id	sid	tid	token	lemma	pos
ejpam-1203	1	1	9_devamanoharan.dvi	9_devamanoharan.dvi	NUM
ejpam-1203	1	2	european	european	PROPN
ejpam-1203	1	3	journal	journal	PROPN
ejpam-1203	1	4	of	of	ADP
ejpam-1203	1	5	pure	pure	ADJ
ejpam-1203	1	6	and	and	CCONJ
ejpam-1203	1	7	applied	apply	VERB
ejpam-1203	1	8	mathematics	mathematic	NOUN
ejpam-1203	1	9	vol	vol	NOUN
ejpam-1203	1	10	.	.	PROPN
ejpam-1203	2	1	5	5	NUM
ejpam-1203	2	2	,	,	PUNCT
ejpam-1203	2	3	no	no	INTJ
ejpam-1203	2	4	.	.	NOUN
ejpam-1203	2	5	4	4	NUM
ejpam-1203	2	6	,	,	PUNCT
ejpam-1203	2	7	2012	2012	NUM
ejpam-1203	2	8	,	,	PUNCT
ejpam-1203	2	9	554	554	NUM
ejpam-1203	2	10	-	-	SYM
ejpam-1203	2	11	566	566	NUM
ejpam-1203	2	12	issn	issn	PROPN
ejpam-1203	2	13	1307	1307	NUM
ejpam-1203	2	14	-	-	SYM
ejpam-1203	2	15	5543	5543	NUM
ejpam-1203	2	16	–	–	PUNCT
ejpam-1203	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-1203	2	18	ρ	ρ	VERB
ejpam-1203	2	19	-	-	PUNCT
ejpam-1203	2	20	closed	closed	ADJ
ejpam-1203	2	21	sets	set	NOUN
ejpam-1203	2	22	in	in	ADP
ejpam-1203	2	23	topological	topological	ADJ
ejpam-1203	2	24	spaces	space	NOUN
ejpam-1203	2	25	c.	c.	PROPN
ejpam-1203	2	26	devamanoharan1,∗	devamanoharan1,∗	PROPN
ejpam-1203	2	27	,	,	PUNCT
ejpam-1203	2	28	s.pious	s.pious	ADJ
ejpam-1203	2	29	missier1	missier1	NOUN
ejpam-1203	2	30	and	and	CCONJ
ejpam-1203	2	31	s.	s.	PROPN
ejpam-1203	2	32	jafari2	jafari2	PROPN
ejpam-1203	2	33	1	1	NUM
ejpam-1203	2	34	post	post	NOUN
ejpam-1203	2	35	graduate	graduate	NOUN
ejpam-1203	2	36	and	and	CCONJ
ejpam-1203	2	37	research	research	NOUN
ejpam-1203	2	38	department	department	PROPN
ejpam-1203	2	39	of	of	ADP
ejpam-1203	2	40	mathematics	mathematics	PROPN
ejpam-1203	2	41	,	,	PUNCT
ejpam-1203	2	42	v.o.chidambaram	v.o.chidambaram	PROPN
ejpam-1203	2	43	college	college	PROPN
ejpam-1203	2	44	,	,	PUNCT
ejpam-1203	2	45	thoothukudi	thoothukudi	NOUN
ejpam-1203	2	46	628	628	NUM
ejpam-1203	2	47	008	008	NUM
ejpam-1203	2	48	,	,	PUNCT
ejpam-1203	2	49	tamil	tamil	PROPN
ejpam-1203	2	50	nadu	nadu	PROPN
ejpam-1203	2	51	,	,	PUNCT
ejpam-1203	2	52	india	india	PROPN
ejpam-1203	2	53	.	.	PROPN
ejpam-1203	2	54	2	2	NUM
ejpam-1203	2	55	college	college	NOUN
ejpam-1203	2	56	of	of	ADP
ejpam-1203	2	57	vestsjaelland	vestsjaelland	PROPN
ejpam-1203	2	58	south	south	NOUN
ejpam-1203	2	59	,	,	PUNCT
ejpam-1203	2	60	herrestraede	herrestraede	NOUN
ejpam-1203	2	61	11	11	NUM
ejpam-1203	2	62	,	,	PUNCT
ejpam-1203	2	63	4200	4200	NUM
ejpam-1203	2	64	slagelse	slagelse	NOUN
ejpam-1203	2	65	,	,	PUNCT
ejpam-1203	2	66	denmark	denmark	NOUN
ejpam-1203	2	67	.	.	PUNCT
ejpam-1203	3	1	abstract	abstract	ADJ
ejpam-1203	3	2	.	.	PUNCT
ejpam-1203	4	1	in	in	ADP
ejpam-1203	4	2	this	this	DET
ejpam-1203	4	3	paper	paper	NOUN
ejpam-1203	4	4	,	,	PUNCT
ejpam-1203	4	5	we	we	PRON
ejpam-1203	4	6	introduce	introduce	VERB
ejpam-1203	4	7	and	and	CCONJ
ejpam-1203	4	8	study	study	VERB
ejpam-1203	4	9	new	new	ADJ
ejpam-1203	4	10	classes	class	NOUN
ejpam-1203	4	11	of	of	ADP
ejpam-1203	4	12	sets	set	NOUN
ejpam-1203	4	13	called	call	VERB
ejpam-1203	4	14	ρ	ρ	NOUN
ejpam-1203	4	15	-	-	PUNCT
ejpam-1203	4	16	closed	closed	ADJ
ejpam-1203	4	17	sets	set	NOUN
ejpam-1203	4	18	and	and	CCONJ
ejpam-1203	4	19	ρs	ρs	NOUN
ejpam-1203	4	20	-	-	PUNCT
ejpam-1203	4	21	closed	closed	ADJ
ejpam-1203	4	22	sets	set	NOUN
ejpam-1203	4	23	,	,	PUNCT
ejpam-1203	4	24	ρ	ρ	ADJ
ejpam-1203	4	25	-	-	ADJ
ejpam-1203	4	26	open	open	ADJ
ejpam-1203	4	27	sets	set	NOUN
ejpam-1203	4	28	and	and	CCONJ
ejpam-1203	4	29	ρs	ρs	NOUN
ejpam-1203	4	30	-	-	PUNCT
ejpam-1203	4	31	open	open	ADJ
ejpam-1203	4	32	sets	set	NOUN
ejpam-1203	4	33	.	.	PUNCT
ejpam-1203	5	1	moreover	moreover	ADV
ejpam-1203	5	2	,	,	PUNCT
ejpam-1203	5	3	we	we	PRON
ejpam-1203	5	4	present	present	VERB
ejpam-1203	5	5	two	two	NUM
ejpam-1203	5	6	new	new	ADJ
ejpam-1203	5	7	types	type	NOUN
ejpam-1203	5	8	of	of	ADP
ejpam-1203	5	9	continuities	continuity	NOUN
ejpam-1203	5	10	called	call	VERB
ejpam-1203	5	11	ρcontinuity	ρcontinuity	NOUN
ejpam-1203	5	12	and	and	CCONJ
ejpam-1203	5	13	ρs	ρs	NOUN
ejpam-1203	5	14	-	-	PUNCT
ejpam-1203	5	15	continuity	continuity	NOUN
ejpam-1203	5	16	and	and	CCONJ
ejpam-1203	5	17	investigate	investigate	VERB
ejpam-1203	5	18	some	some	PRON
ejpam-1203	5	19	of	of	ADP
ejpam-1203	5	20	their	their	PRON
ejpam-1203	5	21	fundamental	fundamental	ADJ
ejpam-1203	5	22	properties	property	NOUN
ejpam-1203	5	23	.	.	PUNCT
ejpam-1203	6	1	2010	2010	NUM
ejpam-1203	6	2	mathematics	mathematic	NOUN
ejpam-1203	6	3	subject	subject	NOUN
ejpam-1203	6	4	classifications	classification	NOUN
ejpam-1203	6	5	:	:	PUNCT
ejpam-1203	6	6	54a05	54a05	NUM
ejpam-1203	6	7	,	,	PUNCT
ejpam-1203	6	8	54c08	54c08	NUM
ejpam-1203	6	9	key	key	ADJ
ejpam-1203	6	10	words	word	NOUN
ejpam-1203	6	11	and	and	CCONJ
ejpam-1203	6	12	phrases	phrase	NOUN
ejpam-1203	6	13	:	:	PUNCT
ejpam-1203	6	14	ρ	ρ	NOUN
ejpam-1203	6	15	-	-	PUNCT
ejpam-1203	6	16	closed	closed	ADJ
ejpam-1203	6	17	,	,	PUNCT
ejpam-1203	6	18	ρs	ρs	NOUN
ejpam-1203	6	19	-	-	PUNCT
ejpam-1203	6	20	closed	closed	ADJ
ejpam-1203	6	21	,	,	PUNCT
ejpam-1203	6	22	ρ	ρ	NOUN
ejpam-1203	6	23	-	-	ADJ
ejpam-1203	6	24	open	open	ADJ
ejpam-1203	6	25	,	,	PUNCT
ejpam-1203	6	26	ρs	ρs	NOUN
ejpam-1203	6	27	-	-	ADJ
ejpam-1203	6	28	open	open	ADJ
ejpam-1203	6	29	,	,	PUNCT
ejpam-1203	6	30	ρ	ρ	NOUN
ejpam-1203	6	31	-	-	PUNCT
ejpam-1203	6	32	continuity	continuity	NOUN
ejpam-1203	6	33	andρs	andρs	NOUN
ejpam-1203	6	34	-	-	PUNCT
ejpam-1203	6	35	continuity	continuity	NOUN
ejpam-1203	6	36	1	1	NUM
ejpam-1203	6	37	.	.	PUNCT
ejpam-1203	6	38	introduction	introduction	NOUN
ejpam-1203	6	39	the	the	DET
ejpam-1203	6	40	study	study	NOUN
ejpam-1203	6	41	of	of	ADP
ejpam-1203	6	42	generalized	generalized	ADJ
ejpam-1203	6	43	closed	close	VERB
ejpam-1203	6	44	sets	set	NOUN
ejpam-1203	6	45	in	in	ADP
ejpam-1203	6	46	a	a	DET
ejpam-1203	6	47	topological	topological	ADJ
ejpam-1203	6	48	space	space	NOUN
ejpam-1203	6	49	was	be	AUX
ejpam-1203	6	50	initiated	initiate	VERB
ejpam-1203	6	51	by	by	ADP
ejpam-1203	6	52	levine	levine	PROPN
ejpam-1203	6	53	in	in	ADP
ejpam-1203	6	54	[	[	X
ejpam-1203	6	55	7	7	NUM
ejpam-1203	6	56	]	]	PUNCT
ejpam-1203	6	57	and	and	CCONJ
ejpam-1203	6	58	the	the	DET
ejpam-1203	6	59	concept	concept	NOUN
ejpam-1203	6	60	of	of	ADP
ejpam-1203	6	61	t1/2	t1/2	ADJ
ejpam-1203	6	62	spaces	space	NOUN
ejpam-1203	6	63	was	be	AUX
ejpam-1203	6	64	introduced	introduce	VERB
ejpam-1203	6	65	.	.	PUNCT
ejpam-1203	7	1	in	in	ADP
ejpam-1203	7	2	1996	1996	NUM
ejpam-1203	7	3	,	,	PUNCT
ejpam-1203	7	4	h.maki	h.maki	NOUN
ejpam-1203	7	5	,	,	PUNCT
ejpam-1203	7	6	j.	j.	PROPN
ejpam-1203	7	7	umehara	umehara	PROPN
ejpam-1203	7	8	and	and	CCONJ
ejpam-1203	7	9	t.	t.	PROPN
ejpam-1203	7	10	noiri	noiri	PROPN
ejpam-1203	7	11	[	[	X
ejpam-1203	7	12	9	9	NUM
ejpam-1203	7	13	]	]	PUNCT
ejpam-1203	7	14	introduced	introduce	VERB
ejpam-1203	7	15	the	the	DET
ejpam-1203	7	16	class	class	NOUN
ejpam-1203	7	17	of	of	ADP
ejpam-1203	7	18	pregeneralized	pregeneralize	VERB
ejpam-1203	7	19	closed	close	VERB
ejpam-1203	7	20	sets	set	NOUN
ejpam-1203	7	21	and	and	CCONJ
ejpam-1203	7	22	used	use	VERB
ejpam-1203	7	23	them	they	PRON
ejpam-1203	7	24	to	to	PART
ejpam-1203	7	25	obtain	obtain	VERB
ejpam-1203	7	26	properties	property	NOUN
ejpam-1203	7	27	of	of	ADP
ejpam-1203	7	28	pre	pre	ADJ
ejpam-1203	7	29	-	-	ADJ
ejpam-1203	7	30	t1/2	t1/2	ADJ
ejpam-1203	7	31	spaces	space	NOUN
ejpam-1203	7	32	.	.	PUNCT
ejpam-1203	8	1	the	the	DET
ejpam-1203	8	2	modified	modify	VERB
ejpam-1203	8	3	forms	form	NOUN
ejpam-1203	8	4	of	of	ADP
ejpam-1203	8	5	generalized	generalized	ADJ
ejpam-1203	8	6	closed	closed	ADJ
ejpam-1203	8	7	sets	set	NOUN
ejpam-1203	8	8	and	and	CCONJ
ejpam-1203	8	9	generalized	generalized	ADJ
ejpam-1203	8	10	continuity	continuity	NOUN
ejpam-1203	8	11	were	be	AUX
ejpam-1203	8	12	studied	study	VERB
ejpam-1203	8	13	by	by	ADP
ejpam-1203	8	14	k.	k.	PROPN
ejpam-1203	8	15	balachandran	balachandran	PROPN
ejpam-1203	8	16	,	,	PUNCT
ejpam-1203	8	17	p.	p.	PROPN
ejpam-1203	8	18	sundaram	sundaram	PROPN
ejpam-1203	8	19	and	and	CCONJ
ejpam-1203	8	20	h.	h.	PROPN
ejpam-1203	8	21	maki	maki	PROPN
ejpam-1203	9	1	[	[	X
ejpam-1203	9	2	2	2	NUM
ejpam-1203	9	3	]	]	PUNCT
ejpam-1203	9	4	.	.	PUNCT
ejpam-1203	10	1	in	in	ADP
ejpam-1203	10	2	2008	2008	NUM
ejpam-1203	10	3	,	,	PUNCT
ejpam-1203	10	4	s.	s.	PROPN
ejpam-1203	10	5	jafari	jafari	PROPN
ejpam-1203	10	6	,	,	PUNCT
ejpam-1203	10	7	t.	t.	PROPN
ejpam-1203	10	8	noiri	noiri	PROPN
ejpam-1203	10	9	,	,	PUNCT
ejpam-1203	10	10	n.	n.	PROPN
ejpam-1203	10	11	rajesh	rajesh	PROPN
ejpam-1203	10	12	and	and	CCONJ
ejpam-1203	10	13	m.l	m.l	PROPN
ejpam-1203	10	14	.	.	PROPN
ejpam-1203	10	15	thivagar	thivagar	PROPN
ejpam-1203	11	1	[	[	X
ejpam-1203	11	2	5	5	NUM
ejpam-1203	11	3	]	]	PUNCT
ejpam-1203	11	4	introduced	introduce	VERB
ejpam-1203	11	5	the	the	DET
ejpam-1203	11	6	concept	concept	NOUN
ejpam-1203	11	7	of	of	ADP
ejpam-1203	11	8	g̃-closed	g̃-closed	ADJ
ejpam-1203	11	9	sets	set	NOUN
ejpam-1203	11	10	and	and	CCONJ
ejpam-1203	11	11	their	their	PRON
ejpam-1203	11	12	properties	property	NOUN
ejpam-1203	11	13	.	.	PUNCT
ejpam-1203	12	1	in	in	ADP
ejpam-1203	12	2	this	this	DET
ejpam-1203	12	3	paper	paper	NOUN
ejpam-1203	12	4	,	,	PUNCT
ejpam-1203	12	5	we	we	PRON
ejpam-1203	12	6	introduce	introduce	VERB
ejpam-1203	12	7	new	new	ADJ
ejpam-1203	12	8	classes	class	NOUN
ejpam-1203	12	9	of	of	ADP
ejpam-1203	12	10	sets	set	NOUN
ejpam-1203	12	11	called	call	VERB
ejpam-1203	12	12	ρ	ρ	NOUN
ejpam-1203	12	13	-	-	PUNCT
ejpam-1203	12	14	closed	closed	ADJ
ejpam-1203	12	15	sets	set	NOUN
ejpam-1203	12	16	for	for	ADP
ejpam-1203	12	17	topological	topological	ADJ
ejpam-1203	12	18	spaces	space	NOUN
ejpam-1203	12	19	.	.	PUNCT
ejpam-1203	13	1	2	2	X
ejpam-1203	13	2	.	.	NUM
ejpam-1203	13	3	preliminaries	preliminary	NOUN
ejpam-1203	13	4	throughout	throughout	ADP
ejpam-1203	13	5	this	this	DET
ejpam-1203	13	6	paper	paper	NOUN
ejpam-1203	13	7	(	(	PUNCT
ejpam-1203	13	8	x	x	X
ejpam-1203	13	9	,	,	PUNCT
ejpam-1203	13	10	τ	τ	PROPN
ejpam-1203	13	11	)	)	PUNCT
ejpam-1203	13	12	,	,	PUNCT
ejpam-1203	13	13	(	(	PUNCT
ejpam-1203	13	14	y	y	X
ejpam-1203	13	15	,	,	PUNCT
ejpam-1203	13	16	σ)and	σ)and	NOUN
ejpam-1203	13	17	(	(	PUNCT
ejpam-1203	13	18	z	z	PROPN
ejpam-1203	13	19	,	,	PUNCT
ejpam-1203	13	20	η	η	NOUN
ejpam-1203	13	21	)	)	PUNCT
ejpam-1203	13	22	will	will	AUX
ejpam-1203	13	23	always	always	ADV
ejpam-1203	13	24	denote	denote	VERB
ejpam-1203	13	25	topological	topological	ADJ
ejpam-1203	13	26	spaces	space	NOUN
ejpam-1203	13	27	on	on	ADP
ejpam-1203	13	28	which	which	PRON
ejpam-1203	13	29	no	no	DET
ejpam-1203	13	30	separation	separation	NOUN
ejpam-1203	13	31	axioms	axiom	NOUN
ejpam-1203	13	32	are	be	AUX
ejpam-1203	13	33	assumed	assume	VERB
ejpam-1203	13	34	,	,	PUNCT
ejpam-1203	13	35	unless	unless	SCONJ
ejpam-1203	13	36	otherwise	otherwise	ADV
ejpam-1203	13	37	mentioned	mention	VERB
ejpam-1203	13	38	.	.	PUNCT
ejpam-1203	14	1	when	when	SCONJ
ejpam-1203	14	2	a	a	PRON
ejpam-1203	14	3	is	be	AUX
ejpam-1203	14	4	a	a	DET
ejpam-1203	14	5	subset	subset	NOUN
ejpam-1203	14	6	of	of	ADP
ejpam-1203	14	7	(	(	PUNCT
ejpam-1203	14	8	x	x	PROPN
ejpam-1203	14	9	,	,	PUNCT
ejpam-1203	14	10	τ	τ	PROPN
ejpam-1203	14	11	)	)	PUNCT
ejpam-1203	14	12	,	,	PUNCT
ejpam-1203	14	13	cl(a	cl(a	NUM
ejpam-1203	14	14	)	)	PUNCT
ejpam-1203	14	15	,	,	PUNCT
ejpam-1203	14	16	int(a	int(a	PROPN
ejpam-1203	14	17	)	)	PUNCT
ejpam-1203	14	18	and	and	CCONJ
ejpam-1203	14	19	d[a	d[a	ADJ
ejpam-1203	14	20	]	]	X
ejpam-1203	14	21	denote	denote	VERB
ejpam-1203	14	22	the	the	DET
ejpam-1203	14	23	closure	closure	NOUN
ejpam-1203	14	24	,	,	PUNCT
ejpam-1203	14	25	the	the	DET
ejpam-1203	14	26	interior	interior	NOUN
ejpam-1203	14	27	and	and	CCONJ
ejpam-1203	14	28	the	the	DET
ejpam-1203	14	29	derived	derived	ADJ
ejpam-1203	14	30	set	set	NOUN
ejpam-1203	14	31	of	of	ADP
ejpam-1203	14	32	a	a	PRON
ejpam-1203	14	33	,	,	PUNCT
ejpam-1203	14	34	respectively	respectively	ADV
ejpam-1203	14	35	.	.	PUNCT
ejpam-1203	15	1	we	we	PRON
ejpam-1203	15	2	recall	recall	VERB
ejpam-1203	15	3	some	some	DET
ejpam-1203	15	4	known	known	ADJ
ejpam-1203	15	5	definitions	definition	NOUN
ejpam-1203	15	6	needed	need	VERB
ejpam-1203	15	7	in	in	ADP
ejpam-1203	15	8	this	this	DET
ejpam-1203	15	9	paper	paper	NOUN
ejpam-1203	15	10	.	.	PUNCT
ejpam-1203	16	1	definition	definition	NOUN
ejpam-1203	16	2	1	1	NUM
ejpam-1203	16	3	.	.	PUNCT
ejpam-1203	17	1	let	let	AUX
ejpam-1203	17	2	(	(	PUNCT
ejpam-1203	17	3	x	x	X
ejpam-1203	17	4	,	,	PUNCT
ejpam-1203	17	5	τ	τ	X
ejpam-1203	17	6	)	)	PUNCT
ejpam-1203	17	7	be	be	VERB
ejpam-1203	17	8	a	a	DET
ejpam-1203	17	9	topological	topological	ADJ
ejpam-1203	17	10	space	space	NOUN
ejpam-1203	17	11	.	.	PUNCT
ejpam-1203	18	1	a	a	DET
ejpam-1203	18	2	subset	subset	NOUN
ejpam-1203	18	3	a	a	PRON
ejpam-1203	18	4	of	of	ADP
ejpam-1203	18	5	the	the	DET
ejpam-1203	18	6	space	space	NOUN
ejpam-1203	18	7	x	x	PRON
ejpam-1203	18	8	is	be	AUX
ejpam-1203	18	9	said	say	VERB
ejpam-1203	18	10	to	to	PART
ejpam-1203	18	11	be	be	AUX
ejpam-1203	18	12	∗corresponding	∗corresponde	VERB
ejpam-1203	18	13	author	author	NOUN
ejpam-1203	18	14	.	.	PUNCT
ejpam-1203	19	1	email	email	NOUN
ejpam-1203	19	2	addresses	address	NOUN
ejpam-1203	19	3	:	:	PUNCT
ejpam-1203	19	4	kan	kan	PROPN
ejpam-1203	19	5	hidev	hidev	PROPN
ejpam-1203	19	6	�	�	PROPN
ejpam-1203	19	7	gmail	gmail	NOUN
ejpam-1203	19	8	.	.	PUNCT
ejpam-1203	20	1	om	om	PROPN
ejpam-1203	20	2	(	(	PUNCT
ejpam-1203	20	3	c.devamanoharan	c.devamanoharan	ADJ
ejpam-1203	20	4	)	)	PUNCT
ejpam-1203	20	5	,	,	PUNCT
ejpam-1203	20	6	spmissier	spmissier	PROPN
ejpam-1203	20	7	�	�	PROPN
ejpam-1203	20	8	yahoo	yahoo	PROPN
ejpam-1203	20	9	.	.	PUNCT
ejpam-1203	21	1	om	om	PROPN
ejpam-1203	21	2	(	(	PUNCT
ejpam-1203	21	3	s.	s.	PROPN
ejpam-1203	21	4	missier	missier	PROPN
ejpam-1203	21	5	)	)	PUNCT
ejpam-1203	21	6	,	,	PUNCT
ejpam-1203	21	7	jafari�stofanet.dk	jafari�stofanet.dk	PROPN
ejpam-1203	21	8	(	(	PUNCT
ejpam-1203	21	9	s.jafari	s.jafari	ADJ
ejpam-1203	21	10	)	)	PUNCT
ejpam-1203	21	11	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1203	22	1	554	554	NUM
ejpam-1203	22	2	c	c	X
ejpam-1203	22	3	©	©	VERB
ejpam-1203	22	4	2012	2012	NUM
ejpam-1203	22	5	ejpam	ejpam	VERB
ejpam-1203	22	6	all	all	DET
ejpam-1203	22	7	rights	right	NOUN
ejpam-1203	22	8	reserved	reserve	VERB
ejpam-1203	22	9	.	.	PUNCT
ejpam-1203	23	1	c.	c.	PROPN
ejpam-1203	23	2	devamanoharan	devamanoharan	PROPN
ejpam-1203	23	3	,	,	PUNCT
ejpam-1203	23	4	s.	s.	PROPN
ejpam-1203	23	5	missier	missier	PROPN
ejpam-1203	23	6	,	,	PUNCT
ejpam-1203	23	7	s.	s.	PROPN
ejpam-1203	23	8	jafari	jafari	PROPN
ejpam-1203	23	9	/	/	SYM
ejpam-1203	23	10	eur	eur	PROPN
ejpam-1203	23	11	.	.	PUNCT
ejpam-1203	24	1	j.	j.	PROPN
ejpam-1203	24	2	pure	pure	PROPN
ejpam-1203	24	3	appl	appl	PROPN
ejpam-1203	24	4	.	.	PROPN
ejpam-1203	24	5	math	math	PROPN
ejpam-1203	24	6	,	,	PUNCT
ejpam-1203	24	7	5	5	NUM
ejpam-1203	24	8	(	(	PUNCT
ejpam-1203	24	9	2012	2012	NUM
ejpam-1203	24	10	)	)	PUNCT
ejpam-1203	24	11	,	,	PUNCT
ejpam-1203	24	12	554	554	NUM
ejpam-1203	24	13	-	-	SYM
ejpam-1203	24	14	566	566	NUM
ejpam-1203	24	15	555	555	NUM
ejpam-1203	24	16	1	1	NUM
ejpam-1203	24	17	.	.	PUNCT
ejpam-1203	25	1	preopen	preopen	ADJ
ejpam-1203	26	1	[	[	X
ejpam-1203	26	2	8	8	NUM
ejpam-1203	26	3	]	]	X
ejpam-1203	26	4	if	if	SCONJ
ejpam-1203	26	5	a⊆	a⊆	ADP
ejpam-1203	26	6	int(cl(a	int(cl(a	PROPN
ejpam-1203	26	7	)	)	PUNCT
ejpam-1203	26	8	)	)	PUNCT
ejpam-1203	27	1	and	and	CCONJ
ejpam-1203	27	2	preclosed	preclose	VERB
ejpam-1203	27	3	if	if	SCONJ
ejpam-1203	27	4	cl(int(a	cl(int(a	NOUN
ejpam-1203	27	5	)	)	PUNCT
ejpam-1203	27	6	)	)	PUNCT
ejpam-1203	28	1	⊆	⊆	NUM
ejpam-1203	28	2	a.	a.	NOUN
ejpam-1203	28	3	2	2	NUM
ejpam-1203	28	4	.	.	PUNCT
ejpam-1203	28	5	semi	semi	ADJ
ejpam-1203	28	6	-	-	ADJ
ejpam-1203	28	7	open	open	ADJ
ejpam-1203	28	8	[	[	X
ejpam-1203	28	9	6	6	NUM
ejpam-1203	28	10	]	]	X
ejpam-1203	28	11	if	if	SCONJ
ejpam-1203	28	12	a⊆	a⊆	PROPN
ejpam-1203	28	13	cl(int(a	cl(int(a	NOUN
ejpam-1203	28	14	)	)	PUNCT
ejpam-1203	28	15	)	)	PUNCT
ejpam-1203	28	16	and	and	CCONJ
ejpam-1203	28	17	semi	semi	ADJ
ejpam-1203	28	18	-	-	ADJ
ejpam-1203	28	19	closed	closed	ADJ
ejpam-1203	28	20	if	if	SCONJ
ejpam-1203	28	21	int(cl(a	int(cl(a	PROPN
ejpam-1203	28	22	)	)	PUNCT
ejpam-1203	28	23	)	)	PUNCT
ejpam-1203	29	1	⊆	⊆	NUM
ejpam-1203	29	2	a.	a.	NOUN
ejpam-1203	29	3	3	3	NUM
ejpam-1203	29	4	.	.	PUNCT
ejpam-1203	30	1	α	α	X
ejpam-1203	30	2	-	-	ADJ
ejpam-1203	30	3	open	open	ADJ
ejpam-1203	30	4	[	[	X
ejpam-1203	30	5	10	10	NUM
ejpam-1203	30	6	]	]	X
ejpam-1203	30	7	if	if	SCONJ
ejpam-1203	30	8	a⊆	a⊆	ADP
ejpam-1203	30	9	int(cl(int(a	int(cl(int(a	PROPN
ejpam-1203	30	10	)	)	PUNCT
ejpam-1203	30	11	)	)	PUNCT
ejpam-1203	30	12	)	)	PUNCT
ejpam-1203	31	1	and	and	CCONJ
ejpam-1203	31	2	α	α	X
ejpam-1203	31	3	-	-	PUNCT
ejpam-1203	31	4	closed	closed	ADJ
ejpam-1203	31	5	if	if	SCONJ
ejpam-1203	31	6	cl(int(cl(a	cl(int(cl(a	NOUN
ejpam-1203	31	7	)	)	PUNCT
ejpam-1203	31	8	)	)	PUNCT
ejpam-1203	31	9	)	)	PUNCT
ejpam-1203	32	1	⊆	⊆	NUM
ejpam-1203	32	2	a.	a.	NOUN
ejpam-1203	32	3	4	4	NUM
ejpam-1203	32	4	.	.	PUNCT
ejpam-1203	32	5	semi	semi	ADV
ejpam-1203	32	6	preopen	preopen	ADJ
ejpam-1203	32	7	[	[	X
ejpam-1203	32	8	1	1	NUM
ejpam-1203	32	9	]	]	X
ejpam-1203	32	10	if	if	SCONJ
ejpam-1203	32	11	a⊆	a⊆	NOUN
ejpam-1203	32	12	cl(int(cl(a	cl(int(cl(a	NOUN
ejpam-1203	32	13	)	)	PUNCT
ejpam-1203	32	14	)	)	PUNCT
ejpam-1203	32	15	)	)	PUNCT
ejpam-1203	32	16	and	and	CCONJ
ejpam-1203	32	17	semi	semi	ADV
ejpam-1203	32	18	preclosed	preclose	VERB
ejpam-1203	32	19	if	if	SCONJ
ejpam-1203	32	20	int(cl(int(a	int(cl(int(a	PROPN
ejpam-1203	32	21	)	)	PUNCT
ejpam-1203	32	22	)	)	PUNCT
ejpam-1203	32	23	)	)	PUNCT
ejpam-1203	33	1	⊆	⊆	NUM
ejpam-1203	33	2	a.	a.	NOUN
ejpam-1203	33	3	5	5	NUM
ejpam-1203	33	4	.	.	PUNCT
ejpam-1203	33	5	regular	regular	ADJ
ejpam-1203	33	6	open	open	ADJ
ejpam-1203	33	7	[	[	X
ejpam-1203	33	8	13	13	NUM
ejpam-1203	33	9	]	]	PUNCT
ejpam-1203	33	10	if	if	SCONJ
ejpam-1203	33	11	a=	a=	ADV
ejpam-1203	33	12	int(cl(a	int(cl(a	PROPN
ejpam-1203	33	13	)	)	PUNCT
ejpam-1203	33	14	)	)	PUNCT
ejpam-1203	33	15	and	and	CCONJ
ejpam-1203	33	16	regular	regular	ADJ
ejpam-1203	33	17	closed	close	VERB
ejpam-1203	33	18	if	if	SCONJ
ejpam-1203	33	19	a=	a=	NOUN
ejpam-1203	33	20	cl(int(a	cl(int(a	PROPN
ejpam-1203	33	21	)	)	PUNCT
ejpam-1203	33	22	)	)	PUNCT
ejpam-1203	33	23	.	.	PUNCT
ejpam-1203	34	1	6	6	NUM
ejpam-1203	34	2	.	.	X
ejpam-1203	35	1	π	π	X
ejpam-1203	35	2	-	-	PUNCT
ejpam-1203	35	3	open	open	ADJ
ejpam-1203	35	4	[	[	X
ejpam-1203	35	5	17	17	NUM
ejpam-1203	35	6	]	]	PUNCT
ejpam-1203	35	7	if	if	SCONJ
ejpam-1203	35	8	it	it	PRON
ejpam-1203	35	9	is	be	AUX
ejpam-1203	35	10	the	the	DET
ejpam-1203	35	11	finite	finite	PROPN
ejpam-1203	35	12	union	union	NOUN
ejpam-1203	35	13	of	of	ADP
ejpam-1203	35	14	regular	regular	ADJ
ejpam-1203	35	15	open	open	ADJ
ejpam-1203	35	16	sets	set	NOUN
ejpam-1203	35	17	.	.	PUNCT
ejpam-1203	36	1	definition	definition	NOUN
ejpam-1203	36	2	2	2	NUM
ejpam-1203	36	3	(	(	PUNCT
ejpam-1203	36	4	[	[	X
ejpam-1203	36	5	8	8	NUM
ejpam-1203	36	6	]	]	PUNCT
ejpam-1203	36	7	)	)	PUNCT
ejpam-1203	36	8	.	.	PUNCT
ejpam-1203	37	1	let	let	VERB
ejpam-1203	37	2	(	(	PUNCT
ejpam-1203	37	3	x	x	X
ejpam-1203	37	4	,	,	PUNCT
ejpam-1203	37	5	τ	τ	X
ejpam-1203	37	6	)	)	PUNCT
ejpam-1203	37	7	be	be	VERB
ejpam-1203	37	8	a	a	DET
ejpam-1203	37	9	topological	topological	ADJ
ejpam-1203	37	10	space	space	NOUN
ejpam-1203	37	11	and	and	CCONJ
ejpam-1203	37	12	a⊆	a⊆	PROPN
ejpam-1203	37	13	x	x	X
ejpam-1203	37	14	.	.	PUNCT
ejpam-1203	38	1	1	1	X
ejpam-1203	38	2	.	.	X
ejpam-1203	38	3	the	the	DET
ejpam-1203	38	4	pre	pre	NOUN
ejpam-1203	38	5	-	-	NOUN
ejpam-1203	38	6	interior	interior	ADJ
ejpam-1203	38	7	of	of	ADP
ejpam-1203	38	8	a	a	PRON
ejpam-1203	38	9	,	,	PUNCT
ejpam-1203	38	10	denoted	denote	VERB
ejpam-1203	38	11	by	by	ADP
ejpam-1203	38	12	pint(a	pint(a	PROPN
ejpam-1203	38	13	)	)	PUNCT
ejpam-1203	38	14	,	,	PUNCT
ejpam-1203	38	15	is	be	AUX
ejpam-1203	38	16	the	the	DET
ejpam-1203	38	17	union	union	NOUN
ejpam-1203	38	18	of	of	ADP
ejpam-1203	38	19	all	all	DET
ejpam-1203	38	20	preopen	preopen	ADJ
ejpam-1203	38	21	subsets	subset	NOUN
ejpam-1203	38	22	of	of	ADP
ejpam-1203	38	23	a.	a.	NOUN
ejpam-1203	38	24	2	2	NUM
ejpam-1203	38	25	.	.	PUNCT
ejpam-1203	39	1	the	the	DET
ejpam-1203	39	2	pre	pre	NOUN
ejpam-1203	39	3	-	-	NOUN
ejpam-1203	39	4	closure	closure	NOUN
ejpam-1203	39	5	of	of	ADP
ejpam-1203	39	6	a	a	PRON
ejpam-1203	39	7	,	,	PUNCT
ejpam-1203	39	8	denoted	denote	VERB
ejpam-1203	39	9	by	by	ADP
ejpam-1203	39	10	pcl(a	pcl(a	PROPN
ejpam-1203	39	11	)	)	PUNCT
ejpam-1203	39	12	,	,	PUNCT
ejpam-1203	39	13	is	be	AUX
ejpam-1203	39	14	the	the	DET
ejpam-1203	39	15	intersection	intersection	NOUN
ejpam-1203	39	16	of	of	ADP
ejpam-1203	39	17	all	all	DET
ejpam-1203	39	18	preclosed	preclose	VERB
ejpam-1203	39	19	sets	set	NOUN
ejpam-1203	39	20	containing	contain	VERB
ejpam-1203	39	21	a.	a.	PROPN
ejpam-1203	39	22	lemma	lemma	PROPN
ejpam-1203	39	23	1	1	NUM
ejpam-1203	39	24	(	(	PUNCT
ejpam-1203	39	25	[	[	X
ejpam-1203	39	26	1	1	NUM
ejpam-1203	39	27	]	]	PUNCT
ejpam-1203	39	28	)	)	PUNCT
ejpam-1203	39	29	.	.	PUNCT
ejpam-1203	40	1	for	for	ADP
ejpam-1203	40	2	any	any	DET
ejpam-1203	40	3	subset	subset	NOUN
ejpam-1203	40	4	a	a	PRON
ejpam-1203	40	5	of	of	ADP
ejpam-1203	40	6	x	x	PRON
ejpam-1203	40	7	,	,	PUNCT
ejpam-1203	40	8	the	the	DET
ejpam-1203	40	9	following	follow	VERB
ejpam-1203	40	10	relations	relation	NOUN
ejpam-1203	40	11	hold	hold	VERB
ejpam-1203	40	12	.	.	PUNCT
ejpam-1203	41	1	1	1	X
ejpam-1203	41	2	.	.	X
ejpam-1203	41	3	scl(a	scl(a	X
ejpam-1203	41	4	)	)	PUNCT
ejpam-1203	42	1	=	=	PUNCT
ejpam-1203	42	2	a∪	a∪	PROPN
ejpam-1203	42	3	int(cl(a	int(cl(a	PROPN
ejpam-1203	42	4	)	)	PUNCT
ejpam-1203	42	5	)	)	PUNCT
ejpam-1203	42	6	.	.	PUNCT
ejpam-1203	43	1	2	2	X
ejpam-1203	43	2	.	.	X
ejpam-1203	43	3	αcl(a	αcl(a	NUM
ejpam-1203	43	4	)	)	PUNCT
ejpam-1203	43	5	=	=	SYM
ejpam-1203	43	6	a∪	a∪	PRON
ejpam-1203	43	7	cl(int(cl(a	cl(int(cl(a	NOUN
ejpam-1203	43	8	)	)	PUNCT
ejpam-1203	43	9	)	)	PUNCT
ejpam-1203	43	10	)	)	PUNCT
ejpam-1203	43	11	.	.	PUNCT
ejpam-1203	44	1	3	3	X
ejpam-1203	44	2	.	.	X
ejpam-1203	44	3	pcl(a	pcl(a	NUM
ejpam-1203	44	4	)	)	PUNCT
ejpam-1203	44	5	=	=	PUNCT
ejpam-1203	44	6	a∪	a∪	ADP
ejpam-1203	44	7	cl(int(a	cl(int(a	PROPN
ejpam-1203	44	8	)	)	PUNCT
ejpam-1203	44	9	)	)	PUNCT
ejpam-1203	44	10	.	.	PUNCT
ejpam-1203	45	1	4	4	X
ejpam-1203	45	2	.	.	X
ejpam-1203	45	3	spcl(a	spcl(a	NUM
ejpam-1203	45	4	)	)	PUNCT
ejpam-1203	45	5	=	=	PUNCT
ejpam-1203	45	6	a∪	a∪	PROPN
ejpam-1203	45	7	int(cl(int(a	int(cl(int(a	NOUN
ejpam-1203	45	8	)	)	PUNCT
ejpam-1203	45	9	)	)	PUNCT
ejpam-1203	45	10	)	)	PUNCT
ejpam-1203	45	11	.	.	PUNCT
ejpam-1203	46	1	definition	definition	NOUN
ejpam-1203	46	2	3	3	X
ejpam-1203	46	3	.	.	PUNCT
ejpam-1203	47	1	let	let	AUX
ejpam-1203	47	2	(	(	PUNCT
ejpam-1203	47	3	x	x	X
ejpam-1203	47	4	,	,	PUNCT
ejpam-1203	47	5	τ	τ	X
ejpam-1203	47	6	)	)	PUNCT
ejpam-1203	47	7	be	be	VERB
ejpam-1203	47	8	a	a	DET
ejpam-1203	47	9	topological	topological	ADJ
ejpam-1203	47	10	space	space	NOUN
ejpam-1203	47	11	.	.	PUNCT
ejpam-1203	48	1	a	a	DET
ejpam-1203	48	2	subset	subset	NOUN
ejpam-1203	48	3	a⊆	a⊆	NOUN
ejpam-1203	48	4	x	x	VERB
ejpam-1203	48	5	is	be	AUX
ejpam-1203	48	6	said	say	VERB
ejpam-1203	48	7	to	to	PART
ejpam-1203	48	8	be	be	AUX
ejpam-1203	48	9	1	1	NUM
ejpam-1203	48	10	.	.	PUNCT
ejpam-1203	48	11	generalized	generalize	VERB
ejpam-1203	48	12	closed	close	VERB
ejpam-1203	48	13	(	(	PUNCT
ejpam-1203	48	14	briely	briely	ADV
ejpam-1203	48	15	g	g	NOUN
ejpam-1203	48	16	-	-	PUNCT
ejpam-1203	48	17	closed)[7	closed)[7	X
ejpam-1203	48	18	]	]	PUNCT
ejpam-1203	48	19	if	if	SCONJ
ejpam-1203	48	20	cl(a	cl(a	NUM
ejpam-1203	48	21	)	)	PUNCT
ejpam-1203	48	22	⊆	⊆	NUM
ejpam-1203	48	23	u	u	NOUN
ejpam-1203	48	24	whenever	whenever	SCONJ
ejpam-1203	48	25	a⊆	a⊆	VERB
ejpam-1203	48	26	u	u	NOUN
ejpam-1203	48	27	and	and	CCONJ
ejpam-1203	48	28	u	u	NOUN
ejpam-1203	48	29	is	be	AUX
ejpam-1203	48	30	open	open	ADJ
ejpam-1203	48	31	in	in	ADP
ejpam-1203	48	32	x	x	X
ejpam-1203	48	33	.	.	PUNCT
ejpam-1203	49	1	2	2	X
ejpam-1203	49	2	.	.	NUM
ejpam-1203	49	3	generalized	generalize	VERB
ejpam-1203	49	4	preclosed	preclose	VERB
ejpam-1203	49	5	(	(	PUNCT
ejpam-1203	49	6	briely	briely	ADV
ejpam-1203	49	7	gp	gp	NOUN
ejpam-1203	49	8	-	-	PUNCT
ejpam-1203	49	9	closed)[11	closed)[11	ADV
ejpam-1203	49	10	]	]	PUNCT
ejpam-1203	49	11	if	if	SCONJ
ejpam-1203	49	12	pcl(a	pcl(a	X
ejpam-1203	49	13	)	)	PUNCT
ejpam-1203	49	14	⊆	⊆	NUM
ejpam-1203	49	15	u	u	NOUN
ejpam-1203	49	16	whenever	whenever	SCONJ
ejpam-1203	49	17	a⊆	a⊆	VERB
ejpam-1203	49	18	u	u	NOUN
ejpam-1203	49	19	and	and	CCONJ
ejpam-1203	49	20	u	u	NOUN
ejpam-1203	49	21	is	be	AUX
ejpam-1203	49	22	open	open	ADJ
ejpam-1203	49	23	in	in	ADP
ejpam-1203	49	24	x	x	X
ejpam-1203	49	25	.	.	PUNCT
ejpam-1203	50	1	3	3	X
ejpam-1203	50	2	.	.	NUM
ejpam-1203	50	3	generalized	generalize	VERB
ejpam-1203	50	4	preregular	preregular	NOUN
ejpam-1203	50	5	closed	close	VERB
ejpam-1203	50	6	(	(	PUNCT
ejpam-1203	50	7	briely	briely	ADV
ejpam-1203	50	8	gpr	gpr	PROPN
ejpam-1203	50	9	-	-	PUNCT
ejpam-1203	50	10	closed)[4	closed)[4	X
ejpam-1203	50	11	]	]	PUNCT
ejpam-1203	50	12	if	if	SCONJ
ejpam-1203	50	13	pcl(a	pcl(a	X
ejpam-1203	50	14	)	)	PUNCT
ejpam-1203	51	1	⊆	⊆	NUM
ejpam-1203	51	2	u	u	NOUN
ejpam-1203	51	3	whenever	whenever	SCONJ
ejpam-1203	51	4	a⊆	a⊆	VERB
ejpam-1203	51	5	u	u	NOUN
ejpam-1203	51	6	and	and	CCONJ
ejpam-1203	51	7	u	u	NOUN
ejpam-1203	51	8	is	be	AUX
ejpam-1203	51	9	regular	regular	ADJ
ejpam-1203	51	10	open	open	ADJ
ejpam-1203	51	11	in	in	ADP
ejpam-1203	51	12	x	x	X
ejpam-1203	51	13	.	.	PUNCT
ejpam-1203	52	1	4	4	X
ejpam-1203	52	2	.	.	NUM
ejpam-1203	52	3	pregeneralized	pregeneralize	VERB
ejpam-1203	52	4	closed	closed	ADJ
ejpam-1203	52	5	(	(	PUNCT
ejpam-1203	52	6	briely	briely	ADV
ejpam-1203	52	7	pg	pg	VERB
ejpam-1203	52	8	-	-	PUNCT
ejpam-1203	52	9	closed)[9	closed)[9	NUM
ejpam-1203	52	10	]	]	PUNCT
ejpam-1203	52	11	if	if	SCONJ
ejpam-1203	52	12	pcl(a	pcl(a	X
ejpam-1203	52	13	)	)	PUNCT
ejpam-1203	53	1	⊆	⊆	NUM
ejpam-1203	53	2	u	u	NOUN
ejpam-1203	53	3	whenever	whenever	SCONJ
ejpam-1203	53	4	a⊆	a⊆	VERB
ejpam-1203	53	5	u	u	NOUN
ejpam-1203	53	6	and	and	CCONJ
ejpam-1203	53	7	u	u	NOUN
ejpam-1203	53	8	is	be	AUX
ejpam-1203	53	9	preopen	preopen	ADJ
ejpam-1203	53	10	in	in	ADP
ejpam-1203	53	11	x	x	X
ejpam-1203	53	12	.	.	PUNCT
ejpam-1203	54	1	5	5	X
ejpam-1203	54	2	.	.	NUM
ejpam-1203	54	3	g*-preclosed	g*-preclosed	ADJ
ejpam-1203	54	4	(	(	PUNCT
ejpam-1203	54	5	briely	briely	ADV
ejpam-1203	54	6	g*p	g*p	PROPN
ejpam-1203	54	7	-	-	PUNCT
ejpam-1203	54	8	closed)[15	closed)[15	NOUN
ejpam-1203	54	9	]	]	PUNCT
ejpam-1203	54	10	if	if	SCONJ
ejpam-1203	54	11	pcl(a	pcl(a	X
ejpam-1203	54	12	)	)	PUNCT
ejpam-1203	55	1	⊆	⊆	NUM
ejpam-1203	55	2	u	u	NOUN
ejpam-1203	55	3	whenever	whenever	SCONJ
ejpam-1203	55	4	a⊆	a⊆	VERB
ejpam-1203	55	5	u	u	NOUN
ejpam-1203	55	6	and	and	CCONJ
ejpam-1203	55	7	u	u	NOUN
ejpam-1203	55	8	is	be	AUX
ejpam-1203	55	9	g	g	NOUN
ejpam-1203	55	10	-	-	PUNCT
ejpam-1203	55	11	open	open	ADJ
ejpam-1203	55	12	in	in	ADP
ejpam-1203	55	13	x	x	X
ejpam-1203	55	14	.	.	PROPN
ejpam-1203	55	15	6	6	NUM
ejpam-1203	55	16	.	.	NUM
ejpam-1203	55	17	generalized	generalize	VERB
ejpam-1203	55	18	semi	semi	ADV
ejpam-1203	55	19	-	-	ADJ
ejpam-1203	55	20	preclosed	preclosed	ADJ
ejpam-1203	55	21	(	(	PUNCT
ejpam-1203	55	22	briely	briely	ADV
ejpam-1203	55	23	gsp	gsp	VERB
ejpam-1203	55	24	-	-	PUNCT
ejpam-1203	55	25	closed)[3	closed)[3	NUM
ejpam-1203	55	26	]	]	PUNCT
ejpam-1203	55	27	if	if	SCONJ
ejpam-1203	55	28	spcl(a	spcl(a	NUM
ejpam-1203	55	29	)	)	PUNCT
ejpam-1203	55	30	⊆	⊆	NUM
ejpam-1203	55	31	u	u	NOUN
ejpam-1203	55	32	whenever	whenever	SCONJ
ejpam-1203	55	33	a⊆	a⊆	VERB
ejpam-1203	55	34	u	u	NOUN
ejpam-1203	55	35	and	and	CCONJ
ejpam-1203	55	36	u	u	NOUN
ejpam-1203	55	37	is	be	AUX
ejpam-1203	55	38	open	open	ADJ
ejpam-1203	55	39	in	in	ADP
ejpam-1203	55	40	x	x	X
ejpam-1203	55	41	.	.	PUNCT
ejpam-1203	56	1	7	7	X
ejpam-1203	56	2	.	.	PUNCT
ejpam-1203	56	3	pre	pre	VERB
ejpam-1203	56	4	semi	semi	ADV
ejpam-1203	56	5	closed	closed	ADJ
ejpam-1203	56	6	[	[	X
ejpam-1203	56	7	16	16	NUM
ejpam-1203	56	8	]	]	PUNCT
ejpam-1203	56	9	if	if	SCONJ
ejpam-1203	56	10	spcl(a	spcl(a	NUM
ejpam-1203	56	11	)	)	PUNCT
ejpam-1203	56	12	⊆	⊆	NUM
ejpam-1203	56	13	u	u	NOUN
ejpam-1203	56	14	whenever	whenever	SCONJ
ejpam-1203	56	15	a⊆	a⊆	VERB
ejpam-1203	56	16	u	u	NOUN
ejpam-1203	56	17	and	and	CCONJ
ejpam-1203	56	18	u	u	NOUN
ejpam-1203	56	19	is	be	AUX
ejpam-1203	56	20	g	g	NOUN
ejpam-1203	56	21	-	-	PUNCT
ejpam-1203	56	22	open	open	ADJ
ejpam-1203	56	23	in	in	ADP
ejpam-1203	56	24	x	x	X
ejpam-1203	56	25	.	.	PUNCT
ejpam-1203	56	26	8	8	NUM
ejpam-1203	56	27	.	.	X
ejpam-1203	57	1	πgp	πgp	X
ejpam-1203	57	2	-	-	PUNCT
ejpam-1203	57	3	closed	closed	ADJ
ejpam-1203	58	1	[	[	X
ejpam-1203	58	2	12	12	NUM
ejpam-1203	58	3	]	]	PUNCT
ejpam-1203	58	4	if	if	SCONJ
ejpam-1203	58	5	pcl(a	pcl(a	X
ejpam-1203	58	6	)	)	PUNCT
ejpam-1203	59	1	⊆	⊆	NUM
ejpam-1203	59	2	u	u	NOUN
ejpam-1203	59	3	whenever	whenever	SCONJ
ejpam-1203	59	4	a⊆	a⊆	VERB
ejpam-1203	59	5	u	u	NOUN
ejpam-1203	59	6	and	and	CCONJ
ejpam-1203	59	7	u	u	NOUN
ejpam-1203	59	8	is	be	AUX
ejpam-1203	59	9	π	π	NOUN
ejpam-1203	59	10	-	-	NOUN
ejpam-1203	59	11	open	open	ADJ
ejpam-1203	59	12	in	in	ADP
ejpam-1203	59	13	x	x	X
ejpam-1203	59	14	.	.	PUNCT
ejpam-1203	60	1	c.	c.	PROPN
ejpam-1203	60	2	devamanoharan	devamanoharan	PROPN
ejpam-1203	60	3	,	,	PUNCT
ejpam-1203	60	4	s.	s.	PROPN
ejpam-1203	60	5	missier	missier	PROPN
ejpam-1203	60	6	,	,	PUNCT
ejpam-1203	60	7	s.	s.	PROPN
ejpam-1203	60	8	jafari	jafari	PROPN
ejpam-1203	60	9	/	/	SYM
ejpam-1203	60	10	eur	eur	PROPN
ejpam-1203	60	11	.	.	PUNCT
ejpam-1203	61	1	j.	j.	PROPN
ejpam-1203	61	2	pure	pure	PROPN
ejpam-1203	61	3	appl	appl	PROPN
ejpam-1203	61	4	.	.	PROPN
ejpam-1203	61	5	math	math	PROPN
ejpam-1203	61	6	,	,	PUNCT
ejpam-1203	61	7	5	5	NUM
ejpam-1203	61	8	(	(	PUNCT
ejpam-1203	61	9	2012	2012	NUM
ejpam-1203	61	10	)	)	PUNCT
ejpam-1203	61	11	,	,	PUNCT
ejpam-1203	61	12	554	554	NUM
ejpam-1203	61	13	-	-	SYM
ejpam-1203	61	14	566	566	NUM
ejpam-1203	61	15	556	556	NUM
ejpam-1203	61	16	9	9	NUM
ejpam-1203	61	17	.	.	PUNCT
ejpam-1203	62	1	ĝ-closed	ĝ-close	VERB
ejpam-1203	63	1	[	[	X
ejpam-1203	63	2	14	14	NUM
ejpam-1203	63	3	]	]	X
ejpam-1203	63	4	if	if	SCONJ
ejpam-1203	63	5	cl(a	cl(a	NUM
ejpam-1203	63	6	)	)	PUNCT
ejpam-1203	63	7	⊆	⊆	NUM
ejpam-1203	63	8	u	u	NOUN
ejpam-1203	63	9	whenever	whenever	SCONJ
ejpam-1203	63	10	a⊆	a⊆	VERB
ejpam-1203	63	11	u	u	NOUN
ejpam-1203	63	12	and	and	CCONJ
ejpam-1203	63	13	u	u	NOUN
ejpam-1203	63	14	is	be	AUX
ejpam-1203	63	15	semi	semi	ADV
ejpam-1203	63	16	open	open	ADJ
ejpam-1203	63	17	in	in	ADP
ejpam-1203	63	18	x	x	X
ejpam-1203	63	19	.	.	PUNCT
ejpam-1203	63	20	10	10	NUM
ejpam-1203	63	21	.	.	X
ejpam-1203	64	1	*	*	PUNCT
ejpam-1203	64	2	g	g	NOUN
ejpam-1203	64	3	-	-	PUNCT
ejpam-1203	64	4	closed	closed	ADJ
ejpam-1203	64	5	[	[	X
ejpam-1203	64	6	5	5	NUM
ejpam-1203	64	7	]	]	PUNCT
ejpam-1203	64	8	if	if	SCONJ
ejpam-1203	64	9	cl(a	cl(a	NUM
ejpam-1203	64	10	)	)	PUNCT
ejpam-1203	64	11	⊆	⊆	NUM
ejpam-1203	64	12	u	u	NOUN
ejpam-1203	64	13	whenever	whenever	SCONJ
ejpam-1203	64	14	a⊆	a⊆	VERB
ejpam-1203	64	15	u	u	NOUN
ejpam-1203	64	16	and	and	CCONJ
ejpam-1203	64	17	u	u	NOUN
ejpam-1203	64	18	is	be	AUX
ejpam-1203	64	19	ĝ	ĝ	X
ejpam-1203	64	20	-open	-open	VERB
ejpam-1203	64	21	in	in	ADP
ejpam-1203	64	22	x	x	X
ejpam-1203	64	23	.	.	PUNCT
ejpam-1203	65	1	11	11	NUM
ejpam-1203	65	2	.	.	PUNCT
ejpam-1203	66	1	#	#	ADJ
ejpam-1203	66	2	gsemi	gsemi	NOUN
ejpam-1203	66	3	closed	closed	ADJ
ejpam-1203	66	4	(	(	PUNCT
ejpam-1203	66	5	briely	briely	ADV
ejpam-1203	66	6	#	#	ADJ
ejpam-1203	66	7	gs	gs	NOUN
ejpam-1203	66	8	-	-	PUNCT
ejpam-1203	66	9	closed)[5	closed)[5	X
ejpam-1203	66	10	]	]	PUNCT
ejpam-1203	66	11	if	if	SCONJ
ejpam-1203	66	12	scl(a	scl(a	X
ejpam-1203	66	13	)	)	PUNCT
ejpam-1203	66	14	⊆	⊆	NUM
ejpam-1203	66	15	u	u	NOUN
ejpam-1203	66	16	whenever	whenever	SCONJ
ejpam-1203	66	17	a⊆	a⊆	VERB
ejpam-1203	66	18	u	u	NOUN
ejpam-1203	66	19	and	and	CCONJ
ejpam-1203	66	20	u	u	NOUN
ejpam-1203	66	21	is	be	AUX
ejpam-1203	66	22	*	*	PUNCT
ejpam-1203	66	23	g	g	NOUN
ejpam-1203	66	24	-	-	PUNCT
ejpam-1203	66	25	open	open	ADJ
ejpam-1203	66	26	in	in	ADP
ejpam-1203	66	27	x	x	X
ejpam-1203	66	28	.	.	PUNCT
ejpam-1203	66	29	12	12	NUM
ejpam-1203	66	30	.	.	PUNCT
ejpam-1203	67	1	g̃-closed	g̃-close	VERB
ejpam-1203	67	2	set	set	NOUN
ejpam-1203	67	3	[	[	X
ejpam-1203	67	4	5	5	NUM
ejpam-1203	67	5	]	]	PUNCT
ejpam-1203	67	6	if	if	SCONJ
ejpam-1203	67	7	cl(a	cl(a	NUM
ejpam-1203	67	8	)	)	PUNCT
ejpam-1203	67	9	⊆	⊆	NUM
ejpam-1203	67	10	u	u	NOUN
ejpam-1203	67	11	whenever	whenever	SCONJ
ejpam-1203	67	12	a⊆	a⊆	VERB
ejpam-1203	67	13	u	u	NOUN
ejpam-1203	67	14	and	and	CCONJ
ejpam-1203	67	15	u	u	NOUN
ejpam-1203	67	16	is	be	AUX
ejpam-1203	67	17	#	#	SYM
ejpam-1203	67	18	gs	gs	NOUN
ejpam-1203	67	19	-	-	PUNCT
ejpam-1203	67	20	open	open	ADJ
ejpam-1203	67	21	in	in	ADP
ejpam-1203	67	22	x	x	X
ejpam-1203	67	23	.	.	PUNCT
ejpam-1203	68	1	the	the	DET
ejpam-1203	68	2	complements	complement	NOUN
ejpam-1203	68	3	of	of	ADP
ejpam-1203	68	4	the	the	DET
ejpam-1203	68	5	above	above	ADJ
ejpam-1203	68	6	mentioned	mention	VERB
ejpam-1203	68	7	sets	set	NOUN
ejpam-1203	68	8	are	be	AUX
ejpam-1203	68	9	called	call	VERB
ejpam-1203	68	10	their	their	PRON
ejpam-1203	68	11	respective	respective	ADJ
ejpam-1203	68	12	open	open	ADJ
ejpam-1203	68	13	sets	set	NOUN
ejpam-1203	68	14	.	.	PUNCT
ejpam-1203	69	1	definition	definition	NOUN
ejpam-1203	69	2	4	4	NUM
ejpam-1203	69	3	.	.	PUNCT
ejpam-1203	70	1	a	a	DET
ejpam-1203	70	2	function	function	NOUN
ejpam-1203	70	3	f	f	NOUN
ejpam-1203	70	4	:	:	PUNCT
ejpam-1203	70	5	(	(	PUNCT
ejpam-1203	70	6	x	x	X
ejpam-1203	70	7	,	,	PUNCT
ejpam-1203	70	8	τ)→	τ)→	PROPN
ejpam-1203	70	9	(	(	PUNCT
ejpam-1203	70	10	y	y	PROPN
ejpam-1203	70	11	,	,	PUNCT
ejpam-1203	70	12	σ	σ	PROPN
ejpam-1203	70	13	)	)	PUNCT
ejpam-1203	70	14	is	be	AUX
ejpam-1203	70	15	said	say	VERB
ejpam-1203	70	16	to	to	PART
ejpam-1203	70	17	be	be	AUX
ejpam-1203	70	18	g	g	NOUN
ejpam-1203	70	19	-	-	ADJ
ejpam-1203	70	20	continuous	continuous	ADJ
ejpam-1203	70	21	[	[	X
ejpam-1203	70	22	2	2	NUM
ejpam-1203	70	23	]	]	PUNCT
ejpam-1203	70	24	if	if	SCONJ
ejpam-1203	70	25	f	f	PROPN
ejpam-1203	70	26	−1(v	−1(v	PROPN
ejpam-1203	70	27	)	)	PUNCT
ejpam-1203	70	28	is	be	AUX
ejpam-1203	70	29	g	g	NOUN
ejpam-1203	70	30	-	-	PUNCT
ejpam-1203	70	31	closed	closed	ADJ
ejpam-1203	70	32	in	in	ADP
ejpam-1203	70	33	(	(	PUNCT
ejpam-1203	70	34	x	x	INTJ
ejpam-1203	70	35	,	,	PUNCT
ejpam-1203	70	36	τ	τ	PROPN
ejpam-1203	70	37	)	)	PUNCT
ejpam-1203	70	38	for	for	ADP
ejpam-1203	70	39	every	every	DET
ejpam-1203	70	40	closed	close	VERB
ejpam-1203	70	41	set	set	VERB
ejpam-1203	70	42	v	v	NOUN
ejpam-1203	70	43	of	of	ADP
ejpam-1203	70	44	(	(	PUNCT
ejpam-1203	70	45	y	y	PROPN
ejpam-1203	70	46	,	,	PUNCT
ejpam-1203	70	47	σ	σ	PROPN
ejpam-1203	70	48	)	)	PUNCT
ejpam-1203	70	49	.	.	PUNCT
ejpam-1203	71	1	3	3	X
ejpam-1203	71	2	.	.	X
ejpam-1203	71	3	basic	basic	ADJ
ejpam-1203	71	4	properties	property	NOUN
ejpam-1203	71	5	of	of	ADP
ejpam-1203	71	6	ρ	ρ	PROPN
ejpam-1203	71	7	-	-	PUNCT
ejpam-1203	71	8	closed	closed	ADJ
ejpam-1203	71	9	sets	set	NOUN
ejpam-1203	71	10	we	we	PRON
ejpam-1203	71	11	introduce	introduce	VERB
ejpam-1203	71	12	the	the	DET
ejpam-1203	71	13	following	following	ADJ
ejpam-1203	71	14	definition	definition	NOUN
ejpam-1203	71	15	.	.	PUNCT
ejpam-1203	72	1	definition	definition	NOUN
ejpam-1203	72	2	5	5	NUM
ejpam-1203	72	3	.	.	PUNCT
ejpam-1203	73	1	a	a	DET
ejpam-1203	73	2	subset	subset	NOUN
ejpam-1203	73	3	a	a	PRON
ejpam-1203	73	4	of	of	ADP
ejpam-1203	73	5	a	a	DET
ejpam-1203	73	6	space	space	NOUN
ejpam-1203	73	7	(	(	PUNCT
ejpam-1203	73	8	x	x	X
ejpam-1203	73	9	,	,	PUNCT
ejpam-1203	73	10	τ	τ	X
ejpam-1203	73	11	)	)	PUNCT
ejpam-1203	73	12	is	be	AUX
ejpam-1203	73	13	said	say	VERB
ejpam-1203	73	14	to	to	PART
ejpam-1203	73	15	be	be	AUX
ejpam-1203	73	16	ρ	ρ	NOUN
ejpam-1203	73	17	-	-	PUNCT
ejpam-1203	73	18	closed	closed	ADJ
ejpam-1203	73	19	in	in	ADP
ejpam-1203	73	20	(	(	PUNCT
ejpam-1203	73	21	x	x	INTJ
ejpam-1203	73	22	,	,	PUNCT
ejpam-1203	73	23	τ	τ	PROPN
ejpam-1203	73	24	)	)	PUNCT
ejpam-1203	73	25	if	if	SCONJ
ejpam-1203	73	26	pcl(a	pcl(a	NOUN
ejpam-1203	73	27	)	)	PUNCT
ejpam-1203	73	28	⊆	⊆	NUM
ejpam-1203	73	29	int(u	int(u	PROPN
ejpam-1203	73	30	)	)	PUNCT
ejpam-1203	73	31	whenever	whenever	SCONJ
ejpam-1203	73	32	a⊆	a⊆	VERB
ejpam-1203	73	33	u	u	NOUN
ejpam-1203	73	34	and	and	CCONJ
ejpam-1203	73	35	u	u	NOUN
ejpam-1203	73	36	is	be	AUX
ejpam-1203	73	37	g̃-open	g̃-open	NOUN
ejpam-1203	73	38	in	in	ADP
ejpam-1203	73	39	(	(	PUNCT
ejpam-1203	73	40	x	x	INTJ
ejpam-1203	73	41	,	,	PUNCT
ejpam-1203	73	42	τ	τ	PROPN
ejpam-1203	73	43	)	)	PUNCT
ejpam-1203	73	44	.	.	PUNCT
ejpam-1203	74	1	theorem	theorem	NOUN
ejpam-1203	74	2	1	1	NUM
ejpam-1203	74	3	.	.	PUNCT
ejpam-1203	75	1	every	every	DET
ejpam-1203	75	2	open	open	ADJ
ejpam-1203	75	3	and	and	CCONJ
ejpam-1203	75	4	preclosed	preclose	VERB
ejpam-1203	75	5	subset	subset	NOUN
ejpam-1203	75	6	of	of	ADP
ejpam-1203	75	7	(	(	PUNCT
ejpam-1203	75	8	x	x	INTJ
ejpam-1203	75	9	,	,	PUNCT
ejpam-1203	75	10	τ	τ	X
ejpam-1203	75	11	)	)	PUNCT
ejpam-1203	75	12	is	be	AUX
ejpam-1203	75	13	ρ	ρ	NOUN
ejpam-1203	75	14	-	-	PUNCT
ejpam-1203	75	15	closed	closed	ADJ
ejpam-1203	75	16	.	.	PUNCT
ejpam-1203	76	1	proof	proof	NOUN
ejpam-1203	76	2	.	.	PUNCT
ejpam-1203	77	1	let	let	VERB
ejpam-1203	77	2	a	a	DET
ejpam-1203	77	3	be	be	AUX
ejpam-1203	77	4	an	an	DET
ejpam-1203	77	5	open	open	ADJ
ejpam-1203	77	6	and	and	CCONJ
ejpam-1203	77	7	preclosed	preclose	VERB
ejpam-1203	77	8	subset	subset	NOUN
ejpam-1203	77	9	of	of	ADP
ejpam-1203	77	10	(	(	PUNCT
ejpam-1203	77	11	x	x	PROPN
ejpam-1203	77	12	,	,	PUNCT
ejpam-1203	77	13	τ	τ	PROPN
ejpam-1203	77	14	)	)	PUNCT
ejpam-1203	77	15	.	.	PUNCT
ejpam-1203	78	1	let	let	VERB
ejpam-1203	78	2	a⊆	a⊆	PUNCT
ejpam-1203	78	3	u	u	NOUN
ejpam-1203	78	4	and	and	CCONJ
ejpam-1203	78	5	u	u	NOUN
ejpam-1203	78	6	be	be	VERB
ejpam-1203	78	7	g̃-open	g̃-open	NOUN
ejpam-1203	78	8	in	in	ADP
ejpam-1203	78	9	x	x	X
ejpam-1203	78	10	.	.	PUNCT
ejpam-1203	79	1	then	then	ADV
ejpam-1203	79	2	pcl(a	pcl(a	X
ejpam-1203	79	3	)	)	PUNCT
ejpam-1203	79	4	=	=	PUNCT
ejpam-1203	80	1	a=	a=	VERB
ejpam-1203	80	2	int(a	int(a	X
ejpam-1203	80	3	)	)	PUNCT
ejpam-1203	80	4	⊆	⊆	NUM
ejpam-1203	80	5	int(u	int(u	NUM
ejpam-1203	80	6	)	)	PUNCT
ejpam-1203	80	7	.	.	PUNCT
ejpam-1203	81	1	hence	hence	ADV
ejpam-1203	81	2	a	a	PRON
ejpam-1203	81	3	is	be	AUX
ejpam-1203	81	4	ρ	ρ	NOUN
ejpam-1203	81	5	-	-	PUNCT
ejpam-1203	81	6	closed	closed	ADJ
ejpam-1203	81	7	.	.	PUNCT
ejpam-1203	82	1	the	the	DET
ejpam-1203	82	2	converse	converse	NOUN
ejpam-1203	82	3	of	of	ADP
ejpam-1203	82	4	the	the	DET
ejpam-1203	82	5	above	above	ADJ
ejpam-1203	82	6	theorem	theorem	NOUN
ejpam-1203	82	7	need	need	AUX
ejpam-1203	82	8	not	not	PART
ejpam-1203	82	9	be	be	AUX
ejpam-1203	82	10	true	true	ADJ
ejpam-1203	82	11	as	as	SCONJ
ejpam-1203	82	12	it	it	PRON
ejpam-1203	82	13	is	be	AUX
ejpam-1203	82	14	seen	see	VERB
ejpam-1203	82	15	from	from	ADP
ejpam-1203	82	16	the	the	DET
ejpam-1203	82	17	following	follow	VERB
ejpam-1203	82	18	example	example	NOUN
ejpam-1203	82	19	.	.	PUNCT
ejpam-1203	83	1	example	example	NOUN
ejpam-1203	84	1	1	1	NUM
ejpam-1203	84	2	.	.	PUNCT
ejpam-1203	84	3	let	let	VERB
ejpam-1203	84	4	x	x	PUNCT
ejpam-1203	84	5	=	=	PRON
ejpam-1203	84	6	{	{	PUNCT
ejpam-1203	84	7	a	a	PRON
ejpam-1203	84	8	,	,	PUNCT
ejpam-1203	84	9	b	b	NOUN
ejpam-1203	84	10	,	,	PUNCT
ejpam-1203	84	11	c	c	NOUN
ejpam-1203	84	12	}	}	PUNCT
ejpam-1203	84	13	and	and	CCONJ
ejpam-1203	84	14	τ	τ	PROPN
ejpam-1203	84	15	=	=	PUNCT
ejpam-1203	84	16	{	{	PUNCT
ejpam-1203	84	17	φ	φ	PROPN
ejpam-1203	84	18	,	,	PUNCT
ejpam-1203	84	19	{	{	PUNCT
ejpam-1203	84	20	a	a	X
ejpam-1203	84	21	}	}	PUNCT
ejpam-1203	84	22	,	,	PUNCT
ejpam-1203	84	23	{	{	PUNCT
ejpam-1203	84	24	c	c	X
ejpam-1203	84	25	,	,	PUNCT
ejpam-1203	84	26	a	a	PRON
ejpam-1203	84	27	}	}	PUNCT
ejpam-1203	84	28	,	,	PUNCT
ejpam-1203	84	29	x	x	SYM
ejpam-1203	84	30	}	}	PUNCT
ejpam-1203	84	31	.	.	PUNCT
ejpam-1203	85	1	then	then	ADV
ejpam-1203	85	2	the	the	DET
ejpam-1203	85	3	set	set	NOUN
ejpam-1203	85	4	a=	a=	NOUN
ejpam-1203	85	5	{	{	PUNCT
ejpam-1203	85	6	a	a	PRON
ejpam-1203	85	7	,	,	PUNCT
ejpam-1203	85	8	b	b	NOUN
ejpam-1203	85	9	}	}	PUNCT
ejpam-1203	85	10	is	be	AUX
ejpam-1203	85	11	ρ	ρ	NOUN
ejpam-1203	85	12	-	-	PUNCT
ejpam-1203	85	13	closed	closed	ADJ
ejpam-1203	85	14	but	but	CCONJ
ejpam-1203	85	15	it	it	PRON
ejpam-1203	85	16	is	be	AUX
ejpam-1203	85	17	neither	neither	CCONJ
ejpam-1203	85	18	open	open	ADJ
ejpam-1203	85	19	set	set	VERB
ejpam-1203	85	20	nor	nor	CCONJ
ejpam-1203	85	21	preclosed	preclose	VERB
ejpam-1203	85	22	set	set	NOUN
ejpam-1203	85	23	in	in	ADP
ejpam-1203	85	24	(	(	PUNCT
ejpam-1203	85	25	x	x	INTJ
ejpam-1203	85	26	,	,	PUNCT
ejpam-1203	85	27	τ	τ	PROPN
ejpam-1203	85	28	)	)	PUNCT
ejpam-1203	85	29	.	.	PUNCT
ejpam-1203	86	1	theorem	theorem	NOUN
ejpam-1203	86	2	2	2	NUM
ejpam-1203	86	3	.	.	PUNCT
ejpam-1203	87	1	every	every	DET
ejpam-1203	87	2	ρ	ρ	PROPN
ejpam-1203	87	3	-	-	PUNCT
ejpam-1203	87	4	closed	closed	ADJ
ejpam-1203	87	5	set	set	NOUN
ejpam-1203	87	6	is	be	AUX
ejpam-1203	87	7	gp	gp	NOUN
ejpam-1203	87	8	-	-	ADJ
ejpam-1203	87	9	closed	closed	ADJ
ejpam-1203	87	10	.	.	PUNCT
ejpam-1203	88	1	proof	proof	NOUN
ejpam-1203	88	2	.	.	PUNCT
ejpam-1203	89	1	let	let	VERB
ejpam-1203	89	2	a	a	DET
ejpam-1203	89	3	be	be	AUX
ejpam-1203	89	4	any	any	DET
ejpam-1203	89	5	ρ	ρ	NOUN
ejpam-1203	89	6	-	-	PUNCT
ejpam-1203	89	7	closed	closed	ADJ
ejpam-1203	89	8	set	set	NOUN
ejpam-1203	89	9	in	in	ADP
ejpam-1203	89	10	x	x	X
ejpam-1203	89	11	.	.	PUNCT
ejpam-1203	90	1	let	let	VERB
ejpam-1203	90	2	a	a	DET
ejpam-1203	90	3	⊆	⊆	NUM
ejpam-1203	90	4	u	u	NOUN
ejpam-1203	90	5	and	and	CCONJ
ejpam-1203	90	6	u	u	NOUN
ejpam-1203	90	7	be	be	VERB
ejpam-1203	90	8	open	open	ADJ
ejpam-1203	90	9	in	in	ADP
ejpam-1203	90	10	x	x	X
ejpam-1203	90	11	.	.	PUNCT
ejpam-1203	91	1	every	every	DET
ejpam-1203	91	2	open	open	ADJ
ejpam-1203	91	3	set	set	NOUN
ejpam-1203	91	4	is	be	AUX
ejpam-1203	91	5	g̃-open	g̃-open	NOUN
ejpam-1203	91	6	and	and	CCONJ
ejpam-1203	91	7	thus	thus	ADV
ejpam-1203	91	8	a	a	PRON
ejpam-1203	91	9	is	be	AUX
ejpam-1203	91	10	ρ	ρ	NOUN
ejpam-1203	91	11	-	-	PUNCT
ejpam-1203	91	12	closed	closed	ADJ
ejpam-1203	91	13	.	.	PUNCT
ejpam-1203	92	1	therefore	therefore	ADV
ejpam-1203	92	2	pcl(a	pcl(a	X
ejpam-1203	92	3	)	)	PUNCT
ejpam-1203	92	4	⊆	⊆	NUM
ejpam-1203	92	5	int(u	int(u	PROPN
ejpam-1203	92	6	)	)	PUNCT
ejpam-1203	92	7	=	=	SYM
ejpam-1203	92	8	u	u	NOUN
ejpam-1203	92	9	.	.	PUNCT
ejpam-1203	93	1	hence	hence	ADV
ejpam-1203	93	2	a	a	PRON
ejpam-1203	93	3	is	be	AUX
ejpam-1203	93	4	gp	gp	NOUN
ejpam-1203	93	5	-	-	ADJ
ejpam-1203	93	6	closed	closed	ADJ
ejpam-1203	93	7	.	.	PUNCT
ejpam-1203	94	1	the	the	DET
ejpam-1203	94	2	converse	converse	NOUN
ejpam-1203	94	3	of	of	ADP
ejpam-1203	94	4	the	the	DET
ejpam-1203	94	5	above	above	ADJ
ejpam-1203	94	6	theorem	theorem	NOUN
ejpam-1203	94	7	need	need	AUX
ejpam-1203	94	8	not	not	PART
ejpam-1203	94	9	be	be	AUX
ejpam-1203	94	10	true	true	ADJ
ejpam-1203	94	11	as	as	SCONJ
ejpam-1203	94	12	it	it	PRON
ejpam-1203	94	13	is	be	AUX
ejpam-1203	94	14	seen	see	VERB
ejpam-1203	94	15	from	from	ADP
ejpam-1203	94	16	the	the	DET
ejpam-1203	94	17	following	follow	VERB
ejpam-1203	94	18	example	example	NOUN
ejpam-1203	94	19	.	.	PUNCT
ejpam-1203	95	1	example	example	NOUN
ejpam-1203	96	1	2	2	NUM
ejpam-1203	96	2	.	.	PUNCT
ejpam-1203	96	3	let	let	VERB
ejpam-1203	96	4	x	x	PUNCT
ejpam-1203	96	5	=	=	PRON
ejpam-1203	96	6	{	{	PUNCT
ejpam-1203	96	7	a	a	PRON
ejpam-1203	96	8	,	,	PUNCT
ejpam-1203	96	9	b	b	NOUN
ejpam-1203	96	10	,	,	PUNCT
ejpam-1203	96	11	c	c	NOUN
ejpam-1203	96	12	,	,	PUNCT
ejpam-1203	96	13	d	d	NOUN
ejpam-1203	96	14	}	}	PUNCT
ejpam-1203	96	15	and	and	CCONJ
ejpam-1203	96	16	τ	τ	PROPN
ejpam-1203	96	17	=	=	PUNCT
ejpam-1203	96	18	{	{	PUNCT
ejpam-1203	96	19	φ	φ	PROPN
ejpam-1203	96	20	,	,	PUNCT
ejpam-1203	96	21	{	{	PUNCT
ejpam-1203	96	22	c	c	NOUN
ejpam-1203	96	23	}	}	PUNCT
ejpam-1203	96	24	,	,	PUNCT
ejpam-1203	96	25	{	{	PUNCT
ejpam-1203	96	26	a	a	DET
ejpam-1203	96	27	,	,	PUNCT
ejpam-1203	96	28	b	b	NOUN
ejpam-1203	96	29	}	}	PUNCT
ejpam-1203	96	30	,	,	PUNCT
ejpam-1203	96	31	{	{	PUNCT
ejpam-1203	96	32	a	a	DET
ejpam-1203	96	33	,	,	PUNCT
ejpam-1203	96	34	b	b	NOUN
ejpam-1203	96	35	,	,	PUNCT
ejpam-1203	96	36	c	c	NOUN
ejpam-1203	96	37	}	}	PUNCT
ejpam-1203	96	38	,	,	PUNCT
ejpam-1203	96	39	x	x	NOUN
ejpam-1203	96	40	}	}	PUNCT
ejpam-1203	96	41	.	.	PUNCT
ejpam-1203	97	1	then	then	ADV
ejpam-1203	97	2	the	the	DET
ejpam-1203	97	3	set	set	NOUN
ejpam-1203	97	4	a	a	X
ejpam-1203	97	5	=	=	X
ejpam-1203	97	6	{	{	PUNCT
ejpam-1203	97	7	a	a	PRON
ejpam-1203	97	8	}	}	PUNCT
ejpam-1203	97	9	is	be	AUX
ejpam-1203	97	10	gp	gp	NOUN
ejpam-1203	97	11	-	-	ADJ
ejpam-1203	97	12	closed	closed	ADJ
ejpam-1203	97	13	but	but	CCONJ
ejpam-1203	97	14	not	not	PART
ejpam-1203	97	15	ρ	ρ	NOUN
ejpam-1203	97	16	-	-	PUNCT
ejpam-1203	97	17	closed	closed	ADJ
ejpam-1203	97	18	in	in	ADP
ejpam-1203	97	19	(	(	PUNCT
ejpam-1203	97	20	x	x	INTJ
ejpam-1203	97	21	,	,	PUNCT
ejpam-1203	97	22	τ	τ	PROPN
ejpam-1203	97	23	)	)	PUNCT
ejpam-1203	97	24	.	.	PUNCT
ejpam-1203	98	1	theorem	theorem	NOUN
ejpam-1203	98	2	3	3	NUM
ejpam-1203	98	3	.	.	PUNCT
ejpam-1203	99	1	every	every	DET
ejpam-1203	99	2	ρ	ρ	PROPN
ejpam-1203	99	3	-	-	PUNCT
ejpam-1203	99	4	closed	closed	ADJ
ejpam-1203	99	5	set	set	NOUN
ejpam-1203	99	6	is	be	AUX
ejpam-1203	99	7	gpr	gpr	NOUN
ejpam-1203	99	8	-	-	PUNCT
ejpam-1203	99	9	closed	closed	ADJ
ejpam-1203	99	10	.	.	PUNCT
ejpam-1203	100	1	proof	proof	NOUN
ejpam-1203	100	2	.	.	PUNCT
ejpam-1203	101	1	let	let	VERB
ejpam-1203	101	2	a	a	DET
ejpam-1203	101	3	be	be	AUX
ejpam-1203	101	4	any	any	DET
ejpam-1203	101	5	ρ	ρ	NOUN
ejpam-1203	101	6	-	-	PUNCT
ejpam-1203	101	7	closed	closed	ADJ
ejpam-1203	101	8	set	set	NOUN
ejpam-1203	101	9	.	.	PUNCT
ejpam-1203	102	1	let	let	VERB
ejpam-1203	102	2	a	a	DET
ejpam-1203	102	3	⊆	⊆	NUM
ejpam-1203	102	4	u	u	NOUN
ejpam-1203	102	5	and	and	CCONJ
ejpam-1203	102	6	u	u	NOUN
ejpam-1203	102	7	be	be	VERB
ejpam-1203	102	8	regular	regular	ADV
ejpam-1203	102	9	open	open	ADJ
ejpam-1203	102	10	.	.	PUNCT
ejpam-1203	103	1	observe	observe	VERB
ejpam-1203	103	2	that	that	SCONJ
ejpam-1203	103	3	every	every	DET
ejpam-1203	103	4	regular	regular	ADJ
ejpam-1203	103	5	open	open	ADJ
ejpam-1203	103	6	set	set	NOUN
ejpam-1203	103	7	is	be	AUX
ejpam-1203	103	8	open	open	ADJ
ejpam-1203	103	9	and	and	CCONJ
ejpam-1203	103	10	every	every	DET
ejpam-1203	103	11	open	open	ADJ
ejpam-1203	103	12	set	set	NOUN
ejpam-1203	103	13	is	be	AUX
ejpam-1203	103	14	g̃-open	g̃-open	NOUN
ejpam-1203	103	15	and	and	CCONJ
ejpam-1203	103	16	therefore	therefore	ADV
ejpam-1203	103	17	a	a	PRON
ejpam-1203	103	18	is	be	AUX
ejpam-1203	103	19	ρ	ρ	NOUN
ejpam-1203	103	20	-	-	PUNCT
ejpam-1203	103	21	closed	closed	ADJ
ejpam-1203	103	22	.	.	PUNCT
ejpam-1203	104	1	it	it	PRON
ejpam-1203	104	2	follows	follow	VERB
ejpam-1203	104	3	that	that	SCONJ
ejpam-1203	104	4	pcl(a	pcl(a	X
ejpam-1203	104	5	)	)	PUNCT
ejpam-1203	104	6	⊆	⊆	NUM
ejpam-1203	104	7	int(u	int(u	PROPN
ejpam-1203	104	8	)	)	PUNCT
ejpam-1203	104	9	=	=	SYM
ejpam-1203	104	10	u	u	NOUN
ejpam-1203	104	11	.	.	PUNCT
ejpam-1203	105	1	hence	hence	ADV
ejpam-1203	105	2	a	a	PRON
ejpam-1203	105	3	is	be	AUX
ejpam-1203	105	4	gpr	gpr	NOUN
ejpam-1203	105	5	-	-	PUNCT
ejpam-1203	105	6	closed	closed	ADJ
ejpam-1203	105	7	.	.	PUNCT
ejpam-1203	106	1	the	the	DET
ejpam-1203	106	2	converse	converse	NOUN
ejpam-1203	106	3	of	of	ADP
ejpam-1203	106	4	the	the	DET
ejpam-1203	106	5	above	above	ADJ
ejpam-1203	106	6	theorem	theorem	NOUN
ejpam-1203	106	7	need	need	AUX
ejpam-1203	106	8	not	not	PART
ejpam-1203	106	9	be	be	AUX
ejpam-1203	106	10	true	true	ADJ
ejpam-1203	106	11	as	as	SCONJ
ejpam-1203	106	12	it	it	PRON
ejpam-1203	106	13	is	be	AUX
ejpam-1203	106	14	seen	see	VERB
ejpam-1203	106	15	from	from	ADP
ejpam-1203	106	16	the	the	DET
ejpam-1203	106	17	following	follow	VERB
ejpam-1203	106	18	example	example	NOUN
ejpam-1203	106	19	.	.	PUNCT
ejpam-1203	107	1	c.	c.	PROPN
ejpam-1203	107	2	devamanoharan	devamanoharan	PROPN
ejpam-1203	107	3	,	,	PUNCT
ejpam-1203	107	4	s.	s.	PROPN
ejpam-1203	107	5	missier	missier	PROPN
ejpam-1203	107	6	,	,	PUNCT
ejpam-1203	107	7	s.	s.	PROPN
ejpam-1203	107	8	jafari	jafari	PROPN
ejpam-1203	107	9	/	/	SYM
ejpam-1203	107	10	eur	eur	PROPN
ejpam-1203	107	11	.	.	PUNCT
ejpam-1203	108	1	j.	j.	PROPN
ejpam-1203	108	2	pure	pure	PROPN
ejpam-1203	108	3	appl	appl	PROPN
ejpam-1203	108	4	.	.	PROPN
ejpam-1203	108	5	math	math	PROPN
ejpam-1203	108	6	,	,	PUNCT
ejpam-1203	108	7	5	5	NUM
ejpam-1203	108	8	(	(	PUNCT
ejpam-1203	108	9	2012	2012	NUM
ejpam-1203	108	10	)	)	PUNCT
ejpam-1203	108	11	,	,	PUNCT
ejpam-1203	108	12	554	554	NUM
ejpam-1203	108	13	-	-	SYM
ejpam-1203	108	14	566	566	NUM
ejpam-1203	108	15	557	557	NUM
ejpam-1203	108	16	example	example	NOUN
ejpam-1203	108	17	3	3	NUM
ejpam-1203	108	18	.	.	PUNCT
ejpam-1203	109	1	let	let	VERB
ejpam-1203	109	2	x	x	PUNCT
ejpam-1203	109	3	=	=	PRON
ejpam-1203	109	4	{	{	PUNCT
ejpam-1203	109	5	a	a	PRON
ejpam-1203	109	6	,	,	PUNCT
ejpam-1203	109	7	b	b	NOUN
ejpam-1203	109	8	,	,	PUNCT
ejpam-1203	109	9	c	c	NOUN
ejpam-1203	109	10	}	}	PUNCT
ejpam-1203	109	11	and	and	CCONJ
ejpam-1203	109	12	τ	τ	PROPN
ejpam-1203	109	13	=	=	PUNCT
ejpam-1203	109	14	{	{	PUNCT
ejpam-1203	109	15	φ	φ	PROPN
ejpam-1203	109	16	,	,	PUNCT
ejpam-1203	109	17	{	{	PUNCT
ejpam-1203	109	18	a	a	X
ejpam-1203	109	19	}	}	PUNCT
ejpam-1203	109	20	,	,	PUNCT
ejpam-1203	109	21	{	{	PUNCT
ejpam-1203	109	22	b	b	NOUN
ejpam-1203	109	23	}	}	PUNCT
ejpam-1203	109	24	,	,	PUNCT
ejpam-1203	109	25	{	{	PUNCT
ejpam-1203	109	26	a	a	DET
ejpam-1203	109	27	,	,	PUNCT
ejpam-1203	109	28	b	b	NOUN
ejpam-1203	109	29	}	}	PUNCT
ejpam-1203	109	30	,	,	PUNCT
ejpam-1203	109	31	x	x	SYM
ejpam-1203	109	32	}	}	PUNCT
ejpam-1203	109	33	.	.	PUNCT
ejpam-1203	110	1	then	then	ADV
ejpam-1203	110	2	the	the	DET
ejpam-1203	110	3	set	set	NOUN
ejpam-1203	110	4	a	a	X
ejpam-1203	110	5	=	=	X
ejpam-1203	110	6	{	{	PUNCT
ejpam-1203	110	7	a	a	PROPN
ejpam-1203	110	8	,	,	PUNCT
ejpam-1203	110	9	b	b	X
ejpam-1203	110	10	}	}	PUNCT
ejpam-1203	110	11	is	be	AUX
ejpam-1203	110	12	gprclosed	gprclose	VERB
ejpam-1203	110	13	but	but	CCONJ
ejpam-1203	110	14	not	not	PART
ejpam-1203	110	15	ρ	ρ	NOUN
ejpam-1203	110	16	-	-	PUNCT
ejpam-1203	110	17	closed	closed	ADJ
ejpam-1203	110	18	in	in	ADP
ejpam-1203	110	19	(	(	PUNCT
ejpam-1203	110	20	x	x	INTJ
ejpam-1203	110	21	,	,	PUNCT
ejpam-1203	110	22	τ	τ	PROPN
ejpam-1203	110	23	)	)	PUNCT
ejpam-1203	110	24	.	.	PUNCT
ejpam-1203	111	1	theorem	theorem	ADJ
ejpam-1203	111	2	4	4	NUM
ejpam-1203	111	3	.	.	PUNCT
ejpam-1203	111	4	everyρ	everyρ	NOUN
ejpam-1203	111	5	-	-	PUNCT
ejpam-1203	111	6	closed	close	VERB
ejpam-1203	111	7	set	set	NOUN
ejpam-1203	111	8	is	be	AUX
ejpam-1203	111	9	gsp	gsp	VERB
ejpam-1203	111	10	-	-	PUNCT
ejpam-1203	111	11	closed	closed	ADJ
ejpam-1203	111	12	.	.	PUNCT
ejpam-1203	112	1	proof	proof	NOUN
ejpam-1203	112	2	.	.	PUNCT
ejpam-1203	113	1	let	let	VERB
ejpam-1203	113	2	a	a	DET
ejpam-1203	113	3	be	be	AUX
ejpam-1203	113	4	any	any	DET
ejpam-1203	113	5	ρ	ρ	NOUN
ejpam-1203	113	6	-	-	PUNCT
ejpam-1203	113	7	closed	closed	ADJ
ejpam-1203	113	8	set	set	NOUN
ejpam-1203	113	9	.	.	PUNCT
ejpam-1203	114	1	let	let	VERB
ejpam-1203	114	2	a⊆	a⊆	PUNCT
ejpam-1203	114	3	u	u	NOUN
ejpam-1203	114	4	and	and	CCONJ
ejpam-1203	114	5	u	u	NOUN
ejpam-1203	114	6	be	be	VERB
ejpam-1203	114	7	open	open	ADJ
ejpam-1203	114	8	.	.	PUNCT
ejpam-1203	115	1	since	since	SCONJ
ejpam-1203	115	2	every	every	DET
ejpam-1203	115	3	open	open	ADJ
ejpam-1203	115	4	set	set	NOUN
ejpam-1203	115	5	is	be	AUX
ejpam-1203	115	6	g̃-open	g̃-open	NOUN
ejpam-1203	115	7	and	and	CCONJ
ejpam-1203	115	8	thus	thus	ADV
ejpam-1203	115	9	a	a	PRON
ejpam-1203	115	10	is	be	AUX
ejpam-1203	115	11	ρ	ρ	NOUN
ejpam-1203	115	12	-	-	PUNCT
ejpam-1203	115	13	closed	closed	ADJ
ejpam-1203	115	14	.	.	PUNCT
ejpam-1203	116	1	therefore	therefore	ADV
ejpam-1203	116	2	pcl(a	pcl(a	X
ejpam-1203	116	3	)	)	PUNCT
ejpam-1203	116	4	⊆	⊆	NUM
ejpam-1203	116	5	int(u	int(u	PROPN
ejpam-1203	116	6	)	)	PUNCT
ejpam-1203	116	7	=	=	SYM
ejpam-1203	116	8	u	u	NOUN
ejpam-1203	116	9	and	and	CCONJ
ejpam-1203	116	10	so	so	ADV
ejpam-1203	116	11	spcl(a	spcl(a	ADJ
ejpam-1203	116	12	)	)	PUNCT
ejpam-1203	116	13	⊆	⊆	NUM
ejpam-1203	116	14	u	u	NOUN
ejpam-1203	116	15	.	.	PUNCT
ejpam-1203	117	1	hence	hence	ADV
ejpam-1203	117	2	a	a	PRON
ejpam-1203	117	3	is	be	AUX
ejpam-1203	117	4	gsp	gsp	VERB
ejpam-1203	117	5	-	-	PUNCT
ejpam-1203	117	6	closed	closed	ADJ
ejpam-1203	117	7	.	.	PUNCT
ejpam-1203	118	1	the	the	DET
ejpam-1203	118	2	converse	converse	NOUN
ejpam-1203	118	3	of	of	ADP
ejpam-1203	118	4	this	this	DET
ejpam-1203	118	5	theorem	theorem	NOUN
ejpam-1203	118	6	need	need	AUX
ejpam-1203	118	7	not	not	PART
ejpam-1203	118	8	be	be	AUX
ejpam-1203	118	9	true	true	ADJ
ejpam-1203	118	10	as	as	SCONJ
ejpam-1203	118	11	it	it	PRON
ejpam-1203	118	12	is	be	AUX
ejpam-1203	118	13	seen	see	VERB
ejpam-1203	118	14	from	from	ADP
ejpam-1203	118	15	the	the	DET
ejpam-1203	118	16	following	follow	VERB
ejpam-1203	118	17	example	example	NOUN
ejpam-1203	118	18	.	.	PUNCT
ejpam-1203	119	1	example	example	NOUN
ejpam-1203	120	1	4	4	NUM
ejpam-1203	120	2	.	.	PUNCT
ejpam-1203	120	3	let	let	VERB
ejpam-1203	120	4	x	x	PUNCT
ejpam-1203	120	5	=	=	PRON
ejpam-1203	120	6	{	{	PUNCT
ejpam-1203	120	7	a	a	PRON
ejpam-1203	120	8	,	,	PUNCT
ejpam-1203	120	9	b	b	NOUN
ejpam-1203	120	10	,	,	PUNCT
ejpam-1203	120	11	c	c	NOUN
ejpam-1203	120	12	,	,	PUNCT
ejpam-1203	120	13	d	d	X
ejpam-1203	120	14	,	,	PUNCT
ejpam-1203	120	15	e	e	NOUN
ejpam-1203	120	16	}	}	PUNCT
ejpam-1203	120	17	and	and	CCONJ
ejpam-1203	120	18	τ	τ	PROPN
ejpam-1203	120	19	=	=	PUNCT
ejpam-1203	120	20	{	{	PUNCT
ejpam-1203	120	21	φ	φ	PROPN
ejpam-1203	120	22	,	,	PUNCT
ejpam-1203	120	23	{	{	PUNCT
ejpam-1203	120	24	a	a	DET
ejpam-1203	120	25	,	,	PUNCT
ejpam-1203	120	26	b	b	NOUN
ejpam-1203	120	27	}	}	PUNCT
ejpam-1203	120	28	,	,	PUNCT
ejpam-1203	120	29	{	{	PUNCT
ejpam-1203	120	30	c	c	X
ejpam-1203	120	31	,	,	PUNCT
ejpam-1203	120	32	d	d	NOUN
ejpam-1203	120	33	}	}	PUNCT
ejpam-1203	120	34	,	,	PUNCT
ejpam-1203	120	35	{	{	PUNCT
ejpam-1203	120	36	a	a	PRON
ejpam-1203	120	37	,	,	PUNCT
ejpam-1203	120	38	b	b	NOUN
ejpam-1203	120	39	,	,	PUNCT
ejpam-1203	120	40	c	c	NOUN
ejpam-1203	120	41	,	,	PUNCT
ejpam-1203	120	42	d	d	NOUN
ejpam-1203	120	43	}	}	PUNCT
ejpam-1203	120	44	,	,	PUNCT
ejpam-1203	120	45	x	x	SYM
ejpam-1203	120	46	}	}	PUNCT
ejpam-1203	120	47	.	.	PUNCT
ejpam-1203	121	1	then	then	ADV
ejpam-1203	121	2	the	the	DET
ejpam-1203	121	3	set	set	NOUN
ejpam-1203	121	4	a=	a=	NOUN
ejpam-1203	121	5	{	{	PUNCT
ejpam-1203	121	6	a	a	DET
ejpam-1203	121	7	,	,	PUNCT
ejpam-1203	121	8	b	b	NOUN
ejpam-1203	121	9	}	}	PUNCT
ejpam-1203	121	10	is	be	AUX
ejpam-1203	121	11	gspclosed	gspclose	VERB
ejpam-1203	121	12	but	but	CCONJ
ejpam-1203	121	13	not	not	PART
ejpam-1203	121	14	ρ	ρ	NOUN
ejpam-1203	121	15	-	-	PUNCT
ejpam-1203	121	16	closed	closed	ADJ
ejpam-1203	121	17	in	in	ADP
ejpam-1203	121	18	(	(	PUNCT
ejpam-1203	121	19	x	x	INTJ
ejpam-1203	121	20	,	,	PUNCT
ejpam-1203	121	21	τ	τ	PROPN
ejpam-1203	121	22	)	)	PUNCT
ejpam-1203	121	23	.	.	PUNCT
ejpam-1203	122	1	theorem	theorem	ADJ
ejpam-1203	122	2	5	5	NUM
ejpam-1203	122	3	.	.	PUNCT
ejpam-1203	123	1	every	every	DET
ejpam-1203	123	2	ρ	ρ	PROPN
ejpam-1203	123	3	-	-	PUNCT
ejpam-1203	123	4	closed	closed	ADJ
ejpam-1203	123	5	set	set	NOUN
ejpam-1203	123	6	is	be	AUX
ejpam-1203	123	7	πgp	πgp	ADJ
ejpam-1203	123	8	-	-	PUNCT
ejpam-1203	123	9	closed	closed	ADJ
ejpam-1203	123	10	.	.	PUNCT
ejpam-1203	124	1	proof	proof	NOUN
ejpam-1203	124	2	.	.	PUNCT
ejpam-1203	125	1	let	let	VERB
ejpam-1203	125	2	a	a	DET
ejpam-1203	125	3	be	be	AUX
ejpam-1203	125	4	any	any	DET
ejpam-1203	125	5	ρ	ρ	NOUN
ejpam-1203	125	6	-	-	PUNCT
ejpam-1203	125	7	closed	closed	ADJ
ejpam-1203	125	8	set	set	NOUN
ejpam-1203	125	9	.	.	PUNCT
ejpam-1203	126	1	let	let	VERB
ejpam-1203	126	2	a	a	DET
ejpam-1203	126	3	⊆	⊆	NUM
ejpam-1203	126	4	u	u	NOUN
ejpam-1203	126	5	and	and	CCONJ
ejpam-1203	126	6	u	u	PRON
ejpam-1203	126	7	be	be	VERB
ejpam-1203	126	8	π	π	NOUN
ejpam-1203	126	9	-	-	ADJ
ejpam-1203	126	10	open	open	ADJ
ejpam-1203	126	11	.	.	PUNCT
ejpam-1203	127	1	since	since	SCONJ
ejpam-1203	127	2	every	every	DET
ejpam-1203	127	3	π	π	PROPN
ejpam-1203	127	4	-	-	ADJ
ejpam-1203	127	5	open	open	ADJ
ejpam-1203	127	6	set	set	NOUN
ejpam-1203	127	7	is	be	AUX
ejpam-1203	127	8	open	open	ADJ
ejpam-1203	127	9	and	and	CCONJ
ejpam-1203	127	10	every	every	DET
ejpam-1203	127	11	open	open	ADJ
ejpam-1203	127	12	set	set	NOUN
ejpam-1203	127	13	is	be	AUX
ejpam-1203	127	14	g̃-open	g̃-open	NOUN
ejpam-1203	127	15	and	and	CCONJ
ejpam-1203	127	16	therefore	therefore	ADV
ejpam-1203	127	17	a	a	PRON
ejpam-1203	127	18	is	be	AUX
ejpam-1203	127	19	ρ	ρ	NOUN
ejpam-1203	127	20	-	-	PUNCT
ejpam-1203	127	21	closed	closed	ADJ
ejpam-1203	127	22	.	.	PUNCT
ejpam-1203	128	1	this	this	PRON
ejpam-1203	128	2	means	mean	VERB
ejpam-1203	128	3	that	that	SCONJ
ejpam-1203	128	4	pcl(a	pcl(a	X
ejpam-1203	128	5	)	)	PUNCT
ejpam-1203	128	6	⊆	⊆	NUM
ejpam-1203	128	7	int(u	int(u	PROPN
ejpam-1203	128	8	)	)	PUNCT
ejpam-1203	128	9	=	=	SYM
ejpam-1203	128	10	u	u	NOUN
ejpam-1203	128	11	.	.	PUNCT
ejpam-1203	129	1	hence	hence	ADV
ejpam-1203	129	2	a	a	PRON
ejpam-1203	129	3	is	be	AUX
ejpam-1203	129	4	πgp	πgp	VERB
ejpam-1203	129	5	-	-	PUNCT
ejpam-1203	129	6	closed	closed	ADJ
ejpam-1203	129	7	.	.	PUNCT
ejpam-1203	130	1	the	the	DET
ejpam-1203	130	2	converse	converse	NOUN
ejpam-1203	130	3	of	of	ADP
ejpam-1203	130	4	the	the	DET
ejpam-1203	130	5	above	above	ADJ
ejpam-1203	130	6	theorem	theorem	NOUN
ejpam-1203	130	7	need	need	AUX
ejpam-1203	130	8	not	not	PART
ejpam-1203	130	9	be	be	AUX
ejpam-1203	130	10	true	true	ADJ
ejpam-1203	130	11	as	as	SCONJ
ejpam-1203	130	12	it	it	PRON
ejpam-1203	130	13	is	be	AUX
ejpam-1203	130	14	seen	see	VERB
ejpam-1203	130	15	from	from	ADP
ejpam-1203	130	16	the	the	DET
ejpam-1203	130	17	following	follow	VERB
ejpam-1203	130	18	example	example	NOUN
ejpam-1203	130	19	.	.	PUNCT
ejpam-1203	131	1	example	example	NOUN
ejpam-1203	132	1	5	5	NUM
ejpam-1203	132	2	.	.	PUNCT
ejpam-1203	132	3	let	let	VERB
ejpam-1203	132	4	x	x	PUNCT
ejpam-1203	132	5	=	=	PRON
ejpam-1203	132	6	{	{	PUNCT
ejpam-1203	132	7	a	a	PRON
ejpam-1203	132	8	,	,	PUNCT
ejpam-1203	132	9	b	b	NOUN
ejpam-1203	132	10	,	,	PUNCT
ejpam-1203	132	11	c	c	NOUN
ejpam-1203	132	12	}	}	PUNCT
ejpam-1203	132	13	and	and	CCONJ
ejpam-1203	132	14	τ	τ	PROPN
ejpam-1203	132	15	=	=	PUNCT
ejpam-1203	132	16	{	{	PUNCT
ejpam-1203	132	17	φ	φ	PROPN
ejpam-1203	132	18	,	,	PUNCT
ejpam-1203	132	19	{	{	PUNCT
ejpam-1203	132	20	a	a	X
ejpam-1203	132	21	}	}	PUNCT
ejpam-1203	132	22	,	,	PUNCT
ejpam-1203	132	23	{	{	PUNCT
ejpam-1203	132	24	a	a	DET
ejpam-1203	132	25	,	,	PUNCT
ejpam-1203	132	26	b	b	NOUN
ejpam-1203	132	27	}	}	PUNCT
ejpam-1203	132	28	,	,	PUNCT
ejpam-1203	132	29	{	{	PUNCT
ejpam-1203	132	30	a	a	X
ejpam-1203	132	31	,	,	PUNCT
ejpam-1203	132	32	c	c	NOUN
ejpam-1203	132	33	}	}	PUNCT
ejpam-1203	132	34	,	,	PUNCT
ejpam-1203	132	35	x	x	SYM
ejpam-1203	132	36	}	}	PUNCT
ejpam-1203	132	37	.	.	PUNCT
ejpam-1203	133	1	then	then	ADV
ejpam-1203	133	2	the	the	DET
ejpam-1203	133	3	set	set	NOUN
ejpam-1203	133	4	a	a	X
ejpam-1203	133	5	=	=	X
ejpam-1203	133	6	{	{	PUNCT
ejpam-1203	133	7	a	a	PROPN
ejpam-1203	133	8	,	,	PUNCT
ejpam-1203	133	9	b	b	NOUN
ejpam-1203	133	10	}	}	PUNCT
ejpam-1203	133	11	is	be	AUX
ejpam-1203	133	12	πgp	πgp	VERB
ejpam-1203	133	13	-	-	PUNCT
ejpam-1203	133	14	closed	closed	ADJ
ejpam-1203	133	15	but	but	CCONJ
ejpam-1203	133	16	not	not	PART
ejpam-1203	133	17	ρ	ρ	NOUN
ejpam-1203	133	18	-	-	PUNCT
ejpam-1203	133	19	closed	closed	ADJ
ejpam-1203	133	20	in	in	ADP
ejpam-1203	133	21	(	(	PUNCT
ejpam-1203	133	22	x	x	INTJ
ejpam-1203	133	23	,	,	PUNCT
ejpam-1203	133	24	τ	τ	PROPN
ejpam-1203	133	25	)	)	PUNCT
ejpam-1203	133	26	.	.	PUNCT
ejpam-1203	134	1	remark	remark	PROPN
ejpam-1203	134	2	1	1	NUM
ejpam-1203	134	3	.	.	PUNCT
ejpam-1203	135	1	ρ	ρ	NOUN
ejpam-1203	135	2	-	-	PUNCT
ejpam-1203	135	3	closedness	closedness	NOUN
ejpam-1203	135	4	and	and	CCONJ
ejpam-1203	135	5	preclosedness	preclosedness	NOUN
ejpam-1203	135	6	are	be	AUX
ejpam-1203	135	7	independent	independent	ADJ
ejpam-1203	135	8	concepts	concept	NOUN
ejpam-1203	135	9	as	as	SCONJ
ejpam-1203	135	10	we	we	PRON
ejpam-1203	135	11	illustrate	illustrate	VERB
ejpam-1203	135	12	by	by	ADP
ejpam-1203	135	13	means	mean	NOUN
ejpam-1203	135	14	of	of	ADP
ejpam-1203	135	15	the	the	DET
ejpam-1203	135	16	following	follow	VERB
ejpam-1203	135	17	examples	example	NOUN
ejpam-1203	135	18	.	.	PUNCT
ejpam-1203	136	1	example	example	NOUN
ejpam-1203	137	1	6	6	NUM
ejpam-1203	137	2	.	.	NOUN
ejpam-1203	137	3	1	1	NUM
ejpam-1203	137	4	.	.	X
ejpam-1203	138	1	as	as	SCONJ
ejpam-1203	138	2	in	in	ADP
ejpam-1203	138	3	example	example	NOUN
ejpam-1203	138	4	1	1	NUM
ejpam-1203	138	5	,	,	PUNCT
ejpam-1203	138	6	the	the	DET
ejpam-1203	138	7	set	set	NOUN
ejpam-1203	138	8	a=	a=	NOUN
ejpam-1203	138	9	{	{	PUNCT
ejpam-1203	138	10	a	a	PRON
ejpam-1203	138	11	,	,	PUNCT
ejpam-1203	138	12	b	b	NOUN
ejpam-1203	138	13	}	}	PUNCT
ejpam-1203	138	14	is	be	AUX
ejpam-1203	138	15	ρ	ρ	NOUN
ejpam-1203	138	16	-	-	PUNCT
ejpam-1203	138	17	closed	closed	ADJ
ejpam-1203	138	18	but	but	CCONJ
ejpam-1203	138	19	not	not	PART
ejpam-1203	138	20	preclosed	preclose	VERB
ejpam-1203	138	21	in	in	ADP
ejpam-1203	138	22	(	(	PUNCT
ejpam-1203	138	23	x	x	INTJ
ejpam-1203	138	24	,	,	PUNCT
ejpam-1203	138	25	τ	τ	PROPN
ejpam-1203	138	26	)	)	PUNCT
ejpam-1203	138	27	.	.	PUNCT
ejpam-1203	139	1	2	2	X
ejpam-1203	139	2	.	.	X
ejpam-1203	139	3	let	let	VERB
ejpam-1203	139	4	x	x	PUNCT
ejpam-1203	139	5	=	=	PRON
ejpam-1203	139	6	{	{	PUNCT
ejpam-1203	139	7	a	a	PRON
ejpam-1203	139	8	,	,	PUNCT
ejpam-1203	139	9	b	b	NOUN
ejpam-1203	139	10	,	,	PUNCT
ejpam-1203	139	11	c	c	NOUN
ejpam-1203	139	12	,	,	PUNCT
ejpam-1203	139	13	d	d	X
ejpam-1203	139	14	,	,	PUNCT
ejpam-1203	139	15	e	e	NOUN
ejpam-1203	139	16	}	}	PUNCT
ejpam-1203	139	17	and	and	CCONJ
ejpam-1203	139	18	τ	τ	PROPN
ejpam-1203	139	19	=	=	PUNCT
ejpam-1203	139	20	{	{	PUNCT
ejpam-1203	139	21	φ	φ	PROPN
ejpam-1203	139	22	,	,	PUNCT
ejpam-1203	139	23	{	{	PUNCT
ejpam-1203	139	24	a	a	DET
ejpam-1203	139	25	,	,	PUNCT
ejpam-1203	139	26	b	b	NOUN
ejpam-1203	139	27	}	}	PUNCT
ejpam-1203	139	28	,	,	PUNCT
ejpam-1203	139	29	{	{	PUNCT
ejpam-1203	139	30	a	a	DET
ejpam-1203	139	31	,	,	PUNCT
ejpam-1203	139	32	b	b	NOUN
ejpam-1203	139	33	,	,	PUNCT
ejpam-1203	139	34	c	c	NOUN
ejpam-1203	139	35	,	,	PUNCT
ejpam-1203	139	36	}	}	PUNCT
ejpam-1203	139	37	,	,	PUNCT
ejpam-1203	139	38	{	{	PUNCT
ejpam-1203	139	39	a	a	DET
ejpam-1203	139	40	,	,	PUNCT
ejpam-1203	139	41	b	b	NOUN
ejpam-1203	139	42	,	,	PUNCT
ejpam-1203	139	43	d	d	NOUN
ejpam-1203	139	44	}	}	PUNCT
ejpam-1203	139	45	,	,	PUNCT
ejpam-1203	139	46	{	{	PUNCT
ejpam-1203	139	47	a	a	PRON
ejpam-1203	139	48	,	,	PUNCT
ejpam-1203	139	49	b	b	NOUN
ejpam-1203	139	50	,	,	PUNCT
ejpam-1203	139	51	c	c	NOUN
ejpam-1203	139	52	,	,	PUNCT
ejpam-1203	139	53	d	d	NOUN
ejpam-1203	139	54	}	}	PUNCT
ejpam-1203	139	55	,	,	PUNCT
ejpam-1203	139	56	x	x	SYM
ejpam-1203	139	57	}	}	PUNCT
ejpam-1203	139	58	.	.	PUNCT
ejpam-1203	140	1	then	then	ADV
ejpam-1203	140	2	the	the	DET
ejpam-1203	140	3	set	set	NOUN
ejpam-1203	140	4	a=	a=	NOUN
ejpam-1203	140	5	{	{	PUNCT
ejpam-1203	140	6	a	a	PRON
ejpam-1203	140	7	}	}	PUNCT
ejpam-1203	140	8	is	be	AUX
ejpam-1203	140	9	preclosed	preclose	VERB
ejpam-1203	140	10	but	but	CCONJ
ejpam-1203	140	11	not	not	PART
ejpam-1203	140	12	ρ	ρ	NOUN
ejpam-1203	140	13	-	-	PUNCT
ejpam-1203	140	14	closed	closed	ADJ
ejpam-1203	140	15	in	in	ADP
ejpam-1203	140	16	(	(	PUNCT
ejpam-1203	140	17	x	x	INTJ
ejpam-1203	140	18	,	,	PUNCT
ejpam-1203	140	19	τ	τ	PROPN
ejpam-1203	140	20	)	)	PUNCT
ejpam-1203	140	21	.	.	PUNCT
ejpam-1203	141	1	remark	remark	PROPN
ejpam-1203	141	2	2	2	NUM
ejpam-1203	141	3	.	.	PUNCT
ejpam-1203	141	4	ρ	ρ	VERB
ejpam-1203	141	5	-	-	PUNCT
ejpam-1203	141	6	closed	closed	ADJ
ejpam-1203	141	7	sets	set	NOUN
ejpam-1203	141	8	are	be	AUX
ejpam-1203	141	9	independent	independent	ADJ
ejpam-1203	141	10	concepts	concept	NOUN
ejpam-1203	141	11	of	of	ADP
ejpam-1203	141	12	semi	semi	ADJ
ejpam-1203	141	13	-	-	ADJ
ejpam-1203	141	14	closed	closed	ADJ
ejpam-1203	141	15	sets	set	NOUN
ejpam-1203	141	16	and	and	CCONJ
ejpam-1203	141	17	semi	semi	ADJ
ejpam-1203	141	18	-	-	ADJ
ejpam-1203	141	19	preclosed	preclosed	ADJ
ejpam-1203	141	20	sets	set	NOUN
ejpam-1203	141	21	as	as	SCONJ
ejpam-1203	141	22	we	we	PRON
ejpam-1203	141	23	illustrate	illustrate	VERB
ejpam-1203	141	24	by	by	ADP
ejpam-1203	141	25	means	mean	NOUN
ejpam-1203	141	26	of	of	ADP
ejpam-1203	141	27	the	the	DET
ejpam-1203	141	28	following	follow	VERB
ejpam-1203	141	29	example	example	NOUN
ejpam-1203	141	30	.	.	PUNCT
ejpam-1203	142	1	example	example	NOUN
ejpam-1203	143	1	7	7	NUM
ejpam-1203	143	2	.	.	PUNCT
ejpam-1203	144	1	let	let	VERB
ejpam-1203	144	2	x	x	PUNCT
ejpam-1203	144	3	=	=	PRON
ejpam-1203	144	4	{	{	PUNCT
ejpam-1203	144	5	a	a	PRON
ejpam-1203	144	6	,	,	PUNCT
ejpam-1203	144	7	b	b	NOUN
ejpam-1203	144	8	,	,	PUNCT
ejpam-1203	144	9	c	c	NOUN
ejpam-1203	144	10	,	,	PUNCT
ejpam-1203	144	11	d	d	NOUN
ejpam-1203	144	12	}	}	PUNCT
ejpam-1203	144	13	and	and	CCONJ
ejpam-1203	144	14	τ	τ	PROPN
ejpam-1203	144	15	=	=	PUNCT
ejpam-1203	144	16	{	{	PUNCT
ejpam-1203	144	17	φ	φ	PROPN
ejpam-1203	144	18	,	,	PUNCT
ejpam-1203	144	19	{	{	PUNCT
ejpam-1203	144	20	b	b	NOUN
ejpam-1203	144	21	}	}	PUNCT
ejpam-1203	144	22	,	,	PUNCT
ejpam-1203	144	23	{	{	PUNCT
ejpam-1203	144	24	c	c	X
ejpam-1203	144	25	}	}	PUNCT
ejpam-1203	144	26	,	,	PUNCT
ejpam-1203	144	27	{	{	PUNCT
ejpam-1203	144	28	b	b	X
ejpam-1203	144	29	,	,	PUNCT
ejpam-1203	144	30	c	c	NOUN
ejpam-1203	144	31	}	}	PUNCT
ejpam-1203	144	32	,	,	PUNCT
ejpam-1203	144	33	{	{	PUNCT
ejpam-1203	144	34	b	b	X
ejpam-1203	144	35	,	,	PUNCT
ejpam-1203	144	36	c	c	NOUN
ejpam-1203	144	37	,	,	PUNCT
ejpam-1203	144	38	d	d	NOUN
ejpam-1203	144	39	}	}	PUNCT
ejpam-1203	144	40	,	,	PUNCT
ejpam-1203	144	41	x	x	SYM
ejpam-1203	144	42	}	}	PUNCT
ejpam-1203	144	43	.	.	PUNCT
ejpam-1203	145	1	then	then	ADV
ejpam-1203	145	2	the	the	DET
ejpam-1203	145	3	set	set	NOUN
ejpam-1203	145	4	a	a	X
ejpam-1203	145	5	=	=	X
ejpam-1203	145	6	{	{	PUNCT
ejpam-1203	145	7	a	a	PROPN
ejpam-1203	145	8	,	,	PUNCT
ejpam-1203	145	9	b	b	NOUN
ejpam-1203	145	10	,	,	PUNCT
ejpam-1203	145	11	c	c	NOUN
ejpam-1203	145	12	}	}	PUNCT
ejpam-1203	145	13	is	be	AUX
ejpam-1203	145	14	ρ	ρ	NOUN
ejpam-1203	145	15	-	-	PUNCT
ejpam-1203	145	16	closed	closed	ADJ
ejpam-1203	145	17	but	but	CCONJ
ejpam-1203	145	18	neither	neither	CCONJ
ejpam-1203	145	19	semi	semi	ADV
ejpam-1203	145	20	-	-	ADJ
ejpam-1203	145	21	closed	closed	ADJ
ejpam-1203	145	22	nor	nor	CCONJ
ejpam-1203	145	23	semi	semi	ADJ
ejpam-1203	145	24	-	-	ADJ
ejpam-1203	145	25	preclosed	preclosed	ADJ
ejpam-1203	145	26	.	.	PUNCT
ejpam-1203	146	1	the	the	DET
ejpam-1203	146	2	set	set	PROPN
ejpam-1203	146	3	b	b	PROPN
ejpam-1203	146	4	=	=	X
ejpam-1203	146	5	{	{	PUNCT
ejpam-1203	146	6	c	c	NOUN
ejpam-1203	146	7	,	,	PUNCT
ejpam-1203	146	8	d	d	NOUN
ejpam-1203	146	9	}	}	PUNCT
ejpam-1203	146	10	is	be	AUX
ejpam-1203	146	11	both	both	PRON
ejpam-1203	146	12	semi	semi	ADJ
ejpam-1203	146	13	-	-	ADJ
ejpam-1203	146	14	closed	closed	ADJ
ejpam-1203	146	15	and	and	CCONJ
ejpam-1203	146	16	semi	semi	ADJ
ejpam-1203	146	17	-	-	ADJ
ejpam-1203	146	18	preclosed	preclosed	ADJ
ejpam-1203	146	19	but	but	CCONJ
ejpam-1203	146	20	not	not	PART
ejpam-1203	146	21	ρ	ρ	NOUN
ejpam-1203	146	22	-	-	PUNCT
ejpam-1203	146	23	closed	closed	ADJ
ejpam-1203	146	24	.	.	PUNCT
ejpam-1203	147	1	remark	remark	NOUN
ejpam-1203	147	2	3	3	NUM
ejpam-1203	147	3	.	.	PUNCT
ejpam-1203	148	1	ρ	ρ	NOUN
ejpam-1203	148	2	-	-	PUNCT
ejpam-1203	148	3	closedness	closedness	NOUN
ejpam-1203	148	4	and	and	CCONJ
ejpam-1203	148	5	presemiclosedness	presemiclosedness	NOUN
ejpam-1203	148	6	are	be	AUX
ejpam-1203	148	7	independent	independent	ADJ
ejpam-1203	148	8	concepts	concept	NOUN
ejpam-1203	148	9	as	as	SCONJ
ejpam-1203	148	10	we	we	PRON
ejpam-1203	148	11	illustrate	illustrate	VERB
ejpam-1203	148	12	by	by	ADP
ejpam-1203	148	13	means	mean	NOUN
ejpam-1203	148	14	of	of	ADP
ejpam-1203	148	15	the	the	DET
ejpam-1203	148	16	following	follow	VERB
ejpam-1203	148	17	examples	example	NOUN
ejpam-1203	148	18	.	.	PUNCT
ejpam-1203	149	1	c.	c.	PROPN
ejpam-1203	149	2	devamanoharan	devamanoharan	PROPN
ejpam-1203	149	3	,	,	PUNCT
ejpam-1203	149	4	s.	s.	PROPN
ejpam-1203	149	5	missier	missier	PROPN
ejpam-1203	149	6	,	,	PUNCT
ejpam-1203	149	7	s.	s.	PROPN
ejpam-1203	149	8	jafari	jafari	PROPN
ejpam-1203	149	9	/	/	SYM
ejpam-1203	149	10	eur	eur	PROPN
ejpam-1203	149	11	.	.	PUNCT
ejpam-1203	150	1	j.	j.	PROPN
ejpam-1203	150	2	pure	pure	PROPN
ejpam-1203	150	3	appl	appl	PROPN
ejpam-1203	150	4	.	.	PROPN
ejpam-1203	150	5	math	math	PROPN
ejpam-1203	150	6	,	,	PUNCT
ejpam-1203	150	7	5	5	NUM
ejpam-1203	150	8	(	(	PUNCT
ejpam-1203	150	9	2012	2012	NUM
ejpam-1203	150	10	)	)	PUNCT
ejpam-1203	150	11	,	,	PUNCT
ejpam-1203	150	12	554	554	NUM
ejpam-1203	150	13	-	-	SYM
ejpam-1203	150	14	566	566	NUM
ejpam-1203	150	15	558	558	NUM
ejpam-1203	150	16	example	example	NOUN
ejpam-1203	150	17	8	8	NUM
ejpam-1203	150	18	.	.	NOUN
ejpam-1203	150	19	1	1	NUM
ejpam-1203	150	20	.	.	X
ejpam-1203	151	1	let	let	VERB
ejpam-1203	151	2	x	x	PUNCT
ejpam-1203	151	3	=	=	PRON
ejpam-1203	151	4	{	{	PUNCT
ejpam-1203	151	5	a	a	PRON
ejpam-1203	151	6	,	,	PUNCT
ejpam-1203	151	7	b	b	NOUN
ejpam-1203	151	8	,	,	PUNCT
ejpam-1203	151	9	c	c	NOUN
ejpam-1203	151	10	}	}	PUNCT
ejpam-1203	151	11	and	and	CCONJ
ejpam-1203	151	12	τ	τ	PROPN
ejpam-1203	151	13	=	=	PUNCT
ejpam-1203	151	14	{	{	PUNCT
ejpam-1203	151	15	φ	φ	PROPN
ejpam-1203	151	16	,	,	PUNCT
ejpam-1203	151	17	{	{	PUNCT
ejpam-1203	151	18	a	a	X
ejpam-1203	151	19	}	}	PUNCT
ejpam-1203	151	20	,	,	PUNCT
ejpam-1203	151	21	{	{	PUNCT
ejpam-1203	151	22	c	c	NOUN
ejpam-1203	151	23	}	}	PUNCT
ejpam-1203	151	24	,	,	PUNCT
ejpam-1203	151	25	{	{	PUNCT
ejpam-1203	151	26	c	c	X
ejpam-1203	151	27	,	,	PUNCT
ejpam-1203	151	28	a	a	PRON
ejpam-1203	151	29	}	}	PUNCT
ejpam-1203	151	30	,	,	PUNCT
ejpam-1203	151	31	x	x	SYM
ejpam-1203	151	32	}	}	PUNCT
ejpam-1203	151	33	.	.	PUNCT
ejpam-1203	152	1	then	then	ADV
ejpam-1203	152	2	the	the	DET
ejpam-1203	152	3	set	set	NOUN
ejpam-1203	152	4	a=	a=	NOUN
ejpam-1203	152	5	{	{	PUNCT
ejpam-1203	152	6	c	c	X
ejpam-1203	152	7	}	}	PUNCT
ejpam-1203	152	8	is	be	AUX
ejpam-1203	152	9	presemiclosed	presemiclose	VERB
ejpam-1203	152	10	but	but	CCONJ
ejpam-1203	152	11	not	not	PART
ejpam-1203	152	12	ρ	ρ	NOUN
ejpam-1203	152	13	-	-	PUNCT
ejpam-1203	152	14	closed	closed	ADJ
ejpam-1203	152	15	in	in	ADP
ejpam-1203	152	16	(	(	PUNCT
ejpam-1203	152	17	x	x	INTJ
ejpam-1203	152	18	,	,	PUNCT
ejpam-1203	152	19	τ	τ	PROPN
ejpam-1203	152	20	)	)	PUNCT
ejpam-1203	152	21	.	.	PUNCT
ejpam-1203	153	1	2	2	X
ejpam-1203	153	2	.	.	X
ejpam-1203	153	3	let	let	VERB
ejpam-1203	153	4	x	x	PUNCT
ejpam-1203	153	5	=	=	PRON
ejpam-1203	153	6	{	{	PUNCT
ejpam-1203	153	7	a	a	PRON
ejpam-1203	153	8	,	,	PUNCT
ejpam-1203	153	9	b	b	NOUN
ejpam-1203	153	10	,	,	PUNCT
ejpam-1203	153	11	c	c	NOUN
ejpam-1203	153	12	}	}	PUNCT
ejpam-1203	153	13	and	and	CCONJ
ejpam-1203	153	14	τ	τ	PROPN
ejpam-1203	153	15	=	=	PUNCT
ejpam-1203	153	16	{	{	PUNCT
ejpam-1203	153	17	φ	φ	PROPN
ejpam-1203	153	18	,	,	PUNCT
ejpam-1203	153	19	{	{	PUNCT
ejpam-1203	153	20	c	c	NOUN
ejpam-1203	153	21	}	}	PUNCT
ejpam-1203	153	22	,	,	PUNCT
ejpam-1203	153	23	x	x	SYM
ejpam-1203	153	24	}	}	PUNCT
ejpam-1203	153	25	.	.	PUNCT
ejpam-1203	154	1	then	then	ADV
ejpam-1203	154	2	the	the	DET
ejpam-1203	154	3	set	set	ADJ
ejpam-1203	154	4	a=	a=	PROPN
ejpam-1203	154	5	{	{	PUNCT
ejpam-1203	154	6	b	b	NOUN
ejpam-1203	154	7	,	,	PUNCT
ejpam-1203	154	8	c	c	NOUN
ejpam-1203	154	9	}	}	PUNCT
ejpam-1203	154	10	is	be	AUX
ejpam-1203	154	11	ρ	ρ	NOUN
ejpam-1203	154	12	-	-	PUNCT
ejpam-1203	154	13	closed	closed	ADJ
ejpam-1203	154	14	but	but	CCONJ
ejpam-1203	154	15	not	not	PART
ejpam-1203	154	16	presemiclosed	presemiclose	VERB
ejpam-1203	154	17	in	in	ADP
ejpam-1203	154	18	(	(	PUNCT
ejpam-1203	154	19	x	x	INTJ
ejpam-1203	154	20	,	,	PUNCT
ejpam-1203	154	21	τ	τ	PROPN
ejpam-1203	154	22	)	)	PUNCT
ejpam-1203	154	23	.	.	PUNCT
ejpam-1203	155	1	remark	remark	PROPN
ejpam-1203	155	2	4	4	NUM
ejpam-1203	155	3	.	.	PUNCT
ejpam-1203	156	1	ρ	ρ	NOUN
ejpam-1203	156	2	-	-	PUNCT
ejpam-1203	156	3	closedness	closedness	NOUN
ejpam-1203	156	4	and	and	CCONJ
ejpam-1203	156	5	g	g	NOUN
ejpam-1203	156	6	-	-	PUNCT
ejpam-1203	156	7	closedness	closedness	NOUN
ejpam-1203	156	8	are	be	AUX
ejpam-1203	156	9	independent	independent	ADJ
ejpam-1203	156	10	concepts	concept	NOUN
ejpam-1203	156	11	as	as	SCONJ
ejpam-1203	156	12	we	we	PRON
ejpam-1203	156	13	illustrate	illustrate	VERB
ejpam-1203	156	14	by	by	ADP
ejpam-1203	156	15	means	mean	NOUN
ejpam-1203	156	16	of	of	ADP
ejpam-1203	156	17	the	the	DET
ejpam-1203	156	18	following	follow	VERB
ejpam-1203	156	19	examples	example	NOUN
ejpam-1203	156	20	.	.	PUNCT
ejpam-1203	157	1	example	example	NOUN
ejpam-1203	157	2	9	9	NUM
ejpam-1203	157	3	.	.	NOUN
ejpam-1203	157	4	1	1	NUM
ejpam-1203	157	5	.	.	X
ejpam-1203	158	1	let	let	AUX
ejpam-1203	158	2	(	(	PUNCT
ejpam-1203	158	3	x	x	X
ejpam-1203	158	4	,	,	PUNCT
ejpam-1203	158	5	κ	κ	NOUN
ejpam-1203	158	6	)	)	PUNCT
ejpam-1203	158	7	be	be	VERB
ejpam-1203	158	8	a	a	DET
ejpam-1203	158	9	digital	digital	ADJ
ejpam-1203	158	10	topology	topology	NOUN
ejpam-1203	158	11	.	.	PUNCT
ejpam-1203	159	1	then	then	ADV
ejpam-1203	159	2	the	the	DET
ejpam-1203	159	3	set	set	NOUN
ejpam-1203	159	4	a	a	X
ejpam-1203	159	5	=	=	PUNCT
ejpam-1203	159	6	{	{	PUNCT
ejpam-1203	159	7	4	4	NUM
ejpam-1203	159	8	}	}	PUNCT
ejpam-1203	159	9	is	be	AUX
ejpam-1203	159	10	closed	close	VERB
ejpam-1203	159	11	in	in	ADP
ejpam-1203	159	12	(	(	PUNCT
ejpam-1203	159	13	x	x	INTJ
ejpam-1203	159	14	,	,	PUNCT
ejpam-1203	159	15	κ	κ	NOUN
ejpam-1203	159	16	)	)	PUNCT
ejpam-1203	159	17	and	and	CCONJ
ejpam-1203	159	18	thus	thus	ADV
ejpam-1203	159	19	gclosed	gclose	VERB
ejpam-1203	159	20	.	.	PUNCT
ejpam-1203	160	1	but	but	CCONJ
ejpam-1203	160	2	the	the	DET
ejpam-1203	160	3	set	set	NOUN
ejpam-1203	160	4	a	a	PRON
ejpam-1203	160	5	is	be	AUX
ejpam-1203	160	6	not	not	PART
ejpam-1203	160	7	ρ	ρ	NOUN
ejpam-1203	160	8	-	-	PUNCT
ejpam-1203	160	9	closed	closed	ADJ
ejpam-1203	160	10	in	in	ADP
ejpam-1203	160	11	(	(	PUNCT
ejpam-1203	160	12	x	x	INTJ
ejpam-1203	160	13	,	,	PUNCT
ejpam-1203	160	14	κ	κ	NOUN
ejpam-1203	160	15	)	)	PUNCT
ejpam-1203	160	16	,	,	PUNCT
ejpam-1203	160	17	because	because	SCONJ
ejpam-1203	160	18	there	there	PRON
ejpam-1203	160	19	is	be	VERB
ejpam-1203	160	20	a	a	DET
ejpam-1203	160	21	g̃-open	g̃-open	NOUN
ejpam-1203	160	22	set	set	VERB
ejpam-1203	160	23	u	u	NOUN
ejpam-1203	160	24	=	=	PUNCT
ejpam-1203	160	25	{	{	PUNCT
ejpam-1203	160	26	1,2,3,4	1,2,3,4	NUM
ejpam-1203	160	27	}	}	PUNCT
ejpam-1203	160	28	containing	contain	VERB
ejpam-1203	160	29	{	{	PUNCT
ejpam-1203	160	30	4	4	NUM
ejpam-1203	160	31	}	}	PUNCT
ejpam-1203	160	32	,	,	PUNCT
ejpam-1203	160	33	is	be	AUX
ejpam-1203	160	34	not	not	PART
ejpam-1203	160	35	open	open	ADJ
ejpam-1203	160	36	in	in	ADP
ejpam-1203	160	37	(	(	PUNCT
ejpam-1203	160	38	x	x	INTJ
ejpam-1203	160	39	,	,	PUNCT
ejpam-1203	160	40	κ	κ	NOUN
ejpam-1203	160	41	)	)	PUNCT
ejpam-1203	160	42	such	such	ADJ
ejpam-1203	160	43	that	that	DET
ejpam-1203	160	44	pcl(a	pcl(a	NOUN
ejpam-1203	160	45	)	)	PUNCT
ejpam-1203	160	46	=	=	NOUN
ejpam-1203	160	47	{	{	PUNCT
ejpam-1203	160	48	4	4	NUM
ejpam-1203	160	49	}	}	PUNCT
ejpam-1203	160	50	*	*	PUNCT
ejpam-1203	160	51	int(u	int(u	PROPN
ejpam-1203	160	52	)	)	PUNCT
ejpam-1203	160	53	=	=	PUNCT
ejpam-1203	160	54	{	{	PUNCT
ejpam-1203	160	55	1,2,3	1,2,3	NUM
ejpam-1203	160	56	}	}	PUNCT
ejpam-1203	160	57	.	.	PUNCT
ejpam-1203	161	1	2	2	X
ejpam-1203	161	2	.	.	X
ejpam-1203	161	3	let	let	VERB
ejpam-1203	161	4	x	x	PUNCT
ejpam-1203	161	5	=	=	PRON
ejpam-1203	161	6	{	{	PUNCT
ejpam-1203	161	7	a	a	PRON
ejpam-1203	161	8	,	,	PUNCT
ejpam-1203	161	9	b	b	NOUN
ejpam-1203	161	10	,	,	PUNCT
ejpam-1203	161	11	c	c	NOUN
ejpam-1203	161	12	,	,	PUNCT
ejpam-1203	161	13	d	d	X
ejpam-1203	161	14	,	,	PUNCT
ejpam-1203	161	15	e	e	NOUN
ejpam-1203	161	16	}	}	PUNCT
ejpam-1203	161	17	and	and	CCONJ
ejpam-1203	161	18	τ	τ	PROPN
ejpam-1203	161	19	=	=	PUNCT
ejpam-1203	161	20	{	{	PUNCT
ejpam-1203	161	21	φ	φ	PROPN
ejpam-1203	161	22	,	,	PUNCT
ejpam-1203	161	23	{	{	PUNCT
ejpam-1203	161	24	a	a	DET
ejpam-1203	161	25	,	,	PUNCT
ejpam-1203	161	26	b	b	NOUN
ejpam-1203	161	27	}	}	PUNCT
ejpam-1203	161	28	,	,	PUNCT
ejpam-1203	161	29	{	{	PUNCT
ejpam-1203	161	30	a	a	DET
ejpam-1203	161	31	,	,	PUNCT
ejpam-1203	161	32	b	b	NOUN
ejpam-1203	161	33	,	,	PUNCT
ejpam-1203	161	34	d	d	NOUN
ejpam-1203	161	35	}	}	PUNCT
ejpam-1203	161	36	,	,	PUNCT
ejpam-1203	161	37	{	{	PUNCT
ejpam-1203	161	38	a	a	PRON
ejpam-1203	161	39	,	,	PUNCT
ejpam-1203	161	40	b	b	NOUN
ejpam-1203	161	41	,	,	PUNCT
ejpam-1203	161	42	c	c	NOUN
ejpam-1203	161	43	,	,	PUNCT
ejpam-1203	161	44	d	d	NOUN
ejpam-1203	161	45	}	}	PUNCT
ejpam-1203	161	46	,	,	PUNCT
ejpam-1203	161	47	{	{	PUNCT
ejpam-1203	161	48	a	a	PRON
ejpam-1203	161	49	,	,	PUNCT
ejpam-1203	161	50	b	b	NOUN
ejpam-1203	161	51	,	,	PUNCT
ejpam-1203	161	52	d	d	X
ejpam-1203	161	53	,	,	PUNCT
ejpam-1203	161	54	e	e	NOUN
ejpam-1203	161	55	,	,	PUNCT
ejpam-1203	161	56	}	}	PUNCT
ejpam-1203	161	57	,	,	PUNCT
ejpam-1203	161	58	x	x	X
ejpam-1203	161	59	}	}	PUNCT
ejpam-1203	161	60	.	.	PUNCT
ejpam-1203	162	1	then	then	ADV
ejpam-1203	162	2	the	the	DET
ejpam-1203	162	3	set	set	NOUN
ejpam-1203	162	4	a=	a=	NOUN
ejpam-1203	162	5	{	{	PUNCT
ejpam-1203	162	6	a	a	X
ejpam-1203	162	7	,	,	PUNCT
ejpam-1203	162	8	c	c	NOUN
ejpam-1203	162	9	,	,	PUNCT
ejpam-1203	162	10	d	d	X
ejpam-1203	162	11	}	}	PUNCT
ejpam-1203	162	12	is	be	AUX
ejpam-1203	162	13	ρ	ρ	NOUN
ejpam-1203	162	14	-	-	PUNCT
ejpam-1203	162	15	closed	closed	ADJ
ejpam-1203	162	16	but	but	CCONJ
ejpam-1203	162	17	not	not	PART
ejpam-1203	162	18	g	g	NOUN
ejpam-1203	162	19	-	-	PUNCT
ejpam-1203	162	20	closed	closed	ADJ
ejpam-1203	162	21	in	in	ADP
ejpam-1203	162	22	(	(	PUNCT
ejpam-1203	162	23	x	x	INTJ
ejpam-1203	162	24	,	,	PUNCT
ejpam-1203	162	25	τ	τ	PROPN
ejpam-1203	162	26	)	)	PUNCT
ejpam-1203	162	27	.	.	PUNCT
ejpam-1203	163	1	remark	remark	PROPN
ejpam-1203	163	2	5	5	NUM
ejpam-1203	163	3	.	.	PUNCT
ejpam-1203	164	1	ρ	ρ	NOUN
ejpam-1203	164	2	-	-	PUNCT
ejpam-1203	164	3	closedness	closedness	NOUN
ejpam-1203	164	4	and	and	CCONJ
ejpam-1203	164	5	pg	pg	NOUN
ejpam-1203	164	6	-	-	PUNCT
ejpam-1203	164	7	closedness	closedness	NOUN
ejpam-1203	164	8	are	be	AUX
ejpam-1203	164	9	independent	independent	ADJ
ejpam-1203	164	10	concepts	concept	NOUN
ejpam-1203	164	11	as	as	SCONJ
ejpam-1203	164	12	we	we	PRON
ejpam-1203	164	13	illustrate	illustrate	VERB
ejpam-1203	164	14	by	by	ADP
ejpam-1203	164	15	means	mean	NOUN
ejpam-1203	164	16	of	of	ADP
ejpam-1203	164	17	the	the	DET
ejpam-1203	164	18	following	follow	VERB
ejpam-1203	164	19	example	example	NOUN
ejpam-1203	164	20	.	.	PUNCT
ejpam-1203	165	1	example	example	NOUN
ejpam-1203	166	1	10	10	NUM
ejpam-1203	166	2	.	.	PUNCT
ejpam-1203	167	1	let	let	VERB
ejpam-1203	167	2	x	x	PUNCT
ejpam-1203	167	3	=	=	PRON
ejpam-1203	167	4	{	{	PUNCT
ejpam-1203	167	5	a	a	PRON
ejpam-1203	167	6	,	,	PUNCT
ejpam-1203	167	7	b	b	NOUN
ejpam-1203	167	8	,	,	PUNCT
ejpam-1203	167	9	c	c	NOUN
ejpam-1203	167	10	,	,	PUNCT
ejpam-1203	167	11	d	d	NOUN
ejpam-1203	167	12	}	}	PUNCT
ejpam-1203	167	13	=	=	SYM
ejpam-1203	167	14	y	y	PROPN
ejpam-1203	167	15	and	and	CCONJ
ejpam-1203	167	16	τ	τ	PROPN
ejpam-1203	167	17	=	=	X
ejpam-1203	167	18	{	{	PUNCT
ejpam-1203	167	19	φ	φ	PROPN
ejpam-1203	167	20	,	,	PUNCT
ejpam-1203	167	21	{	{	PUNCT
ejpam-1203	167	22	b	b	NOUN
ejpam-1203	167	23	,	,	PUNCT
ejpam-1203	167	24	c	c	NOUN
ejpam-1203	167	25	}	}	PUNCT
ejpam-1203	167	26	,	,	PUNCT
ejpam-1203	167	27	{	{	PUNCT
ejpam-1203	167	28	a	a	DET
ejpam-1203	167	29	,	,	PUNCT
ejpam-1203	167	30	b	b	NOUN
ejpam-1203	167	31	,	,	PUNCT
ejpam-1203	167	32	c	c	NOUN
ejpam-1203	167	33	}	}	PUNCT
ejpam-1203	167	34	,	,	PUNCT
ejpam-1203	167	35	{	{	PUNCT
ejpam-1203	167	36	b	b	X
ejpam-1203	167	37	,	,	PUNCT
ejpam-1203	167	38	c	c	NOUN
ejpam-1203	167	39	,	,	PUNCT
ejpam-1203	167	40	d	d	NOUN
ejpam-1203	167	41	}	}	PUNCT
ejpam-1203	167	42	,	,	PUNCT
ejpam-1203	167	43	x	x	SYM
ejpam-1203	167	44	}	}	PUNCT
ejpam-1203	167	45	and	and	CCONJ
ejpam-1203	167	46	σ	σ	NUM
ejpam-1203	167	47	=	=	SYM
ejpam-1203	167	48	{	{	PUNCT
ejpam-1203	167	49	φ	φ	PROPN
ejpam-1203	167	50	,	,	PUNCT
ejpam-1203	167	51	{	{	PUNCT
ejpam-1203	167	52	b	b	NOUN
ejpam-1203	167	53	}	}	PUNCT
ejpam-1203	167	54	,	,	PUNCT
ejpam-1203	167	55	{	{	PUNCT
ejpam-1203	167	56	c	c	X
ejpam-1203	167	57	}	}	PUNCT
ejpam-1203	167	58	,	,	PUNCT
ejpam-1203	167	59	{	{	PUNCT
ejpam-1203	167	60	b	b	X
ejpam-1203	167	61	,	,	PUNCT
ejpam-1203	167	62	c	c	NOUN
ejpam-1203	167	63	}	}	PUNCT
ejpam-1203	167	64	,	,	PUNCT
ejpam-1203	167	65	y	y	PROPN
ejpam-1203	167	66	}	}	PUNCT
ejpam-1203	167	67	.	.	PUNCT
ejpam-1203	168	1	then	then	ADV
ejpam-1203	168	2	the	the	DET
ejpam-1203	168	3	set	set	NOUN
ejpam-1203	168	4	a=	a=	NOUN
ejpam-1203	168	5	{	{	PUNCT
ejpam-1203	168	6	c	c	X
ejpam-1203	168	7	}	}	PUNCT
ejpam-1203	168	8	is	be	AUX
ejpam-1203	168	9	pg	pg	ADJ
ejpam-1203	168	10	-	-	PUNCT
ejpam-1203	168	11	closed	closed	ADJ
ejpam-1203	168	12	but	but	CCONJ
ejpam-1203	168	13	not	not	PART
ejpam-1203	168	14	ρ	ρ	NOUN
ejpam-1203	168	15	-	-	PUNCT
ejpam-1203	168	16	closed	closed	ADJ
ejpam-1203	168	17	in	in	ADP
ejpam-1203	168	18	(	(	PUNCT
ejpam-1203	168	19	x	x	INTJ
ejpam-1203	168	20	,	,	PUNCT
ejpam-1203	168	21	τ	τ	PROPN
ejpam-1203	168	22	)	)	PUNCT
ejpam-1203	168	23	and	and	CCONJ
ejpam-1203	168	24	the	the	DET
ejpam-1203	168	25	set	set	NOUN
ejpam-1203	168	26	b	b	PROPN
ejpam-1203	168	27	=	=	X
ejpam-1203	168	28	{	{	PUNCT
ejpam-1203	168	29	a	a	DET
ejpam-1203	168	30	,	,	PUNCT
ejpam-1203	168	31	b	b	NOUN
ejpam-1203	168	32	,	,	PUNCT
ejpam-1203	168	33	c	c	NOUN
ejpam-1203	168	34	}	}	PUNCT
ejpam-1203	168	35	is	be	AUX
ejpam-1203	168	36	ρ	ρ	NOUN
ejpam-1203	168	37	-	-	PUNCT
ejpam-1203	168	38	closed	closed	ADJ
ejpam-1203	168	39	but	but	CCONJ
ejpam-1203	168	40	not	not	PART
ejpam-1203	168	41	pg	pg	ADJ
ejpam-1203	168	42	-	-	PUNCT
ejpam-1203	168	43	closed	closed	ADJ
ejpam-1203	168	44	in	in	ADP
ejpam-1203	168	45	(	(	PUNCT
ejpam-1203	168	46	x	x	INTJ
ejpam-1203	168	47	,	,	PUNCT
ejpam-1203	168	48	τ	τ	PROPN
ejpam-1203	168	49	)	)	PUNCT
ejpam-1203	168	50	.	.	PUNCT
ejpam-1203	169	1	remark	remark	PROPN
ejpam-1203	169	2	6	6	NUM
ejpam-1203	169	3	.	.	PUNCT
ejpam-1203	170	1	ρ	ρ	NOUN
ejpam-1203	170	2	-	-	PUNCT
ejpam-1203	170	3	closedness	closedness	NOUN
ejpam-1203	170	4	and	and	CCONJ
ejpam-1203	170	5	g*p	g*p	PROPN
ejpam-1203	170	6	-	-	PUNCT
ejpam-1203	170	7	closedness	closedness	NOUN
ejpam-1203	170	8	are	be	AUX
ejpam-1203	170	9	independent	independent	ADJ
ejpam-1203	170	10	concepts	concept	NOUN
ejpam-1203	170	11	as	as	SCONJ
ejpam-1203	170	12	we	we	PRON
ejpam-1203	170	13	illustrate	illustrate	VERB
ejpam-1203	170	14	by	by	ADP
ejpam-1203	170	15	means	mean	NOUN
ejpam-1203	170	16	of	of	ADP
ejpam-1203	170	17	the	the	DET
ejpam-1203	170	18	following	follow	VERB
ejpam-1203	170	19	example	example	NOUN
ejpam-1203	170	20	.	.	PUNCT
ejpam-1203	171	1	example	example	NOUN
ejpam-1203	172	1	11	11	NUM
ejpam-1203	172	2	.	.	PUNCT
ejpam-1203	173	1	let	let	VERB
ejpam-1203	173	2	x	x	PUNCT
ejpam-1203	173	3	=	=	PRON
ejpam-1203	173	4	{	{	PUNCT
ejpam-1203	173	5	a	a	PRON
ejpam-1203	173	6	,	,	PUNCT
ejpam-1203	173	7	b	b	NOUN
ejpam-1203	173	8	,	,	PUNCT
ejpam-1203	173	9	c	c	NOUN
ejpam-1203	173	10	,	,	PUNCT
ejpam-1203	173	11	d	d	X
ejpam-1203	173	12	,	,	PUNCT
ejpam-1203	173	13	e	e	NOUN
ejpam-1203	173	14	}	}	PUNCT
ejpam-1203	173	15	and	and	CCONJ
ejpam-1203	173	16	τ	τ	PROPN
ejpam-1203	173	17	=	=	PUNCT
ejpam-1203	173	18	{	{	PUNCT
ejpam-1203	173	19	φ	φ	PROPN
ejpam-1203	173	20	,	,	PUNCT
ejpam-1203	173	21	{	{	PUNCT
ejpam-1203	173	22	b	b	NOUN
ejpam-1203	173	23	}	}	PUNCT
ejpam-1203	173	24	,	,	PUNCT
ejpam-1203	173	25	{	{	PUNCT
ejpam-1203	173	26	d	d	X
ejpam-1203	173	27	,	,	PUNCT
ejpam-1203	173	28	e	e	NOUN
ejpam-1203	173	29	}	}	PUNCT
ejpam-1203	173	30	,	,	PUNCT
ejpam-1203	173	31	{	{	PUNCT
ejpam-1203	173	32	b	b	X
ejpam-1203	173	33	,	,	PUNCT
ejpam-1203	173	34	d	d	NOUN
ejpam-1203	173	35	,	,	PUNCT
ejpam-1203	173	36	e	e	NOUN
ejpam-1203	173	37	}	}	PUNCT
ejpam-1203	173	38	,	,	PUNCT
ejpam-1203	173	39	{	{	PUNCT
ejpam-1203	173	40	a	a	PRON
ejpam-1203	173	41	,	,	PUNCT
ejpam-1203	173	42	c	c	NOUN
ejpam-1203	173	43	,	,	PUNCT
ejpam-1203	173	44	d	d	X
ejpam-1203	173	45	,	,	PUNCT
ejpam-1203	173	46	e	e	NOUN
ejpam-1203	173	47	}	}	PUNCT
ejpam-1203	173	48	,	,	PUNCT
ejpam-1203	173	49	x	x	NOUN
ejpam-1203	173	50	}	}	PUNCT
ejpam-1203	173	51	.	.	PUNCT
ejpam-1203	174	1	then	then	ADV
ejpam-1203	174	2	the	the	DET
ejpam-1203	174	3	set	set	NOUN
ejpam-1203	174	4	a=	a=	NOUN
ejpam-1203	174	5	{	{	PUNCT
ejpam-1203	174	6	a	a	PRON
ejpam-1203	174	7	,	,	PUNCT
ejpam-1203	174	8	b	b	NOUN
ejpam-1203	174	9	,	,	PUNCT
ejpam-1203	174	10	d	d	X
ejpam-1203	174	11	,	,	PUNCT
ejpam-1203	174	12	e	e	NOUN
ejpam-1203	174	13	}	}	PUNCT
ejpam-1203	174	14	is	be	AUX
ejpam-1203	174	15	ρ	ρ	NOUN
ejpam-1203	174	16	-	-	PUNCT
ejpam-1203	174	17	closed	closed	ADJ
ejpam-1203	174	18	but	but	CCONJ
ejpam-1203	174	19	not	not	PART
ejpam-1203	174	20	g*p	g*p	PROPN
ejpam-1203	174	21	-	-	PUNCT
ejpam-1203	174	22	closed	close	VERB
ejpam-1203	174	23	and	and	CCONJ
ejpam-1203	174	24	the	the	DET
ejpam-1203	174	25	set	set	NOUN
ejpam-1203	174	26	b	b	PROPN
ejpam-1203	174	27	=	=	SYM
ejpam-1203	174	28	{	{	PUNCT
ejpam-1203	174	29	d	d	NOUN
ejpam-1203	174	30	}	}	PUNCT
ejpam-1203	174	31	is	be	AUX
ejpam-1203	174	32	g*p	g*p	PROPN
ejpam-1203	174	33	-	-	PUNCT
ejpam-1203	174	34	closed	closed	ADJ
ejpam-1203	174	35	but	but	CCONJ
ejpam-1203	174	36	not	not	PART
ejpam-1203	174	37	ρ	ρ	NOUN
ejpam-1203	174	38	-	-	PUNCT
ejpam-1203	174	39	closed	closed	ADJ
ejpam-1203	174	40	in	in	ADP
ejpam-1203	174	41	(	(	PUNCT
ejpam-1203	174	42	x	x	INTJ
ejpam-1203	174	43	,	,	PUNCT
ejpam-1203	174	44	τ	τ	PROPN
ejpam-1203	174	45	)	)	PUNCT
ejpam-1203	174	46	.	.	PUNCT
ejpam-1203	175	1	remark	remark	PROPN
ejpam-1203	175	2	7	7	NUM
ejpam-1203	175	3	.	.	PUNCT
ejpam-1203	176	1	ρ	ρ	NOUN
ejpam-1203	176	2	-	-	PUNCT
ejpam-1203	176	3	closedness	closedness	NOUN
ejpam-1203	176	4	and	and	CCONJ
ejpam-1203	176	5	α	α	VERB
ejpam-1203	176	6	-	-	PUNCT
ejpam-1203	176	7	closedness	closedness	NOUN
ejpam-1203	176	8	are	be	AUX
ejpam-1203	176	9	independent	independent	ADJ
ejpam-1203	176	10	concepts	concept	NOUN
ejpam-1203	176	11	as	as	SCONJ
ejpam-1203	176	12	we	we	PRON
ejpam-1203	176	13	illustrate	illustrate	VERB
ejpam-1203	176	14	by	by	ADP
ejpam-1203	176	15	means	mean	NOUN
ejpam-1203	176	16	of	of	ADP
ejpam-1203	176	17	the	the	DET
ejpam-1203	176	18	following	follow	VERB
ejpam-1203	176	19	examples	example	NOUN
ejpam-1203	176	20	.	.	PUNCT
ejpam-1203	177	1	example	example	NOUN
ejpam-1203	177	2	12	12	NUM
ejpam-1203	177	3	.	.	NOUN
ejpam-1203	178	1	1	1	NUM
ejpam-1203	178	2	.	.	X
ejpam-1203	179	1	as	as	ADP
ejpam-1203	179	2	in	in	ADP
ejpam-1203	179	3	example	example	NOUN
ejpam-1203	179	4	9(1	9(1	NUM
ejpam-1203	179	5	)	)	PUNCT
ejpam-1203	179	6	,	,	PUNCT
ejpam-1203	179	7	the	the	DET
ejpam-1203	179	8	set	set	NOUN
ejpam-1203	179	9	a=	a=	NOUN
ejpam-1203	179	10	{	{	PUNCT
ejpam-1203	179	11	4	4	NUM
ejpam-1203	179	12	}	}	PUNCT
ejpam-1203	179	13	is	be	AUX
ejpam-1203	179	14	α	α	PRON
ejpam-1203	179	15	-	-	PUNCT
ejpam-1203	179	16	closed	closed	ADJ
ejpam-1203	179	17	but	but	CCONJ
ejpam-1203	179	18	not	not	PART
ejpam-1203	179	19	ρ	ρ	NOUN
ejpam-1203	179	20	-	-	PUNCT
ejpam-1203	179	21	closed	closed	ADJ
ejpam-1203	179	22	in	in	ADP
ejpam-1203	179	23	(	(	PUNCT
ejpam-1203	179	24	x	x	INTJ
ejpam-1203	179	25	,	,	PUNCT
ejpam-1203	179	26	κ	κ	NOUN
ejpam-1203	179	27	)	)	PUNCT
ejpam-1203	179	28	.	.	PUNCT
ejpam-1203	180	1	2	2	X
ejpam-1203	180	2	.	.	X
ejpam-1203	180	3	x	x	SYM
ejpam-1203	180	4	=	=	NOUN
ejpam-1203	180	5	{	{	PUNCT
ejpam-1203	180	6	a	a	PRON
ejpam-1203	180	7	,	,	PUNCT
ejpam-1203	180	8	b	b	NOUN
ejpam-1203	180	9	,	,	PUNCT
ejpam-1203	180	10	c	c	NOUN
ejpam-1203	180	11	}	}	PUNCT
ejpam-1203	180	12	and	and	CCONJ
ejpam-1203	180	13	τ	τ	PROPN
ejpam-1203	180	14	=	=	PUNCT
ejpam-1203	180	15	{	{	PUNCT
ejpam-1203	180	16	φ	φ	PROPN
ejpam-1203	180	17	,	,	PUNCT
ejpam-1203	180	18	{	{	PUNCT
ejpam-1203	180	19	c	c	NOUN
ejpam-1203	180	20	}	}	PUNCT
ejpam-1203	180	21	,	,	PUNCT
ejpam-1203	180	22	{	{	PUNCT
ejpam-1203	180	23	b	b	X
ejpam-1203	180	24	,	,	PUNCT
ejpam-1203	180	25	c	c	NOUN
ejpam-1203	180	26	}	}	PUNCT
ejpam-1203	180	27	,	,	PUNCT
ejpam-1203	180	28	y	y	PROPN
ejpam-1203	180	29	}	}	PUNCT
ejpam-1203	180	30	.	.	PUNCT
ejpam-1203	181	1	then	then	ADV
ejpam-1203	181	2	the	the	DET
ejpam-1203	181	3	set	set	NOUN
ejpam-1203	181	4	a	a	X
ejpam-1203	181	5	=	=	X
ejpam-1203	181	6	{	{	PUNCT
ejpam-1203	181	7	c	c	NOUN
ejpam-1203	181	8	,	,	PUNCT
ejpam-1203	181	9	a	a	PRON
ejpam-1203	181	10	}	}	PUNCT
ejpam-1203	181	11	is	be	AUX
ejpam-1203	181	12	ρ	ρ	NOUN
ejpam-1203	181	13	-	-	PUNCT
ejpam-1203	181	14	closed	closed	ADJ
ejpam-1203	181	15	but	but	CCONJ
ejpam-1203	181	16	not	not	PART
ejpam-1203	181	17	α	α	NOUN
ejpam-1203	181	18	-	-	VERB
ejpam-1203	181	19	closed	closed	ADJ
ejpam-1203	181	20	in	in	ADP
ejpam-1203	181	21	(	(	PUNCT
ejpam-1203	181	22	x	x	INTJ
ejpam-1203	181	23	,	,	PUNCT
ejpam-1203	181	24	τ	τ	PROPN
ejpam-1203	181	25	)	)	PUNCT
ejpam-1203	181	26	.	.	PUNCT
ejpam-1203	182	1	c.	c.	PROPN
ejpam-1203	182	2	devamanoharan	devamanoharan	PROPN
ejpam-1203	182	3	,	,	PUNCT
ejpam-1203	182	4	s.	s.	PROPN
ejpam-1203	182	5	missier	missier	PROPN
ejpam-1203	182	6	,	,	PUNCT
ejpam-1203	182	7	s.	s.	PROPN
ejpam-1203	182	8	jafari	jafari	PROPN
ejpam-1203	182	9	/	/	SYM
ejpam-1203	182	10	eur	eur	PROPN
ejpam-1203	182	11	.	.	PUNCT
ejpam-1203	183	1	j.	j.	PROPN
ejpam-1203	183	2	pure	pure	PROPN
ejpam-1203	183	3	appl	appl	PROPN
ejpam-1203	183	4	.	.	PROPN
ejpam-1203	183	5	math	math	PROPN
ejpam-1203	183	6	,	,	PUNCT
ejpam-1203	183	7	5	5	NUM
ejpam-1203	183	8	(	(	PUNCT
ejpam-1203	183	9	2012	2012	NUM
ejpam-1203	183	10	)	)	PUNCT
ejpam-1203	183	11	,	,	PUNCT
ejpam-1203	183	12	554	554	NUM
ejpam-1203	183	13	-	-	SYM
ejpam-1203	183	14	566	566	NUM
ejpam-1203	183	15	559	559	NUM
ejpam-1203	183	16	definition	definition	NOUN
ejpam-1203	183	17	6	6	NUM
ejpam-1203	183	18	.	.	PUNCT
ejpam-1203	184	1	a	a	DET
ejpam-1203	184	2	subset	subset	NOUN
ejpam-1203	184	3	a	a	PRON
ejpam-1203	184	4	of	of	ADP
ejpam-1203	184	5	(	(	PUNCT
ejpam-1203	184	6	x	x	PROPN
ejpam-1203	184	7	,	,	PUNCT
ejpam-1203	184	8	τ	τ	X
ejpam-1203	184	9	)	)	PUNCT
ejpam-1203	184	10	is	be	AUX
ejpam-1203	184	11	said	say	VERB
ejpam-1203	184	12	to	to	PART
ejpam-1203	184	13	be	be	AUX
ejpam-1203	184	14	ρs	ρs	ADV
ejpam-1203	184	15	-	-	PUNCT
ejpam-1203	184	16	closed	closed	ADJ
ejpam-1203	184	17	in	in	ADP
ejpam-1203	184	18	(	(	PUNCT
ejpam-1203	184	19	x	x	INTJ
ejpam-1203	184	20	,	,	PUNCT
ejpam-1203	184	21	τ	τ	PROPN
ejpam-1203	184	22	)	)	PUNCT
ejpam-1203	184	23	if	if	SCONJ
ejpam-1203	184	24	pcl(a	pcl(a	NUM
ejpam-1203	184	25	)	)	PUNCT
ejpam-1203	184	26	⊆	⊆	NUM
ejpam-1203	184	27	int(cl(u	int(cl(u	PROPN
ejpam-1203	184	28	)	)	PUNCT
ejpam-1203	184	29	)	)	PUNCT
ejpam-1203	185	1	whenever	whenever	SCONJ
ejpam-1203	185	2	a⊆	a⊆	VERB
ejpam-1203	185	3	u	u	NOUN
ejpam-1203	185	4	and	and	CCONJ
ejpam-1203	185	5	u	u	NOUN
ejpam-1203	185	6	is	be	AUX
ejpam-1203	185	7	g̃-open	g̃-open	NOUN
ejpam-1203	185	8	in	in	ADP
ejpam-1203	185	9	(	(	PUNCT
ejpam-1203	185	10	x	x	INTJ
ejpam-1203	185	11	,	,	PUNCT
ejpam-1203	185	12	τ	τ	PROPN
ejpam-1203	185	13	)	)	PUNCT
ejpam-1203	185	14	.	.	PUNCT
ejpam-1203	186	1	theorem	theorem	VERB
ejpam-1203	186	2	6	6	NUM
ejpam-1203	186	3	.	.	PUNCT
ejpam-1203	186	4	everyρ	everyρ	NOUN
ejpam-1203	186	5	-	-	PUNCT
ejpam-1203	186	6	closed	close	VERB
ejpam-1203	186	7	set	set	VERB
ejpam-1203	186	8	isρs	isρs	ADV
ejpam-1203	186	9	-	-	PUNCT
ejpam-1203	186	10	closed	close	VERB
ejpam-1203	186	11	set	set	NOUN
ejpam-1203	186	12	.	.	PUNCT
ejpam-1203	187	1	proof	proof	NOUN
ejpam-1203	187	2	.	.	PUNCT
ejpam-1203	188	1	let	let	VERB
ejpam-1203	188	2	a	a	DET
ejpam-1203	188	3	be	be	AUX
ejpam-1203	188	4	any	any	DET
ejpam-1203	188	5	ρ	ρ	NOUN
ejpam-1203	188	6	-	-	PUNCT
ejpam-1203	188	7	closed	closed	ADJ
ejpam-1203	188	8	set	set	NOUN
ejpam-1203	188	9	.	.	PUNCT
ejpam-1203	189	1	let	let	VERB
ejpam-1203	189	2	a	a	DET
ejpam-1203	189	3	⊆	⊆	NUM
ejpam-1203	189	4	u	u	NOUN
ejpam-1203	189	5	and	and	CCONJ
ejpam-1203	189	6	u	u	PRON
ejpam-1203	189	7	be	be	VERB
ejpam-1203	189	8	g̃-open	g̃-open	NOUN
ejpam-1203	189	9	in	in	ADP
ejpam-1203	189	10	x	x	X
ejpam-1203	189	11	.	.	PUNCT
ejpam-1203	190	1	since	since	SCONJ
ejpam-1203	190	2	a	a	PRON
ejpam-1203	190	3	is	be	AUX
ejpam-1203	190	4	ρ	ρ	NOUN
ejpam-1203	190	5	-	-	PUNCT
ejpam-1203	190	6	closed	closed	ADJ
ejpam-1203	190	7	,	,	PUNCT
ejpam-1203	190	8	pcl(a	pcl(a	PROPN
ejpam-1203	190	9	)	)	PUNCT
ejpam-1203	190	10	⊆	⊆	NUM
ejpam-1203	190	11	int(u	int(u	PROPN
ejpam-1203	190	12	)	)	PUNCT
ejpam-1203	190	13	⊆	⊆	NUM
ejpam-1203	190	14	int(cl(u	int(cl(u	PROPN
ejpam-1203	190	15	)	)	PUNCT
ejpam-1203	190	16	)	)	PUNCT
ejpam-1203	190	17	.	.	PUNCT
ejpam-1203	191	1	hence	hence	ADV
ejpam-1203	191	2	a	a	PRON
ejpam-1203	191	3	is	be	AUX
ejpam-1203	191	4	ρs	ρs	ADV
ejpam-1203	191	5	-	-	PUNCT
ejpam-1203	191	6	closed	closed	ADJ
ejpam-1203	191	7	.	.	PUNCT
ejpam-1203	192	1	the	the	DET
ejpam-1203	192	2	converse	converse	NOUN
ejpam-1203	192	3	of	of	ADP
ejpam-1203	192	4	the	the	DET
ejpam-1203	192	5	above	above	ADJ
ejpam-1203	192	6	theorem	theorem	NOUN
ejpam-1203	192	7	need	need	AUX
ejpam-1203	192	8	not	not	PART
ejpam-1203	192	9	be	be	AUX
ejpam-1203	192	10	true	true	ADJ
ejpam-1203	192	11	as	as	SCONJ
ejpam-1203	192	12	it	it	PRON
ejpam-1203	192	13	is	be	AUX
ejpam-1203	192	14	seen	see	VERB
ejpam-1203	192	15	from	from	ADP
ejpam-1203	192	16	the	the	DET
ejpam-1203	192	17	following	follow	VERB
ejpam-1203	192	18	example	example	NOUN
ejpam-1203	192	19	.	.	PUNCT
ejpam-1203	193	1	example	example	NOUN
ejpam-1203	193	2	13	13	NUM
ejpam-1203	193	3	.	.	PUNCT
ejpam-1203	194	1	as	as	SCONJ
ejpam-1203	194	2	in	in	ADP
ejpam-1203	194	3	example	example	NOUN
ejpam-1203	194	4	2	2	NUM
ejpam-1203	194	5	,	,	PUNCT
ejpam-1203	194	6	the	the	DET
ejpam-1203	194	7	set	set	NOUN
ejpam-1203	194	8	a=	a=	NOUN
ejpam-1203	194	9	{	{	PUNCT
ejpam-1203	194	10	a	a	X
ejpam-1203	194	11	,	,	PUNCT
ejpam-1203	194	12	c	c	NOUN
ejpam-1203	194	13	}	}	PUNCT
ejpam-1203	194	14	is	be	AUX
ejpam-1203	194	15	ρs	ρs	ADV
ejpam-1203	194	16	-	-	PUNCT
ejpam-1203	194	17	closed	closed	ADJ
ejpam-1203	194	18	but	but	CCONJ
ejpam-1203	194	19	not	not	PART
ejpam-1203	194	20	ρ	ρ	NOUN
ejpam-1203	194	21	-	-	PUNCT
ejpam-1203	194	22	closed	closed	ADJ
ejpam-1203	194	23	in	in	ADP
ejpam-1203	194	24	(	(	PUNCT
ejpam-1203	194	25	x	x	INTJ
ejpam-1203	194	26	,	,	PUNCT
ejpam-1203	194	27	τ	τ	PROPN
ejpam-1203	194	28	)	)	PUNCT
ejpam-1203	194	29	.	.	PUNCT
ejpam-1203	195	1	remark	remark	PROPN
ejpam-1203	195	2	8	8	NUM
ejpam-1203	195	3	.	.	PUNCT
ejpam-1203	195	4	from	from	ADP
ejpam-1203	195	5	the	the	DET
ejpam-1203	195	6	above	above	ADJ
ejpam-1203	195	7	discussions	discussion	NOUN
ejpam-1203	195	8	and	and	CCONJ
ejpam-1203	195	9	known	know	VERB
ejpam-1203	195	10	results	result	NOUN
ejpam-1203	195	11	should	should	AUX
ejpam-1203	195	12	be	be	AUX
ejpam-1203	195	13	accompanied	accompany	VERB
ejpam-1203	195	14	by	by	ADP
ejpam-1203	195	15	a	a	DET
ejpam-1203	195	16	reference	reference	NOUN
ejpam-1203	195	17	we	we	PRON
ejpam-1203	195	18	have	have	VERB
ejpam-1203	195	19	the	the	DET
ejpam-1203	195	20	following	follow	VERB
ejpam-1203	195	21	implications	implication	NOUN
ejpam-1203	195	22	a→	a→	PUNCT
ejpam-1203	195	23	b	b	X
ejpam-1203	195	24	(	(	PUNCT
ejpam-1203	195	25	a=	a=	NOUN
ejpam-1203	195	26	b	b	X
ejpam-1203	195	27	)	)	PUNCT
ejpam-1203	195	28	represents	represent	VERB
ejpam-1203	195	29	a	a	DET
ejpam-1203	195	30	implies	implie	NOUN
ejpam-1203	195	31	b	b	NOUN
ejpam-1203	195	32	but	but	CCONJ
ejpam-1203	195	33	not	not	PART
ejpam-1203	195	34	conversely	conversely	ADV
ejpam-1203	195	35	(	(	PUNCT
ejpam-1203	195	36	a	a	PRON
ejpam-1203	195	37	and	and	CCONJ
ejpam-1203	195	38	b	b	NOUN
ejpam-1203	195	39	are	be	AUX
ejpam-1203	195	40	independent	independent	ADJ
ejpam-1203	195	41	of	of	ADP
ejpam-1203	195	42	each	each	DET
ejpam-1203	195	43	other	other	ADJ
ejpam-1203	195	44	)	)	PUNCT
ejpam-1203	195	45	.	.	PUNCT
ejpam-1203	196	1	see	see	VERB
ejpam-1203	196	2	figure	figure	NOUN
ejpam-1203	196	3	1	1	NUM
ejpam-1203	196	4	.	.	PUNCT
ejpam-1203	196	5	figure	figure	NOUN
ejpam-1203	196	6	1	1	NUM
ejpam-1203	196	7	:	:	PUNCT
ejpam-1203	196	8	impli	impli	PROPN
ejpam-1203	196	9	ations	ation	NOUN
ejpam-1203	196	10	.	.	PUNCT
ejpam-1203	197	1	4	4	X
ejpam-1203	197	2	.	.	X
ejpam-1203	197	3	properties	property	NOUN
ejpam-1203	197	4	of	of	ADP
ejpam-1203	197	5	ρ	ρ	PROPN
ejpam-1203	197	6	-	-	PUNCT
ejpam-1203	197	7	closed	closed	ADJ
ejpam-1203	197	8	sets	set	NOUN
ejpam-1203	197	9	definition	definition	NOUN
ejpam-1203	197	10	7	7	NUM
ejpam-1203	197	11	.	.	PUNCT
ejpam-1203	198	1	the	the	DET
ejpam-1203	198	2	intersection	intersection	NOUN
ejpam-1203	198	3	of	of	ADP
ejpam-1203	198	4	all	all	DET
ejpam-1203	198	5	g̃-open	g̃-open	NOUN
ejpam-1203	198	6	subsets	subset	NOUN
ejpam-1203	198	7	of	of	ADP
ejpam-1203	198	8	(	(	PUNCT
ejpam-1203	198	9	x	x	INTJ
ejpam-1203	198	10	,	,	PUNCT
ejpam-1203	198	11	τ	τ	X
ejpam-1203	198	12	)	)	PUNCT
ejpam-1203	198	13	containing	contain	VERB
ejpam-1203	198	14	a	a	PRON
ejpam-1203	198	15	is	be	AUX
ejpam-1203	198	16	called	call	VERB
ejpam-1203	198	17	g̃-kernel	g̃-kernel	PROPN
ejpam-1203	198	18	of	of	ADP
ejpam-1203	198	19	a	a	PRON
ejpam-1203	198	20	and	and	CCONJ
ejpam-1203	198	21	denoted	denote	VERB
ejpam-1203	198	22	by	by	ADP
ejpam-1203	198	23	g̃−ker(a	g̃−ker(a	NUM
ejpam-1203	198	24	)	)	PUNCT
ejpam-1203	198	25	.	.	PUNCT
ejpam-1203	199	1	theorem	theorem	VERB
ejpam-1203	199	2	7	7	NUM
ejpam-1203	199	3	.	.	PUNCT
ejpam-1203	200	1	if	if	SCONJ
ejpam-1203	200	2	a	a	DET
ejpam-1203	200	3	subset	subset	NOUN
ejpam-1203	200	4	a	a	PRON
ejpam-1203	200	5	of	of	ADP
ejpam-1203	200	6	(	(	PUNCT
ejpam-1203	200	7	x	x	PROPN
ejpam-1203	200	8	,	,	PUNCT
ejpam-1203	200	9	τ	τ	X
ejpam-1203	200	10	)	)	PUNCT
ejpam-1203	200	11	is	be	AUX
ejpam-1203	200	12	ρ	ρ	NOUN
ejpam-1203	200	13	-	-	PUNCT
ejpam-1203	200	14	closed	closed	ADJ
ejpam-1203	200	15	then	then	ADV
ejpam-1203	200	16	pcl(a	pcl(a	NUM
ejpam-1203	200	17	)	)	PUNCT
ejpam-1203	200	18	⊆g̃−ker(a	⊆g̃−ker(a	PROPN
ejpam-1203	200	19	)	)	PUNCT
ejpam-1203	200	20	.	.	PUNCT
ejpam-1203	201	1	proof	proof	NOUN
ejpam-1203	201	2	.	.	PUNCT
ejpam-1203	202	1	suppose	suppose	VERB
ejpam-1203	202	2	that	that	SCONJ
ejpam-1203	202	3	a	a	PRON
ejpam-1203	202	4	is	be	AUX
ejpam-1203	202	5	ρ	ρ	NOUN
ejpam-1203	202	6	-	-	PUNCT
ejpam-1203	202	7	closed	closed	ADJ
ejpam-1203	202	8	.	.	PUNCT
ejpam-1203	203	1	then	then	ADV
ejpam-1203	203	2	pcl(a	pcl(a	X
ejpam-1203	203	3	)	)	PUNCT
ejpam-1203	203	4	⊆	⊆	NUM
ejpam-1203	203	5	int(u	int(u	PROPN
ejpam-1203	203	6	)	)	PUNCT
ejpam-1203	203	7	whenever	whenever	SCONJ
ejpam-1203	203	8	a	a	DET
ejpam-1203	203	9	⊆	⊆	NUM
ejpam-1203	203	10	u	u	NOUN
ejpam-1203	203	11	and	and	CCONJ
ejpam-1203	203	12	u	u	NOUN
ejpam-1203	203	13	is	be	AUX
ejpam-1203	203	14	g̃open	g̃open	ADJ
ejpam-1203	203	15	.	.	PUNCT
ejpam-1203	204	1	let	let	VERB
ejpam-1203	204	2	x	x	PUNCT
ejpam-1203	204	3	∈	∈	PROPN
ejpam-1203	204	4	pcl(a	pcl(a	PROPN
ejpam-1203	204	5	)	)	PUNCT
ejpam-1203	204	6	and	and	CCONJ
ejpam-1203	204	7	suppose	suppose	VERB
ejpam-1203	204	8	x	x	X
ejpam-1203	204	9	/∈g̃−ker(a	/∈g̃−ker(a	ADJ
ejpam-1203	204	10	)	)	PUNCT
ejpam-1203	204	11	.	.	PUNCT
ejpam-1203	205	1	then	then	ADV
ejpam-1203	205	2	there	there	PRON
ejpam-1203	205	3	is	be	VERB
ejpam-1203	205	4	a	a	DET
ejpam-1203	205	5	g̃-open	g̃-open	NOUN
ejpam-1203	205	6	set	set	VERB
ejpam-1203	205	7	u	u	NOUN
ejpam-1203	205	8	containing	contain	VERB
ejpam-1203	205	9	a	a	DET
ejpam-1203	205	10	such	such	ADJ
ejpam-1203	205	11	that	that	PRON
ejpam-1203	205	12	x	x	SYM
ejpam-1203	205	13	/∈	/∈	PUNCT
ejpam-1203	205	14	u	u	PROPN
ejpam-1203	205	15	.	.	PUNCT
ejpam-1203	206	1	but	but	CCONJ
ejpam-1203	206	2	u	u	NOUN
ejpam-1203	206	3	is	be	AUX
ejpam-1203	206	4	a	a	DET
ejpam-1203	206	5	g̃-open	g̃-open	NOUN
ejpam-1203	206	6	set	set	VERB
ejpam-1203	206	7	containing	contain	VERB
ejpam-1203	206	8	a.	a.	NOUN
ejpam-1203	206	9	it	it	PRON
ejpam-1203	206	10	follows	follow	VERB
ejpam-1203	206	11	that	that	SCONJ
ejpam-1203	206	12	x	x	SYM
ejpam-1203	206	13	/∈	/∈	PUNCT
ejpam-1203	206	14	pcl(a	pcl(a	NOUN
ejpam-1203	206	15	)	)	PUNCT
ejpam-1203	206	16	and	and	CCONJ
ejpam-1203	206	17	this	this	PRON
ejpam-1203	206	18	is	be	AUX
ejpam-1203	206	19	a	a	DET
ejpam-1203	206	20	contradiction	contradiction	NOUN
ejpam-1203	206	21	.	.	PUNCT
ejpam-1203	207	1	the	the	DET
ejpam-1203	207	2	converse	converse	NOUN
ejpam-1203	207	3	of	of	ADP
ejpam-1203	207	4	the	the	DET
ejpam-1203	207	5	above	above	ADJ
ejpam-1203	207	6	theorem	theorem	NOUN
ejpam-1203	207	7	need	need	AUX
ejpam-1203	207	8	not	not	PART
ejpam-1203	207	9	be	be	AUX
ejpam-1203	207	10	true	true	ADJ
ejpam-1203	207	11	as	as	SCONJ
ejpam-1203	207	12	it	it	PRON
ejpam-1203	207	13	is	be	AUX
ejpam-1203	207	14	seen	see	VERB
ejpam-1203	207	15	from	from	ADP
ejpam-1203	207	16	the	the	DET
ejpam-1203	207	17	following	follow	VERB
ejpam-1203	207	18	example	example	NOUN
ejpam-1203	207	19	.	.	PUNCT
ejpam-1203	208	1	example	example	NOUN
ejpam-1203	209	1	14	14	NUM
ejpam-1203	209	2	.	.	PUNCT
ejpam-1203	210	1	let	let	VERB
ejpam-1203	210	2	x	x	PUNCT
ejpam-1203	210	3	=	=	PRON
ejpam-1203	210	4	{	{	PUNCT
ejpam-1203	210	5	a	a	PRON
ejpam-1203	210	6	,	,	PUNCT
ejpam-1203	210	7	b	b	NOUN
ejpam-1203	210	8	,	,	PUNCT
ejpam-1203	210	9	c	c	NOUN
ejpam-1203	210	10	,	,	PUNCT
ejpam-1203	210	11	d	d	X
ejpam-1203	210	12	,	,	PUNCT
ejpam-1203	210	13	e	e	NOUN
ejpam-1203	210	14	}	}	PUNCT
ejpam-1203	210	15	and	and	CCONJ
ejpam-1203	210	16	τ	τ	PROPN
ejpam-1203	210	17	=	=	PUNCT
ejpam-1203	210	18	{	{	PUNCT
ejpam-1203	210	19	φ	φ	PROPN
ejpam-1203	210	20	,	,	PUNCT
ejpam-1203	210	21	{	{	PUNCT
ejpam-1203	210	22	c	c	NOUN
ejpam-1203	210	23	}	}	PUNCT
ejpam-1203	210	24	,	,	PUNCT
ejpam-1203	210	25	{	{	PUNCT
ejpam-1203	210	26	e	e	NOUN
ejpam-1203	210	27	}	}	PUNCT
ejpam-1203	210	28	,	,	PUNCT
ejpam-1203	210	29	{	{	PUNCT
ejpam-1203	210	30	a	a	DET
ejpam-1203	210	31	,	,	PUNCT
ejpam-1203	210	32	b	b	NOUN
ejpam-1203	210	33	}	}	PUNCT
ejpam-1203	210	34	,	,	PUNCT
ejpam-1203	210	35	{	{	PUNCT
ejpam-1203	210	36	c	c	X
ejpam-1203	210	37	,	,	PUNCT
ejpam-1203	210	38	e	e	NOUN
ejpam-1203	210	39	}	}	PUNCT
ejpam-1203	210	40	,	,	PUNCT
ejpam-1203	210	41	{	{	PUNCT
ejpam-1203	210	42	a	a	DET
ejpam-1203	210	43	,	,	PUNCT
ejpam-1203	210	44	b	b	NOUN
ejpam-1203	210	45	,	,	PUNCT
ejpam-1203	210	46	c	c	NOUN
ejpam-1203	210	47	}	}	PUNCT
ejpam-1203	210	48	,	,	PUNCT
ejpam-1203	210	49	{	{	PUNCT
ejpam-1203	210	50	a	a	PRON
ejpam-1203	210	51	,	,	PUNCT
ejpam-1203	210	52	b	b	NOUN
ejpam-1203	210	53	,	,	PUNCT
ejpam-1203	210	54	e	e	NOUN
ejpam-1203	210	55	}	}	PUNCT
ejpam-1203	210	56	,	,	PUNCT
ejpam-1203	210	57	{	{	PUNCT
ejpam-1203	210	58	a	a	DET
ejpam-1203	210	59	,	,	PUNCT
ejpam-1203	210	60	b	b	NOUN
ejpam-1203	210	61	,	,	PUNCT
ejpam-1203	210	62	c	c	X
ejpam-1203	210	63	,	,	PUNCT
ejpam-1203	210	64	e	e	NOUN
ejpam-1203	210	65	}	}	PUNCT
ejpam-1203	210	66	,	,	PUNCT
ejpam-1203	210	67	x	x	SYM
ejpam-1203	210	68	}	}	PUNCT
ejpam-1203	210	69	.	.	PUNCT
ejpam-1203	211	1	then	then	ADV
ejpam-1203	211	2	the	the	DET
ejpam-1203	211	3	set	set	NOUN
ejpam-1203	211	4	a=	a=	NOUN
ejpam-1203	211	5	{	{	PUNCT
ejpam-1203	211	6	a	a	PRON
ejpam-1203	211	7	}	}	PUNCT
ejpam-1203	211	8	satisfies	satisfie	NOUN
ejpam-1203	211	9	pcl(a	pcl(a	NUM
ejpam-1203	211	10	)	)	PUNCT
ejpam-1203	211	11	⊆g̃−ker(a	⊆g̃−ker(a	PROPN
ejpam-1203	211	12	)	)	PUNCT
ejpam-1203	211	13	.	.	PUNCT
ejpam-1203	212	1	but	but	CCONJ
ejpam-1203	212	2	a	a	PRON
ejpam-1203	212	3	is	be	AUX
ejpam-1203	212	4	not	not	PART
ejpam-1203	212	5	ρ	ρ	NOUN
ejpam-1203	212	6	-	-	PUNCT
ejpam-1203	212	7	closed	closed	ADJ
ejpam-1203	212	8	(	(	PUNCT
ejpam-1203	212	9	x	x	X
ejpam-1203	212	10	,	,	PUNCT
ejpam-1203	212	11	τ	τ	PROPN
ejpam-1203	212	12	)	)	PUNCT
ejpam-1203	212	13	.	.	PUNCT
ejpam-1203	213	1	c.	c.	PROPN
ejpam-1203	213	2	devamanoharan	devamanoharan	PROPN
ejpam-1203	213	3	,	,	PUNCT
ejpam-1203	213	4	s.	s.	PROPN
ejpam-1203	213	5	missier	missier	PROPN
ejpam-1203	213	6	,	,	PUNCT
ejpam-1203	213	7	s.	s.	PROPN
ejpam-1203	213	8	jafari	jafari	PROPN
ejpam-1203	213	9	/	/	SYM
ejpam-1203	213	10	eur	eur	PROPN
ejpam-1203	213	11	.	.	PUNCT
ejpam-1203	214	1	j.	j.	PROPN
ejpam-1203	214	2	pure	pure	PROPN
ejpam-1203	214	3	appl	appl	PROPN
ejpam-1203	214	4	.	.	PROPN
ejpam-1203	214	5	math	math	PROPN
ejpam-1203	214	6	,	,	PUNCT
ejpam-1203	214	7	5	5	NUM
ejpam-1203	214	8	(	(	PUNCT
ejpam-1203	214	9	2012	2012	NUM
ejpam-1203	214	10	)	)	PUNCT
ejpam-1203	214	11	,	,	PUNCT
ejpam-1203	214	12	554	554	NUM
ejpam-1203	214	13	-	-	SYM
ejpam-1203	214	14	566	566	NUM
ejpam-1203	214	15	560	560	NUM
ejpam-1203	214	16	remark	remark	NOUN
ejpam-1203	214	17	9	9	NUM
ejpam-1203	214	18	.	.	PUNCT
ejpam-1203	215	1	the	the	DET
ejpam-1203	215	2	union	union	NOUN
ejpam-1203	215	3	(	(	PUNCT
ejpam-1203	215	4	intersection	intersection	NOUN
ejpam-1203	215	5	)	)	PUNCT
ejpam-1203	215	6	of	of	ADP
ejpam-1203	215	7	two	two	NUM
ejpam-1203	215	8	ρ	ρ	ADJ
ejpam-1203	215	9	-	-	PUNCT
ejpam-1203	215	10	closed	close	VERB
ejpam-1203	215	11	sets	set	NOUN
ejpam-1203	215	12	need	need	AUX
ejpam-1203	215	13	not	not	PART
ejpam-1203	215	14	be	be	AUX
ejpam-1203	215	15	ρ	ρ	NOUN
ejpam-1203	215	16	-	-	PUNCT
ejpam-1203	215	17	closed	closed	ADJ
ejpam-1203	215	18	.	.	PUNCT
ejpam-1203	215	19	example	example	NOUN
ejpam-1203	216	1	15	15	NUM
ejpam-1203	216	2	.	.	PUNCT
ejpam-1203	217	1	let	let	VERB
ejpam-1203	217	2	x	x	PUNCT
ejpam-1203	217	3	=	=	PRON
ejpam-1203	217	4	{	{	PUNCT
ejpam-1203	217	5	a	a	PRON
ejpam-1203	217	6	,	,	PUNCT
ejpam-1203	217	7	b	b	NOUN
ejpam-1203	217	8	,	,	PUNCT
ejpam-1203	217	9	c	c	NOUN
ejpam-1203	217	10	,	,	PUNCT
ejpam-1203	217	11	d	d	NOUN
ejpam-1203	217	12	}	}	PUNCT
ejpam-1203	217	13	and	and	CCONJ
ejpam-1203	217	14	τ	τ	PROPN
ejpam-1203	217	15	=	=	PUNCT
ejpam-1203	217	16	{	{	PUNCT
ejpam-1203	217	17	φ	φ	PROPN
ejpam-1203	217	18	,	,	PUNCT
ejpam-1203	217	19	{	{	PUNCT
ejpam-1203	217	20	b	b	NOUN
ejpam-1203	217	21	,	,	PUNCT
ejpam-1203	217	22	c	c	NOUN
ejpam-1203	217	23	}	}	PUNCT
ejpam-1203	217	24	,	,	PUNCT
ejpam-1203	217	25	{	{	PUNCT
ejpam-1203	217	26	a	a	DET
ejpam-1203	217	27	,	,	PUNCT
ejpam-1203	217	28	b	b	NOUN
ejpam-1203	217	29	,	,	PUNCT
ejpam-1203	217	30	c	c	NOUN
ejpam-1203	217	31	}	}	PUNCT
ejpam-1203	217	32	,	,	PUNCT
ejpam-1203	217	33	{	{	PUNCT
ejpam-1203	217	34	b	b	X
ejpam-1203	217	35	,	,	PUNCT
ejpam-1203	217	36	c	c	NOUN
ejpam-1203	217	37	,	,	PUNCT
ejpam-1203	217	38	d	d	NOUN
ejpam-1203	217	39	}	}	PUNCT
ejpam-1203	217	40	,	,	PUNCT
ejpam-1203	217	41	x	x	SYM
ejpam-1203	217	42	}	}	PUNCT
ejpam-1203	217	43	.	.	PUNCT
ejpam-1203	218	1	1	1	X
ejpam-1203	218	2	.	.	X
ejpam-1203	218	3	let	let	VERB
ejpam-1203	218	4	a=	a=	VERB
ejpam-1203	218	5	{	{	PUNCT
ejpam-1203	218	6	a	a	DET
ejpam-1203	218	7	,	,	PUNCT
ejpam-1203	218	8	b	b	NOUN
ejpam-1203	218	9	}	}	PUNCT
ejpam-1203	218	10	and	and	CCONJ
ejpam-1203	218	11	b	b	X
ejpam-1203	218	12	=	=	NOUN
ejpam-1203	218	13	{	{	PUNCT
ejpam-1203	218	14	a	a	X
ejpam-1203	218	15	,	,	PUNCT
ejpam-1203	218	16	c	c	NOUN
ejpam-1203	218	17	}	}	PUNCT
ejpam-1203	218	18	.	.	PUNCT
ejpam-1203	219	1	here	here	ADV
ejpam-1203	219	2	a	a	PRON
ejpam-1203	219	3	and	and	CCONJ
ejpam-1203	219	4	b	b	NOUN
ejpam-1203	219	5	are	be	AUX
ejpam-1203	219	6	ρ	ρ	ADJ
ejpam-1203	219	7	-	-	PUNCT
ejpam-1203	219	8	closed	closed	ADJ
ejpam-1203	219	9	sets	set	NOUN
ejpam-1203	219	10	.	.	PUNCT
ejpam-1203	220	1	but	but	CCONJ
ejpam-1203	220	2	a∪b	a∪b	NOUN
ejpam-1203	220	3	=	=	X
ejpam-1203	220	4	{	{	PUNCT
ejpam-1203	220	5	a	a	DET
ejpam-1203	220	6	,	,	PUNCT
ejpam-1203	220	7	b	b	NOUN
ejpam-1203	220	8	,	,	PUNCT
ejpam-1203	220	9	c	c	NOUN
ejpam-1203	220	10	}	}	PUNCT
ejpam-1203	220	11	is	be	AUX
ejpam-1203	220	12	not	not	PART
ejpam-1203	220	13	ρ	ρ	NOUN
ejpam-1203	220	14	-	-	PUNCT
ejpam-1203	220	15	closed	closed	ADJ
ejpam-1203	220	16	.	.	PUNCT
ejpam-1203	221	1	2	2	X
ejpam-1203	221	2	.	.	X
ejpam-1203	221	3	let	let	VERB
ejpam-1203	221	4	a	a	PRON
ejpam-1203	221	5	=	=	X
ejpam-1203	221	6	{	{	PUNCT
ejpam-1203	221	7	a	a	X
ejpam-1203	221	8	,	,	PUNCT
ejpam-1203	221	9	c	c	NOUN
ejpam-1203	221	10	}	}	PUNCT
ejpam-1203	221	11	and	and	CCONJ
ejpam-1203	221	12	b	b	X
ejpam-1203	221	13	=	=	SYM
ejpam-1203	221	14	{	{	PUNCT
ejpam-1203	221	15	c	c	NOUN
ejpam-1203	221	16	,	,	PUNCT
ejpam-1203	221	17	d	d	NOUN
ejpam-1203	221	18	}	}	PUNCT
ejpam-1203	221	19	.	.	PUNCT
ejpam-1203	222	1	here	here	ADV
ejpam-1203	222	2	a	a	PRON
ejpam-1203	222	3	and	and	CCONJ
ejpam-1203	222	4	b	b	NOUN
ejpam-1203	222	5	are	be	AUX
ejpam-1203	222	6	ρ	ρ	ADJ
ejpam-1203	222	7	-	-	PUNCT
ejpam-1203	222	8	closed	closed	ADJ
ejpam-1203	222	9	sets	set	NOUN
ejpam-1203	222	10	.	.	PUNCT
ejpam-1203	223	1	but	but	CCONJ
ejpam-1203	223	2	a∩	a∩	PROPN
ejpam-1203	223	3	b	b	PROPN
ejpam-1203	223	4	=	=	PRON
ejpam-1203	223	5	{	{	PUNCT
ejpam-1203	223	6	c	c	NOUN
ejpam-1203	223	7	}	}	PUNCT
ejpam-1203	223	8	is	be	AUX
ejpam-1203	223	9	not	not	PART
ejpam-1203	223	10	ρ	ρ	NOUN
ejpam-1203	223	11	-	-	PUNCT
ejpam-1203	223	12	closed	closed	ADJ
ejpam-1203	223	13	.	.	PUNCT
ejpam-1203	224	1	theorem	theorem	VERB
ejpam-1203	224	2	8	8	NUM
ejpam-1203	224	3	.	.	PUNCT
ejpam-1203	225	1	if	if	SCONJ
ejpam-1203	225	2	a	a	DET
ejpam-1203	225	3	set	set	NOUN
ejpam-1203	225	4	a	a	PRON
ejpam-1203	225	5	is	be	AUX
ejpam-1203	225	6	ρ	ρ	NOUN
ejpam-1203	225	7	-	-	PUNCT
ejpam-1203	225	8	closed	closed	ADJ
ejpam-1203	225	9	,	,	PUNCT
ejpam-1203	225	10	then	then	ADV
ejpam-1203	225	11	pcl(a)−	pcl(a)−	VERB
ejpam-1203	225	12	a	a	DET
ejpam-1203	225	13	contains	contain	VERB
ejpam-1203	225	14	no	no	DET
ejpam-1203	225	15	nonempty	nonempty	ADV
ejpam-1203	225	16	closed	close	VERB
ejpam-1203	225	17	set	set	NOUN
ejpam-1203	225	18	.	.	PUNCT
ejpam-1203	226	1	proof	proof	NOUN
ejpam-1203	226	2	.	.	PUNCT
ejpam-1203	227	1	let	let	VERB
ejpam-1203	227	2	f	f	PROPN
ejpam-1203	227	3	⊆	⊆	NUM
ejpam-1203	227	4	pcl(a	pcl(a	PROPN
ejpam-1203	227	5	)	)	PUNCT
ejpam-1203	227	6	−	−	NOUN
ejpam-1203	227	7	a	a	DET
ejpam-1203	227	8	be	be	AUX
ejpam-1203	227	9	a	a	DET
ejpam-1203	227	10	nonempty	nonempty	ADV
ejpam-1203	227	11	closed	close	VERB
ejpam-1203	227	12	set	set	NOUN
ejpam-1203	227	13	.	.	PUNCT
ejpam-1203	228	1	then	then	ADV
ejpam-1203	228	2	f	f	PROPN
ejpam-1203	228	3	⊆	⊆	NUM
ejpam-1203	228	4	pcl(a	pcl(a	PROPN
ejpam-1203	228	5	)	)	PUNCT
ejpam-1203	228	6	and	and	CCONJ
ejpam-1203	228	7	a	a	DET
ejpam-1203	228	8	⊆	⊆	NUM
ejpam-1203	228	9	x	x	SYM
ejpam-1203	228	10	−	−	PROPN
ejpam-1203	228	11	f	f	NOUN
ejpam-1203	228	12	.	.	PUNCT
ejpam-1203	229	1	since	since	SCONJ
ejpam-1203	229	2	x	x	PRON
ejpam-1203	229	3	−	−	PROPN
ejpam-1203	229	4	f	f	PROPN
ejpam-1203	229	5	is	be	AUX
ejpam-1203	229	6	g̃-open	g̃-open	PROPN
ejpam-1203	229	7	,	,	PUNCT
ejpam-1203	229	8	then	then	ADV
ejpam-1203	229	9	a	a	PRON
ejpam-1203	229	10	is	be	AUX
ejpam-1203	229	11	ρ	ρ	NOUN
ejpam-1203	229	12	-	-	PUNCT
ejpam-1203	229	13	closed	closed	ADJ
ejpam-1203	229	14	.	.	PUNCT
ejpam-1203	230	1	therefore	therefore	ADV
ejpam-1203	230	2	pcl(a	pcl(a	X
ejpam-1203	230	3	)	)	PUNCT
ejpam-1203	230	4	⊆	⊆	NUM
ejpam-1203	230	5	int(x	int(x	PROPN
ejpam-1203	230	6	−	−	NOUN
ejpam-1203	230	7	f	f	NOUN
ejpam-1203	230	8	)	)	PUNCT
ejpam-1203	231	1	=	=	PUNCT
ejpam-1203	232	1	x	x	PUNCT
ejpam-1203	232	2	−	−	PROPN
ejpam-1203	232	3	cl(f	cl(f	PROPN
ejpam-1203	232	4	)	)	PUNCT
ejpam-1203	232	5	,	,	PUNCT
ejpam-1203	232	6	cl(f	cl(f	PROPN
ejpam-1203	232	7	)	)	PUNCT
ejpam-1203	233	1	⊆	⊆	NUM
ejpam-1203	233	2	x	x	SYM
ejpam-1203	233	3	−	−	NOUN
ejpam-1203	233	4	pcl(a	pcl(a	PROPN
ejpam-1203	233	5	)	)	PUNCT
ejpam-1203	233	6	.	.	PUNCT
ejpam-1203	234	1	and	and	CCONJ
ejpam-1203	234	2	so	so	ADV
ejpam-1203	234	3	f	f	PROPN
ejpam-1203	235	1	⊆	⊆	NUM
ejpam-1203	235	2	x	x	SYM
ejpam-1203	235	3	−	−	NOUN
ejpam-1203	235	4	pcl(a	pcl(a	PROPN
ejpam-1203	235	5	)	)	PUNCT
ejpam-1203	236	1	,	,	PUNCT
ejpam-1203	236	2	f	f	PROPN
ejpam-1203	236	3	⊆	⊆	NUM
ejpam-1203	236	4	pcl(a	pcl(a	PROPN
ejpam-1203	236	5	)	)	PUNCT
ejpam-1203	236	6	∩	∩	NOUN
ejpam-1203	236	7	(	(	PUNCT
ejpam-1203	236	8	x	x	SYM
ejpam-1203	236	9	−	−	NOUN
ejpam-1203	236	10	pcl(a	pcl(a	NUM
ejpam-1203	236	11	)	)	PUNCT
ejpam-1203	236	12	)	)	PUNCT
ejpam-1203	237	1	=	=	PRON
ejpam-1203	237	2	{	{	PUNCT
ejpam-1203	237	3	;	;	PUNCT
ejpam-1203	237	4	}	}	PUNCT
ejpam-1203	237	5	.	.	PUNCT
ejpam-1203	238	1	hence	hence	ADV
ejpam-1203	238	2	pcl(a)−	pcl(a)−	VERB
ejpam-1203	238	3	a	a	DET
ejpam-1203	238	4	contains	contain	VERB
ejpam-1203	238	5	no	no	DET
ejpam-1203	238	6	nonempty	nonempty	ADV
ejpam-1203	238	7	closed	close	VERB
ejpam-1203	238	8	set	set	NOUN
ejpam-1203	238	9	.	.	PUNCT
ejpam-1203	239	1	the	the	DET
ejpam-1203	239	2	converse	converse	NOUN
ejpam-1203	239	3	of	of	ADP
ejpam-1203	239	4	the	the	DET
ejpam-1203	239	5	above	above	ADJ
ejpam-1203	239	6	theorem	theorem	NOUN
ejpam-1203	239	7	need	need	AUX
ejpam-1203	239	8	not	not	PART
ejpam-1203	239	9	be	be	AUX
ejpam-1203	239	10	true	true	ADJ
ejpam-1203	239	11	as	as	SCONJ
ejpam-1203	239	12	it	it	PRON
ejpam-1203	239	13	is	be	AUX
ejpam-1203	239	14	seen	see	VERB
ejpam-1203	239	15	from	from	ADP
ejpam-1203	239	16	the	the	DET
ejpam-1203	239	17	following	follow	VERB
ejpam-1203	239	18	example	example	NOUN
ejpam-1203	239	19	.	.	PUNCT
ejpam-1203	240	1	example	example	NOUN
ejpam-1203	241	1	16	16	NUM
ejpam-1203	241	2	.	.	PUNCT
ejpam-1203	242	1	let	let	VERB
ejpam-1203	242	2	x	x	PUNCT
ejpam-1203	242	3	=	=	PRON
ejpam-1203	242	4	{	{	PUNCT
ejpam-1203	242	5	a	a	PRON
ejpam-1203	242	6	,	,	PUNCT
ejpam-1203	242	7	b	b	NOUN
ejpam-1203	242	8	,	,	PUNCT
ejpam-1203	242	9	c	c	NOUN
ejpam-1203	242	10	,	,	PUNCT
ejpam-1203	242	11	d	d	NOUN
ejpam-1203	242	12	}	}	PUNCT
ejpam-1203	242	13	and	and	CCONJ
ejpam-1203	242	14	τ	τ	PROPN
ejpam-1203	242	15	=	=	PUNCT
ejpam-1203	242	16	{	{	PUNCT
ejpam-1203	242	17	φ	φ	PROPN
ejpam-1203	242	18	,	,	PUNCT
ejpam-1203	242	19	{	{	PUNCT
ejpam-1203	242	20	c	c	NOUN
ejpam-1203	242	21	}	}	PUNCT
ejpam-1203	242	22	,	,	PUNCT
ejpam-1203	242	23	{	{	PUNCT
ejpam-1203	242	24	a	a	DET
ejpam-1203	242	25	,	,	PUNCT
ejpam-1203	242	26	b	b	NOUN
ejpam-1203	242	27	}	}	PUNCT
ejpam-1203	242	28	,	,	PUNCT
ejpam-1203	242	29	{	{	PUNCT
ejpam-1203	242	30	a	a	PRON
ejpam-1203	242	31	,	,	PUNCT
ejpam-1203	242	32	b	b	NOUN
ejpam-1203	242	33	,	,	PUNCT
ejpam-1203	242	34	c	c	NOUN
ejpam-1203	242	35	}	}	PUNCT
ejpam-1203	242	36	,	,	PUNCT
ejpam-1203	242	37	x	x	NOUN
ejpam-1203	242	38	}	}	PUNCT
ejpam-1203	242	39	.	.	PUNCT
ejpam-1203	243	1	let	let	VERB
ejpam-1203	243	2	a	a	PRON
ejpam-1203	243	3	=	=	X
ejpam-1203	243	4	{	{	PUNCT
ejpam-1203	243	5	a	a	NOUN
ejpam-1203	243	6	}	}	PUNCT
ejpam-1203	243	7	.	.	PUNCT
ejpam-1203	244	1	then	then	ADV
ejpam-1203	244	2	pcl(a)−	pcl(a)−	VERB
ejpam-1203	244	3	a	a	DET
ejpam-1203	244	4	contains	contain	VERB
ejpam-1203	244	5	no	no	DET
ejpam-1203	244	6	nonempty	nonempty	ADV
ejpam-1203	244	7	closed	close	VERB
ejpam-1203	244	8	set	set	NOUN
ejpam-1203	244	9	.	.	PUNCT
ejpam-1203	245	1	but	but	CCONJ
ejpam-1203	245	2	a	a	PRON
ejpam-1203	245	3	is	be	AUX
ejpam-1203	245	4	not	not	PART
ejpam-1203	245	5	ρ	ρ	NOUN
ejpam-1203	245	6	-	-	PUNCT
ejpam-1203	245	7	closed	closed	ADJ
ejpam-1203	245	8	in	in	ADP
ejpam-1203	245	9	(	(	PUNCT
ejpam-1203	245	10	x	x	INTJ
ejpam-1203	245	11	,	,	PUNCT
ejpam-1203	245	12	τ	τ	PROPN
ejpam-1203	245	13	)	)	PUNCT
ejpam-1203	245	14	.	.	PUNCT
ejpam-1203	246	1	theorem	theorem	VERB
ejpam-1203	246	2	9	9	NUM
ejpam-1203	246	3	.	.	PUNCT
ejpam-1203	247	1	if	if	SCONJ
ejpam-1203	247	2	a	a	DET
ejpam-1203	247	3	set	set	NOUN
ejpam-1203	247	4	a	a	PRON
ejpam-1203	247	5	is	be	AUX
ejpam-1203	247	6	ρ	ρ	NOUN
ejpam-1203	247	7	-	-	PUNCT
ejpam-1203	247	8	closed	closed	ADJ
ejpam-1203	247	9	,	,	PUNCT
ejpam-1203	247	10	then	then	ADV
ejpam-1203	247	11	pcl(a)−	pcl(a)−	VERB
ejpam-1203	247	12	a	a	DET
ejpam-1203	247	13	contains	contain	VERB
ejpam-1203	247	14	no	no	DET
ejpam-1203	247	15	nonempty	nonempty	ADV
ejpam-1203	247	16	g̃-closed	g̃-close	VERB
ejpam-1203	247	17	set	set	NOUN
ejpam-1203	247	18	.	.	PUNCT
ejpam-1203	248	1	proof	proof	NOUN
ejpam-1203	248	2	.	.	PUNCT
ejpam-1203	249	1	let	let	VERB
ejpam-1203	249	2	f	f	PRON
ejpam-1203	249	3	be	be	AUX
ejpam-1203	249	4	a	a	DET
ejpam-1203	249	5	nonempty	nonempty	ADV
ejpam-1203	249	6	g̃-closed	g̃-close	VERB
ejpam-1203	249	7	set	set	NOUN
ejpam-1203	249	8	such	such	ADJ
ejpam-1203	249	9	that	that	SCONJ
ejpam-1203	249	10	f	f	PROPN
ejpam-1203	249	11	⊆	⊆	NUM
ejpam-1203	249	12	pcl(a)−	pcl(a)−	NOUN
ejpam-1203	249	13	a.	a.	NOUN
ejpam-1203	249	14	then	then	ADV
ejpam-1203	249	15	f	f	PROPN
ejpam-1203	249	16	⊆	⊆	NUM
ejpam-1203	249	17	pcl(a	pcl(a	NUM
ejpam-1203	249	18	)	)	PUNCT
ejpam-1203	249	19	and	and	CCONJ
ejpam-1203	249	20	a⊆	a⊆	VERB
ejpam-1203	249	21	x	x	PUNCT
ejpam-1203	250	1	−	−	PROPN
ejpam-1203	250	2	f	f	X
ejpam-1203	250	3	.	.	PUNCT
ejpam-1203	251	1	we	we	PRON
ejpam-1203	251	2	have	have	VERB
ejpam-1203	251	3	pcl(a	pcl(a	NOUN
ejpam-1203	251	4	)	)	PUNCT
ejpam-1203	251	5	⊆	⊆	NUM
ejpam-1203	251	6	int(x	int(x	PROPN
ejpam-1203	251	7	−	−	NOUN
ejpam-1203	251	8	f	f	NOUN
ejpam-1203	251	9	)	)	PUNCT
ejpam-1203	251	10	,	,	PUNCT
ejpam-1203	251	11	pcl(a	pcl(a	PROPN
ejpam-1203	251	12	)	)	PUNCT
ejpam-1203	251	13	⊆	⊆	NUM
ejpam-1203	251	14	x	x	SYM
ejpam-1203	251	15	−	−	PROPN
ejpam-1203	251	16	cl(f	cl(f	NUM
ejpam-1203	251	17	)	)	PUNCT
ejpam-1203	251	18	,	,	PUNCT
ejpam-1203	251	19	cl(f	cl(f	PROPN
ejpam-1203	251	20	)	)	PUNCT
ejpam-1203	252	1	⊆	⊆	NUM
ejpam-1203	252	2	x	x	SYM
ejpam-1203	252	3	−	−	NOUN
ejpam-1203	252	4	pcl(a	pcl(a	PROPN
ejpam-1203	252	5	)	)	PUNCT
ejpam-1203	252	6	.	.	PUNCT
ejpam-1203	253	1	therefore	therefore	ADV
ejpam-1203	253	2	f	f	PROPN
ejpam-1203	253	3	⊆	⊆	NUM
ejpam-1203	253	4	pcl(a)∩	pcl(a)∩	PROPN
ejpam-1203	253	5	(	(	PUNCT
ejpam-1203	253	6	x	x	X
ejpam-1203	253	7	−	−	NOUN
ejpam-1203	253	8	pcl(a	pcl(a	PROPN
ejpam-1203	253	9	)	)	PUNCT
ejpam-1203	253	10	)	)	PUNCT
ejpam-1203	253	11	=	=	PRON
ejpam-1203	253	12	{	{	PUNCT
ejpam-1203	253	13	;	;	PUNCT
ejpam-1203	253	14	}	}	PUNCT
ejpam-1203	253	15	.	.	PUNCT
ejpam-1203	254	1	hence	hence	ADV
ejpam-1203	254	2	pcl(a)−	pcl(a)−	VERB
ejpam-1203	254	3	a	a	DET
ejpam-1203	254	4	contains	contain	VERB
ejpam-1203	254	5	no	no	DET
ejpam-1203	254	6	nonempty	nonempty	ADV
ejpam-1203	254	7	g̃-closed	g̃-close	VERB
ejpam-1203	254	8	set	set	NOUN
ejpam-1203	254	9	.	.	PUNCT
ejpam-1203	255	1	the	the	DET
ejpam-1203	255	2	converse	converse	NOUN
ejpam-1203	255	3	of	of	ADP
ejpam-1203	255	4	the	the	DET
ejpam-1203	255	5	above	above	ADJ
ejpam-1203	255	6	theorem	theorem	NOUN
ejpam-1203	255	7	need	need	AUX
ejpam-1203	255	8	not	not	PART
ejpam-1203	255	9	be	be	AUX
ejpam-1203	255	10	true	true	ADJ
ejpam-1203	255	11	as	as	SCONJ
ejpam-1203	255	12	it	it	PRON
ejpam-1203	255	13	is	be	AUX
ejpam-1203	255	14	seen	see	VERB
ejpam-1203	255	15	from	from	ADP
ejpam-1203	255	16	the	the	DET
ejpam-1203	255	17	following	follow	VERB
ejpam-1203	255	18	example	example	NOUN
ejpam-1203	255	19	.	.	PUNCT
ejpam-1203	256	1	example	example	NOUN
ejpam-1203	256	2	17	17	NUM
ejpam-1203	256	3	.	.	PUNCT
ejpam-1203	257	1	let	let	VERB
ejpam-1203	257	2	x	x	PUNCT
ejpam-1203	257	3	=	=	PRON
ejpam-1203	257	4	{	{	PUNCT
ejpam-1203	257	5	a	a	PRON
ejpam-1203	257	6	,	,	PUNCT
ejpam-1203	257	7	b	b	NOUN
ejpam-1203	257	8	,	,	PUNCT
ejpam-1203	257	9	c	c	NOUN
ejpam-1203	257	10	,	,	PUNCT
ejpam-1203	257	11	d	d	NOUN
ejpam-1203	257	12	}	}	PUNCT
ejpam-1203	257	13	and	and	CCONJ
ejpam-1203	257	14	τ	τ	PROPN
ejpam-1203	257	15	=	=	PUNCT
ejpam-1203	257	16	{	{	PUNCT
ejpam-1203	257	17	φ	φ	PROPN
ejpam-1203	257	18	,	,	PUNCT
ejpam-1203	257	19	{	{	PUNCT
ejpam-1203	257	20	c	c	NOUN
ejpam-1203	257	21	}	}	PUNCT
ejpam-1203	257	22	,	,	PUNCT
ejpam-1203	257	23	{	{	PUNCT
ejpam-1203	257	24	a	a	DET
ejpam-1203	257	25	,	,	PUNCT
ejpam-1203	257	26	b	b	NOUN
ejpam-1203	257	27	}	}	PUNCT
ejpam-1203	257	28	,	,	PUNCT
ejpam-1203	257	29	{	{	PUNCT
ejpam-1203	257	30	a	a	DET
ejpam-1203	257	31	,	,	PUNCT
ejpam-1203	257	32	b	b	NOUN
ejpam-1203	257	33	,	,	PUNCT
ejpam-1203	257	34	c	c	NOUN
ejpam-1203	257	35	}	}	PUNCT
ejpam-1203	257	36	,	,	PUNCT
ejpam-1203	257	37	x	x	NOUN
ejpam-1203	257	38	}	}	PUNCT
ejpam-1203	257	39	.	.	PUNCT
ejpam-1203	258	1	let	let	VERB
ejpam-1203	258	2	a={a	a={a	NOUN
ejpam-1203	258	3	}	}	PUNCT
ejpam-1203	258	4	.	.	PUNCT
ejpam-1203	259	1	then	then	ADV
ejpam-1203	259	2	pcl(a)−	pcl(a)−	VERB
ejpam-1203	259	3	a	a	DET
ejpam-1203	259	4	contains	contain	VERB
ejpam-1203	259	5	no	no	DET
ejpam-1203	259	6	nonempty	nonempty	ADV
ejpam-1203	259	7	g̃-closed	g̃-close	VERB
ejpam-1203	259	8	set	set	NOUN
ejpam-1203	259	9	.	.	PUNCT
ejpam-1203	260	1	but	but	CCONJ
ejpam-1203	260	2	a	a	PRON
ejpam-1203	260	3	is	be	AUX
ejpam-1203	260	4	not	not	PART
ejpam-1203	260	5	ρ	ρ	NOUN
ejpam-1203	260	6	-	-	PUNCT
ejpam-1203	260	7	closed	closed	ADJ
ejpam-1203	260	8	in	in	ADP
ejpam-1203	260	9	(	(	PUNCT
ejpam-1203	260	10	x	x	INTJ
ejpam-1203	260	11	,	,	PUNCT
ejpam-1203	260	12	τ	τ	PROPN
ejpam-1203	260	13	)	)	PUNCT
ejpam-1203	260	14	.	.	PUNCT
ejpam-1203	261	1	theorem	theorem	VERB
ejpam-1203	261	2	10	10	NUM
ejpam-1203	261	3	.	.	PUNCT
ejpam-1203	262	1	if	if	SCONJ
ejpam-1203	262	2	a	a	PRON
ejpam-1203	262	3	is	be	AUX
ejpam-1203	262	4	ρ	ρ	NOUN
ejpam-1203	262	5	-	-	PUNCT
ejpam-1203	262	6	closed	closed	ADJ
ejpam-1203	262	7	and	and	CCONJ
ejpam-1203	262	8	a⊆	a⊆	VERB
ejpam-1203	262	9	b	b	X
ejpam-1203	262	10	⊆	⊆	NUM
ejpam-1203	262	11	pcl(a	pcl(a	NUM
ejpam-1203	262	12	)	)	PUNCT
ejpam-1203	262	13	,	,	PUNCT
ejpam-1203	262	14	then	then	ADV
ejpam-1203	262	15	b	b	PROPN
ejpam-1203	262	16	is	be	AUX
ejpam-1203	262	17	ρ	ρ	NOUN
ejpam-1203	262	18	-	-	PUNCT
ejpam-1203	262	19	closed	closed	ADJ
ejpam-1203	262	20	.	.	PUNCT
ejpam-1203	263	1	proof	proof	NOUN
ejpam-1203	263	2	.	.	PUNCT
ejpam-1203	264	1	let	let	VERB
ejpam-1203	264	2	u	u	PRON
ejpam-1203	264	3	be	be	AUX
ejpam-1203	264	4	a	a	DET
ejpam-1203	264	5	g̃-open	g̃-open	NOUN
ejpam-1203	264	6	set	set	NOUN
ejpam-1203	264	7	of	of	ADP
ejpam-1203	264	8	x	x	PUNCT
ejpam-1203	264	9	such	such	ADJ
ejpam-1203	264	10	that	that	DET
ejpam-1203	264	11	b	b	PROPN
ejpam-1203	264	12	⊆	⊆	NUM
ejpam-1203	264	13	u	u	NOUN
ejpam-1203	264	14	.	.	PUNCT
ejpam-1203	265	1	then	then	ADV
ejpam-1203	265	2	a⊆	a⊆	VERB
ejpam-1203	265	3	u	u	NOUN
ejpam-1203	265	4	and	and	CCONJ
ejpam-1203	265	5	since	since	SCONJ
ejpam-1203	265	6	a	a	PRON
ejpam-1203	265	7	is	be	AUX
ejpam-1203	265	8	ρ	ρ	NOUN
ejpam-1203	265	9	-	-	ADJ
ejpam-1203	265	10	closed	closed	ADJ
ejpam-1203	265	11	,	,	PUNCT
ejpam-1203	265	12	we	we	PRON
ejpam-1203	265	13	have	have	VERB
ejpam-1203	265	14	pcl(a	pcl(a	NOUN
ejpam-1203	265	15	)	)	PUNCT
ejpam-1203	265	16	⊆	⊆	NUM
ejpam-1203	265	17	int(u	int(u	NUM
ejpam-1203	265	18	)	)	PUNCT
ejpam-1203	265	19	.	.	PUNCT
ejpam-1203	266	1	now	now	ADV
ejpam-1203	266	2	pcl(b	pcl(b	PROPN
ejpam-1203	266	3	)	)	PUNCT
ejpam-1203	266	4	⊆	⊆	NUM
ejpam-1203	266	5	pcl(pcl(a	pcl(pcl(a	NUM
ejpam-1203	266	6	)	)	PUNCT
ejpam-1203	266	7	)	)	PUNCT
ejpam-1203	267	1	=	=	SYM
ejpam-1203	267	2	pcl(a	pcl(a	X
ejpam-1203	267	3	)	)	PUNCT
ejpam-1203	267	4	⊆	⊆	NUM
ejpam-1203	267	5	int(u	int(u	NUM
ejpam-1203	267	6	)	)	PUNCT
ejpam-1203	267	7	.	.	PUNCT
ejpam-1203	268	1	hence	hence	ADV
ejpam-1203	268	2	b	b	PROPN
ejpam-1203	268	3	is	be	AUX
ejpam-1203	268	4	ρ	ρ	NOUN
ejpam-1203	268	5	-	-	PUNCT
ejpam-1203	268	6	closed	closed	ADJ
ejpam-1203	268	7	.	.	PUNCT
ejpam-1203	269	1	theorem	theorem	VERB
ejpam-1203	269	2	11	11	NUM
ejpam-1203	269	3	.	.	PUNCT
ejpam-1203	270	1	if	if	SCONJ
ejpam-1203	270	2	a	a	DET
ejpam-1203	270	3	subset	subset	NOUN
ejpam-1203	270	4	a	a	PRON
ejpam-1203	270	5	of	of	ADP
ejpam-1203	270	6	(	(	PUNCT
ejpam-1203	270	7	x	x	PROPN
ejpam-1203	270	8	,	,	PUNCT
ejpam-1203	270	9	τ	τ	X
ejpam-1203	270	10	)	)	PUNCT
ejpam-1203	270	11	is	be	AUX
ejpam-1203	270	12	g̃open	g̃open	VERB
ejpam-1203	270	13	and	and	CCONJ
ejpam-1203	270	14	ρ	ρ	VERB
ejpam-1203	270	15	-	-	PUNCT
ejpam-1203	270	16	closed	closed	ADJ
ejpam-1203	270	17	,	,	PUNCT
ejpam-1203	270	18	then	then	ADV
ejpam-1203	270	19	a	a	PRON
ejpam-1203	270	20	is	be	AUX
ejpam-1203	270	21	preclosed	preclose	VERB
ejpam-1203	270	22	in	in	ADP
ejpam-1203	270	23	(	(	PUNCT
ejpam-1203	270	24	x	x	INTJ
ejpam-1203	270	25	,	,	PUNCT
ejpam-1203	270	26	τ	τ	PROPN
ejpam-1203	270	27	)	)	PUNCT
ejpam-1203	270	28	.	.	PUNCT
ejpam-1203	271	1	proof	proof	NOUN
ejpam-1203	271	2	.	.	PUNCT
ejpam-1203	272	1	if	if	SCONJ
ejpam-1203	272	2	a	a	DET
ejpam-1203	272	3	subset	subset	NOUN
ejpam-1203	272	4	a	a	PRON
ejpam-1203	272	5	of	of	ADP
ejpam-1203	272	6	(	(	PUNCT
ejpam-1203	272	7	x	x	PROPN
ejpam-1203	272	8	,	,	PUNCT
ejpam-1203	272	9	τ	τ	X
ejpam-1203	272	10	)	)	PUNCT
ejpam-1203	272	11	is	be	AUX
ejpam-1203	272	12	g̃-open	g̃-open	NOUN
ejpam-1203	272	13	and	and	CCONJ
ejpam-1203	272	14	ρ	ρ	NOUN
ejpam-1203	272	15	-	-	PUNCT
ejpam-1203	272	16	closed	closed	ADJ
ejpam-1203	272	17	.	.	PUNCT
ejpam-1203	273	1	then	then	ADV
ejpam-1203	273	2	pcl(a	pcl(a	X
ejpam-1203	273	3	)	)	PUNCT
ejpam-1203	273	4	⊆	⊆	NUM
ejpam-1203	273	5	int(a	int(a	PROPN
ejpam-1203	273	6	)	)	PUNCT
ejpam-1203	273	7	⊆	⊆	NUM
ejpam-1203	273	8	a.	a.	NOUN
ejpam-1203	273	9	hence	hence	ADV
ejpam-1203	273	10	a	a	PRON
ejpam-1203	273	11	is	be	AUX
ejpam-1203	273	12	preclosed	preclose	VERB
ejpam-1203	273	13	is	be	AUX
ejpam-1203	273	14	(	(	PUNCT
ejpam-1203	273	15	x	x	INTJ
ejpam-1203	273	16	,	,	PUNCT
ejpam-1203	273	17	τ	τ	PROPN
ejpam-1203	273	18	)	)	PUNCT
ejpam-1203	273	19	.	.	PUNCT
ejpam-1203	274	1	lemma	lemma	PROPN
ejpam-1203	274	2	2	2	NUM
ejpam-1203	274	3	(	(	PUNCT
ejpam-1203	274	4	[	[	X
ejpam-1203	274	5	4	4	NUM
ejpam-1203	274	6	]	]	PUNCT
ejpam-1203	274	7	)	)	PUNCT
ejpam-1203	274	8	.	.	PUNCT
ejpam-1203	275	1	if	if	SCONJ
ejpam-1203	275	2	a	a	PRON
ejpam-1203	275	3	is	be	AUX
ejpam-1203	275	4	regular	regular	ADJ
ejpam-1203	275	5	open	open	ADJ
ejpam-1203	275	6	and	and	CCONJ
ejpam-1203	275	7	gpr	gpr	NOUN
ejpam-1203	275	8	-	-	PUNCT
ejpam-1203	275	9	closed	closed	ADJ
ejpam-1203	275	10	,	,	PUNCT
ejpam-1203	275	11	then	then	ADV
ejpam-1203	275	12	a	a	PRON
ejpam-1203	275	13	is	be	AUX
ejpam-1203	275	14	preclosed	preclose	VERB
ejpam-1203	275	15	.	.	PUNCT
ejpam-1203	276	1	theorem	theorem	NOUN
ejpam-1203	276	2	12	12	NUM
ejpam-1203	276	3	.	.	PUNCT
ejpam-1203	277	1	a	a	DET
ejpam-1203	277	2	regular	regular	ADJ
ejpam-1203	277	3	open	open	ADJ
ejpam-1203	277	4	set	set	NOUN
ejpam-1203	277	5	of	of	ADP
ejpam-1203	277	6	(	(	PUNCT
ejpam-1203	277	7	x	x	PROPN
ejpam-1203	277	8	,	,	PUNCT
ejpam-1203	277	9	τ	τ	X
ejpam-1203	277	10	)	)	PUNCT
ejpam-1203	277	11	is	be	AUX
ejpam-1203	277	12	gpr	gpr	NOUN
ejpam-1203	277	13	-	-	PUNCT
ejpam-1203	277	14	closed	close	VERB
ejpam-1203	277	15	if	if	SCONJ
ejpam-1203	277	16	and	and	CCONJ
ejpam-1203	277	17	only	only	ADV
ejpam-1203	277	18	if	if	SCONJ
ejpam-1203	277	19	a	a	PRON
ejpam-1203	277	20	is	be	AUX
ejpam-1203	277	21	ρ	ρ	NOUN
ejpam-1203	277	22	-	-	PUNCT
ejpam-1203	277	23	closed	closed	ADJ
ejpam-1203	277	24	in	in	ADP
ejpam-1203	277	25	(	(	PUNCT
ejpam-1203	277	26	x	x	INTJ
ejpam-1203	277	27	,	,	PUNCT
ejpam-1203	277	28	τ	τ	PROPN
ejpam-1203	277	29	)	)	PUNCT
ejpam-1203	277	30	.	.	PUNCT
ejpam-1203	278	1	c.	c.	PROPN
ejpam-1203	278	2	devamanoharan	devamanoharan	PROPN
ejpam-1203	278	3	,	,	PUNCT
ejpam-1203	278	4	s.	s.	PROPN
ejpam-1203	278	5	missier	missier	PROPN
ejpam-1203	278	6	,	,	PUNCT
ejpam-1203	278	7	s.	s.	PROPN
ejpam-1203	278	8	jafari	jafari	PROPN
ejpam-1203	278	9	/	/	SYM
ejpam-1203	278	10	eur	eur	PROPN
ejpam-1203	278	11	.	.	PUNCT
ejpam-1203	279	1	j.	j.	PROPN
ejpam-1203	279	2	pure	pure	PROPN
ejpam-1203	279	3	appl	appl	PROPN
ejpam-1203	279	4	.	.	PROPN
ejpam-1203	279	5	math	math	PROPN
ejpam-1203	279	6	,	,	PUNCT
ejpam-1203	279	7	5	5	NUM
ejpam-1203	279	8	(	(	PUNCT
ejpam-1203	279	9	2012	2012	NUM
ejpam-1203	279	10	)	)	PUNCT
ejpam-1203	279	11	,	,	PUNCT
ejpam-1203	279	12	554	554	NUM
ejpam-1203	279	13	-	-	SYM
ejpam-1203	279	14	566	566	NUM
ejpam-1203	279	15	561	561	NUM
ejpam-1203	279	16	proof	proof	NOUN
ejpam-1203	279	17	.	.	PUNCT
ejpam-1203	280	1	let	let	VERB
ejpam-1203	280	2	a	a	DET
ejpam-1203	280	3	⊆	⊆	NUM
ejpam-1203	280	4	u	u	NOUN
ejpam-1203	280	5	and	and	CCONJ
ejpam-1203	280	6	u	u	PRON
ejpam-1203	280	7	be	be	VERB
ejpam-1203	280	8	g̃-open	g̃-open	NOUN
ejpam-1203	280	9	in	in	ADP
ejpam-1203	280	10	(	(	PUNCT
ejpam-1203	280	11	x	x	INTJ
ejpam-1203	280	12	,	,	PUNCT
ejpam-1203	280	13	τ	τ	PROPN
ejpam-1203	280	14	)	)	PUNCT
ejpam-1203	280	15	.	.	PUNCT
ejpam-1203	281	1	since	since	SCONJ
ejpam-1203	281	2	a	a	PRON
ejpam-1203	281	3	is	be	AUX
ejpam-1203	281	4	regular	regular	ADJ
ejpam-1203	281	5	open	open	ADJ
ejpam-1203	281	6	and	and	CCONJ
ejpam-1203	281	7	gpr	gpr	NOUN
ejpam-1203	281	8	-	-	PUNCT
ejpam-1203	281	9	closed	closed	ADJ
ejpam-1203	281	10	,	,	PUNCT
ejpam-1203	281	11	a	a	PRON
ejpam-1203	281	12	is	be	AUX
ejpam-1203	281	13	preclosed	preclose	VERB
ejpam-1203	281	14	by	by	ADP
ejpam-1203	281	15	lemma	lemma	PROPN
ejpam-1203	281	16	2	2	NUM
ejpam-1203	281	17	.	.	PUNCT
ejpam-1203	282	1	since	since	SCONJ
ejpam-1203	282	2	every	every	DET
ejpam-1203	282	3	regular	regular	ADJ
ejpam-1203	282	4	open	open	NOUN
ejpam-1203	282	5	is	be	AUX
ejpam-1203	282	6	open	open	ADJ
ejpam-1203	282	7	,	,	PUNCT
ejpam-1203	282	8	therefore	therefore	ADV
ejpam-1203	282	9	a	a	PRON
ejpam-1203	282	10	is	be	AUX
ejpam-1203	282	11	open	open	ADJ
ejpam-1203	282	12	and	and	CCONJ
ejpam-1203	282	13	preclosed	preclose	VERB
ejpam-1203	282	14	.	.	PUNCT
ejpam-1203	283	1	hence	hence	ADV
ejpam-1203	283	2	by	by	ADP
ejpam-1203	283	3	theorem	theorem	NOUN
ejpam-1203	283	4	1	1	NUM
ejpam-1203	283	5	,	,	PUNCT
ejpam-1203	283	6	a	a	PRON
ejpam-1203	283	7	is	be	AUX
ejpam-1203	283	8	ρ	ρ	NOUN
ejpam-1203	283	9	-	-	PUNCT
ejpam-1203	283	10	closed	closed	ADJ
ejpam-1203	283	11	.	.	PUNCT
ejpam-1203	284	1	by	by	ADP
ejpam-1203	284	2	theorem	theorem	NOUN
ejpam-1203	284	3	3	3	NUM
ejpam-1203	284	4	,	,	PUNCT
ejpam-1203	284	5	the	the	DET
ejpam-1203	284	6	converse	converse	NOUN
ejpam-1203	284	7	is	be	AUX
ejpam-1203	284	8	obvious	obvious	ADJ
ejpam-1203	284	9	.	.	PUNCT
ejpam-1203	285	1	theorem	theorem	NOUN
ejpam-1203	285	2	13	13	NUM
ejpam-1203	285	3	.	.	PUNCT
ejpam-1203	286	1	let	let	VERB
ejpam-1203	286	2	a	a	PRON
ejpam-1203	286	3	be	be	AUX
ejpam-1203	286	4	ρ	ρ	NOUN
ejpam-1203	286	5	-	-	ADJ
ejpam-1203	286	6	closed	closed	ADJ
ejpam-1203	286	7	in	in	ADP
ejpam-1203	286	8	(	(	PUNCT
ejpam-1203	286	9	x	x	INTJ
ejpam-1203	286	10	,	,	PUNCT
ejpam-1203	286	11	τ	τ	PROPN
ejpam-1203	286	12	)	)	PUNCT
ejpam-1203	286	13	then	then	ADV
ejpam-1203	286	14	a	a	PRON
ejpam-1203	286	15	is	be	AUX
ejpam-1203	286	16	preclosed	preclose	VERB
ejpam-1203	286	17	if	if	SCONJ
ejpam-1203	286	18	and	and	CCONJ
ejpam-1203	286	19	only	only	ADV
ejpam-1203	286	20	if	if	SCONJ
ejpam-1203	286	21	pcl(a)−a	pcl(a)−a	PROPN
ejpam-1203	286	22	is	be	AUX
ejpam-1203	286	23	g̃-closed	g̃-close	VERB
ejpam-1203	286	24	.	.	PUNCT
ejpam-1203	287	1	proof	proof	NOUN
ejpam-1203	287	2	.	.	PUNCT
ejpam-1203	288	1	necessity	necessity	NOUN
ejpam-1203	288	2	.	.	PUNCT
ejpam-1203	289	1	let	let	VERB
ejpam-1203	289	2	a	a	PRON
ejpam-1203	289	3	be	be	AUX
ejpam-1203	289	4	preclosed	preclose	VERB
ejpam-1203	289	5	.	.	PUNCT
ejpam-1203	290	1	then	then	ADV
ejpam-1203	290	2	pcl(a	pcl(a	X
ejpam-1203	290	3	)	)	PUNCT
ejpam-1203	290	4	=	=	NOUN
ejpam-1203	290	5	a.	a.	NOUN
ejpam-1203	290	6	hence	hence	ADV
ejpam-1203	290	7	pcl(a)−	pcl(a)−	VERB
ejpam-1203	290	8	a	a	PRON
ejpam-1203	290	9	=	=	X
ejpam-1203	290	10	{	{	PUNCT
ejpam-1203	290	11	;	;	PUNCT
ejpam-1203	290	12	}	}	PUNCT
ejpam-1203	290	13	which	which	PRON
ejpam-1203	290	14	is	be	AUX
ejpam-1203	290	15	g̃-closed	g̃-close	VERB
ejpam-1203	290	16	.	.	PUNCT
ejpam-1203	291	1	sufficiency	sufficiency	PROPN
ejpam-1203	291	2	.	.	PUNCT
ejpam-1203	292	1	suppose	suppose	VERB
ejpam-1203	292	2	pcl(a	pcl(a	X
ejpam-1203	292	3	)	)	PUNCT
ejpam-1203	292	4	−	−	NOUN
ejpam-1203	292	5	a	a	PRON
ejpam-1203	292	6	is	be	AUX
ejpam-1203	292	7	g̃-closed	g̃-close	VERB
ejpam-1203	292	8	.	.	PUNCT
ejpam-1203	293	1	since	since	SCONJ
ejpam-1203	293	2	a	a	PRON
ejpam-1203	293	3	is	be	AUX
ejpam-1203	293	4	ρ	ρ	NOUN
ejpam-1203	293	5	-	-	PUNCT
ejpam-1203	293	6	closed	closed	ADJ
ejpam-1203	293	7	and	and	CCONJ
ejpam-1203	293	8	by	by	ADP
ejpam-1203	293	9	theorem	theorem	NOUN
ejpam-1203	293	10	9	9	NUM
ejpam-1203	293	11	,	,	PUNCT
ejpam-1203	293	12	pcl(a)−	pcl(a)−	NOUN
ejpam-1203	293	13	a=	a=	PROPN
ejpam-1203	293	14	{	{	PUNCT
ejpam-1203	293	15	;	;	PUNCT
ejpam-1203	293	16	}	}	PUNCT
ejpam-1203	293	17	.	.	PUNCT
ejpam-1203	294	1	then	then	ADV
ejpam-1203	294	2	pcl(a	pcl(a	X
ejpam-1203	294	3	)	)	PUNCT
ejpam-1203	294	4	=	=	NOUN
ejpam-1203	295	1	a.	a.	NOUN
ejpam-1203	295	2	this	this	PRON
ejpam-1203	295	3	means	mean	VERB
ejpam-1203	295	4	that	that	SCONJ
ejpam-1203	295	5	a	a	PRON
ejpam-1203	295	6	is	be	AUX
ejpam-1203	295	7	preclosed	preclose	VERB
ejpam-1203	295	8	.	.	PUNCT
ejpam-1203	296	1	theorem	theorem	VERB
ejpam-1203	296	2	14	14	NUM
ejpam-1203	296	3	.	.	PUNCT
ejpam-1203	297	1	an	an	DET
ejpam-1203	297	2	open	open	ADJ
ejpam-1203	297	3	set	set	NOUN
ejpam-1203	297	4	a	a	PRON
ejpam-1203	297	5	of	of	ADP
ejpam-1203	297	6	(	(	PUNCT
ejpam-1203	297	7	x	x	PROPN
ejpam-1203	297	8	,	,	PUNCT
ejpam-1203	297	9	τ	τ	X
ejpam-1203	297	10	)	)	PUNCT
ejpam-1203	297	11	is	be	AUX
ejpam-1203	297	12	gp	gp	NOUN
ejpam-1203	297	13	-	-	ADJ
ejpam-1203	297	14	closed	closed	ADJ
ejpam-1203	297	15	if	if	SCONJ
ejpam-1203	297	16	and	and	CCONJ
ejpam-1203	297	17	only	only	ADV
ejpam-1203	297	18	if	if	SCONJ
ejpam-1203	297	19	a	a	PRON
ejpam-1203	297	20	is	be	AUX
ejpam-1203	297	21	ρ	ρ	NOUN
ejpam-1203	297	22	-	-	PUNCT
ejpam-1203	297	23	closed	closed	ADJ
ejpam-1203	297	24	.	.	PUNCT
ejpam-1203	298	1	proof	proof	NOUN
ejpam-1203	298	2	.	.	PUNCT
ejpam-1203	299	1	let	let	VERB
ejpam-1203	299	2	a	a	DET
ejpam-1203	299	3	be	be	AUX
ejpam-1203	299	4	an	an	DET
ejpam-1203	299	5	open	open	ADJ
ejpam-1203	299	6	and	and	CCONJ
ejpam-1203	299	7	gp	gp	NOUN
ejpam-1203	299	8	-	-	PUNCT
ejpam-1203	299	9	closed	closed	ADJ
ejpam-1203	299	10	set	set	NOUN
ejpam-1203	299	11	.	.	PUNCT
ejpam-1203	300	1	let	let	VERB
ejpam-1203	300	2	a	a	DET
ejpam-1203	300	3	⊆	⊆	NUM
ejpam-1203	300	4	u	u	NOUN
ejpam-1203	300	5	and	and	CCONJ
ejpam-1203	300	6	u	u	PRON
ejpam-1203	300	7	be	be	VERB
ejpam-1203	300	8	g̃-open	g̃-open	NOUN
ejpam-1203	300	9	in	in	ADP
ejpam-1203	300	10	x	x	X
ejpam-1203	300	11	.	.	PUNCT
ejpam-1203	301	1	since	since	SCONJ
ejpam-1203	301	2	a	a	PRON
ejpam-1203	301	3	is	be	AUX
ejpam-1203	301	4	open	open	ADJ
ejpam-1203	301	5	,	,	PUNCT
ejpam-1203	301	6	a	a	DET
ejpam-1203	301	7	=	=	SYM
ejpam-1203	301	8	int(a	int(a	NOUN
ejpam-1203	301	9	)	)	PUNCT
ejpam-1203	301	10	⊆	⊆	NUM
ejpam-1203	301	11	int(u	int(u	NUM
ejpam-1203	301	12	)	)	PUNCT
ejpam-1203	301	13	.	.	PUNCT
ejpam-1203	302	1	observe	observe	VERB
ejpam-1203	302	2	that	that	SCONJ
ejpam-1203	302	3	int(u	int(u	ADV
ejpam-1203	302	4	)	)	PUNCT
ejpam-1203	302	5	is	be	AUX
ejpam-1203	302	6	open	open	ADJ
ejpam-1203	302	7	and	and	CCONJ
ejpam-1203	302	8	thus	thus	ADV
ejpam-1203	302	9	a	a	PRON
ejpam-1203	302	10	is	be	AUX
ejpam-1203	302	11	gp	gp	NOUN
ejpam-1203	302	12	-	-	ADJ
ejpam-1203	302	13	closed	closed	ADJ
ejpam-1203	302	14	.	.	PUNCT
ejpam-1203	303	1	hence	hence	ADV
ejpam-1203	303	2	pcl(a	pcl(a	NUM
ejpam-1203	303	3	)	)	PUNCT
ejpam-1203	303	4	⊆	⊆	NUM
ejpam-1203	303	5	int(u	int(u	PROPN
ejpam-1203	303	6	)	)	PUNCT
ejpam-1203	303	7	and	and	CCONJ
ejpam-1203	303	8	a	a	PRON
ejpam-1203	303	9	is	be	AUX
ejpam-1203	303	10	an	an	DET
ejpam-1203	303	11	ρ	ρ	NOUN
ejpam-1203	303	12	-	-	PUNCT
ejpam-1203	303	13	closed	closed	ADJ
ejpam-1203	303	14	set	set	NOUN
ejpam-1203	303	15	.	.	PUNCT
ejpam-1203	304	1	conversely	conversely	ADV
ejpam-1203	304	2	,	,	PUNCT
ejpam-1203	304	3	by	by	ADP
ejpam-1203	304	4	theorem	theorem	NOUN
ejpam-1203	304	5	2	2	NUM
ejpam-1203	304	6	,	,	PUNCT
ejpam-1203	304	7	every	every	DET
ejpam-1203	304	8	ρ	ρ	NOUN
ejpam-1203	304	9	-	-	PUNCT
ejpam-1203	304	10	closed	closed	ADJ
ejpam-1203	304	11	set	set	NOUN
ejpam-1203	304	12	is	be	AUX
ejpam-1203	304	13	gp	gp	NOUN
ejpam-1203	304	14	-	-	ADJ
ejpam-1203	304	15	closed	closed	ADJ
ejpam-1203	304	16	.	.	PUNCT
ejpam-1203	305	1	theorem	theorem	VERB
ejpam-1203	305	2	15	15	NUM
ejpam-1203	305	3	.	.	PUNCT
ejpam-1203	306	1	if	if	SCONJ
ejpam-1203	306	2	a	a	DET
ejpam-1203	306	3	subset	subset	NOUN
ejpam-1203	306	4	a	a	PRON
ejpam-1203	306	5	of	of	ADP
ejpam-1203	306	6	(	(	PUNCT
ejpam-1203	306	7	x	x	PROPN
ejpam-1203	306	8	,	,	PUNCT
ejpam-1203	306	9	τ	τ	X
ejpam-1203	306	10	)	)	PUNCT
ejpam-1203	306	11	is	be	AUX
ejpam-1203	306	12	open	open	ADJ
ejpam-1203	306	13	and	and	CCONJ
ejpam-1203	306	14	regular	regular	ADJ
ejpam-1203	306	15	closed	close	VERB
ejpam-1203	306	16	then	then	ADV
ejpam-1203	306	17	a	a	PRON
ejpam-1203	306	18	is	be	AUX
ejpam-1203	306	19	ρ	ρ	NOUN
ejpam-1203	306	20	-	-	PUNCT
ejpam-1203	306	21	closed	closed	ADJ
ejpam-1203	306	22	.	.	PUNCT
ejpam-1203	307	1	proof	proof	NOUN
ejpam-1203	307	2	.	.	PUNCT
ejpam-1203	308	1	let	let	VERB
ejpam-1203	308	2	a	a	DET
ejpam-1203	308	3	be	be	AUX
ejpam-1203	308	4	an	an	DET
ejpam-1203	308	5	open	open	ADJ
ejpam-1203	308	6	and	and	CCONJ
ejpam-1203	308	7	regular	regular	ADJ
ejpam-1203	308	8	closed	closed	ADJ
ejpam-1203	308	9	set	set	NOUN
ejpam-1203	308	10	.	.	PUNCT
ejpam-1203	309	1	since	since	SCONJ
ejpam-1203	309	2	regular	regular	ADJ
ejpam-1203	309	3	closed	closed	ADJ
ejpam-1203	309	4	set	set	NOUN
ejpam-1203	309	5	is	be	AUX
ejpam-1203	309	6	preclosed	preclose	VERB
ejpam-1203	309	7	.	.	PUNCT
ejpam-1203	310	1	then	then	ADV
ejpam-1203	310	2	a	a	PRON
ejpam-1203	310	3	is	be	AUX
ejpam-1203	310	4	open	open	ADJ
ejpam-1203	310	5	and	and	CCONJ
ejpam-1203	310	6	preclosed	preclose	VERB
ejpam-1203	310	7	.	.	PUNCT
ejpam-1203	311	1	by	by	ADP
ejpam-1203	311	2	theorem	theorem	NOUN
ejpam-1203	311	3	1	1	NUM
ejpam-1203	311	4	,	,	PUNCT
ejpam-1203	311	5	a	a	PRON
ejpam-1203	311	6	is	be	AUX
ejpam-1203	311	7	ρ	ρ	NOUN
ejpam-1203	311	8	-	-	PUNCT
ejpam-1203	311	9	closed	closed	ADJ
ejpam-1203	311	10	.	.	PUNCT
ejpam-1203	312	1	lemma	lemma	PROPN
ejpam-1203	312	2	3	3	NUM
ejpam-1203	312	3	(	(	PUNCT
ejpam-1203	312	4	[	[	X
ejpam-1203	312	5	5	5	NUM
ejpam-1203	312	6	]	]	NUM
ejpam-1203	312	7	)	)	PUNCT
ejpam-1203	312	8	.	.	PUNCT
ejpam-1203	313	1	every	every	DET
ejpam-1203	313	2	g̃-closed	g̃-close	VERB
ejpam-1203	313	3	set	set	NOUN
ejpam-1203	313	4	is	be	AUX
ejpam-1203	313	5	preclosed	preclose	VERB
ejpam-1203	313	6	.	.	PUNCT
ejpam-1203	314	1	theorem	theorem	VERB
ejpam-1203	314	2	16	16	NUM
ejpam-1203	314	3	.	.	PUNCT
ejpam-1203	315	1	if	if	SCONJ
ejpam-1203	315	2	a	a	DET
ejpam-1203	315	3	subset	subset	NOUN
ejpam-1203	315	4	a	a	PRON
ejpam-1203	315	5	of	of	ADP
ejpam-1203	315	6	(	(	PUNCT
ejpam-1203	315	7	x	x	PROPN
ejpam-1203	315	8	,	,	PUNCT
ejpam-1203	315	9	τ	τ	X
ejpam-1203	315	10	)	)	PUNCT
ejpam-1203	315	11	is	be	AUX
ejpam-1203	315	12	open	open	ADJ
ejpam-1203	315	13	and	and	CCONJ
ejpam-1203	315	14	g̃-closed	g̃-close	VERB
ejpam-1203	315	15	,	,	PUNCT
ejpam-1203	315	16	then	then	ADV
ejpam-1203	315	17	a	a	DET
ejpam-1203	315	18	isρ	isρ	NOUN
ejpam-1203	315	19	-	-	PUNCT
ejpam-1203	315	20	closed	closed	ADJ
ejpam-1203	315	21	.	.	PUNCT
ejpam-1203	316	1	proof	proof	NOUN
ejpam-1203	316	2	.	.	PUNCT
ejpam-1203	317	1	let	let	VERB
ejpam-1203	317	2	a	a	PRON
ejpam-1203	317	3	be	be	AUX
ejpam-1203	317	4	open	open	ADJ
ejpam-1203	317	5	and	and	CCONJ
ejpam-1203	317	6	g̃-closed	g̃-closed	ADJ
ejpam-1203	317	7	.	.	PUNCT
ejpam-1203	318	1	then	then	ADV
ejpam-1203	318	2	by	by	ADP
ejpam-1203	318	3	lemma	lemma	PROPN
ejpam-1203	318	4	3	3	NUM
ejpam-1203	318	5	,	,	PUNCT
ejpam-1203	318	6	a	a	PRON
ejpam-1203	318	7	is	be	AUX
ejpam-1203	318	8	open	open	ADJ
ejpam-1203	318	9	and	and	CCONJ
ejpam-1203	318	10	preclosed	preclose	VERB
ejpam-1203	318	11	.	.	PUNCT
ejpam-1203	319	1	hence	hence	ADV
ejpam-1203	319	2	by	by	ADP
ejpam-1203	319	3	theorem	theorem	NOUN
ejpam-1203	319	4	1	1	NUM
ejpam-1203	319	5	,	,	PUNCT
ejpam-1203	319	6	a	a	PRON
ejpam-1203	319	7	is	be	AUX
ejpam-1203	319	8	ρ	ρ	NOUN
ejpam-1203	319	9	-	-	PUNCT
ejpam-1203	319	10	closed	closed	ADJ
ejpam-1203	319	11	.	.	PUNCT
ejpam-1203	320	1	theorem	theorem	VERB
ejpam-1203	320	2	17	17	NUM
ejpam-1203	320	3	.	.	PUNCT
ejpam-1203	321	1	in	in	ADP
ejpam-1203	321	2	a	a	DET
ejpam-1203	321	3	topological	topological	ADJ
ejpam-1203	321	4	space	space	NOUN
ejpam-1203	321	5	x	x	X
ejpam-1203	321	6	,	,	PUNCT
ejpam-1203	321	7	for	for	SCONJ
ejpam-1203	321	8	each	each	DET
ejpam-1203	321	9	x	x	SYM
ejpam-1203	321	10	∈	∈	PROPN
ejpam-1203	321	11	x	x	X
ejpam-1203	321	12	,	,	PUNCT
ejpam-1203	321	13	{	{	PUNCT
ejpam-1203	321	14	x	x	NOUN
ejpam-1203	321	15	}	}	PUNCT
ejpam-1203	321	16	is	be	AUX
ejpam-1203	321	17	g̃-closed	g̃-close	VERB
ejpam-1203	321	18	or	or	CCONJ
ejpam-1203	321	19	its	its	PRON
ejpam-1203	321	20	complement	complement	NOUN
ejpam-1203	321	21	x	x	NOUN
ejpam-1203	321	22	−{x	−{x	NOUN
ejpam-1203	321	23	}	}	PUNCT
ejpam-1203	321	24	isρ	isρ	NOUN
ejpam-1203	321	25	-	-	PUNCT
ejpam-1203	321	26	closed	closed	ADJ
ejpam-1203	321	27	in	in	ADP
ejpam-1203	321	28	(	(	PUNCT
ejpam-1203	321	29	x	x	INTJ
ejpam-1203	321	30	,	,	PUNCT
ejpam-1203	321	31	τ	τ	PROPN
ejpam-1203	321	32	)	)	PUNCT
ejpam-1203	321	33	.	.	PUNCT
ejpam-1203	322	1	proof	proof	NOUN
ejpam-1203	322	2	.	.	PUNCT
ejpam-1203	323	1	suppose	suppose	VERB
ejpam-1203	323	2	that	that	SCONJ
ejpam-1203	323	3	{	{	PUNCT
ejpam-1203	323	4	x	x	X
ejpam-1203	323	5	}	}	PUNCT
ejpam-1203	323	6	is	be	AUX
ejpam-1203	323	7	not	not	PART
ejpam-1203	323	8	g̃	g̃	PROPN
ejpam-1203	323	9	closed	close	VERB
ejpam-1203	323	10	in	in	ADP
ejpam-1203	323	11	(	(	PUNCT
ejpam-1203	323	12	x	x	INTJ
ejpam-1203	323	13	,	,	PUNCT
ejpam-1203	323	14	τ	τ	PROPN
ejpam-1203	323	15	)	)	PUNCT
ejpam-1203	323	16	.	.	PUNCT
ejpam-1203	324	1	then	then	ADV
ejpam-1203	324	2	x	x	X
ejpam-1203	324	3	−	−	PROPN
ejpam-1203	324	4	{	{	PUNCT
ejpam-1203	324	5	x	x	NOUN
ejpam-1203	324	6	}	}	PUNCT
ejpam-1203	324	7	is	be	AUX
ejpam-1203	324	8	not	not	PART
ejpam-1203	324	9	g̃-open	g̃-open	ADJ
ejpam-1203	324	10	and	and	CCONJ
ejpam-1203	325	1	the	the	DET
ejpam-1203	325	2	only	only	ADJ
ejpam-1203	325	3	g̃-open	g̃-open	NOUN
ejpam-1203	325	4	set	set	VERB
ejpam-1203	325	5	containing	contain	VERB
ejpam-1203	325	6	x	x	PART
ejpam-1203	325	7	−	−	PROPN
ejpam-1203	325	8	{	{	PUNCT
ejpam-1203	325	9	x	x	NOUN
ejpam-1203	325	10	}	}	PUNCT
ejpam-1203	325	11	is	be	AUX
ejpam-1203	325	12	x	x	X
ejpam-1203	325	13	.	.	PUNCT
ejpam-1203	326	1	therefore	therefore	ADV
ejpam-1203	326	2	pcl(x	pcl(x	PROPN
ejpam-1203	326	3	−	−	PROPN
ejpam-1203	326	4	{	{	PUNCT
ejpam-1203	326	5	x	x	NOUN
ejpam-1203	326	6	}	}	PUNCT
ejpam-1203	326	7	)	)	PUNCT
ejpam-1203	326	8	⊆	⊆	NUM
ejpam-1203	326	9	x	x	NOUN
ejpam-1203	326	10	and	and	CCONJ
ejpam-1203	326	11	int(x	int(x	NOUN
ejpam-1203	326	12	)	)	PUNCT
ejpam-1203	327	1	=	=	SYM
ejpam-1203	327	2	x	x	PROPN
ejpam-1203	327	3	and	and	CCONJ
ejpam-1203	327	4	pcl(x	pcl(x	PROPN
ejpam-1203	327	5	−	−	PROPN
ejpam-1203	327	6	{	{	PUNCT
ejpam-1203	327	7	x})⊆	x})⊆	PROPN
ejpam-1203	327	8	int(x	int(x	PROPN
ejpam-1203	327	9	)	)	PUNCT
ejpam-1203	327	10	.	.	PUNCT
ejpam-1203	328	1	hence	hence	ADV
ejpam-1203	328	2	x	x	X
ejpam-1203	328	3	−	−	PROPN
ejpam-1203	328	4	{	{	PUNCT
ejpam-1203	328	5	x	x	NOUN
ejpam-1203	328	6	}	}	PUNCT
ejpam-1203	328	7	is	be	AUX
ejpam-1203	328	8	ρ	ρ	NOUN
ejpam-1203	328	9	-	-	PUNCT
ejpam-1203	328	10	closed	closed	ADJ
ejpam-1203	328	11	in	in	ADP
ejpam-1203	328	12	(	(	PUNCT
ejpam-1203	328	13	x	x	INTJ
ejpam-1203	328	14	,	,	PUNCT
ejpam-1203	328	15	τ	τ	PROPN
ejpam-1203	328	16	)	)	PUNCT
ejpam-1203	328	17	.	.	PUNCT
ejpam-1203	329	1	definition	definition	NOUN
ejpam-1203	329	2	8	8	NUM
ejpam-1203	329	3	.	.	NOUN
ejpam-1203	329	4	1	1	NUM
ejpam-1203	329	5	.	.	PUNCT
ejpam-1203	330	1	the	the	DET
ejpam-1203	330	2	union	union	NOUN
ejpam-1203	330	3	of	of	ADP
ejpam-1203	330	4	all	all	DET
ejpam-1203	330	5	ρ	ρ	ADJ
ejpam-1203	330	6	-	-	ADJ
ejpam-1203	330	7	open	open	ADJ
ejpam-1203	330	8	sets	set	NOUN
ejpam-1203	330	9	,	,	PUNCT
ejpam-1203	330	10	each	each	PRON
ejpam-1203	330	11	contained	contain	VERB
ejpam-1203	330	12	in	in	ADP
ejpam-1203	330	13	a	a	DET
ejpam-1203	330	14	set	set	NOUN
ejpam-1203	330	15	a	a	PRON
ejpam-1203	330	16	in	in	ADP
ejpam-1203	330	17	a	a	DET
ejpam-1203	330	18	topological	topological	ADJ
ejpam-1203	330	19	space	space	NOUN
ejpam-1203	330	20	x	x	PRON
ejpam-1203	330	21	is	be	AUX
ejpam-1203	330	22	called	call	VERB
ejpam-1203	330	23	the	the	DET
ejpam-1203	330	24	ρ	ρ	NOUN
ejpam-1203	330	25	-	-	NOUN
ejpam-1203	330	26	interior	interior	NOUN
ejpam-1203	330	27	of	of	ADP
ejpam-1203	330	28	a	a	PRON
ejpam-1203	330	29	and	and	CCONJ
ejpam-1203	330	30	is	be	AUX
ejpam-1203	330	31	denoted	denote	VERB
ejpam-1203	330	32	by	by	ADP
ejpam-1203	330	33	ρ−	ρ−	PROPN
ejpam-1203	330	34	int(a	int(a	PROPN
ejpam-1203	330	35	)	)	PUNCT
ejpam-1203	330	36	.	.	PUNCT
ejpam-1203	331	1	2	2	X
ejpam-1203	331	2	.	.	X
ejpam-1203	331	3	the	the	DET
ejpam-1203	331	4	intersection	intersection	NOUN
ejpam-1203	331	5	of	of	ADP
ejpam-1203	331	6	all	all	DET
ejpam-1203	331	7	ρ	ρ	PROPN
ejpam-1203	331	8	-	-	PUNCT
ejpam-1203	331	9	closed	close	VERB
ejpam-1203	331	10	sets	set	NOUN
ejpam-1203	331	11	each	each	PRON
ejpam-1203	331	12	containing	contain	VERB
ejpam-1203	331	13	a	a	DET
ejpam-1203	331	14	set	set	NOUN
ejpam-1203	331	15	a	a	PRON
ejpam-1203	331	16	in	in	ADP
ejpam-1203	331	17	topological	topological	ADJ
ejpam-1203	331	18	space	space	NOUN
ejpam-1203	331	19	x	x	PUNCT
ejpam-1203	331	20	is	be	AUX
ejpam-1203	331	21	called	call	VERB
ejpam-1203	331	22	theρ	theρ	NOUN
ejpam-1203	331	23	-	-	PUNCT
ejpam-1203	331	24	closure	closure	NOUN
ejpam-1203	331	25	of	of	ADP
ejpam-1203	331	26	a	a	PRON
ejpam-1203	331	27	and	and	CCONJ
ejpam-1203	331	28	is	be	AUX
ejpam-1203	331	29	denoted	denote	VERB
ejpam-1203	331	30	byρ−	byρ−	PROPN
ejpam-1203	331	31	cl(a	cl(a	NUM
ejpam-1203	331	32	)	)	PUNCT
ejpam-1203	331	33	.	.	PUNCT
ejpam-1203	332	1	c.	c.	PROPN
ejpam-1203	332	2	devamanoharan	devamanoharan	PROPN
ejpam-1203	332	3	,	,	PUNCT
ejpam-1203	332	4	s.	s.	PROPN
ejpam-1203	332	5	missier	missier	PROPN
ejpam-1203	332	6	,	,	PUNCT
ejpam-1203	332	7	s.	s.	PROPN
ejpam-1203	332	8	jafari	jafari	PROPN
ejpam-1203	332	9	/	/	SYM
ejpam-1203	332	10	eur	eur	PROPN
ejpam-1203	332	11	.	.	PUNCT
ejpam-1203	333	1	j.	j.	PROPN
ejpam-1203	333	2	pure	pure	PROPN
ejpam-1203	333	3	appl	appl	PROPN
ejpam-1203	333	4	.	.	PROPN
ejpam-1203	333	5	math	math	PROPN
ejpam-1203	333	6	,	,	PUNCT
ejpam-1203	333	7	5	5	NUM
ejpam-1203	333	8	(	(	PUNCT
ejpam-1203	333	9	2012	2012	NUM
ejpam-1203	333	10	)	)	PUNCT
ejpam-1203	333	11	,	,	PUNCT
ejpam-1203	333	12	554	554	NUM
ejpam-1203	333	13	-	-	SYM
ejpam-1203	333	14	566	566	NUM
ejpam-1203	333	15	562	562	NUM
ejpam-1203	333	16	lemma	lemma	PROPN
ejpam-1203	333	17	4	4	NUM
ejpam-1203	333	18	.	.	PUNCT
ejpam-1203	334	1	if	if	SCONJ
ejpam-1203	334	2	a	a	DET
ejpam-1203	334	3	subset	subset	NOUN
ejpam-1203	334	4	a	a	PRON
ejpam-1203	334	5	of	of	ADP
ejpam-1203	334	6	(	(	PUNCT
ejpam-1203	334	7	x	x	PROPN
ejpam-1203	334	8	,	,	PUNCT
ejpam-1203	334	9	τ	τ	X
ejpam-1203	334	10	)	)	PUNCT
ejpam-1203	334	11	is	be	AUX
ejpam-1203	334	12	ρ	ρ	NOUN
ejpam-1203	334	13	-	-	PUNCT
ejpam-1203	334	14	closed	closed	ADJ
ejpam-1203	334	15	then	then	ADV
ejpam-1203	334	16	a=	a=	VERB
ejpam-1203	334	17	ρ	ρ	PROPN
ejpam-1203	334	18	−	−	NOUN
ejpam-1203	334	19	cl(a	cl(a	NUM
ejpam-1203	334	20	)	)	PUNCT
ejpam-1203	334	21	.	.	PUNCT
ejpam-1203	335	1	the	the	DET
ejpam-1203	335	2	converse	converse	NOUN
ejpam-1203	335	3	of	of	ADP
ejpam-1203	335	4	the	the	DET
ejpam-1203	335	5	above	above	ADJ
ejpam-1203	335	6	lemma	lemma	PROPN
ejpam-1203	335	7	need	need	AUX
ejpam-1203	335	8	not	not	PART
ejpam-1203	335	9	be	be	AUX
ejpam-1203	335	10	true	true	ADJ
ejpam-1203	335	11	as	as	SCONJ
ejpam-1203	335	12	it	it	PRON
ejpam-1203	335	13	is	be	AUX
ejpam-1203	335	14	seen	see	VERB
ejpam-1203	335	15	from	from	ADP
ejpam-1203	335	16	the	the	DET
ejpam-1203	335	17	following	follow	VERB
ejpam-1203	335	18	example	example	NOUN
ejpam-1203	335	19	.	.	PUNCT
ejpam-1203	336	1	example	example	NOUN
ejpam-1203	337	1	18	18	NUM
ejpam-1203	337	2	.	.	PUNCT
ejpam-1203	338	1	let	let	VERB
ejpam-1203	338	2	x	x	PUNCT
ejpam-1203	338	3	=	=	PRON
ejpam-1203	338	4	{	{	PUNCT
ejpam-1203	338	5	a	a	PRON
ejpam-1203	338	6	,	,	PUNCT
ejpam-1203	338	7	b	b	NOUN
ejpam-1203	338	8	,	,	PUNCT
ejpam-1203	338	9	c	c	NOUN
ejpam-1203	338	10	}	}	PUNCT
ejpam-1203	338	11	and	and	CCONJ
ejpam-1203	338	12	τ	τ	PROPN
ejpam-1203	338	13	=	=	PUNCT
ejpam-1203	338	14	{	{	PUNCT
ejpam-1203	338	15	φ	φ	PROPN
ejpam-1203	338	16	,	,	PUNCT
ejpam-1203	338	17	{	{	PUNCT
ejpam-1203	338	18	c	c	NOUN
ejpam-1203	338	19	}	}	PUNCT
ejpam-1203	338	20	,	,	PUNCT
ejpam-1203	338	21	x	x	PUNCT
ejpam-1203	338	22	}	}	PUNCT
ejpam-1203	338	23	.	.	PUNCT
ejpam-1203	339	1	if	if	SCONJ
ejpam-1203	339	2	we	we	PRON
ejpam-1203	339	3	consider	consider	VERB
ejpam-1203	339	4	a=	a=	ADJ
ejpam-1203	339	5	{	{	PUNCT
ejpam-1203	339	6	c	c	NOUN
ejpam-1203	339	7	}	}	PUNCT
ejpam-1203	339	8	then	then	ADV
ejpam-1203	339	9	a=	a=	VERB
ejpam-1203	339	10	ρ	ρ	PROPN
ejpam-1203	339	11	−	−	NOUN
ejpam-1203	339	12	cl(a	cl(a	NUM
ejpam-1203	339	13	)	)	PUNCT
ejpam-1203	339	14	but	but	CCONJ
ejpam-1203	339	15	a	a	PRON
ejpam-1203	339	16	is	be	AUX
ejpam-1203	339	17	not	not	PART
ejpam-1203	339	18	ρ	ρ	NOUN
ejpam-1203	339	19	-	-	PUNCT
ejpam-1203	339	20	closed	closed	ADJ
ejpam-1203	339	21	in	in	ADP
ejpam-1203	339	22	(	(	PUNCT
ejpam-1203	339	23	x	x	INTJ
ejpam-1203	339	24	,	,	PUNCT
ejpam-1203	339	25	τ	τ	PROPN
ejpam-1203	339	26	)	)	PUNCT
ejpam-1203	339	27	.	.	PUNCT
ejpam-1203	340	1	definition	definition	NOUN
ejpam-1203	340	2	9	9	NUM
ejpam-1203	340	3	.	.	NOUN
ejpam-1203	340	4	1	1	NUM
ejpam-1203	340	5	.	.	X
ejpam-1203	341	1	let	let	AUX
ejpam-1203	341	2	(	(	PUNCT
ejpam-1203	341	3	x	x	X
ejpam-1203	341	4	,	,	PUNCT
ejpam-1203	341	5	τ	τ	X
ejpam-1203	341	6	)	)	PUNCT
ejpam-1203	341	7	be	be	VERB
ejpam-1203	341	8	a	a	DET
ejpam-1203	341	9	topological	topological	ADJ
ejpam-1203	341	10	space	space	NOUN
ejpam-1203	341	11	,	,	PUNCT
ejpam-1203	341	12	a⊆	a⊆	VERB
ejpam-1203	341	13	x	x	PUNCT
ejpam-1203	341	14	and	and	CCONJ
ejpam-1203	341	15	x	x	SYM
ejpam-1203	341	16	∈	∈	NOUN
ejpam-1203	341	17	x	x	X
ejpam-1203	341	18	.	.	PUNCT
ejpam-1203	342	1	then	then	ADV
ejpam-1203	342	2	x	x	X
ejpam-1203	342	3	is	be	AUX
ejpam-1203	342	4	said	say	VERB
ejpam-1203	342	5	to	to	PART
ejpam-1203	342	6	be	be	AUX
ejpam-1203	342	7	a	a	DET
ejpam-1203	342	8	pre	pre	ADJ
ejpam-1203	342	9	-	-	ADJ
ejpam-1203	342	10	limit	limit	ADJ
ejpam-1203	342	11	point	point	NOUN
ejpam-1203	342	12	of	of	ADP
ejpam-1203	342	13	a	a	PRON
ejpam-1203	342	14	if	if	SCONJ
ejpam-1203	342	15	every	every	DET
ejpam-1203	342	16	preopen	preopen	ADJ
ejpam-1203	342	17	set	set	NOUN
ejpam-1203	342	18	containing	contain	VERB
ejpam-1203	342	19	x	x	AUX
ejpam-1203	342	20	contains	contain	VERB
ejpam-1203	342	21	a	a	DET
ejpam-1203	342	22	point	point	NOUN
ejpam-1203	342	23	of	of	ADP
ejpam-1203	342	24	a	a	DET
ejpam-1203	342	25	different	different	ADJ
ejpam-1203	342	26	from	from	ADP
ejpam-1203	342	27	x.	x.	NOUN
ejpam-1203	342	28	2	2	NUM
ejpam-1203	342	29	.	.	PUNCT
ejpam-1203	343	1	let	let	AUX
ejpam-1203	343	2	(	(	PUNCT
ejpam-1203	343	3	x	x	X
ejpam-1203	343	4	,	,	PUNCT
ejpam-1203	343	5	τ	τ	X
ejpam-1203	343	6	)	)	PUNCT
ejpam-1203	343	7	be	be	VERB
ejpam-1203	343	8	a	a	DET
ejpam-1203	343	9	topological	topological	ADJ
ejpam-1203	343	10	space	space	NOUN
ejpam-1203	343	11	and	and	CCONJ
ejpam-1203	343	12	a⊆	a⊆	PROPN
ejpam-1203	343	13	x	x	X
ejpam-1203	343	14	.	.	PUNCT
ejpam-1203	344	1	the	the	DET
ejpam-1203	344	2	set	set	NOUN
ejpam-1203	344	3	of	of	ADP
ejpam-1203	344	4	all	all	DET
ejpam-1203	344	5	prelimit	prelimit	NOUN
ejpam-1203	344	6	points	point	NOUN
ejpam-1203	344	7	of	of	ADP
ejpam-1203	344	8	a	a	PRON
ejpam-1203	344	9	is	be	AUX
ejpam-1203	344	10	said	say	VERB
ejpam-1203	344	11	to	to	PART
ejpam-1203	344	12	be	be	AUX
ejpam-1203	344	13	a	a	DET
ejpam-1203	344	14	pre	pre	ADJ
ejpam-1203	344	15	-	-	ADJ
ejpam-1203	344	16	derived	derived	ADJ
ejpam-1203	344	17	set	set	NOUN
ejpam-1203	344	18	of	of	ADP
ejpam-1203	344	19	a	a	PRON
ejpam-1203	344	20	and	and	CCONJ
ejpam-1203	344	21	is	be	AUX
ejpam-1203	344	22	denoted	denote	VERB
ejpam-1203	344	23	by	by	ADP
ejpam-1203	344	24	dp[a	dp[a	PROPN
ejpam-1203	344	25	]	]	PUNCT
ejpam-1203	344	26	.	.	PUNCT
ejpam-1203	345	1	theorem	theorem	VERB
ejpam-1203	345	2	18	18	NUM
ejpam-1203	345	3	.	.	PUNCT
ejpam-1203	346	1	if	if	SCONJ
ejpam-1203	346	2	d[a]⊆	d[a]⊆	PROPN
ejpam-1203	346	3	dp[a	dp[a	PROPN
ejpam-1203	346	4	]	]	PUNCT
ejpam-1203	346	5	for	for	ADP
ejpam-1203	346	6	each	each	PRON
ejpam-1203	346	7	subset	subset	VERB
ejpam-1203	346	8	a	a	PRON
ejpam-1203	346	9	of	of	ADP
ejpam-1203	346	10	a	a	DET
ejpam-1203	346	11	space	space	NOUN
ejpam-1203	346	12	(	(	PUNCT
ejpam-1203	346	13	x	x	X
ejpam-1203	346	14	,	,	PUNCT
ejpam-1203	346	15	τ	τ	PROPN
ejpam-1203	346	16	)	)	PUNCT
ejpam-1203	346	17	,	,	PUNCT
ejpam-1203	346	18	then	then	ADV
ejpam-1203	346	19	the	the	DET
ejpam-1203	346	20	union	union	NOUN
ejpam-1203	346	21	of	of	ADP
ejpam-1203	346	22	two	two	NUM
ejpam-1203	346	23	ρ	ρ	ADJ
ejpam-1203	346	24	-	-	PUNCT
ejpam-1203	346	25	closed	closed	ADJ
ejpam-1203	346	26	sets	set	NOUN
ejpam-1203	346	27	is	be	AUX
ejpam-1203	346	28	ρ	ρ	NOUN
ejpam-1203	346	29	-	-	PUNCT
ejpam-1203	346	30	closed	closed	ADJ
ejpam-1203	346	31	.	.	PUNCT
ejpam-1203	347	1	proof	proof	NOUN
ejpam-1203	347	2	.	.	PUNCT
ejpam-1203	348	1	let	let	VERB
ejpam-1203	348	2	a	a	PRON
ejpam-1203	348	3	and	and	CCONJ
ejpam-1203	348	4	b	b	NOUN
ejpam-1203	348	5	be	be	AUX
ejpam-1203	348	6	ρ	ρ	VERB
ejpam-1203	348	7	-	-	PUNCT
ejpam-1203	348	8	closed	closed	ADJ
ejpam-1203	348	9	subsets	subset	NOUN
ejpam-1203	348	10	of	of	ADP
ejpam-1203	348	11	x	x	PUNCT
ejpam-1203	348	12	and	and	CCONJ
ejpam-1203	348	13	u	u	NOUN
ejpam-1203	348	14	be	be	VERB
ejpam-1203	348	15	a	a	DET
ejpam-1203	348	16	g̃-open	g̃-open	NOUN
ejpam-1203	348	17	set	set	VERB
ejpam-1203	349	1	such	such	DET
ejpam-1203	349	2	that	that	SCONJ
ejpam-1203	349	3	a∪	a∪	PROPN
ejpam-1203	349	4	b	b	NOUN
ejpam-1203	349	5	⊆	⊆	NUM
ejpam-1203	349	6	u	u	NOUN
ejpam-1203	349	7	then	then	ADV
ejpam-1203	349	8	pcl(a	pcl(a	PROPN
ejpam-1203	349	9	)	)	PUNCT
ejpam-1203	349	10	⊆	⊆	NUM
ejpam-1203	349	11	int(u	int(u	PROPN
ejpam-1203	349	12	)	)	PUNCT
ejpam-1203	349	13	and	and	CCONJ
ejpam-1203	349	14	pcl(b	pcl(b	PROPN
ejpam-1203	349	15	)	)	PUNCT
ejpam-1203	349	16	⊆	⊆	NUM
ejpam-1203	349	17	int(u	int(u	NUM
ejpam-1203	349	18	)	)	PUNCT
ejpam-1203	349	19	.	.	PUNCT
ejpam-1203	350	1	for	for	ADP
ejpam-1203	350	2	each	each	DET
ejpam-1203	350	3	subset	subset	VERB
ejpam-1203	350	4	a	a	PRON
ejpam-1203	350	5	of	of	ADP
ejpam-1203	350	6	x	x	PRON
ejpam-1203	350	7	we	we	PRON
ejpam-1203	350	8	havedp[a	havedp[a	VERB
ejpam-1203	350	9	]	]	PUNCT
ejpam-1203	350	10	⊆	⊆	NUM
ejpam-1203	350	11	d[a	d[a	PROPN
ejpam-1203	350	12	]	]	PUNCT
ejpam-1203	350	13	.	.	PUNCT
ejpam-1203	351	1	thus	thus	ADV
ejpam-1203	351	2	cl(a	cl(a	NUM
ejpam-1203	351	3	)	)	PUNCT
ejpam-1203	351	4	=	=	SYM
ejpam-1203	351	5	pcl(a	pcl(a	PROPN
ejpam-1203	351	6	)	)	PUNCT
ejpam-1203	351	7	and	and	CCONJ
ejpam-1203	351	8	cl(b	cl(b	NOUN
ejpam-1203	351	9	)	)	PUNCT
ejpam-1203	351	10	=	=	SYM
ejpam-1203	351	11	pcl(b	pcl(b	PROPN
ejpam-1203	351	12	)	)	PUNCT
ejpam-1203	351	13	.	.	PUNCT
ejpam-1203	352	1	therefore	therefore	ADV
ejpam-1203	352	2	cl(a	cl(a	X
ejpam-1203	352	3	∪	∪	X
ejpam-1203	352	4	b	b	NOUN
ejpam-1203	352	5	)	)	PUNCT
ejpam-1203	352	6	=	=	SYM
ejpam-1203	352	7	cl(a	cl(a	X
ejpam-1203	352	8	)	)	PUNCT
ejpam-1203	352	9	∪	∪	ADJ
ejpam-1203	352	10	cl(b	cl(b	NOUN
ejpam-1203	352	11	)	)	PUNCT
ejpam-1203	352	12	=	=	SYM
ejpam-1203	352	13	pcl(a	pcl(a	PROPN
ejpam-1203	352	14	)	)	PUNCT
ejpam-1203	352	15	∪	∪	NOUN
ejpam-1203	352	16	pcl(b	pcl(b	PROPN
ejpam-1203	352	17	)	)	PUNCT
ejpam-1203	352	18	⊆	⊆	NUM
ejpam-1203	352	19	int(u	int(u	NUM
ejpam-1203	352	20	)	)	PUNCT
ejpam-1203	352	21	.	.	PUNCT
ejpam-1203	353	1	but	but	CCONJ
ejpam-1203	353	2	pcl(a	pcl(a	NUM
ejpam-1203	353	3	∪	∪	X
ejpam-1203	353	4	b	b	NOUN
ejpam-1203	353	5	)	)	PUNCT
ejpam-1203	353	6	⊆	⊆	NUM
ejpam-1203	353	7	cl(a	cl(a	X
ejpam-1203	353	8	∪	∪	X
ejpam-1203	353	9	b	b	NOUN
ejpam-1203	353	10	)	)	PUNCT
ejpam-1203	353	11	.	.	PUNCT
ejpam-1203	354	1	so	so	ADV
ejpam-1203	354	2	pcl(a∪	pcl(a∪	PROPN
ejpam-1203	354	3	b	b	X
ejpam-1203	354	4	)	)	PUNCT
ejpam-1203	354	5	⊆	⊆	NUM
ejpam-1203	354	6	int(u	int(u	PROPN
ejpam-1203	354	7	)	)	PUNCT
ejpam-1203	354	8	and	and	CCONJ
ejpam-1203	354	9	hence	hence	ADV
ejpam-1203	354	10	a∪	a∪	PROPN
ejpam-1203	355	1	b	b	NOUN
ejpam-1203	355	2	is	be	AUX
ejpam-1203	355	3	ρ	ρ	NOUN
ejpam-1203	355	4	-	-	PUNCT
ejpam-1203	355	5	closed	closed	ADJ
ejpam-1203	355	6	.	.	PUNCT
ejpam-1203	356	1	theorem	theorem	NOUN
ejpam-1203	356	2	19	19	NUM
ejpam-1203	356	3	.	.	PUNCT
ejpam-1203	357	1	a	a	DET
ejpam-1203	357	2	subset	subset	NOUN
ejpam-1203	357	3	a	a	PRON
ejpam-1203	357	4	of	of	ADP
ejpam-1203	357	5	(	(	PUNCT
ejpam-1203	357	6	x	x	PROPN
ejpam-1203	357	7	,	,	PUNCT
ejpam-1203	357	8	τ	τ	X
ejpam-1203	357	9	)	)	PUNCT
ejpam-1203	357	10	is	be	AUX
ejpam-1203	357	11	both	both	CCONJ
ejpam-1203	357	12	open	open	ADJ
ejpam-1203	357	13	and	and	CCONJ
ejpam-1203	357	14	ρ	ρ	VERB
ejpam-1203	357	15	-	-	PUNCT
ejpam-1203	357	16	closed	closed	ADJ
ejpam-1203	357	17	,	,	PUNCT
ejpam-1203	357	18	then	then	ADV
ejpam-1203	357	19	a	a	PRON
ejpam-1203	357	20	is	be	AUX
ejpam-1203	357	21	regular	regular	ADJ
ejpam-1203	357	22	open	open	ADJ
ejpam-1203	357	23	.	.	PUNCT
ejpam-1203	358	1	proof	proof	NOUN
ejpam-1203	358	2	.	.	PUNCT
ejpam-1203	359	1	suppose	suppose	VERB
ejpam-1203	359	2	a	a	PRON
ejpam-1203	359	3	is	be	AUX
ejpam-1203	359	4	open	open	ADJ
ejpam-1203	359	5	and	and	CCONJ
ejpam-1203	359	6	ρ	ρ	VERB
ejpam-1203	359	7	-	-	PUNCT
ejpam-1203	359	8	closed	closed	ADJ
ejpam-1203	359	9	.	.	PUNCT
ejpam-1203	360	1	then	then	ADV
ejpam-1203	360	2	a	a	PRON
ejpam-1203	360	3	is	be	AUX
ejpam-1203	360	4	g̃-open	g̃-open	NOUN
ejpam-1203	360	5	and	and	CCONJ
ejpam-1203	360	6	ρ	ρ	NOUN
ejpam-1203	360	7	-	-	PUNCT
ejpam-1203	360	8	closed	closed	ADJ
ejpam-1203	360	9	.	.	PUNCT
ejpam-1203	361	1	by	by	ADP
ejpam-1203	361	2	theorem	theorem	NOUN
ejpam-1203	361	3	16	16	NUM
ejpam-1203	361	4	,	,	PUNCT
ejpam-1203	361	5	a	a	PRON
ejpam-1203	361	6	is	be	AUX
ejpam-1203	361	7	preclosed	preclose	VERB
ejpam-1203	361	8	.	.	PUNCT
ejpam-1203	362	1	hence	hence	ADV
ejpam-1203	362	2	pcl(a	pcl(a	NUM
ejpam-1203	362	3	)	)	PUNCT
ejpam-1203	362	4	=	=	SYM
ejpam-1203	363	1	a.	a.	NOUN
ejpam-1203	363	2	since	since	SCONJ
ejpam-1203	363	3	a	a	PRON
ejpam-1203	363	4	is	be	AUX
ejpam-1203	363	5	open	open	ADJ
ejpam-1203	363	6	,	,	PUNCT
ejpam-1203	363	7	cl(a	cl(a	NUM
ejpam-1203	363	8	)	)	PUNCT
ejpam-1203	363	9	=	=	SYM
ejpam-1203	363	10	a.	a.	NOUN
ejpam-1203	363	11	therefore	therefore	ADV
ejpam-1203	363	12	int(a	int(a	PROPN
ejpam-1203	363	13	)	)	PUNCT
ejpam-1203	363	14	=	=	SYM
ejpam-1203	363	15	int(cl(a	int(cl(a	PROPN
ejpam-1203	363	16	)	)	PUNCT
ejpam-1203	363	17	)	)	PUNCT
ejpam-1203	363	18	implies	imply	VERB
ejpam-1203	363	19	a=	a=	ADJ
ejpam-1203	363	20	int(cl(a	int(cl(a	PROPN
ejpam-1203	363	21	)	)	PUNCT
ejpam-1203	363	22	)	)	PUNCT
ejpam-1203	363	23	and	and	CCONJ
ejpam-1203	363	24	hence	hence	ADV
ejpam-1203	363	25	a	a	PRON
ejpam-1203	363	26	is	be	AUX
ejpam-1203	363	27	regular	regular	ADJ
ejpam-1203	363	28	open	open	ADJ
ejpam-1203	363	29	.	.	PUNCT
ejpam-1203	364	1	the	the	DET
ejpam-1203	364	2	converse	converse	NOUN
ejpam-1203	364	3	of	of	ADP
ejpam-1203	364	4	the	the	DET
ejpam-1203	364	5	above	above	ADJ
ejpam-1203	364	6	theorem	theorem	NOUN
ejpam-1203	364	7	need	need	AUX
ejpam-1203	364	8	not	not	PART
ejpam-1203	364	9	be	be	AUX
ejpam-1203	364	10	true	true	ADJ
ejpam-1203	364	11	as	as	SCONJ
ejpam-1203	364	12	it	it	PRON
ejpam-1203	364	13	is	be	AUX
ejpam-1203	364	14	seen	see	VERB
ejpam-1203	364	15	from	from	ADP
ejpam-1203	364	16	the	the	DET
ejpam-1203	364	17	following	follow	VERB
ejpam-1203	364	18	example	example	NOUN
ejpam-1203	364	19	.	.	PUNCT
ejpam-1203	365	1	example	example	NOUN
ejpam-1203	365	2	19	19	NUM
ejpam-1203	365	3	.	.	PUNCT
ejpam-1203	366	1	as	as	ADP
ejpam-1203	366	2	in	in	ADP
ejpam-1203	366	3	example	example	NOUN
ejpam-1203	366	4	8(1	8(1	NOUN
ejpam-1203	366	5	)	)	PUNCT
ejpam-1203	366	6	,	,	PUNCT
ejpam-1203	366	7	the	the	DET
ejpam-1203	366	8	set	set	NOUN
ejpam-1203	366	9	a=	a=	NOUN
ejpam-1203	366	10	{	{	PUNCT
ejpam-1203	366	11	a	a	PRON
ejpam-1203	366	12	}	}	PUNCT
ejpam-1203	366	13	is	be	AUX
ejpam-1203	366	14	regular	regular	ADJ
ejpam-1203	366	15	open	open	ADJ
ejpam-1203	366	16	but	but	CCONJ
ejpam-1203	366	17	not	not	PART
ejpam-1203	366	18	ρ	ρ	NOUN
ejpam-1203	366	19	-	-	PUNCT
ejpam-1203	366	20	closed	closed	ADJ
ejpam-1203	366	21	in	in	ADP
ejpam-1203	366	22	(	(	PUNCT
ejpam-1203	366	23	x	x	INTJ
ejpam-1203	366	24	,	,	PUNCT
ejpam-1203	366	25	τ	τ	PROPN
ejpam-1203	366	26	)	)	PUNCT
ejpam-1203	366	27	.	.	PUNCT
ejpam-1203	367	1	it	it	PRON
ejpam-1203	367	2	should	should	AUX
ejpam-1203	367	3	be	be	AUX
ejpam-1203	367	4	noticed	notice	VERB
ejpam-1203	367	5	that	that	SCONJ
ejpam-1203	367	6	in	in	ADP
ejpam-1203	367	7	a	a	DET
ejpam-1203	367	8	locally	locally	ADV
ejpam-1203	367	9	indiscrete	indiscrete	ADJ
ejpam-1203	367	10	space	space	NOUN
ejpam-1203	367	11	openness	openness	NOUN
ejpam-1203	367	12	andρ	andρ	NOUN
ejpam-1203	367	13	-	-	PUNCT
ejpam-1203	367	14	closedness	closedness	NOUN
ejpam-1203	367	15	are	be	AUX
ejpam-1203	367	16	equivalent	equivalent	ADJ
ejpam-1203	367	17	.	.	PUNCT
ejpam-1203	368	1	moreover	moreover	ADV
ejpam-1203	368	2	,	,	PUNCT
ejpam-1203	368	3	it	it	PRON
ejpam-1203	368	4	is	be	AUX
ejpam-1203	368	5	well	well	ADV
ejpam-1203	368	6	-	-	PUNCT
ejpam-1203	368	7	known	know	VERB
ejpam-1203	368	8	that	that	SCONJ
ejpam-1203	368	9	if	if	SCONJ
ejpam-1203	368	10	(	(	PUNCT
ejpam-1203	368	11	x	x	X
ejpam-1203	368	12	,	,	PUNCT
ejpam-1203	368	13	τ	τ	X
ejpam-1203	368	14	)	)	PUNCT
ejpam-1203	368	15	is	be	AUX
ejpam-1203	368	16	locally	locally	ADV
ejpam-1203	368	17	indiscrete	indiscrete	ADJ
ejpam-1203	368	18	and	and	CCONJ
ejpam-1203	368	19	t0	t0	NOUN
ejpam-1203	368	20	,	,	PUNCT
ejpam-1203	368	21	then	then	ADV
ejpam-1203	368	22	(	(	PUNCT
ejpam-1203	368	23	x	x	X
ejpam-1203	368	24	,	,	PUNCT
ejpam-1203	368	25	τ	τ	X
ejpam-1203	368	26	)	)	PUNCT
ejpam-1203	368	27	must	must	AUX
ejpam-1203	368	28	be	be	AUX
ejpam-1203	368	29	discrete	discrete	ADJ
ejpam-1203	368	30	.	.	PUNCT
ejpam-1203	369	1	definition	definition	NOUN
ejpam-1203	369	2	10	10	NUM
ejpam-1203	369	3	.	.	PUNCT
ejpam-1203	370	1	a	a	DET
ejpam-1203	370	2	space	space	NOUN
ejpam-1203	370	3	x	x	PUNCT
ejpam-1203	370	4	is	be	AUX
ejpam-1203	370	5	called	call	VERB
ejpam-1203	370	6	a	a	DET
ejpam-1203	370	7	pg̃-space	pg̃-space	NOUN
ejpam-1203	370	8	if	if	SCONJ
ejpam-1203	370	9	the	the	DET
ejpam-1203	370	10	intersection	intersection	NOUN
ejpam-1203	370	11	of	of	ADP
ejpam-1203	370	12	a	a	DET
ejpam-1203	370	13	preclosed	preclose	VERB
ejpam-1203	370	14	set	set	NOUN
ejpam-1203	370	15	with	with	ADP
ejpam-1203	370	16	a	a	DET
ejpam-1203	370	17	g̃-closed	g̃-close	VERB
ejpam-1203	370	18	set	set	NOUN
ejpam-1203	370	19	is	be	AUX
ejpam-1203	370	20	g̃-closed	g̃-close	VERB
ejpam-1203	370	21	.	.	PUNCT
ejpam-1203	370	22	example	example	NOUN
ejpam-1203	371	1	20	20	NUM
ejpam-1203	371	2	.	.	PUNCT
ejpam-1203	372	1	let	let	VERB
ejpam-1203	372	2	x	x	PUNCT
ejpam-1203	372	3	=	=	PRON
ejpam-1203	372	4	{	{	PUNCT
ejpam-1203	372	5	a	a	PRON
ejpam-1203	372	6	,	,	PUNCT
ejpam-1203	372	7	b	b	NOUN
ejpam-1203	372	8	,	,	PUNCT
ejpam-1203	372	9	c	c	NOUN
ejpam-1203	372	10	,	,	PUNCT
ejpam-1203	372	11	d	d	NOUN
ejpam-1203	372	12	}	}	PUNCT
ejpam-1203	372	13	and	and	CCONJ
ejpam-1203	372	14	τ	τ	PROPN
ejpam-1203	372	15	=	=	PUNCT
ejpam-1203	372	16	{	{	PUNCT
ejpam-1203	372	17	φ	φ	PROPN
ejpam-1203	372	18	,	,	PUNCT
ejpam-1203	372	19	{	{	PUNCT
ejpam-1203	372	20	a	a	X
ejpam-1203	372	21	}	}	PUNCT
ejpam-1203	372	22	,	,	PUNCT
ejpam-1203	372	23	{	{	PUNCT
ejpam-1203	372	24	b	b	NOUN
ejpam-1203	372	25	}	}	PUNCT
ejpam-1203	372	26	,	,	PUNCT
ejpam-1203	372	27	{	{	PUNCT
ejpam-1203	372	28	a	a	DET
ejpam-1203	372	29	,	,	PUNCT
ejpam-1203	372	30	b	b	NOUN
ejpam-1203	372	31	}	}	PUNCT
ejpam-1203	372	32	,	,	PUNCT
ejpam-1203	372	33	{	{	PUNCT
ejpam-1203	372	34	a	a	DET
ejpam-1203	372	35	,	,	PUNCT
ejpam-1203	372	36	b	b	NOUN
ejpam-1203	372	37	,	,	PUNCT
ejpam-1203	372	38	c	c	NOUN
ejpam-1203	372	39	}	}	PUNCT
ejpam-1203	372	40	,	,	PUNCT
ejpam-1203	372	41	{	{	PUNCT
ejpam-1203	372	42	a	a	PRON
ejpam-1203	372	43	,	,	PUNCT
ejpam-1203	372	44	b	b	NOUN
ejpam-1203	372	45	,	,	PUNCT
ejpam-1203	372	46	d	d	NOUN
ejpam-1203	372	47	}	}	PUNCT
ejpam-1203	372	48	,	,	PUNCT
ejpam-1203	372	49	x	x	SYM
ejpam-1203	372	50	}	}	PUNCT
ejpam-1203	372	51	.	.	PUNCT
ejpam-1203	373	1	then	then	ADV
ejpam-1203	373	2	(	(	PUNCT
ejpam-1203	373	3	x	x	X
ejpam-1203	373	4	,	,	PUNCT
ejpam-1203	373	5	τ	τ	X
ejpam-1203	373	6	)	)	PUNCT
ejpam-1203	373	7	is	be	AUX
ejpam-1203	373	8	a	a	DET
ejpam-1203	373	9	pg̃-space	pg̃-space	NOUN
ejpam-1203	373	10	.	.	PUNCT
ejpam-1203	374	1	but	but	CCONJ
ejpam-1203	374	2	,	,	PUNCT
ejpam-1203	374	3	let	let	VERB
ejpam-1203	374	4	τ	τ	PROPN
ejpam-1203	374	5	=	=	PUNCT
ejpam-1203	374	6	{	{	PUNCT
ejpam-1203	374	7	φ	φ	PROPN
ejpam-1203	374	8	,	,	PUNCT
ejpam-1203	374	9	{	{	PUNCT
ejpam-1203	374	10	a	a	X
ejpam-1203	374	11	}	}	PUNCT
ejpam-1203	374	12	,	,	PUNCT
ejpam-1203	374	13	{	{	PUNCT
ejpam-1203	374	14	a	a	DET
ejpam-1203	374	15	,	,	PUNCT
ejpam-1203	374	16	b	b	NOUN
ejpam-1203	374	17	}	}	PUNCT
ejpam-1203	374	18	,	,	PUNCT
ejpam-1203	374	19	{	{	PUNCT
ejpam-1203	374	20	a	a	DET
ejpam-1203	374	21	,	,	PUNCT
ejpam-1203	374	22	b	b	NOUN
ejpam-1203	374	23	,	,	PUNCT
ejpam-1203	374	24	c	c	NOUN
ejpam-1203	374	25	}	}	PUNCT
ejpam-1203	374	26	,	,	PUNCT
ejpam-1203	374	27	x	x	SYM
ejpam-1203	374	28	}	}	PUNCT
ejpam-1203	374	29	then	then	ADV
ejpam-1203	374	30	(	(	PUNCT
ejpam-1203	374	31	x	x	X
ejpam-1203	374	32	,	,	PUNCT
ejpam-1203	374	33	τ	τ	X
ejpam-1203	374	34	)	)	PUNCT
ejpam-1203	374	35	is	be	AUX
ejpam-1203	374	36	not	not	PART
ejpam-1203	374	37	a	a	DET
ejpam-1203	374	38	pg̃-space	pg̃-space	NOUN
ejpam-1203	374	39	.	.	PUNCT
ejpam-1203	375	1	theorem	theorem	NOUN
ejpam-1203	375	2	20	20	NUM
ejpam-1203	375	3	.	.	PUNCT
ejpam-1203	376	1	for	for	ADP
ejpam-1203	376	2	a	a	DET
ejpam-1203	376	3	subset	subset	NOUN
ejpam-1203	376	4	a	a	PRON
ejpam-1203	376	5	of	of	ADP
ejpam-1203	376	6	a	a	DET
ejpam-1203	376	7	pg̃-space	pg̃-space	NOUN
ejpam-1203	376	8	(	(	PUNCT
ejpam-1203	376	9	x	x	NOUN
ejpam-1203	376	10	,	,	PUNCT
ejpam-1203	376	11	τ	τ	PROPN
ejpam-1203	376	12	)	)	PUNCT
ejpam-1203	376	13	the	the	DET
ejpam-1203	376	14	following	follow	VERB
ejpam-1203	376	15	are	be	AUX
ejpam-1203	376	16	equivalent	equivalent	ADJ
ejpam-1203	376	17	.	.	PUNCT
ejpam-1203	377	1	1	1	X
ejpam-1203	377	2	.	.	X
ejpam-1203	377	3	a	a	PRON
ejpam-1203	377	4	is	be	AUX
ejpam-1203	377	5	ρ	ρ	NOUN
ejpam-1203	377	6	-	-	PUNCT
ejpam-1203	377	7	closed	closed	ADJ
ejpam-1203	377	8	.	.	PUNCT
ejpam-1203	378	1	c.	c.	PROPN
ejpam-1203	378	2	devamanoharan	devamanoharan	PROPN
ejpam-1203	378	3	,	,	PUNCT
ejpam-1203	378	4	s.	s.	PROPN
ejpam-1203	378	5	missier	missier	PROPN
ejpam-1203	378	6	,	,	PUNCT
ejpam-1203	378	7	s.	s.	PROPN
ejpam-1203	378	8	jafari	jafari	PROPN
ejpam-1203	378	9	/	/	SYM
ejpam-1203	378	10	eur	eur	PROPN
ejpam-1203	378	11	.	.	PUNCT
ejpam-1203	379	1	j.	j.	PROPN
ejpam-1203	379	2	pure	pure	PROPN
ejpam-1203	379	3	appl	appl	PROPN
ejpam-1203	379	4	.	.	PROPN
ejpam-1203	379	5	math	math	PROPN
ejpam-1203	379	6	,	,	PUNCT
ejpam-1203	379	7	5	5	NUM
ejpam-1203	379	8	(	(	PUNCT
ejpam-1203	379	9	2012	2012	NUM
ejpam-1203	379	10	)	)	PUNCT
ejpam-1203	379	11	,	,	PUNCT
ejpam-1203	379	12	554	554	NUM
ejpam-1203	379	13	-	-	SYM
ejpam-1203	379	14	566	566	NUM
ejpam-1203	379	15	563	563	NUM
ejpam-1203	379	16	2	2	NUM
ejpam-1203	379	17	.	.	PUNCT
ejpam-1203	380	1	c	c	NOUN
ejpam-1203	380	2	l({x})∩	l({x})∩	PRON
ejpam-1203	380	3	a	a	PRON
ejpam-1203	380	4	6=	6=	NUM
ejpam-1203	380	5	φ	φ	NOUN
ejpam-1203	380	6	for	for	ADP
ejpam-1203	380	7	each	each	DET
ejpam-1203	380	8	x	x	SYM
ejpam-1203	380	9	∈	∈	PROPN
ejpam-1203	380	10	pcl(a	pcl(a	PROPN
ejpam-1203	380	11	)	)	PUNCT
ejpam-1203	380	12	.	.	PUNCT
ejpam-1203	381	1	3	3	X
ejpam-1203	381	2	.	.	X
ejpam-1203	381	3	pcl(a)−	pcl(a)−	VERB
ejpam-1203	381	4	a	a	PRON
ejpam-1203	381	5	contains	contain	VERB
ejpam-1203	381	6	no	no	DET
ejpam-1203	381	7	nonempty	nonempty	ADV
ejpam-1203	381	8	g̃-closed	g̃-close	VERB
ejpam-1203	381	9	sets	set	NOUN
ejpam-1203	381	10	.	.	PUNCT
ejpam-1203	382	1	proof	proof	NOUN
ejpam-1203	382	2	.	.	PUNCT
ejpam-1203	383	1	1⇒	1⇒	PROPN
ejpam-1203	383	2	2	2	NUM
ejpam-1203	383	3	:	:	PUNCT
ejpam-1203	383	4	let	let	VERB
ejpam-1203	383	5	a	a	PRON
ejpam-1203	383	6	be	be	AUX
ejpam-1203	383	7	ρ	ρ	NOUN
ejpam-1203	383	8	-	-	PUNCT
ejpam-1203	383	9	closed	closed	ADJ
ejpam-1203	383	10	and	and	CCONJ
ejpam-1203	383	11	x	x	PART
ejpam-1203	383	12	∈	∈	PROPN
ejpam-1203	383	13	pcl(a	pcl(a	PROPN
ejpam-1203	383	14	)	)	PUNCT
ejpam-1203	383	15	.	.	PUNCT
ejpam-1203	384	1	if	if	SCONJ
ejpam-1203	384	2	cl({x	cl({x	NOUN
ejpam-1203	384	3	}	}	PUNCT
ejpam-1203	384	4	)	)	PUNCT
ejpam-1203	385	1	∩	∩	NOUN
ejpam-1203	385	2	a	a	DET
ejpam-1203	385	3	=	=	SYM
ejpam-1203	385	4	φ	φ	PROPN
ejpam-1203	385	5	,	,	PUNCT
ejpam-1203	385	6	then	then	ADV
ejpam-1203	385	7	a	a	DET
ejpam-1203	385	8	⊆	⊆	NUM
ejpam-1203	385	9	x	x	SYM
ejpam-1203	385	10	−	−	NOUN
ejpam-1203	385	11	cl({x	cl({x	NOUN
ejpam-1203	385	12	}	}	PUNCT
ejpam-1203	385	13	)	)	PUNCT
ejpam-1203	385	14	.	.	PUNCT
ejpam-1203	386	1	since	since	SCONJ
ejpam-1203	386	2	cl({x	cl({x	NOUN
ejpam-1203	386	3	}	}	PUNCT
ejpam-1203	386	4	)	)	PUNCT
ejpam-1203	386	5	is	be	AUX
ejpam-1203	386	6	closed	close	VERB
ejpam-1203	386	7	,	,	PUNCT
ejpam-1203	386	8	x	x	PUNCT
ejpam-1203	386	9	−	−	NOUN
ejpam-1203	386	10	cl({x	cl({x	NOUN
ejpam-1203	386	11	}	}	PUNCT
ejpam-1203	386	12	)	)	PUNCT
ejpam-1203	386	13	is	be	AUX
ejpam-1203	386	14	open	open	ADJ
ejpam-1203	386	15	and	and	CCONJ
ejpam-1203	386	16	so	so	ADV
ejpam-1203	386	17	g̃-open	g̃-open	VERB
ejpam-1203	386	18	and	and	CCONJ
ejpam-1203	386	19	thus	thus	ADV
ejpam-1203	386	20	a	a	PRON
ejpam-1203	386	21	is	be	AUX
ejpam-1203	386	22	ρ	ρ	NOUN
ejpam-1203	386	23	-	-	PUNCT
ejpam-1203	386	24	closed	closed	ADJ
ejpam-1203	386	25	.	.	PUNCT
ejpam-1203	387	1	pcl(a	pcl(a	X
ejpam-1203	387	2	)	)	PUNCT
ejpam-1203	387	3	⊆	⊆	NUM
ejpam-1203	387	4	int(x	int(x	PROPN
ejpam-1203	387	5	−	−	PROPN
ejpam-1203	387	6	cl({x	cl({x	NOUN
ejpam-1203	387	7	}	}	PUNCT
ejpam-1203	387	8	)	)	PUNCT
ejpam-1203	387	9	)	)	PUNCT
ejpam-1203	387	10	,	,	PUNCT
ejpam-1203	387	11	x	x	X
ejpam-1203	387	12	/∈	/∈	PUNCT
ejpam-1203	388	1	pcl(a	pcl(a	X
ejpam-1203	388	2	)	)	PUNCT
ejpam-1203	388	3	which	which	PRON
ejpam-1203	388	4	is	be	AUX
ejpam-1203	388	5	a	a	DET
ejpam-1203	388	6	contradiction	contradiction	NOUN
ejpam-1203	388	7	.	.	PUNCT
ejpam-1203	389	1	therefore	therefore	ADV
ejpam-1203	389	2	cl({x})∩	cl({x})∩	VERB
ejpam-1203	389	3	a	a	DET
ejpam-1203	389	4	6=	6=	NUM
ejpam-1203	389	5	φ	φ	PROPN
ejpam-1203	389	6	.	.	PUNCT
ejpam-1203	390	1	2⇒	2⇒	PROPN
ejpam-1203	390	2	3	3	NUM
ejpam-1203	390	3	:	:	PUNCT
ejpam-1203	390	4	let	let	VERB
ejpam-1203	390	5	cl({x	cl({x	NOUN
ejpam-1203	390	6	}	}	PUNCT
ejpam-1203	390	7	)	)	PUNCT
ejpam-1203	390	8	∩	∩	PROPN
ejpam-1203	390	9	a	a	DET
ejpam-1203	390	10	6=	6=	NUM
ejpam-1203	390	11	φ	φ	NOUN
ejpam-1203	390	12	for	for	ADP
ejpam-1203	390	13	each	each	DET
ejpam-1203	390	14	x	x	SYM
ejpam-1203	390	15	∈	∈	PROPN
ejpam-1203	390	16	pcl(a	pcl(a	PROPN
ejpam-1203	390	17	)	)	PUNCT
ejpam-1203	390	18	and	and	CCONJ
ejpam-1203	390	19	k	k	PROPN
ejpam-1203	390	20	⊆	⊆	NUM
ejpam-1203	390	21	pcl(a)−	pcl(a)−	NOUN
ejpam-1203	390	22	a	a	DET
ejpam-1203	390	23	be	be	AUX
ejpam-1203	390	24	a	a	DET
ejpam-1203	390	25	non	non	X
ejpam-1203	390	26	empty	empty	ADJ
ejpam-1203	390	27	g̃-closed	g̃-closed	ADJ
ejpam-1203	390	28	set	set	NOUN
ejpam-1203	390	29	,	,	PUNCT
ejpam-1203	390	30	then	then	ADV
ejpam-1203	390	31	k	k	PROPN
ejpam-1203	390	32	⊆	⊆	NUM
ejpam-1203	390	33	pcl(a	pcl(a	NUM
ejpam-1203	390	34	)	)	PUNCT
ejpam-1203	390	35	and	and	CCONJ
ejpam-1203	390	36	a⊆	a⊆	VERB
ejpam-1203	390	37	x	x	PUNCT
ejpam-1203	390	38	−k	−k	ADJ
ejpam-1203	390	39	.	.	PUNCT
ejpam-1203	391	1	if	if	SCONJ
ejpam-1203	391	2	there	there	PRON
ejpam-1203	391	3	exist	exist	VERB
ejpam-1203	391	4	an	an	DET
ejpam-1203	391	5	x	x	SYM
ejpam-1203	391	6	∈	∈	PROPN
ejpam-1203	391	7	k	k	NOUN
ejpam-1203	391	8	then	then	ADV
ejpam-1203	391	9	by	by	ADP
ejpam-1203	391	10	(	(	PUNCT
ejpam-1203	391	11	2	2	X
ejpam-1203	391	12	)	)	PUNCT
ejpam-1203	391	13	cl({x})∩a	cl({x})∩a	PROPN
ejpam-1203	391	14	6=	6=	ADP
ejpam-1203	391	15	φ	φ	PROPN
ejpam-1203	391	16	.	.	PUNCT
ejpam-1203	392	1	cl({x})∩a⊆	cl({x})∩a⊆	NUM
ejpam-1203	392	2	k∩a⊆	k∩a⊆	PROPN
ejpam-1203	392	3	(	(	PUNCT
ejpam-1203	392	4	pcl(a)−a)∩a	pcl(a)−a)∩a	ADJ
ejpam-1203	392	5	which	which	PRON
ejpam-1203	392	6	is	be	AUX
ejpam-1203	392	7	a	a	DET
ejpam-1203	392	8	contradiction	contradiction	NOUN
ejpam-1203	392	9	.	.	PUNCT
ejpam-1203	393	1	hence	hence	ADV
ejpam-1203	393	2	pcl(a)−a	pcl(a)−a	PROPN
ejpam-1203	393	3	contains	contain	VERB
ejpam-1203	393	4	no	no	DET
ejpam-1203	393	5	nonempty	nonempty	ADV
ejpam-1203	393	6	g̃-closed	g̃-close	VERB
ejpam-1203	393	7	sets	set	NOUN
ejpam-1203	393	8	.	.	PUNCT
ejpam-1203	394	1	3⇒	3⇒	NUM
ejpam-1203	394	2	1	1	NUM
ejpam-1203	394	3	:	:	PUNCT
ejpam-1203	394	4	let	let	VERB
ejpam-1203	394	5	pcl(a	pcl(a	NUM
ejpam-1203	394	6	)	)	PUNCT
ejpam-1203	394	7	−	−	NOUN
ejpam-1203	394	8	a	a	PRON
ejpam-1203	394	9	contains	contain	VERB
ejpam-1203	394	10	no	no	DET
ejpam-1203	394	11	nonempty	nonempty	ADV
ejpam-1203	394	12	g̃-closed	g̃-close	VERB
ejpam-1203	394	13	set	set	NOUN
ejpam-1203	394	14	and	and	CCONJ
ejpam-1203	394	15	a	a	DET
ejpam-1203	394	16	⊆	⊆	NUM
ejpam-1203	394	17	u	u	NOUN
ejpam-1203	394	18	and	and	CCONJ
ejpam-1203	394	19	u	u	NOUN
ejpam-1203	394	20	be	be	VERB
ejpam-1203	394	21	g̃	g̃	PROPN
ejpam-1203	394	22	open	open	ADJ
ejpam-1203	394	23	in	in	ADP
ejpam-1203	394	24	x	x	X
ejpam-1203	394	25	.	.	PUNCT
ejpam-1203	395	1	if	if	SCONJ
ejpam-1203	395	2	pcl(a	pcl(a	NUM
ejpam-1203	395	3	)	)	PUNCT
ejpam-1203	395	4	*	*	PUNCT
ejpam-1203	396	1	int(u	int(u	PROPN
ejpam-1203	396	2	)	)	PUNCT
ejpam-1203	396	3	,	,	PUNCT
ejpam-1203	396	4	then	then	ADV
ejpam-1203	396	5	pcl(a	pcl(a	NUM
ejpam-1203	396	6	)	)	PUNCT
ejpam-1203	396	7	∩	∩	NOUN
ejpam-1203	396	8	(	(	PUNCT
ejpam-1203	396	9	int(u))c	int(u))c	PROPN
ejpam-1203	396	10	6=	6=	PROPN
ejpam-1203	396	11	φ	φ	PROPN
ejpam-1203	396	12	.	.	PUNCT
ejpam-1203	397	1	since	since	SCONJ
ejpam-1203	397	2	the	the	DET
ejpam-1203	397	3	space	space	NOUN
ejpam-1203	397	4	is	be	AUX
ejpam-1203	397	5	a	a	DET
ejpam-1203	397	6	pg̃-space	pg̃-space	NOUN
ejpam-1203	397	7	,	,	PUNCT
ejpam-1203	397	8	pcl(a)]∩(int(u))c	pcl(a)]∩(int(u))c	PROPN
ejpam-1203	397	9	is	be	AUX
ejpam-1203	397	10	a	a	DET
ejpam-1203	397	11	nonempty	nonempty	ADV
ejpam-1203	397	12	g̃-closed	g̃-close	VERB
ejpam-1203	397	13	subset	subset	NOUN
ejpam-1203	397	14	of	of	ADP
ejpam-1203	397	15	pcl(a)−a	pcl(a)−a	PROPN
ejpam-1203	397	16	which	which	PRON
ejpam-1203	397	17	is	be	AUX
ejpam-1203	397	18	a	a	DET
ejpam-1203	397	19	contradiction	contradiction	NOUN
ejpam-1203	397	20	.	.	PUNCT
ejpam-1203	398	1	hence	hence	ADV
ejpam-1203	398	2	a	a	PRON
ejpam-1203	398	3	is	be	AUX
ejpam-1203	398	4	ρ	ρ	NOUN
ejpam-1203	398	5	-	-	PUNCT
ejpam-1203	398	6	closed	closed	ADJ
ejpam-1203	398	7	.	.	PUNCT
ejpam-1203	399	1	5	5	X
ejpam-1203	399	2	.	.	X
ejpam-1203	399	3	ρ	ρ	VERB
ejpam-1203	399	4	-	-	ADJ
ejpam-1203	399	5	open	open	ADJ
ejpam-1203	399	6	sets	set	NOUN
ejpam-1203	399	7	and	and	CCONJ
ejpam-1203	399	8	ρs	ρs	NOUN
ejpam-1203	399	9	-	-	PUNCT
ejpam-1203	399	10	open	open	ADJ
ejpam-1203	399	11	sets	set	NOUN
ejpam-1203	399	12	definition	definition	NOUN
ejpam-1203	399	13	11	11	NUM
ejpam-1203	399	14	.	.	PUNCT
ejpam-1203	400	1	1	1	NUM
ejpam-1203	400	2	.	.	X
ejpam-1203	400	3	a	a	DET
ejpam-1203	400	4	subset	subset	NOUN
ejpam-1203	400	5	a	a	PRON
ejpam-1203	400	6	of	of	ADP
ejpam-1203	400	7	(	(	PUNCT
ejpam-1203	400	8	x	x	PROPN
ejpam-1203	400	9	,	,	PUNCT
ejpam-1203	400	10	τ	τ	X
ejpam-1203	400	11	)	)	PUNCT
ejpam-1203	400	12	is	be	AUX
ejpam-1203	400	13	said	say	VERB
ejpam-1203	400	14	to	to	ADP
ejpam-1203	400	15	beρ	beρ	NOUN
ejpam-1203	400	16	-	-	PUNCT
ejpam-1203	400	17	open	open	ADJ
ejpam-1203	400	18	in	in	ADP
ejpam-1203	400	19	(	(	PUNCT
ejpam-1203	400	20	x	x	INTJ
ejpam-1203	400	21	,	,	PUNCT
ejpam-1203	400	22	τ	τ	X
ejpam-1203	400	23	)	)	PUNCT
ejpam-1203	400	24	if	if	SCONJ
ejpam-1203	400	25	its	its	PRON
ejpam-1203	400	26	complement	complement	NOUN
ejpam-1203	400	27	x	x	PUNCT
ejpam-1203	400	28	−	−	NOUN
ejpam-1203	400	29	a	a	PRON
ejpam-1203	400	30	is	be	AUX
ejpam-1203	400	31	ρ	ρ	NOUN
ejpam-1203	400	32	-	-	PUNCT
ejpam-1203	400	33	closed	closed	ADJ
ejpam-1203	400	34	in	in	ADP
ejpam-1203	400	35	(	(	PUNCT
ejpam-1203	400	36	x	x	INTJ
ejpam-1203	400	37	,	,	PUNCT
ejpam-1203	400	38	τ	τ	PROPN
ejpam-1203	400	39	)	)	PUNCT
ejpam-1203	400	40	.	.	PUNCT
ejpam-1203	401	1	2	2	X
ejpam-1203	401	2	.	.	X
ejpam-1203	401	3	a	a	DET
ejpam-1203	401	4	subset	subset	NOUN
ejpam-1203	401	5	a	a	PRON
ejpam-1203	401	6	of	of	ADP
ejpam-1203	401	7	(	(	PUNCT
ejpam-1203	401	8	x	x	PROPN
ejpam-1203	401	9	,	,	PUNCT
ejpam-1203	401	10	τ	τ	X
ejpam-1203	401	11	)	)	PUNCT
ejpam-1203	401	12	is	be	AUX
ejpam-1203	401	13	said	say	VERB
ejpam-1203	401	14	to	to	PART
ejpam-1203	401	15	be	be	AUX
ejpam-1203	401	16	ρs	ρs	ADV
ejpam-1203	401	17	-	-	NOUN
ejpam-1203	401	18	open	open	ADJ
ejpam-1203	401	19	in	in	ADP
ejpam-1203	401	20	(	(	PUNCT
ejpam-1203	401	21	x	x	INTJ
ejpam-1203	401	22	,	,	PUNCT
ejpam-1203	401	23	τ	τ	X
ejpam-1203	401	24	)	)	PUNCT
ejpam-1203	401	25	if	if	SCONJ
ejpam-1203	401	26	its	its	PRON
ejpam-1203	401	27	complement	complement	NOUN
ejpam-1203	401	28	x	x	PUNCT
ejpam-1203	401	29	−	−	PROPN
ejpam-1203	401	30	a	a	DET
ejpam-1203	401	31	isρs	isρs	ADV
ejpam-1203	401	32	-	-	PUNCT
ejpam-1203	401	33	closed	close	VERB
ejpam-1203	401	34	in	in	ADP
ejpam-1203	401	35	(	(	PUNCT
ejpam-1203	401	36	x	x	INTJ
ejpam-1203	401	37	,	,	PUNCT
ejpam-1203	401	38	τ	τ	PROPN
ejpam-1203	401	39	)	)	PUNCT
ejpam-1203	401	40	.	.	PUNCT
ejpam-1203	402	1	theorem	theorem	NOUN
ejpam-1203	402	2	21	21	NUM
ejpam-1203	402	3	.	.	PUNCT
ejpam-1203	403	1	let	let	AUX
ejpam-1203	403	2	(	(	PUNCT
ejpam-1203	403	3	x	x	X
ejpam-1203	403	4	,	,	PUNCT
ejpam-1203	403	5	τ	τ	X
ejpam-1203	403	6	)	)	PUNCT
ejpam-1203	403	7	be	be	VERB
ejpam-1203	403	8	a	a	DET
ejpam-1203	403	9	topological	topological	ADJ
ejpam-1203	403	10	space	space	NOUN
ejpam-1203	403	11	and	and	CCONJ
ejpam-1203	403	12	a⊆	a⊆	PROPN
ejpam-1203	403	13	x	x	X
ejpam-1203	403	14	.	.	PUNCT
ejpam-1203	404	1	1	1	X
ejpam-1203	404	2	.	.	X
ejpam-1203	404	3	a	a	PRON
ejpam-1203	404	4	is	be	AUX
ejpam-1203	404	5	an	an	DET
ejpam-1203	404	6	ρ	ρ	NOUN
ejpam-1203	404	7	-	-	PUNCT
ejpam-1203	404	8	open	open	ADJ
ejpam-1203	404	9	set	set	NOUN
ejpam-1203	404	10	if	if	SCONJ
ejpam-1203	404	11	and	and	CCONJ
ejpam-1203	404	12	only	only	ADV
ejpam-1203	404	13	if	if	SCONJ
ejpam-1203	404	14	cl(k	cl(k	NOUN
ejpam-1203	404	15	)	)	PUNCT
ejpam-1203	404	16	⊆	⊆	X
ejpam-1203	404	17	pint(a	pint(a	NOUN
ejpam-1203	404	18	)	)	PUNCT
ejpam-1203	404	19	whenever	whenever	SCONJ
ejpam-1203	404	20	k	k	PROPN
ejpam-1203	404	21	⊆	⊆	PROPN
ejpam-1203	404	22	a	a	PRON
ejpam-1203	404	23	and	and	CCONJ
ejpam-1203	404	24	k	k	PROPN
ejpam-1203	404	25	is	be	AUX
ejpam-1203	404	26	g̃-closed	g̃-close	VERB
ejpam-1203	404	27	.	.	PUNCT
ejpam-1203	405	1	2	2	X
ejpam-1203	405	2	.	.	X
ejpam-1203	405	3	a	a	PRON
ejpam-1203	405	4	is	be	AUX
ejpam-1203	405	5	an	an	DET
ejpam-1203	405	6	ρs	ρs	ADV
ejpam-1203	405	7	-	-	PUNCT
ejpam-1203	405	8	open	open	ADJ
ejpam-1203	405	9	set	set	NOUN
ejpam-1203	405	10	if	if	SCONJ
ejpam-1203	405	11	and	and	CCONJ
ejpam-1203	405	12	only	only	ADV
ejpam-1203	405	13	if	if	SCONJ
ejpam-1203	405	14	cl(int(k	cl(int(k	NOUN
ejpam-1203	405	15	)	)	PUNCT
ejpam-1203	405	16	)	)	PUNCT
ejpam-1203	406	1	⊆	⊆	X
ejpam-1203	406	2	pint(a	pint(a	NOUN
ejpam-1203	406	3	)	)	PUNCT
ejpam-1203	406	4	whenever	whenever	SCONJ
ejpam-1203	406	5	k	k	PROPN
ejpam-1203	406	6	⊆	⊆	PROPN
ejpam-1203	406	7	a	a	PRON
ejpam-1203	406	8	and	and	CCONJ
ejpam-1203	406	9	k	k	PROPN
ejpam-1203	406	10	is	be	AUX
ejpam-1203	406	11	g̃-closed	g̃-close	VERB
ejpam-1203	406	12	.	.	PUNCT
ejpam-1203	407	1	3	3	X
ejpam-1203	407	2	.	.	X
ejpam-1203	407	3	if	if	SCONJ
ejpam-1203	407	4	a	a	PRON
ejpam-1203	407	5	is	be	AUX
ejpam-1203	407	6	ρ	ρ	NOUN
ejpam-1203	407	7	-	-	ADJ
ejpam-1203	407	8	open	open	ADJ
ejpam-1203	407	9	,	,	PUNCT
ejpam-1203	407	10	then	then	ADV
ejpam-1203	407	11	a	a	PRON
ejpam-1203	407	12	is	be	AUX
ejpam-1203	407	13	ρs	ρs	ADV
ejpam-1203	407	14	-	-	NOUN
ejpam-1203	407	15	open	open	ADJ
ejpam-1203	407	16	.	.	PUNCT
ejpam-1203	408	1	proof	proof	NOUN
ejpam-1203	408	2	.	.	PUNCT
ejpam-1203	409	1	1	1	X
ejpam-1203	409	2	.	.	X
ejpam-1203	409	3	necessity	necessity	NOUN
ejpam-1203	409	4	.	.	PUNCT
ejpam-1203	410	1	let	let	VERB
ejpam-1203	410	2	a	a	PRON
ejpam-1203	410	3	be	be	AUX
ejpam-1203	410	4	an	an	DET
ejpam-1203	410	5	ρ	ρ	NOUN
ejpam-1203	410	6	-	-	PUNCT
ejpam-1203	410	7	open	open	ADJ
ejpam-1203	410	8	set	set	NOUN
ejpam-1203	410	9	in	in	ADP
ejpam-1203	410	10	(	(	PUNCT
ejpam-1203	410	11	x	x	INTJ
ejpam-1203	410	12	,	,	PUNCT
ejpam-1203	410	13	τ	τ	PROPN
ejpam-1203	410	14	)	)	PUNCT
ejpam-1203	410	15	.	.	PUNCT
ejpam-1203	411	1	let	let	VERB
ejpam-1203	411	2	k	k	PROPN
ejpam-1203	411	3	⊆	⊆	SYM
ejpam-1203	411	4	a	a	PRON
ejpam-1203	411	5	and	and	CCONJ
ejpam-1203	411	6	k	k	PROPN
ejpam-1203	411	7	be	be	AUX
ejpam-1203	411	8	g̃-closed	g̃-close	VERB
ejpam-1203	411	9	.	.	PUNCT
ejpam-1203	412	1	then	then	ADV
ejpam-1203	412	2	x	x	PUNCT
ejpam-1203	412	3	−a	−a	NOUN
ejpam-1203	412	4	is	be	AUX
ejpam-1203	412	5	ρ	ρ	NOUN
ejpam-1203	412	6	-	-	PUNCT
ejpam-1203	412	7	closed	closed	ADJ
ejpam-1203	412	8	and	and	CCONJ
ejpam-1203	412	9	it	it	PRON
ejpam-1203	412	10	is	be	AUX
ejpam-1203	412	11	contained	contain	VERB
ejpam-1203	412	12	in	in	ADP
ejpam-1203	412	13	the	the	DET
ejpam-1203	412	14	g̃-open	g̃-open	NOUN
ejpam-1203	412	15	set	set	VERB
ejpam-1203	412	16	x−k	x−k	PROPN
ejpam-1203	412	17	.	.	PUNCT
ejpam-1203	413	1	therefore	therefore	ADV
ejpam-1203	413	2	pcl(x−a)⊆	pcl(x−a)⊆	PROPN
ejpam-1203	413	3	int(x−k	int(x−k	NOUN
ejpam-1203	413	4	)	)	PUNCT
ejpam-1203	413	5	,	,	PUNCT
ejpam-1203	413	6	x	x	X
ejpam-1203	413	7	−	−	PROPN
ejpam-1203	413	8	pint(a	pint(a	NOUN
ejpam-1203	413	9	)	)	PUNCT
ejpam-1203	413	10	⊆	⊆	NUM
ejpam-1203	413	11	x	x	SYM
ejpam-1203	413	12	−	−	NOUN
ejpam-1203	413	13	cl(k	cl(k	NOUN
ejpam-1203	413	14	)	)	PUNCT
ejpam-1203	413	15	,	,	PUNCT
ejpam-1203	413	16	hence	hence	ADV
ejpam-1203	413	17	cl(k	cl(k	PUNCT
ejpam-1203	413	18	)	)	PUNCT
ejpam-1203	413	19	⊆	⊆	NUM
ejpam-1203	413	20	pint(a	pint(a	NOUN
ejpam-1203	413	21	)	)	PUNCT
ejpam-1203	413	22	.	.	PUNCT
ejpam-1203	414	1	sufficiency	sufficiency	PROPN
ejpam-1203	414	2	.	.	PUNCT
ejpam-1203	415	1	if	if	SCONJ
ejpam-1203	415	2	k	k	PROPN
ejpam-1203	415	3	is	be	AUX
ejpam-1203	415	4	g̃-closed	g̃-close	VERB
ejpam-1203	415	5	set	set	VERB
ejpam-1203	415	6	such	such	ADJ
ejpam-1203	415	7	that	that	DET
ejpam-1203	415	8	cl(k	cl(k	NOUN
ejpam-1203	415	9	)	)	PUNCT
ejpam-1203	416	1	⊆	⊆	X
ejpam-1203	416	2	pint(a	pint(a	NOUN
ejpam-1203	416	3	)	)	PUNCT
ejpam-1203	416	4	whenever	whenever	SCONJ
ejpam-1203	416	5	k	k	PROPN
ejpam-1203	416	6	⊆	⊆	NUM
ejpam-1203	416	7	a.	a.	NOUN
ejpam-1203	416	8	it	it	PRON
ejpam-1203	416	9	follows	follow	VERB
ejpam-1203	416	10	that	that	SCONJ
ejpam-1203	416	11	x	x	PUNCT
ejpam-1203	416	12	−	−	NOUN
ejpam-1203	416	13	a⊆	a⊆	VERB
ejpam-1203	416	14	x	x	PUNCT
ejpam-1203	416	15	−	−	PROPN
ejpam-1203	416	16	k	k	PROPN
ejpam-1203	416	17	and	and	CCONJ
ejpam-1203	416	18	x	x	ADJ
ejpam-1203	416	19	−	−	PROPN
ejpam-1203	416	20	pint(a	pint(a	NOUN
ejpam-1203	416	21	)	)	PUNCT
ejpam-1203	416	22	⊆	⊆	NUM
ejpam-1203	416	23	x	x	SYM
ejpam-1203	416	24	−	−	NOUN
ejpam-1203	416	25	cl(k	cl(k	NOUN
ejpam-1203	416	26	)	)	PUNCT
ejpam-1203	416	27	.	.	PUNCT
ejpam-1203	417	1	therefore	therefore	ADV
ejpam-1203	417	2	pcl(x	pcl(x	PROPN
ejpam-1203	417	3	−	−	PROPN
ejpam-1203	417	4	a	a	NOUN
ejpam-1203	417	5	)	)	PUNCT
ejpam-1203	417	6	⊆	⊆	NUM
ejpam-1203	417	7	int(x	int(x	PROPN
ejpam-1203	417	8	−	−	PROPN
ejpam-1203	417	9	k	k	NOUN
ejpam-1203	417	10	)	)	PUNCT
ejpam-1203	417	11	.	.	PUNCT
ejpam-1203	418	1	hence	hence	ADV
ejpam-1203	418	2	x	x	X
ejpam-1203	418	3	−	−	NOUN
ejpam-1203	418	4	a	a	PRON
ejpam-1203	418	5	is	be	AUX
ejpam-1203	418	6	ρ	ρ	NOUN
ejpam-1203	418	7	-	-	PUNCT
ejpam-1203	418	8	closed	closed	ADJ
ejpam-1203	418	9	and	and	CCONJ
ejpam-1203	418	10	a	a	PRON
ejpam-1203	418	11	becomes	become	VERB
ejpam-1203	418	12	an	an	DET
ejpam-1203	418	13	ρ	ρ	NOUN
ejpam-1203	418	14	-	-	PUNCT
ejpam-1203	418	15	open	open	ADJ
ejpam-1203	418	16	set	set	NOUN
ejpam-1203	418	17	.	.	PUNCT
ejpam-1203	419	1	c.	c.	PROPN
ejpam-1203	419	2	devamanoharan	devamanoharan	PROPN
ejpam-1203	419	3	,	,	PUNCT
ejpam-1203	419	4	s.	s.	PROPN
ejpam-1203	419	5	missier	missier	PROPN
ejpam-1203	419	6	,	,	PUNCT
ejpam-1203	419	7	s.	s.	PROPN
ejpam-1203	419	8	jafari	jafari	PROPN
ejpam-1203	419	9	/	/	SYM
ejpam-1203	419	10	eur	eur	PROPN
ejpam-1203	419	11	.	.	PUNCT
ejpam-1203	420	1	j.	j.	PROPN
ejpam-1203	420	2	pure	pure	PROPN
ejpam-1203	420	3	appl	appl	PROPN
ejpam-1203	420	4	.	.	PROPN
ejpam-1203	420	5	math	math	PROPN
ejpam-1203	420	6	,	,	PUNCT
ejpam-1203	420	7	5	5	NUM
ejpam-1203	420	8	(	(	PUNCT
ejpam-1203	420	9	2012	2012	NUM
ejpam-1203	420	10	)	)	PUNCT
ejpam-1203	420	11	,	,	PUNCT
ejpam-1203	420	12	554	554	NUM
ejpam-1203	420	13	-	-	SYM
ejpam-1203	420	14	566	566	NUM
ejpam-1203	420	15	564	564	NUM
ejpam-1203	420	16	2	2	NUM
ejpam-1203	420	17	.	.	PUNCT
ejpam-1203	421	1	necessity	necessity	NOUN
ejpam-1203	421	2	:	:	PUNCT
ejpam-1203	421	3	let	let	VERB
ejpam-1203	421	4	a	a	PRON
ejpam-1203	421	5	be	be	AUX
ejpam-1203	421	6	an	an	DET
ejpam-1203	421	7	ρs	ρs	ADV
ejpam-1203	421	8	-	-	PUNCT
ejpam-1203	421	9	open	open	ADJ
ejpam-1203	421	10	set	set	NOUN
ejpam-1203	421	11	in	in	ADP
ejpam-1203	421	12	(	(	PUNCT
ejpam-1203	421	13	x	x	INTJ
ejpam-1203	421	14	,	,	PUNCT
ejpam-1203	421	15	τ	τ	PROPN
ejpam-1203	421	16	)	)	PUNCT
ejpam-1203	421	17	.	.	PUNCT
ejpam-1203	422	1	let	let	VERB
ejpam-1203	422	2	k	k	PROPN
ejpam-1203	422	3	⊆	⊆	SYM
ejpam-1203	422	4	a	a	PRON
ejpam-1203	422	5	and	and	CCONJ
ejpam-1203	422	6	k	k	PROPN
ejpam-1203	422	7	be	be	AUX
ejpam-1203	422	8	g̃-closed	g̃-close	VERB
ejpam-1203	422	9	.	.	PUNCT
ejpam-1203	423	1	then	then	ADV
ejpam-1203	423	2	x−a	x−a	PROPN
ejpam-1203	423	3	is	be	AUX
ejpam-1203	423	4	ρs	ρs	ADV
ejpam-1203	423	5	-	-	PUNCT
ejpam-1203	423	6	closed	closed	ADJ
ejpam-1203	423	7	and	and	CCONJ
ejpam-1203	423	8	is	be	AUX
ejpam-1203	423	9	contained	contain	VERB
ejpam-1203	423	10	in	in	ADP
ejpam-1203	423	11	the	the	DET
ejpam-1203	423	12	g̃-open	g̃-open	NOUN
ejpam-1203	423	13	set	set	VERB
ejpam-1203	423	14	x−k	x−k	PROPN
ejpam-1203	423	15	.	.	PUNCT
ejpam-1203	424	1	therefore	therefore	ADV
ejpam-1203	424	2	pcl(x−a)⊆	pcl(x−a)⊆	PROPN
ejpam-1203	424	3	int(cl(x−k	int(cl(x−k	NOUN
ejpam-1203	424	4	)	)	PUNCT
ejpam-1203	424	5	)	)	PUNCT
ejpam-1203	425	1	and	and	CCONJ
ejpam-1203	425	2	so	so	ADV
ejpam-1203	425	3	x	x	PUNCT
ejpam-1203	425	4	−	−	PROPN
ejpam-1203	425	5	pint(a	pint(a	NOUN
ejpam-1203	425	6	)	)	PUNCT
ejpam-1203	426	1	⊆	⊆	NUM
ejpam-1203	426	2	int(x	int(x	PROPN
ejpam-1203	426	3	−	−	PROPN
ejpam-1203	426	4	int(k	int(k	NOUN
ejpam-1203	426	5	)	)	PUNCT
ejpam-1203	426	6	)	)	PUNCT
ejpam-1203	427	1	=	=	PUNCT
ejpam-1203	427	2	x	x	X
ejpam-1203	428	1	−	−	NOUN
ejpam-1203	428	2	cl(int(k	cl(int(k	NOUN
ejpam-1203	428	3	)	)	PUNCT
ejpam-1203	428	4	)	)	PUNCT
ejpam-1203	428	5	.	.	PUNCT
ejpam-1203	429	1	hence	hence	ADV
ejpam-1203	429	2	cl(int(k	cl(int(k	PROPN
ejpam-1203	429	3	)	)	PUNCT
ejpam-1203	430	1	⊆	⊆	NUM
ejpam-1203	430	2	pint(a	pint(a	NOUN
ejpam-1203	430	3	)	)	PUNCT
ejpam-1203	430	4	.	.	PUNCT
ejpam-1203	431	1	sufficiency	sufficiency	NOUN
ejpam-1203	431	2	:	:	PUNCT
ejpam-1203	431	3	if	if	SCONJ
ejpam-1203	431	4	k	k	PROPN
ejpam-1203	431	5	is	be	AUX
ejpam-1203	431	6	g̃-closed	g̃-close	VERB
ejpam-1203	431	7	set	set	VERB
ejpam-1203	431	8	such	such	ADJ
ejpam-1203	431	9	that	that	DET
ejpam-1203	431	10	cl(int(k	cl(int(k	NOUN
ejpam-1203	431	11	)	)	PUNCT
ejpam-1203	431	12	)	)	PUNCT
ejpam-1203	432	1	⊆	⊆	X
ejpam-1203	432	2	pint(a	pint(a	NOUN
ejpam-1203	432	3	)	)	PUNCT
ejpam-1203	432	4	whenever	whenever	SCONJ
ejpam-1203	432	5	k	k	PROPN
ejpam-1203	432	6	⊆	⊆	SYM
ejpam-1203	432	7	a	a	PRON
ejpam-1203	432	8	,	,	PUNCT
ejpam-1203	432	9	it	it	PRON
ejpam-1203	432	10	follows	follow	VERB
ejpam-1203	432	11	that	that	PRON
ejpam-1203	432	12	.	.	PUNCT
ejpam-1203	433	1	x	x	PUNCT
ejpam-1203	434	1	−	−	NOUN
ejpam-1203	434	2	a⊆	a⊆	NOUN
ejpam-1203	434	3	x	x	PUNCT
ejpam-1203	434	4	−	−	PROPN
ejpam-1203	434	5	k	k	NOUN
ejpam-1203	434	6	,	,	PUNCT
ejpam-1203	434	7	x	x	INTJ
ejpam-1203	434	8	−	−	PROPN
ejpam-1203	434	9	pint(a	pint(a	NOUN
ejpam-1203	434	10	)	)	PUNCT
ejpam-1203	434	11	⊆	⊆	NUM
ejpam-1203	434	12	x	x	SYM
ejpam-1203	434	13	−	−	NOUN
ejpam-1203	434	14	cl(int(k	cl(int(k	NOUN
ejpam-1203	434	15	)	)	PUNCT
ejpam-1203	434	16	)	)	PUNCT
ejpam-1203	434	17	and	and	CCONJ
ejpam-1203	434	18	pcl(x	pcl(x	PROPN
ejpam-1203	434	19	−a)⊆	−a)⊆	NOUN
ejpam-1203	434	20	x	x	PUNCT
ejpam-1203	434	21	−	−	PROPN
ejpam-1203	434	22	cl(int(k	cl(int(k	NOUN
ejpam-1203	434	23	)	)	PUNCT
ejpam-1203	434	24	)	)	PUNCT
ejpam-1203	435	1	=	=	SYM
ejpam-1203	435	2	int(cl(x	int(cl(x	PROPN
ejpam-1203	435	3	−k	−k	PROPN
ejpam-1203	435	4	)	)	PUNCT
ejpam-1203	435	5	)	)	PUNCT
ejpam-1203	435	6	.	.	PUNCT
ejpam-1203	436	1	hence	hence	ADV
ejpam-1203	436	2	x	x	PUNCT
ejpam-1203	436	3	−a	−a	NOUN
ejpam-1203	436	4	is	be	AUX
ejpam-1203	436	5	ρs	ρs	ADV
ejpam-1203	436	6	-	-	PUNCT
ejpam-1203	436	7	closed	closed	ADJ
ejpam-1203	436	8	and	and	CCONJ
ejpam-1203	436	9	a	a	PRON
ejpam-1203	436	10	becomes	become	VERB
ejpam-1203	436	11	an	an	DET
ejpam-1203	436	12	ρs	ρs	NOUN
ejpam-1203	436	13	-	-	PUNCT
ejpam-1203	436	14	open	open	ADJ
ejpam-1203	436	15	set	set	NOUN
ejpam-1203	436	16	.	.	PUNCT
ejpam-1203	437	1	3	3	X
ejpam-1203	437	2	.	.	X
ejpam-1203	437	3	let	let	VERB
ejpam-1203	437	4	a	a	PRON
ejpam-1203	437	5	be	be	AUX
ejpam-1203	437	6	an	an	DET
ejpam-1203	437	7	ρ	ρ	NOUN
ejpam-1203	437	8	-	-	NOUN
ejpam-1203	437	9	open	open	ADJ
ejpam-1203	437	10	.	.	PUNCT
ejpam-1203	438	1	let	let	VERB
ejpam-1203	438	2	also	also	ADV
ejpam-1203	438	3	k	k	PROPN
ejpam-1203	438	4	⊆	⊆	NUM
ejpam-1203	438	5	a	a	PRON
ejpam-1203	438	6	and	and	CCONJ
ejpam-1203	438	7	k	k	PROPN
ejpam-1203	438	8	be	be	AUX
ejpam-1203	438	9	g̃-closed	g̃-close	VERB
ejpam-1203	438	10	.	.	PUNCT
ejpam-1203	439	1	since	since	SCONJ
ejpam-1203	439	2	a	a	PRON
ejpam-1203	439	3	is	be	AUX
ejpam-1203	439	4	ρ	ρ	NOUN
ejpam-1203	439	5	-	-	ADJ
ejpam-1203	439	6	open	open	ADJ
ejpam-1203	439	7	we	we	PRON
ejpam-1203	439	8	have	have	VERB
ejpam-1203	439	9	cl(k	cl(k	NOUN
ejpam-1203	439	10	)	)	PUNCT
ejpam-1203	440	1	⊆	⊆	NUM
ejpam-1203	440	2	pint(a	pint(a	NOUN
ejpam-1203	440	3	)	)	PUNCT
ejpam-1203	440	4	.	.	PUNCT
ejpam-1203	441	1	therefore	therefore	ADV
ejpam-1203	441	2	cl(int(k	cl(int(k	PROPN
ejpam-1203	441	3	)	)	PUNCT
ejpam-1203	442	1	⊆	⊆	NUM
ejpam-1203	442	2	pint(a	pint(a	NOUN
ejpam-1203	442	3	)	)	PUNCT
ejpam-1203	442	4	.	.	PUNCT
ejpam-1203	443	1	hence	hence	ADV
ejpam-1203	443	2	by	by	ADP
ejpam-1203	443	3	2	2	NUM
ejpam-1203	443	4	,	,	PUNCT
ejpam-1203	443	5	a	a	PRON
ejpam-1203	443	6	is	be	AUX
ejpam-1203	443	7	ρs	ρs	ADV
ejpam-1203	443	8	-	-	ADJ
ejpam-1203	443	9	open	open	ADJ
ejpam-1203	443	10	.	.	PUNCT
ejpam-1203	444	1	theorem	theorem	NOUN
ejpam-1203	444	2	22	22	NUM
ejpam-1203	444	3	.	.	PUNCT
ejpam-1203	445	1	if	if	SCONJ
ejpam-1203	445	2	pint(a	pint(a	NOUN
ejpam-1203	445	3	)	)	PUNCT
ejpam-1203	445	4	⊆	⊆	NUM
ejpam-1203	445	5	b	b	NUM
ejpam-1203	445	6	⊆	⊆	NUM
ejpam-1203	445	7	a	a	PRON
ejpam-1203	445	8	and	and	CCONJ
ejpam-1203	445	9	a	a	PRON
ejpam-1203	445	10	is	be	AUX
ejpam-1203	445	11	ρ	ρ	NOUN
ejpam-1203	445	12	-	-	ADJ
ejpam-1203	445	13	open	open	ADJ
ejpam-1203	445	14	then	then	ADV
ejpam-1203	445	15	b	b	NOUN
ejpam-1203	445	16	is	be	AUX
ejpam-1203	445	17	ρ	ρ	NOUN
ejpam-1203	445	18	-	-	ADJ
ejpam-1203	445	19	open	open	ADJ
ejpam-1203	445	20	.	.	PUNCT
ejpam-1203	446	1	proof	proof	NOUN
ejpam-1203	446	2	.	.	PUNCT
ejpam-1203	447	1	if	if	SCONJ
ejpam-1203	447	2	pint(a	pint(a	NOUN
ejpam-1203	447	3	)	)	PUNCT
ejpam-1203	447	4	⊆	⊆	NUM
ejpam-1203	447	5	b	b	PROPN
ejpam-1203	447	6	⊆	⊆	NUM
ejpam-1203	447	7	a	a	NOUN
ejpam-1203	447	8	,	,	PUNCT
ejpam-1203	447	9	then	then	ADV
ejpam-1203	447	10	x	x	INTJ
ejpam-1203	447	11	−	−	PROPN
ejpam-1203	447	12	a⊆	a⊆	VERB
ejpam-1203	447	13	x	x	PUNCT
ejpam-1203	448	1	−	−	NOUN
ejpam-1203	448	2	b	b	NOUN
ejpam-1203	448	3	⊆	⊆	NUM
ejpam-1203	448	4	x	x	SYM
ejpam-1203	448	5	−	−	PROPN
ejpam-1203	448	6	pint(a	pint(a	NOUN
ejpam-1203	448	7	)	)	PUNCT
ejpam-1203	448	8	that	that	PRON
ejpam-1203	448	9	is	be	AUX
ejpam-1203	448	10	x	x	X
ejpam-1203	448	11	−	−	VERB
ejpam-1203	448	12	a	a	DET
ejpam-1203	448	13	⊆	⊆	NUM
ejpam-1203	448	14	x	x	SYM
ejpam-1203	448	15	−	−	PROPN
ejpam-1203	448	16	b	b	NOUN
ejpam-1203	448	17	⊆	⊆	NUM
ejpam-1203	448	18	pcl(x	pcl(x	PROPN
ejpam-1203	448	19	−	−	PROPN
ejpam-1203	448	20	a	a	NOUN
ejpam-1203	448	21	)	)	PUNCT
ejpam-1203	448	22	.	.	PUNCT
ejpam-1203	449	1	observe	observe	VERB
ejpam-1203	449	2	that	that	SCONJ
ejpam-1203	449	3	x	x	PUNCT
ejpam-1203	449	4	−	−	NOUN
ejpam-1203	449	5	a	a	PRON
ejpam-1203	449	6	is	be	AUX
ejpam-1203	449	7	ρ	ρ	NOUN
ejpam-1203	449	8	-	-	PUNCT
ejpam-1203	449	9	closed	closed	ADJ
ejpam-1203	449	10	and	and	CCONJ
ejpam-1203	449	11	by	by	ADP
ejpam-1203	449	12	theorem	theorem	NOUN
ejpam-1203	449	13	10	10	NUM
ejpam-1203	449	14	x	x	SYM
ejpam-1203	449	15	−	−	PROPN
ejpam-1203	449	16	b	b	PROPN
ejpam-1203	449	17	is	be	AUX
ejpam-1203	449	18	ρ	ρ	NOUN
ejpam-1203	449	19	-	-	PUNCT
ejpam-1203	449	20	closed	closed	ADJ
ejpam-1203	449	21	and	and	CCONJ
ejpam-1203	449	22	hence	hence	ADV
ejpam-1203	449	23	b	b	PROPN
ejpam-1203	449	24	is	be	AUX
ejpam-1203	449	25	ρ	ρ	NOUN
ejpam-1203	449	26	-	-	ADJ
ejpam-1203	449	27	open	open	ADJ
ejpam-1203	449	28	.	.	PUNCT
ejpam-1203	450	1	theorem	theorem	VERB
ejpam-1203	450	2	23	23	NUM
ejpam-1203	450	3	.	.	PUNCT
ejpam-1203	451	1	if	if	SCONJ
ejpam-1203	451	2	a⊆	a⊆	PROPN
ejpam-1203	451	3	k	k	PROPN
ejpam-1203	451	4	is	be	AUX
ejpam-1203	451	5	ρ	ρ	NOUN
ejpam-1203	451	6	-	-	PUNCT
ejpam-1203	451	7	closed	closed	ADJ
ejpam-1203	451	8	then	then	ADV
ejpam-1203	451	9	pcl(a)−	pcl(a)−	VERB
ejpam-1203	451	10	a	a	PRON
ejpam-1203	451	11	is	be	AUX
ejpam-1203	451	12	ρ	ρ	NOUN
ejpam-1203	451	13	-	-	ADJ
ejpam-1203	451	14	open	open	ADJ
ejpam-1203	451	15	.	.	PUNCT
ejpam-1203	452	1	proof	proof	NOUN
ejpam-1203	452	2	.	.	PUNCT
ejpam-1203	453	1	let	let	VERB
ejpam-1203	453	2	a	a	PRON
ejpam-1203	453	3	be	be	AUX
ejpam-1203	453	4	an	an	DET
ejpam-1203	453	5	ρ	ρ	NOUN
ejpam-1203	453	6	-	-	PUNCT
ejpam-1203	453	7	closed	closed	ADJ
ejpam-1203	453	8	.	.	PUNCT
ejpam-1203	454	1	then	then	ADV
ejpam-1203	454	2	by	by	ADP
ejpam-1203	454	3	theorem	theorem	NOUN
ejpam-1203	454	4	9	9	NUM
ejpam-1203	454	5	,	,	PUNCT
ejpam-1203	454	6	pcl(a)−a	pcl(a)−a	NOUN
ejpam-1203	454	7	contains	contain	VERB
ejpam-1203	454	8	no	no	DET
ejpam-1203	454	9	nonempty	nonempty	ADV
ejpam-1203	454	10	g̃-closed	g̃-close	VERB
ejpam-1203	454	11	set	set	NOUN
ejpam-1203	454	12	.	.	PUNCT
ejpam-1203	455	1	therefore	therefore	ADV
ejpam-1203	455	2	φ	φ	PROPN
ejpam-1203	455	3	=	=	SYM
ejpam-1203	455	4	k	k	PROPN
ejpam-1203	455	5	⊆	⊆	NUM
ejpam-1203	455	6	pcl(a)−	pcl(a)−	NOUN
ejpam-1203	455	7	a	a	PRON
ejpam-1203	455	8	and	and	CCONJ
ejpam-1203	455	9	φ	φ	NOUN
ejpam-1203	455	10	=	=	SYM
ejpam-1203	455	11	k	k	PROPN
ejpam-1203	455	12	is	be	AUX
ejpam-1203	455	13	g̃-closed	g̃-close	VERB
ejpam-1203	455	14	.	.	PUNCT
ejpam-1203	456	1	clearly	clearly	ADV
ejpam-1203	456	2	cl(k	cl(k	PUNCT
ejpam-1203	456	3	)	)	PUNCT
ejpam-1203	457	1	⊆	⊆	X
ejpam-1203	457	2	pint(pcl(a)−	pint(pcl(a)−	VERB
ejpam-1203	457	3	a	a	PRON
ejpam-1203	457	4	)	)	PUNCT
ejpam-1203	457	5	.	.	PUNCT
ejpam-1203	458	1	hence	hence	ADV
ejpam-1203	458	2	by	by	ADP
ejpam-1203	458	3	theorem	theorem	NOUN
ejpam-1203	458	4	21	21	NUM
ejpam-1203	458	5	,	,	PUNCT
ejpam-1203	458	6	pcl(a)−	pcl(a)−	VERB
ejpam-1203	458	7	a	a	PRON
ejpam-1203	458	8	is	be	AUX
ejpam-1203	458	9	ρ	ρ	NOUN
ejpam-1203	458	10	-	-	NOUN
ejpam-1203	458	11	open	open	ADJ
ejpam-1203	458	12	.	.	PUNCT
ejpam-1203	459	1	6	6	NUM
ejpam-1203	459	2	.	.	X
ejpam-1203	459	3	ρ	ρ	NOUN
ejpam-1203	459	4	-	-	PUNCT
ejpam-1203	459	5	continuity	continuity	NOUN
ejpam-1203	459	6	and	and	CCONJ
ejpam-1203	459	7	ρs	ρs	NOUN
ejpam-1203	459	8	-	-	PUNCT
ejpam-1203	459	9	continuity	continuity	NOUN
ejpam-1203	459	10	let	let	VERB
ejpam-1203	459	11	f	f	NOUN
ejpam-1203	459	12	:	:	PUNCT
ejpam-1203	459	13	(	(	PUNCT
ejpam-1203	459	14	x	x	X
ejpam-1203	459	15	,	,	PUNCT
ejpam-1203	459	16	τ	τ	PROPN
ejpam-1203	459	17	)	)	PUNCT
ejpam-1203	459	18	→	→	SYM
ejpam-1203	459	19	(	(	PUNCT
ejpam-1203	459	20	y	y	PROPN
ejpam-1203	459	21	,	,	PUNCT
ejpam-1203	459	22	σ	σ	PROPN
ejpam-1203	459	23	)	)	PUNCT
ejpam-1203	459	24	be	be	VERB
ejpam-1203	459	25	a	a	DET
ejpam-1203	459	26	function	function	NOUN
ejpam-1203	459	27	from	from	ADP
ejpam-1203	459	28	a	a	DET
ejpam-1203	459	29	topological	topological	ADJ
ejpam-1203	459	30	space	space	NOUN
ejpam-1203	459	31	(	(	PUNCT
ejpam-1203	459	32	x	x	X
ejpam-1203	459	33	,	,	PUNCT
ejpam-1203	459	34	τ	τ	PROPN
ejpam-1203	459	35	)	)	PUNCT
ejpam-1203	459	36	into	into	ADP
ejpam-1203	459	37	a	a	DET
ejpam-1203	459	38	topological	topological	ADJ
ejpam-1203	459	39	space	space	NOUN
ejpam-1203	459	40	(	(	PUNCT
ejpam-1203	459	41	y	y	PROPN
ejpam-1203	459	42	,	,	PUNCT
ejpam-1203	459	43	σ	σ	PROPN
ejpam-1203	459	44	)	)	PUNCT
ejpam-1203	459	45	.	.	PUNCT
ejpam-1203	460	1	definition	definition	NOUN
ejpam-1203	460	2	12	12	NUM
ejpam-1203	460	3	.	.	PUNCT
ejpam-1203	461	1	1	1	X
ejpam-1203	461	2	.	.	X
ejpam-1203	462	1	a	a	DET
ejpam-1203	462	2	function	function	NOUN
ejpam-1203	462	3	f	f	NOUN
ejpam-1203	462	4	:	:	PUNCT
ejpam-1203	462	5	(	(	PUNCT
ejpam-1203	462	6	x	x	X
ejpam-1203	462	7	,	,	PUNCT
ejpam-1203	462	8	τ)→	τ)→	PROPN
ejpam-1203	462	9	(	(	PUNCT
ejpam-1203	462	10	y	y	PROPN
ejpam-1203	462	11	,	,	PUNCT
ejpam-1203	462	12	σ	σ	PROPN
ejpam-1203	462	13	)	)	PUNCT
ejpam-1203	462	14	is	be	AUX
ejpam-1203	462	15	said	say	VERB
ejpam-1203	462	16	to	to	PART
ejpam-1203	462	17	be	be	AUX
ejpam-1203	462	18	ρ	ρ	NOUN
ejpam-1203	462	19	-	-	ADJ
ejpam-1203	462	20	continuous	continuous	ADJ
ejpam-1203	462	21	(	(	PUNCT
ejpam-1203	462	22	resp	resp	NOUN
ejpam-1203	462	23	.	.	PUNCT
ejpam-1203	463	1	ρs	ρs	NOUN
ejpam-1203	463	2	-	-	PUNCT
ejpam-1203	463	3	continuous	continuous	ADJ
ejpam-1203	463	4	)	)	PUNCT
ejpam-1203	463	5	if	if	SCONJ
ejpam-1203	463	6	f	f	PROPN
ejpam-1203	463	7	−1(v	−1(v	PROPN
ejpam-1203	463	8	)	)	PUNCT
ejpam-1203	463	9	is	be	AUX
ejpam-1203	463	10	ρ	ρ	NOUN
ejpam-1203	463	11	-	-	PUNCT
ejpam-1203	463	12	closed	closed	ADJ
ejpam-1203	463	13	(	(	PUNCT
ejpam-1203	463	14	resp	resp	NOUN
ejpam-1203	463	15	.	.	PUNCT
ejpam-1203	464	1	ρs	ρs	NOUN
ejpam-1203	464	2	-	-	PUNCT
ejpam-1203	464	3	closed	closed	ADJ
ejpam-1203	464	4	)	)	PUNCT
ejpam-1203	464	5	in	in	ADP
ejpam-1203	464	6	(	(	PUNCT
ejpam-1203	464	7	x	x	INTJ
ejpam-1203	464	8	,	,	PUNCT
ejpam-1203	464	9	τ	τ	PROPN
ejpam-1203	464	10	)	)	PUNCT
ejpam-1203	464	11	for	for	ADP
ejpam-1203	464	12	every	every	DET
ejpam-1203	464	13	closed	close	VERB
ejpam-1203	464	14	set	set	VERB
ejpam-1203	464	15	v	v	NOUN
ejpam-1203	464	16	of	of	ADP
ejpam-1203	464	17	(	(	PUNCT
ejpam-1203	464	18	y	y	PROPN
ejpam-1203	464	19	,	,	PUNCT
ejpam-1203	464	20	σ	σ	PROPN
ejpam-1203	464	21	)	)	PUNCT
ejpam-1203	464	22	.	.	PUNCT
ejpam-1203	465	1	2	2	X
ejpam-1203	465	2	.	.	X
ejpam-1203	465	3	a	a	DET
ejpam-1203	465	4	function	function	NOUN
ejpam-1203	465	5	f	f	NOUN
ejpam-1203	465	6	:	:	PUNCT
ejpam-1203	465	7	(	(	PUNCT
ejpam-1203	465	8	x	x	X
ejpam-1203	465	9	,	,	PUNCT
ejpam-1203	465	10	τ)→	τ)→	PROPN
ejpam-1203	465	11	(	(	PUNCT
ejpam-1203	465	12	y	y	PROPN
ejpam-1203	465	13	,	,	PUNCT
ejpam-1203	465	14	σ	σ	PROPN
ejpam-1203	465	15	)	)	PUNCT
ejpam-1203	465	16	is	be	AUX
ejpam-1203	465	17	said	say	VERB
ejpam-1203	465	18	to	to	PART
ejpam-1203	465	19	be	be	AUX
ejpam-1203	465	20	ρ	ρ	NOUN
ejpam-1203	465	21	-	-	NOUN
ejpam-1203	465	22	irresolute	irresolute	ADJ
ejpam-1203	465	23	(	(	PUNCT
ejpam-1203	465	24	resp	resp	NOUN
ejpam-1203	465	25	.	.	PUNCT
ejpam-1203	466	1	ρs	ρs	NOUN
ejpam-1203	466	2	-	-	PUNCT
ejpam-1203	466	3	irresolute	irresolute	NOUN
ejpam-1203	466	4	)	)	PUNCT
ejpam-1203	466	5	if	if	SCONJ
ejpam-1203	466	6	f	f	PROPN
ejpam-1203	466	7	−1(v	−1(v	PROPN
ejpam-1203	466	8	)	)	PUNCT
ejpam-1203	466	9	is	be	AUX
ejpam-1203	466	10	ρ	ρ	NOUN
ejpam-1203	466	11	-	-	PUNCT
ejpam-1203	466	12	closed	closed	ADJ
ejpam-1203	466	13	(	(	PUNCT
ejpam-1203	466	14	resp	resp	NOUN
ejpam-1203	466	15	.	.	PUNCT
ejpam-1203	467	1	ρs	ρs	NOUN
ejpam-1203	467	2	-	-	PUNCT
ejpam-1203	467	3	closed	closed	ADJ
ejpam-1203	467	4	)	)	PUNCT
ejpam-1203	467	5	in	in	ADP
ejpam-1203	467	6	(	(	PUNCT
ejpam-1203	467	7	x	x	INTJ
ejpam-1203	467	8	,	,	PUNCT
ejpam-1203	467	9	τ	τ	PROPN
ejpam-1203	467	10	)	)	PUNCT
ejpam-1203	467	11	for	for	ADP
ejpam-1203	467	12	every	every	DET
ejpam-1203	467	13	ρ	ρ	NOUN
ejpam-1203	467	14	-	-	PUNCT
ejpam-1203	467	15	closed	closed	ADJ
ejpam-1203	467	16	(	(	PUNCT
ejpam-1203	467	17	resp	resp	NOUN
ejpam-1203	467	18	.	.	PUNCT
ejpam-1203	468	1	ρs	ρs	NOUN
ejpam-1203	468	2	-	-	PUNCT
ejpam-1203	468	3	closed	closed	ADJ
ejpam-1203	468	4	)	)	PUNCT
ejpam-1203	469	1	set	set	VERB
ejpam-1203	469	2	v	v	NUM
ejpam-1203	469	3	of	of	ADP
ejpam-1203	469	4	(	(	PUNCT
ejpam-1203	469	5	y	y	PROPN
ejpam-1203	469	6	,	,	PUNCT
ejpam-1203	469	7	σ	σ	PROPN
ejpam-1203	469	8	)	)	PUNCT
ejpam-1203	469	9	.	.	PUNCT
ejpam-1203	470	1	example	example	NOUN
ejpam-1203	470	2	21	21	NUM
ejpam-1203	470	3	.	.	NOUN
ejpam-1203	471	1	1	1	X
ejpam-1203	471	2	.	.	X
ejpam-1203	472	1	let	let	VERB
ejpam-1203	472	2	x	x	PUNCT
ejpam-1203	472	3	=	=	PRON
ejpam-1203	472	4	{	{	PUNCT
ejpam-1203	472	5	a	a	DET
ejpam-1203	472	6	,	,	PUNCT
ejpam-1203	472	7	b	b	NOUN
ejpam-1203	472	8	,	,	PUNCT
ejpam-1203	472	9	c	c	NOUN
ejpam-1203	472	10	}	}	PUNCT
ejpam-1203	472	11	,	,	PUNCT
ejpam-1203	472	12	τ	τ	X
ejpam-1203	472	13	=	=	PUNCT
ejpam-1203	472	14	{	{	PUNCT
ejpam-1203	472	15	φ	φ	PROPN
ejpam-1203	472	16	,	,	PUNCT
ejpam-1203	472	17	{	{	PUNCT
ejpam-1203	472	18	a	a	X
ejpam-1203	472	19	}	}	PUNCT
ejpam-1203	472	20	,	,	PUNCT
ejpam-1203	472	21	{	{	PUNCT
ejpam-1203	472	22	b	b	NOUN
ejpam-1203	472	23	}	}	PUNCT
ejpam-1203	472	24	,	,	PUNCT
ejpam-1203	472	25	{	{	PUNCT
ejpam-1203	472	26	a	a	DET
ejpam-1203	472	27	,	,	PUNCT
ejpam-1203	472	28	b	b	NOUN
ejpam-1203	472	29	}	}	PUNCT
ejpam-1203	472	30	,	,	PUNCT
ejpam-1203	472	31	x	x	SYM
ejpam-1203	472	32	}	}	PUNCT
ejpam-1203	472	33	and	and	CCONJ
ejpam-1203	472	34	σ	σ	NUM
ejpam-1203	472	35	=	=	SYM
ejpam-1203	472	36	{	{	PUNCT
ejpam-1203	472	37	φ	φ	PROPN
ejpam-1203	472	38	,	,	PUNCT
ejpam-1203	472	39	{	{	PUNCT
ejpam-1203	472	40	c	c	NOUN
ejpam-1203	472	41	}	}	PUNCT
ejpam-1203	472	42	,	,	PUNCT
ejpam-1203	472	43	{	{	PUNCT
ejpam-1203	472	44	b	b	X
ejpam-1203	472	45	,	,	PUNCT
ejpam-1203	472	46	c	c	NOUN
ejpam-1203	472	47	}	}	PUNCT
ejpam-1203	472	48	,	,	PUNCT
ejpam-1203	472	49	x	x	SYM
ejpam-1203	472	50	}	}	PUNCT
ejpam-1203	472	51	.	.	PUNCT
ejpam-1203	473	1	define	define	VERB
ejpam-1203	473	2	f	f	X
ejpam-1203	473	3	:	:	PUNCT
ejpam-1203	473	4	(	(	PUNCT
ejpam-1203	473	5	x	x	X
ejpam-1203	473	6	,	,	PUNCT
ejpam-1203	473	7	τ)→	τ)→	PROPN
ejpam-1203	473	8	(	(	PUNCT
ejpam-1203	473	9	x	x	X
ejpam-1203	473	10	,	,	PUNCT
ejpam-1203	473	11	σ	σ	PROPN
ejpam-1203	473	12	)	)	PUNCT
ejpam-1203	473	13	by	by	ADP
ejpam-1203	473	14	f	f	PROPN
ejpam-1203	473	15	(	(	PUNCT
ejpam-1203	473	16	a	a	X
ejpam-1203	473	17	)	)	PUNCT
ejpam-1203	474	1	=	=	SYM
ejpam-1203	474	2	f	f	X
ejpam-1203	474	3	(	(	PUNCT
ejpam-1203	474	4	b	b	NOUN
ejpam-1203	474	5	)	)	PUNCT
ejpam-1203	474	6	=	=	SYM
ejpam-1203	474	7	b	b	PROPN
ejpam-1203	474	8	and	and	CCONJ
ejpam-1203	474	9	f	f	PROPN
ejpam-1203	474	10	(	(	PUNCT
ejpam-1203	474	11	c	c	NOUN
ejpam-1203	474	12	)	)	PUNCT
ejpam-1203	474	13	=	=	SYM
ejpam-1203	475	1	a	a	PRON
ejpam-1203	475	2	,	,	PUNCT
ejpam-1203	475	3	then	then	ADV
ejpam-1203	475	4	f	f	PROPN
ejpam-1203	475	5	is	be	AUX
ejpam-1203	475	6	ρ	ρ	NOUN
ejpam-1203	475	7	-	-	ADJ
ejpam-1203	475	8	continuous	continuous	ADJ
ejpam-1203	475	9	.	.	PUNCT
ejpam-1203	476	1	2	2	X
ejpam-1203	476	2	.	.	X
ejpam-1203	476	3	let	let	VERB
ejpam-1203	476	4	x	x	PUNCT
ejpam-1203	476	5	=	=	PRON
ejpam-1203	476	6	{	{	PUNCT
ejpam-1203	476	7	a	a	DET
ejpam-1203	476	8	,	,	PUNCT
ejpam-1203	476	9	b	b	NOUN
ejpam-1203	476	10	,	,	PUNCT
ejpam-1203	476	11	c	c	NOUN
ejpam-1203	476	12	}	}	PUNCT
ejpam-1203	476	13	,	,	PUNCT
ejpam-1203	476	14	τ	τ	X
ejpam-1203	476	15	=	=	PUNCT
ejpam-1203	476	16	{	{	PUNCT
ejpam-1203	476	17	φ	φ	PROPN
ejpam-1203	476	18	,	,	PUNCT
ejpam-1203	476	19	{	{	PUNCT
ejpam-1203	476	20	c	c	NOUN
ejpam-1203	476	21	}	}	PUNCT
ejpam-1203	476	22	,	,	PUNCT
ejpam-1203	476	23	{	{	PUNCT
ejpam-1203	476	24	a	a	DET
ejpam-1203	476	25	,	,	PUNCT
ejpam-1203	476	26	b	b	NOUN
ejpam-1203	476	27	}	}	PUNCT
ejpam-1203	476	28	,	,	PUNCT
ejpam-1203	476	29	x	x	SYM
ejpam-1203	476	30	}	}	PUNCT
ejpam-1203	476	31	and	and	CCONJ
ejpam-1203	476	32	σ	σ	NUM
ejpam-1203	476	33	=	=	SYM
ejpam-1203	476	34	{	{	PUNCT
ejpam-1203	476	35	φ	φ	PROPN
ejpam-1203	476	36	,	,	PUNCT
ejpam-1203	476	37	{	{	PUNCT
ejpam-1203	476	38	a	a	DET
ejpam-1203	476	39	,	,	PUNCT
ejpam-1203	476	40	b	b	NOUN
ejpam-1203	476	41	}	}	PUNCT
ejpam-1203	476	42	,	,	PUNCT
ejpam-1203	476	43	x	x	SYM
ejpam-1203	476	44	}	}	PUNCT
ejpam-1203	476	45	.	.	PUNCT
ejpam-1203	477	1	define	define	VERB
ejpam-1203	477	2	f	f	X
ejpam-1203	477	3	:	:	PUNCT
ejpam-1203	477	4	(	(	PUNCT
ejpam-1203	477	5	x	x	X
ejpam-1203	477	6	,	,	PUNCT
ejpam-1203	477	7	τ)→	τ)→	PROPN
ejpam-1203	477	8	(	(	PUNCT
ejpam-1203	477	9	x	x	X
ejpam-1203	477	10	,	,	PUNCT
ejpam-1203	477	11	σ	σ	PROPN
ejpam-1203	477	12	)	)	PUNCT
ejpam-1203	477	13	by	by	ADP
ejpam-1203	477	14	f	f	PROPN
ejpam-1203	477	15	(	(	PUNCT
ejpam-1203	477	16	a	a	NOUN
ejpam-1203	477	17	)	)	PUNCT
ejpam-1203	477	18	=	=	SYM
ejpam-1203	477	19	c	c	X
ejpam-1203	477	20	,	,	PUNCT
ejpam-1203	477	21	f	f	PROPN
ejpam-1203	477	22	(	(	PUNCT
ejpam-1203	477	23	b	b	NOUN
ejpam-1203	477	24	)	)	PUNCT
ejpam-1203	477	25	=	=	SYM
ejpam-1203	477	26	b	b	PROPN
ejpam-1203	477	27	and	and	CCONJ
ejpam-1203	477	28	f	f	PROPN
ejpam-1203	477	29	(	(	PUNCT
ejpam-1203	477	30	c	c	NOUN
ejpam-1203	477	31	)	)	PUNCT
ejpam-1203	477	32	=	=	SYM
ejpam-1203	478	1	a.	a.	NOUN
ejpam-1203	478	2	then	then	ADV
ejpam-1203	478	3	the	the	DET
ejpam-1203	478	4	inverse	inverse	ADJ
ejpam-1203	478	5	image	image	NOUN
ejpam-1203	478	6	of	of	ADP
ejpam-1203	478	7	every	every	DET
ejpam-1203	478	8	ρ	ρ	PROPN
ejpam-1203	478	9	-	-	PUNCT
ejpam-1203	478	10	closed	closed	ADJ
ejpam-1203	478	11	set	set	NOUN
ejpam-1203	478	12	is	be	AUX
ejpam-1203	478	13	ρ	ρ	NOUN
ejpam-1203	478	14	-	-	PUNCT
ejpam-1203	478	15	closed	closed	ADJ
ejpam-1203	478	16	under	under	ADP
ejpam-1203	478	17	f	f	PROPN
ejpam-1203	478	18	.	.	PUNCT
ejpam-1203	479	1	hence	hence	ADV
ejpam-1203	479	2	f	f	PROPN
ejpam-1203	479	3	is	be	AUX
ejpam-1203	479	4	ρ	ρ	NOUN
ejpam-1203	479	5	-	-	PUNCT
ejpam-1203	479	6	irresolute	irresolute	NOUN
ejpam-1203	479	7	.	.	PUNCT
ejpam-1203	480	1	references	reference	NOUN
ejpam-1203	480	2	565	565	NUM
ejpam-1203	480	3	the	the	DET
ejpam-1203	480	4	composition	composition	NOUN
ejpam-1203	480	5	of	of	ADP
ejpam-1203	480	6	two	two	NUM
ejpam-1203	480	7	ρ	ρ	ADJ
ejpam-1203	480	8	-	-	PUNCT
ejpam-1203	480	9	continuous	continuous	ADJ
ejpam-1203	480	10	functions	function	NOUN
ejpam-1203	480	11	need	need	VERB
ejpam-1203	480	12	not	not	PART
ejpam-1203	480	13	beρ	beρ	ADJ
ejpam-1203	480	14	-	-	PUNCT
ejpam-1203	480	15	continuous	continuous	ADJ
ejpam-1203	480	16	as	as	SCONJ
ejpam-1203	480	17	it	it	PRON
ejpam-1203	480	18	is	be	AUX
ejpam-1203	480	19	shown	show	VERB
ejpam-1203	480	20	by	by	ADP
ejpam-1203	480	21	the	the	DET
ejpam-1203	480	22	following	follow	VERB
ejpam-1203	480	23	example	example	NOUN
ejpam-1203	480	24	.	.	PUNCT
ejpam-1203	481	1	example	example	NOUN
ejpam-1203	482	1	22	22	NUM
ejpam-1203	482	2	.	.	PUNCT
ejpam-1203	483	1	let	let	VERB
ejpam-1203	483	2	x	x	PUNCT
ejpam-1203	483	3	=	=	PRON
ejpam-1203	483	4	{	{	PUNCT
ejpam-1203	483	5	a	a	DET
ejpam-1203	483	6	,	,	PUNCT
ejpam-1203	483	7	b	b	NOUN
ejpam-1203	483	8	,	,	PUNCT
ejpam-1203	483	9	c	c	NOUN
ejpam-1203	483	10	}	}	PUNCT
ejpam-1203	483	11	,	,	PUNCT
ejpam-1203	483	12	τ=	τ=	X
ejpam-1203	483	13	{	{	PUNCT
ejpam-1203	483	14	φ	φ	PROPN
ejpam-1203	483	15	,	,	PUNCT
ejpam-1203	483	16	{	{	PUNCT
ejpam-1203	483	17	b	b	NOUN
ejpam-1203	483	18	}	}	PUNCT
ejpam-1203	483	19	,	,	PUNCT
ejpam-1203	483	20	x	x	SYM
ejpam-1203	483	21	}	}	PUNCT
ejpam-1203	483	22	,	,	PUNCT
ejpam-1203	483	23	σ	σ	PROPN
ejpam-1203	483	24	=	=	SYM
ejpam-1203	483	25	{	{	PUNCT
ejpam-1203	483	26	φ	φ	PROPN
ejpam-1203	483	27	,	,	PUNCT
ejpam-1203	483	28	{	{	PUNCT
ejpam-1203	483	29	a	a	DET
ejpam-1203	483	30	,	,	PUNCT
ejpam-1203	483	31	b	b	NOUN
ejpam-1203	483	32	}	}	PUNCT
ejpam-1203	483	33	,	,	PUNCT
ejpam-1203	483	34	x	x	SYM
ejpam-1203	483	35	}	}	PUNCT
ejpam-1203	483	36	and	and	CCONJ
ejpam-1203	483	37	η	η	PROPN
ejpam-1203	483	38	=	=	PROPN
ejpam-1203	483	39	{	{	PUNCT
ejpam-1203	483	40	φ	φ	PROPN
ejpam-1203	483	41	,	,	PUNCT
ejpam-1203	483	42	{	{	PUNCT
ejpam-1203	483	43	a	a	X
ejpam-1203	483	44	}	}	PUNCT
ejpam-1203	483	45	,	,	PUNCT
ejpam-1203	483	46	{	{	PUNCT
ejpam-1203	483	47	a	a	DET
ejpam-1203	483	48	,	,	PUNCT
ejpam-1203	483	49	b	b	NOUN
ejpam-1203	483	50	}	}	PUNCT
ejpam-1203	483	51	,	,	PUNCT
ejpam-1203	483	52	x	x	SYM
ejpam-1203	483	53	}	}	PUNCT
ejpam-1203	483	54	.	.	PUNCT
ejpam-1203	484	1	define	define	VERB
ejpam-1203	484	2	f	f	X
ejpam-1203	484	3	:	:	PUNCT
ejpam-1203	484	4	(	(	PUNCT
ejpam-1203	484	5	x	x	X
ejpam-1203	484	6	,	,	PUNCT
ejpam-1203	484	7	τ)→	τ)→	PROPN
ejpam-1203	484	8	(	(	PUNCT
ejpam-1203	484	9	x	x	X
ejpam-1203	484	10	,	,	PUNCT
ejpam-1203	484	11	σ	σ	PROPN
ejpam-1203	484	12	)	)	PUNCT
ejpam-1203	484	13	by	by	ADP
ejpam-1203	484	14	f	f	PROPN
ejpam-1203	484	15	(	(	PUNCT
ejpam-1203	484	16	a	a	NOUN
ejpam-1203	484	17	)	)	PUNCT
ejpam-1203	484	18	=	=	SYM
ejpam-1203	484	19	c	c	X
ejpam-1203	484	20	,	,	PUNCT
ejpam-1203	484	21	f	f	PROPN
ejpam-1203	484	22	(	(	PUNCT
ejpam-1203	484	23	b	b	NOUN
ejpam-1203	484	24	)	)	PUNCT
ejpam-1203	484	25	=	=	SYM
ejpam-1203	485	1	a	a	PROPN
ejpam-1203	485	2	,	,	PUNCT
ejpam-1203	485	3	f	f	PROPN
ejpam-1203	485	4	(	(	PUNCT
ejpam-1203	485	5	c	c	NOUN
ejpam-1203	485	6	)	)	PUNCT
ejpam-1203	485	7	=	=	SYM
ejpam-1203	485	8	b	b	NOUN
ejpam-1203	485	9	and	and	CCONJ
ejpam-1203	485	10	define	define	VERB
ejpam-1203	485	11	g	g	NOUN
ejpam-1203	485	12	:	:	PUNCT
ejpam-1203	485	13	(	(	PUNCT
ejpam-1203	485	14	x	x	X
ejpam-1203	485	15	,	,	PUNCT
ejpam-1203	485	16	σ)→	σ)→	PROPN
ejpam-1203	485	17	(	(	PUNCT
ejpam-1203	485	18	x	x	PROPN
ejpam-1203	485	19	,	,	PUNCT
ejpam-1203	485	20	η	η	PROPN
ejpam-1203	485	21	)	)	PUNCT
ejpam-1203	485	22	by	by	ADP
ejpam-1203	485	23	g(a	g(a	PROPN
ejpam-1203	485	24	)	)	PUNCT
ejpam-1203	485	25	=	=	SYM
ejpam-1203	486	1	c	c	X
ejpam-1203	486	2	,	,	PUNCT
ejpam-1203	486	3	g(b	g(b	NOUN
ejpam-1203	486	4	)	)	PUNCT
ejpam-1203	486	5	=	=	SYM
ejpam-1203	486	6	a	a	PRON
ejpam-1203	486	7	and	and	CCONJ
ejpam-1203	486	8	g(c	g(c	NOUN
ejpam-1203	486	9	)	)	PUNCT
ejpam-1203	486	10	=	=	SYM
ejpam-1203	487	1	b.	b.	PROPN
ejpam-1203	488	1	then	then	ADV
ejpam-1203	488	2	f	f	PROPN
ejpam-1203	488	3	and	and	CCONJ
ejpam-1203	488	4	g	g	PROPN
ejpam-1203	488	5	are	be	AUX
ejpam-1203	488	6	ρ	ρ	NOUN
ejpam-1203	488	7	-	-	ADJ
ejpam-1203	488	8	continuous	continuous	ADJ
ejpam-1203	488	9	but	but	CCONJ
ejpam-1203	488	10	g	g	PROPN
ejpam-1203	488	11	◦	◦	NOUN
ejpam-1203	488	12	f	f	PROPN
ejpam-1203	488	13	is	be	AUX
ejpam-1203	488	14	not	not	PART
ejpam-1203	488	15	ρ	ρ	NOUN
ejpam-1203	488	16	-	-	ADJ
ejpam-1203	488	17	continuous	continuous	ADJ
ejpam-1203	488	18	.	.	PUNCT
ejpam-1203	489	1	since	since	SCONJ
ejpam-1203	489	2	{	{	PUNCT
ejpam-1203	489	3	c	c	X
ejpam-1203	489	4	}	}	PUNCT
ejpam-1203	489	5	is	be	AUX
ejpam-1203	489	6	closed	close	VERB
ejpam-1203	489	7	in	in	ADP
ejpam-1203	489	8	(	(	PUNCT
ejpam-1203	489	9	x	x	INTJ
ejpam-1203	489	10	,	,	PUNCT
ejpam-1203	489	11	η	η	PROPN
ejpam-1203	489	12	)	)	PUNCT
ejpam-1203	489	13	(	(	PUNCT
ejpam-1203	489	14	g	g	PROPN
ejpam-1203	489	15	◦	◦	NOUN
ejpam-1203	489	16	f	f	PROPN
ejpam-1203	489	17	)	)	PUNCT
ejpam-1203	489	18	−1({c	−1({c	ADV
ejpam-1203	489	19	}	}	PUNCT
ejpam-1203	489	20	)	)	PUNCT
ejpam-1203	490	1	=	=	SYM
ejpam-1203	490	2	f	f	X
ejpam-1203	490	3	−1(g−1({c	−1(g−1({c	NOUN
ejpam-1203	490	4	}	}	PUNCT
ejpam-1203	490	5	)	)	PUNCT
ejpam-1203	490	6	)	)	PUNCT
ejpam-1203	491	1	=	=	PUNCT
ejpam-1203	491	2	f	f	X
ejpam-1203	491	3	−1({a	−1({a	PROPN
ejpam-1203	491	4	}	}	PUNCT
ejpam-1203	491	5	)	)	PUNCT
ejpam-1203	491	6	=	=	PUNCT
ejpam-1203	491	7	{	{	PUNCT
ejpam-1203	491	8	b	b	NOUN
ejpam-1203	491	9	}	}	PUNCT
ejpam-1203	491	10	which	which	PRON
ejpam-1203	491	11	is	be	AUX
ejpam-1203	491	12	not	not	PART
ejpam-1203	491	13	ρ	ρ	NOUN
ejpam-1203	491	14	-	-	PUNCT
ejpam-1203	491	15	closed	closed	ADJ
ejpam-1203	491	16	in	in	ADP
ejpam-1203	491	17	(	(	PUNCT
ejpam-1203	491	18	x	x	INTJ
ejpam-1203	491	19	,	,	PUNCT
ejpam-1203	491	20	τ	τ	PROPN
ejpam-1203	491	21	)	)	PUNCT
ejpam-1203	491	22	.	.	PUNCT
ejpam-1203	492	1	theorem	theorem	NOUN
ejpam-1203	492	2	24	24	NUM
ejpam-1203	492	3	.	.	PUNCT
ejpam-1203	493	1	let	let	VERB
ejpam-1203	493	2	f	f	NOUN
ejpam-1203	493	3	:	:	PUNCT
ejpam-1203	493	4	(	(	PUNCT
ejpam-1203	493	5	x	x	X
ejpam-1203	493	6	,	,	PUNCT
ejpam-1203	493	7	τ)→	τ)→	PROPN
ejpam-1203	493	8	(	(	PUNCT
ejpam-1203	493	9	y	y	PROPN
ejpam-1203	493	10	,	,	PUNCT
ejpam-1203	493	11	σ	σ	PROPN
ejpam-1203	493	12	)	)	PUNCT
ejpam-1203	493	13	and	and	CCONJ
ejpam-1203	493	14	g	g	NOUN
ejpam-1203	493	15	:	:	PUNCT
ejpam-1203	493	16	(	(	PUNCT
ejpam-1203	493	17	y	y	NOUN
ejpam-1203	493	18	,	,	PUNCT
ejpam-1203	493	19	σ)→	σ)→	PROPN
ejpam-1203	493	20	(	(	PUNCT
ejpam-1203	493	21	z	z	PROPN
ejpam-1203	493	22	,	,	PUNCT
ejpam-1203	493	23	η	η	PROPN
ejpam-1203	493	24	)	)	PUNCT
ejpam-1203	493	25	be	be	VERB
ejpam-1203	493	26	two	two	NUM
ejpam-1203	493	27	functions	function	NOUN
ejpam-1203	493	28	.	.	PUNCT
ejpam-1203	494	1	then	then	ADV
ejpam-1203	494	2	1	1	X
ejpam-1203	494	3	.	.	X
ejpam-1203	495	1	g	g	NOUN
ejpam-1203	495	2	◦	◦	NOUN
ejpam-1203	495	3	f	f	PROPN
ejpam-1203	495	4	is	be	AUX
ejpam-1203	495	5	ρ	ρ	NOUN
ejpam-1203	495	6	-	-	ADJ
ejpam-1203	495	7	continuous	continuous	ADJ
ejpam-1203	495	8	if	if	SCONJ
ejpam-1203	495	9	g	g	PROPN
ejpam-1203	495	10	is	be	AUX
ejpam-1203	495	11	continuous	continuous	ADJ
ejpam-1203	495	12	and	and	CCONJ
ejpam-1203	495	13	f	f	PROPN
ejpam-1203	495	14	is	be	AUX
ejpam-1203	495	15	ρ	ρ	NOUN
ejpam-1203	495	16	-	-	ADJ
ejpam-1203	495	17	continuous	continuous	ADJ
ejpam-1203	495	18	.	.	PUNCT
ejpam-1203	496	1	2	2	X
ejpam-1203	496	2	.	.	X
ejpam-1203	496	3	g	g	ADP
ejpam-1203	496	4	◦	◦	NOUN
ejpam-1203	496	5	f	f	X
ejpam-1203	496	6	isρ	isρ	NOUN
ejpam-1203	496	7	-	-	PUNCT
ejpam-1203	496	8	irresolute	irresolute	ADJ
ejpam-1203	496	9	if	if	SCONJ
ejpam-1203	496	10	g	g	PROPN
ejpam-1203	496	11	is	be	AUX
ejpam-1203	496	12	ρ	ρ	NOUN
ejpam-1203	496	13	-	-	PUNCT
ejpam-1203	496	14	irresolute	irresolute	ADJ
ejpam-1203	496	15	and	and	CCONJ
ejpam-1203	496	16	f	f	PROPN
ejpam-1203	496	17	is	be	AUX
ejpam-1203	496	18	ρ	ρ	NOUN
ejpam-1203	496	19	-	-	PUNCT
ejpam-1203	496	20	irresolute	irresolute	ADJ
ejpam-1203	496	21	.	.	PUNCT
ejpam-1203	497	1	3	3	X
ejpam-1203	497	2	.	.	X
ejpam-1203	497	3	g	g	NOUN
ejpam-1203	497	4	◦	◦	NOUN
ejpam-1203	497	5	f	f	PROPN
ejpam-1203	497	6	is	be	AUX
ejpam-1203	497	7	ρ	ρ	NOUN
ejpam-1203	497	8	-	-	ADJ
ejpam-1203	497	9	continuous	continuous	ADJ
ejpam-1203	497	10	if	if	SCONJ
ejpam-1203	497	11	g	g	PROPN
ejpam-1203	497	12	is	be	AUX
ejpam-1203	497	13	ρ	ρ	NOUN
ejpam-1203	497	14	-	-	ADJ
ejpam-1203	497	15	continuous	continuous	ADJ
ejpam-1203	497	16	and	and	CCONJ
ejpam-1203	497	17	f	f	PROPN
ejpam-1203	497	18	is	be	AUX
ejpam-1203	497	19	ρ	ρ	NOUN
ejpam-1203	497	20	-	-	PUNCT
ejpam-1203	497	21	irresolute	irresolute	ADJ
ejpam-1203	497	22	.	.	PUNCT
ejpam-1203	498	1	proof	proof	NOUN
ejpam-1203	498	2	.	.	PUNCT
ejpam-1203	499	1	1	1	X
ejpam-1203	499	2	.	.	X
ejpam-1203	499	3	let	let	VERB
ejpam-1203	499	4	v	v	PART
ejpam-1203	499	5	be	be	AUX
ejpam-1203	499	6	closed	close	VERB
ejpam-1203	499	7	in	in	ADP
ejpam-1203	499	8	(	(	PUNCT
ejpam-1203	499	9	z	z	PROPN
ejpam-1203	499	10	,	,	PUNCT
ejpam-1203	499	11	η	η	PROPN
ejpam-1203	499	12	)	)	PUNCT
ejpam-1203	499	13	.	.	PUNCT
ejpam-1203	500	1	since	since	SCONJ
ejpam-1203	500	2	g	g	PROPN
ejpam-1203	500	3	is	be	AUX
ejpam-1203	500	4	continuous	continuous	ADJ
ejpam-1203	500	5	,	,	PUNCT
ejpam-1203	500	6	g−1(v	g−1(v	PROPN
ejpam-1203	500	7	)	)	PUNCT
ejpam-1203	500	8	is	be	AUX
ejpam-1203	500	9	closed	close	VERB
ejpam-1203	500	10	in	in	ADP
ejpam-1203	500	11	(	(	PUNCT
ejpam-1203	500	12	y	y	PROPN
ejpam-1203	500	13	,	,	PUNCT
ejpam-1203	500	14	σ	σ	PROPN
ejpam-1203	500	15	)	)	PUNCT
ejpam-1203	500	16	.	.	PUNCT
ejpam-1203	501	1	as	as	SCONJ
ejpam-1203	501	2	f	f	PROPN
ejpam-1203	501	3	is	be	AUX
ejpam-1203	501	4	ρ	ρ	NOUN
ejpam-1203	501	5	-	-	ADJ
ejpam-1203	501	6	continuous	continuous	ADJ
ejpam-1203	501	7	,	,	PUNCT
ejpam-1203	501	8	f	f	PROPN
ejpam-1203	501	9	−1(g−1(v	−1(g−1(v	NOUN
ejpam-1203	501	10	)	)	PUNCT
ejpam-1203	501	11	)	)	PUNCT
ejpam-1203	502	1	=	=	PRON
ejpam-1203	502	2	(	(	PUNCT
ejpam-1203	502	3	g	g	PROPN
ejpam-1203	502	4	◦	◦	NOUN
ejpam-1203	502	5	f	f	PROPN
ejpam-1203	502	6	)	)	PUNCT
ejpam-1203	502	7	−1(v	−1(v	PROPN
ejpam-1203	502	8	)	)	PUNCT
ejpam-1203	502	9	is	be	AUX
ejpam-1203	502	10	ρ	ρ	NOUN
ejpam-1203	502	11	-	-	PUNCT
ejpam-1203	502	12	closed	closed	ADJ
ejpam-1203	502	13	in	in	ADP
ejpam-1203	502	14	(	(	PUNCT
ejpam-1203	502	15	x	x	INTJ
ejpam-1203	502	16	,	,	PUNCT
ejpam-1203	502	17	τ	τ	PROPN
ejpam-1203	502	18	)	)	PUNCT
ejpam-1203	502	19	.	.	PUNCT
ejpam-1203	503	1	hence	hence	ADV
ejpam-1203	503	2	g	g	PROPN
ejpam-1203	503	3	◦	◦	PROPN
ejpam-1203	503	4	f	f	PROPN
ejpam-1203	503	5	is	be	AUX
ejpam-1203	503	6	ρcontinuous	ρcontinuous	ADJ
ejpam-1203	503	7	.	.	PUNCT
ejpam-1203	504	1	2	2	X
ejpam-1203	504	2	.	.	X
ejpam-1203	504	3	let	let	VERB
ejpam-1203	504	4	v	v	PART
ejpam-1203	504	5	be	be	AUX
ejpam-1203	504	6	ρ	ρ	NOUN
ejpam-1203	504	7	-	-	ADJ
ejpam-1203	504	8	closed	closed	ADJ
ejpam-1203	504	9	in	in	ADP
ejpam-1203	504	10	(	(	PUNCT
ejpam-1203	504	11	z	z	PROPN
ejpam-1203	504	12	,	,	PUNCT
ejpam-1203	504	13	η	η	PROPN
ejpam-1203	504	14	)	)	PUNCT
ejpam-1203	504	15	.	.	PUNCT
ejpam-1203	505	1	since	since	SCONJ
ejpam-1203	505	2	g	g	PROPN
ejpam-1203	505	3	is	be	AUX
ejpam-1203	505	4	ρ	ρ	NOUN
ejpam-1203	505	5	-	-	PUNCT
ejpam-1203	505	6	irresolute	irresolute	ADJ
ejpam-1203	505	7	,	,	PUNCT
ejpam-1203	505	8	g−1(v	g−1(v	PROPN
ejpam-1203	505	9	)	)	PUNCT
ejpam-1203	505	10	is	be	AUX
ejpam-1203	505	11	ρ	ρ	NOUN
ejpam-1203	505	12	-	-	PUNCT
ejpam-1203	505	13	closed	closed	ADJ
ejpam-1203	505	14	in	in	ADP
ejpam-1203	505	15	(	(	PUNCT
ejpam-1203	505	16	y	y	PROPN
ejpam-1203	505	17	,	,	PUNCT
ejpam-1203	505	18	σ	σ	PROPN
ejpam-1203	505	19	)	)	PUNCT
ejpam-1203	505	20	.	.	PUNCT
ejpam-1203	506	1	as	as	SCONJ
ejpam-1203	506	2	f	f	PROPN
ejpam-1203	506	3	is	be	AUX
ejpam-1203	506	4	ρ	ρ	NOUN
ejpam-1203	506	5	-	-	PUNCT
ejpam-1203	506	6	irresolute	irresolute	ADJ
ejpam-1203	506	7	,	,	PUNCT
ejpam-1203	506	8	f	f	PROPN
ejpam-1203	506	9	−1(g−1(v	−1(g−1(v	NOUN
ejpam-1203	506	10	)	)	PUNCT
ejpam-1203	506	11	)	)	PUNCT
ejpam-1203	507	1	=	=	PRON
ejpam-1203	507	2	(	(	PUNCT
ejpam-1203	507	3	g	g	PROPN
ejpam-1203	507	4	◦	◦	NOUN
ejpam-1203	507	5	f	f	PROPN
ejpam-1203	507	6	)	)	PUNCT
ejpam-1203	507	7	−1(v	−1(v	PROPN
ejpam-1203	507	8	)	)	PUNCT
ejpam-1203	507	9	is	be	AUX
ejpam-1203	507	10	ρ	ρ	NOUN
ejpam-1203	507	11	-	-	PUNCT
ejpam-1203	507	12	closed	closed	ADJ
ejpam-1203	507	13	in	in	ADP
ejpam-1203	507	14	(	(	PUNCT
ejpam-1203	507	15	x	x	INTJ
ejpam-1203	507	16	,	,	PUNCT
ejpam-1203	507	17	τ	τ	PROPN
ejpam-1203	507	18	)	)	PUNCT
ejpam-1203	507	19	therefore	therefore	ADV
ejpam-1203	507	20	g	g	PROPN
ejpam-1203	507	21	◦	◦	PROPN
ejpam-1203	507	22	f	f	PROPN
ejpam-1203	507	23	is	be	AUX
ejpam-1203	507	24	ρ	ρ	NOUN
ejpam-1203	507	25	-	-	PUNCT
ejpam-1203	507	26	irresolute	irresolute	ADJ
ejpam-1203	507	27	.	.	PUNCT
ejpam-1203	508	1	3	3	X
ejpam-1203	508	2	.	.	X
ejpam-1203	508	3	let	let	VERB
ejpam-1203	508	4	v	v	PART
ejpam-1203	508	5	be	be	AUX
ejpam-1203	508	6	closed	close	VERB
ejpam-1203	508	7	in	in	ADP
ejpam-1203	508	8	(	(	PUNCT
ejpam-1203	508	9	z	z	PROPN
ejpam-1203	508	10	,	,	PUNCT
ejpam-1203	508	11	η	η	PROPN
ejpam-1203	508	12	)	)	PUNCT
ejpam-1203	508	13	.	.	PUNCT
ejpam-1203	509	1	since	since	SCONJ
ejpam-1203	509	2	g	g	PROPN
ejpam-1203	509	3	is	be	AUX
ejpam-1203	509	4	ρ	ρ	NOUN
ejpam-1203	509	5	-	-	ADJ
ejpam-1203	509	6	continuous	continuous	ADJ
ejpam-1203	509	7	,	,	PUNCT
ejpam-1203	509	8	g−1(v	g−1(v	PROPN
ejpam-1203	509	9	)	)	PUNCT
ejpam-1203	509	10	is	be	AUX
ejpam-1203	509	11	ρ	ρ	NOUN
ejpam-1203	509	12	-	-	PUNCT
ejpam-1203	509	13	closed	closed	ADJ
ejpam-1203	509	14	in	in	ADP
ejpam-1203	509	15	(	(	PUNCT
ejpam-1203	509	16	y	y	PROPN
ejpam-1203	509	17	,	,	PUNCT
ejpam-1203	509	18	σ	σ	PROPN
ejpam-1203	509	19	)	)	PUNCT
ejpam-1203	509	20	.	.	PUNCT
ejpam-1203	510	1	as	as	SCONJ
ejpam-1203	510	2	f	f	PROPN
ejpam-1203	510	3	is	be	AUX
ejpam-1203	510	4	ρ	ρ	NOUN
ejpam-1203	510	5	-	-	PUNCT
ejpam-1203	510	6	irresolute	irresolute	ADJ
ejpam-1203	510	7	,	,	PUNCT
ejpam-1203	510	8	f	f	PROPN
ejpam-1203	510	9	−1(g−1(v	−1(g−1(v	NOUN
ejpam-1203	510	10	)	)	PUNCT
ejpam-1203	510	11	)	)	PUNCT
ejpam-1203	511	1	=	=	PRON
ejpam-1203	511	2	(	(	PUNCT
ejpam-1203	511	3	g	g	PROPN
ejpam-1203	511	4	◦	◦	NOUN
ejpam-1203	511	5	f	f	PROPN
ejpam-1203	511	6	)	)	PUNCT
ejpam-1203	511	7	−1(v	−1(v	PROPN
ejpam-1203	511	8	)	)	PUNCT
ejpam-1203	511	9	is	be	AUX
ejpam-1203	511	10	ρ	ρ	NOUN
ejpam-1203	511	11	-	-	PUNCT
ejpam-1203	511	12	closed	closed	ADJ
ejpam-1203	511	13	in	in	ADP
ejpam-1203	511	14	(	(	PUNCT
ejpam-1203	511	15	x	x	INTJ
ejpam-1203	511	16	,	,	PUNCT
ejpam-1203	511	17	τ	τ	PROPN
ejpam-1203	511	18	)	)	PUNCT
ejpam-1203	511	19	.	.	PUNCT
ejpam-1203	512	1	therefore	therefore	ADV
ejpam-1203	512	2	g	g	PROPN
ejpam-1203	512	3	◦	◦	PROPN
ejpam-1203	512	4	f	f	PROPN
ejpam-1203	512	5	is	be	AUX
ejpam-1203	512	6	ρ	ρ	NOUN
ejpam-1203	512	7	-	-	ADJ
ejpam-1203	512	8	continuous	continuous	ADJ
ejpam-1203	512	9	.	.	PUNCT
ejpam-1203	513	1	7	7	X
ejpam-1203	513	2	.	.	NUM
ejpam-1203	513	3	references	reference	NOUN
ejpam-1203	513	4	acknowledgements	acknowledgement	VERB
ejpam-1203	513	5	the	the	DET
ejpam-1203	513	6	authors	author	NOUN
ejpam-1203	513	7	thank	thank	VERB
ejpam-1203	513	8	the	the	DET
ejpam-1203	513	9	readers	reader	NOUN
ejpam-1203	513	10	of	of	ADP
ejpam-1203	513	11	european	european	PROPN
ejpam-1203	513	12	journal	journal	PROPN
ejpam-1203	513	13	of	of	ADP
ejpam-1203	513	14	pure	pure	ADJ
ejpam-1203	513	15	and	and	CCONJ
ejpam-1203	513	16	applied	applied	ADJ
ejpam-1203	513	17	mathematics	mathematic	NOUN
ejpam-1203	513	18	,	,	PUNCT
ejpam-1203	513	19	for	for	ADP
ejpam-1203	513	20	making	make	VERB
ejpam-1203	513	21	our	our	PRON
ejpam-1203	513	22	journal	journal	NOUN
ejpam-1203	513	23	successful	successful	ADJ
ejpam-1203	513	24	.	.	PUNCT
ejpam-1203	514	1	references	reference	NOUN
ejpam-1203	514	2	[	[	X
ejpam-1203	514	3	1	1	NUM
ejpam-1203	514	4	]	]	PUNCT
ejpam-1203	514	5	d.andrijevic	d.andrijevic	PROPN
ejpam-1203	514	6	.	.	PUNCT
ejpam-1203	515	1	semipreopen	semipreopen	ADJ
ejpam-1203	515	2	sets	set	NOUN
ejpam-1203	515	3	,	,	PUNCT
ejpam-1203	515	4	mat	mat	PROPN
ejpam-1203	515	5	.	.	PROPN
ejpam-1203	515	6	vesnik	vesnik	PROPN
ejpam-1203	515	7	,	,	PUNCT
ejpam-1203	515	8	38	38	NUM
ejpam-1203	515	9	(	(	PUNCT
ejpam-1203	515	10	1	1	NUM
ejpam-1203	515	11	)	)	PUNCT
ejpam-1203	515	12	,	,	PUNCT
ejpam-1203	515	13	24	24	NUM
ejpam-1203	515	14	-	-	SYM
ejpam-1203	515	15	32	32	NUM
ejpam-1203	515	16	.	.	PUNCT
ejpam-1203	515	17	1986	1986	NUM
ejpam-1203	515	18	.	.	PUNCT
ejpam-1203	516	1	[	[	X
ejpam-1203	516	2	2	2	NUM
ejpam-1203	516	3	]	]	PUNCT
ejpam-1203	516	4	k.	k.	PROPN
ejpam-1203	516	5	balachandran	balachandran	PROPN
ejpam-1203	516	6	,	,	PUNCT
ejpam-1203	516	7	p.	p.	PROPN
ejpam-1203	516	8	sundaram	sundaram	PROPN
ejpam-1203	516	9	and	and	CCONJ
ejpam-1203	516	10	h.	h.	PROPN
ejpam-1203	516	11	maki	maki	PROPN
ejpam-1203	516	12	.	.	PUNCT
ejpam-1203	517	1	on	on	ADP
ejpam-1203	517	2	generalized	generalized	ADJ
ejpam-1203	517	3	continuous	continuous	ADJ
ejpam-1203	517	4	maps	map	NOUN
ejpam-1203	517	5	in	in	ADP
ejpam-1203	517	6	topological	topological	ADJ
ejpam-1203	517	7	spaces	space	NOUN
ejpam-1203	517	8	,	,	PUNCT
ejpam-1203	517	9	mem	mem	X
ejpam-1203	517	10	fac	fac	PROPN
ejpam-1203	517	11	.	.	PUNCT
ejpam-1203	517	12	sci	sci	PROPN
ejpam-1203	517	13	.	.	PUNCT
ejpam-1203	517	14	kochi	kochi	PROPN
ejpam-1203	517	15	univ.ser	univ.ser	PROPN
ejpam-1203	517	16	.	.	PUNCT
ejpam-1203	518	1	a.	a.	PROPN
ejpam-1203	518	2	math	math	PROPN
ejpam-1203	518	3	12	12	NUM
ejpam-1203	518	4	.	.	PUNCT
ejpam-1203	519	1	5	5	NUM
ejpam-1203	519	2	-	-	SYM
ejpam-1203	519	3	13	13	NUM
ejpam-1203	519	4	.	.	PUNCT
ejpam-1203	520	1	1991	1991	NUM
ejpam-1203	520	2	.	.	PUNCT
ejpam-1203	521	1	[	[	X
ejpam-1203	521	2	3	3	X
ejpam-1203	521	3	]	]	PUNCT
ejpam-1203	521	4	j.	j.	PROPN
ejpam-1203	521	5	dontchev	dontchev	PROPN
ejpam-1203	521	6	.	.	PUNCT
ejpam-1203	522	1	on	on	ADP
ejpam-1203	522	2	generalizing	generalize	VERB
ejpam-1203	522	3	semi	semi	ADJ
ejpam-1203	522	4	-	-	ADJ
ejpam-1203	522	5	preopen	preopen	ADJ
ejpam-1203	522	6	sets	set	NOUN
ejpam-1203	522	7	,	,	PUNCT
ejpam-1203	522	8	mem.fac.sci	mem.fac.sci	PROPN
ejpam-1203	522	9	.	.	PUNCT
ejpam-1203	523	1	kochi	kochi	PROPN
ejpam-1203	523	2	univ.ser.a.maths	univ.ser.a.math	NOUN
ejpam-1203	523	3	16	16	NUM
ejpam-1203	523	4	,	,	PUNCT
ejpam-1203	523	5	35	35	NUM
ejpam-1203	523	6	-	-	SYM
ejpam-1203	523	7	48	48	NUM
ejpam-1203	523	8	.	.	PUNCT
ejpam-1203	523	9	1995	1995	NUM
ejpam-1203	523	10	.	.	PUNCT
ejpam-1203	524	1	references	reference	NOUN
ejpam-1203	524	2	566	566	NUM
ejpam-1203	524	3	[	[	X
ejpam-1203	524	4	4	4	NUM
ejpam-1203	524	5	]	]	X
ejpam-1203	524	6	y.	y.	PROPN
ejpam-1203	524	7	gnanambal	gnanambal	PROPN
ejpam-1203	524	8	.	.	PUNCT
ejpam-1203	525	1	generalized	generalize	VERB
ejpam-1203	525	2	pre	pre	ADJ
ejpam-1203	525	3	-	-	ADJ
ejpam-1203	525	4	regular	regular	ADJ
ejpam-1203	525	5	closed	closed	ADJ
ejpam-1203	525	6	sets	set	NOUN
ejpam-1203	525	7	in	in	ADP
ejpam-1203	525	8	topological	topological	ADJ
ejpam-1203	525	9	spaces	space	NOUN
ejpam-1203	525	10	,	,	PUNCT
ejpam-1203	525	11	indian	indian	PROPN
ejpam-1203	525	12	j.	j.	PROPN
ejpam-1203	525	13	pure	pure	PROPN
ejpam-1203	525	14	appl	appl	PROPN
ejpam-1203	525	15	.	.	PUNCT
ejpam-1203	526	1	maths	maths	PROPN
ejpam-1203	526	2	.	.	PUNCT
ejpam-1203	526	3	,	,	PUNCT
ejpam-1203	526	4	28	28	NUM
ejpam-1203	526	5	(	(	PUNCT
ejpam-1203	526	6	3	3	NUM
ejpam-1203	526	7	)	)	PUNCT
ejpam-1203	526	8	,	,	PUNCT
ejpam-1203	526	9	351	351	NUM
ejpam-1203	526	10	-	-	SYM
ejpam-1203	526	11	360	360	NUM
ejpam-1203	526	12	.	.	PUNCT
ejpam-1203	527	1	1997	1997	NUM
ejpam-1203	527	2	.	.	PUNCT
ejpam-1203	528	1	[	[	X
ejpam-1203	528	2	5	5	X
ejpam-1203	528	3	]	]	PUNCT
ejpam-1203	528	4	s.	s.	PROPN
ejpam-1203	528	5	jafari	jafari	PROPN
ejpam-1203	528	6	,	,	PUNCT
ejpam-1203	528	7	t.	t.	PROPN
ejpam-1203	528	8	noiri	noiri	PROPN
ejpam-1203	528	9	,	,	PUNCT
ejpam-1203	528	10	n.	n.	PROPN
ejpam-1203	528	11	rajesh	rajesh	PROPN
ejpam-1203	528	12	and	and	CCONJ
ejpam-1203	528	13	m.l	m.l	PROPN
ejpam-1203	528	14	.	.	PROPN
ejpam-1203	528	15	thivagar	thivagar	NOUN
ejpam-1203	528	16	.	.	PUNCT
ejpam-1203	529	1	another	another	DET
ejpam-1203	529	2	generalization	generalization	NOUN
ejpam-1203	529	3	of	of	ADP
ejpam-1203	529	4	closed	closed	ADJ
ejpam-1203	529	5	sets	set	NOUN
ejpam-1203	529	6	,	,	PUNCT
ejpam-1203	529	7	kochi	kochi	NOUN
ejpam-1203	529	8	j.math	j.math	NOUN
ejpam-1203	529	9	,	,	PUNCT
ejpam-1203	529	10	3	3	NUM
ejpam-1203	529	11	,	,	PUNCT
ejpam-1203	529	12	25	25	NUM
ejpam-1203	529	13	-	-	SYM
ejpam-1203	529	14	38	38	NUM
ejpam-1203	529	15	.	.	PUNCT
ejpam-1203	529	16	2008	2008	NUM
ejpam-1203	529	17	.	.	PUNCT
ejpam-1203	530	1	[	[	X
ejpam-1203	530	2	6	6	NUM
ejpam-1203	530	3	]	]	X
ejpam-1203	530	4	n.	n.	PROPN
ejpam-1203	530	5	levine	levine	PROPN
ejpam-1203	530	6	.	.	PUNCT
ejpam-1203	531	1	semi	semi	ADJ
ejpam-1203	531	2	-	-	ADJ
ejpam-1203	531	3	open	open	ADJ
ejpam-1203	531	4	sets	set	NOUN
ejpam-1203	531	5	,	,	PUNCT
ejpam-1203	531	6	semi	semi	ADJ
ejpam-1203	531	7	-	-	NOUN
ejpam-1203	531	8	continuity	continuity	NOUN
ejpam-1203	531	9	in	in	ADP
ejpam-1203	531	10	topological	topological	ADJ
ejpam-1203	531	11	spaces	space	NOUN
ejpam-1203	531	12	,	,	PUNCT
ejpam-1203	531	13	amer	amer	PROPN
ejpam-1203	531	14	math	math	PROPN
ejpam-1203	531	15	,	,	PUNCT
ejpam-1203	531	16	monthly	monthly	ADV
ejpam-1203	531	17	,	,	PUNCT
ejpam-1203	531	18	70	70	NUM
ejpam-1203	531	19	,	,	PUNCT
ejpam-1203	531	20	36	36	NUM
ejpam-1203	531	21	-	-	SYM
ejpam-1203	531	22	41	41	NUM
ejpam-1203	531	23	.	.	PUNCT
ejpam-1203	531	24	1963	1963	NUM
ejpam-1203	531	25	.	.	PUNCT
ejpam-1203	532	1	[	[	X
ejpam-1203	532	2	7	7	X
ejpam-1203	532	3	]	]	X
ejpam-1203	532	4	n.	n.	PROPN
ejpam-1203	532	5	levine	levine	PROPN
ejpam-1203	532	6	.	.	PUNCT
ejpam-1203	533	1	generalized	generalize	VERB
ejpam-1203	533	2	closed	closed	ADJ
ejpam-1203	533	3	sets	set	NOUN
ejpam-1203	533	4	in	in	ADP
ejpam-1203	533	5	topology	topology	NOUN
ejpam-1203	533	6	,	,	PUNCT
ejpam-1203	533	7	rend	rend	VERB
ejpam-1203	533	8	circ	circ	NOUN
ejpam-1203	533	9	.	.	PUNCT
ejpam-1203	534	1	math	math	NOUN
ejpam-1203	534	2	palermo	palermo	PROPN
ejpam-1203	534	3	,	,	PUNCT
ejpam-1203	534	4	19	19	NUM
ejpam-1203	534	5	(	(	PUNCT
ejpam-1203	534	6	2	2	NUM
ejpam-1203	534	7	)	)	PUNCT
ejpam-1203	534	8	.	.	PUNCT
ejpam-1203	535	1	89	89	NUM
ejpam-1203	535	2	-	-	SYM
ejpam-1203	535	3	96	96	NUM
ejpam-1203	535	4	.	.	PUNCT
ejpam-1203	535	5	1970	1970	NUM
ejpam-1203	535	6	.	.	PUNCT
ejpam-1203	536	1	[	[	X
ejpam-1203	536	2	8	8	NUM
ejpam-1203	536	3	]	]	X
ejpam-1203	536	4	a.s	a.s	PROPN
ejpam-1203	536	5	.	.	PROPN
ejpam-1203	536	6	mashour	mashour	PROPN
ejpam-1203	536	7	,	,	PUNCT
ejpam-1203	536	8	m.e	m.e	PROPN
ejpam-1203	536	9	.	.	PROPN
ejpam-1203	536	10	abd	abd	PROPN
ejpam-1203	536	11	elmonsef	elmonsef	PROPN
ejpam-1203	536	12	and	and	CCONJ
ejpam-1203	536	13	s.n	s.n	PROPN
ejpam-1203	536	14	.	.	PROPN
ejpam-1203	536	15	el	el	PROPN
ejpam-1203	536	16	-	-	PUNCT
ejpam-1203	536	17	deep	deep	ADJ
ejpam-1203	536	18	.	.	PUNCT
ejpam-1203	537	1	on	on	ADP
ejpam-1203	537	2	precontinuous	precontinuous	ADJ
ejpam-1203	537	3	and	and	CCONJ
ejpam-1203	537	4	weak	weak	ADJ
ejpam-1203	537	5	pre	pre	ADJ
ejpam-1203	537	6	continuous	continuous	ADJ
ejpam-1203	537	7	mappings	mapping	NOUN
ejpam-1203	537	8	,	,	PUNCT
ejpam-1203	537	9	proc	proc	NOUN
ejpam-1203	537	10	,	,	PUNCT
ejpam-1203	537	11	math	math	NOUN
ejpam-1203	537	12	,	,	PUNCT
ejpam-1203	537	13	phys	phy	NOUN
ejpam-1203	537	14	.	.	PUNCT
ejpam-1203	537	15	soc	soc	PROPN
ejpam-1203	537	16	.	.	PUNCT
ejpam-1203	537	17	egypt	egypt	PROPN
ejpam-1203	537	18	.	.	PROPN
ejpam-1203	537	19	,	,	PUNCT
ejpam-1203	537	20	53	53	NUM
ejpam-1203	537	21	,	,	PUNCT
ejpam-1203	537	22	47	47	NUM
ejpam-1203	537	23	-	-	SYM
ejpam-1203	537	24	53	53	NUM
ejpam-1203	537	25	.	.	NUM
ejpam-1203	537	26	1982	1982	NUM
ejpam-1203	537	27	.	.	PUNCT
ejpam-1203	538	1	[	[	X
ejpam-1203	538	2	9	9	NUM
ejpam-1203	538	3	]	]	X
ejpam-1203	538	4	h.	h.	NOUN
ejpam-1203	538	5	maki	maki	PROPN
ejpam-1203	538	6	,	,	PUNCT
ejpam-1203	538	7	j.	j.	PROPN
ejpam-1203	538	8	umehara	umehara	PROPN
ejpam-1203	538	9	and	and	CCONJ
ejpam-1203	538	10	t.	t.	PROPN
ejpam-1203	538	11	noiri	noiri	PROPN
ejpam-1203	538	12	.	.	PUNCT
ejpam-1203	539	1	every	every	DET
ejpam-1203	539	2	topological	topological	ADJ
ejpam-1203	539	3	space	space	NOUN
ejpam-1203	539	4	in	in	ADP
ejpam-1203	539	5	pret1/2	pret1/2	PROPN
ejpam-1203	539	6	,	,	PUNCT
ejpam-1203	539	7	mem.fac.sci	mem.fac.sci	PROPN
ejpam-1203	539	8	,	,	PUNCT
ejpam-1203	539	9	kochi	kochi	PROPN
ejpam-1203	539	10	univ	univ	ADJ
ejpam-1203	539	11	ser.a.maths	ser.a.math	NOUN
ejpam-1203	539	12	.	.	PUNCT
ejpam-1203	540	1	(	(	PUNCT
ejpam-1203	540	2	17	17	NUM
ejpam-1203	540	3	)	)	PUNCT
ejpam-1203	540	4	.	.	PUNCT
ejpam-1203	541	1	33	33	NUM
ejpam-1203	541	2	-	-	SYM
ejpam-1203	541	3	42	42	NUM
ejpam-1203	541	4	.	.	PUNCT
ejpam-1203	541	5	1996	1996	NUM
ejpam-1203	541	6	.	.	PUNCT
ejpam-1203	542	1	[	[	X
ejpam-1203	542	2	10	10	NUM
ejpam-1203	542	3	]	]	X
ejpam-1203	542	4	o.	o.	PROPN
ejpam-1203	542	5	njastad	njastad	PROPN
ejpam-1203	542	6	.	.	PUNCT
ejpam-1203	543	1	on	on	ADP
ejpam-1203	543	2	some	some	DET
ejpam-1203	543	3	classes	class	NOUN
ejpam-1203	543	4	of	of	ADP
ejpam-1203	543	5	nearly	nearly	ADV
ejpam-1203	543	6	open	open	ADJ
ejpam-1203	543	7	sets	set	NOUN
ejpam-1203	543	8	,	,	PUNCT
ejpam-1203	543	9	pacific	pacific	PROPN
ejpam-1203	543	10	j.	j.	PROPN
ejpam-1203	543	11	math	math	PROPN
ejpam-1203	543	12	.	.	PUNCT
ejpam-1203	544	1	15	15	NUM
ejpam-1203	544	2	,	,	PUNCT
ejpam-1203	544	3	961	961	NUM
ejpam-1203	544	4	-	-	SYM
ejpam-1203	544	5	970	970	NUM
ejpam-1203	544	6	.	.	PUNCT
ejpam-1203	545	1	1965	1965	NUM
ejpam-1203	545	2	.	.	PUNCT
ejpam-1203	546	1	[	[	X
ejpam-1203	546	2	11	11	NUM
ejpam-1203	546	3	]	]	PUNCT
ejpam-1203	546	4	t.noiri	t.noiri	NOUN
ejpam-1203	546	5	,	,	PUNCT
ejpam-1203	546	6	h.maki	h.maki	NOUN
ejpam-1203	546	7	and	and	CCONJ
ejpam-1203	546	8	j.umehara	j.umehara	NOUN
ejpam-1203	546	9	.	.	PUNCT
ejpam-1203	547	1	generalized	generalize	VERB
ejpam-1203	547	2	preclosed	preclose	VERB
ejpam-1203	547	3	functions	function	NOUN
ejpam-1203	547	4	,	,	PUNCT
ejpam-1203	547	5	mem.fac.sci	mem.fac.sci	PROPN
ejpam-1203	547	6	.	.	PUNCT
ejpam-1203	548	1	kochi.univ.ser	kochi.univ.ser	NOUN
ejpam-1203	548	2	a.maths	a.math	NOUN
ejpam-1203	548	3	.	.	PUNCT
ejpam-1203	548	4	,	,	PUNCT
ejpam-1203	548	5	19.13	19.13	NUM
ejpam-1203	548	6	-	-	SYM
ejpam-1203	548	7	20	20	NUM
ejpam-1203	548	8	.	.	PUNCT
ejpam-1203	549	1	1998	1998	NUM
ejpam-1203	549	2	.	.	PUNCT
ejpam-1203	550	1	[	[	X
ejpam-1203	550	2	12	12	NUM
ejpam-1203	550	3	]	]	X
ejpam-1203	550	4	j.h	j.h	PROPN
ejpam-1203	550	5	.	.	PROPN
ejpam-1203	550	6	park	park	PROPN
ejpam-1203	550	7	.	.	PUNCT
ejpam-1203	551	1	on	on	ADP
ejpam-1203	551	2	πgp	πgp	X
ejpam-1203	551	3	-	-	PUNCT
ejpam-1203	551	4	closed	closed	ADJ
ejpam-1203	551	5	sets	set	NOUN
ejpam-1203	551	6	in	in	ADP
ejpam-1203	551	7	topological	topological	ADJ
ejpam-1203	551	8	spaces	space	NOUN
ejpam-1203	551	9	,	,	PUNCT
ejpam-1203	551	10	indian	indian	ADJ
ejpam-1203	551	11	j.pure	j.pure	NOUN
ejpam-1203	551	12	appl	appl	PROPN
ejpam-1203	551	13	.	.	PUNCT
ejpam-1203	551	14	math	math	NOUN
ejpam-1203	551	15	(	(	PUNCT
ejpam-1203	551	16	to	to	PART
ejpam-1203	551	17	appear	appear	VERB
ejpam-1203	551	18	)	)	PUNCT
ejpam-1203	551	19	.	.	PUNCT
ejpam-1203	552	1	[	[	X
ejpam-1203	552	2	13	13	NUM
ejpam-1203	552	3	]	]	SYM
ejpam-1203	552	4	m.h.stone	m.h.stone	NOUN
ejpam-1203	552	5	.	.	PUNCT
ejpam-1203	553	1	application	application	NOUN
ejpam-1203	553	2	of	of	ADP
ejpam-1203	553	3	the	the	DET
ejpam-1203	553	4	theory	theory	NOUN
ejpam-1203	553	5	boolean	boolean	ADJ
ejpam-1203	553	6	rings	ring	NOUN
ejpam-1203	553	7	to	to	ADP
ejpam-1203	553	8	general	general	ADJ
ejpam-1203	553	9	topology	topology	NOUN
ejpam-1203	553	10	,	,	PUNCT
ejpam-1203	553	11	trans.amer.math.soc	trans.amer.math.soc	PROPN
ejpam-1203	553	12	.	.	PROPN
ejpam-1203	553	13	,41	,41	PROPN
ejpam-1203	553	14	,	,	PUNCT
ejpam-1203	553	15	375	375	NUM
ejpam-1203	553	16	-	-	SYM
ejpam-1203	553	17	381	381	NUM
ejpam-1203	553	18	.	.	PUNCT
ejpam-1203	553	19	1937	1937	NUM
ejpam-1203	553	20	.	.	PUNCT
ejpam-1203	554	1	[	[	X
ejpam-1203	554	2	14	14	NUM
ejpam-1203	554	3	]	]	X
ejpam-1203	554	4	m.k.r.s	m.k.r.s	PROPN
ejpam-1203	554	5	veerakumar	veerakumar	PROPN
ejpam-1203	554	6	.	.	PROPN
ejpam-1203	554	7	ĝ	ĝ	PROPN
ejpam-1203	555	1	-closed	-close	VERB
ejpam-1203	555	2	sets	set	NOUN
ejpam-1203	555	3	in	in	ADP
ejpam-1203	555	4	topological	topological	ADJ
ejpam-1203	555	5	spaces	space	NOUN
ejpam-1203	555	6	.	.	PUNCT
ejpam-1203	556	1	bull	bull	PROPN
ejpam-1203	556	2	allahabad	allahabad	PROPN
ejpam-1203	556	3	.	.	PUNCT
ejpam-1203	557	1	soc.18	soc.18	PROPN
ejpam-1203	557	2	,	,	PUNCT
ejpam-1203	557	3	99112	99112	NUM
ejpam-1203	557	4	.	.	PUNCT
ejpam-1203	558	1	2003	2003	NUM
ejpam-1203	558	2	.	.	PUNCT
ejpam-1203	559	1	[	[	X
ejpam-1203	559	2	15	15	NUM
ejpam-1203	559	3	]	]	X
ejpam-1203	559	4	m.k.r.s	m.k.r.s	PROPN
ejpam-1203	559	5	veerakumar	veerakumar	PROPN
ejpam-1203	559	6	.	.	PROPN
ejpam-1203	560	1	g*-preclosed	g*-preclose	VERB
ejpam-1203	560	2	sets	set	NOUN
ejpam-1203	560	3	,	,	PUNCT
ejpam-1203	560	4	acta	acta	PROPN
ejpam-1203	560	5	ciencia	ciencia	PROPN
ejpam-1203	560	6	indica(mathematics	indica(mathematics	PROPN
ejpam-1203	560	7	)	)	PUNCT
ejpam-1203	560	8	meerut	meerut	PROPN
ejpam-1203	560	9	,	,	PUNCT
ejpam-1203	560	10	xxviii	xxviii	PROPN
ejpam-1203	560	11	(	(	PUNCT
ejpam-1203	560	12	m	m	NOUN
ejpam-1203	560	13	)	)	PUNCT
ejpam-1203	560	14	(	(	PUNCT
ejpam-1203	560	15	1	1	NUM
ejpam-1203	560	16	)	)	PUNCT
ejpam-1203	560	17	.	.	PUNCT
ejpam-1203	561	1	51	51	NUM
ejpam-1203	561	2	-	-	SYM
ejpam-1203	561	3	60	60	NUM
ejpam-1203	561	4	.	.	PUNCT
ejpam-1203	561	5	2002	2002	NUM
ejpam-1203	561	6	.	.	PUNCT
ejpam-1203	562	1	[	[	X
ejpam-1203	562	2	16	16	NUM
ejpam-1203	562	3	]	]	X
ejpam-1203	562	4	m.k.r.s	m.k.r.s	PROPN
ejpam-1203	562	5	veerakumar	veerakumar	PROPN
ejpam-1203	562	6	.	.	PUNCT
ejpam-1203	563	1	pre	pre	ADJ
ejpam-1203	563	2	-	-	ADJ
ejpam-1203	563	3	semi	semi	ADJ
ejpam-1203	563	4	-	-	ADJ
ejpam-1203	563	5	closed	closed	ADJ
ejpam-1203	563	6	,	,	PUNCT
ejpam-1203	563	7	indian	indian	PROPN
ejpam-1203	563	8	j.	j.	PROPN
ejpam-1203	563	9	math	math	PROPN
ejpam-1203	563	10	,	,	PUNCT
ejpam-1203	563	11	44(2	44(2	NOUN
ejpam-1203	563	12	)	)	PUNCT
ejpam-1203	563	13	.	.	PUNCT
ejpam-1203	564	1	165	165	NUM
ejpam-1203	564	2	-	-	SYM
ejpam-1203	564	3	181	181	NUM
ejpam-1203	564	4	.	.	PUNCT
ejpam-1203	565	1	2002	2002	NUM
ejpam-1203	565	2	.	.	PUNCT
ejpam-1203	566	1	[	[	X
ejpam-1203	566	2	17	17	NUM
ejpam-1203	566	3	]	]	X
ejpam-1203	566	4	v.zaitov	v.zaitov	NOUN
ejpam-1203	566	5	.	.	PUNCT
ejpam-1203	567	1	on	on	ADP
ejpam-1203	567	2	certain	certain	ADJ
ejpam-1203	567	3	classes	class	NOUN
ejpam-1203	567	4	of	of	ADP
ejpam-1203	567	5	topological	topological	ADJ
ejpam-1203	567	6	spaces	space	NOUN
ejpam-1203	567	7	and	and	CCONJ
ejpam-1203	567	8	their	their	PRON
ejpam-1203	567	9	bicompactification	bicompactification	NOUN
ejpam-1203	567	10	,	,	PUNCT
ejpam-1203	567	11	dokl	dokl	NOUN
ejpam-1203	567	12	akad	akad	PROPN
ejpam-1203	567	13	nauk	nauk	PROPN
ejpam-1203	567	14	sssr	sssr	NOUN
ejpam-1203	567	15	.	.	PUNCT
ejpam-1203	568	1	178	178	NUM
ejpam-1203	568	2	:	:	PUNCT
ejpam-1203	568	3	778	778	NUM
ejpam-1203	568	4	-	-	SYM
ejpam-1203	568	5	9	9	NUM
ejpam-1203	568	6	.	.	NUM
ejpam-1203	568	7	1968	1968	NUM
ejpam-1203	568	8	.	.	PUNCT