id	sid	tid	token	lemma	pos
ejpam-4060	1	1	european	european	PROPN
ejpam-4060	1	2	journal	journal	PROPN
ejpam-4060	1	3	of	of	ADP
ejpam-4060	1	4	pure	pure	ADJ
ejpam-4060	1	5	and	and	CCONJ
ejpam-4060	1	6	applied	apply	VERB
ejpam-4060	1	7	mathematics	mathematic	NOUN
ejpam-4060	1	8	vol	vol	NOUN
ejpam-4060	1	9	.	.	PUNCT
ejpam-4060	2	1	14	14	NUM
ejpam-4060	2	2	,	,	PUNCT
ejpam-4060	2	3	no	no	INTJ
ejpam-4060	2	4	.	.	NOUN
ejpam-4060	2	5	4	4	NUM
ejpam-4060	2	6	,	,	PUNCT
ejpam-4060	2	7	2021	2021	NUM
ejpam-4060	2	8	,	,	PUNCT
ejpam-4060	2	9	1275	1275	NUM
ejpam-4060	2	10	-	-	SYM
ejpam-4060	2	11	1282	1282	NUM
ejpam-4060	2	12	issn	issn	PROPN
ejpam-4060	2	13	1307	1307	NUM
ejpam-4060	2	14	-	-	SYM
ejpam-4060	2	15	5543	5543	NUM
ejpam-4060	2	16	–	–	PUNCT
ejpam-4060	2	17	ejpam.com	ejpam.com	X
ejpam-4060	2	18	published	publish	VERB
ejpam-4060	2	19	by	by	ADP
ejpam-4060	2	20	new	new	PROPN
ejpam-4060	2	21	york	york	PROPN
ejpam-4060	2	22	business	business	PROPN
ejpam-4060	2	23	global	global	PROPN
ejpam-4060	2	24	on	on	ADP
ejpam-4060	2	25	ψgs	ψgs	ADV
ejpam-4060	2	26	-	-	PUNCT
ejpam-4060	2	27	closed	close	VERB
ejpam-4060	2	28	sets	set	NOUN
ejpam-4060	2	29	in	in	ADP
ejpam-4060	2	30	bitopological	bitopological	ADJ
ejpam-4060	2	31	spaces	space	NOUN
ejpam-4060	3	1	lezel	lezel	ADJ
ejpam-4060	3	2	mernilo	mernilo	PROPN
ejpam-4060	3	3	tutanes	tutane	NOUN
ejpam-4060	3	4	mathematics	mathematics	PROPN
ejpam-4060	3	5	department	department	PROPN
ejpam-4060	3	6	,	,	PUNCT
ejpam-4060	3	7	college	college	NOUN
ejpam-4060	3	8	of	of	ADP
ejpam-4060	3	9	arts	art	NOUN
ejpam-4060	3	10	and	and	CCONJ
ejpam-4060	3	11	sciences	sciences	PROPN
ejpam-4060	3	12	,	,	PUNCT
ejpam-4060	3	13	bukidnon	bukidnon	NOUN
ejpam-4060	3	14	state	state	PROPN
ejpam-4060	3	15	university	university	PROPN
ejpam-4060	3	16	,	,	PUNCT
ejpam-4060	3	17	malaybalay	malaybalay	NOUN
ejpam-4060	3	18	city	city	NOUN
ejpam-4060	3	19	,	,	PUNCT
ejpam-4060	3	20	bukidnon	bukidnon	NOUN
ejpam-4060	3	21	,	,	PUNCT
ejpam-4060	3	22	philippines	philippine	NOUN
ejpam-4060	3	23	abstract	abstract	ADJ
ejpam-4060	3	24	.	.	PUNCT
ejpam-4060	4	1	in	in	ADP
ejpam-4060	4	2	this	this	DET
ejpam-4060	4	3	paper	paper	NOUN
ejpam-4060	4	4	,	,	PUNCT
ejpam-4060	4	5	the	the	DET
ejpam-4060	4	6	properties	property	NOUN
ejpam-4060	4	7	of	of	ADP
ejpam-4060	4	8	ψgs	ψgs	ADV
ejpam-4060	4	9	-	-	PUNCT
ejpam-4060	4	10	closed	close	VERB
ejpam-4060	4	11	sets	set	NOUN
ejpam-4060	4	12	in	in	ADP
ejpam-4060	4	13	bitopological	bitopological	ADJ
ejpam-4060	4	14	spaces	space	NOUN
ejpam-4060	4	15	are	be	AUX
ejpam-4060	4	16	investigated	investigate	VERB
ejpam-4060	4	17	.	.	PUNCT
ejpam-4060	5	1	the	the	DET
ejpam-4060	5	2	relationships	relationship	NOUN
ejpam-4060	5	3	between	between	ADP
ejpam-4060	5	4	ψgs	ψgs	ADV
ejpam-4060	5	5	-	-	PUNCT
ejpam-4060	5	6	closed	close	VERB
ejpam-4060	5	7	set	set	VERB
ejpam-4060	5	8	and	and	CCONJ
ejpam-4060	5	9	other	other	ADJ
ejpam-4060	5	10	closed	closed	ADJ
ejpam-4060	5	11	sets	set	NOUN
ejpam-4060	5	12	in	in	ADP
ejpam-4060	5	13	bitopological	bitopological	ADJ
ejpam-4060	5	14	spaces	space	NOUN
ejpam-4060	5	15	are	be	AUX
ejpam-4060	5	16	established	establish	VERB
ejpam-4060	5	17	and	and	CCONJ
ejpam-4060	5	18	some	some	DET
ejpam-4060	5	19	properties	property	NOUN
ejpam-4060	5	20	of	of	ADP
ejpam-4060	5	21	ψgs	ψgs	NOUN
ejpam-4060	5	22	-	-	PUNCT
ejpam-4060	5	23	closure	closure	NOUN
ejpam-4060	5	24	and	and	CCONJ
ejpam-4060	5	25	ψgs	ψgs	ADV
ejpam-4060	5	26	-	-	PUNCT
ejpam-4060	5	27	interior	interior	ADJ
ejpam-4060	5	28	are	be	AUX
ejpam-4060	5	29	provided	provide	VERB
ejpam-4060	5	30	.	.	PUNCT
ejpam-4060	6	1	2020	2020	NUM
ejpam-4060	6	2	mathematics	mathematic	NOUN
ejpam-4060	6	3	subject	subject	NOUN
ejpam-4060	6	4	classifications	classification	NOUN
ejpam-4060	6	5	:	:	PUNCT
ejpam-4060	6	6	18f60	18f60	NUM
ejpam-4060	6	7	,	,	PUNCT
ejpam-4060	6	8	05c69	05c69	NUM
ejpam-4060	6	9	,	,	PUNCT
ejpam-4060	6	10	30h80	30h80	NUM
ejpam-4060	6	11	key	key	ADJ
ejpam-4060	6	12	words	word	NOUN
ejpam-4060	6	13	and	and	CCONJ
ejpam-4060	6	14	phrases	phrase	NOUN
ejpam-4060	6	15	:	:	PUNCT
ejpam-4060	6	16	bitopological	bitopological	ADJ
ejpam-4060	6	17	spaces	space	NOUN
ejpam-4060	6	18	,	,	PUNCT
ejpam-4060	6	19	ψgs	ψgs	ADV
ejpam-4060	6	20	-	-	PUNCT
ejpam-4060	6	21	closed	close	VERB
ejpam-4060	6	22	sets	set	NOUN
ejpam-4060	6	23	,	,	PUNCT
ejpam-4060	6	24	ψgs	ψgs	ADJ
ejpam-4060	6	25	-	-	PUNCT
ejpam-4060	6	26	interior	interior	ADJ
ejpam-4060	6	27	,	,	PUNCT
ejpam-4060	6	28	ψgs	ψgs	NOUN
ejpam-4060	6	29	-	-	PUNCT
ejpam-4060	6	30	closure	closure	NOUN
ejpam-4060	6	31	1	1	NUM
ejpam-4060	6	32	.	.	PUNCT
ejpam-4060	6	33	introduction	introduction	NOUN
ejpam-4060	6	34	over	over	ADP
ejpam-4060	6	35	the	the	DET
ejpam-4060	6	36	years	year	NOUN
ejpam-4060	6	37	,	,	PUNCT
ejpam-4060	6	38	many	many	ADJ
ejpam-4060	6	39	researchers	researcher	NOUN
ejpam-4060	6	40	have	have	AUX
ejpam-4060	6	41	introduced	introduce	VERB
ejpam-4060	6	42	different	different	ADJ
ejpam-4060	6	43	types	type	NOUN
ejpam-4060	6	44	of	of	ADP
ejpam-4060	6	45	sets	set	NOUN
ejpam-4060	6	46	in	in	ADP
ejpam-4060	6	47	topological	topological	ADJ
ejpam-4060	6	48	spaces	space	NOUN
ejpam-4060	6	49	.	.	PUNCT
ejpam-4060	7	1	one	one	NUM
ejpam-4060	7	2	of	of	ADP
ejpam-4060	7	3	these	these	DET
ejpam-4060	7	4	sets	set	NOUN
ejpam-4060	7	5	is	be	AUX
ejpam-4060	7	6	the	the	DET
ejpam-4060	7	7	semi	semi	ADJ
ejpam-4060	7	8	-	-	ADJ
ejpam-4060	7	9	open	open	ADJ
ejpam-4060	7	10	set	set	NOUN
ejpam-4060	7	11	,	,	PUNCT
ejpam-4060	7	12	which	which	PRON
ejpam-4060	7	13	was	be	AUX
ejpam-4060	7	14	introduced	introduce	VERB
ejpam-4060	7	15	and	and	CCONJ
ejpam-4060	7	16	studied	study	VERB
ejpam-4060	7	17	by	by	ADP
ejpam-4060	7	18	levine	levine	PROPN
ejpam-4060	7	19	[	[	X
ejpam-4060	7	20	12	12	NUM
ejpam-4060	7	21	]	]	PUNCT
ejpam-4060	7	22	.	.	PUNCT
ejpam-4060	8	1	thereafter	thereafter	ADV
ejpam-4060	8	2	,	,	PUNCT
ejpam-4060	8	3	the	the	DET
ejpam-4060	8	4	notion	notion	NOUN
ejpam-4060	8	5	of	of	ADP
ejpam-4060	8	6	generalized	generalized	ADJ
ejpam-4060	8	7	closed	closed	ADJ
ejpam-4060	8	8	sets	set	NOUN
ejpam-4060	8	9	(	(	PUNCT
ejpam-4060	8	10	briefly	briefly	ADV
ejpam-4060	8	11	,	,	PUNCT
ejpam-4060	8	12	g	g	NOUN
ejpam-4060	8	13	-	-	PUNCT
ejpam-4060	8	14	closed	close	VERB
ejpam-4060	8	15	set	set	NOUN
ejpam-4060	8	16	)	)	PUNCT
ejpam-4060	8	17	in	in	ADP
ejpam-4060	8	18	topological	topological	ADJ
ejpam-4060	8	19	spaces	space	NOUN
ejpam-4060	8	20	was	be	AUX
ejpam-4060	8	21	introduced	introduce	VERB
ejpam-4060	8	22	and	and	CCONJ
ejpam-4060	8	23	investigated	investigate	VERB
ejpam-4060	8	24	in	in	ADP
ejpam-4060	8	25	[	[	X
ejpam-4060	8	26	13	13	NUM
ejpam-4060	8	27	]	]	PUNCT
ejpam-4060	8	28	.	.	PUNCT
ejpam-4060	9	1	in	in	ADP
ejpam-4060	9	2	2000	2000	NUM
ejpam-4060	9	3	,	,	PUNCT
ejpam-4060	9	4	the	the	DET
ejpam-4060	9	5	concepts	concept	NOUN
ejpam-4060	9	6	between	between	ADP
ejpam-4060	9	7	closed	closed	ADJ
ejpam-4060	9	8	sets	set	NOUN
ejpam-4060	9	9	and	and	CCONJ
ejpam-4060	9	10	g	g	NOUN
ejpam-4060	9	11	-	-	PUNCT
ejpam-4060	9	12	closed	close	VERB
ejpam-4060	9	13	sets	set	NOUN
ejpam-4060	9	14	in	in	ADP
ejpam-4060	9	15	topological	topological	ADJ
ejpam-4060	9	16	spaces	space	NOUN
ejpam-4060	9	17	were	be	AUX
ejpam-4060	9	18	studied	study	VERB
ejpam-4060	9	19	in	in	ADP
ejpam-4060	9	20	[	[	X
ejpam-4060	9	21	10	10	NUM
ejpam-4060	9	22	]	]	PUNCT
ejpam-4060	9	23	and	and	CCONJ
ejpam-4060	9	24	a	a	DET
ejpam-4060	9	25	few	few	ADJ
ejpam-4060	9	26	years	year	NOUN
ejpam-4060	9	27	later	later	ADV
ejpam-4060	9	28	,	,	PUNCT
ejpam-4060	9	29	the	the	DET
ejpam-4060	9	30	same	same	ADJ
ejpam-4060	9	31	author	author	NOUN
ejpam-4060	10	1	[	[	X
ejpam-4060	10	2	11	11	NUM
ejpam-4060	10	3	]	]	PUNCT
ejpam-4060	10	4	studied	study	VERB
ejpam-4060	10	5	ψclosed	ψclose	VERB
ejpam-4060	10	6	sets	set	NOUN
ejpam-4060	10	7	in	in	ADP
ejpam-4060	10	8	topological	topological	ADJ
ejpam-4060	10	9	spaces	space	NOUN
ejpam-4060	10	10	.	.	PUNCT
ejpam-4060	11	1	ramya	ramya	PROPN
ejpam-4060	11	2	and	and	CCONJ
ejpam-4060	11	3	parvathi	parvathi	PROPN
ejpam-4060	11	4	introduced	introduce	VERB
ejpam-4060	11	5	a	a	DET
ejpam-4060	11	6	new	new	ADJ
ejpam-4060	11	7	concept	concept	NOUN
ejpam-4060	11	8	of	of	ADP
ejpam-4060	11	9	ψgeneralized	ψgeneralize	VERB
ejpam-4060	11	10	closed	close	VERB
ejpam-4060	11	11	(	(	PUNCT
ejpam-4060	11	12	briefly	briefly	ADV
ejpam-4060	11	13	,	,	PUNCT
ejpam-4060	11	14	ψg	ψg	NOUN
ejpam-4060	11	15	-	-	PUNCT
ejpam-4060	11	16	closed	closed	ADJ
ejpam-4060	11	17	)	)	PUNCT
ejpam-4060	11	18	sets	set	NOUN
ejpam-4060	11	19	in	in	ADP
ejpam-4060	11	20	topological	topological	ADJ
ejpam-4060	11	21	spaces	space	NOUN
ejpam-4060	11	22	.	.	PUNCT
ejpam-4060	12	1	recently	recently	ADV
ejpam-4060	12	2	,	,	PUNCT
ejpam-4060	12	3	a	a	DET
ejpam-4060	12	4	new	new	ADJ
ejpam-4060	12	5	class	class	NOUN
ejpam-4060	12	6	of	of	ADP
ejpam-4060	12	7	sets	set	NOUN
ejpam-4060	12	8	namely	namely	ADV
ejpam-4060	12	9	ψ	ψ	VERB
ejpam-4060	12	10	generalized	generalized	ADJ
ejpam-4060	12	11	semi	semi	ADJ
ejpam-4060	12	12	-	-	ADJ
ejpam-4060	12	13	closed	closed	ADJ
ejpam-4060	12	14	(	(	PUNCT
ejpam-4060	12	15	briefly	briefly	ADV
ejpam-4060	12	16	,	,	PUNCT
ejpam-4060	12	17	ψgsclosed	ψgsclosed	ADJ
ejpam-4060	12	18	)	)	PUNCT
ejpam-4060	12	19	sets	set	NOUN
ejpam-4060	12	20	were	be	AUX
ejpam-4060	12	21	introduced	introduce	VERB
ejpam-4060	12	22	in	in	ADP
ejpam-4060	12	23	topological	topological	ADJ
ejpam-4060	12	24	spaces	space	NOUN
ejpam-4060	12	25	and	and	CCONJ
ejpam-4060	12	26	some	some	PRON
ejpam-4060	12	27	of	of	ADP
ejpam-4060	12	28	their	their	PRON
ejpam-4060	12	29	basic	basic	ADJ
ejpam-4060	12	30	properties	property	NOUN
ejpam-4060	12	31	were	be	AUX
ejpam-4060	12	32	investigated	investigate	VERB
ejpam-4060	12	33	.	.	PUNCT
ejpam-4060	13	1	nowadays	nowadays	ADV
ejpam-4060	13	2	,	,	PUNCT
ejpam-4060	13	3	a	a	DET
ejpam-4060	13	4	new	new	ADJ
ejpam-4060	13	5	concept	concept	NOUN
ejpam-4060	13	6	coined	coin	VERB
ejpam-4060	13	7	from	from	ADP
ejpam-4060	13	8	topological	topological	ADJ
ejpam-4060	13	9	spaces	space	NOUN
ejpam-4060	13	10	is	be	AUX
ejpam-4060	13	11	the	the	DET
ejpam-4060	13	12	so	so	ADV
ejpam-4060	13	13	-	-	PUNCT
ejpam-4060	13	14	called	call	VERB
ejpam-4060	13	15	bitopological	bitopological	ADJ
ejpam-4060	13	16	spaces	space	NOUN
ejpam-4060	13	17	(	(	PUNCT
ejpam-4060	13	18	briefly	briefly	ADV
ejpam-4060	13	19	,	,	PUNCT
ejpam-4060	13	20	bts	bts	PROPN
ejpam-4060	13	21	)	)	PUNCT
ejpam-4060	13	22	.	.	PUNCT
ejpam-4060	14	1	bose	bose	VERB
ejpam-4060	15	1	[	[	X
ejpam-4060	15	2	2	2	NUM
ejpam-4060	15	3	]	]	PUNCT
ejpam-4060	15	4	,	,	PUNCT
ejpam-4060	15	5	studied	study	VERB
ejpam-4060	15	6	semi	semi	ADJ
ejpam-4060	15	7	continuity	continuity	NOUN
ejpam-4060	15	8	and	and	CCONJ
ejpam-4060	15	9	semi	semi	ADJ
ejpam-4060	15	10	open	open	ADJ
ejpam-4060	15	11	mappings	mapping	NOUN
ejpam-4060	15	12	in	in	ADP
ejpam-4060	15	13	bts	bt	NOUN
ejpam-4060	15	14	.	.	PUNCT
ejpam-4060	16	1	thereafter	thereafter	ADV
ejpam-4060	16	2	,	,	PUNCT
ejpam-4060	16	3	in	in	ADP
ejpam-4060	16	4	[	[	X
ejpam-4060	16	5	7	7	NUM
ejpam-4060	16	6	]	]	PUNCT
ejpam-4060	16	7	and	and	CCONJ
ejpam-4060	16	8	[	[	X
ejpam-4060	16	9	8	8	NUM
ejpam-4060	16	10	]	]	PUNCT
ejpam-4060	16	11	,	,	PUNCT
ejpam-4060	16	12	the	the	DET
ejpam-4060	16	13	concepts	concept	NOUN
ejpam-4060	16	14	on	on	ADP
ejpam-4060	16	15	generalized	generalized	ADJ
ejpam-4060	16	16	closed	closed	ADJ
ejpam-4060	16	17	and	and	CCONJ
ejpam-4060	16	18	semi	semi	ADV
ejpam-4060	16	19	open	open	ADJ
ejpam-4060	16	20	sets	set	NOUN
ejpam-4060	16	21	in	in	ADP
ejpam-4060	16	22	bitopological	bitopological	ADJ
ejpam-4060	16	23	spaces	space	NOUN
ejpam-4060	16	24	were	be	AUX
ejpam-4060	16	25	investigated	investigate	VERB
ejpam-4060	16	26	.	.	PUNCT
ejpam-4060	17	1	the	the	DET
ejpam-4060	17	2	concepts	concept	NOUN
ejpam-4060	17	3	of	of	ADP
ejpam-4060	17	4	bitopological	bitopological	ADJ
ejpam-4060	17	5	spaces	space	NOUN
ejpam-4060	17	6	have	have	AUX
ejpam-4060	17	7	been	be	AUX
ejpam-4060	17	8	widely	widely	ADV
ejpam-4060	17	9	investigated	investigate	VERB
ejpam-4060	17	10	up	up	ADP
ejpam-4060	17	11	to	to	ADP
ejpam-4060	17	12	other	other	ADJ
ejpam-4060	17	13	types	type	NOUN
ejpam-4060	17	14	of	of	ADP
ejpam-4060	17	15	spaces	space	NOUN
ejpam-4060	17	16	,	,	PUNCT
ejpam-4060	17	17	like	like	ADP
ejpam-4060	17	18	soft	soft	ADJ
ejpam-4060	17	19	bitopological	bitopological	ADJ
ejpam-4060	17	20	spaces	space	NOUN
ejpam-4060	17	21	.	.	PUNCT
ejpam-4060	18	1	the	the	DET
ejpam-4060	18	2	researcher	researcher	NOUN
ejpam-4060	18	3	of	of	ADP
ejpam-4060	18	4	this	this	DET
ejpam-4060	18	5	present	present	ADJ
ejpam-4060	18	6	study	study	NOUN
ejpam-4060	18	7	was	be	AUX
ejpam-4060	18	8	inspired	inspire	VERB
ejpam-4060	18	9	by	by	ADP
ejpam-4060	18	10	the	the	DET
ejpam-4060	18	11	work	work	NOUN
ejpam-4060	18	12	of	of	ADP
ejpam-4060	18	13	şenel	şenel	NOUN
ejpam-4060	18	14	and	and	CCONJ
ejpam-4060	18	15	cagman	cagman	NOUN
ejpam-4060	18	16	where	where	SCONJ
ejpam-4060	18	17	in	in	ADP
ejpam-4060	18	18	[	[	X
ejpam-4060	18	19	5	5	X
ejpam-4060	18	20	]	]	PUNCT
ejpam-4060	18	21	they	they	PRON
ejpam-4060	18	22	studied	study	VERB
ejpam-4060	18	23	soft	soft	ADJ
ejpam-4060	18	24	closed	closed	ADJ
ejpam-4060	18	25	sets	set	NOUN
ejpam-4060	18	26	on	on	ADP
ejpam-4060	18	27	soft	soft	ADJ
ejpam-4060	18	28	bitopological	bitopological	ADJ
ejpam-4060	18	29	spaces	space	NOUN
ejpam-4060	18	30	.	.	PUNCT
ejpam-4060	19	1	thereafter	thereafter	ADV
ejpam-4060	19	2	in	in	ADP
ejpam-4060	19	3	[	[	X
ejpam-4060	19	4	6	6	NUM
ejpam-4060	19	5	]	]	PUNCT
ejpam-4060	19	6	they	they	PRON
ejpam-4060	19	7	investigated	investigate	VERB
ejpam-4060	19	8	soft	soft	ADJ
ejpam-4060	19	9	topological	topological	ADJ
ejpam-4060	19	10	subspaces	subspace	NOUN
ejpam-4060	19	11	.	.	PUNCT
ejpam-4060	20	1	in	in	ADP
ejpam-4060	20	2	addition	addition	NOUN
ejpam-4060	20	3	,	,	PUNCT
ejpam-4060	20	4	in	in	ADP
ejpam-4060	20	5	[	[	X
ejpam-4060	20	6	3	3	X
ejpam-4060	20	7	]	]	X
ejpam-4060	20	8	a	a	DET
ejpam-4060	20	9	new	new	ADJ
ejpam-4060	20	10	approach	approach	NOUN
ejpam-4060	20	11	to	to	ADP
ejpam-4060	20	12	hausdorff	hausdorff	NOUN
ejpam-4060	20	13	space	space	NOUN
ejpam-4060	20	14	theory	theory	NOUN
ejpam-4060	20	15	via	via	ADP
ejpam-4060	20	16	the	the	DET
ejpam-4060	20	17	soft	soft	ADJ
ejpam-4060	20	18	sets	set	NOUN
ejpam-4060	20	19	was	be	AUX
ejpam-4060	20	20	investigated	investigate	VERB
ejpam-4060	20	21	by	by	ADP
ejpam-4060	20	22	şenel	şenel	NOUN
ejpam-4060	20	23	and	and	CCONJ
ejpam-4060	20	24	further	far	ADV
ejpam-4060	20	25	studied	study	VERB
ejpam-4060	20	26	soft	soft	ADJ
ejpam-4060	20	27	topology	topology	NOUN
ejpam-4060	20	28	generated	generate	VERB
ejpam-4060	20	29	by	by	ADP
ejpam-4060	20	30	l	l	ADJ
ejpam-4060	20	31	-	-	ADJ
ejpam-4060	20	32	soft	soft	ADJ
ejpam-4060	20	33	sets	set	NOUN
ejpam-4060	20	34	in	in	ADP
ejpam-4060	20	35	[	[	X
ejpam-4060	20	36	4	4	NUM
ejpam-4060	20	37	]	]	PUNCT
ejpam-4060	20	38	.	.	PUNCT
ejpam-4060	21	1	with	with	ADP
ejpam-4060	21	2	all	all	DET
ejpam-4060	21	3	these	these	DET
ejpam-4060	21	4	concepts	concept	NOUN
ejpam-4060	21	5	in	in	ADP
ejpam-4060	21	6	doi	doi	NOUN
ejpam-4060	21	7	:	:	PUNCT
ejpam-4060	21	8	https://doi.org/10.29020/nybg.ejpam.v14i4.4060	https://doi.org/10.29020/nybg.ejpam.v14i4.4060	NOUN
ejpam-4060	21	9	email	email	NOUN
ejpam-4060	21	10	address	address	NOUN
ejpam-4060	21	11	:	:	PUNCT
ejpam-4060	22	1	lmernilotutanes@gmail.com	lmernilotutanes@gmail.com	X
ejpam-4060	22	2	(	(	PUNCT
ejpam-4060	22	3	l.m.tutanes	l.m.tutane	NOUN
ejpam-4060	22	4	)	)	PUNCT
ejpam-4060	22	5	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-4060	22	6	1275	1275	NUM
ejpam-4060	23	1	©	©	PROPN
ejpam-4060	23	2	2021	2021	NUM
ejpam-4060	23	3	ejpam	ejpam	VERB
ejpam-4060	23	4	all	all	DET
ejpam-4060	23	5	rights	right	NOUN
ejpam-4060	23	6	reserved	reserve	VERB
ejpam-4060	23	7	.	.	PUNCT
ejpam-4060	24	1	l.m.tutanes	l.m.tutane	NOUN
ejpam-4060	24	2	/	/	SYM
ejpam-4060	24	3	eur	eur	PROPN
ejpam-4060	24	4	.	.	PUNCT
ejpam-4060	25	1	j.	j.	PROPN
ejpam-4060	25	2	pure	pure	PROPN
ejpam-4060	25	3	appl	appl	PROPN
ejpam-4060	25	4	.	.	PROPN
ejpam-4060	25	5	math	math	PROPN
ejpam-4060	25	6	,	,	PUNCT
ejpam-4060	25	7	14	14	NUM
ejpam-4060	25	8	(	(	PUNCT
ejpam-4060	25	9	4	4	NUM
ejpam-4060	25	10	)	)	PUNCT
ejpam-4060	25	11	(	(	PUNCT
ejpam-4060	25	12	2021	2021	NUM
ejpam-4060	25	13	)	)	PUNCT
ejpam-4060	25	14	,	,	PUNCT
ejpam-4060	25	15	1275	1275	NUM
ejpam-4060	25	16	-	-	SYM
ejpam-4060	25	17	1282	1282	NUM
ejpam-4060	25	18	1276	1276	NUM
ejpam-4060	25	19	mind	mind	NOUN
ejpam-4060	25	20	,	,	PUNCT
ejpam-4060	25	21	we	we	PRON
ejpam-4060	25	22	are	be	AUX
ejpam-4060	25	23	motivated	motivated	ADJ
ejpam-4060	25	24	to	to	PART
ejpam-4060	25	25	define	define	VERB
ejpam-4060	25	26	and	and	CCONJ
ejpam-4060	25	27	introduce	introduce	VERB
ejpam-4060	25	28	ψgs	ψgs	ADV
ejpam-4060	25	29	-	-	PUNCT
ejpam-4060	25	30	closed	close	VERB
ejpam-4060	25	31	sets	set	NOUN
ejpam-4060	25	32	in	in	ADP
ejpam-4060	25	33	bitopological	bitopological	ADJ
ejpam-4060	25	34	spaces	space	NOUN
ejpam-4060	25	35	and	and	CCONJ
ejpam-4060	25	36	will	will	AUX
ejpam-4060	25	37	intend	intend	VERB
ejpam-4060	25	38	to	to	PART
ejpam-4060	25	39	further	far	ADV
ejpam-4060	25	40	study	study	VERB
ejpam-4060	25	41	in	in	ADP
ejpam-4060	25	42	other	other	ADJ
ejpam-4060	25	43	spaces	space	NOUN
ejpam-4060	25	44	such	such	ADJ
ejpam-4060	25	45	as	as	ADP
ejpam-4060	25	46	soft	soft	ADJ
ejpam-4060	25	47	bitopological	bitopological	ADJ
ejpam-4060	25	48	spaces	space	NOUN
ejpam-4060	25	49	.	.	PUNCT
ejpam-4060	26	1	moreover	moreover	ADV
ejpam-4060	26	2	,	,	PUNCT
ejpam-4060	26	3	we	we	PRON
ejpam-4060	26	4	are	be	AUX
ejpam-4060	26	5	interested	interested	ADJ
ejpam-4060	26	6	to	to	PART
ejpam-4060	26	7	find	find	VERB
ejpam-4060	26	8	the	the	DET
ejpam-4060	26	9	properties	property	NOUN
ejpam-4060	26	10	of	of	ADP
ejpam-4060	26	11	ψgs	ψgs	ADV
ejpam-4060	26	12	-	-	PUNCT
ejpam-4060	26	13	closed	close	VERB
ejpam-4060	26	14	sets	set	NOUN
ejpam-4060	26	15	in	in	ADP
ejpam-4060	26	16	bts	bt	NOUN
ejpam-4060	26	17	and	and	CCONJ
ejpam-4060	26	18	their	their	PRON
ejpam-4060	26	19	relationship	relationship	NOUN
ejpam-4060	26	20	to	to	ADP
ejpam-4060	26	21	other	other	ADJ
ejpam-4060	26	22	existing	exist	VERB
ejpam-4060	26	23	sets	set	NOUN
ejpam-4060	26	24	and	and	CCONJ
ejpam-4060	26	25	will	will	AUX
ejpam-4060	26	26	intend	intend	VERB
ejpam-4060	26	27	to	to	PART
ejpam-4060	26	28	investigate	investigate	VERB
ejpam-4060	26	29	the	the	DET
ejpam-4060	26	30	properties	property	NOUN
ejpam-4060	26	31	of	of	ADP
ejpam-4060	26	32	ψgsinterior	ψgsinterior	PROPN
ejpam-4060	26	33	and	and	CCONJ
ejpam-4060	26	34	ψgs	ψgs	NOUN
ejpam-4060	26	35	-	-	PUNCT
ejpam-4060	26	36	closure	closure	NOUN
ejpam-4060	26	37	of	of	ADP
ejpam-4060	26	38	a	a	DET
ejpam-4060	26	39	set	set	NOUN
ejpam-4060	26	40	.	.	PUNCT
ejpam-4060	27	1	in	in	ADP
ejpam-4060	27	2	general	general	ADJ
ejpam-4060	27	3	,	,	PUNCT
ejpam-4060	27	4	this	this	DET
ejpam-4060	27	5	study	study	NOUN
ejpam-4060	27	6	establishes	establish	VERB
ejpam-4060	27	7	some	some	DET
ejpam-4060	27	8	properties	property	NOUN
ejpam-4060	27	9	of	of	ADP
ejpam-4060	27	10	ψgs	ψgs	ADV
ejpam-4060	27	11	-	-	PUNCT
ejpam-4060	27	12	closed	close	VERB
ejpam-4060	27	13	set	set	NOUN
ejpam-4060	27	14	in	in	ADP
ejpam-4060	27	15	bitopological	bitopological	ADJ
ejpam-4060	27	16	spaces	space	NOUN
ejpam-4060	27	17	.	.	PUNCT
ejpam-4060	28	1	specifically	specifically	ADV
ejpam-4060	28	2	,	,	PUNCT
ejpam-4060	28	3	this	this	DET
ejpam-4060	28	4	study	study	NOUN
ejpam-4060	28	5	investigates	investigate	VERB
ejpam-4060	28	6	some	some	DET
ejpam-4060	28	7	properties	property	NOUN
ejpam-4060	28	8	of	of	ADP
ejpam-4060	28	9	ψgs	ψgs	ADV
ejpam-4060	28	10	-	-	PUNCT
ejpam-4060	28	11	closed	close	VERB
ejpam-4060	28	12	set	set	NOUN
ejpam-4060	28	13	in	in	ADP
ejpam-4060	28	14	bts	bt	NOUN
ejpam-4060	28	15	;	;	PUNCT
ejpam-4060	28	16	establishes	establish	VERB
ejpam-4060	28	17	the	the	DET
ejpam-4060	28	18	relationships	relationship	NOUN
ejpam-4060	28	19	between	between	ADP
ejpam-4060	28	20	ψgs	ψgs	ADV
ejpam-4060	28	21	-	-	PUNCT
ejpam-4060	28	22	closed	close	VERB
ejpam-4060	28	23	set	set	VERB
ejpam-4060	28	24	and	and	CCONJ
ejpam-4060	28	25	other	other	ADJ
ejpam-4060	28	26	closed	closed	ADJ
ejpam-4060	28	27	sets	set	NOUN
ejpam-4060	28	28	in	in	ADP
ejpam-4060	28	29	bts	bt	NOUN
ejpam-4060	28	30	;	;	PUNCT
ejpam-4060	28	31	and	and	CCONJ
ejpam-4060	28	32	provides	provide	VERB
ejpam-4060	28	33	some	some	DET
ejpam-4060	28	34	properties	property	NOUN
ejpam-4060	28	35	of	of	ADP
ejpam-4060	28	36	ψgs	ψgs	NOUN
ejpam-4060	28	37	-	-	PUNCT
ejpam-4060	28	38	closure	closure	NOUN
ejpam-4060	28	39	and	and	CCONJ
ejpam-4060	28	40	ψgs	ψgs	ADV
ejpam-4060	28	41	-	-	NOUN
ejpam-4060	28	42	interior	interior	ADJ
ejpam-4060	28	43	in	in	ADP
ejpam-4060	28	44	bts	bt	NOUN
ejpam-4060	28	45	.	.	PUNCT
ejpam-4060	29	1	the	the	DET
ejpam-4060	29	2	major	major	ADJ
ejpam-4060	29	3	contributions	contribution	NOUN
ejpam-4060	29	4	of	of	ADP
ejpam-4060	29	5	this	this	DET
ejpam-4060	29	6	study	study	NOUN
ejpam-4060	29	7	are	be	AUX
ejpam-4060	29	8	the	the	DET
ejpam-4060	29	9	original	original	ADJ
ejpam-4060	29	10	results	result	NOUN
ejpam-4060	29	11	on	on	ADP
ejpam-4060	29	12	ψgs	ψgs	ADV
ejpam-4060	29	13	-	-	PUNCT
ejpam-4060	29	14	closed	close	VERB
ejpam-4060	29	15	set	set	NOUN
ejpam-4060	29	16	in	in	ADP
ejpam-4060	29	17	bts	bt	NOUN
ejpam-4060	29	18	.	.	PUNCT
ejpam-4060	30	1	the	the	DET
ejpam-4060	30	2	findings	finding	NOUN
ejpam-4060	30	3	reveal	reveal	VERB
ejpam-4060	30	4	that	that	SCONJ
ejpam-4060	30	5	every	every	DET
ejpam-4060	30	6	(	(	PUNCT
ejpam-4060	30	7	i	i	NOUN
ejpam-4060	30	8	,	,	PUNCT
ejpam-4060	30	9	j)-ψ	j)-ψ	PROPN
ejpam-4060	30	10	-	-	ADJ
ejpam-4060	30	11	closed	closed	ADJ
ejpam-4060	30	12	set	set	NOUN
ejpam-4060	30	13	,	,	PUNCT
ejpam-4060	30	14	τi	τi	ADP
ejpam-4060	30	15	closed	close	VERB
ejpam-4060	30	16	set	set	VERB
ejpam-4060	30	17	,	,	PUNCT
ejpam-4060	30	18	regular	regular	ADJ
ejpam-4060	30	19	-	-	PUNCT
ejpam-4060	30	20	closed	close	VERB
ejpam-4060	30	21	set	set	NOUN
ejpam-4060	30	22	,	,	PUNCT
ejpam-4060	30	23	semi	semi	ADJ
ejpam-4060	30	24	-	-	ADJ
ejpam-4060	30	25	closed	closed	ADJ
ejpam-4060	30	26	set	set	NOUN
ejpam-4060	30	27	,	,	PUNCT
ejpam-4060	30	28	α	α	NOUN
ejpam-4060	30	29	-	-	PUNCT
ejpam-4060	30	30	closed	closed	ADJ
ejpam-4060	30	31	set	set	NOUN
ejpam-4060	30	32	,	,	PUNCT
ejpam-4060	30	33	ψ	ψ	ADJ
ejpam-4060	30	34	-	-	ADJ
ejpam-4060	30	35	closed	closed	ADJ
ejpam-4060	30	36	set	set	NOUN
ejpam-4060	30	37	,	,	PUNCT
ejpam-4060	30	38	αgs	αgs	NOUN
ejpam-4060	30	39	-	-	PUNCT
ejpam-4060	30	40	closed	closed	ADJ
ejpam-4060	30	41	set	set	NOUN
ejpam-4060	30	42	in	in	ADP
ejpam-4060	30	43	(	(	PUNCT
ejpam-4060	30	44	x	x	NOUN
ejpam-4060	30	45	,	,	PUNCT
ejpam-4060	30	46	τi	τi	PROPN
ejpam-4060	30	47	)	)	PUNCT
ejpam-4060	30	48	is	be	AUX
ejpam-4060	30	49	(	(	PUNCT
ejpam-4060	30	50	i	i	INTJ
ejpam-4060	30	51	,	,	PUNCT
ejpam-4060	30	52	j)-ψgs	j)-ψgs	ADV
ejpam-4060	30	53	-	-	PUNCT
ejpam-4060	30	54	closed	closed	ADJ
ejpam-4060	30	55	where	where	SCONJ
ejpam-4060	30	56	i	i	PRON
ejpam-4060	30	57	,	,	PUNCT
ejpam-4060	30	58	j	j	PROPN
ejpam-4060	30	59	∈	∈	PROPN
ejpam-4060	30	60	{	{	PUNCT
ejpam-4060	30	61	1	1	NUM
ejpam-4060	30	62	,	,	PUNCT
ejpam-4060	30	63	2	2	NUM
ejpam-4060	30	64	}	}	PUNCT
ejpam-4060	30	65	.	.	PUNCT
ejpam-4060	31	1	hence	hence	ADV
ejpam-4060	31	2	,	,	PUNCT
ejpam-4060	31	3	(	(	PUNCT
ejpam-4060	31	4	i	i	INTJ
ejpam-4060	31	5	,	,	PUNCT
ejpam-4060	31	6	j)-ψgs	j)-ψgs	ADV
ejpam-4060	31	7	-	-	PUNCT
ejpam-4060	31	8	closed	closed	ADJ
ejpam-4060	31	9	set	set	NOUN
ejpam-4060	31	10	is	be	AUX
ejpam-4060	31	11	bigger	big	ADJ
ejpam-4060	31	12	than	than	ADP
ejpam-4060	31	13	those	those	PRON
ejpam-4060	31	14	of	of	ADP
ejpam-4060	31	15	the	the	DET
ejpam-4060	31	16	mentioned	mention	VERB
ejpam-4060	31	17	sets	set	NOUN
ejpam-4060	31	18	.	.	PUNCT
ejpam-4060	32	1	also	also	ADV
ejpam-4060	32	2	,	,	PUNCT
ejpam-4060	32	3	it	it	PRON
ejpam-4060	32	4	was	be	AUX
ejpam-4060	32	5	found	find	VERB
ejpam-4060	32	6	out	out	ADP
ejpam-4060	32	7	that	that	SCONJ
ejpam-4060	32	8	the	the	DET
ejpam-4060	32	9	intersection	intersection	NOUN
ejpam-4060	32	10	of	of	ADP
ejpam-4060	32	11	(	(	PUNCT
ejpam-4060	32	12	i	i	PROPN
ejpam-4060	32	13	,	,	PUNCT
ejpam-4060	32	14	j)-ψgs	j)-ψgs	ADV
ejpam-4060	32	15	-	-	PUNCT
ejpam-4060	32	16	closed	closed	ADJ
ejpam-4060	32	17	sets	set	NOUN
ejpam-4060	32	18	is	be	AUX
ejpam-4060	32	19	(	(	PUNCT
ejpam-4060	32	20	i	i	NOUN
ejpam-4060	32	21	,	,	PUNCT
ejpam-4060	32	22	j)-ψgs	j)-ψgs	ADV
ejpam-4060	32	23	-	-	PUNCT
ejpam-4060	32	24	closed	closed	ADJ
ejpam-4060	32	25	.	.	PUNCT
ejpam-4060	33	1	furthermore	furthermore	ADV
ejpam-4060	33	2	,	,	PUNCT
ejpam-4060	33	3	the	the	DET
ejpam-4060	33	4	results	result	NOUN
ejpam-4060	33	5	on	on	ADP
ejpam-4060	33	6	ψgs	ψgs	NOUN
ejpam-4060	33	7	-	-	PUNCT
ejpam-4060	33	8	closure	closure	NOUN
ejpam-4060	33	9	and	and	CCONJ
ejpam-4060	33	10	ψgs	ψgs	ADV
ejpam-4060	33	11	-	-	NOUN
ejpam-4060	33	12	interior	interior	ADJ
ejpam-4060	33	13	in	in	ADP
ejpam-4060	33	14	bts	bt	NOUN
ejpam-4060	33	15	are	be	AUX
ejpam-4060	33	16	analogous	analogous	ADJ
ejpam-4060	33	17	to	to	ADP
ejpam-4060	33	18	that	that	PRON
ejpam-4060	33	19	in	in	ADP
ejpam-4060	33	20	other	other	ADJ
ejpam-4060	33	21	spaces	space	NOUN
ejpam-4060	33	22	.	.	PUNCT
ejpam-4060	34	1	we	we	PRON
ejpam-4060	34	2	are	be	AUX
ejpam-4060	34	3	motivated	motivated	ADJ
ejpam-4060	34	4	to	to	PART
ejpam-4060	34	5	have	have	VERB
ejpam-4060	34	6	the	the	DET
ejpam-4060	34	7	results	result	NOUN
ejpam-4060	34	8	or	or	CCONJ
ejpam-4060	34	9	theorems	theorem	NOUN
ejpam-4060	34	10	since	since	SCONJ
ejpam-4060	34	11	these	these	DET
ejpam-4060	34	12	results	result	NOUN
ejpam-4060	34	13	could	could	AUX
ejpam-4060	34	14	also	also	ADV
ejpam-4060	34	15	be	be	AUX
ejpam-4060	34	16	applied	apply	VERB
ejpam-4060	34	17	in	in	ADP
ejpam-4060	34	18	other	other	ADJ
ejpam-4060	34	19	spaces	space	NOUN
ejpam-4060	34	20	to	to	PART
ejpam-4060	34	21	come	come	VERB
ejpam-4060	34	22	up	up	ADP
ejpam-4060	34	23	with	with	ADP
ejpam-4060	34	24	analogous	analogous	ADJ
ejpam-4060	34	25	results	result	NOUN
ejpam-4060	34	26	or	or	CCONJ
ejpam-4060	34	27	theorems	theorem	NOUN
ejpam-4060	34	28	.	.	PUNCT
ejpam-4060	35	1	this	this	DET
ejpam-4060	35	2	study	study	NOUN
ejpam-4060	35	3	could	could	AUX
ejpam-4060	35	4	serve	serve	VERB
ejpam-4060	35	5	as	as	ADP
ejpam-4060	35	6	a	a	DET
ejpam-4060	35	7	resource	resource	NOUN
ejpam-4060	35	8	material	material	NOUN
ejpam-4060	35	9	for	for	ADP
ejpam-4060	35	10	future	future	ADJ
ejpam-4060	35	11	researches	research	NOUN
ejpam-4060	35	12	and	and	CCONJ
ejpam-4060	35	13	possible	possible	ADJ
ejpam-4060	35	14	applications	application	NOUN
ejpam-4060	35	15	.	.	PUNCT
ejpam-4060	36	1	this	this	PRON
ejpam-4060	36	2	may	may	AUX
ejpam-4060	36	3	encourage	encourage	VERB
ejpam-4060	36	4	other	other	ADJ
ejpam-4060	36	5	mathematics	mathematics	NOUN
ejpam-4060	36	6	enthusiasts	enthusiast	NOUN
ejpam-4060	36	7	to	to	PART
ejpam-4060	36	8	come	come	VERB
ejpam-4060	36	9	up	up	ADP
ejpam-4060	36	10	with	with	ADP
ejpam-4060	36	11	more	more	ADJ
ejpam-4060	36	12	results	result	NOUN
ejpam-4060	36	13	and	and	CCONJ
ejpam-4060	36	14	to	to	PART
ejpam-4060	36	15	establish	establish	VERB
ejpam-4060	36	16	possible	possible	ADJ
ejpam-4060	36	17	research	research	NOUN
ejpam-4060	36	18	directions	direction	NOUN
ejpam-4060	36	19	for	for	ADP
ejpam-4060	36	20	further	further	ADJ
ejpam-4060	36	21	study	study	NOUN
ejpam-4060	36	22	.	.	PUNCT
ejpam-4060	37	1	2	2	X
ejpam-4060	37	2	.	.	X
ejpam-4060	37	3	preliminaries	preliminary	NOUN
ejpam-4060	37	4	in	in	ADP
ejpam-4060	37	5	this	this	DET
ejpam-4060	37	6	section	section	NOUN
ejpam-4060	37	7	,	,	PUNCT
ejpam-4060	37	8	some	some	DET
ejpam-4060	37	9	basic	basic	ADJ
ejpam-4060	37	10	definitions	definition	NOUN
ejpam-4060	37	11	and	and	CCONJ
ejpam-4060	37	12	some	some	DET
ejpam-4060	37	13	known	know	VERB
ejpam-4060	37	14	results	result	NOUN
ejpam-4060	37	15	are	be	AUX
ejpam-4060	37	16	provided	provide	VERB
ejpam-4060	37	17	.	.	PUNCT
ejpam-4060	38	1	examples	example	NOUN
ejpam-4060	38	2	are	be	AUX
ejpam-4060	38	3	also	also	ADV
ejpam-4060	38	4	given	give	VERB
ejpam-4060	38	5	for	for	ADP
ejpam-4060	38	6	a	a	DET
ejpam-4060	38	7	clearer	clear	ADJ
ejpam-4060	38	8	understanding	understanding	NOUN
ejpam-4060	38	9	of	of	ADP
ejpam-4060	38	10	several	several	ADJ
ejpam-4060	38	11	terms	term	NOUN
ejpam-4060	38	12	defined	define	VERB
ejpam-4060	38	13	.	.	PUNCT
ejpam-4060	39	1	a	a	DET
ejpam-4060	39	2	collection	collection	NOUN
ejpam-4060	39	3	τ	τ	PROPN
ejpam-4060	39	4	of	of	ADP
ejpam-4060	39	5	subsets	subset	NOUN
ejpam-4060	39	6	of	of	ADP
ejpam-4060	39	7	a	a	DET
ejpam-4060	39	8	nonempty	nonempty	ADV
ejpam-4060	39	9	set	set	VERB
ejpam-4060	39	10	x	x	PUNCT
ejpam-4060	39	11	is	be	AUX
ejpam-4060	39	12	a	a	DET
ejpam-4060	39	13	topology	topology	NOUN
ejpam-4060	39	14	on	on	ADP
ejpam-4060	39	15	x	x	PUNCT
ejpam-4060	39	16	if	if	SCONJ
ejpam-4060	39	17	∅	∅	NOUN
ejpam-4060	39	18	,	,	PUNCT
ejpam-4060	39	19	x	x	SYM
ejpam-4060	39	20	∈	∈	PROPN
ejpam-4060	39	21	τ	τ	X
ejpam-4060	39	22	,	,	PUNCT
ejpam-4060	39	23	{	{	PUNCT
ejpam-4060	39	24	mω	mω	X
ejpam-4060	39	25	:	:	PUNCT
ejpam-4060	39	26	ω	ω	NUM
ejpam-4060	39	27	∈	∈	PROPN
ejpam-4060	39	28	ω	ω	PROPN
ejpam-4060	39	29	}	}	PUNCT
ejpam-4060	39	30	⊆	⊆	NUM
ejpam-4060	39	31	τ	τ	PROPN
ejpam-4060	39	32	implies	imply	VERB
ejpam-4060	39	33	∪ω∈ωmω	∪ω∈ωmω	PROPN
ejpam-4060	39	34	∈	∈	PROPN
ejpam-4060	39	35	τ	τ	X
ejpam-4060	39	36	,	,	PUNCT
ejpam-4060	39	37	and	and	CCONJ
ejpam-4060	39	38	a	a	DET
ejpam-4060	39	39	,	,	PUNCT
ejpam-4060	39	40	b	b	X
ejpam-4060	39	41	∈	∈	PROPN
ejpam-4060	39	42	τ	τ	X
ejpam-4060	39	43	implies	imply	VERB
ejpam-4060	39	44	a	a	DET
ejpam-4060	39	45	∩	∩	ADJ
ejpam-4060	39	46	b	b	X
ejpam-4060	39	47	∈	∈	PROPN
ejpam-4060	39	48	τ	τ	X
ejpam-4060	39	49	.	.	PUNCT
ejpam-4060	40	1	if	if	SCONJ
ejpam-4060	40	2	τ	τ	PROPN
ejpam-4060	40	3	is	be	AUX
ejpam-4060	40	4	a	a	DET
ejpam-4060	40	5	topology	topology	NOUN
ejpam-4060	40	6	on	on	ADP
ejpam-4060	40	7	x	x	NOUN
ejpam-4060	40	8	,	,	PUNCT
ejpam-4060	40	9	then	then	ADV
ejpam-4060	40	10	(	(	PUNCT
ejpam-4060	40	11	x	x	X
ejpam-4060	40	12	,	,	PUNCT
ejpam-4060	40	13	τ	τ	X
ejpam-4060	40	14	)	)	PUNCT
ejpam-4060	40	15	is	be	AUX
ejpam-4060	40	16	called	call	VERB
ejpam-4060	40	17	a	a	DET
ejpam-4060	40	18	topological	topological	ADJ
ejpam-4060	40	19	space	space	NOUN
ejpam-4060	40	20	,	,	PUNCT
ejpam-4060	40	21	and	and	CCONJ
ejpam-4060	40	22	the	the	DET
ejpam-4060	40	23	elements	element	NOUN
ejpam-4060	40	24	of	of	ADP
ejpam-4060	40	25	τ	τ	PROPN
ejpam-4060	40	26	are	be	AUX
ejpam-4060	40	27	called	call	VERB
ejpam-4060	40	28	τ	τ	X
ejpam-4060	40	29	-open	-open	PROPN
ejpam-4060	40	30	(	(	PUNCT
ejpam-4060	40	31	or	or	CCONJ
ejpam-4060	40	32	simply	simply	ADV
ejpam-4060	40	33	open	open	ADJ
ejpam-4060	40	34	)	)	PUNCT
ejpam-4060	40	35	sets	set	NOUN
ejpam-4060	40	36	.	.	PUNCT
ejpam-4060	41	1	a	a	DET
ejpam-4060	41	2	subset	subset	NOUN
ejpam-4060	41	3	f	f	NOUN
ejpam-4060	41	4	of	of	ADP
ejpam-4060	41	5	x	x	PROPN
ejpam-4060	41	6	is	be	AUX
ejpam-4060	41	7	said	say	VERB
ejpam-4060	41	8	to	to	PART
ejpam-4060	41	9	be	be	AUX
ejpam-4060	41	10	τ	τ	X
ejpam-4060	41	11	-closed	-close	VERB
ejpam-4060	41	12	(	(	PUNCT
ejpam-4060	41	13	or	or	CCONJ
ejpam-4060	41	14	simply	simply	ADV
ejpam-4060	41	15	closed	closed	ADJ
ejpam-4060	41	16	)	)	PUNCT
ejpam-4060	41	17	if	if	SCONJ
ejpam-4060	41	18	its	its	PRON
ejpam-4060	41	19	complement	complement	NOUN
ejpam-4060	41	20	x∖f	x∖f	PROPN
ejpam-4060	41	21	is	be	AUX
ejpam-4060	41	22	open	open	ADJ
ejpam-4060	41	23	.	.	PUNCT
ejpam-4060	42	1	the	the	DET
ejpam-4060	42	2	interior	interior	NOUN
ejpam-4060	42	3	of	of	ADP
ejpam-4060	42	4	a	a	PRON
ejpam-4060	42	5	,	,	PUNCT
ejpam-4060	42	6	denoted	denote	VERB
ejpam-4060	42	7	by	by	ADP
ejpam-4060	42	8	int(a	int(a	PROPN
ejpam-4060	42	9	)	)	PUNCT
ejpam-4060	42	10	,	,	PUNCT
ejpam-4060	42	11	is	be	AUX
ejpam-4060	42	12	the	the	DET
ejpam-4060	42	13	union	union	NOUN
ejpam-4060	42	14	of	of	ADP
ejpam-4060	42	15	all	all	DET
ejpam-4060	42	16	open	open	ADJ
ejpam-4060	42	17	sets	set	NOUN
ejpam-4060	42	18	contained	contain	VERB
ejpam-4060	42	19	in	in	ADP
ejpam-4060	42	20	a.	a.	NOUN
ejpam-4060	42	21	that	that	PRON
ejpam-4060	42	22	is	be	AUX
ejpam-4060	42	23	,	,	PUNCT
ejpam-4060	42	24	int(a	int(a	PROPN
ejpam-4060	42	25	)	)	PUNCT
ejpam-4060	42	26	=	=	SYM
ejpam-4060	42	27	⋃	⋃	NOUN
ejpam-4060	42	28	{	{	PUNCT
ejpam-4060	42	29	o	o	NOUN
ejpam-4060	42	30	∈	∈	PROPN
ejpam-4060	42	31	τ	τ	X
ejpam-4060	42	32	:	:	PUNCT
ejpam-4060	42	33	o	o	X
ejpam-4060	42	34	⊆	⊆	NUM
ejpam-4060	42	35	a	a	PRON
ejpam-4060	42	36	}	}	PUNCT
ejpam-4060	42	37	.	.	PUNCT
ejpam-4060	43	1	the	the	DET
ejpam-4060	43	2	closure	closure	NOUN
ejpam-4060	43	3	of	of	ADP
ejpam-4060	43	4	a	a	PRON
ejpam-4060	43	5	,	,	PUNCT
ejpam-4060	43	6	denoted	denote	VERB
ejpam-4060	43	7	by	by	ADP
ejpam-4060	43	8	cl(a	cl(a	NOUN
ejpam-4060	43	9	)	)	PUNCT
ejpam-4060	43	10	,	,	PUNCT
ejpam-4060	43	11	is	be	AUX
ejpam-4060	43	12	the	the	DET
ejpam-4060	43	13	intersection	intersection	NOUN
ejpam-4060	43	14	of	of	ADP
ejpam-4060	43	15	all	all	DET
ejpam-4060	43	16	closed	closed	ADJ
ejpam-4060	43	17	sets	set	NOUN
ejpam-4060	43	18	containing	contain	VERB
ejpam-4060	43	19	a.	a.	NOUN
ejpam-4060	43	20	that	that	PRON
ejpam-4060	43	21	is	be	AUX
ejpam-4060	43	22	,	,	PUNCT
ejpam-4060	43	23	cl(a	cl(a	X
ejpam-4060	43	24	)	)	PUNCT
ejpam-4060	43	25	=	=	SYM
ejpam-4060	43	26	⋂	⋂	PROPN
ejpam-4060	43	27	{	{	PUNCT
ejpam-4060	43	28	f	f	NOUN
ejpam-4060	43	29	⊆	⊆	NUM
ejpam-4060	43	30	x	x	X
ejpam-4060	43	31	:	:	PUNCT
ejpam-4060	43	32	f	f	PROPN
ejpam-4060	43	33	is	be	AUX
ejpam-4060	43	34	closed	closed	ADJ
ejpam-4060	43	35	and	and	CCONJ
ejpam-4060	43	36	f	f	PROPN
ejpam-4060	43	37	⊇	⊇	PROPN
ejpam-4060	43	38	a	a	PROPN
ejpam-4060	43	39	}	}	PUNCT
ejpam-4060	43	40	.	.	PUNCT
ejpam-4060	44	1	now	now	ADV
ejpam-4060	44	2	,	,	PUNCT
ejpam-4060	44	3	if	if	SCONJ
ejpam-4060	44	4	τ1	τ1	NOUN
ejpam-4060	44	5	and	and	CCONJ
ejpam-4060	44	6	τ2	τ2	NOUN
ejpam-4060	44	7	are	be	AUX
ejpam-4060	44	8	arbitrary	arbitrary	ADJ
ejpam-4060	44	9	topologies	topology	NOUN
ejpam-4060	44	10	on	on	ADP
ejpam-4060	44	11	x	x	PUNCT
ejpam-4060	44	12	then	then	ADV
ejpam-4060	44	13	(	(	PUNCT
ejpam-4060	44	14	x	x	NOUN
ejpam-4060	44	15	,	,	PUNCT
ejpam-4060	44	16	τ1	τ1	NOUN
ejpam-4060	44	17	,	,	PUNCT
ejpam-4060	44	18	τ2	τ2	NOUN
ejpam-4060	44	19	)	)	PUNCT
ejpam-4060	44	20	is	be	AUX
ejpam-4060	44	21	called	call	VERB
ejpam-4060	44	22	a	a	DET
ejpam-4060	44	23	bitopological	bitopological	ADJ
ejpam-4060	44	24	space	space	NOUN
ejpam-4060	44	25	.	.	PUNCT
ejpam-4060	45	1	the	the	DET
ejpam-4060	45	2	interior	interior	NOUN
ejpam-4060	45	3	of	of	ADP
ejpam-4060	45	4	a	a	PRON
ejpam-4060	45	5	and	and	CCONJ
ejpam-4060	45	6	the	the	DET
ejpam-4060	45	7	closure	closure	NOUN
ejpam-4060	45	8	of	of	ADP
ejpam-4060	45	9	a	a	PRON
ejpam-4060	45	10	with	with	ADP
ejpam-4060	45	11	respect	respect	NOUN
ejpam-4060	45	12	to	to	ADP
ejpam-4060	45	13	τi	τi	PROPN
ejpam-4060	45	14	are	be	AUX
ejpam-4060	45	15	denoted	denote	VERB
ejpam-4060	45	16	by	by	ADP
ejpam-4060	45	17	inti(a	inti(a	NOUN
ejpam-4060	45	18	)	)	PUNCT
ejpam-4060	45	19	and	and	CCONJ
ejpam-4060	45	20	cli(a	cli(a	PROPN
ejpam-4060	45	21	)	)	PUNCT
ejpam-4060	45	22	,	,	PUNCT
ejpam-4060	45	23	respectively	respectively	ADV
ejpam-4060	45	24	.	.	PUNCT
ejpam-4060	46	1	note	note	VERB
ejpam-4060	46	2	that	that	SCONJ
ejpam-4060	46	3	through	through	ADP
ejpam-4060	46	4	out	out	ADP
ejpam-4060	46	5	this	this	DET
ejpam-4060	46	6	context	context	NOUN
ejpam-4060	47	1	i	i	PRON
ejpam-4060	47	2	,	,	PUNCT
ejpam-4060	47	3	j	j	PROPN
ejpam-4060	47	4	∈	∈	PROPN
ejpam-4060	47	5	{	{	PUNCT
ejpam-4060	47	6	1	1	NUM
ejpam-4060	47	7	,	,	PUNCT
ejpam-4060	47	8	2	2	NUM
ejpam-4060	47	9	}	}	PUNCT
ejpam-4060	47	10	such	such	ADJ
ejpam-4060	47	11	that	that	SCONJ
ejpam-4060	47	12	i	i	PRON
ejpam-4060	47	13	̸=	̸=	PROPN
ejpam-4060	47	14	j.	j.	PROPN
ejpam-4060	47	15	definition	definition	NOUN
ejpam-4060	47	16	1	1	NUM
ejpam-4060	47	17	.	.	PUNCT
ejpam-4060	48	1	let	let	VERB
ejpam-4060	48	2	(	(	PUNCT
ejpam-4060	48	3	x	x	NOUN
ejpam-4060	48	4	,	,	PUNCT
ejpam-4060	48	5	τ	τ	X
ejpam-4060	48	6	)	)	PUNCT
ejpam-4060	48	7	be	be	VERB
ejpam-4060	48	8	a	a	DET
ejpam-4060	48	9	topological	topological	ADJ
ejpam-4060	48	10	space	space	NOUN
ejpam-4060	48	11	.	.	PUNCT
ejpam-4060	49	1	a	a	DET
ejpam-4060	49	2	subset	subset	NOUN
ejpam-4060	49	3	a	a	PRON
ejpam-4060	49	4	of	of	ADP
ejpam-4060	49	5	x	x	PRON
ejpam-4060	49	6	is	be	AUX
ejpam-4060	49	7	called	call	VERB
ejpam-4060	49	8	(	(	PUNCT
ejpam-4060	49	9	i	i	NOUN
ejpam-4060	49	10	)	)	PUNCT
ejpam-4060	49	11	semi	semi	ADJ
ejpam-4060	49	12	-	-	ADJ
ejpam-4060	49	13	open	open	ADJ
ejpam-4060	49	14	set	set	NOUN
ejpam-4060	49	15	[	[	X
ejpam-4060	49	16	12	12	NUM
ejpam-4060	49	17	]	]	X
ejpam-4060	49	18	if	if	SCONJ
ejpam-4060	49	19	a	a	DET
ejpam-4060	49	20	⊆	⊆	NUM
ejpam-4060	49	21	cl(int(a	cl(int(a	NOUN
ejpam-4060	49	22	)	)	PUNCT
ejpam-4060	49	23	)	)	PUNCT
ejpam-4060	50	1	;	;	PUNCT
ejpam-4060	50	2	l.m.tutanes	l.m.tutane	NOUN
ejpam-4060	50	3	/	/	SYM
ejpam-4060	50	4	eur	eur	PROPN
ejpam-4060	50	5	.	.	PUNCT
ejpam-4060	51	1	j.	j.	PROPN
ejpam-4060	51	2	pure	pure	PROPN
ejpam-4060	51	3	appl	appl	PROPN
ejpam-4060	51	4	.	.	PROPN
ejpam-4060	51	5	math	math	PROPN
ejpam-4060	51	6	,	,	PUNCT
ejpam-4060	51	7	14	14	NUM
ejpam-4060	51	8	(	(	PUNCT
ejpam-4060	51	9	4	4	NUM
ejpam-4060	51	10	)	)	PUNCT
ejpam-4060	51	11	(	(	PUNCT
ejpam-4060	51	12	2021	2021	NUM
ejpam-4060	51	13	)	)	PUNCT
ejpam-4060	51	14	,	,	PUNCT
ejpam-4060	51	15	1275	1275	NUM
ejpam-4060	51	16	-	-	SYM
ejpam-4060	51	17	1282	1282	NUM
ejpam-4060	51	18	1277	1277	NUM
ejpam-4060	51	19	(	(	PUNCT
ejpam-4060	51	20	ii	ii	NOUN
ejpam-4060	51	21	)	)	PUNCT
ejpam-4060	51	22	regular	regular	ADJ
ejpam-4060	51	23	-	-	PUNCT
ejpam-4060	51	24	open	open	NOUN
ejpam-4060	51	25	set	set	NOUN
ejpam-4060	51	26	[	[	X
ejpam-4060	51	27	19	19	NUM
ejpam-4060	51	28	]	]	X
ejpam-4060	51	29	if	if	SCONJ
ejpam-4060	51	30	a	a	PRON
ejpam-4060	51	31	=	=	SYM
ejpam-4060	51	32	int(cl(a	int(cl(a	PROPN
ejpam-4060	51	33	)	)	PUNCT
ejpam-4060	51	34	)	)	PUNCT
ejpam-4060	51	35	;	;	PUNCT
ejpam-4060	51	36	(	(	PUNCT
ejpam-4060	51	37	iii	iii	X
ejpam-4060	51	38	)	)	PUNCT
ejpam-4060	51	39	α	α	NOUN
ejpam-4060	51	40	-	-	ADJ
ejpam-4060	51	41	open	open	ADJ
ejpam-4060	51	42	set	set	NOUN
ejpam-4060	52	1	[	[	X
ejpam-4060	52	2	16	16	NUM
ejpam-4060	52	3	]	]	PUNCT
ejpam-4060	52	4	if	if	SCONJ
ejpam-4060	52	5	a	a	DET
ejpam-4060	52	6	⊆	⊆	NUM
ejpam-4060	52	7	int(cl(int(a	int(cl(int(a	NOUN
ejpam-4060	52	8	)	)	PUNCT
ejpam-4060	52	9	)	)	PUNCT
ejpam-4060	52	10	)	)	PUNCT
ejpam-4060	52	11	;	;	PUNCT
ejpam-4060	52	12	(	(	PUNCT
ejpam-4060	52	13	iv	iv	X
ejpam-4060	52	14	)	)	PUNCT
ejpam-4060	52	15	semi	semi	ADJ
ejpam-4060	52	16	-	-	ADJ
ejpam-4060	52	17	generalized	generalized	ADJ
ejpam-4060	52	18	closed	close	VERB
ejpam-4060	52	19	(	(	PUNCT
ejpam-4060	52	20	briefly	briefly	ADV
ejpam-4060	52	21	,	,	PUNCT
ejpam-4060	52	22	sg	sg	ADV
ejpam-4060	52	23	-	-	PUNCT
ejpam-4060	52	24	closed	closed	ADJ
ejpam-4060	52	25	)	)	PUNCT
ejpam-4060	52	26	set	set	NOUN
ejpam-4060	52	27	[	[	X
ejpam-4060	52	28	1	1	X
ejpam-4060	52	29	]	]	PUNCT
ejpam-4060	52	30	if	if	SCONJ
ejpam-4060	52	31	scl(a	scl(a	X
ejpam-4060	52	32	)	)	PUNCT
ejpam-4060	52	33	⊆	⊆	NUM
ejpam-4060	52	34	u	u	NOUN
ejpam-4060	52	35	whenever	whenever	SCONJ
ejpam-4060	52	36	a	a	DET
ejpam-4060	52	37	⊆	⊆	NUM
ejpam-4060	52	38	u	u	NOUN
ejpam-4060	52	39	and	and	CCONJ
ejpam-4060	52	40	u	u	NOUN
ejpam-4060	52	41	is	be	AUX
ejpam-4060	52	42	semi	semi	ADJ
ejpam-4060	52	43	-	-	ADJ
ejpam-4060	52	44	open	open	ADJ
ejpam-4060	52	45	in	in	ADP
ejpam-4060	52	46	(	(	PUNCT
ejpam-4060	52	47	x	x	NOUN
ejpam-4060	52	48	,	,	PUNCT
ejpam-4060	52	49	τ	τ	PROPN
ejpam-4060	52	50	)	)	PUNCT
ejpam-4060	52	51	;	;	PUNCT
ejpam-4060	52	52	(	(	PUNCT
ejpam-4060	52	53	v	v	NOUN
ejpam-4060	52	54	)	)	PUNCT
ejpam-4060	52	55	αgs	αgs	NOUN
ejpam-4060	52	56	-	-	PUNCT
ejpam-4060	52	57	closed	close	VERB
ejpam-4060	52	58	set	set	NOUN
ejpam-4060	52	59	[	[	X
ejpam-4060	52	60	18	18	NUM
ejpam-4060	52	61	]	]	PUNCT
ejpam-4060	52	62	if	if	SCONJ
ejpam-4060	52	63	αcl(a	αcl(a	NUM
ejpam-4060	52	64	)	)	PUNCT
ejpam-4060	52	65	⊆	⊆	NUM
ejpam-4060	52	66	u	u	NOUN
ejpam-4060	52	67	whenever	whenever	SCONJ
ejpam-4060	52	68	a	a	DET
ejpam-4060	52	69	⊆	⊆	NUM
ejpam-4060	52	70	u	u	NOUN
ejpam-4060	52	71	and	and	CCONJ
ejpam-4060	52	72	u	u	NOUN
ejpam-4060	52	73	is	be	AUX
ejpam-4060	52	74	semi	semi	ADJ
ejpam-4060	52	75	-	-	ADJ
ejpam-4060	52	76	open	open	ADJ
ejpam-4060	52	77	in	in	ADP
ejpam-4060	52	78	(	(	PUNCT
ejpam-4060	52	79	x	x	NOUN
ejpam-4060	52	80	,	,	PUNCT
ejpam-4060	52	81	τ	τ	PROPN
ejpam-4060	52	82	)	)	PUNCT
ejpam-4060	52	83	;	;	PUNCT
ejpam-4060	52	84	(	(	PUNCT
ejpam-4060	52	85	vi	vi	NOUN
ejpam-4060	52	86	)	)	PUNCT
ejpam-4060	52	87	ψ	ψ	ADJ
ejpam-4060	52	88	-	-	ADJ
ejpam-4060	52	89	closed	closed	ADJ
ejpam-4060	52	90	set	set	NOUN
ejpam-4060	52	91	[	[	X
ejpam-4060	52	92	11	11	NUM
ejpam-4060	52	93	]	]	PUNCT
ejpam-4060	52	94	if	if	SCONJ
ejpam-4060	52	95	scl(a	scl(a	X
ejpam-4060	52	96	)	)	PUNCT
ejpam-4060	52	97	⊆	⊆	NUM
ejpam-4060	52	98	u	u	NOUN
ejpam-4060	52	99	whenever	whenever	SCONJ
ejpam-4060	52	100	a	a	DET
ejpam-4060	52	101	⊆	⊆	NUM
ejpam-4060	52	102	u	u	NOUN
ejpam-4060	52	103	and	and	CCONJ
ejpam-4060	52	104	u	u	NOUN
ejpam-4060	52	105	is	be	AUX
ejpam-4060	52	106	sg	sg	ADV
ejpam-4060	52	107	-	-	PUNCT
ejpam-4060	52	108	open	open	ADJ
ejpam-4060	52	109	in	in	ADP
ejpam-4060	52	110	(	(	PUNCT
ejpam-4060	52	111	x	x	NOUN
ejpam-4060	52	112	,	,	PUNCT
ejpam-4060	52	113	τ	τ	PROPN
ejpam-4060	52	114	)	)	PUNCT
ejpam-4060	52	115	;	;	PUNCT
ejpam-4060	52	116	and	and	CCONJ
ejpam-4060	52	117	(	(	PUNCT
ejpam-4060	52	118	vii	vii	PROPN
ejpam-4060	52	119	)	)	PUNCT
ejpam-4060	52	120	ψ	ψ	PROPN
ejpam-4060	52	121	generalized	generalize	VERB
ejpam-4060	52	122	semi	semi	ADJ
ejpam-4060	52	123	-	-	ADJ
ejpam-4060	52	124	closed	closed	ADJ
ejpam-4060	52	125	(	(	PUNCT
ejpam-4060	52	126	briefly	briefly	ADV
ejpam-4060	52	127	,	,	PUNCT
ejpam-4060	52	128	ψgs	ψgs	ADV
ejpam-4060	52	129	-	-	PUNCT
ejpam-4060	52	130	closed	closed	ADJ
ejpam-4060	52	131	)	)	PUNCT
ejpam-4060	52	132	set	set	NOUN
ejpam-4060	52	133	[	[	X
ejpam-4060	52	134	9	9	NUM
ejpam-4060	52	135	]	]	PUNCT
ejpam-4060	52	136	if	if	SCONJ
ejpam-4060	52	137	ψcl(a	ψcl(a	PROPN
ejpam-4060	52	138	)	)	PUNCT
ejpam-4060	52	139	⊆	⊆	NUM
ejpam-4060	52	140	u	u	NOUN
ejpam-4060	52	141	whenever	whenever	SCONJ
ejpam-4060	52	142	a	a	DET
ejpam-4060	52	143	⊆	⊆	NUM
ejpam-4060	52	144	u	u	NOUN
ejpam-4060	52	145	and	and	CCONJ
ejpam-4060	52	146	u	u	NOUN
ejpam-4060	52	147	is	be	AUX
ejpam-4060	52	148	semi	semi	ADJ
ejpam-4060	52	149	-	-	ADJ
ejpam-4060	52	150	open	open	ADJ
ejpam-4060	52	151	in	in	ADP
ejpam-4060	52	152	(	(	PUNCT
ejpam-4060	52	153	x	x	NOUN
ejpam-4060	52	154	,	,	PUNCT
ejpam-4060	52	155	τ	τ	PROPN
ejpam-4060	52	156	)	)	PUNCT
ejpam-4060	52	157	.	.	PUNCT
ejpam-4060	53	1	the	the	DET
ejpam-4060	53	2	complement	complement	NOUN
ejpam-4060	53	3	of	of	ADP
ejpam-4060	53	4	semi	semi	ADJ
ejpam-4060	53	5	-	-	ADJ
ejpam-4060	53	6	open	open	ADJ
ejpam-4060	53	7	(	(	PUNCT
ejpam-4060	53	8	resp	resp	NOUN
ejpam-4060	53	9	.	.	PUNCT
ejpam-4060	54	1	regular	regular	ADJ
ejpam-4060	54	2	-	-	PUNCT
ejpam-4060	54	3	open	open	ADJ
ejpam-4060	54	4	,	,	PUNCT
ejpam-4060	54	5	α	α	NOUN
ejpam-4060	54	6	-	-	ADJ
ejpam-4060	54	7	open	open	ADJ
ejpam-4060	54	8	,	,	PUNCT
ejpam-4060	54	9	gs	gs	NOUN
ejpam-4060	54	10	-	-	PUNCT
ejpam-4060	54	11	closed	closed	ADJ
ejpam-4060	54	12	,	,	PUNCT
ejpam-4060	54	13	αgs	αgs	NOUN
ejpam-4060	54	14	-	-	PUNCT
ejpam-4060	54	15	closed	closed	ADJ
ejpam-4060	54	16	,	,	PUNCT
ejpam-4060	54	17	ψclosed	ψclose	VERB
ejpam-4060	54	18	,	,	PUNCT
ejpam-4060	54	19	and	and	CCONJ
ejpam-4060	54	20	ψgs	ψgs	ADV
ejpam-4060	54	21	-	-	PUNCT
ejpam-4060	54	22	closed	closed	ADJ
ejpam-4060	54	23	)	)	PUNCT
ejpam-4060	54	24	set	set	NOUN
ejpam-4060	54	25	is	be	AUX
ejpam-4060	54	26	called	call	VERB
ejpam-4060	54	27	semi	semi	ADJ
ejpam-4060	54	28	-	-	ADJ
ejpam-4060	54	29	closed	closed	ADJ
ejpam-4060	54	30	(	(	PUNCT
ejpam-4060	54	31	resp	resp	NOUN
ejpam-4060	54	32	.	.	PUNCT
ejpam-4060	55	1	regular	regular	ADJ
ejpam-4060	55	2	-	-	PUNCT
ejpam-4060	55	3	closed	closed	ADJ
ejpam-4060	55	4	,	,	PUNCT
ejpam-4060	55	5	α	α	NOUN
ejpam-4060	55	6	-	-	PUNCT
ejpam-4060	55	7	closed	closed	ADJ
ejpam-4060	55	8	,	,	PUNCT
ejpam-4060	55	9	gs	gs	NOUN
ejpam-4060	55	10	-	-	PUNCT
ejpam-4060	55	11	open	open	ADJ
ejpam-4060	55	12	,	,	PUNCT
ejpam-4060	55	13	αgs	αgs	NOUN
ejpam-4060	55	14	-	-	ADJ
ejpam-4060	55	15	open	open	ADJ
ejpam-4060	55	16	,	,	PUNCT
ejpam-4060	55	17	ψ	ψ	NOUN
ejpam-4060	55	18	-	-	ADJ
ejpam-4060	55	19	open	open	ADJ
ejpam-4060	55	20	,	,	PUNCT
ejpam-4060	55	21	and	and	CCONJ
ejpam-4060	55	22	ψgs	ψgs	ADV
ejpam-4060	55	23	-	-	PUNCT
ejpam-4060	55	24	open	open	ADJ
ejpam-4060	55	25	)	)	PUNCT
ejpam-4060	55	26	set	set	NOUN
ejpam-4060	55	27	.	.	PUNCT
ejpam-4060	55	28	definition	definition	NOUN
ejpam-4060	55	29	2	2	NUM
ejpam-4060	55	30	.	.	PUNCT
ejpam-4060	56	1	let	let	AUX
ejpam-4060	56	2	(	(	PUNCT
ejpam-4060	56	3	x	x	NOUN
ejpam-4060	56	4	,	,	PUNCT
ejpam-4060	56	5	τ1	τ1	NOUN
ejpam-4060	56	6	,	,	PUNCT
ejpam-4060	56	7	τ2	τ2	PROPN
ejpam-4060	56	8	)	)	PUNCT
ejpam-4060	56	9	be	be	VERB
ejpam-4060	56	10	a	a	DET
ejpam-4060	56	11	bitopological	bitopological	ADJ
ejpam-4060	56	12	space	space	NOUN
ejpam-4060	56	13	.	.	PUNCT
ejpam-4060	57	1	a	a	DET
ejpam-4060	57	2	subset	subset	NOUN
ejpam-4060	57	3	a	a	PRON
ejpam-4060	57	4	of	of	ADP
ejpam-4060	57	5	x	x	PRON
ejpam-4060	57	6	is	be	AUX
ejpam-4060	57	7	called	call	VERB
ejpam-4060	57	8	(	(	PUNCT
ejpam-4060	57	9	i	i	NOUN
ejpam-4060	57	10	)	)	PUNCT
ejpam-4060	57	11	(	(	PUNCT
ejpam-4060	57	12	i	i	PROPN
ejpam-4060	57	13	,	,	PUNCT
ejpam-4060	57	14	j)-semi	j)-semi	VERB
ejpam-4060	57	15	open	open	ADJ
ejpam-4060	57	16	set	set	ADJ
ejpam-4060	57	17	[	[	X
ejpam-4060	57	18	15	15	NUM
ejpam-4060	57	19	]	]	X
ejpam-4060	57	20	if	if	SCONJ
ejpam-4060	57	21	a	a	DET
ejpam-4060	57	22	⊆	⊆	NUM
ejpam-4060	57	23	clj(inti(a	clj(inti(a	NOUN
ejpam-4060	57	24	)	)	PUNCT
ejpam-4060	57	25	)	)	PUNCT
ejpam-4060	58	1	;	;	PUNCT
ejpam-4060	58	2	(	(	PUNCT
ejpam-4060	58	3	ii	ii	NOUN
ejpam-4060	58	4	)	)	PUNCT
ejpam-4060	58	5	(	(	PUNCT
ejpam-4060	58	6	i	i	PROPN
ejpam-4060	58	7	,	,	PUNCT
ejpam-4060	58	8	j)-semi	j)-semi	VERB
ejpam-4060	58	9	generalized	generalize	VERB
ejpam-4060	58	10	closed	closed	ADJ
ejpam-4060	58	11	(	(	PUNCT
ejpam-4060	58	12	briefly	briefly	ADV
ejpam-4060	58	13	,	,	PUNCT
ejpam-4060	58	14	(	(	PUNCT
ejpam-4060	58	15	i	i	NOUN
ejpam-4060	58	16	,	,	PUNCT
ejpam-4060	58	17	j)-sg	j)-sg	NOUN
ejpam-4060	58	18	closed	closed	ADJ
ejpam-4060	58	19	)	)	PUNCT
ejpam-4060	58	20	set	set	VERB
ejpam-4060	58	21	[	[	X
ejpam-4060	58	22	17	17	NUM
ejpam-4060	58	23	]	]	PUNCT
ejpam-4060	58	24	if	if	SCONJ
ejpam-4060	58	25	(	(	PUNCT
ejpam-4060	58	26	i	i	NOUN
ejpam-4060	58	27	,	,	PUNCT
ejpam-4060	58	28	j)-scl(a	j)-scl(a	PROPN
ejpam-4060	58	29	)	)	PUNCT
ejpam-4060	58	30	⊆	⊆	NUM
ejpam-4060	58	31	u	u	NOUN
ejpam-4060	58	32	whenever	whenever	SCONJ
ejpam-4060	58	33	a	a	DET
ejpam-4060	58	34	⊆	⊆	NUM
ejpam-4060	58	35	u	u	NOUN
ejpam-4060	58	36	and	and	CCONJ
ejpam-4060	58	37	u	u	NOUN
ejpam-4060	58	38	is	be	AUX
ejpam-4060	58	39	(	(	PUNCT
ejpam-4060	58	40	i	i	PROPN
ejpam-4060	58	41	,	,	PUNCT
ejpam-4060	58	42	j)-semi	j)-semi	VERB
ejpam-4060	58	43	open	open	ADJ
ejpam-4060	58	44	;	;	PUNCT
ejpam-4060	58	45	and	and	CCONJ
ejpam-4060	58	46	(	(	PUNCT
ejpam-4060	58	47	iii	iii	X
ejpam-4060	58	48	)	)	PUNCT
ejpam-4060	58	49	(	(	PUNCT
ejpam-4060	58	50	i	i	PROPN
ejpam-4060	58	51	,	,	PUNCT
ejpam-4060	58	52	j)-ψ	j)-ψ	PROPN
ejpam-4060	58	53	-	-	ADJ
ejpam-4060	58	54	closed	closed	ADJ
ejpam-4060	58	55	set	set	NOUN
ejpam-4060	58	56	[	[	X
ejpam-4060	58	57	20	20	NUM
ejpam-4060	58	58	]	]	PUNCT
ejpam-4060	58	59	if	if	SCONJ
ejpam-4060	58	60	(	(	PUNCT
ejpam-4060	58	61	i	i	NOUN
ejpam-4060	58	62	,	,	PUNCT
ejpam-4060	58	63	j)-scl(a	j)-scl(a	PROPN
ejpam-4060	58	64	)	)	PUNCT
ejpam-4060	58	65	⊆	⊆	NUM
ejpam-4060	58	66	u	u	NOUN
ejpam-4060	58	67	whenever	whenever	SCONJ
ejpam-4060	58	68	a	a	DET
ejpam-4060	58	69	⊆	⊆	NUM
ejpam-4060	58	70	u	u	NOUN
ejpam-4060	58	71	and	and	CCONJ
ejpam-4060	58	72	u	u	NOUN
ejpam-4060	58	73	is	be	AUX
ejpam-4060	58	74	(	(	PUNCT
ejpam-4060	58	75	i	i	NOUN
ejpam-4060	58	76	,	,	PUNCT
ejpam-4060	58	77	j)-sg	j)-sg	NOUN
ejpam-4060	58	78	open	open	ADJ
ejpam-4060	58	79	.	.	PUNCT
ejpam-4060	59	1	the	the	DET
ejpam-4060	59	2	complement	complement	NOUN
ejpam-4060	59	3	of	of	ADP
ejpam-4060	59	4	(	(	PUNCT
ejpam-4060	59	5	i	i	PROPN
ejpam-4060	59	6	,	,	PUNCT
ejpam-4060	59	7	j)-semi	j)-semi	VERB
ejpam-4060	59	8	open	open	ADJ
ejpam-4060	59	9	(	(	PUNCT
ejpam-4060	59	10	resp	resp	NOUN
ejpam-4060	59	11	.	.	PUNCT
ejpam-4060	60	1	(	(	PUNCT
ejpam-4060	60	2	i	i	NOUN
ejpam-4060	60	3	,	,	PUNCT
ejpam-4060	60	4	j)-sg	j)-sg	NOUN
ejpam-4060	60	5	closed	close	VERB
ejpam-4060	60	6	and	and	CCONJ
ejpam-4060	60	7	(	(	PUNCT
ejpam-4060	60	8	i	i	NOUN
ejpam-4060	60	9	,	,	PUNCT
ejpam-4060	60	10	j)-ψ	j)-ψ	PROPN
ejpam-4060	60	11	-	-	ADJ
ejpam-4060	60	12	closed	closed	ADJ
ejpam-4060	60	13	)	)	PUNCT
ejpam-4060	60	14	set	set	NOUN
ejpam-4060	60	15	is	be	AUX
ejpam-4060	60	16	called	call	VERB
ejpam-4060	60	17	(	(	PUNCT
ejpam-4060	60	18	i	i	PROPN
ejpam-4060	60	19	,	,	PUNCT
ejpam-4060	60	20	j)-semi	j)-semi	X
ejpam-4060	60	21	closed	closed	ADJ
ejpam-4060	60	22	(	(	PUNCT
ejpam-4060	60	23	resp	resp	NOUN
ejpam-4060	60	24	.	.	PUNCT
ejpam-4060	61	1	(	(	PUNCT
ejpam-4060	61	2	i	i	NOUN
ejpam-4060	61	3	,	,	PUNCT
ejpam-4060	61	4	j)-sg	j)-sg	VERB
ejpam-4060	61	5	open	open	ADJ
ejpam-4060	61	6	and	and	CCONJ
ejpam-4060	61	7	(	(	PUNCT
ejpam-4060	61	8	i	i	NOUN
ejpam-4060	61	9	,	,	PUNCT
ejpam-4060	61	10	j)-ψ	j)-ψ	PROPN
ejpam-4060	61	11	-	-	ADJ
ejpam-4060	61	12	open	open	ADJ
ejpam-4060	61	13	)	)	PUNCT
ejpam-4060	61	14	set	set	NOUN
ejpam-4060	61	15	.	.	PUNCT
ejpam-4060	62	1	the	the	DET
ejpam-4060	62	2	next	next	ADJ
ejpam-4060	62	3	result	result	NOUN
ejpam-4060	62	4	was	be	AUX
ejpam-4060	62	5	proven	prove	VERB
ejpam-4060	62	6	in	in	ADP
ejpam-4060	62	7	[	[	X
ejpam-4060	62	8	14	14	NUM
ejpam-4060	62	9	]	]	PUNCT
ejpam-4060	62	10	.	.	PUNCT
ejpam-4060	63	1	lemma	lemma	PROPN
ejpam-4060	63	2	1	1	X
ejpam-4060	63	3	.	.	PUNCT
ejpam-4060	64	1	if	if	SCONJ
ejpam-4060	64	2	a	a	DET
ejpam-4060	64	3	subset	subset	NOUN
ejpam-4060	64	4	a	a	PRON
ejpam-4060	64	5	of	of	ADP
ejpam-4060	64	6	x	x	PUNCT
ejpam-4060	64	7	is	be	AUX
ejpam-4060	64	8	semi	semi	ADJ
ejpam-4060	64	9	-	-	ADJ
ejpam-4060	64	10	open	open	ADJ
ejpam-4060	64	11	(	(	PUNCT
ejpam-4060	64	12	respectively	respectively	ADV
ejpam-4060	64	13	,	,	PUNCT
ejpam-4060	64	14	semi	semi	ADJ
ejpam-4060	64	15	-	-	ADJ
ejpam-4060	64	16	closed	closed	ADJ
ejpam-4060	64	17	,	,	PUNCT
ejpam-4060	64	18	sg	sg	NOUN
ejpam-4060	64	19	-	-	PUNCT
ejpam-4060	64	20	closed	closed	ADJ
ejpam-4060	64	21	,	,	PUNCT
ejpam-4060	64	22	gs	gs	NOUN
ejpam-4060	64	23	-	-	PUNCT
ejpam-4060	64	24	closed	closed	ADJ
ejpam-4060	64	25	,	,	PUNCT
ejpam-4060	64	26	g	g	NOUN
ejpam-4060	64	27	-	-	PUNCT
ejpam-4060	64	28	closed	closed	ADJ
ejpam-4060	64	29	,	,	PUNCT
ejpam-4060	64	30	ψ	ψ	ADJ
ejpam-4060	64	31	-	-	ADJ
ejpam-4060	64	32	closed	closed	ADJ
ejpam-4060	64	33	)	)	PUNCT
ejpam-4060	64	34	set	set	VERB
ejpam-4060	64	35	in	in	ADP
ejpam-4060	64	36	(	(	PUNCT
ejpam-4060	64	37	x	x	NOUN
ejpam-4060	64	38	,	,	PUNCT
ejpam-4060	64	39	τi	τi	ADP
ejpam-4060	64	40	)	)	PUNCT
ejpam-4060	64	41	for	for	ADP
ejpam-4060	64	42	i	i	PRON
ejpam-4060	64	43	∈	∈	PROPN
ejpam-4060	64	44	{	{	PUNCT
ejpam-4060	64	45	1	1	NUM
ejpam-4060	64	46	,	,	PUNCT
ejpam-4060	64	47	2	2	NUM
ejpam-4060	64	48	}	}	PUNCT
ejpam-4060	64	49	,	,	PUNCT
ejpam-4060	64	50	then	then	ADV
ejpam-4060	64	51	it	it	PRON
ejpam-4060	64	52	is	be	AUX
ejpam-4060	64	53	semi	semi	ADJ
ejpam-4060	64	54	-	-	ADJ
ejpam-4060	64	55	open	open	ADJ
ejpam-4060	64	56	(	(	PUNCT
ejpam-4060	64	57	respectively	respectively	ADV
ejpam-4060	64	58	,	,	PUNCT
ejpam-4060	64	59	semiclosed	semiclose	VERB
ejpam-4060	64	60	,	,	PUNCT
ejpam-4060	64	61	sg	sg	ADV
ejpam-4060	64	62	-	-	PUNCT
ejpam-4060	64	63	closed	closed	ADJ
ejpam-4060	64	64	,	,	PUNCT
ejpam-4060	64	65	gs	gs	NOUN
ejpam-4060	64	66	-	-	PUNCT
ejpam-4060	64	67	closed	closed	ADJ
ejpam-4060	64	68	,	,	PUNCT
ejpam-4060	64	69	g	g	NOUN
ejpam-4060	64	70	-	-	PUNCT
ejpam-4060	64	71	closed	closed	ADJ
ejpam-4060	64	72	,	,	PUNCT
ejpam-4060	64	73	ψ	ψ	ADJ
ejpam-4060	64	74	-	-	ADJ
ejpam-4060	64	75	closed	closed	ADJ
ejpam-4060	64	76	)	)	PUNCT
ejpam-4060	64	77	set	set	VERB
ejpam-4060	64	78	in	in	ADP
ejpam-4060	64	79	(	(	PUNCT
ejpam-4060	64	80	x	x	NOUN
ejpam-4060	64	81	,	,	PUNCT
ejpam-4060	64	82	τ1	τ1	NOUN
ejpam-4060	64	83	,	,	PUNCT
ejpam-4060	64	84	τ2	τ2	NOUN
ejpam-4060	64	85	)	)	PUNCT
ejpam-4060	64	86	.	.	PUNCT
ejpam-4060	65	1	the	the	DET
ejpam-4060	65	2	next	next	ADJ
ejpam-4060	65	3	theorem	theorem	NOUN
ejpam-4060	65	4	is	be	AUX
ejpam-4060	65	5	a	a	DET
ejpam-4060	65	6	composition	composition	NOUN
ejpam-4060	65	7	of	of	ADP
ejpam-4060	65	8	several	several	ADJ
ejpam-4060	65	9	results	result	NOUN
ejpam-4060	65	10	from	from	ADP
ejpam-4060	65	11	gowsalya	gowsalya	NOUN
ejpam-4060	65	12	,	,	PUNCT
ejpam-4060	65	13	s.	s.	PROPN
ejpam-4060	65	14	and	and	CCONJ
ejpam-4060	65	15	balamani	balamani	PROPN
ejpam-4060	65	16	,	,	PUNCT
ejpam-4060	65	17	n.	n.	NOUN
ejpam-4060	65	18	in	in	ADP
ejpam-4060	65	19	[	[	PUNCT
ejpam-4060	65	20	9	9	NUM
ejpam-4060	65	21	]	]	PUNCT
ejpam-4060	65	22	.	.	PUNCT
ejpam-4060	66	1	theorem	theorem	NOUN
ejpam-4060	66	2	1	1	X
ejpam-4060	66	3	.	.	PUNCT
ejpam-4060	67	1	let	let	VERB
ejpam-4060	67	2	(	(	PUNCT
ejpam-4060	67	3	x	x	NOUN
ejpam-4060	67	4	,	,	PUNCT
ejpam-4060	67	5	τ1	τ1	NOUN
ejpam-4060	67	6	,	,	PUNCT
ejpam-4060	67	7	τ2	τ2	NOUN
ejpam-4060	67	8	)	)	PUNCT
ejpam-4060	67	9	be	be	AUX
ejpam-4060	67	10	bitopological	bitopological	ADJ
ejpam-4060	67	11	space	space	NOUN
ejpam-4060	67	12	.	.	PUNCT
ejpam-4060	68	1	then	then	ADV
ejpam-4060	68	2	(	(	PUNCT
ejpam-4060	68	3	i	i	NOUN
ejpam-4060	68	4	)	)	PUNCT
ejpam-4060	68	5	every	every	DET
ejpam-4060	68	6	semi	semi	ADJ
ejpam-4060	68	7	-	-	ADJ
ejpam-4060	68	8	closed	closed	ADJ
ejpam-4060	68	9	set	set	NOUN
ejpam-4060	68	10	in	in	ADP
ejpam-4060	68	11	(	(	PUNCT
ejpam-4060	68	12	x	x	NOUN
ejpam-4060	68	13	,	,	PUNCT
ejpam-4060	68	14	τ	τ	X
ejpam-4060	68	15	)	)	PUNCT
ejpam-4060	68	16	is	be	AUX
ejpam-4060	68	17	ψgs	ψgs	ADV
ejpam-4060	68	18	-	-	PUNCT
ejpam-4060	68	19	closed	closed	ADJ
ejpam-4060	68	20	in	in	ADP
ejpam-4060	68	21	(	(	PUNCT
ejpam-4060	68	22	x	x	NOUN
ejpam-4060	68	23	,	,	PUNCT
ejpam-4060	68	24	τ	τ	PROPN
ejpam-4060	68	25	)	)	PUNCT
ejpam-4060	68	26	.	.	PUNCT
ejpam-4060	69	1	(	(	PUNCT
ejpam-4060	69	2	ii	ii	NOUN
ejpam-4060	69	3	)	)	PUNCT
ejpam-4060	69	4	every	every	DET
ejpam-4060	69	5	closed	close	VERB
ejpam-4060	69	6	set	set	VERB
ejpam-4060	69	7	in	in	ADP
ejpam-4060	69	8	(	(	PUNCT
ejpam-4060	69	9	x	x	NOUN
ejpam-4060	69	10	,	,	PUNCT
ejpam-4060	69	11	τ	τ	X
ejpam-4060	69	12	)	)	PUNCT
ejpam-4060	69	13	is	be	AUX
ejpam-4060	69	14	ψgs	ψgs	ADV
ejpam-4060	69	15	-	-	PUNCT
ejpam-4060	69	16	closed	close	VERB
ejpam-4060	69	17	set	set	NOUN
ejpam-4060	69	18	in	in	ADP
ejpam-4060	69	19	(	(	PUNCT
ejpam-4060	69	20	x	x	NOUN
ejpam-4060	69	21	,	,	PUNCT
ejpam-4060	69	22	τ	τ	PROPN
ejpam-4060	69	23	)	)	PUNCT
ejpam-4060	69	24	.	.	PUNCT
ejpam-4060	70	1	(	(	PUNCT
ejpam-4060	70	2	iii	iii	X
ejpam-4060	70	3	)	)	PUNCT
ejpam-4060	70	4	every	every	DET
ejpam-4060	70	5	regular	regular	ADJ
ejpam-4060	70	6	-	-	PUNCT
ejpam-4060	70	7	closed	close	VERB
ejpam-4060	70	8	set	set	NOUN
ejpam-4060	70	9	in	in	ADP
ejpam-4060	70	10	(	(	PUNCT
ejpam-4060	70	11	x	x	NOUN
ejpam-4060	70	12	,	,	PUNCT
ejpam-4060	70	13	τ	τ	X
ejpam-4060	70	14	)	)	PUNCT
ejpam-4060	70	15	is	be	AUX
ejpam-4060	70	16	ψgs	ψgs	ADV
ejpam-4060	70	17	-	-	PUNCT
ejpam-4060	70	18	closed	closed	ADJ
ejpam-4060	70	19	in	in	ADP
ejpam-4060	70	20	(	(	PUNCT
ejpam-4060	70	21	x	x	NOUN
ejpam-4060	70	22	,	,	PUNCT
ejpam-4060	70	23	τ	τ	PROPN
ejpam-4060	70	24	)	)	PUNCT
ejpam-4060	70	25	.	.	PUNCT
ejpam-4060	71	1	(	(	PUNCT
ejpam-4060	71	2	iv	iv	X
ejpam-4060	71	3	)	)	PUNCT
ejpam-4060	71	4	every	every	DET
ejpam-4060	71	5	α	α	X
ejpam-4060	71	6	-	-	ADJ
ejpam-4060	71	7	closed	closed	ADJ
ejpam-4060	71	8	set	set	NOUN
ejpam-4060	71	9	in	in	ADP
ejpam-4060	71	10	(	(	PUNCT
ejpam-4060	71	11	x	x	NOUN
ejpam-4060	71	12	,	,	PUNCT
ejpam-4060	71	13	τ	τ	X
ejpam-4060	71	14	)	)	PUNCT
ejpam-4060	71	15	is	be	AUX
ejpam-4060	71	16	ψgs	ψgs	ADV
ejpam-4060	71	17	-	-	PUNCT
ejpam-4060	71	18	closed	closed	ADJ
ejpam-4060	71	19	in	in	ADP
ejpam-4060	71	20	(	(	PUNCT
ejpam-4060	71	21	x	x	NOUN
ejpam-4060	71	22	,	,	PUNCT
ejpam-4060	71	23	τ	τ	PROPN
ejpam-4060	71	24	)	)	PUNCT
ejpam-4060	71	25	.	.	PUNCT
ejpam-4060	72	1	(	(	PUNCT
ejpam-4060	72	2	v	v	NOUN
ejpam-4060	72	3	)	)	PUNCT
ejpam-4060	72	4	every	every	DET
ejpam-4060	72	5	ψ	ψ	ADJ
ejpam-4060	72	6	-	-	ADJ
ejpam-4060	72	7	closed	closed	ADJ
ejpam-4060	72	8	set	set	NOUN
ejpam-4060	72	9	in	in	ADP
ejpam-4060	72	10	(	(	PUNCT
ejpam-4060	72	11	x	x	NOUN
ejpam-4060	72	12	,	,	PUNCT
ejpam-4060	72	13	τ	τ	X
ejpam-4060	72	14	)	)	PUNCT
ejpam-4060	72	15	is	be	AUX
ejpam-4060	72	16	ψgs	ψgs	ADV
ejpam-4060	72	17	-	-	PUNCT
ejpam-4060	72	18	closed	closed	ADJ
ejpam-4060	72	19	in	in	ADP
ejpam-4060	72	20	(	(	PUNCT
ejpam-4060	72	21	x	x	NOUN
ejpam-4060	72	22	,	,	PUNCT
ejpam-4060	72	23	τ	τ	PROPN
ejpam-4060	72	24	)	)	PUNCT
ejpam-4060	72	25	.	.	PUNCT
ejpam-4060	73	1	(	(	PUNCT
ejpam-4060	73	2	vi	vi	X
ejpam-4060	73	3	)	)	PUNCT
ejpam-4060	73	4	every	every	DET
ejpam-4060	73	5	αgs	αgs	NOUN
ejpam-4060	73	6	-	-	PUNCT
ejpam-4060	73	7	closed	closed	ADJ
ejpam-4060	73	8	set	set	NOUN
ejpam-4060	73	9	in	in	ADP
ejpam-4060	73	10	(	(	PUNCT
ejpam-4060	73	11	x	x	NOUN
ejpam-4060	73	12	,	,	PUNCT
ejpam-4060	73	13	τ	τ	X
ejpam-4060	73	14	)	)	PUNCT
ejpam-4060	73	15	is	be	AUX
ejpam-4060	73	16	ψgs	ψgs	ADV
ejpam-4060	73	17	-	-	PUNCT
ejpam-4060	73	18	closed	closed	ADJ
ejpam-4060	73	19	in	in	ADP
ejpam-4060	73	20	(	(	PUNCT
ejpam-4060	73	21	x	x	NOUN
ejpam-4060	73	22	,	,	PUNCT
ejpam-4060	73	23	τ	τ	PROPN
ejpam-4060	73	24	)	)	PUNCT
ejpam-4060	73	25	.	.	PUNCT
ejpam-4060	74	1	l.m.tutanes	l.m.tutane	NOUN
ejpam-4060	74	2	/	/	SYM
ejpam-4060	74	3	eur	eur	PROPN
ejpam-4060	74	4	.	.	PUNCT
ejpam-4060	75	1	j.	j.	PROPN
ejpam-4060	75	2	pure	pure	PROPN
ejpam-4060	75	3	appl	appl	PROPN
ejpam-4060	75	4	.	.	PROPN
ejpam-4060	75	5	math	math	PROPN
ejpam-4060	75	6	,	,	PUNCT
ejpam-4060	75	7	14	14	NUM
ejpam-4060	75	8	(	(	PUNCT
ejpam-4060	75	9	4	4	NUM
ejpam-4060	75	10	)	)	PUNCT
ejpam-4060	75	11	(	(	PUNCT
ejpam-4060	75	12	2021	2021	NUM
ejpam-4060	75	13	)	)	PUNCT
ejpam-4060	75	14	,	,	PUNCT
ejpam-4060	75	15	1275	1275	NUM
ejpam-4060	75	16	-	-	SYM
ejpam-4060	75	17	1282	1282	NUM
ejpam-4060	75	18	1278	1278	NUM
ejpam-4060	75	19	3	3	NUM
ejpam-4060	75	20	.	.	PUNCT
ejpam-4060	75	21	ψgs	ψgs	ADV
ejpam-4060	75	22	-	-	PUNCT
ejpam-4060	75	23	closed	close	VERB
ejpam-4060	75	24	sets	set	NOUN
ejpam-4060	75	25	and	and	CCONJ
ejpam-4060	75	26	its	its	PRON
ejpam-4060	75	27	relationship	relationship	NOUN
ejpam-4060	75	28	to	to	ADP
ejpam-4060	75	29	other	other	ADJ
ejpam-4060	75	30	closed	closed	ADJ
ejpam-4060	75	31	sets	set	NOUN
ejpam-4060	75	32	in	in	ADP
ejpam-4060	75	33	bts	bt	NOUN
ejpam-4060	75	34	in	in	ADP
ejpam-4060	75	35	this	this	DET
ejpam-4060	75	36	section	section	NOUN
ejpam-4060	75	37	,	,	PUNCT
ejpam-4060	75	38	some	some	DET
ejpam-4060	75	39	properties	property	NOUN
ejpam-4060	75	40	of	of	ADP
ejpam-4060	75	41	ψgs	ψgs	ADV
ejpam-4060	75	42	-	-	PUNCT
ejpam-4060	75	43	closed	close	VERB
ejpam-4060	75	44	sets	set	NOUN
ejpam-4060	75	45	in	in	ADP
ejpam-4060	75	46	bts	bt	NOUN
ejpam-4060	75	47	are	be	AUX
ejpam-4060	75	48	investigated	investigate	VERB
ejpam-4060	75	49	.	.	PUNCT
ejpam-4060	76	1	moreover	moreover	ADV
ejpam-4060	76	2	,	,	PUNCT
ejpam-4060	76	3	the	the	DET
ejpam-4060	76	4	relationship	relationship	NOUN
ejpam-4060	76	5	to	to	ADP
ejpam-4060	76	6	some	some	DET
ejpam-4060	76	7	other	other	ADJ
ejpam-4060	76	8	existing	exist	VERB
ejpam-4060	76	9	closed	closed	ADJ
ejpam-4060	76	10	sets	set	NOUN
ejpam-4060	76	11	in	in	ADP
ejpam-4060	76	12	bts	bt	NOUN
ejpam-4060	76	13	is	be	AUX
ejpam-4060	76	14	established	establish	VERB
ejpam-4060	76	15	.	.	PUNCT
ejpam-4060	77	1	definition	definition	NOUN
ejpam-4060	77	2	3	3	NUM
ejpam-4060	77	3	.	.	PUNCT
ejpam-4060	78	1	a	a	DET
ejpam-4060	78	2	subset	subset	NOUN
ejpam-4060	78	3	a	a	PRON
ejpam-4060	78	4	of	of	ADP
ejpam-4060	78	5	a	a	DET
ejpam-4060	78	6	bitopological	bitopological	ADJ
ejpam-4060	78	7	space	space	NOUN
ejpam-4060	78	8	(	(	PUNCT
ejpam-4060	78	9	x	x	NOUN
ejpam-4060	78	10	,	,	PUNCT
ejpam-4060	78	11	τ1	τ1	NOUN
ejpam-4060	78	12	,	,	PUNCT
ejpam-4060	78	13	τ2	τ2	NOUN
ejpam-4060	78	14	)	)	PUNCT
ejpam-4060	78	15	is	be	AUX
ejpam-4060	78	16	called	call	VERB
ejpam-4060	78	17	(	(	PUNCT
ejpam-4060	78	18	i	i	PROPN
ejpam-4060	78	19	,	,	PUNCT
ejpam-4060	78	20	j)-ψ	j)-ψ	PROPN
ejpam-4060	78	21	generalized	generalize	VERB
ejpam-4060	78	22	semi	semi	ADV
ejpam-4060	78	23	-	-	ADJ
ejpam-4060	78	24	closed	closed	ADJ
ejpam-4060	78	25	(	(	PUNCT
ejpam-4060	78	26	briefly	briefly	ADV
ejpam-4060	78	27	,	,	PUNCT
ejpam-4060	78	28	(	(	PUNCT
ejpam-4060	78	29	i	i	INTJ
ejpam-4060	78	30	,	,	PUNCT
ejpam-4060	78	31	j)-ψgs	j)-ψgs	ADV
ejpam-4060	78	32	-	-	PUNCT
ejpam-4060	78	33	closed	closed	ADJ
ejpam-4060	78	34	)	)	PUNCT
ejpam-4060	78	35	set	set	VERB
ejpam-4060	78	36	if	if	SCONJ
ejpam-4060	78	37	(	(	PUNCT
ejpam-4060	78	38	i	i	NOUN
ejpam-4060	78	39	,	,	PUNCT
ejpam-4060	78	40	j)-ψcl(a	j)-ψcl(a	PROPN
ejpam-4060	78	41	)	)	PUNCT
ejpam-4060	78	42	⊆	⊆	NUM
ejpam-4060	78	43	u	u	NOUN
ejpam-4060	78	44	whenever	whenever	SCONJ
ejpam-4060	78	45	a	a	DET
ejpam-4060	78	46	⊆	⊆	NUM
ejpam-4060	78	47	u	u	NOUN
ejpam-4060	78	48	and	and	CCONJ
ejpam-4060	78	49	u	u	NOUN
ejpam-4060	78	50	is	be	AUX
ejpam-4060	78	51	(	(	PUNCT
ejpam-4060	78	52	i	i	PROPN
ejpam-4060	78	53	,	,	PUNCT
ejpam-4060	78	54	j)-semi	j)-semi	NOUN
ejpam-4060	78	55	-	-	PUNCT
ejpam-4060	78	56	open	open	ADJ
ejpam-4060	78	57	in	in	ADP
ejpam-4060	78	58	(	(	PUNCT
ejpam-4060	78	59	x	x	NOUN
ejpam-4060	78	60	,	,	PUNCT
ejpam-4060	78	61	τ1	τ1	NOUN
ejpam-4060	78	62	,	,	PUNCT
ejpam-4060	78	63	τ2	τ2	NOUN
ejpam-4060	78	64	)	)	PUNCT
ejpam-4060	78	65	,	,	PUNCT
ejpam-4060	78	66	i	i	PRON
ejpam-4060	78	67	,	,	PUNCT
ejpam-4060	78	68	j	j	PROPN
ejpam-4060	78	69	∈	∈	PROPN
ejpam-4060	78	70	{	{	PUNCT
ejpam-4060	78	71	1	1	NUM
ejpam-4060	78	72	,	,	PUNCT
ejpam-4060	78	73	2	2	NUM
ejpam-4060	78	74	}	}	PUNCT
ejpam-4060	78	75	where	where	SCONJ
ejpam-4060	78	76	i	i	PRON
ejpam-4060	78	77	̸=	̸=	PROPN
ejpam-4060	78	78	j.	j.	PROPN
ejpam-4060	78	79	the	the	DET
ejpam-4060	78	80	complement	complement	NOUN
ejpam-4060	78	81	of	of	ADP
ejpam-4060	78	82	(	(	PUNCT
ejpam-4060	78	83	i	i	PROPN
ejpam-4060	78	84	,	,	PUNCT
ejpam-4060	78	85	j)-ψgs	j)-ψgs	ADV
ejpam-4060	78	86	-	-	PUNCT
ejpam-4060	78	87	closed	closed	ADJ
ejpam-4060	78	88	set	set	NOUN
ejpam-4060	78	89	is	be	AUX
ejpam-4060	78	90	called	call	VERB
ejpam-4060	78	91	(	(	PUNCT
ejpam-4060	78	92	i	i	PROPN
ejpam-4060	78	93	,	,	PUNCT
ejpam-4060	78	94	j)-ψgs	j)-ψgs	ADV
ejpam-4060	78	95	-	-	PUNCT
ejpam-4060	78	96	open	open	ADJ
ejpam-4060	78	97	set	set	NOUN
ejpam-4060	78	98	.	.	PUNCT
ejpam-4060	79	1	example	example	NOUN
ejpam-4060	80	1	1	1	NUM
ejpam-4060	80	2	.	.	PUNCT
ejpam-4060	81	1	let	let	AUX
ejpam-4060	81	2	(	(	PUNCT
ejpam-4060	81	3	x	x	NOUN
ejpam-4060	81	4	,	,	PUNCT
ejpam-4060	81	5	τ1	τ1	NOUN
ejpam-4060	81	6	,	,	PUNCT
ejpam-4060	81	7	τ2	τ2	PROPN
ejpam-4060	81	8	)	)	PUNCT
ejpam-4060	81	9	be	be	VERB
ejpam-4060	81	10	a	a	DET
ejpam-4060	81	11	bitopological	bitopological	ADJ
ejpam-4060	81	12	space	space	NOUN
ejpam-4060	81	13	such	such	ADJ
ejpam-4060	81	14	that	that	SCONJ
ejpam-4060	81	15	x	x	X
ejpam-4060	81	16	=	=	X
ejpam-4060	81	17	{	{	PUNCT
ejpam-4060	81	18	a	a	PRON
ejpam-4060	81	19	,	,	PUNCT
ejpam-4060	81	20	b	b	NOUN
ejpam-4060	81	21	,	,	PUNCT
ejpam-4060	81	22	c	c	NOUN
ejpam-4060	81	23	}	}	PUNCT
ejpam-4060	81	24	,	,	PUNCT
ejpam-4060	81	25	τ1	τ1	NOUN
ejpam-4060	81	26	=	=	SYM
ejpam-4060	81	27	{	{	PUNCT
ejpam-4060	81	28	∅	∅	NOUN
ejpam-4060	81	29	,	,	PUNCT
ejpam-4060	81	30	x	x	X
ejpam-4060	81	31	,	,	PUNCT
ejpam-4060	81	32	{	{	PUNCT
ejpam-4060	81	33	a	a	X
ejpam-4060	81	34	}	}	PUNCT
ejpam-4060	81	35	,	,	PUNCT
ejpam-4060	81	36	{	{	PUNCT
ejpam-4060	81	37	b	b	NOUN
ejpam-4060	81	38	}	}	PUNCT
ejpam-4060	81	39	,	,	PUNCT
ejpam-4060	81	40	{	{	PUNCT
ejpam-4060	81	41	a	a	DET
ejpam-4060	81	42	,	,	PUNCT
ejpam-4060	81	43	b	b	NOUN
ejpam-4060	81	44	}	}	PUNCT
ejpam-4060	81	45	}	}	PUNCT
ejpam-4060	81	46	,	,	PUNCT
ejpam-4060	81	47	and	and	CCONJ
ejpam-4060	81	48	τ2	τ2	NOUN
ejpam-4060	81	49	=	=	SYM
ejpam-4060	81	50	{	{	PUNCT
ejpam-4060	81	51	∅	∅	NOUN
ejpam-4060	81	52	,	,	PUNCT
ejpam-4060	81	53	x	x	X
ejpam-4060	81	54	,	,	PUNCT
ejpam-4060	81	55	{	{	PUNCT
ejpam-4060	81	56	a	a	X
ejpam-4060	81	57	}	}	PUNCT
ejpam-4060	81	58	,	,	PUNCT
ejpam-4060	81	59	{	{	PUNCT
ejpam-4060	81	60	a	a	DET
ejpam-4060	81	61	,	,	PUNCT
ejpam-4060	81	62	b	b	NOUN
ejpam-4060	81	63	}	}	PUNCT
ejpam-4060	81	64	,	,	PUNCT
ejpam-4060	81	65	{	{	PUNCT
ejpam-4060	81	66	a	a	PRON
ejpam-4060	81	67	,	,	PUNCT
ejpam-4060	81	68	c	c	NOUN
ejpam-4060	81	69	}	}	PUNCT
ejpam-4060	81	70	}	}	PUNCT
ejpam-4060	81	71	and	and	CCONJ
ejpam-4060	81	72	a	a	DET
ejpam-4060	81	73	=	=	X
ejpam-4060	81	74	{	{	PUNCT
ejpam-4060	81	75	b	b	NOUN
ejpam-4060	81	76	,	,	PUNCT
ejpam-4060	81	77	c	c	NOUN
ejpam-4060	81	78	}	}	PUNCT
ejpam-4060	81	79	.	.	PUNCT
ejpam-4060	82	1	note	note	VERB
ejpam-4060	82	2	that	that	SCONJ
ejpam-4060	82	3	x	x	PRON
ejpam-4060	82	4	is	be	AUX
ejpam-4060	82	5	the	the	DET
ejpam-4060	82	6	only	only	ADJ
ejpam-4060	82	7	(	(	PUNCT
ejpam-4060	82	8	1	1	NUM
ejpam-4060	82	9	,	,	PUNCT
ejpam-4060	82	10	2)-semi	2)-semi	NUM
ejpam-4060	82	11	open	open	ADJ
ejpam-4060	82	12	set	set	NOUN
ejpam-4060	82	13	containing	contain	VERB
ejpam-4060	82	14	a	a	PRON
ejpam-4060	82	15	=	=	SYM
ejpam-4060	82	16	{	{	PUNCT
ejpam-4060	82	17	b	b	NOUN
ejpam-4060	82	18	,	,	PUNCT
ejpam-4060	82	19	c	c	NOUN
ejpam-4060	82	20	}	}	PUNCT
ejpam-4060	82	21	.	.	PUNCT
ejpam-4060	83	1	since	since	SCONJ
ejpam-4060	83	2	a	a	PRON
ejpam-4060	83	3	=	=	SYM
ejpam-4060	83	4	{	{	PUNCT
ejpam-4060	83	5	b	b	NOUN
ejpam-4060	83	6	,	,	PUNCT
ejpam-4060	83	7	c	c	NOUN
ejpam-4060	83	8	}	}	PUNCT
ejpam-4060	83	9	is	be	AUX
ejpam-4060	83	10	a	a	DET
ejpam-4060	83	11	ψ	ψ	NOUN
ejpam-4060	83	12	closed	close	VERB
ejpam-4060	83	13	set	set	NOUN
ejpam-4060	83	14	,	,	PUNCT
ejpam-4060	83	15	it	it	PRON
ejpam-4060	83	16	follows	follow	VERB
ejpam-4060	83	17	that	that	SCONJ
ejpam-4060	83	18	(	(	PUNCT
ejpam-4060	83	19	i	i	NOUN
ejpam-4060	83	20	,	,	PUNCT
ejpam-4060	83	21	j)-ψcl({b	j)-ψcl({b	PROPN
ejpam-4060	83	22	,	,	PUNCT
ejpam-4060	83	23	c	c	NOUN
ejpam-4060	83	24	}	}	PUNCT
ejpam-4060	83	25	)	)	PUNCT
ejpam-4060	84	1	=	=	PRON
ejpam-4060	84	2	{	{	PUNCT
ejpam-4060	84	3	b	b	NOUN
ejpam-4060	84	4	,	,	PUNCT
ejpam-4060	84	5	c	c	NOUN
ejpam-4060	84	6	}	}	PUNCT
ejpam-4060	84	7	⊆	⊆	NUM
ejpam-4060	84	8	x.	x.	NOUN
ejpam-4060	84	9	thus	thus	ADV
ejpam-4060	84	10	a	a	X
ejpam-4060	84	11	=	=	SYM
ejpam-4060	84	12	{	{	PUNCT
ejpam-4060	84	13	b	b	NOUN
ejpam-4060	84	14	,	,	PUNCT
ejpam-4060	84	15	c	c	NOUN
ejpam-4060	84	16	}	}	PUNCT
ejpam-4060	84	17	is	be	AUX
ejpam-4060	84	18	a	a	DET
ejpam-4060	84	19	(	(	PUNCT
ejpam-4060	84	20	1	1	NUM
ejpam-4060	84	21	,	,	PUNCT
ejpam-4060	84	22	2)-ψ	2)-ψ	NUM
ejpam-4060	84	23	generalized	generalize	VERB
ejpam-4060	84	24	semi	semi	ADV
ejpam-4060	84	25	closed	closed	ADJ
ejpam-4060	84	26	set	set	NOUN
ejpam-4060	84	27	.	.	PUNCT
ejpam-4060	85	1	similarly	similarly	ADV
ejpam-4060	85	2	,	,	PUNCT
ejpam-4060	85	3	∅	∅	NOUN
ejpam-4060	85	4	,	,	PUNCT
ejpam-4060	85	5	{	{	PUNCT
ejpam-4060	85	6	b	b	NOUN
ejpam-4060	85	7	}	}	PUNCT
ejpam-4060	85	8	,	,	PUNCT
ejpam-4060	85	9	{	{	PUNCT
ejpam-4060	85	10	c	c	NOUN
ejpam-4060	85	11	}	}	PUNCT
ejpam-4060	85	12	and	and	CCONJ
ejpam-4060	85	13	x	x	X
ejpam-4060	85	14	are	be	AUX
ejpam-4060	85	15	(	(	PUNCT
ejpam-4060	85	16	1	1	NUM
ejpam-4060	85	17	,	,	PUNCT
ejpam-4060	85	18	2)-ψ	2)-ψ	NUM
ejpam-4060	85	19	generalized	generalize	VERB
ejpam-4060	85	20	semi	semi	ADJ
ejpam-4060	85	21	closed	closed	ADJ
ejpam-4060	85	22	sets	set	NOUN
ejpam-4060	85	23	.	.	PUNCT
ejpam-4060	86	1	throughout	throughout	ADP
ejpam-4060	86	2	this	this	DET
ejpam-4060	86	3	context	context	NOUN
ejpam-4060	86	4	,	,	PUNCT
ejpam-4060	86	5	the	the	DET
ejpam-4060	86	6	open	open	ADJ
ejpam-4060	86	7	(	(	PUNCT
ejpam-4060	86	8	resp	resp	NOUN
ejpam-4060	86	9	.	.	PROPN
ejpam-4060	86	10	,	,	PUNCT
ejpam-4060	86	11	closed	closed	ADJ
ejpam-4060	86	12	)	)	PUNCT
ejpam-4060	86	13	set	set	VERB
ejpam-4060	86	14	in	in	ADP
ejpam-4060	86	15	(	(	PUNCT
ejpam-4060	86	16	x	x	NOUN
ejpam-4060	86	17	,	,	PUNCT
ejpam-4060	86	18	τ1	τ1	NOUN
ejpam-4060	86	19	,	,	PUNCT
ejpam-4060	86	20	τ2	τ2	NOUN
ejpam-4060	86	21	)	)	PUNCT
ejpam-4060	86	22	is	be	AUX
ejpam-4060	86	23	denoted	denote	VERB
ejpam-4060	86	24	by	by	ADP
ejpam-4060	86	25	(	(	PUNCT
ejpam-4060	86	26	i	i	NOUN
ejpam-4060	86	27	,	,	PUNCT
ejpam-4060	86	28	j)open	j)open	PROPN
ejpam-4060	86	29	(	(	PUNCT
ejpam-4060	86	30	resp	resp	NOUN
ejpam-4060	86	31	.	.	PUNCT
ejpam-4060	87	1	,	,	PUNCT
ejpam-4060	87	2	(	(	PUNCT
ejpam-4060	87	3	i	i	NOUN
ejpam-4060	87	4	,	,	PUNCT
ejpam-4060	87	5	j)-closed	j)-closed	ADJ
ejpam-4060	87	6	)	)	PUNCT
ejpam-4060	87	7	set	set	NOUN
ejpam-4060	87	8	.	.	PUNCT
ejpam-4060	88	1	proposition	proposition	NOUN
ejpam-4060	88	2	1	1	NUM
ejpam-4060	88	3	.	.	PUNCT
ejpam-4060	89	1	every	every	DET
ejpam-4060	89	2	(	(	PUNCT
ejpam-4060	89	3	i	i	NOUN
ejpam-4060	89	4	,	,	PUNCT
ejpam-4060	89	5	j)-ψ	j)-ψ	PROPN
ejpam-4060	89	6	-	-	ADJ
ejpam-4060	89	7	closed	closed	ADJ
ejpam-4060	89	8	set	set	NOUN
ejpam-4060	89	9	is	be	AUX
ejpam-4060	89	10	(	(	PUNCT
ejpam-4060	89	11	i	i	PROPN
ejpam-4060	89	12	,	,	PUNCT
ejpam-4060	89	13	j)-ψgs	j)-ψgs	ADV
ejpam-4060	89	14	-	-	PUNCT
ejpam-4060	89	15	closed	closed	ADJ
ejpam-4060	89	16	.	.	PUNCT
ejpam-4060	90	1	proof	proof	NOUN
ejpam-4060	90	2	.	.	PUNCT
ejpam-4060	91	1	let	let	VERB
ejpam-4060	91	2	a	a	DET
ejpam-4060	91	3	be	be	AUX
ejpam-4060	91	4	(	(	PUNCT
ejpam-4060	91	5	i	i	NOUN
ejpam-4060	91	6	,	,	PUNCT
ejpam-4060	91	7	j)-ψ	j)-ψ	PROPN
ejpam-4060	91	8	-	-	ADJ
ejpam-4060	91	9	closed	closed	ADJ
ejpam-4060	91	10	set	set	NOUN
ejpam-4060	91	11	and	and	CCONJ
ejpam-4060	91	12	u	u	PRON
ejpam-4060	91	13	be	be	AUX
ejpam-4060	91	14	(	(	PUNCT
ejpam-4060	91	15	i	i	NOUN
ejpam-4060	91	16	,	,	PUNCT
ejpam-4060	91	17	j)-semi	j)-semi	NOUN
ejpam-4060	91	18	-	-	PUNCT
ejpam-4060	91	19	open	open	ADJ
ejpam-4060	91	20	in	in	ADP
ejpam-4060	91	21	(	(	PUNCT
ejpam-4060	91	22	x	x	NOUN
ejpam-4060	91	23	,	,	PUNCT
ejpam-4060	91	24	τ1	τ1	NOUN
ejpam-4060	91	25	,	,	PUNCT
ejpam-4060	91	26	τ2	τ2	NOUN
ejpam-4060	91	27	)	)	PUNCT
ejpam-4060	91	28	such	such	ADJ
ejpam-4060	91	29	that	that	SCONJ
ejpam-4060	91	30	a	a	DET
ejpam-4060	91	31	⊆	⊆	NUM
ejpam-4060	91	32	u	u	NOUN
ejpam-4060	91	33	.	.	PUNCT
ejpam-4060	92	1	then	then	ADV
ejpam-4060	92	2	(	(	PUNCT
ejpam-4060	92	3	i	i	NOUN
ejpam-4060	92	4	,	,	PUNCT
ejpam-4060	92	5	j)-ψcl(a	j)-ψcl(a	PROPN
ejpam-4060	92	6	)	)	PUNCT
ejpam-4060	92	7	=	=	PUNCT
ejpam-4060	92	8	a	a	DET
ejpam-4060	92	9	⊆	⊆	NUM
ejpam-4060	92	10	u	u	NOUN
ejpam-4060	92	11	.	.	PUNCT
ejpam-4060	93	1	hence	hence	ADV
ejpam-4060	93	2	a	a	PRON
ejpam-4060	93	3	is	be	AUX
ejpam-4060	93	4	(	(	PUNCT
ejpam-4060	93	5	i	i	NOUN
ejpam-4060	93	6	,	,	PUNCT
ejpam-4060	93	7	j)-ψgs	j)-ψgs	ADV
ejpam-4060	93	8	-	-	PUNCT
ejpam-4060	93	9	closed	closed	ADJ
ejpam-4060	93	10	in	in	ADP
ejpam-4060	93	11	(	(	PUNCT
ejpam-4060	93	12	x	x	NOUN
ejpam-4060	93	13	,	,	PUNCT
ejpam-4060	93	14	τ1	τ1	NOUN
ejpam-4060	93	15	,	,	PUNCT
ejpam-4060	93	16	τ2	τ2	NOUN
ejpam-4060	93	17	)	)	PUNCT
ejpam-4060	93	18	.	.	PUNCT
ejpam-4060	94	1	theorem	theorem	NOUN
ejpam-4060	94	2	2	2	NUM
ejpam-4060	94	3	.	.	PUNCT
ejpam-4060	95	1	every	every	DET
ejpam-4060	95	2	ψgs	ψgs	ADV
ejpam-4060	95	3	-	-	PUNCT
ejpam-4060	95	4	closed	close	VERB
ejpam-4060	95	5	set	set	NOUN
ejpam-4060	95	6	in	in	ADP
ejpam-4060	95	7	(	(	PUNCT
ejpam-4060	95	8	x	x	NOUN
ejpam-4060	95	9	,	,	PUNCT
ejpam-4060	95	10	τi	τi	PROPN
ejpam-4060	95	11	)	)	PUNCT
ejpam-4060	95	12	is	be	AUX
ejpam-4060	95	13	ψgs	ψgs	ADV
ejpam-4060	95	14	-	-	PUNCT
ejpam-4060	95	15	closed	close	VERB
ejpam-4060	95	16	set	set	NOUN
ejpam-4060	95	17	in	in	ADP
ejpam-4060	95	18	(	(	PUNCT
ejpam-4060	95	19	x	x	NOUN
ejpam-4060	95	20	,	,	PUNCT
ejpam-4060	95	21	τ1	τ1	NOUN
ejpam-4060	95	22	,	,	PUNCT
ejpam-4060	95	23	τ2	τ2	NOUN
ejpam-4060	95	24	)	)	PUNCT
ejpam-4060	95	25	.	.	PUNCT
ejpam-4060	96	1	proof	proof	NOUN
ejpam-4060	96	2	.	.	PUNCT
ejpam-4060	97	1	let	let	VERB
ejpam-4060	97	2	a	a	DET
ejpam-4060	97	3	be	be	AUX
ejpam-4060	97	4	ψgs	ψgs	ADV
ejpam-4060	97	5	-	-	PUNCT
ejpam-4060	97	6	closed	close	VERB
ejpam-4060	97	7	set	set	NOUN
ejpam-4060	97	8	in	in	ADP
ejpam-4060	97	9	(	(	PUNCT
ejpam-4060	97	10	x	x	NOUN
ejpam-4060	97	11	,	,	PUNCT
ejpam-4060	97	12	τi	τi	PROPN
ejpam-4060	97	13	)	)	PUNCT
ejpam-4060	97	14	.	.	PUNCT
ejpam-4060	98	1	then	then	ADV
ejpam-4060	98	2	ψcl(a	ψcl(a	PROPN
ejpam-4060	98	3	)	)	PUNCT
ejpam-4060	98	4	⊆	⊆	NUM
ejpam-4060	98	5	u	u	NOUN
ejpam-4060	98	6	where	where	SCONJ
ejpam-4060	98	7	u	u	NOUN
ejpam-4060	98	8	is	be	AUX
ejpam-4060	98	9	semi	semi	ADJ
ejpam-4060	98	10	-	-	ADJ
ejpam-4060	98	11	open	open	ADJ
ejpam-4060	98	12	in	in	ADP
ejpam-4060	98	13	τi	τi	ADP
ejpam-4060	98	14	such	such	ADJ
ejpam-4060	98	15	that	that	SCONJ
ejpam-4060	98	16	a	a	DET
ejpam-4060	98	17	⊆	⊆	NUM
ejpam-4060	98	18	u	u	NOUN
ejpam-4060	98	19	.	.	PUNCT
ejpam-4060	99	1	since	since	SCONJ
ejpam-4060	99	2	,	,	PUNCT
ejpam-4060	99	3	for	for	ADP
ejpam-4060	99	4	each	each	DET
ejpam-4060	99	5	i	i	PRON
ejpam-4060	99	6	∈	∈	PROPN
ejpam-4060	99	7	{	{	PUNCT
ejpam-4060	99	8	1	1	NUM
ejpam-4060	99	9	,	,	PUNCT
ejpam-4060	99	10	2	2	NUM
ejpam-4060	99	11	}	}	PUNCT
ejpam-4060	99	12	,	,	PUNCT
ejpam-4060	99	13	every	every	DET
ejpam-4060	99	14	semi	semi	ADJ
ejpam-4060	99	15	-	-	ADJ
ejpam-4060	99	16	open	open	ADJ
ejpam-4060	99	17	in	in	ADP
ejpam-4060	99	18	(	(	PUNCT
ejpam-4060	99	19	x	x	NOUN
ejpam-4060	99	20	,	,	PUNCT
ejpam-4060	99	21	τi	τi	PROPN
ejpam-4060	99	22	)	)	PUNCT
ejpam-4060	99	23	is	be	AUX
ejpam-4060	99	24	semi	semi	ADJ
ejpam-4060	99	25	-	-	ADJ
ejpam-4060	99	26	open	open	ADJ
ejpam-4060	99	27	in	in	ADP
ejpam-4060	99	28	(	(	PUNCT
ejpam-4060	99	29	x	x	NOUN
ejpam-4060	99	30	,	,	PUNCT
ejpam-4060	99	31	τ1	τ1	NOUN
ejpam-4060	99	32	,	,	PUNCT
ejpam-4060	99	33	τ2	τ2	PROPN
ejpam-4060	99	34	)	)	PUNCT
ejpam-4060	99	35	by	by	ADP
ejpam-4060	99	36	lemma	lemma	PROPN
ejpam-4060	99	37	1	1	NUM
ejpam-4060	99	38	,	,	PUNCT
ejpam-4060	99	39	it	it	PRON
ejpam-4060	99	40	follows	follow	VERB
ejpam-4060	99	41	that	that	SCONJ
ejpam-4060	99	42	u	u	NOUN
ejpam-4060	99	43	is	be	AUX
ejpam-4060	99	44	semi	semi	ADJ
ejpam-4060	99	45	-	-	ADJ
ejpam-4060	99	46	open	open	ADJ
ejpam-4060	99	47	in	in	ADP
ejpam-4060	99	48	(	(	PUNCT
ejpam-4060	99	49	x	x	NOUN
ejpam-4060	99	50	,	,	PUNCT
ejpam-4060	99	51	τ1	τ1	NOUN
ejpam-4060	99	52	,	,	PUNCT
ejpam-4060	99	53	τ2	τ2	NOUN
ejpam-4060	99	54	)	)	PUNCT
ejpam-4060	99	55	.	.	PUNCT
ejpam-4060	100	1	moreover	moreover	ADV
ejpam-4060	100	2	,	,	PUNCT
ejpam-4060	100	3	by	by	ADP
ejpam-4060	100	4	lemma	lemma	PROPN
ejpam-4060	100	5	1	1	NUM
ejpam-4060	100	6	,	,	PUNCT
ejpam-4060	100	7	every	every	DET
ejpam-4060	100	8	ψ	ψ	NOUN
ejpam-4060	100	9	-	-	PUNCT
ejpam-4060	100	10	closed	closed	ADJ
ejpam-4060	100	11	in	in	ADP
ejpam-4060	100	12	τi	τi	ADV
ejpam-4060	100	13	is	be	AUX
ejpam-4060	100	14	ψ	ψ	NOUN
ejpam-4060	100	15	-	-	VERB
ejpam-4060	100	16	closed	closed	ADJ
ejpam-4060	100	17	in	in	ADP
ejpam-4060	100	18	(	(	PUNCT
ejpam-4060	100	19	x	x	NOUN
ejpam-4060	100	20	,	,	PUNCT
ejpam-4060	100	21	τ1	τ1	NOUN
ejpam-4060	100	22	,	,	PUNCT
ejpam-4060	100	23	τ2	τ2	NOUN
ejpam-4060	100	24	)	)	PUNCT
ejpam-4060	100	25	.	.	PUNCT
ejpam-4060	101	1	thus	thus	ADV
ejpam-4060	101	2	(	(	PUNCT
ejpam-4060	101	3	i	i	PRON
ejpam-4060	101	4	,	,	PUNCT
ejpam-4060	101	5	j)-ψcl(a	j)-ψcl(a	PROPN
ejpam-4060	101	6	)	)	PUNCT
ejpam-4060	101	7	⊆	⊆	NUM
ejpam-4060	101	8	ψcl(a	ψcl(a	X
ejpam-4060	101	9	)	)	PUNCT
ejpam-4060	101	10	⊆	⊆	NUM
ejpam-4060	101	11	u	u	NOUN
ejpam-4060	101	12	.	.	PUNCT
ejpam-4060	102	1	hence	hence	ADV
ejpam-4060	102	2	a	a	PRON
ejpam-4060	102	3	is	be	AUX
ejpam-4060	102	4	a	a	DET
ejpam-4060	102	5	ψgs	ψgs	ADV
ejpam-4060	102	6	-	-	PUNCT
ejpam-4060	102	7	closed	close	VERB
ejpam-4060	102	8	set	set	NOUN
ejpam-4060	102	9	in	in	ADP
ejpam-4060	102	10	(	(	PUNCT
ejpam-4060	102	11	x	x	NOUN
ejpam-4060	102	12	,	,	PUNCT
ejpam-4060	102	13	τ1	τ1	NOUN
ejpam-4060	102	14	,	,	PUNCT
ejpam-4060	102	15	τ2	τ2	NOUN
ejpam-4060	102	16	)	)	PUNCT
ejpam-4060	102	17	.	.	PUNCT
ejpam-4060	103	1	the	the	DET
ejpam-4060	103	2	following	follow	VERB
ejpam-4060	103	3	corollary	corollary	NOUN
ejpam-4060	103	4	follows	follow	VERB
ejpam-4060	103	5	from	from	ADP
ejpam-4060	103	6	theorem	theorem	ADJ
ejpam-4060	103	7	1	1	NUM
ejpam-4060	103	8	and	and	CCONJ
ejpam-4060	103	9	theorem	theorem	VERB
ejpam-4060	103	10	2	2	NUM
ejpam-4060	103	11	.	.	PUNCT
ejpam-4060	103	12	corollary	corollary	ADJ
ejpam-4060	103	13	1	1	NUM
ejpam-4060	103	14	.	.	PUNCT
ejpam-4060	104	1	let	let	AUX
ejpam-4060	104	2	(	(	PUNCT
ejpam-4060	104	3	x	x	NOUN
ejpam-4060	104	4	,	,	PUNCT
ejpam-4060	104	5	τi	τi	PROPN
ejpam-4060	104	6	)	)	PUNCT
ejpam-4060	104	7	be	be	AUX
ejpam-4060	104	8	a	a	DET
ejpam-4060	104	9	topological	topological	ADJ
ejpam-4060	104	10	space	space	NOUN
ejpam-4060	104	11	and	and	CCONJ
ejpam-4060	104	12	(	(	PUNCT
ejpam-4060	104	13	x	x	NOUN
ejpam-4060	104	14	,	,	PUNCT
ejpam-4060	104	15	τ1	τ1	NOUN
ejpam-4060	104	16	,	,	PUNCT
ejpam-4060	104	17	τ2	τ2	NOUN
ejpam-4060	104	18	)	)	PUNCT
ejpam-4060	104	19	be	be	AUX
ejpam-4060	104	20	bitopological	bitopological	ADJ
ejpam-4060	104	21	space	space	NOUN
ejpam-4060	104	22	.	.	PUNCT
ejpam-4060	105	1	then	then	ADV
ejpam-4060	105	2	the	the	DET
ejpam-4060	105	3	following	follow	VERB
ejpam-4060	105	4	statements	statement	NOUN
ejpam-4060	105	5	hold	hold	VERB
ejpam-4060	105	6	.	.	PUNCT
ejpam-4060	106	1	(	(	PUNCT
ejpam-4060	106	2	i	i	NOUN
ejpam-4060	106	3	)	)	PUNCT
ejpam-4060	106	4	every	every	DET
ejpam-4060	106	5	τi	τi	NOUN
ejpam-4060	106	6	closed	close	VERB
ejpam-4060	106	7	set	set	VERB
ejpam-4060	106	8	is	be	AUX
ejpam-4060	106	9	(	(	PUNCT
ejpam-4060	106	10	i	i	PROPN
ejpam-4060	106	11	,	,	PUNCT
ejpam-4060	106	12	j)-ψgs	j)-ψgs	ADV
ejpam-4060	106	13	-	-	PUNCT
ejpam-4060	106	14	closed	closed	ADJ
ejpam-4060	106	15	set	set	NOUN
ejpam-4060	106	16	.	.	PUNCT
ejpam-4060	107	1	(	(	PUNCT
ejpam-4060	107	2	ii	ii	NOUN
ejpam-4060	107	3	)	)	PUNCT
ejpam-4060	107	4	every	every	DET
ejpam-4060	107	5	regular	regular	ADJ
ejpam-4060	107	6	-	-	PUNCT
ejpam-4060	107	7	closed	close	VERB
ejpam-4060	107	8	set	set	NOUN
ejpam-4060	107	9	in	in	ADP
ejpam-4060	107	10	(	(	PUNCT
ejpam-4060	107	11	x	x	NOUN
ejpam-4060	107	12	,	,	PUNCT
ejpam-4060	107	13	τi	τi	PROPN
ejpam-4060	107	14	)	)	PUNCT
ejpam-4060	107	15	is	be	AUX
ejpam-4060	107	16	(	(	PUNCT
ejpam-4060	107	17	i	i	INTJ
ejpam-4060	107	18	,	,	PUNCT
ejpam-4060	107	19	j)-ψgs	j)-ψgs	ADV
ejpam-4060	107	20	-	-	PUNCT
ejpam-4060	107	21	closed	closed	ADJ
ejpam-4060	107	22	.	.	PUNCT
ejpam-4060	108	1	(	(	PUNCT
ejpam-4060	108	2	iii	iii	NOUN
ejpam-4060	108	3	)	)	PUNCT
ejpam-4060	108	4	every	every	DET
ejpam-4060	108	5	semi	semi	ADJ
ejpam-4060	108	6	-	-	ADJ
ejpam-4060	108	7	closed	closed	ADJ
ejpam-4060	108	8	set	set	NOUN
ejpam-4060	108	9	in	in	ADP
ejpam-4060	108	10	(	(	PUNCT
ejpam-4060	108	11	x	x	NOUN
ejpam-4060	108	12	,	,	PUNCT
ejpam-4060	108	13	τi	τi	PROPN
ejpam-4060	108	14	)	)	PUNCT
ejpam-4060	108	15	is	be	AUX
ejpam-4060	108	16	(	(	PUNCT
ejpam-4060	108	17	i	i	INTJ
ejpam-4060	108	18	,	,	PUNCT
ejpam-4060	108	19	j)-ψgs	j)-ψgs	ADV
ejpam-4060	108	20	-	-	PUNCT
ejpam-4060	108	21	closed	closed	ADJ
ejpam-4060	108	22	.	.	PUNCT
ejpam-4060	109	1	(	(	PUNCT
ejpam-4060	109	2	iv	iv	X
ejpam-4060	109	3	)	)	PUNCT
ejpam-4060	109	4	every	every	DET
ejpam-4060	109	5	α	α	X
ejpam-4060	109	6	-	-	ADJ
ejpam-4060	109	7	closed	closed	ADJ
ejpam-4060	109	8	set	set	NOUN
ejpam-4060	109	9	in	in	ADP
ejpam-4060	109	10	(	(	PUNCT
ejpam-4060	109	11	x	x	NOUN
ejpam-4060	109	12	,	,	PUNCT
ejpam-4060	109	13	τi	τi	PROPN
ejpam-4060	109	14	)	)	PUNCT
ejpam-4060	109	15	is	be	AUX
ejpam-4060	109	16	(	(	PUNCT
ejpam-4060	109	17	i	i	INTJ
ejpam-4060	109	18	,	,	PUNCT
ejpam-4060	109	19	j)-ψgs	j)-ψgs	ADV
ejpam-4060	109	20	-	-	PUNCT
ejpam-4060	109	21	closed	closed	ADJ
ejpam-4060	109	22	.	.	PUNCT
ejpam-4060	110	1	(	(	PUNCT
ejpam-4060	110	2	v	v	NOUN
ejpam-4060	110	3	)	)	PUNCT
ejpam-4060	110	4	every	every	DET
ejpam-4060	110	5	ψ	ψ	ADJ
ejpam-4060	110	6	-	-	ADJ
ejpam-4060	110	7	closed	closed	ADJ
ejpam-4060	110	8	set	set	NOUN
ejpam-4060	110	9	in	in	ADP
ejpam-4060	110	10	(	(	PUNCT
ejpam-4060	110	11	x	x	NOUN
ejpam-4060	110	12	,	,	PUNCT
ejpam-4060	110	13	τi	τi	PROPN
ejpam-4060	110	14	)	)	PUNCT
ejpam-4060	110	15	is	be	AUX
ejpam-4060	110	16	(	(	PUNCT
ejpam-4060	110	17	i	i	INTJ
ejpam-4060	110	18	,	,	PUNCT
ejpam-4060	110	19	j)-ψgs	j)-ψgs	ADV
ejpam-4060	110	20	-	-	PUNCT
ejpam-4060	110	21	closed	closed	ADJ
ejpam-4060	110	22	.	.	PUNCT
ejpam-4060	111	1	(	(	PUNCT
ejpam-4060	111	2	vi	vi	NOUN
ejpam-4060	111	3	)	)	PUNCT
ejpam-4060	111	4	every	every	DET
ejpam-4060	111	5	αgs	αgs	NOUN
ejpam-4060	111	6	-	-	PUNCT
ejpam-4060	111	7	closed	closed	ADJ
ejpam-4060	111	8	set	set	NOUN
ejpam-4060	111	9	in	in	ADP
ejpam-4060	111	10	(	(	PUNCT
ejpam-4060	111	11	x	x	NOUN
ejpam-4060	111	12	,	,	PUNCT
ejpam-4060	111	13	τi	τi	PROPN
ejpam-4060	111	14	)	)	PUNCT
ejpam-4060	111	15	is	be	AUX
ejpam-4060	111	16	(	(	PUNCT
ejpam-4060	111	17	i	i	INTJ
ejpam-4060	111	18	,	,	PUNCT
ejpam-4060	111	19	j)-ψgs	j)-ψgs	ADV
ejpam-4060	111	20	-	-	PUNCT
ejpam-4060	111	21	closed	closed	ADJ
ejpam-4060	111	22	.	.	PUNCT
ejpam-4060	112	1	l.m.tutanes	l.m.tutane	NOUN
ejpam-4060	112	2	/	/	SYM
ejpam-4060	112	3	eur	eur	PROPN
ejpam-4060	112	4	.	.	PUNCT
ejpam-4060	113	1	j.	j.	PROPN
ejpam-4060	113	2	pure	pure	PROPN
ejpam-4060	113	3	appl	appl	PROPN
ejpam-4060	113	4	.	.	PROPN
ejpam-4060	113	5	math	math	PROPN
ejpam-4060	113	6	,	,	PUNCT
ejpam-4060	113	7	14	14	NUM
ejpam-4060	113	8	(	(	PUNCT
ejpam-4060	113	9	4	4	NUM
ejpam-4060	113	10	)	)	PUNCT
ejpam-4060	113	11	(	(	PUNCT
ejpam-4060	113	12	2021	2021	NUM
ejpam-4060	113	13	)	)	PUNCT
ejpam-4060	113	14	,	,	PUNCT
ejpam-4060	113	15	1275	1275	NUM
ejpam-4060	113	16	-	-	SYM
ejpam-4060	113	17	1282	1282	NUM
ejpam-4060	113	18	1279	1279	NUM
ejpam-4060	113	19	theorem	theorem	NOUN
ejpam-4060	113	20	3	3	X
ejpam-4060	113	21	.	.	PUNCT
ejpam-4060	113	22	let	let	VERB
ejpam-4060	113	23	a	a	DET
ejpam-4060	113	24	be	be	AUX
ejpam-4060	113	25	a	a	DET
ejpam-4060	113	26	(	(	PUNCT
ejpam-4060	113	27	i	i	NOUN
ejpam-4060	113	28	,	,	PUNCT
ejpam-4060	113	29	j)-ψ	j)-ψ	PROPN
ejpam-4060	113	30	-	-	ADJ
ejpam-4060	113	31	closed	closed	ADJ
ejpam-4060	113	32	set	set	NOUN
ejpam-4060	113	33	and	and	CCONJ
ejpam-4060	113	34	a	a	DET
ejpam-4060	113	35	⊆	⊆	NUM
ejpam-4060	113	36	b	b	SYM
ejpam-4060	113	37	⊆	⊆	NUM
ejpam-4060	113	38	(	(	PUNCT
ejpam-4060	113	39	i	i	PROPN
ejpam-4060	113	40	,	,	PUNCT
ejpam-4060	113	41	j)-ψcl(a	j)-ψcl(a	PROPN
ejpam-4060	113	42	)	)	PUNCT
ejpam-4060	113	43	.	.	PUNCT
ejpam-4060	114	1	then	then	ADV
ejpam-4060	114	2	b	b	PROPN
ejpam-4060	114	3	is	be	AUX
ejpam-4060	114	4	also	also	ADV
ejpam-4060	114	5	a	a	DET
ejpam-4060	114	6	(	(	PUNCT
ejpam-4060	114	7	i	i	NOUN
ejpam-4060	114	8	,	,	PUNCT
ejpam-4060	114	9	j)-ψgs	j)-ψgs	ADV
ejpam-4060	114	10	-	-	PUNCT
ejpam-4060	114	11	closed	closed	ADJ
ejpam-4060	114	12	set	set	NOUN
ejpam-4060	114	13	.	.	PUNCT
ejpam-4060	115	1	proof	proof	NOUN
ejpam-4060	115	2	.	.	PUNCT
ejpam-4060	116	1	let	let	VERB
ejpam-4060	116	2	a	a	DET
ejpam-4060	116	3	be	be	AUX
ejpam-4060	116	4	a	a	DET
ejpam-4060	116	5	(	(	PUNCT
ejpam-4060	116	6	i	i	NOUN
ejpam-4060	116	7	,	,	PUNCT
ejpam-4060	116	8	j)-ψ	j)-ψ	PROPN
ejpam-4060	116	9	-	-	ADJ
ejpam-4060	116	10	closed	closed	ADJ
ejpam-4060	116	11	set	set	NOUN
ejpam-4060	116	12	and	and	CCONJ
ejpam-4060	116	13	a	a	DET
ejpam-4060	116	14	⊆	⊆	NUM
ejpam-4060	116	15	(	(	PUNCT
ejpam-4060	116	16	i	i	PROPN
ejpam-4060	116	17	,	,	PUNCT
ejpam-4060	116	18	j)-ψcl(a	j)-ψcl(a	PROPN
ejpam-4060	116	19	)	)	PUNCT
ejpam-4060	116	20	.	.	PUNCT
ejpam-4060	117	1	suppose	suppose	VERB
ejpam-4060	117	2	u	u	PRON
ejpam-4060	117	3	is	be	AUX
ejpam-4060	117	4	(	(	PUNCT
ejpam-4060	117	5	i	i	PROPN
ejpam-4060	117	6	,	,	PUNCT
ejpam-4060	117	7	j)-semiopen	j)-semiopen	VERB
ejpam-4060	117	8	such	such	ADJ
ejpam-4060	117	9	that	that	SCONJ
ejpam-4060	117	10	b	b	PROPN
ejpam-4060	117	11	⊆	⊆	NUM
ejpam-4060	117	12	u	u	NOUN
ejpam-4060	117	13	.	.	PUNCT
ejpam-4060	118	1	we	we	PRON
ejpam-4060	118	2	want	want	VERB
ejpam-4060	118	3	to	to	PART
ejpam-4060	118	4	show	show	VERB
ejpam-4060	118	5	(	(	PUNCT
ejpam-4060	118	6	i	i	PROPN
ejpam-4060	118	7	,	,	PUNCT
ejpam-4060	118	8	j)-ψcl(b	j)-ψcl(b	PROPN
ejpam-4060	118	9	)	)	PUNCT
ejpam-4060	118	10	⊆	⊆	NUM
ejpam-4060	118	11	u	u	NOUN
ejpam-4060	118	12	.	.	PUNCT
ejpam-4060	119	1	since	since	SCONJ
ejpam-4060	119	2	a	a	DET
ejpam-4060	119	3	⊆	⊆	NUM
ejpam-4060	119	4	b	b	NOUN
ejpam-4060	119	5	and	and	CCONJ
ejpam-4060	119	6	b	b	NOUN
ejpam-4060	119	7	⊆	⊆	NUM
ejpam-4060	119	8	u	u	NOUN
ejpam-4060	119	9	,	,	PUNCT
ejpam-4060	119	10	it	it	PRON
ejpam-4060	119	11	follows	follow	VERB
ejpam-4060	119	12	that	that	SCONJ
ejpam-4060	119	13	a	a	DET
ejpam-4060	119	14	⊆	⊆	NUM
ejpam-4060	119	15	u	u	NOUN
ejpam-4060	119	16	.	.	PUNCT
ejpam-4060	120	1	also	also	ADV
ejpam-4060	120	2	,	,	PUNCT
ejpam-4060	120	3	by	by	ADP
ejpam-4060	120	4	proposition	proposition	NOUN
ejpam-4060	120	5	1	1	NUM
ejpam-4060	120	6	,	,	PUNCT
ejpam-4060	120	7	a	a	PRON
ejpam-4060	120	8	is	be	AUX
ejpam-4060	120	9	a	a	DET
ejpam-4060	120	10	(	(	PUNCT
ejpam-4060	120	11	i	i	NOUN
ejpam-4060	120	12	,	,	PUNCT
ejpam-4060	120	13	j)-ψgs	j)-ψgs	ADV
ejpam-4060	120	14	-	-	PUNCT
ejpam-4060	120	15	closed	closed	ADJ
ejpam-4060	120	16	set	set	NOUN
ejpam-4060	120	17	since	since	SCONJ
ejpam-4060	120	18	a	a	PRON
ejpam-4060	120	19	is	be	AUX
ejpam-4060	120	20	a	a	DET
ejpam-4060	120	21	(	(	PUNCT
ejpam-4060	120	22	i	i	NOUN
ejpam-4060	120	23	,	,	PUNCT
ejpam-4060	120	24	j)-ψ	j)-ψ	PROPN
ejpam-4060	120	25	-	-	ADJ
ejpam-4060	120	26	closed	closed	ADJ
ejpam-4060	120	27	set	set	NOUN
ejpam-4060	120	28	;	;	PUNCT
ejpam-4060	120	29	and	and	CCONJ
ejpam-4060	120	30	so	so	ADV
ejpam-4060	120	31	(	(	PUNCT
ejpam-4060	120	32	i	i	NOUN
ejpam-4060	120	33	,	,	PUNCT
ejpam-4060	120	34	j)-ψcl(a	j)-ψcl(a	PROPN
ejpam-4060	120	35	)	)	PUNCT
ejpam-4060	120	36	⊆	⊆	NUM
ejpam-4060	120	37	u	u	NOUN
ejpam-4060	120	38	.	.	PUNCT
ejpam-4060	121	1	note	note	VERB
ejpam-4060	121	2	that	that	SCONJ
ejpam-4060	121	3	b	b	X
ejpam-4060	121	4	⊆	⊆	NUM
ejpam-4060	121	5	(	(	PUNCT
ejpam-4060	121	6	i	i	PROPN
ejpam-4060	121	7	,	,	PUNCT
ejpam-4060	121	8	j)-ψcl(a	j)-ψcl(a	PROPN
ejpam-4060	121	9	)	)	PUNCT
ejpam-4060	121	10	implies	imply	VERB
ejpam-4060	121	11	(	(	PUNCT
ejpam-4060	121	12	i	i	PRON
ejpam-4060	121	13	,	,	PUNCT
ejpam-4060	121	14	j)-ψcl(b	j)-ψcl(b	PROPN
ejpam-4060	121	15	)	)	PUNCT
ejpam-4060	121	16	⊆	⊆	NUM
ejpam-4060	121	17	(	(	PUNCT
ejpam-4060	121	18	i	i	NOUN
ejpam-4060	121	19	,	,	PUNCT
ejpam-4060	121	20	j)-ψcl((i	j)-ψcl((i	NOUN
ejpam-4060	121	21	,	,	PUNCT
ejpam-4060	121	22	j)-ψcl(a	j)-ψcl(a	PROPN
ejpam-4060	121	23	)	)	PUNCT
ejpam-4060	121	24	)	)	PUNCT
ejpam-4060	122	1	=	=	PUNCT
ejpam-4060	122	2	(	(	PUNCT
ejpam-4060	122	3	i	i	NOUN
ejpam-4060	122	4	,	,	PUNCT
ejpam-4060	122	5	j)-ψcl(a	j)-ψcl(a	PROPN
ejpam-4060	122	6	)	)	PUNCT
ejpam-4060	122	7	⊆	⊆	NUM
ejpam-4060	122	8	u.	u.	NOUN
ejpam-4060	122	9	theorem	theorem	NOUN
ejpam-4060	122	10	4	4	X
ejpam-4060	122	11	.	.	PUNCT
ejpam-4060	123	1	let	let	VERB
ejpam-4060	123	2	{	{	PUNCT
ejpam-4060	123	3	ak|ak	ak|ak	X
ejpam-4060	123	4	is	be	AUX
ejpam-4060	123	5	(	(	PUNCT
ejpam-4060	123	6	i	i	PROPN
ejpam-4060	123	7	,	,	PUNCT
ejpam-4060	123	8	j)-ψgs	j)-ψgs	ADV
ejpam-4060	123	9	-	-	PUNCT
ejpam-4060	123	10	closed	closed	ADJ
ejpam-4060	123	11	set	set	NOUN
ejpam-4060	123	12	,	,	PUNCT
ejpam-4060	123	13	k	k	PROPN
ejpam-4060	123	14	∈	∈	PROPN
ejpam-4060	123	15	n	n	CCONJ
ejpam-4060	123	16	}	}	PUNCT
ejpam-4060	123	17	.	.	PUNCT
ejpam-4060	124	1	then	then	ADV
ejpam-4060	124	2	⋂∞	⋂∞	NOUN
ejpam-4060	124	3	k=1ak	k=1ak	X
ejpam-4060	124	4	is	be	AUX
ejpam-4060	124	5	(	(	PUNCT
ejpam-4060	124	6	i	i	PROPN
ejpam-4060	124	7	,	,	PUNCT
ejpam-4060	124	8	j)-ψgsclosed	j)-ψgsclose	VERB
ejpam-4060	124	9	set	set	NOUN
ejpam-4060	124	10	.	.	PUNCT
ejpam-4060	125	1	proof	proof	NOUN
ejpam-4060	125	2	.	.	PUNCT
ejpam-4060	126	1	suppose	suppose	VERB
ejpam-4060	126	2	u	u	PRON
ejpam-4060	126	3	=	=	SYM
ejpam-4060	126	4	⋂∞	⋂∞	NOUN
ejpam-4060	126	5	k=1	k=1	PUNCT
ejpam-4060	126	6	uk	uk	PROPN
ejpam-4060	126	7	is	be	AUX
ejpam-4060	126	8	(	(	PUNCT
ejpam-4060	126	9	i	i	PROPN
ejpam-4060	126	10	,	,	PUNCT
ejpam-4060	126	11	j)-semi	j)-semi	NOUN
ejpam-4060	126	12	-	-	PUNCT
ejpam-4060	126	13	open	open	ADJ
ejpam-4060	126	14	such	such	ADJ
ejpam-4060	126	15	that	that	DET
ejpam-4060	126	16	⋂∞	⋂∞	NOUN
ejpam-4060	126	17	k=1ak	k=1ak	VERB
ejpam-4060	126	18	⊆	⊆	NUM
ejpam-4060	126	19	u	u	NOUN
ejpam-4060	126	20	.	.	PUNCT
ejpam-4060	127	1	we	we	PRON
ejpam-4060	127	2	want	want	VERB
ejpam-4060	127	3	to	to	PART
ejpam-4060	127	4	show	show	VERB
ejpam-4060	127	5	that	that	SCONJ
ejpam-4060	127	6	(	(	PUNCT
ejpam-4060	127	7	i	i	PRON
ejpam-4060	127	8	,	,	PUNCT
ejpam-4060	127	9	j)-ψcl	j)-ψcl	PROPN
ejpam-4060	127	10	(	(	PUNCT
ejpam-4060	127	11	⋂∞	⋂∞	NUM
ejpam-4060	127	12	k=1ak	k=1ak	NUM
ejpam-4060	127	13	)	)	PUNCT
ejpam-4060	127	14	⊆	⊆	NUM
ejpam-4060	127	15	u	u	NOUN
ejpam-4060	127	16	.	.	PUNCT
ejpam-4060	128	1	from	from	ADP
ejpam-4060	128	2	our	our	PRON
ejpam-4060	128	3	assumption	assumption	NOUN
ejpam-4060	128	4	,	,	PUNCT
ejpam-4060	128	5	ak	ak	PROPN
ejpam-4060	128	6	is	be	AUX
ejpam-4060	128	7	(	(	PUNCT
ejpam-4060	128	8	i	i	PROPN
ejpam-4060	128	9	,	,	PUNCT
ejpam-4060	128	10	j)-ψgs	j)-ψgs	ADV
ejpam-4060	128	11	-	-	PUNCT
ejpam-4060	128	12	closed	closed	ADJ
ejpam-4060	128	13	set	set	NOUN
ejpam-4060	128	14	for	for	ADP
ejpam-4060	128	15	each	each	DET
ejpam-4060	128	16	k	k	PROPN
ejpam-4060	128	17	∈	∈	PROPN
ejpam-4060	128	18	n.	n.	NOUN
ejpam-4060	128	19	it	it	PRON
ejpam-4060	128	20	follows	follow	VERB
ejpam-4060	128	21	that	that	SCONJ
ejpam-4060	128	22	(	(	PUNCT
ejpam-4060	128	23	i	i	PRON
ejpam-4060	128	24	,	,	PUNCT
ejpam-4060	128	25	j)-ψcl(ak	j)-ψcl(ak	PROPN
ejpam-4060	128	26	)	)	PUNCT
ejpam-4060	128	27	⊆	⊆	NUM
ejpam-4060	128	28	uk	uk	PROPN
ejpam-4060	128	29	for	for	ADP
ejpam-4060	128	30	each	each	DET
ejpam-4060	128	31	k	k	NOUN
ejpam-4060	128	32	such	such	ADJ
ejpam-4060	128	33	that	that	SCONJ
ejpam-4060	128	34	ak	ak	PROPN
ejpam-4060	128	35	⊆	⊆	NUM
ejpam-4060	128	36	uk	uk	PROPN
ejpam-4060	128	37	where	where	SCONJ
ejpam-4060	128	38	uk	uk	PROPN
ejpam-4060	128	39	is	be	AUX
ejpam-4060	128	40	(	(	PUNCT
ejpam-4060	128	41	i	i	PROPN
ejpam-4060	128	42	,	,	PUNCT
ejpam-4060	128	43	j)-semi	j)-semi	NOUN
ejpam-4060	128	44	-	-	PUNCT
ejpam-4060	128	45	open	open	ADJ
ejpam-4060	128	46	.	.	PUNCT
ejpam-4060	129	1	now	now	ADV
ejpam-4060	129	2	,	,	PUNCT
ejpam-4060	129	3	(	(	PUNCT
ejpam-4060	129	4	i	i	PROPN
ejpam-4060	129	5	,	,	PUNCT
ejpam-4060	129	6	j)-ψcl	j)-ψcl	PROPN
ejpam-4060	129	7	(	(	PUNCT
ejpam-4060	129	8	∞⋂	∞⋂	PROPN
ejpam-4060	129	9	k=1	k=1	PROPN
ejpam-4060	129	10	ak	ak	PROPN
ejpam-4060	129	11	)	)	PUNCT
ejpam-4060	129	12	⊆	⊆	PROPN
ejpam-4060	129	13	∞⋂	∞⋂	PROPN
ejpam-4060	129	14	k=1	k=1	PROPN
ejpam-4060	129	15	(	(	PUNCT
ejpam-4060	129	16	i	i	PROPN
ejpam-4060	129	17	,	,	PUNCT
ejpam-4060	129	18	j)-ψcl(ak	j)-ψcl(ak	PROPN
ejpam-4060	129	19	)	)	PUNCT
ejpam-4060	129	20	⊆	⊆	NUM
ejpam-4060	129	21	∞⋂	∞⋂	PROPN
ejpam-4060	129	22	k=1	k=1	PROPN
ejpam-4060	129	23	uk	uk	PROPN
ejpam-4060	129	24	=	=	NOUN
ejpam-4060	129	25	u.	u.	PROPN
ejpam-4060	129	26	note	note	VERB
ejpam-4060	129	27	that	that	SCONJ
ejpam-4060	129	28	if	if	SCONJ
ejpam-4060	129	29	ak	ak	PROPN
ejpam-4060	129	30	is	be	AUX
ejpam-4060	129	31	(	(	PUNCT
ejpam-4060	129	32	i	i	PROPN
ejpam-4060	129	33	,	,	PUNCT
ejpam-4060	129	34	j)-ψgs	j)-ψgs	ADV
ejpam-4060	129	35	-	-	PUNCT
ejpam-4060	129	36	closed	closed	ADJ
ejpam-4060	129	37	set	set	NOUN
ejpam-4060	129	38	,	,	PUNCT
ejpam-4060	129	39	then	then	ADV
ejpam-4060	129	40	by	by	ADP
ejpam-4060	129	41	definition	definition	NOUN
ejpam-4060	129	42	3	3	NUM
ejpam-4060	129	43	,	,	PUNCT
ejpam-4060	129	44	x∖ak	x∖ak	PROPN
ejpam-4060	129	45	is	be	AUX
ejpam-4060	129	46	(	(	PUNCT
ejpam-4060	129	47	i	i	NOUN
ejpam-4060	129	48	,	,	PUNCT
ejpam-4060	129	49	j)-ψgs	j)-ψgs	ADV
ejpam-4060	129	50	-	-	PUNCT
ejpam-4060	129	51	open	open	ADJ
ejpam-4060	129	52	set	set	NOUN
ejpam-4060	129	53	.	.	PUNCT
ejpam-4060	130	1	moreover	moreover	ADV
ejpam-4060	130	2	,	,	PUNCT
ejpam-4060	130	3	by	by	ADP
ejpam-4060	130	4	de	de	ADP
ejpam-4060	130	5	morganś	morganś	ADJ
ejpam-4060	130	6	law	law	NOUN
ejpam-4060	130	7	,	,	PUNCT
ejpam-4060	130	8	x∖	x∖	PROPN
ejpam-4060	130	9	(	(	PUNCT
ejpam-4060	130	10	⋂∞	⋂∞	NUM
ejpam-4060	130	11	k=1ak	k=1ak	NUM
ejpam-4060	130	12	)	)	PUNCT
ejpam-4060	130	13	=	=	SYM
ejpam-4060	130	14	⋃∞	⋃∞	X
ejpam-4060	130	15	k=1(x∖ak	k=1(x∖ak	PROPN
ejpam-4060	130	16	)	)	PUNCT
ejpam-4060	130	17	.	.	PUNCT
ejpam-4060	131	1	hence	hence	ADV
ejpam-4060	131	2	the	the	DET
ejpam-4060	131	3	following	follow	VERB
ejpam-4060	131	4	corollary	corollary	NOUN
ejpam-4060	131	5	follows	follow	VERB
ejpam-4060	131	6	.	.	PUNCT
ejpam-4060	132	1	corollary	corollary	ADJ
ejpam-4060	132	2	2	2	NUM
ejpam-4060	132	3	.	.	PUNCT
ejpam-4060	133	1	if	if	SCONJ
ejpam-4060	133	2	{	{	PUNCT
ejpam-4060	133	3	bk|bk	bk|bk	NOUN
ejpam-4060	133	4	is	be	AUX
ejpam-4060	133	5	(	(	PUNCT
ejpam-4060	133	6	i	i	NOUN
ejpam-4060	133	7	,	,	PUNCT
ejpam-4060	133	8	j)-ψgs	j)-ψgs	ADV
ejpam-4060	133	9	-	-	PUNCT
ejpam-4060	133	10	open	open	ADJ
ejpam-4060	133	11	set	set	NOUN
ejpam-4060	133	12	,	,	PUNCT
ejpam-4060	133	13	k	k	PROPN
ejpam-4060	133	14	∈	∈	PROPN
ejpam-4060	133	15	n	n	CCONJ
ejpam-4060	133	16	}	}	PUNCT
ejpam-4060	133	17	,	,	PUNCT
ejpam-4060	133	18	then	then	ADV
ejpam-4060	133	19	⋃∞	⋃∞	PUNCT
ejpam-4060	133	20	k=1bk	k=1bk	PROPN
ejpam-4060	133	21	is	be	AUX
ejpam-4060	133	22	(	(	PUNCT
ejpam-4060	133	23	i	i	INTJ
ejpam-4060	133	24	,	,	PUNCT
ejpam-4060	133	25	j)-ψgs	j)-ψgs	ADV
ejpam-4060	133	26	-	-	PUNCT
ejpam-4060	133	27	open	open	ADJ
ejpam-4060	133	28	set	set	NOUN
ejpam-4060	133	29	.	.	PUNCT
ejpam-4060	134	1	4	4	X
ejpam-4060	134	2	.	.	X
ejpam-4060	134	3	ψgs	ψgs	NOUN
ejpam-4060	134	4	-	-	PUNCT
ejpam-4060	134	5	closure	closure	NOUN
ejpam-4060	134	6	and	and	CCONJ
ejpam-4060	134	7	ψgs	ψgs	ADV
ejpam-4060	134	8	-	-	NOUN
ejpam-4060	134	9	interior	interior	ADJ
ejpam-4060	134	10	in	in	ADP
ejpam-4060	134	11	bts	bt	NOUN
ejpam-4060	134	12	in	in	ADP
ejpam-4060	134	13	this	this	DET
ejpam-4060	134	14	section	section	NOUN
ejpam-4060	134	15	,	,	PUNCT
ejpam-4060	134	16	the	the	DET
ejpam-4060	134	17	ψgs	ψgs	NOUN
ejpam-4060	134	18	-	-	PUNCT
ejpam-4060	134	19	closure	closure	NOUN
ejpam-4060	134	20	and	and	CCONJ
ejpam-4060	134	21	ψgs	ψgs	ADV
ejpam-4060	134	22	-	-	PUNCT
ejpam-4060	134	23	interior	interior	ADJ
ejpam-4060	134	24	in	in	ADP
ejpam-4060	134	25	bitopological	bitopological	ADJ
ejpam-4060	134	26	spaces	space	NOUN
ejpam-4060	134	27	are	be	AUX
ejpam-4060	134	28	introduced	introduce	VERB
ejpam-4060	134	29	and	and	CCONJ
ejpam-4060	134	30	some	some	PRON
ejpam-4060	134	31	of	of	ADP
ejpam-4060	134	32	their	their	PRON
ejpam-4060	134	33	properties	property	NOUN
ejpam-4060	134	34	are	be	AUX
ejpam-4060	134	35	explored	explore	VERB
ejpam-4060	134	36	.	.	PUNCT
ejpam-4060	135	1	definition	definition	NOUN
ejpam-4060	135	2	4	4	NUM
ejpam-4060	135	3	.	.	PUNCT
ejpam-4060	136	1	let	let	AUX
ejpam-4060	136	2	(	(	PUNCT
ejpam-4060	136	3	x	x	NOUN
ejpam-4060	136	4	,	,	PUNCT
ejpam-4060	136	5	τ1	τ1	NOUN
ejpam-4060	136	6	,	,	PUNCT
ejpam-4060	136	7	τ2	τ2	PROPN
ejpam-4060	136	8	)	)	PUNCT
ejpam-4060	136	9	be	be	VERB
ejpam-4060	136	10	a	a	DET
ejpam-4060	136	11	bitopological	bitopological	ADJ
ejpam-4060	136	12	space	space	NOUN
ejpam-4060	136	13	and	and	CCONJ
ejpam-4060	136	14	a	a	DET
ejpam-4060	136	15	⊆	⊆	NUM
ejpam-4060	136	16	x.	x.	NOUN
ejpam-4060	136	17	an	an	DET
ejpam-4060	136	18	element	element	NOUN
ejpam-4060	136	19	x	x	SYM
ejpam-4060	136	20	∈	∈	PROPN
ejpam-4060	136	21	a	a	PRON
ejpam-4060	136	22	is	be	AUX
ejpam-4060	136	23	called	call	VERB
ejpam-4060	136	24	(	(	PUNCT
ejpam-4060	136	25	i	i	PROPN
ejpam-4060	136	26	,	,	PUNCT
ejpam-4060	136	27	j)-ψgs	j)-ψgs	ADJ
ejpam-4060	136	28	-	-	ADJ
ejpam-4060	136	29	interior	interior	ADJ
ejpam-4060	136	30	point	point	NOUN
ejpam-4060	136	31	of	of	ADP
ejpam-4060	136	32	a	a	PRON
ejpam-4060	136	33	if	if	SCONJ
ejpam-4060	136	34	there	there	PRON
ejpam-4060	136	35	exists	exist	VERB
ejpam-4060	136	36	a	a	DET
ejpam-4060	136	37	(	(	PUNCT
ejpam-4060	136	38	i	i	NOUN
ejpam-4060	136	39	,	,	PUNCT
ejpam-4060	136	40	j)-ψgs	j)-ψgs	ADV
ejpam-4060	136	41	-	-	ADJ
ejpam-4060	136	42	open	open	ADJ
ejpam-4060	136	43	set	set	ADJ
ejpam-4060	136	44	o	o	NOUN
ejpam-4060	137	1	such	such	ADJ
ejpam-4060	137	2	that	that	SCONJ
ejpam-4060	137	3	x	x	SYM
ejpam-4060	137	4	∈	∈	NOUN
ejpam-4060	137	5	o	o	NOUN
ejpam-4060	137	6	⊆	⊆	NUM
ejpam-4060	137	7	a.	a.	NOUN
ejpam-4060	137	8	the	the	DET
ejpam-4060	137	9	set	set	NOUN
ejpam-4060	137	10	of	of	ADP
ejpam-4060	137	11	all	all	DET
ejpam-4060	137	12	(	(	PUNCT
ejpam-4060	137	13	i	i	NOUN
ejpam-4060	137	14	,	,	PUNCT
ejpam-4060	137	15	j)-ψgs	j)-ψgs	ADJ
ejpam-4060	137	16	-	-	ADJ
ejpam-4060	137	17	interior	interior	ADJ
ejpam-4060	137	18	points	point	NOUN
ejpam-4060	137	19	of	of	ADP
ejpam-4060	137	20	a	a	PRON
ejpam-4060	137	21	is	be	AUX
ejpam-4060	137	22	called	call	VERB
ejpam-4060	137	23	the	the	DET
ejpam-4060	137	24	(	(	PUNCT
ejpam-4060	137	25	i	i	PROPN
ejpam-4060	137	26	,	,	PUNCT
ejpam-4060	137	27	j)-ψgs	j)-ψgs	ADV
ejpam-4060	137	28	-	-	ADJ
ejpam-4060	137	29	interior	interior	ADJ
ejpam-4060	137	30	of	of	ADP
ejpam-4060	137	31	a	a	PRON
ejpam-4060	137	32	and	and	CCONJ
ejpam-4060	137	33	is	be	AUX
ejpam-4060	137	34	denoted	denote	VERB
ejpam-4060	137	35	by	by	ADP
ejpam-4060	137	36	(	(	PUNCT
ejpam-4060	137	37	i	i	INTJ
ejpam-4060	137	38	,	,	PUNCT
ejpam-4060	137	39	j)-ψgs	j)-ψgs	ADV
ejpam-4060	137	40	-	-	PUNCT
ejpam-4060	137	41	int(a	int(a	NOUN
ejpam-4060	137	42	)	)	PUNCT
ejpam-4060	137	43	.	.	PUNCT
ejpam-4060	138	1	theorem	theorem	NOUN
ejpam-4060	138	2	5	5	NUM
ejpam-4060	138	3	.	.	PUNCT
ejpam-4060	139	1	the	the	DET
ejpam-4060	139	2	ψgs	ψgs	ADV
ejpam-4060	139	3	-	-	PUNCT
ejpam-4060	139	4	interior	interior	NOUN
ejpam-4060	139	5	of	of	ADP
ejpam-4060	139	6	a	a	DET
ejpam-4060	139	7	subset	subset	NOUN
ejpam-4060	139	8	a	a	PRON
ejpam-4060	139	9	of	of	ADP
ejpam-4060	139	10	x	x	SYM
ejpam-4060	139	11	is	be	AUX
ejpam-4060	139	12	the	the	DET
ejpam-4060	139	13	countable	countable	ADJ
ejpam-4060	139	14	union	union	NOUN
ejpam-4060	139	15	of	of	ADP
ejpam-4060	139	16	ψgs	ψgs	ADV
ejpam-4060	139	17	-	-	PUNCT
ejpam-4060	139	18	open	open	ADJ
ejpam-4060	139	19	sets	set	NOUN
ejpam-4060	139	20	contained	contain	VERB
ejpam-4060	139	21	in	in	ADP
ejpam-4060	139	22	a	a	PRON
ejpam-4060	139	23	,	,	PUNCT
ejpam-4060	139	24	that	that	ADV
ejpam-4060	139	25	is	is	ADV
ejpam-4060	139	26	,	,	PUNCT
ejpam-4060	139	27	(	(	PUNCT
ejpam-4060	139	28	i	i	PRON
ejpam-4060	139	29	,	,	PUNCT
ejpam-4060	139	30	j)-ψgs	j)-ψgs	ADV
ejpam-4060	139	31	-	-	PUNCT
ejpam-4060	139	32	int(a	int(a	NOUN
ejpam-4060	139	33	)	)	PUNCT
ejpam-4060	140	1	=	=	SYM
ejpam-4060	140	2	∪{o	∪{o	VERB
ejpam-4060	140	3	:	:	PUNCT
ejpam-4060	140	4	o	o	NOUN
ejpam-4060	140	5	is	be	AUX
ejpam-4060	140	6	(	(	PUNCT
ejpam-4060	140	7	i	i	NOUN
ejpam-4060	140	8	,	,	PUNCT
ejpam-4060	140	9	j)-ψgs	j)-ψgs	ADV
ejpam-4060	140	10	-	-	PUNCT
ejpam-4060	140	11	open	open	ADJ
ejpam-4060	140	12	and	and	CCONJ
ejpam-4060	140	13	o	o	X
ejpam-4060	140	14	⊆	⊆	NUM
ejpam-4060	140	15	a	a	PRON
ejpam-4060	140	16	}	}	PUNCT
ejpam-4060	140	17	.	.	PUNCT
ejpam-4060	141	1	l.m.tutanes	l.m.tutane	NOUN
ejpam-4060	141	2	/	/	SYM
ejpam-4060	141	3	eur	eur	PROPN
ejpam-4060	141	4	.	.	PUNCT
ejpam-4060	142	1	j.	j.	PROPN
ejpam-4060	142	2	pure	pure	PROPN
ejpam-4060	142	3	appl	appl	PROPN
ejpam-4060	142	4	.	.	PROPN
ejpam-4060	142	5	math	math	PROPN
ejpam-4060	142	6	,	,	PUNCT
ejpam-4060	142	7	14	14	NUM
ejpam-4060	142	8	(	(	PUNCT
ejpam-4060	142	9	4	4	NUM
ejpam-4060	142	10	)	)	PUNCT
ejpam-4060	142	11	(	(	PUNCT
ejpam-4060	142	12	2021	2021	NUM
ejpam-4060	142	13	)	)	PUNCT
ejpam-4060	142	14	,	,	PUNCT
ejpam-4060	142	15	1275	1275	NUM
ejpam-4060	142	16	-	-	SYM
ejpam-4060	142	17	1282	1282	NUM
ejpam-4060	142	18	1280	1280	NUM
ejpam-4060	142	19	proof	proof	NOUN
ejpam-4060	142	20	.	.	PUNCT
ejpam-4060	143	1	let	let	VERB
ejpam-4060	143	2	x	x	X
ejpam-4060	143	3	∈	∈	PROPN
ejpam-4060	143	4	(	(	PUNCT
ejpam-4060	143	5	i	i	NOUN
ejpam-4060	143	6	,	,	PUNCT
ejpam-4060	143	7	j)-ψgs	j)-ψgs	ADV
ejpam-4060	143	8	-	-	PUNCT
ejpam-4060	143	9	int(a	int(a	NOUN
ejpam-4060	143	10	)	)	PUNCT
ejpam-4060	143	11	.	.	PUNCT
ejpam-4060	144	1	then	then	ADV
ejpam-4060	144	2	there	there	PRON
ejpam-4060	144	3	exists	exist	VERB
ejpam-4060	144	4	a	a	DET
ejpam-4060	144	5	(	(	PUNCT
ejpam-4060	144	6	i	i	NOUN
ejpam-4060	144	7	,	,	PUNCT
ejpam-4060	144	8	j)-ψgs	j)-ψgs	ADV
ejpam-4060	144	9	-	-	ADJ
ejpam-4060	144	10	open	open	ADJ
ejpam-4060	144	11	set	set	ADJ
ejpam-4060	144	12	o	o	NOUN
ejpam-4060	144	13	such	such	ADJ
ejpam-4060	144	14	that	that	SCONJ
ejpam-4060	144	15	x	x	SYM
ejpam-4060	144	16	∈	∈	NOUN
ejpam-4060	144	17	o	o	NOUN
ejpam-4060	144	18	⊆	⊆	NUM
ejpam-4060	144	19	a	a	DET
ejpam-4060	144	20	implying	implying	ADJ
ejpam-4060	144	21	x	x	SYM
ejpam-4060	144	22	∈	∈	PROPN
ejpam-4060	144	23	∪{o	∪{o	PROPN
ejpam-4060	144	24	:	:	PUNCT
ejpam-4060	144	25	o	o	NOUN
ejpam-4060	144	26	is	be	AUX
ejpam-4060	144	27	(	(	PUNCT
ejpam-4060	144	28	i	i	NOUN
ejpam-4060	144	29	,	,	PUNCT
ejpam-4060	144	30	j)-ψgs	j)-ψgs	ADV
ejpam-4060	144	31	-	-	PUNCT
ejpam-4060	144	32	open	open	ADJ
ejpam-4060	144	33	and	and	CCONJ
ejpam-4060	144	34	o	o	X
ejpam-4060	144	35	⊆	⊆	NUM
ejpam-4060	144	36	a	a	PRON
ejpam-4060	144	37	}	}	PUNCT
ejpam-4060	144	38	.	.	PUNCT
ejpam-4060	145	1	next	next	ADV
ejpam-4060	145	2	,	,	PUNCT
ejpam-4060	145	3	suppose	suppose	VERB
ejpam-4060	145	4	y	y	PROPN
ejpam-4060	145	5	∈	∈	PROPN
ejpam-4060	145	6	∪{o	∪{o	PROPN
ejpam-4060	145	7	:	:	PUNCT
ejpam-4060	145	8	o	o	NOUN
ejpam-4060	145	9	is	be	AUX
ejpam-4060	145	10	(	(	PUNCT
ejpam-4060	145	11	i	i	NOUN
ejpam-4060	145	12	,	,	PUNCT
ejpam-4060	145	13	j)-ψgs	j)-ψgs	ADV
ejpam-4060	145	14	-	-	PUNCT
ejpam-4060	145	15	open	open	ADJ
ejpam-4060	145	16	and	and	CCONJ
ejpam-4060	145	17	o	o	X
ejpam-4060	145	18	⊆	⊆	NUM
ejpam-4060	145	19	a	a	PRON
ejpam-4060	145	20	}	}	PUNCT
ejpam-4060	145	21	.	.	PUNCT
ejpam-4060	146	1	then	then	ADV
ejpam-4060	146	2	there	there	PRON
ejpam-4060	146	3	exists	exist	VERB
ejpam-4060	146	4	(	(	PUNCT
ejpam-4060	146	5	i	i	PRON
ejpam-4060	146	6	,	,	PUNCT
ejpam-4060	146	7	j)-ψgs	j)-ψgs	ADV
ejpam-4060	146	8	-	-	ADJ
ejpam-4060	146	9	open	open	ADJ
ejpam-4060	146	10	set	set	VERB
ejpam-4060	146	11	o0	o0	NOUN
ejpam-4060	146	12	⊆	⊆	NUM
ejpam-4060	146	13	a	a	DET
ejpam-4060	146	14	such	such	ADJ
ejpam-4060	146	15	that	that	SCONJ
ejpam-4060	146	16	y	y	PROPN
ejpam-4060	146	17	∈	∈	PROPN
ejpam-4060	146	18	o0	o0	NOUN
ejpam-4060	146	19	.	.	PUNCT
ejpam-4060	147	1	thus	thus	ADV
ejpam-4060	147	2	y	y	PROPN
ejpam-4060	147	3	∈	∈	PROPN
ejpam-4060	147	4	(	(	PUNCT
ejpam-4060	147	5	i	i	NOUN
ejpam-4060	147	6	,	,	PUNCT
ejpam-4060	147	7	j)-ψgs	j)-ψgs	ADV
ejpam-4060	147	8	-	-	PUNCT
ejpam-4060	147	9	int(a	int(a	NOUN
ejpam-4060	147	10	)	)	PUNCT
ejpam-4060	147	11	.	.	PUNCT
ejpam-4060	148	1	the	the	DET
ejpam-4060	148	2	previous	previous	ADJ
ejpam-4060	148	3	theorem	theorem	NOUN
ejpam-4060	148	4	implies	imply	VERB
ejpam-4060	148	5	that	that	SCONJ
ejpam-4060	148	6	(	(	PUNCT
ejpam-4060	148	7	i	i	PRON
ejpam-4060	148	8	,	,	PUNCT
ejpam-4060	148	9	j)-ψgs	j)-ψgs	ADV
ejpam-4060	148	10	-	-	PUNCT
ejpam-4060	148	11	int(a	int(a	NOUN
ejpam-4060	148	12	)	)	PUNCT
ejpam-4060	148	13	is	be	AUX
ejpam-4060	148	14	contained	contain	VERB
ejpam-4060	148	15	in	in	ADP
ejpam-4060	148	16	a	a	PRON
ejpam-4060	148	17	,	,	PUNCT
ejpam-4060	148	18	where	where	SCONJ
ejpam-4060	148	19	a	a	PRON
ejpam-4060	148	20	is	be	AUX
ejpam-4060	148	21	any	any	DET
ejpam-4060	148	22	subset	subset	NOUN
ejpam-4060	148	23	of	of	ADP
ejpam-4060	148	24	x	x	PRON
ejpam-4060	148	25	,	,	PUNCT
ejpam-4060	148	26	being	be	AUX
ejpam-4060	148	27	the	the	DET
ejpam-4060	148	28	union	union	NOUN
ejpam-4060	148	29	of	of	ADP
ejpam-4060	148	30	all	all	DET
ejpam-4060	148	31	(	(	PUNCT
ejpam-4060	148	32	i	i	NOUN
ejpam-4060	148	33	,	,	PUNCT
ejpam-4060	148	34	j)-ψgs	j)-ψgs	ADV
ejpam-4060	148	35	-	-	PUNCT
ejpam-4060	148	36	open	open	ADJ
ejpam-4060	148	37	sets	set	NOUN
ejpam-4060	148	38	contained	contain	VERB
ejpam-4060	148	39	in	in	ADP
ejpam-4060	148	40	a.	a.	NOUN
ejpam-4060	148	41	now	now	ADV
ejpam-4060	148	42	corollary	corollary	ADJ
ejpam-4060	148	43	2	2	NUM
ejpam-4060	148	44	entails	entail	VERB
ejpam-4060	148	45	that	that	SCONJ
ejpam-4060	148	46	the	the	DET
ejpam-4060	148	47	arbitrary	arbitrary	ADJ
ejpam-4060	148	48	union	union	NOUN
ejpam-4060	148	49	of	of	ADP
ejpam-4060	148	50	(	(	PUNCT
ejpam-4060	148	51	i	i	PROPN
ejpam-4060	148	52	,	,	PUNCT
ejpam-4060	148	53	j)-ψgs	j)-ψgs	ADV
ejpam-4060	148	54	-	-	PUNCT
ejpam-4060	148	55	open	open	ADJ
ejpam-4060	148	56	sets	set	NOUN
ejpam-4060	148	57	is	be	AUX
ejpam-4060	148	58	also	also	ADV
ejpam-4060	148	59	(	(	PUNCT
ejpam-4060	148	60	i	i	INTJ
ejpam-4060	148	61	,	,	PUNCT
ejpam-4060	148	62	j)-ψgs	j)-ψgs	ADV
ejpam-4060	148	63	-	-	ADJ
ejpam-4060	148	64	open	open	ADJ
ejpam-4060	148	65	,	,	PUNCT
ejpam-4060	148	66	hence	hence	ADV
ejpam-4060	148	67	we	we	PRON
ejpam-4060	148	68	can	can	AUX
ejpam-4060	148	69	say	say	VERB
ejpam-4060	148	70	that	that	PRON
ejpam-4060	148	71	(	(	PUNCT
ejpam-4060	148	72	i	i	PRON
ejpam-4060	148	73	,	,	PUNCT
ejpam-4060	148	74	j)-ψgs	j)-ψgs	ADV
ejpam-4060	148	75	-	-	PUNCT
ejpam-4060	148	76	int(a	int(a	NOUN
ejpam-4060	148	77	)	)	PUNCT
ejpam-4060	148	78	is	be	AUX
ejpam-4060	148	79	(	(	PUNCT
ejpam-4060	148	80	i	i	NOUN
ejpam-4060	148	81	,	,	PUNCT
ejpam-4060	148	82	j)-ψgs	j)-ψgs	ADV
ejpam-4060	148	83	-	-	ADJ
ejpam-4060	148	84	open	open	ADJ
ejpam-4060	148	85	.	.	PUNCT
ejpam-4060	149	1	consequently	consequently	ADV
ejpam-4060	149	2	,	,	PUNCT
ejpam-4060	149	3	(	(	PUNCT
ejpam-4060	149	4	i	i	INTJ
ejpam-4060	149	5	,	,	PUNCT
ejpam-4060	149	6	j)-ψgs	j)-ψgs	ADV
ejpam-4060	149	7	-	-	PUNCT
ejpam-4060	149	8	int(a	int(a	NOUN
ejpam-4060	149	9	)	)	PUNCT
ejpam-4060	149	10	is	be	AUX
ejpam-4060	149	11	the	the	DET
ejpam-4060	149	12	largest	large	ADJ
ejpam-4060	149	13	(	(	PUNCT
ejpam-4060	149	14	i	i	NOUN
ejpam-4060	149	15	,	,	PUNCT
ejpam-4060	149	16	j)-ψgs	j)-ψgs	ADV
ejpam-4060	149	17	-	-	ADJ
ejpam-4060	149	18	open	open	ADJ
ejpam-4060	149	19	set	set	NOUN
ejpam-4060	149	20	contained	contain	VERB
ejpam-4060	149	21	in	in	ADP
ejpam-4060	149	22	a	a	PRON
ejpam-4060	149	23	,	,	PUNCT
ejpam-4060	149	24	as	as	SCONJ
ejpam-4060	149	25	stated	state	VERB
ejpam-4060	149	26	in	in	ADP
ejpam-4060	149	27	the	the	DET
ejpam-4060	149	28	following	follow	VERB
ejpam-4060	149	29	remark	remark	NOUN
ejpam-4060	149	30	.	.	PUNCT
ejpam-4060	150	1	remark	remark	PROPN
ejpam-4060	150	2	1	1	NUM
ejpam-4060	150	3	.	.	PUNCT
ejpam-4060	151	1	let	let	AUX
ejpam-4060	151	2	(	(	PUNCT
ejpam-4060	151	3	x	x	NOUN
ejpam-4060	151	4	,	,	PUNCT
ejpam-4060	151	5	τ1	τ1	NOUN
ejpam-4060	151	6	,	,	PUNCT
ejpam-4060	151	7	τ2	τ2	PROPN
ejpam-4060	151	8	)	)	PUNCT
ejpam-4060	151	9	be	be	VERB
ejpam-4060	151	10	a	a	DET
ejpam-4060	151	11	bitopological	bitopological	ADJ
ejpam-4060	151	12	space	space	NOUN
ejpam-4060	151	13	and	and	CCONJ
ejpam-4060	151	14	a	a	PRON
ejpam-4060	151	15	,	,	PUNCT
ejpam-4060	151	16	b	b	PROPN
ejpam-4060	151	17	⊆	⊆	NUM
ejpam-4060	151	18	x.	x.	NOUN
ejpam-4060	151	19	then	then	ADV
ejpam-4060	151	20	the	the	DET
ejpam-4060	151	21	following	follow	VERB
ejpam-4060	151	22	hold	hold	NOUN
ejpam-4060	151	23	:	:	PUNCT
ejpam-4060	151	24	(	(	PUNCT
ejpam-4060	151	25	i	i	NOUN
ejpam-4060	151	26	)	)	PUNCT
ejpam-4060	151	27	(	(	PUNCT
ejpam-4060	151	28	i	i	NOUN
ejpam-4060	151	29	,	,	PUNCT
ejpam-4060	151	30	j)-ψgs	j)-ψgs	ADV
ejpam-4060	151	31	-	-	PUNCT
ejpam-4060	151	32	int(a	int(a	NOUN
ejpam-4060	151	33	)	)	PUNCT
ejpam-4060	151	34	⊆	⊆	PROPN
ejpam-4060	151	35	a	a	PRON
ejpam-4060	151	36	;	;	PUNCT
ejpam-4060	151	37	(	(	PUNCT
ejpam-4060	151	38	ii	ii	NOUN
ejpam-4060	151	39	)	)	PUNCT
ejpam-4060	151	40	(	(	PUNCT
ejpam-4060	151	41	i	i	NOUN
ejpam-4060	151	42	,	,	PUNCT
ejpam-4060	151	43	j)-ψgs	j)-ψgs	ADV
ejpam-4060	151	44	-	-	PUNCT
ejpam-4060	151	45	int(a	int(a	NOUN
ejpam-4060	151	46	)	)	PUNCT
ejpam-4060	151	47	is	be	AUX
ejpam-4060	151	48	(	(	PUNCT
ejpam-4060	151	49	i	i	NOUN
ejpam-4060	151	50	,	,	PUNCT
ejpam-4060	151	51	j)-ψgs	j)-ψgs	ADV
ejpam-4060	151	52	-	-	PUNCT
ejpam-4060	151	53	open	open	ADJ
ejpam-4060	151	54	set	set	NOUN
ejpam-4060	151	55	;	;	PUNCT
ejpam-4060	151	56	and	and	CCONJ
ejpam-4060	151	57	(	(	PUNCT
ejpam-4060	151	58	iii	iii	X
ejpam-4060	151	59	)	)	PUNCT
ejpam-4060	151	60	if	if	SCONJ
ejpam-4060	151	61	b	b	PROPN
ejpam-4060	151	62	⊆	⊆	SYM
ejpam-4060	151	63	a	a	DET
ejpam-4060	151	64	such	such	ADJ
ejpam-4060	151	65	that	that	DET
ejpam-4060	151	66	b	b	NOUN
ejpam-4060	151	67	is	be	AUX
ejpam-4060	151	68	(	(	PUNCT
ejpam-4060	151	69	i	i	NOUN
ejpam-4060	151	70	,	,	PUNCT
ejpam-4060	151	71	j)-ψgs	j)-ψgs	ADV
ejpam-4060	151	72	-	-	PUNCT
ejpam-4060	151	73	open	open	ADJ
ejpam-4060	151	74	set	set	NOUN
ejpam-4060	151	75	,	,	PUNCT
ejpam-4060	151	76	then	then	ADV
ejpam-4060	151	77	b	b	PROPN
ejpam-4060	151	78	⊆	⊆	NUM
ejpam-4060	151	79	(	(	PUNCT
ejpam-4060	151	80	i	i	NOUN
ejpam-4060	151	81	,	,	PUNCT
ejpam-4060	151	82	j)-ψgs	j)-ψgs	ADV
ejpam-4060	151	83	-	-	PUNCT
ejpam-4060	151	84	int(a	int(a	NOUN
ejpam-4060	151	85	)	)	PUNCT
ejpam-4060	151	86	.	.	PUNCT
ejpam-4060	152	1	theorem	theorem	VERB
ejpam-4060	152	2	6	6	NUM
ejpam-4060	152	3	.	.	PUNCT
ejpam-4060	153	1	let	let	AUX
ejpam-4060	153	2	(	(	PUNCT
ejpam-4060	153	3	x	x	NOUN
ejpam-4060	153	4	,	,	PUNCT
ejpam-4060	153	5	τ1	τ1	NOUN
ejpam-4060	153	6	,	,	PUNCT
ejpam-4060	153	7	τ2	τ2	PROPN
ejpam-4060	153	8	)	)	PUNCT
ejpam-4060	153	9	be	be	VERB
ejpam-4060	153	10	a	a	DET
ejpam-4060	153	11	bitopological	bitopological	ADJ
ejpam-4060	153	12	space	space	NOUN
ejpam-4060	153	13	and	and	CCONJ
ejpam-4060	153	14	a	a	DET
ejpam-4060	153	15	⊆	⊆	NUM
ejpam-4060	153	16	x.	x.	NOUN
ejpam-4060	153	17	a	a	PRON
ejpam-4060	153	18	is	be	AUX
ejpam-4060	153	19	(	(	PUNCT
ejpam-4060	153	20	i	i	NOUN
ejpam-4060	153	21	,	,	PUNCT
ejpam-4060	153	22	j)-ψgs	j)-ψgs	ADV
ejpam-4060	153	23	-	-	PUNCT
ejpam-4060	153	24	open	open	ADJ
ejpam-4060	153	25	set	set	NOUN
ejpam-4060	153	26	,	,	PUNCT
ejpam-4060	153	27	if	if	SCONJ
ejpam-4060	153	28	and	and	CCONJ
ejpam-4060	153	29	only	only	ADV
ejpam-4060	153	30	if	if	SCONJ
ejpam-4060	153	31	(	(	PUNCT
ejpam-4060	153	32	i	i	NOUN
ejpam-4060	153	33	,	,	PUNCT
ejpam-4060	153	34	j)-ψgs	j)-ψgs	ADV
ejpam-4060	153	35	-	-	PUNCT
ejpam-4060	153	36	int(a	int(a	NOUN
ejpam-4060	153	37	)	)	PUNCT
ejpam-4060	153	38	=	=	NOUN
ejpam-4060	153	39	a.	a.	NOUN
ejpam-4060	153	40	proof	proof	NOUN
ejpam-4060	153	41	.	.	PUNCT
ejpam-4060	154	1	let	let	VERB
ejpam-4060	154	2	a	a	DET
ejpam-4060	154	3	be	be	AUX
ejpam-4060	154	4	(	(	PUNCT
ejpam-4060	154	5	i	i	NOUN
ejpam-4060	154	6	,	,	PUNCT
ejpam-4060	154	7	j)-ψgs	j)-ψgs	ADV
ejpam-4060	154	8	-	-	ADJ
ejpam-4060	154	9	open	open	ADJ
ejpam-4060	154	10	set	set	NOUN
ejpam-4060	154	11	and	and	CCONJ
ejpam-4060	154	12	x	x	SYM
ejpam-4060	154	13	∈	∈	NOUN
ejpam-4060	154	14	a.	a.	NOUN
ejpam-4060	154	15	note	note	NOUN
ejpam-4060	154	16	that	that	SCONJ
ejpam-4060	154	17	by	by	ADP
ejpam-4060	154	18	remark	remark	NOUN
ejpam-4060	154	19	1	1	NUM
ejpam-4060	154	20	(	(	PUNCT
ejpam-4060	154	21	i	i	NOUN
ejpam-4060	154	22	)	)	PUNCT
ejpam-4060	154	23	,	,	PUNCT
ejpam-4060	154	24	(	(	PUNCT
ejpam-4060	154	25	i	i	INTJ
ejpam-4060	154	26	,	,	PUNCT
ejpam-4060	154	27	j)-ψgs	j)-ψgs	ADV
ejpam-4060	154	28	-	-	PUNCT
ejpam-4060	154	29	int(a	int(a	NOUN
ejpam-4060	154	30	)	)	PUNCT
ejpam-4060	154	31	⊆	⊆	NUM
ejpam-4060	154	32	a.	a.	NOUN
ejpam-4060	154	33	hence	hence	ADV
ejpam-4060	154	34	it	it	PRON
ejpam-4060	154	35	suffices	suffice	VERB
ejpam-4060	154	36	to	to	PART
ejpam-4060	154	37	show	show	VERB
ejpam-4060	154	38	a	a	DET
ejpam-4060	154	39	⊆	⊆	NUM
ejpam-4060	154	40	(	(	PUNCT
ejpam-4060	154	41	i	i	NOUN
ejpam-4060	154	42	,	,	PUNCT
ejpam-4060	154	43	j)-ψgs	j)-ψgs	ADV
ejpam-4060	154	44	-	-	PUNCT
ejpam-4060	154	45	int(a	int(a	NOUN
ejpam-4060	154	46	)	)	PUNCT
ejpam-4060	154	47	.	.	PUNCT
ejpam-4060	155	1	suppose	suppose	VERB
ejpam-4060	155	2	x	x	X
ejpam-4060	155	3	/∈	/∈	PUNCT
ejpam-4060	155	4	(	(	PUNCT
ejpam-4060	155	5	i	i	NOUN
ejpam-4060	155	6	,	,	PUNCT
ejpam-4060	155	7	j)-ψgs	j)-ψgs	ADV
ejpam-4060	155	8	-	-	PUNCT
ejpam-4060	155	9	int(a	int(a	NOUN
ejpam-4060	155	10	)	)	PUNCT
ejpam-4060	155	11	.	.	PUNCT
ejpam-4060	156	1	then	then	ADV
ejpam-4060	156	2	x	x	X
ejpam-4060	156	3	/∈	/∈	PUNCT
ejpam-4060	157	1	o	o	NOUN
ejpam-4060	157	2	for	for	ADP
ejpam-4060	157	3	all	all	DET
ejpam-4060	157	4	(	(	PUNCT
ejpam-4060	157	5	i	i	NOUN
ejpam-4060	157	6	,	,	PUNCT
ejpam-4060	157	7	j)-ψgs	j)-ψgs	ADV
ejpam-4060	157	8	-	-	PUNCT
ejpam-4060	157	9	open	open	ADJ
ejpam-4060	157	10	sets	set	NOUN
ejpam-4060	157	11	o	o	NOUN
ejpam-4060	158	1	such	such	ADJ
ejpam-4060	158	2	that	that	SCONJ
ejpam-4060	158	3	a	a	DET
ejpam-4060	158	4	⊆	⊆	NUM
ejpam-4060	158	5	o.	o.	NOUN
ejpam-4060	158	6	it	it	PRON
ejpam-4060	158	7	follows	follow	VERB
ejpam-4060	158	8	that	that	SCONJ
ejpam-4060	158	9	x	x	PROPN
ejpam-4060	158	10	∈	∈	PROPN
ejpam-4060	158	11	x∖o	x∖o	PROPN
ejpam-4060	158	12	such	such	ADJ
ejpam-4060	158	13	that	that	DET
ejpam-4060	158	14	a∩(x∖o	a∩(x∖o	NOUN
ejpam-4060	158	15	)	)	PUNCT
ejpam-4060	158	16	=	=	PUNCT
ejpam-4060	158	17	∅.	∅.	ADP
ejpam-4060	158	18	this	this	PRON
ejpam-4060	158	19	is	be	AUX
ejpam-4060	158	20	a	a	DET
ejpam-4060	158	21	contradiction	contradiction	NOUN
ejpam-4060	158	22	since	since	SCONJ
ejpam-4060	158	23	x	x	PROPN
ejpam-4060	158	24	∈	∈	PROPN
ejpam-4060	158	25	a∩x∖o	a∩x∖o	PROPN
ejpam-4060	158	26	.	.	PUNCT
ejpam-4060	159	1	thus	thus	ADV
ejpam-4060	159	2	x	x	X
ejpam-4060	159	3	∈	∈	PROPN
ejpam-4060	159	4	(	(	PUNCT
ejpam-4060	159	5	i	i	NOUN
ejpam-4060	159	6	,	,	PUNCT
ejpam-4060	159	7	j)-ψgs	j)-ψgs	ADV
ejpam-4060	159	8	-	-	PUNCT
ejpam-4060	159	9	int(a	int(a	NOUN
ejpam-4060	159	10	)	)	PUNCT
ejpam-4060	159	11	.	.	PUNCT
ejpam-4060	160	1	consequently	consequently	ADV
ejpam-4060	160	2	,	,	PUNCT
ejpam-4060	160	3	(	(	PUNCT
ejpam-4060	160	4	i	i	INTJ
ejpam-4060	160	5	,	,	PUNCT
ejpam-4060	160	6	j)-ψgs	j)-ψgs	ADV
ejpam-4060	160	7	-	-	PUNCT
ejpam-4060	160	8	int(a	int(a	NOUN
ejpam-4060	160	9	)	)	PUNCT
ejpam-4060	160	10	=	=	VERB
ejpam-4060	160	11	a.	a.	NOUN
ejpam-4060	160	12	conversely	conversely	ADV
ejpam-4060	160	13	,	,	PUNCT
ejpam-4060	160	14	suppose	suppose	VERB
ejpam-4060	160	15	(	(	PUNCT
ejpam-4060	160	16	i	i	NOUN
ejpam-4060	160	17	,	,	PUNCT
ejpam-4060	160	18	j)-ψgs	j)-ψgs	ADV
ejpam-4060	160	19	-	-	PUNCT
ejpam-4060	160	20	int(a	int(a	NOUN
ejpam-4060	160	21	)	)	PUNCT
ejpam-4060	160	22	=	=	PUNCT
ejpam-4060	161	1	a.	a.	NOUN
ejpam-4060	161	2	by	by	ADP
ejpam-4060	161	3	remark	remark	NOUN
ejpam-4060	161	4	1	1	NUM
ejpam-4060	161	5	(	(	PUNCT
ejpam-4060	161	6	ii	ii	NOUN
ejpam-4060	161	7	)	)	PUNCT
ejpam-4060	161	8	,	,	PUNCT
ejpam-4060	161	9	(	(	PUNCT
ejpam-4060	161	10	i	i	INTJ
ejpam-4060	161	11	,	,	PUNCT
ejpam-4060	161	12	j)-ψgs	j)-ψgs	ADV
ejpam-4060	161	13	-	-	PUNCT
ejpam-4060	161	14	int(a	int(a	NOUN
ejpam-4060	161	15	)	)	PUNCT
ejpam-4060	161	16	is	be	AUX
ejpam-4060	161	17	(	(	PUNCT
ejpam-4060	161	18	i	i	NOUN
ejpam-4060	161	19	,	,	PUNCT
ejpam-4060	161	20	j)-ψgs	j)-ψgs	ADV
ejpam-4060	161	21	-	-	PUNCT
ejpam-4060	161	22	open	open	ADJ
ejpam-4060	161	23	set	set	NOUN
ejpam-4060	161	24	,	,	PUNCT
ejpam-4060	161	25	and	and	CCONJ
ejpam-4060	161	26	so	so	ADV
ejpam-4060	161	27	a	a	PRON
ejpam-4060	161	28	is	be	AUX
ejpam-4060	161	29	(	(	PUNCT
ejpam-4060	161	30	i	i	NOUN
ejpam-4060	161	31	,	,	PUNCT
ejpam-4060	161	32	j)-ψgs	j)-ψgs	ADV
ejpam-4060	161	33	-	-	PUNCT
ejpam-4060	161	34	open	open	ADJ
ejpam-4060	161	35	set	set	NOUN
ejpam-4060	161	36	.	.	PUNCT
ejpam-4060	162	1	definition	definition	NOUN
ejpam-4060	162	2	5	5	NUM
ejpam-4060	162	3	.	.	PUNCT
ejpam-4060	163	1	let	let	VERB
ejpam-4060	163	2	a	a	DET
ejpam-4060	163	3	⊆	⊆	NUM
ejpam-4060	163	4	x.	x.	NOUN
ejpam-4060	163	5	then	then	ADV
ejpam-4060	163	6	x	x	SYM
ejpam-4060	163	7	∈	∈	PROPN
ejpam-4060	163	8	x	x	X
ejpam-4060	163	9	is	be	AUX
ejpam-4060	163	10	(	(	PUNCT
ejpam-4060	163	11	i	i	NOUN
ejpam-4060	163	12	,	,	PUNCT
ejpam-4060	163	13	j)-ψgs	j)-ψgs	ADV
ejpam-4060	163	14	-	-	PUNCT
ejpam-4060	163	15	adherent	adherent	ADJ
ejpam-4060	163	16	to	to	ADP
ejpam-4060	163	17	a	a	DET
ejpam-4060	163	18	if	if	SCONJ
ejpam-4060	163	19	v	v	NOUN
ejpam-4060	163	20	∩a	∩a	PROPN
ejpam-4060	163	21	̸=	̸=	PROPN
ejpam-4060	163	22	∅	∅	NOUN
ejpam-4060	163	23	for	for	ADP
ejpam-4060	163	24	every	every	DET
ejpam-4060	163	25	(	(	PUNCT
ejpam-4060	163	26	i	i	NOUN
ejpam-4060	163	27	,	,	PUNCT
ejpam-4060	163	28	j)-ψgs	j)-ψgs	ADV
ejpam-4060	163	29	-	-	ADJ
ejpam-4060	163	30	open	open	ADJ
ejpam-4060	163	31	set	set	VERB
ejpam-4060	163	32	v	v	NOUN
ejpam-4060	163	33	containing	contain	VERB
ejpam-4060	163	34	x.	x.	NOUN
ejpam-4060	163	35	the	the	DET
ejpam-4060	163	36	set	set	NOUN
ejpam-4060	163	37	of	of	ADP
ejpam-4060	163	38	all	all	DET
ejpam-4060	163	39	(	(	PUNCT
ejpam-4060	163	40	i	i	NOUN
ejpam-4060	163	41	,	,	PUNCT
ejpam-4060	163	42	j)-ψgs	j)-ψgs	ADJ
ejpam-4060	163	43	-	-	PUNCT
ejpam-4060	163	44	adherent	adherent	ADJ
ejpam-4060	163	45	points	point	NOUN
ejpam-4060	163	46	of	of	ADP
ejpam-4060	163	47	a	a	PRON
ejpam-4060	163	48	is	be	AUX
ejpam-4060	163	49	called	call	VERB
ejpam-4060	163	50	the	the	DET
ejpam-4060	163	51	(	(	PUNCT
ejpam-4060	163	52	i	i	NOUN
ejpam-4060	163	53	,	,	PUNCT
ejpam-4060	163	54	j)-ψgs	j)-ψgs	ADV
ejpam-4060	163	55	-	-	PUNCT
ejpam-4060	163	56	closure	closure	NOUN
ejpam-4060	163	57	of	of	ADP
ejpam-4060	163	58	a	a	PRON
ejpam-4060	163	59	and	and	CCONJ
ejpam-4060	163	60	is	be	AUX
ejpam-4060	163	61	denoted	denote	VERB
ejpam-4060	163	62	by	by	ADP
ejpam-4060	163	63	(	(	PUNCT
ejpam-4060	163	64	i	i	INTJ
ejpam-4060	163	65	,	,	PUNCT
ejpam-4060	163	66	j)-ψgs	j)-ψgs	ADV
ejpam-4060	163	67	-	-	PUNCT
ejpam-4060	163	68	cl(a	cl(a	NUM
ejpam-4060	163	69	)	)	PUNCT
ejpam-4060	163	70	.	.	PUNCT
ejpam-4060	164	1	theorem	theorem	VERB
ejpam-4060	164	2	7	7	NUM
ejpam-4060	164	3	.	.	PUNCT
ejpam-4060	165	1	the	the	DET
ejpam-4060	165	2	(	(	PUNCT
ejpam-4060	165	3	i	i	NOUN
ejpam-4060	165	4	,	,	PUNCT
ejpam-4060	165	5	j)-ψgs	j)-ψgs	ADV
ejpam-4060	165	6	-	-	PUNCT
ejpam-4060	165	7	closure	closure	NOUN
ejpam-4060	165	8	of	of	ADP
ejpam-4060	165	9	a	a	DET
ejpam-4060	165	10	subset	subset	NOUN
ejpam-4060	165	11	a	a	PRON
ejpam-4060	165	12	of	of	ADP
ejpam-4060	165	13	x	x	SYM
ejpam-4060	165	14	is	be	AUX
ejpam-4060	165	15	the	the	DET
ejpam-4060	165	16	countable	countable	ADJ
ejpam-4060	165	17	intersection	intersection	NOUN
ejpam-4060	165	18	of	of	ADP
ejpam-4060	165	19	(	(	PUNCT
ejpam-4060	165	20	i	i	PROPN
ejpam-4060	165	21	,	,	PUNCT
ejpam-4060	165	22	j)-ψgs	j)-ψgs	ADV
ejpam-4060	165	23	-	-	PUNCT
ejpam-4060	165	24	closed	closed	ADJ
ejpam-4060	165	25	sets	set	NOUN
ejpam-4060	165	26	containing	contain	VERB
ejpam-4060	165	27	a	a	PRON
ejpam-4060	165	28	,	,	PUNCT
ejpam-4060	165	29	that	that	ADV
ejpam-4060	165	30	is	is	ADV
ejpam-4060	165	31	,	,	PUNCT
ejpam-4060	165	32	(	(	PUNCT
ejpam-4060	165	33	i	i	PRON
ejpam-4060	165	34	,	,	PUNCT
ejpam-4060	165	35	j)-ψgs	j)-ψgs	ADV
ejpam-4060	165	36	-	-	PUNCT
ejpam-4060	165	37	cl(a	cl(a	NUM
ejpam-4060	165	38	)	)	PUNCT
ejpam-4060	165	39	=	=	SYM
ejpam-4060	165	40	⋂	⋂	PROPN
ejpam-4060	165	41	{	{	PUNCT
ejpam-4060	165	42	f	f	NOUN
ejpam-4060	165	43	:	:	PUNCT
ejpam-4060	165	44	f	f	PROPN
ejpam-4060	165	45	is	be	AUX
ejpam-4060	165	46	(	(	PUNCT
ejpam-4060	165	47	i	i	NOUN
ejpam-4060	165	48	,	,	PUNCT
ejpam-4060	165	49	j)-ψgs	j)-ψgs	ADV
ejpam-4060	165	50	-	-	PUNCT
ejpam-4060	165	51	closed	closed	ADJ
ejpam-4060	165	52	and	and	CCONJ
ejpam-4060	165	53	a	a	DET
ejpam-4060	165	54	⊆	⊆	NUM
ejpam-4060	165	55	f	f	NOUN
ejpam-4060	165	56	}	}	PUNCT
ejpam-4060	165	57	.	.	PUNCT
ejpam-4060	166	1	proof	proof	NOUN
ejpam-4060	166	2	.	.	PUNCT
ejpam-4060	167	1	let	let	VERB
ejpam-4060	167	2	x	x	X
ejpam-4060	167	3	∈	∈	PROPN
ejpam-4060	167	4	(	(	PUNCT
ejpam-4060	167	5	i	i	NOUN
ejpam-4060	167	6	,	,	PUNCT
ejpam-4060	167	7	j)-ψgs	j)-ψgs	ADV
ejpam-4060	167	8	-	-	PUNCT
ejpam-4060	167	9	cl(a	cl(a	NUM
ejpam-4060	167	10	)	)	PUNCT
ejpam-4060	167	11	.	.	PUNCT
ejpam-4060	168	1	then	then	ADV
ejpam-4060	168	2	o	o	X
ejpam-4060	168	3	∩	∩	PROPN
ejpam-4060	168	4	a	a	DET
ejpam-4060	168	5	̸=	̸=	PROPN
ejpam-4060	168	6	∅	∅	NOUN
ejpam-4060	168	7	for	for	ADP
ejpam-4060	168	8	every	every	DET
ejpam-4060	168	9	(	(	PUNCT
ejpam-4060	168	10	i	i	NOUN
ejpam-4060	168	11	,	,	PUNCT
ejpam-4060	168	12	j)-ψgs	j)-ψgs	ADV
ejpam-4060	168	13	-	-	ADJ
ejpam-4060	168	14	open	open	ADJ
ejpam-4060	168	15	set	set	VERB
ejpam-4060	168	16	o	o	NOUN
ejpam-4060	168	17	containing	contain	VERB
ejpam-4060	168	18	x.	x.	NOUN
ejpam-4060	168	19	suppose	suppose	VERB
ejpam-4060	168	20	x	x	X
ejpam-4060	168	21	/∈	/∈	PUNCT
ejpam-4060	169	1	∩{f	∩{f	NOUN
ejpam-4060	169	2	:	:	PUNCT
ejpam-4060	169	3	f	f	PROPN
ejpam-4060	169	4	is	be	AUX
ejpam-4060	169	5	(	(	PUNCT
ejpam-4060	169	6	i	i	NOUN
ejpam-4060	169	7	,	,	PUNCT
ejpam-4060	169	8	j)-ψgs	j)-ψgs	ADV
ejpam-4060	169	9	-	-	PUNCT
ejpam-4060	169	10	closed	closed	ADJ
ejpam-4060	169	11	and	and	CCONJ
ejpam-4060	169	12	a	a	DET
ejpam-4060	169	13	⊆	⊆	NUM
ejpam-4060	169	14	f	f	NOUN
ejpam-4060	169	15	}	}	PUNCT
ejpam-4060	169	16	.	.	PUNCT
ejpam-4060	170	1	it	it	PRON
ejpam-4060	170	2	follows	follow	VERB
ejpam-4060	170	3	that	that	SCONJ
ejpam-4060	170	4	there	there	PRON
ejpam-4060	170	5	exists	exist	VERB
ejpam-4060	170	6	(	(	PUNCT
ejpam-4060	170	7	i	i	PRON
ejpam-4060	170	8	,	,	PUNCT
ejpam-4060	170	9	j)-ψgs	j)-ψgs	ADV
ejpam-4060	170	10	-	-	PUNCT
ejpam-4060	170	11	closed	closed	ADJ
ejpam-4060	170	12	f0	f0	NOUN
ejpam-4060	170	13	such	such	ADJ
ejpam-4060	170	14	that	that	SCONJ
ejpam-4060	170	15	a	a	DET
ejpam-4060	170	16	⊆	⊆	NUM
ejpam-4060	170	17	f0	f0	NOUN
ejpam-4060	170	18	and	and	CCONJ
ejpam-4060	170	19	x	x	SYM
ejpam-4060	170	20	∈	∈	PROPN
ejpam-4060	170	21	x∖f0	x∖f0	PROPN
ejpam-4060	170	22	.	.	PUNCT
ejpam-4060	171	1	note	note	VERB
ejpam-4060	171	2	that	that	SCONJ
ejpam-4060	171	3	x∖f0	x∖f0	PROPN
ejpam-4060	171	4	is	be	AUX
ejpam-4060	171	5	(	(	PUNCT
ejpam-4060	171	6	i	i	INTJ
ejpam-4060	171	7	,	,	PUNCT
ejpam-4060	171	8	j)-ψgs	j)-ψgs	ADV
ejpam-4060	171	9	-	-	ADJ
ejpam-4060	171	10	open	open	ADJ
ejpam-4060	171	11	set	set	NOUN
ejpam-4060	171	12	containing	contain	VERB
ejpam-4060	171	13	x	x	PUNCT
ejpam-4060	171	14	such	such	ADJ
ejpam-4060	171	15	that	that	PRON
ejpam-4060	171	16	(	(	PUNCT
ejpam-4060	171	17	x∖f0	x∖f0	X
ejpam-4060	171	18	)	)	PUNCT
ejpam-4060	171	19	∩a	∩a	NOUN
ejpam-4060	172	1	=	=	PUNCT
ejpam-4060	173	1	∅	∅	NOUN
ejpam-4060	173	2	,	,	PUNCT
ejpam-4060	173	3	a	a	DET
ejpam-4060	173	4	contradiction	contradiction	NOUN
ejpam-4060	173	5	.	.	PUNCT
ejpam-4060	174	1	thus	thus	ADV
ejpam-4060	174	2	x	x	SYM
ejpam-4060	174	3	∈	∈	PROPN
ejpam-4060	174	4	∩{f	∩{f	NOUN
ejpam-4060	174	5	:	:	PUNCT
ejpam-4060	174	6	f	f	PROPN
ejpam-4060	174	7	is	be	AUX
ejpam-4060	174	8	(	(	PUNCT
ejpam-4060	174	9	i	i	NOUN
ejpam-4060	174	10	,	,	PUNCT
ejpam-4060	174	11	j)-ψgs	j)-ψgs	ADV
ejpam-4060	174	12	-	-	PUNCT
ejpam-4060	174	13	closed	closed	ADJ
ejpam-4060	174	14	and	and	CCONJ
ejpam-4060	174	15	a	a	DET
ejpam-4060	174	16	⊆	⊆	NUM
ejpam-4060	174	17	f	f	NOUN
ejpam-4060	174	18	}	}	PUNCT
ejpam-4060	174	19	.	.	PUNCT
ejpam-4060	175	1	references	reference	NOUN
ejpam-4060	175	2	1281	1281	NUM
ejpam-4060	175	3	next	next	ADV
ejpam-4060	175	4	,	,	PUNCT
ejpam-4060	175	5	let	let	VERB
ejpam-4060	175	6	y	y	PROPN
ejpam-4060	175	7	∈	∈	PROPN
ejpam-4060	175	8	∩{f	∩{f	PROPN
ejpam-4060	175	9	:	:	PUNCT
ejpam-4060	175	10	f	f	PROPN
ejpam-4060	175	11	is	be	AUX
ejpam-4060	175	12	(	(	PUNCT
ejpam-4060	175	13	i	i	NOUN
ejpam-4060	175	14	,	,	PUNCT
ejpam-4060	175	15	j)-ψgs	j)-ψgs	ADV
ejpam-4060	175	16	-	-	PUNCT
ejpam-4060	175	17	closed	closed	ADJ
ejpam-4060	175	18	and	and	CCONJ
ejpam-4060	175	19	a	a	DET
ejpam-4060	175	20	⊆	⊆	NUM
ejpam-4060	175	21	f	f	NOUN
ejpam-4060	175	22	}	}	PUNCT
ejpam-4060	175	23	.	.	PUNCT
ejpam-4060	176	1	then	then	ADV
ejpam-4060	176	2	y	y	PROPN
ejpam-4060	176	3	∈	∈	PROPN
ejpam-4060	176	4	f	f	PROPN
ejpam-4060	176	5	for	for	ADP
ejpam-4060	176	6	all	all	PRON
ejpam-4060	176	7	(	(	PUNCT
ejpam-4060	176	8	i	i	PROPN
ejpam-4060	176	9	,	,	PUNCT
ejpam-4060	176	10	j)-ψgsclosed	j)-ψgsclose	VERB
ejpam-4060	176	11	such	such	ADJ
ejpam-4060	176	12	that	that	SCONJ
ejpam-4060	176	13	a	a	DET
ejpam-4060	176	14	⊆	⊆	NUM
ejpam-4060	176	15	f	f	X
ejpam-4060	176	16	.	.	PUNCT
ejpam-4060	177	1	suppose	suppose	VERB
ejpam-4060	177	2	on	on	ADP
ejpam-4060	177	3	the	the	DET
ejpam-4060	177	4	contrary	contrary	NOUN
ejpam-4060	177	5	,	,	PUNCT
ejpam-4060	177	6	y	y	PROPN
ejpam-4060	177	7	/∈	/∈	PUNCT
ejpam-4060	178	1	(	(	PUNCT
ejpam-4060	178	2	i	i	NOUN
ejpam-4060	178	3	,	,	PUNCT
ejpam-4060	178	4	j)-ψgs	j)-ψgs	ADV
ejpam-4060	178	5	-	-	PUNCT
ejpam-4060	178	6	cl(a	cl(a	NUM
ejpam-4060	178	7	)	)	PUNCT
ejpam-4060	178	8	.	.	PUNCT
ejpam-4060	179	1	it	it	PRON
ejpam-4060	179	2	implies	imply	VERB
ejpam-4060	179	3	that	that	SCONJ
ejpam-4060	179	4	u	u	PROPN
ejpam-4060	179	5	∩	∩	NOUN
ejpam-4060	179	6	a	a	DET
ejpam-4060	179	7	=	=	NOUN
ejpam-4060	179	8	∅	∅	NOUN
ejpam-4060	179	9	for	for	ADP
ejpam-4060	179	10	some	some	PRON
ejpam-4060	179	11	(	(	PUNCT
ejpam-4060	179	12	i	i	NOUN
ejpam-4060	179	13	,	,	PUNCT
ejpam-4060	179	14	j)-ψgs	j)-ψgs	ADV
ejpam-4060	179	15	-	-	PUNCT
ejpam-4060	179	16	closed	closed	ADJ
ejpam-4060	179	17	set	set	ADJ
ejpam-4060	179	18	u	u	NOUN
ejpam-4060	179	19	containing	contain	VERB
ejpam-4060	179	20	y.	y.	NOUN
ejpam-4060	179	21	hence	hence	ADV
ejpam-4060	179	22	there	there	PRON
ejpam-4060	179	23	exists	exist	VERB
ejpam-4060	179	24	(	(	PUNCT
ejpam-4060	179	25	i	i	PROPN
ejpam-4060	179	26	,	,	PUNCT
ejpam-4060	179	27	j)-ψgsclosed	j)-ψgsclose	VERB
ejpam-4060	179	28	set	set	VERB
ejpam-4060	179	29	x∖u	x∖u	PROPN
ejpam-4060	180	1	such	such	ADJ
ejpam-4060	180	2	that	that	DET
ejpam-4060	180	3	y	y	PROPN
ejpam-4060	180	4	/∈	/∈	PUNCT
ejpam-4060	180	5	x∖u	x∖u	PROPN
ejpam-4060	180	6	and	and	CCONJ
ejpam-4060	180	7	a	a	DET
ejpam-4060	180	8	⊆	⊆	NUM
ejpam-4060	180	9	x∖u	x∖u	PROPN
ejpam-4060	180	10	,	,	PUNCT
ejpam-4060	180	11	a	a	DET
ejpam-4060	180	12	contradiction	contradiction	NOUN
ejpam-4060	180	13	.	.	PUNCT
ejpam-4060	181	1	consequently	consequently	ADV
ejpam-4060	181	2	,	,	PUNCT
ejpam-4060	181	3	y	y	PROPN
ejpam-4060	181	4	∈	∈	PROPN
ejpam-4060	181	5	(	(	PUNCT
ejpam-4060	181	6	i	i	NOUN
ejpam-4060	181	7	,	,	PUNCT
ejpam-4060	181	8	j)-ψgs	j)-ψgs	ADV
ejpam-4060	181	9	-	-	PUNCT
ejpam-4060	181	10	cl(a	cl(a	NUM
ejpam-4060	181	11	)	)	PUNCT
ejpam-4060	181	12	.	.	PUNCT
ejpam-4060	182	1	theorem	theorem	NOUN
ejpam-4060	182	2	7	7	NUM
ejpam-4060	182	3	indicates	indicate	VERB
ejpam-4060	182	4	that	that	SCONJ
ejpam-4060	182	5	(	(	PUNCT
ejpam-4060	182	6	i	i	PRON
ejpam-4060	182	7	,	,	PUNCT
ejpam-4060	182	8	j)-ψgs	j)-ψgs	ADV
ejpam-4060	182	9	-	-	PUNCT
ejpam-4060	182	10	cl(a	cl(a	X
ejpam-4060	182	11	)	)	PUNCT
ejpam-4060	182	12	contains	contain	VERB
ejpam-4060	182	13	a	a	PRON
ejpam-4060	182	14	since	since	SCONJ
ejpam-4060	182	15	the	the	DET
ejpam-4060	182	16	intersection	intersection	NOUN
ejpam-4060	182	17	of	of	ADP
ejpam-4060	182	18	all	all	DET
ejpam-4060	182	19	(	(	PUNCT
ejpam-4060	182	20	i	i	NOUN
ejpam-4060	182	21	,	,	PUNCT
ejpam-4060	182	22	j)-ψgs	j)-ψgs	ADV
ejpam-4060	182	23	-	-	PUNCT
ejpam-4060	182	24	closed	closed	ADJ
ejpam-4060	182	25	sets	set	NOUN
ejpam-4060	182	26	contains	contain	VERB
ejpam-4060	182	27	a.	a.	NOUN
ejpam-4060	182	28	now	now	ADV
ejpam-4060	182	29	theorem	theorem	VERB
ejpam-4060	182	30	4	4	NUM
ejpam-4060	182	31	implies	imply	VERB
ejpam-4060	182	32	that	that	SCONJ
ejpam-4060	182	33	the	the	DET
ejpam-4060	182	34	arbitrary	arbitrary	ADJ
ejpam-4060	182	35	intersection	intersection	NOUN
ejpam-4060	182	36	of	of	ADP
ejpam-4060	182	37	(	(	PUNCT
ejpam-4060	182	38	i	i	PROPN
ejpam-4060	182	39	,	,	PUNCT
ejpam-4060	182	40	j)-ψgs	j)-ψgs	ADV
ejpam-4060	182	41	-	-	PUNCT
ejpam-4060	182	42	closed	closed	ADJ
ejpam-4060	182	43	sets	set	NOUN
ejpam-4060	182	44	is	be	AUX
ejpam-4060	182	45	also	also	ADV
ejpam-4060	182	46	(	(	PUNCT
ejpam-4060	182	47	i	i	INTJ
ejpam-4060	182	48	,	,	PUNCT
ejpam-4060	182	49	j)-ψgs	j)-ψgs	ADV
ejpam-4060	182	50	-	-	PUNCT
ejpam-4060	182	51	closed	closed	ADJ
ejpam-4060	182	52	,	,	PUNCT
ejpam-4060	182	53	thus	thus	ADV
ejpam-4060	182	54	it	it	PRON
ejpam-4060	182	55	follows	follow	VERB
ejpam-4060	182	56	that	that	SCONJ
ejpam-4060	182	57	(	(	PUNCT
ejpam-4060	182	58	i	i	PRON
ejpam-4060	182	59	,	,	PUNCT
ejpam-4060	182	60	j)-ψgs	j)-ψgs	ADV
ejpam-4060	182	61	-	-	PUNCT
ejpam-4060	182	62	cl(a	cl(a	X
ejpam-4060	182	63	)	)	PUNCT
ejpam-4060	182	64	is	be	AUX
ejpam-4060	182	65	(	(	PUNCT
ejpam-4060	182	66	i	i	INTJ
ejpam-4060	182	67	,	,	PUNCT
ejpam-4060	182	68	j)-ψgs	j)-ψgs	ADV
ejpam-4060	182	69	-	-	PUNCT
ejpam-4060	182	70	closed	closed	ADJ
ejpam-4060	182	71	.	.	PUNCT
ejpam-4060	183	1	hence	hence	ADV
ejpam-4060	183	2	,	,	PUNCT
ejpam-4060	183	3	(	(	PUNCT
ejpam-4060	183	4	i	i	INTJ
ejpam-4060	183	5	,	,	PUNCT
ejpam-4060	183	6	j)-ψgs	j)-ψgs	ADV
ejpam-4060	183	7	-	-	PUNCT
ejpam-4060	183	8	cl(a	cl(a	NUM
ejpam-4060	183	9	)	)	PUNCT
ejpam-4060	183	10	is	be	AUX
ejpam-4060	183	11	the	the	DET
ejpam-4060	183	12	smallest	small	ADJ
ejpam-4060	183	13	(	(	PUNCT
ejpam-4060	183	14	i	i	NOUN
ejpam-4060	183	15	,	,	PUNCT
ejpam-4060	183	16	j)-ψgs	j)-ψgs	ADV
ejpam-4060	183	17	-	-	PUNCT
ejpam-4060	183	18	closed	closed	ADJ
ejpam-4060	183	19	set	set	NOUN
ejpam-4060	183	20	that	that	PRON
ejpam-4060	183	21	contains	contain	VERB
ejpam-4060	183	22	a	a	PRON
ejpam-4060	183	23	,	,	PUNCT
ejpam-4060	183	24	as	as	SCONJ
ejpam-4060	183	25	stated	state	VERB
ejpam-4060	183	26	in	in	ADP
ejpam-4060	183	27	the	the	DET
ejpam-4060	183	28	following	follow	VERB
ejpam-4060	183	29	remark	remark	NOUN
ejpam-4060	183	30	.	.	PUNCT
ejpam-4060	184	1	remark	remark	PROPN
ejpam-4060	184	2	2	2	NUM
ejpam-4060	184	3	.	.	PUNCT
ejpam-4060	185	1	let	let	AUX
ejpam-4060	185	2	(	(	PUNCT
ejpam-4060	185	3	x	x	NOUN
ejpam-4060	185	4	,	,	PUNCT
ejpam-4060	185	5	τ1	τ1	NOUN
ejpam-4060	185	6	,	,	PUNCT
ejpam-4060	185	7	τ2	τ2	PROPN
ejpam-4060	185	8	)	)	PUNCT
ejpam-4060	185	9	be	be	VERB
ejpam-4060	185	10	a	a	DET
ejpam-4060	185	11	bitopological	bitopological	ADJ
ejpam-4060	185	12	space	space	NOUN
ejpam-4060	185	13	and	and	CCONJ
ejpam-4060	185	14	a	a	PRON
ejpam-4060	185	15	,	,	PUNCT
ejpam-4060	185	16	b	b	PROPN
ejpam-4060	185	17	⊆	⊆	NUM
ejpam-4060	185	18	x.	x.	NOUN
ejpam-4060	185	19	then	then	ADV
ejpam-4060	185	20	the	the	DET
ejpam-4060	185	21	following	follow	VERB
ejpam-4060	185	22	hold	hold	NOUN
ejpam-4060	185	23	:	:	PUNCT
ejpam-4060	185	24	(	(	PUNCT
ejpam-4060	185	25	i	i	NOUN
ejpam-4060	185	26	)	)	PUNCT
ejpam-4060	185	27	a	a	PRON
ejpam-4060	185	28	⊆	⊆	NUM
ejpam-4060	185	29	(	(	PUNCT
ejpam-4060	185	30	i	i	NOUN
ejpam-4060	185	31	,	,	PUNCT
ejpam-4060	185	32	j)-ψgs	j)-ψgs	ADV
ejpam-4060	185	33	-	-	PUNCT
ejpam-4060	185	34	cl(a	cl(a	NUM
ejpam-4060	185	35	)	)	PUNCT
ejpam-4060	185	36	;	;	PUNCT
ejpam-4060	185	37	(	(	PUNCT
ejpam-4060	185	38	ii	ii	NOUN
ejpam-4060	185	39	)	)	PUNCT
ejpam-4060	185	40	(	(	PUNCT
ejpam-4060	185	41	i	i	NOUN
ejpam-4060	185	42	,	,	PUNCT
ejpam-4060	185	43	j)-ψgs	j)-ψgs	ADV
ejpam-4060	185	44	-	-	PUNCT
ejpam-4060	185	45	cl(a	cl(a	X
ejpam-4060	185	46	)	)	PUNCT
ejpam-4060	185	47	is	be	AUX
ejpam-4060	185	48	(	(	PUNCT
ejpam-4060	185	49	i	i	INTJ
ejpam-4060	185	50	,	,	PUNCT
ejpam-4060	185	51	j)-ψgs	j)-ψgs	ADV
ejpam-4060	185	52	-	-	PUNCT
ejpam-4060	185	53	closed	closed	ADJ
ejpam-4060	185	54	set	set	NOUN
ejpam-4060	185	55	;	;	PUNCT
ejpam-4060	185	56	and	and	CCONJ
ejpam-4060	185	57	(	(	PUNCT
ejpam-4060	185	58	iii	iii	X
ejpam-4060	185	59	)	)	PUNCT
ejpam-4060	185	60	if	if	SCONJ
ejpam-4060	185	61	a	a	DET
ejpam-4060	185	62	⊆	⊆	NUM
ejpam-4060	185	63	b	b	NOUN
ejpam-4060	185	64	such	such	DET
ejpam-4060	185	65	that	that	DET
ejpam-4060	185	66	b	b	NOUN
ejpam-4060	185	67	is	be	AUX
ejpam-4060	185	68	(	(	PUNCT
ejpam-4060	185	69	i	i	NOUN
ejpam-4060	185	70	,	,	PUNCT
ejpam-4060	185	71	j)-ψgs	j)-ψgs	ADV
ejpam-4060	185	72	-	-	PUNCT
ejpam-4060	185	73	closed	closed	ADJ
ejpam-4060	185	74	set	set	NOUN
ejpam-4060	185	75	,	,	PUNCT
ejpam-4060	185	76	then	then	ADV
ejpam-4060	185	77	(	(	PUNCT
ejpam-4060	185	78	i	i	NOUN
ejpam-4060	185	79	,	,	PUNCT
ejpam-4060	185	80	j)-ψgs	j)-ψgs	ADV
ejpam-4060	185	81	-	-	PUNCT
ejpam-4060	185	82	cl(a	cl(a	NUM
ejpam-4060	185	83	)	)	PUNCT
ejpam-4060	185	84	⊆	⊆	PROPN
ejpam-4060	185	85	b.	b.	NOUN
ejpam-4060	185	86	theorem	theorem	VERB
ejpam-4060	185	87	8	8	NUM
ejpam-4060	185	88	.	.	PUNCT
ejpam-4060	186	1	a	a	PRON
ejpam-4060	186	2	is	be	AUX
ejpam-4060	186	3	(	(	PUNCT
ejpam-4060	186	4	i	i	PROPN
ejpam-4060	186	5	,	,	PUNCT
ejpam-4060	186	6	j)-ψgs	j)-ψgs	ADV
ejpam-4060	186	7	-	-	PUNCT
ejpam-4060	186	8	closed	closed	ADJ
ejpam-4060	186	9	set	set	NOUN
ejpam-4060	186	10	,	,	PUNCT
ejpam-4060	186	11	if	if	SCONJ
ejpam-4060	186	12	and	and	CCONJ
ejpam-4060	186	13	only	only	ADV
ejpam-4060	186	14	if	if	SCONJ
ejpam-4060	186	15	(	(	PUNCT
ejpam-4060	186	16	i	i	NOUN
ejpam-4060	186	17	,	,	PUNCT
ejpam-4060	186	18	j)-ψgs	j)-ψgs	ADV
ejpam-4060	186	19	-	-	PUNCT
ejpam-4060	186	20	cl(a	cl(a	NUM
ejpam-4060	186	21	)	)	PUNCT
ejpam-4060	186	22	=	=	SYM
ejpam-4060	186	23	a.	a.	NOUN
ejpam-4060	186	24	proof	proof	NOUN
ejpam-4060	186	25	.	.	PUNCT
ejpam-4060	187	1	let	let	VERB
ejpam-4060	187	2	a	a	DET
ejpam-4060	187	3	be	be	AUX
ejpam-4060	187	4	(	(	PUNCT
ejpam-4060	187	5	i	i	NOUN
ejpam-4060	187	6	,	,	PUNCT
ejpam-4060	187	7	j)-ψgs	j)-ψgs	ADV
ejpam-4060	187	8	-	-	PUNCT
ejpam-4060	187	9	closed	closed	ADJ
ejpam-4060	187	10	set	set	NOUN
ejpam-4060	187	11	and	and	CCONJ
ejpam-4060	187	12	x	x	SYM
ejpam-4060	187	13	∈	∈	PROPN
ejpam-4060	187	14	(	(	PUNCT
ejpam-4060	187	15	i	i	NOUN
ejpam-4060	187	16	,	,	PUNCT
ejpam-4060	187	17	j)-ψgs	j)-ψgs	ADV
ejpam-4060	187	18	-	-	PUNCT
ejpam-4060	187	19	cl(a	cl(a	NUM
ejpam-4060	187	20	)	)	PUNCT
ejpam-4060	187	21	.	.	PUNCT
ejpam-4060	188	1	then	then	ADV
ejpam-4060	188	2	for	for	ADP
ejpam-4060	188	3	all	all	PRON
ejpam-4060	188	4	(	(	PUNCT
ejpam-4060	188	5	i	i	NOUN
ejpam-4060	188	6	,	,	PUNCT
ejpam-4060	188	7	j)-ψgsopen	j)-ψgsopen	PUNCT
ejpam-4060	188	8	set	set	VERB
ejpam-4060	188	9	u	u	PRON
ejpam-4060	188	10	containing	contain	VERB
ejpam-4060	188	11	x	x	PRON
ejpam-4060	188	12	,	,	PUNCT
ejpam-4060	188	13	we	we	PRON
ejpam-4060	188	14	have	have	VERB
ejpam-4060	188	15	u	u	NOUN
ejpam-4060	188	16	∩	∩	NOUN
ejpam-4060	188	17	a	a	DET
ejpam-4060	188	18	̸=	̸=	PROPN
ejpam-4060	188	19	∅.	∅.	ADV
ejpam-4060	188	20	suppose	suppose	VERB
ejpam-4060	188	21	on	on	ADP
ejpam-4060	188	22	the	the	DET
ejpam-4060	188	23	contrary	contrary	NOUN
ejpam-4060	188	24	,	,	PUNCT
ejpam-4060	188	25	x	x	PUNCT
ejpam-4060	188	26	/∈	/∈	PUNCT
ejpam-4060	189	1	a.	a.	NOUN
ejpam-4060	189	2	then	then	ADV
ejpam-4060	189	3	x	x	SYM
ejpam-4060	189	4	∈	∈	PROPN
ejpam-4060	189	5	x∖a	x∖a	PROPN
ejpam-4060	189	6	where	where	SCONJ
ejpam-4060	189	7	x∖a	x∖a	PROPN
ejpam-4060	189	8	is	be	AUX
ejpam-4060	189	9	(	(	PUNCT
ejpam-4060	189	10	i	i	NOUN
ejpam-4060	189	11	,	,	PUNCT
ejpam-4060	189	12	j)-ψgs	j)-ψgs	ADV
ejpam-4060	189	13	-	-	PUNCT
ejpam-4060	189	14	open	open	ADJ
ejpam-4060	189	15	and	and	CCONJ
ejpam-4060	189	16	(	(	PUNCT
ejpam-4060	189	17	x∖a	x∖a	PROPN
ejpam-4060	189	18	)	)	PUNCT
ejpam-4060	189	19	∩	∩	NOUN
ejpam-4060	189	20	a	a	DET
ejpam-4060	189	21	=	=	NOUN
ejpam-4060	189	22	∅	∅	NOUN
ejpam-4060	189	23	,	,	PUNCT
ejpam-4060	189	24	a	a	DET
ejpam-4060	189	25	contradiction	contradiction	NOUN
ejpam-4060	189	26	since	since	SCONJ
ejpam-4060	189	27	x	x	PROPN
ejpam-4060	189	28	∈	∈	PROPN
ejpam-4060	189	29	(	(	PUNCT
ejpam-4060	189	30	i	i	NOUN
ejpam-4060	189	31	,	,	PUNCT
ejpam-4060	189	32	j)-ψgs	j)-ψgs	ADV
ejpam-4060	189	33	-	-	PUNCT
ejpam-4060	189	34	cl(a	cl(a	NUM
ejpam-4060	189	35	)	)	PUNCT
ejpam-4060	189	36	.	.	PUNCT
ejpam-4060	190	1	thus	thus	ADV
ejpam-4060	190	2	x	x	X
ejpam-4060	190	3	∈	∈	PROPN
ejpam-4060	190	4	a	a	PRON
ejpam-4060	190	5	,	,	PUNCT
ejpam-4060	190	6	and	and	CCONJ
ejpam-4060	190	7	so	so	ADV
ejpam-4060	190	8	(	(	PUNCT
ejpam-4060	190	9	i	i	NOUN
ejpam-4060	190	10	,	,	PUNCT
ejpam-4060	190	11	j)-ψgs	j)-ψgs	ADV
ejpam-4060	190	12	-	-	PUNCT
ejpam-4060	190	13	cl(a	cl(a	NUM
ejpam-4060	190	14	)	)	PUNCT
ejpam-4060	190	15	⊆	⊆	NUM
ejpam-4060	190	16	a.	a.	NOUN
ejpam-4060	190	17	note	note	NOUN
ejpam-4060	190	18	that	that	SCONJ
ejpam-4060	190	19	by	by	ADP
ejpam-4060	190	20	remark	remark	NOUN
ejpam-4060	190	21	2	2	NUM
ejpam-4060	190	22	(	(	PUNCT
ejpam-4060	190	23	i	i	NOUN
ejpam-4060	190	24	)	)	PUNCT
ejpam-4060	190	25	,	,	PUNCT
ejpam-4060	190	26	a	a	DET
ejpam-4060	190	27	⊆	⊆	NUM
ejpam-4060	190	28	(	(	PUNCT
ejpam-4060	190	29	i	i	NOUN
ejpam-4060	190	30	,	,	PUNCT
ejpam-4060	190	31	j)-ψgs	j)-ψgs	ADV
ejpam-4060	190	32	-	-	PUNCT
ejpam-4060	190	33	cl(a	cl(a	NUM
ejpam-4060	190	34	)	)	PUNCT
ejpam-4060	190	35	,	,	PUNCT
ejpam-4060	190	36	and	and	CCONJ
ejpam-4060	190	37	hence	hence	ADV
ejpam-4060	190	38	(	(	PUNCT
ejpam-4060	190	39	i	i	INTJ
ejpam-4060	190	40	,	,	PUNCT
ejpam-4060	190	41	j)-ψgs	j)-ψgs	ADV
ejpam-4060	190	42	-	-	PUNCT
ejpam-4060	190	43	cl(a	cl(a	NUM
ejpam-4060	190	44	)	)	PUNCT
ejpam-4060	190	45	=	=	SYM
ejpam-4060	190	46	a.	a.	NOUN
ejpam-4060	190	47	conversely	conversely	ADV
ejpam-4060	190	48	,	,	PUNCT
ejpam-4060	190	49	suppose	suppose	VERB
ejpam-4060	190	50	(	(	PUNCT
ejpam-4060	190	51	i	i	NOUN
ejpam-4060	190	52	,	,	PUNCT
ejpam-4060	190	53	j)-ψgs	j)-ψgs	ADV
ejpam-4060	190	54	-	-	PUNCT
ejpam-4060	190	55	cl(a	cl(a	NUM
ejpam-4060	190	56	)	)	PUNCT
ejpam-4060	190	57	=	=	PUNCT
ejpam-4060	190	58	a.	a.	NOUN
ejpam-4060	190	59	by	by	ADP
ejpam-4060	190	60	remark	remark	NOUN
ejpam-4060	190	61	2	2	NUM
ejpam-4060	190	62	(	(	PUNCT
ejpam-4060	190	63	ii	ii	NOUN
ejpam-4060	190	64	)	)	PUNCT
ejpam-4060	190	65	,	,	PUNCT
ejpam-4060	190	66	(	(	PUNCT
ejpam-4060	190	67	i	i	INTJ
ejpam-4060	190	68	,	,	PUNCT
ejpam-4060	190	69	j)-ψgs	j)-ψgs	ADV
ejpam-4060	190	70	-	-	PUNCT
ejpam-4060	190	71	cl(a	cl(a	X
ejpam-4060	190	72	)	)	PUNCT
ejpam-4060	190	73	is	be	AUX
ejpam-4060	190	74	(	(	PUNCT
ejpam-4060	190	75	i	i	INTJ
ejpam-4060	190	76	,	,	PUNCT
ejpam-4060	190	77	j)-ψgs	j)-ψgs	ADV
ejpam-4060	190	78	-	-	PUNCT
ejpam-4060	190	79	closed	closed	ADJ
ejpam-4060	190	80	set	set	NOUN
ejpam-4060	190	81	,	,	PUNCT
ejpam-4060	190	82	and	and	CCONJ
ejpam-4060	190	83	so	so	ADV
ejpam-4060	190	84	a	a	PRON
ejpam-4060	190	85	is	be	AUX
ejpam-4060	190	86	(	(	PUNCT
ejpam-4060	190	87	i	i	NOUN
ejpam-4060	190	88	,	,	PUNCT
ejpam-4060	190	89	j)-ψgs	j)-ψgs	ADV
ejpam-4060	190	90	-	-	PUNCT
ejpam-4060	190	91	closed	closed	ADJ
ejpam-4060	190	92	set	set	NOUN
ejpam-4060	190	93	.	.	PUNCT
ejpam-4060	191	1	acknowledgements	acknowledgement	NOUN
ejpam-4060	191	2	we	we	PRON
ejpam-4060	191	3	are	be	AUX
ejpam-4060	191	4	thankful	thankful	ADJ
ejpam-4060	191	5	to	to	ADP
ejpam-4060	191	6	the	the	DET
ejpam-4060	191	7	bukidnon	bukidnon	NOUN
ejpam-4060	191	8	state	state	PROPN
ejpam-4060	191	9	university	university	PROPN
ejpam-4060	191	10	research	research	NOUN
ejpam-4060	191	11	unit	unit	NOUN
ejpam-4060	191	12	for	for	ADP
ejpam-4060	191	13	the	the	DET
ejpam-4060	191	14	financial	financial	ADJ
ejpam-4060	191	15	assistance	assistance	NOUN
ejpam-4060	191	16	.	.	PUNCT
ejpam-4060	192	1	references	reference	NOUN
ejpam-4060	192	2	[	[	X
ejpam-4060	192	3	1	1	X
ejpam-4060	192	4	]	]	PUNCT
ejpam-4060	192	5	p.	p.	NOUN
ejpam-4060	192	6	bhattacharyya	bhattacharyya	PROPN
ejpam-4060	192	7	and	and	CCONJ
ejpam-4060	192	8	b.k	b.k	PROPN
ejpam-4060	192	9	.	.	PROPN
ejpam-4060	193	1	lahiri	lahiri	PROPN
ejpam-4060	193	2	.	.	PUNCT
ejpam-4060	194	1	semi	semi	ADJ
ejpam-4060	194	2	-	-	ADJ
ejpam-4060	194	3	generalized	generalized	ADJ
ejpam-4060	194	4	closed	closed	ADJ
ejpam-4060	194	5	sets	set	NOUN
ejpam-4060	194	6	in	in	ADP
ejpam-4060	194	7	topology	topology	NOUN
ejpam-4060	194	8	.	.	PUNCT
ejpam-4060	195	1	indian	indian	PROPN
ejpam-4060	195	2	j.	j.	PROPN
ejpam-4060	195	3	math	math	PROPN
ejpam-4060	195	4	.	.	PUNCT
ejpam-4060	195	5	,	,	PUNCT
ejpam-4060	196	1	29:376–382	29:376–382	NUM
ejpam-4060	196	2	,	,	PUNCT
ejpam-4060	196	3	1987	1987	NUM
ejpam-4060	196	4	.	.	PUNCT
ejpam-4060	197	1	[	[	X
ejpam-4060	197	2	2	2	X
ejpam-4060	197	3	]	]	PUNCT
ejpam-4060	197	4	s.	s.	PROPN
ejpam-4060	197	5	bose	bose	PROPN
ejpam-4060	197	6	.	.	PUNCT
ejpam-4060	198	1	semi	semi	VERB
ejpam-4060	198	2	open	open	ADJ
ejpam-4060	198	3	sets	set	NOUN
ejpam-4060	198	4	,	,	PUNCT
ejpam-4060	198	5	semi	semi	ADV
ejpam-4060	198	6	continuity	continuity	NOUN
ejpam-4060	198	7	and	and	CCONJ
ejpam-4060	198	8	semi	semi	ADJ
ejpam-4060	198	9	open	open	ADJ
ejpam-4060	198	10	mappings	mapping	NOUN
ejpam-4060	198	11	in	in	ADP
ejpam-4060	198	12	bitopological	bitopological	ADJ
ejpam-4060	198	13	spaces	space	NOUN
ejpam-4060	198	14	.	.	PUNCT
ejpam-4060	199	1	bull	bull	NOUN
ejpam-4060	199	2	.	.	PUNCT
ejpam-4060	200	1	cal	cal	PROPN
ejpam-4060	200	2	.	.	PUNCT
ejpam-4060	201	1	math	math	NOUN
ejpam-4060	201	2	.	.	PUNCT
ejpam-4060	202	1	soc	soc	PROPN
ejpam-4060	202	2	.	.	PUNCT
ejpam-4060	202	3	,	,	PUNCT
ejpam-4060	202	4	73:237–246	73:237–246	PROPN
ejpam-4060	202	5	,	,	PUNCT
ejpam-4060	202	6	1981	1981	NUM
ejpam-4060	202	7	.	.	PUNCT
ejpam-4060	203	1	[	[	X
ejpam-4060	203	2	3	3	X
ejpam-4060	203	3	]	]	X
ejpam-4060	203	4	g.	g.	PROPN
ejpam-4060	203	5	şenel	şenel	PROPN
ejpam-4060	203	6	.	.	PUNCT
ejpam-4060	204	1	a	a	DET
ejpam-4060	204	2	new	new	ADJ
ejpam-4060	204	3	approach	approach	NOUN
ejpam-4060	204	4	to	to	ADP
ejpam-4060	204	5	hausdorff	hausdorff	NOUN
ejpam-4060	204	6	space	space	NOUN
ejpam-4060	204	7	theory	theory	NOUN
ejpam-4060	204	8	via	via	ADP
ejpam-4060	204	9	the	the	DET
ejpam-4060	204	10	soft	soft	ADJ
ejpam-4060	204	11	sets	set	NOUN
ejpam-4060	204	12	.	.	PUNCT
ejpam-4060	205	1	mathematical	mathematical	ADJ
ejpam-4060	205	2	problems	problem	NOUN
ejpam-4060	205	3	in	in	ADP
ejpam-4060	205	4	engineering	engineering	NOUN
ejpam-4060	205	5	,	,	PUNCT
ejpam-4060	205	6	9:1–6	9:1–6	NUM
ejpam-4060	205	7	,	,	PUNCT
ejpam-4060	205	8	2016	2016	NUM
ejpam-4060	205	9	.	.	PUNCT
ejpam-4060	206	1	references	reference	NOUN
ejpam-4060	206	2	1282	1282	NUM
ejpam-4060	206	3	[	[	X
ejpam-4060	206	4	4	4	NUM
ejpam-4060	206	5	]	]	X
ejpam-4060	206	6	g.	g.	PROPN
ejpam-4060	206	7	şenel	şenel	PROPN
ejpam-4060	206	8	.	.	PUNCT
ejpam-4060	207	1	soft	soft	ADJ
ejpam-4060	207	2	topology	topology	NOUN
ejpam-4060	207	3	generated	generate	VERB
ejpam-4060	207	4	by	by	ADP
ejpam-4060	207	5	l	l	NOUN
ejpam-4060	207	6	-	-	ADJ
ejpam-4060	207	7	soft	soft	ADJ
ejpam-4060	207	8	sets	set	NOUN
ejpam-4060	207	9	.	.	PUNCT
ejpam-4060	208	1	journal	journal	NOUN
ejpam-4060	208	2	of	of	ADP
ejpam-4060	208	3	new	new	ADJ
ejpam-4060	208	4	theory	theory	NOUN
ejpam-4060	208	5	,	,	PUNCT
ejpam-4060	208	6	4(24):88	4(24):88	PROPN
ejpam-4060	208	7	–	–	PUNCT
ejpam-4060	208	8	100	100	NUM
ejpam-4060	208	9	,	,	PUNCT
ejpam-4060	208	10	2018	2018	NUM
ejpam-4060	208	11	.	.	PUNCT
ejpam-4060	209	1	[	[	X
ejpam-4060	209	2	5	5	X
ejpam-4060	209	3	]	]	PUNCT
ejpam-4060	209	4	g.	g.	NOUN
ejpam-4060	209	5	şenel	şenel	PROPN
ejpam-4060	209	6	and	and	CCONJ
ejpam-4060	209	7	n.	n.	PROPN
ejpam-4060	209	8	cagman	cagman	PROPN
ejpam-4060	209	9	.	.	PUNCT
ejpam-4060	210	1	soft	soft	ADJ
ejpam-4060	210	2	closed	closed	ADJ
ejpam-4060	210	3	sets	set	NOUN
ejpam-4060	210	4	on	on	ADP
ejpam-4060	210	5	soft	soft	ADJ
ejpam-4060	210	6	bitopological	bitopological	ADJ
ejpam-4060	210	7	space	space	NOUN
ejpam-4060	210	8	.	.	PUNCT
ejpam-4060	211	1	journal	journal	NOUN
ejpam-4060	211	2	of	of	ADP
ejpam-4060	211	3	new	new	ADJ
ejpam-4060	211	4	results	result	NOUN
ejpam-4060	211	5	in	in	ADP
ejpam-4060	211	6	science	science	NOUN
ejpam-4060	211	7	,	,	PUNCT
ejpam-4060	211	8	3(5):57–66	3(5):57–66	NUM
ejpam-4060	211	9	,	,	PUNCT
ejpam-4060	211	10	2014	2014	NUM
ejpam-4060	211	11	.	.	PUNCT
ejpam-4060	212	1	[	[	X
ejpam-4060	212	2	6	6	NUM
ejpam-4060	212	3	]	]	PUNCT
ejpam-4060	212	4	g.	g.	NOUN
ejpam-4060	212	5	şenel	şenel	PROPN
ejpam-4060	212	6	and	and	CCONJ
ejpam-4060	212	7	n.	n.	PROPN
ejpam-4060	212	8	cagman	cagman	PROPN
ejpam-4060	212	9	.	.	PUNCT
ejpam-4060	213	1	soft	soft	ADJ
ejpam-4060	213	2	topological	topological	ADJ
ejpam-4060	213	3	subspaces	subspace	NOUN
ejpam-4060	213	4	.	.	PUNCT
ejpam-4060	214	1	annals	annal	NOUN
ejpam-4060	214	2	of	of	ADP
ejpam-4060	214	3	fuzzy	fuzzy	ADJ
ejpam-4060	214	4	mathematics	mathematic	NOUN
ejpam-4060	214	5	and	and	CCONJ
ejpam-4060	214	6	informatics	informatic	NOUN
ejpam-4060	214	7	,	,	PUNCT
ejpam-4060	214	8	10(4):525–535	10(4):525–535	NUM
ejpam-4060	214	9	,	,	PUNCT
ejpam-4060	214	10	2015	2015	NUM
ejpam-4060	214	11	.	.	PUNCT
ejpam-4060	215	1	[	[	X
ejpam-4060	215	2	7	7	X
ejpam-4060	215	3	]	]	X
ejpam-4060	215	4	t.	t.	NOUN
ejpam-4060	215	5	fukutake	fukutake	NOUN
ejpam-4060	215	6	.	.	PUNCT
ejpam-4060	216	1	on	on	ADP
ejpam-4060	216	2	generalized	generalized	ADJ
ejpam-4060	216	3	closed	closed	ADJ
ejpam-4060	216	4	sets	set	NOUN
ejpam-4060	216	5	in	in	ADP
ejpam-4060	216	6	bitopological	bitopological	ADJ
ejpam-4060	216	7	spaces	space	NOUN
ejpam-4060	216	8	.	.	PUNCT
ejpam-4060	217	1	bull	bull	NOUN
ejpam-4060	217	2	.	.	PUNCT
ejpam-4060	218	1	fukuoka	fukuoka	PROPN
ejpam-4060	218	2	.	.	PUNCT
ejpam-4060	219	1	univ	univ	PROPN
ejpam-4060	219	2	.	.	PROPN
ejpam-4060	220	1	of	of	ADP
ejpam-4060	220	2	educ	educ	PROPN
ejpam-4060	220	3	.	.	PUNCT
ejpam-4060	221	1	,	,	PUNCT
ejpam-4060	221	2	35:19–28	35:19–28	PROPN
ejpam-4060	221	3	,	,	PUNCT
ejpam-4060	221	4	1985	1985	NUM
ejpam-4060	221	5	.	.	PUNCT
ejpam-4060	222	1	[	[	X
ejpam-4060	222	2	8	8	X
ejpam-4060	222	3	]	]	PUNCT
ejpam-4060	222	4	t.	t.	NOUN
ejpam-4060	222	5	fukutake	fukutake	NOUN
ejpam-4060	222	6	.	.	PUNCT
ejpam-4060	223	1	semi	semi	ADV
ejpam-4060	223	2	open	open	ADJ
ejpam-4060	223	3	sets	set	NOUN
ejpam-4060	223	4	on	on	ADP
ejpam-4060	223	5	bitopological	bitopological	ADJ
ejpam-4060	223	6	spaces	space	NOUN
ejpam-4060	223	7	.	.	PUNCT
ejpam-4060	224	1	bull	bull	NOUN
ejpam-4060	224	2	.	.	PUNCT
ejpam-4060	225	1	fukuoka	fukuoka	PROPN
ejpam-4060	225	2	.	.	PUNCT
ejpam-4060	226	1	univ	univ	PROPN
ejpam-4060	226	2	.	.	PROPN
ejpam-4060	227	1	of	of	ADP
ejpam-4060	227	2	educ	educ	PROPN
ejpam-4060	227	3	.	.	PUNCT
ejpam-4060	227	4	,	,	PUNCT
ejpam-4060	227	5	38:1–7	38:1–7	NUM
ejpam-4060	227	6	,	,	PUNCT
ejpam-4060	227	7	1989	1989	NUM
ejpam-4060	227	8	.	.	PUNCT
ejpam-4060	228	1	[	[	X
ejpam-4060	228	2	9	9	NUM
ejpam-4060	228	3	]	]	PUNCT
ejpam-4060	228	4	s.	s.	PROPN
ejpam-4060	228	5	gowsalya	gowsalya	PROPN
ejpam-4060	228	6	and	and	CCONJ
ejpam-4060	228	7	n.	n.	PROPN
ejpam-4060	228	8	balamani	balamani	PROPN
ejpam-4060	228	9	.	.	PUNCT
ejpam-4060	229	1	ψgs	ψgs	ADV
ejpam-4060	229	2	-	-	PUNCT
ejpam-4060	229	3	closed	close	VERB
ejpam-4060	229	4	sets	set	NOUN
ejpam-4060	229	5	in	in	ADP
ejpam-4060	229	6	topological	topological	ADJ
ejpam-4060	229	7	spaces	space	NOUN
ejpam-4060	229	8	.	.	PUNCT
ejpam-4060	230	1	international	international	ADJ
ejpam-4060	230	2	journal	journal	PROPN
ejpam-4060	230	3	of	of	ADP
ejpam-4060	230	4	advance	advance	PROPN
ejpam-4060	230	5	foundation	foundation	NOUN
ejpam-4060	230	6	and	and	CCONJ
ejpam-4060	230	7	research	research	NOUN
ejpam-4060	230	8	in	in	ADP
ejpam-4060	230	9	computer	computer	NOUN
ejpam-4060	230	10	,	,	PUNCT
ejpam-4060	230	11	3(4):52–61	3(4):52–61	NUM
ejpam-4060	230	12	,	,	PUNCT
ejpam-4060	230	13	2016	2016	NUM
ejpam-4060	230	14	.	.	PUNCT
ejpam-4060	231	1	[	[	X
ejpam-4060	231	2	10	10	NUM
ejpam-4060	231	3	]	]	PUNCT
ejpam-4060	231	4	m.	m.	NOUN
ejpam-4060	231	5	veera	veera	NOUN
ejpam-4060	231	6	kumar	kumar	PROPN
ejpam-4060	231	7	.	.	PROPN
ejpam-4060	232	1	between	between	ADP
ejpam-4060	232	2	closed	closed	ADJ
ejpam-4060	232	3	and	and	CCONJ
ejpam-4060	232	4	g	g	NOUN
ejpam-4060	232	5	-	-	PUNCT
ejpam-4060	232	6	closed	close	VERB
ejpam-4060	232	7	sets	set	NOUN
ejpam-4060	232	8	.	.	PUNCT
ejpam-4060	233	1	mem.fac	mem.fac	NOUN
ejpam-4060	233	2	sci	sci	PROPN
ejpam-4060	233	3	.	.	PUNCT
ejpam-4060	234	1	kochiuniv.math	kochiuniv.math	PROPN
ejpam-4060	234	2	.	.	PROPN
ejpam-4060	234	3	,	,	PUNCT
ejpam-4060	234	4	(	(	PUNCT
ejpam-4060	234	5	21):1–19	21):1–19	NUM
ejpam-4060	234	6	,	,	PUNCT
ejpam-4060	234	7	2000	2000	NUM
ejpam-4060	234	8	.	.	PUNCT
ejpam-4060	235	1	[	[	X
ejpam-4060	235	2	11	11	NUM
ejpam-4060	235	3	]	]	PUNCT
ejpam-4060	235	4	m.	m.	NOUN
ejpam-4060	235	5	veera	veera	NOUN
ejpam-4060	235	6	kumar	kumar	PROPN
ejpam-4060	235	7	.	.	PUNCT
ejpam-4060	235	8	between	between	ADP
ejpam-4060	235	9	ψ	ψ	X
ejpam-4060	235	10	-	-	ADJ
ejpam-4060	235	11	closed	closed	ADJ
ejpam-4060	235	12	sets	set	NOUN
ejpam-4060	235	13	and	and	CCONJ
ejpam-4060	235	14	gsp	gsp	NOUN
ejpam-4060	235	15	-	-	PUNCT
ejpam-4060	235	16	closed	close	VERB
ejpam-4060	235	17	sets	set	NOUN
ejpam-4060	235	18	spaces	space	NOUN
ejpam-4060	235	19	.	.	PUNCT
ejpam-4060	236	1	antarctica	antarctica	PROPN
ejpam-4060	236	2	.	.	PUNCT
ejpam-4060	237	1	j.math	j.math	PROPN
ejpam-4060	237	2	.	.	PROPN
ejpam-4060	237	3	,	,	PUNCT
ejpam-4060	238	1	2(1):123–141	2(1):123–141	NUM
ejpam-4060	238	2	,	,	PUNCT
ejpam-4060	238	3	2005	2005	NUM
ejpam-4060	238	4	.	.	PUNCT
ejpam-4060	239	1	[	[	X
ejpam-4060	239	2	12	12	NUM
ejpam-4060	239	3	]	]	X
ejpam-4060	239	4	n.	n.	PROPN
ejpam-4060	239	5	levine	levine	PROPN
ejpam-4060	239	6	.	.	PUNCT
ejpam-4060	240	1	semi	semi	ADJ
ejpam-4060	240	2	-	-	ADJ
ejpam-4060	240	3	open	open	ADJ
ejpam-4060	240	4	sets	set	NOUN
ejpam-4060	240	5	and	and	CCONJ
ejpam-4060	240	6	semi	semi	ADJ
ejpam-4060	240	7	-	-	NOUN
ejpam-4060	240	8	continuity	continuity	NOUN
ejpam-4060	240	9	in	in	ADP
ejpam-4060	240	10	topological	topological	ADJ
ejpam-4060	240	11	spaces	space	NOUN
ejpam-4060	240	12	.	.	PUNCT
ejpam-4060	241	1	amer	amer	PROPN
ejpam-4060	241	2	.	.	PUNCT
ejpam-4060	241	3	math	math	PROPN
ejpam-4060	241	4	.	.	PUNCT
ejpam-4060	242	1	monthly	monthly	ADV
ejpam-4060	242	2	,	,	PUNCT
ejpam-4060	242	3	(	(	PUNCT
ejpam-4060	242	4	70):36–41	70):36–41	NOUN
ejpam-4060	242	5	,	,	PUNCT
ejpam-4060	242	6	1963	1963	NUM
ejpam-4060	242	7	.	.	PUNCT
ejpam-4060	243	1	[	[	X
ejpam-4060	243	2	13	13	NUM
ejpam-4060	243	3	]	]	X
ejpam-4060	243	4	n.	n.	PROPN
ejpam-4060	243	5	levine	levine	PROPN
ejpam-4060	243	6	.	.	PUNCT
ejpam-4060	244	1	generalized	generalize	VERB
ejpam-4060	244	2	closed	close	VERB
ejpam-4060	244	3	sets	set	NOUN
ejpam-4060	244	4	in	in	ADP
ejpam-4060	244	5	topological	topological	ADJ
ejpam-4060	244	6	spaces	space	NOUN
ejpam-4060	244	7	.	.	PUNCT
ejpam-4060	245	1	rend	rend	VERB
ejpam-4060	245	2	.	.	PUNCT
ejpam-4060	246	1	circ	circ	PROPN
ejpam-4060	246	2	.	.	PUNCT
ejpam-4060	247	1	mat	mat	NOUN
ejpam-4060	247	2	.	.	PUNCT
ejpam-4060	247	3	palermo	palermo	PROPN
ejpam-4060	247	4	,	,	PUNCT
ejpam-4060	247	5	19(2):89–96	19(2):89–96	NUM
ejpam-4060	247	6	,	,	PUNCT
ejpam-4060	247	7	1970	1970	NUM
ejpam-4060	247	8	.	.	PUNCT
ejpam-4060	248	1	[	[	X
ejpam-4060	248	2	14	14	NUM
ejpam-4060	248	3	]	]	X
ejpam-4060	248	4	y.	y.	PROPN
ejpam-4060	248	5	mahdi	mahdi	PROPN
ejpam-4060	248	6	.	.	PUNCT
ejpam-4060	249	1	semi	semi	ADJ
ejpam-4060	249	2	-	-	ADJ
ejpam-4060	249	3	open	open	ADJ
ejpam-4060	249	4	and	and	CCONJ
ejpam-4060	249	5	semi	semi	ADJ
ejpam-4060	249	6	-	-	ADJ
ejpam-4060	249	7	closed	closed	ADJ
ejpam-4060	249	8	sets	set	NOUN
ejpam-4060	249	9	in	in	ADP
ejpam-4060	249	10	bitopological	bitopological	ADJ
ejpam-4060	249	11	spaces	space	NOUN
ejpam-4060	249	12	.	.	PUNCT
ejpam-4060	250	1	in	in	ADP
ejpam-4060	250	2	first	first	ADJ
ejpam-4060	250	3	science	science	NOUN
ejpam-4060	250	4	conference	conference	NOUN
ejpam-4060	250	5	of	of	ADP
ejpam-4060	250	6	education	education	PROPN
ejpam-4060	250	7	college	college	NOUN
ejpam-4060	250	8	,	,	PUNCT
ejpam-4060	250	9	pages	page	NOUN
ejpam-4060	250	10	18–19	18–19	NUM
ejpam-4060	250	11	,	,	PUNCT
ejpam-4060	250	12	hillah	hillah	NOUN
ejpam-4060	250	13	,	,	PUNCT
ejpam-4060	250	14	2007	2007	NUM
ejpam-4060	250	15	.	.	PUNCT
ejpam-4060	251	1	babylon	babylon	PROPN
ejpam-4060	251	2	univ	univ	PROPN
ejpam-4060	251	3	.	.	PUNCT
ejpam-4060	252	1	[	[	X
ejpam-4060	252	2	15	15	NUM
ejpam-4060	252	3	]	]	X
ejpam-4060	252	4	y.	y.	PROPN
ejpam-4060	252	5	k.	k.	PROPN
ejpam-4060	252	6	mahdi	mahdi	PROPN
ejpam-4060	252	7	.	.	PUNCT
ejpam-4060	253	1	semi	semi	ADJ
ejpam-4060	253	2	-	-	ADJ
ejpam-4060	253	3	open	open	ADJ
ejpam-4060	253	4	and	and	CCONJ
ejpam-4060	253	5	semi	semi	ADJ
ejpam-4060	253	6	-	-	ADJ
ejpam-4060	253	7	closed	closed	ADJ
ejpam-4060	253	8	set	set	NOUN
ejpam-4060	253	9	in	in	ADP
ejpam-4060	253	10	bitopological	bitopological	ADJ
ejpam-4060	253	11	spaces	space	NOUN
ejpam-4060	253	12	.	.	PUNCT
ejpam-4060	254	1	the	the	DET
ejpam-4060	254	2	first	first	ADJ
ejpam-4060	254	3	scientific	scientific	ADJ
ejpam-4060	254	4	conference	conference	NOUN
ejpam-4060	254	5	of	of	ADP
ejpam-4060	254	6	the	the	DET
ejpam-4060	254	7	faculty	faculty	NOUN
ejpam-4060	254	8	of	of	ADP
ejpam-4060	254	9	physical	physical	ADJ
ejpam-4060	254	10	education	education	NOUN
ejpam-4060	254	11	,	,	PUNCT
ejpam-4060	254	12	18:1–8	18:1–8	NUM
ejpam-4060	254	13	,	,	PUNCT
ejpam-4060	254	14	2007	2007	NUM
ejpam-4060	254	15	.	.	PUNCT
ejpam-4060	255	1	[	[	X
ejpam-4060	255	2	16	16	NUM
ejpam-4060	255	3	]	]	X
ejpam-4060	255	4	o.	o.	PROPN
ejpam-4060	255	5	njastad	njastad	PROPN
ejpam-4060	255	6	.	.	PUNCT
ejpam-4060	256	1	on	on	ADP
ejpam-4060	256	2	some	some	DET
ejpam-4060	256	3	classes	class	NOUN
ejpam-4060	256	4	of	of	ADP
ejpam-4060	256	5	nearly	nearly	ADV
ejpam-4060	256	6	open	open	ADJ
ejpam-4060	256	7	sets	set	NOUN
ejpam-4060	256	8	.	.	PUNCT
ejpam-4060	257	1	pacific	pacific	PROPN
ejpam-4060	257	2	j.	j.	PROPN
ejpam-4060	257	3	math	math	PROPN
ejpam-4060	257	4	.	.	PUNCT
ejpam-4060	257	5	,	,	PUNCT
ejpam-4060	257	6	15:961–970	15:961–970	PROPN
ejpam-4060	257	7	,	,	PUNCT
ejpam-4060	257	8	1965	1965	NUM
ejpam-4060	257	9	.	.	PUNCT
ejpam-4060	258	1	[	[	X
ejpam-4060	258	2	17	17	NUM
ejpam-4060	258	3	]	]	X
ejpam-4060	258	4	h.m	h.m	PROPN
ejpam-4060	258	5	.	.	PUNCT
ejpam-4060	258	6	abu	abu	PROPN
ejpam-4060	258	7	-	-	PUNCT
ejpam-4060	258	8	donia	donia	PROPN
ejpam-4060	258	9	o.a	o.a	PROPN
ejpam-4060	258	10	.	.	PROPN
ejpam-4060	258	11	el	el	PROPN
ejpam-4060	258	12	-	-	PUNCT
ejpam-4060	258	13	tantawi	tantawi	PROPN
ejpam-4060	258	14	.	.	PUNCT
ejpam-4060	259	1	generalized	generalized	ADJ
ejpam-4060	259	2	separation	separation	NOUN
ejpam-4060	259	3	axioms	axiom	NOUN
ejpam-4060	259	4	in	in	ADP
ejpam-4060	259	5	bitopological	bitopological	ADJ
ejpam-4060	259	6	spaces	space	NOUN
ejpam-4060	259	7	.	.	PUNCT
ejpam-4060	260	1	arab	arab	PROPN
ejpam-4060	260	2	.	.	PUNCT
ejpam-4060	261	1	j.	j.	PROPN
ejpam-4060	261	2	sci	sci	PROPN
ejpam-4060	261	3	.	.	PUNCT
ejpam-4060	262	1	eng	eng	PROPN
ejpam-4060	262	2	.	.	PROPN
ejpam-4060	262	3	,	,	PUNCT
ejpam-4060	262	4	1:117–129	1:117–129	NUM
ejpam-4060	262	5	,	,	PUNCT
ejpam-4060	262	6	2005	2005	NUM
ejpam-4060	262	7	.	.	PUNCT
ejpam-4060	263	1	[	[	X
ejpam-4060	263	2	18	18	NUM
ejpam-4060	263	3	]	]	PUNCT
ejpam-4060	263	4	m.	m.	NOUN
ejpam-4060	263	5	rajamani	rajamani	NOUN
ejpam-4060	263	6	and	and	CCONJ
ejpam-4060	263	7	k.	k.	PROPN
ejpam-4060	263	8	vishwanathan	vishwanathan	PROPN
ejpam-4060	263	9	.	.	PUNCT
ejpam-4060	264	1	αgs	αgs	NOUN
ejpam-4060	264	2	-	-	PUNCT
ejpam-4060	264	3	closed	close	VERB
ejpam-4060	264	4	sets	set	NOUN
ejpam-4060	264	5	in	in	ADP
ejpam-4060	264	6	topological	topological	ADJ
ejpam-4060	264	7	spaces	space	NOUN
ejpam-4060	264	8	.	.	PUNCT
ejpam-4060	265	1	acta	acta	PROPN
ejpam-4060	265	2	cienia	cienia	PROPN
ejpam-4060	265	3	indica	indica	PROPN
ejpam-4060	265	4	,	,	PUNCT
ejpam-4060	265	5	xxxm(3):521–526	xxxm(3):521–526	PROPN
ejpam-4060	265	6	,	,	PUNCT
ejpam-4060	265	7	2004	2004	NUM
ejpam-4060	265	8	.	.	PUNCT
ejpam-4060	266	1	[	[	X
ejpam-4060	266	2	19	19	NUM
ejpam-4060	266	3	]	]	PUNCT
ejpam-4060	266	4	m.	m.	NOUN
ejpam-4060	266	5	stone	stone	NOUN
ejpam-4060	266	6	.	.	PUNCT
ejpam-4060	267	1	application	application	NOUN
ejpam-4060	267	2	of	of	ADP
ejpam-4060	267	3	the	the	DET
ejpam-4060	267	4	theory	theory	NOUN
ejpam-4060	267	5	of	of	ADP
ejpam-4060	267	6	boolean	boolean	ADJ
ejpam-4060	267	7	rings	ring	NOUN
ejpam-4060	267	8	to	to	ADP
ejpam-4060	267	9	general	general	ADJ
ejpam-4060	267	10	topology	topology	NOUN
ejpam-4060	267	11	.	.	PUNCT
ejpam-4060	268	1	trans	trans	PROPN
ejpam-4060	268	2	.	.	PROPN
ejpam-4060	268	3	amer.math	amer.math	NUM
ejpam-4060	268	4	.	.	PUNCT
ejpam-4060	268	5	soc	soc	PROPN
ejpam-4060	268	6	.	.	PUNCT
ejpam-4060	268	7	,	,	PUNCT
ejpam-4060	268	8	41:374–481	41:374–481	PROPN
ejpam-4060	268	9	,	,	PUNCT
ejpam-4060	268	10	1937	1937	NUM
ejpam-4060	268	11	.	.	PUNCT
ejpam-4060	269	1	[	[	X
ejpam-4060	269	2	20	20	NUM
ejpam-4060	269	3	]	]	PUNCT
ejpam-4060	269	4	r.	r.	PROPN
ejpam-4060	269	5	nithya	nithya	PROPN
ejpam-4060	269	6	kalyani	kalyani	PROPN
ejpam-4060	269	7	veronica	veronica	PROPN
ejpam-4060	269	8	viayan	viayan	NOUN
ejpam-4060	269	9	.	.	PUNCT
ejpam-4060	270	1	a	a	DET
ejpam-4060	270	2	study	study	NOUN
ejpam-4060	270	3	on	on	ADP
ejpam-4060	270	4	(	(	PUNCT
ejpam-4060	270	5	i	i	PROPN
ejpam-4060	270	6	,	,	PUNCT
ejpam-4060	270	7	j)-ψ⋆	j)-ψ⋆	PROPN
ejpam-4060	270	8	,	,	PUNCT
ejpam-4060	270	9	and	and	CCONJ
ejpam-4060	270	10	(	(	PUNCT
ejpam-4060	270	11	i	i	INTJ
ejpam-4060	270	12	,	,	PUNCT
ejpam-4060	270	13	j)-ψ	j)-ψ	PROPN
ejpam-4060	270	14	closed	close	VERB
ejpam-4060	270	15	sets	set	NOUN
ejpam-4060	270	16	in	in	ADP
ejpam-4060	270	17	bitopological	bitopological	ADJ
ejpam-4060	270	18	spaces	space	NOUN
ejpam-4060	270	19	.	.	PUNCT
ejpam-4060	271	1	international	international	ADJ
ejpam-4060	271	2	journal	journal	NOUN
ejpam-4060	271	3	of	of	ADP
ejpam-4060	271	4	computer	computer	NOUN
ejpam-4060	271	5	application	application	NOUN
ejpam-4060	271	6	,	,	PUNCT
ejpam-4060	271	7	4:40–48	4:40–48	NUM
ejpam-4060	271	8	,	,	PUNCT
ejpam-4060	271	9	2013	2013	NUM
ejpam-4060	271	10	.	.	PUNCT