id	sid	tid	token	lemma	pos
ejpam-2522	1	1	compile	compile	NOUN
ejpam-2522	1	2	/	/	SYM
ejpam-2522	1	3	output.dvi	output.dvi	NOUN
ejpam-2522	1	4	european	european	ADJ
ejpam-2522	1	5	journal	journal	NOUN
ejpam-2522	1	6	of	of	ADP
ejpam-2522	1	7	pure	pure	ADJ
ejpam-2522	1	8	and	and	CCONJ
ejpam-2522	1	9	applied	apply	VERB
ejpam-2522	1	10	mathematics	mathematic	NOUN
ejpam-2522	1	11	vol	vol	NOUN
ejpam-2522	1	12	.	.	PROPN
ejpam-2522	2	1	9	9	NUM
ejpam-2522	2	2	,	,	PUNCT
ejpam-2522	2	3	no	no	INTJ
ejpam-2522	2	4	.	.	NOUN
ejpam-2522	2	5	1	1	NUM
ejpam-2522	2	6	,	,	PUNCT
ejpam-2522	2	7	2016	2016	NUM
ejpam-2522	2	8	,	,	PUNCT
ejpam-2522	2	9	27	27	NUM
ejpam-2522	2	10	-	-	SYM
ejpam-2522	2	11	33	33	NUM
ejpam-2522	2	12	issn	issn	PROPN
ejpam-2522	2	13	1307	1307	NUM
ejpam-2522	2	14	-	-	SYM
ejpam-2522	2	15	5543	5543	NUM
ejpam-2522	2	16	–	–	PUNCT
ejpam-2522	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-2522	2	18	a	a	DET
ejpam-2522	2	19	note	note	NOUN
ejpam-2522	2	20	on	on	ADP
ejpam-2522	2	21	αgrw	αgrw	NOUN
ejpam-2522	2	22	-	-	PUNCT
ejpam-2522	2	23	closed	close	VERB
ejpam-2522	2	24	sets	set	NOUN
ejpam-2522	2	25	ennis	ennis	PROPN
ejpam-2522	2	26	rosas1	rosas1	PROPN
ejpam-2522	2	27	,	,	PUNCT
ejpam-2522	2	28	n.selvanayaki2∗	n.selvanayaki2∗	NOUN
ejpam-2522	2	29	,	,	PUNCT
ejpam-2522	2	30	and	and	CCONJ
ejpam-2522	2	31	gnanambal	gnanambal	ADJ
ejpam-2522	2	32	ilango3	ilango3	NOUN
ejpam-2522	2	33	1	1	NUM
ejpam-2522	2	34	departamento	departamento	NOUN
ejpam-2522	2	35	de	de	PROPN
ejpam-2522	2	36	matemáticas	matemáticas	NOUN
ejpam-2522	2	37	,	,	PUNCT
ejpam-2522	2	38	universidad	universidad	PROPN
ejpam-2522	2	39	de	de	X
ejpam-2522	2	40	oriente	oriente	PROPN
ejpam-2522	2	41	,	,	PUNCT
ejpam-2522	2	42	cumaná	cumaná	PROPN
ejpam-2522	2	43	,	,	PUNCT
ejpam-2522	2	44	venezuela	venezuela	PROPN
ejpam-2522	2	45	and	and	CCONJ
ejpam-2522	2	46	facultad	facultad	PROPN
ejpam-2522	2	47	de	de	PROPN
ejpam-2522	2	48	ciencias	ciencias	PROPN
ejpam-2522	2	49	básicas	básicas	PROPN
ejpam-2522	2	50	,	,	PUNCT
ejpam-2522	2	51	universidad	universidad	PROPN
ejpam-2522	2	52	del	del	PROPN
ejpam-2522	2	53	atlántico	atlántico	PROPN
ejpam-2522	2	54	,	,	PUNCT
ejpam-2522	2	55	barranquilla	barranquilla	PROPN
ejpam-2522	2	56	,	,	PUNCT
ejpam-2522	2	57	colombia	colombia	PROPN
ejpam-2522	2	58	.	.	PUNCT
ejpam-2522	3	1	ãű2	ãű2	PROPN
ejpam-2522	3	2	department	department	PROPN
ejpam-2522	3	3	of	of	ADP
ejpam-2522	3	4	mathematics	mathematics	PROPN
ejpam-2522	3	5	,	,	PUNCT
ejpam-2522	3	6	akshaya	akshaya	PROPN
ejpam-2522	3	7	college	college	PROPN
ejpam-2522	3	8	of	of	ADP
ejpam-2522	3	9	engineering	engineering	NOUN
ejpam-2522	3	10	and	and	CCONJ
ejpam-2522	3	11	technology	technology	NOUN
ejpam-2522	3	12	,	,	PUNCT
ejpam-2522	3	13	coimbatore	coimbatore	PROPN
ejpam-2522	3	14	,	,	PUNCT
ejpam-2522	3	15	tamil	tamil	PROPN
ejpam-2522	3	16	nadu	nadu	PROPN
ejpam-2522	3	17	,	,	PUNCT
ejpam-2522	3	18	india	india	PROPN
ejpam-2522	3	19	.	.	PROPN
ejpam-2522	4	1	3	3	NUM
ejpam-2522	4	2	department	department	NOUN
ejpam-2522	4	3	of	of	ADP
ejpam-2522	4	4	mathematics	mathematic	NOUN
ejpam-2522	4	5	,	,	PUNCT
ejpam-2522	4	6	government	government	NOUN
ejpam-2522	4	7	arts	arts	PROPN
ejpam-2522	4	8	college	college	PROPN
ejpam-2522	4	9	,	,	PUNCT
ejpam-2522	4	10	coimbatore	coimbatore	PROPN
ejpam-2522	4	11	,	,	PUNCT
ejpam-2522	4	12	tamilnadu	tamilnadu	NOUN
ejpam-2522	4	13	,	,	PUNCT
ejpam-2522	4	14	india	india	PROPN
ejpam-2522	4	15	.	.	PUNCT
ejpam-2522	5	1	abstract	abstract	PROPN
ejpam-2522	5	2	.	.	PUNCT
ejpam-2522	6	1	in	in	ADP
ejpam-2522	6	2	this	this	DET
ejpam-2522	6	3	paper	paper	NOUN
ejpam-2522	6	4	,	,	PUNCT
ejpam-2522	6	5	some	some	DET
ejpam-2522	6	6	properties	property	NOUN
ejpam-2522	6	7	of	of	ADP
ejpam-2522	6	8	αgrw	αgrw	NOUN
ejpam-2522	6	9	-	-	PUNCT
ejpam-2522	6	10	closed	close	VERB
ejpam-2522	6	11	sets	set	NOUN
ejpam-2522	6	12	are	be	AUX
ejpam-2522	6	13	discussed	discuss	VERB
ejpam-2522	6	14	and	and	CCONJ
ejpam-2522	6	15	also	also	ADV
ejpam-2522	6	16	some	some	DET
ejpam-2522	6	17	characterizations	characterization	NOUN
ejpam-2522	6	18	of	of	ADP
ejpam-2522	6	19	αgrw	αgrw	NOUN
ejpam-2522	6	20	-	-	PUNCT
ejpam-2522	6	21	closed	close	VERB
ejpam-2522	6	22	sets	set	NOUN
ejpam-2522	6	23	are	be	AUX
ejpam-2522	6	24	studied	study	VERB
ejpam-2522	6	25	in	in	ADP
ejpam-2522	6	26	topological	topological	ADJ
ejpam-2522	6	27	spaces	space	NOUN
ejpam-2522	6	28	.	.	PUNCT
ejpam-2522	7	1	2010	2010	NUM
ejpam-2522	7	2	mathematics	mathematic	NOUN
ejpam-2522	7	3	subject	subject	NOUN
ejpam-2522	7	4	classifications	classification	NOUN
ejpam-2522	7	5	:	:	PUNCT
ejpam-2522	7	6	54a05	54a05	NUM
ejpam-2522	7	7	key	key	ADJ
ejpam-2522	7	8	words	word	NOUN
ejpam-2522	7	9	and	and	CCONJ
ejpam-2522	7	10	phrases	phrase	NOUN
ejpam-2522	7	11	:	:	PUNCT
ejpam-2522	7	12	αgrw	αgrw	ADJ
ejpam-2522	7	13	-	-	PUNCT
ejpam-2522	7	14	closed	close	VERB
ejpam-2522	7	15	sets	set	NOUN
ejpam-2522	7	16	,	,	PUNCT
ejpam-2522	7	17	rsker(a	rsker(a	NOUN
ejpam-2522	7	18	)	)	PUNCT
ejpam-2522	7	19	,	,	PUNCT
ejpam-2522	7	20	s	s	X
ejpam-2522	7	21	-	-	ADJ
ejpam-2522	7	22	normal	normal	ADJ
ejpam-2522	7	23	space	space	NOUN
ejpam-2522	7	24	1	1	NUM
ejpam-2522	7	25	.	.	PUNCT
ejpam-2522	7	26	introduction	introduction	NOUN
ejpam-2522	7	27	in	in	ADP
ejpam-2522	7	28	2013	2013	NUM
ejpam-2522	7	29	,	,	PUNCT
ejpam-2522	7	30	αgrw	αgrw	NOUN
ejpam-2522	7	31	-	-	PUNCT
ejpam-2522	7	32	closed	close	VERB
ejpam-2522	7	33	sets	set	NOUN
ejpam-2522	7	34	are	be	AUX
ejpam-2522	7	35	introduced	introduce	VERB
ejpam-2522	7	36	and	and	CCONJ
ejpam-2522	7	37	studied	study	VERB
ejpam-2522	7	38	by	by	ADP
ejpam-2522	7	39	selvanayaki	selvanayaki	PROPN
ejpam-2522	7	40	and	and	CCONJ
ejpam-2522	7	41	gnanambal	gnanambal	ADJ
ejpam-2522	7	42	ilango	ilango	NOUN
ejpam-2522	8	1	[	[	X
ejpam-2522	8	2	14	14	NUM
ejpam-2522	8	3	]	]	PUNCT
ejpam-2522	8	4	and	and	CCONJ
ejpam-2522	8	5	some	some	DET
ejpam-2522	8	6	basic	basic	ADJ
ejpam-2522	8	7	properties	property	NOUN
ejpam-2522	8	8	of	of	ADP
ejpam-2522	8	9	αgrw	αgrw	NOUN
ejpam-2522	8	10	-	-	PUNCT
ejpam-2522	8	11	closed	close	VERB
ejpam-2522	8	12	sets	set	NOUN
ejpam-2522	8	13	are	be	AUX
ejpam-2522	8	14	investigated	investigate	VERB
ejpam-2522	8	15	.	.	PUNCT
ejpam-2522	9	1	the	the	DET
ejpam-2522	9	2	class	class	NOUN
ejpam-2522	9	3	of	of	ADP
ejpam-2522	9	4	αgrwclosed	αgrwclose	VERB
ejpam-2522	9	5	sets	set	NOUN
ejpam-2522	9	6	properly	properly	ADV
ejpam-2522	9	7	lies	lie	VERB
ejpam-2522	9	8	between	between	ADP
ejpam-2522	9	9	the	the	DET
ejpam-2522	9	10	class	class	NOUN
ejpam-2522	9	11	of	of	ADP
ejpam-2522	9	12	rw	rw	NOUN
ejpam-2522	9	13	-	-	PUNCT
ejpam-2522	9	14	closed	close	VERB
ejpam-2522	9	15	sets	set	NOUN
ejpam-2522	9	16	and	and	CCONJ
ejpam-2522	9	17	the	the	DET
ejpam-2522	9	18	class	class	NOUN
ejpam-2522	9	19	of	of	ADP
ejpam-2522	9	20	gprw	gprw	ADJ
ejpam-2522	9	21	-	-	PUNCT
ejpam-2522	9	22	closed	close	VERB
ejpam-2522	9	23	sets	set	NOUN
ejpam-2522	9	24	.	.	PUNCT
ejpam-2522	10	1	in	in	ADP
ejpam-2522	10	2	2007	2007	NUM
ejpam-2522	10	3	,	,	PUNCT
ejpam-2522	10	4	benchalli	benchalli	NOUN
ejpam-2522	10	5	and	and	CCONJ
ejpam-2522	10	6	wali	wali	VERB
ejpam-2522	10	7	[	[	X
ejpam-2522	10	8	1	1	NUM
ejpam-2522	10	9	]	]	PUNCT
ejpam-2522	10	10	have	have	AUX
ejpam-2522	10	11	introduced	introduce	VERB
ejpam-2522	10	12	a	a	DET
ejpam-2522	10	13	new	new	ADJ
ejpam-2522	10	14	type	type	NOUN
ejpam-2522	10	15	of	of	ADP
ejpam-2522	10	16	kernel	kernel	NOUN
ejpam-2522	10	17	known	know	VERB
ejpam-2522	10	18	as	as	ADP
ejpam-2522	10	19	regular	regular	ADJ
ejpam-2522	10	20	semi	semi	ADV
ejpam-2522	10	21	kernel.the	kernel.the	DET
ejpam-2522	10	22	aim	aim	NOUN
ejpam-2522	10	23	of	of	ADP
ejpam-2522	10	24	this	this	DET
ejpam-2522	10	25	paper	paper	NOUN
ejpam-2522	10	26	is	be	AUX
ejpam-2522	10	27	to	to	PART
ejpam-2522	10	28	study	study	VERB
ejpam-2522	10	29	some	some	DET
ejpam-2522	10	30	properties	property	NOUN
ejpam-2522	10	31	of	of	ADP
ejpam-2522	10	32	αgrw	αgrw	NOUN
ejpam-2522	10	33	-	-	PUNCT
ejpam-2522	10	34	closed	close	VERB
ejpam-2522	10	35	sets	set	NOUN
ejpam-2522	10	36	and	and	CCONJ
ejpam-2522	10	37	some	some	DET
ejpam-2522	10	38	characterizations	characterization	NOUN
ejpam-2522	10	39	of	of	ADP
ejpam-2522	10	40	it	it	PRON
ejpam-2522	10	41	.	.	PUNCT
ejpam-2522	11	1	throughout	throughout	ADP
ejpam-2522	11	2	this	this	DET
ejpam-2522	11	3	paper	paper	NOUN
ejpam-2522	11	4	,	,	PUNCT
ejpam-2522	11	5	space	space	NOUN
ejpam-2522	11	6	(	(	PUNCT
ejpam-2522	11	7	x	x	X
ejpam-2522	11	8	,	,	PUNCT
ejpam-2522	11	9	τ	τ	X
ejpam-2522	11	10	)	)	PUNCT
ejpam-2522	11	11	(	(	PUNCT
ejpam-2522	11	12	or	or	CCONJ
ejpam-2522	11	13	simply	simply	ADV
ejpam-2522	11	14	x	x	X
ejpam-2522	11	15	)	)	PUNCT
ejpam-2522	11	16	always	always	ADV
ejpam-2522	11	17	means	mean	VERB
ejpam-2522	11	18	a	a	DET
ejpam-2522	11	19	topological	topological	ADJ
ejpam-2522	11	20	space	space	NOUN
ejpam-2522	11	21	on	on	ADP
ejpam-2522	11	22	which	which	PRON
ejpam-2522	11	23	no	no	DET
ejpam-2522	11	24	separation	separation	NOUN
ejpam-2522	11	25	axioms	axiom	NOUN
ejpam-2522	11	26	are	be	AUX
ejpam-2522	11	27	assumed	assume	VERB
ejpam-2522	11	28	unless	unless	SCONJ
ejpam-2522	11	29	explicitly	explicitly	ADV
ejpam-2522	11	30	stated	state	VERB
ejpam-2522	11	31	.	.	PUNCT
ejpam-2522	12	1	for	for	ADP
ejpam-2522	12	2	a	a	DET
ejpam-2522	12	3	subset	subset	NOUN
ejpam-2522	12	4	a	a	PRON
ejpam-2522	12	5	of	of	ADP
ejpam-2522	12	6	a	a	DET
ejpam-2522	12	7	space	space	NOUN
ejpam-2522	12	8	x	x	SYM
ejpam-2522	12	9	,	,	PUNCT
ejpam-2522	12	10	cl(a	cl(a	NUM
ejpam-2522	12	11	)	)	PUNCT
ejpam-2522	12	12	,	,	PUNCT
ejpam-2522	12	13	int(a	int(a	PROPN
ejpam-2522	12	14	)	)	PUNCT
ejpam-2522	12	15	and	and	CCONJ
ejpam-2522	12	16	x	x	PART
ejpam-2522	12	17	−a	−a	NOUN
ejpam-2522	12	18	(	(	PUNCT
ejpam-2522	12	19	or	or	CCONJ
ejpam-2522	12	20	ac)denote	ac)denote	VERB
ejpam-2522	12	21	the	the	DET
ejpam-2522	12	22	closure	closure	NOUN
ejpam-2522	12	23	of	of	ADP
ejpam-2522	12	24	a	a	PRON
ejpam-2522	12	25	,	,	PUNCT
ejpam-2522	12	26	the	the	DET
ejpam-2522	12	27	interior	interior	NOUN
ejpam-2522	12	28	of	of	ADP
ejpam-2522	12	29	a	a	PRON
ejpam-2522	12	30	and	and	CCONJ
ejpam-2522	12	31	the	the	DET
ejpam-2522	12	32	complement	complement	NOUN
ejpam-2522	12	33	of	of	ADP
ejpam-2522	12	34	a	a	PRON
ejpam-2522	12	35	in	in	ADP
ejpam-2522	12	36	x	x	X
ejpam-2522	12	37	,	,	PUNCT
ejpam-2522	12	38	respectively	respectively	ADV
ejpam-2522	12	39	.	.	PUNCT
ejpam-2522	13	1	2	2	X
ejpam-2522	13	2	.	.	X
ejpam-2522	13	3	preliminaries	preliminary	NOUN
ejpam-2522	13	4	definition	definition	NOUN
ejpam-2522	13	5	1	1	NUM
ejpam-2522	13	6	.	.	PUNCT
ejpam-2522	14	1	a	a	DET
ejpam-2522	14	2	subset	subset	NOUN
ejpam-2522	14	3	a	a	PRON
ejpam-2522	14	4	of	of	ADP
ejpam-2522	14	5	a	a	DET
ejpam-2522	14	6	topological	topological	ADJ
ejpam-2522	14	7	space	space	NOUN
ejpam-2522	14	8	(	(	PUNCT
ejpam-2522	14	9	x	x	X
ejpam-2522	14	10	,	,	PUNCT
ejpam-2522	14	11	τ	τ	X
ejpam-2522	14	12	)	)	PUNCT
ejpam-2522	14	13	is	be	AUX
ejpam-2522	14	14	called	call	VERB
ejpam-2522	14	15	(	(	PUNCT
ejpam-2522	14	16	i	i	NOUN
ejpam-2522	14	17	)	)	PUNCT
ejpam-2522	14	18	regular	regular	ADJ
ejpam-2522	14	19	open	open	ADJ
ejpam-2522	14	20	[	[	X
ejpam-2522	14	21	15	15	NUM
ejpam-2522	14	22	]	]	X
ejpam-2522	14	23	if	if	SCONJ
ejpam-2522	14	24	a=	a=	ADV
ejpam-2522	14	25	int(cl(a	int(cl(a	PROPN
ejpam-2522	14	26	)	)	PUNCT
ejpam-2522	14	27	)	)	PUNCT
ejpam-2522	15	1	and	and	CCONJ
ejpam-2522	15	2	regular	regular	ADJ
ejpam-2522	15	3	closed	close	VERB
ejpam-2522	15	4	if	if	SCONJ
ejpam-2522	15	5	a=	a=	NOUN
ejpam-2522	15	6	cl(int(a	cl(int(a	PROPN
ejpam-2522	15	7	)	)	PUNCT
ejpam-2522	15	8	)	)	PUNCT
ejpam-2522	15	9	.	.	PUNCT
ejpam-2522	16	1	∗corresponding	∗corresponde	VERB
ejpam-2522	16	2	author	author	NOUN
ejpam-2522	16	3	.	.	PUNCT
ejpam-2522	17	1	email	email	NOUN
ejpam-2522	17	2	addresses	address	NOUN
ejpam-2522	17	3	:	:	PUNCT
ejpam-2522	17	4	ennisrafael@gmail.com	ennisrafael@gmail.com	X
ejpam-2522	17	5	(	(	PUNCT
ejpam-2522	17	6	ennis	ennis	PROPN
ejpam-2522	17	7	rosas	rosas	PROPN
ejpam-2522	17	8	)	)	PUNCT
ejpam-2522	17	9	,	,	PUNCT
ejpam-2522	17	10	selvanayaki.nataraj@gmail.com	selvanayaki.nataraj@gmail.com	X
ejpam-2522	17	11	(	(	PUNCT
ejpam-2522	17	12	n.	n.	NOUN
ejpam-2522	17	13	selvanayaki	selvanayaki	PROPN
ejpam-2522	17	14	)	)	PUNCT
ejpam-2522	17	15	and	and	CCONJ
ejpam-2522	17	16	gnanamilango@yahoo.co.in	gnanamilango@yahoo.co.in	PROPN
ejpam-2522	17	17	(	(	PUNCT
ejpam-2522	17	18	gnanambal	gnanambal	ADJ
ejpam-2522	17	19	ilango	ilango	NOUN
ejpam-2522	17	20	)	)	PUNCT
ejpam-2522	17	21	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2522	18	1	27	27	NUM
ejpam-2522	18	2	c	c	X
ejpam-2522	18	3	©	©	PROPN
ejpam-2522	18	4	2016	2016	NUM
ejpam-2522	18	5	ejpam	ejpam	VERB
ejpam-2522	18	6	all	all	DET
ejpam-2522	18	7	rights	right	NOUN
ejpam-2522	18	8	reserved	reserve	VERB
ejpam-2522	18	9	.	.	PUNCT
ejpam-2522	19	1	ennis	ennis	PROPN
ejpam-2522	19	2	rosas	rosas	PROPN
ejpam-2522	19	3	,	,	PUNCT
ejpam-2522	19	4	n.	n.	PROPN
ejpam-2522	19	5	selvanayaki	selvanayaki	PROPN
ejpam-2522	19	6	,	,	PUNCT
ejpam-2522	19	7	gnanambal	gnanambal	PROPN
ejpam-2522	19	8	ilango	ilango	PROPN
ejpam-2522	19	9	/	/	SYM
ejpam-2522	19	10	eur	eur	PROPN
ejpam-2522	19	11	.	.	PUNCT
ejpam-2522	20	1	j.	j.	PROPN
ejpam-2522	20	2	pure	pure	PROPN
ejpam-2522	20	3	appl	appl	PROPN
ejpam-2522	20	4	.	.	PROPN
ejpam-2522	20	5	math	math	PROPN
ejpam-2522	20	6	,	,	PUNCT
ejpam-2522	20	7	9	9	NUM
ejpam-2522	20	8	(	(	PUNCT
ejpam-2522	20	9	2016	2016	NUM
ejpam-2522	20	10	)	)	PUNCT
ejpam-2522	20	11	,	,	PUNCT
ejpam-2522	20	12	27	27	NUM
ejpam-2522	20	13	-	-	SYM
ejpam-2522	20	14	33	33	NUM
ejpam-2522	20	15	28	28	NUM
ejpam-2522	20	16	(	(	PUNCT
ejpam-2522	20	17	ii	ii	NOUN
ejpam-2522	20	18	)	)	PUNCT
ejpam-2522	20	19	semi	semi	ADJ
ejpam-2522	20	20	-	-	ADJ
ejpam-2522	20	21	open	open	ADJ
ejpam-2522	20	22	[	[	X
ejpam-2522	20	23	7	7	NUM
ejpam-2522	20	24	]	]	X
ejpam-2522	20	25	if	if	SCONJ
ejpam-2522	20	26	a⊆	a⊆	PROPN
ejpam-2522	20	27	cl(int(a	cl(int(a	NOUN
ejpam-2522	20	28	)	)	PUNCT
ejpam-2522	20	29	)	)	PUNCT
ejpam-2522	20	30	and	and	CCONJ
ejpam-2522	20	31	semi	semi	ADJ
ejpam-2522	20	32	-	-	ADJ
ejpam-2522	20	33	closed	closed	ADJ
ejpam-2522	20	34	if	if	SCONJ
ejpam-2522	20	35	int(cl(a	int(cl(a	PROPN
ejpam-2522	20	36	)	)	PUNCT
ejpam-2522	20	37	)	)	PUNCT
ejpam-2522	21	1	⊆	⊆	NUM
ejpam-2522	21	2	a.	a.	NOUN
ejpam-2522	21	3	(	(	PUNCT
ejpam-2522	21	4	iii	iii	NOUN
ejpam-2522	21	5	)	)	PUNCT
ejpam-2522	21	6	α	α	NOUN
ejpam-2522	21	7	-	-	ADJ
ejpam-2522	21	8	open	open	ADJ
ejpam-2522	21	9	[	[	X
ejpam-2522	21	10	13	13	NUM
ejpam-2522	21	11	]	]	X
ejpam-2522	21	12	if	if	SCONJ
ejpam-2522	21	13	a⊆	a⊆	ADP
ejpam-2522	21	14	int(cl(int(a	int(cl(int(a	PROPN
ejpam-2522	21	15	)	)	PUNCT
ejpam-2522	21	16	)	)	PUNCT
ejpam-2522	21	17	)	)	PUNCT
ejpam-2522	21	18	and	and	CCONJ
ejpam-2522	21	19	α	α	X
ejpam-2522	21	20	-	-	ADJ
ejpam-2522	21	21	closed	closed	ADJ
ejpam-2522	21	22	[	[	X
ejpam-2522	21	23	12	12	NUM
ejpam-2522	21	24	]	]	PUNCT
ejpam-2522	21	25	if	if	SCONJ
ejpam-2522	21	26	cl(int(cl(a	cl(int(cl(a	NOUN
ejpam-2522	21	27	)	)	PUNCT
ejpam-2522	21	28	)	)	PUNCT
ejpam-2522	21	29	)	)	PUNCT
ejpam-2522	22	1	⊆	⊆	NUM
ejpam-2522	22	2	a.	a.	NOUN
ejpam-2522	22	3	definition	definition	NOUN
ejpam-2522	22	4	2	2	NUM
ejpam-2522	22	5	(	(	PUNCT
ejpam-2522	22	6	[	[	X
ejpam-2522	22	7	2	2	NUM
ejpam-2522	22	8	]	]	NUM
ejpam-2522	22	9	)	)	PUNCT
ejpam-2522	22	10	.	.	PUNCT
ejpam-2522	23	1	a	a	DET
ejpam-2522	23	2	subset	subset	NOUN
ejpam-2522	23	3	a	a	PRON
ejpam-2522	23	4	of	of	ADP
ejpam-2522	23	5	a	a	DET
ejpam-2522	23	6	space	space	NOUN
ejpam-2522	23	7	(	(	PUNCT
ejpam-2522	23	8	x	x	X
ejpam-2522	23	9	,	,	PUNCT
ejpam-2522	23	10	τ	τ	X
ejpam-2522	23	11	)	)	PUNCT
ejpam-2522	23	12	is	be	AUX
ejpam-2522	23	13	called	call	VERB
ejpam-2522	23	14	regular	regular	ADJ
ejpam-2522	23	15	semi	semi	ADJ
ejpam-2522	23	16	-	-	ADJ
ejpam-2522	23	17	open	open	ADJ
ejpam-2522	23	18	if	if	SCONJ
ejpam-2522	23	19	there	there	PRON
ejpam-2522	23	20	is	be	VERB
ejpam-2522	23	21	a	a	DET
ejpam-2522	23	22	regular	regular	ADJ
ejpam-2522	23	23	open	open	ADJ
ejpam-2522	23	24	set	set	NOUN
ejpam-2522	23	25	u	u	PRON
ejpam-2522	23	26	such	such	ADJ
ejpam-2522	23	27	that	that	SCONJ
ejpam-2522	23	28	u	u	PROPN
ejpam-2522	23	29	⊆	⊆	NUM
ejpam-2522	23	30	a⊆	a⊆	PROPN
ejpam-2522	23	31	cl(u	cl(u	NOUN
ejpam-2522	23	32	)	)	PUNCT
ejpam-2522	23	33	.	.	PUNCT
ejpam-2522	24	1	the	the	DET
ejpam-2522	24	2	family	family	NOUN
ejpam-2522	24	3	of	of	ADP
ejpam-2522	24	4	all	all	DET
ejpam-2522	24	5	regular	regular	ADJ
ejpam-2522	24	6	semi	semi	ADJ
ejpam-2522	24	7	-	-	ADJ
ejpam-2522	24	8	open	open	ADJ
ejpam-2522	24	9	sets	set	NOUN
ejpam-2522	24	10	of	of	ADP
ejpam-2522	24	11	x	x	SYM
ejpam-2522	24	12	is	be	AUX
ejpam-2522	24	13	denoted	denote	VERB
ejpam-2522	24	14	by	by	ADP
ejpam-2522	24	15	rso(x	rso(x	PROPN
ejpam-2522	24	16	)	)	PUNCT
ejpam-2522	24	17	.	.	PUNCT
ejpam-2522	25	1	definition	definition	NOUN
ejpam-2522	25	2	3	3	NUM
ejpam-2522	25	3	(	(	PUNCT
ejpam-2522	25	4	noiri	noiri	ADV
ejpam-2522	25	5	[	[	X
ejpam-2522	25	6	10	10	NUM
ejpam-2522	25	7	]	]	NUM
ejpam-2522	25	8	)	)	PUNCT
ejpam-2522	25	9	.	.	PUNCT
ejpam-2522	26	1	a	a	DET
ejpam-2522	26	2	subset	subset	NOUN
ejpam-2522	26	3	a	a	PRON
ejpam-2522	26	4	of	of	ADP
ejpam-2522	26	5	a	a	DET
ejpam-2522	26	6	space	space	NOUN
ejpam-2522	26	7	(	(	PUNCT
ejpam-2522	26	8	x	x	X
ejpam-2522	26	9	,	,	PUNCT
ejpam-2522	26	10	τ	τ	X
ejpam-2522	26	11	)	)	PUNCT
ejpam-2522	26	12	is	be	AUX
ejpam-2522	26	13	said	say	VERB
ejpam-2522	26	14	to	to	PART
ejpam-2522	26	15	be	be	AUX
ejpam-2522	26	16	semi	semi	ADJ
ejpam-2522	26	17	-	-	ADJ
ejpam-2522	26	18	regular	regular	ADJ
ejpam-2522	26	19	open	open	ADJ
ejpam-2522	26	20	if	if	SCONJ
ejpam-2522	26	21	it	it	PRON
ejpam-2522	26	22	is	be	AUX
ejpam-2522	26	23	both	both	PRON
ejpam-2522	26	24	semi	semi	ADJ
ejpam-2522	26	25	-	-	ADJ
ejpam-2522	26	26	open	open	ADJ
ejpam-2522	26	27	and	and	CCONJ
ejpam-2522	26	28	semi	semi	ADJ
ejpam-2522	26	29	-	-	ADJ
ejpam-2522	26	30	closed	closed	ADJ
ejpam-2522	26	31	.	.	PUNCT
ejpam-2522	27	1	the	the	DET
ejpam-2522	27	2	family	family	NOUN
ejpam-2522	27	3	of	of	ADP
ejpam-2522	27	4	all	all	DET
ejpam-2522	27	5	semi	semi	ADJ
ejpam-2522	27	6	-	-	ADJ
ejpam-2522	27	7	regular	regular	ADJ
ejpam-2522	27	8	open	open	ADJ
ejpam-2522	27	9	sets	set	NOUN
ejpam-2522	27	10	of	of	ADP
ejpam-2522	27	11	x	x	SYM
ejpam-2522	27	12	is	be	AUX
ejpam-2522	27	13	denoted	denote	VERB
ejpam-2522	27	14	by	by	ADP
ejpam-2522	27	15	sr(x	sr(x	NOUN
ejpam-2522	27	16	)	)	PUNCT
ejpam-2522	27	17	.	.	PUNCT
ejpam-2522	28	1	on	on	ADP
ejpam-2522	28	2	other	other	ADJ
ejpam-2522	28	3	hand	hand	NOUN
ejpam-2522	28	4	,	,	PUNCT
ejpam-2522	28	5	maio	maio	PROPN
ejpam-2522	28	6	and	and	CCONJ
ejpam-2522	28	7	noiri	noiri	PROPN
ejpam-2522	28	8	defined	define	VERB
ejpam-2522	28	9	a	a	DET
ejpam-2522	28	10	subset	subset	NOUN
ejpam-2522	28	11	a	a	PRON
ejpam-2522	28	12	of	of	ADP
ejpam-2522	28	13	x	x	PRON
ejpam-2522	28	14	to	to	PART
ejpam-2522	28	15	be	be	AUX
ejpam-2522	28	16	semi	semi	ADJ
ejpam-2522	28	17	-	-	ADJ
ejpam-2522	28	18	regular	regular	ADJ
ejpam-2522	28	19	open	open	ADJ
ejpam-2522	28	20	if	if	SCONJ
ejpam-2522	28	21	a=	a=	ADV
ejpam-2522	28	22	sint(scl(a	sint(scl(a	ADJ
ejpam-2522	28	23	)	)	PUNCT
ejpam-2522	28	24	)	)	PUNCT
ejpam-2522	28	25	.	.	PUNCT
ejpam-2522	29	1	however	however	ADV
ejpam-2522	29	2	,	,	PUNCT
ejpam-2522	29	3	these	these	DET
ejpam-2522	29	4	three	three	NUM
ejpam-2522	29	5	notions	notion	NOUN
ejpam-2522	29	6	are	be	AUX
ejpam-2522	29	7	equivalent	equivalent	ADJ
ejpam-2522	29	8	,	,	PUNCT
ejpam-2522	29	9	which	which	PRON
ejpam-2522	29	10	is	be	AUX
ejpam-2522	29	11	given	give	VERB
ejpam-2522	29	12	in	in	ADP
ejpam-2522	29	13	the	the	DET
ejpam-2522	29	14	following	follow	VERB
ejpam-2522	29	15	theorem	theorem	NOUN
ejpam-2522	29	16	.	.	PUNCT
ejpam-2522	30	1	theorem	theorem	NOUN
ejpam-2522	30	2	1	1	NUM
ejpam-2522	30	3	(	(	PUNCT
ejpam-2522	30	4	[	[	X
ejpam-2522	30	5	10	10	NUM
ejpam-2522	30	6	]	]	NUM
ejpam-2522	30	7	)	)	PUNCT
ejpam-2522	30	8	.	.	PUNCT
ejpam-2522	31	1	for	for	ADP
ejpam-2522	31	2	a	a	DET
ejpam-2522	31	3	subset	subset	NOUN
ejpam-2522	31	4	a	a	PRON
ejpam-2522	31	5	of	of	ADP
ejpam-2522	31	6	a	a	DET
ejpam-2522	31	7	space	space	NOUN
ejpam-2522	31	8	x	x	SYM
ejpam-2522	31	9	,	,	PUNCT
ejpam-2522	31	10	the	the	DET
ejpam-2522	31	11	followings	following	NOUN
ejpam-2522	31	12	are	be	AUX
ejpam-2522	31	13	equivalent	equivalent	ADJ
ejpam-2522	31	14	:	:	PUNCT
ejpam-2522	31	15	(	(	PUNCT
ejpam-2522	31	16	i	i	NOUN
ejpam-2522	31	17	)	)	PUNCT
ejpam-2522	31	18	a∈	a∈	PROPN
ejpam-2522	31	19	sr(x	sr(x	PROPN
ejpam-2522	31	20	)	)	PUNCT
ejpam-2522	32	1	(=	(=	ADP
ejpam-2522	32	2	rso(x	rso(x	PROPN
ejpam-2522	32	3	)	)	PUNCT
ejpam-2522	32	4	)	)	PUNCT
ejpam-2522	32	5	,	,	PUNCT
ejpam-2522	32	6	(	(	PUNCT
ejpam-2522	32	7	ii	ii	NOUN
ejpam-2522	32	8	)	)	PUNCT
ejpam-2522	32	9	a=	a=	ADV
ejpam-2522	32	10	sint(scl(a	sint(scl(a	X
ejpam-2522	32	11	)	)	PUNCT
ejpam-2522	32	12	)	)	PUNCT
ejpam-2522	32	13	,	,	PUNCT
ejpam-2522	32	14	(	(	PUNCT
ejpam-2522	32	15	iii	iii	X
ejpam-2522	32	16	)	)	PUNCT
ejpam-2522	32	17	there	there	PRON
ejpam-2522	32	18	exists	exist	VERB
ejpam-2522	32	19	a	a	DET
ejpam-2522	32	20	regular	regular	ADJ
ejpam-2522	32	21	open	open	ADJ
ejpam-2522	32	22	set	set	NOUN
ejpam-2522	32	23	u	u	NOUN
ejpam-2522	32	24	of	of	ADP
ejpam-2522	32	25	x	x	SYM
ejpam-2522	32	26	such	such	ADJ
ejpam-2522	32	27	that	that	SCONJ
ejpam-2522	32	28	u	u	PROPN
ejpam-2522	32	29	⊆	⊆	NUM
ejpam-2522	32	30	a⊆	a⊆	PROPN
ejpam-2522	32	31	cl(u	cl(u	NOUN
ejpam-2522	32	32	)	)	PUNCT
ejpam-2522	32	33	.	.	PUNCT
ejpam-2522	33	1	definition	definition	NOUN
ejpam-2522	33	2	4	4	NUM
ejpam-2522	33	3	.	.	PUNCT
ejpam-2522	34	1	a	a	DET
ejpam-2522	34	2	subset	subset	NOUN
ejpam-2522	34	3	a	a	PRON
ejpam-2522	34	4	of	of	ADP
ejpam-2522	34	5	a	a	DET
ejpam-2522	34	6	topological	topological	ADJ
ejpam-2522	34	7	space	space	NOUN
ejpam-2522	34	8	(	(	PUNCT
ejpam-2522	34	9	x	x	X
ejpam-2522	34	10	,	,	PUNCT
ejpam-2522	34	11	τ	τ	X
ejpam-2522	34	12	)	)	PUNCT
ejpam-2522	34	13	is	be	AUX
ejpam-2522	34	14	called	call	VERB
ejpam-2522	34	15	(	(	PUNCT
ejpam-2522	34	16	i	i	NOUN
ejpam-2522	34	17	)	)	PUNCT
ejpam-2522	34	18	generalized	generalize	VERB
ejpam-2522	34	19	closed	closed	ADJ
ejpam-2522	34	20	(	(	PUNCT
ejpam-2522	34	21	briefly	briefly	NOUN
ejpam-2522	34	22	g	g	NOUN
ejpam-2522	34	23	-	-	PUNCT
ejpam-2522	34	24	closed	closed	ADJ
ejpam-2522	34	25	)	)	PUNCT
ejpam-2522	35	1	[	[	X
ejpam-2522	35	2	8	8	NUM
ejpam-2522	35	3	]	]	X
ejpam-2522	35	4	if	if	SCONJ
ejpam-2522	35	5	cl(a	cl(a	NUM
ejpam-2522	35	6	)	)	PUNCT
ejpam-2522	35	7	⊆	⊆	NUM
ejpam-2522	35	8	u	u	NOUN
ejpam-2522	35	9	whenever	whenever	SCONJ
ejpam-2522	35	10	a⊆	a⊆	VERB
ejpam-2522	35	11	u	u	NOUN
ejpam-2522	35	12	and	and	CCONJ
ejpam-2522	35	13	u	u	NOUN
ejpam-2522	35	14	is	be	AUX
ejpam-2522	35	15	open	open	ADJ
ejpam-2522	35	16	in	in	ADP
ejpam-2522	35	17	x	x	X
ejpam-2522	35	18	.	.	PUNCT
ejpam-2522	36	1	(	(	PUNCT
ejpam-2522	36	2	ii	ii	NOUN
ejpam-2522	36	3	)	)	PUNCT
ejpam-2522	36	4	α	α	PROPN
ejpam-2522	36	5	-	-	PUNCT
ejpam-2522	36	6	generalized	generalize	VERB
ejpam-2522	36	7	closed	close	VERB
ejpam-2522	36	8	(	(	PUNCT
ejpam-2522	36	9	briefly	briefly	ADV
ejpam-2522	36	10	αg	αg	NOUN
ejpam-2522	36	11	-	-	PUNCT
ejpam-2522	36	12	closed)[11	closed)[11	NOUN
ejpam-2522	36	13	]	]	PUNCT
ejpam-2522	36	14	if	if	SCONJ
ejpam-2522	36	15	αcl(a	αcl(a	NUM
ejpam-2522	36	16	)	)	PUNCT
ejpam-2522	36	17	⊆	⊆	NUM
ejpam-2522	36	18	u	u	NOUN
ejpam-2522	36	19	whenever	whenever	SCONJ
ejpam-2522	36	20	a⊆	a⊆	VERB
ejpam-2522	36	21	u	u	NOUN
ejpam-2522	36	22	and	and	CCONJ
ejpam-2522	36	23	u	u	NOUN
ejpam-2522	36	24	is	be	AUX
ejpam-2522	36	25	open	open	ADJ
ejpam-2522	36	26	in	in	ADP
ejpam-2522	36	27	x	x	X
ejpam-2522	36	28	.	.	PUNCT
ejpam-2522	37	1	(	(	PUNCT
ejpam-2522	37	2	iii	iii	NOUN
ejpam-2522	37	3	)	)	PUNCT
ejpam-2522	37	4	α	α	NOUN
ejpam-2522	37	5	-	-	PUNCT
ejpam-2522	37	6	generalized	generalize	VERB
ejpam-2522	37	7	regular	regular	ADJ
ejpam-2522	37	8	weakly	weakly	ADJ
ejpam-2522	37	9	closed	closed	ADJ
ejpam-2522	37	10	(	(	PUNCT
ejpam-2522	37	11	briefly	briefly	ADV
ejpam-2522	37	12	αgrw	αgrw	ADJ
ejpam-2522	37	13	-	-	PUNCT
ejpam-2522	37	14	closed)[14	closed)[14	NOUN
ejpam-2522	37	15	]	]	PUNCT
ejpam-2522	37	16	if	if	SCONJ
ejpam-2522	37	17	αcl(a	αcl(a	NUM
ejpam-2522	37	18	)	)	PUNCT
ejpam-2522	37	19	⊆	⊆	NUM
ejpam-2522	37	20	u	u	NOUN
ejpam-2522	37	21	whenever	whenever	SCONJ
ejpam-2522	37	22	a⊆	a⊆	VERB
ejpam-2522	37	23	u	u	NOUN
ejpam-2522	37	24	and	and	CCONJ
ejpam-2522	37	25	u	u	NOUN
ejpam-2522	37	26	is	be	AUX
ejpam-2522	37	27	regular	regular	ADJ
ejpam-2522	37	28	semi	semi	ADJ
ejpam-2522	37	29	-	-	ADJ
ejpam-2522	37	30	open	open	ADJ
ejpam-2522	37	31	in	in	ADP
ejpam-2522	37	32	x	x	X
ejpam-2522	37	33	.	.	PUNCT
ejpam-2522	38	1	the	the	DET
ejpam-2522	38	2	set	set	NOUN
ejpam-2522	38	3	of	of	ADP
ejpam-2522	38	4	all	all	DET
ejpam-2522	38	5	αgrw	αgrw	NOUN
ejpam-2522	38	6	-	-	PUNCT
ejpam-2522	38	7	closed	close	VERB
ejpam-2522	38	8	sets	set	NOUN
ejpam-2522	38	9	in	in	ADP
ejpam-2522	38	10	(	(	PUNCT
ejpam-2522	38	11	x	x	INTJ
ejpam-2522	38	12	,	,	PUNCT
ejpam-2522	38	13	τ	τ	X
ejpam-2522	38	14	)	)	PUNCT
ejpam-2522	38	15	is	be	AUX
ejpam-2522	38	16	denoted	denote	VERB
ejpam-2522	38	17	by	by	ADP
ejpam-2522	38	18	αgrwc(x	αgrwc(x	NOUN
ejpam-2522	38	19	)	)	PUNCT
ejpam-2522	38	20	.	.	PUNCT
ejpam-2522	39	1	definition	definition	NOUN
ejpam-2522	39	2	5	5	NUM
ejpam-2522	39	3	(	(	PUNCT
ejpam-2522	39	4	[	[	X
ejpam-2522	39	5	9	9	NUM
ejpam-2522	39	6	]	]	NUM
ejpam-2522	39	7	)	)	PUNCT
ejpam-2522	39	8	.	.	PUNCT
ejpam-2522	40	1	a	a	DET
ejpam-2522	40	2	topological	topological	ADJ
ejpam-2522	40	3	space	space	NOUN
ejpam-2522	40	4	(	(	PUNCT
ejpam-2522	40	5	x	x	X
ejpam-2522	40	6	,	,	PUNCT
ejpam-2522	40	7	τ	τ	X
ejpam-2522	40	8	)	)	PUNCT
ejpam-2522	40	9	is	be	AUX
ejpam-2522	40	10	said	say	VERB
ejpam-2522	40	11	to	to	PART
ejpam-2522	40	12	be	be	AUX
ejpam-2522	40	13	s	s	NOUN
ejpam-2522	40	14	-	-	ADJ
ejpam-2522	40	15	normal	normal	ADJ
ejpam-2522	40	16	if	if	SCONJ
ejpam-2522	40	17	for	for	ADP
ejpam-2522	40	18	each	each	DET
ejpam-2522	40	19	pair	pair	NOUN
ejpam-2522	40	20	of	of	ADP
ejpam-2522	40	21	disjoint	disjoint	NOUN
ejpam-2522	40	22	closed	closed	ADJ
ejpam-2522	40	23	sets	set	NOUN
ejpam-2522	40	24	a	a	PRON
ejpam-2522	40	25	and	and	CCONJ
ejpam-2522	40	26	b	b	NOUN
ejpam-2522	40	27	,	,	PUNCT
ejpam-2522	40	28	there	there	PRON
ejpam-2522	40	29	exists	exist	VERB
ejpam-2522	40	30	disjoint	disjoint	ADJ
ejpam-2522	40	31	semi	semi	ADJ
ejpam-2522	40	32	-	-	ADJ
ejpam-2522	40	33	open	open	ADJ
ejpam-2522	40	34	sets	set	NOUN
ejpam-2522	40	35	u	u	NOUN
ejpam-2522	40	36	,	,	PUNCT
ejpam-2522	40	37	v	v	ADP
ejpam-2522	40	38	such	such	ADJ
ejpam-2522	40	39	that	that	PRON
ejpam-2522	40	40	a⊆	a⊆	PROPN
ejpam-2522	40	41	u	u	NOUN
ejpam-2522	40	42	and	and	CCONJ
ejpam-2522	40	43	b	b	NOUN
ejpam-2522	40	44	⊆	⊆	NUM
ejpam-2522	40	45	v	v	NOUN
ejpam-2522	40	46	.	.	PUNCT
ejpam-2522	41	1	definition	definition	NOUN
ejpam-2522	41	2	6	6	NUM
ejpam-2522	41	3	(	(	PUNCT
ejpam-2522	41	4	[	[	X
ejpam-2522	41	5	1	1	NUM
ejpam-2522	41	6	]	]	NUM
ejpam-2522	41	7	)	)	PUNCT
ejpam-2522	41	8	.	.	PUNCT
ejpam-2522	42	1	the	the	DET
ejpam-2522	42	2	intersection	intersection	NOUN
ejpam-2522	42	3	of	of	ADP
ejpam-2522	42	4	all	all	DET
ejpam-2522	42	5	regular	regular	ADJ
ejpam-2522	42	6	semi	semi	ADJ
ejpam-2522	42	7	-	-	ADJ
ejpam-2522	42	8	open	open	ADJ
ejpam-2522	42	9	subsets	subset	NOUN
ejpam-2522	42	10	of	of	ADP
ejpam-2522	42	11	(	(	PUNCT
ejpam-2522	42	12	x	x	INTJ
ejpam-2522	42	13	,	,	PUNCT
ejpam-2522	42	14	τ	τ	X
ejpam-2522	42	15	)	)	PUNCT
ejpam-2522	42	16	containing	contain	VERB
ejpam-2522	42	17	a	a	PRON
ejpam-2522	42	18	is	be	AUX
ejpam-2522	42	19	called	call	VERB
ejpam-2522	42	20	the	the	DET
ejpam-2522	42	21	regular	regular	ADJ
ejpam-2522	42	22	semi	semi	ADJ
ejpam-2522	42	23	-	-	NOUN
ejpam-2522	42	24	kernel	kernel	NOUN
ejpam-2522	42	25	of	of	ADP
ejpam-2522	42	26	a	a	PRON
ejpam-2522	42	27	and	and	CCONJ
ejpam-2522	42	28	is	be	AUX
ejpam-2522	42	29	denoted	denote	VERB
ejpam-2522	42	30	by	by	ADP
ejpam-2522	42	31	rsker(a	rsker(a	NOUN
ejpam-2522	42	32	)	)	PUNCT
ejpam-2522	42	33	.	.	PUNCT
ejpam-2522	43	1	theorem	theorem	ADJ
ejpam-2522	43	2	2	2	NUM
ejpam-2522	43	3	(	(	PUNCT
ejpam-2522	43	4	[	[	X
ejpam-2522	43	5	3	3	NUM
ejpam-2522	43	6	]	]	PUNCT
ejpam-2522	43	7	)	)	PUNCT
ejpam-2522	43	8	.	.	PUNCT
ejpam-2522	44	1	if	if	SCONJ
ejpam-2522	44	2	a	a	PRON
ejpam-2522	44	3	is	be	AUX
ejpam-2522	44	4	open	open	ADJ
ejpam-2522	44	5	and	and	CCONJ
ejpam-2522	44	6	s	s	VERB
ejpam-2522	44	7	is	be	AUX
ejpam-2522	44	8	semi	semi	ADJ
ejpam-2522	44	9	-	-	ADJ
ejpam-2522	44	10	open	open	ADJ
ejpam-2522	44	11	in	in	ADP
ejpam-2522	44	12	a	a	DET
ejpam-2522	44	13	topological	topological	ADJ
ejpam-2522	44	14	space	space	NOUN
ejpam-2522	44	15	x	x	NOUN
ejpam-2522	44	16	,	,	PUNCT
ejpam-2522	44	17	then	then	ADV
ejpam-2522	44	18	a∩s	a∩s	PROPN
ejpam-2522	44	19	is	be	AUX
ejpam-2522	44	20	semi	semi	ADJ
ejpam-2522	44	21	-	-	ADJ
ejpam-2522	44	22	open	open	ADJ
ejpam-2522	44	23	in	in	ADP
ejpam-2522	44	24	x	x	X
ejpam-2522	44	25	.	.	PUNCT
ejpam-2522	45	1	lemma	lemma	PROPN
ejpam-2522	45	2	1	1	NUM
ejpam-2522	45	3	(	(	PUNCT
ejpam-2522	45	4	[	[	X
ejpam-2522	45	5	1	1	NUM
ejpam-2522	45	6	]	]	PUNCT
ejpam-2522	45	7	)	)	PUNCT
ejpam-2522	45	8	.	.	PUNCT
ejpam-2522	46	1	let	let	AUX
ejpam-2522	46	2	a⊆	a⊆	VERB
ejpam-2522	46	3	y	y	PROPN
ejpam-2522	46	4	⊆	⊆	NUM
ejpam-2522	46	5	x	x	SYM
ejpam-2522	46	6	,	,	PUNCT
ejpam-2522	46	7	where	where	SCONJ
ejpam-2522	46	8	x	x	PRON
ejpam-2522	46	9	is	be	AUX
ejpam-2522	46	10	a	a	DET
ejpam-2522	46	11	topological	topological	ADJ
ejpam-2522	46	12	space	space	NOUN
ejpam-2522	46	13	and	and	CCONJ
ejpam-2522	46	14	y	y	PROPN
ejpam-2522	46	15	is	be	AUX
ejpam-2522	46	16	an	an	DET
ejpam-2522	46	17	open	open	ADJ
ejpam-2522	46	18	subspace	subspace	NOUN
ejpam-2522	46	19	of	of	ADP
ejpam-2522	46	20	x	x	X
ejpam-2522	46	21	.	.	PUNCT
ejpam-2522	47	1	if	if	SCONJ
ejpam-2522	47	2	a∈	a∈	PROPN
ejpam-2522	47	3	rso(x	rso(x	PROPN
ejpam-2522	47	4	)	)	PUNCT
ejpam-2522	47	5	,	,	PUNCT
ejpam-2522	47	6	then	then	ADV
ejpam-2522	47	7	a∈	a∈	PROPN
ejpam-2522	47	8	rso(y	rso(y	PROPN
ejpam-2522	47	9	)	)	PUNCT
ejpam-2522	47	10	.	.	PUNCT
ejpam-2522	48	1	lemma	lemma	PROPN
ejpam-2522	48	2	2	2	NUM
ejpam-2522	48	3	(	(	PUNCT
ejpam-2522	48	4	[	[	X
ejpam-2522	48	5	1	1	NUM
ejpam-2522	48	6	]	]	PUNCT
ejpam-2522	48	7	)	)	PUNCT
ejpam-2522	48	8	.	.	PUNCT
ejpam-2522	49	1	let	let	VERB
ejpam-2522	49	2	y	y	PRON
ejpam-2522	49	3	be	be	AUX
ejpam-2522	49	4	regular	regular	ADV
ejpam-2522	49	5	open	open	ADJ
ejpam-2522	49	6	in	in	ADP
ejpam-2522	49	7	x	x	PUNCT
ejpam-2522	49	8	and	and	CCONJ
ejpam-2522	49	9	u	u	NOUN
ejpam-2522	49	10	be	be	VERB
ejpam-2522	49	11	a	a	DET
ejpam-2522	49	12	subset	subset	NOUN
ejpam-2522	49	13	of	of	ADP
ejpam-2522	49	14	y	y	PROPN
ejpam-2522	49	15	.	.	PUNCT
ejpam-2522	50	1	then	then	ADV
ejpam-2522	50	2	u	u	PRON
ejpam-2522	50	3	is	be	AUX
ejpam-2522	50	4	regular	regular	ADJ
ejpam-2522	50	5	semi	semi	ADJ
ejpam-2522	50	6	-	-	ADJ
ejpam-2522	50	7	open	open	ADJ
ejpam-2522	50	8	in	in	ADP
ejpam-2522	50	9	x	x	PUNCT
ejpam-2522	50	10	if	if	SCONJ
ejpam-2522	51	1	and	and	CCONJ
ejpam-2522	51	2	only	only	ADV
ejpam-2522	51	3	if	if	SCONJ
ejpam-2522	51	4	u	u	NOUN
ejpam-2522	51	5	is	be	AUX
ejpam-2522	51	6	regular	regular	ADJ
ejpam-2522	51	7	semi	semi	ADJ
ejpam-2522	51	8	-	-	ADJ
ejpam-2522	51	9	open	open	ADJ
ejpam-2522	51	10	in	in	ADP
ejpam-2522	51	11	the	the	DET
ejpam-2522	51	12	subspace	subspace	NOUN
ejpam-2522	51	13	y	y	PROPN
ejpam-2522	51	14	.	.	PUNCT
ejpam-2522	52	1	lemma	lemma	PROPN
ejpam-2522	52	2	3	3	NUM
ejpam-2522	52	3	(	(	PUNCT
ejpam-2522	52	4	[	[	X
ejpam-2522	52	5	6	6	NUM
ejpam-2522	52	6	]	]	PUNCT
ejpam-2522	52	7	)	)	PUNCT
ejpam-2522	52	8	.	.	PUNCT
ejpam-2522	53	1	let	let	VERB
ejpam-2522	53	2	x	x	PRON
ejpam-2522	53	3	be	be	AUX
ejpam-2522	53	4	a	a	DET
ejpam-2522	53	5	point	point	NOUN
ejpam-2522	53	6	of	of	ADP
ejpam-2522	53	7	(	(	PUNCT
ejpam-2522	53	8	x	x	INTJ
ejpam-2522	53	9	,	,	PUNCT
ejpam-2522	53	10	τ	τ	PROPN
ejpam-2522	53	11	)	)	PUNCT
ejpam-2522	53	12	.	.	PUNCT
ejpam-2522	54	1	then	then	ADV
ejpam-2522	54	2	{	{	PUNCT
ejpam-2522	54	3	x	x	X
ejpam-2522	54	4	}	}	PUNCT
ejpam-2522	54	5	is	be	AUX
ejpam-2522	54	6	either	either	CCONJ
ejpam-2522	54	7	nowhere	nowhere	ADV
ejpam-2522	54	8	dense	dense	ADJ
ejpam-2522	54	9	or	or	CCONJ
ejpam-2522	54	10	pre	pre	ADJ
ejpam-2522	54	11	-	-	ADJ
ejpam-2522	54	12	open	open	ADJ
ejpam-2522	54	13	.	.	PUNCT
ejpam-2522	55	1	lemma	lemma	PROPN
ejpam-2522	55	2	4	4	NUM
ejpam-2522	55	3	(	(	PUNCT
ejpam-2522	55	4	[	[	X
ejpam-2522	55	5	5	5	NUM
ejpam-2522	55	6	]	]	PUNCT
ejpam-2522	55	7	)	)	PUNCT
ejpam-2522	55	8	.	.	PUNCT
ejpam-2522	56	1	if	if	SCONJ
ejpam-2522	56	2	a	a	PRON
ejpam-2522	56	3	is	be	AUX
ejpam-2522	56	4	regular	regular	ADJ
ejpam-2522	56	5	semi	semi	ADJ
ejpam-2522	56	6	-	-	ADJ
ejpam-2522	56	7	open	open	ADJ
ejpam-2522	56	8	in	in	ADP
ejpam-2522	56	9	(	(	PUNCT
ejpam-2522	56	10	x	x	INTJ
ejpam-2522	56	11	,	,	PUNCT
ejpam-2522	56	12	τ	τ	PROPN
ejpam-2522	56	13	)	)	PUNCT
ejpam-2522	56	14	,	,	PUNCT
ejpam-2522	56	15	then	then	ADV
ejpam-2522	56	16	x	x	PUNCT
ejpam-2522	56	17	−	−	NOUN
ejpam-2522	56	18	a	a	PRON
ejpam-2522	56	19	is	be	AUX
ejpam-2522	56	20	also	also	ADV
ejpam-2522	56	21	regular	regular	ADJ
ejpam-2522	56	22	semi	semi	ADJ
ejpam-2522	56	23	-	-	ADJ
ejpam-2522	56	24	open	open	ADJ
ejpam-2522	56	25	.	.	PUNCT
ejpam-2522	57	1	lemma	lemma	PROPN
ejpam-2522	57	2	5	5	NUM
ejpam-2522	57	3	(	(	PUNCT
ejpam-2522	57	4	[	[	X
ejpam-2522	57	5	1	1	NUM
ejpam-2522	57	6	]	]	PUNCT
ejpam-2522	57	7	)	)	PUNCT
ejpam-2522	57	8	.	.	PUNCT
ejpam-2522	58	1	for	for	ADP
ejpam-2522	58	2	any	any	DET
ejpam-2522	58	3	subset	subset	NOUN
ejpam-2522	58	4	a	a	PRON
ejpam-2522	58	5	of	of	ADP
ejpam-2522	58	6	(	(	PUNCT
ejpam-2522	58	7	x	x	PROPN
ejpam-2522	58	8	,	,	PUNCT
ejpam-2522	58	9	τ	τ	PROPN
ejpam-2522	58	10	)	)	PUNCT
ejpam-2522	58	11	,	,	PUNCT
ejpam-2522	58	12	a⊆	a⊆	VERB
ejpam-2522	58	13	rsker(a	rsker(a	NOUN
ejpam-2522	58	14	)	)	PUNCT
ejpam-2522	58	15	.	.	PUNCT
ejpam-2522	59	1	ennis	ennis	PROPN
ejpam-2522	59	2	rosas	rosas	PROPN
ejpam-2522	59	3	,	,	PUNCT
ejpam-2522	59	4	n.	n.	PROPN
ejpam-2522	59	5	selvanayaki	selvanayaki	PROPN
ejpam-2522	59	6	,	,	PUNCT
ejpam-2522	59	7	gnanambal	gnanambal	PROPN
ejpam-2522	59	8	ilango	ilango	PROPN
ejpam-2522	59	9	/	/	SYM
ejpam-2522	59	10	eur	eur	PROPN
ejpam-2522	59	11	.	.	PUNCT
ejpam-2522	60	1	j.	j.	PROPN
ejpam-2522	60	2	pure	pure	PROPN
ejpam-2522	60	3	appl	appl	PROPN
ejpam-2522	60	4	.	.	PROPN
ejpam-2522	60	5	math	math	PROPN
ejpam-2522	60	6	,	,	PUNCT
ejpam-2522	60	7	9	9	NUM
ejpam-2522	60	8	(	(	PUNCT
ejpam-2522	60	9	2016	2016	NUM
ejpam-2522	60	10	)	)	PUNCT
ejpam-2522	60	11	,	,	PUNCT
ejpam-2522	60	12	27	27	NUM
ejpam-2522	60	13	-	-	SYM
ejpam-2522	60	14	33	33	NUM
ejpam-2522	60	15	29	29	NUM
ejpam-2522	60	16	3	3	NUM
ejpam-2522	60	17	.	.	PUNCT
ejpam-2522	60	18	αgrw	αgrw	ADJ
ejpam-2522	60	19	-	-	PUNCT
ejpam-2522	60	20	closed	close	VERB
ejpam-2522	60	21	sets	set	NOUN
ejpam-2522	60	22	proposition	proposition	NOUN
ejpam-2522	60	23	1	1	NUM
ejpam-2522	60	24	.	.	PUNCT
ejpam-2522	61	1	in	in	ADP
ejpam-2522	61	2	a	a	DET
ejpam-2522	61	3	space	space	NOUN
ejpam-2522	61	4	(	(	PUNCT
ejpam-2522	61	5	x	x	X
ejpam-2522	61	6	,	,	PUNCT
ejpam-2522	61	7	τ	τ	PROPN
ejpam-2522	61	8	)	)	PUNCT
ejpam-2522	61	9	,	,	PUNCT
ejpam-2522	61	10	if	if	SCONJ
ejpam-2522	61	11	rso(x	rso(x	X
ejpam-2522	61	12	)	)	PUNCT
ejpam-2522	61	13	=	=	PUNCT
ejpam-2522	61	14	{	{	PUNCT
ejpam-2522	61	15	;	;	PUNCT
ejpam-2522	61	16	,	,	PUNCT
ejpam-2522	61	17	x	x	X
ejpam-2522	61	18	}	}	PUNCT
ejpam-2522	61	19	,	,	PUNCT
ejpam-2522	61	20	then	then	ADV
ejpam-2522	61	21	every	every	DET
ejpam-2522	61	22	subset	subset	NOUN
ejpam-2522	61	23	of	of	ADP
ejpam-2522	61	24	x	x	PUNCT
ejpam-2522	61	25	is	be	AUX
ejpam-2522	61	26	an	an	DET
ejpam-2522	61	27	αgrw	αgrw	NOUN
ejpam-2522	61	28	-	-	PUNCT
ejpam-2522	61	29	closed	close	VERB
ejpam-2522	61	30	set	set	NOUN
ejpam-2522	61	31	.	.	PUNCT
ejpam-2522	62	1	proof	proof	NOUN
ejpam-2522	62	2	.	.	PUNCT
ejpam-2522	63	1	let	let	VERB
ejpam-2522	63	2	rso(x	rso(x	PRON
ejpam-2522	63	3	)	)	PUNCT
ejpam-2522	63	4	=	=	PUNCT
ejpam-2522	63	5	{	{	PUNCT
ejpam-2522	63	6	;	;	PUNCT
ejpam-2522	63	7	,	,	PUNCT
ejpam-2522	63	8	x	x	SYM
ejpam-2522	63	9	}	}	PUNCT
ejpam-2522	63	10	and	and	CCONJ
ejpam-2522	63	11	a	a	DET
ejpam-2522	63	12	be	be	AUX
ejpam-2522	63	13	any	any	DET
ejpam-2522	63	14	subset	subset	NOUN
ejpam-2522	63	15	of	of	ADP
ejpam-2522	63	16	x	x	X
ejpam-2522	63	17	.	.	PUNCT
ejpam-2522	63	18	suppose	suppose	VERB
ejpam-2522	63	19	a=	a=	ADV
ejpam-2522	63	20	;	;	PUNCT
ejpam-2522	63	21	,	,	PUNCT
ejpam-2522	63	22	then	then	ADV
ejpam-2522	63	23	a	a	PRON
ejpam-2522	63	24	is	be	AUX
ejpam-2522	63	25	an	an	DET
ejpam-2522	63	26	αgrwclosed	αgrwclose	VERB
ejpam-2522	63	27	set	set	NOUN
ejpam-2522	63	28	in	in	ADP
ejpam-2522	63	29	x.	x.	NOUN
ejpam-2522	63	30	suppose	suppose	VERB
ejpam-2522	63	31	a	a	DET
ejpam-2522	63	32	6=	6=	NUM
ejpam-2522	63	33	;	;	PUNCT
ejpam-2522	63	34	,	,	PUNCT
ejpam-2522	63	35	then	then	ADV
ejpam-2522	63	36	x	x	PUNCT
ejpam-2522	63	37	is	be	AUX
ejpam-2522	63	38	the	the	DET
ejpam-2522	63	39	only	only	ADJ
ejpam-2522	63	40	regular	regular	ADJ
ejpam-2522	63	41	semi	semi	ADJ
ejpam-2522	63	42	-	-	ADJ
ejpam-2522	63	43	open	open	ADJ
ejpam-2522	63	44	set	set	NOUN
ejpam-2522	63	45	containing	contain	VERB
ejpam-2522	63	46	a	a	PRON
ejpam-2522	63	47	and	and	CCONJ
ejpam-2522	63	48	so	so	ADV
ejpam-2522	63	49	αcl(a	αcl(a	NUM
ejpam-2522	63	50	)	)	PUNCT
ejpam-2522	63	51	⊆	⊆	NUM
ejpam-2522	63	52	x	x	X
ejpam-2522	63	53	.	.	PUNCT
ejpam-2522	64	1	hence	hence	ADV
ejpam-2522	64	2	a	a	PRON
ejpam-2522	64	3	is	be	AUX
ejpam-2522	64	4	αgrw	αgrw	NOUN
ejpam-2522	64	5	-	-	PUNCT
ejpam-2522	64	6	closed	closed	ADJ
ejpam-2522	64	7	.	.	PUNCT
ejpam-2522	65	1	remark	remark	NOUN
ejpam-2522	65	2	1	1	NUM
ejpam-2522	65	3	.	.	PUNCT
ejpam-2522	66	1	the	the	DET
ejpam-2522	66	2	converse	converse	NOUN
ejpam-2522	66	3	of	of	ADP
ejpam-2522	66	4	the	the	DET
ejpam-2522	66	5	above	above	ADJ
ejpam-2522	66	6	proposition	proposition	NOUN
ejpam-2522	66	7	need	need	AUX
ejpam-2522	66	8	not	not	PART
ejpam-2522	66	9	be	be	AUX
ejpam-2522	66	10	true	true	ADJ
ejpam-2522	66	11	as	as	SCONJ
ejpam-2522	66	12	seen	see	VERB
ejpam-2522	66	13	from	from	ADP
ejpam-2522	66	14	the	the	DET
ejpam-2522	66	15	following	follow	VERB
ejpam-2522	66	16	example	example	NOUN
ejpam-2522	66	17	.	.	PUNCT
ejpam-2522	67	1	example	example	NOUN
ejpam-2522	68	1	1	1	NUM
ejpam-2522	68	2	.	.	PUNCT
ejpam-2522	68	3	let	let	VERB
ejpam-2522	68	4	x	x	PUNCT
ejpam-2522	68	5	=	=	PRON
ejpam-2522	68	6	{	{	PUNCT
ejpam-2522	68	7	a	a	PRON
ejpam-2522	68	8	,	,	PUNCT
ejpam-2522	68	9	b	b	NOUN
ejpam-2522	68	10	,	,	PUNCT
ejpam-2522	68	11	c	c	NOUN
ejpam-2522	68	12	}	}	PUNCT
ejpam-2522	68	13	with	with	ADP
ejpam-2522	68	14	topology	topology	NOUN
ejpam-2522	68	15	τ	τ	X
ejpam-2522	68	16	=	=	PUNCT
ejpam-2522	68	17	{	{	PUNCT
ejpam-2522	68	18	;	;	PUNCT
ejpam-2522	68	19	,	,	PUNCT
ejpam-2522	68	20	{	{	PUNCT
ejpam-2522	68	21	a	a	X
ejpam-2522	68	22	}	}	PUNCT
ejpam-2522	68	23	,	,	PUNCT
ejpam-2522	68	24	{	{	PUNCT
ejpam-2522	68	25	b	b	NOUN
ejpam-2522	68	26	,	,	PUNCT
ejpam-2522	68	27	c	c	NOUN
ejpam-2522	68	28	}	}	PUNCT
ejpam-2522	68	29	,	,	PUNCT
ejpam-2522	68	30	x	x	SYM
ejpam-2522	68	31	}	}	PUNCT
ejpam-2522	68	32	.	.	PUNCT
ejpam-2522	69	1	then	then	ADV
ejpam-2522	69	2	every	every	DET
ejpam-2522	69	3	subset	subset	NOUN
ejpam-2522	69	4	of	of	ADP
ejpam-2522	69	5	x	x	PUNCT
ejpam-2522	69	6	is	be	AUX
ejpam-2522	69	7	αgrw	αgrw	NOUN
ejpam-2522	69	8	-	-	PUNCT
ejpam-2522	69	9	closed	close	VERB
ejpam-2522	69	10	in	in	ADP
ejpam-2522	69	11	x	x	X
ejpam-2522	69	12	but	but	CCONJ
ejpam-2522	69	13	rso(x	rso(x	NOUN
ejpam-2522	69	14	)	)	PUNCT
ejpam-2522	69	15	=	=	PUNCT
ejpam-2522	69	16	{	{	PUNCT
ejpam-2522	69	17	;	;	PUNCT
ejpam-2522	69	18	,	,	PUNCT
ejpam-2522	69	19	{	{	PUNCT
ejpam-2522	69	20	a	a	X
ejpam-2522	69	21	}	}	PUNCT
ejpam-2522	69	22	,	,	PUNCT
ejpam-2522	69	23	{	{	PUNCT
ejpam-2522	69	24	b	b	NOUN
ejpam-2522	69	25	,	,	PUNCT
ejpam-2522	69	26	c	c	NOUN
ejpam-2522	69	27	}	}	PUNCT
ejpam-2522	69	28	,	,	PUNCT
ejpam-2522	69	29	x	x	SYM
ejpam-2522	69	30	}	}	PUNCT
ejpam-2522	69	31	.	.	PUNCT
ejpam-2522	70	1	proposition	proposition	NOUN
ejpam-2522	70	2	2	2	NUM
ejpam-2522	70	3	.	.	PUNCT
ejpam-2522	71	1	every	every	DET
ejpam-2522	71	2	subset	subset	NOUN
ejpam-2522	71	3	of	of	ADP
ejpam-2522	71	4	(	(	PUNCT
ejpam-2522	71	5	x	x	INTJ
ejpam-2522	71	6	,	,	PUNCT
ejpam-2522	71	7	τ	τ	X
ejpam-2522	71	8	)	)	PUNCT
ejpam-2522	71	9	is	be	AUX
ejpam-2522	71	10	αgrw	αgrw	NOUN
ejpam-2522	71	11	-	-	PUNCT
ejpam-2522	71	12	closed	close	VERB
ejpam-2522	71	13	if	if	SCONJ
ejpam-2522	71	14	and	and	CCONJ
ejpam-2522	71	15	only	only	ADV
ejpam-2522	71	16	if	if	SCONJ
ejpam-2522	71	17	rso(x	rso(x	PROPN
ejpam-2522	71	18	,	,	PUNCT
ejpam-2522	71	19	τ	τ	PROPN
ejpam-2522	71	20	)	)	PUNCT
ejpam-2522	71	21	⊆	⊆	NUM
ejpam-2522	71	22	{	{	PUNCT
ejpam-2522	71	23	f	f	NOUN
ejpam-2522	71	24	⊆	⊆	NUM
ejpam-2522	71	25	x	x	SYM
ejpam-2522	71	26	:	:	PUNCT
ejpam-2522	71	27	f	f	X
ejpam-2522	71	28	c	c	X
ejpam-2522	71	29	∈	∈	PROPN
ejpam-2522	71	30	τα	τα	NOUN
ejpam-2522	71	31	}	}	PUNCT
ejpam-2522	71	32	,	,	PUNCT
ejpam-2522	71	33	where	where	SCONJ
ejpam-2522	71	34	τα	τα	NOUN
ejpam-2522	71	35	is	be	AUX
ejpam-2522	71	36	the	the	DET
ejpam-2522	71	37	topology	topology	NOUN
ejpam-2522	71	38	generated	generate	VERB
ejpam-2522	71	39	by	by	ADP
ejpam-2522	71	40	the	the	DET
ejpam-2522	71	41	α	α	NOUN
ejpam-2522	71	42	-	-	ADJ
ejpam-2522	71	43	open	open	ADJ
ejpam-2522	71	44	sets	set	NOUN
ejpam-2522	71	45	in	in	ADP
ejpam-2522	71	46	(	(	PUNCT
ejpam-2522	71	47	x	x	INTJ
ejpam-2522	71	48	,	,	PUNCT
ejpam-2522	71	49	τ	τ	PROPN
ejpam-2522	71	50	)	)	PUNCT
ejpam-2522	71	51	.	.	PUNCT
ejpam-2522	72	1	proof	proof	NOUN
ejpam-2522	72	2	.	.	PUNCT
ejpam-2522	73	1	suppose	suppose	VERB
ejpam-2522	73	2	that	that	SCONJ
ejpam-2522	73	3	every	every	DET
ejpam-2522	73	4	subset	subset	NOUN
ejpam-2522	73	5	of	of	ADP
ejpam-2522	73	6	(	(	PUNCT
ejpam-2522	73	7	x	x	INTJ
ejpam-2522	73	8	,	,	PUNCT
ejpam-2522	73	9	τ	τ	X
ejpam-2522	73	10	)	)	PUNCT
ejpam-2522	73	11	is	be	AUX
ejpam-2522	73	12	αgrw	αgrw	NOUN
ejpam-2522	73	13	-	-	PUNCT
ejpam-2522	73	14	closed	closed	ADJ
ejpam-2522	73	15	.	.	PUNCT
ejpam-2522	74	1	let	let	VERB
ejpam-2522	74	2	u	u	PRON
ejpam-2522	74	3	∈	∈	PROPN
ejpam-2522	74	4	rso(x	rso(x	PROPN
ejpam-2522	74	5	,	,	PUNCT
ejpam-2522	74	6	τ	τ	PROPN
ejpam-2522	74	7	)	)	PUNCT
ejpam-2522	74	8	.	.	PUNCT
ejpam-2522	75	1	since	since	SCONJ
ejpam-2522	75	2	u	u	PROPN
ejpam-2522	75	3	⊆	⊆	NUM
ejpam-2522	75	4	u	u	NOUN
ejpam-2522	75	5	and	and	CCONJ
ejpam-2522	75	6	u	u	NOUN
ejpam-2522	75	7	is	be	AUX
ejpam-2522	75	8	αgrw	αgrw	NOUN
ejpam-2522	75	9	-	-	PUNCT
ejpam-2522	75	10	closed	closed	ADJ
ejpam-2522	75	11	,	,	PUNCT
ejpam-2522	75	12	we	we	PRON
ejpam-2522	75	13	have	have	VERB
ejpam-2522	75	14	αcl(u	αcl(u	NOUN
ejpam-2522	75	15	)	)	PUNCT
ejpam-2522	75	16	⊆	⊆	NUM
ejpam-2522	75	17	u	u	NOUN
ejpam-2522	75	18	.	.	PUNCT
ejpam-2522	76	1	thus	thus	ADV
ejpam-2522	76	2	u	u	X
ejpam-2522	76	3	∈	∈	PROPN
ejpam-2522	76	4	{	{	PUNCT
ejpam-2522	76	5	f	f	NOUN
ejpam-2522	76	6	⊆	⊆	NUM
ejpam-2522	76	7	x	x	SYM
ejpam-2522	76	8	:	:	PUNCT
ejpam-2522	76	9	f	f	X
ejpam-2522	76	10	c	c	X
ejpam-2522	76	11	∈	∈	PROPN
ejpam-2522	76	12	τα	τα	NOUN
ejpam-2522	76	13	}	}	PUNCT
ejpam-2522	76	14	and	and	CCONJ
ejpam-2522	76	15	hence	hence	ADV
ejpam-2522	76	16	rso(x	rso(x	PROPN
ejpam-2522	76	17	,	,	PUNCT
ejpam-2522	76	18	τ	τ	PROPN
ejpam-2522	76	19	)	)	PUNCT
ejpam-2522	76	20	⊆	⊆	NUM
ejpam-2522	76	21	{	{	PUNCT
ejpam-2522	76	22	f	f	NOUN
ejpam-2522	76	23	⊆	⊆	NUM
ejpam-2522	76	24	x	x	SYM
ejpam-2522	76	25	:	:	PUNCT
ejpam-2522	76	26	f	f	X
ejpam-2522	76	27	c	c	X
ejpam-2522	76	28	∈	∈	PROPN
ejpam-2522	76	29	τα	τα	NOUN
ejpam-2522	76	30	}	}	PUNCT
ejpam-2522	76	31	.	.	PUNCT
ejpam-2522	77	1	conversely	conversely	ADV
ejpam-2522	77	2	,	,	PUNCT
ejpam-2522	77	3	assume	assume	VERB
ejpam-2522	77	4	that	that	SCONJ
ejpam-2522	77	5	rso(x	rso(x	PROPN
ejpam-2522	77	6	,	,	PUNCT
ejpam-2522	77	7	τ	τ	PROPN
ejpam-2522	77	8	)	)	PUNCT
ejpam-2522	77	9	⊆	⊆	NUM
ejpam-2522	77	10	{	{	PUNCT
ejpam-2522	77	11	f	f	NOUN
ejpam-2522	77	12	⊆	⊆	NUM
ejpam-2522	77	13	x	x	SYM
ejpam-2522	77	14	:	:	PUNCT
ejpam-2522	77	15	f	f	X
ejpam-2522	77	16	c	c	X
ejpam-2522	77	17	∈	∈	PROPN
ejpam-2522	77	18	τα	τα	NOUN
ejpam-2522	77	19	}	}	PUNCT
ejpam-2522	77	20	.	.	PUNCT
ejpam-2522	78	1	let	let	VERB
ejpam-2522	78	2	a	a	DET
ejpam-2522	78	3	be	be	AUX
ejpam-2522	78	4	any	any	DET
ejpam-2522	78	5	subset	subset	NOUN
ejpam-2522	78	6	of	of	ADP
ejpam-2522	78	7	(	(	PUNCT
ejpam-2522	78	8	x	x	INTJ
ejpam-2522	78	9	,	,	PUNCT
ejpam-2522	78	10	τ	τ	X
ejpam-2522	78	11	)	)	PUNCT
ejpam-2522	78	12	such	such	ADJ
ejpam-2522	78	13	that	that	SCONJ
ejpam-2522	78	14	a⊆	a⊆	PROPN
ejpam-2522	78	15	u	u	NOUN
ejpam-2522	78	16	,	,	PUNCT
ejpam-2522	78	17	where	where	SCONJ
ejpam-2522	78	18	u	u	NOUN
ejpam-2522	78	19	is	be	AUX
ejpam-2522	78	20	regular	regular	ADJ
ejpam-2522	78	21	semi	semi	ADJ
ejpam-2522	78	22	-	-	ADJ
ejpam-2522	78	23	open	open	ADJ
ejpam-2522	78	24	.	.	PUNCT
ejpam-2522	79	1	thus	thus	ADV
ejpam-2522	79	2	u	u	NOUN
ejpam-2522	79	3	is	be	AUX
ejpam-2522	79	4	α	α	NOUN
ejpam-2522	79	5	-	-	PUNCT
ejpam-2522	79	6	closed	closed	ADJ
ejpam-2522	79	7	and	and	CCONJ
ejpam-2522	79	8	so	so	ADV
ejpam-2522	79	9	αcl(a	αcl(a	NUM
ejpam-2522	79	10	)	)	PUNCT
ejpam-2522	79	11	⊆	⊆	NUM
ejpam-2522	79	12	u	u	NOUN
ejpam-2522	79	13	.	.	PUNCT
ejpam-2522	80	1	hence	hence	ADV
ejpam-2522	80	2	a	a	PRON
ejpam-2522	80	3	is	be	AUX
ejpam-2522	80	4	αgrw	αgrw	NOUN
ejpam-2522	80	5	-	-	PUNCT
ejpam-2522	80	6	closed	close	VERB
ejpam-2522	80	7	in	in	ADP
ejpam-2522	80	8	x.	x.	NOUN
ejpam-2522	80	9	proposition	proposition	NOUN
ejpam-2522	80	10	3	3	X
ejpam-2522	80	11	.	.	PUNCT
ejpam-2522	81	1	if	if	SCONJ
ejpam-2522	81	2	a	a	PRON
ejpam-2522	81	3	is	be	AUX
ejpam-2522	81	4	both	both	CCONJ
ejpam-2522	81	5	open	open	ADJ
ejpam-2522	81	6	and	and	CCONJ
ejpam-2522	81	7	g	g	NOUN
ejpam-2522	81	8	-	-	PUNCT
ejpam-2522	81	9	closed	closed	ADJ
ejpam-2522	81	10	in	in	ADP
ejpam-2522	81	11	x	x	SYM
ejpam-2522	81	12	,	,	PUNCT
ejpam-2522	81	13	then	then	ADV
ejpam-2522	81	14	it	it	PRON
ejpam-2522	81	15	is	be	AUX
ejpam-2522	81	16	αgrw	αgrw	NOUN
ejpam-2522	81	17	-	-	PUNCT
ejpam-2522	81	18	closed	close	VERB
ejpam-2522	81	19	in	in	ADP
ejpam-2522	81	20	x.	x.	NOUN
ejpam-2522	81	21	proof	proof	NOUN
ejpam-2522	81	22	.	.	PUNCT
ejpam-2522	82	1	let	let	VERB
ejpam-2522	82	2	a	a	PRON
ejpam-2522	82	3	be	be	AUX
ejpam-2522	82	4	open	open	ADJ
ejpam-2522	82	5	and	and	CCONJ
ejpam-2522	82	6	g	g	NOUN
ejpam-2522	82	7	-	-	PUNCT
ejpam-2522	82	8	closed	closed	ADJ
ejpam-2522	82	9	in	in	ADP
ejpam-2522	82	10	x.	x.	NOUN
ejpam-2522	82	11	let	let	VERB
ejpam-2522	82	12	a	a	DET
ejpam-2522	82	13	⊆	⊆	NUM
ejpam-2522	82	14	u	u	NOUN
ejpam-2522	82	15	and	and	CCONJ
ejpam-2522	82	16	u	u	NOUN
ejpam-2522	82	17	be	be	VERB
ejpam-2522	82	18	regular	regular	ADJ
ejpam-2522	82	19	semi	semi	ADJ
ejpam-2522	82	20	-	-	ADJ
ejpam-2522	82	21	open	open	ADJ
ejpam-2522	82	22	in	in	ADP
ejpam-2522	82	23	x.	x.	NOUN
ejpam-2522	82	24	now	now	ADV
ejpam-2522	82	25	a⊆	a⊆	VERB
ejpam-2522	82	26	a	a	PRON
ejpam-2522	82	27	,	,	PUNCT
ejpam-2522	82	28	we	we	PRON
ejpam-2522	82	29	have	have	VERB
ejpam-2522	82	30	cl(a	cl(a	X
ejpam-2522	82	31	)	)	PUNCT
ejpam-2522	82	32	⊆	⊆	NUM
ejpam-2522	82	33	a.	a.	NOUN
ejpam-2522	82	34	this	this	PRON
ejpam-2522	82	35	implies	imply	VERB
ejpam-2522	82	36	αcl(a	αcl(a	NUM
ejpam-2522	82	37	)	)	PUNCT
ejpam-2522	82	38	⊆	⊆	NUM
ejpam-2522	82	39	u	u	NOUN
ejpam-2522	82	40	.	.	PUNCT
ejpam-2522	83	1	hence	hence	ADV
ejpam-2522	83	2	a	a	PRON
ejpam-2522	83	3	is	be	AUX
ejpam-2522	83	4	αgrw	αgrw	NOUN
ejpam-2522	83	5	-	-	PUNCT
ejpam-2522	83	6	closed	close	VERB
ejpam-2522	83	7	in	in	ADP
ejpam-2522	83	8	x	x	X
ejpam-2522	83	9	.	.	PUNCT
ejpam-2522	83	10	remark	remark	PROPN
ejpam-2522	83	11	2	2	NUM
ejpam-2522	83	12	.	.	PUNCT
ejpam-2522	84	1	if	if	SCONJ
ejpam-2522	84	2	a	a	PRON
ejpam-2522	84	3	is	be	AUX
ejpam-2522	84	4	both	both	CCONJ
ejpam-2522	84	5	open	open	ADJ
ejpam-2522	84	6	and	and	CCONJ
ejpam-2522	84	7	αgrw	αgrw	NOUN
ejpam-2522	84	8	-	-	PUNCT
ejpam-2522	84	9	closed	close	VERB
ejpam-2522	84	10	in	in	ADP
ejpam-2522	84	11	x	x	SYM
ejpam-2522	84	12	,	,	PUNCT
ejpam-2522	84	13	then	then	ADV
ejpam-2522	84	14	a	a	DET
ejpam-2522	84	15	need	need	NOUN
ejpam-2522	84	16	not	not	PART
ejpam-2522	84	17	be	be	AUX
ejpam-2522	84	18	g	g	NOUN
ejpam-2522	84	19	-	-	PUNCT
ejpam-2522	84	20	closed	closed	ADJ
ejpam-2522	84	21	in	in	ADP
ejpam-2522	84	22	x	x	X
ejpam-2522	84	23	.	.	PUNCT
ejpam-2522	84	24	example	example	NOUN
ejpam-2522	85	1	2	2	NUM
ejpam-2522	85	2	.	.	PUNCT
ejpam-2522	85	3	let	let	VERB
ejpam-2522	85	4	x	x	PUNCT
ejpam-2522	85	5	=	=	PRON
ejpam-2522	85	6	{	{	PUNCT
ejpam-2522	85	7	a	a	PRON
ejpam-2522	85	8	,	,	PUNCT
ejpam-2522	85	9	b	b	NOUN
ejpam-2522	85	10	,	,	PUNCT
ejpam-2522	85	11	c	c	NOUN
ejpam-2522	85	12	}	}	PUNCT
ejpam-2522	85	13	with	with	ADP
ejpam-2522	85	14	topology	topology	NOUN
ejpam-2522	85	15	τ	τ	X
ejpam-2522	85	16	=	=	PUNCT
ejpam-2522	85	17	{	{	PUNCT
ejpam-2522	85	18	;	;	PUNCT
ejpam-2522	85	19	,	,	PUNCT
ejpam-2522	85	20	{	{	PUNCT
ejpam-2522	85	21	a	a	X
ejpam-2522	85	22	}	}	PUNCT
ejpam-2522	85	23	,	,	PUNCT
ejpam-2522	85	24	{	{	PUNCT
ejpam-2522	85	25	b	b	NOUN
ejpam-2522	85	26	}	}	PUNCT
ejpam-2522	85	27	,	,	PUNCT
ejpam-2522	85	28	{	{	PUNCT
ejpam-2522	85	29	a	a	DET
ejpam-2522	85	30	,	,	PUNCT
ejpam-2522	85	31	b	b	NOUN
ejpam-2522	85	32	}	}	PUNCT
ejpam-2522	85	33	,	,	PUNCT
ejpam-2522	85	34	x	x	SYM
ejpam-2522	85	35	}	}	PUNCT
ejpam-2522	85	36	.then	.then	X
ejpam-2522	85	37	a=	a=	VERB
ejpam-2522	85	38	{	{	PUNCT
ejpam-2522	85	39	a	a	DET
ejpam-2522	85	40	,	,	PUNCT
ejpam-2522	85	41	b	b	NOUN
ejpam-2522	85	42	}	}	PUNCT
ejpam-2522	85	43	is	be	AUX
ejpam-2522	85	44	both	both	CCONJ
ejpam-2522	85	45	open	open	ADJ
ejpam-2522	85	46	and	and	CCONJ
ejpam-2522	85	47	αgrw	αgrw	NOUN
ejpam-2522	85	48	-	-	PUNCT
ejpam-2522	85	49	closed	closed	ADJ
ejpam-2522	85	50	but	but	CCONJ
ejpam-2522	85	51	not	not	PART
ejpam-2522	85	52	g	g	NOUN
ejpam-2522	85	53	-	-	PUNCT
ejpam-2522	85	54	closed	closed	ADJ
ejpam-2522	85	55	.	.	PUNCT
ejpam-2522	86	1	proposition	proposition	NOUN
ejpam-2522	86	2	4	4	NUM
ejpam-2522	86	3	.	.	PUNCT
ejpam-2522	87	1	if	if	SCONJ
ejpam-2522	87	2	a	a	PRON
ejpam-2522	87	3	is	be	AUX
ejpam-2522	87	4	regular	regular	ADJ
ejpam-2522	87	5	semi	semi	ADJ
ejpam-2522	87	6	-	-	ADJ
ejpam-2522	87	7	open	open	ADJ
ejpam-2522	87	8	and	and	CCONJ
ejpam-2522	87	9	αgrw	αgrw	NOUN
ejpam-2522	87	10	-	-	PUNCT
ejpam-2522	87	11	closed	closed	ADJ
ejpam-2522	87	12	,	,	PUNCT
ejpam-2522	87	13	then	then	ADV
ejpam-2522	87	14	a	a	PRON
ejpam-2522	87	15	is	be	AUX
ejpam-2522	87	16	α	α	PRON
ejpam-2522	87	17	-	-	PUNCT
ejpam-2522	87	18	closed	closed	ADJ
ejpam-2522	87	19	.	.	PUNCT
ejpam-2522	88	1	proof	proof	NOUN
ejpam-2522	88	2	.	.	PUNCT
ejpam-2522	89	1	suppose	suppose	VERB
ejpam-2522	89	2	a	a	PRON
ejpam-2522	89	3	is	be	AUX
ejpam-2522	89	4	regular	regular	ADJ
ejpam-2522	89	5	semi	semi	ADJ
ejpam-2522	89	6	-	-	ADJ
ejpam-2522	89	7	open	open	ADJ
ejpam-2522	89	8	and	and	CCONJ
ejpam-2522	89	9	αgrw	αgrw	NOUN
ejpam-2522	89	10	-	-	PUNCT
ejpam-2522	89	11	closed	closed	ADJ
ejpam-2522	89	12	.	.	PUNCT
ejpam-2522	90	1	we	we	PRON
ejpam-2522	90	2	have	have	VERB
ejpam-2522	90	3	αcl(a	αcl(a	NUM
ejpam-2522	90	4	)	)	PUNCT
ejpam-2522	90	5	⊆	⊆	NUM
ejpam-2522	90	6	a.	a.	NOUN
ejpam-2522	90	7	since	since	SCONJ
ejpam-2522	90	8	a⊆	a⊆	PROPN
ejpam-2522	90	9	αcl(a	αcl(a	NOUN
ejpam-2522	90	10	)	)	PUNCT
ejpam-2522	90	11	always	always	ADV
ejpam-2522	90	12	,	,	PUNCT
ejpam-2522	90	13	αcl(a	αcl(a	NUM
ejpam-2522	90	14	)	)	PUNCT
ejpam-2522	90	15	=	=	SYM
ejpam-2522	90	16	a.	a.	NOUN
ejpam-2522	90	17	hence	hence	ADV
ejpam-2522	90	18	a	a	PRON
ejpam-2522	90	19	is	be	AUX
ejpam-2522	90	20	α	α	PRON
ejpam-2522	90	21	-	-	PUNCT
ejpam-2522	90	22	closed	closed	ADJ
ejpam-2522	90	23	.	.	PUNCT
ejpam-2522	91	1	example	example	NOUN
ejpam-2522	92	1	3	3	NUM
ejpam-2522	92	2	.	.	PUNCT
ejpam-2522	93	1	in	in	ADP
ejpam-2522	93	2	example	example	NOUN
ejpam-2522	93	3	2	2	NUM
ejpam-2522	93	4	,	,	PUNCT
ejpam-2522	93	5	the	the	DET
ejpam-2522	93	6	set	set	NOUN
ejpam-2522	93	7	{	{	PUNCT
ejpam-2522	93	8	b	b	NOUN
ejpam-2522	93	9	,	,	PUNCT
ejpam-2522	93	10	c	c	NOUN
ejpam-2522	93	11	}	}	PUNCT
ejpam-2522	93	12	is	be	AUX
ejpam-2522	93	13	α	α	PRON
ejpam-2522	93	14	-	-	PUNCT
ejpam-2522	93	15	closed	closed	ADJ
ejpam-2522	93	16	and	and	CCONJ
ejpam-2522	93	17	αgrw	αgrw	NOUN
ejpam-2522	93	18	-	-	PUNCT
ejpam-2522	93	19	closed	close	VERB
ejpam-2522	93	20	but	but	CCONJ
ejpam-2522	93	21	is	be	AUX
ejpam-2522	93	22	not	not	PART
ejpam-2522	93	23	regular	regular	ADJ
ejpam-2522	93	24	semi	semi	ADJ
ejpam-2522	93	25	-	-	ADJ
ejpam-2522	93	26	open	open	ADJ
ejpam-2522	93	27	.	.	PUNCT
ejpam-2522	94	1	corollary	corollary	ADJ
ejpam-2522	94	2	1	1	NUM
ejpam-2522	94	3	.	.	PUNCT
ejpam-2522	95	1	let	let	VERB
ejpam-2522	95	2	a	a	PRON
ejpam-2522	95	3	be	be	AUX
ejpam-2522	95	4	regular	regular	ADJ
ejpam-2522	95	5	semi	semi	ADJ
ejpam-2522	95	6	-	-	ADJ
ejpam-2522	95	7	open	open	ADJ
ejpam-2522	95	8	and	and	CCONJ
ejpam-2522	95	9	αgrw	αgrw	NOUN
ejpam-2522	95	10	-	-	PUNCT
ejpam-2522	95	11	closed	close	VERB
ejpam-2522	95	12	in	in	ADP
ejpam-2522	95	13	x.	x.	NOUN
ejpam-2522	95	14	then	then	ADV
ejpam-2522	95	15	a∩	a∩	PROPN
ejpam-2522	95	16	f	f	PROPN
ejpam-2522	95	17	is	be	AUX
ejpam-2522	95	18	αgrw	αgrw	NOUN
ejpam-2522	95	19	-	-	PUNCT
ejpam-2522	95	20	closed	close	VERB
ejpam-2522	95	21	in	in	ADP
ejpam-2522	95	22	x	x	NOUN
ejpam-2522	95	23	,	,	PUNCT
ejpam-2522	95	24	where	where	SCONJ
ejpam-2522	95	25	f	f	PROPN
ejpam-2522	95	26	is	be	AUX
ejpam-2522	95	27	α	α	PRON
ejpam-2522	95	28	-	-	PUNCT
ejpam-2522	95	29	closed	closed	ADJ
ejpam-2522	95	30	.	.	PUNCT
ejpam-2522	96	1	ennis	ennis	PROPN
ejpam-2522	96	2	rosas	rosas	PROPN
ejpam-2522	96	3	,	,	PUNCT
ejpam-2522	96	4	n.	n.	PROPN
ejpam-2522	96	5	selvanayaki	selvanayaki	PROPN
ejpam-2522	96	6	,	,	PUNCT
ejpam-2522	96	7	gnanambal	gnanambal	PROPN
ejpam-2522	96	8	ilango	ilango	PROPN
ejpam-2522	96	9	/	/	SYM
ejpam-2522	96	10	eur	eur	PROPN
ejpam-2522	96	11	.	.	PUNCT
ejpam-2522	97	1	j.	j.	PROPN
ejpam-2522	97	2	pure	pure	PROPN
ejpam-2522	97	3	appl	appl	PROPN
ejpam-2522	97	4	.	.	PROPN
ejpam-2522	97	5	math	math	PROPN
ejpam-2522	97	6	,	,	PUNCT
ejpam-2522	97	7	9	9	NUM
ejpam-2522	97	8	(	(	PUNCT
ejpam-2522	97	9	2016	2016	NUM
ejpam-2522	97	10	)	)	PUNCT
ejpam-2522	97	11	,	,	PUNCT
ejpam-2522	97	12	27	27	NUM
ejpam-2522	97	13	-	-	SYM
ejpam-2522	97	14	33	33	NUM
ejpam-2522	97	15	30	30	NUM
ejpam-2522	97	16	proof	proof	NOUN
ejpam-2522	97	17	.	.	PUNCT
ejpam-2522	98	1	since	since	SCONJ
ejpam-2522	98	2	a	a	PRON
ejpam-2522	98	3	is	be	AUX
ejpam-2522	98	4	regular	regular	ADJ
ejpam-2522	98	5	semi	semi	ADJ
ejpam-2522	98	6	-	-	ADJ
ejpam-2522	98	7	open	open	ADJ
ejpam-2522	98	8	and	and	CCONJ
ejpam-2522	98	9	αgrw	αgrw	NOUN
ejpam-2522	98	10	-	-	PUNCT
ejpam-2522	98	11	closed	close	VERB
ejpam-2522	98	12	then	then	ADV
ejpam-2522	98	13	by	by	ADP
ejpam-2522	98	14	proposition	proposition	NOUN
ejpam-2522	98	15	4	4	NUM
ejpam-2522	98	16	,	,	PUNCT
ejpam-2522	98	17	we	we	PRON
ejpam-2522	98	18	have	have	VERB
ejpam-2522	98	19	a	a	PRON
ejpam-2522	98	20	is	be	AUX
ejpam-2522	98	21	α	α	PRON
ejpam-2522	98	22	-	-	PUNCT
ejpam-2522	98	23	closed	closed	ADJ
ejpam-2522	98	24	.	.	PUNCT
ejpam-2522	99	1	therefore	therefore	ADV
ejpam-2522	99	2	a∩	a∩	PROPN
ejpam-2522	99	3	f	f	PROPN
ejpam-2522	99	4	is	be	AUX
ejpam-2522	99	5	α	α	NOUN
ejpam-2522	99	6	-	-	VERB
ejpam-2522	99	7	closed	closed	ADJ
ejpam-2522	99	8	,	,	PUNCT
ejpam-2522	99	9	since	since	SCONJ
ejpam-2522	99	10	f	f	PROPN
ejpam-2522	99	11	is	be	AUX
ejpam-2522	99	12	α	α	PRON
ejpam-2522	99	13	-	-	PUNCT
ejpam-2522	99	14	closed	closed	ADJ
ejpam-2522	99	15	.	.	PUNCT
ejpam-2522	100	1	hence	hence	ADV
ejpam-2522	100	2	a∩	a∩	PROPN
ejpam-2522	100	3	f	f	PROPN
ejpam-2522	100	4	is	be	AUX
ejpam-2522	100	5	αgrw	αgrw	NOUN
ejpam-2522	100	6	-	-	PUNCT
ejpam-2522	100	7	closed	closed	ADJ
ejpam-2522	100	8	.	.	PUNCT
ejpam-2522	101	1	proposition	proposition	NOUN
ejpam-2522	101	2	5	5	NUM
ejpam-2522	101	3	.	.	PUNCT
ejpam-2522	102	1	if	if	SCONJ
ejpam-2522	102	2	a	a	PRON
ejpam-2522	102	3	is	be	AUX
ejpam-2522	102	4	both	both	CCONJ
ejpam-2522	102	5	open	open	ADJ
ejpam-2522	102	6	and	and	CCONJ
ejpam-2522	102	7	αg	αg	NOUN
ejpam-2522	102	8	-	-	PUNCT
ejpam-2522	102	9	closed	closed	ADJ
ejpam-2522	102	10	,	,	PUNCT
ejpam-2522	102	11	then	then	ADV
ejpam-2522	102	12	a	a	PRON
ejpam-2522	102	13	is	be	AUX
ejpam-2522	102	14	αgrw	αgrw	NOUN
ejpam-2522	102	15	-	-	PUNCT
ejpam-2522	102	16	closed	closed	ADJ
ejpam-2522	102	17	.	.	PUNCT
ejpam-2522	103	1	proof	proof	NOUN
ejpam-2522	103	2	.	.	PUNCT
ejpam-2522	104	1	let	let	VERB
ejpam-2522	104	2	a	a	DET
ejpam-2522	104	3	be	be	AUX
ejpam-2522	104	4	an	an	DET
ejpam-2522	104	5	open	open	ADJ
ejpam-2522	104	6	and	and	CCONJ
ejpam-2522	104	7	αg	αg	NOUN
ejpam-2522	104	8	-	-	PUNCT
ejpam-2522	104	9	closed	closed	ADJ
ejpam-2522	104	10	.	.	PUNCT
ejpam-2522	105	1	let	let	VERB
ejpam-2522	105	2	a⊆	a⊆	PUNCT
ejpam-2522	105	3	u	u	NOUN
ejpam-2522	105	4	and	and	CCONJ
ejpam-2522	105	5	u	u	NOUN
ejpam-2522	105	6	be	be	VERB
ejpam-2522	105	7	regular	regular	ADJ
ejpam-2522	105	8	semi	semi	ADJ
ejpam-2522	105	9	-	-	ADJ
ejpam-2522	105	10	open	open	ADJ
ejpam-2522	105	11	.	.	PUNCT
ejpam-2522	106	1	now	now	ADV
ejpam-2522	106	2	a⊆	a⊆	VERB
ejpam-2522	106	3	a	a	PRON
ejpam-2522	106	4	and	and	CCONJ
ejpam-2522	106	5	by	by	ADP
ejpam-2522	106	6	hypothesis	hypothesis	NOUN
ejpam-2522	106	7	αcl(a	αcl(a	NUM
ejpam-2522	106	8	)	)	PUNCT
ejpam-2522	106	9	⊆	⊆	NUM
ejpam-2522	106	10	a.	a.	NOUN
ejpam-2522	106	11	therefore	therefore	ADV
ejpam-2522	106	12	αcl(a	αcl(a	NUM
ejpam-2522	106	13	)	)	PUNCT
ejpam-2522	106	14	⊆	⊆	NUM
ejpam-2522	106	15	u	u	NOUN
ejpam-2522	106	16	.	.	PUNCT
ejpam-2522	107	1	hence	hence	ADV
ejpam-2522	107	2	a	a	PRON
ejpam-2522	107	3	is	be	AUX
ejpam-2522	107	4	αgrw	αgrw	NOUN
ejpam-2522	107	5	-	-	PUNCT
ejpam-2522	107	6	closed	closed	ADJ
ejpam-2522	107	7	.	.	PUNCT
ejpam-2522	108	1	remark	remark	NOUN
ejpam-2522	108	2	3	3	NUM
ejpam-2522	108	3	.	.	PUNCT
ejpam-2522	109	1	if	if	SCONJ
ejpam-2522	109	2	a	a	PRON
ejpam-2522	109	3	is	be	AUX
ejpam-2522	109	4	both	both	CCONJ
ejpam-2522	109	5	open	open	ADJ
ejpam-2522	109	6	and	and	CCONJ
ejpam-2522	109	7	αgrw	αgrw	NOUN
ejpam-2522	109	8	-	-	PUNCT
ejpam-2522	109	9	closed	closed	ADJ
ejpam-2522	109	10	,	,	PUNCT
ejpam-2522	109	11	then	then	ADV
ejpam-2522	109	12	a	a	DET
ejpam-2522	109	13	need	need	NOUN
ejpam-2522	109	14	not	not	PART
ejpam-2522	109	15	be	be	AUX
ejpam-2522	109	16	αg	αg	NOUN
ejpam-2522	109	17	-	-	PUNCT
ejpam-2522	109	18	closed	closed	ADJ
ejpam-2522	109	19	.	.	PUNCT
ejpam-2522	109	20	example	example	NOUN
ejpam-2522	110	1	4	4	X
ejpam-2522	110	2	.	.	PUNCT
ejpam-2522	110	3	let	let	VERB
ejpam-2522	110	4	x	x	PUNCT
ejpam-2522	110	5	=	=	PRON
ejpam-2522	110	6	{	{	PUNCT
ejpam-2522	110	7	a	a	PRON
ejpam-2522	110	8	,	,	PUNCT
ejpam-2522	110	9	b	b	NOUN
ejpam-2522	110	10	,	,	PUNCT
ejpam-2522	110	11	c	c	NOUN
ejpam-2522	110	12	,	,	PUNCT
ejpam-2522	110	13	d	d	NOUN
ejpam-2522	110	14	}	}	PUNCT
ejpam-2522	110	15	with	with	ADP
ejpam-2522	110	16	topology	topology	NOUN
ejpam-2522	110	17	τ	τ	X
ejpam-2522	110	18	=	=	PUNCT
ejpam-2522	110	19	{	{	PUNCT
ejpam-2522	110	20	;	;	PUNCT
ejpam-2522	110	21	,	,	PUNCT
ejpam-2522	110	22	{	{	PUNCT
ejpam-2522	110	23	a	a	X
ejpam-2522	110	24	}	}	PUNCT
ejpam-2522	110	25	,	,	PUNCT
ejpam-2522	110	26	{	{	PUNCT
ejpam-2522	110	27	b	b	NOUN
ejpam-2522	110	28	}	}	PUNCT
ejpam-2522	110	29	,	,	PUNCT
ejpam-2522	110	30	{	{	PUNCT
ejpam-2522	110	31	a	a	DET
ejpam-2522	110	32	,	,	PUNCT
ejpam-2522	110	33	b	b	NOUN
ejpam-2522	110	34	}	}	PUNCT
ejpam-2522	110	35	,	,	PUNCT
ejpam-2522	110	36	{	{	PUNCT
ejpam-2522	110	37	a	a	DET
ejpam-2522	110	38	,	,	PUNCT
ejpam-2522	110	39	b	b	NOUN
ejpam-2522	110	40	,	,	PUNCT
ejpam-2522	110	41	c	c	NOUN
ejpam-2522	110	42	}	}	PUNCT
ejpam-2522	110	43	,	,	PUNCT
ejpam-2522	110	44	x	x	SYM
ejpam-2522	110	45	}	}	PUNCT
ejpam-2522	110	46	.	.	PUNCT
ejpam-2522	111	1	then	then	ADV
ejpam-2522	111	2	the	the	DET
ejpam-2522	111	3	subsets	subset	NOUN
ejpam-2522	111	4	{	{	PUNCT
ejpam-2522	111	5	a	a	DET
ejpam-2522	111	6	,	,	PUNCT
ejpam-2522	111	7	b	b	NOUN
ejpam-2522	111	8	}	}	PUNCT
ejpam-2522	111	9	and	and	CCONJ
ejpam-2522	111	10	{	{	PUNCT
ejpam-2522	111	11	a	a	PRON
ejpam-2522	111	12	,	,	PUNCT
ejpam-2522	111	13	b	b	NOUN
ejpam-2522	111	14	,	,	PUNCT
ejpam-2522	111	15	c	c	NOUN
ejpam-2522	111	16	}	}	PUNCT
ejpam-2522	111	17	are	be	AUX
ejpam-2522	111	18	αgrw	αgrw	NOUN
ejpam-2522	111	19	-	-	PUNCT
ejpam-2522	111	20	closed	closed	ADJ
ejpam-2522	111	21	and	and	CCONJ
ejpam-2522	111	22	open	open	ADJ
ejpam-2522	111	23	but	but	CCONJ
ejpam-2522	111	24	not	not	PART
ejpam-2522	111	25	αg	αg	ADV
ejpam-2522	111	26	-	-	PUNCT
ejpam-2522	111	27	closed	closed	ADJ
ejpam-2522	111	28	.	.	PUNCT
ejpam-2522	112	1	remark	remark	NOUN
ejpam-2522	112	2	4	4	NUM
ejpam-2522	112	3	.	.	NOUN
ejpam-2522	112	4	difference	difference	NOUN
ejpam-2522	112	5	of	of	ADP
ejpam-2522	112	6	two	two	NUM
ejpam-2522	112	7	αgrw	αgrw	ADJ
ejpam-2522	112	8	-	-	PUNCT
ejpam-2522	112	9	closed	close	VERB
ejpam-2522	112	10	sets	set	NOUN
ejpam-2522	112	11	is	be	AUX
ejpam-2522	112	12	not	not	PART
ejpam-2522	112	13	generally	generally	ADV
ejpam-2522	112	14	αgrw	αgrw	ADJ
ejpam-2522	112	15	-	-	PUNCT
ejpam-2522	112	16	closed	closed	ADJ
ejpam-2522	112	17	.	.	PUNCT
ejpam-2522	113	1	example	example	NOUN
ejpam-2522	114	1	5	5	NUM
ejpam-2522	114	2	.	.	PUNCT
ejpam-2522	114	3	let	let	VERB
ejpam-2522	114	4	x	x	PUNCT
ejpam-2522	114	5	=	=	PRON
ejpam-2522	114	6	{	{	PUNCT
ejpam-2522	114	7	a	a	PRON
ejpam-2522	114	8	,	,	PUNCT
ejpam-2522	114	9	b	b	NOUN
ejpam-2522	114	10	,	,	PUNCT
ejpam-2522	114	11	c	c	NOUN
ejpam-2522	114	12	,	,	PUNCT
ejpam-2522	114	13	d	d	NOUN
ejpam-2522	114	14	}	}	PUNCT
ejpam-2522	114	15	with	with	ADP
ejpam-2522	114	16	topology	topology	NOUN
ejpam-2522	114	17	τ=	τ=	PUNCT
ejpam-2522	114	18	{	{	PUNCT
ejpam-2522	114	19	;	;	PUNCT
ejpam-2522	114	20	,	,	PUNCT
ejpam-2522	114	21	{	{	PUNCT
ejpam-2522	114	22	a	a	X
ejpam-2522	114	23	}	}	PUNCT
ejpam-2522	114	24	,	,	PUNCT
ejpam-2522	114	25	{	{	PUNCT
ejpam-2522	114	26	b	b	NOUN
ejpam-2522	114	27	}	}	PUNCT
ejpam-2522	114	28	,	,	PUNCT
ejpam-2522	114	29	{	{	PUNCT
ejpam-2522	114	30	a	a	DET
ejpam-2522	114	31	,	,	PUNCT
ejpam-2522	114	32	b	b	NOUN
ejpam-2522	114	33	}	}	PUNCT
ejpam-2522	114	34	,	,	PUNCT
ejpam-2522	114	35	{	{	PUNCT
ejpam-2522	114	36	a	a	DET
ejpam-2522	114	37	,	,	PUNCT
ejpam-2522	114	38	b	b	NOUN
ejpam-2522	114	39	,	,	PUNCT
ejpam-2522	114	40	c	c	NOUN
ejpam-2522	114	41	}	}	PUNCT
ejpam-2522	114	42	,	,	PUNCT
ejpam-2522	114	43	x	x	SYM
ejpam-2522	114	44	}	}	PUNCT
ejpam-2522	114	45	.	.	PUNCT
ejpam-2522	115	1	then	then	ADV
ejpam-2522	115	2	the	the	DET
ejpam-2522	115	3	sets	set	NOUN
ejpam-2522	115	4	a=	a=	VERB
ejpam-2522	115	5	{	{	PUNCT
ejpam-2522	115	6	a	a	X
ejpam-2522	115	7	,	,	PUNCT
ejpam-2522	115	8	c	c	NOUN
ejpam-2522	115	9	,	,	PUNCT
ejpam-2522	115	10	d	d	NOUN
ejpam-2522	115	11	}	}	PUNCT
ejpam-2522	115	12	and	and	CCONJ
ejpam-2522	115	13	b	b	X
ejpam-2522	115	14	=	=	SYM
ejpam-2522	115	15	{	{	PUNCT
ejpam-2522	115	16	c	c	NOUN
ejpam-2522	115	17	,	,	PUNCT
ejpam-2522	115	18	d	d	NOUN
ejpam-2522	115	19	}	}	PUNCT
ejpam-2522	115	20	are	be	AUX
ejpam-2522	115	21	αgrw	αgrw	NOUN
ejpam-2522	115	22	-	-	PUNCT
ejpam-2522	115	23	closed	close	VERB
ejpam-2522	115	24	but	but	CCONJ
ejpam-2522	115	25	a−	a−	PROPN
ejpam-2522	115	26	b	b	PROPN
ejpam-2522	116	1	=	=	PUNCT
ejpam-2522	116	2	{	{	PUNCT
ejpam-2522	116	3	a	a	PRON
ejpam-2522	116	4	}	}	PUNCT
ejpam-2522	116	5	is	be	AUX
ejpam-2522	116	6	not	not	PART
ejpam-2522	116	7	αgrw	αgrw	NOUN
ejpam-2522	116	8	-	-	PUNCT
ejpam-2522	116	9	closed	closed	ADJ
ejpam-2522	116	10	.	.	PUNCT
ejpam-2522	117	1	proposition	proposition	NOUN
ejpam-2522	117	2	6	6	NUM
ejpam-2522	117	3	.	.	PUNCT
ejpam-2522	118	1	let	let	VERB
ejpam-2522	118	2	b	b	NOUN
ejpam-2522	118	3	⊆	⊆	NUM
ejpam-2522	118	4	a⊆	a⊆	X
ejpam-2522	118	5	x	x	X
ejpam-2522	118	6	.	.	PUNCT
ejpam-2522	119	1	if	if	SCONJ
ejpam-2522	119	2	a	a	PRON
ejpam-2522	119	3	is	be	AUX
ejpam-2522	119	4	open	open	ADJ
ejpam-2522	119	5	in	in	ADP
ejpam-2522	119	6	x	x	X
ejpam-2522	119	7	,	,	PUNCT
ejpam-2522	119	8	then	then	ADV
ejpam-2522	119	9	a∈	a∈	PROPN
ejpam-2522	119	10	αgrwc(x	αgrwc(x	PROPN
ejpam-2522	119	11	)	)	PUNCT
ejpam-2522	119	12	implies	imply	VERB
ejpam-2522	119	13	a∈	a∈	PROPN
ejpam-2522	119	14	αgrwc(y	αgrwc(y	PROPN
ejpam-2522	119	15	)	)	PUNCT
ejpam-2522	119	16	.	.	PUNCT
ejpam-2522	120	1	proof	proof	NOUN
ejpam-2522	120	2	.	.	PUNCT
ejpam-2522	121	1	let	let	VERB
ejpam-2522	121	2	a	a	PRON
ejpam-2522	121	3	be	be	AUX
ejpam-2522	121	4	αgrw	αgrw	NOUN
ejpam-2522	121	5	-	-	PUNCT
ejpam-2522	121	6	closed	close	VERB
ejpam-2522	121	7	in	in	ADP
ejpam-2522	121	8	x	x	PUNCT
ejpam-2522	121	9	and	and	CCONJ
ejpam-2522	121	10	let	let	VERB
ejpam-2522	121	11	a⊆	a⊆	VERB
ejpam-2522	121	12	g	g	NOUN
ejpam-2522	121	13	where	where	SCONJ
ejpam-2522	121	14	g	g	PROPN
ejpam-2522	121	15	is	be	AUX
ejpam-2522	121	16	regular	regular	ADJ
ejpam-2522	121	17	semi	semi	ADJ
ejpam-2522	121	18	-	-	ADJ
ejpam-2522	121	19	open	open	ADJ
ejpam-2522	121	20	in	in	ADP
ejpam-2522	121	21	y	y	PROPN
ejpam-2522	121	22	.	.	PUNCT
ejpam-2522	122	1	then	then	ADV
ejpam-2522	122	2	g	g	PROPN
ejpam-2522	122	3	=	=	SYM
ejpam-2522	122	4	u	u	PROPN
ejpam-2522	122	5	∩	∩	PROPN
ejpam-2522	122	6	y	y	PROPN
ejpam-2522	122	7	,	,	PUNCT
ejpam-2522	122	8	where	where	SCONJ
ejpam-2522	122	9	u	u	NOUN
ejpam-2522	122	10	is	be	AUX
ejpam-2522	122	11	regular	regular	ADJ
ejpam-2522	122	12	semi	semi	ADJ
ejpam-2522	122	13	-	-	ADJ
ejpam-2522	122	14	open	open	ADJ
ejpam-2522	122	15	in	in	ADP
ejpam-2522	122	16	x	x	PUNCT
ejpam-2522	122	17	by	by	ADP
ejpam-2522	122	18	lemma	lemma	PROPN
ejpam-2522	122	19	1	1	NUM
ejpam-2522	122	20	.	.	PUNCT
ejpam-2522	123	1	this	this	PRON
ejpam-2522	123	2	implies	imply	VERB
ejpam-2522	123	3	a	a	DET
ejpam-2522	123	4	⊆	⊆	NUM
ejpam-2522	123	5	u	u	NOUN
ejpam-2522	123	6	.	.	PUNCT
ejpam-2522	124	1	since	since	SCONJ
ejpam-2522	124	2	a	a	PRON
ejpam-2522	124	3	is	be	AUX
ejpam-2522	124	4	αgrw	αgrw	NOUN
ejpam-2522	124	5	-	-	PUNCT
ejpam-2522	124	6	closed	close	VERB
ejpam-2522	124	7	in	in	ADP
ejpam-2522	124	8	x	x	SYM
ejpam-2522	124	9	,	,	PUNCT
ejpam-2522	124	10	αcl(a	αcl(a	PROPN
ejpam-2522	124	11	)	)	PUNCT
ejpam-2522	124	12	⊆	⊆	NUM
ejpam-2522	124	13	u	u	NOUN
ejpam-2522	124	14	and	and	CCONJ
ejpam-2522	124	15	so	so	ADV
ejpam-2522	124	16	αcl(a	αcl(a	NUM
ejpam-2522	124	17	)	)	PUNCT
ejpam-2522	124	18	∩	∩	NOUN
ejpam-2522	124	19	y	y	PROPN
ejpam-2522	124	20	⊆	⊆	NUM
ejpam-2522	124	21	u	u	NOUN
ejpam-2522	124	22	∩	∩	PROPN
ejpam-2522	124	23	y	y	PROPN
ejpam-2522	124	24	.	.	PUNCT
ejpam-2522	125	1	therefore	therefore	ADV
ejpam-2522	125	2	αcly	αcly	ADV
ejpam-2522	125	3	(	(	PUNCT
ejpam-2522	125	4	a	a	X
ejpam-2522	125	5	)	)	PUNCT
ejpam-2522	125	6	⊆	⊆	NUM
ejpam-2522	125	7	g.	g.	NOUN
ejpam-2522	125	8	hence	hence	ADV
ejpam-2522	125	9	a∈	a∈	PROPN
ejpam-2522	125	10	αgrwc(y	αgrwc(y	PROPN
ejpam-2522	125	11	)	)	PUNCT
ejpam-2522	125	12	.	.	PUNCT
ejpam-2522	126	1	proposition	proposition	NOUN
ejpam-2522	126	2	7	7	NUM
ejpam-2522	126	3	.	.	PUNCT
ejpam-2522	126	4	suppose	suppose	VERB
ejpam-2522	126	5	b	b	SYM
ejpam-2522	126	6	⊆	⊆	NUM
ejpam-2522	126	7	a	a	DET
ejpam-2522	126	8	⊆	⊆	NUM
ejpam-2522	126	9	x	x	SYM
ejpam-2522	126	10	,	,	PUNCT
ejpam-2522	126	11	b	b	PROPN
ejpam-2522	126	12	is	be	AUX
ejpam-2522	126	13	αgrw	αgrw	ADJ
ejpam-2522	126	14	-	-	PUNCT
ejpam-2522	126	15	closed	close	VERB
ejpam-2522	126	16	relative	relative	ADJ
ejpam-2522	126	17	to	to	ADP
ejpam-2522	126	18	a	a	PRON
ejpam-2522	126	19	and	and	CCONJ
ejpam-2522	126	20	a	a	PRON
ejpam-2522	126	21	is	be	AUX
ejpam-2522	126	22	both	both	PRON
ejpam-2522	126	23	regular	regular	ADJ
ejpam-2522	126	24	open	open	ADJ
ejpam-2522	126	25	and	and	CCONJ
ejpam-2522	126	26	αgrw	αgrw	NOUN
ejpam-2522	126	27	-	-	PUNCT
ejpam-2522	126	28	closed	close	VERB
ejpam-2522	126	29	subset	subset	NOUN
ejpam-2522	126	30	of	of	ADP
ejpam-2522	126	31	x	x	X
ejpam-2522	126	32	.	.	PUNCT
ejpam-2522	127	1	then	then	ADV
ejpam-2522	127	2	b	b	PROPN
ejpam-2522	127	3	is	be	AUX
ejpam-2522	127	4	αgrw	αgrw	NOUN
ejpam-2522	127	5	-	-	PUNCT
ejpam-2522	127	6	closed	close	VERB
ejpam-2522	127	7	in	in	ADP
ejpam-2522	127	8	x	x	X
ejpam-2522	127	9	.	.	PUNCT
ejpam-2522	128	1	proof	proof	NOUN
ejpam-2522	128	2	.	.	PUNCT
ejpam-2522	129	1	let	let	VERB
ejpam-2522	129	2	b	b	NOUN
ejpam-2522	129	3	⊆	⊆	NUM
ejpam-2522	129	4	u	u	NOUN
ejpam-2522	129	5	and	and	CCONJ
ejpam-2522	129	6	u	u	NOUN
ejpam-2522	129	7	be	be	VERB
ejpam-2522	129	8	regular	regular	ADJ
ejpam-2522	129	9	semi	semi	ADJ
ejpam-2522	129	10	-	-	ADJ
ejpam-2522	129	11	open	open	ADJ
ejpam-2522	129	12	in	in	ADP
ejpam-2522	129	13	x	x	X
ejpam-2522	129	14	.	.	PUNCT
ejpam-2522	130	1	then	then	ADV
ejpam-2522	130	2	we	we	PRON
ejpam-2522	130	3	have	have	VERB
ejpam-2522	130	4	b	b	NUM
ejpam-2522	130	5	⊆	⊆	NUM
ejpam-2522	130	6	a∩	a∩	PROPN
ejpam-2522	130	7	u	u	NOUN
ejpam-2522	130	8	.	.	PUNCT
ejpam-2522	131	1	since	since	SCONJ
ejpam-2522	131	2	a	a	PRON
ejpam-2522	131	3	is	be	AUX
ejpam-2522	131	4	open	open	ADJ
ejpam-2522	131	5	and	and	CCONJ
ejpam-2522	131	6	u	u	NOUN
ejpam-2522	131	7	is	be	AUX
ejpam-2522	131	8	semi	semi	ADJ
ejpam-2522	131	9	-	-	ADJ
ejpam-2522	131	10	open	open	ADJ
ejpam-2522	131	11	in	in	ADP
ejpam-2522	131	12	x	x	PUNCT
ejpam-2522	131	13	by	by	ADP
ejpam-2522	131	14	theorem	theorem	NOUN
ejpam-2522	131	15	2	2	NUM
ejpam-2522	131	16	,	,	PUNCT
ejpam-2522	131	17	a∩	a∩	PROPN
ejpam-2522	131	18	u	u	NOUN
ejpam-2522	131	19	is	be	AUX
ejpam-2522	131	20	semi	semi	ADJ
ejpam-2522	131	21	-	-	ADJ
ejpam-2522	131	22	open	open	ADJ
ejpam-2522	131	23	in	in	ADP
ejpam-2522	131	24	x	x	X
ejpam-2522	131	25	.	.	PUNCT
ejpam-2522	132	1	since	since	SCONJ
ejpam-2522	132	2	every	every	DET
ejpam-2522	132	3	regularopen	regularopen	NOUN
ejpam-2522	132	4	set	set	NOUN
ejpam-2522	132	5	is	be	AUX
ejpam-2522	132	6	regular	regular	ADJ
ejpam-2522	132	7	semi	semi	ADJ
ejpam-2522	132	8	-	-	ADJ
ejpam-2522	132	9	open	open	ADJ
ejpam-2522	132	10	and	and	CCONJ
ejpam-2522	132	11	every	every	DET
ejpam-2522	132	12	regular	regular	ADJ
ejpam-2522	132	13	semi	semi	ADJ
ejpam-2522	132	14	-	-	ADJ
ejpam-2522	132	15	open	open	ADJ
ejpam-2522	132	16	set	set	NOUN
ejpam-2522	132	17	is	be	AUX
ejpam-2522	132	18	semi	semi	ADJ
ejpam-2522	132	19	-	-	ADJ
ejpam-2522	132	20	closed	closed	ADJ
ejpam-2522	132	21	,	,	PUNCT
ejpam-2522	132	22	a	a	PRON
ejpam-2522	132	23	and	and	CCONJ
ejpam-2522	132	24	u	u	NOUN
ejpam-2522	132	25	are	be	AUX
ejpam-2522	132	26	semi	semi	ADJ
ejpam-2522	132	27	-	-	ADJ
ejpam-2522	132	28	closed	closed	ADJ
ejpam-2522	132	29	.	.	PUNCT
ejpam-2522	133	1	therefore	therefore	ADV
ejpam-2522	133	2	a∩	a∩	PROPN
ejpam-2522	133	3	u	u	PROPN
ejpam-2522	133	4	is	be	AUX
ejpam-2522	133	5	semi	semi	ADJ
ejpam-2522	133	6	-	-	ADJ
ejpam-2522	133	7	closed	closed	ADJ
ejpam-2522	133	8	in	in	ADP
ejpam-2522	133	9	x	x	X
ejpam-2522	133	10	.	.	PUNCT
ejpam-2522	134	1	thus	thus	ADV
ejpam-2522	134	2	a∩	a∩	PROPN
ejpam-2522	134	3	u	u	NOUN
ejpam-2522	134	4	is	be	AUX
ejpam-2522	134	5	regular	regular	ADJ
ejpam-2522	134	6	semi	semi	ADJ
ejpam-2522	134	7	-	-	ADJ
ejpam-2522	134	8	open	open	ADJ
ejpam-2522	134	9	in	in	ADP
ejpam-2522	134	10	x	x	X
ejpam-2522	134	11	.	.	PUNCT
ejpam-2522	135	1	also	also	ADV
ejpam-2522	135	2	a∩	a∩	VERB
ejpam-2522	135	3	u	u	NOUN
ejpam-2522	135	4	⊆	⊆	NUM
ejpam-2522	135	5	a	a	DET
ejpam-2522	135	6	⊆	⊆	NUM
ejpam-2522	135	7	x	x	NOUN
ejpam-2522	135	8	and	and	CCONJ
ejpam-2522	135	9	a	a	PRON
ejpam-2522	135	10	is	be	AUX
ejpam-2522	135	11	open	open	ADJ
ejpam-2522	135	12	subspace	subspace	NOUN
ejpam-2522	135	13	of	of	ADP
ejpam-2522	135	14	x	x	PUNCT
ejpam-2522	135	15	by	by	ADP
ejpam-2522	135	16	lemma	lemma	PROPN
ejpam-2522	135	17	1	1	NUM
ejpam-2522	135	18	,	,	PUNCT
ejpam-2522	135	19	a∩	a∩	PROPN
ejpam-2522	135	20	u	u	NOUN
ejpam-2522	135	21	is	be	AUX
ejpam-2522	135	22	regular	regular	ADJ
ejpam-2522	135	23	semi	semi	ADJ
ejpam-2522	135	24	-	-	ADJ
ejpam-2522	135	25	open	open	ADJ
ejpam-2522	135	26	in	in	ADP
ejpam-2522	135	27	a.	a.	NOUN
ejpam-2522	135	28	since	since	SCONJ
ejpam-2522	135	29	b	b	PROPN
ejpam-2522	135	30	is	be	AUX
ejpam-2522	135	31	αgrw	αgrw	ADJ
ejpam-2522	135	32	-	-	PUNCT
ejpam-2522	135	33	closed	close	VERB
ejpam-2522	135	34	relative	relative	ADJ
ejpam-2522	135	35	to	to	ADP
ejpam-2522	135	36	a	a	DET
ejpam-2522	135	37	,	,	PUNCT
ejpam-2522	135	38	αcla(b	αcla(b	NUM
ejpam-2522	135	39	)	)	PUNCT
ejpam-2522	135	40	⊆	⊆	NUM
ejpam-2522	135	41	a∩	a∩	PROPN
ejpam-2522	135	42	u	u	NOUN
ejpam-2522	135	43	.	.	PUNCT
ejpam-2522	136	1	but	but	CCONJ
ejpam-2522	136	2	αcla(b	αcla(b	NUM
ejpam-2522	136	3	)	)	PUNCT
ejpam-2522	136	4	=	=	SYM
ejpam-2522	136	5	a∩αcl(b	a∩αcl(b	PROPN
ejpam-2522	136	6	)	)	PUNCT
ejpam-2522	136	7	.	.	PUNCT
ejpam-2522	137	1	this	this	PRON
ejpam-2522	137	2	implies	imply	VERB
ejpam-2522	137	3	a∩αcl(b	a∩αcl(b	SYM
ejpam-2522	137	4	)	)	PUNCT
ejpam-2522	137	5	⊆	⊆	NUM
ejpam-2522	137	6	a∩	a∩	PROPN
ejpam-2522	137	7	u	u	NOUN
ejpam-2522	137	8	and	and	CCONJ
ejpam-2522	137	9	we	we	PRON
ejpam-2522	137	10	have	have	VERB
ejpam-2522	137	11	a∩αcl(b	a∩αcl(b	SYM
ejpam-2522	137	12	)	)	PUNCT
ejpam-2522	137	13	⊆	⊆	NUM
ejpam-2522	137	14	u	u	NOUN
ejpam-2522	137	15	.	.	PUNCT
ejpam-2522	138	1	since	since	SCONJ
ejpam-2522	138	2	a	a	PRON
ejpam-2522	138	3	is	be	AUX
ejpam-2522	138	4	regular	regular	ADJ
ejpam-2522	138	5	open	open	ADJ
ejpam-2522	138	6	and	and	CCONJ
ejpam-2522	138	7	αgrw	αgrw	NOUN
ejpam-2522	138	8	-	-	PUNCT
ejpam-2522	138	9	closed	close	VERB
ejpam-2522	138	10	by	by	ADP
ejpam-2522	138	11	proposition	proposition	NOUN
ejpam-2522	138	12	4	4	NUM
ejpam-2522	138	13	,	,	PUNCT
ejpam-2522	138	14	αcl(a	αcl(a	NUM
ejpam-2522	138	15	)	)	PUNCT
ejpam-2522	138	16	=	=	PUNCT
ejpam-2522	138	17	a	a	PRON
ejpam-2522	138	18	and	and	CCONJ
ejpam-2522	138	19	so	so	ADV
ejpam-2522	138	20	αcl(b	αcl(b	PROPN
ejpam-2522	138	21	)	)	PUNCT
ejpam-2522	138	22	⊆	⊆	NUM
ejpam-2522	138	23	a.	a.	NOUN
ejpam-2522	138	24	thus	thus	ADV
ejpam-2522	138	25	αcl(b	αcl(b	NUM
ejpam-2522	138	26	)	)	PUNCT
ejpam-2522	138	27	⊆	⊆	NUM
ejpam-2522	138	28	u	u	NOUN
ejpam-2522	138	29	and	and	CCONJ
ejpam-2522	138	30	hence	hence	ADV
ejpam-2522	138	31	b	b	PROPN
ejpam-2522	138	32	is	be	AUX
ejpam-2522	138	33	αgrw	αgrw	NOUN
ejpam-2522	138	34	-	-	PUNCT
ejpam-2522	138	35	closed	close	VERB
ejpam-2522	138	36	in	in	ADP
ejpam-2522	138	37	x.	x.	NOUN
ejpam-2522	138	38	proposition	proposition	NOUN
ejpam-2522	138	39	8	8	NUM
ejpam-2522	138	40	.	.	PUNCT
ejpam-2522	139	1	if	if	SCONJ
ejpam-2522	139	2	a	a	DET
ejpam-2522	139	3	subset	subset	NOUN
ejpam-2522	139	4	a	a	PRON
ejpam-2522	139	5	of	of	ADP
ejpam-2522	139	6	(	(	PUNCT
ejpam-2522	139	7	x	x	PROPN
ejpam-2522	139	8	,	,	PUNCT
ejpam-2522	139	9	τ	τ	X
ejpam-2522	139	10	)	)	PUNCT
ejpam-2522	139	11	is	be	AUX
ejpam-2522	139	12	αgrw	αgrw	NOUN
ejpam-2522	139	13	-	-	PUNCT
ejpam-2522	139	14	closed	closed	ADJ
ejpam-2522	139	15	,	,	PUNCT
ejpam-2522	139	16	then	then	ADV
ejpam-2522	139	17	αcl(a	αcl(a	NUM
ejpam-2522	139	18	)	)	PUNCT
ejpam-2522	139	19	−	−	NOUN
ejpam-2522	139	20	a	a	PRON
ejpam-2522	139	21	contains	contain	VERB
ejpam-2522	139	22	no	no	DET
ejpam-2522	139	23	non	non	ADJ
ejpam-2522	139	24	-	-	ADJ
ejpam-2522	139	25	empty	empty	ADJ
ejpam-2522	139	26	regular	regular	ADJ
ejpam-2522	139	27	closed	closed	ADJ
ejpam-2522	139	28	set	set	NOUN
ejpam-2522	139	29	.	.	PUNCT
ejpam-2522	140	1	proof	proof	NOUN
ejpam-2522	140	2	.	.	PUNCT
ejpam-2522	141	1	suppose	suppose	VERB
ejpam-2522	141	2	that	that	SCONJ
ejpam-2522	141	3	a	a	DET
ejpam-2522	141	4	isαgrw	isαgrw	NOUN
ejpam-2522	141	5	-	-	PUNCT
ejpam-2522	141	6	closed	closed	ADJ
ejpam-2522	141	7	in	in	ADP
ejpam-2522	141	8	(	(	PUNCT
ejpam-2522	141	9	x	x	INTJ
ejpam-2522	141	10	,	,	PUNCT
ejpam-2522	141	11	τ	τ	PROPN
ejpam-2522	141	12	)	)	PUNCT
ejpam-2522	141	13	and	and	CCONJ
ejpam-2522	141	14	f	f	PROPN
ejpam-2522	141	15	be	be	AUX
ejpam-2522	141	16	a	a	DET
ejpam-2522	141	17	regular	regular	ADJ
ejpam-2522	141	18	closed	closed	ADJ
ejpam-2522	141	19	subset	subset	NOUN
ejpam-2522	141	20	ofαcl(a)−a	ofαcl(a)−a	NUM
ejpam-2522	141	21	.	.	PUNCT
ejpam-2522	142	1	then	then	ADV
ejpam-2522	142	2	a⊆	a⊆	VERB
ejpam-2522	142	3	f	f	PROPN
ejpam-2522	142	4	c	c	PROPN
ejpam-2522	142	5	.	.	PUNCT
ejpam-2522	143	1	since	since	SCONJ
ejpam-2522	143	2	every	every	DET
ejpam-2522	143	3	regular	regular	ADJ
ejpam-2522	143	4	open	open	ADJ
ejpam-2522	143	5	set	set	NOUN
ejpam-2522	143	6	is	be	AUX
ejpam-2522	143	7	regular	regular	ADJ
ejpam-2522	143	8	semi	semi	ADJ
ejpam-2522	143	9	-	-	ADJ
ejpam-2522	143	10	open	open	ADJ
ejpam-2522	143	11	and	and	CCONJ
ejpam-2522	143	12	a	a	PRON
ejpam-2522	143	13	is	be	AUX
ejpam-2522	143	14	αgrw	αgrw	NOUN
ejpam-2522	143	15	-	-	PUNCT
ejpam-2522	143	16	closed	close	VERB
ejpam-2522	143	17	,	,	PUNCT
ejpam-2522	143	18	αcl(a	αcl(a	NUM
ejpam-2522	143	19	)	)	PUNCT
ejpam-2522	143	20	⊆	⊆	NUM
ejpam-2522	143	21	f	f	PROPN
ejpam-2522	143	22	c	c	NOUN
ejpam-2522	143	23	.	.	PUNCT
ejpam-2522	144	1	consequently	consequently	ADV
ejpam-2522	144	2	f	f	PROPN
ejpam-2522	145	1	⊆	⊆	NUM
ejpam-2522	145	2	[	[	X
ejpam-2522	145	3	αcl(a)]c	αcl(a)]c	NOUN
ejpam-2522	145	4	.	.	PUNCT
ejpam-2522	146	1	thus	thus	ADV
ejpam-2522	146	2	f	f	PROPN
ejpam-2522	146	3	⊆	⊆	NUM
ejpam-2522	146	4	αcl(a)∩	αcl(a)∩	PROPN
ejpam-2522	146	5	[	[	X
ejpam-2522	146	6	αcl(a)]c	αcl(a)]c	NOUN
ejpam-2522	146	7	=	=	X
ejpam-2522	146	8	;	;	PUNCT
ejpam-2522	146	9	.	.	PUNCT
ejpam-2522	146	10	hence	hence	ADV
ejpam-2522	146	11	αcl(a)−	αcl(a)−	VERB
ejpam-2522	146	12	a	a	DET
ejpam-2522	146	13	contains	contain	VERB
ejpam-2522	146	14	no	no	DET
ejpam-2522	146	15	non	non	ADJ
ejpam-2522	146	16	-	-	ADJ
ejpam-2522	146	17	empty	empty	ADJ
ejpam-2522	146	18	regular	regular	ADJ
ejpam-2522	146	19	closed	closed	ADJ
ejpam-2522	146	20	set	set	NOUN
ejpam-2522	146	21	.	.	PUNCT
ejpam-2522	147	1	ennis	ennis	PROPN
ejpam-2522	147	2	rosas	rosas	PROPN
ejpam-2522	147	3	,	,	PUNCT
ejpam-2522	147	4	n.	n.	PROPN
ejpam-2522	147	5	selvanayaki	selvanayaki	PROPN
ejpam-2522	147	6	,	,	PUNCT
ejpam-2522	147	7	gnanambal	gnanambal	PROPN
ejpam-2522	147	8	ilango	ilango	PROPN
ejpam-2522	147	9	/	/	SYM
ejpam-2522	147	10	eur	eur	PROPN
ejpam-2522	147	11	.	.	PUNCT
ejpam-2522	148	1	j.	j.	PROPN
ejpam-2522	148	2	pure	pure	PROPN
ejpam-2522	148	3	appl	appl	PROPN
ejpam-2522	148	4	.	.	PROPN
ejpam-2522	148	5	math	math	PROPN
ejpam-2522	148	6	,	,	PUNCT
ejpam-2522	148	7	9	9	NUM
ejpam-2522	148	8	(	(	PUNCT
ejpam-2522	148	9	2016	2016	NUM
ejpam-2522	148	10	)	)	PUNCT
ejpam-2522	148	11	,	,	PUNCT
ejpam-2522	148	12	27	27	NUM
ejpam-2522	148	13	-	-	SYM
ejpam-2522	148	14	33	33	NUM
ejpam-2522	148	15	31	31	NUM
ejpam-2522	148	16	remark	remark	NOUN
ejpam-2522	148	17	5	5	NUM
ejpam-2522	148	18	.	.	PUNCT
ejpam-2522	149	1	the	the	DET
ejpam-2522	149	2	converse	converse	NOUN
ejpam-2522	149	3	of	of	ADP
ejpam-2522	149	4	the	the	DET
ejpam-2522	149	5	above	above	ADJ
ejpam-2522	149	6	proposition	proposition	NOUN
ejpam-2522	149	7	need	need	AUX
ejpam-2522	149	8	not	not	PART
ejpam-2522	149	9	be	be	AUX
ejpam-2522	149	10	true	true	ADJ
ejpam-2522	149	11	.	.	PUNCT
ejpam-2522	150	1	in	in	ADP
ejpam-2522	150	2	example	example	NOUN
ejpam-2522	150	3	2	2	NUM
ejpam-2522	150	4	,	,	PUNCT
ejpam-2522	150	5	let	let	VERB
ejpam-2522	150	6	a	a	DET
ejpam-2522	150	7	=	=	X
ejpam-2522	150	8	{	{	PUNCT
ejpam-2522	150	9	a	a	NOUN
ejpam-2522	150	10	}	}	PUNCT
ejpam-2522	150	11	.	.	PUNCT
ejpam-2522	151	1	then	then	ADV
ejpam-2522	151	2	αcl(a)−a=	αcl(a)−a=	X
ejpam-2522	151	3	{	{	PUNCT
ejpam-2522	151	4	c	c	AUX
ejpam-2522	151	5	}	}	PUNCT
ejpam-2522	151	6	does	do	AUX
ejpam-2522	151	7	not	not	PART
ejpam-2522	151	8	contain	contain	VERB
ejpam-2522	151	9	non	non	ADJ
ejpam-2522	151	10	-	-	ADJ
ejpam-2522	151	11	empty	empty	ADJ
ejpam-2522	151	12	regular	regular	ADJ
ejpam-2522	151	13	closed	closed	ADJ
ejpam-2522	151	14	set	set	NOUN
ejpam-2522	151	15	,	,	PUNCT
ejpam-2522	151	16	but	but	CCONJ
ejpam-2522	151	17	a	a	PRON
ejpam-2522	151	18	is	be	AUX
ejpam-2522	151	19	not	not	PART
ejpam-2522	151	20	an	an	DET
ejpam-2522	151	21	αgrw	αgrw	NOUN
ejpam-2522	151	22	-	-	PUNCT
ejpam-2522	151	23	closed	close	VERB
ejpam-2522	151	24	set	set	NOUN
ejpam-2522	151	25	.	.	PUNCT
ejpam-2522	152	1	proposition	proposition	NOUN
ejpam-2522	152	2	9	9	NUM
ejpam-2522	152	3	.	.	PUNCT
ejpam-2522	153	1	let	let	AUX
ejpam-2522	153	2	a⊆	a⊆	VERB
ejpam-2522	153	3	y	y	PROPN
ejpam-2522	153	4	⊆	⊆	NUM
ejpam-2522	153	5	x	x	PUNCT
ejpam-2522	153	6	and	and	CCONJ
ejpam-2522	153	7	y	y	PROPN
ejpam-2522	153	8	is	be	AUX
ejpam-2522	153	9	regular	regular	ADJ
ejpam-2522	153	10	open	open	ADJ
ejpam-2522	153	11	in	in	ADP
ejpam-2522	153	12	x	x	SYM
ejpam-2522	153	13	then	then	ADV
ejpam-2522	153	14	a	a	PRON
ejpam-2522	153	15	is	be	AUX
ejpam-2522	153	16	αgrw	αgrw	NOUN
ejpam-2522	153	17	-	-	PUNCT
ejpam-2522	153	18	closed	close	VERB
ejpam-2522	153	19	in	in	ADP
ejpam-2522	153	20	y	y	PROPN
ejpam-2522	153	21	whenever	whenever	SCONJ
ejpam-2522	153	22	a	a	PRON
ejpam-2522	153	23	is	be	AUX
ejpam-2522	153	24	αgrw	αgrw	NOUN
ejpam-2522	153	25	-	-	PUNCT
ejpam-2522	153	26	closed	close	VERB
ejpam-2522	153	27	in	in	ADP
ejpam-2522	153	28	x	x	X
ejpam-2522	153	29	.	.	PUNCT
ejpam-2522	154	1	proof	proof	NOUN
ejpam-2522	154	2	.	.	PUNCT
ejpam-2522	155	1	let	let	VERB
ejpam-2522	155	2	a	a	PRON
ejpam-2522	155	3	be	be	AUX
ejpam-2522	155	4	αgrw	αgrw	NOUN
ejpam-2522	155	5	-	-	PUNCT
ejpam-2522	155	6	closed	close	VERB
ejpam-2522	155	7	in	in	ADP
ejpam-2522	155	8	x	x	PUNCT
ejpam-2522	155	9	and	and	CCONJ
ejpam-2522	155	10	y	y	PROPN
ejpam-2522	155	11	be	be	AUX
ejpam-2522	155	12	regular	regular	ADJ
ejpam-2522	155	13	open	open	ADJ
ejpam-2522	155	14	subset	subset	NOUN
ejpam-2522	155	15	of	of	ADP
ejpam-2522	155	16	x	x	X
ejpam-2522	155	17	.	.	PUNCT
ejpam-2522	156	1	let	let	VERB
ejpam-2522	156	2	u	u	PRON
ejpam-2522	156	3	be	be	AUX
ejpam-2522	156	4	any	any	DET
ejpam-2522	156	5	regular	regular	ADJ
ejpam-2522	156	6	semi	semi	ADJ
ejpam-2522	156	7	-	-	ADJ
ejpam-2522	156	8	open	open	ADJ
ejpam-2522	156	9	set	set	NOUN
ejpam-2522	156	10	in	in	ADP
ejpam-2522	156	11	y	y	PROPN
ejpam-2522	156	12	such	such	ADJ
ejpam-2522	156	13	that	that	PRON
ejpam-2522	156	14	a⊆	a⊆	PROPN
ejpam-2522	156	15	u	u	NOUN
ejpam-2522	156	16	.	.	PUNCT
ejpam-2522	157	1	by	by	ADP
ejpam-2522	157	2	lemma	lemma	PROPN
ejpam-2522	157	3	2	2	NUM
ejpam-2522	157	4	,	,	PUNCT
ejpam-2522	157	5	u	u	NOUN
ejpam-2522	157	6	is	be	AUX
ejpam-2522	157	7	regular	regular	ADJ
ejpam-2522	157	8	semi	semi	ADJ
ejpam-2522	157	9	-	-	ADJ
ejpam-2522	157	10	open	open	ADJ
ejpam-2522	157	11	in	in	ADP
ejpam-2522	157	12	x	x	X
ejpam-2522	157	13	.	.	PUNCT
ejpam-2522	158	1	then	then	ADV
ejpam-2522	158	2	we	we	PRON
ejpam-2522	158	3	have	have	VERB
ejpam-2522	158	4	αcl(a	αcl(a	NUM
ejpam-2522	158	5	)	)	PUNCT
ejpam-2522	158	6	⊆	⊆	NUM
ejpam-2522	158	7	u	u	NOUN
ejpam-2522	158	8	.	.	PUNCT
ejpam-2522	159	1	that	that	PRON
ejpam-2522	159	2	is	be	AUX
ejpam-2522	159	3	y	y	PROPN
ejpam-2522	159	4	∩	∩	ADJ
ejpam-2522	159	5	αcl(a	αcl(a	NUM
ejpam-2522	159	6	)	)	PUNCT
ejpam-2522	160	1	⊆	⊆	NUM
ejpam-2522	160	2	y	y	PROPN
ejpam-2522	160	3	∩	∩	ADJ
ejpam-2522	160	4	u	u	NOUN
ejpam-2522	160	5	=	=	PROPN
ejpam-2522	160	6	u	u	PROPN
ejpam-2522	160	7	.	.	PUNCT
ejpam-2522	161	1	thus	thus	ADV
ejpam-2522	161	2	αcly	αcly	ADV
ejpam-2522	161	3	(	(	PUNCT
ejpam-2522	161	4	a	a	X
ejpam-2522	161	5	)	)	PUNCT
ejpam-2522	161	6	⊆	⊆	NUM
ejpam-2522	161	7	u	u	NOUN
ejpam-2522	161	8	and	and	CCONJ
ejpam-2522	161	9	hence	hence	ADV
ejpam-2522	161	10	a	a	PRON
ejpam-2522	161	11	is	be	AUX
ejpam-2522	161	12	αgrw	αgrw	NOUN
ejpam-2522	161	13	-	-	PUNCT
ejpam-2522	161	14	closed	close	VERB
ejpam-2522	161	15	in	in	ADP
ejpam-2522	161	16	y	y	PROPN
ejpam-2522	161	17	.	.	PUNCT
ejpam-2522	162	1	proposition	proposition	NOUN
ejpam-2522	162	2	10	10	NUM
ejpam-2522	162	3	.	.	PUNCT
ejpam-2522	163	1	a	a	DET
ejpam-2522	163	2	subset	subset	NOUN
ejpam-2522	163	3	a	a	PRON
ejpam-2522	163	4	of	of	ADP
ejpam-2522	163	5	(	(	PUNCT
ejpam-2522	163	6	x	x	PROPN
ejpam-2522	163	7	,	,	PUNCT
ejpam-2522	163	8	τ	τ	X
ejpam-2522	163	9	)	)	PUNCT
ejpam-2522	163	10	is	be	AUX
ejpam-2522	163	11	αgrw	αgrw	NOUN
ejpam-2522	163	12	-	-	PUNCT
ejpam-2522	163	13	closed	close	VERB
ejpam-2522	163	14	if	if	SCONJ
ejpam-2522	163	15	and	and	CCONJ
ejpam-2522	163	16	only	only	ADV
ejpam-2522	163	17	if	if	SCONJ
ejpam-2522	163	18	αcl(a	αcl(a	NUM
ejpam-2522	163	19	)	)	PUNCT
ejpam-2522	163	20	⊆	⊆	NUM
ejpam-2522	163	21	rsker(a	rsker(a	NOUN
ejpam-2522	163	22	)	)	PUNCT
ejpam-2522	163	23	.	.	PUNCT
ejpam-2522	164	1	proof	proof	NOUN
ejpam-2522	164	2	.	.	PUNCT
ejpam-2522	165	1	suppose	suppose	VERB
ejpam-2522	165	2	that	that	SCONJ
ejpam-2522	165	3	a	a	PRON
ejpam-2522	165	4	is	be	AUX
ejpam-2522	165	5	αgrw	αgrw	NOUN
ejpam-2522	165	6	-	-	PUNCT
ejpam-2522	165	7	closed	closed	ADJ
ejpam-2522	165	8	.	.	PUNCT
ejpam-2522	166	1	let	let	VERB
ejpam-2522	166	2	x	x	SYM
ejpam-2522	166	3	∈	∈	PROPN
ejpam-2522	166	4	αcl(a	αcl(a	NUM
ejpam-2522	166	5	)	)	PUNCT
ejpam-2522	166	6	.	.	PUNCT
ejpam-2522	167	1	suppose	suppose	VERB
ejpam-2522	168	1	x	x	X
ejpam-2522	168	2	/∈	/∈	PUNCT
ejpam-2522	168	3	rsker(a	rsker(a	NOUN
ejpam-2522	168	4	)	)	PUNCT
ejpam-2522	168	5	,	,	PUNCT
ejpam-2522	168	6	then	then	ADV
ejpam-2522	168	7	there	there	PRON
ejpam-2522	168	8	is	be	VERB
ejpam-2522	168	9	a	a	DET
ejpam-2522	168	10	regular	regular	ADJ
ejpam-2522	168	11	semi	semi	ADJ
ejpam-2522	168	12	-	-	ADJ
ejpam-2522	168	13	open	open	ADJ
ejpam-2522	168	14	set	set	NOUN
ejpam-2522	168	15	u	u	NOUN
ejpam-2522	168	16	containing	contain	VERB
ejpam-2522	168	17	a	a	DET
ejpam-2522	168	18	such	such	ADJ
ejpam-2522	168	19	that	that	PRON
ejpam-2522	168	20	x	x	SYM
ejpam-2522	168	21	/∈	/∈	PUNCT
ejpam-2522	168	22	u	u	INTJ
ejpam-2522	168	23	.	.	PUNCT
ejpam-2522	169	1	since	since	SCONJ
ejpam-2522	169	2	u	u	NOUN
ejpam-2522	169	3	is	be	AUX
ejpam-2522	169	4	regular	regular	ADJ
ejpam-2522	169	5	semi	semi	ADJ
ejpam-2522	169	6	-	-	ADJ
ejpam-2522	169	7	open	open	ADJ
ejpam-2522	169	8	containing	contain	VERB
ejpam-2522	169	9	a	a	PRON
ejpam-2522	169	10	,	,	PUNCT
ejpam-2522	169	11	we	we	PRON
ejpam-2522	169	12	have	have	VERB
ejpam-2522	169	13	x	x	X
ejpam-2522	169	14	/∈	/∈	PUNCT
ejpam-2522	169	15	αcl(a	αcl(a	NUM
ejpam-2522	169	16	)	)	PUNCT
ejpam-2522	169	17	,	,	PUNCT
ejpam-2522	169	18	which	which	PRON
ejpam-2522	169	19	is	be	AUX
ejpam-2522	169	20	a	a	DET
ejpam-2522	169	21	contradiction	contradiction	NOUN
ejpam-2522	169	22	.	.	PUNCT
ejpam-2522	170	1	thus	thus	ADV
ejpam-2522	170	2	αcl(a	αcl(a	NUM
ejpam-2522	170	3	)	)	PUNCT
ejpam-2522	170	4	⊆	⊆	NUM
ejpam-2522	170	5	rsker(a	rsker(a	NOUN
ejpam-2522	170	6	)	)	PUNCT
ejpam-2522	170	7	.	.	PUNCT
ejpam-2522	171	1	conversely	conversely	ADV
ejpam-2522	171	2	,	,	PUNCT
ejpam-2522	171	3	let	let	VERB
ejpam-2522	171	4	αcl(a	αcl(a	NUM
ejpam-2522	171	5	)	)	PUNCT
ejpam-2522	171	6	⊆	⊆	NUM
ejpam-2522	171	7	rsker(a	rsker(a	NOUN
ejpam-2522	171	8	)	)	PUNCT
ejpam-2522	171	9	.	.	PUNCT
ejpam-2522	172	1	if	if	SCONJ
ejpam-2522	172	2	u	u	NOUN
ejpam-2522	172	3	is	be	AUX
ejpam-2522	172	4	any	any	DET
ejpam-2522	172	5	regular	regular	ADJ
ejpam-2522	172	6	semi	semi	ADJ
ejpam-2522	172	7	-	-	ADJ
ejpam-2522	172	8	open	open	ADJ
ejpam-2522	172	9	set	set	NOUN
ejpam-2522	172	10	containing	contain	VERB
ejpam-2522	172	11	a	a	DET
ejpam-2522	172	12	,	,	PUNCT
ejpam-2522	172	13	then	then	ADV
ejpam-2522	172	14	αcl(a	αcl(a	NUM
ejpam-2522	172	15	)	)	PUNCT
ejpam-2522	172	16	⊆	⊆	NUM
ejpam-2522	172	17	rsker(a	rsker(a	NOUN
ejpam-2522	172	18	)	)	PUNCT
ejpam-2522	172	19	⊆	⊆	NUM
ejpam-2522	172	20	u	u	NOUN
ejpam-2522	172	21	.	.	PUNCT
ejpam-2522	173	1	therefore	therefore	ADV
ejpam-2522	173	2	a	a	PRON
ejpam-2522	173	3	is	be	AUX
ejpam-2522	173	4	αgrw	αgrw	NOUN
ejpam-2522	173	5	-	-	PUNCT
ejpam-2522	173	6	closed	closed	ADJ
ejpam-2522	173	7	.	.	PUNCT
ejpam-2522	174	1	remark	remark	NOUN
ejpam-2522	174	2	6	6	NUM
ejpam-2522	174	3	(	(	PUNCT
ejpam-2522	174	4	[	[	X
ejpam-2522	174	5	4	4	NUM
ejpam-2522	174	6	]	]	NUM
ejpam-2522	174	7	)	)	PUNCT
ejpam-2522	174	8	.	.	PUNCT
ejpam-2522	175	1	in	in	ADP
ejpam-2522	175	2	the	the	DET
ejpam-2522	175	3	notion	notion	NOUN
ejpam-2522	175	4	of	of	ADP
ejpam-2522	175	5	lemma	lemma	PROPN
ejpam-2522	175	6	3	3	NUM
ejpam-2522	175	7	,	,	PUNCT
ejpam-2522	175	8	we	we	PRON
ejpam-2522	175	9	may	may	AUX
ejpam-2522	175	10	consider	consider	VERB
ejpam-2522	175	11	the	the	DET
ejpam-2522	175	12	following	follow	VERB
ejpam-2522	175	13	decomposition	decomposition	NOUN
ejpam-2522	175	14	of	of	ADP
ejpam-2522	175	15	a	a	DET
ejpam-2522	175	16	given	give	VERB
ejpam-2522	175	17	topological	topological	ADJ
ejpam-2522	175	18	space	space	NOUN
ejpam-2522	175	19	(	(	PUNCT
ejpam-2522	175	20	x	x	X
ejpam-2522	175	21	,	,	PUNCT
ejpam-2522	175	22	τ	τ	PROPN
ejpam-2522	175	23	)	)	PUNCT
ejpam-2522	175	24	,	,	PUNCT
ejpam-2522	175	25	namely	namely	ADV
ejpam-2522	175	26	x	x	PUNCT
ejpam-2522	176	1	=	=	SYM
ejpam-2522	176	2	x1	x1	PROPN
ejpam-2522	176	3	∪	∪	VERB
ejpam-2522	176	4	x2	x2	PROPN
ejpam-2522	176	5	,	,	PUNCT
ejpam-2522	176	6	where	where	SCONJ
ejpam-2522	176	7	x1	x1	ADV
ejpam-2522	176	8	=	=	SYM
ejpam-2522	176	9	{	{	PUNCT
ejpam-2522	176	10	x	x	SYM
ejpam-2522	176	11	∈	∈	PROPN
ejpam-2522	176	12	x	x	X
ejpam-2522	176	13	:	:	PUNCT
ejpam-2522	176	14	{	{	PUNCT
ejpam-2522	176	15	x	x	X
ejpam-2522	176	16	}	}	PUNCT
ejpam-2522	176	17	is	be	AUX
ejpam-2522	176	18	nowhere	nowhere	ADV
ejpam-2522	176	19	dense	dense	ADJ
ejpam-2522	176	20	}	}	PUNCT
ejpam-2522	176	21	and	and	CCONJ
ejpam-2522	176	22	x2	x2	PROPN
ejpam-2522	176	23	=	=	PRON
ejpam-2522	176	24	{	{	PUNCT
ejpam-2522	176	25	x	x	SYM
ejpam-2522	176	26	∈	∈	PROPN
ejpam-2522	176	27	x	x	X
ejpam-2522	176	28	:	:	PUNCT
ejpam-2522	176	29	{	{	PUNCT
ejpam-2522	176	30	x	x	X
ejpam-2522	176	31	}	}	PUNCT
ejpam-2522	176	32	is	be	AUX
ejpam-2522	176	33	preopen	preopen	ADJ
ejpam-2522	176	34	}	}	PUNCT
ejpam-2522	176	35	.	.	PUNCT
ejpam-2522	177	1	proposition	proposition	NOUN
ejpam-2522	177	2	11	11	NUM
ejpam-2522	177	3	.	.	PUNCT
ejpam-2522	178	1	for	for	ADP
ejpam-2522	178	2	any	any	DET
ejpam-2522	178	3	subset	subset	NOUN
ejpam-2522	178	4	a	a	PRON
ejpam-2522	178	5	of	of	ADP
ejpam-2522	178	6	(	(	PUNCT
ejpam-2522	178	7	x	x	PROPN
ejpam-2522	178	8	,	,	PUNCT
ejpam-2522	178	9	τ	τ	PROPN
ejpam-2522	178	10	)	)	PUNCT
ejpam-2522	178	11	,	,	PUNCT
ejpam-2522	178	12	x2	x2	PROPN
ejpam-2522	178	13	∩αcl(a	∩αcl(a	PRON
ejpam-2522	178	14	)	)	PUNCT
ejpam-2522	178	15	⊆	⊆	NUM
ejpam-2522	178	16	rsker(a	rsker(a	NOUN
ejpam-2522	178	17	)	)	PUNCT
ejpam-2522	178	18	.	.	PUNCT
ejpam-2522	179	1	proof	proof	NOUN
ejpam-2522	179	2	.	.	PUNCT
ejpam-2522	180	1	let	let	VERB
ejpam-2522	180	2	x	x	SYM
ejpam-2522	180	3	∈	∈	PROPN
ejpam-2522	180	4	x2	x2	PROPN
ejpam-2522	180	5	∩	∩	NOUN
ejpam-2522	180	6	αcl(a	αcl(a	NUM
ejpam-2522	180	7	)	)	PUNCT
ejpam-2522	180	8	and	and	CCONJ
ejpam-2522	180	9	suppose	suppose	VERB
ejpam-2522	180	10	that	that	SCONJ
ejpam-2522	180	11	x	x	X
ejpam-2522	180	12	/∈	/∈	PUNCT
ejpam-2522	180	13	rsker(a	rsker(a	NOUN
ejpam-2522	180	14	)	)	PUNCT
ejpam-2522	180	15	.	.	PUNCT
ejpam-2522	181	1	then	then	ADV
ejpam-2522	181	2	there	there	PRON
ejpam-2522	181	3	is	be	VERB
ejpam-2522	181	4	a	a	DET
ejpam-2522	181	5	regular	regular	ADJ
ejpam-2522	181	6	semiopen	semiopen	ADJ
ejpam-2522	181	7	set	set	NOUN
ejpam-2522	181	8	u	u	NOUN
ejpam-2522	181	9	containing	contain	VERB
ejpam-2522	181	10	a	a	DET
ejpam-2522	181	11	such	such	ADJ
ejpam-2522	181	12	that	that	PRON
ejpam-2522	181	13	x	x	SYM
ejpam-2522	181	14	/∈	/∈	PUNCT
ejpam-2522	181	15	u	u	INTJ
ejpam-2522	181	16	.	.	PUNCT
ejpam-2522	182	1	if	if	SCONJ
ejpam-2522	182	2	f	f	PROPN
ejpam-2522	182	3	=	=	PUNCT
ejpam-2522	182	4	x	x	SYM
ejpam-2522	182	5	−u	−u	PROPN
ejpam-2522	182	6	,	,	PUNCT
ejpam-2522	182	7	then	then	ADV
ejpam-2522	182	8	f	f	PROPN
ejpam-2522	182	9	is	be	AUX
ejpam-2522	182	10	regular	regular	ADJ
ejpam-2522	182	11	semi	semi	ADJ
ejpam-2522	182	12	-	-	ADJ
ejpam-2522	182	13	closed	closed	ADJ
ejpam-2522	182	14	and	and	CCONJ
ejpam-2522	182	15	so	so	ADV
ejpam-2522	182	16	f	f	PROPN
ejpam-2522	182	17	is	be	AUX
ejpam-2522	182	18	semi	semi	ADJ
ejpam-2522	182	19	-	-	ADJ
ejpam-2522	182	20	closed	closed	ADJ
ejpam-2522	182	21	.	.	PUNCT
ejpam-2522	183	1	we	we	PRON
ejpam-2522	183	2	have	have	VERB
ejpam-2522	183	3	scl({x	scl({x	NOUN
ejpam-2522	183	4	}	}	PUNCT
ejpam-2522	183	5	)	)	PUNCT
ejpam-2522	184	1	=	=	PRON
ejpam-2522	184	2	{	{	PUNCT
ejpam-2522	184	3	x	x	NOUN
ejpam-2522	184	4	}	}	PUNCT
ejpam-2522	184	5	∪	∪	ADP
ejpam-2522	184	6	int(cl({x	int(cl({x	NOUN
ejpam-2522	184	7	}	}	PUNCT
ejpam-2522	184	8	)	)	PUNCT
ejpam-2522	184	9	)	)	PUNCT
ejpam-2522	185	1	⊆	⊆	NUM
ejpam-2522	185	2	f	f	NOUN
ejpam-2522	185	3	.	.	PUNCT
ejpam-2522	186	1	since	since	SCONJ
ejpam-2522	186	2	αcl({x	αcl({x	NOUN
ejpam-2522	186	3	}	}	PUNCT
ejpam-2522	186	4	)	)	PUNCT
ejpam-2522	186	5	⊆	⊆	NUM
ejpam-2522	186	6	αcl(a	αcl(a	NUM
ejpam-2522	186	7	)	)	PUNCT
ejpam-2522	186	8	,	,	PUNCT
ejpam-2522	186	9	we	we	PRON
ejpam-2522	186	10	have	have	VERB
ejpam-2522	186	11	int(cl({x	int(cl({x	NOUN
ejpam-2522	186	12	}	}	PUNCT
ejpam-2522	186	13	)	)	PUNCT
ejpam-2522	186	14	)	)	PUNCT
ejpam-2522	187	1	⊆	⊆	NUM
ejpam-2522	187	2	a∪	a∪	X
ejpam-2522	187	3	int(cl(a	int(cl(a	PROPN
ejpam-2522	187	4	)	)	PUNCT
ejpam-2522	187	5	)	)	PUNCT
ejpam-2522	187	6	.	.	PUNCT
ejpam-2522	188	1	again	again	ADV
ejpam-2522	188	2	since	since	SCONJ
ejpam-2522	188	3	x	x	PROPN
ejpam-2522	188	4	∈	∈	PROPN
ejpam-2522	188	5	x2	x2	PROPN
ejpam-2522	188	6	,	,	PUNCT
ejpam-2522	188	7	we	we	PRON
ejpam-2522	188	8	have	have	VERB
ejpam-2522	188	9	x	x	NOUN
ejpam-2522	188	10	/∈	/∈	PUNCT
ejpam-2522	189	1	x1	x1	PROPN
ejpam-2522	189	2	and	and	CCONJ
ejpam-2522	189	3	so	so	ADV
ejpam-2522	189	4	int(cl({x	int(cl({x	PROPN
ejpam-2522	189	5	}	}	PUNCT
ejpam-2522	189	6	)	)	PUNCT
ejpam-2522	189	7	)	)	PUNCT
ejpam-2522	190	1	6=	6=	NUM
ejpam-2522	190	2	;	;	PUNCT
ejpam-2522	190	3	.	.	PUNCT
ejpam-2522	191	1	therefore	therefore	ADV
ejpam-2522	191	2	there	there	PRON
ejpam-2522	191	3	has	have	VERB
ejpam-2522	191	4	to	to	PART
ejpam-2522	191	5	be	be	AUX
ejpam-2522	191	6	some	some	DET
ejpam-2522	191	7	point	point	NOUN
ejpam-2522	191	8	y	y	PROPN
ejpam-2522	191	9	∈	∈	PROPN
ejpam-2522	191	10	a∩	a∩	PROPN
ejpam-2522	191	11	int(cl({x	int(cl({x	PROPN
ejpam-2522	191	12	}	}	PUNCT
ejpam-2522	191	13	)	)	PUNCT
ejpam-2522	191	14	)	)	PUNCT
ejpam-2522	191	15	and	and	CCONJ
ejpam-2522	191	16	hence	hence	ADV
ejpam-2522	191	17	y	y	PROPN
ejpam-2522	191	18	∈	∈	PROPN
ejpam-2522	191	19	f∩a	f∩a	PROPN
ejpam-2522	191	20	,	,	PUNCT
ejpam-2522	191	21	a	a	DET
ejpam-2522	191	22	contradiction	contradiction	NOUN
ejpam-2522	191	23	.	.	PUNCT
ejpam-2522	192	1	thus	thus	ADV
ejpam-2522	192	2	x	x	X
ejpam-2522	192	3	∈	∈	NUM
ejpam-2522	192	4	rsker(a	rsker(a	NOUN
ejpam-2522	192	5	)	)	PUNCT
ejpam-2522	192	6	.	.	PUNCT
ejpam-2522	193	1	hence	hence	ADV
ejpam-2522	193	2	x2	x2	PROPN
ejpam-2522	193	3	∩αcl(a	∩αcl(a	PRON
ejpam-2522	193	4	)	)	PUNCT
ejpam-2522	193	5	⊆	⊆	NUM
ejpam-2522	193	6	rsker(a	rsker(a	NOUN
ejpam-2522	193	7	)	)	PUNCT
ejpam-2522	193	8	.	.	PUNCT
ejpam-2522	194	1	proposition	proposition	NOUN
ejpam-2522	194	2	12	12	NUM
ejpam-2522	194	3	.	.	PUNCT
ejpam-2522	195	1	for	for	ADP
ejpam-2522	195	2	any	any	DET
ejpam-2522	195	3	subset	subset	NOUN
ejpam-2522	195	4	a	a	PRON
ejpam-2522	195	5	of	of	ADP
ejpam-2522	195	6	(	(	PUNCT
ejpam-2522	195	7	x	x	PROPN
ejpam-2522	195	8	,	,	PUNCT
ejpam-2522	195	9	τ	τ	PROPN
ejpam-2522	195	10	)	)	PUNCT
ejpam-2522	195	11	,	,	PUNCT
ejpam-2522	195	12	if	if	SCONJ
ejpam-2522	195	13	x1	x1	PROPN
ejpam-2522	195	14	∩αcl(a	∩αcl(a	NOUN
ejpam-2522	195	15	)	)	PUNCT
ejpam-2522	195	16	⊆	⊆	NUM
ejpam-2522	195	17	a	a	PRON
ejpam-2522	195	18	,	,	PUNCT
ejpam-2522	195	19	then	then	ADV
ejpam-2522	195	20	a	a	PRON
ejpam-2522	195	21	is	be	AUX
ejpam-2522	195	22	αgrw	αgrw	NOUN
ejpam-2522	195	23	-	-	PUNCT
ejpam-2522	195	24	closed	close	VERB
ejpam-2522	195	25	in	in	ADP
ejpam-2522	195	26	x	x	X
ejpam-2522	195	27	.	.	PUNCT
ejpam-2522	196	1	proof	proof	NOUN
ejpam-2522	196	2	.	.	PUNCT
ejpam-2522	197	1	suppose	suppose	VERB
ejpam-2522	197	2	that	that	SCONJ
ejpam-2522	197	3	x1	x1	PROPN
ejpam-2522	197	4	∩	∩	ADJ
ejpam-2522	197	5	αcl(a	αcl(a	NUM
ejpam-2522	197	6	)	)	PUNCT
ejpam-2522	197	7	⊆	⊆	NUM
ejpam-2522	197	8	a.	a.	NOUN
ejpam-2522	197	9	then	then	ADV
ejpam-2522	197	10	x1	x1	NUM
ejpam-2522	197	11	∩	∩	ADJ
ejpam-2522	197	12	αcl(a	αcl(a	NUM
ejpam-2522	197	13	)	)	PUNCT
ejpam-2522	197	14	⊆	⊆	NUM
ejpam-2522	197	15	rsker(a	rsker(a	NOUN
ejpam-2522	197	16	)	)	PUNCT
ejpam-2522	197	17	,	,	PUNCT
ejpam-2522	197	18	since	since	SCONJ
ejpam-2522	197	19	a	a	DET
ejpam-2522	197	20	⊆	⊆	NUM
ejpam-2522	197	21	rsker(a	rsker(a	NOUN
ejpam-2522	197	22	)	)	PUNCT
ejpam-2522	197	23	.	.	PUNCT
ejpam-2522	198	1	now	now	ADV
ejpam-2522	198	2	αcl(a	αcl(a	NUM
ejpam-2522	198	3	)	)	PUNCT
ejpam-2522	198	4	=	=	SYM
ejpam-2522	198	5	x	x	SYM
ejpam-2522	198	6	∩αcl(a	∩αcl(a	NUM
ejpam-2522	198	7	)	)	PUNCT
ejpam-2522	198	8	=	=	SYM
ejpam-2522	198	9	(	(	PUNCT
ejpam-2522	198	10	x1∪x2)∩αcl(a	x1∪x2)∩αcl(a	X
ejpam-2522	198	11	)	)	PUNCT
ejpam-2522	199	1	=	=	SYM
ejpam-2522	199	2	(	(	PUNCT
ejpam-2522	199	3	x1∩αcl(a))∪(x2∩αcl(a	x1∩αcl(a))∪(x2∩αcl(a	PROPN
ejpam-2522	199	4	)	)	PUNCT
ejpam-2522	199	5	)	)	PUNCT
ejpam-2522	200	1	⊆	⊆	NUM
ejpam-2522	200	2	rsker(a	rsker(a	NOUN
ejpam-2522	200	3	)	)	PUNCT
ejpam-2522	200	4	,	,	PUNCT
ejpam-2522	200	5	since	since	SCONJ
ejpam-2522	200	6	x1	x1	PROPN
ejpam-2522	200	7	∩αcl(a	∩αcl(a	NOUN
ejpam-2522	200	8	)	)	PUNCT
ejpam-2522	200	9	⊆	⊆	NUM
ejpam-2522	200	10	rsker(a	rsker(a	NOUN
ejpam-2522	200	11	)	)	PUNCT
ejpam-2522	200	12	and	and	CCONJ
ejpam-2522	200	13	by	by	ADP
ejpam-2522	200	14	proposition	proposition	NOUN
ejpam-2522	200	15	11	11	NUM
ejpam-2522	200	16	.	.	PUNCT
ejpam-2522	201	1	thus	thus	ADV
ejpam-2522	201	2	a	a	PRON
ejpam-2522	201	3	is	be	AUX
ejpam-2522	201	4	αgrw	αgrw	NOUN
ejpam-2522	201	5	-	-	PUNCT
ejpam-2522	201	6	closed	close	VERB
ejpam-2522	201	7	by	by	ADP
ejpam-2522	201	8	proposition	proposition	NOUN
ejpam-2522	201	9	10	10	NUM
ejpam-2522	201	10	.	.	PUNCT
ejpam-2522	202	1	proposition	proposition	NOUN
ejpam-2522	202	2	13	13	NUM
ejpam-2522	202	3	.	.	PUNCT
ejpam-2522	203	1	let	let	VERB
ejpam-2522	203	2	x	x	PRON
ejpam-2522	203	3	be	be	AUX
ejpam-2522	203	4	a	a	DET
ejpam-2522	203	5	regular	regular	ADJ
ejpam-2522	203	6	space	space	NOUN
ejpam-2522	203	7	in	in	ADP
ejpam-2522	203	8	which	which	PRON
ejpam-2522	203	9	every	every	DET
ejpam-2522	203	10	regular	regular	ADJ
ejpam-2522	203	11	semi	semi	ADJ
ejpam-2522	203	12	-	-	ADJ
ejpam-2522	203	13	open	open	ADJ
ejpam-2522	203	14	subset	subset	NOUN
ejpam-2522	203	15	is	be	AUX
ejpam-2522	203	16	open	open	ADJ
ejpam-2522	203	17	.	.	PUNCT
ejpam-2522	204	1	if	if	SCONJ
ejpam-2522	204	2	a	a	PRON
ejpam-2522	204	3	is	be	AUX
ejpam-2522	204	4	compact	compact	ADJ
ejpam-2522	204	5	subset	subset	NOUN
ejpam-2522	204	6	of	of	ADP
ejpam-2522	204	7	x	x	X
ejpam-2522	204	8	,	,	PUNCT
ejpam-2522	204	9	then	then	ADV
ejpam-2522	204	10	a	a	PRON
ejpam-2522	204	11	is	be	AUX
ejpam-2522	204	12	αgrw	αgrw	NOUN
ejpam-2522	204	13	-	-	PUNCT
ejpam-2522	204	14	closed	closed	ADJ
ejpam-2522	204	15	.	.	PUNCT
ejpam-2522	205	1	proof	proof	NOUN
ejpam-2522	205	2	.	.	PUNCT
ejpam-2522	206	1	let	let	VERB
ejpam-2522	206	2	a⊆	a⊆	PROPN
ejpam-2522	206	3	u	u	NOUN
ejpam-2522	206	4	and	and	CCONJ
ejpam-2522	206	5	u	u	NOUN
ejpam-2522	206	6	be	be	VERB
ejpam-2522	206	7	regular	regular	ADJ
ejpam-2522	206	8	semi	semi	ADJ
ejpam-2522	206	9	-	-	ADJ
ejpam-2522	206	10	open	open	ADJ
ejpam-2522	206	11	.	.	PUNCT
ejpam-2522	207	1	by	by	ADP
ejpam-2522	207	2	assumption	assumption	NOUN
ejpam-2522	207	3	u	u	NOUN
ejpam-2522	207	4	is	be	AUX
ejpam-2522	207	5	open	open	ADJ
ejpam-2522	207	6	in	in	ADP
ejpam-2522	207	7	x	x	X
ejpam-2522	207	8	.	.	PUNCT
ejpam-2522	208	1	since	since	SCONJ
ejpam-2522	208	2	a	a	PRON
ejpam-2522	208	3	is	be	AUX
ejpam-2522	208	4	a	a	DET
ejpam-2522	208	5	compact	compact	ADJ
ejpam-2522	208	6	subset	subset	NOUN
ejpam-2522	208	7	of	of	ADP
ejpam-2522	208	8	a	a	DET
ejpam-2522	208	9	regular	regular	ADJ
ejpam-2522	208	10	space	space	NOUN
ejpam-2522	208	11	x	x	NOUN
ejpam-2522	208	12	,	,	PUNCT
ejpam-2522	208	13	then	then	ADV
ejpam-2522	208	14	there	there	PRON
ejpam-2522	208	15	exists	exist	VERB
ejpam-2522	208	16	a	a	DET
ejpam-2522	208	17	closed	closed	ADJ
ejpam-2522	208	18	set	set	VERB
ejpam-2522	208	19	v	v	ADP
ejpam-2522	208	20	such	such	ADJ
ejpam-2522	208	21	that	that	PRON
ejpam-2522	208	22	a⊆	a⊆	VERB
ejpam-2522	208	23	v	v	NOUN
ejpam-2522	208	24	=	=	NOUN
ejpam-2522	208	25	cl(v	cl(v	X
ejpam-2522	208	26	)	)	PUNCT
ejpam-2522	208	27	⊆	⊆	NUM
ejpam-2522	208	28	u	u	NOUN
ejpam-2522	208	29	.	.	PUNCT
ejpam-2522	209	1	thus	thus	ADV
ejpam-2522	209	2	cl(v	cl(v	NOUN
ejpam-2522	209	3	)	)	PUNCT
ejpam-2522	209	4	⊆	⊆	NUM
ejpam-2522	209	5	u	u	NOUN
ejpam-2522	209	6	and	and	CCONJ
ejpam-2522	209	7	so	so	ADV
ejpam-2522	209	8	αcl(a	αcl(a	NUM
ejpam-2522	209	9	)	)	PUNCT
ejpam-2522	209	10	⊆	⊆	NUM
ejpam-2522	209	11	u	u	NOUN
ejpam-2522	209	12	.	.	PUNCT
ejpam-2522	210	1	hence	hence	ADV
ejpam-2522	210	2	a	a	PRON
ejpam-2522	210	3	is	be	AUX
ejpam-2522	210	4	αgrw	αgrw	NOUN
ejpam-2522	210	5	-	-	PUNCT
ejpam-2522	210	6	closed	close	VERB
ejpam-2522	210	7	.	.	PUNCT
ejpam-2522	211	1	references	reference	NOUN
ejpam-2522	211	2	32	32	NUM
ejpam-2522	211	3	proposition	proposition	NOUN
ejpam-2522	211	4	14	14	NUM
ejpam-2522	211	5	.	.	PUNCT
ejpam-2522	212	1	if	if	SCONJ
ejpam-2522	212	2	(	(	PUNCT
ejpam-2522	212	3	x	x	X
ejpam-2522	212	4	,	,	PUNCT
ejpam-2522	212	5	τ	τ	X
ejpam-2522	212	6	)	)	PUNCT
ejpam-2522	212	7	is	be	AUX
ejpam-2522	212	8	s	s	NOUN
ejpam-2522	212	9	-	-	ADJ
ejpam-2522	212	10	normal	normal	ADJ
ejpam-2522	212	11	and	and	CCONJ
ejpam-2522	212	12	f	f	PROPN
ejpam-2522	212	13	∩	∩	NOUN
ejpam-2522	212	14	a	a	X
ejpam-2522	212	15	=	=	X
ejpam-2522	212	16	;	;	PUNCT
ejpam-2522	212	17	,	,	PUNCT
ejpam-2522	212	18	where	where	SCONJ
ejpam-2522	212	19	f	f	PROPN
ejpam-2522	212	20	is	be	AUX
ejpam-2522	212	21	regular	regular	ADJ
ejpam-2522	212	22	semi	semi	ADJ
ejpam-2522	212	23	-	-	ADJ
ejpam-2522	212	24	open	open	ADJ
ejpam-2522	212	25	and	and	CCONJ
ejpam-2522	212	26	a	a	PRON
ejpam-2522	212	27	is	be	AUX
ejpam-2522	212	28	αgrw	αgrw	NOUN
ejpam-2522	212	29	-	-	PUNCT
ejpam-2522	212	30	closed	closed	ADJ
ejpam-2522	212	31	,	,	PUNCT
ejpam-2522	212	32	then	then	ADV
ejpam-2522	212	33	there	there	PRON
ejpam-2522	212	34	exist	exist	VERB
ejpam-2522	212	35	disjoint	disjoint	NOUN
ejpam-2522	212	36	semi	semi	ADJ
ejpam-2522	212	37	-	-	ADJ
ejpam-2522	212	38	open	open	ADJ
ejpam-2522	212	39	sets	set	NOUN
ejpam-2522	212	40	s1	s1	NOUN
ejpam-2522	212	41	and	and	CCONJ
ejpam-2522	212	42	s2	s2	VERB
ejpam-2522	212	43	such	such	ADJ
ejpam-2522	212	44	that	that	DET
ejpam-2522	212	45	a⊆	a⊆	PROPN
ejpam-2522	212	46	s1	s1	NOUN
ejpam-2522	212	47	and	and	CCONJ
ejpam-2522	212	48	f	f	PROPN
ejpam-2522	212	49	⊆	⊆	NUM
ejpam-2522	212	50	s2	s2	PROPN
ejpam-2522	212	51	.	.	PUNCT
ejpam-2522	213	1	proof	proof	NOUN
ejpam-2522	213	2	.	.	PUNCT
ejpam-2522	214	1	since	since	SCONJ
ejpam-2522	214	2	f	f	PROPN
ejpam-2522	214	3	is	be	AUX
ejpam-2522	214	4	regular	regular	ADJ
ejpam-2522	214	5	semi	semi	ADJ
ejpam-2522	214	6	-	-	ADJ
ejpam-2522	214	7	open	open	ADJ
ejpam-2522	214	8	and	and	CCONJ
ejpam-2522	214	9	f	f	PROPN
ejpam-2522	214	10	∩	∩	NOUN
ejpam-2522	214	11	a=	a=	VERB
ejpam-2522	214	12	;	;	PUNCT
ejpam-2522	214	13	.	.	PUNCT
ejpam-2522	215	1	then	then	ADV
ejpam-2522	215	2	a⊆	a⊆	VERB
ejpam-2522	215	3	f	f	PROPN
ejpam-2522	215	4	c	c	PROPN
ejpam-2522	215	5	and	and	CCONJ
ejpam-2522	215	6	so	so	ADV
ejpam-2522	215	7	αcl(a	αcl(a	NUM
ejpam-2522	215	8	)	)	PUNCT
ejpam-2522	215	9	⊆	⊆	NUM
ejpam-2522	215	10	f	f	PROPN
ejpam-2522	215	11	c	c	NOUN
ejpam-2522	215	12	.	.	PUNCT
ejpam-2522	216	1	thus	thus	ADV
ejpam-2522	216	2	αcl(a	αcl(a	NUM
ejpam-2522	216	3	)	)	PUNCT
ejpam-2522	216	4	∩	∩	NOUN
ejpam-2522	216	5	f	f	PROPN
ejpam-2522	216	6	=	=	PUNCT
ejpam-2522	216	7	;	;	PUNCT
ejpam-2522	216	8	.	.	PUNCT
ejpam-2522	217	1	since	since	SCONJ
ejpam-2522	217	2	αcl(a	αcl(a	NUM
ejpam-2522	217	3	)	)	PUNCT
ejpam-2522	217	4	and	and	CCONJ
ejpam-2522	217	5	f	f	PROPN
ejpam-2522	217	6	are	be	AUX
ejpam-2522	217	7	semi	semi	ADJ
ejpam-2522	217	8	-	-	ADJ
ejpam-2522	217	9	closed	closed	ADJ
ejpam-2522	217	10	and	and	CCONJ
ejpam-2522	217	11	x	x	X
ejpam-2522	217	12	is	be	AUX
ejpam-2522	217	13	s	s	NOUN
ejpam-2522	217	14	-	-	ADJ
ejpam-2522	217	15	normal	normal	ADJ
ejpam-2522	217	16	,	,	PUNCT
ejpam-2522	217	17	there	there	PRON
ejpam-2522	217	18	exist	exist	VERB
ejpam-2522	217	19	semi	semi	ADJ
ejpam-2522	217	20	-	-	ADJ
ejpam-2522	217	21	open	open	ADJ
ejpam-2522	217	22	sets	set	NOUN
ejpam-2522	217	23	s1	s1	NOUN
ejpam-2522	217	24	and	and	CCONJ
ejpam-2522	217	25	s2	s2	VERB
ejpam-2522	217	26	such	such	ADJ
ejpam-2522	217	27	that	that	DET
ejpam-2522	217	28	αcl(a	αcl(a	NUM
ejpam-2522	217	29	)	)	PUNCT
ejpam-2522	217	30	⊆	⊆	NUM
ejpam-2522	217	31	s1	s1	NOUN
ejpam-2522	217	32	and	and	CCONJ
ejpam-2522	217	33	f	f	PROPN
ejpam-2522	217	34	⊆	⊆	NUM
ejpam-2522	217	35	s2	s2	PROPN
ejpam-2522	217	36	.	.	PUNCT
ejpam-2522	218	1	this	this	PRON
ejpam-2522	218	2	implies	imply	VERB
ejpam-2522	218	3	a⊆	a⊆	PROPN
ejpam-2522	218	4	s1	s1	NOUN
ejpam-2522	218	5	and	and	CCONJ
ejpam-2522	218	6	f	f	PROPN
ejpam-2522	218	7	⊆	⊆	NUM
ejpam-2522	218	8	s2	s2	PROPN
ejpam-2522	218	9	.	.	PUNCT
ejpam-2522	218	10	remark	remark	PROPN
ejpam-2522	218	11	7	7	NUM
ejpam-2522	218	12	.	.	PUNCT
ejpam-2522	218	13	disjoint	disjoint	VERB
ejpam-2522	218	14	αgrw	αgrw	NOUN
ejpam-2522	218	15	-	-	PUNCT
ejpam-2522	218	16	closed	close	VERB
ejpam-2522	218	17	sets	set	NOUN
ejpam-2522	218	18	in	in	ADP
ejpam-2522	218	19	a	a	DET
ejpam-2522	218	20	semi	semi	ADJ
ejpam-2522	218	21	-	-	ADJ
ejpam-2522	218	22	normal	normal	ADJ
ejpam-2522	218	23	space	space	NOUN
ejpam-2522	218	24	can	can	AUX
ejpam-2522	218	25	not	not	PART
ejpam-2522	218	26	be	be	AUX
ejpam-2522	218	27	separated	separate	VERB
ejpam-2522	218	28	by	by	ADP
ejpam-2522	218	29	semi	semi	ADJ
ejpam-2522	218	30	-	-	ADJ
ejpam-2522	218	31	open	open	ADJ
ejpam-2522	218	32	sets	set	NOUN
ejpam-2522	218	33	.	.	PUNCT
ejpam-2522	219	1	in	in	ADP
ejpam-2522	219	2	example	example	NOUN
ejpam-2522	219	3	1	1	NUM
ejpam-2522	219	4	,	,	PUNCT
ejpam-2522	219	5	the	the	DET
ejpam-2522	219	6	space	space	NOUN
ejpam-2522	219	7	(	(	PUNCT
ejpam-2522	219	8	x	x	X
ejpam-2522	219	9	,	,	PUNCT
ejpam-2522	219	10	τ	τ	X
ejpam-2522	219	11	)	)	PUNCT
ejpam-2522	219	12	is	be	AUX
ejpam-2522	219	13	s	s	NOUN
ejpam-2522	219	14	-	-	ADJ
ejpam-2522	219	15	normal	normal	ADJ
ejpam-2522	219	16	,	,	PUNCT
ejpam-2522	219	17	but	but	CCONJ
ejpam-2522	219	18	{	{	PUNCT
ejpam-2522	219	19	a	a	PRON
ejpam-2522	219	20	,	,	PUNCT
ejpam-2522	219	21	b	b	NOUN
ejpam-2522	219	22	}	}	PUNCT
ejpam-2522	219	23	and	and	CCONJ
ejpam-2522	219	24	{	{	PUNCT
ejpam-2522	219	25	c	c	X
ejpam-2522	219	26	}	}	PUNCT
ejpam-2522	219	27	are	be	AUX
ejpam-2522	219	28	disjoint	disjoint	ADJ
ejpam-2522	219	29	αgrw	αgrw	NOUN
ejpam-2522	219	30	-	-	PUNCT
ejpam-2522	219	31	closed	close	VERB
ejpam-2522	219	32	sets	set	NOUN
ejpam-2522	219	33	which	which	PRON
ejpam-2522	219	34	can	can	AUX
ejpam-2522	219	35	not	not	PART
ejpam-2522	219	36	be	be	AUX
ejpam-2522	219	37	separated	separate	VERB
ejpam-2522	219	38	by	by	ADP
ejpam-2522	219	39	disjoint	disjoint	NOUN
ejpam-2522	219	40	semi	semi	ADJ
ejpam-2522	219	41	-	-	ADJ
ejpam-2522	219	42	open	open	ADJ
ejpam-2522	219	43	sets	set	NOUN
ejpam-2522	219	44	.	.	PUNCT
ejpam-2522	220	1	proposition	proposition	NOUN
ejpam-2522	220	2	15	15	NUM
ejpam-2522	220	3	.	.	PUNCT
ejpam-2522	221	1	if	if	SCONJ
ejpam-2522	221	2	(	(	PUNCT
ejpam-2522	221	3	x	x	X
ejpam-2522	221	4	,	,	PUNCT
ejpam-2522	221	5	τ	τ	X
ejpam-2522	221	6	)	)	PUNCT
ejpam-2522	221	7	is	be	AUX
ejpam-2522	221	8	normal	normal	ADJ
ejpam-2522	221	9	in	in	ADP
ejpam-2522	221	10	which	which	PRON
ejpam-2522	221	11	every	every	DET
ejpam-2522	221	12	α	α	NOUN
ejpam-2522	221	13	-	-	PUNCT
ejpam-2522	221	14	closed	closed	ADJ
ejpam-2522	221	15	set	set	NOUN
ejpam-2522	221	16	is	be	AUX
ejpam-2522	221	17	closed	close	VERB
ejpam-2522	221	18	and	and	CCONJ
ejpam-2522	221	19	f	f	PROPN
ejpam-2522	221	20	∩	∩	NOUN
ejpam-2522	221	21	a	a	X
ejpam-2522	221	22	=	=	X
ejpam-2522	221	23	;	;	PUNCT
ejpam-2522	221	24	,	,	PUNCT
ejpam-2522	221	25	where	where	SCONJ
ejpam-2522	221	26	f	f	PROPN
ejpam-2522	221	27	is	be	AUX
ejpam-2522	221	28	regular	regular	ADV
ejpam-2522	221	29	closed	closed	ADJ
ejpam-2522	221	30	and	and	CCONJ
ejpam-2522	221	31	a	a	PRON
ejpam-2522	221	32	is	be	AUX
ejpam-2522	221	33	αgrw	αgrw	NOUN
ejpam-2522	221	34	-	-	PUNCT
ejpam-2522	221	35	closed	close	VERB
ejpam-2522	221	36	then	then	ADV
ejpam-2522	221	37	there	there	PRON
ejpam-2522	221	38	exist	exist	VERB
ejpam-2522	221	39	disjoint	disjoint	ADJ
ejpam-2522	221	40	open	open	ADJ
ejpam-2522	221	41	sets	set	NOUN
ejpam-2522	221	42	o1	o1	NOUN
ejpam-2522	221	43	and	and	CCONJ
ejpam-2522	221	44	o2	o2	PROPN
ejpam-2522	221	45	such	such	ADJ
ejpam-2522	221	46	that	that	DET
ejpam-2522	221	47	a⊆	a⊆	PROPN
ejpam-2522	221	48	o1	o1	NOUN
ejpam-2522	221	49	and	and	CCONJ
ejpam-2522	221	50	f	f	NOUN
ejpam-2522	221	51	⊆	⊆	NUM
ejpam-2522	221	52	o2	o2	PROPN
ejpam-2522	221	53	.	.	PUNCT
ejpam-2522	222	1	proof	proof	NOUN
ejpam-2522	222	2	.	.	PUNCT
ejpam-2522	223	1	similar	similar	ADJ
ejpam-2522	223	2	to	to	ADP
ejpam-2522	223	3	proposition	proposition	NOUN
ejpam-2522	223	4	14	14	NUM
ejpam-2522	223	5	.	.	PUNCT
ejpam-2522	224	1	references	reference	NOUN
ejpam-2522	224	2	[	[	X
ejpam-2522	224	3	1	1	X
ejpam-2522	224	4	]	]	PUNCT
ejpam-2522	224	5	s.	s.	PROPN
ejpam-2522	224	6	s.	s.	PROPN
ejpam-2522	224	7	benchalli	benchalli	PROPN
ejpam-2522	224	8	and	and	CCONJ
ejpam-2522	224	9	r.	r.	PROPN
ejpam-2522	224	10	s.	s.	PROPN
ejpam-2522	224	11	walli	walli	PROPN
ejpam-2522	224	12	.	.	PUNCT
ejpam-2522	225	1	on	on	ADP
ejpam-2522	225	2	rw	rw	NOUN
ejpam-2522	225	3	-	-	PUNCT
ejpam-2522	225	4	closed	close	VERB
ejpam-2522	225	5	sets	set	NOUN
ejpam-2522	225	6	in	in	ADP
ejpam-2522	225	7	topological	topological	ADJ
ejpam-2522	225	8	spaces	space	NOUN
ejpam-2522	225	9	.	.	PUNCT
ejpam-2522	226	1	bulletin	bulletin	NOUN
ejpam-2522	226	2	of	of	ADP
ejpam-2522	226	3	the	the	DET
ejpam-2522	226	4	malaysian	malaysian	PROPN
ejpam-2522	226	5	mathematical	mathematical	PROPN
ejpam-2522	226	6	sciences	sciences	PROPN
ejpam-2522	226	7	society	society	NOUN
ejpam-2522	226	8	,	,	PUNCT
ejpam-2522	226	9	30(2):99–110	30(2):99–110	PROPN
ejpam-2522	226	10	,	,	PUNCT
ejpam-2522	226	11	2007	2007	NUM
ejpam-2522	226	12	.	.	PUNCT
ejpam-2522	227	1	[	[	X
ejpam-2522	227	2	2	2	X
ejpam-2522	227	3	]	]	PUNCT
ejpam-2522	227	4	d.	d.	PROPN
ejpam-2522	227	5	e.	e.	PROPN
ejpam-2522	227	6	cameron	cameron	PROPN
ejpam-2522	227	7	.	.	PUNCT
ejpam-2522	228	1	properties	property	NOUN
ejpam-2522	228	2	of	of	ADP
ejpam-2522	228	3	s	s	NOUN
ejpam-2522	228	4	-	-	PUNCT
ejpam-2522	228	5	closed	closed	ADJ
ejpam-2522	228	6	spaces	space	NOUN
ejpam-2522	228	7	.	.	PUNCT
ejpam-2522	229	1	proceedings	proceeding	NOUN
ejpam-2522	229	2	of	of	ADP
ejpam-2522	229	3	the	the	DET
ejpam-2522	229	4	american	american	PROPN
ejpam-2522	229	5	mathematical	mathematical	PROPN
ejpam-2522	229	6	society	society	NOUN
ejpam-2522	229	7	,	,	PUNCT
ejpam-2522	229	8	72:581–586	72:581–586	PROPN
ejpam-2522	229	9	,	,	PUNCT
ejpam-2522	229	10	1978	1978	NUM
ejpam-2522	229	11	.	.	PUNCT
ejpam-2522	230	1	[	[	X
ejpam-2522	230	2	3	3	X
ejpam-2522	230	3	]	]	PUNCT
ejpam-2522	230	4	s.	s.	PROPN
ejpam-2522	230	5	g.	g.	PROPN
ejpam-2522	230	6	crossley	crossley	PROPN
ejpam-2522	230	7	and	and	CCONJ
ejpam-2522	230	8	s.	s.	PROPN
ejpam-2522	230	9	k.	k.	PROPN
ejpam-2522	230	10	hildebrand	hildebrand	PROPN
ejpam-2522	230	11	.	.	PUNCT
ejpam-2522	231	1	semi	semi	ADJ
ejpam-2522	231	2	-	-	NOUN
ejpam-2522	231	3	closure	closure	ADJ
ejpam-2522	231	4	.	.	PUNCT
ejpam-2522	232	1	texas	texas	PROPN
ejpam-2522	232	2	journal	journal	PROPN
ejpam-2522	232	3	of	of	ADP
ejpam-2522	232	4	science	science	NOUN
ejpam-2522	232	5	,	,	PUNCT
ejpam-2522	232	6	22:99–112	22:99–112	NUM
ejpam-2522	232	7	,	,	PUNCT
ejpam-2522	232	8	1971	1971	NUM
ejpam-2522	232	9	.	.	PUNCT
ejpam-2522	233	1	[	[	X
ejpam-2522	233	2	4	4	X
ejpam-2522	233	3	]	]	PUNCT
ejpam-2522	233	4	j.	j.	PROPN
ejpam-2522	233	5	dontchev	dontchev	PROPN
ejpam-2522	233	6	and	and	CCONJ
ejpam-2522	233	7	h.	h.	PROPN
ejpam-2522	233	8	maki	maki	PROPN
ejpam-2522	233	9	.	.	PUNCT
ejpam-2522	234	1	on	on	ADP
ejpam-2522	234	2	sg	sg	ADV
ejpam-2522	234	3	-	-	PUNCT
ejpam-2522	234	4	closed	close	VERB
ejpam-2522	234	5	sets	set	NOUN
ejpam-2522	234	6	and	and	CCONJ
ejpam-2522	234	7	semi	semi	ADJ
ejpam-2522	234	8	-	-	ADJ
ejpam-2522	234	9	λ	λ	ADJ
ejpam-2522	234	10	closed	closed	ADJ
ejpam-2522	234	11	sets	set	NOUN
ejpam-2522	234	12	.	.	PUNCT
ejpam-2522	235	1	questions	question	NOUN
ejpam-2522	235	2	and	and	CCONJ
ejpam-2522	235	3	answers	answer	NOUN
ejpam-2522	235	4	in	in	ADP
ejpam-2522	235	5	general	general	ADJ
ejpam-2522	235	6	topology	topology	NOUN
ejpam-2522	235	7	,	,	PUNCT
ejpam-2522	235	8	15:259–266	15:259–266	NUM
ejpam-2522	235	9	,	,	PUNCT
ejpam-2522	235	10	1997	1997	NUM
ejpam-2522	235	11	.	.	PUNCT
ejpam-2522	236	1	[	[	X
ejpam-2522	236	2	5	5	X
ejpam-2522	236	3	]	]	PUNCT
ejpam-2522	236	4	g.	g.	PROPN
ejpam-2522	236	5	l.	l.	PROPN
ejpam-2522	236	6	garg	garg	PROPN
ejpam-2522	236	7	and	and	CCONJ
ejpam-2522	236	8	d.	d.	PROPN
ejpam-2522	236	9	sivaraj	sivaraj	PROPN
ejpam-2522	236	10	.	.	PUNCT
ejpam-2522	237	1	on	on	ADP
ejpam-2522	237	2	sc	sc	PROPN
ejpam-2522	237	3	-	-	ADJ
ejpam-2522	237	4	compact	compact	ADJ
ejpam-2522	237	5	and	and	CCONJ
ejpam-2522	237	6	s	s	NOUN
ejpam-2522	237	7	-	-	PUNCT
ejpam-2522	237	8	closed	closed	ADJ
ejpam-2522	237	9	spaces	space	NOUN
ejpam-2522	237	10	.	.	PUNCT
ejpam-2522	238	1	bollettino	bollettino	PROPN
ejpam-2522	238	2	dell’unione	dell’unione	PROPN
ejpam-2522	238	3	matematica	matematica	PROPN
ejpam-2522	238	4	italiana	italiana	PROPN
ejpam-2522	238	5	,	,	PUNCT
ejpam-2522	238	6	6(3b):321–332	6(3b):321–332	PROPN
ejpam-2522	238	7	,	,	PUNCT
ejpam-2522	238	8	1984	1984	NUM
ejpam-2522	238	9	.	.	PUNCT
ejpam-2522	239	1	[	[	X
ejpam-2522	239	2	6	6	NUM
ejpam-2522	239	3	]	]	PUNCT
ejpam-2522	239	4	d.	d.	PROPN
ejpam-2522	239	5	s.	s.	PROPN
ejpam-2522	239	6	jankovic	jankovic	PROPN
ejpam-2522	239	7	and	and	CCONJ
ejpam-2522	239	8	i.	i.	PROPN
ejpam-2522	239	9	l.	l.	PROPN
ejpam-2522	239	10	reilly	reilly	PROPN
ejpam-2522	239	11	.	.	PUNCT
ejpam-2522	240	1	on	on	ADP
ejpam-2522	240	2	semi	semi	ADJ
ejpam-2522	240	3	separation	separation	NOUN
ejpam-2522	240	4	properties	property	NOUN
ejpam-2522	240	5	.	.	PUNCT
ejpam-2522	241	1	indian	indian	ADJ
ejpam-2522	241	2	journal	journal	PROPN
ejpam-2522	241	3	of	of	ADP
ejpam-2522	241	4	pure	pure	ADJ
ejpam-2522	241	5	and	and	CCONJ
ejpam-2522	241	6	applied	applied	ADJ
ejpam-2522	241	7	mathematics	mathematic	NOUN
ejpam-2522	241	8	,	,	PUNCT
ejpam-2522	241	9	16:957–964	16:957–964	PROPN
ejpam-2522	241	10	,	,	PUNCT
ejpam-2522	241	11	1985	1985	NUM
ejpam-2522	241	12	.	.	PUNCT
ejpam-2522	242	1	[	[	X
ejpam-2522	242	2	7	7	X
ejpam-2522	242	3	]	]	X
ejpam-2522	242	4	n.	n.	PROPN
ejpam-2522	242	5	levine	levine	PROPN
ejpam-2522	242	6	.	.	PUNCT
ejpam-2522	243	1	semi	semi	ADJ
ejpam-2522	243	2	-	-	ADJ
ejpam-2522	243	3	open	open	ADJ
ejpam-2522	243	4	sets	set	NOUN
ejpam-2522	243	5	and	and	CCONJ
ejpam-2522	243	6	semi	semi	ADJ
ejpam-2522	243	7	-	-	NOUN
ejpam-2522	243	8	continuity	continuity	NOUN
ejpam-2522	243	9	in	in	ADP
ejpam-2522	243	10	topological	topological	ADJ
ejpam-2522	243	11	spaces	space	NOUN
ejpam-2522	243	12	.	.	PUNCT
ejpam-2522	244	1	the	the	DET
ejpam-2522	244	2	american	american	PROPN
ejpam-2522	244	3	mathematical	mathematical	PROPN
ejpam-2522	244	4	monthly	monthly	ADV
ejpam-2522	244	5	,	,	PUNCT
ejpam-2522	244	6	70:36–41	70:36–41	NUM
ejpam-2522	244	7	,	,	PUNCT
ejpam-2522	244	8	1963	1963	NUM
ejpam-2522	244	9	.	.	PUNCT
ejpam-2522	245	1	[	[	X
ejpam-2522	245	2	8	8	NUM
ejpam-2522	245	3	]	]	X
ejpam-2522	245	4	n.	n.	PROPN
ejpam-2522	245	5	levine	levine	PROPN
ejpam-2522	245	6	.	.	PUNCT
ejpam-2522	246	1	generalized	generalize	VERB
ejpam-2522	246	2	closed	closed	ADJ
ejpam-2522	246	3	sets	set	NOUN
ejpam-2522	246	4	in	in	ADP
ejpam-2522	246	5	topology	topology	NOUN
ejpam-2522	246	6	.	.	PUNCT
ejpam-2522	247	1	rendiconti	rendiconti	VERB
ejpam-2522	247	2	del	del	PROPN
ejpam-2522	247	3	circolo	circolo	PROPN
ejpam-2522	247	4	matematico	matematico	NOUN
ejpam-2522	247	5	di	di	NOUN
ejpam-2522	247	6	palermo	palermo	NOUN
ejpam-2522	247	7	,	,	PUNCT
ejpam-2522	247	8	19:89–96	19:89–96	NUM
ejpam-2522	247	9	,	,	PUNCT
ejpam-2522	247	10	1970	1970	NUM
ejpam-2522	247	11	.	.	PUNCT
ejpam-2522	248	1	[	[	X
ejpam-2522	248	2	9	9	NUM
ejpam-2522	248	3	]	]	PUNCT
ejpam-2522	248	4	s.	s.	PROPN
ejpam-2522	248	5	n.	n.	PROPN
ejpam-2522	248	6	maheshwari	maheshwari	PROPN
ejpam-2522	248	7	and	and	CCONJ
ejpam-2522	248	8	r.	r.	PROPN
ejpam-2522	248	9	prasad	prasad	PROPN
ejpam-2522	248	10	.	.	PUNCT
ejpam-2522	249	1	on	on	ADP
ejpam-2522	249	2	s	s	NOUN
ejpam-2522	249	3	-	-	ADJ
ejpam-2522	249	4	normal	normal	ADJ
ejpam-2522	249	5	spaces	space	NOUN
ejpam-2522	249	6	.	.	PUNCT
ejpam-2522	250	1	bulletin	bulletin	NOUN
ejpam-2522	250	2	mathematique	mathematique	PROPN
ejpam-2522	250	3	de	de	PROPN
ejpam-2522	250	4	la	la	PROPN
ejpam-2522	250	5	societe	societe	PROPN
ejpam-2522	250	6	des	des	PROPN
ejpam-2522	250	7	sciences	sciences	PROPN
ejpam-2522	250	8	mathematiques	mathematiques	PROPN
ejpam-2522	250	9	de	de	PROPN
ejpam-2522	250	10	roumanie	roumanie	PROPN
ejpam-2522	250	11	,	,	PUNCT
ejpam-2522	250	12	22:27–29	22:27–29	NUM
ejpam-2522	250	13	,	,	PUNCT
ejpam-2522	250	14	1978	1978	NUM
ejpam-2522	250	15	.	.	PUNCT
ejpam-2522	251	1	references	reference	NOUN
ejpam-2522	251	2	33	33	NUM
ejpam-2522	251	3	[	[	SYM
ejpam-2522	251	4	10	10	NUM
ejpam-2522	251	5	]	]	X
ejpam-2522	251	6	g.	g.	PROPN
ejpam-2522	251	7	di	di	PROPN
ejpam-2522	251	8	maio	maio	PROPN
ejpam-2522	251	9	and	and	CCONJ
ejpam-2522	251	10	t.	t.	PROPN
ejpam-2522	251	11	noiri	noiri	PROPN
ejpam-2522	251	12	.	.	PUNCT
ejpam-2522	252	1	on	on	ADP
ejpam-2522	252	2	s	s	NOUN
ejpam-2522	252	3	-	-	PUNCT
ejpam-2522	252	4	closed	closed	ADJ
ejpam-2522	252	5	spaces	space	NOUN
ejpam-2522	252	6	.	.	PUNCT
ejpam-2522	253	1	indian	indian	ADJ
ejpam-2522	253	2	journal	journal	PROPN
ejpam-2522	253	3	of	of	ADP
ejpam-2522	253	4	pure	pure	ADJ
ejpam-2522	253	5	and	and	CCONJ
ejpam-2522	253	6	applied	applied	ADJ
ejpam-2522	253	7	mathematics	mathematic	NOUN
ejpam-2522	253	8	,	,	PUNCT
ejpam-2522	253	9	18(3):226–233	18(3):226–233	NUM
ejpam-2522	253	10	,	,	PUNCT
ejpam-2522	253	11	1987	1987	NUM
ejpam-2522	253	12	.	.	PUNCT
ejpam-2522	254	1	[	[	X
ejpam-2522	254	2	11	11	NUM
ejpam-2522	254	3	]	]	X
ejpam-2522	254	4	h.	h.	PROPN
ejpam-2522	254	5	maki	maki	PROPN
ejpam-2522	254	6	,	,	PUNCT
ejpam-2522	254	7	r.	r.	PROPN
ejpam-2522	254	8	devi	devi	PROPN
ejpam-2522	254	9	,	,	PUNCT
ejpam-2522	254	10	and	and	CCONJ
ejpam-2522	254	11	k.	k.	PROPN
ejpam-2522	254	12	balachandran	balachandran	PROPN
ejpam-2522	254	13	.	.	PUNCT
ejpam-2522	255	1	generalized	generalize	VERB
ejpam-2522	255	2	α	α	PRON
ejpam-2522	255	3	-	-	PUNCT
ejpam-2522	255	4	closed	closed	ADJ
ejpam-2522	255	5	sets	set	NOUN
ejpam-2522	255	6	in	in	ADP
ejpam-2522	255	7	topology	topology	NOUN
ejpam-2522	255	8	.	.	PUNCT
ejpam-2522	256	1	buletin	buletin	PROPN
ejpam-2522	256	2	of	of	ADP
ejpam-2522	256	3	fukuoka	fukuoka	PROPN
ejpam-2522	256	4	university	university	PROPN
ejpam-2522	256	5	of	of	ADP
ejpam-2522	256	6	education	education	PROPN
ejpam-2522	256	7	part	part	PROPN
ejpam-2522	256	8	-	-	PUNCT
ejpam-2522	256	9	iii	iii	NOUN
ejpam-2522	256	10	,	,	PUNCT
ejpam-2522	256	11	42:13–21	42:13–21	NUM
ejpam-2522	256	12	,	,	PUNCT
ejpam-2522	256	13	1993	1993	NUM
ejpam-2522	256	14	.	.	PUNCT
ejpam-2522	257	1	[	[	X
ejpam-2522	257	2	12	12	NUM
ejpam-2522	257	3	]	]	PUNCT
ejpam-2522	257	4	a.	a.	NOUN
ejpam-2522	257	5	s.	s.	PROPN
ejpam-2522	257	6	mashhour	mashhour	PROPN
ejpam-2522	257	7	,	,	PUNCT
ejpam-2522	257	8	i.	i.	PROPN
ejpam-2522	257	9	a.	a.	PROPN
ejpam-2522	257	10	hasanein	hasanein	PROPN
ejpam-2522	257	11	,	,	PUNCT
ejpam-2522	257	12	and	and	CCONJ
ejpam-2522	257	13	s.	s.	PROPN
ejpam-2522	257	14	n.	n.	PROPN
ejpam-2522	257	15	el	el	PROPN
ejpam-2522	257	16	-	-	PROPN
ejpam-2522	257	17	deeb	deeb	PROPN
ejpam-2522	257	18	.	.	PUNCT
ejpam-2522	258	1	α	α	X
ejpam-2522	258	2	-	-	ADJ
ejpam-2522	258	3	continuous	continuous	ADJ
ejpam-2522	258	4	and	and	CCONJ
ejpam-2522	258	5	α	α	NOUN
ejpam-2522	258	6	-	-	ADJ
ejpam-2522	258	7	open	open	ADJ
ejpam-2522	258	8	mappings	mapping	NOUN
ejpam-2522	258	9	.	.	PUNCT
ejpam-2522	259	1	acta	acta	PROPN
ejpam-2522	259	2	mathematica	mathematica	PROPN
ejpam-2522	259	3	hungarica	hungarica	PROPN
ejpam-2522	259	4	,	,	PUNCT
ejpam-2522	259	5	41:213–218	41:213–218	PROPN
ejpam-2522	259	6	,	,	PUNCT
ejpam-2522	259	7	1983	1983	NUM
ejpam-2522	259	8	.	.	PUNCT
ejpam-2522	260	1	[	[	X
ejpam-2522	260	2	13	13	NUM
ejpam-2522	260	3	]	]	X
ejpam-2522	260	4	o.	o.	PROPN
ejpam-2522	260	5	njastad	njastad	PROPN
ejpam-2522	260	6	.	.	PUNCT
ejpam-2522	261	1	on	on	ADP
ejpam-2522	261	2	some	some	DET
ejpam-2522	261	3	classes	class	NOUN
ejpam-2522	261	4	of	of	ADP
ejpam-2522	261	5	nearly	nearly	ADV
ejpam-2522	261	6	open	open	ADJ
ejpam-2522	261	7	sets	set	NOUN
ejpam-2522	261	8	.	.	PUNCT
ejpam-2522	262	1	pacific	pacific	PROPN
ejpam-2522	262	2	journal	journal	PROPN
ejpam-2522	262	3	of	of	ADP
ejpam-2522	262	4	mathematics	mathematic	NOUN
ejpam-2522	262	5	,	,	PUNCT
ejpam-2522	262	6	15:961	15:961	NUM
ejpam-2522	262	7	–	–	PUNCT
ejpam-2522	262	8	970	970	NUM
ejpam-2522	262	9	,	,	PUNCT
ejpam-2522	262	10	1965	1965	NUM
ejpam-2522	262	11	.	.	PUNCT
ejpam-2522	263	1	[	[	X
ejpam-2522	263	2	14	14	NUM
ejpam-2522	263	3	]	]	X
ejpam-2522	263	4	n.	n.	NOUN
ejpam-2522	263	5	selvanayaki	selvanayaki	PROPN
ejpam-2522	263	6	and	and	CCONJ
ejpam-2522	263	7	g.	g.	PROPN
ejpam-2522	263	8	ilango	ilango	PROPN
ejpam-2522	263	9	.	.	PUNCT
ejpam-2522	264	1	on	on	ADP
ejpam-2522	264	2	α	α	NOUN
ejpam-2522	264	3	-	-	PUNCT
ejpam-2522	264	4	generalized	generalize	VERB
ejpam-2522	264	5	regular	regular	ADJ
ejpam-2522	264	6	weakly	weakly	ADJ
ejpam-2522	264	7	closed	closed	ADJ
ejpam-2522	264	8	sets	set	NOUN
ejpam-2522	264	9	in	in	ADP
ejpam-2522	264	10	topological	topological	ADJ
ejpam-2522	264	11	spaces	space	NOUN
ejpam-2522	264	12	.	.	PUNCT
ejpam-2522	265	1	scientia	scientia	PROPN
ejpam-2522	265	2	magna	magna	PROPN
ejpam-2522	265	3	,	,	PUNCT
ejpam-2522	265	4	9(1):52–58	9(1):52–58	NUM
ejpam-2522	265	5	,	,	PUNCT
ejpam-2522	265	6	2013	2013	NUM
ejpam-2522	265	7	.	.	PUNCT
ejpam-2522	266	1	[	[	X
ejpam-2522	266	2	15	15	NUM
ejpam-2522	266	3	]	]	X
ejpam-2522	266	4	m.	m.	NOUN
ejpam-2522	266	5	stone	stone	NOUN
ejpam-2522	266	6	.	.	PUNCT
ejpam-2522	267	1	application	application	NOUN
ejpam-2522	267	2	of	of	ADP
ejpam-2522	267	3	the	the	DET
ejpam-2522	267	4	theory	theory	NOUN
ejpam-2522	267	5	of	of	ADP
ejpam-2522	267	6	boolean	boolean	ADJ
ejpam-2522	267	7	rings	ring	NOUN
ejpam-2522	267	8	to	to	ADP
ejpam-2522	267	9	general	general	ADJ
ejpam-2522	267	10	topology	topology	NOUN
ejpam-2522	267	11	.	.	PUNCT
ejpam-2522	268	1	transactions	transaction	NOUN
ejpam-2522	268	2	of	of	ADP
ejpam-2522	268	3	the	the	DET
ejpam-2522	268	4	american	american	PROPN
ejpam-2522	268	5	mathematical	mathematical	PROPN
ejpam-2522	268	6	society	society	NOUN
ejpam-2522	268	7	,	,	PUNCT
ejpam-2522	268	8	41:374–481	41:374–481	PROPN
ejpam-2522	268	9	,	,	PUNCT
ejpam-2522	268	10	1937	1937	NUM
ejpam-2522	268	11	.	.	PUNCT