	7	)	)	PUNCT
ejpam-108	106	8	and	and	CCONJ
ejpam-108	106	9	g	g	NOUN
ejpam-108	106	10	=	=	PUNCT
ejpam-108	106	11	g−1(cl(w	g−1(cl(w	NOUN
ejpam-108	106	12	)	)	PUNCT
ejpam-108	106	13	)	)	PUNCT
ejpam-108	106	14	.	.	PUNCT
ejpam-108	107	1	then	then	ADV
ejpam-108	107	2	u	u	NOUN
ejpam-108	107	3	and	and	CCONJ
ejpam-108	107	4	g	g	PROPN
ejpam-108	107	5	contain	contain	VERB
ejpam-108	107	6	x	x	X
ejpam-108	107	7	.	.	PUNCT
ejpam-108	108	1	set	set	VERB
ejpam-108	108	2	a=	a=	PROPN
ejpam-108	108	3	u	u	NOUN
ejpam-108	108	4	∩	∩	X
ejpam-108	108	5	g.	g.	PROPN
ejpam-108	108	6	a	a	PRON
ejpam-108	108	7	is	be	AUX
ejpam-108	108	8	b	b	NOUN
ejpam-108	108	9	-	-	PUNCT
ejpam-108	108	10	open	open	ADJ
ejpam-108	108	11	in	in	ADP
ejpam-108	108	12	x	x	X
ejpam-108	108	13	.	.	PUNCT
ejpam-108	109	1	and	and	CCONJ
ejpam-108	109	2	f	f	PROPN
ejpam-108	109	3	(	(	PUNCT
ejpam-108	109	4	a)∩	a)∩	X
ejpam-108	109	5	g(a	g(a	PROPN
ejpam-108	109	6	)	)	PUNCT
ejpam-108	110	1	⊆	⊆	NUM
ejpam-108	110	2	f	f	X
ejpam-108	110	3	(	(	PUNCT
ejpam-108	110	4	u)∩	u)∩	PROPN
ejpam-108	110	5	g(g	g(g	PROPN
ejpam-108	110	6	)	)	PUNCT
ejpam-108	110	7	⊆	⊆	NUM
ejpam-108	110	8	cl(v	cl(v	NOUN
ejpam-108	110	9	)	)	PUNCT
ejpam-108	110	10	∩cl(w	∩cl(w	PROPN
ejpam-108	110	11	)	)	PUNCT
ejpam-108	110	12	=	=	SYM
ejpam-108	111	1	φ	φ	PROPN
ejpam-108	111	2	.	.	PUNCT
ejpam-108	112	1	hence	hence	ADV
ejpam-108	112	2	f	f	PROPN
ejpam-108	112	3	(	(	PUNCT
ejpam-108	112	4	a)∩g(a	a)∩g(a	PROPN
ejpam-108	112	5	)	)	PUNCT
ejpam-108	112	6	=	=	PUNCT
ejpam-108	112	7	φ	φ	PROPN
ejpam-108	112	8	and	and	CCONJ
ejpam-108	112	9	a∩e	a∩e	NUM
ejpam-108	112	10	=	=	SYM
ejpam-108	112	11	φ	φ	PROPN
ejpam-108	112	12	where	where	SCONJ
ejpam-108	112	13	a	a	PRON
ejpam-108	112	14	is	be	AUX
ejpam-108	112	15	b	b	NOUN
ejpam-108	112	16	-	-	PUNCT
ejpam-108	112	17	open	open	ADJ
ejpam-108	112	18	therefore	therefore	ADV
ejpam-108	112	19	x	x	X
ejpam-108	112	20	/∈	/∈	PUNCT
ejpam-108	112	21	bcl(e	bcl(e	PROPN
ejpam-108	112	22	)	)	PUNCT
ejpam-108	112	23	.	.	PUNCT
ejpam-108	113	1	thus	thus	ADV
ejpam-108	113	2	e	e	X
ejpam-108	113	3	is	be	AUX
ejpam-108	113	4	b	b	NOUN
ejpam-108	113	5	-	-	PUNCT
ejpam-108	113	6	closed	closed	ADJ
ejpam-108	113	7	in	in	ADP
ejpam-108	113	8	x	x	X
ejpam-108	113	9	.	.	PUNCT
ejpam-108	114	1	a	a	DET
ejpam-108	114	2	subset	subset	NOUN
ejpam-108	114	3	a	a	PRON
ejpam-108	114	4	of	of	ADP
ejpam-108	114	5	a	a	DET
ejpam-108	114	6	topological	topological	ADJ
ejpam-108	114	7	space	space	NOUN
ejpam-108	114	8	x	x	PRON
ejpam-108	114	9	is	be	AUX
ejpam-108	114	10	said	say	VERB
ejpam-108	114	11	to	to	PART
ejpam-108	114	12	be	be	AUX
ejpam-108	114	13	b	b	NOUN
ejpam-108	114	14	-	-	PUNCT
ejpam-108	114	15	dense	dense	ADJ
ejpam-108	114	16	in	in	ADP
ejpam-108	114	17	x	x	SYM
ejpam-108	114	18	if	if	SCONJ
ejpam-108	114	19	bcl(a	bcl(a	PROPN
ejpam-108	114	20	)	)	PUNCT
ejpam-108	114	21	=	=	SYM
ejpam-108	115	1	x	x	X
ejpam-108	115	2	.	.	PUNCT
ejpam-108	116	1	theorem	theorem	VERB
ejpam-108	116	2	2.8	2.8	NUM
ejpam-108	116	3	.	.	PUNCT
ejpam-108	117	1	let	let	VERB
ejpam-108	117	2	f	f	NOUN
ejpam-108	117	3	:	:	PUNCT
ejpam-108	117	4	x	x	X
ejpam-108	117	5	→	→	SYM
ejpam-108	117	6	y	y	PROPN
ejpam-108	117	7	is	be	AUX
ejpam-108	117	8	contra	contra	PROPN
ejpam-108	117	9	b	b	PROPN
ejpam-108	117	10	-	-	PUNCT
ejpam-108	117	11	continuous	continuous	ADJ
ejpam-108	117	12	and	and	CCONJ
ejpam-108	117	13	g	g	NOUN
ejpam-108	117	14	:	:	PUNCT
ejpam-108	117	15	x	x	X
ejpam-108	117	16	→	→	SYM
ejpam-108	117	17	y	y	PROPN
ejpam-108	117	18	is	be	AUX
ejpam-108	117	19	contra	contra	PROPN
ejpam-108	117	20	continuous	continuous	ADJ
ejpam-108	117	21	.	.	PUNCT
ejpam-108	118	1	if	if	SCONJ
ejpam-108	118	2	y	y	PROPN
ejpam-108	118	3	is	be	AUX
ejpam-108	118	4	urysohn	urysohn	ADJ
ejpam-108	118	5	,	,	PUNCT
ejpam-108	118	6	and	and	CCONJ
ejpam-108	118	7	f	f	PROPN
ejpam-108	118	8	=	=	SYM
ejpam-108	118	9	g	g	PROPN
ejpam-108	118	10	on	on	ADP
ejpam-108	118	11	b	b	NOUN
ejpam-108	118	12	-	-	PUNCT
ejpam-108	118	13	dense	dense	ADJ
ejpam-108	118	14	set	set	NOUN
ejpam-108	118	15	a⊆	a⊆	PROPN
ejpam-108	118	16	x	x	INTJ
ejpam-108	118	17	,	,	PUNCT
ejpam-108	118	18	then	then	ADV
ejpam-108	118	19	f	f	PROPN
ejpam-108	118	20	=	=	SYM
ejpam-108	118	21	g	g	PROPN
ejpam-108	118	22	on	on	ADP
ejpam-108	118	23	x	x	X
ejpam-108	118	24	.	.	PUNCT
ejpam-108	119	1	proof	proof	NOUN
ejpam-108	119	2	.	.	PUNCT
ejpam-108	120	1	since	since	SCONJ
ejpam-108	120	2	f	f	PROPN
ejpam-108	120	3	is	be	AUX
ejpam-108	120	4	contra	contra	PROPN
ejpam-108	120	5	b	b	PROPN
ejpam-108	120	6	-	-	PUNCT
ejpam-108	120	7	continuous	continuous	ADJ
ejpam-108	120	8	,	,	PUNCT
ejpam-108	120	9	g	g	PROPN
ejpam-108	120	10	contra	contra	PROPN
ejpam-108	120	11	continuous	continuous	ADJ
ejpam-108	120	12	functions	function	NOUN
ejpam-108	120	13	and	and	CCONJ
ejpam-108	120	14	y	y	PROPN
ejpam-108	120	15	is	be	AUX
ejpam-108	120	16	urysohn	urysohn	PRON
ejpam-108	120	17	by	by	ADP
ejpam-108	120	18	the	the	DET
ejpam-108	120	19	previous	previous	ADJ
ejpam-108	120	20	theorem	theorem	NOUN
ejpam-108	120	21	e	e	NOUN
ejpam-108	120	22	=	=	SYM
ejpam-108	120	23	{	{	PUNCT
ejpam-108	120	24	x	x	SYM
ejpam-108	120	25	∈	∈	PROPN
ejpam-108	120	26	x	x	X
ejpam-108	120	27	:	:	PUNCT
ejpam-108	120	28	f	f	X
ejpam-108	120	29	(	(	PUNCT
ejpam-108	120	30	x	x	X
ejpam-108	120	31	)	)	PUNCT
ejpam-108	120	32	=	=	SYM
ejpam-108	120	33	g(x	g(x	NOUN
ejpam-108	120	34	)	)	PUNCT
ejpam-108	120	35	}	}	PUNCT
ejpam-108	120	36	is	be	AUX
ejpam-108	120	37	b	b	NOUN
ejpam-108	120	38	-	-	PUNCT
ejpam-108	120	39	closed	closed	ADJ
ejpam-108	120	40	in	in	ADP
ejpam-108	120	41	x	x	X
ejpam-108	120	42	.	.	PUNCT
ejpam-108	121	1	we	we	PRON
ejpam-108	121	2	have	have	VERB
ejpam-108	121	3	f	f	NOUN
ejpam-108	121	4	=	=	SYM
ejpam-108	121	5	g	g	PROPN
ejpam-108	121	6	on	on	ADP
ejpam-108	121	7	b	b	NOUN
ejpam-108	121	8	-	-	PUNCT
ejpam-108	121	9	dense	dense	ADJ
ejpam-108	121	10	set	set	NOUN
ejpam-108	121	11	a	a	DET
ejpam-108	121	12	⊆	⊆	NUM
ejpam-108	121	13	x	x	SYM
ejpam-108	121	14	.	.	PUNCT
ejpam-108	122	1	since	since	SCONJ
ejpam-108	122	2	a	a	DET
ejpam-108	122	3	⊆	⊆	NUM
ejpam-108	122	4	e	e	NOUN
ejpam-108	122	5	and	and	CCONJ
ejpam-108	122	6	a	a	PRON
ejpam-108	122	7	is	be	AUX
ejpam-108	122	8	b	b	NOUN
ejpam-108	122	9	-	-	PUNCT
ejpam-108	122	10	dense	dense	ADJ
ejpam-108	122	11	set	set	NOUN
ejpam-108	122	12	in	in	ADP
ejpam-108	122	13	x	x	SYM
ejpam-108	122	14	,	,	PUNCT
ejpam-108	122	15	then	then	ADV
ejpam-108	122	16	x	x	X
ejpam-108	122	17	=	=	SYM
ejpam-108	122	18	bcl(a	bcl(a	PROPN
ejpam-108	122	19	)	)	PUNCT
ejpam-108	122	20	⊆	⊆	NUM
ejpam-108	122	21	bcl(e	bcl(e	PROPN
ejpam-108	122	22	)	)	PUNCT
ejpam-108	122	23	=	=	SYM
ejpam-108	122	24	e.	e.	PROPN
ejpam-108	123	1	hence	hence	ADV
ejpam-108	123	2	f	f	PROPN
ejpam-108	124	1	=	=	SYM
ejpam-108	124	2	g	g	PROPN
ejpam-108	124	3	on	on	ADP
ejpam-108	124	4	x	x	X
ejpam-108	124	5	.	.	PUNCT
ejpam-108	125	1	definition	definition	NOUN
ejpam-108	125	2	2.9	2.9	NUM
ejpam-108	125	3	.	.	PUNCT
ejpam-108	126	1	[	[	X
ejpam-108	126	2	11	11	NUM
ejpam-108	126	3	]	]	PUNCT
ejpam-108	126	4	a	a	DET
ejpam-108	126	5	space	space	NOUN
ejpam-108	126	6	x	x	PUNCT
ejpam-108	126	7	is	be	AUX
ejpam-108	126	8	called	call	VERB
ejpam-108	126	9	b	b	ADV
ejpam-108	126	10	-	-	PUNCT
ejpam-108	126	11	connected	connected	ADJ
ejpam-108	126	12	provided	provide	VERB
ejpam-108	126	13	that	that	SCONJ
ejpam-108	126	14	x	x	PRON
ejpam-108	126	15	is	be	AUX
ejpam-108	126	16	not	not	PART
ejpam-108	126	17	the	the	DET
ejpam-108	126	18	union	union	NOUN
ejpam-108	126	19	of	of	ADP
ejpam-108	126	20	two	two	NUM
ejpam-108	126	21	disjoint	disjoint	NOUN
ejpam-108	126	22	nonempty	nonempty	X
ejpam-108	126	23	b	b	X
ejpam-108	126	24	-	-	PUNCT
ejpam-108	126	25	open	open	ADJ
ejpam-108	126	26	sets	set	NOUN
ejpam-108	126	27	.	.	PUNCT
ejpam-108	127	1	theorem	theorem	VERB
ejpam-108	127	2	2.10	2.10	NUM
ejpam-108	127	3	.	.	PUNCT
ejpam-108	128	1	if	if	SCONJ
ejpam-108	128	2	f	f	PROPN
ejpam-108	128	3	:	:	PUNCT
ejpam-108	128	4	x	x	X
ejpam-108	128	5	→	→	SYM
ejpam-108	128	6	y	y	PROPN
ejpam-108	128	7	is	be	AUX
ejpam-108	128	8	a	a	DET
ejpam-108	128	9	contra	contra	PROPN
ejpam-108	128	10	b	b	NOUN
ejpam-108	128	11	-	-	PUNCT
ejpam-108	128	12	continuous	continuous	ADJ
ejpam-108	128	13	function	function	NOUN
ejpam-108	128	14	from	from	ADP
ejpam-108	128	15	a	a	DET
ejpam-108	128	16	b	b	NOUN
ejpam-108	128	17	-	-	PUNCT
ejpam-108	128	18	connected	connect	VERB
ejpam-108	128	19	space	space	NOUN
ejpam-108	128	20	x	x	X
ejpam-108	128	21	onto	onto	ADP
ejpam-108	128	22	any	any	DET
ejpam-108	128	23	space	space	NOUN
ejpam-108	128	24	y	y	PROPN
ejpam-108	128	25	,	,	PUNCT
ejpam-108	128	26	then	then	ADV
ejpam-108	128	27	y	y	PROPN
ejpam-108	128	28	is	be	AUX
ejpam-108	128	29	not	not	PART
ejpam-108	128	30	a	a	DET
ejpam-108	128	31	discrete	discrete	ADJ
ejpam-108	128	32	space	space	NOUN
ejpam-108	128	33	.	.	PUNCT
ejpam-108	129	1	a.	a.	PROPN
ejpam-108	129	2	al	al	PROPN
ejpam-108	129	3	-	-	PUNCT
ejpam-108	129	4	omari	omari	PROPN
ejpam-108	129	5	and	and	CCONJ
ejpam-108	129	6	s.	s.	PROPN
ejpam-108	129	7	noorani	noorani	PROPN
ejpam-108	129	8	/	/	SYM
ejpam-108	129	9	eur	eur	PROPN
ejpam-108	129	10	.	.	PUNCT
ejpam-108	130	1	j.	j.	PROPN
ejpam-108	130	2	pure	pure	PROPN
ejpam-108	130	3	appl	appl	PROPN
ejpam-108	130	4	.	.	PROPN
ejpam-108	130	5	math	math	PROPN
ejpam-108	130	6	,	,	PUNCT
ejpam-108	130	7	2	2	NUM
ejpam-108	130	8	(	(	PUNCT
ejpam-108	130	9	2009	2009	NUM
ejpam-108	130	10	)	)	PUNCT
ejpam-108	130	11	,	,	PUNCT
ejpam-108	130	12	(	(	PUNCT
ejpam-108	130	13	213	213	NUM
ejpam-108	130	14	-	-	SYM
ejpam-108	130	15	230	230	NUM
ejpam-108	130	16	)	)	PUNCT
ejpam-108	130	17	218	218	NUM
ejpam-108	130	18	proof	proof	NOUN
ejpam-108	130	19	.	.	PUNCT
ejpam-108	130	20	suppose	suppose	VERB
ejpam-108	130	21	that	that	SCONJ
ejpam-108	130	22	y	y	PROPN
ejpam-108	130	23	is	be	AUX
ejpam-108	130	24	discrete	discrete	ADJ
ejpam-108	130	25	.	.	PUNCT
ejpam-108	131	1	let	let	VERB
ejpam-108	131	2	a	a	DET
ejpam-108	131	3	be	be	AUX
ejpam-108	131	4	a	a	DET
ejpam-108	131	5	proper	proper	ADJ
ejpam-108	131	6	nonempty	nonempty	ADV
ejpam-108	131	7	open	open	ADJ
ejpam-108	131	8	and	and	CCONJ
ejpam-108	131	9	closed	closed	ADJ
ejpam-108	131	10	subset	subset	NOUN
ejpam-108	131	11	of	of	ADP
ejpam-108	131	12	y	y	PROPN
ejpam-108	131	13	.	.	PUNCT
ejpam-108	132	1	then	then	ADV
ejpam-108	132	2	f	f	PROPN
ejpam-108	132	3	−1(a	−1(a	CCONJ
ejpam-108	132	4	)	)	PUNCT
ejpam-108	132	5	is	be	AUX
ejpam-108	132	6	a	a	DET
ejpam-108	132	7	proper	proper	ADJ
ejpam-108	132	8	nonempty	nonempty	ADJ
ejpam-108	132	9	b	b	NOUN
ejpam-108	132	10	-	-	PUNCT
ejpam-108	132	11	clopen	clopen	ADJ
ejpam-108	132	12	subset	subset	NOUN
ejpam-108	132	13	of	of	ADP
ejpam-108	132	14	x	x	SYM
ejpam-108	132	15	,	,	PUNCT
ejpam-108	132	16	which	which	PRON
ejpam-108	132	17	is	be	AUX
ejpam-108	132	18	a	a	DET
ejpam-108	132	19	contradiction	contradiction	NOUN
ejpam-108	132	20	to	to	ADP
ejpam-108	132	21	the	the	DET
ejpam-108	132	22	fact	fact	NOUN
ejpam-108	132	23	that	that	SCONJ
ejpam-108	132	24	x	x	PRON
ejpam-108	132	25	is	be	AUX
ejpam-108	132	26	b	b	NOUN
ejpam-108	132	27	-	-	PUNCT
ejpam-108	132	28	connected	connect	VERB
ejpam-108	132	29	.	.	PUNCT
ejpam-108	133	1	3	3	X
ejpam-108	133	2	.	.	X
ejpam-108	133	3	almost	almost	ADV
ejpam-108	133	4	contra	contra	PROPN
ejpam-108	133	5	-	-	PUNCT
ejpam-108	133	6	b	b	ADJ
ejpam-108	133	7	-	-	PUNCT
ejpam-108	133	8	continuous	continuous	ADJ
ejpam-108	133	9	functions	function	NOUN
ejpam-108	133	10	in	in	ADP
ejpam-108	133	11	this	this	DET
ejpam-108	133	12	section	section	NOUN
ejpam-108	133	13	,	,	PUNCT
ejpam-108	133	14	we	we	PRON
ejpam-108	133	15	introduce	introduce	VERB
ejpam-108	133	16	a	a	DET
ejpam-108	133	17	new	new	ADJ
ejpam-108	133	18	type	type	NOUN
ejpam-108	133	19	of	of	ADP
ejpam-108	133	20	continuity	continuity	NOUN
ejpam-108	133	21	called	call	VERB
ejpam-108	133	22	almost	almost	ADV
ejpam-108	133	23	contra	contra	PROPN
ejpam-108	133	24	-	-	ADJ
ejpam-108	133	25	bcontinuity	bcontinuity	NOUN
ejpam-108	133	26	which	which	PRON
ejpam-108	133	27	is	be	AUX
ejpam-108	133	28	weaker	weak	ADJ
ejpam-108	133	29	than	than	ADP
ejpam-108	133	30	almost	almost	ADV
ejpam-108	133	31	contra	contra	NOUN
ejpam-108	133	32	-	-	NOUN
ejpam-108	133	33	precontinuity	precontinuity	NOUN
ejpam-108	133	34	[	[	X
ejpam-108	133	35	8	8	NUM
ejpam-108	133	36	]	]	PUNCT
ejpam-108	133	37	and	and	CCONJ
ejpam-108	133	38	stronger	strong	ADJ
ejpam-108	133	39	than	than	ADP
ejpam-108	133	40	almost	almost	ADV
ejpam-108	133	41	contra	contra	X
ejpam-108	133	42	-	-	PROPN
ejpam-108	133	43	β	β	X
ejpam-108	133	44	-continuity	-continuity	NOUN
ejpam-108	133	45	[	[	X
ejpam-108	133	46	4	4	NUM
ejpam-108	133	47	]	]	PUNCT
ejpam-108	133	48	.	.	PUNCT
ejpam-108	134	1	definition	definition	NOUN
ejpam-108	134	2	3.1	3.1	NUM
ejpam-108	134	3	.	.	PUNCT
ejpam-108	135	1	a	a	DET
ejpam-108	135	2	function	function	NOUN
ejpam-108	135	3	f	f	NOUN
ejpam-108	135	4	:	:	PUNCT
ejpam-108	135	5	x	x	X
ejpam-108	135	6	→	→	SYM
ejpam-108	135	7	y	y	PROPN
ejpam-108	135	8	is	be	AUX
ejpam-108	135	9	said	say	VERB
ejpam-108	135	10	to	to	PART
ejpam-108	135	11	be	be	AUX
ejpam-108	135	12	almost	almost	ADV
ejpam-108	135	13	contra	contra	ADJ
ejpam-108	135	14	-	-	PUNCT
ejpam-108	135	15	b	b	NOUN
ejpam-108	135	16	-	-	PUNCT
ejpam-108	135	17	continuous	continuous	ADJ
ejpam-108	135	18	(	(	PUNCT
ejpam-108	135	19	resp	resp	NOUN
ejpam-108	135	20	.	.	PUNCT
ejpam-108	136	1	almost	almost	ADV
ejpam-108	136	2	contra	contra	ADJ
ejpam-108	136	3	-	-	NOUN
ejpam-108	136	4	precontinuous	precontinuous	ADJ
ejpam-108	137	1	[	[	X
ejpam-108	137	2	8	8	NUM
ejpam-108	137	3	]	]	PUNCT
ejpam-108	137	4	,	,	PUNCT
ejpam-108	137	5	almost	almost	ADV
ejpam-108	137	6	contra	contra	PROPN
ejpam-108	137	7	-	-	PUNCT
ejpam-108	137	8	β	β	X
ejpam-108	137	9	-continuous	-continuous	ADJ
ejpam-108	137	10	[	[	X
ejpam-108	137	11	4	4	NUM
ejpam-108	137	12	]	]	SYM
ejpam-108	137	13	)	)	PUNCT
ejpam-108	137	14	f	f	PROPN
ejpam-108	137	15	−1(v	−1(v	PROPN
ejpam-108	137	16	)	)	PUNCT
ejpam-108	137	17	∈	∈	PROPN
ejpam-108	137	18	bc(x	bc(x	NOUN
ejpam-108	137	19	)	)	PUNCT
ejpam-108	137	20	(	(	PUNCT
ejpam-108	137	21	resp	resp	NOUN
ejpam-108	137	22	.	.	PUNCT
ejpam-108	138	1	f	f	PROPN
ejpam-108	138	2	−1(v	−1(v	PROPN
ejpam-108	138	3	)	)	PUNCT
ejpam-108	138	4	∈	∈	PROPN
ejpam-108	138	5	pc(x	pc(x	NOUN
ejpam-108	138	6	)	)	PUNCT
ejpam-108	138	7	,	,	PUNCT
ejpam-108	138	8	f	f	PROPN
ejpam-108	138	9	−1(v	−1(v	PROPN
ejpam-108	138	10	)	)	PUNCT
ejpam-108	138	11	∈	∈	PROPN
ejpam-108	138	12	βc(x	βc(x	PUNCT
ejpam-108	138	13	)	)	PUNCT
ejpam-108	138	14	)	)	PUNCT
ejpam-108	138	15	for	for	ADP
ejpam-108	138	16	every	every	DET
ejpam-108	138	17	v	v	NOUN
ejpam-108	138	18	∈	∈	NOUN
ejpam-108	138	19	ro(x	ro(x	PUNCT
ejpam-108	138	20	)	)	PUNCT
ejpam-108	138	21	.	.	PUNCT
ejpam-108	139	1	lemma	lemma	PROPN
ejpam-108	139	2	3.2	3.2	NUM
ejpam-108	139	3	.	.	PUNCT
ejpam-108	140	1	[	[	X
ejpam-108	140	2	3	3	X
ejpam-108	140	3	]	]	PUNCT
ejpam-108	140	4	let	let	VERB
ejpam-108	140	5	a	a	PRON
ejpam-108	140	6	be	be	AUX
ejpam-108	140	7	a	a	DET
ejpam-108	140	8	subset	subset	NOUN
ejpam-108	140	9	of	of	ADP
ejpam-108	140	10	a	a	DET
ejpam-108	140	11	space	space	NOUN
ejpam-108	140	12	x	x	X
ejpam-108	140	13	.	.	PUNCT
ejpam-108	141	1	then	then	ADV
ejpam-108	141	2	1	1	X
ejpam-108	141	3	.	.	X
ejpam-108	141	4	bcl(a	bcl(a	VERB
ejpam-108	141	5	)	)	PUNCT
ejpam-108	141	6	=	=	SYM
ejpam-108	141	7	sc	sc	PROPN
ejpam-108	141	8	l(a	l(a	PROPN
ejpam-108	141	9	)	)	PUNCT
ejpam-108	141	10	∩	∩	NOUN
ejpam-108	141	11	pcl(a	pcl(a	X
ejpam-108	141	12	)	)	PUNCT
ejpam-108	141	13	=	=	PUNCT
ejpam-108	141	14	a∪	a∪	PROPN
ejpam-108	142	1	[	[	X
ejpam-108	142	2	int(cl(a))∩	int(cl(a))∩	PROPN
ejpam-108	142	3	cl(int(a	cl(int(a	PROPN
ejpam-108	142	4	)	)	PUNCT
ejpam-108	142	5	)	)	PUNCT
ejpam-108	143	1	]	]	X
ejpam-108	143	2	;	;	PUNCT
ejpam-108	143	3	2	2	X
ejpam-108	143	4	.	.	X
ejpam-108	143	5	bint(a	bint(a	NUM
ejpam-108	143	6	)	)	PUNCT
ejpam-108	143	7	=	=	VERB
ejpam-108	143	8	sint(a)∪	sint(a)∪	VERB
ejpam-108	143	9	pint(a	pint(a	NOUN
ejpam-108	143	10	)	)	PUNCT
ejpam-108	144	1	=	=	SYM
ejpam-108	144	2	a∩	a∩	PROPN
ejpam-108	145	1	[	[	X
ejpam-108	145	2	int(cl(a))∪	int(cl(a))∪	NOUN
ejpam-108	145	3	cl(int(a	cl(int(a	PROPN
ejpam-108	145	4	)	)	PUNCT
ejpam-108	145	5	)	)	PUNCT
ejpam-108	145	6	.	.	PUNCT
ejpam-108	146	1	lemma	lemma	PROPN
ejpam-108	146	2	3.3	3.3	NUM
ejpam-108	146	3	.	.	PUNCT
ejpam-108	147	1	for	for	ADP
ejpam-108	147	2	a	a	DET
ejpam-108	147	3	subset	subset	NOUN
ejpam-108	147	4	v	v	NOUN
ejpam-108	147	5	of	of	ADP
ejpam-108	147	6	a	a	DET
ejpam-108	147	7	topological	topological	ADJ
ejpam-108	147	8	space	space	NOUN
ejpam-108	147	9	y	y	PROPN
ejpam-108	147	10	,	,	PUNCT
ejpam-108	147	11	the	the	DET
ejpam-108	147	12	following	follow	VERB
ejpam-108	147	13	hold	hold	NOUN
ejpam-108	147	14	:	:	PUNCT
ejpam-108	147	15	αcl(v	αcl(v	X
ejpam-108	147	16	)	)	PUNCT
ejpam-108	147	17	=	=	SYM
ejpam-108	147	18	cl(v	cl(v	NOUN
ejpam-108	147	19	)	)	PUNCT
ejpam-108	147	20	for	for	ADP
ejpam-108	147	21	every	every	DET
ejpam-108	147	22	v	v	PROPN
ejpam-108	147	23	∈	∈	NOUN
ejpam-108	147	24	bo(y	bo(y	NUM
ejpam-108	147	25	)	)	PUNCT
ejpam-108	147	26	.	.	PUNCT
ejpam-108	148	1	a.	a.	PROPN
ejpam-108	148	2	al	al	PROPN
ejpam-108	148	3	-	-	PUNCT
ejpam-108	148	4	omari	omari	PROPN
ejpam-108	148	5	and	and	CCONJ
ejpam-108	148	6	s.	s.	PROPN
ejpam-108	148	7	noorani	noorani	PROPN
ejpam-108	148	8	/	/	SYM
ejpam-108	148	9	eur	eur	PROPN
ejpam-108	148	10	.	.	PUNCT
ejpam-108	149	1	j.	j.	PROPN
ejpam-108	149	2	pure	pure	PROPN
ejpam-108	149	3	appl	appl	PROPN
ejpam-108	149	4	.	.	PROPN
ejpam-108	149	5	math	math	PROPN
ejpam-108	149	6	,	,	PUNCT
ejpam-108	149	7	2	2	NUM
ejpam-108	149	8	(	(	PUNCT
ejpam-108	149	9	2009	2009	NUM
ejpam-108	149	10	)	)	PUNCT
ejpam-108	149	11	,	,	PUNCT
ejpam-108	149	12	(	(	PUNCT
ejpam-108	149	13	213	213	NUM
ejpam-108	149	14	-	-	SYM
ejpam-108	149	15	230	230	NUM
ejpam-108	149	16	)	)	PUNCT
ejpam-108	149	17	219	219	NUM
ejpam-108	149	18	proof	proof	NOUN
ejpam-108	149	19	.	.	PUNCT
ejpam-108	150	1	since	since	SCONJ
ejpam-108	150	2	v	v	NUM
ejpam-108	150	3	∈	∈	PROPN
ejpam-108	150	4	bo(y	bo(y	NUM
ejpam-108	150	5	)	)	PUNCT
ejpam-108	150	6	,	,	PUNCT
ejpam-108	150	7	then	then	ADV
ejpam-108	150	8	v	v	X
ejpam-108	150	9	=	=	SYM
ejpam-108	150	10	bint(v	bint(v	PROPN
ejpam-108	150	11	)	)	PUNCT
ejpam-108	150	12	=	=	NOUN
ejpam-108	150	13	sint(v	sint(v	NOUN
ejpam-108	150	14	)	)	PUNCT
ejpam-108	150	15	∪	∪	NOUN
ejpam-108	150	16	pint(v	pint(v	NOUN
ejpam-108	150	17	)	)	PUNCT
ejpam-108	150	18	=	=	SYM
ejpam-108	150	19	bint(v	bint(v	PROPN
ejpam-108	150	20	)	)	PUNCT
ejpam-108	150	21	=	=	SYM
ejpam-108	150	22	v	v	NUM
ejpam-108	150	23	∩	∩	NOUN
ejpam-108	150	24	[	[	X
ejpam-108	150	25	int(cl(v	int(cl(v	NOUN
ejpam-108	150	26	)	)	PUNCT
ejpam-108	150	27	)	)	PUNCT
ejpam-108	150	28	∪	∪	NOUN
ejpam-108	150	29	cl(int(v	cl(int(v	NOUN
ejpam-108	150	30	)	)	PUNCT
ejpam-108	150	31	)	)	PUNCT
ejpam-108	151	1	=	=	PRON
ejpam-108	151	2	cl(v	cl(v	NOUN
ejpam-108	151	3	∩	∩	NOUN
ejpam-108	151	4	[	[	X
ejpam-108	151	5	int(cl(v	int(cl(v	NOUN
ejpam-108	151	6	)	)	PUNCT
ejpam-108	151	7	)	)	PUNCT
ejpam-108	151	8	∪	∪	NOUN
ejpam-108	151	9	cl(int(v	cl(int(v	NOUN
ejpam-108	151	10	)	)	PUNCT
ejpam-108	151	11	)	)	PUNCT
ejpam-108	151	12	)	)	PUNCT
ejpam-108	152	1	⊆	⊆	NUM
ejpam-108	152	2	cl(v	cl(v	NOUN
ejpam-108	152	3	)	)	PUNCT
ejpam-108	152	4	∩	∩	NOUN
ejpam-108	152	5	cl(int(cl(v	cl(int(cl(v	NOUN
ejpam-108	152	6	)	)	PUNCT
ejpam-108	152	7	)	)	PUNCT
ejpam-108	152	8	∪	∪	NOUN
ejpam-108	152	9	cl(int(v	cl(int(v	NOUN
ejpam-108	152	10	)	)	PUNCT
ejpam-108	152	11	)	)	PUNCT
ejpam-108	152	12	)	)	PUNCT
ejpam-108	153	1	⊆	⊆	NUM
ejpam-108	153	2	cl(v	cl(v	NOUN
ejpam-108	153	3	)	)	PUNCT
ejpam-108	153	4	∩	∩	NOUN
ejpam-108	153	5	cl(int(cl(v	cl(int(cl(v	NOUN
ejpam-108	153	6	)	)	PUNCT
ejpam-108	153	7	)	)	PUNCT
ejpam-108	153	8	)	)	PUNCT
ejpam-108	153	9	∪	∪	NOUN
ejpam-108	153	10	cl(int(v	cl(int(v	NOUN
ejpam-108	153	11	)	)	PUNCT
ejpam-108	153	12	)	)	PUNCT
ejpam-108	154	1	⊆	⊆	X
ejpam-108	154	2	(	(	PUNCT
ejpam-108	154	3	cl(v	cl(v	X
ejpam-108	154	4	)	)	PUNCT
ejpam-108	154	5	∩	∩	NOUN
ejpam-108	154	6	cl(int(cl(v	cl(int(cl(v	NOUN
ejpam-108	154	7	)	)	PUNCT
ejpam-108	154	8	)	)	PUNCT
ejpam-108	154	9	)	)	PUNCT
ejpam-108	154	10	)	)	PUNCT
ejpam-108	154	11	∪	∪	X
ejpam-108	154	12	(	(	PUNCT
ejpam-108	154	13	cl(v	cl(v	NOUN
ejpam-108	154	14	)	)	PUNCT
ejpam-108	154	15	∩	∩	NOUN
ejpam-108	154	16	(	(	PUNCT
ejpam-108	154	17	cl(int(v	cl(int(v	NOUN
ejpam-108	154	18	)	)	PUNCT
ejpam-108	154	19	)	)	PUNCT
ejpam-108	154	20	)	)	PUNCT
ejpam-108	155	1	⊆	⊆	NUM
ejpam-108	155	2	cl(int(cl(v	cl(int(cl(v	NOUN
ejpam-108	155	3	)	)	PUNCT
ejpam-108	155	4	)	)	PUNCT
ejpam-108	155	5	)	)	PUNCT
ejpam-108	155	6	∪	∪	NOUN
ejpam-108	155	7	cl(int(v	cl(int(v	NOUN
ejpam-108	155	8	)	)	PUNCT
ejpam-108	155	9	)	)	PUNCT
ejpam-108	156	1	⊆	⊆	NUM
ejpam-108	156	2	cl(int(cl(v	cl(int(cl(v	NOUN
ejpam-108	156	3	)	)	PUNCT
ejpam-108	156	4	)	)	PUNCT
ejpam-108	156	5	)	)	PUNCT
ejpam-108	157	1	⊆	⊆	NUM
ejpam-108	157	2	cl(int(cl(v	cl(int(cl(v	NOUN
ejpam-108	157	3	)	)	PUNCT
ejpam-108	157	4	)	)	PUNCT
ejpam-108	157	5	)	)	PUNCT
ejpam-108	157	6	∪	∪	ADP
ejpam-108	157	7	v	v	NOUN
ejpam-108	157	8	=	=	SYM
ejpam-108	157	9	αcl(v	αcl(v	NOUN
ejpam-108	157	10	)	)	PUNCT
ejpam-108	157	11	and	and	CCONJ
ejpam-108	157	12	also	also	ADV
ejpam-108	157	13	αcl(v	αcl(v	ADJ
ejpam-108	157	14	)	)	PUNCT
ejpam-108	157	15	⊆	⊆	NUM
ejpam-108	157	16	cl(v	cl(v	NOUN
ejpam-108	157	17	)	)	PUNCT
ejpam-108	157	18	for	for	ADP
ejpam-108	157	19	every	every	DET
ejpam-108	157	20	subset	subset	NOUN
ejpam-108	157	21	v	v	ADP
ejpam-108	157	22	⊆	⊆	NUM
ejpam-108	157	23	x	x	SYM
ejpam-108	157	24	.	.	PUNCT
ejpam-108	158	1	hence	hence	ADV
ejpam-108	158	2	αcl(v	αcl(v	X
ejpam-108	158	3	)	)	PUNCT
ejpam-108	159	1	=	=	SYM
ejpam-108	159	2	cl(v	cl(v	NOUN
ejpam-108	159	3	)	)	PUNCT
ejpam-108	159	4	for	for	ADP
ejpam-108	159	5	every	every	DET
ejpam-108	159	6	v	v	PROPN
ejpam-108	159	7	∈	∈	NOUN
ejpam-108	159	8	bo(y	bo(y	NUM
ejpam-108	159	9	)	)	PUNCT
ejpam-108	159	10	.	.	PUNCT
ejpam-108	160	1	definition	definition	NOUN
ejpam-108	160	2	3.4	3.4	NUM
ejpam-108	160	3	.	.	PUNCT
ejpam-108	161	1	a	a	DET
ejpam-108	161	2	subfamily	subfamily	ADV
ejpam-108	161	3	mx	mx	NOUN
ejpam-108	161	4	of	of	ADP
ejpam-108	161	5	the	the	DET
ejpam-108	161	6	power	power	NOUN
ejpam-108	161	7	set	set	NOUN
ejpam-108	161	8	p(x	p(x	PROPN
ejpam-108	161	9	)	)	PUNCT
ejpam-108	161	10	of	of	ADP
ejpam-108	161	11	a	a	DET
ejpam-108	161	12	nonempty	nonempty	ADV
ejpam-108	161	13	set	set	VERB
ejpam-108	161	14	x	x	PUNCT
ejpam-108	161	15	is	be	AUX
ejpam-108	161	16	called	call	VERB
ejpam-108	161	17	a	a	DET
ejpam-108	161	18	minimal	minimal	ADJ
ejpam-108	161	19	structure	structure	NOUN
ejpam-108	161	20	(	(	PUNCT
ejpam-108	161	21	briefly	briefly	NOUN
ejpam-108	161	22	m	m	NOUN
ejpam-108	161	23	-	-	NOUN
ejpam-108	161	24	structure	structure	NOUN
ejpam-108	161	25	)	)	PUNCT
ejpam-108	161	26	on	on	ADP
ejpam-108	161	27	x	x	X
ejpam-108	162	1	[	[	X
ejpam-108	162	2	18	18	NUM
ejpam-108	162	3	]	]	PUNCT
ejpam-108	162	4	if	if	SCONJ
ejpam-108	162	5	;	;	PUNCT
ejpam-108	162	6	φ	φ	PROPN
ejpam-108	162	7	∈	∈	PROPN
ejpam-108	162	8	mx	mx	PROPN
ejpam-108	162	9	and	and	CCONJ
ejpam-108	162	10	x	x	PROPN
ejpam-108	162	11	∈	∈	PROPN
ejpam-108	162	12	mx	mx	PROPN
ejpam-108	162	13	.	.	PUNCT
ejpam-108	163	1	by	by	ADP
ejpam-108	163	2	(	(	PUNCT
ejpam-108	163	3	x	x	INTJ
ejpam-108	163	4	;	;	PUNCT
ejpam-108	163	5	mx	mx	PROPN
ejpam-108	163	6	)	)	PUNCT
ejpam-108	163	7	,	,	PUNCT
ejpam-108	163	8	we	we	PRON
ejpam-108	163	9	denote	denote	VERB
ejpam-108	163	10	a	a	DET
ejpam-108	163	11	nonempty	nonempty	ADV
ejpam-108	163	12	set	set	VERB
ejpam-108	163	13	x	x	PUNCT
ejpam-108	163	14	with	with	ADP
ejpam-108	163	15	a	a	DET
ejpam-108	163	16	minimal	minimal	ADJ
ejpam-108	163	17	structure	structure	NOUN
ejpam-108	163	18	mx	mx	NOUN
ejpam-108	163	19	on	on	ADP
ejpam-108	163	20	x	x	PUNCT
ejpam-108	163	21	and	and	CCONJ
ejpam-108	163	22	call	call	VERB
ejpam-108	163	23	it	it	PRON
ejpam-108	163	24	an	an	DET
ejpam-108	163	25	m	m	NOUN
ejpam-108	163	26	-	-	NOUN
ejpam-108	163	27	space	space	NOUN
ejpam-108	163	28	.	.	PUNCT
ejpam-108	164	1	each	each	DET
ejpam-108	164	2	member	member	NOUN
ejpam-108	164	3	of	of	ADP
ejpam-108	164	4	mx	mx	PROPN
ejpam-108	164	5	is	be	AUX
ejpam-108	164	6	said	say	VERB
ejpam-108	164	7	to	to	PART
ejpam-108	164	8	be	be	AUX
ejpam-108	164	9	mx	mx	PROPN
ejpam-108	164	10	-open	-open	ADJ
ejpam-108	164	11	(	(	PUNCT
ejpam-108	164	12	or	or	CCONJ
ejpam-108	164	13	briefly	briefly	NOUN
ejpam-108	164	14	m	m	NOUN
ejpam-108	164	15	-	-	VERB
ejpam-108	164	16	open	open	ADJ
ejpam-108	164	17	)	)	PUNCT
ejpam-108	164	18	and	and	CCONJ
ejpam-108	164	19	the	the	DET
ejpam-108	164	20	complement	complement	NOUN
ejpam-108	164	21	of	of	ADP
ejpam-108	164	22	an	an	DET
ejpam-108	164	23	mx	mx	PROPN
ejpam-108	164	24	-open	-open	NOUN
ejpam-108	164	25	set	set	NOUN
ejpam-108	164	26	is	be	AUX
ejpam-108	164	27	said	say	VERB
ejpam-108	164	28	to	to	PART
ejpam-108	164	29	be	be	AUX
ejpam-108	164	30	mx	mx	NOUN
ejpam-108	164	31	-closed	-close	VERB
ejpam-108	164	32	(	(	PUNCT
ejpam-108	164	33	or	or	CCONJ
ejpam-108	164	34	briefly	briefly	NOUN
ejpam-108	164	35	m	m	NOUN
ejpam-108	164	36	-	-	PUNCT
ejpam-108	164	37	closed	closed	ADJ
ejpam-108	164	38	)	)	PUNCT
ejpam-108	164	39	.	.	PUNCT
ejpam-108	165	1	definition	definition	NOUN
ejpam-108	165	2	3.5	3.5	NUM
ejpam-108	165	3	.	.	PUNCT
ejpam-108	166	1	a	a	DET
ejpam-108	166	2	function	function	NOUN
ejpam-108	166	3	f	f	NOUN
ejpam-108	166	4	:	:	PUNCT
ejpam-108	166	5	(	(	PUNCT
ejpam-108	166	6	x	x	X
ejpam-108	166	7	;	;	PUNCT
ejpam-108	166	8	mx	mx	PROPN
ejpam-108	166	9	)	)	PUNCT
ejpam-108	166	10	→	→	PUNCT
ejpam-108	166	11	(	(	PUNCT
ejpam-108	166	12	y	y	PROPN
ejpam-108	166	13	;	;	PUNCT
ejpam-108	166	14	σ	σ	PROPN
ejpam-108	166	15	)	)	PUNCT
ejpam-108	166	16	is	be	AUX
ejpam-108	166	17	said	say	VERB
ejpam-108	166	18	to	to	PART
ejpam-108	166	19	be	be	AUX
ejpam-108	166	20	almost	almost	ADV
ejpam-108	166	21	contra	contra	PROPN
ejpam-108	166	22	mcontinuous	mcontinuous	ADJ
ejpam-108	166	23	[	[	X
ejpam-108	166	24	18	18	NUM
ejpam-108	166	25	]	]	PUNCT
ejpam-108	166	26	if	if	SCONJ
ejpam-108	166	27	f	f	PROPN
ejpam-108	166	28	−1(v	−1(v	X
ejpam-108	166	29	)	)	PUNCT
ejpam-108	167	1	=	=	SYM
ejpam-108	167	2	mx	mx	PROPN
ejpam-108	167	3	-cl	-cl	INTJ
ejpam-108	167	4	(	(	PUNCT
ejpam-108	167	5	f	f	PROPN
ejpam-108	167	6	−1(v	−1(v	PROPN
ejpam-108	167	7	)	)	PUNCT
ejpam-108	167	8	)	)	PUNCT
ejpam-108	168	1	for	for	ADP
ejpam-108	168	2	every	every	DET
ejpam-108	168	3	regular	regular	ADJ
ejpam-108	168	4	open	open	ADJ
ejpam-108	168	5	set	set	NOUN
ejpam-108	168	6	v	v	NUM
ejpam-108	168	7	of	of	ADP
ejpam-108	168	8	(	(	PUNCT
ejpam-108	168	9	y	y	PROPN
ejpam-108	168	10	;	;	PUNCT
ejpam-108	168	11	σ	σ	PROPN
ejpam-108	168	12	)	)	PUNCT
ejpam-108	168	13	.	.	PUNCT
ejpam-108	169	1	theorem	theorem	VERB
ejpam-108	169	2	3.6	3.6	NUM
ejpam-108	169	3	.	.	PUNCT
ejpam-108	170	1	[	[	X
ejpam-108	170	2	19	19	NUM
ejpam-108	170	3	]	]	PUNCT
ejpam-108	170	4	for	for	ADP
ejpam-108	170	5	a	a	DET
ejpam-108	170	6	function	function	NOUN
ejpam-108	170	7	f	f	NOUN
ejpam-108	170	8	:	:	PUNCT
ejpam-108	170	9	(	(	PUNCT
ejpam-108	170	10	x	x	X
ejpam-108	170	11	,	,	PUNCT
ejpam-108	170	12	mx	mx	PROPN
ejpam-108	170	13	)	)	PUNCT
ejpam-108	170	14	→	→	SYM
ejpam-108	170	15	(	(	PUNCT
ejpam-108	170	16	y	y	PROPN
ejpam-108	170	17	,	,	PUNCT
ejpam-108	170	18	σ	σ	PROPN
ejpam-108	170	19	)	)	PUNCT
ejpam-108	170	20	,	,	PUNCT
ejpam-108	170	21	the	the	DET
ejpam-108	170	22	following	follow	VERB
ejpam-108	170	23	properties	property	NOUN
ejpam-108	170	24	are	be	AUX
ejpam-108	170	25	equivalent	equivalent	ADJ
ejpam-108	170	26	:	:	PUNCT
ejpam-108	170	27	1	1	X
ejpam-108	170	28	.	.	X
ejpam-108	170	29	f	f	PROPN
ejpam-108	170	30	is	be	AUX
ejpam-108	170	31	almost	almost	ADV
ejpam-108	170	32	contra	contra	PROPN
ejpam-108	170	33	m	m	PROPN
ejpam-108	170	34	-	-	ADJ
ejpam-108	170	35	continuous	continuous	ADJ
ejpam-108	170	36	;	;	PUNCT
ejpam-108	170	37	2	2	NUM
ejpam-108	170	38	.	.	X
ejpam-108	170	39	f	f	PROPN
ejpam-108	170	40	−1(cl(v	−1(cl(v	PROPN
ejpam-108	170	41	)	)	PUNCT
ejpam-108	170	42	)	)	PUNCT
ejpam-108	171	1	=	=	PUNCT
ejpam-108	171	2	mx	mx	PROPN
ejpam-108	171	3	−	−	PROPN
ejpam-108	171	4	int	int	NOUN
ejpam-108	171	5	(	(	PUNCT
ejpam-108	171	6	f	f	NOUN
ejpam-108	171	7	−1(cl(v	−1(cl(v	PROPN
ejpam-108	171	8	)	)	PUNCT
ejpam-108	171	9	)	)	PUNCT
ejpam-108	171	10	)	)	PUNCT
ejpam-108	172	1	for	for	ADP
ejpam-108	172	2	every	every	DET
ejpam-108	172	3	v	v	NOUN
ejpam-108	172	4	∈	∈	NOUN
ejpam-108	172	5	β(y	β(y	PROPN
ejpam-108	172	6	)	)	PUNCT
ejpam-108	172	7	;	;	PUNCT
ejpam-108	172	8	a.	a.	PROPN
ejpam-108	172	9	al	al	PROPN
ejpam-108	172	10	-	-	PUNCT
ejpam-108	172	11	omari	omari	PROPN
ejpam-108	172	12	and	and	CCONJ
ejpam-108	172	13	s.	s.	PROPN
ejpam-108	172	14	noorani	noorani	PROPN
ejpam-108	172	15	/	/	SYM
ejpam-108	172	16	eur	eur	PROPN
ejpam-108	172	17	.	.	PUNCT
ejpam-108	173	1	j.	j.	PROPN
ejpam-108	173	2	pure	pure	PROPN
ejpam-108	173	3	appl	appl	PROPN
ejpam-108	173	4	.	.	PROPN
ejpam-108	173	5	math	math	PROPN
ejpam-108	173	6	,	,	PUNCT
ejpam-108	173	7	2	2	NUM
ejpam-108	173	8	(	(	PUNCT
ejpam-108	173	9	2009	2009	NUM
ejpam-108	173	10	)	)	PUNCT
ejpam-108	173	11	,	,	PUNCT
ejpam-108	173	12	(	(	PUNCT
ejpam-108	173	13	213	213	NUM
ejpam-108	173	14	-	-	SYM
ejpam-108	173	15	230	230	NUM
ejpam-108	173	16	)	)	PUNCT
ejpam-108	173	17	220	220	NUM
ejpam-108	173	18	3	3	NUM
ejpam-108	173	19	.	.	PUNCT
ejpam-108	174	1	f	f	PROPN
ejpam-108	174	2	−1(cl(v	−1(cl(v	PROPN
ejpam-108	174	3	)	)	PUNCT
ejpam-108	174	4	)	)	PUNCT
ejpam-108	175	1	=	=	PUNCT
ejpam-108	175	2	mx	mx	PROPN
ejpam-108	175	3	−	−	PROPN
ejpam-108	175	4	int	int	NOUN
ejpam-108	175	5	(	(	PUNCT
ejpam-108	175	6	f	f	NOUN
ejpam-108	175	7	−1(cl(v	−1(cl(v	PROPN
ejpam-108	175	8	)	)	PUNCT
ejpam-108	175	9	)	)	PUNCT
ejpam-108	175	10	)	)	PUNCT
ejpam-108	176	1	for	for	ADP
ejpam-108	176	2	every	every	DET
ejpam-108	176	3	v	v	NOUN
ejpam-108	176	4	∈	∈	NOUN
ejpam-108	176	5	so(y	so(y	X
ejpam-108	176	6	)	)	PUNCT
ejpam-108	176	7	;	;	PUNCT
ejpam-108	176	8	4	4	X
ejpam-108	176	9	.	.	X
ejpam-108	176	10	f	f	PROPN
ejpam-108	176	11	−1(int(cl(v	−1(int(cl(v	PROPN
ejpam-108	176	12	)	)	PUNCT
ejpam-108	176	13	)	)	PUNCT
ejpam-108	176	14	)	)	PUNCT
ejpam-108	177	1	=	=	PUNCT
ejpam-108	177	2	mx	mx	PROPN
ejpam-108	177	3	−	−	PROPN
ejpam-108	177	4	int	int	NOUN
ejpam-108	177	5	(	(	PUNCT
ejpam-108	177	6	f	f	NOUN
ejpam-108	177	7	−1(int(cl(v	−1(int(cl(v	PROPN
ejpam-108	177	8	)	)	PUNCT
ejpam-108	177	9	)	)	PUNCT
ejpam-108	177	10	)	)	PUNCT
ejpam-108	177	11	)	)	PUNCT
ejpam-108	178	1	for	for	ADP
ejpam-108	178	2	every	every	DET
ejpam-108	178	3	v	v	NOUN
ejpam-108	178	4	∈	∈	NOUN
ejpam-108	178	5	po(y	po(y	NUM
ejpam-108	178	6	)	)	PUNCT
ejpam-108	178	7	.	.	PUNCT
ejpam-108	179	1	for	for	ADP
ejpam-108	179	2	more	more	ADJ
ejpam-108	179	3	properties	property	NOUN
ejpam-108	179	4	of	of	ADP
ejpam-108	179	5	almost	almost	ADV
ejpam-108	179	6	contra	contra	PROPN
ejpam-108	179	7	m	m	PROPN
ejpam-108	179	8	-	-	ADJ
ejpam-108	179	9	continuous	continuous	ADJ
ejpam-108	179	10	the	the	DET
ejpam-108	179	11	reader	reader	NOUN
ejpam-108	179	12	should	should	AUX
ejpam-108	179	13	refer	refer	VERB
ejpam-108	179	14	to	to	ADP
ejpam-108	179	15	[	[	X
ejpam-108	179	16	19	19	NUM
ejpam-108	179	17	]	]	PUNCT
ejpam-108	179	18	.	.	PUNCT
ejpam-108	180	1	corollary	corollary	ADJ
ejpam-108	180	2	3.7	3.7	NUM
ejpam-108	180	3	.	.	PUNCT
ejpam-108	181	1	for	for	ADP
ejpam-108	181	2	a	a	DET
ejpam-108	181	3	function	function	NOUN
ejpam-108	181	4	f	f	NOUN
ejpam-108	181	5	:	:	PUNCT
ejpam-108	181	6	x	x	X
ejpam-108	181	7	→	→	SYM
ejpam-108	181	8	y	y	PROPN
ejpam-108	181	9	,	,	PUNCT
ejpam-108	181	10	the	the	DET
ejpam-108	181	11	following	follow	VERB
ejpam-108	181	12	properties	property	NOUN
ejpam-108	181	13	are	be	AUX
ejpam-108	181	14	equivalent	equivalent	ADJ
ejpam-108	181	15	:	:	PUNCT
ejpam-108	181	16	1	1	X
ejpam-108	181	17	.	.	X
ejpam-108	181	18	f	f	PROPN
ejpam-108	181	19	is	be	AUX
ejpam-108	181	20	almost	almost	ADV
ejpam-108	181	21	contra	contra	PROPN
ejpam-108	181	22	b	b	NOUN
ejpam-108	181	23	-	-	ADJ
ejpam-108	181	24	continuous	continuous	ADJ
ejpam-108	181	25	;	;	PUNCT
ejpam-108	181	26	2	2	NUM
ejpam-108	181	27	.	.	X
ejpam-108	181	28	f	f	PROPN
ejpam-108	181	29	−1(cl(v	−1(cl(v	PROPN
ejpam-108	181	30	)	)	PUNCT
ejpam-108	181	31	)	)	PUNCT
ejpam-108	181	32	is	be	AUX
ejpam-108	181	33	b	b	NOUN
ejpam-108	181	34	-	-	PUNCT
ejpam-108	181	35	open	open	ADJ
ejpam-108	181	36	in	in	ADP
ejpam-108	181	37	x	x	PUNCT
ejpam-108	181	38	for	for	ADP
ejpam-108	181	39	every	every	DET
ejpam-108	181	40	v	v	NOUN
ejpam-108	181	41	∈	∈	NOUN
ejpam-108	181	42	bo(y	bo(y	NUM
ejpam-108	181	43	)	)	PUNCT
ejpam-108	181	44	;	;	PUNCT
ejpam-108	182	1	3	3	X
ejpam-108	182	2	.	.	X
ejpam-108	182	3	f	f	PROPN
ejpam-108	183	1	−1(αcl(v	−1(αcl(v	NOUN
ejpam-108	183	2	)	)	PUNCT
ejpam-108	183	3	)	)	PUNCT
ejpam-108	183	4	is	be	AUX
ejpam-108	183	5	b	b	NOUN
ejpam-108	183	6	-	-	PUNCT
ejpam-108	183	7	open	open	ADJ
ejpam-108	183	8	in	in	ADP
ejpam-108	183	9	x	x	PUNCT
ejpam-108	183	10	for	for	ADP
ejpam-108	183	11	every	every	DET
ejpam-108	183	12	v	v	NOUN
ejpam-108	183	13	∈	∈	NOUN
ejpam-108	183	14	bo(y	bo(y	NUM
ejpam-108	183	15	)	)	PUNCT
ejpam-108	183	16	.	.	PUNCT
ejpam-108	184	1	definition	definition	NOUN
ejpam-108	184	2	3.8	3.8	NUM
ejpam-108	184	3	.	.	PUNCT
ejpam-108	185	1	[	[	X
ejpam-108	185	2	26	26	NUM
ejpam-108	185	3	]	]	PUNCT
ejpam-108	185	4	a	a	DET
ejpam-108	185	5	function	function	NOUN
ejpam-108	185	6	f	f	NOUN
ejpam-108	185	7	:	:	PUNCT
ejpam-108	185	8	x	x	X
ejpam-108	185	9	→	→	SYM
ejpam-108	185	10	y	y	PROPN
ejpam-108	185	11	is	be	AUX
ejpam-108	185	12	said	say	VERB
ejpam-108	185	13	to	to	PART
ejpam-108	185	14	be	be	AUX
ejpam-108	185	15	r	r	NOUN
ejpam-108	185	16	-	-	PUNCT
ejpam-108	185	17	map	map	NOUN
ejpam-108	185	18	if	if	SCONJ
ejpam-108	185	19	f	f	PROPN
ejpam-108	185	20	−1(v	−1(v	PROPN
ejpam-108	185	21	)	)	PUNCT
ejpam-108	185	22	is	be	AUX
ejpam-108	185	23	regular	regular	ADJ
ejpam-108	185	24	open	open	ADJ
ejpam-108	185	25	in	in	ADP
ejpam-108	185	26	x	x	PUNCT
ejpam-108	185	27	for	for	ADP
ejpam-108	185	28	each	each	DET
ejpam-108	185	29	regular	regular	ADJ
ejpam-108	185	30	open	open	ADJ
ejpam-108	185	31	set	set	VERB
ejpam-108	185	32	v	v	NOUN
ejpam-108	185	33	of	of	ADP
ejpam-108	185	34	y	y	PROPN
ejpam-108	185	35	.	.	PUNCT
ejpam-108	186	1	recall	recall	VERB
ejpam-108	186	2	that	that	SCONJ
ejpam-108	186	3	a	a	DET
ejpam-108	186	4	function	function	NOUN
ejpam-108	186	5	f	f	NOUN
ejpam-108	186	6	:	:	PUNCT
ejpam-108	186	7	x	x	X
ejpam-108	186	8	→	→	SYM
ejpam-108	186	9	y	y	PROPN
ejpam-108	186	10	is	be	AUX
ejpam-108	186	11	almost	almost	ADV
ejpam-108	186	12	-	-	PUNCT
ejpam-108	186	13	continuous	continuous	ADJ
ejpam-108	186	14	if	if	SCONJ
ejpam-108	186	15	f	f	PROPN
ejpam-108	186	16	−1(v	−1(v	PROPN
ejpam-108	186	17	)	)	PUNCT
ejpam-108	186	18	is	be	AUX
ejpam-108	186	19	open	open	ADJ
ejpam-108	186	20	in	in	ADP
ejpam-108	186	21	x	x	PUNCT
ejpam-108	186	22	for	for	ADP
ejpam-108	186	23	each	each	DET
ejpam-108	186	24	regular	regular	ADJ
ejpam-108	186	25	open	open	ADJ
ejpam-108	186	26	set	set	VERB
ejpam-108	186	27	v	v	NOUN
ejpam-108	186	28	of	of	ADP
ejpam-108	186	29	y	y	PROPN
ejpam-108	186	30	.	.	PUNCT
ejpam-108	187	1	theorem	theorem	VERB
ejpam-108	187	2	3.9	3.9	NUM
ejpam-108	187	3	.	.	PUNCT
ejpam-108	188	1	if	if	SCONJ
ejpam-108	188	2	a	a	DET
ejpam-108	188	3	function	function	NOUN
ejpam-108	188	4	f	f	NOUN
ejpam-108	188	5	:	:	PUNCT
ejpam-108	188	6	x	x	X
ejpam-108	188	7	→	→	SYM
ejpam-108	188	8	y	y	PROPN
ejpam-108	188	9	is	be	AUX
ejpam-108	188	10	almost	almost	ADV
ejpam-108	188	11	contra	contra	PROPN
ejpam-108	188	12	-	-	PUNCT
ejpam-108	188	13	b	b	NOUN
ejpam-108	188	14	-	-	PUNCT
ejpam-108	188	15	continuous	continuous	ADJ
ejpam-108	188	16	and	and	CCONJ
ejpam-108	188	17	almost	almost	ADV
ejpam-108	188	18	continuous	continuous	ADJ
ejpam-108	188	19	,	,	PUNCT
ejpam-108	188	20	then	then	ADV
ejpam-108	188	21	f	f	PROPN
ejpam-108	188	22	is	be	AUX
ejpam-108	188	23	r	r	NOUN
ejpam-108	188	24	-	-	PUNCT
ejpam-108	188	25	map	map	NOUN
ejpam-108	188	26	.	.	PUNCT
ejpam-108	189	1	proof	proof	NOUN
ejpam-108	189	2	.	.	PUNCT
ejpam-108	190	1	let	let	VERB
ejpam-108	190	2	v	v	PART
ejpam-108	190	3	be	be	AUX
ejpam-108	190	4	any	any	DET
ejpam-108	190	5	regular	regular	ADJ
ejpam-108	190	6	open	open	ADJ
ejpam-108	190	7	set	set	NOUN
ejpam-108	190	8	in	in	ADP
ejpam-108	190	9	y	y	PROPN
ejpam-108	190	10	.	.	PUNCT
ejpam-108	191	1	since	since	SCONJ
ejpam-108	191	2	f	f	PROPN
ejpam-108	191	3	is	be	AUX
ejpam-108	191	4	almost	almost	ADV
ejpam-108	191	5	contra	contra	PROPN
ejpam-108	191	6	-	-	PUNCT
ejpam-108	191	7	b	b	NOUN
ejpam-108	191	8	-	-	PUNCT
ejpam-108	191	9	continuous	continuous	ADJ
ejpam-108	191	10	and	and	CCONJ
ejpam-108	191	11	contra	contra	PROPN
ejpam-108	191	12	continuous	continuous	ADJ
ejpam-108	191	13	f	f	PROPN
ejpam-108	191	14	−1(v	−1(v	PROPN
ejpam-108	191	15	)	)	PUNCT
ejpam-108	191	16	is	be	AUX
ejpam-108	191	17	b	b	NOUN
ejpam-108	191	18	-	-	PUNCT
ejpam-108	191	19	closed	closed	ADJ
ejpam-108	191	20	and	and	CCONJ
ejpam-108	191	21	open	open	ADJ
ejpam-108	191	22	,	,	PUNCT
ejpam-108	191	23	thus	thus	ADV
ejpam-108	191	24	bcl	bcl	NOUN
ejpam-108	191	25	(	(	PUNCT
ejpam-108	191	26	f	f	PROPN
ejpam-108	191	27	−1(v	−1(v	PROPN
ejpam-108	191	28	)	)	PUNCT
ejpam-108	191	29	)	)	PUNCT
ejpam-108	192	1	=	=	PUNCT
ejpam-108	192	2	f	f	PROPN
ejpam-108	192	3	−1(v	−1(v	NOUN
ejpam-108	192	4	)	)	PUNCT
ejpam-108	193	1	=	=	SYM
ejpam-108	193	2	int	int	NOUN
ejpam-108	193	3	(	(	PUNCT
ejpam-108	193	4	(	(	PUNCT
ejpam-108	193	5	f	f	X
ejpam-108	193	6	−1(v	−1(v	PROPN
ejpam-108	193	7	)	)	PUNCT
ejpam-108	193	8	)	)	PUNCT
ejpam-108	193	9	,	,	PUNCT
ejpam-108	193	10	by	by	ADP
ejpam-108	193	11	lemma	lemma	PROPN
ejpam-108	193	12	3.2	3.2	NUM
ejpam-108	193	13	we	we	PRON
ejpam-108	193	14	have	have	VERB
ejpam-108	193	15	bcl	bcl	NOUN
ejpam-108	193	16	(	(	PUNCT
ejpam-108	193	17	f	f	PROPN
ejpam-108	193	18	−1(v	−1(v	PROPN
ejpam-108	193	19	)	)	PUNCT
ejpam-108	193	20	)	)	PUNCT
ejpam-108	194	1	=	=	PUNCT
ejpam-108	194	2	f	f	PROPN
ejpam-108	194	3	−1(v	−1(v	NOUN
ejpam-108	194	4	)	)	PUNCT
ejpam-108	194	5	∪	∪	ADP
ejpam-108	194	6	[	[	X
ejpam-108	194	7	cl(int	cl(int	X
ejpam-108	194	8	(	(	PUNCT
ejpam-108	194	9	f	f	PROPN
ejpam-108	194	10	−1(v	−1(v	PROPN
ejpam-108	194	11	)	)	PUNCT
ejpam-108	194	12	)	)	PUNCT
ejpam-108	194	13	)	)	PUNCT
ejpam-108	194	14	∩	∩	NOUN
ejpam-108	194	15	int(cl	int(cl	X
ejpam-108	194	16	(	(	PUNCT
ejpam-108	194	17	f	f	PROPN
ejpam-108	194	18	−1(v	−1(v	PROPN
ejpam-108	194	19	)	)	PUNCT
ejpam-108	194	20	)	)	PUNCT
ejpam-108	194	21	)	)	PUNCT
ejpam-108	194	22	]	]	PUNCT
ejpam-108	195	1	=	=	PUNCT
ejpam-108	195	2	f	f	PROPN
ejpam-108	195	3	−1(v	−1(v	NOUN
ejpam-108	195	4	)	)	PUNCT
ejpam-108	195	5	∪	∪	ADP
ejpam-108	195	6	[	[	X
ejpam-108	195	7	cl	cl	NOUN
ejpam-108	195	8	(	(	PUNCT
ejpam-108	195	9	f	f	PROPN
ejpam-108	195	10	−1(v	−1(v	PROPN
ejpam-108	195	11	)	)	PUNCT
ejpam-108	195	12	)	)	PUNCT
ejpam-108	195	13	∩	∩	NOUN
ejpam-108	195	14	int(cl	int(cl	X
ejpam-108	195	15	(	(	PUNCT
ejpam-108	195	16	f	f	PROPN
ejpam-108	195	17	−1(v	−1(v	PROPN
ejpam-108	195	18	)	)	PUNCT
ejpam-108	195	19	)	)	PUNCT
ejpam-108	195	20	)	)	PUNCT
ejpam-108	195	21	]	]	PUNCT
ejpam-108	196	1	=	=	PUNCT
ejpam-108	196	2	f	f	PROPN
ejpam-108	196	3	−1(v	−1(v	PROPN
ejpam-108	196	4	)	)	PUNCT
ejpam-108	196	5	∪	∪	ADP
ejpam-108	196	6	int(cl	int(cl	PROPN
ejpam-108	196	7	(	(	PUNCT
ejpam-108	196	8	f	f	PROPN
ejpam-108	196	9	−1(v	−1(v	PROPN
ejpam-108	196	10	)	)	PUNCT
ejpam-108	196	11	)	)	PUNCT
ejpam-108	196	12	)	)	PUNCT
ejpam-108	197	1	=	=	SYM
ejpam-108	197	2	int(cl	int(cl	PROPN
ejpam-108	197	3	(	(	PUNCT
ejpam-108	197	4	f	f	PROPN
ejpam-108	197	5	−1(v	−1(v	PROPN
ejpam-108	197	6	)	)	PUNCT
ejpam-108	197	7	)	)	PUNCT
ejpam-108	197	8	)	)	PUNCT
ejpam-108	198	1	=	=	PUNCT
ejpam-108	198	2	f	f	PROPN
ejpam-108	198	3	−1(v	−1(v	NOUN
ejpam-108	198	4	)	)	PUNCT
ejpam-108	198	5	.	.	PUNCT
ejpam-108	199	1	we	we	PRON
ejpam-108	199	2	obtain	obtain	VERB
ejpam-108	199	3	that	that	SCONJ
ejpam-108	199	4	f	f	PROPN
ejpam-108	199	5	is	be	AUX
ejpam-108	199	6	r	r	NOUN
ejpam-108	199	7	-	-	PUNCT
ejpam-108	199	8	map	map	NOUN
ejpam-108	199	9	.	.	PUNCT
ejpam-108	200	1	a.	a.	PROPN
ejpam-108	200	2	al	al	PROPN
ejpam-108	200	3	-	-	PUNCT
ejpam-108	200	4	omari	omari	PROPN
ejpam-108	200	5	and	and	CCONJ
ejpam-108	200	6	s.	s.	PROPN
ejpam-108	200	7	noorani	noorani	PROPN
ejpam-108	200	8	/	/	SYM
ejpam-108	200	9	eur	eur	PROPN
ejpam-108	200	10	.	.	PUNCT
ejpam-108	201	1	j.	j.	PROPN
ejpam-108	201	2	pure	pure	PROPN
ejpam-108	201	3	appl	appl	PROPN
ejpam-108	201	4	.	.	PROPN
ejpam-108	201	5	math	math	PROPN
ejpam-108	201	6	,	,	PUNCT
ejpam-108	201	7	2	2	NUM
ejpam-108	201	8	(	(	PUNCT
ejpam-108	201	9	2009	2009	NUM
ejpam-108	201	10	)	)	PUNCT
ejpam-108	201	11	,	,	PUNCT
ejpam-108	201	12	(	(	PUNCT
ejpam-108	201	13	213	213	NUM
ejpam-108	201	14	-	-	SYM
ejpam-108	201	15	230	230	NUM
ejpam-108	201	16	)	)	PUNCT
ejpam-108	201	17	221	221	NUM
ejpam-108	201	18	definition	definition	NOUN
ejpam-108	201	19	3.10	3.10	NUM
ejpam-108	201	20	.	.	PUNCT
ejpam-108	202	1	[	[	X
ejpam-108	202	2	11	11	NUM
ejpam-108	202	3	]	]	PUNCT
ejpam-108	202	4	a	a	DET
ejpam-108	202	5	space	space	NOUN
ejpam-108	202	6	x	x	PUNCT
ejpam-108	202	7	is	be	AUX
ejpam-108	202	8	said	say	VERB
ejpam-108	202	9	to	to	PART
ejpam-108	202	10	be	be	AUX
ejpam-108	202	11	b	b	NOUN
ejpam-108	202	12	-	-	ADJ
ejpam-108	202	13	compact	compact	ADJ
ejpam-108	202	14	(	(	PUNCT
ejpam-108	202	15	resp	resp	NOUN
ejpam-108	202	16	.	.	PUNCT
ejpam-108	203	1	b	b	X
ejpam-108	203	2	-	-	PUNCT
ejpam-108	203	3	lindelöf	lindelöf	NOUN
ejpam-108	203	4	,	,	PUNCT
ejpam-108	203	5	countably	countably	ADV
ejpam-108	203	6	b	b	X
ejpam-108	203	7	-	-	PUNCT
ejpam-108	203	8	compact	compact	ADJ
ejpam-108	203	9	)	)	PUNCT
ejpam-108	203	10	if	if	SCONJ
ejpam-108	203	11	every	every	DET
ejpam-108	203	12	b	b	NOUN
ejpam-108	203	13	-	-	PUNCT
ejpam-108	203	14	open	open	ADJ
ejpam-108	203	15	(	(	PUNCT
ejpam-108	203	16	resp	resp	NOUN
ejpam-108	203	17	.	.	PUNCT
ejpam-108	204	1	b	b	X
ejpam-108	204	2	-	-	PUNCT
ejpam-108	204	3	open	open	ADJ
ejpam-108	204	4	,	,	PUNCT
ejpam-108	204	5	countable	countable	ADJ
ejpam-108	204	6	b	b	NOUN
ejpam-108	204	7	-	-	ADJ
ejpam-108	204	8	open	open	ADJ
ejpam-108	204	9	)	)	PUNCT
ejpam-108	204	10	cover	cover	NOUN
ejpam-108	204	11	of	of	ADP
ejpam-108	204	12	x	x	PUNCT
ejpam-108	204	13	has	have	VERB
ejpam-108	204	14	a	a	DET
ejpam-108	204	15	finite	finite	NOUN
ejpam-108	204	16	(	(	PUNCT
ejpam-108	204	17	resp	resp	NOUN
ejpam-108	204	18	.	.	PUNCT
ejpam-108	205	1	a	a	DET
ejpam-108	205	2	countable	countable	ADJ
ejpam-108	205	3	,	,	PUNCT
ejpam-108	205	4	a	a	DET
ejpam-108	205	5	finite	finite	NOUN
ejpam-108	205	6	)	)	PUNCT
ejpam-108	205	7	subcover	subcover	PROPN
ejpam-108	205	8	.	.	PUNCT
ejpam-108	206	1	definition	definition	NOUN
ejpam-108	206	2	3.11	3.11	NUM
ejpam-108	206	3	.	.	PUNCT
ejpam-108	207	1	a	a	DET
ejpam-108	207	2	space	space	NOUN
ejpam-108	207	3	x	x	PUNCT
ejpam-108	207	4	is	be	AUX
ejpam-108	207	5	said	say	VERB
ejpam-108	207	6	to	to	PART
ejpam-108	207	7	be	be	AUX
ejpam-108	207	8	s	s	NOUN
ejpam-108	207	9	-	-	NOUN
ejpam-108	207	10	lindelöf	lindelöf	NOUN
ejpam-108	207	11	[	[	X
ejpam-108	207	12	10	10	NUM
ejpam-108	207	13	]	]	X
ejpam-108	207	14	(	(	PUNCT
ejpam-108	207	15	resp	resp	NOUN
ejpam-108	207	16	.	.	PUNCT
ejpam-108	208	1	s	s	X
ejpam-108	208	2	-	-	PUNCT
ejpam-108	208	3	closed	closed	ADJ
ejpam-108	209	1	[	[	X
ejpam-108	209	2	21	21	NUM
ejpam-108	209	3	]	]	X
ejpam-108	209	4	,	,	PUNCT
ejpam-108	209	5	countably	countably	ADV
ejpam-108	209	6	s	s	VERB
ejpam-108	209	7	-	-	PUNCT
ejpam-108	209	8	closed	closed	ADJ
ejpam-108	210	1	[	[	X
ejpam-108	210	2	6	6	NUM
ejpam-108	210	3	]	]	PUNCT
ejpam-108	210	4	)	)	PUNCT
ejpam-108	210	5	if	if	SCONJ
ejpam-108	210	6	every	every	DET
ejpam-108	210	7	regular	regular	ADJ
ejpam-108	210	8	closed	closed	ADJ
ejpam-108	210	9	(	(	PUNCT
ejpam-108	210	10	resp	resp	NOUN
ejpam-108	210	11	.	.	PUNCT
ejpam-108	211	1	regular	regular	ADJ
ejpam-108	211	2	closed	closed	ADJ
ejpam-108	211	3	,	,	PUNCT
ejpam-108	211	4	countable	countable	ADJ
ejpam-108	211	5	regular	regular	ADJ
ejpam-108	211	6	closed	closed	ADJ
ejpam-108	211	7	)	)	PUNCT
ejpam-108	211	8	cover	cover	NOUN
ejpam-108	211	9	of	of	ADP
ejpam-108	211	10	x	x	PUNCT
ejpam-108	211	11	has	have	VERB
ejpam-108	211	12	a	a	DET
ejpam-108	211	13	countable	countable	ADJ
ejpam-108	211	14	(	(	PUNCT
ejpam-108	211	15	resp	resp	NOUN
ejpam-108	211	16	.	.	PUNCT
ejpam-108	212	1	a	a	DET
ejpam-108	212	2	finite	finite	NOUN
ejpam-108	212	3	,	,	PUNCT
ejpam-108	212	4	a	a	DET
ejpam-108	212	5	finite	finite	NOUN
ejpam-108	212	6	)	)	PUNCT
ejpam-108	212	7	subcover	subcover	PROPN
ejpam-108	212	8	.	.	PUNCT
ejpam-108	212	9	theorem	theorem	VERB
ejpam-108	212	10	3.12	3.12	NUM
ejpam-108	212	11	.	.	PUNCT
ejpam-108	213	1	let	let	VERB
ejpam-108	213	2	f	f	NOUN
ejpam-108	213	3	:	:	PUNCT
ejpam-108	213	4	x	x	X
ejpam-108	213	5	→	→	SYM
ejpam-108	213	6	y	y	X
ejpam-108	213	7	be	be	AUX
ejpam-108	213	8	an	an	DET
ejpam-108	213	9	almost	almost	ADV
ejpam-108	213	10	contra	contra	ADJ
ejpam-108	213	11	-	-	PUNCT
ejpam-108	213	12	b	b	NOUN
ejpam-108	213	13	-	-	PUNCT
ejpam-108	213	14	continuous	continuous	ADJ
ejpam-108	213	15	surjection	surjection	NOUN
ejpam-108	213	16	.	.	PUNCT
ejpam-108	214	1	the	the	DET
ejpam-108	214	2	following	follow	VERB
ejpam-108	214	3	statements	statement	NOUN
ejpam-108	214	4	hold	hold	VERB
ejpam-108	214	5	:	:	PUNCT
ejpam-108	215	1	1	1	X
ejpam-108	215	2	.	.	X
ejpam-108	216	1	if	if	SCONJ
ejpam-108	216	2	x	x	PRON
ejpam-108	216	3	is	be	AUX
ejpam-108	216	4	b	b	NOUN
ejpam-108	216	5	-	-	ADJ
ejpam-108	216	6	compact	compact	ADJ
ejpam-108	216	7	,	,	PUNCT
ejpam-108	216	8	then	then	ADV
ejpam-108	216	9	y	y	PROPN
ejpam-108	216	10	is	be	AUX
ejpam-108	216	11	s	s	NOUN
ejpam-108	216	12	-	-	PUNCT
ejpam-108	216	13	closed	closed	ADJ
ejpam-108	216	14	;	;	PUNCT
ejpam-108	217	1	2	2	X
ejpam-108	217	2	.	.	X
ejpam-108	217	3	if	if	SCONJ
ejpam-108	217	4	x	x	PRON
ejpam-108	217	5	is	be	AUX
ejpam-108	217	6	b	b	NOUN
ejpam-108	217	7	-	-	PUNCT
ejpam-108	217	8	lindelöf	lindelöf	NOUN
ejpam-108	217	9	,	,	PUNCT
ejpam-108	217	10	then	then	ADV
ejpam-108	217	11	y	y	PROPN
ejpam-108	217	12	is	be	AUX
ejpam-108	217	13	s	s	NOUN
ejpam-108	217	14	-	-	NOUN
ejpam-108	217	15	lindelöf	lindelöf	NOUN
ejpam-108	217	16	;	;	PUNCT
ejpam-108	217	17	3	3	X
ejpam-108	217	18	.	.	X
ejpam-108	218	1	if	if	SCONJ
ejpam-108	218	2	x	x	PRON
ejpam-108	218	3	is	be	AUX
ejpam-108	218	4	countably	countably	ADV
ejpam-108	218	5	b	b	NOUN
ejpam-108	218	6	-	-	PUNCT
ejpam-108	218	7	compact	compact	ADJ
ejpam-108	218	8	,	,	PUNCT
ejpam-108	218	9	then	then	ADV
ejpam-108	218	10	y	y	PROPN
ejpam-108	218	11	is	be	AUX
ejpam-108	218	12	countably	countably	ADV
ejpam-108	218	13	s	s	NOUN
ejpam-108	218	14	-	-	PUNCT
ejpam-108	218	15	closed	closed	ADJ
ejpam-108	218	16	.	.	PUNCT
ejpam-108	219	1	proof	proof	NOUN
ejpam-108	219	2	.	.	PUNCT
ejpam-108	220	1	we	we	PRON
ejpam-108	220	2	prove	prove	VERB
ejpam-108	220	3	only	only	ADV
ejpam-108	220	4	(	(	PUNCT
ejpam-108	220	5	1	1	NUM
ejpam-108	220	6	)	)	PUNCT
ejpam-108	220	7	.	.	PUNCT
ejpam-108	221	1	let	let	VERB
ejpam-108	221	2	{	{	PUNCT
ejpam-108	221	3	vα	vα	X
ejpam-108	221	4	:	:	PUNCT
ejpam-108	221	5	α	α	PROPN
ejpam-108	221	6	∈	∈	PROPN
ejpam-108	222	1	i	i	PRON
ejpam-108	222	2	}	}	PUNCT
ejpam-108	222	3	be	be	VERB
ejpam-108	222	4	any	any	DET
ejpam-108	222	5	regular	regular	ADJ
ejpam-108	222	6	closed	closed	ADJ
ejpam-108	222	7	cover	cover	NOUN
ejpam-108	222	8	of	of	ADP
ejpam-108	222	9	y	y	PROPN
ejpam-108	222	10	.	.	PUNCT
ejpam-108	223	1	since	since	SCONJ
ejpam-108	223	2	f	f	PROPN
ejpam-108	223	3	is	be	AUX
ejpam-108	223	4	almost	almost	ADV
ejpam-108	223	5	contra	contra	PROPN
ejpam-108	223	6	-	-	PUNCT
ejpam-108	223	7	b	b	NOUN
ejpam-108	223	8	-continuous	-continuous	ADJ
ejpam-108	223	9	,	,	PUNCT
ejpam-108	223	10	then	then	ADV
ejpam-108	223	11	{	{	PUNCT
ejpam-108	223	12	f	f	PROPN
ejpam-108	223	13	−1(vα	−1(vα	PROPN
ejpam-108	223	14	)	)	PUNCT
ejpam-108	223	15	:	:	PUNCT
ejpam-108	224	1	α	α	X
ejpam-108	224	2	∈	∈	PROPN
ejpam-108	225	1	i	i	PRON
ejpam-108	225	2	}	}	PUNCT
ejpam-108	225	3	is	be	AUX
ejpam-108	225	4	a	a	DET
ejpam-108	225	5	b	b	NOUN
ejpam-108	225	6	-	-	PUNCT
ejpam-108	225	7	open	open	ADJ
ejpam-108	225	8	cover	cover	NOUN
ejpam-108	225	9	of	of	ADP
ejpam-108	225	10	x	x	X
ejpam-108	225	11	and	and	CCONJ
ejpam-108	225	12	hence	hence	ADV
ejpam-108	225	13	there	there	PRON
ejpam-108	225	14	exists	exist	VERB
ejpam-108	225	15	a	a	DET
ejpam-108	225	16	finite	finite	NOUN
ejpam-108	225	17	subset	subset	VERB
ejpam-108	225	18	i0	i0	PROPN
ejpam-108	225	19	of	of	ADP
ejpam-108	225	20	i	i	PRON
ejpam-108	225	21	such	such	ADJ
ejpam-108	225	22	that	that	SCONJ
ejpam-108	225	23	x	x	X
ejpam-108	225	24	=	=	SYM
ejpam-108	225	25	∪	∪	X
ejpam-108	225	26	{	{	PUNCT
ejpam-108	225	27	f	f	PROPN
ejpam-108	225	28	−1(vα	−1(vα	PROPN
ejpam-108	225	29	)	)	PUNCT
ejpam-108	225	30	:	:	PUNCT
ejpam-108	225	31	α	α	PROPN
ejpam-108	225	32	∈	∈	PROPN
ejpam-108	225	33	i0	i0	PROPN
ejpam-108	225	34	}	}	PUNCT
ejpam-108	225	35	therefore	therefore	ADV
ejpam-108	225	36	we	we	PRON
ejpam-108	225	37	have	have	VERB
ejpam-108	225	38	y	y	NOUN
ejpam-108	225	39	=	=	PUNCT
ejpam-108	225	40	∪{vα	∪{vα	NOUN
ejpam-108	225	41	:	:	PUNCT
ejpam-108	225	42	α	α	PROPN
ejpam-108	225	43	∈	∈	PROPN
ejpam-108	225	44	i0	i0	PROPN
ejpam-108	225	45	}	}	PUNCT
ejpam-108	225	46	and	and	CCONJ
ejpam-108	225	47	y	y	PROPN
ejpam-108	225	48	is	be	AUX
ejpam-108	225	49	s	s	NOUN
ejpam-108	225	50	-	-	PUNCT
ejpam-108	225	51	closed	closed	ADJ
ejpam-108	225	52	.	.	PUNCT
ejpam-108	226	1	definition	definition	NOUN
ejpam-108	226	2	3.13	3.13	NUM
ejpam-108	226	3	.	.	PUNCT
ejpam-108	227	1	[	[	X
ejpam-108	227	2	22	22	NUM
ejpam-108	227	3	]	]	PUNCT
ejpam-108	227	4	a	a	DET
ejpam-108	227	5	space	space	NOUN
ejpam-108	227	6	x	x	PUNCT
ejpam-108	227	7	is	be	AUX
ejpam-108	227	8	said	say	VERB
ejpam-108	227	9	to	to	PART
ejpam-108	227	10	be	be	AUX
ejpam-108	227	11	nearly	nearly	ADV
ejpam-108	227	12	compact	compact	ADJ
ejpam-108	227	13	(	(	PUNCT
ejpam-108	227	14	resp	resp	NOUN
ejpam-108	227	15	.	.	PUNCT
ejpam-108	228	1	nearly	nearly	ADV
ejpam-108	228	2	countably	countably	ADV
ejpam-108	228	3	compact	compact	ADJ
ejpam-108	228	4	,	,	PUNCT
ejpam-108	228	5	nearly	nearly	ADV
ejpam-108	228	6	lindelöf	lindelöf	NOUN
ejpam-108	228	7	)	)	PUNCT
ejpam-108	228	8	if	if	SCONJ
ejpam-108	228	9	every	every	DET
ejpam-108	228	10	regular	regular	ADJ
ejpam-108	228	11	open	open	ADJ
ejpam-108	228	12	(	(	PUNCT
ejpam-108	228	13	resp	resp	NOUN
ejpam-108	228	14	.	.	PUNCT
ejpam-108	229	1	countable	countable	ADJ
ejpam-108	229	2	regular	regular	ADJ
ejpam-108	229	3	open	open	ADJ
ejpam-108	229	4	,	,	PUNCT
ejpam-108	229	5	regular	regular	ADJ
ejpam-108	229	6	open	open	ADJ
ejpam-108	229	7	)	)	PUNCT
ejpam-108	229	8	cover	cover	NOUN
ejpam-108	229	9	of	of	ADP
ejpam-108	229	10	x	x	PUNCT
ejpam-108	229	11	has	have	VERB
ejpam-108	229	12	a	a	DET
ejpam-108	229	13	finite	finite	NOUN
ejpam-108	229	14	(	(	PUNCT
ejpam-108	229	15	resp	resp	NOUN
ejpam-108	229	16	.	.	PUNCT
ejpam-108	230	1	a	a	DET
ejpam-108	230	2	finite	finite	NOUN
ejpam-108	230	3	,	,	PUNCT
ejpam-108	230	4	a	a	DET
ejpam-108	230	5	countably	countably	ADJ
ejpam-108	230	6	)	)	PUNCT
ejpam-108	230	7	subcover	subcover	PROPN
ejpam-108	230	8	.	.	PUNCT
ejpam-108	230	9	theorem	theorem	VERB
ejpam-108	230	10	3.14	3.14	NUM
ejpam-108	230	11	.	.	PUNCT
ejpam-108	231	1	let	let	VERB
ejpam-108	231	2	f	f	NOUN
ejpam-108	231	3	:	:	PUNCT
ejpam-108	231	4	x	x	X
ejpam-108	231	5	→	→	SYM
ejpam-108	231	6	y	y	X
ejpam-108	231	7	be	be	AUX
ejpam-108	231	8	an	an	DET
ejpam-108	231	9	almost	almost	ADV
ejpam-108	231	10	contra	contra	ADJ
ejpam-108	231	11	-	-	PUNCT
ejpam-108	231	12	b	b	NOUN
ejpam-108	231	13	-	-	PUNCT
ejpam-108	231	14	continuous	continuous	ADJ
ejpam-108	231	15	and	and	CCONJ
ejpam-108	231	16	almost	almost	ADV
ejpam-108	231	17	continuous	continuous	ADJ
ejpam-108	231	18	surjection	surjection	NOUN
ejpam-108	231	19	and	and	CCONJ
ejpam-108	231	20	x	x	NOUN
ejpam-108	231	21	is	be	AUX
ejpam-108	231	22	s	s	NOUN
ejpam-108	231	23	-	-	PROPN
ejpam-108	231	24	closed(resp	closed(resp	ADJ
ejpam-108	231	25	.	.	PUNCT
ejpam-108	232	1	nearly	nearly	ADV
ejpam-108	232	2	compact	compact	ADJ
ejpam-108	232	3	,	,	PUNCT
ejpam-108	232	4	nearly	nearly	ADV
ejpam-108	232	5	lindelöf	lindelöf	NOUN
ejpam-108	232	6	,	,	PUNCT
ejpam-108	232	7	nearly	nearly	ADV
ejpam-108	232	8	countably	countably	ADV
ejpam-108	232	9	compact	compact	ADJ
ejpam-108	232	10	,	,	PUNCT
ejpam-108	232	11	countably	countably	ADV
ejpam-108	232	12	s	s	NOUN
ejpam-108	232	13	-	-	PUNCT
ejpam-108	232	14	closed	closed	ADJ
ejpam-108	232	15	,	,	PUNCT
ejpam-108	232	16	s	s	NOUN
ejpam-108	232	17	-	-	NOUN
ejpam-108	232	18	lindelöf	lindelöf	NOUN
ejpam-108	232	19	)	)	PUNCT
ejpam-108	232	20	then	then	ADV
ejpam-108	232	21	y	y	PROPN
ejpam-108	232	22	is	be	AUX
ejpam-108	232	23	s	s	NOUN
ejpam-108	232	24	-	-	PUNCT
ejpam-108	232	25	closed	closed	ADJ
ejpam-108	232	26	(	(	PUNCT
ejpam-108	232	27	resp	resp	NOUN
ejpam-108	232	28	.	.	PUNCT
ejpam-108	233	1	nearly	nearly	ADV
ejpam-108	233	2	countably	countably	ADV
ejpam-108	233	3	compact	compact	ADJ
ejpam-108	233	4	,	,	PUNCT
ejpam-108	233	5	nearly	nearly	ADV
ejpam-108	233	6	lindelöf	lindelöf	NOUN
ejpam-108	233	7	,	,	PUNCT
ejpam-108	233	8	nearly	nearly	ADV
ejpam-108	233	9	countably	countably	ADV
ejpam-108	233	10	compact	compact	ADJ
ejpam-108	233	11	,	,	PUNCT
ejpam-108	233	12	countably	countably	ADV
ejpam-108	233	13	s	s	NOUN
ejpam-108	233	14	-	-	PUNCT
ejpam-108	233	15	closed	closed	ADJ
ejpam-108	233	16	,	,	PUNCT
ejpam-108	233	17	s	s	NOUN
ejpam-108	233	18	-	-	NOUN
ejpam-108	233	19	lindelöf	lindelöf	NOUN
ejpam-108	233	20	)	)	PUNCT
ejpam-108	233	21	.	.	PUNCT
ejpam-108	234	1	a.	a.	PROPN
ejpam-108	234	2	al	al	PROPN
ejpam-108	234	3	-	-	PUNCT
ejpam-108	234	4	omari	omari	PROPN
ejpam-108	234	5	and	and	CCONJ
ejpam-108	234	6	s.	s.	PROPN
ejpam-108	234	7	noorani	noorani	PROPN
ejpam-108	234	8	/	/	SYM
ejpam-108	234	9	eur	eur	PROPN
ejpam-108	234	10	.	.	PUNCT
ejpam-108	235	1	j.	j.	PROPN
ejpam-108	235	2	pure	pure	PROPN
ejpam-108	235	3	appl	appl	PROPN
ejpam-108	235	4	.	.	PROPN
ejpam-108	235	5	math	math	PROPN
ejpam-108	235	6	,	,	PUNCT
ejpam-108	235	7	2	2	NUM
ejpam-108	235	8	(	(	PUNCT
ejpam-108	235	9	2009	2009	NUM
ejpam-108	235	10	)	)	PUNCT
ejpam-108	235	11	,	,	PUNCT
ejpam-108	235	12	(	(	PUNCT
ejpam-108	235	13	213	213	NUM
ejpam-108	235	14	-	-	SYM
ejpam-108	235	15	230	230	NUM
ejpam-108	235	16	)	)	PUNCT
ejpam-108	235	17	222	222	NUM
ejpam-108	235	18	proof	proof	NOUN
ejpam-108	235	19	.	.	PUNCT
ejpam-108	236	1	let	let	VERB
ejpam-108	236	2	v	v	PART
ejpam-108	236	3	be	be	AUX
ejpam-108	236	4	any	any	DET
ejpam-108	236	5	regular	regular	ADJ
ejpam-108	236	6	closed	closed	ADJ
ejpam-108	236	7	set	set	NOUN
ejpam-108	236	8	on	on	ADP
ejpam-108	236	9	y	y	PROPN
ejpam-108	236	10	.	.	PUNCT
ejpam-108	237	1	then	then	ADV
ejpam-108	237	2	since	since	SCONJ
ejpam-108	237	3	f	f	PROPN
ejpam-108	237	4	is	be	AUX
ejpam-108	237	5	almost	almost	ADV
ejpam-108	237	6	contra	contra	ADJ
ejpam-108	237	7	-	-	ADJ
ejpam-108	237	8	bcontinuous	bcontinuous	ADJ
ejpam-108	237	9	and	and	CCONJ
ejpam-108	237	10	almost	almost	ADV
ejpam-108	237	11	continuous	continuous	ADJ
ejpam-108	237	12	,	,	PUNCT
ejpam-108	237	13	then	then	ADV
ejpam-108	237	14	by	by	ADP
ejpam-108	237	15	theorem	theorem	NOUN
ejpam-108	237	16	3.9	3.9	NUM
ejpam-108	237	17	f	f	NOUN
ejpam-108	237	18	is	be	AUX
ejpam-108	237	19	r	r	NOUN
ejpam-108	237	20	-	-	PUNCT
ejpam-108	237	21	map	map	NOUN
ejpam-108	237	22	.	.	PUNCT
ejpam-108	238	1	hence	hence	ADV
ejpam-108	238	2	f	f	PROPN
ejpam-108	238	3	−1(v	−1(v	PROPN
ejpam-108	238	4	)	)	PUNCT
ejpam-108	238	5	is	be	AUX
ejpam-108	238	6	regular	regular	ADV
ejpam-108	238	7	closed	closed	ADJ
ejpam-108	238	8	in	in	ADP
ejpam-108	238	9	x	x	X
ejpam-108	238	10	.	.	PUNCT
ejpam-108	239	1	let	let	VERB
ejpam-108	239	2	{	{	PUNCT
ejpam-108	239	3	vα	vα	X
ejpam-108	239	4	:	:	PUNCT
ejpam-108	239	5	α	α	PROPN
ejpam-108	239	6	∈	∈	PROPN
ejpam-108	240	1	i	i	PRON
ejpam-108	240	2	}	}	PUNCT
ejpam-108	240	3	be	be	VERB
ejpam-108	240	4	any	any	DET
ejpam-108	240	5	regular	regular	ADJ
ejpam-108	240	6	closed	closed	ADJ
ejpam-108	240	7	cover	cover	NOUN
ejpam-108	240	8	of	of	ADP
ejpam-108	240	9	y	y	PROPN
ejpam-108	240	10	.	.	PUNCT
ejpam-108	241	1	then	then	ADV
ejpam-108	241	2	{	{	PUNCT
ejpam-108	241	3	f	f	PROPN
ejpam-108	241	4	−1(vα	−1(vα	PROPN
ejpam-108	241	5	)	)	PUNCT
ejpam-108	241	6	:	:	PUNCT
ejpam-108	242	1	α	α	X
ejpam-108	242	2	∈	∈	PROPN
ejpam-108	243	1	i	i	PRON
ejpam-108	243	2	}	}	PUNCT
ejpam-108	243	3	is	be	AUX
ejpam-108	243	4	a	a	DET
ejpam-108	243	5	regular	regular	ADJ
ejpam-108	243	6	closed	closed	ADJ
ejpam-108	243	7	cover	cover	NOUN
ejpam-108	243	8	of	of	ADP
ejpam-108	243	9	x	x	X
ejpam-108	243	10	and	and	CCONJ
ejpam-108	243	11	since	since	SCONJ
ejpam-108	243	12	x	x	PRON
ejpam-108	243	13	is	be	AUX
ejpam-108	243	14	s	s	NOUN
ejpam-108	243	15	-	-	PUNCT
ejpam-108	243	16	closed	closed	ADJ
ejpam-108	243	17	,	,	PUNCT
ejpam-108	243	18	there	there	PRON
ejpam-108	243	19	exists	exist	VERB
ejpam-108	243	20	a	a	DET
ejpam-108	243	21	finite	finite	NOUN
ejpam-108	243	22	subset	subset	VERB
ejpam-108	243	23	i0	i0	PROPN
ejpam-108	243	24	of	of	ADP
ejpam-108	243	25	i	i	PRON
ejpam-108	243	26	such	such	ADJ
ejpam-108	243	27	that	that	SCONJ
ejpam-108	243	28	x	x	X
ejpam-108	243	29	=	=	SYM
ejpam-108	243	30	∪	∪	X
ejpam-108	243	31	{	{	PUNCT
ejpam-108	243	32	f	f	PROPN
ejpam-108	243	33	−1(vα	−1(vα	PROPN
ejpam-108	243	34	)	)	PUNCT
ejpam-108	243	35	:	:	PUNCT
ejpam-108	243	36	α	α	PROPN
ejpam-108	243	37	∈	∈	PROPN
ejpam-108	243	38	i0	i0	PROPN
ejpam-108	243	39	}	}	PUNCT
ejpam-108	243	40	.	.	PUNCT
ejpam-108	244	1	since	since	SCONJ
ejpam-108	244	2	f	f	PROPN
ejpam-108	244	3	is	be	AUX
ejpam-108	244	4	surjection	surjection	NOUN
ejpam-108	244	5	,	,	PUNCT
ejpam-108	244	6	we	we	PRON
ejpam-108	244	7	obtain	obtain	VERB
ejpam-108	244	8	y	y	NOUN
ejpam-108	244	9	=	=	PUNCT
ejpam-108	245	1	∪{vα	∪{vα	NOUN
ejpam-108	245	2	:	:	PUNCT
ejpam-108	245	3	α	α	PROPN
ejpam-108	245	4	∈	∈	PROPN
ejpam-108	245	5	i0	i0	PROPN
ejpam-108	245	6	}	}	PUNCT
ejpam-108	245	7	.	.	PUNCT
ejpam-108	246	1	this	this	PRON
ejpam-108	246	2	shows	show	VERB
ejpam-108	246	3	that	that	SCONJ
ejpam-108	246	4	y	y	PROPN
ejpam-108	246	5	is	be	AUX
ejpam-108	246	6	s	s	NOUN
ejpam-108	246	7	-	-	PUNCT
ejpam-108	246	8	closed	closed	ADJ
ejpam-108	246	9	.	.	PUNCT
ejpam-108	247	1	the	the	DET
ejpam-108	247	2	other	other	ADJ
ejpam-108	247	3	proofs	proof	NOUN
ejpam-108	247	4	are	be	AUX
ejpam-108	247	5	similar	similar	ADJ
ejpam-108	247	6	.	.	PUNCT
ejpam-108	248	1	theorem	theorem	VERB
ejpam-108	248	2	3.15	3.15	NUM
ejpam-108	248	3	.	.	PUNCT
ejpam-108	249	1	if	if	SCONJ
ejpam-108	249	2	f	f	PROPN
ejpam-108	249	3	:	:	PUNCT
ejpam-108	249	4	x	x	X
ejpam-108	249	5	→	→	SYM
ejpam-108	249	6	y	y	PROPN
ejpam-108	249	7	is	be	AUX
ejpam-108	249	8	contra	contra	PROPN
ejpam-108	249	9	-	-	PUNCT
ejpam-108	249	10	b	b	NOUN
ejpam-108	249	11	-	-	PUNCT
ejpam-108	249	12	continuous	continuous	ADJ
ejpam-108	249	13	and	and	CCONJ
ejpam-108	249	14	a	a	PRON
ejpam-108	249	15	is	be	AUX
ejpam-108	249	16	b	b	NOUN
ejpam-108	249	17	-	-	ADJ
ejpam-108	249	18	compact	compact	ADJ
ejpam-108	249	19	relative	relative	NOUN
ejpam-108	249	20	to	to	ADP
ejpam-108	249	21	x	x	PRON
ejpam-108	249	22	,	,	PUNCT
ejpam-108	249	23	then	then	ADV
ejpam-108	249	24	f	f	X
ejpam-108	249	25	(	(	PUNCT
ejpam-108	249	26	a	a	PRON
ejpam-108	249	27	)	)	PUNCT
ejpam-108	249	28	is	be	AUX
ejpam-108	249	29	strongly	strongly	ADV
ejpam-108	249	30	s	s	NOUN
ejpam-108	249	31	-	-	PUNCT
ejpam-108	249	32	closed	closed	ADJ
ejpam-108	249	33	in	in	ADP
ejpam-108	249	34	y	y	PROPN
ejpam-108	249	35	.	.	PUNCT
ejpam-108	250	1	proof	proof	NOUN
ejpam-108	250	2	.	.	PUNCT
ejpam-108	251	1	let	let	VERB
ejpam-108	251	2	{	{	PUNCT
ejpam-108	251	3	vi	vi	VERB
ejpam-108	251	4	:	:	PUNCT
ejpam-108	251	5	i	i	PRON
ejpam-108	251	6	∈	∈	PROPN
ejpam-108	252	1	i	i	PRON
ejpam-108	252	2	}	}	PUNCT
ejpam-108	252	3	be	be	VERB
ejpam-108	252	4	any	any	DET
ejpam-108	252	5	cover	cover	NOUN
ejpam-108	252	6	of	of	ADP
ejpam-108	252	7	f	f	PROPN
ejpam-108	252	8	(	(	PUNCT
ejpam-108	252	9	a	a	NOUN
ejpam-108	252	10	)	)	PUNCT
ejpam-108	252	11	by	by	ADP
ejpam-108	252	12	closed	closed	ADJ
ejpam-108	252	13	sets	set	NOUN
ejpam-108	252	14	of	of	ADP
ejpam-108	252	15	the	the	DET
ejpam-108	252	16	subspace	subspace	NOUN
ejpam-108	252	17	f	f	PROPN
ejpam-108	252	18	(	(	PUNCT
ejpam-108	252	19	a	a	NOUN
ejpam-108	252	20	)	)	PUNCT
ejpam-108	252	21	.	.	PUNCT
ejpam-108	253	1	for	for	ADP
ejpam-108	253	2	i	i	PRON
ejpam-108	253	3	∈	∈	PROPN
ejpam-108	253	4	i	i	PRON
ejpam-108	253	5	,	,	PUNCT
ejpam-108	253	6	there	there	PRON
ejpam-108	253	7	exists	exist	VERB
ejpam-108	253	8	a	a	DET
ejpam-108	253	9	closed	closed	ADJ
ejpam-108	253	10	set	set	VERB
ejpam-108	253	11	ai	ai	NOUN
ejpam-108	253	12	of	of	ADP
ejpam-108	253	13	y	y	PRON
ejpam-108	253	14	such	such	ADJ
ejpam-108	253	15	that	that	PRON
ejpam-108	253	16	vi	vi	NOUN
ejpam-108	253	17	=	=	NOUN
ejpam-108	253	18	ai	ai	PROPN
ejpam-108	253	19	∩	∩	ADJ
ejpam-108	253	20	f	f	X
ejpam-108	253	21	(	(	PUNCT
ejpam-108	253	22	a	a	NOUN
ejpam-108	253	23	)	)	PUNCT
ejpam-108	253	24	.	.	PUNCT
ejpam-108	254	1	for	for	ADP
ejpam-108	254	2	each	each	DET
ejpam-108	254	3	x	x	SYM
ejpam-108	254	4	∈	∈	PROPN
ejpam-108	254	5	a	a	PRON
ejpam-108	254	6	,	,	PUNCT
ejpam-108	254	7	there	there	PRON
ejpam-108	254	8	exists	exist	VERB
ejpam-108	254	9	i(x	i(x	NOUN
ejpam-108	254	10	)	)	PUNCT
ejpam-108	254	11	∈	∈	PROPN
ejpam-108	255	1	i	i	PRON
ejpam-108	255	2	such	such	VERB
ejpam-108	255	3	that	that	SCONJ
ejpam-108	255	4	f	f	PROPN
ejpam-108	255	5	(	(	PUNCT
ejpam-108	255	6	x	x	X
ejpam-108	255	7	)	)	PUNCT
ejpam-108	255	8	∈	∈	NOUN
ejpam-108	255	9	ai(x	ai(x	NUM
ejpam-108	255	10	)	)	PUNCT
ejpam-108	255	11	and	and	CCONJ
ejpam-108	255	12	by	by	ADP
ejpam-108	255	13	theorem	theorem	NOUN
ejpam-108	255	14	3.1	3.1	NUM
ejpam-108	255	15	in	in	ADP
ejpam-108	255	16	[	[	PUNCT
ejpam-108	255	17	13	13	NUM
ejpam-108	255	18	]	]	PUNCT
ejpam-108	255	19	,	,	PUNCT
ejpam-108	255	20	there	there	PRON
ejpam-108	255	21	exists	exist	VERB
ejpam-108	255	22	ux	ux	PROPN
ejpam-108	255	23	∈	∈	PROPN
ejpam-108	255	24	bo(x	bo(x	NUM
ejpam-108	255	25	,	,	PUNCT
ejpam-108	255	26	x	x	X
ejpam-108	255	27	)	)	PUNCT
ejpam-108	255	28	such	such	ADJ
ejpam-108	255	29	that	that	SCONJ
ejpam-108	255	30	f	f	PROPN
ejpam-108	255	31	(	(	PUNCT
ejpam-108	255	32	ux	ux	PROPN
ejpam-108	255	33	)	)	PUNCT
ejpam-108	255	34	⊆	⊆	NUM
ejpam-108	255	35	ai(x	ai(x	NUM
ejpam-108	255	36	)	)	PUNCT
ejpam-108	255	37	.	.	PUNCT
ejpam-108	256	1	since	since	SCONJ
ejpam-108	256	2	the	the	DET
ejpam-108	256	3	family	family	NOUN
ejpam-108	256	4	{	{	PUNCT
ejpam-108	256	5	ux	ux	NOUN
ejpam-108	256	6	:	:	PUNCT
ejpam-108	256	7	x	x	X
ejpam-108	256	8	∈	∈	PROPN
ejpam-108	256	9	a	a	PRON
ejpam-108	256	10	}	}	PUNCT
ejpam-108	256	11	is	be	AUX
ejpam-108	256	12	a	a	DET
ejpam-108	256	13	cover	cover	NOUN
ejpam-108	256	14	of	of	ADP
ejpam-108	256	15	a	a	PRON
ejpam-108	256	16	by	by	ADP
ejpam-108	256	17	b	b	NOUN
ejpam-108	256	18	-	-	PUNCT
ejpam-108	256	19	open	open	ADJ
ejpam-108	256	20	sets	set	NOUN
ejpam-108	256	21	of	of	ADP
ejpam-108	256	22	x	x	SYM
ejpam-108	256	23	,	,	PUNCT
ejpam-108	256	24	there	there	PRON
ejpam-108	256	25	exists	exist	VERB
ejpam-108	256	26	a	a	DET
ejpam-108	256	27	finite	finite	NOUN
ejpam-108	256	28	subset	subset	VERB
ejpam-108	256	29	a0	a0	NOUN
ejpam-108	256	30	of	of	ADP
ejpam-108	256	31	a	a	DET
ejpam-108	256	32	such	such	ADJ
ejpam-108	256	33	that	that	DET
ejpam-108	256	34	a⊆	a⊆	PROPN
ejpam-108	256	35	∪{ux	∪{ux	NOUN
ejpam-108	256	36	:	:	PUNCT
ejpam-108	256	37	x	x	SYM
ejpam-108	256	38	∈	∈	PROPN
ejpam-108	256	39	a0	a0	PROPN
ejpam-108	256	40	}	}	PUNCT
ejpam-108	256	41	.	.	PUNCT
ejpam-108	257	1	therefore	therefore	ADV
ejpam-108	257	2	,	,	PUNCT
ejpam-108	257	3	we	we	PRON
ejpam-108	257	4	obtain	obtain	VERB
ejpam-108	257	5	f	f	X
ejpam-108	257	6	(	(	PUNCT
ejpam-108	257	7	a	a	NOUN
ejpam-108	257	8	)	)	PUNCT
ejpam-108	257	9	⊆	⊆	NUM
ejpam-108	257	10	∪	∪	NOUN
ejpam-108	257	11	{	{	PUNCT
ejpam-108	257	12	f	f	PROPN
ejpam-108	257	13	(	(	PUNCT
ejpam-108	257	14	ux	ux	PROPN
ejpam-108	257	15	)	)	PUNCT
ejpam-108	257	16	:	:	PUNCT
ejpam-108	258	1	x	x	X
ejpam-108	258	2	∈	∈	PROPN
ejpam-108	258	3	a0	a0	PROPN
ejpam-108	258	4	}	}	PUNCT
ejpam-108	258	5	.	.	PUNCT
ejpam-108	259	1	which	which	PRON
ejpam-108	259	2	is	be	AUX
ejpam-108	259	3	a	a	DET
ejpam-108	259	4	subset	subset	NOUN
ejpam-108	259	5	of	of	ADP
ejpam-108	259	6	∪{ai(x	∪{ai(x	NOUN
ejpam-108	259	7	)	)	PUNCT
ejpam-108	259	8	:	:	PUNCT
ejpam-108	260	1	x	x	X
ejpam-108	260	2	∈	∈	PROPN
ejpam-108	260	3	a0	a0	PROPN
ejpam-108	260	4	}	}	PUNCT
ejpam-108	260	5	.	.	PUNCT
ejpam-108	261	1	thus	thus	ADV
ejpam-108	261	2	f	f	X
ejpam-108	261	3	(	(	PUNCT
ejpam-108	261	4	a	a	NOUN
ejpam-108	261	5	)	)	PUNCT
ejpam-108	261	6	=	=	SYM
ejpam-108	261	7	∪{vi(x	∪{vi(x	ADJ
ejpam-108	261	8	)	)	PUNCT
ejpam-108	261	9	:	:	PUNCT
ejpam-108	262	1	x	x	X
ejpam-108	262	2	∈	∈	PROPN
ejpam-108	262	3	a0	a0	NOUN
ejpam-108	262	4	}	}	PUNCT
ejpam-108	262	5	and	and	CCONJ
ejpam-108	262	6	hence	hence	ADV
ejpam-108	262	7	f	f	X
ejpam-108	262	8	(	(	PUNCT
ejpam-108	262	9	a	a	X
ejpam-108	262	10	)	)	PUNCT
ejpam-108	262	11	is	be	AUX
ejpam-108	262	12	strongly	strongly	ADV
ejpam-108	262	13	s	s	NOUN
ejpam-108	262	14	-	-	PUNCT
ejpam-108	262	15	closed	closed	ADJ
ejpam-108	262	16	.	.	PUNCT
ejpam-108	263	1	corollary	corollary	NOUN
ejpam-108	263	2	3.16	3.16	NUM
ejpam-108	263	3	.	.	PUNCT
ejpam-108	264	1	if	if	SCONJ
ejpam-108	264	2	f	f	PROPN
ejpam-108	264	3	:	:	PUNCT
ejpam-108	264	4	x	x	X
ejpam-108	264	5	→	→	SYM
ejpam-108	264	6	y	y	PROPN
ejpam-108	264	7	is	be	AUX
ejpam-108	264	8	contra	contra	PROPN
ejpam-108	264	9	-	-	PUNCT
ejpam-108	264	10	b	b	ADJ
ejpam-108	264	11	-	-	PUNCT
ejpam-108	264	12	continuous	continuous	ADJ
ejpam-108	264	13	surjection	surjection	NOUN
ejpam-108	264	14	and	and	CCONJ
ejpam-108	264	15	x	x	NOUN
ejpam-108	264	16	is	be	AUX
ejpam-108	264	17	b	b	NOUN
ejpam-108	264	18	-	-	ADJ
ejpam-108	264	19	compact	compact	ADJ
ejpam-108	264	20	then	then	ADV
ejpam-108	264	21	y	y	PROPN
ejpam-108	264	22	is	be	AUX
ejpam-108	264	23	strongly	strongly	ADV
ejpam-108	264	24	s	s	NOUN
ejpam-108	264	25	-	-	PUNCT
ejpam-108	264	26	closed	closed	ADJ
ejpam-108	264	27	.	.	PUNCT
ejpam-108	265	1	definition	definition	NOUN
ejpam-108	265	2	3.17	3.17	NUM
ejpam-108	265	3	.	.	PUNCT
ejpam-108	266	1	a	a	DET
ejpam-108	266	2	function	function	NOUN
ejpam-108	266	3	f	f	NOUN
ejpam-108	266	4	:	:	PUNCT
ejpam-108	266	5	x	x	X
ejpam-108	266	6	→	→	SYM
ejpam-108	266	7	y	y	PROPN
ejpam-108	266	8	is	be	AUX
ejpam-108	266	9	almost	almost	ADV
ejpam-108	266	10	weakly	weakly	ADV
ejpam-108	266	11	continuous	continuous	ADJ
ejpam-108	266	12	[	[	X
ejpam-108	266	13	12	12	NUM
ejpam-108	266	14	]	]	PUNCT
ejpam-108	266	15	(	(	PUNCT
ejpam-108	266	16	resp	resp	NOUN
ejpam-108	266	17	.	.	PUNCT
ejpam-108	267	1	almost	almost	ADV
ejpam-108	267	2	weakly	weakly	ADV
ejpam-108	267	3	b	b	NOUN
ejpam-108	267	4	-	-	ADJ
ejpam-108	267	5	continuous	continuous	ADJ
ejpam-108	267	6	)	)	PUNCT
ejpam-108	267	7	if	if	SCONJ
ejpam-108	267	8	for	for	ADP
ejpam-108	267	9	each	each	DET
ejpam-108	267	10	x	x	SYM
ejpam-108	267	11	∈	∈	PROPN
ejpam-108	267	12	x	x	X
ejpam-108	267	13	and	and	CCONJ
ejpam-108	267	14	each	each	DET
ejpam-108	267	15	open	open	ADJ
ejpam-108	267	16	set	set	VERB
ejpam-108	267	17	v	v	NOUN
ejpam-108	267	18	containing	contain	VERB
ejpam-108	267	19	f	f	X
ejpam-108	267	20	(	(	PUNCT
ejpam-108	267	21	x	x	X
ejpam-108	267	22	)	)	PUNCT
ejpam-108	267	23	there	there	PRON
ejpam-108	267	24	exists	exist	VERB
ejpam-108	267	25	u	u	PROPN
ejpam-108	267	26	∈	∈	PROPN
ejpam-108	267	27	po(x	po(x	PUNCT
ejpam-108	267	28	,	,	PUNCT
ejpam-108	267	29	x	x	X
ejpam-108	267	30	)	)	PUNCT
ejpam-108	267	31	(	(	PUNCT
ejpam-108	267	32	resp	resp	NOUN
ejpam-108	267	33	.	.	PUNCT
ejpam-108	268	1	u	u	PROPN
ejpam-108	268	2	∈	∈	PROPN
ejpam-108	268	3	bo(x	bo(x	NUM
ejpam-108	268	4	,	,	PUNCT
ejpam-108	268	5	x	x	NOUN
ejpam-108	268	6	)	)	PUNCT
ejpam-108	268	7	)	)	PUNCT
ejpam-108	269	1	such	such	ADJ
ejpam-108	269	2	that	that	SCONJ
ejpam-108	269	3	f	f	PROPN
ejpam-108	269	4	(	(	PUNCT
ejpam-108	269	5	u)⊆	u)⊆	NUM
ejpam-108	269	6	cl(v	cl(v	NOUN
ejpam-108	269	7	)	)	PUNCT
ejpam-108	269	8	.	.	PUNCT
ejpam-108	270	1	definition	definition	NOUN
ejpam-108	270	2	3.18	3.18	NUM
ejpam-108	270	3	.	.	PUNCT
ejpam-108	271	1	[	[	X
ejpam-108	271	2	9	9	NUM
ejpam-108	271	3	]	]	PUNCT
ejpam-108	271	4	a	a	DET
ejpam-108	271	5	function	function	NOUN
ejpam-108	271	6	f	f	NOUN
ejpam-108	271	7	:	:	PUNCT
ejpam-108	271	8	x	x	X
ejpam-108	271	9	→	→	SYM
ejpam-108	271	10	y	y	PROPN
ejpam-108	271	11	is	be	AUX
ejpam-108	271	12	(	(	PUNCT
ejpam-108	271	13	θ	θ	PROPN
ejpam-108	271	14	,	,	PUNCT
ejpam-108	271	15	s)-continuous	s)-continuous	ADJ
ejpam-108	271	16	if	if	SCONJ
ejpam-108	271	17	the	the	DET
ejpam-108	271	18	preimage	preimage	NOUN
ejpam-108	271	19	of	of	ADP
ejpam-108	271	20	every	every	DET
ejpam-108	271	21	regular	regular	ADJ
ejpam-108	271	22	open	open	ADJ
ejpam-108	271	23	subset	subset	NOUN
ejpam-108	271	24	of	of	ADP
ejpam-108	271	25	y	y	PROPN
ejpam-108	271	26	is	be	AUX
ejpam-108	271	27	closed	close	VERB
ejpam-108	271	28	in	in	ADP
ejpam-108	271	29	x.	x.	NOUN
ejpam-108	271	30	the	the	DET
ejpam-108	271	31	following	follow	VERB
ejpam-108	271	32	examples	example	NOUN
ejpam-108	271	33	will	will	AUX
ejpam-108	271	34	show	show	VERB
ejpam-108	271	35	that	that	SCONJ
ejpam-108	271	36	the	the	DET
ejpam-108	271	37	concepts	concept	NOUN
ejpam-108	271	38	of	of	ADP
ejpam-108	271	39	almost	almost	ADV
ejpam-108	271	40	,	,	PUNCT
ejpam-108	271	41	contra	contra	PROPN
ejpam-108	271	42	-	-	ADJ
ejpam-108	271	43	b	b	NOUN
ejpam-108	271	44	-	-	PUNCT
ejpam-108	271	45	continuity	continuity	NOUN
ejpam-108	271	46	,	,	PUNCT
ejpam-108	271	47	almost	almost	ADV
ejpam-108	271	48	contra	contra	PROPN
ejpam-108	271	49	-	-	PUNCT
ejpam-108	271	50	b	b	NOUN
ejpam-108	271	51	-	-	PUNCT
ejpam-108	271	52	continuity	continuity	NOUN
ejpam-108	271	53	,	,	PUNCT
ejpam-108	271	54	almost	almost	ADV
ejpam-108	271	55	weak	weak	ADJ
ejpam-108	271	56	b	b	NOUN
ejpam-108	271	57	-	-	PUNCT
ejpam-108	271	58	continuity	continuity	NOUN
ejpam-108	271	59	,	,	PUNCT
ejpam-108	271	60	almost	almost	ADV
ejpam-108	271	61	contra	contra	NOUN
ejpam-108	271	62	-	-	NOUN
ejpam-108	271	63	precontinuity	precontinuity	NOUN
ejpam-108	271	64	,	,	PUNCT
ejpam-108	271	65	almost	almost	ADV
ejpam-108	271	66	weak	weak	ADJ
ejpam-108	271	67	-	-	PUNCT
ejpam-108	271	68	continuity	continuity	NOUN
ejpam-108	271	69	are	be	AUX
ejpam-108	271	70	independent	independent	ADJ
ejpam-108	271	71	from	from	ADP
ejpam-108	271	72	each	each	DET
ejpam-108	271	73	other	other	ADJ
ejpam-108	271	74	.	.	PUNCT
ejpam-108	272	1	a.	a.	PROPN
ejpam-108	272	2	al	al	PROPN
ejpam-108	272	3	-	-	PUNCT
ejpam-108	272	4	omari	omari	PROPN
ejpam-108	272	5	and	and	CCONJ
ejpam-108	272	6	s.	s.	PROPN
ejpam-108	272	7	noorani	noorani	PROPN
ejpam-108	272	8	/	/	SYM
ejpam-108	272	9	eur	eur	PROPN
ejpam-108	272	10	.	.	PUNCT
ejpam-108	273	1	j.	j.	PROPN
ejpam-108	273	2	pure	pure	PROPN
ejpam-108	273	3	appl	appl	PROPN
ejpam-108	273	4	.	.	PROPN
ejpam-108	273	5	math	math	PROPN
ejpam-108	273	6	,	,	PUNCT
ejpam-108	273	7	2	2	NUM
ejpam-108	273	8	(	(	PUNCT
ejpam-108	273	9	2009	2009	NUM
ejpam-108	273	10	)	)	PUNCT
ejpam-108	273	11	,	,	PUNCT
ejpam-108	273	12	(	(	PUNCT
ejpam-108	273	13	213	213	NUM
ejpam-108	273	14	-	-	SYM
ejpam-108	273	15	230	230	NUM
ejpam-108	273	16	)	)	PUNCT
ejpam-108	273	17	223	223	NUM
ejpam-108	273	18	example	example	NOUN
ejpam-108	273	19	3.19	3.19	NUM
ejpam-108	273	20	.	.	PUNCT
ejpam-108	274	1	let	let	VERB
ejpam-108	274	2	x	x	PUNCT
ejpam-108	274	3	=	=	PRON
ejpam-108	274	4	{	{	PUNCT
ejpam-108	274	5	a	a	DET
ejpam-108	274	6	,	,	PUNCT
ejpam-108	274	7	b	b	NOUN
ejpam-108	274	8	,	,	PUNCT
ejpam-108	274	9	c	c	NOUN
ejpam-108	274	10	}	}	PUNCT
ejpam-108	274	11	,	,	PUNCT
ejpam-108	274	12	τ=	τ=	X
ejpam-108	274	13	{	{	PUNCT
ejpam-108	274	14	x	x	PROPN
ejpam-108	274	15	,	,	PUNCT
ejpam-108	274	16	φ	φ	PROPN
ejpam-108	274	17	,	,	PUNCT
ejpam-108	274	18	{	{	PUNCT
ejpam-108	274	19	a	a	X
ejpam-108	274	20	}	}	PUNCT
ejpam-108	274	21	,	,	PUNCT
ejpam-108	274	22	{	{	PUNCT
ejpam-108	274	23	b	b	NOUN
ejpam-108	274	24	}	}	PUNCT
ejpam-108	274	25	,	,	PUNCT
ejpam-108	274	26	{	{	PUNCT
ejpam-108	274	27	a	a	PRON
ejpam-108	274	28	,	,	PUNCT
ejpam-108	274	29	b	b	NOUN
ejpam-108	274	30	}	}	PUNCT
ejpam-108	274	31	}	}	PUNCT
ejpam-108	274	32	and	and	CCONJ
ejpam-108	274	33	σ	σ	X
ejpam-108	274	34	=	=	SYM
ejpam-108	274	35	{	{	PUNCT
ejpam-108	274	36	x	x	PROPN
ejpam-108	274	37	,	,	PUNCT
ejpam-108	274	38	φ	φ	PROPN
ejpam-108	274	39	,	,	PUNCT
ejpam-108	274	40	{	{	PUNCT
ejpam-108	274	41	b	b	NOUN
ejpam-108	274	42	}	}	PUNCT
ejpam-108	274	43	,	,	PUNCT
ejpam-108	274	44	{	{	PUNCT
ejpam-108	274	45	c	c	X
ejpam-108	274	46	}	}	PUNCT
ejpam-108	274	47	,	,	PUNCT
ejpam-108	274	48	{	{	PUNCT
ejpam-108	274	49	b	b	X
ejpam-108	274	50	,	,	PUNCT
ejpam-108	274	51	c	c	NOUN
ejpam-108	274	52	}	}	PUNCT
ejpam-108	274	53	}	}	PUNCT
ejpam-108	274	54	.	.	PUNCT
ejpam-108	275	1	then	then	ADV
ejpam-108	275	2	rc(x	rc(x	VERB
ejpam-108	275	3	,	,	PUNCT
ejpam-108	275	4	τ	τ	X
ejpam-108	275	5	)	)	PUNCT
ejpam-108	275	6	=	=	PRON
ejpam-108	276	1	{	{	PUNCT
ejpam-108	276	2	x	x	PROPN
ejpam-108	276	3	,	,	PUNCT
ejpam-108	276	4	φ	φ	PROPN
ejpam-108	276	5	,	,	PUNCT
ejpam-108	276	6	{	{	PUNCT
ejpam-108	276	7	b	b	NOUN
ejpam-108	276	8	,	,	PUNCT
ejpam-108	276	9	c	c	NOUN
ejpam-108	276	10	}	}	PUNCT
ejpam-108	276	11	,	,	PUNCT
ejpam-108	276	12	{	{	PUNCT
ejpam-108	276	13	a	a	PRON
ejpam-108	276	14	,	,	PUNCT
ejpam-108	276	15	c	c	NOUN
ejpam-108	276	16	}	}	PUNCT
ejpam-108	276	17	}	}	PUNCT
ejpam-108	276	18	and	and	CCONJ
ejpam-108	276	19	bo(x	bo(x	NUM
ejpam-108	276	20	,	,	PUNCT
ejpam-108	276	21	σ	σ	PROPN
ejpam-108	276	22	)	)	PUNCT
ejpam-108	276	23	=	=	PRON
ejpam-108	276	24	{	{	PUNCT
ejpam-108	276	25	x	x	PROPN
ejpam-108	276	26	,	,	PUNCT
ejpam-108	276	27	φ	φ	PROPN
ejpam-108	276	28	,	,	PUNCT
ejpam-108	276	29	{	{	PUNCT
ejpam-108	276	30	b	b	NOUN
ejpam-108	276	31	}	}	PUNCT
ejpam-108	276	32	,	,	PUNCT
ejpam-108	276	33	{	{	PUNCT
ejpam-108	276	34	c	c	X
ejpam-108	276	35	}	}	PUNCT
ejpam-108	276	36	,	,	PUNCT
ejpam-108	276	37	{	{	PUNCT
ejpam-108	276	38	b	b	X
ejpam-108	276	39	,	,	PUNCT
ejpam-108	276	40	c	c	NOUN
ejpam-108	276	41	}	}	PUNCT
ejpam-108	276	42	,	,	PUNCT
ejpam-108	276	43	{	{	PUNCT
ejpam-108	276	44	a	a	X
ejpam-108	276	45	,	,	PUNCT
ejpam-108	276	46	c	c	NOUN
ejpam-108	276	47	}	}	PUNCT
ejpam-108	276	48	,	,	PUNCT
ejpam-108	276	49	{	{	PUNCT
ejpam-108	276	50	a	a	PRON
ejpam-108	276	51	,	,	PUNCT
ejpam-108	276	52	b	b	NOUN
ejpam-108	276	53	}	}	PUNCT
ejpam-108	276	54	}	}	PUNCT
ejpam-108	276	55	,	,	PUNCT
ejpam-108	276	56	po(x	po(x	PUNCT
ejpam-108	276	57	,	,	PUNCT
ejpam-108	276	58	σ	σ	X
ejpam-108	276	59	)	)	PUNCT
ejpam-108	276	60	=	=	PRON
ejpam-108	276	61	{	{	PUNCT
ejpam-108	276	62	x	x	PROPN
ejpam-108	276	63	,	,	PUNCT
ejpam-108	276	64	φ	φ	PROPN
ejpam-108	276	65	,	,	PUNCT
ejpam-108	276	66	{	{	PUNCT
ejpam-108	276	67	b	b	NOUN
ejpam-108	276	68	}	}	PUNCT
ejpam-108	276	69	,	,	PUNCT
ejpam-108	276	70	{	{	PUNCT
ejpam-108	276	71	c	c	X
ejpam-108	276	72	}	}	PUNCT
ejpam-108	276	73	,	,	PUNCT
ejpam-108	276	74	{	{	PUNCT
ejpam-108	276	75	b	b	X
ejpam-108	276	76	,	,	PUNCT
ejpam-108	276	77	c	c	NOUN
ejpam-108	276	78	}	}	PUNCT
ejpam-108	276	79	}	}	PUNCT
ejpam-108	276	80	.	.	PUNCT
ejpam-108	277	1	let	let	VERB
ejpam-108	277	2	f	f	NOUN
ejpam-108	277	3	:	:	PUNCT
ejpam-108	277	4	(	(	PUNCT
ejpam-108	277	5	x	x	X
ejpam-108	277	6	,	,	PUNCT
ejpam-108	277	7	σ	σ	PROPN
ejpam-108	277	8	)	)	PUNCT
ejpam-108	277	9	→	→	SYM
ejpam-108	277	10	(	(	PUNCT
ejpam-108	277	11	x	x	X
ejpam-108	277	12	,	,	PUNCT
ejpam-108	277	13	τ	τ	X
ejpam-108	277	14	)	)	PUNCT
ejpam-108	277	15	be	be	VERB
ejpam-108	277	16	the	the	DET
ejpam-108	277	17	identity	identity	NOUN
ejpam-108	277	18	function	function	NOUN
ejpam-108	277	19	.	.	PUNCT
ejpam-108	278	1	then	then	ADV
ejpam-108	278	2	f	f	PROPN
ejpam-108	278	3	is	be	AUX
ejpam-108	278	4	almost	almost	ADV
ejpam-108	278	5	contra	contra	ADJ
ejpam-108	278	6	-	-	ADJ
ejpam-108	278	7	bcontinuous	bcontinuous	ADJ
ejpam-108	278	8	function	function	NOUN
ejpam-108	278	9	which	which	PRON
ejpam-108	278	10	is	be	AUX
ejpam-108	278	11	not	not	PART
ejpam-108	278	12	almost	almost	ADV
ejpam-108	278	13	contra	contra	ADJ
ejpam-108	278	14	-	-	ADJ
ejpam-108	278	15	precontinuous	precontinuous	ADJ
ejpam-108	278	16	,	,	PUNCT
ejpam-108	278	17	since	since	SCONJ
ejpam-108	278	18	{	{	PUNCT
ejpam-108	278	19	a	a	PRON
ejpam-108	278	20	,	,	PUNCT
ejpam-108	278	21	c	c	NOUN
ejpam-108	278	22	}	}	PUNCT
ejpam-108	278	23	is	be	AUX
ejpam-108	278	24	a	a	DET
ejpam-108	278	25	regular	regular	ADJ
ejpam-108	278	26	closed	closed	ADJ
ejpam-108	278	27	set	set	NOUN
ejpam-108	278	28	of	of	ADP
ejpam-108	278	29	(	(	PUNCT
ejpam-108	278	30	x	x	PROPN
ejpam-108	278	31	,	,	PUNCT
ejpam-108	278	32	τ	τ	PROPN
ejpam-108	278	33	)	)	PUNCT
ejpam-108	278	34	and	and	CCONJ
ejpam-108	278	35	f	f	PROPN
ejpam-108	278	36	−1({a	−1({a	PROPN
ejpam-108	278	37	,	,	PUNCT
ejpam-108	278	38	c	c	NOUN
ejpam-108	278	39	}	}	PUNCT
ejpam-108	278	40	)	)	PUNCT
ejpam-108	279	1	=	=	PRON
ejpam-108	279	2	{	{	PUNCT
ejpam-108	279	3	a	a	X
ejpam-108	279	4	,	,	PUNCT
ejpam-108	279	5	c	c	NOUN
ejpam-108	279	6	}	}	PUNCT
ejpam-108	279	7	/∈	/∈	PUNCT
ejpam-108	279	8	po(x	po(x	NUM
ejpam-108	279	9	,	,	PUNCT
ejpam-108	279	10	σ	σ	PROPN
ejpam-108	279	11	)	)	PUNCT
ejpam-108	279	12	.	.	PUNCT
ejpam-108	280	1	example	example	NOUN
ejpam-108	281	1	3.20	3.20	NUM
ejpam-108	281	2	.	.	PUNCT
ejpam-108	282	1	let	let	VERB
ejpam-108	282	2	x	x	PUNCT
ejpam-108	282	3	=	=	PRON
ejpam-108	282	4	{	{	PUNCT
ejpam-108	282	5	a	a	PRON
ejpam-108	282	6	,	,	PUNCT
ejpam-108	282	7	b	b	PROPN
ejpam-108	282	8	,	,	PUNCT
ejpam-108	282	9	c},τ	c},τ	PROPN
ejpam-108	282	10	=	=	SYM
ejpam-108	282	11	{	{	PUNCT
ejpam-108	282	12	x	x	PROPN
ejpam-108	282	13	,	,	PUNCT
ejpam-108	282	14	φ	φ	PROPN
ejpam-108	282	15	,	,	PUNCT
ejpam-108	282	16	{	{	PUNCT
ejpam-108	282	17	a	a	X
ejpam-108	282	18	}	}	PUNCT
ejpam-108	282	19	,	,	PUNCT
ejpam-108	282	20	{	{	PUNCT
ejpam-108	282	21	b	b	NOUN
ejpam-108	282	22	}	}	PUNCT
ejpam-108	282	23	,	,	PUNCT
ejpam-108	282	24	{	{	PUNCT
ejpam-108	282	25	a	a	DET
ejpam-108	282	26	,	,	PUNCT
ejpam-108	282	27	b	b	NOUN
ejpam-108	282	28	}	}	PUNCT
ejpam-108	282	29	}	}	PUNCT
ejpam-108	282	30	.	.	PUNCT
ejpam-108	283	1	then	then	ADV
ejpam-108	283	2	rc(x	rc(x	VERB
ejpam-108	283	3	,	,	PUNCT
ejpam-108	283	4	τ	τ	X
ejpam-108	283	5	)	)	PUNCT
ejpam-108	283	6	=	=	PRON
ejpam-108	284	1	{	{	PUNCT
ejpam-108	284	2	x	x	PROPN
ejpam-108	284	3	,	,	PUNCT
ejpam-108	284	4	φ	φ	PROPN
ejpam-108	284	5	,	,	PUNCT
ejpam-108	284	6	{	{	PUNCT
ejpam-108	284	7	b	b	NOUN
ejpam-108	284	8	,	,	PUNCT
ejpam-108	284	9	c	c	NOUN
ejpam-108	284	10	}	}	PUNCT
ejpam-108	284	11	,	,	PUNCT
ejpam-108	284	12	{	{	PUNCT
ejpam-108	284	13	a	a	PRON
ejpam-108	284	14	,	,	PUNCT
ejpam-108	284	15	c	c	NOUN
ejpam-108	284	16	}	}	PUNCT
ejpam-108	284	17	}	}	PUNCT
ejpam-108	284	18	and	and	CCONJ
ejpam-108	284	19	bo(x	bo(x	NUM
ejpam-108	284	20	,	,	PUNCT
ejpam-108	284	21	τ	τ	X
ejpam-108	284	22	)	)	PUNCT
ejpam-108	284	23	=	=	PRON
ejpam-108	284	24	{	{	PUNCT
ejpam-108	284	25	x	x	PROPN
ejpam-108	284	26	,	,	PUNCT
ejpam-108	284	27	φ	φ	PROPN
ejpam-108	284	28	,	,	PUNCT
ejpam-108	284	29	{	{	PUNCT
ejpam-108	284	30	a	a	X
ejpam-108	284	31	}	}	PUNCT
ejpam-108	284	32	,	,	PUNCT
ejpam-108	284	33	{	{	PUNCT
ejpam-108	284	34	b	b	NOUN
ejpam-108	284	35	}	}	PUNCT
ejpam-108	284	36	,	,	PUNCT
ejpam-108	284	37	{	{	PUNCT
ejpam-108	284	38	b	b	X
ejpam-108	284	39	,	,	PUNCT
ejpam-108	284	40	c	c	NOUN
ejpam-108	284	41	}	}	PUNCT
ejpam-108	284	42	,	,	PUNCT
ejpam-108	284	43	{	{	PUNCT
ejpam-108	284	44	a	a	X
ejpam-108	284	45	,	,	PUNCT
ejpam-108	284	46	c	c	NOUN
ejpam-108	284	47	}	}	PUNCT
ejpam-108	284	48	,	,	PUNCT
ejpam-108	284	49	{	{	PUNCT
ejpam-108	284	50	a	a	PRON
ejpam-108	284	51	,	,	PUNCT
ejpam-108	284	52	b	b	NOUN
ejpam-108	284	53	}	}	PUNCT
ejpam-108	284	54	}	}	PUNCT
ejpam-108	284	55	,	,	PUNCT
ejpam-108	284	56	let	let	VERB
ejpam-108	284	57	f	f	PRON
ejpam-108	284	58	:	:	PUNCT
ejpam-108	284	59	(	(	PUNCT
ejpam-108	284	60	x	x	X
ejpam-108	284	61	,	,	PUNCT
ejpam-108	284	62	τ	τ	PROPN
ejpam-108	284	63	)	)	PUNCT
ejpam-108	284	64	→	→	SYM
ejpam-108	284	65	(	(	PUNCT
ejpam-108	284	66	x	x	X
ejpam-108	284	67	,	,	PUNCT
ejpam-108	284	68	τ	τ	X
ejpam-108	284	69	)	)	PUNCT
ejpam-108	284	70	be	be	VERB
ejpam-108	284	71	the	the	DET
ejpam-108	284	72	identity	identity	NOUN
ejpam-108	284	73	function	function	NOUN
ejpam-108	284	74	.	.	PUNCT
ejpam-108	285	1	then	then	ADV
ejpam-108	285	2	f	f	PROPN
ejpam-108	285	3	is	be	AUX
ejpam-108	285	4	almost	almost	ADV
ejpam-108	285	5	contra	contra	PROPN
ejpam-108	285	6	-	-	PUNCT
ejpam-108	285	7	b	b	ADJ
ejpam-108	285	8	-	-	PUNCT
ejpam-108	285	9	continuous	continuous	ADJ
ejpam-108	285	10	function	function	NOUN
ejpam-108	285	11	which	which	PRON
ejpam-108	285	12	is	be	AUX
ejpam-108	285	13	not	not	PART
ejpam-108	285	14	contra	contra	ADJ
ejpam-108	285	15	-	-	NOUN
ejpam-108	285	16	bcontinuous	bcontinuous	ADJ
ejpam-108	285	17	,	,	PUNCT
ejpam-108	285	18	since	since	SCONJ
ejpam-108	285	19	{	{	PUNCT
ejpam-108	285	20	c	c	X
ejpam-108	285	21	}	}	PUNCT
ejpam-108	285	22	is	be	AUX
ejpam-108	285	23	a	a	DET
ejpam-108	285	24	closed	closed	ADJ
ejpam-108	285	25	set	set	NOUN
ejpam-108	285	26	of	of	ADP
ejpam-108	285	27	(	(	PUNCT
ejpam-108	285	28	x	x	PROPN
ejpam-108	285	29	,	,	PUNCT
ejpam-108	285	30	τ	τ	PROPN
ejpam-108	285	31	)	)	PUNCT
ejpam-108	285	32	and	and	CCONJ
ejpam-108	285	33	f	f	PROPN
ejpam-108	285	34	−1({c	−1({c	PROPN
ejpam-108	285	35	}	}	PUNCT
ejpam-108	285	36	)	)	PUNCT
ejpam-108	286	1	=	=	PRON
ejpam-108	286	2	{	{	PUNCT
ejpam-108	286	3	c	c	NOUN
ejpam-108	286	4	}	}	PUNCT
ejpam-108	286	5	/∈	/∈	PUNCT
ejpam-108	287	1	bo(x	bo(x	NUM
ejpam-108	287	2	,	,	PUNCT
ejpam-108	287	3	σ	σ	PROPN
ejpam-108	287	4	)	)	PUNCT
ejpam-108	287	5	.	.	PUNCT
ejpam-108	288	1	example	example	NOUN
ejpam-108	289	1	3.21	3.21	NUM
ejpam-108	289	2	.	.	PUNCT
ejpam-108	290	1	let	let	VERB
ejpam-108	290	2	x	x	PUNCT
ejpam-108	290	3	=	=	PRON
ejpam-108	290	4	{	{	PUNCT
ejpam-108	290	5	a	a	PRON
ejpam-108	290	6	,	,	PUNCT
ejpam-108	290	7	b	b	PROPN
ejpam-108	290	8	,	,	PUNCT
ejpam-108	290	9	c},τ	c},τ	PROPN
ejpam-108	290	10	=	=	SYM
ejpam-108	290	11	{	{	PUNCT
ejpam-108	290	12	x	x	PROPN
ejpam-108	290	13	,	,	PUNCT
ejpam-108	290	14	φ	φ	PROPN
ejpam-108	290	15	,	,	PUNCT
ejpam-108	290	16	{	{	PUNCT
ejpam-108	290	17	a	a	X
ejpam-108	290	18	}	}	PUNCT
ejpam-108	290	19	,	,	PUNCT
ejpam-108	290	20	{	{	PUNCT
ejpam-108	290	21	b	b	NOUN
ejpam-108	290	22	}	}	PUNCT
ejpam-108	290	23	,	,	PUNCT
ejpam-108	290	24	{	{	PUNCT
ejpam-108	290	25	a	a	DET
ejpam-108	290	26	,	,	PUNCT
ejpam-108	290	27	b	b	NOUN
ejpam-108	290	28	}	}	PUNCT
ejpam-108	290	29	}	}	PUNCT
ejpam-108	290	30	.	.	PUNCT
ejpam-108	291	1	then	then	ADV
ejpam-108	291	2	rc(x	rc(x	VERB
ejpam-108	291	3	,	,	PUNCT
ejpam-108	291	4	τ	τ	X
ejpam-108	291	5	)	)	PUNCT
ejpam-108	291	6	=	=	PRON
ejpam-108	292	1	{	{	PUNCT
ejpam-108	292	2	x	x	PROPN
ejpam-108	292	3	,	,	PUNCT
ejpam-108	292	4	φ	φ	PROPN
ejpam-108	292	5	,	,	PUNCT
ejpam-108	292	6	{	{	PUNCT
ejpam-108	292	7	b	b	NOUN
ejpam-108	292	8	,	,	PUNCT
ejpam-108	292	9	c	c	NOUN
ejpam-108	292	10	}	}	PUNCT
ejpam-108	292	11	,	,	PUNCT
ejpam-108	292	12	{	{	PUNCT
ejpam-108	292	13	a	a	PRON
ejpam-108	292	14	,	,	PUNCT
ejpam-108	292	15	c	c	NOUN
ejpam-108	292	16	}	}	PUNCT
ejpam-108	292	17	}	}	PUNCT
ejpam-108	292	18	and	and	CCONJ
ejpam-108	292	19	y	y	PROPN
ejpam-108	292	20	=	=	PUNCT
ejpam-108	292	21	{	{	PUNCT
ejpam-108	292	22	1	1	NUM
ejpam-108	292	23	,	,	PUNCT
ejpam-108	292	24	2	2	NUM
ejpam-108	292	25	}	}	PUNCT
ejpam-108	292	26	(	(	PUNCT
ejpam-108	292	27	y	y	PROPN
ejpam-108	292	28	,	,	PUNCT
ejpam-108	292	29	σ	σ	PROPN
ejpam-108	292	30	)	)	PUNCT
ejpam-108	292	31	=	=	PRON
ejpam-108	292	32	{	{	PUNCT
ejpam-108	292	33	y	y	PROPN
ejpam-108	292	34	,	,	PUNCT
ejpam-108	292	35	φ	φ	PROPN
ejpam-108	292	36	,	,	PUNCT
ejpam-108	292	37	{	{	PUNCT
ejpam-108	292	38	1	1	NUM
ejpam-108	292	39	}	}	PUNCT
ejpam-108	292	40	}	}	PUNCT
ejpam-108	292	41	,	,	PUNCT
ejpam-108	292	42	bo(y	bo(y	NUM
ejpam-108	292	43	,	,	PUNCT
ejpam-108	292	44	σ	σ	X
ejpam-108	292	45	)	)	PUNCT
ejpam-108	292	46	=	=	PRON
ejpam-108	292	47	{	{	PUNCT
ejpam-108	292	48	y	y	PROPN
ejpam-108	292	49	,	,	PUNCT
ejpam-108	292	50	φ	φ	PROPN
ejpam-108	292	51	,	,	PUNCT
ejpam-108	292	52	{	{	PUNCT
ejpam-108	292	53	1	1	NUM
ejpam-108	292	54	}	}	PUNCT
ejpam-108	292	55	}	}	PUNCT
ejpam-108	292	56	let	let	VERB
ejpam-108	292	57	f	f	PRON
ejpam-108	292	58	:	:	PUNCT
ejpam-108	292	59	(	(	PUNCT
ejpam-108	292	60	y	y	NOUN
ejpam-108	292	61	,	,	PUNCT
ejpam-108	292	62	σ)→	σ)→	PROPN
ejpam-108	292	63	(	(	PUNCT
ejpam-108	292	64	x	x	PROPN
ejpam-108	292	65	,	,	PUNCT
ejpam-108	292	66	τ	τ	X
ejpam-108	292	67	)	)	PUNCT
ejpam-108	292	68	be	be	AUX
ejpam-108	292	69	defined	define	VERB
ejpam-108	292	70	by	by	ADP
ejpam-108	292	71	f	f	PROPN
ejpam-108	292	72	(	(	PUNCT
ejpam-108	292	73	1	1	NUM
ejpam-108	292	74	)	)	PUNCT
ejpam-108	292	75	=	=	PUNCT
ejpam-108	293	1	a	a	PROPN
ejpam-108	293	2	and	and	CCONJ
ejpam-108	293	3	f	f	PROPN
ejpam-108	293	4	(	(	PUNCT
ejpam-108	293	5	2	2	NUM
ejpam-108	293	6	)	)	PUNCT
ejpam-108	293	7	=	=	SYM
ejpam-108	294	1	c.	c.	NOUN
ejpam-108	294	2	then	then	ADV
ejpam-108	294	3	function	function	NOUN
ejpam-108	294	4	is	be	AUX
ejpam-108	294	5	almost	almost	ADV
ejpam-108	294	6	weak	weak	ADJ
ejpam-108	294	7	-	-	PUNCT
ejpam-108	294	8	b	b	NOUN
ejpam-108	294	9	-	-	PUNCT
ejpam-108	294	10	continuous	continuous	ADJ
ejpam-108	294	11	,	,	PUNCT
ejpam-108	294	12	and	and	CCONJ
ejpam-108	294	13	f	f	PROPN
ejpam-108	294	14	is	be	AUX
ejpam-108	294	15	not	not	PART
ejpam-108	294	16	almost	almost	ADV
ejpam-108	294	17	contra	contra	ADJ
ejpam-108	294	18	-	-	PUNCT
ejpam-108	294	19	b	b	NOUN
ejpam-108	294	20	-	-	PUNCT
ejpam-108	294	21	continuous	continuous	ADJ
ejpam-108	294	22	since	since	SCONJ
ejpam-108	294	23	{	{	PUNCT
ejpam-108	294	24	b	b	NOUN
ejpam-108	294	25	,	,	PUNCT
ejpam-108	294	26	c	c	NOUN
ejpam-108	294	27	}	}	PUNCT
ejpam-108	294	28	is	be	AUX
ejpam-108	294	29	a	a	DET
ejpam-108	294	30	regular	regular	ADJ
ejpam-108	294	31	closed	closed	ADJ
ejpam-108	294	32	set	set	NOUN
ejpam-108	294	33	of	of	ADP
ejpam-108	294	34	(	(	PUNCT
ejpam-108	294	35	x	x	PROPN
ejpam-108	294	36	,	,	PUNCT
ejpam-108	294	37	τ	τ	PROPN
ejpam-108	294	38	)	)	PUNCT
ejpam-108	294	39	and	and	CCONJ
ejpam-108	294	40	f	f	PROPN
ejpam-108	294	41	−1({b	−1({b	PROPN
ejpam-108	294	42	,	,	PUNCT
ejpam-108	294	43	c	c	NOUN
ejpam-108	294	44	}	}	PUNCT
ejpam-108	294	45	)	)	PUNCT
ejpam-108	294	46	=	=	PRON
ejpam-108	294	47	{	{	PUNCT
ejpam-108	294	48	2	2	NUM
ejpam-108	294	49	}	}	PUNCT
ejpam-108	294	50	/∈	/∈	PUNCT
ejpam-108	294	51	bo(y	bo(y	NUM
ejpam-108	294	52	,	,	PUNCT
ejpam-108	294	53	σ	σ	PROPN
ejpam-108	294	54	)	)	PUNCT
ejpam-108	294	55	.	.	PUNCT
ejpam-108	295	1	example	example	NOUN
ejpam-108	296	1	3.22	3.22	NUM
ejpam-108	296	2	.	.	PUNCT
ejpam-108	297	1	in	in	ADP
ejpam-108	297	2	example	example	NOUN
ejpam-108	297	3	3.19	3.19	NUM
ejpam-108	297	4	f	f	NOUN
ejpam-108	297	5	is	be	AUX
ejpam-108	297	6	almost	almost	ADV
ejpam-108	297	7	weak	weak	ADJ
ejpam-108	297	8	-	-	PUNCT
ejpam-108	297	9	b	b	NOUN
ejpam-108	297	10	-	-	PUNCT
ejpam-108	297	11	continuous	continuous	ADJ
ejpam-108	297	12	,	,	PUNCT
ejpam-108	297	13	and	and	CCONJ
ejpam-108	297	14	it	it	PRON
ejpam-108	297	15	is	be	AUX
ejpam-108	297	16	not	not	PART
ejpam-108	297	17	almost	almost	ADV
ejpam-108	297	18	weak	weak	ADJ
ejpam-108	297	19	-	-	PUNCT
ejpam-108	297	20	continuous	continuous	ADJ
ejpam-108	297	21	,	,	PUNCT
ejpam-108	297	22	since	since	SCONJ
ejpam-108	297	23	if	if	SCONJ
ejpam-108	297	24	a	a	DET
ejpam-108	297	25	∈	∈	NOUN
ejpam-108	297	26	x	x	X
ejpam-108	297	27	and	and	CCONJ
ejpam-108	297	28	f	f	PROPN
ejpam-108	297	29	(	(	PUNCT
ejpam-108	297	30	a	a	X
ejpam-108	297	31	)	)	PUNCT
ejpam-108	297	32	∈	∈	PROPN
ejpam-108	297	33	{	{	PUNCT
ejpam-108	297	34	a	a	NOUN
ejpam-108	297	35	}	}	PUNCT
ejpam-108	297	36	it	it	PRON
ejpam-108	297	37	clear	clear	ADJ
ejpam-108	297	38	that	that	SCONJ
ejpam-108	297	39	does	do	AUX
ejpam-108	297	40	not	not	PART
ejpam-108	297	41	exist	exist	VERB
ejpam-108	297	42	u	u	PRON
ejpam-108	297	43	∈	∈	NOUN
ejpam-108	297	44	po(x	po(x	PUNCT
ejpam-108	297	45	,	,	PUNCT
ejpam-108	297	46	x	x	X
ejpam-108	297	47	)	)	PUNCT
ejpam-108	298	1	such	such	ADJ
ejpam-108	298	2	that	that	SCONJ
ejpam-108	298	3	f	f	PROPN
ejpam-108	298	4	(	(	PUNCT
ejpam-108	298	5	{	{	PUNCT
ejpam-108	298	6	u})⊆	u})⊆	PROPN
ejpam-108	298	7	cl({a	cl({a	ADJ
ejpam-108	298	8	}	}	PUNCT
ejpam-108	298	9	)	)	PUNCT
ejpam-108	298	10	=	=	PRON
ejpam-108	299	1	{	{	PUNCT
ejpam-108	299	2	a	a	X
ejpam-108	299	3	,	,	PUNCT
ejpam-108	299	4	c	c	NOUN
ejpam-108	299	5	}	}	PUNCT
ejpam-108	299	6	.	.	PUNCT
ejpam-108	300	1	we	we	PRON
ejpam-108	300	2	have	have	VERB
ejpam-108	300	3	the	the	DET
ejpam-108	300	4	following	follow	VERB
ejpam-108	300	5	relation	relation	NOUN
ejpam-108	300	6	for	for	ADP
ejpam-108	300	7	the	the	DET
ejpam-108	300	8	functions	function	NOUN
ejpam-108	300	9	defined	define	VERB
ejpam-108	300	10	above	above	ADV
ejpam-108	300	11	:	:	PUNCT
ejpam-108	300	12	diagram	diagram	NOUN
ejpam-108	300	13	i	i	PRON
ejpam-108	300	14	contra	contra	PROPN
ejpam-108	300	15	-	-	ADJ
ejpam-108	300	16	continuity	continuity	ADJ
ejpam-108	300	17	�	�	PROPN
ejpam-108	300	18	�	�	PROPN
ejpam-108	300	19	//	//	SYM
ejpam-108	300	20	(	(	PUNCT
ejpam-108	300	21	θ	θ	PROPN
ejpam-108	300	22	,	,	PUNCT
ejpam-108	300	23	s)-continuity	s)-continuity	NOUN
ejpam-108	300	24	�	�	PROPN
ejpam-108	300	25	�	�	PROPN
ejpam-108	300	26	//	//	NUM
ejpam-108	300	27	weak	weak	ADJ
ejpam-108	300	28	continuity	continuity	NOUN
ejpam-108	300	29	�	�	PROPN
ejpam-108	300	30	�	�	PROPN
ejpam-108	300	31	contra	contra	PROPN
ejpam-108	300	32	-	-	NOUN
ejpam-108	300	33	precontinuity	precontinuity	NOUN
ejpam-108	300	34	//	//	SYM
ejpam-108	300	35	�	�	PROPN
ejpam-108	300	36	�	�	PROPN
ejpam-108	300	37	almost	almost	ADV
ejpam-108	300	38	contra	contra	PROPN
ejpam-108	300	39	-	-	NOUN
ejpam-108	300	40	precontinuity	precontinuity	NOUN
ejpam-108	300	41	//	//	SYM
ejpam-108	300	42	�	�	PROPN
ejpam-108	300	43	�	�	PROPN
ejpam-108	300	44	almost	almost	ADV
ejpam-108	300	45	weak	weak	ADJ
ejpam-108	300	46	continuity	continuity	NOUN
ejpam-108	300	47	�	�	PROPN
ejpam-108	300	48	�	�	PROPN
ejpam-108	300	49	contra	contra	PROPN
ejpam-108	300	50	-	-	PUNCT
ejpam-108	300	51	b	b	NOUN
ejpam-108	300	52	-	-	PUNCT
ejpam-108	300	53	continuity	continuity	NOUN
ejpam-108	300	54	//	//	NOUN
ejpam-108	300	55	almost	almost	ADV
ejpam-108	300	56	contra	contra	PROPN
ejpam-108	300	57	-	-	PUNCT
ejpam-108	300	58	b	b	NOUN
ejpam-108	300	59	-	-	PUNCT
ejpam-108	300	60	continuity	continuity	NOUN
ejpam-108	300	61	//	//	NOUN
ejpam-108	300	62	almost	almost	ADV
ejpam-108	300	63	weak	weak	ADJ
ejpam-108	300	64	b	b	X
ejpam-108	300	65	-	-	PUNCT
ejpam-108	300	66	continuity	continuity	NOUN
ejpam-108	300	67	a.	a.	NOUN
ejpam-108	300	68	al	al	PROPN
ejpam-108	300	69	-	-	PUNCT
ejpam-108	300	70	omari	omari	PROPN
ejpam-108	300	71	and	and	CCONJ
ejpam-108	300	72	s.	s.	PROPN
ejpam-108	300	73	noorani	noorani	PROPN
ejpam-108	300	74	/	/	SYM
ejpam-108	300	75	eur	eur	PROPN
ejpam-108	300	76	.	.	PUNCT
ejpam-108	301	1	j.	j.	PROPN
ejpam-108	301	2	pure	pure	PROPN
ejpam-108	301	3	appl	appl	PROPN
ejpam-108	301	4	.	.	PROPN
ejpam-108	301	5	math	math	PROPN
ejpam-108	301	6	,	,	PUNCT
ejpam-108	301	7	2	2	NUM
ejpam-108	301	8	(	(	PUNCT
ejpam-108	301	9	2009	2009	NUM
ejpam-108	301	10	)	)	PUNCT
ejpam-108	301	11	,	,	PUNCT
ejpam-108	301	12	(	(	PUNCT
ejpam-108	301	13	213	213	NUM
ejpam-108	301	14	-	-	SYM
ejpam-108	301	15	230	230	NUM
ejpam-108	301	16	)	)	PUNCT
ejpam-108	301	17	224	224	NUM
ejpam-108	301	18	4	4	NUM
ejpam-108	301	19	.	.	PUNCT
ejpam-108	302	1	b	b	X
ejpam-108	302	2	-	-	PUNCT
ejpam-108	302	3	regular	regular	ADJ
ejpam-108	302	4	graphs	graph	NOUN
ejpam-108	302	5	we	we	PRON
ejpam-108	302	6	introduce	introduce	VERB
ejpam-108	302	7	the	the	DET
ejpam-108	302	8	following	follow	VERB
ejpam-108	302	9	relatively	relatively	ADV
ejpam-108	302	10	new	new	ADJ
ejpam-108	302	11	definition	definition	NOUN
ejpam-108	302	12	:	:	PUNCT
ejpam-108	302	13	definition	definition	NOUN
ejpam-108	302	14	4.1	4.1	NUM
ejpam-108	302	15	.	.	PUNCT
ejpam-108	303	1	the	the	DET
ejpam-108	303	2	graph	graph	NOUN
ejpam-108	303	3	g	g	PROPN
ejpam-108	303	4	(	(	PUNCT
ejpam-108	303	5	f	f	PROPN
ejpam-108	303	6	)	)	PUNCT
ejpam-108	303	7	of	of	ADP
ejpam-108	303	8	a	a	DET
ejpam-108	303	9	function	function	NOUN
ejpam-108	303	10	f	f	NOUN
ejpam-108	303	11	:	:	PUNCT
ejpam-108	303	12	x	x	X
ejpam-108	303	13	→	→	SYM
ejpam-108	303	14	y	y	PROPN
ejpam-108	303	15	is	be	AUX
ejpam-108	303	16	said	say	VERB
ejpam-108	303	17	to	to	PART
ejpam-108	303	18	be	be	AUX
ejpam-108	303	19	b	b	NOUN
ejpam-108	303	20	-	-	ADJ
ejpam-108	303	21	regular	regular	ADJ
ejpam-108	303	22	(	(	PUNCT
ejpam-108	303	23	resp	resp	NOUN
ejpam-108	303	24	.	.	PUNCT
ejpam-108	304	1	strongly	strongly	ADV
ejpam-108	304	2	contra	contra	PROPN
ejpam-108	304	3	-	-	PUNCT
ejpam-108	304	4	b	b	NOUN
ejpam-108	304	5	-	-	PUNCT
ejpam-108	304	6	closed	closed	ADJ
ejpam-108	304	7	)	)	PUNCT
ejpam-108	304	8	graph	graph	NOUN
ejpam-108	304	9	if	if	SCONJ
ejpam-108	304	10	for	for	ADP
ejpam-108	304	11	each	each	DET
ejpam-108	304	12	(	(	PUNCT
ejpam-108	304	13	x	x	PROPN
ejpam-108	304	14	,	,	PUNCT
ejpam-108	304	15	y	y	PROPN
ejpam-108	304	16	)	)	PUNCT
ejpam-108	304	17	∈	∈	PROPN
ejpam-108	304	18	(	(	PUNCT
ejpam-108	304	19	x	x	NOUN
ejpam-108	304	20	,	,	PUNCT
ejpam-108	304	21	y	y	PROPN
ejpam-108	304	22	)	)	PUNCT
ejpam-108	304	23	−	−	PROPN
ejpam-108	305	1	g	g	PROPN
ejpam-108	305	2	(	(	PUNCT
ejpam-108	305	3	f	f	PROPN
ejpam-108	305	4	)	)	PUNCT
ejpam-108	305	5	,	,	PUNCT
ejpam-108	305	6	there	there	PRON
ejpam-108	305	7	exist	exist	VERB
ejpam-108	305	8	u	u	PROPN
ejpam-108	305	9	∈	∈	PROPN
ejpam-108	305	10	bo(x	bo(x	NUM
ejpam-108	305	11	,	,	PUNCT
ejpam-108	305	12	x	x	X
ejpam-108	305	13	)	)	PUNCT
ejpam-108	305	14	and	and	CCONJ
ejpam-108	305	15	a	a	DET
ejpam-108	305	16	regular	regular	ADJ
ejpam-108	305	17	open	open	ADJ
ejpam-108	305	18	(	(	PUNCT
ejpam-108	305	19	resp	resp	NOUN
ejpam-108	305	20	,	,	PUNCT
ejpam-108	305	21	regular	regular	ADJ
ejpam-108	305	22	closed	closed	ADJ
ejpam-108	305	23	)	)	PUNCT
ejpam-108	305	24	set	set	VERB
ejpam-108	305	25	v	v	NOUN
ejpam-108	305	26	of	of	ADP
ejpam-108	305	27	y	y	PROPN
ejpam-108	305	28	containing	contain	VERB
ejpam-108	305	29	y	y	PRON
ejpam-108	305	30	such	such	ADJ
ejpam-108	305	31	that	that	PRON
ejpam-108	305	32	(	(	PUNCT
ejpam-108	305	33	u	u	NOUN
ejpam-108	305	34	×	×	PROPN
ejpam-108	305	35	v	v	NOUN
ejpam-108	305	36	)	)	PUNCT
ejpam-108	305	37	∩	∩	ADJ
ejpam-108	305	38	g	g	PROPN
ejpam-108	305	39	(	(	PUNCT
ejpam-108	305	40	f	f	PROPN
ejpam-108	305	41	)	)	PUNCT
ejpam-108	306	1	=	=	SYM
ejpam-108	306	2	φ	φ	PROPN
ejpam-108	306	3	.	.	PUNCT
ejpam-108	307	1	lemma	lemma	PROPN
ejpam-108	307	2	4.2	4.2	NUM
ejpam-108	307	3	.	.	PUNCT
ejpam-108	308	1	[	[	X
ejpam-108	308	2	13	13	NUM
ejpam-108	308	3	]	]	PUNCT
ejpam-108	308	4	the	the	DET
ejpam-108	308	5	graph	graph	NOUN
ejpam-108	308	6	g	g	PROPN
ejpam-108	308	7	(	(	PUNCT
ejpam-108	308	8	f	f	PROPN
ejpam-108	308	9	)	)	PUNCT
ejpam-108	308	10	of	of	ADP
ejpam-108	308	11	f	f	PROPN
ejpam-108	308	12	:	:	PUNCT
ejpam-108	308	13	x	x	X
ejpam-108	308	14	→	→	SYM
ejpam-108	308	15	y	y	PROPN
ejpam-108	308	16	is	be	AUX
ejpam-108	308	17	contra	contra	PROPN
ejpam-108	308	18	-	-	VERB
ejpam-108	308	19	bclosed	bclose	VERB
ejpam-108	308	20	in	in	ADP
ejpam-108	308	21	x	x	SYM
ejpam-108	308	22	×	×	PROPN
ejpam-108	308	23	y	y	PROPN
ejpam-108	308	24	if	if	SCONJ
ejpam-108	309	1	and	and	CCONJ
ejpam-108	309	2	only	only	ADV
ejpam-108	309	3	if	if	SCONJ
ejpam-108	309	4	for	for	ADP
ejpam-108	309	5	each	each	DET
ejpam-108	309	6	(	(	PUNCT
ejpam-108	309	7	x	x	PROPN
ejpam-108	309	8	,	,	PUNCT
ejpam-108	309	9	y	y	PROPN
ejpam-108	309	10	)	)	PUNCT
ejpam-108	309	11	∈	∈	PROPN
ejpam-108	309	12	(	(	PUNCT
ejpam-108	309	13	x	x	SYM
ejpam-108	309	14	×	×	PROPN
ejpam-108	309	15	y	y	PROPN
ejpam-108	309	16	)	)	PUNCT
ejpam-108	309	17	−	−	PROPN
ejpam-108	310	1	g	g	PROPN
ejpam-108	310	2	(	(	PUNCT
ejpam-108	310	3	f	f	PROPN
ejpam-108	310	4	)	)	PUNCT
ejpam-108	310	5	,	,	PUNCT
ejpam-108	310	6	there	there	PRON
ejpam-108	310	7	exists	exist	VERB
ejpam-108	310	8	u	u	PROPN
ejpam-108	310	9	∈	∈	PROPN
ejpam-108	310	10	bo(x	bo(x	NUM
ejpam-108	310	11	,	,	PUNCT
ejpam-108	310	12	x	x	X
ejpam-108	310	13	)	)	PUNCT
ejpam-108	310	14	and	and	CCONJ
ejpam-108	310	15	v	v	ADP
ejpam-108	310	16	∈	∈	PROPN
ejpam-108	310	17	c(y	c(y	PROPN
ejpam-108	310	18	,	,	PUNCT
ejpam-108	310	19	y	y	NOUN
ejpam-108	310	20	)	)	PUNCT
ejpam-108	310	21	such	such	ADJ
ejpam-108	310	22	that	that	SCONJ
ejpam-108	310	23	f	f	PROPN
ejpam-108	310	24	(	(	PUNCT
ejpam-108	310	25	u)∩	u)∩	PROPN
ejpam-108	310	26	v	v	X
ejpam-108	310	27	=	=	SYM
ejpam-108	310	28	φ	φ	PROPN
ejpam-108	310	29	.	.	PUNCT
ejpam-108	310	30	theorem	theorem	VERB
ejpam-108	310	31	4.3	4.3	NUM
ejpam-108	310	32	.	.	PUNCT
ejpam-108	311	1	[	[	X
ejpam-108	311	2	13	13	NUM
ejpam-108	311	3	]	]	PUNCT
ejpam-108	311	4	if	if	SCONJ
ejpam-108	311	5	f	f	PROPN
ejpam-108	311	6	:	:	PUNCT
ejpam-108	311	7	x	x	X
ejpam-108	311	8	→	→	SYM
ejpam-108	311	9	y	y	PROPN
ejpam-108	311	10	is	be	AUX
ejpam-108	311	11	contra	contra	PROPN
ejpam-108	311	12	-	-	PUNCT
ejpam-108	311	13	b	b	NOUN
ejpam-108	311	14	-	-	PUNCT
ejpam-108	311	15	continuous	continuous	ADJ
ejpam-108	311	16	and	and	CCONJ
ejpam-108	311	17	y	y	PROPN
ejpam-108	311	18	is	be	AUX
ejpam-108	311	19	urysohn	urysohn	ADJ
ejpam-108	311	20	,	,	PUNCT
ejpam-108	311	21	then	then	ADV
ejpam-108	311	22	g	g	PROPN
ejpam-108	311	23	(	(	PUNCT
ejpam-108	311	24	f	f	PROPN
ejpam-108	311	25	)	)	PUNCT
ejpam-108	311	26	is	be	AUX
ejpam-108	311	27	contra	contra	PROPN
ejpam-108	311	28	-	-	PUNCT
ejpam-108	311	29	b	b	NOUN
ejpam-108	311	30	-	-	PUNCT
ejpam-108	311	31	closed	closed	ADJ
ejpam-108	311	32	in	in	ADP
ejpam-108	311	33	x	x	PUNCT
ejpam-108	311	34	×	×	PROPN
ejpam-108	311	35	y	y	PROPN
ejpam-108	311	36	.	.	PUNCT
ejpam-108	312	1	the	the	DET
ejpam-108	312	2	following	follow	VERB
ejpam-108	312	3	results	result	NOUN
ejpam-108	312	4	can	can	AUX
ejpam-108	312	5	be	be	AUX
ejpam-108	312	6	easily	easily	ADV
ejpam-108	312	7	verified	verify	VERB
ejpam-108	312	8	.	.	PUNCT
ejpam-108	313	1	lemma	lemma	PROPN
ejpam-108	313	2	4.4	4.4	NUM
ejpam-108	313	3	.	.	PUNCT
ejpam-108	314	1	let	let	VERB
ejpam-108	314	2	g	g	NOUN
ejpam-108	314	3	(	(	PUNCT
ejpam-108	314	4	f	f	PROPN
ejpam-108	314	5	)	)	PUNCT
ejpam-108	314	6	be	be	AUX
ejpam-108	314	7	the	the	DET
ejpam-108	314	8	graph	graph	NOUN
ejpam-108	314	9	of	of	ADP
ejpam-108	314	10	f	f	PROPN
ejpam-108	314	11	,	,	PUNCT
ejpam-108	314	12	for	for	ADP
ejpam-108	314	13	any	any	DET
ejpam-108	314	14	subset	subset	NOUN
ejpam-108	314	15	a	a	PRON
ejpam-108	314	16	⊆	⊆	NUM
ejpam-108	314	17	x	x	NOUN
ejpam-108	314	18	and	and	CCONJ
ejpam-108	314	19	b	b	NOUN
ejpam-108	314	20	⊆	⊆	NUM
ejpam-108	314	21	y	y	PROPN
ejpam-108	314	22	,	,	PUNCT
ejpam-108	314	23	we	we	PRON
ejpam-108	314	24	have	have	VERB
ejpam-108	314	25	f	f	PROPN
ejpam-108	314	26	(	(	PUNCT
ejpam-108	314	27	a)∩	a)∩	X
ejpam-108	314	28	b	b	X
ejpam-108	314	29	=	=	SYM
ejpam-108	314	30	φ	φ	PROPN
ejpam-108	315	1	if	if	SCONJ
ejpam-108	315	2	and	and	CCONJ
ejpam-108	315	3	only	only	ADV
ejpam-108	315	4	if	if	SCONJ
ejpam-108	315	5	(	(	PUNCT
ejpam-108	315	6	a×	a×	ADJ
ejpam-108	315	7	b)∩	b)∩	NOUN
ejpam-108	315	8	g	g	PROPN
ejpam-108	315	9	(	(	PUNCT
ejpam-108	315	10	f	f	PROPN
ejpam-108	315	11	)	)	PUNCT
ejpam-108	315	12	=	=	PUNCT
ejpam-108	316	1	φ	φ	PROPN
ejpam-108	316	2	lemma	lemma	PROPN
ejpam-108	316	3	4.5	4.5	NUM
ejpam-108	316	4	.	.	PUNCT
ejpam-108	317	1	the	the	DET
ejpam-108	317	2	graph	graph	NOUN
ejpam-108	317	3	g	g	PROPN
ejpam-108	317	4	(	(	PUNCT
ejpam-108	317	5	f	f	PROPN
ejpam-108	317	6	)	)	PUNCT
ejpam-108	317	7	of	of	ADP
ejpam-108	317	8	f	f	PROPN
ejpam-108	317	9	:	:	PUNCT
ejpam-108	317	10	x	x	X
ejpam-108	317	11	→	→	SYM
ejpam-108	317	12	y	y	PROPN
ejpam-108	317	13	is	be	AUX
ejpam-108	317	14	b	b	NOUN
ejpam-108	317	15	-	-	ADJ
ejpam-108	317	16	regular	regular	ADJ
ejpam-108	317	17	in	in	ADP
ejpam-108	317	18	x	x	SYM
ejpam-108	317	19	×	×	PROPN
ejpam-108	317	20	y	y	PROPN
ejpam-108	317	21	if	if	SCONJ
ejpam-108	317	22	and	and	CCONJ
ejpam-108	317	23	only	only	ADV
ejpam-108	317	24	if	if	SCONJ
ejpam-108	317	25	for	for	ADP
ejpam-108	317	26	each	each	DET
ejpam-108	317	27	(	(	PUNCT
ejpam-108	317	28	x	x	PROPN
ejpam-108	317	29	,	,	PUNCT
ejpam-108	317	30	y	y	PROPN
ejpam-108	317	31	)	)	PUNCT
ejpam-108	317	32	∈	∈	PROPN
ejpam-108	317	33	(	(	PUNCT
ejpam-108	317	34	x	x	SYM
ejpam-108	317	35	×	×	PROPN
ejpam-108	317	36	y	y	PROPN
ejpam-108	317	37	)	)	PUNCT
ejpam-108	317	38	−	−	PROPN
ejpam-108	318	1	g	g	PROPN
ejpam-108	318	2	(	(	PUNCT
ejpam-108	318	3	f	f	PROPN
ejpam-108	318	4	)	)	PUNCT
ejpam-108	318	5	,	,	PUNCT
ejpam-108	318	6	there	there	PRON
ejpam-108	318	7	exists	exist	VERB
ejpam-108	318	8	u	u	PROPN
ejpam-108	318	9	∈	∈	PROPN
ejpam-108	318	10	bo(x	bo(x	NUM
ejpam-108	318	11	,	,	PUNCT
ejpam-108	318	12	x	x	X
ejpam-108	318	13	)	)	PUNCT
ejpam-108	318	14	and	and	CCONJ
ejpam-108	318	15	v	v	ADP
ejpam-108	318	16	∈	∈	PROPN
ejpam-108	318	17	ro(y	ro(y	X
ejpam-108	318	18	,	,	PUNCT
ejpam-108	318	19	y	y	NOUN
ejpam-108	318	20	)	)	PUNCT
ejpam-108	319	1	such	such	ADJ
ejpam-108	319	2	that	that	SCONJ
ejpam-108	319	3	f	f	PROPN
ejpam-108	319	4	(	(	PUNCT
ejpam-108	319	5	u)∩	u)∩	PROPN
ejpam-108	319	6	v	v	X
ejpam-108	319	7	=	=	SYM
ejpam-108	319	8	φ	φ	PROPN
ejpam-108	319	9	.	.	PUNCT
ejpam-108	319	10	lemma	lemma	PROPN
ejpam-108	319	11	4.6	4.6	NUM
ejpam-108	319	12	.	.	PUNCT
ejpam-108	320	1	if	if	SCONJ
ejpam-108	320	2	a	a	PRON
ejpam-108	320	3	and	and	CCONJ
ejpam-108	320	4	b	b	NOUN
ejpam-108	320	5	are	be	AUX
ejpam-108	320	6	open	open	ADJ
ejpam-108	320	7	sets	set	NOUN
ejpam-108	320	8	with	with	ADP
ejpam-108	320	9	a∩	a∩	PROPN
ejpam-108	320	10	b	b	PROPN
ejpam-108	320	11	=	=	SYM
ejpam-108	320	12	φ	φ	PROPN
ejpam-108	320	13	,	,	PUNCT
ejpam-108	320	14	then	then	ADV
ejpam-108	320	15	cl(a)∩	cl(a)∩	PROPN
ejpam-108	320	16	int(cl(b	int(cl(b	PROPN
ejpam-108	320	17	)	)	PUNCT
ejpam-108	320	18	)	)	PUNCT
ejpam-108	321	1	=	=	PUNCT
ejpam-108	321	2	φ	φ	PROPN
ejpam-108	321	3	theorem	theorem	VERB
ejpam-108	321	4	4.7	4.7	NUM
ejpam-108	321	5	.	.	PUNCT
ejpam-108	322	1	if	if	SCONJ
ejpam-108	322	2	f	f	PROPN
ejpam-108	322	3	:	:	PUNCT
ejpam-108	322	4	x	x	X
ejpam-108	322	5	→	→	SYM
ejpam-108	322	6	y	y	PROPN
ejpam-108	322	7	is	be	AUX
ejpam-108	322	8	almost	almost	ADV
ejpam-108	322	9	contra	contra	PROPN
ejpam-108	322	10	-	-	PUNCT
ejpam-108	322	11	b	b	NOUN
ejpam-108	322	12	-	-	PUNCT
ejpam-108	322	13	continuous	continuous	ADJ
ejpam-108	322	14	and	and	CCONJ
ejpam-108	322	15	y	y	PROPN
ejpam-108	322	16	is	be	AUX
ejpam-108	322	17	t2	t2	NOUN
ejpam-108	322	18	,	,	PUNCT
ejpam-108	322	19	then	then	ADV
ejpam-108	322	20	g	g	PROPN
ejpam-108	322	21	(	(	PUNCT
ejpam-108	322	22	f	f	PROPN
ejpam-108	322	23	)	)	PUNCT
ejpam-108	322	24	is	be	AUX
ejpam-108	322	25	b	b	NOUN
ejpam-108	322	26	-	-	ADJ
ejpam-108	322	27	regular	regular	ADJ
ejpam-108	322	28	in	in	ADP
ejpam-108	322	29	x	x	SYM
ejpam-108	322	30	×	×	PROPN
ejpam-108	322	31	y	y	PROPN
ejpam-108	322	32	.	.	PUNCT
ejpam-108	323	1	proof	proof	NOUN
ejpam-108	323	2	.	.	PUNCT
ejpam-108	324	1	let	let	VERB
ejpam-108	324	2	(	(	PUNCT
ejpam-108	324	3	x	x	X
ejpam-108	324	4	,	,	PUNCT
ejpam-108	324	5	y	y	PROPN
ejpam-108	324	6	)	)	PUNCT
ejpam-108	324	7	∈	∈	PROPN
ejpam-108	324	8	(	(	PUNCT
ejpam-108	324	9	x	x	SYM
ejpam-108	324	10	×	×	PROPN
ejpam-108	324	11	y	y	PROPN
ejpam-108	324	12	)	)	PUNCT
ejpam-108	324	13	−	−	PROPN
ejpam-108	325	1	g	g	PROPN
ejpam-108	325	2	(	(	PUNCT
ejpam-108	325	3	f	f	PROPN
ejpam-108	325	4	)	)	PUNCT
ejpam-108	325	5	.	.	PUNCT
ejpam-108	326	1	it	it	PRON
ejpam-108	326	2	follows	follow	VERB
ejpam-108	326	3	that	that	SCONJ
ejpam-108	327	1	f	f	PROPN
ejpam-108	327	2	(	(	PUNCT
ejpam-108	327	3	x	x	X
ejpam-108	327	4	)	)	PUNCT
ejpam-108	327	5	6=	6=	PUNCT
ejpam-108	328	1	y.	y.	NOUN
ejpam-108	328	2	since	since	SCONJ
ejpam-108	328	3	y	y	PROPN
ejpam-108	328	4	is	be	AUX
ejpam-108	328	5	t2	t2	NOUN
ejpam-108	328	6	,	,	PUNCT
ejpam-108	328	7	there	there	PRON
ejpam-108	328	8	exists	exist	VERB
ejpam-108	328	9	open	open	ADJ
ejpam-108	328	10	sets	set	NOUN
ejpam-108	328	11	v	v	ADP
ejpam-108	328	12	and	and	CCONJ
ejpam-108	328	13	w	w	NOUN
ejpam-108	328	14	containing	contain	VERB
ejpam-108	328	15	f	f	PROPN
ejpam-108	328	16	(	(	PUNCT
ejpam-108	328	17	x	x	NOUN
ejpam-108	328	18	)	)	PUNCT
ejpam-108	328	19	and	and	CCONJ
ejpam-108	328	20	y	y	PROPN
ejpam-108	328	21	respectively	respectively	ADV
ejpam-108	328	22	,	,	PUNCT
ejpam-108	328	23	such	such	ADJ
ejpam-108	328	24	that	that	PRON
ejpam-108	328	25	v	v	NOUN
ejpam-108	328	26	∩w	∩w	NOUN
ejpam-108	328	27	=	=	PUNCT
ejpam-108	329	1	φ	φ	PROPN
ejpam-108	329	2	.	.	PUNCT
ejpam-108	330	1	then	then	ADV
ejpam-108	330	2	int(cl(v	int(cl(v	NOUN
ejpam-108	330	3	)	)	PUNCT
ejpam-108	330	4	)	)	PUNCT
ejpam-108	330	5	∩	∩	PROPN
ejpam-108	330	6	int(cl(w	int(cl(w	PROPN
ejpam-108	330	7	)	)	PUNCT
ejpam-108	330	8	)	)	PUNCT
ejpam-108	331	1	=	=	PUNCT
ejpam-108	331	2	φ	φ	PROPN
ejpam-108	331	3	.	.	PUNCT
ejpam-108	332	1	since	since	SCONJ
ejpam-108	332	2	f	f	PROPN
ejpam-108	332	3	is	be	AUX
ejpam-108	332	4	almost	almost	ADV
ejpam-108	332	5	contra	contra	PROPN
ejpam-108	332	6	-	-	PUNCT
ejpam-108	332	7	b	b	NOUN
ejpam-108	332	8	-	-	PUNCT
ejpam-108	332	9	continuous	continuous	ADJ
ejpam-108	332	10	,	,	PUNCT
ejpam-108	332	11	we	we	PRON
ejpam-108	332	12	have	have	VERB
ejpam-108	332	13	a.	a.	PROPN
ejpam-108	332	14	al	al	PROPN
ejpam-108	332	15	-	-	PUNCT
ejpam-108	332	16	omari	omari	PROPN
ejpam-108	332	17	and	and	CCONJ
ejpam-108	332	18	s.	s.	PROPN
ejpam-108	332	19	noorani	noorani	PROPN
ejpam-108	332	20	/	/	SYM
ejpam-108	332	21	eur	eur	PROPN
ejpam-108	332	22	.	.	PUNCT
ejpam-108	333	1	j.	j.	PROPN
ejpam-108	333	2	pure	pure	PROPN
ejpam-108	333	3	appl	appl	PROPN
ejpam-108	333	4	.	.	PROPN
ejpam-108	333	5	math	math	PROPN
ejpam-108	333	6	,	,	PUNCT
ejpam-108	333	7	2	2	NUM
ejpam-108	333	8	(	(	PUNCT
ejpam-108	333	9	2009	2009	NUM
ejpam-108	333	10	)	)	PUNCT
ejpam-108	333	11	,	,	PUNCT
ejpam-108	333	12	(	(	PUNCT
ejpam-108	333	13	213	213	NUM
ejpam-108	333	14	-	-	SYM
ejpam-108	333	15	230	230	NUM
ejpam-108	333	16	)	)	PUNCT
ejpam-108	333	17	225	225	NUM
ejpam-108	333	18	f	f	NOUN
ejpam-108	333	19	−1(int(cl(v	−1(int(cl(v	NOUN
ejpam-108	333	20	)	)	PUNCT
ejpam-108	333	21	)	)	PUNCT
ejpam-108	333	22	)	)	PUNCT
ejpam-108	333	23	is	be	AUX
ejpam-108	333	24	b	b	NOUN
ejpam-108	333	25	-	-	PUNCT
ejpam-108	333	26	closed	closed	ADJ
ejpam-108	333	27	in	in	ADP
ejpam-108	333	28	x	x	PUNCT
ejpam-108	333	29	containing	contain	VERB
ejpam-108	333	30	x	x	PUNCT
ejpam-108	333	31	.	.	PUNCT
ejpam-108	334	1	take	take	VERB
ejpam-108	334	2	u	u	NOUN
ejpam-108	334	3	=	=	PUNCT
ejpam-108	334	4	f	f	PROPN
ejpam-108	334	5	−1(int(cl(v	−1(int(cl(v	NOUN
ejpam-108	334	6	)	)	PUNCT
ejpam-108	334	7	)	)	PUNCT
ejpam-108	334	8	)	)	PUNCT
ejpam-108	334	9	.	.	PUNCT
ejpam-108	335	1	then	then	ADV
ejpam-108	335	2	f	f	PROPN
ejpam-108	335	3	(	(	PUNCT
ejpam-108	335	4	u	u	NOUN
ejpam-108	335	5	)	)	PUNCT
ejpam-108	335	6	⊆	⊆	NUM
ejpam-108	335	7	int(cl(v	int(cl(v	NOUN
ejpam-108	335	8	)	)	PUNCT
ejpam-108	335	9	)	)	PUNCT
ejpam-108	335	10	.	.	PUNCT
ejpam-108	336	1	therefore	therefore	ADV
ejpam-108	336	2	f	f	PROPN
ejpam-108	336	3	(	(	PUNCT
ejpam-108	336	4	u	u	NOUN
ejpam-108	336	5	)	)	PUNCT
ejpam-108	336	6	∩	∩	ADJ
ejpam-108	336	7	int(cl(w	int(cl(w	PROPN
ejpam-108	336	8	)	)	PUNCT
ejpam-108	336	9	)	)	PUNCT
ejpam-108	337	1	=	=	SYM
ejpam-108	337	2	φ	φ	NUM
ejpam-108	337	3	,	,	PUNCT
ejpam-108	337	4	and	and	CCONJ
ejpam-108	337	5	int(cl(w	int(cl(w	PROPN
ejpam-108	337	6	)	)	PUNCT
ejpam-108	337	7	)	)	PUNCT
ejpam-108	338	1	∈	∈	PROPN
ejpam-108	338	2	ro(y	ro(y	NOUN
ejpam-108	338	3	)	)	PUNCT
ejpam-108	338	4	.	.	PUNCT
ejpam-108	339	1	hence	hence	ADV
ejpam-108	339	2	g	g	PROPN
ejpam-108	339	3	(	(	PUNCT
ejpam-108	339	4	f	f	PROPN
ejpam-108	339	5	)	)	PUNCT
ejpam-108	339	6	is	be	AUX
ejpam-108	339	7	b	b	NOUN
ejpam-108	339	8	-	-	ADJ
ejpam-108	339	9	regular	regular	ADJ
ejpam-108	339	10	in	in	ADP
ejpam-108	339	11	x	x	SYM
ejpam-108	339	12	×	×	PROPN
ejpam-108	339	13	y	y	PROPN
ejpam-108	339	14	.	.	PUNCT
ejpam-108	340	1	definition	definition	NOUN
ejpam-108	340	2	4.8	4.8	NUM
ejpam-108	340	3	.	.	PUNCT
ejpam-108	341	1	[	[	X
ejpam-108	341	2	11	11	NUM
ejpam-108	341	3	]	]	PUNCT
ejpam-108	341	4	a	a	DET
ejpam-108	341	5	space	space	NOUN
ejpam-108	341	6	x	x	PUNCT
ejpam-108	341	7	is	be	AUX
ejpam-108	341	8	said	say	VERB
ejpam-108	341	9	to	to	PART
ejpam-108	341	10	be	be	AUX
ejpam-108	341	11	b	b	NOUN
ejpam-108	341	12	-	-	PUNCT
ejpam-108	341	13	t1	t1	NOUN
ejpam-108	341	14	if	if	SCONJ
ejpam-108	341	15	each	each	DET
ejpam-108	341	16	pair	pair	NOUN
ejpam-108	341	17	of	of	ADP
ejpam-108	341	18	distinct	distinct	ADJ
ejpam-108	341	19	points	point	NOUN
ejpam-108	341	20	x	x	PUNCT
ejpam-108	341	21	and	and	CCONJ
ejpam-108	341	22	y	y	PROPN
ejpam-108	341	23	of	of	ADP
ejpam-108	341	24	x	x	SYM
ejpam-108	341	25	,	,	PUNCT
ejpam-108	341	26	there	there	PRON
ejpam-108	341	27	exists	exist	VERB
ejpam-108	341	28	b	b	ADJ
ejpam-108	341	29	-	-	PUNCT
ejpam-108	341	30	open	open	ADJ
ejpam-108	341	31	sets	set	NOUN
ejpam-108	341	32	u	u	NOUN
ejpam-108	341	33	and	and	CCONJ
ejpam-108	341	34	v	v	ADP
ejpam-108	341	35	containing	contain	VERB
ejpam-108	341	36	x	x	PROPN
ejpam-108	341	37	and	and	CCONJ
ejpam-108	341	38	y	y	PROPN
ejpam-108	341	39	respectively	respectively	ADV
ejpam-108	341	40	such	such	ADJ
ejpam-108	341	41	that	that	SCONJ
ejpam-108	341	42	y	y	PROPN
ejpam-108	341	43	/∈	/∈	PUNCT
ejpam-108	341	44	u	u	PROPN
ejpam-108	341	45	and	and	CCONJ
ejpam-108	341	46	x	x	NOUN
ejpam-108	341	47	/∈	/∈	NOUN
ejpam-108	341	48	v	v	X
ejpam-108	341	49	.	.	PUNCT
ejpam-108	342	1	theorem	theorem	NOUN
ejpam-108	342	2	4.9	4.9	NUM
ejpam-108	342	3	.	.	PUNCT
ejpam-108	343	1	let	let	VERB
ejpam-108	343	2	f	f	NOUN
ejpam-108	343	3	:	:	PUNCT
ejpam-108	343	4	x	x	X
ejpam-108	343	5	→	→	SYM
ejpam-108	343	6	y	y	PROPN
ejpam-108	343	7	have	have	VERB
ejpam-108	343	8	a	a	DET
ejpam-108	343	9	b	b	NOUN
ejpam-108	343	10	-	-	PUNCT
ejpam-108	343	11	regular	regular	ADJ
ejpam-108	343	12	graph	graph	NOUN
ejpam-108	343	13	.	.	PUNCT
ejpam-108	344	1	if	if	SCONJ
ejpam-108	344	2	f	f	PROPN
ejpam-108	344	3	is	be	AUX
ejpam-108	344	4	injection	injection	NOUN
ejpam-108	344	5	then	then	ADV
ejpam-108	344	6	x	x	PUNCT
ejpam-108	344	7	is	be	AUX
ejpam-108	344	8	b	b	NOUN
ejpam-108	344	9	-	-	PUNCT
ejpam-108	344	10	t1	t1	NOUN
ejpam-108	344	11	.	.	PUNCT
ejpam-108	345	1	proof	proof	NOUN
ejpam-108	345	2	.	.	PUNCT
ejpam-108	346	1	let	let	VERB
ejpam-108	346	2	x	x	PRON
ejpam-108	346	3	and	and	CCONJ
ejpam-108	346	4	y	y	PROPN
ejpam-108	346	5	be	be	AUX
ejpam-108	346	6	any	any	DET
ejpam-108	346	7	two	two	NUM
ejpam-108	346	8	distinct	distinct	ADJ
ejpam-108	346	9	points	point	NOUN
ejpam-108	346	10	of	of	ADP
ejpam-108	346	11	x	x	X
ejpam-108	346	12	.	.	PUNCT
ejpam-108	347	1	since	since	SCONJ
ejpam-108	347	2	f	f	PROPN
ejpam-108	347	3	is	be	AUX
ejpam-108	347	4	injection	injection	NOUN
ejpam-108	347	5	,	,	PUNCT
ejpam-108	347	6	then	then	ADV
ejpam-108	347	7	we	we	PRON
ejpam-108	347	8	have	have	VERB
ejpam-108	347	9	(	(	PUNCT
ejpam-108	347	10	x	x	X
ejpam-108	347	11	,	,	PUNCT
ejpam-108	347	12	f	f	PROPN
ejpam-108	347	13	(	(	PUNCT
ejpam-108	347	14	y	y	NOUN
ejpam-108	347	15	)	)	PUNCT
ejpam-108	347	16	)	)	PUNCT
ejpam-108	348	1	∈	∈	PROPN
ejpam-108	348	2	(	(	PUNCT
ejpam-108	348	3	x	x	SYM
ejpam-108	348	4	×	×	PROPN
ejpam-108	348	5	y	y	PROPN
ejpam-108	348	6	)	)	PUNCT
ejpam-108	348	7	−	−	PROPN
ejpam-108	349	1	g	g	PROPN
ejpam-108	349	2	(	(	PUNCT
ejpam-108	349	3	f	f	PROPN
ejpam-108	349	4	)	)	PUNCT
ejpam-108	349	5	.	.	PUNCT
ejpam-108	350	1	by	by	ADP
ejpam-108	350	2	definition	definition	NOUN
ejpam-108	350	3	of	of	ADP
ejpam-108	350	4	b	b	NOUN
ejpam-108	350	5	-	-	PUNCT
ejpam-108	350	6	regular	regular	ADJ
ejpam-108	350	7	graph	graph	NOUN
ejpam-108	350	8	,	,	PUNCT
ejpam-108	350	9	there	there	PRON
ejpam-108	350	10	exist	exist	VERB
ejpam-108	350	11	a	a	DET
ejpam-108	350	12	b	b	NOUN
ejpam-108	350	13	-	-	PUNCT
ejpam-108	350	14	closed	closed	ADJ
ejpam-108	350	15	set	set	ADJ
ejpam-108	350	16	u	u	NOUN
ejpam-108	350	17	of	of	ADP
ejpam-108	350	18	x	x	PUNCT
ejpam-108	350	19	and	and	CCONJ
ejpam-108	350	20	v	v	NOUN
ejpam-108	350	21	∈	∈	NOUN
ejpam-108	350	22	ro(y	ro(y	X
ejpam-108	350	23	)	)	PUNCT
ejpam-108	350	24	such	such	ADJ
ejpam-108	350	25	that	that	SCONJ
ejpam-108	350	26	(	(	PUNCT
ejpam-108	350	27	x	x	X
ejpam-108	350	28	,	,	PUNCT
ejpam-108	350	29	f	f	PROPN
ejpam-108	350	30	(	(	PUNCT
ejpam-108	350	31	y	y	NOUN
ejpam-108	350	32	)	)	PUNCT
ejpam-108	350	33	)	)	PUNCT
ejpam-108	351	1	∈	∈	PROPN
ejpam-108	352	1	u	u	NOUN
ejpam-108	352	2	×	×	PROPN
ejpam-108	352	3	v	v	NOUN
ejpam-108	352	4	and	and	CCONJ
ejpam-108	352	5	f	f	PROPN
ejpam-108	352	6	(	(	PUNCT
ejpam-108	352	7	u	u	NOUN
ejpam-108	352	8	)	)	PUNCT
ejpam-108	352	9	∩	∩	ADJ
ejpam-108	352	10	v	v	NOUN
ejpam-108	352	11	=	=	SYM
ejpam-108	352	12	φ	φ	PROPN
ejpam-108	352	13	.	.	PUNCT
ejpam-108	353	1	therefore	therefore	ADV
ejpam-108	353	2	we	we	PRON
ejpam-108	353	3	have	have	VERB
ejpam-108	353	4	u	u	NOUN
ejpam-108	353	5	∩	∩	NOUN
ejpam-108	353	6	f	f	PROPN
ejpam-108	353	7	−1(v	−1(v	PROPN
ejpam-108	353	8	)	)	PUNCT
ejpam-108	354	1	=	=	SYM
ejpam-108	354	2	φ	φ	PROPN
ejpam-108	354	3	and	and	CCONJ
ejpam-108	354	4	y	y	PROPN
ejpam-108	354	5	/∈	/∈	PUNCT
ejpam-108	355	1	u	u	PROPN
ejpam-108	355	2	.	.	PUNCT
ejpam-108	356	1	thus	thus	ADV
ejpam-108	356	2	y	y	PROPN
ejpam-108	356	3	∈	∈	PROPN
ejpam-108	356	4	x	x	PUNCT
ejpam-108	356	5	−	−	NOUN
ejpam-108	356	6	u	u	NOUN
ejpam-108	356	7	and	and	CCONJ
ejpam-108	356	8	x	x	NOUN
ejpam-108	356	9	/∈	/∈	PUNCT
ejpam-108	356	10	x	x	PUNCT
ejpam-108	356	11	−	−	NOUN
ejpam-108	356	12	u	u	NOUN
ejpam-108	356	13	and	and	CCONJ
ejpam-108	356	14	x	x	SYM
ejpam-108	356	15	−	−	NOUN
ejpam-108	356	16	u	u	PROPN
ejpam-108	356	17	∈	∈	PROPN
ejpam-108	356	18	bo(x	bo(x	NUM
ejpam-108	356	19	)	)	PUNCT
ejpam-108	356	20	.	.	PUNCT
ejpam-108	357	1	this	this	PRON
ejpam-108	357	2	implies	imply	VERB
ejpam-108	357	3	that	that	SCONJ
ejpam-108	357	4	x	x	PRON
ejpam-108	357	5	is	be	AUX
ejpam-108	357	6	b	b	NOUN
ejpam-108	357	7	-	-	PUNCT
ejpam-108	357	8	t1	t1	NOUN
ejpam-108	357	9	.	.	PUNCT
ejpam-108	358	1	definition	definition	NOUN
ejpam-108	358	2	4.10	4.10	NUM
ejpam-108	358	3	.	.	PUNCT
ejpam-108	359	1	[	[	X
ejpam-108	359	2	23	23	NUM
ejpam-108	359	3	]	]	PUNCT
ejpam-108	359	4	a	a	DET
ejpam-108	359	5	space	space	NOUN
ejpam-108	359	6	x	x	PUNCT
ejpam-108	359	7	is	be	AUX
ejpam-108	359	8	said	say	VERB
ejpam-108	359	9	to	to	PART
ejpam-108	359	10	be	be	AUX
ejpam-108	359	11	weakly	weakly	ADJ
ejpam-108	359	12	hausdorff	hausdorff	NOUN
ejpam-108	359	13	if	if	SCONJ
ejpam-108	359	14	each	each	DET
ejpam-108	359	15	element	element	NOUN
ejpam-108	359	16	of	of	ADP
ejpam-108	359	17	x	x	PUNCT
ejpam-108	359	18	is	be	AUX
ejpam-108	359	19	an	an	DET
ejpam-108	359	20	intersection	intersection	NOUN
ejpam-108	359	21	of	of	ADP
ejpam-108	359	22	regular	regular	ADJ
ejpam-108	359	23	closed	closed	ADJ
ejpam-108	359	24	sets	set	NOUN
ejpam-108	359	25	.	.	PUNCT
ejpam-108	360	1	theorem	theorem	NOUN
ejpam-108	360	2	4.11	4.11	NUM
ejpam-108	360	3	.	.	PUNCT
ejpam-108	361	1	let	let	VERB
ejpam-108	361	2	f	f	NOUN
ejpam-108	361	3	:	:	PUNCT
ejpam-108	361	4	x	x	X
ejpam-108	361	5	→	→	SYM
ejpam-108	361	6	y	y	PROPN
ejpam-108	361	7	have	have	VERB
ejpam-108	361	8	a	a	DET
ejpam-108	361	9	b	b	NOUN
ejpam-108	361	10	-	-	PUNCT
ejpam-108	361	11	regular	regular	ADJ
ejpam-108	361	12	graph	graph	NOUN
ejpam-108	361	13	.	.	PUNCT
ejpam-108	362	1	if	if	SCONJ
ejpam-108	362	2	f	f	PROPN
ejpam-108	362	3	is	be	AUX
ejpam-108	362	4	surjection	surjection	PROPN
ejpam-108	362	5	then	then	ADV
ejpam-108	362	6	y	y	PROPN
ejpam-108	362	7	is	be	AUX
ejpam-108	362	8	weakly	weakly	ADJ
ejpam-108	362	9	hausdorff	hausdorff	NOUN
ejpam-108	362	10	.	.	PUNCT
ejpam-108	363	1	proof	proof	NOUN
ejpam-108	363	2	.	.	PUNCT
ejpam-108	364	1	let	let	VERB
ejpam-108	364	2	y1	y1	INTJ
ejpam-108	364	3	and	and	CCONJ
ejpam-108	364	4	y2	y2	NOUN
ejpam-108	364	5	be	be	AUX
ejpam-108	364	6	any	any	DET
ejpam-108	364	7	two	two	NUM
ejpam-108	364	8	distinct	distinct	ADJ
ejpam-108	364	9	points	point	NOUN
ejpam-108	364	10	of	of	ADP
ejpam-108	364	11	y	y	PROPN
ejpam-108	364	12	.	.	PUNCT
ejpam-108	365	1	since	since	SCONJ
ejpam-108	365	2	f	f	PROPN
ejpam-108	365	3	is	be	AUX
ejpam-108	365	4	surjective	surjective	ADJ
ejpam-108	365	5	f	f	X
ejpam-108	365	6	(	(	PUNCT
ejpam-108	365	7	x	x	NOUN
ejpam-108	365	8	)	)	PUNCT
ejpam-108	365	9	=	=	SYM
ejpam-108	365	10	y1	y1	NOUN
ejpam-108	365	11	for	for	ADP
ejpam-108	365	12	some	some	DET
ejpam-108	365	13	x	x	SYM
ejpam-108	365	14	∈	∈	PROPN
ejpam-108	365	15	x	x	X
ejpam-108	365	16	and	and	CCONJ
ejpam-108	365	17	(	(	PUNCT
ejpam-108	365	18	x	x	INTJ
ejpam-108	365	19	,	,	PUNCT
ejpam-108	365	20	y2	y2	PROPN
ejpam-108	365	21	)	)	PUNCT
ejpam-108	365	22	∈	∈	PROPN
ejpam-108	365	23	(	(	PUNCT
ejpam-108	365	24	x	x	SYM
ejpam-108	365	25	×	×	PROPN
ejpam-108	365	26	y	y	PROPN
ejpam-108	365	27	)	)	PUNCT
ejpam-108	366	1	−	−	PROPN
ejpam-108	366	2	g	g	PROPN
ejpam-108	366	3	(	(	PUNCT
ejpam-108	366	4	f	f	PROPN
ejpam-108	366	5	)	)	PUNCT
ejpam-108	366	6	.	.	PUNCT
ejpam-108	367	1	by	by	ADP
ejpam-108	367	2	definition	definition	NOUN
ejpam-108	367	3	of	of	ADP
ejpam-108	367	4	b	b	NOUN
ejpam-108	367	5	-	-	PUNCT
ejpam-108	367	6	regular	regular	ADJ
ejpam-108	367	7	graph	graph	NOUN
ejpam-108	367	8	,	,	PUNCT
ejpam-108	367	9	there	there	PRON
ejpam-108	367	10	exist	exist	VERB
ejpam-108	367	11	a	a	DET
ejpam-108	367	12	b	b	NOUN
ejpam-108	367	13	-	-	PUNCT
ejpam-108	367	14	closed	closed	ADJ
ejpam-108	367	15	set	set	ADJ
ejpam-108	367	16	u	u	NOUN
ejpam-108	367	17	of	of	ADP
ejpam-108	367	18	x	x	X
ejpam-108	367	19	and	and	CCONJ
ejpam-108	367	20	f	f	PROPN
ejpam-108	367	21	∈	∈	PROPN
ejpam-108	367	22	ro(y	ro(y	X
ejpam-108	367	23	)	)	PUNCT
ejpam-108	367	24	such	such	ADJ
ejpam-108	367	25	that	that	SCONJ
ejpam-108	367	26	(	(	PUNCT
ejpam-108	367	27	x	x	X
ejpam-108	367	28	,	,	PUNCT
ejpam-108	367	29	y2	y2	PROPN
ejpam-108	367	30	)	)	PUNCT
ejpam-108	367	31	∈	∈	PROPN
ejpam-108	367	32	u×f	u×f	PROPN
ejpam-108	367	33	and	and	CCONJ
ejpam-108	367	34	f	f	PROPN
ejpam-108	367	35	(	(	PUNCT
ejpam-108	367	36	u)∩f	u)∩f	PROPN
ejpam-108	367	37	=	=	SYM
ejpam-108	367	38	φ	φ	PROPN
ejpam-108	367	39	.	.	PUNCT
ejpam-108	368	1	since	since	SCONJ
ejpam-108	368	2	f	f	PROPN
ejpam-108	368	3	(	(	PUNCT
ejpam-108	368	4	x	x	X
ejpam-108	368	5	)	)	PUNCT
ejpam-108	368	6	∈	∈	PROPN
ejpam-108	368	7	f	f	X
ejpam-108	368	8	(	(	PUNCT
ejpam-108	368	9	u	u	NOUN
ejpam-108	368	10	)	)	PUNCT
ejpam-108	368	11	.	.	PUNCT
ejpam-108	369	1	hence	hence	ADV
ejpam-108	369	2	y1	y1	INTJ
ejpam-108	369	3	/∈	/∈	PUNCT
ejpam-108	370	1	f	f	INTJ
ejpam-108	370	2	.	.	PUNCT
ejpam-108	371	1	then	then	ADV
ejpam-108	371	2	y2	y2	INTJ
ejpam-108	371	3	/∈	/∈	PUNCT
ejpam-108	372	1	y	y	NOUN
ejpam-108	373	1	−	−	PROPN
ejpam-108	373	2	f	f	PROPN
ejpam-108	373	3	∈	∈	PROPN
ejpam-108	373	4	rc(y	rc(y	X
ejpam-108	373	5	)	)	PUNCT
ejpam-108	373	6	and	and	CCONJ
ejpam-108	373	7	y1	y1	NOUN
ejpam-108	373	8	∈	∈	PROPN
ejpam-108	374	1	y	y	NOUN
ejpam-108	374	2	−	−	PROPN
ejpam-108	375	1	f	f	PROPN
ejpam-108	375	2	.	.	PUNCT
ejpam-108	376	1	this	this	PRON
ejpam-108	376	2	implies	imply	VERB
ejpam-108	376	3	that	that	SCONJ
ejpam-108	376	4	y	y	PROPN
ejpam-108	376	5	is	be	AUX
ejpam-108	376	6	weakly	weakly	ADJ
ejpam-108	376	7	hausdorff	hausdorff	NOUN
ejpam-108	376	8	.	.	PUNCT
ejpam-108	377	1	lemma	lemma	PROPN
ejpam-108	377	2	4.12	4.12	NUM
ejpam-108	377	3	.	.	PUNCT
ejpam-108	378	1	the	the	DET
ejpam-108	378	2	graph	graph	NOUN
ejpam-108	378	3	g	g	PROPN
ejpam-108	378	4	(	(	PUNCT
ejpam-108	378	5	f	f	PROPN
ejpam-108	378	6	)	)	PUNCT
ejpam-108	378	7	of	of	ADP
ejpam-108	378	8	f	f	PROPN
ejpam-108	378	9	:	:	PUNCT
ejpam-108	378	10	x	x	X
ejpam-108	378	11	→	→	SYM
ejpam-108	378	12	y	y	PROPN
ejpam-108	378	13	is	be	AUX
ejpam-108	378	14	strongly	strongly	ADV
ejpam-108	378	15	contra	contra	ADJ
ejpam-108	378	16	-	-	ADJ
ejpam-108	378	17	bclosed	bclosed	ADJ
ejpam-108	378	18	graph	graph	NOUN
ejpam-108	378	19	in	in	ADP
ejpam-108	378	20	x	x	PUNCT
ejpam-108	378	21	×	×	PROPN
ejpam-108	378	22	y	y	PROPN
ejpam-108	378	23	if	if	SCONJ
ejpam-108	379	1	and	and	CCONJ
ejpam-108	379	2	only	only	ADV
ejpam-108	379	3	if	if	SCONJ
ejpam-108	379	4	for	for	ADP
ejpam-108	379	5	each	each	DET
ejpam-108	379	6	(	(	PUNCT
ejpam-108	379	7	x	x	PROPN
ejpam-108	379	8	,	,	PUNCT
ejpam-108	379	9	y	y	PROPN
ejpam-108	379	10	)	)	PUNCT
ejpam-108	379	11	∈	∈	PROPN
ejpam-108	379	12	(	(	PUNCT
ejpam-108	379	13	x	x	SYM
ejpam-108	379	14	×	×	PROPN
ejpam-108	379	15	y	y	PROPN
ejpam-108	379	16	)	)	PUNCT
ejpam-108	379	17	−	−	PROPN
ejpam-108	380	1	g	g	PROPN
ejpam-108	380	2	(	(	PUNCT
ejpam-108	380	3	f	f	PROPN
ejpam-108	380	4	)	)	PUNCT
ejpam-108	380	5	,	,	PUNCT
ejpam-108	380	6	there	there	PRON
ejpam-108	380	7	exists	exist	VERB
ejpam-108	380	8	u	u	PROPN
ejpam-108	380	9	∈	∈	PROPN
ejpam-108	380	10	bo(x	bo(x	NUM
ejpam-108	380	11	,	,	PUNCT
ejpam-108	380	12	x	x	X
ejpam-108	380	13	)	)	PUNCT
ejpam-108	380	14	and	and	CCONJ
ejpam-108	380	15	v	v	ADP
ejpam-108	380	16	∈	∈	PROPN
ejpam-108	380	17	rc(y	rc(y	NOUN
ejpam-108	380	18	,	,	PUNCT
ejpam-108	380	19	y	y	NOUN
ejpam-108	380	20	)	)	PUNCT
ejpam-108	380	21	such	such	ADJ
ejpam-108	380	22	that	that	SCONJ
ejpam-108	380	23	f	f	PROPN
ejpam-108	380	24	(	(	PUNCT
ejpam-108	380	25	u)∩	u)∩	PROPN
ejpam-108	380	26	v	v	X
ejpam-108	380	27	=	=	SYM
ejpam-108	380	28	φ	φ	PROPN
ejpam-108	380	29	.	.	PUNCT
ejpam-108	380	30	a.	a.	PROPN
ejpam-108	380	31	al	al	PROPN
ejpam-108	380	32	-	-	PUNCT
ejpam-108	380	33	omari	omari	PROPN
ejpam-108	380	34	and	and	CCONJ
ejpam-108	380	35	s.	s.	PROPN
ejpam-108	380	36	noorani	noorani	PROPN
ejpam-108	380	37	/	/	SYM
ejpam-108	380	38	eur	eur	PROPN
ejpam-108	380	39	.	.	PUNCT
ejpam-108	381	1	j.	j.	PROPN
ejpam-108	381	2	pure	pure	PROPN
ejpam-108	381	3	appl	appl	PROPN
ejpam-108	381	4	.	.	PROPN
ejpam-108	381	5	math	math	PROPN
ejpam-108	381	6	,	,	PUNCT
ejpam-108	381	7	2	2	NUM
ejpam-108	381	8	(	(	PUNCT
ejpam-108	381	9	2009	2009	NUM
ejpam-108	381	10	)	)	PUNCT
ejpam-108	381	11	,	,	PUNCT
ejpam-108	381	12	(	(	PUNCT
ejpam-108	381	13	213	213	NUM
ejpam-108	381	14	-	-	SYM
ejpam-108	381	15	230	230	NUM
ejpam-108	381	16	)	)	PUNCT
ejpam-108	381	17	226	226	NUM
ejpam-108	381	18	theorem	theorem	VERB
ejpam-108	381	19	4.13	4.13	NUM
ejpam-108	381	20	.	.	PUNCT
ejpam-108	382	1	if	if	SCONJ
ejpam-108	382	2	f	f	PROPN
ejpam-108	382	3	:	:	PUNCT
ejpam-108	382	4	x	x	X
ejpam-108	382	5	→	→	SYM
ejpam-108	382	6	y	y	PROPN
ejpam-108	382	7	is	be	AUX
ejpam-108	382	8	almost	almost	ADV
ejpam-108	382	9	weakly	weakly	ADJ
ejpam-108	382	10	-	-	PUNCT
ejpam-108	382	11	b	b	NOUN
ejpam-108	382	12	-	-	PUNCT
ejpam-108	382	13	continuous	continuous	ADJ
ejpam-108	382	14	and	and	CCONJ
ejpam-108	382	15	y	y	PROPN
ejpam-108	382	16	is	be	AUX
ejpam-108	382	17	urysohn	urysohn	ADJ
ejpam-108	382	18	,	,	PUNCT
ejpam-108	382	19	then	then	ADV
ejpam-108	382	20	g	g	PROPN
ejpam-108	382	21	(	(	PUNCT
ejpam-108	382	22	f	f	PROPN
ejpam-108	382	23	)	)	PUNCT
ejpam-108	382	24	is	be	AUX
ejpam-108	382	25	strongly	strongly	ADV
ejpam-108	382	26	contra	contra	PROPN
ejpam-108	382	27	-	-	PUNCT
ejpam-108	382	28	b	b	NOUN
ejpam-108	382	29	-	-	PUNCT
ejpam-108	382	30	closed	closed	ADJ
ejpam-108	382	31	in	in	ADP
ejpam-108	382	32	x	x	PUNCT
ejpam-108	382	33	×	×	PROPN
ejpam-108	382	34	y	y	PROPN
ejpam-108	382	35	.	.	PUNCT
ejpam-108	383	1	proof	proof	NOUN
ejpam-108	383	2	.	.	PUNCT
ejpam-108	384	1	suppose	suppose	VERB
ejpam-108	384	2	that	that	SCONJ
ejpam-108	384	3	(	(	PUNCT
ejpam-108	384	4	x	x	X
ejpam-108	384	5	,	,	PUNCT
ejpam-108	384	6	y	y	PROPN
ejpam-108	384	7	)	)	PUNCT
ejpam-108	384	8	∈	∈	PROPN
ejpam-108	384	9	(	(	PUNCT
ejpam-108	384	10	x	x	SYM
ejpam-108	384	11	×	×	PROPN
ejpam-108	384	12	y	y	PROPN
ejpam-108	384	13	)	)	PUNCT
ejpam-108	385	1	−	−	PROPN
ejpam-108	386	1	g	g	PROPN
ejpam-108	386	2	(	(	PUNCT
ejpam-108	386	3	f	f	PROPN
ejpam-108	386	4	)	)	PUNCT
ejpam-108	386	5	.	.	PUNCT
ejpam-108	387	1	then	then	ADV
ejpam-108	387	2	y	y	PROPN
ejpam-108	387	3	6=	6=	PROPN
ejpam-108	387	4	f	f	PROPN
ejpam-108	387	5	(	(	PUNCT
ejpam-108	387	6	x	x	NOUN
ejpam-108	387	7	)	)	PUNCT
ejpam-108	387	8	.	.	PUNCT
ejpam-108	388	1	since	since	SCONJ
ejpam-108	388	2	y	y	PROPN
ejpam-108	388	3	is	be	AUX
ejpam-108	388	4	urysohn	urysohn	ADJ
ejpam-108	388	5	,	,	PUNCT
ejpam-108	388	6	there	there	PRON
ejpam-108	388	7	exist	exist	VERB
ejpam-108	388	8	open	open	ADJ
ejpam-108	388	9	sets	set	NOUN
ejpam-108	388	10	v	v	NOUN
ejpam-108	388	11	and	and	CCONJ
ejpam-108	388	12	w	w	NOUN
ejpam-108	388	13	in	in	ADP
ejpam-108	388	14	y	y	NOUN
ejpam-108	388	15	containing	contain	VERB
ejpam-108	388	16	y	y	PROPN
ejpam-108	388	17	and	and	CCONJ
ejpam-108	388	18	f	f	PROPN
ejpam-108	388	19	(	(	PUNCT
ejpam-108	388	20	x	x	NOUN
ejpam-108	388	21	)	)	PUNCT
ejpam-108	388	22	,	,	PUNCT
ejpam-108	388	23	respectively	respectively	ADV
ejpam-108	388	24	,	,	PUNCT
ejpam-108	388	25	such	such	ADJ
ejpam-108	388	26	that	that	SCONJ
ejpam-108	388	27	cl(v	cl(v	NOUN
ejpam-108	388	28	)	)	PUNCT
ejpam-108	388	29	∩cl(w	∩cl(w	PROPN
ejpam-108	388	30	)	)	PUNCT
ejpam-108	389	1	=	=	SYM
ejpam-108	389	2	φ	φ	PROPN
ejpam-108	389	3	.	.	PUNCT
ejpam-108	390	1	since	since	SCONJ
ejpam-108	390	2	f	f	PROPN
ejpam-108	390	3	is	be	AUX
ejpam-108	390	4	almost	almost	ADV
ejpam-108	390	5	weakly	weakly	ADJ
ejpam-108	390	6	-	-	PUNCT
ejpam-108	390	7	b	b	NOUN
ejpam-108	390	8	-	-	PUNCT
ejpam-108	390	9	continuous	continuous	ADJ
ejpam-108	390	10	there	there	PRON
ejpam-108	390	11	exists	exist	VERB
ejpam-108	390	12	u	u	PROPN
ejpam-108	390	13	∈	∈	PROPN
ejpam-108	390	14	bo(x	bo(x	NUM
ejpam-108	390	15	,	,	PUNCT
ejpam-108	390	16	x	x	X
ejpam-108	390	17	)	)	PUNCT
ejpam-108	390	18	such	such	ADJ
ejpam-108	390	19	that	that	SCONJ
ejpam-108	390	20	f	f	PROPN
ejpam-108	390	21	(	(	PUNCT
ejpam-108	390	22	u	u	NOUN
ejpam-108	390	23	)	)	PUNCT
ejpam-108	390	24	⊆	⊆	NUM
ejpam-108	390	25	cl(w	cl(w	NOUN
ejpam-108	390	26	)	)	PUNCT
ejpam-108	390	27	.	.	PUNCT
ejpam-108	391	1	this	this	PRON
ejpam-108	391	2	shows	show	VERB
ejpam-108	391	3	that	that	SCONJ
ejpam-108	391	4	f	f	PROPN
ejpam-108	391	5	(	(	PUNCT
ejpam-108	391	6	u	u	NOUN
ejpam-108	391	7	)	)	PUNCT
ejpam-108	391	8	)	)	PUNCT
ejpam-108	391	9	∩	∩	NOUN
ejpam-108	391	10	cl(v	cl(v	NOUN
ejpam-108	391	11	)	)	PUNCT
ejpam-108	391	12	=	=	SYM
ejpam-108	391	13	f	f	X
ejpam-108	391	14	(	(	PUNCT
ejpam-108	391	15	u	u	NOUN
ejpam-108	391	16	)	)	PUNCT
ejpam-108	391	17	∩	∩	ADJ
ejpam-108	391	18	cl(int(v	cl(int(v	NOUN
ejpam-108	391	19	)	)	PUNCT
ejpam-108	391	20	)	)	PUNCT
ejpam-108	392	1	=	=	PUNCT
ejpam-108	393	1	φ	φ	PROPN
ejpam-108	393	2	with	with	ADP
ejpam-108	393	3	cl(int(v	cl(int(v	NOUN
ejpam-108	393	4	)	)	PUNCT
ejpam-108	393	5	)	)	PUNCT
ejpam-108	394	1	∈	∈	PROPN
ejpam-108	394	2	rc(y	rc(y	PROPN
ejpam-108	394	3	,	,	PUNCT
ejpam-108	394	4	y	y	NOUN
ejpam-108	394	5	)	)	PUNCT
ejpam-108	394	6	and	and	CCONJ
ejpam-108	394	7	hence	hence	ADV
ejpam-108	394	8	by	by	ADP
ejpam-108	394	9	lemma	lemma	PROPN
ejpam-108	394	10	4.12	4.12	NUM
ejpam-108	394	11	we	we	PRON
ejpam-108	394	12	have	have	VERB
ejpam-108	394	13	g	g	NOUN
ejpam-108	394	14	(	(	PUNCT
ejpam-108	394	15	f	f	PROPN
ejpam-108	394	16	)	)	PUNCT
ejpam-108	394	17	is	be	AUX
ejpam-108	394	18	strongly	strongly	ADV
ejpam-108	394	19	contra	contra	PROPN
ejpam-108	394	20	-	-	PUNCT
ejpam-108	394	21	b	b	NOUN
ejpam-108	394	22	-	-	PUNCT
ejpam-108	394	23	closed	closed	ADJ
ejpam-108	394	24	.	.	PUNCT
ejpam-108	395	1	theorem	theorem	VERB
ejpam-108	395	2	4.14	4.14	NUM
ejpam-108	395	3	.	.	PUNCT
ejpam-108	396	1	if	if	SCONJ
ejpam-108	396	2	f	f	PROPN
ejpam-108	396	3	:	:	PUNCT
ejpam-108	396	4	x	x	X
ejpam-108	396	5	→	→	SYM
ejpam-108	396	6	y	y	PROPN
ejpam-108	396	7	is	be	AUX
ejpam-108	396	8	almost	almost	ADV
ejpam-108	396	9	contra	contra	PROPN
ejpam-108	396	10	-	-	PUNCT
ejpam-108	396	11	b	b	NOUN
ejpam-108	396	12	-	-	PUNCT
ejpam-108	396	13	continuous	continuous	ADJ
ejpam-108	396	14	,	,	PUNCT
ejpam-108	396	15	then	then	ADV
ejpam-108	396	16	f	f	PROPN
ejpam-108	396	17	is	be	AUX
ejpam-108	396	18	almost	almost	ADV
ejpam-108	396	19	weakly	weakly	ADJ
ejpam-108	396	20	-	-	PUNCT
ejpam-108	396	21	bcontinuous	bcontinuous	ADJ
ejpam-108	396	22	.	.	PUNCT
ejpam-108	397	1	proof	proof	NOUN
ejpam-108	397	2	.	.	PUNCT
ejpam-108	398	1	let	let	VERB
ejpam-108	398	2	x	x	PUNCT
ejpam-108	398	3	∈	∈	PROPN
ejpam-108	398	4	x	x	X
ejpam-108	398	5	and	and	CCONJ
ejpam-108	398	6	v	v	X
ejpam-108	398	7	be	be	AUX
ejpam-108	398	8	any	any	DET
ejpam-108	398	9	open	open	ADJ
ejpam-108	398	10	set	set	NOUN
ejpam-108	398	11	of	of	ADP
ejpam-108	398	12	y	y	PROPN
ejpam-108	398	13	containing	contain	VERB
ejpam-108	398	14	f	f	PROPN
ejpam-108	398	15	(	(	PUNCT
ejpam-108	398	16	x	x	NOUN
ejpam-108	398	17	)	)	PUNCT
ejpam-108	398	18	.	.	PUNCT
ejpam-108	399	1	then	then	ADV
ejpam-108	399	2	cl(v	cl(v	NOUN
ejpam-108	399	3	)	)	PUNCT
ejpam-108	399	4	is	be	AUX
ejpam-108	399	5	a	a	DET
ejpam-108	399	6	regular	regular	ADJ
ejpam-108	399	7	closed	closed	ADJ
ejpam-108	399	8	set	set	NOUN
ejpam-108	399	9	of	of	ADP
ejpam-108	399	10	y	y	PROPN
ejpam-108	399	11	containing	contain	VERB
ejpam-108	399	12	f	f	PROPN
ejpam-108	399	13	(	(	PUNCT
ejpam-108	399	14	x	x	NOUN
ejpam-108	399	15	)	)	PUNCT
ejpam-108	399	16	.	.	PUNCT
ejpam-108	400	1	since	since	SCONJ
ejpam-108	400	2	f	f	PROPN
ejpam-108	400	3	almost	almost	ADV
ejpam-108	400	4	contra	contra	PROPN
ejpam-108	400	5	-	-	PUNCT
ejpam-108	400	6	b	b	NOUN
ejpam-108	400	7	-	-	PUNCT
ejpam-108	400	8	continuous	continuous	ADJ
ejpam-108	400	9	by	by	ADP
ejpam-108	400	10	theorem	theorem	ADJ
ejpam-108	400	11	3.1	3.1	NUM
ejpam-108	400	12	(	(	PUNCT
ejpam-108	400	13	3	3	NUM
ejpam-108	400	14	)	)	PUNCT
ejpam-108	400	15	in	in	ADP
ejpam-108	400	16	[	[	X
ejpam-108	400	17	19	19	NUM
ejpam-108	400	18	]	]	PUNCT
ejpam-108	400	19	there	there	PRON
ejpam-108	400	20	exists	exist	VERB
ejpam-108	400	21	u	u	PROPN
ejpam-108	400	22	∈	∈	PROPN
ejpam-108	400	23	bo(x	bo(x	NUM
ejpam-108	400	24	,	,	PUNCT
ejpam-108	400	25	x	x	X
ejpam-108	400	26	)	)	PUNCT
ejpam-108	400	27	such	such	ADJ
ejpam-108	400	28	that	that	SCONJ
ejpam-108	400	29	f	f	PROPN
ejpam-108	400	30	(	(	PUNCT
ejpam-108	400	31	u	u	NOUN
ejpam-108	400	32	)	)	PUNCT
ejpam-108	400	33	⊆	⊆	NUM
ejpam-108	400	34	cl(v	cl(v	NOUN
ejpam-108	400	35	)	)	PUNCT
ejpam-108	400	36	.	.	PUNCT
ejpam-108	401	1	therefore	therefore	ADV
ejpam-108	401	2	f	f	PROPN
ejpam-108	401	3	is	be	AUX
ejpam-108	401	4	almost	almost	ADV
ejpam-108	401	5	weakly	weakly	ADJ
ejpam-108	401	6	-	-	PUNCT
ejpam-108	401	7	b	b	NOUN
ejpam-108	401	8	-	-	PUNCT
ejpam-108	401	9	continuous	continuous	ADJ
ejpam-108	401	10	.	.	PUNCT
ejpam-108	402	1	corollary	corollary	ADJ
ejpam-108	402	2	4.15	4.15	NUM
ejpam-108	402	3	.	.	PUNCT
ejpam-108	403	1	if	if	SCONJ
ejpam-108	403	2	f	f	PROPN
ejpam-108	403	3	:	:	PUNCT
ejpam-108	403	4	x	x	X
ejpam-108	403	5	→	→	SYM
ejpam-108	403	6	y	y	PROPN
ejpam-108	403	7	is	be	AUX
ejpam-108	403	8	almost	almost	ADV
ejpam-108	403	9	contra	contra	PROPN
ejpam-108	403	10	-	-	PUNCT
ejpam-108	403	11	b	b	NOUN
ejpam-108	403	12	-	-	PUNCT
ejpam-108	403	13	continuous	continuous	ADJ
ejpam-108	403	14	and	and	CCONJ
ejpam-108	403	15	y	y	PROPN
ejpam-108	403	16	is	be	AUX
ejpam-108	403	17	urysohn	urysohn	ADJ
ejpam-108	403	18	,	,	PUNCT
ejpam-108	403	19	then	then	ADV
ejpam-108	403	20	g	g	PROPN
ejpam-108	403	21	(	(	PUNCT
ejpam-108	403	22	f	f	PROPN
ejpam-108	403	23	)	)	PUNCT
ejpam-108	403	24	is	be	AUX
ejpam-108	403	25	strongly	strongly	ADV
ejpam-108	403	26	contra	contra	PROPN
ejpam-108	403	27	-	-	PUNCT
ejpam-108	403	28	b	b	NOUN
ejpam-108	403	29	-	-	PUNCT
ejpam-108	403	30	closed	closed	ADJ
ejpam-108	403	31	.	.	PUNCT
ejpam-108	404	1	definition	definition	NOUN
ejpam-108	404	2	4.16	4.16	NUM
ejpam-108	404	3	.	.	PUNCT
ejpam-108	405	1	[	[	X
ejpam-108	405	2	7	7	X
ejpam-108	405	3	]	]	X
ejpam-108	405	4	a	a	DET
ejpam-108	405	5	function	function	NOUN
ejpam-108	405	6	f	f	NOUN
ejpam-108	405	7	:	:	PUNCT
ejpam-108	405	8	x	x	X
ejpam-108	405	9	→	→	SYM
ejpam-108	405	10	y	y	PROPN
ejpam-108	405	11	is	be	AUX
ejpam-108	405	12	called	call	VERB
ejpam-108	405	13	almost	almost	ADV
ejpam-108	405	14	-	-	PUNCT
ejpam-108	405	15	b	b	NOUN
ejpam-108	405	16	-	-	PUNCT
ejpam-108	405	17	continuous	continuous	ADJ
ejpam-108	405	18	if	if	SCONJ
ejpam-108	405	19	f	f	PROPN
ejpam-108	405	20	−1(v	−1(v	PROPN
ejpam-108	405	21	)	)	PUNCT
ejpam-108	406	1	b	b	X
ejpam-108	406	2	-	-	PUNCT
ejpam-108	406	3	open	open	ADJ
ejpam-108	406	4	in	in	ADP
ejpam-108	406	5	x	x	PUNCT
ejpam-108	406	6	for	for	ADP
ejpam-108	406	7	every	every	DET
ejpam-108	406	8	regular	regular	ADJ
ejpam-108	406	9	open	open	ADJ
ejpam-108	406	10	set	set	NOUN
ejpam-108	406	11	v	v	NOUN
ejpam-108	406	12	of	of	ADP
ejpam-108	406	13	y	y	PROPN
ejpam-108	406	14	.	.	PUNCT
ejpam-108	407	1	the	the	DET
ejpam-108	407	2	following	following	ADJ
ejpam-108	407	3	result	result	NOUN
ejpam-108	407	4	can	can	AUX
ejpam-108	407	5	be	be	AUX
ejpam-108	407	6	easily	easily	ADV
ejpam-108	407	7	verified	verify	VERB
ejpam-108	407	8	.	.	PUNCT
ejpam-108	408	1	lemma	lemma	PROPN
ejpam-108	408	2	4.17	4.17	NUM
ejpam-108	408	3	.	.	PUNCT
ejpam-108	409	1	[	[	X
ejpam-108	409	2	7	7	X
ejpam-108	409	3	]	]	X
ejpam-108	409	4	a	a	DET
ejpam-108	409	5	function	function	NOUN
ejpam-108	409	6	f	f	NOUN
ejpam-108	409	7	:	:	PUNCT
ejpam-108	409	8	x	x	X
ejpam-108	409	9	→	→	SYM
ejpam-108	409	10	y	y	PROPN
ejpam-108	409	11	is	be	AUX
ejpam-108	409	12	almost	almost	ADV
ejpam-108	409	13	b	b	NOUN
ejpam-108	409	14	-	-	ADJ
ejpam-108	409	15	continuous	continuous	ADJ
ejpam-108	409	16	,	,	PUNCT
ejpam-108	409	17	if	if	SCONJ
ejpam-108	409	18	and	and	CCONJ
ejpam-108	409	19	only	only	ADV
ejpam-108	409	20	if	if	SCONJ
ejpam-108	409	21	for	for	ADP
ejpam-108	409	22	each	each	DET
ejpam-108	409	23	x	x	SYM
ejpam-108	409	24	∈	∈	PROPN
ejpam-108	409	25	x	x	X
ejpam-108	409	26	and	and	CCONJ
ejpam-108	409	27	each	each	DET
ejpam-108	409	28	regular	regular	ADJ
ejpam-108	409	29	open	open	ADJ
ejpam-108	409	30	set	set	VERB
ejpam-108	409	31	v	v	NOUN
ejpam-108	409	32	of	of	ADP
ejpam-108	409	33	y	y	PROPN
ejpam-108	409	34	containing	contain	VERB
ejpam-108	409	35	f	f	PROPN
ejpam-108	409	36	(	(	PUNCT
ejpam-108	409	37	x	x	NOUN
ejpam-108	409	38	)	)	PUNCT
ejpam-108	409	39	,	,	PUNCT
ejpam-108	409	40	there	there	PRON
ejpam-108	409	41	exists	exist	VERB
ejpam-108	409	42	u	u	PROPN
ejpam-108	409	43	∈	∈	PROPN
ejpam-108	409	44	bo(x	bo(x	NUM
ejpam-108	409	45	,	,	PUNCT
ejpam-108	409	46	x	x	X
ejpam-108	409	47	)	)	PUNCT
ejpam-108	409	48	such	such	ADJ
ejpam-108	409	49	that	that	SCONJ
ejpam-108	409	50	f	f	PROPN
ejpam-108	409	51	(	(	PUNCT
ejpam-108	409	52	u)⊆	u)⊆	PROPN
ejpam-108	409	53	v	v	NOUN
ejpam-108	409	54	.	.	PUNCT
ejpam-108	410	1	theorem	theorem	VERB
ejpam-108	410	2	4.18	4.18	NUM
ejpam-108	410	3	.	.	PUNCT
ejpam-108	411	1	if	if	SCONJ
ejpam-108	411	2	f	f	PROPN
ejpam-108	411	3	:	:	PUNCT
ejpam-108	411	4	x	x	X
ejpam-108	411	5	→	→	SYM
ejpam-108	411	6	y	y	PROPN
ejpam-108	411	7	is	be	AUX
ejpam-108	411	8	almost	almost	ADV
ejpam-108	411	9	b	b	NOUN
ejpam-108	411	10	-	-	ADJ
ejpam-108	411	11	continuous	continuous	ADJ
ejpam-108	411	12	,	,	PUNCT
ejpam-108	411	13	and	and	CCONJ
ejpam-108	411	14	y	y	PROPN
ejpam-108	411	15	is	be	AUX
ejpam-108	411	16	hausdorff	hausdorff	NOUN
ejpam-108	411	17	,	,	PUNCT
ejpam-108	411	18	then	then	ADV
ejpam-108	411	19	g	g	PROPN
ejpam-108	411	20	(	(	PUNCT
ejpam-108	411	21	f	f	PROPN
ejpam-108	411	22	)	)	PUNCT
ejpam-108	411	23	is	be	AUX
ejpam-108	411	24	strongly	strongly	ADV
ejpam-108	411	25	contra	contra	PROPN
ejpam-108	411	26	-	-	PUNCT
ejpam-108	411	27	b	b	NOUN
ejpam-108	411	28	-	-	PUNCT
ejpam-108	411	29	closed	closed	ADJ
ejpam-108	411	30	.	.	PUNCT
ejpam-108	412	1	a.	a.	PROPN
ejpam-108	412	2	al	al	PROPN
ejpam-108	412	3	-	-	PUNCT
ejpam-108	412	4	omari	omari	PROPN
ejpam-108	412	5	and	and	CCONJ
ejpam-108	412	6	s.	s.	PROPN
ejpam-108	412	7	noorani	noorani	PROPN
ejpam-108	412	8	/	/	SYM
ejpam-108	412	9	eur	eur	PROPN
ejpam-108	412	10	.	.	PUNCT
ejpam-108	413	1	j.	j.	PROPN
ejpam-108	413	2	pure	pure	PROPN
ejpam-108	413	3	appl	appl	PROPN
ejpam-108	413	4	.	.	PROPN
ejpam-108	413	5	math	math	PROPN
ejpam-108	413	6	,	,	PUNCT
ejpam-108	413	7	2	2	NUM
ejpam-108	413	8	(	(	PUNCT
ejpam-108	413	9	2009	2009	NUM
ejpam-108	413	10	)	)	PUNCT
ejpam-108	413	11	,	,	PUNCT
ejpam-108	413	12	(	(	PUNCT
ejpam-108	413	13	213	213	NUM
ejpam-108	413	14	-	-	SYM
ejpam-108	413	15	230	230	NUM
ejpam-108	413	16	)	)	PUNCT
ejpam-108	413	17	227	227	NUM
ejpam-108	413	18	proof	proof	NOUN
ejpam-108	413	19	.	.	PUNCT
ejpam-108	413	20	suppose	suppose	VERB
ejpam-108	413	21	that	that	SCONJ
ejpam-108	413	22	(	(	PUNCT
ejpam-108	413	23	x	x	X
ejpam-108	413	24	,	,	PUNCT
ejpam-108	413	25	y	y	PROPN
ejpam-108	413	26	)	)	PUNCT
ejpam-108	413	27	∈	∈	PROPN
ejpam-108	413	28	(	(	PUNCT
ejpam-108	413	29	x×y	x×y	PROPN
ejpam-108	413	30	)	)	PUNCT
ejpam-108	413	31	−g	−g	NOUN
ejpam-108	413	32	(	(	PUNCT
ejpam-108	413	33	f	f	PROPN
ejpam-108	413	34	)	)	PUNCT
ejpam-108	413	35	.	.	PUNCT
ejpam-108	414	1	then	then	ADV
ejpam-108	414	2	y	y	PROPN
ejpam-108	414	3	6=	6=	PROPN
ejpam-108	414	4	f	f	PROPN
ejpam-108	414	5	(	(	PUNCT
ejpam-108	414	6	x	x	NOUN
ejpam-108	414	7	)	)	PUNCT
ejpam-108	414	8	.	.	PUNCT
ejpam-108	415	1	since	since	SCONJ
ejpam-108	415	2	y	y	PROPN
ejpam-108	415	3	is	be	AUX
ejpam-108	415	4	hausdorff	hausdorff	NOUN
ejpam-108	415	5	,	,	PUNCT
ejpam-108	415	6	there	there	PRON
ejpam-108	415	7	exist	exist	VERB
ejpam-108	415	8	open	open	ADJ
ejpam-108	415	9	sets	set	NOUN
ejpam-108	415	10	v	v	NOUN
ejpam-108	415	11	and	and	CCONJ
ejpam-108	415	12	w	w	NOUN
ejpam-108	415	13	in	in	ADP
ejpam-108	415	14	y	y	NOUN
ejpam-108	415	15	containing	contain	VERB
ejpam-108	415	16	y	y	PROPN
ejpam-108	415	17	and	and	CCONJ
ejpam-108	415	18	f	f	PROPN
ejpam-108	415	19	(	(	PUNCT
ejpam-108	415	20	x	x	NOUN
ejpam-108	415	21	)	)	PUNCT
ejpam-108	415	22	,	,	PUNCT
ejpam-108	415	23	respectively	respectively	ADV
ejpam-108	415	24	,	,	PUNCT
ejpam-108	415	25	such	such	ADJ
ejpam-108	415	26	that	that	DET
ejpam-108	415	27	v	v	NOUN
ejpam-108	415	28	∩w	∩w	NOUN
ejpam-108	415	29	=	=	SYM
ejpam-108	415	30	φ	φ	PROPN
ejpam-108	415	31	,	,	PUNCT
ejpam-108	415	32	hence	hence	ADV
ejpam-108	415	33	cl(v	cl(v	NOUN
ejpam-108	415	34	)	)	PUNCT
ejpam-108	415	35	∩	∩	ADJ
ejpam-108	415	36	int(cl(w	int(cl(w	PROPN
ejpam-108	415	37	)	)	PUNCT
ejpam-108	415	38	)	)	PUNCT
ejpam-108	416	1	=	=	PUNCT
ejpam-108	416	2	φ	φ	PROPN
ejpam-108	416	3	.	.	PUNCT
ejpam-108	417	1	since	since	SCONJ
ejpam-108	417	2	f	f	PROPN
ejpam-108	417	3	is	be	AUX
ejpam-108	417	4	almost	almost	ADV
ejpam-108	417	5	b	b	NOUN
ejpam-108	417	6	-	-	ADJ
ejpam-108	417	7	continuous	continuous	ADJ
ejpam-108	417	8	,	,	PUNCT
ejpam-108	417	9	and	and	CCONJ
ejpam-108	417	10	w	w	NOUN
ejpam-108	417	11	is	be	AUX
ejpam-108	417	12	regular	regular	ADJ
ejpam-108	417	13	open	open	ADJ
ejpam-108	417	14	by	by	ADP
ejpam-108	417	15	lemma	lemma	PROPN
ejpam-108	417	16	4.17	4.17	NUM
ejpam-108	417	17	there	there	ADV
ejpam-108	417	18	exists	exist	VERB
ejpam-108	417	19	u	u	PROPN
ejpam-108	417	20	∈	∈	PROPN
ejpam-108	417	21	bo(x	bo(x	NUM
ejpam-108	417	22	,	,	PUNCT
ejpam-108	417	23	x	x	X
ejpam-108	417	24	)	)	PUNCT
ejpam-108	417	25	such	such	ADJ
ejpam-108	417	26	that	that	SCONJ
ejpam-108	417	27	f	f	PROPN
ejpam-108	417	28	(	(	PUNCT
ejpam-108	417	29	u	u	NOUN
ejpam-108	417	30	)	)	PUNCT
ejpam-108	417	31	=	=	NOUN
ejpam-108	417	32	w	w	PROPN
ejpam-108	417	33	⊆	⊆	NUM
ejpam-108	417	34	int(cl(w	int(cl(w	PROPN
ejpam-108	417	35	)	)	PUNCT
ejpam-108	417	36	)	)	PUNCT
ejpam-108	417	37	.	.	PUNCT
ejpam-108	418	1	this	this	PRON
ejpam-108	418	2	shows	show	VERB
ejpam-108	418	3	that	that	SCONJ
ejpam-108	419	1	f	f	PROPN
ejpam-108	419	2	(	(	PUNCT
ejpam-108	419	3	u)∩	u)∩	PROPN
ejpam-108	419	4	cl(v	cl(v	X
ejpam-108	419	5	)	)	PUNCT
ejpam-108	419	6	=	=	PUNCT
ejpam-108	419	7	φ	φ	PROPN
ejpam-108	419	8	and	and	CCONJ
ejpam-108	419	9	hence	hence	ADV
ejpam-108	419	10	by	by	ADP
ejpam-108	419	11	lemma	lemma	PROPN
ejpam-108	419	12	4.12	4.12	NUM
ejpam-108	419	13	we	we	PRON
ejpam-108	419	14	have	have	VERB
ejpam-108	419	15	g	g	NOUN
ejpam-108	419	16	(	(	PUNCT
ejpam-108	419	17	f	f	PROPN
ejpam-108	419	18	)	)	PUNCT
ejpam-108	419	19	is	be	AUX
ejpam-108	419	20	strongly	strongly	ADV
ejpam-108	419	21	contra	contra	PROPN
ejpam-108	419	22	-	-	PUNCT
ejpam-108	419	23	b	b	NOUN
ejpam-108	419	24	-	-	PUNCT
ejpam-108	419	25	closed	closed	ADJ
ejpam-108	419	26	.	.	PUNCT
ejpam-108	420	1	we	we	PRON
ejpam-108	420	2	recall	recall	VERB
ejpam-108	420	3	that	that	SCONJ
ejpam-108	420	4	a	a	DET
ejpam-108	420	5	topological	topological	ADJ
ejpam-108	420	6	space	space	NOUN
ejpam-108	420	7	(	(	PUNCT
ejpam-108	420	8	x	x	X
ejpam-108	420	9	,	,	PUNCT
ejpam-108	420	10	τ	τ	X
ejpam-108	420	11	)	)	PUNCT
ejpam-108	420	12	is	be	AUX
ejpam-108	420	13	said	say	VERB
ejpam-108	420	14	to	to	PART
ejpam-108	420	15	be	be	AUX
ejpam-108	420	16	extremally	extremally	ADV
ejpam-108	420	17	disconnected	disconnected	ADJ
ejpam-108	420	18	(	(	PUNCT
ejpam-108	420	19	briefly	briefly	NOUN
ejpam-108	420	20	e.d	e.d	PROPN
ejpam-108	420	21	.	.	PUNCT
ejpam-108	420	22	)	)	PUNCT
ejpam-108	421	1	if	if	SCONJ
ejpam-108	421	2	the	the	DET
ejpam-108	421	3	closure	closure	NOUN
ejpam-108	421	4	of	of	ADP
ejpam-108	421	5	every	every	DET
ejpam-108	421	6	open	open	ADJ
ejpam-108	421	7	set	set	NOUN
ejpam-108	421	8	of	of	ADP
ejpam-108	421	9	x	x	PUNCT
ejpam-108	421	10	is	be	AUX
ejpam-108	421	11	open	open	ADJ
ejpam-108	421	12	in	in	ADP
ejpam-108	421	13	x	x	X
ejpam-108	421	14	.	.	PUNCT
ejpam-108	421	15	theorem	theorem	PROPN
ejpam-108	421	16	4.19	4.19	NUM
ejpam-108	421	17	.	.	PUNCT
ejpam-108	422	1	let	let	VERB
ejpam-108	422	2	y	y	PRON
ejpam-108	422	3	be	be	AUX
ejpam-108	422	4	e.d	e.d	PROPN
ejpam-108	422	5	.	.	PROPN
ejpam-108	423	1	then	then	ADV
ejpam-108	423	2	,	,	PUNCT
ejpam-108	423	3	a	a	DET
ejpam-108	423	4	function	function	NOUN
ejpam-108	423	5	f	f	NOUN
ejpam-108	424	1	:	:	PUNCT
ejpam-108	424	2	x	x	X
ejpam-108	424	3	→	→	SYM
ejpam-108	424	4	y	y	PROPN
ejpam-108	424	5	is	be	AUX
ejpam-108	424	6	almost	almost	ADV
ejpam-108	424	7	contra	contra	PROPN
ejpam-108	424	8	-	-	PUNCT
ejpam-108	424	9	b	b	NOUN
ejpam-108	424	10	-	-	PUNCT
ejpam-108	424	11	continuous	continuous	ADJ
ejpam-108	424	12	if	if	SCONJ
ejpam-108	424	13	and	and	CCONJ
ejpam-108	424	14	only	only	ADV
ejpam-108	424	15	if	if	SCONJ
ejpam-108	424	16	it	it	PRON
ejpam-108	424	17	is	be	AUX
ejpam-108	424	18	almost	almost	ADV
ejpam-108	424	19	b	b	NOUN
ejpam-108	424	20	-	-	PUNCT
ejpam-108	424	21	continuous	continuous	ADJ
ejpam-108	424	22	.	.	PUNCT
ejpam-108	425	1	proof	proof	NOUN
ejpam-108	425	2	.	.	PUNCT
ejpam-108	426	1	let	let	VERB
ejpam-108	426	2	x	x	PUNCT
ejpam-108	426	3	∈	∈	PROPN
ejpam-108	426	4	x	x	X
ejpam-108	426	5	and	and	CCONJ
ejpam-108	426	6	v	v	X
ejpam-108	426	7	be	be	AUX
ejpam-108	426	8	any	any	DET
ejpam-108	426	9	regular	regular	ADJ
ejpam-108	426	10	open	open	ADJ
ejpam-108	426	11	set	set	NOUN
ejpam-108	426	12	of	of	ADP
ejpam-108	426	13	y	y	PROPN
ejpam-108	426	14	containing	contain	VERB
ejpam-108	426	15	f	f	PROPN
ejpam-108	426	16	(	(	PUNCT
ejpam-108	426	17	x	x	NOUN
ejpam-108	426	18	)	)	PUNCT
ejpam-108	426	19	.	.	PUNCT
ejpam-108	427	1	since	since	SCONJ
ejpam-108	427	2	y	y	PROPN
ejpam-108	427	3	is	be	AUX
ejpam-108	427	4	e.d	e.d	PROPN
ejpam-108	427	5	.	.	PROPN
ejpam-108	427	6	then	then	ADV
ejpam-108	427	7	v	v	NOUN
ejpam-108	427	8	is	be	AUX
ejpam-108	427	9	clopen	clopen	ADJ
ejpam-108	427	10	.	.	PUNCT
ejpam-108	428	1	by	by	ADP
ejpam-108	428	2	theorem	theorem	ADJ
ejpam-108	428	3	3.1	3.1	NUM
ejpam-108	428	4	(	(	PUNCT
ejpam-108	428	5	3	3	NUM
ejpam-108	428	6	)	)	PUNCT
ejpam-108	428	7	in	in	ADP
ejpam-108	428	8	[	[	X
ejpam-108	428	9	19	19	NUM
ejpam-108	428	10	]	]	PUNCT
ejpam-108	428	11	,	,	PUNCT
ejpam-108	428	12	there	there	PRON
ejpam-108	428	13	exists	exist	VERB
ejpam-108	428	14	u	u	PROPN
ejpam-108	428	15	∈	∈	PROPN
ejpam-108	428	16	bo(x	bo(x	NUM
ejpam-108	428	17	,	,	PUNCT
ejpam-108	428	18	x	x	X
ejpam-108	428	19	)	)	PUNCT
ejpam-108	428	20	such	such	ADJ
ejpam-108	428	21	that	that	SCONJ
ejpam-108	428	22	f	f	PROPN
ejpam-108	428	23	(	(	PUNCT
ejpam-108	428	24	u)⊆	u)⊆	PROPN
ejpam-108	428	25	v	v	NOUN
ejpam-108	428	26	.	.	PUNCT
ejpam-108	429	1	then	then	ADV
ejpam-108	429	2	lemma	lemma	PROPN
ejpam-108	429	3	4.17	4.17	NUM
ejpam-108	429	4	,	,	PUNCT
ejpam-108	429	5	implies	imply	VERB
ejpam-108	429	6	that	that	SCONJ
ejpam-108	429	7	f	f	PROPN
ejpam-108	429	8	is	be	AUX
ejpam-108	429	9	almost	almost	ADV
ejpam-108	429	10	b	b	NOUN
ejpam-108	429	11	-	-	PUNCT
ejpam-108	429	12	continuous	continuous	ADJ
ejpam-108	429	13	.	.	PUNCT
ejpam-108	430	1	conversely	conversely	ADV
ejpam-108	430	2	let	let	VERB
ejpam-108	430	3	f	f	PRON
ejpam-108	430	4	be	be	AUX
ejpam-108	430	5	any	any	DET
ejpam-108	430	6	regular	regular	ADJ
ejpam-108	430	7	closed	closed	ADJ
ejpam-108	430	8	set	set	NOUN
ejpam-108	430	9	of	of	ADP
ejpam-108	430	10	y	y	PROPN
ejpam-108	430	11	.	.	PUNCT
ejpam-108	431	1	since	since	SCONJ
ejpam-108	431	2	y	y	PROPN
ejpam-108	431	3	is	be	AUX
ejpam-108	431	4	e.d	e.d	PROPN
ejpam-108	431	5	.	.	PROPN
ejpam-108	432	1	then	then	ADV
ejpam-108	432	2	f	f	PROPN
ejpam-108	432	3	is	be	AUX
ejpam-108	432	4	also	also	ADV
ejpam-108	432	5	regular	regular	ADJ
ejpam-108	432	6	open	open	ADJ
ejpam-108	432	7	and	and	CCONJ
ejpam-108	432	8	f	f	PROPN
ejpam-108	432	9	−1(f	−1(f	PROPN
ejpam-108	432	10	)	)	PUNCT
ejpam-108	432	11	is	be	AUX
ejpam-108	432	12	b	b	NOUN
ejpam-108	432	13	-	-	PUNCT
ejpam-108	432	14	open	open	ADJ
ejpam-108	432	15	in	in	ADP
ejpam-108	432	16	x	x	X
ejpam-108	432	17	.	.	PUNCT
ejpam-108	433	1	this	this	PRON
ejpam-108	433	2	show	show	VERB
ejpam-108	433	3	that	that	SCONJ
ejpam-108	433	4	f	f	PROPN
ejpam-108	433	5	are	be	AUX
ejpam-108	433	6	almost	almost	ADV
ejpam-108	433	7	contra	contra	PROPN
ejpam-108	433	8	-	-	PUNCT
ejpam-108	433	9	b	b	NOUN
ejpam-108	433	10	-	-	PUNCT
ejpam-108	433	11	continuous	continuous	ADJ
ejpam-108	433	12	.	.	PUNCT
ejpam-108	434	1	the	the	DET
ejpam-108	434	2	following	follow	VERB
ejpam-108	434	3	examples	example	NOUN
ejpam-108	434	4	will	will	AUX
ejpam-108	434	5	show	show	VERB
ejpam-108	434	6	that	that	SCONJ
ejpam-108	434	7	the	the	DET
ejpam-108	434	8	concepts	concept	NOUN
ejpam-108	434	9	of	of	ADP
ejpam-108	434	10	almost	almost	ADV
ejpam-108	434	11	-	-	PUNCT
ejpam-108	434	12	b	b	NOUN
ejpam-108	434	13	-	-	PUNCT
ejpam-108	434	14	continuity	continuity	NOUN
ejpam-108	434	15	and	and	CCONJ
ejpam-108	434	16	almost	almost	ADV
ejpam-108	434	17	contra	contra	PROPN
ejpam-108	434	18	-	-	ADJ
ejpam-108	434	19	b	b	NOUN
ejpam-108	434	20	-	-	PUNCT
ejpam-108	434	21	continuity	continuity	NOUN
ejpam-108	434	22	,	,	PUNCT
ejpam-108	434	23	is	be	AUX
ejpam-108	434	24	independent	independent	ADJ
ejpam-108	434	25	.	.	PUNCT
ejpam-108	434	26	example	example	NOUN
ejpam-108	435	1	4.20	4.20	NUM
ejpam-108	435	2	.	.	PUNCT
ejpam-108	436	1	let	let	VERB
ejpam-108	436	2	x	x	PUNCT
ejpam-108	436	3	=	=	PRON
ejpam-108	436	4	{	{	PUNCT
ejpam-108	436	5	a	a	PRON
ejpam-108	436	6	,	,	PUNCT
ejpam-108	436	7	b	b	NOUN
ejpam-108	436	8	,	,	PUNCT
ejpam-108	436	9	c	c	NOUN
ejpam-108	436	10	}	}	PUNCT
ejpam-108	436	11	=	=	SYM
ejpam-108	436	12	y	y	PROPN
ejpam-108	436	13	,	,	PUNCT
ejpam-108	436	14	τ	τ	PROPN
ejpam-108	436	15	=	=	PUNCT
ejpam-108	436	16	{	{	PUNCT
ejpam-108	436	17	φ	φ	PROPN
ejpam-108	436	18	,	,	PUNCT
ejpam-108	436	19	x	x	INTJ
ejpam-108	436	20	,	,	PUNCT
ejpam-108	436	21	{	{	PUNCT
ejpam-108	436	22	a	a	NOUN
ejpam-108	436	23	}	}	PUNCT
ejpam-108	436	24	,	,	PUNCT
ejpam-108	436	25	{	{	PUNCT
ejpam-108	436	26	b	b	NOUN
ejpam-108	436	27	}	}	PUNCT
ejpam-108	436	28	,	,	PUNCT
ejpam-108	436	29	{	{	PUNCT
ejpam-108	436	30	a	a	PRON
ejpam-108	436	31	,	,	PUNCT
ejpam-108	436	32	b	b	NOUN
ejpam-108	436	33	}	}	PUNCT
ejpam-108	436	34	}	}	PUNCT
ejpam-108	436	35	and	and	CCONJ
ejpam-108	436	36	σ	σ	X
ejpam-108	436	37	=	=	SYM
ejpam-108	436	38	{	{	PUNCT
ejpam-108	436	39	φ	φ	PROPN
ejpam-108	436	40	,	,	PUNCT
ejpam-108	436	41	y	y	PROPN
ejpam-108	436	42	,	,	PUNCT
ejpam-108	436	43	{	{	PUNCT
ejpam-108	436	44	a	a	X
ejpam-108	436	45	}	}	PUNCT
ejpam-108	436	46	}	}	PUNCT
ejpam-108	436	47	,	,	PUNCT
ejpam-108	436	48	then	then	ADV
ejpam-108	436	49	ro(x	ro(x	PUNCT
ejpam-108	436	50	,	,	PUNCT
ejpam-108	436	51	τ	τ	X
ejpam-108	436	52	)	)	PUNCT
ejpam-108	436	53	=	=	PRON
ejpam-108	436	54	{	{	PUNCT
ejpam-108	436	55	φ	φ	PROPN
ejpam-108	436	56	,	,	PUNCT
ejpam-108	436	57	x	x	INTJ
ejpam-108	436	58	,	,	PUNCT
ejpam-108	436	59	{	{	PUNCT
ejpam-108	436	60	a	a	NOUN
ejpam-108	436	61	}	}	PUNCT
ejpam-108	436	62	,	,	PUNCT
ejpam-108	436	63	{	{	PUNCT
ejpam-108	436	64	b	b	X
ejpam-108	436	65	}	}	PUNCT
ejpam-108	436	66	}	}	PUNCT
ejpam-108	436	67	,	,	PUNCT
ejpam-108	436	68	bo(y	bo(y	NUM
ejpam-108	436	69	,	,	PUNCT
ejpam-108	436	70	σ	σ	X
ejpam-108	436	71	)	)	PUNCT
ejpam-108	436	72	=	=	PRON
ejpam-108	436	73	{	{	PUNCT
ejpam-108	436	74	φ	φ	PROPN
ejpam-108	436	75	,	,	PUNCT
ejpam-108	436	76	x	x	INTJ
ejpam-108	436	77	,	,	PUNCT
ejpam-108	436	78	{	{	PUNCT
ejpam-108	436	79	a	a	NOUN
ejpam-108	436	80	}	}	PUNCT
ejpam-108	436	81	,	,	PUNCT
ejpam-108	436	82	{	{	PUNCT
ejpam-108	436	83	a	a	DET
ejpam-108	436	84	,	,	PUNCT
ejpam-108	436	85	b	b	NOUN
ejpam-108	436	86	}	}	PUNCT
ejpam-108	436	87	,	,	PUNCT
ejpam-108	436	88	{	{	PUNCT
ejpam-108	436	89	a	a	PRON
ejpam-108	436	90	,	,	PUNCT
ejpam-108	436	91	c	c	NOUN
ejpam-108	436	92	}	}	PUNCT
ejpam-108	436	93	}	}	PUNCT
ejpam-108	436	94	.	.	PUNCT
ejpam-108	437	1	then	then	ADV
ejpam-108	437	2	it	it	PRON
ejpam-108	437	3	is	be	AUX
ejpam-108	437	4	clear	clear	ADJ
ejpam-108	437	5	that	that	SCONJ
ejpam-108	437	6	(	(	PUNCT
ejpam-108	437	7	x	x	X
ejpam-108	437	8	,	,	PUNCT
ejpam-108	437	9	τ	τ	X
ejpam-108	437	10	)	)	PUNCT
ejpam-108	437	11	is	be	AUX
ejpam-108	437	12	not	not	PART
ejpam-108	437	13	extremally	extremally	ADV
ejpam-108	437	14	disconnected	disconnect	VERB
ejpam-108	437	15	.	.	PUNCT
ejpam-108	438	1	let	let	VERB
ejpam-108	438	2	function	function	VERB
ejpam-108	438	3	f	f	X
ejpam-108	438	4	:	:	PUNCT
ejpam-108	438	5	(	(	PUNCT
ejpam-108	438	6	y	y	PROPN
ejpam-108	438	7	,	,	PUNCT
ejpam-108	438	8	σ	σ	PROPN
ejpam-108	438	9	)	)	PUNCT
ejpam-108	438	10	→	→	SYM
ejpam-108	438	11	(	(	PUNCT
ejpam-108	438	12	x	x	X
ejpam-108	438	13	,	,	PUNCT
ejpam-108	438	14	τ	τ	PROPN
ejpam-108	438	15	)	)	PUNCT
ejpam-108	438	16	as	as	SCONJ
ejpam-108	438	17	follows	follow	VERB
ejpam-108	438	18	:	:	PUNCT
ejpam-108	439	1	f	f	X
ejpam-108	439	2	(	(	PUNCT
ejpam-108	439	3	a	a	X
ejpam-108	439	4	)	)	PUNCT
ejpam-108	439	5	=	=	SYM
ejpam-108	439	6	c	c	X
ejpam-108	439	7	,	,	PUNCT
ejpam-108	439	8	f	f	PROPN
ejpam-108	439	9	(	(	PUNCT
ejpam-108	439	10	b	b	NOUN
ejpam-108	439	11	)	)	PUNCT
ejpam-108	439	12	=	=	SYM
ejpam-108	439	13	b	b	PROPN
ejpam-108	439	14	and	and	CCONJ
ejpam-108	439	15	f	f	PROPN
ejpam-108	439	16	(	(	PUNCT
ejpam-108	439	17	c	c	NOUN
ejpam-108	439	18	)	)	PUNCT
ejpam-108	439	19	=	=	SYM
ejpam-108	440	1	a.	a.	NOUN
ejpam-108	440	2	then	then	ADV
ejpam-108	440	3	f	f	PROPN
ejpam-108	440	4	is	be	AUX
ejpam-108	440	5	almostcontra	almostcontra	ADJ
ejpam-108	440	6	-	-	ADJ
ejpam-108	440	7	b	b	NOUN
ejpam-108	440	8	-	-	PUNCT
ejpam-108	440	9	continuous	continuous	ADJ
ejpam-108	440	10	and	and	CCONJ
ejpam-108	440	11	f	f	NOUN
ejpam-108	440	12	is	be	AUX
ejpam-108	440	13	not	not	PART
ejpam-108	440	14	almost	almost	ADV
ejpam-108	440	15	-	-	PUNCT
ejpam-108	440	16	b	b	NOUN
ejpam-108	440	17	-	-	PUNCT
ejpam-108	440	18	continuous	continuous	ADJ
ejpam-108	440	19	,	,	PUNCT
ejpam-108	440	20	since	since	SCONJ
ejpam-108	440	21	{	{	PUNCT
ejpam-108	440	22	a	a	PRON
ejpam-108	440	23	}	}	PUNCT
ejpam-108	440	24	is	be	AUX
ejpam-108	440	25	regular	regular	ADJ
ejpam-108	440	26	open	open	ADJ
ejpam-108	440	27	and	and	CCONJ
ejpam-108	440	28	f	f	PROPN
ejpam-108	440	29	−1({a	−1({a	PROPN
ejpam-108	440	30	}	}	PUNCT
ejpam-108	440	31	)	)	PUNCT
ejpam-108	441	1	=	=	PRON
ejpam-108	441	2	{	{	PUNCT
ejpam-108	441	3	c	c	X
ejpam-108	441	4	}	}	PUNCT
ejpam-108	441	5	is	be	AUX
ejpam-108	441	6	not	not	PART
ejpam-108	441	7	b	b	NOUN
ejpam-108	441	8	-	-	PUNCT
ejpam-108	441	9	open	open	ADJ
ejpam-108	441	10	.	.	PUNCT
ejpam-108	442	1	but	but	CCONJ
ejpam-108	442	2	if	if	SCONJ
ejpam-108	442	3	we	we	PRON
ejpam-108	442	4	define	define	VERB
ejpam-108	442	5	g	g	NOUN
ejpam-108	442	6	:	:	PUNCT
ejpam-108	442	7	(	(	PUNCT
ejpam-108	442	8	y	y	PROPN
ejpam-108	442	9	,	,	PUNCT
ejpam-108	442	10	σ	σ	PROPN
ejpam-108	442	11	)	)	PUNCT
ejpam-108	442	12	→	→	SYM
ejpam-108	442	13	(	(	PUNCT
ejpam-108	442	14	x	x	X
ejpam-108	442	15	,	,	PUNCT
ejpam-108	442	16	τ	τ	PROPN
ejpam-108	442	17	)	)	PUNCT
ejpam-108	442	18	as	as	ADP
ejpam-108	442	19	g(y	g(y	NOUN
ejpam-108	442	20	)	)	PUNCT
ejpam-108	442	21	=	=	SYM
ejpam-108	442	22	a	a	PRON
ejpam-108	442	23	for	for	ADP
ejpam-108	442	24	all	all	DET
ejpam-108	442	25	y	y	PROPN
ejpam-108	442	26	∈	∈	PROPN
ejpam-108	442	27	y	y	PROPN
ejpam-108	442	28	,	,	PUNCT
ejpam-108	442	29	then	then	ADV
ejpam-108	442	30	g	g	PROPN
ejpam-108	442	31	almost	almost	ADV
ejpam-108	442	32	-	-	PUNCT
ejpam-108	442	33	b	b	NOUN
ejpam-108	442	34	-	-	PUNCT
ejpam-108	442	35	continuous	continuous	ADJ
ejpam-108	442	36	but	but	CCONJ
ejpam-108	442	37	g	g	NOUN
ejpam-108	442	38	is	be	AUX
ejpam-108	442	39	not	not	PART
ejpam-108	442	40	almost	almost	ADV
ejpam-108	442	41	-	-	PUNCT
ejpam-108	442	42	contra	contra	ADJ
ejpam-108	442	43	-	-	PUNCT
ejpam-108	442	44	b	b	NOUN
ejpam-108	442	45	-	-	PUNCT
ejpam-108	442	46	continuous	continuous	ADJ
ejpam-108	442	47	since	since	SCONJ
ejpam-108	442	48	f	f	PROPN
ejpam-108	442	49	−1({a	−1({a	PROPN
ejpam-108	442	50	}	}	PUNCT
ejpam-108	442	51	)	)	PUNCT
ejpam-108	443	1	=	=	PRON
ejpam-108	443	2	{	{	PUNCT
ejpam-108	443	3	a	a	PRON
ejpam-108	443	4	}	}	PUNCT
ejpam-108	443	5	is	be	AUX
ejpam-108	443	6	not	not	PART
ejpam-108	443	7	b	b	NOUN
ejpam-108	443	8	-	-	PUNCT
ejpam-108	443	9	closed	closed	ADJ
ejpam-108	443	10	.	.	PUNCT
ejpam-108	444	1	references	reference	NOUN
ejpam-108	444	2	228	228	NUM
ejpam-108	444	3	definition	definition	NOUN
ejpam-108	444	4	4.21	4.21	NUM
ejpam-108	444	5	.	.	PUNCT
ejpam-108	445	1	[	[	X
ejpam-108	445	2	11	11	NUM
ejpam-108	445	3	]	]	PUNCT
ejpam-108	445	4	a	a	DET
ejpam-108	445	5	space	space	NOUN
ejpam-108	445	6	x	x	PUNCT
ejpam-108	445	7	is	be	AUX
ejpam-108	445	8	said	say	VERB
ejpam-108	445	9	to	to	PART
ejpam-108	445	10	be	be	AUX
ejpam-108	445	11	b	b	NOUN
ejpam-108	445	12	-	-	PUNCT
ejpam-108	445	13	t2	t2	NOUN
ejpam-108	445	14	if	if	SCONJ
ejpam-108	445	15	for	for	ADP
ejpam-108	445	16	each	each	DET
ejpam-108	445	17	pair	pair	NOUN
ejpam-108	445	18	of	of	ADP
ejpam-108	445	19	distinct	distinct	ADJ
ejpam-108	445	20	points	point	NOUN
ejpam-108	445	21	x	x	PUNCT
ejpam-108	445	22	and	and	CCONJ
ejpam-108	445	23	y	y	PROPN
ejpam-108	445	24	in	in	ADP
ejpam-108	445	25	x	x	SYM
ejpam-108	445	26	,	,	PUNCT
ejpam-108	445	27	there	there	PRON
ejpam-108	445	28	exist	exist	VERB
ejpam-108	445	29	u	u	PROPN
ejpam-108	445	30	∈	∈	PROPN
ejpam-108	445	31	bo(x	bo(x	NUM
ejpam-108	445	32	,	,	PUNCT
ejpam-108	445	33	x	x	X
ejpam-108	445	34	)	)	PUNCT
ejpam-108	445	35	and	and	CCONJ
ejpam-108	445	36	v	v	ADP
ejpam-108	445	37	∈	∈	PROPN
ejpam-108	445	38	bo(x	bo(x	NUM
ejpam-108	445	39	,	,	PUNCT
ejpam-108	445	40	y	y	NOUN
ejpam-108	445	41	)	)	PUNCT
ejpam-108	445	42	such	such	ADJ
ejpam-108	445	43	that	that	SCONJ
ejpam-108	445	44	u	u	PROPN
ejpam-108	445	45	∩	∩	NOUN
ejpam-108	445	46	v	v	NOUN
ejpam-108	445	47	=	=	SYM
ejpam-108	445	48	φ	φ	PROPN
ejpam-108	445	49	.	.	PUNCT
ejpam-108	445	50	theorem	theorem	VERB
ejpam-108	445	51	4.22	4.22	NUM
ejpam-108	445	52	.	.	PUNCT
ejpam-108	446	1	if	if	SCONJ
ejpam-108	446	2	f	f	PROPN
ejpam-108	446	3	:	:	PUNCT
ejpam-108	446	4	x	x	X
ejpam-108	446	5	→	→	SYM
ejpam-108	446	6	y	y	PROPN
ejpam-108	446	7	is	be	AUX
ejpam-108	446	8	an	an	DET
ejpam-108	446	9	injective	injective	ADJ
ejpam-108	446	10	almost	almost	ADV
ejpam-108	446	11	contra	contra	PROPN
ejpam-108	446	12	-	-	PUNCT
ejpam-108	446	13	b	b	ADJ
ejpam-108	446	14	-	-	PUNCT
ejpam-108	446	15	continuous	continuous	ADJ
ejpam-108	446	16	function	function	NOUN
ejpam-108	446	17	with	with	ADP
ejpam-108	446	18	the	the	DET
ejpam-108	446	19	strongly	strongly	ADV
ejpam-108	446	20	contra	contra	ADJ
ejpam-108	446	21	-	-	PUNCT
ejpam-108	446	22	b	b	NOUN
ejpam-108	446	23	-	-	PUNCT
ejpam-108	446	24	closed	closed	ADJ
ejpam-108	446	25	graph	graph	NOUN
ejpam-108	446	26	,	,	PUNCT
ejpam-108	446	27	then	then	ADV
ejpam-108	446	28	(	(	PUNCT
ejpam-108	446	29	x	x	X
ejpam-108	446	30	,	,	PUNCT
ejpam-108	446	31	τ	τ	X
ejpam-108	446	32	)	)	PUNCT
ejpam-108	446	33	is	be	AUX
ejpam-108	446	34	b	b	NOUN
ejpam-108	446	35	-	-	PUNCT
ejpam-108	446	36	t2	t2	NOUN
ejpam-108	446	37	.	.	PUNCT
ejpam-108	447	1	proof	proof	NOUN
ejpam-108	447	2	.	.	PUNCT
ejpam-108	448	1	let	let	VERB
ejpam-108	448	2	x	x	PRON
ejpam-108	448	3	and	and	CCONJ
ejpam-108	448	4	y	y	PROPN
ejpam-108	448	5	be	be	AUX
ejpam-108	448	6	distinct	distinct	ADJ
ejpam-108	448	7	points	point	NOUN
ejpam-108	448	8	of	of	ADP
ejpam-108	448	9	x	x	X
ejpam-108	448	10	.	.	PUNCT
ejpam-108	449	1	since	since	SCONJ
ejpam-108	449	2	f	f	PROPN
ejpam-108	449	3	is	be	AUX
ejpam-108	449	4	injective	injective	ADJ
ejpam-108	449	5	,	,	PUNCT
ejpam-108	449	6	we	we	PRON
ejpam-108	449	7	have	have	VERB
ejpam-108	449	8	f	f	PROPN
ejpam-108	449	9	(	(	PUNCT
ejpam-108	449	10	x	x	X
ejpam-108	449	11	)	)	PUNCT
ejpam-108	449	12	6=	6=	ADP
ejpam-108	450	1	f	f	PROPN
ejpam-108	450	2	(	(	PUNCT
ejpam-108	450	3	y	y	PROPN
ejpam-108	450	4	)	)	PUNCT
ejpam-108	450	5	.	.	PUNCT
ejpam-108	451	1	then	then	ADV
ejpam-108	451	2	we	we	PRON
ejpam-108	451	3	have	have	VERB
ejpam-108	451	4	(	(	PUNCT
ejpam-108	451	5	x	x	X
ejpam-108	451	6	,	,	PUNCT
ejpam-108	451	7	f	f	PROPN
ejpam-108	451	8	(	(	PUNCT
ejpam-108	451	9	y	y	NOUN
ejpam-108	451	10	)	)	PUNCT
ejpam-108	451	11	)	)	PUNCT
ejpam-108	452	1	∈	∈	PROPN
ejpam-108	452	2	(	(	PUNCT
ejpam-108	452	3	x	x	SYM
ejpam-108	452	4	×	×	PROPN
ejpam-108	452	5	y	y	PROPN
ejpam-108	452	6	)	)	PUNCT
ejpam-108	452	7	−	−	PROPN
ejpam-108	453	1	g	g	PROPN
ejpam-108	453	2	(	(	PUNCT
ejpam-108	453	3	f	f	PROPN
ejpam-108	453	4	)	)	PUNCT
ejpam-108	453	5	.	.	PUNCT
ejpam-108	454	1	since	since	SCONJ
ejpam-108	454	2	g	g	PROPN
ejpam-108	454	3	(	(	PUNCT
ejpam-108	454	4	f	f	PROPN
ejpam-108	454	5	)	)	PUNCT
ejpam-108	454	6	is	be	AUX
ejpam-108	454	7	strongly	strongly	ADV
ejpam-108	454	8	contra	contra	ADJ
ejpam-108	454	9	-	-	ADJ
ejpam-108	454	10	bclosed	bclosed	ADJ
ejpam-108	454	11	,	,	PUNCT
ejpam-108	454	12	by	by	ADP
ejpam-108	454	13	lemma	lemma	PROPN
ejpam-108	454	14	4.12	4.12	NUM
ejpam-108	454	15	there	there	ADV
ejpam-108	454	16	exists	exist	VERB
ejpam-108	454	17	u	u	PROPN
ejpam-108	454	18	∈	∈	PROPN
ejpam-108	454	19	bo(x	bo(x	NUM
ejpam-108	454	20	,	,	PUNCT
ejpam-108	454	21	x	x	X
ejpam-108	454	22	)	)	PUNCT
ejpam-108	454	23	and	and	CCONJ
ejpam-108	454	24	a	a	DET
ejpam-108	454	25	regular	regular	ADJ
ejpam-108	454	26	closed	closed	ADJ
ejpam-108	454	27	set	set	VERB
ejpam-108	454	28	v	v	NOUN
ejpam-108	454	29	containing	contain	VERB
ejpam-108	454	30	f	f	PROPN
ejpam-108	454	31	(	(	PUNCT
ejpam-108	454	32	y	y	NOUN
ejpam-108	454	33	)	)	PUNCT
ejpam-108	454	34	such	such	ADJ
ejpam-108	454	35	that	that	SCONJ
ejpam-108	454	36	f	f	PROPN
ejpam-108	454	37	(	(	PUNCT
ejpam-108	454	38	u)∩v	u)∩v	PROPN
ejpam-108	454	39	=	=	SYM
ejpam-108	454	40	φ	φ	PROPN
ejpam-108	454	41	.	.	PUNCT
ejpam-108	455	1	since	since	SCONJ
ejpam-108	455	2	f	f	PROPN
ejpam-108	455	3	is	be	AUX
ejpam-108	455	4	almost	almost	ADV
ejpam-108	455	5	contra	contra	PROPN
ejpam-108	455	6	-	-	PUNCT
ejpam-108	455	7	b	b	NOUN
ejpam-108	455	8	-	-	PUNCT
ejpam-108	455	9	continuous	continuous	ADJ
ejpam-108	455	10	,	,	PUNCT
ejpam-108	455	11	by	by	ADP
ejpam-108	455	12	theorem	theorem	ADJ
ejpam-108	455	13	3.1	3.1	NUM
ejpam-108	455	14	(	(	PUNCT
ejpam-108	455	15	3	3	NUM
ejpam-108	455	16	)	)	PUNCT
ejpam-108	455	17	in	in	ADP
ejpam-108	455	18	[	[	X
ejpam-108	455	19	19	19	NUM
ejpam-108	455	20	]	]	PUNCT
ejpam-108	455	21	there	there	PRON
ejpam-108	455	22	exists	exist	VERB
ejpam-108	455	23	g	g	PROPN
ejpam-108	455	24	∈	∈	PROPN
ejpam-108	455	25	bo(x	bo(x	NUM
ejpam-108	455	26	,	,	PUNCT
ejpam-108	455	27	y	y	NOUN
ejpam-108	455	28	)	)	PUNCT
ejpam-108	455	29	such	such	ADJ
ejpam-108	455	30	that	that	SCONJ
ejpam-108	455	31	f	f	PROPN
ejpam-108	455	32	(	(	PUNCT
ejpam-108	455	33	g	g	NOUN
ejpam-108	455	34	)	)	PUNCT
ejpam-108	455	35	⊆	⊆	NUM
ejpam-108	455	36	v	v	NOUN
ejpam-108	455	37	.	.	PUNCT
ejpam-108	456	1	therefore	therefore	ADV
ejpam-108	456	2	we	we	PRON
ejpam-108	456	3	have	have	VERB
ejpam-108	456	4	f	f	PROPN
ejpam-108	456	5	(	(	PUNCT
ejpam-108	456	6	u)∩	u)∩	PROPN
ejpam-108	456	7	f	f	PROPN
ejpam-108	456	8	(	(	PUNCT
ejpam-108	456	9	g	g	NOUN
ejpam-108	456	10	)	)	PUNCT
ejpam-108	457	1	=	=	SYM
ejpam-108	457	2	φ	φ	PROPN
ejpam-108	457	3	,	,	PUNCT
ejpam-108	457	4	hence	hence	ADV
ejpam-108	457	5	u	u	NOUN
ejpam-108	457	6	∩	∩	NOUN
ejpam-108	457	7	g	g	PROPN
ejpam-108	457	8	=	=	SYM
ejpam-108	457	9	φ	φ	PROPN
ejpam-108	457	10	.	.	PUNCT
ejpam-108	458	1	this	this	PRON
ejpam-108	458	2	shows	show	VERB
ejpam-108	458	3	that	that	SCONJ
ejpam-108	458	4	(	(	PUNCT
ejpam-108	458	5	x	x	X
ejpam-108	458	6	,	,	PUNCT
ejpam-108	458	7	τ	τ	X
ejpam-108	458	8	)	)	PUNCT
ejpam-108	458	9	is	be	AUX
ejpam-108	458	10	b	b	NOUN
ejpam-108	458	11	-	-	PUNCT
ejpam-108	458	12	t2	t2	NOUN
ejpam-108	458	13	.	.	PUNCT
ejpam-108	459	1	acknowledgements	acknowledgement	NOUN
ejpam-108	459	2	.	.	PUNCT
ejpam-108	460	1	this	this	DET
ejpam-108	460	2	work	work	NOUN
ejpam-108	460	3	is	be	AUX
ejpam-108	460	4	financially	financially	ADV
ejpam-108	460	5	supported	support	VERB
ejpam-108	460	6	by	by	ADP
ejpam-108	460	7	the	the	DET
ejpam-108	460	8	ministry	ministry	PROPN
ejpam-108	460	9	of	of	ADP
ejpam-108	460	10	higher	high	ADJ
ejpam-108	460	11	education	education	NOUN
ejpam-108	460	12	,	,	PUNCT
ejpam-108	460	13	malaysia	malaysia	PROPN
ejpam-108	460	14	under	under	ADP
ejpam-108	460	15	frgs	frgs	PROPN
ejpam-108	460	16	grant	grant	VERB
ejpam-108	460	17	no	no	DET
ejpam-108	460	18	:	:	PUNCT
ejpam-108	460	19	ukm	ukm	VERB
ejpam-108	460	20	-	-	PUNCT
ejpam-108	460	21	st-06	st-06	NOUN
ejpam-108	460	22	-	-	PUNCT
ejpam-108	460	23	frgs0008	frgs0008	NOUN
ejpam-108	460	24	-	-	PUNCT
ejpam-108	460	25	2008	2008	NUM
ejpam-108	460	26	.	.	PUNCT
ejpam-108	461	1	we	we	PRON
ejpam-108	461	2	also	also	ADV
ejpam-108	461	3	would	would	AUX
ejpam-108	461	4	like	like	VERB
ejpam-108	461	5	to	to	PART
ejpam-108	461	6	thank	thank	VERB
ejpam-108	461	7	the	the	DET
ejpam-108	461	8	referees	referee	NOUN
ejpam-108	461	9	for	for	ADP
ejpam-108	461	10	useful	useful	ADJ
ejpam-108	461	11	comments	comment	NOUN
ejpam-108	461	12	and	and	CCONJ
ejpam-108	461	13	suggestions	suggestion	NOUN
ejpam-108	461	14	.	.	PUNCT
ejpam-108	462	1	references	reference	NOUN
ejpam-108	462	2	[	[	X
ejpam-108	462	3	1	1	NUM
ejpam-108	462	4	]	]	X
ejpam-108	462	5	a.al	a.al	PROPN
ejpam-108	462	6	-	-	NOUN
ejpam-108	462	7	omari	omari	ADJ
ejpam-108	462	8	and	and	CCONJ
ejpam-108	462	9	m.s.m.noorani	m.s.m.noorani	PROPN
ejpam-108	462	10	,	,	PUNCT
ejpam-108	462	11	"	"	PUNCT
ejpam-108	462	12	on	on	ADP
ejpam-108	462	13	generalzed	generalzed	ADJ
ejpam-108	462	14	b	b	X
ejpam-108	462	15	-	-	PUNCT
ejpam-108	462	16	closed	closed	ADJ
ejpam-108	462	17	sets	set	NOUN
ejpam-108	462	18	"	"	PUNCT
ejpam-108	462	19	,	,	PUNCT
ejpam-108	462	20	bull	bull	NOUN
ejpam-108	462	21	.	.	PUNCT
ejpam-108	463	1	malaysian	malaysian	ADJ
ejpam-108	463	2	math	math	PROPN
ejpam-108	463	3	.	.	PUNCT
ejpam-108	464	1	sc	sc	PROPN
ejpam-108	464	2	.	.	PROPN
ejpam-108	464	3	soc	soc	PROPN
ejpam-108	464	4	.	.	PUNCT
ejpam-108	465	1	32(1)(2009	32(1)(2009	NUM
ejpam-108	465	2	)	)	PUNCT
ejpam-108	465	3	1	1	NUM
ejpam-108	465	4	-	-	SYM
ejpam-108	465	5	12	12	NUM
ejpam-108	465	6	.	.	PUNCT
ejpam-108	466	1	[	[	X
ejpam-108	466	2	2	2	NUM
ejpam-108	466	3	]	]	PUNCT
ejpam-108	466	4	m.	m.	NOUN
ejpam-108	466	5	e.	e.	PROPN
ejpam-108	466	6	abd	abd	PROPN
ejpam-108	467	1	el	el	PROPN
ejpam-108	467	2	-	-	PROPN
ejpam-108	467	3	monsef	monsef	PROPN
ejpam-108	467	4	,	,	PUNCT
ejpam-108	467	5	s.	s.	PROPN
ejpam-108	467	6	n.	n.	PROPN
ejpam-108	467	7	el	el	PROPN
ejpam-108	467	8	-	-	PUNCT
ejpam-108	467	9	deeb	deeb	PROPN
ejpam-108	467	10	and	and	CCONJ
ejpam-108	467	11	r.	r.	PROPN
ejpam-108	467	12	a.	a.	PROPN
ejpam-108	467	13	mahmoud	mahmoud	PROPN
ejpam-108	467	14	,	,	PUNCT
ejpam-108	467	15	"	"	PUNCT
ejpam-108	467	16	β	β	X
ejpam-108	467	17	-open	-open	NOUN
ejpam-108	467	18	sets	set	NOUN
ejpam-108	467	19	and	and	CCONJ
ejpam-108	467	20	β	β	PRON
ejpam-108	467	21	-continuous	-continuous	ADJ
ejpam-108	467	22	mappings	mapping	NOUN
ejpam-108	467	23	"	"	PUNCT
ejpam-108	467	24	,	,	PUNCT
ejpam-108	467	25	bull	bull	NOUN
ejpam-108	467	26	.	.	PUNCT
ejpam-108	468	1	fac	fac	PROPN
ejpam-108	468	2	.	.	PUNCT
ejpam-108	469	1	sci	sci	PROPN
ejpam-108	469	2	.	.	PUNCT
ejpam-108	469	3	assuit	assuit	PROPN
ejpam-108	469	4	univ	univ	PROPN
ejpam-108	469	5	.	.	PROPN
ejpam-108	470	1	12	12	NUM
ejpam-108	470	2	(	(	PUNCT
ejpam-108	470	3	1983	1983	NUM
ejpam-108	470	4	)	)	PUNCT
ejpam-108	470	5	,	,	PUNCT
ejpam-108	470	6	77	77	NUM
ejpam-108	470	7	-	-	SYM
ejpam-108	470	8	90	90	NUM
ejpam-108	470	9	.	.	PUNCT
ejpam-108	471	1	[	[	X
ejpam-108	471	2	3	3	X
ejpam-108	471	3	]	]	X
ejpam-108	471	4	d.	d.	PROPN
ejpam-108	471	5	andrijević	andrijević	PROPN
ejpam-108	471	6	,	,	PUNCT
ejpam-108	471	7	"	"	PUNCT
ejpam-108	471	8	on	on	ADP
ejpam-108	471	9	b	b	X
ejpam-108	471	10	-	-	PUNCT
ejpam-108	471	11	open	open	ADJ
ejpam-108	471	12	sets	set	NOUN
ejpam-108	471	13	"	"	PUNCT
ejpam-108	471	14	,	,	PUNCT
ejpam-108	471	15	mat	mat	PROPN
ejpam-108	471	16	.	.	PROPN
ejpam-108	471	17	vesnik	vesnik	PROPN
ejpam-108	471	18	48	48	NUM
ejpam-108	471	19	(	(	PUNCT
ejpam-108	471	20	1996	1996	NUM
ejpam-108	471	21	)	)	PUNCT
ejpam-108	471	22	,	,	PUNCT
ejpam-108	471	23	59	59	NUM
ejpam-108	471	24	-	-	SYM
ejpam-108	471	25	64	64	NUM
ejpam-108	471	26	.	.	PUNCT
ejpam-108	472	1	[	[	X
ejpam-108	472	2	4	4	NUM
ejpam-108	472	3	]	]	PUNCT
ejpam-108	472	4	m.	m.	NOUN
ejpam-108	472	5	caldas	caldas	PROPN
ejpam-108	472	6	and	and	CCONJ
ejpam-108	472	7	s.	s.	PROPN
ejpam-108	472	8	jafri	jafri	PROPN
ejpam-108	472	9	,	,	PUNCT
ejpam-108	472	10	"	"	PUNCT
ejpam-108	472	11	some	some	DET
ejpam-108	472	12	properties	property	NOUN
ejpam-108	472	13	of	of	ADP
ejpam-108	472	14	contra	contra	PROPN
ejpam-108	472	15	-	-	ADJ
ejpam-108	472	16	β	β	X
ejpam-108	472	17	-continuous	-continuous	ADJ
ejpam-108	472	18	functions	function	NOUN
ejpam-108	472	19	"	"	PUNCT
ejpam-108	472	20	,	,	PUNCT
ejpam-108	472	21	mem	mem	PROPN
ejpam-108	472	22	.	.	PUNCT
ejpam-108	472	23	fac	fac	PROPN
ejpam-108	472	24	.	.	PUNCT
ejpam-108	473	1	sci	sci	PROPN
ejpam-108	473	2	.	.	PUNCT
ejpam-108	474	1	koch	koch	PROPN
ejpam-108	474	2	univ	univ	PROPN
ejpam-108	474	3	.	.	PUNCT
ejpam-108	475	1	(	(	PUNCT
ejpam-108	475	2	math	math	NOUN
ejpam-108	475	3	)	)	PUNCT
ejpam-108	475	4	22	22	NUM
ejpam-108	475	5	(	(	PUNCT
ejpam-108	475	6	2001	2001	NUM
ejpam-108	475	7	)	)	PUNCT
ejpam-108	475	8	,	,	PUNCT
ejpam-108	475	9	19	19	NUM
ejpam-108	475	10	-	-	SYM
ejpam-108	475	11	28	28	NUM
ejpam-108	475	12	.	.	PUNCT
ejpam-108	476	1	[	[	X
ejpam-108	476	2	5	5	X
ejpam-108	476	3	]	]	PUNCT
ejpam-108	476	4	j.	j.	PROPN
ejpam-108	476	5	dontchev	dontchev	PROPN
ejpam-108	476	6	,	,	PUNCT
ejpam-108	476	7	"	"	PUNCT
ejpam-108	476	8	contra	contra	ADJ
ejpam-108	476	9	-	-	ADJ
ejpam-108	476	10	continuous	continuous	ADJ
ejpam-108	476	11	functions	function	NOUN
ejpam-108	476	12	and	and	CCONJ
ejpam-108	476	13	strongly	strongly	ADV
ejpam-108	476	14	s	s	NOUN
ejpam-108	476	15	-	-	PUNCT
ejpam-108	476	16	closed	closed	ADJ
ejpam-108	476	17	spaces	space	NOUN
ejpam-108	476	18	"	"	PUNCT
ejpam-108	476	19	,	,	PUNCT
ejpam-108	476	20	internat.j	internat.j	PROPN
ejpam-108	476	21	.	.	PUNCT
ejpam-108	476	22	math	math	PROPN
ejpam-108	476	23	.	.	PUNCT
ejpam-108	477	1	math	math	NOUN
ejpam-108	477	2	.	.	PUNCT
ejpam-108	478	1	sci	sci	PROPN
ejpam-108	478	2	.	.	PROPN
ejpam-108	478	3	19	19	NUM
ejpam-108	478	4	(	(	PUNCT
ejpam-108	478	5	1996	1996	NUM
ejpam-108	478	6	)	)	PUNCT
ejpam-108	478	7	,	,	PUNCT
ejpam-108	478	8	303	303	NUM
ejpam-108	478	9	-	-	SYM
ejpam-108	478	10	310	310	NUM
ejpam-108	478	11	.	.	PUNCT
ejpam-108	479	1	[	[	X
ejpam-108	479	2	6	6	NUM
ejpam-108	479	3	]	]	PUNCT
ejpam-108	479	4	k.	k.	NOUN
ejpam-108	479	5	dlaska	dlaska	PROPN
ejpam-108	479	6	,	,	PUNCT
ejpam-108	479	7	n.	n.	NOUN
ejpam-108	479	8	ergun	ergun	NOUN
ejpam-108	479	9	and	and	CCONJ
ejpam-108	479	10	m.	m.	NOUN
ejpam-108	479	11	ganster	ganster	NOUN
ejpam-108	479	12	,	,	PUNCT
ejpam-108	479	13	"	"	PUNCT
ejpam-108	479	14	countably	countably	ADV
ejpam-108	479	15	s	s	NOUN
ejpam-108	479	16	-	-	PUNCT
ejpam-108	479	17	closd	closd	ADJ
ejpam-108	479	18	spaces	space	NOUN
ejpam-108	479	19	"	"	PUNCT
ejpam-108	479	20	,	,	PUNCT
ejpam-108	479	21	math	math	NOUN
ejpam-108	479	22	.	.	PUNCT
ejpam-108	480	1	slovaca	slovaca	NOUN
ejpam-108	480	2	44	44	NUM
ejpam-108	480	3	(	(	PUNCT
ejpam-108	480	4	1994	1994	NUM
ejpam-108	480	5	)	)	PUNCT
ejpam-108	480	6	,	,	PUNCT
ejpam-108	480	7	337	337	NUM
ejpam-108	480	8	-	-	SYM
ejpam-108	480	9	348	348	NUM
ejpam-108	480	10	.	.	PUNCT
ejpam-108	481	1	references	reference	NOUN
ejpam-108	481	2	229	229	NUM
ejpam-108	482	1	[	[	X
ejpam-108	482	2	7	7	NUM
ejpam-108	482	3	]	]	PUNCT
ejpam-108	482	4	a.	a.	NOUN
ejpam-108	482	5	keskin	keskin	PROPN
ejpam-108	482	6	and	and	CCONJ
ejpam-108	482	7	t.	t.	PROPN
ejpam-108	482	8	noiri	noiri	PROPN
ejpam-108	482	9	,	,	PUNCT
ejpam-108	482	10	"	"	PUNCT
ejpam-108	482	11	almost	almost	ADV
ejpam-108	482	12	b	b	X
ejpam-108	482	13	-	-	PUNCT
ejpam-108	482	14	continuous	continuous	ADJ
ejpam-108	482	15	functions	function	NOUN
ejpam-108	482	16	"	"	PUNCT
ejpam-108	482	17	,	,	PUNCT
ejpam-108	482	18	chaos	chaos	NOUN
ejpam-108	482	19	solitions	solition	NOUN
ejpam-108	482	20	fractals	fractal	NOUN
ejpam-108	482	21	(	(	PUNCT
ejpam-108	482	22	2007	2007	NUM
ejpam-108	482	23	)	)	PUNCT
ejpam-108	482	24	,	,	PUNCT
ejpam-108	482	25	doi:10.1016	doi:10.1016	PROPN
ejpam-108	482	26	/	/	SYM
ejpam-108	482	27	j.chaos.2007.11.012	j.chaos.2007.11.012	PROPN
ejpam-108	482	28	[	[	X
ejpam-108	482	29	8	8	NUM
ejpam-108	482	30	]	]	PUNCT
ejpam-108	482	31	s.	s.	PROPN
ejpam-108	482	32	jafari	jafari	PROPN
ejpam-108	482	33	and	and	CCONJ
ejpam-108	482	34	t.	t.	PROPN
ejpam-108	482	35	noiri	noiri	PROPN
ejpam-108	482	36	,	,	PUNCT
ejpam-108	482	37	"	"	PUNCT
ejpam-108	482	38	on	on	ADP
ejpam-108	482	39	contra	contra	ADJ
ejpam-108	482	40	-	-	ADJ
ejpam-108	482	41	precontinuous	precontinuous	ADJ
ejpam-108	482	42	functions	function	NOUN
ejpam-108	482	43	"	"	PUNCT
ejpam-108	482	44	,	,	PUNCT
ejpam-108	482	45	bull	bull	NOUN
ejpam-108	482	46	.	.	PUNCT
ejpam-108	483	1	malaysian	malaysian	ADJ
ejpam-108	483	2	math	math	PROPN
ejpam-108	483	3	.	.	PUNCT
ejpam-108	484	1	sc	sc	PROPN
ejpam-108	484	2	.	.	PROPN
ejpam-108	484	3	soc	soc	PROPN
ejpam-108	484	4	.	.	PUNCT
ejpam-108	485	1	25	25	NUM
ejpam-108	485	2	(	(	PUNCT
ejpam-108	485	3	2002	2002	NUM
ejpam-108	485	4	)	)	PUNCT
ejpam-108	485	5	,	,	PUNCT
ejpam-108	485	6	115	115	NUM
ejpam-108	485	7	-	-	SYM
ejpam-108	485	8	128	128	NUM
ejpam-108	485	9	.	.	PUNCT
ejpam-108	486	1	[	[	X
ejpam-108	486	2	9	9	NUM
ejpam-108	486	3	]	]	X
ejpam-108	486	4	j.e	j.e	PROPN
ejpam-108	486	5	.	.	PROPN
ejpam-108	486	6	joseph	joseph	PROPN
ejpam-108	486	7	and	and	CCONJ
ejpam-108	486	8	m.h	m.h	PROPN
ejpam-108	486	9	.	.	PROPN
ejpam-108	486	10	kwack	kwack	PROPN
ejpam-108	486	11	,	,	PUNCT
ejpam-108	486	12	"	"	PUNCT
ejpam-108	486	13	on	on	ADP
ejpam-108	486	14	s	s	NOUN
ejpam-108	486	15	-	-	PUNCT
ejpam-108	486	16	closed	closed	ADJ
ejpam-108	486	17	spaces	space	NOUN
ejpam-108	486	18	"	"	PUNCT
ejpam-108	486	19	,	,	PUNCT
ejpam-108	486	20	proc	proc	PROPN
ejpam-108	486	21	.	.	PUNCT
ejpam-108	487	1	amer	amer	PROPN
ejpam-108	487	2	.	.	PUNCT
ejpam-108	487	3	math	math	PROPN
ejpam-108	487	4	.	.	PUNCT
ejpam-108	488	1	soc	soc	PROPN
ejpam-108	488	2	.	.	PUNCT
ejpam-108	489	1	80(1980),341	80(1980),341	NUM
ejpam-108	489	2	-	-	SYM
ejpam-108	489	3	348	348	NUM
ejpam-108	489	4	.	.	PUNCT
ejpam-108	490	1	[	[	X
ejpam-108	490	2	10	10	NUM
ejpam-108	490	3	]	]	X
ejpam-108	490	4	e.	e.	PROPN
ejpam-108	490	5	ekici	ekici	PROPN
ejpam-108	490	6	,	,	PUNCT
ejpam-108	490	7	"	"	PUNCT
ejpam-108	490	8	almost	almost	ADV
ejpam-108	490	9	contra	contra	ADJ
ejpam-108	490	10	-	-	ADJ
ejpam-108	490	11	precontinuous	precontinuous	ADJ
ejpam-108	490	12	functions	function	NOUN
ejpam-108	490	13	"	"	PUNCT
ejpam-108	490	14	,	,	PUNCT
ejpam-108	490	15	bull	bull	NOUN
ejpam-108	490	16	.	.	PUNCT
ejpam-108	491	1	malaysian	malaysian	ADJ
ejpam-108	491	2	math	math	PROPN
ejpam-108	491	3	.	.	PUNCT
ejpam-108	492	1	sc	sc	PROPN
ejpam-108	492	2	.	.	PUNCT
ejpam-108	492	3	soc	soc	PROPN
ejpam-108	492	4	.	.	PUNCT
ejpam-108	493	1	27(1	27(1	NUM
ejpam-108	493	2	)	)	PUNCT
ejpam-108	493	3	(	(	PUNCT
ejpam-108	493	4	2004	2004	NUM
ejpam-108	493	5	)	)	PUNCT
ejpam-108	493	6	,	,	PUNCT
ejpam-108	493	7	53	53	NUM
ejpam-108	493	8	-	-	SYM
ejpam-108	493	9	65	65	NUM
ejpam-108	493	10	.	.	PUNCT
ejpam-108	494	1	[	[	X
ejpam-108	494	2	11	11	NUM
ejpam-108	494	3	]	]	X
ejpam-108	494	4	e.	e.	PROPN
ejpam-108	494	5	ekici	ekici	PROPN
ejpam-108	494	6	and	and	CCONJ
ejpam-108	494	7	m.	m.	NOUN
ejpam-108	494	8	caldas	caldas	PROPN
ejpam-108	494	9	,	,	PUNCT
ejpam-108	494	10	"	"	PUNCT
ejpam-108	494	11	slightly	slightly	ADV
ejpam-108	494	12	γ	γ	ADJ
ejpam-108	494	13	-	-	ADJ
ejpam-108	494	14	continuous	continuous	ADJ
ejpam-108	494	15	functions	function	NOUN
ejpam-108	494	16	"	"	PUNCT
ejpam-108	494	17	,	,	PUNCT
ejpam-108	494	18	bol	bol	NOUN
ejpam-108	494	19	.	.	PUNCT
ejpam-108	495	1	soc	soc	PROPN
ejpam-108	495	2	.	.	PUNCT
ejpam-108	496	1	paran	paran	PROPN
ejpam-108	496	2	.	.	PUNCT
ejpam-108	497	1	mat	mat	PROPN
ejpam-108	497	2	.	.	PUNCT
ejpam-108	498	1	22(2	22(2	NUM
ejpam-108	498	2	)	)	PUNCT
ejpam-108	498	3	(	(	PUNCT
ejpam-108	498	4	2004	2004	NUM
ejpam-108	498	5	)	)	PUNCT
ejpam-108	498	6	,	,	PUNCT
ejpam-108	498	7	63	63	NUM
ejpam-108	498	8	-	-	SYM
ejpam-108	498	9	74	74	NUM
ejpam-108	498	10	.	.	PUNCT
ejpam-108	499	1	[	[	X
ejpam-108	499	2	12	12	NUM
ejpam-108	499	3	]	]	PUNCT
ejpam-108	499	4	v.	v.	CCONJ
ejpam-108	499	5	popa	popa	NOUN
ejpam-108	499	6	and	and	CCONJ
ejpam-108	499	7	t.	t.	NOUN
ejpam-108	499	8	noiri	noiri	PROPN
ejpam-108	499	9	,	,	PUNCT
ejpam-108	499	10	"	"	PUNCT
ejpam-108	499	11	almost	almost	ADV
ejpam-108	499	12	weakly	weakly	ADJ
ejpam-108	499	13	continuous	continuous	ADJ
ejpam-108	499	14	functions	function	NOUN
ejpam-108	499	15	"	"	PUNCT
ejpam-108	499	16	,	,	PUNCT
ejpam-108	499	17	demonstratio	demonstratio	PROPN
ejpam-108	499	18	math	math	PROPN
ejpam-108	499	19	.	.	PUNCT
ejpam-108	500	1	25	25	NUM
ejpam-108	500	2	(	(	PUNCT
ejpam-108	500	3	1992	1992	NUM
ejpam-108	500	4	)	)	PUNCT
ejpam-108	500	5	,	,	PUNCT
ejpam-108	500	6	241	241	NUM
ejpam-108	500	7	-	-	SYM
ejpam-108	500	8	251	251	NUM
ejpam-108	500	9	.	.	PUNCT
ejpam-108	501	1	[	[	X
ejpam-108	501	2	13	13	NUM
ejpam-108	501	3	]	]	SYM
ejpam-108	501	4	a.a	a.a	PROPN
ejpam-108	501	5	.	.	PROPN
ejpam-108	501	6	nasef	nasef	PROPN
ejpam-108	501	7	,	,	PUNCT
ejpam-108	501	8	"	"	PUNCT
ejpam-108	501	9	some	some	DET
ejpam-108	501	10	properties	property	NOUN
ejpam-108	501	11	of	of	ADP
ejpam-108	501	12	contra	contra	PROPN
ejpam-108	501	13	-	-	PUNCT
ejpam-108	501	14	γ	γ	ADJ
ejpam-108	501	15	-	-	ADJ
ejpam-108	501	16	continuous	continuous	ADJ
ejpam-108	501	17	functions	function	NOUN
ejpam-108	501	18	"	"	PUNCT
ejpam-108	501	19	,	,	PUNCT
ejpam-108	501	20	chaos	chaos	NOUN
ejpam-108	501	21	solitons	soliton	NOUN
ejpam-108	501	22	fractals	fractal	NOUN
ejpam-108	501	23	24	24	NUM
ejpam-108	501	24	(	(	PUNCT
ejpam-108	501	25	2005	2005	NUM
ejpam-108	501	26	)	)	PUNCT
ejpam-108	501	27	,	,	PUNCT
ejpam-108	501	28	471	471	NUM
ejpam-108	501	29	-	-	SYM
ejpam-108	501	30	477	477	NUM
ejpam-108	501	31	.	.	PUNCT
ejpam-108	502	1	[	[	X
ejpam-108	502	2	14	14	NUM
ejpam-108	502	3	]	]	X
ejpam-108	502	4	o.	o.	NOUN
ejpam-108	502	5	njåstad	njåstad	PROPN
ejpam-108	502	6	,	,	PUNCT
ejpam-108	502	7	"	"	PUNCT
ejpam-108	502	8	on	on	ADP
ejpam-108	502	9	some	some	DET
ejpam-108	502	10	classes	class	NOUN
ejpam-108	502	11	of	of	ADP
ejpam-108	502	12	nearly	nearly	ADV
ejpam-108	502	13	open	open	ADJ
ejpam-108	502	14	sets	set	NOUN
ejpam-108	502	15	"	"	PUNCT
ejpam-108	502	16	,	,	PUNCT
ejpam-108	502	17	pacific	pacific	PROPN
ejpam-108	502	18	j.	j.	PROPN
ejpam-108	502	19	math	math	PROPN
ejpam-108	502	20	.	.	PUNCT
ejpam-108	503	1	15	15	NUM
ejpam-108	503	2	(	(	PUNCT
ejpam-108	503	3	1965	1965	NUM
ejpam-108	503	4	)	)	PUNCT
ejpam-108	503	5	,	,	PUNCT
ejpam-108	503	6	961	961	NUM
ejpam-108	503	7	-	-	SYM
ejpam-108	503	8	970	970	NUM
ejpam-108	503	9	.	.	PUNCT
ejpam-108	504	1	[	[	X
ejpam-108	504	2	15	15	NUM
ejpam-108	504	3	]	]	X
ejpam-108	504	4	t.	t.	PROPN
ejpam-108	504	5	noiri	noiri	PROPN
ejpam-108	504	6	,	,	PUNCT
ejpam-108	504	7	"	"	PUNCT
ejpam-108	504	8	on	on	ADP
ejpam-108	504	9	almost	almost	ADV
ejpam-108	504	10	continuous	continuous	ADJ
ejpam-108	504	11	functions	function	NOUN
ejpam-108	504	12	"	"	PUNCT
ejpam-108	504	13	,	,	PUNCT
ejpam-108	504	14	indian	indian	PROPN
ejpam-108	504	15	j.	j.	PROPN
ejpam-108	504	16	pure	pure	PROPN
ejpam-108	504	17	appl	appl	PROPN
ejpam-108	504	18	.	.	PUNCT
ejpam-108	504	19	math	math	NOUN
ejpam-108	504	20	.	.	PUNCT
ejpam-108	505	1	20	20	NUM
ejpam-108	505	2	(	(	PUNCT
ejpam-108	505	3	1989	1989	NUM
ejpam-108	505	4	)	)	PUNCT
ejpam-108	505	5	,	,	PUNCT
ejpam-108	505	6	571576	571576	NUM
ejpam-108	505	7	.	.	PUNCT
ejpam-108	506	1	[	[	X
ejpam-108	506	2	16	16	NUM
ejpam-108	506	3	]	]	PUNCT
ejpam-108	506	4	v.	v.	CCONJ
ejpam-108	506	5	popa	popa	NOUN
ejpam-108	506	6	and	and	CCONJ
ejpam-108	506	7	t.	t.	NOUN
ejpam-108	506	8	noiri	noiri	PROPN
ejpam-108	506	9	,	,	PUNCT
ejpam-108	506	10	"	"	PUNCT
ejpam-108	506	11	on	on	ADP
ejpam-108	506	12	the	the	DET
ejpam-108	506	13	definitions	definition	NOUN
ejpam-108	506	14	of	of	ADP
ejpam-108	506	15	some	some	DET
ejpam-108	506	16	generalized	generalized	ADJ
ejpam-108	506	17	forms	form	NOUN
ejpam-108	506	18	of	of	ADP
ejpam-108	506	19	continuity	continuity	NOUN
ejpam-108	506	20	under	under	ADP
ejpam-108	506	21	minimal	minimal	ADJ
ejpam-108	506	22	conditions	condition	NOUN
ejpam-108	506	23	"	"	PUNCT
ejpam-108	506	24	,	,	PUNCT
ejpam-108	506	25	mem	mem	X
ejpam-108	506	26	.	.	PUNCT
ejpam-108	506	27	fac	fac	PROPN
ejpam-108	506	28	.	.	PUNCT
ejpam-108	506	29	sci	sci	PROPN
ejpam-108	506	30	.	.	PROPN
ejpam-108	506	31	kochi	kochi	PROPN
ejpam-108	506	32	univ	univ	PROPN
ejpam-108	506	33	.	.	PUNCT
ejpam-108	506	34	ser	ser	PROPN
ejpam-108	506	35	.	.	PUNCT
ejpam-108	506	36	math	math	NOUN
ejpam-108	506	37	.	.	PUNCT
ejpam-108	507	1	22	22	NUM
ejpam-108	507	2	(	(	PUNCT
ejpam-108	507	3	2001	2001	NUM
ejpam-108	507	4	)	)	PUNCT
ejpam-108	507	5	,	,	PUNCT
ejpam-108	507	6	31	31	NUM
ejpam-108	507	7	-	-	SYM
ejpam-108	507	8	41	41	NUM
ejpam-108	507	9	.	.	PUNCT
ejpam-108	508	1	[	[	X
ejpam-108	508	2	17	17	NUM
ejpam-108	508	3	]	]	PUNCT
ejpam-108	508	4	t.	t.	PROPN
ejpam-108	508	5	noiri	noiri	PROPN
ejpam-108	508	6	and	and	CCONJ
ejpam-108	508	7	v.	v.	ADP
ejpam-108	508	8	popa	popa	NOUN
ejpam-108	508	9	,	,	PUNCT
ejpam-108	508	10	"	"	PUNCT
ejpam-108	508	11	a	a	DET
ejpam-108	508	12	unified	unified	ADJ
ejpam-108	508	13	theory	theory	NOUN
ejpam-108	508	14	of	of	ADP
ejpam-108	508	15	contra	contra	PROPN
ejpam-108	508	16	-	-	NOUN
ejpam-108	508	17	continuity	continuity	NOUN
ejpam-108	508	18	for	for	ADP
ejpam-108	508	19	functions	function	NOUN
ejpam-108	508	20	"	"	PUNCT
ejpam-108	508	21	,	,	PUNCT
ejpam-108	508	22	ann	ann	PROPN
ejpam-108	508	23	.	.	PROPN
ejpam-108	508	24	univ	univ	PROPN
ejpam-108	508	25	.	.	PUNCT
ejpam-108	509	1	sci	sci	PROPN
ejpam-108	509	2	.	.	PUNCT
ejpam-108	510	1	budapest	budapest	PROPN
ejpam-108	510	2	44	44	NUM
ejpam-108	510	3	(	(	PUNCT
ejpam-108	510	4	2002	2002	NUM
ejpam-108	510	5	)	)	PUNCT
ejpam-108	510	6	,	,	PUNCT
ejpam-108	510	7	115	115	NUM
ejpam-108	510	8	-	-	SYM
ejpam-108	510	9	137	137	NUM
ejpam-108	510	10	.	.	PUNCT
ejpam-108	511	1	[	[	X
ejpam-108	511	2	18	18	NUM
ejpam-108	511	3	]	]	PUNCT
ejpam-108	511	4	t.	t.	PROPN
ejpam-108	511	5	noiri	noiri	PROPN
ejpam-108	511	6	and	and	CCONJ
ejpam-108	511	7	v.	v.	ADP
ejpam-108	511	8	popa	popa	NOUN
ejpam-108	511	9	,	,	PUNCT
ejpam-108	511	10	"	"	PUNCT
ejpam-108	511	11	on	on	ADP
ejpam-108	511	12	m	m	ADJ
ejpam-108	511	13	-	-	PUNCT
ejpam-108	511	14	quasi	quasi	ADJ
ejpam-108	511	15	irresolute	irresolute	PROPN
ejpam-108	511	16	functions	function	NOUN
ejpam-108	511	17	"	"	PUNCT
ejpam-108	511	18	,	,	PUNCT
ejpam-108	511	19	math	math	NOUN
ejpam-108	511	20	.	.	PUNCT
ejpam-108	512	1	moravica	moravica	PROPN
ejpam-108	512	2	9	9	NUM
ejpam-108	512	3	(	(	PUNCT
ejpam-108	512	4	2005	2005	NUM
ejpam-108	512	5	)	)	PUNCT
ejpam-108	512	6	,	,	PUNCT
ejpam-108	512	7	25	25	NUM
ejpam-108	512	8	-	-	SYM
ejpam-108	512	9	41	41	NUM
ejpam-108	512	10	.	.	PUNCT
ejpam-108	513	1	[	[	X
ejpam-108	513	2	19	19	NUM
ejpam-108	513	3	]	]	X
ejpam-108	513	4	t.	t.	PROPN
ejpam-108	513	5	noiri	noiri	PROPN
ejpam-108	513	6	and	and	CCONJ
ejpam-108	513	7	v.	v.	ADP
ejpam-108	513	8	popa	popa	NOUN
ejpam-108	513	9	,	,	PUNCT
ejpam-108	513	10	"	"	PUNCT
ejpam-108	513	11	a	a	DET
ejpam-108	513	12	unified	unified	ADJ
ejpam-108	513	13	theory	theory	NOUN
ejpam-108	513	14	of	of	ADP
ejpam-108	513	15	almost	almost	ADV
ejpam-108	513	16	contra	contra	NOUN
ejpam-108	513	17	-	-	NOUN
ejpam-108	513	18	continuity	continuity	NOUN
ejpam-108	513	19	for	for	ADP
ejpam-108	513	20	functions	function	NOUN
ejpam-108	513	21	"	"	PUNCT
ejpam-108	513	22	,	,	PUNCT
ejpam-108	513	23	kochi	kochi	PROPN
ejpam-108	513	24	j.	j.	PROPN
ejpam-108	513	25	math	math	PROPN
ejpam-108	513	26	.	.	PUNCT
ejpam-108	514	1	3	3	NUM
ejpam-108	514	2	(	(	PUNCT
ejpam-108	514	3	2008	2008	NUM
ejpam-108	514	4	)	)	PUNCT
ejpam-108	514	5	,	,	PUNCT
ejpam-108	514	6	125	125	NUM
ejpam-108	514	7	-	-	SYM
ejpam-108	514	8	138	138	NUM
ejpam-108	514	9	.	.	PUNCT
ejpam-108	515	1	[	[	X
ejpam-108	515	2	20	20	NUM
ejpam-108	515	3	]	]	PUNCT
ejpam-108	515	4	t.	t.	PROPN
ejpam-108	515	5	noiri	noiri	PROPN
ejpam-108	515	6	,	,	PUNCT
ejpam-108	515	7	a.	a.	PROPN
ejpam-108	515	8	al	al	PROPN
ejpam-108	515	9	-	-	PUNCT
ejpam-108	515	10	omari	omari	PROPN
ejpam-108	515	11	and	and	CCONJ
ejpam-108	515	12	m.s.m	m.s.m	PROPN
ejpam-108	515	13	.	.	PROPN
ejpam-108	515	14	noorani	noorani	PROPN
ejpam-108	515	15	,	,	PUNCT
ejpam-108	515	16	"	"	PUNCT
ejpam-108	515	17	weakly	weakly	ADJ
ejpam-108	515	18	b	b	X
ejpam-108	515	19	-	-	PUNCT
ejpam-108	515	20	open	open	ADJ
ejpam-108	515	21	functions	function	NOUN
ejpam-108	515	22	"	"	PUNCT
ejpam-108	515	23	,	,	PUNCT
ejpam-108	515	24	mathematica	mathematica	PROPN
ejpam-108	515	25	balkanica	balkanica	PROPN
ejpam-108	515	26	23	23	NUM
ejpam-108	515	27	(	(	PUNCT
ejpam-108	515	28	2009),fasc	2009),fasc	NUM
ejpam-108	515	29	(	(	PUNCT
ejpam-108	515	30	1	1	NUM
ejpam-108	515	31	-	-	SYM
ejpam-108	515	32	2	2	NUM
ejpam-108	515	33	)	)	PUNCT
ejpam-108	515	34	1	1	NUM
ejpam-108	515	35	-	-	SYM
ejpam-108	515	36	14	14	NUM
ejpam-108	515	37	.	.	PUNCT
ejpam-108	516	1	[	[	X
ejpam-108	516	2	21	21	NUM
ejpam-108	516	3	]	]	PUNCT
ejpam-108	516	4	t.	t.	PROPN
ejpam-108	516	5	thompson	thompson	PROPN
ejpam-108	516	6	,	,	PUNCT
ejpam-108	516	7	"	"	PUNCT
ejpam-108	516	8	s	s	NOUN
ejpam-108	516	9	-	-	PUNCT
ejpam-108	516	10	closed	closed	ADJ
ejpam-108	516	11	spaces	space	NOUN
ejpam-108	516	12	"	"	PUNCT
ejpam-108	516	13	,	,	PUNCT
ejpam-108	516	14	proc	proc	PROPN
ejpam-108	516	15	.	.	PUNCT
ejpam-108	517	1	amer	amer	PROPN
ejpam-108	517	2	.	.	PUNCT
ejpam-108	517	3	math	math	PROPN
ejpam-108	517	4	.	.	PUNCT
ejpam-108	518	1	soc	soc	PROPN
ejpam-108	518	2	.	.	PUNCT
ejpam-108	519	1	60	60	NUM
ejpam-108	519	2	(	(	PUNCT
ejpam-108	519	3	1976	1976	NUM
ejpam-108	519	4	)	)	PUNCT
ejpam-108	519	5	,	,	PUNCT
ejpam-108	519	6	335	335	NUM
ejpam-108	519	7	-	-	SYM
ejpam-108	519	8	338	338	NUM
ejpam-108	519	9	.	.	PUNCT
ejpam-108	520	1	[	[	X
ejpam-108	520	2	22	22	NUM
ejpam-108	520	3	]	]	PUNCT
ejpam-108	520	4	m.	m.	NOUN
ejpam-108	520	5	singal	singal	NOUN
ejpam-108	520	6	and	and	CCONJ
ejpam-108	520	7	a.	a.	PROPN
ejpam-108	520	8	mathur	mathur	PROPN
ejpam-108	520	9	,	,	PUNCT
ejpam-108	520	10	"	"	PUNCT
ejpam-108	520	11	on	on	ADP
ejpam-108	520	12	nearly	nearly	ADV
ejpam-108	520	13	-	-	PUNCT
ejpam-108	520	14	compact	compact	ADJ
ejpam-108	520	15	spaces	space	NOUN
ejpam-108	520	16	"	"	PUNCT
ejpam-108	520	17	,	,	PUNCT
ejpam-108	520	18	boll	boll	NOUN
ejpam-108	520	19	.	.	PUNCT
ejpam-108	520	20	un	un	PROPN
ejpam-108	520	21	.	.	PROPN
ejpam-108	520	22	mat	mat	PROPN
ejpam-108	520	23	.	.	PUNCT
ejpam-108	520	24	ital	ital	PROPN
ejpam-108	520	25	.	.	PUNCT
ejpam-108	521	1	serie	serie	PROPN
ejpam-108	521	2	9	9	NUM
ejpam-108	521	3	(	(	PUNCT
ejpam-108	521	4	46)(1969	46)(1969	NUM
ejpam-108	521	5	)	)	PUNCT
ejpam-108	521	6	,	,	PUNCT
ejpam-108	521	7	702	702	NUM
ejpam-108	521	8	-	-	SYM
ejpam-108	521	9	710	710	NUM
ejpam-108	521	10	.	.	PUNCT
ejpam-108	522	1	references	reference	NOUN
ejpam-108	522	2	230	230	NUM
ejpam-108	523	1	[	[	SYM
ejpam-108	523	2	23	23	NUM
ejpam-108	523	3	]	]	PUNCT
ejpam-108	523	4	t.	t.	PROPN
ejpam-108	523	5	soundararajan	soundararajan	PROPN
ejpam-108	523	6	,	,	PUNCT
ejpam-108	523	7	"	"	PUNCT
ejpam-108	523	8	weakly	weakly	ADJ
ejpam-108	523	9	hausdorff	hausdorff	NOUN
ejpam-108	523	10	spaces	space	NOUN
ejpam-108	523	11	and	and	CCONJ
ejpam-108	523	12	the	the	DET
ejpam-108	523	13	cardinality	cardinality	NOUN
ejpam-108	523	14	of	of	ADP
ejpam-108	523	15	topological	topological	ADJ
ejpam-108	523	16	spaces	space	NOUN
ejpam-108	523	17	in	in	ADP
ejpam-108	523	18	general	general	ADJ
ejpam-108	523	19	topology	topology	NOUN
ejpam-108	523	20	and	and	CCONJ
ejpam-108	523	21	its	its	PRON
ejpam-108	523	22	relation	relation	NOUN
ejpam-108	523	23	to	to	ADP
ejpam-108	523	24	modern	modern	ADJ
ejpam-108	523	25	analysis	analysis	NOUN
ejpam-108	523	26	and	and	CCONJ
ejpam-108	523	27	algebra	algebra	NOUN
ejpam-108	523	28	"	"	PUNCT
ejpam-108	523	29	,	,	PUNCT
ejpam-108	523	30	boll.un.iii	boll.un.iii	NOUN
ejpam-108	523	31	,	,	PUNCT
ejpam-108	523	32	proc	proc	NOUN
ejpam-108	523	33	.	.	PUNCT
ejpam-108	523	34	conf	conf	NOUN
ejpam-108	523	35	.	.	PUNCT
ejpam-108	524	1	kanpur(1968	kanpur(1968	NOUN
ejpam-108	524	2	)	)	PUNCT
ejpam-108	524	3	academia	academia	NOUN
ejpam-108	524	4	,	,	PUNCT
ejpam-108	524	5	prague	prague	NOUN
ejpam-108	524	6	(	(	PUNCT
ejpam-108	524	7	1971	1971	NUM
ejpam-108	524	8	)	)	PUNCT
ejpam-108	524	9	,	,	PUNCT
ejpam-108	524	10	301	301	NUM
ejpam-108	524	11	-	-	SYM
ejpam-108	524	12	306	306	NUM
ejpam-108	524	13	.	.	PUNCT
ejpam-108	525	1	[	[	X
ejpam-108	525	2	24	24	NUM
ejpam-108	525	3	]	]	X
ejpam-108	525	4	n.	n.	PROPN
ejpam-108	525	5	levine	levine	PROPN
ejpam-108	525	6	,	,	PUNCT
ejpam-108	525	7	"	"	PUNCT
ejpam-108	525	8	semi	semi	ADJ
ejpam-108	525	9	-	-	ADJ
ejpam-108	525	10	open	open	ADJ
ejpam-108	525	11	sets	set	NOUN
ejpam-108	525	12	and	and	CCONJ
ejpam-108	525	13	semi	semi	ADJ
ejpam-108	525	14	-	-	NOUN
ejpam-108	525	15	continuity	continuity	NOUN
ejpam-108	525	16	in	in	ADP
ejpam-108	525	17	topological	topological	ADJ
ejpam-108	525	18	spaces	space	NOUN
ejpam-108	525	19	"	"	PUNCT
ejpam-108	525	20	,	,	PUNCT
ejpam-108	525	21	amer	amer	PROPN
ejpam-108	525	22	.	.	PROPN
ejpam-108	525	23	math	math	PROPN
ejpam-108	525	24	.	.	PUNCT
ejpam-108	526	1	monthly	monthly	ADJ
ejpam-108	526	2	70	70	NUM
ejpam-108	526	3	(	(	PUNCT
ejpam-108	526	4	1963	1963	NUM
ejpam-108	526	5	)	)	PUNCT
ejpam-108	526	6	,	,	PUNCT
ejpam-108	526	7	36	36	NUM
ejpam-108	526	8	-	-	SYM
ejpam-108	526	9	41	41	NUM
ejpam-108	526	10	.	.	PUNCT
ejpam-108	527	1	[	[	X
ejpam-108	527	2	25	25	NUM
ejpam-108	527	3	]	]	PUNCT
ejpam-108	527	4	a.	a.	NOUN
ejpam-108	527	5	s.	s.	PROPN
ejpam-108	527	6	mashhour	mashhour	PROPN
ejpam-108	527	7	,	,	PUNCT
ejpam-108	527	8	m.	m.	PROPN
ejpam-108	527	9	e.	e.	PROPN
ejpam-108	527	10	abd	abd	PROPN
ejpam-108	527	11	el	el	PROPN
ejpam-108	527	12	-	-	PROPN
ejpam-108	527	13	monsef	monsef	PROPN
ejpam-108	527	14	and	and	CCONJ
ejpam-108	527	15	s.	s.	PROPN
ejpam-108	527	16	n.	n.	PROPN
ejpam-108	527	17	el	el	PROPN
ejpam-108	527	18	-	-	PROPN
ejpam-108	527	19	deeb	deeb	PROPN
ejpam-108	527	20	,	,	PUNCT
ejpam-108	527	21	"	"	PUNCT
ejpam-108	527	22	on	on	ADP
ejpam-108	527	23	precontinuous	precontinuous	ADJ
ejpam-108	527	24	and	and	CCONJ
ejpam-108	527	25	weak	weak	ADJ
ejpam-108	527	26	precontinuous	precontinuous	ADJ
ejpam-108	527	27	functions	function	NOUN
ejpam-108	527	28	"	"	PUNCT
ejpam-108	527	29	,	,	PUNCT
ejpam-108	527	30	proc	proc	PROPN
ejpam-108	527	31	.	.	PUNCT
ejpam-108	528	1	math	math	NOUN
ejpam-108	528	2	.	.	PUNCT
ejpam-108	529	1	phys	phy	NOUN
ejpam-108	529	2	.	.	PUNCT
ejpam-108	530	1	soc	soc	PROPN
ejpam-108	530	2	.	.	PUNCT
ejpam-108	531	1	egypt	egypt	PROPN
ejpam-108	531	2	51	51	NUM
ejpam-108	531	3	(	(	PUNCT
ejpam-108	531	4	1982	1982	NUM
ejpam-108	531	5	)	)	PUNCT
ejpam-108	531	6	,	,	PUNCT
ejpam-108	531	7	47	47	NUM
ejpam-108	531	8	-	-	SYM
ejpam-108	531	9	53	53	NUM
ejpam-108	531	10	.	.	PUNCT
ejpam-108	532	1	[	[	X
ejpam-108	532	2	26	26	NUM
ejpam-108	532	3	]	]	X
ejpam-108	532	4	f.h	f.h	PROPN
ejpam-108	532	5	.	.	PROPN
ejpam-108	532	6	khwdr	khwdr	PROPN
ejpam-108	532	7	and	and	CCONJ
ejpam-108	532	8	t.	t.	PROPN
ejpam-108	532	9	noiri	noiri	PROPN
ejpam-108	532	10	,	,	PUNCT
ejpam-108	532	11	"	"	PUNCT
ejpam-108	532	12	on	on	ADP
ejpam-108	532	13	θ	θ	PROPN
ejpam-108	532	14	-irresolute	-irresolute	NOUN
ejpam-108	532	15	functions	function	NOUN
ejpam-108	532	16	"	"	PUNCT
ejpam-108	532	17	,	,	PUNCT
ejpam-108	532	18	indian	indian	PROPN
ejpam-108	532	19	j.	j.	PROPN
ejpam-108	532	20	of	of	ADP
ejpam-108	532	21	math	math	NOUN
ejpam-108	532	22	.	.	PUNCT
ejpam-108	533	1	28(3	28(3	NUM
ejpam-108	533	2	)	)	PUNCT
ejpam-108	533	3	(	(	PUNCT
ejpam-108	533	4	1986	1986	NUM
ejpam-108	533	5	)	)	PUNCT
ejpam-108	533	6	,	,	PUNCT
ejpam-108	533	7	211	211	NUM
ejpam-108	533	8	-	-	SYM
ejpam-108	533	9	217	217	NUM
ejpam-108	533	10	.	.	PUNCT
ejpam-108	534	1	[	[	X
ejpam-108	534	2	27	27	NUM
ejpam-108	534	3	]	]	X
ejpam-108	534	4	s.	s.	PROPN
ejpam-108	534	5	willard	willard	PROPN
ejpam-108	534	6	,	,	PUNCT
ejpam-108	534	7	general	general	ADJ
ejpam-108	534	8	topology	topology	NOUN
ejpam-108	534	9	spaces	space	VERB
ejpam-108	534	10	,	,	PUNCT
ejpam-108	534	11	addison	addison	PROPN
ejpam-108	534	12	wesley	wesley	PROPN
ejpam-108	534	13	,	,	PUNCT
ejpam-108	534	14	1970	1970	NUM
ejpam-108	534	15	.	.	PUNCT