id	sid	tid	token	lemma	pos
ejpam-289	1	1	2_289_kilicman.dvi	2_289_kilicman.dvi	NUM
ejpam-289	1	2	european	european	ADJ
ejpam-289	1	3	journal	journal	NOUN
ejpam-289	1	4	of	of	ADP
ejpam-289	1	5	pure	pure	ADJ
ejpam-289	1	6	and	and	CCONJ
ejpam-289	1	7	applied	apply	VERB
ejpam-289	1	8	mathematics	mathematic	NOUN
ejpam-289	1	9	vol	vol	NOUN
ejpam-289	1	10	.	.	PROPN
ejpam-289	2	1	2	2	NUM
ejpam-289	2	2	,	,	PUNCT
ejpam-289	2	3	no	no	INTJ
ejpam-289	2	4	.	.	NOUN
ejpam-289	2	5	3	3	NUM
ejpam-289	2	6	,	,	PUNCT
ejpam-289	2	7	2009	2009	NUM
ejpam-289	2	8	,	,	PUNCT
ejpam-289	2	9	(	(	PUNCT
ejpam-289	2	10	325	325	NUM
ejpam-289	2	11	-	-	SYM
ejpam-289	2	12	337	337	NUM
ejpam-289	2	13	)	)	PUNCT
ejpam-289	2	14	issn	issn	PROPN
ejpam-289	2	15	1307	1307	NUM
ejpam-289	2	16	-	-	SYM
ejpam-289	2	17	5543	5543	NUM
ejpam-289	2	18	–	–	PUNCT
ejpam-289	2	19	www.ejpam.com	www.ejpam.com	X
ejpam-289	2	20	a	a	DET
ejpam-289	2	21	note	note	NOUN
ejpam-289	2	22	on	on	ADP
ejpam-289	2	23	pairwise	pairwise	NOUN
ejpam-289	2	24	continuous	continuous	ADJ
ejpam-289	2	25	mappings	mapping	NOUN
ejpam-289	2	26	and	and	CCONJ
ejpam-289	2	27	bitopological	bitopological	ADJ
ejpam-289	2	28	spaces	space	NOUN
ejpam-289	2	29	adem	adem	PROPN
ejpam-289	2	30	kılıçman1∗	kılıçman1∗	PROPN
ejpam-289	2	31	and	and	CCONJ
ejpam-289	2	32	zabidin	zabidin	VERB
ejpam-289	2	33	salleh2	salleh2	NOUN
ejpam-289	2	34	1	1	NUM
ejpam-289	2	35	department	department	NOUN
ejpam-289	2	36	of	of	ADP
ejpam-289	2	37	mathematics	mathematics	PROPN
ejpam-289	2	38	and	and	CCONJ
ejpam-289	2	39	institute	institute	PROPN
ejpam-289	2	40	for	for	ADP
ejpam-289	2	41	mathematical	mathematical	ADJ
ejpam-289	2	42	research	research	NOUN
ejpam-289	2	43	,	,	PUNCT
ejpam-289	2	44	university	university	NOUN
ejpam-289	2	45	putra	putra	PROPN
ejpam-289	2	46	malaysia	malaysia	PROPN
ejpam-289	2	47	,	,	PUNCT
ejpam-289	2	48	43400	43400	NUM
ejpam-289	2	49	upm	upm	PROPN
ejpam-289	2	50	,	,	PUNCT
ejpam-289	2	51	serdang	serdang	PROPN
ejpam-289	2	52	,	,	PUNCT
ejpam-289	2	53	selangor	selangor	PROPN
ejpam-289	2	54	,	,	PUNCT
ejpam-289	2	55	malaysia	malaysia	PROPN
ejpam-289	2	56	2	2	NUM
ejpam-289	2	57	department	department	NOUN
ejpam-289	2	58	of	of	ADP
ejpam-289	2	59	mathematics	mathematic	NOUN
ejpam-289	2	60	,	,	PUNCT
ejpam-289	2	61	faculty	faculty	NOUN
ejpam-289	2	62	of	of	ADP
ejpam-289	2	63	science	science	NOUN
ejpam-289	2	64	and	and	CCONJ
ejpam-289	2	65	technology	technology	NOUN
ejpam-289	2	66	,	,	PUNCT
ejpam-289	2	67	university	university	PROPN
ejpam-289	2	68	malaysia	malaysia	PROPN
ejpam-289	2	69	terengganu	terengganu	PROPN
ejpam-289	2	70	,	,	PUNCT
ejpam-289	2	71	21030	21030	NUM
ejpam-289	2	72	kuala	kuala	PROPN
ejpam-289	2	73	terengganu	terengganu	PROPN
ejpam-289	2	74	,	,	PUNCT
ejpam-289	2	75	terengganu	terengganu	PROPN
ejpam-289	2	76	,	,	PUNCT
ejpam-289	2	77	malaysia	malaysia	PROPN
ejpam-289	2	78	abstract	abstract	NOUN
ejpam-289	2	79	.	.	PUNCT
ejpam-289	3	1	we	we	PRON
ejpam-289	3	2	shall	shall	AUX
ejpam-289	3	3	continue	continue	VERB
ejpam-289	3	4	the	the	DET
ejpam-289	3	5	study	study	NOUN
ejpam-289	3	6	of	of	ADP
ejpam-289	3	7	bitopological	bitopological	ADJ
ejpam-289	3	8	separation	separation	NOUN
ejpam-289	3	9	axioms	axiom	NOUN
ejpam-289	3	10	that	that	PRON
ejpam-289	3	11	was	be	AUX
ejpam-289	3	12	begun	begin	VERB
ejpam-289	3	13	by	by	ADP
ejpam-289	3	14	kelly	kelly	PROPN
ejpam-289	3	15	and	and	CCONJ
ejpam-289	3	16	obtained	obtain	VERB
ejpam-289	3	17	some	some	DET
ejpam-289	3	18	results	result	NOUN
ejpam-289	3	19	.	.	PUNCT
ejpam-289	4	1	furthermore	furthermore	ADV
ejpam-289	4	2	,	,	PUNCT
ejpam-289	4	3	we	we	PRON
ejpam-289	4	4	introduce	introduce	VERB
ejpam-289	4	5	a	a	DET
ejpam-289	4	6	concept	concept	NOUN
ejpam-289	4	7	of	of	ADP
ejpam-289	4	8	pairwise	pairwise	NOUN
ejpam-289	4	9	lindelöf	lindelöf	NOUN
ejpam-289	4	10	bitopological	bitopological	ADJ
ejpam-289	4	11	spaces	space	NOUN
ejpam-289	4	12	,	,	PUNCT
ejpam-289	4	13	namely	namely	ADV
ejpam-289	4	14	,	,	PUNCT
ejpam-289	4	15	p2	p2	ADJ
ejpam-289	4	16	-	-	PUNCT
ejpam-289	4	17	lindelöf	lindelöf	NOUN
ejpam-289	4	18	spaces	space	NOUN
ejpam-289	4	19	and	and	CCONJ
ejpam-289	4	20	their	their	PRON
ejpam-289	4	21	properties	property	NOUN
ejpam-289	4	22	are	be	AUX
ejpam-289	4	23	established	establish	VERB
ejpam-289	4	24	.	.	PUNCT
ejpam-289	5	1	we	we	PRON
ejpam-289	5	2	also	also	ADV
ejpam-289	5	3	show	show	VERB
ejpam-289	5	4	that	that	SCONJ
ejpam-289	5	5	a	a	DET
ejpam-289	5	6	p2	p2	ADJ
ejpam-289	5	7	-	-	PUNCT
ejpam-289	5	8	lindelöf	lindelöf	NOUN
ejpam-289	5	9	space	space	NOUN
ejpam-289	5	10	is	be	AUX
ejpam-289	5	11	not	not	PART
ejpam-289	5	12	a	a	DET
ejpam-289	5	13	hereditary	hereditary	ADJ
ejpam-289	5	14	property	property	NOUN
ejpam-289	5	15	.	.	PUNCT
ejpam-289	6	1	finally	finally	ADV
ejpam-289	6	2	,	,	PUNCT
ejpam-289	6	3	we	we	PRON
ejpam-289	6	4	show	show	VERB
ejpam-289	6	5	that	that	SCONJ
ejpam-289	6	6	a	a	DET
ejpam-289	6	7	p2	p2	ADJ
ejpam-289	6	8	-	-	PUNCT
ejpam-289	6	9	lindelöf	lindelöf	NOUN
ejpam-289	6	10	space	space	NOUN
ejpam-289	6	11	is	be	AUX
ejpam-289	6	12	a	a	DET
ejpam-289	6	13	p2	p2	ADJ
ejpam-289	6	14	-	-	PUNCT
ejpam-289	6	15	topological	topological	ADJ
ejpam-289	6	16	property	property	NOUN
ejpam-289	6	17	.	.	PUNCT
ejpam-289	7	1	2000	2000	NUM
ejpam-289	7	2	mathematics	mathematic	NOUN
ejpam-289	7	3	subject	subject	NOUN
ejpam-289	7	4	classifications	classification	NOUN
ejpam-289	7	5	:	:	PUNCT
ejpam-289	7	6	54e55	54e55	NUM
ejpam-289	7	7	key	key	ADJ
ejpam-289	7	8	words	word	NOUN
ejpam-289	7	9	and	and	CCONJ
ejpam-289	7	10	phrases	phrase	NOUN
ejpam-289	7	11	:	:	PUNCT
ejpam-289	7	12	bitopological	bitopological	ADJ
ejpam-289	7	13	space	space	NOUN
ejpam-289	7	14	,	,	PUNCT
ejpam-289	7	15	p2	p2	NOUN
ejpam-289	7	16	-	-	PUNCT
ejpam-289	7	17	compact	compact	ADJ
ejpam-289	7	18	,	,	PUNCT
ejpam-289	7	19	p2	p2	NOUN
ejpam-289	7	20	-	-	PUNCT
ejpam-289	7	21	lindelöf	lindelöf	NOUN
ejpam-289	7	22	,	,	PUNCT
ejpam-289	7	23	p1	p1	NOUN
ejpam-289	7	24	-	-	PUNCT
ejpam-289	7	25	regular	regular	ADJ
ejpam-289	7	26	,	,	PUNCT
ejpam-289	7	27	p2	p2	NOUN
ejpam-289	7	28	-	-	PUNCT
ejpam-289	7	29	normal	normal	ADJ
ejpam-289	7	30	,	,	PUNCT
ejpam-289	7	31	p2	p2	NOUN
ejpam-289	7	32	-	-	PUNCT
ejpam-289	7	33	continuity	continuity	NOUN
ejpam-289	7	34	,	,	PUNCT
ejpam-289	7	35	p2	p2	NOUN
ejpam-289	7	36	-	-	PUNCT
ejpam-289	7	37	homeomorphism	homeomorphism	NOUN
ejpam-289	7	38	.	.	PUNCT
ejpam-289	8	1	∗corresponding	∗corresponde	VERB
ejpam-289	8	2	author	author	NOUN
ejpam-289	8	3	.	.	PUNCT
ejpam-289	9	1	email	email	NOUN
ejpam-289	9	2	addresses	address	NOUN
ejpam-289	9	3	:	:	PUNCT
ejpam-289	9	4	akili	akili	NOUN
ejpam-289	9	5	man�putra.upm.edu.my	man�putra.upm.edu.my	NOUN
ejpam-289	9	6	(	(	PUNCT
ejpam-289	9	7	a.	a.	NOUN
ejpam-289	9	8	kılıçman	kılıçman	PROPN
ejpam-289	9	9	)	)	PUNCT
ejpam-289	9	10	,	,	PUNCT
ejpam-289	9	11	zabidin�umt.edu.my	zabidin�umt.edu.my	NUM
ejpam-289	9	12	(	(	PUNCT
ejpam-289	9	13	z.	z.	PROPN
ejpam-289	9	14	salleh	salleh	PROPN
ejpam-289	9	15	)	)	PUNCT
ejpam-289	9	16	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-289	10	1	325	325	NUM
ejpam-289	10	2	c	c	X
ejpam-289	10	3	©	©	PROPN
ejpam-289	10	4	2009	2009	NUM
ejpam-289	10	5	ejpam	ejpam	NOUN
ejpam-289	10	6	all	all	DET
ejpam-289	10	7	rights	right	NOUN
ejpam-289	10	8	reserved	reserve	VERB
ejpam-289	10	9	.	.	PUNCT
ejpam-289	11	1	a.	a.	PROPN
ejpam-289	11	2	kılıçman	kılıçman	PROPN
ejpam-289	11	3	and	and	CCONJ
ejpam-289	11	4	z.	z.	PROPN
ejpam-289	11	5	salleh	salleh	PROPN
ejpam-289	11	6	/	/	PUNCT
ejpam-289	11	7	eur	eur	PROPN
ejpam-289	11	8	.	.	PUNCT
ejpam-289	12	1	j.	j.	PROPN
ejpam-289	12	2	pure	pure	PROPN
ejpam-289	12	3	appl	appl	PROPN
ejpam-289	12	4	.	.	PROPN
ejpam-289	12	5	math	math	PROPN
ejpam-289	12	6	,	,	PUNCT
ejpam-289	12	7	2	2	NUM
ejpam-289	12	8	(	(	PUNCT
ejpam-289	12	9	2009	2009	NUM
ejpam-289	12	10	)	)	PUNCT
ejpam-289	12	11	,	,	PUNCT
ejpam-289	12	12	(	(	PUNCT
ejpam-289	12	13	325	325	NUM
ejpam-289	12	14	-	-	SYM
ejpam-289	12	15	337	337	NUM
ejpam-289	12	16	)	)	PUNCT
ejpam-289	12	17	326	326	NUM
ejpam-289	12	18	1	1	NUM
ejpam-289	12	19	.	.	PUNCT
ejpam-289	12	20	introduction	introduction	NOUN
ejpam-289	12	21	a	a	DET
ejpam-289	12	22	bitopological	bitopological	ADJ
ejpam-289	12	23	space	space	NOUN
ejpam-289	12	24	(	(	PUNCT
ejpam-289	12	25	x	x	X
ejpam-289	12	26	,	,	PUNCT
ejpam-289	12	27	p	p	X
ejpam-289	12	28	,	,	PUNCT
ejpam-289	12	29	q	q	NOUN
ejpam-289	12	30	)	)	PUNCT
ejpam-289	12	31	is	be	AUX
ejpam-289	12	32	known	know	VERB
ejpam-289	12	33	as	as	ADP
ejpam-289	12	34	a	a	DET
ejpam-289	12	35	set	set	NOUN
ejpam-289	12	36	x	x	PUNCT
ejpam-289	12	37	together	together	ADV
ejpam-289	12	38	with	with	ADP
ejpam-289	12	39	two	two	NUM
ejpam-289	12	40	arbitrary	arbitrary	ADJ
ejpam-289	12	41	topologies	topology	NOUN
ejpam-289	12	42	p	p	NOUN
ejpam-289	12	43	and	and	CCONJ
ejpam-289	12	44	q	q	PROPN
ejpam-289	12	45	which	which	PRON
ejpam-289	12	46	are	be	AUX
ejpam-289	12	47	defined	define	VERB
ejpam-289	12	48	on	on	ADP
ejpam-289	12	49	x	x	X
ejpam-289	12	50	,	,	PUNCT
ejpam-289	12	51	for	for	ADP
ejpam-289	12	52	the	the	DET
ejpam-289	12	53	detail	detail	NOUN
ejpam-289	12	54	definitions	definition	NOUN
ejpam-289	12	55	,	,	PUNCT
ejpam-289	12	56	terminologies	terminology	NOUN
ejpam-289	12	57	and	and	CCONJ
ejpam-289	12	58	notations	notation	NOUN
ejpam-289	12	59	we	we	PRON
ejpam-289	12	60	refer	refer	VERB
ejpam-289	12	61	to	to	ADP
ejpam-289	12	62	[	[	X
ejpam-289	12	63	1	1	NUM
ejpam-289	12	64	]	]	PUNCT
ejpam-289	12	65	.	.	PUNCT
ejpam-289	13	1	in	in	ADP
ejpam-289	13	2	[	[	X
ejpam-289	13	3	3	3	NUM
ejpam-289	13	4	]	]	PUNCT
ejpam-289	13	5	and	and	CCONJ
ejpam-289	13	6	[	[	X
ejpam-289	13	7	4	4	NUM
ejpam-289	13	8	]	]	PUNCT
ejpam-289	13	9	,	,	PUNCT
ejpam-289	13	10	the	the	DET
ejpam-289	13	11	authors	author	NOUN
ejpam-289	13	12	introduced	introduce	VERB
ejpam-289	13	13	and	and	CCONJ
ejpam-289	13	14	studied	study	VERB
ejpam-289	13	15	the	the	DET
ejpam-289	13	16	idea	idea	NOUN
ejpam-289	13	17	of	of	ADP
ejpam-289	13	18	pairwise	pairwise	NOUN
ejpam-289	13	19	continuity	continuity	NOUN
ejpam-289	13	20	and	and	CCONJ
ejpam-289	13	21	pairwise	pairwise	NOUN
ejpam-289	13	22	lindelöfness	lindelöfness	NOUN
ejpam-289	13	23	in	in	ADP
ejpam-289	13	24	bitopological	bitopological	ADJ
ejpam-289	13	25	spaces	space	NOUN
ejpam-289	13	26	and	and	CCONJ
ejpam-289	13	27	give	give	VERB
ejpam-289	13	28	some	some	DET
ejpam-289	13	29	results	result	NOUN
ejpam-289	13	30	concerning	concern	VERB
ejpam-289	13	31	these	these	DET
ejpam-289	13	32	ideas	idea	NOUN
ejpam-289	13	33	.	.	PUNCT
ejpam-289	14	1	recently	recently	ADV
ejpam-289	14	2	the	the	DET
ejpam-289	14	3	authors	author	NOUN
ejpam-289	14	4	in	in	ADP
ejpam-289	14	5	[	[	X
ejpam-289	14	6	5	5	NUM
ejpam-289	14	7	]	]	PUNCT
ejpam-289	14	8	,	,	PUNCT
ejpam-289	14	9	[	[	X
ejpam-289	14	10	6	6	NUM
ejpam-289	14	11	]	]	PUNCT
ejpam-289	14	12	introduced	introduce	VERB
ejpam-289	14	13	and	and	CCONJ
ejpam-289	14	14	studied	study	VERB
ejpam-289	14	15	the	the	DET
ejpam-289	14	16	notion	notion	NOUN
ejpam-289	14	17	of	of	ADP
ejpam-289	14	18	pairwise	pairwise	NOUN
ejpam-289	14	19	almost	almost	ADV
ejpam-289	14	20	lindelöf	lindelöf	VERB
ejpam-289	14	21	and	and	CCONJ
ejpam-289	14	22	pairwise	pairwise	NOUN
ejpam-289	14	23	weakly	weakly	ADJ
ejpam-289	14	24	lindelöf	lindelöf	NOUN
ejpam-289	14	25	spaces	space	NOUN
ejpam-289	14	26	in	in	ADP
ejpam-289	14	27	bitopological	bitopological	ADJ
ejpam-289	14	28	spaces	space	NOUN
ejpam-289	14	29	.	.	PUNCT
ejpam-289	15	1	in	in	ADP
ejpam-289	15	2	this	this	DET
ejpam-289	15	3	paper	paper	NOUN
ejpam-289	15	4	,	,	PUNCT
ejpam-289	15	5	we	we	PRON
ejpam-289	15	6	are	be	AUX
ejpam-289	15	7	concerned	concerned	ADJ
ejpam-289	15	8	with	with	ADP
ejpam-289	15	9	another	another	DET
ejpam-289	15	10	concept	concept	NOUN
ejpam-289	15	11	of	of	ADP
ejpam-289	15	12	pairwise	pairwise	NOUN
ejpam-289	15	13	regular	regular	ADJ
ejpam-289	15	14	lindelöfness	lindelöfness	NOUN
ejpam-289	15	15	and	and	CCONJ
ejpam-289	15	16	pairwise	pairwise	NOUN
ejpam-289	15	17	continuity	continuity	NOUN
ejpam-289	15	18	in	in	ADP
ejpam-289	15	19	bitopological	bitopological	ADJ
ejpam-289	15	20	spaces	space	NOUN
ejpam-289	15	21	.	.	PUNCT
ejpam-289	16	1	in	in	ADP
ejpam-289	16	2	section	section	NOUN
ejpam-289	16	3	3	3	NUM
ejpam-289	16	4	,	,	PUNCT
ejpam-289	16	5	we	we	PRON
ejpam-289	16	6	shall	shall	AUX
ejpam-289	16	7	introduce	introduce	VERB
ejpam-289	16	8	another	another	DET
ejpam-289	16	9	concept	concept	NOUN
ejpam-289	16	10	of	of	ADP
ejpam-289	16	11	pairwise	pairwise	NOUN
ejpam-289	16	12	regular	regular	ADV
ejpam-289	16	13	and	and	CCONJ
ejpam-289	16	14	pairwise	pairwise	VERB
ejpam-289	16	15	normal	normal	ADJ
ejpam-289	16	16	bitopological	bitopological	ADJ
ejpam-289	16	17	spaces	space	NOUN
ejpam-289	16	18	,	,	PUNCT
ejpam-289	16	19	i.e.	i.e.	X
ejpam-289	16	20	,	,	PUNCT
ejpam-289	16	21	p1	p1	NOUN
ejpam-289	16	22	-	-	PUNCT
ejpam-289	16	23	regular	regular	ADJ
ejpam-289	16	24	spaces	space	NOUN
ejpam-289	16	25	and	and	CCONJ
ejpam-289	16	26	p2	p2	NOUN
ejpam-289	16	27	-	-	PUNCT
ejpam-289	16	28	normal	normal	ADJ
ejpam-289	16	29	spaces	space	NOUN
ejpam-289	16	30	and	and	CCONJ
ejpam-289	16	31	obtain	obtain	VERB
ejpam-289	16	32	a	a	DET
ejpam-289	16	33	result	result	NOUN
ejpam-289	16	34	.	.	PUNCT
ejpam-289	17	1	furthermore	furthermore	ADV
ejpam-289	17	2	,	,	PUNCT
ejpam-289	17	3	some	some	DET
ejpam-289	17	4	examples	example	NOUN
ejpam-289	17	5	will	will	AUX
ejpam-289	17	6	be	be	AUX
ejpam-289	17	7	given	give	VERB
ejpam-289	17	8	to	to	PART
ejpam-289	17	9	describe	describe	VERB
ejpam-289	17	10	its	its	PRON
ejpam-289	17	11	properties	property	NOUN
ejpam-289	17	12	.	.	PUNCT
ejpam-289	18	1	in	in	ADP
ejpam-289	18	2	section	section	NOUN
ejpam-289	18	3	4	4	NUM
ejpam-289	18	4	,	,	PUNCT
ejpam-289	18	5	we	we	PRON
ejpam-289	18	6	shall	shall	AUX
ejpam-289	18	7	define	define	VERB
ejpam-289	18	8	another	another	DET
ejpam-289	18	9	concept	concept	NOUN
ejpam-289	18	10	of	of	ADP
ejpam-289	18	11	pairwise	pairwise	NOUN
ejpam-289	18	12	lindelöf	lindelöf	NOUN
ejpam-289	18	13	spaces	space	NOUN
ejpam-289	18	14	,	,	PUNCT
ejpam-289	18	15	i.e.	i.e.	X
ejpam-289	18	16	,	,	PUNCT
ejpam-289	18	17	p2lindelöf	p2lindelöf	NOUN
ejpam-289	18	18	spaces	space	NOUN
ejpam-289	18	19	.	.	PUNCT
ejpam-289	19	1	we	we	PRON
ejpam-289	19	2	obtain	obtain	VERB
ejpam-289	19	3	a	a	DET
ejpam-289	19	4	result	result	NOUN
ejpam-289	19	5	about	about	ADP
ejpam-289	19	6	subset	subset	NOUN
ejpam-289	19	7	of	of	ADP
ejpam-289	19	8	such	such	ADJ
ejpam-289	19	9	spaces	space	NOUN
ejpam-289	19	10	.	.	PUNCT
ejpam-289	20	1	the	the	DET
ejpam-289	20	2	main	main	ADJ
ejpam-289	20	3	result	result	NOUN
ejpam-289	20	4	we	we	PRON
ejpam-289	20	5	are	be	AUX
ejpam-289	20	6	obtain	obtain	ADJ
ejpam-289	20	7	here	here	ADV
ejpam-289	20	8	is	be	AUX
ejpam-289	20	9	every	every	DET
ejpam-289	20	10	p1	p1	NOUN
ejpam-289	20	11	-	-	PUNCT
ejpam-289	20	12	regular	regular	ADJ
ejpam-289	20	13	and	and	CCONJ
ejpam-289	20	14	p2	p2	NOUN
ejpam-289	20	15	-	-	PUNCT
ejpam-289	20	16	lindelöf	lindelöf	NOUN
ejpam-289	20	17	bitopological	bitopological	ADJ
ejpam-289	20	18	space	space	NOUN
ejpam-289	20	19	is	be	AUX
ejpam-289	20	20	p2	p2	NOUN
ejpam-289	20	21	-	-	PUNCT
ejpam-289	20	22	normal	normal	ADJ
ejpam-289	20	23	.	.	PUNCT
ejpam-289	21	1	in	in	ADP
ejpam-289	21	2	section	section	NOUN
ejpam-289	21	3	5	5	NUM
ejpam-289	21	4	,	,	PUNCT
ejpam-289	21	5	we	we	PRON
ejpam-289	21	6	extend	extend	VERB
ejpam-289	21	7	idea	idea	NOUN
ejpam-289	21	8	of	of	ADP
ejpam-289	21	9	continuity	continuity	NOUN
ejpam-289	21	10	to	to	ADP
ejpam-289	21	11	a	a	DET
ejpam-289	21	12	bitopological	bitopological	ADJ
ejpam-289	21	13	space	space	NOUN
ejpam-289	21	14	,	,	PUNCT
ejpam-289	21	15	namely	namely	ADV
ejpam-289	21	16	,	,	PUNCT
ejpam-289	21	17	p2continuity	p2continuity	NOUN
ejpam-289	21	18	and	and	CCONJ
ejpam-289	21	19	study	study	VERB
ejpam-289	21	20	their	their	PRON
ejpam-289	21	21	properties	property	NOUN
ejpam-289	21	22	where	where	SCONJ
ejpam-289	21	23	the	the	DET
ejpam-289	21	24	purpose	purpose	NOUN
ejpam-289	21	25	is	be	AUX
ejpam-289	21	26	to	to	PART
ejpam-289	21	27	study	study	VERB
ejpam-289	21	28	the	the	DET
ejpam-289	21	29	effect	effect	NOUN
ejpam-289	21	30	of	of	ADP
ejpam-289	21	31	mapping	mapping	NOUN
ejpam-289	21	32	and	and	CCONJ
ejpam-289	21	33	p2	p2	NOUN
ejpam-289	21	34	-	-	PUNCT
ejpam-289	21	35	continuity	continuity	NOUN
ejpam-289	21	36	on	on	ADP
ejpam-289	21	37	p2	p2	NOUN
ejpam-289	21	38	-	-	PUNCT
ejpam-289	21	39	lindelöf	lindelöf	NOUN
ejpam-289	21	40	bitopological	bitopological	ADJ
ejpam-289	21	41	spaces	space	NOUN
ejpam-289	21	42	.	.	PUNCT
ejpam-289	22	1	we	we	PRON
ejpam-289	22	2	also	also	ADV
ejpam-289	22	3	show	show	VERB
ejpam-289	22	4	that	that	SCONJ
ejpam-289	22	5	this	this	DET
ejpam-289	22	6	mapping	mapping	NOUN
ejpam-289	22	7	preserve	preserve	VERB
ejpam-289	22	8	p2	p2	NOUN
ejpam-289	22	9	-	-	PUNCT
ejpam-289	22	10	lindelöf	lindelöf	NOUN
ejpam-289	22	11	property	property	NOUN
ejpam-289	22	12	.	.	PUNCT
ejpam-289	23	1	the	the	DET
ejpam-289	23	2	main	main	ADJ
ejpam-289	23	3	result	result	NOUN
ejpam-289	23	4	here	here	ADV
ejpam-289	23	5	is	be	AUX
ejpam-289	23	6	that	that	SCONJ
ejpam-289	23	7	the	the	DET
ejpam-289	23	8	image	image	NOUN
ejpam-289	23	9	of	of	ADP
ejpam-289	23	10	a	a	DET
ejpam-289	23	11	p2	p2	ADJ
ejpam-289	23	12	-	-	PUNCT
ejpam-289	23	13	lindelöf	lindelöf	NOUN
ejpam-289	23	14	space	space	NOUN
ejpam-289	23	15	under	under	ADP
ejpam-289	23	16	a	a	DET
ejpam-289	23	17	p2	p2	ADJ
ejpam-289	23	18	-	-	PUNCT
ejpam-289	23	19	continuous	continuous	ADJ
ejpam-289	23	20	function	function	NOUN
ejpam-289	23	21	is	be	AUX
ejpam-289	23	22	p2	p2	NOUN
ejpam-289	23	23	-	-	PUNCT
ejpam-289	23	24	lindelöf	lindelöf	NOUN
ejpam-289	23	25	.	.	PUNCT
ejpam-289	24	1	a.	a.	PROPN
ejpam-289	24	2	kılıçman	kılıçman	PROPN
ejpam-289	24	3	and	and	CCONJ
ejpam-289	24	4	z.	z.	PROPN
ejpam-289	24	5	salleh	salleh	PROPN
ejpam-289	24	6	/	/	PUNCT
ejpam-289	24	7	eur	eur	PROPN
ejpam-289	24	8	.	.	PUNCT
ejpam-289	25	1	j.	j.	PROPN
ejpam-289	25	2	pure	pure	PROPN
ejpam-289	25	3	appl	appl	PROPN
ejpam-289	25	4	.	.	PROPN
ejpam-289	25	5	math	math	PROPN
ejpam-289	25	6	,	,	PUNCT
ejpam-289	25	7	2	2	NUM
ejpam-289	25	8	(	(	PUNCT
ejpam-289	25	9	2009	2009	NUM
ejpam-289	25	10	)	)	PUNCT
ejpam-289	25	11	,	,	PUNCT
ejpam-289	25	12	(	(	PUNCT
ejpam-289	25	13	325	325	NUM
ejpam-289	25	14	-	-	SYM
ejpam-289	25	15	337	337	NUM
ejpam-289	25	16	)	)	PUNCT
ejpam-289	25	17	327	327	NUM
ejpam-289	25	18	2	2	NUM
ejpam-289	25	19	.	.	PUNCT
ejpam-289	25	20	preliminaries	preliminary	NOUN
ejpam-289	25	21	throughout	throughout	ADP
ejpam-289	25	22	this	this	DET
ejpam-289	25	23	paper	paper	NOUN
ejpam-289	25	24	,	,	PUNCT
ejpam-289	25	25	all	all	DET
ejpam-289	25	26	spaces	space	NOUN
ejpam-289	25	27	(	(	PUNCT
ejpam-289	25	28	x	x	X
ejpam-289	25	29	,	,	PUNCT
ejpam-289	25	30	p	p	NOUN
ejpam-289	25	31	)	)	PUNCT
ejpam-289	25	32	and	and	CCONJ
ejpam-289	25	33	(	(	PUNCT
ejpam-289	25	34	x	x	INTJ
ejpam-289	25	35	,	,	PUNCT
ejpam-289	25	36	p	p	X
ejpam-289	25	37	,	,	PUNCT
ejpam-289	25	38	q	q	NOUN
ejpam-289	25	39	)	)	PUNCT
ejpam-289	25	40	(	(	PUNCT
ejpam-289	25	41	or	or	CCONJ
ejpam-289	25	42	simply	simply	ADV
ejpam-289	25	43	x	x	X
ejpam-289	25	44	)	)	PUNCT
ejpam-289	25	45	are	be	AUX
ejpam-289	25	46	always	always	ADV
ejpam-289	25	47	meant	mean	VERB
ejpam-289	25	48	topological	topological	ADJ
ejpam-289	25	49	spaces	space	NOUN
ejpam-289	25	50	and	and	CCONJ
ejpam-289	25	51	bitopological	bitopological	ADJ
ejpam-289	25	52	spaces	space	NOUN
ejpam-289	25	53	,	,	PUNCT
ejpam-289	25	54	respectively	respectively	ADV
ejpam-289	25	55	.	.	PUNCT
ejpam-289	26	1	in	in	ADP
ejpam-289	26	2	this	this	DET
ejpam-289	26	3	paper	paper	NOUN
ejpam-289	26	4	,	,	PUNCT
ejpam-289	26	5	we	we	PRON
ejpam-289	26	6	shall	shall	AUX
ejpam-289	26	7	use	use	VERB
ejpam-289	26	8	pto	pto	PROPN
ejpam-289	26	9	denote	denote	PROPN
ejpam-289	26	10	pairwise	pairwise	NOUN
ejpam-289	26	11	.	.	PUNCT
ejpam-289	27	1	for	for	ADP
ejpam-289	27	2	instance	instance	NOUN
ejpam-289	27	3	,	,	PUNCT
ejpam-289	27	4	p	p	X
ejpam-289	27	5	-	-	PUNCT
ejpam-289	27	6	lindelöf	lindelöf	NOUN
ejpam-289	27	7	stands	stand	VERB
ejpam-289	27	8	for	for	ADP
ejpam-289	27	9	pairwise	pairwise	NOUN
ejpam-289	27	10	lindelöf	lindelöf	NOUN
ejpam-289	27	11	.	.	PUNCT
ejpam-289	28	1	while	while	SCONJ
ejpam-289	28	2	p1and	p1and	NOUN
ejpam-289	28	3	p2are	p2are	PROPN
ejpam-289	28	4	used	use	VERB
ejpam-289	28	5	to	to	PART
ejpam-289	28	6	denote	denote	VERB
ejpam-289	28	7	other	other	ADJ
ejpam-289	28	8	concepts	concept	NOUN
ejpam-289	28	9	of	of	ADP
ejpam-289	28	10	pairwise	pairwise	NOUN
ejpam-289	28	11	.	.	PUNCT
ejpam-289	29	1	sometimes	sometimes	ADV
ejpam-289	29	2	the	the	DET
ejpam-289	29	3	authors	author	NOUN
ejpam-289	29	4	write	write	VERB
ejpam-289	29	5	the	the	DET
ejpam-289	29	6	term	term	NOUN
ejpam-289	29	7	“	"	PUNCT
ejpam-289	29	8	pairwise	pairwise	NOUN
ejpam-289	29	9	lindelöf	lindelöf	NOUN
ejpam-289	29	10	spaces	space	NOUN
ejpam-289	29	11	"	"	PUNCT
ejpam-289	29	12	which	which	PRON
ejpam-289	29	13	means	mean	VERB
ejpam-289	29	14	that	that	SCONJ
ejpam-289	29	15	pairwise	pairwise	NOUN
ejpam-289	29	16	lindelöf	lindelöf	NOUN
ejpam-289	29	17	bitopological	bitopological	ADJ
ejpam-289	29	18	spaces	space	NOUN
ejpam-289	29	19	.	.	PUNCT
ejpam-289	30	1	kelly	kelly	PROPN
ejpam-289	31	1	[	[	X
ejpam-289	31	2	1	1	X
ejpam-289	31	3	]	]	PUNCT
ejpam-289	31	4	was	be	AUX
ejpam-289	31	5	the	the	DET
ejpam-289	31	6	first	first	ADJ
ejpam-289	31	7	one	one	NUM
ejpam-289	31	8	who	who	PRON
ejpam-289	31	9	introduced	introduce	VERB
ejpam-289	31	10	the	the	DET
ejpam-289	31	11	idea	idea	NOUN
ejpam-289	31	12	of	of	ADP
ejpam-289	31	13	p	p	NOUN
ejpam-289	31	14	-	-	PUNCT
ejpam-289	31	15	regular	regular	ADJ
ejpam-289	31	16	spaces	space	NOUN
ejpam-289	31	17	and	and	CCONJ
ejpam-289	31	18	pnormal	pnormal	ADJ
ejpam-289	31	19	spaces	space	NOUN
ejpam-289	31	20	.	.	PUNCT
ejpam-289	32	1	later	later	ADV
ejpam-289	32	2	these	these	DET
ejpam-289	32	3	spaces	space	NOUN
ejpam-289	32	4	will	will	AUX
ejpam-289	32	5	be	be	AUX
ejpam-289	32	6	generalized	generalize	VERB
ejpam-289	32	7	to	to	ADP
ejpam-289	32	8	p1	p1	NOUN
ejpam-289	32	9	-	-	PUNCT
ejpam-289	32	10	regular	regular	ADJ
ejpam-289	32	11	spaces	space	NOUN
ejpam-289	32	12	and	and	CCONJ
ejpam-289	32	13	p2normal	p2normal	ADJ
ejpam-289	32	14	spaces	space	NOUN
ejpam-289	32	15	respectively	respectively	ADV
ejpam-289	32	16	.	.	PUNCT
ejpam-289	33	1	definition	definition	NOUN
ejpam-289	33	2	2.1	2.1	NUM
ejpam-289	33	3	(	(	PUNCT
ejpam-289	33	4	kelly	kelly	PROPN
ejpam-289	33	5	)	)	PUNCT
ejpam-289	33	6	.	.	PUNCT
ejpam-289	34	1	in	in	ADP
ejpam-289	34	2	a	a	DET
ejpam-289	34	3	space	space	NOUN
ejpam-289	34	4	(	(	PUNCT
ejpam-289	34	5	x	x	X
ejpam-289	34	6	,	,	PUNCT
ejpam-289	34	7	p	p	X
ejpam-289	34	8	,	,	PUNCT
ejpam-289	34	9	q	q	NOUN
ejpam-289	34	10	)	)	PUNCT
ejpam-289	34	11	,	,	PUNCT
ejpam-289	34	12	p	p	NOUN
ejpam-289	34	13	is	be	AUX
ejpam-289	34	14	said	say	VERB
ejpam-289	34	15	to	to	PART
ejpam-289	34	16	be	be	AUX
ejpam-289	34	17	regular	regular	ADJ
ejpam-289	34	18	with	with	ADP
ejpam-289	34	19	respect	respect	NOUN
ejpam-289	34	20	to	to	ADP
ejpam-289	34	21	q	q	NOUN
ejpam-289	34	22	if	if	SCONJ
ejpam-289	34	23	,	,	PUNCT
ejpam-289	34	24	for	for	ADP
ejpam-289	34	25	each	each	DET
ejpam-289	34	26	point	point	NOUN
ejpam-289	34	27	x	x	X
ejpam-289	34	28	∈	∈	NOUN
ejpam-289	34	29	x	x	X
ejpam-289	34	30	,	,	PUNCT
ejpam-289	34	31	there	there	PRON
ejpam-289	34	32	is	be	VERB
ejpam-289	34	33	a	a	DET
ejpam-289	34	34	p	p	NOUN
ejpam-289	34	35	-neighbourhood	-neighbourhood	NOUN
ejpam-289	34	36	base	base	NOUN
ejpam-289	34	37	ofq	ofq	NOUN
ejpam-289	34	38	-	-	PUNCT
ejpam-289	34	39	closed	close	VERB
ejpam-289	34	40	sets	set	NOUN
ejpam-289	34	41	,	,	PUNCT
ejpam-289	34	42	or	or	CCONJ
ejpam-289	34	43	,	,	PUNCT
ejpam-289	34	44	as	as	SCONJ
ejpam-289	34	45	is	be	AUX
ejpam-289	34	46	easily	easily	ADV
ejpam-289	34	47	seen	see	VERB
ejpam-289	34	48	to	to	PART
ejpam-289	34	49	be	be	AUX
ejpam-289	34	50	equivalent	equivalent	ADJ
ejpam-289	34	51	,	,	PUNCT
ejpam-289	34	52	if	if	SCONJ
ejpam-289	34	53	,	,	PUNCT
ejpam-289	34	54	for	for	ADP
ejpam-289	34	55	each	each	DET
ejpam-289	34	56	point	point	NOUN
ejpam-289	34	57	x	x	X
ejpam-289	34	58	∈	∈	NOUN
ejpam-289	34	59	x	x	X
ejpam-289	34	60	and	and	CCONJ
ejpam-289	34	61	each	each	DET
ejpam-289	34	62	p	p	NOUN
ejpam-289	34	63	-closed	-close	VERB
ejpam-289	34	64	set	set	NOUN
ejpam-289	34	65	p	p	NOUN
ejpam-289	34	66	such	such	ADJ
ejpam-289	34	67	that	that	PRON
ejpam-289	34	68	x	x	X
ejpam-289	34	69	/∈	/∈	PUNCT
ejpam-289	35	1	p	p	X
ejpam-289	35	2	,	,	PUNCT
ejpam-289	35	3	there	there	PRON
ejpam-289	35	4	are	be	VERB
ejpam-289	35	5	a	a	DET
ejpam-289	35	6	p	p	NOUN
ejpam-289	35	7	-open	-open	ADJ
ejpam-289	35	8	set	set	NOUN
ejpam-289	35	9	u	u	NOUN
ejpam-289	35	10	and	and	CCONJ
ejpam-289	35	11	a	a	DET
ejpam-289	35	12	q	q	ADJ
ejpam-289	35	13	-	-	PUNCT
ejpam-289	35	14	open	open	ADJ
ejpam-289	35	15	set	set	VERB
ejpam-289	35	16	v	v	ADP
ejpam-289	35	17	such	such	ADJ
ejpam-289	35	18	that	that	SCONJ
ejpam-289	35	19	x	x	SYM
ejpam-289	35	20	∈	∈	PROPN
ejpam-289	35	21	u	u	NOUN
ejpam-289	35	22	,	,	PUNCT
ejpam-289	35	23	p	p	PROPN
ejpam-289	35	24	⊆	⊆	NUM
ejpam-289	35	25	v	v	NOUN
ejpam-289	35	26	,	,	PUNCT
ejpam-289	35	27	and	and	CCONJ
ejpam-289	35	28	u	u	NOUN
ejpam-289	35	29	∩	∩	NOUN
ejpam-289	35	30	v	v	NOUN
ejpam-289	35	31	=	=	PUNCT
ejpam-289	35	32	;	;	PUNCT
ejpam-289	35	33	.	.	PUNCT
ejpam-289	36	1	similarly	similarly	ADV
ejpam-289	36	2	,	,	PUNCT
ejpam-289	36	3	(	(	PUNCT
ejpam-289	36	4	x	x	X
ejpam-289	36	5	,	,	PUNCT
ejpam-289	36	6	p	p	X
ejpam-289	36	7	,	,	PUNCT
ejpam-289	36	8	q	q	NOUN
ejpam-289	36	9	)	)	PUNCT
ejpam-289	36	10	is	be	AUX
ejpam-289	36	11	,	,	PUNCT
ejpam-289	36	12	or	or	CCONJ
ejpam-289	36	13	p	p	NOUN
ejpam-289	36	14	and	and	CCONJ
ejpam-289	36	15	q	q	NOUN
ejpam-289	36	16	are	be	AUX
ejpam-289	36	17	,	,	PUNCT
ejpam-289	36	18	p	p	NOUN
ejpam-289	36	19	-	-	PUNCT
ejpam-289	36	20	regular	regular	ADJ
ejpam-289	36	21	if	if	SCONJ
ejpam-289	36	22	p	p	NOUN
ejpam-289	36	23	is	be	AUX
ejpam-289	36	24	regular	regular	ADJ
ejpam-289	36	25	with	with	ADP
ejpam-289	36	26	respect	respect	NOUN
ejpam-289	36	27	to	to	ADP
ejpam-289	36	28	q	q	NOUN
ejpam-289	36	29	and	and	CCONJ
ejpam-289	36	30	vice	vice	ADV
ejpam-289	36	31	versa	versa	ADV
ejpam-289	36	32	.	.	PUNCT
ejpam-289	37	1	definition	definition	NOUN
ejpam-289	37	2	2.2	2.2	NUM
ejpam-289	37	3	(	(	PUNCT
ejpam-289	37	4	kelly	kelly	PROPN
ejpam-289	37	5	)	)	PUNCT
ejpam-289	37	6	.	.	PUNCT
ejpam-289	38	1	a	a	DET
ejpam-289	38	2	bitopological	bitopological	ADJ
ejpam-289	38	3	space	space	NOUN
ejpam-289	38	4	(	(	PUNCT
ejpam-289	38	5	x	x	X
ejpam-289	38	6	,	,	PUNCT
ejpam-289	38	7	p	p	X
ejpam-289	38	8	,	,	PUNCT
ejpam-289	38	9	q	q	NOUN
ejpam-289	38	10	)	)	PUNCT
ejpam-289	38	11	is	be	AUX
ejpam-289	38	12	said	say	VERB
ejpam-289	38	13	to	to	PART
ejpam-289	38	14	be	be	AUX
ejpam-289	38	15	p	p	NOUN
ejpam-289	38	16	-	-	PUNCT
ejpam-289	38	17	normal	normal	ADJ
ejpam-289	38	18	if	if	SCONJ
ejpam-289	38	19	,	,	PUNCT
ejpam-289	38	20	given	give	VERB
ejpam-289	38	21	a	a	DET
ejpam-289	38	22	p	p	NOUN
ejpam-289	38	23	-closed	-close	VERB
ejpam-289	38	24	set	set	NOUN
ejpam-289	38	25	a	a	PRON
ejpam-289	38	26	and	and	CCONJ
ejpam-289	38	27	a	a	DET
ejpam-289	38	28	q	q	ADV
ejpam-289	38	29	-	-	PUNCT
ejpam-289	38	30	closed	closed	ADJ
ejpam-289	38	31	set	set	NOUN
ejpam-289	38	32	b	b	NOUN
ejpam-289	38	33	with	with	ADP
ejpam-289	38	34	a∩	a∩	PROPN
ejpam-289	38	35	b	b	PROPN
ejpam-289	38	36	=	=	PUNCT
ejpam-289	38	37	;	;	PUNCT
ejpam-289	38	38	,	,	PUNCT
ejpam-289	38	39	there	there	PRON
ejpam-289	38	40	exist	exist	VERB
ejpam-289	38	41	a	a	DET
ejpam-289	38	42	q	q	ADJ
ejpam-289	38	43	-	-	PUNCT
ejpam-289	38	44	open	open	ADJ
ejpam-289	38	45	set	set	NOUN
ejpam-289	38	46	u	u	NOUN
ejpam-289	38	47	and	and	CCONJ
ejpam-289	38	48	a	a	DET
ejpam-289	38	49	p	p	NOUN
ejpam-289	38	50	-open	-open	NOUN
ejpam-289	38	51	set	set	VERB
ejpam-289	38	52	v	v	ADP
ejpam-289	38	53	such	such	ADJ
ejpam-289	38	54	that	that	PRON
ejpam-289	38	55	a⊆	a⊆	PROPN
ejpam-289	38	56	u	u	PROPN
ejpam-289	38	57	,	,	PUNCT
ejpam-289	38	58	b	b	PROPN
ejpam-289	38	59	⊆	⊆	NUM
ejpam-289	38	60	v	v	NOUN
ejpam-289	38	61	,	,	PUNCT
ejpam-289	38	62	and	and	CCONJ
ejpam-289	38	63	u	u	NOUN
ejpam-289	38	64	∩	∩	NOUN
ejpam-289	38	65	v	v	NOUN
ejpam-289	38	66	=	=	PUNCT
ejpam-289	38	67	;	;	PUNCT
ejpam-289	38	68	.	.	PUNCT
ejpam-289	39	1	further	far	ADV
ejpam-289	39	2	,	,	PUNCT
ejpam-289	39	3	in	in	ADP
ejpam-289	39	4	[	[	X
ejpam-289	39	5	3	3	X
ejpam-289	39	6	]	]	PUNCT
ejpam-289	39	7	the	the	DET
ejpam-289	39	8	authors	author	NOUN
ejpam-289	39	9	introduced	introduce	VERB
ejpam-289	39	10	the	the	DET
ejpam-289	39	11	concept	concept	NOUN
ejpam-289	39	12	of	of	ADP
ejpam-289	39	13	p1	p1	NOUN
ejpam-289	39	14	-	-	ADJ
ejpam-289	39	15	normal	normal	ADJ
ejpam-289	39	16	spaces	space	NOUN
ejpam-289	39	17	.	.	PUNCT
ejpam-289	40	1	moreover	moreover	ADV
ejpam-289	40	2	in	in	ADP
ejpam-289	40	3	the	the	DET
ejpam-289	40	4	same	same	ADJ
ejpam-289	40	5	paper	paper	NOUN
ejpam-289	40	6	,	,	PUNCT
ejpam-289	40	7	the	the	DET
ejpam-289	40	8	authors	author	NOUN
ejpam-289	40	9	also	also	ADV
ejpam-289	40	10	introduced	introduce	VERB
ejpam-289	40	11	the	the	DET
ejpam-289	40	12	concept	concept	NOUN
ejpam-289	40	13	of	of	ADP
ejpam-289	40	14	p	p	NOUN
ejpam-289	40	15	-	-	PUNCT
ejpam-289	40	16	lindelöf	lindelöf	NOUN
ejpam-289	40	17	spaces	space	NOUN
ejpam-289	40	18	and	and	CCONJ
ejpam-289	40	19	p1	p1	NOUN
ejpam-289	40	20	-	-	PUNCT
ejpam-289	40	21	lindelöf	lindelöf	NOUN
ejpam-289	40	22	spaces	space	NOUN
ejpam-289	40	23	as	as	ADP
ejpam-289	40	24	the	the	DET
ejpam-289	40	25	following	following	NOUN
ejpam-289	40	26	.	.	PUNCT
ejpam-289	41	1	a.	a.	PROPN
ejpam-289	41	2	kılıçman	kılıçman	PROPN
ejpam-289	41	3	and	and	CCONJ
ejpam-289	41	4	z.	z.	PROPN
ejpam-289	41	5	salleh	salleh	PROPN
ejpam-289	41	6	/	/	PUNCT
ejpam-289	41	7	eur	eur	PROPN
ejpam-289	41	8	.	.	PUNCT
ejpam-289	42	1	j.	j.	PROPN
ejpam-289	42	2	pure	pure	PROPN
ejpam-289	42	3	appl	appl	PROPN
ejpam-289	42	4	.	.	PROPN
ejpam-289	42	5	math	math	PROPN
ejpam-289	42	6	,	,	PUNCT
ejpam-289	42	7	2	2	NUM
ejpam-289	42	8	(	(	PUNCT
ejpam-289	42	9	2009	2009	NUM
ejpam-289	42	10	)	)	PUNCT
ejpam-289	42	11	,	,	PUNCT
ejpam-289	42	12	(	(	PUNCT
ejpam-289	42	13	325	325	NUM
ejpam-289	42	14	-	-	SYM
ejpam-289	42	15	337	337	NUM
ejpam-289	42	16	)	)	PUNCT
ejpam-289	42	17	328	328	NUM
ejpam-289	42	18	definition	definition	NOUN
ejpam-289	42	19	2.3	2.3	NUM
ejpam-289	42	20	(	(	PUNCT
ejpam-289	42	21	see	see	VERB
ejpam-289	42	22	[	[	X
ejpam-289	42	23	3	3	NUM
ejpam-289	42	24	]	]	PUNCT
ejpam-289	42	25	)	)	PUNCT
ejpam-289	42	26	.	.	PUNCT
ejpam-289	43	1	a	a	DET
ejpam-289	43	2	bitopological	bitopological	ADJ
ejpam-289	43	3	space	space	NOUN
ejpam-289	43	4	(	(	PUNCT
ejpam-289	43	5	x	x	X
ejpam-289	43	6	,	,	PUNCT
ejpam-289	43	7	p	p	X
ejpam-289	43	8	,	,	PUNCT
ejpam-289	43	9	q	q	NOUN
ejpam-289	43	10	)	)	PUNCT
ejpam-289	43	11	is	be	AUX
ejpam-289	43	12	said	say	VERB
ejpam-289	43	13	to	to	PART
ejpam-289	43	14	be	be	AUX
ejpam-289	43	15	p	p	NOUN
ejpam-289	43	16	-	-	PUNCT
ejpam-289	43	17	lindelöf	lindelöf	NOUN
ejpam-289	43	18	if	if	SCONJ
ejpam-289	43	19	the	the	DET
ejpam-289	43	20	topological	topological	ADJ
ejpam-289	43	21	space	space	NOUN
ejpam-289	43	22	(	(	PUNCT
ejpam-289	43	23	x	x	X
ejpam-289	43	24	,	,	PUNCT
ejpam-289	43	25	p	p	NOUN
ejpam-289	43	26	)	)	PUNCT
ejpam-289	43	27	and	and	CCONJ
ejpam-289	43	28	(	(	PUNCT
ejpam-289	43	29	x	x	X
ejpam-289	43	30	,	,	PUNCT
ejpam-289	43	31	q	q	X
ejpam-289	43	32	)	)	PUNCT
ejpam-289	43	33	are	be	AUX
ejpam-289	43	34	both	both	PRON
ejpam-289	43	35	lindelöf	lindelöf	NOUN
ejpam-289	43	36	.	.	PUNCT
ejpam-289	44	1	equivalently	equivalently	ADV
ejpam-289	44	2	,	,	PUNCT
ejpam-289	44	3	(	(	PUNCT
ejpam-289	44	4	x	x	X
ejpam-289	44	5	,	,	PUNCT
ejpam-289	44	6	p	p	X
ejpam-289	44	7	,	,	PUNCT
ejpam-289	44	8	q	q	NOUN
ejpam-289	44	9	)	)	PUNCT
ejpam-289	44	10	is	be	AUX
ejpam-289	44	11	p	p	NOUN
ejpam-289	44	12	-	-	PUNCT
ejpam-289	44	13	lindelöf	lindelöf	NOUN
ejpam-289	44	14	if	if	SCONJ
ejpam-289	44	15	every	every	DET
ejpam-289	44	16	p	p	NOUN
ejpam-289	44	17	-open	-open	ADJ
ejpam-289	44	18	cover	cover	NOUN
ejpam-289	44	19	of	of	ADP
ejpam-289	44	20	x	x	PUNCT
ejpam-289	44	21	can	can	AUX
ejpam-289	44	22	be	be	AUX
ejpam-289	44	23	reduced	reduce	VERB
ejpam-289	44	24	to	to	ADP
ejpam-289	44	25	a	a	DET
ejpam-289	44	26	countable	countable	ADJ
ejpam-289	44	27	p	p	NOUN
ejpam-289	44	28	-open	-open	ADJ
ejpam-289	44	29	cover	cover	NOUN
ejpam-289	44	30	and	and	CCONJ
ejpam-289	44	31	every	every	DET
ejpam-289	44	32	q	q	ADJ
ejpam-289	44	33	-	-	PUNCT
ejpam-289	44	34	open	open	ADJ
ejpam-289	44	35	cover	cover	NOUN
ejpam-289	44	36	of	of	ADP
ejpam-289	44	37	x	x	PRON
ejpam-289	44	38	can	can	AUX
ejpam-289	44	39	be	be	AUX
ejpam-289	44	40	reduced	reduce	VERB
ejpam-289	44	41	to	to	ADP
ejpam-289	44	42	a	a	DET
ejpam-289	44	43	countable	countable	ADJ
ejpam-289	44	44	q	q	ADJ
ejpam-289	44	45	-	-	PUNCT
ejpam-289	44	46	open	open	ADJ
ejpam-289	44	47	cover	cover	NOUN
ejpam-289	44	48	.	.	PUNCT
ejpam-289	45	1	definition	definition	NOUN
ejpam-289	45	2	2.4	2.4	NUM
ejpam-289	45	3	(	(	PUNCT
ejpam-289	45	4	see	see	VERB
ejpam-289	45	5	[	[	X
ejpam-289	45	6	3	3	NUM
ejpam-289	45	7	]	]	PUNCT
ejpam-289	45	8	)	)	PUNCT
ejpam-289	45	9	.	.	PUNCT
ejpam-289	46	1	in	in	ADP
ejpam-289	46	2	a	a	DET
ejpam-289	46	3	bitopological	bitopological	ADJ
ejpam-289	46	4	space	space	NOUN
ejpam-289	46	5	(	(	PUNCT
ejpam-289	46	6	x	x	X
ejpam-289	46	7	,	,	PUNCT
ejpam-289	46	8	p	p	X
ejpam-289	46	9	,	,	PUNCT
ejpam-289	46	10	q	q	NOUN
ejpam-289	46	11	)	)	PUNCT
ejpam-289	46	12	,	,	PUNCT
ejpam-289	46	13	p	p	NOUN
ejpam-289	46	14	is	be	AUX
ejpam-289	46	15	said	say	VERB
ejpam-289	46	16	to	to	PART
ejpam-289	46	17	be	be	AUX
ejpam-289	46	18	lindelöf	lindelöf	NOUN
ejpam-289	46	19	with	with	ADP
ejpam-289	46	20	respect	respect	NOUN
ejpam-289	46	21	toq	toq	VERB
ejpam-289	46	22	if	if	SCONJ
ejpam-289	46	23	,	,	PUNCT
ejpam-289	46	24	everyp	everyp	VERB
ejpam-289	46	25	-open	-open	ADJ
ejpam-289	46	26	cover	cover	NOUN
ejpam-289	46	27	of	of	ADP
ejpam-289	46	28	x	x	PUNCT
ejpam-289	46	29	can	can	AUX
ejpam-289	46	30	be	be	AUX
ejpam-289	46	31	reduced	reduce	VERB
ejpam-289	46	32	to	to	ADP
ejpam-289	46	33	a	a	DET
ejpam-289	46	34	countableq	countableq	NOUN
ejpam-289	46	35	-	-	PUNCT
ejpam-289	46	36	open	open	ADJ
ejpam-289	46	37	cover	cover	NOUN
ejpam-289	46	38	and	and	CCONJ
ejpam-289	46	39	similarly	similarly	ADV
ejpam-289	46	40	,	,	PUNCT
ejpam-289	46	41	(	(	PUNCT
ejpam-289	46	42	x	x	X
ejpam-289	46	43	,	,	PUNCT
ejpam-289	46	44	p	p	X
ejpam-289	46	45	,	,	PUNCT
ejpam-289	46	46	q	q	NOUN
ejpam-289	46	47	)	)	PUNCT
ejpam-289	46	48	is	be	AUX
ejpam-289	46	49	,	,	PUNCT
ejpam-289	46	50	or	or	CCONJ
ejpam-289	46	51	p	p	NOUN
ejpam-289	46	52	and	and	CCONJ
ejpam-289	46	53	q	q	NOUN
ejpam-289	46	54	are	be	AUX
ejpam-289	46	55	,	,	PUNCT
ejpam-289	46	56	p1	p1	NOUN
ejpam-289	46	57	-	-	PUNCT
ejpam-289	46	58	lindelöf	lindelöf	NOUN
ejpam-289	46	59	if	if	SCONJ
ejpam-289	46	60	p	p	NOUN
ejpam-289	46	61	is	be	AUX
ejpam-289	46	62	lindelöf	lindelöf	NOUN
ejpam-289	46	63	with	with	ADP
ejpam-289	46	64	respect	respect	NOUN
ejpam-289	46	65	to	to	ADP
ejpam-289	46	66	q	q	NOUN
ejpam-289	46	67	and	and	CCONJ
ejpam-289	46	68	vice	vice	ADV
ejpam-289	46	69	versa	versa	ADV
ejpam-289	46	70	.	.	PUNCT
ejpam-289	47	1	3	3	X
ejpam-289	47	2	.	.	X
ejpam-289	47	3	bitopological	bitopological	ADJ
ejpam-289	47	4	separation	separation	NOUN
ejpam-289	47	5	axioms	axiom	NOUN
ejpam-289	47	6	in	in	ADP
ejpam-289	47	7	this	this	DET
ejpam-289	47	8	section	section	NOUN
ejpam-289	47	9	,	,	PUNCT
ejpam-289	47	10	we	we	PRON
ejpam-289	47	11	shall	shall	AUX
ejpam-289	47	12	introduce	introduce	VERB
ejpam-289	47	13	the	the	DET
ejpam-289	47	14	concept	concept	NOUN
ejpam-289	47	15	of	of	ADP
ejpam-289	47	16	p1	p1	NOUN
ejpam-289	47	17	-	-	PUNCT
ejpam-289	47	18	regular	regular	ADJ
ejpam-289	47	19	spaces	space	NOUN
ejpam-289	47	20	and	and	CCONJ
ejpam-289	47	21	p2	p2	NOUN
ejpam-289	47	22	-	-	PUNCT
ejpam-289	47	23	normal	normal	ADJ
ejpam-289	47	24	spaces	space	NOUN
ejpam-289	47	25	.	.	PUNCT
ejpam-289	48	1	before	before	ADP
ejpam-289	48	2	that	that	SCONJ
ejpam-289	48	3	we	we	PRON
ejpam-289	48	4	need	need	VERB
ejpam-289	48	5	the	the	DET
ejpam-289	48	6	following	follow	VERB
ejpam-289	48	7	definition	definition	NOUN
ejpam-289	48	8	.	.	PUNCT
ejpam-289	49	1	definition	definition	NOUN
ejpam-289	49	2	3.1	3.1	NUM
ejpam-289	49	3	.	.	PUNCT
ejpam-289	50	1	let	let	VERB
ejpam-289	50	2	(	(	PUNCT
ejpam-289	50	3	x	x	INTJ
ejpam-289	50	4	,	,	PUNCT
ejpam-289	50	5	p	p	X
ejpam-289	50	6	,	,	PUNCT
ejpam-289	50	7	q	q	NOUN
ejpam-289	50	8	)	)	PUNCT
ejpam-289	50	9	be	be	AUX
ejpam-289	50	10	a	a	DET
ejpam-289	50	11	bitopological	bitopological	ADJ
ejpam-289	50	12	space	space	NOUN
ejpam-289	50	13	.	.	PUNCT
ejpam-289	51	1	(	(	PUNCT
ejpam-289	51	2	i	i	NOUN
ejpam-289	51	3	)	)	PUNCT
ejpam-289	51	4	a	a	DET
ejpam-289	51	5	set	set	NOUN
ejpam-289	51	6	h	h	NOUN
ejpam-289	51	7	is	be	AUX
ejpam-289	51	8	said	say	VERB
ejpam-289	51	9	to	to	PART
ejpam-289	51	10	be	be	AUX
ejpam-289	51	11	p1	p1	NOUN
ejpam-289	51	12	-	-	ADJ
ejpam-289	51	13	open	open	ADJ
ejpam-289	51	14	if	if	SCONJ
ejpam-289	51	15	h	h	NOUN
ejpam-289	51	16	is	be	AUX
ejpam-289	51	17	(	(	PUNCT
ejpam-289	51	18	p	p	NOUN
ejpam-289	51	19	∪q)-open	∪q)-open	ADJ
ejpam-289	51	20	in	in	ADP
ejpam-289	51	21	x	x	X
ejpam-289	51	22	.	.	PUNCT
ejpam-289	52	1	(	(	PUNCT
ejpam-289	52	2	ii	ii	NOUN
ejpam-289	52	3	)	)	PUNCT
ejpam-289	52	4	a	a	DET
ejpam-289	52	5	set	set	NOUN
ejpam-289	52	6	m	m	VERB
ejpam-289	52	7	is	be	AUX
ejpam-289	52	8	said	say	VERB
ejpam-289	52	9	to	to	PART
ejpam-289	52	10	be	be	AUX
ejpam-289	52	11	p1	p1	NOUN
ejpam-289	52	12	-	-	PUNCT
ejpam-289	52	13	closed	closed	ADJ
ejpam-289	52	14	if	if	SCONJ
ejpam-289	52	15	m	m	NOUN
ejpam-289	52	16	is	be	AUX
ejpam-289	52	17	(	(	PUNCT
ejpam-289	52	18	p	p	PRON
ejpam-289	52	19	∪q)-closed	∪q)-close	VERB
ejpam-289	52	20	in	in	ADP
ejpam-289	52	21	x	x	PROPN
ejpam-289	52	22	.	.	PUNCT
ejpam-289	53	1	definition	definition	NOUN
ejpam-289	53	2	3.2	3.2	NUM
ejpam-289	53	3	.	.	PUNCT
ejpam-289	54	1	a	a	DET
ejpam-289	54	2	bitopological	bitopological	ADJ
ejpam-289	54	3	space	space	NOUN
ejpam-289	54	4	(	(	PUNCT
ejpam-289	54	5	x	x	X
ejpam-289	54	6	,	,	PUNCT
ejpam-289	54	7	p	p	X
ejpam-289	54	8	,	,	PUNCT
ejpam-289	54	9	q	q	NOUN
ejpam-289	54	10	)	)	PUNCT
ejpam-289	54	11	is	be	AUX
ejpam-289	54	12	said	say	VERB
ejpam-289	54	13	to	to	PART
ejpam-289	54	14	be	be	AUX
ejpam-289	54	15	p1	p1	NOUN
ejpam-289	54	16	-	-	ADJ
ejpam-289	54	17	regular	regular	ADJ
ejpam-289	54	18	if	if	SCONJ
ejpam-289	54	19	for	for	ADP
ejpam-289	54	20	each	each	DET
ejpam-289	54	21	point	point	NOUN
ejpam-289	54	22	x	x	X
ejpam-289	54	23	∈	∈	NOUN
ejpam-289	54	24	x	x	X
ejpam-289	54	25	,	,	PUNCT
ejpam-289	54	26	there	there	PRON
ejpam-289	54	27	is	be	VERB
ejpam-289	54	28	a	a	DET
ejpam-289	54	29	p1	p1	ADJ
ejpam-289	54	30	-	-	PUNCT
ejpam-289	54	31	neighbourhood	neighbourhood	NOUN
ejpam-289	54	32	base	base	NOUN
ejpam-289	54	33	of	of	ADP
ejpam-289	54	34	p1	p1	NOUN
ejpam-289	54	35	-	-	PUNCT
ejpam-289	54	36	closed	close	VERB
ejpam-289	54	37	sets	set	NOUN
ejpam-289	54	38	,	,	PUNCT
ejpam-289	54	39	or	or	CCONJ
ejpam-289	54	40	,	,	PUNCT
ejpam-289	54	41	as	as	SCONJ
ejpam-289	54	42	is	be	AUX
ejpam-289	54	43	easily	easily	ADV
ejpam-289	54	44	seen	see	VERB
ejpam-289	54	45	to	to	PART
ejpam-289	54	46	be	be	AUX
ejpam-289	54	47	equivalent	equivalent	ADJ
ejpam-289	54	48	,	,	PUNCT
ejpam-289	54	49	if	if	SCONJ
ejpam-289	54	50	,	,	PUNCT
ejpam-289	54	51	for	for	ADP
ejpam-289	54	52	each	each	DET
ejpam-289	54	53	point	point	NOUN
ejpam-289	54	54	x	x	X
ejpam-289	54	55	∈	∈	NOUN
ejpam-289	54	56	x	x	X
ejpam-289	54	57	and	and	CCONJ
ejpam-289	54	58	each	each	DET
ejpam-289	54	59	p1	p1	NOUN
ejpam-289	54	60	-	-	PUNCT
ejpam-289	54	61	closed	close	VERB
ejpam-289	54	62	set	set	NOUN
ejpam-289	54	63	p	p	PRON
ejpam-289	54	64	such	such	ADJ
ejpam-289	54	65	that	that	PRON
ejpam-289	54	66	x	x	X
ejpam-289	54	67	/∈	/∈	PUNCT
ejpam-289	55	1	p	p	X
ejpam-289	55	2	,	,	PUNCT
ejpam-289	55	3	there	there	PRON
ejpam-289	55	4	are	be	VERB
ejpam-289	55	5	p1	p1	NOUN
ejpam-289	55	6	-	-	PUNCT
ejpam-289	55	7	open	open	ADJ
ejpam-289	55	8	sets	set	VERB
ejpam-289	55	9	u	u	NOUN
ejpam-289	55	10	and	and	CCONJ
ejpam-289	55	11	v	v	ADP
ejpam-289	55	12	such	such	ADJ
ejpam-289	55	13	that	that	SCONJ
ejpam-289	55	14	x	x	SYM
ejpam-289	55	15	∈	∈	PROPN
ejpam-289	55	16	u	u	NOUN
ejpam-289	55	17	,	,	PUNCT
ejpam-289	55	18	p	p	PROPN
ejpam-289	55	19	⊆	⊆	NUM
ejpam-289	55	20	v	v	NOUN
ejpam-289	55	21	,	,	PUNCT
ejpam-289	55	22	and	and	CCONJ
ejpam-289	55	23	u	u	NOUN
ejpam-289	55	24	∩	∩	NOUN
ejpam-289	55	25	v	v	NOUN
ejpam-289	55	26	=	=	PUNCT
ejpam-289	55	27	;	;	PUNCT
ejpam-289	55	28	.	.	PUNCT
ejpam-289	56	1	note	note	VERB
ejpam-289	56	2	that	that	SCONJ
ejpam-289	56	3	,	,	PUNCT
ejpam-289	56	4	below	below	ADP
ejpam-289	56	5	we	we	PRON
ejpam-289	56	6	shall	shall	AUX
ejpam-289	56	7	use	use	VERB
ejpam-289	56	8	the	the	DET
ejpam-289	56	9	notation	notation	NOUN
ejpam-289	56	10	p1	p1	NOUN
ejpam-289	56	11	-	-	PUNCT
ejpam-289	56	12	cl	cl	NOUN
ejpam-289	56	13	(	(	PUNCT
ejpam-289	56	14	u	u	NOUN
ejpam-289	56	15	)	)	PUNCT
ejpam-289	56	16	,	,	PUNCT
ejpam-289	56	17	which	which	PRON
ejpam-289	56	18	means	mean	VERB
ejpam-289	56	19	that	that	SCONJ
ejpam-289	56	20	,	,	PUNCT
ejpam-289	56	21	the	the	DET
ejpam-289	56	22	closure	closure	NOUN
ejpam-289	56	23	of	of	ADP
ejpam-289	56	24	u	u	NOUN
ejpam-289	56	25	with	with	ADP
ejpam-289	56	26	respect	respect	NOUN
ejpam-289	56	27	to	to	ADP
ejpam-289	56	28	p	p	NOUN
ejpam-289	56	29	∪q	∪q	NUM
ejpam-289	56	30	,	,	PUNCT
ejpam-289	56	31	or	or	CCONJ
ejpam-289	56	32	,	,	PUNCT
ejpam-289	56	33	in	in	ADP
ejpam-289	56	34	other	other	ADJ
ejpam-289	56	35	words	word	NOUN
ejpam-289	56	36	(	(	PUNCT
ejpam-289	56	37	p	p	NOUN
ejpam-289	56	38	∪q)-cl	∪q)-cl	PROPN
ejpam-289	56	39	(	(	PUNCT
ejpam-289	56	40	u	u	NOUN
ejpam-289	56	41	)	)	PUNCT
ejpam-289	56	42	.	.	PUNCT
ejpam-289	57	1	a.	a.	PROPN
ejpam-289	57	2	kılıçman	kılıçman	PROPN
ejpam-289	57	3	and	and	CCONJ
ejpam-289	57	4	z.	z.	PROPN
ejpam-289	57	5	salleh	salleh	PROPN
ejpam-289	57	6	/	/	PUNCT
ejpam-289	57	7	eur	eur	PROPN
ejpam-289	57	8	.	.	PUNCT
ejpam-289	58	1	j.	j.	PROPN
ejpam-289	58	2	pure	pure	PROPN
ejpam-289	58	3	appl	appl	PROPN
ejpam-289	58	4	.	.	PROPN
ejpam-289	58	5	math	math	PROPN
ejpam-289	58	6	,	,	PUNCT
ejpam-289	58	7	2	2	NUM
ejpam-289	58	8	(	(	PUNCT
ejpam-289	58	9	2009	2009	NUM
ejpam-289	58	10	)	)	PUNCT
ejpam-289	58	11	,	,	PUNCT
ejpam-289	58	12	(	(	PUNCT
ejpam-289	58	13	325	325	NUM
ejpam-289	58	14	-	-	SYM
ejpam-289	58	15	337	337	NUM
ejpam-289	58	16	)	)	PUNCT
ejpam-289	58	17	329	329	NUM
ejpam-289	58	18	theorem	theorem	VERB
ejpam-289	58	19	3.1	3.1	NUM
ejpam-289	58	20	.	.	PUNCT
ejpam-289	59	1	a	a	DET
ejpam-289	59	2	bitopological	bitopological	ADJ
ejpam-289	59	3	space	space	NOUN
ejpam-289	59	4	(	(	PUNCT
ejpam-289	59	5	x	x	X
ejpam-289	59	6	,	,	PUNCT
ejpam-289	59	7	p	p	X
ejpam-289	59	8	,	,	PUNCT
ejpam-289	59	9	q	q	NOUN
ejpam-289	59	10	)	)	PUNCT
ejpam-289	59	11	is	be	AUX
ejpam-289	59	12	p1	p1	NOUN
ejpam-289	59	13	-	-	ADJ
ejpam-289	59	14	regular	regular	ADJ
ejpam-289	59	15	if	if	SCONJ
ejpam-289	59	16	and	and	CCONJ
ejpam-289	59	17	only	only	ADV
ejpam-289	59	18	if	if	SCONJ
ejpam-289	59	19	for	for	ADP
ejpam-289	59	20	each	each	DET
ejpam-289	59	21	point	point	NOUN
ejpam-289	59	22	x	x	X
ejpam-289	59	23	∈	∈	PROPN
ejpam-289	59	24	x	x	X
ejpam-289	59	25	and	and	CCONJ
ejpam-289	59	26	p1	p1	NOUN
ejpam-289	59	27	-	-	PUNCT
ejpam-289	59	28	open	open	ADJ
ejpam-289	59	29	set	set	NOUN
ejpam-289	59	30	h	h	NOUN
ejpam-289	59	31	containing	contain	VERB
ejpam-289	59	32	x	x	X
ejpam-289	59	33	,	,	PUNCT
ejpam-289	59	34	there	there	PRON
ejpam-289	59	35	exists	exist	VERB
ejpam-289	59	36	a	a	DET
ejpam-289	59	37	p1	p1	NOUN
ejpam-289	59	38	-	-	PUNCT
ejpam-289	59	39	open	open	ADJ
ejpam-289	59	40	set	set	NOUN
ejpam-289	59	41	u	u	PRON
ejpam-289	59	42	such	such	ADJ
ejpam-289	59	43	that	that	SCONJ
ejpam-289	59	44	x	x	SYM
ejpam-289	59	45	∈	∈	NOUN
ejpam-289	59	46	u	u	NOUN
ejpam-289	59	47	⊆	⊆	NUM
ejpam-289	59	48	p1cl	p1cl	X
ejpam-289	59	49	(	(	PUNCT
ejpam-289	59	50	u)⊆	u)⊆	NUM
ejpam-289	59	51	h.	h.	NOUN
ejpam-289	59	52	proof	proof	NOUN
ejpam-289	59	53	.	.	PUNCT
ejpam-289	60	1	(	(	PUNCT
ejpam-289	60	2	⇒	⇒	PROPN
ejpam-289	60	3	)	)	PUNCT
ejpam-289	60	4	:	:	PUNCT
ejpam-289	60	5	suppose	suppose	VERB
ejpam-289	60	6	(	(	PUNCT
ejpam-289	60	7	x	x	X
ejpam-289	60	8	,	,	PUNCT
ejpam-289	60	9	p	p	X
ejpam-289	60	10	,	,	PUNCT
ejpam-289	60	11	q	q	NOUN
ejpam-289	60	12	)	)	PUNCT
ejpam-289	60	13	is	be	AUX
ejpam-289	60	14	p1	p1	NOUN
ejpam-289	60	15	-	-	NOUN
ejpam-289	60	16	regular	regular	ADJ
ejpam-289	60	17	.	.	PUNCT
ejpam-289	61	1	let	let	VERB
ejpam-289	61	2	x	x	PUNCT
ejpam-289	61	3	∈	∈	PROPN
ejpam-289	61	4	x	x	X
ejpam-289	61	5	and	and	CCONJ
ejpam-289	61	6	h	h	NOUN
ejpam-289	61	7	is	be	AUX
ejpam-289	61	8	a	a	DET
ejpam-289	61	9	p1	p1	NOUN
ejpam-289	61	10	-	-	PUNCT
ejpam-289	61	11	open	open	ADJ
ejpam-289	61	12	set	set	NOUN
ejpam-289	61	13	containing	contain	VERB
ejpam-289	61	14	x	x	X
ejpam-289	61	15	.	.	PUNCT
ejpam-289	62	1	then	then	ADV
ejpam-289	62	2	g	g	PROPN
ejpam-289	62	3	=	=	SYM
ejpam-289	62	4	x	x	SYM
ejpam-289	62	5	�	�	NOUN
ejpam-289	62	6	h	h	NOUN
ejpam-289	62	7	is	be	AUX
ejpam-289	62	8	a	a	DET
ejpam-289	62	9	p1	p1	NOUN
ejpam-289	62	10	-	-	PUNCT
ejpam-289	62	11	closed	close	VERB
ejpam-289	62	12	set	set	NOUN
ejpam-289	63	1	which	which	DET
ejpam-289	63	2	x	x	SYM
ejpam-289	63	3	/∈	/∈	PROPN
ejpam-289	63	4	g.	g.	PROPN
ejpam-289	63	5	since	since	SCONJ
ejpam-289	63	6	(	(	PUNCT
ejpam-289	63	7	x	x	INTJ
ejpam-289	63	8	,	,	PUNCT
ejpam-289	63	9	p	p	X
ejpam-289	63	10	,	,	PUNCT
ejpam-289	63	11	q	q	NOUN
ejpam-289	63	12	)	)	PUNCT
ejpam-289	63	13	is	be	AUX
ejpam-289	63	14	p1	p1	NOUN
ejpam-289	63	15	-	-	PUNCT
ejpam-289	63	16	regular	regular	ADJ
ejpam-289	63	17	,	,	PUNCT
ejpam-289	63	18	then	then	ADV
ejpam-289	63	19	there	there	PRON
ejpam-289	63	20	are	be	VERB
ejpam-289	63	21	p1	p1	NOUN
ejpam-289	63	22	-	-	PUNCT
ejpam-289	63	23	open	open	ADJ
ejpam-289	63	24	sets	set	VERB
ejpam-289	63	25	u	u	NOUN
ejpam-289	63	26	and	and	CCONJ
ejpam-289	63	27	v	v	ADP
ejpam-289	63	28	such	such	ADJ
ejpam-289	63	29	that	that	SCONJ
ejpam-289	63	30	x	x	SYM
ejpam-289	63	31	∈	∈	PROPN
ejpam-289	63	32	u	u	NOUN
ejpam-289	63	33	,	,	PUNCT
ejpam-289	63	34	g	g	PROPN
ejpam-289	63	35	⊆	⊆	NUM
ejpam-289	63	36	v	v	NOUN
ejpam-289	63	37	,	,	PUNCT
ejpam-289	63	38	and	and	CCONJ
ejpam-289	63	39	u	u	NOUN
ejpam-289	63	40	∩	∩	NOUN
ejpam-289	63	41	v	v	NOUN
ejpam-289	63	42	=	=	PUNCT
ejpam-289	63	43	;	;	PUNCT
ejpam-289	63	44	.	.	PUNCT
ejpam-289	64	1	since	since	SCONJ
ejpam-289	64	2	u	u	PRON
ejpam-289	64	3	⊆	⊆	NUM
ejpam-289	64	4	x	x	X
ejpam-289	64	5	�	�	PROPN
ejpam-289	64	6	v	v	NOUN
ejpam-289	64	7	,	,	PUNCT
ejpam-289	64	8	then	then	ADV
ejpam-289	64	9	p1	p1	NOUN
ejpam-289	64	10	-	-	PUNCT
ejpam-289	64	11	cl	cl	NOUN
ejpam-289	64	12	(	(	PUNCT
ejpam-289	64	13	u	u	NOUN
ejpam-289	64	14	)	)	PUNCT
ejpam-289	64	15	⊆	⊆	NUM
ejpam-289	64	16	p1	p1	NOUN
ejpam-289	64	17	-	-	PUNCT
ejpam-289	64	18	cl	cl	NOUN
ejpam-289	64	19	(	(	PUNCT
ejpam-289	64	20	x	x	X
ejpam-289	64	21	�	�	NOUN
ejpam-289	64	22	v	v	NOUN
ejpam-289	64	23	)	)	PUNCT
ejpam-289	64	24	=	=	SYM
ejpam-289	64	25	x	x	SYM
ejpam-289	64	26	�	�	PROPN
ejpam-289	64	27	v	v	NUM
ejpam-289	64	28	⊆	⊆	NUM
ejpam-289	64	29	x	x	SYM
ejpam-289	64	30	�	�	PROPN
ejpam-289	64	31	g	g	NOUN
ejpam-289	64	32	=	=	PROPN
ejpam-289	64	33	h.	h.	PROPN
ejpam-289	64	34	thus	thus	ADV
ejpam-289	64	35	,	,	PUNCT
ejpam-289	64	36	x	x	PUNCT
ejpam-289	64	37	∈	∈	PROPN
ejpam-289	64	38	u	u	NOUN
ejpam-289	64	39	⊆	⊆	NUM
ejpam-289	64	40	p1	p1	NOUN
ejpam-289	64	41	-	-	NOUN
ejpam-289	64	42	cl	cl	NOUN
ejpam-289	64	43	(	(	PUNCT
ejpam-289	64	44	u)⊆	u)⊆	PROPN
ejpam-289	64	45	h	h	NOUN
ejpam-289	64	46	as	as	SCONJ
ejpam-289	64	47	desired	desire	VERB
ejpam-289	64	48	.	.	PUNCT
ejpam-289	65	1	(	(	PUNCT
ejpam-289	65	2	⇐	⇐	PROPN
ejpam-289	65	3	)	)	PUNCT
ejpam-289	65	4	:	:	PUNCT
ejpam-289	65	5	suppose	suppose	VERB
ejpam-289	65	6	the	the	DET
ejpam-289	65	7	condition	condition	NOUN
ejpam-289	65	8	holds	hold	VERB
ejpam-289	65	9	.	.	PUNCT
ejpam-289	66	1	let	let	VERB
ejpam-289	66	2	x	x	SYM
ejpam-289	66	3	∈	∈	PROPN
ejpam-289	66	4	x	x	X
ejpam-289	66	5	and	and	CCONJ
ejpam-289	66	6	p	p	NOUN
ejpam-289	66	7	is	be	AUX
ejpam-289	66	8	a	a	DET
ejpam-289	66	9	p1	p1	NOUN
ejpam-289	66	10	-	-	PUNCT
ejpam-289	66	11	closed	close	VERB
ejpam-289	66	12	set	set	NOUN
ejpam-289	66	13	such	such	ADJ
ejpam-289	66	14	that	that	PRON
ejpam-289	66	15	x	x	PUNCT
ejpam-289	66	16	/∈	/∈	PUNCT
ejpam-289	67	1	p.	p.	NOUN
ejpam-289	67	2	then	then	ADV
ejpam-289	67	3	x	x	SYM
ejpam-289	67	4	∈	∈	PROPN
ejpam-289	67	5	x	x	SYM
ejpam-289	67	6	�	�	PROPN
ejpam-289	67	7	p	p	NOUN
ejpam-289	67	8	,	,	PUNCT
ejpam-289	67	9	and	and	CCONJ
ejpam-289	67	10	by	by	ADP
ejpam-289	67	11	hypothesis	hypothesis	NOUN
ejpam-289	67	12	there	there	PRON
ejpam-289	67	13	exists	exist	VERB
ejpam-289	67	14	a	a	DET
ejpam-289	67	15	p1	p1	NOUN
ejpam-289	67	16	-	-	PUNCT
ejpam-289	67	17	open	open	ADJ
ejpam-289	67	18	set	set	NOUN
ejpam-289	67	19	u	u	PRON
ejpam-289	67	20	such	such	ADJ
ejpam-289	67	21	that	that	SCONJ
ejpam-289	67	22	x	x	SYM
ejpam-289	67	23	∈	∈	PROPN
ejpam-289	67	24	u	u	NOUN
ejpam-289	67	25	⊆	⊆	NUM
ejpam-289	67	26	p1	p1	NOUN
ejpam-289	67	27	-	-	PUNCT
ejpam-289	67	28	cl	cl	NOUN
ejpam-289	67	29	(	(	PUNCT
ejpam-289	67	30	u	u	NOUN
ejpam-289	67	31	)	)	PUNCT
ejpam-289	67	32	⊆	⊆	NUM
ejpam-289	67	33	x	x	SYM
ejpam-289	67	34	�	�	NOUN
ejpam-289	67	35	p.	p.	NOUN
ejpam-289	67	36	it	it	PRON
ejpam-289	67	37	follows	follow	VERB
ejpam-289	67	38	that	that	SCONJ
ejpam-289	67	39	x	x	PUNCT
ejpam-289	67	40	∈	∈	PROPN
ejpam-289	67	41	u	u	NOUN
ejpam-289	67	42	,	,	PUNCT
ejpam-289	67	43	p	p	PROPN
ejpam-289	67	44	⊆	⊆	NUM
ejpam-289	67	45	x	x	SYM
ejpam-289	67	46	�	�	PROPN
ejpam-289	67	47	p1	p1	NOUN
ejpam-289	67	48	-	-	NOUN
ejpam-289	67	49	cl	cl	NOUN
ejpam-289	67	50	(	(	PUNCT
ejpam-289	67	51	u	u	NOUN
ejpam-289	67	52	)	)	PUNCT
ejpam-289	67	53	and	and	CCONJ
ejpam-289	67	54	u	u	PROPN
ejpam-289	67	55	∩	∩	NOUN
ejpam-289	67	56	�	�	PROPN
ejpam-289	67	57	x	x	SYM
ejpam-289	67	58	�	�	PROPN
ejpam-289	67	59	p1cl	p1cl	PUNCT
ejpam-289	67	60	(	(	PUNCT
ejpam-289	67	61	u	u	NOUN
ejpam-289	67	62	)	)	PUNCT
ejpam-289	67	63	�	�	PROPN
ejpam-289	67	64	=	=	PUNCT
ejpam-289	67	65	;	;	PUNCT
ejpam-289	67	66	.	.	PUNCT
ejpam-289	68	1	this	this	PRON
ejpam-289	68	2	completes	complete	VERB
ejpam-289	68	3	the	the	DET
ejpam-289	68	4	proof	proof	NOUN
ejpam-289	68	5	.	.	PUNCT
ejpam-289	69	1	definition	definition	NOUN
ejpam-289	69	2	3.3	3.3	NUM
ejpam-289	69	3	.	.	PUNCT
ejpam-289	70	1	a	a	DET
ejpam-289	70	2	bitopological	bitopological	ADJ
ejpam-289	70	3	space	space	NOUN
ejpam-289	70	4	(	(	PUNCT
ejpam-289	70	5	x	x	X
ejpam-289	70	6	,	,	PUNCT
ejpam-289	70	7	p	p	X
ejpam-289	70	8	,	,	PUNCT
ejpam-289	70	9	q	q	NOUN
ejpam-289	70	10	)	)	PUNCT
ejpam-289	70	11	is	be	AUX
ejpam-289	70	12	said	say	VERB
ejpam-289	70	13	to	to	PART
ejpam-289	70	14	be	be	AUX
ejpam-289	70	15	p2	p2	NOUN
ejpam-289	70	16	-	-	PUNCT
ejpam-289	70	17	normal	normal	ADJ
ejpam-289	70	18	if	if	SCONJ
ejpam-289	70	19	given	give	VERB
ejpam-289	70	20	p1	p1	NOUN
ejpam-289	70	21	-	-	PUNCT
ejpam-289	70	22	closed	close	VERB
ejpam-289	70	23	sets	set	NOUN
ejpam-289	70	24	a	a	PRON
ejpam-289	70	25	and	and	CCONJ
ejpam-289	70	26	b	b	NOUN
ejpam-289	70	27	with	with	ADP
ejpam-289	70	28	a∩	a∩	PROPN
ejpam-289	70	29	b	b	PROPN
ejpam-289	70	30	=	=	PUNCT
ejpam-289	70	31	;	;	PUNCT
ejpam-289	70	32	,	,	PUNCT
ejpam-289	70	33	there	there	PRON
ejpam-289	70	34	exist	exist	VERB
ejpam-289	70	35	p1	p1	NOUN
ejpam-289	70	36	-	-	PUNCT
ejpam-289	70	37	open	open	ADJ
ejpam-289	70	38	sets	set	VERB
ejpam-289	70	39	u	u	NOUN
ejpam-289	70	40	and	and	CCONJ
ejpam-289	70	41	v	v	ADP
ejpam-289	70	42	such	such	ADJ
ejpam-289	70	43	that	that	PRON
ejpam-289	70	44	a⊆	a⊆	PROPN
ejpam-289	70	45	u	u	PROPN
ejpam-289	70	46	,	,	PUNCT
ejpam-289	70	47	b	b	PROPN
ejpam-289	70	48	⊆	⊆	NUM
ejpam-289	70	49	v	v	NOUN
ejpam-289	70	50	,	,	PUNCT
ejpam-289	70	51	and	and	CCONJ
ejpam-289	70	52	u	u	NOUN
ejpam-289	70	53	∩	∩	NOUN
ejpam-289	70	54	v	v	NOUN
ejpam-289	70	55	=	=	PUNCT
ejpam-289	70	56	;	;	PUNCT
ejpam-289	70	57	.	.	PUNCT
ejpam-289	71	1	theorem	theorem	VERB
ejpam-289	71	2	3.2	3.2	NUM
ejpam-289	71	3	.	.	PUNCT
ejpam-289	72	1	a	a	DET
ejpam-289	72	2	space	space	NOUN
ejpam-289	72	3	(	(	PUNCT
ejpam-289	72	4	x	x	X
ejpam-289	72	5	,	,	PUNCT
ejpam-289	72	6	p	p	X
ejpam-289	72	7	,	,	PUNCT
ejpam-289	72	8	q	q	NOUN
ejpam-289	72	9	)	)	PUNCT
ejpam-289	72	10	is	be	AUX
ejpam-289	72	11	p2	p2	NOUN
ejpam-289	72	12	-	-	PUNCT
ejpam-289	72	13	normal	normal	ADJ
ejpam-289	72	14	if	if	SCONJ
ejpam-289	72	15	and	and	CCONJ
ejpam-289	72	16	only	only	ADV
ejpam-289	72	17	if	if	SCONJ
ejpam-289	72	18	given	give	VERB
ejpam-289	72	19	a	a	DET
ejpam-289	72	20	p1	p1	NOUN
ejpam-289	72	21	-	-	PUNCT
ejpam-289	72	22	closed	close	VERB
ejpam-289	72	23	set	set	NOUN
ejpam-289	72	24	c	c	NOUN
ejpam-289	72	25	and	and	CCONJ
ejpam-289	72	26	a	a	DET
ejpam-289	72	27	p1	p1	NOUN
ejpam-289	72	28	-	-	PUNCT
ejpam-289	72	29	open	open	ADJ
ejpam-289	72	30	set	set	NOUN
ejpam-289	72	31	d	d	ADP
ejpam-289	72	32	such	such	ADJ
ejpam-289	72	33	that	that	SCONJ
ejpam-289	72	34	c	c	PROPN
ejpam-289	72	35	⊆	⊆	NUM
ejpam-289	72	36	d	d	NOUN
ejpam-289	72	37	,	,	PUNCT
ejpam-289	72	38	there	there	PRON
ejpam-289	72	39	are	be	VERB
ejpam-289	72	40	a	a	DET
ejpam-289	72	41	p1	p1	NOUN
ejpam-289	72	42	-	-	PUNCT
ejpam-289	72	43	open	open	NOUN
ejpam-289	72	44	set	set	NOUN
ejpam-289	72	45	g	g	NOUN
ejpam-289	72	46	and	and	CCONJ
ejpam-289	72	47	a	a	DET
ejpam-289	72	48	p1	p1	NOUN
ejpam-289	72	49	-	-	PUNCT
ejpam-289	72	50	closed	close	VERB
ejpam-289	72	51	set	set	NOUN
ejpam-289	72	52	f	f	PROPN
ejpam-289	72	53	such	such	ADJ
ejpam-289	72	54	that	that	SCONJ
ejpam-289	72	55	c	c	PROPN
ejpam-289	72	56	⊆	⊆	NUM
ejpam-289	72	57	g	g	ADP
ejpam-289	72	58	⊆	⊆	NUM
ejpam-289	72	59	f	f	SYM
ejpam-289	72	60	⊆	⊆	NUM
ejpam-289	72	61	d.	d.	PROPN
ejpam-289	72	62	proof	proof	NOUN
ejpam-289	72	63	.	.	PUNCT
ejpam-289	73	1	(	(	PUNCT
ejpam-289	73	2	⇒	⇒	PROPN
ejpam-289	73	3	)	)	PUNCT
ejpam-289	73	4	:	:	PUNCT
ejpam-289	73	5	suppose	suppose	VERB
ejpam-289	73	6	(	(	PUNCT
ejpam-289	73	7	x	x	X
ejpam-289	73	8	,	,	PUNCT
ejpam-289	73	9	p	p	X
ejpam-289	73	10	,	,	PUNCT
ejpam-289	73	11	q	q	NOUN
ejpam-289	73	12	)	)	PUNCT
ejpam-289	73	13	is	be	AUX
ejpam-289	73	14	p2	p2	NOUN
ejpam-289	73	15	-	-	PUNCT
ejpam-289	73	16	normal	normal	ADJ
ejpam-289	73	17	.	.	PUNCT
ejpam-289	74	1	let	let	VERB
ejpam-289	74	2	c	c	PRON
ejpam-289	74	3	be	be	AUX
ejpam-289	74	4	a	a	DET
ejpam-289	74	5	p1	p1	NOUN
ejpam-289	74	6	-	-	PUNCT
ejpam-289	74	7	closed	close	VERB
ejpam-289	74	8	set	set	NOUN
ejpam-289	74	9	and	and	CCONJ
ejpam-289	74	10	d	d	ADP
ejpam-289	74	11	a	a	DET
ejpam-289	74	12	p1	p1	NOUN
ejpam-289	74	13	-	-	PUNCT
ejpam-289	74	14	open	open	NOUN
ejpam-289	74	15	set	set	NOUN
ejpam-289	74	16	such	such	ADJ
ejpam-289	74	17	that	that	SCONJ
ejpam-289	74	18	c	c	PROPN
ejpam-289	74	19	⊆	⊆	NUM
ejpam-289	74	20	d.	d.	PROPN
ejpam-289	74	21	then	then	ADV
ejpam-289	74	22	k	k	PROPN
ejpam-289	74	23	=	=	PUNCT
ejpam-289	74	24	x	x	SYM
ejpam-289	74	25	�	�	PROPN
ejpam-289	74	26	d	d	PROPN
ejpam-289	74	27	is	be	AUX
ejpam-289	74	28	a	a	DET
ejpam-289	74	29	p1	p1	NOUN
ejpam-289	74	30	-	-	PUNCT
ejpam-289	74	31	closed	close	VERB
ejpam-289	74	32	set	set	NOUN
ejpam-289	74	33	with	with	ADP
ejpam-289	74	34	k	k	PROPN
ejpam-289	74	35	∩	∩	ADJ
ejpam-289	74	36	c	c	NOUN
ejpam-289	74	37	=	=	PUNCT
ejpam-289	74	38	;	;	PUNCT
ejpam-289	74	39	.	.	PUNCT
ejpam-289	75	1	since	since	SCONJ
ejpam-289	75	2	(	(	PUNCT
ejpam-289	75	3	x	x	INTJ
ejpam-289	75	4	,	,	PUNCT
ejpam-289	75	5	p	p	X
ejpam-289	75	6	,	,	PUNCT
ejpam-289	75	7	q	q	NOUN
ejpam-289	75	8	)	)	PUNCT
ejpam-289	75	9	is	be	AUX
ejpam-289	75	10	p2	p2	NOUN
ejpam-289	75	11	-	-	PUNCT
ejpam-289	75	12	normal	normal	ADJ
ejpam-289	75	13	,	,	PUNCT
ejpam-289	75	14	there	there	PRON
ejpam-289	75	15	exists	exist	VERB
ejpam-289	75	16	p1	p1	NOUN
ejpam-289	75	17	-	-	PUNCT
ejpam-289	75	18	open	open	ADJ
ejpam-289	75	19	sets	set	VERB
ejpam-289	75	20	u	u	NOUN
ejpam-289	75	21	and	and	CCONJ
ejpam-289	75	22	g	g	NOUN
ejpam-289	75	23	such	such	ADJ
ejpam-289	75	24	that	that	SCONJ
ejpam-289	75	25	k	k	PROPN
ejpam-289	75	26	⊆	⊆	NUM
ejpam-289	75	27	u	u	NOUN
ejpam-289	75	28	,	,	PUNCT
ejpam-289	75	29	c	c	PROPN
ejpam-289	75	30	⊆	⊆	NUM
ejpam-289	75	31	g	g	NOUN
ejpam-289	75	32	,	,	PUNCT
ejpam-289	75	33	and	and	CCONJ
ejpam-289	75	34	u	u	NOUN
ejpam-289	75	35	∩	∩	NOUN
ejpam-289	75	36	g	g	NOUN
ejpam-289	75	37	=	=	PUNCT
ejpam-289	75	38	;	;	PUNCT
ejpam-289	75	39	.	.	PUNCT
ejpam-289	76	1	hence	hence	ADV
ejpam-289	76	2	g	g	PROPN
ejpam-289	76	3	⊆	⊆	NUM
ejpam-289	76	4	x	x	SYM
ejpam-289	76	5	�	�	NOUN
ejpam-289	76	6	u	u	PRON
ejpam-289	76	7	⊆	⊆	NUM
ejpam-289	76	8	x	x	SYM
ejpam-289	76	9	�	�	PROPN
ejpam-289	76	10	k	k	NOUN
ejpam-289	76	11	=	=	SYM
ejpam-289	76	12	d.	d.	PROPN
ejpam-289	76	13	thus	thus	ADV
ejpam-289	76	14	c	c	VERB
ejpam-289	76	15	⊆	⊆	NUM
ejpam-289	76	16	g	g	PROPN
ejpam-289	76	17	⊆	⊆	NUM
ejpam-289	76	18	x	x	SYM
ejpam-289	76	19	�	�	NOUN
ejpam-289	76	20	u	u	NOUN
ejpam-289	76	21	⊆	⊆	NUM
ejpam-289	76	22	d	d	NOUN
ejpam-289	76	23	and	and	CCONJ
ejpam-289	76	24	the	the	DET
ejpam-289	76	25	a.	a.	NOUN
ejpam-289	76	26	kılıçman	kılıçman	NOUN
ejpam-289	76	27	and	and	CCONJ
ejpam-289	76	28	z.	z.	PROPN
ejpam-289	76	29	salleh	salleh	PROPN
ejpam-289	76	30	/	/	PUNCT
ejpam-289	76	31	eur	eur	PROPN
ejpam-289	76	32	.	.	PUNCT
ejpam-289	77	1	j.	j.	PROPN
ejpam-289	77	2	pure	pure	PROPN
ejpam-289	77	3	appl	appl	PROPN
ejpam-289	77	4	.	.	PROPN
ejpam-289	77	5	math	math	PROPN
ejpam-289	77	6	,	,	PUNCT
ejpam-289	77	7	2	2	NUM
ejpam-289	77	8	(	(	PUNCT
ejpam-289	77	9	2009	2009	NUM
ejpam-289	77	10	)	)	PUNCT
ejpam-289	77	11	,	,	PUNCT
ejpam-289	77	12	(	(	PUNCT
ejpam-289	77	13	325	325	NUM
ejpam-289	77	14	-	-	SYM
ejpam-289	77	15	337	337	NUM
ejpam-289	77	16	)	)	PUNCT
ejpam-289	77	17	330	330	NUM
ejpam-289	77	18	result	result	NOUN
ejpam-289	77	19	follows	follow	VERB
ejpam-289	77	20	by	by	ADP
ejpam-289	77	21	taking	take	VERB
ejpam-289	77	22	x	x	X
ejpam-289	77	23	�	�	NOUN
ejpam-289	77	24	u	u	NOUN
ejpam-289	77	25	=	=	PROPN
ejpam-289	77	26	f	f	PROPN
ejpam-289	77	27	.	.	PUNCT
ejpam-289	78	1	(	(	PUNCT
ejpam-289	78	2	⇐	⇐	NOUN
ejpam-289	78	3	)	)	PUNCT
ejpam-289	78	4	:	:	PUNCT
ejpam-289	78	5	suppose	suppose	VERB
ejpam-289	78	6	the	the	DET
ejpam-289	78	7	condition	condition	NOUN
ejpam-289	78	8	holds	hold	VERB
ejpam-289	78	9	.	.	PUNCT
ejpam-289	79	1	let	let	VERB
ejpam-289	79	2	a	a	PRON
ejpam-289	79	3	and	and	CCONJ
ejpam-289	79	4	b	b	NOUN
ejpam-289	79	5	are	be	AUX
ejpam-289	79	6	p1	p1	NOUN
ejpam-289	79	7	-	-	PUNCT
ejpam-289	79	8	closed	close	VERB
ejpam-289	79	9	sets	set	NOUN
ejpam-289	79	10	with	with	ADP
ejpam-289	79	11	a∩	a∩	PROPN
ejpam-289	79	12	b	b	PROPN
ejpam-289	79	13	=	=	PUNCT
ejpam-289	79	14	;	;	PUNCT
ejpam-289	79	15	.	.	PUNCT
ejpam-289	80	1	then	then	ADV
ejpam-289	80	2	d	d	X
ejpam-289	80	3	=	=	SYM
ejpam-289	80	4	x	x	SYM
ejpam-289	80	5	�	�	PROPN
ejpam-289	80	6	a	a	PRON
ejpam-289	80	7	is	be	AUX
ejpam-289	80	8	a	a	DET
ejpam-289	80	9	p1	p1	NOUN
ejpam-289	80	10	-	-	PUNCT
ejpam-289	80	11	open	open	NOUN
ejpam-289	80	12	set	set	NOUN
ejpam-289	80	13	with	with	ADP
ejpam-289	80	14	b	b	PROPN
ejpam-289	80	15	⊆	⊆	NUM
ejpam-289	80	16	d.	d.	NOUN
ejpam-289	80	17	by	by	ADP
ejpam-289	80	18	hypothesis	hypothesis	NOUN
ejpam-289	80	19	,	,	PUNCT
ejpam-289	80	20	there	there	PRON
ejpam-289	80	21	are	be	VERB
ejpam-289	80	22	a	a	DET
ejpam-289	80	23	p1	p1	NOUN
ejpam-289	80	24	-	-	PUNCT
ejpam-289	80	25	open	open	NOUN
ejpam-289	80	26	set	set	NOUN
ejpam-289	80	27	g	g	NOUN
ejpam-289	80	28	and	and	CCONJ
ejpam-289	80	29	a	a	DET
ejpam-289	80	30	p1	p1	NOUN
ejpam-289	80	31	-	-	PUNCT
ejpam-289	80	32	closed	close	VERB
ejpam-289	80	33	set	set	NOUN
ejpam-289	80	34	f	f	PROPN
ejpam-289	81	1	such	such	ADJ
ejpam-289	81	2	that	that	PRON
ejpam-289	81	3	b	b	NOUN
ejpam-289	81	4	⊆	⊆	NUM
ejpam-289	81	5	g	g	NOUN
ejpam-289	81	6	⊆	⊆	NUM
ejpam-289	81	7	f	f	SYM
ejpam-289	81	8	⊆	⊆	NUM
ejpam-289	81	9	d.	d.	PROPN
ejpam-289	81	10	it	it	PRON
ejpam-289	81	11	follows	follow	VERB
ejpam-289	81	12	that	that	SCONJ
ejpam-289	81	13	a=	a=	PROPN
ejpam-289	81	14	x	x	X
ejpam-289	81	15	�	�	X
ejpam-289	81	16	d	d	SYM
ejpam-289	81	17	⊆	⊆	NUM
ejpam-289	81	18	x	x	SYM
ejpam-289	81	19	�	�	PROPN
ejpam-289	81	20	f	f	PROPN
ejpam-289	81	21	,	,	PUNCT
ejpam-289	81	22	b	b	PROPN
ejpam-289	81	23	⊆	⊆	NUM
ejpam-289	81	24	g	g	NOUN
ejpam-289	81	25	and	and	CCONJ
ejpam-289	81	26	(	(	PUNCT
ejpam-289	81	27	x	x	X
ejpam-289	81	28	�	�	NOUN
ejpam-289	81	29	f	f	NOUN
ejpam-289	81	30	)	)	PUNCT
ejpam-289	81	31	∩	∩	PROPN
ejpam-289	81	32	g	g	PROPN
ejpam-289	81	33	=	=	X
ejpam-289	81	34	;	;	PUNCT
ejpam-289	81	35	where	where	SCONJ
ejpam-289	81	36	x	x	X
ejpam-289	81	37	�	�	PROPN
ejpam-289	81	38	f	f	PROPN
ejpam-289	81	39	and	and	CCONJ
ejpam-289	81	40	g	g	PROPN
ejpam-289	81	41	are	be	AUX
ejpam-289	81	42	p1	p1	ADJ
ejpam-289	81	43	-	-	PUNCT
ejpam-289	81	44	open	open	ADJ
ejpam-289	81	45	sets	set	NOUN
ejpam-289	81	46	.	.	PUNCT
ejpam-289	82	1	this	this	PRON
ejpam-289	82	2	completes	complete	VERB
ejpam-289	82	3	the	the	DET
ejpam-289	82	4	proof	proof	NOUN
ejpam-289	82	5	.	.	PUNCT
ejpam-289	83	1	example	example	NOUN
ejpam-289	83	2	3.1	3.1	NUM
ejpam-289	83	3	.	.	PUNCT
ejpam-289	84	1	consider	consider	VERB
ejpam-289	84	2	x	x	PUNCT
ejpam-289	84	3	=	=	PRON
ejpam-289	84	4	{	{	PUNCT
ejpam-289	84	5	a	a	PRON
ejpam-289	84	6	,	,	PUNCT
ejpam-289	84	7	b	b	NOUN
ejpam-289	84	8	,	,	PUNCT
ejpam-289	84	9	c	c	NOUN
ejpam-289	84	10	}	}	PUNCT
ejpam-289	84	11	with	with	ADP
ejpam-289	84	12	topologies	topology	NOUN
ejpam-289	84	13	p	p	NOUN
ejpam-289	84	14	=	=	X
ejpam-289	84	15	{	{	PUNCT
ejpam-289	84	16	;	;	PUNCT
ejpam-289	84	17	,	,	PUNCT
ejpam-289	84	18	{	{	PUNCT
ejpam-289	84	19	a	a	NOUN
ejpam-289	84	20	}	}	PUNCT
ejpam-289	84	21	,	,	PUNCT
ejpam-289	84	22	{	{	PUNCT
ejpam-289	84	23	c	c	NOUN
ejpam-289	84	24	}	}	PUNCT
ejpam-289	84	25	,	,	PUNCT
ejpam-289	84	26	{	{	PUNCT
ejpam-289	84	27	a	a	X
ejpam-289	84	28	,	,	PUNCT
ejpam-289	84	29	c	c	NOUN
ejpam-289	84	30	}	}	PUNCT
ejpam-289	84	31	,	,	PUNCT
ejpam-289	84	32	x	x	X
ejpam-289	84	33	}	}	PUNCT
ejpam-289	84	34	and	and	CCONJ
ejpam-289	84	35	q	q	NOUN
ejpam-289	84	36	=	=	X
ejpam-289	84	37	{	{	PUNCT
ejpam-289	84	38	;	;	PUNCT
ejpam-289	84	39	,	,	PUNCT
ejpam-289	84	40	{	{	PUNCT
ejpam-289	84	41	a	a	NOUN
ejpam-289	84	42	}	}	PUNCT
ejpam-289	84	43	,	,	PUNCT
ejpam-289	84	44	{	{	PUNCT
ejpam-289	84	45	b	b	NOUN
ejpam-289	84	46	}	}	PUNCT
ejpam-289	84	47	,	,	PUNCT
ejpam-289	84	48	{	{	PUNCT
ejpam-289	84	49	a	a	DET
ejpam-289	84	50	,	,	PUNCT
ejpam-289	84	51	b	b	NOUN
ejpam-289	84	52	}	}	PUNCT
ejpam-289	84	53	,	,	PUNCT
ejpam-289	84	54	{	{	PUNCT
ejpam-289	84	55	b	b	X
ejpam-289	84	56	,	,	PUNCT
ejpam-289	84	57	c	c	NOUN
ejpam-289	84	58	}	}	PUNCT
ejpam-289	84	59	,	,	PUNCT
ejpam-289	84	60	x	x	X
ejpam-289	84	61	}	}	PUNCT
ejpam-289	84	62	defined	define	VERB
ejpam-289	84	63	on	on	ADP
ejpam-289	84	64	x	x	X
ejpam-289	84	65	.	.	PUNCT
ejpam-289	85	1	then	then	ADV
ejpam-289	85	2	p	p	X
ejpam-289	85	3	∪q	∪q	PROPN
ejpam-289	85	4	=	=	SYM
ejpam-289	85	5	{	{	PUNCT
ejpam-289	85	6	;	;	PUNCT
ejpam-289	85	7	,	,	PUNCT
ejpam-289	85	8	{	{	PUNCT
ejpam-289	85	9	a	a	NOUN
ejpam-289	85	10	}	}	PUNCT
ejpam-289	85	11	,	,	PUNCT
ejpam-289	85	12	{	{	PUNCT
ejpam-289	85	13	b	b	NOUN
ejpam-289	85	14	}	}	PUNCT
ejpam-289	85	15	,	,	PUNCT
ejpam-289	85	16	{	{	PUNCT
ejpam-289	85	17	c	c	NOUN
ejpam-289	85	18	}	}	PUNCT
ejpam-289	85	19	,	,	PUNCT
ejpam-289	85	20	{	{	PUNCT
ejpam-289	85	21	a	a	DET
ejpam-289	85	22	,	,	PUNCT
ejpam-289	85	23	b	b	NOUN
ejpam-289	85	24	}	}	PUNCT
ejpam-289	85	25	,	,	PUNCT
ejpam-289	85	26	{	{	PUNCT
ejpam-289	85	27	a	a	X
ejpam-289	85	28	,	,	PUNCT
ejpam-289	85	29	c	c	NOUN
ejpam-289	85	30	}	}	PUNCT
ejpam-289	85	31	,	,	PUNCT
ejpam-289	85	32	{	{	PUNCT
ejpam-289	85	33	b	b	X
ejpam-289	85	34	,	,	PUNCT
ejpam-289	85	35	c	c	NOUN
ejpam-289	85	36	}	}	PUNCT
ejpam-289	85	37	,	,	PUNCT
ejpam-289	85	38	x	x	X
ejpam-289	85	39	}	}	PUNCT
ejpam-289	85	40	.	.	PUNCT
ejpam-289	86	1	observe	observe	VERB
ejpam-289	86	2	that	that	SCONJ
ejpam-289	86	3	p	p	NOUN
ejpam-289	86	4	∪q	∪q	NUM
ejpam-289	86	5	is	be	AUX
ejpam-289	86	6	a	a	DET
ejpam-289	86	7	discrete	discrete	ADJ
ejpam-289	86	8	topology	topology	NOUN
ejpam-289	86	9	and	and	CCONJ
ejpam-289	86	10	p1	p1	NOUN
ejpam-289	86	11	-	-	PUNCT
ejpam-289	86	12	closed	closed	ADJ
ejpam-289	86	13	subsets	subset	NOUN
ejpam-289	86	14	of	of	ADP
ejpam-289	86	15	x	x	X
ejpam-289	86	16	are	be	AUX
ejpam-289	86	17	;	;	PUNCT
ejpam-289	86	18	,	,	PUNCT
ejpam-289	86	19	{	{	PUNCT
ejpam-289	86	20	a	a	NOUN
ejpam-289	86	21	}	}	PUNCT
ejpam-289	86	22	,	,	PUNCT
ejpam-289	86	23	{	{	PUNCT
ejpam-289	86	24	b	b	NOUN
ejpam-289	86	25	}	}	PUNCT
ejpam-289	86	26	,	,	PUNCT
ejpam-289	86	27	{	{	PUNCT
ejpam-289	86	28	c	c	NOUN
ejpam-289	86	29	}	}	PUNCT
ejpam-289	86	30	,	,	PUNCT
ejpam-289	86	31	{	{	PUNCT
ejpam-289	86	32	a	a	DET
ejpam-289	86	33	,	,	PUNCT
ejpam-289	86	34	b	b	NOUN
ejpam-289	86	35	}	}	PUNCT
ejpam-289	86	36	,	,	PUNCT
ejpam-289	86	37	{	{	PUNCT
ejpam-289	86	38	a	a	X
ejpam-289	86	39	,	,	PUNCT
ejpam-289	86	40	c	c	NOUN
ejpam-289	86	41	}	}	PUNCT
ejpam-289	86	42	,	,	PUNCT
ejpam-289	86	43	{	{	PUNCT
ejpam-289	86	44	b	b	X
ejpam-289	86	45	,	,	PUNCT
ejpam-289	86	46	c	c	NOUN
ejpam-289	86	47	}	}	PUNCT
ejpam-289	86	48	and	and	CCONJ
ejpam-289	86	49	x	x	X
ejpam-289	86	50	.	.	PUNCT
ejpam-289	87	1	it	it	PRON
ejpam-289	87	2	follows	follow	VERB
ejpam-289	87	3	that	that	SCONJ
ejpam-289	87	4	(	(	PUNCT
ejpam-289	87	5	x	x	X
ejpam-289	87	6	,	,	PUNCT
ejpam-289	87	7	p	p	X
ejpam-289	87	8	,	,	PUNCT
ejpam-289	87	9	q	q	X
ejpam-289	87	10	)	)	PUNCT
ejpam-289	87	11	does	do	AUX
ejpam-289	87	12	satisfy	satisfy	VERB
ejpam-289	87	13	the	the	DET
ejpam-289	87	14	condition	condition	NOUN
ejpam-289	87	15	in	in	ADP
ejpam-289	87	16	definition	definition	NOUN
ejpam-289	87	17	of	of	ADP
ejpam-289	87	18	p1	p1	NOUN
ejpam-289	87	19	-	-	PUNCT
ejpam-289	87	20	regular	regular	ADJ
ejpam-289	87	21	and	and	CCONJ
ejpam-289	87	22	p2	p2	NOUN
ejpam-289	87	23	-	-	PUNCT
ejpam-289	87	24	normal	normal	ADJ
ejpam-289	87	25	.	.	PUNCT
ejpam-289	88	1	hence	hence	ADV
ejpam-289	88	2	(	(	PUNCT
ejpam-289	88	3	x	x	INTJ
ejpam-289	88	4	,	,	PUNCT
ejpam-289	88	5	p	p	X
ejpam-289	88	6	,	,	PUNCT
ejpam-289	88	7	q	q	NOUN
ejpam-289	88	8	)	)	PUNCT
ejpam-289	88	9	is	be	AUX
ejpam-289	88	10	p1	p1	NOUN
ejpam-289	88	11	-	-	ADJ
ejpam-289	88	12	regular	regular	ADJ
ejpam-289	88	13	and	and	CCONJ
ejpam-289	88	14	p2	p2	NOUN
ejpam-289	88	15	-	-	PUNCT
ejpam-289	88	16	normal	normal	ADJ
ejpam-289	88	17	space	space	NOUN
ejpam-289	88	18	.	.	PUNCT
ejpam-289	89	1	example	example	NOUN
ejpam-289	89	2	3.2	3.2	NUM
ejpam-289	89	3	.	.	PUNCT
ejpam-289	90	1	consider	consider	VERB
ejpam-289	90	2	x	x	PUNCT
ejpam-289	90	3	=	=	PRON
ejpam-289	90	4	{	{	PUNCT
ejpam-289	90	5	a	a	PRON
ejpam-289	90	6	,	,	PUNCT
ejpam-289	90	7	b	b	NOUN
ejpam-289	90	8	,	,	PUNCT
ejpam-289	90	9	c	c	NOUN
ejpam-289	90	10	,	,	PUNCT
ejpam-289	90	11	d	d	NOUN
ejpam-289	90	12	}	}	PUNCT
ejpam-289	90	13	with	with	ADP
ejpam-289	90	14	topologies	topology	NOUN
ejpam-289	90	15	p	p	NOUN
ejpam-289	90	16	=	=	X
ejpam-289	90	17	{	{	PUNCT
ejpam-289	90	18	;	;	PUNCT
ejpam-289	90	19	,	,	PUNCT
ejpam-289	90	20	{	{	PUNCT
ejpam-289	90	21	a	a	DET
ejpam-289	90	22	,	,	PUNCT
ejpam-289	90	23	b	b	NOUN
ejpam-289	90	24	}	}	PUNCT
ejpam-289	90	25	,	,	PUNCT
ejpam-289	90	26	x	x	NOUN
ejpam-289	90	27	}	}	PUNCT
ejpam-289	90	28	and	and	CCONJ
ejpam-289	90	29	q	q	NOUN
ejpam-289	90	30	=	=	X
ejpam-289	90	31	{	{	PUNCT
ejpam-289	90	32	;	;	PUNCT
ejpam-289	90	33	,	,	PUNCT
ejpam-289	90	34	{	{	PUNCT
ejpam-289	90	35	a	a	NOUN
ejpam-289	90	36	}	}	PUNCT
ejpam-289	90	37	,	,	PUNCT
ejpam-289	90	38	{	{	PUNCT
ejpam-289	90	39	b	b	X
ejpam-289	90	40	,	,	PUNCT
ejpam-289	90	41	c	c	NOUN
ejpam-289	90	42	,	,	PUNCT
ejpam-289	90	43	d	d	NOUN
ejpam-289	90	44	}	}	PUNCT
ejpam-289	90	45	,	,	PUNCT
ejpam-289	90	46	x	x	X
ejpam-289	90	47	}	}	PUNCT
ejpam-289	90	48	defined	define	VERB
ejpam-289	90	49	on	on	ADP
ejpam-289	90	50	x	x	X
ejpam-289	90	51	.	.	PUNCT
ejpam-289	91	1	then	then	ADV
ejpam-289	91	2	p	p	X
ejpam-289	91	3	∪q	∪q	PROPN
ejpam-289	91	4	=	=	SYM
ejpam-289	91	5	{	{	PUNCT
ejpam-289	91	6	;	;	PUNCT
ejpam-289	91	7	,	,	PUNCT
ejpam-289	91	8	{	{	PUNCT
ejpam-289	91	9	a	a	NOUN
ejpam-289	91	10	}	}	PUNCT
ejpam-289	91	11	,	,	PUNCT
ejpam-289	91	12	{	{	PUNCT
ejpam-289	91	13	a	a	DET
ejpam-289	91	14	,	,	PUNCT
ejpam-289	91	15	b	b	NOUN
ejpam-289	91	16	}	}	PUNCT
ejpam-289	91	17	,	,	PUNCT
ejpam-289	91	18	{	{	PUNCT
ejpam-289	91	19	b	b	X
ejpam-289	91	20	,	,	PUNCT
ejpam-289	91	21	c	c	NOUN
ejpam-289	91	22	,	,	PUNCT
ejpam-289	91	23	d	d	NOUN
ejpam-289	91	24	}	}	PUNCT
ejpam-289	91	25	,	,	PUNCT
ejpam-289	91	26	x	x	X
ejpam-289	91	27	}	}	PUNCT
ejpam-289	91	28	.	.	PUNCT
ejpam-289	92	1	observe	observe	VERB
ejpam-289	92	2	that	that	SCONJ
ejpam-289	92	3	p1	p1	NOUN
ejpam-289	92	4	-	-	PUNCT
ejpam-289	92	5	closed	closed	ADJ
ejpam-289	92	6	subsets	subset	NOUN
ejpam-289	92	7	of	of	ADP
ejpam-289	92	8	x	x	X
ejpam-289	92	9	are	be	AUX
ejpam-289	92	10	;	;	PUNCT
ejpam-289	92	11	,	,	PUNCT
ejpam-289	92	12	{	{	PUNCT
ejpam-289	92	13	a	a	NOUN
ejpam-289	92	14	}	}	PUNCT
ejpam-289	92	15	,	,	PUNCT
ejpam-289	92	16	{	{	PUNCT
ejpam-289	92	17	b	b	X
ejpam-289	92	18	,	,	PUNCT
ejpam-289	92	19	c	c	NOUN
ejpam-289	92	20	,	,	PUNCT
ejpam-289	92	21	d	d	NOUN
ejpam-289	92	22	}	}	PUNCT
ejpam-289	92	23	,	,	PUNCT
ejpam-289	92	24	{	{	PUNCT
ejpam-289	92	25	c	c	X
ejpam-289	92	26	,	,	PUNCT
ejpam-289	92	27	d	d	NOUN
ejpam-289	92	28	}	}	PUNCT
ejpam-289	92	29	and	and	CCONJ
ejpam-289	92	30	x	x	X
ejpam-289	92	31	.	.	PUNCT
ejpam-289	93	1	hence	hence	ADV
ejpam-289	93	2	(	(	PUNCT
ejpam-289	93	3	x	x	INTJ
ejpam-289	93	4	,	,	PUNCT
ejpam-289	93	5	p	p	X
ejpam-289	93	6	,	,	PUNCT
ejpam-289	93	7	q	q	NOUN
ejpam-289	93	8	)	)	PUNCT
ejpam-289	93	9	is	be	AUX
ejpam-289	93	10	p2	p2	NOUN
ejpam-289	93	11	-	-	PUNCT
ejpam-289	93	12	normal	normal	ADJ
ejpam-289	93	13	as	as	SCONJ
ejpam-289	93	14	we	we	PRON
ejpam-289	93	15	can	can	AUX
ejpam-289	93	16	checks	check	VERB
ejpam-289	93	17	.	.	PUNCT
ejpam-289	94	1	however	however	ADV
ejpam-289	94	2	(	(	PUNCT
ejpam-289	94	3	x	x	INTJ
ejpam-289	94	4	,	,	PUNCT
ejpam-289	94	5	p	p	X
ejpam-289	94	6	,	,	PUNCT
ejpam-289	94	7	q	q	NOUN
ejpam-289	94	8	)	)	PUNCT
ejpam-289	94	9	is	be	AUX
ejpam-289	94	10	not	not	PART
ejpam-289	94	11	p1	p1	NOUN
ejpam-289	94	12	-	-	NOUN
ejpam-289	94	13	regular	regular	ADJ
ejpam-289	94	14	since	since	SCONJ
ejpam-289	94	15	the	the	DET
ejpam-289	94	16	p1	p1	NOUN
ejpam-289	94	17	-	-	PUNCT
ejpam-289	94	18	closed	close	VERB
ejpam-289	94	19	set	set	NOUN
ejpam-289	94	20	p	p	NOUN
ejpam-289	94	21	=	=	X
ejpam-289	94	22	{	{	PUNCT
ejpam-289	94	23	c	c	NOUN
ejpam-289	94	24	,	,	PUNCT
ejpam-289	94	25	d	d	NOUN
ejpam-289	94	26	}	}	PUNCT
ejpam-289	94	27	satisfy	satisfy	NOUN
ejpam-289	94	28	b	b	PROPN
ejpam-289	94	29	/∈	/∈	PUNCT
ejpam-289	95	1	p	p	X
ejpam-289	95	2	,	,	PUNCT
ejpam-289	95	3	but	but	CCONJ
ejpam-289	95	4	do	do	AUX
ejpam-289	95	5	not	not	PART
ejpam-289	95	6	exist	exist	VERB
ejpam-289	95	7	the	the	DET
ejpam-289	95	8	p1	p1	NOUN
ejpam-289	95	9	-	-	PUNCT
ejpam-289	95	10	open	open	ADJ
ejpam-289	95	11	sets	set	VERB
ejpam-289	95	12	u	u	NOUN
ejpam-289	95	13	and	and	CCONJ
ejpam-289	95	14	v	v	ADP
ejpam-289	95	15	such	such	ADJ
ejpam-289	95	16	that	that	PRON
ejpam-289	95	17	b	b	PROPN
ejpam-289	95	18	∈	∈	PROPN
ejpam-289	95	19	u	u	NOUN
ejpam-289	95	20	,	,	PUNCT
ejpam-289	95	21	p	p	ADJ
ejpam-289	95	22	⊆	⊆	NUM
ejpam-289	95	23	v	v	NOUN
ejpam-289	95	24	and	and	CCONJ
ejpam-289	95	25	u	u	NOUN
ejpam-289	95	26	∩	∩	NOUN
ejpam-289	95	27	v	v	NOUN
ejpam-289	95	28	=	=	PUNCT
ejpam-289	95	29	;	;	PUNCT
ejpam-289	95	30	.	.	PUNCT
ejpam-289	96	1	note	note	VERB
ejpam-289	96	2	that	that	SCONJ
ejpam-289	96	3	p	p	NOUN
ejpam-289	96	4	∪q	∪q	NUM
ejpam-289	96	5	is	be	AUX
ejpam-289	96	6	not	not	PART
ejpam-289	96	7	a	a	DET
ejpam-289	96	8	topology	topology	NOUN
ejpam-289	96	9	of	of	ADP
ejpam-289	96	10	x	x	PUNCT
ejpam-289	96	11	since	since	SCONJ
ejpam-289	96	12	{	{	PUNCT
ejpam-289	96	13	a	a	DET
ejpam-289	96	14	,	,	PUNCT
ejpam-289	96	15	b	b	NOUN
ejpam-289	96	16	}	}	PUNCT
ejpam-289	96	17	,	,	PUNCT
ejpam-289	96	18	{	{	PUNCT
ejpam-289	96	19	b	b	X
ejpam-289	96	20	,	,	PUNCT
ejpam-289	96	21	c	c	NOUN
ejpam-289	96	22	,	,	PUNCT
ejpam-289	96	23	d	d	NOUN
ejpam-289	96	24	}	}	PUNCT
ejpam-289	96	25	∈	∈	PROPN
ejpam-289	96	26	p	p	NOUN
ejpam-289	96	27	∪q	∪q	PROPN
ejpam-289	96	28	,	,	PUNCT
ejpam-289	96	29	but	but	CCONJ
ejpam-289	96	30	{	{	PUNCT
ejpam-289	96	31	a	a	PRON
ejpam-289	96	32	,	,	PUNCT
ejpam-289	96	33	b	b	NOUN
ejpam-289	96	34	}	}	PUNCT
ejpam-289	96	35	∩	∩	ADJ
ejpam-289	96	36	{	{	PUNCT
ejpam-289	96	37	b	b	NOUN
ejpam-289	96	38	,	,	PUNCT
ejpam-289	96	39	c	c	NOUN
ejpam-289	96	40	,	,	PUNCT
ejpam-289	96	41	d	d	NOUN
ejpam-289	96	42	}	}	PUNCT
ejpam-289	96	43	=	=	SYM
ejpam-289	96	44	{	{	PUNCT
ejpam-289	96	45	b	b	NOUN
ejpam-289	96	46	}	}	PUNCT
ejpam-289	96	47	/∈	/∈	PUNCT
ejpam-289	97	1	p	p	NOUN
ejpam-289	97	2	∪q	∪q	NUM
ejpam-289	97	3	.	.	PUNCT
ejpam-289	97	4	a.	a.	PROPN
ejpam-289	97	5	kılıçman	kılıçman	PROPN
ejpam-289	97	6	and	and	CCONJ
ejpam-289	97	7	z.	z.	PROPN
ejpam-289	97	8	salleh	salleh	PROPN
ejpam-289	97	9	/	/	PUNCT
ejpam-289	97	10	eur	eur	PROPN
ejpam-289	97	11	.	.	PUNCT
ejpam-289	98	1	j.	j.	PROPN
ejpam-289	98	2	pure	pure	PROPN
ejpam-289	98	3	appl	appl	PROPN
ejpam-289	98	4	.	.	PROPN
ejpam-289	98	5	math	math	PROPN
ejpam-289	98	6	,	,	PUNCT
ejpam-289	98	7	2	2	NUM
ejpam-289	98	8	(	(	PUNCT
ejpam-289	98	9	2009	2009	NUM
ejpam-289	98	10	)	)	PUNCT
ejpam-289	98	11	,	,	PUNCT
ejpam-289	98	12	(	(	PUNCT
ejpam-289	98	13	325	325	NUM
ejpam-289	98	14	-	-	SYM
ejpam-289	98	15	337	337	NUM
ejpam-289	98	16	)	)	PUNCT
ejpam-289	98	17	331	331	NUM
ejpam-289	98	18	4	4	NUM
ejpam-289	98	19	.	.	PUNCT
ejpam-289	99	1	on	on	ADP
ejpam-289	99	2	p2	p2	ADJ
ejpam-289	99	3	-	-	PUNCT
ejpam-289	99	4	lindelöf	lindelöf	NOUN
ejpam-289	99	5	spaces	space	NOUN
ejpam-289	99	6	in	in	ADP
ejpam-289	99	7	this	this	DET
ejpam-289	99	8	section	section	NOUN
ejpam-289	99	9	,	,	PUNCT
ejpam-289	99	10	we	we	PRON
ejpam-289	99	11	shall	shall	AUX
ejpam-289	99	12	introduce	introduce	VERB
ejpam-289	99	13	a	a	DET
ejpam-289	99	14	new	new	ADJ
ejpam-289	99	15	concept	concept	NOUN
ejpam-289	99	16	of	of	ADP
ejpam-289	99	17	pairwise	pairwise	NOUN
ejpam-289	99	18	compact	compact	ADJ
ejpam-289	99	19	spaces	space	NOUN
ejpam-289	99	20	and	and	CCONJ
ejpam-289	99	21	pairwise	pairwise	NOUN
ejpam-289	99	22	lindelöf	lindelöf	NOUN
ejpam-289	99	23	spaces	space	NOUN
ejpam-289	99	24	as	as	ADP
ejpam-289	99	25	the	the	DET
ejpam-289	99	26	following	following	NOUN
ejpam-289	99	27	.	.	PUNCT
ejpam-289	100	1	definition	definition	NOUN
ejpam-289	100	2	4.1	4.1	NUM
ejpam-289	100	3	.	.	PUNCT
ejpam-289	101	1	a	a	DET
ejpam-289	101	2	bitopological	bitopological	ADJ
ejpam-289	101	3	space	space	NOUN
ejpam-289	101	4	(	(	PUNCT
ejpam-289	101	5	x	x	X
ejpam-289	101	6	,	,	PUNCT
ejpam-289	101	7	p	p	X
ejpam-289	101	8	,	,	PUNCT
ejpam-289	101	9	q	q	NOUN
ejpam-289	101	10	)	)	PUNCT
ejpam-289	101	11	is	be	AUX
ejpam-289	101	12	said	say	VERB
ejpam-289	101	13	to	to	PART
ejpam-289	101	14	be	be	AUX
ejpam-289	101	15	p2	p2	NOUN
ejpam-289	101	16	-	-	ADJ
ejpam-289	101	17	compact	compact	ADJ
ejpam-289	101	18	if	if	SCONJ
ejpam-289	101	19	every	every	DET
ejpam-289	101	20	p1	p1	NOUN
ejpam-289	101	21	-	-	PUNCT
ejpam-289	101	22	open	open	ADJ
ejpam-289	101	23	cover	cover	NOUN
ejpam-289	101	24	of	of	ADP
ejpam-289	101	25	x	x	PUNCT
ejpam-289	101	26	has	have	VERB
ejpam-289	101	27	a	a	DET
ejpam-289	101	28	finite	finite	ADJ
ejpam-289	101	29	subcover	subcover	PROPN
ejpam-289	101	30	.	.	PUNCT
ejpam-289	102	1	definition	definition	NOUN
ejpam-289	102	2	4.2	4.2	NUM
ejpam-289	102	3	.	.	PUNCT
ejpam-289	103	1	a	a	DET
ejpam-289	103	2	bitopological	bitopological	ADJ
ejpam-289	103	3	space	space	NOUN
ejpam-289	103	4	(	(	PUNCT
ejpam-289	103	5	x	x	X
ejpam-289	103	6	,	,	PUNCT
ejpam-289	103	7	p	p	X
ejpam-289	103	8	,	,	PUNCT
ejpam-289	103	9	q	q	NOUN
ejpam-289	103	10	)	)	PUNCT
ejpam-289	103	11	is	be	AUX
ejpam-289	103	12	said	say	VERB
ejpam-289	103	13	to	to	PART
ejpam-289	103	14	be	be	AUX
ejpam-289	103	15	p2	p2	NOUN
ejpam-289	103	16	-	-	PUNCT
ejpam-289	103	17	lindelöf	lindelöf	NOUN
ejpam-289	103	18	if	if	SCONJ
ejpam-289	103	19	every	every	DET
ejpam-289	103	20	p1	p1	NOUN
ejpam-289	103	21	-	-	PUNCT
ejpam-289	103	22	open	open	ADJ
ejpam-289	103	23	cover	cover	NOUN
ejpam-289	103	24	of	of	ADP
ejpam-289	103	25	x	x	PUNCT
ejpam-289	103	26	has	have	VERB
ejpam-289	103	27	a	a	DET
ejpam-289	103	28	countable	countable	ADJ
ejpam-289	103	29	subcover	subcover	NOUN
ejpam-289	103	30	.	.	PUNCT
ejpam-289	104	1	it	it	PRON
ejpam-289	104	2	is	be	AUX
ejpam-289	104	3	very	very	ADV
ejpam-289	104	4	clear	clear	ADJ
ejpam-289	104	5	that	that	SCONJ
ejpam-289	104	6	,	,	PUNCT
ejpam-289	104	7	every	every	DET
ejpam-289	104	8	p2	p2	ADJ
ejpam-289	104	9	-	-	PUNCT
ejpam-289	104	10	compact	compact	ADJ
ejpam-289	104	11	space	space	NOUN
ejpam-289	104	12	is	be	AUX
ejpam-289	104	13	p2	p2	NOUN
ejpam-289	104	14	-	-	PUNCT
ejpam-289	104	15	lindelöf	lindelöf	NOUN
ejpam-289	104	16	but	but	CCONJ
ejpam-289	104	17	not	not	PART
ejpam-289	104	18	the	the	DET
ejpam-289	104	19	converse	converse	NOUN
ejpam-289	104	20	by	by	ADP
ejpam-289	104	21	the	the	DET
ejpam-289	104	22	following	follow	VERB
ejpam-289	104	23	counter	counter	NOUN
ejpam-289	104	24	-	-	NOUN
ejpam-289	104	25	example	example	NOUN
ejpam-289	104	26	.	.	PUNCT
ejpam-289	105	1	example	example	NOUN
ejpam-289	105	2	4.1	4.1	NUM
ejpam-289	105	3	.	.	PUNCT
ejpam-289	106	1	letb	letb	PROPN
ejpam-289	106	2	be	be	AUX
ejpam-289	106	3	the	the	DET
ejpam-289	106	4	collection	collection	NOUN
ejpam-289	106	5	of	of	ADP
ejpam-289	106	6	open	open	ADJ
ejpam-289	106	7	-	-	PUNCT
ejpam-289	106	8	closed	close	VERB
ejpam-289	106	9	intervals	interval	NOUN
ejpam-289	106	10	in	in	ADP
ejpam-289	106	11	the	the	DET
ejpam-289	106	12	real	real	ADJ
ejpam-289	106	13	line	line	NOUN
ejpam-289	106	14	r	r	NOUN
ejpam-289	106	15	b	b	NOUN
ejpam-289	106	16	=	=	PRON
ejpam-289	106	17	{	{	PUNCT
ejpam-289	106	18	(	(	PUNCT
ejpam-289	106	19	a	a	PROPN
ejpam-289	106	20	,	,	PUNCT
ejpam-289	106	21	b	b	NOUN
ejpam-289	106	22	]	]	X
ejpam-289	106	23	:	:	PUNCT
ejpam-289	106	24	a	a	DET
ejpam-289	106	25	,	,	PUNCT
ejpam-289	106	26	b	b	X
ejpam-289	106	27	∈	∈	PROPN
ejpam-289	106	28	r	r	NOUN
ejpam-289	106	29	,	,	PUNCT
ejpam-289	106	30	a	a	DET
ejpam-289	106	31	<	<	X
ejpam-289	106	32	b	b	NOUN
ejpam-289	106	33	}	}	PUNCT
ejpam-289	106	34	.	.	PUNCT
ejpam-289	107	1	hence	hence	ADV
ejpam-289	107	2	b	b	X
ejpam-289	107	3	is	be	AUX
ejpam-289	107	4	a	a	DET
ejpam-289	107	5	base	base	NOUN
ejpam-289	107	6	for	for	ADP
ejpam-289	107	7	the	the	DET
ejpam-289	107	8	upper	upper	ADJ
ejpam-289	107	9	limit	limit	NOUN
ejpam-289	107	10	topology	topology	NOUN
ejpam-289	107	11	p	p	NOUN
ejpam-289	107	12	on	on	ADP
ejpam-289	107	13	r.	r.	PROPN
ejpam-289	107	14	similarly	similarly	ADV
ejpam-289	107	15	,	,	PUNCT
ejpam-289	107	16	the	the	DET
ejpam-289	107	17	collection	collection	NOUN
ejpam-289	107	18	of	of	ADP
ejpam-289	107	19	closed	closed	ADJ
ejpam-289	107	20	-	-	PUNCT
ejpam-289	107	21	open	open	ADJ
ejpam-289	107	22	intervals	interval	NOUN
ejpam-289	107	23	,	,	PUNCT
ejpam-289	107	24	b∗	b∗	ADJ
ejpam-289	107	25	=	=	PUNCT
ejpam-289	107	26	{	{	PUNCT
ejpam-289	108	1	[	[	X
ejpam-289	108	2	c	c	X
ejpam-289	108	3	,	,	PUNCT
ejpam-289	108	4	d	d	NOUN
ejpam-289	108	5	)	)	PUNCT
ejpam-289	108	6	:	:	PUNCT
ejpam-289	108	7	c	c	X
ejpam-289	108	8	,	,	PUNCT
ejpam-289	108	9	d	d	PROPN
ejpam-289	108	10	∈	∈	PROPN
ejpam-289	108	11	r	r	NOUN
ejpam-289	108	12	,	,	PUNCT
ejpam-289	108	13	c	c	NOUN
ejpam-289	108	14	<	<	X
ejpam-289	108	15	d	d	X
ejpam-289	108	16	}	}	PUNCT
ejpam-289	108	17	is	be	AUX
ejpam-289	108	18	a	a	DET
ejpam-289	108	19	base	base	NOUN
ejpam-289	108	20	for	for	ADP
ejpam-289	108	21	the	the	DET
ejpam-289	108	22	lower	low	ADJ
ejpam-289	108	23	limit	limit	NOUN
ejpam-289	108	24	topologyq	topologyq	NOUN
ejpam-289	108	25	on	on	ADP
ejpam-289	108	26	r.	r.	PROPN
ejpam-289	108	27	observe	observe	VERB
ejpam-289	108	28	thatb	thatb	PROPN
ejpam-289	108	29	∪b∗	∪b∗	NUM
ejpam-289	108	30	is	be	AUX
ejpam-289	108	31	the	the	DET
ejpam-289	108	32	set	set	NOUN
ejpam-289	108	33	of	of	ADP
ejpam-289	108	34	the	the	DET
ejpam-289	108	35	form	form	NOUN
ejpam-289	108	36	(	(	PUNCT
ejpam-289	108	37	a	a	DET
ejpam-289	108	38	,	,	PUNCT
ejpam-289	108	39	b	b	NOUN
ejpam-289	108	40	]	]	PUNCT
ejpam-289	108	41	,	,	PUNCT
ejpam-289	108	42	[	[	X
ejpam-289	108	43	a	a	DET
ejpam-289	108	44	,	,	PUNCT
ejpam-289	108	45	b	b	NOUN
ejpam-289	108	46	)	)	PUNCT
ejpam-289	108	47	,	,	PUNCT
ejpam-289	108	48	(	(	PUNCT
ejpam-289	108	49	a	a	DET
ejpam-289	108	50	,	,	PUNCT
ejpam-289	108	51	d	d	NOUN
ejpam-289	108	52	)	)	PUNCT
ejpam-289	108	53	,	,	PUNCT
ejpam-289	109	1	[	[	X
ejpam-289	109	2	c	c	X
ejpam-289	109	3	,	,	PUNCT
ejpam-289	109	4	b	b	NOUN
ejpam-289	109	5	]	]	PUNCT
ejpam-289	109	6	and	and	CCONJ
ejpam-289	109	7	(	(	PUNCT
ejpam-289	109	8	a	a	DET
ejpam-289	109	9	,	,	PUNCT
ejpam-289	109	10	b	b	NOUN
ejpam-289	109	11	]	]	X
ejpam-289	109	12	∪	∪	ADP
ejpam-289	109	13	[	[	X
ejpam-289	109	14	c	c	X
ejpam-289	109	15	,	,	PUNCT
ejpam-289	109	16	d	d	NOUN
ejpam-289	109	17	)	)	PUNCT
ejpam-289	109	18	,	,	PUNCT
ejpam-289	109	19	i.e.	i.e.	X
ejpam-289	109	20	,	,	PUNCT
ejpam-289	109	21	b	b	PROPN
ejpam-289	109	22	∪b∗	∪b∗	NUM
ejpam-289	109	23	is	be	AUX
ejpam-289	109	24	a	a	DET
ejpam-289	109	25	base	base	NOUN
ejpam-289	109	26	for	for	ADP
ejpam-289	109	27	the	the	DET
ejpam-289	109	28	p	p	NOUN
ejpam-289	109	29	∪q	∪q	NUM
ejpam-289	109	30	.	.	PUNCT
ejpam-289	110	1	thus	thus	ADV
ejpam-289	110	2	(	(	PUNCT
ejpam-289	110	3	r	r	NOUN
ejpam-289	110	4	,	,	PUNCT
ejpam-289	110	5	p	p	NOUN
ejpam-289	110	6	,	,	PUNCT
ejpam-289	110	7	q	q	NOUN
ejpam-289	110	8	)	)	PUNCT
ejpam-289	110	9	is	be	AUX
ejpam-289	110	10	a	a	DET
ejpam-289	110	11	p2	p2	ADJ
ejpam-289	110	12	-	-	PUNCT
ejpam-289	110	13	lindelöf	lindelöf	NOUN
ejpam-289	110	14	space	space	NOUN
ejpam-289	110	15	.	.	PUNCT
ejpam-289	111	1	but	but	CCONJ
ejpam-289	111	2	(	(	PUNCT
ejpam-289	111	3	r	r	NOUN
ejpam-289	111	4	,	,	PUNCT
ejpam-289	111	5	p	p	NOUN
ejpam-289	111	6	,	,	PUNCT
ejpam-289	111	7	q	q	NOUN
ejpam-289	111	8	)	)	PUNCT
ejpam-289	111	9	is	be	AUX
ejpam-289	111	10	not	not	PART
ejpam-289	111	11	p2	p2	ADJ
ejpam-289	111	12	-	-	PUNCT
ejpam-289	111	13	compact	compact	ADJ
ejpam-289	111	14	since	since	SCONJ
ejpam-289	111	15	for	for	ADP
ejpam-289	111	16	example	example	NOUN
ejpam-289	111	17	{	{	PUNCT
ejpam-289	111	18	(	(	PUNCT
ejpam-289	111	19	n	n	CCONJ
ejpam-289	111	20	,	,	PUNCT
ejpam-289	111	21	n+	n+	ADP
ejpam-289	111	22	1	1	NUM
ejpam-289	111	23	]	]	PUNCT
ejpam-289	111	24	:	:	PUNCT
ejpam-289	111	25	n	n	CCONJ
ejpam-289	111	26	∈	∈	PROPN
ejpam-289	111	27	z	z	AUX
ejpam-289	111	28	}	}	PUNCT
ejpam-289	111	29	is	be	AUX
ejpam-289	111	30	a	a	DET
ejpam-289	111	31	p1	p1	NOUN
ejpam-289	111	32	-	-	PUNCT
ejpam-289	111	33	open	open	ADJ
ejpam-289	111	34	cover	cover	NOUN
ejpam-289	111	35	of	of	ADP
ejpam-289	111	36	r	r	NOUN
ejpam-289	111	37	contains	contain	VERB
ejpam-289	111	38	no	no	DET
ejpam-289	111	39	finite	finite	PROPN
ejpam-289	111	40	subcover	subcover	PROPN
ejpam-289	111	41	.	.	PUNCT
ejpam-289	112	1	lemma	lemma	PROPN
ejpam-289	112	2	4.1	4.1	NUM
ejpam-289	112	3	.	.	PUNCT
ejpam-289	113	1	every	every	DET
ejpam-289	113	2	p1	p1	NOUN
ejpam-289	113	3	-	-	PUNCT
ejpam-289	113	4	closed	closed	ADJ
ejpam-289	113	5	subset	subset	NOUN
ejpam-289	113	6	of	of	ADP
ejpam-289	113	7	a	a	DET
ejpam-289	113	8	p2	p2	ADJ
ejpam-289	113	9	-	-	PUNCT
ejpam-289	113	10	lindelöf	lindelöf	NOUN
ejpam-289	113	11	bitopological	bitopological	ADJ
ejpam-289	113	12	space	space	NOUN
ejpam-289	113	13	is	be	AUX
ejpam-289	113	14	p2	p2	NOUN
ejpam-289	113	15	-	-	PUNCT
ejpam-289	113	16	lindelöf	lindelöf	NOUN
ejpam-289	113	17	.	.	PUNCT
ejpam-289	114	1	proof	proof	NOUN
ejpam-289	114	2	.	.	PUNCT
ejpam-289	115	1	let	let	VERB
ejpam-289	115	2	(	(	PUNCT
ejpam-289	115	3	x	x	INTJ
ejpam-289	115	4	,	,	PUNCT
ejpam-289	115	5	p	p	X
ejpam-289	115	6	,	,	PUNCT
ejpam-289	115	7	q	q	NOUN
ejpam-289	115	8	)	)	PUNCT
ejpam-289	115	9	be	be	AUX
ejpam-289	115	10	a	a	DET
ejpam-289	115	11	p2	p2	ADJ
ejpam-289	115	12	-	-	PUNCT
ejpam-289	115	13	lindelöf	lindelöf	NOUN
ejpam-289	115	14	bitopological	bitopological	ADJ
ejpam-289	115	15	space	space	NOUN
ejpam-289	115	16	and	and	CCONJ
ejpam-289	115	17	let	let	VERB
ejpam-289	115	18	f	f	PROPN
ejpam-289	115	19	is	be	AUX
ejpam-289	115	20	a	a	DET
ejpam-289	115	21	p1	p1	NOUN
ejpam-289	115	22	-	-	PUNCT
ejpam-289	115	23	closed	closed	ADJ
ejpam-289	115	24	subset	subset	NOUN
ejpam-289	115	25	of	of	ADP
ejpam-289	115	26	x	x	X
ejpam-289	115	27	.	.	PUNCT
ejpam-289	116	1	if	if	SCONJ
ejpam-289	116	2	�	�	PROPN
ejpam-289	116	3	uα	uα	X
ejpam-289	116	4	:	:	PUNCT
ejpam-289	116	5	α	α	PROPN
ejpam-289	116	6	∈∆	∈∆	NOUN
ejpam-289	116	7	is	be	AUX
ejpam-289	116	8	a	a	DET
ejpam-289	116	9	p1	p1	NOUN
ejpam-289	116	10	-	-	PUNCT
ejpam-289	116	11	open	open	ADJ
ejpam-289	116	12	cover	cover	NOUN
ejpam-289	116	13	of	of	ADP
ejpam-289	116	14	f	f	PROPN
ejpam-289	116	15	,	,	PUNCT
ejpam-289	116	16	then	then	ADV
ejpam-289	116	17	x	x	X
ejpam-289	116	18	=	=	SYM
ejpam-289	116	19	�	�	PROPN
ejpam-289	116	20	⋃	⋃	NOUN
ejpam-289	116	21	α∈∆	α∈∆	PROPN
ejpam-289	116	22	uα	uα	PROPN
ejpam-289	116	23	�	�	PROPN
ejpam-289	116	24	⋃	⋃	PROPN
ejpam-289	116	25	(	(	PUNCT
ejpam-289	116	26	x	x	X
ejpam-289	116	27	�	�	X
ejpam-289	116	28	f	f	NUM
ejpam-289	116	29	)	)	PUNCT
ejpam-289	116	30	.	.	PUNCT
ejpam-289	117	1	hence	hence	ADV
ejpam-289	117	2	the	the	DET
ejpam-289	117	3	collection	collection	NOUN
ejpam-289	117	4	�	�	PROPN
ejpam-289	117	5	uα	uα	PROPN
ejpam-289	117	6	:	:	PUNCT
ejpam-289	117	7	α	α	PROPN
ejpam-289	117	8	∈∆	∈∆	NOUN
ejpam-289	117	9	and	and	CCONJ
ejpam-289	117	10	x	x	PART
ejpam-289	117	11	�	�	PROPN
ejpam-289	117	12	f	f	PROPN
ejpam-289	117	13	forms	form	VERB
ejpam-289	117	14	a	a	DET
ejpam-289	117	15	p1	p1	NOUN
ejpam-289	117	16	-	-	PUNCT
ejpam-289	117	17	open	open	ADJ
ejpam-289	117	18	cover	cover	NOUN
ejpam-289	117	19	of	of	ADP
ejpam-289	117	20	x	x	X
ejpam-289	117	21	.	.	PUNCT
ejpam-289	118	1	since	since	SCONJ
ejpam-289	118	2	(	(	PUNCT
ejpam-289	118	3	x	x	INTJ
ejpam-289	118	4	,	,	PUNCT
ejpam-289	118	5	p	p	X
ejpam-289	118	6	,	,	PUNCT
ejpam-289	118	7	q	q	NOUN
ejpam-289	118	8	)	)	PUNCT
ejpam-289	118	9	is	be	AUX
ejpam-289	118	10	p2	p2	NOUN
ejpam-289	118	11	-	-	PUNCT
ejpam-289	118	12	lindelöf	lindelöf	NOUN
ejpam-289	118	13	,	,	PUNCT
ejpam-289	118	14	there	there	PRON
ejpam-289	118	15	will	will	AUX
ejpam-289	118	16	be	be	AUX
ejpam-289	118	17	a	a	DET
ejpam-289	118	18	countable	countable	ADJ
ejpam-289	118	19	subcover	subcover	NOUN
ejpam-289	118	20	¦	¦	PROPN
ejpam-289	118	21	x	x	SYM
ejpam-289	118	22	�	�	PROPN
ejpam-289	118	23	f	f	PROPN
ejpam-289	118	24	,	,	PUNCT
ejpam-289	118	25	uα1	uα1	NOUN
ejpam-289	118	26	,	,	PUNCT
ejpam-289	118	27	uα2	uα2	ADV
ejpam-289	118	28	,	,	PUNCT
ejpam-289	118	29	.	.	PUNCT
ejpam-289	118	30	.	.	PUNCT
ejpam-289	118	31	.	.	PUNCT
ejpam-289	119	1	©	©	PROPN
ejpam-289	119	2	.	.	PUNCT
ejpam-289	120	1	but	but	CCONJ
ejpam-289	120	2	a.	a.	NOUN
ejpam-289	120	3	kılıçman	kılıçman	PROPN
ejpam-289	120	4	and	and	CCONJ
ejpam-289	120	5	z.	z.	PROPN
ejpam-289	120	6	salleh	salleh	PROPN
ejpam-289	120	7	/	/	PUNCT
ejpam-289	120	8	eur	eur	PROPN
ejpam-289	120	9	.	.	PUNCT
ejpam-289	121	1	j.	j.	PROPN
ejpam-289	121	2	pure	pure	PROPN
ejpam-289	121	3	appl	appl	PROPN
ejpam-289	121	4	.	.	PROPN
ejpam-289	121	5	math	math	PROPN
ejpam-289	121	6	,	,	PUNCT
ejpam-289	121	7	2	2	NUM
ejpam-289	121	8	(	(	PUNCT
ejpam-289	121	9	2009	2009	NUM
ejpam-289	121	10	)	)	PUNCT
ejpam-289	121	11	,	,	PUNCT
ejpam-289	121	12	(	(	PUNCT
ejpam-289	121	13	325	325	NUM
ejpam-289	121	14	-	-	SYM
ejpam-289	121	15	337	337	NUM
ejpam-289	121	16	)	)	PUNCT
ejpam-289	121	17	332	332	NUM
ejpam-289	121	18	f	f	NOUN
ejpam-289	121	19	and	and	CCONJ
ejpam-289	121	20	x	x	PROPN
ejpam-289	121	21	�	�	PROPN
ejpam-289	121	22	f	f	NOUN
ejpam-289	121	23	are	be	AUX
ejpam-289	121	24	disjoint	disjoint	ADJ
ejpam-289	121	25	;	;	PUNCT
ejpam-289	121	26	hence	hence	ADV
ejpam-289	121	27	the	the	DET
ejpam-289	121	28	subcollection	subcollection	NOUN
ejpam-289	121	29	of	of	ADP
ejpam-289	121	30	p1	p1	NOUN
ejpam-289	121	31	-	-	PUNCT
ejpam-289	121	32	open	open	NOUN
ejpam-289	121	33	set	set	NOUN
ejpam-289	121	34	¦	¦	PROPN
ejpam-289	121	35	uαi	uαi	NOUN
ejpam-289	121	36	:	:	PUNCT
ejpam-289	121	37	i	i	PRON
ejpam-289	121	38	∈	∈	PROPN
ejpam-289	121	39	n	n	PRON
ejpam-289	121	40	©	©	PROPN
ejpam-289	121	41	also	also	ADV
ejpam-289	121	42	cover	cover	VERB
ejpam-289	121	43	f	f	PROPN
ejpam-289	121	44	,	,	PUNCT
ejpam-289	121	45	and	and	CCONJ
ejpam-289	121	46	so	so	ADV
ejpam-289	121	47	�	�	PROPN
ejpam-289	121	48	uα	uα	PROPN
ejpam-289	121	49	:	:	PUNCT
ejpam-289	121	50	α	α	PROPN
ejpam-289	121	51	∈∆	∈∆	NOUN
ejpam-289	121	52	has	have	VERB
ejpam-289	121	53	a	a	DET
ejpam-289	121	54	countable	countable	ADJ
ejpam-289	121	55	subcover	subcover	NOUN
ejpam-289	121	56	.	.	PUNCT
ejpam-289	122	1	this	this	PRON
ejpam-289	122	2	completes	complete	VERB
ejpam-289	122	3	the	the	DET
ejpam-289	122	4	proof	proof	NOUN
ejpam-289	122	5	.	.	PUNCT
ejpam-289	123	1	theorem	theorem	VERB
ejpam-289	123	2	4.1	4.1	NUM
ejpam-289	123	3	.	.	PUNCT
ejpam-289	124	1	every	every	DET
ejpam-289	124	2	p1	p1	NOUN
ejpam-289	124	3	-	-	PUNCT
ejpam-289	124	4	regular	regular	ADJ
ejpam-289	124	5	and	and	CCONJ
ejpam-289	124	6	p2	p2	NOUN
ejpam-289	124	7	-	-	PUNCT
ejpam-289	124	8	lindelöf	lindelöf	NOUN
ejpam-289	124	9	bitopological	bitopological	ADJ
ejpam-289	124	10	space	space	NOUN
ejpam-289	124	11	(	(	PUNCT
ejpam-289	124	12	x	x	X
ejpam-289	124	13	,	,	PUNCT
ejpam-289	124	14	p	p	X
ejpam-289	124	15	,	,	PUNCT
ejpam-289	124	16	q	q	NOUN
ejpam-289	124	17	)	)	PUNCT
ejpam-289	124	18	is	be	AUX
ejpam-289	124	19	p2normal	p2normal	ADJ
ejpam-289	124	20	.	.	PUNCT
ejpam-289	125	1	proof	proof	NOUN
ejpam-289	125	2	.	.	PUNCT
ejpam-289	126	1	let	let	VERB
ejpam-289	126	2	a	a	PRON
ejpam-289	126	3	and	and	CCONJ
ejpam-289	126	4	b	b	NOUN
ejpam-289	126	5	are	be	AUX
ejpam-289	126	6	p1	p1	NOUN
ejpam-289	126	7	-	-	PUNCT
ejpam-289	126	8	closed	close	VERB
ejpam-289	126	9	sets	set	NOUN
ejpam-289	126	10	in	in	ADP
ejpam-289	126	11	x	x	PUNCT
ejpam-289	126	12	with	with	ADP
ejpam-289	126	13	a∩	a∩	PROPN
ejpam-289	126	14	b	b	PROPN
ejpam-289	126	15	=	=	PUNCT
ejpam-289	126	16	;	;	PUNCT
ejpam-289	126	17	.	.	PUNCT
ejpam-289	127	1	since	since	SCONJ
ejpam-289	127	2	(	(	PUNCT
ejpam-289	127	3	x	x	INTJ
ejpam-289	127	4	,	,	PUNCT
ejpam-289	127	5	p	p	X
ejpam-289	127	6	,	,	PUNCT
ejpam-289	127	7	q	q	NOUN
ejpam-289	127	8	)	)	PUNCT
ejpam-289	127	9	is	be	AUX
ejpam-289	127	10	p1	p1	NOUN
ejpam-289	127	11	-	-	PUNCT
ejpam-289	127	12	regular	regular	ADJ
ejpam-289	127	13	,	,	PUNCT
ejpam-289	127	14	then	then	ADV
ejpam-289	127	15	by	by	ADP
ejpam-289	127	16	theorem	theorem	NOUN
ejpam-289	127	17	3.1	3.1	NUM
ejpam-289	127	18	,	,	PUNCT
ejpam-289	127	19	for	for	ADP
ejpam-289	127	20	each	each	PRON
ejpam-289	127	21	x	x	PUNCT
ejpam-289	127	22	in	in	ADP
ejpam-289	127	23	b	b	PROPN
ejpam-289	127	24	and	and	CCONJ
ejpam-289	127	25	p1	p1	NOUN
ejpam-289	127	26	-	-	PUNCT
ejpam-289	127	27	open	open	ADJ
ejpam-289	127	28	set	set	NOUN
ejpam-289	127	29	x	x	PRON
ejpam-289	127	30	�	�	X
ejpam-289	127	31	a	a	DET
ejpam-289	127	32	containing	containing	NOUN
ejpam-289	127	33	x	x	SYM
ejpam-289	127	34	,	,	PUNCT
ejpam-289	127	35	there	there	PRON
ejpam-289	127	36	is	be	VERB
ejpam-289	127	37	a	a	DET
ejpam-289	127	38	p1	p1	NOUN
ejpam-289	127	39	-	-	PUNCT
ejpam-289	127	40	open	open	ADJ
ejpam-289	127	41	set	set	NOUN
ejpam-289	127	42	px	px	ADP
ejpam-289	127	43	such	such	ADJ
ejpam-289	127	44	that	that	SCONJ
ejpam-289	127	45	x	x	SYM
ejpam-289	127	46	∈	∈	NOUN
ejpam-289	127	47	px	px	VERB
ejpam-289	127	48	⊆	⊆	NUM
ejpam-289	127	49	p1cl(px)⊆	p1cl(px)⊆	NOUN
ejpam-289	127	50	x	x	SYM
ejpam-289	127	51	�	�	PROPN
ejpam-289	127	52	a	a	PRON
ejpam-289	127	53	,	,	PUNCT
ejpam-289	127	54	i.e.	i.e.	X
ejpam-289	127	55	,	,	PUNCT
ejpam-289	127	56	p1	p1	ADJ
ejpam-289	127	57	-	-	PUNCT
ejpam-289	127	58	cl	cl	NOUN
ejpam-289	127	59	�	�	PROPN
ejpam-289	127	60	px	px	PROPN
ejpam-289	127	61	�	�	PROPN
ejpam-289	127	62	∩	∩	NOUN
ejpam-289	127	63	a=	a=	NOUN
ejpam-289	127	64	;	;	PUNCT
ejpam-289	127	65	.	.	PUNCT
ejpam-289	128	1	the	the	DET
ejpam-289	128	2	collection	collection	NOUN
ejpam-289	128	3	{	{	PUNCT
ejpam-289	128	4	px	px	X
ejpam-289	128	5	:	:	PUNCT
ejpam-289	128	6	x	x	SYM
ejpam-289	128	7	∈	∈	PROPN
ejpam-289	128	8	b	b	NOUN
ejpam-289	128	9	}	}	PUNCT
ejpam-289	128	10	forms	form	VERB
ejpam-289	128	11	a	a	DET
ejpam-289	128	12	p1	p1	NOUN
ejpam-289	128	13	-	-	PUNCT
ejpam-289	128	14	open	open	ADJ
ejpam-289	128	15	cover	cover	NOUN
ejpam-289	128	16	of	of	ADP
ejpam-289	128	17	b.	b.	PROPN
ejpam-289	128	18	since	since	SCONJ
ejpam-289	128	19	(	(	PUNCT
ejpam-289	128	20	x	x	INTJ
ejpam-289	128	21	,	,	PUNCT
ejpam-289	128	22	p	p	X
ejpam-289	128	23	,	,	PUNCT
ejpam-289	128	24	q	q	NOUN
ejpam-289	128	25	)	)	PUNCT
ejpam-289	128	26	is	be	AUX
ejpam-289	128	27	p2	p2	NOUN
ejpam-289	128	28	-	-	PUNCT
ejpam-289	128	29	lindelöf	lindelöf	NOUN
ejpam-289	128	30	,	,	PUNCT
ejpam-289	128	31	then	then	ADV
ejpam-289	128	32	b	b	PROPN
ejpam-289	128	33	is	be	AUX
ejpam-289	128	34	also	also	ADV
ejpam-289	128	35	p2	p2	ADJ
ejpam-289	128	36	-	-	PUNCT
ejpam-289	128	37	lindelöf	lindelöf	NOUN
ejpam-289	128	38	by	by	ADP
ejpam-289	128	39	lemma	lemma	PROPN
ejpam-289	128	40	4.1	4.1	NUM
ejpam-289	128	41	.	.	PUNCT
ejpam-289	129	1	hence	hence	ADV
ejpam-289	129	2	we	we	PRON
ejpam-289	129	3	obtain	obtain	VERB
ejpam-289	129	4	a	a	DET
ejpam-289	129	5	countable	countable	ADJ
ejpam-289	129	6	p1	p1	NOUN
ejpam-289	129	7	-	-	PUNCT
ejpam-289	129	8	open	open	ADJ
ejpam-289	129	9	cover	cover	NOUN
ejpam-289	129	10	of	of	ADP
ejpam-289	129	11	b	b	NOUN
ejpam-289	129	12	,	,	PUNCT
ejpam-289	129	13	which	which	PRON
ejpam-289	129	14	we	we	PRON
ejpam-289	129	15	denote	denote	VERB
ejpam-289	129	16	by	by	ADP
ejpam-289	129	17	�	�	PROPN
ejpam-289	129	18	pi	pi	NOUN
ejpam-289	129	19	:	:	PUNCT
ejpam-289	130	1	i	i	PRON
ejpam-289	130	2	∈	∈	PROPN
ejpam-289	130	3	n	n	INTJ
ejpam-289	130	4	.	.	PUNCT
ejpam-289	131	1	similarly	similarly	ADV
ejpam-289	131	2	,	,	PUNCT
ejpam-289	131	3	for	for	ADP
ejpam-289	131	4	each	each	DET
ejpam-289	131	5	y	y	PROPN
ejpam-289	131	6	in	in	ADP
ejpam-289	131	7	a	a	DET
ejpam-289	131	8	and	and	CCONJ
ejpam-289	131	9	p1	p1	NOUN
ejpam-289	131	10	-	-	PUNCT
ejpam-289	131	11	open	open	ADJ
ejpam-289	131	12	set	set	NOUN
ejpam-289	131	13	x	x	NOUN
ejpam-289	131	14	�	�	PROPN
ejpam-289	131	15	b	b	NOUN
ejpam-289	131	16	containing	contain	VERB
ejpam-289	131	17	y	y	NOUN
ejpam-289	131	18	,	,	PUNCT
ejpam-289	131	19	there	there	PRON
ejpam-289	131	20	is	be	VERB
ejpam-289	131	21	a	a	DET
ejpam-289	131	22	p1	p1	NOUN
ejpam-289	131	23	-	-	PUNCT
ejpam-289	131	24	open	open	NOUN
ejpam-289	131	25	set	set	NOUN
ejpam-289	131	26	q	q	PROPN
ejpam-289	131	27	y	y	PROPN
ejpam-289	131	28	such	such	ADJ
ejpam-289	131	29	that	that	SCONJ
ejpam-289	131	30	y	y	PROPN
ejpam-289	131	31	∈	∈	PROPN
ejpam-289	131	32	q	q	PROPN
ejpam-289	131	33	y	y	PROPN
ejpam-289	131	34	⊆	⊆	NUM
ejpam-289	131	35	p1cl	p1cl	PUNCT
ejpam-289	131	36	�	�	PROPN
ejpam-289	131	37	q	q	PROPN
ejpam-289	131	38	y	y	PROPN
ejpam-289	131	39	�	�	PROPN
ejpam-289	131	40	⊆	⊆	NUM
ejpam-289	131	41	x	x	SYM
ejpam-289	131	42	�	�	PROPN
ejpam-289	131	43	b	b	NUM
ejpam-289	131	44	,	,	PUNCT
ejpam-289	131	45	i.e.	i.e.	X
ejpam-289	131	46	,	,	PUNCT
ejpam-289	131	47	p1	p1	ADJ
ejpam-289	131	48	-	-	PUNCT
ejpam-289	131	49	cl	cl	NOUN
ejpam-289	131	50	�	�	PROPN
ejpam-289	131	51	q	q	PROPN
ejpam-289	131	52	y	y	PROPN
ejpam-289	131	53	�	�	PROPN
ejpam-289	131	54	∩b	∩b	PROPN
ejpam-289	131	55	=	=	PUNCT
ejpam-289	131	56	;	;	PUNCT
ejpam-289	131	57	.	.	PUNCT
ejpam-289	132	1	the	the	DET
ejpam-289	132	2	collection	collection	NOUN
ejpam-289	132	3	¦	¦	PROPN
ejpam-289	132	4	q	q	ADJ
ejpam-289	132	5	y	y	NOUN
ejpam-289	132	6	:	:	PUNCT
ejpam-289	132	7	y	y	PROPN
ejpam-289	132	8	∈	∈	PROPN
ejpam-289	132	9	a	a	DET
ejpam-289	132	10	©	©	PROPN
ejpam-289	132	11	forms	form	VERB
ejpam-289	132	12	a	a	DET
ejpam-289	132	13	p1	p1	NOUN
ejpam-289	132	14	-	-	PUNCT
ejpam-289	132	15	open	open	ADJ
ejpam-289	132	16	cover	cover	NOUN
ejpam-289	132	17	of	of	ADP
ejpam-289	132	18	a.	a.	NOUN
ejpam-289	132	19	since	since	SCONJ
ejpam-289	132	20	(	(	PUNCT
ejpam-289	132	21	x	x	INTJ
ejpam-289	132	22	,	,	PUNCT
ejpam-289	132	23	p	p	X
ejpam-289	132	24	,	,	PUNCT
ejpam-289	132	25	q	q	NOUN
ejpam-289	132	26	)	)	PUNCT
ejpam-289	132	27	is	be	AUX
ejpam-289	132	28	p2	p2	NOUN
ejpam-289	132	29	-	-	PUNCT
ejpam-289	132	30	lindelöf	lindelöf	NOUN
ejpam-289	132	31	,	,	PUNCT
ejpam-289	132	32	then	then	ADV
ejpam-289	132	33	a	a	PRON
ejpam-289	132	34	is	be	AUX
ejpam-289	132	35	also	also	ADV
ejpam-289	132	36	p2	p2	ADJ
ejpam-289	132	37	-	-	PUNCT
ejpam-289	132	38	lindelöf	lindelöf	NOUN
ejpam-289	132	39	by	by	ADP
ejpam-289	132	40	lemma	lemma	PROPN
ejpam-289	132	41	4.1	4.1	NUM
ejpam-289	132	42	.	.	PUNCT
ejpam-289	133	1	hence	hence	ADV
ejpam-289	133	2	we	we	PRON
ejpam-289	133	3	obtain	obtain	VERB
ejpam-289	133	4	a	a	DET
ejpam-289	133	5	countable	countable	ADJ
ejpam-289	133	6	p1	p1	NOUN
ejpam-289	133	7	-	-	PUNCT
ejpam-289	133	8	open	open	ADJ
ejpam-289	133	9	cover	cover	NOUN
ejpam-289	133	10	of	of	ADP
ejpam-289	133	11	a	a	PRON
ejpam-289	133	12	,	,	PUNCT
ejpam-289	133	13	which	which	PRON
ejpam-289	133	14	we	we	PRON
ejpam-289	133	15	denote	denote	VERB
ejpam-289	133	16	by	by	ADP
ejpam-289	133	17	�	�	PROPN
ejpam-289	133	18	q	q	PROPN
ejpam-289	134	1	i	i	PRON
ejpam-289	134	2	:	:	PUNCT
ejpam-289	134	3	i	i	PROPN
ejpam-289	134	4	∈	∈	PROPN
ejpam-289	134	5	n	n	INTJ
ejpam-289	134	6	.	.	PUNCT
ejpam-289	135	1	let	let	VERB
ejpam-289	135	2	un	un	PROPN
ejpam-289	135	3	=	=	PROPN
ejpam-289	135	4	qn	qn	NOUN
ejpam-289	135	5	�	�	PROPN
ejpam-289	135	6	⋃	⋃	PROPN
ejpam-289	135	7	�	�	PROPN
ejpam-289	135	8	p1cl	p1cl	PUNCT
ejpam-289	135	9	�	�	PROPN
ejpam-289	135	10	vi	vi	X
ejpam-289	135	11	�	�	PROPN
ejpam-289	135	12	:	:	PUNCT
ejpam-289	135	13	i	i	PRON
ejpam-289	135	14	≤	≤	PUNCT
ejpam-289	135	15	n	n	CCONJ
ejpam-289	136	1	and	and	CCONJ
ejpam-289	136	2	vn	vn	PROPN
ejpam-289	136	3	=	=	PUNCT
ejpam-289	136	4	pn	pn	PROPN
ejpam-289	136	5	�	�	PROPN
ejpam-289	136	6	⋃	⋃	PROPN
ejpam-289	136	7	�	�	PROPN
ejpam-289	136	8	p1cl	p1cl	PUNCT
ejpam-289	136	9	�	�	PROPN
ejpam-289	136	10	ui	ui	PROPN
ejpam-289	136	11	�	�	PROPN
ejpam-289	136	12	:	:	PUNCT
ejpam-289	136	13	i	i	PRON
ejpam-289	136	14	≤	≤	PUNCT
ejpam-289	136	15	n	n	X
ejpam-289	136	16	.	.	PUNCT
ejpam-289	137	1	since	since	SCONJ
ejpam-289	137	2	un	un	PROPN
ejpam-289	137	3	∩	∩	PROPN
ejpam-289	137	4	p1	p1	PROPN
ejpam-289	137	5	-	-	PUNCT
ejpam-289	137	6	cl	cl	NOUN
ejpam-289	137	7	�	�	PROPN
ejpam-289	137	8	vm	vm	PROPN
ejpam-289	137	9	�	�	PROPN
ejpam-289	137	10	=	=	PUNCT
ejpam-289	137	11	;	;	PUNCT
ejpam-289	137	12	for	for	ADP
ejpam-289	137	13	m	m	PROPN
ejpam-289	137	14	≤	≤	NOUN
ejpam-289	137	15	n	n	CCONJ
ejpam-289	137	16	,	,	PUNCT
ejpam-289	137	17	it	it	PRON
ejpam-289	137	18	follows	follow	VERB
ejpam-289	137	19	that	that	SCONJ
ejpam-289	137	20	un	un	PROPN
ejpam-289	137	21	∩	∩	PROPN
ejpam-289	137	22	vm	vm	PROPN
ejpam-289	137	23	=	=	PUNCT
ejpam-289	137	24	;	;	PUNCT
ejpam-289	137	25	for	for	ADP
ejpam-289	137	26	m≤	m≤	NOUN
ejpam-289	137	27	n.	n.	NOUN
ejpam-289	137	28	similarly	similarly	ADV
ejpam-289	137	29	,	,	PUNCT
ejpam-289	137	30	vm	vm	PROPN
ejpam-289	137	31	∩	∩	PROPN
ejpam-289	137	32	p1	p1	NOUN
ejpam-289	137	33	-	-	PUNCT
ejpam-289	137	34	cl	cl	NOUN
ejpam-289	137	35	�	�	PROPN
ejpam-289	137	36	un	un	PROPN
ejpam-289	137	37	�	�	PROPN
ejpam-289	137	38	=	=	PUNCT
ejpam-289	137	39	;	;	PUNCT
ejpam-289	137	40	for	for	ADP
ejpam-289	137	41	n	n	PRON
ejpam-289	137	42	≤	≤	NOUN
ejpam-289	137	43	m	m	ADP
ejpam-289	137	44	,	,	PUNCT
ejpam-289	137	45	it	it	PRON
ejpam-289	137	46	follows	follow	VERB
ejpam-289	137	47	that	that	SCONJ
ejpam-289	137	48	vm	vm	PROPN
ejpam-289	137	49	∩	∩	PROPN
ejpam-289	137	50	un	un	PROPN
ejpam-289	137	51	=	=	X
ejpam-289	137	52	;	;	PUNCT
ejpam-289	137	53	for	for	ADP
ejpam-289	137	54	n	n	PRON
ejpam-289	137	55	≤	≤	NUM
ejpam-289	137	56	m.	m.	NOUN
ejpam-289	137	57	thus	thus	ADV
ejpam-289	137	58	un	un	PROPN
ejpam-289	137	59	∩	∩	PROPN
ejpam-289	137	60	vm	vm	PROPN
ejpam-289	137	61	=	=	PUNCT
ejpam-289	137	62	;	;	PUNCT
ejpam-289	137	63	for	for	ADP
ejpam-289	137	64	all	all	DET
ejpam-289	137	65	m	m	NOUN
ejpam-289	137	66	and	and	CCONJ
ejpam-289	137	67	n	n	CCONJ
ejpam-289	137	68	,	,	PUNCT
ejpam-289	137	69	and	and	CCONJ
ejpam-289	137	70	consequently	consequently	ADV
ejpam-289	137	71	u	u	X
ejpam-289	137	72	=	=	PUNCT
ejpam-289	137	73	⋃	⋃	PROPN
ejpam-289	137	74	�	�	PROPN
ejpam-289	137	75	un	un	PROPN
ejpam-289	137	76	:	:	PUNCT
ejpam-289	137	77	n	n	CCONJ
ejpam-289	137	78	∈	∈	NOUN
ejpam-289	137	79	n	n	VERB
ejpam-289	137	80	is	be	AUX
ejpam-289	137	81	disjoint	disjoint	PROPN
ejpam-289	137	82	a.	a.	NOUN
ejpam-289	137	83	kılıçman	kılıçman	PROPN
ejpam-289	137	84	and	and	CCONJ
ejpam-289	137	85	z.	z.	PROPN
ejpam-289	137	86	salleh	salleh	PROPN
ejpam-289	137	87	/	/	PUNCT
ejpam-289	137	88	eur	eur	PROPN
ejpam-289	137	89	.	.	PUNCT
ejpam-289	138	1	j.	j.	PROPN
ejpam-289	138	2	pure	pure	PROPN
ejpam-289	138	3	appl	appl	PROPN
ejpam-289	138	4	.	.	PROPN
ejpam-289	138	5	math	math	PROPN
ejpam-289	138	6	,	,	PUNCT
ejpam-289	138	7	2	2	NUM
ejpam-289	138	8	(	(	PUNCT
ejpam-289	138	9	2009	2009	NUM
ejpam-289	138	10	)	)	PUNCT
ejpam-289	138	11	,	,	PUNCT
ejpam-289	138	12	(	(	PUNCT
ejpam-289	138	13	325	325	NUM
ejpam-289	138	14	-	-	SYM
ejpam-289	138	15	337	337	NUM
ejpam-289	138	16	)	)	PUNCT
ejpam-289	138	17	333	333	NUM
ejpam-289	138	18	from	from	ADP
ejpam-289	138	19	v	v	NOUN
ejpam-289	138	20	=	=	SYM
ejpam-289	138	21	⋃	⋃	PROPN
ejpam-289	138	22	�	�	PROPN
ejpam-289	138	23	vn	vn	NOUN
ejpam-289	138	24	:	:	PUNCT
ejpam-289	138	25	n	n	CCONJ
ejpam-289	138	26	∈	∈	PROPN
ejpam-289	138	27	n	n	X
ejpam-289	138	28	.	.	PUNCT
ejpam-289	139	1	finally	finally	ADV
ejpam-289	139	2	,	,	PUNCT
ejpam-289	139	3	p1	p1	NOUN
ejpam-289	139	4	-	-	PUNCT
ejpam-289	139	5	cl	cl	NOUN
ejpam-289	139	6	�	�	PROPN
ejpam-289	139	7	vi	vi	PROPN
ejpam-289	139	8	�	�	PROPN
ejpam-289	139	9	∩	∩	PROPN
ejpam-289	139	10	a	a	PRON
ejpam-289	139	11	and	and	CCONJ
ejpam-289	139	12	p1	p1	NOUN
ejpam-289	139	13	-	-	PUNCT
ejpam-289	139	14	cl	cl	NOUN
ejpam-289	139	15	�	�	PROPN
ejpam-289	139	16	ui	ui	PROPN
ejpam-289	139	17	�	�	PROPN
ejpam-289	139	18	∩	∩	PROPN
ejpam-289	139	19	b	b	NUM
ejpam-289	139	20	are	be	AUX
ejpam-289	139	21	empty	empty	ADJ
ejpam-289	139	22	set	set	NOUN
ejpam-289	139	23	for	for	ADP
ejpam-289	139	24	all	all	DET
ejpam-289	139	25	i	i	PRON
ejpam-289	139	26	and	and	CCONJ
ejpam-289	139	27	hence	hence	ADV
ejpam-289	139	28	the	the	DET
ejpam-289	139	29	set	set	NOUN
ejpam-289	139	30	u	u	NOUN
ejpam-289	139	31	contains	contain	VERB
ejpam-289	139	32	a	a	PRON
ejpam-289	139	33	and	and	CCONJ
ejpam-289	139	34	is	be	AUX
ejpam-289	139	35	p1	p1	NOUN
ejpam-289	139	36	-	-	ADJ
ejpam-289	139	37	open	open	ADJ
ejpam-289	139	38	,	,	PUNCT
ejpam-289	139	39	whilst	whilst	SCONJ
ejpam-289	139	40	the	the	DET
ejpam-289	139	41	set	set	NOUN
ejpam-289	139	42	v	v	NOUN
ejpam-289	139	43	contains	contain	VERB
ejpam-289	139	44	b	b	NOUN
ejpam-289	139	45	and	and	CCONJ
ejpam-289	139	46	is	be	AUX
ejpam-289	139	47	p1	p1	NOUN
ejpam-289	139	48	-	-	NOUN
ejpam-289	139	49	open	open	ADJ
ejpam-289	139	50	.	.	PUNCT
ejpam-289	140	1	the	the	DET
ejpam-289	140	2	proof	proof	NOUN
ejpam-289	140	3	is	be	AUX
ejpam-289	140	4	complete	complete	ADJ
ejpam-289	140	5	.	.	PUNCT
ejpam-289	141	1	5	5	X
ejpam-289	141	2	.	.	X
ejpam-289	141	3	on	on	ADP
ejpam-289	141	4	p2	p2	NOUN
ejpam-289	141	5	-	-	PUNCT
ejpam-289	141	6	continuous	continuous	ADJ
ejpam-289	141	7	functions	function	NOUN
ejpam-289	141	8	now	now	ADV
ejpam-289	141	9	we	we	PRON
ejpam-289	141	10	shall	shall	AUX
ejpam-289	141	11	give	give	VERB
ejpam-289	141	12	another	another	DET
ejpam-289	141	13	concept	concept	NOUN
ejpam-289	141	14	of	of	ADP
ejpam-289	141	15	pairwise	pairwise	NOUN
ejpam-289	141	16	continuous	continuous	ADJ
ejpam-289	141	17	functions	function	NOUN
ejpam-289	141	18	and	and	CCONJ
ejpam-289	141	19	pairwise	pairwise	NOUN
ejpam-289	141	20	homeomorphism	homeomorphism	PROPN
ejpam-289	141	21	in	in	ADP
ejpam-289	141	22	the	the	DET
ejpam-289	141	23	sense	sense	NOUN
ejpam-289	141	24	of	of	ADP
ejpam-289	141	25	a.	a.	NOUN
ejpam-289	141	26	tallafha	tallafha	NOUN
ejpam-289	142	1	[	[	X
ejpam-289	142	2	5	5	NUM
ejpam-289	142	3	]	]	PUNCT
ejpam-289	142	4	and	and	CCONJ
ejpam-289	142	5	study	study	VERB
ejpam-289	142	6	its	its	PRON
ejpam-289	142	7	properties	property	NOUN
ejpam-289	142	8	.	.	PUNCT
ejpam-289	143	1	definition	definition	NOUN
ejpam-289	143	2	5.1	5.1	NUM
ejpam-289	143	3	.	.	PUNCT
ejpam-289	144	1	a	a	DET
ejpam-289	144	2	function	function	NOUN
ejpam-289	144	3	f	f	NOUN
ejpam-289	144	4	:	:	PUNCT
ejpam-289	144	5	(	(	PUNCT
ejpam-289	144	6	x	x	X
ejpam-289	144	7	,	,	PUNCT
ejpam-289	144	8	p	p	X
ejpam-289	144	9	,	,	PUNCT
ejpam-289	144	10	q	q	NOUN
ejpam-289	144	11	)	)	PUNCT
ejpam-289	144	12	→	→	SYM
ejpam-289	144	13	(	(	PUNCT
ejpam-289	144	14	y	y	NOUN
ejpam-289	144	15	,	,	PUNCT
ejpam-289	144	16	r	r	NOUN
ejpam-289	144	17	,	,	PUNCT
ejpam-289	144	18	t	t	PROPN
ejpam-289	144	19	)	)	PUNCT
ejpam-289	144	20	is	be	AUX
ejpam-289	144	21	said	say	VERB
ejpam-289	144	22	to	to	PART
ejpam-289	144	23	be	be	AUX
ejpam-289	144	24	p2	p2	NOUN
ejpam-289	144	25	-	-	PUNCT
ejpam-289	144	26	continuous	continuous	ADJ
ejpam-289	144	27	if	if	SCONJ
ejpam-289	144	28	the	the	DET
ejpam-289	144	29	inverse	inverse	NOUN
ejpam-289	144	30	image	image	NOUN
ejpam-289	144	31	f	f	PROPN
ejpam-289	144	32	−1	−1	NOUN
ejpam-289	144	33	(	(	PUNCT
ejpam-289	144	34	u	u	NOUN
ejpam-289	144	35	)	)	PUNCT
ejpam-289	144	36	∈	∈	PROPN
ejpam-289	144	37	p	p	NOUN
ejpam-289	144	38	∪q	∪q	NUM
ejpam-289	144	39	for	for	ADP
ejpam-289	144	40	every	every	DET
ejpam-289	144	41	u	u	PROPN
ejpam-289	144	42	∈	∈	PROPN
ejpam-289	144	43	r	r	NOUN
ejpam-289	144	44	∪t	∪t	NUM
ejpam-289	144	45	,	,	PUNCT
ejpam-289	144	46	or	or	CCONJ
ejpam-289	144	47	equivalently	equivalently	ADV
ejpam-289	144	48	,	,	PUNCT
ejpam-289	144	49	f	f	PROPN
ejpam-289	144	50	−1	−1	NOUN
ejpam-289	144	51	(	(	PUNCT
ejpam-289	144	52	u	u	NOUN
ejpam-289	144	53	)	)	PUNCT
ejpam-289	144	54	is	be	AUX
ejpam-289	144	55	p1	p1	NOUN
ejpam-289	144	56	-	-	PUNCT
ejpam-289	144	57	open	open	ADJ
ejpam-289	144	58	in	in	ADP
ejpam-289	144	59	x	x	PUNCT
ejpam-289	144	60	for	for	SCONJ
ejpam-289	144	61	every	every	DET
ejpam-289	144	62	u	u	NOUN
ejpam-289	144	63	is	be	AUX
ejpam-289	144	64	p1	p1	NOUN
ejpam-289	144	65	-	-	PUNCT
ejpam-289	144	66	open	open	ADJ
ejpam-289	144	67	in	in	ADP
ejpam-289	144	68	y	y	PROPN
ejpam-289	144	69	.	.	PUNCT
ejpam-289	145	1	definition	definition	NOUN
ejpam-289	145	2	5.2	5.2	NUM
ejpam-289	145	3	.	.	PUNCT
ejpam-289	146	1	a	a	DET
ejpam-289	146	2	function	function	NOUN
ejpam-289	146	3	f	f	NOUN
ejpam-289	146	4	:	:	PUNCT
ejpam-289	146	5	(	(	PUNCT
ejpam-289	146	6	x	x	X
ejpam-289	146	7	,	,	PUNCT
ejpam-289	146	8	p	p	NOUN
ejpam-289	146	9	,	,	PUNCT
ejpam-289	146	10	q)→	q)→	PROPN
ejpam-289	146	11	(	(	PUNCT
ejpam-289	146	12	y	y	PROPN
ejpam-289	146	13	,	,	PUNCT
ejpam-289	146	14	r	r	NOUN
ejpam-289	146	15	,	,	PUNCT
ejpam-289	146	16	t	t	PROPN
ejpam-289	146	17	)	)	PUNCT
ejpam-289	146	18	is	be	AUX
ejpam-289	146	19	said	say	VERB
ejpam-289	146	20	to	to	PART
ejpam-289	146	21	be	be	AUX
ejpam-289	146	22	p2	p2	NOUN
ejpam-289	146	23	-	-	PUNCT
ejpam-289	146	24	homeomorphism	homeomorphism	NOUN
ejpam-289	146	25	if	if	SCONJ
ejpam-289	146	26	f	f	PROPN
ejpam-289	146	27	is	be	AUX
ejpam-289	146	28	bijection	bijection	NOUN
ejpam-289	146	29	,	,	PUNCT
ejpam-289	146	30	p2	p2	NOUN
ejpam-289	146	31	-	-	PUNCT
ejpam-289	146	32	continuous	continuous	ADJ
ejpam-289	146	33	and	and	CCONJ
ejpam-289	146	34	f	f	NOUN
ejpam-289	146	35	−1	−1	NOUN
ejpam-289	146	36	:	:	PUNCT
ejpam-289	146	37	(	(	PUNCT
ejpam-289	146	38	y	y	NOUN
ejpam-289	146	39	,	,	PUNCT
ejpam-289	146	40	r	r	NOUN
ejpam-289	146	41	,	,	PUNCT
ejpam-289	146	42	t	t	NOUN
ejpam-289	146	43	)	)	PUNCT
ejpam-289	146	44	→	→	SYM
ejpam-289	146	45	(	(	PUNCT
ejpam-289	146	46	x	x	INTJ
ejpam-289	146	47	,	,	PUNCT
ejpam-289	146	48	p	p	X
ejpam-289	146	49	,	,	PUNCT
ejpam-289	146	50	q	q	NOUN
ejpam-289	146	51	)	)	PUNCT
ejpam-289	146	52	is	be	AUX
ejpam-289	146	53	p2	p2	NOUN
ejpam-289	146	54	-	-	PUNCT
ejpam-289	146	55	continuous	continuous	ADJ
ejpam-289	146	56	.	.	PUNCT
ejpam-289	147	1	the	the	DET
ejpam-289	147	2	bitopological	bitopological	ADJ
ejpam-289	147	3	spaces	space	NOUN
ejpam-289	147	4	(	(	PUNCT
ejpam-289	147	5	x	x	INTJ
ejpam-289	147	6	,	,	PUNCT
ejpam-289	147	7	p	p	X
ejpam-289	147	8	,	,	PUNCT
ejpam-289	147	9	q	q	PROPN
ejpam-289	147	10	)	)	PUNCT
ejpam-289	147	11	and	and	CCONJ
ejpam-289	147	12	(	(	PUNCT
ejpam-289	147	13	y	y	NOUN
ejpam-289	147	14	,	,	PUNCT
ejpam-289	147	15	r	r	NOUN
ejpam-289	147	16	,	,	PUNCT
ejpam-289	147	17	t	t	PROPN
ejpam-289	147	18	)	)	PUNCT
ejpam-289	147	19	are	be	AUX
ejpam-289	147	20	then	then	ADV
ejpam-289	147	21	called	call	VERB
ejpam-289	147	22	p2	p2	NOUN
ejpam-289	147	23	-	-	PUNCT
ejpam-289	147	24	homeomorphic	homeomorphic	ADJ
ejpam-289	147	25	.	.	PUNCT
ejpam-289	148	1	a.	a.	PROPN
ejpam-289	148	2	tallafha	tallafha	PROPN
ejpam-289	148	3	et	et	PROPN
ejpam-289	148	4	.	.	PUNCT
ejpam-289	149	1	al	al	PROPN
ejpam-289	149	2	.	.	PUNCT
ejpam-289	150	1	[	[	X
ejpam-289	150	2	5	5	NUM
ejpam-289	150	3	]	]	PUNCT
ejpam-289	150	4	called	call	VERB
ejpam-289	150	5	p2	p2	NOUN
ejpam-289	150	6	-	-	PUNCT
ejpam-289	150	7	continuous	continuous	ADJ
ejpam-289	150	8	function	function	NOUN
ejpam-289	150	9	in	in	ADP
ejpam-289	150	10	definition	definition	NOUN
ejpam-289	150	11	5.1	5.1	NUM
ejpam-289	150	12	as	as	ADP
ejpam-289	150	13	pcontinuous	pcontinuous	ADJ
ejpam-289	150	14	function	function	NOUN
ejpam-289	150	15	and	and	CCONJ
ejpam-289	150	16	p2	p2	NOUN
ejpam-289	150	17	-	-	PUNCT
ejpam-289	150	18	homeomorphism	homeomorphism	NOUN
ejpam-289	150	19	in	in	ADP
ejpam-289	150	20	definition	definition	NOUN
ejpam-289	150	21	5.2	5.2	NUM
ejpam-289	150	22	as	as	ADP
ejpam-289	150	23	p	p	NOUN
ejpam-289	150	24	-	-	PUNCT
ejpam-289	150	25	homeomorphism	homeomorphism	NOUN
ejpam-289	150	26	.	.	PUNCT
ejpam-289	151	1	theorem	theorem	VERB
ejpam-289	151	2	5.1	5.1	NUM
ejpam-289	151	3	.	.	PUNCT
ejpam-289	152	1	if	if	SCONJ
ejpam-289	152	2	(	(	PUNCT
ejpam-289	152	3	x	x	INTJ
ejpam-289	152	4	,	,	PUNCT
ejpam-289	152	5	p	p	X
ejpam-289	152	6	,	,	PUNCT
ejpam-289	152	7	q	q	PROPN
ejpam-289	152	8	)	)	PUNCT
ejpam-289	152	9	and	and	CCONJ
ejpam-289	152	10	(	(	PUNCT
ejpam-289	152	11	y	y	NOUN
ejpam-289	152	12	,	,	PUNCT
ejpam-289	152	13	r	r	NOUN
ejpam-289	152	14	,	,	PUNCT
ejpam-289	152	15	t	t	PROPN
ejpam-289	152	16	)	)	PUNCT
ejpam-289	152	17	are	be	AUX
ejpam-289	152	18	bitopological	bitopological	ADJ
ejpam-289	152	19	spaces	space	NOUN
ejpam-289	152	20	and	and	CCONJ
ejpam-289	152	21	f	f	NOUN
ejpam-289	152	22	:	:	PUNCT
ejpam-289	152	23	(	(	PUNCT
ejpam-289	152	24	x	x	X
ejpam-289	152	25	,	,	PUNCT
ejpam-289	152	26	p	p	NOUN
ejpam-289	152	27	,	,	PUNCT
ejpam-289	152	28	q)→	q)→	PROPN
ejpam-289	152	29	(	(	PUNCT
ejpam-289	152	30	y	y	PROPN
ejpam-289	152	31	,	,	PUNCT
ejpam-289	152	32	r	r	NOUN
ejpam-289	152	33	,	,	PUNCT
ejpam-289	152	34	t	t	PROPN
ejpam-289	152	35	)	)	PUNCT
ejpam-289	152	36	be	be	AUX
ejpam-289	152	37	a	a	DET
ejpam-289	152	38	function	function	NOUN
ejpam-289	152	39	,	,	PUNCT
ejpam-289	152	40	then	then	ADV
ejpam-289	152	41	the	the	DET
ejpam-289	152	42	following	following	ADJ
ejpam-289	152	43	statements	statement	NOUN
ejpam-289	152	44	are	be	AUX
ejpam-289	152	45	equivalent	equivalent	ADJ
ejpam-289	152	46	:	:	PUNCT
ejpam-289	152	47	(	(	PUNCT
ejpam-289	152	48	i	i	NOUN
ejpam-289	152	49	)	)	PUNCT
ejpam-289	152	50	f	f	PROPN
ejpam-289	152	51	is	be	AUX
ejpam-289	152	52	p2	p2	NOUN
ejpam-289	152	53	-	-	PUNCT
ejpam-289	152	54	continuous	continuous	ADJ
ejpam-289	152	55	,	,	PUNCT
ejpam-289	152	56	(	(	PUNCT
ejpam-289	152	57	ii	ii	NOUN
ejpam-289	152	58	)	)	PUNCT
ejpam-289	152	59	for	for	ADP
ejpam-289	152	60	each	each	DET
ejpam-289	152	61	x	x	SYM
ejpam-289	152	62	∈	∈	PROPN
ejpam-289	152	63	x	x	X
ejpam-289	152	64	and	and	CCONJ
ejpam-289	152	65	each	each	DET
ejpam-289	152	66	p1	p1	NOUN
ejpam-289	152	67	-	-	PUNCT
ejpam-289	152	68	open	open	NOUN
ejpam-289	152	69	set	set	VERB
ejpam-289	152	70	v	v	NOUN
ejpam-289	152	71	in	in	ADP
ejpam-289	152	72	y	y	PROPN
ejpam-289	152	73	containing	contain	VERB
ejpam-289	152	74	f	f	PROPN
ejpam-289	152	75	(	(	PUNCT
ejpam-289	152	76	x	x	NOUN
ejpam-289	152	77	)	)	PUNCT
ejpam-289	152	78	,	,	PUNCT
ejpam-289	152	79	there	there	PRON
ejpam-289	152	80	exists	exist	VERB
ejpam-289	152	81	a	a	DET
ejpam-289	152	82	p1	p1	NOUN
ejpam-289	152	83	-	-	PUNCT
ejpam-289	152	84	open	open	ADJ
ejpam-289	152	85	set	set	NOUN
ejpam-289	152	86	u	u	NOUN
ejpam-289	152	87	in	in	ADP
ejpam-289	152	88	x	x	PUNCT
ejpam-289	152	89	containing	contain	VERB
ejpam-289	152	90	x	x	PUNCT
ejpam-289	152	91	such	such	ADJ
ejpam-289	152	92	that	that	SCONJ
ejpam-289	152	93	f	f	PROPN
ejpam-289	152	94	(	(	PUNCT
ejpam-289	152	95	u)⊆	u)⊆	PROPN
ejpam-289	152	96	v	v	NOUN
ejpam-289	152	97	.	.	PUNCT
ejpam-289	153	1	(	(	PUNCT
ejpam-289	153	2	iii	iii	X
ejpam-289	153	3	)	)	PUNCT
ejpam-289	153	4	f	f	NOUN
ejpam-289	153	5	−1	−1	NOUN
ejpam-289	153	6	(	(	PUNCT
ejpam-289	153	7	v	v	NOUN
ejpam-289	153	8	)	)	PUNCT
ejpam-289	153	9	is	be	AUX
ejpam-289	153	10	p1	p1	NOUN
ejpam-289	153	11	-	-	PUNCT
ejpam-289	153	12	closed	closed	ADJ
ejpam-289	153	13	in	in	ADP
ejpam-289	153	14	x	x	PUNCT
ejpam-289	153	15	for	for	ADP
ejpam-289	153	16	every	every	DET
ejpam-289	153	17	p1	p1	NOUN
ejpam-289	153	18	-	-	PUNCT
ejpam-289	153	19	closed	close	VERB
ejpam-289	153	20	set	set	VERB
ejpam-289	153	21	v	v	NOUN
ejpam-289	153	22	in	in	ADP
ejpam-289	153	23	y	y	PROPN
ejpam-289	153	24	,	,	PUNCT
ejpam-289	153	25	(	(	PUNCT
ejpam-289	153	26	iv	iv	X
ejpam-289	153	27	)	)	PUNCT
ejpam-289	153	28	for	for	ADP
ejpam-289	153	29	every	every	DET
ejpam-289	153	30	a⊆	a⊆	PROPN
ejpam-289	153	31	x	x	SYM
ejpam-289	153	32	,	,	PUNCT
ejpam-289	153	33	f	f	PROPN
ejpam-289	153	34	�	�	PROPN
ejpam-289	153	35	p1cl	p1cl	PUNCT
ejpam-289	153	36	(	(	PUNCT
ejpam-289	153	37	a	a	X
ejpam-289	153	38	)	)	PUNCT
ejpam-289	153	39	�	�	PROPN
ejpam-289	153	40	⊆	⊆	NUM
ejpam-289	153	41	p1	p1	NOUN
ejpam-289	153	42	-	-	PUNCT
ejpam-289	153	43	cl	cl	NOUN
ejpam-289	153	44	�	�	PROPN
ejpam-289	153	45	f	f	PROPN
ejpam-289	153	46	(	(	PUNCT
ejpam-289	153	47	a	a	PRON
ejpam-289	153	48	)	)	PUNCT
ejpam-289	153	49	�	�	PROPN
ejpam-289	153	50	,	,	PUNCT
ejpam-289	153	51	a.	a.	NOUN
ejpam-289	153	52	kılıçman	kılıçman	PROPN
ejpam-289	153	53	and	and	CCONJ
ejpam-289	153	54	z.	z.	PROPN
ejpam-289	153	55	salleh	salleh	PROPN
ejpam-289	153	56	/	/	PUNCT
ejpam-289	153	57	eur	eur	PROPN
ejpam-289	153	58	.	.	PUNCT
ejpam-289	154	1	j.	j.	PROPN
ejpam-289	154	2	pure	pure	PROPN
ejpam-289	154	3	appl	appl	PROPN
ejpam-289	154	4	.	.	PROPN
ejpam-289	154	5	math	math	PROPN
ejpam-289	154	6	,	,	PUNCT
ejpam-289	154	7	2	2	NUM
ejpam-289	154	8	(	(	PUNCT
ejpam-289	154	9	2009	2009	NUM
ejpam-289	154	10	)	)	PUNCT
ejpam-289	154	11	,	,	PUNCT
ejpam-289	154	12	(	(	PUNCT
ejpam-289	154	13	325	325	NUM
ejpam-289	154	14	-	-	SYM
ejpam-289	154	15	337	337	NUM
ejpam-289	154	16	)	)	PUNCT
ejpam-289	154	17	334	334	NUM
ejpam-289	154	18	(	(	PUNCT
ejpam-289	154	19	v	v	NOUN
ejpam-289	154	20	)	)	PUNCT
ejpam-289	154	21	for	for	ADP
ejpam-289	154	22	every	every	DET
ejpam-289	154	23	b	b	PROPN
ejpam-289	154	24	⊆	⊆	NUM
ejpam-289	154	25	y	y	PROPN
ejpam-289	154	26	,	,	PUNCT
ejpam-289	154	27	p1	p1	NOUN
ejpam-289	154	28	-	-	PUNCT
ejpam-289	154	29	cl	cl	NOUN
ejpam-289	154	30	�	�	PROPN
ejpam-289	154	31	f	f	PROPN
ejpam-289	154	32	−1	−1	NOUN
ejpam-289	154	33	(	(	PUNCT
ejpam-289	154	34	b	b	NOUN
ejpam-289	154	35	)	)	PUNCT
ejpam-289	154	36	�	�	PROPN
ejpam-289	154	37	⊆	⊆	NUM
ejpam-289	154	38	f	f	NOUN
ejpam-289	154	39	−1	−1	NOUN
ejpam-289	154	40	�	�	PROPN
ejpam-289	154	41	p1cl	p1cl	PUNCT
ejpam-289	154	42	(	(	PUNCT
ejpam-289	154	43	b	b	X
ejpam-289	154	44	)	)	PUNCT
ejpam-289	154	45	�	�	PROPN
ejpam-289	154	46	.	.	PUNCT
ejpam-289	155	1	proof	proof	NOUN
ejpam-289	155	2	.	.	PUNCT
ejpam-289	156	1	(	(	PUNCT
ejpam-289	156	2	i	i	NOUN
ejpam-289	156	3	)	)	PUNCT
ejpam-289	156	4	⇔	⇔	PROPN
ejpam-289	156	5	(	(	PUNCT
ejpam-289	156	6	ii	ii	PROPN
ejpam-289	156	7	)	)	PUNCT
ejpam-289	156	8	:	:	PUNCT
ejpam-289	156	9	let	let	VERB
ejpam-289	156	10	x	x	X
ejpam-289	156	11	∈	∈	PROPN
ejpam-289	156	12	x	x	X
ejpam-289	156	13	and	and	CCONJ
ejpam-289	156	14	v	v	NOUN
ejpam-289	156	15	is	be	AUX
ejpam-289	156	16	a	a	DET
ejpam-289	156	17	p1	p1	NOUN
ejpam-289	156	18	-	-	PUNCT
ejpam-289	156	19	open	open	ADJ
ejpam-289	156	20	set	set	NOUN
ejpam-289	156	21	in	in	ADP
ejpam-289	156	22	y	y	NOUN
ejpam-289	156	23	containing	contain	VERB
ejpam-289	156	24	f	f	PROPN
ejpam-289	156	25	(	(	PUNCT
ejpam-289	156	26	x	x	NOUN
ejpam-289	156	27	)	)	PUNCT
ejpam-289	156	28	.	.	PUNCT
ejpam-289	157	1	by	by	ADP
ejpam-289	157	2	(	(	PUNCT
ejpam-289	157	3	i	i	NOUN
ejpam-289	157	4	)	)	PUNCT
ejpam-289	157	5	,	,	PUNCT
ejpam-289	157	6	f	f	PROPN
ejpam-289	157	7	−1	−1	NOUN
ejpam-289	157	8	(	(	PUNCT
ejpam-289	157	9	v	v	NOUN
ejpam-289	157	10	)	)	PUNCT
ejpam-289	157	11	is	be	AUX
ejpam-289	157	12	a	a	DET
ejpam-289	157	13	p1	p1	NOUN
ejpam-289	157	14	-	-	PUNCT
ejpam-289	157	15	open	open	NOUN
ejpam-289	157	16	set	set	NOUN
ejpam-289	157	17	in	in	ADP
ejpam-289	157	18	x	x	PUNCT
ejpam-289	157	19	containing	contain	VERB
ejpam-289	157	20	x	x	PUNCT
ejpam-289	157	21	.	.	PUNCT
ejpam-289	158	1	take	take	VERB
ejpam-289	158	2	u	u	NOUN
ejpam-289	158	3	=	=	PUNCT
ejpam-289	158	4	f	f	X
ejpam-289	158	5	−1	−1	NOUN
ejpam-289	158	6	(	(	PUNCT
ejpam-289	158	7	v	v	NOUN
ejpam-289	158	8	)	)	PUNCT
ejpam-289	158	9	,	,	PUNCT
ejpam-289	158	10	and	and	CCONJ
ejpam-289	158	11	then	then	ADV
ejpam-289	158	12	f	f	PROPN
ejpam-289	158	13	(	(	PUNCT
ejpam-289	158	14	u	u	NOUN
ejpam-289	158	15	)	)	PUNCT
ejpam-289	158	16	=	=	SYM
ejpam-289	158	17	f	f	X
ejpam-289	158	18	�	�	PROPN
ejpam-289	158	19	f	f	PROPN
ejpam-289	158	20	−1	−1	NOUN
ejpam-289	158	21	(	(	PUNCT
ejpam-289	158	22	v	v	NOUN
ejpam-289	158	23	)	)	PUNCT
ejpam-289	158	24	�	�	PROPN
ejpam-289	158	25	⊆	⊆	NUM
ejpam-289	158	26	v	v	NOUN
ejpam-289	158	27	.	.	PUNCT
ejpam-289	159	1	conversely	conversely	ADV
ejpam-289	159	2	,	,	PUNCT
ejpam-289	159	3	let	let	VERB
ejpam-289	159	4	u	u	PRON
ejpam-289	159	5	be	be	AUX
ejpam-289	159	6	a	a	DET
ejpam-289	159	7	p1	p1	NOUN
ejpam-289	159	8	-	-	PUNCT
ejpam-289	159	9	open	open	ADJ
ejpam-289	159	10	set	set	NOUN
ejpam-289	159	11	in	in	ADP
ejpam-289	159	12	y	y	PROPN
ejpam-289	159	13	and	and	CCONJ
ejpam-289	159	14	let	let	VERB
ejpam-289	159	15	x	x	PUNCT
ejpam-289	159	16	∈	∈	PROPN
ejpam-289	159	17	f	f	PROPN
ejpam-289	159	18	−1	−1	NOUN
ejpam-289	159	19	(	(	PUNCT
ejpam-289	159	20	u	u	NOUN
ejpam-289	159	21	)	)	PUNCT
ejpam-289	159	22	.	.	PUNCT
ejpam-289	160	1	then	then	ADV
ejpam-289	160	2	f	f	PROPN
ejpam-289	160	3	(	(	PUNCT
ejpam-289	160	4	x	x	X
ejpam-289	160	5	)	)	PUNCT
ejpam-289	160	6	∈	∈	PROPN
ejpam-289	160	7	u	u	NOUN
ejpam-289	160	8	and	and	CCONJ
ejpam-289	160	9	by	by	ADP
ejpam-289	160	10	(	(	PUNCT
ejpam-289	160	11	ii	ii	NOUN
ejpam-289	160	12	)	)	PUNCT
ejpam-289	160	13	,	,	PUNCT
ejpam-289	160	14	there	there	PRON
ejpam-289	160	15	exists	exist	VERB
ejpam-289	160	16	a	a	DET
ejpam-289	160	17	p1	p1	NOUN
ejpam-289	160	18	-	-	PUNCT
ejpam-289	160	19	open	open	NOUN
ejpam-289	160	20	set	set	VERB
ejpam-289	160	21	v	v	NOUN
ejpam-289	160	22	in	in	ADP
ejpam-289	160	23	x	x	PUNCT
ejpam-289	160	24	containing	contain	VERB
ejpam-289	160	25	x	x	PUNCT
ejpam-289	160	26	such	such	ADJ
ejpam-289	160	27	that	that	SCONJ
ejpam-289	160	28	f	f	PROPN
ejpam-289	160	29	(	(	PUNCT
ejpam-289	160	30	v	v	NOUN
ejpam-289	160	31	)	)	PUNCT
ejpam-289	160	32	⊆	⊆	NUM
ejpam-289	160	33	u	u	NOUN
ejpam-289	160	34	.	.	PUNCT
ejpam-289	161	1	hence	hence	ADV
ejpam-289	161	2	x	x	SYM
ejpam-289	161	3	∈	∈	NOUN
ejpam-289	161	4	v	v	ADP
ejpam-289	161	5	⊆	⊆	NUM
ejpam-289	161	6	f	f	SYM
ejpam-289	161	7	−1	−1	NOUN
ejpam-289	161	8	(	(	PUNCT
ejpam-289	161	9	u	u	NOUN
ejpam-289	161	10	)	)	PUNCT
ejpam-289	161	11	and	and	CCONJ
ejpam-289	161	12	f	f	NUM
ejpam-289	161	13	−1	−1	NOUN
ejpam-289	161	14	(	(	PUNCT
ejpam-289	161	15	u	u	NOUN
ejpam-289	161	16	)	)	PUNCT
ejpam-289	161	17	=	=	PUNCT
ejpam-289	161	18	⋃	⋃	PROPN
ejpam-289	161	19	x∈	x∈	PROPN
ejpam-289	161	20	f	f	PROPN
ejpam-289	161	21	−1(u	−1(u	PROPN
ejpam-289	161	22	)	)	PUNCT
ejpam-289	161	23	v	v	NOUN
ejpam-289	161	24	.	.	PUNCT
ejpam-289	162	1	this	this	PRON
ejpam-289	162	2	shows	show	VERB
ejpam-289	162	3	that	that	SCONJ
ejpam-289	162	4	f	f	PROPN
ejpam-289	162	5	−1	−1	NOUN
ejpam-289	162	6	(	(	PUNCT
ejpam-289	162	7	u	u	NOUN
ejpam-289	162	8	)	)	PUNCT
ejpam-289	162	9	is	be	AUX
ejpam-289	162	10	p1	p1	NOUN
ejpam-289	162	11	-	-	PUNCT
ejpam-289	162	12	open	open	ADJ
ejpam-289	162	13	set	set	NOUN
ejpam-289	162	14	in	in	ADP
ejpam-289	162	15	x	x	X
ejpam-289	162	16	.	.	PUNCT
ejpam-289	163	1	thus	thus	ADV
ejpam-289	163	2	f	f	PROPN
ejpam-289	163	3	is	be	AUX
ejpam-289	163	4	p2	p2	NOUN
ejpam-289	163	5	-	-	PUNCT
ejpam-289	163	6	continuous	continuous	ADJ
ejpam-289	163	7	.	.	PUNCT
ejpam-289	164	1	(	(	PUNCT
ejpam-289	164	2	i)⇔	i)⇔	PROPN
ejpam-289	164	3	(	(	PUNCT
ejpam-289	164	4	iii	iii	NOUN
ejpam-289	164	5	)	)	PUNCT
ejpam-289	164	6	:	:	PUNCT
ejpam-289	164	7	let	let	VERB
ejpam-289	164	8	v	v	NOUN
ejpam-289	164	9	is	be	AUX
ejpam-289	164	10	p1	p1	NOUN
ejpam-289	164	11	-	-	PUNCT
ejpam-289	164	12	closed	close	VERB
ejpam-289	164	13	set	set	NOUN
ejpam-289	164	14	in	in	ADP
ejpam-289	164	15	y	y	PROPN
ejpam-289	164	16	.	.	PUNCT
ejpam-289	165	1	then	then	ADV
ejpam-289	165	2	y	y	PROPN
ejpam-289	165	3	�	�	PROPN
ejpam-289	165	4	v	v	PROPN
ejpam-289	165	5	is	be	AUX
ejpam-289	165	6	p1	p1	NOUN
ejpam-289	165	7	-	-	PUNCT
ejpam-289	165	8	open	open	ADJ
ejpam-289	165	9	set	set	NOUN
ejpam-289	165	10	in	in	ADP
ejpam-289	165	11	y	y	PROPN
ejpam-289	165	12	.	.	PUNCT
ejpam-289	166	1	hence	hence	ADV
ejpam-289	166	2	f	f	PROPN
ejpam-289	166	3	−1	−1	NOUN
ejpam-289	166	4	(	(	PUNCT
ejpam-289	166	5	y	y	PROPN
ejpam-289	166	6	�	�	PROPN
ejpam-289	166	7	v	v	NOUN
ejpam-289	166	8	)	)	PUNCT
ejpam-289	166	9	is	be	AUX
ejpam-289	166	10	p1	p1	NOUN
ejpam-289	166	11	-	-	PUNCT
ejpam-289	166	12	open	open	ADJ
ejpam-289	166	13	set	set	NOUN
ejpam-289	166	14	in	in	ADP
ejpam-289	166	15	x	x	PUNCT
ejpam-289	166	16	by	by	ADP
ejpam-289	166	17	(	(	PUNCT
ejpam-289	166	18	i	i	NOUN
ejpam-289	166	19	)	)	PUNCT
ejpam-289	166	20	.	.	PUNCT
ejpam-289	167	1	since	since	SCONJ
ejpam-289	167	2	f	f	PROPN
ejpam-289	167	3	−1	−1	NOUN
ejpam-289	167	4	(	(	PUNCT
ejpam-289	167	5	v	v	NOUN
ejpam-289	167	6	)	)	PUNCT
ejpam-289	167	7	=	=	SYM
ejpam-289	167	8	x	x	SYM
ejpam-289	167	9	�	�	PROPN
ejpam-289	167	10	f	f	PROPN
ejpam-289	167	11	−1	−1	NOUN
ejpam-289	167	12	(	(	PUNCT
ejpam-289	167	13	y	y	PROPN
ejpam-289	167	14	�	�	PROPN
ejpam-289	167	15	v	v	NUM
ejpam-289	167	16	)	)	PUNCT
ejpam-289	167	17	,	,	PUNCT
ejpam-289	167	18	it	it	PRON
ejpam-289	167	19	follows	follow	VERB
ejpam-289	167	20	that	that	SCONJ
ejpam-289	167	21	f	f	PROPN
ejpam-289	167	22	−1	−1	NOUN
ejpam-289	167	23	(	(	PUNCT
ejpam-289	167	24	v	v	NOUN
ejpam-289	167	25	)	)	PUNCT
ejpam-289	167	26	is	be	AUX
ejpam-289	167	27	p1	p1	NOUN
ejpam-289	167	28	-	-	PUNCT
ejpam-289	167	29	closed	closed	ADJ
ejpam-289	167	30	in	in	ADP
ejpam-289	167	31	x	x	X
ejpam-289	167	32	.	.	PUNCT
ejpam-289	168	1	the	the	DET
ejpam-289	168	2	converse	converse	NOUN
ejpam-289	168	3	can	can	AUX
ejpam-289	168	4	be	be	AUX
ejpam-289	168	5	proved	prove	VERB
ejpam-289	168	6	similarly	similarly	ADV
ejpam-289	168	7	.	.	PUNCT
ejpam-289	169	1	(	(	PUNCT
ejpam-289	169	2	iii	iii	X
ejpam-289	169	3	)	)	PUNCT
ejpam-289	169	4	⇒	⇒	NOUN
ejpam-289	169	5	(	(	PUNCT
ejpam-289	169	6	iv	iv	NUM
ejpam-289	169	7	)	)	PUNCT
ejpam-289	169	8	:	:	PUNCT
ejpam-289	169	9	let	let	VERB
ejpam-289	169	10	v	v	PART
ejpam-289	169	11	be	be	AUX
ejpam-289	169	12	any	any	DET
ejpam-289	169	13	p1	p1	NOUN
ejpam-289	169	14	-	-	PUNCT
ejpam-289	169	15	closed	close	VERB
ejpam-289	169	16	set	set	NOUN
ejpam-289	169	17	in	in	ADP
ejpam-289	169	18	y	y	NOUN
ejpam-289	169	19	containing	contain	VERB
ejpam-289	169	20	f	f	PROPN
ejpam-289	169	21	(	(	PUNCT
ejpam-289	169	22	a	a	NOUN
ejpam-289	169	23	)	)	PUNCT
ejpam-289	169	24	.	.	PUNCT
ejpam-289	170	1	then	then	ADV
ejpam-289	170	2	f	f	PROPN
ejpam-289	170	3	−1	−1	NOUN
ejpam-289	170	4	(	(	PUNCT
ejpam-289	170	5	v	v	NOUN
ejpam-289	170	6	)	)	PUNCT
ejpam-289	170	7	is	be	AUX
ejpam-289	170	8	a	a	DET
ejpam-289	170	9	p1	p1	NOUN
ejpam-289	170	10	-	-	PUNCT
ejpam-289	170	11	closed	close	VERB
ejpam-289	170	12	set	set	NOUN
ejpam-289	170	13	in	in	ADP
ejpam-289	170	14	x	x	PUNCT
ejpam-289	170	15	containing	contain	VERB
ejpam-289	170	16	a	a	PRON
ejpam-289	170	17	by	by	ADP
ejpam-289	170	18	(	(	PUNCT
ejpam-289	170	19	iii	iii	NOUN
ejpam-289	170	20	)	)	PUNCT
ejpam-289	170	21	.	.	PUNCT
ejpam-289	171	1	hence	hence	ADV
ejpam-289	171	2	,	,	PUNCT
ejpam-289	171	3	p1	p1	NOUN
ejpam-289	171	4	-	-	NOUN
ejpam-289	171	5	cl	cl	NOUN
ejpam-289	171	6	(	(	PUNCT
ejpam-289	171	7	a	a	NOUN
ejpam-289	171	8	)	)	PUNCT
ejpam-289	171	9	⊆	⊆	NUM
ejpam-289	171	10	f	f	SYM
ejpam-289	171	11	−1	−1	NOUN
ejpam-289	171	12	(	(	PUNCT
ejpam-289	171	13	v	v	NOUN
ejpam-289	171	14	)	)	PUNCT
ejpam-289	171	15	,	,	PUNCT
ejpam-289	171	16	and	and	CCONJ
ejpam-289	171	17	it	it	PRON
ejpam-289	171	18	follows	follow	VERB
ejpam-289	171	19	that	that	SCONJ
ejpam-289	171	20	f	f	PROPN
ejpam-289	171	21	�	�	PROPN
ejpam-289	171	22	p1cl	p1cl	PUNCT
ejpam-289	171	23	(	(	PUNCT
ejpam-289	171	24	a	a	X
ejpam-289	171	25	)	)	PUNCT
ejpam-289	171	26	�	�	PROPN
ejpam-289	171	27	⊆	⊆	NUM
ejpam-289	171	28	f	f	PROPN
ejpam-289	171	29	�	�	PROPN
ejpam-289	171	30	f	f	PROPN
ejpam-289	171	31	−1	−1	NOUN
ejpam-289	171	32	(	(	PUNCT
ejpam-289	171	33	v	v	NOUN
ejpam-289	171	34	)	)	PUNCT
ejpam-289	171	35	�	�	PROPN
ejpam-289	171	36	⊆	⊆	NUM
ejpam-289	171	37	v	v	NOUN
ejpam-289	171	38	.	.	PUNCT
ejpam-289	172	1	since	since	SCONJ
ejpam-289	172	2	this	this	PRON
ejpam-289	172	3	is	be	AUX
ejpam-289	172	4	true	true	ADJ
ejpam-289	172	5	for	for	ADP
ejpam-289	172	6	any	any	DET
ejpam-289	172	7	p1	p1	NOUN
ejpam-289	172	8	-	-	PUNCT
ejpam-289	172	9	closed	close	VERB
ejpam-289	172	10	set	set	VERB
ejpam-289	172	11	v	v	NOUN
ejpam-289	172	12	in	in	ADP
ejpam-289	172	13	y	y	PROPN
ejpam-289	172	14	containing	contain	VERB
ejpam-289	172	15	f	f	PROPN
ejpam-289	172	16	(	(	PUNCT
ejpam-289	172	17	a	a	PROPN
ejpam-289	172	18	)	)	PUNCT
ejpam-289	172	19	,	,	PUNCT
ejpam-289	172	20	we	we	PRON
ejpam-289	172	21	have	have	VERB
ejpam-289	172	22	f	f	PROPN
ejpam-289	172	23	�	�	PROPN
ejpam-289	172	24	p1cl	p1cl	PUNCT
ejpam-289	172	25	(	(	PUNCT
ejpam-289	172	26	a	a	X
ejpam-289	172	27	)	)	PUNCT
ejpam-289	172	28	�	�	PROPN
ejpam-289	172	29	⊆	⊆	NUM
ejpam-289	172	30	p1	p1	NOUN
ejpam-289	172	31	-	-	PUNCT
ejpam-289	172	32	cl	cl	NOUN
ejpam-289	172	33	�	�	PROPN
ejpam-289	172	34	f	f	PROPN
ejpam-289	172	35	(	(	PUNCT
ejpam-289	172	36	a	a	PROPN
ejpam-289	172	37	)	)	PUNCT
ejpam-289	172	38	�	�	PROPN
ejpam-289	172	39	.	.	PUNCT
ejpam-289	173	1	(	(	PUNCT
ejpam-289	173	2	iv)⇒	iv)⇒	X
ejpam-289	173	3	(	(	PUNCT
ejpam-289	173	4	v	v	NOUN
ejpam-289	173	5	)	)	PUNCT
ejpam-289	173	6	:	:	PUNCT
ejpam-289	173	7	let	let	VERB
ejpam-289	173	8	b	b	PRON
ejpam-289	173	9	⊆	⊆	NUM
ejpam-289	173	10	y	y	PROPN
ejpam-289	173	11	and	and	CCONJ
ejpam-289	173	12	a=	a=	PROPN
ejpam-289	173	13	f	f	X
ejpam-289	173	14	−1	−1	NOUN
ejpam-289	173	15	(	(	PUNCT
ejpam-289	173	16	b	b	NOUN
ejpam-289	173	17	)	)	PUNCT
ejpam-289	173	18	.	.	PUNCT
ejpam-289	174	1	then	then	ADV
ejpam-289	174	2	f	f	X
ejpam-289	174	3	(	(	PUNCT
ejpam-289	174	4	a	a	NOUN
ejpam-289	174	5	)	)	PUNCT
ejpam-289	174	6	⊆	⊆	NUM
ejpam-289	174	7	b	b	NOUN
ejpam-289	174	8	,	,	PUNCT
ejpam-289	174	9	and	and	CCONJ
ejpam-289	174	10	by	by	ADP
ejpam-289	174	11	(	(	PUNCT
ejpam-289	174	12	iv	iv	X
ejpam-289	174	13	)	)	PUNCT
ejpam-289	174	14	,	,	PUNCT
ejpam-289	174	15	f	f	PROPN
ejpam-289	174	16	�	�	PROPN
ejpam-289	174	17	p1cl	p1cl	PUNCT
ejpam-289	174	18	(	(	PUNCT
ejpam-289	174	19	a	a	X
ejpam-289	174	20	)	)	PUNCT
ejpam-289	174	21	�	�	PROPN
ejpam-289	174	22	⊆	⊆	NUM
ejpam-289	174	23	p1	p1	NOUN
ejpam-289	174	24	-	-	PUNCT
ejpam-289	174	25	cl	cl	NOUN
ejpam-289	174	26	�	�	PROPN
ejpam-289	174	27	f	f	PROPN
ejpam-289	174	28	(	(	PUNCT
ejpam-289	174	29	a	a	PRON
ejpam-289	174	30	)	)	PUNCT
ejpam-289	174	31	�	�	PROPN
ejpam-289	174	32	⊆	⊆	NUM
ejpam-289	174	33	p1	p1	NOUN
ejpam-289	174	34	-	-	PUNCT
ejpam-289	174	35	cl	cl	NOUN
ejpam-289	174	36	(	(	PUNCT
ejpam-289	174	37	b	b	NOUN
ejpam-289	174	38	)	)	PUNCT
ejpam-289	174	39	.	.	PUNCT
ejpam-289	175	1	this	this	PRON
ejpam-289	175	2	means	mean	VERB
ejpam-289	175	3	p1	p1	NOUN
ejpam-289	175	4	-	-	NOUN
ejpam-289	175	5	cl	cl	NOUN
ejpam-289	175	6	(	(	PUNCT
ejpam-289	175	7	a)⊆	a)⊆	PROPN
ejpam-289	175	8	f	f	PROPN
ejpam-289	175	9	−1	−1	PROPN
ejpam-289	175	10	�	�	PROPN
ejpam-289	175	11	f	f	PROPN
ejpam-289	175	12	�	�	PROPN
ejpam-289	175	13	p1cl	p1cl	PUNCT
ejpam-289	175	14	(	(	PUNCT
ejpam-289	175	15	a	a	X
ejpam-289	175	16	)	)	PUNCT
ejpam-289	175	17	�	�	PROPN
ejpam-289	175	18	�	�	PROPN
ejpam-289	175	19	⊆	⊆	NUM
ejpam-289	175	20	f	f	NOUN
ejpam-289	175	21	−1	−1	NOUN
ejpam-289	175	22	�	�	PROPN
ejpam-289	175	23	p1cl	p1cl	PUNCT
ejpam-289	175	24	(	(	PUNCT
ejpam-289	175	25	b	b	X
ejpam-289	175	26	)	)	PUNCT
ejpam-289	175	27	�	�	PROPN
ejpam-289	175	28	.	.	PUNCT
ejpam-289	176	1	thus	thus	ADV
ejpam-289	176	2	we	we	PRON
ejpam-289	176	3	have	have	AUX
ejpam-289	176	4	p1	p1	NOUN
ejpam-289	176	5	−	−	PROPN
ejpam-289	176	6	cl	cl	NOUN
ejpam-289	176	7	�	�	PROPN
ejpam-289	176	8	f	f	PROPN
ejpam-289	176	9	−1	−1	NOUN
ejpam-289	176	10	(	(	PUNCT
ejpam-289	176	11	b	b	NOUN
ejpam-289	176	12	)	)	PUNCT
ejpam-289	176	13	�	�	PROPN
ejpam-289	177	1	⊆	⊆	NUM
ejpam-289	177	2	f	f	PROPN
ejpam-289	177	3	−1	−1	NOUN
ejpam-289	177	4	�	�	PROPN
ejpam-289	177	5	p1cl	p1cl	PUNCT
ejpam-289	177	6	(	(	PUNCT
ejpam-289	177	7	b	b	X
ejpam-289	177	8	)	)	PUNCT
ejpam-289	177	9	�	�	NOUN
ejpam-289	177	10	by	by	ADP
ejpam-289	177	11	substituting	substitute	VERB
ejpam-289	177	12	a=	a=	PROPN
ejpam-289	177	13	f	f	X
ejpam-289	177	14	−1	−1	NOUN
ejpam-289	177	15	(	(	PUNCT
ejpam-289	177	16	b	b	NOUN
ejpam-289	177	17	)	)	PUNCT
ejpam-289	177	18	.	.	PUNCT
ejpam-289	178	1	a.	a.	PROPN
ejpam-289	178	2	kılıçman	kılıçman	PROPN
ejpam-289	178	3	and	and	CCONJ
ejpam-289	178	4	z.	z.	PROPN
ejpam-289	178	5	salleh	salleh	PROPN
ejpam-289	178	6	/	/	PUNCT
ejpam-289	178	7	eur	eur	PROPN
ejpam-289	178	8	.	.	PUNCT
ejpam-289	179	1	j.	j.	PROPN
ejpam-289	179	2	pure	pure	PROPN
ejpam-289	179	3	appl	appl	PROPN
ejpam-289	179	4	.	.	PROPN
ejpam-289	179	5	math	math	PROPN
ejpam-289	179	6	,	,	PUNCT
ejpam-289	179	7	2	2	NUM
ejpam-289	179	8	(	(	PUNCT
ejpam-289	179	9	2009	2009	NUM
ejpam-289	179	10	)	)	PUNCT
ejpam-289	179	11	,	,	PUNCT
ejpam-289	179	12	(	(	PUNCT
ejpam-289	179	13	325	325	NUM
ejpam-289	179	14	-	-	SYM
ejpam-289	179	15	337	337	NUM
ejpam-289	179	16	)	)	PUNCT
ejpam-289	179	17	335	335	NUM
ejpam-289	179	18	(	(	PUNCT
ejpam-289	179	19	v	v	NOUN
ejpam-289	179	20	)	)	PUNCT
ejpam-289	179	21	⇒	⇒	NOUN
ejpam-289	179	22	(	(	PUNCT
ejpam-289	179	23	iii	iii	NOUN
ejpam-289	179	24	)	)	PUNCT
ejpam-289	179	25	:	:	PUNCT
ejpam-289	179	26	let	let	VERB
ejpam-289	179	27	v	v	PART
ejpam-289	179	28	be	be	AUX
ejpam-289	179	29	a	a	DET
ejpam-289	179	30	p1	p1	NOUN
ejpam-289	179	31	-	-	PUNCT
ejpam-289	179	32	closed	close	VERB
ejpam-289	179	33	set	set	NOUN
ejpam-289	179	34	in	in	ADP
ejpam-289	179	35	y	y	PROPN
ejpam-289	179	36	.	.	PUNCT
ejpam-289	180	1	then	then	ADV
ejpam-289	180	2	v	v	X
ejpam-289	180	3	=	=	SYM
ejpam-289	180	4	p1	p1	NOUN
ejpam-289	180	5	-	-	PUNCT
ejpam-289	180	6	cl	cl	NOUN
ejpam-289	180	7	(	(	PUNCT
ejpam-289	180	8	v	v	NOUN
ejpam-289	180	9	)	)	PUNCT
ejpam-289	180	10	.	.	PUNCT
ejpam-289	181	1	by	by	ADP
ejpam-289	181	2	(	(	PUNCT
ejpam-289	181	3	v	v	NOUN
ejpam-289	181	4	)	)	PUNCT
ejpam-289	181	5	,	,	PUNCT
ejpam-289	181	6	p1cl	p1cl	PUNCT
ejpam-289	181	7	�	�	PROPN
ejpam-289	181	8	f	f	PROPN
ejpam-289	181	9	−1	−1	NOUN
ejpam-289	181	10	(	(	PUNCT
ejpam-289	181	11	v	v	NOUN
ejpam-289	181	12	)	)	PUNCT
ejpam-289	181	13	�	�	PROPN
ejpam-289	181	14	⊆	⊆	NUM
ejpam-289	181	15	f	f	NOUN
ejpam-289	181	16	−1	−1	NOUN
ejpam-289	181	17	�	�	PROPN
ejpam-289	181	18	p1cl	p1cl	PUNCT
ejpam-289	181	19	(	(	PUNCT
ejpam-289	181	20	v	v	NOUN
ejpam-289	181	21	)	)	PUNCT
ejpam-289	181	22	�	�	PROPN
ejpam-289	181	23	=	=	SYM
ejpam-289	181	24	f	f	X
ejpam-289	181	25	−1	−1	NOUN
ejpam-289	181	26	(	(	PUNCT
ejpam-289	181	27	v	v	NOUN
ejpam-289	181	28	)	)	PUNCT
ejpam-289	181	29	.	.	PUNCT
ejpam-289	182	1	since	since	SCONJ
ejpam-289	182	2	f	f	PROPN
ejpam-289	182	3	−1	−1	NOUN
ejpam-289	182	4	(	(	PUNCT
ejpam-289	182	5	v	v	NOUN
ejpam-289	182	6	)	)	PUNCT
ejpam-289	182	7	⊆	⊆	NUM
ejpam-289	182	8	p1	p1	NOUN
ejpam-289	182	9	-	-	PUNCT
ejpam-289	182	10	cl	cl	NOUN
ejpam-289	182	11	�	�	PROPN
ejpam-289	182	12	f	f	PROPN
ejpam-289	182	13	−1	−1	NOUN
ejpam-289	182	14	(	(	PUNCT
ejpam-289	182	15	v	v	NOUN
ejpam-289	182	16	)	)	PUNCT
ejpam-289	182	17	�	�	PROPN
ejpam-289	182	18	,	,	PUNCT
ejpam-289	182	19	we	we	PRON
ejpam-289	182	20	have	have	VERB
ejpam-289	182	21	f	f	NUM
ejpam-289	182	22	−1	−1	NOUN
ejpam-289	182	23	(	(	PUNCT
ejpam-289	182	24	v	v	NOUN
ejpam-289	182	25	)	)	PUNCT
ejpam-289	182	26	=	=	SYM
ejpam-289	182	27	p1	p1	ADJ
ejpam-289	182	28	-	-	PUNCT
ejpam-289	182	29	cl	cl	NOUN
ejpam-289	182	30	�	�	PROPN
ejpam-289	182	31	f	f	PROPN
ejpam-289	182	32	−1	−1	NOUN
ejpam-289	182	33	(	(	PUNCT
ejpam-289	182	34	v	v	NOUN
ejpam-289	182	35	)	)	PUNCT
ejpam-289	182	36	�	�	PROPN
ejpam-289	182	37	.	.	PUNCT
ejpam-289	183	1	therefore	therefore	ADV
ejpam-289	183	2	f	f	PROPN
ejpam-289	183	3	−1	−1	NOUN
ejpam-289	183	4	(	(	PUNCT
ejpam-289	183	5	v	v	NOUN
ejpam-289	183	6	)	)	PUNCT
ejpam-289	183	7	is	be	AUX
ejpam-289	183	8	p1	p1	NOUN
ejpam-289	183	9	-	-	PUNCT
ejpam-289	183	10	closed	closed	ADJ
ejpam-289	183	11	in	in	ADP
ejpam-289	183	12	x	x	X
ejpam-289	183	13	.	.	PUNCT
ejpam-289	184	1	definition	definition	NOUN
ejpam-289	184	2	5.3	5.3	NUM
ejpam-289	184	3	.	.	PUNCT
ejpam-289	185	1	a	a	DET
ejpam-289	185	2	function	function	NOUN
ejpam-289	185	3	f	f	NOUN
ejpam-289	185	4	:	:	PUNCT
ejpam-289	185	5	(	(	PUNCT
ejpam-289	185	6	x	x	X
ejpam-289	185	7	,	,	PUNCT
ejpam-289	185	8	p	p	NOUN
ejpam-289	185	9	,	,	PUNCT
ejpam-289	185	10	q)→	q)→	PROPN
ejpam-289	185	11	(	(	PUNCT
ejpam-289	185	12	y	y	PROPN
ejpam-289	185	13	,	,	PUNCT
ejpam-289	185	14	r	r	NOUN
ejpam-289	185	15	,	,	PUNCT
ejpam-289	185	16	t	t	PROPN
ejpam-289	185	17	)	)	PUNCT
ejpam-289	185	18	is	be	AUX
ejpam-289	185	19	said	say	VERB
ejpam-289	185	20	to	to	PART
ejpam-289	185	21	be	be	AUX
ejpam-289	185	22	p2	p2	NOUN
ejpam-289	185	23	-	-	PUNCT
ejpam-289	185	24	open	open	ADJ
ejpam-289	185	25	if	if	SCONJ
ejpam-289	185	26	f	f	PROPN
ejpam-289	185	27	(	(	PUNCT
ejpam-289	185	28	u	u	NOUN
ejpam-289	185	29	)	)	PUNCT
ejpam-289	185	30	is	be	AUX
ejpam-289	185	31	p1	p1	NOUN
ejpam-289	185	32	-	-	PUNCT
ejpam-289	185	33	open	open	ADJ
ejpam-289	185	34	in	in	ADP
ejpam-289	185	35	y	y	PROPN
ejpam-289	185	36	for	for	SCONJ
ejpam-289	185	37	every	every	DET
ejpam-289	185	38	u	u	NOUN
ejpam-289	185	39	is	be	AUX
ejpam-289	185	40	p1	p1	NOUN
ejpam-289	185	41	-	-	NOUN
ejpam-289	185	42	open	open	ADJ
ejpam-289	185	43	in	in	ADP
ejpam-289	185	44	x	x	X
ejpam-289	185	45	,	,	PUNCT
ejpam-289	185	46	and	and	CCONJ
ejpam-289	185	47	p2	p2	NOUN
ejpam-289	185	48	-	-	PUNCT
ejpam-289	185	49	closed	closed	ADJ
ejpam-289	185	50	if	if	SCONJ
ejpam-289	185	51	f	f	PROPN
ejpam-289	185	52	(	(	PUNCT
ejpam-289	185	53	v	v	NOUN
ejpam-289	185	54	)	)	PUNCT
ejpam-289	185	55	is	be	AUX
ejpam-289	185	56	p1	p1	NOUN
ejpam-289	185	57	-	-	PUNCT
ejpam-289	185	58	closed	closed	ADJ
ejpam-289	185	59	in	in	ADP
ejpam-289	185	60	y	y	PROPN
ejpam-289	185	61	for	for	ADP
ejpam-289	185	62	every	every	DET
ejpam-289	185	63	v	v	NOUN
ejpam-289	185	64	is	be	AUX
ejpam-289	185	65	p1	p1	NOUN
ejpam-289	185	66	-	-	PUNCT
ejpam-289	185	67	closed	closed	ADJ
ejpam-289	185	68	in	in	ADP
ejpam-289	185	69	x	x	X
ejpam-289	185	70	.	.	PUNCT
ejpam-289	186	1	theorem	theorem	VERB
ejpam-289	186	2	5.2	5.2	NUM
ejpam-289	186	3	.	.	PUNCT
ejpam-289	187	1	let	let	VERB
ejpam-289	187	2	f	f	NOUN
ejpam-289	187	3	:	:	PUNCT
ejpam-289	187	4	(	(	PUNCT
ejpam-289	187	5	x	x	X
ejpam-289	187	6	,	,	PUNCT
ejpam-289	187	7	p	p	X
ejpam-289	187	8	,	,	PUNCT
ejpam-289	187	9	q	q	NOUN
ejpam-289	187	10	)	)	PUNCT
ejpam-289	187	11	→	→	SYM
ejpam-289	187	12	(	(	PUNCT
ejpam-289	187	13	y	y	NOUN
ejpam-289	187	14	,	,	PUNCT
ejpam-289	187	15	r	r	NOUN
ejpam-289	187	16	,	,	PUNCT
ejpam-289	187	17	t	t	PROPN
ejpam-289	187	18	)	)	PUNCT
ejpam-289	187	19	be	be	AUX
ejpam-289	187	20	a	a	DET
ejpam-289	187	21	p2	p2	NOUN
ejpam-289	187	22	-	-	PUNCT
ejpam-289	187	23	continuous	continuous	ADJ
ejpam-289	187	24	,	,	PUNCT
ejpam-289	187	25	surjective	surjective	ADJ
ejpam-289	187	26	and	and	CCONJ
ejpam-289	187	27	p2open	p2open	ADJ
ejpam-289	187	28	function	function	NOUN
ejpam-289	187	29	.	.	PUNCT
ejpam-289	188	1	if	if	SCONJ
ejpam-289	188	2	(	(	PUNCT
ejpam-289	188	3	x	x	INTJ
ejpam-289	188	4	,	,	PUNCT
ejpam-289	188	5	p	p	X
ejpam-289	188	6	,	,	PUNCT
ejpam-289	188	7	q	q	NOUN
ejpam-289	188	8	)	)	PUNCT
ejpam-289	188	9	is	be	AUX
ejpam-289	188	10	p2	p2	NOUN
ejpam-289	188	11	-	-	PUNCT
ejpam-289	188	12	lindelöf	lindelöf	NOUN
ejpam-289	188	13	,	,	PUNCT
ejpam-289	188	14	then	then	ADV
ejpam-289	188	15	(	(	PUNCT
ejpam-289	188	16	y	y	NOUN
ejpam-289	188	17	,	,	PUNCT
ejpam-289	188	18	r	r	NOUN
ejpam-289	188	19	,	,	PUNCT
ejpam-289	188	20	t	t	PROPN
ejpam-289	188	21	)	)	PUNCT
ejpam-289	188	22	is	be	AUX
ejpam-289	188	23	p2	p2	NOUN
ejpam-289	188	24	-	-	PUNCT
ejpam-289	188	25	lindelöf	lindelöf	NOUN
ejpam-289	188	26	.	.	PUNCT
ejpam-289	189	1	proof	proof	NOUN
ejpam-289	189	2	.	.	PUNCT
ejpam-289	190	1	let	let	VERB
ejpam-289	190	2	(	(	PUNCT
ejpam-289	190	3	x	x	INTJ
ejpam-289	190	4	,	,	PUNCT
ejpam-289	190	5	p	p	X
ejpam-289	190	6	,	,	PUNCT
ejpam-289	190	7	q	q	NOUN
ejpam-289	190	8	)	)	PUNCT
ejpam-289	190	9	is	be	AUX
ejpam-289	190	10	a	a	DET
ejpam-289	190	11	p2	p2	ADJ
ejpam-289	190	12	-	-	PUNCT
ejpam-289	190	13	lindelöf	lindelöf	NOUN
ejpam-289	190	14	space	space	NOUN
ejpam-289	190	15	.	.	PUNCT
ejpam-289	191	1	suppose	suppose	VERB
ejpam-289	191	2	�	�	PROPN
ejpam-289	191	3	gi	gi	NOUN
ejpam-289	191	4	:	:	PUNCT
ejpam-289	192	1	i	i	PRON
ejpam-289	192	2	∈∆	∈∆	VERB
ejpam-289	192	3	is	be	AUX
ejpam-289	192	4	a	a	DET
ejpam-289	192	5	p1	p1	NOUN
ejpam-289	192	6	-	-	PUNCT
ejpam-289	192	7	open	open	ADJ
ejpam-289	192	8	cover	cover	NOUN
ejpam-289	192	9	of	of	ADP
ejpam-289	192	10	y	y	PROPN
ejpam-289	192	11	,	,	PUNCT
ejpam-289	192	12	i.e.	i.e.	X
ejpam-289	192	13	,	,	PUNCT
ejpam-289	192	14	y	y	PROPN
ejpam-289	192	15	⊆	⊆	NUM
ejpam-289	192	16	⋃	⋃	SCONJ
ejpam-289	192	17	i∈∆	i∈∆	NOUN
ejpam-289	192	18	gi	gi	VERB
ejpam-289	192	19	with	with	ADP
ejpam-289	192	20	gi	gi	NOUN
ejpam-289	192	21	∈	∈	PROPN
ejpam-289	192	22	r	r	NOUN
ejpam-289	192	23	∪t	∪t	NUM
ejpam-289	192	24	.	.	PUNCT
ejpam-289	193	1	since	since	SCONJ
ejpam-289	193	2	f	f	PROPN
ejpam-289	193	3	:	:	PUNCT
ejpam-289	193	4	(	(	PUNCT
ejpam-289	193	5	x	x	X
ejpam-289	193	6	,	,	PUNCT
ejpam-289	193	7	p	p	X
ejpam-289	193	8	,	,	PUNCT
ejpam-289	193	9	q	q	NOUN
ejpam-289	193	10	)	)	PUNCT
ejpam-289	193	11	→	→	SYM
ejpam-289	193	12	(	(	PUNCT
ejpam-289	193	13	y	y	NOUN
ejpam-289	193	14	,	,	PUNCT
ejpam-289	193	15	r	r	NOUN
ejpam-289	193	16	,	,	PUNCT
ejpam-289	193	17	t	t	PROPN
ejpam-289	193	18	)	)	PUNCT
ejpam-289	193	19	is	be	AUX
ejpam-289	193	20	p2	p2	NOUN
ejpam-289	193	21	-	-	PUNCT
ejpam-289	193	22	continuous	continuous	ADJ
ejpam-289	193	23	and	and	CCONJ
ejpam-289	193	24	surjective	surjective	ADJ
ejpam-289	193	25	,	,	PUNCT
ejpam-289	193	26	then	then	ADV
ejpam-289	193	27	f	f	PROPN
ejpam-289	193	28	−1	−1	NOUN
ejpam-289	193	29	�	�	PROPN
ejpam-289	193	30	gi	gi	NOUN
ejpam-289	193	31	�	�	PROPN
ejpam-289	193	32	∈	∈	PROPN
ejpam-289	193	33	p	p	PROPN
ejpam-289	193	34	∪q	∪q	PUNCT
ejpam-289	193	35	and	and	CCONJ
ejpam-289	193	36	x	x	X
ejpam-289	193	37	=	=	SYM
ejpam-289	193	38	f	f	SYM
ejpam-289	193	39	−1	−1	NOUN
ejpam-289	193	40	(	(	PUNCT
ejpam-289	193	41	y	y	PROPN
ejpam-289	193	42	)	)	PUNCT
ejpam-289	193	43	⊆	⊆	NUM
ejpam-289	193	44	f	f	NOUN
ejpam-289	193	45	−1	−1	NOUN
ejpam-289	193	46	⋃	⋃	SCONJ
ejpam-289	193	47	i∈∆	i∈∆	NOUN
ejpam-289	193	48	gi	gi	X
ejpam-289	193	49	!	!	PUNCT
ejpam-289	194	1	=	=	PUNCT
ejpam-289	194	2	⋃	⋃	VERB
ejpam-289	194	3	i∈∆	i∈∆	NOUN
ejpam-289	194	4	f	f	NOUN
ejpam-289	194	5	−1	−1	NOUN
ejpam-289	194	6	�	�	PROPN
ejpam-289	194	7	gi	gi	PROPN
ejpam-289	194	8	�	�	PROPN
ejpam-289	194	9	.	.	PUNCT
ejpam-289	195	1	hence	hence	ADV
ejpam-289	195	2	�	�	PROPN
ejpam-289	195	3	f	f	PROPN
ejpam-289	195	4	−1	−1	NOUN
ejpam-289	195	5	�	�	PROPN
ejpam-289	195	6	gi	gi	NOUN
ejpam-289	195	7	�	�	PROPN
ejpam-289	195	8	:	:	PUNCT
ejpam-289	195	9	i	i	PRON
ejpam-289	195	10	∈∆	∈∆	VERB
ejpam-289	195	11	is	be	AUX
ejpam-289	195	12	a	a	DET
ejpam-289	195	13	p1	p1	NOUN
ejpam-289	195	14	-	-	PUNCT
ejpam-289	195	15	open	open	ADJ
ejpam-289	195	16	cover	cover	NOUN
ejpam-289	195	17	of	of	ADP
ejpam-289	195	18	x	x	X
ejpam-289	195	19	.	.	PUNCT
ejpam-289	196	1	but	but	CCONJ
ejpam-289	196	2	(	(	PUNCT
ejpam-289	196	3	x	x	X
ejpam-289	196	4	,	,	PUNCT
ejpam-289	196	5	p	p	X
ejpam-289	196	6	,	,	PUNCT
ejpam-289	196	7	q	q	NOUN
ejpam-289	196	8	)	)	PUNCT
ejpam-289	196	9	is	be	AUX
ejpam-289	196	10	p2	p2	NOUN
ejpam-289	196	11	-	-	PUNCT
ejpam-289	196	12	lindelöf	lindelöf	NOUN
ejpam-289	196	13	,	,	PUNCT
ejpam-289	196	14	so	so	CCONJ
ejpam-289	196	15	there	there	PRON
ejpam-289	196	16	exists	exist	VERB
ejpam-289	196	17	a	a	DET
ejpam-289	196	18	countable	countable	ADJ
ejpam-289	196	19	subcover	subcover	NOUN
ejpam-289	196	20	of	of	ADP
ejpam-289	196	21	x	x	PRON
ejpam-289	196	22	,	,	PUNCT
ejpam-289	196	23	say	say	VERB
ejpam-289	196	24	¦	¦	PROPN
ejpam-289	196	25	f	f	PROPN
ejpam-289	196	26	−1	−1	NOUN
ejpam-289	196	27	�	�	PROPN
ejpam-289	196	28	gin	gin	PROPN
ejpam-289	196	29	�	�	PROPN
ejpam-289	196	30	:	:	PUNCT
ejpam-289	197	1	n	n	X
ejpam-289	197	2	∈	∈	PROPN
ejpam-289	197	3	n	n	CCONJ
ejpam-289	197	4	©	©	PROPN
ejpam-289	197	5	such	such	ADJ
ejpam-289	197	6	that	that	SCONJ
ejpam-289	197	7	x	x	SYM
ejpam-289	197	8	⊆	⊆	NUM
ejpam-289	197	9	⋃	⋃	NOUN
ejpam-289	197	10	n∈n	n∈n	NOUN
ejpam-289	197	11	f	f	NOUN
ejpam-289	197	12	−1	−1	NOUN
ejpam-289	197	13	�	�	PROPN
ejpam-289	197	14	gin	gin	PROPN
ejpam-289	197	15	�	�	PROPN
ejpam-289	197	16	.	.	PUNCT
ejpam-289	198	1	accordingly	accordingly	ADV
ejpam-289	198	2	,	,	PUNCT
ejpam-289	198	3	y	y	PROPN
ejpam-289	198	4	=	=	SYM
ejpam-289	198	5	f	f	PROPN
ejpam-289	198	6	(	(	PUNCT
ejpam-289	198	7	x	x	SYM
ejpam-289	198	8	)	)	PUNCT
ejpam-289	198	9	⊆	⊆	NUM
ejpam-289	198	10	f	f	NOUN
ejpam-289	198	11	⋃	⋃	NOUN
ejpam-289	198	12	n∈n	n∈n	NOUN
ejpam-289	198	13	f	f	NOUN
ejpam-289	198	14	−1	−1	NOUN
ejpam-289	198	15	�	�	PROPN
ejpam-289	198	16	gin	gin	NOUN
ejpam-289	198	17	�	�	PROPN
ejpam-289	198	18	!	!	PUNCT
ejpam-289	199	1	=	=	PUNCT
ejpam-289	200	1	⋃	⋃	NOUN
ejpam-289	200	2	n∈n	n∈n	NOUN
ejpam-289	200	3	f	f	PROPN
ejpam-289	200	4	�	�	PROPN
ejpam-289	200	5	f	f	PROPN
ejpam-289	200	6	−1	−1	PROPN
ejpam-289	200	7	�	�	PROPN
ejpam-289	200	8	gin	gin	PROPN
ejpam-289	200	9	�	�	PROPN
ejpam-289	200	10	�	�	PROPN
ejpam-289	200	11	⊆	⊆	NUM
ejpam-289	200	12	⋃	⋃	NOUN
ejpam-289	200	13	n∈n	n∈n	ADJ
ejpam-289	200	14	gin	gin	NOUN
ejpam-289	200	15	.	.	PUNCT
ejpam-289	201	1	thus	thus	ADV
ejpam-289	201	2	we	we	PRON
ejpam-289	201	3	obtain	obtain	VERB
ejpam-289	201	4	¦	¦	NOUN
ejpam-289	201	5	gin	gin	NOUN
ejpam-289	201	6	:	:	PUNCT
ejpam-289	201	7	n	n	X
ejpam-289	201	8	∈	∈	PROPN
ejpam-289	201	9	n	n	PRON
ejpam-289	201	10	©	©	PROPN
ejpam-289	201	11	is	be	AUX
ejpam-289	201	12	a	a	DET
ejpam-289	201	13	countable	countable	ADJ
ejpam-289	201	14	subcover	subcover	NOUN
ejpam-289	201	15	of	of	ADP
ejpam-289	201	16	y	y	PROPN
ejpam-289	201	17	since	since	SCONJ
ejpam-289	201	18	f	f	PROPN
ejpam-289	201	19	:	:	PUNCT
ejpam-289	201	20	(	(	PUNCT
ejpam-289	201	21	x	x	X
ejpam-289	201	22	,	,	PUNCT
ejpam-289	201	23	p	p	X
ejpam-289	201	24	,	,	PUNCT
ejpam-289	201	25	q	q	NOUN
ejpam-289	201	26	)	)	PUNCT
ejpam-289	201	27	→	→	SYM
ejpam-289	201	28	(	(	PUNCT
ejpam-289	201	29	y	y	NOUN
ejpam-289	201	30	,	,	PUNCT
ejpam-289	201	31	r	r	NOUN
ejpam-289	201	32	,	,	PUNCT
ejpam-289	201	33	t	t	PROPN
ejpam-289	201	34	)	)	PUNCT
ejpam-289	201	35	is	be	AUX
ejpam-289	201	36	a	a	DET
ejpam-289	201	37	p2	p2	NOUN
ejpam-289	201	38	-	-	PUNCT
ejpam-289	201	39	open	open	ADJ
ejpam-289	201	40	function	function	NOUN
ejpam-289	201	41	.	.	PUNCT
ejpam-289	202	1	this	this	PRON
ejpam-289	202	2	shows	show	VERB
ejpam-289	202	3	that	that	SCONJ
ejpam-289	202	4	(	(	PUNCT
ejpam-289	202	5	y	y	NOUN
ejpam-289	202	6	,	,	PUNCT
ejpam-289	202	7	r	r	NOUN
ejpam-289	202	8	,	,	PUNCT
ejpam-289	202	9	t	t	PROPN
ejpam-289	202	10	)	)	PUNCT
ejpam-289	202	11	is	be	AUX
ejpam-289	202	12	p2	p2	NOUN
ejpam-289	202	13	-	-	PUNCT
ejpam-289	202	14	lindelöf	lindelöf	NOUN
ejpam-289	202	15	.	.	PUNCT
ejpam-289	202	16	example	example	NOUN
ejpam-289	203	1	5.1	5.1	NUM
ejpam-289	203	2	.	.	PUNCT
ejpam-289	204	1	consider	consider	VERB
ejpam-289	204	2	x	x	PUNCT
ejpam-289	204	3	=	=	PRON
ejpam-289	204	4	{	{	PUNCT
ejpam-289	204	5	a	a	PRON
ejpam-289	204	6	,	,	PUNCT
ejpam-289	204	7	b	b	NOUN
ejpam-289	204	8	,	,	PUNCT
ejpam-289	204	9	c	c	NOUN
ejpam-289	204	10	,	,	PUNCT
ejpam-289	204	11	d	d	NOUN
ejpam-289	204	12	}	}	PUNCT
ejpam-289	204	13	with	with	ADP
ejpam-289	204	14	p	p	NOUN
ejpam-289	204	15	is	be	AUX
ejpam-289	204	16	discrete	discrete	ADJ
ejpam-289	204	17	topology	topology	NOUN
ejpam-289	204	18	and	and	CCONJ
ejpam-289	204	19	topology	topology	NOUN
ejpam-289	204	20	q	q	NOUN
ejpam-289	205	1	=	=	PUNCT
ejpam-289	205	2	{	{	PUNCT
ejpam-289	205	3	;	;	PUNCT
ejpam-289	205	4	,	,	PUNCT
ejpam-289	205	5	{	{	PUNCT
ejpam-289	205	6	a	a	NOUN
ejpam-289	205	7	}	}	PUNCT
ejpam-289	205	8	,	,	PUNCT
ejpam-289	205	9	{	{	PUNCT
ejpam-289	205	10	a	a	DET
ejpam-289	205	11	,	,	PUNCT
ejpam-289	205	12	b	b	NOUN
ejpam-289	205	13	}	}	PUNCT
ejpam-289	205	14	,	,	PUNCT
ejpam-289	205	15	{	{	PUNCT
ejpam-289	205	16	a	a	DET
ejpam-289	205	17	,	,	PUNCT
ejpam-289	205	18	b	b	NOUN
ejpam-289	205	19	,	,	PUNCT
ejpam-289	205	20	c	c	NOUN
ejpam-289	205	21	}	}	PUNCT
ejpam-289	205	22	,	,	PUNCT
ejpam-289	205	23	x	x	X
ejpam-289	205	24	}	}	PUNCT
ejpam-289	205	25	on	on	ADP
ejpam-289	205	26	x	x	X
ejpam-289	205	27	,	,	PUNCT
ejpam-289	205	28	and	and	CCONJ
ejpam-289	205	29	y	y	PROPN
ejpam-289	205	30	=	=	SYM
ejpam-289	205	31	�	�	PROPN
ejpam-289	205	32	x	x	SYM
ejpam-289	205	33	,	,	PUNCT
ejpam-289	205	34	y	y	PROPN
ejpam-289	205	35	,	,	PUNCT
ejpam-289	205	36	z	z	PROPN
ejpam-289	205	37	,	,	PUNCT
ejpam-289	205	38	w	w	NOUN
ejpam-289	205	39	with	with	ADP
ejpam-289	205	40	topologies	topology	NOUN
ejpam-289	205	41	r	r	NOUN
ejpam-289	205	42	=	=	SYM
ejpam-289	205	43	�	�	PROPN
ejpam-289	205	44	;	;	PUNCT
ejpam-289	205	45	,	,	PUNCT
ejpam-289	205	46	{	{	PUNCT
ejpam-289	205	47	x	x	NOUN
ejpam-289	205	48	}	}	PUNCT
ejpam-289	205	49	,	,	PUNCT
ejpam-289	205	50	�	�	PROPN
ejpam-289	205	51	y	y	PROPN
ejpam-289	205	52	,	,	PUNCT
ejpam-289	205	53	�	�	PROPN
ejpam-289	205	54	x	x	SYM
ejpam-289	205	55	,	,	PUNCT
ejpam-289	205	56	y	y	PROPN
ejpam-289	205	57	,	,	PUNCT
ejpam-289	205	58	�	�	PROPN
ejpam-289	205	59	y	y	PROPN
ejpam-289	205	60	,	,	PUNCT
ejpam-289	205	61	z	z	PROPN
ejpam-289	205	62	,	,	PUNCT
ejpam-289	205	63	w	w	PROPN
ejpam-289	205	64	,	,	PUNCT
ejpam-289	205	65	y	y	PROPN
ejpam-289	205	66	and	and	CCONJ
ejpam-289	205	67	t	t	PROPN
ejpam-289	205	68	=	=	SYM
ejpam-289	205	69	�	�	PROPN
ejpam-289	205	70	;	;	PUNCT
ejpam-289	205	71	,	,	PUNCT
ejpam-289	205	72	{	{	PUNCT
ejpam-289	205	73	x	x	NOUN
ejpam-289	205	74	}	}	PUNCT
ejpam-289	205	75	,	,	PUNCT
ejpam-289	205	76	�	�	PROPN
ejpam-289	205	77	y	y	PROPN
ejpam-289	205	78	,	,	PUNCT
ejpam-289	205	79	z	z	PROPN
ejpam-289	205	80	,	,	PUNCT
ejpam-289	205	81	w	w	PROPN
ejpam-289	205	82	,	,	PUNCT
ejpam-289	205	83	y	y	PROPN
ejpam-289	205	84	on	on	ADP
ejpam-289	205	85	y	y	PROPN
ejpam-289	205	86	.	.	PUNCT
ejpam-289	206	1	observe	observe	VERB
ejpam-289	206	2	that	that	SCONJ
ejpam-289	206	3	p	p	NOUN
ejpam-289	206	4	∪q	∪q	NUM
ejpam-289	206	5	is	be	AUX
ejpam-289	206	6	a	a	DET
ejpam-289	206	7	discrete	discrete	ADJ
ejpam-289	206	8	topology	topology	NOUN
ejpam-289	206	9	and	and	CCONJ
ejpam-289	206	10	r	r	NOUN
ejpam-289	206	11	∪t	∪t	NUM
ejpam-289	206	12	=	=	SYM
ejpam-289	206	13	�	�	PROPN
ejpam-289	206	14	;	;	PUNCT
ejpam-289	206	15	,	,	PUNCT
ejpam-289	206	16	{	{	PUNCT
ejpam-289	206	17	x	x	NOUN
ejpam-289	206	18	}	}	PUNCT
ejpam-289	206	19	,	,	PUNCT
ejpam-289	206	20	�	�	PROPN
ejpam-289	206	21	y	y	PROPN
ejpam-289	206	22	,	,	PUNCT
ejpam-289	206	23	�	�	PROPN
ejpam-289	206	24	x	x	SYM
ejpam-289	206	25	,	,	PUNCT
ejpam-289	206	26	y	y	PROPN
ejpam-289	206	27	,	,	PUNCT
ejpam-289	206	28	�	�	PROPN
ejpam-289	206	29	y	y	PROPN
ejpam-289	206	30	,	,	PUNCT
ejpam-289	206	31	z	z	PROPN
ejpam-289	206	32	,	,	PUNCT
ejpam-289	206	33	w	w	PROPN
ejpam-289	206	34	,	,	PUNCT
ejpam-289	206	35	y	y	PROPN
ejpam-289	206	36	a.	a.	NOUN
ejpam-289	206	37	kılıçman	kılıçman	PROPN
ejpam-289	206	38	and	and	CCONJ
ejpam-289	206	39	z.	z.	PROPN
ejpam-289	206	40	salleh	salleh	PROPN
ejpam-289	206	41	/	/	PUNCT
ejpam-289	206	42	eur	eur	PROPN
ejpam-289	206	43	.	.	PUNCT
ejpam-289	207	1	j.	j.	PROPN
ejpam-289	207	2	pure	pure	PROPN
ejpam-289	207	3	appl	appl	PROPN
ejpam-289	207	4	.	.	PROPN
ejpam-289	207	5	math	math	PROPN
ejpam-289	207	6	,	,	PUNCT
ejpam-289	207	7	2	2	NUM
ejpam-289	207	8	(	(	PUNCT
ejpam-289	207	9	2009	2009	NUM
ejpam-289	207	10	)	)	PUNCT
ejpam-289	207	11	,	,	PUNCT
ejpam-289	207	12	(	(	PUNCT
ejpam-289	207	13	325	325	NUM
ejpam-289	207	14	-	-	SYM
ejpam-289	207	15	337	337	NUM
ejpam-289	207	16	)	)	PUNCT
ejpam-289	207	17	336	336	NUM
ejpam-289	207	18	on	on	ADP
ejpam-289	207	19	y	y	PROPN
ejpam-289	207	20	.	.	PUNCT
ejpam-289	208	1	define	define	VERB
ejpam-289	208	2	a	a	DET
ejpam-289	208	3	function	function	NOUN
ejpam-289	208	4	f	f	NOUN
ejpam-289	208	5	:	:	PUNCT
ejpam-289	208	6	(	(	PUNCT
ejpam-289	208	7	x	x	X
ejpam-289	208	8	,	,	PUNCT
ejpam-289	208	9	p	p	X
ejpam-289	208	10	,	,	PUNCT
ejpam-289	208	11	q	q	NOUN
ejpam-289	208	12	)	)	PUNCT
ejpam-289	208	13	→	→	SYM
ejpam-289	208	14	(	(	PUNCT
ejpam-289	208	15	y	y	NOUN
ejpam-289	208	16	,	,	PUNCT
ejpam-289	208	17	r	r	NOUN
ejpam-289	208	18	,	,	PUNCT
ejpam-289	208	19	t	t	PROPN
ejpam-289	208	20	)	)	PUNCT
ejpam-289	208	21	by	by	ADP
ejpam-289	208	22	f	f	PROPN
ejpam-289	208	23	(	(	PUNCT
ejpam-289	208	24	a	a	NOUN
ejpam-289	208	25	)	)	PUNCT
ejpam-289	208	26	=	=	SYM
ejpam-289	208	27	y	y	PROPN
ejpam-289	208	28	,	,	PUNCT
ejpam-289	208	29	f	f	PROPN
ejpam-289	208	30	(	(	PUNCT
ejpam-289	208	31	b	b	NOUN
ejpam-289	208	32	)	)	PUNCT
ejpam-289	209	1	=	=	SYM
ejpam-289	209	2	f	f	X
ejpam-289	209	3	(	(	PUNCT
ejpam-289	209	4	d	d	NOUN
ejpam-289	209	5	)	)	PUNCT
ejpam-289	209	6	=	=	SYM
ejpam-289	209	7	z	z	PROPN
ejpam-289	209	8	and	and	CCONJ
ejpam-289	209	9	f	f	PROPN
ejpam-289	209	10	(	(	PUNCT
ejpam-289	209	11	c	c	NOUN
ejpam-289	209	12	)	)	PUNCT
ejpam-289	209	13	=	=	SYM
ejpam-289	210	1	w.	w.	NOUN
ejpam-289	210	2	thus	thus	ADV
ejpam-289	210	3	the	the	DET
ejpam-289	210	4	function	function	NOUN
ejpam-289	210	5	f	f	NOUN
ejpam-289	210	6	:	:	PUNCT
ejpam-289	210	7	(	(	PUNCT
ejpam-289	210	8	x	x	X
ejpam-289	210	9	,	,	PUNCT
ejpam-289	210	10	p	p	NOUN
ejpam-289	210	11	,	,	PUNCT
ejpam-289	210	12	q)→	q)→	PROPN
ejpam-289	210	13	(	(	PUNCT
ejpam-289	210	14	y	y	PROPN
ejpam-289	210	15	,	,	PUNCT
ejpam-289	210	16	r	r	NOUN
ejpam-289	210	17	,	,	PUNCT
ejpam-289	210	18	t	t	PROPN
ejpam-289	210	19	)	)	PUNCT
ejpam-289	210	20	is	be	AUX
ejpam-289	210	21	p2	p2	NOUN
ejpam-289	210	22	-	-	PUNCT
ejpam-289	210	23	continuous	continuous	ADJ
ejpam-289	210	24	since	since	SCONJ
ejpam-289	210	25	the	the	DET
ejpam-289	210	26	inverse	inverse	NOUN
ejpam-289	210	27	image	image	NOUN
ejpam-289	210	28	of	of	ADP
ejpam-289	210	29	each	each	DET
ejpam-289	210	30	member	member	NOUN
ejpam-289	210	31	of	of	ADP
ejpam-289	210	32	r	r	NOUN
ejpam-289	210	33	∪t	∪t	NUM
ejpam-289	210	34	on	on	ADP
ejpam-289	210	35	y	y	PROPN
ejpam-289	210	36	is	be	AUX
ejpam-289	210	37	a	a	DET
ejpam-289	210	38	member	member	NOUN
ejpam-289	210	39	of	of	ADP
ejpam-289	210	40	p	p	NOUN
ejpam-289	210	41	∪q	∪q	PUNCT
ejpam-289	210	42	on	on	ADP
ejpam-289	210	43	x	x	X
ejpam-289	210	44	.	.	PUNCT
ejpam-289	210	45	example	example	NOUN
ejpam-289	210	46	5.2	5.2	NUM
ejpam-289	210	47	.	.	PUNCT
ejpam-289	211	1	consider	consider	VERB
ejpam-289	211	2	x	x	PUNCT
ejpam-289	211	3	=	=	PRON
ejpam-289	211	4	{	{	PUNCT
ejpam-289	211	5	a	a	PRON
ejpam-289	211	6	,	,	PUNCT
ejpam-289	211	7	b	b	NOUN
ejpam-289	211	8	,	,	PUNCT
ejpam-289	211	9	c	c	NOUN
ejpam-289	211	10	,	,	PUNCT
ejpam-289	211	11	d	d	NOUN
ejpam-289	211	12	}	}	PUNCT
ejpam-289	211	13	with	with	ADP
ejpam-289	211	14	p	p	NOUN
ejpam-289	211	15	=	=	PUNCT
ejpam-289	211	16	{	{	PUNCT
ejpam-289	211	17	;	;	PUNCT
ejpam-289	211	18	,	,	PUNCT
ejpam-289	211	19	{	{	PUNCT
ejpam-289	211	20	a	a	NOUN
ejpam-289	211	21	}	}	PUNCT
ejpam-289	211	22	,	,	PUNCT
ejpam-289	211	23	x	x	NOUN
ejpam-289	211	24	}	}	PUNCT
ejpam-289	211	25	and	and	CCONJ
ejpam-289	211	26	topology	topology	NOUN
ejpam-289	211	27	q	q	NOUN
ejpam-289	211	28	=	=	PUNCT
ejpam-289	211	29	{	{	PUNCT
ejpam-289	211	30	;	;	PUNCT
ejpam-289	211	31	,	,	PUNCT
ejpam-289	211	32	{	{	PUNCT
ejpam-289	211	33	a	a	NOUN
ejpam-289	211	34	}	}	PUNCT
ejpam-289	211	35	,	,	PUNCT
ejpam-289	211	36	{	{	PUNCT
ejpam-289	211	37	a	a	DET
ejpam-289	211	38	,	,	PUNCT
ejpam-289	211	39	b	b	NOUN
ejpam-289	211	40	}	}	PUNCT
ejpam-289	211	41	,	,	PUNCT
ejpam-289	211	42	{	{	PUNCT
ejpam-289	211	43	a	a	DET
ejpam-289	211	44	,	,	PUNCT
ejpam-289	211	45	b	b	NOUN
ejpam-289	211	46	,	,	PUNCT
ejpam-289	211	47	c	c	NOUN
ejpam-289	211	48	}	}	PUNCT
ejpam-289	211	49	,	,	PUNCT
ejpam-289	211	50	x	x	X
ejpam-289	211	51	}	}	PUNCT
ejpam-289	211	52	on	on	ADP
ejpam-289	211	53	x	x	X
ejpam-289	211	54	,	,	PUNCT
ejpam-289	211	55	and	and	CCONJ
ejpam-289	211	56	y	y	PROPN
ejpam-289	211	57	=	=	SYM
ejpam-289	211	58	�	�	PROPN
ejpam-289	211	59	x	x	SYM
ejpam-289	211	60	,	,	PUNCT
ejpam-289	211	61	y	y	PROPN
ejpam-289	211	62	,	,	PUNCT
ejpam-289	211	63	z	z	PROPN
ejpam-289	211	64	,	,	PUNCT
ejpam-289	211	65	w	w	NOUN
ejpam-289	211	66	with	with	ADP
ejpam-289	211	67	topologies	topology	NOUN
ejpam-289	211	68	r	r	NOUN
ejpam-289	211	69	=	=	SYM
ejpam-289	211	70	�	�	PROPN
ejpam-289	211	71	;	;	PUNCT
ejpam-289	211	72	,	,	PUNCT
ejpam-289	211	73	{	{	PUNCT
ejpam-289	211	74	x	x	NOUN
ejpam-289	211	75	}	}	PUNCT
ejpam-289	211	76	,	,	PUNCT
ejpam-289	211	77	�	�	PROPN
ejpam-289	211	78	y	y	PROPN
ejpam-289	211	79	,	,	PUNCT
ejpam-289	211	80	�	�	PROPN
ejpam-289	211	81	x	x	SYM
ejpam-289	211	82	,	,	PUNCT
ejpam-289	211	83	y	y	PROPN
ejpam-289	211	84	,	,	PUNCT
ejpam-289	211	85	�	�	PROPN
ejpam-289	211	86	y	y	PROPN
ejpam-289	211	87	,	,	PUNCT
ejpam-289	211	88	z	z	PROPN
ejpam-289	211	89	,	,	PUNCT
ejpam-289	211	90	w	w	PROPN
ejpam-289	211	91	,	,	PUNCT
ejpam-289	211	92	y	y	PROPN
ejpam-289	211	93	and	and	CCONJ
ejpam-289	211	94	t	t	PROPN
ejpam-289	211	95	=	=	SYM
ejpam-289	211	96	�	�	PROPN
ejpam-289	211	97	;	;	PUNCT
ejpam-289	211	98	,	,	PUNCT
ejpam-289	211	99	{	{	PUNCT
ejpam-289	211	100	x	x	NOUN
ejpam-289	211	101	}	}	PUNCT
ejpam-289	211	102	,	,	PUNCT
ejpam-289	211	103	�	�	PROPN
ejpam-289	211	104	y	y	PROPN
ejpam-289	211	105	,	,	PUNCT
ejpam-289	211	106	z	z	PROPN
ejpam-289	211	107	,	,	PUNCT
ejpam-289	211	108	w	w	PROPN
ejpam-289	211	109	,	,	PUNCT
ejpam-289	211	110	y	y	PROPN
ejpam-289	211	111	on	on	ADP
ejpam-289	211	112	y	y	PROPN
ejpam-289	211	113	.	.	PUNCT
ejpam-289	212	1	observe	observe	VERB
ejpam-289	212	2	that	that	SCONJ
ejpam-289	212	3	p	p	NOUN
ejpam-289	212	4	∪q	∪q	X
ejpam-289	212	5	=	=	SYM
ejpam-289	212	6	{	{	PUNCT
ejpam-289	212	7	;	;	PUNCT
ejpam-289	212	8	,	,	PUNCT
ejpam-289	212	9	{	{	PUNCT
ejpam-289	212	10	a	a	NOUN
ejpam-289	212	11	}	}	PUNCT
ejpam-289	212	12	,	,	PUNCT
ejpam-289	212	13	{	{	PUNCT
ejpam-289	212	14	a	a	DET
ejpam-289	212	15	,	,	PUNCT
ejpam-289	212	16	b	b	NOUN
ejpam-289	212	17	}	}	PUNCT
ejpam-289	212	18	,	,	PUNCT
ejpam-289	212	19	{	{	PUNCT
ejpam-289	212	20	a	a	DET
ejpam-289	212	21	,	,	PUNCT
ejpam-289	212	22	b	b	NOUN
ejpam-289	212	23	,	,	PUNCT
ejpam-289	212	24	c	c	NOUN
ejpam-289	212	25	}	}	PUNCT
ejpam-289	212	26	,	,	PUNCT
ejpam-289	212	27	x	x	X
ejpam-289	212	28	}	}	PUNCT
ejpam-289	212	29	and	and	CCONJ
ejpam-289	212	30	r	r	NOUN
ejpam-289	212	31	∪t	∪t	NUM
ejpam-289	212	32	=	=	SYM
ejpam-289	212	33	�	�	PROPN
ejpam-289	212	34	;	;	PUNCT
ejpam-289	212	35	,	,	PUNCT
ejpam-289	212	36	{	{	PUNCT
ejpam-289	212	37	x	x	NOUN
ejpam-289	212	38	}	}	PUNCT
ejpam-289	212	39	,	,	PUNCT
ejpam-289	212	40	�	�	PROPN
ejpam-289	212	41	y	y	PROPN
ejpam-289	212	42	,	,	PUNCT
ejpam-289	212	43	�	�	PROPN
ejpam-289	212	44	x	x	SYM
ejpam-289	212	45	,	,	PUNCT
ejpam-289	212	46	y	y	PROPN
ejpam-289	212	47	,	,	PUNCT
ejpam-289	212	48	�	�	PROPN
ejpam-289	212	49	y	y	PROPN
ejpam-289	212	50	,	,	PUNCT
ejpam-289	212	51	z	z	PROPN
ejpam-289	212	52	,	,	PUNCT
ejpam-289	212	53	w	w	PROPN
ejpam-289	212	54	,	,	PUNCT
ejpam-289	212	55	y	y	PROPN
ejpam-289	212	56	on	on	ADP
ejpam-289	212	57	y	y	PROPN
ejpam-289	212	58	.	.	PUNCT
ejpam-289	213	1	define	define	VERB
ejpam-289	213	2	a	a	DET
ejpam-289	213	3	function	function	NOUN
ejpam-289	213	4	g	g	NOUN
ejpam-289	213	5	:	:	PUNCT
ejpam-289	213	6	(	(	PUNCT
ejpam-289	213	7	x	x	X
ejpam-289	213	8	,	,	PUNCT
ejpam-289	213	9	p	p	NOUN
ejpam-289	213	10	,	,	PUNCT
ejpam-289	213	11	q)→	q)→	PROPN
ejpam-289	213	12	(	(	PUNCT
ejpam-289	213	13	y	y	PROPN
ejpam-289	213	14	,	,	PUNCT
ejpam-289	213	15	r	r	NOUN
ejpam-289	213	16	,	,	PUNCT
ejpam-289	213	17	t	t	PROPN
ejpam-289	213	18	)	)	PUNCT
ejpam-289	213	19	by	by	ADP
ejpam-289	213	20	g	g	PROPN
ejpam-289	213	21	(	(	PUNCT
ejpam-289	213	22	a	a	NOUN
ejpam-289	213	23	)	)	PUNCT
ejpam-289	213	24	=	=	SYM
ejpam-289	213	25	g	g	PROPN
ejpam-289	213	26	(	(	PUNCT
ejpam-289	213	27	b	b	NOUN
ejpam-289	213	28	)	)	PUNCT
ejpam-289	214	1	=	=	SYM
ejpam-289	214	2	x	x	X
ejpam-289	214	3	,	,	PUNCT
ejpam-289	214	4	g	g	PROPN
ejpam-289	214	5	(	(	PUNCT
ejpam-289	214	6	c	c	NOUN
ejpam-289	214	7	)	)	PUNCT
ejpam-289	214	8	=	=	SYM
ejpam-289	214	9	z	z	NOUN
ejpam-289	214	10	and	and	CCONJ
ejpam-289	214	11	g	g	PROPN
ejpam-289	214	12	(	(	PUNCT
ejpam-289	214	13	d	d	NOUN
ejpam-289	214	14	)	)	PUNCT
ejpam-289	214	15	=	=	SYM
ejpam-289	214	16	w.	w.	NOUN
ejpam-289	214	17	thus	thus	ADV
ejpam-289	214	18	the	the	DET
ejpam-289	214	19	function	function	NOUN
ejpam-289	214	20	g	g	NOUN
ejpam-289	214	21	:	:	PUNCT
ejpam-289	214	22	(	(	PUNCT
ejpam-289	214	23	x	x	X
ejpam-289	214	24	,	,	PUNCT
ejpam-289	214	25	p	p	X
ejpam-289	214	26	,	,	PUNCT
ejpam-289	214	27	q	q	NOUN
ejpam-289	214	28	)	)	PUNCT
ejpam-289	214	29	→	→	SYM
ejpam-289	214	30	(	(	PUNCT
ejpam-289	214	31	y	y	NOUN
ejpam-289	214	32	,	,	PUNCT
ejpam-289	214	33	r	r	NOUN
ejpam-289	214	34	,	,	PUNCT
ejpam-289	214	35	t	t	PROPN
ejpam-289	214	36	)	)	PUNCT
ejpam-289	214	37	is	be	AUX
ejpam-289	214	38	not	not	PART
ejpam-289	214	39	p2	p2	NOUN
ejpam-289	214	40	-	-	PUNCT
ejpam-289	214	41	continuous	continuous	ADJ
ejpam-289	214	42	since	since	SCONJ
ejpam-289	214	43	�	�	PROPN
ejpam-289	214	44	y	y	PROPN
ejpam-289	214	45	,	,	PUNCT
ejpam-289	214	46	z	z	PROPN
ejpam-289	214	47	,	,	PUNCT
ejpam-289	214	48	w	w	PROPN
ejpam-289	214	49	∈	∈	PROPN
ejpam-289	214	50	r	r	NOUN
ejpam-289	214	51	∪t	∪t	NUM
ejpam-289	214	52	but	but	CCONJ
ejpam-289	214	53	its	its	PRON
ejpam-289	214	54	inverse	inverse	NOUN
ejpam-289	214	55	image	image	NOUN
ejpam-289	214	56	g−1	g−1	PROPN
ejpam-289	214	57	�	�	PROPN
ejpam-289	214	58	�	�	PROPN
ejpam-289	214	59	y	y	PROPN
ejpam-289	214	60	,	,	PUNCT
ejpam-289	214	61	z	z	PROPN
ejpam-289	214	62	,	,	PUNCT
ejpam-289	214	63	w	w	PROPN
ejpam-289	214	64	�	�	PROPN
ejpam-289	214	65	=	=	PUNCT
ejpam-289	214	66	{	{	PUNCT
ejpam-289	214	67	c	c	NOUN
ejpam-289	214	68	,	,	PUNCT
ejpam-289	214	69	d	d	NOUN
ejpam-289	214	70	}	}	PUNCT
ejpam-289	214	71	/∈	/∈	PUNCT
ejpam-289	215	1	p	p	NOUN
ejpam-289	215	2	∪q	∪q	NUM
ejpam-289	215	3	.	.	PUNCT
ejpam-289	215	4	example	example	NOUN
ejpam-289	215	5	5.3	5.3	NUM
ejpam-289	215	6	.	.	PUNCT
ejpam-289	216	1	consider	consider	VERB
ejpam-289	216	2	a	a	DET
ejpam-289	216	3	function	function	NOUN
ejpam-289	216	4	f	f	NOUN
ejpam-289	216	5	:	:	PUNCT
ejpam-289	216	6	(	(	PUNCT
ejpam-289	216	7	x	x	X
ejpam-289	216	8	,	,	PUNCT
ejpam-289	216	9	p	p	X
ejpam-289	216	10	,	,	PUNCT
ejpam-289	216	11	q	q	NOUN
ejpam-289	216	12	)	)	PUNCT
ejpam-289	216	13	→	→	SYM
ejpam-289	216	14	(	(	PUNCT
ejpam-289	216	15	y	y	NOUN
ejpam-289	216	16	,	,	PUNCT
ejpam-289	216	17	r	r	NOUN
ejpam-289	216	18	,	,	PUNCT
ejpam-289	216	19	t	t	PROPN
ejpam-289	216	20	)	)	PUNCT
ejpam-289	216	21	as	as	ADP
ejpam-289	216	22	in	in	ADP
ejpam-289	216	23	example	example	NOUN
ejpam-289	216	24	5.1	5.1	NUM
ejpam-289	216	25	.	.	PUNCT
ejpam-289	217	1	observe	observe	VERB
ejpam-289	217	2	that	that	SCONJ
ejpam-289	217	3	the	the	DET
ejpam-289	217	4	function	function	NOUN
ejpam-289	217	5	f	f	NOUN
ejpam-289	217	6	:	:	PUNCT
ejpam-289	217	7	(	(	PUNCT
ejpam-289	217	8	x	x	X
ejpam-289	217	9	,	,	PUNCT
ejpam-289	217	10	p	p	NOUN
ejpam-289	217	11	,	,	PUNCT
ejpam-289	217	12	q)→	q)→	PROPN
ejpam-289	217	13	(	(	PUNCT
ejpam-289	217	14	y	y	PROPN
ejpam-289	217	15	,	,	PUNCT
ejpam-289	217	16	r	r	NOUN
ejpam-289	217	17	,	,	PUNCT
ejpam-289	217	18	t	t	PROPN
ejpam-289	217	19	)	)	PUNCT
ejpam-289	217	20	is	be	AUX
ejpam-289	217	21	not	not	PART
ejpam-289	217	22	p2	p2	NOUN
ejpam-289	217	23	-	-	PUNCT
ejpam-289	217	24	open	open	ADJ
ejpam-289	217	25	since	since	SCONJ
ejpam-289	217	26	{	{	PUNCT
ejpam-289	217	27	b	b	X
ejpam-289	217	28	}	}	PUNCT
ejpam-289	217	29	∈	∈	PROPN
ejpam-289	217	30	p	p	NOUN
ejpam-289	217	31	∪q	∪q	NUM
ejpam-289	217	32	but	but	CCONJ
ejpam-289	217	33	f	f	PROPN
ejpam-289	217	34	(	(	PUNCT
ejpam-289	217	35	{	{	PUNCT
ejpam-289	217	36	b	b	NOUN
ejpam-289	217	37	}	}	PUNCT
ejpam-289	217	38	)	)	PUNCT
ejpam-289	218	1	=	=	PRON
ejpam-289	218	2	{	{	PUNCT
ejpam-289	218	3	z	z	NOUN
ejpam-289	218	4	}	}	PUNCT
ejpam-289	218	5	/∈	/∈	PUNCT
ejpam-289	219	1	r	r	NOUN
ejpam-289	219	2	∪t	∪t	NUM
ejpam-289	219	3	.	.	PUNCT
ejpam-289	220	1	example	example	NOUN
ejpam-289	220	2	5.4	5.4	NUM
ejpam-289	220	3	.	.	PUNCT
ejpam-289	221	1	consider	consider	VERB
ejpam-289	221	2	a	a	DET
ejpam-289	221	3	function	function	NOUN
ejpam-289	221	4	g	g	NOUN
ejpam-289	221	5	:	:	PUNCT
ejpam-289	221	6	(	(	PUNCT
ejpam-289	221	7	x	x	X
ejpam-289	221	8	,	,	PUNCT
ejpam-289	221	9	p	p	X
ejpam-289	221	10	,	,	PUNCT
ejpam-289	221	11	q	q	NOUN
ejpam-289	221	12	)	)	PUNCT
ejpam-289	221	13	→	→	SYM
ejpam-289	221	14	(	(	PUNCT
ejpam-289	221	15	y	y	NOUN
ejpam-289	221	16	,	,	PUNCT
ejpam-289	221	17	r	r	NOUN
ejpam-289	221	18	,	,	PUNCT
ejpam-289	221	19	t	t	PROPN
ejpam-289	221	20	)	)	PUNCT
ejpam-289	221	21	as	as	ADP
ejpam-289	221	22	in	in	ADP
ejpam-289	221	23	example	example	NOUN
ejpam-289	221	24	5.2	5.2	NUM
ejpam-289	221	25	.	.	PUNCT
ejpam-289	222	1	observe	observe	VERB
ejpam-289	222	2	that	that	SCONJ
ejpam-289	222	3	the	the	DET
ejpam-289	222	4	function	function	NOUN
ejpam-289	222	5	g	g	NOUN
ejpam-289	222	6	:	:	PUNCT
ejpam-289	222	7	(	(	PUNCT
ejpam-289	222	8	x	x	X
ejpam-289	222	9	,	,	PUNCT
ejpam-289	222	10	p	p	NOUN
ejpam-289	222	11	,	,	PUNCT
ejpam-289	222	12	q)→	q)→	PROPN
ejpam-289	222	13	(	(	PUNCT
ejpam-289	222	14	y	y	PROPN
ejpam-289	222	15	,	,	PUNCT
ejpam-289	222	16	r	r	NOUN
ejpam-289	222	17	,	,	PUNCT
ejpam-289	222	18	t	t	PROPN
ejpam-289	222	19	)	)	PUNCT
ejpam-289	222	20	is	be	AUX
ejpam-289	222	21	not	not	PART
ejpam-289	222	22	p2	p2	NOUN
ejpam-289	222	23	-	-	PUNCT
ejpam-289	222	24	open	open	ADJ
ejpam-289	222	25	since	since	SCONJ
ejpam-289	222	26	{	{	PUNCT
ejpam-289	222	27	a	a	PRON
ejpam-289	222	28	,	,	PUNCT
ejpam-289	222	29	b	b	NOUN
ejpam-289	222	30	,	,	PUNCT
ejpam-289	222	31	c	c	NOUN
ejpam-289	222	32	}	}	PUNCT
ejpam-289	222	33	∈	∈	PROPN
ejpam-289	222	34	p	p	NOUN
ejpam-289	222	35	∪q	∪q	NUM
ejpam-289	222	36	but	but	CCONJ
ejpam-289	222	37	g	g	PROPN
ejpam-289	222	38	(	(	PUNCT
ejpam-289	222	39	{	{	PUNCT
ejpam-289	222	40	a	a	PRON
ejpam-289	222	41	,	,	PUNCT
ejpam-289	222	42	b	b	NOUN
ejpam-289	222	43	,	,	PUNCT
ejpam-289	222	44	c	c	NOUN
ejpam-289	222	45	}	}	PUNCT
ejpam-289	222	46	)	)	PUNCT
ejpam-289	222	47	=	=	PRON
ejpam-289	223	1	{	{	PUNCT
ejpam-289	223	2	x	x	X
ejpam-289	223	3	,	,	PUNCT
ejpam-289	223	4	z	z	NOUN
ejpam-289	223	5	}	}	PUNCT
ejpam-289	223	6	/∈	/∈	PUNCT
ejpam-289	223	7	r	r	NOUN
ejpam-289	223	8	∪t	∪t	NUM
ejpam-289	223	9	.	.	PUNCT
ejpam-289	224	1	example	example	NOUN
ejpam-289	224	2	5.5	5.5	NUM
ejpam-289	224	3	.	.	PUNCT
ejpam-289	225	1	the	the	DET
ejpam-289	225	2	function	function	NOUN
ejpam-289	225	3	f	f	NOUN
ejpam-289	225	4	:	:	PUNCT
ejpam-289	225	5	(	(	PUNCT
ejpam-289	225	6	x	x	X
ejpam-289	225	7	,	,	PUNCT
ejpam-289	225	8	p	p	X
ejpam-289	225	9	,	,	PUNCT
ejpam-289	225	10	q	q	NOUN
ejpam-289	225	11	)	)	PUNCT
ejpam-289	225	12	→	→	SYM
ejpam-289	225	13	(	(	PUNCT
ejpam-289	225	14	y	y	NOUN
ejpam-289	225	15	,	,	PUNCT
ejpam-289	225	16	r	r	NOUN
ejpam-289	225	17	,	,	PUNCT
ejpam-289	225	18	t	t	PROPN
ejpam-289	225	19	)	)	PUNCT
ejpam-289	225	20	in	in	ADP
ejpam-289	225	21	example	example	NOUN
ejpam-289	225	22	5.1	5.1	NUM
ejpam-289	225	23	is	be	AUX
ejpam-289	225	24	not	not	PART
ejpam-289	225	25	p2homeomorphism	p2homeomorphism	NOUN
ejpam-289	225	26	since	since	SCONJ
ejpam-289	225	27	f	f	PROPN
ejpam-289	225	28	−1	−1	NOUN
ejpam-289	225	29	:	:	PUNCT
ejpam-289	225	30	(	(	PUNCT
ejpam-289	225	31	y	y	NOUN
ejpam-289	225	32	,	,	PUNCT
ejpam-289	225	33	r	r	NOUN
ejpam-289	225	34	,	,	PUNCT
ejpam-289	225	35	t	t	NOUN
ejpam-289	225	36	)	)	PUNCT
ejpam-289	225	37	→	→	SYM
ejpam-289	225	38	(	(	PUNCT
ejpam-289	225	39	x	x	INTJ
ejpam-289	225	40	,	,	PUNCT
ejpam-289	225	41	p	p	X
ejpam-289	225	42	,	,	PUNCT
ejpam-289	225	43	q	q	NOUN
ejpam-289	225	44	)	)	PUNCT
ejpam-289	225	45	is	be	AUX
ejpam-289	225	46	not	not	PART
ejpam-289	225	47	p2	p2	ADJ
ejpam-289	225	48	-	-	PUNCT
ejpam-289	225	49	continuous	continuous	ADJ
ejpam-289	225	50	,	,	PUNCT
ejpam-289	225	51	and	and	CCONJ
ejpam-289	225	52	the	the	DET
ejpam-289	225	53	function	function	NOUN
ejpam-289	225	54	g	g	NOUN
ejpam-289	225	55	:	:	PUNCT
ejpam-289	225	56	(	(	PUNCT
ejpam-289	225	57	x	x	X
ejpam-289	225	58	,	,	PUNCT
ejpam-289	225	59	p	p	NOUN
ejpam-289	225	60	,	,	PUNCT
ejpam-289	225	61	q)→	q)→	PROPN
ejpam-289	225	62	(	(	PUNCT
ejpam-289	225	63	y	y	PROPN
ejpam-289	225	64	,	,	PUNCT
ejpam-289	225	65	r	r	NOUN
ejpam-289	225	66	,	,	PUNCT
ejpam-289	225	67	t	t	PROPN
ejpam-289	225	68	)	)	PUNCT
ejpam-289	225	69	in	in	ADP
ejpam-289	225	70	example	example	NOUN
ejpam-289	225	71	5.2	5.2	NUM
ejpam-289	225	72	is	be	AUX
ejpam-289	225	73	not	not	PART
ejpam-289	225	74	p2	p2	NOUN
ejpam-289	225	75	-	-	PUNCT
ejpam-289	225	76	homeomorphism	homeomorphism	NOUN
ejpam-289	225	77	since	since	SCONJ
ejpam-289	225	78	it	it	PRON
ejpam-289	225	79	is	be	AUX
ejpam-289	225	80	not	not	PART
ejpam-289	225	81	p2	p2	ADJ
ejpam-289	225	82	-	-	PUNCT
ejpam-289	225	83	continuous	continuous	ADJ
ejpam-289	225	84	.	.	PUNCT
ejpam-289	226	1	recall	recall	NOUN
ejpam-289	226	2	that	that	PRON
ejpam-289	226	3	,	,	PUNCT
ejpam-289	226	4	a	a	DET
ejpam-289	226	5	property	property	NOUN
ejpam-289	226	6	p	p	NOUN
ejpam-289	226	7	of	of	ADP
ejpam-289	226	8	sets	set	NOUN
ejpam-289	226	9	is	be	AUX
ejpam-289	226	10	called	call	VERB
ejpam-289	226	11	topological	topological	ADJ
ejpam-289	226	12	property	property	NOUN
ejpam-289	226	13	if	if	SCONJ
ejpam-289	226	14	whenever	whenever	SCONJ
ejpam-289	226	15	a	a	DET
ejpam-289	226	16	topological	topological	ADJ
ejpam-289	226	17	space	space	NOUN
ejpam-289	226	18	(	(	PUNCT
ejpam-289	226	19	x	x	X
ejpam-289	226	20	,	,	PUNCT
ejpam-289	226	21	τ	τ	X
ejpam-289	226	22	)	)	PUNCT
ejpam-289	226	23	has	have	VERB
ejpam-289	226	24	property	property	NOUN
ejpam-289	226	25	p	p	NOUN
ejpam-289	226	26	,	,	PUNCT
ejpam-289	226	27	then	then	ADV
ejpam-289	226	28	every	every	DET
ejpam-289	226	29	space	space	NOUN
ejpam-289	226	30	homeomorphic	homeomorphic	ADJ
ejpam-289	226	31	to	to	ADP
ejpam-289	226	32	(	(	PUNCT
ejpam-289	226	33	x	x	X
ejpam-289	226	34	,	,	PUNCT
ejpam-289	226	35	τ	τ	X
ejpam-289	226	36	)	)	PUNCT
ejpam-289	226	37	also	also	ADV
ejpam-289	226	38	has	have	VERB
ejpam-289	226	39	property	property	NOUN
ejpam-289	226	40	p.	p.	NOUN
ejpam-289	226	41	in	in	ADP
ejpam-289	226	42	the	the	DET
ejpam-289	226	43	case	case	NOUN
ejpam-289	226	44	of	of	ADP
ejpam-289	226	45	bitopological	bitopological	ADJ
ejpam-289	226	46	space	space	NOUN
ejpam-289	226	47	(	(	PUNCT
ejpam-289	226	48	x	x	X
ejpam-289	226	49	,	,	PUNCT
ejpam-289	226	50	p	p	X
ejpam-289	226	51	,	,	PUNCT
ejpam-289	226	52	q	q	NOUN
ejpam-289	226	53	)	)	PUNCT
ejpam-289	226	54	,	,	PUNCT
ejpam-289	226	55	there	there	PRON
ejpam-289	226	56	are	be	VERB
ejpam-289	226	57	three	three	NUM
ejpam-289	226	58	types	type	NOUN
ejpam-289	226	59	of	of	ADP
ejpam-289	226	60	topological	topological	ADJ
ejpam-289	226	61	properties	property	NOUN
ejpam-289	226	62	since	since	SCONJ
ejpam-289	226	63	now	now	ADV
ejpam-289	226	64	we	we	PRON
ejpam-289	226	65	have	have	VERB
ejpam-289	226	66	three	three	NUM
ejpam-289	226	67	types	type	NOUN
ejpam-289	226	68	of	of	ADP
ejpam-289	226	69	pairwise	pairwise	PROPN
ejpam-289	226	70	homeomorphism	homeomorphism	NOUN
ejpam-289	226	71	.	.	PUNCT
ejpam-289	227	1	references	reference	NOUN
ejpam-289	227	2	337	337	NUM
ejpam-289	227	3	the	the	DET
ejpam-289	227	4	first	first	ADJ
ejpam-289	227	5	two	two	NUM
ejpam-289	227	6	types	type	NOUN
ejpam-289	227	7	,	,	PUNCT
ejpam-289	227	8	the	the	DET
ejpam-289	227	9	reader	reader	NOUN
ejpam-289	227	10	is	be	AUX
ejpam-289	227	11	suggested	suggest	VERB
ejpam-289	227	12	to	to	PART
ejpam-289	227	13	refer	refer	VERB
ejpam-289	227	14	[	[	X
ejpam-289	227	15	3	3	X
ejpam-289	227	16	]	]	PUNCT
ejpam-289	227	17	for	for	ADP
ejpam-289	227	18	the	the	DET
ejpam-289	227	19	detail	detail	NOUN
ejpam-289	227	20	.	.	PUNCT
ejpam-289	228	1	now	now	ADV
ejpam-289	228	2	if	if	SCONJ
ejpam-289	228	3	p2homeomorphism	p2homeomorphism	NOUN
ejpam-289	228	4	considered	consider	VERB
ejpam-289	228	5	,	,	PUNCT
ejpam-289	228	6	we	we	PRON
ejpam-289	228	7	shall	shall	AUX
ejpam-289	228	8	call	call	VERB
ejpam-289	228	9	such	such	ADJ
ejpam-289	228	10	property	property	NOUN
ejpam-289	228	11	as	as	ADP
ejpam-289	228	12	p2	p2	NOUN
ejpam-289	228	13	-	-	PUNCT
ejpam-289	228	14	topological	topological	ADJ
ejpam-289	228	15	property	property	NOUN
ejpam-289	228	16	.	.	PUNCT
ejpam-289	229	1	it	it	PRON
ejpam-289	229	2	is	be	AUX
ejpam-289	229	3	very	very	ADV
ejpam-289	229	4	clear	clear	ADJ
ejpam-289	229	5	that	that	SCONJ
ejpam-289	229	6	,	,	PUNCT
ejpam-289	229	7	theorem	theorem	VERB
ejpam-289	229	8	5.2	5.2	NUM
ejpam-289	229	9	yields	yield	NOUN
ejpam-289	229	10	the	the	DET
ejpam-289	229	11	following	follow	VERB
ejpam-289	229	12	corollary	corollary	NOUN
ejpam-289	229	13	.	.	PUNCT
ejpam-289	230	1	corollary	corollary	ADJ
ejpam-289	230	2	5.1	5.1	NUM
ejpam-289	230	3	.	.	PUNCT
ejpam-289	231	1	a	a	DET
ejpam-289	231	2	p2	p2	ADJ
ejpam-289	231	3	-	-	PUNCT
ejpam-289	231	4	lindelöf	lindelöf	NOUN
ejpam-289	231	5	property	property	NOUN
ejpam-289	231	6	is	be	AUX
ejpam-289	231	7	p2	p2	NOUN
ejpam-289	231	8	-	-	PUNCT
ejpam-289	231	9	topological	topological	ADJ
ejpam-289	231	10	property	property	NOUN
ejpam-289	231	11	.	.	PUNCT
ejpam-289	232	1	references	reference	NOUN
ejpam-289	232	2	[	[	X
ejpam-289	232	3	1	1	X
ejpam-289	232	4	]	]	PUNCT
ejpam-289	232	5	j.	j.	PROPN
ejpam-289	232	6	c.	c.	PROPN
ejpam-289	232	7	kelly	kelly	PROPN
ejpam-289	232	8	,	,	PUNCT
ejpam-289	232	9	bitopological	bitopological	ADJ
ejpam-289	232	10	spaces	space	NOUN
ejpam-289	232	11	,	,	PUNCT
ejpam-289	232	12	proc	proc	NOUN
ejpam-289	232	13	.	.	PUNCT
ejpam-289	233	1	london	london	PROPN
ejpam-289	233	2	math	math	PROPN
ejpam-289	233	3	.	.	PUNCT
ejpam-289	234	1	soc	soc	PROPN
ejpam-289	234	2	.	.	PUNCT
ejpam-289	234	3	,	,	PUNCT
ejpam-289	234	4	(	(	PUNCT
ejpam-289	234	5	3	3	X
ejpam-289	234	6	)	)	PUNCT
ejpam-289	234	7	13	13	NUM
ejpam-289	234	8	(	(	PUNCT
ejpam-289	234	9	1963	1963	NUM
ejpam-289	234	10	)	)	PUNCT
ejpam-289	234	11	,	,	PUNCT
ejpam-289	234	12	71	71	NUM
ejpam-289	234	13	-	-	SYM
ejpam-289	234	14	89	89	NUM
ejpam-289	234	15	.	.	PUNCT
ejpam-289	235	1	[	[	X
ejpam-289	235	2	2	2	X
ejpam-289	235	3	]	]	PUNCT
ejpam-289	235	4	j.	j.	PROPN
ejpam-289	235	5	l.	l.	PROPN
ejpam-289	235	6	kelly	kelly	PROPN
ejpam-289	235	7	,	,	PUNCT
ejpam-289	235	8	general	general	ADJ
ejpam-289	235	9	topology	topology	NOUN
ejpam-289	235	10	,	,	PUNCT
ejpam-289	235	11	springer	springer	NOUN
ejpam-289	235	12	-	-	PUNCT
ejpam-289	235	13	verlag	verlag	PROPN
ejpam-289	235	14	,	,	PUNCT
ejpam-289	235	15	new	new	PROPN
ejpam-289	235	16	york	york	PROPN
ejpam-289	235	17	,	,	PUNCT
ejpam-289	235	18	1955	1955	NUM
ejpam-289	235	19	.	.	PUNCT
ejpam-289	236	1	[	[	X
ejpam-289	236	2	3	3	NUM
ejpam-289	236	3	]	]	PUNCT
ejpam-289	236	4	a.	a.	NOUN
ejpam-289	236	5	kılıçman	kılıçman	PROPN
ejpam-289	236	6	and	and	CCONJ
ejpam-289	236	7	z.	z.	PROPN
ejpam-289	236	8	salleh	salleh	PROPN
ejpam-289	236	9	,	,	PUNCT
ejpam-289	236	10	on	on	ADP
ejpam-289	236	11	pairwise	pairwise	NOUN
ejpam-289	236	12	lindelöf	lindelöf	NOUN
ejpam-289	236	13	bitopological	bitopological	ADJ
ejpam-289	236	14	spaces	space	NOUN
ejpam-289	236	15	,	,	PUNCT
ejpam-289	236	16	topology	topology	NOUN
ejpam-289	236	17	&	&	CCONJ
ejpam-289	236	18	its	its	PRON
ejpam-289	236	19	appl	appl	PROPN
ejpam-289	236	20	.	.	PROPN
ejpam-289	236	21	,	,	PUNCT
ejpam-289	236	22	154	154	NUM
ejpam-289	236	23	(	(	PUNCT
ejpam-289	236	24	8)	8)	NUM
ejpam-289	236	25	(	(	PUNCT
ejpam-289	236	26	2007	2007	NUM
ejpam-289	236	27	)	)	PUNCT
ejpam-289	236	28	,	,	PUNCT
ejpam-289	236	29	1600	1600	NUM
ejpam-289	236	30	-	-	SYM
ejpam-289	236	31	1607	1607	NUM
ejpam-289	236	32	.	.	PUNCT
ejpam-289	237	1	[	[	X
ejpam-289	237	2	4	4	NUM
ejpam-289	237	3	]	]	PUNCT
ejpam-289	237	4	a.	a.	NOUN
ejpam-289	237	5	kılıçman	kılıçman	PROPN
ejpam-289	237	6	and	and	CCONJ
ejpam-289	237	7	z.	z.	PROPN
ejpam-289	237	8	salleh	salleh	PROPN
ejpam-289	237	9	,	,	PUNCT
ejpam-289	237	10	mappings	mapping	NOUN
ejpam-289	237	11	and	and	CCONJ
ejpam-289	237	12	pairwise	pairwise	NOUN
ejpam-289	237	13	continuity	continuity	NOUN
ejpam-289	237	14	on	on	ADP
ejpam-289	237	15	pairwise	pairwise	NOUN
ejpam-289	237	16	lindelöf	lindelöf	NOUN
ejpam-289	237	17	bitopological	bitopological	ADJ
ejpam-289	237	18	spaces	space	NOUN
ejpam-289	237	19	,	,	PUNCT
ejpam-289	237	20	albanian	albanian	PROPN
ejpam-289	237	21	j.	j.	PROPN
ejpam-289	237	22	math	math	PROPN
ejpam-289	237	23	.	.	PROPN
ejpam-289	237	24	,	,	PUNCT
ejpam-289	237	25	1(2	1(2	NUM
ejpam-289	237	26	)	)	PUNCT
ejpam-289	237	27	(	(	PUNCT
ejpam-289	237	28	2007	2007	NUM
ejpam-289	237	29	)	)	PUNCT
ejpam-289	237	30	,	,	PUNCT
ejpam-289	237	31	115–120	115–120	NUM
ejpam-289	237	32	.	.	PUNCT
ejpam-289	238	1	[	[	X
ejpam-289	238	2	5	5	NUM
ejpam-289	238	3	]	]	PUNCT
ejpam-289	238	4	a.	a.	NOUN
ejpam-289	238	5	kılıçman	kılıçman	PROPN
ejpam-289	238	6	and	and	CCONJ
ejpam-289	238	7	z.	z.	PROPN
ejpam-289	238	8	salleh	salleh	PROPN
ejpam-289	238	9	,	,	PUNCT
ejpam-289	238	10	pairwise	pairwise	PROPN
ejpam-289	238	11	almost	almost	ADV
ejpam-289	238	12	lindelöf	lindelöf	VERB
ejpam-289	238	13	bitopological	bitopological	ADJ
ejpam-289	238	14	spaces	space	NOUN
ejpam-289	238	15	,	,	PUNCT
ejpam-289	238	16	journal	journal	NOUN
ejpam-289	238	17	of	of	ADP
ejpam-289	238	18	malaysian	malaysian	PROPN
ejpam-289	238	19	mathematical	mathematical	PROPN
ejpam-289	238	20	sciences	sciences	PROPN
ejpam-289	238	21	,	,	PUNCT
ejpam-289	238	22	1(2)(2007	1(2)(2007	NUM
ejpam-289	238	23	)	)	PUNCT
ejpam-289	238	24	,	,	PUNCT
ejpam-289	238	25	227–238	227–238	NUM
ejpam-289	238	26	.	.	PUNCT
ejpam-289	239	1	[	[	X
ejpam-289	239	2	6	6	NUM
ejpam-289	239	3	]	]	PUNCT
ejpam-289	239	4	a.	a.	NOUN
ejpam-289	239	5	kılıçman	kılıçman	NOUN
ejpam-289	239	6	and	and	CCONJ
ejpam-289	239	7	z.	z.	PROPN
ejpam-289	239	8	salleh	salleh	PROPN
ejpam-289	239	9	,	,	PUNCT
ejpam-289	239	10	pairwise	pairwise	VERB
ejpam-289	239	11	weakly	weakly	ADJ
ejpam-289	239	12	lindelöf	lindelöf	NOUN
ejpam-289	239	13	bitopological	bitopological	ADJ
ejpam-289	239	14	spaces	space	NOUN
ejpam-289	239	15	,	,	PUNCT
ejpam-289	239	16	abstract	abstract	ADJ
ejpam-289	239	17	and	and	CCONJ
ejpam-289	239	18	applied	apply	VERB
ejpam-289	239	19	analysis	analysis	NOUN
ejpam-289	239	20	,	,	PUNCT
ejpam-289	239	21	volume	volume	NOUN
ejpam-289	239	22	2008	2008	NUM
ejpam-289	239	23	,	,	PUNCT
ejpam-289	239	24	article	article	NOUN
ejpam-289	239	25	i	i	PROPN
ejpam-289	239	26	d	d	PROPN
ejpam-289	239	27	184243	184243	NUM
ejpam-289	239	28	,	,	PUNCT
ejpam-289	239	29	13	13	NUM
ejpam-289	239	30	pages	page	NOUN
ejpam-289	239	31	doi:10.1155/2008/184243	doi:10.1155/2008/184243	PROPN
ejpam-289	239	32	.	.	PUNCT
ejpam-289	240	1	[	[	X
ejpam-289	240	2	7	7	X
ejpam-289	240	3	]	]	X
ejpam-289	240	4	w.	w.	PROPN
ejpam-289	240	5	j.	j.	PROPN
ejpam-289	240	6	pervin	pervin	PROPN
ejpam-289	240	7	,	,	PUNCT
ejpam-289	240	8	foundations	foundation	NOUN
ejpam-289	240	9	of	of	ADP
ejpam-289	240	10	general	general	ADJ
ejpam-289	240	11	topology	topology	NOUN
ejpam-289	240	12	,	,	PUNCT
ejpam-289	240	13	academic	academic	ADJ
ejpam-289	240	14	press	press	PROPN
ejpam-289	240	15	,	,	PUNCT
ejpam-289	240	16	inc	inc	PROPN
ejpam-289	240	17	.	.	PROPN
ejpam-289	240	18	,	,	PUNCT
ejpam-289	240	19	london	london	PROPN
ejpam-289	240	20	,	,	PUNCT
ejpam-289	240	21	1964	1964	NUM
ejpam-289	240	22	.	.	PUNCT
ejpam-289	241	1	[	[	X
ejpam-289	241	2	8	8	NUM
ejpam-289	241	3	]	]	PUNCT
ejpam-289	241	4	a.	a.	NOUN
ejpam-289	241	5	tallafha	tallafha	PROPN
ejpam-289	241	6	,	,	PUNCT
ejpam-289	241	7	a.	a.	PROPN
ejpam-289	241	8	al	al	PROPN
ejpam-289	241	9	-	-	PUNCT
ejpam-289	241	10	bsoul	bsoul	PROPN
ejpam-289	241	11	and	and	CCONJ
ejpam-289	241	12	a.	a.	NOUN
ejpam-289	241	13	fora	fora	PROPN
ejpam-289	241	14	,	,	PUNCT
ejpam-289	241	15	countable	countable	ADJ
ejpam-289	241	16	dense	dense	ADJ
ejpam-289	241	17	homogeneous	homogeneous	ADJ
ejpam-289	241	18	bitopological	bitopological	ADJ
ejpam-289	241	19	spaces	space	NOUN
ejpam-289	241	20	,	,	PUNCT
ejpam-289	241	21	tr	tr	VERB
ejpam-289	241	22	.	.	PROPN
ejpam-289	241	23	j.	j.	PROPN
ejpam-289	241	24	math	math	PROPN
ejpam-289	241	25	.	.	PUNCT
ejpam-289	242	1	,	,	PUNCT
ejpam-289	242	2	23	23	NUM
ejpam-289	242	3	(	(	PUNCT
ejpam-289	242	4	1999	1999	NUM
ejpam-289	242	5	)	)	PUNCT
ejpam-289	242	6	,	,	PUNCT
ejpam-289	242	7	233	233	NUM
ejpam-289	242	8	-	-	SYM
ejpam-289	242	9	242	242	NUM
ejpam-289	242	10	c	c	NOUN
ejpam-289	242	11	©	©	PROPN
ejpam-289	242	12	tübi̇tak	tübi̇tak	NOUN
ejpam-289	242	13	.	.	PUNCT
ejpam-289	243	1	[	[	X
ejpam-289	243	2	9	9	NUM
ejpam-289	243	3	]	]	PUNCT
ejpam-289	243	4	s.	s.	PROPN
ejpam-289	243	5	willard	willard	PROPN
ejpam-289	243	6	,	,	PUNCT
ejpam-289	243	7	general	general	ADJ
ejpam-289	243	8	topology	topology	NOUN
ejpam-289	243	9	,	,	PUNCT
ejpam-289	243	10	addison	addison	PROPN
ejpam-289	243	11	-	-	PUNCT
ejpam-289	243	12	wesley	wesley	PROPN
ejpam-289	243	13	,	,	PUNCT
ejpam-289	243	14	canada	canada	PROPN
ejpam-289	243	15	,	,	PUNCT
ejpam-289	243	16	1970	1970	NUM
ejpam-289	243	17	.	.	PUNCT