id	sid	tid	token	lemma	pos
ejpam-3649	1	1	european	european	PROPN
ejpam-3649	1	2	journal	journal	PROPN
ejpam-3649	1	3	of	of	ADP
ejpam-3649	1	4	pure	pure	ADJ
ejpam-3649	1	5	and	and	CCONJ
ejpam-3649	1	6	applied	apply	VERB
ejpam-3649	1	7	mathematics	mathematic	NOUN
ejpam-3649	1	8	vol	vol	NOUN
ejpam-3649	1	9	.	.	PROPN
ejpam-3649	2	1	13	13	NUM
ejpam-3649	2	2	,	,	PUNCT
ejpam-3649	2	3	no	no	INTJ
ejpam-3649	2	4	.	.	NOUN
ejpam-3649	2	5	2	2	NUM
ejpam-3649	2	6	,	,	PUNCT
ejpam-3649	2	7	2020	2020	NUM
ejpam-3649	2	8	,	,	PUNCT
ejpam-3649	2	9	269	269	NUM
ejpam-3649	2	10	-	-	SYM
ejpam-3649	2	11	279	279	NUM
ejpam-3649	2	12	issn	issn	PROPN
ejpam-3649	2	13	1307	1307	NUM
ejpam-3649	2	14	-	-	SYM
ejpam-3649	2	15	5543	5543	NUM
ejpam-3649	2	16	–	–	PUNCT
ejpam-3649	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3649	2	18	published	publish	VERB
ejpam-3649	2	19	by	by	ADP
ejpam-3649	2	20	new	new	PROPN
ejpam-3649	2	21	york	york	PROPN
ejpam-3649	2	22	business	business	PROPN
ejpam-3649	2	23	global	global	ADJ
ejpam-3649	2	24	on	on	ADP
ejpam-3649	2	25	generalized	generalized	ADJ
ejpam-3649	2	26	β	β	X
ejpam-3649	2	27	-	-	ADJ
ejpam-3649	2	28	open	open	ADJ
ejpam-3649	2	29	sets	set	NOUN
ejpam-3649	2	30	in	in	ADP
ejpam-3649	2	31	ideal	ideal	ADJ
ejpam-3649	2	32	bitopological	bitopological	ADJ
ejpam-3649	2	33	space	space	NOUN
ejpam-3649	2	34	ibtissam	ibtissam	NOUN
ejpam-3649	2	35	bukhatwa1,2,∗	bukhatwa1,2,∗	PROPN
ejpam-3649	2	36	,	,	PUNCT
ejpam-3649	2	37	sibel	sibel	PROPN
ejpam-3649	2	38	demiralp1	demiralp1	PROPN
ejpam-3649	2	39	1	1	NUM
ejpam-3649	2	40	department	department	NOUN
ejpam-3649	2	41	of	of	ADP
ejpam-3649	2	42	mathematics	mathematics	PROPN
ejpam-3649	2	43	,	,	PUNCT
ejpam-3649	2	44	university	university	PROPN
ejpam-3649	2	45	of	of	ADP
ejpam-3649	2	46	kastamonu	kastamonu	NOUN
ejpam-3649	2	47	,	,	PUNCT
ejpam-3649	2	48	kastamonu	kastamonu	NOUN
ejpam-3649	2	49	37150	37150	NUM
ejpam-3649	2	50	,	,	PUNCT
ejpam-3649	2	51	turkey	turkey	PROPN
ejpam-3649	2	52	2	2	NUM
ejpam-3649	2	53	department	department	NOUN
ejpam-3649	2	54	of	of	ADP
ejpam-3649	2	55	mathematics	mathematic	NOUN
ejpam-3649	2	56	,	,	PUNCT
ejpam-3649	2	57	university	university	NOUN
ejpam-3649	2	58	of	of	ADP
ejpam-3649	2	59	benghazi	benghazi	NOUN
ejpam-3649	2	60	,	,	PUNCT
ejpam-3649	2	61	benghazi	benghazi	NOUN
ejpam-3649	2	62	16063	16063	NUM
ejpam-3649	3	1	,	,	PUNCT
ejpam-3649	3	2	libya	libya	PROPN
ejpam-3649	3	3	abstract	abstract	NOUN
ejpam-3649	3	4	.	.	PUNCT
ejpam-3649	4	1	in	in	ADP
ejpam-3649	4	2	this	this	DET
ejpam-3649	4	3	article	article	NOUN
ejpam-3649	4	4	,	,	PUNCT
ejpam-3649	4	5	we	we	PRON
ejpam-3649	4	6	introduce	introduce	VERB
ejpam-3649	4	7	and	and	CCONJ
ejpam-3649	4	8	study	study	VERB
ejpam-3649	4	9	the	the	DET
ejpam-3649	4	10	concepts	concept	NOUN
ejpam-3649	4	11	of	of	ADP
ejpam-3649	4	12	γij	γij	NOUN
ejpam-3649	4	13	-	-	PUNCT
ejpam-3649	4	14	semi	semi	NOUN
ejpam-3649	4	15	-	-	ADJ
ejpam-3649	4	16	i	i	ADV
ejpam-3649	4	17	-	-	PUNCT
ejpam-3649	4	18	open	open	ADJ
ejpam-3649	4	19	sets	set	NOUN
ejpam-3649	4	20	and	and	CCONJ
ejpam-3649	4	21	γijβi	γijβi	NOUN
ejpam-3649	4	22	-	-	PUNCT
ejpam-3649	4	23	open	open	ADJ
ejpam-3649	4	24	sets	set	NOUN
ejpam-3649	4	25	by	by	ADP
ejpam-3649	4	26	generalizing	generalize	VERB
ejpam-3649	4	27	(	(	PUNCT
ejpam-3649	4	28	i	i	PROPN
ejpam-3649	4	29	,	,	PUNCT
ejpam-3649	4	30	j)-semi	j)-semi	PROPN
ejpam-3649	4	31	-	-	PUNCT
ejpam-3649	4	32	i	i	PRON
ejpam-3649	4	33	-	-	PUNCT
ejpam-3649	4	34	open	open	ADJ
ejpam-3649	4	35	sets	set	NOUN
ejpam-3649	4	36	and	and	CCONJ
ejpam-3649	4	37	(	(	PUNCT
ejpam-3649	4	38	ij)-βi	ij)-βi	NOUN
ejpam-3649	4	39	-	-	ADJ
ejpam-3649	4	40	open	open	ADJ
ejpam-3649	4	41	sets	set	NOUN
ejpam-3649	4	42	,	,	PUNCT
ejpam-3649	4	43	respectively	respectively	ADV
ejpam-3649	4	44	,	,	PUNCT
ejpam-3649	4	45	in	in	ADP
ejpam-3649	4	46	ideal	ideal	ADJ
ejpam-3649	4	47	bitopological	bitopological	ADJ
ejpam-3649	4	48	spaces	space	NOUN
ejpam-3649	4	49	with	with	ADP
ejpam-3649	4	50	an	an	DET
ejpam-3649	4	51	operation	operation	NOUN
ejpam-3649	4	52	γ	γ	X
ejpam-3649	4	53	:	:	PUNCT
ejpam-3649	4	54	τ	τ	PROPN
ejpam-3649	4	55	→	→	SYM
ejpam-3649	4	56	p	p	X
ejpam-3649	4	57	(	(	PUNCT
ejpam-3649	4	58	x	x	NOUN
ejpam-3649	4	59	)	)	PUNCT
ejpam-3649	4	60	.	.	PUNCT
ejpam-3649	5	1	further	far	ADV
ejpam-3649	5	2	,	,	PUNCT
ejpam-3649	5	3	we	we	PRON
ejpam-3649	5	4	describe	describe	VERB
ejpam-3649	5	5	and	and	CCONJ
ejpam-3649	5	6	study	study	VERB
ejpam-3649	5	7	(	(	PUNCT
ejpam-3649	5	8	γ	γ	X
ejpam-3649	5	9	,	,	PUNCT
ejpam-3649	5	10	δ)ij	δ)ij	PROPN
ejpam-3649	5	11	-	-	PUNCT
ejpam-3649	5	12	semii	semii	NOUN
ejpam-3649	5	13	-	-	PUNCT
ejpam-3649	5	14	continuous	continuous	ADJ
ejpam-3649	5	15	and	and	CCONJ
ejpam-3649	5	16	(	(	PUNCT
ejpam-3649	5	17	γ	γ	PROPN
ejpam-3649	5	18	,	,	PUNCT
ejpam-3649	5	19	δ)ij	δ)ij	PROPN
ejpam-3649	5	20	-	-	PUNCT
ejpam-3649	5	21	βi	βi	ADV
ejpam-3649	5	22	-	-	PUNCT
ejpam-3649	5	23	continuous	continuous	ADJ
ejpam-3649	5	24	functions	function	NOUN
ejpam-3649	5	25	in	in	ADP
ejpam-3649	5	26	ideal	ideal	ADJ
ejpam-3649	5	27	bitopological	bitopological	ADJ
ejpam-3649	5	28	spaces	space	NOUN
ejpam-3649	5	29	and	and	CCONJ
ejpam-3649	5	30	their	their	PRON
ejpam-3649	5	31	related	related	ADJ
ejpam-3649	5	32	notions	notion	NOUN
ejpam-3649	5	33	.	.	PUNCT
ejpam-3649	6	1	in	in	ADP
ejpam-3649	6	2	addition	addition	NOUN
ejpam-3649	6	3	,	,	PUNCT
ejpam-3649	6	4	various	various	ADJ
ejpam-3649	6	5	examples	example	NOUN
ejpam-3649	6	6	and	and	CCONJ
ejpam-3649	6	7	counterexamples	counterexample	NOUN
ejpam-3649	6	8	are	be	AUX
ejpam-3649	6	9	given	give	VERB
ejpam-3649	6	10	for	for	ADP
ejpam-3649	6	11	answers	answer	NOUN
ejpam-3649	6	12	to	to	ADP
ejpam-3649	6	13	some	some	DET
ejpam-3649	6	14	questions	question	NOUN
ejpam-3649	6	15	raised	raise	VERB
ejpam-3649	6	16	in	in	ADP
ejpam-3649	6	17	this	this	DET
ejpam-3649	6	18	study	study	NOUN
ejpam-3649	6	19	.	.	PUNCT
ejpam-3649	7	1	2020	2020	NUM
ejpam-3649	7	2	mathematics	mathematic	NOUN
ejpam-3649	7	3	subject	subject	NOUN
ejpam-3649	7	4	classifications	classification	NOUN
ejpam-3649	7	5	:	:	PUNCT
ejpam-3649	7	6	54a05	54a05	NUM
ejpam-3649	7	7	,	,	PUNCT
ejpam-3649	7	8	54a10	54a10	NUM
ejpam-3649	7	9	,	,	PUNCT
ejpam-3649	7	10	54c05	54c05	NUM
ejpam-3649	7	11	,	,	PUNCT
ejpam-3649	7	12	54e55	54e55	NUM
ejpam-3649	7	13	key	key	ADJ
ejpam-3649	7	14	words	word	NOUN
ejpam-3649	7	15	and	and	CCONJ
ejpam-3649	7	16	phrases	phrase	NOUN
ejpam-3649	7	17	:	:	PUNCT
ejpam-3649	7	18	ideal	ideal	ADJ
ejpam-3649	7	19	bitopological	bitopological	ADJ
ejpam-3649	7	20	space	space	NOUN
ejpam-3649	7	21	,	,	PUNCT
ejpam-3649	7	22	intγi(a	intγi(a	PROPN
ejpam-3649	7	23	)	)	PUNCT
ejpam-3649	7	24	,	,	PUNCT
ejpam-3649	7	25	clγi(a),γij	clγi(a),γij	NOUN
ejpam-3649	7	26	-	-	PUNCT
ejpam-3649	7	27	semi	semi	ADJ
ejpam-3649	7	28	-	-	ADJ
ejpam-3649	7	29	i	i	ADV
ejpam-3649	7	30	-	-	PUNCT
ejpam-3649	7	31	open	open	ADJ
ejpam-3649	7	32	sets	set	NOUN
ejpam-3649	7	33	,	,	PUNCT
ejpam-3649	7	34	γij	γij	NOUN
ejpam-3649	7	35	-	-	PUNCT
ejpam-3649	7	36	βi	βi	PRON
ejpam-3649	7	37	-	-	PUNCT
ejpam-3649	7	38	open	open	ADJ
ejpam-3649	7	39	sets	set	NOUN
ejpam-3649	7	40	,	,	PUNCT
ejpam-3649	7	41	(	(	PUNCT
ejpam-3649	7	42	γ	γ	X
ejpam-3649	7	43	,	,	PUNCT
ejpam-3649	7	44	δ)ij	δ)ij	PROPN
ejpam-3649	7	45	-	-	PUNCT
ejpam-3649	7	46	βi−continuous	βi−continuous	ADJ
ejpam-3649	7	47	functions	function	NOUN
ejpam-3649	7	48	.	.	PUNCT
ejpam-3649	8	1	1	1	X
ejpam-3649	8	2	.	.	X
ejpam-3649	8	3	introduction	introduction	NOUN
ejpam-3649	8	4	kelly	kelly	PROPN
ejpam-3649	9	1	[	[	X
ejpam-3649	9	2	11	11	NUM
ejpam-3649	9	3	]	]	PUNCT
ejpam-3649	9	4	in	in	ADP
ejpam-3649	9	5	1963	1963	NUM
ejpam-3649	9	6	,	,	PUNCT
ejpam-3649	9	7	introduced	introduce	VERB
ejpam-3649	9	8	the	the	DET
ejpam-3649	9	9	triple	triple	ADJ
ejpam-3649	9	10	(	(	PUNCT
ejpam-3649	9	11	x	x	NOUN
ejpam-3649	9	12	,	,	PUNCT
ejpam-3649	9	13	τ1	τ1	NOUN
ejpam-3649	9	14	,	,	PUNCT
ejpam-3649	9	15	τ2	τ2	NOUN
ejpam-3649	9	16	)	)	PUNCT
ejpam-3649	9	17	as	as	ADP
ejpam-3649	9	18	bitopological	bitopological	ADJ
ejpam-3649	9	19	space	space	NOUN
ejpam-3649	9	20	,	,	PUNCT
ejpam-3649	9	21	where	where	SCONJ
ejpam-3649	9	22	x	x	PRON
ejpam-3649	9	23	is	be	AUX
ejpam-3649	9	24	a	a	DET
ejpam-3649	9	25	nonempty	nonempty	ADJ
ejpam-3649	9	26	set	set	VERB
ejpam-3649	9	27	,	,	PUNCT
ejpam-3649	9	28	τ1	τ1	NOUN
ejpam-3649	9	29	and	and	CCONJ
ejpam-3649	9	30	τ2	τ2	NOUN
ejpam-3649	9	31	are	be	AUX
ejpam-3649	9	32	topologies	topology	NOUN
ejpam-3649	9	33	on	on	ADP
ejpam-3649	9	34	x.	x.	PROPN
ejpam-3649	9	35	levine	levine	PROPN
ejpam-3649	10	1	[	[	X
ejpam-3649	10	2	17	17	NUM
ejpam-3649	10	3	]	]	PUNCT
ejpam-3649	10	4	in	in	ADP
ejpam-3649	10	5	1963	1963	NUM
ejpam-3649	10	6	,	,	PUNCT
ejpam-3649	10	7	introduced	introduce	VERB
ejpam-3649	10	8	the	the	DET
ejpam-3649	10	9	notion	notion	NOUN
ejpam-3649	10	10	of	of	ADP
ejpam-3649	10	11	semi	semi	ADJ
ejpam-3649	10	12	-	-	ADJ
ejpam-3649	10	13	open	open	ADJ
ejpam-3649	10	14	sets	set	NOUN
ejpam-3649	10	15	in	in	ADP
ejpam-3649	10	16	bitopological	bitopological	ADJ
ejpam-3649	10	17	spaces	space	NOUN
ejpam-3649	10	18	.	.	PUNCT
ejpam-3649	11	1	khedr	khedr	PROPN
ejpam-3649	12	1	[	[	X
ejpam-3649	12	2	14	14	NUM
ejpam-3649	12	3	]	]	PUNCT
ejpam-3649	12	4	in	in	ADP
ejpam-3649	12	5	1992	1992	NUM
ejpam-3649	12	6	,	,	PUNCT
ejpam-3649	12	7	defined	define	VERB
ejpam-3649	12	8	semi	semi	ADJ
ejpam-3649	12	9	-	-	ADJ
ejpam-3649	12	10	preopen	preopen	ADJ
ejpam-3649	12	11	(	(	PUNCT
ejpam-3649	12	12	β	β	NOUN
ejpam-3649	12	13	-	-	PUNCT
ejpam-3649	12	14	open)sets	open)set	NOUN
ejpam-3649	12	15	in	in	ADP
ejpam-3649	12	16	bitopological	bitopological	ADJ
ejpam-3649	12	17	spaces	space	NOUN
ejpam-3649	12	18	.	.	PUNCT
ejpam-3649	13	1	k.	k.	PROPN
ejpam-3649	13	2	kuraowski	kuraowski	PROPN
ejpam-3649	13	3	[	[	X
ejpam-3649	13	4	15	15	NUM
ejpam-3649	13	5	]	]	PUNCT
ejpam-3649	13	6	in	in	ADP
ejpam-3649	13	7	1966	1966	NUM
ejpam-3649	13	8	,	,	PUNCT
ejpam-3649	13	9	studied	study	VERB
ejpam-3649	13	10	and	and	CCONJ
ejpam-3649	13	11	applied	apply	VERB
ejpam-3649	13	12	the	the	DET
ejpam-3649	13	13	concept	concept	NOUN
ejpam-3649	13	14	of	of	ADP
ejpam-3649	13	15	ideals	ideal	NOUN
ejpam-3649	13	16	on	on	ADP
ejpam-3649	13	17	topological	topological	ADJ
ejpam-3649	13	18	spaces	space	NOUN
ejpam-3649	13	19	.	.	PUNCT
ejpam-3649	14	1	an	an	DET
ejpam-3649	14	2	ideal	ideal	NOUN
ejpam-3649	14	3	i	i	PRON
ejpam-3649	14	4	on	on	ADP
ejpam-3649	14	5	a	a	DET
ejpam-3649	14	6	topological	topological	ADJ
ejpam-3649	14	7	space	space	NOUN
ejpam-3649	14	8	(	(	PUNCT
ejpam-3649	14	9	x	x	X
ejpam-3649	14	10	,	,	PUNCT
ejpam-3649	14	11	τ	τ	X
ejpam-3649	14	12	)	)	PUNCT
ejpam-3649	14	13	is	be	AUX
ejpam-3649	14	14	a	a	DET
ejpam-3649	14	15	collection	collection	NOUN
ejpam-3649	14	16	of	of	ADP
ejpam-3649	14	17	subsets	subset	NOUN
ejpam-3649	14	18	of	of	ADP
ejpam-3649	14	19	x	x	PUNCT
ejpam-3649	14	20	having	have	VERB
ejpam-3649	14	21	the	the	DET
ejpam-3649	14	22	heredity	heredity	NOUN
ejpam-3649	14	23	property	property	NOUN
ejpam-3649	14	24	(	(	PUNCT
ejpam-3649	14	25	i	i	NOUN
ejpam-3649	14	26	)	)	PUNCT
ejpam-3649	15	1	if	if	SCONJ
ejpam-3649	15	2	a	a	DET
ejpam-3649	15	3	∈	∈	X
ejpam-3649	15	4	i	i	PRON
ejpam-3649	15	5	and	and	CCONJ
ejpam-3649	15	6	b	b	PROPN
ejpam-3649	15	7	⊂	⊂	PROPN
ejpam-3649	15	8	a	a	PRON
ejpam-3649	15	9	then	then	ADV
ejpam-3649	15	10	b	b	X
ejpam-3649	15	11	∈	∈	PROPN
ejpam-3649	16	1	i	i	PRON
ejpam-3649	16	2	and	and	CCONJ
ejpam-3649	16	3	(	(	PUNCT
ejpam-3649	16	4	ii	ii	NOUN
ejpam-3649	16	5	)	)	PUNCT
ejpam-3649	16	6	if	if	SCONJ
ejpam-3649	16	7	a	a	DET
ejpam-3649	16	8	∈	∈	X
ejpam-3649	16	9	i	i	PRON
ejpam-3649	16	10	and	and	CCONJ
ejpam-3649	16	11	b	b	X
ejpam-3649	16	12	∈	∈	PROPN
ejpam-3649	16	13	i	i	PRON
ejpam-3649	16	14	then	then	ADV
ejpam-3649	16	15	a	a	DET
ejpam-3649	16	16	∪	∪	X
ejpam-3649	16	17	b	b	PROPN
ejpam-3649	16	18	∈	∈	PROPN
ejpam-3649	16	19	i.	i.	NOUN
ejpam-3649	16	20	ekici	ekici	PROPN
ejpam-3649	17	1	[	[	X
ejpam-3649	17	2	5	5	NUM
ejpam-3649	17	3	]	]	PUNCT
ejpam-3649	17	4	in	in	ADP
ejpam-3649	17	5	2012	2012	NUM
ejpam-3649	17	6	,	,	PUNCT
ejpam-3649	17	7	studied	study	VERB
ejpam-3649	17	8	the	the	DET
ejpam-3649	17	9	concept	concept	NOUN
ejpam-3649	17	10	of	of	ADP
ejpam-3649	17	11	semi	semi	ADJ
ejpam-3649	17	12	-	-	ADJ
ejpam-3649	17	13	i	i	ADV
ejpam-3649	17	14	-	-	PUNCT
ejpam-3649	17	15	open	open	ADJ
ejpam-3649	17	16	sets	set	NOUN
ejpam-3649	17	17	in	in	ADP
ejpam-3649	17	18	ideal	ideal	ADJ
ejpam-3649	17	19	topological	topological	ADJ
ejpam-3649	17	20	spaces	space	NOUN
ejpam-3649	17	21	.	.	PUNCT
ejpam-3649	18	1	if	if	SCONJ
ejpam-3649	18	2	i	i	PRON
ejpam-3649	18	3	is	be	AUX
ejpam-3649	18	4	an	an	DET
ejpam-3649	18	5	ideal	ideal	NOUN
ejpam-3649	18	6	on	on	ADP
ejpam-3649	18	7	x	x	SYM
ejpam-3649	18	8	then	then	ADV
ejpam-3649	18	9	(	(	PUNCT
ejpam-3649	18	10	x	x	NOUN
ejpam-3649	18	11	,	,	PUNCT
ejpam-3649	18	12	τ1	τ1	NOUN
ejpam-3649	18	13	,	,	PUNCT
ejpam-3649	18	14	τ2	τ2	PROPN
ejpam-3649	18	15	,	,	PUNCT
ejpam-3649	18	16	i	i	PRON
ejpam-3649	18	17	)	)	PUNCT
ejpam-3649	18	18	is	be	AUX
ejpam-3649	18	19	called	call	VERB
ejpam-3649	18	20	an	an	DET
ejpam-3649	18	21	ideal	ideal	ADJ
ejpam-3649	18	22	bitopological	bitopological	ADJ
ejpam-3649	18	23	space	space	NOUN
ejpam-3649	18	24	.	.	PUNCT
ejpam-3649	18	25	kasahara.s	kasahara.s	PUNCT
ejpam-3649	19	1	[	[	X
ejpam-3649	19	2	10	10	NUM
ejpam-3649	19	3	]	]	PUNCT
ejpam-3649	19	4	in	in	ADP
ejpam-3649	19	5	1979	1979	NUM
ejpam-3649	19	6	described	describe	VERB
ejpam-3649	19	7	an	an	DET
ejpam-3649	19	8	operation	operation	NOUN
ejpam-3649	19	9	γ	γ	NOUN
ejpam-3649	19	10	on	on	ADP
ejpam-3649	19	11	τ	τ	PROPN
ejpam-3649	19	12	as	as	ADP
ejpam-3649	19	13	a	a	DET
ejpam-3649	19	14	mapping	mapping	NOUN
ejpam-3649	19	15	γ	γ	X
ejpam-3649	19	16	:	:	PUNCT
ejpam-3649	19	17	τ	τ	PROPN
ejpam-3649	19	18	→	→	SYM
ejpam-3649	19	19	p	p	X
ejpam-3649	19	20	(	(	PUNCT
ejpam-3649	19	21	x	x	X
ejpam-3649	19	22	)	)	PUNCT
ejpam-3649	19	23	such	such	ADJ
ejpam-3649	19	24	that	that	SCONJ
ejpam-3649	19	25	u	u	NOUN
ejpam-3649	19	26	⊆	⊆	NUM
ejpam-3649	19	27	uγ	uγ	ADV
ejpam-3649	19	28	,	,	PUNCT
ejpam-3649	19	29	for	for	ADP
ejpam-3649	19	30	each	each	DET
ejpam-3649	19	31	u	u	PROPN
ejpam-3649	19	32	∈	∈	PROPN
ejpam-3649	19	33	τ	τ	X
ejpam-3649	19	34	.	.	PUNCT
ejpam-3649	20	1	khedr	khedr	PROPN
ejpam-3649	21	1	[	[	X
ejpam-3649	21	2	12	12	NUM
ejpam-3649	21	3	]	]	PUNCT
ejpam-3649	21	4	in	in	ADP
ejpam-3649	21	5	1984	1984	NUM
ejpam-3649	21	6	,	,	PUNCT
ejpam-3649	21	7	extended	extend	VERB
ejpam-3649	21	8	the	the	DET
ejpam-3649	21	9	operation	operation	NOUN
ejpam-3649	21	10	γ	γ	NOUN
ejpam-3649	21	11	to	to	ADP
ejpam-3649	21	12	bitopological	bitopological	ADJ
ejpam-3649	21	13	space	space	NOUN
ejpam-3649	21	14	as	as	ADP
ejpam-3649	21	15	a	a	DET
ejpam-3649	21	16	mapping	mapping	NOUN
ejpam-3649	21	17	γ	γ	NOUN
ejpam-3649	21	18	:	:	PUNCT
ejpam-3649	21	19	τ1∪τ2	τ1∪τ2	X
ejpam-3649	21	20	→	→	X
ejpam-3649	21	21	p	p	X
ejpam-3649	21	22	(	(	PUNCT
ejpam-3649	21	23	x	x	NOUN
ejpam-3649	21	24	)	)	PUNCT
ejpam-3649	21	25	such	such	ADJ
ejpam-3649	21	26	that	that	PRON
ejpam-3649	21	27	for	for	ADP
ejpam-3649	21	28	each	each	DET
ejpam-3649	21	29	u	u	PROPN
ejpam-3649	21	30	∈	∈	PROPN
ejpam-3649	21	31	τ1	τ1	NOUN
ejpam-3649	21	32	∪	∪	X
ejpam-3649	21	33	τ2	τ2	PROPN
ejpam-3649	21	34	,	,	PUNCT
ejpam-3649	21	35	where	where	SCONJ
ejpam-3649	21	36	uγ	uγ	ADP
ejpam-3649	21	37	denotes	denote	VERB
ejpam-3649	21	38	the	the	DET
ejpam-3649	21	39	value	value	NOUN
ejpam-3649	21	40	of	of	ADP
ejpam-3649	21	41	γ	γ	NOUN
ejpam-3649	21	42	at	at	ADP
ejpam-3649	21	43	u	u	PROPN
ejpam-3649	21	44	.	.	PUNCT
ejpam-3649	22	1	for	for	ADP
ejpam-3649	22	2	example	example	NOUN
ejpam-3649	22	3	the	the	DET
ejpam-3649	22	4	operations	operation	NOUN
ejpam-3649	22	5	uγ	uγ	ADP
ejpam-3649	22	6	=	=	SYM
ejpam-3649	22	7	u	u	PROPN
ejpam-3649	22	8	,	,	PUNCT
ejpam-3649	22	9	uγ	uγ	PROPN
ejpam-3649	22	10	=	=	PUNCT
ejpam-3649	22	11	cli(u	cli(u	PROPN
ejpam-3649	22	12	)	)	PUNCT
ejpam-3649	22	13	,	,	PUNCT
ejpam-3649	22	14	uγ	uγ	ADP
ejpam-3649	22	15	=	=	PUNCT
ejpam-3649	22	16	intj(cli(u	intj(cli(u	NOUN
ejpam-3649	22	17	)	)	PUNCT
ejpam-3649	22	18	)	)	PUNCT
ejpam-3649	22	19	for	for	ADP
ejpam-3649	22	20	u	u	PROPN
ejpam-3649	22	21	∈	∈	PROPN
ejpam-3649	22	22	τj	τj	ADP
ejpam-3649	22	23	are	be	AUX
ejpam-3649	22	24	operations	operation	NOUN
ejpam-3649	22	25	on	on	ADP
ejpam-3649	22	26	τ1	τ1	NOUN
ejpam-3649	22	27	∪	∪	X
ejpam-3649	22	28	τ2	τ2	PROPN
ejpam-3649	22	29	.	.	PUNCT
ejpam-3649	23	1	caldas	caldas	PROPN
ejpam-3649	24	1	[	[	X
ejpam-3649	24	2	3	3	X
ejpam-3649	24	3	]	]	PUNCT
ejpam-3649	24	4	in	in	ADP
ejpam-3649	24	5	2013	2013	NUM
ejpam-3649	24	6	,	,	PUNCT
ejpam-3649	24	7	introduced	introduce	VERB
ejpam-3649	24	8	the	the	DET
ejpam-3649	24	9	notion	notion	NOUN
ejpam-3649	24	10	of	of	ADP
ejpam-3649	24	11	β	β	ADJ
ejpam-3649	24	12	-	-	ADJ
ejpam-3649	24	13	open	open	ADJ
ejpam-3649	24	14	sets	set	NOUN
ejpam-3649	24	15	in	in	ADP
ejpam-3649	24	16	ideal	ideal	ADJ
ejpam-3649	24	17	bitopological	bitopological	ADJ
ejpam-3649	24	18	spaces	space	NOUN
ejpam-3649	24	19	.	.	PUNCT
ejpam-3649	25	1	csaszar	csaszar	PROPN
ejpam-3649	26	1	[	[	X
ejpam-3649	26	2	4	4	X
ejpam-3649	26	3	]	]	PUNCT
ejpam-3649	26	4	in	in	ADP
ejpam-3649	26	5	1997	1997	NUM
ejpam-3649	26	6	,	,	PUNCT
ejpam-3649	26	7	defined	define	VERB
ejpam-3649	26	8	generalized	generalized	ADJ
ejpam-3649	26	9	open	open	ADJ
ejpam-3649	26	10	sets	set	NOUN
ejpam-3649	26	11	in	in	ADP
ejpam-3649	26	12	generalized	generalized	ADJ
ejpam-3649	26	13	topological	topological	ADJ
ejpam-3649	26	14	spaces	space	NOUN
ejpam-3649	26	15	.	.	PUNCT
ejpam-3649	27	1	∗corresponding	∗corresponde	VERB
ejpam-3649	27	2	author	author	NOUN
ejpam-3649	27	3	.	.	PUNCT
ejpam-3649	28	1	doi	doi	NOUN
ejpam-3649	28	2	:	:	PUNCT
ejpam-3649	28	3	https://doi.org/10.29020/nybg.ejpam.v13i2.3649	https://doi.org/10.29020/nybg.ejpam.v13i2.3649	VERB
ejpam-3649	28	4	email	email	NOUN
ejpam-3649	28	5	addresses	address	NOUN
ejpam-3649	28	6	:	:	PUNCT
ejpam-3649	28	7	i.bukhatwa@gmail.com	i.bukhatwa@gmail.com	PROPN
ejpam-3649	28	8	(	(	PUNCT
ejpam-3649	28	9	i.	i.	PROPN
ejpam-3649	28	10	bukhatwa	bukhatwa	PROPN
ejpam-3649	28	11	)	)	PUNCT
ejpam-3649	28	12	,	,	PUNCT
ejpam-3649	28	13	sdemiralp@kastamonu.edu.tr	sdemiralp@kastamonu.edu.tr	INTJ
ejpam-3649	28	14	(	(	PUNCT
ejpam-3649	28	15	s.	s.	PROPN
ejpam-3649	28	16	demiralp	demiralp	PROPN
ejpam-3649	28	17	)	)	PUNCT
ejpam-3649	28	18	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3649	29	1	269	269	NUM
ejpam-3649	29	2	c	c	NOUN
ejpam-3649	29	3	©	©	NOUN
ejpam-3649	29	4	2020	2020	NUM
ejpam-3649	29	5	ejpam	ejpam	VERB
ejpam-3649	29	6	all	all	DET
ejpam-3649	29	7	rights	right	NOUN
ejpam-3649	29	8	reserved	reserve	VERB
ejpam-3649	29	9	.	.	PUNCT
ejpam-3649	30	1	i.	i.	PROPN
ejpam-3649	30	2	bukhatwa	bukhatwa	PROPN
ejpam-3649	30	3	,	,	PUNCT
ejpam-3649	30	4	s.	s.	PROPN
ejpam-3649	30	5	demiralp	demiralp	PROPN
ejpam-3649	30	6	/	/	SYM
ejpam-3649	30	7	eur	eur	PROPN
ejpam-3649	30	8	.	.	PUNCT
ejpam-3649	31	1	j.	j.	PROPN
ejpam-3649	31	2	pure	pure	PROPN
ejpam-3649	31	3	appl	appl	PROPN
ejpam-3649	31	4	.	.	PROPN
ejpam-3649	31	5	math	math	PROPN
ejpam-3649	31	6	,	,	PUNCT
ejpam-3649	31	7	13	13	NUM
ejpam-3649	31	8	(	(	PUNCT
ejpam-3649	31	9	2	2	NUM
ejpam-3649	31	10	)	)	PUNCT
ejpam-3649	31	11	(	(	PUNCT
ejpam-3649	31	12	2020	2020	NUM
ejpam-3649	31	13	)	)	PUNCT
ejpam-3649	31	14	,	,	PUNCT
ejpam-3649	31	15	269	269	NUM
ejpam-3649	31	16	-	-	SYM
ejpam-3649	31	17	279	279	NUM
ejpam-3649	31	18	270	270	NUM
ejpam-3649	31	19	2	2	NUM
ejpam-3649	31	20	.	.	PUNCT
ejpam-3649	31	21	preliminaries	preliminary	NOUN
ejpam-3649	31	22	throughout	throughout	ADP
ejpam-3649	31	23	the	the	DET
ejpam-3649	31	24	paper	paper	NOUN
ejpam-3649	31	25	,	,	PUNCT
ejpam-3649	31	26	(	(	PUNCT
ejpam-3649	31	27	x	x	NOUN
ejpam-3649	31	28	,	,	PUNCT
ejpam-3649	31	29	τ1	τ1	NOUN
ejpam-3649	31	30	,	,	PUNCT
ejpam-3649	31	31	τ2	τ2	NOUN
ejpam-3649	31	32	)	)	PUNCT
ejpam-3649	31	33	always	always	ADV
ejpam-3649	31	34	mean	mean	VERB
ejpam-3649	31	35	bitopological	bitopological	ADJ
ejpam-3649	31	36	space	space	NOUN
ejpam-3649	31	37	on	on	ADP
ejpam-3649	31	38	with	with	ADP
ejpam-3649	31	39	no	no	DET
ejpam-3649	31	40	separation	separation	NOUN
ejpam-3649	31	41	axioms	axiom	NOUN
ejpam-3649	31	42	are	be	AUX
ejpam-3649	31	43	supposed	suppose	VERB
ejpam-3649	31	44	in	in	ADP
ejpam-3649	31	45	this	this	DET
ejpam-3649	31	46	space	space	NOUN
ejpam-3649	31	47	,	,	PUNCT
ejpam-3649	31	48	also	also	ADV
ejpam-3649	31	49	(	(	PUNCT
ejpam-3649	31	50	x	x	NOUN
ejpam-3649	31	51	,	,	PUNCT
ejpam-3649	31	52	τ1	τ1	NOUN
ejpam-3649	31	53	,	,	PUNCT
ejpam-3649	31	54	τ2	τ2	PROPN
ejpam-3649	31	55	,	,	PUNCT
ejpam-3649	31	56	i	i	PRON
ejpam-3649	31	57	)	)	PUNCT
ejpam-3649	31	58	be	be	VERB
ejpam-3649	31	59	an	an	DET
ejpam-3649	31	60	ideal	ideal	ADJ
ejpam-3649	31	61	bitopological	bitopological	ADJ
ejpam-3649	31	62	space	space	NOUN
ejpam-3649	31	63	.	.	PUNCT
ejpam-3649	32	1	let	let	VERB
ejpam-3649	32	2	a	a	DET
ejpam-3649	32	3	be	be	AUX
ejpam-3649	32	4	a	a	DET
ejpam-3649	32	5	subset	subset	NOUN
ejpam-3649	32	6	of	of	ADP
ejpam-3649	32	7	x	x	PRON
ejpam-3649	32	8	,	,	PUNCT
ejpam-3649	32	9	by	by	ADP
ejpam-3649	32	10	inti(a	inti(a	NOUN
ejpam-3649	32	11	)	)	PUNCT
ejpam-3649	33	1	[	[	X
ejpam-3649	33	2	10	10	NUM
ejpam-3649	33	3	]	]	PUNCT
ejpam-3649	33	4	and	and	CCONJ
ejpam-3649	33	5	cli(a	cli(a	PROPN
ejpam-3649	33	6	)	)	PUNCT
ejpam-3649	34	1	[	[	X
ejpam-3649	34	2	20	20	NUM
ejpam-3649	34	3	]	]	PUNCT
ejpam-3649	34	4	we	we	PRON
ejpam-3649	34	5	denote	denote	VERB
ejpam-3649	34	6	respectively	respectively	ADV
ejpam-3649	34	7	the	the	DET
ejpam-3649	34	8	interior	interior	ADJ
ejpam-3649	34	9	and	and	CCONJ
ejpam-3649	34	10	closure	closure	NOUN
ejpam-3649	34	11	of	of	ADP
ejpam-3649	34	12	a	a	PRON
ejpam-3649	34	13	with	with	ADP
ejpam-3649	34	14	regard	regard	NOUN
ejpam-3649	34	15	to	to	AUX
ejpam-3649	34	16	τi	τi	VERB
ejpam-3649	34	17	for	for	ADP
ejpam-3649	34	18	i	i	PROPN
ejpam-3649	34	19	=	=	SYM
ejpam-3649	34	20	1	1	NUM
ejpam-3649	34	21	,	,	PUNCT
ejpam-3649	34	22	2	2	NUM
ejpam-3649	34	23	.	.	X
ejpam-3649	34	24	a	a	DET
ejpam-3649	34	25	subset	subset	NOUN
ejpam-3649	34	26	a	a	PRON
ejpam-3649	34	27	of	of	ADP
ejpam-3649	34	28	a	a	DET
ejpam-3649	34	29	bitopological	bitopological	ADJ
ejpam-3649	34	30	space	space	NOUN
ejpam-3649	34	31	will	will	AUX
ejpam-3649	34	32	be	be	AUX
ejpam-3649	34	33	called	call	VERB
ejpam-3649	34	34	a	a	DET
ejpam-3649	34	35	γi	γi	NOUN
ejpam-3649	34	36	-	-	PUNCT
ejpam-3649	34	37	open	open	ADJ
ejpam-3649	34	38	set	set	NOUN
ejpam-3649	34	39	if	if	SCONJ
ejpam-3649	34	40	for	for	ADP
ejpam-3649	34	41	each	each	DET
ejpam-3649	34	42	x	x	SYM
ejpam-3649	34	43	∈	∈	PROPN
ejpam-3649	34	44	a	a	PRON
ejpam-3649	34	45	,	,	PUNCT
ejpam-3649	34	46	there	there	PRON
ejpam-3649	34	47	exists	exist	VERB
ejpam-3649	34	48	an	an	DET
ejpam-3649	34	49	τi	τi	NOUN
ejpam-3649	34	50	-	-	PUNCT
ejpam-3649	34	51	open	open	ADJ
ejpam-3649	34	52	set	set	NOUN
ejpam-3649	34	53	u	u	PRON
ejpam-3649	34	54	such	such	ADJ
ejpam-3649	34	55	that	that	SCONJ
ejpam-3649	34	56	x	x	SYM
ejpam-3649	34	57	∈	∈	PROPN
ejpam-3649	34	58	u	u	NOUN
ejpam-3649	34	59	and	and	CCONJ
ejpam-3649	34	60	uγ	uγ	ADV
ejpam-3649	34	61	⊆	⊆	NUM
ejpam-3649	34	62	a.	a.	NOUN
ejpam-3649	34	63	let	let	VERB
ejpam-3649	34	64	τγi	τγi	NOUN
ejpam-3649	34	65	denotes	denote	VERB
ejpam-3649	34	66	the	the	DET
ejpam-3649	34	67	set	set	NOUN
ejpam-3649	34	68	of	of	ADP
ejpam-3649	34	69	all	all	DET
ejpam-3649	34	70	γi	γi	NOUN
ejpam-3649	34	71	-	-	PUNCT
ejpam-3649	34	72	open	open	ADJ
ejpam-3649	34	73	set	set	NOUN
ejpam-3649	34	74	in	in	ADP
ejpam-3649	34	75	x.	x.	NOUN
ejpam-3649	34	76	obviously	obviously	ADV
ejpam-3649	34	77	,	,	PUNCT
ejpam-3649	34	78	we	we	PRON
ejpam-3649	34	79	have	have	AUX
ejpam-3649	34	80	τγi	τγi	VERB
ejpam-3649	35	1	⊆	⊆	NUM
ejpam-3649	35	2	τi	τi	NOUN
ejpam-3649	36	1	[	[	X
ejpam-3649	36	2	13	13	NUM
ejpam-3649	36	3	]	]	PUNCT
ejpam-3649	36	4	.	.	PUNCT
ejpam-3649	37	1	complement	complement	NOUN
ejpam-3649	37	2	of	of	ADP
ejpam-3649	37	3	all	all	DET
ejpam-3649	37	4	γi	γi	ADJ
ejpam-3649	37	5	-	-	PUNCT
ejpam-3649	37	6	open	open	ADJ
ejpam-3649	37	7	sets	set	NOUN
ejpam-3649	37	8	are	be	AUX
ejpam-3649	37	9	called	call	VERB
ejpam-3649	37	10	γi	γi	ADV
ejpam-3649	37	11	-	-	PUNCT
ejpam-3649	37	12	closed	closed	ADJ
ejpam-3649	37	13	.	.	PUNCT
ejpam-3649	38	1	assumed	assume	VERB
ejpam-3649	38	2	(	(	PUNCT
ejpam-3649	38	3	x	x	NOUN
ejpam-3649	38	4	,	,	PUNCT
ejpam-3649	38	5	τ1	τ1	NOUN
ejpam-3649	38	6	,	,	PUNCT
ejpam-3649	38	7	τ2	τ2	PROPN
ejpam-3649	38	8	,	,	PUNCT
ejpam-3649	38	9	i	i	PROPN
ejpam-3649	38	10	)	)	PUNCT
ejpam-3649	38	11	as	as	ADP
ejpam-3649	38	12	an	an	DET
ejpam-3649	38	13	ideal	ideal	ADJ
ejpam-3649	38	14	bitopological	bitopological	ADJ
ejpam-3649	38	15	space	space	NOUN
ejpam-3649	38	16	and	and	CCONJ
ejpam-3649	38	17	if	if	SCONJ
ejpam-3649	38	18	p	p	X
ejpam-3649	38	19	(	(	PUNCT
ejpam-3649	38	20	x	x	X
ejpam-3649	38	21	)	)	PUNCT
ejpam-3649	38	22	is	be	AUX
ejpam-3649	38	23	the	the	DET
ejpam-3649	38	24	set	set	NOUN
ejpam-3649	38	25	of	of	ADP
ejpam-3649	38	26	all	all	DET
ejpam-3649	38	27	subsets	subset	NOUN
ejpam-3649	38	28	of	of	ADP
ejpam-3649	38	29	x	x	PRON
ejpam-3649	38	30	,	,	PUNCT
ejpam-3649	38	31	a	a	DET
ejpam-3649	38	32	set	set	NOUN
ejpam-3649	38	33	operator	operator	NOUN
ejpam-3649	38	34	(	(	PUNCT
ejpam-3649	38	35	·	·	PUNCT
ejpam-3649	38	36	)	)	PUNCT
ejpam-3649	38	37	∗i	∗i	PROPN
ejpam-3649	38	38	:	:	PUNCT
ejpam-3649	38	39	p	p	X
ejpam-3649	38	40	(	(	PUNCT
ejpam-3649	38	41	x)→	x)→	PROPN
ejpam-3649	38	42	p	p	X
ejpam-3649	38	43	(	(	PUNCT
ejpam-3649	38	44	x	x	X
ejpam-3649	38	45	)	)	PUNCT
ejpam-3649	38	46	named	name	VERB
ejpam-3649	38	47	the	the	DET
ejpam-3649	38	48	local	local	ADJ
ejpam-3649	38	49	function	function	NOUN
ejpam-3649	38	50	of	of	ADP
ejpam-3649	38	51	a	a	DET
ejpam-3649	38	52	[	[	X
ejpam-3649	38	53	22	22	NUM
ejpam-3649	38	54	]	]	PUNCT
ejpam-3649	38	55	with	with	ADP
ejpam-3649	38	56	regard	regard	NOUN
ejpam-3649	38	57	to	to	ADP
ejpam-3649	38	58	τi	τi	VERB
ejpam-3649	38	59	and	and	CCONJ
ejpam-3649	38	60	τ	τ	PROPN
ejpam-3649	38	61	.	.	PUNCT
ejpam-3649	39	1	the	the	DET
ejpam-3649	39	2	definition	definition	NOUN
ejpam-3649	39	3	of	of	ADP
ejpam-3649	39	4	local	local	ADJ
ejpam-3649	39	5	function	function	NOUN
ejpam-3649	39	6	is	be	AUX
ejpam-3649	39	7	given	give	VERB
ejpam-3649	39	8	as	as	ADP
ejpam-3649	39	9	:	:	PUNCT
ejpam-3649	39	10	for	for	ADP
ejpam-3649	39	11	a	a	DET
ejpam-3649	39	12	⊂	⊂	PROPN
ejpam-3649	39	13	x	x	NOUN
ejpam-3649	39	14	,	,	PUNCT
ejpam-3649	39	15	a∗i	a∗i	X
ejpam-3649	39	16	(	(	PUNCT
ejpam-3649	39	17	τi	τi	ADP
ejpam-3649	39	18	,	,	PUNCT
ejpam-3649	39	19	i	i	NOUN
ejpam-3649	39	20	)	)	PUNCT
ejpam-3649	39	21	=	=	PRON
ejpam-3649	40	1	{	{	PUNCT
ejpam-3649	40	2	x	x	SYM
ejpam-3649	40	3	∈	∈	PROPN
ejpam-3649	40	4	x|u	x|u	PUNCT
ejpam-3649	40	5	∩	∩	PROPN
ejpam-3649	40	6	a	a	X
ejpam-3649	40	7	/∈	/∈	PUNCT
ejpam-3649	41	1	i	i	PRON
ejpam-3649	41	2	,	,	PUNCT
ejpam-3649	41	3	for	for	ADP
ejpam-3649	41	4	all	all	DET
ejpam-3649	41	5	u	u	PROPN
ejpam-3649	41	6	∈	∈	PROPN
ejpam-3649	41	7	τi(x	τi(x	NUM
ejpam-3649	41	8	)	)	PUNCT
ejpam-3649	41	9	}	}	PUNCT
ejpam-3649	42	1	where	where	SCONJ
ejpam-3649	42	2	,	,	PUNCT
ejpam-3649	42	3	τi(x	τi(x	NUM
ejpam-3649	42	4	)	)	PUNCT
ejpam-3649	42	5	=	=	PRON
ejpam-3649	42	6	{	{	PUNCT
ejpam-3649	42	7	u	u	NOUN
ejpam-3649	42	8	∈	∈	PROPN
ejpam-3649	42	9	τi|x	τi|x	NOUN
ejpam-3649	42	10	∈	∈	NOUN
ejpam-3649	42	11	u	u	NOUN
ejpam-3649	42	12	}	}	PUNCT
ejpam-3649	42	13	.	.	PUNCT
ejpam-3649	43	1	observe	observe	VERB
ejpam-3649	43	2	additionally	additionally	ADV
ejpam-3649	43	3	that	that	SCONJ
ejpam-3649	43	4	closure	closure	NOUN
ejpam-3649	43	5	operator	operator	NOUN
ejpam-3649	43	6	for	for	ADP
ejpam-3649	43	7	τ∗i	τ∗i	PUNCT
ejpam-3649	43	8	(	(	PUNCT
ejpam-3649	43	9	i	i	NOUN
ejpam-3649	43	10	)	)	PUNCT
ejpam-3649	43	11	accurate	accurate	ADJ
ejpam-3649	43	12	than	than	ADP
ejpam-3649	43	13	τi	τi	NUM
ejpam-3649	43	14	is	be	AUX
ejpam-3649	43	15	defined	define	VERB
ejpam-3649	43	16	by	by	ADP
ejpam-3649	43	17	cl∗i	cl∗i	PROPN
ejpam-3649	43	18	(	(	PUNCT
ejpam-3649	43	19	a	a	X
ejpam-3649	43	20	)	)	PUNCT
ejpam-3649	43	21	=	=	NOUN
ejpam-3649	43	22	a∪a∗i	a∪a∗i	NOUN
ejpam-3649	43	23	.	.	PUNCT
ejpam-3649	44	1	the	the	DET
ejpam-3649	44	2	interior	interior	NOUN
ejpam-3649	44	3	of	of	ADP
ejpam-3649	44	4	a	a	PRON
ejpam-3649	44	5	in	in	ADP
ejpam-3649	44	6	τ∗i	τ∗i	PUNCT
ejpam-3649	44	7	(	(	PUNCT
ejpam-3649	44	8	i	i	NOUN
ejpam-3649	44	9	)	)	PUNCT
ejpam-3649	44	10	is	be	AUX
ejpam-3649	44	11	denoted	denote	VERB
ejpam-3649	44	12	by	by	ADP
ejpam-3649	44	13	int∗i	int∗i	PROPN
ejpam-3649	44	14	(	(	PUNCT
ejpam-3649	44	15	a	a	NOUN
ejpam-3649	44	16	)	)	PUNCT
ejpam-3649	44	17	and	and	CCONJ
ejpam-3649	44	18	int∗γi(a	int∗γi(a	PROPN
ejpam-3649	44	19	∗	∗	NOUN
ejpam-3649	44	20	i	i	PRON
ejpam-3649	44	21	)	)	PUNCT
ejpam-3649	44	22	denotes	denote	VERB
ejpam-3649	44	23	the	the	DET
ejpam-3649	44	24	interior	interior	NOUN
ejpam-3649	44	25	of	of	ADP
ejpam-3649	44	26	a∗i	a∗i	NUM
ejpam-3649	44	27	with	with	ADP
ejpam-3649	44	28	respect	respect	NOUN
ejpam-3649	44	29	to	to	ADP
ejpam-3649	44	30	topology	topology	NOUN
ejpam-3649	44	31	τi	τi	NOUN
ejpam-3649	44	32	,	,	PUNCT
ejpam-3649	44	33	where	where	SCONJ
ejpam-3649	44	34	a∗i	a∗i	PRON
ejpam-3649	44	35	=	=	SYM
ejpam-3649	44	36	{	{	PUNCT
ejpam-3649	44	37	x	x	PROPN
ejpam-3649	44	38	∈	∈	PROPN
ejpam-3649	44	39	x|u	x|u	PUNCT
ejpam-3649	45	1	∩	∩	PROPN
ejpam-3649	45	2	a	a	X
ejpam-3649	45	3	/∈	/∈	PUNCT
ejpam-3649	45	4	i	i	NOUN
ejpam-3649	45	5	}	}	PUNCT
ejpam-3649	45	6	,	,	PUNCT
ejpam-3649	45	7	for	for	ADP
ejpam-3649	45	8	every	every	DET
ejpam-3649	45	9	u	u	PROPN
ejpam-3649	45	10	∈	∈	PROPN
ejpam-3649	45	11	τi	τi	NOUN
ejpam-3649	45	12	.	.	PUNCT
ejpam-3649	46	1	the	the	DET
ejpam-3649	46	2	interiorγi	interiorγi	NOUN
ejpam-3649	46	3	of	of	ADP
ejpam-3649	46	4	a	a	PRON
ejpam-3649	46	5	is	be	AUX
ejpam-3649	46	6	denoted	denote	VERB
ejpam-3649	46	7	by	by	ADP
ejpam-3649	46	8	intγi(a	intγi(a	PROPN
ejpam-3649	46	9	)	)	PUNCT
ejpam-3649	46	10	and	and	CCONJ
ejpam-3649	46	11	described	describe	VERB
ejpam-3649	46	12	to	to	PART
ejpam-3649	46	13	be	be	AUX
ejpam-3649	46	14	the	the	DET
ejpam-3649	46	15	union	union	NOUN
ejpam-3649	46	16	of	of	ADP
ejpam-3649	46	17	all	all	DET
ejpam-3649	46	18	γi	γi	ADJ
ejpam-3649	46	19	-	-	PUNCT
ejpam-3649	46	20	open	open	ADJ
ejpam-3649	46	21	sets	set	NOUN
ejpam-3649	46	22	of	of	ADP
ejpam-3649	46	23	x	x	PUNCT
ejpam-3649	46	24	contained	contain	VERB
ejpam-3649	46	25	in	in	ADP
ejpam-3649	46	26	a.	a.	NOUN
ejpam-3649	46	27	the	the	DET
ejpam-3649	46	28	closureγi	closureγi	NOUN
ejpam-3649	46	29	of	of	ADP
ejpam-3649	46	30	a	a	PRON
ejpam-3649	46	31	is	be	AUX
ejpam-3649	46	32	denoted	denote	VERB
ejpam-3649	46	33	by	by	ADP
ejpam-3649	46	34	clγi(a	clγi(a	PROPN
ejpam-3649	46	35	)	)	PUNCT
ejpam-3649	46	36	and	and	CCONJ
ejpam-3649	46	37	defined	define	VERB
ejpam-3649	46	38	to	to	PART
ejpam-3649	46	39	be	be	AUX
ejpam-3649	46	40	the	the	DET
ejpam-3649	46	41	intersection	intersection	NOUN
ejpam-3649	46	42	of	of	ADP
ejpam-3649	46	43	all	all	DET
ejpam-3649	46	44	γi	γi	ADJ
ejpam-3649	46	45	-	-	PUNCT
ejpam-3649	46	46	closed	closed	ADJ
ejpam-3649	46	47	sets	set	NOUN
ejpam-3649	46	48	containing	contain	VERB
ejpam-3649	46	49	a.	a.	NOUN
ejpam-3649	46	50	currently	currently	ADV
ejpam-3649	46	51	,	,	PUNCT
ejpam-3649	46	52	several	several	ADJ
ejpam-3649	46	53	results	result	NOUN
ejpam-3649	46	54	and	and	CCONJ
ejpam-3649	46	55	definitions	definition	NOUN
ejpam-3649	46	56	from	from	ADP
ejpam-3649	46	57	[	[	X
ejpam-3649	46	58	2	2	NUM
ejpam-3649	46	59	,	,	PUNCT
ejpam-3649	46	60	3	3	NUM
ejpam-3649	46	61	,	,	PUNCT
ejpam-3649	46	62	7	7	NUM
ejpam-3649	46	63	,	,	PUNCT
ejpam-3649	46	64	13	13	NUM
ejpam-3649	46	65	,	,	PUNCT
ejpam-3649	46	66	17	17	NUM
ejpam-3649	46	67	]	]	PUNCT
ejpam-3649	46	68	are	be	AUX
ejpam-3649	46	69	recalled	recall	VERB
ejpam-3649	46	70	to	to	PART
ejpam-3649	46	71	be	be	AUX
ejpam-3649	46	72	used	use	VERB
ejpam-3649	46	73	in	in	ADP
ejpam-3649	46	74	this	this	DET
ejpam-3649	46	75	article	article	NOUN
ejpam-3649	46	76	.	.	PUNCT
ejpam-3649	47	1	definition	definition	NOUN
ejpam-3649	47	2	1	1	NUM
ejpam-3649	47	3	.	.	PUNCT
ejpam-3649	48	1	[	[	X
ejpam-3649	48	2	8	8	NUM
ejpam-3649	48	3	]	]	X
ejpam-3649	48	4	a	a	DET
ejpam-3649	48	5	subset	subset	NOUN
ejpam-3649	48	6	a	a	PRON
ejpam-3649	48	7	of	of	ADP
ejpam-3649	48	8	a	a	DET
ejpam-3649	48	9	bitopological	bitopological	ADJ
ejpam-3649	48	10	space	space	NOUN
ejpam-3649	48	11	(	(	PUNCT
ejpam-3649	48	12	x	x	NOUN
ejpam-3649	48	13	,	,	PUNCT
ejpam-3649	48	14	τ1	τ1	NOUN
ejpam-3649	48	15	,	,	PUNCT
ejpam-3649	48	16	τ2	τ2	NOUN
ejpam-3649	48	17	)	)	PUNCT
ejpam-3649	48	18	with	with	ADP
ejpam-3649	48	19	operation	operation	NOUN
ejpam-3649	48	20	γ	γ	NOUN
ejpam-3649	48	21	on	on	ADV
ejpam-3649	48	22	τ1∪τ2	τ1∪τ2	PROPN
ejpam-3649	48	23	is	be	AUX
ejpam-3649	48	24	named	name	VERB
ejpam-3649	48	25	:	:	PUNCT
ejpam-3649	48	26	1	1	X
ejpam-3649	48	27	.	.	X
ejpam-3649	48	28	γij	γij	VERB
ejpam-3649	48	29	-	-	PUNCT
ejpam-3649	48	30	semi	semi	ADV
ejpam-3649	48	31	-	-	ADJ
ejpam-3649	48	32	open	open	ADJ
ejpam-3649	48	33	set	set	NOUN
ejpam-3649	48	34	if	if	SCONJ
ejpam-3649	48	35	a	a	DET
ejpam-3649	48	36	⊆	⊆	NUM
ejpam-3649	48	37	clγj	clγj	NOUN
ejpam-3649	48	38	(	(	PUNCT
ejpam-3649	48	39	intγi(a	intγi(a	PROPN
ejpam-3649	48	40	)	)	PUNCT
ejpam-3649	48	41	)	)	PUNCT
ejpam-3649	48	42	,	,	PUNCT
ejpam-3649	48	43	where	where	SCONJ
ejpam-3649	48	44	i	i	PRON
ejpam-3649	48	45	6=	6=	VERB
ejpam-3649	48	46	j	j	PROPN
ejpam-3649	48	47	and	and	CCONJ
ejpam-3649	48	48	i	i	PROPN
ejpam-3649	48	49	,	,	PUNCT
ejpam-3649	48	50	j	j	PROPN
ejpam-3649	48	51	=	=	SYM
ejpam-3649	48	52	1	1	NUM
ejpam-3649	48	53	,	,	PUNCT
ejpam-3649	48	54	2	2	NUM
ejpam-3649	48	55	.	.	NOUN
ejpam-3649	48	56	2	2	NUM
ejpam-3649	48	57	.	.	X
ejpam-3649	48	58	γij	γij	VERB
ejpam-3649	48	59	-	-	PUNCT
ejpam-3649	48	60	β	β	NOUN
ejpam-3649	48	61	-	-	ADJ
ejpam-3649	48	62	open	open	ADJ
ejpam-3649	48	63	set	set	NOUN
ejpam-3649	48	64	if	if	SCONJ
ejpam-3649	48	65	a	a	DET
ejpam-3649	48	66	⊆	⊆	NUM
ejpam-3649	48	67	clγj	clγj	NOUN
ejpam-3649	48	68	(	(	PUNCT
ejpam-3649	48	69	intγi(clγj	intγi(clγj	PROPN
ejpam-3649	48	70	(	(	PUNCT
ejpam-3649	48	71	a	a	NOUN
ejpam-3649	48	72	)	)	PUNCT
ejpam-3649	48	73	)	)	PUNCT
ejpam-3649	48	74	)	)	PUNCT
ejpam-3649	48	75	,	,	PUNCT
ejpam-3649	48	76	where	where	SCONJ
ejpam-3649	48	77	i	i	PRON
ejpam-3649	48	78	6=	6=	VERB
ejpam-3649	48	79	j	j	PROPN
ejpam-3649	48	80	and	and	CCONJ
ejpam-3649	48	81	i	i	PROPN
ejpam-3649	48	82	,	,	PUNCT
ejpam-3649	48	83	j	j	PROPN
ejpam-3649	48	84	=	=	SYM
ejpam-3649	48	85	1	1	NUM
ejpam-3649	48	86	,	,	PUNCT
ejpam-3649	48	87	2	2	NUM
ejpam-3649	48	88	.	.	X
ejpam-3649	48	89	definition	definition	NOUN
ejpam-3649	48	90	2	2	NUM
ejpam-3649	48	91	.	.	PUNCT
ejpam-3649	49	1	[	[	X
ejpam-3649	49	2	3	3	X
ejpam-3649	49	3	]	]	PUNCT
ejpam-3649	49	4	a	a	DET
ejpam-3649	49	5	subset	subset	NOUN
ejpam-3649	49	6	a	a	PRON
ejpam-3649	49	7	of	of	ADP
ejpam-3649	49	8	an	an	DET
ejpam-3649	49	9	ideal	ideal	ADJ
ejpam-3649	49	10	bitopological	bitopological	ADJ
ejpam-3649	49	11	space	space	NOUN
ejpam-3649	49	12	(	(	PUNCT
ejpam-3649	49	13	x	x	NOUN
ejpam-3649	49	14	,	,	PUNCT
ejpam-3649	49	15	τ1	τ1	NOUN
ejpam-3649	49	16	,	,	PUNCT
ejpam-3649	49	17	τ2	τ2	PROPN
ejpam-3649	49	18	,	,	PUNCT
ejpam-3649	49	19	i	i	PRON
ejpam-3649	49	20	)	)	PUNCT
ejpam-3649	49	21	is	be	AUX
ejpam-3649	49	22	called	call	VERB
ejpam-3649	49	23	1	1	NUM
ejpam-3649	49	24	.	.	PUNCT
ejpam-3649	50	1	(	(	PUNCT
ejpam-3649	50	2	i	i	NOUN
ejpam-3649	50	3	,	,	PUNCT
ejpam-3649	50	4	j)-semi	j)-semi	PROPN
ejpam-3649	50	5	-	-	PUNCT
ejpam-3649	50	6	i−open	i−open	NOUN
ejpam-3649	50	7	set	set	VERB
ejpam-3649	50	8	if	if	SCONJ
ejpam-3649	50	9	a	a	DET
ejpam-3649	50	10	⊆	⊆	NUM
ejpam-3649	50	11	cl∗j	cl∗j	ADJ
ejpam-3649	50	12	(	(	PUNCT
ejpam-3649	50	13	inti(a	inti(a	NOUN
ejpam-3649	50	14	)	)	PUNCT
ejpam-3649	50	15	)	)	PUNCT
ejpam-3649	50	16	,	,	PUNCT
ejpam-3649	50	17	where	where	SCONJ
ejpam-3649	50	18	i	i	PRON
ejpam-3649	50	19	6=	6=	VERB
ejpam-3649	50	20	j	j	PROPN
ejpam-3649	50	21	and	and	CCONJ
ejpam-3649	50	22	i	i	PROPN
ejpam-3649	50	23	,	,	PUNCT
ejpam-3649	50	24	j	j	PROPN
ejpam-3649	50	25	=	=	SYM
ejpam-3649	50	26	1	1	NUM
ejpam-3649	50	27	,	,	PUNCT
ejpam-3649	50	28	2	2	NUM
ejpam-3649	50	29	.	.	NOUN
ejpam-3649	50	30	2	2	NUM
ejpam-3649	50	31	.	.	PUNCT
ejpam-3649	51	1	(	(	PUNCT
ejpam-3649	51	2	i	i	PROPN
ejpam-3649	51	3	,	,	PUNCT
ejpam-3649	51	4	j)-βi	j)-βi	NOUN
ejpam-3649	51	5	-	-	ADJ
ejpam-3649	51	6	open	open	ADJ
ejpam-3649	51	7	set	set	NOUN
ejpam-3649	51	8	if	if	SCONJ
ejpam-3649	51	9	a	a	DET
ejpam-3649	51	10	⊆	⊆	NUM
ejpam-3649	51	11	clj	clj	NOUN
ejpam-3649	51	12	(	(	PUNCT
ejpam-3649	51	13	inti(cl∗j	inti(cl∗j	PROPN
ejpam-3649	51	14	(	(	PUNCT
ejpam-3649	51	15	a	a	NOUN
ejpam-3649	51	16	)	)	PUNCT
ejpam-3649	51	17	)	)	PUNCT
ejpam-3649	51	18	)	)	PUNCT
ejpam-3649	51	19	,	,	PUNCT
ejpam-3649	51	20	where	where	SCONJ
ejpam-3649	51	21	i	i	PRON
ejpam-3649	51	22	6=	6=	VERB
ejpam-3649	51	23	j	j	PROPN
ejpam-3649	51	24	and	and	CCONJ
ejpam-3649	51	25	i	i	PROPN
ejpam-3649	51	26	,	,	PUNCT
ejpam-3649	51	27	j	j	PROPN
ejpam-3649	51	28	=	=	SYM
ejpam-3649	51	29	1	1	NUM
ejpam-3649	51	30	,	,	PUNCT
ejpam-3649	51	31	2	2	NUM
ejpam-3649	51	32	.	.	X
ejpam-3649	51	33	definition	definition	NOUN
ejpam-3649	51	34	3	3	NUM
ejpam-3649	51	35	.	.	PUNCT
ejpam-3649	52	1	[	[	X
ejpam-3649	52	2	16	16	NUM
ejpam-3649	52	3	]	]	X
ejpam-3649	52	4	let	let	AUX
ejpam-3649	52	5	(	(	PUNCT
ejpam-3649	52	6	x	x	NOUN
ejpam-3649	52	7	,	,	PUNCT
ejpam-3649	52	8	τ1	τ1	NOUN
ejpam-3649	52	9	,	,	PUNCT
ejpam-3649	52	10	τ2	τ2	PROPN
ejpam-3649	52	11	,	,	PUNCT
ejpam-3649	52	12	i	i	PRON
ejpam-3649	52	13	)	)	PUNCT
ejpam-3649	52	14	be	be	VERB
ejpam-3649	52	15	an	an	DET
ejpam-3649	52	16	ideal	ideal	ADJ
ejpam-3649	52	17	bitopological	bitopological	ADJ
ejpam-3649	52	18	space	space	NOUN
ejpam-3649	52	19	with	with	ADP
ejpam-3649	52	20	an	an	DET
ejpam-3649	52	21	operation	operation	NOUN
ejpam-3649	52	22	γ	γ	NOUN
ejpam-3649	52	23	on	on	ADP
ejpam-3649	52	24	τ1∪τ2	τ1∪τ2	PROPN
ejpam-3649	52	25	.	.	PUNCT
ejpam-3649	53	1	the	the	DET
ejpam-3649	53	2	γ	γ	PROPN
ejpam-3649	53	3	-	-	ADJ
ejpam-3649	53	4	local	local	ADJ
ejpam-3649	53	5	function	function	NOUN
ejpam-3649	53	6	of	of	ADP
ejpam-3649	53	7	a	a	PRON
ejpam-3649	53	8	with	with	ADP
ejpam-3649	53	9	regard	regard	NOUN
ejpam-3649	53	10	to	to	ADP
ejpam-3649	53	11	γ	γ	PROPN
ejpam-3649	53	12	and	and	CCONJ
ejpam-3649	53	13	i	i	PRON
ejpam-3649	53	14	is	be	AUX
ejpam-3649	53	15	described	describe	VERB
ejpam-3649	53	16	as	as	ADP
ejpam-3649	53	17	giving	give	VERB
ejpam-3649	53	18	,	,	PUNCT
ejpam-3649	53	19	for	for	ADP
ejpam-3649	53	20	a	a	DET
ejpam-3649	53	21	⊂	⊂	PROPN
ejpam-3649	53	22	x	x	SYM
ejpam-3649	53	23	,	,	PUNCT
ejpam-3649	53	24	a∗γi(γ	a∗γi(γ	NOUN
ejpam-3649	53	25	,	,	PUNCT
ejpam-3649	53	26	i	i	NOUN
ejpam-3649	53	27	)	)	PUNCT
ejpam-3649	53	28	=	=	PRON
ejpam-3649	54	1	{	{	PUNCT
ejpam-3649	54	2	x	x	SYM
ejpam-3649	54	3	∈	∈	PROPN
ejpam-3649	54	4	x|u	x|u	PUNCT
ejpam-3649	55	1	∩a	∩a	PROPN
ejpam-3649	55	2	/∈	/∈	PUNCT
ejpam-3649	56	1	i	i	PRON
ejpam-3649	56	2	,	,	PUNCT
ejpam-3649	56	3	for	for	ADP
ejpam-3649	56	4	every	every	DET
ejpam-3649	56	5	u	u	PROPN
ejpam-3649	56	6	∈	∈	PROPN
ejpam-3649	56	7	τγi(x	τγi(x	PROPN
ejpam-3649	56	8	)	)	PUNCT
ejpam-3649	56	9	}	}	PUNCT
ejpam-3649	56	10	where	where	SCONJ
ejpam-3649	56	11	τγi(x	τγi(x	NOUN
ejpam-3649	56	12	)	)	PUNCT
ejpam-3649	56	13	=	=	PRON
ejpam-3649	57	1	{	{	PUNCT
ejpam-3649	57	2	u	u	NOUN
ejpam-3649	57	3	∈	∈	PROPN
ejpam-3649	57	4	τγi	τγi	NOUN
ejpam-3649	57	5	|x	|x	NOUN
ejpam-3649	57	6	∈	∈	PROPN
ejpam-3649	57	7	u	u	NOUN
ejpam-3649	57	8	}	}	PUNCT
ejpam-3649	57	9	.	.	PUNCT
ejpam-3649	58	1	in	in	ADP
ejpam-3649	58	2	the	the	DET
ejpam-3649	58	3	case	case	NOUN
ejpam-3649	58	4	of	of	ADP
ejpam-3649	58	5	no	no	DET
ejpam-3649	58	6	ambiguity	ambiguity	NOUN
ejpam-3649	58	7	,	,	PUNCT
ejpam-3649	58	8	we	we	PRON
ejpam-3649	58	9	will	will	AUX
ejpam-3649	58	10	replace	replace	VERB
ejpam-3649	58	11	a∗γi(γ	a∗γi(γ	NOUN
ejpam-3649	58	12	,	,	PUNCT
ejpam-3649	58	13	i	i	NOUN
ejpam-3649	58	14	)	)	PUNCT
ejpam-3649	58	15	by	by	ADP
ejpam-3649	58	16	a∗γi	a∗γi	PROPN
ejpam-3649	58	17	.	.	PUNCT
ejpam-3649	59	1	definition	definition	NOUN
ejpam-3649	59	2	4	4	NUM
ejpam-3649	59	3	.	.	PUNCT
ejpam-3649	60	1	[	[	X
ejpam-3649	60	2	22	22	NUM
ejpam-3649	60	3	]	]	PUNCT
ejpam-3649	60	4	let	let	AUX
ejpam-3649	60	5	(	(	PUNCT
ejpam-3649	60	6	x	x	NOUN
ejpam-3649	60	7	,	,	PUNCT
ejpam-3649	60	8	τ1	τ1	NOUN
ejpam-3649	60	9	,	,	PUNCT
ejpam-3649	60	10	τ2	τ2	PROPN
ejpam-3649	60	11	,	,	PUNCT
ejpam-3649	60	12	i	i	PRON
ejpam-3649	60	13	)	)	PUNCT
ejpam-3649	60	14	be	be	VERB
ejpam-3649	60	15	an	an	DET
ejpam-3649	60	16	ideal	ideal	ADJ
ejpam-3649	60	17	bitopological	bitopological	ADJ
ejpam-3649	60	18	space	space	NOUN
ejpam-3649	60	19	with	with	ADP
ejpam-3649	60	20	an	an	DET
ejpam-3649	60	21	operation	operation	NOUN
ejpam-3649	60	22	γ	γ	X
ejpam-3649	60	23	and	and	CCONJ
ejpam-3649	60	24	(	(	PUNCT
ejpam-3649	60	25	y	y	PROPN
ejpam-3649	60	26	,	,	PUNCT
ejpam-3649	60	27	σ1	σ1	PROPN
ejpam-3649	60	28	,	,	PUNCT
ejpam-3649	60	29	σ2	σ2	PROPN
ejpam-3649	60	30	)	)	PUNCT
ejpam-3649	60	31	be	be	VERB
ejpam-3649	60	32	a	a	DET
ejpam-3649	60	33	bitopological	bitopological	ADJ
ejpam-3649	60	34	space	space	NOUN
ejpam-3649	60	35	with	with	ADP
ejpam-3649	60	36	an	an	DET
ejpam-3649	60	37	operation	operation	NOUN
ejpam-3649	60	38	δ	δ	PROPN
ejpam-3649	60	39	.	.	PUNCT
ejpam-3649	61	1	then	then	ADV
ejpam-3649	61	2	a	a	DET
ejpam-3649	61	3	function	function	NOUN
ejpam-3649	61	4	f	f	NOUN
ejpam-3649	61	5	:	:	PUNCT
ejpam-3649	61	6	(	(	PUNCT
ejpam-3649	61	7	x	x	NOUN
ejpam-3649	61	8	,	,	PUNCT
ejpam-3649	61	9	τ1	τ1	NOUN
ejpam-3649	61	10	,	,	PUNCT
ejpam-3649	61	11	τ2	τ2	ADJ
ejpam-3649	61	12	,	,	PUNCT
ejpam-3649	61	13	i)→	i)→	ADJ
ejpam-3649	61	14	(	(	PUNCT
ejpam-3649	61	15	y	y	PROPN
ejpam-3649	61	16	,	,	PUNCT
ejpam-3649	61	17	σ1	σ1	PROPN
ejpam-3649	61	18	,	,	PUNCT
ejpam-3649	61	19	σ2	σ2	PROPN
ejpam-3649	61	20	)	)	PUNCT
ejpam-3649	61	21	is	be	AUX
ejpam-3649	61	22	called	call	VERB
ejpam-3649	61	23	pairwise	pairwise	NOUN
ejpam-3649	61	24	(	(	PUNCT
ejpam-3649	61	25	γ	γ	NOUN
ejpam-3649	61	26	,	,	PUNCT
ejpam-3649	61	27	δ)i	δ)i	ADJ
ejpam-3649	61	28	-	-	ADJ
ejpam-3649	61	29	continuous	continuous	ADJ
ejpam-3649	61	30	function	function	NOUN
ejpam-3649	61	31	if	if	SCONJ
ejpam-3649	61	32	f−1(v	f−1(v	PROPN
ejpam-3649	61	33	)	)	PUNCT
ejpam-3649	61	34	is	be	AUX
ejpam-3649	61	35	γi	γi	NOUN
ejpam-3649	61	36	-	-	PUNCT
ejpam-3649	61	37	open	open	ADJ
ejpam-3649	61	38	in	in	ADP
ejpam-3649	61	39	x	x	PUNCT
ejpam-3649	61	40	for	for	ADP
ejpam-3649	61	41	all	all	PRON
ejpam-3649	61	42	δi	δi	ADV
ejpam-3649	61	43	-	-	PUNCT
ejpam-3649	61	44	open	open	ADJ
ejpam-3649	61	45	set	set	VERB
ejpam-3649	61	46	v	v	NOUN
ejpam-3649	61	47	in	in	ADP
ejpam-3649	61	48	y	y	PROPN
ejpam-3649	61	49	,	,	PUNCT
ejpam-3649	61	50	for	for	ADP
ejpam-3649	61	51	i	i	PROPN
ejpam-3649	61	52	=	=	SYM
ejpam-3649	61	53	1	1	NUM
ejpam-3649	61	54	,	,	PUNCT
ejpam-3649	61	55	2	2	NUM
ejpam-3649	61	56	.	.	X
ejpam-3649	61	57	definition	definition	NOUN
ejpam-3649	61	58	5	5	NUM
ejpam-3649	61	59	.	.	PUNCT
ejpam-3649	62	1	[	[	X
ejpam-3649	62	2	3	3	X
ejpam-3649	62	3	]	]	PUNCT
ejpam-3649	62	4	a	a	DET
ejpam-3649	62	5	function	function	NOUN
ejpam-3649	62	6	f	f	NOUN
ejpam-3649	62	7	:	:	PUNCT
ejpam-3649	62	8	(	(	PUNCT
ejpam-3649	62	9	x	x	NOUN
ejpam-3649	62	10	,	,	PUNCT
ejpam-3649	62	11	τ1	τ1	NOUN
ejpam-3649	62	12	,	,	PUNCT
ejpam-3649	62	13	τ2	τ2	PROPN
ejpam-3649	62	14	,	,	PUNCT
ejpam-3649	62	15	i	i	NOUN
ejpam-3649	62	16	)	)	PUNCT
ejpam-3649	62	17	→	→	SYM
ejpam-3649	62	18	(	(	PUNCT
ejpam-3649	62	19	y	y	PROPN
ejpam-3649	62	20	,	,	PUNCT
ejpam-3649	62	21	σ1	σ1	PROPN
ejpam-3649	62	22	,	,	PUNCT
ejpam-3649	62	23	σ2	σ2	PROPN
ejpam-3649	62	24	)	)	PUNCT
ejpam-3649	62	25	is	be	AUX
ejpam-3649	62	26	called	call	VERB
ejpam-3649	62	27	to	to	PART
ejpam-3649	62	28	be	be	AUX
ejpam-3649	62	29	(	(	PUNCT
ejpam-3649	62	30	i	i	PROPN
ejpam-3649	62	31	,	,	PUNCT
ejpam-3649	62	32	j)-semi	j)-semi	ADJ
ejpam-3649	62	33	-	-	ADJ
ejpam-3649	62	34	icontinuous	icontinuous	ADJ
ejpam-3649	62	35	function	function	NOUN
ejpam-3649	62	36	(	(	PUNCT
ejpam-3649	62	37	resp.(i	resp.(i	NUM
ejpam-3649	62	38	,	,	PUNCT
ejpam-3649	62	39	j)-βi−continuous	j)-βi−continuous	PROPN
ejpam-3649	62	40	)	)	PUNCT
ejpam-3649	62	41	if	if	SCONJ
ejpam-3649	62	42	f−1(v	f−1(v	PROPN
ejpam-3649	62	43	)	)	PUNCT
ejpam-3649	62	44	is	be	AUX
ejpam-3649	62	45	(	(	PUNCT
ejpam-3649	62	46	i	i	PROPN
ejpam-3649	62	47	,	,	PUNCT
ejpam-3649	62	48	j)-semi	j)-semi	PROPN
ejpam-3649	62	49	-	-	PUNCT
ejpam-3649	62	50	i	i	PROPN
ejpam-3649	62	51	-	-	PUNCT
ejpam-3649	62	52	open(resp.(i	open(resp.(i	PROPN
ejpam-3649	62	53	,	,	PUNCT
ejpam-3649	62	54	j)βi	j)βi	PROPN
ejpam-3649	62	55	-	-	ADJ
ejpam-3649	62	56	open	open	ADJ
ejpam-3649	62	57	)	)	PUNCT
ejpam-3649	62	58	in	in	ADP
ejpam-3649	62	59	x	x	PUNCT
ejpam-3649	62	60	for	for	ADP
ejpam-3649	62	61	all	all	DET
ejpam-3649	62	62	γi	γi	NOUN
ejpam-3649	62	63	-	-	PUNCT
ejpam-3649	62	64	open	open	ADJ
ejpam-3649	62	65	set	set	VERB
ejpam-3649	62	66	v	v	NOUN
ejpam-3649	62	67	in	in	ADP
ejpam-3649	62	68	y	y	PROPN
ejpam-3649	62	69	,	,	PUNCT
ejpam-3649	62	70	where	where	SCONJ
ejpam-3649	62	71	i	i	PRON
ejpam-3649	62	72	6=	6=	VERB
ejpam-3649	62	73	j	j	PROPN
ejpam-3649	62	74	and	and	CCONJ
ejpam-3649	62	75	i	i	PROPN
ejpam-3649	62	76	,	,	PUNCT
ejpam-3649	62	77	j	j	PROPN
ejpam-3649	62	78	=	=	SYM
ejpam-3649	62	79	1	1	NUM
ejpam-3649	62	80	,	,	PUNCT
ejpam-3649	62	81	2	2	NUM
ejpam-3649	62	82	.	.	PUNCT
ejpam-3649	62	83	throughout	throughout	ADP
ejpam-3649	62	84	the	the	DET
ejpam-3649	62	85	article	article	NOUN
ejpam-3649	62	86	,	,	PUNCT
ejpam-3649	62	87	we	we	PRON
ejpam-3649	62	88	suppose	suppose	VERB
ejpam-3649	62	89	that	that	SCONJ
ejpam-3649	62	90	i	i	PRON
ejpam-3649	62	91	6=	6=	PROPN
ejpam-3649	62	92	j	j	PROPN
ejpam-3649	62	93	,	,	PUNCT
ejpam-3649	62	94	and	and	CCONJ
ejpam-3649	62	95	i	i	PRON
ejpam-3649	62	96	,	,	PUNCT
ejpam-3649	62	97	j	j	PROPN
ejpam-3649	62	98	=	=	SYM
ejpam-3649	62	99	1	1	NUM
ejpam-3649	62	100	,	,	PUNCT
ejpam-3649	62	101	2	2	NUM
ejpam-3649	62	102	.	.	PUNCT
ejpam-3649	62	103	i.	i.	PROPN
ejpam-3649	62	104	bukhatwa	bukhatwa	PROPN
ejpam-3649	62	105	,	,	PUNCT
ejpam-3649	62	106	s.	s.	PROPN
ejpam-3649	62	107	demiralp	demiralp	PROPN
ejpam-3649	62	108	/	/	SYM
ejpam-3649	62	109	eur	eur	PROPN
ejpam-3649	62	110	.	.	PUNCT
ejpam-3649	63	1	j.	j.	PROPN
ejpam-3649	63	2	pure	pure	PROPN
ejpam-3649	63	3	appl	appl	PROPN
ejpam-3649	63	4	.	.	PROPN
ejpam-3649	63	5	math	math	PROPN
ejpam-3649	63	6	,	,	PUNCT
ejpam-3649	63	7	13	13	NUM
ejpam-3649	63	8	(	(	PUNCT
ejpam-3649	63	9	2	2	NUM
ejpam-3649	63	10	)	)	PUNCT
ejpam-3649	63	11	(	(	PUNCT
ejpam-3649	63	12	2020	2020	NUM
ejpam-3649	63	13	)	)	PUNCT
ejpam-3649	63	14	,	,	PUNCT
ejpam-3649	63	15	269	269	NUM
ejpam-3649	63	16	-	-	SYM
ejpam-3649	63	17	279	279	NUM
ejpam-3649	63	18	271	271	NUM
ejpam-3649	63	19	3	3	NUM
ejpam-3649	63	20	.	.	PUNCT
ejpam-3649	63	21	γij	γij	NOUN
ejpam-3649	63	22	-	-	PUNCT
ejpam-3649	63	23	βi−open	βi−open	NOUN
ejpam-3649	63	24	sets	set	VERB
ejpam-3649	63	25	this	this	DET
ejpam-3649	63	26	section	section	NOUN
ejpam-3649	63	27	deals	deal	VERB
ejpam-3649	63	28	with	with	ADP
ejpam-3649	63	29	the	the	DET
ejpam-3649	63	30	concept	concept	NOUN
ejpam-3649	63	31	of	of	ADP
ejpam-3649	63	32	γij	γij	NOUN
ejpam-3649	63	33	-	-	PUNCT
ejpam-3649	63	34	βi	βi	PRON
ejpam-3649	63	35	-	-	PUNCT
ejpam-3649	63	36	open	open	ADJ
ejpam-3649	63	37	sets	set	NOUN
ejpam-3649	63	38	and	and	CCONJ
ejpam-3649	63	39	some	some	PRON
ejpam-3649	63	40	of	of	ADP
ejpam-3649	63	41	their	their	PRON
ejpam-3649	63	42	characterizations	characterization	NOUN
ejpam-3649	63	43	in	in	ADP
ejpam-3649	63	44	an	an	DET
ejpam-3649	63	45	ideal	ideal	ADJ
ejpam-3649	63	46	bitopological	bitopological	ADJ
ejpam-3649	63	47	space	space	NOUN
ejpam-3649	63	48	.	.	PUNCT
ejpam-3649	64	1	definition	definition	NOUN
ejpam-3649	64	2	6	6	NUM
ejpam-3649	64	3	.	.	PUNCT
ejpam-3649	65	1	a	a	DET
ejpam-3649	65	2	subset	subset	NOUN
ejpam-3649	65	3	a	a	PRON
ejpam-3649	65	4	of	of	ADP
ejpam-3649	65	5	an	an	DET
ejpam-3649	65	6	ideal	ideal	ADJ
ejpam-3649	65	7	bitopological	bitopological	ADJ
ejpam-3649	65	8	space	space	NOUN
ejpam-3649	65	9	(	(	PUNCT
ejpam-3649	65	10	x	x	NOUN
ejpam-3649	65	11	,	,	PUNCT
ejpam-3649	65	12	τ1	τ1	NOUN
ejpam-3649	65	13	,	,	PUNCT
ejpam-3649	65	14	τ2	τ2	PROPN
ejpam-3649	65	15	,	,	PUNCT
ejpam-3649	65	16	i	i	PROPN
ejpam-3649	65	17	)	)	PUNCT
ejpam-3649	65	18	,	,	PUNCT
ejpam-3649	65	19	with	with	ADP
ejpam-3649	65	20	an	an	DET
ejpam-3649	65	21	operation	operation	NOUN
ejpam-3649	65	22	γ	γ	NOUN
ejpam-3649	65	23	on	on	ADP
ejpam-3649	65	24	τ1	τ1	NOUN
ejpam-3649	65	25	∪	∪	X
ejpam-3649	65	26	τ2	τ2	NOUN
ejpam-3649	65	27	,	,	PUNCT
ejpam-3649	65	28	is	be	AUX
ejpam-3649	65	29	said	say	VERB
ejpam-3649	65	30	to	to	PART
ejpam-3649	65	31	be	be	AUX
ejpam-3649	65	32	γij	γij	NOUN
ejpam-3649	65	33	-	-	PUNCT
ejpam-3649	65	34	semi	semi	NOUN
ejpam-3649	65	35	-	-	ADJ
ejpam-3649	65	36	i	i	PRON
ejpam-3649	65	37	-	-	PUNCT
ejpam-3649	65	38	open	open	NOUN
ejpam-3649	65	39	set	set	NOUN
ejpam-3649	65	40	if	if	SCONJ
ejpam-3649	65	41	a	a	DET
ejpam-3649	65	42	⊆	⊆	NUM
ejpam-3649	65	43	cl∗γj	cl∗γj	PROPN
ejpam-3649	65	44	(	(	PUNCT
ejpam-3649	65	45	intγi	intγi	PROPN
ejpam-3649	65	46	(	(	PUNCT
ejpam-3649	65	47	a	a	NOUN
ejpam-3649	65	48	)	)	PUNCT
ejpam-3649	65	49	)	)	PUNCT
ejpam-3649	65	50	.	.	PUNCT
ejpam-3649	66	1	example	example	NOUN
ejpam-3649	67	1	1	1	X
ejpam-3649	67	2	.	.	PUNCT
ejpam-3649	67	3	let	let	VERB
ejpam-3649	67	4	x	x	PUNCT
ejpam-3649	67	5	=	=	PRON
ejpam-3649	67	6	{	{	PUNCT
ejpam-3649	67	7	a	a	PRON
ejpam-3649	67	8	,	,	PUNCT
ejpam-3649	67	9	b	b	NOUN
ejpam-3649	67	10	,	,	PUNCT
ejpam-3649	67	11	c	c	NOUN
ejpam-3649	67	12	,	,	PUNCT
ejpam-3649	67	13	d	d	NOUN
ejpam-3649	67	14	}	}	PUNCT
ejpam-3649	67	15	and	and	CCONJ
ejpam-3649	67	16	(	(	PUNCT
ejpam-3649	67	17	x	x	NOUN
ejpam-3649	67	18	,	,	PUNCT
ejpam-3649	67	19	τ1	τ1	NOUN
ejpam-3649	67	20	,	,	PUNCT
ejpam-3649	67	21	τ2	τ2	PROPN
ejpam-3649	67	22	)	)	PUNCT
ejpam-3649	67	23	be	be	VERB
ejpam-3649	67	24	a	a	DET
ejpam-3649	67	25	bitopological	bitopological	ADJ
ejpam-3649	67	26	space	space	NOUN
ejpam-3649	67	27	with	with	ADP
ejpam-3649	67	28	τ1	τ1	NOUN
ejpam-3649	67	29	=	=	SYM
ejpam-3649	67	30	{	{	PUNCT
ejpam-3649	67	31	∅	∅	NOUN
ejpam-3649	67	32	,	,	PUNCT
ejpam-3649	67	33	x	x	X
ejpam-3649	67	34	,	,	PUNCT
ejpam-3649	67	35	{	{	PUNCT
ejpam-3649	67	36	b	b	NOUN
ejpam-3649	67	37	}	}	PUNCT
ejpam-3649	67	38	,	,	PUNCT
ejpam-3649	67	39	{	{	PUNCT
ejpam-3649	67	40	c	c	X
ejpam-3649	67	41	,	,	PUNCT
ejpam-3649	67	42	d	d	NOUN
ejpam-3649	67	43	}	}	PUNCT
ejpam-3649	67	44	,	,	PUNCT
ejpam-3649	67	45	{	{	PUNCT
ejpam-3649	67	46	b	b	X
ejpam-3649	67	47	,	,	PUNCT
ejpam-3649	67	48	c	c	NOUN
ejpam-3649	67	49	,	,	PUNCT
ejpam-3649	67	50	d	d	NOUN
ejpam-3649	67	51	}	}	PUNCT
ejpam-3649	67	52	}	}	PUNCT
ejpam-3649	67	53	,	,	PUNCT
ejpam-3649	67	54	τ2	τ2	NOUN
ejpam-3649	67	55	=	=	SYM
ejpam-3649	67	56	{	{	PUNCT
ejpam-3649	67	57	∅	∅	NOUN
ejpam-3649	67	58	,	,	PUNCT
ejpam-3649	67	59	x	x	X
ejpam-3649	67	60	,	,	PUNCT
ejpam-3649	67	61	{	{	PUNCT
ejpam-3649	67	62	a	a	X
ejpam-3649	67	63	}	}	PUNCT
ejpam-3649	67	64	,	,	PUNCT
ejpam-3649	67	65	{	{	PUNCT
ejpam-3649	67	66	b	b	NOUN
ejpam-3649	67	67	}	}	PUNCT
ejpam-3649	67	68	,	,	PUNCT
ejpam-3649	67	69	{	{	PUNCT
ejpam-3649	67	70	a	a	PRON
ejpam-3649	67	71	,	,	PUNCT
ejpam-3649	67	72	b	b	NOUN
ejpam-3649	67	73	}	}	PUNCT
ejpam-3649	67	74	,	,	PUNCT
ejpam-3649	67	75	{	{	PUNCT
ejpam-3649	67	76	a	a	PRON
ejpam-3649	67	77	,	,	PUNCT
ejpam-3649	67	78	c	c	NOUN
ejpam-3649	67	79	,	,	PUNCT
ejpam-3649	67	80	d	d	NOUN
ejpam-3649	67	81	}	}	PUNCT
ejpam-3649	67	82	}	}	PUNCT
ejpam-3649	67	83	and	and	CCONJ
ejpam-3649	67	84	i	i	PRON
ejpam-3649	67	85	=	=	PUNCT
ejpam-3649	67	86	{	{	PUNCT
ejpam-3649	67	87	∅	∅	NOUN
ejpam-3649	67	88	,	,	PUNCT
ejpam-3649	67	89	{	{	PUNCT
ejpam-3649	67	90	a	a	X
ejpam-3649	67	91	}	}	PUNCT
ejpam-3649	67	92	}	}	PUNCT
ejpam-3649	67	93	and	and	CCONJ
ejpam-3649	67	94	let	let	VERB
ejpam-3649	67	95	uγ	uγ	ADP
ejpam-3649	67	96	=	=	PUNCT
ejpam-3649	67	97	clj(u	clj(u	PROPN
ejpam-3649	67	98	)	)	PUNCT
ejpam-3649	67	99	for	for	ADP
ejpam-3649	67	100	u	u	PROPN
ejpam-3649	67	101	∈	∈	PROPN
ejpam-3649	67	102	τi	τi	NOUN
ejpam-3649	67	103	.	.	PUNCT
ejpam-3649	68	1	then	then	ADV
ejpam-3649	68	2	we	we	PRON
ejpam-3649	68	3	have	have	VERB
ejpam-3649	68	4	,	,	PUNCT
ejpam-3649	68	5	γ12	γ12	NOUN
ejpam-3649	68	6	-	-	PUNCT
ejpam-3649	68	7	semi	semi	NOUN
ejpam-3649	68	8	-	-	ADJ
ejpam-3649	68	9	i	i	NOUN
ejpam-3649	68	10	-	-	PUNCT
ejpam-3649	68	11	open	open	ADJ
ejpam-3649	68	12	sets	set	NOUN
ejpam-3649	68	13	are	be	AUX
ejpam-3649	68	14	∅	∅	NOUN
ejpam-3649	68	15	,	,	PUNCT
ejpam-3649	68	16	x	x	X
ejpam-3649	68	17	,	,	PUNCT
ejpam-3649	68	18	{	{	PUNCT
ejpam-3649	68	19	b	b	NOUN
ejpam-3649	68	20	}	}	PUNCT
ejpam-3649	68	21	,	,	PUNCT
ejpam-3649	68	22	{	{	PUNCT
ejpam-3649	68	23	c	c	X
ejpam-3649	68	24	,	,	PUNCT
ejpam-3649	68	25	d	d	NOUN
ejpam-3649	68	26	}	}	PUNCT
ejpam-3649	68	27	,	,	PUNCT
ejpam-3649	68	28	{	{	PUNCT
ejpam-3649	68	29	b	b	X
ejpam-3649	68	30	,	,	PUNCT
ejpam-3649	68	31	c	c	NOUN
ejpam-3649	68	32	,	,	PUNCT
ejpam-3649	68	33	d	d	NOUN
ejpam-3649	68	34	}	}	PUNCT
ejpam-3649	68	35	.	.	PUNCT
ejpam-3649	69	1	definition	definition	NOUN
ejpam-3649	69	2	7	7	NUM
ejpam-3649	69	3	.	.	PUNCT
ejpam-3649	70	1	a	a	DET
ejpam-3649	70	2	subset	subset	NOUN
ejpam-3649	70	3	a	a	PRON
ejpam-3649	70	4	of	of	ADP
ejpam-3649	70	5	an	an	DET
ejpam-3649	70	6	ideal	ideal	ADJ
ejpam-3649	70	7	bitopological	bitopological	ADJ
ejpam-3649	70	8	space	space	NOUN
ejpam-3649	70	9	(	(	PUNCT
ejpam-3649	70	10	x	x	NOUN
ejpam-3649	70	11	,	,	PUNCT
ejpam-3649	70	12	τ1	τ1	NOUN
ejpam-3649	70	13	,	,	PUNCT
ejpam-3649	70	14	τ2	τ2	PROPN
ejpam-3649	70	15	,	,	PUNCT
ejpam-3649	70	16	i	i	PRON
ejpam-3649	70	17	)	)	PUNCT
ejpam-3649	70	18	is	be	AUX
ejpam-3649	70	19	said	say	VERB
ejpam-3649	70	20	to	to	PART
ejpam-3649	70	21	be	be	AUX
ejpam-3649	70	22	γij	γij	ADV
ejpam-3649	70	23	-	-	PUNCT
ejpam-3649	70	24	βiopen	βiopen	NOUN
ejpam-3649	70	25	set	set	NOUN
ejpam-3649	70	26	if	if	SCONJ
ejpam-3649	70	27	a	a	DET
ejpam-3649	70	28	⊆	⊆	NUM
ejpam-3649	70	29	clγj	clγj	NOUN
ejpam-3649	70	30	(	(	PUNCT
ejpam-3649	70	31	intγi(cl∗γj	intγi(cl∗γj	PROPN
ejpam-3649	70	32	(	(	PUNCT
ejpam-3649	70	33	a	a	NOUN
ejpam-3649	70	34	)	)	PUNCT
ejpam-3649	70	35	)	)	PUNCT
ejpam-3649	70	36	)	)	PUNCT
ejpam-3649	70	37	.	.	PUNCT
ejpam-3649	71	1	the	the	DET
ejpam-3649	71	2	set	set	NOUN
ejpam-3649	71	3	consisting	consist	VERB
ejpam-3649	71	4	of	of	ADP
ejpam-3649	71	5	all	all	DET
ejpam-3649	71	6	γij	γij	VERB
ejpam-3649	71	7	-	-	PUNCT
ejpam-3649	71	8	βi	βi	PRON
ejpam-3649	71	9	-	-	PUNCT
ejpam-3649	71	10	open	open	ADJ
ejpam-3649	71	11	sets	set	NOUN
ejpam-3649	71	12	in	in	ADP
ejpam-3649	71	13	x	x	PUNCT
ejpam-3649	71	14	will	will	AUX
ejpam-3649	71	15	be	be	AUX
ejpam-3649	71	16	denoted	denote	VERB
ejpam-3649	71	17	by	by	ADP
ejpam-3649	71	18	γij	γij	ADV
ejpam-3649	71	19	-	-	PUNCT
ejpam-3649	71	20	βio(x	βio(x	NUM
ejpam-3649	71	21	)	)	PUNCT
ejpam-3649	71	22	.	.	PUNCT
ejpam-3649	72	1	definition	definition	NOUN
ejpam-3649	72	2	8	8	NUM
ejpam-3649	72	3	.	.	PUNCT
ejpam-3649	73	1	a	a	DET
ejpam-3649	73	2	subset	subset	NOUN
ejpam-3649	73	3	a	a	PRON
ejpam-3649	73	4	of	of	ADP
ejpam-3649	73	5	an	an	DET
ejpam-3649	73	6	ideal	ideal	ADJ
ejpam-3649	73	7	bitopological	bitopological	ADJ
ejpam-3649	73	8	space	space	NOUN
ejpam-3649	73	9	(	(	PUNCT
ejpam-3649	73	10	x	x	NOUN
ejpam-3649	73	11	,	,	PUNCT
ejpam-3649	73	12	τ1	τ1	NOUN
ejpam-3649	73	13	,	,	PUNCT
ejpam-3649	73	14	τ2	τ2	PROPN
ejpam-3649	73	15	,	,	PUNCT
ejpam-3649	73	16	i	i	PRON
ejpam-3649	73	17	)	)	PUNCT
ejpam-3649	73	18	is	be	AUX
ejpam-3649	73	19	called	call	VERB
ejpam-3649	73	20	γij	γij	ADV
ejpam-3649	73	21	-	-	PUNCT
ejpam-3649	73	22	βi	βi	PRON
ejpam-3649	73	23	-	-	PUNCT
ejpam-3649	73	24	closed	close	VERB
ejpam-3649	73	25	set	set	NOUN
ejpam-3649	73	26	if	if	SCONJ
ejpam-3649	73	27	the	the	DET
ejpam-3649	73	28	complement	complement	NOUN
ejpam-3649	73	29	ac	ac	PROPN
ejpam-3649	73	30	is	be	AUX
ejpam-3649	73	31	a	a	DET
ejpam-3649	73	32	γij	γij	VERB
ejpam-3649	73	33	-	-	PUNCT
ejpam-3649	73	34	βi	βi	ADV
ejpam-3649	73	35	-	-	PUNCT
ejpam-3649	73	36	open	open	ADJ
ejpam-3649	73	37	set	set	NOUN
ejpam-3649	73	38	.	.	PUNCT
ejpam-3649	74	1	equivalently	equivalently	ADV
ejpam-3649	74	2	,	,	PUNCT
ejpam-3649	74	3	a	a	PRON
ejpam-3649	74	4	is	be	AUX
ejpam-3649	74	5	called	call	VERB
ejpam-3649	74	6	γij	γij	ADV
ejpam-3649	74	7	-	-	PUNCT
ejpam-3649	74	8	βi	βi	PRON
ejpam-3649	74	9	-	-	PUNCT
ejpam-3649	74	10	closed	close	VERB
ejpam-3649	74	11	set	set	NOUN
ejpam-3649	74	12	if	if	SCONJ
ejpam-3649	74	13	a	a	DET
ejpam-3649	74	14	⊇	⊇	ADJ
ejpam-3649	74	15	intγi(clγj	intγi(clγj	PROPN
ejpam-3649	74	16	(	(	PUNCT
ejpam-3649	74	17	int	int	NOUN
ejpam-3649	74	18	∗	∗	NOUN
ejpam-3649	74	19	γi(a	γi(a	PUNCT
ejpam-3649	74	20	)	)	PUNCT
ejpam-3649	74	21	)	)	PUNCT
ejpam-3649	74	22	)	)	PUNCT
ejpam-3649	74	23	.	.	PUNCT
ejpam-3649	75	1	the	the	DET
ejpam-3649	75	2	set	set	NOUN
ejpam-3649	75	3	consisting	consist	VERB
ejpam-3649	75	4	of	of	ADP
ejpam-3649	75	5	all	all	DET
ejpam-3649	75	6	γij	γij	VERB
ejpam-3649	75	7	-	-	PUNCT
ejpam-3649	75	8	βi	βi	PRON
ejpam-3649	75	9	-	-	PUNCT
ejpam-3649	75	10	closed	close	VERB
ejpam-3649	75	11	sets	set	NOUN
ejpam-3649	75	12	in	in	ADP
ejpam-3649	75	13	x	x	X
ejpam-3649	75	14	will	will	AUX
ejpam-3649	75	15	be	be	AUX
ejpam-3649	75	16	denoted	denote	VERB
ejpam-3649	75	17	by	by	ADP
ejpam-3649	75	18	γij	γij	NOUN
ejpam-3649	75	19	-	-	PUNCT
ejpam-3649	75	20	βic(x	βic(x	NOUN
ejpam-3649	75	21	)	)	PUNCT
ejpam-3649	75	22	.	.	PUNCT
ejpam-3649	76	1	theorem	theorem	NOUN
ejpam-3649	76	2	1	1	X
ejpam-3649	76	3	.	.	PUNCT
ejpam-3649	77	1	let	let	AUX
ejpam-3649	77	2	(	(	PUNCT
ejpam-3649	77	3	x	x	NOUN
ejpam-3649	77	4	,	,	PUNCT
ejpam-3649	77	5	τ1	τ1	NOUN
ejpam-3649	77	6	,	,	PUNCT
ejpam-3649	77	7	τ2	τ2	PROPN
ejpam-3649	77	8	,	,	PUNCT
ejpam-3649	77	9	i	i	PRON
ejpam-3649	77	10	)	)	PUNCT
ejpam-3649	77	11	be	be	VERB
ejpam-3649	77	12	an	an	DET
ejpam-3649	77	13	ideal	ideal	ADJ
ejpam-3649	77	14	bitopological	bitopological	ADJ
ejpam-3649	77	15	space	space	NOUN
ejpam-3649	77	16	,	,	PUNCT
ejpam-3649	77	17	(	(	PUNCT
ejpam-3649	77	18	i	i	NOUN
ejpam-3649	77	19	)	)	PUNCT
ejpam-3649	77	20	every	every	DET
ejpam-3649	77	21	γij	γij	VERB
ejpam-3649	77	22	-	-	PUNCT
ejpam-3649	77	23	semi	semi	NOUN
ejpam-3649	77	24	-	-	ADJ
ejpam-3649	77	25	i	i	PRON
ejpam-3649	77	26	-	-	PUNCT
ejpam-3649	77	27	open	open	ADJ
ejpam-3649	77	28	set	set	NOUN
ejpam-3649	77	29	is	be	AUX
ejpam-3649	77	30	γij	γij	ADV
ejpam-3649	77	31	-	-	PUNCT
ejpam-3649	77	32	βi	βi	PRON
ejpam-3649	77	33	-	-	NOUN
ejpam-3649	77	34	open	open	ADJ
ejpam-3649	77	35	.	.	PUNCT
ejpam-3649	78	1	(	(	PUNCT
ejpam-3649	78	2	ii	ii	NOUN
ejpam-3649	78	3	)	)	PUNCT
ejpam-3649	78	4	every	every	DET
ejpam-3649	78	5	γij	γij	PROPN
ejpam-3649	78	6	-	-	PUNCT
ejpam-3649	78	7	βi	βi	PRON
ejpam-3649	78	8	-	-	PUNCT
ejpam-3649	78	9	open	open	ADJ
ejpam-3649	78	10	set	set	NOUN
ejpam-3649	78	11	is	be	AUX
ejpam-3649	78	12	γij	γij	NOUN
ejpam-3649	78	13	-	-	PUNCT
ejpam-3649	78	14	β	β	NOUN
ejpam-3649	78	15	-	-	ADJ
ejpam-3649	78	16	open	open	ADJ
ejpam-3649	78	17	.	.	PUNCT
ejpam-3649	79	1	proof	proof	NOUN
ejpam-3649	79	2	.	.	PUNCT
ejpam-3649	80	1	(	(	PUNCT
ejpam-3649	80	2	i	i	NOUN
ejpam-3649	80	3	)	)	PUNCT
ejpam-3649	80	4	let	let	VERB
ejpam-3649	80	5	a	a	PRON
ejpam-3649	80	6	be	be	AUX
ejpam-3649	80	7	a	a	DET
ejpam-3649	80	8	subset	subset	NOUN
ejpam-3649	80	9	of	of	ADP
ejpam-3649	80	10	x.	x.	NOUN
ejpam-3649	80	11	if	if	SCONJ
ejpam-3649	80	12	a	a	PRON
ejpam-3649	80	13	is	be	AUX
ejpam-3649	80	14	γij	γij	NOUN
ejpam-3649	80	15	-	-	PUNCT
ejpam-3649	80	16	semi	semi	NOUN
ejpam-3649	80	17	-	-	ADJ
ejpam-3649	80	18	i	i	PRON
ejpam-3649	80	19	-	-	PUNCT
ejpam-3649	80	20	open	open	ADJ
ejpam-3649	80	21	,	,	PUNCT
ejpam-3649	80	22	then	then	ADV
ejpam-3649	80	23	a	a	DET
ejpam-3649	80	24	⊆	⊆	NUM
ejpam-3649	80	25	cl∗γj	cl∗γj	PROPN
ejpam-3649	80	26	(	(	PUNCT
ejpam-3649	80	27	intγi(a	intγi(a	PROPN
ejpam-3649	80	28	)	)	PUNCT
ejpam-3649	80	29	)	)	PUNCT
ejpam-3649	81	1	⊆	⊆	NUM
ejpam-3649	81	2	intγi(a	intγi(a	NOUN
ejpam-3649	81	3	)	)	PUNCT
ejpam-3649	81	4	∪	∪	NOUN
ejpam-3649	81	5	(	(	PUNCT
ejpam-3649	81	6	intγi(a))∗γj	intγi(a))∗γj	NUM
ejpam-3649	81	7	⊆	⊆	NUM
ejpam-3649	81	8	(	(	PUNCT
ejpam-3649	81	9	intγi(a	intγi(a	NOUN
ejpam-3649	81	10	)	)	PUNCT
ejpam-3649	81	11	)	)	PUNCT
ejpam-3649	81	12	∪	∪	ADP
ejpam-3649	81	13	clγj	clγj	PROPN
ejpam-3649	81	14	(	(	PUNCT
ejpam-3649	81	15	intγi(a	intγi(a	NOUN
ejpam-3649	81	16	)	)	PUNCT
ejpam-3649	81	17	)	)	PUNCT
ejpam-3649	82	1	⊆	⊆	NUM
ejpam-3649	82	2	clγj	clγj	NOUN
ejpam-3649	82	3	(	(	PUNCT
ejpam-3649	82	4	intγi(a	intγi(a	PROPN
ejpam-3649	82	5	)	)	PUNCT
ejpam-3649	82	6	)	)	PUNCT
ejpam-3649	83	1	⊆	⊆	NUM
ejpam-3649	83	2	clγj	clγj	NOUN
ejpam-3649	83	3	(	(	PUNCT
ejpam-3649	83	4	intγi(a	intγi(a	NOUN
ejpam-3649	83	5	∪a∗γj	∪a∗γj	PUNCT
ejpam-3649	83	6	)	)	PUNCT
ejpam-3649	83	7	)	)	PUNCT
ejpam-3649	84	1	⊆	⊆	NUM
ejpam-3649	84	2	clγj	clγj	NOUN
ejpam-3649	84	3	(	(	PUNCT
ejpam-3649	84	4	intγi(cl	intγi(cl	NOUN
ejpam-3649	84	5	∗	∗	NOUN
ejpam-3649	84	6	γj	γj	PROPN
ejpam-3649	84	7	(	(	PUNCT
ejpam-3649	84	8	a	a	NOUN
ejpam-3649	84	9	)	)	PUNCT
ejpam-3649	84	10	)	)	PUNCT
ejpam-3649	84	11	)	)	PUNCT
ejpam-3649	84	12	.	.	PUNCT
ejpam-3649	85	1	therefore	therefore	ADV
ejpam-3649	85	2	,	,	PUNCT
ejpam-3649	85	3	a	a	PRON
ejpam-3649	85	4	is	be	AUX
ejpam-3649	85	5	a	a	DET
ejpam-3649	85	6	γij	γij	VERB
ejpam-3649	85	7	-	-	PUNCT
ejpam-3649	85	8	βi	βi	ADV
ejpam-3649	85	9	-	-	PUNCT
ejpam-3649	85	10	open	open	ADJ
ejpam-3649	85	11	set	set	NOUN
ejpam-3649	85	12	.	.	PUNCT
ejpam-3649	86	1	(	(	PUNCT
ejpam-3649	86	2	ii	ii	NOUN
ejpam-3649	86	3	)	)	PUNCT
ejpam-3649	86	4	let	let	VERB
ejpam-3649	86	5	a	a	PRON
ejpam-3649	86	6	be	be	AUX
ejpam-3649	86	7	a	a	DET
ejpam-3649	86	8	subset	subset	NOUN
ejpam-3649	86	9	of	of	ADP
ejpam-3649	86	10	x.	x.	NOUN
ejpam-3649	86	11	if	if	SCONJ
ejpam-3649	86	12	a	a	PRON
ejpam-3649	86	13	is	be	AUX
ejpam-3649	86	14	γij	γij	NOUN
ejpam-3649	86	15	-	-	PUNCT
ejpam-3649	86	16	βi	βi	PRON
ejpam-3649	86	17	-	-	NOUN
ejpam-3649	86	18	open	open	ADJ
ejpam-3649	86	19	,	,	PUNCT
ejpam-3649	86	20	then	then	ADV
ejpam-3649	86	21	a	a	DET
ejpam-3649	86	22	⊆	⊆	NUM
ejpam-3649	86	23	clγj	clγj	NOUN
ejpam-3649	86	24	(	(	PUNCT
ejpam-3649	86	25	intγi(cl	intγi(cl	NOUN
ejpam-3649	86	26	∗	∗	NOUN
ejpam-3649	86	27	γj	γj	PROPN
ejpam-3649	86	28	(	(	PUNCT
ejpam-3649	86	29	a	a	NOUN
ejpam-3649	86	30	)	)	PUNCT
ejpam-3649	86	31	)	)	PUNCT
ejpam-3649	86	32	)	)	PUNCT
ejpam-3649	87	1	⊆	⊆	NUM
ejpam-3649	87	2	clγj	clγj	NOUN
ejpam-3649	87	3	(	(	PUNCT
ejpam-3649	87	4	intγi(a∗γj	intγi(a∗γj	ADJ
ejpam-3649	87	5	∪a	∪a	NUM
ejpam-3649	87	6	)	)	PUNCT
ejpam-3649	87	7	)	)	PUNCT
ejpam-3649	87	8	⊆	⊆	NUM
ejpam-3649	87	9	clγj	clγj	NOUN
ejpam-3649	87	10	(	(	PUNCT
ejpam-3649	87	11	intγi(clγj	intγi(clγj	PROPN
ejpam-3649	87	12	(	(	PUNCT
ejpam-3649	87	13	a	a	NOUN
ejpam-3649	87	14	)	)	PUNCT
ejpam-3649	87	15	∪a	∪a	NUM
ejpam-3649	87	16	)	)	PUNCT
ejpam-3649	87	17	)	)	PUNCT
ejpam-3649	88	1	⊆	⊆	NUM
ejpam-3649	88	2	clγj	clγj	NOUN
ejpam-3649	88	3	(	(	PUNCT
ejpam-3649	88	4	intγi(clγj	intγi(clγj	PROPN
ejpam-3649	88	5	(	(	PUNCT
ejpam-3649	88	6	a	a	NOUN
ejpam-3649	88	7	)	)	PUNCT
ejpam-3649	88	8	)	)	PUNCT
ejpam-3649	88	9	)	)	PUNCT
ejpam-3649	88	10	.	.	PUNCT
ejpam-3649	89	1	therefore	therefore	ADV
ejpam-3649	89	2	,	,	PUNCT
ejpam-3649	89	3	a	a	PRON
ejpam-3649	89	4	is	be	AUX
ejpam-3649	89	5	a	a	DET
ejpam-3649	89	6	γij	γij	VERB
ejpam-3649	89	7	-	-	PUNCT
ejpam-3649	89	8	β	β	NOUN
ejpam-3649	89	9	-	-	ADJ
ejpam-3649	89	10	open	open	ADJ
ejpam-3649	89	11	set	set	NOUN
ejpam-3649	89	12	.	.	PUNCT
ejpam-3649	90	1	but	but	CCONJ
ejpam-3649	90	2	generally	generally	ADV
ejpam-3649	90	3	the	the	DET
ejpam-3649	90	4	convers	conver	NOUN
ejpam-3649	90	5	of	of	ADP
ejpam-3649	90	6	this	this	DET
ejpam-3649	90	7	theorem	theorem	NOUN
ejpam-3649	90	8	is	be	AUX
ejpam-3649	90	9	not	not	PART
ejpam-3649	90	10	true	true	ADJ
ejpam-3649	90	11	as	as	ADP
ejpam-3649	90	12	giving	give	VERB
ejpam-3649	90	13	in	in	ADP
ejpam-3649	90	14	the	the	DET
ejpam-3649	90	15	next	next	ADJ
ejpam-3649	90	16	example	example	NOUN
ejpam-3649	90	17	.	.	PUNCT
ejpam-3649	91	1	i.	i.	PROPN
ejpam-3649	91	2	bukhatwa	bukhatwa	PROPN
ejpam-3649	91	3	,	,	PUNCT
ejpam-3649	91	4	s.	s.	PROPN
ejpam-3649	91	5	demiralp	demiralp	PROPN
ejpam-3649	91	6	/	/	SYM
ejpam-3649	91	7	eur	eur	PROPN
ejpam-3649	91	8	.	.	PUNCT
ejpam-3649	92	1	j.	j.	PROPN
ejpam-3649	92	2	pure	pure	PROPN
ejpam-3649	92	3	appl	appl	PROPN
ejpam-3649	92	4	.	.	PROPN
ejpam-3649	92	5	math	math	PROPN
ejpam-3649	92	6	,	,	PUNCT
ejpam-3649	92	7	13	13	NUM
ejpam-3649	92	8	(	(	PUNCT
ejpam-3649	92	9	2	2	NUM
ejpam-3649	92	10	)	)	PUNCT
ejpam-3649	92	11	(	(	PUNCT
ejpam-3649	92	12	2020	2020	NUM
ejpam-3649	92	13	)	)	PUNCT
ejpam-3649	92	14	,	,	PUNCT
ejpam-3649	92	15	269	269	NUM
ejpam-3649	92	16	-	-	SYM
ejpam-3649	92	17	279	279	NUM
ejpam-3649	92	18	272	272	NUM
ejpam-3649	92	19	example	example	NOUN
ejpam-3649	92	20	2	2	NUM
ejpam-3649	92	21	.	.	PUNCT
ejpam-3649	93	1	from	from	ADP
ejpam-3649	93	2	example	example	NOUN
ejpam-3649	93	3	1	1	NUM
ejpam-3649	93	4	,	,	PUNCT
ejpam-3649	93	5	let	let	VERB
ejpam-3649	93	6	a	a	DET
ejpam-3649	93	7	=	=	X
ejpam-3649	93	8	{	{	PUNCT
ejpam-3649	93	9	c	c	NOUN
ejpam-3649	93	10	}	}	PUNCT
ejpam-3649	93	11	or	or	CCONJ
ejpam-3649	93	12	a	a	DET
ejpam-3649	93	13	=	=	SYM
ejpam-3649	93	14	{	{	PUNCT
ejpam-3649	93	15	b	b	NOUN
ejpam-3649	93	16	,	,	PUNCT
ejpam-3649	93	17	d	d	NOUN
ejpam-3649	93	18	}	}	PUNCT
ejpam-3649	93	19	.	.	PUNCT
ejpam-3649	94	1	calculations	calculation	NOUN
ejpam-3649	94	2	show	show	VERB
ejpam-3649	94	3	that	that	SCONJ
ejpam-3649	94	4	a	a	PRON
ejpam-3649	94	5	is	be	AUX
ejpam-3649	94	6	γ12	γ12	NOUN
ejpam-3649	94	7	-	-	PUNCT
ejpam-3649	94	8	βi	βi	PRON
ejpam-3649	94	9	-	-	PUNCT
ejpam-3649	94	10	open	open	ADJ
ejpam-3649	94	11	,	,	PUNCT
ejpam-3649	94	12	however	however	ADV
ejpam-3649	94	13	,	,	PUNCT
ejpam-3649	94	14	it	it	PRON
ejpam-3649	94	15	is	be	AUX
ejpam-3649	94	16	not	not	PART
ejpam-3649	94	17	γ12	γ12	NOUN
ejpam-3649	94	18	-	-	PUNCT
ejpam-3649	94	19	semi	semi	NOUN
ejpam-3649	94	20	-	-	ADJ
ejpam-3649	94	21	i	i	NOUN
ejpam-3649	94	22	-	-	PUNCT
ejpam-3649	94	23	open	open	ADJ
ejpam-3649	94	24	.	.	PUNCT
ejpam-3649	95	1	conclusion	conclusion	NOUN
ejpam-3649	95	2	1	1	NUM
ejpam-3649	95	3	.	.	PUNCT
ejpam-3649	96	1	let	let	AUX
ejpam-3649	96	2	(	(	PUNCT
ejpam-3649	96	3	x	x	NOUN
ejpam-3649	96	4	,	,	PUNCT
ejpam-3649	96	5	τ1	τ1	NOUN
ejpam-3649	96	6	,	,	PUNCT
ejpam-3649	96	7	τ2	τ2	PROPN
ejpam-3649	96	8	,	,	PUNCT
ejpam-3649	96	9	i	i	PRON
ejpam-3649	96	10	)	)	PUNCT
ejpam-3649	96	11	be	be	VERB
ejpam-3649	96	12	an	an	DET
ejpam-3649	96	13	ideal	ideal	ADJ
ejpam-3649	96	14	bitopological	bitopological	ADJ
ejpam-3649	96	15	space	space	NOUN
ejpam-3649	96	16	.	.	PUNCT
ejpam-3649	97	1	then	then	ADV
ejpam-3649	97	2	every	every	DET
ejpam-3649	97	3	γij	γij	VERB
ejpam-3649	97	4	-	-	PUNCT
ejpam-3649	97	5	semi	semi	NOUN
ejpam-3649	97	6	-	-	ADJ
ejpam-3649	97	7	iopen	iopen	ADJ
ejpam-3649	97	8	set	set	NOUN
ejpam-3649	97	9	is	be	AUX
ejpam-3649	97	10	γij	γij	NOUN
ejpam-3649	97	11	-	-	PUNCT
ejpam-3649	97	12	β	β	NOUN
ejpam-3649	97	13	-	-	ADJ
ejpam-3649	97	14	open	open	ADJ
ejpam-3649	97	15	.	.	PUNCT
ejpam-3649	98	1	theorem	theorem	NOUN
ejpam-3649	98	2	2	2	NUM
ejpam-3649	98	3	.	.	X
ejpam-3649	99	1	let	let	AUX
ejpam-3649	99	2	(	(	PUNCT
ejpam-3649	99	3	x	x	NOUN
ejpam-3649	99	4	,	,	PUNCT
ejpam-3649	99	5	τ1	τ1	NOUN
ejpam-3649	99	6	,	,	PUNCT
ejpam-3649	99	7	τ2	τ2	PROPN
ejpam-3649	99	8	,	,	PUNCT
ejpam-3649	99	9	i	i	PRON
ejpam-3649	99	10	)	)	PUNCT
ejpam-3649	99	11	be	be	VERB
ejpam-3649	99	12	an	an	DET
ejpam-3649	99	13	ideal	ideal	ADJ
ejpam-3649	99	14	bitopological	bitopological	ADJ
ejpam-3649	99	15	space	space	NOUN
ejpam-3649	99	16	.	.	PUNCT
ejpam-3649	100	1	then	then	ADV
ejpam-3649	100	2	(	(	PUNCT
ejpam-3649	100	3	i	i	NOUN
ejpam-3649	100	4	)	)	PUNCT
ejpam-3649	100	5	the	the	DET
ejpam-3649	100	6	union	union	NOUN
ejpam-3649	100	7	of	of	ADP
ejpam-3649	100	8	any	any	DET
ejpam-3649	100	9	γij	γij	VERB
ejpam-3649	100	10	-	-	PUNCT
ejpam-3649	100	11	βi	βi	PRON
ejpam-3649	100	12	-	-	PUNCT
ejpam-3649	100	13	open	open	ADJ
ejpam-3649	100	14	sets	set	NOUN
ejpam-3649	100	15	is	be	AUX
ejpam-3649	100	16	γij	γij	ADV
ejpam-3649	100	17	-	-	PUNCT
ejpam-3649	100	18	βi	βi	PRON
ejpam-3649	100	19	-	-	PUNCT
ejpam-3649	100	20	open	open	ADJ
ejpam-3649	100	21	set	set	NOUN
ejpam-3649	100	22	.	.	PUNCT
ejpam-3649	101	1	(	(	PUNCT
ejpam-3649	101	2	ii	ii	X
ejpam-3649	101	3	)	)	PUNCT
ejpam-3649	101	4	the	the	DET
ejpam-3649	101	5	intersection	intersection	NOUN
ejpam-3649	101	6	of	of	ADP
ejpam-3649	101	7	any	any	DET
ejpam-3649	101	8	γij	γij	VERB
ejpam-3649	101	9	-	-	PUNCT
ejpam-3649	101	10	βi	βi	PRON
ejpam-3649	101	11	-	-	PUNCT
ejpam-3649	101	12	closed	close	VERB
ejpam-3649	101	13	sets	set	NOUN
ejpam-3649	101	14	is	be	AUX
ejpam-3649	101	15	γij	γij	ADV
ejpam-3649	101	16	-	-	PUNCT
ejpam-3649	101	17	βi	βi	PRON
ejpam-3649	101	18	-	-	PUNCT
ejpam-3649	101	19	closed	close	VERB
ejpam-3649	101	20	set	set	NOUN
ejpam-3649	101	21	.	.	PUNCT
ejpam-3649	102	1	proof	proof	NOUN
ejpam-3649	102	2	.	.	PUNCT
ejpam-3649	103	1	(	(	PUNCT
ejpam-3649	103	2	i	i	NOUN
ejpam-3649	103	3	)	)	PUNCT
ejpam-3649	103	4	let	let	VERB
ejpam-3649	103	5	aα	aα	PRON
ejpam-3649	103	6	∈	∈	VERB
ejpam-3649	103	7	γij	γij	NOUN
ejpam-3649	103	8	-	-	PUNCT
ejpam-3649	103	9	βio(x	βio(x	NOUN
ejpam-3649	103	10	)	)	PUNCT
ejpam-3649	103	11	for	for	ADP
ejpam-3649	103	12	each	each	DET
ejpam-3649	103	13	α	α	PROPN
ejpam-3649	103	14	∈	∈	PROPN
ejpam-3649	103	15	λ	λ	PROPN
ejpam-3649	103	16	,	,	PUNCT
ejpam-3649	103	17	where	where	SCONJ
ejpam-3649	103	18	λ	λ	PROPN
ejpam-3649	103	19	is	be	AUX
ejpam-3649	103	20	an	an	DET
ejpam-3649	103	21	index	index	NOUN
ejpam-3649	103	22	set	set	NOUN
ejpam-3649	103	23	.	.	PUNCT
ejpam-3649	104	1	then	then	ADV
ejpam-3649	104	2	aα	aα	NOUN
ejpam-3649	104	3	⊆	⊆	NUM
ejpam-3649	104	4	clγj	clγj	NOUN
ejpam-3649	104	5	(	(	PUNCT
ejpam-3649	104	6	intγi(cl∗γj	intγi(cl∗γj	PROPN
ejpam-3649	104	7	(	(	PUNCT
ejpam-3649	104	8	aα	aα	NOUN
ejpam-3649	104	9	)	)	PUNCT
ejpam-3649	104	10	)	)	PUNCT
ejpam-3649	104	11	)	)	PUNCT
ejpam-3649	104	12	.	.	PUNCT
ejpam-3649	105	1	therefore	therefore	ADV
ejpam-3649	105	2	,	,	PUNCT
ejpam-3649	105	3	∪α∈λaα	∪α∈λaα	PROPN
ejpam-3649	105	4	⊆	⊆	NUM
ejpam-3649	105	5	∪α∈λ{clγj	∪α∈λ{clγj	PROPN
ejpam-3649	105	6	(	(	PUNCT
ejpam-3649	105	7	intγi(cl∗γj	intγi(cl∗γj	PROPN
ejpam-3649	105	8	(	(	PUNCT
ejpam-3649	105	9	aα	aα	NOUN
ejpam-3649	105	10	)	)	PUNCT
ejpam-3649	105	11	)	)	PUNCT
ejpam-3649	105	12	)	)	PUNCT
ejpam-3649	105	13	}	}	PUNCT
ejpam-3649	105	14	⊆	⊆	NUM
ejpam-3649	105	15	{	{	PUNCT
ejpam-3649	105	16	clγj	clγj	NOUN
ejpam-3649	105	17	(	(	PUNCT
ejpam-3649	105	18	intγi(∪α∈λcl	intγi(∪α∈λcl	NOUN
ejpam-3649	105	19	∗	∗	NOUN
ejpam-3649	105	20	γj	γj	PROPN
ejpam-3649	105	21	(	(	PUNCT
ejpam-3649	105	22	aα	aα	NOUN
ejpam-3649	105	23	)	)	PUNCT
ejpam-3649	105	24	)	)	PUNCT
ejpam-3649	105	25	)	)	PUNCT
ejpam-3649	105	26	}	}	PUNCT
ejpam-3649	105	27	⊆	⊆	NUM
ejpam-3649	105	28	{	{	PUNCT
ejpam-3649	105	29	clγj	clγj	NOUN
ejpam-3649	105	30	(	(	PUNCT
ejpam-3649	105	31	intγi(cl∗γj	intγi(cl∗γj	PROPN
ejpam-3649	105	32	(	(	PUNCT
ejpam-3649	105	33	∪α∈λaα	∪α∈λaα	PROPN
ejpam-3649	105	34	)	)	PUNCT
ejpam-3649	105	35	)	)	PUNCT
ejpam-3649	105	36	)	)	PUNCT
ejpam-3649	105	37	}	}	PUNCT
ejpam-3649	105	38	.	.	PUNCT
ejpam-3649	106	1	then	then	ADV
ejpam-3649	106	2	∪α∈λaα	∪α∈λaα	PROPN
ejpam-3649	106	3	is	be	AUX
ejpam-3649	106	4	γij	γij	ADV
ejpam-3649	106	5	-	-	PUNCT
ejpam-3649	106	6	βi	βi	PRON
ejpam-3649	106	7	-	-	NOUN
ejpam-3649	106	8	open	open	ADJ
ejpam-3649	106	9	.	.	PUNCT
ejpam-3649	107	1	(	(	PUNCT
ejpam-3649	107	2	ii	ii	X
ejpam-3649	107	3	)	)	PUNCT
ejpam-3649	107	4	the	the	DET
ejpam-3649	107	5	proof	proof	NOUN
ejpam-3649	107	6	follows	follow	VERB
ejpam-3649	107	7	by	by	ADP
ejpam-3649	107	8	using	use	VERB
ejpam-3649	107	9	(	(	PUNCT
ejpam-3649	107	10	i	i	NOUN
ejpam-3649	107	11	)	)	PUNCT
ejpam-3649	107	12	and	and	CCONJ
ejpam-3649	107	13	taking	take	VERB
ejpam-3649	107	14	complement	complement	NOUN
ejpam-3649	107	15	.	.	PUNCT
ejpam-3649	108	1	the	the	DET
ejpam-3649	108	2	intersection	intersection	NOUN
ejpam-3649	108	3	of	of	ADP
ejpam-3649	108	4	any	any	DET
ejpam-3649	108	5	two	two	NUM
ejpam-3649	108	6	γij	γij	VERB
ejpam-3649	108	7	-	-	PUNCT
ejpam-3649	108	8	βi	βi	PRON
ejpam-3649	108	9	-	-	PUNCT
ejpam-3649	108	10	open	open	ADJ
ejpam-3649	108	11	sets	set	NOUN
ejpam-3649	108	12	may	may	AUX
ejpam-3649	108	13	not	not	PART
ejpam-3649	108	14	be	be	AUX
ejpam-3649	108	15	an	an	DET
ejpam-3649	108	16	γij	γij	VERB
ejpam-3649	108	17	-	-	PUNCT
ejpam-3649	108	18	βi	βi	PRON
ejpam-3649	108	19	-	-	PUNCT
ejpam-3649	108	20	open	open	NOUN
ejpam-3649	108	21	set	set	NOUN
ejpam-3649	108	22	as	as	ADP
ejpam-3649	108	23	showing	show	VERB
ejpam-3649	108	24	in	in	ADP
ejpam-3649	108	25	the	the	DET
ejpam-3649	108	26	next	next	ADJ
ejpam-3649	108	27	example	example	NOUN
ejpam-3649	108	28	.	.	PUNCT
ejpam-3649	109	1	example	example	NOUN
ejpam-3649	110	1	3	3	X
ejpam-3649	110	2	.	.	PUNCT
ejpam-3649	110	3	let	let	VERB
ejpam-3649	110	4	x	x	PUNCT
ejpam-3649	110	5	=	=	PRON
ejpam-3649	110	6	{	{	PUNCT
ejpam-3649	110	7	a	a	PRON
ejpam-3649	110	8	,	,	PUNCT
ejpam-3649	110	9	b	b	NOUN
ejpam-3649	110	10	,	,	PUNCT
ejpam-3649	110	11	c	c	NOUN
ejpam-3649	110	12	,	,	PUNCT
ejpam-3649	110	13	d	d	NOUN
ejpam-3649	110	14	}	}	PUNCT
ejpam-3649	110	15	,	,	PUNCT
ejpam-3649	110	16	τ1	τ1	NOUN
ejpam-3649	110	17	=	=	SYM
ejpam-3649	110	18	{	{	PUNCT
ejpam-3649	110	19	∅	∅	NOUN
ejpam-3649	110	20	,	,	PUNCT
ejpam-3649	110	21	x	x	X
ejpam-3649	110	22	,	,	PUNCT
ejpam-3649	110	23	{	{	PUNCT
ejpam-3649	110	24	a	a	X
ejpam-3649	110	25	}	}	PUNCT
ejpam-3649	110	26	,	,	PUNCT
ejpam-3649	110	27	{	{	PUNCT
ejpam-3649	110	28	d	d	NOUN
ejpam-3649	110	29	}	}	PUNCT
ejpam-3649	110	30	,	,	PUNCT
ejpam-3649	110	31	{	{	PUNCT
ejpam-3649	110	32	a	a	DET
ejpam-3649	110	33	,	,	PUNCT
ejpam-3649	110	34	d	d	NOUN
ejpam-3649	110	35	}	}	PUNCT
ejpam-3649	110	36	,	,	PUNCT
ejpam-3649	110	37	{	{	PUNCT
ejpam-3649	110	38	a	a	PRON
ejpam-3649	110	39	,	,	PUNCT
ejpam-3649	110	40	c	c	NOUN
ejpam-3649	110	41	,	,	PUNCT
ejpam-3649	110	42	d	d	NOUN
ejpam-3649	110	43	}	}	PUNCT
ejpam-3649	110	44	}	}	PUNCT
ejpam-3649	110	45	,	,	PUNCT
ejpam-3649	110	46	τ2	τ2	NOUN
ejpam-3649	110	47	=	=	SYM
ejpam-3649	110	48	{	{	PUNCT
ejpam-3649	110	49	∅	∅	NOUN
ejpam-3649	110	50	,	,	PUNCT
ejpam-3649	110	51	x	x	NOUN
ejpam-3649	110	52	}	}	PUNCT
ejpam-3649	110	53	and	and	CCONJ
ejpam-3649	110	54	i	i	PRON
ejpam-3649	110	55	=	=	PUNCT
ejpam-3649	110	56	{	{	PUNCT
ejpam-3649	110	57	∅	∅	NOUN
ejpam-3649	110	58	,	,	PUNCT
ejpam-3649	110	59	{	{	PUNCT
ejpam-3649	110	60	b	b	NOUN
ejpam-3649	110	61	}	}	PUNCT
ejpam-3649	110	62	,	,	PUNCT
ejpam-3649	110	63	{	{	PUNCT
ejpam-3649	110	64	c	c	X
ejpam-3649	110	65	}	}	PUNCT
ejpam-3649	110	66	,	,	PUNCT
ejpam-3649	110	67	{	{	PUNCT
ejpam-3649	110	68	b	b	X
ejpam-3649	110	69	,	,	PUNCT
ejpam-3649	110	70	c	c	NOUN
ejpam-3649	110	71	}	}	PUNCT
ejpam-3649	110	72	}	}	PUNCT
ejpam-3649	110	73	.	.	PUNCT
ejpam-3649	111	1	let	let	AUX
ejpam-3649	111	2	define	define	VERB
ejpam-3649	111	3	an	an	DET
ejpam-3649	111	4	operation	operation	NOUN
ejpam-3649	111	5	γ	γ	NOUN
ejpam-3649	111	6	:	:	PUNCT
ejpam-3649	111	7	τ1	τ1	VERB
ejpam-3649	111	8	∪	∪	NOUN
ejpam-3649	111	9	τ2	τ2	NOUN
ejpam-3649	111	10	→	→	SYM
ejpam-3649	111	11	p	p	X
ejpam-3649	111	12	(	(	PUNCT
ejpam-3649	111	13	x	x	X
ejpam-3649	111	14	)	)	PUNCT
ejpam-3649	111	15	such	such	ADJ
ejpam-3649	111	16	that	that	SCONJ
ejpam-3649	111	17	uγ	uγ	ADP
ejpam-3649	111	18	=	=	SYM
ejpam-3649	111	19	u	u	NOUN
ejpam-3649	111	20	for	for	ADP
ejpam-3649	111	21	all	all	DET
ejpam-3649	111	22	u	u	PROPN
ejpam-3649	111	23	∈	∈	NOUN
ejpam-3649	111	24	τi	τi	NOUN
ejpam-3649	111	25	.	.	PUNCT
ejpam-3649	112	1	then	then	ADV
ejpam-3649	112	2	we	we	PRON
ejpam-3649	112	3	have	have	VERB
ejpam-3649	112	4	{	{	PUNCT
ejpam-3649	112	5	a	a	PRON
ejpam-3649	112	6	,	,	PUNCT
ejpam-3649	112	7	c	c	NOUN
ejpam-3649	112	8	}	}	PUNCT
ejpam-3649	112	9	and	and	CCONJ
ejpam-3649	112	10	{	{	PUNCT
ejpam-3649	112	11	c	c	X
ejpam-3649	112	12	,	,	PUNCT
ejpam-3649	112	13	d	d	NOUN
ejpam-3649	112	14	}	}	PUNCT
ejpam-3649	112	15	are	be	AUX
ejpam-3649	112	16	γ12	γ12	NOUN
ejpam-3649	112	17	-	-	PUNCT
ejpam-3649	112	18	βi	βi	PRON
ejpam-3649	112	19	-	-	PUNCT
ejpam-3649	112	20	open	open	ADJ
ejpam-3649	112	21	sets	set	NOUN
ejpam-3649	112	22	but	but	CCONJ
ejpam-3649	112	23	{	{	PUNCT
ejpam-3649	112	24	c	c	X
ejpam-3649	112	25	}	}	PUNCT
ejpam-3649	112	26	is	be	AUX
ejpam-3649	112	27	not	not	PART
ejpam-3649	112	28	γ12	γ12	NOUN
ejpam-3649	112	29	-	-	PUNCT
ejpam-3649	112	30	βi	βi	PRON
ejpam-3649	112	31	-	-	PUNCT
ejpam-3649	112	32	open	open	ADJ
ejpam-3649	112	33	.	.	PUNCT
ejpam-3649	113	1	definition	definition	NOUN
ejpam-3649	113	2	9	9	NUM
ejpam-3649	113	3	.	.	PUNCT
ejpam-3649	114	1	let	let	AUX
ejpam-3649	114	2	(	(	PUNCT
ejpam-3649	114	3	x	x	NOUN
ejpam-3649	114	4	,	,	PUNCT
ejpam-3649	114	5	τ1	τ1	NOUN
ejpam-3649	114	6	,	,	PUNCT
ejpam-3649	114	7	τ2	τ2	PROPN
ejpam-3649	114	8	,	,	PUNCT
ejpam-3649	114	9	i	i	PRON
ejpam-3649	114	10	)	)	PUNCT
ejpam-3649	114	11	be	be	VERB
ejpam-3649	114	12	an	an	DET
ejpam-3649	114	13	ideal	ideal	ADJ
ejpam-3649	114	14	bitopological	bitopological	ADJ
ejpam-3649	114	15	space	space	NOUN
ejpam-3649	114	16	with	with	ADP
ejpam-3649	114	17	an	an	DET
ejpam-3649	114	18	operation	operation	NOUN
ejpam-3649	114	19	γ	γ	NOUN
ejpam-3649	114	20	,	,	PUNCT
ejpam-3649	114	21	a	a	DET
ejpam-3649	114	22	⊂	⊂	X
ejpam-3649	114	23	x	x	X
ejpam-3649	114	24	and	and	CCONJ
ejpam-3649	114	25	x	x	ADJ
ejpam-3649	114	26	be	be	AUX
ejpam-3649	114	27	a	a	DET
ejpam-3649	114	28	point	point	NOUN
ejpam-3649	114	29	of	of	ADP
ejpam-3649	114	30	x.	x.	NOUN
ejpam-3649	114	31	then	then	ADV
ejpam-3649	114	32	(	(	PUNCT
ejpam-3649	114	33	i	i	NOUN
ejpam-3649	114	34	)	)	PUNCT
ejpam-3649	114	35	x	x	VERB
ejpam-3649	114	36	is	be	AUX
ejpam-3649	114	37	called	call	VERB
ejpam-3649	114	38	an	an	DET
ejpam-3649	114	39	βi	βi	NOUN
ejpam-3649	114	40	-	-	PUNCT
ejpam-3649	114	41	interiorγij	interiorγij	ADJ
ejpam-3649	114	42	point	point	NOUN
ejpam-3649	114	43	of	of	ADP
ejpam-3649	114	44	a	a	PRON
ejpam-3649	114	45	if	if	SCONJ
ejpam-3649	114	46	there	there	PRON
ejpam-3649	114	47	exists	exist	VERB
ejpam-3649	114	48	any	any	DET
ejpam-3649	114	49	u	u	PROPN
ejpam-3649	114	50	∈	∈	PROPN
ejpam-3649	114	51	γij	γij	NOUN
ejpam-3649	114	52	-	-	PUNCT
ejpam-3649	114	53	βio(x	βio(x	X
ejpam-3649	114	54	)	)	PUNCT
ejpam-3649	114	55	such	such	ADJ
ejpam-3649	114	56	that	that	SCONJ
ejpam-3649	114	57	x	x	SYM
ejpam-3649	114	58	∈	∈	PROPN
ejpam-3649	114	59	u	u	NOUN
ejpam-3649	114	60	⊂	⊂	PROPN
ejpam-3649	114	61	a.	a.	PROPN
ejpam-3649	114	62	(	(	PUNCT
ejpam-3649	114	63	ii	ii	PROPN
ejpam-3649	114	64	)	)	PUNCT
ejpam-3649	114	65	the	the	DET
ejpam-3649	114	66	set	set	NOUN
ejpam-3649	114	67	of	of	ADP
ejpam-3649	114	68	all	all	DET
ejpam-3649	114	69	βi	βi	NOUN
ejpam-3649	114	70	-	-	PUNCT
ejpam-3649	114	71	interiorγij	interiorγij	NOUN
ejpam-3649	114	72	points	point	NOUN
ejpam-3649	114	73	of	of	ADP
ejpam-3649	114	74	a	a	PRON
ejpam-3649	114	75	is	be	AUX
ejpam-3649	114	76	called	call	VERB
ejpam-3649	114	77	γij	γij	ADV
ejpam-3649	114	78	-	-	PUNCT
ejpam-3649	114	79	βi	βi	NOUN
ejpam-3649	114	80	-	-	NOUN
ejpam-3649	114	81	interior	interior	NOUN
ejpam-3649	114	82	of	of	ADP
ejpam-3649	114	83	a	a	PRON
ejpam-3649	114	84	and	and	CCONJ
ejpam-3649	114	85	is	be	AUX
ejpam-3649	114	86	represented	represent	VERB
ejpam-3649	114	87	by	by	ADP
ejpam-3649	114	88	βi	βi	NOUN
ejpam-3649	114	89	-	-	NOUN
ejpam-3649	114	90	intγij	intγij	NOUN
ejpam-3649	114	91	(	(	PUNCT
ejpam-3649	114	92	a	a	NOUN
ejpam-3649	114	93	)	)	PUNCT
ejpam-3649	114	94	.	.	PUNCT
ejpam-3649	115	1	theorem	theorem	NOUN
ejpam-3649	115	2	3	3	X
ejpam-3649	115	3	.	.	PUNCT
ejpam-3649	116	1	let	let	VERB
ejpam-3649	116	2	a	a	PRON
ejpam-3649	116	3	and	and	CCONJ
ejpam-3649	116	4	b	b	NOUN
ejpam-3649	116	5	be	be	AUX
ejpam-3649	116	6	subsets	subset	NOUN
ejpam-3649	116	7	of	of	ADP
ejpam-3649	116	8	(	(	PUNCT
ejpam-3649	116	9	x	x	NOUN
ejpam-3649	116	10	,	,	PUNCT
ejpam-3649	116	11	τ1	τ1	NOUN
ejpam-3649	116	12	,	,	PUNCT
ejpam-3649	116	13	τ2	τ2	PROPN
ejpam-3649	116	14	,	,	PUNCT
ejpam-3649	116	15	i	i	PROPN
ejpam-3649	116	16	)	)	PUNCT
ejpam-3649	116	17	.	.	PUNCT
ejpam-3649	117	1	then	then	ADV
ejpam-3649	117	2	the	the	DET
ejpam-3649	117	3	following	follow	VERB
ejpam-3649	117	4	properties	property	NOUN
ejpam-3649	117	5	hold	hold	VERB
ejpam-3649	117	6	:	:	PUNCT
ejpam-3649	117	7	1	1	X
ejpam-3649	117	8	)	)	PUNCT
ejpam-3649	117	9	βi	βi	NOUN
ejpam-3649	117	10	-	-	NOUN
ejpam-3649	117	11	intγij	intγij	NOUN
ejpam-3649	117	12	(	(	PUNCT
ejpam-3649	117	13	a	a	X
ejpam-3649	117	14	)	)	PUNCT
ejpam-3649	117	15	=	=	SYM
ejpam-3649	118	1	∪{u	∪{u	VERB
ejpam-3649	118	2	:	:	PUNCT
ejpam-3649	118	3	u	u	X
ejpam-3649	118	4	⊂	⊂	PROPN
ejpam-3649	118	5	a	a	PROPN
ejpam-3649	118	6	and	and	CCONJ
ejpam-3649	118	7	u	u	NOUN
ejpam-3649	118	8	∈	∈	PROPN
ejpam-3649	118	9	γij	γij	NOUN
ejpam-3649	118	10	-	-	PUNCT
ejpam-3649	118	11	βio(x	βio(x	NUM
ejpam-3649	118	12	)	)	PUNCT
ejpam-3649	118	13	}	}	PUNCT
ejpam-3649	118	14	.	.	PUNCT
ejpam-3649	119	1	i.	i.	PROPN
ejpam-3649	119	2	bukhatwa	bukhatwa	PROPN
ejpam-3649	119	3	,	,	PUNCT
ejpam-3649	119	4	s.	s.	PROPN
ejpam-3649	119	5	demiralp	demiralp	PROPN
ejpam-3649	119	6	/	/	SYM
ejpam-3649	119	7	eur	eur	PROPN
ejpam-3649	119	8	.	.	PUNCT
ejpam-3649	120	1	j.	j.	PROPN
ejpam-3649	120	2	pure	pure	PROPN
ejpam-3649	120	3	appl	appl	PROPN
ejpam-3649	120	4	.	.	PROPN
ejpam-3649	120	5	math	math	PROPN
ejpam-3649	120	6	,	,	PUNCT
ejpam-3649	120	7	13	13	NUM
ejpam-3649	120	8	(	(	PUNCT
ejpam-3649	120	9	2	2	NUM
ejpam-3649	120	10	)	)	PUNCT
ejpam-3649	120	11	(	(	PUNCT
ejpam-3649	120	12	2020	2020	NUM
ejpam-3649	120	13	)	)	PUNCT
ejpam-3649	120	14	,	,	PUNCT
ejpam-3649	120	15	269	269	NUM
ejpam-3649	120	16	-	-	SYM
ejpam-3649	120	17	279	279	NUM
ejpam-3649	120	18	273	273	NUM
ejpam-3649	120	19	2	2	NUM
ejpam-3649	120	20	)	)	PUNCT
ejpam-3649	120	21	βi	βi	NOUN
ejpam-3649	120	22	-	-	NOUN
ejpam-3649	120	23	intγij	intγij	NOUN
ejpam-3649	120	24	(	(	PUNCT
ejpam-3649	120	25	a	a	NOUN
ejpam-3649	120	26	)	)	PUNCT
ejpam-3649	120	27	is	be	AUX
ejpam-3649	120	28	the	the	DET
ejpam-3649	120	29	largest	large	ADJ
ejpam-3649	120	30	γij	γij	VERB
ejpam-3649	120	31	-	-	PUNCT
ejpam-3649	120	32	βi	βi	PRON
ejpam-3649	120	33	-	-	PUNCT
ejpam-3649	120	34	open	open	ADJ
ejpam-3649	120	35	subset	subset	NOUN
ejpam-3649	120	36	of	of	ADP
ejpam-3649	120	37	x	x	PRON
ejpam-3649	120	38	contained	contain	VERB
ejpam-3649	120	39	in	in	ADP
ejpam-3649	120	40	a.	a.	NOUN
ejpam-3649	120	41	3	3	NUM
ejpam-3649	120	42	)	)	PUNCT
ejpam-3649	120	43	a	a	PRON
ejpam-3649	120	44	is	be	AUX
ejpam-3649	120	45	γij	γij	NOUN
ejpam-3649	120	46	-	-	PUNCT
ejpam-3649	120	47	βi	βi	PRON
ejpam-3649	120	48	-	-	NOUN
ejpam-3649	120	49	open	open	ADJ
ejpam-3649	120	50	if	if	SCONJ
ejpam-3649	120	51	and	and	CCONJ
ejpam-3649	120	52	only	only	ADV
ejpam-3649	120	53	if	if	SCONJ
ejpam-3649	120	54	a	a	DET
ejpam-3649	120	55	=	=	ADJ
ejpam-3649	120	56	βi	βi	NOUN
ejpam-3649	120	57	-	-	NOUN
ejpam-3649	120	58	intγij	intγij	NOUN
ejpam-3649	120	59	(	(	PUNCT
ejpam-3649	120	60	a	a	NOUN
ejpam-3649	120	61	)	)	PUNCT
ejpam-3649	120	62	.	.	PUNCT
ejpam-3649	121	1	the	the	DET
ejpam-3649	121	2	proof	proof	NOUN
ejpam-3649	121	3	will	will	AUX
ejpam-3649	121	4	be	be	AUX
ejpam-3649	121	5	obtained	obtain	VERB
ejpam-3649	121	6	directly	directly	ADV
ejpam-3649	121	7	from	from	ADP
ejpam-3649	121	8	the	the	DET
ejpam-3649	121	9	definition	definition	NOUN
ejpam-3649	121	10	and	and	CCONJ
ejpam-3649	121	11	thus	thus	ADV
ejpam-3649	121	12	the	the	DET
ejpam-3649	121	13	proof	proof	NOUN
ejpam-3649	121	14	is	be	AUX
ejpam-3649	121	15	omitted	omit	VERB
ejpam-3649	121	16	.	.	PUNCT
ejpam-3649	122	1	definition	definition	NOUN
ejpam-3649	122	2	10	10	NUM
ejpam-3649	122	3	.	.	PUNCT
ejpam-3649	123	1	let	let	AUX
ejpam-3649	123	2	(	(	PUNCT
ejpam-3649	123	3	x	x	NOUN
ejpam-3649	123	4	,	,	PUNCT
ejpam-3649	123	5	τ1	τ1	NOUN
ejpam-3649	123	6	,	,	PUNCT
ejpam-3649	123	7	τ2	τ2	PROPN
ejpam-3649	123	8	,	,	PUNCT
ejpam-3649	123	9	i	i	PRON
ejpam-3649	123	10	)	)	PUNCT
ejpam-3649	123	11	be	be	VERB
ejpam-3649	123	12	an	an	DET
ejpam-3649	123	13	ideal	ideal	ADJ
ejpam-3649	123	14	bitopological	bitopological	ADJ
ejpam-3649	123	15	space	space	NOUN
ejpam-3649	123	16	with	with	ADP
ejpam-3649	123	17	an	an	DET
ejpam-3649	123	18	operation	operation	NOUN
ejpam-3649	123	19	γ	γ	NOUN
ejpam-3649	123	20	,	,	PUNCT
ejpam-3649	123	21	a	a	DET
ejpam-3649	123	22	⊂	⊂	X
ejpam-3649	123	23	x	x	X
ejpam-3649	123	24	and	and	CCONJ
ejpam-3649	123	25	x	x	ADJ
ejpam-3649	123	26	be	be	AUX
ejpam-3649	123	27	a	a	DET
ejpam-3649	123	28	point	point	NOUN
ejpam-3649	123	29	of	of	ADP
ejpam-3649	123	30	x.	x.	NOUN
ejpam-3649	123	31	then	then	ADV
ejpam-3649	123	32	,	,	PUNCT
ejpam-3649	123	33	1	1	X
ejpam-3649	123	34	.	.	X
ejpam-3649	124	1	x	x	PRON
ejpam-3649	124	2	is	be	AUX
ejpam-3649	124	3	called	call	VERB
ejpam-3649	124	4	an	an	DET
ejpam-3649	124	5	γij	γij	VERB
ejpam-3649	124	6	-	-	PUNCT
ejpam-3649	124	7	βi	βi	NOUN
ejpam-3649	124	8	-	-	PUNCT
ejpam-3649	124	9	cluster	cluster	NOUN
ejpam-3649	124	10	point	point	NOUN
ejpam-3649	124	11	of	of	ADP
ejpam-3649	124	12	a	a	DET
ejpam-3649	124	13	if	if	SCONJ
ejpam-3649	124	14	u	u	PROPN
ejpam-3649	124	15	∩	∩	NOUN
ejpam-3649	124	16	a	a	DET
ejpam-3649	124	17	6=	6=	NOUN
ejpam-3649	124	18	∅	∅	NOUN
ejpam-3649	124	19	for	for	ADP
ejpam-3649	124	20	every	every	DET
ejpam-3649	124	21	u	u	PROPN
ejpam-3649	124	22	∈	∈	PROPN
ejpam-3649	124	23	γij	γij	NOUN
ejpam-3649	124	24	-	-	PUNCT
ejpam-3649	124	25	βio(x	βio(x	X
ejpam-3649	124	26	)	)	PUNCT
ejpam-3649	124	27	such	such	ADJ
ejpam-3649	124	28	that	that	SCONJ
ejpam-3649	124	29	x	x	SYM
ejpam-3649	124	30	∈	∈	PROPN
ejpam-3649	124	31	u	u	NOUN
ejpam-3649	124	32	.	.	PUNCT
ejpam-3649	125	1	2	2	X
ejpam-3649	125	2	.	.	X
ejpam-3649	125	3	the	the	DET
ejpam-3649	125	4	set	set	NOUN
ejpam-3649	125	5	of	of	ADP
ejpam-3649	125	6	all	all	DET
ejpam-3649	125	7	γij	γij	VERB
ejpam-3649	125	8	-	-	PUNCT
ejpam-3649	125	9	βi	βi	NOUN
ejpam-3649	125	10	-	-	PUNCT
ejpam-3649	125	11	cluster	cluster	NOUN
ejpam-3649	125	12	points	point	NOUN
ejpam-3649	125	13	of	of	ADP
ejpam-3649	125	14	a	a	PRON
ejpam-3649	125	15	is	be	AUX
ejpam-3649	125	16	called	call	VERB
ejpam-3649	125	17	γij	γij	ADV
ejpam-3649	125	18	-	-	PUNCT
ejpam-3649	125	19	βi	βi	NOUN
ejpam-3649	125	20	-	-	PUNCT
ejpam-3649	125	21	cluster	cluster	NOUN
ejpam-3649	125	22	of	of	ADP
ejpam-3649	125	23	a	a	PRON
ejpam-3649	125	24	and	and	CCONJ
ejpam-3649	125	25	is	be	AUX
ejpam-3649	125	26	represented	represent	VERB
ejpam-3649	125	27	by	by	ADP
ejpam-3649	125	28	βi	βi	NOUN
ejpam-3649	125	29	-	-	PUNCT
ejpam-3649	125	30	clγij	clγij	NOUN
ejpam-3649	125	31	(	(	PUNCT
ejpam-3649	125	32	a	a	NOUN
ejpam-3649	125	33	)	)	PUNCT
ejpam-3649	125	34	.	.	PUNCT
ejpam-3649	126	1	theorem	theorem	ADJ
ejpam-3649	126	2	4	4	NUM
ejpam-3649	126	3	.	.	PUNCT
ejpam-3649	127	1	let	let	VERB
ejpam-3649	127	2	a	a	PRON
ejpam-3649	127	3	and	and	CCONJ
ejpam-3649	127	4	b	b	NOUN
ejpam-3649	127	5	be	be	AUX
ejpam-3649	127	6	subsets	subset	NOUN
ejpam-3649	127	7	of	of	ADP
ejpam-3649	127	8	(	(	PUNCT
ejpam-3649	127	9	x	x	NOUN
ejpam-3649	127	10	,	,	PUNCT
ejpam-3649	127	11	τ1	τ1	NOUN
ejpam-3649	127	12	,	,	PUNCT
ejpam-3649	127	13	τ2	τ2	PROPN
ejpam-3649	127	14	,	,	PUNCT
ejpam-3649	127	15	i	i	PROPN
ejpam-3649	127	16	)	)	PUNCT
ejpam-3649	127	17	.	.	PUNCT
ejpam-3649	128	1	then	then	ADV
ejpam-3649	128	2	the	the	DET
ejpam-3649	128	3	following	follow	VERB
ejpam-3649	128	4	properties	property	NOUN
ejpam-3649	128	5	hold	hold	VERB
ejpam-3649	128	6	:	:	PUNCT
ejpam-3649	128	7	1	1	X
ejpam-3649	128	8	)	)	PUNCT
ejpam-3649	128	9	βi	βi	NOUN
ejpam-3649	128	10	-	-	PUNCT
ejpam-3649	128	11	clγij	clγij	NOUN
ejpam-3649	128	12	(	(	PUNCT
ejpam-3649	128	13	a	a	X
ejpam-3649	128	14	)	)	PUNCT
ejpam-3649	128	15	=	=	VERB
ejpam-3649	129	1	∩{v	∩{v	NOUN
ejpam-3649	129	2	:	:	PUNCT
ejpam-3649	129	3	a	a	DET
ejpam-3649	129	4	⊂	⊂	PROPN
ejpam-3649	129	5	v	v	NOUN
ejpam-3649	129	6	and	and	CCONJ
ejpam-3649	129	7	v	v	ADP
ejpam-3649	129	8	∈	∈	PROPN
ejpam-3649	129	9	γij	γij	NOUN
ejpam-3649	129	10	-	-	PUNCT
ejpam-3649	129	11	βic(a	βic(a	PROPN
ejpam-3649	129	12	)	)	PUNCT
ejpam-3649	129	13	.	.	PUNCT
ejpam-3649	130	1	2	2	X
ejpam-3649	130	2	)	)	PUNCT
ejpam-3649	130	3	βi	βi	NOUN
ejpam-3649	130	4	-	-	PUNCT
ejpam-3649	130	5	clγij	clγij	NOUN
ejpam-3649	130	6	(	(	PUNCT
ejpam-3649	130	7	a	a	X
ejpam-3649	130	8	)	)	PUNCT
ejpam-3649	130	9	is	be	AUX
ejpam-3649	130	10	the	the	DET
ejpam-3649	130	11	smallest	small	ADJ
ejpam-3649	130	12	γij	γij	VERB
ejpam-3649	130	13	-	-	PUNCT
ejpam-3649	130	14	βi	βi	PRON
ejpam-3649	130	15	-	-	PUNCT
ejpam-3649	130	16	closed	close	VERB
ejpam-3649	130	17	subset	subset	NOUN
ejpam-3649	130	18	of	of	ADP
ejpam-3649	130	19	x	x	PUNCT
ejpam-3649	130	20	containing	contain	VERB
ejpam-3649	130	21	a.	a.	NOUN
ejpam-3649	130	22	3	3	NUM
ejpam-3649	130	23	)	)	PUNCT
ejpam-3649	130	24	a	a	PRON
ejpam-3649	130	25	is	be	AUX
ejpam-3649	130	26	γij	γij	NOUN
ejpam-3649	130	27	-	-	PUNCT
ejpam-3649	130	28	βi	βi	PRON
ejpam-3649	130	29	-	-	PUNCT
ejpam-3649	130	30	closed	closed	ADJ
ejpam-3649	130	31	if	if	SCONJ
ejpam-3649	130	32	and	and	CCONJ
ejpam-3649	130	33	only	only	ADV
ejpam-3649	130	34	if	if	SCONJ
ejpam-3649	130	35	a	a	DET
ejpam-3649	130	36	=	=	ADJ
ejpam-3649	130	37	βi	βi	NOUN
ejpam-3649	130	38	-	-	PUNCT
ejpam-3649	130	39	clγij	clγij	NOUN
ejpam-3649	130	40	(	(	PUNCT
ejpam-3649	130	41	a	a	X
ejpam-3649	130	42	)	)	PUNCT
ejpam-3649	130	43	the	the	DET
ejpam-3649	130	44	proof	proof	NOUN
ejpam-3649	130	45	will	will	AUX
ejpam-3649	130	46	be	be	AUX
ejpam-3649	130	47	obtained	obtain	VERB
ejpam-3649	130	48	directly	directly	ADV
ejpam-3649	130	49	from	from	ADP
ejpam-3649	130	50	the	the	DET
ejpam-3649	130	51	definition	definition	NOUN
ejpam-3649	130	52	and	and	CCONJ
ejpam-3649	130	53	thus	thus	ADV
ejpam-3649	130	54	the	the	DET
ejpam-3649	130	55	proof	proof	NOUN
ejpam-3649	130	56	is	be	AUX
ejpam-3649	130	57	omitted	omit	VERB
ejpam-3649	130	58	.	.	PUNCT
ejpam-3649	131	1	theorem	theorem	NOUN
ejpam-3649	131	2	5	5	NUM
ejpam-3649	131	3	.	.	PUNCT
ejpam-3649	132	1	let	let	AUX
ejpam-3649	132	2	(	(	PUNCT
ejpam-3649	132	3	x	x	NOUN
ejpam-3649	132	4	,	,	PUNCT
ejpam-3649	132	5	τ1	τ1	NOUN
ejpam-3649	132	6	,	,	PUNCT
ejpam-3649	132	7	τ2	τ2	PROPN
ejpam-3649	132	8	,	,	PUNCT
ejpam-3649	132	9	i	i	PRON
ejpam-3649	132	10	)	)	PUNCT
ejpam-3649	132	11	be	be	VERB
ejpam-3649	132	12	an	an	DET
ejpam-3649	132	13	ideal	ideal	ADJ
ejpam-3649	132	14	bitopological	bitopological	ADJ
ejpam-3649	132	15	space	space	NOUN
ejpam-3649	132	16	with	with	ADP
ejpam-3649	132	17	an	an	DET
ejpam-3649	132	18	operation	operation	NOUN
ejpam-3649	132	19	γ	γ	NOUN
ejpam-3649	132	20	and	and	CCONJ
ejpam-3649	132	21	a	a	DET
ejpam-3649	132	22	⊂	⊂	PROPN
ejpam-3649	132	23	x.	x.	NOUN
ejpam-3649	132	24	then	then	ADV
ejpam-3649	132	25	,	,	PUNCT
ejpam-3649	132	26	(	(	PUNCT
ejpam-3649	132	27	i	i	NOUN
ejpam-3649	132	28	)	)	PUNCT
ejpam-3649	132	29	if	if	SCONJ
ejpam-3649	132	30	i	i	PRON
ejpam-3649	132	31	=	=	SYM
ejpam-3649	132	32	{	{	PUNCT
ejpam-3649	132	33	∅	∅	NOUN
ejpam-3649	132	34	}	}	PUNCT
ejpam-3649	132	35	,	,	PUNCT
ejpam-3649	132	36	then	then	ADV
ejpam-3649	132	37	a	a	PRON
ejpam-3649	132	38	is	be	AUX
ejpam-3649	132	39	γij	γij	NOUN
ejpam-3649	132	40	-	-	PUNCT
ejpam-3649	132	41	βi	βi	PRON
ejpam-3649	132	42	-	-	NOUN
ejpam-3649	132	43	open	open	ADJ
ejpam-3649	132	44	if	if	SCONJ
ejpam-3649	132	45	and	and	CCONJ
ejpam-3649	132	46	only	only	ADV
ejpam-3649	132	47	if	if	SCONJ
ejpam-3649	132	48	a	a	PRON
ejpam-3649	132	49	is	be	AUX
ejpam-3649	132	50	γij	γij	NOUN
ejpam-3649	132	51	-	-	PUNCT
ejpam-3649	132	52	β	β	NOUN
ejpam-3649	132	53	-	-	ADJ
ejpam-3649	132	54	open	open	ADJ
ejpam-3649	132	55	.	.	PUNCT
ejpam-3649	133	1	(	(	PUNCT
ejpam-3649	133	2	ii	ii	NOUN
ejpam-3649	133	3	)	)	PUNCT
ejpam-3649	133	4	if	if	SCONJ
ejpam-3649	133	5	i	i	PRON
ejpam-3649	133	6	=	=	NOUN
ejpam-3649	133	7	p	p	X
ejpam-3649	133	8	(	(	PUNCT
ejpam-3649	133	9	x	x	NOUN
ejpam-3649	133	10	)	)	PUNCT
ejpam-3649	133	11	,	,	PUNCT
ejpam-3649	133	12	then	then	ADV
ejpam-3649	133	13	a	a	PRON
ejpam-3649	133	14	is	be	AUX
ejpam-3649	133	15	γij	γij	NOUN
ejpam-3649	133	16	-	-	PUNCT
ejpam-3649	133	17	βi	βi	PRON
ejpam-3649	133	18	-	-	NOUN
ejpam-3649	133	19	open	open	ADJ
ejpam-3649	133	20	if	if	SCONJ
ejpam-3649	133	21	and	and	CCONJ
ejpam-3649	133	22	only	only	ADV
ejpam-3649	133	23	if	if	SCONJ
ejpam-3649	133	24	a	a	PRON
ejpam-3649	133	25	is	be	AUX
ejpam-3649	133	26	γij	γij	NOUN
ejpam-3649	133	27	-	-	PUNCT
ejpam-3649	133	28	semi	semi	ADV
ejpam-3649	133	29	-	-	ADJ
ejpam-3649	133	30	open	open	ADJ
ejpam-3649	133	31	.	.	PUNCT
ejpam-3649	134	1	proof	proof	NOUN
ejpam-3649	134	2	.	.	PUNCT
ejpam-3649	135	1	(	(	PUNCT
ejpam-3649	135	2	i	i	NOUN
ejpam-3649	135	3	)	)	PUNCT
ejpam-3649	135	4	we	we	PRON
ejpam-3649	135	5	have	have	VERB
ejpam-3649	135	6	just	just	ADV
ejpam-3649	135	7	to	to	PART
ejpam-3649	135	8	show	show	VERB
ejpam-3649	135	9	that	that	SCONJ
ejpam-3649	135	10	if	if	SCONJ
ejpam-3649	135	11	i	i	PRON
ejpam-3649	135	12	=	=	SYM
ejpam-3649	135	13	{	{	PUNCT
ejpam-3649	135	14	∅	∅	NOUN
ejpam-3649	135	15	}	}	PUNCT
ejpam-3649	135	16	and	and	CCONJ
ejpam-3649	135	17	a	a	PRON
ejpam-3649	135	18	is	be	AUX
ejpam-3649	135	19	γij	γij	NOUN
ejpam-3649	135	20	-	-	PUNCT
ejpam-3649	135	21	β	β	NOUN
ejpam-3649	135	22	-	-	ADJ
ejpam-3649	135	23	open	open	ADJ
ejpam-3649	135	24	,	,	PUNCT
ejpam-3649	135	25	then	then	ADV
ejpam-3649	135	26	a	a	PRON
ejpam-3649	135	27	is	be	AUX
ejpam-3649	135	28	γij	γij	NOUN
ejpam-3649	135	29	-	-	PUNCT
ejpam-3649	135	30	βi	βi	PRON
ejpam-3649	135	31	-	-	NOUN
ejpam-3649	135	32	open	open	ADJ
ejpam-3649	135	33	.	.	PUNCT
ejpam-3649	136	1	if	if	SCONJ
ejpam-3649	136	2	i	i	PRON
ejpam-3649	136	3	=	=	SYM
ejpam-3649	136	4	{	{	PUNCT
ejpam-3649	136	5	∅	∅	NOUN
ejpam-3649	136	6	}	}	PUNCT
ejpam-3649	136	7	,	,	PUNCT
ejpam-3649	136	8	then	then	ADV
ejpam-3649	136	9	a∗γj	a∗γj	PROPN
ejpam-3649	136	10	=	=	SYM
ejpam-3649	136	11	clγj	clγj	PROPN
ejpam-3649	136	12	(	(	PUNCT
ejpam-3649	136	13	a	a	NOUN
ejpam-3649	136	14	)	)	PUNCT
ejpam-3649	136	15	for	for	ADP
ejpam-3649	136	16	all	all	PRON
ejpam-3649	136	17	subset	subset	VERB
ejpam-3649	136	18	a	a	PRON
ejpam-3649	136	19	of	of	ADP
ejpam-3649	136	20	x.	x.	PROPN
ejpam-3649	136	21	assumed	assume	VERB
ejpam-3649	136	22	a	a	PRON
ejpam-3649	136	23	to	to	PART
ejpam-3649	136	24	be	be	AUX
ejpam-3649	136	25	γij	γij	NOUN
ejpam-3649	136	26	-	-	PUNCT
ejpam-3649	136	27	β	β	NOUN
ejpam-3649	136	28	-	-	ADJ
ejpam-3649	136	29	open	open	ADJ
ejpam-3649	136	30	set	set	NOUN
ejpam-3649	136	31	,	,	PUNCT
ejpam-3649	136	32	then	then	ADV
ejpam-3649	136	33	a	a	DET
ejpam-3649	136	34	⊆	⊆	NUM
ejpam-3649	136	35	clγj	clγj	NOUN
ejpam-3649	136	36	(	(	PUNCT
ejpam-3649	136	37	intγi(clγj	intγi(clγj	PROPN
ejpam-3649	136	38	(	(	PUNCT
ejpam-3649	136	39	a	a	NOUN
ejpam-3649	136	40	)	)	PUNCT
ejpam-3649	136	41	)	)	PUNCT
ejpam-3649	136	42	)	)	PUNCT
ejpam-3649	137	1	⊆	⊆	NUM
ejpam-3649	137	2	clγj	clγj	NOUN
ejpam-3649	137	3	(	(	PUNCT
ejpam-3649	137	4	intγi(a∗γj	intγi(a∗γj	ADJ
ejpam-3649	137	5	)	)	PUNCT
ejpam-3649	137	6	)	)	PUNCT
ejpam-3649	138	1	⊆	⊆	NUM
ejpam-3649	138	2	clγj	clγj	NOUN
ejpam-3649	138	3	(	(	PUNCT
ejpam-3649	138	4	intγi(a	intγi(a	NOUN
ejpam-3649	138	5	∗	∗	NOUN
ejpam-3649	138	6	γj	γj	ADP
ejpam-3649	138	7	∪a	∪a	NUM
ejpam-3649	138	8	)	)	PUNCT
ejpam-3649	138	9	)	)	PUNCT
ejpam-3649	138	10	⊆	⊆	NUM
ejpam-3649	138	11	clγj	clγj	NOUN
ejpam-3649	138	12	(	(	PUNCT
ejpam-3649	138	13	intγi(cl∗γj	intγi(cl∗γj	PROPN
ejpam-3649	138	14	(	(	PUNCT
ejpam-3649	138	15	a	a	NOUN
ejpam-3649	138	16	)	)	PUNCT
ejpam-3649	138	17	)	)	PUNCT
ejpam-3649	138	18	)	)	PUNCT
ejpam-3649	138	19	.	.	PUNCT
ejpam-3649	139	1	therefore	therefore	ADV
ejpam-3649	139	2	,	,	PUNCT
ejpam-3649	139	3	a	a	PRON
ejpam-3649	139	4	is	be	AUX
ejpam-3649	139	5	γij	γij	NOUN
ejpam-3649	139	6	-	-	PUNCT
ejpam-3649	139	7	βi	βi	PRON
ejpam-3649	139	8	-	-	NOUN
ejpam-3649	139	9	open	open	ADJ
ejpam-3649	139	10	.	.	PUNCT
ejpam-3649	140	1	(	(	PUNCT
ejpam-3649	140	2	ii	ii	NOUN
ejpam-3649	140	3	)	)	PUNCT
ejpam-3649	140	4	let	let	VERB
ejpam-3649	140	5	i	i	PRON
ejpam-3649	140	6	=	=	NOUN
ejpam-3649	140	7	p	p	X
ejpam-3649	140	8	(	(	PUNCT
ejpam-3649	140	9	x	x	NOUN
ejpam-3649	140	10	)	)	PUNCT
ejpam-3649	140	11	,	,	PUNCT
ejpam-3649	140	12	then	then	ADV
ejpam-3649	140	13	a∗γj	a∗γj	PROPN
ejpam-3649	140	14	=	=	SYM
ejpam-3649	140	15	{	{	PUNCT
ejpam-3649	140	16	∅	∅	NOUN
ejpam-3649	140	17	}	}	PUNCT
ejpam-3649	140	18	for	for	ADP
ejpam-3649	140	19	any	any	DET
ejpam-3649	140	20	subset	subset	NOUN
ejpam-3649	140	21	a	a	PRON
ejpam-3649	140	22	of	of	ADP
ejpam-3649	140	23	x.	x.	NOUN
ejpam-3649	140	24	let	let	VERB
ejpam-3649	140	25	a	a	PRON
ejpam-3649	140	26	be	be	AUX
ejpam-3649	140	27	γij	γij	NOUN
ejpam-3649	140	28	-	-	PUNCT
ejpam-3649	140	29	semi	semi	ADV
ejpam-3649	140	30	-	-	ADJ
ejpam-3649	140	31	open	open	ADJ
ejpam-3649	140	32	.	.	PUNCT
ejpam-3649	141	1	then	then	ADV
ejpam-3649	141	2	a	a	DET
ejpam-3649	141	3	⊆	⊆	NUM
ejpam-3649	141	4	clγj	clγj	NOUN
ejpam-3649	141	5	(	(	PUNCT
ejpam-3649	141	6	intγi(a	intγi(a	NOUN
ejpam-3649	141	7	)	)	PUNCT
ejpam-3649	141	8	)	)	PUNCT
ejpam-3649	142	1	=	=	PRON
ejpam-3649	142	2	clγj	clγj	INTJ
ejpam-3649	142	3	(	(	PUNCT
ejpam-3649	142	4	intγi(a∪a∗γj	intγi(a∪a∗γj	PROPN
ejpam-3649	142	5	)	)	PUNCT
ejpam-3649	142	6	)	)	PUNCT
ejpam-3649	143	1	=	=	PRON
ejpam-3649	143	2	clγj	clγj	INTJ
ejpam-3649	143	3	(	(	PUNCT
ejpam-3649	143	4	intγi(cl	intγi(cl	NOUN
ejpam-3649	143	5	∗	∗	NOUN
ejpam-3649	143	6	γj	γj	PROPN
ejpam-3649	143	7	(	(	PUNCT
ejpam-3649	143	8	a	a	NOUN
ejpam-3649	143	9	)	)	PUNCT
ejpam-3649	143	10	)	)	PUNCT
ejpam-3649	143	11	)	)	PUNCT
ejpam-3649	143	12	.	.	PUNCT
ejpam-3649	144	1	therefore	therefore	ADV
ejpam-3649	144	2	,	,	PUNCT
ejpam-3649	144	3	a	a	PRON
ejpam-3649	144	4	is	be	AUX
ejpam-3649	144	5	γij	γij	NOUN
ejpam-3649	144	6	-	-	PUNCT
ejpam-3649	144	7	βi	βi	PRON
ejpam-3649	144	8	-open	-open	NOUN
ejpam-3649	144	9	.	.	PUNCT
ejpam-3649	145	1	i.	i.	PROPN
ejpam-3649	145	2	bukhatwa	bukhatwa	PROPN
ejpam-3649	145	3	,	,	PUNCT
ejpam-3649	145	4	s.	s.	PROPN
ejpam-3649	145	5	demiralp	demiralp	PROPN
ejpam-3649	145	6	/	/	SYM
ejpam-3649	145	7	eur	eur	PROPN
ejpam-3649	145	8	.	.	PUNCT
ejpam-3649	146	1	j.	j.	PROPN
ejpam-3649	146	2	pure	pure	PROPN
ejpam-3649	146	3	appl	appl	PROPN
ejpam-3649	146	4	.	.	PROPN
ejpam-3649	146	5	math	math	PROPN
ejpam-3649	146	6	,	,	PUNCT
ejpam-3649	146	7	13	13	NUM
ejpam-3649	146	8	(	(	PUNCT
ejpam-3649	146	9	2	2	NUM
ejpam-3649	146	10	)	)	PUNCT
ejpam-3649	146	11	(	(	PUNCT
ejpam-3649	146	12	2020	2020	NUM
ejpam-3649	146	13	)	)	PUNCT
ejpam-3649	146	14	,	,	PUNCT
ejpam-3649	146	15	269	269	NUM
ejpam-3649	146	16	-	-	SYM
ejpam-3649	146	17	279	279	NUM
ejpam-3649	146	18	274	274	NUM
ejpam-3649	146	19	theorem	theorem	NOUN
ejpam-3649	146	20	6	6	NUM
ejpam-3649	146	21	.	.	PUNCT
ejpam-3649	147	1	let	let	AUX
ejpam-3649	147	2	(	(	PUNCT
ejpam-3649	147	3	x	x	NOUN
ejpam-3649	147	4	,	,	PUNCT
ejpam-3649	147	5	τ1	τ1	NOUN
ejpam-3649	147	6	,	,	PUNCT
ejpam-3649	147	7	τ2	τ2	PROPN
ejpam-3649	147	8	,	,	PUNCT
ejpam-3649	147	9	i	i	PRON
ejpam-3649	147	10	)	)	PUNCT
ejpam-3649	147	11	be	be	VERB
ejpam-3649	147	12	an	an	DET
ejpam-3649	147	13	ideal	ideal	ADJ
ejpam-3649	147	14	bitopological	bitopological	ADJ
ejpam-3649	147	15	space	space	NOUN
ejpam-3649	147	16	with	with	ADP
ejpam-3649	147	17	an	an	DET
ejpam-3649	147	18	operation	operation	NOUN
ejpam-3649	147	19	γ	γ	NOUN
ejpam-3649	147	20	and	and	CCONJ
ejpam-3649	147	21	a	a	DET
ejpam-3649	147	22	⊂	⊂	PROPN
ejpam-3649	147	23	x.	x.	NOUN
ejpam-3649	147	24	then	then	ADV
ejpam-3649	147	25	a	a	PRON
ejpam-3649	147	26	is	be	AUX
ejpam-3649	147	27	γij	γij	NOUN
ejpam-3649	147	28	-	-	PUNCT
ejpam-3649	147	29	βi	βi	PRON
ejpam-3649	147	30	-	-	NOUN
ejpam-3649	147	31	open	open	ADJ
ejpam-3649	147	32	if	if	SCONJ
ejpam-3649	147	33	and	and	CCONJ
ejpam-3649	147	34	only	only	ADV
ejpam-3649	147	35	if	if	SCONJ
ejpam-3649	147	36	clγj	clγj	PROPN
ejpam-3649	147	37	(	(	PUNCT
ejpam-3649	147	38	a	a	X
ejpam-3649	147	39	)	)	PUNCT
ejpam-3649	148	1	=	=	NOUN
ejpam-3649	148	2	clγj	clγj	INTJ
ejpam-3649	148	3	(	(	PUNCT
ejpam-3649	148	4	intγi(cl	intγi(cl	NOUN
ejpam-3649	148	5	∗	∗	NOUN
ejpam-3649	148	6	γj	γj	PROPN
ejpam-3649	148	7	(	(	PUNCT
ejpam-3649	148	8	a	a	NOUN
ejpam-3649	148	9	)	)	PUNCT
ejpam-3649	148	10	)	)	PUNCT
ejpam-3649	148	11	)	)	PUNCT
ejpam-3649	148	12	.	.	PUNCT
ejpam-3649	149	1	proof	proof	NOUN
ejpam-3649	149	2	.	.	PUNCT
ejpam-3649	150	1	let	let	VERB
ejpam-3649	150	2	a	a	PRON
ejpam-3649	150	3	be	be	AUX
ejpam-3649	150	4	an	an	DET
ejpam-3649	150	5	γij	γij	VERB
ejpam-3649	150	6	-	-	PUNCT
ejpam-3649	150	7	βi	βi	ADV
ejpam-3649	150	8	-	-	PUNCT
ejpam-3649	150	9	open	open	ADJ
ejpam-3649	150	10	subset	subset	NOUN
ejpam-3649	150	11	of	of	ADP
ejpam-3649	150	12	x.	x.	NOUN
ejpam-3649	150	13	then	then	ADV
ejpam-3649	150	14	a	a	DET
ejpam-3649	150	15	⊆	⊆	NUM
ejpam-3649	150	16	clγj	clγj	NOUN
ejpam-3649	150	17	(	(	PUNCT
ejpam-3649	150	18	intγi(cl	intγi(cl	NOUN
ejpam-3649	150	19	∗	∗	NOUN
ejpam-3649	150	20	γj	γj	PROPN
ejpam-3649	150	21	(	(	PUNCT
ejpam-3649	150	22	a	a	NOUN
ejpam-3649	150	23	)	)	PUNCT
ejpam-3649	150	24	)	)	PUNCT
ejpam-3649	150	25	)	)	PUNCT
ejpam-3649	150	26	.	.	PUNCT
ejpam-3649	151	1	hence	hence	ADV
ejpam-3649	151	2	clγj	clγj	INTJ
ejpam-3649	151	3	(	(	PUNCT
ejpam-3649	151	4	a	a	NOUN
ejpam-3649	151	5	)	)	PUNCT
ejpam-3649	151	6	⊆	⊆	NUM
ejpam-3649	151	7	clγj	clγj	NOUN
ejpam-3649	151	8	(	(	PUNCT
ejpam-3649	151	9	intγi(cl∗γj	intγi(cl∗γj	PROPN
ejpam-3649	151	10	(	(	PUNCT
ejpam-3649	151	11	a	a	NOUN
ejpam-3649	151	12	)	)	PUNCT
ejpam-3649	151	13	)	)	PUNCT
ejpam-3649	151	14	)	)	PUNCT
ejpam-3649	151	15	.	.	PUNCT
ejpam-3649	152	1	since	since	SCONJ
ejpam-3649	152	2	a∗γj	a∗γj	PROPN
ejpam-3649	152	3	∪a	∪a	NUM
ejpam-3649	152	4	⊆	⊆	NUM
ejpam-3649	152	5	clγj	clγj	NOUN
ejpam-3649	152	6	(	(	PUNCT
ejpam-3649	152	7	a	a	NOUN
ejpam-3649	152	8	)	)	PUNCT
ejpam-3649	152	9	,	,	PUNCT
ejpam-3649	152	10	then	then	ADV
ejpam-3649	152	11	we	we	PRON
ejpam-3649	152	12	have	have	VERB
ejpam-3649	152	13	,	,	PUNCT
ejpam-3649	152	14	clγj	clγj	INTJ
ejpam-3649	152	15	(	(	PUNCT
ejpam-3649	152	16	a	a	NOUN
ejpam-3649	152	17	)	)	PUNCT
ejpam-3649	152	18	⊆	⊆	NUM
ejpam-3649	152	19	clγj	clγj	NOUN
ejpam-3649	152	20	(	(	PUNCT
ejpam-3649	152	21	intγi(cl∗γj	intγi(cl∗γj	PROPN
ejpam-3649	152	22	(	(	PUNCT
ejpam-3649	152	23	a	a	NOUN
ejpam-3649	152	24	)	)	PUNCT
ejpam-3649	152	25	)	)	PUNCT
ejpam-3649	152	26	)	)	PUNCT
ejpam-3649	153	1	⊆	⊆	NUM
ejpam-3649	153	2	clγj	clγj	NOUN
ejpam-3649	153	3	(	(	PUNCT
ejpam-3649	153	4	intγi(clγj	intγi(clγj	PROPN
ejpam-3649	153	5	(	(	PUNCT
ejpam-3649	153	6	a	a	NOUN
ejpam-3649	153	7	)	)	PUNCT
ejpam-3649	153	8	)	)	PUNCT
ejpam-3649	153	9	)	)	PUNCT
ejpam-3649	154	1	⊆	⊆	NUM
ejpam-3649	154	2	clγj	clγj	NOUN
ejpam-3649	154	3	(	(	PUNCT
ejpam-3649	154	4	a	a	NOUN
ejpam-3649	154	5	)	)	PUNCT
ejpam-3649	154	6	.	.	PUNCT
ejpam-3649	155	1	therefore	therefore	ADV
ejpam-3649	155	2	,	,	PUNCT
ejpam-3649	155	3	clγj	clγj	INTJ
ejpam-3649	155	4	(	(	PUNCT
ejpam-3649	155	5	a	a	NOUN
ejpam-3649	155	6	)	)	PUNCT
ejpam-3649	155	7	=	=	NOUN
ejpam-3649	155	8	clγj	clγj	INTJ
ejpam-3649	155	9	(	(	PUNCT
ejpam-3649	155	10	intγi(cl	intγi(cl	NOUN
ejpam-3649	155	11	∗	∗	NOUN
ejpam-3649	155	12	γj	γj	PROPN
ejpam-3649	155	13	(	(	PUNCT
ejpam-3649	155	14	a	a	NOUN
ejpam-3649	155	15	)	)	PUNCT
ejpam-3649	155	16	)	)	PUNCT
ejpam-3649	155	17	)	)	PUNCT
ejpam-3649	155	18	.	.	PUNCT
ejpam-3649	156	1	the	the	DET
ejpam-3649	156	2	convers	conver	NOUN
ejpam-3649	156	3	is	be	AUX
ejpam-3649	156	4	obvious	obvious	ADJ
ejpam-3649	156	5	.	.	PUNCT
ejpam-3649	157	1	4	4	X
ejpam-3649	157	2	.	.	X
ejpam-3649	157	3	(	(	PUNCT
ejpam-3649	157	4	γ	γ	X
ejpam-3649	157	5	,	,	PUNCT
ejpam-3649	157	6	δ)ij	δ)ij	PROPN
ejpam-3649	157	7	-	-	PUNCT
ejpam-3649	157	8	βi	βi	ADV
ejpam-3649	157	9	-	-	PUNCT
ejpam-3649	157	10	continuous	continuous	ADJ
ejpam-3649	157	11	functions	function	NOUN
ejpam-3649	157	12	in	in	ADP
ejpam-3649	157	13	this	this	DET
ejpam-3649	157	14	section	section	NOUN
ejpam-3649	157	15	the	the	DET
ejpam-3649	157	16	concept	concept	NOUN
ejpam-3649	157	17	of	of	ADP
ejpam-3649	157	18	(	(	PUNCT
ejpam-3649	157	19	γ	γ	X
ejpam-3649	157	20	,	,	PUNCT
ejpam-3649	157	21	δ)ij	δ)ij	PROPN
ejpam-3649	157	22	-	-	PUNCT
ejpam-3649	157	23	βi	βi	ADV
ejpam-3649	157	24	-	-	PUNCT
ejpam-3649	157	25	continuous	continuous	ADJ
ejpam-3649	157	26	function	function	NOUN
ejpam-3649	157	27	in	in	ADP
ejpam-3649	157	28	ideal	ideal	ADJ
ejpam-3649	157	29	bitopological	bitopological	ADJ
ejpam-3649	157	30	spaces	space	NOUN
ejpam-3649	157	31	are	be	AUX
ejpam-3649	157	32	introduced	introduce	VERB
ejpam-3649	157	33	along	along	ADP
ejpam-3649	157	34	with	with	ADP
ejpam-3649	157	35	some	some	DET
ejpam-3649	157	36	characterizations	characterization	NOUN
ejpam-3649	157	37	via	via	ADP
ejpam-3649	157	38	related	related	ADJ
ejpam-3649	157	39	notions	notion	NOUN
ejpam-3649	157	40	.	.	PUNCT
ejpam-3649	158	1	throughout	throughout	ADP
ejpam-3649	158	2	this	this	DET
ejpam-3649	158	3	section	section	NOUN
ejpam-3649	158	4	,	,	PUNCT
ejpam-3649	158	5	let	let	VERB
ejpam-3649	158	6	(	(	PUNCT
ejpam-3649	158	7	x	x	NOUN
ejpam-3649	158	8	,	,	PUNCT
ejpam-3649	158	9	τ1	τ1	NOUN
ejpam-3649	158	10	,	,	PUNCT
ejpam-3649	158	11	τ2	τ2	PROPN
ejpam-3649	158	12	,	,	PUNCT
ejpam-3649	158	13	i	i	PRON
ejpam-3649	158	14	)	)	PUNCT
ejpam-3649	158	15	be	be	VERB
ejpam-3649	158	16	an	an	DET
ejpam-3649	158	17	ideal	ideal	ADJ
ejpam-3649	158	18	bitopological	bitopological	ADJ
ejpam-3649	158	19	space	space	NOUN
ejpam-3649	158	20	with	with	ADP
ejpam-3649	158	21	an	an	DET
ejpam-3649	158	22	operation	operation	NOUN
ejpam-3649	158	23	γ	γ	NOUN
ejpam-3649	158	24	,	,	PUNCT
ejpam-3649	158	25	and	and	CCONJ
ejpam-3649	158	26	(	(	PUNCT
ejpam-3649	158	27	y	y	PROPN
ejpam-3649	158	28	,	,	PUNCT
ejpam-3649	158	29	σ1	σ1	PROPN
ejpam-3649	158	30	,	,	PUNCT
ejpam-3649	158	31	σ2	σ2	PROPN
ejpam-3649	158	32	)	)	PUNCT
ejpam-3649	158	33	be	be	VERB
ejpam-3649	158	34	a	a	DET
ejpam-3649	158	35	bitopological	bitopological	ADJ
ejpam-3649	158	36	space	space	NOUN
ejpam-3649	158	37	with	with	ADP
ejpam-3649	158	38	an	an	DET
ejpam-3649	158	39	operation	operation	NOUN
ejpam-3649	158	40	δ	δ	PROPN
ejpam-3649	158	41	.	.	PUNCT
ejpam-3649	159	1	definition	definition	NOUN
ejpam-3649	159	2	11	11	NUM
ejpam-3649	159	3	.	.	PUNCT
ejpam-3649	160	1	a	a	DET
ejpam-3649	160	2	function	function	NOUN
ejpam-3649	160	3	f	f	NOUN
ejpam-3649	160	4	:	:	PUNCT
ejpam-3649	160	5	(	(	PUNCT
ejpam-3649	160	6	x	x	NOUN
ejpam-3649	160	7	,	,	PUNCT
ejpam-3649	160	8	τ1	τ1	NOUN
ejpam-3649	160	9	,	,	PUNCT
ejpam-3649	160	10	τ2	τ2	ADJ
ejpam-3649	160	11	,	,	PUNCT
ejpam-3649	160	12	i)→	i)→	ADJ
ejpam-3649	160	13	(	(	PUNCT
ejpam-3649	160	14	y	y	PROPN
ejpam-3649	160	15	,	,	PUNCT
ejpam-3649	160	16	σ1	σ1	PROPN
ejpam-3649	160	17	,	,	PUNCT
ejpam-3649	160	18	σ2	σ2	PROPN
ejpam-3649	160	19	)	)	PUNCT
ejpam-3649	160	20	is	be	AUX
ejpam-3649	160	21	called	call	VERB
ejpam-3649	160	22	(	(	PUNCT
ejpam-3649	160	23	γ	γ	PROPN
ejpam-3649	160	24	,	,	PUNCT
ejpam-3649	160	25	δ)ij	δ)ij	PROPN
ejpam-3649	160	26	-	-	PUNCT
ejpam-3649	160	27	semi	semi	NOUN
ejpam-3649	160	28	-	-	ADJ
ejpam-3649	160	29	i	i	ADV
ejpam-3649	160	30	-	-	PUNCT
ejpam-3649	160	31	continuous	continuous	ADJ
ejpam-3649	160	32	function	function	NOUN
ejpam-3649	160	33	(	(	PUNCT
ejpam-3649	160	34	resp	resp	NOUN
ejpam-3649	160	35	.	.	PUNCT
ejpam-3649	161	1	(	(	PUNCT
ejpam-3649	161	2	γ	γ	X
ejpam-3649	161	3	,	,	PUNCT
ejpam-3649	161	4	δ)ij	δ)ij	PROPN
ejpam-3649	161	5	-	-	PUNCT
ejpam-3649	161	6	βi	βi	PROPN
ejpam-3649	161	7	continuous	continuous	ADJ
ejpam-3649	161	8	)	)	PUNCT
ejpam-3649	161	9	if	if	SCONJ
ejpam-3649	161	10	f−1(v	f−1(v	PROPN
ejpam-3649	161	11	)	)	PUNCT
ejpam-3649	161	12	is	be	AUX
ejpam-3649	161	13	γij	γij	NOUN
ejpam-3649	161	14	-	-	PUNCT
ejpam-3649	161	15	semi	semi	NOUN
ejpam-3649	161	16	-	-	ADJ
ejpam-3649	161	17	i	i	PRON
ejpam-3649	161	18	-	-	PUNCT
ejpam-3649	161	19	open	open	ADJ
ejpam-3649	161	20	(	(	PUNCT
ejpam-3649	161	21	resp	resp	NOUN
ejpam-3649	161	22	.	.	PUNCT
ejpam-3649	162	1	γij	γij	VERB
ejpam-3649	162	2	-	-	PUNCT
ejpam-3649	162	3	βi	βi	PRON
ejpam-3649	162	4	open	open	ADJ
ejpam-3649	162	5	)	)	PUNCT
ejpam-3649	162	6	in	in	ADP
ejpam-3649	162	7	x	x	PUNCT
ejpam-3649	162	8	for	for	ADP
ejpam-3649	162	9	all	all	PRON
ejpam-3649	162	10	δi	δi	ADV
ejpam-3649	162	11	-	-	PUNCT
ejpam-3649	162	12	open	open	ADJ
ejpam-3649	162	13	set	set	VERB
ejpam-3649	162	14	v	v	NOUN
ejpam-3649	162	15	in	in	ADP
ejpam-3649	162	16	y	y	PROPN
ejpam-3649	162	17	.	.	PUNCT
ejpam-3649	163	1	generally	generally	ADV
ejpam-3649	163	2	every	every	DET
ejpam-3649	163	3	(	(	PUNCT
ejpam-3649	163	4	γ	γ	X
ejpam-3649	163	5	,	,	PUNCT
ejpam-3649	163	6	δ)ij	δ)ij	PROPN
ejpam-3649	163	7	-	-	PUNCT
ejpam-3649	163	8	semi	semi	NOUN
ejpam-3649	163	9	-	-	ADJ
ejpam-3649	163	10	i	i	ADV
ejpam-3649	163	11	-	-	PUNCT
ejpam-3649	163	12	continuous	continuous	ADJ
ejpam-3649	163	13	function	function	NOUN
ejpam-3649	163	14	is	be	AUX
ejpam-3649	163	15	(	(	PUNCT
ejpam-3649	163	16	γ	γ	X
ejpam-3649	163	17	,	,	PUNCT
ejpam-3649	163	18	δ)ij	δ)ij	PROPN
ejpam-3649	163	19	-	-	PUNCT
ejpam-3649	163	20	βi	βi	ADV
ejpam-3649	163	21	-	-	PUNCT
ejpam-3649	163	22	continuous	continuous	ADJ
ejpam-3649	163	23	,	,	PUNCT
ejpam-3649	163	24	but	but	CCONJ
ejpam-3649	163	25	the	the	DET
ejpam-3649	163	26	convers	conver	NOUN
ejpam-3649	163	27	is	be	AUX
ejpam-3649	163	28	not	not	PART
ejpam-3649	163	29	true	true	ADJ
ejpam-3649	163	30	as	as	ADP
ejpam-3649	163	31	giving	give	VERB
ejpam-3649	163	32	in	in	ADP
ejpam-3649	163	33	next	next	ADJ
ejpam-3649	163	34	example	example	NOUN
ejpam-3649	163	35	.	.	PUNCT
ejpam-3649	164	1	example	example	NOUN
ejpam-3649	165	1	4	4	NUM
ejpam-3649	165	2	.	.	PUNCT
ejpam-3649	165	3	let	let	VERB
ejpam-3649	165	4	x	x	PUNCT
ejpam-3649	165	5	=	=	PRON
ejpam-3649	165	6	{	{	PUNCT
ejpam-3649	165	7	a	a	PRON
ejpam-3649	165	8	,	,	PUNCT
ejpam-3649	165	9	b	b	NOUN
ejpam-3649	165	10	,	,	PUNCT
ejpam-3649	165	11	c	c	NOUN
ejpam-3649	165	12	,	,	PUNCT
ejpam-3649	165	13	d	d	AUX
ejpam-3649	165	14	}	}	PUNCT
ejpam-3649	165	15	be	be	AUX
ejpam-3649	165	16	a	a	DET
ejpam-3649	165	17	set	set	NOUN
ejpam-3649	165	18	and	and	CCONJ
ejpam-3649	165	19	(	(	PUNCT
ejpam-3649	165	20	x	x	NOUN
ejpam-3649	165	21	,	,	PUNCT
ejpam-3649	165	22	τ1	τ1	NOUN
ejpam-3649	165	23	,	,	PUNCT
ejpam-3649	165	24	τ2	τ2	PROPN
ejpam-3649	165	25	,	,	PUNCT
ejpam-3649	165	26	i	i	PRON
ejpam-3649	165	27	)	)	PUNCT
ejpam-3649	165	28	be	be	VERB
ejpam-3649	165	29	an	an	DET
ejpam-3649	165	30	ideal	ideal	ADJ
ejpam-3649	165	31	bitopological	bitopological	ADJ
ejpam-3649	165	32	space	space	NOUN
ejpam-3649	165	33	with	with	ADP
ejpam-3649	165	34	τ1	τ1	NOUN
ejpam-3649	165	35	=	=	SYM
ejpam-3649	165	36	{	{	PUNCT
ejpam-3649	165	37	∅	∅	NOUN
ejpam-3649	165	38	,	,	PUNCT
ejpam-3649	165	39	x	x	X
ejpam-3649	165	40	,	,	PUNCT
ejpam-3649	165	41	{	{	PUNCT
ejpam-3649	165	42	b	b	NOUN
ejpam-3649	165	43	}	}	PUNCT
ejpam-3649	165	44	,	,	PUNCT
ejpam-3649	165	45	{	{	PUNCT
ejpam-3649	165	46	c	c	X
ejpam-3649	165	47	,	,	PUNCT
ejpam-3649	165	48	d	d	NOUN
ejpam-3649	165	49	}	}	PUNCT
ejpam-3649	165	50	,	,	PUNCT
ejpam-3649	165	51	{	{	PUNCT
ejpam-3649	165	52	b	b	X
ejpam-3649	165	53	,	,	PUNCT
ejpam-3649	165	54	c	c	NOUN
ejpam-3649	165	55	,	,	PUNCT
ejpam-3649	165	56	d	d	NOUN
ejpam-3649	165	57	}	}	PUNCT
ejpam-3649	165	58	}	}	PUNCT
ejpam-3649	165	59	,	,	PUNCT
ejpam-3649	165	60	τ2	τ2	NOUN
ejpam-3649	165	61	=	=	SYM
ejpam-3649	165	62	{	{	PUNCT
ejpam-3649	165	63	∅	∅	NOUN
ejpam-3649	165	64	,	,	PUNCT
ejpam-3649	165	65	x	x	X
ejpam-3649	165	66	,	,	PUNCT
ejpam-3649	165	67	{	{	PUNCT
ejpam-3649	165	68	a	a	X
ejpam-3649	165	69	}	}	PUNCT
ejpam-3649	165	70	,	,	PUNCT
ejpam-3649	165	71	{	{	PUNCT
ejpam-3649	165	72	a	a	DET
ejpam-3649	165	73	,	,	PUNCT
ejpam-3649	165	74	b	b	NOUN
ejpam-3649	165	75	}	}	PUNCT
ejpam-3649	165	76	,	,	PUNCT
ejpam-3649	165	77	{	{	PUNCT
ejpam-3649	165	78	a	a	PRON
ejpam-3649	165	79	,	,	PUNCT
ejpam-3649	165	80	c	c	NOUN
ejpam-3649	165	81	,	,	PUNCT
ejpam-3649	165	82	d	d	NOUN
ejpam-3649	165	83	}	}	PUNCT
ejpam-3649	165	84	}	}	PUNCT
ejpam-3649	165	85	,	,	PUNCT
ejpam-3649	165	86	i	i	PRON
ejpam-3649	165	87	=	=	NOUN
ejpam-3649	165	88	{	{	PUNCT
ejpam-3649	165	89	∅	∅	NOUN
ejpam-3649	165	90	,	,	PUNCT
ejpam-3649	165	91	{	{	PUNCT
ejpam-3649	165	92	b	b	NOUN
ejpam-3649	165	93	}	}	PUNCT
ejpam-3649	165	94	}	}	PUNCT
ejpam-3649	165	95	,	,	PUNCT
ejpam-3649	165	96	uγ	uγ	PROPN
ejpam-3649	165	97	=	=	PUNCT
ejpam-3649	165	98	clj	clj	PROPN
ejpam-3649	165	99	(	(	PUNCT
ejpam-3649	165	100	u	u	NOUN
ejpam-3649	165	101	)	)	PUNCT
ejpam-3649	165	102	for	for	ADP
ejpam-3649	165	103	u	u	PROPN
ejpam-3649	165	104	∈	∈	PROPN
ejpam-3649	165	105	τi	τi	NOUN
ejpam-3649	165	106	.	.	PUNCT
ejpam-3649	166	1	let	let	VERB
ejpam-3649	166	2	y	y	NOUN
ejpam-3649	166	3	=	=	PUNCT
ejpam-3649	166	4	{	{	PUNCT
ejpam-3649	166	5	p	p	X
ejpam-3649	166	6	,	,	PUNCT
ejpam-3649	166	7	q	q	ADJ
ejpam-3649	166	8	,	,	PUNCT
ejpam-3649	166	9	r	r	NOUN
ejpam-3649	166	10	,	,	PUNCT
ejpam-3649	166	11	s	s	AUX
ejpam-3649	166	12	}	}	PUNCT
ejpam-3649	166	13	be	be	AUX
ejpam-3649	166	14	a	a	DET
ejpam-3649	166	15	set	set	NOUN
ejpam-3649	166	16	and	and	CCONJ
ejpam-3649	166	17	(	(	PUNCT
ejpam-3649	166	18	y	y	PROPN
ejpam-3649	166	19	,	,	PUNCT
ejpam-3649	166	20	σ1	σ1	PROPN
ejpam-3649	166	21	,	,	PUNCT
ejpam-3649	166	22	σ2	σ2	PROPN
ejpam-3649	166	23	)	)	PUNCT
ejpam-3649	166	24	be	be	VERB
ejpam-3649	166	25	a	a	DET
ejpam-3649	166	26	bitopological	bitopological	ADJ
ejpam-3649	166	27	space	space	NOUN
ejpam-3649	166	28	with	with	ADP
ejpam-3649	166	29	σ1	σ1	PROPN
ejpam-3649	166	30	=	=	SYM
ejpam-3649	166	31	{	{	PUNCT
ejpam-3649	166	32	∅	∅	NOUN
ejpam-3649	166	33	,	,	PUNCT
ejpam-3649	166	34	y	y	PROPN
ejpam-3649	166	35	,	,	PUNCT
ejpam-3649	166	36	{	{	PUNCT
ejpam-3649	166	37	q	q	X
ejpam-3649	166	38	}	}	PUNCT
ejpam-3649	166	39	,	,	PUNCT
ejpam-3649	166	40	{	{	PUNCT
ejpam-3649	166	41	r	r	NOUN
ejpam-3649	166	42	,	,	PUNCT
ejpam-3649	166	43	s	s	PART
ejpam-3649	166	44	}	}	PUNCT
ejpam-3649	166	45	,	,	PUNCT
ejpam-3649	166	46	{	{	PUNCT
ejpam-3649	166	47	q	q	X
ejpam-3649	166	48	,	,	PUNCT
ejpam-3649	166	49	r	r	NOUN
ejpam-3649	166	50	,	,	PUNCT
ejpam-3649	166	51	s	s	PART
ejpam-3649	166	52	}	}	PUNCT
ejpam-3649	166	53	}	}	PUNCT
ejpam-3649	166	54	,	,	PUNCT
ejpam-3649	166	55	σ2	σ2	PROPN
ejpam-3649	166	56	=	=	SYM
ejpam-3649	166	57	{	{	PUNCT
ejpam-3649	166	58	∅	∅	NOUN
ejpam-3649	166	59	,	,	PUNCT
ejpam-3649	166	60	y	y	PROPN
ejpam-3649	166	61	,	,	PUNCT
ejpam-3649	166	62	{	{	PUNCT
ejpam-3649	166	63	p	p	X
ejpam-3649	166	64	}	}	PUNCT
ejpam-3649	166	65	,	,	PUNCT
ejpam-3649	166	66	{	{	PUNCT
ejpam-3649	166	67	p	p	X
ejpam-3649	166	68	,	,	PUNCT
ejpam-3649	166	69	q	q	NOUN
ejpam-3649	166	70	}	}	PUNCT
ejpam-3649	166	71	,	,	PUNCT
ejpam-3649	166	72	{	{	PUNCT
ejpam-3649	166	73	p	p	X
ejpam-3649	166	74	,	,	PUNCT
ejpam-3649	166	75	r	r	NOUN
ejpam-3649	166	76	,	,	PUNCT
ejpam-3649	166	77	s	s	PART
ejpam-3649	166	78	}	}	PUNCT
ejpam-3649	166	79	}	}	PUNCT
ejpam-3649	166	80	,	,	PUNCT
ejpam-3649	166	81	v	v	ADP
ejpam-3649	166	82	δ	δ	PROPN
ejpam-3649	166	83	=	=	PUNCT
ejpam-3649	166	84	v	v	PROPN
ejpam-3649	166	85	for	for	ADP
ejpam-3649	166	86	v	v	PROPN
ejpam-3649	166	87	∈	∈	PROPN
ejpam-3649	166	88	σi	σi	NOUN
ejpam-3649	166	89	.	.	PUNCT
ejpam-3649	167	1	let	let	AUX
ejpam-3649	167	2	define	define	VERB
ejpam-3649	167	3	f	f	X
ejpam-3649	167	4	:	:	PUNCT
ejpam-3649	167	5	(	(	PUNCT
ejpam-3649	167	6	x	x	NOUN
ejpam-3649	167	7	,	,	PUNCT
ejpam-3649	167	8	τ1	τ1	NOUN
ejpam-3649	167	9	,	,	PUNCT
ejpam-3649	167	10	τ2	τ2	PROPN
ejpam-3649	167	11	,	,	PUNCT
ejpam-3649	167	12	i	i	NOUN
ejpam-3649	167	13	)	)	PUNCT
ejpam-3649	167	14	→	→	SYM
ejpam-3649	167	15	(	(	PUNCT
ejpam-3649	167	16	y	y	PROPN
ejpam-3649	167	17	,	,	PUNCT
ejpam-3649	167	18	σ1	σ1	PROPN
ejpam-3649	167	19	,	,	PUNCT
ejpam-3649	167	20	σ2	σ2	NOUN
ejpam-3649	167	21	)	)	PUNCT
ejpam-3649	167	22	such	such	ADJ
ejpam-3649	167	23	that	that	DET
ejpam-3649	167	24	f(a	f(a	NOUN
ejpam-3649	167	25	)	)	PUNCT
ejpam-3649	168	1	=	=	SYM
ejpam-3649	168	2	p	p	NOUN
ejpam-3649	168	3	,	,	PUNCT
ejpam-3649	168	4	f(b	f(b	PROPN
ejpam-3649	168	5	)	)	PUNCT
ejpam-3649	168	6	=	=	SYM
ejpam-3649	169	1	q	q	X
ejpam-3649	169	2	,	,	PUNCT
ejpam-3649	169	3	f(c	f(c	PROPN
ejpam-3649	169	4	)	)	PUNCT
ejpam-3649	169	5	=	=	SYM
ejpam-3649	169	6	r	r	NOUN
ejpam-3649	169	7	and	and	CCONJ
ejpam-3649	169	8	f(d	f(d	PROPN
ejpam-3649	169	9	)	)	PUNCT
ejpam-3649	169	10	=	=	PUNCT
ejpam-3649	170	1	s.	s.	PROPN
ejpam-3649	170	2	then	then	ADV
ejpam-3649	170	3	f	f	PROPN
ejpam-3649	170	4	is	be	AUX
ejpam-3649	170	5	(	(	PUNCT
ejpam-3649	170	6	γ	γ	X
ejpam-3649	170	7	,	,	PUNCT
ejpam-3649	170	8	δ)12	δ)12	PROPN
ejpam-3649	170	9	-	-	PUNCT
ejpam-3649	170	10	βi	βi	ADV
ejpam-3649	170	11	-	-	PUNCT
ejpam-3649	170	12	continuous	continuous	ADJ
ejpam-3649	170	13	but	but	CCONJ
ejpam-3649	170	14	not	not	PART
ejpam-3649	170	15	(	(	PUNCT
ejpam-3649	170	16	γ	γ	X
ejpam-3649	170	17	,	,	PUNCT
ejpam-3649	170	18	δ)12	δ)12	NOUN
ejpam-3649	170	19	-	-	PUNCT
ejpam-3649	170	20	semi	semi	NOUN
ejpam-3649	170	21	-	-	ADJ
ejpam-3649	170	22	i	i	NOUN
ejpam-3649	170	23	-	-	NOUN
ejpam-3649	170	24	continuous	continuous	ADJ
ejpam-3649	170	25	because	because	SCONJ
ejpam-3649	170	26	{	{	PUNCT
ejpam-3649	170	27	p	p	X
ejpam-3649	170	28	}	}	PUNCT
ejpam-3649	170	29	is	be	AUX
ejpam-3649	170	30	δi	δi	ADV
ejpam-3649	170	31	-	-	PUNCT
ejpam-3649	170	32	open	open	ADJ
ejpam-3649	170	33	set	set	NOUN
ejpam-3649	170	34	and	and	CCONJ
ejpam-3649	170	35	f−1({p	f−1({p	NOUN
ejpam-3649	170	36	}	}	PUNCT
ejpam-3649	170	37	)	)	PUNCT
ejpam-3649	171	1	=	=	PRON
ejpam-3649	171	2	{	{	PUNCT
ejpam-3649	171	3	a	a	X
ejpam-3649	171	4	}	}	PUNCT
ejpam-3649	171	5	which	which	PRON
ejpam-3649	171	6	is	be	AUX
ejpam-3649	171	7	γ12	γ12	NOUN
ejpam-3649	171	8	-	-	PUNCT
ejpam-3649	171	9	βi	βi	PRON
ejpam-3649	171	10	-	-	PUNCT
ejpam-3649	171	11	open	open	ADJ
ejpam-3649	171	12	in	in	ADP
ejpam-3649	171	13	x	x	X
ejpam-3649	171	14	but	but	CCONJ
ejpam-3649	171	15	not	not	PART
ejpam-3649	171	16	γ12	γ12	NOUN
ejpam-3649	171	17	-	-	PUNCT
ejpam-3649	171	18	semi	semi	NOUN
ejpam-3649	171	19	-	-	ADJ
ejpam-3649	171	20	i	i	PRON
ejpam-3649	171	21	-	-	PUNCT
ejpam-3649	171	22	open	open	ADJ
ejpam-3649	171	23	in	in	ADP
ejpam-3649	171	24	x.	x.	NOUN
ejpam-3649	171	25	theorem	theorem	VERB
ejpam-3649	171	26	7	7	NUM
ejpam-3649	171	27	.	.	X
ejpam-3649	171	28	for	for	ADP
ejpam-3649	171	29	any	any	DET
ejpam-3649	171	30	function	function	NOUN
ejpam-3649	171	31	f	f	NOUN
ejpam-3649	171	32	:	:	PUNCT
ejpam-3649	171	33	(	(	PUNCT
ejpam-3649	171	34	x	x	NOUN
ejpam-3649	171	35	,	,	PUNCT
ejpam-3649	171	36	τ1	τ1	NOUN
ejpam-3649	171	37	,	,	PUNCT
ejpam-3649	171	38	τ2	τ2	PROPN
ejpam-3649	171	39	,	,	PUNCT
ejpam-3649	171	40	i	i	NOUN
ejpam-3649	171	41	)	)	PUNCT
ejpam-3649	171	42	→	→	SYM
ejpam-3649	171	43	(	(	PUNCT
ejpam-3649	171	44	y	y	PROPN
ejpam-3649	171	45	,	,	PUNCT
ejpam-3649	171	46	σ1	σ1	PROPN
ejpam-3649	171	47	,	,	PUNCT
ejpam-3649	171	48	σ2	σ2	NOUN
ejpam-3649	171	49	)	)	PUNCT
ejpam-3649	171	50	,	,	PUNCT
ejpam-3649	171	51	the	the	DET
ejpam-3649	171	52	next	next	ADJ
ejpam-3649	171	53	properties	property	NOUN
ejpam-3649	171	54	are	be	AUX
ejpam-3649	171	55	equivalent	equivalent	ADJ
ejpam-3649	171	56	,	,	PUNCT
ejpam-3649	171	57	1	1	X
ejpam-3649	171	58	)	)	PUNCT
ejpam-3649	171	59	f	f	PROPN
ejpam-3649	171	60	is	be	AUX
ejpam-3649	171	61	(	(	PUNCT
ejpam-3649	171	62	γ	γ	X
ejpam-3649	171	63	,	,	PUNCT
ejpam-3649	171	64	δ)ij	δ)ij	PROPN
ejpam-3649	171	65	-	-	PUNCT
ejpam-3649	171	66	βi	βi	ADV
ejpam-3649	171	67	-	-	ADJ
ejpam-3649	171	68	continuous	continuous	ADJ
ejpam-3649	171	69	2	2	NUM
ejpam-3649	171	70	)	)	PUNCT
ejpam-3649	171	71	for	for	ADP
ejpam-3649	171	72	all	all	DET
ejpam-3649	171	73	x	x	SYM
ejpam-3649	171	74	∈	∈	PROPN
ejpam-3649	171	75	x	x	X
ejpam-3649	171	76	and	and	CCONJ
ejpam-3649	171	77	every	every	DET
ejpam-3649	171	78	δi	δi	ADV
ejpam-3649	171	79	-	-	PUNCT
ejpam-3649	171	80	open	open	ADJ
ejpam-3649	171	81	set	set	VERB
ejpam-3649	171	82	v	v	NOUN
ejpam-3649	171	83	in	in	ADP
ejpam-3649	171	84	y	y	NOUN
ejpam-3649	171	85	containing	contain	VERB
ejpam-3649	171	86	f(x	f(x	PROPN
ejpam-3649	171	87	)	)	PUNCT
ejpam-3649	171	88	,	,	PUNCT
ejpam-3649	171	89	there	there	PRON
ejpam-3649	171	90	exists	exist	VERB
ejpam-3649	171	91	a	a	DET
ejpam-3649	171	92	γij	γij	ADV
ejpam-3649	171	93	-	-	PUNCT
ejpam-3649	171	94	βiopen	βiopen	NOUN
ejpam-3649	171	95	set	set	NOUN
ejpam-3649	171	96	u	u	PROPN
ejpam-3649	171	97	of	of	ADP
ejpam-3649	171	98	x	x	PUNCT
ejpam-3649	171	99	containing	contain	VERB
ejpam-3649	171	100	x	x	PUNCT
ejpam-3649	171	101	such	such	ADJ
ejpam-3649	171	102	that	that	DET
ejpam-3649	171	103	f(u	f(u	PROPN
ejpam-3649	171	104	)	)	PUNCT
ejpam-3649	172	1	⊂	⊂	PROPN
ejpam-3649	172	2	v	v	PROPN
ejpam-3649	172	3	.	.	PUNCT
ejpam-3649	172	4	i.	i.	PROPN
ejpam-3649	172	5	bukhatwa	bukhatwa	PROPN
ejpam-3649	172	6	,	,	PUNCT
ejpam-3649	172	7	s.	s.	PROPN
ejpam-3649	172	8	demiralp	demiralp	PROPN
ejpam-3649	172	9	/	/	SYM
ejpam-3649	172	10	eur	eur	PROPN
ejpam-3649	172	11	.	.	PUNCT
ejpam-3649	173	1	j.	j.	PROPN
ejpam-3649	173	2	pure	pure	PROPN
ejpam-3649	173	3	appl	appl	PROPN
ejpam-3649	173	4	.	.	PROPN
ejpam-3649	173	5	math	math	PROPN
ejpam-3649	173	6	,	,	PUNCT
ejpam-3649	173	7	13	13	NUM
ejpam-3649	173	8	(	(	PUNCT
ejpam-3649	173	9	2	2	NUM
ejpam-3649	173	10	)	)	PUNCT
ejpam-3649	173	11	(	(	PUNCT
ejpam-3649	173	12	2020	2020	NUM
ejpam-3649	173	13	)	)	PUNCT
ejpam-3649	173	14	,	,	PUNCT
ejpam-3649	173	15	269	269	NUM
ejpam-3649	173	16	-	-	SYM
ejpam-3649	173	17	279	279	NUM
ejpam-3649	173	18	275	275	NUM
ejpam-3649	173	19	proof	proof	NOUN
ejpam-3649	173	20	.	.	PUNCT
ejpam-3649	174	1	(	(	PUNCT
ejpam-3649	174	2	1⇒	1⇒	NOUN
ejpam-3649	174	3	2	2	X
ejpam-3649	174	4	)	)	PUNCT
ejpam-3649	174	5	let	let	VERB
ejpam-3649	174	6	v	v	NOUN
ejpam-3649	174	7	is	be	AUX
ejpam-3649	174	8	δi	δi	ADV
ejpam-3649	174	9	-	-	PUNCT
ejpam-3649	174	10	open	open	ADJ
ejpam-3649	174	11	in	in	ADP
ejpam-3649	174	12	y	y	PROPN
ejpam-3649	174	13	such	such	ADJ
ejpam-3649	174	14	that	that	SCONJ
ejpam-3649	174	15	f(x	f(x	PROPN
ejpam-3649	174	16	)	)	PUNCT
ejpam-3649	174	17	∈	∈	PROPN
ejpam-3649	174	18	v	v	NOUN
ejpam-3649	174	19	.	.	PUNCT
ejpam-3649	175	1	since	since	SCONJ
ejpam-3649	175	2	f	f	PROPN
ejpam-3649	175	3	is	be	AUX
ejpam-3649	175	4	(	(	PUNCT
ejpam-3649	175	5	γ	γ	X
ejpam-3649	175	6	,	,	PUNCT
ejpam-3649	175	7	δ)ij	δ)ij	PROPN
ejpam-3649	175	8	-	-	PUNCT
ejpam-3649	175	9	βi	βi	ADV
ejpam-3649	175	10	-	-	PUNCT
ejpam-3649	175	11	continuous	continuous	ADJ
ejpam-3649	175	12	,	,	PUNCT
ejpam-3649	175	13	f−1(v	f−1(v	PROPN
ejpam-3649	175	14	)	)	PUNCT
ejpam-3649	175	15	is	be	AUX
ejpam-3649	175	16	γij	γij	ADV
ejpam-3649	175	17	-	-	PUNCT
ejpam-3649	175	18	βi	βi	PRON
ejpam-3649	175	19	-	-	PUNCT
ejpam-3649	175	20	open	open	NOUN
ejpam-3649	175	21	set	set	NOUN
ejpam-3649	175	22	in	in	ADP
ejpam-3649	175	23	x.	x.	NOUN
ejpam-3649	175	24	let	let	VERB
ejpam-3649	175	25	u	u	NOUN
ejpam-3649	175	26	=	=	NOUN
ejpam-3649	175	27	f−1(v	f−1(v	PROPN
ejpam-3649	175	28	)	)	PUNCT
ejpam-3649	175	29	.	.	PUNCT
ejpam-3649	176	1	then	then	ADV
ejpam-3649	176	2	f(x	f(x	PROPN
ejpam-3649	176	3	)	)	PUNCT
ejpam-3649	176	4	∈	∈	PROPN
ejpam-3649	176	5	f(u	f(u	PROPN
ejpam-3649	176	6	)	)	PUNCT
ejpam-3649	177	1	⊂	⊂	PROPN
ejpam-3649	177	2	v.	v.	PROPN
ejpam-3649	177	3	(	(	PUNCT
ejpam-3649	177	4	2⇒	2⇒	PROPN
ejpam-3649	177	5	1	1	NUM
ejpam-3649	177	6	)	)	PUNCT
ejpam-3649	177	7	let	let	VERB
ejpam-3649	177	8	v	v	PART
ejpam-3649	177	9	be	be	AUX
ejpam-3649	177	10	δi	δi	ADV
ejpam-3649	177	11	-	-	PUNCT
ejpam-3649	177	12	open	open	ADJ
ejpam-3649	177	13	set	set	NOUN
ejpam-3649	177	14	in	in	ADP
ejpam-3649	177	15	y	y	PROPN
ejpam-3649	177	16	and	and	CCONJ
ejpam-3649	177	17	x	x	PROPN
ejpam-3649	177	18	∈	∈	PROPN
ejpam-3649	177	19	f−1(v	f−1(v	NOUN
ejpam-3649	177	20	)	)	PUNCT
ejpam-3649	177	21	.	.	PUNCT
ejpam-3649	178	1	then	then	ADV
ejpam-3649	178	2	v	v	NOUN
ejpam-3649	178	3	is	be	AUX
ejpam-3649	178	4	δi	δi	ADV
ejpam-3649	178	5	-	-	PUNCT
ejpam-3649	178	6	open	open	ADJ
ejpam-3649	178	7	set	set	NOUN
ejpam-3649	178	8	in	in	ADP
ejpam-3649	178	9	y	y	PROPN
ejpam-3649	178	10	and	and	CCONJ
ejpam-3649	179	1	f(x	f(x	PROPN
ejpam-3649	179	2	)	)	PUNCT
ejpam-3649	179	3	∈	∈	PROPN
ejpam-3649	179	4	v	v	NOUN
ejpam-3649	179	5	.	.	PUNCT
ejpam-3649	180	1	from	from	ADP
ejpam-3649	180	2	the	the	DET
ejpam-3649	180	3	hypothesis	hypothesis	NOUN
ejpam-3649	180	4	,	,	PUNCT
ejpam-3649	180	5	there	there	PRON
ejpam-3649	180	6	exists	exist	VERB
ejpam-3649	180	7	an	an	DET
ejpam-3649	180	8	γij	γij	VERB
ejpam-3649	180	9	-	-	PUNCT
ejpam-3649	180	10	βi	βi	PRON
ejpam-3649	180	11	-	-	PUNCT
ejpam-3649	180	12	open	open	ADJ
ejpam-3649	180	13	set	set	VERB
ejpam-3649	180	14	u	u	NOUN
ejpam-3649	180	15	in	in	ADP
ejpam-3649	180	16	x	x	PUNCT
ejpam-3649	180	17	containing	contain	VERB
ejpam-3649	180	18	x	x	PUNCT
ejpam-3649	180	19	such	such	ADJ
ejpam-3649	180	20	that	that	DET
ejpam-3649	180	21	f(u	f(u	PROPN
ejpam-3649	180	22	)	)	PUNCT
ejpam-3649	181	1	⊂	⊂	PROPN
ejpam-3649	181	2	v	v	NOUN
ejpam-3649	181	3	.	.	PUNCT
ejpam-3649	182	1	then	then	ADV
ejpam-3649	182	2	x	x	SYM
ejpam-3649	182	3	∈	∈	PROPN
ejpam-3649	182	4	u	u	NOUN
ejpam-3649	182	5	∈	∈	PROPN
ejpam-3649	182	6	f−1(v	f−1(v	NOUN
ejpam-3649	182	7	)	)	PUNCT
ejpam-3649	182	8	,	,	PUNCT
ejpam-3649	182	9	i.e.	i.e.	X
ejpam-3649	182	10	f−1(v	f−1(v	PROPN
ejpam-3649	182	11	)	)	PUNCT
ejpam-3649	182	12	is	be	AUX
ejpam-3649	182	13	γij	γij	ADV
ejpam-3649	182	14	-	-	PUNCT
ejpam-3649	182	15	βi	βi	PRON
ejpam-3649	182	16	-	-	PUNCT
ejpam-3649	182	17	open	open	NOUN
ejpam-3649	182	18	set	set	NOUN
ejpam-3649	182	19	in	in	ADP
ejpam-3649	182	20	x.	x.	NOUN
ejpam-3649	182	21	therefore	therefore	ADV
ejpam-3649	182	22	,	,	PUNCT
ejpam-3649	182	23	f	f	PROPN
ejpam-3649	182	24	is	be	AUX
ejpam-3649	182	25	(	(	PUNCT
ejpam-3649	182	26	γ	γ	X
ejpam-3649	182	27	,	,	PUNCT
ejpam-3649	182	28	δ)ij	δ)ij	PROPN
ejpam-3649	182	29	-	-	PUNCT
ejpam-3649	182	30	βi	βi	ADV
ejpam-3649	182	31	-	-	PUNCT
ejpam-3649	182	32	continuous	continuous	ADJ
ejpam-3649	182	33	.	.	PUNCT
ejpam-3649	183	1	theorem	theorem	ADJ
ejpam-3649	183	2	8	8	NUM
ejpam-3649	183	3	.	.	PUNCT
ejpam-3649	184	1	let	let	VERB
ejpam-3649	184	2	f	f	NOUN
ejpam-3649	184	3	:	:	PUNCT
ejpam-3649	184	4	(	(	PUNCT
ejpam-3649	184	5	x	x	NOUN
ejpam-3649	184	6	,	,	PUNCT
ejpam-3649	184	7	τ1	τ1	NOUN
ejpam-3649	184	8	,	,	PUNCT
ejpam-3649	184	9	τ2	τ2	ADJ
ejpam-3649	184	10	,	,	PUNCT
ejpam-3649	184	11	i)→	i)→	ADJ
ejpam-3649	184	12	(	(	PUNCT
ejpam-3649	184	13	y	y	PROPN
ejpam-3649	184	14	,	,	PUNCT
ejpam-3649	184	15	σ1	σ1	PROPN
ejpam-3649	184	16	,	,	PUNCT
ejpam-3649	184	17	σ2	σ2	PROPN
ejpam-3649	184	18	)	)	PUNCT
ejpam-3649	184	19	be	be	VERB
ejpam-3649	184	20	a	a	DET
ejpam-3649	184	21	(	(	PUNCT
ejpam-3649	184	22	γ	γ	X
ejpam-3649	184	23	,	,	PUNCT
ejpam-3649	184	24	δ)ij	δ)ij	PROPN
ejpam-3649	184	25	-	-	PUNCT
ejpam-3649	184	26	βi	βi	ADV
ejpam-3649	184	27	-	-	PUNCT
ejpam-3649	184	28	continuous	continuous	ADJ
ejpam-3649	184	29	function	function	NOUN
ejpam-3649	184	30	.	.	PUNCT
ejpam-3649	185	1	then	then	ADV
ejpam-3649	185	2	the	the	DET
ejpam-3649	185	3	next	next	ADJ
ejpam-3649	185	4	properties	property	NOUN
ejpam-3649	185	5	are	be	AUX
ejpam-3649	185	6	equivalent	equivalent	ADJ
ejpam-3649	185	7	:	:	PUNCT
ejpam-3649	185	8	1	1	X
ejpam-3649	185	9	)	)	PUNCT
ejpam-3649	185	10	the	the	DET
ejpam-3649	185	11	inverse	inverse	ADJ
ejpam-3649	185	12	image	image	NOUN
ejpam-3649	185	13	of	of	ADP
ejpam-3649	185	14	every	every	DET
ejpam-3649	185	15	δi	δi	ADV
ejpam-3649	185	16	-	-	PUNCT
ejpam-3649	185	17	closed	closed	ADJ
ejpam-3649	185	18	set	set	NOUN
ejpam-3649	185	19	in	in	ADP
ejpam-3649	185	20	y	y	PROPN
ejpam-3649	185	21	is	be	AUX
ejpam-3649	185	22	γij	γij	ADV
ejpam-3649	185	23	-	-	PUNCT
ejpam-3649	185	24	βi	βi	PRON
ejpam-3649	185	25	-	-	PUNCT
ejpam-3649	185	26	closed	close	VERB
ejpam-3649	185	27	set	set	NOUN
ejpam-3649	185	28	in	in	ADP
ejpam-3649	185	29	x	x	PROPN
ejpam-3649	185	30	,	,	PUNCT
ejpam-3649	185	31	2	2	X
ejpam-3649	185	32	)	)	PUNCT
ejpam-3649	185	33	f(βi	f(βi	NOUN
ejpam-3649	185	34	-	-	PUNCT
ejpam-3649	185	35	clγij	clγij	NOUN
ejpam-3649	185	36	(	(	PUNCT
ejpam-3649	185	37	u	u	NOUN
ejpam-3649	185	38	)	)	PUNCT
ejpam-3649	185	39	)	)	PUNCT
ejpam-3649	186	1	⊂	⊂	PROPN
ejpam-3649	186	2	clδj	clδj	PROPN
ejpam-3649	186	3	(	(	PUNCT
ejpam-3649	186	4	f(u	f(u	PROPN
ejpam-3649	186	5	)	)	PUNCT
ejpam-3649	186	6	)	)	PUNCT
ejpam-3649	186	7	,	,	PUNCT
ejpam-3649	186	8	for	for	ADP
ejpam-3649	186	9	all	all	DET
ejpam-3649	186	10	subset	subset	VERB
ejpam-3649	186	11	u	u	NOUN
ejpam-3649	186	12	of	of	ADP
ejpam-3649	186	13	x	x	PROPN
ejpam-3649	186	14	,	,	PUNCT
ejpam-3649	186	15	3	3	NUM
ejpam-3649	186	16	)	)	PUNCT
ejpam-3649	186	17	βi	βi	NOUN
ejpam-3649	186	18	-	-	PUNCT
ejpam-3649	186	19	clγij	clγij	NOUN
ejpam-3649	186	20	(	(	PUNCT
ejpam-3649	186	21	f	f	X
ejpam-3649	186	22	−1(v	−1(v	PROPN
ejpam-3649	186	23	)	)	PUNCT
ejpam-3649	186	24	)	)	PUNCT
ejpam-3649	187	1	⊂	⊂	PRON
ejpam-3649	187	2	f−1(clδj	f−1(clδj	PROPN
ejpam-3649	187	3	(	(	PUNCT
ejpam-3649	187	4	v	v	NOUN
ejpam-3649	187	5	)	)	PUNCT
ejpam-3649	187	6	)	)	PUNCT
ejpam-3649	187	7	,	,	PUNCT
ejpam-3649	187	8	for	for	ADP
ejpam-3649	187	9	each	each	DET
ejpam-3649	187	10	subset	subset	NOUN
ejpam-3649	187	11	v	v	NOUN
ejpam-3649	187	12	of	of	ADP
ejpam-3649	187	13	y	y	PROPN
ejpam-3649	187	14	.	.	PUNCT
ejpam-3649	188	1	proof	proof	NOUN
ejpam-3649	188	2	.	.	PUNCT
ejpam-3649	189	1	(	(	PUNCT
ejpam-3649	189	2	1⇒	1⇒	NOUN
ejpam-3649	189	3	2	2	X
ejpam-3649	189	4	)	)	PUNCT
ejpam-3649	189	5	let	let	VERB
ejpam-3649	189	6	u	u	PRON
ejpam-3649	189	7	⊂	⊂	PROPN
ejpam-3649	189	8	x.	x.	PROPN
ejpam-3649	190	1	since	since	SCONJ
ejpam-3649	190	2	clδj	clδj	PROPN
ejpam-3649	190	3	(	(	PUNCT
ejpam-3649	190	4	f(u	f(u	PROPN
ejpam-3649	190	5	)	)	PUNCT
ejpam-3649	190	6	)	)	PUNCT
ejpam-3649	190	7	is	be	AUX
ejpam-3649	190	8	an	an	DET
ejpam-3649	190	9	δi	δi	ADV
ejpam-3649	190	10	-	-	PUNCT
ejpam-3649	190	11	closed	close	VERB
ejpam-3649	190	12	set	set	NOUN
ejpam-3649	190	13	in	in	ADP
ejpam-3649	190	14	y	y	PROPN
ejpam-3649	190	15	,	,	PUNCT
ejpam-3649	190	16	from	from	ADP
ejpam-3649	190	17	the	the	DET
ejpam-3649	190	18	hypothesis	hypothesis	NOUN
ejpam-3649	190	19	,	,	PUNCT
ejpam-3649	190	20	we	we	PRON
ejpam-3649	190	21	have	have	AUX
ejpam-3649	190	22	f−1(clδj	f−1(clδj	PROPN
ejpam-3649	190	23	(	(	PUNCT
ejpam-3649	190	24	f(u	f(u	PROPN
ejpam-3649	190	25	)	)	PUNCT
ejpam-3649	190	26	)	)	PUNCT
ejpam-3649	190	27	)	)	PUNCT
ejpam-3649	190	28	is	be	AUX
ejpam-3649	190	29	γij	γij	ADV
ejpam-3649	190	30	-	-	PUNCT
ejpam-3649	190	31	βi	βi	PRON
ejpam-3649	190	32	-	-	PUNCT
ejpam-3649	190	33	closed	close	VERB
ejpam-3649	190	34	set	set	NOUN
ejpam-3649	190	35	in	in	ADP
ejpam-3649	190	36	x.	x.	NOUN
ejpam-3649	190	37	also	also	ADV
ejpam-3649	190	38	u	u	PROPN
ejpam-3649	190	39	⊂	⊂	PROPN
ejpam-3649	190	40	f−1(clδj	f−1(clδj	PROPN
ejpam-3649	190	41	(	(	PUNCT
ejpam-3649	190	42	f(u	f(u	PROPN
ejpam-3649	190	43	)	)	PUNCT
ejpam-3649	190	44	)	)	PUNCT
ejpam-3649	190	45	)	)	PUNCT
ejpam-3649	190	46	and	and	CCONJ
ejpam-3649	190	47	βi	βi	NOUN
ejpam-3649	190	48	-	-	PUNCT
ejpam-3649	190	49	clδi(u	clδi(u	NOUN
ejpam-3649	190	50	)	)	PUNCT
ejpam-3649	190	51	is	be	AUX
ejpam-3649	190	52	the	the	DET
ejpam-3649	190	53	smallest	small	ADJ
ejpam-3649	190	54	γij	γij	VERB
ejpam-3649	190	55	-	-	PUNCT
ejpam-3649	190	56	βi	βi	PRON
ejpam-3649	190	57	-	-	PUNCT
ejpam-3649	190	58	closed	close	VERB
ejpam-3649	190	59	set	set	NOUN
ejpam-3649	190	60	containing	contain	VERB
ejpam-3649	190	61	u	u	NOUN
ejpam-3649	190	62	.	.	PUNCT
ejpam-3649	191	1	therefore	therefore	ADV
ejpam-3649	191	2	,	,	PUNCT
ejpam-3649	191	3	βi	βi	PRON
ejpam-3649	191	4	−	−	PROPN
ejpam-3649	191	5	clδi(u	clδi(u	PROPN
ejpam-3649	191	6	)	)	PUNCT
ejpam-3649	191	7	⊂	⊂	PROPN
ejpam-3649	191	8	f−1(clδi(f(u	f−1(clδi(f(u	PROPN
ejpam-3649	191	9	)	)	PUNCT
ejpam-3649	191	10	)	)	PUNCT
ejpam-3649	191	11	)	)	PUNCT
ejpam-3649	191	12	.	.	PUNCT
ejpam-3649	192	1	this	this	PRON
ejpam-3649	192	2	implies	imply	VERB
ejpam-3649	192	3	that	that	SCONJ
ejpam-3649	192	4	f(βi	f(βi	NOUN
ejpam-3649	192	5	-	-	PUNCT
ejpam-3649	192	6	clγij	clγij	NOUN
ejpam-3649	192	7	(	(	PUNCT
ejpam-3649	192	8	u	u	NOUN
ejpam-3649	192	9	)	)	PUNCT
ejpam-3649	192	10	)	)	PUNCT
ejpam-3649	192	11	⊂	⊂	PROPN
ejpam-3649	192	12	clδi(f(u	clδi(f(u	PROPN
ejpam-3649	192	13	)	)	PUNCT
ejpam-3649	192	14	)	)	PUNCT
ejpam-3649	192	15	.	.	PUNCT
ejpam-3649	193	1	(	(	PUNCT
ejpam-3649	193	2	2⇒	2⇒	NOUN
ejpam-3649	193	3	3	3	NUM
ejpam-3649	193	4	)	)	PUNCT
ejpam-3649	193	5	let	let	VERB
ejpam-3649	193	6	v	v	ADP
ejpam-3649	193	7	⊂	⊂	PROPN
ejpam-3649	193	8	y	y	PROPN
ejpam-3649	193	9	.	.	PUNCT
ejpam-3649	194	1	then	then	ADV
ejpam-3649	194	2	f−1(v	f−1(v	PROPN
ejpam-3649	194	3	)	)	PUNCT
ejpam-3649	195	1	⊂	⊂	PROPN
ejpam-3649	195	2	x.	x.	NOUN
ejpam-3649	195	3	from	from	ADP
ejpam-3649	195	4	the	the	DET
ejpam-3649	195	5	hypothesis	hypothesis	NOUN
ejpam-3649	195	6	,	,	PUNCT
ejpam-3649	195	7	f(βi	f(βi	PROPN
ejpam-3649	195	8	−	−	NOUN
ejpam-3649	195	9	clγij	clγij	NOUN
ejpam-3649	195	10	(	(	PUNCT
ejpam-3649	195	11	f−1(v	f−1(v	PROPN
ejpam-3649	195	12	)	)	PUNCT
ejpam-3649	195	13	)	)	PUNCT
ejpam-3649	195	14	)	)	PUNCT
ejpam-3649	196	1	⊂	⊂	PROPN
ejpam-3649	196	2	clδj	clδj	PROPN
ejpam-3649	196	3	(	(	PUNCT
ejpam-3649	196	4	f(f−1(v	f(f−1(v	PROPN
ejpam-3649	196	5	)	)	PUNCT
ejpam-3649	196	6	)	)	PUNCT
ejpam-3649	196	7	)	)	PUNCT
ejpam-3649	197	1	⊂	⊂	PROPN
ejpam-3649	197	2	clδj	clδj	PROPN
ejpam-3649	197	3	(	(	PUNCT
ejpam-3649	197	4	v	v	NOUN
ejpam-3649	197	5	)	)	PUNCT
ejpam-3649	197	6	.	.	PUNCT
ejpam-3649	198	1	hence	hence	ADV
ejpam-3649	198	2	βi	βi	NOUN
ejpam-3649	198	3	-	-	PUNCT
ejpam-3649	198	4	clγij	clγij	NOUN
ejpam-3649	198	5	(	(	PUNCT
ejpam-3649	198	6	f	f	X
ejpam-3649	198	7	−1(v	−1(v	PROPN
ejpam-3649	198	8	)	)	PUNCT
ejpam-3649	198	9	)	)	PUNCT
ejpam-3649	199	1	⊂	⊂	PRON
ejpam-3649	199	2	f−1(clδj	f−1(clδj	PROPN
ejpam-3649	199	3	(	(	PUNCT
ejpam-3649	199	4	v	v	NOUN
ejpam-3649	199	5	)	)	PUNCT
ejpam-3649	199	6	)	)	PUNCT
ejpam-3649	199	7	.	.	PUNCT
ejpam-3649	200	1	(	(	PUNCT
ejpam-3649	200	2	3⇒	3⇒	NUM
ejpam-3649	200	3	1	1	NUM
ejpam-3649	200	4	)	)	PUNCT
ejpam-3649	200	5	let	let	VERB
ejpam-3649	200	6	v	v	PART
ejpam-3649	200	7	be	be	AUX
ejpam-3649	200	8	a	a	DET
ejpam-3649	200	9	δi	δi	ADV
ejpam-3649	200	10	-	-	PUNCT
ejpam-3649	200	11	closed	close	VERB
ejpam-3649	200	12	set	set	NOUN
ejpam-3649	200	13	in	in	ADP
ejpam-3649	200	14	y	y	PROPN
ejpam-3649	200	15	.	.	PUNCT
ejpam-3649	201	1	from	from	ADP
ejpam-3649	201	2	the	the	DET
ejpam-3649	201	3	hypothesis	hypothesis	NOUN
ejpam-3649	201	4	,	,	PUNCT
ejpam-3649	201	5	βi	βi	PRON
ejpam-3649	201	6	−	−	NOUN
ejpam-3649	201	7	clδi(f	clδi(f	INTJ
ejpam-3649	201	8	−1(v	−1(v	NOUN
ejpam-3649	201	9	)	)	PUNCT
ejpam-3649	201	10	)	)	PUNCT
ejpam-3649	202	1	⊂	⊂	PRON
ejpam-3649	202	2	f−1(clδj	f−1(clδj	PROPN
ejpam-3649	202	3	(	(	PUNCT
ejpam-3649	202	4	v	v	NOUN
ejpam-3649	202	5	)	)	PUNCT
ejpam-3649	202	6	)	)	PUNCT
ejpam-3649	203	1	=	=	SYM
ejpam-3649	203	2	f−1(v	f−1(v	PROPN
ejpam-3649	203	3	)	)	PUNCT
ejpam-3649	203	4	.	.	PUNCT
ejpam-3649	204	1	therefore	therefore	ADV
ejpam-3649	204	2	,	,	PUNCT
ejpam-3649	204	3	f−1(v	f−1(v	PROPN
ejpam-3649	204	4	)	)	PUNCT
ejpam-3649	205	1	=	=	PUNCT
ejpam-3649	205	2	βi	βi	NOUN
ejpam-3649	205	3	-	-	PUNCT
ejpam-3649	205	4	clγij	clγij	NOUN
ejpam-3649	205	5	(	(	PUNCT
ejpam-3649	205	6	f	f	X
ejpam-3649	205	7	−1(v	−1(v	PROPN
ejpam-3649	205	8	)	)	PUNCT
ejpam-3649	205	9	)	)	PUNCT
ejpam-3649	205	10	and	and	CCONJ
ejpam-3649	205	11	so	so	ADV
ejpam-3649	205	12	f−1(v	f−1(v	PROPN
ejpam-3649	205	13	)	)	PUNCT
ejpam-3649	205	14	is	be	AUX
ejpam-3649	205	15	γij	γij	ADV
ejpam-3649	205	16	-	-	PUNCT
ejpam-3649	205	17	βi	βi	PRON
ejpam-3649	205	18	-	-	PUNCT
ejpam-3649	205	19	closed	close	VERB
ejpam-3649	205	20	set	set	NOUN
ejpam-3649	205	21	in	in	ADP
ejpam-3649	205	22	x.	x.	NOUN
ejpam-3649	205	23	theorem	theorem	VERB
ejpam-3649	205	24	9	9	NUM
ejpam-3649	205	25	.	.	PUNCT
ejpam-3649	206	1	the	the	DET
ejpam-3649	206	2	function	function	NOUN
ejpam-3649	206	3	f	f	NOUN
ejpam-3649	206	4	:	:	PUNCT
ejpam-3649	206	5	(	(	PUNCT
ejpam-3649	206	6	x	x	NOUN
ejpam-3649	206	7	,	,	PUNCT
ejpam-3649	206	8	τ1	τ1	NOUN
ejpam-3649	206	9	,	,	PUNCT
ejpam-3649	206	10	τ2	τ2	PROPN
ejpam-3649	206	11	,	,	PUNCT
ejpam-3649	206	12	i	i	NOUN
ejpam-3649	206	13	)	)	PUNCT
ejpam-3649	206	14	→	→	SYM
ejpam-3649	206	15	(	(	PUNCT
ejpam-3649	206	16	y	y	PROPN
ejpam-3649	206	17	,	,	PUNCT
ejpam-3649	206	18	σ1	σ1	PROPN
ejpam-3649	206	19	,	,	PUNCT
ejpam-3649	206	20	σ2	σ2	PROPN
ejpam-3649	206	21	)	)	PUNCT
ejpam-3649	206	22	is	be	AUX
ejpam-3649	206	23	(	(	PUNCT
ejpam-3649	206	24	γ	γ	X
ejpam-3649	206	25	,	,	PUNCT
ejpam-3649	206	26	δ)ij	δ)ij	PROPN
ejpam-3649	206	27	-	-	PUNCT
ejpam-3649	206	28	βi	βi	ADV
ejpam-3649	206	29	-	-	PUNCT
ejpam-3649	206	30	continuous	continuous	ADJ
ejpam-3649	206	31	function	function	NOUN
ejpam-3649	206	32	if	if	SCONJ
ejpam-3649	206	33	and	and	CCONJ
ejpam-3649	206	34	only	only	ADV
ejpam-3649	206	35	if	if	SCONJ
ejpam-3649	206	36	f−1(intδi(v	f−1(intδi(v	PROPN
ejpam-3649	206	37	)	)	PUNCT
ejpam-3649	206	38	)	)	PUNCT
ejpam-3649	207	1	⊂	⊂	PROPN
ejpam-3649	207	2	βi	βi	PROPN
ejpam-3649	207	3	−	−	PROPN
ejpam-3649	207	4	intγijf−1(v	intγijf−1(v	NOUN
ejpam-3649	207	5	)	)	PUNCT
ejpam-3649	207	6	for	for	ADP
ejpam-3649	207	7	all	all	DET
ejpam-3649	207	8	δi	δi	ADV
ejpam-3649	207	9	-	-	PUNCT
ejpam-3649	207	10	open	open	ADJ
ejpam-3649	207	11	set	set	NOUN
ejpam-3649	207	12	of	of	ADP
ejpam-3649	207	13	y.	y.	PROPN
ejpam-3649	207	14	i.	i.	PROPN
ejpam-3649	207	15	bukhatwa	bukhatwa	PROPN
ejpam-3649	207	16	,	,	PUNCT
ejpam-3649	207	17	s.	s.	PROPN
ejpam-3649	207	18	demiralp	demiralp	PROPN
ejpam-3649	207	19	/	/	SYM
ejpam-3649	207	20	eur	eur	PROPN
ejpam-3649	207	21	.	.	PUNCT
ejpam-3649	208	1	j.	j.	PROPN
ejpam-3649	208	2	pure	pure	PROPN
ejpam-3649	208	3	appl	appl	PROPN
ejpam-3649	208	4	.	.	PROPN
ejpam-3649	208	5	math	math	PROPN
ejpam-3649	208	6	,	,	PUNCT
ejpam-3649	208	7	13	13	NUM
ejpam-3649	208	8	(	(	PUNCT
ejpam-3649	208	9	2	2	NUM
ejpam-3649	208	10	)	)	PUNCT
ejpam-3649	208	11	(	(	PUNCT
ejpam-3649	208	12	2020	2020	NUM
ejpam-3649	208	13	)	)	PUNCT
ejpam-3649	208	14	,	,	PUNCT
ejpam-3649	208	15	269	269	NUM
ejpam-3649	208	16	-	-	SYM
ejpam-3649	208	17	279	279	NUM
ejpam-3649	208	18	276	276	NUM
ejpam-3649	208	19	proof	proof	NOUN
ejpam-3649	208	20	.	.	PUNCT
ejpam-3649	209	1	let	let	VERB
ejpam-3649	209	2	f	f	PROPN
ejpam-3649	209	3	is	be	AUX
ejpam-3649	209	4	a	a	DET
ejpam-3649	209	5	(	(	PUNCT
ejpam-3649	209	6	γ	γ	X
ejpam-3649	209	7	,	,	PUNCT
ejpam-3649	209	8	δ)ij	δ)ij	PROPN
ejpam-3649	209	9	-	-	PUNCT
ejpam-3649	209	10	βi	βi	ADV
ejpam-3649	209	11	-	-	PUNCT
ejpam-3649	209	12	continuous	continuous	ADJ
ejpam-3649	209	13	function	function	NOUN
ejpam-3649	209	14	and	and	CCONJ
ejpam-3649	209	15	v	v	AUX
ejpam-3649	209	16	be	be	AUX
ejpam-3649	209	17	an	an	DET
ejpam-3649	209	18	δi	δi	ADV
ejpam-3649	209	19	-	-	PUNCT
ejpam-3649	209	20	open	open	ADJ
ejpam-3649	209	21	set	set	NOUN
ejpam-3649	209	22	in	in	ADP
ejpam-3649	209	23	y	y	PROPN
ejpam-3649	209	24	.	.	PUNCT
ejpam-3649	210	1	then	then	ADV
ejpam-3649	210	2	f−1(intδi(v	f−1(intδi(v	PROPN
ejpam-3649	210	3	)	)	PUNCT
ejpam-3649	210	4	)	)	PUNCT
ejpam-3649	210	5	is	be	AUX
ejpam-3649	210	6	a	a	DET
ejpam-3649	210	7	γij	γij	VERB
ejpam-3649	210	8	-	-	PUNCT
ejpam-3649	210	9	βi	βi	PRON
ejpam-3649	210	10	-	-	PUNCT
ejpam-3649	210	11	open	open	NOUN
ejpam-3649	210	12	set	set	NOUN
ejpam-3649	210	13	in	in	ADP
ejpam-3649	210	14	x.	x.	NOUN
ejpam-3649	210	15	therefore	therefore	ADV
ejpam-3649	210	16	,	,	PUNCT
ejpam-3649	210	17	f−1(intδi(v	f−1(intδi(v	PROPN
ejpam-3649	210	18	)	)	PUNCT
ejpam-3649	210	19	)	)	PUNCT
ejpam-3649	211	1	⊂	⊂	PROPN
ejpam-3649	211	2	βi	βi	PRON
ejpam-3649	212	1	−	−	NOUN
ejpam-3649	212	2	intγijf−1(intδi(v	intγijf−1(intδi(v	ADJ
ejpam-3649	212	3	)	)	PUNCT
ejpam-3649	212	4	)	)	PUNCT
ejpam-3649	213	1	⊂	⊂	PROPN
ejpam-3649	213	2	βi	βi	PRON
ejpam-3649	213	3	−	−	PROPN
ejpam-3649	213	4	intγijf−1((v	intγijf−1((v	PROPN
ejpam-3649	213	5	)	)	PUNCT
ejpam-3649	213	6	)	)	PUNCT
ejpam-3649	213	7	.	.	PUNCT
ejpam-3649	214	1	if	if	SCONJ
ejpam-3649	214	2	f−1(intδi(v	f−1(intδi(v	PROPN
ejpam-3649	214	3	)	)	PUNCT
ejpam-3649	214	4	)	)	PUNCT
ejpam-3649	215	1	⊂	⊂	PROPN
ejpam-3649	215	2	βi	βi	PROPN
ejpam-3649	215	3	-	-	PUNCT
ejpam-3649	215	4	intγijf	intγijf	PROPN
ejpam-3649	215	5	−1((v	−1((v	NOUN
ejpam-3649	215	6	)	)	PUNCT
ejpam-3649	215	7	)	)	PUNCT
ejpam-3649	215	8	and	and	CCONJ
ejpam-3649	215	9	v	v	AUX
ejpam-3649	215	10	be	be	AUX
ejpam-3649	215	11	a	a	DET
ejpam-3649	215	12	δi	δi	ADV
ejpam-3649	215	13	-	-	PUNCT
ejpam-3649	215	14	open	open	ADJ
ejpam-3649	215	15	set	set	NOUN
ejpam-3649	215	16	of	of	ADP
ejpam-3649	215	17	y	y	PROPN
ejpam-3649	215	18	,	,	PUNCT
ejpam-3649	215	19	then	then	ADV
ejpam-3649	215	20	f−1(v	f−1(v	PROPN
ejpam-3649	215	21	)	)	PUNCT
ejpam-3649	216	1	=	=	SYM
ejpam-3649	216	2	f−1(intδi(v	f−1(intδi(v	PROPN
ejpam-3649	216	3	)	)	PUNCT
ejpam-3649	216	4	)	)	PUNCT
ejpam-3649	217	1	⊂	⊂	PROPN
ejpam-3649	217	2	βi	βi	PRON
ejpam-3649	217	3	−	−	PROPN
ejpam-3649	217	4	intγijf−1((v	intγijf−1((v	PROPN
ejpam-3649	217	5	)	)	PUNCT
ejpam-3649	217	6	)	)	PUNCT
ejpam-3649	217	7	.	.	PUNCT
ejpam-3649	218	1	therefore	therefore	ADV
ejpam-3649	218	2	,	,	PUNCT
ejpam-3649	218	3	f−1(v	f−1(v	PROPN
ejpam-3649	218	4	)	)	PUNCT
ejpam-3649	218	5	is	be	AUX
ejpam-3649	218	6	γij	γij	ADV
ejpam-3649	218	7	-	-	PUNCT
ejpam-3649	218	8	βi	βi	PRON
ejpam-3649	218	9	-	-	PUNCT
ejpam-3649	218	10	open	open	NOUN
ejpam-3649	218	11	set	set	NOUN
ejpam-3649	218	12	in	in	ADP
ejpam-3649	218	13	x	x	PUNCT
ejpam-3649	219	1	and	and	CCONJ
ejpam-3649	219	2	so	so	ADV
ejpam-3649	219	3	f	f	PROPN
ejpam-3649	219	4	is	be	AUX
ejpam-3649	219	5	a	a	DET
ejpam-3649	219	6	(	(	PUNCT
ejpam-3649	219	7	γ	γ	X
ejpam-3649	219	8	,	,	PUNCT
ejpam-3649	219	9	δ)ij	δ)ij	PROPN
ejpam-3649	219	10	-	-	PUNCT
ejpam-3649	219	11	βi	βi	ADV
ejpam-3649	219	12	-	-	PUNCT
ejpam-3649	219	13	continuous	continuous	ADJ
ejpam-3649	219	14	function	function	NOUN
ejpam-3649	219	15	.	.	PUNCT
ejpam-3649	220	1	note	note	VERB
ejpam-3649	220	2	that	that	SCONJ
ejpam-3649	220	3	,	,	PUNCT
ejpam-3649	220	4	the	the	DET
ejpam-3649	220	5	composition	composition	NOUN
ejpam-3649	220	6	of	of	ADP
ejpam-3649	220	7	two	two	NUM
ejpam-3649	220	8	(	(	PUNCT
ejpam-3649	220	9	γ	γ	X
ejpam-3649	220	10	,	,	PUNCT
ejpam-3649	220	11	δ)ij	δ)ij	PROPN
ejpam-3649	220	12	-	-	PUNCT
ejpam-3649	220	13	βi	βi	ADV
ejpam-3649	220	14	-	-	PUNCT
ejpam-3649	220	15	continuous	continuous	ADJ
ejpam-3649	220	16	functions	function	NOUN
ejpam-3649	220	17	need	need	VERB
ejpam-3649	220	18	not	not	PART
ejpam-3649	220	19	to	to	PART
ejpam-3649	220	20	be	be	AUX
ejpam-3649	220	21	(	(	PUNCT
ejpam-3649	220	22	γ	γ	X
ejpam-3649	220	23	,	,	PUNCT
ejpam-3649	220	24	δ)ij	δ)ij	PROPN
ejpam-3649	220	25	-	-	PUNCT
ejpam-3649	220	26	βi	βi	ADV
ejpam-3649	220	27	-	-	PUNCT
ejpam-3649	220	28	continuous	continuous	ADJ
ejpam-3649	220	29	,	,	PUNCT
ejpam-3649	220	30	in	in	ADP
ejpam-3649	220	31	general	general	ADJ
ejpam-3649	220	32	.	.	PUNCT
ejpam-3649	221	1	example	example	NOUN
ejpam-3649	222	1	5	5	NUM
ejpam-3649	222	2	.	.	PUNCT
ejpam-3649	223	1	let	let	VERB
ejpam-3649	223	2	(	(	PUNCT
ejpam-3649	223	3	x	x	NOUN
ejpam-3649	223	4	,	,	PUNCT
ejpam-3649	223	5	τ1	τ1	NOUN
ejpam-3649	223	6	,	,	PUNCT
ejpam-3649	223	7	τ2	τ2	PROPN
ejpam-3649	223	8	,	,	PUNCT
ejpam-3649	223	9	i	i	PROPN
ejpam-3649	223	10	)	)	PUNCT
ejpam-3649	223	11	and	and	CCONJ
ejpam-3649	223	12	(	(	PUNCT
ejpam-3649	223	13	x	x	X
ejpam-3649	223	14	,	,	PUNCT
ejpam-3649	223	15	σ1	σ1	PROPN
ejpam-3649	223	16	,	,	PUNCT
ejpam-3649	223	17	σ2	σ2	NOUN
ejpam-3649	223	18	,	,	PUNCT
ejpam-3649	223	19	ζ	ζ	NOUN
ejpam-3649	223	20	)	)	PUNCT
ejpam-3649	223	21	be	be	VERB
ejpam-3649	223	22	two	two	NUM
ejpam-3649	223	23	ideal	ideal	ADJ
ejpam-3649	223	24	bitopological	bitopological	ADJ
ejpam-3649	223	25	spaces	space	NOUN
ejpam-3649	223	26	such	such	ADJ
ejpam-3649	223	27	that	that	SCONJ
ejpam-3649	223	28	x	x	X
ejpam-3649	224	1	=	=	X
ejpam-3649	224	2	{	{	PUNCT
ejpam-3649	224	3	a	a	PRON
ejpam-3649	224	4	,	,	PUNCT
ejpam-3649	224	5	b	b	NOUN
ejpam-3649	224	6	,	,	PUNCT
ejpam-3649	224	7	c	c	NOUN
ejpam-3649	224	8	}	}	PUNCT
ejpam-3649	224	9	,	,	PUNCT
ejpam-3649	224	10	τ1	τ1	NOUN
ejpam-3649	224	11	=	=	SYM
ejpam-3649	224	12	{	{	PUNCT
ejpam-3649	224	13	∅	∅	NOUN
ejpam-3649	224	14	,	,	PUNCT
ejpam-3649	224	15	x	x	X
ejpam-3649	224	16	,	,	PUNCT
ejpam-3649	224	17	{	{	PUNCT
ejpam-3649	224	18	a	a	PRON
ejpam-3649	224	19	,	,	PUNCT
ejpam-3649	224	20	b	b	NOUN
ejpam-3649	224	21	}	}	PUNCT
ejpam-3649	224	22	}	}	PUNCT
ejpam-3649	224	23	,	,	PUNCT
ejpam-3649	224	24	τ2	τ2	NOUN
ejpam-3649	224	25	=	=	SYM
ejpam-3649	224	26	{	{	PUNCT
ejpam-3649	224	27	∅	∅	NOUN
ejpam-3649	224	28	,	,	PUNCT
ejpam-3649	224	29	x	x	X
ejpam-3649	224	30	,	,	PUNCT
ejpam-3649	224	31	{	{	PUNCT
ejpam-3649	224	32	a	a	X
ejpam-3649	224	33	}	}	PUNCT
ejpam-3649	224	34	,	,	PUNCT
ejpam-3649	224	35	{	{	PUNCT
ejpam-3649	224	36	a	a	DET
ejpam-3649	224	37	,	,	PUNCT
ejpam-3649	224	38	b	b	NOUN
ejpam-3649	224	39	}	}	PUNCT
ejpam-3649	224	40	}	}	PUNCT
ejpam-3649	224	41	,	,	PUNCT
ejpam-3649	224	42	i	i	PRON
ejpam-3649	224	43	=	=	NOUN
ejpam-3649	224	44	{	{	PUNCT
ejpam-3649	224	45	∅	∅	NOUN
ejpam-3649	224	46	,	,	PUNCT
ejpam-3649	224	47	{	{	PUNCT
ejpam-3649	224	48	b	b	NOUN
ejpam-3649	224	49	}	}	PUNCT
ejpam-3649	224	50	}	}	PUNCT
ejpam-3649	224	51	,	,	PUNCT
ejpam-3649	224	52	uγ	uγ	ADV
ejpam-3649	224	53	=	=	SYM
ejpam-3649	224	54	{	{	PUNCT
ejpam-3649	224	55	clj(u	clj(u	NOUN
ejpam-3649	224	56	)	)	PUNCT
ejpam-3649	224	57	for	for	ADP
ejpam-3649	224	58	u	u	PROPN
ejpam-3649	224	59	∈	∈	PROPN
ejpam-3649	224	60	τi	τi	PROPN
ejpam-3649	224	61	,	,	PUNCT
ejpam-3649	224	62	b	b	X
ejpam-3649	224	63	/∈	/∈	PUNCT
ejpam-3649	224	64	u	u	PROPN
ejpam-3649	224	65	u	u	NOUN
ejpam-3649	224	66	,	,	PUNCT
ejpam-3649	224	67	b	b	PROPN
ejpam-3649	224	68	∈	∈	PROPN
ejpam-3649	224	69	u	u	NOUN
ejpam-3649	224	70	and	and	CCONJ
ejpam-3649	224	71	σ1	σ1	NOUN
ejpam-3649	224	72	=	=	SYM
ejpam-3649	224	73	{	{	PUNCT
ejpam-3649	224	74	∅	∅	NOUN
ejpam-3649	224	75	,	,	PUNCT
ejpam-3649	224	76	x	x	X
ejpam-3649	224	77	,	,	PUNCT
ejpam-3649	224	78	{	{	PUNCT
ejpam-3649	224	79	b	b	NOUN
ejpam-3649	224	80	}	}	PUNCT
ejpam-3649	224	81	,	,	PUNCT
ejpam-3649	224	82	{	{	PUNCT
ejpam-3649	224	83	b	b	X
ejpam-3649	224	84	,	,	PUNCT
ejpam-3649	224	85	c	c	NOUN
ejpam-3649	224	86	}	}	PUNCT
ejpam-3649	224	87	}	}	PUNCT
ejpam-3649	224	88	,	,	PUNCT
ejpam-3649	224	89	σ2	σ2	PROPN
ejpam-3649	224	90	=	=	SYM
ejpam-3649	224	91	{	{	PUNCT
ejpam-3649	224	92	∅	∅	NOUN
ejpam-3649	224	93	,	,	PUNCT
ejpam-3649	224	94	x	x	X
ejpam-3649	224	95	,	,	PUNCT
ejpam-3649	224	96	{	{	PUNCT
ejpam-3649	224	97	b	b	NOUN
ejpam-3649	224	98	,	,	PUNCT
ejpam-3649	224	99	c	c	NOUN
ejpam-3649	224	100	}	}	PUNCT
ejpam-3649	224	101	}	}	PUNCT
ejpam-3649	224	102	,	,	PUNCT
ejpam-3649	224	103	ζ	ζ	NOUN
ejpam-3649	224	104	=	=	SYM
ejpam-3649	224	105	{	{	PUNCT
ejpam-3649	224	106	∅	∅	NOUN
ejpam-3649	224	107	,	,	PUNCT
ejpam-3649	224	108	{	{	PUNCT
ejpam-3649	224	109	a	a	X
ejpam-3649	224	110	}	}	PUNCT
ejpam-3649	224	111	}	}	PUNCT
ejpam-3649	224	112	,	,	PUNCT
ejpam-3649	224	113	v	v	ADP
ejpam-3649	224	114	δ	δ	PROPN
ejpam-3649	224	115	=	=	PUNCT
ejpam-3649	224	116	v	v	PROPN
ejpam-3649	224	117	for	for	ADP
ejpam-3649	224	118	v	v	PROPN
ejpam-3649	224	119	∈	∈	PROPN
ejpam-3649	224	120	σi	σi	NOUN
ejpam-3649	224	121	.	.	PUNCT
ejpam-3649	225	1	let	let	AUX
ejpam-3649	225	2	define	define	VERB
ejpam-3649	225	3	f	f	X
ejpam-3649	225	4	:	:	PUNCT
ejpam-3649	225	5	(	(	PUNCT
ejpam-3649	225	6	x	x	NOUN
ejpam-3649	225	7	,	,	PUNCT
ejpam-3649	225	8	τ1	τ1	NOUN
ejpam-3649	225	9	,	,	PUNCT
ejpam-3649	225	10	τ2	τ2	PROPN
ejpam-3649	225	11	,	,	PUNCT
ejpam-3649	225	12	i	i	NOUN
ejpam-3649	225	13	)	)	PUNCT
ejpam-3649	225	14	→	→	SYM
ejpam-3649	225	15	(	(	PUNCT
ejpam-3649	225	16	x	x	X
ejpam-3649	225	17	,	,	PUNCT
ejpam-3649	225	18	σ1	σ1	PROPN
ejpam-3649	225	19	,	,	PUNCT
ejpam-3649	225	20	σ2	σ2	NOUN
ejpam-3649	225	21	)	)	PUNCT
ejpam-3649	225	22	such	such	ADJ
ejpam-3649	225	23	that	that	DET
ejpam-3649	225	24	f(a	f(a	NOUN
ejpam-3649	225	25	)	)	PUNCT
ejpam-3649	226	1	=	=	SYM
ejpam-3649	226	2	b	b	PROPN
ejpam-3649	226	3	,	,	PUNCT
ejpam-3649	226	4	f(b	f(b	PROPN
ejpam-3649	226	5	)	)	PUNCT
ejpam-3649	226	6	=	=	SYM
ejpam-3649	226	7	a	a	PRON
ejpam-3649	226	8	and	and	CCONJ
ejpam-3649	226	9	f(c	f(c	PROPN
ejpam-3649	226	10	)	)	PUNCT
ejpam-3649	226	11	=	=	SYM
ejpam-3649	226	12	c	c	NOUN
ejpam-3649	226	13	and	and	CCONJ
ejpam-3649	226	14	let	let	VERB
ejpam-3649	226	15	(	(	PUNCT
ejpam-3649	226	16	x	x	NOUN
ejpam-3649	226	17	,	,	PUNCT
ejpam-3649	226	18	ς1	ς1	NOUN
ejpam-3649	226	19	,	,	PUNCT
ejpam-3649	226	20	ς2	ς2	PROPN
ejpam-3649	226	21	)	)	PUNCT
ejpam-3649	226	22	be	be	VERB
ejpam-3649	226	23	a	a	DET
ejpam-3649	226	24	bitopological	bitopological	ADJ
ejpam-3649	226	25	space	space	NOUN
ejpam-3649	226	26	such	such	ADJ
ejpam-3649	226	27	that	that	SCONJ
ejpam-3649	226	28	ς1	ς1	NOUN
ejpam-3649	226	29	=	=	SYM
ejpam-3649	226	30	{	{	PUNCT
ejpam-3649	226	31	∅	∅	NOUN
ejpam-3649	226	32	,	,	PUNCT
ejpam-3649	226	33	x	x	X
ejpam-3649	226	34	,	,	PUNCT
ejpam-3649	226	35	{	{	PUNCT
ejpam-3649	226	36	a	a	X
ejpam-3649	226	37	}	}	PUNCT
ejpam-3649	226	38	,	,	PUNCT
ejpam-3649	226	39	{	{	PUNCT
ejpam-3649	226	40	c}{a	c}{a	PROPN
ejpam-3649	226	41	,	,	PUNCT
ejpam-3649	226	42	c	c	NOUN
ejpam-3649	226	43	}	}	PUNCT
ejpam-3649	226	44	}	}	PUNCT
ejpam-3649	226	45	,	,	PUNCT
ejpam-3649	226	46	ς2	ς2	PROPN
ejpam-3649	226	47	=	=	SYM
ejpam-3649	226	48	{	{	PUNCT
ejpam-3649	226	49	∅	∅	NOUN
ejpam-3649	226	50	,	,	PUNCT
ejpam-3649	226	51	x	x	X
ejpam-3649	226	52	,	,	PUNCT
ejpam-3649	226	53	{	{	PUNCT
ejpam-3649	226	54	b	b	NOUN
ejpam-3649	226	55	,	,	PUNCT
ejpam-3649	226	56	c	c	NOUN
ejpam-3649	226	57	}	}	PUNCT
ejpam-3649	226	58	}	}	PUNCT
ejpam-3649	226	59	,	,	PUNCT
ejpam-3649	226	60	w	w	PROPN
ejpam-3649	226	61	ξ	ξ	X
ejpam-3649	226	62	=	=	SYM
ejpam-3649	226	63	{	{	PUNCT
ejpam-3649	226	64	clj(w	clj(w	NOUN
ejpam-3649	226	65	)	)	PUNCT
ejpam-3649	226	66	for	for	ADP
ejpam-3649	226	67	w	w	PROPN
ejpam-3649	226	68	∈	∈	PROPN
ejpam-3649	226	69	τi	τi	NOUN
ejpam-3649	226	70	,	,	PUNCT
ejpam-3649	226	71	c	c	NOUN
ejpam-3649	226	72	/∈	/∈	PUNCT
ejpam-3649	226	73	w	w	PROPN
ejpam-3649	226	74	w	w	PROPN
ejpam-3649	226	75	,	,	PUNCT
ejpam-3649	226	76	c	c	PROPN
ejpam-3649	226	77	∈	∈	PROPN
ejpam-3649	226	78	w	w	NOUN
ejpam-3649	226	79	and	and	CCONJ
ejpam-3649	226	80	define	define	VERB
ejpam-3649	226	81	g	g	NOUN
ejpam-3649	226	82	:	:	PUNCT
ejpam-3649	226	83	(	(	PUNCT
ejpam-3649	226	84	x	x	NOUN
ejpam-3649	226	85	,	,	PUNCT
ejpam-3649	226	86	τ1	τ1	NOUN
ejpam-3649	226	87	,	,	PUNCT
ejpam-3649	226	88	τ2	τ2	PROPN
ejpam-3649	226	89	,	,	PUNCT
ejpam-3649	226	90	i	i	NOUN
ejpam-3649	226	91	)	)	PUNCT
ejpam-3649	226	92	→	→	SYM
ejpam-3649	226	93	(	(	PUNCT
ejpam-3649	226	94	x	x	X
ejpam-3649	226	95	,	,	PUNCT
ejpam-3649	226	96	ς1	ς1	NOUN
ejpam-3649	226	97	,	,	PUNCT
ejpam-3649	226	98	ς2	ς2	PROPN
ejpam-3649	226	99	)	)	PUNCT
ejpam-3649	226	100	such	such	ADJ
ejpam-3649	226	101	that	that	PRON
ejpam-3649	226	102	g(a	g(a	PROPN
ejpam-3649	226	103	)	)	PUNCT
ejpam-3649	226	104	=	=	SYM
ejpam-3649	226	105	b	b	PROPN
ejpam-3649	226	106	,	,	PUNCT
ejpam-3649	226	107	g(b	g(b	NOUN
ejpam-3649	226	108	)	)	PUNCT
ejpam-3649	226	109	=	=	SYM
ejpam-3649	226	110	c	c	NOUN
ejpam-3649	226	111	and	and	CCONJ
ejpam-3649	226	112	g(c	g(c	NOUN
ejpam-3649	226	113	)	)	PUNCT
ejpam-3649	226	114	=	=	PUNCT
ejpam-3649	227	1	a.	a.	NOUN
ejpam-3649	227	2	then	then	ADV
ejpam-3649	227	3	f	f	PROPN
ejpam-3649	227	4	is	be	AUX
ejpam-3649	227	5	(	(	PUNCT
ejpam-3649	227	6	γ	γ	X
ejpam-3649	227	7	,	,	PUNCT
ejpam-3649	227	8	δ)12	δ)12	PROPN
ejpam-3649	227	9	-	-	PUNCT
ejpam-3649	227	10	βi	βi	ADV
ejpam-3649	227	11	-	-	PUNCT
ejpam-3649	227	12	continuous	continuous	ADJ
ejpam-3649	227	13	function	function	NOUN
ejpam-3649	227	14	and	and	CCONJ
ejpam-3649	227	15	g	g	NOUN
ejpam-3649	227	16	is	be	AUX
ejpam-3649	227	17	(	(	PUNCT
ejpam-3649	227	18	δ	δ	PROPN
ejpam-3649	227	19	,	,	PUNCT
ejpam-3649	227	20	ξ)12	ξ)12	PROPN
ejpam-3649	227	21	-	-	PUNCT
ejpam-3649	227	22	βi	βi	ADV
ejpam-3649	227	23	-	-	PUNCT
ejpam-3649	227	24	continuous	continuous	ADJ
ejpam-3649	227	25	function	function	NOUN
ejpam-3649	227	26	but	but	CCONJ
ejpam-3649	227	27	the	the	DET
ejpam-3649	227	28	composition	composition	NOUN
ejpam-3649	227	29	g	g	PROPN
ejpam-3649	227	30	◦	◦	NOUN
ejpam-3649	227	31	f	f	X
ejpam-3649	227	32	is	be	AUX
ejpam-3649	227	33	not	not	PART
ejpam-3649	227	34	(	(	PUNCT
ejpam-3649	227	35	γ	γ	X
ejpam-3649	227	36	,	,	PUNCT
ejpam-3649	227	37	ξ)12	ξ)12	NOUN
ejpam-3649	227	38	-	-	PUNCT
ejpam-3649	227	39	βi−continuous	βi−continuous	ADJ
ejpam-3649	227	40	function	function	NOUN
ejpam-3649	227	41	because	because	SCONJ
ejpam-3649	227	42	{	{	PUNCT
ejpam-3649	227	43	a	a	PRON
ejpam-3649	227	44	}	}	PUNCT
ejpam-3649	227	45	is	be	AUX
ejpam-3649	227	46	ξ1	ξ1	NOUN
ejpam-3649	227	47	-	-	PUNCT
ejpam-3649	227	48	open	open	NOUN
ejpam-3649	227	49	set	set	NOUN
ejpam-3649	227	50	and	and	CCONJ
ejpam-3649	227	51	(	(	PUNCT
ejpam-3649	227	52	g	g	NOUN
ejpam-3649	227	53	◦	◦	NOUN
ejpam-3649	227	54	f)−1({a	f)−1({a	NOUN
ejpam-3649	227	55	}	}	PUNCT
ejpam-3649	227	56	)	)	PUNCT
ejpam-3649	227	57	=	=	PRON
ejpam-3649	228	1	{	{	PUNCT
ejpam-3649	228	2	c	c	NOUN
ejpam-3649	228	3	}	}	PUNCT
ejpam-3649	228	4	/∈	/∈	PUNCT
ejpam-3649	228	5	γ12	γ12	NOUN
ejpam-3649	228	6	-	-	PUNCT
ejpam-3649	228	7	βio(x	βio(x	NUM
ejpam-3649	228	8	)	)	PUNCT
ejpam-3649	228	9	.	.	PUNCT
ejpam-3649	229	1	definition	definition	NOUN
ejpam-3649	229	2	12	12	NUM
ejpam-3649	229	3	.	.	PUNCT
ejpam-3649	230	1	a	a	DET
ejpam-3649	230	2	function	function	NOUN
ejpam-3649	230	3	(	(	PUNCT
ejpam-3649	230	4	x	x	NOUN
ejpam-3649	230	5	,	,	PUNCT
ejpam-3649	230	6	τ1	τ1	NOUN
ejpam-3649	230	7	,	,	PUNCT
ejpam-3649	230	8	τ2	τ2	PROPN
ejpam-3649	230	9	,	,	PUNCT
ejpam-3649	230	10	i	i	NOUN
ejpam-3649	230	11	)	)	PUNCT
ejpam-3649	230	12	→	→	SYM
ejpam-3649	230	13	(	(	PUNCT
ejpam-3649	230	14	y	y	PROPN
ejpam-3649	230	15	,	,	PUNCT
ejpam-3649	230	16	σ1	σ1	PROPN
ejpam-3649	230	17	,	,	PUNCT
ejpam-3649	230	18	σ2	σ2	PROPN
ejpam-3649	230	19	)	)	PUNCT
ejpam-3649	230	20	is	be	AUX
ejpam-3649	230	21	said	say	VERB
ejpam-3649	230	22	to	to	PART
ejpam-3649	230	23	be	be	AUX
ejpam-3649	230	24	pairwise	pairwise	NOUN
ejpam-3649	230	25	(	(	PUNCT
ejpam-3649	230	26	γ	γ	NOUN
ejpam-3649	230	27	,	,	PUNCT
ejpam-3649	230	28	δ)i	δ)i	ADJ
ejpam-3649	230	29	-	-	ADJ
ejpam-3649	230	30	βicontinuous	βicontinuous	ADJ
ejpam-3649	230	31	function	function	NOUN
ejpam-3649	230	32	if	if	SCONJ
ejpam-3649	230	33	f−1(v	f−1(v	PROPN
ejpam-3649	230	34	)	)	PUNCT
ejpam-3649	230	35	is	be	AUX
ejpam-3649	230	36	γi	γi	NOUN
ejpam-3649	230	37	-	-	PUNCT
ejpam-3649	230	38	βi	βi	ADV
ejpam-3649	230	39	-	-	NOUN
ejpam-3649	230	40	open	open	ADJ
ejpam-3649	230	41	in	in	ADP
ejpam-3649	230	42	x	x	PUNCT
ejpam-3649	230	43	for	for	ADP
ejpam-3649	230	44	every	every	DET
ejpam-3649	230	45	δi	δi	ADV
ejpam-3649	230	46	-	-	PUNCT
ejpam-3649	230	47	open	open	ADJ
ejpam-3649	230	48	set	set	VERB
ejpam-3649	230	49	v	v	NOUN
ejpam-3649	230	50	in	in	ADP
ejpam-3649	230	51	y	y	PROPN
ejpam-3649	230	52	.	.	PUNCT
ejpam-3649	231	1	note	note	VERB
ejpam-3649	231	2	that	that	SCONJ
ejpam-3649	231	3	the	the	DET
ejpam-3649	231	4	notion	notion	NOUN
ejpam-3649	231	5	of	of	ADP
ejpam-3649	231	6	pairwise	pairwise	NOUN
ejpam-3649	231	7	(	(	PUNCT
ejpam-3649	231	8	γ	γ	NOUN
ejpam-3649	231	9	,	,	PUNCT
ejpam-3649	231	10	δ)i	δ)i	NOUN
ejpam-3649	231	11	-	-	PUNCT
ejpam-3649	231	12	βi	βi	ADV
ejpam-3649	231	13	-	-	ADJ
ejpam-3649	231	14	continuous	continuous	ADJ
ejpam-3649	231	15	and	and	CCONJ
ejpam-3649	231	16	(	(	PUNCT
ejpam-3649	231	17	γ	γ	PROPN
ejpam-3649	231	18	,	,	PUNCT
ejpam-3649	231	19	δ)ij	δ)ij	PROPN
ejpam-3649	231	20	-	-	PUNCT
ejpam-3649	231	21	βi	βi	ADV
ejpam-3649	231	22	-	-	ADJ
ejpam-3649	231	23	continuous	continuous	ADJ
ejpam-3649	231	24	are	be	AUX
ejpam-3649	231	25	independent	independent	ADJ
ejpam-3649	231	26	.	.	PUNCT
ejpam-3649	231	27	example	example	NOUN
ejpam-3649	232	1	6	6	NUM
ejpam-3649	232	2	.	.	PUNCT
ejpam-3649	233	1	let	let	VERB
ejpam-3649	233	2	x	x	PUNCT
ejpam-3649	233	3	=	=	PRON
ejpam-3649	233	4	{	{	PUNCT
ejpam-3649	233	5	a	a	PRON
ejpam-3649	233	6	,	,	PUNCT
ejpam-3649	233	7	b	b	NOUN
ejpam-3649	233	8	,	,	PUNCT
ejpam-3649	233	9	c	c	NOUN
ejpam-3649	233	10	}	}	PUNCT
ejpam-3649	233	11	,	,	PUNCT
ejpam-3649	233	12	τ1	τ1	NOUN
ejpam-3649	233	13	=	=	SYM
ejpam-3649	233	14	{	{	PUNCT
ejpam-3649	233	15	∅	∅	NOUN
ejpam-3649	233	16	,	,	PUNCT
ejpam-3649	233	17	x	x	X
ejpam-3649	233	18	,	,	PUNCT
ejpam-3649	233	19	{	{	PUNCT
ejpam-3649	233	20	b	b	NOUN
ejpam-3649	233	21	}	}	PUNCT
ejpam-3649	233	22	,	,	PUNCT
ejpam-3649	233	23	{	{	PUNCT
ejpam-3649	233	24	b	b	X
ejpam-3649	233	25	,	,	PUNCT
ejpam-3649	233	26	c	c	NOUN
ejpam-3649	233	27	}	}	PUNCT
ejpam-3649	233	28	}	}	PUNCT
ejpam-3649	234	1	,	,	PUNCT
ejpam-3649	234	2	τ2	τ2	NOUN
ejpam-3649	234	3	=	=	SYM
ejpam-3649	234	4	{	{	PUNCT
ejpam-3649	234	5	∅	∅	NOUN
ejpam-3649	234	6	,	,	PUNCT
ejpam-3649	234	7	x	x	X
ejpam-3649	234	8	,	,	PUNCT
ejpam-3649	234	9	{	{	PUNCT
ejpam-3649	234	10	b	b	NOUN
ejpam-3649	234	11	,	,	PUNCT
ejpam-3649	234	12	c	c	NOUN
ejpam-3649	234	13	}	}	PUNCT
ejpam-3649	234	14	}	}	PUNCT
ejpam-3649	234	15	,	,	PUNCT
ejpam-3649	234	16	i	i	PRON
ejpam-3649	234	17	=	=	NOUN
ejpam-3649	234	18	{	{	PUNCT
ejpam-3649	234	19	∅	∅	NOUN
ejpam-3649	234	20	,	,	PUNCT
ejpam-3649	234	21	{	{	PUNCT
ejpam-3649	234	22	a	a	X
ejpam-3649	234	23	}	}	PUNCT
ejpam-3649	234	24	}	}	PUNCT
ejpam-3649	234	25	with	with	ADP
ejpam-3649	234	26	operation	operation	NOUN
ejpam-3649	234	27	uγ	uγ	ADP
ejpam-3649	234	28	=	=	SYM
ejpam-3649	234	29	u	u	PROPN
ejpam-3649	234	30	for	for	ADP
ejpam-3649	234	31	u	u	PROPN
ejpam-3649	234	32	∈	∈	PROPN
ejpam-3649	234	33	τi	τi	NOUN
ejpam-3649	234	34	and	and	CCONJ
ejpam-3649	234	35	let	let	VERB
ejpam-3649	234	36	(	(	PUNCT
ejpam-3649	234	37	x	x	NOUN
ejpam-3649	234	38	,	,	PUNCT
ejpam-3649	234	39	σ1	σ1	PROPN
ejpam-3649	234	40	,	,	PUNCT
ejpam-3649	234	41	σ2	σ2	PROPN
ejpam-3649	234	42	)	)	PUNCT
ejpam-3649	234	43	be	be	VERB
ejpam-3649	234	44	a	a	DET
ejpam-3649	234	45	bitopological	bitopological	ADJ
ejpam-3649	234	46	space	space	NOUN
ejpam-3649	234	47	such	such	ADJ
ejpam-3649	234	48	that	that	SCONJ
ejpam-3649	234	49	σ1	σ1	NOUN
ejpam-3649	234	50	=	=	SYM
ejpam-3649	234	51	{	{	PUNCT
ejpam-3649	234	52	∅	∅	NOUN
ejpam-3649	234	53	,	,	PUNCT
ejpam-3649	234	54	x	x	X
ejpam-3649	234	55	,	,	PUNCT
ejpam-3649	234	56	{	{	PUNCT
ejpam-3649	234	57	a	a	X
ejpam-3649	234	58	}	}	PUNCT
ejpam-3649	234	59	,	,	PUNCT
ejpam-3649	234	60	{	{	PUNCT
ejpam-3649	234	61	c	c	X
ejpam-3649	234	62	}	}	PUNCT
ejpam-3649	234	63	,	,	PUNCT
ejpam-3649	234	64	{	{	PUNCT
ejpam-3649	234	65	a	a	PRON
ejpam-3649	234	66	,	,	PUNCT
ejpam-3649	234	67	c	c	NOUN
ejpam-3649	234	68	}	}	PUNCT
ejpam-3649	234	69	}	}	PUNCT
ejpam-3649	234	70	,	,	PUNCT
ejpam-3649	234	71	σ2	σ2	PROPN
ejpam-3649	234	72	=	=	SYM
ejpam-3649	234	73	{	{	PUNCT
ejpam-3649	234	74	∅	∅	NOUN
ejpam-3649	234	75	,	,	PUNCT
ejpam-3649	234	76	x	x	X
ejpam-3649	234	77	,	,	PUNCT
ejpam-3649	234	78	{	{	PUNCT
ejpam-3649	234	79	b	b	NOUN
ejpam-3649	234	80	,	,	PUNCT
ejpam-3649	234	81	c	c	NOUN
ejpam-3649	234	82	}	}	PUNCT
ejpam-3649	234	83	}	}	PUNCT
ejpam-3649	234	84	with	with	ADP
ejpam-3649	234	85	operation	operation	NOUN
ejpam-3649	234	86	v	v	ADP
ejpam-3649	234	87	δ	δ	PROPN
ejpam-3649	234	88	=	=	PRON
ejpam-3649	234	89	{	{	PUNCT
ejpam-3649	234	90	clj(v	clj(v	NOUN
ejpam-3649	234	91	)	)	PUNCT
ejpam-3649	234	92	for	for	ADP
ejpam-3649	234	93	v	v	NOUN
ejpam-3649	234	94	∈	∈	PROPN
ejpam-3649	234	95	σj	σj	NOUN
ejpam-3649	234	96	,	,	PUNCT
ejpam-3649	234	97	c	c	PROPN
ejpam-3649	234	98	/∈	/∈	PUNCT
ejpam-3649	235	1	v	v	NUM
ejpam-3649	235	2	v	v	NOUN
ejpam-3649	235	3	,	,	PUNCT
ejpam-3649	235	4	c	c	PROPN
ejpam-3649	235	5	∈	∈	PROPN
ejpam-3649	235	6	v	v	NOUN
ejpam-3649	235	7	and	and	CCONJ
ejpam-3649	235	8	define	define	VERB
ejpam-3649	235	9	f	f	X
ejpam-3649	235	10	:	:	PUNCT
ejpam-3649	235	11	(	(	PUNCT
ejpam-3649	235	12	x	x	NOUN
ejpam-3649	235	13	,	,	PUNCT
ejpam-3649	235	14	τ1	τ1	NOUN
ejpam-3649	235	15	,	,	PUNCT
ejpam-3649	235	16	τ2	τ2	PROPN
ejpam-3649	235	17	,	,	PUNCT
ejpam-3649	235	18	i	i	NOUN
ejpam-3649	235	19	)	)	PUNCT
ejpam-3649	235	20	→	→	SYM
ejpam-3649	235	21	(	(	PUNCT
ejpam-3649	235	22	x	x	X
ejpam-3649	235	23	,	,	PUNCT
ejpam-3649	235	24	σ1	σ1	PROPN
ejpam-3649	235	25	,	,	PUNCT
ejpam-3649	235	26	σ2	σ2	NOUN
ejpam-3649	235	27	)	)	PUNCT
ejpam-3649	235	28	such	such	ADJ
ejpam-3649	235	29	that	that	DET
ejpam-3649	235	30	f(a	f(a	NOUN
ejpam-3649	235	31	)	)	PUNCT
ejpam-3649	236	1	=	=	SYM
ejpam-3649	236	2	b	b	PROPN
ejpam-3649	236	3	,	,	PUNCT
ejpam-3649	236	4	f(b	f(b	PROPN
ejpam-3649	236	5	)	)	PUNCT
ejpam-3649	236	6	=	=	SYM
ejpam-3649	236	7	c	c	NOUN
ejpam-3649	236	8	and	and	CCONJ
ejpam-3649	236	9	f(c	f(c	PROPN
ejpam-3649	236	10	)	)	PUNCT
ejpam-3649	236	11	=	=	PUNCT
ejpam-3649	237	1	a	a	PRON
ejpam-3649	237	2	then	then	ADV
ejpam-3649	237	3	f	f	X
ejpam-3649	237	4	is	be	AUX
ejpam-3649	237	5	(	(	PUNCT
ejpam-3649	237	6	γ	γ	X
ejpam-3649	237	7	,	,	PUNCT
ejpam-3649	237	8	δ)12	δ)12	PROPN
ejpam-3649	237	9	-	-	PUNCT
ejpam-3649	237	10	βi	βi	ADV
ejpam-3649	237	11	-	-	PUNCT
ejpam-3649	237	12	continuous	continuous	ADJ
ejpam-3649	237	13	function	function	NOUN
ejpam-3649	237	14	but	but	CCONJ
ejpam-3649	237	15	it	it	PRON
ejpam-3649	237	16	is	be	AUX
ejpam-3649	237	17	not	not	PART
ejpam-3649	237	18	(	(	PUNCT
ejpam-3649	237	19	γ	γ	X
ejpam-3649	237	20	,	,	PUNCT
ejpam-3649	237	21	δ)1	δ)1	NOUN
ejpam-3649	237	22	-	-	PUNCT
ejpam-3649	237	23	βi	βi	ADV
ejpam-3649	237	24	-	-	PUNCT
ejpam-3649	237	25	continuous	continuous	ADJ
ejpam-3649	237	26	function	function	NOUN
ejpam-3649	237	27	since	since	SCONJ
ejpam-3649	237	28	{	{	PUNCT
ejpam-3649	237	29	a	a	DET
ejpam-3649	237	30	}	}	PUNCT
ejpam-3649	237	31	∈	∈	PROPN
ejpam-3649	237	32	δ1	δ1	NOUN
ejpam-3649	237	33	-	-	PUNCT
ejpam-3649	237	34	open	open	ADJ
ejpam-3649	237	35	and	and	CCONJ
ejpam-3649	237	36	f−1({a	f−1({a	NOUN
ejpam-3649	237	37	}	}	PUNCT
ejpam-3649	237	38	)	)	PUNCT
ejpam-3649	237	39	=	=	PRON
ejpam-3649	238	1	{	{	PUNCT
ejpam-3649	238	2	c	c	NOUN
ejpam-3649	238	3	}	}	PUNCT
ejpam-3649	238	4	which	which	PRON
ejpam-3649	238	5	is	be	AUX
ejpam-3649	238	6	not	not	PART
ejpam-3649	238	7	(	(	PUNCT
ejpam-3649	238	8	γ	γ	X
ejpam-3649	238	9	,	,	PUNCT
ejpam-3649	238	10	δ)1	δ)1	NOUN
ejpam-3649	238	11	-	-	PUNCT
ejpam-3649	238	12	βi	βi	PRON
ejpam-3649	238	13	-	-	PUNCT
ejpam-3649	238	14	open	open	ADJ
ejpam-3649	238	15	.	.	PUNCT
ejpam-3649	239	1	references	reference	NOUN
ejpam-3649	239	2	277	277	NUM
ejpam-3649	239	3	theorem	theorem	VERB
ejpam-3649	239	4	10	10	NUM
ejpam-3649	239	5	.	.	PUNCT
ejpam-3649	240	1	let	let	VERB
ejpam-3649	240	2	f	f	NOUN
ejpam-3649	240	3	:	:	PUNCT
ejpam-3649	240	4	(	(	PUNCT
ejpam-3649	240	5	x	x	NOUN
ejpam-3649	240	6	,	,	PUNCT
ejpam-3649	240	7	τ1	τ1	NOUN
ejpam-3649	240	8	,	,	PUNCT
ejpam-3649	240	9	τ2	τ2	ADJ
ejpam-3649	240	10	,	,	PUNCT
ejpam-3649	240	11	i)→	i)→	ADJ
ejpam-3649	240	12	(	(	PUNCT
ejpam-3649	240	13	y	y	PROPN
ejpam-3649	240	14	,	,	PUNCT
ejpam-3649	240	15	σ1	σ1	PROPN
ejpam-3649	240	16	,	,	PUNCT
ejpam-3649	240	17	σ2	σ2	NOUN
ejpam-3649	240	18	)	)	PUNCT
ejpam-3649	240	19	and	and	CCONJ
ejpam-3649	240	20	g	g	NOUN
ejpam-3649	240	21	:	:	PUNCT
ejpam-3649	240	22	(	(	PUNCT
ejpam-3649	240	23	x	x	NOUN
ejpam-3649	240	24	,	,	PUNCT
ejpam-3649	240	25	τ1	τ1	NOUN
ejpam-3649	240	26	,	,	PUNCT
ejpam-3649	240	27	τ2	τ2	ADJ
ejpam-3649	240	28	,	,	PUNCT
ejpam-3649	240	29	i)→	i)→	ADJ
ejpam-3649	240	30	(	(	PUNCT
ejpam-3649	240	31	z	z	NOUN
ejpam-3649	240	32	,	,	PUNCT
ejpam-3649	240	33	`	`	PUNCT
ejpam-3649	240	34	1	1	NUM
ejpam-3649	240	35	,	,	PUNCT
ejpam-3649	240	36	`	`	PUNCT
ejpam-3649	240	37	2	2	NUM
ejpam-3649	240	38	)	)	PUNCT
ejpam-3649	240	39	.	.	PUNCT
ejpam-3649	241	1	then	then	ADV
ejpam-3649	241	2	g	g	PROPN
ejpam-3649	241	3	◦	◦	PROPN
ejpam-3649	241	4	f	f	X
ejpam-3649	241	5	is	be	AUX
ejpam-3649	241	6	(	(	PUNCT
ejpam-3649	241	7	γ	γ	X
ejpam-3649	241	8	,	,	PUNCT
ejpam-3649	241	9	ξ)ij	ξ)ij	PROPN
ejpam-3649	241	10	-	-	PUNCT
ejpam-3649	241	11	βi	βi	ADV
ejpam-3649	241	12	-	-	ADJ
ejpam-3649	241	13	continuous	continuous	ADJ
ejpam-3649	241	14	if	if	SCONJ
ejpam-3649	241	15	f	f	PROPN
ejpam-3649	241	16	is	be	AUX
ejpam-3649	241	17	(	(	PUNCT
ejpam-3649	241	18	γ	γ	X
ejpam-3649	241	19	,	,	PUNCT
ejpam-3649	241	20	δ)ij	δ)ij	PROPN
ejpam-3649	241	21	-	-	PUNCT
ejpam-3649	241	22	βi	βi	ADV
ejpam-3649	241	23	-	-	PUNCT
ejpam-3649	241	24	continuous	continuous	ADJ
ejpam-3649	241	25	and	and	CCONJ
ejpam-3649	241	26	g	g	NOUN
ejpam-3649	241	27	is	be	AUX
ejpam-3649	241	28	pairwise	pairwise	NOUN
ejpam-3649	241	29	(	(	PUNCT
ejpam-3649	241	30	δ	δ	PROPN
ejpam-3649	241	31	,	,	PUNCT
ejpam-3649	241	32	ξ)i	ξ)i	ADJ
ejpam-3649	241	33	-	-	ADJ
ejpam-3649	241	34	βicontinuous	βicontinuous	ADJ
ejpam-3649	241	35	.	.	PUNCT
ejpam-3649	242	1	proof	proof	NOUN
ejpam-3649	242	2	.	.	PUNCT
ejpam-3649	243	1	let	let	VERB
ejpam-3649	243	2	w	w	PROPN
ejpam-3649	243	3	∈	∈	PROPN
ejpam-3649	243	4	ξi	ξi	NOUN
ejpam-3649	243	5	-	-	PUNCT
ejpam-3649	243	6	open	open	ADJ
ejpam-3649	243	7	set	set	NOUN
ejpam-3649	243	8	in	in	ADP
ejpam-3649	243	9	z.	z.	PROPN
ejpam-3649	243	10	since	since	SCONJ
ejpam-3649	243	11	g	g	PROPN
ejpam-3649	243	12	is	be	AUX
ejpam-3649	243	13	pairwise	pairwise	NOUN
ejpam-3649	243	14	(	(	PUNCT
ejpam-3649	243	15	δ	δ	PROPN
ejpam-3649	243	16	,	,	PUNCT
ejpam-3649	243	17	ξ)i	ξ)i	ADJ
ejpam-3649	244	1	-	-	ADJ
ejpam-3649	244	2	continuous	continuous	ADJ
ejpam-3649	244	3	,	,	PUNCT
ejpam-3649	244	4	then	then	ADV
ejpam-3649	244	5	g−1(w	g−1(w	PROPN
ejpam-3649	244	6	)	)	PUNCT
ejpam-3649	244	7	∈	∈	PROPN
ejpam-3649	244	8	δi	δi	ADV
ejpam-3649	244	9	-	-	PUNCT
ejpam-3649	244	10	open	open	ADJ
ejpam-3649	244	11	set	set	NOUN
ejpam-3649	244	12	in	in	ADP
ejpam-3649	244	13	y	y	PROPN
ejpam-3649	244	14	.	.	PUNCT
ejpam-3649	245	1	on	on	ADP
ejpam-3649	245	2	the	the	DET
ejpam-3649	245	3	other	other	ADJ
ejpam-3649	245	4	hand	hand	NOUN
ejpam-3649	245	5	,	,	PUNCT
ejpam-3649	245	6	since	since	SCONJ
ejpam-3649	245	7	f	f	PROPN
ejpam-3649	245	8	is	be	AUX
ejpam-3649	245	9	(	(	PUNCT
ejpam-3649	245	10	γ	γ	X
ejpam-3649	245	11	,	,	PUNCT
ejpam-3649	245	12	δ)ij	δ)ij	PROPN
ejpam-3649	245	13	-	-	PUNCT
ejpam-3649	245	14	βi	βi	ADV
ejpam-3649	245	15	-	-	PUNCT
ejpam-3649	245	16	continuous	continuous	ADJ
ejpam-3649	245	17	,	,	PUNCT
ejpam-3649	245	18	f−1(g−1(w	f−1(g−1(w	PUNCT
ejpam-3649	245	19	)	)	PUNCT
ejpam-3649	245	20	)	)	PUNCT
ejpam-3649	245	21	∈	∈	PROPN
ejpam-3649	245	22	γijβio(x	γijβio(x	PROPN
ejpam-3649	245	23	)	)	PUNCT
ejpam-3649	245	24	.	.	PUNCT
ejpam-3649	246	1	therefore	therefore	ADV
ejpam-3649	246	2	,	,	PUNCT
ejpam-3649	246	3	we	we	PRON
ejpam-3649	246	4	obtain	obtain	VERB
ejpam-3649	246	5	that	that	PRON
ejpam-3649	246	6	g	g	PROPN
ejpam-3649	246	7	◦	◦	NOUN
ejpam-3649	246	8	f	f	X
ejpam-3649	246	9	is	be	AUX
ejpam-3649	246	10	(	(	PUNCT
ejpam-3649	246	11	γ	γ	X
ejpam-3649	246	12	,	,	PUNCT
ejpam-3649	246	13	ξ)ij	ξ)ij	PROPN
ejpam-3649	246	14	-	-	PUNCT
ejpam-3649	246	15	βi	βi	ADV
ejpam-3649	246	16	-	-	PUNCT
ejpam-3649	246	17	continuous	continuous	ADJ
ejpam-3649	246	18	.	.	PUNCT
ejpam-3649	247	1	5	5	X
ejpam-3649	247	2	.	.	X
ejpam-3649	247	3	conclusion	conclusion	NOUN
ejpam-3649	247	4	in	in	ADP
ejpam-3649	247	5	this	this	DET
ejpam-3649	247	6	study	study	NOUN
ejpam-3649	247	7	,	,	PUNCT
ejpam-3649	247	8	we	we	PRON
ejpam-3649	247	9	defined	define	VERB
ejpam-3649	247	10	the	the	DET
ejpam-3649	247	11	notion	notion	NOUN
ejpam-3649	247	12	of	of	ADP
ejpam-3649	247	13	γij	γij	NOUN
ejpam-3649	247	14	-	-	PUNCT
ejpam-3649	247	15	semi	semi	NOUN
ejpam-3649	247	16	-	-	ADJ
ejpam-3649	247	17	i	i	ADV
ejpam-3649	247	18	-	-	PUNCT
ejpam-3649	247	19	open	open	ADJ
ejpam-3649	247	20	sets	set	NOUN
ejpam-3649	247	21	and	and	CCONJ
ejpam-3649	247	22	γij	γij	NOUN
ejpam-3649	247	23	-	-	PUNCT
ejpam-3649	247	24	βi	βi	PRON
ejpam-3649	247	25	-	-	PUNCT
ejpam-3649	247	26	open	open	ADJ
ejpam-3649	247	27	sets	set	NOUN
ejpam-3649	247	28	by	by	ADP
ejpam-3649	247	29	generalizing	generalize	VERB
ejpam-3649	247	30	(	(	PUNCT
ejpam-3649	247	31	i	i	PROPN
ejpam-3649	247	32	,	,	PUNCT
ejpam-3649	247	33	j)-semi	j)-semi	PROPN
ejpam-3649	247	34	-	-	PUNCT
ejpam-3649	247	35	i	i	PRON
ejpam-3649	247	36	-	-	PUNCT
ejpam-3649	247	37	open	open	ADJ
ejpam-3649	247	38	sets	set	NOUN
ejpam-3649	247	39	and	and	CCONJ
ejpam-3649	247	40	(	(	PUNCT
ejpam-3649	247	41	ij)-βi	ij)-βi	NOUN
ejpam-3649	247	42	-	-	ADJ
ejpam-3649	247	43	open	open	ADJ
ejpam-3649	247	44	sets	set	NOUN
ejpam-3649	247	45	in	in	ADP
ejpam-3649	247	46	ideal	ideal	ADJ
ejpam-3649	247	47	bitopological	bitopological	ADJ
ejpam-3649	247	48	spaces	space	NOUN
ejpam-3649	247	49	with	with	ADP
ejpam-3649	247	50	an	an	DET
ejpam-3649	247	51	operation	operation	NOUN
ejpam-3649	247	52	γ	γ	X
ejpam-3649	247	53	:	:	PUNCT
ejpam-3649	247	54	τ	τ	PROPN
ejpam-3649	247	55	→	→	SYM
ejpam-3649	247	56	p	p	X
ejpam-3649	247	57	(	(	PUNCT
ejpam-3649	247	58	x	x	NOUN
ejpam-3649	247	59	)	)	PUNCT
ejpam-3649	247	60	.	.	PUNCT
ejpam-3649	248	1	we	we	PRON
ejpam-3649	248	2	show	show	VERB
ejpam-3649	248	3	that	that	SCONJ
ejpam-3649	248	4	every	every	DET
ejpam-3649	248	5	γij	γij	VERB
ejpam-3649	248	6	-	-	PUNCT
ejpam-3649	248	7	semi	semi	NOUN
ejpam-3649	248	8	-	-	ADJ
ejpam-3649	248	9	i	i	PRON
ejpam-3649	248	10	-	-	PUNCT
ejpam-3649	248	11	open	open	ADJ
ejpam-3649	248	12	set	set	NOUN
ejpam-3649	248	13	is	be	AUX
ejpam-3649	248	14	a	a	DET
ejpam-3649	248	15	γij	γij	NOUN
ejpam-3649	248	16	-	-	PUNCT
ejpam-3649	248	17	βiopen	βiopen	NOUN
ejpam-3649	248	18	but	but	CCONJ
ejpam-3649	248	19	the	the	DET
ejpam-3649	248	20	converse	converse	NOUN
ejpam-3649	248	21	is	be	AUX
ejpam-3649	248	22	not	not	PART
ejpam-3649	248	23	always	always	ADV
ejpam-3649	248	24	true	true	ADJ
ejpam-3649	248	25	.	.	PUNCT
ejpam-3649	249	1	then	then	ADV
ejpam-3649	249	2	we	we	PRON
ejpam-3649	249	3	described	describe	VERB
ejpam-3649	249	4	the	the	DET
ejpam-3649	249	5	notions	notion	NOUN
ejpam-3649	249	6	γij	γij	VERB
ejpam-3649	249	7	-	-	PUNCT
ejpam-3649	249	8	βi	βi	NOUN
ejpam-3649	249	9	-	-	ADJ
ejpam-3649	249	10	interior	interior	ADJ
ejpam-3649	249	11	and	and	CCONJ
ejpam-3649	249	12	γij	γij	NOUN
ejpam-3649	249	13	-	-	PUNCT
ejpam-3649	249	14	βi	βi	NOUN
ejpam-3649	249	15	-	-	PUNCT
ejpam-3649	249	16	cluster	cluster	NOUN
ejpam-3649	249	17	of	of	ADP
ejpam-3649	249	18	a	a	DET
ejpam-3649	249	19	set	set	NOUN
ejpam-3649	249	20	a.	a.	NOUN
ejpam-3649	249	21	finally	finally	ADV
ejpam-3649	249	22	we	we	PRON
ejpam-3649	249	23	characterized	characterize	VERB
ejpam-3649	249	24	(	(	PUNCT
ejpam-3649	249	25	γ	γ	X
ejpam-3649	249	26	,	,	PUNCT
ejpam-3649	249	27	δ)ij	δ)ij	PROPN
ejpam-3649	249	28	-	-	PUNCT
ejpam-3649	249	29	semi	semi	NOUN
ejpam-3649	249	30	-	-	ADJ
ejpam-3649	249	31	i	i	NOUN
ejpam-3649	249	32	-	-	PUNCT
ejpam-3649	249	33	continuous	continuous	ADJ
ejpam-3649	249	34	and	and	CCONJ
ejpam-3649	249	35	(	(	PUNCT
ejpam-3649	249	36	γ	γ	PROPN
ejpam-3649	249	37	,	,	PUNCT
ejpam-3649	249	38	δ)ij	δ)ij	PROPN
ejpam-3649	249	39	-	-	PUNCT
ejpam-3649	249	40	βi	βi	ADV
ejpam-3649	249	41	-	-	PUNCT
ejpam-3649	249	42	continuous	continuous	ADJ
ejpam-3649	249	43	functions	function	NOUN
ejpam-3649	249	44	and	and	CCONJ
ejpam-3649	249	45	showed	show	VERB
ejpam-3649	249	46	that	that	SCONJ
ejpam-3649	249	47	any	any	DET
ejpam-3649	249	48	(	(	PUNCT
ejpam-3649	249	49	γ	γ	X
ejpam-3649	249	50	,	,	PUNCT
ejpam-3649	249	51	δ)ij	δ)ij	PROPN
ejpam-3649	249	52	-	-	PUNCT
ejpam-3649	249	53	semi	semi	NOUN
ejpam-3649	249	54	-	-	ADJ
ejpam-3649	249	55	i	i	ADV
ejpam-3649	249	56	-	-	PUNCT
ejpam-3649	249	57	continuous	continuous	ADJ
ejpam-3649	249	58	function	function	NOUN
ejpam-3649	249	59	is	be	AUX
ejpam-3649	249	60	a	a	DET
ejpam-3649	249	61	(	(	PUNCT
ejpam-3649	249	62	γ	γ	X
ejpam-3649	249	63	,	,	PUNCT
ejpam-3649	249	64	δ)ij	δ)ij	PROPN
ejpam-3649	249	65	-	-	PUNCT
ejpam-3649	249	66	βi	βi	ADV
ejpam-3649	249	67	-	-	PUNCT
ejpam-3649	249	68	continuous	continuous	ADJ
ejpam-3649	249	69	but	but	CCONJ
ejpam-3649	249	70	the	the	DET
ejpam-3649	249	71	converse	converse	NOUN
ejpam-3649	249	72	is	be	AUX
ejpam-3649	249	73	not	not	PART
ejpam-3649	249	74	always	always	ADV
ejpam-3649	249	75	true	true	ADJ
ejpam-3649	249	76	.	.	PUNCT
ejpam-3649	250	1	also	also	ADV
ejpam-3649	250	2	it	it	PRON
ejpam-3649	250	3	is	be	AUX
ejpam-3649	250	4	shown	show	VERB
ejpam-3649	250	5	that	that	SCONJ
ejpam-3649	250	6	the	the	DET
ejpam-3649	250	7	composition	composition	NOUN
ejpam-3649	250	8	of	of	ADP
ejpam-3649	250	9	two	two	NUM
ejpam-3649	250	10	(	(	PUNCT
ejpam-3649	250	11	γ	γ	X
ejpam-3649	250	12	,	,	PUNCT
ejpam-3649	250	13	δ)ij	δ)ij	PROPN
ejpam-3649	250	14	-	-	PUNCT
ejpam-3649	250	15	βi	βi	ADV
ejpam-3649	250	16	-	-	PUNCT
ejpam-3649	250	17	continuous	continuous	ADJ
ejpam-3649	250	18	functions	function	NOUN
ejpam-3649	250	19	need	need	VERB
ejpam-3649	250	20	not	not	PART
ejpam-3649	250	21	to	to	PART
ejpam-3649	250	22	be	be	AUX
ejpam-3649	250	23	(	(	PUNCT
ejpam-3649	250	24	γ	γ	X
ejpam-3649	250	25	,	,	PUNCT
ejpam-3649	250	26	δ)ij	δ)ij	PROPN
ejpam-3649	250	27	-	-	PUNCT
ejpam-3649	250	28	βi	βi	ADV
ejpam-3649	250	29	-	-	PUNCT
ejpam-3649	250	30	continuous	continuous	ADJ
ejpam-3649	250	31	.	.	PUNCT
ejpam-3649	251	1	consequently	consequently	ADV
ejpam-3649	251	2	the	the	DET
ejpam-3649	251	3	following	follow	VERB
ejpam-3649	251	4	diagrams	diagram	NOUN
ejpam-3649	251	5	are	be	AUX
ejpam-3649	251	6	true	true	ADJ
ejpam-3649	251	7	:	:	PUNCT
ejpam-3649	251	8	γij	γij	ADJ
ejpam-3649	251	9	-	-	PUNCT
ejpam-3649	251	10	semi	semi	NOUN
ejpam-3649	251	11	-	-	ADJ
ejpam-3649	251	12	i	i	PRON
ejpam-3649	251	13	-	-	PUNCT
ejpam-3649	251	14	open	open	ADJ
ejpam-3649	251	15	−→	−→	NOUN
ejpam-3649	251	16	γij	γij	VERB
ejpam-3649	251	17	-	-	PUNCT
ejpam-3649	251	18	βi	βi	PRON
ejpam-3649	251	19	-	-	PUNCT
ejpam-3649	251	20	open	open	ADJ
ejpam-3649	251	21	−→	−→	NOUN
ejpam-3649	251	22	γij	γij	NOUN
ejpam-3649	251	23	-	-	PUNCT
ejpam-3649	251	24	β	β	NOUN
ejpam-3649	251	25	-	-	ADJ
ejpam-3649	251	26	open	open	ADJ
ejpam-3649	251	27	γij	γij	NOUN
ejpam-3649	251	28	-	-	PUNCT
ejpam-3649	251	29	βi	βi	NOUN
ejpam-3649	251	30	-	-	PUNCT
ejpam-3649	251	31	open←→	open←→	NOUN
ejpam-3649	251	32	γij	γij	NOUN
ejpam-3649	251	33	-	-	PUNCT
ejpam-3649	251	34	β	β	NOUN
ejpam-3649	251	35	-	-	ADJ
ejpam-3649	251	36	open	open	ADJ
ejpam-3649	251	37	(	(	PUNCT
ejpam-3649	251	38	i	i	NOUN
ejpam-3649	251	39	=	=	NOUN
ejpam-3649	251	40	{	{	PUNCT
ejpam-3649	251	41	∅	∅	NOUN
ejpam-3649	251	42	}	}	PUNCT
ejpam-3649	251	43	)	)	PUNCT
ejpam-3649	251	44	γij	γij	VERB
ejpam-3649	251	45	-	-	PUNCT
ejpam-3649	251	46	βi	βi	NOUN
ejpam-3649	251	47	-	-	PUNCT
ejpam-3649	251	48	open←→	open←→	NOUN
ejpam-3649	251	49	γij	γij	NOUN
ejpam-3649	251	50	-	-	PUNCT
ejpam-3649	251	51	semi	semi	NOUN
ejpam-3649	251	52	-	-	ADJ
ejpam-3649	251	53	open	open	ADJ
ejpam-3649	251	54	(	(	PUNCT
ejpam-3649	251	55	i	i	NOUN
ejpam-3649	251	56	=	=	NOUN
ejpam-3649	251	57	p	p	X
ejpam-3649	251	58	(	(	PUNCT
ejpam-3649	251	59	x	x	NOUN
ejpam-3649	251	60	)	)	PUNCT
ejpam-3649	251	61	)	)	PUNCT
ejpam-3649	251	62	(	(	PUNCT
ejpam-3649	251	63	γ	γ	X
ejpam-3649	251	64	,	,	PUNCT
ejpam-3649	251	65	δ)ij	δ)ij	PROPN
ejpam-3649	251	66	-	-	PUNCT
ejpam-3649	251	67	semi	semi	NOUN
ejpam-3649	251	68	-	-	ADJ
ejpam-3649	251	69	i	i	ADV
ejpam-3649	251	70	-	-	PUNCT
ejpam-3649	251	71	continuous	continuous	ADJ
ejpam-3649	251	72	−→	−→	NOUN
ejpam-3649	251	73	(	(	PUNCT
ejpam-3649	251	74	γ	γ	X
ejpam-3649	251	75	,	,	PUNCT
ejpam-3649	251	76	δ)ij	δ)ij	PROPN
ejpam-3649	251	77	-	-	PUNCT
ejpam-3649	251	78	βi	βi	ADV
ejpam-3649	251	79	-	-	ADJ
ejpam-3649	251	80	continuous	continuous	ADJ
ejpam-3649	251	81	these	these	DET
ejpam-3649	251	82	notations	notation	NOUN
ejpam-3649	251	83	,	,	PUNCT
ejpam-3649	251	84	defined	define	VERB
ejpam-3649	251	85	in	in	ADP
ejpam-3649	251	86	this	this	DET
ejpam-3649	251	87	study	study	NOUN
ejpam-3649	251	88	,	,	PUNCT
ejpam-3649	251	89	can	can	AUX
ejpam-3649	251	90	be	be	AUX
ejpam-3649	251	91	extended	extend	VERB
ejpam-3649	251	92	to	to	ADP
ejpam-3649	251	93	other	other	ADJ
ejpam-3649	251	94	practicable	practicable	ADJ
ejpam-3649	251	95	research	research	NOUN
ejpam-3649	251	96	fields	field	NOUN
ejpam-3649	251	97	of	of	ADP
ejpam-3649	251	98	topology	topology	NOUN
ejpam-3649	251	99	such	such	ADJ
ejpam-3649	251	100	as	as	ADP
ejpam-3649	251	101	fuzzy	fuzzy	ADJ
ejpam-3649	251	102	topology	topology	NOUN
ejpam-3649	251	103	,	,	PUNCT
ejpam-3649	251	104	soft	soft	ADJ
ejpam-3649	251	105	topology	topology	NOUN
ejpam-3649	251	106	,	,	PUNCT
ejpam-3649	251	107	intuitionistic	intuitionistic	ADJ
ejpam-3649	251	108	topology	topology	NOUN
ejpam-3649	251	109	and	and	CCONJ
ejpam-3649	251	110	so	so	ADV
ejpam-3649	251	111	on	on	ADV
ejpam-3649	251	112	.	.	PUNCT
ejpam-3649	252	1	also	also	ADV
ejpam-3649	252	2	generalized	generalized	ADJ
ejpam-3649	252	3	seperation	seperation	NOUN
ejpam-3649	252	4	axioms	axiom	NOUN
ejpam-3649	252	5	can	can	AUX
ejpam-3649	252	6	be	be	AUX
ejpam-3649	252	7	introduced	introduce	VERB
ejpam-3649	252	8	by	by	ADP
ejpam-3649	252	9	the	the	DET
ejpam-3649	252	10	concept	concept	NOUN
ejpam-3649	252	11	of	of	ADP
ejpam-3649	252	12	generalized	generalized	ADJ
ejpam-3649	252	13	β	β	X
ejpam-3649	252	14	-	-	ADJ
ejpam-3649	252	15	open	open	ADJ
ejpam-3649	252	16	set	set	NOUN
ejpam-3649	252	17	.	.	PUNCT
ejpam-3649	253	1	references	reference	NOUN
ejpam-3649	253	2	[	[	X
ejpam-3649	253	3	1	1	NUM
ejpam-3649	253	4	]	]	PUNCT
ejpam-3649	253	5	b.	b.	PROPN
ejpam-3649	253	6	ahmad	ahmad	PROPN
ejpam-3649	253	7	and	and	CCONJ
ejpam-3649	253	8	s.	s.	PROPN
ejpam-3649	253	9	hussain	hussain	PROPN
ejpam-3649	253	10	.	.	PUNCT
ejpam-3649	254	1	γ	γ	X
ejpam-3649	254	2	-	-	PUNCT
ejpam-3649	254	3	semi	semi	ADJ
ejpam-3649	254	4	-	-	ADJ
ejpam-3649	254	5	open	open	ADJ
ejpam-3649	254	6	sets	set	NOUN
ejpam-3649	254	7	in	in	ADP
ejpam-3649	254	8	topological	topological	PROPN
ejpam-3649	254	9	spaces	space	NOUN
ejpam-3649	254	10	ii	ii	PROPN
ejpam-3649	254	11	.	.	PROPN
ejpam-3649	255	1	southeast	southeast	PROPN
ejpam-3649	255	2	asian	asian	ADJ
ejpam-3649	255	3	bull	bull	PROPN
ejpam-3649	255	4	.	.	PUNCT
ejpam-3649	256	1	math	math	NOUN
ejpam-3649	256	2	34	34	NUM
ejpam-3649	256	3	,	,	PUNCT
ejpam-3649	256	4	no	no	INTJ
ejpam-3649	256	5	.	.	NOUN
ejpam-3649	256	6	6	6	NUM
ejpam-3649	256	7	,	,	PUNCT
ejpam-3649	256	8	997	997	NUM
ejpam-3649	256	9	-	-	SYM
ejpam-3649	256	10	1008	1008	NUM
ejpam-3649	256	11	,	,	PUNCT
ejpam-3649	256	12	2010	2010	NUM
ejpam-3649	256	13	.	.	PUNCT
ejpam-3649	257	1	[	[	X
ejpam-3649	257	2	2	2	NUM
ejpam-3649	257	3	]	]	X
ejpam-3649	257	4	b.	b.	PROPN
ejpam-3649	257	5	bhattacharya	bhattacharya	PROPN
ejpam-3649	257	6	and	and	CCONJ
ejpam-3649	257	7	a.	a.	PROPN
ejpam-3649	257	8	paul	paul	PROPN
ejpam-3649	257	9	.	.	PUNCT
ejpam-3649	258	1	a	a	DET
ejpam-3649	258	2	new	new	ADJ
ejpam-3649	258	3	approach	approach	NOUN
ejpam-3649	258	4	of	of	ADP
ejpam-3649	258	5	γ	γ	X
ejpam-3649	258	6	-	-	ADJ
ejpam-3649	258	7	open	open	ADJ
ejpam-3649	258	8	sets	set	NOUN
ejpam-3649	258	9	in	in	ADP
ejpam-3649	258	10	bitopological	bitopological	ADJ
ejpam-3649	258	11	spaces	space	NOUN
ejpam-3649	258	12	,	,	PUNCT
ejpam-3649	258	13	gen	gen	PROPN
ejpam-3649	258	14	.	.	PROPN
ejpam-3649	258	15	math	math	PROPN
ejpam-3649	258	16	.	.	PUNCT
ejpam-3649	259	1	notes	note	NOUN
ejpam-3649	259	2	20(2	20(2	NUM
ejpam-3649	259	3	)	)	PUNCT
ejpam-3649	259	4	,	,	PUNCT
ejpam-3649	259	5	95	95	NUM
ejpam-3649	259	6	-	-	SYM
ejpam-3649	259	7	110	110	NUM
ejpam-3649	259	8	,	,	PUNCT
ejpam-3649	259	9	2014	2014	NUM
ejpam-3649	259	10	.	.	PUNCT
ejpam-3649	260	1	[	[	X
ejpam-3649	260	2	3	3	NUM
ejpam-3649	260	3	]	]	X
ejpam-3649	260	4	m.	m.	NOUN
ejpam-3649	260	5	caldas	caldas	PROPN
ejpam-3649	260	6	,	,	PUNCT
ejpam-3649	260	7	s.	s.	PROPN
ejpam-3649	260	8	jafari	jafari	PROPN
ejpam-3649	260	9	and	and	CCONJ
ejpam-3649	260	10	n.	n.	PROPN
ejpam-3649	260	11	rajesh	rajesh	PROPN
ejpam-3649	260	12	.	.	PUNCT
ejpam-3649	261	1	some	some	DET
ejpam-3649	261	2	fundamental	fundamental	ADJ
ejpam-3649	261	3	properties	property	NOUN
ejpam-3649	261	4	of	of	ADP
ejpam-3649	261	5	β	β	ADJ
ejpam-3649	261	6	-	-	ADJ
ejpam-3649	261	7	open	open	ADJ
ejpam-3649	261	8	sets	set	NOUN
ejpam-3649	261	9	in	in	ADP
ejpam-3649	261	10	ideal	ideal	ADJ
ejpam-3649	261	11	bitopological	bitopological	ADJ
ejpam-3649	261	12	spaces	space	NOUN
ejpam-3649	261	13	.	.	PUNCT
ejpam-3649	262	1	european	european	ADJ
ejpam-3649	262	2	journal	journal	PROPN
ejpam-3649	262	3	of	of	ADP
ejpam-3649	262	4	pure	pure	ADJ
ejpam-3649	262	5	and	and	CCONJ
ejpam-3649	262	6	applied	applied	ADJ
ejpam-3649	262	7	mathematics	mathematic	NOUN
ejpam-3649	262	8	,	,	PUNCT
ejpam-3649	262	9	6(2	6(2	NUM
ejpam-3649	262	10	)	)	PUNCT
ejpam-3649	262	11	,	,	PUNCT
ejpam-3649	262	12	247	247	NUM
ejpam-3649	262	13	-	-	SYM
ejpam-3649	262	14	255	255	NUM
ejpam-3649	262	15	,	,	PUNCT
ejpam-3649	262	16	2013	2013	NUM
ejpam-3649	262	17	.	.	PUNCT
ejpam-3649	263	1	[	[	X
ejpam-3649	263	2	4	4	NUM
ejpam-3649	263	3	]	]	ADJ
ejpam-3649	263	4	a.csaszar	a.csaszar	NOUN
ejpam-3649	263	5	.	.	PUNCT
ejpam-3649	264	1	generalized	generalize	VERB
ejpam-3649	264	2	open	open	ADJ
ejpam-3649	264	3	sets	set	NOUN
ejpam-3649	264	4	.	.	PUNCT
ejpam-3649	265	1	acta	acta	PROPN
ejpam-3649	265	2	mathematica	mathematica	PROPN
ejpam-3649	265	3	hungarica	hungarica	PROPN
ejpam-3649	265	4	,	,	PUNCT
ejpam-3649	265	5	75(1	75(1	NOUN
ejpam-3649	265	6	-	-	PUNCT
ejpam-3649	265	7	2	2	NUM
ejpam-3649	265	8	)	)	PUNCT
ejpam-3649	265	9	,	,	PUNCT
ejpam-3649	265	10	65	65	NUM
ejpam-3649	265	11	-	-	SYM
ejpam-3649	265	12	87	87	NUM
ejpam-3649	265	13	,	,	PUNCT
ejpam-3649	265	14	1997	1997	NUM
ejpam-3649	265	15	.	.	PUNCT
ejpam-3649	266	1	references	reference	NOUN
ejpam-3649	266	2	278	278	NUM
ejpam-3649	267	1	[	[	X
ejpam-3649	267	2	5	5	NUM
ejpam-3649	267	3	]	]	PUNCT
ejpam-3649	267	4	e.	e.	PROPN
ejpam-3649	267	5	ekici	ekici	PROPN
ejpam-3649	267	6	.	.	PUNCT
ejpam-3649	268	1	on	on	ADP
ejpam-3649	268	2	pre	pre	ADJ
ejpam-3649	268	3	-	-	ADJ
ejpam-3649	268	4	i	i	PRON
ejpam-3649	268	5	-	-	PUNCT
ejpam-3649	268	6	open	open	ADJ
ejpam-3649	268	7	sets	set	NOUN
ejpam-3649	268	8	,	,	PUNCT
ejpam-3649	268	9	semi	semi	ADJ
ejpam-3649	268	10	-	-	ADJ
ejpam-3649	268	11	i	i	ADV
ejpam-3649	268	12	-	-	PUNCT
ejpam-3649	268	13	open	open	ADJ
ejpam-3649	268	14	sets	set	NOUN
ejpam-3649	268	15	and	and	CCONJ
ejpam-3649	268	16	bi	bi	ADJ
ejpam-3649	268	17	-	-	ADJ
ejpam-3649	268	18	open	open	ADJ
ejpam-3649	268	19	sets	set	NOUN
ejpam-3649	268	20	in	in	ADP
ejpam-3649	268	21	ideal	ideal	ADJ
ejpam-3649	268	22	topological	topological	ADJ
ejpam-3649	268	23	spaces	space	NOUN
ejpam-3649	268	24	.	.	PUNCT
ejpam-3649	269	1	acta	acta	PROPN
ejpam-3649	269	2	universitatis	universitatis	PROPN
ejpam-3649	269	3	apulensis	apulensis	NOUN
ejpam-3649	269	4	,	,	PUNCT
ejpam-3649	269	5	30	30	NUM
ejpam-3649	269	6	,	,	PUNCT
ejpam-3649	269	7	293	293	NUM
ejpam-3649	269	8	-	-	SYM
ejpam-3649	269	9	303	303	NUM
ejpam-3649	269	10	,	,	PUNCT
ejpam-3649	269	11	2012	2012	NUM
ejpam-3649	269	12	.	.	PUNCT
ejpam-3649	270	1	[	[	X
ejpam-3649	270	2	6	6	NUM
ejpam-3649	270	3	]	]	PUNCT
ejpam-3649	270	4	s.	s.	PROPN
ejpam-3649	270	5	d.	d.	PROPN
ejpam-3649	270	6	jyoti	jyoti	PROPN
ejpam-3649	270	7	.	.	PUNCT
ejpam-3649	271	1	bi	bi	ADJ
ejpam-3649	271	2	-	-	ADJ
ejpam-3649	271	3	open	open	ADJ
ejpam-3649	271	4	sets	set	NOUN
ejpam-3649	271	5	in	in	ADP
ejpam-3649	271	6	ideal	ideal	ADJ
ejpam-3649	271	7	bitopological	bitopological	ADJ
ejpam-3649	271	8	space	space	NOUN
ejpam-3649	271	9	.	.	PUNCT
ejpam-3649	272	1	international	international	ADJ
ejpam-3649	272	2	journal	journal	NOUN
ejpam-3649	272	3	of	of	ADP
ejpam-3649	272	4	pure	pure	ADJ
ejpam-3649	272	5	and	and	CCONJ
ejpam-3649	272	6	applied	apply	VERB
ejpam-3649	272	7	mathematics	mathematic	NOUN
ejpam-3649	272	8	105(1	105(1	NUM
ejpam-3649	272	9	)	)	PUNCT
ejpam-3649	272	10	,	,	PUNCT
ejpam-3649	272	11	7	7	NUM
ejpam-3649	272	12	-	-	SYM
ejpam-3649	272	13	18	18	NUM
ejpam-3649	272	14	,	,	PUNCT
ejpam-3649	272	15	(	(	PUNCT
ejpam-3649	272	16	2015	2015	NUM
ejpam-3649	272	17	)	)	PUNCT
ejpam-3649	272	18	.	.	PUNCT
ejpam-3649	273	1	[	[	X
ejpam-3649	273	2	7	7	X
ejpam-3649	273	3	]	]	X
ejpam-3649	273	4	s.	s.	PROPN
ejpam-3649	273	5	jafari	jafari	PROPN
ejpam-3649	273	6	and	and	CCONJ
ejpam-3649	273	7	n.	n.	PROPN
ejpam-3649	273	8	rajesh	rajesh	PROPN
ejpam-3649	273	9	.	.	PUNCT
ejpam-3649	274	1	on	on	ADP
ejpam-3649	274	2	qi	qi	NOUN
ejpam-3649	274	3	-	-	PUNCT
ejpam-3649	274	4	open	open	ADJ
ejpam-3649	274	5	sets	set	NOUN
ejpam-3649	274	6	in	in	ADP
ejpam-3649	274	7	ideal	ideal	ADJ
ejpam-3649	274	8	bitopological	bitopological	ADJ
ejpam-3649	274	9	spaces.university	spaces.university	NOUN
ejpam-3649	274	10	of	of	ADP
ejpam-3649	274	11	bacau	bacau	NOUN
ejpam-3649	274	12	,	,	PUNCT
ejpam-3649	274	13	faculty	faculty	NOUN
ejpam-3649	274	14	of	of	ADP
ejpam-3649	274	15	sciences	science	NOUN
ejpam-3649	274	16	,	,	PUNCT
ejpam-3649	274	17	scientific	scientific	ADJ
ejpam-3649	274	18	studies	study	NOUN
ejpam-3649	274	19	and	and	CCONJ
ejpam-3649	274	20	research	research	NOUN
ejpam-3649	274	21	,	,	PUNCT
ejpam-3649	274	22	series	series	NOUN
ejpam-3649	274	23	mathematics	mathematics	PROPN
ejpam-3649	274	24	and	and	CCONJ
ejpam-3649	274	25	informatics	informatic	NOUN
ejpam-3649	274	26	20(2	20(2	NUM
ejpam-3649	274	27	)	)	PUNCT
ejpam-3649	274	28	,	,	PUNCT
ejpam-3649	274	29	29	29	NUM
ejpam-3649	274	30	-	-	SYM
ejpam-3649	274	31	38	38	NUM
ejpam-3649	274	32	,	,	PUNCT
ejpam-3649	274	33	2010	2010	NUM
ejpam-3649	274	34	.	.	PUNCT
ejpam-3649	275	1	[	[	X
ejpam-3649	275	2	8	8	NUM
ejpam-3649	275	3	]	]	X
ejpam-3649	275	4	m.	m.	NOUN
ejpam-3649	275	5	ilkhan	ilkhan	PROPN
ejpam-3649	275	6	,	,	PUNCT
ejpam-3649	275	7	m.	m.	PROPN
ejpam-3649	275	8	akyigit	akyigit	PROPN
ejpam-3649	275	9	,	,	PUNCT
ejpam-3649	275	10	and	and	CCONJ
ejpam-3649	275	11	e.	e.	PROPN
ejpam-3649	275	12	e.	e.	PROPN
ejpam-3649	275	13	kara	kara	PROPN
ejpam-3649	275	14	,	,	PUNCT
ejpam-3649	275	15	on	on	ADP
ejpam-3649	275	16	new	new	ADJ
ejpam-3649	275	17	types	type	NOUN
ejpam-3649	275	18	of	of	ADP
ejpam-3649	275	19	sets	set	NOUN
ejpam-3649	275	20	via	via	ADP
ejpam-3649	275	21	γ	γ	ADJ
ejpam-3649	275	22	-	-	ADJ
ejpam-3649	275	23	open	open	ADJ
ejpam-3649	275	24	sets	set	NOUN
ejpam-3649	275	25	in	in	ADP
ejpam-3649	275	26	bitopological	bitopological	ADJ
ejpam-3649	275	27	spaces	space	NOUN
ejpam-3649	275	28	,	,	PUNCT
ejpam-3649	275	29	communications	communication	NOUN
ejpam-3649	275	30	series	series	NOUN
ejpam-3649	275	31	a1	a1	NOUN
ejpam-3649	275	32	mathematics	mathematic	NOUN
ejpam-3649	275	33	and	and	CCONJ
ejpam-3649	275	34	statistics	statistic	NOUN
ejpam-3649	275	35	,	,	PUNCT
ejpam-3649	275	36	67(1	67(1	NOUN
ejpam-3649	275	37	)	)	PUNCT
ejpam-3649	275	38	,	,	PUNCT
ejpam-3649	275	39	225	225	NUM
ejpam-3649	275	40	-	-	SYM
ejpam-3649	275	41	234	234	NUM
ejpam-3649	275	42	,	,	PUNCT
ejpam-3649	275	43	(	(	PUNCT
ejpam-3649	275	44	2017	2017	NUM
ejpam-3649	275	45	)	)	PUNCT
ejpam-3649	275	46	.	.	PUNCT
ejpam-3649	276	1	[	[	X
ejpam-3649	276	2	9	9	NUM
ejpam-3649	276	3	]	]	PUNCT
ejpam-3649	276	4	m.	m.	NOUN
ejpam-3649	276	5	kar	kar	PROPN
ejpam-3649	276	6	,	,	PUNCT
ejpam-3649	276	7	s.	s.	PROPN
ejpam-3649	276	8	thakur	thakur	PROPN
ejpam-3649	276	9	,	,	PUNCT
ejpam-3649	276	10	s.	s.	PROPN
ejpam-3649	276	11	rana	rana	PROPN
ejpam-3649	276	12	,	,	PUNCT
ejpam-3649	276	13	and	and	CCONJ
ejpam-3649	276	14	j.	j.	PROPN
ejpam-3649	276	15	maitra	maitra	PROPN
ejpam-3649	276	16	.	.	PUNCT
ejpam-3649	277	1	i	i	PRON
ejpam-3649	277	2	-	-	PUNCT
ejpam-3649	277	3	continuous	continuous	ADJ
ejpam-3649	277	4	functions	function	NOUN
ejpam-3649	277	5	in	in	ADP
ejpam-3649	277	6	ideal	ideal	ADJ
ejpam-3649	277	7	bitopological	bitopological	ADJ
ejpam-3649	277	8	spaces	space	NOUN
ejpam-3649	277	9	.	.	PUNCT
ejpam-3649	278	1	american	american	ADJ
ejpam-3649	278	2	journal	journal	PROPN
ejpam-3649	278	3	of	of	ADP
ejpam-3649	278	4	engineering	engineering	NOUN
ejpam-3649	278	5	research	research	NOUN
ejpam-3649	278	6	,	,	PUNCT
ejpam-3649	278	7	3(3	3(3	NUM
ejpam-3649	278	8	)	)	PUNCT
ejpam-3649	278	9	,	,	PUNCT
ejpam-3649	278	10	51	51	NUM
ejpam-3649	278	11	-	-	SYM
ejpam-3649	278	12	55	55	NUM
ejpam-3649	278	13	,	,	PUNCT
ejpam-3649	278	14	2014	2014	NUM
ejpam-3649	278	15	.	.	PUNCT
ejpam-3649	279	1	[	[	X
ejpam-3649	279	2	10	10	NUM
ejpam-3649	279	3	]	]	X
ejpam-3649	279	4	s.	s.	PROPN
ejpam-3649	279	5	kasahara	kasahara	PROPN
ejpam-3649	279	6	.	.	PUNCT
ejpam-3649	280	1	operation	operation	NOUN
ejpam-3649	280	2	-	-	PUNCT
ejpam-3649	280	3	compact	compact	ADJ
ejpam-3649	280	4	spaces	space	NOUN
ejpam-3649	280	5	,	,	PUNCT
ejpam-3649	280	6	math	math	NOUN
ejpam-3649	280	7	.	.	PUNCT
ejpam-3649	281	1	japon	japon	PROPN
ejpam-3649	281	2	,	,	PUNCT
ejpam-3649	281	3	24	24	NUM
ejpam-3649	281	4	,	,	PUNCT
ejpam-3649	281	5	97	97	NUM
ejpam-3649	281	6	-	-	SYM
ejpam-3649	281	7	105	105	NUM
ejpam-3649	281	8	,	,	PUNCT
ejpam-3649	281	9	1979	1979	NUM
ejpam-3649	281	10	.	.	PUNCT
ejpam-3649	282	1	[	[	X
ejpam-3649	282	2	11	11	NUM
ejpam-3649	282	3	]	]	PUNCT
ejpam-3649	282	4	j.	j.	PROPN
ejpam-3649	282	5	kelly	kelly	PROPN
ejpam-3649	282	6	.	.	PUNCT
ejpam-3649	283	1	bitopological	bitopological	ADJ
ejpam-3649	283	2	spaces	space	NOUN
ejpam-3649	283	3	.	.	PUNCT
ejpam-3649	284	1	proceedings	proceeding	NOUN
ejpam-3649	284	2	of	of	ADP
ejpam-3649	284	3	the	the	DET
ejpam-3649	284	4	london	london	PROPN
ejpam-3649	284	5	mathematical	mathematical	ADJ
ejpam-3649	284	6	society	society	NOUN
ejpam-3649	284	7	,	,	PUNCT
ejpam-3649	284	8	3(1	3(1	NUM
ejpam-3649	284	9	)	)	PUNCT
ejpam-3649	284	10	,	,	PUNCT
ejpam-3649	284	11	71	71	NUM
ejpam-3649	284	12	-	-	SYM
ejpam-3649	284	13	89	89	NUM
ejpam-3649	284	14	,	,	PUNCT
ejpam-3649	284	15	1963	1963	NUM
ejpam-3649	284	16	.	.	PUNCT
ejpam-3649	285	1	[	[	X
ejpam-3649	285	2	12	12	NUM
ejpam-3649	285	3	]	]	X
ejpam-3649	285	4	f.	f.	PROPN
ejpam-3649	285	5	khedr	khedr	PROPN
ejpam-3649	285	6	.	.	PUNCT
ejpam-3649	286	1	operation	operation	NOUN
ejpam-3649	286	2	on	on	ADP
ejpam-3649	286	3	bitopologies	bitopologie	NOUN
ejpam-3649	286	4	,	,	PUNCT
ejpam-3649	286	5	delta	delta	PROPN
ejpam-3649	286	6	j.	j.	PROPN
ejpam-3649	286	7	sci	sci	PROPN
ejpam-3649	286	8	,	,	PUNCT
ejpam-3649	286	9	8(1	8(1	NOUN
ejpam-3649	286	10	)	)	PUNCT
ejpam-3649	286	11	,	,	PUNCT
ejpam-3649	286	12	309	309	NUM
ejpam-3649	286	13	-	-	SYM
ejpam-3649	286	14	320	320	NUM
ejpam-3649	286	15	,	,	PUNCT
ejpam-3649	286	16	1984	1984	NUM
ejpam-3649	286	17	.	.	PUNCT
ejpam-3649	287	1	[	[	X
ejpam-3649	287	2	13	13	NUM
ejpam-3649	287	3	]	]	X
ejpam-3649	287	4	f.	f.	PROPN
ejpam-3649	287	5	khedr	khedr	PROPN
ejpam-3649	287	6	and	and	CCONJ
ejpam-3649	287	7	k.	k.	PROPN
ejpam-3649	287	8	abdelhakiem	abdelhakiem	PROPN
ejpam-3649	287	9	.	.	PUNCT
ejpam-3649	288	1	operations	operation	NOUN
ejpam-3649	288	2	on	on	ADP
ejpam-3649	288	3	bitopological	bitopological	ADJ
ejpam-3649	288	4	spaces	space	NOUN
ejpam-3649	288	5	.	.	PUNCT
ejpam-3649	289	1	fasciculi	fasciculi	PROPN
ejpam-3649	289	2	mathematici	mathematici	PROPN
ejpam-3649	289	3	,	,	PUNCT
ejpam-3649	289	4	(	(	PUNCT
ejpam-3649	289	5	45	45	NUM
ejpam-3649	289	6	)	)	PUNCT
ejpam-3649	289	7	,	,	PUNCT
ejpam-3649	289	8	47	47	NUM
ejpam-3649	289	9	-	-	SYM
ejpam-3649	289	10	57	57	NUM
ejpam-3649	289	11	,	,	PUNCT
ejpam-3649	289	12	2010	2010	NUM
ejpam-3649	289	13	.	.	PUNCT
ejpam-3649	290	1	[	[	X
ejpam-3649	290	2	14	14	NUM
ejpam-3649	290	3	]	]	X
ejpam-3649	290	4	f.	f.	PROPN
ejpam-3649	290	5	khedr	khedr	PROPN
ejpam-3649	290	6	,	,	PUNCT
ejpam-3649	290	7	s.	s.	PROPN
ejpam-3649	290	8	al	al	PROPN
ejpam-3649	290	9	-	-	PUNCT
ejpam-3649	290	10	areefi	areefi	PROPN
ejpam-3649	290	11	and	and	CCONJ
ejpam-3649	290	12	t.	t.	PROPN
ejpam-3649	290	13	noiri	noiri	PROPN
ejpam-3649	290	14	.	.	PUNCT
ejpam-3649	291	1	precontinuity	precontinuity	NOUN
ejpam-3649	291	2	and	and	CCONJ
ejpam-3649	291	3	semi	semi	NOUN
ejpam-3649	291	4	-	-	NOUN
ejpam-3649	291	5	precontinuity	precontinuity	NOUN
ejpam-3649	291	6	in	in	ADP
ejpam-3649	291	7	bitopological	bitopological	ADJ
ejpam-3649	291	8	spaces	space	NOUN
ejpam-3649	291	9	.	.	PUNCT
ejpam-3649	292	1	indian	indian	ADJ
ejpam-3649	292	2	journal	journal	PROPN
ejpam-3649	292	3	of	of	ADP
ejpam-3649	292	4	pure	pure	ADJ
ejpam-3649	292	5	and	and	CCONJ
ejpam-3649	292	6	applied	applied	ADJ
ejpam-3649	292	7	mathematics	mathematic	NOUN
ejpam-3649	292	8	,	,	PUNCT
ejpam-3649	292	9	23,625	23,625	NUM
ejpam-3649	292	10	-	-	SYM
ejpam-3649	292	11	625	625	NUM
ejpam-3649	292	12	,	,	PUNCT
ejpam-3649	292	13	1992	1992	NUM
ejpam-3649	292	14	.	.	PUNCT
ejpam-3649	293	1	[	[	X
ejpam-3649	293	2	15	15	NUM
ejpam-3649	293	3	]	]	PUNCT
ejpam-3649	293	4	k.	k.	PROPN
ejpam-3649	293	5	kuratowski	kuratowski	PROPN
ejpam-3649	293	6	.	.	PUNCT
ejpam-3649	294	1	topology	topology	NOUN
ejpam-3649	294	2	,	,	PUNCT
ejpam-3649	294	3	academic	academic	ADJ
ejpam-3649	294	4	press	press	NOUN
ejpam-3649	294	5	,	,	PUNCT
ejpam-3649	294	6	new	new	PROPN
ejpam-3649	294	7	york	york	PROPN
ejpam-3649	294	8	.	.	PUNCT
ejpam-3649	295	1	1966	1966	NUM
ejpam-3649	295	2	.	.	PUNCT
ejpam-3649	296	1	[	[	X
ejpam-3649	296	2	16	16	NUM
ejpam-3649	296	3	]	]	PUNCT
ejpam-3649	296	4	j.	j.	PROPN
ejpam-3649	296	5	k.	k.	PROPN
ejpam-3649	296	6	maitra	maitra	PROPN
ejpam-3649	296	7	and	and	CCONJ
ejpam-3649	296	8	h.	h.	PROPN
ejpam-3649	296	9	k.	k.	PROPN
ejpam-3649	296	10	tripathi	tripathi	PROPN
ejpam-3649	296	11	,	,	PUNCT
ejpam-3649	296	12	local	local	ADJ
ejpam-3649	296	13	function	function	NOUN
ejpam-3649	296	14	in	in	ADP
ejpam-3649	296	15	generalized	generalized	ADJ
ejpam-3649	296	16	ideal	ideal	ADJ
ejpam-3649	296	17	topological	topological	ADJ
ejpam-3649	296	18	spaces	space	NOUN
ejpam-3649	296	19	,	,	PUNCT
ejpam-3649	296	20	vislesana	vislesana	NUM
ejpam-3649	296	21	,	,	PUNCT
ejpam-3649	296	22	11(1	11(1	NUM
ejpam-3649	296	23	)	)	PUNCT
ejpam-3649	296	24	,	,	PUNCT
ejpam-3649	296	25	191195	191195	NUM
ejpam-3649	296	26	,	,	PUNCT
ejpam-3649	296	27	(	(	PUNCT
ejpam-3649	296	28	2014	2014	NUM
ejpam-3649	296	29	)	)	PUNCT
ejpam-3649	296	30	.	.	PUNCT
ejpam-3649	297	1	[	[	X
ejpam-3649	297	2	17	17	NUM
ejpam-3649	297	3	]	]	X
ejpam-3649	297	4	n.	n.	PROPN
ejpam-3649	297	5	levine	levine	PROPN
ejpam-3649	297	6	.	.	PUNCT
ejpam-3649	298	1	semi	semi	ADJ
ejpam-3649	298	2	-	-	ADJ
ejpam-3649	298	3	open	open	ADJ
ejpam-3649	298	4	sets	set	NOUN
ejpam-3649	298	5	and	and	CCONJ
ejpam-3649	298	6	semi	semi	ADJ
ejpam-3649	298	7	continuity	continuity	NOUN
ejpam-3649	298	8	in	in	ADP
ejpam-3649	298	9	topological	topological	ADJ
ejpam-3649	298	10	spaces	space	NOUN
ejpam-3649	298	11	,	,	PUNCT
ejpam-3649	298	12	amer	amer	PROPN
ejpam-3649	298	13	.	.	PUNCT
ejpam-3649	299	1	math.70	math.70	PROPN
ejpam-3649	299	2	,	,	PUNCT
ejpam-3649	299	3	36	36	NUM
ejpam-3649	299	4	-	-	SYM
ejpam-3649	299	5	41	41	NUM
ejpam-3649	299	6	,	,	PUNCT
ejpam-3649	299	7	1963	1963	NUM
ejpam-3649	299	8	.	.	PUNCT
ejpam-3649	300	1	[	[	X
ejpam-3649	300	2	18	18	NUM
ejpam-3649	300	3	]	]	PUNCT
ejpam-3649	300	4	t.	t.	PROPN
ejpam-3649	300	5	noiri	noiri	PROPN
ejpam-3649	300	6	,	,	PUNCT
ejpam-3649	300	7	m.	m.	NOUN
ejpam-3649	300	8	rajamani	rajamani	NOUN
ejpam-3649	300	9	and	and	CCONJ
ejpam-3649	300	10	m.	m.	NOUN
ejpam-3649	300	11	maheswari	maheswari	PROPN
ejpam-3649	300	12	..	..	PUNCT
ejpam-3649	300	13	a	a	DET
ejpam-3649	300	14	decomposition	decomposition	NOUN
ejpam-3649	300	15	of	of	ADP
ejpam-3649	300	16	pairwise	pairwise	NOUN
ejpam-3649	300	17	continuity	continuity	NOUN
ejpam-3649	300	18	via	via	ADP
ejpam-3649	300	19	ideals	ideal	NOUN
ejpam-3649	300	20	.	.	PUNCT
ejpam-3649	301	1	boletim	boletim	PROPN
ejpam-3649	301	2	da	da	PROPN
ejpam-3649	301	3	sociedade	sociedade	PROPN
ejpam-3649	301	4	paranaense	paranaense	PROPN
ejpam-3649	301	5	de	de	PROPN
ejpam-3649	301	6	matemtica	matemtica	PROPN
ejpam-3649	301	7	,	,	PUNCT
ejpam-3649	301	8	34(1	34(1	NUM
ejpam-3649	301	9	)	)	PUNCT
ejpam-3649	301	10	,	,	PUNCT
ejpam-3649	301	11	141	141	NUM
ejpam-3649	301	12	-	-	SYM
ejpam-3649	301	13	149,(2016	149,(2016	NUM
ejpam-3649	301	14	)	)	PUNCT
ejpam-3649	301	15	.	.	PUNCT
ejpam-3649	302	1	[	[	X
ejpam-3649	302	2	19	19	NUM
ejpam-3649	302	3	]	]	PUNCT
ejpam-3649	302	4	s.	s.	PROPN
ejpam-3649	302	5	maheshwari	maheshwari	PROPN
ejpam-3649	302	6	,	,	PUNCT
ejpam-3649	302	7	and	and	CCONJ
ejpam-3649	302	8	r.	r.	PROPN
ejpam-3649	302	9	prasad	prasad	PROPN
ejpam-3649	302	10	.	.	PUNCT
ejpam-3649	303	1	semi	semi	ADJ
ejpam-3649	303	2	-	-	ADJ
ejpam-3649	303	3	open	open	ADJ
ejpam-3649	303	4	sets	set	NOUN
ejpam-3649	303	5	and	and	CCONJ
ejpam-3649	303	6	semi	semi	ADJ
ejpam-3649	303	7	-	-	ADJ
ejpam-3649	303	8	continuous	continuous	ADJ
ejpam-3649	303	9	function	function	NOUN
ejpam-3649	303	10	in	in	ADP
ejpam-3649	303	11	bitopological	bitopological	ADJ
ejpam-3649	303	12	spaces	space	NOUN
ejpam-3649	303	13	,	,	PUNCT
ejpam-3649	303	14	26	26	NUM
ejpam-3649	303	15	,	,	PUNCT
ejpam-3649	303	16	29	29	NUM
ejpam-3649	303	17	-	-	SYM
ejpam-3649	303	18	37	37	NUM
ejpam-3649	303	19	,	,	PUNCT
ejpam-3649	303	20	1977	1977	NUM
ejpam-3649	303	21	.	.	PUNCT
ejpam-3649	304	1	[	[	X
ejpam-3649	304	2	20	20	NUM
ejpam-3649	304	3	]	]	PUNCT
ejpam-3649	304	4	h.	h.	PROPN
ejpam-3649	304	5	ogata	ogata	PROPN
ejpam-3649	304	6	.	.	PUNCT
ejpam-3649	305	1	operations	operation	NOUN
ejpam-3649	305	2	on	on	ADP
ejpam-3649	305	3	topological	topological	ADJ
ejpam-3649	305	4	spaces	space	NOUN
ejpam-3649	305	5	and	and	CCONJ
ejpam-3649	305	6	associated	associate	VERB
ejpam-3649	305	7	topology	topology	NOUN
ejpam-3649	305	8	.	.	PUNCT
ejpam-3649	306	1	math	math	NOUN
ejpam-3649	306	2	.	.	PUNCT
ejpam-3649	307	1	japon	japon	PROPN
ejpam-3649	307	2	.	.	PUNCT
ejpam-3649	308	1	36	36	NUM
ejpam-3649	308	2	,	,	PUNCT
ejpam-3649	308	3	175	175	NUM
ejpam-3649	308	4	-	-	SYM
ejpam-3649	308	5	184	184	NUM
ejpam-3649	308	6	,	,	PUNCT
ejpam-3649	308	7	1991	1991	NUM
ejpam-3649	308	8	.	.	PUNCT
ejpam-3649	309	1	[	[	X
ejpam-3649	309	2	21	21	NUM
ejpam-3649	309	3	]	]	X
ejpam-3649	309	4	s.	s.	PROPN
ejpam-3649	309	5	tahiliani	tahiliani	PROPN
ejpam-3649	309	6	.	.	PUNCT
ejpam-3649	310	1	operation	operation	NOUN
ejpam-3649	310	2	approach	approach	NOUN
ejpam-3649	310	3	to	to	ADP
ejpam-3649	310	4	β	β	ADJ
ejpam-3649	310	5	-	-	ADJ
ejpam-3649	310	6	open	open	ADJ
ejpam-3649	310	7	sets	set	NOUN
ejpam-3649	310	8	and	and	CCONJ
ejpam-3649	310	9	applications	application	NOUN
ejpam-3649	310	10	.	.	PUNCT
ejpam-3649	311	1	mathematical	mathematical	ADJ
ejpam-3649	311	2	communications	communication	NOUN
ejpam-3649	311	3	16	16	NUM
ejpam-3649	311	4	,	,	PUNCT
ejpam-3649	311	5	no	no	INTJ
ejpam-3649	311	6	.	.	NOUN
ejpam-3649	311	7	2	2	NUM
ejpam-3649	311	8	,	,	PUNCT
ejpam-3649	311	9	577	577	NUM
ejpam-3649	311	10	-	-	SYM
ejpam-3649	311	11	591	591	NUM
ejpam-3649	311	12	,	,	PUNCT
ejpam-3649	311	13	2011	2011	NUM
ejpam-3649	311	14	.	.	PUNCT
ejpam-3649	312	1	references	reference	NOUN
ejpam-3649	312	2	279	279	NUM
ejpam-3649	312	3	[	[	X
ejpam-3649	312	4	22	22	NUM
ejpam-3649	312	5	]	]	PUNCT
ejpam-3649	312	6	r.	r.	PROPN
ejpam-3649	312	7	vaidyanathaswamy	vaidyanathaswamy	PROPN
ejpam-3649	312	8	.	.	PUNCT
ejpam-3649	313	1	the	the	DET
ejpam-3649	313	2	localisation	localisation	NOUN
ejpam-3649	313	3	theory	theory	NOUN
ejpam-3649	313	4	in	in	ADP
ejpam-3649	313	5	set	set	NOUN
ejpam-3649	313	6	topology	topology	NOUN
ejpam-3649	313	7	,	,	PUNCT
ejpam-3649	313	8	proceedings	proceeding	NOUN
ejpam-3649	313	9	of	of	ADP
ejpam-3649	313	10	the	the	DET
ejpam-3649	313	11	indian	indian	ADJ
ejpam-3649	313	12	acadamic	acadamic	NOUN
ejpam-3649	313	13	of	of	ADP
ejpam-3649	313	14	sciences	science	NOUN
ejpam-3649	313	15	,	,	PUNCT
ejpam-3649	313	16	20	20	NUM
ejpam-3649	313	17	,	,	PUNCT
ejpam-3649	313	18	51	51	NUM
ejpam-3649	313	19	-	-	SYM
ejpam-3649	313	20	61	61	NUM
ejpam-3649	313	21	,	,	PUNCT
ejpam-3649	313	22	1945	1945	NUM
ejpam-3649	313	23	.	.	PUNCT