id	sid	tid	token	lemma	pos
ejpam-1200	1	1	european	european	PROPN
ejpam-1200	1	2	journal	journal	PROPN
ejpam-1200	1	3	of	of	ADP
ejpam-1200	1	4	pure	pure	ADJ
ejpam-1200	1	5	and	and	CCONJ
ejpam-1200	1	6	applied	apply	VERB
ejpam-1200	1	7	mathematics	mathematic	NOUN
ejpam-1200	1	8	vol	vol	NOUN
ejpam-1200	1	9	.	.	PROPN
ejpam-1200	2	1	6	6	NUM
ejpam-1200	2	2	,	,	PUNCT
ejpam-1200	2	3	no	no	INTJ
ejpam-1200	2	4	.	.	NOUN
ejpam-1200	2	5	2	2	NUM
ejpam-1200	2	6	,	,	PUNCT
ejpam-1200	2	7	2013	2013	NUM
ejpam-1200	2	8	,	,	PUNCT
ejpam-1200	2	9	247	247	NUM
ejpam-1200	2	10	-	-	SYM
ejpam-1200	2	11	255	255	NUM
ejpam-1200	2	12	issn	issn	PROPN
ejpam-1200	2	13	1307	1307	NUM
ejpam-1200	2	14	-	-	SYM
ejpam-1200	2	15	5543	5543	NUM
ejpam-1200	2	16	–	–	PUNCT
ejpam-1200	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-1200	2	18	some	some	DET
ejpam-1200	2	19	fundamental	fundamental	ADJ
ejpam-1200	2	20	properties	property	NOUN
ejpam-1200	2	21	of	of	ADP
ejpam-1200	2	22	β	β	ADJ
ejpam-1200	2	23	-	-	ADJ
ejpam-1200	2	24	open	open	ADJ
ejpam-1200	2	25	sets	set	NOUN
ejpam-1200	2	26	in	in	ADP
ejpam-1200	2	27	ideal	ideal	ADJ
ejpam-1200	2	28	bitopological	bitopological	ADJ
ejpam-1200	2	29	spaces	space	NOUN
ejpam-1200	2	30	m.	m.	NOUN
ejpam-1200	2	31	caldas1	caldas1	PROPN
ejpam-1200	2	32	,	,	PUNCT
ejpam-1200	2	33	s.	s.	PROPN
ejpam-1200	2	34	jafari2	jafari2	PROPN
ejpam-1200	2	35	and	and	CCONJ
ejpam-1200	2	36	n.	n.	PROPN
ejpam-1200	2	37	rajesh3,∗	rajesh3,∗	PROPN
ejpam-1200	2	38	1	1	NUM
ejpam-1200	2	39	departamento	departamento	PROPN
ejpam-1200	2	40	de	de	PROPN
ejpam-1200	2	41	matematica	matematica	PROPN
ejpam-1200	2	42	aplicada	aplicada	PROPN
ejpam-1200	2	43	,	,	PUNCT
ejpam-1200	2	44	universidade	universidade	PROPN
ejpam-1200	2	45	federal	federal	PROPN
ejpam-1200	2	46	fluminense	fluminense	PROPN
ejpam-1200	2	47	,	,	PUNCT
ejpam-1200	2	48	rua	rua	PROPN
ejpam-1200	2	49	mario	mario	PROPN
ejpam-1200	2	50	santos	santos	PROPN
ejpam-1200	2	51	braga	braga	PROPN
ejpam-1200	2	52	,	,	PUNCT
ejpam-1200	2	53	s	s	PROPN
ejpam-1200	2	54	/	/	SYM
ejpam-1200	2	55	n	n	CCONJ
ejpam-1200	2	56	,	,	PUNCT
ejpam-1200	2	57	24020	24020	NUM
ejpam-1200	2	58	-	-	SYM
ejpam-1200	2	59	140	140	NUM
ejpam-1200	2	60	,	,	PUNCT
ejpam-1200	2	61	niteroi	niteroi	NOUN
ejpam-1200	2	62	,	,	PUNCT
ejpam-1200	2	63	rj	rj	PROPN
ejpam-1200	2	64	brasil	brasil	PROPN
ejpam-1200	2	65	2	2	NUM
ejpam-1200	2	66	college	college	NOUN
ejpam-1200	2	67	of	of	ADP
ejpam-1200	2	68	vestsjaelland	vestsjaelland	PROPN
ejpam-1200	2	69	south	south	NOUN
ejpam-1200	2	70	,	,	PUNCT
ejpam-1200	2	71	herrestraede	herrestraede	NOUN
ejpam-1200	2	72	11	11	NUM
ejpam-1200	2	73	,	,	PUNCT
ejpam-1200	2	74	4200	4200	NUM
ejpam-1200	2	75	slagelse	slagelse	NOUN
ejpam-1200	2	76	,	,	PUNCT
ejpam-1200	2	77	denmark	denmark	PROPN
ejpam-1200	2	78	3	3	NUM
ejpam-1200	2	79	department	department	NOUN
ejpam-1200	2	80	of	of	ADP
ejpam-1200	2	81	mathematics	mathematic	NOUN
ejpam-1200	2	82	,	,	PUNCT
ejpam-1200	2	83	rajah	rajah	VERB
ejpam-1200	2	84	serfoji	serfoji	ADJ
ejpam-1200	2	85	govt	govt	NOUN
ejpam-1200	2	86	.	.	PUNCT
ejpam-1200	3	1	college	college	NOUN
ejpam-1200	3	2	,	,	PUNCT
ejpam-1200	3	3	thanjavur-613005	thanjavur-613005	NOUN
ejpam-1200	3	4	,	,	PUNCT
ejpam-1200	3	5	tamilnadu	tamilnadu	ADJ
ejpam-1200	3	6	,	,	PUNCT
ejpam-1200	3	7	india	india	PROPN
ejpam-1200	3	8	abstract	abstract	NOUN
ejpam-1200	3	9	.	.	PUNCT
ejpam-1200	4	1	in	in	ADP
ejpam-1200	4	2	this	this	DET
ejpam-1200	4	3	paper	paper	NOUN
ejpam-1200	4	4	we	we	PRON
ejpam-1200	4	5	introduce	introduce	VERB
ejpam-1200	4	6	and	and	CCONJ
ejpam-1200	4	7	characterize	characterize	VERB
ejpam-1200	4	8	the	the	DET
ejpam-1200	4	9	concepts	concept	NOUN
ejpam-1200	4	10	of	of	ADP
ejpam-1200	4	11	β	β	ADJ
ejpam-1200	4	12	-	-	ADJ
ejpam-1200	4	13	open	open	ADJ
ejpam-1200	4	14	sets	set	NOUN
ejpam-1200	4	15	and	and	CCONJ
ejpam-1200	4	16	their	their	PRON
ejpam-1200	4	17	related	related	ADJ
ejpam-1200	4	18	notions	notion	NOUN
ejpam-1200	4	19	in	in	ADP
ejpam-1200	4	20	ideal	ideal	ADJ
ejpam-1200	4	21	bitopological	bitopological	ADJ
ejpam-1200	4	22	spaces	space	NOUN
ejpam-1200	4	23	.	.	PUNCT
ejpam-1200	5	1	2010	2010	NUM
ejpam-1200	5	2	mathematics	mathematic	NOUN
ejpam-1200	5	3	subject	subject	NOUN
ejpam-1200	5	4	classifications	classification	NOUN
ejpam-1200	5	5	:	:	PUNCT
ejpam-1200	5	6	54d10	54d10	NUM
ejpam-1200	5	7	key	key	ADJ
ejpam-1200	5	8	words	word	NOUN
ejpam-1200	5	9	and	and	CCONJ
ejpam-1200	5	10	phrases	phrase	NOUN
ejpam-1200	5	11	:	:	PUNCT
ejpam-1200	5	12	ideal	ideal	ADJ
ejpam-1200	5	13	bitopological	bitopological	ADJ
ejpam-1200	5	14	spaces	space	NOUN
ejpam-1200	5	15	,	,	PUNCT
ejpam-1200	5	16	(	(	PUNCT
ejpam-1200	5	17	i	i	PRON
ejpam-1200	5	18	,	,	PUNCT
ejpam-1200	5	19	j)−β−i	j)−β−i	PROPN
ejpam-1200	5	20	-open	-open	NOUN
ejpam-1200	5	21	sets	set	NOUN
ejpam-1200	5	22	,	,	PUNCT
ejpam-1200	5	23	(	(	PUNCT
ejpam-1200	5	24	i	i	PRON
ejpam-1200	5	25	,	,	PUNCT
ejpam-1200	5	26	j)−β−i	j)−β−i	PROPN
ejpam-1200	5	27	-closed	-close	VERB
ejpam-1200	5	28	sets	set	NOUN
ejpam-1200	5	29	.	.	PUNCT
ejpam-1200	6	1	1	1	X
ejpam-1200	6	2	.	.	X
ejpam-1200	6	3	introduction	introduction	NOUN
ejpam-1200	6	4	kuratowski	kuratowski	NOUN
ejpam-1200	7	1	[	[	X
ejpam-1200	7	2	7	7	NUM
ejpam-1200	7	3	]	]	PUNCT
ejpam-1200	7	4	and	and	CCONJ
ejpam-1200	7	5	vaidyanathasamy	vaidyanathasamy	ADJ
ejpam-1200	8	1	[	[	X
ejpam-1200	8	2	9	9	NUM
ejpam-1200	8	3	]	]	PUNCT
ejpam-1200	8	4	introduced	introduce	VERB
ejpam-1200	8	5	and	and	CCONJ
ejpam-1200	8	6	investigated	investigate	VERB
ejpam-1200	8	7	the	the	DET
ejpam-1200	8	8	concept	concept	NOUN
ejpam-1200	8	9	of	of	ADP
ejpam-1200	8	10	ideals	ideal	NOUN
ejpam-1200	8	11	in	in	ADP
ejpam-1200	8	12	topological	topological	ADJ
ejpam-1200	8	13	spaces	space	NOUN
ejpam-1200	8	14	.	.	PUNCT
ejpam-1200	9	1	an	an	DET
ejpam-1200	9	2	ideal	ideal	NOUN
ejpam-1200	9	3	i	i	PRON
ejpam-1200	9	4	on	on	ADP
ejpam-1200	9	5	a	a	DET
ejpam-1200	9	6	topological	topological	ADJ
ejpam-1200	9	7	space	space	NOUN
ejpam-1200	9	8	(	(	PUNCT
ejpam-1200	9	9	x	x	X
ejpam-1200	9	10	,	,	PUNCT
ejpam-1200	9	11	τ	τ	X
ejpam-1200	9	12	)	)	PUNCT
ejpam-1200	9	13	is	be	AUX
ejpam-1200	9	14	a	a	DET
ejpam-1200	9	15	nonempty	nonempty	ADJ
ejpam-1200	9	16	collection	collection	NOUN
ejpam-1200	9	17	of	of	ADP
ejpam-1200	9	18	subsets	subset	NOUN
ejpam-1200	9	19	of	of	ADP
ejpam-1200	9	20	x	x	PUNCT
ejpam-1200	9	21	which	which	DET
ejpam-1200	9	22	satisfies	satisfy	VERB
ejpam-1200	9	23	(	(	PUNCT
ejpam-1200	9	24	i	i	NOUN
ejpam-1200	9	25	)	)	PUNCT
ejpam-1200	9	26	a	a	PRON
ejpam-1200	9	27	∈	∈	NOUN
ejpam-1200	9	28	i	i	PRON
ejpam-1200	9	29	and	and	CCONJ
ejpam-1200	9	30	b	b	PROPN
ejpam-1200	9	31	⊂	⊂	PROPN
ejpam-1200	9	32	a	a	DET
ejpam-1200	9	33	implies	imply	VERB
ejpam-1200	9	34	b	b	X
ejpam-1200	9	35	∈	∈	ADV
ejpam-1200	10	1	i	i	PRON
ejpam-1200	10	2	and	and	CCONJ
ejpam-1200	10	3	(	(	PUNCT
ejpam-1200	10	4	ii	ii	NOUN
ejpam-1200	10	5	)	)	PUNCT
ejpam-1200	10	6	a	a	DET
ejpam-1200	10	7	∈	∈	PROPN
ejpam-1200	10	8	i	i	PRON
ejpam-1200	10	9	and	and	CCONJ
ejpam-1200	10	10	b	b	X
ejpam-1200	10	11	∈	∈	PROPN
ejpam-1200	11	1	i	i	PRON
ejpam-1200	11	2	implies	imply	VERB
ejpam-1200	11	3	a∪b	a∪b	ADJ
ejpam-1200	11	4	∈	∈	PROPN
ejpam-1200	11	5	i	i	PRON
ejpam-1200	11	6	.	.	PUNCT
ejpam-1200	12	1	given	give	VERB
ejpam-1200	12	2	a	a	DET
ejpam-1200	12	3	bitopological	bitopological	ADJ
ejpam-1200	12	4	space	space	NOUN
ejpam-1200	12	5	(	(	PUNCT
ejpam-1200	12	6	x	x	NOUN
ejpam-1200	12	7	,	,	PUNCT
ejpam-1200	12	8	τ1,τ2	τ1,τ2	PROPN
ejpam-1200	12	9	)	)	PUNCT
ejpam-1200	12	10	with	with	ADP
ejpam-1200	12	11	an	an	DET
ejpam-1200	12	12	ideal	ideal	ADJ
ejpam-1200	12	13	i	i	PRON
ejpam-1200	12	14	on	on	ADP
ejpam-1200	12	15	x	x	X
ejpam-1200	12	16	and	and	CCONJ
ejpam-1200	12	17	if	if	SCONJ
ejpam-1200	12	18	p	p	X
ejpam-1200	12	19	(	(	PUNCT
ejpam-1200	12	20	x	x	X
ejpam-1200	12	21	)	)	PUNCT
ejpam-1200	12	22	is	be	AUX
ejpam-1200	12	23	the	the	DET
ejpam-1200	12	24	set	set	NOUN
ejpam-1200	12	25	of	of	ADP
ejpam-1200	12	26	all	all	DET
ejpam-1200	12	27	subsets	subset	NOUN
ejpam-1200	12	28	of	of	ADP
ejpam-1200	12	29	x	x	PRON
ejpam-1200	12	30	,	,	PUNCT
ejpam-1200	12	31	a	a	DET
ejpam-1200	12	32	set	set	NOUN
ejpam-1200	12	33	operator	operator	NOUN
ejpam-1200	12	34	(	(	PUNCT
ejpam-1200	12	35	.)∗i	.)∗i	NOUN
ejpam-1200	12	36	:	:	PUNCT
ejpam-1200	12	37	p	p	X
ejpam-1200	12	38	(	(	PUNCT
ejpam-1200	12	39	x	x	X
ejpam-1200	12	40	)	)	PUNCT
ejpam-1200	12	41	→p	→p	PROPN
ejpam-1200	12	42	(	(	PUNCT
ejpam-1200	12	43	x	x	PROPN
ejpam-1200	12	44	)	)	PUNCT
ejpam-1200	12	45	,	,	PUNCT
ejpam-1200	12	46	called	call	VERB
ejpam-1200	12	47	the	the	DET
ejpam-1200	12	48	local	local	ADJ
ejpam-1200	12	49	function	function	NOUN
ejpam-1200	12	50	[	[	X
ejpam-1200	12	51	9	9	NUM
ejpam-1200	12	52	]	]	PUNCT
ejpam-1200	12	53	of	of	ADP
ejpam-1200	12	54	a	a	PRON
ejpam-1200	12	55	with	with	ADP
ejpam-1200	12	56	respect	respect	NOUN
ejpam-1200	12	57	to	to	PART
ejpam-1200	12	58	τi	τi	VERB
ejpam-1200	13	1	and	and	CCONJ
ejpam-1200	13	2	i	i	PRON
ejpam-1200	13	3	,	,	PUNCT
ejpam-1200	13	4	is	be	AUX
ejpam-1200	13	5	defined	define	VERB
ejpam-1200	13	6	as	as	SCONJ
ejpam-1200	13	7	follows	follow	VERB
ejpam-1200	13	8	:	:	PUNCT
ejpam-1200	13	9	for	for	ADP
ejpam-1200	13	10	a⊂	a⊂	ADP
ejpam-1200	13	11	x	x	SYM
ejpam-1200	13	12	,	,	PUNCT
ejpam-1200	13	13	a∗i	a∗i	X
ejpam-1200	13	14	(	(	PUNCT
ejpam-1200	13	15	τi	τi	ADP
ejpam-1200	13	16	,	,	PUNCT
ejpam-1200	13	17	i	i	NOUN
ejpam-1200	13	18	)	)	PUNCT
ejpam-1200	14	1	=	=	PRON
ejpam-1200	14	2	{	{	PUNCT
ejpam-1200	14	3	x	x	SYM
ejpam-1200	14	4	∈	∈	PROPN
ejpam-1200	14	5	x	x	X
ejpam-1200	14	6	|u	|u	PROPN
ejpam-1200	14	7	∩a	∩a	PROPN
ejpam-1200	14	8	/∈	/∈	PUNCT
ejpam-1200	15	1	i	i	PRON
ejpam-1200	15	2	for	for	ADP
ejpam-1200	15	3	every	every	DET
ejpam-1200	15	4	u	u	PROPN
ejpam-1200	15	5	∈	∈	PROPN
ejpam-1200	15	6	τi(x	τi(x	NUM
ejpam-1200	15	7	)	)	PUNCT
ejpam-1200	15	8	}	}	PUNCT
ejpam-1200	15	9	,	,	PUNCT
ejpam-1200	15	10	where	where	SCONJ
ejpam-1200	15	11	τi(x	τi(x	NUM
ejpam-1200	15	12	)	)	PUNCT
ejpam-1200	16	1	=	=	PRON
ejpam-1200	16	2	{	{	PUNCT
ejpam-1200	16	3	u	u	NOUN
ejpam-1200	16	4	∈	∈	PROPN
ejpam-1200	16	5	τi|x	τi|x	NOUN
ejpam-1200	16	6	∈	∈	NOUN
ejpam-1200	16	7	u	u	NOUN
ejpam-1200	16	8	}	}	PUNCT
ejpam-1200	16	9	.	.	PUNCT
ejpam-1200	17	1	for	for	ADP
ejpam-1200	17	2	every	every	DET
ejpam-1200	17	3	ideal	ideal	ADJ
ejpam-1200	17	4	topological	topological	ADJ
ejpam-1200	17	5	space	space	NOUN
ejpam-1200	17	6	(	(	PUNCT
ejpam-1200	17	7	x	x	X
ejpam-1200	17	8	,	,	PUNCT
ejpam-1200	17	9	τ	τ	PROPN
ejpam-1200	17	10	,	,	PUNCT
ejpam-1200	17	11	i	i	PROPN
ejpam-1200	17	12	)	)	PUNCT
ejpam-1200	17	13	,	,	PUNCT
ejpam-1200	17	14	there	there	PRON
ejpam-1200	17	15	exists	exist	VERB
ejpam-1200	17	16	a	a	DET
ejpam-1200	17	17	topology	topology	NOUN
ejpam-1200	17	18	τ∗(i	τ∗(i	PROPN
ejpam-1200	17	19	)	)	PUNCT
ejpam-1200	17	20	,	,	PUNCT
ejpam-1200	17	21	finer	fine	ADJ
ejpam-1200	17	22	than	than	ADP
ejpam-1200	17	23	τ	τ	PROPN
ejpam-1200	17	24	,	,	PUNCT
ejpam-1200	17	25	generated	generate	VERB
ejpam-1200	17	26	by	by	ADP
ejpam-1200	17	27	the	the	DET
ejpam-1200	17	28	base	base	NOUN
ejpam-1200	17	29	β(i	β(i	PUNCT
ejpam-1200	17	30	,	,	PUNCT
ejpam-1200	17	31	τ	τ	X
ejpam-1200	17	32	)	)	PUNCT
ejpam-1200	17	33	=	=	PRON
ejpam-1200	17	34	{	{	PUNCT
ejpam-1200	17	35	u\i	u\i	PROPN
ejpam-1200	17	36	|u	|u	PROPN
ejpam-1200	17	37	∈	∈	PROPN
ejpam-1200	17	38	τ	τ	X
ejpam-1200	17	39	and	and	CCONJ
ejpam-1200	17	40	i	i	PRON
ejpam-1200	17	41	∈	∈	PROPN
ejpam-1200	18	1	i	i	PRON
ejpam-1200	18	2	}	}	PUNCT
ejpam-1200	18	3	,	,	PUNCT
ejpam-1200	18	4	but	but	CCONJ
ejpam-1200	18	5	in	in	ADP
ejpam-1200	18	6	general	general	ADJ
ejpam-1200	18	7	β(i	β(i	X
ejpam-1200	18	8	,	,	PUNCT
ejpam-1200	18	9	τ	τ	X
ejpam-1200	18	10	)	)	PUNCT
ejpam-1200	18	11	is	be	AUX
ejpam-1200	18	12	not	not	PART
ejpam-1200	18	13	always	always	ADV
ejpam-1200	18	14	a	a	DET
ejpam-1200	18	15	topology	topology	NOUN
ejpam-1200	19	1	[	[	X
ejpam-1200	19	2	4	4	NUM
ejpam-1200	19	3	]	]	PUNCT
ejpam-1200	19	4	.	.	PUNCT
ejpam-1200	20	1	observe	observe	VERB
ejpam-1200	20	2	additionally	additionally	ADV
ejpam-1200	20	3	that	that	SCONJ
ejpam-1200	20	4	τi	τi	ADP
ejpam-1200	20	5	−	−	NOUN
ejpam-1200	20	6	cl∗(a	cl∗(a	NOUN
ejpam-1200	20	7	)	)	PUNCT
ejpam-1200	20	8	=	=	PUNCT
ejpam-1200	20	9	a∪	a∪	X
ejpam-1200	20	10	a∗i	a∗i	NUM
ejpam-1200	20	11	(	(	PUNCT
ejpam-1200	20	12	τi	τi	ADP
ejpam-1200	20	13	,	,	PUNCT
ejpam-1200	20	14	i	i	PRON
ejpam-1200	20	15	)	)	PUNCT
ejpam-1200	20	16	defines	define	VERB
ejpam-1200	20	17	a	a	DET
ejpam-1200	20	18	kuratowski	kuratowski	ADJ
ejpam-1200	20	19	closure	closure	NOUN
ejpam-1200	20	20	operator	operator	NOUN
ejpam-1200	20	21	for	for	ADP
ejpam-1200	20	22	τ∗(i	τ∗(i	PROPN
ejpam-1200	20	23	)	)	PUNCT
ejpam-1200	20	24	,	,	PUNCT
ejpam-1200	20	25	when	when	SCONJ
ejpam-1200	20	26	there	there	PRON
ejpam-1200	20	27	is	be	VERB
ejpam-1200	20	28	no	no	DET
ejpam-1200	20	29	chance	chance	NOUN
ejpam-1200	20	30	of	of	ADP
ejpam-1200	20	31	confusion	confusion	NOUN
ejpam-1200	20	32	,	,	PUNCT
ejpam-1200	20	33	a∗i	a∗i	NUM
ejpam-1200	20	34	(	(	PUNCT
ejpam-1200	20	35	i	i	NOUN
ejpam-1200	20	36	)	)	PUNCT
ejpam-1200	20	37	is	be	AUX
ejpam-1200	20	38	denoted	denote	VERB
ejpam-1200	20	39	by	by	ADP
ejpam-1200	20	40	a∗i	a∗i	NUM
ejpam-1200	20	41	and	and	CCONJ
ejpam-1200	20	42	τi−	τi−	PUNCT
ejpam-1200	20	43	int∗(a	int∗(a	NOUN
ejpam-1200	20	44	)	)	PUNCT
ejpam-1200	20	45	denotes	denote	VERB
ejpam-1200	20	46	the	the	DET
ejpam-1200	20	47	interior	interior	NOUN
ejpam-1200	20	48	of	of	ADP
ejpam-1200	20	49	a	a	PRON
ejpam-1200	20	50	in	in	ADP
ejpam-1200	20	51	τ∗i	τ∗i	PUNCT
ejpam-1200	20	52	(	(	PUNCT
ejpam-1200	20	53	i	i	NOUN
ejpam-1200	20	54	)	)	PUNCT
ejpam-1200	20	55	.	.	PUNCT
ejpam-1200	21	1	in	in	ADP
ejpam-1200	21	2	this	this	DET
ejpam-1200	21	3	paper	paper	NOUN
ejpam-1200	21	4	we	we	PRON
ejpam-1200	21	5	introduce	introduce	VERB
ejpam-1200	21	6	and	and	CCONJ
ejpam-1200	21	7	characterize	characterize	VERB
ejpam-1200	21	8	the	the	DET
ejpam-1200	21	9	concepts	concept	NOUN
ejpam-1200	21	10	of	of	ADP
ejpam-1200	21	11	β	β	ADJ
ejpam-1200	21	12	-	-	ADJ
ejpam-1200	21	13	open	open	ADJ
ejpam-1200	21	14	sets	set	NOUN
ejpam-1200	21	15	and	and	CCONJ
ejpam-1200	21	16	their	their	PRON
ejpam-1200	21	17	related	related	ADJ
ejpam-1200	21	18	notions	notion	NOUN
ejpam-1200	21	19	in	in	ADP
ejpam-1200	21	20	ideal	ideal	ADJ
ejpam-1200	21	21	bitopological	bitopological	ADJ
ejpam-1200	21	22	spaces	space	NOUN
ejpam-1200	21	23	.	.	PUNCT
ejpam-1200	22	1	∗corresponding	∗corresponde	VERB
ejpam-1200	22	2	author	author	NOUN
ejpam-1200	22	3	.	.	PUNCT
ejpam-1200	23	1	email	email	NOUN
ejpam-1200	23	2	addresses	address	NOUN
ejpam-1200	23	3	:	:	PUNCT
ejpam-1200	23	4	gmamccs@vm.uff.br	gmamccs@vm.uff.br	PROPN
ejpam-1200	23	5	(	(	PUNCT
ejpam-1200	23	6	m.	m.	NOUN
ejpam-1200	23	7	caldas	caldas	PROPN
ejpam-1200	23	8	)	)	PUNCT
ejpam-1200	23	9	,	,	PUNCT
ejpam-1200	23	10	jafari@stofanet.dk	jafari@stofanet.dk	PROPN
ejpam-1200	23	11	(	(	PUNCT
ejpam-1200	23	12	s.	s.	PROPN
ejpam-1200	23	13	jafari	jafari	PROPN
ejpam-1200	23	14	)	)	PUNCT
ejpam-1200	23	15	,	,	PUNCT
ejpam-1200	23	16	nrajesh_topology@yahoo.co.in	nrajesh_topology@yahoo.co.in	X
ejpam-1200	23	17	(	(	PUNCT
ejpam-1200	23	18	n.	n.	PROPN
ejpam-1200	23	19	rajesh	rajesh	PROPN
ejpam-1200	23	20	)	)	PUNCT
ejpam-1200	23	21	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1200	24	1	247	247	NUM
ejpam-1200	24	2	c	c	NOUN
ejpam-1200	24	3	©	©	PROPN
ejpam-1200	24	4	2013	2013	NUM
ejpam-1200	24	5	ejpam	ejpam	NOUN
ejpam-1200	24	6	all	all	DET
ejpam-1200	24	7	rights	right	NOUN
ejpam-1200	24	8	reserved	reserve	VERB
ejpam-1200	24	9	.	.	PUNCT
ejpam-1200	25	1	m.	m.	PROPN
ejpam-1200	25	2	caldas	caldas	PROPN
ejpam-1200	25	3	,	,	PUNCT
ejpam-1200	25	4	s.	s.	PROPN
ejpam-1200	25	5	jafari	jafari	PROPN
ejpam-1200	25	6	,	,	PUNCT
ejpam-1200	25	7	n.	n.	PROPN
ejpam-1200	25	8	rajesh	rajesh	PROPN
ejpam-1200	25	9	/	/	SYM
ejpam-1200	25	10	eur	eur	PROPN
ejpam-1200	25	11	.	.	PUNCT
ejpam-1200	26	1	j.	j.	PROPN
ejpam-1200	26	2	pure	pure	PROPN
ejpam-1200	26	3	appl	appl	PROPN
ejpam-1200	26	4	.	.	PROPN
ejpam-1200	26	5	math	math	PROPN
ejpam-1200	26	6	,	,	PUNCT
ejpam-1200	26	7	6	6	NUM
ejpam-1200	26	8	(	(	PUNCT
ejpam-1200	26	9	2013	2013	NUM
ejpam-1200	26	10	)	)	PUNCT
ejpam-1200	26	11	,	,	PUNCT
ejpam-1200	26	12	247	247	NUM
ejpam-1200	26	13	-	-	SYM
ejpam-1200	26	14	255	255	NUM
ejpam-1200	26	15	248	248	NUM
ejpam-1200	26	16	2	2	NUM
ejpam-1200	26	17	.	.	PUNCT
ejpam-1200	26	18	preiliminaries	preiliminarie	NOUN
ejpam-1200	26	19	for	for	ADP
ejpam-1200	26	20	a	a	DET
ejpam-1200	26	21	subset	subset	NOUN
ejpam-1200	26	22	a	a	PRON
ejpam-1200	26	23	of	of	ADP
ejpam-1200	26	24	a	a	DET
ejpam-1200	26	25	bitopological	bitopological	ADJ
ejpam-1200	26	26	space	space	NOUN
ejpam-1200	26	27	(	(	PUNCT
ejpam-1200	26	28	x	x	NOUN
ejpam-1200	26	29	,	,	PUNCT
ejpam-1200	26	30	τ1,τ2	τ1,τ2	PROPN
ejpam-1200	26	31	)	)	PUNCT
ejpam-1200	27	1	,	,	PUNCT
ejpam-1200	27	2	we	we	PRON
ejpam-1200	27	3	denote	denote	VERB
ejpam-1200	27	4	the	the	DET
ejpam-1200	27	5	closure	closure	NOUN
ejpam-1200	27	6	of	of	ADP
ejpam-1200	27	7	a	a	PRON
ejpam-1200	27	8	and	and	CCONJ
ejpam-1200	27	9	the	the	DET
ejpam-1200	27	10	interior	interior	NOUN
ejpam-1200	27	11	of	of	ADP
ejpam-1200	27	12	a	a	PRON
ejpam-1200	27	13	with	with	ADP
ejpam-1200	27	14	respect	respect	NOUN
ejpam-1200	27	15	to	to	PART
ejpam-1200	27	16	τi	τi	VERB
ejpam-1200	27	17	by	by	ADP
ejpam-1200	27	18	τi	τi	ADP
ejpam-1200	27	19	−cl(a	−cl(a	NOUN
ejpam-1200	27	20	)	)	PUNCT
ejpam-1200	27	21	and	and	CCONJ
ejpam-1200	27	22	τi	τi	VERB
ejpam-1200	27	23	−	−	PROPN
ejpam-1200	27	24	int(a	int(a	PROPN
ejpam-1200	27	25	)	)	PUNCT
ejpam-1200	27	26	,	,	PUNCT
ejpam-1200	27	27	respectively	respectively	ADV
ejpam-1200	27	28	.	.	PUNCT
ejpam-1200	28	1	definition	definition	NOUN
ejpam-1200	28	2	1	1	NUM
ejpam-1200	28	3	.	.	PUNCT
ejpam-1200	29	1	a	a	DET
ejpam-1200	29	2	subset	subset	NOUN
ejpam-1200	29	3	a	a	PRON
ejpam-1200	29	4	of	of	ADP
ejpam-1200	29	5	a	a	DET
ejpam-1200	29	6	bitopological	bitopological	ADJ
ejpam-1200	29	7	space	space	NOUN
ejpam-1200	29	8	(	(	PUNCT
ejpam-1200	29	9	x	x	NOUN
ejpam-1200	29	10	,	,	PUNCT
ejpam-1200	29	11	τ1,τ2	τ1,τ2	PROPN
ejpam-1200	29	12	)	)	PUNCT
ejpam-1200	29	13	is	be	AUX
ejpam-1200	29	14	said	say	VERB
ejpam-1200	29	15	to	to	PART
ejpam-1200	29	16	be	be	AUX
ejpam-1200	29	17	(	(	PUNCT
ejpam-1200	29	18	i	i	NOUN
ejpam-1200	29	19	,	,	PUNCT
ejpam-1200	29	20	j)-semiopen	j)-semiopen	VERB
ejpam-1200	30	1	[	[	X
ejpam-1200	30	2	5	5	NUM
ejpam-1200	30	3	]	]	PUNCT
ejpam-1200	30	4	(	(	PUNCT
ejpam-1200	30	5	resp	resp	NOUN
ejpam-1200	30	6	.	.	PUNCT
ejpam-1200	31	1	(	(	PUNCT
ejpam-1200	31	2	i	i	NOUN
ejpam-1200	31	3	,	,	PUNCT
ejpam-1200	31	4	j)-preopen	j)-preopen	VERB
ejpam-1200	31	5	[	[	X
ejpam-1200	31	6	5	5	NUM
ejpam-1200	31	7	]	]	PUNCT
ejpam-1200	31	8	,	,	PUNCT
ejpam-1200	31	9	(	(	PUNCT
ejpam-1200	31	10	i	i	PROPN
ejpam-1200	31	11	,	,	PUNCT
ejpam-1200	31	12	j)-semi	j)-semi	NOUN
ejpam-1200	31	13	-	-	NOUN
ejpam-1200	31	14	preopen	preopen	ADJ
ejpam-1200	31	15	[	[	X
ejpam-1200	31	16	6	6	NUM
ejpam-1200	31	17	]	]	SYM
ejpam-1200	31	18	)	)	PUNCT
ejpam-1200	31	19	if	if	SCONJ
ejpam-1200	31	20	a⊂	a⊂	PRON
ejpam-1200	31	21	τ	τ	X
ejpam-1200	31	22	j	j	PROPN
ejpam-1200	31	23	−cl(τi	−cl(τi	NOUN
ejpam-1200	31	24	−	−	PROPN
ejpam-1200	31	25	int(a	int(a	NOUN
ejpam-1200	31	26	)	)	PUNCT
ejpam-1200	31	27	)	)	PUNCT
ejpam-1200	31	28	(	(	PUNCT
ejpam-1200	31	29	resp	resp	NOUN
ejpam-1200	31	30	.	.	PUNCT
ejpam-1200	31	31	a⊂	a⊂	X
ejpam-1200	32	1	τi	τi	ADP
ejpam-1200	32	2	−	−	PROPN
ejpam-1200	32	3	int(τ	int(τ	PROPN
ejpam-1200	32	4	j	j	PROPN
ejpam-1200	32	5	−cl(a	−cl(a	NOUN
ejpam-1200	32	6	)	)	PUNCT
ejpam-1200	32	7	)	)	PUNCT
ejpam-1200	32	8	,	,	PUNCT
ejpam-1200	32	9	a⊂	a⊂	PRON
ejpam-1200	32	10	τ	τ	PROPN
ejpam-1200	32	11	j	j	PROPN
ejpam-1200	32	12	−cl(τi	−cl(τi	PROPN
ejpam-1200	32	13	−	−	PROPN
ejpam-1200	32	14	int(τ	int(τ	PROPN
ejpam-1200	32	15	j	j	PROPN
ejpam-1200	32	16	−cl(a	−cl(a	NOUN
ejpam-1200	32	17	)	)	PUNCT
ejpam-1200	32	18	)	)	PUNCT
ejpam-1200	32	19	)	)	PUNCT
ejpam-1200	32	20	)	)	PUNCT
ejpam-1200	32	21	,	,	PUNCT
ejpam-1200	32	22	where	where	SCONJ
ejpam-1200	32	23	i	i	PRON
ejpam-1200	32	24	,	,	PUNCT
ejpam-1200	32	25	j	j	PROPN
ejpam-1200	32	26	=	=	SYM
ejpam-1200	32	27	1	1	NUM
ejpam-1200	32	28	,	,	PUNCT
ejpam-1200	32	29	2	2	NUM
ejpam-1200	32	30	and	and	CCONJ
ejpam-1200	32	31	i	i	PRON
ejpam-1200	32	32	6=	6=	PROPN
ejpam-1200	32	33	j.	j.	PROPN
ejpam-1200	32	34	definition	definition	PROPN
ejpam-1200	32	35	2	2	NUM
ejpam-1200	32	36	.	.	PUNCT
ejpam-1200	32	37	a	a	DET
ejpam-1200	32	38	subset	subset	NOUN
ejpam-1200	32	39	a	a	PRON
ejpam-1200	32	40	of	of	ADP
ejpam-1200	32	41	an	an	DET
ejpam-1200	32	42	ideal	ideal	ADJ
ejpam-1200	32	43	bitopological	bitopological	ADJ
ejpam-1200	32	44	space	space	NOUN
ejpam-1200	32	45	(	(	PUNCT
ejpam-1200	32	46	x	x	X
ejpam-1200	32	47	,	,	PUNCT
ejpam-1200	32	48	τ1,τ2,i	τ1,τ2,i	PROPN
ejpam-1200	32	49	)	)	PUNCT
ejpam-1200	32	50	is	be	AUX
ejpam-1200	32	51	said	say	VERB
ejpam-1200	32	52	to	to	PART
ejpam-1200	32	53	be	be	AUX
ejpam-1200	32	54	(	(	PUNCT
ejpam-1200	32	55	i	i	NOUN
ejpam-1200	32	56	)	)	PUNCT
ejpam-1200	32	57	(	(	PUNCT
ejpam-1200	32	58	i	i	PROPN
ejpam-1200	32	59	,	,	PUNCT
ejpam-1200	32	60	j)-semi	j)-semi	PROPN
ejpam-1200	32	61	-	-	PUNCT
ejpam-1200	32	62	i	i	PRON
ejpam-1200	32	63	-open	-open	NOUN
ejpam-1200	33	1	[	[	X
ejpam-1200	33	2	3	3	NUM
ejpam-1200	33	3	]	]	PUNCT
ejpam-1200	33	4	if	if	SCONJ
ejpam-1200	33	5	a⊂	a⊂	PRON
ejpam-1200	33	6	τ	τ	PROPN
ejpam-1200	33	7	j	j	PROPN
ejpam-1200	33	8	−cl∗(τi	−cl∗(τi	NOUN
ejpam-1200	33	9	−	−	PROPN
ejpam-1200	33	10	int(a	int(a	PROPN
ejpam-1200	33	11	)	)	PUNCT
ejpam-1200	33	12	)	)	PUNCT
ejpam-1200	33	13	.	.	PUNCT
ejpam-1200	34	1	(	(	PUNCT
ejpam-1200	34	2	ii	ii	NOUN
ejpam-1200	34	3	)	)	PUNCT
ejpam-1200	34	4	(	(	PUNCT
ejpam-1200	34	5	i	i	PROPN
ejpam-1200	34	6	,	,	PUNCT
ejpam-1200	34	7	j)-pre	j)-pre	PROPN
ejpam-1200	34	8	-	-	PUNCT
ejpam-1200	34	9	i	i	PRON
ejpam-1200	34	10	-open	-open	NOUN
ejpam-1200	35	1	[	[	X
ejpam-1200	35	2	2	2	NUM
ejpam-1200	35	3	]	]	PUNCT
ejpam-1200	35	4	if	if	SCONJ
ejpam-1200	35	5	a⊂	a⊂	NOUN
ejpam-1200	35	6	τi	τi	VERB
ejpam-1200	35	7	−	−	PROPN
ejpam-1200	35	8	int(τ	int(τ	PROPN
ejpam-1200	35	9	j	j	NOUN
ejpam-1200	35	10	−cl∗(a	−cl∗(a	PROPN
ejpam-1200	35	11	)	)	PUNCT
ejpam-1200	35	12	)	)	PUNCT
ejpam-1200	35	13	.	.	PUNCT
ejpam-1200	36	1	(	(	PUNCT
ejpam-1200	36	2	iii	iii	X
ejpam-1200	36	3	)	)	PUNCT
ejpam-1200	36	4	(	(	PUNCT
ejpam-1200	36	5	i	i	PROPN
ejpam-1200	36	6	,	,	PUNCT
ejpam-1200	36	7	j)−	j)−	PROPN
ejpam-1200	36	8	b−i	b−i	PROPN
ejpam-1200	36	9	-open	-open	NOUN
ejpam-1200	36	10	[	[	X
ejpam-1200	36	11	3	3	NUM
ejpam-1200	36	12	]	]	X
ejpam-1200	36	13	if	if	SCONJ
ejpam-1200	36	14	a⊂	a⊂	NOUN
ejpam-1200	36	15	τi	τi	VERB
ejpam-1200	36	16	−	−	PROPN
ejpam-1200	36	17	int(τ	int(τ	PROPN
ejpam-1200	36	18	j	j	PROPN
ejpam-1200	36	19	−cl∗(a))∪τ	−cl∗(a))∪τ	PROPN
ejpam-1200	36	20	j	j	PROPN
ejpam-1200	36	21	−cl∗(τi	−cl∗(τi	NOUN
ejpam-1200	36	22	−	−	PROPN
ejpam-1200	36	23	int(a	int(a	PROPN
ejpam-1200	36	24	)	)	PUNCT
ejpam-1200	36	25	)	)	PUNCT
ejpam-1200	36	26	.	.	PUNCT
ejpam-1200	37	1	(	(	PUNCT
ejpam-1200	37	2	iv	iv	X
ejpam-1200	37	3	)	)	PUNCT
ejpam-1200	37	4	(	(	PUNCT
ejpam-1200	37	5	i	i	PRON
ejpam-1200	37	6	,	,	PUNCT
ejpam-1200	37	7	j)−α−i	j)−α−i	PROPN
ejpam-1200	37	8	-open	-open	PROPN
ejpam-1200	38	1	[	[	X
ejpam-1200	38	2	3	3	NUM
ejpam-1200	38	3	]	]	X
ejpam-1200	38	4	if	if	SCONJ
ejpam-1200	38	5	a⊂	a⊂	NOUN
ejpam-1200	38	6	τi	τi	VERB
ejpam-1200	38	7	−	−	NOUN
ejpam-1200	38	8	int(τ	int(τ	PROPN
ejpam-1200	38	9	j	j	PROPN
ejpam-1200	38	10	−cl∗(τi	−cl∗(τi	NOUN
ejpam-1200	38	11	−	−	PROPN
ejpam-1200	38	12	int(a	int(a	PROPN
ejpam-1200	38	13	)	)	PUNCT
ejpam-1200	38	14	)	)	PUNCT
ejpam-1200	38	15	)	)	PUNCT
ejpam-1200	38	16	.	.	PUNCT
ejpam-1200	39	1	definition	definition	NOUN
ejpam-1200	39	2	3	3	NUM
ejpam-1200	39	3	.	.	PUNCT
ejpam-1200	40	1	a	a	DET
ejpam-1200	40	2	function	function	NOUN
ejpam-1200	40	3	f	f	NOUN
ejpam-1200	40	4	:	:	PUNCT
ejpam-1200	40	5	(	(	PUNCT
ejpam-1200	40	6	x	x	INTJ
ejpam-1200	40	7	,	,	PUNCT
ejpam-1200	40	8	τ1,τ2,i	τ1,τ2,i	PROPN
ejpam-1200	40	9	)	)	PUNCT
ejpam-1200	40	10	→	→	SYM
ejpam-1200	40	11	(	(	PUNCT
ejpam-1200	40	12	y	y	PROPN
ejpam-1200	40	13	,	,	PUNCT
ejpam-1200	40	14	σ1,σ2	σ1,σ2	PROPN
ejpam-1200	40	15	)	)	PUNCT
ejpam-1200	40	16	is	be	AUX
ejpam-1200	40	17	said	say	VERB
ejpam-1200	40	18	to	to	PART
ejpam-1200	40	19	be	be	AUX
ejpam-1200	40	20	(	(	PUNCT
ejpam-1200	40	21	i	i	NOUN
ejpam-1200	40	22	)	)	PUNCT
ejpam-1200	40	23	(	(	PUNCT
ejpam-1200	40	24	i	i	PROPN
ejpam-1200	40	25	,	,	PUNCT
ejpam-1200	40	26	j)-pre	j)-pre	PROPN
ejpam-1200	40	27	-	-	PUNCT
ejpam-1200	40	28	i	i	PRON
ejpam-1200	40	29	-continuous	-continuous	ADJ
ejpam-1200	40	30	[	[	X
ejpam-1200	40	31	2	2	NUM
ejpam-1200	40	32	]	]	PUNCT
ejpam-1200	40	33	if	if	SCONJ
ejpam-1200	40	34	the	the	DET
ejpam-1200	40	35	inverse	inverse	ADJ
ejpam-1200	40	36	image	image	NOUN
ejpam-1200	40	37	of	of	ADP
ejpam-1200	40	38	every	every	DET
ejpam-1200	40	39	σi	σi	NOUN
ejpam-1200	40	40	-	-	PUNCT
ejpam-1200	40	41	open	open	ADJ
ejpam-1200	40	42	set	set	NOUN
ejpam-1200	40	43	of	of	ADP
ejpam-1200	40	44	y	y	PROPN
ejpam-1200	40	45	is	be	AUX
ejpam-1200	40	46	(	(	PUNCT
ejpam-1200	40	47	i	i	PROPN
ejpam-1200	40	48	,	,	PUNCT
ejpam-1200	40	49	j)-pre	j)-pre	PROPN
ejpam-1200	40	50	-	-	PUNCT
ejpam-1200	40	51	i	i	PRON
ejpam-1200	40	52	open	open	VERB
ejpam-1200	40	53	in	in	ADP
ejpam-1200	40	54	x	x	X
ejpam-1200	40	55	,	,	PUNCT
ejpam-1200	40	56	where	where	SCONJ
ejpam-1200	40	57	i	i	PRON
ejpam-1200	40	58	6=	6=	PROPN
ejpam-1200	40	59	j	j	PROPN
ejpam-1200	40	60	,	,	PUNCT
ejpam-1200	40	61	i	i	PRON
ejpam-1200	40	62	,	,	PUNCT
ejpam-1200	40	63	j=1	j=1	PROPN
ejpam-1200	40	64	,	,	PUNCT
ejpam-1200	40	65	2	2	NUM
ejpam-1200	40	66	.	.	PUNCT
ejpam-1200	40	67	(	(	PUNCT
ejpam-1200	40	68	ii	ii	NOUN
ejpam-1200	40	69	)	)	PUNCT
ejpam-1200	40	70	(	(	PUNCT
ejpam-1200	40	71	i	i	PROPN
ejpam-1200	40	72	,	,	PUNCT
ejpam-1200	40	73	j)-semi	j)-semi	NOUN
ejpam-1200	40	74	-	-	PUNCT
ejpam-1200	40	75	i	i	PRON
ejpam-1200	40	76	-continuous	-continuous	ADJ
ejpam-1200	40	77	[	[	X
ejpam-1200	40	78	3	3	NUM
ejpam-1200	40	79	]	]	PUNCT
ejpam-1200	40	80	if	if	SCONJ
ejpam-1200	40	81	the	the	DET
ejpam-1200	40	82	inverse	inverse	ADJ
ejpam-1200	40	83	image	image	NOUN
ejpam-1200	40	84	of	of	ADP
ejpam-1200	40	85	every	every	DET
ejpam-1200	40	86	σi	σi	NOUN
ejpam-1200	40	87	-	-	PUNCT
ejpam-1200	40	88	open	open	ADJ
ejpam-1200	40	89	set	set	NOUN
ejpam-1200	40	90	of	of	ADP
ejpam-1200	40	91	y	y	PROPN
ejpam-1200	40	92	is	be	AUX
ejpam-1200	40	93	(	(	PUNCT
ejpam-1200	40	94	i	i	PROPN
ejpam-1200	40	95	,	,	PUNCT
ejpam-1200	40	96	j)-semi	j)-semi	NOUN
ejpam-1200	40	97	-	-	PUNCT
ejpam-1200	40	98	i	i	PRON
ejpam-1200	40	99	open	open	VERB
ejpam-1200	40	100	in	in	ADP
ejpam-1200	40	101	x	x	X
ejpam-1200	40	102	,	,	PUNCT
ejpam-1200	40	103	where	where	SCONJ
ejpam-1200	40	104	i	i	PRON
ejpam-1200	40	105	6=	6=	PROPN
ejpam-1200	40	106	j	j	PROPN
ejpam-1200	40	107	,	,	PUNCT
ejpam-1200	40	108	i	i	PRON
ejpam-1200	40	109	,	,	PUNCT
ejpam-1200	40	110	j=1	j=1	PROPN
ejpam-1200	40	111	,	,	PUNCT
ejpam-1200	40	112	2	2	NUM
ejpam-1200	40	113	.	.	PUNCT
ejpam-1200	40	114	(	(	PUNCT
ejpam-1200	40	115	iii	iii	X
ejpam-1200	40	116	)	)	PUNCT
ejpam-1200	40	117	(	(	PUNCT
ejpam-1200	40	118	i	i	PROPN
ejpam-1200	40	119	,	,	PUNCT
ejpam-1200	40	120	j)−	j)−	PROPN
ejpam-1200	40	121	b−i	b−i	PROPN
ejpam-1200	40	122	-continuous	-continuous	ADJ
ejpam-1200	40	123	[	[	X
ejpam-1200	40	124	3	3	NUM
ejpam-1200	40	125	]	]	PUNCT
ejpam-1200	40	126	if	if	SCONJ
ejpam-1200	40	127	the	the	DET
ejpam-1200	40	128	inverse	inverse	ADJ
ejpam-1200	40	129	image	image	NOUN
ejpam-1200	40	130	of	of	ADP
ejpam-1200	40	131	every	every	DET
ejpam-1200	40	132	σi	σi	NOUN
ejpam-1200	40	133	-	-	PUNCT
ejpam-1200	40	134	open	open	ADJ
ejpam-1200	40	135	set	set	NOUN
ejpam-1200	40	136	of	of	ADP
ejpam-1200	40	137	y	y	PROPN
ejpam-1200	40	138	is	be	AUX
ejpam-1200	40	139	(	(	PUNCT
ejpam-1200	40	140	i	i	PROPN
ejpam-1200	40	141	,	,	PUNCT
ejpam-1200	40	142	j)−	j)−	PROPN
ejpam-1200	40	143	b−i	b−i	PROPN
ejpam-1200	40	144	open	open	VERB
ejpam-1200	40	145	in	in	ADP
ejpam-1200	40	146	x	x	X
ejpam-1200	40	147	,	,	PUNCT
ejpam-1200	40	148	where	where	SCONJ
ejpam-1200	40	149	i	i	PRON
ejpam-1200	40	150	6=	6=	PROPN
ejpam-1200	40	151	j	j	PROPN
ejpam-1200	40	152	,	,	PUNCT
ejpam-1200	40	153	i	i	PRON
ejpam-1200	40	154	,	,	PUNCT
ejpam-1200	40	155	j=1	j=1	PROPN
ejpam-1200	40	156	,	,	PUNCT
ejpam-1200	40	157	2	2	NUM
ejpam-1200	40	158	.	.	PUNCT
ejpam-1200	40	159	(	(	PUNCT
ejpam-1200	40	160	iv	iv	X
ejpam-1200	40	161	)	)	PUNCT
ejpam-1200	40	162	(	(	PUNCT
ejpam-1200	40	163	i	i	PRON
ejpam-1200	40	164	,	,	PUNCT
ejpam-1200	40	165	j)−α−i	j)−α−i	PROPN
ejpam-1200	40	166	-continuous	-continuous	ADJ
ejpam-1200	41	1	[	[	X
ejpam-1200	41	2	3	3	NUM
ejpam-1200	41	3	]	]	PUNCT
ejpam-1200	41	4	if	if	SCONJ
ejpam-1200	41	5	the	the	DET
ejpam-1200	41	6	inverse	inverse	ADJ
ejpam-1200	41	7	image	image	NOUN
ejpam-1200	41	8	of	of	ADP
ejpam-1200	41	9	every	every	DET
ejpam-1200	41	10	σi	σi	NOUN
ejpam-1200	41	11	-	-	PUNCT
ejpam-1200	41	12	open	open	ADJ
ejpam-1200	41	13	set	set	NOUN
ejpam-1200	41	14	of	of	ADP
ejpam-1200	41	15	y	y	PROPN
ejpam-1200	41	16	is	be	AUX
ejpam-1200	41	17	(	(	PUNCT
ejpam-1200	41	18	i	i	INTJ
ejpam-1200	41	19	,	,	PUNCT
ejpam-1200	41	20	j)−α−i	j)−α−i	PROPN
ejpam-1200	41	21	open	open	VERB
ejpam-1200	41	22	in	in	ADP
ejpam-1200	41	23	x	x	X
ejpam-1200	41	24	,	,	PUNCT
ejpam-1200	41	25	where	where	SCONJ
ejpam-1200	41	26	i	i	PRON
ejpam-1200	41	27	6=	6=	PROPN
ejpam-1200	41	28	j	j	PROPN
ejpam-1200	41	29	,	,	PUNCT
ejpam-1200	41	30	i	i	PRON
ejpam-1200	41	31	,	,	PUNCT
ejpam-1200	41	32	j=1	j=1	PROPN
ejpam-1200	41	33	,	,	PUNCT
ejpam-1200	41	34	2	2	NUM
ejpam-1200	41	35	.	.	PUNCT
ejpam-1200	41	36	(	(	PUNCT
ejpam-1200	41	37	v	v	NOUN
ejpam-1200	41	38	)	)	PUNCT
ejpam-1200	41	39	pairwise	pairwise	NOUN
ejpam-1200	41	40	semi	semi	ADJ
ejpam-1200	41	41	-	-	ADJ
ejpam-1200	41	42	precontinuous	precontinuous	ADJ
ejpam-1200	42	1	[	[	X
ejpam-1200	42	2	6	6	NUM
ejpam-1200	42	3	]	]	PUNCT
ejpam-1200	42	4	if	if	SCONJ
ejpam-1200	42	5	the	the	DET
ejpam-1200	42	6	inverse	inverse	ADJ
ejpam-1200	42	7	image	image	NOUN
ejpam-1200	42	8	of	of	ADP
ejpam-1200	42	9	every	every	DET
ejpam-1200	42	10	σi	σi	NOUN
ejpam-1200	42	11	-	-	PUNCT
ejpam-1200	42	12	open	open	ADJ
ejpam-1200	42	13	set	set	NOUN
ejpam-1200	42	14	in	in	ADP
ejpam-1200	42	15	(	(	PUNCT
ejpam-1200	42	16	y	y	PROPN
ejpam-1200	42	17	,	,	PUNCT
ejpam-1200	42	18	σ1,σ2	σ1,σ2	PROPN
ejpam-1200	42	19	)	)	PUNCT
ejpam-1200	42	20	is	be	AUX
ejpam-1200	42	21	(	(	PUNCT
ejpam-1200	42	22	i	i	PROPN
ejpam-1200	42	23	,	,	PUNCT
ejpam-1200	42	24	j)-semi	j)-semi	NOUN
ejpam-1200	42	25	-	-	PUNCT
ejpam-1200	42	26	preopen	preopen	ADJ
ejpam-1200	42	27	in	in	ADP
ejpam-1200	42	28	(	(	PUNCT
ejpam-1200	42	29	x	x	INTJ
ejpam-1200	42	30	,	,	PUNCT
ejpam-1200	42	31	τ1,τ2	τ1,τ2	PROPN
ejpam-1200	42	32	)	)	PUNCT
ejpam-1200	42	33	,	,	PUNCT
ejpam-1200	42	34	where	where	SCONJ
ejpam-1200	42	35	i	i	PRON
ejpam-1200	42	36	6=	6=	PROPN
ejpam-1200	42	37	j	j	PROPN
ejpam-1200	42	38	,	,	PUNCT
ejpam-1200	42	39	i	i	PRON
ejpam-1200	42	40	,	,	PUNCT
ejpam-1200	42	41	j=1	j=1	PROPN
ejpam-1200	42	42	,	,	PUNCT
ejpam-1200	42	43	2	2	NUM
ejpam-1200	42	44	.	.	NOUN
ejpam-1200	42	45	3	3	NUM
ejpam-1200	42	46	.	.	X
ejpam-1200	42	47	properties	property	NOUN
ejpam-1200	42	48	of	of	ADP
ejpam-1200	42	49	(	(	PUNCT
ejpam-1200	42	50	i	i	PROPN
ejpam-1200	42	51	,	,	PUNCT
ejpam-1200	42	52	j)−	j)−	PROPN
ejpam-1200	42	53	β	β	PROPN
ejpam-1200	42	54	−i	−i	PROPN
ejpam-1200	42	55	-open	-open	PROPN
ejpam-1200	42	56	sets	set	VERB
ejpam-1200	42	57	definition	definition	NOUN
ejpam-1200	42	58	4	4	NUM
ejpam-1200	42	59	.	.	PUNCT
ejpam-1200	43	1	a	a	DET
ejpam-1200	43	2	subset	subset	NOUN
ejpam-1200	43	3	a	a	PRON
ejpam-1200	43	4	of	of	ADP
ejpam-1200	43	5	an	an	DET
ejpam-1200	43	6	ideal	ideal	ADJ
ejpam-1200	43	7	bitopological	bitopological	ADJ
ejpam-1200	43	8	space	space	NOUN
ejpam-1200	43	9	(	(	PUNCT
ejpam-1200	43	10	x	x	X
ejpam-1200	43	11	,	,	PUNCT
ejpam-1200	43	12	τ1,τ2,i	τ1,τ2,i	PROPN
ejpam-1200	43	13	)	)	PUNCT
ejpam-1200	43	14	is	be	AUX
ejpam-1200	43	15	said	say	VERB
ejpam-1200	43	16	to	to	PART
ejpam-1200	43	17	be	be	AUX
ejpam-1200	43	18	(	(	PUNCT
ejpam-1200	43	19	i	i	PRON
ejpam-1200	43	20	,	,	PUNCT
ejpam-1200	43	21	j)−β−i	j)−β−i	PROPN
ejpam-1200	43	22	open	open	ADJ
ejpam-1200	43	23	if	if	SCONJ
ejpam-1200	43	24	a⊂	a⊂	PRON
ejpam-1200	43	25	τ	τ	PROPN
ejpam-1200	43	26	j	j	PROPN
ejpam-1200	43	27	−cl(τi	−cl(τi	NOUN
ejpam-1200	43	28	−	−	PROPN
ejpam-1200	44	1	int(τ	int(τ	PROPN
ejpam-1200	44	2	j	j	PROPN
ejpam-1200	44	3	−cl∗(a	−cl∗(a	PROPN
ejpam-1200	44	4	)	)	PUNCT
ejpam-1200	44	5	)	)	PUNCT
ejpam-1200	44	6	)	)	PUNCT
ejpam-1200	44	7	,	,	PUNCT
ejpam-1200	44	8	where	where	SCONJ
ejpam-1200	44	9	i	i	PRON
ejpam-1200	44	10	,	,	PUNCT
ejpam-1200	44	11	j	j	PROPN
ejpam-1200	44	12	=	=	SYM
ejpam-1200	44	13	1,2	1,2	NUM
ejpam-1200	44	14	and	and	CCONJ
ejpam-1200	44	15	i	i	PRON
ejpam-1200	44	16	6=	6=	PROPN
ejpam-1200	44	17	j.	j.	PROPN
ejpam-1200	44	18	the	the	DET
ejpam-1200	44	19	family	family	NOUN
ejpam-1200	44	20	of	of	ADP
ejpam-1200	44	21	all	all	PRON
ejpam-1200	44	22	(	(	PUNCT
ejpam-1200	44	23	i	i	PROPN
ejpam-1200	44	24	,	,	PUNCT
ejpam-1200	44	25	j	j	PROPN
ejpam-1200	44	26	)	)	PUNCT
ejpam-1200	44	27	−	−	PROPN
ejpam-1200	44	28	β	β	NOUN
ejpam-1200	45	1	−	−	NOUN
ejpam-1200	45	2	i	i	PRON
ejpam-1200	45	3	-open	-open	VERB
ejpam-1200	45	4	sets	set	NOUN
ejpam-1200	45	5	of	of	ADP
ejpam-1200	45	6	(	(	PUNCT
ejpam-1200	45	7	x	x	INTJ
ejpam-1200	45	8	,	,	PUNCT
ejpam-1200	45	9	τ1,τ2,i	τ1,τ2,i	PROPN
ejpam-1200	45	10	)	)	PUNCT
ejpam-1200	45	11	is	be	AUX
ejpam-1200	45	12	denoted	denote	VERB
ejpam-1200	45	13	by	by	ADP
ejpam-1200	45	14	βio(x	βio(x	X
ejpam-1200	45	15	,	,	PUNCT
ejpam-1200	45	16	τ1,τ2	τ1,τ2	PROPN
ejpam-1200	45	17	)	)	PUNCT
ejpam-1200	45	18	or	or	CCONJ
ejpam-1200	45	19	(	(	PUNCT
ejpam-1200	45	20	i	i	NOUN
ejpam-1200	45	21	,	,	PUNCT
ejpam-1200	45	22	j)−βio(x	j)−βio(x	PROPN
ejpam-1200	45	23	)	)	PUNCT
ejpam-1200	45	24	.	.	PUNCT
ejpam-1200	46	1	also	also	ADV
ejpam-1200	46	2	,	,	PUNCT
ejpam-1200	46	3	the	the	DET
ejpam-1200	46	4	family	family	NOUN
ejpam-1200	46	5	of	of	ADP
ejpam-1200	46	6	all	all	PRON
ejpam-1200	46	7	(	(	PUNCT
ejpam-1200	46	8	i	i	NOUN
ejpam-1200	46	9	,	,	PUNCT
ejpam-1200	46	10	j)−β	j)−β	PRON
ejpam-1200	46	11	−i	−i	ADJ
ejpam-1200	46	12	-open	-open	PROPN
ejpam-1200	46	13	sets	set	NOUN
ejpam-1200	46	14	of	of	ADP
ejpam-1200	46	15	(	(	PUNCT
ejpam-1200	46	16	x	x	INTJ
ejpam-1200	46	17	,	,	PUNCT
ejpam-1200	46	18	τ1,τ2,i	τ1,τ2,i	PROPN
ejpam-1200	46	19	)	)	PUNCT
ejpam-1200	46	20	containing	contain	VERB
ejpam-1200	46	21	x	x	VERB
ejpam-1200	46	22	is	be	AUX
ejpam-1200	46	23	denoted	denote	VERB
ejpam-1200	46	24	by	by	ADP
ejpam-1200	46	25	(	(	PUNCT
ejpam-1200	46	26	i	i	PROPN
ejpam-1200	46	27	,	,	PUNCT
ejpam-1200	46	28	j)−	j)−	PROPN
ejpam-1200	46	29	βio(x	βio(x	PRON
ejpam-1200	46	30	,	,	PUNCT
ejpam-1200	46	31	x	x	NOUN
ejpam-1200	46	32	)	)	PUNCT
ejpam-1200	46	33	.	.	PUNCT
ejpam-1200	47	1	remark	remark	PROPN
ejpam-1200	47	2	1	1	NUM
ejpam-1200	47	3	.	.	PUNCT
ejpam-1200	48	1	let	let	VERB
ejpam-1200	48	2	i	i	PRON
ejpam-1200	48	3	and	and	CCONJ
ejpam-1200	48	4	j	j	PROPN
ejpam-1200	48	5	be	be	VERB
ejpam-1200	48	6	two	two	NUM
ejpam-1200	48	7	ideals	ideal	NOUN
ejpam-1200	48	8	on	on	ADP
ejpam-1200	48	9	(	(	PUNCT
ejpam-1200	48	10	x	x	INTJ
ejpam-1200	48	11	,	,	PUNCT
ejpam-1200	48	12	τ1,τ2	τ1,τ2	PROPN
ejpam-1200	48	13	)	)	PUNCT
ejpam-1200	48	14	.	.	PUNCT
ejpam-1200	49	1	if	if	SCONJ
ejpam-1200	49	2	i	i	PRON
ejpam-1200	49	3	⊂	⊂	PROPN
ejpam-1200	49	4	j	j	PROPN
ejpam-1200	49	5	,	,	PUNCT
ejpam-1200	49	6	then	then	ADV
ejpam-1200	49	7	βj	βj	X
ejpam-1200	49	8	o(x	o(x	ADJ
ejpam-1200	49	9	,	,	PUNCT
ejpam-1200	49	10	τ1,τ2)⊂	τ1,τ2)⊂	PROPN
ejpam-1200	49	11	βio(x	βio(x	X
ejpam-1200	49	12	,	,	PUNCT
ejpam-1200	49	13	τ1,τ2	τ1,τ2	PROPN
ejpam-1200	49	14	)	)	PUNCT
ejpam-1200	49	15	.	.	PUNCT
ejpam-1200	50	1	proposition	proposition	NOUN
ejpam-1200	50	2	1	1	NUM
ejpam-1200	50	3	.	.	PUNCT
ejpam-1200	51	1	(	(	PUNCT
ejpam-1200	51	2	i	i	NOUN
ejpam-1200	51	3	)	)	PUNCT
ejpam-1200	51	4	every	every	PRON
ejpam-1200	51	5	(	(	PUNCT
ejpam-1200	51	6	i	i	NOUN
ejpam-1200	51	7	,	,	PUNCT
ejpam-1200	51	8	j)−	j)−	PROPN
ejpam-1200	51	9	b−i	b−i	PROPN
ejpam-1200	51	10	-open	-open	NOUN
ejpam-1200	51	11	set	set	NOUN
ejpam-1200	51	12	is	be	AUX
ejpam-1200	51	13	(	(	PUNCT
ejpam-1200	51	14	i	i	PROPN
ejpam-1200	51	15	,	,	PUNCT
ejpam-1200	51	16	j)−	j)−	PROPN
ejpam-1200	51	17	β	β	PROPN
ejpam-1200	51	18	−i	−i	PROPN
ejpam-1200	51	19	-open	-open	PROPN
ejpam-1200	51	20	.	.	PUNCT
ejpam-1200	52	1	m.	m.	PROPN
ejpam-1200	52	2	caldas	caldas	PROPN
ejpam-1200	52	3	,	,	PUNCT
ejpam-1200	52	4	s.	s.	PROPN
ejpam-1200	52	5	jafari	jafari	PROPN
ejpam-1200	52	6	,	,	PUNCT
ejpam-1200	52	7	n.	n.	PROPN
ejpam-1200	52	8	rajesh	rajesh	PROPN
ejpam-1200	52	9	/	/	SYM
ejpam-1200	52	10	eur	eur	PROPN
ejpam-1200	52	11	.	.	PUNCT
ejpam-1200	53	1	j.	j.	PROPN
ejpam-1200	53	2	pure	pure	PROPN
ejpam-1200	53	3	appl	appl	PROPN
ejpam-1200	53	4	.	.	PROPN
ejpam-1200	53	5	math	math	PROPN
ejpam-1200	53	6	,	,	PUNCT
ejpam-1200	53	7	6	6	NUM
ejpam-1200	53	8	(	(	PUNCT
ejpam-1200	53	9	2013	2013	NUM
ejpam-1200	53	10	)	)	PUNCT
ejpam-1200	53	11	,	,	PUNCT
ejpam-1200	53	12	247	247	NUM
ejpam-1200	53	13	-	-	SYM
ejpam-1200	53	14	255	255	NUM
ejpam-1200	53	15	249	249	NUM
ejpam-1200	53	16	(	(	PUNCT
ejpam-1200	53	17	ii	ii	NOUN
ejpam-1200	53	18	)	)	PUNCT
ejpam-1200	53	19	every	every	PRON
ejpam-1200	53	20	(	(	PUNCT
ejpam-1200	53	21	i	i	NOUN
ejpam-1200	53	22	,	,	PUNCT
ejpam-1200	53	23	j)−	j)−	PROPN
ejpam-1200	53	24	β	β	PROPN
ejpam-1200	53	25	−i	−i	PROPN
ejpam-1200	53	26	-open	-open	PROPN
ejpam-1200	53	27	set	set	NOUN
ejpam-1200	53	28	is	be	AUX
ejpam-1200	53	29	(	(	PUNCT
ejpam-1200	53	30	i	i	PROPN
ejpam-1200	53	31	,	,	PUNCT
ejpam-1200	53	32	j)-semi	j)-semi	NOUN
ejpam-1200	53	33	-	-	PUNCT
ejpam-1200	53	34	preopen	preopen	ADJ
ejpam-1200	53	35	.	.	PUNCT
ejpam-1200	54	1	proof	proof	NOUN
ejpam-1200	54	2	.	.	PUNCT
ejpam-1200	55	1	the	the	DET
ejpam-1200	55	2	proof	proof	NOUN
ejpam-1200	55	3	follows	follow	VERB
ejpam-1200	55	4	from	from	ADP
ejpam-1200	55	5	the	the	DET
ejpam-1200	55	6	definitions	definition	NOUN
ejpam-1200	55	7	.	.	PUNCT
ejpam-1200	56	1	the	the	DET
ejpam-1200	56	2	following	follow	VERB
ejpam-1200	56	3	example	example	NOUN
ejpam-1200	56	4	shows	show	VERB
ejpam-1200	56	5	that	that	SCONJ
ejpam-1200	56	6	the	the	DET
ejpam-1200	56	7	converses	converse	NOUN
ejpam-1200	56	8	of	of	ADP
ejpam-1200	56	9	proposition	proposition	NOUN
ejpam-1200	56	10	1	1	NUM
ejpam-1200	56	11	is	be	AUX
ejpam-1200	56	12	not	not	PART
ejpam-1200	56	13	true	true	ADJ
ejpam-1200	56	14	in	in	ADP
ejpam-1200	56	15	general	general	ADJ
ejpam-1200	56	16	.	.	PUNCT
ejpam-1200	56	17	example	example	NOUN
ejpam-1200	57	1	1	1	NUM
ejpam-1200	57	2	.	.	PUNCT
ejpam-1200	57	3	let	let	VERB
ejpam-1200	57	4	x	x	PUNCT
ejpam-1200	57	5	=	=	PRON
ejpam-1200	57	6	{	{	PUNCT
ejpam-1200	57	7	a	a	PRON
ejpam-1200	57	8	,	,	PUNCT
ejpam-1200	57	9	b	b	NOUN
ejpam-1200	57	10	,	,	PUNCT
ejpam-1200	57	11	c	c	NOUN
ejpam-1200	57	12	}	}	PUNCT
ejpam-1200	57	13	,	,	PUNCT
ejpam-1200	57	14	τ1	τ1	NOUN
ejpam-1200	57	15	=	=	SYM
ejpam-1200	57	16	{	{	PUNCT
ejpam-1200	57	17	;	;	PUNCT
ejpam-1200	57	18	,	,	PUNCT
ejpam-1200	57	19	{	{	PUNCT
ejpam-1200	57	20	a	a	X
ejpam-1200	57	21	}	}	PUNCT
ejpam-1200	57	22	,	,	PUNCT
ejpam-1200	57	23	x	x	SYM
ejpam-1200	57	24	}	}	PUNCT
ejpam-1200	57	25	,	,	PUNCT
ejpam-1200	57	26	τ2	τ2	NOUN
ejpam-1200	57	27	=	=	SYM
ejpam-1200	57	28	{	{	PUNCT
ejpam-1200	57	29	;	;	PUNCT
ejpam-1200	57	30	,	,	PUNCT
ejpam-1200	57	31	{	{	PUNCT
ejpam-1200	57	32	a	a	X
ejpam-1200	57	33	}	}	PUNCT
ejpam-1200	57	34	,	,	PUNCT
ejpam-1200	57	35	{	{	PUNCT
ejpam-1200	57	36	a	a	DET
ejpam-1200	57	37	,	,	PUNCT
ejpam-1200	57	38	b	b	NOUN
ejpam-1200	57	39	}	}	PUNCT
ejpam-1200	57	40	,	,	PUNCT
ejpam-1200	57	41	x	x	SYM
ejpam-1200	57	42	}	}	PUNCT
ejpam-1200	57	43	and	and	CCONJ
ejpam-1200	57	44	i	i	PRON
ejpam-1200	57	45	=	=	PUNCT
ejpam-1200	57	46	{	{	PUNCT
ejpam-1200	57	47	;	;	PUNCT
ejpam-1200	57	48	,	,	PUNCT
ejpam-1200	57	49	{	{	PUNCT
ejpam-1200	57	50	a	a	X
ejpam-1200	57	51	}	}	PUNCT
ejpam-1200	57	52	}	}	PUNCT
ejpam-1200	57	53	.	.	PUNCT
ejpam-1200	58	1	then	then	ADV
ejpam-1200	58	2	the	the	DET
ejpam-1200	58	3	set	set	NOUN
ejpam-1200	58	4	{	{	PUNCT
ejpam-1200	58	5	a	a	NOUN
ejpam-1200	58	6	,	,	PUNCT
ejpam-1200	58	7	c	c	NOUN
ejpam-1200	58	8	}	}	PUNCT
ejpam-1200	58	9	is	be	AUX
ejpam-1200	58	10	(	(	PUNCT
ejpam-1200	58	11	i	i	NOUN
ejpam-1200	58	12	,	,	PUNCT
ejpam-1200	58	13	j)−	j)−	PROPN
ejpam-1200	58	14	β	β	PROPN
ejpam-1200	58	15	−i	−i	PROPN
ejpam-1200	58	16	-open	-open	PROPN
ejpam-1200	58	17	but	but	CCONJ
ejpam-1200	58	18	not	not	PART
ejpam-1200	58	19	(	(	PUNCT
ejpam-1200	58	20	i	i	NOUN
ejpam-1200	58	21	,	,	PUNCT
ejpam-1200	58	22	j)−	j)−	PROPN
ejpam-1200	58	23	b−i	b−i	PROPN
ejpam-1200	58	24	-open	-open	NOUN
ejpam-1200	58	25	.	.	PUNCT
ejpam-1200	59	1	corollary	corollary	ADJ
ejpam-1200	59	2	1	1	NUM
ejpam-1200	59	3	.	.	PUNCT
ejpam-1200	60	1	(	(	PUNCT
ejpam-1200	60	2	i	i	NOUN
ejpam-1200	60	3	)	)	PUNCT
ejpam-1200	60	4	every	every	PRON
ejpam-1200	60	5	(	(	PUNCT
ejpam-1200	60	6	i	i	NOUN
ejpam-1200	60	7	,	,	PUNCT
ejpam-1200	60	8	j)−α−i	j)−α−i	PROPN
ejpam-1200	60	9	-open	-open	PROPN
ejpam-1200	60	10	set	set	NOUN
ejpam-1200	60	11	is	be	AUX
ejpam-1200	60	12	(	(	PUNCT
ejpam-1200	60	13	i	i	PROPN
ejpam-1200	60	14	,	,	PUNCT
ejpam-1200	60	15	j)−	j)−	PROPN
ejpam-1200	60	16	β	β	PROPN
ejpam-1200	60	17	−i	−i	PROPN
ejpam-1200	60	18	-open	-open	PROPN
ejpam-1200	60	19	.	.	PUNCT
ejpam-1200	61	1	(	(	PUNCT
ejpam-1200	61	2	ii	ii	NOUN
ejpam-1200	61	3	)	)	PUNCT
ejpam-1200	62	1	every	every	PRON
ejpam-1200	62	2	(	(	PUNCT
ejpam-1200	62	3	i	i	NOUN
ejpam-1200	62	4	,	,	PUNCT
ejpam-1200	62	5	j)-semi	j)-semi	PROPN
ejpam-1200	62	6	-	-	PUNCT
ejpam-1200	62	7	i	i	PRON
ejpam-1200	62	8	-open	-open	VERB
ejpam-1200	62	9	set	set	VERB
ejpam-1200	62	10	is	be	AUX
ejpam-1200	62	11	(	(	PUNCT
ejpam-1200	62	12	i	i	PROPN
ejpam-1200	62	13	,	,	PUNCT
ejpam-1200	62	14	j)−	j)−	PROPN
ejpam-1200	62	15	β	β	PROPN
ejpam-1200	62	16	−i	−i	PROPN
ejpam-1200	62	17	-open	-open	PROPN
ejpam-1200	62	18	.	.	PUNCT
ejpam-1200	63	1	(	(	PUNCT
ejpam-1200	63	2	iii	iii	X
ejpam-1200	63	3	)	)	PUNCT
ejpam-1200	63	4	every	every	PRON
ejpam-1200	63	5	(	(	PUNCT
ejpam-1200	63	6	i	i	PROPN
ejpam-1200	63	7	,	,	PUNCT
ejpam-1200	63	8	j)-pre	j)-pre	PROPN
ejpam-1200	63	9	-	-	PUNCT
ejpam-1200	63	10	i	i	PRON
ejpam-1200	63	11	-open	-open	VERB
ejpam-1200	63	12	set	set	VERB
ejpam-1200	63	13	is	be	AUX
ejpam-1200	63	14	(	(	PUNCT
ejpam-1200	63	15	i	i	PROPN
ejpam-1200	63	16	,	,	PUNCT
ejpam-1200	63	17	j)−	j)−	PROPN
ejpam-1200	63	18	β	β	PROPN
ejpam-1200	63	19	−i	−i	PROPN
ejpam-1200	63	20	-open	-open	PROPN
ejpam-1200	63	21	.	.	PUNCT
ejpam-1200	64	1	proposition	proposition	NOUN
ejpam-1200	64	2	2	2	NUM
ejpam-1200	64	3	.	.	X
ejpam-1200	64	4	for	for	ADP
ejpam-1200	64	5	an	an	DET
ejpam-1200	64	6	ideal	ideal	ADJ
ejpam-1200	64	7	bitopological	bitopological	ADJ
ejpam-1200	64	8	space	space	NOUN
ejpam-1200	64	9	(	(	PUNCT
ejpam-1200	64	10	x	x	NOUN
ejpam-1200	64	11	,	,	PUNCT
ejpam-1200	64	12	τ1,τ2,i	τ1,τ2,i	PROPN
ejpam-1200	64	13	)	)	PUNCT
ejpam-1200	64	14	and	and	CCONJ
ejpam-1200	64	15	a⊂	a⊂	ADP
ejpam-1200	64	16	x	x	SYM
ejpam-1200	64	17	,	,	PUNCT
ejpam-1200	64	18	we	we	PRON
ejpam-1200	64	19	have	have	VERB
ejpam-1200	64	20	:	:	PUNCT
ejpam-1200	64	21	(	(	PUNCT
ejpam-1200	64	22	i	i	NOUN
ejpam-1200	64	23	)	)	PUNCT
ejpam-1200	64	24	if	if	SCONJ
ejpam-1200	64	25	i	i	PRON
ejpam-1200	64	26	=	=	X
ejpam-1200	64	27	{	{	PUNCT
ejpam-1200	64	28	;	;	PUNCT
ejpam-1200	64	29	}	}	PUNCT
ejpam-1200	64	30	,	,	PUNCT
ejpam-1200	64	31	then	then	ADV
ejpam-1200	64	32	a	a	PRON
ejpam-1200	64	33	is	be	AUX
ejpam-1200	64	34	(	(	PUNCT
ejpam-1200	64	35	i	i	NOUN
ejpam-1200	64	36	,	,	PUNCT
ejpam-1200	64	37	j)−	j)−	PROPN
ejpam-1200	64	38	β	β	PROPN
ejpam-1200	64	39	−i	−i	PROPN
ejpam-1200	64	40	-open	-open	PROPN
ejpam-1200	64	41	if	if	SCONJ
ejpam-1200	64	42	and	and	CCONJ
ejpam-1200	64	43	only	only	ADV
ejpam-1200	64	44	if	if	SCONJ
ejpam-1200	64	45	a	a	PRON
ejpam-1200	64	46	is	be	AUX
ejpam-1200	64	47	(	(	PUNCT
ejpam-1200	64	48	i	i	PROPN
ejpam-1200	64	49	,	,	PUNCT
ejpam-1200	64	50	j)-semi	j)-semi	NOUN
ejpam-1200	64	51	-	-	PUNCT
ejpam-1200	64	52	preopen	preopen	ADJ
ejpam-1200	64	53	.	.	PUNCT
ejpam-1200	65	1	(	(	PUNCT
ejpam-1200	65	2	ii	ii	NOUN
ejpam-1200	65	3	)	)	PUNCT
ejpam-1200	65	4	if	if	SCONJ
ejpam-1200	65	5	i	i	PRON
ejpam-1200	65	6	=	=	VERB
ejpam-1200	65	7	p	p	X
ejpam-1200	65	8	(	(	PUNCT
ejpam-1200	65	9	x	x	PROPN
ejpam-1200	65	10	)	)	PUNCT
ejpam-1200	65	11	,	,	PUNCT
ejpam-1200	65	12	then	then	ADV
ejpam-1200	65	13	a	a	PRON
ejpam-1200	65	14	is	be	AUX
ejpam-1200	65	15	(	(	PUNCT
ejpam-1200	65	16	i	i	NOUN
ejpam-1200	65	17	,	,	PUNCT
ejpam-1200	65	18	j)−	j)−	PROPN
ejpam-1200	65	19	β	β	PROPN
ejpam-1200	65	20	−i	−i	PROPN
ejpam-1200	65	21	-open	-open	PROPN
ejpam-1200	65	22	if	if	SCONJ
ejpam-1200	65	23	and	and	CCONJ
ejpam-1200	65	24	only	only	ADV
ejpam-1200	65	25	if	if	SCONJ
ejpam-1200	65	26	a	a	PRON
ejpam-1200	65	27	is	be	AUX
ejpam-1200	65	28	(	(	PUNCT
ejpam-1200	65	29	i	i	PRON
ejpam-1200	65	30	,	,	PUNCT
ejpam-1200	65	31	j)-semiopen	j)-semiopen	ADJ
ejpam-1200	65	32	.	.	PUNCT
ejpam-1200	66	1	proof	proof	NOUN
ejpam-1200	66	2	.	.	PUNCT
ejpam-1200	67	1	the	the	DET
ejpam-1200	67	2	proof	proof	NOUN
ejpam-1200	67	3	follows	follow	VERB
ejpam-1200	67	4	from	from	ADP
ejpam-1200	67	5	the	the	DET
ejpam-1200	67	6	fact	fact	NOUN
ejpam-1200	67	7	that	that	SCONJ
ejpam-1200	67	8	(	(	PUNCT
ejpam-1200	67	9	i	i	NOUN
ejpam-1200	67	10	)	)	PUNCT
ejpam-1200	67	11	if	if	SCONJ
ejpam-1200	67	12	i	i	PRON
ejpam-1200	67	13	=	=	X
ejpam-1200	67	14	{	{	PUNCT
ejpam-1200	67	15	;	;	PUNCT
ejpam-1200	67	16	}	}	PUNCT
ejpam-1200	67	17	,	,	PUNCT
ejpam-1200	67	18	then	then	ADV
ejpam-1200	67	19	a∗	a∗	PROPN
ejpam-1200	67	20	=	=	SYM
ejpam-1200	67	21	cl(a	cl(a	X
ejpam-1200	67	22	)	)	PUNCT
ejpam-1200	67	23	.	.	PUNCT
ejpam-1200	68	1	(	(	PUNCT
ejpam-1200	68	2	ii	ii	X
ejpam-1200	68	3	)	)	PUNCT
ejpam-1200	68	4	if	if	SCONJ
ejpam-1200	68	5	i	i	PRON
ejpam-1200	68	6	=	=	VERB
ejpam-1200	68	7	p	p	X
ejpam-1200	68	8	(	(	PUNCT
ejpam-1200	68	9	x	x	PROPN
ejpam-1200	68	10	)	)	PUNCT
ejpam-1200	68	11	,	,	PUNCT
ejpam-1200	68	12	then	then	ADV
ejpam-1200	68	13	a∗	a∗	PROPN
ejpam-1200	68	14	=	=	PUNCT
ejpam-1200	68	15	;	;	PUNCT
ejpam-1200	68	16	for	for	ADP
ejpam-1200	68	17	every	every	DET
ejpam-1200	68	18	subset	subset	NOUN
ejpam-1200	68	19	a	a	PRON
ejpam-1200	68	20	of	of	ADP
ejpam-1200	68	21	x	x	PUNCT
ejpam-1200	68	22	.	.	PUNCT
ejpam-1200	68	23	remark	remark	PROPN
ejpam-1200	68	24	2	2	NUM
ejpam-1200	68	25	.	.	PUNCT
ejpam-1200	69	1	the	the	DET
ejpam-1200	69	2	intersection	intersection	NOUN
ejpam-1200	69	3	of	of	ADP
ejpam-1200	69	4	any	any	DET
ejpam-1200	69	5	two	two	NUM
ejpam-1200	69	6	(	(	PUNCT
ejpam-1200	69	7	i	i	NOUN
ejpam-1200	69	8	,	,	PUNCT
ejpam-1200	69	9	j)−β	j)−β	PRON
ejpam-1200	69	10	−i	−i	ADJ
ejpam-1200	69	11	-open	-open	PROPN
ejpam-1200	69	12	sets	set	NOUN
ejpam-1200	69	13	is	be	AUX
ejpam-1200	69	14	not	not	PART
ejpam-1200	69	15	an	an	DET
ejpam-1200	69	16	(	(	PUNCT
ejpam-1200	69	17	i	i	NOUN
ejpam-1200	69	18	,	,	PUNCT
ejpam-1200	69	19	j)−β	j)−β	PRON
ejpam-1200	69	20	−i	−i	ADJ
ejpam-1200	69	21	-open	-open	NOUN
ejpam-1200	69	22	set	set	VERB
ejpam-1200	69	23	as	as	SCONJ
ejpam-1200	69	24	it	it	PRON
ejpam-1200	69	25	can	can	AUX
ejpam-1200	69	26	be	be	AUX
ejpam-1200	69	27	seen	see	VERB
ejpam-1200	69	28	from	from	ADP
ejpam-1200	69	29	the	the	DET
ejpam-1200	69	30	following	follow	VERB
ejpam-1200	69	31	example	example	NOUN
ejpam-1200	69	32	.	.	PUNCT
ejpam-1200	70	1	example	example	NOUN
ejpam-1200	71	1	2	2	NUM
ejpam-1200	71	2	.	.	PUNCT
ejpam-1200	71	3	let	let	VERB
ejpam-1200	71	4	x	x	PUNCT
ejpam-1200	71	5	=	=	PRON
ejpam-1200	71	6	{	{	PUNCT
ejpam-1200	71	7	a	a	PRON
ejpam-1200	71	8	,	,	PUNCT
ejpam-1200	71	9	b	b	NOUN
ejpam-1200	71	10	,	,	PUNCT
ejpam-1200	71	11	c	c	NOUN
ejpam-1200	71	12	,	,	PUNCT
ejpam-1200	71	13	d	d	NOUN
ejpam-1200	71	14	}	}	PUNCT
ejpam-1200	71	15	,	,	PUNCT
ejpam-1200	71	16	τ1	τ1	NOUN
ejpam-1200	71	17	=	=	SYM
ejpam-1200	71	18	{	{	PUNCT
ejpam-1200	71	19	∅	∅	NOUN
ejpam-1200	71	20	,	,	PUNCT
ejpam-1200	71	21	{	{	PUNCT
ejpam-1200	71	22	a	a	X
ejpam-1200	71	23	}	}	PUNCT
ejpam-1200	71	24	,	,	PUNCT
ejpam-1200	71	25	{	{	PUNCT
ejpam-1200	71	26	b	b	NOUN
ejpam-1200	71	27	}	}	PUNCT
ejpam-1200	71	28	,	,	PUNCT
ejpam-1200	71	29	{	{	PUNCT
ejpam-1200	71	30	a	a	DET
ejpam-1200	71	31	,	,	PUNCT
ejpam-1200	71	32	b	b	NOUN
ejpam-1200	71	33	}	}	PUNCT
ejpam-1200	71	34	,	,	PUNCT
ejpam-1200	71	35	{	{	PUNCT
ejpam-1200	71	36	a	a	DET
ejpam-1200	71	37	,	,	PUNCT
ejpam-1200	71	38	b	b	NOUN
ejpam-1200	71	39	,	,	PUNCT
ejpam-1200	71	40	c	c	NOUN
ejpam-1200	71	41	}	}	PUNCT
ejpam-1200	71	42	,	,	PUNCT
ejpam-1200	71	43	x	x	SYM
ejpam-1200	71	44	}	}	PUNCT
ejpam-1200	71	45	,	,	PUNCT
ejpam-1200	71	46	τ2	τ2	NOUN
ejpam-1200	71	47	=	=	SYM
ejpam-1200	71	48	{	{	PUNCT
ejpam-1200	71	49	∅	∅	NOUN
ejpam-1200	71	50	,	,	PUNCT
ejpam-1200	71	51	x	x	SYM
ejpam-1200	71	52	}	}	PUNCT
ejpam-1200	71	53	and	and	CCONJ
ejpam-1200	71	54	i	i	PRON
ejpam-1200	71	55	=	=	PUNCT
ejpam-1200	71	56	{	{	PUNCT
ejpam-1200	71	57	∅	∅	NOUN
ejpam-1200	71	58	,	,	PUNCT
ejpam-1200	71	59	{	{	PUNCT
ejpam-1200	71	60	c	c	NOUN
ejpam-1200	71	61	}	}	PUNCT
ejpam-1200	71	62	,	,	PUNCT
ejpam-1200	71	63	{	{	PUNCT
ejpam-1200	71	64	d	d	X
ejpam-1200	71	65	}	}	PUNCT
ejpam-1200	71	66	,	,	PUNCT
ejpam-1200	71	67	{	{	PUNCT
ejpam-1200	71	68	c	c	X
ejpam-1200	71	69	,	,	PUNCT
ejpam-1200	71	70	d	d	NOUN
ejpam-1200	71	71	}	}	PUNCT
ejpam-1200	71	72	}	}	PUNCT
ejpam-1200	71	73	.	.	PUNCT
ejpam-1200	72	1	then	then	ADV
ejpam-1200	72	2	the	the	DET
ejpam-1200	72	3	sets	set	NOUN
ejpam-1200	72	4	{	{	PUNCT
ejpam-1200	72	5	a	a	PRON
ejpam-1200	72	6	,	,	PUNCT
ejpam-1200	72	7	c	c	NOUN
ejpam-1200	72	8	}	}	PUNCT
ejpam-1200	72	9	and	and	CCONJ
ejpam-1200	72	10	{	{	PUNCT
ejpam-1200	72	11	b	b	NOUN
ejpam-1200	72	12	,	,	PUNCT
ejpam-1200	72	13	c	c	NOUN
ejpam-1200	72	14	}	}	PUNCT
ejpam-1200	72	15	are	be	AUX
ejpam-1200	72	16	(	(	PUNCT
ejpam-1200	72	17	1	1	NUM
ejpam-1200	72	18	,	,	PUNCT
ejpam-1200	72	19	2)−β−i	2)−β−i	NUM
ejpam-1200	72	20	-open	-open	NOUN
ejpam-1200	72	21	sets	set	NOUN
ejpam-1200	72	22	of	of	ADP
ejpam-1200	72	23	(	(	PUNCT
ejpam-1200	72	24	x	x	INTJ
ejpam-1200	72	25	,	,	PUNCT
ejpam-1200	72	26	τ1,τ2,i	τ1,τ2,i	PROPN
ejpam-1200	72	27	)	)	PUNCT
ejpam-1200	72	28	but	but	CCONJ
ejpam-1200	72	29	their	their	PRON
ejpam-1200	72	30	intersection	intersection	NOUN
ejpam-1200	72	31	{	{	PUNCT
ejpam-1200	72	32	c	c	NOUN
ejpam-1200	72	33	}	}	PUNCT
ejpam-1200	72	34	is	be	AUX
ejpam-1200	72	35	not	not	PART
ejpam-1200	72	36	an	an	DET
ejpam-1200	72	37	(	(	PUNCT
ejpam-1200	72	38	1,2)−	1,2)−	NUM
ejpam-1200	72	39	β	β	X
ejpam-1200	72	40	−i	−i	ADJ
ejpam-1200	72	41	-open	-open	ADJ
ejpam-1200	72	42	set	set	NOUN
ejpam-1200	72	43	of	of	ADP
ejpam-1200	72	44	(	(	PUNCT
ejpam-1200	72	45	x	x	INTJ
ejpam-1200	72	46	,	,	PUNCT
ejpam-1200	72	47	τ1,τ2,i	τ1,τ2,i	PROPN
ejpam-1200	72	48	)	)	PUNCT
ejpam-1200	72	49	.	.	PUNCT
ejpam-1200	73	1	theorem	theorem	NOUN
ejpam-1200	73	2	1	1	NUM
ejpam-1200	73	3	.	.	PUNCT
ejpam-1200	74	1	if	if	SCONJ
ejpam-1200	74	2	{	{	PUNCT
ejpam-1200	74	3	aα}α∈ω	aα}α∈ω	NOUN
ejpam-1200	74	4	is	be	AUX
ejpam-1200	74	5	a	a	DET
ejpam-1200	74	6	family	family	NOUN
ejpam-1200	74	7	of	of	ADP
ejpam-1200	74	8	(	(	PUNCT
ejpam-1200	74	9	i	i	PROPN
ejpam-1200	74	10	,	,	PUNCT
ejpam-1200	74	11	j)−	j)−	PROPN
ejpam-1200	74	12	β	β	PROPN
ejpam-1200	74	13	−i	−i	PROPN
ejpam-1200	74	14	-open	-open	PROPN
ejpam-1200	74	15	sets	set	NOUN
ejpam-1200	74	16	in	in	ADP
ejpam-1200	74	17	(	(	PUNCT
ejpam-1200	74	18	x	x	INTJ
ejpam-1200	74	19	,	,	PUNCT
ejpam-1200	74	20	τ1,τ2,i	τ1,τ2,i	PROPN
ejpam-1200	74	21	)	)	PUNCT
ejpam-1200	74	22	,	,	PUNCT
ejpam-1200	74	23	then	then	ADV
ejpam-1200	74	24	⋃	⋃	NOUN
ejpam-1200	74	25	α∈ω	α∈ω	NOUN
ejpam-1200	74	26	aα	aα	NOUN
ejpam-1200	74	27	is	be	AUX
ejpam-1200	74	28	(	(	PUNCT
ejpam-1200	74	29	i	i	NOUN
ejpam-1200	74	30	,	,	PUNCT
ejpam-1200	74	31	j)−	j)−	PROPN
ejpam-1200	74	32	β	β	PROPN
ejpam-1200	74	33	−i	−i	PROPN
ejpam-1200	74	34	-open	-open	PROPN
ejpam-1200	74	35	in	in	ADP
ejpam-1200	74	36	(	(	PUNCT
ejpam-1200	74	37	x	x	INTJ
ejpam-1200	74	38	,	,	PUNCT
ejpam-1200	74	39	τ1,τ2,i	τ1,τ2,i	PROPN
ejpam-1200	74	40	)	)	PUNCT
ejpam-1200	74	41	.	.	PUNCT
ejpam-1200	75	1	proof	proof	NOUN
ejpam-1200	75	2	.	.	PUNCT
ejpam-1200	76	1	since	since	SCONJ
ejpam-1200	76	2	{	{	PUNCT
ejpam-1200	76	3	aα	aα	NOUN
ejpam-1200	76	4	:	:	PUNCT
ejpam-1200	76	5	α	α	PROPN
ejpam-1200	76	6	∈	∈	PROPN
ejpam-1200	76	7	ω	ω	PROPN
ejpam-1200	76	8	}	}	PUNCT
ejpam-1200	76	9	⊂	⊂	PROPN
ejpam-1200	76	10	(	(	PUNCT
ejpam-1200	76	11	i	i	PRON
ejpam-1200	76	12	,	,	PUNCT
ejpam-1200	76	13	j)−βio(x	j)−βio(x	PROPN
ejpam-1200	76	14	)	)	PUNCT
ejpam-1200	76	15	,	,	PUNCT
ejpam-1200	76	16	then	then	ADV
ejpam-1200	76	17	aα	aα	PROPN
ejpam-1200	76	18	⊂	⊂	PROPN
ejpam-1200	76	19	τ	τ	PROPN
ejpam-1200	77	1	j	j	PROPN
ejpam-1200	77	2	−cl(τi	−cl(τi	PROPN
ejpam-1200	77	3	−	−	PROPN
ejpam-1200	77	4	int(τ	int(τ	PROPN
ejpam-1200	77	5	j	j	PROPN
ejpam-1200	77	6	−cl∗(aα	−cl∗(aα	PROPN
ejpam-1200	77	7	)	)	PUNCT
ejpam-1200	77	8	)	)	PUNCT
ejpam-1200	77	9	)	)	PUNCT
ejpam-1200	78	1	for	for	ADP
ejpam-1200	78	2	every	every	DET
ejpam-1200	78	3	α	α	PROPN
ejpam-1200	78	4	∈	∈	PROPN
ejpam-1200	78	5	ω	ω	PROPN
ejpam-1200	78	6	.	.	PUNCT
ejpam-1200	79	1	thus	thus	ADV
ejpam-1200	79	2	,	,	PUNCT
ejpam-1200	79	3	∪	∪	ADP
ejpam-1200	79	4	α∈ω	α∈ω	NUM
ejpam-1200	79	5	aα	aα	NOUN
ejpam-1200	79	6	⊂	⊂	NOUN
ejpam-1200	79	7	∪	∪	ADP
ejpam-1200	79	8	α∈ω	α∈ω	NOUN
ejpam-1200	79	9	τ	τ	X
ejpam-1200	79	10	j	j	PROPN
ejpam-1200	79	11	−cl(τi	−cl(τi	PROPN
ejpam-1200	79	12	−	−	PROPN
ejpam-1200	80	1	int(τ	int(τ	PROPN
ejpam-1200	80	2	j	j	PROPN
ejpam-1200	80	3	−cl∗(aα)))⊂	−cl∗(aα)))⊂	NOUN
ejpam-1200	80	4	τ	τ	PROPN
ejpam-1200	80	5	j	j	PROPN
ejpam-1200	80	6	−cl(τi	−cl(τi	PROPN
ejpam-1200	80	7	−	−	PROPN
ejpam-1200	80	8	int	int	NOUN
ejpam-1200	80	9	(	(	PUNCT
ejpam-1200	80	10	∪	∪	ADP
ejpam-1200	80	11	α∈ω	α∈ω	NOUN
ejpam-1200	80	12	τ	τ	X
ejpam-1200	80	13	j	j	PROPN
ejpam-1200	80	14	−cl∗(aα	−cl∗(aα	PROPN
ejpam-1200	80	15	)	)	PUNCT
ejpam-1200	80	16	)	)	PUNCT
ejpam-1200	80	17	)	)	PUNCT
ejpam-1200	81	1	=	=	PUNCT
ejpam-1200	81	2	τ	τ	X
ejpam-1200	81	3	j	j	PROPN
ejpam-1200	81	4	−cl(τi	−cl(τi	PROPN
ejpam-1200	81	5	−	−	PROPN
ejpam-1200	81	6	int(τ	int(τ	PROPN
ejpam-1200	81	7	j	j	PROPN
ejpam-1200	81	8	−cl∗	−cl∗	PROPN
ejpam-1200	81	9	(	(	PUNCT
ejpam-1200	81	10	∪	∪	PROPN
ejpam-1200	81	11	α∈ω	α∈ω	NUM
ejpam-1200	81	12	aα	aα	NOUN
ejpam-1200	81	13	)	)	PUNCT
ejpam-1200	81	14	)	)	PUNCT
ejpam-1200	81	15	)	)	PUNCT
ejpam-1200	81	16	.	.	PUNCT
ejpam-1200	82	1	therefore	therefore	ADV
ejpam-1200	82	2	,	,	PUNCT
ejpam-1200	82	3	we	we	PRON
ejpam-1200	82	4	obtain	obtain	VERB
ejpam-1200	82	5	∪	∪	ADJ
ejpam-1200	82	6	α∈ω	α∈ω	NOUN
ejpam-1200	82	7	aα	aα	NOUN
ejpam-1200	82	8	⊂	⊂	PROPN
ejpam-1200	82	9	τ	τ	X
ejpam-1200	82	10	j−cl(τi−	j−cl(τi−	PUNCT
ejpam-1200	83	1	int(τ	int(τ	PROPN
ejpam-1200	83	2	j−cl∗	j−cl∗	PROPN
ejpam-1200	83	3	(	(	PUNCT
ejpam-1200	83	4	∪	∪	ADP
ejpam-1200	83	5	α∈ω	α∈ω	NUM
ejpam-1200	83	6	aα	aα	NOUN
ejpam-1200	83	7	)	)	PUNCT
ejpam-1200	83	8	)	)	PUNCT
ejpam-1200	83	9	)	)	PUNCT
ejpam-1200	83	10	.	.	PUNCT
ejpam-1200	84	1	hence	hence	ADV
ejpam-1200	84	2	any	any	DET
ejpam-1200	84	3	union	union	NOUN
ejpam-1200	84	4	of	of	ADP
ejpam-1200	84	5	(	(	PUNCT
ejpam-1200	84	6	i	i	PROPN
ejpam-1200	84	7	,	,	PUNCT
ejpam-1200	84	8	j)−	j)−	PROPN
ejpam-1200	84	9	β	β	PROPN
ejpam-1200	84	10	−i	−i	PROPN
ejpam-1200	84	11	-open	-open	PROPN
ejpam-1200	84	12	sets	set	NOUN
ejpam-1200	84	13	is	be	AUX
ejpam-1200	84	14	(	(	PUNCT
ejpam-1200	84	15	i	i	NOUN
ejpam-1200	84	16	,	,	PUNCT
ejpam-1200	84	17	j)−	j)−	PROPN
ejpam-1200	84	18	β	β	PROPN
ejpam-1200	84	19	−i	−i	PROPN
ejpam-1200	84	20	-open	-open	PROPN
ejpam-1200	84	21	.	.	PUNCT
ejpam-1200	85	1	theorem	theorem	NOUN
ejpam-1200	85	2	2	2	NUM
ejpam-1200	85	3	.	.	PUNCT
ejpam-1200	85	4	a	a	DET
ejpam-1200	85	5	subset	subset	NOUN
ejpam-1200	85	6	a	a	PRON
ejpam-1200	85	7	of	of	ADP
ejpam-1200	85	8	an	an	DET
ejpam-1200	85	9	ideal	ideal	ADJ
ejpam-1200	85	10	bitopological	bitopological	ADJ
ejpam-1200	85	11	space	space	NOUN
ejpam-1200	85	12	(	(	PUNCT
ejpam-1200	85	13	x	x	X
ejpam-1200	85	14	,	,	PUNCT
ejpam-1200	85	15	τ1,τ2,i	τ1,τ2,i	PROPN
ejpam-1200	85	16	)	)	PUNCT
ejpam-1200	86	1	is	be	AUX
ejpam-1200	86	2	(	(	PUNCT
ejpam-1200	86	3	i	i	INTJ
ejpam-1200	86	4	,	,	PUNCT
ejpam-1200	86	5	j)−β−i	j)−β−i	PROPN
ejpam-1200	86	6	-open	-open	VERB
ejpam-1200	86	7	if	if	SCONJ
ejpam-1200	86	8	and	and	CCONJ
ejpam-1200	86	9	only	only	ADV
ejpam-1200	86	10	if	if	SCONJ
ejpam-1200	86	11	τ	τ	PROPN
ejpam-1200	86	12	j	j	PROPN
ejpam-1200	86	13	−cl(a	−cl(a	PROPN
ejpam-1200	86	14	)	)	PUNCT
ejpam-1200	86	15	=	=	PUNCT
ejpam-1200	87	1	τ	τ	PROPN
ejpam-1200	87	2	j	j	PROPN
ejpam-1200	87	3	−cl(τi	−cl(τi	NOUN
ejpam-1200	87	4	−	−	PROPN
ejpam-1200	87	5	int(τ	int(τ	PROPN
ejpam-1200	87	6	j	j	PROPN
ejpam-1200	87	7	−cl∗(a	−cl∗(a	PROPN
ejpam-1200	87	8	)	)	PUNCT
ejpam-1200	87	9	)	)	PUNCT
ejpam-1200	87	10	)	)	PUNCT
ejpam-1200	87	11	.	.	PUNCT
ejpam-1200	88	1	m.	m.	PROPN
ejpam-1200	88	2	caldas	caldas	PROPN
ejpam-1200	88	3	,	,	PUNCT
ejpam-1200	88	4	s.	s.	PROPN
ejpam-1200	88	5	jafari	jafari	PROPN
ejpam-1200	88	6	,	,	PUNCT
ejpam-1200	88	7	n.	n.	PROPN
ejpam-1200	88	8	rajesh	rajesh	PROPN
ejpam-1200	88	9	/	/	SYM
ejpam-1200	88	10	eur	eur	PROPN
ejpam-1200	88	11	.	.	PUNCT
ejpam-1200	89	1	j.	j.	PROPN
ejpam-1200	89	2	pure	pure	PROPN
ejpam-1200	89	3	appl	appl	PROPN
ejpam-1200	89	4	.	.	PROPN
ejpam-1200	89	5	math	math	PROPN
ejpam-1200	89	6	,	,	PUNCT
ejpam-1200	89	7	6	6	NUM
ejpam-1200	89	8	(	(	PUNCT
ejpam-1200	89	9	2013	2013	NUM
ejpam-1200	89	10	)	)	PUNCT
ejpam-1200	89	11	,	,	PUNCT
ejpam-1200	89	12	247	247	NUM
ejpam-1200	89	13	-	-	SYM
ejpam-1200	89	14	255	255	NUM
ejpam-1200	89	15	250	250	NUM
ejpam-1200	89	16	proof	proof	NOUN
ejpam-1200	89	17	.	.	PUNCT
ejpam-1200	90	1	let	let	VERB
ejpam-1200	90	2	a	a	DET
ejpam-1200	90	3	be	be	AUX
ejpam-1200	90	4	an	an	DET
ejpam-1200	90	5	(	(	PUNCT
ejpam-1200	90	6	i	i	NOUN
ejpam-1200	90	7	,	,	PUNCT
ejpam-1200	90	8	j)−	j)−	PROPN
ejpam-1200	90	9	β	β	PROPN
ejpam-1200	90	10	−i	−i	PROPN
ejpam-1200	90	11	-open	-open	PROPN
ejpam-1200	90	12	subset	subset	NOUN
ejpam-1200	90	13	of	of	ADP
ejpam-1200	90	14	x	x	X
ejpam-1200	90	15	.	.	PUNCT
ejpam-1200	91	1	then	then	ADV
ejpam-1200	91	2	,	,	PUNCT
ejpam-1200	91	3	we	we	PRON
ejpam-1200	91	4	have	have	VERB
ejpam-1200	91	5	a⊂	a⊂	NOUN
ejpam-1200	91	6	τ	τ	PROPN
ejpam-1200	91	7	j	j	PROPN
ejpam-1200	91	8	−cl(τi	−cl(τi	NOUN
ejpam-1200	91	9	−	−	PROPN
ejpam-1200	91	10	int(τ	int(τ	PROPN
ejpam-1200	91	11	j	j	PROPN
ejpam-1200	91	12	−cl∗(a	−cl∗(a	PROPN
ejpam-1200	91	13	)	)	PUNCT
ejpam-1200	91	14	)	)	PUNCT
ejpam-1200	91	15	)	)	PUNCT
ejpam-1200	92	1	and	and	CCONJ
ejpam-1200	92	2	hence	hence	ADV
ejpam-1200	92	3	τ	τ	PROPN
ejpam-1200	92	4	j	j	PROPN
ejpam-1200	92	5	−cl(a)⊂	−cl(a)⊂	PROPN
ejpam-1200	92	6	τ	τ	PROPN
ejpam-1200	92	7	j	j	PROPN
ejpam-1200	92	8	−cl(τi	−cl(τi	PROPN
ejpam-1200	92	9	−	−	PROPN
ejpam-1200	93	1	int(τ	int(τ	PROPN
ejpam-1200	93	2	j	j	PROPN
ejpam-1200	93	3	−cl∗(a)))⊂	−cl∗(a)))⊂	NOUN
ejpam-1200	93	4	τ	τ	PROPN
ejpam-1200	93	5	j	j	PROPN
ejpam-1200	93	6	−cl(τi	−cl(τi	PROPN
ejpam-1200	93	7	−	−	PROPN
ejpam-1200	93	8	int(τ	int(τ	PROPN
ejpam-1200	93	9	j	j	PROPN
ejpam-1200	93	10	−cl(a)))⊂	−cl(a)))⊂	ADV
ejpam-1200	93	11	τ	τ	PROPN
ejpam-1200	93	12	j	j	PROPN
ejpam-1200	93	13	−cl(a	−cl(a	PROPN
ejpam-1200	93	14	)	)	PUNCT
ejpam-1200	93	15	.	.	PUNCT
ejpam-1200	94	1	therefore	therefore	ADV
ejpam-1200	94	2	,	,	PUNCT
ejpam-1200	94	3	τ	τ	PROPN
ejpam-1200	94	4	j	j	PROPN
ejpam-1200	94	5	−cl(a	−cl(a	PROPN
ejpam-1200	94	6	)	)	PUNCT
ejpam-1200	94	7	=	=	PUNCT
ejpam-1200	94	8	τ	τ	PROPN
ejpam-1200	94	9	j	j	PROPN
ejpam-1200	94	10	−cl(τi	−cl(τi	NOUN
ejpam-1200	94	11	−	−	PROPN
ejpam-1200	95	1	int(τ	int(τ	PROPN
ejpam-1200	95	2	j	j	PROPN
ejpam-1200	95	3	−cl∗(a	−cl∗(a	PROPN
ejpam-1200	95	4	)	)	PUNCT
ejpam-1200	95	5	)	)	PUNCT
ejpam-1200	95	6	)	)	PUNCT
ejpam-1200	95	7	.	.	PUNCT
ejpam-1200	96	1	the	the	DET
ejpam-1200	96	2	converse	converse	NOUN
ejpam-1200	96	3	is	be	AUX
ejpam-1200	96	4	obvious	obvious	ADJ
ejpam-1200	96	5	.	.	PUNCT
ejpam-1200	97	1	definition	definition	NOUN
ejpam-1200	97	2	5	5	NUM
ejpam-1200	97	3	.	.	PUNCT
ejpam-1200	98	1	a	a	DET
ejpam-1200	98	2	bitopological	bitopological	ADJ
ejpam-1200	98	3	space	space	NOUN
ejpam-1200	98	4	(	(	PUNCT
ejpam-1200	98	5	x	x	NOUN
ejpam-1200	98	6	,	,	PUNCT
ejpam-1200	98	7	τ1,τ2	τ1,τ2	PROPN
ejpam-1200	98	8	)	)	PUNCT
ejpam-1200	98	9	is	be	AUX
ejpam-1200	98	10	said	say	VERB
ejpam-1200	98	11	to	to	PART
ejpam-1200	98	12	be	be	AUX
ejpam-1200	98	13	pairwise	pairwise	NOUN
ejpam-1200	98	14	extremally	extremally	ADV
ejpam-1200	98	15	disconnected	disconnect	VERB
ejpam-1200	99	1	[	[	X
ejpam-1200	99	2	1	1	X
ejpam-1200	99	3	]	]	X
ejpam-1200	99	4	if	if	SCONJ
ejpam-1200	99	5	τ	τ	PROPN
ejpam-1200	99	6	j	j	PROPN
ejpam-1200	99	7	−cl(a	−cl(a	NOUN
ejpam-1200	99	8	)	)	PUNCT
ejpam-1200	99	9	∈	∈	NOUN
ejpam-1200	99	10	τi	τi	NOUN
ejpam-1200	99	11	for	for	ADP
ejpam-1200	99	12	every	every	DET
ejpam-1200	99	13	a∈	a∈	PROPN
ejpam-1200	99	14	τi	τi	VERB
ejpam-1200	99	15	.	.	PUNCT
ejpam-1200	100	1	proposition	proposition	NOUN
ejpam-1200	100	2	3	3	X
ejpam-1200	100	3	.	.	PUNCT
ejpam-1200	101	1	let	let	AUX
ejpam-1200	101	2	(	(	PUNCT
ejpam-1200	101	3	x	x	INTJ
ejpam-1200	101	4	,	,	PUNCT
ejpam-1200	101	5	τ1,τ2,i	τ1,τ2,i	PROPN
ejpam-1200	101	6	)	)	PUNCT
ejpam-1200	101	7	be	be	AUX
ejpam-1200	101	8	a	a	DET
ejpam-1200	101	9	pairwise	pairwise	NOUN
ejpam-1200	101	10	extremally	extremally	ADV
ejpam-1200	101	11	disconnected	disconnect	VERB
ejpam-1200	101	12	space	space	NOUN
ejpam-1200	101	13	.	.	PUNCT
ejpam-1200	102	1	if	if	SCONJ
ejpam-1200	102	2	a	a	PRON
ejpam-1200	102	3	is	be	AUX
ejpam-1200	102	4	(	(	PUNCT
ejpam-1200	102	5	i	i	PROPN
ejpam-1200	102	6	,	,	PUNCT
ejpam-1200	102	7	j)−β−	j)−β−	NOUN
ejpam-1200	102	8	i	i	PRON
ejpam-1200	102	9	-open	-open	VERB
ejpam-1200	102	10	,	,	PUNCT
ejpam-1200	102	11	then	then	ADV
ejpam-1200	102	12	it	it	PRON
ejpam-1200	102	13	is	be	AUX
ejpam-1200	102	14	(	(	PUNCT
ejpam-1200	102	15	i	i	NOUN
ejpam-1200	102	16	,	,	PUNCT
ejpam-1200	102	17	j)-preopen	j)-preopen	VERB
ejpam-1200	102	18	in	in	ADP
ejpam-1200	102	19	x	x	X
ejpam-1200	102	20	.	.	PUNCT
ejpam-1200	103	1	proof	proof	NOUN
ejpam-1200	103	2	.	.	PUNCT
ejpam-1200	104	1	let	let	VERB
ejpam-1200	104	2	a	a	DET
ejpam-1200	104	3	be	be	AUX
ejpam-1200	104	4	(	(	PUNCT
ejpam-1200	104	5	i	i	NOUN
ejpam-1200	104	6	,	,	PUNCT
ejpam-1200	104	7	j)−	j)−	PROPN
ejpam-1200	104	8	β	β	PROPN
ejpam-1200	104	9	−i	−i	PROPN
ejpam-1200	104	10	-open	-open	PROPN
ejpam-1200	104	11	set	set	NOUN
ejpam-1200	104	12	of	of	ADP
ejpam-1200	104	13	x	x	SYM
ejpam-1200	104	14	,	,	PUNCT
ejpam-1200	104	15	we	we	PRON
ejpam-1200	104	16	have	have	VERB
ejpam-1200	104	17	a	a	DET
ejpam-1200	104	18	⊂	⊂	PROPN
ejpam-1200	104	19	τ	τ	PROPN
ejpam-1200	104	20	j	j	PROPN
ejpam-1200	104	21	−	−	PROPN
ejpam-1200	104	22	cl(τi	cl(τi	PROPN
ejpam-1200	104	23	−	−	PROPN
ejpam-1200	105	1	int(τ	int(τ	PROPN
ejpam-1200	105	2	j	j	PROPN
ejpam-1200	105	3	−	−	PROPN
ejpam-1200	105	4	cl∗(a	cl∗(a	NOUN
ejpam-1200	105	5	)	)	PUNCT
ejpam-1200	105	6	)	)	PUNCT
ejpam-1200	105	7	)	)	PUNCT
ejpam-1200	105	8	.	.	PUNCT
ejpam-1200	106	1	since	since	SCONJ
ejpam-1200	106	2	x	x	PRON
ejpam-1200	106	3	is	be	AUX
ejpam-1200	106	4	pairwise	pairwise	NOUN
ejpam-1200	106	5	extremally	extremally	ADV
ejpam-1200	106	6	disconnected	disconnect	VERB
ejpam-1200	106	7	,	,	PUNCT
ejpam-1200	106	8	for	for	ADP
ejpam-1200	106	9	τi	τi	ADP
ejpam-1200	106	10	−	−	PROPN
ejpam-1200	107	1	int(τ	int(τ	PROPN
ejpam-1200	107	2	j	j	PROPN
ejpam-1200	107	3	−cl∗(a	−cl∗(a	PROPN
ejpam-1200	107	4	)	)	PUNCT
ejpam-1200	107	5	)	)	PUNCT
ejpam-1200	108	1	∈	∈	PROPN
ejpam-1200	108	2	τi	τi	ADV
ejpam-1200	108	3	,	,	PUNCT
ejpam-1200	108	4	we	we	PRON
ejpam-1200	108	5	have	have	VERB
ejpam-1200	108	6	τ	τ	PROPN
ejpam-1200	108	7	j	j	PROPN
ejpam-1200	108	8	−cl(τi	−cl(τi	PROPN
ejpam-1200	108	9	−	−	PROPN
ejpam-1200	108	10	int(τ	int(τ	PROPN
ejpam-1200	108	11	j	j	PROPN
ejpam-1200	108	12	−cl∗(a	−cl∗(a	PROPN
ejpam-1200	108	13	)	)	PUNCT
ejpam-1200	108	14	)	)	PUNCT
ejpam-1200	108	15	)	)	PUNCT
ejpam-1200	109	1	∈	∈	PROPN
ejpam-1200	109	2	τi	τi	VERB
ejpam-1200	109	3	.	.	PUNCT
ejpam-1200	110	1	so	so	ADV
ejpam-1200	110	2	,	,	PUNCT
ejpam-1200	110	3	we	we	PRON
ejpam-1200	110	4	have	have	VERB
ejpam-1200	110	5	a⊂τ	a⊂τ	NOUN
ejpam-1200	110	6	j	j	PROPN
ejpam-1200	110	7	−cl(τi	−cl(τi	NOUN
ejpam-1200	110	8	−	−	PROPN
ejpam-1200	110	9	int(τ	int(τ	PROPN
ejpam-1200	110	10	j	j	PROPN
ejpam-1200	110	11	−cl∗(a)))⊂	−cl∗(a)))⊂	NOUN
ejpam-1200	110	12	τi	τi	ADP
ejpam-1200	110	13	−	−	PROPN
ejpam-1200	110	14	int(τ	int(τ	PROPN
ejpam-1200	110	15	j	j	PROPN
ejpam-1200	110	16	−cl(τi	−cl(τi	NOUN
ejpam-1200	110	17	−	−	PROPN
ejpam-1200	110	18	int(τ	int(τ	PROPN
ejpam-1200	110	19	j	j	PROPN
ejpam-1200	110	20	−cl∗(a	−cl∗(a	PROPN
ejpam-1200	110	21	)	)	PUNCT
ejpam-1200	110	22	)	)	PUNCT
ejpam-1200	110	23	)	)	PUNCT
ejpam-1200	110	24	)	)	PUNCT
ejpam-1200	111	1	⊂τi	⊂τi	INTJ
ejpam-1200	111	2	−	−	PUNCT
ejpam-1200	112	1	int(τ	int(τ	PROPN
ejpam-1200	112	2	j	j	PROPN
ejpam-1200	112	3	−cl(τ	−cl(τ	PROPN
ejpam-1200	112	4	j	j	PROPN
ejpam-1200	112	5	−cl∗(a)))⊂	−cl∗(a)))⊂	NOUN
ejpam-1200	112	6	τi	τi	ADP
ejpam-1200	112	7	−	−	PROPN
ejpam-1200	112	8	int(τ	int(τ	PROPN
ejpam-1200	112	9	j	j	PROPN
ejpam-1200	112	10	−cl(a∪	−cl(a∪	PROPN
ejpam-1200	112	11	a∗	a∗	PROPN
ejpam-1200	112	12	)	)	PUNCT
ejpam-1200	112	13	)	)	PUNCT
ejpam-1200	113	1	=	=	PRON
ejpam-1200	113	2	τi	τi	VERB
ejpam-1200	113	3	−	−	PROPN
ejpam-1200	114	1	int(τ	int(τ	PROPN
ejpam-1200	114	2	j	j	PROPN
ejpam-1200	114	3	−cl(a)∪τ	−cl(a)∪τ	PRON
ejpam-1200	115	1	j	j	PROPN
ejpam-1200	115	2	−cl(a∗))⊂	−cl(a∗))⊂	NOUN
ejpam-1200	115	3	τi	τi	ADP
ejpam-1200	115	4	−	−	PROPN
ejpam-1200	115	5	int(τ	int(τ	PROPN
ejpam-1200	115	6	j	j	PROPN
ejpam-1200	115	7	−cl(a	−cl(a	NOUN
ejpam-1200	115	8	)	)	PUNCT
ejpam-1200	115	9	)	)	PUNCT
ejpam-1200	115	10	;	;	PUNCT
ejpam-1200	115	11	hence	hence	ADV
ejpam-1200	115	12	a	a	PRON
ejpam-1200	115	13	is	be	AUX
ejpam-1200	115	14	(	(	PUNCT
ejpam-1200	115	15	i	i	NOUN
ejpam-1200	115	16	,	,	PUNCT
ejpam-1200	115	17	j)-preopen	j)-preopen	VERB
ejpam-1200	115	18	in	in	ADP
ejpam-1200	115	19	x	x	X
ejpam-1200	115	20	.	.	PUNCT
ejpam-1200	116	1	an	an	DET
ejpam-1200	116	2	ideal	ideal	ADJ
ejpam-1200	116	3	bitopological	bitopological	ADJ
ejpam-1200	116	4	space	space	NOUN
ejpam-1200	116	5	is	be	AUX
ejpam-1200	116	6	said	say	VERB
ejpam-1200	116	7	to	to	PART
ejpam-1200	116	8	satisfy	satisfy	VERB
ejpam-1200	116	9	the	the	DET
ejpam-1200	116	10	condition	condition	NOUN
ejpam-1200	116	11	(	(	PUNCT
ejpam-1200	116	12	a	a	X
ejpam-1200	116	13	)	)	PUNCT
ejpam-1200	116	14	if	if	SCONJ
ejpam-1200	116	15	u	u	PROPN
ejpam-1200	116	16	∩τ	∩τ	NOUN
ejpam-1200	116	17	j	j	PROPN
ejpam-1200	116	18	−cl∗(a)⊂	−cl∗(a)⊂	NUM
ejpam-1200	116	19	τ	τ	PROPN
ejpam-1200	116	20	j	j	PROPN
ejpam-1200	116	21	−cl∗(u	−cl∗(u	PROPN
ejpam-1200	116	22	∩	∩	PROPN
ejpam-1200	116	23	a	a	X
ejpam-1200	116	24	)	)	PUNCT
ejpam-1200	116	25	for	for	ADP
ejpam-1200	116	26	every	every	DET
ejpam-1200	116	27	u	u	PROPN
ejpam-1200	116	28	∈	∈	PROPN
ejpam-1200	116	29	τi	τi	X
ejpam-1200	116	30	.	.	PUNCT
ejpam-1200	117	1	theorem	theorem	VERB
ejpam-1200	117	2	3	3	X
ejpam-1200	117	3	.	.	PUNCT
ejpam-1200	118	1	let	let	AUX
ejpam-1200	118	2	(	(	PUNCT
ejpam-1200	118	3	x	x	INTJ
ejpam-1200	118	4	,	,	PUNCT
ejpam-1200	118	5	τ1,τ2,i	τ1,τ2,i	PROPN
ejpam-1200	118	6	)	)	PUNCT
ejpam-1200	118	7	be	be	AUX
ejpam-1200	118	8	a	a	DET
ejpam-1200	118	9	pairwise	pairwise	NOUN
ejpam-1200	118	10	extremally	extremally	ADV
ejpam-1200	118	11	disconnected	disconnect	VERB
ejpam-1200	118	12	space	space	NOUN
ejpam-1200	118	13	which	which	PRON
ejpam-1200	118	14	satisfies	satisfy	VERB
ejpam-1200	118	15	the	the	DET
ejpam-1200	118	16	condition	condition	NOUN
ejpam-1200	118	17	a	a	PRON
ejpam-1200	118	18	.	.	PUNCT
ejpam-1200	119	1	if	if	SCONJ
ejpam-1200	119	2	a	a	PRON
ejpam-1200	119	3	is	be	AUX
ejpam-1200	119	4	(	(	PUNCT
ejpam-1200	119	5	i	i	PROPN
ejpam-1200	119	6	,	,	PUNCT
ejpam-1200	119	7	j)-semi	j)-semi	NOUN
ejpam-1200	119	8	-	-	PUNCT
ejpam-1200	119	9	i	i	PRON
ejpam-1200	119	10	-open	-open	ADJ
ejpam-1200	119	11	and	and	CCONJ
ejpam-1200	119	12	b	b	NOUN
ejpam-1200	119	13	is	be	AUX
ejpam-1200	119	14	(	(	PUNCT
ejpam-1200	119	15	i	i	PROPN
ejpam-1200	119	16	,	,	PUNCT
ejpam-1200	119	17	j)-pre	j)-pre	PROPN
ejpam-1200	119	18	-	-	PUNCT
ejpam-1200	119	19	i	i	PRON
ejpam-1200	119	20	-open	-open	NOUN
ejpam-1200	119	21	,	,	PUNCT
ejpam-1200	119	22	then	then	ADV
ejpam-1200	119	23	a∩	a∩	PROPN
ejpam-1200	119	24	b	b	PROPN
ejpam-1200	119	25	is	be	AUX
ejpam-1200	119	26	(	(	PUNCT
ejpam-1200	119	27	i	i	NOUN
ejpam-1200	119	28	,	,	PUNCT
ejpam-1200	119	29	j)−	j)−	PROPN
ejpam-1200	119	30	β	β	PROPN
ejpam-1200	119	31	−i	−i	PROPN
ejpam-1200	119	32	open	open	ADJ
ejpam-1200	119	33	.	.	PUNCT
ejpam-1200	120	1	proof	proof	NOUN
ejpam-1200	120	2	.	.	PUNCT
ejpam-1200	121	1	let	let	VERB
ejpam-1200	121	2	a	a	DET
ejpam-1200	121	3	be	be	AUX
ejpam-1200	121	4	(	(	PUNCT
ejpam-1200	121	5	i	i	PROPN
ejpam-1200	121	6	,	,	PUNCT
ejpam-1200	121	7	j)-semi	j)-semi	NOUN
ejpam-1200	121	8	-	-	PUNCT
ejpam-1200	121	9	i	i	PRON
ejpam-1200	121	10	-open	-open	ADJ
ejpam-1200	121	11	and	and	CCONJ
ejpam-1200	121	12	b	b	NOUN
ejpam-1200	121	13	an	an	DET
ejpam-1200	121	14	(	(	PUNCT
ejpam-1200	121	15	i	i	NOUN
ejpam-1200	121	16	,	,	PUNCT
ejpam-1200	121	17	j)-pre	j)-pre	PROPN
ejpam-1200	121	18	-	-	PUNCT
ejpam-1200	121	19	i	i	PRON
ejpam-1200	121	20	-open	-open	VERB
ejpam-1200	121	21	set	set	NOUN
ejpam-1200	121	22	of	of	ADP
ejpam-1200	121	23	x	x	X
ejpam-1200	121	24	.	.	PUNCT
ejpam-1200	122	1	then	then	ADV
ejpam-1200	122	2	a∩	a∩	PROPN
ejpam-1200	122	3	b	b	NOUN
ejpam-1200	122	4	⊂τ	⊂τ	PROPN
ejpam-1200	122	5	j	j	PROPN
ejpam-1200	122	6	−cl∗(τi	−cl∗(τi	NOUN
ejpam-1200	122	7	−	−	PROPN
ejpam-1200	123	1	int(a))∩τi	int(a))∩τi	NOUN
ejpam-1200	123	2	−	−	NUM
ejpam-1200	123	3	int(τ	int(τ	PROPN
ejpam-1200	123	4	j	j	PROPN
ejpam-1200	123	5	−cl∗(b))⊂	−cl∗(b))⊂	PROPN
ejpam-1200	123	6	τ	τ	PROPN
ejpam-1200	123	7	j	j	PROPN
ejpam-1200	123	8	−cl∗(τi	−cl∗(τi	NOUN
ejpam-1200	123	9	−	−	PROPN
ejpam-1200	123	10	int(a)∩τi	int(a)∩τi	NOUN
ejpam-1200	123	11	−	−	PROPN
ejpam-1200	123	12	int(τ	int(τ	PROPN
ejpam-1200	123	13	j	j	PROPN
ejpam-1200	123	14	−cl∗(b	−cl∗(b	PROPN
ejpam-1200	123	15	)	)	PUNCT
ejpam-1200	123	16	)	)	PUNCT
ejpam-1200	124	1	=	=	PUNCT
ejpam-1200	125	1	τ	τ	PROPN
ejpam-1200	125	2	j	j	PROPN
ejpam-1200	125	3	−cl∗(τi	−cl∗(τi	NOUN
ejpam-1200	125	4	−	−	PROPN
ejpam-1200	125	5	int(τi	int(τi	NOUN
ejpam-1200	125	6	−	−	PROPN
ejpam-1200	125	7	int(a))∩τ	int(a))∩τ	PROPN
ejpam-1200	125	8	j	j	PROPN
ejpam-1200	125	9	−cl∗(b)))⊂	−cl∗(b)))⊂	NOUN
ejpam-1200	125	10	τ	τ	PROPN
ejpam-1200	125	11	j	j	PROPN
ejpam-1200	125	12	−cl∗(τi	−cl∗(τi	NOUN
ejpam-1200	125	13	−	−	PROPN
ejpam-1200	125	14	int(τ	int(τ	PROPN
ejpam-1200	125	15	j	j	PROPN
ejpam-1200	125	16	−cl∗(τi	−cl∗(τi	NOUN
ejpam-1200	125	17	−	−	PROPN
ejpam-1200	125	18	int(a)∩	int(a)∩	PROPN
ejpam-1200	125	19	b	b	NOUN
ejpam-1200	125	20	)	)	PUNCT
ejpam-1200	125	21	)	)	PUNCT
ejpam-1200	125	22	)	)	PUNCT
ejpam-1200	126	1	⊂	⊂	PROPN
ejpam-1200	126	2	τ	τ	PROPN
ejpam-1200	127	1	j	j	PROPN
ejpam-1200	127	2	−cl∗(τi	−cl∗(τi	NOUN
ejpam-1200	127	3	−	−	PROPN
ejpam-1200	127	4	int(τ	int(τ	PROPN
ejpam-1200	127	5	j	j	PROPN
ejpam-1200	127	6	−cl∗(a∩	−cl∗(a∩	NUM
ejpam-1200	127	7	b)))⊂	b)))⊂	NOUN
ejpam-1200	127	8	τ	τ	PROPN
ejpam-1200	127	9	j	j	PROPN
ejpam-1200	127	10	−cl(τi	−cl(τi	PROPN
ejpam-1200	127	11	−	−	PROPN
ejpam-1200	127	12	int(τ	int(τ	PROPN
ejpam-1200	127	13	j	j	PROPN
ejpam-1200	127	14	−cl∗(a∩	−cl∗(a∩	NUM
ejpam-1200	127	15	b	b	PROPN
ejpam-1200	127	16	)	)	PUNCT
ejpam-1200	127	17	)	)	PUNCT
ejpam-1200	127	18	)	)	PUNCT
ejpam-1200	127	19	.	.	PUNCT
ejpam-1200	128	1	thus	thus	ADV
ejpam-1200	128	2	,	,	PUNCT
ejpam-1200	128	3	a∩	a∩	PROPN
ejpam-1200	128	4	b	b	PROPN
ejpam-1200	128	5	is	be	AUX
ejpam-1200	128	6	(	(	PUNCT
ejpam-1200	128	7	i	i	NOUN
ejpam-1200	128	8	,	,	PUNCT
ejpam-1200	128	9	j)−	j)−	PROPN
ejpam-1200	128	10	β	β	PROPN
ejpam-1200	128	11	−i	−i	PROPN
ejpam-1200	128	12	-open	-open	VERB
ejpam-1200	128	13	in	in	ADP
ejpam-1200	128	14	x	x	X
ejpam-1200	128	15	.	.	PUNCT
ejpam-1200	129	1	definition	definition	NOUN
ejpam-1200	129	2	6	6	NUM
ejpam-1200	129	3	.	.	PUNCT
ejpam-1200	130	1	in	in	ADP
ejpam-1200	130	2	an	an	DET
ejpam-1200	130	3	ideal	ideal	ADJ
ejpam-1200	130	4	bitopological	bitopological	ADJ
ejpam-1200	130	5	space	space	NOUN
ejpam-1200	130	6	(	(	PUNCT
ejpam-1200	130	7	x	x	NOUN
ejpam-1200	130	8	,	,	PUNCT
ejpam-1200	130	9	τ1,τ2,i	τ1,τ2,i	PROPN
ejpam-1200	130	10	)	)	PUNCT
ejpam-1200	130	11	,	,	PUNCT
ejpam-1200	130	12	a⊂	a⊂	PRON
ejpam-1200	130	13	x	x	VERB
ejpam-1200	130	14	is	be	AUX
ejpam-1200	130	15	said	say	VERB
ejpam-1200	130	16	to	to	PART
ejpam-1200	130	17	be	be	AUX
ejpam-1200	130	18	(	(	PUNCT
ejpam-1200	130	19	i	i	NOUN
ejpam-1200	130	20	,	,	PUNCT
ejpam-1200	130	21	j)−	j)−	PROPN
ejpam-1200	130	22	β	β	PROPN
ejpam-1200	130	23	−i	−i	PROPN
ejpam-1200	130	24	closed	close	VERB
ejpam-1200	130	25	if	if	SCONJ
ejpam-1200	130	26	x\a	x\a	PROPN
ejpam-1200	130	27	is	be	AUX
ejpam-1200	130	28	(	(	PUNCT
ejpam-1200	130	29	i	i	PROPN
ejpam-1200	130	30	,	,	PUNCT
ejpam-1200	130	31	j)−	j)−	PROPN
ejpam-1200	130	32	β	β	PROPN
ejpam-1200	130	33	−i	−i	PROPN
ejpam-1200	130	34	-open	-open	VERB
ejpam-1200	130	35	in	in	ADP
ejpam-1200	130	36	x	x	SYM
ejpam-1200	130	37	,	,	PUNCT
ejpam-1200	130	38	i	i	PRON
ejpam-1200	130	39	,	,	PUNCT
ejpam-1200	130	40	j	j	PROPN
ejpam-1200	131	1	=	=	SYM
ejpam-1200	131	2	1,2	1,2	NUM
ejpam-1200	131	3	and	and	CCONJ
ejpam-1200	131	4	i	i	PRON
ejpam-1200	131	5	6=	6=	PROPN
ejpam-1200	132	1	j.	j.	PROPN
ejpam-1200	132	2	theorem	theorem	VERB
ejpam-1200	132	3	4	4	NUM
ejpam-1200	132	4	.	.	PUNCT
ejpam-1200	133	1	if	if	SCONJ
ejpam-1200	133	2	a	a	PRON
ejpam-1200	133	3	is	be	AUX
ejpam-1200	133	4	an	an	DET
ejpam-1200	133	5	(	(	PUNCT
ejpam-1200	133	6	i	i	NOUN
ejpam-1200	133	7	,	,	PUNCT
ejpam-1200	133	8	j)−	j)−	PROPN
ejpam-1200	133	9	β	β	PROPN
ejpam-1200	133	10	−i	−i	PROPN
ejpam-1200	133	11	-closed	-close	VERB
ejpam-1200	133	12	set	set	NOUN
ejpam-1200	133	13	in	in	ADP
ejpam-1200	133	14	an	an	DET
ejpam-1200	133	15	ideal	ideal	ADJ
ejpam-1200	133	16	bitopological	bitopological	ADJ
ejpam-1200	133	17	space	space	NOUN
ejpam-1200	133	18	(	(	PUNCT
ejpam-1200	133	19	x	x	NOUN
ejpam-1200	133	20	,	,	PUNCT
ejpam-1200	133	21	τ1,τ2,i	τ1,τ2,i	PROPN
ejpam-1200	133	22	)	)	PUNCT
ejpam-1200	134	1	if	if	SCONJ
ejpam-1200	134	2	and	and	CCONJ
ejpam-1200	134	3	only	only	ADV
ejpam-1200	134	4	if	if	SCONJ
ejpam-1200	134	5	τ	τ	PROPN
ejpam-1200	134	6	j	j	PROPN
ejpam-1200	134	7	−	−	PROPN
ejpam-1200	134	8	int(τi	int(τi	VERB
ejpam-1200	134	9	−cl(τ	−cl(τ	PROPN
ejpam-1200	134	10	j	j	NOUN
ejpam-1200	134	11	−	−	PROPN
ejpam-1200	134	12	int∗(a)))⊂	int∗(a)))⊂	NOUN
ejpam-1200	134	13	a.	a.	NOUN
ejpam-1200	134	14	proof	proof	NOUN
ejpam-1200	134	15	.	.	PUNCT
ejpam-1200	135	1	the	the	DET
ejpam-1200	135	2	proof	proof	NOUN
ejpam-1200	135	3	follows	follow	VERB
ejpam-1200	135	4	from	from	ADP
ejpam-1200	135	5	the	the	DET
ejpam-1200	135	6	definitions	definition	NOUN
ejpam-1200	135	7	.	.	PUNCT
ejpam-1200	136	1	m.	m.	PROPN
ejpam-1200	136	2	caldas	caldas	PROPN
ejpam-1200	136	3	,	,	PUNCT
ejpam-1200	136	4	s.	s.	PROPN
ejpam-1200	136	5	jafari	jafari	PROPN
ejpam-1200	136	6	,	,	PUNCT
ejpam-1200	136	7	n.	n.	PROPN
ejpam-1200	136	8	rajesh	rajesh	PROPN
ejpam-1200	136	9	/	/	SYM
ejpam-1200	136	10	eur	eur	PROPN
ejpam-1200	136	11	.	.	PUNCT
ejpam-1200	137	1	j.	j.	PROPN
ejpam-1200	137	2	pure	pure	PROPN
ejpam-1200	137	3	appl	appl	PROPN
ejpam-1200	137	4	.	.	PROPN
ejpam-1200	137	5	math	math	PROPN
ejpam-1200	137	6	,	,	PUNCT
ejpam-1200	137	7	6	6	NUM
ejpam-1200	137	8	(	(	PUNCT
ejpam-1200	137	9	2013	2013	NUM
ejpam-1200	137	10	)	)	PUNCT
ejpam-1200	137	11	,	,	PUNCT
ejpam-1200	137	12	247	247	NUM
ejpam-1200	137	13	-	-	SYM
ejpam-1200	137	14	255	255	NUM
ejpam-1200	137	15	251	251	NUM
ejpam-1200	137	16	theorem	theorem	NOUN
ejpam-1200	137	17	5	5	NUM
ejpam-1200	137	18	.	.	PUNCT
ejpam-1200	138	1	a	a	DET
ejpam-1200	138	2	subset	subset	NOUN
ejpam-1200	138	3	a	a	PRON
ejpam-1200	138	4	of	of	ADP
ejpam-1200	138	5	an	an	DET
ejpam-1200	138	6	ideal	ideal	ADJ
ejpam-1200	138	7	bitopological	bitopological	ADJ
ejpam-1200	138	8	space	space	NOUN
ejpam-1200	138	9	(	(	PUNCT
ejpam-1200	138	10	x	x	X
ejpam-1200	138	11	,	,	PUNCT
ejpam-1200	138	12	τ1,τ2,i	τ1,τ2,i	PROPN
ejpam-1200	138	13	)	)	PUNCT
ejpam-1200	138	14	is	be	AUX
ejpam-1200	138	15	(	(	PUNCT
ejpam-1200	138	16	i	i	INTJ
ejpam-1200	138	17	,	,	PUNCT
ejpam-1200	138	18	j)−β−i	j)−β−i	PROPN
ejpam-1200	138	19	-closed	-close	VERB
ejpam-1200	138	20	,	,	PUNCT
ejpam-1200	138	21	then	then	ADV
ejpam-1200	138	22	τ	τ	PROPN
ejpam-1200	138	23	j	j	PROPN
ejpam-1200	138	24	−	−	PROPN
ejpam-1200	138	25	int(τi	int(τi	VERB
ejpam-1200	138	26	−cl∗(τ	−cl∗(τ	X
ejpam-1200	138	27	j	j	NOUN
ejpam-1200	138	28	−	−	NOUN
ejpam-1200	139	1	int(a)))⊂	int(a)))⊂	NOUN
ejpam-1200	139	2	a	a	DET
ejpam-1200	139	3	proof	proof	NOUN
ejpam-1200	139	4	.	.	PUNCT
ejpam-1200	140	1	the	the	DET
ejpam-1200	140	2	proof	proof	NOUN
ejpam-1200	140	3	follows	follow	VERB
ejpam-1200	140	4	from	from	ADP
ejpam-1200	140	5	the	the	DET
ejpam-1200	140	6	fact	fact	NOUN
ejpam-1200	140	7	that	that	SCONJ
ejpam-1200	140	8	cl∗(a)⊂	cl∗(a)⊂	PROPN
ejpam-1200	140	9	cl(a	cl(a	PUNCT
ejpam-1200	140	10	)	)	PUNCT
ejpam-1200	140	11	for	for	ADP
ejpam-1200	140	12	every	every	DET
ejpam-1200	140	13	subset	subset	NOUN
ejpam-1200	140	14	a	a	PRON
ejpam-1200	140	15	of	of	ADP
ejpam-1200	140	16	x	x	SYM
ejpam-1200	140	17	.	.	PUNCT
ejpam-1200	141	1	theorem	theorem	ADJ
ejpam-1200	141	2	6	6	NUM
ejpam-1200	141	3	.	.	PUNCT
ejpam-1200	141	4	arbitrary	arbitrary	ADJ
ejpam-1200	141	5	intersection	intersection	NOUN
ejpam-1200	141	6	of	of	ADP
ejpam-1200	141	7	(	(	PUNCT
ejpam-1200	141	8	i	i	PROPN
ejpam-1200	141	9	,	,	PUNCT
ejpam-1200	141	10	j)−	j)−	PROPN
ejpam-1200	141	11	β	β	PROPN
ejpam-1200	141	12	−i	−i	PROPN
ejpam-1200	141	13	-closed	-close	VERB
ejpam-1200	141	14	sets	set	NOUN
ejpam-1200	141	15	is	be	AUX
ejpam-1200	141	16	always	always	ADV
ejpam-1200	141	17	(	(	PUNCT
ejpam-1200	141	18	i	i	NOUN
ejpam-1200	141	19	,	,	PUNCT
ejpam-1200	141	20	j)−	j)−	PROPN
ejpam-1200	141	21	β	β	PROPN
ejpam-1200	141	22	−i	−i	PROPN
ejpam-1200	141	23	-closed	-closed	PROPN
ejpam-1200	141	24	.	.	PUNCT
ejpam-1200	142	1	proof	proof	NOUN
ejpam-1200	142	2	.	.	PUNCT
ejpam-1200	143	1	follows	follow	VERB
ejpam-1200	143	2	from	from	ADP
ejpam-1200	143	3	theorems	theorem	NOUN
ejpam-1200	143	4	1	1	NUM
ejpam-1200	143	5	and	and	CCONJ
ejpam-1200	143	6	5	5	NUM
ejpam-1200	143	7	.	.	X
ejpam-1200	143	8	definition	definition	NOUN
ejpam-1200	143	9	7	7	NUM
ejpam-1200	143	10	.	.	PUNCT
ejpam-1200	144	1	let	let	AUX
ejpam-1200	144	2	(	(	PUNCT
ejpam-1200	144	3	x	x	INTJ
ejpam-1200	144	4	,	,	PUNCT
ejpam-1200	144	5	τ1,τ2,i	τ1,τ2,i	PROPN
ejpam-1200	144	6	)	)	PUNCT
ejpam-1200	144	7	be	be	AUX
ejpam-1200	144	8	an	an	DET
ejpam-1200	144	9	ideal	ideal	ADJ
ejpam-1200	144	10	bitopological	bitopological	ADJ
ejpam-1200	144	11	space	space	NOUN
ejpam-1200	144	12	,	,	PUNCT
ejpam-1200	144	13	s	s	VERB
ejpam-1200	144	14	a	a	DET
ejpam-1200	144	15	subset	subset	NOUN
ejpam-1200	144	16	of	of	ADP
ejpam-1200	144	17	x	x	PUNCT
ejpam-1200	144	18	and	and	CCONJ
ejpam-1200	144	19	x	x	ADJ
ejpam-1200	144	20	be	be	AUX
ejpam-1200	144	21	a	a	DET
ejpam-1200	144	22	point	point	NOUN
ejpam-1200	144	23	of	of	ADP
ejpam-1200	144	24	x	x	X
ejpam-1200	144	25	.	.	PUNCT
ejpam-1200	145	1	then	then	ADV
ejpam-1200	145	2	(	(	PUNCT
ejpam-1200	145	3	i	i	NOUN
ejpam-1200	145	4	)	)	PUNCT
ejpam-1200	145	5	x	x	VERB
ejpam-1200	145	6	is	be	AUX
ejpam-1200	145	7	called	call	VERB
ejpam-1200	145	8	an	an	DET
ejpam-1200	145	9	(	(	PUNCT
ejpam-1200	145	10	i	i	NOUN
ejpam-1200	145	11	,	,	PUNCT
ejpam-1200	145	12	j)−	j)−	PROPN
ejpam-1200	145	13	β	β	PROPN
ejpam-1200	145	14	−i	−i	ADJ
ejpam-1200	145	15	-interior	-interior	ADJ
ejpam-1200	145	16	point	point	NOUN
ejpam-1200	145	17	of	of	ADP
ejpam-1200	145	18	s	s	PRON
ejpam-1200	145	19	if	if	SCONJ
ejpam-1200	145	20	there	there	PRON
ejpam-1200	145	21	exists	exist	VERB
ejpam-1200	145	22	v	v	ADP
ejpam-1200	145	23	∈	∈	PROPN
ejpam-1200	145	24	(	(	PUNCT
ejpam-1200	145	25	i	i	PROPN
ejpam-1200	145	26	,	,	PUNCT
ejpam-1200	145	27	j)−	j)−	PROPN
ejpam-1200	145	28	βio(x	βio(x	PRON
ejpam-1200	145	29	,	,	PUNCT
ejpam-1200	145	30	τ1,τ2	τ1,τ2	PROPN
ejpam-1200	145	31	)	)	PUNCT
ejpam-1200	145	32	such	such	ADJ
ejpam-1200	145	33	that	that	SCONJ
ejpam-1200	145	34	x	x	SYM
ejpam-1200	145	35	∈	∈	PROPN
ejpam-1200	145	36	v	v	ADP
ejpam-1200	145	37	⊂	⊂	PROPN
ejpam-1200	145	38	s.	s.	PROPN
ejpam-1200	145	39	(	(	PUNCT
ejpam-1200	145	40	ii	ii	PROPN
ejpam-1200	145	41	)	)	PUNCT
ejpam-1200	145	42	the	the	DET
ejpam-1200	145	43	set	set	NOUN
ejpam-1200	145	44	of	of	ADP
ejpam-1200	145	45	all	all	PRON
ejpam-1200	145	46	(	(	PUNCT
ejpam-1200	145	47	i	i	NOUN
ejpam-1200	145	48	,	,	PUNCT
ejpam-1200	145	49	j)−	j)−	PROPN
ejpam-1200	145	50	β	β	PROPN
ejpam-1200	145	51	−i	−i	ADJ
ejpam-1200	145	52	-interior	-interior	ADJ
ejpam-1200	145	53	points	point	NOUN
ejpam-1200	145	54	of	of	ADP
ejpam-1200	145	55	s	s	NOUN
ejpam-1200	145	56	is	be	AUX
ejpam-1200	145	57	called	call	VERB
ejpam-1200	145	58	(	(	PUNCT
ejpam-1200	145	59	i	i	PROPN
ejpam-1200	145	60	,	,	PUNCT
ejpam-1200	146	1	j)−	j)−	PROPN
ejpam-1200	146	2	β	β	PROPN
ejpam-1200	146	3	−i	−i	ADJ
ejpam-1200	146	4	-interior	-interior	NOUN
ejpam-1200	146	5	of	of	ADP
ejpam-1200	146	6	s	s	PRON
ejpam-1200	146	7	and	and	CCONJ
ejpam-1200	146	8	is	be	AUX
ejpam-1200	146	9	denoted	denote	VERB
ejpam-1200	146	10	by	by	ADP
ejpam-1200	146	11	(	(	PUNCT
ejpam-1200	146	12	i	i	PROPN
ejpam-1200	146	13	,	,	PUNCT
ejpam-1200	146	14	j)−	j)−	PROPN
ejpam-1200	146	15	βi	βi	PUNCT
ejpam-1200	146	16	int(s	int(s	PROPN
ejpam-1200	146	17	)	)	PUNCT
ejpam-1200	146	18	.	.	PUNCT
ejpam-1200	147	1	theorem	theorem	VERB
ejpam-1200	147	2	7	7	NUM
ejpam-1200	147	3	.	.	PUNCT
ejpam-1200	147	4	let	let	VERB
ejpam-1200	147	5	a	a	PRON
ejpam-1200	147	6	and	and	CCONJ
ejpam-1200	147	7	b	b	NOUN
ejpam-1200	147	8	be	be	AUX
ejpam-1200	147	9	subsets	subset	NOUN
ejpam-1200	147	10	of	of	ADP
ejpam-1200	147	11	(	(	PUNCT
ejpam-1200	147	12	x	x	INTJ
ejpam-1200	147	13	,	,	PUNCT
ejpam-1200	147	14	τ1,τ2,i	τ1,τ2,i	PROPN
ejpam-1200	147	15	)	)	PUNCT
ejpam-1200	147	16	.	.	PUNCT
ejpam-1200	148	1	then	then	ADV
ejpam-1200	148	2	the	the	DET
ejpam-1200	148	3	following	follow	VERB
ejpam-1200	148	4	properties	property	NOUN
ejpam-1200	148	5	hold	hold	VERB
ejpam-1200	148	6	:	:	PUNCT
ejpam-1200	148	7	(	(	PUNCT
ejpam-1200	148	8	i	i	NOUN
ejpam-1200	148	9	)	)	PUNCT
ejpam-1200	148	10	(	(	PUNCT
ejpam-1200	148	11	i	i	PROPN
ejpam-1200	148	12	,	,	PUNCT
ejpam-1200	148	13	j)−	j)−	PROPN
ejpam-1200	148	14	βi	βi	PUNCT
ejpam-1200	148	15	int(a	int(a	PROPN
ejpam-1200	148	16	)	)	PUNCT
ejpam-1200	148	17	=	=	SYM
ejpam-1200	149	1	∪{t	∪{t	PROPN
ejpam-1200	149	2	:	:	PUNCT
ejpam-1200	150	1	t	t	X
ejpam-1200	150	2	⊂	⊂	PROPN
ejpam-1200	150	3	a	a	PROPN
ejpam-1200	150	4	and	and	CCONJ
ejpam-1200	150	5	t	t	NOUN
ejpam-1200	150	6	∈	∈	PROPN
ejpam-1200	150	7	(	(	PUNCT
ejpam-1200	150	8	i	i	NOUN
ejpam-1200	150	9	,	,	PUNCT
ejpam-1200	150	10	j)−	j)−	PROPN
ejpam-1200	150	11	βio(x	βio(x	PRON
ejpam-1200	150	12	)	)	PUNCT
ejpam-1200	150	13	}	}	PUNCT
ejpam-1200	150	14	.	.	PUNCT
ejpam-1200	151	1	(	(	PUNCT
ejpam-1200	151	2	ii	ii	NOUN
ejpam-1200	151	3	)	)	PUNCT
ejpam-1200	151	4	(	(	PUNCT
ejpam-1200	151	5	i	i	PROPN
ejpam-1200	151	6	,	,	PUNCT
ejpam-1200	151	7	j)−	j)−	PROPN
ejpam-1200	151	8	βi	βi	PUNCT
ejpam-1200	151	9	int(a	int(a	PROPN
ejpam-1200	151	10	)	)	PUNCT
ejpam-1200	151	11	is	be	AUX
ejpam-1200	151	12	the	the	DET
ejpam-1200	151	13	largest	large	ADJ
ejpam-1200	151	14	(	(	PUNCT
ejpam-1200	151	15	i	i	NOUN
ejpam-1200	151	16	,	,	PUNCT
ejpam-1200	151	17	j)−	j)−	PROPN
ejpam-1200	151	18	β	β	PROPN
ejpam-1200	151	19	−i	−i	PROPN
ejpam-1200	151	20	-open	-open	PROPN
ejpam-1200	151	21	subset	subset	NOUN
ejpam-1200	151	22	of	of	ADP
ejpam-1200	151	23	x	x	PUNCT
ejpam-1200	151	24	contained	contain	VERB
ejpam-1200	151	25	in	in	ADP
ejpam-1200	151	26	a.	a.	NOUN
ejpam-1200	151	27	(	(	PUNCT
ejpam-1200	151	28	iii	iii	NOUN
ejpam-1200	151	29	)	)	PUNCT
ejpam-1200	151	30	a	a	PRON
ejpam-1200	151	31	is	be	AUX
ejpam-1200	151	32	(	(	PUNCT
ejpam-1200	151	33	i	i	NOUN
ejpam-1200	151	34	,	,	PUNCT
ejpam-1200	151	35	j)−	j)−	PROPN
ejpam-1200	151	36	β	β	PROPN
ejpam-1200	151	37	−i	−i	PROPN
ejpam-1200	151	38	-open	-open	PROPN
ejpam-1200	151	39	if	if	SCONJ
ejpam-1200	151	40	and	and	CCONJ
ejpam-1200	151	41	only	only	ADV
ejpam-1200	151	42	if	if	SCONJ
ejpam-1200	151	43	a=	a=	PROPN
ejpam-1200	151	44	(	(	PUNCT
ejpam-1200	151	45	i	i	NOUN
ejpam-1200	151	46	,	,	PUNCT
ejpam-1200	151	47	j)−	j)−	PROPN
ejpam-1200	151	48	βi	βi	PROPN
ejpam-1200	151	49	int(a	int(a	PROPN
ejpam-1200	151	50	)	)	PUNCT
ejpam-1200	151	51	.	.	PUNCT
ejpam-1200	152	1	(	(	PUNCT
ejpam-1200	152	2	iv	iv	X
ejpam-1200	152	3	)	)	PUNCT
ejpam-1200	152	4	(	(	PUNCT
ejpam-1200	152	5	i	i	PROPN
ejpam-1200	152	6	,	,	PUNCT
ejpam-1200	152	7	j)−	j)−	PROPN
ejpam-1200	152	8	βi	βi	PROPN
ejpam-1200	152	9	int((i	int((i	PROPN
ejpam-1200	152	10	,	,	PUNCT
ejpam-1200	152	11	j)−	j)−	PROPN
ejpam-1200	152	12	βi	βi	PROPN
ejpam-1200	152	13	int(a	int(a	PROPN
ejpam-1200	152	14	)	)	PUNCT
ejpam-1200	152	15	)	)	PUNCT
ejpam-1200	153	1	=	=	PUNCT
ejpam-1200	153	2	(	(	PUNCT
ejpam-1200	153	3	i	i	PROPN
ejpam-1200	153	4	,	,	PUNCT
ejpam-1200	153	5	j)−	j)−	PROPN
ejpam-1200	153	6	βi	βi	PROPN
ejpam-1200	153	7	int(a	int(a	PROPN
ejpam-1200	153	8	)	)	PUNCT
ejpam-1200	153	9	.	.	PUNCT
ejpam-1200	154	1	(	(	PUNCT
ejpam-1200	154	2	v	v	NOUN
ejpam-1200	154	3	)	)	PUNCT
ejpam-1200	154	4	if	if	SCONJ
ejpam-1200	154	5	a⊂	a⊂	NOUN
ejpam-1200	154	6	b	b	NOUN
ejpam-1200	154	7	,	,	PUNCT
ejpam-1200	154	8	then	then	ADV
ejpam-1200	154	9	(	(	PUNCT
ejpam-1200	154	10	i	i	PROPN
ejpam-1200	154	11	,	,	PUNCT
ejpam-1200	154	12	j)−	j)−	PROPN
ejpam-1200	154	13	βi	βi	PRON
ejpam-1200	154	14	int(a)⊂	int(a)⊂	PROPN
ejpam-1200	154	15	(	(	PUNCT
ejpam-1200	154	16	i	i	PROPN
ejpam-1200	154	17	,	,	PUNCT
ejpam-1200	154	18	j)−	j)−	PROPN
ejpam-1200	154	19	βi	βi	PRON
ejpam-1200	154	20	int(b	int(b	PROPN
ejpam-1200	154	21	)	)	PUNCT
ejpam-1200	154	22	.	.	PUNCT
ejpam-1200	155	1	(	(	PUNCT
ejpam-1200	155	2	vi	vi	X
ejpam-1200	155	3	)	)	PUNCT
ejpam-1200	155	4	(	(	PUNCT
ejpam-1200	155	5	i	i	PROPN
ejpam-1200	155	6	,	,	PUNCT
ejpam-1200	155	7	j)−	j)−	PROPN
ejpam-1200	155	8	βi	βi	PROPN
ejpam-1200	155	9	int(a∩	int(a∩	PROPN
ejpam-1200	155	10	b)⊂	b)⊂	PROPN
ejpam-1200	155	11	(	(	PUNCT
ejpam-1200	155	12	i	i	PROPN
ejpam-1200	155	13	,	,	PUNCT
ejpam-1200	155	14	j)−	j)−	PROPN
ejpam-1200	155	15	βi	βi	PRON
ejpam-1200	155	16	int(a)∩	int(a)∩	PROPN
ejpam-1200	155	17	(	(	PUNCT
ejpam-1200	155	18	i	i	PROPN
ejpam-1200	155	19	,	,	PUNCT
ejpam-1200	155	20	j)−	j)−	PROPN
ejpam-1200	155	21	βi	βi	PRON
ejpam-1200	155	22	int(b	int(b	PROPN
ejpam-1200	155	23	)	)	PUNCT
ejpam-1200	155	24	.	.	PUNCT
ejpam-1200	156	1	(	(	PUNCT
ejpam-1200	156	2	vii	vii	PROPN
ejpam-1200	156	3	)	)	PUNCT
ejpam-1200	156	4	(	(	PUNCT
ejpam-1200	156	5	i	i	PROPN
ejpam-1200	156	6	,	,	PUNCT
ejpam-1200	156	7	j)−	j)−	PROPN
ejpam-1200	156	8	βi	βi	NUM
ejpam-1200	156	9	int(a∪	int(a∪	NOUN
ejpam-1200	156	10	b)⊃	b)⊃	NOUN
ejpam-1200	156	11	(	(	PUNCT
ejpam-1200	156	12	i	i	PROPN
ejpam-1200	156	13	,	,	PUNCT
ejpam-1200	156	14	j)−	j)−	PROPN
ejpam-1200	156	15	βi	βi	PROPN
ejpam-1200	156	16	int(a)∪	int(a)∪	PROPN
ejpam-1200	156	17	(	(	PUNCT
ejpam-1200	156	18	i	i	NOUN
ejpam-1200	156	19	,	,	PUNCT
ejpam-1200	156	20	j)−	j)−	PROPN
ejpam-1200	156	21	βi	βi	PRON
ejpam-1200	156	22	int(b	int(b	PROPN
ejpam-1200	156	23	)	)	PUNCT
ejpam-1200	156	24	.	.	PUNCT
ejpam-1200	157	1	proof	proof	NOUN
ejpam-1200	157	2	.	.	PUNCT
ejpam-1200	158	1	(	(	PUNCT
ejpam-1200	158	2	vi	vi	NOUN
ejpam-1200	158	3	)	)	PUNCT
ejpam-1200	158	4	.	.	PUNCT
ejpam-1200	159	1	since	since	SCONJ
ejpam-1200	159	2	a∩	a∩	PROPN
ejpam-1200	159	3	b	b	PROPN
ejpam-1200	159	4	⊂	⊂	PROPN
ejpam-1200	159	5	a	a	PROPN
ejpam-1200	159	6	and	and	CCONJ
ejpam-1200	159	7	a∩	a∩	PROPN
ejpam-1200	159	8	b	b	PROPN
ejpam-1200	159	9	⊂	⊂	PROPN
ejpam-1200	159	10	b	b	PROPN
ejpam-1200	159	11	,	,	PUNCT
ejpam-1200	159	12	by	by	ADP
ejpam-1200	159	13	(	(	PUNCT
ejpam-1200	159	14	iv	iv	X
ejpam-1200	159	15	)	)	PUNCT
ejpam-1200	159	16	,	,	PUNCT
ejpam-1200	159	17	we	we	PRON
ejpam-1200	159	18	have	have	VERB
ejpam-1200	159	19	(	(	PUNCT
ejpam-1200	159	20	i	i	PROPN
ejpam-1200	159	21	,	,	PUNCT
ejpam-1200	159	22	j	j	PROPN
ejpam-1200	159	23	)	)	PUNCT
ejpam-1200	160	1	−	−	PROPN
ejpam-1200	160	2	βi	βi	SYM
ejpam-1200	160	3	int(a	int(a	PROPN
ejpam-1200	160	4	∩	∩	ADJ
ejpam-1200	160	5	b	b	X
ejpam-1200	160	6	)	)	PUNCT
ejpam-1200	160	7	⊂	⊂	PROPN
ejpam-1200	160	8	(	(	PUNCT
ejpam-1200	160	9	i	i	PROPN
ejpam-1200	160	10	,	,	PUNCT
ejpam-1200	160	11	j	j	PROPN
ejpam-1200	160	12	)	)	PUNCT
ejpam-1200	160	13	−	−	PROPN
ejpam-1200	160	14	βi	βi	PROPN
ejpam-1200	160	15	int(a	int(a	PROPN
ejpam-1200	160	16	)	)	PUNCT
ejpam-1200	160	17	and	and	CCONJ
ejpam-1200	160	18	(	(	PUNCT
ejpam-1200	160	19	i	i	PROPN
ejpam-1200	160	20	,	,	PUNCT
ejpam-1200	160	21	j	j	PROPN
ejpam-1200	160	22	)	)	PUNCT
ejpam-1200	160	23	−	−	PROPN
ejpam-1200	160	24	βi	βi	SYM
ejpam-1200	160	25	int(a	int(a	PROPN
ejpam-1200	160	26	∩	∩	ADJ
ejpam-1200	160	27	b	b	X
ejpam-1200	160	28	)	)	PUNCT
ejpam-1200	160	29	⊂	⊂	PROPN
ejpam-1200	160	30	(	(	PUNCT
ejpam-1200	160	31	i	i	PROPN
ejpam-1200	160	32	,	,	PUNCT
ejpam-1200	160	33	j	j	PROPN
ejpam-1200	160	34	)	)	PUNCT
ejpam-1200	160	35	−	−	PROPN
ejpam-1200	160	36	βi	βi	NOUN
ejpam-1200	160	37	int(b	int(b	PROPN
ejpam-1200	160	38	)	)	PUNCT
ejpam-1200	160	39	.	.	PUNCT
ejpam-1200	161	1	therefore	therefore	ADV
ejpam-1200	161	2	,	,	PUNCT
ejpam-1200	161	3	(	(	PUNCT
ejpam-1200	161	4	i	i	PROPN
ejpam-1200	161	5	,	,	PUNCT
ejpam-1200	161	6	j)−	j)−	PROPN
ejpam-1200	161	7	βi	βi	PROPN
ejpam-1200	161	8	int(a∩	int(a∩	PROPN
ejpam-1200	161	9	b)⊂	b)⊂	PROPN
ejpam-1200	161	10	(	(	PUNCT
ejpam-1200	161	11	i	i	PROPN
ejpam-1200	161	12	,	,	PUNCT
ejpam-1200	161	13	j)−	j)−	PROPN
ejpam-1200	161	14	βi	βi	PRON
ejpam-1200	161	15	int(a)∩	int(a)∩	PROPN
ejpam-1200	161	16	(	(	PUNCT
ejpam-1200	161	17	i	i	PROPN
ejpam-1200	161	18	,	,	PUNCT
ejpam-1200	161	19	j)−	j)−	PROPN
ejpam-1200	161	20	βi	βi	PRON
ejpam-1200	161	21	int(b	int(b	PROPN
ejpam-1200	161	22	)	)	PUNCT
ejpam-1200	161	23	.	.	PUNCT
ejpam-1200	162	1	(	(	PUNCT
ejpam-1200	162	2	vii	vii	PROPN
ejpam-1200	162	3	)	)	PUNCT
ejpam-1200	162	4	.	.	PUNCT
ejpam-1200	163	1	we	we	PRON
ejpam-1200	163	2	have	have	VERB
ejpam-1200	163	3	(	(	PUNCT
ejpam-1200	163	4	i	i	NOUN
ejpam-1200	163	5	,	,	PUNCT
ejpam-1200	163	6	j)−	j)−	PROPN
ejpam-1200	163	7	βi	βi	PRON
ejpam-1200	163	8	int(a)⊂	int(a)⊂	PROPN
ejpam-1200	163	9	(	(	PUNCT
ejpam-1200	163	10	i	i	PROPN
ejpam-1200	163	11	,	,	PUNCT
ejpam-1200	163	12	j)−	j)−	PROPN
ejpam-1200	163	13	βi	βi	PROPN
ejpam-1200	163	14	int(a∪	int(a∪	NOUN
ejpam-1200	163	15	b	b	X
ejpam-1200	163	16	)	)	PUNCT
ejpam-1200	163	17	and	and	CCONJ
ejpam-1200	163	18	(	(	PUNCT
ejpam-1200	163	19	i	i	NOUN
ejpam-1200	163	20	,	,	PUNCT
ejpam-1200	163	21	j)−	j)−	PROPN
ejpam-1200	163	22	βi	βi	PROPN
ejpam-1200	163	23	int(b)⊂	int(b)⊂	PROPN
ejpam-1200	163	24	(	(	PUNCT
ejpam-1200	163	25	i	i	PROPN
ejpam-1200	163	26	,	,	PUNCT
ejpam-1200	163	27	j)−	j)−	PROPN
ejpam-1200	163	28	βi	βi	PROPN
ejpam-1200	163	29	int(a∪	int(a∪	NOUN
ejpam-1200	163	30	b	b	NOUN
ejpam-1200	163	31	)	)	PUNCT
ejpam-1200	163	32	.	.	PUNCT
ejpam-1200	164	1	then	then	ADV
ejpam-1200	164	2	we	we	PRON
ejpam-1200	164	3	obtain	obtain	VERB
ejpam-1200	164	4	(	(	PUNCT
ejpam-1200	164	5	i	i	NOUN
ejpam-1200	164	6	,	,	PUNCT
ejpam-1200	164	7	j)−	j)−	PROPN
ejpam-1200	164	8	βi	βi	PROPN
ejpam-1200	164	9	int(a)∪	int(a)∪	PROPN
ejpam-1200	165	1	(	(	PUNCT
ejpam-1200	165	2	i	i	PROPN
ejpam-1200	165	3	,	,	PUNCT
ejpam-1200	165	4	j)−	j)−	PROPN
ejpam-1200	165	5	βi	βi	PROPN
ejpam-1200	165	6	int(b)⊂	int(b)⊂	PROPN
ejpam-1200	165	7	(	(	PUNCT
ejpam-1200	165	8	i	i	PROPN
ejpam-1200	165	9	,	,	PUNCT
ejpam-1200	165	10	j)−	j)−	PROPN
ejpam-1200	165	11	βi	βi	PROPN
ejpam-1200	165	12	int(a∪	int(a∪	NOUN
ejpam-1200	165	13	b	b	NOUN
ejpam-1200	165	14	)	)	PUNCT
ejpam-1200	165	15	.	.	PUNCT
ejpam-1200	166	1	the	the	DET
ejpam-1200	166	2	other	other	ADJ
ejpam-1200	166	3	proofs	proof	NOUN
ejpam-1200	166	4	are	be	AUX
ejpam-1200	166	5	obvious	obvious	ADJ
ejpam-1200	166	6	.	.	PUNCT
ejpam-1200	167	1	definition	definition	NOUN
ejpam-1200	167	2	8	8	NUM
ejpam-1200	167	3	.	.	PUNCT
ejpam-1200	168	1	let	let	AUX
ejpam-1200	168	2	(	(	PUNCT
ejpam-1200	168	3	x	x	INTJ
ejpam-1200	168	4	,	,	PUNCT
ejpam-1200	168	5	τ1,τ2,i	τ1,τ2,i	PROPN
ejpam-1200	168	6	)	)	PUNCT
ejpam-1200	168	7	be	be	AUX
ejpam-1200	168	8	an	an	DET
ejpam-1200	168	9	ideal	ideal	ADJ
ejpam-1200	168	10	bitopological	bitopological	ADJ
ejpam-1200	168	11	space	space	NOUN
ejpam-1200	168	12	,	,	PUNCT
ejpam-1200	168	13	s	s	VERB
ejpam-1200	168	14	a	a	DET
ejpam-1200	168	15	subset	subset	NOUN
ejpam-1200	168	16	of	of	ADP
ejpam-1200	168	17	x	x	PUNCT
ejpam-1200	168	18	and	and	CCONJ
ejpam-1200	168	19	x	x	ADJ
ejpam-1200	168	20	be	be	AUX
ejpam-1200	168	21	a	a	DET
ejpam-1200	168	22	point	point	NOUN
ejpam-1200	168	23	of	of	ADP
ejpam-1200	168	24	x	x	X
ejpam-1200	168	25	.	.	PUNCT
ejpam-1200	169	1	then	then	ADV
ejpam-1200	169	2	(	(	PUNCT
ejpam-1200	169	3	i	i	NOUN
ejpam-1200	169	4	)	)	PUNCT
ejpam-1200	169	5	x	x	VERB
ejpam-1200	169	6	is	be	AUX
ejpam-1200	169	7	called	call	VERB
ejpam-1200	169	8	an	an	DET
ejpam-1200	169	9	(	(	PUNCT
ejpam-1200	169	10	i	i	NOUN
ejpam-1200	169	11	,	,	PUNCT
ejpam-1200	169	12	j)−β−i	j)−β−i	PROPN
ejpam-1200	169	13	-cluster	-cluster	NOUN
ejpam-1200	169	14	point	point	NOUN
ejpam-1200	169	15	of	of	ADP
ejpam-1200	169	16	s	s	PRON
ejpam-1200	169	17	if	if	SCONJ
ejpam-1200	169	18	v	v	PROPN
ejpam-1200	169	19	∩s	∩s	PROPN
ejpam-1200	169	20	6=	6=	PROPN
ejpam-1200	169	21	;	;	PUNCT
ejpam-1200	169	22	for	for	ADP
ejpam-1200	169	23	every	every	DET
ejpam-1200	169	24	v	v	NOUN
ejpam-1200	169	25	∈	∈	NOUN
ejpam-1200	169	26	(	(	PUNCT
ejpam-1200	169	27	i	i	NOUN
ejpam-1200	169	28	,	,	PUNCT
ejpam-1200	169	29	j)−βio(x	j)−βio(x	PROPN
ejpam-1200	169	30	,	,	PUNCT
ejpam-1200	169	31	x	x	NOUN
ejpam-1200	169	32	)	)	PUNCT
ejpam-1200	169	33	.	.	PUNCT
ejpam-1200	170	1	(	(	PUNCT
ejpam-1200	170	2	ii	ii	X
ejpam-1200	170	3	)	)	PUNCT
ejpam-1200	170	4	the	the	DET
ejpam-1200	170	5	set	set	NOUN
ejpam-1200	170	6	of	of	ADP
ejpam-1200	170	7	all	all	DET
ejpam-1200	170	8	(	(	PUNCT
ejpam-1200	170	9	i	i	NOUN
ejpam-1200	170	10	,	,	PUNCT
ejpam-1200	170	11	j)−	j)−	PROPN
ejpam-1200	170	12	β	β	PROPN
ejpam-1200	170	13	−i	−i	ADJ
ejpam-1200	170	14	-cluster	-cluster	NOUN
ejpam-1200	170	15	points	point	NOUN
ejpam-1200	170	16	of	of	ADP
ejpam-1200	170	17	s	s	NOUN
ejpam-1200	170	18	is	be	AUX
ejpam-1200	170	19	called	call	VERB
ejpam-1200	170	20	(	(	PUNCT
ejpam-1200	170	21	i	i	PROPN
ejpam-1200	170	22	,	,	PUNCT
ejpam-1200	171	1	j)−	j)−	PROPN
ejpam-1200	171	2	β	β	PROPN
ejpam-1200	171	3	−i	−i	ADJ
ejpam-1200	171	4	-closure	-closure	NOUN
ejpam-1200	171	5	of	of	ADP
ejpam-1200	171	6	s	s	PRON
ejpam-1200	171	7	and	and	CCONJ
ejpam-1200	171	8	is	be	AUX
ejpam-1200	171	9	denoted	denote	VERB
ejpam-1200	171	10	by	by	ADP
ejpam-1200	171	11	(	(	PUNCT
ejpam-1200	171	12	i	i	PROPN
ejpam-1200	171	13	,	,	PUNCT
ejpam-1200	171	14	j)−	j)−	PROPN
ejpam-1200	171	15	βi	βi	PRON
ejpam-1200	171	16	cl(s	cl(s	PROPN
ejpam-1200	171	17	)	)	PUNCT
ejpam-1200	171	18	.	.	PUNCT
ejpam-1200	172	1	m.	m.	PROPN
ejpam-1200	172	2	caldas	caldas	PROPN
ejpam-1200	172	3	,	,	PUNCT
ejpam-1200	172	4	s.	s.	PROPN
ejpam-1200	172	5	jafari	jafari	PROPN
ejpam-1200	172	6	,	,	PUNCT
ejpam-1200	172	7	n.	n.	PROPN
ejpam-1200	172	8	rajesh	rajesh	PROPN
ejpam-1200	172	9	/	/	SYM
ejpam-1200	172	10	eur	eur	PROPN
ejpam-1200	172	11	.	.	PUNCT
ejpam-1200	173	1	j.	j.	PROPN
ejpam-1200	173	2	pure	pure	PROPN
ejpam-1200	173	3	appl	appl	PROPN
ejpam-1200	173	4	.	.	PROPN
ejpam-1200	173	5	math	math	PROPN
ejpam-1200	173	6	,	,	PUNCT
ejpam-1200	173	7	6	6	NUM
ejpam-1200	173	8	(	(	PUNCT
ejpam-1200	173	9	2013	2013	NUM
ejpam-1200	173	10	)	)	PUNCT
ejpam-1200	173	11	,	,	PUNCT
ejpam-1200	173	12	247	247	NUM
ejpam-1200	173	13	-	-	SYM
ejpam-1200	173	14	255	255	NUM
ejpam-1200	173	15	252	252	NUM
ejpam-1200	173	16	theorem	theorem	NOUN
ejpam-1200	173	17	8	8	NUM
ejpam-1200	173	18	.	.	PUNCT
ejpam-1200	174	1	let	let	VERB
ejpam-1200	174	2	a	a	PRON
ejpam-1200	174	3	and	and	CCONJ
ejpam-1200	174	4	b	b	NOUN
ejpam-1200	174	5	be	be	AUX
ejpam-1200	174	6	subsets	subset	NOUN
ejpam-1200	174	7	of	of	ADP
ejpam-1200	174	8	(	(	PUNCT
ejpam-1200	174	9	x	x	INTJ
ejpam-1200	174	10	,	,	PUNCT
ejpam-1200	174	11	τ1,τ2,i	τ1,τ2,i	PROPN
ejpam-1200	174	12	)	)	PUNCT
ejpam-1200	174	13	.	.	PUNCT
ejpam-1200	175	1	then	then	ADV
ejpam-1200	175	2	the	the	DET
ejpam-1200	175	3	following	follow	VERB
ejpam-1200	175	4	properties	property	NOUN
ejpam-1200	175	5	hold	hold	VERB
ejpam-1200	175	6	:	:	PUNCT
ejpam-1200	175	7	(	(	PUNCT
ejpam-1200	175	8	i	i	NOUN
ejpam-1200	175	9	)	)	PUNCT
ejpam-1200	175	10	(	(	PUNCT
ejpam-1200	175	11	i	i	PROPN
ejpam-1200	175	12	,	,	PUNCT
ejpam-1200	175	13	j)−	j)−	PROPN
ejpam-1200	175	14	βi	βi	PRON
ejpam-1200	175	15	cl(a	cl(a	NUM
ejpam-1200	175	16	)	)	PUNCT
ejpam-1200	175	17	=	=	SYM
ejpam-1200	175	18	∩{f	∩{f	NOUN
ejpam-1200	175	19	:	:	PUNCT
ejpam-1200	175	20	a⊂	a⊂	X
ejpam-1200	175	21	f	f	NOUN
ejpam-1200	175	22	and	and	CCONJ
ejpam-1200	175	23	f	f	PROPN
ejpam-1200	175	24	∈	∈	PROPN
ejpam-1200	175	25	(	(	PUNCT
ejpam-1200	175	26	i	i	NOUN
ejpam-1200	175	27	,	,	PUNCT
ejpam-1200	175	28	j)−	j)−	PROPN
ejpam-1200	175	29	βi	βi	PROPN
ejpam-1200	175	30	c(x	c(x	PROPN
ejpam-1200	175	31	)	)	PUNCT
ejpam-1200	175	32	}	}	PUNCT
ejpam-1200	175	33	.	.	PUNCT
ejpam-1200	176	1	(	(	PUNCT
ejpam-1200	176	2	ii	ii	NOUN
ejpam-1200	176	3	)	)	PUNCT
ejpam-1200	176	4	(	(	PUNCT
ejpam-1200	176	5	i	i	PROPN
ejpam-1200	176	6	,	,	PUNCT
ejpam-1200	176	7	j)−	j)−	PROPN
ejpam-1200	176	8	βi	βi	PRON
ejpam-1200	176	9	cl(a	cl(a	NUM
ejpam-1200	176	10	)	)	PUNCT
ejpam-1200	176	11	is	be	AUX
ejpam-1200	176	12	the	the	DET
ejpam-1200	176	13	smallest	small	ADJ
ejpam-1200	176	14	(	(	PUNCT
ejpam-1200	176	15	i	i	NOUN
ejpam-1200	176	16	,	,	PUNCT
ejpam-1200	176	17	j)−	j)−	PROPN
ejpam-1200	176	18	β	β	PROPN
ejpam-1200	176	19	−i	−i	PROPN
ejpam-1200	176	20	-closed	-closed	PROPN
ejpam-1200	176	21	subset	subset	NOUN
ejpam-1200	176	22	of	of	ADP
ejpam-1200	176	23	x	x	SYM
ejpam-1200	176	24	containing	contain	VERB
ejpam-1200	176	25	a.	a.	NOUN
ejpam-1200	176	26	(	(	PUNCT
ejpam-1200	176	27	iii	iii	NOUN
ejpam-1200	176	28	)	)	PUNCT
ejpam-1200	176	29	a	a	PRON
ejpam-1200	176	30	is	be	AUX
ejpam-1200	176	31	(	(	PUNCT
ejpam-1200	176	32	i	i	NOUN
ejpam-1200	176	33	,	,	PUNCT
ejpam-1200	176	34	j)−	j)−	PROPN
ejpam-1200	176	35	β	β	PROPN
ejpam-1200	176	36	−i	−i	PROPN
ejpam-1200	176	37	-closed	-close	VERB
ejpam-1200	176	38	if	if	SCONJ
ejpam-1200	176	39	and	and	CCONJ
ejpam-1200	176	40	only	only	ADV
ejpam-1200	176	41	if	if	SCONJ
ejpam-1200	176	42	a=	a=	PROPN
ejpam-1200	176	43	(	(	PUNCT
ejpam-1200	176	44	i	i	NOUN
ejpam-1200	176	45	,	,	PUNCT
ejpam-1200	176	46	j)−	j)−	PROPN
ejpam-1200	176	47	βi	βi	PRON
ejpam-1200	176	48	cl(a	cl(a	NUM
ejpam-1200	176	49	)	)	PUNCT
ejpam-1200	176	50	.	.	PUNCT
ejpam-1200	177	1	(	(	PUNCT
ejpam-1200	177	2	iv	iv	X
ejpam-1200	177	3	)	)	PUNCT
ejpam-1200	177	4	(	(	PUNCT
ejpam-1200	177	5	i	i	PROPN
ejpam-1200	177	6	,	,	PUNCT
ejpam-1200	177	7	j)−	j)−	PROPN
ejpam-1200	177	8	βi	βi	PUNCT
ejpam-1200	177	9	cl((i	cl((i	NOUN
ejpam-1200	177	10	,	,	PUNCT
ejpam-1200	177	11	j)−	j)−	PROPN
ejpam-1200	177	12	βi	βi	PRON
ejpam-1200	177	13	cl(a	cl(a	NUM
ejpam-1200	177	14	)	)	PUNCT
ejpam-1200	177	15	=	=	SYM
ejpam-1200	177	16	(	(	PUNCT
ejpam-1200	177	17	i	i	PROPN
ejpam-1200	177	18	,	,	PUNCT
ejpam-1200	177	19	j)−	j)−	PROPN
ejpam-1200	177	20	βi	βi	PRON
ejpam-1200	177	21	cl(a	cl(a	NUM
ejpam-1200	177	22	)	)	PUNCT
ejpam-1200	177	23	.	.	PUNCT
ejpam-1200	178	1	(	(	PUNCT
ejpam-1200	178	2	v	v	NOUN
ejpam-1200	178	3	)	)	PUNCT
ejpam-1200	178	4	if	if	SCONJ
ejpam-1200	178	5	a⊂	a⊂	NOUN
ejpam-1200	178	6	b	b	NOUN
ejpam-1200	178	7	,	,	PUNCT
ejpam-1200	178	8	then	then	ADV
ejpam-1200	178	9	(	(	PUNCT
ejpam-1200	178	10	i	i	PROPN
ejpam-1200	178	11	,	,	PUNCT
ejpam-1200	178	12	j)−	j)−	PROPN
ejpam-1200	178	13	βi	βi	PROPN
ejpam-1200	178	14	cl(a)⊂	cl(a)⊂	PROPN
ejpam-1200	178	15	(	(	PUNCT
ejpam-1200	178	16	i	i	PROPN
ejpam-1200	178	17	,	,	PUNCT
ejpam-1200	178	18	j)−	j)−	PROPN
ejpam-1200	178	19	βi	βi	NUM
ejpam-1200	178	20	cl(b	cl(b	NOUN
ejpam-1200	178	21	)	)	PUNCT
ejpam-1200	178	22	.	.	PUNCT
ejpam-1200	179	1	(	(	PUNCT
ejpam-1200	179	2	vi	vi	X
ejpam-1200	179	3	)	)	PUNCT
ejpam-1200	179	4	(	(	PUNCT
ejpam-1200	179	5	i	i	PROPN
ejpam-1200	179	6	,	,	PUNCT
ejpam-1200	179	7	j)−	j)−	PROPN
ejpam-1200	179	8	βi	βi	PROPN
ejpam-1200	179	9	cl(a∪	cl(a∪	PROPN
ejpam-1200	179	10	b)⊃	b)⊃	NOUN
ejpam-1200	179	11	(	(	PUNCT
ejpam-1200	179	12	i	i	PROPN
ejpam-1200	179	13	,	,	PUNCT
ejpam-1200	179	14	j)−	j)−	PROPN
ejpam-1200	179	15	βi	βi	PUNCT
ejpam-1200	179	16	cl(a)∪	cl(a)∪	PROPN
ejpam-1200	179	17	(	(	PUNCT
ejpam-1200	179	18	i	i	PROPN
ejpam-1200	179	19	,	,	PUNCT
ejpam-1200	179	20	j)−	j)−	PROPN
ejpam-1200	179	21	βi	βi	NUM
ejpam-1200	179	22	cl(b	cl(b	NOUN
ejpam-1200	179	23	)	)	PUNCT
ejpam-1200	179	24	.	.	PUNCT
ejpam-1200	180	1	(	(	PUNCT
ejpam-1200	180	2	vii	vii	PROPN
ejpam-1200	180	3	)	)	PUNCT
ejpam-1200	180	4	]	]	PUNCT
ejpam-1200	181	1	(	(	PUNCT
ejpam-1200	181	2	i	i	PRON
ejpam-1200	181	3	,	,	PUNCT
ejpam-1200	181	4	j)−	j)−	PROPN
ejpam-1200	181	5	βi	βi	PROPN
ejpam-1200	181	6	cl(a∩	cl(a∩	PROPN
ejpam-1200	181	7	b)⊂	b)⊂	PROPN
ejpam-1200	181	8	(	(	PUNCT
ejpam-1200	181	9	i	i	PROPN
ejpam-1200	181	10	,	,	PUNCT
ejpam-1200	181	11	j)−	j)−	PROPN
ejpam-1200	181	12	βi	βi	PRON
ejpam-1200	181	13	cl(a)∩	cl(a)∩	PROPN
ejpam-1200	181	14	(	(	PUNCT
ejpam-1200	181	15	i	i	PROPN
ejpam-1200	181	16	,	,	PUNCT
ejpam-1200	181	17	j)−	j)−	PROPN
ejpam-1200	181	18	βi	βi	NUM
ejpam-1200	181	19	cl(b	cl(b	NOUN
ejpam-1200	181	20	)	)	PUNCT
ejpam-1200	181	21	.	.	PUNCT
ejpam-1200	182	1	proof	proof	NOUN
ejpam-1200	182	2	.	.	PUNCT
ejpam-1200	183	1	the	the	DET
ejpam-1200	183	2	proofs	proof	NOUN
ejpam-1200	183	3	follows	follow	VERB
ejpam-1200	183	4	from	from	ADP
ejpam-1200	183	5	the	the	DET
ejpam-1200	183	6	definitions	definition	NOUN
ejpam-1200	183	7	.	.	PUNCT
ejpam-1200	184	1	theorem	theorem	NOUN
ejpam-1200	184	2	9	9	NUM
ejpam-1200	184	3	.	.	PUNCT
ejpam-1200	185	1	let	let	AUX
ejpam-1200	185	2	(	(	PUNCT
ejpam-1200	185	3	x	x	INTJ
ejpam-1200	185	4	,	,	PUNCT
ejpam-1200	185	5	τ1,τ2,i	τ1,τ2,i	PROPN
ejpam-1200	185	6	)	)	PUNCT
ejpam-1200	185	7	be	be	AUX
ejpam-1200	185	8	an	an	DET
ejpam-1200	185	9	ideal	ideal	ADJ
ejpam-1200	185	10	bitopological	bitopological	ADJ
ejpam-1200	185	11	space	space	NOUN
ejpam-1200	185	12	and	and	CCONJ
ejpam-1200	185	13	a⊂	a⊂	NOUN
ejpam-1200	185	14	x	x	X
ejpam-1200	185	15	.	.	PUNCT
ejpam-1200	186	1	a	a	DET
ejpam-1200	186	2	point	point	NOUN
ejpam-1200	186	3	x	x	X
ejpam-1200	186	4	∈	∈	PROPN
ejpam-1200	186	5	(	(	PUNCT
ejpam-1200	186	6	i	i	PROPN
ejpam-1200	186	7	,	,	PUNCT
ejpam-1200	186	8	j)−	j)−	PROPN
ejpam-1200	186	9	βi	βi	PRON
ejpam-1200	186	10	cl(a	cl(a	NUM
ejpam-1200	186	11	)	)	PUNCT
ejpam-1200	186	12	if	if	SCONJ
ejpam-1200	186	13	and	and	CCONJ
ejpam-1200	186	14	only	only	ADV
ejpam-1200	186	15	if	if	SCONJ
ejpam-1200	186	16	u	u	PROPN
ejpam-1200	186	17	∩	∩	VERB
ejpam-1200	186	18	a	a	DET
ejpam-1200	186	19	6=	6=	NOUN
ejpam-1200	186	20	;	;	PUNCT
ejpam-1200	186	21	for	for	ADP
ejpam-1200	186	22	every	every	DET
ejpam-1200	186	23	u	u	PROPN
ejpam-1200	186	24	∈	∈	PROPN
ejpam-1200	186	25	(	(	PUNCT
ejpam-1200	186	26	i	i	NOUN
ejpam-1200	186	27	,	,	PUNCT
ejpam-1200	186	28	j)−	j)−	PROPN
ejpam-1200	186	29	βio(x	βio(x	PRON
ejpam-1200	186	30	,	,	PUNCT
ejpam-1200	186	31	x	x	NOUN
ejpam-1200	186	32	)	)	PUNCT
ejpam-1200	186	33	.	.	PUNCT
ejpam-1200	187	1	proof	proof	NOUN
ejpam-1200	187	2	.	.	PUNCT
ejpam-1200	188	1	suppose	suppose	VERB
ejpam-1200	188	2	that	that	SCONJ
ejpam-1200	188	3	x	x	SYM
ejpam-1200	188	4	∈	∈	PROPN
ejpam-1200	188	5	(	(	PUNCT
ejpam-1200	188	6	i	i	PROPN
ejpam-1200	188	7	,	,	PUNCT
ejpam-1200	188	8	j)−	j)−	PROPN
ejpam-1200	188	9	βi	βi	PRON
ejpam-1200	188	10	cl(a	cl(a	NUM
ejpam-1200	188	11	)	)	PUNCT
ejpam-1200	188	12	.	.	PUNCT
ejpam-1200	189	1	we	we	PRON
ejpam-1200	189	2	shall	shall	AUX
ejpam-1200	189	3	show	show	VERB
ejpam-1200	189	4	that	that	SCONJ
ejpam-1200	189	5	u	u	PROPN
ejpam-1200	189	6	∩	∩	NOUN
ejpam-1200	189	7	a	a	DET
ejpam-1200	189	8	6=	6=	NOUN
ejpam-1200	189	9	;	;	PUNCT
ejpam-1200	189	10	for	for	ADP
ejpam-1200	189	11	every	every	DET
ejpam-1200	189	12	u	u	PROPN
ejpam-1200	189	13	∈	∈	PROPN
ejpam-1200	189	14	(	(	PUNCT
ejpam-1200	189	15	i	i	NOUN
ejpam-1200	189	16	,	,	PUNCT
ejpam-1200	189	17	j)−βio(x	j)−βio(x	PROPN
ejpam-1200	189	18	,	,	PUNCT
ejpam-1200	189	19	x	x	X
ejpam-1200	189	20	)	)	PUNCT
ejpam-1200	189	21	.	.	PUNCT
ejpam-1200	190	1	suppose	suppose	VERB
ejpam-1200	190	2	that	that	SCONJ
ejpam-1200	190	3	there	there	PRON
ejpam-1200	190	4	exists	exist	VERB
ejpam-1200	190	5	u	u	PROPN
ejpam-1200	190	6	∈	∈	PROPN
ejpam-1200	190	7	(	(	PUNCT
ejpam-1200	190	8	i	i	NOUN
ejpam-1200	190	9	,	,	PUNCT
ejpam-1200	190	10	j)−βio(x	j)−βio(x	PROPN
ejpam-1200	190	11	,	,	PUNCT
ejpam-1200	190	12	x	x	X
ejpam-1200	190	13	)	)	PUNCT
ejpam-1200	190	14	such	such	ADJ
ejpam-1200	190	15	that	that	DET
ejpam-1200	190	16	u	u	NOUN
ejpam-1200	190	17	∩a=	∩a=	PUNCT
ejpam-1200	190	18	;	;	PUNCT
ejpam-1200	190	19	.	.	PUNCT
ejpam-1200	191	1	then	then	ADV
ejpam-1200	191	2	a⊂	a⊂	VERB
ejpam-1200	191	3	x\u	x\u	PROPN
ejpam-1200	191	4	and	and	CCONJ
ejpam-1200	191	5	x\u	x\u	PROPN
ejpam-1200	191	6	is	be	AUX
ejpam-1200	191	7	(	(	PUNCT
ejpam-1200	191	8	i	i	NOUN
ejpam-1200	191	9	,	,	PUNCT
ejpam-1200	191	10	j)−	j)−	PROPN
ejpam-1200	191	11	β	β	PROPN
ejpam-1200	191	12	−i	−i	PROPN
ejpam-1200	191	13	-closed	-closed	PROPN
ejpam-1200	191	14	.	.	PUNCT
ejpam-1200	192	1	since	since	SCONJ
ejpam-1200	192	2	a⊂	a⊂	PRON
ejpam-1200	192	3	x\u	x\u	PROPN
ejpam-1200	192	4	,	,	PUNCT
ejpam-1200	192	5	(	(	PUNCT
ejpam-1200	192	6	i	i	NOUN
ejpam-1200	192	7	,	,	PUNCT
ejpam-1200	192	8	j)−	j)−	PROPN
ejpam-1200	192	9	βi	βi	PROPN
ejpam-1200	192	10	cl(a)⊂	cl(a)⊂	PROPN
ejpam-1200	192	11	(	(	PUNCT
ejpam-1200	192	12	i	i	NOUN
ejpam-1200	192	13	,	,	PUNCT
ejpam-1200	192	14	j)−	j)−	PROPN
ejpam-1200	192	15	βi	βi	PROPN
ejpam-1200	192	16	cl(x\u	cl(x\u	PROPN
ejpam-1200	192	17	)	)	PUNCT
ejpam-1200	192	18	.	.	PUNCT
ejpam-1200	193	1	since	since	SCONJ
ejpam-1200	193	2	x	x	PROPN
ejpam-1200	193	3	∈	∈	PROPN
ejpam-1200	193	4	(	(	PUNCT
ejpam-1200	193	5	i	i	PROPN
ejpam-1200	193	6	,	,	PUNCT
ejpam-1200	193	7	j)−	j)−	PROPN
ejpam-1200	193	8	βi	βi	PRON
ejpam-1200	193	9	cl(a	cl(a	NUM
ejpam-1200	193	10	)	)	PUNCT
ejpam-1200	193	11	,	,	PUNCT
ejpam-1200	193	12	we	we	PRON
ejpam-1200	193	13	have	have	VERB
ejpam-1200	193	14	x	x	SYM
ejpam-1200	193	15	∈	∈	PROPN
ejpam-1200	193	16	(	(	PUNCT
ejpam-1200	193	17	i	i	PROPN
ejpam-1200	193	18	,	,	PUNCT
ejpam-1200	193	19	j)−	j)−	PROPN
ejpam-1200	193	20	βi	βi	PROPN
ejpam-1200	193	21	cl(x\u	cl(x\u	PROPN
ejpam-1200	193	22	)	)	PUNCT
ejpam-1200	193	23	.	.	PUNCT
ejpam-1200	194	1	since	since	SCONJ
ejpam-1200	194	2	x\u	x\u	PROPN
ejpam-1200	194	3	is	be	AUX
ejpam-1200	194	4	(	(	PUNCT
ejpam-1200	194	5	i	i	NOUN
ejpam-1200	194	6	,	,	PUNCT
ejpam-1200	194	7	j)−	j)−	PROPN
ejpam-1200	194	8	β	β	PROPN
ejpam-1200	194	9	−i	−i	PROPN
ejpam-1200	194	10	-closed	-closed	PROPN
ejpam-1200	194	11	,	,	PUNCT
ejpam-1200	194	12	we	we	PRON
ejpam-1200	194	13	have	have	VERB
ejpam-1200	194	14	x	x	PROPN
ejpam-1200	194	15	∈	∈	PROPN
ejpam-1200	194	16	x\u	x\u	NOUN
ejpam-1200	194	17	;	;	PUNCT
ejpam-1200	194	18	hence	hence	ADV
ejpam-1200	194	19	x	x	NOUN
ejpam-1200	194	20	/∈	/∈	PUNCT
ejpam-1200	194	21	u	u	NOUN
ejpam-1200	194	22	,	,	PUNCT
ejpam-1200	194	23	which	which	PRON
ejpam-1200	194	24	is	be	AUX
ejpam-1200	194	25	a	a	DET
ejpam-1200	194	26	contradiction	contradiction	NOUN
ejpam-1200	194	27	that	that	SCONJ
ejpam-1200	194	28	x	x	PUNCT
ejpam-1200	194	29	∈	∈	PROPN
ejpam-1200	194	30	u	u	NOUN
ejpam-1200	194	31	.	.	PUNCT
ejpam-1200	195	1	therefore	therefore	ADV
ejpam-1200	195	2	,	,	PUNCT
ejpam-1200	195	3	u	u	PROPN
ejpam-1200	195	4	∩a	∩a	PROPN
ejpam-1200	195	5	6=	6=	PROPN
ejpam-1200	195	6	;	;	PUNCT
ejpam-1200	195	7	.	.	PUNCT
ejpam-1200	196	1	conversely	conversely	ADV
ejpam-1200	196	2	,	,	PUNCT
ejpam-1200	196	3	suppose	suppose	VERB
ejpam-1200	196	4	that	that	SCONJ
ejpam-1200	196	5	u	u	PROPN
ejpam-1200	196	6	∩	∩	NOUN
ejpam-1200	196	7	a	a	DET
ejpam-1200	196	8	6=	6=	NOUN
ejpam-1200	196	9	;	;	PUNCT
ejpam-1200	196	10	for	for	ADP
ejpam-1200	196	11	every	every	DET
ejpam-1200	196	12	u	u	PROPN
ejpam-1200	196	13	∈	∈	PROPN
ejpam-1200	196	14	(	(	PUNCT
ejpam-1200	196	15	i	i	PROPN
ejpam-1200	196	16	,	,	PUNCT
ejpam-1200	196	17	j	j	PROPN
ejpam-1200	196	18	)	)	PUNCT
ejpam-1200	196	19	−	−	PROPN
ejpam-1200	196	20	βio(x	βio(x	X
ejpam-1200	196	21	,	,	PUNCT
ejpam-1200	196	22	x	x	NOUN
ejpam-1200	196	23	)	)	PUNCT
ejpam-1200	196	24	.	.	PUNCT
ejpam-1200	197	1	we	we	PRON
ejpam-1200	197	2	shall	shall	AUX
ejpam-1200	197	3	show	show	VERB
ejpam-1200	197	4	that	that	SCONJ
ejpam-1200	197	5	x	x	SYM
ejpam-1200	197	6	∈	∈	PROPN
ejpam-1200	197	7	(	(	PUNCT
ejpam-1200	197	8	i	i	PROPN
ejpam-1200	197	9	,	,	PUNCT
ejpam-1200	197	10	j	j	PROPN
ejpam-1200	197	11	)	)	PUNCT
ejpam-1200	197	12	−	−	PROPN
ejpam-1200	197	13	βi	βi	PRON
ejpam-1200	197	14	cl(a	cl(a	NUM
ejpam-1200	197	15	)	)	PUNCT
ejpam-1200	197	16	.	.	PUNCT
ejpam-1200	198	1	suppose	suppose	VERB
ejpam-1200	198	2	that	that	SCONJ
ejpam-1200	198	3	x	x	X
ejpam-1200	198	4	/∈	/∈	INTJ
ejpam-1200	198	5	(	(	PUNCT
ejpam-1200	198	6	i	i	NOUN
ejpam-1200	198	7	,	,	PUNCT
ejpam-1200	198	8	j)−	j)−	PROPN
ejpam-1200	198	9	βi	βi	PRON
ejpam-1200	198	10	cl(a	cl(a	NUM
ejpam-1200	198	11	)	)	PUNCT
ejpam-1200	198	12	.	.	PUNCT
ejpam-1200	199	1	then	then	ADV
ejpam-1200	199	2	there	there	PRON
ejpam-1200	199	3	exists	exist	VERB
ejpam-1200	199	4	u	u	PROPN
ejpam-1200	199	5	∈	∈	PROPN
ejpam-1200	199	6	(	(	PUNCT
ejpam-1200	199	7	i	i	PROPN
ejpam-1200	199	8	,	,	PUNCT
ejpam-1200	199	9	j)−	j)−	PROPN
ejpam-1200	199	10	βio(x	βio(x	PRON
ejpam-1200	199	11	,	,	PUNCT
ejpam-1200	199	12	x	x	X
ejpam-1200	199	13	)	)	PUNCT
ejpam-1200	199	14	such	such	ADJ
ejpam-1200	199	15	that	that	SCONJ
ejpam-1200	199	16	u	u	PROPN
ejpam-1200	199	17	∩	∩	NOUN
ejpam-1200	199	18	a=	a=	VERB
ejpam-1200	199	19	empt	empt	NOUN
ejpam-1200	199	20	yset	yset	NOUN
ejpam-1200	199	21	.	.	PUNCT
ejpam-1200	200	1	this	this	PRON
ejpam-1200	200	2	is	be	AUX
ejpam-1200	200	3	a	a	DET
ejpam-1200	200	4	contradiction	contradiction	NOUN
ejpam-1200	200	5	to	to	ADP
ejpam-1200	200	6	u	u	NOUN
ejpam-1200	200	7	∩	∩	NOUN
ejpam-1200	200	8	a	a	DET
ejpam-1200	200	9	6=	6=	NOUN
ejpam-1200	200	10	;	;	PUNCT
ejpam-1200	200	11	;	;	PUNCT
ejpam-1200	201	1	hence	hence	ADV
ejpam-1200	201	2	x	x	X
ejpam-1200	201	3	∈	∈	PROPN
ejpam-1200	201	4	(	(	PUNCT
ejpam-1200	201	5	i	i	PROPN
ejpam-1200	201	6	,	,	PUNCT
ejpam-1200	201	7	j)−	j)−	PROPN
ejpam-1200	201	8	βi	βi	PRON
ejpam-1200	201	9	cl(a	cl(a	NUM
ejpam-1200	201	10	)	)	PUNCT
ejpam-1200	201	11	.	.	PUNCT
ejpam-1200	201	12	theorem	theorem	ADJ
ejpam-1200	201	13	10	10	NUM
ejpam-1200	201	14	.	.	PUNCT
ejpam-1200	202	1	let	let	AUX
ejpam-1200	202	2	(	(	PUNCT
ejpam-1200	202	3	x	x	INTJ
ejpam-1200	202	4	,	,	PUNCT
ejpam-1200	202	5	τ1,τ2,i	τ1,τ2,i	PROPN
ejpam-1200	202	6	)	)	PUNCT
ejpam-1200	202	7	be	be	AUX
ejpam-1200	202	8	an	an	DET
ejpam-1200	202	9	ideal	ideal	ADJ
ejpam-1200	202	10	bitopological	bitopological	ADJ
ejpam-1200	202	11	space	space	NOUN
ejpam-1200	202	12	and	and	CCONJ
ejpam-1200	202	13	a⊂	a⊂	PRON
ejpam-1200	202	14	x	x	X
ejpam-1200	202	15	.	.	PUNCT
ejpam-1200	203	1	then	then	ADV
ejpam-1200	203	2	the	the	DET
ejpam-1200	203	3	following	follow	VERB
ejpam-1200	203	4	propeties	propetie	NOUN
ejpam-1200	203	5	hold	hold	VERB
ejpam-1200	203	6	:	:	PUNCT
ejpam-1200	203	7	(	(	PUNCT
ejpam-1200	203	8	i	i	NOUN
ejpam-1200	203	9	)	)	PUNCT
ejpam-1200	203	10	(	(	PUNCT
ejpam-1200	203	11	i	i	PROPN
ejpam-1200	203	12	,	,	PUNCT
ejpam-1200	203	13	j)−	j)−	PROPN
ejpam-1200	203	14	βi	βi	PROPN
ejpam-1200	203	15	int(x\a	int(x\a	PROPN
ejpam-1200	203	16	)	)	PUNCT
ejpam-1200	203	17	=	=	SYM
ejpam-1200	204	1	x\(i	x\(i	PROPN
ejpam-1200	204	2	,	,	PUNCT
ejpam-1200	204	3	j)−	j)−	PROPN
ejpam-1200	204	4	βi	βi	PRON
ejpam-1200	204	5	cl(a	cl(a	NUM
ejpam-1200	204	6	)	)	PUNCT
ejpam-1200	204	7	;	;	PUNCT
ejpam-1200	204	8	(	(	PUNCT
ejpam-1200	204	9	ii	ii	NOUN
ejpam-1200	204	10	)	)	PUNCT
ejpam-1200	204	11	(	(	PUNCT
ejpam-1200	204	12	i	i	PROPN
ejpam-1200	204	13	,	,	PUNCT
ejpam-1200	204	14	j)−	j)−	PROPN
ejpam-1200	204	15	βi	βi	PRON
ejpam-1200	204	16	cl(x\a	cl(x\a	ADV
ejpam-1200	204	17	)	)	PUNCT
ejpam-1200	205	1	=	=	SYM
ejpam-1200	205	2	x\(i	x\(i	PROPN
ejpam-1200	205	3	,	,	PUNCT
ejpam-1200	205	4	j)−	j)−	PROPN
ejpam-1200	205	5	βi	βi	PROPN
ejpam-1200	205	6	int(a	int(a	PROPN
ejpam-1200	205	7	)	)	PUNCT
ejpam-1200	205	8	.	.	PUNCT
ejpam-1200	206	1	proof	proof	NOUN
ejpam-1200	206	2	.	.	PUNCT
ejpam-1200	207	1	(	(	PUNCT
ejpam-1200	207	2	i	i	NOUN
ejpam-1200	207	3	)	)	PUNCT
ejpam-1200	207	4	.	.	PUNCT
ejpam-1200	208	1	let	let	VERB
ejpam-1200	208	2	x	x	X
ejpam-1200	208	3	∈	∈	PROPN
ejpam-1200	208	4	(	(	PUNCT
ejpam-1200	208	5	i	i	NOUN
ejpam-1200	208	6	,	,	PUNCT
ejpam-1200	208	7	j)−βi	j)−βi	PROPN
ejpam-1200	208	8	cl(a	cl(a	NUM
ejpam-1200	208	9	)	)	PUNCT
ejpam-1200	208	10	.	.	PUNCT
ejpam-1200	209	1	there	there	PRON
ejpam-1200	209	2	exists	exist	VERB
ejpam-1200	209	3	v	v	ADP
ejpam-1200	209	4	∈	∈	PROPN
ejpam-1200	209	5	(	(	PUNCT
ejpam-1200	209	6	i	i	NOUN
ejpam-1200	209	7	,	,	PUNCT
ejpam-1200	209	8	j)−βio(x	j)−βio(x	PROPN
ejpam-1200	209	9	,	,	PUNCT
ejpam-1200	209	10	x	x	X
ejpam-1200	209	11	)	)	PUNCT
ejpam-1200	209	12	such	such	ADJ
ejpam-1200	209	13	that	that	SCONJ
ejpam-1200	209	14	v∩a	v∩a	NOUN
ejpam-1200	209	15	6=	6=	NUM
ejpam-1200	209	16	;	;	PUNCT
ejpam-1200	209	17	;	;	PUNCT
ejpam-1200	209	18	hence	hence	ADV
ejpam-1200	209	19	we	we	PRON
ejpam-1200	209	20	obtain	obtain	VERB
ejpam-1200	209	21	x	x	SYM
ejpam-1200	209	22	∈	∈	PROPN
ejpam-1200	209	23	(	(	PUNCT
ejpam-1200	209	24	i	i	PROPN
ejpam-1200	209	25	,	,	PUNCT
ejpam-1200	209	26	j)−	j)−	PROPN
ejpam-1200	209	27	βi	βi	PROPN
ejpam-1200	209	28	int(x\a	int(x\a	PROPN
ejpam-1200	209	29	)	)	PUNCT
ejpam-1200	209	30	.	.	PUNCT
ejpam-1200	210	1	this	this	PRON
ejpam-1200	210	2	shows	show	VERB
ejpam-1200	210	3	that	that	SCONJ
ejpam-1200	210	4	x\(i	x\(i	PROPN
ejpam-1200	210	5	,	,	PUNCT
ejpam-1200	210	6	j)−	j)−	PROPN
ejpam-1200	210	7	βi	βi	PROPN
ejpam-1200	210	8	cl(a)⊂	cl(a)⊂	PROPN
ejpam-1200	210	9	(	(	PUNCT
ejpam-1200	210	10	i	i	NOUN
ejpam-1200	210	11	,	,	PUNCT
ejpam-1200	210	12	j)−	j)−	PROPN
ejpam-1200	210	13	βi	βi	PROPN
ejpam-1200	210	14	int(x\a	int(x\a	PROPN
ejpam-1200	210	15	)	)	PUNCT
ejpam-1200	210	16	.	.	PUNCT
ejpam-1200	211	1	let	let	VERB
ejpam-1200	211	2	x	x	X
ejpam-1200	211	3	∈	∈	PROPN
ejpam-1200	211	4	(	(	PUNCT
ejpam-1200	211	5	i	i	PROPN
ejpam-1200	211	6	,	,	PUNCT
ejpam-1200	211	7	j)−	j)−	PROPN
ejpam-1200	211	8	βi	βi	PROPN
ejpam-1200	211	9	int(x\a	int(x\a	PROPN
ejpam-1200	211	10	)	)	PUNCT
ejpam-1200	211	11	.	.	PUNCT
ejpam-1200	212	1	since	since	SCONJ
ejpam-1200	212	2	(	(	PUNCT
ejpam-1200	212	3	i	i	PROPN
ejpam-1200	212	4	,	,	PUNCT
ejpam-1200	212	5	j)−	j)−	PROPN
ejpam-1200	212	6	βi	βi	PROPN
ejpam-1200	212	7	int(x\a)∩	int(x\a)∩	PROPN
ejpam-1200	212	8	a=	a=	PROPN
ejpam-1200	212	9	;	;	PUNCT
ejpam-1200	212	10	,	,	PUNCT
ejpam-1200	212	11	we	we	PRON
ejpam-1200	212	12	obtain	obtain	VERB
ejpam-1200	212	13	x	x	X
ejpam-1200	212	14	/∈	/∈	PUNCT
ejpam-1200	213	1	(	(	PUNCT
ejpam-1200	213	2	i	i	NOUN
ejpam-1200	213	3	,	,	PUNCT
ejpam-1200	213	4	j)−	j)−	PROPN
ejpam-1200	213	5	βi	βi	PRON
ejpam-1200	213	6	cl(a	cl(a	NUM
ejpam-1200	213	7	)	)	PUNCT
ejpam-1200	213	8	;	;	PUNCT
ejpam-1200	213	9	hence	hence	ADV
ejpam-1200	213	10	x	x	X
ejpam-1200	213	11	∈	∈	PROPN
ejpam-1200	213	12	x\(i	x\(i	PROPN
ejpam-1200	213	13	,	,	PUNCT
ejpam-1200	213	14	j)−	j)−	PROPN
ejpam-1200	213	15	βi	βi	PRON
ejpam-1200	213	16	cl(a	cl(a	NUM
ejpam-1200	213	17	)	)	PUNCT
ejpam-1200	213	18	.	.	PUNCT
ejpam-1200	214	1	therefore	therefore	ADV
ejpam-1200	214	2	,	,	PUNCT
ejpam-1200	214	3	we	we	PRON
ejpam-1200	214	4	obtain	obtain	VERB
ejpam-1200	214	5	(	(	PUNCT
ejpam-1200	214	6	i	i	NOUN
ejpam-1200	214	7	,	,	PUNCT
ejpam-1200	214	8	j)−	j)−	PROPN
ejpam-1200	214	9	βi	βi	PROPN
ejpam-1200	214	10	int(x\a	int(x\a	PROPN
ejpam-1200	214	11	)	)	PUNCT
ejpam-1200	215	1	=	=	SYM
ejpam-1200	215	2	x\(i	x\(i	PROPN
ejpam-1200	215	3	,	,	PUNCT
ejpam-1200	215	4	j)−	j)−	PROPN
ejpam-1200	215	5	βi	βi	PRON
ejpam-1200	215	6	cl(a	cl(a	NUM
ejpam-1200	215	7	)	)	PUNCT
ejpam-1200	215	8	.	.	PUNCT
ejpam-1200	216	1	(	(	PUNCT
ejpam-1200	216	2	ii	ii	NOUN
ejpam-1200	216	3	)	)	PUNCT
ejpam-1200	216	4	.	.	PUNCT
ejpam-1200	217	1	follows	follow	VERB
ejpam-1200	217	2	from	from	ADP
ejpam-1200	217	3	(	(	PUNCT
ejpam-1200	217	4	i	i	NOUN
ejpam-1200	217	5	)	)	PUNCT
ejpam-1200	217	6	.	.	PUNCT
ejpam-1200	218	1	proposition	proposition	NOUN
ejpam-1200	218	2	4	4	NUM
ejpam-1200	218	3	.	.	PUNCT
ejpam-1200	219	1	the	the	DET
ejpam-1200	219	2	product	product	NOUN
ejpam-1200	219	3	of	of	ADP
ejpam-1200	219	4	two	two	NUM
ejpam-1200	219	5	(	(	PUNCT
ejpam-1200	219	6	i	i	NOUN
ejpam-1200	219	7	,	,	PUNCT
ejpam-1200	219	8	j)−	j)−	PROPN
ejpam-1200	219	9	β	β	PROPN
ejpam-1200	219	10	−i	−i	PROPN
ejpam-1200	219	11	-open	-open	PROPN
ejpam-1200	219	12	sets	set	NOUN
ejpam-1200	219	13	is	be	AUX
ejpam-1200	219	14	(	(	PUNCT
ejpam-1200	219	15	i	i	NOUN
ejpam-1200	219	16	,	,	PUNCT
ejpam-1200	219	17	j)−	j)−	PROPN
ejpam-1200	219	18	β	β	PROPN
ejpam-1200	219	19	−i	−i	PROPN
ejpam-1200	219	20	-open	-open	PROPN
ejpam-1200	219	21	.	.	PUNCT
ejpam-1200	220	1	proof	proof	NOUN
ejpam-1200	220	2	.	.	PUNCT
ejpam-1200	221	1	the	the	DET
ejpam-1200	221	2	proof	proof	NOUN
ejpam-1200	221	3	follows	follow	VERB
ejpam-1200	221	4	from	from	ADP
ejpam-1200	221	5	lemma	lemma	PROPN
ejpam-1200	221	6	3.3	3.3	NUM
ejpam-1200	221	7	of	of	ADP
ejpam-1200	221	8	[	[	X
ejpam-1200	221	9	10	10	NUM
ejpam-1200	221	10	]	]	PUNCT
ejpam-1200	221	11	.	.	PUNCT
ejpam-1200	222	1	m.	m.	PROPN
ejpam-1200	222	2	caldas	caldas	PROPN
ejpam-1200	222	3	,	,	PUNCT
ejpam-1200	222	4	s.	s.	PROPN
ejpam-1200	222	5	jafari	jafari	PROPN
ejpam-1200	222	6	,	,	PUNCT
ejpam-1200	222	7	n.	n.	PROPN
ejpam-1200	222	8	rajesh	rajesh	PROPN
ejpam-1200	222	9	/	/	SYM
ejpam-1200	222	10	eur	eur	PROPN
ejpam-1200	222	11	.	.	PUNCT
ejpam-1200	223	1	j.	j.	PROPN
ejpam-1200	223	2	pure	pure	PROPN
ejpam-1200	223	3	appl	appl	PROPN
ejpam-1200	223	4	.	.	PROPN
ejpam-1200	223	5	math	math	PROPN
ejpam-1200	223	6	,	,	PUNCT
ejpam-1200	223	7	6	6	NUM
ejpam-1200	223	8	(	(	PUNCT
ejpam-1200	223	9	2013	2013	NUM
ejpam-1200	223	10	)	)	PUNCT
ejpam-1200	223	11	,	,	PUNCT
ejpam-1200	223	12	247	247	NUM
ejpam-1200	223	13	-	-	SYM
ejpam-1200	223	14	255	255	NUM
ejpam-1200	223	15	253	253	NUM
ejpam-1200	223	16	4	4	NUM
ejpam-1200	223	17	.	.	PUNCT
ejpam-1200	224	1	(	(	PUNCT
ejpam-1200	224	2	i	i	NOUN
ejpam-1200	224	3	,	,	PUNCT
ejpam-1200	224	4	j)−	j)−	PROPN
ejpam-1200	224	5	β	β	PROPN
ejpam-1200	224	6	−i	−i	PROPN
ejpam-1200	224	7	-continuous	-continuous	ADJ
ejpam-1200	224	8	functions	function	NOUN
ejpam-1200	224	9	definition	definition	NOUN
ejpam-1200	224	10	9	9	NUM
ejpam-1200	224	11	.	.	PUNCT
ejpam-1200	225	1	a	a	DET
ejpam-1200	225	2	function	function	NOUN
ejpam-1200	225	3	f	f	NOUN
ejpam-1200	225	4	:	:	PUNCT
ejpam-1200	225	5	(	(	PUNCT
ejpam-1200	225	6	x	x	INTJ
ejpam-1200	225	7	,	,	PUNCT
ejpam-1200	225	8	τ1,τ2,i	τ1,τ2,i	PROPN
ejpam-1200	225	9	)	)	PUNCT
ejpam-1200	225	10	→	→	SYM
ejpam-1200	225	11	(	(	PUNCT
ejpam-1200	225	12	y	y	PROPN
ejpam-1200	225	13	,	,	PUNCT
ejpam-1200	225	14	σ1,σ2	σ1,σ2	PROPN
ejpam-1200	225	15	)	)	PUNCT
ejpam-1200	225	16	is	be	AUX
ejpam-1200	225	17	said	say	VERB
ejpam-1200	225	18	to	to	PART
ejpam-1200	225	19	be	be	AUX
ejpam-1200	225	20	(	(	PUNCT
ejpam-1200	225	21	i	i	PRON
ejpam-1200	225	22	,	,	PUNCT
ejpam-1200	225	23	j)−β	j)−β	ADJ
ejpam-1200	225	24	−i	−i	ADV
ejpam-1200	225	25	-continuous	-continuous	ADJ
ejpam-1200	225	26	if	if	SCONJ
ejpam-1200	225	27	the	the	DET
ejpam-1200	225	28	inverse	inverse	ADJ
ejpam-1200	225	29	image	image	NOUN
ejpam-1200	225	30	of	of	ADP
ejpam-1200	225	31	every	every	DET
ejpam-1200	225	32	σi	σi	NOUN
ejpam-1200	225	33	-	-	PUNCT
ejpam-1200	225	34	open	open	ADJ
ejpam-1200	225	35	set	set	NOUN
ejpam-1200	225	36	of	of	ADP
ejpam-1200	225	37	y	y	PROPN
ejpam-1200	225	38	is	be	AUX
ejpam-1200	225	39	(	(	PUNCT
ejpam-1200	225	40	i	i	INTJ
ejpam-1200	225	41	,	,	PUNCT
ejpam-1200	225	42	j)−β	j)−β	PRON
ejpam-1200	225	43	−i	−i	ADJ
ejpam-1200	225	44	-open	-open	NOUN
ejpam-1200	225	45	in	in	ADP
ejpam-1200	225	46	x	x	SYM
ejpam-1200	225	47	,	,	PUNCT
ejpam-1200	225	48	where	where	SCONJ
ejpam-1200	225	49	i	i	PRON
ejpam-1200	225	50	6=	6=	PROPN
ejpam-1200	225	51	j	j	PROPN
ejpam-1200	225	52	,	,	PUNCT
ejpam-1200	225	53	i	i	PRON
ejpam-1200	225	54	,	,	PUNCT
ejpam-1200	225	55	j	j	PROPN
ejpam-1200	225	56	=	=	SYM
ejpam-1200	225	57	1	1	NUM
ejpam-1200	225	58	,	,	PUNCT
ejpam-1200	225	59	2	2	NUM
ejpam-1200	225	60	.	.	X
ejpam-1200	225	61	proposition	proposition	NOUN
ejpam-1200	225	62	5	5	NUM
ejpam-1200	225	63	.	.	PUNCT
ejpam-1200	226	1	every	every	PRON
ejpam-1200	226	2	(	(	PUNCT
ejpam-1200	226	3	i	i	PROPN
ejpam-1200	226	4	,	,	PUNCT
ejpam-1200	226	5	j	j	PROPN
ejpam-1200	226	6	)	)	PUNCT
ejpam-1200	226	7	−	−	PROPN
ejpam-1200	226	8	b	b	X
ejpam-1200	227	1	−	−	NOUN
ejpam-1200	227	2	i	i	PRON
ejpam-1200	227	3	-continuous	-continuous	ADJ
ejpam-1200	227	4	function	function	NOUN
ejpam-1200	227	5	is	be	AUX
ejpam-1200	227	6	(	(	PUNCT
ejpam-1200	227	7	i	i	PROPN
ejpam-1200	227	8	,	,	PUNCT
ejpam-1200	227	9	j	j	PROPN
ejpam-1200	227	10	)	)	PUNCT
ejpam-1200	227	11	−	−	PROPN
ejpam-1200	228	1	β	β	NOUN
ejpam-1200	228	2	−	−	NOUN
ejpam-1200	229	1	i	i	PRON
ejpam-1200	229	2	-continuous	-continuous	ADJ
ejpam-1200	229	3	but	but	CCONJ
ejpam-1200	229	4	not	not	PART
ejpam-1200	229	5	conversely	conversely	ADV
ejpam-1200	229	6	.	.	PUNCT
ejpam-1200	230	1	proof	proof	NOUN
ejpam-1200	230	2	.	.	PUNCT
ejpam-1200	231	1	the	the	DET
ejpam-1200	231	2	proof	proof	NOUN
ejpam-1200	231	3	follows	follow	VERB
ejpam-1200	231	4	from	from	ADP
ejpam-1200	231	5	proposition	proposition	NOUN
ejpam-1200	231	6	1	1	NUM
ejpam-1200	231	7	.	.	PUNCT
ejpam-1200	232	1	the	the	DET
ejpam-1200	232	2	following	follow	VERB
ejpam-1200	232	3	example	example	NOUN
ejpam-1200	232	4	shows	show	VERB
ejpam-1200	232	5	that	that	SCONJ
ejpam-1200	232	6	the	the	DET
ejpam-1200	232	7	converse	converse	NOUN
ejpam-1200	232	8	of	of	ADP
ejpam-1200	232	9	proposition	proposition	NOUN
ejpam-1200	232	10	5	5	NUM
ejpam-1200	232	11	is	be	AUX
ejpam-1200	232	12	not	not	PART
ejpam-1200	232	13	true	true	ADJ
ejpam-1200	232	14	,	,	PUNCT
ejpam-1200	232	15	in	in	ADP
ejpam-1200	232	16	general	general	ADJ
ejpam-1200	232	17	.	.	PUNCT
ejpam-1200	233	1	example	example	NOUN
ejpam-1200	234	1	3	3	X
ejpam-1200	234	2	.	.	PUNCT
ejpam-1200	234	3	let	let	VERB
ejpam-1200	234	4	x	x	PUNCT
ejpam-1200	234	5	=	=	PRON
ejpam-1200	234	6	{	{	PUNCT
ejpam-1200	234	7	a	a	PRON
ejpam-1200	234	8	,	,	PUNCT
ejpam-1200	234	9	b	b	NOUN
ejpam-1200	234	10	,	,	PUNCT
ejpam-1200	234	11	c	c	NOUN
ejpam-1200	234	12	}	}	PUNCT
ejpam-1200	234	13	,	,	PUNCT
ejpam-1200	234	14	τ1	τ1	NOUN
ejpam-1200	234	15	=	=	SYM
ejpam-1200	234	16	{	{	PUNCT
ejpam-1200	234	17	;	;	PUNCT
ejpam-1200	234	18	,	,	PUNCT
ejpam-1200	234	19	{	{	PUNCT
ejpam-1200	234	20	a	a	X
ejpam-1200	234	21	}	}	PUNCT
ejpam-1200	234	22	,	,	PUNCT
ejpam-1200	234	23	x	x	SYM
ejpam-1200	234	24	}	}	PUNCT
ejpam-1200	234	25	,	,	PUNCT
ejpam-1200	234	26	τ2	τ2	NOUN
ejpam-1200	234	27	=	=	SYM
ejpam-1200	234	28	{	{	PUNCT
ejpam-1200	234	29	;	;	PUNCT
ejpam-1200	234	30	,	,	PUNCT
ejpam-1200	234	31	{	{	PUNCT
ejpam-1200	234	32	a	a	X
ejpam-1200	234	33	}	}	PUNCT
ejpam-1200	234	34	,	,	PUNCT
ejpam-1200	234	35	{	{	PUNCT
ejpam-1200	234	36	a	a	DET
ejpam-1200	234	37	,	,	PUNCT
ejpam-1200	234	38	b	b	NOUN
ejpam-1200	234	39	}	}	PUNCT
ejpam-1200	234	40	,	,	PUNCT
ejpam-1200	234	41	x	x	SYM
ejpam-1200	234	42	}	}	PUNCT
ejpam-1200	234	43	,	,	PUNCT
ejpam-1200	234	44	σ1	σ1	NOUN
ejpam-1200	234	45	=	=	PUNCT
ejpam-1200	234	46	{	{	PUNCT
ejpam-1200	234	47	;	;	PUNCT
ejpam-1200	234	48	,	,	PUNCT
ejpam-1200	234	49	{	{	PUNCT
ejpam-1200	234	50	a	a	NOUN
ejpam-1200	234	51	,	,	PUNCT
ejpam-1200	234	52	c	c	NOUN
ejpam-1200	234	53	}	}	PUNCT
ejpam-1200	234	54	,	,	PUNCT
ejpam-1200	234	55	x	x	SYM
ejpam-1200	234	56	}	}	PUNCT
ejpam-1200	234	57	,	,	PUNCT
ejpam-1200	234	58	σ2	σ2	NOUN
ejpam-1200	234	59	=	=	PUNCT
ejpam-1200	234	60	{	{	PUNCT
ejpam-1200	234	61	;	;	PUNCT
ejpam-1200	234	62	,	,	PUNCT
ejpam-1200	234	63	{	{	PUNCT
ejpam-1200	234	64	a	a	X
ejpam-1200	234	65	}	}	PUNCT
ejpam-1200	234	66	,	,	PUNCT
ejpam-1200	234	67	x	x	SYM
ejpam-1200	234	68	}	}	PUNCT
ejpam-1200	234	69	and	and	CCONJ
ejpam-1200	234	70	i	i	PRON
ejpam-1200	234	71	=	=	PUNCT
ejpam-1200	234	72	{	{	PUNCT
ejpam-1200	234	73	;	;	PUNCT
ejpam-1200	234	74	,	,	PUNCT
ejpam-1200	234	75	{	{	PUNCT
ejpam-1200	234	76	a	a	X
ejpam-1200	234	77	}	}	PUNCT
ejpam-1200	234	78	}	}	PUNCT
ejpam-1200	234	79	.	.	PUNCT
ejpam-1200	235	1	then	then	ADV
ejpam-1200	235	2	the	the	DET
ejpam-1200	235	3	identity	identity	NOUN
ejpam-1200	235	4	function	function	NOUN
ejpam-1200	235	5	f	f	NOUN
ejpam-1200	235	6	:	:	PUNCT
ejpam-1200	235	7	(	(	PUNCT
ejpam-1200	235	8	x	x	INTJ
ejpam-1200	235	9	,	,	PUNCT
ejpam-1200	235	10	τ1,τ2,i	τ1,τ2,i	PROPN
ejpam-1200	235	11	)	)	PUNCT
ejpam-1200	235	12	→	→	SYM
ejpam-1200	235	13	(	(	PUNCT
ejpam-1200	235	14	y	y	PROPN
ejpam-1200	235	15	,	,	PUNCT
ejpam-1200	235	16	σ1,σ2	σ1,σ2	PROPN
ejpam-1200	235	17	)	)	PUNCT
ejpam-1200	235	18	is	be	AUX
ejpam-1200	235	19	(	(	PUNCT
ejpam-1200	235	20	1	1	NUM
ejpam-1200	235	21	,	,	PUNCT
ejpam-1200	235	22	2)−	2)−	NUM
ejpam-1200	235	23	β	β	PUNCT
ejpam-1200	235	24	−i	−i	PROPN
ejpam-1200	235	25	-continuous	-continuous	ADJ
ejpam-1200	235	26	but	but	CCONJ
ejpam-1200	235	27	not	not	PART
ejpam-1200	235	28	(	(	PUNCT
ejpam-1200	235	29	1	1	NUM
ejpam-1200	235	30	,	,	PUNCT
ejpam-1200	235	31	2)−	2)−	NUM
ejpam-1200	235	32	b−i	b−i	PROPN
ejpam-1200	235	33	-continuous	-continuous	ADJ
ejpam-1200	235	34	.	.	PUNCT
ejpam-1200	235	35	corollary	corollary	ADJ
ejpam-1200	235	36	2	2	NUM
ejpam-1200	235	37	.	.	PUNCT
ejpam-1200	236	1	(	(	PUNCT
ejpam-1200	236	2	i	i	NOUN
ejpam-1200	236	3	)	)	PUNCT
ejpam-1200	236	4	every	every	PRON
ejpam-1200	236	5	(	(	PUNCT
ejpam-1200	236	6	i	i	NOUN
ejpam-1200	236	7	,	,	PUNCT
ejpam-1200	236	8	j)−α−i	j)−α−i	PROPN
ejpam-1200	236	9	-continuous	-continuous	ADJ
ejpam-1200	236	10	function	function	NOUN
ejpam-1200	236	11	is	be	AUX
ejpam-1200	236	12	(	(	PUNCT
ejpam-1200	236	13	i	i	X
ejpam-1200	236	14	,	,	PUNCT
ejpam-1200	236	15	j)−β−i	j)−β−i	PROPN
ejpam-1200	236	16	-continuous	-continuous	ADJ
ejpam-1200	236	17	but	but	CCONJ
ejpam-1200	236	18	not	not	PART
ejpam-1200	236	19	conversely	conversely	ADV
ejpam-1200	236	20	.	.	PUNCT
ejpam-1200	237	1	(	(	PUNCT
ejpam-1200	237	2	ii	ii	NOUN
ejpam-1200	237	3	)	)	PUNCT
ejpam-1200	237	4	every	every	PRON
ejpam-1200	237	5	(	(	PUNCT
ejpam-1200	237	6	i	i	NOUN
ejpam-1200	237	7	,	,	PUNCT
ejpam-1200	237	8	j)-semi	j)-semi	NOUN
ejpam-1200	237	9	-	-	PUNCT
ejpam-1200	237	10	i	i	PRON
ejpam-1200	237	11	-continuous	-continuous	ADJ
ejpam-1200	237	12	function	function	NOUN
ejpam-1200	237	13	is	be	AUX
ejpam-1200	237	14	(	(	PUNCT
ejpam-1200	237	15	i	i	PROPN
ejpam-1200	237	16	,	,	PUNCT
ejpam-1200	237	17	j)−	j)−	PROPN
ejpam-1200	237	18	β	β	NOUN
ejpam-1200	237	19	-	-	ADJ
ejpam-1200	237	20	continuous	continuous	ADJ
ejpam-1200	237	21	but	but	CCONJ
ejpam-1200	237	22	not	not	PART
ejpam-1200	237	23	conversely	conversely	ADV
ejpam-1200	237	24	.	.	PUNCT
ejpam-1200	238	1	(	(	PUNCT
ejpam-1200	238	2	iii	iii	X
ejpam-1200	238	3	)	)	PUNCT
ejpam-1200	238	4	every	every	PRON
ejpam-1200	238	5	(	(	PUNCT
ejpam-1200	238	6	i	i	PROPN
ejpam-1200	238	7	,	,	PUNCT
ejpam-1200	238	8	j)-pre	j)-pre	PROPN
ejpam-1200	238	9	-	-	ADJ
ejpam-1200	238	10	i	i	PRON
ejpam-1200	238	11	-continuous	-continuous	ADJ
ejpam-1200	238	12	function	function	NOUN
ejpam-1200	238	13	is	be	AUX
ejpam-1200	238	14	(	(	PUNCT
ejpam-1200	238	15	i	i	NOUN
ejpam-1200	238	16	,	,	PUNCT
ejpam-1200	238	17	j)−	j)−	PROPN
ejpam-1200	238	18	β	β	PROPN
ejpam-1200	238	19	−i	−i	PROPN
ejpam-1200	238	20	-continuous	-continuous	ADJ
ejpam-1200	238	21	but	but	CCONJ
ejpam-1200	238	22	not	not	PART
ejpam-1200	238	23	conversely	conversely	ADV
ejpam-1200	238	24	.	.	PUNCT
ejpam-1200	239	1	theorem	theorem	ADJ
ejpam-1200	239	2	11	11	NUM
ejpam-1200	239	3	.	.	PUNCT
ejpam-1200	240	1	for	for	ADP
ejpam-1200	240	2	a	a	DET
ejpam-1200	240	3	function	function	NOUN
ejpam-1200	240	4	f	f	NOUN
ejpam-1200	240	5	:	:	PUNCT
ejpam-1200	240	6	(	(	PUNCT
ejpam-1200	240	7	x	x	X
ejpam-1200	240	8	,	,	PUNCT
ejpam-1200	240	9	τ1,τ2,i	τ1,τ2,i	PROPN
ejpam-1200	240	10	)	)	PUNCT
ejpam-1200	240	11	→	→	SYM
ejpam-1200	240	12	(	(	PUNCT
ejpam-1200	240	13	y	y	NOUN
ejpam-1200	240	14	,	,	PUNCT
ejpam-1200	240	15	σ1,σ2	σ1,σ2	PROPN
ejpam-1200	240	16	)	)	PUNCT
ejpam-1200	240	17	,	,	PUNCT
ejpam-1200	240	18	the	the	DET
ejpam-1200	240	19	following	follow	VERB
ejpam-1200	240	20	statements	statement	NOUN
ejpam-1200	240	21	are	be	AUX
ejpam-1200	240	22	equivalent	equivalent	ADJ
ejpam-1200	240	23	:	:	PUNCT
ejpam-1200	240	24	(	(	PUNCT
ejpam-1200	240	25	i	i	NOUN
ejpam-1200	240	26	)	)	PUNCT
ejpam-1200	240	27	f	f	PROPN
ejpam-1200	240	28	is	be	AUX
ejpam-1200	240	29	(	(	PUNCT
ejpam-1200	240	30	i	i	NOUN
ejpam-1200	240	31	,	,	PUNCT
ejpam-1200	240	32	j)−	j)−	PROPN
ejpam-1200	240	33	β	β	PROPN
ejpam-1200	240	34	−i	−i	PROPN
ejpam-1200	240	35	-continuous	-continuous	ADJ
ejpam-1200	240	36	.	.	PUNCT
ejpam-1200	241	1	(	(	PUNCT
ejpam-1200	241	2	ii	ii	NOUN
ejpam-1200	241	3	)	)	PUNCT
ejpam-1200	241	4	for	for	ADP
ejpam-1200	241	5	each	each	DET
ejpam-1200	241	6	point	point	NOUN
ejpam-1200	241	7	x	x	PUNCT
ejpam-1200	241	8	in	in	ADP
ejpam-1200	241	9	x	x	X
ejpam-1200	241	10	and	and	CCONJ
ejpam-1200	241	11	each	each	DET
ejpam-1200	241	12	σi	σi	NOUN
ejpam-1200	241	13	-	-	PUNCT
ejpam-1200	241	14	open	open	ADJ
ejpam-1200	241	15	set	set	ADJ
ejpam-1200	241	16	f	f	PROPN
ejpam-1200	241	17	in	in	ADP
ejpam-1200	241	18	y	y	PRON
ejpam-1200	242	1	such	such	ADJ
ejpam-1200	242	2	that	that	SCONJ
ejpam-1200	242	3	f	f	PROPN
ejpam-1200	242	4	(	(	PUNCT
ejpam-1200	242	5	x	x	X
ejpam-1200	242	6	)	)	PUNCT
ejpam-1200	242	7	∈	∈	PROPN
ejpam-1200	242	8	f	f	X
ejpam-1200	242	9	,	,	PUNCT
ejpam-1200	242	10	there	there	PRON
ejpam-1200	242	11	exists	exist	VERB
ejpam-1200	242	12	an	an	DET
ejpam-1200	242	13	(	(	PUNCT
ejpam-1200	242	14	i	i	NOUN
ejpam-1200	242	15	,	,	PUNCT
ejpam-1200	242	16	j)−	j)−	PROPN
ejpam-1200	242	17	β	β	PROPN
ejpam-1200	242	18	−i	−i	PROPN
ejpam-1200	242	19	-open	-open	PROPN
ejpam-1200	242	20	set	set	VERB
ejpam-1200	242	21	a	a	PRON
ejpam-1200	242	22	in	in	ADP
ejpam-1200	242	23	x	x	PUNCT
ejpam-1200	242	24	such	such	ADJ
ejpam-1200	242	25	that	that	SCONJ
ejpam-1200	242	26	x	x	SYM
ejpam-1200	242	27	∈	∈	PROPN
ejpam-1200	242	28	a	a	X
ejpam-1200	242	29	,	,	PUNCT
ejpam-1200	242	30	f	f	PROPN
ejpam-1200	242	31	(	(	PUNCT
ejpam-1200	242	32	a)⊂	a)⊂	PROPN
ejpam-1200	242	33	f.	f.	PROPN
ejpam-1200	242	34	(	(	PUNCT
ejpam-1200	242	35	iii	iii	X
ejpam-1200	242	36	)	)	PUNCT
ejpam-1200	242	37	the	the	DET
ejpam-1200	242	38	inverse	inverse	ADJ
ejpam-1200	242	39	image	image	NOUN
ejpam-1200	242	40	of	of	ADP
ejpam-1200	242	41	each	each	DET
ejpam-1200	242	42	σi	σi	NOUN
ejpam-1200	242	43	-	-	PUNCT
ejpam-1200	242	44	closed	closed	ADJ
ejpam-1200	242	45	set	set	NOUN
ejpam-1200	242	46	in	in	ADP
ejpam-1200	242	47	y	y	PROPN
ejpam-1200	242	48	is	be	AUX
ejpam-1200	242	49	(	(	PUNCT
ejpam-1200	242	50	i	i	PROPN
ejpam-1200	242	51	,	,	PUNCT
ejpam-1200	242	52	j)−	j)−	PROPN
ejpam-1200	242	53	β	β	PROPN
ejpam-1200	242	54	−i	−i	PROPN
ejpam-1200	242	55	-closed	-close	VERB
ejpam-1200	242	56	in	in	ADP
ejpam-1200	242	57	x	x	X
ejpam-1200	242	58	.	.	PUNCT
ejpam-1200	243	1	(	(	PUNCT
ejpam-1200	243	2	iv	iv	X
ejpam-1200	243	3	)	)	PUNCT
ejpam-1200	243	4	for	for	ADP
ejpam-1200	243	5	each	each	PRON
ejpam-1200	243	6	subset	subset	VERB
ejpam-1200	243	7	a	a	PRON
ejpam-1200	243	8	of	of	ADP
ejpam-1200	243	9	x	x	SYM
ejpam-1200	243	10	,	,	PUNCT
ejpam-1200	243	11	f	f	PROPN
ejpam-1200	243	12	(	(	PUNCT
ejpam-1200	243	13	(	(	PUNCT
ejpam-1200	243	14	i	i	PROPN
ejpam-1200	243	15	,	,	PUNCT
ejpam-1200	243	16	j)−	j)−	PROPN
ejpam-1200	243	17	βi	βi	NOUN
ejpam-1200	243	18	cl(a))⊂	cl(a))⊂	NOUN
ejpam-1200	243	19	σi	σi	PROPN
ejpam-1200	243	20	−cl	−cl	PROPN
ejpam-1200	243	21	(	(	PUNCT
ejpam-1200	243	22	f	f	PROPN
ejpam-1200	243	23	(	(	PUNCT
ejpam-1200	243	24	a	a	NOUN
ejpam-1200	243	25	)	)	PUNCT
ejpam-1200	243	26	)	)	PUNCT
ejpam-1200	243	27	.	.	PUNCT
ejpam-1200	244	1	(	(	PUNCT
ejpam-1200	244	2	v	v	NOUN
ejpam-1200	244	3	)	)	PUNCT
ejpam-1200	244	4	for	for	ADP
ejpam-1200	244	5	each	each	DET
ejpam-1200	244	6	subset	subset	NOUN
ejpam-1200	244	7	b	b	PROPN
ejpam-1200	244	8	of	of	ADP
ejpam-1200	244	9	y	y	PROPN
ejpam-1200	244	10	,	,	PUNCT
ejpam-1200	244	11	(	(	PUNCT
ejpam-1200	244	12	i	i	PROPN
ejpam-1200	244	13	,	,	PUNCT
ejpam-1200	244	14	j)−	j)−	PROPN
ejpam-1200	244	15	βi	βi	PROPN
ejpam-1200	244	16	cl	cl	PROPN
ejpam-1200	244	17	(	(	PUNCT
ejpam-1200	244	18	f	f	X
ejpam-1200	244	19	−1(b))⊂	−1(b))⊂	PROPN
ejpam-1200	244	20	f	f	PROPN
ejpam-1200	244	21	−1(σi	−1(σi	NOUN
ejpam-1200	244	22	−cl(b	−cl(b	ADP
ejpam-1200	244	23	)	)	PUNCT
ejpam-1200	244	24	)	)	PUNCT
ejpam-1200	244	25	.	.	PUNCT
ejpam-1200	245	1	(	(	PUNCT
ejpam-1200	245	2	vi	vi	X
ejpam-1200	245	3	)	)	PUNCT
ejpam-1200	245	4	for	for	ADP
ejpam-1200	245	5	each	each	DET
ejpam-1200	245	6	subset	subset	NOUN
ejpam-1200	245	7	c	c	PROPN
ejpam-1200	245	8	of	of	ADP
ejpam-1200	245	9	y	y	PROPN
ejpam-1200	245	10	,	,	PUNCT
ejpam-1200	245	11	f	f	PROPN
ejpam-1200	245	12	−1(σi	−1(σi	NOUN
ejpam-1200	245	13	−	−	PROPN
ejpam-1200	246	1	int(c))⊂	int(c))⊂	NOUN
ejpam-1200	246	2	(	(	PUNCT
ejpam-1200	246	3	i	i	PROPN
ejpam-1200	246	4	,	,	PUNCT
ejpam-1200	246	5	j)−	j)−	PROPN
ejpam-1200	246	6	βi	βi	NUM
ejpam-1200	246	7	int	int	PROPN
ejpam-1200	246	8	(	(	PUNCT
ejpam-1200	246	9	f	f	PROPN
ejpam-1200	246	10	−1(c	−1(c	PROPN
ejpam-1200	246	11	)	)	PUNCT
ejpam-1200	246	12	)	)	PUNCT
ejpam-1200	246	13	.	.	PUNCT
ejpam-1200	247	1	proof	proof	NOUN
ejpam-1200	247	2	.	.	PUNCT
ejpam-1200	248	1	(	(	PUNCT
ejpam-1200	248	2	i)⇒(ii	i)⇒(ii	ADV
ejpam-1200	248	3	):	):	PUNCT
ejpam-1200	248	4	let	let	VERB
ejpam-1200	248	5	x	x	PUNCT
ejpam-1200	248	6	∈	∈	PROPN
ejpam-1200	248	7	x	x	X
ejpam-1200	248	8	and	and	CCONJ
ejpam-1200	248	9	f	f	PROPN
ejpam-1200	248	10	be	be	AUX
ejpam-1200	248	11	a	a	DET
ejpam-1200	248	12	σi	σi	NOUN
ejpam-1200	248	13	-	-	PUNCT
ejpam-1200	248	14	open	open	ADJ
ejpam-1200	248	15	set	set	NOUN
ejpam-1200	248	16	of	of	ADP
ejpam-1200	248	17	y	y	PROPN
ejpam-1200	248	18	containing	contain	VERB
ejpam-1200	248	19	f	f	PROPN
ejpam-1200	248	20	(	(	PUNCT
ejpam-1200	248	21	x	x	NOUN
ejpam-1200	248	22	)	)	PUNCT
ejpam-1200	248	23	.	.	PUNCT
ejpam-1200	249	1	by	by	ADP
ejpam-1200	249	2	(	(	PUNCT
ejpam-1200	249	3	i	i	NOUN
ejpam-1200	249	4	)	)	PUNCT
ejpam-1200	249	5	,	,	PUNCT
ejpam-1200	249	6	f	f	PROPN
ejpam-1200	249	7	−1(f	−1(f	PROPN
ejpam-1200	249	8	)	)	PUNCT
ejpam-1200	249	9	is	be	AUX
ejpam-1200	249	10	(	(	PUNCT
ejpam-1200	249	11	i	i	NOUN
ejpam-1200	249	12	,	,	PUNCT
ejpam-1200	249	13	j)−	j)−	PROPN
ejpam-1200	249	14	β	β	PROPN
ejpam-1200	249	15	−i	−i	PROPN
ejpam-1200	249	16	-open	-open	VERB
ejpam-1200	249	17	in	in	ADP
ejpam-1200	249	18	x	x	X
ejpam-1200	249	19	.	.	PUNCT
ejpam-1200	250	1	let	let	VERB
ejpam-1200	250	2	a=	a=	PROPN
ejpam-1200	250	3	f	f	X
ejpam-1200	250	4	−1(f	−1(f	PROPN
ejpam-1200	250	5	)	)	PUNCT
ejpam-1200	250	6	.	.	PUNCT
ejpam-1200	251	1	then	then	ADV
ejpam-1200	251	2	x	x	X
ejpam-1200	251	3	∈	∈	PROPN
ejpam-1200	251	4	a	a	PRON
ejpam-1200	251	5	and	and	CCONJ
ejpam-1200	251	6	f	f	PROPN
ejpam-1200	251	7	(	(	PUNCT
ejpam-1200	251	8	a)⊂	a)⊂	PROPN
ejpam-1200	251	9	f	f	X
ejpam-1200	251	10	.	.	PUNCT
ejpam-1200	252	1	(	(	PUNCT
ejpam-1200	252	2	ii)⇒(i	ii)⇒(i	NOUN
ejpam-1200	252	3	):	):	PUNCT
ejpam-1200	252	4	let	let	VERB
ejpam-1200	252	5	f	f	PRON
ejpam-1200	252	6	be	be	AUX
ejpam-1200	252	7	σi	σi	NOUN
ejpam-1200	252	8	-	-	ADJ
ejpam-1200	252	9	open	open	ADJ
ejpam-1200	252	10	in	in	ADP
ejpam-1200	252	11	y	y	PROPN
ejpam-1200	252	12	and	and	CCONJ
ejpam-1200	252	13	let	let	VERB
ejpam-1200	252	14	x	x	SYM
ejpam-1200	252	15	∈	∈	PROPN
ejpam-1200	252	16	f	f	X
ejpam-1200	252	17	−1(f	−1(f	PROPN
ejpam-1200	252	18	)	)	PUNCT
ejpam-1200	252	19	.	.	PUNCT
ejpam-1200	253	1	then	then	ADV
ejpam-1200	253	2	f	f	PROPN
ejpam-1200	253	3	(	(	PUNCT
ejpam-1200	253	4	x	x	X
ejpam-1200	253	5	)	)	PUNCT
ejpam-1200	253	6	∈	∈	PROPN
ejpam-1200	253	7	f	f	X
ejpam-1200	253	8	.	.	PUNCT
ejpam-1200	254	1	by	by	ADP
ejpam-1200	254	2	(	(	PUNCT
ejpam-1200	254	3	ii	ii	NOUN
ejpam-1200	254	4	)	)	PUNCT
ejpam-1200	254	5	,	,	PUNCT
ejpam-1200	254	6	there	there	PRON
ejpam-1200	254	7	is	be	VERB
ejpam-1200	254	8	an	an	DET
ejpam-1200	254	9	(	(	PUNCT
ejpam-1200	254	10	i	i	NOUN
ejpam-1200	254	11	,	,	PUNCT
ejpam-1200	255	1	j)−	j)−	PROPN
ejpam-1200	256	1	β	β	PROPN
ejpam-1200	257	1	−	−	PROPN
ejpam-1200	258	1	i	i	PRON
ejpam-1200	258	2	-open	-open	AUX
ejpam-1200	258	3	set	set	VERB
ejpam-1200	258	4	ux	ux	ADV
ejpam-1200	258	5	in	in	ADP
ejpam-1200	258	6	x	x	X
ejpam-1200	259	1	such	such	ADJ
ejpam-1200	259	2	that	that	SCONJ
ejpam-1200	259	3	x	x	SYM
ejpam-1200	259	4	∈	∈	NOUN
ejpam-1200	259	5	ux	ux	NOUN
ejpam-1200	259	6	and	and	CCONJ
ejpam-1200	259	7	f	f	PROPN
ejpam-1200	259	8	(	(	PUNCT
ejpam-1200	259	9	ux	ux	PROPN
ejpam-1200	259	10	)	)	PUNCT
ejpam-1200	259	11	⊂	⊂	PROPN
ejpam-1200	260	1	f	f	PROPN
ejpam-1200	260	2	.	.	PUNCT
ejpam-1200	261	1	then	then	ADV
ejpam-1200	261	2	x	x	SYM
ejpam-1200	261	3	∈	∈	PROPN
ejpam-1200	261	4	ux	ux	PROPN
ejpam-1200	261	5	⊂	⊂	PROPN
ejpam-1200	261	6	f	f	PROPN
ejpam-1200	261	7	−1(f	−1(f	PROPN
ejpam-1200	261	8	)	)	PUNCT
ejpam-1200	261	9	.	.	PUNCT
ejpam-1200	262	1	hence	hence	ADV
ejpam-1200	262	2	f	f	PROPN
ejpam-1200	262	3	−1(f	−1(f	PROPN
ejpam-1200	262	4	)	)	PUNCT
ejpam-1200	262	5	is	be	AUX
ejpam-1200	262	6	(	(	PUNCT
ejpam-1200	262	7	i	i	NOUN
ejpam-1200	262	8	,	,	PUNCT
ejpam-1200	262	9	j)−	j)−	PROPN
ejpam-1200	262	10	β	β	PROPN
ejpam-1200	262	11	−i	−i	PROPN
ejpam-1200	262	12	-open	-open	VERB
ejpam-1200	262	13	in	in	ADP
ejpam-1200	262	14	x	x	X
ejpam-1200	262	15	.	.	PUNCT
ejpam-1200	263	1	(	(	PUNCT
ejpam-1200	263	2	i)⇔(iii	i)⇔(iii	NOUN
ejpam-1200	263	3	):	):	PUNCT
ejpam-1200	263	4	this	this	PRON
ejpam-1200	263	5	follows	follow	VERB
ejpam-1200	263	6	due	due	ADP
ejpam-1200	263	7	to	to	ADP
ejpam-1200	263	8	the	the	DET
ejpam-1200	263	9	fact	fact	NOUN
ejpam-1200	263	10	that	that	SCONJ
ejpam-1200	263	11	for	for	ADP
ejpam-1200	263	12	any	any	DET
ejpam-1200	263	13	subset	subset	NOUN
ejpam-1200	263	14	b	b	PROPN
ejpam-1200	263	15	of	of	ADP
ejpam-1200	263	16	y	y	PROPN
ejpam-1200	263	17	,	,	PUNCT
ejpam-1200	263	18	f	f	PROPN
ejpam-1200	263	19	−1(y	−1(y	PUNCT
ejpam-1200	263	20	\b	\b	ADJ
ejpam-1200	263	21	)	)	PUNCT
ejpam-1200	264	1	=	=	PUNCT
ejpam-1200	265	1	x\	x\	PROPN
ejpam-1200	265	2	f	f	PROPN
ejpam-1200	265	3	−1(b	−1(b	NOUN
ejpam-1200	265	4	)	)	PUNCT
ejpam-1200	265	5	.	.	PUNCT
ejpam-1200	266	1	(	(	PUNCT
ejpam-1200	266	2	iii)⇒(iv	iii)⇒(iv	NOUN
ejpam-1200	266	3	):	):	PUNCT
ejpam-1200	266	4	let	let	VERB
ejpam-1200	266	5	a	a	PRON
ejpam-1200	266	6	be	be	AUX
ejpam-1200	266	7	a	a	DET
ejpam-1200	266	8	subset	subset	NOUN
ejpam-1200	266	9	of	of	ADP
ejpam-1200	266	10	x	x	X
ejpam-1200	266	11	.	.	PUNCT
ejpam-1200	267	1	since	since	SCONJ
ejpam-1200	267	2	a	a	DET
ejpam-1200	267	3	⊂	⊂	PROPN
ejpam-1200	267	4	f	f	X
ejpam-1200	267	5	−1	−1	PROPN
ejpam-1200	267	6	(	(	PUNCT
ejpam-1200	267	7	f	f	PROPN
ejpam-1200	267	8	(	(	PUNCT
ejpam-1200	267	9	a	a	NOUN
ejpam-1200	267	10	)	)	PUNCT
ejpam-1200	267	11	)	)	PUNCT
ejpam-1200	267	12	we	we	PRON
ejpam-1200	267	13	have	have	VERB
ejpam-1200	267	14	a	a	PRON
ejpam-1200	267	15	⊂	⊂	PROPN
ejpam-1200	267	16	f	f	X
ejpam-1200	267	17	−1(σi	−1(σi	NOUN
ejpam-1200	268	1	−	−	PROPN
ejpam-1200	269	1	cl	cl	NOUN
ejpam-1200	269	2	(	(	PUNCT
ejpam-1200	269	3	f	f	X
ejpam-1200	269	4	(	(	PUNCT
ejpam-1200	269	5	a	a	NOUN
ejpam-1200	269	6	)	)	PUNCT
ejpam-1200	269	7	)	)	PUNCT
ejpam-1200	269	8	)	)	PUNCT
ejpam-1200	269	9	.	.	PUNCT
ejpam-1200	270	1	now	now	ADV
ejpam-1200	270	2	,	,	PUNCT
ejpam-1200	270	3	σi	σi	PRON
ejpam-1200	270	4	−	−	PROPN
ejpam-1200	270	5	cl	cl	NOUN
ejpam-1200	270	6	(	(	PUNCT
ejpam-1200	270	7	f	f	X
ejpam-1200	270	8	(	(	PUNCT
ejpam-1200	270	9	a	a	NOUN
ejpam-1200	270	10	)	)	PUNCT
ejpam-1200	270	11	)	)	PUNCT
ejpam-1200	270	12	is	be	AUX
ejpam-1200	270	13	σi	σi	NOUN
ejpam-1200	270	14	-	-	PUNCT
ejpam-1200	270	15	closed	closed	ADJ
ejpam-1200	270	16	in	in	ADP
ejpam-1200	270	17	y	y	PROPN
ejpam-1200	270	18	and	and	CCONJ
ejpam-1200	270	19	hence	hence	ADV
ejpam-1200	270	20	(	(	PUNCT
ejpam-1200	270	21	i	i	PROPN
ejpam-1200	270	22	,	,	PUNCT
ejpam-1200	270	23	j)−	j)−	PROPN
ejpam-1200	270	24	βi	βi	PRON
ejpam-1200	270	25	cl(a	cl(a	NUM
ejpam-1200	270	26	)	)	PUNCT
ejpam-1200	271	1	⊂	⊂	PROPN
ejpam-1200	271	2	f	f	PROPN
ejpam-1200	271	3	−1(σi	−1(σi	ADV
ejpam-1200	271	4	−	−	PROPN
ejpam-1200	271	5	cl	cl	NOUN
ejpam-1200	271	6	(	(	PUNCT
ejpam-1200	271	7	f	f	X
ejpam-1200	271	8	(	(	PUNCT
ejpam-1200	271	9	a	a	NOUN
ejpam-1200	271	10	)	)	PUNCT
ejpam-1200	271	11	)	)	PUNCT
ejpam-1200	271	12	)	)	PUNCT
ejpam-1200	271	13	for	for	ADP
ejpam-1200	271	14	(	(	PUNCT
ejpam-1200	271	15	i	i	PROPN
ejpam-1200	271	16	,	,	PUNCT
ejpam-1200	271	17	j)−	j)−	PROPN
ejpam-1200	271	18	βi	βi	PRON
ejpam-1200	271	19	cl(a	cl(a	NUM
ejpam-1200	271	20	)	)	PUNCT
ejpam-1200	271	21	is	be	AUX
ejpam-1200	271	22	the	the	DET
ejpam-1200	271	23	smallest	small	ADJ
ejpam-1200	271	24	(	(	PUNCT
ejpam-1200	271	25	i	i	NOUN
ejpam-1200	271	26	,	,	PUNCT
ejpam-1200	271	27	j)−	j)−	PROPN
ejpam-1200	271	28	β	β	PROPN
ejpam-1200	271	29	−i	−i	PROPN
ejpam-1200	271	30	-closed	-close	VERB
ejpam-1200	271	31	set	set	NOUN
ejpam-1200	271	32	containing	contain	VERB
ejpam-1200	271	33	a.	a.	NOUN
ejpam-1200	271	34	then	then	ADV
ejpam-1200	271	35	f	f	X
ejpam-1200	271	36	(	(	PUNCT
ejpam-1200	271	37	(	(	PUNCT
ejpam-1200	271	38	i	i	PROPN
ejpam-1200	271	39	,	,	PUNCT
ejpam-1200	271	40	j)−	j)−	PROPN
ejpam-1200	271	41	βi	βi	NOUN
ejpam-1200	271	42	cl(a))⊂	cl(a))⊂	NOUN
ejpam-1200	271	43	σi	σi	PROPN
ejpam-1200	271	44	−cl	−cl	PROPN
ejpam-1200	271	45	(	(	PUNCT
ejpam-1200	271	46	f	f	PROPN
ejpam-1200	271	47	(	(	PUNCT
ejpam-1200	271	48	a	a	NOUN
ejpam-1200	271	49	)	)	PUNCT
ejpam-1200	271	50	)	)	PUNCT
ejpam-1200	271	51	.	.	PUNCT
ejpam-1200	272	1	m.	m.	PROPN
ejpam-1200	272	2	caldas	caldas	PROPN
ejpam-1200	272	3	,	,	PUNCT
ejpam-1200	272	4	s.	s.	PROPN
ejpam-1200	272	5	jafari	jafari	PROPN
ejpam-1200	272	6	,	,	PUNCT
ejpam-1200	272	7	n.	n.	PROPN
ejpam-1200	272	8	rajesh	rajesh	PROPN
ejpam-1200	272	9	/	/	SYM
ejpam-1200	272	10	eur	eur	PROPN
ejpam-1200	272	11	.	.	PUNCT
ejpam-1200	273	1	j.	j.	PROPN
ejpam-1200	273	2	pure	pure	PROPN
ejpam-1200	273	3	appl	appl	PROPN
ejpam-1200	273	4	.	.	PROPN
ejpam-1200	273	5	math	math	PROPN
ejpam-1200	273	6	,	,	PUNCT
ejpam-1200	273	7	6	6	NUM
ejpam-1200	273	8	(	(	PUNCT
ejpam-1200	273	9	2013	2013	NUM
ejpam-1200	273	10	)	)	PUNCT
ejpam-1200	273	11	,	,	PUNCT
ejpam-1200	273	12	247	247	NUM
ejpam-1200	273	13	-	-	SYM
ejpam-1200	273	14	255	255	NUM
ejpam-1200	273	15	254	254	NUM
ejpam-1200	273	16	(	(	PUNCT
ejpam-1200	273	17	iv)⇒(iii	iv)⇒(iii	NOUN
ejpam-1200	273	18	):	):	PUNCT
ejpam-1200	273	19	let	let	VERB
ejpam-1200	273	20	f	f	PRON
ejpam-1200	273	21	be	be	AUX
ejpam-1200	273	22	any	any	DET
ejpam-1200	273	23	(	(	PUNCT
ejpam-1200	273	24	i	i	NOUN
ejpam-1200	273	25	,	,	PUNCT
ejpam-1200	273	26	j)−	j)−	PROPN
ejpam-1200	273	27	β	β	PROPN
ejpam-1200	273	28	−i	−i	PROPN
ejpam-1200	273	29	-closed	-closed	PROPN
ejpam-1200	273	30	subset	subset	NOUN
ejpam-1200	273	31	of	of	ADP
ejpam-1200	273	32	y	y	PROPN
ejpam-1200	273	33	.	.	PUNCT
ejpam-1200	274	1	then	then	ADV
ejpam-1200	274	2	f	f	X
ejpam-1200	274	3	(	(	PUNCT
ejpam-1200	274	4	(	(	PUNCT
ejpam-1200	274	5	i	i	PROPN
ejpam-1200	274	6	,	,	PUNCT
ejpam-1200	274	7	j)−	j)−	PROPN
ejpam-1200	274	8	βi	βi	PROPN
ejpam-1200	274	9	cl	cl	PROPN
ejpam-1200	274	10	(	(	PUNCT
ejpam-1200	274	11	f	f	X
ejpam-1200	275	1	−1(f)))⊂	−1(f)))⊂	ADV
ejpam-1200	275	2	σi	σi	PROPN
ejpam-1200	275	3	−cl	−cl	PROPN
ejpam-1200	275	4	(	(	PUNCT
ejpam-1200	275	5	f	f	PROPN
ejpam-1200	275	6	(	(	PUNCT
ejpam-1200	275	7	f	f	PROPN
ejpam-1200	275	8	−1(f	−1(f	PROPN
ejpam-1200	275	9	)	)	PUNCT
ejpam-1200	275	10	)	)	PUNCT
ejpam-1200	275	11	)	)	PUNCT
ejpam-1200	276	1	=	=	PRON
ejpam-1200	276	2	σi	σi	NUM
ejpam-1200	276	3	−cl(f	−cl(f	PROPN
ejpam-1200	276	4	)	)	PUNCT
ejpam-1200	277	1	=	=	SYM
ejpam-1200	277	2	f	f	PROPN
ejpam-1200	277	3	.	.	PUNCT
ejpam-1200	278	1	therefore	therefore	ADV
ejpam-1200	278	2	,	,	PUNCT
ejpam-1200	278	3	(	(	PUNCT
ejpam-1200	278	4	i	i	PROPN
ejpam-1200	278	5	,	,	PUNCT
ejpam-1200	278	6	j)−	j)−	PROPN
ejpam-1200	278	7	βi	βi	PROPN
ejpam-1200	278	8	cl	cl	PROPN
ejpam-1200	278	9	(	(	PUNCT
ejpam-1200	278	10	f	f	X
ejpam-1200	278	11	−1(f))⊂	−1(f))⊂	PROPN
ejpam-1200	278	12	f	f	PROPN
ejpam-1200	278	13	−1(f	−1(f	PROPN
ejpam-1200	278	14	)	)	PUNCT
ejpam-1200	278	15	.	.	PUNCT
ejpam-1200	279	1	consequently	consequently	ADV
ejpam-1200	279	2	,	,	PUNCT
ejpam-1200	279	3	f	f	PROPN
ejpam-1200	279	4	−1(f	−1(f	PROPN
ejpam-1200	279	5	)	)	PUNCT
ejpam-1200	279	6	is	be	AUX
ejpam-1200	279	7	(	(	PUNCT
ejpam-1200	279	8	i	i	NOUN
ejpam-1200	279	9	,	,	PUNCT
ejpam-1200	279	10	j)−	j)−	PROPN
ejpam-1200	279	11	β	β	PROPN
ejpam-1200	279	12	−i	−i	PROPN
ejpam-1200	279	13	-closed	-close	VERB
ejpam-1200	279	14	in	in	ADP
ejpam-1200	279	15	x	x	X
ejpam-1200	279	16	.	.	PUNCT
ejpam-1200	280	1	(	(	PUNCT
ejpam-1200	280	2	iv)⇒(v	iv)⇒(v	ADV
ejpam-1200	280	3	):	):	PUNCT
ejpam-1200	280	4	let	let	VERB
ejpam-1200	280	5	b	b	X
ejpam-1200	280	6	be	be	AUX
ejpam-1200	280	7	any	any	DET
ejpam-1200	280	8	subset	subset	NOUN
ejpam-1200	280	9	of	of	ADP
ejpam-1200	280	10	y	y	PROPN
ejpam-1200	280	11	.	.	PUNCT
ejpam-1200	281	1	now	now	ADV
ejpam-1200	281	2	,	,	PUNCT
ejpam-1200	281	3	f	f	PROPN
ejpam-1200	281	4	(	(	PUNCT
ejpam-1200	281	5	(	(	PUNCT
ejpam-1200	281	6	i	i	PROPN
ejpam-1200	281	7	,	,	PUNCT
ejpam-1200	281	8	j)−	j)−	PROPN
ejpam-1200	281	9	βi	βi	PROPN
ejpam-1200	281	10	cl	cl	PROPN
ejpam-1200	281	11	(	(	PUNCT
ejpam-1200	281	12	f	f	X
ejpam-1200	281	13	−1(b)))⊂	−1(b)))⊂	NOUN
ejpam-1200	281	14	σi	σi	PROPN
ejpam-1200	281	15	−cl	−cl	PROPN
ejpam-1200	281	16	(	(	PUNCT
ejpam-1200	281	17	f	f	PROPN
ejpam-1200	281	18	(	(	PUNCT
ejpam-1200	281	19	f	f	X
ejpam-1200	282	1	−1(b)))⊂	−1(b)))⊂	NOUN
ejpam-1200	282	2	σi	σi	INTJ
ejpam-1200	282	3	−cl(b	−cl(b	ADP
ejpam-1200	282	4	)	)	PUNCT
ejpam-1200	282	5	.	.	PUNCT
ejpam-1200	283	1	consequently	consequently	ADV
ejpam-1200	283	2	,	,	PUNCT
ejpam-1200	283	3	(	(	PUNCT
ejpam-1200	283	4	i	i	PROPN
ejpam-1200	283	5	,	,	PUNCT
ejpam-1200	283	6	j)−	j)−	PROPN
ejpam-1200	283	7	βi	βi	PROPN
ejpam-1200	283	8	cl	cl	PROPN
ejpam-1200	283	9	(	(	PUNCT
ejpam-1200	283	10	f	f	X
ejpam-1200	283	11	−1(b))⊂	−1(b))⊂	PROPN
ejpam-1200	283	12	f	f	PROPN
ejpam-1200	283	13	−1(σi	−1(σi	NOUN
ejpam-1200	283	14	−cl(b	−cl(b	ADP
ejpam-1200	283	15	)	)	PUNCT
ejpam-1200	283	16	)	)	PUNCT
ejpam-1200	283	17	.	.	PUNCT
ejpam-1200	284	1	(	(	PUNCT
ejpam-1200	284	2	v)⇒(iv	v)⇒(iv	NUM
ejpam-1200	284	3	):	):	PUNCT
ejpam-1200	284	4	let	let	VERB
ejpam-1200	284	5	b	b	NOUN
ejpam-1200	284	6	=	=	SYM
ejpam-1200	284	7	f	f	PROPN
ejpam-1200	284	8	(	(	PUNCT
ejpam-1200	284	9	a	a	NOUN
ejpam-1200	284	10	)	)	PUNCT
ejpam-1200	284	11	,	,	PUNCT
ejpam-1200	284	12	where	where	SCONJ
ejpam-1200	284	13	a	a	PRON
ejpam-1200	284	14	is	be	AUX
ejpam-1200	284	15	a	a	DET
ejpam-1200	284	16	subset	subset	NOUN
ejpam-1200	284	17	of	of	ADP
ejpam-1200	284	18	x	x	X
ejpam-1200	284	19	.	.	PUNCT
ejpam-1200	285	1	then	then	ADV
ejpam-1200	285	2	,	,	PUNCT
ejpam-1200	285	3	(	(	PUNCT
ejpam-1200	285	4	i	i	PROPN
ejpam-1200	285	5	,	,	PUNCT
ejpam-1200	285	6	j)−	j)−	PROPN
ejpam-1200	285	7	βi	βi	PROPN
ejpam-1200	285	8	cl(a)⊂	cl(a)⊂	PROPN
ejpam-1200	285	9	(	(	PUNCT
ejpam-1200	285	10	i	i	PROPN
ejpam-1200	285	11	,	,	PUNCT
ejpam-1200	285	12	j)−	j)−	PROPN
ejpam-1200	285	13	βi	βi	PROPN
ejpam-1200	285	14	cl	cl	PROPN
ejpam-1200	285	15	(	(	PUNCT
ejpam-1200	285	16	f	f	X
ejpam-1200	285	17	−1(b))⊂	−1(b))⊂	PROPN
ejpam-1200	285	18	f	f	PROPN
ejpam-1200	285	19	−1(σi	−1(σi	NOUN
ejpam-1200	285	20	−cl(b	−cl(b	ADP
ejpam-1200	285	21	)	)	PUNCT
ejpam-1200	285	22	)	)	PUNCT
ejpam-1200	286	1	=	=	SYM
ejpam-1200	286	2	f	f	PROPN
ejpam-1200	286	3	−1(σi	−1(σi	PROPN
ejpam-1200	286	4	−cl	−cl	PROPN
ejpam-1200	286	5	(	(	PUNCT
ejpam-1200	286	6	f	f	X
ejpam-1200	286	7	(	(	PUNCT
ejpam-1200	286	8	a	a	NOUN
ejpam-1200	286	9	)	)	PUNCT
ejpam-1200	286	10	)	)	PUNCT
ejpam-1200	286	11	)	)	PUNCT
ejpam-1200	286	12	.	.	PUNCT
ejpam-1200	287	1	this	this	PRON
ejpam-1200	287	2	shows	show	VERB
ejpam-1200	287	3	that	that	SCONJ
ejpam-1200	287	4	f	f	PROPN
ejpam-1200	287	5	(	(	PUNCT
ejpam-1200	287	6	(	(	PUNCT
ejpam-1200	287	7	i	i	PROPN
ejpam-1200	287	8	,	,	PUNCT
ejpam-1200	287	9	j)−	j)−	PROPN
ejpam-1200	287	10	βi	βi	NOUN
ejpam-1200	287	11	cl(a))⊂	cl(a))⊂	NOUN
ejpam-1200	287	12	σi	σi	PROPN
ejpam-1200	287	13	−cl	−cl	PROPN
ejpam-1200	287	14	(	(	PUNCT
ejpam-1200	287	15	f	f	PROPN
ejpam-1200	287	16	(	(	PUNCT
ejpam-1200	287	17	a	a	NOUN
ejpam-1200	287	18	)	)	PUNCT
ejpam-1200	287	19	)	)	PUNCT
ejpam-1200	287	20	.	.	PUNCT
ejpam-1200	288	1	(	(	PUNCT
ejpam-1200	288	2	i)⇒(vi	i)⇒(vi	X
ejpam-1200	288	3	):	):	PUNCT
ejpam-1200	288	4	let	let	VERB
ejpam-1200	288	5	b	b	X
ejpam-1200	288	6	be	be	AUX
ejpam-1200	288	7	a	a	DET
ejpam-1200	288	8	σi	σi	NOUN
ejpam-1200	288	9	-	-	PUNCT
ejpam-1200	288	10	open	open	ADJ
ejpam-1200	288	11	set	set	NOUN
ejpam-1200	288	12	in	in	ADP
ejpam-1200	288	13	y	y	PROPN
ejpam-1200	288	14	.	.	PUNCT
ejpam-1200	289	1	clearly	clearly	ADV
ejpam-1200	289	2	,	,	PUNCT
ejpam-1200	289	3	f	f	PROPN
ejpam-1200	289	4	−1(σi	−1(σi	ADV
ejpam-1200	289	5	−	−	PROPN
ejpam-1200	289	6	int(b	int(b	NOUN
ejpam-1200	289	7	)	)	PUNCT
ejpam-1200	289	8	)	)	PUNCT
ejpam-1200	289	9	is	be	AUX
ejpam-1200	289	10	(	(	PUNCT
ejpam-1200	289	11	i	i	INTJ
ejpam-1200	289	12	,	,	PUNCT
ejpam-1200	289	13	j)−β	j)−β	PRON
ejpam-1200	289	14	−i	−i	PROPN
ejpam-1200	289	15	-open	-open	PROPN
ejpam-1200	290	1	and	and	CCONJ
ejpam-1200	290	2	we	we	PRON
ejpam-1200	290	3	have	have	VERB
ejpam-1200	290	4	f	f	PROPN
ejpam-1200	290	5	−1(σi	−1(σi	NOUN
ejpam-1200	290	6	−	−	PROPN
ejpam-1200	290	7	int(b))⊂	int(b))⊂	NOUN
ejpam-1200	291	1	(	(	PUNCT
ejpam-1200	291	2	i	i	NOUN
ejpam-1200	291	3	,	,	PUNCT
ejpam-1200	291	4	j)−	j)−	PROPN
ejpam-1200	291	5	βi	βi	NUM
ejpam-1200	291	6	int	int	PROPN
ejpam-1200	291	7	(	(	PUNCT
ejpam-1200	291	8	f	f	PROPN
ejpam-1200	291	9	−1(σi	−1(σi	NOUN
ejpam-1200	292	1	−	−	PROPN
ejpam-1200	293	1	int(b)))⊂	int(b)))⊂	PROPN
ejpam-1200	293	2	(	(	PUNCT
ejpam-1200	293	3	i	i	PROPN
ejpam-1200	293	4	,	,	PUNCT
ejpam-1200	293	5	j)−	j)−	PROPN
ejpam-1200	293	6	βi	βi	PROPN
ejpam-1200	293	7	int	int	PROPN
ejpam-1200	293	8	(	(	PUNCT
ejpam-1200	293	9	f	f	PROPN
ejpam-1200	293	10	−1(b	−1(b	NOUN
ejpam-1200	293	11	)	)	PUNCT
ejpam-1200	293	12	)	)	PUNCT
ejpam-1200	293	13	.	.	PUNCT
ejpam-1200	294	1	(	(	PUNCT
ejpam-1200	294	2	vi)⇒(i	vi)⇒(i	ADV
ejpam-1200	294	3	):	):	PUNCT
ejpam-1200	294	4	let	let	VERB
ejpam-1200	294	5	b	b	X
ejpam-1200	294	6	be	be	AUX
ejpam-1200	294	7	a	a	DET
ejpam-1200	294	8	σi	σi	NOUN
ejpam-1200	294	9	-	-	PUNCT
ejpam-1200	294	10	open	open	ADJ
ejpam-1200	294	11	set	set	NOUN
ejpam-1200	294	12	in	in	ADP
ejpam-1200	294	13	y	y	PROPN
ejpam-1200	294	14	.	.	PUNCT
ejpam-1200	295	1	then	then	ADV
ejpam-1200	295	2	σi	σi	INTJ
ejpam-1200	295	3	−	−	PROPN
ejpam-1200	295	4	int(b	int(b	PROPN
ejpam-1200	295	5	)	)	PUNCT
ejpam-1200	295	6	=	=	SYM
ejpam-1200	295	7	b	b	PROPN
ejpam-1200	295	8	and	and	CCONJ
ejpam-1200	295	9	f	f	PROPN
ejpam-1200	295	10	−1(b)\	−1(b)\	PROPN
ejpam-1200	295	11	f	f	PROPN
ejpam-1200	296	1	−1(σi−int(b))⊂	−1(σi−int(b))⊂	PROPN
ejpam-1200	296	2	(	(	PUNCT
ejpam-1200	296	3	i	i	NOUN
ejpam-1200	296	4	,	,	PUNCT
ejpam-1200	296	5	j)−βi	j)−βi	PROPN
ejpam-1200	296	6	int	int	PROPN
ejpam-1200	296	7	(	(	PUNCT
ejpam-1200	296	8	f	f	PROPN
ejpam-1200	296	9	−1(b	−1(b	NOUN
ejpam-1200	296	10	)	)	PUNCT
ejpam-1200	296	11	)	)	PUNCT
ejpam-1200	296	12	.	.	PUNCT
ejpam-1200	297	1	hence	hence	ADV
ejpam-1200	297	2	we	we	PRON
ejpam-1200	297	3	have	have	VERB
ejpam-1200	297	4	f	f	NOUN
ejpam-1200	297	5	−1(b	−1(b	ADJ
ejpam-1200	297	6	)	)	PUNCT
ejpam-1200	297	7	=	=	SYM
ejpam-1200	297	8	(	(	PUNCT
ejpam-1200	297	9	i	i	NOUN
ejpam-1200	297	10	,	,	PUNCT
ejpam-1200	297	11	j)−βi	j)−βi	PROPN
ejpam-1200	297	12	int	int	PROPN
ejpam-1200	297	13	(	(	PUNCT
ejpam-1200	297	14	f	f	PROPN
ejpam-1200	297	15	−1(b	−1(b	NOUN
ejpam-1200	297	16	)	)	PUNCT
ejpam-1200	297	17	)	)	PUNCT
ejpam-1200	297	18	.	.	PUNCT
ejpam-1200	298	1	this	this	PRON
ejpam-1200	298	2	shows	show	VERB
ejpam-1200	298	3	that	that	SCONJ
ejpam-1200	298	4	f	f	PROPN
ejpam-1200	298	5	−1(b	−1(b	NOUN
ejpam-1200	298	6	)	)	PUNCT
ejpam-1200	298	7	is	be	AUX
ejpam-1200	298	8	(	(	PUNCT
ejpam-1200	298	9	i	i	NOUN
ejpam-1200	298	10	,	,	PUNCT
ejpam-1200	298	11	j)−	j)−	PROPN
ejpam-1200	298	12	β	β	PROPN
ejpam-1200	298	13	−i	−i	PROPN
ejpam-1200	298	14	-open	-open	VERB
ejpam-1200	298	15	in	in	ADP
ejpam-1200	298	16	x	x	X
ejpam-1200	298	17	.	.	PUNCT
ejpam-1200	299	1	if	if	SCONJ
ejpam-1200	299	2	i	i	PRON
ejpam-1200	299	3	=	=	X
ejpam-1200	299	4	{	{	PUNCT
ejpam-1200	299	5	;	;	PUNCT
ejpam-1200	299	6	}	}	PUNCT
ejpam-1200	299	7	in	in	ADP
ejpam-1200	299	8	theorem	theorem	NOUN
ejpam-1200	299	9	11	11	NUM
ejpam-1200	299	10	,	,	PUNCT
ejpam-1200	299	11	we	we	PRON
ejpam-1200	299	12	get	get	VERB
ejpam-1200	299	13	the	the	DET
ejpam-1200	299	14	following	follow	VERB
ejpam-1200	299	15	corollary	corollary	NOUN
ejpam-1200	299	16	3	3	NUM
ejpam-1200	299	17	(	(	PUNCT
ejpam-1200	299	18	[	[	X
ejpam-1200	299	19	6	6	NUM
ejpam-1200	299	20	,	,	PUNCT
ejpam-1200	299	21	theorem	theorem	VERB
ejpam-1200	299	22	5.1	5.1	NUM
ejpam-1200	299	23	]	]	PUNCT
ejpam-1200	299	24	)	)	PUNCT
ejpam-1200	299	25	.	.	PUNCT
ejpam-1200	300	1	for	for	ADP
ejpam-1200	300	2	a	a	DET
ejpam-1200	300	3	function	function	NOUN
ejpam-1200	300	4	f	f	NOUN
ejpam-1200	300	5	:	:	PUNCT
ejpam-1200	300	6	(	(	PUNCT
ejpam-1200	300	7	x	x	X
ejpam-1200	300	8	,	,	PUNCT
ejpam-1200	300	9	τ1,τ2	τ1,τ2	PROPN
ejpam-1200	300	10	)	)	PUNCT
ejpam-1200	300	11	→	→	SYM
ejpam-1200	300	12	(	(	PUNCT
ejpam-1200	300	13	y	y	NOUN
ejpam-1200	300	14	,	,	PUNCT
ejpam-1200	300	15	σ1,σ2	σ1,σ2	PROPN
ejpam-1200	300	16	)	)	PUNCT
ejpam-1200	300	17	,	,	PUNCT
ejpam-1200	300	18	the	the	DET
ejpam-1200	300	19	following	follow	VERB
ejpam-1200	300	20	statements	statement	NOUN
ejpam-1200	300	21	are	be	AUX
ejpam-1200	300	22	equivalent	equivalent	ADJ
ejpam-1200	300	23	:	:	PUNCT
ejpam-1200	300	24	(	(	PUNCT
ejpam-1200	300	25	i	i	NOUN
ejpam-1200	300	26	)	)	PUNCT
ejpam-1200	300	27	f	f	PROPN
ejpam-1200	300	28	is	be	AUX
ejpam-1200	300	29	pairwise	pairwise	NOUN
ejpam-1200	300	30	semi	semi	ADJ
ejpam-1200	300	31	-	-	ADJ
ejpam-1200	300	32	precontinuous	precontinuous	ADJ
ejpam-1200	300	33	;	;	PUNCT
ejpam-1200	300	34	(	(	PUNCT
ejpam-1200	300	35	ii	ii	NOUN
ejpam-1200	300	36	)	)	PUNCT
ejpam-1200	300	37	for	for	ADP
ejpam-1200	300	38	each	each	DET
ejpam-1200	300	39	point	point	NOUN
ejpam-1200	300	40	x	x	PUNCT
ejpam-1200	300	41	in	in	ADP
ejpam-1200	300	42	x	x	X
ejpam-1200	300	43	and	and	CCONJ
ejpam-1200	300	44	each	each	DET
ejpam-1200	300	45	σi	σi	NOUN
ejpam-1200	300	46	-	-	PUNCT
ejpam-1200	300	47	open	open	ADJ
ejpam-1200	300	48	set	set	ADJ
ejpam-1200	300	49	f	f	PROPN
ejpam-1200	300	50	in	in	ADP
ejpam-1200	300	51	y	y	PRON
ejpam-1200	301	1	such	such	ADJ
ejpam-1200	301	2	that	that	SCONJ
ejpam-1200	301	3	f	f	PROPN
ejpam-1200	301	4	(	(	PUNCT
ejpam-1200	301	5	x	x	X
ejpam-1200	301	6	)	)	PUNCT
ejpam-1200	301	7	∈	∈	PROPN
ejpam-1200	302	1	f	f	X
ejpam-1200	302	2	,	,	PUNCT
ejpam-1200	302	3	there	there	PRON
ejpam-1200	302	4	is	be	VERB
ejpam-1200	302	5	an	an	DET
ejpam-1200	302	6	(	(	PUNCT
ejpam-1200	302	7	i	i	NOUN
ejpam-1200	302	8	,	,	PUNCT
ejpam-1200	302	9	j)semi	j)semi	PROPN
ejpam-1200	302	10	-	-	ADJ
ejpam-1200	302	11	preopen	preopen	NOUN
ejpam-1200	302	12	set	set	VERB
ejpam-1200	302	13	a	a	PRON
ejpam-1200	302	14	in	in	ADP
ejpam-1200	302	15	x	x	PUNCT
ejpam-1200	302	16	such	such	ADJ
ejpam-1200	302	17	that	that	SCONJ
ejpam-1200	302	18	x	x	SYM
ejpam-1200	302	19	∈	∈	PROPN
ejpam-1200	302	20	a	a	X
ejpam-1200	302	21	,	,	PUNCT
ejpam-1200	302	22	f	f	PROPN
ejpam-1200	302	23	(	(	PUNCT
ejpam-1200	302	24	a)⊂	a)⊂	PROPN
ejpam-1200	302	25	f	f	X
ejpam-1200	302	26	;	;	PUNCT
ejpam-1200	302	27	(	(	PUNCT
ejpam-1200	302	28	iii	iii	X
ejpam-1200	302	29	)	)	PUNCT
ejpam-1200	302	30	the	the	DET
ejpam-1200	302	31	inverse	inverse	ADJ
ejpam-1200	302	32	image	image	NOUN
ejpam-1200	302	33	of	of	ADP
ejpam-1200	302	34	each	each	DET
ejpam-1200	302	35	σi	σi	NOUN
ejpam-1200	302	36	-	-	PUNCT
ejpam-1200	302	37	closed	closed	ADJ
ejpam-1200	302	38	set	set	NOUN
ejpam-1200	302	39	in	in	ADP
ejpam-1200	302	40	y	y	PROPN
ejpam-1200	302	41	is	be	AUX
ejpam-1200	302	42	(	(	PUNCT
ejpam-1200	302	43	i	i	PROPN
ejpam-1200	302	44	,	,	PUNCT
ejpam-1200	302	45	j)-semi	j)-semi	NOUN
ejpam-1200	302	46	-	-	PUNCT
ejpam-1200	302	47	preclosed	preclose	VERB
ejpam-1200	302	48	in	in	ADP
ejpam-1200	302	49	x	x	SYM
ejpam-1200	302	50	;	;	PUNCT
ejpam-1200	302	51	(	(	PUNCT
ejpam-1200	302	52	iv	iv	X
ejpam-1200	302	53	)	)	PUNCT
ejpam-1200	302	54	for	for	ADP
ejpam-1200	302	55	each	each	PRON
ejpam-1200	302	56	subset	subset	VERB
ejpam-1200	302	57	a	a	PRON
ejpam-1200	302	58	of	of	ADP
ejpam-1200	302	59	x	x	SYM
ejpam-1200	302	60	,	,	PUNCT
ejpam-1200	302	61	f	f	PROPN
ejpam-1200	302	62	(	(	PUNCT
ejpam-1200	302	63	(	(	PUNCT
ejpam-1200	302	64	i	i	NOUN
ejpam-1200	302	65	,	,	PUNCT
ejpam-1200	302	66	j)−	j)−	PROPN
ejpam-1200	302	67	sp	sp	ADP
ejpam-1200	302	68	cl(a))⊂	cl(a))⊂	NOUN
ejpam-1200	302	69	σi	σi	PROPN
ejpam-1200	302	70	−cl	−cl	PROPN
ejpam-1200	302	71	(	(	PUNCT
ejpam-1200	302	72	f	f	PROPN
ejpam-1200	302	73	(	(	PUNCT
ejpam-1200	302	74	a	a	NOUN
ejpam-1200	302	75	)	)	PUNCT
ejpam-1200	302	76	)	)	PUNCT
ejpam-1200	302	77	;	;	PUNCT
ejpam-1200	302	78	(	(	PUNCT
ejpam-1200	302	79	v	v	NOUN
ejpam-1200	302	80	)	)	PUNCT
ejpam-1200	302	81	for	for	ADP
ejpam-1200	302	82	each	each	DET
ejpam-1200	302	83	subset	subset	NOUN
ejpam-1200	302	84	b	b	PROPN
ejpam-1200	302	85	of	of	ADP
ejpam-1200	302	86	y	y	PROPN
ejpam-1200	302	87	,	,	PUNCT
ejpam-1200	302	88	(	(	PUNCT
ejpam-1200	302	89	i	i	NOUN
ejpam-1200	302	90	,	,	PUNCT
ejpam-1200	302	91	j)−	j)−	PROPN
ejpam-1200	302	92	sp	sp	ADP
ejpam-1200	302	93	cl	cl	NOUN
ejpam-1200	302	94	(	(	PUNCT
ejpam-1200	302	95	f	f	PROPN
ejpam-1200	302	96	−1(b))⊂	−1(b))⊂	PROPN
ejpam-1200	302	97	f	f	PROPN
ejpam-1200	302	98	−1(σi	−1(σi	NOUN
ejpam-1200	302	99	−cl(b	−cl(b	ADP
ejpam-1200	302	100	)	)	PUNCT
ejpam-1200	302	101	)	)	PUNCT
ejpam-1200	302	102	.	.	PUNCT
ejpam-1200	303	1	theorem	theorem	NOUN
ejpam-1200	303	2	12	12	NUM
ejpam-1200	303	3	.	.	PUNCT
ejpam-1200	304	1	let	let	VERB
ejpam-1200	304	2	f	f	NOUN
ejpam-1200	304	3	:	:	PUNCT
ejpam-1200	304	4	(	(	PUNCT
ejpam-1200	304	5	x	x	INTJ
ejpam-1200	304	6	,	,	PUNCT
ejpam-1200	304	7	τ1,τ2,i	τ1,τ2,i	PROPN
ejpam-1200	304	8	)	)	PUNCT
ejpam-1200	304	9	→	→	SYM
ejpam-1200	304	10	(	(	PUNCT
ejpam-1200	304	11	y	y	PROPN
ejpam-1200	304	12	,	,	PUNCT
ejpam-1200	304	13	σ1,σ2	σ1,σ2	PROPN
ejpam-1200	304	14	)	)	PUNCT
ejpam-1200	304	15	be	be	AUX
ejpam-1200	304	16	a	a	DET
ejpam-1200	304	17	function	function	NOUN
ejpam-1200	304	18	.	.	PUNCT
ejpam-1200	305	1	if	if	SCONJ
ejpam-1200	305	2	g	g	NOUN
ejpam-1200	305	3	:	:	PUNCT
ejpam-1200	305	4	(	(	PUNCT
ejpam-1200	305	5	x	x	INTJ
ejpam-1200	305	6	,	,	PUNCT
ejpam-1200	305	7	τ1,τ2,i	τ1,τ2,i	PROPN
ejpam-1200	305	8	)	)	PUNCT
ejpam-1200	305	9	→	→	SYM
ejpam-1200	305	10	(	(	PUNCT
ejpam-1200	305	11	x×y	x×y	PROPN
ejpam-1200	305	12	,	,	PUNCT
ejpam-1200	305	13	σ1×σ2	σ1×σ2	PROPN
ejpam-1200	305	14	)	)	PUNCT
ejpam-1200	305	15	defined	define	VERB
ejpam-1200	305	16	by	by	ADP
ejpam-1200	305	17	g(x	g(x	NOUN
ejpam-1200	305	18	)	)	PUNCT
ejpam-1200	305	19	=	=	SYM
ejpam-1200	305	20	(	(	PUNCT
ejpam-1200	305	21	x	x	INTJ
ejpam-1200	305	22	,	,	PUNCT
ejpam-1200	305	23	f	f	PROPN
ejpam-1200	305	24	(	(	PUNCT
ejpam-1200	305	25	x	x	NOUN
ejpam-1200	305	26	)	)	PUNCT
ejpam-1200	305	27	)	)	PUNCT
ejpam-1200	305	28	is	be	AUX
ejpam-1200	305	29	an	an	DET
ejpam-1200	305	30	(	(	PUNCT
ejpam-1200	305	31	i	i	NOUN
ejpam-1200	305	32	,	,	PUNCT
ejpam-1200	305	33	j)−β−i	j)−β−i	PROPN
ejpam-1200	305	34	-continuous	-continuous	ADJ
ejpam-1200	305	35	function	function	NOUN
ejpam-1200	305	36	,	,	PUNCT
ejpam-1200	305	37	then	then	ADV
ejpam-1200	305	38	f	f	PROPN
ejpam-1200	305	39	is	be	AUX
ejpam-1200	305	40	(	(	PUNCT
ejpam-1200	305	41	i	i	NOUN
ejpam-1200	305	42	,	,	PUNCT
ejpam-1200	305	43	j)−	j)−	PROPN
ejpam-1200	305	44	β	β	PROPN
ejpam-1200	305	45	−i	−i	PROPN
ejpam-1200	305	46	-continuous	-continuous	ADJ
ejpam-1200	305	47	.	.	PUNCT
ejpam-1200	306	1	proof	proof	NOUN
ejpam-1200	306	2	.	.	PUNCT
ejpam-1200	307	1	let	let	VERB
ejpam-1200	307	2	v	v	PART
ejpam-1200	307	3	be	be	AUX
ejpam-1200	307	4	a	a	DET
ejpam-1200	307	5	σi	σi	NOUN
ejpam-1200	307	6	-	-	PUNCT
ejpam-1200	307	7	open	open	ADJ
ejpam-1200	307	8	set	set	NOUN
ejpam-1200	307	9	of	of	ADP
ejpam-1200	307	10	y	y	PROPN
ejpam-1200	307	11	.	.	PUNCT
ejpam-1200	308	1	then	then	ADV
ejpam-1200	308	2	f	f	PROPN
ejpam-1200	308	3	−1(v	−1(v	PROPN
ejpam-1200	308	4	)	)	PUNCT
ejpam-1200	309	1	=	=	PUNCT
ejpam-1200	309	2	x	x	NOUN
ejpam-1200	309	3	∩	∩	X
ejpam-1200	309	4	f	f	PROPN
ejpam-1200	309	5	−1(v	−1(v	PROPN
ejpam-1200	309	6	)	)	PUNCT
ejpam-1200	310	1	=	=	PUNCT
ejpam-1200	310	2	g−1(x	g−1(x	NOUN
ejpam-1200	311	1	×	×	NOUN
ejpam-1200	311	2	v	v	NOUN
ejpam-1200	311	3	)	)	PUNCT
ejpam-1200	311	4	.	.	PUNCT
ejpam-1200	312	1	since	since	SCONJ
ejpam-1200	312	2	g	g	PROPN
ejpam-1200	312	3	is	be	AUX
ejpam-1200	312	4	an	an	DET
ejpam-1200	312	5	(	(	PUNCT
ejpam-1200	312	6	i	i	NOUN
ejpam-1200	312	7	,	,	PUNCT
ejpam-1200	312	8	j)−	j)−	PROPN
ejpam-1200	312	9	β	β	PROPN
ejpam-1200	312	10	−i	−i	PROPN
ejpam-1200	312	11	-continuous	-continuous	ADJ
ejpam-1200	312	12	function	function	NOUN
ejpam-1200	312	13	and	and	CCONJ
ejpam-1200	312	14	x	x	SYM
ejpam-1200	312	15	×	×	NOUN
ejpam-1200	312	16	v	v	NOUN
ejpam-1200	312	17	is	be	AUX
ejpam-1200	312	18	a	a	DET
ejpam-1200	312	19	τi	τi	ADJ
ejpam-1200	312	20	×σi	×σi	NOUN
ejpam-1200	312	21	-	-	PUNCT
ejpam-1200	312	22	open	open	ADJ
ejpam-1200	312	23	set	set	NOUN
ejpam-1200	312	24	of	of	ADP
ejpam-1200	312	25	x	x	SYM
ejpam-1200	312	26	×	×	PROPN
ejpam-1200	312	27	y	y	PROPN
ejpam-1200	312	28	,	,	PUNCT
ejpam-1200	312	29	f	f	PROPN
ejpam-1200	312	30	−1(v	−1(v	PROPN
ejpam-1200	312	31	)	)	PUNCT
ejpam-1200	312	32	is	be	AUX
ejpam-1200	312	33	an	an	DET
ejpam-1200	312	34	(	(	PUNCT
ejpam-1200	312	35	i	i	NOUN
ejpam-1200	312	36	,	,	PUNCT
ejpam-1200	312	37	j)−	j)−	PROPN
ejpam-1200	312	38	β	β	PROPN
ejpam-1200	312	39	−i	−i	PROPN
ejpam-1200	312	40	-open	-open	PROPN
ejpam-1200	312	41	set	set	NOUN
ejpam-1200	312	42	of	of	ADP
ejpam-1200	312	43	x	x	X
ejpam-1200	312	44	.	.	PUNCT
ejpam-1200	313	1	hence	hence	ADV
ejpam-1200	313	2	f	f	PROPN
ejpam-1200	313	3	is	be	AUX
ejpam-1200	313	4	(	(	PUNCT
ejpam-1200	313	5	i	i	NOUN
ejpam-1200	313	6	,	,	PUNCT
ejpam-1200	313	7	j)−	j)−	PROPN
ejpam-1200	313	8	β	β	PROPN
ejpam-1200	313	9	−i	−i	PROPN
ejpam-1200	313	10	-continuous	-continuous	ADJ
ejpam-1200	313	11	.	.	PUNCT
ejpam-1200	314	1	definition	definition	NOUN
ejpam-1200	314	2	10	10	NUM
ejpam-1200	314	3	.	.	PUNCT
ejpam-1200	315	1	a	a	DET
ejpam-1200	315	2	bitopological	bitopological	ADJ
ejpam-1200	315	3	space	space	NOUN
ejpam-1200	315	4	(	(	PUNCT
ejpam-1200	315	5	x	x	NOUN
ejpam-1200	315	6	,	,	PUNCT
ejpam-1200	315	7	τ1,τ2	τ1,τ2	PROPN
ejpam-1200	315	8	)	)	PUNCT
ejpam-1200	315	9	is	be	AUX
ejpam-1200	315	10	said	say	VERB
ejpam-1200	315	11	to	to	PART
ejpam-1200	315	12	be	be	AUX
ejpam-1200	315	13	pairwise	pairwise	NOUN
ejpam-1200	315	14	connected	connect	VERB
ejpam-1200	315	15	[	[	X
ejpam-1200	315	16	8	8	NUM
ejpam-1200	315	17	]	]	X
ejpam-1200	315	18	if	if	SCONJ
ejpam-1200	315	19	it	it	PRON
ejpam-1200	315	20	can	can	AUX
ejpam-1200	315	21	not	not	PART
ejpam-1200	315	22	be	be	AUX
ejpam-1200	315	23	expressed	express	VERB
ejpam-1200	315	24	as	as	ADP
ejpam-1200	315	25	the	the	DET
ejpam-1200	315	26	union	union	NOUN
ejpam-1200	315	27	of	of	ADP
ejpam-1200	315	28	two	two	NUM
ejpam-1200	315	29	nonempty	nonempty	ADJ
ejpam-1200	315	30	disjoint	disjoint	NOUN
ejpam-1200	315	31	sets	set	NOUN
ejpam-1200	315	32	u	u	NOUN
ejpam-1200	315	33	and	and	CCONJ
ejpam-1200	315	34	v	v	ADP
ejpam-1200	315	35	such	such	ADJ
ejpam-1200	315	36	that	that	SCONJ
ejpam-1200	315	37	u	u	NOUN
ejpam-1200	315	38	is	be	AUX
ejpam-1200	315	39	τi	τi	ADJ
ejpam-1200	315	40	-	-	PUNCT
ejpam-1200	315	41	open	open	ADJ
ejpam-1200	315	42	and	and	CCONJ
ejpam-1200	315	43	v	v	NOUN
ejpam-1200	315	44	is	be	AUX
ejpam-1200	315	45	τ	τ	PROPN
ejpam-1200	315	46	j	j	NOUN
ejpam-1200	315	47	-	-	NOUN
ejpam-1200	315	48	open	open	ADJ
ejpam-1200	315	49	,	,	PUNCT
ejpam-1200	315	50	where	where	SCONJ
ejpam-1200	315	51	i	i	PRON
ejpam-1200	315	52	,	,	PUNCT
ejpam-1200	315	53	j	j	PROPN
ejpam-1200	315	54	=	=	PUNCT
ejpam-1200	315	55	{	{	PUNCT
ejpam-1200	315	56	1	1	NUM
ejpam-1200	315	57	,	,	PUNCT
ejpam-1200	315	58	2	2	NUM
ejpam-1200	315	59	}	}	PUNCT
ejpam-1200	315	60	.	.	PUNCT
ejpam-1200	316	1	references	reference	NOUN
ejpam-1200	316	2	255	255	NUM
ejpam-1200	316	3	definition	definition	NOUN
ejpam-1200	316	4	11	11	NUM
ejpam-1200	316	5	.	.	PUNCT
ejpam-1200	317	1	an	an	DET
ejpam-1200	317	2	ideal	ideal	ADJ
ejpam-1200	317	3	bitopological	bitopological	ADJ
ejpam-1200	317	4	space	space	NOUN
ejpam-1200	317	5	(	(	PUNCT
ejpam-1200	317	6	x	x	X
ejpam-1200	317	7	,	,	PUNCT
ejpam-1200	317	8	τ1,τ2,i	τ1,τ2,i	PROPN
ejpam-1200	317	9	)	)	PUNCT
ejpam-1200	317	10	is	be	AUX
ejpam-1200	317	11	said	say	VERB
ejpam-1200	317	12	to	to	PART
ejpam-1200	317	13	be	be	AUX
ejpam-1200	317	14	(	(	PUNCT
ejpam-1200	317	15	i	i	NOUN
ejpam-1200	317	16	,	,	PUNCT
ejpam-1200	317	17	j)−	j)−	PROPN
ejpam-1200	317	18	β	β	PROPN
ejpam-1200	317	19	−i	−i	PROPN
ejpam-1200	317	20	-connected	-connected	PROPN
ejpam-1200	317	21	if	if	SCONJ
ejpam-1200	317	22	it	it	PRON
ejpam-1200	317	23	can	can	AUX
ejpam-1200	317	24	not	not	PART
ejpam-1200	317	25	be	be	AUX
ejpam-1200	317	26	expressed	express	VERB
ejpam-1200	317	27	as	as	ADP
ejpam-1200	317	28	the	the	DET
ejpam-1200	317	29	union	union	NOUN
ejpam-1200	317	30	of	of	ADP
ejpam-1200	317	31	two	two	NUM
ejpam-1200	317	32	nonempty	nonempty	ADJ
ejpam-1200	317	33	disjoint	disjoint	NOUN
ejpam-1200	317	34	sets	set	NOUN
ejpam-1200	317	35	u	u	NOUN
ejpam-1200	317	36	and	and	CCONJ
ejpam-1200	317	37	v	v	ADP
ejpam-1200	317	38	such	such	ADJ
ejpam-1200	317	39	that	that	SCONJ
ejpam-1200	317	40	u	u	NOUN
ejpam-1200	317	41	is	be	AUX
ejpam-1200	317	42	(	(	PUNCT
ejpam-1200	317	43	i	i	NOUN
ejpam-1200	317	44	,	,	PUNCT
ejpam-1200	317	45	j)−	j)−	PROPN
ejpam-1200	317	46	β	β	PROPN
ejpam-1200	317	47	−i	−i	PROPN
ejpam-1200	317	48	-open	-open	PROPN
ejpam-1200	317	49	and	and	CCONJ
ejpam-1200	317	50	v	v	NOUN
ejpam-1200	317	51	is	be	AUX
ejpam-1200	317	52	(	(	PUNCT
ejpam-1200	317	53	i	i	NOUN
ejpam-1200	317	54	,	,	PUNCT
ejpam-1200	317	55	j)−	j)−	PROPN
ejpam-1200	317	56	β	β	PROPN
ejpam-1200	317	57	−i	−i	PROPN
ejpam-1200	317	58	-open	-open	PROPN
ejpam-1200	317	59	.	.	PUNCT
ejpam-1200	318	1	theorem	theorem	NOUN
ejpam-1200	318	2	13	13	NUM
ejpam-1200	318	3	.	.	PUNCT
ejpam-1200	319	1	let	let	VERB
ejpam-1200	319	2	f	f	NOUN
ejpam-1200	319	3	:	:	PUNCT
ejpam-1200	319	4	(	(	PUNCT
ejpam-1200	319	5	x	x	X
ejpam-1200	319	6	,	,	PUNCT
ejpam-1200	319	7	τ1,τ2,i	τ1,τ2,i	PROPN
ejpam-1200	319	8	)	)	PUNCT
ejpam-1200	320	1	→	→	SYM
ejpam-1200	320	2	(	(	PUNCT
ejpam-1200	320	3	y	y	PROPN
ejpam-1200	320	4	,	,	PUNCT
ejpam-1200	320	5	σ1,σ2	σ1,σ2	PROPN
ejpam-1200	320	6	)	)	PUNCT
ejpam-1200	320	7	is	be	AUX
ejpam-1200	320	8	(	(	PUNCT
ejpam-1200	320	9	i	i	NOUN
ejpam-1200	320	10	,	,	PUNCT
ejpam-1200	320	11	j)−	j)−	PROPN
ejpam-1200	321	1	β	β	PROPN
ejpam-1200	321	2	−	−	PROPN
ejpam-1200	322	1	i	i	PRON
ejpam-1200	322	2	-continuous	-continuous	ADJ
ejpam-1200	322	3	surjection	surjection	NOUN
ejpam-1200	322	4	and	and	CCONJ
ejpam-1200	322	5	(	(	PUNCT
ejpam-1200	322	6	x	x	INTJ
ejpam-1200	322	7	,	,	PUNCT
ejpam-1200	322	8	τ1,τ2,i	τ1,τ2,i	PROPN
ejpam-1200	322	9	)	)	PUNCT
ejpam-1200	322	10	is	be	AUX
ejpam-1200	322	11	(	(	PUNCT
ejpam-1200	322	12	i	i	NOUN
ejpam-1200	322	13	,	,	PUNCT
ejpam-1200	322	14	j)−	j)−	PROPN
ejpam-1200	322	15	β	β	PROPN
ejpam-1200	322	16	−i	−i	PROPN
ejpam-1200	322	17	-connected	-connected	PROPN
ejpam-1200	322	18	,	,	PUNCT
ejpam-1200	322	19	then	then	ADV
ejpam-1200	322	20	(	(	PUNCT
ejpam-1200	322	21	y	y	NOUN
ejpam-1200	322	22	,	,	PUNCT
ejpam-1200	322	23	σ1,σ2	σ1,σ2	PROPN
ejpam-1200	322	24	)	)	PUNCT
ejpam-1200	322	25	is	be	AUX
ejpam-1200	322	26	pairwise	pairwise	NOUN
ejpam-1200	322	27	connected	connect	VERB
ejpam-1200	322	28	.	.	PUNCT
ejpam-1200	323	1	proof	proof	NOUN
ejpam-1200	323	2	.	.	PUNCT
ejpam-1200	324	1	suppose	suppose	VERB
ejpam-1200	324	2	y	y	PRON
ejpam-1200	324	3	is	be	AUX
ejpam-1200	324	4	not	not	PART
ejpam-1200	324	5	pairwise	pairwise	NOUN
ejpam-1200	324	6	connected	connect	VERB
ejpam-1200	324	7	,	,	PUNCT
ejpam-1200	324	8	then	then	ADV
ejpam-1200	324	9	y	y	PROPN
ejpam-1200	324	10	=	=	PUNCT
ejpam-1200	325	1	a∪	a∪	PROPN
ejpam-1200	326	1	b	b	NUM
ejpam-1200	326	2	where	where	SCONJ
ejpam-1200	326	3	a∩	a∩	PROPN
ejpam-1200	326	4	b	b	PROPN
ejpam-1200	326	5	=	=	X
ejpam-1200	326	6	;	;	PUNCT
ejpam-1200	326	7	,	,	PUNCT
ejpam-1200	326	8	a	a	DET
ejpam-1200	326	9	6=	6=	NOUN
ejpam-1200	326	10	;	;	PUNCT
ejpam-1200	326	11	,	,	PUNCT
ejpam-1200	326	12	b	b	PROPN
ejpam-1200	326	13	6=	6=	NUM
ejpam-1200	326	14	;	;	PUNCT
ejpam-1200	326	15	and	and	CCONJ
ejpam-1200	326	16	a	a	DET
ejpam-1200	326	17	∈	∈	NOUN
ejpam-1200	326	18	σi	σi	X
ejpam-1200	326	19	,	,	PUNCT
ejpam-1200	326	20	b	b	PROPN
ejpam-1200	326	21	∈	∈	PROPN
ejpam-1200	326	22	σ	σ	PROPN
ejpam-1200	326	23	j	j	PROPN
ejpam-1200	326	24	.	.	PUNCT
ejpam-1200	327	1	since	since	SCONJ
ejpam-1200	327	2	f	f	PROPN
ejpam-1200	327	3	is	be	AUX
ejpam-1200	327	4	(	(	PUNCT
ejpam-1200	327	5	i	i	PROPN
ejpam-1200	327	6	,	,	PUNCT
ejpam-1200	328	1	j)−	j)−	PROPN
ejpam-1200	328	2	β	β	PROPN
ejpam-1200	328	3	−	−	PROPN
ejpam-1200	328	4	i	i	PRON
ejpam-1200	328	5	-continuous	-continuous	ADJ
ejpam-1200	328	6	f	f	PROPN
ejpam-1200	328	7	−1(a	−1(a	ADP
ejpam-1200	328	8	)	)	PUNCT
ejpam-1200	328	9	∈	∈	PROPN
ejpam-1200	328	10	(	(	PUNCT
ejpam-1200	328	11	i	i	NOUN
ejpam-1200	328	12	,	,	PUNCT
ejpam-1200	328	13	j)−	j)−	PROPN
ejpam-1200	328	14	βio(x	βio(x	X
ejpam-1200	328	15	)	)	PUNCT
ejpam-1200	328	16	and	and	CCONJ
ejpam-1200	328	17	f	f	PROPN
ejpam-1200	328	18	−1(b	−1(b	ADJ
ejpam-1200	328	19	)	)	PUNCT
ejpam-1200	328	20	∈	∈	PROPN
ejpam-1200	328	21	(	(	PUNCT
ejpam-1200	328	22	i	i	NOUN
ejpam-1200	328	23	,	,	PUNCT
ejpam-1200	328	24	j)−	j)−	PROPN
ejpam-1200	328	25	βio(x	βio(x	NUM
ejpam-1200	328	26	)	)	PUNCT
ejpam-1200	328	27	,	,	PUNCT
ejpam-1200	328	28	such	such	ADJ
ejpam-1200	328	29	that	that	SCONJ
ejpam-1200	328	30	f	f	PROPN
ejpam-1200	328	31	−1(a	−1(a	ADP
ejpam-1200	328	32	)	)	PUNCT
ejpam-1200	328	33	6=	6=	NUM
ejpam-1200	328	34	;	;	PUNCT
ejpam-1200	328	35	,	,	PUNCT
ejpam-1200	328	36	f	f	PROPN
ejpam-1200	328	37	−1(b	−1(b	ADJ
ejpam-1200	328	38	)	)	PUNCT
ejpam-1200	328	39	6=	6=	NUM
ejpam-1200	328	40	;	;	PUNCT
ejpam-1200	328	41	.	.	PUNCT
ejpam-1200	329	1	f	f	PROPN
ejpam-1200	329	2	−1(a	−1(a	PROPN
ejpam-1200	329	3	)	)	PUNCT
ejpam-1200	329	4	∩	∩	NOUN
ejpam-1200	329	5	f	f	X
ejpam-1200	329	6	−1(b	−1(b	NOUN
ejpam-1200	329	7	)	)	PUNCT
ejpam-1200	329	8	=	=	SYM
ejpam-1200	329	9	;	;	PUNCT
ejpam-1200	329	10	and	and	CCONJ
ejpam-1200	329	11	f	f	PROPN
ejpam-1200	329	12	−1(a)∪	−1(a)∪	PROPN
ejpam-1200	329	13	f	f	X
ejpam-1200	329	14	−1(b	−1(b	NOUN
ejpam-1200	329	15	)	)	PUNCT
ejpam-1200	330	1	=	=	SYM
ejpam-1200	330	2	x	x	NOUN
ejpam-1200	330	3	,	,	PUNCT
ejpam-1200	330	4	which	which	PRON
ejpam-1200	330	5	implies	imply	VERB
ejpam-1200	330	6	that	that	SCONJ
ejpam-1200	330	7	x	x	PRON
ejpam-1200	330	8	is	be	AUX
ejpam-1200	330	9	not	not	PART
ejpam-1200	330	10	(	(	PUNCT
ejpam-1200	330	11	i	i	NOUN
ejpam-1200	330	12	,	,	PUNCT
ejpam-1200	330	13	j)−	j)−	PROPN
ejpam-1200	330	14	β	β	PROPN
ejpam-1200	330	15	−i	−i	PROPN
ejpam-1200	330	16	-connected	-connected	PROPN
ejpam-1200	330	17	.	.	PUNCT
ejpam-1200	331	1	references	reference	NOUN
ejpam-1200	331	2	[	[	X
ejpam-1200	331	3	1	1	NUM
ejpam-1200	331	4	]	]	X
ejpam-1200	331	5	g.	g.	PROPN
ejpam-1200	331	6	balasubramanian	balasubramanian	PROPN
ejpam-1200	331	7	.	.	PUNCT
ejpam-1200	332	1	extremally	extremally	ADV
ejpam-1200	332	2	disconnected	disconnect	VERB
ejpam-1200	332	3	bitopological	bitopological	ADJ
ejpam-1200	332	4	spaces	space	NOUN
ejpam-1200	332	5	,	,	PUNCT
ejpam-1200	332	6	bulletin	bulletin	NOUN
ejpam-1200	332	7	of	of	ADP
ejpam-1200	332	8	the	the	DET
ejpam-1200	332	9	calcutta	calcutta	PROPN
ejpam-1200	332	10	mathematical	mathematical	ADJ
ejpam-1200	332	11	society	society	NOUN
ejpam-1200	332	12	,	,	PUNCT
ejpam-1200	332	13	83	83	NUM
ejpam-1200	332	14	,	,	PUNCT
ejpam-1200	332	15	247	247	NUM
ejpam-1200	332	16	-	-	SYM
ejpam-1200	332	17	252	252	NUM
ejpam-1200	332	18	.	.	NOUN
ejpam-1200	332	19	1991	1991	NUM
ejpam-1200	332	20	.	.	PUNCT
ejpam-1200	333	1	[	[	X
ejpam-1200	333	2	2	2	NUM
ejpam-1200	333	3	]	]	PUNCT
ejpam-1200	333	4	m.	m.	NOUN
ejpam-1200	333	5	caldas	caldas	PROPN
ejpam-1200	333	6	,	,	PUNCT
ejpam-1200	333	7	s.	s.	PROPN
ejpam-1200	333	8	jafari	jafari	PROPN
ejpam-1200	333	9	and	and	CCONJ
ejpam-1200	333	10	n.	n.	PROPN
ejpam-1200	333	11	rajesh	rajesh	PROPN
ejpam-1200	333	12	.	.	PUNCT
ejpam-1200	334	1	preopen	preopen	ADJ
ejpam-1200	334	2	sets	set	NOUN
ejpam-1200	334	3	in	in	ADP
ejpam-1200	334	4	ideal	ideal	ADJ
ejpam-1200	334	5	bitopological	bitopological	ADJ
ejpam-1200	334	6	spaces	space	NOUN
ejpam-1200	334	7	,	,	PUNCT
ejpam-1200	334	8	bulletin	bulletin	NOUN
ejpam-1200	334	9	of	of	ADP
ejpam-1200	334	10	parana	parana	PROPN
ejpam-1200	334	11	’s	’s	PART
ejpam-1200	334	12	mathematical	mathematical	ADJ
ejpam-1200	334	13	society	society	NOUN
ejpam-1200	334	14	,	,	PUNCT
ejpam-1200	334	15	29(2	29(2	NUM
ejpam-1200	334	16	)	)	PUNCT
ejpam-1200	334	17	,	,	PUNCT
ejpam-1200	334	18	61	61	NUM
ejpam-1200	334	19	-	-	SYM
ejpam-1200	334	20	68	68	NUM
ejpam-1200	334	21	.	.	PUNCT
ejpam-1200	334	22	2011	2011	NUM
ejpam-1200	334	23	.	.	PUNCT
ejpam-1200	335	1	[	[	X
ejpam-1200	335	2	3	3	NUM
ejpam-1200	335	3	]	]	X
ejpam-1200	335	4	m.	m.	NOUN
ejpam-1200	335	5	caldas	caldas	PROPN
ejpam-1200	335	6	,	,	PUNCT
ejpam-1200	335	7	s.	s.	PROPN
ejpam-1200	335	8	jafari	jafari	PROPN
ejpam-1200	335	9	and	and	CCONJ
ejpam-1200	335	10	n.	n.	PROPN
ejpam-1200	335	11	rajesh	rajesh	PROPN
ejpam-1200	335	12	.	.	PUNCT
ejpam-1200	336	1	semiopen	semiopen	VERB
ejpam-1200	336	2	sets	set	NOUN
ejpam-1200	336	3	in	in	ADP
ejpam-1200	336	4	ideal	ideal	ADJ
ejpam-1200	336	5	bitopological	bitopological	ADJ
ejpam-1200	336	6	spaces	space	NOUN
ejpam-1200	336	7	(	(	PUNCT
ejpam-1200	336	8	to	to	PART
ejpam-1200	336	9	appear	appear	VERB
ejpam-1200	336	10	in	in	ADP
ejpam-1200	336	11	cubo	cubo	NOUN
ejpam-1200	336	12	mathematics	mathematic	NOUN
ejpam-1200	336	13	journal	journal	PROPN
ejpam-1200	336	14	)	)	PUNCT
ejpam-1200	336	15	.	.	PUNCT
ejpam-1200	337	1	[	[	X
ejpam-1200	337	2	4	4	X
ejpam-1200	337	3	]	]	X
ejpam-1200	337	4	d.	d.	PROPN
ejpam-1200	337	5	jankovic	jankovic	PROPN
ejpam-1200	337	6	and	and	CCONJ
ejpam-1200	337	7	t.	t.	PROPN
ejpam-1200	337	8	r.	r.	PROPN
ejpam-1200	337	9	hamlett	hamlett	PROPN
ejpam-1200	337	10	.	.	PUNCT
ejpam-1200	338	1	new	new	ADJ
ejpam-1200	338	2	topologies	topology	NOUN
ejpam-1200	338	3	from	from	ADP
ejpam-1200	338	4	old	old	ADJ
ejpam-1200	338	5	via	via	ADP
ejpam-1200	338	6	ideals	ideal	NOUN
ejpam-1200	338	7	,	,	PUNCT
ejpam-1200	338	8	american	american	PROPN
ejpam-1200	338	9	mathematical	mathematical	PROPN
ejpam-1200	338	10	monthly	monthly	ADV
ejpam-1200	338	11	,	,	PUNCT
ejpam-1200	338	12	97	97	NUM
ejpam-1200	338	13	,	,	PUNCT
ejpam-1200	338	14	295	295	NUM
ejpam-1200	338	15	-	-	SYM
ejpam-1200	338	16	310	310	NUM
ejpam-1200	338	17	.	.	NOUN
ejpam-1200	338	18	1990	1990	NUM
ejpam-1200	338	19	.	.	PUNCT
ejpam-1200	339	1	[	[	X
ejpam-1200	339	2	5	5	NUM
ejpam-1200	339	3	]	]	PUNCT
ejpam-1200	339	4	m.	m.	NOUN
ejpam-1200	339	5	jelic	jelic	NOUN
ejpam-1200	339	6	,	,	PUNCT
ejpam-1200	339	7	feeble	feeble	ADJ
ejpam-1200	339	8	p	p	ADJ
ejpam-1200	339	9	-	-	PUNCT
ejpam-1200	339	10	continuous	continuous	ADJ
ejpam-1200	339	11	mappings	mapping	NOUN
ejpam-1200	339	12	.	.	PUNCT
ejpam-1200	340	1	rendicondi	rendicondi	PROPN
ejpam-1200	340	2	del	del	PROPN
ejpam-1200	340	3	circolo	circolo	PROPN
ejpam-1200	340	4	matematico	matematico	NOUN
ejpam-1200	340	5	di	di	NOUN
ejpam-1200	340	6	palermo	palermo	NOUN
ejpam-1200	340	7	,	,	PUNCT
ejpam-1200	340	8	24	24	NUM
ejpam-1200	340	9	,	,	PUNCT
ejpam-1200	340	10	387	387	NUM
ejpam-1200	340	11	-	-	SYM
ejpam-1200	340	12	395	395	NUM
ejpam-1200	340	13	.	.	PUNCT
ejpam-1200	340	14	1990	1990	NUM
ejpam-1200	341	1	[	[	X
ejpam-1200	341	2	6	6	NUM
ejpam-1200	341	3	]	]	X
ejpam-1200	341	4	f.	f.	PROPN
ejpam-1200	341	5	khedr	khedr	PROPN
ejpam-1200	341	6	,	,	PUNCT
ejpam-1200	341	7	s.	s.	PROPN
ejpam-1200	341	8	al	al	PROPN
ejpam-1200	341	9	-	-	PUNCT
ejpam-1200	341	10	areefi	areefi	PROPN
ejpam-1200	341	11	and	and	CCONJ
ejpam-1200	341	12	t.	t.	PROPN
ejpam-1200	341	13	noiri	noiri	PROPN
ejpam-1200	341	14	.	.	PUNCT
ejpam-1200	342	1	precontinuity	precontinuity	NOUN
ejpam-1200	342	2	and	and	CCONJ
ejpam-1200	342	3	semi	semi	NOUN
ejpam-1200	342	4	-	-	NOUN
ejpam-1200	342	5	precontinuity	precontinuity	NOUN
ejpam-1200	342	6	in	in	ADP
ejpam-1200	342	7	bitopological	bitopological	ADJ
ejpam-1200	342	8	spaces	space	NOUN
ejpam-1200	342	9	,	,	PUNCT
ejpam-1200	342	10	indian	indian	ADJ
ejpam-1200	342	11	journal	journal	NOUN
ejpam-1200	342	12	of	of	ADP
ejpam-1200	342	13	pure	pure	ADJ
ejpam-1200	342	14	and	and	CCONJ
ejpam-1200	342	15	applied	apply	VERB
ejpam-1200	342	16	mathematics	mathematic	NOUN
ejpam-1200	342	17	23(9	23(9	NUM
ejpam-1200	342	18	)	)	PUNCT
ejpam-1200	342	19	,	,	PUNCT
ejpam-1200	342	20	624	624	NUM
ejpam-1200	342	21	-	-	SYM
ejpam-1200	342	22	633	633	NUM
ejpam-1200	342	23	.	.	PUNCT
ejpam-1200	342	24	1992	1992	NUM
ejpam-1200	342	25	.	.	PUNCT
ejpam-1200	343	1	[	[	X
ejpam-1200	343	2	7	7	X
ejpam-1200	343	3	]	]	PUNCT
ejpam-1200	343	4	k.	k.	PROPN
ejpam-1200	343	5	kuratowski	kuratowski	PROPN
ejpam-1200	343	6	.	.	PUNCT
ejpam-1200	344	1	topology	topology	NOUN
ejpam-1200	344	2	,	,	PUNCT
ejpam-1200	344	3	academic	academic	ADJ
ejpam-1200	344	4	press	press	NOUN
ejpam-1200	344	5	,	,	PUNCT
ejpam-1200	344	6	new	new	PROPN
ejpam-1200	344	7	york	york	PROPN
ejpam-1200	344	8	.	.	PUNCT
ejpam-1200	345	1	1966	1966	NUM
ejpam-1200	345	2	.	.	PUNCT
ejpam-1200	346	1	[	[	X
ejpam-1200	346	2	8	8	NUM
ejpam-1200	346	3	]	]	X
ejpam-1200	346	4	w.	w.	PROPN
ejpam-1200	346	5	j.	j.	PROPN
ejpam-1200	346	6	pervine	pervine	PROPN
ejpam-1200	346	7	.	.	PUNCT
ejpam-1200	347	1	connectedness	connectedness	NOUN
ejpam-1200	347	2	in	in	ADP
ejpam-1200	347	3	bitopological	bitopological	ADJ
ejpam-1200	347	4	spaces	space	NOUN
ejpam-1200	347	5	.	.	PUNCT
ejpam-1200	348	1	indagationes	indagatione	NOUN
ejpam-1200	348	2	mathematicae	mathematicae	PROPN
ejpam-1200	348	3	,	,	PUNCT
ejpam-1200	348	4	29	29	NUM
ejpam-1200	348	5	,	,	PUNCT
ejpam-1200	348	6	369372	369372	NUM
ejpam-1200	348	7	.	.	PUNCT
ejpam-1200	349	1	1967	1967	NUM
ejpam-1200	349	2	.	.	PUNCT
ejpam-1200	350	1	[	[	X
ejpam-1200	350	2	9	9	NUM
ejpam-1200	350	3	]	]	X
ejpam-1200	350	4	r.	r.	NOUN
ejpam-1200	350	5	vaidyanathaswamy	vaidyanathaswamy	PROPN
ejpam-1200	350	6	.	.	PUNCT
ejpam-1200	351	1	the	the	DET
ejpam-1200	351	2	localisation	localisation	NOUN
ejpam-1200	351	3	theory	theory	NOUN
ejpam-1200	351	4	in	in	ADP
ejpam-1200	351	5	set	set	NOUN
ejpam-1200	351	6	topology	topology	NOUN
ejpam-1200	351	7	,	,	PUNCT
ejpam-1200	351	8	proceedings	proceeding	NOUN
ejpam-1200	351	9	of	of	ADP
ejpam-1200	351	10	the	the	DET
ejpam-1200	351	11	indian	indian	ADJ
ejpam-1200	351	12	acadamic	acadamic	NOUN
ejpam-1200	351	13	of	of	ADP
ejpam-1200	351	14	sciences	science	NOUN
ejpam-1200	351	15	,	,	PUNCT
ejpam-1200	351	16	20	20	NUM
ejpam-1200	351	17	,	,	PUNCT
ejpam-1200	351	18	51	51	NUM
ejpam-1200	351	19	-	-	SYM
ejpam-1200	351	20	61	61	NUM
ejpam-1200	351	21	.	.	PUNCT
ejpam-1200	351	22	1945	1945	NUM
ejpam-1200	351	23	.	.	PUNCT
ejpam-1200	352	1	[	[	X
ejpam-1200	352	2	10	10	NUM
ejpam-1200	352	3	]	]	X
ejpam-1200	352	4	s.	s.	PROPN
ejpam-1200	352	5	yuksel	yuksel	PROPN
ejpam-1200	352	6	,	,	PUNCT
ejpam-1200	352	7	a.	a.	PROPN
ejpam-1200	352	8	h.	h.	PROPN
ejpam-1200	352	9	kocaman	kocaman	PROPN
ejpam-1200	352	10	and	and	CCONJ
ejpam-1200	352	11	a.	a.	NOUN
ejpam-1200	352	12	acıkgoz	acıkgoz	PROPN
ejpam-1200	352	13	.	.	PUNCT
ejpam-1200	353	1	on	on	ADP
ejpam-1200	353	2	β−i	β−i	NOUN
ejpam-1200	353	3	-irresolute	-irresolute	NOUN
ejpam-1200	353	4	functions	function	NOUN
ejpam-1200	353	5	,	,	PUNCT
ejpam-1200	353	6	far	far	PROPN
ejpam-1200	353	7	east	east	PROPN
ejpam-1200	353	8	journal	journal	PROPN
ejpam-1200	353	9	of	of	ADP
ejpam-1200	353	10	mathematical	mathematical	ADJ
ejpam-1200	353	11	sciences	science	NOUN
ejpam-1200	353	12	.	.	PUNCT
ejpam-1200	353	13	26(3	26(3	NUM
ejpam-1200	353	14	)	)	PUNCT
ejpam-1200	353	15	,	,	PUNCT
ejpam-1200	353	16	673	673	NUM
ejpam-1200	353	17	-	-	SYM
ejpam-1200	353	18	684	684	NUM
ejpam-1200	353	19	.	.	PUNCT
ejpam-1200	353	20	2007	2007	NUM
ejpam-1200	353	21	.	.	PUNCT